Find the magnitudes of sides x and y.

Answer:

100 square feet

Step-by-step explanation:

[tex]9*12-2*4=\\108-2*4=\\108-8=\\100 ft^2[/tex]

Complete Question:

When a new charter school opened in 2000, there were 240 students enrolled. Write a formula for the function N ( t ) , representing the number of students attending this charter school t years after 2000, assuming that the student population:

a) Increased by 44 students per year

b) Decreased by 32 students per year

c) Increased by 40 students every 2 years

d) Decreased by 24 students every 4 years

e) Remained constant

f) Increased by 5 students every semester (twice in a year)

Answer:

a) N(t) = 240 + 44t

b) N(t) = 240 - 32t

c) N(t) = 240 + 20t

d) N(t) = 240 - 6t

e) N(t) = 240

f) N(t) = 240 + 10t

Step-by-step explanation:

The original population of the students in year 2000 is 240.

I.e. [tex]N_0 = 240[/tex]

Let the number of years = t

a) If the population increased by 44 students every year, the population, after t years, would have increased by 44t

Therefore, [tex]N(t) = N_o + 44t[/tex]

N(t) = 240 + 44t

b) If the population decreased by 32 students per year, the population, after t years, would have decreased by 32t

Therefore, [tex]N(t) = N_o - 32t[/tex]

N(t) = 240 - 32t

c) If the population Increased by 40 students every 2 years and increase is uniform per year, the population will increase by 40/2 = 20 students in 1 year. So in t years, the population would increase by 20 t.

Therefore,

[tex]N(t) = N_o + 20t\\N(t) = 240 + 20 t[/tex]

d) Decreased by 24 students every 4 years

In 1 year, it decreases by 24/4 = 6 students

In t years, it decreases by 6t students

[tex]N(t) = N_o - 6t\\N(t) = 240 - 6 t[/tex]

e) Remained constant

[tex]N(t) = N_o\\N(t) = 240[/tex]

f) If the population increases by 5 students twice in a year

In 1 year, it increases by 5*2 = 10 students

In t years, it increases by 10t students

[tex]N(t) = N_o + 10t\\N(t) = 240 + 10 t[/tex]

Answer:

w and y are knights

Step-by-step explanation:

Of the six natives, W and Y are the knights.

In mathematics, reasoning entails making logical deductions from data or presumptions. Making sense of something can be defined as gaining comprehension of a situation, setting, or idea by relating it to what is already known or has already happened.

Given that you meet a group of six natives, U, V, W, X, Y, and Z, who speak to you as follows. U says: None of us is a knight. V says: At least three of us are knights. W says: At most three of us are knights. X says: Exactly five of us are knights. Y says: Exactly two of us are knights. Z says: Exactly one of us is a knight.

From the given data it is concluded that W and Y are the knights because their statement is W says: At most three of us are knights and Y says: Exactly two of us are knights.

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Answer:

42

Step-by-step explanation:

Number of students whose favorite class is Math:

60*0.85=51

Number of students whose favorite class is Science:

15% is equal to 0.15.

60*0.15=9

Subtract number of students who like science from number of students who like math.

51-9=42

42 more students in the survey prefer math over science.

Answer:

42

Step-by-step explanation:

85% math

15% science

Subtract

85-15 = 70

The difference is 70 %

70% of 60 students

.70 * 60 = 42

There is a 42 student difference

Answer:

P(X = 2) = 0.22.

Step-by-step explanation:

We are given with the following probability distribution below;

          X                                         P(X)

          1                                          0.05

          2                                         0.22

          3                                         0.35

          4                                         0.30

          5                                        0.08    

       Total                                       1        

As the sum of all the probabilities is equal to 1, which means that this is a valid probability distribution.

Now, from the table above P(X = 2) = 0.22.

Hence, the probability that the X is equal to 2 is 0.22 or 22%.

Answer:

  54

Step-by-step explanation:

  [tex](\sqrt{6} + \sqrt{24})^2=(\sqrt{6}+2\sqrt{6})^2\\\\=(3\sqrt{6})^2=(3^2)(6)=\boxed{54}[/tex]

Answer:

  x = 6

Step-by-step explanation:

Compare the given formula to the equations shown in the attachment. First of all, you see that all of the numbers are scaled by a factor of 4. Removing that gives ...

  [tex]r=\dfrac{6.6}{1+1.1\cos{\theta}}=\dfrac{1.1\cdot6}{1+1.1\cos{\theta}}[/tex]

This matches the formula for the hyperbola with e=1.1 and d=6, for a directrix of x = 6.

Answer:

N = 53°

Step-by-step explanation:

1. 55 + 72 = 127°

2. 180° - 127° = 53°

3. Angle N is 53°

I hope this helps in any way:)

Answer:

5/11, 2/3, 7/8

Step-by-step explanation:

you can just do the numerator divided by the denominator to get a decimal, which can help you rank the fractions easier. hope this helps

Answer:

6026

Step-by-step explanation:

6072 × (1 - 0.76%)

6072 × 0.9924

= 6025.8528

Round to the whole number.

The enrollment for next semester will be 6026.

Answer:

5249 years

Step-by-step explanation:

Half-Life of Carbon-14 is approximately 5730 years.

When we want to determine the age of a fossil using carbon dating, we use the formula:

[tex]t=\dfrac{\ln(N/N_0)}{-0.693} \cdot t_{1/2}[/tex]

Where:

In this case:

N(t)=100

[tex]N_o=53\\t_{1/2}\approx 5730$ years[/tex]

Therefore, the age of the mummy

[tex]t=\dfrac{\ln(53/100)}{-0.693} \cdot 5730\\=5249.43$ years\\t \approx 5249$ years[/tex]

Answer:

the answer is 6349 :)

Step-by-step explanation:

Someone put the correct answer in the comments so I figured I would put it here so you wouldn't miss it :) (It is correct I have tested it)

Answer:

9.392

Step-by-step explanation:

3.1415 + 6.25 = 9.3915

Rounded to the thousandths place, this would be ≈ 9.392

The sum of the given decimal numbers is rounded to the nearest thousandths place as 9.392.

Given that, 3.1415 + 6.25.

Here, sum of the given decimals is 9.3915.

Rounding a number means the process of making a number simpler such that its value remains close to what it was. The result obtained after rounding off a number is less accurate, but easier to use. While rounding a number, we consider the place value of digits in a number.

To round 9.3915 to the nearest thousandths consider the ten thousandths' digit of 9.3915, which is 5. So, the thousandths place value of 9.3915 increase by 1 and ten thousandths place becomes 0.

That, 9.392

Therefore, the sum of the given decimal numbers is rounded to the nearest thousandths place as 9.392.

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Answer:

[tex]h(x) = 80x^2 + 560x[/tex]

Step-by-step explanation:

To find the function h(x), that represents the total number of seats, we just need to multiply the functions f(x) (number of rows) and g(x) (number of seats per row):

[tex]h(x) = f(x) * g(x)[/tex]

[tex]h(x) = 80x * (x+7)[/tex]

[tex]h(x) = 80x*x + 80x*7[/tex]

[tex]h(x) = 80x^2 + 560x[/tex]

So the function that represents the total number of seats is:

[tex]h(x) = 80x^2 + 560x[/tex]

Answer: A

Step-by-step explanation:

Answer:

B ). IF = IT

Step-by-step explanation:

IG is perpendicular to FT, means that the line IG divides the line FT into two equal parts without remainder.

Line IG does not only divide line FT, it also bisect the arc FT into two equally parts also.

It also divide the segment of the circle FIT into two equal parts.

So to the correct answer to the question, IF = IT

Answer:

Right-angle triangle

Step-by-step explanation:

Answer:

second one

Step-by-step explanation:

The output is result we get after applying a rule or a relation

In a function it's labelled y and we get it by inputting a value in the function

The second function fits the definition of an output

Answer:

an output is a special type of of relation for which there is a rule that pairs each input with one output

Answer:

A.18/25

B.72% of them brought in their permission slips

C.0.72

D.There the exact same value and we would divide by 100 to go from percentage to decimal and multiply by 100 to go to decimal to percentage Sign.

Step-by-step explanation:

Answer: [tex]C. f(x) = 3(2^x)[/tex].

Step-by-step explanation:

If the graph of function y=f(x) is vertically stretched by a scale factor of 'k', then the new function will be :

[tex]Y=kf(x)[/tex]

The given function : [tex]f(x)=2^x[/tex]

If the given function vertically stretched by a scale factor of '3', then the new function will be :

[tex]Y=3f(x)=3(2^x)[/tex]

Hence, the correct option is [tex]C. f(x) = 3(2^x)[/tex].

Answer:

x² + 9x + 8

Step-by-step explanation:

Step 1: FOIL

x² + 8x + x + 8

Step 2: Combine like terms

x² + 9x + 8

Answer:

x^2 + 9x + 8

Step-by-step explanation:

(x + 1)(x + 8)

x(x + 1) +8(x + 1)

x^2 + x + 8x +8

x^2 + 9x + 8

Answer:

They are dependent because we have to select from people who are given cards.

Step By Step Explanation:

So we'll take away people not given cards first den find the probability of selecting people with cards over the total number of people present .

Probability we'll be equal to = number of people with card(C) two persons/total number of people

Where C represent combination

Answer:

C. 5

Step-by-step explanation:

Triangle BED is enlarged by scale factor 4.

(25-x)/4 = x

Multiply both sides by 4.

25-x = 4x

Add x on both sides.

25 = 5x

Divide both sides by 5.

5 = x

Answer:

P(10 packet) = 0.000976

Therefore, there is a 0.000976 probability of packet loss if the number of packets in residence is limited to 10.

Step-by-step explanation:

We are given an M/M/1 queuing system

The mean arrival rate is

λ = 500 packets/second

The mean service rate is

μ = 1000 packets/second

The number of packets in residence is

n = 10

The probability of packet loss is given by

P(n packet) = ρⁿ

When n is the number of packets and ρ is the gateway utilization

The gateway utilization is given by

ρ = λ/μ

Where λ is the mean arrival rate and μ is the mean service rate.

ρ = 500/1000

ρ =0.50

So, the probability is

P(10 packet) = (0.50)¹⁰

P(10 packet) = 0.000976

Therefore, there is a 0.000976 probability of packet loss if the number of packets in residence is limited to 10.

Answer:

the 3rd option is the answer

Step-by-step explanation:

I hope the attached file is self-explanatory

Answer:

3/4

Step-by-step explanation:

Use [tex]\frac{rise}{run}[/tex]. From the bottom red point, you have to go up 3 and left 4 to get to the top point. That's your answer.

Answer: 0.1435

Step-by-step explanation:

Given : Mean = 479 pounds

Standard deviation = 40 pounds.

Let  X denote the weights of cows.

[tex]X\sim N(\mu=479,\sigma=40)[/tex]

The cow transport truck holds 15 cows and can hold a maximum weight of 7350.

i.e. mean weight of cow in this case =[tex]\overline{x}=\dfrac{7350}{15}=490\text{ pounds}[/tex]

If 15 cows are randomly selected from the very large herd to go on the truck, what is the probability their total weight will be over the maximum allowed of 7350 will be:-

[tex]P(\overline{x}>490)=P(\dfrac{\overline{x}-\mu}{\dfrac{\sigma}{\sqrt{n}}}>\dfrac{490-479}{\dfrac{40}{\sqrt{15}}})\\\\=P(z>1.065)\ \ [\because\ z=\dfrac{\overline{x}-\mu}{\dfrac{\sigma}{\sqrt{n}}}]\\\\=1-P(z\leq1.065)\\\\=1- 0.8565=0.1435\ \ [\text{By z-table}][/tex]

Hence, If 15 cows are randomly selected from the very large herd to go on the truck,  the probability their total weight will be over the maximum allowed of 7350 = 0.1435

So, the probability their mean weight will be over 479 is [tex]0.53836.[/tex]

A Z-score is a numerical measurement that describes a value's relationship to the mean of a group of values. Z-score is measured in terms of standard deviations from the mean.

It is given that,

[tex]\mu=479\\\sigma=40\\n=15\\X=maximum\ weight=7350[/tex]

Then,

[tex]\bar{x}=\frac{\sum x}{n}\\ =\frac{7350}{15}\\ =490[/tex]

Now, calculating Z-score:

[tex]Z=\frac{\bar{x}-\mu}{\frac{\sigma}{\sqrt{n} } } \\Z=\frac{490-479}{\frac{40}{\sqrt{15} } }\\ Z=1.07[/tex]

Using z table =1.07

[tex]P(Z < 1.07)=0.46164\\P(Z > 1.07)=1-P(Z < 1.07)\\=1-0.46164\\=0.53836[/tex]

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Answer:

area = 36 ft²

Step-by-step explanation:

no figure has been given ..

therefore,  area of a triangle = 1/2 * b * h

assume b = 6 ft

assume h = 12 ft

area = 1/2 * 6 * 12

area = 36 ft²

Answer:

87.5%

Step-by-step explanation:

Total parts = 8

Part 6 = 1

Parts not 6 = 7

P(not 6) = 7/8

In %age:

=> 87.5%

Answer:

87.5%

Step-by-step explanation:

The numbers not 6 on the spinner are 2, 3, 4, 5, 7, 8, and 9.

7 numbers out of 8 are not 6.

7/8 = 0.875

P(not 6) = 87.5%

Answer:

The value of y is - 11

Step-by-step explanation:

The first statement is written as

6y + x = -62.......... equation 1

The second statement is written as

x - y = 15 ........ equation 2

To find y make x the subject in the second equation and substitute it into the first equation

That's

x = 15 + y

6y + x = - 62

6y + 15 + y = -62

7y = -62 - 15

7y = - 77

Divide both sides by 7

y = - 11

Hope this helps you.

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▹ Answer

#3. 1.89/100

▹ Step-by-Step Explanation

1.89 → hundreths place so..

1.89/100 is the correct answer

Hope this helps!

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