Which equation best represents the relationship between X and Y in the graph?
A- y = 3x + 3
B- y = 3x - 1
C- y = 1/3x + 3
D- y = 1/3x - 1

The number of square inches to make up half the cookie cake is 76.93 in² area.

The diameter of the circular cookie cake is 14 inches, so its radius will be r = 7 inches. Using the formula for area of circle we have:

area of cookies cake = 3.14 × 7 in × 7 in

area of cookies cake = 153.84 in²

half the area of the cookie cake = 153.84 in²/2

half the area of the cookie cake = 76.93 in²

Therefore, the number of square inches to make up half the cookie cake is 76.93 in² area.

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Answer:

[tex]10 = -4( - 1) + b[/tex]

[tex]10 = 4 + b[/tex]

[tex]b = 6[/tex]

[tex]y = - 4x + 6[/tex]

The equation of the line in slope-intercept form is y = -4x + 6.

The equation of a line in slope-intercept form is given by y = mx + b, where m is the slope and b is the y-intercept.

Given that the slope is -4 and the line passes through the point (-1, 10), we can substitute these values into the equation.

Using the point-slope formula (y - y1) = m(x - x1), we can rewrite it as (y - 10) = -4(x - (-1)). Simplifying this equation, we get y - 10 = -4x - 4, and rearranging it, we have y = -4x + 6. Therefore, the equation of the line in slope-intercept form is y = -4x + 6.

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a.He will win a prize.

b.Tina needs to walk 4 more miles to meet the goal for the Bike Riding activity and win a prize.

a. How to find the distance Tony runs in one week?

To find the distance Tony runs in one week, we need to multiply the distance he runs in one day (which is 1/2 mile) by the number of days in a week (7):

Distance run in 1 week = 1/2 mile per day x 7 days = 3.5 miles

Since Tony has run a total of 3.5 miles in a week, he has met the goal for the Swimming activity, which requires running 1 mile in 2 weeks. Therefore, he will win a prize.

b. How to find the total distance walked by Tina in one week?

To find the total distance walked by Tina in one week, we need to multiply the distance she walks to the library and back (which is 1 mile each way) by the number of times she walks per week (which is 3):

Distance walked in 1 week = 2 miles per walk x 3 walks = 6 miles

Since Tina has walked a total of 6 miles in a week, she has met the goal for the Walking activity, which requires walking 6 miles in 2 weeks. Therefore, she will win a prize.

To find out how much more Tina needs to walk to meet the goal for the Bike Riding activity, we need to subtract the distance she has already walked (6 miles) from the total distance required (10 miles):

Distance left to walk = 10 miles - 6 miles = 4 miles

Therefore, Tina needs to walk 4 more miles to meet the goal for the Bike Riding activity and win a prize.

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The equation of the tangent line of f(x) = (ln x)⁴ at x = 4 is y = (3/16)ln 2 x - (3/4)ln 2 + 256ln⁴ 2.

We may calculate the derivative of a power function using the power rule of differentiation. Since many functions may be expressed as power functions or can be made simpler using power functions, the power rule is a helpful tool in calculus. We can quickly determine the derivatives of these functions using the power rule and apply them to issues in physics, economics, and engineering.

The slope of the tangent line at x = 4 is determined using the derivative as follows:

f(x) = (ln x)⁴

f'(x) = 4(ln x)³ (1/x)

At x = 4, we have:

f'(4) = 4(ln 4)³ (1/4) = (3/16)ln 2

Now, the equation of the tangent line is:

y - 256ln⁴ 2 = (3/16)ln 2(x - 4)

y = (3/16)ln 2 x - (3/4)ln 2 + 256ln⁴ 2

Hence, the equation of the tangent line of f(x) = (ln x)⁴ at x = 4 is y = (3/16)ln 2 x - (3/4)ln 2 + 256ln⁴ 2.

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The answer is , (a)  For equation 1 Use the quadratic formula , (b) For equation 2 use of Factor out the common factor , (c) For equation 3 use of Complete the square.

A quadratic equation is a type of equation in algebra that contains a variable of degree 2, meaning that the highest power of the variable is 2.

Quadratic equations can have two real roots, one real root, or two complex roots, depending on the value of the discriminant (b² - 4ac). If discriminant is positive, equation has two real roots, if it is zero, equation has one real root (a "double root"), and if it is negative, equation has two complex roots.

Inga can use the following steps to solve the quadratic equation 2x² + 12x - 3 = 0:

Therefore, steps that Inga could use to solve quadratic equation are given:

Use the quadratic formula

Factor out the common factor

Complete the square

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Answer:

Looking at the number line, we can see that R is to the left of P, and S is to the right of P. Also, Q is to the left of R, and S is to the right of Q.

So, the first statement "R x P > S" is not true, because S is to the right of both R and P.

The second statement "S > Q x R" is also not true, because Q is to the left of R, and S is to the right of both Q and R.

The third statement "Q x R > S" is true, because Q is to the left of R, and S is to the right of both Q and R. Therefore, the correct statement is:

Q x R > S

40 students have red hair.

We have,

Red color= 5%

Black = 25%

Brown = 40%

Blonde= 30%

Total middle school students = 800

So, the number of red haired student

= 5% of 800

= 5/100 x 800

= 5 x 8

= 40 students

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Laila: The amount of surplus corn

Thiago: The amount of corn eaten

According to graph the vertical axis of Laila's Graph is surplus popcorn and the vertical axis of Thiago's Graph is popcorn eaten. This can be seen on the graph (graph in image attached below)

Therefore, the correct vertical axis label that accurately represent the situation is:

The amount of surplus popcorn for Laila's graph.

The amount of popcorn eaten for Thiago's graph

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The question is incomplete, complete question in image attached.

According to the question the magnitude of the resulting force is 5.83.

Magnitude is a measure of the size or intensity of a physical quantity. It is an expression of how large or small a quantity is in comparison to a reference value. Magnitude is typically used in physics and astronomy, but it can also be used in other areas such as engineering and seismology. Magnitude is not an absolute measurement; rather, it is a relative measure of how much larger or smaller one quantity is compared to another. For example, the magnitude of a star's brightness is a measure of how much brighter it is compared to other stars.

The magnitude of the resulting force can be calculated using the Pythagorean theorem. The formula for calculating the magnitude of a vector is:
[tex]\sqrt[]{(x2 + y2)}[/tex]
In this case, x = 5 and y = -3, which gives us:
[tex]\sqrt{(52 + (-3)2)}[/tex] = [tex]\sqrt{(25 + 9)}[/tex] = √[tex]\sqrt{(34)}[/tex] = 5.83.
Therefore, the magnitude of the resulting force is 5.83.

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Answer:Let's assume the number of haircuts Hayley needs to perform in a month for the total amount paid to either salon to be the same is denoted as 'x'.

For self-employment at The Princeton Salon:

Hayley would pay a fixed monthly rent of $774 to rent a station and keep all of her earnings.

For working at a franchise:

Hayley would have to pay $9 to the salon for every haircut she performs.

Based on the given information, we can set up the following equation to find the value of 'x':

Number of haircuts * Cost per haircut at franchise = Monthly rent at The Princeton Salon

x * 9 = 774

Solving for 'x':

x = 774/9

x ≈ 86.00

So, Hayley would need to perform approximately 86 haircuts in a month for the total amount paid to either salon to be the same.

Now, to calculate the total amount paid to either salon, we can use the following formulas:

Total amount paid at The Princeton Salon = Monthly rent + Earnings (which would be all of her earnings, as mentioned in the prompt)

Total amount paid at the franchise = Cost per haircut * Number of haircuts

Plugging in the values:

Total amount paid at The Princeton Salon = $774 + (Earnings from haircuts)

Total amount paid at the franchise = $9 * 86

Since the total amount paid to either salon is the same, we can equate the two equations:

$774 + Earnings from haircuts = $9 * 86

Solving for Earnings from haircuts:

Earnings from haircuts = $9 * 86 - $774

Earnings from haircuts = $774

So, Hayley would pay a total of $774 in earnings from haircuts, regardless of whether she chooses self-employment at The Princeton Salon or working at the franchise. The number of haircuts she needs to perform to reach this amount is 86.

Step-by-step explanation:

The 90% CI for the mean tension μ of all the screens produced on this day = (292.32, 320.32).

A confidence interval is a range of values that is likely to contain the true value of a population parameter with a certain degree of confidence. It is calculated from a sample of data, and provides a measure of the precision and uncertainty of the estimate.

a. Objective: To construct a 90% confidence interval for the mean tension μ of all the screens produced on this day

STATE: State the parameter you want to estimate and the confidence level.

Parameter: In the given problem we are asked to estimate the mean tension μ of all the screens produced on this day, by listing a range of plausible values. Hence, the parameter of interest is the true mean tension of the population (μ).

Confidence level: As mentioned in the problem, we need to estimate the range of plausible values that the true mean tension (μ) can take with 90% confidence. Hence,

Confidence level = 90%

PLAN: Identify the appropriate inference method and check conditions.

Name of procedure: Statistical inference by Confidence interval approach - Since the population standard deviation is unknown, the underlying distribution would be assumed to follow a t distribution with n - 1 degrees of freedom.

Check conditions:

- The data is normally distributed; although the sample size is small.

From the summary statistics and dot plot, the data does appear to be symmetric and approximately normally distributed.

- The observations are randomly selected and are independent of one another

This is ensured the data collection

The population variance is unknown

Since the conditions are met, we may construct the 90% CI as folllows:

General Formula:

Sample Mean ±  Margin of Error

= Sample Mean ± [tex]t_{n-1}[/tex]SE

Specific Formula:

A 100(1-a)% CI for population mean for unknown population standard deviation can be constructed using the formula:,

[tex]\bar x \± t_{a,n-1}\frac{s}{\sqrt{n} }[/tex]

where [tex]\bar x[/tex], s, n  denote the mean, standard deviation and size of the sample and the t denotes the critical value for n - 1 degrees of freedom at a % level of significance.

Work:

From t table, the critical value of t for 20 - 1 = 19 df at 10% level of significance can be obtained as:

Table is mentioned below

Substituting the descriptive and the critical value in the CI formula:

306.32 ± (1.729) [tex](\frac{36.209}{\sqrt{20} } )[/tex]

306.32 ±  (1.729)(8.097)

≈ 306.32 ±  14

≈ (292.32,320.32)

The 90% CI for the mean tension μ of all the screens produced on this day = (292.32, 320.32)

CONCLUDE:

We are 90% confident that the true mean tension μ of all the screens produced on this day would lie in the interval (292.32, 320.32).

b. Given:

The manufacturer’s goal is to produce screens with an average tension of 300 mV. Here, we need to test:

[tex]H_{0}[/tex] : μ= 300   Vs     [tex]H_{a}[/tex] :  μ ≠ 300

Using the Confidence Interval approach for testing the hypothesis,

Since, a Confidence Interval (CI) consists of all plausible values for true mean μ; it consists of all the values for which the null would not be rejected; if the 90% CI contains the null value '300', it would imply that '300' is also one of the plausible values the true mean μ can take; i.e. there would be a pretty good chance that μ is indeed equal to '300'; hence, we would fail to reject H0 based on such a CI.

Here, we find that the 90% CI for μ (292.32, 320.32) does contain the null value '300'. And hence, we fail to reject Họ: = H=300  at 10% level of significance. Hence, based on the interval, we may state that there is not enough convincing evidence that the screens produced this day don’t meet the manufacturer’s goal.

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The complete question is:

a) you would need $450,332.81 in your account at the beginning. b)  the total money that will be pulled out of the account is $600,000.

a) To calculate the amount needed in the account at the beginning, we can use the present value formula:

PV = PMT * ((1 - (1 + r)^-n) / r)

Where PV is the present value, PMT is the annual payment, r is the annual interest rate, and n is the number of periods.

Plugging in the values, we get:

PV = 40000 * ((1 - (1 + 0.05)^-15) / 0.05)

PV = $450,332.81

Therefore, you would need $450,332.81 in your account at the beginning.

b) To calculate the total money that will be pulled out of the account, we can simply multiply the annual payment by the number of years:

Total money = PMT * n

Total money = 40000 * 15

Total money = $600,000

Therefore, the total money that will be pulled out of the account is $600,000.

c) To calculate the amount of money that is interest, we can subtract the initial investment from the total money pulled out:

Interest = Total money - Initial investment

Interest = $600,000 - $450,332.81

Interest = $149,667.19

Therefore, $149,667.19 of the money pulled out is interest.

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The image vertices of K′L′M′N′ under a rotation of 270° clockwise are:

K′(0, 0), L′(−2, 5), M′(5, 5), N′(3, 0).

What is coordinates?

Coordinates are numerical values used to represent the position of a point in a particular space or system. coordinates are used to identify the position of a point in a given plane or space. Typically, two or three numbers are used to describe the location of a point in a two-dimensional or three-dimensional space, respectively.

To rotate a point by 270° clockwise about the origin, we can swap the coordinates and negate the new x-coordinate. Let's apply this transformation to each vertex of the polygon:

For point K(0, 0), we have K′(0, 0) (since the origin is its own image under any rotation).

For point L(5, 2), we have L′(−2, 5) (swapping the coordinates gives (2, 5), and negating the x-coordinate gives (−2, 5)).

For point M(5, −5), we have M′(5, 5) (swapping the coordinates gives (−5, 5), and negating the x-coordinate gives (5, 5)).

For point N(0, −3), we have N′(3, 0) (swapping the coordinates gives (−3, 0), and negating the x-coordinate gives (3, 0)).

Therefore, the image vertices of K′L′M′N′ under a rotation of 270° clockwise are:

=> K′(0, 0), L′(−2, 5), M′(5, 5), N′(3, 0)

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After the exchange, Peter will have 45 dollars & James will have 40 dollars.

What is an equation?

In mathematics, an equation shows that two expressions are equal. It consists of variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. An equation is typically written with an equal sign (=) between the two expressions

First, let's find the total amount of money they have together:

45 + 40 = 85 dollars

Now, let's say Peter gives x dollars to James. Then, James will give x dollars to Peter as well.

After the exchange, Peter will have 45 - x + x = 45 dollars.

Similarly, James will have 40 + x - x = 40 dollars.

So, no matter how much they exchange, they will always have a total of 85 dollars.

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The equation of the parabola with vertex at point (2, -11) and passes through the point (0, 5) is y = 4(x - 2)² - 11.

A straight line can be used to symbolise a function that is linear, meaning that for each unit change in the input, the output (y) changes by a fixed amount (x). While a parabola can be used to depict a function, a quadratic function has an output (y) that changes by a non-constant amount for each unit change in the input (x). In other words, a quadratic function curves because of the squared term in its equation.

Given, the parabola has vertex at point (2, -11) and passes through the point (0, 5).

Thus, the equation of parabola in vertex form is:

y = a(x - 2)² - 11

Now, the parabola passes through the point (0, 5) we have:

5 = a(0 - 2)² - 11

5 = 4a - 11

16 = 4a

a = 4

Hence, the equation of the parabola with vertex at point (2, -11) and passes through the point (0, 5) is y = 4(x - 2)² - 11.

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according to the question the given fraction can be solved with equation 1/3 x (15+6) is equal to 7.

To represent a whole, any quantity of equal parts or fractions can be utilised. In standard English, fractions show how many units there are of a particular size. 8, 3/4. Fractions are part of a whole. In mathematics, numbers are stated as a ratio between the numerator compared to the denominator. These can all be expressed as simple fractions as integers. A fraction appears in a complex fraction's numerator or denominator. The numerators of true fractions are smaller than the denominators. A sum that is a fraction of a total is called a fraction. You can analyse something by dissecting it into smaller pieces. For instance, the number 12 is used to symbolise half of a whole number or object.

given,

To evaluate the fraction 1/3 x (15+6), we need to perform the addition inside the parentheses first and then multiply the result by 1/3.

So, 15+6 equals 21.

Then, we can write:

1/3 x (15+6) = 1/3 x 21

Multiplying 1/3 by 21 gives:

1/3 x 21 = 7

Therefore, 1/3 x (15+6) is equal to 7.

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Answer:5

Step-by-step explanation: hope this helps

All the intersection points are determined as (-65, 0, 3.48).

To find the intersection points of the two given functions, we can set them equal to each other and solve for the values of x and y that satisfy the equation.

Setting y = 3x² + x - 10 equal to y = x³ + 6x² + d, we get:

3x² + x - 10 = x³ + 6x² + d

Rearranging this equation, we get:

x³ + 3x² - x + d - 10 = 0 ...........(1)

Now, since we are given that the two graphs intersect at x = -5, we can substitute x = -5 into equation (1) to find the value of d.

Substituting x = -5 into equation (1), we get:

(-5)³ + 3(-5)² - (-5) + d - 10 = 0

-125 + 3(25) + 5 + d - 10 = 0

75 + d - 10 = 0

65 + d = 0

d = -65

So the value of d is -65.

Now that we have the value of d, we can substitute it back into equation (1) to find the other intersection points.

Substituting d = -65 into equation (1), we get:

x³ + 3x² - x - 75 = 0 ...........(2)

Solve equation (2), using graphing system.

roots = (3.48, 0)

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Answer: To solve this problem, we can use the binomial distribution formula. Let X be the number of blue jelly beans in a bag of 200 jelly beans. Then X follows a binomial distribution with parameters n = 200 and p = 0.15, where p is the probability of drawing a blue jelly bean.

The probability of getting more than 20% blue jelly beans in a bag can be calculated as:

P(X > 0.2*200) = P(X > 40)

We can use the normal approximation to the binomial distribution, since n is large (200) and p is not too close to 0 or 1. Using the mean and variance of the binomial distribution, we can calculate the corresponding mean and standard deviation of the normal distribution as follows:

μ = np = 200 * 0.15 = 30

σ = sqrt(np(1-p)) = sqrt(200 * 0.15 * (1-0.15)) = 4.07

Then, we can standardize the random variable X as:

Z = (X - μ) / σ

So, we have:

P(X > 40) = P((X - μ) / σ > (40 - μ) / σ)

= P(Z > (40 - 30) / 4.07)

= P(Z > 2.46)

Using a standard normal distribution table or a calculator, we find that P(Z > 2.46) is approximately 0.007. Therefore, the probability that a bag will contain more than 20% blue jelly beans is about 0.007 or 0.7%.

Step-by-step explanation:

The rational inequality f(x) > 0 has the solution x > - 7

A rational inequality is an inequality in the form of a fraction

Given the function f(x) = (x + 7)/(x² - 4x + 3)

To find the value of x for which the function f(x) > 0, we proceed as follows

Given that f(x) > 0

So, this means that

(x + 7)/(x² - 4x + 3) > 0

This implies that

x + 7 > 0

Subtracting 7 from both sides, we have that

x + 7 - 7 > 0 - 7

x + 0 > - 7

x > - 7

So, f(x) > 0 has the solution x > - 7

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Answer:

Step-by-step explanation:

BD is craxking treys and cracking treys is gd dissing bd you can look it up i ffrom o block and bd is the opps im telling so you wont lose yo life so please play right if you gdk be gdk if u gd be gd we aint bd ofn

Answer:

all numbers greater than 8

Step-by-step explanation:

simply pick any number greater than 8, since the > symbol is in front of 8. By the way, you cannot pick 8. :) I hope this helps!

The third quartile range is the difference between the median height of the third grade class and the fourth grade class, so the answer is two times.

Answer:

171 > 117

Step-by-step explanation:

171 is greater than 117 meaning the alligator is eating the bigger number, 171.

In a case whereby Gary wants to make a circular pond in his yard and put a low fence around the edge. If Gary has 124 feet of fencing,  the closest to the area of the largest circular pond he can make with the fencing is 1471.61ft^2

We were told that he will bw making a pond which is circular in nature, then We can assume that the radius is R, then 2 πR = 136

R= 136/2 π

R= 68/π

The the are of the pond= πR^2

=  π * (68/π)^2

=1471.61ft^2

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Average Minutes Per Night Spent On Homework

0 20

48 60

190

Average Minutes Per Night Spent Watching TV

0 10

20 30

50

11. What is the median for TV time?

12. What is the range of times that the middle 50% of the sophomores spend on TV per night?

13. What percent of the sophomores spend more than 30 minutes per night watc

The measure of  angle CFE is determined as 29⁰.

The measure of angle CFE is calculated by applying the following formula.

The intersecting chord theorem, also known as the intersecting chords inside and outside theorem, is a geometric property that applies to chords (line segments that connect two points on the circumference of a circle) that intersect inside or outside a circle.

Based on the angle of intersecting chord theorem, we will have the following equation.

m∠CFE = ¹/₂( arc angle CE )

arc CE = 360 - 302 (sum of angles in a circle)

arc CE = 58⁰

m∠CFE = ¹/₂ x 58

m∠CFE = 29⁰

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The discount allowed for a cash payment of GH 5,600.00 is given as follows:

GHC 280.00.

The discount allowed for a cash payment of GH 5,600.00 is obtained applying the proportions in the context of the problem.

There is a 5% discount, hence the value of the discount is obtained as follows:

0.05 x 5600 = GHC 280.00.

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Using the proportions we know that the value of h would be 15 units when b is 10 units.

An online application called a proportion calculator solves two fractions for the parameter x.

It uses cross-multiplication to assess whether two fractions are equivalent.

A proportion is an equation that sets two ratios at the same value.

For instance, you could express the ratio as follows: 1: 3 if there is 1 boy and 3 girls. (for every boy there are 3 girls) There are 1 in 4 boys and 3 in 4 girls. 0.25 are male. (by dividing 1 by 4).

So, according to the given similar triangle, the proportions would be:

4/b = 6/h

Now, insert the given values:

4/10 = 6/h

Solve as follows:

4/10 = 6/h

4h = 60

h = 60/4

h = 15

Therefore, using the proportions we know that the value of h would be 15 units when b is 10 units.

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