A rectangular prism has a volume of 160 cubic centimeters and a height of 4 centimeters. What is the area of its base?

The equation 5(x + 1) - x = 3(x - 1) + 7 has one solution which is x = -1.

An equation is the statement of two expressions located on two sides connected with an equal to sign. The two sides of an equation is usually called as left hand side and right hand side.

The given equation is,

5(x + 1) - x = 3(x - 1) + 7

Using the distributive property,

5(x + 1) = 5x + 5 and 3(x - 1) = 3x - 3

Substituting,

5x + 5 - x = 3x - 3 + 7

(5x - x) + 5 = 3x + (-3 + 7)

4x + 5 = 3x + 4

4x - 3x = 4 - 5

x = -1

Hence the solution of the given equation is -1.

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The area of the shaded sector is 4π square units.

To find the area of the shaded sector, we need to calculate the central angle formed by the sector. In this case, we are given that the angle JIK is 90 degrees, which means it forms a quarter of a full circle.

Since a full circle has 360 degrees, the central angle of the shaded sector is 90 degrees.

Next, we need to determine the radius of the circle. The line segment IJ represents the radius of the circle, and it is given as 4 units.

The formula to calculate the area of a sector is A = (θ/360) * π * r², where θ is the central angle and r is the radius of the circle.

Plugging in the values, we have A = (90/360) * π * 4².

Simplifying, A = (1/4) * π * 16.

Further simplifying, A = (1/4) * π * 16.

Canceling out the common factors, A = π * 4.

Hence, the area of the shaded sector is 4π square units.

Therefore, the area of the shaded sector, expressed as a fraction times π, is 4π/1.

In summary, the area of the shaded sector is 4π square units, or 4π/1 when expressed as a fraction times π.

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Answer:

y = T(x) = 8 + (9/shirt)x

Step-by-step explanation:

Represent "total amount" by T(x).  Then:

y = T(x) = 8 + (9/shirt)x

Here the shipping cost ($8) is a fixed cost and the cost of the x shirts is ($9/shirt)(x), where x is the number of shirts bought.

Note that this is a linear equation, and that 8 represents the vertical intercept and (9/shirt) the slope of the line representing the total cost.

The equation that shows the relationship between the number of T-shirts Manuel buys, x, and the total amount he will pay, y is y = 9x + 8.

The total amount Manuel will pay consists of the cost of the T-shirts and the shipping cost.

The cost of the T-shirts is $9 each, and the shipping cost is a flat $8.

The equation that shows the relationship between the number of T-shirts Manuel buys (x) and the total amount he will pay (y) can be written as y = 9x + 8.

Hence, y = 9x + 8 is the equation that shows the relationship between the number of T-shirts Manuel buys, x, and the total amount he will pay, y.

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The height of the part of the post that is above the ground is 10 - 3(1/3)

= 6(2/3) feet.

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Answer:

adult ticket $39 and youth ticket $21

Hope it helped

PLS mark BRAINLIEST

Answer:

A=82

C=83

X+y=60

X=30+50+80

X=80

Answer:

5089.3cm³

Step-by-step explanation:

Volume of cylinder

=  πr2h

= π×92×20

= 1620π

= 5089.3

\(Answer:\large\boxed{y=\frac{2}{3} x+6}\)

Step-by-step explanation:

First let's convert 2x - 3y = 12 into \(y = mx + b\)  form.

In order to do this, solve for y.

\(2x-3y=12\)

\(-3y=-2x+12\)

\(y=\frac{2}{3} x-4\)

This shows us that the slope is   \(\boxed{\frac{2}{3}}\)

Now we use the point-slope formula:

\((y-y1)=m(x-x1)\)

where m is the slope and y1 and x1 are the point the line passes through

Using the point (-6,2) and slope, 2/3, we can find the equation:

\((y-2)=\frac{2}{3} (x-(-6))\)

\((y-2)=\frac{2}{3} (x+6)\)

\((y-2)=\frac{2}{3} x+4\)

\(\large\boxed{y=\frac{2}{3} x+6}\)

Answer:

Julio debe $ 41225 al banco por concepto del préstamo para invertir en su casa.

Step-by-step explanation:

Dada la falta de información, asumimos que el préstamo fue realizado sin tasa de interés, de modo que la deuda solo sea el monto inicial menos las cuotas pagadas por quien recibe el préstamo, la cantidad de dinero que adeuda al banco es:

\(x = \$\,100000 - \$\,32950 - \$\,25825\)

\(x = \$ \,41225\)

Julio debe $ 41225 al banco por concepto del préstamo para invertir en su casa.

Answer:

3.67 hours

Step-by-step explanation:

Speed is the ratio of distance to time, it is given by the formula:

Speed = Distance / time

For annike her average speed was 11 miles per hour and she started at  7 am.

At 8 am (time = 1 hr i.e 7 am to 8 am) the distance she would have covered is given as:

11 miles/hr = distance / 1 hr

Distance = 11 miles per hr × 1 hr = 11 miles

After 8 am, the distance traveled at time t is:

11 = distance/t

distance = 11t

Total distance = 11t + 11

For Celia she started at 8 am at 14 miles per hour, at time t, the distance traveled is:

14 = distance/t

Distance = 14t  

Given that both bikers traveled the same distance, hence:

14t = 11t + 11

3t = 11

t = 11/3

t = 3.67 hours

Answer:

B

Step-by-step explanation:

Functions/equations for straight lines are in the form:

\(y=mx+c\)

Where m is the slope/gradient and where c is the y-intercept.

All we have to do for this equation s just a simple switch of 2 terms to make it in this format. By the way g(x) and y are the same.

g(x) = 19.60+1.74x

Swap 19.60 and 1.74x:

g(x)=1.74x+19.60

Now we can see that m = 1.74 not 1.74x

Answer:

100 x 25 x 4 = 10000\(m^{3}\)

Step-by-step explanation:

A= π r^2 = π*21^2 ≈ 1385.44236

Comment: RMS value is equal to the average value. This means that the signal does not have any high-frequency content. It can be inferred that the function y(t) does not oscillate. When the RMS value is less than the average value, it means that the signal has a lesser amount of high-frequency content.

Average and rms values for the function y(t)=25+10sin6πt over the time periods (a) 0 to 0.1 s, (b) 0.4 to 0.5 s, (c) 0 to 1/3 s, and (d) 0 to 20 s are as follows:

a) For t=0 to t=0.1s:

Average value, y_avg = 25

RMS value, y_RMS = 25.1987

Comment: RMS value is greater than the average value. This means that the signal has a considerable amount of high-frequency content. It can be inferred that the function y(t) oscillates rapidly.

b) For t=0.4 to t=0.5s:

Average value, y_avg = 25

RMS value, y_RMS = 28.2843

Comment: RMS value is greater than the average value. This means that the signal has a considerable amount of high-frequency content. It can be inferred that the function y(t) oscillates rapidly.

c) For t=0 to t=1/3 s:

Average value, y_avg = 25

RMS value, y_RMS = 23.7176

Comment: RMS value is less than the average value. This means that the signal has a lesser amount of high-frequency content. It can be inferred that the function y(t) oscillates slowly.

d) For t=0 to t=20 s:

Average value, y_avg = 25

RMS value, y_RMS = 25

Comment: RMS value is equal to the average value. This means that the signal does not have any high-frequency content. It can be inferred that the function y(t) does not oscillate. Comment on the nature and meaning of the results in terms of analysis of dynamic signals.The results indicate that the function y(t) oscillates rapidly at the start and end of the time period and slowly in the middle. When the RMS value is greater than the average value, it means that the signal has a considerable amount of high-frequency content.

On the other hand, when the RMS value is less than the average value, it means that the signal has a lesser amount of high-frequency content.

Furthermore, if the RMS value is equal to the average value, it means that the signal does not have any high-frequency content.

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Answer:

116 yards

Step-by-step explanation:

You first need to determine the length of string needed (in feet). So 6ft per baloon and she needs 58 baloons. 6 x 58 = 348 ft

You need to put this answer into yards. 3ft = 1 yard

So divide 348 by 3 and you get 116 yards of string needed

Answer:

116 yards

Step-by-step explanation:

There are three feet in a yard, so two yards for each balloon. If you then multiply the number of ballons by 2 (yards) you get 116 yards.

Answer:

Your answer is: k = 5+12/x

Isolate the variable by dividing each side by factors that don't contain the variable.

Step-by-step explanation:

Hope this helped : )

Answer:

1 - 4sqrt3

2 - 6sqrt2

3 - 6sqrt7

4 - 7sqrt2

5 - 5sqrt6

6 - 2sqrt30

Step-by-step explanation:

The length of the actual hotdog is 15 cm

The graph that completes the question is added as an attachment

The length of the hotdog in the figure is given as

Length = 9 units

The scale is given as

Scale: 6 units = 10 cm

So, we have

6 * 9 units = 10 * 9 cm

Divide both sides by 6

So, we have

9 units = 15 cm

Substitute 9 units = 15 cm in Length = 9 units

Length = 15 cm

Hence, the length of the actual hotdog is 15 cm

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Answer:

Step-by-step explanation:

the first one is the right one

Answer:

C.  30(-2)= -60 is the correct answer

Step-by-step explanation:

(i)The impulse response h(t) is a quadratic function that opens downward and has roots at t = -1. (ii)Therefore, by evaluating the convolution integral with the given input signal x(t) and impulse response h(t), we can determine the output signal y(t) and sketch its graph based on the obtained expression.

i. To sketch the signals x(t) and h(t), we can analyze their mathematical expressions. The input signal x(t) is a linear function with negative slope from t = 0 to t = 4, and it is zero for t > 4. The impulse response h(t) is a quadratic function that opens downward and has roots at t = -1. We can plot the graphs of x(t) and h(t) based on these characteristics.

ii. To determine the output signal y(t), we can use the convolution integral, which is given by the expression:

y(t) = ∫[x(τ)h(t-τ)] dτ

In this case, we substitute the expressions for x(t) and h(t) into the convolution integral. By performing the convolution integral calculation, we obtain the expression for y(t) as a function of t.

To sketch the output signal y(t), we can plot the graph of y(t) based on the obtained expression. The shape of the output signal will depend on the specific values of t and the coefficients in the expressions for x(t) and h(t).

Therefore, by evaluating the convolution integral with the given input signal x(t) and impulse response h(t), we can determine the output signal y(t) and sketch its graph based on the obtained expression.

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First let's make the picture of the movement of the little sister:

The green line represents the first trip and the red line represents the trip back.

Since she traveled 1000m and then came back 300m, we have that:

therefore, the little sister displaced 700 meters and she traveled 1300m

No, statistics and quantitative data are not necessarily more valid and objective than qualitative research.

While quantitative data can provide precise numerical measurements, it may not capture the full complexity of a particular phenomenon or experience. Qualitative research, on the other hand, can offer rich and nuanced insights into human behavior and attitudes. It allows for a deeper understanding of the context and meaning behind the data.

Ultimately, the choice between quantitative and qualitative research depends on the research question and the goals of the study. Both methods have their strengths and limitations, and it is important to consider them carefully when designing a study.

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The ordered pairs which are on the graph of 7x - y = 2 as required in the task content are; Choices B and C; (-1, -9) and (0, -2).

It follows from the task content that the ordered pairs which are on the graph of 7x - y = 2 be determined.

Hence, by testing each pair as follows; we have;

Ultimately, the required ordered pairs are; (-1, -9) and (0, -2).

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the center of the ball rests on the table which implies that the y-coordinate of the center of the ball is zero since we have selected the table as the reference plane

the bottom of the ball as its reference point, the y-axis along a vertical line, and the positive direction as pointing upward can be calculated as follows:The y-coordinate of the ball = (y-coordinate of the center of the ball) - (the radius of the ball)As per the given problem, the center of the ball rests on the table which implies that the y-coordinate of the center of the ball is zero since we have selected the table as the reference plane.Hence, the y-coordinate of the ball = 0 - 2= -2Therefore, the y-coordinate of the ball is -2.

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The distribution of weights of adult dogs is strongly skewed right, with a mean of 15 pounds and a standard deviation of 4 pounds.

A right-skewed distribution means that the tail of the distribution extends towards larger values, indicating a larger number of lighter dogs and fewer heavier dogs. In this case, the mean weight of adult dogs is 15 pounds, indicating the central tendency of the distribution.

The standard deviation of 4 pounds measures the variability or spread of the weights around the mean. A larger standard deviation suggests a wider range of weights in the distribution.

Understanding the shape, mean, and standard deviation of the weight distribution provides valuable information about the characteristics of the breed.

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The equation of the curve that passes through the point (0, 1) and has a slope of 5xy at any point (x, y) is y = (5/2) * x^2y + 1. This equation represents a curve where the y-coordinate is a function of the x-coordinate, satisfying the conditions.

To determine an equation of the curve that satisfies the conditions, we can integrate the slope function with respect to x to obtain the equation of the curve. Let's proceed with the calculations:

We have:

Point: (0, 1)

Slope: 5xy

We can start by integrating the slope function to find the equation of the curve:

∫(dy/dx) dx = ∫(5xy) dx

Integrating both sides:

∫dy = ∫(5xy) dx

Integrating with respect to y on the left side gives us:

y = ∫(5xy) dx

To solve this integral, we treat y as a constant and integrate with respect to x:

y = 5∫(xy) dx

Using the power rule of integration, where the integral of x^n dx is (1/(n+1)) * x^(n+1), we integrate x with respect to x and get:

y = 5 * (1/2) * x^2y + C

Applying the initial condition (0, 1), we substitute x = 0 and y = 1 into the equation to find the value of the constant C:

1 = 5 * (1/2) * (0)^2 * 1 + C

1 = C

Therefore, the equation of the curve that passes through the point (0, 1) and has a slope of 5xy at any point (x, y) is:

y = 5 * (1/2) * x^2y + 1

Simplifying further, we have:

y = (5/2) * x^2y + 1

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Answer:

18 pounds = 48 pizzas

18 pounds = 48 pizzas 22.5 pounds = 60 pizzas

18 pounds = 48 pizzas 22.5 pounds = 60 pizzas 27 pounds = 72 pizzas

Step-by-step explanation:

1) because they are ratios you multiply 18 and 8 (18 × 8 = 144) then you divide 144 by 3 (144÷3 =48)

2) now you do the same thing multiply 22.5 and 48 (22.5 × 48= 1,080) and divide 1,080 by 18 (1,080 ÷ 18= 60)

3) multiply 27 times 60 (27 × 60= 1,620) now divide 1,620 by 22.5 (1,620 ÷ 22.5= 72)

The table is:

Cheese   Number of Pizzas

3 pounds          8

18 pounds        48

22.5 pounds    60

27 pounds        72

It is the quantity of an amount of something at a rate of one of another quantity.

In 2 hours, a man can walk for 6 miles

In 1 hour, a man will walk for 3 miles.

We have,

3 pounds bag of cheese makes 8 pizzas.

This means,

3 pounds = 8 pizzas

1 pound = 8/3 pizzas

Now,

1 pound = 8/3 pizzas

Multiply 18 on both sides.

18 pounds = 18 x 8/3

18 pounds = 48 pizzas

1 pound = 8/3 pizzas

Multiply 22.5 on both sides.

22.5 pounds = 22.5 x 8/3

22.5 pounds = 60 pizzas

1 pound = 8/3 pizzas

Multiply 27 on both sides.

27 pounds = 27 x 8/3

27 pounds = 72 pizzas

Thus,

The number of Pizzas for 3 pounds is 8.

The number of Pizzas for 18 pounds is 48.

The number of Pizzas for 22.5 pounds is 60.

The number of Pizzas for 27 pounds is 71.

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Answer:

233,905 doctors

Step-by-step explanation:

if 23.3% = 54500

100% = 233,905.5794

= 233,905 doctors