how will the volume of the pyramid change if each side is multiplied by a factor of one-half?

Answer:

Step-by-step explanation:

\(a_1=14\\a_2=22\\\\d=a_2-a_1=22-14=8\\\\a_n=a_1+d(n-1)\\\\a_{75}=14+8(75-1)=14+8\cdot74=14+592=606\)

Answer:

30

Step-by-step explanation:

If you plug in 5 for x and 3 for y then the equation would be 3(5)+5(3) or 15+15.

Answer:

Area of Shaded Region = (25π - 24) cm²

Step-by-step explanation:

See attachment

From the attached, the following observations are made;

Radius, r = 5cm

Base of triangles = 6cm.

Required

Area of shaded region.

If the distance between the base of the triangle to the outline of the circle is 1cm then the height of the triangle is 1cm less than the radius

Height = 5cm - 1cm

Height = 4cm

To calculate the area of the shaded region, we first calculate the area of the circle.

Area = πr²

Substitute 5 for r

Area = π * 5²

Area = π * 25

Area = 25π cm²

Then we calculate the area of both triangles

Area of 1 triangle is calculated as follows.

Area = ½ * base * height

Substitute 4 for height and 6 for base.

Area = ½ * 4 * 6

Area = 2 * 6

Area = 12cm²

Since both triangles are equal.

Area of two triangles = 2 * Area of 1 triangle

Area = 2 * 12cm²

Area = 24cm²

Having calculated the area of the circle and that of both triangles.

Area of shaded region = Area of Circle - Area of Triangles

Area of Shaded Region = 25π cm² - 24 cm²

Area of Shaded Region = (25π - 24) cm²

Answer:

The third one

Step-by-step explanation:

Using the Poisson Approximation the probability are:

a)  0.6321

b)  0.3679

c) 0.2642

The Poisson distribution is utilized to compute the likelihood of a particular amount of occurrences happening over a set period. The Poisson approximation will be used to answer the given question, and it is a form of a probability distribution that can be used to approximate the probability of particular events that occur infrequently, and it is suitable for both continuous and discrete variables.

a) The probability of having at least one student with the same birthday as Brad using the Poisson Approximation.

Let the number of other students with the same birthday as Brad be represented by x. Here, x is a discrete variable with a Poisson distribution that follows a Poisson distribution with an average of λ, which is equal to 1:

λ = average number of students having the same birthday as Brad = 1.

Using the Poisson distribution formula, the probability of having at least one student with the same birthday as Brad is given by:

P(X >= 1) = 1 - P(X = 0)

= 1 - e ^ (-λ)P(X = 0)

= (e^(-λ))(λ^0) / 0!

= e^(-λ)

= e^(-1)

= 0.3679

Therefore, the probability of having at least one student with the same birthday as Brad is:

P(X >= 1) = 1 - P(X = 0)

= 1 - 0.3679

= 0.6321

b) The probability of having exactly one student with the same birthday as Brad using Poisson Approximation

P(X = 1) = (e^(-λ))(λ^1) / 1!

= e^(-1)(1) / 1!

= e^(-1)

= 0.3679

Therefore, the probability of having exactly one student with the same birthday as Brad is:

P(X = 1)

= e^(-1)

= 0.3679

c) The probability of having at least two students with the same birthday as Brad using Poisson Approximation

P(X >= 2) = 1 - P(X < 2)

= 1 - [P(X = 0) + P(X = 1)]

= 1 - [e^(-λ)(λ^0) / 0! + e^(-λ)(λ^1) / 1!]

= 1 - [e^(-1) + e^(-1)(1) / 1!]

= 1 - [e^(-1) + e^(-1)]

= 1 - 2e^(-1)

= 0.2642

Exact probability: 1 - (364/365)^180 = 0.4406

Poisson Approximation Probability: 0.6321

The exact probability is 0.4406, which is less than the Poisson approximation probability, which is 0.6321.

This result indicates that the Poisson approximation formula overestimates the likelihood of having at least one student with the same birthday as Brad.

Exact probability: (364/365)^179(1/365) = 0.3775

Poisson Approximation Probability: 0.3679

The exact probability is 0.3775, which is quite similar to the Poisson approximation probability, which is 0.3679.

This result indicates that the Poisson approximation formula provides a reasonably precise estimate of the likelihood of having exactly one student with the same birthday as Brad.

Exact probability: 1 - [1 + 364/365 + ... + (364!/347!)/365^34] = 0.1827

Poisson Approximation Probability: 0.2642

The exact probability is 0.1827, which is less than the Poisson approximation probability, which is 0.2642.

This result indicates that the Poisson approximation formula overestimates the likelihood of having at least two students with the same birthday as Brad.

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Answer:

15

Step-by-step explanation:

Use this formula \(\sqrt{(x2 - x1)^2 + (y2 - y1)^2}\)

Plug in points (-9, 7) (0, -5) and solve

\(\sqrt{(0 - -9)^2 + (-5 - 7)^2} \\\\\sqrt{(9)^2 + (-12)^2} \\\\\sqrt{81 + 144} \\\\\sqrt{225}\)

√225 = 15

Hope this helps ya!!

Answer:

A) 1

Step-by-step explanation:

1/2 × 1 = 1/2

3/6 is the same value as 1/2

Answer:

-3

Step-by-step explanation:

What you do is divide the 12 by 4, which equals 3. But then dividing a negative by a positive still gives you a negative, so you add in the negative after the quotient. So your answer would be -3.

Answer:

It equals -3

Step-by-step explanation:

Have an amazing day or night!

Answer:

yass

Step-by-step explanation: 5+1 = 6 <3 i need points-

Answer:

24/49

Step-by-step explanation:

The options to get 2 of different color is picking blue then red or red then blue.  

Starting with picking blue then red.

The chance to pull blue first is 3/7.  Then since the marble is replaced the chance to pull red next is 4/7.  

The chance to get those in that specific order is the product of the two fractions.   (3/7) * (4/7) = 12 / 49

The second option of getting red then blue will be the same as above but 4/7 then 3/7 with the same result of 12/49.  

To finish, add the two probabilities together 12/49 + 12/49 = 24/49.  

Hi!

We can use point-slope form to solve this.

\(y-y_{1} =m(x -x_{1})\)

\(y_{1}\) and \(x_{1}\) will be from one of the points.

First, we have to find \(m\), the slope. We can use the slope equation to get this.

\(\frac{y_{1} -y_{2} }{x_{1} -x_{2} }\)

Plug in your points:

\(\frac{4-0}{8-(-8)} =\frac{4-0}{8+8} =\frac{4}{16} =\frac{1}{4}\)

Your slope is \(\frac{1}{4}\)

Now plug points and slope into point-slope equation. We will use (8, 4).

\(y-4=\frac{1}{4} (x-8)\)

Now, if you want to get it into y = mx + b form, you have to solve for y:

\(y-4=\frac{1}{4} (x-8)\)

\(y-4=\frac{1}{4} x-2\)

\(y=\frac{1}{4} +2\)

Your equation is \(y=\frac{1}{4} +2\)

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The inequality 24 > f - 6 is solved to give 30 > f

An inequality can be described an an non- equal comparison between elements, numbers or mathematical expressions.

It is mostly used to compare two numbers, elements or expression on the number line based on their sizes or magnitudes.

From the information given, we have that;

24 > f - 6

First, collect like terms

24 + 6 > f

Now, add the like terms

30 > f

The variable 'f' is greater than 30 and is given as the solution to the inequality

Hence, the value of 'f' is greater than 30

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The solution set of the given homogeneous system in parametric vector form is (x1,x2,x3)=(s,-2,-5)

Parametric vector form:

If there are m-free variables in the homogeneous equation, the solution set can be expressed as the span of m vectors:

x = s1v1 + s2v2 + ··· + sm vm. This is called a parametric equation or a parametric vector form of the solution.

A common parametric vector form uses the free variables as the parameters s1 through sm

Given is a system of equations

We are to solve them in parametric form.

x1 + 3x2 + x3 = 0 --------(1)

-4x1 + 9x2 + 2x3 = 0 ---------(2)

-3x2 - 6x3 = 0--------(3)

From equation(3)

-3x2=6x3

x2=-2x3

substitute in equation(1) and equation(2)

x1+3(-2x3)+x3=0

x1-6x3+x3=0

x1-5x3=0

x1=5x3

So the solution in parametric form is (x1,x2,x3) = (s,-2,5) for all real values.

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The 40-year-old should have $76800 in capital. The 35-year-old should be saving $$10,320 for retirement.

The capital that a 40 year old has to have with an income of 32000 is

capital income at age 40 * income

= 2.4 * 32000

Capital = $76800

b. At 35 the savings income has to be

percentage of savings income * income

= 12% * $86000

= $10,320

c. There is no specified value for education earnings.

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(A) Circular orbits of stable particles are possible at radii greater than three times the Schwarzschild radius for the non-rotating spherically symmetric mass.

This represents the radius of a black hole's event horizon, within which nothing can escape. The Schwarzschild radius is the event horizon radius of a black hole with mass M.

M can be calculated using the formula: r+ = 2Mwhere r+ is the radius of the event horizon.

(B)  1/2 M -1/2 3M (²) ¹² (1-³) dT = R³ R. This is the required expression.

Tau is the proper time of the particle moving around a circular orbit. Hence, by making use of the formula given above:1/2 M -1/2 3M (²) ¹² (1-³) dT = R³ dt.

(C) Time passes differently in different gravitational fields, and it follows that the period as measured at infinity should be larger than that measured by the particle.

The principle of equivalence can be defined as the connection between gravitational forces and the forces we observe in non-inertial frames of reference. It's basically the idea that an accelerating reference frame feels identical to a gravitational force.

(D) The period of the orbit as measured by an observer at infinity is 16π M^(1/2) and the period of the orbit as measured by the particle is 16π M^(1/2)(1 + 9/64 M²).

The period of orbit as measured by an observer at infinity can be calculated using the formula: T = 2π R³/2/√(M). Substitute the given values in the above formula: T = 2π (8M)³/2/√(M)= 16π M^(1/2).The period of the orbit as measured by the particle can be calculated using the formula: T = 2π R/√(1-3M/R).

Substitute the given values in the above formula: T = 2π (8M)/√(1-3M/(8M))= 16π M^(1/2)(1 + 9/64 M²).

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Answer: 1.17600521 rad

Step-by-step explanation:

To find the angle (in radians) that the ladder makes with the building, we can use the right triangle formed by the ladder, the building, and the ground. The ladder acts as the hypotenuse of the right triangle, with a length of 13 feet. The height from the ground to the second-floor window is the side opposite the angle we want to find, which has a length of 12 feet.

We can use the sine function to find the angle, θ:

sin(θ) = opposite side / hypotenuse

sin(θ) = 12 / 13

Now, to find the angle θ in radians, we can use the inverse sine function (arcsin):

θ = arcsin(12/13)

Plug the value into a calculator to get the angle in radians:

θ ≈ 1.17600521 rad

Answer:

θ ≈ 1.17600521 rad

Step-by-step explanation:

The correct options that could be an example of a function with a domain (-∞0,00) and a range (-∞,4) are given below.Option A. V = -(0.25)x - 4 Option B. V = − (0.25)x+4

A function can be defined as a special relation where each input has exactly one output. The set of values that a function takes as input is known as the domain of the function. The set of all output values that are obtained by evaluating a function is known as the range of the function.

From the given options, only option A and option B are the functions that satisfy the condition.Both of the options are linear equations and graph of linear equation is always a straight line. By solving both of the given options, we will get the range as (-∞, 4) and domain as (-∞, 0).Hence, the correct options that could be an example of a function with a domain (-∞0,00) and a range (-∞,4) are option A and option B.

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Answer:

1,010 seconds

Step-by-step explanation:

50.5 per lap

50.5 * 20 = 1010

Answer:

1010 seconds to do 20 laps

Step-by-step explanation:

Answer:

The value of y is 48.

Step-by-step explanation:

You have to substitute the values into the equation :

\(y = mx\)

\(let \: m = 8,x = 6\)

\(y = 8 \times 6\)

\(y = 48\)

Question:

(a) Write a linear equation that describes the problem

(b). If the cheerleading squad collects 6000 plastic bottles, how many cans will it need to collect to reach the goal?

Answer:

a. \(0.10x + 0.05y = 500\)

b. 2000 cans

Step-by-step explanation:

We have the following:

\(Cost = \$0.10\) per aluminum

\(Cost = \$0.05\) per plastic bottle

\(Total = \$500\)

Solving (a): The linear equation.

If 1 aluminum can costs $0.10,

x cans would cost $0.10x

If 1 plastic bottle costs $0.05,

y bottles would cost $0.05y

Total Cost:

\(Aluminum + Plastic = Total\)

\(0.10x + 0.05y = 500\)

b.

If y = 6000.

Solve for x

We have:

\(0.10x + 0.05y = 500\)

Substitute 6000 for y

\(0.10x + 0.05* 6000 = 500\)

\(0.10x + 300= 500\)

Collect Like Terms

\(0.10x = 500 - 300\)

\(0.10x = 200\)

Solve for x

\(x = 200/0.10\)

\(x = 2000\)

Answer:

y=2/3x-5

Step-by-step explanation:

Answer:

15

Step-by-step explanation:

36/3 +3

12 +3

15

Some other expressions that could equal 15 are 5+10, 20-5, 2x5+5

Answer:

1 times 15 equals 15

3 times 5 equals 15

5 times 3 equals 15

15 times 1 equals 15

Step-by-step explanation:

36 divided by 3 is 12 plus 3 is 15

3 x 5 is equal event because it is equal

Answer:

c.) x = -3

Step-by-step explanation:

Solve for x:

-10 x = 2 (9 - 2 x)

Hint: | Write the linear polynomial on the left hand side in standard form.

Expand out terms of the right hand side:

-10 x = 18 - 4 x

Hint: | Move terms with x to the left hand side.

Add 4 x to both sides:

4 x - 10 x = (4 x - 4 x) + 18

Hint: | Look for the difference of two identical terms.

4 x - 4 x = 0:

4 x - 10 x = 18

Hint: | Combine like terms in 4 x - 10 x.

4 x - 10 x = -6 x:

-6 x = 18

Hint: | Divide both sides by a constant to simplify the equation.

Divide both sides of -6 x = 18 by -6:

(-6 x)/(-6) = 18/(-6)

Hint: | Any nonzero number divided by itself is one.

(-6)/(-6) = 1:

x = 18/(-6)

Hint: | Reduce 18/(-6) to lowest terms. Start by finding the GCD of 18 and -6.

The gcd of 18 and -6 is 6, so 18/(-6) = (6×3)/(6 (-1)) = 6/6×3/(-1) = 3/(-1):

x = 3/(-1)

Hint: | Simplify the sign of 3/(-1).

Multiply numerator and denominator of 3/(-1) by -1:

Answer: x = -3

Answer:

Step-by-step explanation:

The three numbers that are chosen by Levi are 5, 9 and 10.

It should be noted that the factors of 20 are 1, 2, 4, 5, 10 and 20.

Possible sum of factors of 20 are: 3, 5, 6, 7, 9, 11, 12, 14, 15, 21, 22, and 24.

Difference between 24 and a possible sum of factors of 24 are:

(21, 19, 18, 17, 15, 13, 12, 10, 9, 3, 2 , 0.)

The square numbers less than 24 are ( 1, 4, 9, 16).

Therefore the square number is 9.

And sum of the factors of 20 is 24 -9 = 15.

Therefore, the factors of 20 are = 5 and 10

Thus the given numbers are 5, 9 and 10.

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Answer:

Step-by-step explanation:

5.27=3.40+.85x

1.87=.85x

2.2=x

Answer:

105

Step-by-step explanation:

2x17=34

17x2.5=42.5

1.5x17=25.5

1/2x2x2x1.5=3

34+42.5+25.5+3=105

Answer Po Ba Ay 11.33?

Step-by-step explanation:

Calc

Due to length restriction we kindly invite to check the explanation for further details about the analysis of three quadratic equations and inherent rigid transformations.

Herein we find the graph of the parent quadratic equation f(x) = x² and two proposed resulting functions, whose difference with the former one have to be explained in terms of the kind of rigid transformations they have.

By comparing them, we find that both functions g(x) and h(x) are the result of a rigid transformation of the form f'(x) = k · f(x), where the transformation is a simple vertical dilation for k > 1, simple vertical contraction for 0 < k < 1, vertical contraction and reflection around the x-axis for - 1 < k < 0 and vertical dilation and reflection around the x-axis for k < - 1.

Function g(x) is the result of dilating f(x) by a factor of 3 and function h(x) is the result of dilating and reflecting f(x) around the x-axis by a factor of - 3.

The tables for each quadratic function are summarized below:

g(x):

 x             - 2             - 1               0             1                2

g(x)            12               3              0             3               12

f(x):

 x             - 2             - 1               0             1                2

g(x)          - 12            - 3               0           - 3            - 12

Lastly, we prepare the graph with the three functions in the image attached below.

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We need to find the average acceleration, this is given by the next formula:

Where:

vf = final velocity

vi = initial velocity

t = time.

Hence, we can replace using:

vf = 22 m/s

vi = 4 m/s

t = 3s

Then:

Hence, the average acceleration is 6 m/s²