Ralph has 3/4 gallons of paint. He wants to store all of the paint equally among 5 containers. How much paint, in gallons, will Ralph store in each container?

Answer:

Step-by-step explanation:

If Cara's calculation of the sum of the squared differences i.e. 1370 from the mean is incorrect, that would be the first error she made in computing the variance.

As the steps for finding the variance are not provided, it is difficult to determine the first error Cara made.

However, the formula for calculating the variance is:

Variance = (sum of the squared differences from the mean) / (number of observations)

The first error Cara may have made is in calculating the sum of the squared differences from the mean.

The correct steps to find the variance are:

Find the mean:

Mean = (87 + 46 + 90 + 78 + 89) / 5 = 78

Calculate the differences from the mean for each observation:

87 - 78 = 9

46 - 78 = -32

90 - 78 = 12

78 - 78 = 0

89 - 78 = 11

Square each difference:

[tex]9^2 = 81[/tex]

[tex](-32)^2 = 1024[/tex]

[tex]12^2 = 144[/tex]

[tex]0^2 = 0[/tex]

[tex]11^2 = 121[/tex]

Find the sum of the squared differences:

81 + 1024 + 144 + 0 + 121 = 1370

Divide the sum of squared differences by the number of observations:

Variance = 1370 / 5 = 274.

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The correct answer is option B. Translate 1 to the left, scale vertically by 1/2, then reflect over the y-axis.

The process of modifying the shape, location, or features of a graph is often referred to as graph transformation. Graphs are visual representations of mathematical functions or data point connections, often represented on a coordinate plane.

Translations, reflections, rotations, dilations, and other changes to the look of a graph are examples of graph transformations.

For the given problem, Transformation to get the desired result can be carried out as:

Hence, to convert the graph of "y = k(x)" to the graph of "y = -k(x + 1)," the correct sequence of transformations is to translate 1 unit to the left, scale vertically by 1/2, and then reflect across the y-axis, which is option B.

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Thus, the area of unshaded portion for the given values of triangle is found as 48.6 sq. m.

Three sides, three angles, plus three vertices make up a triangle.

Area of triangle  = 1/2*base *height

Area of unshaded portion = complete area - area of shaded triangle

Area of unshaded portion = 1/2*(20)*(8.1) - 1/2*8*(8.1)

Area of unshaded portion = 81 - 32.4

Area of unshaded portion = 48.6

Thus, the area of unshaded portion for the given values of triangle is found as 48.6 sq. m.

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Answer: 64 sqaure centimetres.

Step-by-step explanation:

- Surface area means the area of all exterior sides of a 3D dimensional shape. This means we'll have to find the area of every face and then add them all together.

Top and Bottom

4 x 4 = 16

16 x 2 = 32

Both faces are the same so once we find the area of one, we can just double it.

North, South, East and West Side

4 x 2 = 8

8 x 4 = 32

All four remaining faces had the same dimensions, meaning that once you found one, you just had to multiply that answer by 4.

To find the overall surface area add all the areas you have.

32 + 32 = 64

or

16 +_16 + 8 + 8 + 8 + 8 = 64

The rate of change of the area is 20π square inches per second.

The area of the shaded region can be calculated as the difference between the areas of the outer circle and the inner circle:

A = πr^2 - πr'^2

where r is the radius of the outer circle, r' is the radius of the inner circle, and π is the constant pi.

To find the rate of change of the area, we can take the derivative of both sides of the equation with respect to time t:

dA/dt = d/dt (πr^2) - d/dt (πr'^2)

Using the chain rule, we can express the derivatives in terms of the rates of change of the radii:

dA/dt = 2πr (dr/dt) - 2πr' (dr'/dt)

Substituting the given values at the instant when r=4 inches and r'=3 inches, we have:

dA/dt = 2π(4)(2) - 2π(3)(-1) = 20π

Therefore, the rate of change of the area is 20π square inches per second.

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Original number = $\frac{3}{4}$. The original number expressed as a common fraction is $\frac{3}{4}$.

1. Reciprocal: This is the result of switching the numerator and denominator of a fraction (or dividing 1 by a whole number).
2. Original number: This is the number we're trying to find.
3. Common fraction: This is a fraction where the numerator and denominator are both integers (whole numbers).

Step 1: Set up the equation using the given information.

One more than the reciprocal of the original number is $\frac{7}{3}$. We can express this as an equation:

Reciprocal of the original number + 1 = $\frac{7}{3}$

Step 2: Solve for the reciprocal of the original number.

Reciprocal of the original number = $\frac{7}{3}$ - 1

Step 3: Simplify the equation.

Reciprocal of the original number = $\frac{7}{3}$ - $\frac{3}{3}$

Reciprocal of the original number = $\frac{4}{3}$

Step 4: Find the original number.

Since we have the reciprocal of the original number, we can find the original number by taking the reciprocal of this value:

Original number = $\frac{1}{(\frac{4}{3})}$

Step 5: Simplify the expression.

Original number = $\frac{1}{1} \times \frac{3}{4}$

Original number = $\frac{3}{4}$

The original number expressed as a common fraction is $\frac{3}{4}$.

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The score to be made on the 4th quiz in order to have a mean quiz score of exactly 90 is equal to 88.

Let us consider the score that Tim needs to get on his fourth quiz be x.

Score he needs to get in order to have a mean quiz score of 90,

Set up an equation using the formula for the mean ,

(mean score) = (sum of scores) / (number of scores)

If Tim wants his mean quiz score to be 90, then we have,

⇒ 90 = (86 + 92 + 94 + x) / 4

Multiplying both sides by 4, we get,

⇒360 = 86 + 92 + 94 + x

Simplifying this equation, we get,

⇒ x = 360 - 272

⇒ x = 88

Therefore, Tim needs to get a score of 88 on his fourth quiz in order to have a mean quiz score of exactly 90.

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Duri can make 72 cupcakes on his own and Habib can make 36 cupcakes on her own, assuming they have enough of all the other ingredients.

To determine how many cupcakes each person can make on their own, we need to check if they have enough of all the other ingredients required to make 12 cupcakes.

Terrance has 1 cup of flour and 6 eggs, which is not enough to make 12 cupcakes.

Duri has 12 cups of flour and 1000 grams of butter, which is more than enough to make 12 cupcakes. However, the recipe requires 3/4 cup of sugar, 2 eggs, and 3/4 cup of milk, which we do not know if Duri has enough of.

Habib has 3 cups of milk and 6 cups of sugar, which is enough to make 12 cupcakes.

Anika has 1 cup of sugar and 4 cups of milk, which is not enough to make 12 cupcakes.

Therefore, only Duri and Habib have enough ingredients to make 12 cupcakes on their own.

To determine how many cupcakes they can make, we need to calculate how much of each ingredient is required for one cupcake and then divide the available ingredients by that amount.

For one cupcake, we need:

1/6 cups of flour

1/16 cup of sugar

1/6 eggs

1/16 cups of milk

125/12 grams of butter

Duri has 12 cups of flour and 1000 grams of butter, which is enough to make 72 cupcakes. Habib has 6 cups of sugar and 3 cups of milk, which is enough to make 36 cupcakes.

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The game owner should charge option (a) $0.55 to make it a fair game

To determine how much the game owner should charge to make it a fair game, we need to calculate the average value of each package. We can do this by finding the total value of all the packages and dividing it by the total number of packages.

The total value of the 30 packages worth $.65 each is:

30 x $.65 = $19.50

The total value of the 10 packages worth $.60 each is:

10 x $.60 = $6.00

The total value of the 15 packages worth $.30 each is:

15 x $.30 = $4.50

The total value of all the packages is

$19.50 + $6.00 + $4.50 = $30.00

The total number of packages is

30 + 10 + 15 = 55

The average value of each package is

$30.00 / 55 = $0.55

Therefore, the correct option is (a) $0.55

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Answer:

Step-by-step explanation:

1 + 1 divided by 3 x 3.5 = 4.66 or 4 2/3

Answer:

9.955

Step-by-step explanation:

The probability that a student who did not complete the homework passed the test is 0.25.

The measure of angle I in the triangle HIJ using given measurements is equal to 46.05 degrees.

In the triangle HIJ,

The measure of angle J is equal to 90 degrees.

This implies ,

HI is the hypotenuse.

JH is the opposite side to angle I.

In triangle HIJ,

Using trigonometric ratio we get,

sin ∠I = Opposite side / Hypotenuse

Substitute the values we have,

⇒ sin ∠I = 4.8 / 6.7

⇒ sin ∠I = 0.72

Now , take sin⁻¹ both the side of the equation we get,

⇒sin⁻¹(sin ∠I) = sin⁻¹( 0.72 )

Here sin⁻¹(sin ∠I) = ∠I

⇒∠I = sin⁻¹( 0.72 )

⇒∠I = 46.05 degrees

Therefore, the measure of angle I is equal to 46.05 degrees.

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Answer: y=1/2x-3

Step-by-step explanation:

I'm assuming you're trying to find it in slope intercept form!

y=mx+b

y=1/2x-3

easy

a) The probability that a simple random sample of 50 ten-gram portions results in a mean of at least 3.6 insect fragments is approximately 0.027.

b) This result is somewhat unusual, as only about 2.7% of samples would be expected to have a mean of at least 3.6 insect fragments. However, it is not necessarily a cause for concern, as it is within the range of expected variation.

c) More information about the distribution of insect fragments in the population and the context in which the samples were collected would be needed to draw more definitive conclusions.

To answer this question, we would need to know the distribution of insect fragments in the population from which the samples are drawn. Let's assume that this distribution is approximately normal with a mean of 3.2 insect fragments and a standard deviation of 0.8 insect fragments, as suggested by FDA guidelines for chocolate.

The distribution of the sample means for samples of size n can be approximated by a normal distribution with mean µ and standard deviation σ/√n. In this case, µ = 3.2 and σ/√n = 0.8/√50 = 0.113.

To find the probability that a sample of 50 ten-gram portions has a mean of at least 3.6 insect fragments, we need to find the area under the normal curve to the right of 3.6. Using a standard normal distribution table or a calculator, we find that this probability is approximately 0.027.

This result is somewhat unusual, as only about 2.7% of samples would be expected to have a mean of at least 3.6 insect fragments. However, it is not necessarily a cause for concern, as it is within the range of expected variation. If the sample mean was much higher, say 4.0 or 4.5, it would be more concerning and warrant further investigation.

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The point of tangency is (-3, -2).

To find the point of  tangency , we really want to find the convergence point between the line and the circle. We can begin by tracking down the situation of the circle with focus (- 1,2).

A circle's equation for its center (a,b) and radius (r) is as follows:

[tex](x - a)^2 + (y - b)^2 = r^2[/tex]

Plugging in the values for the center and solving for r, we get:

[tex](x + 1)^2 + (y - 2)^2 = r^2[/tex]

Now we need to find the intersection point between this circle and the line 2x+3y=-22. We can do this by substituting y = (-2/3)x - (22/3) into the equation of the circle:

[tex](x + 1)^2 + ((-2/3)x - (16/3))^2 = r^2[/tex]

Expanding and simplifying, we get:

[tex]10x^2 + 24x + 44 = 9r^2[/tex]

Next, we can make use of the fact that the line intersects the circle at a tangent. This indicates that the distance between the intersection point and the center of the circle is the same as its radius. The distance between the center of the circle and the line can be determined using the distance formula:

distance = [tex]|2x + 3y - (-22)\sqrt{2^2 + 3^2}| = |2x + 3y + 22| \sqrt(13)[/tex]

Setting this equal to the radius r, we get:

[tex]|2x + 3y + 22| \sqrt{13} = \sqrt{10x^2 + 24x + 44} / 3[/tex]

Squaring both sides and simplifying, we get:

[tex]36(2x + 3y + 22)^2 = 13(10x^2 + 24x + 44)[/tex]

Expanding and simplifying, we get:

[tex]26x^2 + 36xy + 45y^2 + 52x + 132y + 240 = 0[/tex]

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

x = (-18y - 13 ± [tex]\sqrt{169 - 720y^2[/tex])) / 13

Substituting this into the equation for the line, we get:

2(-18y - 13 ± [tex]\sqrt{169 - 720y^2))[/tex] / 13 + 3y = -22

Simplifying, we get:

y = -2

Substituting y = -2 into the equation for x, we get:

x = -3

Therefore, the point of tangency is (-3, -2).

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Answer:

3(n + 6) = 2(n + 6) + (n + 6)

3(n + 6) = 3n + 18

Answer:

f(x + 1) + 2

Step-by-step explanation:

All the points are translated 1 unit to the left and 2 units up.
To write a translation along the x-axis, movement to the right would be written as f(x - a), where a is the amount translated, and movement to the left would be written as f(x + a). In this case, we would need to write the translation as f(x + 1), since it is moving 1 unit to the left.
As for translations along the y-axis, movement upward would be written as f(x) + a, and movement downward would be written as f(x) - a. Thus, the transformation rule to describe the path the pre-image made to arrive at the image would be f(x + 1) + 2.

P.S. I'm a bit rusty with this stuff, so I apologize in advance if I messed something up.

The probability regarding fewer than 30 people out of 250 people will consider working from home is 3.36%.

In order to calculate the probability for the given condition we need to perform binomial distribution

P(X < 30) = Σ P(X = x)

For x = 0 to 29

Here,

X = number of people from the sample who work from home

P = probability of an adult working from home

Given,

X = 250

P = 0.15

Now performing approximation to binomial distribution, leads to approximate X like a normal random variable with mean

Therefore,

μ = np

μ = 250 x 0.15

μ =  37.5

Now we have to evaluate the standard deviation

σ = √(np(1-p))

σ = √ 250 x 0.15 x (1 - 0.15)

σ ≈  4.08

Then we can proceed to standardized X

Z = (X - μ) / σ

P(X < 30) = P(Z < (30 - μ) / σ) = P(Z < (30 - 37.5) / 4.08)

≈ P(Z < -1.84)

Using standard distribution table

P(Z < -1.84) ≈ 0.0336

Converting it into percentage

0.0336 x 100

= 3.36%

The probability regarding fewer than 30 people out of 250 people will consider working from home is 3.36%.

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Step-by-step explanation:

Volume of rect prism = L X W X H = 4 X 9 X 10 = 360 cm^3

It will take Tom and Nelson 1.875 hours, or 1 hour and 52.5 minutes, to complete the report working together.

To solve this problem, we can use the concept of work done. Let's assume that a report is a unit of work, and Tom and Nelson each do a fraction of the work in one hour.

Tom can do the entire report in 3 hours, which means he can do 1/3 of the report in one hour. Similarly, Nelson can do 1/5 of the report in one hour.

If they work together, the fraction of the report they can do in one hour is the sum of their individual fractions:

1/3 + 1/5 = 8/15

So, together they can do 8/15 of the report in one hour. To find out how long it will take them to do the entire report working together, we can use the formula:

time = work ÷ rate

where work is 1 (the whole report) and rate is 8/15 (the fraction of the report they can do in one hour).

time = 1 ÷ (8/15)

time = 1.875 hours

Therefore, it will take Tom and Nelson 1.875 hours, or 1 hour and 52.5 minutes, to complete the report working together.

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Answer:

15 1/2

Step-by-step explanation:

hope this helped

Answer:

9) Keep the denominators the same, and subtract the numerators. Then simplify if necessary.

[tex] \frac{3x + 2}{x + 5} - \frac{2x - 3}{x + 5} [/tex]

[tex] = \frac{3x + 2 - (2x - 3)}{x + 5} [/tex]

[tex] = \frac{3x + 2 - 2x + 3}{x + 5} [/tex]

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

10) Find the LCD. Rewrite each rational expression as an equivalent expression with the LCD as the denominator. Add the numerators and write the sum over the LCD. Then simplify if necessary.

[tex] \frac{4x}{x - 2} + \frac{x - 4}{x - 5} [/tex]

[tex] = \frac{4x(x - 5) + (x - 4)(x - 2)}{(x - 2)(x - 5)} [/tex]

[tex] = \frac{4 {x}^{2} - 20x + {x}^{2} - 6x + 8 }{(x - 2)(x - 5)} [/tex]

[tex] = \frac{5 {x}^{2} - 26x + 8}{(x - 2)(x - 5)} [/tex]

[tex] = \frac{5 {x}^{2} - 26x + 8 }{ {x}^{2} - 7x + 10} [/tex]

Answer:

50 meters/21.91 seconds = 2.282 m/sec

If you choose not to make a payment during the 24-month period, your balance at the end of the promotion will be $3,637.16.

Explain month

A month is a unit of time equal to one-twelfth of a year, or approximately 30.44 days. It is often used to represent periodic phenomena, such as interest rates or seasonal trends, and to calculate the duration between two dates. The number of months between two dates is calculated by dividing the difference in days by 30.44.

According to the given information

If you do not make any payments during the 24-month period, your balance will increase each month due to the interest that accrues. After 24 months, your balance will be:

$2299.99 * (1 + 0.020825)²⁴ = $3,637.16

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The bearing of C from A is 90 degrees when B is equidistant from A and C.

In navigation and geometry, bearing refers to the direction or angle between two points, measured clockwise from a fixed reference direction. Typically, bearings are measured in degrees, with 0 degrees indicating a direction due north, 90 degrees indicating a direction due east, 180 degrees indicating a direction due south, and 270 degrees indicating a direction due west. Bearings can be expressed as either magnetic bearings or true bearings, depending on the reference direction used.

Let's assume that the distance from B to A and from B to C is the same.

To find the bearing of C from A, we can use the fact that the interior angles of a triangle sum up to 180 degrees. Therefore, we can first find the bearing of A from C:

180 - 129 = 51

This means that the bearing of C from A is 51 degrees in the opposite direction of the bearing of A from C. Since the bearing of A from C is 219, the bearing of C from A is:

219 - 180 + 51 = 90 degrees

Therefore, the bearing of C from A is 90 degrees.

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The statement that is equivalent to each other would be =

2×(4+2)-6 = 14÷(3.5×2)+4. That is option A.

An equivalent equation is the type of equation that appears different but has the same answer when simplified or solved.

The first part;

=2×(4+2)-6

= 2×(6)-6

= 12-6 = 6

The second part;

= 14÷(3.5×2)+4

= 14÷7+4

= 2+4

= 6

Therefore, 2×(4+2)-6 = 14÷(3.5×2)+4. is a true statement.

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(a) True. We can use partial fraction decomposition to write X(x² + 4)/(x² - 4) as (A/(x+2)) + (B/(x-2)).

(b) True. We can use partial fraction decomposition to write X² + 4/(x(x² - 4)) as (A/x) + (B/(x+2)) + (C/(x-2)).

(c) True. We can use partial fraction decomposition to write X² + 4/(x²(x - 4)) as (A/x²) + (B/x) + (C/(x-4)).

(d) False. We can use partial fraction decomposition to write X² - 4/(x(x² + 4)) as (A/x) + (Bx+C)/(x²+4).

(a) We want to write X(x² + 4)/(x² - 4) in the form (A/(x+2)) + (B/(x-2)). First, we find A and B by multiplying both sides by the common denominator (x+2)(x-2):

X(x² + 4) = A(x-2) + B(x+2)

Expanding both sides gives:

Xx² + 4X = Ax - 2A + Bx + 2B

Grouping terms by x gives:

Xx² + (A+B)x + (-2A+2B) = 4X

Now we have a system of two equations:

A + B = 0 (coefficients of x)

-2A + 2B = 4X (constant terms)

Solving for A and B gives:

A = -B

-2A + 2B = 4X

-2A + 2(-A) = 4X

-4A = 4X

A = -X

Therefore, B = X. Thus,

X(x² + 4)/(x² - 4) = (-X/(x+2)) + (X/(x-2))

(b) We want to write X² + 4/(x(x² - 4)) in the form (A/x) + (B/(x+2)) + (C/(x-2)). First, we find A, B, and C by multiplying both sides by the common denominator x(x+2)(x-2):

X² + 4 = A(x+2)(x-2) + Bx(x-2) + Cx(x+2)

Expanding both sides gives:

X² + 4 = Ax² - 4A + Bx² - 2Bx + Cx^2 + 2Cx

Grouping terms by powers of x gives:

(X² + 4) = (A+B+C)x² + (-2B+2C)x - 4A

Now we have a system of three equations:

A + B + C = 0 (coefficients of x²)

-2B + 2C = 0 (coefficients of x)

-4A = 4 (constant terms)

Solving for A, B, and C gives:

A = -1/4

B = 1/4

C = 1/4

Therefore,

X² + 4/(x(x² - 4)) = (-1/(4x)) + (1/(4(x+2))) + (1/(4(x-2)))

(c) We want to write X² + 4/(x²(x - 4)) in the form (A/x²) + (B/x) + (C/(x-4)). First, we find A, B, and C by multiplying both sides by the common denominator x²(x-4):

X²(x-4) + 4x² = Ax(x-4) + Bx²(x-4) + Cx²

Expanding both sides gives:

X²x - 4X² + 4x² = Ax² - 4Ax + Bx³ - 4Bx² + Cx²

Grouping terms by powers of x gives:

(X² + 4) = (B)x³ + (A-4B)x² + (-4A+C)x

Now that we have a common denominator of (x² - 4), we can combine the two fractions and simplify:

X(x² + 4) - 2(x² - 4) = A(x - 2) + B(x + 2)

Expanding and simplifying the left side:

x³ + 4x - 2x² + 8 = Ax - 2A + Bx + 2B

Grouping the like terms on each side:

x³ - 2x² + Ax + Bx + 4x - 2A + 2B + 8 = 0

Now we have a polynomial equation that we can use to solve for A and B. We can do this by equating the coefficients of like terms on both sides. Specifically, we can equate the coefficients of x² and x:

x³ - 2x² + Ax + Bx + 4x - 2A + 2B + 8 = 0

Coefficients of x²: -2 = A

Coefficients of x: 4 = B

Therefore, we have:

X(x² + 4)/(x² - 4) = (-2x)/(x² - 4) + (4)/(x² - 4)

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