How many terms are in the expression 3x+y−23−5

Answers

Answer 1

Answer:

There are 4 terms

Step-by-step explanation:

“Terms are single numbers, variables, or the product of a number and variables. Examples of terms: 9 a 9a 9a. y y y.”


Related Questions

Notywered Points out 200 euro Individuals from high income countries are more likely to meet physical activity guidelines compared to individuals from low income countries because they have more access to the resources and facilities needed to be active Select one: a. Trueb. False

Answers

The answer is True, individuals from high-income countries more likely to meet physical activity guidelines compared to individuals from low-income countries because they have more access to resources and facilities needed to be active.

Individuals from high-income countries are more likely to meet physical activity guidelines compared to individuals from low-income countries because they have more access to the resources and facilities needed to be active. This is because higher-income countries generally have better infrastructure, more public spaces for physical activities, and greater access to fitness facilities, which enable individuals to engage in regular exercise and maintain an active lifestyle.

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Use properties to rewrite the given equation. Which equations have the same solution as 2.3p – 10.1 = 6.5p – 4 – 0.01p? Select two options. 2.3p – 10.1 = 6.4p – 4 2.3p – 10.1 = 6.49p – 4 230p – 1010 = 650p – 400 – p 23p – 101 = 65p – 40 – p 2.3p – 14.1 = 6.4p – 4

Answers

Answer:

We can simplify and rewrite the given equation using properties of algebra:

2.3p – 10.1 = 6.5p – 4 – 0.01p

2.3p – 10.1 = 6.49p – 4

2.3p - 6.49p = -4 + 10.1

-4.19p = 6.1

p = -6.1 / 4.19

p ≈ -1.4568

Therefore, the equation 2.3p – 10.1 = 6.5p – 4 – 0.01p is equivalent to the equation -4.19p = 6.1, which has the solution p ≈ -1.4568.

Now, we can check which of the given equations have the same solution as -4.19p = 6.1:

- 2.3p – 10.1 = 6.4p – 4

Simplifying:

-8.7p = 6.1

p = -0.7011

This equation does not have the same solution as -4.19p = 6.1.

- 2.3p – 10.1 = 6.49p – 4

Simplifying:

-8.79p = 6.1

p = -0.6932

This equation does not have the same solution as -4.19p = 6.1.

- 230p – 1010 = 650p – 400 – p

Simplifying:

229p = 610

p = 610/229

p ≈ 2.6620

This equation does not have the same solution as -4.19p = 6.1.

- 23p – 101 = 65p – 40 – p

Simplifying:

23p + p - 65p = -40 + 101

-41p = 61

p = -61/41

p ≈ -1.4878

This equation does have the same solution as -4.19p = 6.1.

- 2.3p – 14.1 = 6.4p – 4

Simplifying:

-8.7p = 9.1

p = -1.0517

This equation does not have the same solution as -4.19p = 6.1.

Therefore, the equations that have the same solution as 2.3p – 10.1 = 6.5p – 4 – 0.01p are:

- 23p – 101 = 65p – 40 – p

Please mark me the brainliest

Answer:

It's B & C on Edge

:) pls star 5 and thanks!!!!!!!!!!!!!!!!

Or
The diameter of a circle is 8 inches. What is the circle's circumference?
3. 14

Answers

Answer:

Circumference of the circle = 25.12 inches

Step-by-step explanation:

Given, the diameter of the circle = 8 inches

so the radius is given by the formula

∴ d = 2r

→ 8=2×r

→r = 4 inches     [i]

circumference of the circle =2πr     [ii]

substituting the value of r in equation [ii]

we get,

circumference of the circle = 2×3.14×4

                                             = 25.14 inches

so the circumference of the circle is  25.14 inches

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Question #8
A student flips a coin 100 times. The coin lands on heads 62 times.
Which statement is true?
A
The experimental probability of landing on heads is 12% less than the theoretical probability of
landing on heads.
B
The experimental probability of landing on heads is the same as the theoretical probability of
landing on heads.
C
The experimental probability of landing on heads is 12% greater than the theoretical probability of
landing on heads.
D
The student needs to repeat the experiment because the experimental and theoretical probability
are not the same, but they should be.

Answers

The experimental probability of landing on heads is 12% greater than the theoretical probability of landing on heads. The correct option is C

To solve this problem

Flipping a fair coin, the theoretical chance of landing on heads is 0.5, or 50%. The experimental probability is the ratio of the total number of coin flips to the number of times the coin landed on heads.

The experiment's experimental probability is 62/100 = 0.62 or 62% since the student flipped the coin 100 times and it came up heads 62 times.

We can see that by comparing the experimental and theoretical probabilities, 62% - 50% = 12%

So the experimental probability is 12% greater than the theoretical probability.

Therefore, The experimental probability of landing on heads is 12% greater than the theoretical probability of landing on heads.

Therefore, The correct option is C

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A survey found that 4 out
of 10 students will work a
summer job. If there are
340 students at the
school, about how many
will work a summer job?

Answers

If 4 out of 10 students work a summer job, then the proportion of students who will work a summer job is 4/10 or 0.4.

To calculate the number of students who will work a summer job in a school with 340 students, we can multiply the proportion who will work (0.4) by the total number of students:

0.4 x 340 = 136

So, about 136 students will work a summer job.

Find the largest three-digit number that can be written in the form 3m+2n where m and n are the positive integers.
ExponentAn exponent, also called power or index, is the magnitude by which a number is multiplied by itself.
It is denoted in the form xn, where x is multiplied by x for n times.
It can be clearly expressed as:

Answers

The largest three-digit number that can be written in the form 3m + 2n is 1997.

To find the largest three-digit number that can be written in the form 3m + 2n, we need to maximize both m and n while staying within the constraints of being positive integers.

Let's start by considering the maximum value for m. Since m is multiplied by 3, we want m to be as large as possible while still being a positive integer. The largest positive integer value for m in this case is 333, as 334 would result in a four-digit number.

Next, let's consider the maximum value for n. Similarly, we want n to be as large as possible while still being a positive integer. The largest positive integer value for n is 499, as 500 would also result in a four-digit number.

Now, let's substitute these values into the expression 3m + 2n:

3(333) + 2(499) = 999 + 998 = 1997

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calculate the slope of the lines that pass through 5,-8 and -3,-4

Answers

Slope  of the lines that pass through points (5,-8) and (-3,-4) is -1/2

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

We have to find slope  of the lines that pass through (5,-8) and (-3,-4)

Slope = -4-(-8)/-3-5

=-4+8/-8

=-4/8

=-1/2

Hence,  slope of the lines that pass through (5,-8) and (-3,-4) is -1/2

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Karl has taken a three-year personal loan of $5000 at 7.25% per year, compounded monthly. The loan requires monthly payments. What is the total amount Karl will pay to the bank?

Answers

≈≈≈Answer:

Step-by-step explanation:

To calculate the total amount Karl will pay to the bank, we need to find the monthly payment and then multiply it by the total number of payments over three years.

First, we need to calculate the monthly interest rate. Since the loan is compounded monthly, we divide the annual interest rate by 12:

Monthly interest rate = 7.25% / 12 = 0.006041667

Next, we need to calculate the total number of payments Karl will make over the course of the loan. Since he will be making monthly payments for three years, there will be a total of:

Total number of payments = 3 years x 12 months/year = 36 payments

To calculate the monthly payment, we can use the formula for the present value of an annuity:

Monthly payment = P * (r / (1 - (1 + r)^(-n)))

where P is the principal amount (in this case, $5000), r is the monthly interest rate, and n is the total number of payments.

Plugging in the values, we get:

Monthly payment = [tex]5000 * \frac{0.006041667}{(1-(1+0.006041667^{-36} )} = $154.96[/tex]

Finally, we can calculate the total amount Karl will pay to the bank by multiplying the monthly payment by the total number of payments:

Total amount paid = Monthly payment x Total number of payments = $154.96 x 36 = $5,578.56

Therefore, the total amount Karl will pay to the bank is $5,578.56

A normal education system that cannot accommodate individuals with inabilities. They require segregated facilities and a different education system.
1.
holistic social rights approach
2.
charity
3.
lay
4.
traditional medical approach

Answers

A normal education system that cannot accommodate individuals with inabilities often follows a traditional medical approach. This approach focuses on the diagnosis and treatment of disabilities, rather than considering the individual's needs in a holistic manner. As a result, these individuals require segregated facilities and a different education system.

A holistic social rights approach would emphasize the importance of including all individuals, regardless of their abilities, in a comprehensive education system. This approach seeks to ensure equal opportunities for all and recognizes the inherent dignity and worth of each person.

In contrast, the charity model views individuals with inabilities as recipients of benevolence from others. This can lead to a patronizing and disempowering attitude towards these individuals, and reinforces the idea that they should be segregated and provided with different facilities.

Lastly, the term "lay" refers to non-expert individuals or those without specialized knowledge in a specific field. Laypeople might not fully understand the nuances and complexities involved in accommodating individuals with inabilities within the education system. This lack of understanding can perpetuate the idea that segregated facilities and a different education system are necessary, instead of promoting inclusion and equal opportunities for all.

In summary, a normal education system that cannot accommodate individuals with inabilities often follows a traditional medical approach, which is in contrast to a holistic social rights approach. The charity model reinforces segregation, and the opinions of laypeople may perpetuate the need for segregated facilities and a different education system.

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you wish to test the following claim ( ) at a significance level of . you obtain 25.4% successes in a sample of size from the first population. you obtain 20.3% successes in a sample of size from the second population. for this test, you should not use the continuity correction, and you should use the normal distribution as an approximation for the binomial distribution. what is the test statistic for this sample? (report answer accurate to three decimal places.) test statistic

Answers

The test statistic for this sample is z = (0.254 - 0.203) / (p_hat * (1 - p_hat) * (1/n1 + 1/n2))

Based on the given information, we can set up the hypotheses as follows:

Null hypothesis: p1 - p2 = 0
Alternative hypothesis: p1 - p2 > 0

where p1 represents the proportion of successes in the first population and p2 represents the proportion of successes in the second population.

Since the sample sizes are large (n1 and n2 are not given, but we can assume they are large enough for the normal approximation to hold), we can use the normal distribution to approximate the sampling distribution of the difference in sample proportions.

The test statistic for this sample can be calculated as follows:

z = (p1 - p2) / sqrt(p_hat * (1 - p_hat) * (1/n1 + 1/n2))

where p_hat = (x1 + x2) / (n1 + n2), x1 and x2 are the number of successes in the two samples respectively.

Plugging in the given values, we get:

p_hat = (0.254n1 + 0.203n2) / (n1 + n2)
z = (0.254 - 0.203) / sqrt(p_hat * (1 - p_hat) * (1/n1 + 1/n2))

Since the significance level is not given, we cannot determine the critical value for the test. However, we can use the test statistic to calculate the p-value for the test, which is the probability of observing a difference in sample proportions as extreme as the one we observed (or more extreme) under the null hypothesis.

Once we have the p-value, we can compare it to the significance level to make a decision about whether to reject or fail to reject the null hypothesis.

Note: It is important to mention that using the normal approximation without the continuity correction may not always be accurate, especially when the sample sizes are small or the proportion of successes is close to 0 or 1. In such cases, it is recommended to use other methods (such as exact tests or simulation) that do not rely on the normal approximation.

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Which of the following statements is false concerning the hypothesis testing procedure for a regression model?The F-test statistic is used.An α level must be selected.The null hypothesis is that the true slope coefficient is equal to zero.The null hypothesis is rejected if the adjusted r2 is above the critical value.The alternative hypothesis is that the true slope coefficient is not equal to zero.

Answers

The statements that is false concerning the hypothesis testing procedure for a regression model is "The null hypothesis is rejected if the adjusted r2 is above the critical value".

The statement that the null hypothesis is rejected if the adjusted r2 is above the critical value is false concerning the hypothesis testing procedure for a regression model.

The F-test statistic is used to test the overall significance of the regression model, and an α level must be selected to determine the level of significance.

The null hypothesis is that the true slope coefficient is equal to zero, which means that there is no linear relationship between the dependent variable and the independent variable.

The alternative hypothesis is that the true slope coefficient is not equal to zero, which means that there is a linear relationship between the dependent variable and the independent variable.

The adjusted R-squared value is a measure of the goodness of fit of the regression model and represents the proportion of the variation in the dependent variable that is explained by the independent variable(s) in the model.

The null hypothesis is rejected if the F-test statistic is above the critical value, which indicates that the regression model is statistically significant and the independent variable(s) have a significant linear relationship with the dependent variable.

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Find the standard equation of the sphere that has the point (5,−1,6) and (2,−2,−4) as endpoints of a diameter. Center of the Sphere is (If necessary, write your answer as a decimal.) Radius of the Sphere is Equation of the Sphere is

Answers

The radius of the sphere is approximately 5.22. The equation of the sphere is x^2 + y^2 + z^2 - 7x + 3y - 2z = 14.6784.

To find the centre of the sphere, we first need to find the midpoint of the diameter. Using the midpoint formula, we have:
Midpoint = ((5+2)/2, (-1-2)/2, (6+(-4))/2) = (3.5, -1.5, 1)
Therefore, the centre of the sphere is (3.5, -1.5, 1).
To find the radius of the sphere, we need to find the distance between the centre and one of the endpoints of the diameter. Using the distance formula, we have:
r = √[(5-3.5)^2 + (-1-(-1.5))^2 + (6-1)^2] = √[(1.5)^2 + (0.5)^2 + (5)^2] = √(27.25) ≈ 5.22
Therefore, the radius of the sphere is approximately 5.22.
The standard equation of a sphere with centre (h,k,l) and radius r is:
(x-h)^2 + (y-k)^2 + (z-l)^2 = r^2
Plugging in the values we found, we have:
(x-3.5)^2 + (y-(-1.5))^2 + (z-1)^2 = (5.22)^2
Expanding and simplifying, we get:
x^2 - 7x + 12.25 + y^2 + 3y + 2.25 + z^2 - 2z + 1 = 27.3284
Rearranging and simplifying further, we get:
x^2 + y^2 + z^2 - 7x + 3y - 2z = 14.6784
Therefore, the equation of the sphere is x^2 + y^2 + z^2 - 7x + 3y - 2z = 14.6784.

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Question 2: Binomial Distribution (50 Points) Supposed on a particular day you have made B digital bank transactions using your mobile phone app. Let the random variable X denotes the number of failed digital bank transactions while using your phone app. If the probability of a failing transaction is A/20 and transactions are independent from each other, answer the following questions: a) What is the probability distribution of X? (10 points) b) Find P(X SA). (10 points) c) Find P( XA). (10 points) d) What is the expected value and variance of X? (10 points) e) Find P[X = (A+1) X2 A). (10 points)

Answers

We can substitute these expressions into the conditional probability formula to get the desired probability.

a) The probability distribution of X is a binomial distribution with parameters B and p = A/20, denoted by X ~ Bin(B, A/20).

b) P(X ≤ A) can be calculated using the cumulative distribution function (CDF) of the binomial distribution:

P(X ≤ A) = F(A; B, A/20) = Σ(k=0 to A) (B choose k) * (A/20)^k * (1 - A/20)^(B-k)

where (B choose k) denotes the binomial coefficient "B choose k". Alternatively, we can use software or a binomial probability table to find the probability directly.

c) P(X > A) can be found by subtracting P(X ≤ A) from 1:

P(X > A) = 1 - P(X ≤ A)

d) The expected value and variance of X can be calculated using the formulae for the mean and variance of a binomial distribution:

E(X) = Bp = B(A/20)

Var(X) = Bp(1-p) = B(A/20)(1 - A/20)

e) P(X = (A+1) | X < 2A) can be found using the conditional probability formula:

P(X = (A+1) | X < 2A) = P(X = (A+1) and X < 2A) / P(X < 2A)

We can simplify this expression by noting that P(X = (A+1) and X < 2A) = P(X = (A+1)), since if X is greater than (A+1), it cannot be less than 2A. Therefore, we can write:

P(X = (A+1) | X < 2A) = P(X = (A+1)) / P(X < 2A)

Using the formula for the probability mass function (PMF) of the binomial distribution, we can find P(X = (A+1)):

P(X = (A+1)) = (B choose (A+1)) * (A/20)^(A+1) * (1 - A/20)^(B-(A+1))

Similarly, we can use the CDF of the binomial distribution to find P(X < 2A):

P(X < 2A) = F(2A-1; B, A/20) = Σ(k=0 to 2A-1) (B choose k) * (A/20)^k * (1 - A/20)^(B-k)

Finally, we can substitute these expressions into the conditional probability formula to get the desired probability.

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You take out a compound interest loan of $200,000 at 6% annual interest to pay off your house. The period is 30 years. What payment is required each month?

Answers

The required monthly payment for this compound-interest loan is approximately $1,199.10.

Calculating the monthly payment for a compound-interest loan, you will need to use the following formula:

Monthly Payment = [tex]P (r  (1 + r)^n) / ((1 + r)^n - 1)[/tex]

Where:
P, principal amount = $200,000
r, monthly interest rate = annual rate / 12
n, total number of payments = 30 years × 12 payments per year

For this loan:
P = $200,000
Annual Rate = 6% = 0.06
Monthly Rate (r) = 0.06 / 12 = 0.005
Number of Payments (n) = 30 * 12 = 360

Now, putting in the values into the formula:

Monthly Payment = 200,000 × (0.005 × [tex](1 + 0.005)^{360}) / ((1 + 0.005)^{360} - 1)[/tex]
Calculating this, you get:

Monthly Payment ≈ $1,199.10

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You invest $200 every quarter for 20 years in an annuity that pays 5% interest compounded quarterly. What is the final value of the annuity?

Answers

The final value of the annuity after 20 years of quarterly payments at a 5% interest rate compounded quarterly is:

$29,238.49.

To calculate the final value of the annuity, we can use the formula:

FV = P * ((1 + r/n)^(n*t) - 1) / (r/n)

Where:
FV = Final value of the annuity
P = Quarterly payment ($200)
r = Annual interest rate (5%)
n = Number of compounding periods per year (4)
t = Number of years (20)

Plugging in the values, we get:

FV = 200 * ((1 + 0.05/4)^(4*20) - 1) / (0.05/4)
FV = $29,238.49

Therefore, the final value of the annuity after 20 years of quarterly payments at a 5% interest rate compounded quarterly is equal to $29,238.49.

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This sentence is from the passage.
"With an estimated 100 billion galaxies in the universe,
each outfitted with some 100 billion to 200 billion
stars, we have a stellar inventory of 10 far-flung suns:
so many stars to yearn toward, so many ways to get
lost in the dark." (Paragraph 5)
What does the comment "so many stars to yearn
toward, so many ways to get lost in the dark" suggest
about efforts to understand the universe?
1. Trying to understand the universe is unlikely
to produce any meaningful results.
O2. Trying to understand the universe is as
tempting to human curiosity as it is daunting.
3. Trying to understand the universe should
begin with getting an accurate count of the
number of stars.
O4. Trying to understand the universe should
become easier when humans are able to
travel greater distances in space.

Answers

The meaning of the statement is : Trying to understand the universe is as tempting to human curiosity as it is daunting. Option 2

How to explain the phrase

The use of "so many stars to yearn toward" suggests a multitude of stars existing in the universe, sparking fascination amongst humankind. Herein lies an implication of our innate desire for exploration and comprehension of the cosmos, urging us to seek knowledge about countless celestial bodies.

Yet, the phrase "so many ways to get lost in the dark" hints at the vastness of the universe, teeming with infinite stellar objects that present significant challenges in their study and analysis. It is this immense scope that gives rise to the difficulty of bridging the gaps in our understanding of space.

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Algebra Tina had $145. She spent $40 on fruit at the farmer's market. Solve the equation 40+ c = 145 to find the amount Tina has left ​

Answers

Okay so since the equation is 40+c=145 you take 40 from the left side and subtract it from 145, this will get you an answer of 105 so c (the amount she has left) is $105

Q2 + Let S be the part of the hyperbolic paraboloid z = x2-y located between the cylinders x² + y2 = 1 and x2 + y2 = 25. Calculate the area of the surfaces

Answers

Therefore, the area of the surface S is approximately 1.14 square units.

Here We can parametrize the  hyperbolic-paraboloid surface S as follows:

r(u,v) = (u, v, [tex]u^2[/tex] - v)

Here u is restricted to the interval [−1, 1] and v is restricted to the interval [−5, 5].

The area of the surface, we need to compute the magnitude of the cross product of the partial derivatives of r with respect to u and v:

|ru x rv| = |(1, 0, 2u) x (0, 1, -1)| = |(2u, 1, 0)| = [tex]\sqrt{(4u^2 + 1)}[/tex]

Therefore, the area of the surface is given by the double integral:

A = ∬S dS = ∫[tex]-5^5 * -1^1 \sqrt{ (4u^2 + 1)}[/tex] du/dv

We can evaluate this integral by making the substitution w = [tex]2u^2 + 1,[/tex] ,which gives:

A = ∫[tex]1^2 *1/4 \sqrt{w} dw[/tex]

= [tex](2/3) * w^{({3/2)}} |1^2 *1/4[/tex]

= [tex](2/3)(2 * \sqrt{5} - 1)[/tex]

So the area of the surface S is approximately 1.14 square units.

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A soccer player has a large cylindrical water cooler that measures 2.5 feet in diameter and is 5 feet tall. If there are approximately 7.48 gallons of water in a cubic foot, how many gallons of water are in the water cooler when it is completely full? Use π = 3.14 and round to the nearest hundredth.

98.13 gallons
733.98 gallons
24.53 gallons
183.49 gallons

Answers

The volume in gallons of the water cooler is 183.49 gallons

How many gallons of water are in the water cooler when it is completely full?

We know that the volume of a cylinder of radius R and height H is.

V = pi*R²*H

Where pi = 3.14

Here we know that the diameter is 2.5 ft, then the radius is:

R = 2.5ft/2 = 1.25ft

And the height is 5ft

So the volume is:

V = 3.14*(1.25ft)²*5ft = 24.53125 ft³

And we know that

1ft³ =  7.48 gallons

Then we can do a change of units to get:

24.53125*7.48 gal = 183.49 gal

That is the correct option.

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the table shows information about masses of some dogs work at the minimum and maximum auto dogs that have a more 27kg

Answers

The minimum number of dogs that have more than 27 kg is 4, and the maximum number of dogs that have more than 27 kg is 26.

We have,

To determine the minimum and maximum number of dogs that have more than 27 kg, we need to first find the cumulative frequency for the mass data.

Mass(x)     frequency   Cumulative frequency

0 ≤ x ≤10    3                 3

10 ≤ x ≤20 9                 12

20 ≤ x ≤ 30 13                25

30 ≤ x ≤ 40 4                29

Now, we can see that there are a total of 29 dogs.

To find the minimum and maximum number of dogs that have more than 27 kg, we can use the cumulative frequency table as follows:

The minimum number of dogs that have more than 27 kg is the frequency of dogs in the 30 ≤ x ≤ 40 category, which is 4.

The maximum number of dogs that have more than 27 kg is the total number of dogs minus the cumulative frequency for the 0 ≤ x ≤ 27 category, which is 3.

Now,

The maximum number of dogs that have more than 27 kg is:

29 - 3 = 26.

Thus,

The minimum number of dogs that have more than 27 kg is 4, and the maximum number of dogs that have more than 27 kg is 26.

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Use Wallis's Formulas to evaluate the integral.

∫ cos^7 (x) dx

Answers

The value of the integral ∫ [tex]cos^7(x) dx[/tex] is[tex](3\pi /32).[/tex]

Wallis's formulas are used to evaluate integrals of the form:

∫ [tex]sin^{n(x)} cos^{m(x)} dx[/tex]

where n and m are non-negative integers. We can use the trigonometric identity[tex]cos^{2(x)] + sin^{2(x)} = 1[/tex] to convert the powers of cosine to powers of sine.

Here, we have m = 7, so we can use the identity [tex]cos^{2(x)} = 1 - sin^{2(x)}[/tex] to write:

[tex]cos^{7(x)} = cos^{6(x)}[/tex] × [tex]cos(x)[/tex]

[tex]= (1 - sin^2(x))^3[/tex] ×[tex]cos(x)[/tex]

Now, we can use a substitution of [tex]u = sin(x), du = cos(x) dx[/tex]to convert the integral to a form that can be evaluated using Wallis's formulas:

∫ [tex]cos^7(x) dx =[/tex] ∫ [tex](1 - sin^2(x))^3[/tex] × [tex]cos(x) dx[/tex]

= ∫ [tex](1 - u^2)^3 du[/tex]

Using Wallis's formulas, we have:

∫ [tex](1 - u^2)^3 du = (1/8)[/tex]× β[tex](4, 4)[/tex]

[tex]= (1/8)[/tex] ×[tex][(3\pi /4) / sin(3\pi /4)][/tex]

[tex]= (3\pi /32)[/tex]

Substituting [tex]u = sin(x)[/tex], we have:

∫ [tex]cos^7(x) dx =[/tex] ∫ [tex](1 - u^2)^3 du = (3π/32)[/tex]

Therefore, the value of the integral ∫ [tex]cos^7(x) dx[/tex] is [tex](3\pi /32).[/tex]

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(question/equation in the photo) PLEASE PLEASE HELP ITS DUE TMR ​

Answers

Answer:

The perimeter of the quarter circle is 24.997 cm

Step-by-step explanation:

Given, the radius of the circle = 7 cm

The perimeter of the circle = 2πr

and perimeter of the quarter circle = 2r + C

where r is the radius and C is the circumference of the sector of a circle

Circumference of the sector =  ∅/360°(2πr)

                                           C  = 90°/360°(2×3.142×7)

                                            C = 10.997 cm

perimeter of the quarter circle = 2r + C  

                                                   = 2×7 + 10.997

                                                   = 24.997 cm

The perimeter of the quarter circle will be 24.997 cm

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Marcus is 5 7 /24 feet tall. Ben is 5 13/ 16 feet tall. Which of the two boys is taller? Give your answer and complete the justification using decimal representations of the mixed numbers. Round decimal entries to four decimal places.

Answers

The taller of the two boys is Ben if Marcus is 5 7 /24 feet tall and Ben is 5 13/ 16 feet tall.

Which of the two boys is taller?

From the question, we have the following parameters that can be used in our computation:

Marcus is 5 7 /24 feet tall. Ben is 5 13/ 16 feet tall.

This means that

Marcus = 5 7 /24 feet tall

Ben = 5 13/ 16 feet tall.

Express the heights as decimals

So, we have

Marcus = 5.292 feet tall

Ben = 5.8125 feet tall.

When the above values are compared, we have

5.8125 feet tall > 5.292 feet tall

Hence, the taller of the two boys is Ben

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Which value Makes the equation true 64/100=6/10+?/100
A.4 B.6 C.40 D.58

Answers

The value that makes the equation true is A. 4.

What is a fraction?

A fraction is a given number expressed as it numerator divided by its denominator. For example; a/b where a is the numerator and b is the denominator. The types of fraction are: proper, improper and mixed fractions.

In the given question, let the required value be represented by t.

So that;

64/100 = 6/10 + t/100

find the LCM, to have;

64/100 = (60 + t)/100

cross multiply

100*64 = 100*(60 + t)

divide through by 100,

64 = 60 + t

t = 64 - 60

 = 4

t = 4

The value that makes the equation true is A. 4.

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Elyssa has 4 cups of popcorn for her movie party. She puts 1/3 of a cup of popcorn into each bag for her guests. If she has 10 people at the party, will she have enough popcorn for everyone? Explain?

Answers

Answer:

Yes.

Step-by-step explanation:

Elyssa has a total of 4 cups of popcorn for her party. She is putting 1/3 of a cup of popcorn into each bag for her guests.

To find out if she has enough popcorn for everyone, we need to calculate how much popcorn will be needed for all 10 guests.

If each guest gets 1/3 of a cup of popcorn, then for 10 guests, Elyssa will need:

(1/3) x 10 = 10/3 = 3 1/3 cups of popcorn

However, Elyssa only has 4 cups of popcorn. Since 4 cups is greater than 3 1/3 cups, Elyssa will have enough popcorn for all of her guests.

Therefore, Elyssa will have enough popcorn for everyone at her party.

Consider the utility function U = 29192 + 92 to: a) Construct ordinary and compensated demand functions for Q1. (5 points) b) Construct the indirect utility function. (3 points) c) Apply Roy's identity to derive the demand for Q1. (2 points) II. Consider an Industry with 3 identical firms in which the ith firm's total cost function is C = aq + bqiq (i= 1,...,3, where q = -191. Derive the industry's supply function. (10 points) =

Answers

The industry's supply function for 3 identical firms with total cost function C=aq+bq^2 and q=-191 is: Qs = -1/6b - 1/3a - 191/6.

What is indirect utility function?

The indirect utility function is a mathematical function that expresses the maximum utility that a consumer can achieve, given a certain level of income and prices of goods and services

a) The ordinary demand function for Q1 is obtained by maximizing U with respect to Q1 subject to the budget constraint. Let p1 be the price of Q1, and let M be the consumer's income. Then the budget constraint is given by:

p1Q1 + M = 0

Solving for Q1, we get:

Q1 = -M/p1

Substituting this into U, we get:

U = 29192 + 92(-M/p1)

To obtain the ordinary demand function for Q1, we differentiate U with respect to p1 and solve for Q1:

dU/dp1 = -92M/p1^2

Setting this equal to the price of Q1, we get:

p1 = 92M/Q1^2

Solving for Q1, we get the ordinary demand function for Q1:

Q1 = sqrt(92M/p1)

The compensated demand function for Q1 is obtained by finding the cost of maintaining the consumer's utility level after a change in the price of Q1. This is given by:

C(Q1',p1,U) = min{p1Q1' + p2Q2 : U(Q1',Q2) = U}

where p2 is the price of some other good, and U(Q1',Q2) is the utility function with Q1' replacing Q1.

The compensated demand function for Q1 is then obtained by differentiating C with respect to p1 and solving for Q1:

dC/dp1 = -Q1'

Setting this equal to the price of Q1, we get:

p1 = -dC/dQ1' = -d/dQ1'(p1Q1' + p2Q2)

Solving for Q1', we get the compensated demand function for Q1:

Q1' = (p1/p2)Q2

b) The indirect utility function is given by:

V(p1,p2,M) = max{U(Q1,Q2) : p1Q1 + p2Q2 = M}

Using the utility function U = 29192 + 92, the budget constraint p1Q1 + p2Q2 = M, and the ordinary demand function for Q1, we can solve for the indirect utility function:

V(p1,p2,M) = U(Q1(p1,p2,M),Q2(p1,p2,M)) = 29192 + 92(Q1(p1,p2,M))

Substituting the ordinary demand function for Q1 into this equation, we get:

V(p1,p2,M) = 29192 + 92(sqrt(92M/p1))

c) Roy's identity states that the derivative of the indirect utility function with respect to the price of a good gives the compensated demand function for that good:

dV/dp1 = Q1'

Using the indirect utility function derived in part b, we can solve for the demand function for Q1:

dV/dp1 = 92M/(p1^2 sqrt(92M/p1)) = Q1'

Simplifying, we get:

Q1' = 92sqrt(92M/p1)

II. The industry's supply function is obtained by adding the output of each firm at a given price level:

Q = Q1 + Q2 + Q3

where Qi is the output of the ith firm. To find the output of each firm, we need to solve for the profit-maximizing level of output:

πi = piqi - Ci(qi)

where πi is the profit of the ith firm, pi is the price of the good, qi is the output of the ith firm, and Ci

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Complete Question:

I. Consider the utility function U(Q1) = 29192 + 92Q1, where Q1 is the quantity consumed of a certain good.

a) Construct the ordinary and compensated demand functions for Q1.

b) Construct the indirect utility function.

c) Apply Roy's identity to derive the demand for Q1.

II. Consider an industry with 3 identical firms in which the ith firm's total cost function is C = aq + bq^2 (i=1,...,3), where q is the quantity produced by the firm and a, b are positive constants. The market demand curve is given by Qd = 200 - 2P, where Qd is the total quantity demanded in the market and P is the market price. Each firm takes the market price as given.

Derive the industry's supply function.

Please note that the point values given in the original prompt are also included for reference.

Select the degree of this equation. 3x² + 5x = 2 . A. 1st degree B. 2nd degree C. 3rd degree D. 4th degree E. 5th degree​

Answers

Answer:

b) 2nd degree

Step-by-step explanation:

Degree of the polynomial:

     Highest exponent of the variable x, is the degree of the polynomial.

 Highest power is 2. So the degree is 2.

(1 point) Use the ratio test to determine whether ? + 2 converges or diverges (a) Find the ratio of successive terms. Write your answer as a fully simplified fraction. For n 2 11. +! lim = lim 00 00 (b) Evaluate the limit in the previous part. Enter co as infinity and -20 as -infinity. If the limit does not exist, enter DNE. Lim a. (c) By the ratio test, does the series converge, diverge, or is the test Inconclusive? Choose 00 (1 point) For the following alternating series, Σα, = 0. 45 - (0. 45) (0. 45) (0. 45) 31 +. 5! 7! how many terms do you have to compute in order for your approximation your partial sum) to be within 0. 0000001 from the convergent value of that series?

Answers

To ensure that the error is less than 0.0000001, we need to compute at least the first 6 terms of the series. This will give us a partial sum that is within 0.0000001 of the actual sum.

(a) The ratio of successive terms of the series is:

[tex]|a[n+1]/a[n]| = |(-1)^(n+1)*(n+2)/(n+1)(1/2)|[/tex]

Simplifying this expression, we get:

[tex]|a[n+1]/a[n]| = (n+2)/(2(n+1))[/tex]

(b) To evaluate the limit of this expression as n approaches infinity, we can divide the numerator and denominator by n:

[tex]|a[n+1]/a[n]| = [(n/n)(1+2/n)] / [(2/n)(1+1/n)][/tex]

Taking the limit as n approaches infinity, we get:

[tex]lim n- > ∞ |a[n+1]/a[n]| = lim n- > ∞ [(n/n)(1+2/n)] / [(2/n)(1+1/n)[/tex]]

= 1/2

Therefore, the limit of the ratio of successive terms is 1/2.

(c) Since the limit of the ratio of successive terms is less than 1, by the ratio test, the series ? + 2 converges.

To approximate the alternating series Σα, = 0. 45 - (0. 45) (0. 45) (0. 45) 31 +. 5! 7! within 0.0000001 of the convergent value, we need to determine how many terms of the series we need to compute. We can use the alternating series error bound theorem to estimate the error:

|Rn| <= |an+1|

where Rn is the error term (the difference between the nth partial sum and the actual sum), and an+1 is the first neglected term in the series.

To find the first neglected term, we can look at the pattern of the series:

a0 = 0.45

a1 = -0.2025

a2 = 0.025641

a3 = -0.0007716

a4 = 0.00003857

a5 = -0.00000298

The absolute value of the terms is decreasing, so the error is bounded by the absolute value of the first neglected term. In this case, the first neglected term is a6 = 0.00000025.

Therefore, to ensure that the error is less than 0.0000001, we need to compute at least the first 6 terms of the series. This will give us a partial sum that is within 0.0000001 of the actual sum.

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Solve the integral equations: (a) t - 2f(2)= S e---)f(t – 7)dt (b) f(t) = cost + Stef(t – T)dt = е

Answers

(a) The is the solution to the integral equation is:

f(t) = (t-2)/2 + (1/2) e^(7-t) f(t-7) - (1/2) S e^(7-t) f'(t-7) dt

(b) The is the solution to the integral equation is:

f(t) = L^-1[F(s)] = (1/2) sin(t) + (1/2) cos(t-T) u(t-T)
where u(t-T) is the unit step function.

To solve integral equations, we need to use techniques such as integration by substitution or integration by parts. Let's start with the given equations:

(a) t - 2f(2)= S e---)f(t – 7)dt

To solve this integral equation, we need to integrate the function on the right-hand side with respect to t. Let u = t - 7, then du = dt. The integral becomes:

S e---)f(t – 7)dt = S e---)f(u)du

We can then apply integration by parts, using u = f(u) and dv = e^-u du, which gives us:

S e^-u f(u) du = -e^-u f(u) + S e^-u f'(u) du

Substituting back in for u, we get:

S e---)f(t – 7)dt = -e^(7-t) f(t-7) + S e^(7-t) f'(t-7) dt

Now we can substitute this into the original equation:

t - 2f(2) = -e^(7-t) f(t-7) + S e^(7-t) f'(t-7) dt

To solve for f(t), we need to isolate it on one side of the equation. Rearranging, we get:

f(t) = (t-2)/2 + (1/2) e^(7-t) f(t-7) - (1/2) S e^(7-t) f'(t-7) dt

This is the solution to the integral equation (a).

(b) f(t) = cost + Stef(t – T)dt = е

To solve this integral equation, we can take the derivative of both sides with respect to t. Using the chain rule, we get:

f'(t) = -sinf(t) + s e^(-T) f(t-T)

Now we can substitute this back into the original equation:

f(t) = cost + S e^(-T) f(t-T)dt

To solve for f(t), we need to isolate it on one side of the equation. Rearranging, we get:

f(t) - S e^(-T) f(t-T) = cost

Now we can take the Laplace transform of both sides of the equation:

L[f(t) - S e^(-T) f(t-T)] = L[cos(t)]

Using the properties of the Laplace transform, we get:

F(s) - e^(-Ts) F(s) e^(-Ts) = s/(s^2 + 1)

Simplifying, we get:

F(s) = s/(s^2 + 1) / (1 - e^(-Ts))

Now we can take the inverse Laplace transform to get the solution to the integral equation:

f(t) = L^-1[F(s)] = (1/2) sin(t) + (1/2) cos(t-T) u(t-T)

where u(t-T) is the unit step function. This is the solution to the integral equation (b).

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If the diameter of a circle is 8.4 in., find the area and the circumference of the circle. Use 3.14 for pi. Round your answers to the nearest hundredth.

Answers

Answer:

Area of the circle = 55.39 in²

Circumference of the circle = 26.38 in

Step-by-step explanation:

Given, the diameter of the circle = 8.4

so the radius is given by the formula

∴ d = 2r

→ 8.4 = 2×r

→r=4.2 in      [i]

Area of the circle = π×r²     [ii]

substituting the value of r in equation [ii]

we get,

area of circle = 3.14×(4.2)²

                      =55.39 in²

                     

circumference of the circle =2πr     [iii]

substituting the value of r in equation [iii]

we get,

circumference of the circle = 2×3.14×4.2

                                             = 26.38 in

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