Alex is drawing rectangles with different areas on a centimetre grid.He can draw 2 different rectangles with an area of 6cm² how many different rectangles could Alex draw with an area of 5cm²give a reason for your answer?

Answer:

Step-by-step explanation:

The cost of one ticket will be  £8.20

Explanation

Suppose, the cost of one ticket is  

As the offer says "buy 3 tickets and get a ticket free" , it means they actually need to pay for 3 tickets.

So, the total cost of 3 tickets  

Each of four friends pay £6.15 , so the total amount they pay  

=£6.15*4=£24.60

Thus, the equation will be .....

=3x=24.60

=x=24.60/3=8.20

 So, the cost of one ticket will be  £8.20

a) we reject the null hypothesis at the 5% significance level. The P-value is less than 0.01. b) This interval does not contain zero, we can conclude that the difference in means is statistically significant at the 5% level. c) The power of the test is 0.31. d)  we need a sample size of 23 in each group to achieve a power of 0.95.

(a) To test the hypothesis H0: μ1 = μ2 against H1: μ1 ≠ μ2, we can use a two-sample t-test assuming equal variances. The test statistic is given by:

t = (X1 - X2) / \(\sqrt{s^{2}p*(1/n1 + 1/n2) }\)  

where X1 and X2 are the sample means, s²p is the pooled sample variance, n1 and n2 are the sample sizes, and t follows a t-distribution with degrees of freedom df = n1 + n2 - 2.

The pooled sample variance is given by:

s²p = [(n1 - 1) * s1² + (n2 - 1) * s2²] / (n1 + n2 - 2)

where s1² and s2² are the sample variances for the first and second sample, respectively.

Using the given values, we have:

X1 = 4.7, X2 = 7.8

s1² = 4, s2² = 6.25

n1 = n2 = 15

s²p = [(15 - 1) * 4 + (15 - 1) * 6.25] / (15 + 15 - 2) = 4.625

Substituting these values into the formula for t, we get:

t = (4.7 - 7.8) / \(\sqrt{4.625*(1/15 + 1/15)}\) = -3.23

The P-value for this test is the probability of obtaining a t-value more extreme than -3.23 under the null hypothesis. This can be calculated using a t-distribution with 28 degrees of freedom (df = n1 + n2 - 2), or by using software or a t-table. For α = 0.05, the critical values are ±2.048. Since -3.23 is outside this range, we reject the null hypothesis at the 5% significance level. The P-value is less than 0.01.

(b) To construct a confidence interval for the difference in means, we can use the formula:

(X1 - X2) ± tα/2, \(\sqrt{s^{2}p*(1/n1 + 1/n2) }\)  

where tα/2 is the t-value with α/2 area to the right (or left) under the t-distribution with degrees of freedom df = n1 + n2 - 2, and s²p is the pooled sample variance as before.

Using the same values as before and α = 0.05, we have:

tα/2 = 2.048 (from the t-table)

(X1 - X2) ± 2.048 *  \(\sqrt{4.625*(1/15 + 1/15)}\)

= -3.126 to -0.474

We can interpret this interval as follows: we are 95% confident that the true difference in means falls between -3.126 and -0.474. Since this interval does not contain zero, we can conclude that the difference in means is statistically significant at the 5% level.

(c) The power of the test is the probability of correctly rejecting the null hypothesis when the alternative hypothesis is true. It depends on several factors, including the sample sizes, the level of significance, the effect size (i.e., the difference between the population means), and the variability of the data.

To calculate the power of the test for a true difference in means of 3, we need to specify the effect size and the sample sizes. Assuming equal variances and a two-sided test with a level of significance of 0.05, we can use a standard formula or a statistical software to calculate the power of the test. For example, using the R statistical software, we can use the power.t.test function. the power of the test is approximately 0.31, which means that there is a 31% chance of correctly rejecting the null hypothesis if the true difference in means is 3.

d) To determine the sample size needed to achieve a desired level of power, we need to specify the effect size, the level of significance, the desired power, and the variability of the data. Assuming equal variances and a two-sided test with a level of significance of 0.05, we can use a standard formula or a statistical software to calculate the sample size needed to achieve a desired power. For example, using the R statistical software, we can use the power.t.test function. we need a sample size of approximately 23 in each group to achieve a power of 0.95, assuming a true difference in means of -2 and a standard deviation of 4.5 (the average of the two sample standard deviations).

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When bisecting a segment using a compass, Sasha's next step would be to swing an arc that intersects the segment. Correct option is B.

To bisect a segment, Sasha needs to find the midpoint of the segment. The compass can help her achieve this by creating two arcs with the same radius from each endpoint of the segment. The intersection of these arcs will be the midpoint of the segment.

Sasha's first step is to place the compass on one endpoint of the segment and open it to a width larger than the length of the segment. Then, she places the compass on the other endpoint and draws an arc that intersects the first arc.

The next step is to swing an arc with the same radius from the other endpoint of the segment, again intersecting the first arc. The intersection of these two arcs will give the midpoint of the segment, which can be marked with a straightedge.

Therefore, Sasha's next step in bisecting a segment using a compass is to swing an arc that intersects the segment.

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Answer:

7:00pm

Step-by-step explanation:

Answer:

Step-by-step explanation:

3:3:2 = 3x +2x +3x = 8x

112 = 8x

x = 14

alex = 3x = 3(14) = 42

sara = alex = 42

henry = 2x = 28

Answer:

the probability is 3/5

Step-by-step explanation:

you have the numbers 2, 4, 6

and the numbers 3, 5

the 1 doesn't count, the question says numbers greater than or equal to 2

so, the remaining numbers add up to 3/5

Answer:

Isosceles triangle. An Isosceles triangle is a triangle that has 2 equal sides and 2 equal angles

Step-by-step explanation:

The algorithm is designed to find out whether the child wins or loses in a game where two players take turns to pick balls. The algorithm takes the number of balls remaining in the box as input and returns True if the child wins, otherwise False.

The algorithm assumes that both players play optimally. The algorithm works by recursively picking balls from the box and checking whether the child or the game owner wins the game.

This is a recursive problem where each player plays optimally. There are two players in the game. The child will pick the balls first and then the game owner takes turns. Both will pick the balls optimally in order to win.

In each turn, k balls can be picked from the box. The winner is the one who picks the last ball. If the child picks the last ball, they win otherwise the game owner wins.

The algorithm is as follows:

Algorithm - Pick Balls

1. Define a recursive function called PickBalls(n). The function takes one parameter as input, which is the number of balls remaining in the box.

2. Check if the number of balls remaining is less than or equal to k. If yes, then return True as the game has ended and the child has won.

3. If the number of balls is greater than k, then pick k balls from the box.

4. If the child picks the last ball, then return True.

5. If the child does not pick the last ball, then the game owner picks the balls recursively.

6. If the game owner picks the last ball, then return False. Otherwise, return True.

Explanation: We are designing a recursive algorithm to find out whether the child will win or lose in a game where two players take turns to pick balls. The algorithm takes the number of balls remaining in the box as input and returns True if the child wins, otherwise False. We are assuming that both players play optimally. The algorithm works as follows:

If the number of balls remaining in the box is less than or equal to k, then the child can pick all the balls and win the game. Therefore, the function returns True.

If the number of balls remaining in the box is greater than k, then the child picks k balls from the box. If the child picks the last ball, then they win the game. Therefore, the function returns True.

If the child does not pick the last ball, then the game owner picks the balls recursively. If the game owner picks the last ball, then they win the game. Therefore, the function returns False. If the game owner does not pick the last ball, then the child picks again and the process repeats itself. If the child eventually picks the last ball, then they win the game. Therefore, the function returns True.

Conclusion: The algorithm is designed to find out whether the child wins or loses in a game where two players take turns to pick balls. The algorithm takes the number of balls remaining in the box as input and returns True if the child wins, otherwise False. The algorithm assumes that both players play optimally. The algorithm works by recursively picking balls from the box and checking whether the child or the game owner wins the game.

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The option B is a correct option which is y = 26x and y = -0.030(x-500)2 15,900 represent the quadratic and linear function.

According to the statement

we have given that Vertex

(h,k) = (500, 15900)

And One of the points on the graph

(x,y) = (0,8400)

FIRST PART: we have to find the quadratic function

We can find the quadratic function by parabola's equation formula

y = a (x - h)² + k  -(1)

Input the numbers to the formula, to find the value of a

y = a (x - h)² + k

8400 = a(0 - 500)² + 15900

8400 = a (500)² + 15900

8400 = 250000a + 15900

-250000a = 15900 - 8400

-250000a = 7500

a = 7500/-250000

a = 0.03

Now,

Submit a to the formula (1)

y = a (x - h)² + k

y = 0.03 (x - 500)² + 15900

this is the quadratic equation.

SECOND PART: Find the linear function

the total cost = cost each helmet × the number of helmet

y = 26x

So,

The option B is a correct option which is y = 26x and y = -0.030(x-500)2 15,900 represent the quadratic and linear function.

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Disclaimer: This question was incomplete. Please find the full content below.

Question: A company plans to sell bicycle helmets for $26 each. The company's business manager estimates that the cost, y, of making x helmets is a quadratic function with a y-intercept of 8,400 and a vertex of (500, 15900)

x= number of helmets

y = amount in dollars

Which system models this situation?

a) y = 26x and y = 8,400(x-500)2+15,900

b) y = 26x and y = -0.030(x-500)2+15,900

c) y = x/26 and y = -0.030(x-500)2+15,900

d) y = x/26 and y =8,400(x-500)2+15,900

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Answer:

B. y = 26x and y = -0.030(x-500)2+15,900

Step-by-step explanation:

Answer:

22

Step-by-step explanation:

21 23 19 25 83 23 21

Removing the outlier of 83

21 23 19 25 23 21

Find the mean

Add the numbers and divide by the number of numbers

(21+ 23+ 19+ 25+ 23+ 21)/6

132/6

22

a) The relationship between b and c is that c cannot be zero.

b) b can be any nonzero constant and c is equal to 2.5 in this case.

In two dimensions, the compatibility equations for strain are,0

∂εx/∂y + ∂γxy/∂x = 0

∂εy/∂x + ∂γxy/∂y = 0

where εx and εy are the normal strains in the x and y directions, respectively, and γxy is the shear strain.

Using the given strain field, we can calculate the strains,

εx = -4.5cx² + 10.5cy

εy = 1.5cx² - 7.5cy²

γxy = 1.5bxy

Taking partial derivatives and plugging them into the compatibility equations, we get,

⇒ -9cx + 0 = 0

⇒ 0 + (-15cy) = 0

These equations must be satisfied for the strain field to be compatible. From the first equation,

We get cx = 0, which means c cannot be zero.

From the second equation, we get cy = 0,

Which means b can be any nonzero constant.

For part b:

We are asked to find the displacements u and v corresponding to the given strain field at points (3, 7), assuming they are zero at point (0, 0) and using c = 2.5.

To find the displacement components,

We need to integrate the strains with respect to x and y. We get,

u = ∫∫εx dx dy = ∫(10.5cy) dy = 5.25cy²

v = ∫∫εy dx dy = ∫(1.5cx² ) dx - ∫(7.5cy²) dy = 0.5cx³ - 2.5cy³

Plugging in the values of c and b, we get,

u = 5.25(2.5)(7)²  = 767.62

v = 0.5(2.5)(3)³ - 2.5(7)³ = -8583.75

Therefore,

The displacements at points (3, 7) are u = 767.62 and v = -8583.75.

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The p-value for a test concerning a mean is 0.064.

What is p-value?

A p-value, also known as a probability value, is a numerical representation of the likelihood that your data would have occurred under the null hypothesis of your statistical test.

As per question given,

This is two tail list then z = 1.85.

p (z > 1.85) = 1 - p (z < 1.85)

                  = 1 - 0.9678

                  = 0.0322

Thus, the p-value is

p-value = 2 × 0.0322

            = 0.064

Hence, the p-value for a test concerning a mean is 0.064.

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Explanation

We are given a triangle

and then asked to determine the value of x

To do so, we know that the total angles in a triangle are 180 degrees

Thus

The value of x is 41 degrees

Answer:

x = 9

Step-by-step explanation:

2/3x = 6

Multiply each side by 3/2

3/2 * 2/3x = 6 * 3/2

x = 18/2

x = 9

Answer: uses a visual representation of the logical flow of steps needed to reach a conclusion.

Step-by-step explanation:

A flowchart proof is a visual representation that is made of boxes with which arrows are used to show the flow of steps which take place. It uses a visual representation of the logical flow of steps needed to reach a conclusion.

The true facts which are the statements, will be placed in the boxes that are drawn. The arrows in flowchart proof shows the progression of statements made.

A flowchart proof uses a visual representation of the logical flow of steps needed to reach a conclusion.

Here, we have to find the definition or the use of the flowchart proof.

It is a method to prove any theorems or corollaries in a more easily understandable way.

In the flowchart proof, the statements are written in an order of series with the reasoning behind the statement written below them.

The statements are usually written inside a box and underneath it will be the logical reasoning.

So the correct option is that it uses a visual representation of the logical flow of steps needed to reach a conclusion.

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Answer:

The correct answer: F (Scalene) and A (Acute)

Step-by-step explanation:

F. (Scalene):  By definition, a scalene triangle is a triangle that has no equal sides, and no equal angles. This definition matches your given triangle, since it has no equal sides and angles.

A. (Acute): By definition, an acute triangle is a triangle in which all the internal angles are less than 90 degrees. This definition matches your given triangle, since all of the internal angles are less than 90 degrees.

The given triangle is not obtuse, equilateral, right, and isoceles.

It is not an obtuse triangle because none of the angles are greater than 90 degrees.

It is not an equilateral triangle because its sides are not equal.

It is not a right triangle because none of its internal angles measure 90 degrees.

And it is not an isoceles triangle because by definition, an isoceles triangle must have two equal sides. Your given triangle has no equal sides.

Answer:

the answer is d.

Step-by-step explanation:

each variable is being divided by negative two.

32/-2 = -16

-16/-2 = 8

8/-2 = -4

-4/-2 = 2

2/-2 = -1

Answer:

-5

Step-by-step explanation:

when you eat 5 pieces of candy per day then the sequence will be

125, 120, 115, 110, 105......

And Then, the common difference will be -5

The price of the item after the first month can be expressed as 300 - (0.20 * 300) or 300 * (1 - 0.20). The price of the item after the second month can be expressed as (300 - (0.20 * 300)) - (0.25 * (300 - (0.20 * 300))) or 300 * (1 - 0.20) * (1 - 0.25).

Expression 1: Price after the first month = 300 - (20% of 300)

We subtract 20% of the original price, which is equivalent to multiplying 300 by 0.20 and subtracting it from 300. This represents a 20% decrease in price.

Expression 2: Price after the first month = 300 * (1 - 20%)

We calculate the new price by multiplying the original price by 1 minus 20% (which is 0.20). This represents a 20% decrease in price.

Math drawing:

Let's consider a bar graph where the length of the bar represents the original price (300). We can visualize a 20% decrease by shading out 20% of the length of the bar.

[300] ------X------- (X represents the 20% decrease portion)

Expression 1: Price after the second month = (300 - 20%) - (25% of (300 - 20%))

We first calculate the price after the first month using one of the expressions from question 1. Then, we subtract 25% of that new price. This represents a 25% decrease in the already decreased price.

Expression 2: Price after the second month = 300 * (1 - 20%) * (1 - 25%)

We calculate the new price by multiplying the original price by (1 - 20%) to represent the first month's decrease, and then further multiply it by (1 - 25%) to represent the second month's decrease.

Math drawing:

Using the same bar graph from before, we can visualize a 25% decrease from the already decreased price (represented by the shaded portion).

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The equations represent the line that is perpendicular to the line 5x − 2y = −6 and passes through the point (5, −4) is y = (-2/5)x + 2

The given equation of the line is

5x - 2y = -6

Ax + By = C1

Bx - Ay = C2

are perpendicular.

Then the perpendicular to the line 5x - 2y = -6 is 2x + 5y = C2

We have to find the value of C2

The line is passing through the point (5, -4)

Substitute the values in the equation and find the value of C2

2(5) + 5(-4) = C2

C2 = 10 -20

= -10

The equation will be 2x + 5y = -10

Rearrange the terms and make it slope intercept form

2x + 5y = -10

5y = -10 -2x

5y = -2x - 10

y = (-2/5)x - 2

Hence,  equations represent the line that is perpendicular to the line 5x − 2y = −6 and passes through the point (5, −4) is y = (-2/5)x + 2

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Answer:

g(x) has a larger slope

Step-by-step explanation:

If you look closely, g(x) has a slope of 5.

The series estimate of the sum is between 1.000020993 and 1.000031132.

The given series is S = \(1/1^5 + 1/2^5 + 1/3^5\) + ...

We need to compute the 4th partial sum S4.

S4 =\(1/1^5 + 1/2^5 + 1/3^5 + 1/4^5\)

Using a calculator, we get:

S4 ≈ 1.000015873

To estimate the error in using S4 as an approximation of the sum of the series, we can use the integral test. Let f(x) = 1/\(x^5\).

Then, ∫f(x) dx from 4 to ∞ = ∫(1/\(x^5\)) dx from 4 to ∞

= [-1/(\(4x^4\))] from 4 to ∞

= (1/\(4^4\)) - (1/∞)

= 1/256

Since f(x) is positive, decreasing, and continuous for x ≥ 1, the integral test applies and we have:

S - S4 = ∫f(x) dx from 4 to ∞

≥ 1/256

Therefore, the error in using S4 as an approximation of the sum of the series is at least 1/256.

To find a better estimate of the sum, we can use the following inequality:

S_n + ∫f(x) dx from n+1 to ∞ ≤ S ≤ S_n + ∫f(x) dx from n to ∞

where Sn is the nth partial sum of the series.

For n = 4, we have:

S4 + ∫f(x) dx from 5 to ∞ ≤ S ≤ S4 + ∫f(x) dx from 4 to ∞

Substituting the values, we get:

1.000015873 + ∫(1/\(x^5\)) dx from 5 to ∞ ≤ S ≤ 1.000015873 + ∫(1/\(x^5\)) dx from 4 to ∞

Simplifying the integral, we get:

1.000015873 + [(1/\(4^4\)) - (1/5^4)] ≤ S ≤ 1.000015873 + (1/\(4^4\))

Solving for the bounds, we get:

1.000015873 + 0.00000512 ≤ S ≤ 1.000015873 + 0.000015259

1.000020993 ≤ S ≤ 1.000031132

Therefore, a better estimate of the sum is between 1.000020993 and 1.000031132.

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Answer:  The surface area is reduced by a factor of 16/25

Step-by-step explanation:  The area is the square measurements. So squaring the factor of the linear measurement change is the quick way is to determine the factor for the area.

The longer way-- if you had to prove your conclusion:

Compute the area of each side, add all the five sides of the prisms and find the ratio.

The area of the large prism is 500 square units.

The area of the smaller prism is 320 square units

320/500 = 32/50,  reduce again  16/25

Answer:

B. 16/25

Step-by-step explanation:

Just took the Pre-Test on Edg (2020-2021)!

Answer:

Step-by-step explanation:

Given the equation x + 5 = 1, to get the solution to the equation, we need to find the value of x

Step 1: Subtract 5 from both sides of the equation

x+5-5 = 1-5

x = 1-5

Step 2: Find the value of the unknown variable x

x = -4

The solution to the equation is x = -4

Answer:

85

Step-by-step explanation:

8+3+4

Answer:

140

Step-by-step explanation:

The measure of arc of FH is 140.

The arc of a circle between two distinct locations is known as a circular arc.

One of these arcs, the minor arc, subtends an angle at the circle's center that is less than radians (180 degrees), and the other arc, the major arc, subtends an angle higher than radians if the two points are not exactly opposite one another.

A circle's arc is referred to as a portion or section of its circumference. A chord of a circle is a straight line that joins the two ends of the arc. A semicircular arc is one whose length is exactly half that of a circle.

Therefore, The measure of arc of FH is 140.

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Answer:

Step-by-step explanation:

KALIS2007

Answer:

7500

Step-by-step explanation:

Answer:

The problem seems to be incomplete, after an online search I couldn't find the complete question, to be able to solve the question, I will assume that the known measure is the width W.

For a rectangular prism of length L and width W, the surface area is calculated as:

S = W*L

For the assumption we took, we have:

W = 39.5ft

And we also know that S = 158 ft^2

And we want to find the missing dimension, in this case is L, then we need to solve:

158 ft^2 = W*L

We just need to divide both sides by the known measure, W

We get:

(158 ft^2)/W = L

So you just need to replace the known value, and can find the missing one.