Data were collected on income (in dollars) for a random sample of 490 residents in a city. The mean income was 42200 with a standard deviation of 7200. The data were positively skewed.
(a) Would the median income be higher or lower than 42200 dollars?
A. The median income is higher.
B. The mean and median incomes are the same.
C. The median income is lower
D. Insufficient information to determine.
(b) What is the standardized score (z-score) for an income value of 34500?
A. -1.06944444444444
B. 1.06944444444444
C. -15.7142857142857
D. Standardized score cannot be computed because the distribution is skewed.
(c) Suppose that you express all values in the data in thousand dollars. What would the resulting mean income be?
A. 422
B. 4.22
C. 42.2
D. None of the above.

Answer:

31

Step-by-step explanation:

The solution of expression 20 divided by cos70° is,

⇒ 20 divided by cos70° = 58.82

We have to given that,

A number 20 divided by cos70°.

We can simplify the expression as,

20 divided by cos70°

⇒ 20 ÷ cos 70°

⇒ 20 / cos 70°

⇒ 20 / 0.34

⇒ 20 x 100 / 0.34x100

⇒ 2000/34

⇒ 58.82

Therefore, The solution of expression 20 divided by cos70° is,

⇒ 20 divided by cos70° = 58.82

Learn more about the divide visit:

https://brainly.com/question/28119824

#SPJ6

The given demand function is x = 300 - p - p = $5(4p)^(1.13), where x represents the quantity demanded and p represents the price. To find the rate of change in demand x with respect to price p, we need to take the derivative of the demand function with respect to p.

We use the power rule of differentiation and the chain rule to differentiate the given demand function. The derivative is dx/dp = -1 - 51.13(4p)^0.13. We plug in the price p = 5 to get the rate of change in demand x for a price of $5, which is approximately -9.27 units per dollar. This means that if the price increases by $1, the quantity demanded will decrease by approximately 9.27 units. Similarly, if the price decreases by $1, the quantity demanded will increase by approximately 9.27 units.

In summary, the rate of change in demand gives us information about how sensitive the quantity demanded is to changes in price. A larger absolute value of the rate of change indicates a higher degree of sensitivity, or elasticity, of demand to price changes.

Learn more about function here:

https://brainly.com/question/30721594

#SPJ11

Answer:

$8

Step-by-step explanation:

First we have to see how much you are paid per car. To do this we divide the money earned ($20), by the number of cars washed (5).

20÷5=4

This tells us you earn $4 per car. So, to find the amount you would earn buy washing 2 cars, you multiply the money earned per car by 2.

4·2=8

This means you would earn $8.

Would you please mark my answer brainliest if it helped you? :D

With linear relationship, His rate is 7 hot dogs per minute. The number of hot dogs he eat every 3 minutes is 21 hot dogs. He have eaten hot dogs 13 minutes after you arrive is 95 hot dogs.

A straight-line link between two variables is referred to statistically as a linear relationship (or linear association). Both a graphical representation of a linear relationship, in which the variable and constant are connected by a straight line, and a mathematical representation, in which the dependent variable is determined by multiplying the independent variable by the slope coefficient and a constant.

A polynomial or non-linear (curved) relationship can be contrasted with a linear relationship.

The given parameters are;

Number of hot dogs Uncle Blake has eaten after 4 minutes = 32 hot dogs

Number of hot dogs eaten after 10 minutes = 74 hot dogs

Therefore, we have that the points on a graph of hot dog eaten are;

(4, 32), and (10, 74)

Which gives;

The rate of hot dogs eats = (74-32)/(10-4)

The rate of hot dogs eats = 42/6

His rate is 7 hot dogs/minute

He eat hot dogs in every 3 minutes

n = 7.t

n = 7.3

n = 21

The equation to calculate hot dogs eaten in times after our arrival is

n - 32 = 7·(t - 4)

n = 7·t - 28 + 32

n = 7·t + 4

He have eaten hot dogs 13 minutes after our arrive

n = 7·t + 4

n = 7*13 + 4

n = 91 + 4

n = 95

The number of hot dog he had eaten after 13 minutes at our arrival = 95 hot dogs

To learn more about linear relationship visit:

https://brainly.com/question/25678940

#SPJ4

Answer: y = -2x + 8

Step-by-step explanation:

gradient = change in y/ change in x = 8/-4 = -2

y = -2x + c

substitute values in

8 = 0 + c

c = 8

y = -2x + 8

The graph of a line passes through the points (0, 8) and (4, 0), the equation of the line is y = -2x + 8

The line is the distance between two points. The equation of a line in slope-intercept form is y = mx + b

Slope = -8/4
Slope = -2

Determine the y-intercept

Since the y-intercept is the point where the line cross the y-axis, hence b = 8.

FInd the required equation

y = -2x + 8

Hence if the graph of a line passes through the points (0, 8) and (4, 0), the equation of the line is y = -2x + 8

Learn more on equation of a line here: https://brainly.com/question/18831322

The congressional decision to fund an authorized program with a specific sum of money is called an appropriation.Appropriations play a significant role in shaping government spending and implementing policies and programs.

An appropriation refers to the act of setting aside a specific amount of funds by Congress for a particular purpose or program. It is a legislative action that determines the amount of money allocated to support authorized activities or initiatives. When Congress passes an appropriation bill, it authorizes the expenditure of funds for specific programs or agencies. This decision is crucial in the budgeting process, as it determines the financial resources available for various government programs and ensures that authorized activities receive the necessary funding.

Learn more about appropriation bill here:

https://brainly.com/question/29254157

#SPJ11

The velocity of a particle when it moves on a straight line along the x-axis will be V= 42 m/s

Velocity is defined as the ratio of the distance moved by the object in a particular time. The velocity is a vector quantity so it needs both the magnitude and the direction.  

Here we have a displacement function:-

F(t)=3t⁴-5t³+6t-7

So to find out the velocity we will differentiate the above equation with respect to t.

d(F(t)/dt=12t³-15t²+6

V=12t³-15t²+6

Put the value of t=2 seconds

V=12x(2x2x2)-15x(2x2)+6

V=42 meters per second

Hence the velocity of a particle when it moves on a straight line along the x-axis will be V= 42 m/s

To know more about Velocity follow

https://brainly.com/question/25749514

#SPJ1

By Completing the square method, the value of y = 1.6i +0.7

The given quadratic equation is 40y²-56y=-124

So, we have :

40y²-56y=-124

40y²-56y + 124 = 0

Dividing the whole equation by 4, we get:

10y² - 14y + 31 = 0

Now, Dividing the whole equation by 10, we get:

\(y^{2} - \frac{7}{5} y+ \frac{31}{10} = 0\)

By completing the square method,

Adding and Subtracting \(\frac{7^{2} }{10^{2} } = \frac{49}{100}\) to the equation, we get:

\(y^{2} - \frac{7}{5} y+ \frac{31}{10} + \frac{49}{100} - \frac{49}{100} = 0\\\\y^{2} - \frac{7}5y} +\frac{49}{100} + (\frac{31}{10} -\frac{49}{100} ) =0\\\)

\((y -\frac{7}{10} )^{2} +\frac{261}{100} =0\)

\((y -\frac{7}{10} )^{2}= -\frac{261}{100} \\\\(y -\frac{7}{10} )^{2}= -2.61\\\\(y -\frac{7}{10} ) = 1.61i\\\\y = 1.6i +0.7\)

Hence, the value of y = 1.6i +0.7

To read more about Completing the square method, visit  https://brainly.com/question/4822356

#SPJ9

Answer:

3

Step-by-step explanation:

.......................

Answer:

3

Step-by-step explanation:

The formula of to calculate slope of a linear function is

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

where m is the slope and so lets take any two points from the table to calculate the slope. Lets take,

(0 , 4) and (1 , 7) and lets plug it in the formula

\(m=\frac{y_2-y_1}{x_2-x_1}\\\\m=\frac{7-4}{1-0}\\\\m=3\)

So the slope of the function is 3

To find the displacement and total distance traveled by the object from t=0 to t=6, we need to integrate the velocity function over the given time interval.

The displacement can be found by integrating the velocity function v(t) with respect to t over the interval [0, 6]. The integral of v(t) represents the net change in position of the object during this time interval.

The total distance traveled can be determined by considering the absolute value of the velocity function over the interval [0, 6]. This accounts for both the forward and backward movements of the object.

Now, let's calculate the displacement and total distance traveled using the given velocity function v(t) = t^2 - (1/t) - 12 over the interval [0, 6].

To find the displacement, we integrate the velocity function as follows:

Displacement = ∫[0,6] (t^2 - (1/t) - 12) dt.

To find the total distance traveled, we integrate the absolute value of the velocity function as follows:

Total distance = ∫[0,6] |t^2 - (1/t) - 12| dt.

By evaluating these integrals, we can determine the displacement and total distance traveled by the object from t=0 to t=6.

Learn more about Velocity here:

brainly.com/question/31968174

#SPJ11

The possible approximate lengths of b are: 2.3 units and 7.8 units

We know that the law of sines for triangle is:

The ratios of the length of all sides of a triangle to the sine of the respective opposite angles are in proportion.

This means, for triangle ABC,

\(\frac{sin~ A}{a} =\frac{sin~B}{b} =\frac{sin~ C}{c}\)

where a is the length of side BC,

b is the length of side AC,

c is the length of side AB.

For triangle ABC consider an equation from sine law,

\(\frac{sin~ A}{a} =\frac{sin~ C}{c}\)

here, c = 5.4, a = 3.3, and m∠A = 20°

\(\frac{sin~ 20}{3.3} =\frac{sin~ C}{5.4}\\\\\frac{0.3420}{3.3} =\frac{sin~ C}{5.4}\)

0.3420 × 5.4 = 3.3 × sin(C)

sin(C) = 0.5596

∠C = arcsin(0.5596)

∠C = 34.03°  OR 145.9°

∠C ≈ 34° OR 146°

We know that the sum of all angles of triangle is 180 degrees.

so, ∠A + ∠B + ∠C = 180°

when m∠C = 34°,

20° + ∠B + 34.03° = 180°

∠B = 125.97°

m∠B = 126°

when m∠C = 146°,

20° + ∠B + 146° = 180°

m∠B = 14°

Now consider equation,

\(\frac{sin~ A}{a} =\frac{sin~ B}{b}\\\\\frac{sin~20^{\circ}}{3.3} =\frac{sin~ 126^{\circ}}{b}\)

b × 0.3420 = 0.8090 × 3.3

b = 7.8 units

when m∠B = 14°,

\(\frac{sin~20^{\circ}}{3.3} =\frac{sin~ 14^{\circ}}{b}\)

b × 0.3420 = 0.2419 × 3.3

b = 2.3 units

Learn more about the law of sines here:

https://brainly.com/question/17289163

#SPJ4

The complete question is:

Law of sines: StartFraction sine (uppercase A) Over a EndFraction = StartFraction sine (uppercase B) Over b EndFraction = StartFraction sine (uppercase C) Over c EndFraction

In ΔABC, c = 5.4, a = 3.3, and measure of angle A = 20 degrees. What are the possible approximate lengths of b? Use the law of sines to find the answer.

2.0 units and 4.6 units

2.1 units and 8.7 units

2.3 units and 7.8 units

2.6 units and 6.6 units

Answer:

134

Step-by-step explanation:

268/2=134

since its equal both rows should have the same number.

The answers are, a) -2x² + 28x - 35, b) x = 7, c) p = $50 and d) P = $63

a) The profit function P(x) is given by the difference between the revenue function R(x) and the cost function C(x):

R(x) = p(x) · x

P(x) = R(x) - C(x)

First, let's substitute the given price function p(x) = 64 - 2x into the revenue function:

R(x) = (64 - 2x) · x

= 64x - 2x²

Now, substitute the cost function C(x) = 35 + 36x into the profit function:

P(x) = R(x) - C(x)

= (64x - 2x²) - (35 + 36x)

= 64x - 2x² - 35 - 36x

= -2x² + 28x - 35

b) To find the number of units that produces the maximum profit, we need to find the value of x that maximizes the profit function P(x).

This can be done by finding the vertex of the parabola represented by the quadratic function P(x) = -2x² + 28x - 35.

The x-coordinate of the vertex of a quadratic function in the form P(x) = ax² + bx + c is given by:

x = -b / (2a)

In this case, a = -2, b = 28, and c = -35:

x = -b / (2a)

= -28 / (2 · -2)

= -28 / -4

= 7

Therefore, the number of units that produces maximum profit is x = 7.

c) To find the price per unit that produces maximum profit, we can substitute the value x = 7 into the price function p(x) = 64 - 2x:

p = 64 - 2x

= 64 - 2 · 7

= 64 - 14

= 50

Therefore, the price per unit that produces maximum profit is p = $50.

d) To find the maximum profit, we substitute the value x = 7 into the profit function P(x):

P(x) = -2x² + 28x - 35

= -2 · 7² + 28 · 7 - 35

= -2 · 49 + 196 - 35

= -98 + 196 - 35

= 63

Therefore, the maximum profit is P = $63.

Learn more about function click;

https://brainly.com/question/30721594

#SPJ1

Answer:

No

Step-by-step explanation:

As you probably know, triangles have 3 sides. The longest side is called the hypotenuse. In this case, the hypotenuse is 10.3. Now, you might or might not know the pythagorean theorem, which states that the a² + b² =c ².

In this case, we can say that 4.4 is a and 8.3 is b. Now if we square 4.4 and add it to 8.3 squared, we get 88.25. However, if you square 10.3, you get 106.09. Thus, the values cannot be this way. So, your answer is no.

Answer:

\( \huge{ \orange{y + 3 = 2(x + 7)}}\)

Step-by-step explanation:

To find an equation of a line in point slope form when given the slope and a point we use the formula

\(y - y_1 = m(x - x_1) \\ \)

where

m is the slope

( x1 , y1) is the point

From the question we have

\(y - - 3 = 2(x - - 7) \\ y + 3 = 2(x + 7)\)

Hope this helps you

The correct option is False. The standard formulas for the derivatives of sine and cosine are true when the angle is in radians. These formulas are derived based on the properties of the trigonometric functions in the context of radians. The derivatives of sine and cosine with respect to an angle measured in radians are as follows:

\(\[\frac{d}{dx}(\sin(x)) = \cos(x)\]\)

\(\[\frac{d}{dx}(\cos(x)) = -\sin(x)\]\)

If the angle is measured in degrees, these formulas would not hold true. To differentiate trigonometric functions when the angle is measured in degrees, conversion factors and additional adjustments would be necessary.

To know more about functions visit-

brainly.com/question/2273042

#SPJ11

The correct inequality is \(40n-240>160:n>10 months\)

It is given that Albert has saved $\(720\), and every month he saves $\(80\) more. John has saved $\(480\), and every month he saves $\(120\) more.

We will solve this problem using Arithmetic progression

For Albert:

\(a_{m}=720,d=80\\a_{n} =720+80n,n>m\)

For John:

\(a_{m} =480,d=120\\a_{n} =480+120n,n>m\)

John saved money=\(160\) more than Albert

\(480+120n-(720+80n)>160\\-240+40n>160\\40n-240>160:n>10 months\)

Therefore the correct inequality is \(40n-240>160:n>10 months\)

Learn  more about Arithmetic progression from here:

https://brainly.in/question/22234492

Answer:

She earned 1,076 dollars and 25 cents.

Step-by-step explanation:

x =  7.25 * 4,500 / 100

x = 7.25 * 45

x = 326.25

So commission earned is 326.25 $

We need to add this to her base salary for the week, so:

750 + 326.25 = 1, 076.25

Therefore she earned 1,076 dollars and 25 cents.

Hopes this helps ;p

Answer: false

Step-by-step explanation:

False

To determine the fair amount the player should win, we need to calculate the probability of drawing a diamond from a standard 52-card deck. There are 13 diamonds in a deck, and 52 total cards, so the probability of drawing a diamond is 13/52, or 1/4. This means that there is a 25% chance of winning the game.
To make the game fair, the expected value of the game must be zero. The expected value is calculated by multiplying the amount won by the probability of winning, and subtracting the amount lost by the probability of losing. In this case, the amount lost is $52, and the probability of losing is 75%, or 3/4.
So, the expected value equation would be:
0 = (amount won)(1/4) - ($52)(3/4)
Solving for the amount won, we get:
Amount won = $208/1 = $208
Therefore, in order for this game to be fair, the player should win $208 when they draw a diamond. This makes the expected value of the game zero, ensuring that it is a fair game for both the player and the house.
Answer more than 100 words: To summarize, the amount the player should win in order for the game to be fair is $208. This calculation is based on the probability of drawing a diamond from a standard 52-card deck, which is 1/4 or 25%. By calculating the expected value of the game, we can determine the amount the player should win in order for the game to be fair. The expected value equation takes into account both the probability of winning and the amount lost when losing. By setting the expected value equal to zero and solving for the amount won, we can determine the fair amount the player should win. This ensures that the game is fair for both the player and the house, as the expected value is zero.
In a fair game, the expected value of the game should be zero, meaning the player neither wins nor loses money on average. To determine the winning amount, let's analyze the probabilities and outcomes of the game.
A standard 52-card deck has 13 diamonds and 39 non-diamond cards. The probability of drawing a diamond is 13/52 or 1/4, and the probability of drawing a non-diamond is 39/52 or 3/4. If the player loses, they lose $52.
Let X be the winning amount if the player draws a diamond. The expected value (EV) is given by:
EV = (probability of winning) * (winning amount) + (probability of losing) * (losing amount)
Since the game is fair, EV = 0. Therefore:
0 = (1/4) * X + (3/4) * (-52)
To solve for X, multiply both sides by 4:
0 = X - 3 * 52
Now, add 3 * 52 to both sides to find the winning amount:
X = 3 * 52
X = $156
In order for this game to be fair, the player should win $156 when they draw a diamond.

To know more about Deck visit:

https://brainly.com/question/20362559

#SPJ11

The statement "Integration by parts can only be used when there is a polynomial or exponential" is false. Integration by parts is a technique in calculus that can be applied to a wide range of functions beyond polynomials and exponentials.

Integration by parts is a method used to evaluate integrals that involve the product of two functions. It is based on the product rule for differentiation. While it is commonly used with polynomials and exponentials due to their simple derivative and antiderivative properties, integration by parts can be used with other types of functions as well.

The technique of integration by parts can be applied to functions that are differentiable or have well-defined antiderivatives. It involves selecting one function to differentiate and another function to integrate. The choice of functions depends on their properties and simplification of the resulting integral.

Functions such as trigonometric functions, logarithmic functions, inverse trigonometric functions, and more can also be integrated using the integration by parts method. Therefore, integration by parts is not limited to only polynomials or exponentials, but can be applied to a wide range of functions in calculus.

Learn more about calculus here:

https://brainly.com/question/22810844

#SPJ11

Answers:

18:12

3:2

Step-by-step explanation:

9:6 = 9 * 2 : 6 * 2 = 18:12

9:6 = 9/3 : 6/3 = 3:2

Hope this helps.

Check the picture below.

Notice it's simply a 5x4 rectangle, and surely you know how to get its area.

Answer:

12 is 1/5 of 60

Step-by-step explanation:

12 x 5 is 60.

Answer:

1 25/ 26

2 3/4

3 35/24

6 9/2

8 2/5

Step-by-step explanation:

The required original price of the coat is given as £95.

The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.

here,
let the original price of the coat be x,
According to the question
x - 17% of x = 78.85
x - 0.17x = 78.85
0.83x = 78.85
x = 78.85 / 0.83
x = £95

Hence, the cost of the coat before the sale is £95.

Learn more about percentages here:

brainly.com/question/13450942

#SPJ1