A teacher records the amount of time it took a random sample of students to finish a test and their scores on that test. Let x be the score and y be the amount of time. Conduct a hypothesis test of the claim that there is a linear correlation between the variables, using a 0.10 level of significance. Find the PERCENTAGE OF THE VARIANCE IN THE Y-VALUES THAT CAN BE EXPLAINED BY THEIR LINEAR RELATIONSHIP WITH THE X-VALUES.

Answer:   A) a² = b² - w² + 2wx

Step-by-step explanation:

b² - (w - x)² = a² - x²

b² - (w² - 2wx + x²) = a² - x²

b² - w² + 2wx - x² = a² - x²

b² - w² + 2wx       = a²

Answer:

There is sufficient evidence that there is linear  correlation between two variable

Step-by-step explanation:

From the question we are told

   The significance level is  [tex]\alpha = 0.01[/tex]

   The critical value  is  [tex]a = 0.590[/tex]

   The  test statistics is  [tex]r = 0.591[/tex](linear correlation coefficient )

Now  from the data given in the value we see that

     [tex]r > a[/tex] so  the null hypothesis is rejected

Hence the conclusion is that there is  sufficient evidence that there is linear   correlation between two variable  

Answer: 7.5

Step-by-step explanation:

All you have to do is divide the base/width by area.

Answer:

The answer is

Step-by-step explanation:

Area of a rectangle = length × width

From the question

Area = 90 in²

Width = 12 in

To find the length substitute these values into the formula and solve for the length

We have

90 = 12l

Divide both sides by 12

[tex] \frac{12l}{12} = \frac{90}{12} [/tex]

We have the final answer as

Hope this helps you

Answer: 80

Step-by-step explanation:

A) The first domino is 3, the second is 4. Hence 34.

B) The first domino is 5, the second is 1. Hence 51.

C) The first domino is 6, the second is 11. Hence 71.

D) The first domino is 7, the second is 10. Hence 80.

Answer:

  all real numbers

Step-by-step explanation:

The domain of any polynomial function is "all real numbers." There is no value of x for which y is undefined.

Answer:

1 week= 7 days

number of days= 9

number of weeks= 1 week and 2 days

hope it helps :)

please mark it the brainliest!

Answer:

1 week and 2 days

Step-by-step explanation:

Answer:

0.185185185185185185.........

Step-by-step explanation:

i used a  calculator, to the nearst tenth is 0.18 to the nearest 100th is 0.185 also the 185 is repeating so u put a line over the numbers 185

Answer:

3 ÷ 162 = 0.01851851851

If you meant 162 ÷ 3 it is 54

If niether of the two answers above didnt answer your question, then sorry

Answer:

Any equation shown in the explanation

Step-by-step explanation:

Hello!

Combining like terms means combining terms with the same variables.

So combing all x's, all y's, all numbers, etc.

2/3x - 9 - 2x + 2 = 1

combine the x's

-1 1/3 x - 9 + 2 = 1

combine normal numbers

-1 1/3 x - 7 = 1

Add 7 to both sides

-1 1/3x = 8

Make mixed number into improper fraction

-4/3x = 8

Multiply both sides by 3

-4x = 24

Divide both sides by -4

x = -6

The answer would be any of the equation I showed above

Hope this helps!

Answer:

Part A: The student forgot to distribute the subtraction across the entire polynomial.

Part B: 8[tex]x^{2}[/tex]-6[tex]x^{2}[/tex]-7x+x-2-3 = 2[tex]x^{2}[/tex]-6x-5

Part C: The terms are 2[tex]x^{2}[/tex], -6x, and -5. The coefficient of [tex]x^{2}[/tex] is 2. The coefficient of x is -6.  

Step-by-step explanation:

Part A: When subtracting polynomials you have to make sure the subtraction is distributed to every term in the second polynomial.

Part B: Distributing the subtraction across the entire term we see that we need to subtract 6[tex]x^{2}[/tex], add x, and subtract 3. Then we just do the math and we get the answer.

Part C: Since they're asking for the simplified polynomial, they want the answer to the subtraction problem.  The terms are separated by + and - signs and the coefficients  are the numbers being multiplied against variables.

Answer:

The number of ways to distribute 30 batteries among the six different types is 33,649.

Step-by-step explanation:

It is provided that a camera shop stocks six different types of batteries, one of which is type A7b.

Also, the camera shop has only twelve A7b batteries but at least 30 of each of the other types.

Combinations would be used to determine the number of ways to distribute 30 batteries among the six different types. Here repetition is allowed.

[tex]C(n+r-1, r)={n+r-1\choose r}=\frac{(n+r-1)!}{r!(n-1)!}[/tex]

The number of A7b batteries is 12.

Then the number of ways to distribute 30 batteries among the six different types is:

[tex]C(n+(r-k)-1, (r-k))={n+(r-k)-1\choose (r-k)}=\frac{(n+(r-k)-1)!}{(r-k)!(n-1)!}[/tex]

The number of ways is:

[tex]C(n+(r-k)-1, (r-k))={n+(r-k)-1\choose (r-k)}[/tex]

                                          [tex]=\frac{(n+(r-k)-1)!}{(r-k)!(n-1)!}\\\\=\frac{(6+(30-12)-1)!}{(30-12)!\times (6-1)!}\\\\=\frac{23!}{18!\times 5!}\\\\=\frac{23\times 22\times 21\times 20\times 19\times 18!}{18!\times 5!}\\\\=\frac{23\times 22\times 21\times 20\times 19}{ 5!}\\\\=33649[/tex]

Thus, the number of ways to distribute 30 batteries among the six different types is 33,649.

Answer:

Step-by-step explanation:

[tex] \sf{2(4x + 3)}[/tex]

Distribute 2 through the parentheses

⇒[tex] \sf{2 \times 4x + 2 \times 3}[/tex]

⇒[tex] \sf{8x + 6}[/tex]

Hope I helped!

Best regards!!

Answer:

your answer is 8x + 16

............

Answer:

a is the right answer

Step-by-step explanation:

please give 5 star i need it

Answer:

Step-by-step explanation:

hello, you know that

[tex]\sqrt[5]{x^5}=x[/tex]

so, I can write

[tex]\sqrt[5]{2^5}=\sqrt[5]{32}=2\\\\\sqrt[5]{3^5}=\sqrt[5]{243}=3\\\\\sqrt[5]{4^5}=\sqrt[5]{1024}=4\\\\\sqrt[5]{5^5}=\sqrt[5]{3125}=5[/tex]

So, the winners are 32, 243, 1024, 3125 !!

You know that [tex]i^2=-1[/tex], right?

[tex]\sqrt{-9}=\sqrt{(3i)^2}=3i[/tex]

So, the answer is 3i

Thank you

Answer:

Length of the rectangular prism = 4 meters

But other possible values = (-5meters or - 9 meters)

Step-by-step explanation:

The volume of a rectangular prism = Length × Width × Height

From the question above,

Length = x meters

Width = x - 1 meters

Height = x + 11 meters

Volume of the Rectangular prism = 180 cubic meters

Hence,

(x) × (x - 1) × (x + 11) = 180

We expand the brackets

(x)(x - 1) (x + 11) = 180

x² - x(x + 11) = 180

x² (x + 11) - x(x + 11) = 180

x³ + 11x² - x² + 11x =180

x³ +10x² - 11x = 180

x³ + 10x² - 11x -180 = 0

The above is a polynomial

We solve this polynomial to find x

x³ + 10x² - 11x -180 = 0

(x - 4)(x + 5) (x + 9) = 0

x - 4 = 0

x = 4

x + 5 = 0

x = -5

x + 9 = 0

x = -9

We are asked to find the various values for the length hence,

From the above question, we are told that

Length = x meters

Therefore, the length of this rectangular prism = 4 meters or -5 meters or -9 meters.

Answer:

(1, 4)

Step-by-step explanation:

Answer:

The answer is Zero ( 0 ).

Step-by-step explanation:

Some of the property of log are as follows :

1. [tex]\text{log a}-\text{log b}=\text{log} \dfrac{\text{a}}{\text{b}}[/tex]

2. [tex]\text{log a}+\text{log b}=\text{log}(a{\cdot} b)[/tex]

3. [tex]\text{log}a^n=n\ \text{log} a[/tex]

Now coming to question,

(a) [tex]\text{log 5}-\text{log 8}=\text{log} \dfrac{\text{5}}{\text{8}}[/tex] (using property 1)

(b) [tex]\text{log 1}+\text{log 3}=\text{log}(1{\cdot} 3)=\text{log} 3[/tex] (using property 2)

(c) [tex]\text{log} 4=\text{log} 2^2=2\ \text{log} 2[/tex] (using property 3)

Hence, this is the required solution.

Answer:

π

Step-by-step explanation:

Any other irrational number, actually, so √2 would also do the trick.

Answer:

Pi, since pi is irrational

Step-by-step explanation:

Any irrational number, such as √2

Answer:

Reflect of X-axis -> diolate by a factor of 2

Remember to say thanks and mark brainliest

The sequence of similarity transformations is Reflection of Triangle ABC across the x-axis and a dilation of Triangle ABC by a scale factor of 2

What is Reflection and Dilation?

Reflection is a type of transformation that flips a shape along a line of reflection, also known as a mirror line, such that each point is at the same distance from the mirror line as its mirrored point. The line of reflection is the line that a figure is reflected over. If a point is on the line of reflection then the image is the same as the pre-image. Images are always congruent to pre-images.

The reflection of point (x, y) across the x-axis is (x, -y). When you reflect a point across the y-axis, the y-coordinate remains the same, but the x-coordinate is taken to be the additive inverse. The reflection of point (x, y) across the y-axis is (-x, y).

Resizing an item uses a transition called Dilation. Dilation is used to enlarge or contract the items. The result of this transformation is an image with the same shape as the original. However, there is a variation in the shape's size. Dilation transformations ensure that the shape will stay the same and that corresponding angles will be congruent

Given data ,

Let the triangle be ΔABC

Now , the coordinates of the triangle ABC is given as

A = A ( -4 , 2 )

B = B ( -2 , 4 )

C = C ( 0 , 2 )

And , the triangle be ΔDEF

Now , the coordinates of triangle DEF is given as

D = D ( -8 , -4 )

E = E ( -4 , -8 )

F = F ( 0 , -4 )

Now , on reflecting the triangle ABC along the x-axis , we get

The reflected triangle be A'B'C' will be the reflection of point (x, y) across the x-axis is (x, -y)

So ,

A' = A' ( -4 , -2 )

B' = B' ( -2 , -4 )

C' = C' ( 0 , -2 )

Now , on dilating the triangle A'B'C' with a scale factor of 2 , we get

D = 2 x A'

D = D ( -8 , -4 )

E = 2 x B'

E = E ( -4 , -8 )

F = 2 x C'

F = F ( 0 , -4 )

Therefore , the coordinates of the triangle DEF is

D = D ( -8 , -4 )

E = E ( -4 , -8 )

F = F ( 0 , -4 )

So , the triangle ABC is transformed into triangle DEF by a reflection across x-axis and a dilation by a scale factor of 2.

Hence , The sequence of similarity transformations is Reflection of Triangle ABC across the x-axis and a dilation of Triangle ABC by a scale factor of 2

To learn more about reflection and dilation click :

https://brainly.com/question/4681298

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Answer;

=-6p-10

Step-by-step explanation:

Lesson: It's about the using properties to simplify expression.

First, you apply by the rule.

-12-6p+2

Then, subtract by the numbers.

-12-6=-6

-6p-12+2← (group like terms)

And finally, add or subtract by the numbers.

-12+2 =-10

12-2=10

Answer:  -6p-10

Hope this helps!

Answer:

x = 1/25

Step-by-step explanation:

2/5x+1/x=35

[tex]2/5x+1/x=35[/tex]

taking 1/x common

[tex]1/x(2/5+1)=35[/tex]

[tex](2+5)/5=35x\\7/5 = 35x\\x = 7/(5*35) = 1/(5*5) = 1/25[/tex]

Thus, value of x is 1/25

Answer:

Option (B)

Step-by-step explanation:

Since all the four rays A, E, D and F are diverging from a point C in the different directions.

Therefore, sum of all the angles formed at a point C will be equal to 360°

m∠1 + m∠4 + m∠6 + m∠9 = 360°

25° + 34° + 146° + m∠9 = 360°

m∠9 = 360° - 205°

        = 155°

Therefore, measure of angle 9 is 155°.

Option (B) will be the correct option.

Answer:

Step-by-step explanation:

The general equation of a circle is expressed as x²+y²+2gx+2fy+c = 0 with centre at C (-g, -f).

Given the equation of the circles x²+y²−2x+4y+1  =0  and x²+y²+4x+2y+4  =0, to  get the centre of both circles, we will compare both equations with the general form of the equation above as shown;

For the circle with equation x²+y²−2x+4y+1  =0:

2gx = -2x

2g = -2

Divide both sides by 2:

2g/2 = -2/2

g = -1

Also, 2fy = 4y

2f = 4

f = 2

The centre of the circle is (-(-1), -2) = (1, -2)

For the circle with equation x²+y²+4x+2y+4  =0:

2gx = 4x

2g = 4

Divide both sides by 2:

2g/2 = 4/2

g = 2

Also, 2fy = 2y

2f = 2

f = 1

The centre of the circle is (-2, -1)

Next is to find the equation of a line containing the two centres (1, -2) and (-2.-1).

The standard equation of a line is expressed as y = mx+c where;

m is the slope

c is the intercept

Slope m = Δy/Δx = y₂-y₁/x₂-x₁

from both centres, x₁= 1, y₁= -2, x₂ = -2 and y₂ = -1

m = -1-(-2)/-2-1

m = -1+2/-3

m = -1/3

The slope of the line is -1/3

To get the intercept c, we will substitute any of the points and the slope into the equation of the line above.

Substituting the point (-2, -1) and slope of -1/3 into the equation y = mx+c

-1 = -1/3(-2)+c

-1 = 2/3+c

c = -1-2/3

c = -5/3

Finally, we will substitute m = -1/3 and c = 05/3 into the equation y = mx+c.

y = -1/3 x + (-5/3)

y = -x/3-5/3

Multiply through by 3

3y = -x-5

3y+x = -5

Hence the equation of the line containing the centers of the two circles is 3y+x = -5

Answer:

The correct answer is:

It is a continuous random variable. (B)

Step-by-step explanation:

Continuous random variables are variables that take on infinite possibility of values, hence the number of possible outcomes of a random variable cannot be counted. For instance, in this example, the amount of rainfall measured using a rain guage or a pluviometer has infinite possibilities of outcomes. it can either be 22.3 Liters, 20.1 Liters etc, up to infinity, in fact between 20 and 21 litres, there is an infinite possibility of outcomes.

Discrete random variables are variables that have a finite possibility of outcomes. the possibilities of occurrences can be counted. For example, if a coin is tossed, the coin can either land on its head or tail, hence there are two possibilities, making the variables discrete

The correct answer is:

It is a continuous random variable (B)

Step-by-step explanation:

Continuous Random Variables are variables that take on a number of possibilities of values that cannot be counted. The values have infinite possibilities. In this example, the height of a Giraffe measured in meters can be an unlimited possibility if values say, 10.5m, 15.22m 12.0m etc. The possibilities are endless.

Discrete Random variables are variables that take on a number of possibility of occurrences that can be counted. For instance, if a dice is rolled, the possibilities can either be a 1, 2, 3, 4, 5 or 6. There are six values that can be gotten, nothing in-between.

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Answer:

d) 205

Step-by-step explanation:

Step(i):-

x             :   100      150      200      250      300

p(X=x)    :   0.10     0.20    0.30     0.30      0.10

Step(ii):-

Let 'X' be the discrete random variable

Expected value of the random variable

   E(X) = ∑ x P(X=x)

           =  100 X 0.10 + 150 X 0.20 + 200 X 0.30 +250 X 0.30 + 300 X 0.10

          =   205

Final answer:-

The expected value     E(X) = 205

Answer: B. a = b .

First of all, let's think that a is equal to b.

Then, let's link up these two triangles.

Now, we have a parallelogram.

x+y = a+60

and 75 = b . So, a = b. Then, a is also = 75.

Now apply the basic triangle rule.

75+75+x=180 .. x = 30 degree.

and for the other triangle....

y+75+60=180 .. y= 45 degree...

Now, let's consider that we want to write a as b.

So, x+b+75=180 ...x+b=105

and..

y+b+60=180...y+b = 120..

Then, let's exit the b from these two equations.

-1/  x+b=105

    y+b=120

Finally, we found this: y-x =15

and we have already found y and x values.

y was 45 and x was 30 degree.

So when we put these two numbers into that equation y-x=15

we found the value of 15.

So, our answer is a=b.

Answer:

[tex]\huge \boxed{\mathrm{B.} \ a=b}[/tex]

Step-by-step explanation:

The two triangles form a parallelogram.

A parallelogram has opposite angles equal.

75 = b

Adjacent angles in a parallelogram are supplementary to one another.

They add up to 180 degrees.

a + 60 + 75 = 180

a + 135 = 180

Subtract 135 from both sides.

a = 75

Therefore, a = b.

Answer: 300%

Step-by-step explanation:

percent of increase: new/old×100%-100%

Since it is percent of increase, you need to subtract the original percent (100%) from the current percent.

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

new (current)=2000

old (original)=500

 new/old×100%-100%

=2000/500×100%-100%

=4×100%-100%

=400%-100%

=300%

Hope this helps!! :)

Please let me know if you have any question or need further explanation

Answer: d) Neither of the answers are correct

Step-by-step explanation:

Law of Cosines: a² = b² + c² - 2bc · cos A

Note: The letters can be swapped but the letters on the outside must be the same.

Answer:

Decimal

Step-by-step explanation:

When using decimals the bigger number is greater.

Example) .3 > .2

If there are more 0's in front of the number in a decimal it is smaller.

Example) .003 > .0003

The reason why it is harder to visualize that a fraction is greater is because there are two numbers to look at. You basically have to take an extra step and divide.

Answer:

The amount of jobs from fitting industry shall decline in 5.5 percent from 2015 to 2025.

Step-by-step explanation:

Due to the assumption of a yearly average rate, a linear function model shall be used. The expected amount of jobs ([tex]n[/tex]) after a certain amount of years (t) is given by the following formula:

[tex]n = n_{o} + \frac{\Delta n}{\Delta t}\cdot t[/tex]

Where:

[tex]n_{o}[/tex] - Initial amount of jobs in pipe fitting industry, measured in thousands.

[tex]\frac{\Delta n}{\Delta t}[/tex] - Average yearly rate, measured in thousands per year. (A decline is indicated by a negative sign)

If [tex]n_{o} = 546.5[/tex], [tex]t = 2025-2015 = 10\,years[/tex] and [tex]\frac{\Delta n}{\Delta t} = -3\,\frac{1}{years}[/tex], then:

[tex]n = 546.5+\left(-3\,\frac{1}{year}\right)\cdot (10\,years)[/tex]

[tex]n = 516.5[/tex]

The percent change in jobs from pipe fitting industry is calculated as follows:

[tex]\%n = \left(1-\frac{n}{n_{o}}\right)\times 100\,\%[/tex]

[tex]\% n = \left(1-\frac{516.5}{546.5}\right)\times 100\,\%[/tex]

[tex]\%n = 5.5\,\%[/tex]

The amount of jobs from fitting industry shall decline in 5.5 percent from 2015 to 2025.

First set up the ratio 2/5 = 10/x where x is the number of girls.

Now, we can use cross-products to find the missing value.

So we have (2)(x) = (5)(10).

Simplifying, we have 2x = 50.

Dividing both sides by 2, we find that x = 25.

So there are 25 girls in the class if there are 10 boys.