A rectangle with a length of 10 inches and a width of 6 inches is rotated around its length. What is the volume of the resulting solid in terms of Pi?

The image of the bar chart is missing and so i have attached it.

Answer:

Bus = 75

Cycle = 20

Walk = 45

Step-by-step explanation:

We are told that 50 students said they travel to school by car.

However, in the bar chart, we see that we have a portion for boys and girls

Under car, when we count along the y-axis, we will see that, there are 6 units for boys and 4 units for girls.

Thus, to find the value of a unit since number of people that took cars is 50, we have;

(6x + 4x)/2 = 50

Where x is the value of one unit. Thus;

10x/2 = 50

5x = 50

x = 50/5

x = 10

Thus, a unit is 10

Under bus;

Boys have 7 units while girls have 8 units.

Thus;

Frequency by bus = ((7 × 10) + (8 × 10))/2 = 150/2 = 75

Under cycle;

Boys have 1 unit while girls have 3 units.

Thus;

Frequency by cycle = ((1 × 10) + (3 × 10))/2 = 20

Under walk;

Boys have 5 units while girls have 4 units.

Thus;

Frequency by cycle = ((5 × 10) + (4 × 10))/2 = 45

Answer:

5n-3n= 14-6

2n=8

n=8/2

n=4

..............................................

-----------------------------------

14 + 3n = 5n - 6

3n - 5 = -6 - 14

-2n = -6 - 14

-2n = - 20

n = 10

<3

It took Torrin 15.75 minutes to ride to school

Torrin house is 3.54 km away from school

An exponential equation is an expression that shows how numbers and variables using mathematical operators.

Let d represent the distance from Torrin home to school.

Let x represent the time it takes Torrin riding at 13.5 km/h and y represent the time it takes Torrin riding at 10.5 km/h

Torrin took a total of 36 min (0.6 hour) to ride to school and back, Hence:

x + y = 36    (1)

Also:

13.5 = d/x

d = 13.5x

10.5 = d/y

d = 10.5y

13.5x = 10.5y      (2)

Solving equation 1 and 2 simultaneously:

x = 0.2625 hours = 15.75 minutes

y = 0.3375 hour = 20.25 minutes

d = 10.5y = 10.5(0.3375) = 3.54 km

It took Torrin 15.75 minutes to ride to school

Torrin house is 3.54 km away from school

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No.1

Set those two equations equal to each other.

-7/4 x - 4 = -1/4 x + 2

x on one side, constant on other side.

-6/4 x = 6

x = -4

now put x value into any of the two equations given

y = -7/4 * -4 - 4 = 7 - 4 = 3

(-4,3)

No.2

Set those two equations equal to each other.

x + 2 = -1/5 x - 4

x on one side, constant on other side.

6/5 x = -6

x = -5

now put x value into any of the two equations given

y = -5 + 2 = -3

(-5,-3)

Answer:

45 times

Step-by-step explanation:

There are nine pink sections and 11 sections total. The probability of landing on a pink section is 9/11.

Multiply the probability by 55

\(\frac{9}{11}\) × \(\frac{55}{1}\)

Cancel the 11 and 55. The 11 becomes a 1 and 55 becomes a 5

\(\frac{9}{ 1}\) × \(\frac{5}{1}\)

45

Answer:

58%

Step-by-step explanation:

47/81 x 100%

≈ 58%

Hope it helps : )

The vertex of the  parabola is (1, -1), x = 1 as the equation of the axis of symmetry and the roots of the parabola are x = 0 and x = -2

The graph represents the given parabola

As a general rule:

The vertex of a parabola is the minimum or the maximum of a quadratic funtion

In this case, we have

Minimum = (1, -1)

This means that the vertex of the given parabola is (1, -1)

The equation of the axis of symmetry is the x-coordinate of the vertex

In this case, we have

x = 1 as the equation of the axis of symmetry

These are the points where the graph crosse the x-axis

In this case, the roots of the parabola are x = 0 and x = -2

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To find the value of z corresponding to a cumulative standardized normal distribution of 0.2090, we can use a standard normal distribution table or a calculator. The value of z is approximately -0.82 when rounded to two decimal places.

In a standard normal distribution, the cumulative standardized normal distribution represents the area under the curve to the left of a given z-score. In this case, we are given a cumulative probability of 0.2090, which indicates that 20.90% of the area under the curve lies to the left of the corresponding z-score.

By referring to a standard normal distribution table or using a calculator that provides the cumulative distribution function (CDF) for the standard normal distribution, we can find the closest corresponding z-score. In this case, the value of z that corresponds to a cumulative probability of 0.2090 is approximately -0.82 when rounded to two decimal places.

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Answer:

Step-by-step explanation:

It would be either A or C

Most likely A Hope this helps ya <3

The word describing 5 in the given expression is a coefficient.

An expression, in math, is a sentence with a minimum of two numbers and at least one math operation in it.

Given that an expression 5n, we need determine the word used for number 5,

We know that, the numbers connected to a variable by multiplication is called a coefficient.

Here,

5n = 5 × n,

n = variable, 5 = coefficient.

Hence the word describing 5 in the given expression is a coefficient.

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Answer:

8.1

Step-by-step explanation:

Subtract 2.9 to get Y alone.

11 - 2.9 = 8.1

Answer:

cool!!

Step-by-step explanation:

Answer:

X = 65.

Step-by-step explanation:

The range is the greatest number - least, so we have:

X - 12 = 53

X = 53 + 12 = 65.

Answer:

I think x=65

Step-by-step explanation:

Hope this helped have an amazing day/month/year!

Answer:

An exponential function has the form `f(x) = ab^x`, where `a` and `b` are constants. To find the exponential function that passes through the points `(-2,1)` and `(-1,2)`, we can use these points to set up a system of equations to solve for the values of `a` and `b`.

Substituting the coordinates of the first point into the equation for an exponential function gives us:

`1 = ab^(-2)`

Substituting the coordinates of the second point into the equation for an exponential function gives us:

`2 = ab^(-1)`

Dividing these two equations gives us:

`(2)/(1) = (ab^(-1))/(ab^(-2))`

`2 = b`

Now that we know that `b=2`, we can substitute this value back into either equation to solve for `a`. Substituting into the first equation gives us:

`1 = a(2)^(-2)`

`1 = a(1/4)`

`a = 4`

So, the exponential function that passes through the points `(-2, 1)` and `(-1, 2)` is given by:

`f(x) = 4 * 2^x`.

To find the exponential function for the graph passing through (-2,1) and (-1,2), we need to use the general form of an exponential function, which is:

y = a * b^x

where:

a is the initial value or the y-intercept of the function

b is the base of the exponential function

x is the variable or the exponent

To determine the values of a and b, we need to use the two given points and solve for the corresponding equations. Substituting the first point (-2,1), we get:

1 = a * b^(-2)

Substituting the second point (-1,2), we get:

2 = a * b^(-1)

Now, we can solve for a and b by eliminating one variable. Dividing the second equation by the first equation, we get:

2/1 = a * b^(-1) / (a * b^(-2))

2 = b

Substituting this value of b into the first equation, we get:

1 = a * 2^(-2)

a = 4

Therefore, the exponential function that passes through (-2,1) and (-1,2) is:

y = 4 * 2^x

or

f(x) = 4 * 2^x

Answer:

molar mass of carbon-12

Step-by-step explanation:

Answer:

10:4, 15:6, 20:8

hope that helps.

The graph of the linear equation, 5x - 9y = -7, is in the attachment below.

The linear equation that models a graph can be written in  slope-intercept equation as y = mx + b. The value of the slope, which is the rise over the run of the line is represented as m, while the value of b, which is where the line intercepts the y-axis is b.

Given the linear equation, 5x - 9y = -7, rewrite in slope-intercept form:

5x - 9y = -7

-9y = -5x - 7

-9y/-9 = -5x/-9 - 7/-9

y = 5/9x + 7/9

This means the rise over the run of the line, m is 5/9, while the y-intercept of the graph, b is 7/9.

The graph is shown below.

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Answer:

1. 7x

2. 8x - 1

3. 6x + 12

4. 3x + 4

5. 13x - 7

Step-by-Step Explanation:

Hope this helps!

Answer:

1. 7x

2. 8x -1

3. 6x+12

4. 3x + 4

5. 13x -7

Step-by-step explanation:

It is given that:

1. 4x + 3x

  7x

2. 3x + 5x - 1

   8x -1

3.  5 + 2x + 7 + 4x

   2x+4x+5+7

   6x+12

4. 4 - 2x + 5x

   4 + 3x

  3x + 4

5. 10x - 5 + 3x - 2

   10x + 3x -5 -2

   13x - 7

Therefore,

1. 7x

2. 8x -1

3. 6x+12

4. 3x + 4

5. 13x -7

Answer:

\(120^{0}\)

Step-by-step explanation:

Given: pentagon (5 sided polygon), two interior angles = \(90^{0}\) each, other three interior angles are congruent.

Sum of angles in a polygon = (n - 2) × \(180^{0}\)

where n is the number of sides of the polygon.

For a pentagon, n = 5, so that;

Sum of angles in a pentagon = (5 - 2) × \(180^{0}\)

                                                = 3  × \(180^{0}\)

                                                = \(540^{0}\)

Sum of angles in a pentagon is \(540^{0}\).

Since two interior angles are right angle, the measure of one of its three congruent interior angles can be determined by;

\(540^{0}\) - (2 × \(90^{0}\))  = \(540^{0}\) - \(180^{0}\)

                       = \(360^{0}\)

So that;

the measure of the interior angle = \(\frac{360^{0} }{3}\)

                                                        = \(120^{0}\)

The measure of one of its three congruent interior angles is \(120^{0}\).

Answer:

y = 3 may I please get brainliest?

Step-by-step explanation:

y= -3x+5

y= -3(2/3)+5

-3(2/3) = -2

y= -2+5

-2+5 = 3

y=3

The artist sold 32 smaller candles and 20 larger candles.

An equation is a mathematical statement that shows the equality of two expressions. It contains an equals sign (=) and at least one variable. An equation can be true or false depending on the values of the variables. Solving an equation involves finding the value or values of the variable that make the equation true. Equations are used to model relationships between different quantities in a wide range of fields, including mathematics, physics, chemistry, economics, and engineering.

A. Let's represent the number of smaller candles sold as x and the number of larger candles sold as y. We know that x + y = 52 (since a total of 52 candles were sold) and 4x + 7y = 269 (since the total sales was $269 and smaller candles sell for $4 and larger candles sell for $7). We can use these two equations to solve for x and y.

Multiplying the first equation by 4, we get 4x + 4y = 208. Subtracting this from the second equation, we get:

4x + 7y - (4x + 4y) = 269 - 208

3y = 61

y = 20.33

This means that the artist sold 20.33 larger candles. However, since we cannot sell a fractional part of a candle, we need to round this down to 20. Similarly, we can find x by subtracting y from 52:

x = 52 - y = 52 - 20 = 32

So the artist sold 32 smaller candles and 20 larger candles.

B. The answer is reasonable since the number of smaller candles sold is larger than the number of larger candles sold, and the total sales amount is closer to the price of the smaller candle than the larger candle. This implies that the artist's records are likely accurate.

Therefore, the artist sold 32 smaller candles and 20 larger candles.

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The volume of the solid obtained by rotating the region bounded by the curves x = 5y^2, y = 2, x = 0 about the y-axis is 125π/7 cubic units.The region bounded by the curves x = 5y^2, y = 2, x = 0 is a parabola that opens to the right. When this region is rotated about the y-axis, a solid is created. The volume of the solid can be found using the formula V = π∫[a,b] (f(y))^2 dy.

To solve this problem, we will use the formula for finding the volume of a solid of revolution about the y-axis, which is:

V = π∫[a,b] (f(y))^2 dy, where f(y) is the equation of the curve being revolved, and [a,b] is the interval of y-values.

To find the interval of y-values, we need to solve for the y-value of the point where the parabola x = 5y^2 intersects the line

y = 2:5y^2 = 2

=> y^2 = 2/5

=> y = ±√(2/5).

Since we are revolving about the y-axis, our interval of integration will be [0, √(2/5)].

We can now set up the integral:

V = π∫[0, √(2/5)] (5y^2)^2 dy = π∫[0, √(2/5)] 25y^4 dy = 125π/7.

The volume of the solid obtained by rotating the region bounded by the curves x = 5y^2, y = 2, x = 0 about the y-axis is 125π/7 cubic units.

We are given the region bounded by the curves x = 5y^2, y = 2, x = 0, and we are asked to find the volume of the solid obtained by rotating this region about the y-axis.

To do this, we will use the formula for finding the volume of a solid of revolution about the y-axis, which is:V = π∫[a,b] (f(y))^2 dy, where f(y) is the equation of the curve being revolved, and [a,b] is the interval of y-values.First, we need to determine the interval of y-values.

To do this, we need to find the y-value of the point where the parabola x = 5y^2 intersects the line

y = 2:5y^2 = 2

=> y^2 = 2/5

=> y = ±√(2/5).

Since we are revolving about the y-axis, our interval of integration will be [0, √(2/5)].We can now set up the integral:V = π∫[0, √(2/5)] (5y^2)^2 dy = π∫[0, √(2/5)] 25y^4 dy = 125π/7.

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Answer: 5x2x2x3x3 is the answer to your question

Probability that the mean childhood asthma prevalence for the sample is greater than 2.6% is 0.0357 or 3.57 %.

What is Probability ?

Probability is the measure of likelihood of an event.

For a Normal Distribution ,

the z-score formula is given by

\(\rm Z = \dfrac{X - \mu }{\sigma}\)

Here \(\rm \mu\\\) is the mean and \(\rm \sigma\\\) is the standard deviation .

It is the measure of the deviation of the data from its central tendency.

Each z-score has a probability value.

It is given in the question that

Mean of 2.16% =  \(\rm \mu\\\) = 2.16

Standard deviation of 1.36% means that  \(\rm \sigma\\\) = 1.36

For Sample of 31 the value of standard deviation is \(\rm s = \dfrac{\sigma}{\sqrt{n}}\)

s = 1.36/√31

s = 0.2442

Substituting the values

Z = (2.6 -2.16)/0.2442

Z =1.8

the p value from the graph of z and p , 0.9643

To determine value of probability  more than X is 1 - 0.9643= 0.0357

the

Probability that the mean childhood asthma prevalence for the sample is greater than 2.6% is 0.0357.

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Answer:

__________-3<Y<4______________

Given that cot(0) = 4/3 and theta is in Quadrant I, what is sin(theta)?

we have that

If angle theta is in quadrant I , then the value of sin(theta) is positive

Remember that

tan(theta)=1/cot(theta)

so

tan(theta)=3/4

substitute in the expression above

is positive because is quadrant I

remember that

sec(theta)=1/cos(theta)

so

cos(theta)=4/5

tan(theta)=3/4

tan(theta)=sin(theta)/cos(theta)

substitute given values

3/4=sin(theta)/(4/5)

sin(theta)=(3/4)*(4/5)=3/5

the answer is

Answer: 1.  x = 2

2. x = -2

Step-by-step explanation:

The proofing of the line segments AD,E(eff) illustrate that bisect each other at right angles.

Based on the information given, it should be noted that the line segment that is given is parallel to the third side.

This will be illustrated as:

DE = D(eff)(AB = AC) Also, A(eff)= AE

A(eff) = 1/2AB, AE = 1/2AC

DE = AE = A(eff)=D(eff)

This illustrates that the line segments AD,E(eff) bisect each other at right angles.

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Answer:

30, 60, 120, 180

Step-by-step explanation:

hope this helps

The correct value of p(x<8) is 1.875.

To determine how probable something is gonna occur, use probability. It is a number between 0 and 1, where 0 denotes the absence of a possibility and 1 denotes the existence of one. By dividing the number of favorable outcomes by the entire number of potential possibilities, the probability of an occurrence is determined.

To find the probability that is greater than 8, we need to integrate this probability density function from 5.5 to 20.5:

P(X < 8) = ∫[5.5,20.5] f(x) dx

= ∫[5.5,20.5] (1/8) dx

= [x/8] from 5.5 to 20.5

= (20.5/8) - (5.5/8)

= 15/8

= 1.875.

Therefore, the correct probability is 1.875.

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You would need to wait approximately 51.33 years from now to grow your initial investment of $39,000 to $174,000 at an interest rate of 10% per year.

To calculate the number of periods (years) required to grow an initial investment to a desired future value, we can use the formula for compound interest:

FV = PV * \((1 + r)^n\)

Where:

FV is the future value

PV is the present value (initial investment)

r is the interest rate per period

n is the number of periods

In this case:

PV = $39,000

FV = $174,000

r = 10% per year

Let's calculate the number of periods (years):

FV = PV * \((1 + r)^n\)

174,000 = 39,000 * \((1 + 0.10)^n\)

Divide both sides by 39,000:

4.4615 = \((1.10)^n\)

Take the logarithm of both sides to solve for n:

log(4.4615) = n * log(1.10)

n ≈ log(4.4615) / log(1.10)

n ≈ 2.1270 / 0.0414

n ≈ 51.33 (rounded to two decimal places)

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