approximately 60% of mathematics students do their homework on time. in a class of 100 students, what is the mean, variance, and standard deviation if we assume normality and use the normal distribution as an approximation of the binomial distribution? answer choices rounded to the nearest whole number

From the inequality concept ( -7 / 10) > ( -5 / 6).

When two expressions are connected by a sign like "not equal to," "greater than," or "less than," it is said to be inequitable. The inequality shows the greater than and less than relation between variables and the numbers.

Given fractional numbers are -5/6 and -7/10. The numbers in the form of inequality will be calculated as:-

-7 / 10 = -0.7

-5 / 6 = -0.84

-0.7 > -0.84

-7 / 10 > -5 / 6

Therefore, from the inequality concept ( -7 / 10) > ( -5 / 6).

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Answer: -3/2

Step-by-step explanation:

rise / run . the line is decreasing vertically by 3 and increasing horizontally by 2.

Answer:

Step-by-step explanation:

It is 35%

First turn the question into a fraction which is 112/320, and now since it is asking for percentage we multiply the whole fraction by 100 which will look like this:

112/320 X 100.

If you put that into the calculator you will get 35. But you can also do it mentally.

If you choose to do it mentally, we go left to right so 112 X 100 = 11200 and then divide 11200 by 320 and you get 35.

Answer:

I believe its 1. -18 meters

Step-by-step explanation:

first find how many meters the elevator is descending per minute. to do this:

what is 12% of 75?

(75×.12) = 9

the elevator is descending 9 meters per minute.

9×2=18

The range of values of x as shown in the figure is -9 < x < 15

Inequality expressions

Inequality are expressions not separated by an equal sign.

The required inequality expression is given as:

⇒ |9x - 27| < 108

For the positive inequality

⇒ 9x - 27 < 108

⇒ 9x < 108 +27

⇒ 9x < 135

⇒ x < 15

For the negative inequality

⇒ -9x +  27 < 108

⇒ -9x < 108 - 27

⇒ -9x < 91

⇒ x > -9

⇒ -9 < x

Hence the range of values of x as shown in the diagram is -9 < x < 15

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The probability that a randomly selected barista has a salary less than $13 thousand is approximately 0.0228.

In this scenario, we are given that the salaries of coffee shop baristas follow a normal distribution with a mean of $16 thousand per year and a standard deviation of $1 thousand. To find the probability of a randomly selected barista earning less than $13 thousand, we need to calculate the area under the normal distribution curve to the left of $13 thousand. By standardizing the value using the z-score formula and referring to a standard normal distribution table or using statistical software, we find that the probability is approximately 0.0228. This means there is a 2.28% chance that a randomly selected barista earns less than $13 thousand.

To delve deeper into the topic of probability and normal distribution, it's useful to understand how z-scores are calculated and applied. Z-scores are a way to standardize values in a normal distribution, allowing us to compare and calculate probabilities. By subtracting the mean from the observed value and dividing it by the standard deviation, we obtain the z-score. This score tells us how many standard deviations away from the mean a particular value is. Using z-scores, we can refer to a standard normal distribution table or use statistical software to determine probabilities accurately.

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Answer:

x = 2

Explanation:

The given expression is

7x - 4 - 3x = -3x + 10

First, we need to add the like terms on the left side

(7x - 3x) - 4 = -3x + 10

4x - 4 = -3x + 10

Add 4 to both sides

4x - 4 + 4 = -3x + 10 + 4

4x = -3x + 14

Add 3x to both sides

4x + 3x = -3x + 14 + 3x

7x = 14

Finally, divide by 7

7x/7 = 14/7

x = 2

Therefore, the answer is x = 2

Answer:

12x - 24

Step-by-step explanation:

Since the perimeter of a square 4 times a side length we can do 4 times 3x - 6 or 4(3x - 6) and use the distributive property to get 12x - 24.

The correct options that could be an example of a function with a domain (-∞0,00) and a range (-∞,4) are given below.Option A. V = -(0.25)x - 4 Option B. V = − (0.25)x+4

A function can be defined as a special relation where each input has exactly one output. The set of values that a function takes as input is known as the domain of the function. The set of all output values that are obtained by evaluating a function is known as the range of the function.

From the given options, only option A and option B are the functions that satisfy the condition.Both of the options are linear equations and graph of linear equation is always a straight line. By solving both of the given options, we will get the range as (-∞, 4) and domain as (-∞, 0).Hence, the correct options that could be an example of a function with a domain (-∞0,00) and a range (-∞,4) are option A and option B.

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To find the radius of the crystal ball, we can use the formula for the volume of a sphere: V = (4/3) * π * r^3, where V is the volume and r is the radius.

Given that the volume of the crystal ball is 113.14 cm³, we can solve for r:

113.14 = (4/3) * π * r^3

To find the radius, we can rearrange the equation:

r^3 = (3/4) * (113.14 / π)

r = (3/4) * (113.14 / π)^(1/3)

Using a calculator, we can evaluate the expression to find the approximate value of the radius.

To find the volume of foam required to fill the vacant space inside the box, we need the volume of the box. However, the dimensions of the box are not provided in the question, so we cannot calculate the volume of foam accurately.

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The proportion of trick-or-treaters who were not dressed as cowboys is 10/13.

If three out of every thirteen trick-or-treaters were dressed as cowboys, it means that the proportion of trick-or-treaters dressed as cowboys is 3/13.

To find the proportion of trick-or-treaters who were not dressed as cowboys.

we subtract the proportion dressed as cowboys from 1 (since the total proportion of trick-or-treaters must sum to 1).

Proportion not dressed as cowboys = 1 - Proportion dressed as cowboys

Proportion not dressed as cowboys = 1 - (3/13)

Proportion not dressed as cowboys = (13/13) - (3/13)

Proportion not dressed as cowboys = 10/13

Therefore, the proportion of trick-or-treaters who were not dressed as cowboys is 10/13.

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Answer:

the equation of this line is x = -5

Step-by-step explanation:

An equation of the tangent line to the curve \(x e^y+y e^x=4\) at the point (0, 4) is \(y=-(4+e^4) x+4\).

A tangent is described as a line that intersects a circle or an ellipse only at one point. If a line touches a curve at P, the point "P" is known as the point of tangency.

Now according to the question;

To obtain the tangent at a given point, we must first obtain the slope at that point by obtaining the differentiation value at that point  \(\left.y^{\prime}\right|_{x=0, y=4}\) as-

Consider the given equation;

\(x e^y+y e^x=4\)

Differentiate both side with respect to x;

\(\begin{aligned}&\frac{d}{d x}\left(x e^y+y e^x\right)=\frac{d}{d x} 4 \\&\frac{d}{d x} x e^y+\frac{d}{d x} y e^x=0\end{aligned}\)

Now apply product rule;

\(\begin{aligned}&e^y \frac{d}{d x} x+x \frac{d}{d x} e^y+e^x \frac{d}{d x} y+y \frac{d}{d x} e^x=0 \\&e^y \frac{d}{d x} x+x \frac{d}{d y} e^y \cdot y^{\prime}+e^x y^{\prime}+y \frac{d}{d x} e^x=0\end{aligned}\)

Applying exponential and power rule;

\(\begin{aligned}&e^y \cdot 1+x e^y \cdot y^{\prime}+e^x y^{\prime}+y e^x=0 \\&\left(x e^y+e^x\right) y^{\prime}=-y e^x-e^y\end{aligned}\)

Solve the value of y'

\(y^{\prime}=\frac{-y e^x-e^y}{x e^y+e^x}\)

Now, find the value of slope m.

\(m=\left.y^{\prime}\right|_{x=0, y=4}\)

\(\frac{-4 \cdot e^0-e^4}{0 e^4+e^0}=-4-e^4\)

Now, using the point-slope formula, obtain the line equation as follows.

\(\begin{aligned}&\left(y-y_1\right)=m\left(x-x_1\right) \\&(y-4)=-(4+e^4) \cdot(x-0) \\&y=-(4+e^4) x+4\end{aligned}\)

Therefore, an equation of the tangent line to the curve is   \(y=-(4+e^4) x+4\).

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Answer:

=64x^14+169

Step-by-step explanation:

happy to help ya :)

Answer:

1 to 1/3

Step-by-step explanation:

The ratio is simply the relation between two groups of things. For example you have 1/3 cups of water for every cup of flour. As we can see, when we add just one cup of flour, the amount of water needed increases by 1/3. this means that the very minimum of water needed is 1/3. (since the ratio must be simple) This means that it takes 3 cups of flour to make a whole cup of water. this also means that in relation to the 1/3 cup of water, 1 cup of flour is needed. this means the ratio is 1 to 1/3 because for every cup of flour, 1/3 cup of water is needed. Hope this helps!!!

If your APR is 28.92 percent, then 2.41 percent monthly interest rate is applied.

Monthly interest rate = APR / 12 months ( 1 year )

                                   = 28.92 / 12 = 2.41 %

For example, if you currently owe $500 on your credit card throughout the month and your current APR is 17.99%, you can calculate your monthly interest rate by dividing the 17.99% by 12, which is approximately 1.49%. Then multiply $500 x 0.0149 for an amount of $7.45 each month.

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49.2 calories are in  would that contribute per serving .

What does a calorie mean ?

Carbohydrates provide 4 calories per gram.

              1 gm Carbohydrates = 4 calories

 then 12.3 gm Carbohydrates  = 12.3 * 4

                                             = 49.2 calories

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The walking distance saved across walking the lot is 19.6ft

The Pythagoras theorem which is also referred to as the Pythagorean theorem explains the relationship between the three sides of a right-angled triangle.

The formula is given as;

a² = y² + z²

Substituting the values into the equation;

48² = x² + (x + 6)²

2304 = x² + x² + 12x + 36

2304 = 2x² + 12x + 36

solving for x;

x = 30.8ft

The walking distance will be x + (x + 6) = 30.8 + (30.8 + 6) = 67.8ft

The walking distance saved will be 67.8ft - 48 ft = 19.6ft

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Answer:

285.28571429 minutes

Step-by-step explanation:

Let us represent

The number of minutes you talk = t

C1 = Cost in dollars of the first plan

C2 = Cost in dollars of the second plan

First plan

The first plan charges a rate of 26 cents per minute

Converting cents to dollars

100 cents = 1 dollars

26 cents =

26/100 cents

=$ 0.26

C1 = $0.26 × t

C1 = 0.26t .......... Equation 1

Second Plan

The second plan charges a monthly fee of $39.95 plus 12 cents per minute

Converting 12 cents to dollars

100 cents = 1 dollars

12 cents =

12/100

= $0.12

C2 = $39.95 + 0.12t........Equation 2

Find the number of talk minutes that would produce the same cost for both plans

We would Equate C1 to C2

C1 = C2

0.26t = $39.95 + 0.12t

Collect like terms

0.26t - 0.12t = $39.95

= 0.14t = $39.95

Divide both sides by 0.14

= t = $34.95/0.14

t = 285.28571429 minutes

Therefore, the number of talk minutes that would produce the same cost for both plans is 285.28571429 minutes.

The height of the bottom of the hole after the second day is -35 11/12 feet

Given:

Day 1 height = -45 1/4 feet

Day 2 height = -45 1/4 + 9 1/3

= - 181/4 + 28/3

= (-543 + 112) / 12

= -431/12

= -35 11/12 feet

Therefore, the height of the bottom of the hole after the second day is -35 11/12 feet

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he fourth constraint restricts the total length of the extra-large beams that are produced each week to 7,000 feet and it is given by$$\sum_{j=1}^3 x_{4j} \le 7000.$$

A linear programming problem can be formulated in order to address the machine scheduling problem as shown below:

Variables:$x_{ij}$ is the number of beams of size $i$ produced on machine $j$.Objective function:

The objective of the linear programming problem is to minimize the total weekly cost of using the machines,

which is given by$$\min 30\sum_{i=1}^4\sum_{j=1}^3x_{ij}+\min 50\sum_{i=1}^4\sum_{j=1}^3x_{ij}+\min 80\sum_{i=1}^4\sum_{j=1}^3x_{ij}$$Subject to:

The first constraint restricts the total length of the small beams that are produced each week to 12,000 feet and it is given by$$\sum_{j=1}^3 x_{1j} \le 12000.$$

The second constraint restricts the total length of the medium beams that are produced each week to 6,000 feet and it is given by$$\sum_{j=1}^3 x_{2j} \le 6000.$$

The third constraint restricts the total length of the large beams that are produced each week to 5,000 feet and it is given by$$\sum_{j=1}^3 x_{3j} \le 5000.

$$TThe fifth constraint restricts the number of hours that each machine is used to 50 and it is given by$$\sum_{i=1}^4 x_{ij} \le 50, \quad j = 1,2,3.$$

The last constraint specifies that $x_{ij} \ge 0$ for all $i$ and $j.$Thus, the linear program is given by\begin{align*}\min 30\sum_{i=1}^4\sum_{j=1}^3x_{ij}+\min 50\sum_{i=1}^4\sum_{j=1}^3x_{ij}+\min 80\sum_{i=1}^4\sum_{j=1}^3x_{ij}&\\\text{subject to}&&\\ \sum_{j=1}^3 x_{1j} &\le 12000,\\ \sum_{j=1}^3 x_{2j} &\le 6000,\\ \sum_{j=1}^3 x_{3j} &\le 5000,\\ \sum_{j=1}^3 x_{4j} &\le 7000,\\ \sum_{i=1}^4 x_{ij} &\le 50, &&j = 1,2,3,\\ x_{ij} &\ge 0 &&i = 1,2,3,4; j = 1,2,3.\end{align*}.

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The solution to the system of equations, y = -3x + 4 and y = 2x - 6 is: B.(2, -2).

The solution to the system of equations is a point with the coordinate, (x, y), which will make both equations true.

Given the system:

y = -3x + 4 --> eqn. 1

y = 2x - 6 --> eqn. 2

Therefore:

-3x + 4 = 2x - 6

Combine like terms

-3x - 2x = -4 - 6

-5x = -10

x = 2

Substitute x = 2 into equation 2:

y = 2(2) - 6

y = 4 - 6

y = -2

The solution is: B. (2, -2)

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Answer:

Step-by-step explanation:

Answer:

1/4 is your answer.

Step-by-step explanation:

The fraction 1/4 will let Edna find the x-coordinate for point H.

When the point is (x, y) and the two ends of the segment are (x1, y1) and (x2, y2), the following equation can be used:

x = x1 + [m / (m + n)] × (x2 - x1)

y = y2 + [m / (m + n) ] × (y2 - y1)

m:n is the ratio in which the point divides the line.

It is given that point H divides the line FG into two at the ratio of 1:3, where F and G are at (4, 9) and (7, 2) respectively.

Therefore, m = 1 and n = 3.

We can now use this to find the fraction. It is known that the formula for finding the fraction is m/m+n. Therefore, the fraction is:

m/m+n = 1/1+3

= 1/4

This is the fraction that can be used to find the coordinates of H. The fraction is 1/4.

Thus, we have found the fraction 1/4 will let Edna find the x-coordinate for point H. The correct answer is option A.

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Answer:

\(\large\boxed{\sf 64\ cm }\)

Step-by-step explanation:

Here it is given that the side of a square is 16cm , and we need to find the perimeter of the square .

As we know that ,

\(\sf\qquad\longrightarrow \bigg\lgroup Perimeter_{square} = 4(side) \bigg\rgroup\)

• On substituting the respective values ,

\(\sf\qquad\longrightarrow Perimeter = 4(side)\\ \\\)

\(\sf\qquad\longrightarrow Perimeter = 4\times 16cm \\\\\)

\(\sf\qquad\longrightarrow \pink{ Perimeter = 64cm } \)

Perimeter:-

\(\\ \rm\hookrightarrow 4a\)

\(\\ \rm\hookrightarrow 4(16)\)

\(\\ \rm\hookrightarrow 64cm\)

Answer:

36 is your least common denominator. Hope this helps

Step-by-step explanation: