Solve each proportion.
(z-1)/3 = 8/(z+1)

Answer:

100 meters

Step-by-step explanation:

0.1 x 1000 = 100 m

\(g(x) = 3^x + 4\) is a parallel shift of f(x) upwards by 4 units. \(h(x) = (1/4)^x - 4\) is a parallel shift of f(x) downwards by 4 units and has a steeper graph. \(j(x) = 3^{(x + 6)} - 2\) is a horizontal shift of f(x) to the left by 6 units and a vertical shift downwards by 2 units.

\(g(x) = 3^x + 4:\)

The function \(g(x) = 3^x + 4\) is obtained by shifting the graph of \(f(x) = 3^x\) upwards by 4 units. This means that the graph of g(x) will lie entirely above the graph of f(x) and will be parallel to it. The y-values of g(x) will be 4 units higher than the corresponding y-values of f(x) for any given x.

\(h(x) = (1/4)^x - 4:\)

The function \(h(x) = (1/4)^x - 4\) is obtained by shifting the graph of \(f(x) = 3^x\) downwards by 4 units. This means that the graph of h(x) will lie entirely below the graph of f(x) and will be parallel to it. The y-values of h(x) will be 4 units lower than the corresponding y-values of f(x) for any given x. Additionally, the base of the exponential function changes from 3 to 1/4, causing the graph to be steeper.

\(j(x) = 3^{(x + 6)} - 2:\)

The function \(j(x) = 3^{(x + 6)} - 2\) is obtained by shifting the graph of \(f(x) = 3^x\) horizontally to the left by 6 units and then shifting it downwards by 2 units. This means that the graph of j(x) will have the same shape as f(x) but will be shifted to the left by 6 units and down by 2 units. The y-values of j(x) will be 2 units lower than the corresponding y-values of f(x) for any given x.

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The mean score of 90, and percentile of Bob's score of 80, gives Bob's exam score as approximately 92.5%

The Z-Score of the 80th percentile is 0.8416

The formula for Z-Score is presented as follows;

\(z = \frac{x - \mu}{ \sigma} \)

Where;

\( \sigma = The \: standard \: deviation\)

\( \mu = The \: mean = 90\%\)

x = The given score

Taking the mean as a proportion, we have;

\( \sigma = \sqrt{\frac{\mu \cdot (1-\mu)}{n}}\)

Which gives;

\( \sigma = \sqrt{\frac{0.9 \times (1-0.9)}{100}}= 0.03\)

Therefore, when z = 0.8416, gives;

\(0.8416 = \frac{x - 0.9}{ 0.03} \)

x = 0.8416 × 0.03 + 0.9 ≈ 0.925

Therefore;

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Answer:

58/21 is added to -7/3 to get 3/7

The statement that is true on the system of equations is that A. The system has no solution.

There is no solution in the given system of equations because the lines formed by the equations are parallel to each other. This means that they will never intersect with each other.

A solution is only derived at the points where the systems of equations intersect with each other. As there is no point where these equations intersect, it means there is no solution for these system of equations.

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Answer:

50

Step-by-step explanation:

A person travels to work at an average speed of 40 mph, and returns home at 60 mph. the average speed for the entire trip is 48 mph.

To find the average speed for the entire trip, we need to use the formula:

average speed = total distance / total time

Let's assume that the distance to work is d.

The time it takes to travel to work is:

time = distance / speed = d / 40

The time it takes to return home is:

time = distance / speed = d / 60

The total distance for the round trip is:

total distance = d + d = 2d

The total time for the round trip is:

total time = d/40 + d/60

We can simplify the total time by finding a common denominator:

total time = (3d/120) + (2d/120) = 5d/120 = d/24

Now we can plug in the values for total distance and total time:

average speed = (2d) / (d/24) = 48 mph

Therefore, the average speed for the entire trip is 48 mph.

To find the average speed for the entire trip, we can use the harmonic mean formula for two rates: average speed = (2 * speed1 * speed2) / (speed1 + speed2). In this case, speed1 is 40 mph (to work) and speed2 is 60 mph (returning home).

Using the formula: average speed = (2 * 40 * 60) / (40 + 60) = (4800) / (100) = 48 mph.

So, the average speed for the entire trip is 48 mph.

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Answer:

1 is the result of equation.

Step-by-step explanation:

Given that,

→ x = 1

The equation will be,

→ [{((x × 2) + 4) ÷ 2} - 2]

Then the result of the eq. will be,

→ [{((1 × 2) + 4) ÷ 2} - 2]

→ [{(2 + 4) ÷ 2} - 2]

→ [{6 ÷ 2} - 2]

→ [3 - 2] = 1

Hence, 1 is the value of equation.

Answer:

a

Step-by-step explanation:

Answer:

10.75 would be a 64 ring size in the US

The total erasing cost is 5.

The erasing cost refers to the cost associated with removing or eliminating something. In this case, the question states that the total erasing cost is 5. However, without further context or information, it is unclear what specifically is being erased and what the units of the cost are.

To provide a more detailed explanation, it would be helpful to have additional information about the context or problem at hand. Please provide more details or clarify the question so that I can assist you more effectively in determining the specific meaning and explanation behind the total erasing cost of 5.

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Answer:

Your answer is 40√3.

Answer:

The car is 13 years old

Step-by-step explanation:

Lets say Car is x and the Truck is y, so the trucks age = x + 3 = y

    Lets find the value of the Car or x

x + 3 = 1/2(x + 7)------- >

first we will divide x by 1/2 and 7 by 1/2, So...

x + 3 = (x / 1/2 + 7 / 1/2)------- >

x + 3 = 1/2x + 3.5------->

next Isolate variable x,

x + 1/2x = 3 + 3.5

1/2x = 6.5, So...

x = 13 and in turn, y = 13 + 3

:)

Answer: C.5

Step-by-step explanation:

For the mutual fund investment, the chosen options are a starting amount of $900 and a rate of annual return of 7%.
To calculate Khalid's weekly profits based on the number of weeks, a function is determined using the given data. The graph of Khalid's profits is plotted alongside Harper's profits.
The solution to the system of equations is found by determining the point where Harper's and Khalid's profit functions intersect. This represents the week when their profits are equal.
The average rate of change of Khalid's profits from week 3 to week 6 is calculated, representing the rate at which his profits are changing over that period.

The chosen options for the mutual fund investment are a starting amount of $900 and a rate of annual return of 7%. To calculate the future value of the investment after 30 years, we can use the compound interest formula: FV = PV * (1 + r)^n. Plugging in the values, we get FV = 900 * (1 + 0.07)^30 = $6,084.38.
To calculate Khalid's weekly profits based on the number of weeks, we can observe the given table and identify the pattern. The function for Khalid's profits can be determined by fitting a curve to the given data points. Plotting Khalid's profits on the same graph as Harper's profits allows for a visual comparison.
The solution to the equation h(x) = k(x) represents the point where Harper's and Khalid's profit functions intersect. It indicates the week when.
their profits are equal. By finding the x-coordinate of this point, the specific week can be determined.
The average rate of change of Khalid's profits from week 3 to week 6 can be calculated by finding the slope of the line passing through those two points. It represents the average rate at which Khalid's profits are changing over that specific period, indicating the growth or decline in his business during that time.

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The equation illustrates the given information is 5x+4y=200

Cement= a bag x kg

Gravel =a bag of y kg

An equation can be defined as a mathematical statement consisting of an equal symbol between two algebraic expressions that have the same value.

and the total is 200kg

Therefore we get the equation is

5x+4y=200

Therefore the equation illustrates the given information is 5x+4y=200.

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A light-year is the distance light can travel in one year. It is equal to 9.46 trillion kilometers or 5.88 trillion miles. This is equal to about 6 trillion kilometers (3.7 trillion miles). It is the most common unit used to measure interstellar distances.

1. One light-year is equal to the distance light can travel in one year.

2. Distance light can travel in one year = speed of light x time

3. Speed of light = 300,000 km/sec

4. Time = 1 year

5. Distance light can travel in one year = 300,000 km/sec x 1 year

6. Distance light can travel in one year = 9.46 trillion km

7.The annual distance that light can cover is 5.88 trillion miles.

A light-year is a unit of distance used to measure interstellar distances. It is equal to 9.46 trillion kilometers, or 5.88 trillion miles. This is equal to approximately 6 trillion kilometers (3.7 trillion miles). This is calculated by multiplying the speed of light (300,000 km/sec) by one year (365.25 days). Light-years are commonly used to measure distances between stars and galaxies.

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Answer:

y=2x-1

Step-by-step explanation:

The equation for a line (slope-intercept form) is:

y=mx+b

m: slope

b: y-intercept

x and y: (x, y) coordinate pair

In this scenario, since we are given the slope and a point on the line, we can solve for the y-intercept:

y=2x+b

5=2(3)+b

5=6+b

Subtract 6 from both sides

b=-1

Therefore the equation of the line is:

y=2x-1

Answer

480

Step-by-step explanation:

Congrats on your first question!

The investment is 480 because

(80 / 100) x 1000 = 80 x 6 = 480

The total is 1480.

The amount that can be saved by purchasing ten notebooks at the sale price is 95 cents.

The information stated that the notebook are in sale for 2 at 99 cents. The cost for each notebook will be:

= 99 cents / 2

= 49.5 cents

The amount they can be saved will be:

= (59 × 10) - (49.5 × 10)

= 590 - 495

= 95 cents

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Answer:

1

Step-by-step explanation:

To evaluate, substitute x = - \(\frac{2}{3}\) into f(x), that is

f(- \(\frac{2}{3}\) )

= 3(- \(\frac{2}{3}\) )² + 2(- \(\frac{2}{3}\) ) + 1

= 3(\(\frac{4}{9}\) ) - \(\frac{4}{3}\) + 1

= \(\frac{4}{3}\) - \(\frac{4}{3}\) + 1

= 0 + 1

= 1

Answer:

1

Step-by-step explanation:

f(x) = 3x² + 2x + 1

f(-2/3) = 3x² + 2x +1

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

Substitute the value in for all the x's

f(-2/3) = 3(4/9) + 2(-2/3) + 1

f(-2/3) = 12/9 + (-4/3) + 1

f(-2/3) = 4/3 + (-4/3) + 1                

Subtracting 4/3 by (-4/3) gets you 0 so I didn't write it down.

f(-2/3) = 1

So, the answer I got is 1

James has $37.67 now after all his expenses

James had $x, his brother had $y, and his sister had $z when the morning began.

By using algebra,

James's sibling had twice as much money as James.

Now, x =y/2..... (i)

James had $27 fewer dollars than his sister did.

So, x = z - 27 ........ (ii)

⇒  {From equation (1)}

⇒ y/2 = z -27

⇒ y = 2z - 54

⇒ 2z - y =54 ..........(3)

Now, James and his sister each received $12 from his brother.

James now has $(x + 12), his brother now has $(y -24), and his sister now has $(z + 12).

Given that James' sister has twice as much money as James' brother after payoff,

So, z+12/2 = y-24

⇒ z + 12 = 2y - 48

⇒ 2y - z = 50 ......... (4)

The result of resolving equations (3) and (4) is

3y = 54 + 100 = 154

⇒ y =  51.33.

The result of equation (3) is now z = 52.67.

And from equation (1), x = 51.3/2= 25.67

So, now, James has (25.67 + 12) = $37.67

Hence, James has $37.67 now after all his expenses

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The "d" format specifier is used to denote a signed decimal integer in various programming languages and formatting systems.

When used in format strings or printf-style functions, the "d" specifier indicates that the corresponding argument should be formatted as a signed decimal integer. It allows for the representation of both positive and negative whole numbers, including zero.

For example, in C programming, the printf function can be used with the "%d" format specifier to display a signed decimal integer value. Similarly, in other languages such as Python, the "{:d}" format specifier can be used with the format() function or string interpolation to represent a signed decimal integer.

Using the "d" specifier ensures that the output is formatted as a base-10 representation of a signed integer, taking into account the sign of the number.

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Answer:

#1 is the 1st option. #2 is the 4th option.

Step-by-step explanation:

Have a great day mate!

Answer:

8 7/14 - 9/14= 55/7

7 - 5/9 = 58/9

6 17/20 - 4 =  57/20

Answer:

very funny and 14

Step-by-step explanation:

Answer:

14

Step-by-step explanation:

7 plus 7? how old are you?

The required  cost of each shirt is $21.28.

A mathematical statement known as an equation is made up of two expressions joined together by the equal symbol. A formula would be 3x - 5 = 16, for instance. When this equation is solved, we discover that the value of the quantity x is 7.

The total cost of 3 identical shirts, including shipping, is $71.83. So we can write the equation as:

3s + 7.99 = 71.83

To solve for the cost of each shirt, we need to isolate the variable "s" on one side of the equation. We can start by subtracting 7.99 from both sides:

3s = 63.84

Then, we can divide both sides by 3:

s = 21.28

Therefore, the cost of each shirt is $21.28.

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You could solve using the Law of Sines. You could also use SohCahToa to find the missing angle.

Answer:

E

Step-by-step explanation:

the weight of the packaging materials is 12 oz. There are 16 oz in a pound. If the vase weighs 3 lb 11 oz, it would take 5 more oz to reach the next pound, and there was another 7 oz after that. You would then do 5 + 7, which is 12, so the packaging materials weigh 12 oz.

Answer:

b^2√30b

Step-by-step explanation:

√30b^5 - Original

Break down the radical with its factors (factor tree)

√3*2*5*b*b*b*b*b  

See what perfect squares you can take out (Can take out four b terms)  You cant take out any perfect squares involving 30 since there are no perfect squares

b^2√3*2*5*b

b^2√30b