Following is the probability distribution for age of a student at a certain public high school.
X
13
14
15
16
17
18
P(x) 0.09 0.22 0.24 0.28 0.15 0.02

(a) Find the variance of the ages. Round the answer to at least four decimal places.
The variance of the ages is

Answer: here

Step-by-step explanation:

−21−24

Answer: negative 21 Negative 224

-21-24

Answer: About 800 thousand

The more accurate value is 807,528 but this is also an approximation.

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

Work Shown:

[tex]t = \text{number of years since the year 2000}[/tex]

[tex]P_0 = \text{population (in millions) in the year 2000}[/tex]

[tex]P = P_0(1.2)^t\\\\5 = P_0(1.2)^{10}\\\\5 \approx P_0*6.1917364224\\\\P_0 \approx \frac{5}{6.1917364224}\\\\P_0 \approx 0.80752791444922\\\\P_0 \approx 0.807528\\\\[/tex]

That's the rough population of wild pigs (in millions) for the year 2000.

Multiply by [tex]10^6[/tex] to get it in terms of units instead.

[tex]0.807528\times10^6 = 807,528[/tex]

There were roughly 800 thousand wild pigs in the year 2000.

Answer:

  sh.299,449.72

Step-by-step explanation:

The future value of an ordinary annuity with annual payments P earning interest rate r compounded annually for t years is ...

  FV = P((1+r)^t -1)/r

For the given numbers, the future value is ...

  FV = sh.25000(1.07^9 -1)/0.07 ≈ sh.299,449.72

Answer: x = 2/23

Step-by-step explanation:

[tex]46x-23x=2[/tex]

[tex]\mathrm{Add\:like\:terms:}\:46x-23x=23x[/tex]

[tex]23x=2[/tex]

[tex]\mathrm{Divide\:both\:sides\:by\:}23[/tex]

[tex]\frac{23x}{23}=\frac{2}{23}[/tex]

[tex]$$Simplify[/tex]

[tex]\bold{x=\frac{2}{23}}[/tex]

Answer:

Step-by-step explanation:

Inthis question we are given with one equation that is 46x - 23x = 2 and we have asked to find the value of x or solve for x .

So , from here we are solving :

[tex] \longmapsto \: 46x - 23x = 2[/tex]

Step 1 : Taking 23x common at left hand side :

[tex] \longmapsto \: 23x(2 - 1) = 2[/tex]

Step 2 : Subtracting 1 with 2 :

[tex] \longmapsto \:23x = 2[/tex]

Step 3 : Transposing 23 to right hand side :

[tex] \longmapsto \: \red{ \boxed{x = \frac{2}{23} }}[/tex]

Verifying the answer :

We are verifying our answer by substituting the value of x in the given equation .

[tex] \longmapsto \: 46(\frac{2}{23}) - 23( \frac{2}{23} ) = 2[/tex]

Now , calculating :

[tex] \longmapsto \: \cancel{46}(\frac{2}{ \cancel{23}}) - \cancel{23}( \frac{2}{ \cancel{23}} ) = 2[/tex]

[tex] \longmapsto \: 4 - 2 = 2[/tex]

[tex] \longmapsto \: 2 = 2[/tex]

[tex] \longmapsto \: L.H.S = R.H.S[/tex]

[tex] \longmapsto \: Hence, \: Verified . \: [/tex]

[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$530000\\ r=rate\to 4\%\to \frac{4}{100}\dotfill &0.04\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{quarterly, thus four} \end{array}\dotfill &4\\ t=years \end{cases} \\\\\\ A=530000\left(1+\frac{0.04}{4}\right)^{4\cdot t}\implies A=530000(1.01)^{4t} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{\textit{after 12 years}}{t=12}\implies A=530000(1.01)^{4(12)}\implies A=530000(1.01)^{48} \\\\\\ A\approx 854479.82~\hfill \underset{\textit{interest in the account}}{\stackrel{854479.82~~ - ~~530000}{\approx 324479.82}}[/tex]

The mode is 78

Mode: The digit that has been repeated the most in a specific data.

To determine the mode of the data, let's arrange the data in ascending order.

Arranging the data in ascending form, we get:

In the ascending data, we can see that: (Refer to underlined and bolded text)

Since 78 has been repeated the most, 78 is the mode of the data.

Answer:

hopefully this helps :] 16th line down I think

Answer:

A rectangle with sides lengths 4cm and 6cm and a rectangle with side lengths 2cm and 12 cm...

Answer:

5/6

Step-by-step explanation:

since there already is a common denominator all you have to do is add the numerators

The frequency count that should be recorded for the soup category is 6.

Subtraction is the process of taking one number away from another number. The sign used to represent subtraction is -.

The frequency count on the table should be equal to the number of students. Thus, in order to determine the frequency count for the soup category, subtract 22 from the total frequency count.

The frequency count for the soup category = 22 - (5 + 8 + 2 + 1 ) = 6

To learn more about subtraction, please check: https://brainly.com/question/915789

Answer:

648 cubic centimeters

Step-by-step explanation:

6×9×12=648

Answer:

648 cubic centimeters

Step-by-step explanation:

All you need to do is multiply all of the measures that they show you.

6 x 9 x 12 which equals 648

The areas of the square pyramid are the amount of space on it

The given parameters are:

Base (b) = 12 cm

Slant height (l) = 12.8 cm

The lateral surface area is calculated using:

L = 2bl

So, we have:

L = 2 * 12 * 12.8

Evaluate the product

L = 307.2

This is calculated using:

T = L + b^2

So, we have:

T = 307.2 + 12^2

Evaluate

T = 451.2

Hence, the total surface area is 451.2 square cm

Read more about areas at:

https://brainly.com/question/24487155

Answer:

3.6 m/h

Step-by-step explanation:

Distance (d) = 9 Km

Time (t) = 2.5 hour

Speed ( s )

Speed = Distance / Time

s = d / t

s = 9 / 2.5

s = 90 / 25

s = 18 / 5

s = 3.6 Km/h

Answer:

Soln:

Step-by-step explanation:

Here,

Base(b) =9

Opposite/Perpendicular (p)= x

Hypotenus (h) = 24

We know,

(p)^2 = (h)^2 - (b)^2

(x)^2 = (24)^2 - (9)^2

x^2 = 576 - 81

x^2 = 495

x = root under 495

Answer:

1- 22.2486  2- No

Step-by-step explanation:
1:

[tex]b = \sqrt{ c^{2}- a^{2}[/tex]

C is the hypotenuse, or longest side of the triangle (24).

A is the one length we have besides the hypotenuse(9).

[tex]b = \sqrt{ 24^{2}- 9^{2}[/tex]

b = 22.2486

2:
No, because if it was a Pythagorean triple, it would follow the equation [tex]a^{2} +b^{2} =c^{2}[/tex].

[tex]9^{2} + 22.2485^{2} \neq 24^{2}[/tex].

Answer:

D.  1  1/2 feet

Step-by-step explanation:

Multiply the numbers to find the length of wire used.

Correct choice is D

Answer:

1080 seconds.

Step-by-step explanation:

There are 60 seconds in a minute. As provided in the question, Lillian spent eighteen minutes, so 18x60=1080.

Answer:

1,080 seconds

Step-by-step explanation:

Answer:

The distance is 20 units

Step-by-step explanation:

Answer:

15% interest

Step-by-step explanation:

because it's 15 out of 100 so that would be 15%

The town should be located 13.4 units from each other

The formula for calculating the distance between two points is expressed as:
√(x2-x1)²+(y2-y1)²

The midpoint of two coordinates is expressed as:
[tex]m(x, y)=(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2} )[/tex]

Substitute the given coordinate

[tex]m(x, y)=(\frac{3+15}{2}, \frac{1+7}{2} )\\m(x,y)=(9,4)[/tex]

Hence the town should be located at coordinate (9, 4)

Calculate the distance

D =  √(15-3)²+(7-1)²

D =  √(12)²+(6)²

D = 13.4units

Hene the town should be located 13.4 units from each other

Learn more on midpoint here: https://brainly.com/question/24431553

Answer:

Parallel lines never intersect. Perpendicular lines are lines that intersect.

Step-by-step explanation:

Hope this helps.

Answer:

Perpendicular lines meet at a 90 degree angle while parallel lines will never touch

Step-by-step explanation:

The twenty units of potatoes illustrates the measure of central tendency  and probability

Start by sorting the dataset:

0.19; 0.28; 0.55;

0.62; 0.68; 0.77;

0.88; 0.89; 0.98;

0.99; 1.11; 1.22;

1.22; 1.22; 1.33;

1.44; 1.48; 1.68;

1.77; 1.99

The highest occuring element is 1.22 with a frequency of 3

The two middle elements are 0.99 and 1.11.

The mean of these two middle elements is: 0.5 * (0.99 + 1.11) = 1.05

The mean of the whole dataset is:

Mean = (0.19+ 0.28+ 0.55+ 0.62+ 0.68+ 0.77+ 0.88+ 0.89+ 0.98+ 0.99+ 1.11+ 1.22+1.22+ 1.22+ 1.33+ 1.44+ 1.48+ 1.68+1.77+1.99)/20

Mean = 1.06

Hence, the modal weight is 1.22, the mean is 1.06, and the median is 1.05

(a) at least 1.1 kg

There are 10 potatoes that weigh at least 1.1 kg.

So, the probability is:

P = 10/20

P = 0.5

(b) more than 3.5kg

There are 0 potatoes that weigh more than 3.5 kg.

So, the probability is:

P = 0/20

P = 0

(c) below 0.50kg

There are 2 potatoes that weigh below 0.50 kg.

So, the probability is:

P = 2/20

P = 0.1

The Variance of the weight.

This is calculated as:

Var = [tex]\sum[/tex](x - mean)^2/n

This gives

Var = [(0.19 - 1.06)^2 + (0.28 - 1.06)^2 + (0.55 - 1.06)^2 + (0.62 - 1.06)^2 + (0.68 - 1.06)^2 + (0.77 - 1.06)^2 + (0.88 - 1.06)^2 + (0.89 - 1.06)^2 + (0.98 - 1.06)^2 + (0.99 - 1.06)^2 + (1.11 - 1.06)^2 + (1.22 - 1.06)^2 + (1.22 - 1.06)^2 + (1.22 - 1.06)^2 + (1.33 - 1.06)^2 + (1.44 - 1.06)^2 + (1.48 - 1.06)^2 + (1.68 - 1.06)^2 + (1.77 - 1.06)^2 + (1.99 - 1.06)^2]/20

Evaluate

Var = 0.22

This means that:

The expectation of the squared deviation of the random variable from the mean is 0.22 kg

Read more about measure of central tendency at:

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Answer:

0.22 kg

Step-by-step explanation:

Answer:

12 cups

Step-by-step explanation:

The ratio he uses is

2 parts strong coffee

3 parts milk

Let's say he makes a recipe exactly like the amounts of the ratio.

2 cups strong coffee

3 cups milk

Total: 2 cups + 3 cups = 5 cups

He wants to make 30 cups, so 5 cups is not enough.

Let's double the amounts of the recipe keeping the same ratio of 2 to 3.

2 × 2 = 4 cups strong coffee

3 × 2 = 6 cups milk

Total: 4 cups + 6 cups = 10 cups

He wants to make 30 cups, so 10 cups is not enough.

We can keep on going up by multiplying the numbers in the ratio by larger numbers, but there is a quicker way.

We need to multiply both numbers in the ratio by a number, let's call it x, so that when both numbers in the ratio are multiplled by x, and the ingredients are added, we end up with 30 cups.

Multiply both numbers in the ratio by x.

2x cups of strong coffee

3x cups of milk

Now add: the total amount will be 5x cups

We want 30 cups, so

5x = 30

Solve for x.

x = 30/5 = 6

x, the multiplier we need is 6.

2x cups strong coffee = 2(6) cups = 12 cups

3x cups milk = 3(6) cups = 18 cups

Answer: 12 cups

Answer: TThere is no picture

Step-by-step explanation:

Answer:

$600

Step-by-step explanation:

This can be modeled as an exponential equation.

General form of an exponential function: [tex]y=ab^x[/tex]

where:

Therefore:

[tex]\implies 75=a(0.5)^3[/tex]

[tex]\implies 75=0.125a[/tex]

[tex]\implies a=\dfrac{75}{0.125}[/tex]

[tex]\implies a=600[/tex]

Therefore, the computer initially cost $600.

Answer:

15

Step-by-step explanation:

hope this helps

Answer:

[tex]x= \dfrac 72, ~~y= -2[/tex]

Step by step explanation:

[tex]4x+5y=4~~~...(i)\\\\2x-y=9~~~...(ii)\\\\\text{Multiply eq (ii) by 2 to isolate x:}\\\\4x-2y=18~~~.....(iii)\\\\(iii)-(i):\\\\4x-2y-4x-5y=18-4\\\\\implies -7y=14\\\\\implies y = -\dfrac{14}7 = -2\\\\\text{Substitute}~ y=-2~ \text{in equation (iii):}\\\\4x-2(-2) = 18\\\\\implies 4x +4 = 18\\\\\implies 4x = 18-4\\\\\implies 4x = 14\\\\\implies x = \dfrac{14}4 = \dfrac 72\\\\\text{Hence}~ (x,y) =\left(\dfrac 72 , -2 \right)[/tex]

Step-by-step explanation:

4x+5y=4 (equation 1)

2x-y=9 (equation2)

solving equation 1 and 2 and multiplying equation 2 by 2

4x+5y=4

4x-2y=18

- + -

________

7y= -14

y= -2

putting the value of y in equation 2

2x-y=9

2x+2=9

2x=7

x=3.5

Answer:

  yes; 2 m = 200 cm

Step-by-step explanation:

The SI prefix "centi-" signifies 1/100. That is 300 cm = 300/100 m = 3 m.

If the ceiling is 3 meters high, a sculpture that is 2 meters tall will have no difficulty fitting into the room.

Answer:

there would be around 40,000 colony of bats

There to be about 13,286,025 bats in the colony after 12 years if the growth rate remains constant.

An exponential function's curve is created by a pattern of data called exponential growth, which exhibits higher increases over time.

y = a(1+r)ˣ,

where a is the initial population and r is the rate in decimals and x is the time period.

To solve this problem, we need to use the formula for exponential growth:

N = N₀ (1 + r)ˣ

where:

N is the final number of bats after x years

N₀ is the initial number of bats

r is the annual growth rate (expressed as a decimal)

x is the number of years.

We can use the information given in the problem to find the values of N0, r, and t for the first two time periods:

For the first 4 years:

2025 = N₀(1 + r)⁴

For the next 2 years (6 years in total):

18225 = N₀ (1 + r)⁶

To solve for N₀ and r, we can divide the second equation by the first equation:

18225/2025 = (N₀ (1 + r)⁶) / (N₀(1 + r)⁴)

9 = (1 + r)²

Taking the square root of both sides, we get:

1 + r = 3

r = 2 (since r is expressed as a decimal)

Now that we know r, we can use either of the two original equations to find N₀. Let's use the first equation:

2025 = N₀(1 + 2)⁴

2025 = N₀(81)

N₀ = 25

So the initial number of bats was 25, and the annual growth rate is 200% (or 2 as a decimal).

Now we can use the formula to find the number of bats after 12 years:

N = 25 (1 + 2)¹²

N = 25 (531441)

N = 13,286,025

Therefore, we can expect there to be about 13,286,025 bats in the colony after 12 years if the growth rate remains constant.

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