What is the value of x?

Answer: 1

Step-by-step explanation:

3(x-2) = 4x+2

3x-6 = 4x+2

To move 3x, deduct it on both sides of the equation.

3x - 6 - (3x) = 4x + 2 - (3x)

0 - 6 = [1]x +2

Given:-

[tex] \: [/tex]

Solution:-

[tex] \: [/tex]

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[tex] \: [/tex]

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hope it helps ⸙

Kim Chung owes $176 in federal income taxes.

What is the interest?

In finance, interest refers to the fee that a borrower pays to a lender for the use of money or assets. It is a cost of borrowing money, usually expressed as a percentage of the principal amount borrowed (or invested).

To calculate the federal income tax owed by Kim Chung, we need to first determine his taxable income.

Kim Chung's taxable income is calculated as follows:

Total Income = $2,897 (wages) + $57 (interest) = $2,954

Adjustments = $0

Adjusted Gross Income (AGI) = Total Income - Adjustments = $2,954 - $0 = $2,954

Since Kim Chung's parents claim him as a dependent, his standard deduction for tax year 2022 is $1,150.

Taxable Income = AGI - Standard Deduction = $2,954 - $1,150 = $1,804

To determine the federal income tax owed, we need to use the tax tables provided by the IRS for tax year 2022.

According to the tax tables, the tax on $1,804 of taxable income is $176.

Therefore, Kim Chung owes $176 in federal income taxes.

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Answer:

x=36

y=6

system of equations

A professional golfer to make about 40.7 holes over 5 rounds of golf with the new club, while an amateur golfer would only make about 1.6.

First, let's define some variables to represent the probabilities of making a hole for a professional golfer and an amateur golfer:

Let p be the probability that a professional golfer makes a hole with the new club.

Let q be the probability that an amateur golfer makes a hole with the new club.

According to the company's claims, we know that:

p = 1.2q (since the professional golfer makes a hole 120% of the time, which is 1.2 times the probability of the amateur golfer making a hole)

Next, we need to determine the probability of each golfer making a hole during one round of golf, which consists of 18 holes. Let's assume that each hole is independent of the others, meaning that the outcome of one hole does not affect the outcome of another. In that case, the probability of making at least one hole in a round can be calculated using the complement rule:

The probability that a professional golfer makes at least one hole in a round is 1 minus the probability that the golfer misses every hole: [tex]1 - (1-p)^{18} .[/tex]

The probability that an amateur golfer makes at least one hole in a round is[tex]1 - (1-q)^{18} .[/tex]

Now, let's use these probabilities to calculate the expected number of holes each golfer will make in 5 rounds of golf:

The expected number of holes made by a professional golfer in 5 rounds is 5 times the expected number of holes made in one round, which is [tex](1 - (1-p)^{18} )\times18.[/tex]

The expected number of holes made by an amateur golfer in 5 rounds is 5 times the expected number of holes made in one round, which is [tex](1 - (1-q)^{18} )\times18.[/tex]

We can simplify these expressions using the relationship between p and q:

The expected number of holes made by a professional golfer in 5 rounds is [tex]518(1 - (1-1.2q)^{18} ).[/tex]

The expected number of holes made by an amateur golfer in 5 rounds is [tex]518(1 - (1-q)^{18} ).[/tex]

We can now evaluate these expressions using the values of p and q:

[tex]p = 1.2q, so q = p/1.2[/tex]

Substituting this into the expressions above, we get:

The expected number of holes made by a professional golfer in 5 rounds is[tex]518(1 - (1-1.2(p/1.2))^{18} ) = 518(1 - (1-p)^{18} ).[/tex]

The expected number of holes made by an amateur golfer in 5 rounds is [tex]518(1 - (1-p/1.2)^{18} ).[/tex]

Finally, we can evaluate these expressions using the given probabilities:

The expected number of holes made by a professional golfer in 5 rounds is[tex]518(1 - (1-1.2q)^{18} ) = 518(1 - (1-1.2(0.1))^{18} ) = 40.7.[/tex]

The expected number of holes made by an amateur golfer in 5 rounds is [tex]518(1 - (1-q)^{18} ) = 518(1 - (1-0.1/1.2)^{18} ) = 1.6.[/tex]

So according to these calculations, we would expect a professional golfer to make about 40.7 holes over 5 rounds of golf with the new club, while an amateur golfer would only make about 1.6

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(a) The probability that X = n is 2^n-1 / 2^N - 1.

(b) ɸ(t) = E[2^tx] = ∑_{n=1}^N 2^tx P(X=n) = ∑_{n=1}^N 2^tx (2^n-1 / 2^N - 1) = (2^t / 2^N - 1) ∑_{n=1}^N 2^(n-1)t = (2^t / 2^N - 1) (2^Nt - 1) / (2^t - 1) = 2^Nt / (2^N - 1)

(c) The probability that X = n and Y = m is 2^(n-m-1) / 2^N - 1.

(d) This is the same as finding the probability that the difference between the maximum and minimum elements of a subset of {1,...,N} is k. If k = 0, then the only subsets with maximum and minimum elements differing by k are the single-element subsets, so P(W=k) = N / 2^N - 1. If k > 0, then there are (N-k) choices for the minimum element m and 2^(k-1) subsets of {m+1,...,m+k-1}, so P(W=k) = (N-k) 2^(k-1) / 2^N - 1.

To find the probability mass function of X, we need to find the probability that X = n for each n ∈ {1,...,N}. This is the same as finding the probability that the maximum element of a subset of {1,...,N} is n. There are 2^n-1 subsets of {1,...,n-1}, and each of these subsets can be combined with n to form a subset of {1,...,N} with maximum element n. Therefore, the probability that X = n is 2^n-1 / 2^N - 1.

To find the value of ɸ(t) for any t ∈ R, we need to compute the expected value of 2^tx. Using the formula for expected value, we get:

ɸ(t) = E[2^tx] = ∑_{n=1}^N 2^tx P(X=n) = ∑_{n=1}^N 2^tx (2^n-1 / 2^N - 1) = (2^t / 2^N - 1) ∑_{n=1}^N 2^(n-1)t = (2^t / 2^N - 1) (2^Nt - 1) / (2^t - 1) = 2^Nt / (2^N - 1)

To find the joint probability mass function of (X,Y), we need to find the probability that X = n and Y = m for each n,m ∈ {1,...,N}. If n = m, then the only subset of {1,...,N} with maximum element n and minimum element m is {n}, so P(X=n, Y=m) = 1 / 2^N - 1. If n ≠ m, then there are 2^(n-m-1) subsets of {m+1,...,n-1}, and each of these subsets can be combined with m and n to form a subset of {1,...,N} with maximum element n and minimum element m. Therefore, the probability that X = n and Y = m is 2^(n-m-1) / 2^N - 1.

To find the probability mass function of W = X - Y, we need to find the probability that W = k for each k ∈ {0,...,N-1}. This is the same as finding the probability that the difference between the maximum and minimum elements of a subset of {1,...,N} is k. If k = 0, then the only subsets with maximum and minimum elements differing by k are the single-element subsets, so P(W=k) = N / 2^N - 1. If k > 0, then there are (N-k) choices for the minimum element m and 2^(k-1) subsets of {m+1,...,m+k-1}, so P(W=k) = (N-k) 2^(k-1) / 2^N - 1.

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Answer:

7 and 4

Step-by-step explanation:

take away 3 each time so

10-3=7

7-3=4

The solution of the inequaltiy is v <= 6 or v >= 2.

To solve the compound inequality 4v+3<=27 or 2v-4>=0, we need to solve each inequality separately and then combine the solutions.

For the first inequality, 4v+3<=27, we can isolate the variable on one side of the inequality by subtracting 3 from both sides:

4v <= 24

Next, we can divide both sides by 4 to get:

v <= 6

For the second inequality, 2v-4>=0, we can isolate the variable on one side of the inequality by adding 4 to both sides:

2v >= 4

Next, we can divide both sides by 2 to get:

v >= 2

Now, we can combine the solutions to get the final solution for the compound inequality:

v <= 6 or v >= 2

This means that the solution set includes all values of v that are less than or equal to 6 or greater than or equal to 2.

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The total number of months he made deposits and multiply that by the monthly deposit amount.

Chase started an IRA at the age of 26 and deposited $400 each month until he retired at the age of 65. To determine the amount of money Chase deposited over the length of the investment, we need to calculate the total number of months he made deposits and multiply that by the monthly deposit amount.

Number of months = (Retirement age - Starting age) * 12
Number of months = (65 - 26) * 12
Number of months = 468

Total deposits = Number of months * Monthly deposit amount
Total deposits = 468 * 400
Total deposits = $187,200

To determine how much Chase made in interest upon retirement, we need to subtract the total deposits from the retirement savings.

Interest = Retirement savings - Total deposits
Interest = $838,879.58 - $187,200
Interest = $651,679.58

Therefore, Chase deposited a total of $187,200 over the length of the investment and made $651,679.58 in interest upon retirement.

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airplane A

To compare the rate of speed of Airplane A and Airplane B, we need to calculate the speed of Airplane B first.

The formula to calculate distance is:

distance = rate x time

For Airplane A, we know:

distance = 1662 miles

time = 6 hours

So, we can rearrange the formula to solve for the rate:

rate = distance / time = 1662 / 6 = 277 miles per hour

For Airplane B, we know:

y = 922/3

x = rate of speed over 6 hours

We can use the formula to solve for x:

distance = rate x time

922/3 = x * 6

x = (922/3) / 6 = 153.67 miles per hour

Comparing the rates of the two airplanes, we can see that Airplane A traveled at a faster rate with 277 miles per hour compared to Airplane B's rate of 153.67 miles per hour. Therefore, Airplane A traveled at a faster rate.

a) Null hypothesis: Sex and risk of a lower-extremity injury in interscholastic soccer are not related variables. Alternative hypothesis: Sex and risk of a lower-extremity injury in interscholastic soccer are related variables. So the option E is correct.

b) There is insufficient information to draw the conclusion that the variables are connected even though the value is greater than the 0.05 threshold for significance.

c) The difference between these percentage are fairly similar which suggests that sex and risk of lower-extremity Injury in  interscholastic soccer are not related.

a) The null and alternative hypotheses about sex and the risk of a lower-extremity Injury while playing interscholastic soccer is:

Null hypothesis: Sex and lower-extremity injury risk in interscholastic soccer are unrelated factors. Alternative hypothesis: sex and the likelihood of sustaining a lower-extremity injury in collegiate soccer are associated variables.

So the option E is correct.

b) The conclusion is that there is no significant relationship between the gender of the athlete and the risk of lower-extremity injuries. This conclusion is based on the fact that the chi-square statistic (1.63) and the corresponding p-value (0.202) are both greater than the 1.63 X standard for significance. This indicates that there is not enough evidence to show that the variables are related.

c) Of 997 participants in girls' soccer, 79 experienced lower-extremity injuries. Of 1,664 participants in boys' soccer, 156 experienced lower-extremity injuries.

Girls = 79/997 × 100 = 7.92%

Boys = 156/1664 × 100 = 9.38%

The difference between the two percentages is consistent with the conclusion that there is no significant relationship between the gender of the athlete and the risk of lower-extremity injuries because the difference between the two percentages is small.

This indicates that the risk of lower-extremity injuries is relatively similar for both boys and girls, which is consistent with the conclusion that there is no significant relationship between gender and the risk of lower-extremity injuries.

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The complete question is:

Researchers studied a random sample of high school students who participated in interscholastic athletics to learn about the risk of lower-extremity injuries (anywhere between hip and toe) for interscholastic athletes. Of 997 participants in girls' soccer, 79 experienced lower-extremity injuries. Of 1,664 participants in boys' soccer, 156 experienced lower-extremity injuries.

(a) Write null and alternative hypotheses about sex and the risk of a lower-extremity Injury while playing interscholastic soccer.

A. Null hypothesis: Sex and risk of a lower-extremity injury in interscholastic soccer are related variables. Alternative hypothesis: Sex and risk of a lower-extremity Injury in interscholastic soccer are not related variables.

B. Null hypothesis: Sex and risk of a lower extremity injury in interscholastic soccer are explanatory variables. Alternative hypothesis: Sex and risk of a lower-extremity injury in interscholastic soccer are not explanatory variables.

C. Null hypothesis: Sex and risk of a lower extremity injury in interscholastic soccer are not explanatory variables. Alternative hypothesis: Sex and risk of a lower-extremity injury in interscholastic soccer are explanatory variables.

D. Null hypothesis: There is a weak relationship between sex and risk of a lower-extremity injury in interscholastic soccer. Alternative hypothesis: There is a strong relationship between sex and risk of a lower-extremity injury in interscholastic soccer

E. Null hypothesis: Sex and risk of a lower-extremity injury in interscholastic soccer are not related variables. Alternative hypothesis: Sex and risk of a lower-extremity injury in interscholastic soccer are related variables.

(b) For these data, the value of the chi-square statistic is 1. 63, and the p-value for the chi-square test is 0. 202. Based on these results, state a conclusion about the two variables in this situation and explain how you came to this conclusion. The p-value is greater than the 1. 63 X standard for significance, so there is not sufficient evidence to be able to conclude that the variables are related.

(c) For each sex separately, calculate the percent of participants who had a lower-extremity injury. (Round your answers to one decimal place. ) girls 7.9% boys 9.4%. Explain how the difference between these percentages is consistent with the conclusion you stated in part (b). These percentages are fairly similar , which suggests that sex and risk of a lower-extremity injury in interscholastic soccer are not related

The two linearly independent solutions are y₁(x) = 1 - (x²/3) + (x⁴/81) - (x⁶/2187) + … and y₂(x) = x - (x³/9) + (x⁵/405) - (x⁷/21870) + ...

We can use the power series method to find the two solutions of the given differential equation:

Let y = ∑anxn be a power series solution. Then, we have:

y' = ∑nanxn-1

y'' = ∑nan(n-1)xn-2

Substituting these into the differential equation and equating coefficients of like powers of x, we get:

3x∑nan(n-1)xn-1 + ∑anxn = 0

Simplifying, we obtain:

∑[3nan(n-1) + an-1]xn = 0

Since x ≠ 0, the coefficients of like powers of x must be zero. This gives us the recurrence relation:

an = -an-1/(3n(n-1)), n ≥ 1

Using this recurrence relation and the initial condition y(0) = 1, we can find the power series solution:

y₁(x) = 1 - (x²/3) + (x⁴/81) - (x⁶/2187) + ...

To find a second linearly independent solution, we can use the method of reduction of order. Let y₂(x) = v(x)y₁(x). Then, we have:

y₂' = v'y₁ + vy₁'

y₂'' = v''y₁ + 2v'y₁' + vy₁''

Substituting these into the differential equation and simplifying, we get:

v''y1x + (2v'y1' + vy1'')x + 3vy1 = 0

Since y₁(x) is a solution, we have:

y₁'' + (1/3x)y₁ = 0

Multiplying by y1 and integrating, we obtain:

(y₁')² + y₁²/3 = C

where C is a constant of integration. Using the initial condition y₂(0) = 0, we can find the second solution:

y₂(x) = x - (x³/9) + (x⁵/405) - (x⁷/21870) + ...

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Answer: 50 total stamps = 30 Postcard Stamps + 20 Letter Stamps

Step-by-step explanation:

Postcard Stamp = Ps

Letter Stamp = Ls

Ps = 20c

Ls = 33c

50 total stamps = $12.60

50 total stamps = X Ps + Y Ls

12.60 = 30 Ps + 20 Ls

$12.60 = 30(20c) + 20(33c)

50 total stamps = 30 Postcard Stamps + 20 Letter Stamps

Answer:

You have 30 postcard stamps and 20 letter stamps.

Step-by-step explanation:

To solve this you'll need to set up a system of equations. Let's use P for postcard stamps and L for letter stamps

Remember, since the price is in cents, it'll be 0.2 and 0.33.

The equations can be in any order, this is just the order I chose.

0.2P + 0.33L = 12.60

P + L = 50

Your next step is to cancel out one of the variables to solve for the other. Let's cancel out P and solve for L. (You can switch these if you want, you'll still get the same answsrs.) Remember to multiply by a negative so the variable cancels out.

Here's what your work will look like:

0.2P + 0.33L = 12.60

-0.2(P + L = 50)

Here's what your new equations will look like after distributing:

0.2P + 0.33L = 12.60

-0.2P - 0.2L = -10

Now add these two equations together. When you do so, the P cancels out, and you can now solve for L.

Here's what your new equation will look like after adding the two equations:

0.13L = 2.6

Now, divide both sides by 0.13 to get what L equals. After doing so, you should get L = 20. This means that you have 20 letter stamps.

Your last step is to plug the value of L (which is 20) into either of your original equations to solve for how many postcard stamps you have. Let's use our second equation, P + L = 50. (You can use either original equation and get the same answer, but this one is more simpler to use.)

Here's what your work will look like:

P + 20 = 50

Subtract 20 from both sides:

P = 30. This means you have 30 postcard stamps.

Hope this helps!

The answer is 0(zero)

The remainder when dividing 4x4 - 2x2 by x3 - x2 + 1 can be found using polynomial long division.

The calculation is shown below:

Therefore, the remainder when dividing.

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The final expression after collecting terms is: 19zx^(2) - 3z^(2)x + 2z^(2)y

Explanation: To collect terms in an expression, we need to combine like terms. Like terms are terms that have the same variables with the same exponents. In the given expression, the like terms are 13zx^(2) and 6zx^(2). We can combine these terms by adding their coefficients:

13zx^(2) + 6zx^(2) = 19zx^(2)

The other terms, 2z^(2)y and -3z^(2)x, do not have any like terms, so we cannot combine them with any other terms. Therefore, the final expression after collecting terms is:

19zx^(2) - 3z^(2)x + 2z^(2)y

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Mengxi invested $4,200 in the term deposit paying 5% /year and $5,800 in Canada Savings Bonds paying 3.5% /year. The total interest earned is $413.

Let's assume that Mengxi invests x dollars in the term deposit paying 5% /year, and the remaining (10000 - x) dollars in Canada Savings Bonds paying 3.5% /year.

At the end of the year, Mengxi earns a total of $413 in simple interest. The interest earned from the investment in the term deposit is calculated as 0.05x, while the interest earned from the investment in Canada Savings Bonds is 0.035(10000 - x).

Thus, we can write the following equation to represent the total interest earned:

0.05x + 0.035(10000 - x) = 413

Simplifying the equation, we get:

0.015x + 350 = 413

0.015x = 63

x = 4200

Therefore, Mengxi invested $4,200 in the term deposit paying 5% /year, and $5,800 (10000 - 4200) in Canada Savings Bonds paying 3.5% /year.

To check the answer, we can calculate the interest earned from each investment and add them up:

0.05(4200) + 0.035(5800) = 210 + 203 = 413

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The simplified expression is u^(3) - v^(3).

To perform the indicated operation on the algebraic expressions, we need to multiply each term in the first expression by each term in the second expression and then simplify the resulting expression.

Step 1: Multiply each term in the first expression by each term in the second expression:

(u)(u^(2)) + (u)(uv) + (u)(v^(2)) - (v)(u^(2)) - (v)(uv) - (v)(v^(2))

Step 2: Simplify the resulting expression by combining like terms:

u^(3) + u^(2)v + uv^(2) - u^(2)v - uv^(2) - v^(3)

Step 3: Simplify further by canceling out terms that are equal but opposite in sign:

u^(3) - v^(3)

Therefore, the simplified expression is u^(3) - v^(3).

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Answer:

990 applicants

Step-by-step explanation:

We know

A university law school accepts 4 out of every 11 applicants.

If the school accepted 360 ​students, find how many applications they received.

To get from 4 to 360, we time 90

We take 11 times 90 = 990 applicants

So, they received 990 applicants.

According to the information, the expressions that would match the descriptions would be both expressions have the same result, so it doesn't matter which description they are associated with. both are the largest and the smallest value.

To find the correct descriptions that match the expressions we must look at the graph. In this case q and n represent two numbers on the number line. In this case, to relate them to a description we must find the number to which they refer:

In accordance with the above, we could say that the descriptions would look like this:

In this case, both expressions have the same result, so it doesn't matter which description they are associated with. both are the largest and the smallest value.

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The possible rational roots of f(x) are ±1, ±2, ±4, ±8, ±1/2, and ±1/4.

The Rational Root Theorem states that if a polynomial [tex]f(x) = anxn + an-1xn-1 + ... + a1x + a0[/tex] has a rational root, then it must be of the form p/q, where p is a factor of the constant term a0 and q is a factor of the leading coefficient an.

For the given polynomial [tex]f(x) = -x + 14x3 - 18x2 - 4x5 - 26x4 + 8[/tex], the constant term is 8 and the leading coefficient is -4.

The factors of 8 are ±1, ±2, ±4, and ±8. The factors of -4 are ±1, ±2, and ±4.

Therefore, the possible rational roots of f(x) are:

p/q = ±1/1, ±2/1, ±4/1, ±8/1, ±1/2, ±2/2, ±4/2, ±8/2, ±1/4, ±2/4, ±4/4, ±8/4

Simplifying gives us the possible rational roots:

±1, ±2, ±4, ±8, ±1/2, ±4/2, ±8/2, ±1/4, ±2/4, ±8/4

Simplifying further gives us the final list of possible rational roots:

±1, ±2, ±4, ±8, ±1/2, ±2, ±4, ±1/4, ±1/2, ±2

Removing duplicates, the final list of possible rational roots is:

±1, ±2, ±4, ±8, ±1/2, ±1/4

Therefore, the possible rational roots of f(x) are ±1, ±2, ±4, ±8, ±1/2, and ±1/4.

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I chose the Quadratic Formula and Graphing because they are both straightforward methods that can give us the exact solutions.

A quadratic equation in the form ax^2 + bx + c = 0 where a > 1 is 2x^2 + 5x + 3 = 0.

To find the number of solutions based on the discriminant, we can use the formula D = b^2 - 4ac. In this case, D = (5)^2 - 4(2)(3) = 25 - 24 = 1. Since D > 0, the quadratic equation has two distinct real solutions.

Two ways to find the specific solutions or show that there is no solution are the Quadratic Formula and Graphing.

The Quadratic Formula is x = (-b ± √D)/2a. Plugging in the values from the equation, we get x = (-5 ± √1)/4 = (-5 ± 1)/4. This gives us the two solutions x = -1 and x = -2.

Graphing is another way to find the solutions. We can graph the equation y = 2x^2 + 5x + 3 and find the x-intercepts, which are the solutions to the equation. The graph shows that the x-intercepts are -1 and -2, which are the same solutions we found using the Quadratic Formula.

I chose the Quadratic Formula and Graphing because they are both straightforward methods that can give us the exact solutions. The Quadratic Formula is a formula that can be applied to any quadratic equation, and Graphing allows us to visually see the solutions. The other methods, such as Factoring, Square Root Property, and Completing the Square, may not always be applicable or may require more steps to find the solutions.

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Answer:

She earns 10 dollars per hour.

Step-by-step explanation:

They substituted h for the amount of hours, since it is unknown. And you can see 10 is multiplied with h. So that is how much she earns an hour.

Answer:

the answer is A

So basically it's simple just use some scientific calculator and put the number one by one with the bracket because there's a rule of mathematics which we call BODMAS

Answer:

D

Step-by-step explanation:

The amount of Kingston's birth weight that was much bigger than Karmichael would be = 1 pound 4 ounces

The weight of Kingston at birth = 9 pounds 2 ounces

The weight of Karmichael at birth = 7 pounds 11 ounces.

Next, the weights are converted to ounces such as:

1 pound = 16 ounces

For 9 pounds = 16×9 = 144 ounces+ 2 ounces = 146 ounces

For 7 pounds = 16×7 = 112 ounce + 11 ounces = 123 ounce

The difference between the birth weight of Kingston and Karmichael = 146-123 = 23 ounce

Convert 23 ounce to pounds = 23/16 = 1 pound 4 ounces

Therefore, amount of Kingston's birth weight that was much bigger than Karmichael would be = 1 pound 4 ounces.

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In answering the question above, the solution is If you know the lengths Pythagorean theorem of the other two sides of the right triangle, you may use these formulae to determine the length of the missing side.

The fundamental Euclidean geometry relationship between the three sides of a right triangle is the Pythagorean Theorem, sometimes referred to as the Pythagorean Theorem. This rule states that the areas of squares with the other two sides added together equal the area of the square with the hypotenuse side. According to the Pythagorean Theorem, the square that spans the hypotenuse (the side that is opposite the right angle) of a right triangle equals the sum of the squares that span its sides. It may also be expressed using the standard algebraic notation, a2 + b2 = c2.

[tex]a^2 + b^2 = c^2[/tex]

where a and b are the lengths of the other two sides, and c is the length of the hypotenuse.

c = √[tex](a^2 + b^2)[/tex]

You may rewrite the formula as follows to get the length of one of the other sides:

a = √[tex](c^2 - b^2)[/tex]

b = √[tex](c^2 - a^2)[/tex]

If you know the lengths of the other two sides of the right triangle, you may use these formulae to determine the length of the missing side.

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Answer:

Step-by-step explanation:

x + 4 + 2x + 23 = 90

3x + 27 = 90

3x = 63

x = 21

x + 4 = 21 + 4 = 25 for <1

2(21) + 23  = 42 + 23 = 65 for <2

Answer:

Step-by-step explanation:

Im not really sure what the heck you doing because im only in 8th grade but right now im in central and i'm kind of good at math but i'll try. Lets see........ I think they would all just be $11.50, but like i said im only in 8th grade and not that good at this kind of math so before you answer it please check with someone else to see if i got it right for you, cause i don't want to give you the wrong answer and you fail it.

Answer:

We can solve for p by isolating it on one side of the inequality symbol. First, we'll subtract 7 from both sides:

55 - 7 < -12p

48 < -12p

Next, we'll divide both sides by -12. Since we're dividing by a negative number, we'll need to flip the direction of the inequality:

48/-12 > p

-4 > p

Therefore, p is greater than -4. Written in interval notation, this solution is p ∈ (-∞, -4).

The cost of producing 2000 bagels is $796.8.

To determine the cost of producing 2000 bagels, we need to plug in the value of x into the given equation and solve for C(x).
C(x) = 300 + 0.25x - 0.4(x/1000)^3
C(2000) = 300 + 0.25(2000) - 0.4(2000/1000)^3
C(2000) = 300 + 500 - 0.4(2)^3
C(2000) = 300 + 500 - 0.4(8)
C(2000) = 300 + 500 - 3.2
C(2000) = 796.8

Therefore, the cost of producing 2000 bagels is $796.8.

In general terms, profit is nothing more than revenues minus costs. This mathematically expressed is:

Profit = Revenues - Costs

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Answer: 10,210$

Step-by-step explanation:
Its simple really. The formula is 800 x 2.65 x 1. 10,210.

Use this next time, good luck :)

Answer: $879.50

Step-by-step explanation:

The simple interest formula is I = prt

Plug values in:

(Percent move decimal over 2 and time has to be in years, so 3 years and 9 months is 3.75 years)

I = (800)(0.0265)(3.75)

I = (21.2)(3.75)

I = 79.5

Add the interest to the principle:

800 + 79.5 = $879.50

Hope this helps!