rewrite the equation 2 x 3 y = 6 in slope-intercept form. y = -2 x 6 y = - x 2 y = 2 x 6 3 y = -2 x 6

Hamilton Corporation's effective tax rate is 22.5%.

The effective tax rate is a measure of a company's tax burden as a percentage of its pre-tax income. It indicates the proportion of pre-tax income that is paid in taxes.

In this case, Hamilton Corporation has a pre-tax income of $100,000 and a tax expense of $22,500. Therefore, the company paid $22,500 in taxes out of its pre-tax income of $100,000.

The effective tax rate is the ratio of the total tax expense to the company's pre-tax income.

Effective Tax Rate = Total Tax Expense / Pre-tax Income

In this case, the pre-tax income is $100,000, and the tax expense is $22,500. Therefore,

Effective Tax Rate = $22,500 / $100,000 = 0.225 or 22.5%

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The sampling distribution of the sample mean can be approximated by a normal distribution by the Central Limit Theorem (CLT) since the sample size is 30.

The Reeses candy company claims that 52% of the Reese's pieces are orange. Assume the company's claim is true. Let X = the number of orange candies in a sample of 30.a) Mean of the sampling distribution of X \[\mu = np = 30 × 0.52 = 15.6\]Standard deviation of the sampling distribution of X \[\sigma = \sqrt {npq} = \sqrt {30 × 0.52 × 0.48} \] \[\sigma \approx 2.12\]b) Standard deviation shows how much the sample proportion varies from the true population proportion, on average. Here, the standard deviation is 2.12, which means that when you take repeated random samples of 30, the sample proportion of orange candies will typically vary by about 2.12 percentage points from the true population proportion of 52%.c) The shape of the sampling distribution of X can be approximated by a normal distribution since the sample size is 30 and np and nq are both greater than 10. Thus, the Central Limit Theorem (CLT) is applicable.d) \[P (X ≤ 12)\] = \[P\left( \frac {X-\mu}{\sigma}\le \frac {12-15.6}{2.12} \right)\] = \[P(z\le -1.679)\] Using standard normal distribution table, we get \[P(z\le -1.679) = 0.0455\]Therefore, the probability that a sample of 30 Reese's pieces would have 12 or less orange candies is 0.0455.2. Let \[\hat{p}\] = the proportion of orange candies in a sample of 30.a) Mean of the sampling distribution of \[\hat{p}\] \[\mu_{\hat{p}}= p=0.52\] Standard deviation of the sampling distribution of \[\hat{p}\] \[\sigma_{\hat{p}} = \sqrt {\frac {pq}{n}} = \sqrt {\frac {0.52 × 0.48}{30}} \] \[\sigma_{\hat{p}} \approx 0.098\]b) Standard deviation shows how much the sample proportion varies from the true population proportion, on average. Here, the standard deviation is 0.098, which means that when you take repeated random samples of 30, the sample proportion of orange candies will typically vary by about 9.8 percentage points from the true population proportion of 52%.c) Since np and nq are both greater than 10, the shape of the sampling distribution of \[\hat{p}\] can be approximated by a normal distribution by CLT.d) \[P(\hat{p} \le 0.40) \] = \[P\left( z \le \frac {0.40-0.52}{0.098} \right) \] = \[P(z\le -1.2245) \] Using standard normal distribution table, we get \[P(z\le -1.2245) = 0.1103\]Therefore, the probability that a sample of 30 Reese's pieces would have a sample proportion, p^, of 0.40 or less orange candies is 0.1103.3. Given that the company claims that the average weight of each piece is μ = 0.8 grams with a standard deviation of σ = 0.05 grams. Let x be the weight of one piece of candy. Therefore, \[\mu_{\bar{x}}=\mu=0.8\] and \[\sigma_{\bar{x}} = \frac {\sigma}{\sqrt{n}} = \frac {0.05}{\sqrt{30}} \] \[\sigma_{\bar{x}} \approx 0.0091\]b) The standard deviation of the sampling distribution of the sample mean is 0.0091. It tells us how much the sample means vary from the true population mean, on average.c) The sampling distribution of the sample mean can be approximated by a normal distribution by the Central Limit Theorem (CLT) since the sample size is 30.

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Answer:

x = 12

Step-by-step explanation:

The midsegment VY is half the sum of the parallel bases , that is

VY = \(\frac{EF+CD}{2}\) , then

3x + 18 = \(\frac{1}{2}\) (x + 96) ← multiply both sides by 2 to clear the fraction

6x + 36 = x + 96 ( subtract x from both sides )

5x + 36 = 96 ( subtract 36 from both sides )

5x = 60 ( divide both sides by 5 )

x = 12

Answer:

The choice D.

\((3b - 1) {x}^{2} + 35x - c\)

Step-by-step explanation:

\(3x(bx + 10) - ( {x}^{2} - 5x + c) \\ \\( 3b {x}^{2} + 30x) + ( - {x}^{2} + 5x - c) \\ \\ 3b {x}^{2} - {x}^{2} + 35x - c \\ \\ = (3b - 1) {x}^{2} + 35x - c\)

I hope I helped you^_^

Answer:

The triple is 9, 12, 15

The hypotenuse is 15.

Step-by-step explanation:

Pythagorean Theorem Formula: a²+b²=c² where a & b are the short legs and c is the hypotenuse.

9²+b²=(b+3)²

81+b²=(b+3)²

Small list of the Pythagorean Triples that contain 9:

9,12,15

9,40,41

So as you can see, there are only 2 examples in my list that contain 9 in them. The only one that fits our criteria is the triple, 9, 12 and, 15

You don't need to use the Pythagorean Formula for this as I have just proved.

Answer:

12 cm

Step-by-step explanation:

I don't think u have to use the phytagores theorem b/c the hypotenuse is 9+3=12. but if u have to use this.

\( {?a}^{2} + {b}^{2} = {c}^{2} \)

\( {9}^{2} + {b}^{2} = {9 + 3}^{2} \)

\(81 + {b}^{2} = 9(9 + 3) + 3(9 + 3)\)

\(81 + {b}^{2} = 81 + 54 + 9\)

\(81 + {b}^{2} = 144\)

\( {b}^{2} = 144 - 81 = 63\)

\( {b}^{2} = \sqrt{53} = b = 7.93\)

so if u found b then u can find c by using the same formula.

\( {a}^{2} + {b}^{2} = {c}^{2} \)

\( {9}^{2} + {7.93}^{2} = {c}^{2} \)

\(81 + 63 = {c}^{2} \)

\( {c}^{2} = 81 + 63 = 144\)

\( \sqrt{c} = \sqrt{144} \)

\(c = 12\)

To find the vector v with the same direction as u and a length of 3, we can scale the vector u by a factor of 3 divided by its magnitude.

Given vector u = (1, 2, -1, 0) and the desired length of v as 3, we first need to calculate the magnitude (or length) of vector u.

The magnitude of a vector is computed using the formula:

∥u∥ = √(u1² + u2²+ u3² + u4²), where u₁, u₂, u₃, and u₄ are the components of vector u.

In this case, the magnitude of vector u is √(1² + 2² + (-1)² + 0²) = √6. To find vector v with the same direction as u and a length of 3, we scale u by the factor 3/√6.

This can be done by multiplying each component of u by the scaling factor.

Therefore, vector v = (3/√6) * (1, 2, -1, 0) = (√6/2, √6, -√6/2, 0).

Hence, vector v has the same direction as u and a length of 3.

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Answer:

15.42

Step-by-step explanation:

The formula for finding the perimeter of a semicircle: r(π+2)

Therefore, 3(π+2)

9.42+6 = 15.42

Answer:

The answer is D.

Step-by-step explanation:

There is only one 8n^2, and that means that it cannot combine with anything.

Answer: A

Step-by-step explanation

2.167x10^4 = 21,670

                   = 9,978

1.1x10^6      = 1100,000

                   = 56,344,000

2.468x10^5 =  246,800

Answer: A. 9,978

Based on the power, move the decimal point that many spaces to the right. (E.g., If it's 4.2 × 10^3, then move the decimal three spaces to the right, and you'd get 4200.)

2.167 × 10^4 = 21670

1.1 × 10^6 = 1100000

2.468 × 10^5 = 246800

Out of all the numbers mentioned in the question, 9,978 is the only one that's less than 2.167 × 10^4 = 21670.

Answer:

8

Step-by-step explanation:

12 ÷ 3 = 4

4 × 2 = 8

:) hope this helps

Answer:

The answer is is 8 inches.

Answer:

3^4

Step-by-step explanation:

when both constants have equal base then powers are added

Answer:

See below

Step-by-step explanation:

If you can't tell just by looking at them, you will need to convert them all to fractions of a common denominator .....in this case (the smallest) common denominator would be 18

1/2 = 9/18  

1/3 = 6/18

1/6 = 3/18

4/9 = 8/ 18             so now you can see least to greatest is

                                    1/6    1/3    1/2   4/9

Answer:

The probability of a passengers waiting at the stop less than 5 minutes and more than 10 minutes is equal to 1/6 and 2/3 respectively.

Probability that the passenger waits less than 5 minutes for the train,

Area under the probability density function (PDF) of the arrival time distribution from 7:00am to 7:05am.

Distribution is uniform,

PDF is a constant function over the interval [7:00am, 7:30am] .

With height 1 / (30 minutes - 0 minutes) = 1/30.

Area under the PDF from 7:00am to 7:05am is,

Probability of waiting less than 5 minutes

= area under PDF from 7:00am to 7:05am

= (1/30) ×(5 - 0) minutes

= 1/6

Probability that the passenger waits less than 5 minutes for the train is 1/6.

Probability that the passenger waits more than 10 minutes for the train is

= Area under the PDF from 7:00am to 7:30am -  area under the PDF from 7:00am to 7:10am.

Area under PDF from 7:00am to 7:30am

= (1/30) × (30 - 0) minutes

= 1

Area under PDF from 7:00am to 7:10am

= (1/30) × (10 - 0) minutes

= 1/3

Area under PDF from 7:10am to 7:30am

= 1 - 1/3

= 2/3

Probability of waiting more than 10 minutes

= area under PDF from 7:10am to 7:30am

= (1/30) × (30 - 10) minutes

= 2/3

Probability that the passenger waits more than 10 minutes for the train is 2/3.

Therefore, the probability of waiting less than 5 minutes and waiting more than 10 minutes is equal to 1/6 and 2/3 respectively.

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Based on the fact that Jessica and her best friend split the money and were able to get $16.32, the total amount that they found was $32.64

The fact that they split the money evenly means that they split it in half which each person getting the same amount.

This means that the total amount they found was twice the amount that Jessica and her best friend got.

The total amount found is therefore:

= Jessica's share + Best friend's share

= 16.32 + 16.32

= $32.64

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a. Proportions in both the left-hand and right-hand tails tend to be relatively small.

The correct answer is: a. Proportions in both the left-hand and right-hand tails tend to be relatively small. This is because a normal distribution is symmetric and bell-shaped, with the majority of the data concentrated around the mean. As a result, the tails of the distribution have fewer data points and smaller proportions compared to the center. This is because a normal distribution is symmetric and bell-shaped, with the majority of the data concentrated around the mean.

So, a. Proportions in both the left-hand and right-hand tails tend to be relatively small.

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The group of participants who are not exposed to the independent variables are the known as the control group.

Good luck! :)

c=14+xh is the  equation that represents the relationship between h and c.

An expression is combination of variables, numbers and operators.

Given that ski resort charges $14 for snowshoe rental, plus an additional dollar per hour.

Let h represent the duration of a rental in hours and c represent the total cost of the rental.

We have to find the  relationship between h and c.

c=14+xh

Here x represents the dollar.

Hence, c=14+xh is the  equation that represents the relationship between h and c.

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The surface area and volume of a pentagonal prism is  5/2 × a² × √(5 + 2√5) + 5ab and (1/4) × (5 + 2√5) × a² × h respectively. We can find the solution in the following manner.

A pentagonal prism is a three-dimensional geometric shape that consists of two parallel pentagons as the top and bottom faces, and five rectangular faces connecting them.

To find the surface area and volume of a pentagonal prism, we need to know its height, the length of the sides of the pentagon, and the length of the rectangular faces.

Let's denote the height of the pentagonal prism as "h", the side length of the pentagon as "a", and the length of the rectangular face as "b".

Surface Area of a Pentagonal Prism:

The surface area of a pentagonal prism is the sum of the areas of its faces. There are two pentagonal faces and five rectangular faces in a pentagonal prism.

Area of each pentagonal face = 5/4 × a² × √(5 + 2√5)

Area of each rectangular face = a × b

Total surface area = 2 × Area of pentagonal face + 5 × Area of rectangular face

= 5/2 × a² × √(5 + 2√5) + 5ab

Volume of a Pentagonal Prism:

The volume of a pentagonal prism is given by the formula:

Volume = (1/4) × (5 + 2√5) × a² × h

Therefore, the surface area and volume of a pentagonal prism can be calculated using the above formulas, given the values of a, b, and h.

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The surface area and volume of a pentagonal prism is sum of the areas of its faces, and (1/4) × (5 + 2√5) × a² × h.

A pentagonal prism is a three-dimensional geometric shape that consists of two parallel pentagons as the top and bottom faces, and five rectangular faces connecting them.

Surface Area of a Pentagonal Prism:

The surface area of a pentagonal prism is the sum of the areas of its faces. There are two pentagonal faces and five rectangular faces in a pentagonal prism.

Total surface area = 2 × Area of pentagonal face + 5 × Area of rectangular face

Volume of a Pentagonal Prism:

The volume of a pentagonal prism is given by the formula:

Volume = (1/4) × (5 + 2√5) × a² × h

Therefore, the surface area and volume of a pentagonal prism can be calculated using the above formulas, given the values of a, b, and h.

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Answer:

2x+20+x+10+2x-5 = 180

5x + 25 = 180

x=31

brainliestpls

The area of the region that lies above the x-axis, below the curve \(x=t^2+7t+8\), y=e^-t with 0≤t≤1 is approximately 2.1185 square units.

To find the area of the region bounded by the x-axis and the curve, we need to integrate the curve between the limits of t=0 and t=1.

∫₀¹ \(e^-t dt = [-e] ^{-t}\)from 0 to 1 = 1 - 1/e

So, the equation of the curve intersects the x-axis when y=0. To find the x-coordinate of the intersection point, we set y=0 in the equation of the curve:

\(0=e^-t\)

t=0

Thus, the intersection point is (8,0). We also need to find the value of t for which the curve is at its lowest point. To find the minimum point of the curve, we take the derivative of the equation of the curve and set it equal to zero.

y' = \(-e^{-t(2t+7)}\)

0 = \(-e^{-t(2t+7)}\)

t = -7/2

Since t is bounded by 0 and 1, the minimum point of the curve lies within the given range of t. Therefore, the area of the region bounded by the x-axis and the curve is given by the definite integral:

∫₀¹\((t^2+7t+8) e^{-t} dt\)

This integral can be evaluated using integration by parts. After integrating, differentiating, and simplifying, we get:

∫₀¹\((t^2+7t+8) e^{-t} dt\)  = 2.1185 (rounded to four decimal places).

Therefore, the area of the region that lies above the x-axis, below the curve\(x=t^2+7t+8\), \(y=e^-t\) with 0≤t≤1 is approximately 2.1185 square units.

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Answer:

1152000 feet

Step-by-step explanation:

6,400x60 mins per hour = 384000 feet in one hour

384000x3 hours = 1152000 in 3 hours

Happy learning!

--Applepi101

Answer:

Answer:

a) The base of the rectangular pyramid shown has an area of

60 square inches

b) A triangular face with a base of 10 inches has an area of 28 square inches.

c) A triangular face with a base of 5 inches has an area of 17.75 square inches.

d) The total surface area of the pyramid is 151.5 square inches.

Step-by-step explanation:

a) Solving for question a, we were given the following parameters

A rectangular pyramid. The rectangular base has a length of 10 inches and a width of 6 inches

The formula used to calculate the rectangular base of a rectangular pyramid =

Length × Width

Where :

Length = 10 inches

Width = 6 inches

Rectangular base = 10 inches × 6 inches

= 60 inches²

Hence, the base of the rectangular pyramid shown has an area of 60 square inches

b) Solving for question b, we have the following values given:

2 triangular sides have a base of 10 inches and height of 5.6 inches.

First step would be to solve for one triangular side first.

The area of the one triangular side = (Base × Height) ÷ 2

= (10 inches × 5.6 inches) ÷ 2

= 56inches² ÷ 2

= 28 inches²

Therefore, for the 2 triangular sides, since they have the same base and height, the other side as well would be 28 inches².

A triangular face with a base of 10 inches has an area of 28 square inches.

c) Solving for question c, the following parameters are given:

2 triangular sides have a base of 5 inches and height of 7.1 inches.

We would be to solving for one triangular side first.

The area of the one triangular side = (Base × Height) ÷ 2

= (5 inches × 7.1 inches) ÷ 2

= 35.5 inches² ÷ 2

= 17.75 inches²

Therefore, for the 2 triangular sides, since they have the same base and height, the other side as well would be 17.75 inches².

A triangular face with a base of 5 inches has an area of 17.75 square inches.

d) Solving for d, it is important to note that, a rectangular pyramid has 5 faces and they are: The rectangular base and 4 triangular faces

The formula for the total surface area of the rectangular pyramid is given as

Total Surface Area of the rectangular pyramid = Rectangular Base + Area of Triangular Side A + Area of Triangular Side B + Area of Triangular Side C + Area of Triangular Side D + Area of Triangular Side E

Total Surface Area of the Rectangular Pyramid = 60 inches² + 28 inches² + 28 inches² + 17.75 inches² + 17.75 inches²

Total surface Area of the Rectangular pyramid = 151.5 inches²

The total surface area of the pyramid is 151.5 square inches.

Step-by-step explanation:

BRAINLIEST PLEASE?

Answer:

50, 28, 17.75, 141.5

Step-by-step explanation:

The formula for the area of the shapes in:

8e). A = a[√(x² + a²)]

8f). A = a² - a[√[(2b)² - a²]]/4

Shape in 8e is a triangle and the height is derived using Pythagoras rule as;

triangle height = √(x² + a²)

Area of the triangle = 1/2 × 2a × √(x² + a²)

Area of the triangle = a[√(x² + a²)]

The shape in 8f is observed to be a triangle area cut out from a square area, thus;

Area of the square = a²

The triangle height = √[(b² - (a/2)²]

triangle height = √[(2b)² - a²]

Area of the triangle = 1/2 × a × √[(2b)² - a²]

Area of the triangle = a[√[(2b)² - a²]]/4

Area for the 8f shape = a² - a[√[(2b)² - a²]]/4

Therefore, the formula for the area of the shapes in:

8e). A = a[√(x² + a²)]

8f). A = a² - a[√[(2b)² - a²]]/4

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Answer:

31+27.5

Step-by-step explanation:

5+26=31 and 26+3/2=27.5

In a Venn diagram, we illustrate the relationships between sets a, b, and c, specifically the relationships a ⊂ b (a is a subset of b) and a ⊂ c (a is a subset of c).

A Venn diagram is a visual representation of sets using overlapping circles. In this case, we have three sets: a, b, and c. To illustrate the relationship a ⊂ b, we draw a circle representing set b and a smaller circle inside it representing set a. This indicates that every element in a is also an element of b, but b may contain additional elements that are not in a. The subset a is completely contained within set b. Similarly, to represent the relationship a ⊂ c, we draw a circle representing set c and a smaller circle inside it representing set a. This indicates that every element in a is also an element of c, but c may contain additional elements that are not in a. The subset a is completely contained within set c. By using the Venn diagram, we visually demonstrate the relationships between sets a, b, and c. The diagram clearly shows that a is a subset of both b and c, indicating that all elements of a are also elements of b and c. However, b and c may have additional elements that are not in a.

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Answer:

Approximately 33%

Step-by-step explanation:

There are 15 students, and 5 of them have either a cat or a dog. Therefore approximately 33%

\(\\ \sf\longmapsto 3x+5+7x+5=180\)

\(\\ \sf\longmapsto 10x+10=180\)

\(\\ \sf\longmapsto x+1=18\)

\(\\ \sf\longmapsto x=17\)

Answer:

\({ \tt{(3x + 5) + (7x + 5) = 180}} \\ \\ { \tt{(3x + 7x) + (5 + 5) = 180}} \\ \\ { \tt{10x + 10 = 180}} \\ \\ { \tt{10x = 170}} \\ \\ { \boxed{ \tt{x = 17}}}\)

• Angle 1 = Angle 4

\({ \tt{ \angle 1 = \angle 4 = 3x + 5}} \\ \\ { \tt{\angle 1 = \angle 4 = (3 \times 17) + 5}} \\ \\ { \boxed{ \rm{\angle 1 = \angle 4 = 56 \degree}}}\)

• Angle 2 = Angle 3

\({ \tt{\angle 2= \angle 3 = 7x + 5}} \\ \\ { \tt{\angle 2 = \angle 3 = (7 \times 17) + 5}} \\ \\ { \boxed{ \rm{\angle 2 = \angle 3 = 124 \degree}}}\)

Answer

\(\frac{573}{400}\)

step-by-step explanation:

\(\frac{1.4325}{1}\) ×  \(\frac{10000}{10000}\)  =  \(\frac{14325}{10000}\)

Simplify

\(\frac{14325}{10000}\) ÷\(\frac{25}{25}\) = \(\frac{573}{400}\)