Sally earns a weekly salary of $450 plus a 6. 5% commission on sales at a boutique. How much would she make in a work week if she sold $650 worth of merchandise?

In this prism, lateral Area =  858.54 m² and surface area = 890.54 m².

Firstly, we will find the lateral area of the prism by applying the formula:

Lateral  area = perimeter × height

Perimeter = sum of all the sides of prism

= 4 + 8 + 8.94  = 20.94 m

Lateral Area = 20.94 * 41  =  858.54 m²

Now, we have to find the surface area of the prism.

Surface area = Lateral Area + 2 × ( Base Area)

Base Area = the area of a triangle with sides 4, 8, and 8.94.

Now, we will calculate the area of the triangle

Firstly, we will find s for calculating the area of triangle and then apply the formula.

s = ( 4 + 8 + 8.94)/2 = 10.47 m

Area of triangle =  [tex]\sqrt{ (10.47 (10.47 - 4)(10.47 - 8)(10.47 - 8.94))}[/tex]

= [tex]\sqrt{(10.47 (6.47)(2.47)(1.53))}[/tex]

= 16 m²

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Correct question:

Use formulas to find the lateral area and surface area of the given prism. Round your answer to the nearest whole number. The figure is not drawn to scale. The bases are right triangles.

The equation of the line that passes though (-2, 0 and have a slope of 1 is y = x + 2.

The equation of a line can be represented in slope in intercept form as follows:

y = mx + b

where

Therefore, the slope of a line is the change in the dependent variable with respect to the change in the independent variables.

Hence,

slope = 1 and the line passes through(-2, 0).

Therefore,

y = x + b

let's find b using (-2, 0)

0 = -2 + b

b = 2

Therefore, the equation is y = x + 2.

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The 85% confidence interval for the population proportion of people who are captured after appearing on the 10 Most Wanted list falls between 0.194 and 0.286.

To construct the 85% confidence interval for the population proportion of people who are captured after appearing on the 10 Most Wanted list, we can use the following formula:

[tex]\hat{p} \pm z^* \sqrt{\frac{\hat{p} (1 - \hat{p})}{n}}[/tex]

where [tex]$\hat{p}$[/tex] is the sample proportion, [tex]$n$[/tex] is the sample size, and [tex]$z^*$[/tex] is the z-score corresponding to the desired level of confidence. Since we are looking for an 85% confidence interval, the z-score is 1.440.

First, we can calculate the sample proportion:

[tex]\hat{p} = \frac{109}{455} = 0.240[/tex]

Next, we can plug in the values into the formula:

[tex]$$ 0.240 \pm 1.440 \sqrt{\frac{0.240 (1 - 0.240)}{455}} $$[/tex]

Simplifying this expression, we get:

[tex]$$ 0.240 \pm 0.046 $$[/tex]

Therefore, the 85% confidence interval for the population proportion of people who are captured after appearing on the 10 Most Wanted list is [tex]$(0.194, 0.286)$[/tex].

We can interpret this interval as follows: if we were to draw many samples of size 455 from the population of people who appear on the 10 Most Wanted list, and construct a 85% confidence interval for the proportion of people who are captured based on each sample, about 85% of these intervals would contain the true population proportion.

Furthermore, we are 85% confident that the true population proportion of people who are captured after appearing on the 10 Most Wanted list falls between 0.194 and 0.286.

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The slope of the equation is 0.6, which means that for every second, the computer downloads 0.6 megabytes of data, option C is correct.

The linear equation that represents the number of megabytes downloaded per second can be determined by dividing the total amount of data downloaded (3 MB) by the time taken to download it (5 seconds). This gives us the rate of download in megabytes per second (MB/s). Therefore, the equation is:

y = 0.6x

where y represents the number of megabytes downloaded per second and x represents the time taken to download the data. The negative slope values in the other options do not make sense, as the number of megabytes downloaded per second should be a positive value, option C is correct.

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In this case, the mean absolute deviation of 8.5 indicates that, on average, the data points deviate from the mean by about 8.5 units.

Mean absolute deviation (MAD) is a statistical measure that represents the average distance between each data point and the mean of the data set. It is calculated by finding the absolute value of the difference between each data point and the mean, and then taking the average of these absolute differences. MAD is a useful measure of the variability or spread of a data set, and is often used as an alternative to the more common measure of standard deviation. Like standard deviation, MAD gives an indication of how spread out the data is, but unlike standard deviation, MAD is less sensitive to extreme values or outliers.

Here,

To find the mean absolute deviation of the data, we first need to calculate the mean (average) of the data:

Mean = (46 + 54 + 43 + 57 + 50 + 62 + 78 + 42) / 8

Mean = 52

The mean of the data is 52.

Next, we need to calculate the absolute deviation of each data point from the mean. The absolute deviation is simply the absolute value of the difference between each data point and the mean:

|46 - 52| = 6

|54 - 52| = 2

|43 - 52| = 9

|57 - 52| = 5

|50 - 52| = 2

|62 - 52| = 10

|78 - 52| = 26

|42 - 52| = 10

Now, we can calculate the mean absolute deviation by taking the average of the absolute deviations:

Mean Absolute Deviation = (6 + 2 + 9 + 5 + 2 + 10 + 26 + 10) / 8

Mean Absolute Deviation = 8.5

The mean absolute deviation of the data is 8.5.

Interpretation: The mean absolute deviation represents the average distance between each data point and the mean of the data. In this case, the mean absolute deviation of 8.5 indicates that, on average, the data points deviate from the mean by about 8.5 units. This means that the data points are relatively spread out, with some points being much higher or lower than the mean.

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When Krissa exercises daily by walking and she aims to walk at a steady rate of 3.4 miles per hour:

a) The equation is d = 3.4t;

b) Krissa will walk 2.13 miles;

c) It will take Krissa 1.6 hours to walk 5.44 miles.

When Krissa exercises daily by walking and she aims to walk at a steady rate of 3.4 miles per hour:

a. The equation that models the relationship between time and distance is:

d = 3.4t

where d is the distance Krissa walks in miles and t is the time she spends walking in hours.

b. To calculate the distance Krissa will walk in 5/8 of an hour, we can substitute t = 5/8 into the equation from part a:

d = 3.4(5/8) = 2.125 miles

Therefore, Krissa will walk 2.125 miles in 5/8 of an hour, rounded to the hundredths.

c. To calculate how long it will take Krissa to walk 5.44 miles, we can rearrange the equation from part a to solve for t:

t = d/3.4

Substituting d = 5.44 into this equation, we get:

t = 5.44/3.4 = 1.6 hours

Therefore, it will take Krissa 1.6 hours to walk 5.44 miles.

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The diameter of the sphere is approximately 20 meters to the nearest tenth of a meter.

The volume of a sphere is given by the formula V = (4/3)πr^3, where r is the radius of the sphere. Since we are given the volume of the sphere, we can solve for the radius as follows:

V = (4/3)π[tex]r^{3}[/tex]

[tex]r^{3}[/tex] = (3V) / (4π)

r = [tex](3V/4\pi )^{1/3}[/tex]

Substituting the given value of the volume, we get:

r = [tex](3*7483/4\pi )^{1/3}[/tex] ≈ 10.0

Therefore, the radius of the sphere is approximately 10 meters. The diameter of the sphere is twice the radius, so the diameter is approximately:

2 x 10 ≈ 20 meters

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The perpendicular distance between the bases of a trapezoid with an area of 337.5 ft² and base lengths of 25 ft and 20 ft is 15 ft.

Area = (1/2) * (Base1 + Base2) * Height

In this case, the area is 337.5 ft², Base1 is 25 ft, and Base2 is 20 ft. We need to solve for the height, which represents the perpendicular distance between the bases.

Plugging in the known values into the formula:

337.5 = (1/2) * (25 + 20) * Height

Simplifying the expression:

337.5 = (1/2) * (45) * Height

Multiplying both sides of the equation by 2 to get rid of the fraction:

675 = 45 * Height

Dividing both sides by 45 to solve for the height:

Height = 675 / 45

Height = 15 ft

Therefore, the perpendicular distance between the bases of the trapezoid is 15 ft.

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In the given diagram, using the intersecting secant theorem, the length of c is 2 cm

From the question, we are to determine the length of segment c

From the intersecting secant theorem, we have that

If two secant segments intersect outside a circle, then the product of the secant segment with its external portion equals the product of the other secant segment with its external portion

Thus,

In the given circle, we can write that

a × b =  c × d

Substitute the values

3 × 12 = c × 18

36 = c × 18

Divide both sides by 18

36 / 18 = (c × 18) / 18

2 = c

Therefore,

c = 2

Hence, the length of c is 2 cm

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The interval 4:00-4:59 represents the most number of cars.

How to determine the interval with the most number of cars based on the given time ranges?

To determine the interval that represents the most number of cars, we need to analyze the given options and find the one with the highest number of cars.

Unfortunately, we don't have any data about the actual number of cars during those intervals. Therefore, we cannot provide a definitive answer to this question. We could only make an educated guess based on certain assumptions.

For instance, if we assume that the traffic is usually higher during rush hour, we could say that the intervals between 4:00-4:59 and 3:00-3:59 are more likely to have the highest number of cars. However, without additional information or data, we cannot provide a more accurate answer.

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Answer:

D

Step-by-step explanation:

If you dilate the figure with the center at (0,0), the sides of the triangle will be twice as long.  Then You translate the figure 7 units to the right.  

Helping in the name of Jesus.

The correct statement is,

⇒ A dilation by a scale factor of 2, centered at the origin, followed by

the translation (x, y) → (x + 7, y)

A transformation that occurs when a figure is moved from one location to another location without changing its size or shape is called translation.

Since, Scale Factor is defined as the ratio of the size of the new image to the size of the old image.

If the scale factor is more than 1, then the image stretches.

If the scale factor is between 0 and 1, then the image shrinks.

If the scale factor is 1, then the original image and the image produced are congruent.

And, The only change in the dilation process is that the distance between the points changes.

It means that the length of the sides of the original image and the dilated image may vary.

Here, By dilation with factor 2 to the small triangle, its sides becomes equal as big triangle.

Now, center the small triangle at origin (0,0).

Then, transform the small triangle to (x + 7, y) i.e., it exactly gets the coordinates of the big triangle.

There are same in terms of sides length and coordinates.

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The value of the domains is given as:

In order to find the results of (fg)(x) and (f/g)(x), we must begin by multiplying and dividing the two functions, respectively:

(fg)(x) = f(x) * g(x) = [tex]3x * 3(x + 1)^2 = 9x(x + 1)^2[/tex]; its domain containing all real numbers.

Similarly, (f/g)(x) = f(x) / g(x) = in a domain that does not [tex]3x / 3(x + 1)^2 = x / (x + 1)^2[/tex]include x = -1 (if g(x) ≠ 0).

Let us now evaluate  (fg)(5) and (f/g)(5):

(fg)(5) =[tex]9(5)(5 + 1)^2 = 9(5)*(6)^2[/tex] = 9(5(36)) = 1620 while  

(f/g)(5) = [tex]5/(5 + 1)^2 = 5/(6)^2[/tex] = 5/36.

Consequently, (fg)(5) equals 1620 and (f/g)(5) is equivalent to 5/36.

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The most likely factor to push the price of a company's stock higher is an increase in demand for the company's stock. Option A.

A stock's price will often increase when there is greater demand than there is supply. Various things, such as good news about the company's financial performance, new product releases or innovations, positive analyst reports, or general market trends, can contribute to this increased demand.

The company's financial performance may benefit from a rise in product demand, but if investors do not view it as a key growth engine for the business, it may not necessarily transfer into a higher stock price.

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The volume of the solid enclosed by the paraboloids z = 4 (x² + y²) and z = 50 – 4 (x² + y²) is approximately 164.93 cubic units.

To find the volume of the solid enclosed by the two paraboloids, we need to first find the intersection of the two surfaces. Setting the equations of the paraboloids equal to each other, we get:

4(x² + y²) = 50 - 4(x² + y²)

Simplifying this equation, we get:

8x² + 8y² = 50

Dividing by 8, we get:

x² + y² = 6.25

This equation represents a circle of radius 2.5 centered at the origin in the xy-plane.

To find the volume of the solid, we can use a double integral in cylindrical coordinates:

V = ∫∫R (50 - 4r²) - 4r² r dr dθ

where R is the region enclosed by the circle x² + y² = 6.25.

Evaluating the integral, we get:

V = ∫0^2π ∫0^2.5 (50 - 8r²) r dr dθ

= 2π [25r² - (4/3)r^4]0^2.5

= 2π [156.25/3]

≈ 164.93 cubic units

Therefore, the volume of the solid enclosed by the paraboloids z = 4 (x² + y²) and z = 50 – 4 (x² + y²) is approximately 164.93 cubic units.

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Answer: There are two solutions to X.. x = -3 and x = 2

Step-by-step explanation:

In this case, a = 1, b = 1, and c = -6, so we have:

x = (-1 ± sqrt(1^2 - 4(1)(-6))) / 2(1)

x = (-1 ± sqrt(1 + 24)) / 2

x = (-1 ± sqrt(25)) / 2

The two solutions are x = (-1 + 5) / 2 = 2 and x = (-1 - 5) / 2 = -3. Therefore, the solutions to the equation X^2 + x - 6 = 0 are x = 2 and x = -3.

Answer:

A= 225π  ft²

Step-by-step explanation:

A = π r²

A= π 15²

A= 225π  ft²

Answer:

706.86

Step-by-step explanation:

1. A=πr^2 : The formula to find the area of a circle.

2. A = π15^2 : Substitute the given radius value into the equation.

3. Insert equation into calculator

706.86 (Rounded to the nearest hundredth)

To find the number of unique types of sneakers, we need to multiply the number of options for each characteristic:

Number of colors: 6

Number of styles: 4

Number of fabrics: 3

Total number of unique types of sneakers = 6 x 4 x 3 = 72

Therefore, the manufacturer makes 72 unique types of sneakers.

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The domain of the function y = (3/x) - 1 is all real numbers except x = 0

The domain of a function consists of all the valid input values for which the function is defined. In the case of the function y = (3/x) - 1, the only restriction on the domain arises from the presence of the variable x in the denominator.

To determine the domain, we need to find the values of x for which the expression 3/x is defined. Division by zero is undefined, so we must exclude any value of x that makes the denominator equal to zero.

In this case, we set the denominator, x, equal to zero and solve for x:

x = 0

Therefore, x cannot be equal to zero. All other real numbers are valid input values for this function. Therefore, the domain of the function y = (3/x) - 1 is all real numbers except x = 0. In interval notation, we can represent the domain as (-∞, 0) ∪ (0, ∞).

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The solution to the equation √8x + 4 = 6 is x = 0.5.

An equation is simply a mathematical formula that expresses the equality of two expressions, using the equals sign as a connection between them.

Given the equation in the question:

√8x + 4 = 6

To solve for x in the equation, isolate the term containing the variable x.

Subtract 4 from both sides of the equation:

√8x + 4 - 4 = 6 - 4

√8x = 6 - 4

√8x = 2

Square both sides of the equation:

( √8x )² = 2²

8x = 4

Divide both sides of the equation by 8:

x = 4/8

x = 1/2

x = 0.5

Therefore, the value of x is 0.5.

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Answer:34

Step-by-step explanation:

Using the t-distribution table with a sample size of 36 and a significance level of 0.05, we find the critical t-value to be ±2.03 (with 34 degrees of freedom, which is n-1).

To explain, we use the t-distribution to find the critical values because the population standard deviation is known. Since the alternative hypothesis is two-tailed (H_A: μ ≠ 40), we need to find two critical values.

With a sample size of 36, the degrees of freedom are 34 (n-1), so we use a t-distribution table with 34 degrees of freedom and a significance level of 0.05. From the table, we find the critical t-value to be ±2.03.

Therefore, if the calculated t-value falls outside of this range, we can reject the null hypothesis H0: μ = 40 in favor of the alternative hypothesis H_A: μ ≠ 40.

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a) Parametrization for the curve of intersection of 9y2 + z2 = 1 and xyz = 1 is:
x = 1/(z(sqrt((1 - z^2)/9)))
y = ±sqrt((1 - z^2)/9)
z = t

b)Parametrization for the curve of intersection of  x=y_and x2 - y2 =z is

x = t
y = t
z = 0
c)Parametrization for the curve of intersection of  x2 + y2 + z = is

x = r cos(t)
y = r sin(t)
z = 1 - r

a) To find the curve of intersection of the two surfaces [tex]9y^2 + z^2 = 1[/tex] and xyz = 1:

We can solve for one variable in terms of the others.

For example, we can solve for y in terms of z and x using the first equation:
[tex]9y^2 + z^2 = 1[/tex]
[tex]9y^2 = 1 - z^2[/tex]
[tex]y^2 = (1 - z^2)/9[/tex]
y = ±sqrt([tex](1 - z^2)/9)[/tex]
Substituting this into the second equation, we get:
x(sqrt((1 - [tex]z^2)/9))z = 1[/tex]
x = 1/(z(sqrt((1 - [tex]z^2)/9)))[/tex]
So, a parametrization for the curve of intersection is:
x = 1/(z(sqrt((1 - [tex]z^2)/9)))[/tex]
y = ±sqrt((1 - z^2)/9)
z = t
This is defined for all t except at z = ±1.
b) To find the curve of intersection of the two surfaces x = y and [tex]x^2 - y^2 = z:[/tex]

We can substitute x = y into the second equation:
[tex]x^2 - y^2 = z[/tex]
[tex]y^2 - y^2 = z[/tex]
z = 0
So the curve of intersection is just the x = y line.

A parametrization for this line is:
x = t
y = t
z = 0
c) To find a parametrization for the surface [tex]x^2 + y^2 + z = 1:[/tex]

We can use cylindrical coordinates:
x = r cos(t)
y = r sin(t)
z = 1 - r
where 0 ≤ r ≤ 1 and 0 ≤ t < 2π.

This parameterization covers the surface of a unit cylinder with its top and bottom caps removed.

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We can be 99% confident that the true average price of all foreclosed homes in Washington, DC is no higher than $460,794.81.

To find the upper 99% confidence limit for the average price of all foreclosed homes in Washington, DC, we can use the formula:

Upper limit = sample mean + (z-score)*(standard error)

First, we need to find the z-score for the 99% confidence level. From a standard normal distribution table, we can find that the z-score for a 99% confidence level is 2.576.

Next, we need to find the standard error, which is the standard deviation of the sample divided by the square root of the sample size:

standard error = standard deviation / √sample size

Plugging in the values given in the problem, we get:

standard error = 220,978 / √40

standard error = 34,955.84

Finally, we can plug in the values for the sample mean, z-score, and standard error into the formula to get the upper limit:

Upper limit = 375,334 + (2.576)*(34,955.84)

Upper limit = 460,794.81

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The probability of Larry has a chance of winning the game is equal to 2/3

Let P be the probability that Larry wins the game.

Set up a system of equations based on the probabilities of each player winning on their turn,

P = 1/2 + 1/2 × (1 - P)

First term corresponds to Larry winning on his first turn, with probability 1/2.

The second term corresponds to Julius winning on his first turn, with probability 1/2,

And then Larry winning with probability (1 - P).

Since they are now in the same position as at the start of the game.

Simplifying the equation, we get,

⇒P = 1/2 + 1/2 - P/2

Multiplying both sides by 2, we get,

⇒2P = 1 + 1 - P

Simplifying further, we get,

⇒3P = 2

⇒ p = 2/3.

Therefore, the probability that Larry wins the game is equal to

P = 2/3.

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To find the number of minutes it will take for both Aquarium A and Aquarium B to contain the same amount of water, we can set up an equation using the given information.

Aquarium A starts with 6 gallons and is filled at 2 gallons per minute. The equation for Aquarium A will be:

A = 6 + 2t

Aquarium B starts with 54 gallons and is filled at 1 gallon per minute. The equation for Aquarium B will be:

B = 54 + 1t

We want to find the time 't' when the amount of water in both aquariums is equal, so we can set the equations equal to each other:

6 + 2t = 54 + 1t

Now, solve for 't':
2t - 1t = 54 - 6
t = 48

After 48 minutes, both Aquarium A and Aquarium B will contain the same amount of water.

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The payback period for the auto is approximately 8 years.

Buy-Rite Pharmacy has purchased an auto for delivering prescriptions. The auto was purchased for $26,000, and it has a useful life of 6 years with a $5,500 salvage value. By delivering prescriptions, the pharmacy aims to increase gross revenues by at least $33,500 per year. The pharmacy will incur a cost of $28,000 per year for these prescriptions.

Using the straight-line method, the annual depreciation of the auto is ($26,000 - $5,500) / 6 = $3,917. This means that the total cost of the auto over 6 years will be $26,000 - $5,500 + ($3,917 x 6) = $43,502.

To calculate the payback period, we need to determine how long it will take for the increased gross revenues to cover the cost of the auto.

The net increase in revenues will be $33,500 - $28,000 = $5,500 per year. Therefore, the payback period is $43,502 / $5,500 = 7.9 years, which is rounded to 8 years.

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the measurement of the couch in the scale drawing would be 15 inches.

We can precisely portray locations, areas, structures, and details in scale drawings at a scale that is either smaller or more feasible than the original.

When a drawing is said to be "to scale," it signifies that each piece is proportionate to the real or hypothetical entity; it may be smaller or larger by a specific amount.

When something is described as being "drawn to scale," we assume that it has been printed or drawn to a conventional scale that is accepted as the norm in the construction sector.

When our awareness of scale improves, we are better able to quickly recognize the spaces, zones, and proposed or existent spatial relationships when looking at a drawing at a given scale.

One metre is equivalent to one metre in the actual world. When an object is depicted at a 1:10 scale, it is 10 times smaller than it would be in real life.

You might also remark that 10 units in real life are equivalent to 1 unit in the illustration.

To determine the measurement of the couch in the scale drawing, we can use the scale factor provided:

1/4 inch = 2 feet

This means that every 1/4 inch in the drawing represents 2 feet in real life.

To find the measurement of the couch in the drawing, we need to convert its actual size to the corresponding size in the drawing using the scale factor.

First, we can convert the actual size of the couch to feet:

10 ft = 10 ft x 12 inches/ft = 120 inches

Next, we can use the scale factor to convert the actual size to the corresponding size in the drawing:

1/4 inch = 2 feet

1 inch = 8 feet (multiplying both sides by 4)

So, 120 inches in real life is equal to:

120 inches / 8 feet per inch = 15 inches in the drawing

Therefore, the measurement of the couch in the scale drawing would be 15 inches.

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To find the angle between two planes, we need to find the cosine of the angle between their normal vectors. The normal vector of the first plane is (4, 0, -1) and the normal vector of the second plane is (24, -1, 0).

Using the dot product formula, we have:

cos(theta) = (4, 0, -1) · (24, -1, 0) / ||(4, 0, -1)|| ||(24, -1, 0)||

= (96 + 0 + 0) / (sqrt(16 + 1) * sqrt(576 + 1))

= 96 / sqrt(33217)

Using a calculator, we get:

cos(theta) ≈ 0.00575

Therefore, the angle between the two planes is:

theta ≈ acos(0.00575)

theta ≈ 89.59 degrees

Rounded to two decimal places, the angle between the two planes is approximately 89.59 degrees.
To find the angle between the two given planes, we first need to rewrite the equations in their standard form and find the normal vectors for each plane.

Plane 1: -4x + y + 7 = 4
Standard form: -4x + y + 0z = -3
Normal vector N1: <-4, 1, 0>

Plane 2: 24x - 6y + 42 = 16
Standard form: 24x - 6y + 0z = -26
Normal vector N2: <24, -6, 0>

Now, we can find the angle θ between the two planes by using the formula:

cos(θ) = (N1 • N2) / (||N1|| ||N2||)

First, calculate the dot product (N1 • N2):
N1 • N2 = (-4 * 24) + (1 * -6) + (0 * 0) = -102

Next, calculate the magnitudes of the normal vectors:
||N1|| = sqrt((-4)^2 + 1^2 + 0^2) = sqrt(17)
||N2|| = sqrt(24^2 + (-6)^2 + 0^2) = sqrt(576+36) = sqrt(612)

Now, we can find cos(θ):
cos(θ) = (-102) / (sqrt(17) * sqrt(612))

Finally, calculate the angle θ (in degrees) by taking the inverse cosine:
θ = arccos((-102) / (sqrt(17) * sqrt(612))) = 44.41° (rounded to two decimal places)

So, the angle between the two planes is 44.41°.

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If the store advertises 60 square foot flooring for $253, then the cost for "per-square foot" is (c) $5.55.

To find the cost per square foot for the flooring, we need to divide the total cost of the flooring including the "installation-fee' by the total square footage of the flooring.

⇒ Total cost of flooring + installation fee = $253 + $80 = $333,

⇒ Total square footage of the flooring = 60 sq. ft.

So, Cost per square foot = (Total cost of flooring and installation fee)/(Total square footage of the flooring),

⇒ Cost per square-foot = 333/60,

⇒ Cost per square foot = $5.55/sq. ft.

Therefore, the correct option is (c).

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Answer:

2(x - 3) < -24

x - 3 < -12

x < -9

The inequality that represents the given statement is 2(x-3) ≤ -24, where x is the unknown number.

The given statement can be translated into an inequality as "twice the difference of a number (x) and 3 is at most -24". Mathematically, this can be represented as 2(x-3) ≤ -24. Simplifying this inequality, we get 2x - 6 ≤ -24, or 2x ≤ -18, which gives x ≤ -9. Therefore, any number less than or equal to -9 satisfies the given statement.

For example, x = -10 satisfies 2(-10-3) = -26, which is less than or equal to -24. However, any number greater than -9 does not satisfy the given statement. For example, x = -8 gives 2(-8-3) = -22, which is greater than -24. Therefore, the solution set for the given inequality is x ≤ -9.

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