True or False: If X Bin(n,p) with np > 10 and n(1 - p) > 10, then 2 = np(1-P) is approximately distributed as N(0,1).

The number of people that attended the game in each cost category is Faculty: 7,000,Alumni: 18,000,Public: 18,000,Veterans: 4,000

To determine the number of people that attended the game in each cost category,  to consider the given information and set up a system of equations to solve for the unknowns. Let's break down the problem step by step.

Let's denote the number of people in each cost category as follows:

Faculty: F

Alumni: A

Public: P

Veterans: V

The number of alumni is 11,000 more than the faculty, so we have the equation:

A = F + 11,000

The number of public plus alumni together was 10 times the number of veterans, so  the equation:

P + A = 10V

The number of faculty plus alumni together was the same as the number of veterans, so we have the equation:

F + A = V

The total number of people attending the game is the sum of the people in each category, so  the equation:

F + A + P + V = 100,000

Now, use these equations to solve for the unknowns.

First, substitute equation 1 into equations 2 and 3:

P + (F + 11,000) = 10V

F + (F + 11,000) = V

Simplify these equations:

P + F + 11,000 = 10V

2F + 11,000 = V

Next, substitute these equations into equation 4:

F + (F + 11,000) + P + (2F + 11,000) = 100,000

Simplify and combine like terms:

4F + 22,000 + P = 100,000

Subtract 22,000 from both sides:

4F + P = 78,000

Now a system of two equations:

P + F + 11,000 = 10V

4F + P = 78,000

solve this system of equations to find the values of F, P, and V.

By solving the system,

F = 7,000

P = 18,000

V = 4,000

Finally, substitute these values back into equation 1 to find the value of A:

A = F + 11,000 = 7,000 + 11,000 = 18,000

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Answer:

y = 4x  the pace is 4 minutes per mile

y = 3x the pace is 3 minutes per mile.

Step-by-step explanation:

The equation for the top graph is:

y = 4x  You find this by taking any point and putting it in the form y/x  For example the point (4,16) would be 16/4 = 4  or the point (10,40) would be 40/10 = 4.  The only point that you cannot use is the point (0,0)

and the equation for the bottom graph is:

y = 3x

The pace of the first equation is 4 minutes for each mile and the second equations pace is 3 minutes for each mile.

Answer:

2,-1

Step-by-step explanation:

You read the X axis first then the Y axis

Answer:

In 2020 the population will be 6,233.

Step-by-step explanation:

Giving the following information:

Present value (PV)= 5,600

Growth rate (g)= 1.8%

Number of periods= 6 years

To calculate the population in 2020, we need to use the following formula:

FV= PV*(1 + g)^n

FV= 5,600*(1.018^6)

FV= 6,232.67 = 6,233

In 2020 the population will be 6,233.

Answer:

F(x) = sqrt(x^2 + 3) ; g(x) = sqrt(X-2)

f(g(x))= √[{√(x-2)²+3}]

         =√[{x-2+3}]

         √(x+1)

Step-by-step explanation:

The number of units produced is increasing at a rate of 150 units per week, the rate of change of cost is 0.85 * 150 = $127.50 per week. The rate of change of profit is -$201,887.50 per week or -$5072.5 per unit per week.

(a) To find the rate of change of cost, we take the derivative of the cost equation with respect to x (units produced):

dC/dt = d(115,000 + 0.85x)/dt = 0.85

Since the number of units produced is increasing at a rate of 150 units per week, the rate of change of cost is 0.85 * 150 = $127.50 per week.

(b) To find the rate of change of revenue, we take the derivative of the revenue equation with respect to x:

dR/dt = d(240x - 101x^2)/dt = 240 - 202x

Substituting x = 1000 (current production), the rate of change of revenue is 240 - 202 * 1000 = -$201,760 per week.

(c) To find the rate of change of profit, we subtract the rate of change of cost from the rate of change of revenue:

dP/dt = dR/dt - dC/dt = (-$201,760) - ($127.50) = -$201,887.50 per week.

Therefore, the rate of change of profit is -$201,887.50 per week or -$5072.5 per unit per week.

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Answer: C

Step-by-step explanation:

Obtuse angles are greater than 90 degrees

The angle, in degrees, of the compass direction of a line connecting will be 53.9 degrees

Your entire distance from the beginning location is your hypotenuse.

We employ the hypotenuse formula because...

The Pythagoras theorem can be used to determine the length of the hypotenuse in a right triangle. According to the theory, the hypotenuse's square is equal to the sum of its two other sides' squares.

R2=A2+B2

R2=17.52+242R2

=306.25+576

R=√882.25

=29.7 meters

However, the assertion that R=A + B is incorrect (the assertion on the figure is FALSE!).

Your direction is northwest.

Now use trigonometry:

sinθ=B/R

sinθ=24/29.70

=0.808

θ=53.9 degrees. This is your angle.

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The correct format of the question is

After an​ accident, police can use the formula \(v=2\sqrt{5L }\) to estimate the​ speed, v, in miles per​ hour, that a car was traveling by measuring the length of the skid​ marks, L, in feet. Estimate the speed of a car that left skid marks 118 ft long. If the posted speed limit is 45 ​mi/h, was the car​ speeding? The speed of a car that left skid marks 118 ft long was about nothing ​mi/h.

Answer:

48.6mi/h, Yes the car was speeding.

Step-by-step explanation:

The speed of the car is given by  \(v=2\sqrt{5L }\)

Skid length (L) = 118ft

V= \(2\sqrt{5*118}\)

  = 2 \(\sqrt{590}\)  

  =  2*24.3

V = 48.6mi/h

Since the speed limit is 45mi/h and the velocity of this driver is 48.6mi/h it is clear that was speeding by 3.6mi/h over speed limit.

Answer:

Step-by-step explanation:

16, 18, 23, 25, 26, 34, 37, 37, 40, 41, 46

( 16 + 18 + 23 + 25 + 26 + 34 + 37 + 37 + 40 + 41 + 46 ) ÷ 11 = 31.181818...

mean ≈ 31

median = 34

mode = 37

100% is equal to the total earnings in a month which is $4000.So 33% is the rent so you say:

If 100%=4000

33%=?

[(33×4000)÷100]=$ 1320

Answer:

21x- 21

Step-by-step explanation:

7 × (x × 3 - 3)

7 × (3x - 3)

21x - 21

I'm not sure if the answer is correct

Answer:

151.4496 cm^2 is the area

It takes a machine at a seafood company 20 seconds to clean 3 pounds of shrimp. The rate of the machine is 0.15 pound per second

An equation is an expression that shows the relationship between two numbers and variables.

An independent variable is a variable that does not depend on any other variable for its value whereas a dependent variable is a variable that depend on any other variable for its value.

It takes a machine at a seafood company 20 seconds to clean 3 pounds of shrimp. Hence:

Rate of the machine = 3 pounds / 20 seconds = 0.15 pound per second

It takes a machine at a seafood company 20 seconds to clean 3 pounds of shrimp. The rate of the machine is 0.15 pound per second

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hello

if the sequence continues as 19, 13, 7, 1, - 5, ...

hence the formula for this sequence is:

n - 6

Answer:

its y=2

Step-by-step explanation:

The corresponding p-value for this statistic lies between 0.05 and 0.1.

The null hypothesis (H0) states that the mean daily food cost for two adults is $110 and H1 states that the mean daily food cost for two adults is greater than $110. This is a one tailed t-test.

We have a sample of size of 14 and the observed t-statistic is 1.76.

Degree of freedom, n = 14 - 1 = 13

Therefore, from t-table, p-value is between 0.1 and 0.05.

The small p-value implies that our null hypothesis is not probable and is thus rejected proving that the mean daily food cost for two adults is greater than $110.

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Answer: 12 refills

Step-by-step explanation:

y = 8.95 + 1.50x

26.95= 8.95 + 1.50x

26.95 - 8.95 = 1.50x

18 = 1.50X

18 / 1.50 = x

X = 12

The number of refills Jalisa purchased are 12.

Two or more expressions with an Equal sign is called as Equation.

Given that Long’s Coffee Shop sells a refill mug for $8.95.

Each refill costs $1.50. Last month,

Number of refills are denoted by x

Jalissa spent $26.95 on a mug and refills.

8.95 + 1.50x=26.95

Subtract 8.95 from both sides

1.50x  = 26.95 - 8.95

1.50x=18

Divide both sides by 1.5

x=18 / 1.50

x = 12

Hence, the number of refills Jalisa purchased are 12.

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The measure of \(\angle D\) is 13.

Vertical angles are formed when two lines meet each other at a point. They are always equal to each other.

given:

\(m\angle C=-3x+58\) and \(m\angle D=x-2\)

As, \(\angle C\) and \(\angle D\) are vertical angles

so,

\(m\angle C= m\angle D\)

\(-3x+58 = x-2\)

\(-3x -x = -2-58\)

\(-4x = -60\)

\(x= 15\)

So, \(m\angle D= x-2= 15-2 = 13\)

Hence, the value of \(m\angle D\) is 13.

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Answer:

11

Step-by-step explanation:

d=√(5-(-6))²+(-7-(-7))²

d=√(11²+0²)

d=11

Answer:

\(\boxed {\boxed {\sf d= 11}}\)

Step-by-step explanation:

We are asked to find the distance between 2 points. We will use the distance formula.

\(d= \sqrt{ (x_2-x_1)^2+(y_2-y_1)^2\)

In this formula, (x₁ , y₁) and (x₂ , y₂) are the points. We are given the points (-6, -7) and (5, -7). If we match the value and the corresponding variable, we see that:

Substitute these values into the formula.

\(d= \sqrt{(5- -6)^2 + (-7--7)^2\)

Solve inside the parentheses. Remember that two back-to-back negative signs become a plus sign.

\(d= \sqrt{ (11)^2+(0)^2\)

Solve the exponents.

\(d= \sqrt{(121)+(0)\)

Add.

\(d= \sqrt{121}\)

\(d=11\)

The distance between (-6, -7) and (5, -7) is 11.

Answer:

1+2=90° .so complementary angle

The mean of the given data is 291.67.2. The median of the given data is 250.3.

The revenue percent of each agency is as follows; Agency 1 - 31.43%, Agency 2 - 11.43%, Agency 3 - 5.71%, Agency 4 - 8.57%, Agency 5 - 20%, Agency 6 - 17.14%.

The arrival revenue for a few travel agencies are listed below:

a. Mean: To get the mean of the above data, we need to add all the data and divide it by the total number of data.

Mean = (550 + 200 + 100 + 150 + 350 + 300) ÷ 6

= 1750 ÷ 6

= 291.67

The mean of the given data is 291.67.

Median: To get the median of the above data, we need to sort the data in ascending order, then we take the middle value or average of middle values if there are even numbers of data.

When the data is sorted in ascending order, it becomes;

100, 150, 200, 300, 350, 550

The median of the given data is (200 + 300) ÷ 2= 250

The median of the given data is 250.

b. Total Revenue Percent = (Individual revenue ÷ Sum of total revenue) × 100%

For Agency 1 Total revenue = $550

Revenue percent = (550 ÷ 1750) × 100%

= 31.43%

For Agency 2 Total revenue = $200

Revenue percent = (200 ÷ 1750) × 100%

= 11.43%

For Agency 3 Total revenue = $100

Revenue percent = (100 ÷ 1750) × 100%

= 5.71%

For Agency 4 Total revenue = $150

Revenue percent = (150 ÷ 1750) × 100%

= 8.57%

For Agency 5 Total revenue = $350

Revenue percent = (350 ÷ 1750) × 100%

= 20%

For Agency 6 Total revenue = $300

Revenue percent = (300 ÷ 1750) × 100%

= 17.14%

Conclusion: 1. The mean of the given data is 291.67.2. The median of the given data is 250.3.

The revenue percent of each agency is as follows; Agency 1 - 31.43%, Agency 2 - 11.43%, Agency 3 - 5.71%, Agency 4 - 8.57%, Agency 5 - 20%, Agency 6 - 17.14%.

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Step-by-step explanation:

1/6y+ 1/6(y+12)-2

hope it helps !

Answer:

A choice.

Step-by-step explanation:

Irrational number is a number that cannot be written in a fraction form. All square roots are classified as an Irrational number unless can be evaluated to Rational number.

From A choice, you cannot evaluate the square root of 7 into any rational number. Therefore, it is an Irrational number.

B choice, even though there is a square root, but you can still evaluate from square root of 4 to 2.

For C and D, both are integers. Integers are classified to be Rational Number. Therefore, C and D both are rational.

The given statement "The mapping x T(S(x)) is a linear transformation from Rp to Rm"  is true. Because it satisfies the properties of linearity, as shown by the computation of T(S(cu + dv)).

To show that the mapping x → T(S(x)) is a linear transformation from Rp to Rm, we need to show that it satisfies the following two properties for all vectors x, y in Rp and all scalars c, d:

Additivity: T(S(cx + dy)) = cT(S(x)) + dT(S(y))

Homogeneity: T(S(cx)) = cT(S(x))

Let's first show the additivity property:

T(S(cx + dy)) = T(S(c(x) + d(y))) [Definition of vector addition]

= T(S(c x) + S(d y)) [By linearity of S]

= T(S(c x)) + T(S(d y)) [By linearity of T]

= c T(S(x)) + d T(S(y)) [By linearity of S and T]

Therefore, T(S(x)) satisfies the additivity property.

Now let's show the homogeneity property:

T(S(cx)) = T(S(c x)) [Definition of scalar multiplication]

= c T(S(x)) [By linearity of S and T]

Therefore, T(S(x)) satisfies the homogeneity property.

Since T(S(x)) satisfies both the additivity and homogeneity properties, it is a linear transformation from Rp to Rm.

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Answer:

\( \sqrt{48} \times \sqrt{3} \\ \sqrt{144} \\ 12\)

a. n-(n - 1) = 1

b. n( n - 1) = n² - n

c. (n - 1) + n = 2n - 1

d. (n - 1) + n = 2n - 1

General Rule for Equation Solving

Given two consecutive numbers , (n - 1) , n

simplifying :

n - (n - 1)

= n -1(n - 1)

= n - n + 1

= 1

multiplying :

n( n -1)

= n² - n

simplifying :

(n-1) + n

= n - 1 + n

= 2n -1

by adding two numbers :

(n - 1) + n

= n -1 + n

= 2n - 1

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Statistical process control technique that permits only 3.4 defects per million opportunities is Six Sigma.

Six Sigma is a statistical technique that emphasizes the necessity of a standardized approach to enhancing and optimizing the efficiency of the production and management processes by reducing the variation and waste within them. It concentrates on controlling a process to ensure that the results of a process are consistent and reliable by using statistical methods. The objective of the Six Sigma process is to produce 3.4 errors or defects per million opportunities. If the process is better than Six Sigma, it is considered more consistent and predictable.
Six Sigma's statistical approach to process control encompasses a range of tools and methods. Six Sigma's primary objective is to increase revenue and profits by developing and delivering high-quality products and services while eliminating defects and reducing waste.
Six Sigma aims to improve quality by detecting and reducing the reasons for variations in production processes. It accomplishes this by developing quality management practices that enable it to assess quality, establish goals, and implement best practices to achieve those goals.
In conclusion, Six Sigma is a process control approach that emphasizes statistical methods for process control and improvement. Six Sigma is used to reduce variability and eliminate waste, and its goal is to achieve 3.4 defects per million opportunities.

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Hence, in response to the provided question, we can say that As a result,  equation the inequality representing the amount of copies you can produce is: x ≤ 41.

A math equation is a mechanism for connecting statements and indicating equivalence with both the equals symbol (=). An equation is an algebraic claim that asserts the equivalency of two formulae in algebra. In the calculation 3x + 5 = 14, for example, the equivalence sign separates the numbers 3x + 5 and 14. To explain the relationship among the two words on each surface of a letter, a formula can really be employed. The software and the logo are usually interchangeable. For instance, 2x - 4 equals 2.

Let x represent the number of copies that can be made. The cost of x copies is $0.30x.

$0.30x ≤ $12.50

To find x, we must divide both sides by $0.30:

x ≤ $12.50 ÷ $0.30

x ≤ 41.67

Because you cannot manufacture a fraction of a copy, the most you can afford to make is 41 copies.

As a result, the inequality representing the amount of copies you can produce is:

x ≤ 41.

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The rate of change remains the same over the mentioned intervals, function f cannot be quadratic or exponential.

Hence, it can be concluded that function f is a linear function.

Based on the given information that the rate of change of function f is the same from x = -9 to x = -4 as it is from x = 1 to x = 6, we can conclude that function f is a linear function.

A linear function is characterized by a constant rate of change, meaning that the change in the function's value is consistent over any given interval.

In this case, the rate of change remains the same from x = -9 to x = -4 and from x = 1 to x = 6.

On the other hand, a quadratic function is characterized by a changing rate of change, meaning that the function's value changes at an increasing or decreasing rate over different intervals.

An exponential function, on the other hand, exhibits a rapid growth or decay with an increasing rate of change.

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