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Answer:

a) $49,200

b)
Housing: $19,680

Food: $8,856

Transportation: $8,856

Other goods and services: $11,808

c) Average real salary is unchanged at $0

Step-by-step explanation:

Since salaries and expenses are reduced by 40% if any of the amounts was originally $x, the reduction is 40% of $x = 0.4x   (1% = 1/100)

Therefore reduced value = original value - reduction amount

= x - 0.4x

= 0.6x

Applying this to the various dollar values provided will help us answer the questions

Real income before reduction
= Salary - expenses

= 82,000 - (32,800 + 14,760 + 14,760 + 19,680)

= 0

So the average individual real income is $0

a) How much does the average individual now earn?
New salary = 0.6 x old salary
= 0.6 x $82,000
=  $49,200

b) How much does the average individual now spend on housing, food, transportation, and other goods and services?

Total expenses after reduction = $19,680 + $8,856 + $8,856 + $11,808

= $49,200

Real income after reduction of salary and expenses
= $49,200 - $49,200 = 0

So the average salary stays the same at $0

The rate of the slower car is 77km/hr

Velocity is the rate of change of displacement with time. It is measured in meter per second and it is a vector quantity.

velocity = displacement/time

displacement = velocity × time

represent the faster car by v1 and the slower car by v2

v1 = v2+16

V2 = v1-16

Total displacement = 680km

680 =( v1+V2)t

680 = (v1+V2)4

v1+v2 = 680/4

v2+16+v2 = 170

2v2 = 170-16

2v2 = 154

v2 = 154/2

v2 = 77km/hr

therefore the rate of the slower car is 77km/hr

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The requreid we can reject the null hypothesis and conclude that at least one of the desserts is significantly more popular than the others.

To conduct an ANOVA analysis, we need to calculate the mean and variance for each group, as well as the overall mean and variance.

Pies: Mean = (5+2+7+4+3)/5 = 4.2
Variance =[tex]((5-4.2)^2 + (2-4.2)^2 + (7-4.2)^2 + (4-4.2)^2 + (3-4.2)^2)/4[/tex]
               = 3.7

Similarly,

Cakes:
Mean =  5, Variance = 6.4

Cookies:
Mean =  6, Variance = 8.8

Overall mean =  5.1, Overall variance =5.1

To calculate the F-statistic, we need to use the formula,
F = (between-group variance)/(within-group variance).

Between-group variance [tex]= ((4.2-5.1)^2 + (5-5.1)^2 + (6-5.1)^2)*5 + ((5-5.1)^2 + (5-5.1)^2)*6 + ((6-5.1)^2)*7[/tex] =5.3

Within-group variance = (3.7+6.4+8.8)/14 = 0.8

F = 5.3/0.8 = 6.6

The appropriate statistic for an ANOVA analysis is the F-statistic. we can reject the null hypothesis and conclude that at least one of the desserts is significantly more popular than the others.

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Answer:

 5/6 - 4 1/2 = 10/3 = 3 1/3

Step-by-step explanation:

their was 10/3 punch left its also equivalent to 3 1/3

The measures of angles 1 and 2 are:

The two lines that go upwards are parallel lines, that means that angles 2 and the 135° one are alternate inverse angles, then these have the same measure:

m∠2 = 135°

And angle 2 and 1 are adjacent, then their measures add up to 180°, this means that:

135° + m∠1 = 180°

Solving that equation for the measure of angle 1 we will get:

m∠1 = 180° - 135° = 45°

These are the measures of the two angles we wanted.

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Answer: The probability that Chang gets dressed with a white shirt and tan pants is 25%.

Step-by-step explanation:Given that Chang has 2 shirts, a white one and a black one, and he also has 2 pairs of pants, one blue and one tan, to determine what is the probability, if Chang gets dressed in the dark, that he winds up wearing the white shirt and tan pants the following calculation must be performed:

Each shirt = 50% chance Each pants = 50% chance 0.50 x 0.50 = X0.25 = X Therefore, the probability that Chang gets dressed with a white shirt and tan pants is 25%.

yes, the answer is actually 180

The solution to the problem is that the number is 46.

In mathematics, expression is defined as the relationship of numbers, variables, and functions using mathematical signs such as addition, subtraction, multiplication, and division.

The equation that can be used to solve the problem is q - 22 = 24.

To solve this equation, we need to isolate q on one side of the equation.

q - 22 = 24

Adding 22 to both sides, we get:

q - 22 + 22 = 24 + 22

Simplifying, we get:

q = 46

Therefore, the solution to the problem is that the number is 46.

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You would end at the point (4, -4).

We have,

Starting at (-1, 2), moving down 6 units would take you to the point (-1, 2-6) = (-1, -4).

From there,

Moving right 5 units would take you to the point (-1+5, -4) = (4, -4).

Therefore,

You would end at the point (4, -4).

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is △ABC equilateral?  well, we dunno, however let's check for all sides' length.

[tex]~\hfill \stackrel{\textit{\large distance between 2 points}}{d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}}~\hfill~ \\\\[-0.35em] ~\dotfill\\\\ A(\stackrel{x_1}{-3}~,~\stackrel{y_1}{2})\qquad B(\stackrel{x_2}{-6}~,~\stackrel{y_2}{-2}) ~\hfill AB=\sqrt{(~~ -6- (-3)~~)^2 + (~~ -2- 2~~)^2} \\\\\\ ~\hfill AB=\sqrt{( -3)^2 + ( -4)^2} \implies AB=\sqrt{ 25 }\implies \boxed{AB=5}[/tex]

[tex]B(\stackrel{x_1}{-6}~,~\stackrel{y_1}{-2})\qquad C(\stackrel{x_2}{0}~,~\stackrel{y_2}{-2}) ~\hfill BC=\sqrt{(~~ 0- (-6)~~)^2 + (~~ -2- (-2)~~)^2} \\\\\\ ~\hfill BC=\sqrt{( 6)^2 + ( 0)^2} \implies BC=\sqrt{ 36 }\implies \boxed{BC=6} \\\\\\ C(\stackrel{x_1}{0}~,~\stackrel{y_1}{-2})\qquad A(\stackrel{x_2}{-3}~,~\stackrel{y_2}{2}) ~\hfill CA=\sqrt{(~~ -3- 0~~)^2 + (~~ 2- (-2)~~)^2} \\\\\\ ~\hfill CA=\sqrt{( -3)^2 + (4)^2} \implies CA=\sqrt{ 25 }\implies \boxed{CA=5}[/tex]

well, not quite.

The probability that a gorilla in this particular zoo will live between 14.3 and 19.4 years is 86% (or 0.86)

From the Empirical Rule, for a Normal Distribution, approximately:

68% of the data falls within one standard deviation of the mean

95% of the data falls within two standard deviations of the mean

99.7% of the data falls within three standard deviations of the mean

To estimate the probability of a gorilla living between 14.3 and 19.4 years, we first need to standardize these values by subtracting the mean and dividing by the standard deviation:

For 14.3 years: (14.3 - 16) / 1.7 = -1.18

For 19.4 years: (19.4 - 16) / 1.7 = 2

Now we can use a standard normal distribution table to find the probabilities associated with these z-scores:

The probability of a gorilla living less than 14.3 years is approximately the same as the probability of a standard normal variable being less than -1.18, which is about 0.12.

The probability of a gorilla living less than 19.4 years is approximately the same as the probability of a standard normal variable being less than 2, which is about 0.98.

Therefore, the probability of a gorilla living between 14.3 and 19.4 years is approximately the difference between these two probabilities: 0.98 - 0.12 = 0.86.

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The range of weights that one crate could weigh is between 127.6 and 154.8 pounds.

Harriet has 6 crates of watermelons.

Each crate alone weighs 17.8 pounds and contains between 32 and 36 watermelons.

The weight of each watermelon is between 3.9 and 4.3 pounds.

One crate of watermelons could weigh between 127.6 pounds

(6 crates x 32 watermelons x 3.9 pounds per watermelon + 17.8 pounds crate weight) and

154.8 pounds (6 crates x 36 watermelons x 4.3 pounds per watermelon + 17.8 pounds crate weight).

Therefore, the range of weights that one crate could weigh is between 127.6 and 154.8 pounds.

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Answer:

The equation Y=970(0.51)^x represents the percentage of change over time. As x increases, Y decreases due to the exponentiation of 0.51. This means that the percentage of change is decreasing over time.

For example, if we plug in x=1, the equation outputs Y=495.7, which represents a 49.43% decrease from the initial value of 970. As x continues to increase, the percentage of change decreases, approaching 0% but never quite reaching it.

Overall, this equation can be used to model a variety of situations where there is a gradual decrease in the percentage of change over time.

The three complex cube roots of w are:

Z1 = 5(cos(70°) + i * sin(70°))

Z2 = 5(cos(190°) + i * sin(190°))

Z3 = 5(cos(310°) + i * sin(310°))

Given that;

To find all the complex cube roots of ,

w = 125(cos 210 deg + i  sin 210 deg)

Now, We know that;

x = r cos θ

y = r sin θ

let's find the modulus of w:

|w| = sqrt(125)

     = 125

Now let's find the argument of w:

arg(w) = 210°

Next, let's find the principal cube root of w. We can do this by taking the cube root of the modulus and dividing the argument by 3:

w^(1/3) = 125^(1/3) (cos(210°)/3 + i sin(210°)/3)

Let's simplify this expression:

w^(1/3) = 5(cos(70°) + i * sin(70°))

Now let's find the other two cube roots. We can do this by adding multiples of 120° to the argument and dividing by 3:

w^(1/3) = 5(cos(70°) + i * sin(70°))

w^(1/3) = 5(cos(190°) + i * sin(190°))

w^(1/3) = 5(cos(310°) + i * sin(310°))

So the three complex cube roots of w are:

w^(1/3) = 5(cos(70°) + i * sin(70°))

w^(1/3) = 5(cos(190°) + i * sin(190°))

w^(1/3) = 5(cos(310°) + i * sin(310°))

Thus, The three complex cube roots of w are:

Z1 = 5(cos(70°) + i * sin(70°))

Z2 = 5(cos(190°) + i * sin(190°))

Z3 = 5(cos(310°) + i * sin(310°))

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An expression that correctly sets up the quadratic formula include the following: C. [tex]x = \frac{-(-2)\; \pm \;\sqrt{(-2)^2 - 4(1)(4)}}{2(1)}[/tex]

In Mathematics and Geometry, a quadratic equation can be defined as a mathematical expression that can be used to define and represent the relationship that exists between two or more variable on a graph.

In Mathematics, the standard form of a quadratic equation is represented by the following equation;

ax² + bx + c = 0

Mathematically, the quadratic formula is represented by this mathematical equation:

[tex]x = \frac{-b\; \pm \;\sqrt{b^2 - 4ac}}{2a}[/tex]

For the given quadratic equation x² + 1 =2x-3, we have:

x² - 2x + 1 + 3 =0

x² - 2x + 4 =0

[tex]x = \frac{-(-2)\; \pm \;\sqrt{(-2)^2 - 4(1)(4)}}{2(1)}[/tex]

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The radius of the circle P is 20 centimetres.

P is in the shape of a circle. Q is in the shape of a quarter circle of radius 20 cm.

The area of Q is 4 times the area of P. Therefore, the radius of circle P can be found as follows:

area of circle Q = πr² / 4

area of circle Q = 3.14 × 20² ÷ 4

area of circle Q = 3.14 × 400 / 4

area of circle Q = 314 cm²

Therefore,

Hence,

area of circle p = πr²

4(314) = 3.14 × r²

r² = 1256 / 3.14

r = √400

r = 20 cm

Therefore, the radius of the circle P is 20 cm.

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Answer: B

Step-by-step explanation:

10 + 22 can be simplified by adding 10 and 22 to get:

10 + 22 = 32

Now, let's check each expression to see which one is equivalent to 10 + 22 = 32:

A. 2(5 + 22) = 2(27) = 54

B. 2(5 + 11) = 2(16) = 32 (This expression is equivalent to 10 + 12)

C. 5(2 + 22) = 5(24) = 120

D. 5(2 + 4) = 5(6) = 30

So, the expression that is equivalent to 10 + 22 is B. 2(5 + 11) = 32.

To measure the bearing from A to  B  you can use the compass with the ruler.

To measure the bearing from B to A, place the thread from B to A, then place the compass and take you reading

To degree the bearing from A to B, take after these steps:

Lastly the bearing from A to B is the point measured clockwise from genuine north to the line between focuses A and B, communicated in degrees. Do the same for bearing from B to A

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The solution to the division is 9a² - 6a + 31 + [(-106a + 259)/(3a² + 2a - 7)].

We have to divide, 27 +  0a³ + 18a² - 2a  + 42 by 3a² + 2a - 7.

So,

                     9a² - 6a + 31

3a² + 2a - 7 ║27 +  0a³ + 18a² - 2a  + 42

                   -(27 + 18a³ - 63a²)

                  _________________  

                            - 18a³ + 81a² - 2a

                             -(-18a³ - 12a² + 42a)

                           ____________________

                                           93a²  - 44a + 42

                                         -(93a² + 62a - 217)

                                                    -106a +259

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The equation of the exponential function that has a y-intercept of 3 and a growth factor of 1.25 will be y = a(1.25)ˣ + 3.

Given that:

y-intercept, c = 3

Growth factor, r = 1.25

The exponent is given as,

y = a(b)ˣ + c           ...1

Put b = 1.25 and c = 3 in equation (1), then

y = a(1.25)ˣ + 3

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The number of second for Adrian to reach the school is A = 36 seconds

Given data ,

Let the speed of Adrian be 5 feet every 4 seconds

So , S = ( 5/4 ) feet/seconds

And , the distance to the school = 45 feer

So , the time taken by Adrian to reach the school is T

where T = distance / speed

T = 45 / ( 5/4 )

T = ( 45 / 5 ) x 4

T = 9 x 4 seconds

T = 36 seconds

Hence , the time is 36 seconds

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The value of z in the intersected secant and tangent is 57 degrees.

When a tangent and a secant intersect outside a circle then the measure of the angle formed is one-half the positive difference of the measures of the intercepted arcs.

A secant touches two point on a circle while a tangent touches one point on a circle.

Therefore,

z = 1 / 2 (156 - 42)

z = 1 / 2 (114)

z = 114 / 2

z = 57 degrees

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Answer:

v = -4

Step-by-step explanation:

2v + 7 = 3

Subtract 7 on both sides

2v = -4

Divided by 2 both sides

v = -4

The linear function which represents a slope of -3 as required in the task content is; A two column table with five rows. The first column, x, has the entries, negative 5, negative 1, 3, 7. The second column, y, has the entries, 32, 24, 16, 8.

It follows that the task requires that a linear function whose slope, i.e rate of change is -2 is to be determined.

Since slope is the rate of change in y with respect to x;

The required linear function is; A two column table with five rows. The first column, x, has the entries, -5, -1, 3, 7. The second column, y, has the entries, 32, 24, 16, 8 so that we have;

Slope = (24 - 32) / (-1 -(-5)) = -8 / 4 = -2.

Remarks: The complete question is such that the required slope is -2.

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Answer: the second option

Step-by-step explanation:

i took the assignment

A down payment on a loan is a payment made upfront by the borrower to reduce the amount of the loan.

The purpose of a down payment is to lower the overall cost of the loan and to reduce the lender's risk.

When you make a down payment on a loan, the amount you owe on the loan is reduced by that amount.

A down payment also reduces the lender's risk.

When you make a down payment, you are showing the lender that you are committed to repaying the loan.

If you default on the loan, the lender will be able to recoup some of their losses by selling the collateral (the car, in this example) that was used to secure the loan.

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The probability of landing on a 9 and then landing on a number less than 8 is 1/8

Given that a spinner, spined twice, we need to find the probability of landing on a 9 and then landing on a number less than 8,

So,

Probability = favorable outcomes / total outcomes

Therefore,

Favorable outcomes = 1 and 2

Total outcomes = 4

So,

P(landing on a 9 and then landing on a number less than 8) = 1/4 x 2/4

= 1/4 x 1/2 = 1/8

Hence, the probability of landing on a 9 and then landing on a number less than 8 is 1/8

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