Coaching companies claim that their courses can raise the SAT scores of high school students. Of course, students who retake the SAT without paying for coaching generally raise their scores. A random sample of students who took the SAT twice found 427 who were coached and 2733 who were uncoached. Starting with their verbal scores on the first and second tries, we have these summary statistics:
Try 1 Try 2 Gain
x s x s x s
Coached 500 92 529 97 29 59
Uncoached 506 101 527 101 21 52
Let's first ask if students who are coached significantly increased their scores.
You could use the information given to carry out either a two-sample t test comparing Try 1 with Try 2 for coached students or a matched pairs t test using Gain. Which is the correct test? Why?
A. Two-sample test, because we are given data for the two samples which is more accurate than the data only on the gain.
B. Matched pairs test, because we are not interested in the difference in mean between the two groups, but the gain that each student has achieved.
C. Two-sample test, because matched pairs test can be performed only if we have information on every individual.
D. Matched pairs test, because we are interested in the difference in mean between the two groups - not the gain that each student has achieved.

#hope it helps ^_^

mark me as brainliest please

Answer:

C. \( \frac{5}{4} \)

D. \( \frac{6}{7} \)

Step-by-step explanation:

C. \(2 - \frac{12}{16} \)

\( = 2 - \frac{3}{4} \)

\( = \frac{8 - 3}{4} \)

\( = \frac{5}{4} \)

D. \( \frac{20}{22} \times \frac{33}{35} \)

\( = \frac{10}{11} \times \frac{33}{35} \)

\( = 10 \times \frac{3}{35} \)

\( = 2 \times \frac{3}{7} \)

\( = \frac{6}{7} \)

Therefore, the quotient when x³ - x² - 3x + 2 is divided by x - 2 is x² - 2x - 5 with a remainder of -3.

To find the quotient when x³ - x² - 3x + 2 is divided by x - 2, we will use the long division method. Here is the solution:  

Step 1: The first term of the quotient is x². Multiply x² by x - 2 to get x³ - 2x². Subtract this product from x³ - x² to get: x² - 3x² = -2x²

Step 2: Bring down the next term of the dividend, which is -3x. The new dividend is -2x² - 3x.

Step 3: The second term of the quotient is -2x. Multiply -2x by x - 2 to get -2x² + 4x. Subtract this product from -2x² - 3x to get -5x.

Step 4: Bring down the last term of the dividend, which is +2. The new dividend is -5x + 2. Step 5: The third term of the quotient is -5. Multiply -5 by x - 2 to get -5x + 10. Subtract this product from -5x + 2 to get -3.

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Answer:

50.75

Step-by-step explanation:

We have:

\(E[g(x)] = \int\limits^{\infty}_{-\infty} {g(x)f(x)} \, dx \\\\= \int\limits^{1}_{-\infty} {g(x)(0)} \, dx+\int\limits^{6}_{1} {g(x)\frac{2}{x} } \, dx+\int\limits^{\infty}_{6} {g(x)(0)} \, dx\\\\= \int\limits^{6}_{1} {g(x)\frac{2}{x} } \, dx\\\\=\int\limits^{6}_{1} {(4x+3)\frac{2}{x} } \, dx\\\\=\int\limits^{6}_{1} {(4x)\frac{2}{x} } \, dx + \int\limits^{6}_{1} {(3)\frac{2}{x} } \, dx\\\\=\int\limits^{6}_{1} {8} \, dx + \int\limits^{6}_{1} {\frac{6}{x} } \, dx\\\\\)

\(=8\int\limits^{6}_{1} \, dx + 6\int\limits^{6}_{1} {\frac{1}{x} } \, dx\\\\= 8[x]^{^6}_{_1} + 6 [ln(x)]^{^6}_{_1}\\\\= 8[6-1] + 6[ln(6) - ln(1)]\\\\= 8(5) + 6(ln(6))\\\\= 40 + 10.75\\\\= 50.74\)

The equation that represents the statement is

2y = 100+9x

A linear equation is an algebraic equation where each term has an exponent of 1 and when this equation is graphed, it always results in a straight line. This is the reason why it is named as a 'linear equation.

If x represents the number of years invested and y represents the investment's value.

I = p×r×t/100

I = 50 × 9 × x/100

I = 9x/2

A = P+1

y = 50+ 9x/2

multiply both sides by 2

2y = 100+9x

therefore the equation of the statement is

2y = 100+9x

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Answer:

d=-6.5

Step-by-step explanation:

2d+13=0

2d=-13

d= -13/2

d=-6.5

Answer:

There are 12 blocks in the bottom layer

Step-by-step explanation:

We see from the diagram that in the bottom layer,

length = 3 cm

width = 4 cm

And that there are 3 blocks for the 3 cm length,

Hence each block has a length of 1 cm (the 3 then make up 3 cm)

And there are 4 blocks for the 4 cm width

Hence the width is also 1 cm (4 of these make up 4 cm width)

Now, to find the total number of blocks,

we just multiply the length and width,

so, (3)(4) = 12

so there are 12 blocks in the bottom layer

Answer:

To fill in the table of values for the equation y = 2x + 1, we can choose different values of x and substitute them into the equation to find the corresponding values of y. For example:

x y

0 1

1 3

2 5

3 7

4 9

To get the value of y, we substitute each value of x into the equation and simplify:

When x = 0:

y = 2(0) + 1 = 1

When x = 1:

y = 2(1) + 1 = 3

When x = 2:

y = 2(2) + 1 = 5

When x = 3:

y = 2(3) + 1 = 7

When x = 4:

y = 2(4) + 1 = 9

Therefore, the table of values for the equation y = 2x + 1 is:

x y

0 1

1 3

2 5

3 7

4 9

Answer:

Step-by-step explanation:

Using midpoint formula

Midpoint is (5, 3)

Answer:

Step-by-step explanation:

A(-1, 7)   B(11, 1)

use the midpoint formula:

mid point = (x₁ + x₂) ,  (y₁ + y₂)

                        2              2

                = (-1 + 11) , (7 - 1)

                        2          2

mid point = 5,  3

The amount of hot chocolate served daily is inversely correlated with the temperature of the city, with more cups being sold once the temperature is between 40 and 50 F.

When two variables change in tandem, the relationship is said to be direct. The variable y increases as the variable x increases. A linear relationship denoted by the equation y = kx is directly proportional.

There is a direct correlation between a circle's radius and area, meaning that when the radius is increased or decreased, the area correspondingly changes. If one variable increases while the other declines or vice versa, the relationship between the two variables is inverse.

For given question-

Jordan created the graph below to illustrate the correlation between a city's temperature and the daily sales of hot chocolate.

As we can see that - when the temperature increases the demand for the ice cream also increases which is the direct relation.

Thus, the amount of hot chocolate served daily is inversely correlated with the temperature of the city, with more cups being sold once the temperature is between 40 and 50 F.

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The diagram for the question is attached:

The contractor has a maximum of 29 hours (rounded down) to complete the job while keeping the total cost under $2000.

To find the number of hours the contractor has for the job while keeping the total cost under $2000, we can use the given cost model equation: C = 43H + 750.

Since the owner wants the total cost to be under $2000, we can set up the inequality:

43H + 750 < 2000

Now, let's solve this inequality for H, the number of hours:

43H < 2000 - 750

43H < 1250

Dividing both sides of the inequality by 43:

H < 1250/43

To determine the maximum number of hours the contractor has for the job, we need to round down the result to the nearest whole number since the contractor cannot work a fraction of an hour.

Using a calculator, we find that 1250 divided by 43 is approximately 29.07. Rounding down to the nearest whole number, we get:

H < 29

Using the cost model equation C = 43H + 750, where C represents the total cost and H represents the number of hours, we set up the inequality 43H + 750 < 2000 to satisfy the owner's requirement of a total cost under $2000.

By solving the inequality and rounding down to the nearest whole number, we find that the contractor has a maximum of 29 hours to complete the job within the specified cost limit.

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We know the equation for a circle is given by

( x-h) ^2 + ( y-k) ^2 = r^2 where ( h,k) is the center and r is the radius

We know the center of the circle is at ( 4,-3)

( x-4) ^2 + ( y--3) ^2 = r^2

( x-4) ^2 + ( y+3) ^2 = r^2

Now we need to find the radius which is the distance from the center to the point (5,1)

r = sqrt( ( x2-x1)^2 + ( y2 - y1) ^2 )

= sqrt( ( 5 - 4) ^2 + ( 1 - -3) ^2)

= sqrt( ( 1^2 + ( ( 1+3) ^2)

= sqrt( 1 + 4^2)

= sqrt( 1+16)

= sqrt( 17)

Squaring each side

r^2 = 17

( x-4) ^2 + ( y+3) ^2 = 17

Answer: C) SAS is correct

Check out the diagram below.

We're given BA = BC as shown in red.

The congruent angles are shown in blue. The larger angle is bisected into smaller equal halves.

The red segments are congruent by the reflexive property.

The angles mentioned are between the sides mentioned, so that's why we can use SAS.

a. To create a pie chart to show the total medal winnings of the Top 10 NOCs at the Beijing 2022 Winter Olympic games:

Obtain the data for the medal winnings of the Top 10 NOCs

Calculate the total medal winnings for each NOC (i.e., the sum of gold, silver, and bronze medals)

Create a pie chart in Excel or any other software by selecting the data and choosing the pie chart option

Add a title and labels to the chart to show the NOCs and their corresponding medal winnings

b. The interpretation of the pie chart produced in Question 8a) depends on the shape and distribution of the chart. Two probable justifications for the behavior of the data are:

Dominance of certain NOCs: The pie chart may show that certain NOCs have a significantly higher share of medal winnings compared to others. This may be due to the dominance of these NOCs in specific sports or events, or due to their superior training and preparation.

Balanced distribution of medals: The pie chart may show a relatively balanced distribution of medal winnings among the Top 10 NOCs. This may indicate a high level of competitiveness and equal opportunities for success among the NOCs.

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Step-by-step explanation:

I just answered this.

we have 2 angles and their connecting side in between that are congruent (identical).

so, it is D. ASA (angle side angle)

just look up the meaning of the acronyms, and it will all be clear and very easy.

The inequality is X > 0 and a word sentence represent the graph is  X  the graph of a number line with an open circle on zero and an arrow pointing to the right.

The inequality X > 0 represents the graph of a number line with an open circle on zero to left and an arrow pointing to the right. This means that any value of X that is greater than zero is a valid solution for the inequality.

In other words, X can be any positive number, such as 1, 2, 3, and so on. However, X cannot be zero or any negative number, as those values do not satisfy the inequality. Therefore, the word sentence that represents this inequality is "X is greater than zero."

This means that X must be a positive number, and it can be any value that is greater than zero.

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The inequality that describes the problem is C. 8x ≤ 16

Inequalities are created through the connection of two expressions. It should be noted that the expressions in an inequality aren't always equal. Inequalities implies that the expressions are not equal. They are denoted by the symbols ≥ < > ≤.

Since Kamari's Sweet Treats, cookies are packaged in boxes of 8 and the most a box can cost is $16. This will be:

8x ≤ 16

The correct option is C.

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Answer:

C) inconsistent

Step-by-step explanation:

3x+y=−5

3y+15=−9x

3x + y = -5

9x + 3y = 15

3x + y = -5

3x + y = 5

The system graphs as two parallel lines.

Answer: C) inconsistent

From the constraint, we have

\(x+y+z=9 \implies z = 9-x-y\)

so that \(s\) depends only on \(x,y\).

\(s = g(x,y) = xy + y(9-x-y) + x(9-x-y) = 9y - y^2 + 9x - x^2 - xy\)

Find the critical points of \(g\).

\(\dfrac{\partial g}{\partial x} = 9 - 2x - y = 0 \implies 2x + y = 9\)

\(\dfrac{\partial g}{\partial y} = 9 - 2y - x = 0\)

Using the given constraint again, we have the condition

\(x+y+z = 2x+y \implies x=z\)

so that

\(x = 9 - x - y \implies y = 9 - 2x\)

and \(s\) depends only on \(x\).

\(s = h(x) = 9(9-2x) - (9-2x)^2 + 9x - x^2 - x(9-2x) = 18x - 3x^2\)

Find the critical points of \(h\).

\(\dfrac{dh}{dx} = 18 - 6x = 0 \implies x=3\)

It follows that \(y = 9-2\cdot3 = 3\) and \(z=3\), so the only critical point of \(s\) is at (3, 3, 3).

Differentiate \(h\) again and check the sign of the second derivative at the critical point.

\(\dfrac{d^2h}{dx^2} = -6 < 0\)

for all \(x\), which indicates a maximum.

We find that

\(\max\left\{xy+yz+xz \mid x+y+z=9\right\} = \boxed{27} \text{ at } (x,y,z) = (3,3,3)\)

The second derivative at the critical point exists

\($\frac{d^{2} h}{d x^{2}}=-6 < 0\) for all x, which suggests a maximum.

Given, the constraint, we have

x + y + z = 9

⇒ z = 9 - x - y

Let s depend only on x, y.

s = g(x, y)

= xy + y(9 - x - y) + x(9 - x - y)

= 9y - y² + 9x - x² - xy

To estimate the critical points of g.

\($&\frac{\partial g}{\partial x}\) = 9 - 2x - y = 0

\($&\frac{\partial g}{\partial y}\) = 9 - 2y - x = 0

Utilizing the given constraint again,

x + y + z = 2x + y

⇒ x = z

x = 9 - x - y  

⇒ y = 9 - 2x, and s depends only on x.

s = h(x) = 9(9 - 2x) - (9 - 2x)² + 9x - x² - x(9 - 2x) = 18x - 3x²

To estimate the critical points of h.

\($\frac{d h}{d x}=18-6 x=0\)

⇒ x = 3

It pursues that y = 9 - 2 \(*\) 3 = 3 and z = 3, so the only critical point of s exists at (3, 3, 3).

Differentiate h again and review the sign of the second derivative at the critical point.

\($\frac{d^{2} h}{d x^{2}}=-6 < 0\)

for all x, which suggests a maximum.

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Answer:

The amount of silver that will be left after 100seconds is 68grams

Half-life is the time required for a quantity to reduce to half of its initial value. The term is commonly used in nuclear physics to describe how quickly unstable atoms undergo radioactive decay or how long stable atoms survive. The term is also used more generally to characterize any type of exponential decay.

Since the half life of the silver is 25 sec

No/2 = 544/2 = 272 grams

at 50seconds

No/4 = 272/2 = 136 grams

at 100seconds

No/8 = 136/2 = 68grams

therefore the gram of silver left after 100 seconds is 68grams

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Answer:

100°

Step-by-step explanation:

tThe sum of all arc measures that make up that circle is 360 degrees.

QS + RQ + RS = 360

QS = 360 - 120 - 140 = 100

An arc angle is the degree measurement of that angle inside the circle, opposite the arc

m∠R = arc QS = 100°

Answer:

∠ R = 50°

Step-by-step explanation:

the inscribed angle R is half the measure of its intercepted arc QS

the sum of the arcs on a circle is 360° , that is

RQ + QS + SR = 360°

120° + QS + 140° = 360°

QS + 260° = 360° ( subtract 260° from both sides )

QS = 100°

Then

∠ R = \(\frac{1}{2}\) × 100° = 50°

The function g( x ) is translated to the left by 9 units and down by 5 units.

Given data ,

Let the first function be represented as f ( x )

where the value of f ( x ) = | x |

Let the translated function be g ( x )

where the value of g ( x ) = | x + 9 | - 5

A translation in the coordinate plane moves every point on a figure a given distance in a given direction. The position of any point (x, y) on the figure changes to (x + a, y + b), where a and b are real numbers.

On translating to the left , f ( x + a )

So , the function f ( x ) is translated 9 units to the left by f ( x + 9 ) = | x + 9 |

Now , when the function is translated 5 units down , f ( x ) - 5

So , the translated function is g ( x ) = | x + 9 | - 5

Hence , the function is translated to the left by 9 and up by 5 units.

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Answer: To find A and B such that g(x) = f(x) is bijective, we need to ensure that g(x) satisfies the conditions for a bijective function, namely, that it is both injective and surjective.

To show that g(x) is injective, we need to show that for any distinct x1, x2 in A, g(x1) ≠ g(x2). We can do this by assuming that g(x1) = g(x2) and then showing that it leads to a contradiction.

So, let's assume that g(x1) = g(x2). Then, we have:

f(x1) = f(x2)

x1(x1-1) = x2(x2-1)

x1^2 - x1 = x2^2 - x2

x1^2 - x2^2 - x1 + x2 = 0

(x1 - x2)(x1 + x2 - 1) = 0

Since x1 and x2 are distinct, we must have x1 + x2 = 1.

But this is impossible, since x1 and x2 are both real numbers, and the sum of two real numbers cannot equal 1 unless one of them is complex. Therefore, our assumption that g(x1) = g(x2) must be false, and g(x) is injective.

To show that g(x) is surjective, we need to show that for any y in B, there exists at least one x in A such that g(x) = y. In other words, we need to find an expression for x in terms of y.

So, let's solve the equation f(x) = y for x:

x(x-1) = y

x^2 - x - y = 0

Using the quadratic formula, we get:

x = (1 ± √(1 + 4y))/2

Since we want to define g(x) on R, we need to ensure that the expression under the square root is non-negative. This means that 1 + 4y ≥ 0, or y ≥ -1/4.

Therefore, we can define A = [-1/4, ∞) and B = [0, ∞), and g(x) = f(x) is a bijective function from A to B.

Answer:

4 19/24

Step-by-step explanation:

3 5/12 + 1 3/8

denominators multiplied by 3 and the numerators

= 3 10/24 + 1 9/24=4 19/24

Step-by-step explanation:

44.2m²

=44.2×100

=4420cm²

Answer:

Parallel: -1/2

Perpendicular: 2

Step-by-step explanation:

The slope of a line parallel to another, always has the same slope as the line that it is parallel to.

The slope of a line perpendicular to another, always has the opposite reciprical to the line that it is perpendicular to.

Answer:

The idea is to transform the expression by multiplying \((\sqrt{x + 1} - \sqrt{x})\) with its conjugate, \((\sqrt{x + 1} + \sqrt{x})\).

Step-by-step explanation:

For any real number \(a\) and \(b\), \((a + b)\, (a - b) = a^{2} - b^{2}\).

The factor \((\sqrt{x + 1} - \sqrt{x})\) is irrational. However, when multiplied with its square root conjugate \((\sqrt{x + 1} + \sqrt{x})\), the product would become rational:

\(\begin{aligned} & (\sqrt{x + 1} - \sqrt{x}) \, (\sqrt{x + 1} + \sqrt{x}) \\ &= (\sqrt{x + 1})^{2} -(\sqrt{x})^{2} \\ &= (x + 1) - (x) = 1\end{aligned}\).

The idea is to multiply \(\sqrt{x}\, (\sqrt{x + 1} - \sqrt{x})\) by \(\displaystyle \frac{\sqrt{x + 1} + \sqrt{x}}{\sqrt{x + 1} + \sqrt{x}}\) so as to make it easier to take the limit.

Since \(\displaystyle \frac{\sqrt{x + 1} + \sqrt{x}}{\sqrt{x + 1} + \sqrt{x}} = 1\), multiplying the expression by this fraction would not change the value of the original expression.

\(\begin{aligned} & \lim\limits_{x \to \infty} \sqrt{x} \, (\sqrt{x + 1} - \sqrt{x}) \\ &= \lim\limits_{x \to \infty} \left[\sqrt{x} \, (\sqrt{x + 1} - \sqrt{x})\cdot \frac{\sqrt{x + 1} + \sqrt{x}}{\sqrt{x + 1} + \sqrt{x}}\right] \\ &= \lim\limits_{x \to \infty} \frac{\sqrt{x}\, ((x + 1) - x)}{\sqrt{x + 1} + \sqrt{x}} \\ &= \lim\limits_{x \to \infty} \frac{\sqrt{x}}{\sqrt{x + 1}+ \sqrt{x}}\end{aligned}\).

The order of \(x\) in both the numerator and the denominator are now both \((1/2)\). Hence, dividing both the numerator and the denominator by \(x^{(1/2)}\) (same as \(\sqrt{x}\)) would ensure that all but the constant terms would approach \(0\) under this limit:

\(\begin{aligned} & \lim\limits_{x \to \infty} \sqrt{x} \, (\sqrt{x + 1} - \sqrt{x}) \\ &= \cdots\\ &= \lim\limits_{x \to \infty} \frac{\sqrt{x}}{\sqrt{x + 1}+ \sqrt{x}} \\ &= \lim\limits_{x \to \infty} \frac{\sqrt{x} / \sqrt{x}}{(\sqrt{x + 1} / \sqrt{x}) + (\sqrt{x} / \sqrt{x})} \\ &= \lim\limits_{x \to \infty}\frac{1}{\sqrt{(x / x) + (1 / x)} + 1} \\ &= \lim\limits_{x \to \infty} \frac{1}{\sqrt{1 + (1/x)} + 1}\end{aligned}\).

By continuity:

\(\begin{aligned} & \lim\limits_{x \to \infty} \sqrt{x} \, (\sqrt{x + 1} - \sqrt{x}) \\ &= \cdots\\ &= \lim\limits_{x \to \infty} \frac{\sqrt{x}}{\sqrt{x + 1}+ \sqrt{x}} \\ &= \cdots \\ &= \lim\limits_{x \to \infty} \frac{1}{\sqrt{1 + (1/x)} + 1} \\ &= \frac{1}{\sqrt{1 + \lim\limits_{x \to \infty}(1/x)} + 1} \\ &= \frac{1}{1 + 1} \\ &= \frac{1}{2}\end{aligned}\).

Answer:

Hello,

Step-by-step explanation:

\(\displaystyle \lim_{x \to \infty} \sqrt{x}*(\sqrt{x+1}-\sqrt{x} ) \\\\\\= \lim_{x \to \infty}\dfrac{ \sqrt{x}*(\sqrt{x+1}-\sqrt{x} )*(\sqrt{x+1}+\sqrt{x} )}{\sqrt{x+1} +\sqrt{x} } \\\\= \lim_{x \to \infty} \dfrac{\sqrt{x} *1}{\sqrt{x+1} +\sqrt{x} } \\\\\\= \lim_{x \to \infty} \dfrac{1} {\sqrt {\dfrac {x+1} {x} }+\sqrt{\dfrac{x}{x} } } \\\\\\=\dfrac{1} {\sqrt {1}+\sqrt{1} } \\\\\\=\dfrac{1} {2} \\\)

Answer:

Bro your question is wrong recheck it. Hope you understand me

The factored form of -g - 15 is -1(g + 15).

In mathematics, factorization refers to the process of expressing an expression or number as a product of its factors. In this case, we will factorize the expression -g - 15.

To factorize -g - 15, we first look for common factors, if any. The given expression does not have any common factors other than 1. Therefore, we proceed with the next steps.

The expression -g - 15 can be factored using the distributive property, which states that for any real numbers a, b, and c, a(b + c) = ab + ac. Applying this property to our expression, we get:

-g - 15 = -1 * g - 1 * 15

Now, the expression is in the form of a difference of two terms, and it can be further factored using the concept of like terms. Like terms are terms that have the same variables raised to the same powers. In our expression, -1 * g and -1 * 15 are like terms because they both have a coefficient of -1.

So, we can factor out -1 from both terms:

-g - 15 = -1(g + 15)

Now, the expression is fully factorized.

Answer: -1(g + 15)

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