"

Suppose X is normally distributed with a mean of u = 12 and a standard deviation of g = 1.4. Find the z-score corresponding to x = 15.5. Show your work.
"

Answer:

x - z = -36

Step-by-step explanation:

Given:  

 x + y                                          y + z

---------- = 32               and         ---------- = 50

     2                                                2

These lead to x + y = 64 and y + z = 100

Subtracting the second equation from the first yields:

 x + y = 64

-(      y + z = 100)

------------------------

   x       - z = -36

Answer:

Step-by-step explanation:

Factor the sum of cubes

a³ + b³ = (a+b)(a² - ab +b²)

= 2a² - 2ab + 2b²

a³ + b³ + 6ab = 2a² + 4ab + 2b²

= 2(a² + 2ab +b²)

= 2(a+b)²

= 8

Answer:

x<_ 4

Step-by-step explanation:

first you distribute 5 to equal 5-35x+5 then you would carry the non variables to one side to be -35x>_-140 and the you would flip the sides because te variable is negative so it would be -35x<_ -140 the divid to get x<_4

c=number of crossings; Q=quarterly pass; S=semi-annual pass; P=pay as you go

P=$2.50c

Q=$12+$0.50c

S=$40

Compare single pay and quarterly ticket:

$2.50c=$12+$0.50c Subtract $0.50c from each side

$2.00c=$12 Divide each side by $2.

c=6 6 crossings is the break even for single pay and quarterly ticket: more crossings favor the ticket.

Compare quarterly and semi-annual tickets:

3 month pro-rated cost of semi annual ticket=$20

$20=$12+$0.50c Subtract 12 from each side

$8=$0.50c Divide each side by $0.50

16=c The break=even point between quarterly and semi annual tickets is 16 crossings per 3 months. More than this favors the semi annual ticket.

ANSWER: The three month pass is the best deal if you cross between 6 and 16 times during the three month period.

I hope this help you

Charlie

Here, we want to check if polynomials is closed under subtraction or not

To check this, we proceed either ways, if the answer is same, then it is closed. If otherwise, then it is not

We have;

As we can see, both results are not equal

If subtraction was closed under polynomials, then the results of both should have been equal. This means Charlie is correct.

Answer:

To regroup means to rearrange groups in place value to carry out an operation.

An inverse variation is the one in which the product of x and y is a constant:

We can find the value of this constant by replace x and y for the given values:

Now, replace k in the initial equation and then solve for y:

It means that the relationship is:

The graph of this relationship is:

To find the Total Cost Function C(x) for a product, we need to integrate the given marginal cost function MC(x). Given that MC(x) = 4x + 20 and the cost of producing 2 units is $78, we can determine the Total Cost Function.

The Total Cost Function C(x) represents the cumulative cost of producing x units. To find C(x), we need to integrate the marginal cost function MC(x) with respect to x.

Integrating MC(x), we get:

C(x) = ∫(MC(x))dx = ∫(4x + 20)dx.

Integrating each term separately, we obtain:

C(x) = 2x² + 20x + C,

where C is the constant of integration.

To find the value of C, we use the given information that the cost of producing 2 units is $78. Substituting x = 2 and C(x) = 78 into the equation, we have:

78 = 2(2)² + 20(2) + C,

78 = 8 + 40 + C,

78 = 48 + C,

C = 78 - 48,

C = 30.

Therefore, the Total Cost Function for the product is:

C(x) = 2x² + 20x + 30.

Hence, the correct answer is option a. C(x) = 2x² + 20x + 30.

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The probability of success, p, is the same for each trial. Each outcome is either a success (P) or a failure (Q). The correct option is A.

Independence is a fundamental notion in probability theory, as in statistics and the theory of stochastic processes.

You should perform x trials until you observe a success.

We have given that,

There are exactly two possible outcomes success and failure.

We have to determine the following is NOT a common characteristic of a binomial distribution.

By process of elimination:-

A binomial experiment is a statistical experiment that must meet certain requirements

All trials are independent.

There are a fixed number of n trials.

The probability of success, p, is the same for each trial.

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Answer:

a=6

b=-2

Step-by-step explanation:

You can use the hint provided on the mathswatch question page, I've attached it below

step 1

h(4) = ax+b = (ax4)+b = 4a+b

it is given in the question that h(4)=22, therefore 4a+b=22

step 2

work out the equation for inverse g

g^-1(x) = \(\frac{x-2}{3}\)

step 3

input 14 into the equation in place of x to find g^-1(x)

\(\frac{x-2}{3} =\frac{14-2}{3} =\frac{12}{3} =4\)

so, g(x)^-1=4

step 4

find h(1):

h(1) = (ax1)+b = a+b

so, h(1)=a+b

step 5

a+b=4 (as it is given in the question that g^-1(14) is equal to h(1))

step 6

Now you have two simultaneous equations:

4a+b=22

a+b=4

then, solve for a:

4a+b=22

- a+b=4  

3a=18

a=6

then, input answer for a into either equation (I've gone with the a+b=4 equation):

6+b=4

-6   - 6

b=-2

(p.s i know this is very late but hope it helps someone)

Answer: 3

Step-by-step explanation:

7 x 3 = 21

Answer:

40

Step-by-step explanation:

i guessed for you, and i got it right.

The correct statement about the function h(x) = -2  square root of x is given as follows:

The function is decreasing on the interval (0, ∞).

The parent function in this problem is given as follows:

f(x) = square root of x.

The domain of this function is for non-negative values, that is, x ≥ 0, and the function is increasing over it's entire interval.

The transformed function is given as follows:

h(x) = -2 square root of x

The product by the negative number means that the function was reflected over the x-axis, meaning that when it was increasing, now it is decreasing.

The domain of the function remains the same, hence the first statement is the correct statement.

The statements are given as follows:

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The predicted sales for week 6 is 740

In the case of linear regression using excel formula, we can find the intercept and the slope value for the regression model.

The equation of linear regression is similar to the slope formula what we have learned before in earlier classes such as linear equations in two variables.

Forecast\($=\mathrm{A}+\mathrm{B}(\mathrm{x})$\)

Where A is the intercept of the data, B is the slope, and X is the period.

Intercept \(=\) INTERCEPT (Range Y, Range X)

The above data generates the equation.

Now the data corresponds to an intercept value of 698 and a slope of 8.

Therefore, for period \($6, x=6$\)

The equation \($=698+(8 * 6)=746$\)

The intermediate calculations are in the table below:

PERIODUNITSFORECAST

____________________

1            700      706

2           724       714

3           720       722

4           728       730

5                         738

6                         740

Therefore, the predicted sales for week 6 is 740.

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Given

The slope of the line is 3.

And, the coodinates of x and y on the graph is (-1,1).

To find the equation of the line using slope point form.

Explanation:

The equation of the line using slope point form is given as,

Then, for m=3 and point (-1,1).

We get,

Hence, the equation of the line is y=3x+4.

Jean would need to pay $10088.55 as property tax on her new home which cost $238500

An equation is an expression that shows the relationship between two or more numbers and variables.

Let x represent the value of Jeans property tax.

Jean's new home are 4. 23% of the value of the home. For a home of $238500:

x = 4.23% of $238500 = 0.0423 * $238500 = $10088.55

Jean would need to pay $10088.55 as property tax on her new home which cost $238500

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Answer:

Solve the equation for  x  by finding  a ,  b , and  c

of the quadratic then applying the quadratic formula.

x = − 2  Double roots

Answer:

12.5 if all the numbers are one set. 15.3 for first row and 10 for last row if they are separate

Step-by-step explanation:

mean is found by adding all the data from the set and then dividing by how many data's there are. Mean can also be called the average of a set of data.

Answer:

are you okay?

Step-by-step explanation:

Answer:

$46.06

Step-by-step explanation:

Divide $49 by 5

9.8

So it costs $9.80 for 1 pound of salmon

Multiply $9.80 by 4.7

$46.06

Hope this helped :)

The area of the kite is \(66 \ cm^2\).

To find the area of a kite, you can use the formula: Area = \(\frac{(diagonal \ 1 \times diagonal \ 2)}{2}\)

In this case, the measurements given are \(6\) cm, \(1\) cm, and \(11\) cm. However, it is unclear which measurements correspond to the diagonals of the kite.

If we assume that the 6 cm and 11 cm measurements are the diagonals, we can calculate the area as follows:

Area = \(\frac{6 \times 11 }{2}\)

= \(66\) cm²

If the \(1\) cm measurement is one of the diagonals, and the other diagonal is unknown, it is not possible to calculate the area accurately without the measurement of the other diagonal. Without knowledge of the lengths of both diagonals of the kite, it is not possible to determine the exact area as it depends on the specific dimensions.

Therefore, the area of the kite is \(66 \ cm^2\).

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Answer:

\(D. \\x>\frac{3}{2}\)

Step-by-step explanation:

12(1/2x - 1/3) > 8 - 2x

6x - 4 > 8 - 2x

6x + 2x - 4 > 8 - 2x + 2x

8x - 4 > 8

8x - 4 + 4 > 8 + 4

8x > 12

8x ÷ 8 > 12 ÷ 8

x  > 1.5

Answer:

mop=11x-38

Lmp=3x+41

we kow that,

Answer:  B. H(t) = -6.9(t - 2.3)² + 112

Step-by-step explanation:

The vertex form of a quadratic equation is: y = a(x - h)² + k

where (h, k) is the vertex   ⇒    k is the maximum height

the distance traveled is when y = 0     ⇒    \(x=\sqrt{\dfrac{-k}{a}}+h\)

Given: H(t) = -7.1(t - 2.3)² + 98

maximum height (k) = 98 feet

distance traveled (x) = \(\sqrt{\dfrac{-98}{-7.1}}+2.3\)    = 6.02 seconds

A) H(t) = -7.5(t - 2.2)² + 112

maximum height (k) = 112 feet

distance traveled (x) = \(\sqrt{\dfrac{-112}{-7.5}}+2.2\)    = 6.06 seconds

B) H(t) = -6.9(t - 2.3)² + 112

maximum height (k) = 112 feet

distance traveled (x) = \(\sqrt{\dfrac{-112}{-6.9}}+2.3\)    = 6.33 seconds

C) H(t) = -6.9(t - 2.4)² + 95

maximum height (k) = 95 feet

This has a lower height than the given equation.

D) H(t) = -7.5(t - 2.3)² + 95

maximum height (k) = 95 feet

This has a lower height than the given equation.

Both options A and B travel higher and stay in the air longer than last year's winner, however option B stays in the air longer than option A.

The answers are 1.67 glucose molecules, 36 glucose molecules, 15 glucose molecules and 8400 times.

When two ratios are equivalent, they are in proportion. It is an equation or statement used to depict that two ratios or fractions are equal.

Given are some questions regarding production of glucose molecules during aerobic metabolism.

1) 1 glucose molecules produces 30 ATP molecules, how many for 50 ATP molecules :-

Using proportionality, let there be x glucose molecules required to produce 50 ATP molecules,

1 / 30 = x / 50

x = 5/3

x = 1.67

Therefore, there are 1.67 glucose molecules required to produce 50 ATP molecules.

2) 1 glucose molecules produces 6 ATP molecules, how many for 216 ATP molecules :-

Using proportionality, let there be x glucose molecules required to produce 216 ATP molecules,

1 / 6 = x / 216

x = 36

Therefore, there are 36 glucose molecules required to produce 216 ATP molecules.

3) 1 glucose molecules produces 30 ATP molecules, how many for 450 ATP molecules :-

Using proportionality, let there be x glucose molecules required to produce 450 ATP molecules,

1 / 30 = x / 450

x = 15

Therefore, there are 15 glucose molecules required to produce 450 ATP molecules.

4) Since, in one day it's 1200 times an ATP molecule is reused in a human body,

We need to find for a week, there are 7 days in a week,

Therefore, an ATP molecule is reused in a human body for a week = 1200 x 7 = 8400 times.

Hence, the answers are 1.67 glucose molecules, 36 glucose molecules, 15 glucose molecules and 8400 times.

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For a real number x, by using mathematical induction it is shown that a\((1 + x)^{2n}\) > 1 + 2nx for every positive integer n.

To prove the inequality a\((1 + x)^{2n}\) > 1 + 2nx  for every positive integer n, we will use mathematical induction.

The inequality holds true for n = 1, and we will assume it is true for some positive integer k.

We will then show that it holds for k + 1, which will complete the proof.

For n = 1, the inequality becomes a\((1 + x)^2\) > 1 + 2x.

This can be expanded as a(1 + 2x + \(x^2\)) > 1 + 2x, which simplifies to a + 2ax + a\(x^2\) > 1 + 2x.

Now, let's assume the inequality holds true for some positive integer k, i.e., a\((1 + x)^{2k}\) > 1 + 2kx.

We need to prove that it holds for k + 1, i.e., a\((1 + x)^{2(k+1)}\) > 1 + 2(k+1)x.

Using the assumption, we have a\((1 + x)^{2k}\) > 1 + 2kx.

Multiplying both sides by \((1 + x)^2\), we get a\((1 + x)^{2k+2}\) > (1 + 2kx)\((1 + x)^2\).

Expanding the right side, we have a\((1 + x)^{2k+2}\) > 1 + 2kx + 2x + 2k\(x^2\) + 2\(x^2\).

Simplifying further, we get a\((1 + x)^{2k+2}\) > 1 + 2(k+1)x + 2k\(x^2\) + 2\(x^2\).

Since k and x are positive, 2k\(x^2\) and 2\(x^2\) are positive as well.

Therefore, we can write a\((1 + x)^{2k+2}\) > 1 + 2(k+1)x + 2k\(x^2\) + 2\(x^2\) > 1 + 2(k+1)x.

This proves that if the inequality holds for some positive integer k, it also holds for k + 1.

Since it holds for n = 1, it holds for all positive integers n by mathematical induction.

Therefore, we have shown that a\((1 + x)^{2n}\) > 1 + 2nx  for every positive integer n.

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Answer:

31

Step-by-step explanation:

Answer:

what are the ratios hope this helps

Step-by-step explanation:

option b ie. 98 degree

if you do angle 2 +10x+8=180

from 10x +8 and 12x -10 we can get the value of X