Geometric series mastery test

Plato/edumentum

Answer: ∠A=144°

Step-by-step explanation:

∠A and ∠B are alternate exterior angles. Alternate exterior angles are congruent to each other. That means ∠A=∠B. Since we are given the measures of ∠A and ∠B, all we have to do is set them equal to each other.

10x+24=6x+72          [subtract both sides by 6x]

4x+24=72                  [subtract both sides by 24]

4x=48                         [divide both sides by 4]

x=12

Now that we found x, we need to plug it into ∠A.

10(12)+24=120+24=144

We know that ∠A=144°.

Answer:

6.132

Step-by-step explanation:

please mark me the brainiest

Answer: 189

All Steps and Information Found in Image.

Hope This Helped!

Answer:

V(sphere) =

[tex] \frac{4 }{3} \pi \:{r}^{3} = 195.43 \\ [/tex]

V(hemisphere) = V(sphere)/2 = 97.715 = 97.7

Answer:

four sixths + three fifths.

Step-by-step explanation:

1 8/30 = 38/30.

4/6 + 3/5

= 20/30 + 18/30 = 38/30.

Answer:

21.42

Step-by-step explanation:

Imagine it as a full circle. 3 x 4 will give you the diameter of a full circle, which is 12. circumference = pi x diameter. so 12 pi (we can work that out later). now for the quater circle, divide it by 4, so 3 pi. Then you have the 2 extra edges which are both 2r, so 6 each. finally, you have 3 pi plus 12 which = 21.42

The distance they(Bobby's cat and dog) will be from each other after 30 minutes is 0.5x miles.

The dog runs twice as fast as the cat. Therefore,

Bobby's cat speed = x

Bobby's dog speed = 2x

Therefore,

speed  = distance / time

30 minutes = 0.5 hours

Therefore,

distance = speed × time

distance covered by the cat = x × 0.5 = 0.5x

distance covered by the dog = 2x × 0.5 = x

Therefore, the distance they will be from each other after 30 minutes is as follows:

distance = x - 0.5x = 0.5x

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Answer:

36

Step-by-step explanation:

triangular numbers are

1, 3, 6, 10, 15, 21, 28, 36, .....

square numbers are

1, 4, 9, 16, 25, 36, ..........

the smallest number that is triangular and square is 36

Step-by-step explanation:

i hope this helps the steps are within the photo

Answer:256960ft

Step-by-step explanation: LENGTHXWIDTH . So you would want to multiply 440x584 and that is 256960 So it is 256960ft I think.

Answer:

297 ft

Step-by-step explanation:

So

Now

The required probability

[tex]\\ \rm\rightarrowtail P(A')^{10}\times P(A)^5\times ^{15}C_{10}[/tex]

[tex]\\ \rm\rightarrowtail (0.33)^{5}\times (0.67)^{10}\times \dfrac{15!}{5!10!}[/tex]

[tex]\\ \rm\rightarrow 0.0039(0.0182)\times\dfrac{15(14)(13)(12)(11)10!}{5!10!}[/tex]

[tex]\\ \rm\rightarrowtail 0.00007098\times \dfrac{360360}{120}[/tex]

[tex]\\ \rm\rightarrowtail 0.00007098(3003)[/tex]

[tex]\\ \rm\rightarrowtail 0.213[/tex]

So probability

Option B

Answer:

b.  21.4 % (nearest tenth)

Step-by-step explanation:

P(lose) = 33% = 0.33

P(win) = 1 - 0.33 = 0.67

Using binomial distribution X ~ B(n, p)

where n is the number of trials and p is the probability of success

⇒ X ~ B(15, 0.67)

Binomial probability formula:

[tex]\sf P(X=x)= \ _nC_x\cdot p^x \cdot(1-p)^{n-x}[/tex]

[tex]\sf \implies P(X=10)=15C10\cdot 0.67^{10} \cdot(1-0.67)^{15-10}[/tex]

                       [tex]\sf =3003 \cdot 0.67^{10} \cdot 0.33^5[/tex]

                       [tex]\sf =0.214226434...[/tex]

Converting to percentage:

0.214266434... x 100% = 21.4 % (nearest tenth)

Answer:

13. True, False, True

14. False, True, True

15. All true

Answer:

See below for answers and explanations

Step-by-step explanation:

Part A

The average rate of change of a function over the interval [tex][a,b][/tex] is equal to [tex]\frac{f(b)-f(a)}{b-a}[/tex], hence:

[tex]\frac{f(b)-f(a)}{b-a}\\\\\frac{f(9)-f(5)}{9-5}\\\\\frac{14-(-4)}{9-5}\\ \\\frac{14+4}{4}\\ \\\frac{18}{4}\\ \\\frac{9}{2}[/tex]

Therefore, the average rate of change of [tex]f(x)[/tex] over the interval [tex][5,9][/tex] is [tex]\frac{9}{2}[/tex].

Part B

Do the same thing as in Part A:

[tex]\frac{f(b)-f(a)}{b-a}\\ \\\frac{f(1)-f(0.25)}{1-0.25}\\ \\\frac{2-5}{0.75}\\ \\\frac{-3}{0.75}\\ \\-4[/tex]

Therefore, the average rate of change of [tex]g(x)[/tex] over the interval [tex][0.25,1][/tex] is [tex]-4[/tex].

Part C

To interpret our answer from Part B in terms of the real world it represents, we say that between 0.25 seconds and 1 second, the ball falls at a rate of 4 feet per second (since our average rate of change is negative).

The average rates of change are:

For a function f(x), the average rate of change on the interval [a, b] is:

[tex]r = \frac{f(b) - f(a)}{b -a}[/tex]

a) Here we have:

[tex]r = \frac{F(9) - F(5)}{9 - 5} = \frac{14 - (-4)}{4} = 4.5[/tex]

b) Now we look at g(x) on the interval [0.25, 1]

Notice that g(0.25) = 5 and g(1) = 2

Then we have:

[tex]r = \frac{2 - 5}{1 - 0.25} = -4[/tex]

c) That average rate of change means that, in average, in that interval in each second the height decreases by 4 ft.

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17 (1/5) × 17,5 = 301

,..,.

Answer:

x = -1, y = -1

Step-by-step explanation:

Given:

[tex]\begin{bmatrix}2x-3y=1\\ x+2y=-3\end{bmatrix}[/tex]

Solve:

[tex]\mathrm{Substitute\:}x=\frac{1+3y}{2}[/tex]

[tex]\begin{bmatrix}\frac{1+3y}{2}+2y=-3\end{bmatrix}[/tex]

Simplify

[tex]\begin{bmatrix}\frac{1+7y}{2}=-3\end{bmatrix}[/tex]

[tex]\mathrm{For\:}x=\frac{1+3y}{2}[/tex]

[tex]\mathrm{Substitute\:}y=-1[/tex]

[tex]x=\frac{1+3\left(-1\right)}{2}[/tex]

[tex]x=-1[/tex]

[tex]The\:solutions\:to\:the\:system\:of\:equations\:are[/tex]

[tex]x=-1,\:y=-1[/tex]

Check Answer:

2(-1)-3(-1) = 1

True

-1+2(-1)= -3

True

~Lenvy~

Answer:

Step-by-step explanation:

5(a + a + b) = 5(2a + b)

use the distributive property:

a(b + c) = ab + ac

= 5 · 2a + 5 · b =10a + 5b

Answer:

[tex]\boxed{\sf{D. \quad 10a+5b}}[/tex]

Step-by-step explanation:

Use a distributive property.

Distributive property:

[tex]\Longrightarrow: \sf{A(B+C)=AB+AC}[/tex]

⇒ a+a=2a

Rewrite the problem down.

[tex]\Longrightarrow: \sf{5(2a+b)}[/tex]

Multiply should be expanded.

⇒ 5*2a=10a

⇒ 5*b=5b

Rewrite the problem.

⇒ = 10a+5b

I hope this helps you! Let me know if my answer is wrong or not.

Answer:

The range is the best measure of variability because the distribution has an outlier.

Either the IQR or the range are good measures of variability because the distribution has no outliers.

The IQR is the best measure of variability because the distribution has an outlier.

Step-by-step explanation:

is this what you was looking for

Answer:

60 + 6n

Step-by-step explanation:

Distribute 6 to both terms:

6 * 10 is 60

6 * n is 6n

Both total are 60 + 6n

Hey there!

6(10 + n)

= 6(10 + 1n)

DISTRIBUTE 6 WITHIN the PARENTHESES

= 6(10) + 6(1n)

= 60 + 6n

= 6n + 60

Therefore, your answer is: 6n + 60

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

Answer:

5 + 3(4)

5+ 12

17

Step-by-step explanation:

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Answer:

17

Step-by-step explanation:

5 + (3 x 4)

5 + (12)

17

You're multiplying 3 by 4 because x = 4. When a variable is on top of a number, you will multiply it. Almost like saying 3(4).

I hope this helped!

Answer:

10 trips

Step-by-step explanation:

50kg in a bag, 4535.92 kg in 5 tons

4535.92kg/50kg = 90.7184

90/10 = 9 trips

but there's still 0.7184 bag left, so the pick-up would need to make 10 trips.

Answer:

114

Step-by-step explanation:

The external angle measure is equal to the half of difference between the larger intercepted arc (5x-12) and the smaller intercepted arc (3x)

32 = (5x-12 -3x)/2

combine like terms in parenthesis and multiply both sides by 2

32·2 = 2x-12

multiply 32·2 = 64, and add 12 to both sides

64 + 12 = 2x

add 64+12 = 76, and divide both sides by 2 to isolate x

76/2 = x

38 = x

The measure of arc AB is 3x.

Substitute x for 38

Measure of arc AB = 3x = 3·38 = 114

Answer:

6 sales

Step-by-step explanation:

(I MADE THIS QUESTION I DIDINT KNOW IF YOU NEEDED IT)

Jake wants to but the new computer(it costs $920). Jake has $560 saved in his bank. Jake also gets $60 whenever he makes a sale at his job. How many sale(s) at his job does Jake need to make? Answer -- Jake needs to make 6 sales of $60 to buy the new computer.

MATH -----

$6 x $60 = $360

$360 + $560 = $920

Step-by-step explanation:

a parallelogram has 2 pairs of equation sides (as a rectangle, just not necessarily with the 90° angles).

so, when one side is 16 cm, then there is a second side with 16cm.

the perimeter is the sum of all 4 sides (the 2 pairs of sides) : 48 cm.

and we know the length of one of these pairs : 2×16 = 32 cm.

what is left for the second pair of sides ?

48 - 32 = 16 cm

so, these 16 cm is the sum of a pair of equally long sides. that means their are

16/2 = 8 cm

long each.

so, the length of the "remaining" side is 8 cm.

The circumference of a circle that was computed when the diameter is 3cm will be 9.426cm.

The circumference of a circle of gotten by the formula:

C = 2πr or πd

where,

r = radius

d = diameter

Since the diameter is given as 3cm, the circumference will be:

= πd

= 3.142 × 3

= 9.426cm

In conclusion, the circumference of the circle is 9.426cm.

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Answer:

Step-by-step explanation:

Answer: She.Was.Playing.By.Ear

Answer:

[tex]\huge\boxed{\sf x < 6}[/tex]

Step-by-step explanation:

Given inequality:

2x - 3 < 9

Add 3 to both sides

2x < 9 + 3

2x < 12

Divide 2 to both sides

x < 6

[tex]\rule[225]{225}{2}[/tex]

Answer:

Step-by-step explanation:

2x − 3 < 9

Solve:

2x − 3 < 9 <== add 3 to both sides

     + 3 + 3

2x < 12 <== divide both sides by 2, to isolate the variable (x)

/2    /2

x < 6

This means that x, can be any number than is smaller than (less than) 6.

A. x = −4

-5 < 6 <== correct

B. x = −3

-3 < 6 <== correct

C. x = −2

-2 < 6 <== correct

D. x = 3

3 < 6 <== correct

Therefore, all these are solutions to the inequality.

Hope this helps!

Answer: yes its a 3:1 ratio

3 cups of strawberries

per 1 cup of mango

Step-by-step explanation:

so the best way i can try to explain it is this...

1 2 they both need a

_ x _ common denominator so

3 6 you need to multiply the smaller one to equal

the bottom number of the other one

oorr divide the big number on the bottom to equal

the smaller number on the bottom of the left

equation.

soooo 2 times (1:3) equals (2:6)

or divide by 2 to (2:6) to equal the denominator of 3 (same as smaller)

Answer:

There is no affirmative formula, but this is the basics

Step-by-step explanation:

DDM Formula=

Stock value = Dividend per share / (Required Rate of Return – Dividend Growth Rate)

Rate of Return = (Dividend Payment / Stock Price) + Dividend Growth Rate.

The P/E Ratio. The price-to-earnings ratio or P/E ratio is a popular metric for valuing stocks that works even when they have no dividends. Regardless of dividends, a company with high earnings and a low price will have a low P/E ratio. Value investors see such stocks as undervalued.

The current price is the most recent selling price of a stock, currency, commodity, or precious metal that is traded on an exchange and is the most reliable indicator of that security's present value.

The formula consists of taking the DPS in the period by (Required Rate of Return – Expected Dividend Growth Rate). For example, the value per share in Year is calculated using the following equation: Value Per Share ($) = $5.15 DPS ÷ (8.0% Ke – 3.0% g) = $103.00.

Briefly, in order to be eligible for payment of stock dividends, you must buy the stock (or already own it) at least two days before the date of record. That's one day before the ex-dividend date.

Answer:

L= 12

Step-by-step explanation:

area= L×B

108= 9×L

108= 9L

Divide both sides by 9

108/9= 9L/9

L= 12

There are 16 fruits in each of the boxes found under the stairs.

An equation is an expression used to show the relationship between two or more numbers and variables.

Let x represent the number of pears, hence:

Number of fruit in first box = 12 + (1/9)x

Number of fruit in second box = number of fruit in third box = (8/9)x ÷ 2 = (4/9)x

Therefore:

12 + (1/9)x = (4/9)x

x = 36

First box = second box = third box = (4/9) * 36 = 16

There are 16 fruits in each of the boxes found under the stairs.

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Answer:

7

Step-by-step explanation: