Exam
AABC ~ AQRS
Find the missing side length, m.
B
10
m
А
6
9
m = [?]

Answer:

23 boxes of toys are being stored.

Step-by-step explanation:

There is a fixed cost of $1200 a month for rent and a variable cost of $5 per box of toys that are stored

This means that for x boxes of toys stored, the total cost is of:

[tex]C(x) = 1200 + 5x[/tex]

If the total cost for this month was $1315, how many boxes of toys are being stored?

This is [tex]x[/tex] for which [tex]C(x) = 1315[/tex]. So

[tex]C(x) = 1200 + 5x[/tex]

[tex]1315 = 1200 + 5x[/tex]

[tex]5x = 115[/tex]

[tex]x = \frac{115}{5}[/tex]

[tex]x = 23[/tex]

23 boxes of toys are being stored.

9514 1404 393

Answer:

  3) y = √10

  4) x = 5√2

Step-by-step explanation:

The side ratios of an isosceles right triangle (one of the "special" right triangles) are ...

  1 : 1 : √2

So, for some multiplier k, they can be made to match the sides in your triangles.

__

3) 1·k : 1·k : k√2 = √5 : √5 : y

Clearly, k = √5, so ...

  y = (√5)(√2)

  y = √10

__

4) k : k : k√2 = x : x : 10

  k = 10/√2 = (5√2)/2

  k = x = (5√2)/2

Answer:

Step-by-step explanation:

The population of bacteria in the culture after 7 hours is approximately 883.

Several real-world phenomena, including population expansion, radioactive decay, compound interest, and the spread of diseases, are modeled using exponential functions. In calculus, where they are used to define the exponential and logarithmic functions—essential ideas in calculus and other fields of mathematics—they also play a significant role.

Using the formula [tex]P_t = P_0 \times 2^{\frac{t}{d}}[/tex], where P_t is the population after t hours, P₀ is the initial population, t is the time in hours and d is the doubling time, we can find the population of bacteria in the culture after 7 hours as follows:

Since the initial population is 470, we have P₀ = 470.

The doubling time is 8 hours, so we have d = 8.

Substituting these values into the formula, we get:

[tex]P_7 = 470 \times 2^{\frac{7}{8}}[/tex]

P₇≈ 882.77

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Step-by-step explanation:

let's see....

3m × 5r = 15mr

15(m × r)

15mr.

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Answer 8 divide by 10 =0.8

0.8x 25=20

Step-by-step explanation: i hope this helps

The equation for the total cost, c, in terms of the number of songs, s, purchased is c = 1.25s and  $25 can purchase 20 songs.

Two or more expressions with an Equal sign is called as Equation.

Let x be the price of each song.

The cost to purchase 8 songs is given as $10, so we can write the equation:

8x = 10

To find the equation for the relationship between the total cost, c, and the number of songs, s, purchased, we can solve for x:

8x = 10

x = 10/8

x = 1.25

So the price of each song is $1.25, and the equation for the total cost, c, in terms of the number of songs, s, purchased is:

c = 1.25s

To find how many songs can be purchased for $25, we can use the equation:

c = 1.25s

Substitute c = $25, and solve for s:

25 = 1.25s

s = 25/1.25

s = 20

Therefore, at this rate, $25 can purchase 20 songs.

Hence, the equation for the total cost, c, in terms of the number of songs, s, purchased is c = 1.25s and  $25 can purchase 20 songs.

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Answer:

(a) 3003 ways

(b) 10897286400 ways

(c) 3002 ways

Step-by-step explanation:

Given

[tex]n = 15[/tex] --- 15 players

Solving (a) Ways of selecting 10 players.

This implies combination.

So, we have:

[tex]r=10[/tex]

Using:

[tex]^nC_r = \frac{n!}{(n-r)!r!}[/tex]

We have:

[tex]^{15}C_{10} = \frac{15!}{(15-10)!10!}[/tex]

[tex]^{15}C_{10} = \frac{15!}{5!10!}[/tex]

Simplify

[tex]^{15}C_{10} = \frac{15*14*13*12*11*10!}{5!10!}[/tex]

[tex]^{15}C_{10} = \frac{15*14*13*12*11}{5!}[/tex]

[tex]^{15}C_{10} = \frac{15*14*13*12*11}{5*4*3*2*1}[/tex]

[tex]^{15}C_{10} = \frac{360360}{120}[/tex]

[tex]^{15}C_{10} = 3003[/tex]

Solving (b) Ways of assigning positions to 10 players.

This implies permutation.

So, we have:

[tex]r=10[/tex]

Using:

[tex]^nP_r = \frac{n!}{(n-r)!}[/tex]

We have:

[tex]^{15}P_{10} = \frac{15!}{(15-10)!}[/tex]

[tex]^{15}P_{10} = \frac{15!}{5!}[/tex]

Solve each factorial

[tex]^{15}P_{10} = \frac{1307674368000}{120}[/tex]

[tex]^{15}P_{10} = 10897286400[/tex]

Solving (c) Ways of choosing at least 1 woman

We have:

[tex]Men = 10[/tex]

[tex]Women = 5[/tex]

Ways of selecting 10 players is: (a) 3003 ways

Since the number of men are 10, there is 1 way of selecting 10 men (i.e. selection without women)

Using complement rule:

At least 1 woman = Total - No woman

[tex]At\ least\ 1\ woman = 3003 - 1[/tex]

[tex]At\ least\ 1\ woman = 3002[/tex]

Answer:

0.60

Step-by-step explanation:

Answer:

.60

Step-by-step explanation:

Answer:

2.5 hours

Step-by-step explanation

it takes 1/2 a hour to write one page so do

5 x 1/2 which is 2.5 since there are 5 pages

Answer:

QUESTION:

what is the y-intercept of the line that goes through (0, 0) (6, 3)

ANSWER:

Use the slope formula and the slope-intercept form to find the slope  m  and y-intercept  b .

Slope: 1/2

y-intercept: (0,0)

Step-by-step explanation:

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Answer:

d

Step-by-step explanation:

if the taxes raise each year

Answer:

X = 2 If the exponent 2 in the 2 does not have the x

Step-by-step explanation:

Answer:

x > 7

Step-by-step explanation:

-5x < -35

(Divide by 5)

-x < -7

(When dividing by a negative number, you flip the sign)

x > 7

The answer of given inequality is x > 7 .

Inequality is the defined as mathematical statements that have a minimum of two terms containing variables or numbers is not equal.

Given,

-5x < -35

Divide by 5 in inequality

-x < -7

Multiply by (-1) in inequality [flip the sign of inequality]

So, x > 7

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Answer:

∡x°=35°

Step-by-step explanation:

x° and 35° are vertical angles, so they are congruent to each other. Therefore, the measure of angle x° is also 35°

Answer:

820          

Step-by-step explanation:

Hi so if your area is 4756, the base would be 820

Answer:

1/5

Step-by-step explanation:

7 + 13 =20

20 + 5 = 25

5 is a fifth of 25

Answer:

[tex]\frac{1}{5}[/tex]

Step-by-step explanation:

There are 25 socks in total, only 5 of these are green.

The proportion would look like this:

[tex]\frac{5}{25}=\frac{1}{5}[/tex]

Answer:

[tex](d)\ \beta = 2\ rad[/tex]

Step-by-step explanation:

Given

[tex]L =2[/tex] -- length of the arc

[tex]r = 1[/tex] --- radius of a unit circle

[tex]\beta =[/tex] the subtended angle

Required

Find [tex]\beta[/tex]

The length of an arc is:

[tex]L = r * \beta[/tex]

This gives:

[tex]2 = 1 * \beta[/tex]

[tex]2 = \beta[/tex]

Make [tex]\bets[/tex][tex]\beta[/tex] the subject

[tex]\beta = 2[/tex]

Hence:

[tex]\beta = 2\ rad[/tex]

Answer:

2rad

Step-by-step explanation:

Answer:

165+x = 180 (linear pair)

Hence x = 15

Answer:

69.08

Step-by-step explanation:

2×3.14=6.28

6.28×11=69.08

Answer:

5

Step-by-step explanation:

5y+155=180

5y=180-155=25

y=5

5y+13x=90

13x=90-25=65

x=5°

Answer:

#8 is one #9 is 4

Step-by-step explanation:

Answer:

12 gallons

Step-by-step explanation:

Answer:

(-5,1)

Step-by-step explanation:

Because if you graph the point and move it 3 units down then that is your awnser.

Answer:

9,386

Step-by-step explanation:

56,316 ÷ 6 = 9,386

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