what is the volume of a cylinder with a diameter of 10 ft and a height of 6 ft

First, we multiply the first equation by 5 and the second equation by 7, then subtract the first equation from the second equation to eliminate y. Next, we substitute x = 11/2 into one of the original equations to solve for y. The solution is (x, y) = (11/2, 2). To find the value of y2, we square the value of y.

A mathematical statement known as an equation utilizes the equal symbol (=) to demonstrate the equality of two expressions. A mathematical equation normally consists of constants, variables, and operations such addition, subtraction, multiplication, and division.

To solve this system of equations, we can use the method of elimination.

First, we will multiply the first equation by 5 and the second equation by 7 to get:

10x - 35y = -15

28x - 35y = 84

Now, we can subtract the first equation from the second equation to eliminate y:

28x - 10x - 35y + 35y = 84 - (-15)

18x = 99

x = 99/18 = 11/2

Next, we can substitute x = 11/2 into one of the original equations to solve for y. We'll use the first equation:

2x - 7y = -3

2(11/2) - 7y = -3

11 - 7y = -3

-7y = -14

y = 2

Therefore, the solution to the system of equations is (x, y) = (11/2, 2).

To find the value of y², we simply square the value of y:

y² = 2² = 4

So the value of y² is 4.

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Answer:

740.48

Step-by-step explanation:

multipky

When trapezoidal prism undergoes a dilation, the size of the prism changes

The height of the image is 52.2 meters

The given parameters are:

A1 = 35 m²

A2 = 315 m²

H1 = 5.8 m

To calculate the height of the image, we make use of the following equivalent ratio

A1 : H1 = A2 : H2

So, we have:

35 : 5.8 = 315 : H

Express as fractions

35/5.8 = 315/H

Make H the subject

H = 315 * 5.8/35

Evaluate the product

H = 52.2

Hence, the height of the image is 52.2 meters

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Answer:

17.4

Step-by-step explanation:

Answer:

P(2): 1/5

P(4): 1/5

P(odd number): 3/5

P(whole number): 5/5

P(6): 0/5

P(2 or 3): 2/5

Step-by-step explanation:

There are 5 equal sections in this circle. So, the probability to land in each section is 1/5.

The odd numbers are 1, 3, and 5. Since each section is 1/5, you add

1/5 + 1/5 + 1/5 = 3/5. That is the probability that you will land in any odd number.

Because all the numbers listed are whole numbers, no matter where the spinner lands it will be a whole number. So, the probability is 5/5 for whole numbers.

Since 6 is not a section, it's probability will be 0/5 (or you can just put 0).

"Or" means you add the two probabilities. Add the probability of landing on 3 (which is 1/5) to the probability of landing on 2 (which is also 1/5). So, you get 2/5.

Answer:

17. 1/5

18. 1/5

19. 3/5

20. 1

21. 2/5

The ratio by mass of copper to zinc in the alloy is 3:1.

To find the ratio by mass of copper to zinc in the alloy, we need to first calculate the total mass of the alloy. We can do this by adding the mass of copper and zinc:

Total mass of alloy = 13.5 g + 4.5 g = 18 g

Now we can find the ratio of copper to zinc by dividing the mass of copper by the mass of zinc:

Ratio of copper to zinc = 13.5 g / 4.5 g = 3:1

Therefore, the ratio by mass of copper to zinc in the alloy is 3:1.

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I hope this helps!

-AxekickNebulite

Answer:

88 would be the answer maybe.....

Answer:

88

Step-by-step explanation:

Answer:

the Answer is 4 and 6

Step-by-step explanation:

4 + 6 = 10 but 4 x 6 = 24

well, let's take a look at the tickmarks on the triangle, the tickmarks mean that AC = CB, both AC and CB stemming out of vertex C, and both twin sides will make twin angles at the "base" or namely ∡A = ∡B, that means that 34 = x - 5, let's also recall that the sum of all interior angles in a triangle is 180°, so

\(34=x-5\implies \boxed{39=x} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\measuredangle A}{34}~~ + ~~\stackrel{\measuredangle B}{34}~~ + ~~\stackrel{\measuredangle C}{4y}~~ = ~~180\implies 68+4y=180 \\\\\\ 4y=112\implies y=\cfrac{112}{4}\implies \boxed{y=28}\)

Answer:

y = 28

Step-by-step explanation:

The dashes on line segments AC and BC indicate that the line segments are equal in length.

Therefore, as the triangle has two sides of equal length, it is an isosceles triangle.

The base angles of an isosceles triangle are equal, therefore ∠A = ∠B.

Interior angles of a triangle sum to 180°.  

Therefore:

⇒ ∠A + ∠B + ∠C = 180°

⇒ 34° + 34° + 4y° = 180°

⇒ 68° + 4y° = 180°

⇒ 4y° = 112°

⇒ y = 112° ÷ 4°

⇒ y = 28

Answer:

The original recipe calls for 1 1/4 cups of dip and 1/2 cup of veggies, so you + both together which is a total of 1 3/4 cups of ingredients.

If Austin wants to use 1 cup of veggies instead of 1/2 cup, he needs to double the recipe. To keep the same ratio of dip to veggies, he will also need to double the amount of dip.

1 3/4 cups (original recipe) x 2 = 3 1/2 cups

Therefore, Austin will need 3 1/2 cups of dip to make the recipe using 1 cup of veggies.

Answer:

B) 68 cm²

Step-by-step explanation:

Answer:

v=20π ft/s

Step-by-step explanation:

Given:

Distance from the security car to the movie theater, D=25 ft

Distance of the reflection from the car, d=30 ft

Speed of rotation of the strobe lights, 2 rev/s

To find the speed at which the reflection of the security strobe lights is moving along the wall of the movie theater, we need to calculate the linear velocity of the reflection when it is 30 ft from the car.

We can start by finding the angular velocity in radians per second. Since the strobe lights rotate at 2 revolutions per second, we can convert this to radians per second.

ω=2πf

=> ω=2π(2)

=> ω=4π rad/s

The distance between the security car and the reflection on the wall of the theater is...

r=30-25= 5 ft

The speed of reflection is given as (this is the linear velocity)...

v=ωr

Plug our know values into the equation.

v=ωr

=> v=(4π)(5)

∴ v=20π ft/s

Thus, the problem is solved.

The speed of the reflection of the security strobe lights along the wall of the movie theater is 2π ft/s.

To solve this problem, we can use the concept of related rates. Let's consider the following variables:

x: Distance between the security car and the movie theater wall

y: Distance between the reflection of the security strobe lights and the security car

θ: Angle between the line connecting the security car and the movie theater wall and the line connecting the security car and the reflection of the strobe lights

We are given:

x = 25 ft (constant)

y = 30 ft (changing)

θ = 2 revolutions per second (constant)

We need to find the speed at which the reflection of the security strobe lights is moving along the wall (dy/dt) when the reflection is 30 ft from the car.

Since we have a right triangle formed by the security car, the movie theater wall, and the reflection of the strobe lights, we can use the Pythagorean theorem:

x^2 + y^2 = z^2

Differentiating both sides of the equation with respect to time (t), we get:

2x(dx/dt) + 2y(dy/dt) = 2z(dz/dt)

Since x is constant, dx/dt = 0. Also, dz/dt is the rate at which the angle θ is changing, which is given as 2 revolutions per second.

Plugging in the known values, we have:

2(25)(0) + 2(30)(dy/dt) = 2(30)(2π)

Simplifying the equation, we find:

60(dy/dt) = 120π

Dividing both sides by 60, we get:

dy/dt = 2π ft/s

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The required length of the curst on the edge of one piece of pizza 1.5 π. Option D is correct.

Perimeter is the measure of the figure on its circumference. The perimeter of a circle is given as 2πr, where r is the radius of the circle.

here,
A pizza has an 18-inch diameter
Circumference of pizza = 18π

The pizza is sliced into 12 pieces, and the length of the crust on the edge of one piece of pizza is given as,
= 18π/12
= 1.5π

Thus, the required length of the curst on the edge of one piece of pizza is 1.5 π.

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Answer: I believe it is a. Sorry if I am incorrect

Step-by-step explanation:

Functions assign outputs to inputs. The domain of a function is the set of all possible inputs for the function. For example, the domain of f(x)=x² is all real numbers, and the domain of g(x)=1/x is all real numbers except for x=0.

The test statistic for this sample and the p-value for this sample is  t = 0.467.

Given:

sample of size n=305

M=83.6

SD=14.9.

Significance level of α = 0.001 . H o : μ = 82.4 H a : μ ≠ 82.4

To find the Test statistic

\(test=\frac{\bar x-\mu}{\frac{s.t}{\sqrt{n} } }\)

    \(=\frac{82.4.6-83.6}{\frac{14.9}{\sqrt{305} } }\)

     \(0.467\)

P-value:

With t = 0.467.

p-value = (1 - 0.467)

0.533 > 0.001

So, fail to reject H₀

Therefore, the failing to reject the Null Hypothesis.

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Answer:

-3

Step-by-step explanation:

This is read as the set of all possible combinations of Heads and Tails, combined with the set of all odd numbers from 1 to 5.

A.

Sample Space:

{Heads, Tails} x {1, 2, 3, 4, 5}

B. Favorable Outcomes: {Heads, 1}, {Heads, 3}, {Tails, 1}, {Tails, 3}, {Tails, 5}

A. The sample space for this event can be represented as a set of all possible outcomes, which can be written as {Heads, Tails} x {1, 2, 3, 4, 5}. This is read as the set of all possible combinations of Heads and Tails, combined with the set of all numbers from 1 to 5.

B. The favorable outcomes for the event of choosing an odd number are {Heads, 1}, {Heads, 3}, {Tails, 1}, {Tails, 3}, {Tails, 5}. This is read as the set of all possible combinations of Heads and Tails, combined with the set of all odd numbers from 1 to 5.

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The factor of the expression using linear interpolation is 208.12 and 11,110.41

Linear interpolation is a method of curve fitting using linear polynomials to construct new data points within the range of a discrete set of known data points.

Now, The linear interpolation is given as:

1. (F/P,17%,34)

2. (A/G,23%,45)

Now, According to the question:

The factor is then calculated as:

\(Factor=(1+17\)%\()^3^4\)

Express 17% as decimal

\(Factor=(1+0.17)^3^4\)

Take the sum of 1 and 0.17

\(Factor=(1.17)^3^4\)

Evaluate the exponent

Factor = 208.12

2.The factor is then calculated as:

\(Factor=(1+23\)%\()^4^5\)

Express 23% as decimal

\(Factor=(1+0.23)^4^5\)

Take the sum of 1 and 0.23

\(Factor=(1.23)^4^5\)

Evaluate the exponent

Factor = 11,110.41

Hence, the factor of the expression using linear interpolation is 208.12 and 11,110.41

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Answer:

−36

Step-by-step explanation:

Answer:

Answer: f(-7) = -167

Step-by-step explanation:

\({ \tt{f(x) = - {3x}^{2} - 20}}\)

• When x is -7, f(x) is f(-7):

\({ \tt{f( {}^{ - }7) = {}^{ - } 3( { {}^{ - }7) }^{2} - 20 }} \\ \\ { \tt{f( {}^{ - } 7) = ( {}^{ - } 3 \times 49) - 20}} \\ \\{ \tt{ f( {}^{ - }7) = {}^{ - } 147 - 20 }} \\ \\ { \boxed{ \tt{f( {}^{ - }7) = {}^{ - } 167 }}}\)

Based on the calculations, the evaluation of this function is equal to -167.

Given the following data:

In this exercise, you're required to evaluate the given function. This ultimately implies that, we would substitute the vale of x into the function as follows.

Note: The value of x is equal to -7.

Substituting the given parameter into the function, we have;

\(f(-7)=-3(-7)^2-20\\\\f(-7)=-3(49)-20\\\\f(-7)=-147-20\)

f(-7) = -167.

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Answer:

  x = 12

Step-by-step explanation:

You want the measure of x, given inscribed angle (5x+1)° subtends an arc of measure (14x-46)°.

An inscribed angle has half the measure of the arc it subtends. This tells us the arc measure is twice the angle measure:

  2(5x +1)° = (14x -46)°

  10x +2 = 14x -46 . . . . . divide by °, eliminate parentheses

  48 = 4x . . . . . . . . add 46-10x

  12 = x . . . . . . divide by 4

The value of x is 12.

__

Additional comment

The angle is 61°; the arc is 122°.

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Answer:

h = 112.5 feets

Step-by-step explanation:

The equation for horizontal distance "h" in feet of a projectile with initial velocity v₀ and initial angle theta is given by :

\(h=\dfrac{v_o^2}{16}\sin\theta\cos\theta\)

We know that, \(2\sin\theta\cos\theta=\sin2\theta\)

So,

\(h=\dfrac{v_o^2}{32}\sin2\theta\)

Now we need to find the maximum horizontal distance possible and at what angle does this occur.

For maximum distance angle should be 45 degrees. Som,

\(h=\dfrac{60^2}{32}\sin2(45)\\\\h=112.5\ \text{feet}\)

So, 112.5 feets is the maximum possible distance.

the radius of convergence is 1 and the interval of convergence is (1, 3) in terms of x-values.

To determine the radius of convergence, we can use the ratio test. The ratio test states that if the limit of the absolute value of the ratio of consecutive terms is less than 1 as n approaches infinity, then the series converges. Applying the ratio test to the given series, we have:

lim(n->∞) |((x - 2)^(n+1)/(n+1)) / ((x - 2)^n/n)| < 1

Simplifying the expression, we get:

lim(n->∞) |(x - 2)n+1 / (n+1)(x - 2)^n| < 1

Taking the absolute value and rearranging, we have:

lim(n->∞) |x - 2| < 1

This implies that the series converges when |x - 2| < 1, which gives us the interval of convergence. The radius of convergence is the distance between the center of the series (x = 2) and the nearest point where the series diverges, which in this case is 1.

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