Today only, a sofa is being sold at a 76% discount. The sale price is $100.80.
What was the price yesterday?

Answer:

<JML=126 degrees, x=42

Step-by-step explanation:

well, something important to note here is that a straight line is allways equal to 180, and you have part of the 180 sitting there on the line being 54 degrees, so all you have to do is do 180-54=126 and that is the measure of <JML, to find x, you just reverse the steps you see, right now 3x=3*x so you want to reverse that and divide 126/3=42.

Angles are supplementary hence their sum is 180°

So

<JML=3x=126°

Answer:

12

Step-by-step explanation:

Number of years since 2003 x=5 years and number of jobs in thousand y=288.

In this method two equation are added or subtracted depending on the sign of variables. After adding or subtracting we create a new equation with one variable. Therefore, we easily get the solution.

while using addition method of algebra, we either add or subtract two equations to obtain a new equation by eliminating one variable. Hence, this method is called elimination method.

Given equation, 7.4x-y= -254

                         12.4x-y = -231

          using addition method

                -5x= -23

                  after solving x=4.6

            x= 5 (nearest whole number)

                     y = 288.04

                y =288

   hence, number of years 5

 number of jobs in thousand =288

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Answer:

The equation of the line segment to the line segment with end point (4, 4) and (-8, 8) is y = x/3 - 4

Step-by-step explanation:

The coordinates of the given points are;

(4, 4) and (-8, 8)

Therefore;

\(Slope, \, m =\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}\)

Where;

y₁ = 4, y₂ = -8, x₁ = 4, x₂ = 8

Therefore, the slope, m of the given line segment = (-8 - 4)/(8 - 4) = -3

The slope of the perpendicular line segment = -1/m = -1/(-3) = 1/3

The mid point of the line segment with endpoint (4, 4) and (-8, 8) is given as follows;

\(Midpoint, M = \left (\dfrac{x_1 + x_2}{2} , \ \dfrac{y_1 + y_2}{2} \right )\)

Therefore, the midpoint  = ((4 + 8)/2, (4 + (-8))/2) = (6, -2)

The equation of the perpendicular line segment in point and slope form is given as follows;

y - (-2) = 1/3 × (x - 6)

Which gives;

y + 2 = x/3 - 6/3 = x/3 - 2

y = x/3 - 2 - 2 = x/3 - 4

The equation of the line segment to the line segment with end point (4, 4) and (-8, 8) is y = x/3 - 4

The probability that a truck drives between 122 and 127 miles in a day is 0.0165, rounded to four decimal places.

To find the probability that a truck drives between 122 and 127 miles in a day, we'll use the z-score formula and standard normal distribution table. Follow these steps:

Step 1: Calculate the z-scores for 122 and 127 miles.
z = (X - μ) / σ

For 122 miles:
z1 = (122 - 90) / 18
z1 = 32 / 18
z1 ≈ 1.78

For 127 miles:
z2 = (127 - 90) / 18
z2 = 37 / 18
z2 ≈ 2.06

Step 2: Use the standard normal distribution table to find the probabilities for z1 and z2.
P(z1) ≈ 0.9625
P(z2) ≈ 0.9803

Step 3: Calculate the probability of a truck driving between 122 and 127 miles.
P(122 ≤ X ≤ 127) = P(z2) - P(z1)
P(122 ≤ X ≤ 127) = 0.9803 - 0.9625
P(122 ≤ X ≤ 127) ≈ 0.0178

So, the probability that a truck drives between 122 and 127 miles in a day is approximately 0.0178 or 1.78%.

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The estimated standard error for a sample of n = 9 scores with ss = 288 is 2. Among your choices, it should be B; s2 = 36 and sM  = 2.

Hope that helps!

Answer:

a fraction in which the numerator is greater than the denominator, such as 5/4.

Step-by-step explanation:

By applying algebra, it can be concluded that the number of candies remaining in the bag can be written as c = 150 - 8s, where s is the number of snacking.

Algebra is a branch of mathematics that uses symbols and mathematical operations, such as addition, subtraction, multiplication, and division to solve problems

Now we apply algebra to solve the problem:

Tyrone takes 8 pieces of candy each time snacking

After snacking 18 times, 6 pieces of candy remained in the bag

So the totals candies eaten = 8 * 18

                                              = 144 candies

Number of candies in the bag = candies eaten + remaining candies

                                                  = 144 + 6

                                                  = 150 candies

If s denotes the number of snacking, then the total number of candies eaten on s snacking = 8s

if c denotes the number of remaining candies, then:

c = total candies - candies eaten

c = 150 - 8s

Thus the number of candies remaining in the bag can be written as c = 150 - 8s, where s is the number of snacking.

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Answer: \(e=-50|t-40|+2000\)

The cable car’s elevation will be 750 feet after 15 minutes or 65 minutes.

Step-by-step explanation:

Given: A cable car begins its trip by moving up a hill. As it moves up, it gains elevation at a constant rate of 50 feet/minute until it reaches the peak at 2,000 feet.

Then, total time taken to reach the peak = (Distance) ÷ (speed)

= (2,000 feet) ÷ ( 50 feet/minute)

= 40 minutes

Then, as the car moves down to the hill’s base, its elevation drops at the same rate.

The equation that models the cable car’s elevation, e, after t minutes is

e= (constant rate)|t- time to reach peak |+ Peak's height

\(e=-50|t-40|+2000\)

When the cable car’s elevation will be 750 feet after minutes, then we have

\(750=-50|t-40|+2000\\\\\Rightarrow\ -50|t-40|=750-2000\\\\\Rightarrow\ -50|t-40|=1250\\\\\Rightarrow|t-40|=-\dfrac{1250}{50}\\\\\Rightarrow|t-40|=-25\\\\\Rightarrow t-40=-25\text{ or }t-40=25\\\\\Rightarrow t=-25+40\text{ or }t=25+40\\\\\Rightarrow t=15\text{ or }t=65\)

Time cannot be negative, so the cable car’s elevation will be 750 feet after 15 minutes or 65 minutes.

If Amy uses 41-cent stamps and 6-cent stamps to mail a gift card to a friend worth of $1.77 , then the number of 41 cent stamp used is 3  and the number of 6 cent stamps used is  9 .

Let the number of 41 cents stamps used in postage is = x ;

let the number of 6 cents stamps used in postage is = y ;

the amount 41 cents in dollars is = $0.41  ;

and amount 6 cents in dollars is = $0.06  ;

Amy used 41-cent stamps , 6-cent stamps to pay $1.77 in postage

it is represented in equation form as  ⇒ 0.41x + 0.06y = 1.77

Multiplying on both sides by 100 , we get

⇒ 41x + 6y = 177  ;

⇒ y = (177 - 41x)/6 ;

We will test for corresponding values of x and y to satisfies this equation and the number of stamps must be whole numbers.

If x = 1 , then y = 26.66

If x = 2 , then y = 15.83

If x = 3 , then y = 9

If x = 4 , then y = 2.16 .

the only values that shows a whole number is : If x = 3 , then y = 9 .

Therefore , Amy used "3" 41-cents stamps and "9" 6-cent stamps .

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The weighted cost of capital for Craig Corporation is 11.6%, i.e., Option D is correct. This is calculated by considering the proportion of each component in the capital structure and multiplying it by its respective cost, resulting in an overall weighted cost of capital.

To calculate the weighted cost of capital, we need to determine the proportion of each component in the company's capital structure and multiply it by its respective cost. In this case, the company's capital structure consists of bonds, preferred stock, and common stock.

The proportion of each component can be calculated by dividing the value of each component by the total capital structure value. For bonds, the proportion is $325,000 / $1,500,000 = 0.2167. For preferred stock, the proportion is $525,000 / $1,500,000 = 0.35. And for common stock, the proportion is $650,000 / $1,500,000 = 0.4333.

Next, we multiply the proportion of each component by its respective cost. The after-tax cost of debt is given as 6%, so the cost of debt is 0.06. The cost of preferred stock is given as 12.9%, so the cost of preferred stock is 0.129. The cost of common stock is given as 14%, so the cost of common stock is 0.14.

Finally, we multiply each component's proportion by its respective cost, and then sum up the results:

(0.2167 * 0.06) + (0.35 * 0.129) + (0.4333 * 0.14) = 0.013 + 0.04515 + 0.060532 = 0.118682

Therefore, the weighted cost of capital for Craig Corporation is 11.6%, i.e., Option D.

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Answer:

5

Step-by-step explanation:

The width of the auxiliary board will be 50 feet.

In its most basic form, a ratio is a comparison between two comparable quantities.

There are two types of proportions One is the direct proportion, whereby increasing one number by a constant k also increases the other quantity by the same constant k, and vice versa.

If one quantity is increased by a constant k, the other will decrease by the same constant k in the case of inverse proportion, and vice versa.

From the given information the width of the auxiliary board can be solved by the proportional method.

Let, The width of the auxiliary board be 'w'.

Therefore, 60 : 150 : : 20 : w.

60/150 = 20/w.

60w = 150×20.

6w = 15×20.

2w = 5×20.

w = 5×10.

w = 50.

So, The width of the board will be 50 feet.

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Sine and cosine functions are two of the most important trigonometric functions. They both relate angles to the ratios of the sides of a right triangle and are used extensively in mathematics and physics. While they are similar in many ways, there are some key differences between them.

The sine function f(x) = sin(x) and cosine function g(x) = cos(x) are periodic functions with a period of 2π. They have several key features in common, including the fact that they both have a midline of y = 0 and a y-intercept of 1 for cos(x) and 0 for sin(x).

The two functions differ in their amplitude and maximum/minimum values. The amplitude of a function is the distance between the maximum or minimum value and the midline, and it is equal to 1 for sin(x) and cos(x). The maximum value of sin(x) is 1, and its minimum value is -1, while the maximum value of cos(x) is 1 and its minimum value is -1.

In terms of Amplitude: The amplitude of the sine function is 1, while the amplitude of the cosine function is also 1.

In all,  their relationship can be described by a phase shift of 90 degrees, and it is possible for a function to be both a sine and cosine function, but only if it is a simple transformation of one of the functions.

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The percent of the total area under the standard normal curve between z = -1.5 and z = -0.7 is 18%.

To find the percent of the total area between two z-scores, we need to calculate the area under the standard normal curve between those two z-scores.

Using a standard normal distribution table or a statistical software, we can find the area to the left of each z-score and subtract the smaller area from the larger area to find the area between the z-scores.

For z = -1.5, the area to the left of z = -1.5 is approximately 0.0668.

For z = -0.7, the area to the left of z = -0.7 is approximately 0.2420.

The area between z = -1.5 and z = -0.7 is:

Area between z = -1.5 and z = -0.7 = Area to the left of z = -0.7 - Area to the left of z = -1.5

= 0.2420 - 0.0668

= 0.1752

To convert this area to a percentage, we multiply by 100:

Percentage of the total area between z = -1.5 and z = -0.7 = 0.1752 * 100 ≈ 17.52%

Rounding to the nearest integer, the percent of the total area between z = -1.5 and z = -0.7 is 18%.

The percent of the total area under the standard normal curve between z = -1.5 and z = -0.7 is approximately 18%.

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Answer:

I think it still exists today but mostly in other countries. Although, there are several examples of racism in today's U.S. schools.

Answer:

X/5 - 5 = f(x) for the domain [0,infinity)

Step-by-step explanation:

Answer:

Yo, the answer would be 95

Step-by-step explanation:

The area of a circle is

A=(pi)r^2     OR       A=(pi)d      (d is diameter)

This means you have to square 5.5, that means multiply it by itself.

5.5*5.5

This is 30.25 which you then multiply by pi

30.25*3.14=94.985

If you round to the nearest hundredth, you get 95. Cheers

Answer:

the anwers wil be 95

Step-by-step explanation:

this by calculating the area of the circle

Answer: The ratio would be 73.6

1   Y is distributed as N(aμ + b, a^2σ^2), as desired.

2  We have shown that under these conditions, E[XY] = E[X]E[Y].

To prove that Y is distributed as N(aμ + b, a^2σ^2), we need to show that the mean and variance of Y match those of a normal distribution with parameters aμ + b and a^2σ^2, respectively.

First, let's find the mean of Y:

E(Y) = E(aX + b) = aE(X) + b = aμ + b

Next, let's find the variance of Y:

Var(Y) = Var(aX + b) = a^2Var(X) = a^2σ^2

Therefore, Y is distributed as N(aμ + b, a^2σ^2), as desired.

We can use the definition of covariance to prove that E[XY] = E[X]E[Y]. By the properties of expected value, we know that:

E[XY] = ∫∫ xy f(x,y) dxdy

where f(x,y) is the joint probability density function of X and Y.

Then, we can use the fact that X and Y are independent to simplify the expression:

E[XY] = ∫∫ xy f(x) f(y) dxdy

= ∫ x f(x) dx ∫ y f(y) dy

= E[X]E[Y]

where f(x) and f(y) are the marginal probability density functions of X and Y, respectively.

Therefore, we have shown that under these conditions, E[XY] = E[X]E[Y].

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Lauren assumed that the Roof Truss Diagram is an accurate representation of the actual roof design that will be used on the shed. She used the given measurements, such as the length of the bottom chord, and the angles in the diagram to calculate the pitch of the roof. If the diagram was not accurate, her calculations would not have been useful in determining the pitch of the actual roof. Therefore, Lauren had to make the assumption that the diagram was a reliable representation of the shed's roof design.

The logical assumption that Darin make about the Roof Truss Diagram is that the rise is 4.6 ft and the run is 9 feet.

A logical assumption is simply an idea that can be inferred, or identified, in a text without the writer stating it in an obvious way. One simple example may be the logical assumption that if you do not turn in your homework, your teacher will be disappointed in you.

Here, we have,

Based on the information provided, it appears that Darin assumed that the Roof Truss Diagram is symmetrical, meaning that both sides of the roof have the same dimensions and angles. This assumption is supported by his calculation that the pitch of both sides of the roof is close to 1/2.

Rise will be:

= 9 × tan 27°

= 9 × 0.5095

= 4.6 feet.

Run will be 9ft

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In the given diagram, the area of the figure is 79.27 square units

From the question, we are to determine the area of the figure shown in the diagram

Area of the figure = Area of the triangle + Area of the semicircle

The area of a triangle is given by the formula,

A = 1/2 b×h

Where b is the base

and h is the height

In the given diagram,

h = 8

b = 10

Thus,

Area of the triangle = 1/2 × 10 × 8

Area of the triangle = 40

The area of a semicircle is given by the formula

Area = 1/2 πr²

Where r is the radius

From the given diagram,

Diameter = 10

Therefore,

Radius = 10/2

Radius = 5

Thus,

Area of the semicircle = 1/2 × π × 5²

Area of the semicircle = 1/2 × π × 25

Area of the semicircle = 12.5π

Then,

Area of the figure = 40 + 12.5π

Area of the figure = 79.2699

Area of the figure = 79.27 square units

Hence,

The area of the figure is 79.27 square units

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Given statement solution is :- We cannot find the missing value from the given options (3656, 2739, 1841, 5418, or 3556).

The given sequence is: 5 2 1 4 0 0 7 2 8 1 m m 7 m 5 m A.

To find the missing value, let's analyze the pattern in the sequence. We can observe the following pattern:

The first number, 5, is the sum of the second and third numbers (2 + 1).

The fourth number, 4, is the sum of the fifth and sixth numbers (0 + 0).

The seventh number, 7, is the sum of the eighth and ninth numbers (2 + 8).

The tenth number, 1, is the sum of the eleventh and twelfth numbers (m + m).

The thirteenth number, 7, is the sum of the fourteenth and fifteenth numbers (m + 5).

The sixteenth number, m, is the sum of the seventeenth and eighteenth numbers (m + A).

Based on this pattern, we can deduce that the missing values are 5 and A.

Now, let's calculate the missing value:

m + A = 5

To find a specific value for m and A, we need more information or equations. Without any additional information, we cannot determine the exact values of m and A. Therefore, we cannot find the missing value from the given options (3656, 2739, 1841, 5418, or 3556).

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a)   The velocity of the object at t = 10.0 s is 645.9 m/s.

b)    The object is at rest at t = -0.87 s and t = 0.62 s.

c)    The acceleration of the object at t = 0.50 s is 7.20 m/s^2.

A. To find the velocity of the object at t = 10.0 s, we need to take the derivative of the position function with respect to time:

v(t) = 3At^2 + 2Bt + C

Plugging in the given constants, we get:

v(10.0) = 3(2.10)(10.0)^2 + 2(1.00)(10.0) - 4.10

v(10.0) = 630.0 + 20.0 - 4.10

v(10.0) = 645.9 m/s

Therefore, the velocity of the object at t = 10.0 s is 645.9 m/s.

B. The object is at rest when its velocity is zero. So, we need to find the value(s) of t that make v(t) = 0. Using the same velocity function from part (A), we can set it equal to zero and solve for t:

3At^2 + 2Bt + C = 0

Plugging in the given constants, we get a quadratic equation:

6.30t^2 + 2.00t - 4.10 = 0

Using the quadratic formula, we can solve for t:

t = (-2.00 ± sqrt(2.00^2 - 4(6.30)(-4.10))) / (2(6.30))

t = (-2.00 ± sqrt(104.80)) / 12.60

t = (-2.00 ± 10.24) / 12.60

t = -0.87 s or 0.62 s

Therefore, the object is at rest at t = -0.87 s and t = 0.62 s.

C. To find the acceleration of the object at t = 0.50 s, we need to take the derivative of the velocity function with respect to time:

a(t) = 6At + 2B

Plugging in the given constants, we get:

a(0.50) = 6(2.10)(0.50) + 2(1.00)

a(0.50) = 7.20 m/s^2

Therefore, the acceleration of the object at t = 0.50 s is 7.20 m/s^2.

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The Number of sodas sold: 174,

The number of hot dogs sold: 58.

Each term in a linear equation has an exponent of 1, and when this algebraic equation is graphed, it always produces a straight line. It is called a "linear equation" for this reason.

Both linear equations with one variable and those with two variables exist.

Given a vendor sold a combined total of 232 sodas and hot dogs.

let S for the number of sodas sold and H for the number of hot dogs sold,

S + H = 232

The number of sodas sold was three times the number of hot dogs sold

S = 3H

substitute the values,

S + H = 232

3H + H = 232

4H = 232

H = 232/4

H = 58

and the number of sodas sold

S = 3H

S = 3*58

S = 174

Hence the number of sodas sold = 174,

and the number of hot dogs sold = 58.

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The angle subtended at the center of the arc is 102⁰

Recall that to find the length of an arc on a circle, we can use the formula L = r *, where r is the radius of the circle, is the central angle, and is the angle between the ends of the arc.  If the central angle is measured in degrees, we can use the formula L = r *, where r is the radius of the circle, is the central angle, and is the angle between the ends of the arc.

Lenght of arc = A/360 *2пr

A = angle at center = ?

п = 22/7 r = radius = 840 feet

⇒1500 = A/360  2 *22/7 * 840

1500 = 36960A/2520

3780000= 36960A

making A the subject we have

3780000/36960 = A

A = 102.27

A= 102⁰

The angle is 102⁰

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Answer:

Step-by-step explanation:

Value of the car at the end of the first year = £9680

Depreciation = 12 %

Original price = £ x

If we reduce 12% of original price from x, we will get £9680

x - 12% of x  = £ 9680

\(x-\frac{12}{100}x=9680\\\\\\\frac{88}{100}x=9680\\\\x=9680*\frac{100}{88}\\\\x = 11000\)

Original price  = £ 11000

Step-by-step explanation:

3-0= 3

2-(-2)= 4

3/4= 0.75