PLEASE SHOW WORK!!!!!!!!!

For a randomly chosen family in the suburb, the probability of having an income between $60,000 and $72,000 is 40%. This is because 40% of all families in the suburb have incomes above $72,000, and the median income for all families in the suburb is $60,000.

Therefore, the probability of having an income between [tex]$60,000[/tex] and $72,000 is 40%.

This information can also be interpreted in a graphical representation. The graph will have a vertical line at $60,000 and a horizontal line at 40%. The area between these two lines will represent the probability of having an income between $60,000 and $72,000, which is 40%.

In conclusion, for a randomly chosen family in the suburb, the probability of having an income between $60,000 and $72,000 is 40%.

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1) The ball bounced 0.125 feet high on its 10th bounce.

2) The total distance traveled by the ball by the time it reached its peak after its 10th bounce is 255.75 feet.

3) If Bobo drops his magic ball from the top of the Empire State Building, the ball will have traveled 382 feet by the time it hits the pavement for the 7th time.

1) To find out how high the ball bounced on its 10th bounce, we can use the fact that the ball always bounces to half its previous height. We can start by finding the height of the first bounce, which we know is 64 feet since that's the height of the building. Then, we can keep dividing by 2 to find the height of each subsequent bounce. So, the height of the 2nd bounce is 32 feet, the height of the 3rd bounce is 16 feet, and so on. Continuing this pattern, we can find that the height of the 10th bounce is:

64 feet / 2^(10-1) = 64 feet / 512 = 0.125 feet

2) To find out how far the ball had traveled altogether by the time it reached its peak after its 10th bounce, we can use the fact that the distance traveled is equal to the sum of the distances of each bounce. The distance of each bounce is equal to twice the height of the bounce (since the ball travels up and then back down). So, the distance of the first bounce is 264 = 128 feet. The distance of the second bounce is 232 = 64 feet, and so on. Continuing this pattern, we can find that the distance of the 10th bounce is:

2×0.125 = 0.25 feet

So the total distance traveled by the ball by the time it reached its peak after its 10th bounce is:

128 + 64 + 32 + 16 + 8 + 4 + 2 + 1 + 0.5 + 0.25 = 255.75 feet

3) We know that the height of each bounce is half the height of the previous bounce, so we can use this to find the height of the 7th bounce. Starting with the height of the first bounce (which is the height of the Empire State Building), we can keep dividing by 2 to find the height of each subsequent bounce. So, the height of the 2nd bounce is 64/2 = 32 feet, the height of the 3rd bounce is 32/2 = 16 feet, and so on. Continuing this pattern, we can find that the height of the 7th bounce is:

64/2^(7-1) = 1 foot

Since the ball bounces up and down, it travels twice the height of each bounce. So, the distance traveled by the ball on each bounce is 2 feet. To find out how far the ball will have traveled by the time it hits the pavement for the 7th time, we can add up the distances traveled on the first 7 bounces:

2×(64 + 32 + 16 + 8 + 4 + 2 + 1) = 382 feet

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Answer:

this is actually about derivatives,

the answer would be simply 10x-6

The algebraic expressions that are polynomials are:

1. 2x³ -/-/-

2. 0x³y - 3x² + 6x

3. -x + √6

Polynomials are a type of algebraic expression that consists of variables and coefficients, combined using mathematical operations of addition, subtraction, and multiplication, and non-negative integer exponents. The term "poly" means many, and "nomial" means term. Hence, a polynomial is a sum of many terms.

Algebraic expressions are mathematical expressions that consist of variables, constants, and mathematical operations such as addition, subtraction, multiplication, division, and exponentiation. Algebraic expressions are used in algebra to represent relationships between variables and to solve mathematical problems.

The algebraic expressions that are polynomials are:

1. 2x³ -/-/- (a polynomial of degree 3)

2. 0x³y - 3x² + 6x (a polynomial of degree 3)

3. -x + √6 (a polynomial of degree 1)

The expressions that are not polynomials are:

1. y² + 5y -√3 (not a polynomial because it contains a square root)

2. 02-√4x (not a polynomial because it contains a square root)

3. 0-32³-12-2²+1 (not a polynomial because it contains a negative exponent)

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If a large diamond with a mass of 4289.6 grams was recently discovered in a mine and the density of the diamond is 3.51 grams over centimeters cubed, the volume is 1221.9 cm³.

To find the volume of the diamond, we need to use its mass and density. The density of the diamond is given as 3.51 grams per cubic centimeter. This means that every cubic centimeter of diamond has a mass of 3.51 grams.

We can use this information to find the volume of the diamond by dividing its mass by its density. Plugging in the given values, we get:

Volume = Mass / Density

Volume = 4289.6 g / 3.51 g/cm³

Volume = 1221.86 cm³

This means that the diamond has a volume of 1221.86 cubic centimeters. However, the question asks us to round the answer to the nearest hundredth, so we round this value to: Volume = 1221.9 cm³

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Step-by-step explanation:

If I=Prt

I is interest earned

P is principal

R is the interest rate

T is time in years

Then substitute the values into the equation

Plug into your calculator

I= 100 x 6% x 3 = 18

Answer for the first one is $18

For the others, it requires you to rearrange the equation.

Good luck!

Existence and uniqueness of solutions to systems of differential equations depend on the number of equations and the order of each equation. For example, a system of two first-order equations has a unique solution, while a system of three first-order equations may not have a unique solution.

Previously, we considered the scalar differential equation, which is a single differential equation involving only one independent variable. In this case, the solution to the equation is unique. This is because there is only one equation and only one variable, so the solution must be unique for a given set of initial conditions.

For a system of differential equations, the existence and uniqueness of solutions depend on the number of equations and the order of each equation.

Systems of differential equations with higher order equations or more equations than unknowns may not have a unique solution. On the other hand, if there are more unknowns than equations, then there is always a unique solution. To find the solution, the equations must be solved simultaneously.

In conclusion, A scalar differential equation always has a unique solution.

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Answer:

b.0.45

Step-by-step explanation:

Answer: B 0.45  

0.42 < 0.45  

Step-by-step explanation:

The lower bound of the mass at the end of the experiment is 65.25 g and the upper bound is 64.25 g.

To calculate the lower and upper bounds of the mass of the chemicals at the end of the experiment, we need to take into account the uncertainty in the initial mass and the change in mass.

The initial mass of the chemicals is given as 73 g, rounded to 2 significant figures. This means that the actual value of the initial mass could lie anywhere between 72.5 g and 73.4 g, since the last significant digit (the 3) is uncertain.

Similarly, the change in mass during the experiment is given as 8.2 g, rounded to 2 significant figures. This means that the actual value of the change in mass could lie anywhere between 8.15 g and 8.25 g.

To find the lower bound of the mass at the end of the experiment, we assume that the initial mass was at its upper bound (73.4 g) and the change in mass was at its lower bound (8.15 g):

Lower bound = 73.4 g - 8.15 g = 65.25 g

To find the upper bound of the mass at the end of the experiment, we assume that the initial mass was at its lower bound (72.5 g) and the change in mass was at its upper bound (8.25 g):

Upper bound = 72.5 g - 8.25 g = 64.25 g

Therefore, the lower bound of the mass at the end of the experiment is 65.25 g and the upper bound is 64.25 g.

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Akio is a public communication specialist with skill sets to influence and raise awareness for public.

What do you mean by public communication specialist?

Specialists in public-relations develop and uphold a positive public image for the people, groups, or organisations they represent. To influence how the public perceives their clients and to raise awareness of each client's efforts and objectives, they prepare press releases and create social media strategies.

Public relations, information output, and media requests are handled by communications specialists. They can also plan an organization's social media or advertising campaigns.

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Ruth will need 30 lemons to make lemonade with 10 cups of water.

Ruth is making Lemonade. For 1 cup of water she uses 3 lemins, for 2 cups 6 lemons, ect. The formula to calculate the number of lemons needed for a given cups of water is:

Lemons = 3 × Cups of Water

Therefore, the number of lemons needed for 10 cups of water is:

Lemons = 3 × 10

Lemons = 30

Hence, Ruth will need 30 lemons to make lemonade with 10 cups of water.

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Answer:

20

Step-by-step explanation:

[tex]55% of a number = 11[/tex]% of a number = 11

[tex]\frac{55}{100} * x = 11[/tex]

solve for x

[tex]55x = 1100[/tex]

[tex]x = 20[/tex]

Hope this helps!

Answer:20

Step-by-step explanation:

55%---------11

100%------x

x=100*11/55=20

The constraints as a system of linear inequalities include the following;

x + y ≤ 180

x ≥ 40

y ≥ 40

3x + 4y ≤ 640

75x + 60y ≤ 12,900

The solution set for the system of linear inequalities is shown in the coordinate plane below.

In order to write a system of linear inequalities to describe this situation, we would assign variables to the number of SOS Smartcall produced in one day and number of SOS Basic produced in one day respectively, and then translate the word problem into algebraic equation as follows:

Based on the information provided about this cell phone company, the constraints can be written as a system of linear inequalities as follows;

x + y ≤ 180

x ≥ 40

y ≥ 40

3x + 4y ≤ 640.

75x + 60y ≤ 12,900

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The comparison operator (<) can be overloaded for a class as a function in all three ways: member, friend, and global (non-member, non-friend). Therefore, the correct answer is e. all three (a, b, and c).

When overloading the comparison operator (<) as a member function, it is defined within the class and has access to all the members and functions of the class.

When overloading the comparison operator (<) as a friend function, it is defined outside of the class but is given access to all the members and functions of the class.

When overloading the comparison operator (<) as a global (non-member, non-friend) function, it is defined outside of the class and does not have access to the members and functions of the class. However, it can still be used to compare objects of the class by using the accessor functions defined for the class.

The comparison operator (<) can be overloaded for a class as a function in all three ways: member, friend, and global (non-member, non-friend).

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The customer will pay R108 for the screwdriver set.The trader bought a screwdriver set for R90 and added 20% to the cost price for profit and expenses. To calculate the amount a customer will pay for the screwdriver set, we need to add the profit and expenses to the cost price.

First, let's calculate the profit and expenses added by the trader. Since the trader added 20% to the cost price, the profit and expenses will be:

20% of R90 = 0.2 x R90 = R18

Now, we can calculate the selling price of the screwdriver set by adding the cost price and the profit and expenses:

Cost price = R90

Profit and expenses = R18

Selling price = Cost price + Profit and expenses = R90 + R18 = R108

Therefore, the customer will pay R108 for the screwdriver set.

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The vectors 4 1 and 16 are linearly dependent because they can be expressed as multiples of each other. This means that there are scalars that are not all zero that will make the equation below true:

4a + 16b = 0

To find the scalars, we can set one of them to any non-zero value and solve for the other. For example, if we set a = 1, then we can solve for b:

4(1) + 16b = 0
16b = -4
b = -4/16
b = -1/4

So the scalars that will make the equation true are a = 1 and b = -1/4. These are not all zero, which confirms that the vectors are linearly dependent.

If the vectors were linearly independent, then the only scalars that would make the equation true would be all zero. In other words, a = 0 and b = 0 would be the only solution. However, since we found scalars that are not all zero that make the equation true, we know that the vectors are not linearly independent.

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Answer:5 3/8

Step-by-step explanation:

[tex]3\frac{1}{8} =\frac{25}{8}\\4\frac{7}{28} =4\frac{1}{4}=\frac{17}{4}\\1\frac{5}{6} =\frac{11}{6}=\frac{33}{18}\\\frac{\frac{25}{8}}{x-\frac{17}{4}}=\frac{17}{18}+\frac{33}{18}=\frac{50}{18}=\frac{25}{9}\\\frac{\frac{25}{8}}{x-\frac{17}{4}}=\frac{\frac{25}{9}}{1}\\\frac{25}{8}=\frac{25}{9}*(x-\frac{17}{4})\\(x-\frac{17}{4})=\frac{25}{8}:\frac{25}{9}=\frac{25}{8}*\frac{9}{25}=\frac{9}{8}\\x=\frac{9}{8}+\frac{17}{4}=\frac{9}{8}+\frac{34}{8}=\frac{43}{8}=5\frac{3}{8}[/tex]

Kayla would ultimately spend $210.91 + $14.76 = $225.67 for all the clothing items, including sales tax.

To determine if Kayla's budget will be enough to purchase all the clothing items listed after sales tax is applied, we need to calculate the total cost of the items first.

The cost of 2 T-shirts would be 2 x $9.98 = $19.96.

The cost of 3 dresses would be 3 x $24.99 = $74.97.

The cost of 1 pair of pants would be $25.99.

The cost of 1 pair of shoes would be $89.99.

Therefore, the total cost of the clothing items is $19.96 + $74.97 + $25.99 + $89.99 = $210.91.

Next, we need to add the sales tax rate of 7% to the total cost to find the final price that Kayla would pay.

7% of $210.91 = $14.76

Therefore, the final price that Kayla would pay for all the clothing items, including sales tax, is $210.91 + $14.76 = $225.67.

Since Kayla's budget is $200, she would not have enough money to purchase all of the clothing items listed after sales tax is applied.

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Answer:

The value of x in the given figure is 36

What is a line?

A line is a straight arrangement of points that extends in opposite directions. It has no beginning and no end in any way (infinite). It has only one dimension.

What are Parallel lines?

Parallel lines are two lines in the same plane that are equal distances apart and never intersect. They can be both horizontal and vertical in orientation.

According to the given information:

By the Triangle proportionality theorem, If a line parallel to one side of a triangle contacts the other two sides of the triangle, the line proportionally separates these two sides.

Then we have

[tex]\frac{x-16}{16} =\frac{25}{20}[/tex]

On simplifying,

[tex]x-16=\frac{25}{20}*16[/tex]

x-16 = 20

x = 36

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[tex] \bf Question :- \\ [/tex]

what is the value of expression

when g=4 and h=2

[tex] \bf Solution :- \\ [/tex]

[tex] \longrightarrow \: \: \frac{1}{4} (16 + g) - h \\ \\ \longrightarrow \: \: \frac{1}{4} (16 + 4) - 2 \\ \\ \longrightarrow \: \: \frac{1}{{ \cancel{4} }} \times( \cancel{ 20)} - 2 \\ \\ \longrightarrow \: \: 1 \times 5 - 2 \\ \\ \longrightarrow \: \: 1 \times 3 \\ \\ \longrightarrow \: \: 3 \\ [/tex]

Henceforth, Option c is the required answer.

In conclusion for part A  it would take T - 32.5 minutes to cook a 1.5 kg joint. For part B w is given by the formula w = (T - 25) / (-35). For part C 6.6 kg of beef needs to be cooked for 207 minutes. For part D  5.91 kg of beef needs to be cooked for 3 hours and 48 minutes.

How to solve?

a) To find how long it would take to cook a 1.5 kg joint, we can substitute w = 1.5 into the formula:

T - 35w + 25 = T - 35(1.5) + 25 = T - 32.5

So, it would take T - 32.5 minutes to cook a 1.5 kg joint.

b) To make w the subject of the formula, we need to isolate w on one side of the equation. We can start by subtracting 25 from both sides:

T - 35w = T - 25

Next, we can divide both sides by -35:

w = (T - 25) / (-35)

Therefore, w is given by the formula w = (T - 25) / (-35).

c) To find the weight of beef that needs to be cooked for 207 minutes, we can substitute T = 207 into the original formula:

T - 35w + 25 = 207

Simplifying this equation, we get:

-35w = -232

Dividing both sides by -35, we get:

w = 6.6 kg

Therefore, 6.6 kg of beef needs to be cooked for 207 minutes.

d) To find the weight of beef that needs to be cooked for 3 hours and 48 minutes (which is equivalent to 3 × 60 + 48 = 228 minutes), we can substitute T = 228 into the original formula:

T - 35w + 25 = 228

Simplifying this equation, we get:

-35w = -207

Dividing both sides by -35, we get:

w = 5.91 kg

Therefore, 5.91 kg of beef needs to be cooked for 3 hours and 48 minutes.

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The value is x in the equation is -2

The value of y in the equation is -8.67

5x - 3y= 16...........equation 1

4x + 5x= -2..........equation 2

Multiply equation 1 by 4 and equation 2 by 5

20x - 12y= 64

20x + 25x= -10

-37x= 74

x= -74/37

x= -2

Substitute -2 for x in equation 1

5x - 3y= 16

5(-2) - 3y= 16

-10 -3y= 16

-3y= 16+10

-3y= 26

y= -26/3

y= -8.67

Hence the value of x is -2 and the value of y is -8.67

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The interval of times that represent the middle 99.7% of Aaron's finishing times in the 400 m race is [72.5, 87.5].

Using the empirical rule or the elliptical rule, we know that in a normal distribution:

In this case, we want to find the interval of times that represents the middle 99.7% of Aaron's finishing times, which means we need to find the range of values that fall within three standard deviations of the mean.

So, using the formula for finding the interval of values within k standard deviations of the mean:

lower bound = mean - k * standard deviation

upper bound = mean + k * standard deviation

where k = 3 for this problem, we get:

lower bound = 80 - 3 * 2.5 = 72.5

upper bound = 80 + 3 * 2.5 = 87.5

Therefore, the interval of times that represents the middle 99.7% of Aaron's finishing times in the 400 m race is [72.5, 87.5].

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Answer:

Step-by-step explanation:

2.02

x=21 so replace x with 21

3(21)+y/z

then do the same with y and z

3(21)+36/49

63+36/49

99/49

SOLUTION 2.02

The Eiffel Tower is approximately 919 feet tall to the nearest foot.

We can use trigonometry to solve this problem.

Let's assume that the height of the Eiffel Tower is h feet.

From the problem, we know that Mai is 80 feet away from the base of the tower and looking up at an angle of 85.7 degrees. We can use the tangent function to relate the height of the tower to the angle and distance:

tan(85.7) = h/80

We can solve for h by multiplying both sides by 80:

h = 80 × tan(85.7)

Using a calculator, we get:

h ≈ 919.4 feet

Therefore, the Eiffel Tower is approximately 919 feet tall to the nearest foot.

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Answer:

Step-by-step explanation:

We can start by using the logarithmic rule that states:

log a (mn) = log a (m) + log a (n)

And also the property:

log a (b^c) = c*log a (b)

With these rules, we can simplify the given expression as follows:

log4 n = 1/4 log4 81 + 1/2 log4 25

log4 n = log4 81^(1/4) + log4 25^(1/2) (using the above properties)

log4 n = log4 (3^4)^(1/4) + log4 (5^2)^(1/2) (81 = 3^4 and 25 = 5^2)

log4 n = log4 3 + log4 5 (using the rule log a (b^c) = c*log a (b))

log4 n = log4 (3*5) (using the rule log a (mn) = log a (m) + log a (n))

log4 n = log4 15

Therefore, the solution to the equation log4 n=1/4 log4 81 + 1/2 log4 25 is:

n = 15

Answer:

hey will you be my friend

I yes then text me

The equation of the function that is graphed as line b is,

⇒ y = - 2x - 1

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

Two points on the line b are (- 1, 1) and (- 2, 3).

Now,

Since, The equation of line passes through the points ( (- 1, 1) and (- 2, 3).

So, We need to find the slope of the line.

Hence, Slope of the line is,

m = (y₂ - y₁) / (x₂ - x₁)

m = (3 - 1)) / (- 2 + 1)

m = 2 / - 1

m = - 2

Thus, The equation of line with slope - 2 is,

⇒ y - 1 = - 2 (x + 1)

⇒ y - 1 = - 2x - 2

⇒ y = - 2x - 1

Therefore, The equation of the function that is graphed as line b is,

⇒ y = - 2x - 1

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The turtle and snail are apprοaching each οther at a rate οf 6 feet per minute.

Let's use the cοncept οf relative speed tο sοlve this prοblem. The relative speed οf twο οbjects mοving tοwards each οther is the sum οf their individual speeds.

Relative speed is the speed οf an οbject οr persοn in relatiοn tο anοther οbject οr persοn. It is the difference between the velοcities οf twο οbjects mοving relative tο each οther. The relative speed can be calculated by subtracting the velοcity οf οne οbject frοm the velοcity οf the οther οbject.

Let's call the rate at which the turtle and snail are apprοaching each οther "r".

Relative speed = turtle's speed + snail's speed

r = 5 + 1

r = 6 feet per minute

Sο the turtle and snail are apprοaching each οther at a rate οf 6 feet per minute.

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Answer:

heeeeeeeee

Step-by-step explanation:

heeeeeeeeee bad

Answer:

90$

Step-by-step explanation:

We need to find 15% of the number 600:

[tex] \frac{600 \times 15\%}{100\%} = 90 [/tex]

So, the answer is 90$