Write the equation of the line that passes through the points (-7,5) and (0,7). Put your answer in fully reduced point-slope form, unless it is a vertical or horizontal line

Answers

Answer 1

The equation of the line that passes through the points (-7,5) and (0,7) is equals to [tex] y = \frac{2}{7} x + 7 [/tex] and in point-slope form 7( y - 5) = 2( x +7).

The equation of a straight line is y = mx+ c, where, m is slope of line

c is known as the y -intercept.

Point-slope form of equation of line is written as y – y₁ = m(x – x₁), where

y is coordinate of second pointy₁ is coordinate of first pointx is coordinate of second pointx₁ is coordinate of first pointm is slope

We have a line that passes through the points say A(-7,5) and B(0,7). We have to write an equation of line in point-slope form. Now, slope of line, [tex]m = \frac{ y_2 - y_1}{x_2- x_1}[/tex]

here, x₁ = -7, y₁ = 5, x₂ = 0, y₂ = 7

=> [tex]m = \frac{ 7 - 5}{0 + 7}[/tex]

[tex]= \frac{2}{7}[/tex]

Using the point slope equation of a line passes through A(-7,5) and B(0,7) is y – y₁ = m(x – x₁).

Substitute all known values, [tex]y - 5 = \frac{2}{7}( x + 7) [/tex]

Cross multiplication, 7( y - 5) = 2( x +7)

=> 7y - 35 = 2x + 14

=> 7y = 2x + 14 + 35

=> 7y = 2x + 49

=> [tex] y = \frac{2}{7} x + 7 [/tex]

Hence, required equation is [tex] y = \frac{2}{7} x + 7 [/tex] but in point slope form 7( y - 5) = 2( x +7).

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Related Questions

When I multiply my number by four and add twenty, I get 4. What is my number?

Answers

The number is -4. We can solve for it using algebraic equations and multiplication.

The problem states that when we multiply our number by four and add twenty, we get 4. We can represent this relationship using an algebraic equation with the variable x representing our unknown number:

4x + 20 = 4

To solve for x, we need to isolate it on one side of the equation. We start by subtracting 20 from both sides of the equation:

4x = -16

Now, we divide both sides by 4:

x = -4

Therefore, our number is -4. We can check this answer by plugging it back into the original equation:

4(-4) + 20 = 4

Simplifying the left side of the equation, we get:

-16 + 20 = 4

4 = 4

This confirms that our answer, x = -4, is correct.

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1)
coin is tossed until for the first time the same result appear twice in succession.
To an outcome requiring n tosses assign a probability2

. Describe the sample space. Evaluate the
probability of the following events:
(a) A= The experiment ends before the 6th toss.
(b) B= An even number of tosses are required.
(c) A∩ B,
c ∩
Don't copy from others.
Don't copy from others

Answers

The probability that the experiment ends before the 6th toss and an even number of tosses are required is 5/16.

The given experiment involves tossing a coin until the first time the same result appears twice in succession. This means that the experiment could end after two tosses if both tosses yield the same result (e.g., heads-heads or tails-tails) or it could continue for many more tosses until this condition is met.

The sample space for this experiment can be represented as a binary tree where the root node represents the first toss and the two branches from the root represent the two possible outcomes (heads or tails). The next level of the tree represents the second toss, with two branches emanating from each branch of the root (one for heads and one for tails). This process continues until the experiment ends with two successive outcomes being the same.

The probability of each outcome in the sample space can be computed by multiplying the probabilities of each individual toss. Since each toss has a probability of 1/2 of resulting in heads or tails, the probability of any particular outcome requiring n tosses is 1/2^n.

(a) A = The experiment ends before the 6th toss.

To calculate the probability of this event, we need to sum the probabilities of all outcomes that end before the 6th toss. This includes outcomes that end after the second, third, fourth, or fifth toss. Thus, we have:

P(A) = P(outcome ends after 2 tosses) + P(outcome ends after 3 tosses) + P(outcome ends after 4 tosses) + P(outcome ends after 5 tosses)

= (1/2^2) + (1/2^3) + (1/2^4) + (1/2^5)

= 15/32

Therefore, the probability that the experiment ends before the 6th toss is 15/32.

(b) B = An even number of tosses are required.

An even number of tosses are required if the experiment ends after the second, fourth, sixth, etc. toss. The probability of this event can be calculated as follows:

P(B) = P(outcome ends after 2 tosses) + P(outcome ends after 4 tosses) + P(outcome ends after 6 tosses) + ...

= (1/2^2) + (1/2^4) + (1/2^6) + ...

This is a geometric series with first term a = 1/4 and common ratio r = 1/16. Using the formula for the sum of an infinite geometric series, we have:

P(B) = a/(1-r) = (1/4)/(1-1/16) = 4/15

Therefore, the probability that an even number of tosses are required is 4/15.

(c) A∩B = The experiment ends before the 6th toss and an even number of tosses are required.

To calculate the probability of this event, we need to consider only the outcomes that satisfy both conditions. These include outcomes that end after the second or fourth toss. Thus, we have:

P(A∩B) = P(outcome ends after 2 tosses) + P(outcome ends after 4 tosses)

= (1/2^2) + (1/2^4)

= 5/16

Therefore, the probability that the experiment ends before the 6th toss and an even number of tosses are required is 5/16.

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a large fish tank at an aquarium needs to be emptied so that it can be cleaned. when its large and small drains are opened together, the tank can be emptied in 4h . by itself, it takes the small drain 6 hr longer to empty the tank than it takes the large drain to empty the tank on its own. how much time would it take for each drain to empty the tank on its own?

Answers

The large drain can empty the tank on its own in 10 hours, while the small drain can empty the tank on its own in 16 hours.

Let's assume that the large drain can empty the tank in x hours. Then, according to the problem statement, the small drain can empty the same tank in x + 6 hours.

When both the large and small drains are opened together, they can empty the tank in 4 hours. This means that their combined rate of emptying the tank is 1/4 tank per hour.

We can set up two equations based on the rates of the individual drains and their combined rate:

1/x + 1/(x+6) = 1/4

Solving for x, we get x = 10 hours, which is the time it takes for the large drain to empty the tank on its own.

To find the time it takes for the small drain to empty the tank on its own, we substitute x = 10 in x+6, which gives us 16 hours.

Therefore, the large drain can empty the tank on its own in 10 hours, while the small drain can empty the tank on its own in 16 hours.

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Pepe and leo deposits money into their savings account at the end of the month the table shows the account balances. If there pattern of savings continue and neither earns interest nor withdraw any of the money , how will the balance compare after a very long time ?

Answers

If Pepe and Leo continue to deposit the same amount of money every month, their balances will be the same and continue to grow at the same rate i.e. Pepe's balance = $3,600 and Leo's balance = $3,600.

If we assume that Pepe and Leo continue to deposit the same amount of money every month and that the interest rate remains constant, we can use a formula to calculate the future value of their savings. The formula for future value is:

FV = PV x (1 + r)n

Where:

FV stands for the savings account's future value.

PV stands for the savings account's initial balance's present value.

The interest rate, r, is considered to be zero in this instance.

The number of months is n.

If we assume that Pepe and Leo deposit $100 each per month, we can use this formula to calculate the future value of their savings after a certain number of months. For example:

After 12 months:

Pepe's balance = $1,200

Leo's balance = $1,200

After 24 months:

Pepe's balance = $2,400

Leo's balance = $2,400

After 36 months:

Pepe's balance = $3,600

Leo's balance = $3,600

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I need the measure of angle b pls help :)?

Answers

Answer:

89

Step-by-step explanation:

it is a straight line mean 180 degrees.

180 subtract 91 is 89

Answer:The measure of angle b is 89 degrees.

Step-by-step explanation:

Types of angles:

• Angles between 0 and 90 degrees (0°< θ <90°) are called acute angles.

• Angles between 90 and 180 degrees (90°< θ <180°) are known as obtuse angles.

• Angles that are 90 degrees (θ = 90°) are right angles.

• Angles that are 180 degrees (θ = 180°) are known as straight angles.

• Angles between 180 and 360 degrees (180°< θ < 360°) are called reflex angles.

• Angles that are 360 degrees (θ = 360°) are full turn.

We know that,

 Angles that are 180 degrees (θ = 180°) are known as straight angles.

In this question ,let

a= 91 and we have to find b=?

here,by straight angle

a+b=180

91+b=180

b=180-91

b=89

this is the required answer.

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Karl and Leonard want to make soup. In order to get the right balance of ingredients for their tastes they bought 3 pounds of potatoes at $3.62 per pound, 5 pounds of cod for $4.56 per pound, and 3 pounds of fish broth for $3.66 per pound. Determine the cost per pound of the soup The cost per pound of the soup is $(Round to the nearest cent)

Answers

The cost per pound of the soup is $4.06 per pound (rounded to the nearest cent).

To find the cost per pound of the soup, we need to calculate the total cost of all the ingredients and divide it by the total weight of the soup.

The total cost of potatoes is 3 pounds × $3.62 per pound = $10.86.

The total cost of cod is 5 pounds × $4.56 per pound = $22.80.

The total cost of fish broth is 3 pounds × $3.66 per pound = $10.98.

So, the total cost of all the ingredients is:

$10.86 + $22.80 + $10.98 = $44.64

The total weight of the soup is 3 + 5 + 3 = 11 pounds.

Thus, the cost per pound of soup is:

$44.64 / 11 pounds = $4.06 per pound

Therefore, the cost per pound of the soup is $4.06 per pound (rounded to the nearest cent).

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if an income of Rs.3 lakhs is to be received after 1 year at 5% rate of interest? Not yet answered A. 1.835 B. None of these C. 1.1 Flag question D. 2.85

Answers

The closest answer is B. None of these

To find the present value of an income of Rs. 3 lakhs to be received after 1 year at a 5% rate of interest, you can use the present value formula:

Present Value (PV) = Future Value (FV) / (1 + Interest Rate) ^ Number of Years

1. Repeat the question in your answer: The present value of an income of Rs. 3 lakhs to be received after 1 year at a 5% rate of interest is:

2. Step-by-step explanation:

Step 1: Identify the values for the formula.
- Future Value (FV) = Rs. 3 lakhs
- Interest Rate = 5% or 0.05
- Number of Years = 1

Step 2: Plug the values into the formula.
PV = Rs. 3,00,000 / (1 + 0.05) ^ 1

Step 3: Calculate the present value.
PV = Rs. 3,00,000 / 1.05

PV ≈ Rs. 2,85,714.29

Based on the given options, the closest answer is B. None of these, as the calculated present value is approximately Rs. 2,85,714.29, which does not match any of the provided options.

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2. Supposed the prevalence of Sudden infant death syndrome (SIDS) is 0.01%. At a local Maternity hospital 3 of the 100 newborn infants died of SIDS following birth. a. What is the probability of 3 dying of SIDS in this situation? b. In this situation would you find it alarming that this many died or would this be expected. Why or why not? (write 1-3 sentences explaining

Answers

The probability of 3 dying of SIDS in this situation is approximately 0.000227. The number of SIDS cases in this hospital is significantly higher than the expected rate.

a. The probability of 3 infants dying of SIDS in this situation can be calculated using the binomial probability formula:
P(X=k) = C(n,k) * p^k * (1-p)^(n-k)
Where:
P(X=k) is the probability of k successes (SIDS cases) in n trials (infants),
C(n,k) is the number of combinations of n items taken k at a time,
p is the probability of SIDS (0.0001),
n = 100 infants,
k = 3 SIDS cases.
P(3 SIDS cases in 100 infants) = C(100,3) * (0.0001)^3 * (1-0.0001)^(100-3)
After calculating, the probability is approximately 0.000227.

b. In this situation, it is alarming that many infants died of SIDS, as the probability of 3 deaths in 100 infants is very low (0.000227), much lower than the prevalence of 0.01%. This indicates that the number of SIDS cases in this hospital is significantly higher than the expected rate.

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Directions: There are 11 questions in 5 pages. No credit will be given without sufficient work 1. Let Z be a standard normally distributed random variable. Find: a. P(Z S 2.32) b. P(Z 2-1.56) c. P(-1.43 SZ 52.47) d. Find : so that P(-:* SZS :) 0.99

Answers

As given below find the suitable option which gives you the answer for the question. "There are 11 questions in 5 pages. No credit will be given without sufficient work 1. Let Z be a standard normally distributed random variable."

1. Let Z be a standard, normally distributed random variable.
a. P(Z ≤ 2.32)
To find this probability, you need to use the standard normal distribution table (also known as the Z-table) to look up the value corresponding to Z = 2.32. The value you find in the table is the probability P(Z ≤ 2.32).
b. P(Z ≥ -1.56)
To find this probability, first look up the value corresponding to Z = -1.56 in the standard normal distribution table. This value represents P(Z ≤ -1.56). Since we want P(Z ≥ -1.56), we need to find the complement, which is 1 - P(Z ≤ -1.56).
c. P(-1.43 ≤ Z ≤ 2.47)
To find this probability, look up the values corresponding to Z = -1.43 and Z = 2.47 in the standard normal distribution table. The difference between these two values will give you the probability P(-1.43 ≤ Z ≤ 2.47).
d. Find z* so that P(-z* ≤ Z ≤ z*) = 0.99
To find the z* value, you need to look up the value in the standard normal distribution table that corresponds to the area of 0.995 (since 0.99 is the area between -z* and z*, and each tail contains 0.005). Once you find the value in the table, look at the corresponding Z value. This value will be your z*.

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The graph below shows a household’s budget. What angle measure was used to construct the section representing insurance?




43.2°

46.8°

36°

72°

Answers

Answer:

[tex].12 \times 360 \: degrees = 43.2 \: degrees[/tex]

right triangles, find the exact values of x and y.​

Answers

Step-by-step explanation:

the main triangle is an isoceles triangle (both legs are equally long). that means that the height y bergen the 2 legs splits the baseline in half.

therefore,

x = 10/2 = 5

Pythagoras gives us y.

c² = a² + b²

c being the Hypotenuse (the side opposite of the 90° angle). in our case 10.

a and b are the legs. in our case x and y.

10² = 5² + y²

100 = 25 + y²

75 = y²

y = sqrt(75) = 8.660254038...

A spinner is divided into 10 equally sized sectors. The sectors are numbered 1 to 10. A randomly selected point is chosen.

What is the probability that the randomly selected point lies in a sector that is a factor of 3?

Enter your answer in the box.

Answers

Answer:

0.2 or 20%

-----------------------

There are two sectors that are factors of 3:

sector 1, sector 3

So out of the 10 sectors, there is a 2/10 probability that the randomly selected point lies in one of these three sectors.

Therefore, the probability is 0.2 or 20%.

Answer:

20%

Step-by-step explanation:

For this question, we must find the numbers from 1-10 that are factors of 3. A factor is a number that, when multiplied by a specific number, gives a specific whole. For instance, in 2*4=8, 2 and 4 would be factors. The number 3 only has two factors: one and itself. Since two of the ten numbers are factors of 3, that is a rate of 2/10, 0.2, or 20%.

Please help me with this my quiz. Thank you :)
Due tomorrow

Answers

Answer:

dark blue

Step-by-step explanation:

A soccer dome shaped like a hemisphere has a volume of 450,000 m^3. What is the area of its field? Use 3. 14 for pi

Answers

As per the given values, the area of the hemisphere is 45065.41 m³

Volume = 450000 m³

Calculating the volume of the hemisphere -

Volume = 2/3 πr³

Substituting the values -

450,000 =2/3 x 3.14 x r³

Solving for r³

r³ = 450000 x 3/(2 x 3.14)

r³ = 214968.1

r = √214968.1

r = 59.9

Calculating the area of the hemisphere -

Area = 4πr²

Substituting the values -

Area = 4 x 3.14 x (59.9)²

= 12.56 x (59.9)²

= 45065.41

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If you don't have a calculator, you may want to approximate (128.012)6/7 by 1286/7 Use the Mean Value Theorem to estimate the error in making this approximation To check that you are on the right track, test your numerical answer below. the magnitude of the error is less than (enter an exact answer)

Answers

The magnitude of the error is less than [tex]$\$ 0.015 \$$[/tex], which is our final exact answer.

We can use the Mean Value Theorem to estimate the error in approximating [tex]$(128.012)^{\frac{6}{7}}$[/tex] by [tex]$128^{\frac{6}{7}}$[/tex]. Let [tex]$f(x) = x^{\frac{6}{7}}$[/tex] and [tex]$a = 128.012$[/tex]. Then, by the Mean Value Theorem, there exists some [tex]$c$[/tex] between [tex]$a$[/tex] and [tex]$128$[/tex] such that:

[tex]$$\frac{f(a)-f(128)}{a-128}=f^{\prime}(c)$$[/tex]

Taking the absolute value of both sides and rearranging, we get:

[tex]$$|f(a)-f(128)|=|a-128| \cdot\left|f^{\prime}(c)\right|$$[/tex]

Now, we can find [tex]$\$ f^{\prime}(x) \$$[/tex] :

[tex]$$f(x)=x^{\frac{6}{7}}=e^{\frac{6}{7} \ln x}$$[/tex]

Using the chain rule, we get:

[tex]$$f^{\prime}(x)=\frac{6}{7} x^{-\frac{1}{7}} e^{\frac{6}{7} \ln x}=\frac{6}{7} x^{-\frac{1}{7}} f(x)$$[/tex]

Plugging in [tex]$\$ \mathrm{c} \$$[/tex] and simplifying, we get:

[tex]$$|f(a)-f(128)|=|128.012-128| \cdot\left|\frac{6}{7} c^{-\frac{1}{7}}\left(\frac{128.012}{c}\right)^{\frac{6}{7}}\right|$$[/tex]

We want to find an upper bound for this expression, so we will use the fact that [tex]$\$ c \$$[/tex] is between [tex]$\$ 128 \$$[/tex] and [tex]$\$ 128.012 \$$[/tex]. Therefore, we have:

[tex]$$|f(a)-f(128)| < 0.012 \cdot \frac{6}{7} 128^{-\frac{1}{7}}(128.012)^{\frac{6}{7}}$$[/tex]

Plugging in the values, we get:

[tex]$$|f(a)-f(128)| < 0.012 \cdot \frac{6}{7} \cdot 128^{-\frac{1}{7}}(128.012)^{\frac{6}{7}} \approx 0.015$$[/tex]

Therefore, the magnitude of the error is less than [tex]$\$ 0.015 \$$[/tex], which is our final exact answer.

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Two concentric circles form a target. The radii of the two circles measure 8 cm and 4 cm. The inner circle is the bullseye of the target. A point on the target is randomly selected.

What is the probability that the randomly selected point is in the bullseye?

Enter your answer as a simplified fraction in the boxes.

Answers

The probability that the randomly selected point is in the bullseye is 0.75, or 75%.

The area of the bullseye is the difference between the areas of the larger and smaller circles:

[tex]A = \pi r_1^2 - \pi r_2^2[/tex]

where [tex]r_1[/tex] is the radius of the larger circle (8 cm) and [tex]r_2[/tex] is the radius of the smaller circle (4 cm).

[tex]A = \pi(8^2 - 4^2)A = \pi(64 - 16)A = 48\pi[/tex]

The area of the entire target (both circles) is:

[tex]A = \pi r_1^2[/tex]

A = 64π

Therefore, the probability of selecting a point in the bullseye is:

P(bullseye) = A(bullseye) / A(target)

P(bullseye) = (48π) / (64π)

P(bullseye) = 3/4 or 0.75

So the probability that the randomly selected point is in the bullseye is 0.75, or 75%.

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Seth bought a pair of shorts. The original cost was $21, but the store was having a sale of 25% off. Seth also had a coupon for 15% off any purchase at checkout. How much did Seth pay for the pair of shorts?

Answers

Answer: $13.39

Step-by-step explanation:

first, you take 25% off 21, by multiplying 21*.25 which is 5.25

next, subtract 5.25 from 21, which gets you 15.75

next, add the 15% off coupon, by multiplying 15.75*.15 which is 2.3625

last, subtract 2.3625 from 15.75, which gets you 13.3875, or $13.39 rounded

One child in the Mumbai study had a height of 59 cm and arm span 60 cm. This child's residual is

Answers

In the context of the Mumbai study, the residual is the difference between the observed value (the child's height or arm span) and the predicted value (based on a statistical model or an average value). Therefore, the residual for this child is -3.1 cm.

To calculate the residual, we need to first determine the predicted arm span for a child with a height of 59 cm using the regression equation from the Mumbai study. Let's assume the regression equation is:

Arm span = 0.9*Height + 10

Plugging in the height of 59 cm, we get:

Arm span = 0.9*59 + 10 = 63.1 cm

The predicted arm span for this child is 63.1 cm.

Now, to calculate the residual, we simply subtract the predicted arm span from the actual arm span:

Residual = Actual arm span - Predicted arm span
Residual = 60 - 63.1
Residual = -3.1 cm

Therefore, the residual for this child is -3.1 cm.

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Use Newton's method to find the root of f(a), starting at x = 0. Compute X1 and 22. Please show - your work and do NOT simplify your answer

Answers

The first two approximations of the root of f(a) using Newton's method starting at x=0 are: X₁ = 1/3 X₂= 19/54

Newton's Method Algorithm: (1) Choose a beginning value x0 (ideally near to a root of f). (2) Create a new estimate xn+1=xnf(xn)f′(xn) for each estimate xn. (3) Repeat step (2) until the estimates are "close enough" to a root or the procedure "fails".

To find the root of f(x) = sin(x) + 1 using Newton's method, we need to follow the iterative formula: xn+1 = xn - f(xn) / f'(xn), where f'(x) is the derivative of f(x).

First, find the derivative of f(x): f'(x) = cos(x)

Now, compute x₁ and x₂ using the formula:

x₁ = x0 - f(x0) / f'(x0) = 0 - (sin(0) + 1) / cos(0) = 0 - 1/1 = -1

x₂ = x1 - f(x1) / f'(x1) = -1 - (sin(-1) + 1) / cos(-1)

The first two approximations of the root of f(a) using Newton's method starting at x=0 are:

X1 = 1/3

X2 = 19/54

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Which of the following are true regarding the specific rule of addition and the general rule of addition?
If the events A and B are mutually exclusive, you can use the special rule of addition.
If the events A and B are not mutually exclusive, you can use the general rule of addition.

Answers

Both statements are true. When events A and B are mutually exclusive, meaning they cannot occur simultaneously, you can use the special rule of addition.

If events A and B are not mutually exclusive, meaning they can occur together, you should use the general rule of addition. The specific rule of addition can only be used when dealing with mutually exclusive events, while the general rule of addition can be used for any two events, whether they are mutually exclusive or not. The specific rule of addition states that the probability of either event A or event B occurring is equal to the sum of their individual probabilities, while the general rule of addition states that the probability of event A or event B occurring is equal to the sum of their individual probabilities minus the probability of their intersection (if they are not mutually exclusive).

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What is 011.4583 as a fraction?

Answers

Answer:

11.4583 = 114583 / 10000

Step-by-step explanation:

Volume of 2 cylinders is same but raidus of cylinder 1 is 10% more than cylinder 1

Answers

The height of the second cylinder should be 56.25% greater than the height of the first cylinder. (Option 1)

Let's assume the radius of the first cylinder to be 'r' and its height to be 'h'. So, its volume can be represented as V1 = πr^2h.

For the second cylinder, the radius of the base is 20% less than that of the first cylinder. So, the radius of the second cylinder can be represented as 0.8r. Let the height of the second cylinder be represented as 'H'. So, its volume can be represented as V2 = π(0.8r)²H.

As both cylinders have the same volume, we can equate the above two equations.

πr²h = π(0.8r)²H

h = (0.8)²H

H = (1/(0.8)²)h

H = (1.5625)h

Therefore, the height of the second cylinder should be 56.25% greater than the height of the first cylinder.

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Complete Question:

Two cylinders have the same volume, but the radius of the base of the second cylinder is 20% less than the radius of the base of the first. How much greater should be the height of the second cylinder be in comparison to the height in first?

Options:

56.25%55.25%56.75%55.75%.

Answer Immediately Please

Answers

Answer:

x = 28.5 units

Step-by-step explanation:

from the angles we understand that they are similar, therefore in proportion, we solve, in fact, with a proportion between the corresponding sides

24 : x = 32 : 38

x = 24 x 38 : 32

x = 912 : 32

x = 28.5 units

-------------------------

check

24 : 28.5 = 32 : 38

0.84 = 0.84

The answer is good

Which of the following is NOT true:
A) It is possible to have Pr(A)=1, Pr(B)= and Pr(A u B)=1.
B) If A is an event such that Pr(A)=1, then A'=Ø.
C) Pr(A/B)=Pr(B|A) if and only if Pr(A)=Pr(B)>0.
D) Pr(A/B)=MMABIA) assuming that both Pr(A) and Pr(B) are greater than 0.
E) none of these

Answers

The set statement that is NOT true is option B) If A is an event such that Pr(A)=1, then A'=Ø.

What is the set about?

In terms of option A, one can have Pr(A)=1, Pr(B)=0, and Pr(A u B)=1. This outcome is true in cases where A and B are not mutually exclusive occurrences, telling us that they have the potential to happen concurrently.

Therefore, If Pr(A) is equal to Pr(B) and both are greater than zero, then Pr(A/B) is one that is equivalent to Pr(B|A). Bayes' theorem, which establishes a connection between conditional probabilities, is an accurate hold to this.

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4. Obtain (a) the half-range cosine series and (b) the half-range sine series for the function f(t) = 0, 0

Answers

This is because the function f(t) is a constant function, which is an even function and has no odd component.

The half-range Fourier series is a representation of a periodic function over a finite interval, where the function is assumed to be even or odd. In the case of the function f(t) = 0, the function is even and the interval is from 0 to π.

(a) The half-range cosine series:

To find the half-range cosine series, we first need to find the Fourier coefficients:

[tex]a_0 &= \frac{2}{\pi} \int_0^{\pi} f(t) dt = \frac{2}{\pi} \int_0^{\pi} 0 dt = 0 \a_n &= \frac{2}{\pi} \int_0^{\pi} f(t) \cos(nt) dt = \frac{2}{\pi} \int_0^{\pi} 0 \cos(nt) dt = 0 \\[/tex]

Since all the Fourier coefficients are zero, the half-range cosine series for f(t) is:

[tex]$\begin{align*}f(t) &= \frac{a_0}{2} + \sum_{n=1}^{\infty} a_n \cos(nt) \&= 0\end{align*}$[/tex]

b) The half-range sine series:

To find the half-range sine series, we need to find the Fourier coefficients:

[tex]b_n &= \frac{2}{\pi} \int_0^{\pi} f(t) \sin(nt) dt = \frac{2}{\pi} \int_0^{\pi} 0 \sin(nt) dt = 0 \\[/tex]

Since all the Fourier coefficients are zero, the half-range sine series for f(t) is:

[tex]$\begin{align*}f(t) &= \sum_{n=1}^{\infty} b_n \sin(nt) \&= 0\end{align*}$[/tex]

Therefore, both the half-range cosine series and the half-range sine series for f(t) are zero. This is because the function f(t) is a constant function, which is an even function and has no odd component.

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the sum of the first three terms of a decreasing geometric progression is 7 and the product is 8. find the common ratio and the first three terms of the g.p​

Answers

Answer:

ratio: 1/2first terms: 4, 2, 1, ...

Step-by-step explanation:

You want the common ratio and first 3 terms of a decreasing geometric progression with the sum of the first three terms being 7, and their product being 8.

Setup

Let the first term be represented by x, and let r represent the common ratio. Then the first three terms are ...

  x, xr, xr²

Their sum is ...

  7 = x +xr +xr²

Their product is ...

  8 = (x)(xr)(xr²) = (xr)³

Solution

Taking the cube root of the product equation, we have ...

  2 = xr

Substituting this into the first equation, we have ...

  7 = x +2 + 2r

  5 = x +2r   ⇒   x = 5 -2r

And substituting back into the above, we get ...

  2 = (5 -2r)(r)

  2r² -5r +2 = 0

  (2r -1)(r -2) = 0

  r = 2 or 1/2

We want r < 1, so r = 1/2.

  x = 5 -2(1/2) = 4

Progression

For x = 4, r = 1/2, the first three terms are ...

  x, xr, xr² = 4, 2, 1

__

Additional comment

The equations are nicely solved by a graphing calculator. In the attached, we used y instead of r. We want the solution with y<1.


The two solutions give rise to terms 4, 2, 1 (decreasing) or 1, 2, 4 (increasing).


Using a 2-D shape and an axis of rotation of your choice, draw the 2-D shape, the axis, and the resulting 3-D shape.

Answers

The 2-D shape used here is a right triangle. When rotated about the axis, this becomes a cone which is 3-D. See the attached.

What is rotation in Math?

In mathematics, rotation is a notion that originated in geometry. Any rotation is a movement of a specific space that retains at least one point.

A rotation differs from the following motions: translations, which have no fixed points, and (hyperplane) reflections, which each have a full (n 1)-dimensional flat of fixed points in an n-dimensional space.

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Mia runs 7/3 miles every day in the morning. Select all the equivalent values, in miles, that show the distance she runs each day.

1.66
2.3333333
2 2/3
1.6777777
2 2/5
2 1/3

Answers

The equivalent distance travelled by Mia is 2.3333... and 2[tex]\frac{1}{3}[/tex] miles.

The distance run by Mia is equivalent to 7/3 miles. We can express the fraction as -

7/3 = 2.3333

7/3 = (3 x 2 + 1)/3 = 2[tex]\frac{1}{3}[/tex]

So, the equivalent distance travelled by Mia is 2.3333... and 2[tex]\frac{1}{3}[/tex] miles.

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Answer: 2.33 and 2 1/3

Step-by-step explanation:

For the given cost function

C(x) = 36100 + 800x + x^2 find:

a) The cost at the production level 1250

b) The average cost at the production level 1250

c) The marginal cost at the production level 1250

d) The production level that will minimize the average cost

e) The minimal average cost

Answers

For a cost function, C(x) = 36100 + 800x + x²

a) The cost at the production level 1250 is equal to 2,598,600.

b) The average cost at the production level 1250 is equal to 2,078.88.

c) The marginal cost at the production level 1250 is equal to 3300 $/unit.

d) The production level, x = 60 that will minimize the average cost.

e) The minimal average cost is equals the 1,461.67.

Let consider C(x) be a total cost function where x is quantity of the product, then,

The average of the total cost is written as:[tex]AC(x)= \frac{C(x)}{x}[/tex]The Marginal cost is written as MC(x) = C'(x).

We have a cost function is written as C(x) = 36100 + 800x + x²

a) The cost at production level 1250, that is x = 1250 is equals to

=> C( 1250) = 36100 + 800× 1250 + 1250²

= 2,598,600

b) The average cost at the production level 1250, that is AC(x) [tex]= \frac{36100 + 800x + x²}{x}[/tex]

[tex]= \frac{36100}{x} + 800 + x[/tex]

Plug the value x = 1250

[tex]= \frac{36100}{1250} + 800 + 1250[/tex]

= 2,078.88

c) The marginal cost at the production level 1250 is equal to the derivative of

[tex]\frac{dC(x)}{dx }[/tex], evaluated for x = 1250,

[tex]\frac{dC(x)}{dx }[/tex] = C'(x)

= 800 + 2x

C'(1250) = 800 + 2× 1250 = 3300$/unit

d) As we know the average cost of the total cost function is,

[tex] A C(x) = \frac{36100}{x} + 800 + x[/tex]

Compute the critical point for minimizing the average cost, differentating the above equation, [tex]AC′(x)= \frac{ d(\frac{36100}{x} + 800 + x)}{dx}[/tex]

[tex]= \frac{- 36100}{x²} + 1[/tex]

For critical value plug AC'(x) = 0

[tex]\frac{- 36100}{x²} + 1 = 0[/tex]

=> x² - 3600 = 0

=> x = ± 60

As the quantity must be positive so x = 60.

e) Now we will compute the minimum average value at x = 60,

[tex] A C(60) = \frac{36100}{60} + 800 + 60[/tex]

= 1,461.67

Hence, required value is 1,461.67.

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Printer A prints 100 pages for $26.99. Printer B prints 275 sheets for $67.99. Which printer has the better rate of cost per page?

Answers

The printer that has a better rate of cost per page would be = printer B.

How to calculate the rate of cost per page for the printers?

For printer A:

The number of pages printed = 100

The cost for the printed pages = $26.99

Cost per page = 26.99/100 = $0.27/page

For printer B:

The number of pages printed = 275

The cost for the printed pages = $67.99

Cost per page =67.99/275

= 0.25

Therefore the printer that has a better rate of cost per page would be = printer B

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