Which accurately shows how to use inverse operations to find the value of a in a + 5 = 14?
O 14+ 5 = a
18 = a
O 14+5= a
19 = a
O14-5-a
8 = a
14-5= a
9=a

The solution of the system of equations is z = -12

The system of equations are:

xy/(x + y) = 1 ...........................(1)

xz/(x + z) = 2...........................(2)

yz/(y + z) = 3...........................(3)

From equation  (1): x + y = xy

=> y = xy - x

y = x(y - 1)

x = y/(y - 1).......................................(4)

From equation (2):

2(x + z) = xz

=> 2x + 2z = xz

2x = xz - 2z

2x = z(x - 2)

z = 2x/(x - 2) ....................................(5)

From equation (3): 3(y + z) = yz

=> 3y + 3z = yz

3y = yz - 3z

3y = z(y - 3)

z = 3y/(y - 3)....................................(6)

We then will compare equation (5) and (6)

2x/(x - 2) = 3y/(y - 3)

2x(y - 3) = 3y(x - 2)

2xy - 6x = 3xy - 6y

6(y - x) = xy .................................(7)

and  xy = x + y in equation 1

6(y - x) = x + y

6y - y - 6x - x = 0

5y - 7x = 0

5y = 7x

x = 5y/7................................................(8) we now use this in equation 4

5y/7 = y/(y - 1)

1/(y - 1) = 5/7

(y - 1) = 7/5

y = 1 + 7/5

y = 12/5    ..........................................(9)

We use this in equation  (8)

x = 5(12/5)/7

x= 12/7 .......................(10)

z = 2x/(x - 2)

z = 2(12/7) ÷ (12/7 - 2)

= 24/7 ÷ -2/7

= 24/7 × (-7/2)

= -24/2 = -12

z = -12.

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The answers are:

27. P(6) = 0.2 , 28. P(even number) = 0.6 , 29. P(6) = 1/10 , 30. P(even number) = 5/10 = 0.5

The experimental probability of getting a 6 is 0.2, because 2 out of 50 displays were 6s.

The experimental probability of getting an even number is 0.6, because 30 out of 50 displays were even numbers.

The theoretical probability of getting a 6 is 1/10, because there is 1 chance out of 10 that the calculator will display a 6.

The theoretical probability of getting an even number is 5/10, because there are 5 chances out of 10 that the calculator will display an even number.

As you can see, the experimental probabilities are close to the theoretical probabilities. This is because the calculator was programmed to randomly display a digit from 0 to 9, so the results should be evenly distributed. However, there is always some chance of variation, so the experimental probabilities may not be exactly equal to the theoretical probabilities.

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Answer:

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Step-by-step explanation:Please help me important question in image

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Answer:

The equation a=0.003x^2+21.3 models the average ages of women when they first married since the year 1940 in the United States. In this equation, a represents the average age and x represents the years since 1940. To estimate the year in which the average age of brides was the youngest, we need to find the minimum value of the quadratic function a=0.003x^2+21.3. This can be done by using the formula x=-b/2a, where b is the coefficient of x and a is the coefficient of x^2. In this case, b=0 and a=0.003, so x=-0/(2*0.003)=0. This means that the average age of brides was the lowest when x=0, which corresponds to the year 1940. The value of a when x=0 is a=0.003*0^2+21.3=21.3, so the average age of brides in 1940 was 21.3 years old. This is consistent with the historical data, which shows that the median age of women at their first wedding in 1940 was 21.5 years old. The average age of brides has been increasing since then, reaching 28.6 years old in 2021.

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The total number of votes casted by the residents of the city is 6,633.

Given that,  the ratio of yes votes to no votes was 5 to 6.

This means that for every 5 yes votes, there were 6 no votes.

Also given that, there were 3618 no votes.

Since the ratio of yes votes to no votes is 5 to 6, we can set up the following proportion:

5/6 = x/3618

Where x is the number of yes votes

Solving for x:

6x = 5 × 3618

6x = 18090

Divide both sides by 6

x = 18090/6

x = 3015

Therefore, the total number of votes will be:

Number of yes votes + number of no votes

= 3015 + 3618

= 6,633

Therefore, the total number of votes is 6,633.

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Given statement solution is :- If the expression is set equal to 10x + 5, then there would be one solution.

If the expression is set equal to 10x + 7, then there would be no solution.

If the expression is set equal to -10x + 5, then there would be one solution.

If the expression 12x - 6x + 5 + 4x is set equal to 10x + 5, then there would be solution(s).

If the expression is set equal to 10x + 5, then there would be one solution.

If the expression is set equal to 10x + 7, then there would be no solution.

If the expression is set equal to -10x + 5, then there would be one solution.

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Answer:

  20°

Step-by-step explanation:

You want to know the measure of external angle 1 in the diagram of a circle, secants, and chord.

The measure of each arc subtended by a chord is shown as 100°. They all have the same measure because the chords are all the same length.

The measure of the remaining arc is ...

  360° -100° -100° -100° = 60°

The measure of angle 1 is half the difference of the measures of the arcs it intercepts:

  angle 1 = 1/2(100° -60°)

  angle 1 = 20°

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The measure of the angle 1 using the appropriate angle theorem is 20°

The measure of the arc subtended by the chord is 100°. Since the length of the chord are equal, then the measure of each arc in the figure is the same.

Since we have three arcs measuring 100°

The measure of the smallest arc would be : (360 - 100) = 60°

Angle 1 = 0.5(100-60) (half the measure of intercepted arc)

Angle 1 = 0.5(40) = 20°

Hence, the measure of angle 1 is 20°

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Answer:

Step-by-step explanation:

Since there are an even number of values in the data set (20), the median is the average of the two middle values. In this case, the two middle values are 14 and 18. The median is therefore (14 + 18) / 2 = 16.

Answer:

θ =  60 degrees

If needed in radians:

θ = π/3

Step-by-step explanation:

2cos(θ) = 1

We are solving for theta.

We can divide 2 on both sides.

2cos(θ) = 1

/2             /2

cos(θ) = 1/2

Now we can use Inverse of cosine to isolate theta.

θ [tex]= cos^-^1(1/2)[/tex]

θ =  60 degrees

If needed in radians:

θ = π/3

The area that was removed from the shape was 3.9 square inches, and the remaining area is 50.1 square inches. (None of the options given)

The area of the parallelogram is given by the formula A_p = b * h, where b is the base and h is the height. In this case, the base is 2 feet or 24 inches, and the height is 2.25 inches. Therefore, the area of the parallelogram is:

A_p = b * h = 24 inches * 2.25 inches = 54 square inches

Next, we compute the area of the cut-out rectangle. The area of a rectangle is given by the formula A_r = L * W, where L is the length and W is the width. In this case, L = 3 inches and W = 1-5/8 inches.

A_r = L * W = 3 inches * 1-5/8 inches

A_r = 3 inches * 13/8 inches

A_r = 3.9 square inches

Therefore, the area that was removed from the parallelogram is 3.9 square inches.

To find the remaining area of the parallelogram that was not cut-out, we simply subtract the area of the cut-out rectangle from the area of the parallelogram:

Remaining area = Area of parallelogram - Area of cut-out rectangle

Remaining area = 54 square inches - 3.9 square inches

Remaining area = 50.1 square inches

None of the answer options provided matches with the correct calculation above.

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Therefore Table 1 represents the function g(x) obtained by shifting f(x) 5 units down.

To shift a function f(x) 5 units down, we need to subtract 5 from the y-values of f(x) or add a constant -5 to the function. This means that the new function g(x) will be f(x) - 5. In other words, we take the table of values for f(x) and subtract 5 from each of the y-values to get the new table of values for g(x).Let's take a look at the given tables of values and see which one represents the function g(x) obtained by shifting f(x) 5 units down.

Table 1:  From this table, we can see that when x = 2, f(x) = 5. If we subtract 5 from this value, we get 0, which is the correct value of g(2). Similarly, when x = 3, f(x) = 7. If we subtract 5 from this value, we get 2, which is the correct value of g(3). Therefore, this table represents the function g(x) obtained by shifting f(x) 5 units down.

Table 2: From this table, we can see that when x = 0, f(x) = 1. If we subtract 5 from this value, we get -4, which is not the correct value of g(0). Therefore, this table does not represent the function g(x) obtained by shifting f(x) 5 units down.

Table 3: From this table, we can see that when x = -2, f(x) = -3. If we subtract 5 from this value, we get -8, which is not the correct value of g(-2). Therefore, this table does not represent the function g(x) obtained by shifting f(x) 5 units down.

Table 4: From this table, we can see that when x = 5, f(x) = 0. If we subtract 5 from this value, we get -5, which is not the correct value of g(5). Therefore, this table does not represent the function g(x) obtained by shifting f(x) 5 units down.In conclusion,

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The volume of the figure is 3300 ft³.

We have,

The figure is a composite of two rectangular boxes.

Now,

Rectangular box volume.

= length x width x height

Now,

One rectanglular box.

= (20 + 4) x 25 x³5

=  24 x 25 x 5

= 3000 ft²

Another rectangular box.

= 4 x 25 x (8 - 5)

= 4 x 25 x 3

= 300 ft³

Now,

The volume of the figure.

= 3000 + 300

= 3300 ft³

Thus,

The volume of the figure is 3300 ft³.

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The measure of the complement of a 1-degree angle is 89 degrees.

The complement of an angle is defined as the angle that, when added to the given angle, results in a sum of 90 degrees. To find the measure of the complement of a 1-degree angle, we need to determine the angle that, when added to 1 degree, equals 90 degrees.

Let's denote the measure of the complement as x degrees. According to the definition, we can set up the equation:

1 degree + x degrees = 90 degrees.

To solve for x, we need to isolate it on one side of the equation. By subtracting 1 degree from both sides, we have:

x degrees = 90 degrees - 1 degree.

Simplifying the right side, we get:

x degrees = 89 degrees.

In summary, when an angle measures 1 degree, its complement measures 89 degrees. Complementary angles are pairs of angles that add up to 90 degrees. In this case, since the given angle measures only 1 degree, its complement is significantly larger, nearly forming a right angle. The concept of complementary angles is fundamental in geometry and can be applied to various problems involving angles and their relationships.

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The correct option is (b) For each Additional one hundred pounds of weight, miles per gallon decreases by 1.4 miles.

The given regression equation is: ý = 38.5 - 1.4x where the weight is the explanatory variable.We are to select the conclusion that is true based on this information regarding weight and miles per gallon (mpg).

Solution:Given regression equation is: ý = 38.5 - 1.4x.

Here, explanatory variable is weight (in hundreds of pounds) and mpg is the response variable. Let us see each option.a) For each additional one pound of weight, mpg stays relatively the same.For each additional one pound of weight, the value of x would increase by 1/100 = 0.01.

Putting this value in the given equation, we get: ý = 38.5 - 1.4 (0.01) x 100= 37.1Since the value of ý is a decreasing function of x, a slight increase in x would lead to a decrease in the value of ý. Hence, this statement is false.b) For each additional one hundred pounds of weight, mpg decreases by 1.4 miles.

For each additional one hundred pounds of weight, the value of x would increase by 1. Putting this value in the given equation, we get: ý = 38.5 - 1.4 (1) x 100= 24.5For every increase of 100 pounds of weight, mpg decreases by 1.4 miles. Hence, this statement is true.

Therefore, the correct option is (b) For each additional one hundred pounds of weight, miles per gallon decreases by 1.4 miles.

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A  graph that represents a Functional relationship between x and y on the given grid.

To draw a graph that represents a functional relationship between x and y on the given grid below, you need to follow the steps mentioned below:

First, draw a horizontal line called the x-axis. The x-axis represents the independent variable, and the values of x are plotted along this axis. Second, draw a vertical line called the y-axis.

The y-axis represents the dependent variable, and the values of y are plotted along this axis. Third, select some values of x, and substitute each value of x into the function to obtain the corresponding values of y. For each (x, y) pair, plot a point on the graph.

Finally, connect the points with a line to obtain the graph that represents the functional relationship between x and y.

Example: Let's say we have a functional relationship given as y = 2x + 3

Now, we can use this equation to calculate the values of y for different values of x. For example, when x = 0, y = 2(0) + 3 = 3.

When x = 1, y = 2(1) + 3 = 5. When x = 2, y = 2(2) + 3 = 7. When x = 3, y = 2(3) + 3 = 9. When x = 4, y = 2(4) + 3 = 11.Now we can plot these points (0, 3), (1, 5), (2, 7), (3, 9), and (4, 11) on the grid, and connect them with a line to obtain the graph as shown below:

Therefore, this is how you can draw a graph that represents a functional relationship between x and y on the given grid.

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Answer: 8  

Step-by-step explanation:

By the pythagorean theorem

Answer:

To find the volume of the shipping box in cubic feet, we need to convert the dimensions from inches to feet and then calculate the volume.

Given:

Length = 36 inches

Width = 24 inches

Height = 18 inches

Converting the dimensions to feet:

Length = 36 inches / 12 inches/foot = 3 feet

Width = 24 inches / 12 inches/foot = 2 feet

Height = 18 inches / 12 inches/foot = 1.5 feet

Now, we can calculate the volume of the box by multiplying the length, width, and height:

Volume = Length * Width * Height

Volume = 3 feet * 2 feet * 1.5 feet

Volume = 9 cubic feet

Therefore, the shipping box can hold 9 cubic feet.

Step-by-step explanation:

First convert the units because it's asking for the cubic feet but they give us the measurements in inches.

To convert inches to feet we divide the number by 12.

36 ÷  12 = 3

24 ÷  12 = 2

18 ÷ 12 = 1.5

Now to find the volume, we multiply it all together.

3 × 2 × 1.5 = 9

It can hold 9 cubic feet.

Hope this helped!

Answer:

this is the answer:

Step-by-step explanation:

Hope it helps:

Kareem uses 300 milliliters of Solution B.

Let's assume Kareem uses "x" milliliters of Solution B.

Since Kareem uses twice as much Solution A as Solution B, he would use 2x milliliters of Solution A.

Solution A contains 10% alcohol, so the amount of alcohol from Solution A is (2x)(0.10) = 0.2x milliliters.

Solution B contains 15% alcohol, so the amount of alcohol from Solution B is (x)(0.15) = 0.15x milliliters.

The resulting mixture has 105 milliliters of pure alcohol, which is the sum of the alcohol from Solution A and Solution B:

0.2x + 0.15x = 105

Combining like terms:

0.35x = 105

Dividing both sides by 0.35:

x = 105 / 0.35

x = 300

Therefore, Kareem uses 300 milliliters of Solution B.

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One bagel costs 485 cents, equivalent to $4.85.

Let t be the price of a piece of toast in cents

Let m be the price of a muffin in cents

Let b be the price of a bagel in cents.

We will form equations to solve:

Multiply Equa 1 by 2:

4t + 2b = 630 --------- (Equ 4)

Subtract Equ 4 from Equ 3:

(t + 2b + 3m) - (4t + 2b) = 725 - 630

-t + 3m = 95

3m - t = 95 --------- (Equ 5)

Multiply Equ 2 by 2:

2b + 4m = 970 ------ (Equ 6)

Add Equ 5 and Equ 6:

(3m - t) + (2b + 4m) = 95 + 970

3m + 2b + 4m - t = 1065

6m + 2b - t = 1065 (------- Equ 7)

Now we have two equations:

Solve Equ 2 for b:

b = 485 - 2m

Substitute b in Equ 7:

6m + 2(485 - 2m) - t = 1065

6m + 970 - 4m - t = 1065

2m - t = 95 ------ (Equ 8)

Subtract Equ 8 from Equ 5:

(3m - t) - (2m - t) = 95 - 95

3m - t - 2m + t = 0

m = 0

Substitute m = 0 into Equ 2:

b + 2(0) = 485

b = 485

Therefore, one bagel costs 485 cents.

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The steady-state average utilization of the server is 0.3333.

a. Customer and server in the system: The two-runway airport system can be modeled as a queuing system, where the customer is the aircraft and the server is the runway. The server serves the customers by allowing them to land and take off from the runway.

The runway capacity is limited, and thus, the number of customers (aircraft) that can be served at any given time is also limited. The server also has a processing rate, which is the time required to service a single customer. In this case, the server has two processing rates, one for landing and one for takeoff.

b. Arrival rate can be tolerated if the average wait in the sky is not to exceed 3 minutes: The time to land an airplane is exponentially distributed, with a mean of 1.5 minutes. Thus, the rate at which planes arrive can be calculated using the formula λ = 1/μ, where λ is the arrival rate and μ is the mean time.

Therefore, λ = 1/1.5 = 0.6667 planes per minute. The average wait in the sky should not exceed 3 minutes. This means that the time a plane spends waiting in the queue should be less than or equal to 1.5 minutes. Using Little’s Law, the average number of customers in the system can be calculated as L = λW, where L is the number of customers, λ is the arrival rate, and W is the waiting time.

Thus, L = 0.6667 × 1.5 = 1.0 customers. Since there are two runways, the system can handle two customers at a time, which means that the utilization rate is 50%.

c. Steady-state average utilization of the server: The steady-state average utilization of the server can be calculated using the formula ρ = λ/μ, where ρ is the utilization rate, λ is the arrival rate, and μ is the service rate. In this case, the utilization rate is the same as the arrival rate since the server is always busy.

Thus, ρ = 0.6667 / 2μ = 0.3333. Since there are two runways, the total utilization rate is 0.6667, which is less than 1.0. This means that the system is not overloaded and can handle the given arrival rate. Therefore, the steady-state average utilization of the server is 0.3333.

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The solution to the inequality |1/4x - 3| - 5 ≥ 4 is x ≥ 48 or x ≤ -28. The graph of the solution is a number line with the regions to the right of 48 and to the left of -28 shaded, indicating the values of x that make the inequality true.

Part A: To solve the inequality |1/4x - 3| - 5 ≥ 4, we can follow these steps:

Step 1: Remove the absolute value brackets and rewrite the inequality as two separate inequalities:

1/4x - 3 - 5 ≥ 4   or   -(1/4x - 3) - 5 ≥ 4

Step 2: Simplify each inequality:

1/4x - 8 ≥ 4   or   -1/4x + 2 - 5 ≥ 4

Step 3: Solve each inequality separately:

1/4x ≥ 12   or   -1/4x - 3 ≥ 4

Step 4: Continue solving each inequality:

x ≥ 48   or   -1/4x ≥ 7

Step 5: Multiply both sides of the second inequality by -4, remembering to reverse the inequality sign when multiplying by a negative number:

x ≤ -28

Part B: The graph of the solution would be a number line with shaded regions. The region to the right of 48 (including 48) would be shaded to represent x ≥ 48. The region to the left of -28 (including -28) would also be shaded to represent x ≤ -28. These shaded regions represent the values of x that satisfy the inequality. The rest of the number line, between -28 and 48, would remain unshaded, indicating that those values of x do not satisfy the inequality.

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Answer:

b. 12 cm

Step-by-step explanation:

The perimeter of any shape is the sum of the lengths of its sides.

We can call the three sides of a triangle a, b, and c.  Thus, the perimeter, P is given by the formula:

P = a + b + c

Thus, we can plug in 3 for a, 4 for b, and 5 for c to find P, the perimeter of the triangle in centimeters:

P = 3 + 4 + 5

P = 7 + 5

P = 12

Thus, the perimeter is 12 cm (answer b.).

The rate of the jet in still air is 1150 miles per hour and what is the rate of the jetstream is 220 miles per hour

An equation is an expression that is used to show how numbers and variables are related using mathematical operators

Let a represent the speed of the jet in still air and b represent the speed of the jet stream.

Flying against the jetstream, a jet travels 7440 miles in 8 hours, hence:

a - b = 7440/8

a - b = 930     (1)

Flying with the jetstream, the same jet travels 12,330 miles in 9 hours, hence:

a + b = 12330/9

a + b = 1370    (2)

From both equations, solving simultaneously:

a = 1150, b = 220

The rate of the jet in still air is 1150 miles per hour and what is the rate of the jetstream is 220 miles per hour

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Answer:

9x^2y^6 square feet.

Step-by-step explanation:

The area of a square is the length of one of its sides multiplied by itself.

If the side length of a square is -3xy^3 feet,

then the area of the square is

-3xy^3 * -3xy^3 = 9x^2y^6

Therefore, the area of the square is 9x^2y^6 square feet.

To find the number of temperatures in the set, we can divide the sum of the temperatures by the mean temperature.

Number of temperatures = Sum of temperatures / Mean temperature

In this case, the sum of temperatures is given as 2,516 and the mean temperature is given as 74 degrees Fahrenheit.

Number of temperatures = 2,516 / 74

Calculating the division:

Number of temperatures ≈ 34.05

Since we cannot have a fraction of a temperature, we need to round the result to the nearest whole number. Therefore, there are approximately 34 temperatures in the set.

Kira has $19, Boris has $75, and Deshuan has $25.

We will denote as follows:

From information, we can set up equations:

B = 3D (Boris has 3 times what Deshuan has)

D = K + 6 (Deshuan has $6 more than Kira)

K + B + D = 119 (The total amount of money they have is $119)

Substituting equation 2 into equation 1, we have:

B = 3(K + 6)

Substituting equations 1 and 2 into equation 3:

K + 3(K + 6) + (K + 6) = 119

K + 3K + 18 + K + 6 = 119

5K + 24 = 119

5K = 119 - 24

5K = 95

K = 95 / 5

K = 19

Using equation 2, we can find D:

D = K + 6

D = 19 + 6

D = 25

Using equation 1, we can find B:

B = 3D

B = 3 * 25

B = 75.

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The calculated value of X in the circle is 6

From the question, we have the following parameters that can be used in our computation:

The circle

The value of X can be calculated using the following intersecting secants equation

5 * (5 + 7) = x * (x + 4)

using the above as a guide, we have the following:

x * (x + 4) = 60

When solved for x, we have

x = 6

Hence, the value of X is 6

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In terms of measures of spread, Group B has a wider IQR than Group A

The comparative dot plots show the points scored in a game by two groups, Group A and Group B. Both groups have a similar spread, with most of the dots clustered around the middle of the distribution. However, there are some differences in the tails of the distribution that affect the measures of spread.

For Group A, the lowest score is 41, and the highest score is 50. The interquartile range (IQR), which is the range containing 50% of the scores, is approximately from 45 to 48. The range, which is the difference between the highest and lowest scores, is 9.

For Group B, the lowest score is 41, and the highest score is 50. The interquartile range (IQR) is approximately from 43 to 49. The range is also 9.

This indicates that Group B has a more variable distribution of scores within the middle 50% of the distribution, indicating a more variable distribution of scores within the middle.

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