A standardized exam consists of three parts: math, writing, and critical reading. Sample data showing the math and writing scores for a sample of 12 students who took the exam follow.
Student Math Writing
1 540 474
2 432 380
3 528 463
4 574 612
5 448 414
6 502 526
7 480 430
8 499 453
9 610 615
10 572 541
11 390 335
12 593 613
(a) Use a 0.05 level of significance and test for a difference between the population mean for the math scores and the population mean for the writing scores. (Use math score − writing score.)
(b) Calculate the test statistic.

[tex]3d=n[/tex]

[tex]10d+5n=325[/tex]

[tex]10d+15d=325[/tex]

[tex]25d=325[/tex]

[tex]d=13[/tex]

[tex]n=39[/tex]

Hope this helps.

頑張って!

Answer:

a = [tex]\frac{9}{2}[/tex]

Step-by-step explanation:

To find the value of a, find the Slope of both the equations.

For lines to be perpendicular to each other    [tex]m_{1}m_{2} = - 1[/tex]

For line 1:

2x + 3y − 6 = 0 represent the line in y=mx +c form

3y = -2x + 6

y = [tex]\frac{-2}{3} x[/tex] + [tex]\frac{6}{3}[/tex]

y = [tex]\frac{-2}{3} x[/tex] + 2

[tex]m_{1}[/tex] = [tex]\frac{-2}{3}[/tex]

For line 2:

ax - 3y = 5

ax = 5 + 3y

ax - 5 = 3y

y = [tex]\frac{ax}{3} - \frac{5}{3}[/tex]

[tex]m_{2}[/tex] = [tex]\frac{a}{3}[/tex]

Apply the condition of perpendicularity:

[tex]\frac{-2}{3}[/tex] * [tex]\frac{a}{3}[/tex] = - 1

[tex]\frac{2a}{9} = 1[/tex]

a = [tex]\frac{9}{2}[/tex]

Answer:

GK = 9x-5

Step-by-step explanation:

GK = GH +HJ + JK

= (GJ - HJ) + (HJ) + (HK - HJ)

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

= 3x-3 + x + 5x-2

= (3x+5x+x)+(-3-2)

GK = 9x-5

Answer:

k = -9

Step-by-step explanation:

Answer:

100 cups of food is for a 25 pound dog

Hey there! I'm happy to help!

Let's call our number n. Here is the information we have.

n×12=84

We want to figure out what n equals. To do this, we have to get it by itself in the equation. What we will do is cancel out the 12 by dividing both sides by 12.

n×12/12=84/12

n=7

Therefore, our number is 7.

Have a wonderful day! :D

Answer:

4

Step-by-step explanation:

3³=27

6-³=1/216

2^5=32

27X1/216x32

=4

Answer:

-4

Step-by-step explanation:

Hello,

x-y=4 <=> x=y+4

so, xy=y(y+4)

[tex]y(y+4)=y^2+4y=(y+2)^2-4[/tex]

so this is minimum for y = -2 and the minimum value is -4

thanks

Answer:

x = ±4

Step-by-step explanation:

Step 1: Write out quadratic

2x² - 5 = 27

Step 2: Add 5 to both sides

2x² = 32

Step 3: Divide both sides by 2

x² = 16

Step 4: Take the square root of both sides

x = ±4

∴ x can equal -4 or 4

Answer:

[tex] \boxed{ \bf \huge \: x =4}[/tex]

[tex] \rm \: Or,[/tex]

[tex] \boxed{\bf \huge \: x = - 4}[/tex]

Step by step explanation:

Given Equation is :-

[tex]\sf \implies \: 2 {x}^{2} - 5 = 27[/tex]

We need to find the value of [tex]x[/tex] using Quadric formula.

Firstly, Subtract 27 from both of the side(s):-

[tex]\sf \implies2 {x}^{2} - 5 - 27 = 27 - 27[/tex]

On Simplification:-

Add -5-27 as (-) and (-) equals to (+). -5-27 would be represented as 5+27, which results to 32.

[tex]\sf\sf \implies2 {x}^{2} - 32 = 0[/tex]

Then, for this equation , a=2, b=0, c=-32.

Put the values :-

That is,

[tex]\sf \implies2 {x}^{2} + 0x + ( - 32) = 0[/tex]

As we know, that the quadratic formula is:-

[tex]\sf \implies \: x = \dfrac{ -b \pm \sqrt{b {}^{2} - 4ac } }{2a} [/tex]

Put the values :-

[tex]\sf \implies \: x = \dfrac{ - 0 \pm \sqrt{0 {}^{2} \: - 4(2) ( - 32)} }{2(2)} [/tex]

On Simplification:-

[tex]\sf \implies \: x = \dfrac{ - 0 {}^{} \pm \sqrt{ {0 } - \: 8 \times - 32}}{2 \times 2} [/tex]

[tex]\sf \implies \: x = \dfrac{ - 0 \pm \: \sqrt{ - 8 \times - 32} }{4}[/tex]

[tex]\sf \implies x = \dfrac{ - {0}^{}\pm \: \sqrt{ + 256} }{4} [/tex]

As 0 has no value here,

[tex]\sf \implies \: x = \dfrac{ \pm \sqrt{256} }{4} [/tex]

On cancelling,

Remove the square of 256 ( √256)

[tex]\sf \implies \: x = \dfrac{ \pm \cancel{ \: 256}}{ \cancel4} [/tex]

[tex]\sf \implies \: x = ± + 4[/tex]

It may be represented as,

[tex]\sf \implies \: x = - 4[/tex]

Or,

[tex]\sf \implies \: x = 4[/tex]

_______________________________

I hope this helps!

Please let me know if you have any questions.

~MisterBrian

Answer:

324 teachers

Step-by-step explanation:

3 teachers of every 50 students

__ teachers of 5400 students

so,

[tex]5400 \div 50 = 108[/tex]

therefore,

[tex]3 \times 108 = 324[/tex]

Answer:

$8.75

Step-by-step explanation:

If you do

$3.50 x 2.5 you get

$8.75

Answer:

3 hours

Step-by-step explanation:

$20 + $16 = $36 base

$36 + $16 = $52

$52 + $16 = $68

3 HOURS

Answer:

0.025 l

Hope it helped u if yes mark me BRAINLIEST

Answer:

40r^6t^9

Step-by-step explanation:

Answer:

7X+7=2(X+1)

7X+7=2X+2

7x-2X =2-7

5X/5 =-5/5

. X =-1

Answer:

(y^3)(z^2)

Step-by-step explanation:

subtract the common based exponents

▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓

[tex]\sf{\dfrac{y^7z^3}{y^4z}}\\\\=\tt{\dfrac{y^7}{y^4}×\dfrac{z^3}{z^1}}\\\\=\tt{y^{(7-4)}×z^{(3-1)}}\\\\=\tt{(y^3)×(z^2)}\\\\\pmb{\green{\boxed{\bold{y^3z^2}}}}[/tex] 

▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓

Answer:

(C) 3 feet

Step-by-step explanation:

We have a function of f(x) here. When Sarina throws the ball, it has been 0 seconds since she threw it.

Since x represents the amount of seconds, we can find the height of the ball (f(x)) by substituting x in as 0.

[tex]-0^2 - 0 + 3[/tex]

0 squared is 0, 0 minus zero is 0, and 0+3 = 3, so

[tex]f(x) = 3[/tex]

Meaning that when Sarina threw the ball, it's height was 3 feet.

Hope this helped!

Answer:

B

Step-by-step explanation:

I've taken a picture of the way I solved it.

The required simplified solution of the given expression is x=21/4. Option B is correct.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

here,
Given expression,
-4 + 5x - 7 = 10 + 3x - 2x,

Adding alike terms and And isolate the terms containing variable x,
-11 + 5x = 10 +x
5x - x = 10 + 11
4x = 21
x = 21 / 4

Thus, the required simplified solution of the given expression is x=21/4. Option B is correct.

Learn more about simplification here:

https://brainly.com/question/12501526

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Answer:

5u-25

Step-by-step explanation:

We have to simplify by distributing 5 to the variable and the number.

5(u-5)

5(u)5(-5)

5u-25

Answer:

1. -9/20

2.  1  7/12

3.  -4  1/3

Step-by-step explanation:

When adding and subtracting fractions with unlike denominators, you must first make them like denominators. To do this we must:

1. Find the Least Common Multiple of the denominators (which is called the Least Common Denominator).

2. Change each fraction (using equivalent fractions) to make their denominators the same as the least common denominator.

3. Then add (or subtract) the fractions, as we wish!

The easiest way to this is by multiplying the denominators. Remember that whatever you do to the bottom, you also do to the top

1. -5/4 +4/5

if we multiply 4 and 5, we get 20. Our denominator will be 20 before we simplify.

our new equation is going to be -25/20 + 16/20. Now we can add these together to get an answer of -9/20. Which is in the simplist form.

One more thing: to make a mixed number an improper fraction, you multiply the whole number by the denominator, and add the numerator.

1X4=4

4+1=5

The improper fraction is 5/4.

To make a Whole number a fraction, multiply the number by the denominator

-5x3=15

The improper is -15/3.

To go from an improper to a mixed, divide the numerator by the denominator. The remainders are going to be the fraction attached.

Answer:

each friend gets 1/36 of the loaf of pumpkin bread

Step-by-step explanation:

1/6 of a loaf

1/6 divided by 6

turn 6 into a fraction → 6/1

1/6 ÷6/1

to divide multiply the reciprocal 6/1 → 1/6

1/6 x 1/6 = 1/36

each friend get 1/36

OR

6/x = 1/6

x= 36

6/36

y(6)+310=y

equals is =

product of is ×

add to is +

Solution for 6x^2+9x=0 equation:

Simplifying

6x2 + 9x = 0

Reorder the terms:

9x + 6x2 = 0

Solving

9x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3x'.

3x(3 + 2x) = 0

Ignore the factor 3.

Subproblem 1

Set the factor 'x' equal to zero and attempt to solve:

Simplifying

x = 0

Solving

x = 0

Move all terms containing x to the left, all other terms to the right.

Simplifying

x = 0

Subproblem 2

Set the factor '(3 + 2x)' equal to zero and attempt to solve:

Simplifying

3 + 2x = 0

Solving

3 + 2x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-3' to each side of the equation.

3 + -3 + 2x = 0 + -3

Combine like terms: 3 + -3 = 0

0 + 2x = 0 + -3

2x = 0 + -3

Combine like terms: 0 + -3 = -3

2x = -3

Divide each side by '2'.

x = -1.5

Simplifying

x = -1.5

Solution

x = {0, -1.5}

Answer:

50

Step-by-step explanation:

Answer:

[tex]2\sqrt7,-2\sqrt7[/tex]

Step-by-step explanation:

So we have the function:

[tex]f(x)=4x^2-6[/tex]

And we want to find all x such that f(x) is 106. So, substitute 106 for f(x):

[tex]106=4x^2-6[/tex]

Add 6 to both sides:

[tex]112=4x^2[/tex]

Divide both sides by 4:

[tex]x^2=28[/tex]

Take the square root of both sides:

[tex]x=\pm\sqrt{28}[/tex]

Simplify the square root:

[tex]x=\pm\sqrt{28}=\pm\sqrt{4\cdot 7}=\pm2\sqrt7[/tex]

So, those are the two values that will satisfy our requirement.

And we're done!

Answer:

Triangle

Step-by-step explanation:

Basically, you have to multiply the base and the height of the triangle, and then divide it by two.

Answer:

O triangle

Step-by-step explanation:

Triangle area = (base*heigth)/2

Answer:

domain is x

range is y

Step-by-step explanation:

The values for the domain of the function appear on the x-axis and the values for the range appear on the y-axis.

A function's range is the set of all values that the function accepts, and its domain is the set of all values for which the function is defined.

The domain is for the independent variable while the range is for the dependent variable.

For example f(x) = x²

Now if we put x = 1 then it is called as domain variable while the value of function at x = 1 its that f(1) = 1 called range variable.

The range is the interval where the function f(x) is defined whereas the domain is the input interval of the independent variable (x).

For example f(x) = x²

Now if we put x = 1 then it is called as domain variable while the value of function at x = 1 its that f(1) = 1 called range variable.

Hence "The values for the domain of the function appear on the x-axis and the values for the range appear on the y-axis".

For more details about the range and domain of the function,

brainly.com/question/28135761

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