Use the long division method to find the result when x³ + 7x² + 15x + 25 is divided by x+ 5.

In the given diagram, using one of the circle theorems, the value of x is 68°

From the question, we are to calculate the value of x in the given diagram.

The diagram shows a circle with O. The angle subtended at the center is 136°. We are to determine the value of the unknown angle x.

From one of circle theorems, we have that

The angle subtended by arc at the center of a circle is twice the angle at the circumference.

Therefore,

We can write that

136° = 2x

Solve for x in the above equation

136° = 2x

Divide both sides of the equation by 2

136° / 2 = 2x / 2

68° = x

Hence,

x = 68°

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The amount of your tax refund is $1,414

To find the tax refund, we need to subtract the amount of federal taxes owed after deductions from the amount of federal taxes already paid.

Tax refund = Federal taxes paid - Federal taxes owed after deductions

Tax refund = $12,042 - $10,628

Tax refund = $1,414

Rounding to the nearest cent, the tax refund is $1,414.00.

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The length of the shorter side of the room is 3.2 inches

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

A rectangular room is 28 feet by 32 feet.

So, the perimeter is

P = 2 * (28 + 32)

Evaluate

P = 120

So, the scale factor from the room to the drawing is

Scale factor = 12/120 i.e. division of perimeters

So, we have

Scale factor = 1/10

The small length of the room is 32 feet

So, we have

Smaller length = 1/10 * 32

Smaller length = 3.2 inches

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The triangles Δ MNO and ΔXYZ are congruent to each other by AAS postulate as two corresponding angles and a corresponding side are equal to each other.

We have,

Two triangles are said to be congruent if the length of the sides is equal, a measure of the angles are equal and they can be superimposed.

Given that YO = NZ.

Consider YO = NZ

Now Add OZ on both sides

YO + OZ = NZ + OZ

YZ = NO

Consider triangles Δ MNO and ΔXYZ.

M ≅ X

N ≅ Y

YO ≅ NZ

Δ MNO ≅ ΔXYZ by AAS postulate.

Therefore, the triangles Δ MNO and ΔXYZ are congruent to each other by AAS postulate as two corresponding angles and a corresponding side are equal to each other.

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complete question:

The congruency of △MNO and △XYZ can be proven using a reflection across the line bisecting OZ. However, this congruency can also be proven using geometric postulates, theorems, and definitions. Prove that the triangles are congruent using a two-column proof and triangle congruency theorems.

Given: M ≅ X

N ≅ Y

YO ≅ NZ

Prove: △MNO ≅ △XYZ

The joint costs allocated to Product B is $240,000.

We must allocate joint costs based on the relative physical quantities produced by each product.

The total physical quantity produced by both products is:

= Quantity of A + Quantity of B

= 10,000 + 40,000

= 50,000 pounds

We will calculate the proportion of physical quantity produced by product A:

= Quantity of B / Total physical quantity

= 40,000 / 50,000

= 0.8

The amount of joint costs allocated to Product B is will be

= Total joint costs x Proportion of

= $300,000 x 0.8

= $240,000.

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Answer: 95 ft²

Step-by-step explanation:

      To solve for the surface area, we will find the area of all the sides and then add them together. We see that we have a square as the base and 4 congruent triangles.

For the square:

      A = LW

      A = (5 ft)(5 ft)

      A = 25 ft²

For one triangle:

      A = [tex]\frac{BH}{2}[/tex]

      A = [tex]\frac{(5\;ft)(7\;ft)}{2}[/tex]

      A = 17.5 ft²

For all four triangles:

      A = 17.5 ft² * 4 = 70 ft²

Total surface area by adding the triangles and square together:

       70 ft² + 25 ft² = 95 ft²

The volume of a rectangular prism would be 100 cubic cm.

Since we know that rectangular prism is a three-dimensional shape that has two at the top and bottom and four are lateral faces.

The volume of a rectangular prism=Length X Width X Height

We are given that base of a rectangular prism is 20 cm sq. . If the height of the prism is 5 cm, then;

Base area = 20 cm sq.

Height = 5 cm

Volume of a rectangular prism=Length X Width X Height

Volume of a rectangular prism= Base area  X Height

Volume of a rectangular prism= 20 x 5

= 100

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Answer:

1. y = 3/2 x - 8

2. 2y-x = -4

3. y = -3/4x-2

4. -5x + 3y = -12

The numerical value of the algebraic expression 1.5 × 6 + 8.3 is 17.3; The factors are 1.5 and 6 & the terms: 1.5 * 6 and 8.3

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

1.5 × 6 + 8.3

The above expression is an algebraic expression and as such the parts of the expressions are

When the expression is evaluated, we have

1.5 × 6 + 8.3 = 17.3

This means that the result of evaluating the expression 1.5 × 6 + 8.3 is 17.3

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The x-coordinate of A” is 2

Here, we want to know;

the x-coordinate of the rotation about the origin of a point 90 degrees clockwise.

A rotation of 90 degrees clockwise about the origin will turn the coordinates (x, y) to (-y, x)

Here, The coordinates of A is (3,-2)

So, upon the assigned rotation, it becomes;

A'' = (2,-3)

So, the x-coordinate of A” is 2

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The Explanation of decimal place value is like place value with whole numbers is shown below.

We know,

Each place value to the left of a whole number is multiplied by ten, but a place value to the right of a decimal number is divided by ten.

For example,

We take whole number 254 where place values are

2- Hundred, 5- Tens and 4- Ones

and, take the decimal 2.369 where the place values are

3- Tenth, 6- hundredth and 9- thousandth

So, both decimal and whole number have similar concept of place value but one is multiplied by 10 and other is divided by 10.

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Answer:$ 24,679.20 or 514.15 a month

Step-by-step explanation: 565(.09) is 50.85 which needs to be deducted from the payment of 565 because he needs to be able to pay for interest. 514.15 is then multiplied by 48 months which will bring you to 24,679.20

The product of the expression is given as  1/4x²y²

Remember that an algebraic expression in mathematics is an expression which is made up of variables and constants, along with algebraic operations (addition, subtraction, etc.). It can be a combination of both variables and constants. Any value that is placed before and multiplied by a variable is a coefficient

The given expression is  (3x⁵y²)/(xy)  * (6xy²) / (9x³y)

Multiply through to have

{(3x⁵y²)(6xy²)} / {(xy)(xy)}

⇒( 18x⁶y⁴) / (72x⁴y²)

Simplify to get

Therefore the value of the expression is 1/4x²y²

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The 96% confidence interval for the population mean μ is approximately (18.06, 20.54).

We have,

To construct a 96% confidence interval about the population mean(μ) with a sample size of n = 57,

we can use the following formula:

CI = x ± z (s/√n)

where x is the sample mean, s is the sample standard deviation, n is the sample size, z is the z-score associated with the desired confidence level (96% in this case), and √n is the square root of the sample size.

The z-score corresponding to a 96% confidence level can be found using a standard normal distribution table or calculator.

For a two-tailed test, the z-score is 1.96.

Substituting the given values, we have:

CI = 19.3 ± 1.96 (4.8/√57)

Calculating the standard error of the mean (s/√n):

s/√n = 4.8/√57 ≈ 0.634

Substituting this value into the formula:

CI = 19.3 ± 1.96*0.634

Calculating the upper and lower bounds of the confidence interval:

lower bound = 19.3 - 1.96*0.634 ≈ 18.06

upper bound = 19.3 + 1.96*0.634 ≈ 20.54

Therefore,

The 96% confidence interval for the population mean μ is approximately (18.06, 20.54).

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To construct a 96% confidence interval for the population mean, use the formula x ± z*(s/√n) with z being the z-score for the 96% level, x being the sample mean, s being the sample standard deviation, and n being the sample size. Substituting the given values will give the lower and upper bound of the confidence interval.

The question is asking for the construction of a 96% confidence interval for a population mean u, given a sample size (n) of 57, a sample mean (x) of 19.3 and a sample standard deviation (s) of 4.8.

To find the confidence interval, we need to use the formula: x ± z*(s/√n) where z is the z-score associated with our confidence level. For a 96% confidence interval, the z-score is approximately 2.05 (you can find this from a standard z-table).

Substituting the given values into the formula gives: 19.3 ± 2.05*(4.8/√57)

Calculating the above expression will give the lower and upper bound of the 96% confidence interval.

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Answer:  B. 78

Step-by-step explanation:

Given:

BC=CD

all the other sides of each triangle are radii, so they are all equal the 2 triangles are congruent.

>Both angles A =78

An angle from the radius is the same as the arc angle it creates.

The arc angle is double only if the angle touches the end of the circle not the radius.  that's why it's not 156

So, <BAC =78   so arc angle BC=78

The area under the curve (since the function of the parabolic expression is y = x - x²) is 1/6 square units.

A parabolic function has an expression represented as f(x) = ax² + bx + c, which allows solving for x using either the factorization method or applying the quadratic formula. By zeroing out this expression, it becomes possible to determine its roots as with any quadratic equation.

In the case of the above function:

To find the area under the curve, above the x-axis, we need to integrate the parabolic expression from 0-1

that is:

∫[0,1](x-x²)dx

This is evaluated using the power rule

∫[0,1](x-x²)dx = [1/2x² - 1/3x³) fro x= 0 to x = 1

inserting the limits of the integration, we have:
[1/2 (1) ² - 1/3 ( 1) ³] - [1/2 (0)² - 1/3 (0) ³]

Simplified, and we have :

Area  = 1/2 - 1/3

Thus, Area under the curve = 1/6

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The person would have to invest approximately $461,044.94 now in an annuity with an annual interest rate of 3.1% to receive monthly payments of $1500 for 20 years.

To calculate the present value of an annuity, we can use the following formula:

[tex]PV = PMT \times \dfrac{(1 - (\dfrac{1}{(1 + r)^n})) }{ r}[/tex]

Where:

PV = present value of the annuity

PMT = monthly payment

r = annual interest rate

n = total number of payments

In this case, the PMT is $1500, the annual interest rate is 3.1%, and the number of payments is 20 years x 12 months per year = 240 payments.

First, we need to convert the annual interest rate to a monthly interest rate by dividing it by 12:

r = 3.1% / 12 = 0.2583%

Next, we can plug in the values and solve for PV:

PV = $1500 x [(1 - (1 / (1 + 0.2583%)²⁴⁰)) / 0.2583%]

PV = $1500 x [(1 - (1 / 1.002152²⁴⁰)) / 0.002583]

PV = $1500 x [(1 - (1 / 4.818681)) / 0.002583]

PV = $1500 x (0.7915 / 0.002583)

PV = $461,044.94

Therefore, the person would have to invest approximately $461,044.94 now in an annuity with an annual interest rate of 3.1% to receive monthly payments of $1500 for 20 years.

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The final velocity of the sled is 4.317 m/s.

Before the snow,

Total mass of sled = 35 + 4.2 = 39.2 kg

Initial velocity of the sled = 5 m/s

Momentum = Mass × Velocity

                   = 39.2 × 5

                   = 196 kg m/s

After the snow,

Total mass = 35 + 4.2 + 6.2 = 45.4 kg

Let v be the final velocity.

By the law of conservation of momentum,

Momentum before snow = momentum after snow

196 = 45.4 v

v = 4.317 m/s

Hence the final velocity is 4.317 m/s.

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Therefore, it is clear that the government should do more to help the poor and middle class, as their incomes have been relatively stagnant for an extended period of time.

Both claims are true, depending on the time period being considered. If we look at the time period over the last few decades, then Claim 1 is accurate, as average household income has risen nearly 30% over the time period, adjusted for inflation.

However, if we look at the past three decades, then Claim 2 is more accurate, as average household income has only risen less than 10%, adjusted for inflation.

Therefore, it is clear that the government should do more to help the poor and middle class, as their incomes have been relatively stagnant for an extended period of time.

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The expected number of lefties top ranked baseball players in a sample of 15 top ranked baseball players, obtained from the 1 to 3 ratio of lefties to righties top ranked baseball players is 5 top ranked baseball players

A ratio is a quantitative comparison between two values that indicates the number of times one quantity is contained in or can contain the other value or quantity.

The ratio or proportion of left handed top ranked baseball players = 1 in 3

Therefore, the ratio of lefties to righties top ranked baseball players = 1 : 3

The number of top ranked baseball players in the sample = 15

The number of the top ranked baseball players in the sample that are left handed is therefore;

Number of left handed baseball players in the sample = (1/3) × 15 = 5

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The probability that more than 8 and less than 12 customers pay in cash is 0.376 or 37.6%.

The probability that more than 8 and less than 12 customers pay in cash is calculated using the binomial probability formula:

where:

n is the number of trials = 15

x = customers who pay in cash

p = paying in cash, which is 0.4 according to the problem

The probability that more than 8 and less than 12 customers pay in cash. is the sum of the probabilities of 9, 10, and 11 customers paying in cash.

Using the binomial probability formula:

P(9) = 15C₉ * 0.4⁹ * 0.6⁶

P(9) = 0.212

P(10) = 15C₁₀ * 0.4¹⁰ * 0.6⁵

P(10) = 0.121

P(11) = 15C₁₁* 0.4¹¹ * 0.6⁴

P(11)= 0.043

Hence;

P(9 or 10 or 11) = 0.212 + 0.121 + 0.043

P(9 or 10 or 11) = 0.376

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The transformation in this problem is a translation combined with a reflection, hence yes, it is a rigid motion, as the side lengths of the transformed figure are equal to the side lengths of the original figure.

Examples of transformations are given as follows:

The dilation is the only transformation that is not a rigid motion, as it changes the side lengths of the figure.

The transformation for this problem has the rule defined as follows:

(x,y) -> (x + 2, -y).

The transformations are defined as follows:

Neither transformation is a dilation, hence it is a rigid motion.

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Answer:

[tex]\huge\boxed{\sf Mean = 11.1 \ hours}[/tex]

Step-by-step explanation:

18, 7, 6, 13, 8, 17, 9

[tex]\displaystyle Mean = \frac{Sum \ of \ data}{No. \ of \ data} \\\\Mean = \frac{18+7+6+13+8+17+9}{7} \\\\Mean = \frac{78}{7} \\\\Mean = 11.1 \ hours\\\\\rule[225]{225}{2}[/tex]

Answer:

11.1

Step-by-step explanation:

The mean is simply the average of a given set of numbers

To find the mean we find the sum of the given numbers and divide that by the number of given values.

Given set of values:

Mean:

The mean of the number of hours the students watched of tv is 11.1 hours

The approximate number of female members of the army reserve in 2019 was 75,467.

If 2 out of every 5 members of the army reserve were female, then the proportion of female army reserve personnel can be represented as:

=  2/5

= 0.4.

Now, we can multiply the proportion to total number of army reserve to get the number of female members which is:

= 0.4 x 188,667

= 75,466.80

= 75,467

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The equivalent expression to  4√3 is  √48 or 6.928.

An equivalent expression is an expression that has equal value to the original given expression.

From the given expression, we can determine its equivalent expression as follows;

The given expression = 4√3

We can square 4 and multiply it by 3 and enclose all with the square root.

4√3 = √(4² x 3 )

= √ ( 16 x 3 )

= √ ( 48 )

= 6.928

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We need 4608 cubes to fill the rectangular prism.

We have,

The rectangular prism has a volume of:

Volume = length x width x height

Volume = 8 in. x 4 in. x 2 1/4 in.

Volume = 72 in³

Each cube has a volume of:

Volume of cube = edge length³

Volume of cube = (1/4 in.)³

Volume of cube = 1/64 in³

To find the number of cubes needed to fill the rectangular prism, we can divide the volume of the prism by the volume of each cube:

Number of cubes = Volume of prism / Volume of a cube

Number of cubes = 72 in³ / (1/64 in³)

Number of cubes = 72 in³ x 64 / 1

Number of cubes = 4608 cubes

Therefore,

We need 4608 cubes to fill the rectangular prism.

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The surface area of the rectangular prism is 220 square inches

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

5 in by 10 in by 4 in

The surface area of the rectangular prism is calculated as

Area = 2 * (5 * 10 + 5 * 4 + 10 * 4)

Evaluate

Area = 220

Hence, teh area is 220 square inches

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