Full-time Ph.D. students receive an average of $12,837 per year. If the average salaries are normally distributed with a standard deviation of $1500, find these probabilities. a. The student makes more than $15,000. b. The student makes between $13,000 and $14,000.

Answer:

A proportion equation is something like:

[tex]\frac{A}{B} = \frac{x}{C}[/tex]

Where A, B, and C are known numbers, and we want to find the value of x.

Now we want two cases where in one of the numerators we have a mixed number, where a mixed number is something like:

1 and 1/3

which actually should be written as:

1 + 1/3

1) a random problem can be:

[tex]\frac{1 + 1/3}{4} = \frac{x}{5}[/tex]

We can see that the numerator on the left is a mixed number.

First, let's rewrite the numerator then:

1 + 1/3

we need to have the same denominator in both numbers, so we can multiply and divide by 3 the number 1:

(3/3)*1 + 1/3

3/3 + 1/3 = 4/3

now we can rewrite our equation as:

[tex]\frac{4/3}{4} = \frac{x}{5}[/tex]

now we can solve this:

[tex]\frac{4/3}{4} = \frac{4}{3*4} = \frac{x}{5} \\\\\frac{1}{3} = \frac{x}{5}[/tex]

now we can multiply both sides by 5 to get:

[tex]\frac{5}{3} = x[/tex]

Now let's look at another example, this time we will have the variable x in the denominator:

[tex]\frac{7}{12} = \frac{3 + 4/7}{x}[/tex]

We can see that we have a mixed number in one numerator.

Let's rewrite that number as a fraction:

3 + 4/7

let's multiply and divide the 3 by 7.

(7/7)*3 + 4/7

21/7 + 4/7

25/7

Then we can rewrite our equation as

[tex]\frac{7}{12} = \frac{25/7}{x}[/tex]

Now we can multiply both sides by x to get:

[tex]\frac{7}{12}*x = \frac{25}{7}[/tex]

Now we need to multiply both sides by (12/7) to get:

[tex]x = \frac{25}{7}*\frac{12}{7} = 300/49[/tex]

Answer:

He must survey 123 adults.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].

The margin of error is:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

Assume that a recent survey suggests that about 87​% of adults have heard of the brand.

This means that [tex]\pi = 0.87[/tex]

90% confidence level

So [tex]\alpha = 0.1[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.1}{2} = 0.95[/tex], so [tex]Z = 1.645[/tex].

How many adults must he survey in order to be 90​% confident that his estimate is within five percentage points of the true population​ percentage?

This is n for which M = 0.05. So

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

[tex]0.05 = 1.645\sqrt{\frac{0.87*0.13}{n}}[/tex]

[tex]0.05\sqrt{n} = 1.645\sqrt{0.87*0.13}[/tex]

[tex]\sqrt{n} = \frac{1.645\sqrt{0.87*0.13}}{0.05}[/tex]

[tex](\sqrt{n})^2 = (\frac{1.645\sqrt{0.87*0.13}}{0.05})^2[/tex]

[tex]n = 122.4[/tex]

Rounding up:

He must survey 123 adults.

Answer:

-1/4 is the least, 0.75 is second, and 1 1/2 is the greatest

Step-by-step explanation:

-1/4 is the least already because it is negative.

1 1/2 is really 1.5 so now compare 0.75 and 1.5.

1.5 is bigger therefore the order  is :

-1/4, 0.75, 1 1/2

Answer:

1/4

Step-by-step explanation:

that is the answer

I found the constant which was -3

a = 1/4

b=-1

Answer:

the value of a in the function's equation is 1/4

Step-by-step explanation:

Plato answer

Step-by-step explanation:

Given:

[tex]\vec{\textbf{F}}(x, y, z) = ye^z\hat{\textbf{i}} + xe^z\hat{\textbf{j}} + xye^z\hat{\textbf{k}}[/tex]

A vector field is conservative if

[tex]\vec{\nabla}\textbf{×}\vec{\text{F}} = 0[/tex]

Looking at the components,

[tex]\left(\vec{\nabla}\textbf{×}\vec{\text{F}}\right)_x = \left(\dfrac{\partial F_z}{\partial y} - \dfrac{\partial F_y}{\partial z}\right)_x[/tex]

[tex]= xe^z - ye^z \neq 0[/tex]

Since the x- component is not equal to zero, then the field is not conservative so there is no scalar potential [tex]\phi[/tex].

Answer:

t is less than or equal to $52, or t <= $52

Step-by-step explanation:

If you can't have more than $52, then use less than symbol (<). The sentence doesn't state that a ticket shouldn't cost $52, so it's safe to assume that you can have exactly $52.

Answer:

24

Explanation:

(23+32)-(3×4)-(52-5)+(7×4)

(55)-(12)-(47)+(28)

Answer:

[tex]a = 4, -4[/tex]

Step-by-step explanation:

Step 1:  Plug in -4 for c

[tex]-a^{2} + c^{2}[/tex]

[tex]-a^{2} + (-4)^{2}[/tex]

[tex]-a^{2} + 16[/tex]

Step 2:  Solve for a

[tex]-a^{2}+16-16=0-16[/tex]

[tex]-a^{2}/-1 = -16/-1[/tex]

[tex]a^{2} = 16[/tex]

[tex]\sqrt{a^{2}} = \sqrt{16}[/tex]

[tex]a = 4, -4[/tex]

Answer:  [tex]a = 4, -4[/tex]

Answer:

Y =-4X +12

Y =-0.625X  -0.75

Step-by-step explanation:

(3,0) and (2,4)....

x1 y1  x2 y2

3 0  2 4

(Y2-Y1) (4)-(0)=   4  ΔY 4

(X2-X1) (2)-(3)=    -1  ΔX -1

slope= -4          

B= 12          

Y =-4X +12    

~~~~~~~~~~~~~~~~~

(-6,3) and (2,-2)​

x1 y1  x2 y2

-6 3  2 -2

(Y2-Y1) (-2)-(3)=   -5  ΔY -5

(X2-X1) (2)-(-6)=    8  ΔX 8

slope= -  5/8    

B= -  3/4    

Y =-0.625X  -0.75    

Answer:

2.334453751

Step-by-step explanation:

Press log on your Casio calculator (if you have one) and plug in 216, then close the parentheses!

Answer:

E &F

Step-by-step explanation:

The rules of a 30-60-90 Triangle is E, and F is just a different value of numbers (but the same ratio).

Answer:

[tex]9[/tex]

Step-by-step explanation:

Step 1:  Find the square root of 81

[tex]\sqrt{81}[/tex]

[tex]\sqrt{9*9}[/tex]

[tex]\sqrt{9^{2}}[/tex]

[tex]9[/tex]

Answer:  [tex]9[/tex]

Answer:

the square root of 81 is 9

Answer: B. Right Scalene

Step-by-step explanation: Right because one of the degrees is 90 and scalene because no of the sides of the triangle are the same length.

Answer:

b

Step-by-step explanation:

Answer:

a) 0.4219 = 42.19% probability that one out of the next four cars needs oil.

b) 0.3115 = 31.15% probability that two out of the next eight cars needs oil.

c) 0.2581 = 25.81% probability that three out of the next 12 cars need oil.

Step-by-step explanation:

For each car, there are only two possible outcomes. Either they need oil, or they do not need it. The probability of a car needing oil is independent of any other car, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

One out of four cars needs to have oil added.

This means that [tex]p = \frac{1}{4} = 0.25[/tex]

a. One out of the next four cars needs oil.

This is P(X = 1) when n = 4. So

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 1) = C_{4,1}.(0.25)^{1}.(0.75)^{3} = 0.4219[/tex]

0.4219 = 42.19% probability that one out of the next four cars needs oil.

b. Two out of the next eight cars needs oil.

This is P(X = 2) when n = 8. So

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 2) = C_{8,2}.(0.25)^{2}.(0.75)^{6} = 0.3115[/tex]

0.3115 = 31.15% probability that two out of the next eight cars needs oil.

c.Three out of the next 12 cars need oil.

This is P(X = 3) when n = 12. So

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 3) = C_{12,3}.(0.25)^{3}.(0.75)^{9} = 0.2581[/tex]

0.2581 = 25.81% probability that three out of the next 12 cars need oil.

Answer:

[tex]G(t) = 120e^{-0.0257t}[/tex]

Step-by-step explanation:

Amount of substance:

The amount of the substance after t minutes is given by:

[tex]G(t) = G(0)e^{-kt}[/tex]

In which G(0) is the initial amount and k is the decay rate.

At the beginning of an experiment, a scientist has 120 grams of radioactive goo.

This means that [tex]G(0) = 120[/tex], so:

[tex]G(t) = G(0)e^{-kt}[/tex]

[tex]G(t) = 120e^{-kt}[/tex]

After 135 minutes, her sample has decayed to 3.75 grams.

This means that [tex]G(135) = 3.75[/tex].

We use this to find k. So

[tex]G(t) = 120e^{-kt}[/tex]

[tex]3.75 = 120e^{-135k}[/tex]

[tex]e^{-135k} = \frac{3.75}{120}[/tex]

[tex]\ln{e^{-135k}} = \ln{\frac{3.75}{120}}[/tex]

[tex]-135k = \ln{\frac{3.75}{120}}[/tex]

[tex]k = -\frac{\ln{\frac{3.75}{120}}}{135}[/tex]

[tex]k = 0.0257[/tex]

So

[tex]G(t) = 120e^{-0.0257t}[/tex]

Answer:

D is your answer

Step-by-step explanation:

Answer:

Here the slope formula m = ( y 2 − y 1 )/( x 2 -x 1 ) = Δy/Δx

Step-by-step explanation:

9514 1404 393

Answer:

2. On a coordinate plane, a hyperbola is shown. One curve opens up and to the right in quadrants 1 and 4, and the other curve opens up and to the left in quadrants 2 and 3

Step-by-step explanation:

Technically, the curve is not a hyperbola. A hyperbola is of the form 1/x; this one is of the form 1/x².

The function can be simplified to ...

  f(x) = 5/x² -5

which is a "hyperbola" with a vertical asymptote at x=0 and a vertical translation of -5 units to bring parts of it into the 3rd and 4th quadrants.

Answer:

44

Step-by-step explanation:

Given that Avi used 11 toothpicks to form a row of 5 attached triangles.

Total number of toothpicks used = 89

Let the total number of triangles formed be represented by x, so that:

11 toothpicks = 5 triangles

It would be observed that only the first triangle starting the pattern has 3 toothpicks. So that;

the average number of toothpicks for 1 triangle = [tex]\frac{11}{5}[/tex]

                                  = 2.2

The number of toothpicks per triangle = 2.0

Thus,

x = [tex]\frac{89}{2.0}[/tex]

  = 44.5

x = 44

The total number of triangles formed is 44.

Answer:

5000 ;

11125

Step-by-step explanation:

Given :

Total principal = 16125

Rates = 8.5% and 4%

Period, t = 2 years

Total interest = 1740

Let :

Principal amount invested at 8.5% = x

Principal amount invested at 4% = 16125 - x

Interest formula :

Interest = principal * rate * time

Hence, mathematically ;

(x * 8.5% * 2) + [(16125 - x) * 4% * 2] = 1740

(0.17x + 1290 - 0.08x ) = 1740

0.09x + 1290 = 1740

0.09x = 1740 - 1290

0.09x = 450

x = 450 / 0.09

x = 5000

Amount invested at 4% :

16125 - 5000 = 11125

Answer:

By the Central Limit Theorem, the distribution of the sample means is approximately normal with mean 41 and standard deviation 2.92, in thousands of dollars.

Step-by-step explanation:

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.

Mean of 41, standard deviation of 28:

This means that [tex]\mu = 41, \sigma = 28[/tex]

Sample of 92:

This means that [tex]n = 92, s = \frac{28}{\sqrt{92}} = 2.92[/tex]

Distribution of the sample means:

By the Central Limit Theorem, the distribution of the sample means is approximately normal with mean 41 and standard deviation 2.92, in thousands of dollars.

Step-by-step explanation:

(-2,-1,0,3,4) are the domain

(x,y)=(domain,range)

simply x components are the domain whereas y components are the range

Answer:

D:20

sqrt(3) is less than 2 thus 10*sqrt(3) is less than 20

Step-by-step explanation:

Answer:

she can make 12 sandwiches

Step-by-step explanation:

3/.25 is the solution

Answer:

An expression is considered simplified only if there is no radical sign in the denominator. If we do have a radical sign, we have to rationalize the denominator . This is achieved by multiplying both the numerator and denominator by the radical in the denominator.

Answer:

Pie( r ^2)

Step-by-step explanation:

Here value of r is in inches

Answer

The Answer is A C D

Step-by-step explanation:

Answer:

A.

Step-by-step explanation:

The Elimination Method is the method for solving a pair of linear equations which reduces one equation to one that has only a single variable.

If the coefficients of one variable are opposites, you add the equations to eliminate a variable, and then solve.

If the coefficients are not opposites, then we multiply one or both equations by a number to create opposite coefficients, and then add the equations to eliminate a variable and solve.

When multiplying the equation by a coefficient, we multiply both sides of the equation (multiplying both sides of the equation by some nonzero number does not change the solution).

So, option B is not allowed (it is not allowed to multiply only one part of the equation)