Derek's collection: 1950, 1952, 1908, 1902, 1955, 1954, 1901, 1910
Paul's collection: 1929, 1935, 1928, 1930, 1925, 1932, 1933, 1920
Find the indicated measures of center and the measures of variation for each data set. Round your answer to the nearest hundredth, if necessary.
Find the mean, median, range, IQR, MAD for Derek's collection and Paul's collection.

ANSWER

C) x = −3 or x = 9

EXPLANATION

The given quadratic function is:

[tex]4 {x}^{2} - 24x - 108[/tex]

To find the zeros, we equate to zero.

[tex]4 {x}^{2} - 24x - 108 = 0[/tex]

Divide through by 4

[tex] {x}^{2} - 6x - 27 = 0[/tex]

Factor to get,

[tex] {x}^{2} + 3x - 9x - 27 = 0[/tex]

[tex]x(x + 3) - 9(x + 3) = 0[/tex]

[tex](x + 3)(x - 9) = 0[/tex]

Use the zero product property,

[tex]x = - 3 \: or \: x = 9[/tex]

ANSWER

C. 9

EXPLANATION

We use the Altitude Theorem,to find the value of a.

According to the altitude theorem, the height of the triangle of the triangle is equal to the geometric mean of the two segment it creates on the hypotenuse.

[tex]6 = \sqrt{4a} [/tex]

Square both sides to get,

[tex]36 = 4a[/tex]

[tex]9 = a[/tex]

The correct choice is option C.

Answer:

C

Step-by-step explanation:

the answer is 9

Answer:

the answer is D:  1800 square in

Step-by-step explanation:

find the area of the triangle

area = 1/2 bh

=1/2 (15 inch) (20 inch)

=150 square inch

***then multiply by 2 which gives you 300 square inch***

find the area of the 3 rectangular faces

A=lw

= (25 in) (15 in)

= 375 square inch

A = lw

= (25 in) (20 in)

= 500 square inch

A = lw

= (25 in) (25 in)

= 625 square inch

then add all 3 rectangular faces which equals to 1500 square inch

then add the triangular and rectangular

300 square inch + 1500 square inch = 1800 square inch

Answer:

The answer for study island would be D. 1,800 in2

hope i helped :)

Answer:

B:  g(x) = x^3 + 1

Step-by-step explanation:

Please  use " ^ " to denote exponentiation:  f(x) = x^3.

This graph starts (increasing) in Quadrant III and grows without bound in Quadrant IV.  It passes thru the origin (0, 0).

If we want to translate the graph 1 unit up, then the function f(x) becomes

g(x) = f(x) + 1, or x^3 + 1.

Answer:B:  g(x) = x^3 + 1

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

Answer:

The answer is 4x-3 because all your doing is subtracting 3x from 4x

B: 292.5; multiply 65x4.5

Using the formula d = rt, the distance traveled by a car moving at 65 miles per hour for 4.5 hours is calculated to be 292.5 miles.

Calculating Distance Traveled

To calculate the distance traveled by a car, we can use the formula d = rt, where d represents distance, r represents average speed (rate), and t represents time.

Given: average speed r = 65 miles/hour, time t = 4.5 hours.

Find: distance d.

We use the formula to solve for d:

d = (65 miles/hour)(4.5 hours) = 292.5 miles

Therefore, the car would travel a distance of 292.5 miles at an average speed of 65 miles per hour over 4.5 hours.

Answer:  [tex]\bold{A)\quad y=5sin\bigg(\dfrac{6}{5}x-\pi\bigg)-4}[/tex]

Step-by-step explanation:

The general form of a sin/cos function is: y = A sin/cos (Bx-C) + D where the period (P) = 2π ÷ B

In the given function, [tex]B=\dfrac{6}{5}[/tex]  →   [tex]P=2\pi \cdot \dfrac{5}{6}=\dfrac{10\pi}{3}[/tex]

Half of that period is: [tex]\dfrac{1}{2}\cdot \dfrac{10\pi}{3}=\large\boxed{\dfrac{5\pi}{3}}[/tex]

Calculate the period for each of the options to find a match:

[tex]A)\quad B=\dfrac{6}{5}:\quad 2\pi \div \dfrac{6}{5}=2\pi \cdot \dfrac{5}{6}=\dfrac{5\pi}{3}\quad \leftarrow\text{THIS WORKS!}\\\\\\B)\quad B=\dfrac{6}{10}:\quad 2\pi \div \dfrac{6}{10}=2\pi \cdot \dfrac{10}{6}=\dfrac{10\pi}{3}\\\\\\C)\quad B=\dfrac{5}{6}:\quad 2\pi \div \dfrac{5}{6}=2\pi \cdot \dfrac{6}{5}=\dfrac{12\pi}{5}\\\\\\D)\quad B=\dfrac{3}{10}:\quad 2\pi \div \dfrac{3}{10}=2\pi \cdot \dfrac{10}{3}=\dfrac{20\pi}{3}[/tex]

Answer: B Or Option 2

Step-by-step explanation: Your Answer Will Be The Second Choice Have A Great Day!

Answer:

option b

6 C 2 + 6

Step-by-step explanation:

Given in the question that,

number of pink beans = 87

number of purple beans = 74

number of white beans = 35

number of black beans = 70

number of orange beans = 25

number of green beans = 47

if two beans selected are different

6 C 2

(6 colours of beans)

if two beans selected are same

6 C 1 = 6

(6 colours of beans)

total sample space will be

6 C 2 + 6

Answer:

The most reasonable Answer is *D.) the bed bugs that survived the DDT years ago, reproduced new generations of chemical resistant offspring.*

Step-by-step explanation:

Answer:

The answer is D) The bed bugs that survived the DDT years ago, reproduced new generations of chemical resistant offspring.

Step-by-step explanation:

The bed bug population has increased because the bed bugs that survived the DDT years ago, reproduced new generations of chemical resistant offspring.

Answer:

slope = 2

Step-by-step explanation:

Calculate the slope m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (- 2, 2) and (x₂, y₂ ) = (- 4, - 2)

m = [tex]\frac{-2-2}{-4+2}[/tex] = [tex]\frac{-4}{-2}[/tex] = 2

hence the numbers are 8 and 13

hope it helps you!!!!!!!!

Final answer:

The two numbers that satisfy the conditions of summing up to 21 and one being 18 less than twice the other are 8 and 13.

Explanation:

To solve the problem, let’s denote the two numbers as x and y. According to the question, the sum of the two numbers is 21, which can be expressed as an equation: x + y = 21. Additionally, we are told that one number is 18 less than two times the other, which gives us another equation: x = 2y - 18.

We can use the method of substitution to solve these equations. First, we will solve the second equation for x, which we already have as x = 2y - 18. Then we will substitute this expression for x in the first equation: (2y - 18) + y = 21. Simplifying we get: 3y - 18 = 21. Adding 18 to both sides gives us 3y = 39. So, dividing both sides by 3 yields y = 13. Now that we have the value of y, we can substitute it back into the equation x = 2y - 18 to get x = 2(13) - 18 which simplifies to x = 8.

Thus, the two numbers in question are 8 and 13.

8+8=16 so 16/5 16÷5=3.2 32%

32% is the answer I think. Hope this helps

Answer:

32%

Step-by-step explanation:

8 + 8 = 16.

16/5

16 ÷ 5

= 3.2

= 32%

Answer: (y-3)(4y-5)

Step-by-step explanation:

4*15= 60. 60= -12 x -5

4(y-12)(y-5)

(y-3)(4y-5)

Answer:

see explanation

Step-by-step explanation:

Given the recursive formula [tex]a_{n}[/tex] = [tex]\frac{a_{n-1} }{4}[/tex] and

[tex]a_{4}[/tex] = 2 [tex]\frac{1}{4}[/tex] = [tex]\frac{9}{4}[/tex], then

[tex]\frac{a_{3} }{4}[/tex] = [tex]\frac{9}{4}[/tex] ( multiply both sides by 4 )

a₃ = 4 × [tex]\frac{9}{4}[/tex] = 9

[tex]\frac{a_{2} }{4}[/tex] = 9 ( multiply both sides by 4 )

a₂ = 36

[tex]\frac{a_{1} }{4}[/tex] = 36 ( multiply both sides by 4 )

a₁ = 144

The first 4 terms are

144, 36, 9, 2 [tex]\frac{1}{4}[/tex]

The first four terms of the recursive formula are 144, 36, 9, 9/4 .

A recursive sequence is an infinite sequence of numbers where each number in the sequence is equal to a fixed linear combination of one or more of its before or after number. In a recursive sequence, the series of the number present follows a particular sequence of logic.

Given series is an = (an-1)/4 and also a4 = 9/4

Putting n = 4 in the given recursive sequence,

⇒ a3/4 = a4

∴  a3 = a4 * 4 = 9/4 * 4 = 9

Again putting n = 3 in the given recursive sequence,

⇒ a2 = 4*a3

∴  a2 = 4 * 9 = 36

Finally putting n = 2 in the recursive sequence,

⇒ a1 = 4 * a2

∴  a1 = 4 * 36 = 144

Therefore, the first four terms of the recursive formula are 144, 36, 9, 9/4 .

To learn more about recursive formula, refer -

https://brainly.com/question/1275192

#SPJ2

Answer:

0.5

Step-by-step explanation:

Its too hard to explain

Answer:

50 =x

Step-by-step explanation:

The two angles are vertical angles, so they are equal

2 (x+10) = 3x-30

Distribute the 2

2x+20 = 3x-30

Subtract 2x from each side

2x-2x+20 = 3x-2x-30

20 = x-30

Add 30 to each side

20+30 = x-30+30

50 =x

Answer:

x = 50

Step-by-step explanation:

We are given a diagram showing two vertically opposite angles and we are to find the value of x.

We know that when two lines intersect each other, vertically opposite angles are formed which are equal to each other.

Therefore, we can write them as:

[tex] 2 ( x + 1 0 ) = 3 x - 3 0 [/tex]

[tex] 2 x + 2 0 = 3 x - 3 0 [/tex]

[tex] 3 x - 2 x = 2 0 + 3 0 [/tex]

x = 50

The answer is probably 14, but I don't know how to prove it correctly, I mean by using the mathematical language. So if it will work, I can try to guess how I got this answer. So if you will draw radiuses, like I did on the screenshot, you will get 2 equal to each other triangles, but the thing is that I have no idea why they should be equal. So if the first step is right the value of x should be equal to 14, as the side below is equal to 14 too. That's it, I guess I helped you at least a little!

The value of x in the chord and arc circle figure is 8[tex]\sqrt{2}[/tex] units.

Given:

Find:

Solution:

As it is given that the radius of the circle is 9 units.

So, from here the diameter is 2*9 units = 18 units.

Now, we will draw a line from A to B, we will then Right triangle.

From the right-angled triangle we can calculate the value of x by Pythagoras Theorem, we get;

[tex]x^{2} = (18)^{2} - (14)^{2}[/tex]

[tex]x^{2} = 324 - 196[/tex]

[tex]x^{2} = 128[/tex]

[tex]x = \sqrt{128} = 8\sqrt{2}[/tex]

Hence, the value of x is 8[tex]\sqrt{2}[/tex] units.

To learn more about chords, refer to:

https://brainly.com/question/1869643

#SPJ2

Answer:

Each side of this equilateral triangle is 12 cm.

A = (1/2)(12)(6√3) = 36√3 cm²

The equilateral triangle, with a perimeter of 36 cm, has a side length of 12 cm. Its area is [tex]\(36\sqrt{3} \, \text{cm}^2\)[/tex], calculated using the formula [tex]\(\frac{\sqrt{3}}{4} \cdot s^2\)[/tex].

For an equilateral triangle, the perimeter (P) is related to the side length (s) by the formula P = 3s. From this, you can find the side length s by dividing the perimeter by 3:

[tex]\[ s = \frac{P}{3} = \frac{36}{3} = 12 \, \text{cm} \][/tex]

Now, you can use the side length to find the area (A) of the equilateral triangle. The formula for the area of an equilateral triangle is:

[tex]\[ A = \frac{\sqrt{3}}{4} \cdot s^2 \][/tex]

Substitute the value of (s):

[tex]\[ A = \frac{\sqrt{3}}{4} \cdot 12^2 \]\[ A = \frac{\sqrt{3}}{4} \cdot 144 \]\[ A = \frac{144\sqrt{3}}{4} \]\[ A = 36\sqrt{3} \, \text{cm}^2 \][/tex]

Therefore, the area of the equilateral triangle is [tex]\(36\sqrt{3} \, \text{cm}^2\)[/tex].

Answer:

It is possible

Step-by-step explanation:

x = 1.5990374 + π     n , for any integer  n

There are 70 degrees in angle A.

Answer:

The answer is option B.

Step-by-step explanation:

Loretta is rolling an unfair 6 sided die with a single number between 1 and 6 on each face and she has a 70% chance of rolling a four.

She is playing a game with a friend and knows that if she rolls a four on three of her next five rolls she will lose the game.

She wants to determine the probability that she rolls a four on three of her next five rolls.

The simulation design that is helpful here is :

B) Using a table of random digits select a digit between 0 and 9. Let 0-6 represent rolling a four and 7-9 represent not rolling a four. Select five digits.

Answer:

I think the answer is B

Answer:

The slope can 1/2 or 0.5

Step-by-step explanation:

Answer:

1/2

Step-by-step explanation:

The slope of a line is defined as ...

slope = (change in y)/(change in x)

Given two points, (x1, y1) and (x2, y2), the slope can be computed using ...

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

It does not matter which points you call point 1 and point 2. You just need to be consistent.

Using the point values in the order given in the problem statement, we have ...

slope = (4 -6)/(1 -5) = -2/-4

slope = 1/2

Answer:

Step-by-step explanation:

Alright.  I can't really explain much but i can get your answer.

AS A DECIMAL: 1.047197551196597746154214461093167628065723133125035273658

As a property:

π/3

Sorry if its wrong... I tried lol

Answer:

The answer would be 2

Step-by-step explanation:

The surface area is 392in squared

Answer:

1.93 x 10^-15

Step-by-step explanation:

You want to move the decimal just past the first real number and count the spaces moved, which is 15. Since the decimal is being moved to the right the spaces moved will be negative. Therefore you remove the zeroes and get 1.93 times 10 to the negative 15th power.

scientific notation means, moving the dot in a way that only one integer is to its left, namely the in this case it'll look like 1.93, so we'll have to move the dot all the way from the left to the right that many slots.

[tex]\bf 0.00000000000000193\implies \stackrel{\textit{moved }\stackrel{\downarrow }{15} \textit{ slots to the right}}{0000000000000001.93}\implies 1.93\times 10^{\stackrel{\downarrow }{-15}}[/tex]

Answer:

a) Similar

b) Perimeter of rectangle 2 is k times the Perimeter of rectangle 1 (Proved Below)

c) Area of rectangle 2 is k^2 times the Area of rectangle 1 (Proved Below)

Step-by-step explanation:

Given:

Rectangle 1 has length = x

Rectangle 1 has width = y

Rectangle 2 has length = kx

Rectangle 2 has width = ky

(a) Are Rectangle 1 and Rectangle 2 similar? Why or why not?

Rectangle 1 and Rectangle 2 are similar because the angles of both rectangles are 90° and the sides of Rectangle 2 is k times the sides of Rectangle 1. So sides of both rectangles is equal to the ratio k.

(b) Write a paragraph proof to show that the perimeter of Rectangle 2 is k times the perimeter of Rectangle 1.

Perimeter of Rectangle = 2*(Length + Width)

Perimeter of Rectangle 1 = 2*(x+y) = 2x+2y

Perimeter of Rectangle 2 = 2*(kx+ky) = 2kx + 2ky

                                          = k(2x+2y)

                                          = k(Perimeter of Rectangle 1)

Hence proved that Perimeter of rectangle 2 is k times the perimeter of rectangle 1.

(c) Write a paragraph proof to show that the area of Rectangle 2 is k^2 times the area of Rectangle 1.

Area of Rectangle = Length * width

Area of Rectangle 1 = x * y

Area of Rectangle 2 = kx*ky

                                  = k^2 (xy)

                                  = k^2 (Area of rectangle 1)

Hence proved that area of rectangle 2 is k^2 times the area of rectangle 1.

Final answer:

Rectangles 1 and 2 are similar due to proportional dimensions. The perimeter of Rectangle 2 is proven to be k times the perimeter of Rectangle 1 by factoring out the scale factor. Similarly, the area of Rectangle 2 is k² times the area of Rectangle 1, as shown by multiplying the scaled dimensions.

Explanation:

(a) Yes, Rectangle 1 and Rectangle 2 are similar because the sides of Rectangle 2 are proportional to the sides of Rectangle 1. This means that the two rectangles have the same shape but different sizes, which is the definition of similarity in geometry.

(b) To prove that the perimeter of Rectangle 2 is k times the perimeter of Rectangle 1, consider the perimeter of Rectangle 1, which is 2x + 2y. When each dimension is multiplied by k, the new length is kx and the new width is ky, so the perimeter of Rectangle 2 is 2(kx) + 2(ky) = 2kx + 2ky. Factoring out the common factor of k gives k(2x + 2y), which is k times the perimeter of Rectangle 1.

(c) For the area of Rectangle 2, the area of Rectangle 1 is xy. After scaling by k, the new dimensions of Rectangle 2 are kx and ky, so its area is (kx)(ky) = k²(xy), which shows that the area of Rectangle 2 is k² times the area of Rectangle 1.

ANSWER

[tex]h= 2 \cos(\pi(t + \frac{1}{2} )) + 5[/tex]

EXPLANATION

The given equation that models the height is

[tex]h(x) = - 2 \sin(\pi(t + \frac{1}{2} )) + 5[/tex]

This is sine a sine function that is reflected in the x-axis.

This function will coincide with the cosine function with the same amplitude, period, phase shift and vertical translation.

The function that can also model this height is

[tex]h= 2 \cos(\pi(t + \frac{1}{2} )) + 5[/tex]

The last choice is correct.