4.(06.07 HC)A teacher is assessing the correlation between the number of hours spent studying and the average score on a science test. The table below shows the data:Number of hours spent studying 0 0.5 1(x)1.5 2 2.5 33.54Score on science test(y)57 62 67727782 879297Part A: Is there any correlation between the number of hours students spent studying and the score on the science test? Justify your answer. (4 points)Part B: Write a function which best fits the data. (3 points)Part C: What does the slope and y-intercept of the plot indicate? (3 points)(10 points)

1) Considering that x is for pounds of apples and y is a total cost of an apple let's find the cost per pound of the apples, given that the y=2.57x +4.5

Let's turn that function into an equation

0=2.57x +4.5 Subtract 2.57x from both sides

-2.57x=4.5 Divide both sides by -2.57

x=-1.75

2) So if no one pie crust is sold, there is going to be a loss of $-1.75, according to that equation.

Therefore, we can infer that the cost per pound of the apples is $1.75

EXPLANATION

Let's see the facts:

The increasing rate is:

The increasing rate is 1.67

In percentage this is:

The percentage of increasing is of 60%.

Answer: is 72 people to 27 animals

Step-by-step explanation:

I can find the ratio by cross multiplying

40/15 to x/27

15x = 1080

x = 72

you can also divide 40/15 for a ratio percent = 8/3

multiply 27 animals x 8/3 = 72

two ways to solve for ratios

Answer:

27

Step-by-step explanation:

Divide 270 by 10

Answer:

2

Step-by-step explanation:

512÷2=256

256÷2=128

128÷2=64

64÷2=32

32÷2=16

16÷2=8

8÷2=4

4÷2=2

2÷2=1

=(2^2)+(2^2)+(2^2)+(2^2)+2

When 2 is multiplied it will make it a perfect square.

512×2=1024

√1024

=32

Answer: 18 combinations

Step-by-step explanation: you want to multiply the amount of ice cream flavors by the amount of children to be able to find the amount of possible combinations. so, 6 children x 3 flavors of ice cream = 18 different combinations. 6 x 3 = 18

The area of the region within the square and without the circle is equal to 13.7 square inches.

In this problem we find the case of figure generated by a square and an inscribed circle. Then, the area of the region is found by subtracting the area of the circle from the area of the square. Then, the area is:

A = L² - 0.25π · D²

Where:

If we know that D = L = 8 in, then the area of the region is:

A = (8 in)² - 0.25π · (8 in)²

A = 64 in² - 50.265 in²

A = 13.735 in²

The area of the region is equal to 13.7 square inches.

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Answer:

No, it is not.

Step-by-step explanation:

A function only has exactly one output for each input. In other words, for each X input, there is only one Y output. In the given set of coordinates, 3 is repeated as an input, which makes this set of coordinates not a function.

. Write the equation for the line: (Hint: there are two points given to you!)

________________________

y= mx + b

the slope is m

or

(y - y1) = m (x - x1)

___________________

points (x,y)

point 1 (4, 4) x1 = 4; y1 = 4

point 2 (3 , -1) x2= 3; y2 = -1

The slope m = (y2- y1) / (x2 -x1)

m=(-1 - 4 )/( 3 - 4)

m= -5/-1 = 5

(In this case, you choose which point you want to put as point one and point two, you will always get the same answer)

____________________

(y - 4) = 5 (x - 4)

y= 5x -20 +4

y= 5x - 16

The equation for the line is y= 5x - 16

__________________

Do you have any questions regarding the solution?

The hypotenuse of a right triangle = 19.31cm

What is Hypotenuse?

The longest side of a right-angled triangle, or the side across from the right angle, is called the hypotenuse. The Pythagorean theorem, which asserts that the square of the length of the hypotenuse equals the sum of the squares of the lengths of the other two sides, can be used to determine the length of the hypotenuse.

Let the measure be,

Perpendicular = 18cm

Base = 7cm

Hypotenuse = ?

To find the Hypotenuse we can Pythagoras Theorem:

Hypotenuse² = Perpendicular²+ Base²

H² = (18)² + (7)²

H² = 324 + 49

H² = 373

H = [tex]\sqrt{373}[/tex]

H = 19.31cm

Hence, The measure of the other leg is²

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No, the ordered pair (-8,1) is not a solution to the equation y=(1/2)x-3.

In the question ,

an equation y=(1/2)x-3 is given ,

if the ordered pair (-8,1) is a solution of the equation , then it should satisfy the equation .

Substituting x=-8 and y=1 in the equation y=(1/2)x-3 , we get

y=(1/2)x-3

1 = (1/2)(-8) -3

1 = -8/2 -3

1 = -4-3

1 ≠ -7

Since 1≠7 , the ordered pair (-8,1) is not a solution to the equation y=(1/2)x-3 .

Therefore , No , the ordered pair (-8,1) is not a solution to the equation y=(1/2)x-3.

The given question is incomplete , the complete question is

Is the ordered pair (-8,1) a solution to the equation y=1/2x-3  ?

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Answer:

Exterior angle = 20 degrees

Interior angle = 160 degrees

================================================

Explanation:

The phrasing "Each exterior angle measure is one eighth the measure of each interior angle" means,

exterior = (1/8)*(interior)

That rearranges to

interior = 8*(exterior)

Let's say x is the measure of the unknown exterior angle. That makes 8x the measure of the interior angle

The two must add to 180 to form a straight line.

interior + exterior = 180

8x + x = 180

9x = 180

x = 180/9

x = 20 is the measure of the exterior angle

8x = 8*20 = 160 is the measure of the interior angle

Note how 160+20 = 180 to verify our answers.

1) Given that an oatmeal cookie has these proportions, let's set a pair of ratios to get that:

Answer:

Since all triangle angles sum to 180 then we can say

2x + 3x + 7x = 180

12x = 180

x = 15

There fore the angles are

2 * 15 3 * 15 and 7 * 15 or

30 45 and 105

Those 3 total 180 degrees

Step-by-step explanation:

Answer:

See below

Step-by-step explanation:

The  equation is

y = [tex]x^{2}[/tex] + x

x equals the step

We see steps: 1, 2,3 and 4

y equals the number of squares that you see in each step.

If you look at step 1, you see [tex]1^{2}[/tex] + 1 = 2

Step 2: [tex]2^{2}[/tex] + 2 = 6

Step 3: [tex]3^{2}[/tex] + 3 = 12

Step 4: [tex]4^{2}[/tex] + 4 = 20

Can you see at each step there is a square of the number and then a little extra?  That little extra equals the number of the stop.

In the equation

y = 4x -2

Step 1

y = 4(1) -2

y = 2  It works!

Step 2:

y = 4x -2

y = 4(2)  - 2

y = 8 - 2

y = 6  It works!

Step 3:

y = 4x -2

y = 4(3) - 2

y = 12 - 2

y = 10  It does not work!

Step 4:

y = 4x -2

y  = 4(4) - 2

y = 16 - 2

y = 14  It does not work!

The equation y= 4x -2  only worked for the first 2 steps.

2, 4, 5, 10 and 20 cast members were possible attendees at the celebration.

The acting teacher provided 20 biscuits and 40 carrot sticks as refreshments in light of this.

What are the factors?

A factor in mathematics is an integer that evenly divides another number by itself, leaving no residue.

2, 4, 5, 10, and 20 make up the factors of 20 and 40.

Additionally, the number of cast members must be greater than one and a divisor of 20 and 40.

Therefore, there could be 2, 4, 5, 10, or 20 cast members.

Therefore, 2, 4, 5, 10 and 20 cast members may have attended the celebration.

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The variable x is 9 and the two adjacent angles have measures of 117° and 63°, respectively.

Parallelograms are quadrilaterals with two pairs of parallel sides of equal length. According to Euclidean geometry, the measures of two adjacent angles in a parallelogram are supplementary. Thus,

13 · x + 7 · x = 180°

Now we clear the variable x:

20 · x = 180°

x = 9

And the missing angles are:

13 · 9 = 117°

7 · 9 = 63°

The value of the variable x is 9 and the measures of the two adjacent angles are 117° and 63°, respectively.

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Answer:

[tex]x = 2[/tex]

Step-by-step explanation:

Let's solve your equation step-by-step.

−3x−9=−15

Step 1: Add 9 to both sides.

−3x−9+9=−15+9

−3x=−6

Step 2: Divide both sides by -3.

−3x/−3 = −6/−3

x=2

Yes the two triangles are necessarily congruent as they are right angled so both the angles are equal and having two sides equal by using SAS rule that is Side, Angle, Side rule by the property of congruency.

Two figures are considered to be "congruent" if they can be positioned precisely over one another. Both of the bread slices are the same size and shape when stacked one on top of the other. Congruent refers to things that are exactly the same size and shape.

If two triangles meet all 5 requirements for congruence, then they are congruent. They are right angle-hypotenuse-side (RAHS), angle-side-angle (ASA), angle-angle-side (AAS), side-side-side (SSS), and side-angle-side (SAS) (RHS).

Here the ΔCED and ΔPOR,

∠CED=∠POR

Side PR=CD

Side ED=PO

by using SAS rule,

ΔCED≅ΔPOR

Yes, the two triangles are inherently congruent because they have right angles, which means that both of their angles are equal, and because their sides are equal according to the SAS rule, which stands for Side, Angle, Side.

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1. x - 3 is not a factor

2. The remainder is 32.

Using the remainder theorem, which states that for a polynomial p(x), if x - a is a factor, then p(a) = 0.

So, p(x) = 2x³ - 4x² - 6 If x - 3 is a factor, then

p(3) = 0

So, substituting x = 3 into the equation, we have

p(3) = 2x³ - 4x² - 6

= 2(3)³ - 4(2)² - 6

= 2(27) - 4(4) - 6

= 54 - 16 - 6

= 54 - 22

= 32

Since p(3) ≠ 0.

x - 3 is not a factor

Since p(3) = 32,

The remainder is 32.

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The lines aren't parallel since they intersect at point B.

Parallel lines never intersect.

For the figure to be a parallelogram, then y must be equal to 12

Here, we want to get the value of y for which the the quadilateral must be a parallelogarm

Mathematically, the diagonals of a parallelogarm bisects each other

That means the lengths on either sides are equal

Mathematically, we can get two equations as follows;

The probability that the transistor will last between 12 and 24 weeks is 0.424

X= lifetime of the transistor in weeks E(X)= 24 weeks

O,= 12 weeks

The anticipated value, variance, and distribution of the random variable X were all provided to us. Finding the parameters alpha and beta is necessary before we can discover the solutions to the difficulties.

X~gamma([tex]\alpha ,\beta[/tex])

E(X)= [tex]\alpha \beta[/tex]                 [tex]\beta[/tex]= [tex]12^{2}/24[/tex]=6 weeks

V(x)= [tex]\alpha \beta ^{2}[/tex]                [tex]\alpha[/tex]=24/6= 4

Now we can find the solutions:

The excel formula used to create Figure one is as follows:

=gammadist(X, [tex]\alpha[/tex], [tex]\beta[/tex], False)

P([tex]12\leq X\leq 24[/tex])

P([tex]12/6\leq G\leq 24/6[/tex])

P([tex]2\leq G\leq 4[/tex])

P= 0.424

Therefore, probability that the transistor will last between 12 and 24 weeks is 0.424

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Answer:

Step-by-step explanation:

0.424 is the probability that the transistor will last between 12 and 24 weeks.

X= lifetime of the transistor in weeks E(X)= 24 weeks

Standard deviation= 12 weeks

Finding the parameters alpha and beta X~gamma(αβ)

E(X)= αβ             β =6 weeks

V(x)=αβ^2           α =24/6= 4

Now we can find the solutions:

The excel formula used to create Figure one is as follows:

=gammadist(X,α,β,False)

P(12≤X≤24)

P(12/6≤G≤24/6)

P= 0.424

Therefore, probability that the transistor will last between 12 and 24 weeks is 0.424

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The shows the expression below simplified 0.0042 - (1.2 x 10-6) as D. 4.1988 x 10^-3.

The concept that is been used is subtraction of the first expression from second expression.

The given expression is 0.0042 - (1.2 x 10-6) and this can be expressed in standard form as ( 4.2 *10^-3) - (1.2 x 10-6)

Then then the subtraction can be done as [ ( 4.2 *10^-3) ] - [ (1.2 x 10^-6) ] = 4.1988 x 10^-3

In conclusion, iif we go through the options., then we can see that the forth option is the best option that match the expression.

Therefore, option D is correct.

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Answer:

23

Step-by-step explanation:

4h = 92

Divide both sides by 4 to get h by itself

h = 23

I WILL USE THE LAWS OF EXPONENTS

[tex] {x}^{n} \times {x}^{m} \\ = {x}^{n + m} [/tex]

AND

[tex] \frac{{x}^{n}}{ {x}^{m} } \\ = {x}^{n - m} [/tex]

[tex] \frac{3 {x}^{ - 2 + 5} }{ {x}^{8} } \\ = \frac{3 {x}^{3} }{ {x}^{8} } \\ = 3 {x}^{3 - 8} \\ = 3 {x}^{ - 5} [/tex]

ATTACHED IS THE SOLUTION.

Answer:

i hope this one is good for you

From the figure, draw from D parallel to AB.

Calculate angle D from triangle DWC = 180 - (90+60) = 180 - 150 = 30

Angle D = 30

Angle W = 90 + 30 = 120

Final answer W = 120