Given f(x) = 6x + 2, find f(x – 3).
A. f(x – 3) = 6x – 1
B. f(x – 3) = 6x – 16
C. f(x - 3) = x - 1
D. f(x – 3) = 6x2 – 16x - 6

Answer:

= c^4 d^8 a^2

Step-by-step explanation:

Apply exponent rule: aa= a^2

= c^3 da^2 cd^7

= c^4 da^2 d^7

= c^4 d^8 a^2

Given:

In a triangle, length of one side is 8 inches and length of another side is 12 inches, and an angle is a right angle.

To find:

The length of the missing side.

Solution:

In a right angle triangle,

[tex]Hypotenuse^2=Perpendicular^2+Base^2[/tex]

Suppose the measures of sides adjacent to the right angle are 8 inches and 12 inches.  

Substituting Perpendicular = 8 inches and Base = 12 inches, we get

[tex]Hypotenuse^2=8^2+12^2[/tex]

[tex]Hypotenuse^2=64+144[/tex]

[tex]Hypotenuse^2=208[/tex]

Taking square root on both sides, we get

[tex]Hypotenuse=\sqrt{208}[/tex]

[tex]Hypotenuse=14.422205[/tex]

[tex]Hypotenuse\approx 14.4[/tex]

The length of the missing side is 14.4 inches. Therefore, the correct option is D.

Answer:

the

Step-by-step explanation:

it's fairly easy actually. You just have to use sin

Answer:

a) Their average weight is of 187 pounds.

b) 0.4562 = 45.62% probability that the maximum safe weight will be exceeded.

c) 0.002 = 0.2% probability that the maximum safe weight will be exceeded

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

a. If 44 people are on the elevator, and their total weight is 8228 pounds, what is their average weight?

8228/44 = 187

Their average weight is of 187 pounds.

b. If a random sample of 44 adult men ride the elevator, what is the probability that the maximum safe weight will be exceeded?

For men, we have that [tex]\mu = 186, \sigma = 60[/tex]

Sample of 44 means that [tex]n = 44, s = \frac{60}{\sqrt{44}}[/tex]

This probability is 1 subtracted by the p-value of Z when X = 187. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{187 - 186}{\frac{60}{\sqrt{44}}}[/tex]

[tex]Z = 0.11[/tex]

[tex]Z = 0.11[/tex] has a p-value of 0.5438.

1 - 0.5438 = 0.4562

0.4562 = 45.62% probability that the maximum safe weight will be exceeded.

c. If a random sample of 44 adult women ride the elevator, what is the probability that the maximum safe weight will be exceeded?

For women, we have that [tex]\mu = 157, \sigma = 69[/tex]

Sample of 44 means that [tex]n = 44, s = \frac{69}{\sqrt{44}}[/tex]

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{187 - 157}{\frac{69}{\sqrt{44}}}[/tex]

[tex]Z = 2.88[/tex]

[tex]Z = 2.88[/tex] has a p-value of 0.998.

1 - 0.998 = 0.002.

0.002 = 0.2% probability that the maximum safe weight will be exceeded

Answer:

(52.30 ; 52.62)

Step-by-step explanation:

Given :

Sample size, n = 20

Mean, xbar = 52.46

Standard deviation, s = 0.42

We assume a t - distribution

The 90% confidence interval

The confidence interval relation :

C.I = xbar ± Tcritical * s/√n

To obtain the Tcritical value :

Degree of freedom, df = n - 1 ; 20 - 1 = 19 ; α = (1 - 0.90) /2 = 0.1/2 = 0.05

Using the T-distribution table, Tcritical = 1.729

We now have :

C.I = 52.46 ± (1.729 * 0.42/√20)

C. I = 52.46 ± 0.1624

C.I = (52.30 ; 52.62)

C. Dilation.

Dilation can resize the image.

Translation will shift the imagine's position but won't change its actual size.

Rotation will mangle with image's orientation but also won't change its size.

Reflection is just a type of rotation which as established, also won't change its size.

Hope this helps.

Answer:

first question is D

second question is D .875

Step-by-step explanation:

35*2.5= 87.5

7 divided by 8= .875

Answer:

D   87.5 miles

D  0.875 = 7/8 so it is a decimal that terminates after 3 dp.

Step-by-step explanation:

We write;

Scale Inch x Miles

2.5 x 35 = 87.5 miles

Why??

87.5 miles is found when we use the scale of 35 miles = 1inch

Answer = D 87.5 miles

The second one we can either multiply by 7/8 or divide by 1-7/8 = 1/8 to show that;

1/ 1/8 = 0.125

1-0.125 = 0.875  

Answer:

Matthew travels 0.0161 meters per second.

Step-by-step explanation:

Given that Matthew travels 42/50 meters In 26/30 minutes, to find the speed of Mathew in meters per second the following calculation must be performed:

42/50 = 0.84

26/30 = 0.86

0.86 x 60 = 52

0.84 meters in 52 seconds

0.84 / 52 = 0.01615

Therefore, Matthew travels 0.0161 meters per second.

Answer:

104 m^2

Step-by-step explanation:

First find the area of the rectangle

A = l*w = 10*8 = 80

Then find the area of the triangle

A = 1/2 bh = 1/2 (8) * 6 = 24

Add the areas together

80+24 = 104 m^2

Answer:

f^-1(x) = sqrt(x+4)

Step-by-step explanation:

y = x^2 -4

Exchange x and y

x = y^2 -4

Add 4 to each side

x+4 = y^2

Take the square root of each side

sqrt(x+4) = y

f^-1(x) = sqrt(x+4)

Answer:

f^-1(x) = sqrt(x+4)

Step-by-step explanation:

Answer:

29Kg

Step-by-step explanation:

P1=2Kg

P2=7Kg

P3=31Kg

P3-P1=29Kg

To find P1, P2 and P3 I started assigning the first prime number, 2, to P1 and tried to assign prime numbers to P2 and P3 so that the sum was 40, increasing them at each step.

I was lucky and I got the result after few steps :-)

Answer:

(11.847 ; 15.813)

Step-by-step explanation:

We are given 12 samples which are :

8, 20, 20, 11, 18, 12, 6, 5, 7, 22, 12, 25

We use a T-distribution to find the confidence interval since the sample size. is small, n < 30

Using a calculator :

The sample mean, xbar = 13.83

Sample standard deviation, s = 6.87

The confidence interval, C.I

C.I = xbar ± Tcritical * s/√n)

Tcritical at 95%, df = n - 1, 12 - 1 = 11

Tcritical(0.05, 11) = 2.20

Hence,

C.I = 13.83 ± 2.20(6.87/√12)

C.I = 13.83 ± 1.9831981

C. I = (13.83 - 1.983 ; 13.83 + 1.983)

C. I = (11.847 ; 15.813)

Answer:

deflation ,,,,

Step-by-step explanation:

Deflation must have existed during the second 9-year period.

Deflation is a decrease in the general price level of goods and services in an economy over a period of time. This means that the purchasing power of money increases, as the same amount of money can buy more goods and services.

The opposite of inflation, which is an overall rise in the cost of goods and services over time, is deflation. Money loses value due to inflation, whereas it gains value due to deflation. Deflation can reduce demand for goods and services, though, if it lasts for a long time. This is because customers may put off purchases in expectation of cheaper costs. A downturn in economic activity may follow, which would be bad for the economy.

Given data ,

Deflation is a decrease in the general price level of goods and services in an economy over a period of time. A decrease in the Consumer Price Index (CPI) is a measure of deflation.

In the first 9-year period, the CPI decreased by 45%, which indicates a significant deflationary period. In the next 9-year period, the CPI decreased by only 5%, which still indicates a deflationary period, but not as severe as the previous one.

Hence , the process is deflation in the second year

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66 because you have to solve the problem next time

Answer:

b 25x6 = 150

25 decreases every month so

150 decreses every 6 month

800-150

650 are the bees remaining after 6 month

Answer:

Moving upwards with an acceleration.

Step-by-step explanation:

weight of the person  = 195 pounds

Apparent weight = 205 pounds

As the weight increases so the scale is moving upwards with some acceleration.

The scale is in elevator which is moving upwards.

Answer:

D, 4√7

Step-by-step explanation:

Answer:

Step-by-step explanation:

c = 16

a = 12

b = ?

a^2 + b^2 = c^2

12^2 + b^2 = 16^2

144 + b^2 = 256

b^2 = 256 - 144

b^2 = 112

b^2 = 16 * 7

sqrt(b^2) = sqrt(16)*sqrt(7)

b = 4 * sqrt(7)

Answer:

Area = 72.62 m²

Step-by-step explanation:

Area of a triangle with the given three sides is given by,

Area = [tex]\sqrt{s(s-a)(s-b)(s-c)}[/tex]

Here, s = [tex]\frac{a+b+c}{2}[/tex]

And a, b, c are the sides of the triangle.

From the question,

a = 20 m, b = 10 m and c = 15 m

s = [tex]\frac{20+10+15}{2}[/tex]

s = 22.5

Substitute these values in the formula,

Area = [tex]\sqrt{22.5(22.5-20)(22.5-10)(22.5-15)}[/tex]

        = [tex]\sqrt{22.5(2.5)(12.5)(7.5)}[/tex]

        = [tex]\sqrt{5273.4375}[/tex]

        = 72.62 m²

Answer:

Percentile rank:

12  =  7th

28 = 21st

35  = 36th

42  = 50th

47  = 64th

49   = 79th

50 =  93rd

- Vth number i.e. 47 is the value that corresponds to the 60th percentile.

Step-by-step explanation:

As we know,

Percentile rank = [(Number of values below x) + 0.5]/total number of values * 100

For 12,

Percentile rank = [0 + 0.5]/7 * 100

= 7th

For 28,

Percentile rank = [1 + 0.5]/7 * 100

= 21st

For 35,

Percentile rank = [2 + 0.5]/7 * 100

= 36th

For 42,

Percentile rank = [3 + 0.5]/7 * 100

= 50th

For 47,

Percentile rank = [4 + 0.5]/7 * 100

= 64th

For 49,

Percentile rank = [5 + 0.5]/7 * 100

= 79th

For 50,

Percentile rank = [6 + 0.5]/7 * 100

= 93rd

Now,

n = 7

60th percentile = 60% of n

So,

60% of n = 60/100 * 7

= 0.6 * 7

= 4.2

After rounding it off,

5th value is the 60th percentile i.e. 47.

Answer:

46.38

Step-by-step explanation:

all the answer are not same but buy calculating its the right answer

Answer:

20%

Step-by-step explanation:

The total number of students is: 4 + 6 + 2 + 2 + 3 + 4 + 6 + 3 = 30 (students)

The probability is: 6/30 = 1/5 = 0.2 = 20%

The probability that the student is a male given that he's a sophomore is approximately 60%.

It is the chance of an event to occur from a total number of outcomes.

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

Example:

The probability of getting a head in tossing a coin.

P(H) = 1/2

We have,

The probability that the student is a male given that it's a sophomore can be calculated using the formula:

P(male | sophomore) = P(male and sophomore) / P(sophomore)

The number of male sophomores is 6, and the total number of sophomores is 6+4=10.

So, the probability of selecting a sophomore is:

P(sophomore)

= (number of sophomores) / (total number of students)

= 10 / 23

The number of male sophomores is 6.

So,

The probability of selecting a male sophomore is:

P(male and sophomore) = 6 / 23

Therefore,

The probability that the student is a male given that it's a sophomore is:

P(male | sophomore)

= (6 / 23) / (10 / 23)

= 6 / 10

= 3 / 5

Rounding to the nearest whole percent, we get:

P(male | sophomore) ≈ 60%

Thus,

The probability that the student is a male given that he's a sophomore is approximately 60%.

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Answer:

Step-by-step explanation:

Part A

The x-intercept are the values of the variable "x" for which the value of the function, f(x) is zero (f(x) = 0)

The given parameters are;

The values of the function, f(x) = The company's profit

The values of the independent variable, "x" = The price of erasers

Therefore, at the x-intercept, where the values of the variable "x" are 0 and 8, the profit of the company, (f(x)) is 0 (the company does not make any profit)

2) The maximum value, which is the highest point of the graph with coordinate (4, 270), gives the company's maximum profit, f(x) = $270, and the price of the eraser, x-value, at which the company makes maximum profit which is at the price of an eraser, x = $4

3) The intervals where the function is increasing is 0 ≤ x ≤ 4

At the interval where the function is increasing, the sale price is increasing and the profits are increasing

The intervals where the function is decreasing is 4 ≤ x ≤ 8

At the interval where the function is decreasing, the sale price is increasing and the profits are decreasing

Part B

The appropriate average rate of change of the graph from x = 1 to x = 4 where f(x) = 120 and 270 respectively is given as follows

Rate of change of the graph from x = 1 to x = 4 is (270 -120)/(4 - 1) = 50

The average rate of change of the graph represents that the as the price of the eraser increases by $1.00 the profits increases by $50.00

THIS WAS NOT MY OWN ANSWER, PLEASE LET oeerivona TAKE THE POINTS!!

Answer: D

Step-by-step explanation:

When a coordinate is reflected over the y-axis, it changes from (x, y) to (-x, y)

The three coordinates of ΔCDE are

After the y-axis reflection, they'll become:

I hope this is correct :\

9514 1404 393

Answer:

  x = 3

Step-by-step explanation:

The two right triangles share angle A, so the similarity statement can be written ...

  ΔABC ~ ΔADE

Corresponding sides are proportional, so we have ...

  BC/DE = AB/AD

  x/12 = 3/(3+9)

  x = 3 . . . . . . . . . . multiply by 12

Answer:

x=3

this is correct!!!

Answer:

✓ x gal of 25% 20-x gal of 5% pure alcohol is x(.25)+(20-x)(.05)=20*.16=3.2 so .25x+1-.05x=3.2 gallons of 25% .20x=2.2 gallons of 5% x=11 gallons of 25%.

Step-by-step explanation:

Hope this helps~ ;D

Answer:

The point-slope form is y - 2 = 1/2 (x - 3)

Step-by-step explanation:

The point-slope form is y - y1 = m (slope) (x - x1). All I did was plug the numbers in the correct locations to get my answer.

Answer:

Exact heights of the next 100 babies born in a region.

Step-by-step explanation:

A discrete random variable involves two key factors ; discrete and randomness ; Hence, a discrete random variable should have a finite or countable Number of outputs or values. It should also stem from a random procedure. Here, the height of the next hundred babies is a random procedure as the next 100 babies in the region are unknown until Given birth too and as such all pregnant women have the chance of having their babies among. Since, we are dealing with exact height values which are countable (100), then we this is a discrete random variable.

Answer:

f (n + 1) = -2 f(n)

Step-by-step explanation: