Which of the following values are solutions to the inequality - 8 - 3x > 2?
I. – 2
II. – 12
III. 5

The cone’s radius r in terms of x is x + 7

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

Volume, V = 3πx^2 + 42πx + 147π

Height, h = 9

The volume of a cone is

V = 1/3πr^2h

Substitute the known values in the above equation, so, we have the following representation

1/3πr^2 * 9 = 3πx^2 + 42πx + 147π

So, we have

3πr^2 = 3πx^2 + 42πx + 147π

Divide by 3π

r^2 = x^2 + 14x + 49

So, we have

r = √(x² + 14x + 49)

Take the square roots of both sides

r = x + 7

Hence, the value of r is x + 7

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(A) You will use 1 cup of red paint and 1 cup of blue paint to make 3 gallons of purple paint. (B) To make 3 gallons of the lighter purple paint, you would use 3 cups of red paint, 6 cups of blue paint, and 13.5 cups of paint in total.

a. To make 3 gallons of purple paint, you need to mix 1 cup of red paint for every cup of blue paint. This means that you will use a total of 1 + 1 = 2 cups of paint for every 3 gallons of purple paint. So, to find out how much red and blue paint you will use, you can set up a proportion:

1 cup red paint : 1 cup blue paint = 2 cups paint : 3 gallons paint

Solving for the unknown quantities, we get:

1 cup red paint = (1 cup red paint / 1 cup blue paint) x 1 cup blue paint = 1 cup red paint

1 cup blue paint = (1 cup blue paint / 1 cup red paint) x 1 cup red paint = 1 cup blue paint

So, you will use 1 cup of red paint and 1 cup of blue paint to make 3 gallons of purple paint.

b. To make a lighter purple paint, you need to add 1/2 cup of white paint for every cup of purple paint and 1/2 cup of blue paint. So, to make 1 gallon of the lighter purple paint, you would need:

1 cup of red paint

2 cups of blue paint

(1/2 cup of white paint + 1 cup of purple paint) x 3 = 4.5 cups of paint in total

To make 3 gallons of the lighter purple paint, you would need to multiply these quantities by 3, giving:

3 cups of red paint

6 cups of blue paint

(1/2 cup of white paint + 1 cup of purple paint) x 9 = 13.5 cups of paint in total

So, to make 3 gallons of the lighter purple paint, you would use 3 cups of red paint, 6 cups of blue paint, and 13.5 cups of paint in total (including 1.5 cups of white paint).

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Answer:

1

Step-by-step explanation:

The interval the value of the function (f - g)(x) is negative is (-∞, 2]

A function is a rule or definition that maps an input variable unto an output such that each input has exactly one output.

The equations on the possible graphs in the question, obtained from a similar question posted online are;

f(x) = x - 3

g(x) = -0.5·x

(f - g)(x) = x - 3 - (-0.5·x) = 1.5·x - 3

(f - g)(x) = 1.5·x - 3

Therefore; The x-intercept of the function (f - g)(x) = 1.5·x - 3 is; (f - g)(x) = 0 1.5·x - 3

1.5·x - 3 = 0

1.5·x = 3

x = 3/1.5 = 2

x = 2

The y-intercept is the point where, x = 0, therefore;

(f - g)(0) = 1.5×0 - 3 = -3

The interval the function is negative is therefore;

The equations of the possible graphs of the function, obtained from a question posted online are;

f(x) = x - 3, g(x) = -0.5·x

The interval the function (f - g)(x) is negative is required

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Answer:

12.08

Step-by-step explanation:

Answer:

\(2262.20 in^3\)

Step-by-step explanation:

Given data

height of cylinder h= 20 in

base radius r= 6 in

We know that the formula for the volume of a cylinder is expresses as

\(volume= \pi r^2h\)

Substituting our data into the expression we have

\(volume= 3.142*6^2*20\\volume= 2262.24 in^2\\\)

To the nearest tenth we have the volume to be

\(2262.20 in^3\)

Answer: 2261.9

use volume of a cylinder formula

Substitute Variables into formula

Multiply

Then round to the nearest 10th

Answer:

$12588.75

Step-by-step explanation:

You must figure out the amount the agency makes on the house before they give the real estate agent their commission then find the amount of commission the real estate agent gets then take that from the agency's total before to get the agency's profit

373,000 X 4.5%

= 16,785 X 25%

= 4196.25

16,785 - 4196.25 = 12588.75

Therefore the agency made $12588.75 on the sale of the house

The probability that a randomly selected steer weighs less than 2030 lbs is approximately 0.9821, or rounded to four decimal places, 0.9821.

The probability that the weight of a randomly selected steer is less than 2030 lbs, we will use the normal distribution, given the mean (µ) is 1400 lbs and the variance (σ²) is 90,000 lbs².

First, let's find the standard deviation (σ) by taking the square root of the variance:
σ = √90,000 = 300 lbs

Next, we'll calculate the z-score for the weight of 2030 lbs:
z = (X - µ) / σ = (2030 - 1400) / 300 = 2.1

Now, we can look up the z-score in a standard normal distribution table or use a calculator to find the probability that the weight of a steer is less than 2030 lbs. The probability for a z-score of 2.1 is approximately 0.9821.

So, the probability that a randomly selected steer weighs less than 2030 lbs is approximately 0.9821, or rounded to four decimal places, 0.9821.

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Step-by-step explanation:

20% = $1.86

1% = 20%/20 = 1.86/20 = $0.093

100% = 1%×100 = 0.093×100 = $9.30

in short : 1.86 × 100/20 = 1.86 × 5 = $9.30

the cost of her dinner without tip was $9.30.

The line integral ∮c F⋅r′ ds is equal to the flux of the curl of F through the surface S bounded by the curve C.

Given: F = [2y, -z, 0] C: the boundary curve of y^2 + z^2 = 4, 0 ≤ x ≤ h

To calculate the line integral using Stokes' theorem, we need to find the curl of F and the surface S bounded by the curve C.

Curl of F: ∇ × F = (dFz/dy - dFy/dz) i + (dFx/dz - dFz/dx) j + (dFy/dx - dFx/dy) k = (0 - (-1)) i + (0 - 0) j + (0 - 2) k = i - 2k

Surface S: The surface S is the region enclosed by the curve C, which is the circular disk defined by y^2 + z^2 = 4. The surface is perpendicular to the x-axis.

Calculate the flux of the curl through S: The flux can be calculated as the surface integral of the dot product between the curl of F and the surface normal vector over the surface S: ∫∫S (∇ × F) ⋅ n dS

Since the surface S is a circular disk, the surface integral simplifies to: ∫∫S (∇ × F) ⋅ n dS = ∫∫S (i - 2k) ⋅ n dS

The unit normal vector to the surface S is n = (n1, n2, n3) = (0, -1, 0).

Calculate the area of S: The area of the circular disk S can be calculated using the formula A = πr^2, where r is the radius of the disk. Given y^2 + z^2 = 4, we can solve for z in terms of y: z = ±√(4 - y^2)

Since the surface S is perpendicular to the x-axis, the limits of integration for y are -2 to 2. Therefore, the radius r is 2.

A = π(2)^2 = 4π

Evaluate the line integral using Stokes' theorem: ∮c F⋅r′ ds = ∫∫S (i - 2k) ⋅ n dS = ∫∫S (0 - 2) dS = -2 ∫∫S dS = -2(A) = -2(4π) = -8π

The line integral ∮c F⋅r′ ds using Stokes' theorem for the given F and C is -8π.

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(a) The displacement is 5 units in the positive direction. (b) The displacement is 8 units in the negative direction. (c) The displacement is 0 units, indicating no change in position.

(a) In the first case, the magnitude of the displacement is 5 units. The direction is positive, which means the object has moved in the positive direction along the chosen axis. This implies that the final position is 5 units greater than the initial position.

(b) In the second case, the magnitude of the displacement is 8 units. The direction is negative, indicating that the object has moved in the negative direction along the chosen axis. This means that the final position is 8 units less than the initial position.

(c) In the third case, the magnitude of the displacement is 0 units. This indicates that there has been no change in position. The object is at the same position as the initial position, so the displacement is zero.

In summary, the displacement can have different magnitudes and directions. Positive displacement indicates movement in the positive direction, negative displacement indicates movement in the negative direction, and zero displacement means no change in position.

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Answer:

-√13/13 or -2.774

Step-by-step explanation:

(3+2-6/√3²+2²)

Answer:

3/4

Step-by-step explanation:

up 3 right 4

Answer:

\(4x^4y^2\sqrt[3]{x^2y^2}\)

Step-by-step explanation:

Recall that \(a^{(\frac{b}{c})}=\sqrt[c]{a^b}\).

Therefore, we have:

\((8x^7y^4)^{\frac{2}{3}}=\sqrt[3]{(8x^7y^4)^2}\)

Use the exponent property \((a^b)^c=a^{(b\cdot c)}\) to simplify:

\((8x^7y^4)^{\frac{2}{3}}=\sqrt[3]{(8x^7y^4)^2}=\sqrt[3]{64x^{14}y^8}=\boxed{4x^4y^2\sqrt[3]{x^2y^2}}\)

Answer:

13ab

Step-by-step explanation:

5ab+9ab = 14ab. 14ab-1ab=13ab.

Good luck

The area of the shaded region is 60 square units.

Area is the entire amount of space occupied by a flat (2-D) surface or an object's form. On a sheet of paper, draw a square using a pencil. It has two dimensions. The area of a form on paper is the area that it occupies.

To find the area of the shaded region, we need to subtract the area of the rectangular region that was removed from the larger rectangular region.

The area of the larger rectangle is:

11 x 8 = 88

The area of the rectangle that was removed is:

7 x 4 = 28

So, the area of the shaded region is:

88 - 28 = 60

Therefore, the area of the shaded region is 60 square units.

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The two limits when x tends to zero are:

\(\lim_{x \to \ 0^-} f(x) = 1\\\\ \lim_{x \to \ 0^+} f(x) = 0\)

Notice that we have a jump at x = 0.

Then we can take two limits, one going from the negative side (where we will go along the blue line)

And other from the positive side (where we go along the orange line).

We will get:

\(\lim_{x \to \ 0^-} f(x) = 1\\\\ \lim_{x \to \ 0^+} f(x) = 0\)

Notice that the two limits are different, that means that the function is not a continuous function.

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Answer:

x-intercept= (5,0)

y-intercept= (0,-2)

Slope= 2/5

Step-by-step explanation:

The pairs that are included in the set of solutions for y = 1/2x + 3/2 are: (3, 3), (−5, −1), and (7, 5).

If a point is located on a line of an equation, then the ordered pair of that point is defined as belonging to the set of solutions for the equation.

Given the equation, y = 1/2x + 3/2, the graph is plotted on a coordinate plane as shown below. It has a slope of 1/2, and a y-intercept of 3/2.

The graph shows that the following pair of the points are located on the line of y = 1/2x + 3/2:

Therefore, it is concluded that the pairs that are included as the solution to y = 1/2x + 3/2 are: (3, 3), (−5, −1), and (7, 5).

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Answer:

V=273

Step-by-step explanation:

V=L*W*H

V=12*6.5*3.5

V=273

Answer:

11/18

Step-by-step explanation:

1 2 + 1 9 = ? The Least Common Multiple (LCM) of 2 and 9 is 18. Multiply the numerator and denominator of each fraction by whatever value will result in the denominator of each fraction being equal to the LCM: 1 2 + 1 9 = 1 × 9 2 × 9 + 1 × 2 9 × 2 = 9 18 + 2 18 Now that the fractions have like denominators, add the numerators: 9 18 + 2 18 = 9 + 2 18 = 11 18 The result is: 1 2 + 1 9 = 11 18

so 11/18 is you answer

Answer:

11/18

Step-by-step explanation:

Get the common denominator by multiplying 2 and 9.

Multiply both sides of 1/2 by 9 to get 9/18, and both sides of 1/9 by 2 to get 2/18.

\(\frac{1}{2} +\frac{1}{9} = \frac{9}{18} + \frac{2}{18} = \frac{11}{18}\)

After adding both fractions you'll get 11/18. That's your answer.

The probability that at least one of the 5 systems will detect the theft when it occurs is what the bank is interested in. To find this probability, we can use the complement rule, which states that the probability of an event occurring is equal to 1 minus the probability of the event not occurring.

Let A be the event that at least one of the 5 alarm systems detects the theft. The complement of A is the event that none of the 5 systems detects the theft, which we will denote by A'.Since each system detects the theft with a probability of 0.88, the probability that any one system does not detect the theft is 1 - 0.88 = 0.12.

Therefore, the probability that none of the 5 systems detect the theft is: P(A') = (0.12)⁵ = 0.00005376Using the complement rule, we can find the probability that at least one of the 5 systems will detect the theft: P(A) = 1 - P(A') = 1 - 0.00005376 = 0.99994624Therefore, the probability that when a theft occurs, at least one of the 5 systems will detect it is approximately 0.99995 when rounded to 5 decimal places.

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The measure of variability that is used when the statistic with the greatest stability is sought is the Standard Deviation.

The Standard Deviation takes into account the dispersion of data points from the mean and provides a measure of the average distance between each data point and the mean. It is widely used in statistical analysis and is considered a robust measure of variability, providing a more precise and stable measure compared to other measures such as Mean Deviation, Quartile Deviation, or Range.

The Standard Deviation is a statistical measure that quantifies the dispersion or variability of a dataset. It takes into account the differences between individual data points and the mean of the dataset. By calculating the average distance between each data point and the mean, it provides a measure of how spread out the data is.

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The 83rd percentile of car speeds over the bridge is 62.08 mph.

To find the 83rd percentile, we need to first find the value of the speed at which 83% of the cars are traveling at or below. We can do this by finding the z-score corresponding to the 83rd percentile using a standard normal distribution table. The formula for finding the z-score is:

z = (x - μ) / σ

where x is the value we are looking for (in this case, the speed at the 83rd percentile), μ is the mean speed (58 mph, which is the midpoint of the range between 52 and 64), and σ is the standard deviation (6 mph, which is half the range).

Using the z-score table, we can find that the z-score corresponding to the 83rd percentile is 0.94. So we can plug in the values we know into the formula and solve for x:

0.94 = (x - 58) / 6

x - 58 = 5.64

x = 63.64

Therefore, the speed at the 83rd percentile is 63.64 mph. Rounded to two decimal places, this is 62.08 mph.

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Answer:

here is no question sorry

The design shear for the beam in kN is 332.64, the nominal shear carried by the concrete section using simplified calculation in KN is 21451651.6, the required spacing of shear reinforcements from simplified calculation is 0.000032, the location of the beam from the support in which shear reinforcement are permitted not to place in the beam is 1220.

1. To determine the design shear for the beam in kN:

The design shear for a simply supported beam can be calculated using the formula:

Vd = 0.6 * (Wd + Wl) * C

Where:

Wd is Superimposed dead load per unit length (given as 35 + 18C kN/m)

Wl is Superimposed live load per unit length (given as 55 + 24G kN/m)

C: Span length (given as 4.2 m)

Substituting the given values, we have:

Vd = 0.6 * ((35 + 18C) + (55 + 24G)) * 4.2

Vd = 332.64

2. To determine the nominal shear carried by the concrete section using simplified calculation in kN:

The nominal shear carried by the concrete section can be calculated using the formula:

Vc = (0.85 * f'c * b * d) / γc

Where:

f'c: Characteristic strength of concrete (taken as 0.85 * f'e = 0.85 * 27.60 MPa)

b: Width of the beam (given as 250 + 50A mm)

d: Effective depth of the beam (taken as L - cover - bar diameter)

γc: Partial safety factor for concrete (taken as 1.5)

Substituting the given values, we have:

Vc = (0.85 * 0.85 * 27.60 MPa * (250 + 50A) mm * (L - 50 mm - 12 mm)) / 1.5

Vc = 21451651.6

3. To determine the required spacing of shear reinforcements from simplified calculation (expressed in multiples of 10mm):

The required spacing of shear reinforcements can be calculated using the formula:

s = (0.87 * fy * Av) / (0.4 * (Vd - Vc))

Where:

fy: Steel yield strength (given as 345 MPa)

Av: Area of shear reinforcement per meter length (taken as (π * (12 mm)^2) / 4)

Vd: Design shear for the beam (calculated in step 1)

Vc: Nominal shear carried by the concrete section (calculated in step 2)

Substituting the given values, we have:

s = (0.87 * 345 MPa * ((π * (12 mm)^2) / 4)) / (0.4 * (Vd - Vc))

s = 0.000032

4. To determine the location of the beam from the support in which shear reinforcement is permitted not to be placed:

The location of the beam from the support where shear reinforcement is not required can be determined based on the formula:

x = (5 * d) / 2

Where:

d: Effective depth of the beam (taken as L - cover - bar diameter)

Substituting the given values, we have:

x = (5 * (L - 50 mm - 12 mm)) / 2

x = 1220

Therefore, the design shear for the beam in kN is 332.64, the nominal shear carried by the concrete section using simplified calculation in KN is 21451651.6, the required spacing of shear reinforcements from simplified calculation is 0.000032, the location of the beam from the support in which shear reinforcement are permitted not to place in the beam is 1220.

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Answer:

(18 is wrong, the slope is 1/3)

Step-by-step explanation:

Using the equation in the top right

11.) (-10-(-4))/(-12-(-20))= -(3/4)

12.) (-8+5)/(0+12)= -(1/4)

13.) (16-(-6))/(15-(-19))=  (11/17)

14.) (-9-9)/(7+6)= -(18/13)

15.) (-15+20)/(-18+18)= No solution

16.) (12+18)/(11-12) = -30

Answer:

The answer is

b≤14

So you make a filled in circle at 14, make the point for left from there.

She had hiccups so she ordered a glass of water. The man noticed so he pulled out a gun to give her a scare. Being startled is said to make hiccups stop. Therefore, she thanked him for ending her hiccups and left.