The Kwik Klean car wash loses $250 on rainy days and gains $1300 on non rainy days. If the probability of rain is 0.12, what is the expected net profit ?

The probability that the randomly drawn card is an odd number (3, 5, 7, 9) or of spade suit is 25/52.

In the question, we are informed that a card is drawn at random from a standard 52-card deck.

We are asked the probability that the randomly drawn card is an odd number (3, 5, 7, 9) or of spade suit.

We assume the event of drawing an odd card from the random pick to be A, and the event of drawing a card of spade suit to be B.

The number of outcomes favorable to event A = 16 {4 odd cards of each of the 4 suits, that is, 4*4 = 16}.

The total number of possible outcomes = 52 {The number of cards in the deck}.

Therefore, the probability of event A, P(A) = 16/52.

The number of outcomes favorable to event B = 13 {The 13 cards of spade suit}.

The total number of possible outcomes = 52 {The number of cards in the deck}.

Therefore, the probability of event B, P(B) = 13/52.

The number of outcomes favorable to events A and B both = 4 {4 odd cards of the spade suit}.

The total number of possible outcomes = 52 {The number of cards in the deck}.

Therefore, the probability of events A and B both, P(A ∩ B) = 4/52.

The probability that the randomly drawn card is an odd number or of spade suit is represented by P(A ∪ B), which is calculated by the formula:

P(A ∪ B) = P(A) + P(B) - P(A ∩ B) = 16/52 + 13/52 - 4/52 = 25/52.

Hence, the probability that the randomly drawn card is an odd number (3, 5, 7, 9) or of spade suit is 25/52.

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Answer:

slope=4x

y intercept=2

Step-by-step explanation:

y=4x+2

The simple equation form is y=mx+b

The y-intercept is the number that is where b is.

In this case 2

and the slope is the number in front of x

in this case is 4

Answer:

Straight or obtuse, I think it's straight but then again I learned this about 5 years ago so sorry :I

Step-by-step explanation:

it's a straight line, right would have a 90 degree angle and the rest would have either (acute) lower than that or (obtuse) bigger than that

Answer:

Step-by-step explanation:

x-int (2/7, 0)

y-int (0, -2)

x-int

7x - 0 = 2

7x = 2

x = 2/7

(2/7, 0)

7(0) - y = 2

-y = 2

y = -2

(0, -2)

Answer:

here you go! 36

Step-by-step explanation:

The monthly payment amount is $217.42 and the finance charge is $413.02.

The payment amount and finance charge can be found by using the formula below

Payment amount formula: PMT = (P x R x (1 + R)^N) / ((1 + R)^N - 1)

Finance charge formula: Finance charge = Total payment - Loan amount

Where P = Loan amount

R = Interest rate per period

N = Number of periods

Given that a loan is made for $4800 with an APR of 12% and payments made monthly for 24 months

Therefore,P = $4800R = 12% / 12 = 1% per month

N = 24

Using the Payment amount formula above: PMT = (P x R x (1 + R)^N) / ((1 + R)^N - 1)

PMT = ($4800 x 0.01 x (1 + 0.01)^24) / ((1 + 0.01)^24 - 1)

PMT = $217.42

Hence, the monthly payment amount is $217.42 (rounded to two decimal places).

Using the finance charge formula above: Finance charge = Total payment - Loan amount

Total payment = Payment amount x Number of periods

Total payment = $217.42 x 24 = $5213.02

Finance charge = $5213.02 - $4800

Finance charge = $413.02

Hence, the finance charge is $413.02 (rounded to two decimal places).

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The dimensions of the kennel and the size of the cylinder indicates;

4.1.1. The two 3D objects which the figure consists of are a triangular prism that lays on top of a rectangular prism at the bottom.

4.1.2. The area of the wood needed to build the dog kennel is approximately 2.85 m²

4.1.3. The number of containers of sealant needed to paint one coat on the dog kennel is approximately 2 containers

4.2. The new height of the water in the container will be approximately 18 cm.

The surface area of a solid is found by adding together the area of the surfaces that enclose the solid.

4.1.1. The two 3D objects in the figure are;

4.1.2. The amount of wood needed is found by finding the surface area, A, of the dog kennel as follows;

A = 2×80×60+2×50×60+50×80+2×0.5×80×40+2×√(40²+40²)×50

A = 22800 + 80·√2×50 = 22800 + 4000·√2

The amount of wood needed = (22800 + 4000·√2) cm²

1 m² = 10,000 cm²

(22800 + 4000·√2) cm² = ((22800 + 4000·√2))/10,000 m²

((22800 + 4000·√2)) cm² = (2.28 + 0.4·√2) m² ≈ 2.85 m²

4.1.3. 500 milliliters of paint is enough to for 1.5 m² area

The number of containers of paint containers required, n, is therefore;

\(n = \dfrac{(2.28 + 0.4\cdot \sqrt{2}) \, m^2 }{1.5 \, m^2/container} = (1.52+0.\overline 6\cdot\sqrt{2} ) \, containers \approx 2 \, containers\)

4.2 Diameter of the base of the water container = 20 cm

Radius of the base = (20 ÷ 2) cm = 10 cm

Height of water in the container = 15 cm

Volume of water added = 1,000 cm³

The new height will be 15 + (1,000/(π×10²)) = (15 + 10/π) cm ≈ 18 cm

The height of the water in the container will rise to approximately 18 centimeters

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Answer:

150 cookies

Step-by-step explanation:

Using the ratio as an equation we can divide 90 by 3 to find the common multiple used to simplify this equation into a more usable ratio.

3 : 5          90 : 5x (x is the common multiple)

90 / 3 = 30, so x is 30

Then we multiply both sides of the original ratio by the common multiple to get our answer.

3 : 5 is equal to 90 : 150

Answer:

$70.80

Step-by-step explanation:

60+18/100*60

70.80

Answer:

60 cents

Step-by-step explanation:

.6 x 5= 3

The corresponding point of f(x) if f(x) is symmetric to the origin is (-2, 3).

The given point is (2,-3) and we need to find the corresponding point of f(x) if f(x) is symmetric to the origin.

The point (x, y) is symmetric to the origin if the point (-x, -y) lies on the graph of the function. Using this fact, we can find the corresponding point of f(x) if f(x) is symmetric to the origin as follows:

Let (x, y) be the corresponding point on the graph of f(x) such that f(x) is symmetric to the origin. Then, (-x, -y) should also lie on the graph of f(x).

Given that (2, -3) lies on the graph of f(x). So, we can write: f(2) = -3

Also, since f(x) is symmetric to the origin, (-2, 3) should lie on the graph of f(x).

Hence, we have:f(-2) = 3

Therefore, the corresponding point of f(x) if f(x) is symmetric to the origin is (-2, 3).

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Since Sylvia receives a net pay of $390.45 biweekly, her annual gross salary is equal to $13,531.7.

In Mathematics, the annual gross salary of an employee simply refers to the total amount of money that is being paid to him or her over a period of fifty two (52) weeks without any revenue.

First of all, we would calculate Sylvia's gross paycheck as follows:

Gross paycheck = $390.45 + $130

Gross paycheck = $520.45

Since Sylvia is paid biweekly, her annual gross salary can be calculated as follows:

Annual gross salary = 52/2 × $520.45

Annual gross salary = 26 × $520.45

Annual gross salary = $13,531.7

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Answer:

0.8497

Step-by-step explanation:

Given that:

n = 10 ; number who wear sunglasses = atleast 6 ; proportion, p = 0.7

Using binomial probability formula :

P(x =x) = nCx * p^x * (1 - p)^(n - x)

P(x ≥ 6) = P(6) + P(7) + P(8) + P(9) + P(10)

To save computation time, we can use a binomial probability calculator :

P(x =6) = 0.2001

P(x = 7) = 0.2668

P(x = 8) = 0.2335

P(x = 9) = 0.1211

P(x = 10) = 0.0282

= 0.2001 + 0.2668 + 0.2335 + 0.1211 + 0.0282

= 0.8497

Answer:

210 \(cm^3\)

Step-by-step explanation:

The formula of solving the volume of a triangular prism is:

volume = (height x base x length)^3 / 2

First, put in the numbers:

V = \(\frac{(2cm*7cm*30cm)^3}{2}\)

V = \(\frac{(14cm*30cm)^3}{2}\)

V = \(\frac{420^3}{2}\)

V = \(210\) \(cm^3\)

Answer:

(2^7)*(7^2)

Step-by-step explanation:

2*2*2*2*2*2*2*7*7=6272where2 is the smallest number by which it becomes a perfect square

Answer:

\(\frac{15}{17}\)

Step-by-step explanation:

Have a nice day

It take 2 minutes to cross this bridge at a constant speed of 20 miles per hour.

The unitary method is a method for figuring out a single unit's value, then multiplying that value by itself to get the required value. An individual or singular unit is referred to as unitary. Because of this, the goal of this method is to determine values in reference to a single unit. The unitary technique can be used, for instance, to determine how many kilometers a car can go on one litre of gas if it can travel 44 km on two litres of gas. A single unit's value is determined using the unitary approach, and the value of the necessary number of units can then be determined using this value.

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The required reflection of the given figure across the line y = x is shown.

Transform the shapes on a coordinate plane by rotating, reflecting, or translating them. Felix Klein introduced transformational geometry, a fresh viewpoint on geometry, in the 19th century.

Here,
A figure on a coordinate plane is shown, and we have to determine the reflection of that figure across the line y = x,

In order to determine the reflection across the line y = x,
The Abscissa inside the line gets interchanged by the ordinate of the corresponding Absciss as.
(x, y) ⇒ (y, x)

Thus, the required reflection of the given figure across the line y = x is shown.

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The side triangle symbol in abstract algebra typically represents the concept of "normal subgroup."

In abstract algebra, a group is a mathematical object consisting of a set of elements and an operation that combines any two elements to form a third element. A subgroup is a subset of a group that also forms a group under the same operation. A normal subgroup is a subgroup that is invariant under conjugation by elements of the larger group.

In other words, for any element of the larger group, if you conjugate the elements of the subgroup by that element and then take the inverse of the element, the resulting set of elements is still a subgroup of the larger group. The symbol for normal subgroup is a triangle with a vertical line on one side.

Therefore, the side triangle symbol in abstract algebra represents the concept of "normal subgroup."

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Completed table is shown below. With this h number, we can calculate the cone's volume as V = (1/3)(72)h\(\pi\) = 49/3h\(\pi\) = 6\(\pi\)h = 131.88.

To complete the table relating the height and volume of cones with a radius of 7 units using the equation\(v = 6\pi h\), we need to substitute the radius value of 7 units into the formula for volume and then solve for height.

Height (h) Volume (V)

1                  131.88

2                  263.76

3                  395.64

4                  527.52

5                  659.4

To obtain volume for each height, we plug in radius value of 7 units into the formula for the volume of a cone, which is given by \(V = (1/3)\pi r^{2} h\). This gives us \(V = (1/3)\pi (7^{2} )h = 49/3\pi h\),

which simplifies to V = 16.33h. Then we substitute this expression for V into given equation \(v = 6\pi h\) to obtain \(16.33h = 6\pi h\), and solve for h to obtain h = 6.56.

Using this value of h, we can obtain the volume of the cone as \(V = (1/3)\pi (7x^{2} )h = \\49/3\pi h = \\6\pi h = \\131.88\)

After that, by multiplying the value of h by 16.33 and rounding to two decimal places, we can determine the volumes for the other heights in the table.

Therefore, the completed table is as shown above.

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Answer:

x=-18/7

Step-by-step explanation:

the weird shapey thing is just the unknown

let's make life easy and just use x

substitute it in and then distribute the fractions

the simplify and solve

To test hypotheses using the binomial distribution, set up hypotheses, determine the significance level, calculate critical values or p-values, and compare them to the significance level to make a decision.

To test hypotheses using the binomial distribution, we can follow these approaches for both non-directional and directional cases:

Set up the null hypothesis (H₀) and alternative hypothesis (H₁) based on the research question.

Determine the significance level (α) for the test.

Calculate the critical values or the rejection regions based on the significance level.

Collect the sample data and calculate the observed test statistic (such as the number of successes in a fixed number of trials).

Calculate the p-value, which is the probability of obtaining a test statistic as extreme as the observed one under the null hypothesis.

Compare the p-value to the significance level. If the p-value is less than or equal to α, reject the null hypothesis. Otherwise, fail to reject the null hypothesis.

Set up the null hypothesis (H₀) and alternative hypothesis (H₁) based on the research question, specifying the direction of the expected effect.

Determine the significance level (α) for the test.

Calculate the critical value or the rejection region for the specified direction.

Collect the sample data and calculate the observed test statistic.

Calculate the p-value for the specified direction.

Compare the p-value to the significance level. If the p-value is less than or equal to α, reject the null hypothesis. Otherwise, fail to reject the null hypothesis.

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Answer:

< PRS and < PRT are congruent supplementary angles.

Step-by-step explanation:

the ''math student'' was wrong. When two lines form to create a 90 degree angle (right angle) they are perpendicular. Angles can be perpendicular. BUT

  Supplementary angles are two angles that measure up to 180 degrees.

Hope this helps!

Answer:

Congruent adjacent angles that form a linear pair are right angles.

Step-by-step explanation:

Congruent adjacent angles that form a linear pair are right angles.

All the attatchments include the directions below:

Prepare a two-way table as shown below.

Enter the number 50 in the two-way table

Prepare a column total and enter 68 for the total number of people who split the check.

The total number of people who do not eat desert are 56, and the total number of people who took the survey are 122. Enter both values.

The remaining values can be found out as shown below.

The two way table shows the characteristics of the given information,

having a sum which is the number of people surveyed.

The completed two-way table is presented as follows;

\(\begin{tabular}{l|c|c|}&Order desert & No desert\\Split the check&50&18\\One person pays&16&38\end{array}\right]\)

Reasons:

Number of people that responded to the survey, U = 122 people

Number of the respondents that ordered dessert and split the check, DS = 50

Number of respondent that prefer splitting the check, S = 68 people

Number that prefer to skip dessert, ND = 56 people

Therefore;

Number that split the check and no dessert, S/ND = S - DS

S/ND = 68 - 50 = 18

Number that do not split the check and no dessert, NS/ND = ND - S/ND

NS/ND = 56 - 18 = 38

Only one person pays, and orders desert, NS/D = The rest of the respondent not excluding the respondent sorted above

Therefore, NS/D = U - S - NS/ND

Which gives

NS/D = 122 - 68 - 38 = 16

The completed two-way table is therefore;

\(\begin{tabular}{l|c|c|}&Order desert & No desert\\Split the check&50&18\\One person pays&16&38\end{array}\right]\)

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Answer:

x + y ≤ 35

10x + 15y ≥ 350

Step-by-step explanation:

Given:

Cost to stay with dog per hour = $10

Car wash per hour = $15

Find:

Equation

Computation:

Assume;

Hour for dog = x

Hour for car = y

So,

x + y ≤ 35

10x + 15y ≥ 350

if it has a diameter of 14 feet, that means its radius is half that or 7 feet.

\(\textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ h=15\\ r=7 \end{cases}\implies V=\pi (7)^2(15) \\\\\\ V=735\pi \implies V\approx 2309.07~ft^3\)

Answer:

75 & 21

Check:

75 + 21 = 96

21 * 4 - 9 = 75

Correct!

Answer:

the smaller number is 21 and the larger number is 75

Step-by-step explanation:

First make a simple equation where x = the smaller number and y = the larger number

ie: 96=x+y

Now make an equation to find the larger number.

ie: y=4x-9

Now substitute the y value in the first equation for the y value in the second equation

ie: 96=x+(4x-9)

Then solve for x

ie: x=21

Then plug in your new x value into the first or second equation to solve for y.

ie: 96=21+y

ie: y=75

Answer:

D

Step-by-step explanation:

The lines are on the same trnasversal and by parallel lines l and m.