The entrance to a museum in Paris is shaped like a square pyramid. The base of the pyramid has a side length of 35 meters, and the height of the pyramid is 22 meters

Answer:

0.0631 = 6.31% probability that his/her vitamin D level will be between 36.84 and 39.73 ng/mL

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

The population average level of vitamin D in US landscapers was found to be 30.8 ng/mL with a standard deviation of 4.371 ng/mL

This means that \(\mu = 30.8, \sigma = 4.371\)

What is the likelihood that his/her vitamin D level will be between 36.84 and 39.73 ng/mL?

This is the pvalue of Z when X = 39.73 subtracted by the pvalue of Z when X = 36.84.

X = 39.73

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{39.73 - 30.8}{4.371}\)

\(Z = 2.04\)

\(Z = 2.04\) has a pvalue of 0.9793

X = 36.84

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{36.84 - 30.8}{4.371}\)

\(Z = 1.38\)

\(Z = 1.38\) has a pvalue of 0.9162

0.9793 - 0.9162 = 0.0631

0.0631 = 6.31% probability that his/her vitamin D level will be between 36.84 and 39.73 ng/mL

Answer:

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Answer: (6,-6)

Step-by-step explanation:

To find the coordinates of point B, we can use the midpoint formula:

Midpoint formula: The midpoint M of a line segment with endpoints (x1, y1) and (x2, y2) is given by:

M = ((x1+x2)/2, (y1+y2)/2)

Here, we know that the midpoint M is (4, -2), and one endpoint A is (2, 2). Let B be the other endpoint, so we can use the midpoint formula to find B:

4 = (2+x2)/2 --> 8 = 2+x2 --> x2 = 6

-2 = (2+y2)/2 --> -4 = 2+y2 --> y2 = -6

Therefore, point B has coordinates (6, -6).

As for the second question, without a graph or information about the equation of line t and point P, it is not possible to determine which points lie on the line passing through P and perpendicular to t.

Evaluating the composition of functions in x = 1 gives:

f(g(1)) = 28

Here we have the two functions:

f(x) = 4x

g(x) = 2x + 5

And we want to find to find the composition f(g(x)), we will get:

f(g(x)) = 4*g(x)

Replacing g(x) there we will get:

f(g(x)) = 4*(2x + 5)

         = 8x + 20

Now we can evaluate that in x = 1, then we will get:

f(g(1)) = 8*1 + 20 = 28

That is what we wanted to find.

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Maybe you're bad at math.

But I don't think that's true.

Try reading the questions more carefully and properly reading/understanding the material.

If you have any future questions, please ask me! I would be glad to help with your geometry work.

Answer:

ΔT =313.5 K - 240.3 K = 73.2 K

Step-by-step explanation:

It's more confortable to work in °C to determine the Absolute value

T°C + 273 = T° K (Kelvin grades)

ΔT = Highest T° in K - Lowest T° in K

We make the conversion to Celsius degree, from Farenheit:

(x F - 32°) . 5/9 = °C

(105 F - 32°) . 5/9 = 40.5°C

(-27 F - 32°) . 5/9 =  - 32.7 °C

40.5°C + 273 = 313.5 K

-32.7 °C + 273 = 240.3 K

Answer: 132 Should be your answer.

Step-by-step explanation: I don't know how to explain very correctly, but I do know that is correct, have a nice day.

Answer:

No it can not

Step-by-step explanation:

Answer:

a = 8

b = 2

c = 48

Step-by-step explanation:

3 cups of flour is needed to make 24 servings.

3:24

Simplify. First, divide 3 from both sides of the ratio.

(3)/3 : (24)/3

1:8

Next, solve for b. You multiply 2 to 8 to get 16. Next, multiply 2 to 1

1 x 2 = b = 2

Finally, multiply 8 to 6 to get c.

8 x 6 = c = 48

~

2(4z−2) = 44

Simplify both sides of the equation.

Distribute:

(2)(4z)+(2)(−2) = 44

8z + −4 = 44

8z − 4 = 44

Add 4 to both sides.

8z − 4 + 4 = 44 + 4

8z = 48

Divide both sides by 8

8z/8    48/8

z = 6

Answer:

z=6

Step-by-step explanation:

The required amount paid in FICA taxes this year would be $2,295. The correct answer is $2,295.

To calculate the FICA taxes paid for the given scenario, we need to multiply the salary by the FICA rate.

Given:

Salary: $30,000

FICA rate: 7.65%

FICA taxes are split between employers and employees, with both parties paying 7.65% of their income to FICA, totaling 15.3% combined.

To calculate the FICA taxes paid by the employee, we multiply the salary by the FICA rate:

$30,000 * 7.65% = $2,295

Therefore, the amount paid in FICA taxes this year would be $2,295. The correct answer is $2,295.

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Answer:

5x+7 > 17 matches with 3.

1+3x > -5 matches with 2.

2x+1 < 3 matches with 1.

5-3x > 11 matches with 4.

Step-by-step explanation:

Answer:

24

Step-by-step explanation:

6x = x + 20

Subtract x from both sides

5x = 20

Divide by 5 on both sides

x = 4

Confirm

4 times 6 equals 24, and 4 + 20 is 24 as well.

Answer: 2/3

Step-by-step explanation:

Answer:

m=−3

Step-by-step explanation:

The maximum volume of the box that can be constructed with \(6 cm^2\) of metal is \(2 cm^3\).

What is volume of rectangle?

A rectangle is a two-dimensional geometric shape with four sides and four right angles. It has a length (l) and a width (w), and its area is given by A = l × w.

Let's denote the side length of the square ends by x and the height of the box by h. Then the length of the box (which is also the width) will be 2x (since there are two square ends).

The surface area of the box and the lid can be expressed in terms of x and h as follows:

The area of the top and bottom square ends is \(2x^2\) (since there are two ends).

The area of the front face (which is covered by the lid) is xh.

The area of the back face is also xh.

The area of each of the two side faces is x(2x) = \(2x^2\).

Therefore, the total surface area of the box and the lid is:

\(SA = 2x^2 + xh + xh + 2x^2\)

\(= 4x^2 + 2xh\)

We know that \(6 cm^2\) of metal are used in the construction of the box and the lid, so we can set up the following equation:

SA + area of lid = 6

Substituting the expression for SA, we get:

\(4x^2 + 2xh + x^2 = 6\)

Simplifying and rearranging, we get:

\(x^2 + xh - 3 = 0\)

We want to maximize the volume of the box, which is given by:

\(V = x^2h\)

Using the equation we derived above, we can express h in terms of x:

\(h = (3 - x^2) / x\)

Substituting this expression for h into the equation for V, we get:

\(V = x^2((3 - x^2) / x)\)

\(= 3x - x^3\)

To find the maximum volume, we need to find the value of x that maximizes this expression. We can do this by taking the derivative of V with respect to x and setting it equal to zero:

\(dV/dx = 3 - 3x^2 = 0\)

Solving for x, we get:

x = 1

To verify that this is a maximum, we can take the second derivative of V with respect to x:

\(d^2V/dx^2 = -6x\)

At x = 1, this is negative, which means that the volume is maximized at x = 1.

Therefore, the maximum volume of the box is:

\(V = 3(1) - (1)^3\)

\(= 2 cm^3\)

So the maximum volume of the box that can be constructed with \(6 cm^2\) of metal is \(2 cm^3.\)

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Answer:

36° , 54° , 90°

Step-by-step explanation:

since the triangle is right then one angle is 90°

the ratio of the smaller angles = 3 : 2 = 3x : 2x ( x is a multiplier )

the sum of the 3 angles in the triangle is 180° , that is

3x + 2x + 90 = 180

5x + 90 = 180 ( subtract 90 from both sides )

5x = 90 ( divide both sides by 5 )

x = 18

Then

3x = 3 × 18 = 54°

2x = 2 × 18 = 36°

the 3 angles measure 36° , 54° , 90°

Answer:

He ate it or he may have ate some in some packs then refilled the other packs.

Step-by-step explanation:

Answer:

Someone else ate them!

Answer:

5

Step-by-step explanation:

Answer:

this list

Step-by-step explanation:

1×12000=12000

2×6000=12000

3×4000=12000

4×3000=12000

5×2400=12000

6×2000=12000

8×1500=12000

10 ×1200=12000

12 ×1000=12000

The calculated value of the probability of B is (c) 0.25

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

P(A or B) = 0.3

P(A and B) = 0.2

P(A/B) =0.8

First, we have

P(A/B) = P(A and B)/P(B)

Substitute the known values in the above equation, so, we have the following representation

0.2/P(B) = 0.8

So, we have

P(B) = 0.2/0.8

Evaluate

P(B) = 0.25

Hence, the probability of B is 0.25

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The members of the given set in this problem are given as follows:

X U (Y ∩ Z) = {p, q, r, 0, 6, 21, 22, 23, 26}

The union and intersection sets of multiple sets are defined as follows:

The intersection of the sets Y and Z for this problem is given as follows:

Y ∩ Z = {0, 6, 23, 26}

(which are the elements that belong to both of the sets).

The union of the above set with the set X is given as follows:

X U (Y ∩ Z) = {p, q, r, 0, 6, 21, 22, 23, 26}

(elements that belong to at least one of the sets).

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Answer:

(1)

\(E(x) = 0.72\)

\(Var(x) = 1.1616\)

\(\sigma = 1.078\)

(2)

\(E(x) = 12\)

\(Var(x) = 1.3\)

\(\sigma = 1.14\)

Step-by-step explanation:

Solving (1):

\(\begin{array}{ccccccc}{Days} & {0} & {1} & {2} & {3} & {4}& {5} \ \\ {Probability} & {0.60} & {0.20} & {0.12} & {0.04} & {0.04} & {0.00} \ \end{array}\)

(a): Mean

This is calculated as:

\(E(x) = \sum x * P(x)\)

So, we have:

\(E(x) = 0 * 0.60 + 1 * 0.20 + 2 * 0.12 + 3 * 0.04 + 4 * 0.04 + 5 * 0.00\)

\(E(x) = 0.72\)

Solving (b): The variance

This is calculated as:

\(Var(x) = E(x^2) - (E(x))^2\)

Where:

\(E(x) = 0.72\)

and \(E(x^2) = \sum x^2 * P(x)\)

So, we have:

\(E(x^2) = 0^2 * 0.60 + 1^2 * 0.20 + 2^2 * 0.12 + 3^2 * 0.04 + 4^2 * 0.04 + 5^2 * 0.00\)

\(E(x^2) = 1.68\)

So, we have:

\(Var(x) = E(x^2) - (E(x))^2\)

\(Var(x) = 1.68 - 0.72^2\)

\(Var(x) = 1.1616\)

Solving (c): The standard deviation.

This is calculated as:

\(\sigma = \sqrt{Var(x)}\)

\(\sigma = \sqrt{1.1616}\)

\(\sigma = 1.078\)

Solving (2):

\(\begin{array}{ccccccc}{x} & {10} & {11} & {12} & {13} & {14}& { } \ \\ {P(x)} & {0.1} & {0.25} & {0.3} & {0.25} & {0.1} & { } \ \end{array}\)

(a): Mean

This is calculated as:

\(E(x) = \sum x * P(x)\)

So, we have:

\(E(x) = 10 * 0.10 + 11 * 0.25 + 12 * 0.3 + 13 * 0.25 + 14 * 0.1\)

\(E(x) = 12\)

Solving (b): The variance

This is calculated as:

\(Var(x) = E(x^2) - (E(x))^2\)

Where:

\(E(x) = 12\)

and \(E(x^2) = \sum x^2 * P(x)\)

So, we have:

\(E(x^2) = 10^2 * 0.10 + 11^2 * 0.25 + 12^2 * 0.3 + 13^2 * 0.25 + 14^2 * 0.1\)

\(E(x^2) = 145.3\)

So, we have:

\(Var(x) = E(x^2) - (E(x))^2\)

\(Var(x) = 145.3 - 12^2\)

\(Var(x) = 1.3\)

Solving (c): The standard deviation.

This is calculated as:

\(\sigma = \sqrt{Var(x)}\)

\(\sigma = \sqrt{1.3}\)

\(\sigma = 1.14\)

The number of students who participated in the survey, based on the histogram showing the number of hours students watch television on the weekend, is 125.

A histogram is a pictorial or graphical representation of categorical data, proportional to the frequency of a variable and whose width is equal to the class interval.

The number of students who watched between 0 - 4 hours = 20

The number of students who watched between 5 - 9 hours = 40

The number of students who watched between 10 - 14 hours = 30

The number of students who watched between 15 - 19 hours = 20

The number of students who watched between 20 - 24 hours = 15

The total number of students who participated = 125

Thus, using the histogram, the total number of students who participated in the survey was 125.

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Step-by-step explanation:

7! = 5040 ways

Answer:

I think the answer is "6" but I could be wrong.

Answer:

the are so many numbers but here's one of them

Step-by-step explanation:

Since the number is less than 700, it cannot begin with a 7 or an 8.

So the hundreds digit can only be a 2 or a 5.

Now the tens digit can be any digit not occupying the hudreds digit. So there would be 3 possibilities, and there remain two possibilities for the units digit.

Hence, the number of such numbers is 2x3x2 which is 12.

The number of two-digit or three-digit numbers that can be made using the digits 1, 7, 8, 5, and 2 will be 150.

A sample is a group of clearly specified components. The number of items in a finite set is denoted by a curly bracket.

The number of two-digit numbers that can be made using the digits 1, 7, 8, 5, and 2 is calculated as,

⇒ 5 x 5

⇒ 25

The number of three-digit numbers that can be made using the digits 1, 7, 8, 5, and 2 is calculated as,

⇒ 5 x 5 x 3

⇒ 125

The number of two-digit or three-digit numbers that can be made using the digits 1, 7, 8, 5, and 2 is calculated as,

⇒ 125 + 25

⇒ 150

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Answer:

x=-2

Step-by-step explanation:

Distribute, add 12 to both side, then simplify

Answer: -2

Let's solve your equation step-by-step.

−2(x+6)=4x:

Step 1: Simplify both sides of the equation.

−2(x + 6) = 4x

(−2)(x) + (−2)(6) = 4x (Distribute)

−2x + (−12) = 4x

−2x − 12 = 4x

Step 2: Subtract 4x from both sides.

−2x − 12 − 4x = 4x − 4x

−6x − 12 = 0

Step 3: Add 12 to both sides.

−6x − 12 + 12 = 0 + 12

−6x = 12

Step 4: Divide both sides by -6.

−6x/−6 = 12/−6

x = −2

An inequality to represent the dollar amounts d in cash and prizes Regan can win is p + d ≥ 500.

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

Given that, Regan won the grand prize at a store giveaway. The grand prize winner is guaranteed to win at least $500 in cash and prizes.

Let d represent the amount of cash in dollars and p represent the amount of prizes.

Since the  grand prize winner is guaranteed to win at least $500,

So, p + d ≥ 500

Therefore, an inequality to represent the dollar amounts d in cash and prizes Regan can win is p + d ≥ 500.

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