The scatterplot illustrates the relationship between high school and college GPAs for a sample of students.

A graph titled Relationship between high school and college G P A s has H S G P A on the x-axis and college G P A on the y-axis. Points are at (2, 4), (2.25, 2.9), (2.5, 2.8), (2.5, 2.8), (2.5, 3), (3, 3), (3.25, 3), (3.25, 3.1), (3.25, 3.2), (3.5, 2.9), (3.5, 3), (3.5, 3.1), (4, 3), (4, 3.1), (4, 3.5).

Which of the following is an accurate description of the scatterplot?

Students with higher high school GPAs have higher college GPAs.
Students with lower high school GPAs repeat their performance and get low college GPAs.
Because college is a fresh start, there is no relationship between high school and college GPAs.
Lower high school GPAs correlate to lower college GPAs, with one exception of a low high school GPA and high college GPA.

Answer:

The common difference is the difference between any two consecutive terms in an arithmetic sequence.

The formula which is used to find the common difference in AP is

d = an - an-1

Here the common difference is

d = a2 - a1 = 8 - 2 = 6

d = a3 - a2 = 14 - 8 = 6

d = a4 - a3 = 20 - 14 = 6

d = a5 - a4 = 26 - 20 = 6

2, 8, 14, 20, 26 … = 2, (2 + 6), (8 + 6), (14 + 6), (20+ 6) …

Therefore, the common difference is 6.

Step-by-step explanation:

The probability of selecting the human characters will be equal to 3 / 7.

Probability is defined as the ratio of the number of favourable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.

Given that:-

The probability will be calculated as:-

Probability = 3 / (3+4)

Probability = 3 / 7

Therefore the probability of selecting the human characters will be equal to 3 / 7.

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The scale factor will be 1.5. The corresponding angles are congruent because the size is changed not the angles.

Dilation is the process of increasing the size of an item without affecting its form. Depending on the scale factor, the object's size can be raised or lowered.

Adnan wants a larger garden.

He draws the triangle ΔPQR to show his original garden.

He wants to enlarge a garden, so he uses a dilation to form the image of the triangle ΔPQ'R'.

He uses vertex P as the center of the dilation.

The ratio of the corresponding sides will be given as

PQ'/PQ = Q'R'/QR = R'P/RP = 1.5

The scale factor will be 1.5.

The corresponding angles are congruent because the size is changed not the angles.

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Answer:

  40

Step-by-step explanation:

The sum of exterior angles of a convex polygon is 360°. This relation lets you write an equation for x.

__

Clockwise from the bottom, the sum of exterior angles is ...

  90° +(x +35)° +(x +15)° +(2x -20)° +(2x)° = 360°

  120° +6x° = 360° . . . . . . . simplify

  6x = 240 . . . . . . . . . . divide by °, subtract 120

  x = 40 . . . . . . . . . . divide by 6

The value of x is 40.

Answer:

x = 40°

Explanation:

The shape is a pentagon. Any polygon's exterior angles sum up to 360°.

Now, they all sum up to 360° :

⇒ (x + 35) + (x + 15) + (2x - 20) + 2x + 90 = 360°

⇒ x + x + 2x + 2x + 35 + 15 -20 + 90 = 360°

⇒ 6x + 120° = 360°

⇒ 6x = 360° - 120°

⇒ 6x = 240°

⇒ x = 240°/6

⇒ x = 40°

Answer:

It's a right triangle ..

Step-by-step explanation:

By using Pythagoras theorem , we can know that it's a right angled triangle or not ..

so , H² = P² + B²

=> 34² = 16² + 30²

=> 1,156 = 256 + 900

=> 1,156 = 1,156

Hence , it's a right triangle

If the trigonometric expression is sin θ = -√2/2. Then the value of angle θ will be 5π/4, 7π/4, and 13π/4.

The connection between the lengths and angles of a triangular shape is the subject of trigonometry.

The trigonometric expression is given below.

sin θ = -√2/2

The expression can be written as

sin θ = -1/√2

Then the value of angle θ will be

θ = sin⁻¹ (-1/√2)

θ = 5π/4, 7π/4, and 13π/4.

Thus, the correct options are B, C, and E.

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Answer:

B,C,E

Step-by-step explanation:

Answer:

7,13,31,85,247......

Step-by-step explanation:

[tex]a_n =3^n + 4[/tex]

        [tex]\sf a_1=3^1 + 4 = 3 + 4 = 7\\\\a_2 = 3^2 + 4 = 9 + 4 = 13\\\\a_3 = 3^3 + 4 = 27 + 4 = 31\\\\a_4 = 3^4 + 4 = 81 + 4 = 85\\\\a_5 = 3^5 + 4 = 243 + 4 = 247[/tex]

Answer:

  f(x) = 4·sin(2/7x) +1

Step-by-step explanation:

The sinusoidal function y = a·sin(kx) +b will have cross its midline at (0, b), and a peak value of (x, y) = (π/(2k), a+b). We can use these facts to find the values of a, k, and b for the sinusoidal function.

__

  (0, b) = (0, 1)   ⇒   b = 1

  (7π/4, 5) = (π/(2k), a+1)

This gives rise to two equations:

  7π/4 = π/(2k)

  k = π/(2(7π/4)) = 2/7

and

  a+1 = 5

  a = 4

Using the found values for the parameters of the function, we have ...

  f(x) = 4·sin(2/7x) +1

Using it's concept, it is found that the inequality represents the domain of the exponential piece is:

d) [tex]x \leq -2[/tex].

The domain of a function is the set that contains all possible input values.

Researching this problem on the internet, we have that the function is divided as follows:

Hence, for the domain of the exponential piece, option d is correct.

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The length of EC shown in the diagram is 66.2.

"To understand the calculation, check below."

ΔBE - ΔAE = ΔAB

ΔAB = 180°- 117°

ΔAB = 63°

Δ[tex]BE-[/tex] Δ[tex]AB-[/tex] Δ[tex]BC[/tex] = Δ[tex]CD[/tex] (Congruent angles)

Δ[tex]CD= 180 - 63 - 15[/tex]

Δ[tex]CD=102[/tex]

[tex]EC = 102 + 63[/tex]

[tex]EC=165[/tex]

[tex]L = 165[/tex] • [tex]2\pi23/360[/tex]

[tex]L = 66.2[/tex]

Therefore, EC = 66.2

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Answer:

S₂₀₀ = 121800

Step-by-step explanation:

the sum to n term of an arithmetic sequence is

[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] [ 2a₁ + (n - 1)d ]

where a₁ is the first term and d the common difference

here a₁ = 12 and d = a₂ - a₁ = 18 - 12 = 6 , then

S₂₀₀ = [tex]\frac{200}{2}[/tex] [ (2 × 12) + (199 × 6) ]

       = 100(24 + 1194)

      = 100 ×1218

     = 121800

Answer:

f(4) = 25

Step-by-step explanation:

substitute x = 4 into f(x)

f(4) = 2(4)² - 7 = 2(16) - 7 = 32 - 7 = 25

The two equation that represents the information is x + y = 150

y = 3x

let

the number of rock music = x

the number of alternative music = y

Therefore,

x + y = 150

y = 3x

The two equation that represent the information are as follows:

x + y = 150

y = 3x

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Answer:

8 times larger than original

Step-by-step explanation:

the volume (V) of a sphere is calculated as

V = [tex]\frac{4}{3}[/tex]πr³

when r = 2 , then

V = [tex]\frac{4}{3}[/tex]π × 2³ = [tex]\frac{4}{3}[/tex]π × 8

when r is doubled , that is r = 4 , then

V = [tex]\frac{4}{3}[/tex]π × 4³ = [tex]\frac{4}{3}[/tex]π × 64

64 is 8 times larger than 8

then new sphere is 8 times larger than original sphere

Answer:

8 times

Step-by-step explanation:

The circumference of the wire is 4x and the area of the circle is 4x^2/π

The length of the wire is given as;

Length = 4x

This represents the circumference.

Hence, the circumference of the wire is 4x

In (a), we have:

Circumference = 4x

Calculate the radius using:

2πr = 4x

Divide through by 2π

r = 2x/π

The area is:

Area = πr^2

This gives

Area = π(2x/π)^2

Evaluate

Area = 4x^2/π

Hence, the area of the circle is 4x^2/π

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Answer:

Step-by-step explanation:

Answer:

It does not matter.

Step-by-step explanation:

How to find a slope with just two points,

Step One: Identify two points on the line.

Step Two: Select one to be (x1, y1) and the other to be (x2, y2).

Step Three: Use the slope equation to calculate the slope.

Example

Let's say that points (15, 8) and (10, 7) are on a straight line. What is the slope of this line?

Step One: Identify two points on the line.

In this example, we are given two points, (15, 8) and (10, 7), on a straight line.

Step Two: Select one to be (x1, y1) and the other to be (x2, y2).

It doesn't matter which we choose, so let's take (15, 8) to be (x2, y2). Let's take the point (10, 7) to be the point (x1, y1).

Step Three: Use the equation to calculate the slope.

Once we've completed step 2, we are ready to calculate the slope using the equation for a slope:

[tex]slope=\frac{y2-y1}{x2-x1} =\frac{8-7}{15-10} =\frac{1}{5}[/tex]

We said that it really doesn't matter which point we choose as (x1, y1) and the which to be (x2, y2). Let's show that this is true. Take the same two points (15, 8) and (10, 7), but this time we will calculate the slope using (15, 8) as (x1, y1) and (10, 7) as the point (x2, y2). Then substitute these into the equation for slope:

[tex]slope=\frac{y2-y1}{x2-x1} =\frac{7-8}{10-15} =\frac{-1}{-5}=\frac{1}{5}[/tex]

We get the same answer as before!

Often you will not be given the two points but will need to identify two points from a graph. In this case, the process is the same, the first step being to identify the points from the graph. Below is an example that begins with a graph.

So therefore it does not matter.

No, it does not matter which point you choose as (x₁, y₁) and which point you choose as (x₂, y₂) when using slope formula. Slope between two points on line remains same regardless of order in which you choose points.

The slope formula is given by slope = (y₂ - y₁) / (x₂ - x₁)

This is because the slope represents the rate at which the y-coordinate changes with respect to the x-coordinate.

If you swap the points (x₁, y₁) and (x₂, y₂), the change in y and the change in x will simply swap as well, but their ratio, which is the slope, will remain unchanged. For example, if the slope between (x₁, y₁) and (x₂, y₂) is m, then the slope between (x₂, y₂) and (x₁, y₁) will also be m.

This property of the slope formula makes it convenient and efficient to calculate the slope between two points, regardless of their order, as it will yield the same result.

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[tex]\rule{300}{1}\\\dashrightarrow\large\blue\textsf{\textbf{\underline{Given question:-}}}[/tex]

   Find the gradient of the line joining (-1,9) and (3,5)

[tex]\dashrightarrow\large\blue\textsf{\textbf{\underline{Answer and how to solve:-}}}[/tex]

Use the slope formula:-

[tex]\boxed{\frac{y_2-y_1}{x_2-x_1}}[/tex]

Replace the letters with the numbers:-

[tex]\boxed{\frac{5-9}{3-(-1)}}[/tex]

[tex]\circ[/tex] On simplification,

[tex]\boxed{\frac{-4}{3+1}}[/tex]

[tex]\circ[/tex] On further simplification,

[tex]\boxed{\frac{-4}{4}}[/tex]

[tex]\circ\sf{SLOPE=-1}[/tex]

[tex]\rule{300}{1}[/tex]

Answer:

352

Step-by-step explanation:

sssplit the shapes and then do regular formula

a = lh

Answer:

Domain: [tex]-3\leq x\leq 3[/tex]

Range: [tex]0\leq y\leq 1.5[/tex]

Increasing: [tex]0\leq x\leq 3[/tex]

Decreasing: [tex]-3\leq x\leq 0[/tex]

No constant intervals

Step-by-step explanation:

Hope this helped

[tex]~~~~~~(2x+34)+(x+71) = 180\\\\\implies 3x + 105=180\\\\\implies 3x = 180-105\\\\\implies 3x = 75\\\\\implies x = \dfrac{75}3\\\\\implies x = 25[/tex]

Answer:

360

Step-by-step explanation:

from the survey:

32/80 - 0.4 love math

0.4*900

= 360

Using the distance formula, each side of the park is 13 units long

The vertices of the park are given as:

(26.5, 12), (38.5, 7), (26.5, 2), (13.5, 2), (1.5, 7), and (13.5, 12).

The length of each side is calculated using the following distance formula:

[tex]d = \sqrt{(x_2 -x_1)^2 + (y_2 -y_1)^2}[/tex]

Using any consecutive points, we have:

[tex]d = \sqrt{(13.5 - 1.5)^2 + (12 -7)^2} = 13[/tex]

Hence, each side of the park is 13 units long

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Answer:

Step-by-step explanation:

Use the nth tern equation of the AP

We have

Find the value of d

Correct choice is a)

Now

Answer:

5  5/9

Step-by-step explanation:

9 goes into 50 4 times and the subtract that from 50

Answer :

5 [tex]\frac{5}{9}[/tex]

Explanation:

50/9= 5.5555555555556 = 5

Now that we have our whole number for the mixed fraction, we need to find our new numerator for the fraction part of the mixed number.

Step 2: Get the new numerator

To work this out we'll use the whole number we calculated in step one (5) and multiply it by the original denominator (9). The result of that multiplication is then subtracted from the original numerator:

50 - (9 x 5) = 5

Step 3: Our mixed fraction

We've now simplified 50/9 to a mixed number. To see it, we just need to put the whole number together with our new numerator and original denominator:

5 [tex]\frac{5}{9}[/tex]

Perimeter of larger sail

Now

Let shorter sail's Perimeter be x

#2

Let they be 2x and 7x

Smaller angle

Answer:

EK = 8

Step-by-step explanation:

Intersecting Chords Formula:  a • b = c • d

BK * KD = EK * KC

4 * 10 = (x+1) * (x-2)

40 = x^2 +x-2x-2

40 = x^2 -x -2

0 = x^2 - x-2-40

0 = x^2 -x -42

Factor

0 = (x-7) (x+6)

Using the zero product property

x-7 = 0   x+6 =0

x=7        x=-6

X is not negative

x=7

EK = x+1

EK = 7+1

EK = 8