A random variable is defined as a process or variable with a numerical outcome. Which of the following are random variables?

i. The amount of rain, in inches, that will fall next Friday in Dallas, TX.
ii. The major of a randomly drawn student from Arizona State University.
iii. The number of books purchased next year by your local library.

a. i only
b. ii only
c. iii only
d. i and iii
e. ii and iii
f. i, ii, and iii

After 9 months each car will have the same number of miles on it.

What is a linear equation?

Each term in a linear equation has an exponent of 1, and when this algebraic equation is graphed, it always produces a straight line. It is called a "linear equation" for this reason.

Here,

Let miles per month be x.

then, by a linear equation, we get

4298 + x(426) = 6129 + x(223)

203x = 1831

x = 9 months

Hence, after 9 months each car will have the same number of miles on it.

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Answer:

Step-by-step explanation:

\(\frac{2}{5} : \frac{1}{15}\\\)

LCM of the denominator = LCM ( 5 , 15 ) = 15

∴ Now we have to multiply LCM by both the fractions , we get ,

\(\frac{2}{5}.15 : \frac{1}{15}.15\\ 6 : 1\)

The correct way to calculate the percent change between the original value of $750 and the new value of $1,000 is option C.

C. (1,000 - 750)/750 = 250/750 = 1/3 ≈ 0.3333 = 33.33%

Therefore, the correct answer is option C, which represents a percent change of approximately 33.33%.

Answer:

168hrs in division terms of every 1 year x 7 etc...

It will always be 24hrs nothing changes set of units to same units.

However because the equivalent to a same length of life as human is 1/7 we can do the reciprocal = 7 and do 24 x 7 = 168 hrs, but as many younger and healthy dogs eat and sleep the same as humans then equivalent would be not a good way to compare a dogs life.

Longer life breeds like Labrador or mixed breed dogs if walked at least 4 times a day and away from other dogs and all day young kids can live older than 20 and have actually be more compared to 4-5 years and so the comparison would be like 96 hrs or 120 hrs, but hours stay 24 a day for all animals as units don't change same units. Day represents a day and a year represents sun rise to sun fall to sun rise again x 365.

Answer:

 P [ Z >  24,1 ] =  72,24 %

Step-by-step explanation:

P [ Z > 24,1 ]  =  1  - P [ Z < 24,1 ]

P [ Z < 24,1 ] = ( Z - μ₀ ) / σ

P [ Z < 24,1 ] = ( 24,1 - 25,4) / 2,1

P [ Z < 24,1 ] = - 1,3/ 2,1

P [ Z <  24,1 ] = - 0,6190  ≈ - 0,62

We look in z-table and find for  z(score) -0,6190

P [ Z <  24,1 ] = 0,27763

Then

P [ Z >  24,1 ] = 1 - 0,27763

P [ Z >  24,1 ] = 0,72237    ⇒    or       P [ Z >  24,1 ] =  72,24 %

Answer:

2. f(x) is a one-to-one function.

Step-by-step explanation:

If a relation passes the vertical line test, it is a function.

If a relation passes the vertical line test and the horizontal line test, then it is a one-to-one function, and its inverse is also a function.

Answer: 2. f(x) is a one-to-one function.

Answer:

The probability is roughly 0.85%.

Step-by-step explanation:

This situation requires the combination of the probabilities in question.

The probability that Steph will make a throw is 90.3%, and from this we can conclude that the amount missed, or the probability of missing will be the remaining, or \(100\%-90.3\%=9.7\%\).

Let's combine the probabilities, remembering a percentage simply means a number over 100:

\(P=\frac{90.3}{100} *\frac{9.7}{100}*\frac{9.7}{100}=\frac{90.3*9.7*9.7}{100*100*100}\\\\P=\frac{8496.327}{1 000 000}=0.008496327\\\\P(\%)=0.008496327*100=0.8496327\%\)

The total value of the prize is $936,000.

The state will need to invest $591,498.96 now at a 5% interest rate to cover the weekly prize payments for 20 years.

The total value of the prize is calculated by multiplying the annual payment by the number of years and is equal to:

=  $900/week x 52 weeks/year x 20 years

= $936,000.

We need to use the present value formula which is: PV = PMT x [1 - (1 + r)^-n] / r

Plugging in the values:

PV = $900 x [1 - (1 + 0.00096154)^-1,040] / 0.00096154

PV = $900 x 657.221075423

PV = $591,498.968.

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So, it says that he ordered 239,021 pounds of flour, but they delivered 451,202 pounds. You are going to subtract the delivered amount to the ordered amount.

451,202 - 239,021 = _________

_________ = The Extra Amount Delivered

451,202 - 239,021 = 212,181

That means, that they had delivered 212,181 extra pounds of flour.

Answer:

y= -1x +1

Step-by-step explanation:

The required equation that represent the hanger is 10 + 5x = 11 and the value of x is 1/5.

Given the diagram of the hanger which one side has 10 + 5x  and other side has 11.

To find the equation, equate the expression of one side to the numerical value of the other side. On solving the equation gives the value of x.

Thus, the equation is 10 + 5x = 11.

Consider the equation 10 + 5x = 11

On subtracting 10 from each side gives,

5x = 1

Divide each side by 5 gives,

x = 1/5.

Hence,  the required equation that represent the hanger is 10 + 5x = 11 and the value of x is 1/5.

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The solution of the system of equations are x = 7 and y = 77

Given data

y = 9x + 14

y = 6x + 35

solving using substitution method to solve the simultaneous equation we have

y = 9x + 14  equation 1

y = 6x + 35  equation 2

equating the both equations will give

9x + 14  = 6x + 35

9x - 6x = 35 - 14

3x = 21

x = 7

plugging x = 7 into equation 1

y = 9x + 14

y = 9 * 7 + 14

y = 63 + 14

y = 77

The solution of the system of equations are x = 7 and y = 77

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Answer: x = 2.

Step-by-step explanation:

By an online search, i found that the question is:

"Given that x satisfies the inequality 20*x > 33,  find the smallest value of x if x is a prime number."

To find the smallest value of x we need to input different possible values of x (where we have the condition that x must be a prime number) and see which one is the first one that makes the inequality true.

The prime numbers are:

2, 3, 5, ....

Let's start with the smaller one, x = 2

So we input it in the inequality and get:

20*2 > 33

40 > 33

this is true.

Then we can have x = 2, which is the smaller prime number that satisfies the inequality.

The area of carpet required to be bought for the living room is 127.75 square feet.

Thus the area of carpet required is 127.75 square feet.

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Answer:70.54

Step-by-step explanation:Add 32 and 32 that will give you 64.Then add 64 and 4.16 that will give you 68.16.Finally, you add 68.16 and 2.38 that will give the answer.

Your answer is: 70.54

Alice is a mathematics major and a computer science major can be classified as an invalid argument

An argument can be invalid even if the conclusion and the premises are all actually true

According to the statement that Alice is a mathematics major. Therefore, Alice is a mathematics major and a computer science major is an invalid argument since a course that can have a combination of math and computer science.

Hence Alice is a mathematics major. Therefore, Alice is a mathematics major and a computer science major can be classified as an invalid argument

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Answer:

8 units, 3 units, √73 units

16 units, 30 units, √50 units

Step-by-step explanation:

Given the above side lengths of a triangle, to determine which triangles are right triangles, we would make use of the Pythagorean theorem which holds that the sum of the square of two smaller legs of a right triangle would give us the square of the length of the longest leg.

That is a² + b² = c²

Thus, let's check each options given.

Let c be the 3rd units given in each option, which is the longest leg.

Option 1:

c² = 8² + 15²

c² = 64 + 225 = 289

c = √289 = 17

∆ with lengths 8 units, 15 units, √75 units is not a right triangle because c ≠ √75, from calculation.

Option 2:

c² = 8² + 3²

c² = 64 + 9 = 73

c = √73 units

∆ with lengths 8 units, 3 units, √73 units is a right triangle because c = √73 from calculation

Option 3:

c² = 16² + 30²

c² = 256 + 900 = 1156

c = √1156 = 34

∆ with lengths 16 units, 30 units, √50 units is not a right triangle because c ≠ √50 units from calculation.

Option 4:

c² = 5² + 7²

c² = 25 + 49 = 74

c = √74 units

∆ with lengths 16 units, 30 units, √50 units is a right triangle because c =  √74 units from calculation.

Therefore, based on the sets of side lengths given, the following are right triangles:

8 units, 3 units, √73 units

16 units, 30 units, √50 units

Answer:

8 units, 3 units, √73 units

16 units, 30 units, √50 units

Step-by-step explanation:

Answer:

\(c = \frac{2}{0.42} \)

Step-by-step explanation:

AB = c

\( \frac{a}{sin \: A} = \frac{c}{sin \: C} \\ \frac{2}{sin \: 25} = \frac{c}{sin \: 90} \\ \frac{2}{0.42} = \frac{c}{1} \\ 0.42 \: c = 2 \\ c = \frac{2}{0.42} \)

Answer:

4.73

Step-by-step explanation:

​

​

Answer:

A. f(x) = 4x + 4

B. f(x) = x - 3.5

Step-by-step explanation:

A. Let's first break down the givens.

When we're given that \(f(a) = b\), for any a and b, that means that the point (a, b) exists on the graph of f(x).

Following this logic, we're given two points on the graph of f(x): (-1, 0) and (7, 2).

Using these two points, we can first find the slope of the function:

\(m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{7 - (-1)}{2 - 0} = \frac82 = 4\)

Now we can substitute one of the points, as well as the slope, to find the equation of the graph:

\(f(x) - y_1 = m(x - x_1)\\\to f(x) - 0 = 4\left(x - (-1)\right)\\\to f(x) = 4x + 4\)

B. Breaking down the givens, we know two things:

- The point (0.5, -3) exists on the graph f(x)

- The slope of the function is the same as the given line y. This is because parallel lines have the same slope. The equation of line y is \(y = x -4\), meaning that the slope is 1.

Substituting the given point and the slope to find the equation of the graph:

\(f(x) - y_1 = m(x - x_1)\\\to f(x) - (-3) = 1(x - 0.5)\\\to f(x) + 3 = x - 0.5\\\to f(x) = x - 3.5\)

Answer:

(4*10)+(7*1/100)=40+7/100=40 7/100

Step-by-step explanation:

The form that most quickly reveals the y intercept is

The y intercept is (0, 21/2)

The y-intercept is the point where a function or a curve intersects the y-axis. In other words, it is the value of the dependent variable (y) when the independent variable (x) is equal to zero.

In the form,  f(x) = 1/2 x² - 5x + 21/2 it is easier to see that eliminating x by plugging in 0 leaves 21/2 which is the y intercept

hence we can easily say that the y intercept is (0, 21/2)

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Answer:

12 gallons fewer

Step-by-step explanation:

3 gallons a minute means 30 gallons in 10 mins

40% less = 18l

new nozzle=18 liters in 10mins

meaning there is a 12 gallon difference

A geometric series is one in which there is a constant between two successive numbers in the series.

When there is a constant between the two successive numbers in the series then it is called a geometric series. In other words, every next term is multiplied by that constant term to form a geometric progression.

The sequence in which every next number is the addition of the constant quantity in the series is termed the arithmetic progression

Suppose the series is given as

2,4,8,16,32,64.........

The common difference is defined as the ratio of the next term to the previous term.

From the above series, the common ratio is calculated as,

Common ratio = 4 / 2

Common ratio = 2

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The formula of the area of the trapezium as subject to x is,

x = 2A/h - y.

Two algebraic expressions having the same value and symbol '=' in between are called an equation.

Given:

The area of the trapezium,

A = (1/2)h(x + y)

To make x the subject of the equation:

2A/h = (x + y)

2A/h - y = x

x = 2A/h - y

Therefore, the formula is x = 2A/h - y.

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Answer:

a) H0: p1 - p2 = 0

H1: p1 - p2 ≠ 0

b) z=-0.58

c) p-value = 0.562

Step-by-step explanation:

We need to determine whether p1 is not equals p2, so the null and alternative hypothesis are:

H0: p1 - p2 = 0

H1: p1 - p2 ≠ 0

Where p1 and p2 are the proportions of the population. Additionally, the proportions of the sample p1' and p2' are calculated as:

\(p1'=\frac{x1}{n1}=\frac{28}{254}=0.1102\\p2'=\frac{x2}{n2}=\frac{38}{301}=0.1262\)

Then, the test statistic is calculated using the following equation:

\(z=\frac{(p1'-p2')-(p1-p2)}{\sqrt{p'(1-p')(\frac{1}{n1}+\frac{1}{n2})} }\)

Where p' is calculated as:

\(p'=\frac{x1+x2}{n1+n2}=\frac{28+38}{254+301}=0.1189\)

So, replacing the values, we get that the test statistic is:

\(z=\frac{(0.1102-0.1262)-(0)}{\sqrt{0.1189(1-0.1189)(\frac{1}{254}+\frac{1}{301})}}=-0.58\)

Finally, using the standard normal table, the p-value is equal to:

\(p-value=2*P(z<-0.58)=2*0.281=0.562\)

The p-value is greater that the value of alpha 0.1, so we can't reject the null hypothesis and there is evidence to said that p1 and p2 are equals.

The domain of a quadratic function is (-∞, +∞), and the range depends on the coefficient a and can be [c, +∞) or (-∞, c] depending on the direction of the parabola.

To determine the domain and range of a quadratic function, we consider the characteristics of the function and its graph.

The domain of a quadratic function, represented by the variable x, is the set of all possible input values for which the function is defined. Since quadratic functions are defined for all real numbers, the domain of a quadratic function is (-∞, +∞) or the set of all real numbers.

The range of a quadratic function, represented by the variable y or f(x), is the set of all possible output values that the function can take. For a quadratic function in the form f(x) = ax^2 + bx + c, where a ≠ 0, the range depends on the coefficient a. If a > 0, the parabola opens upward, and the range is [c, +∞). If a < 0, the parabola opens downward, and the range is (-∞, c].

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we can say that there are 15 male teachers for every 35 female teacher

\(\stackrel{\textit{\large ratio 1}}{\cfrac{15}{35}\qquad \cfrac{male}{female}} ~\hspace{10em} \stackrel{\textit{\large ratio 2}}{\cfrac{\stackrel{3}{~~\begin{matrix} 15 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}}{\underset{7}{~~\begin{matrix} 35 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}}\implies \cfrac{3}{7}\qquad \cfrac{male}{female}}\)

For different function different results are shown below.

A function is a process or a relation that associates each element 'a' of a non-empty set A , at least to a single element 'b' of another non-empty set B.

We have been given a graph of piecewise function. Using that we have to select the function from given choices which is represented by graph.

g(x) = −2x, −2 < x < 0

Answer:

NO. Because g(x) = −2x has negative slope so that means it goes downward also there is no y-intercept in g(x) = −2x but the only graph that has y-intercept in given graph goes upward so that can't be answer.

g(x) = −2, x < −2

Answer:

YES. Because g(x) = −2 is a horizontal line which is only on the left side of x=-2. Graph of this part is present in given graph. So yes it is answer.

g(x) = x − 2, −2 < x < 1

Answer:

NO. Because g(x) = x−2 has y-intercept at y=-2 and slope 1 so that means graph of g(x)= x-2 must be going upward and crossing at y=-2 but there is no such graph. Hence this can't be answer.

g(x) = −2x + 6, x ≥ 1

Answer:

YES. Because g(x) = −2x+6 satisfies the graph which is going downward.

g(x) = x/2+ 1, –2 ≤ x < 1

Answer:

YES. Because g(x) = x/2+ 1 satisfies the graph which is going downward.

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Answer: i think this is the answer sorry if i am wrong.

g(x) = −2, x < −2,

g(x) = −2x + 6, x ≥ 1,

g(x) = x/2  + 1, –2 ≤ x < 1

Step-by-step explanation:

Here is the graph

9514 1404 393

Answer:

  2.1 ft³

Step-by-step explanation:

Put the given radius and height into the volume formula and do the arithmetic.

  V = 1/3πr²h

  V = 1/3(3.14159)(1 ft)²(2 ft) ≈ 2.094 ft³

Rounded to tenths, this is 2.1 cubic feet.

__

The picture cuts off your rounding requirements. If it is hundredths, you need to use 2.09 ft³. If it is thousandths, your answer will depend on the value of pi you are asked to use.

Answer:

T = 5 * ((7 * 10) + (6 * 9) + (3 * 2))

Step-by-step explanation:

The following mathematical expression would calculate the total number of materials in all of the classes which would be represented by the variable T. We would first multiply the quantity of a specific material in a single box by the number of boxes that exist for each separate material and then multiply that number by 5 since there are a total of 5 classrooms and all have the same quantity of the same materials.

T = 5 * ((7 * 10) + (6 * 9) + (3 * 2))

If we were to solve this we would see that there are a total of

T = 5 * ((7 * 10) + (6 * 9) + (3 * 2))

T = 5 * (70 + 54 + 6)

T = 5 * 130

T = 650

650 materials