There is a bag with only red marbles and blue marbles.
The probability of randomly choosing a red marble is
6 over 7 as a fraction.
There are 30 red marbles in the bag and each is equally likely to be chosen.
Work out how many marbles in total there must be.

Answer:

\(AB\) is parallel to \(CD\) (\(AB ||CD\))

Step-by-step explanation:

In a set of parallel lines cut by the traversal, \(\angle AHG\) and \(\angle DGH\) are alternate interior angles. In a set of parallel lines cut by a traversal, alternate interior angles are always equal. Therefore, since \(\angle AHG=\angle DGH=115^{\circ}\) (they are equal), the lines AB and CD must be parallel.

*A set of parallel lines proves that alternate interior angles are always equal, but the converse is also true in that equal alternate interior angles proves a set of parallel lines. This is because if you changed the angle measure of either of the angles, the relative slope of the lines must change and they would no longer be parallel.

Answer:

0.57

Step-by-step explanation:

Given that:

Price of Pecans per pound = 0.95

Harold wants to buy 0.6 pounds of pecans.

To find:

The cost of the required amount of pecans.

Solution:

Here, we can use ratio or unitary method to find the required answer.

0.6 can be written as:

\(\dfrac{6}{10} = \dfrac{3}{5}\)

We are given that, money required to buy 1 pound = 0.95

Multiplying both sides with 0.6 or \(\frac{3}{5}\):

money required to buy \(\frac{3}{5}\) pounds = \(0.95\times \frac{3}{5} = \bold{0.57}\)

Therefore, the answer is:

The cost of 0.6 pounds of pecans = 0.57

Answer:

V = 7385.28

Step-by-step explanation:

Formula of the volume of a cylinder: V = pi*r^2*h

Since you are told to replace pi with 3.14, now plug in the numbers that you are given into the formula...

V = (3.14)(14)^2*(12)

= 7385.28

Notes: Remember you always have to divide your radius in half if it gives you a diameter, BUT since in this question it's given, you don't have to do any extra work :)

Answer:

d > -39

Step-by-step explanation:

hope this helps! :D

have a miraculous day!! <3

Answer:

(a)V=36πh

Explanation:

• Radius = 6 meters

Part A

An equation that represents the volume V as a function of the height h is:

Part B

Using 3.14 as an approximation for π

The graph of the function is attached below: (V is on the y-axis and h is on the x-axis).

Part C

The initial equation for volume is:

When h=1

If you double the height of a cylinder, h=2:

We observe that when the height is doubled, the volume of the cylinder is also doubled.

Part D

The initial equation for volume is:

If the height of the cylinder is multiplied by 1/3, we have:

The volume of the cylinder will be divided by 3.

Using the graph, we observe a horizontal stretch of the graph by 1/3.

Answer:

Since PQRS is a rectangle and the area of PQRS is 84 cm², then:

PQ x PS = 84

Since PQRS is a rectangle, PS = QR, so we can substitute PS for QR:

PQ x QR = 84

We also know that XY is parallel to PS, so triangle RXY is similar to triangle RQS:

RY/QS = XY/PS

9/QS = XY/PS

QS = 9XY/PS

The area of PXYS is 21 cm², so:

XY x PS = 21

Substitute QS for 9XY/PS:

XY x (9XY/QS) = 21

Simplify:

9XY²/QS = 21

XY² = 21QS/9

Substitute QS for PQ, since PQ = QS:

XY² = 21PQ/9

Substitute 84/PQ for PQ in the above equation:

XY² = 21(84/PQ)/9

XY² = 196/PQ

Now we can substitute PQ for 84/XY in the equation PQ x QR = 84:

(84/XY) x QR = 84

QR = XY

Substitute QR for PS in the equation XY x PS = 21:

XY² = 21/XY

Multiply both sides by XY:

XY³ = 21

XY = ∛21

Since RY = 9 cm, we can find QS:

9/QS = ∛21/PS

QS = 9PS/∛21

Now we can substitute QS and XY into the equation XY x PS = 21 and solve for PS:

(∛21) x PS = 21/((9/∛21))

PS = (21/((9/∛21)))/∛21

PS = 7∛21

Finally, we can solve for a and b:

a = PQ - XY = (84/PQ) - (∛21)

Substitute PQ for 84/XY:

a = (XY²/84) - ∛21

Substitute XY for ∛21:

a = (∛21²/84) - ∛21

a = 1/4 - ∛21

b = RY - QS = 9 - (9PS/∛21)

Substitute PS for 7∛21:

b = 9 - (9(7∛21)/∛21)

b = -54/∛21 + 9∛21

Step-by-step explanation:

Answer:

C) 324 cm^3

Step-by-step explanation:

So you know the volume and 2 side lengths. 360 divided by 12 divided by 5 to find the third side. The third side is 360 / 60 (answer of 12x5), which is 6. Surface area of prism is 324 (c)

Answer:

Heres your answer y=x^2 +7x-30

Answer:

y=x^2 +7x-30

Step-by-step explanation:

Hope this helps

Answer:

x+y=-1

2x+2y=8

the correct answer is B

Answer:

(1, 6 )

Step-by-step explanation:

5x + 2y = 17 → (1)

4x + y = 10 → (2)

Multiplying (2) by - 2 and adding to (1) will eliminate the y- term

- 8x - 2y = - 20 → (3)

Add (1) and (3) term by term to eliminate y

- 3x + 0 = - 3

- 3x = - 3 ( divide both sides by - 3 )

x = 1

Substitute x = 1 into either of the 2 equations and solve for x

Substituting into (1)

5(1) + 2y = 17

5 + 2y = 17 ( subtract 5 from both sides )

2y = 12 ( divide both sides by 2 )

y = 6

solution is (1, 6 )

There were 19 teachers sitting in the school auditorium.

The question provides us with the total number of people present in the auditorium, which is 81. It also tells us that 19 of them were teachers. Therefore, the number of students present in the auditorium can be found by subtracting the number of teachers from the total number of people, which is 81 - 19 = 62.

Since the question only asks about the number of teachers present in the auditorium, the answer is simply 19. This is because the question already provides us with the information that there were 19 teachers present.

Alternatively, we can use algebra to solve the problem. Let x be the number of students present in the auditorium. Then, we can write an equation based on the total number of people in the auditorium: x + 19 = 81. Solving for x, we get x = 81 - 19 = 62. Therefore, the number of teachers present in the auditorium is 19.

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Salutem City would need to build 275 more health centers to match the current city with the most health centers per capita.

What is capita?

In the context of the phrase "per capita", capita refers to the per person or per individual basis. It is a Latin term that means "by the head". When used in statistics or economics, per capita is a measure of a particular variable such as income, health centers, or any other quantity, that is divided by the total population of a given area or country. This measure provides a way to compare variables across different populations or regions, taking into account the differences in their sizes.

To determine how many more health centers Salutem City would need to build to claim the most health centers per capita, we can use the following steps:

Calculate the current number of health centers per capita in Salutem City:

Number of health centers per b = (215 centers / 10,000 people) = 0.0215 centers per person

Calculate the number of health centers needed to match the current leader's ratio:

Number of health centers needed = (0.0215 centers per person) * (250,000 people) = 5,375 centers

Calculate the number of additional health centers Salutem City would need to build:

Additional health centers needed = (5,375 centers) - (5,100 centers) = 275 centers

Therefore, Salutem City would need to build 275 more health centers to match the current city with the most health centers per capita.

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Answer: 7

Step-by-step explanation:

Answer: 7 or 5 because 7 is on the bottom but 5 is on the otherside which it looks like its the same value.

The correct form of Pythagoras theorem is: A² + B² = C²

The legs are 12 inches and 5 inches while the hypotenuse is 13 inches

Pythagoras Theorem is defined as the way in which you can find the missing length of a right angled triangle.

The triangle has three sides, the hypotenuse (which is always the longest), Opposite (which doesn't touch the hypotenuse) and the adjacent (which is between the opposite and the hypotenuse).

Pythagoras is in the form of;

a² + b² = c²

Applying Pythagoras Theorem gives us the expression as:

5 = √(13² - 12²)

where:

Legs are 5 inches and 12 inches while the hypotenuse is 13 inches

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Answer:

x = 5

Step-by-step explanation:

Expressing the ratio in fractional form , that is

\(\frac{9}{x}\) = \(\frac{36}{20}\) ( cross- multiply )

36x = 180 ( divide both sides by 36 )

x = 5

Answer:

\(accelaration = \frac{change \: in \: veloity}{time} \\ = \frac{15 - 10}{5} \\ = \frac{5}{5} \\ = 1 \frac{m}{ {s}^{ - 2} } \)

Answer: acceleration = 1 m/s²

Concept:

Here, we need to know how to calculate the acceleration of a body.

a = Δv / Δt = (v₂ - v₁) / (t₂ - t₁)

v = velocity

t = time

unit = m/s²

Solve:

Given information

v₁ = 10 m/s

v₂ = 15 m/s

Δt = 5 seconds

Given expression

a = (v₂ - v₁) / (t₂ - t₁)

Substitute values into the expression

a = (15 - 10) / 5

Simplify values in parentheses

a = 5 / 5

Simplify by division

\(\boxed{a=1}\)

Hope this helps!! :)

Please let me know if you have any questions

a) The relationship between b and c is that c cannot be zero.

b) b can be any nonzero constant and c is equal to 2.5 in this case.

In two dimensions, the compatibility equations for strain are,0

∂εx/∂y + ∂γxy/∂x = 0

∂εy/∂x + ∂γxy/∂y = 0

where εx and εy are the normal strains in the x and y directions, respectively, and γxy is the shear strain.

Using the given strain field, we can calculate the strains,

εx = -4.5cx² + 10.5cy

εy = 1.5cx² - 7.5cy²

γxy = 1.5bxy

Taking partial derivatives and plugging them into the compatibility equations, we get,

⇒ -9cx + 0 = 0

⇒ 0 + (-15cy) = 0

These equations must be satisfied for the strain field to be compatible. From the first equation,

We get cx = 0, which means c cannot be zero.

From the second equation, we get cy = 0,

Which means b can be any nonzero constant.

For part b:

We are asked to find the displacements u and v corresponding to the given strain field at points (3, 7), assuming they are zero at point (0, 0) and using c = 2.5.

To find the displacement components,

We need to integrate the strains with respect to x and y. We get,

u = ∫∫εx dx dy = ∫(10.5cy) dy = 5.25cy²

v = ∫∫εy dx dy = ∫(1.5cx² ) dx - ∫(7.5cy²) dy = 0.5cx³ - 2.5cy³

Plugging in the values of c and b, we get,

u = 5.25(2.5)(7)²  = 767.62

v = 0.5(2.5)(3)³ - 2.5(7)³ = -8583.75

Therefore,

The displacements at points (3, 7) are u = 767.62 and v = -8583.75.

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This problem asks to:

a) Find a model to predict the population P as a function of t (years since 2011).

b) Predict the population in 2022.

To find this information, follow the steps below.

Step 1: Write a general equation for populational growth.

The population growth can be represented as:

Where:

P is the population in time t;

Po is the initial population;

r is the rate of growth;

t is the time.

Step 2: Write the equation that represents the moose population.

Since the problems aks to evaluate the population from 2011. Use the population in 2011 as the initial population.

Then, P0 = 5,800.

Now, to find r, use the information for 2017.

In 2017,

P = 8,000

t = 6 (2017 - 2011)

Then,

To isolate r, first divide both sides by 5,800:

Take the ln from both sides.

Divide both sides by 6:

So,

(a) The equation that represents the moose population over the years is:

Step 3: Predict the population in 2022.

In 2022,

t = 11 (2022 - 2011).

Then,

(b) The moose population in 2022 will be 10,459.

Answer:

(a)

(b) 10,459.

The probability is approximately 0.083. The waiting time between a subway departure schedule and the arrival of a passenger follows a uniform distribution with parameters a=0 and b=9.

We need to find the probability that a randomly selected passenger has a waiting time of fewer than 0.75 minutes.

Using the formula for the uniform distribution, the probability density function is:

f(x) = 1/(b-a) = 1/(9-0) = 1/9

Therefore, the probability of a randomly selected passenger having a waiting time of fewer than 0.75 minutes is:

P(X < 0.75) = (0.75-0)/(9-0) = 0.0833

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The value of the triple integral is 72π.

To evaluate this triple integral in cylindrical coordinates, we first need to express the region E using cylindrical coordinates.

The cylinder x² + y² = 16 can be expressed in cylindrical coordinates as r² = 16, or r = 4. The planes z = -5 and z = 4 define a region of height 9.

So, the region E can be expressed in cylindrical coordinates as:

4 ≤ r ≤ 4

-5 ≤ z ≤ 4

0 ≤ θ ≤ 2π

The integrand √(x² + y²) can be expressed in cylindrical coordinates as r, so the integral becomes:

∭E√x²+y²dV = ∫0²π ∫4⁴ ∫-5⁴ r dz dr dθ

Note that the limits of integration for r are from 0 to 4, which means we are only integrating over the positive x-axis. Since the integrand is an even function of x and y, we can multiply the result by 2 to get the total volume.

The integral with respect to z is easy to evaluate:

∫₋₅⁴ r dz = r(4 - (-5))

= 9r

So the triple integral becomes:

∭E√x²+y²dV = 2 ∫0^2π ∫4⁴ 9r dr dθ

= 2(9) ∫0^²π 4 dθ

= 72π

Therefore, the value of the triple integral is 72π.

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The amount budgeted for dances is approximately $380.00.

Assume that "x" is the budgeted sum for dances. The problem states that there is a 5:7 ratio between the budget for dances and the budget for charitable activities. Hence, we can write:

x/532 = 5/7

We can cross-multiply and simplify to find the answer for "x"

7x = 532 × 5

7x = 2660

x = 2660/7

x ≈ 380.00

The estimated $380.00 planned money for dances is the result.

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Answer:

60

Step-by-step explanation:

The domains of both f(x) and g(x) must be (–∞, ∞).

We have given that,

The function h(x) shown is the result of adding two functions, f(x) and g(x).

We have to determine

The statement could be used to describe the functions.

What is the function?

A function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.

The domain of the function is the set of point at which function is defined.

Therefore, The domains of both f(x) and g(x) must be (–∞, ∞).

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Answer:

y = 2/3x + -4/3

Step-by-step explanation:

4x - 6y - 8 = 0 (Add -4x to both sides)

-6y - 8 = 4x (Add 8 to both sides)

-6y = 4x + 8 (Divide -6 from both sides)

y = 2/3x + -4/3

Answer:

v = 1 or -3

Step-by-step explanation:

2v^2 + 4v = 6

take 2 as common

2(v^2 + 2v = 3)

v^2 + 2v = 3

Now,

v^2 + 2v - 3 = 0

v^2 - v + 3v - 3 = 0

v(v - 1) + 3(v - 1) = 0

(v - 1) (v + 3) = 0

v = 1 or -3

Answer:

<=>v²+2v-3=0

<=>v²-v+3v-3=0

<=>v(v-1)+3(v-1)=0

<=>(v-1)(v+3)=0

<=>*v-1=0

v=1

*v+3=0

v=-3