Find the surface area of the triangular prism.

A drawing of a triangular prism. The base is a right triangle with a base of 4 centimeters, a height 3 centimeters, and a third side of 5 centimeters. The height of the prism is 10 centimeters.

The surface area is ___
square centimeters.

The sample size that required to reduce the standard deviation of the sampling distribution to one-half that standard deviation (0.073) is 120.

As per the data given:

The makers of skittles claim that 20% of skittles candies are orange.

20 % = 0.20

Select a random sample of 30 skittles from a large bag.

[tex]\hat p[/tex] = the proportion of orange skittles in the sample.

The standard deviation of the sampling distribution of [tex]\hat p[/tex] = 0.073

The Standard deviation of the Sampling distribution was reduced to [tex]$= \frac{1}{2} \sigma_{\hat{p}}$[/tex].

[tex]$ \sigma_{\hat p}=\sqrt{\frac{p(1-p)}{n}}=0.073$[/tex]

Divide both sides by 2

We get:

[tex]$\sqrt{\frac{p(1-p)}{n}}=\frac{0.073}{2}[/tex]............... (1)

Now it should become be one - half.

Let [tex]$n_1[/tex] be the new sample size.

[tex]$\sqrt{\frac{p(1-p)}{n_1}}=\frac{0.073}{2}[/tex] ..................2

From (1) and (2) RHS of both equations is equal.

Then equate both equations

[tex]$\frac{1}{2} \sqrt{\frac{p(1-p)}{n}}=\sqrt{\frac{p(1-p)}{n_1}}$[/tex]

Squaring on both sides

We get:

[tex]$\Rightarrow\left(\frac{1}{2}\right)^2 \frac{p(1-p)}{n}=\frac{p(1-p)}{n_1}\end{aligned}$[/tex]

[tex]$\Rightarrow \frac{1}{4 n}=\frac{1}{n_1}$[/tex]

[tex]$\Rightarrow n_1=4 n$[/tex]

[tex]$n_1-[/tex] The new sample size required = 4n

n-The old sample size.

The sample size that required = 4n

= 4 (30)

= 120

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The makers of skittles claim that 20% of skittles candies are orange. Suppose this claim is true. You select a random sample of 30 skittles from a large bag. Let p-hat = the proportion of orange skittles in the sample. The standard deviation of the sampling distribution of p-hat = .073

What sample size would be required to reduce the standard deviation of the sampling distribution to one-half that standard deviation (.073)

Answer:

Yes

Step-by-step explanation:

Dilations shrink or expand a figure.  If the scale factor is one, the two figures will be identical.

The costs of 5 oranges and 15 oranges are R15 and R45

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

Six oranges cost R18,00

This means that the unit rate is

Unit rate = R18,00/6 = R3.00

For 5 oranges, we have

Cost = 5 * R3.00 = R15.00

For 15 oranges, we have

Cost = 15 * R3.00 = R45.00

So, the costs are R15.00 and R45.00

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Using Euler's method, y(0.5) ≈ 0.7052 when h = 0.1 and y(0.5) ≈ 0.6803 when h = 0.05.

What is Euler's method?

Ordinary differential equations (ODE) can be solved using the Euler's method, a first-order numerical technique, with a specified beginning value.

We are given an equation y' = f(x,y), a point ([tex]x_{o} ,y_{o}[/tex]) and a step value h.

We have

f(x,y) = (x − y)^2

Point is (0,0.6)

We need to find y(0.5).

So, using Euler's method with step h = 0.1, we get

⇒[tex]x_{1}[/tex] = [tex]x_{o}[/tex] + h

⇒[tex]x_{1}[/tex] = 0 + 0.1 = 0.1

⇒[tex]y_{1}[/tex] = [tex]y_{o}[/tex] + h * f([tex]x_{o} ,y_{o}[/tex])

⇒[tex]y_{1}[/tex] = 0.6 + 0.1 * (0 - 0.6)^2

⇒[tex]y_{1}[/tex] = 0.636

⇒[tex]x_{2}[/tex] = [tex]x_{1}[/tex] + h

⇒[tex]x_{2}[/tex] = 0.1 + 0.1 = 0.2

⇒[tex]y_{2}[/tex] = [tex]y_{1}[/tex] + h * f([tex]x_{1} ,y_{1}[/tex])

⇒[tex]y_{2}[/tex] = 0.636 + 0.1 * (0.1 - 0.636)^2

⇒[tex]y_{2}[/tex] = 0.6647296

⇒[tex]x_{3}[/tex] = [tex]x_{2}[/tex] + h

⇒[tex]x_{3}[/tex] = 0.2 + 0.1 = 0.3

⇒[tex]y_{3}[/tex] = [tex]y_{2}[/tex] + h * f([tex]x_{2} ,y_{2}[/tex])

⇒[tex]y_{3}[/tex] = 0.6647296 + 0.1 * (0.2 - 0.6647296)^2

⇒[tex]y_{3}[/tex] ≈ 0.6863

⇒[tex]x_{4}[/tex] = [tex]x_{3}[/tex] + h

⇒[tex]x_{4}[/tex] = 0.3 + 0.1 = 0.4

⇒[tex]y_{4}[/tex] = [tex]y_{3}[/tex] + h * f([tex]x_{3} ,y_{3}[/tex])

⇒[tex]y_{4}[/tex] ≈ 0.6863 + 0.1 * (0.3 - 0.6863)^2

⇒[tex]y_{4}[/tex] ≈ 0.7012

⇒[tex]x_{5}[/tex] = [tex]x_{4}[/tex] + h

⇒[tex]x_{5}[/tex] = 0.4 + 0.1 = 0.5

⇒[tex]y_{5}[/tex] = [tex]y_{4}[/tex] + h * f([tex]x_{4} ,y_{4}[/tex])

⇒[tex]y_{5}[/tex] ≈ 0.7012 + 0.1 * (0.5 - 0.7012)^2

⇒[tex]y_{5}[/tex] ≈ 0.7052

So, y(0.5) ≈ 0.7052

Similarly, with step h = 0.5, we will calculate the values till [tex]x_{10}[/tex] and [tex]y_{10}[/tex]

On doing this, we get y(0.5) ≈ 0.6803

Hence, using Euler's method, y(0.5) ≈ 0.7052 when h = 0.1 and y(0.5) ≈ 0.6803 when h = 0.05.

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In the given exercise option a, b and c are in reduced echelon form and option d is in echelon form.

Row echelon form suggests that: Each row's leading (first) entry must be

Each following row's first entry must be on a new column to the right.

All rows with zero entries are listed below rows with non-zero items.

If the leading entry in each column is the only nonzero element in that column, reduced echelon form also results from echelon form conditions.

According to the definitions we see that, in the given exercise option a, b and c are in reduced echelon form and option d is in echelon form.

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m = -2, 0.  The function y = xm is a solution when m = -2 or 0.

For the differential equation xy'' + 2y' = 0, the function y = xm is a solution if m = -2 or 0. This can be seen by substitution and solving the resulting equation. When m = -2, the equation simplifies to 0 = 0, which is true. When m = 0, the equation simplifies to 0 = 2y', which is true when y' = 0. Therefore, the function y = xm is a solution when m = -2 or 0.

To solve for m, first substitute the function y = xm into the differential equation, giving xm'' + 2mx' = 0. Then move all terms containing m to one side of the equation, leaving 0 on the other side. This gives m'' + 2m' = 0, which is a second-order linear differential equation. This equation can be solved using the characteristic equation, which is found by setting the discriminant of the equation equal to 0. The discriminant for this equation is 4 - 4(1)(0) = 4, which is greater than 0. Thus, the equation has two distinct real solutions, which are m = -2 and m = 0. Therefore, the function y = xm is a solution when m = -2 or 0.

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Ha:mu<10  is the appropriate alternative hypothesis that the consumer group wishes to test .

How would you define hypothesis?

An assumption or notion is called a hypothesis when it is put forth with the purpose of debating whether it might be true.

                               In the scientific process, the hypothesis is developed prior to the completion of any relevant study, other than a brief background review.

Ha:mu<10

Because A consumer group is suspicious of this claim, believing that the weight lose is, on average, much less.

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Answer:

12 / 1 and runner B

Step-by-step explanation:

at 13 seconds runner a had only run 156 ft, however runner b had run 200 ft.

The Max height H = [tex]\frac{u^{2} sin^{2} }{2g}[/tex] and the range is R = [tex]\frac{u* sin2thetha }{2g}[/tex].

Any object sent into space with only gravity acting on it is considered a projectile. Gravity is the main force working on a projectile. This doesn't necessary imply that the other troops don't affect it; it merely means that their impact is far less than that of gravity. A projectile's route is known as its trajectory. When a particle is hurled obliquely near the surface of the earth, it flows along a curved route with constant acceleration directed towards the planet's center (we assume that the particle stays close to the surface). Such a particle's motion is referred to as projectile motion, and its route is a projectile.

(A) Time taken by the projectile to reach its maximum height which will be given as -

using the equation of motion (1), we get

Vy= V0 + a*t

So the Max height H = [tex]\frac{u^{2} sin^{2} }{2g}[/tex]

And the range is R = [tex]\frac{u* sin2thetha }{2g}[/tex]

Hence the Max height H = [tex]\frac{u^{2} sin^{2} }{2g}[/tex] and the range is R = [tex]\frac{u* sin2thetha }{2g}[/tex].

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Step-by-step explanation:

a)

Arabica coffee = 750a

Robusta coffee = 1200r

The total amount coffee beans 750a + 1200r = 1000000 kg

b)

The total amount of market price

1.42*750a +0.73*1200r 1000000

1065a + 876r = 1000000 dollars

step by step reading

The coffee variety Arabica yields about 750 kg of coffee beans per hectare, while

Robusta yields about 1200 kg per hectare. Suppose that a plantation has a

hectares of Arabica and r hectares of Robusta.

a. Write an equation relating a and r if the plantation yields 1,200,000 kg of coffee.

b. On August 14, 2003, the world market price of coffee was $1.42 per kg of Arabica

and $0.73 per kg of Robusta. Write an equation relating a and r if the plantation

produces coffee worth $1,200.000. what does that answer that means  it would be

ANSWER

a

Arabica coffee = 750a

Robusta coffee = 1200r

The total amount coffee beans

750a + 1200r = 1.200,000 kg

b)

The total amount of market price

1.42*750a + 0.73*1200r = 1,200.000 ⇒

1065a + 876r = 1,200.000 dollar!!!!!!

Answer: Let's call the bill before the tip "x".

The tip was 20.7% of the bill, so the amount of the tip can be expressed as:

tip = 0.207 * x

The total bill, including the tip, was $31.09, so we can write an equation to represent this:

x + tip = 31.09

Substituting the expression for the tip into this equation, we get:

x + 0.207x = 31.09

Expanding and solving for x, we get:

1.207x = 31.09

x = 31.09 / 1.207

x = 25.76

So the bill before adding the tip was $25.76.

Step-by-step explanation:

The proceeds (discounted value) on the third-party discount note are $4,116.90.

The discounted value of a note is a value that is less than the maturity value.

The maturity value is the face value of the note plus the accumulated interest.

Face value of the note receivable = $4,000

Annual interest rate = 12%

Note issuance date = March 16

Note due date = November 14

The total number of days = 243 days

Discount date = June 11

Discount rate = 11%

March 16 to June 11 = 87 days

Interest on the note = $320 ($4,000 x 243/365 x 0.12)

Maturity value = $4,320 ($4,000 + $320)

Discount period = 156 days (243 - 87)

Discount on the note = $203.10 ($4,320 x 156/365 x 11%)

Discounted value = $4,116.90 ($4,320 - $203.10)

Thus, the man, who holds a note of $4,000 at 12% interest but sells it at a discount rate of 11%, will receive $4,116.90.

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The value of the x is 19.9.

A planar triangle's side's square is equal to the sum of the squares of the other sides minus the product of those sides and the cosine of the angle between them, divided by two.

Given:

The angle C is 98°.

Applying law of cosines:

c² = a² + b² -2ab cosC.

Substituting the values,

c² = (17)² + (13)² -2(17)(13) cos98°.

c² = 458 -  (-0.13917)442

c² = 396.48686

c = 19.9

Hence, x = 19.9.

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The thing that needs to be corrected in the diagram to fix the error is that the third arc should be drawn centered at F.

Given:

Constructing a parallel line to line AB and passing through point P.

To find:

An error occurred in the construction.

The procedure is,

However, the third arc is drawn centered at D. This is wrong.

Therefore, the correct step is that the third arc must be centered at F.

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Checks, debit cards, and electronic payments are considered forms of cashless payments because they allow for the transfer of funds between individuals or businesses without the need for physical currency, such as bills and coins.

Checks are considered cash because they are legal tender and can be deposited into a bank account, allowing the funds to be transferred between parties. Debit cards and electronic payments work in a similar way by deducting funds directly from a bank account or transferring funds electronically. While these forms of payment may not involve physical currency, they represent a transfer of value and can be used to purchase goods and services in the same way as cash.

In summary, checks, debit cards, and electronic payments are considered forms of cash because they facilitate the transfer of value between parties, even though they do not involve physical currency.

Answer:

Debit cards account for 28% of all payments, and credit cards account for 23% of all payments. For these payments, payment details are entered manually during a checkout process, or the physical card is processed at a point of sale (POS) system. There’s usually a debit or credit card processing fee, which the business owner needs to pay.

Step-by-step explanation:

pls tell me if wrong thank you have a great night or day

According to the information, it can be inferred that US President Nixon's visit to China proved that the communist world was not a single entity and had many different positions.

The visit of the President of the United States Richard Nixon to the People's Republic of China is an important event in the political and foreign relations sphere of the United States because it was a way to establish a formal relationship between the United States and the People's Republic of China.

This was significant because it was the first time a US President had visited the PRC, who at the time considered the US one of his main enemies. Additionally, this allowed him to verify to the other states that there were different ways of proposing communism. In this case, Chinese communist thought was moderated, so the relationship with the United States was allowed.

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The value of the last one is 18.

The solution of the diagram can be modelled with an equation. Therefore, let's find the last value.

we will use variable to represent the fruit names.

Hence,

yellow fruit = x

red fruit = y

green fruit = z

Therefore,

x + y + z = 29

2y + z = 26

2z + y = 25

Using substitution,

y = 25 - 2z

2(25 - 2z) + z = 26

50 - 4z + z = 26

50 - 3z = 26

-3z = 26 - 50

-3z = -24

z = 8

y = 25 - 2(8)

y = 25 - 16

y = 9

Therefore,

x + 9 + 8 = 29

x = 29 - 17

x = 12

Finally,

x + 1 / 2x  = 12 + 1 / 2(12) = 12 + 6 = 18

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Answer:

(8,-5)

x=8

y=-5

Step-by-step explanation:

As stated in the preceding statement When 4 points are given in one method for calculating grade point averages (GPA), the resulting mean grade rating is 3.41.

Average While calculating the arithmetic mean, a group of integers is added, their count is divided, and the result is then taken. For instance, the average of 2, 3, 5, 7, and 10 is 5, this is the result of 30 reduced by 6.

The quality points by each grade every course must first be calculated before being added together to determine the GPA.

3 credit hours times 4 points for A equals 12 quality points.

B - ( 3 points x 2 credit hours ) x 2 (because there are 2 courses) = 18 quality points

C - 2 points x 4 credits = 8 quality points

D - 1 point x 3 credits = 3 quality points

Now add up all the quality points = 12 + 18 + 8 + 3 = 41

Add the credit hours as well = 3 + 2 + 4 + 3 = 12

Divide the total kit by total semester credit to calculate the GPA = 41/12 = 3.41

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a. The vector equation for the given line is (x,y,z) = (1,0,7) + t(1,3,1) and the parametric equations are x = 1+t, y = 3t, z = 6+t.

b. The vector equation for the given line is

(3 + 3t)i + (2.3 + 3t)j + (3.6 - t)k and the parametric equation is

x = 3 + 3t, y = 2.3 + 3t, z = 3.6 - t.

What is a parametric equation?

A series of equations known as a parametric equation specifies a point's location in the xy plane in terms of a third variable, which is typically referred to as a parameter.

a. We are given that a line passes through the point (1,0,7) and is perpendicular to the plane x + 3y + z = 2.

Now, since the line is perpendicular to the plane, the normal vector (1,3,1) for the plane is parallel to the line.

So the vector equation for the line is

(x,y,z) = (1,0,7) + t(1,3,1)

The parametric equations for the line are

x = 1+t, y = 3t, z = 6+t

b.  We are given that a line passes through the point (3, 2.3, 3.6) and parallel to the vector 3i + 3j - k.

So the vector equation "r" for the line is

r = (3i + 2.3j + 3.6k) + t(3i + 3j - k)

r = (3 + 3t)i + (2.3 + 3t)j + (3.6 - t)k

The parametric equations for the line are

x = 3 + 3t, y = 2.3 + 3t, z = 3.6 - t

Hence, the required vector and parametric equations have been obtained.

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the quotient of four (4) more than a number (x) and seven (7) is ten (10) equals (x +4)/7 = 10.

Any mathematical statement that includes numbers, variables, and an arithmetic operation between them is known as an expression or algebraic expression. In the phrase 4m + 5, for instance, the terms 4m and 5 are separated from the variable m by the arithmetic sign +.

Given The quotient of four is more than a number and seven is ten.

also given Use x for your variable.

In Mathematics, quotient literally means dividing a particular number by another number i.e the division of two (2) numbers.

Next, we would translate the word problem (sentence) into an algebraic expression as follows;

=> (x +4)/7 = 10

In conclusion, the algebraic expression for the quotient of four (4) more than a number (x) and seven (7) is ten (10) equals (x +4)/7 = 10.

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The first and second models are linear regression models as it follow the general form, while the third model is not a linear regression model

Linear Regression is a statistical method used to model the relationship between a dependent variable (also known as the response or output variable) and one or more independent variables (also known as predictor or input variables). It assumes that there is a linear relationship between the independent variables and the dependent variable.

A linear regression model takes the form:

Y = β0 + β1X1 + β2X2 + ... + βnXn + ε

Where Y is the dependent variable, X1, X2, ..., Xn are the independent variables, β0, β1, β2, ..., βn are the coefficients that represent the slope of the line for each independent variable, and ε is the error term. The goal of linear regression is to estimate the coefficients β0, β1, β2, ..., βn so that the model can be used to make predictions about the dependent variable.

a. Y₁ = A + B₁X₁ + B₂X₂

This is a linear regression model, as the relationship between Y₁ and X₁, X₂ is linear, with the coefficients A, B₁, and B₂.

b. Y₁ = B₁X₁ + A

This is also a linear regression model, as the relationship between Y₁ and X₁ is linear with the coefficients A and B₁.

c. Y₁ = 1 + exp(-B₁ - B2X₁)

This is not a linear regression model, as the relationship between Y₁ and X₁ is not linear. It is not possible to convert it into a linear regression model by suitable algebraic manipulations.

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The ropes should be staked 12 ft away from 16 ft pole and 18 ft away from 24 ft pole.

Two triangles are similar if they have the same ratio of corresponding sides and equal pair of corresponding angles. If two or more figures have the same shape, but their sizes are different, then such objects are called similar figures.

Given that, two vertical poles, one 16 ft high and the other 24 ft high, stand 30 feet apart on a flat field. A worker wants to support both poles by running rope from the ground to the top of each post, we need to find where should the stake be laced to use the least amount of rope,

Let rope of the 16 ft high pole be at x ft and that of 24 ft high pole at (30-x)

The structure of rope and poles are making a set of similar triangles, (refer to figure attached)

We know that, the corresponding sides of the similar triangle are in same ratio,

Therefore,

16 / x = 24 / (30-x)

2 / x = 3 / (30-x)

60 - 2x = 3x

5x = 60

x = 12

30-12 = 18

Hence, the ropes should be staked 12 ft away from 16 ft pole and 18 ft away from 24 ft pole.

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Do u have a screen protector cuz if u do thats probably why

Step-by-step explanation:

Answer:

light diffraction and a dirty phone screen.

Using the principle of alternate angles we can say that the value of x will be 120°.

The intersection of two parallel lines by a transversal produces alternate angles.

The alternate angles are equivalent when a transversal cuts two parallel lines.

The total of all the angles created on a transverse that are inside either of the two parallel lines is always 180 degrees.

Alternate interior angles for non-parallel lines don't have any special characteristics.

Angles of the same size that are found on opposing sides of the transversal line are known as alternate angles.

So, do not observe the given image:
We know that it is the pair of alternate angles that is equal.

Then, x = 120°.

Therefore, using the principle of alternate angles we can say that the value of x will be 120°.

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Answer:

Step-by-step explanation:

We can use similar triangles to find the function that models the length of the woman's shadow. If the woman is standing at a distance d from the base of the lamp, the length of her shadow will be proportional to her height, so the ratio of the shadow length to the height will be equal to the ratio of the distance from the base of the lamp to the height of the lamp.

So, if h is the woman's height and L is the length of her shadow, we have:

L/h = d/13

And since h = 6 feet, we can write:

L = (d/13) * 6

So the function that models the length of the woman's shadow in terms of her distance from the base of the lamp is:

L = (d/13) * 6

Answer:

The player has an annual salary of $305,000, and they have decided to donate 1/8 of their salary to charity. To calculate this, we simply divide their salary by 8.

305,000 / 8 = $38,125

So, the player is donating $38,125 to charity every year. This is calculated by taking 1/8 of their annual salary.

The fraction 1/8 represents one out of eight equal parts of the player's salary, and when this fraction is multiplied by the player's salary, it gives the exact amount that they are donating to charity.