A parking garage charges a 3.50$ base fee plus an hourly rate of 7.00$. If you have at most 21.50$ to pay for parking, how long can you park?

Answer:

\(P = 0.1447\)

Step-by-step explanation:

Given

\(n = 7000\) -- total

\(d = 180\) --- defective

\(r = 6\) --- selected

Required

The probability of rejecting the batch

This means that at least one of the selected piece is defected.

So, we first calculate the probability that all the selected piece are accepted.

So, we have:

\(Pr = \frac{7000 - 180}{7000} * \frac{6999 - 180}{6999}* \frac{6998 - 180}{6998}* \frac{6997 - 180}{6997}* \frac{6996 - 180}{6996}* \frac{6995 - 180}{6995}\)

The denominator decreases by 1 because it is a probability without replacement; 180 is subtracted from the numerator to represent the number of non-defective CDs

So, we have:

\(Pr = \frac{6820}{7000} * \frac{6819}{6999}* \frac{6818}{6998}* \frac{6817}{6997}* \frac{6816}{6996}* \frac{6815}{6995}\)

\(Pr = 0.8553\)

Using the complement rule, the probability that the batch will be rejected is:

\(P = 1 - 0.8553\)

\(P = 0.1447\)

Answer:

a) n less than or equal to 21

b) n greater than or equal to 5

c) n > 3/5

Step-by-step explanation:

i hope this helps!!

Answer:

A.) n ≤ 21

B.) n  ≥ 5

C.) n > 3/5

Step-by-step explanation:

For the first question it says that the number is no more than 21, so it could be equal to or less than 21

For the second question, it says that the number is at least 5, so it could be equal to or greater than 5

Finally, for the last question it says that the number is more than 3/5, so greater than would be the correct inequality symbol to use

Answer:

False, 82 inches is not greater than 5 feet and 10 inches

Step-by-step explanation:

1 feet = 12 inches

5x12=60+10=70

82 is greater than 70.

Answer:

Step-by-step explanation:

I will explain it in a screenshot. That all the way is divided into 5 parts. And 4 of them were by bicycle, and 1 part is by walk. So we divide all the way to 5 and multiply to leftover 1 piece.

Answer:

A. c = 15.9 + 12(y - 2014)

B. c = 15.9 + 12(2025 - 2014)

C. 147.9 gigabytes

D. Unsure what you meant

Step-by-step explanation:

A. In this equation, 'c' represents the flash storage capacity in year 'y' and '15.9' is the flash storage capacity in year 2014. '12' represents the yearly increase in storage and '(y-2014)' represents how many years have passed from 2014.

B.To find the average flash storage capacity of smartphones in 2025, we can use the equation:

c = 15.9 + 12(y - 2014)

We can substitute 'y' with 2025 in the above equation to find the average flash storage capacity of smartphones in 2025

C.

c = 15.9 + 12(2025 - 2014)

c = 15.9 + 12(11)

c = 15.9 + 132

c = 147.9 gigabytes

Answer:

C

Step-by-step explanation:

We know that line CD passes through the two points (0, 2) and (4, 6).

First and foremost, let’s find the slope of the line. We can use the slope formula:

\(\displaystyle m=\frac{y_2-y_1}{x_2-x_1}\)

Where (x₁, y₁) and (x₂, y₂) are our two points.

So, let’s let (0, 2) be (x₁, y₁) and (4, 6) be (x₂, y₂). Substitute appropriately:

\(\displaystyle m=\frac{6-2}{4-0}\)

Evaluate:

\(\displaystyle m=\frac{4}{4}=1\)

Hence, our slope is 1.

Now, we can use the slope-intercept form:

\(\displaystyle y=mx+b\)

Where m is our slope and b is our y-intercept.

Notice from our given points that we are given (0, 2).

So, our y-intercept is 2.

Therefore, we will substitute 1 for m and 2 for b. This yields:

\(\displaystyle y=(1)x+(2)\)

Simplify:

\(\displaystyle y=x+2\)

Hence, our answer is C.

Answer:

4 = x

Step-by-step explanation:

64 = x^3

Take the cube root of each side

64^ (1/3) = x^3 ^ (1/3)

4 = x

Answer:

40 cm

Step-by-step explanation:

volume = length x width x height

10,000 = 25 x 10 x h

h = 10,000/ (25 x 10)

h = 10,000 / 250

h = 40 cm

Answer:

add the like terms then look for a gcf to take out atleast for this one

so -9+7= -2

-5x + 1x = -4x

and -2y

we can take -2 out of all those

so our answer is -2(2x+y+1

The triple integral can be evaluated numerically using the cylindrical coordinates \($(r,\theta,z)$\) with the limits of integration given by the parabolic cylinder and the planes.

The triple integral we need to evaluate is:

\(\begin{equation}\iiint_{S} f(x,y,z) \,dV\end{equation}\)

where S is bounded by the parabolic cylinder \($z=2y^2$\) and the planes x=0, y=0, z=0, and x=2. To evaluate this integral, we will use the cylindrical coordinates \($(r,\theta,z)$\). The Jacobian of the transformation is r, and the volume element is \($r \, dr \, d\theta \, dz$\). The integral then becomes:

\(\begin{equation}\int_0^{2\pi} \int_0^2 \int_0^{2r^2} f(r,\theta,z) r \, dr \, d\theta \, dz\end{equation}\)

The limits of integration for r come from the planes x=0 and x=2, so r goes from 0 to \($\sqrt{2}$\), and for z come from the parabolic cylinder \($z=2r^2$\), so z goes from 0 to \($2r^2$\).

Finally, the integral becomes:

\(\begin{equation}\int_0^{2\pi} \int_0^{\sqrt{2}} \int_0^{2r^2} f(r,\theta,z) r \, dr \, d\theta \, dz\end{equation}\)

which can be evaluated numerically.

The triple integral can be evaluated numerically using the cylindrical coordinates \($(r,\theta,z)$\) with the limits of integration given by the parabolic cylinder and the planes.

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complete question

Evaluate the triple integral where is bounded by the parabolic cylinder \($z=2y^2$\) and the planes x=0, y=0, z=0, and x=2.

Answer: y=-5x-1

Step-by-step explanation:

The two given points are (-1,4) and (1.-6)

We can then use the slope formula (Y2-Y1)/(X2-X1) to find the slope

4-(-6)/ -1-1 = 10/-2 = -5

Slope is -5

We then plug the slope in a set of points to find the y intercept

-5*-1+x = 4

5+x=4

x=-1

Then just add these two together to form the equation of y=mx+b

y=-5x-1

Answer:  2(x+3)^2 - 1

To shift the f(x) function 3 units to the left, the xy axis must move 3 units to the right. This effectively means each x input is 3 units larger than before. That's why we replace every x with x+3.

Step-by-step explanation:

ur gonna go 6 to the left and 5 up

Answer:

6 to the left and 5 up

Step-by-step explanation:

Hope it helps :D

Answer:

THE THIRD COST FUNCTION MOST SUITABLY REPRESENTS THE STATEMENT

Answer:

5x + 1

Step-by-step explanation:

Answer: the answer is = 20x − 4

It is given that the function g(x) is the inverse of f(x) so it follows:

It is given that f(-4)=9 so it follows:

So the value of g(9)-3f(-4) is given by:

Hence the value is -31.

Answer:

meghan has 30 stickers

Step-by-step explanation:

5x3=15 double is 30

Answer:

7 stickers

Step-by-step explanation:

you must multiply 5 by 3 then divide by 2 (you can't have half a sticker so I rounded down to 7) have a great day and I'm sorry if it's wrong

The customer will pay $206.25 for the lamp after the markup.

What is Algebraic expression ?

Algebraic expression can be defined as combination of variables and constants.

The markup on cost is 65%, which means the store wants to increase the cost of the lamp by 65% of its original cost.

To find the increase, we can first calculate 65% of the original cost of the lamp:

65% of $125 = 0.65 * $125 = $81.25

So the store wants to increase the cost of the lamp by $81.25.

To find the selling price of the lamp after markup, we need to add the markup amount to the original cost of the lamp:

Selling price = original cost + markup amount

Selling price = $125 + $81.25 = $206.25

Therefore, the customer will pay $206.25 for the lamp after the markup.

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The transformation that would produce an image with vertices B"(-2, 1), C"(3, 2), D"(0, -1) from the original vertices B(-3,0), C(2, -1), D(-1, 2) is the transformation (x,y) → (X + 1, y + 1).

By applying the transformation (x,y) → (X + 1, y + 1), each point's x-coordinate is shifted one unit to the right (X = x + 1), and each point's y-coordinate is shifted one unit upward (Y = y + 1). This results in the image with the given coordinates B"(-2, 1), C"(3, 2), D"(0, -1).

The other transformations listed do not match the given image coordinates and would not produce the desired result.

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Answer:

(x, y) → (x, −y) → (x + 1, y + 1)

Step-by-step explanation:

Reflect the vertices over the x-axis by applying the transformation (x, y) → (x, -y):

B'(-3, 0) → B'(-3, 0)

C(2, -1) → C(2, 1)

D(-1, 2) → D(-1, -2)

Translate the reflected vertices by (1, 1):

B'(-3, 0) → B″(-3 + 1, 0 + 1) → B″(-2, 1)

C(2, 1) → C″(2 + 1, 1 + 1) → C″(3, 2)

D(-1, -2) → D″(-1 + 1, -2 + 1) → D″(0, -1)

So, the correct sequence of transformations is:

(x, y) → (x, -y) → (x + 1, y + 1)

(Image provided for more proof)

Step-by-step explanation:

\( 5\sqrt{3 } \)

30 60 90 triangle

The location of point R on the number line is 14/5 or Fourteen-fifths.

Fourteen-fifths.

The section formula is a mathematical formula used to find the coordinates of a point that lies on a line segment, given the coordinates of the endpoints and the ratio in which the point divides the segment.

Suppose we have a line segment joining two points A(x1, y1) and B(x2, y2) in a coordinate plane.

Let P(x, y) be a point on the line segment AB that divides it in the ratio m:n.

Then the coordinates of P can be found using the following formula:

x = [(nx1) + (mx2)] / (m + n)

y = [(ny1) + (my2)] / (m + n)

To find the location of point R on the number line using the section formula, follow these steps:
Use the given values: m = 3, n = 2, x1 = -2, and x2 = 6.
Plug the values into the section formula: R = (mx2 + nx1) / (m + n).
Calculate the numerator: \((3 \times  6) + (2 \times  -2) = 18 - 4 = 14.\)
Calculate the denominator: 3 + 2 = 5.
Divide the numerator by the denominator: 14 / 5.

Fourteen-fifths is correct.

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Answer:

A. 14/5

Step-by-step explanation:

The required number of ways is 38,760.

To solve the problem we have to follow the given steps:

Step 1: Choose one person to be the chair of the subcommittee. This can be done in 20 ways.

Step 2: Choose the remaining four members of the subcommittee from the remaining 19 people. This can be done in 19C4 ways.

Step 3: Multiply the number of ways in step 1 and step 2 to get the total number of ways to choose a subcommittee of five people with one person designated as the chair of the subcommittee.

So, the total number of ways to choose a subcommittee of five people with one person designated as the chair of the subcommittee is:

20 × 19C4 = 20 × (19!/4!15!) = 38,760 ways.

Hence, the required number of ways is 38,760.

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The standard form of the rational number -36/216​ is -1/6.

Rational numbers are in the form of p/q, where p and q can be any integer and q ≠ 0. This means that rational numbers include natural numbers, whole numbers, integers, fractions of integers, and decimals (terminating decimals and recurring decimals).

The given rational numbers are 35/15 and -36/216​

If the denominator of a rational number is a positive integer and there is only one other common factor between the numerator and denominator, the number is said to be in the standard form.

(i) Here, 35/15

Divide both the numerator and denominator by 7, we get

7/3

(ii) -36/216​

Divide both the numerator and denominator by 36, we get

-1/6

Therefore, the standard form of the rational number -36/216​ is -1/6.

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"Your question is incomplete, probably the complete question/missing part is:"

Reduce the following rational numbers in standard form.

(i) 35/15

(ii) -36/216​

The solution to the equation \((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2\) is 10.3891

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

\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2\)

Using the following trigonometry ratio

sin²(x) + cos²(x) = 1

We have

\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2 = (\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + 1 + e^2\)

The sum to infinity of a geometric series is

S = a/(1 - r)

So, we have

\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2 = \frac{1/2}{1 - 1/2} + \frac{9/10}{1 - 1/10} + 1 + e^2\)

So, we have

\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2 = 1 + 1 + 1 + e^2\)

Evaluate the sum

\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2 = 3 + e^2\)

This gives

\((\sum\limits^{\infty}_{i=1} \frac{1}{2^i}) + (\sum\limits^{\infty}_{i=1} \frac{9}{10^i}) + \sin^2(\theta) + \cos^2(\theta) + e^2 = 10.3891\)

Hence, the solution to the equation is 10.3891

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Answer:

What is the equation of the graphed line written in standard form?" has four options: 2x + 3y = -6, 2x + 3y = 6, y=-2/3x-2, and y= 2/3x-2. The standard form of a linear equation is Ax + By = C, where A, B, and C are constants. In this case, the first two options, 2x + 3y = -6 and 2x + 3y = 6 are already in standard form. The last two options, y=-2/3x-2 and y= 2/3x-2 are not in standard form. However, without additional information such as a graph or coordinates of points on the line, it is not possible to determine which of these options is the correct equation for the graphed line.

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Compatible numbers are close in value to the real numbers, which simplifies problem-solving and estimation of the solution. 1,7,10/32 has a quotient (integer division) of 53 and a remainder ("leftover") of 14. The dividend is 1,7,10, while the divisor is 32.

Compatible numbers are those that divide equally into each other and are near to the numbers they are replacing. The outcome of a division is the quotient. 55,304 is not too far away from 56,000. 800 splits equally into 56,000 and is reasonably near to 875.

Our minds can occasionally spin when we are asked to find the total (in addition), difference (in subtraction), product (in multiplication), or quotient (in division). By rounding each number to the closest ten, twenty, fifty, or hundred, we employ suitable numbers to make the problem simpler to figure out mentally.

Numbers that are simple to mentally add, subtract, multiply, or divide are said to be compatible. To estimate a calculation, substitute compatible numbers for the actual numbers. Since it is simple to mentally calculate the sum of 800, the numbers 500 and 300 can be added together.

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Answer: -6

Explanation: A loss of 6 yards is a decrease which means that it's negative.

So a loss of 6 yards in football can be written as -6.