Air pressure may be represented as a function of height above the surface of the Earth as shown below.In this function, P0 is air pressure at sea level, and h is measured in meters. Which of the following equations will find the height at which air pressure is 65% of the air pressure at sea level?A.B.C.D.

The transformation of f(x) to g(x) is :

From the question, we have the following parameters that can be used in our computation:

The functions f(x) and g(x)

Where, we have

f(x) = x

g(x) = 1/9x - 2

The graph of the functions f(x) and g(x) are added as an attachment

And we have the transformations to be:

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The standard deviation is 0.07770.

The above table is given.

First, calculate the class mid-point. This is the average of a class interval.

The mid-point x is:

\(x_{1} =\frac{1}{2} (15.3+15.6) = \frac{1}{2} * 30.9 = 15.45\)   ( simplify the equation)

\(x_{2} =\frac{1}{2} (15.6+15.9) = \frac{1}{2} * 31.5 = 15.75\)

\(x_{3} =\frac{1}{2} (15.9+16.2) = \frac{1}{2} * 32.1 = 16.05\)

\(x_{4} =\frac{1}{2} (16.2+16.5) = \frac{1}{2} * 32.7 = 16.35\)

\(x_{5} =\frac{1}{2} (16.5+16.8) = \frac{1}{2} * 33.3 = 16.65\)

So, we know that :

x  15.45   15.75    16.05   16.35   16.65

f     14        25        84       18         9

Calculate the mean:

Mean = \(\frac{15.45 *14 + 15.75 * 25 + 16.05*84 + 16.35 *18 + 16.65 * 9}{14+25+84+18+9}\)

Mean   = \(\frac{2402.4}{150}\)    (by using division)

Mean    = 16.016

The standard deviation is:

σ \(=\frac{\sqrt{(15.45-16.016)^{2} + (15.75-16.016)^{2} + (16.05-16.016)^{2} + (16.35-16.016)^{2} + (16.65-16.016)^{2} } }{14 + 25+84+ 18+ 9}\)

σ  \(=\sqrt{0.00603853333}\)

σ = 0.07770

So, the standard deviation is 0.07770.

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The complete question is:

To study the output of a machine that fills boxes with cereal, a quality control engineer weighed 150 boxes of Brand X cereal. The frequency distribution in the following table summarizes his findings. Find the standard deviation of the weight of the boxes of cereal. (Round your answer to three decimal places.)

Incorrect: Your answer is incorrect.

oz

x = Weight

(ounces) Number of

boxes

15.3 ≤ x < 15.6 14

15.6 ≤ x < 15.9 25

15.9 ≤ x < 16.2 84

16.2 ≤ x < 16.5 18

16.5 ≤ x < 16.8 9

Answer:

24

Step-by-step explanation:

1: Divide 120 by 5 = 24

Answer: 24

Hope this helps.

The number of children are 104 and the number of adult are 130.

A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.

Given that, the admission fee at an amusement park is $1.75 for children and $7.20 for adults.

Let the number of children be c and the number of adults be a.

Now, c+a=234 ------(i)

1.75c+7.20a=1118 ------(ii)

Substitute c=234-a in equation (ii), we get

1.75(234-a)+7.20a=1118

409.5-1.75a+7.20a=1118

5.45a=1118-409.5

5.45a=708.5

a=708.5/5.45

a=130

Substitute a=130 in equation (i), we get c=104

Therefore, the number of children are 104 and the number of adult are 130.

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The probability that you win is 6%, and the two choices are dependent events option (B) is correct.

It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.

It is given that:

A standard deck of playing cards contains 52 total cards, 13 of which are "spades".

The probability of the first draw:

Probability = favorable outcomes/total outcomes

First draw: 1/4

For the second draw:

Second draw = 12/51

The probability that you win = (1/4)(12/51) = 3/51

In percent:

= (3/51)x100

= 5.88 = 6%

Thus, the probability that you win is 6%, and the two choices are dependent on events option (B) is correct.

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Answer:

??

Step-by-step explanation:

Answer:

did u forget to add an attachment

Answer:

The correct answer is x = -8.

Step-by-step explanation:

To solve this equation, we want to get the variable x alone on the left side of the equation.  To do this, we should first add 2 to both sides of the equation.

x/8 - 2 = -3

x/8 -2 + 2 = -3 + 2

x/8 = - 1

Next, we should multiply both sides of the equation by 8 to isolate the variable x.

x = -8

Therefore, the correct answer is x = -8.

If we want to check our answer, we can plug -8 back into the original equation.

-8/8 - 2 = -3

-1 -2 = -3

-3 = -3

Since the two sides match, we know that we got the correct answer.

Hope this helps!

The statement "the sum of a two-digit number is less than the value of the original two-digit number" can be rewritten as conditional statement. If the sum of two digits of a two-digit number is less than the value of the original two-digit number, the number is valid.

A conditional statement, "if p, then q," with p representing the hypothesis and q representing the conclusion. We can identify the hypothesis and conclusion by rewriting the statement "the sum of the digits of a two-digit number is less than the value of the original two-digit number" as an if-then conditional statement.

The hypothesis is the condition that must be satisfied in order to valid the conclusion. In this case, the hypothesis is "the sum of the digits of a two-digit number is less than the value of the original two-digit number".

By combining these, we can rewrite the statement as follows:

If the sum of a two-digit number's digits is less than the value of the original two-digit number, the number is valid.

The hypothesis (the sum of the digits of a two-digit number is less than the value of the original two-digit number) is a sufficient condition for the conclusion, according to this conditional statement (the number is valid). In other words, if the hypothesis is correct, we can be certain that the conclusion is correct as well.

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Answer:

7/5

Step-by-step explanation:

just divide

Answer:

The cookie recipe can be made 7 1/2 times.

Step-by-step explanation:

To solve this you need to change 11 1/4  and 1 1/2 into improper fractions so you can get 45/4 and 3/2. Now you have to flip 3/2 so its 2/3, and you can cross cancel so since the 3 in 2/3 can go into the 45 in 45/4 fifteen times, 45/4 becomes 15/4 and 2/3 becomes 2/1. You can multiply across now, so if you multiply 15 and 2, you get 30, and if you multiply 4 and 1 you get 4, so now you have 30/4. To change 30/4 into a mixed number, you have to divide 30 by 4. Since 4 can go into 30 seven times, your whole number is 7, and since 28 + 2 = 30, your numerator is 2, while the denominator is 4. Also, 2/4 can be simplified to 1/2, so your final result is 7 1/2.

I hope this helps you :D

Charlie 50 miles per hour

Violet 60 miles per hour

It is given that the distance between Memphis and New Orleans is 395 miles. This means, the total distance both covered = 395 miles

Charlie drove for 5.5 hours and Violet drove for 2 hours. Let the speed of Charlie be x miles per hour. Since, the speed of Violet was 10 miles per hour faster than Charlies, the speed of charlie was (x + 10) miles per hour

Since, distance = speed × time

Distance covered by Charlie = 5.5x

Distance covered by Violet = 2(x + 10)

Altogether they covered 395 miles,

So,

395 = Distance covered by Charlie + Distance covered by Violet

395 = 5.5x + 2(x + 10)

395 = 5.5x + 2x + 20

375 = 7.5x

x = 375/7.5

x = 50 mph

Since, x represents the speed of Charlie, the speed of charlie was 50 miles per hour and speed of Violet =

Speed of Charlie +10

50+10 =60

speed of Violet =60mph

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Answer:

D. 564.44 cm^3

Step-by-step explanation:

V = (1/3)(pi)r^2h

V = (1/3)(3.14159)(7 cm)^2(11 cm)

V = 564.44 cm^3

To solve the savings plan balance, we have to calculate the interest for 19 months. The formula for calculating interest for compound interest is given below:$$A = P \left(1 + \frac{r}{n} \right)^{nt}$$where A is the amount, P is the principal, r is the rate of interest, t is the time period and n is the number of times interest compounded in a year.

The given interest rate is 11% per annum, which will be converted into monthly rate and then used in the above formula. Therefore, the monthly rate is $r = \frac{11\%}{12} = 0.0091667$.

The monthly payment is $PMT = $250. We need to find out the amount after 19 months. Therefore, we will use the formula of annuity.

$$A = PMT \frac{(1+r)^t - 1}{r}$$where t is the number of months of the plan and PMT is the monthly payment. Putting all the values in the above equation, we get:

$$A = 250 \times \frac{(1 + 0.0091667)^{19} - 1}{0.0091667}$$$$\Rightarrow

A = 250 \times \frac{1.0091667^{19} - 1}{0.0091667}$$$$\Rightarrow

A =250 \times 14.398$$$$\Rightarrow A = 3599.99$$

Therefore, the savings plan balance after 19 months with an APR of 11% and monthly payments of $250 is $3599.99 (approx).

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Answer:

(-5, 4) The x value is -5, and the y value is 4.

Among the given answer choices, the correct option that represents this range is "0 100 200 none of the answer choices".

To determine the range of the number of RVs that need to be sold each month for the company to make a profit, we need to consider the profit function and find the values of x that result in a positive profit.

The profit function is given by P(x) = -50x + 20,000x - 1,500,000.

To make a profit, the value of P(x) must be greater than zero (P(x) > 0). We can set up the inequality:

-50x + 20,000x - 1,500,000 > 0.

Combining like terms, we have:

19,950x - 1,500,000 > 0.

Now, let's solve this inequality for x:

19,950x > 1,500,000.

Dividing both sides by 19,950, we get:

x > 1,500,000 / 19,950.

Simplifying the right side, we have:

x > 75.

The range of the number of RVs that need to be sold each month for the company to make a profit is x > 75.

Among the given answer choices, the correct option that represents this range is "0 100 200 none of the answer choices".

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One way to write this polar coordinate is to say (2.5, pi/2) meaning we move 2.5 units away from the origin toward the pi/2 direction

pi/2 radians = 90 degrees

An alternative is to write (-2.5, 3pi/2) which is where we aim at the 3pi/2 direction (270 degrees) and walk backward while still facing directly south, and we'll arrive at the same location.

The only graph that represents a function is: Graph D

A function is defined as a relationship or expression that involves one or more variables. It typically has a set of input and outputs.  Each input has only one output. The function is the description of how the inputs relate to the output.

A function is a relation which describes that there should be only one output for each input (or) we can say that a special kind of relation (a set of ordered pairs), which follows a rule i.e., every X-value should be associated with only one y-value is called a function.

From the graphs, we can see that:

Graph A has 2 outputs at x = -2

Graph B has 2 outputs at x = 0

Graph C has two outputs at x = -1

Graph D has a unique output for every input and as such it is a function

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Answer:

[2abc(bc+b-a)–abc(ac+c+b²+a²+c²)–ab(b²+ab²)+a²c²(c–a+1)]/[(a-b)(b-c)(b-a)(c-a)(c-b)]

From the slopes it is confirmed that PQ || RS OR|| SP and therefore it is a parallelogram .

A parallelogram is a quadrilateral in which the opposite sides are parallel.

The coordinates of a quadrilateral is given

To prove that it is a parallelogram

PQ || RS

OR|| SP

The slope of a straight line is given by

\(\rm m = \dfrac{y_2 -y_1}{x_2- x_1}\)

For PQ

m = (-1/6) = -1/6

For QR

m = -6/1 = -6

For RS

m = 1/(-6) = -1/6

For SP

m = -6

From the slopes it is confirmed that

PQ || RS

OR|| SP

and therefore it is a parallelogram

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That both a and b are equally likely, is also not true since the Probability of option b is higher than that of option a.

Option b is more likely to be true. This is because the given information states that the showerhead heights were designed to be 72 inches, which is well above the mean height of 69.5 inches. Therefore, it is reasonable to assume that the majority of the players' heights are below 72 inches. Since the heights of the athletes are normally distributed, the probability of selecting a player at random with a height above 72 inches is relatively low. On the other hand, option a suggests that the mean height of a sample of 20 players is more than 72 inches, which is less likely than option b. Option c, which suggests that both a and b are equally likely, is also not true since the probability of option b is higher than that of option a.

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Answer:

  3 ≤ x < ∞

Step-by-step explanation:

You want the domain of a square root function shifted right 3 units and up 1 unit. It goes through points (3, 1), (4, 2) and (7, 3).

The domain of a function is the set of values of the independent variable for which the function is defined. It is the horizontal extent of the graph.

The graph of the given square root function extends to the right from x=3.

The domain is 3 ≤ x < ∞. In interval notation, it is [3, ∞).

Answer:

the answer is the last one.

9514 1404 393

Answer:

  27

Step-by-step explanation:

The measure of an inscribed angle is half the measure of the arc it subtends.

  ∠P = (RT)/2

  ∠P = 54/2

  ∠P = 27

Answer:

2d+44

Step-by-step explanation:

Multiply all numbers without variables:

11x4=44

Add equations:

2d+44

Hence, the correct answer is 2d+44

Answer:

2d+44

Step-by-step explanation:

Multiply:

11x4=44

Final Equation:

2d+44

Answer:

43 is answer

Step-by-step explanation:

65+x+2+70=180

137+x=180

x=43

Answer:

13

Step-by-step explanation:

cos 13 x 2 = 26

13 is a factor that is more than 4 and less then 26

The factor of the number 26 that is between 4 and 26 is 13. Factors are the numbers that can divide into a number without leaving a remainder. In this case, the factors of 26 are 1, 2, 13, and 26.

In mathematics, a factor of a number is a number that divides into another number without leaving a remainder. In the case of the number 26, its factors include 1, 2, 13, and 26. The factor of 26 that is between 4 and 26 is 13.

To find this, you can go through the factors of 26 one by one. The factors are found by dividing 26 by all the numbers up to 26, and the numbers that give a remainder of 0 are the factors. In this case, 1, 2, 13, and 26 divide evenly into 26, and so are the factors of 26. Of these, only 13 lies between 4 and 26.

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numbers are 20 and 30 or 30 and 20.

A statement that represents the equality between two mathematical expressions. An equation can have one variable or two variables.

sum of two numbers = 50

sum of their reciprocal = 1/12

what is the 2 numbers.

let, one number is X and the other number is Y

as per the given condition, sum of X and Y is 50

X + Y =50 ...... equation 1

again, sum of the reciprocal of X and Y = 1/12

1/ X + 1/ Y = 1/12 ..... equation 2

 (X + Y)/ XY = 1 /12

(X + Y)12 = XY...  equation 3

from equation 1, we can write, Y = 50 - X

putting this value of Y in the equation 3

12X + 12(50 - X) = X(50 -X)

12X + 600 - 12X = 50X - X²

X² - 50X+600= 0

from the formula for quadratic equation, X = [50 ±√ (50² - 4×600)] / 2×1

                                                         X = (50±10) / 2

                                    X = 30, 20

          Y = 50 -30 = 20

      Y = 50- 20 = 30

hence, the 2 numbers are 20 and 30.

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Answer:

C. y=2x+4

Step-by-step explanation:

For every 2 moves on the X axis,4 is moved on the Y axis.