what does it mean by "define a variable".. please help! I don't have much time.

8. To find horsepower, all units need to be converted to the same units.Then, 1 hp = 745.7 watts1 Btu/hr = 0.293 watt500 ft-lbf/sec = 1.35581795 kW5,000 kJ/s = 5,000 kWSo, converting each to kW, we have:5,000 kW - 1.3558 kW - 12.4 x 0.293 kW = 4,631.44 kWNow convert this to hp. 4,631.44 kW = 4,631.44 / 745.7 hp = 6.21 hp to 3 significant figures. Therefore, the answer to the given problem is 6.21 hp to 3 significant figures.

9. we need to calculate the sum of all the given numbers and find the value to the correct significant digits.6.7832 + 1.234 + (2.8723 * 2.3) - 0.97268= 6.7832 + 1.234 + 6.61329 - 0.97268= 13.65881The given numbers have four significant figures (the ones with decimals), so the answer should also have four significant figures. Therefore, the value of the given expression to the correct significant digits is 13.66.10. Stefan-Boltzmann constant expressed in terms of cal/week.ft.mile. K².R².The Stefan-Boltzmann constant, also known as the Stefan constant, is given as σ = 5.670373(21) x 10^-8 W/(m²K^4).Here, the units are in watts per meter squared Kelvin to the fourth power.1 watt = 0.239006 calories/second 1 meter = 3.28084 feet1 week = 604800 seconds1 mile = 5280 feet1 R (Rankine temperature scale) = 1.8 K = 1.8°CThus, σ = 5.670373(21) x 10^-8 W/(m²K^4) can be written as:σ = (5.670373(21) x 10^-8 W)/(m²K^4) × 0.239006 cal/(s·W) × 604800 s/week × (ft/m)^2 × (mi/5280 ft)^2 × (°R/K)^4σ = 0.177134 cal/week·ft^2·mi·K^4·°R^4Hence, the Stefan-Boltzmann constant can be expressed in terms of cal/week·ft^2·mi·K^4·°R^4.

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Answer:

[See Below]

Step-by-step explanation:

✦ Divide by -2 on each side:

  ✧ -2 / -2 = Cancels Out

  ✧ -6 / -2 = 3

So x would be 3, -3.

- |x| Just means absolute value. Which in short just means if it's negative it becomes positive.

~Hope this helps Mate. If you need anything feel free to message me.

Answer:

x = ± 3

Step-by-step explanation:

Answer is ± 3

Answer:

f(-4) = -7

g(-7) = 9

Step-by-step explanation:

f(x) = 2x + 1

f(-4) = 2(-4) + 1 = -8 + 1 = -7

g(x) = x^2 - 40

g(-7) = (-7)^2 - 40 = 49 - 40 = 9

The truck bed is 40cm .

A right-angled triangle is a triangle with one of its angle 90°.

Analysis:

The ramp, the height of the truck bed from ground and the distance of truck bed to the point the ramp makes contact with the ground form a right angle triangle.

So that sin 30 = height of truck bed above ground/length of ramp

sin 30 = height/80

height of the truck = 0.5 x 80 = 40cm

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The number of students in each classroom will be best modeled by a discrete relationship.

What is discrete relationship?

Discrete relationships are those relationships that contain finite or countable elements which means that the elements of such a relationship are distinct.

We are given four choices, from which we need to find the one which can be best modeled by this.

The weight of dog over time, the temperature inside a car and the cost of bananas cannot be modeled by discrete relationship because these are continuous variables.

Hence, the number of students in each classroom will be best modeled by a discrete relationship.

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The major parts of a salary range typically include the minimum, midpoint, and maximum salary for a position. The median salary is often used as a point of reference within a salary range, but is not considered one of the major parts.

The median salary is the salary at which half of the workers in an occupation earn less and half earn more.The midpoint is the average of the minimum and maximum salaries. It is used to calculate the median salary. The median salary is the salary that is in the middle of the minimum and maximum salaries. It is used to calculate the mean salary. The mean salary is the average of all the salaries.

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Answer:

B

Step-by-step explanation:

Graph shrinks, that means for every x value there is a higher y value. So coefficient of x is definitely more than 1. Try to substitute x = 1 to (9x)^2 and (3x)^2.

(3(1))^2 = 9

That each friend on the bus received 4 pieces of candy. The explanation for this is that if Carrie divided 36 pieces of candy by 8 friends, she is essentially performing the operation of division. 36 divided by 8 equals 4. Therefore, each friend received 4 pieces of candy. In conclusion, the answer to the question is 4 pieces of candy per friend.
Each friend received 4 pieces of candy.

To determine how many pieces of candy each friend received, you need to divide the total number of candies (36) by the number of friends (8). Using the formula:

Candies per friend = Total candies / Number of friends
Candies per friend = 36 / 8
Candies per friend = 4

Carrie divided her 36 pieces of candy equally among her eight friends, and each friend received 4 pieces of candy.

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The orientation of the image circle under the transformation w = 1/z is opposite to the orientation of the original circle |z| = 1.

Let's consider the points on the unit circle |z| = 1 in the complex plane. These points are represented by z = cos(θ) + isin(θ), where θ is the angle formed with the positive real axis.

Applying the transformation w = 1/z, we substitute z with its expression on the unit circle:

w = 1/(cos(θ) + isin(θ)).

To simplify, we multiply the numerator and denominator by the conjugate of the denominator:

w = (cos(θ) - isin(θ))/(cos^2(θ) + sin^2(θ)).

Simplifying further, we have:

w = cos(θ) - isin(θ).

The image of each point on the unit circle |z| = 1 corresponds to a point on the circle |w| = 1. However, the angle θ on the unit circle is mapped to the negative angle -θ on the image circle. This means that the image circle has a negative, or clockwise, orientation.

Therefore, the orientation of the image circle under the transformation w = 1/z is opposite to the orientation of the original circle |z| = 1.

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Answer:

Yo espero yo ayuda tu résolve estes équations

Step-by-step explanation:

a) x=8

b) x=-7

c) x=5,1

d) x=5/4

e) x=-3

f) x=5

Lo siento, mi español no son muy bien.

Answer:

TN/TS=NM/RS

\( \frac{240}{120} = \frac{x}{70 } \\ 120x = 16800 \\ x = 140\)

tan 36° can be written as cot 54°, which simplifies to (√3 + 1) / (√3 - 1).

The tangent of 36° can be expressed in terms of its cofunction, which is the cotangent. The cotangent of an angle is equal to the reciprocal of the tangent of that angle. Therefore, we can rewrite tan 36° as cot (90° - 36°).

Now, cot (90° - 36°) can be simplified further. The angle 90° - 36° is equal to 54°. So, we have cot 54°.

The cotangent of 54° can be determined using the unit circle or trigonometric identities. In this case, the exact answer for cot 54° is (√3 + 1) / (√3 - 1).

Hence, tan 36° can be written as cot 54°, which simplifies to (√3 + 1) / (√3 - 1).

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Answer: £150, 90

Step-by-step explanation:

Simplify 240

£150, 90

The probability of getting all heads in three-coin tosses is 1/8 or 0.1251. This means that there is a 12.5% chance that all of Zack’s tulips will be pink.

We know that the formula for finding a probability for any outcome is:

Probability = Number of favorable outcomes ÷ Total number of outcomes.

We know that, when a coin is tossed one time then, there are two sample space: {H,T}.

This means that we can get either a head or a tail when a coin is tossed once. Now, since the coin has been tossed 3 times, hence:

The total number of possible outcomes = 2³ =8

This is due to the fact that there are a total of 2ⁿ possible outcomes when a coin is tossed n times.

The eight outcomes would be as follows:

{HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}

We are asked to find the probability of getting three heads, or tulips be pink. Therefore,

Probability = 1/8.

Therefore, there are 12.5% chances that all of the Zack's tulips would be pink.

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Complete question is:

Read the story. Zack planted an assortment of tulip bulbs in his garden. half of them were pink tulips. this morning, he noticed that 3 of the tulips had started to sprout. how likely is it that all of them will be pink? Zack simulates the situation by flipping a coin 3 times. Each time the coin lands on heads, it represents a pink tulip.

This table shows the results of 100 trials:

number of heads flipped   0   1   2   3

number of trials                  12 37 38 11

Based on zack's results, what is the probability that all of the tulips will be pink?

a. The regular rate of markup on cost is approximately 26%.

b. The rate of markdown on the demonstrator unit is approximately 20%.

c. The operating profit on the demonstrator unit is approximately $3.73.

d. The rate of markup on cost that was actually realized is approximately 0.28%.

a. To calculate the regular rate of markup on cost, we need to find the difference between the selling price and the cost, and then calculate the percentage markup based on the cost.

Let's denote the cost as C.

Selling price = Cost + Markup

$1,690 = C + (26% of C)

To find the cost:

$1,690 = C + 0.26C

$1,690 = 1.26C

C = $1,690 / 1.26

C ≈ $1,341.27

Markup on cost = Selling price - Cost

Markup on cost = $1,690 - $1,341.27

Markup on cost ≈ $348.73

Rate of markup on cost = (Markup on cost / Cost) * 100

Rate of markup on cost = ($348.73 / $1,341.27) * 100

Rate of markup on cost ≈ 26%

The regular rate of markup on cost is approximately 26%.

b. The rate of markdown on the demonstrator unit can be calculated by finding the difference between the original selling price and the clearance price, and then calculating the percentage markdown based on the original selling price.

Original selling price = $1,690

Clearance price = $1,345

Markdown = Original selling price - Clearance price

Markdown = $1,690 - $1,345

Markdown = $345

Rate of markdown on the demonstrator unit = (Markdown / Original selling price) * 100

Rate of markdown on the demonstrator unit = ($345 / $1,690) * 100

Rate of markdown on the demonstrator unit ≈ 20%

The rate of markdown on the demonstrator unit is approximately 20%.

c. Operating profit or loss on the demonstrator unit can be calculated by finding the difference between the clearance price and the cost.

Cost = $1,341.27

Clearance price = $1,345

Operating profit or loss = Clearance price - Cost

Operating profit or loss = $1,345 - $1,341.27

Operating profit or loss ≈ $3.73

The operating profit on the demonstrator unit is approximately $3.73.

d. The rate of markup on cost that was actually realized can be calculated by finding the difference between the actual selling price (clearance price) and the cost, and then calculating the percentage markup based on the cost.

Actual selling price (clearance price) = $1,345

Cost = $1,341.27

Markup on cost that was actually realized = Actual selling price - Cost

Markup on cost that was actually realized = $1,345 - $1,341.27

Markup on cost that was actually realized ≈ $3.73

Rate of markup on cost that was actually realized = (Markup on cost that was actually realized / Cost) * 100

Rate of markup on cost that was actually realized = ($3.73 / $1,341.27) * 100

Rate of markup on cost that was actually realized ≈ 0.2781% ≈ 0.28%

The rate of markup on cost that was actually realized is approximately 0.28%.

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To expand its manufacturing capacity with a $20 million investment in new machinery while maintaining its current capital structure and dividend policy, Gardial GreenLights must seek external equity of $8 million.

The capital structure of Gardial GreenLights is characterized by a 50% debt-to-total-assets ratio. Since the company plans to maintain this ratio, the remaining 50% of the assets must be financed through equity. The investment in new machinery is $20 million, which represents 50% of the total assets needed for expansion. Therefore, the total assets required for expansion would be $40 million (20 million divided by 0.5). To determine the amount of external equity needed, we subtract the company's existing equity from the total assets required. Given that the company's dividend policy entails distributing 25% of the year's net income, we can calculate the retained earnings. This year's net income was $8 million, and 25% of that ($2 million) would be distributed as dividends. Therefore, the retained earnings amount to $6 million ($8 million - $2 million). Since external equity is the difference between the total assets required and retained earnings, Gardial GreenLights must seek external equity of $34 million ($40 million - $6 million) to finance its expansion plans.

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Answer:

angle TRU = angle TRS (RT bisects angle R)

RT = RT (Common side)

RU = RS (given)

so ∆ RUT ≅ ∆ RST (BY SAS)

There is sufficient evidence to conclude that the proportion of sales he makes to women is more than 75%.

At the 1% significance level, the critical value for a one-tailed test with 149 degrees of freedom is 2.326. Since the p-value of 0.0001 is much smaller than 0.01, we reject the null hypothesis that the proportion of sales made to women is equal to 0.75. Therefore, we can conclude that there is sufficient evidence to suggest that the proportion of sales made to women is more than 75%.

Note that we cannot conclude that the proportion of sales made to women is more than 50% because the null hypothesis assumes that the proportion is exactly 75%, not 50%. Furthermore, we have only tested the hypothesis that the proportion is greater than 75%, not whether it is greater than 50%. Therefore, the correct answer is: "There is sufficient evidence to conclude that the proportion of sales he makes to women is more than 75%."

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The true statements for the given function f(x) are:

The value of g(1) is 3 and the y- intercept of g(x) is at the point (0, 1) .

The function g(x) = f( x - 3 )

g (1) = f (1 -3 )

       = f (-2 )

       = 3

g (-1) = f (-1 -3)

       = f (-4)

       = - 1

Substituting , x = 0 to find the y intercept of g(x)

g ( 0 ) = f ( 0 - 3)

          =f (-3)

          =1

The y intercept of g(x) is at the point (0, 1)

Thus, options 1 and 4 are the true statements for the given function.

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Answer:

\(\sf\longrightarrow \boxed{\pink{\sf 3x + 4y -8=0}}\)

Step-by-step explanation:

We need to write the slope intercept form of the equation which passes through (4,-1) and parallel to the line y = -3/4x .

We know that the line parallel to a given line has the same slope . Therefore the slope of the line will be , ( on comparing to Slope Intercept Form ) .

\(\sf\longrightarrow Slope =\dfrac{-3}{4}\)

On using point slope form ,

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

Substitute the respective values ,

\(\sf\longrightarrow y - (-1) = \dfrac{-3}{4}( x - 4 ) \)

Simplify ,

\(\sf\longrightarrow y +1 = \dfrac{-3}{4}x + 3 \)

Multiply both sides by 4 ,

\(\sf\longrightarrow 4y + 4 = -3x + 12 \)

Put all terms on same side , i.e. on LHS ,

\(\sf\longrightarrow \boxed{\pink{\sf 3x + 4y -8=0}}\)

Hence the equation of the line is 3x + 4y - 8 = 0.

Answer:

The slope is 6

Step-by-step explanation:

f(x)=2(3x-7)

Distribute the 2

f(x)=2*3x-2*7

f(x) = 6x -14

This is in slope intercept form

y = mx+b  where m is the slope and b is the y intercept

The slope is 6 and the y intercept is -14

The slope is 6

Answer:

$488778

Step-by-step explanation:

Answer:

$488778

Step-by-step explanation:

For a for interest is;

i = PRT/100

Where;

R is rate

P is Principal

T is time

i is interest

We are given;

R = 12.5% = 0.125.

T = 146 days = (146/364) = 0.4011

i = $245

Thus;

245 = (P × 0.125 × 0.4011)/100

Thus;

P = (245 × 100)/(O.125 × 0.401)

P = $488778

3.a. The slope of the line is -2.

b. The y-intercept of the line is 17.

c. The equation of the line is y=-2x+17.

4. The correlation coefficient is -2.

5. When the number of losses is 20, the week is 6.

6. When the week is 15, the number of losses is -13.

It is calculated by dividing the vertical change (rise) between two points by the horizontal change (run) between the same two points.

3.a. The slope of the line is -2.

This can be determined by calculating the change in the y-values

(15-12=3,

12-10=2,

10-7=3,

7-6=1,

6-3=3,

and 3-1=2)

and dividing by the change in the x-values

(1-2=-1,

2-3=-1,

3-4=-1,

4-5=-1,

5-6=-1,

and 6-7=-1),

which gives us (3+2+3+1+3+2)/-6=-2.33=-2

b. The y-intercept of the line is 17.

This can be determined by finding the y-value when x=0.

Since there is no x=0 value in the table, we can use the equation of the line to calculate the y-value when x=0.

When x=0, y=17.

c. The equation of the line is y=-2x+17.

4. The coefficient of correlation is -2.

This can be determined by using the slope of the line, which is -2.

The coefficient of correlation is equal to the slope of the line, which is -2.

5. When the number of losses is 20, the week is 6.

This can be determined by using the equation of the line and solving for x when y=20.

When y=20,

-2x+17=20,

so 2x=3 and x=3/2, which is 6 weeks.

6. When the week is 15, the number of losses is -13.

This can be determined by using the equation of the line and solving for y when x=15.

When x=15,

y=-2(15)+17

=-13.

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\(\frac{1}{2} x+6(x+15)=12\\\\\frac{1}{2} x+6x+90=12\\\\6\frac{1}{2} x+90=12\\6\frac{1}{2} x=-78\\x=-12\)

\(y=x+15\\y=-12+15\\y=3\)

85.97 cubic centimeters

=====================================================

Work Shown:

\(V = \frac{1}{3}*\pi*r^2*h\\\\V = \frac{1}{3}*\pi*(3.9)^2*(5.4)\\\\V = \frac{1}{3}*(3.9)^2*(5.4)*\pi\\\\V = 27.378\pi\\\\V \approx 27.378*3.14\\\\V \approx 85.96692\\\\V \approx 85.97\\\\\)

The units for the volume are cubic centimeters which we can write shorthand as \(\text{cm}^3\) or as "cubic cm" or as "cc".

The volume 89.97 cubic cm is approximate since pi = 3.14 is approximate. Use more decimal digits of pi to get a more accurate volume.

It is False that based only on the r and p values listed above you can come to the conclusion that age is a moderator of the bivariate relationship between the amount of texting and the number of accidents.

In the given scenario, it is not completely true that based only on the r and p values listed above, you can come to the conclusion that age is a moderator of the bivariate relationship between the amount of texting and the number of accidents.

Let's first understand what is meant by the term "moderator.

"Moderator: A moderator variable is a variable that changes the strength of a connection between two variables. If there is a statistically significant bivariate relationship between the amount of texting during driving and the number of accidents, scientists investigate whether this bivariate relationship is moderated by age.

Therefore, based on the values of r and p, it is difficult to determine if age is a moderator of the bivariate relationship between the amount of texting and the number of accidents.

As we have to analyze other factors also to determine whether the age is a moderator or not, such as the sample size, the effect size, and other aspects to draw a meaningful conclusion.

So, it is False that based only on the r and p values listed above you can come to the conclusion that age is a moderator of the bivariate relationship between the amount of texting and the number of accidents.

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the sum of the terms of the series 36, 24, 16..., we can use the formula for the sum of an infinite geometric series is  is  -36,The limiting sum of a series is 36. If a = 8, we can find the value of r using the formula for the sum of an infinite geometric series is 7 / 9 and the total distance the ball falls is 16 meters.

Given a=−4 and r=2 in a geometric sequence, we can find the values of T3, T8, and Tn by using the formula for the nth term of a geometric sequence:

\(Tn = a * r^(n-1)\)

To find T3:
T3 = -4 * 2^(3-1)
T3 = -4 * 2^2
T3 = -4 * 4
T3 = -16

To find T8:
T8 = -4 * 2^(8-1)
T8 = -4 * 2^7
T8 = -4 * 128
T8 = -512

To find Tn, we need to know the value of n. Please provide the value of n to calculate Tn.

Now, let's move on to the series -3, 15, -75...

To find the common ratio (r), we can divide any term by its previous term. Let's use the second and first terms:

r = 15 / (-3)
r = -5

To find the first term (a), we can use the second term and the common ratio:

-3 = a * (-5)
a = -3 / (-5)
a = 3/5

Now, let's find the 11th term of the sequence:

T11 = a * r^(11-1)
T11 = (3/5) * (-5)^10
T11 = (3/5) * 9765625
T11 = 5859375/5
T11 = 1171875

Moving on to the next question:

1. To find the sum of the terms of the series 36, 24, 16..., we can use the formula for the sum of an infinite geometric series:

Sum = a / (1 - r)

Since this is an infinite series and the common ratio (r) is less than 1 in absolute value, the sum is finite. So, we can find the sum using the given values:

Sum = 36 / (1 - 2)
Sum = 36 / (-1)
Sum = -36

2. The limiting sum of a series is 36. If a = 8, we can find the value of r using the formula for the sum of an infinite geometric series:

Sum = a / (1 - r)

Substituting the given values:

36 = 8 / (1 - r)

Solving for r:

36(1 - r) = 8
36 - 36r = 8
36r = 36 - 8
36r = 28
r = 28 / 36
r = 7 / 9

3. A ball is dropped from 4 m and bounces back to 3/4 of its previous height. If it continues to bounce until it comes to rest, we need to find the total distance the ball falls.

The first fall from 4 m is straightforward, so the distance fallen is 4 m. For each subsequent bounce, the ball reaches 3/4 of its previous height, so the distance fallen decreases by a factor of 3/4 each time.

The total distance fallen can be calculated using the formula for the sum of an infinite geometric series:

Distance = a / (1 - r)

Substituting the given values:

Distance = 4 / (1 - 3/4)

Simplifying:

Distance = 4 / (1/4)
Distance = 4 * 4
Distance = 16 m

Therefore, the total distance the ball falls is 16 meters.
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