Use graph to work out x and y

The ratio of density of cylinder A to cylinder is 8 : 49.

The ratio of the density of the two cylinders is calculated as follows;

The formula for the density of the cylinders is given as;

density = m / (πr²h)

For cylinder A and B;

height = h = h_B = h

mass = m, m_B = 2m_A = 2m

radius, = r, r_B = 4/7r_A = 4/7r

Density of cylinder A = m / (πr²h)

Density of cylinder B = 2m/(π(4/7r)²h = 2m/π16r²h/49  = (2m x 49)/π16r²h

Ratio of the two densities is calculated as;

A/B =  m / (πr²h)     x       π16r²h / (2m x 49)

= 16/(2 x 49)

= 8/49

= 8 : 49

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Answer:

Option A:

A. Each side of 5√x = 10 should be squared.

(5√x)^2 = 10^2

25x = 100, so x = 4

B. x = -6 is an extraneous solution, so x = 2 is the only solution. When solving equations with radicals, you need to check for extraneous solutions.

Option B:

[tex] \sqrt{2x} + 5 = 1[/tex]

does not have any real solutions.

[tex] \sqrt[4]{m + 4} - \sqrt[4]{3m} = 0[/tex]

[tex] \sqrt[4]{m + 4} = \sqrt[4]{3m} [/tex]

[tex]m + 4 = 3m[/tex]

[tex]2m = 4[/tex]

[tex]m = 2[/tex]

Jim can alone finish painting fence in 6 hours, is the required answer of the word problem.

The given question is a word problem which can calculated as,

Tom and Huck paints a fence for four hours.

If Jim had not helped them to finish the work it would have taken Tom and Huck 5 more hours to finish.

That is, in (4+5)hours = 1 (total work)

⇒ in 9 hours = 1 (total) work is done

⇒ in 1 hour = 1/9 work is done

After Jim helped Tom and Huck after 4 hours they finished the work in 2 more hours.

That is, in 6 hours they did the total work.

Total work done by jim is = 1 - (4/9)

Since, Tom and Huck had already worked for 4 hours before Jim.

Thus. Work done by jim is 5/9 in two hours along with tom and Huck.

Work done by three of them in  1 hour is  = 5/9*2 = 5/18

Therefore, work done by Jim in 1 hour = Work done by three of them in 1 hour - Work done by Tom and Huck in one hour

= 5/18 - 1/9

= 1/6

Thus, Jim can alone finish the total work in 6 hours.

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Paolo makes $2 per hour and his earnings is proportional to the hours worked

The graph is added as an attachment

Start by calculating the slope of the graph as follows

Slope = (y2 - y1)/(x2 - x1)

So, we have

Slope = (6 - 0)/(3 - 0)

Evaluate

Slope = 3

This mens that

Paolo makes $2 per hour

Because the graph is a proportional graph, then Paolo's earnings is directly proportional to the number of hours worked

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Answer: y = -3x^2 + 24x - 45

Step-by-step explanation:

To find the equation of the parabola with a vertex of (4, 3) and passing through points (2, -9) and (5, 0), we can use the vertex form of a parabolic equation:

y = a(x - h)^2 + k

Here, (h, k) is the vertex of the parabola. So, we have:

y = a(x - 4)^2 + 3

Now, we need to find the value of 'a' using the two points (2, -9) and (5, 0).

First, let's plug in the point (2, -9):

-9 = a(2 - 4)^2 + 3

-9 = a(-2)^2 + 3

-9 = 4a + 3

Subtract 3 from both sides:

-12 = 4a

Now, divide both sides by 4:

a = -3

Now that we have the value of 'a', we can plug it back into the equation:

y = -3(x - 4)^2 + 3

This is the equation of the parabola in vertex form. To convert it to standard form, we can expand the equation:

y = -3(x^2 - 8x + 16) + 3

y = -3x^2 + 24x - 48 + 3

Now, combine the constants:

y = -3x^2 + 24x - 45

This is the equation of the parabola in standard form.

The measure of the angle of the circle is ∠STR = 224°

Given data ,

Let the measure of the central angle be ∠STR

Now , the measure of the arc angle = 112°

And , Central Angle = 2 x Angle in other segment

So , on simplifying , we get

m∠STR = 2 ( 112 )°

m∠STR = 224°

Hence , the measure of angle is 224°

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Answer:

The answer for Length is D

110m

Step-by-step explanation:

P=2L+2W

L=20+W

400=2(20+W)+2W

400=40+2W+2W

C.L.T

400-40=4W

360=4W

divide both sides by 4

4W/4=360/4

W=90m

L=20+W

L=20+90

L=110m

Answer:

Sure. Here are the steps on how to find the area P(x>290) when the mean is 304 and the standard deviation is 8:

Convert the mean and standard deviation to z-scores.

The z-score is a way of standardizing a distribution so that it has a mean of 0 and a standard deviation of 1. To calculate the z-score for a given value, we use the following formula:

z = (x - μ) / σ

where:

x is the value we are interested in

μ is the mean of the distribution

σ is the standard deviation of the distribution

In this case, the mean is 304 and the standard deviation is 8, so the z-score for 290 is:

z = (290 - 304) / 8 = -2.00

Find the area under the standard normal curve that corresponds to the z-score.

We can use a z-table to find the area under the standard normal curve that corresponds to a given z-score. The z-table is a table that lists the area under the standard normal curve for different z-scores.

Looking up the z-score of -2.00 in the z-table, we find that the area is 0.0228.

Multiply the area by 100 to get the probability.

The area under the standard normal curve is expressed as a percentage. To get the probability, we need to multiply the area by 100.

In this case, the area is 0.0228, so the probability is 2.28%.

Therefore, the area P(x>290) when the mean is 304 and the standard deviation is 8 is 2.28%.

Step-by-step explanation:

Answer:

x=5

Step-by-step explanation:

Multiply 3 on both sides.

Add 8 to both sides.

Divide both sides by -2

The graph of the inequality expression 10x+5y < -4 is attached

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

10x+5y-4

Express properly

So, we have

10x+5y < -4

Next, we plot the graph using a graphing tool

The graph is added as an attacment

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To find the zeros of the equation:

2 = x^2 - 10x

we first need to rearrange the equation into standard quadratic form:

x^2 - 10x - 2 = 0

Now we can use the quadratic formula to solve for x:

x = (-b ± sqrt(b^2 - 4ac)) / 2a

where a = 1, b = -10, and c = -2.

Substituting these values, we get:

x = (-(-10) ± sqrt((-10)^2 - 4(1)(-2))) / 2(1)

Simplifying inside the square root:

x = (10 ± sqrt(100 + 8)) / 2

x = (10 ± sqrt(108)) / 2

x = (10 ± 6√3) / 2

x = 5 ± 3√3

Therefore, the zeros of the equation are:

x = 5 + 3√3 and x = 5 - 3√3

The maximum number of taffy Nadia can buy is 11.

As per the question,

Nadia spends 7 x $0.55 = $3.85 on bags of chips.

She has $8.00 - $3.85 = $4.15 left to spend on taffy.

Now, divide the amount of money she has left by the cost of each taffy to find the maximum number of taffy Nadia can buy:

= $4.15 ÷ $0.35

= 11.857, which rounds down to 11.

Therefore, the maximum number of taffy she can buy is 11.

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Answer:

The answer for the value of x is 9.025 to 3SF

The side length of the square, denoted as x, is found to be approximately 6.38 cm, obtained by working out the relationships between the circle's radius, diameter, and the square's diagonal.

In this mathematics problem, we can solve for x by first understanding the relationship between the square and the circle. Since each vertex of the square is on the circumference of the circle, the diameter of the circle is equal to the diagonal of the square. We can find the diameter of the circle using the formula for the area of a circle, which is A = πr² where r is the radius.

Given the area of the circle as 64 cm², we solve for r, which yields approximately 4.52 cm. The diameter then is twice the radius, approximately 9.05 cm. Now, for a square inscribed in a circle, the diagonal is given by √x² + x² = d². Here, d is the diameter of the circle.

Solving for x, we get that x, the side of the square, is approximately 6.38 cm to three significant figures.

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Answer:

92

Step-by-step explanation:

Since every single triangle is 180 degrees, we can add 46 + 42 and subtract that from 180 to get our answer.

[tex]46+42=88[/tex]

[tex]180-88=92[/tex]

You can check your work by:

[tex]46+42+92=180[/tex]

[tex]180=180[/tex]

So your answer is 92.

Hope this helps!

The distance to the lightbulb is 28.22 meters.

The brightness of a light source decreases as distance from the source increases. This relationship is described by the inverse square law that says brightness of a light source is inversely proportional to the square of the distance from the source.

The formula for calculating brightness is: Brightness = Luminosity / (4π × Distance²)

Given:

Luminosity = 100 W

Brightness = 0.01

We will solve for distance:

Distance² = Luminosity / (4π × Brightness)

Distance² = 100 / (4π × 0.01)

Distance² = 100 / 0.1256

Distance² = 796.178343949

Distance = √796.178343949

Distance = 28.2166323992

Distance = 28.22.

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Answer:7,947 gallons

Step-by-step explanation:

The coordinates of polygon A′B′C′D′ if polygon ABCD is rotated 180°.

A'(0, 0)

B'(-5, -2)

C'(-5, 5)

D'(0, 3)

From the graph we can write the coordinates of ABCD as

A(0, 0),

B( 5, 2)

C(5, -5)

D(0, -3)

Now, the rule for 180 degree rotation is

(x, y) -> (-x, -y)

So, the coordinates of polygon A′B′C′D′ if polygon ABCD is rotated 180°.

A(0, 0) -> A'(0, 0)

B( 5, 2) -> B'(-5, -2)

C(5, -5) -> C'(-5, 5)

D(0, -3) - >D'(0, 3)

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The system of equations 5x - 3y = -26 and x + 2y + 1 = 2 can be solved using the substitution method. The solution of the system of equations is x = -8.2 and y = -5.

An equation is a mathematical statement that expresses two expressions as equal. It consists of two expressions separated by an equals sign (=). Equations are used to describe relationships between different quantities, and to solve problems involving those quantities. Equations may be written in words, symbols, or both. They can be used to solve problems in science, engineering, economics, and other fields.

The system of equations can be solved using substitution method or addition method. In this solution, we will use the substitution method.

Substitution Method:

Step 1: Solve one of the equations for either x or y.

Let us solve the first equation for x.

5x - 3y = -26

5x = -3y - 26

x = (-3y - 26)/5

Step 2: Substitute the expression for x in the second equation.

x + 2y + 1 = 2

(-3y - 26)/5 + 2y + 1 = 2

Step 3: Solve the equation for y.

(-3y - 26)/5 + 2y + 1 = 2

-3y/5 - 26/5 + 2y + 1 = 2

2y - 3y/5 - 26/5 + 1 = 2

-y/5 - 26/5 + 1 = 2

y/5 + 26/5 - 1 = -2

y/5 + 25/5 = -1

y = -5

Step 4: Substitute the value of y in either of the equations to calculate the value of x.

5x - 3(-5) = -26

5x + 15 = -26

5x = -41

x = -41/5

x = -8.2

Therefore, the solution of the system of equations is x = -8.2 and y = -5.

Conclusion:

The system of equations 5x - 3y = -26 and x + 2y + 1 = 2 can be solved using the substitution method. The solution of the system of equations is x = -8.2 and y = -5.

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Thus, the correct options are C, D, and E.

Given: Anna bought 8 tetras and 2 rainbow fish for her aquarium.

To Find: Which option is correct?

Solution: Let's say that the price of tetras is x, which means the price of a rainbow fish will be (x + 6).

Here, we get the equation,

8x +2(x + 6)=37

Now, after simplifying the above equation, we get

10x + 12 =37

By adding -12 on both sides of the equation, we get

10x = 37 - 12 =25

Now, we will divide the equation with 10

x = 25/10

After simplifying the equation, we get

x = 5/2 = 2.5

So, the cost of a tetra will be $2.5, and the cost of a rainbow fist will be $2.5 + $6 = $8.5

Here, option B is false because the cost of each rainbow fish is greater by $6, and here 6 is only taken once.

Option A is false because 4(2.5) is not equal to 8.5.

Option E is true because 37 - 8.5 = 28.5.

Option D is true because the equation that is being used has only one difference which is the selection of variable.

Option C is true because 5(2.5) + 8.5 = 12.5 + 8.5 = 21.

Thus, the correct options are C, D, and E.

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So the minimal transportation cost is $8,700, and it can be achieved by renting 6 buses and 27 vans.

Let's start by defining our variables. Let b be the number of buses and v be the number of vans to be rented. We want to minimize the transportation costs, so our objective function is:

C = 1400b + 100v

We also have two constraints:

The total number of students that can be transported cannot be less than 720:

72b + 9v ≥ 720

The total number of chaperones cannot be more than 45:

3b + v ≤ 45

Now we can solve for b and v. Let's solve the second constraint for v:

v ≤ 45 - 3b

Substituting this inequality into the first constraint, we get:

72b + 9(45 - 3b) ≥ 720

Simplifying and solving for b, we get:

b ≥ 6

So we know that we need to rent at least 6 buses. Since we cannot rent a fraction of a bus or van, b must be an integer. Let's try b = 6 and see if it satisfies the second constraint:

3(6) + v ≤ 45

v ≤ 27

Since v must also be an integer, the largest integer that satisfies this inequality is v = 27. Now we can calculate the total cost:

C = 1400(6) + 100(27) = 8700

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Based on the sample of three sharks measured, we do not have sufficient evidence to support the marine biologist's claim.

To test marine biologists' claims that great white sharks off the coast of Bermuda grow longer than the known average length of 21 feet, a one-sample t-test can be performed.

First, we need to set the null and alternative hypotheses. Let μ be the true average length of a great white shark off Bermuda.

H0:

μ = 21 (true mean length equals 21 feet)

teeth:

μ > 21 (true average length greater than 21 feet)

You can then compute the sample mean and sample standard deviation of the three measured sharks.

x = (24 + 20 + 23) / 3 = 22.33 feet

[tex]s = sqrt(((24-22.33)^2 + (20-22.33)^2 + (23-22.33)^2) / 2) = 1.53 feet[/tex]

You can use the t-test formula to calculate the t-statistic.

t = (x- μ) / (s / sqrt(n)) = (22.33 - 21) / (1.53 / sqrt(3)) = 2.21

This test has n-1 = 2 degrees of freedom.

Using the t-table or the 2 Degrees of Freedom Calculator, we can confirm that the critical value for the one-tailed test at the 5% significance level is 4.303.

The computed t-statistic (2.21) is less than the critical value (4.303), so the null hypothesis is not rejected.

Therefore, based on his three shark samples measured, there is not enough evidence to support a marine biologist's claim that great white sharks off Bermuda grow longer than the known average length of 21 feet at the 5% significance level.  

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I agree with Andre. There are only two unique bases, not seven different faces as Noah suggests.

Both bases are the same, so you only need to calculate their area once and double it.

The other five rectangles have the same height, meaning you can calculate their areas more efficiently.

Noah's approach of finding the area of seven different faces is unnecessary and overcomplicates the problem.

Thus, I agree with Andre because his process is correct and more straightforward.

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Answer:

A

Step-by-step explanation:

Which comparison is true?

A 2.919 > 2.94

B 0.99 <0.569

C 1.27> 1.189

D 3.861 < 3.75

Answer:

$14.43

That's just the answer

By subtracting 62 - 47.57

The average of the points A, B and C with weights 1, 1 and 1

respectively is: (-5/3, -2)

A technique known as a weighted average accounts for the varied levels of significance of the values in a data collection. Each number in the data set is multiplied by a predefined weight before the final computation is completed when calculating a weighted average.

Thus:

Weighted average = [(w₁ × x₁) + (w₂ × x₂) + (w₃ × x₃)]/(w₁ + w₂ + w₃)

Where:

w_i is the weight of the ith point

x_i is the coordinate of the ith point.

Thus:

x-coordinate = [(1 × -4) + (1 × 6) + (1 × -7)]/(1 + 1 + 1)

x-coordinate = -5/3

y-coordinate = [(1 × -5) + (1 × 6) + (1 × -7)]/(1 + 1 + 1)

y-coordinate = -2

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The answer for 2 + 2 in the addition is determined as 4.

Addition is a mathematical operation that involves combining two or more quantities or values to find their total or sum.

Addition is one of the four basic arithmetic operations, along with subtraction, multiplication, and division.

In addition operation, the two or more numbers are often added to produce result called the sum.

For example, in the equation; 2 + 2 = 4.

2 and 2 are the addends, and 4 is the sum.

We can also preform addition on fractions. decimas, percentages, etc.

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Answer:

what’s the company’s profit if each sign sold is $20?

The probability of tuning an engine in 20 minutes or less is 0.5

Given that the time it takes to completely tune an engine of an automobile follows an exponential distribution with a mean of 30 minutes.

Let X be the time taken to tune an engine, then X follows an exponential distribution with mean μ = 30 minutes.

The probability of tuning an engine in 20 minutes or less can be calculated as follows

P(X ≤ 20) = 1 - [tex]e^{-lambda*x}[/tex]

where λ = 1/μ is the rate parameter.

So, substituting the values we get:

P(X ≤ 20) = 1 - [tex]e^{-20/30}[/tex]

= 1 - [tex]e^{-0.6667}[/tex]

Subtract the numbers

= 0.5

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