What’s the value of x?

The correct description of the shape of the distribution is D. Roughly Symmetric.

Symmetric distribution is an often-referenced term in statistics, representing a type of probability with data segments evenly dispersed around the mean. This denotes the perfect mirror image of the right and left halves when the distribution is split; arriving at an equal size and shape on either side when drawn at the midpoint of the line.

Looking at the distribution of a fire department's response time, we can see that the distribution is roughly symmetric because the values on the left seem to match those on the right.

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The measurement of DE is 10 inches.

If we know that E is the point where the diagonals of the rectangle intersect, then we know that DE is equal to half the length of the diagonal BD.

Using the Pythagorean theorem, we can relate the length of the diagonal BD to the sides of the rectangle.

Let's assume that the length of the rectangle is L and the width of the rectangle is W. Then, the length of the diagonal BD is given by:

BD = √(L^2 + W^2)

Since we know that the diagonals of a rectangle are equal, we have:

AC = BD

BD = 20

Therefore, DE = 1/2 BD = 1/2 (20) = 10 inches.

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The coordinates in the solution to the systems of inequalities is (12, 1)

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

y > -4x + 6

y > 1/3x - 7

Next, we plot the graph of the system of the inequalities

See attachment for the graph

From the graph, we have solution to the system to be the shaded region

The coordinates in the solution to the systems of inequalities graphically is (12, 1)

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The graph will look like a circle centered at (2, 1) with radius 3.

To graph the equation [tex]x^2 - 4x + y^2 - 2y - 4 = 0[/tex]  by completing the square, we need to rearrange the terms as follows:

[tex](x^2 - 4x + 4) + (y^2 - 2y + 1) = 9[/tex]

This can be simplified to:

[tex](x - 2)^2 + (y - 1)^2 = 3^2[/tex]

So the equation represents a circle with a center at (2, 1) and a radius 3. To graph the circle, we can plot the center point (2, 1) and then draw a circle with radius 3 around that point.

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Answer:

20

Step-by-step explanation:

She biked an equal amount each day for 8 days to a total of 32 miles. We can write that as 8x = 32. 32/8 = 4 so x = 4. To find how much shell bike in 5 days, we multiply it by x(4). 5*4 = 20.

Answer:

B. More streetlights are installed on one street and people are then asked if they like the change.

Step-by-step explanation:

An experiment is a type of research method that involves manipulating one or more variables and measuring their effects on other variables. In this case, the experiment is to change the color of the product packaging and see how many people like the change. This is because the outcome of the experiment (the number of people who like the change) depends on chance and can be measured using numerical data. The other options are not experiments, but surveys or observations. Surveys involve asking people questions and collecting their opinions or preferences. Observations involve watching and recording people's behavior or reactions without interfering with them.

The claims are this year some of their clients will have a starting salary of at least $38,500 and last year at least one of their clients had a starting salary of exactly $38,500. Correct options are A and B.

Based on the given information, option A can be true. This is because the average starting salary of the job placement agency's clients was $38,500 last year, which means some clients had a starting salary equal to or greater than that amount.

Option B is also true because the mean includes all values, including the value of $38,500, so it is likely that at least one client had that starting salary.

Option C cannot be determined from the given information as it is unclear what percentage of clients had a starting salary above $38,500. Option D is not necessarily true as there is no information on the starting salary of any client exceeding $42,000.

Option E is also not true as the average salary of $38,500 does not guarantee that all clients had that same starting salary. Therefore, the correct answer is A and B, and the rest cannot be determined from the given information.

Correct options are A and B.

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Answer:

a) r(t) = (10, 5, -5) + (5, 5, 0)*t

b) (0, -5, -5)

Step-by-step explanation:

a) 2x + 4 -2y -5 = -3z -6

2x - 2y +3z +5 =0

(10, 5, -5)

(15, 10, -5)

(5, 5, 0)

r = (10, 5, -5) + (5, 5, 0)*t

b) The yz plane is given by the equation x = 0.

x = 0  in the vector equation of a straight line if and only if  t = -2, than r ( - 2) = (0, -5, -5) is the desired intersection point.

Sneha actually got 2475 g of sugar instead of 2500 g.

We have,

If the shopkeeper uses a weight of 990 g for measuring 1 kg, it means that he is using a weight that is 10 g less than the actual weight of 1 kg.

So, the actual weight of 1 kg is 1000 g.

Now,
If Sneha bought 5/2 kg of sugar, she should have received:

= (5/2) x 1000 g

= 2500 g

But since the shopkeeper uses a weight of 990 g for measuring 1 kg, the weight of 5/2 kg would be:

= (5/2) x 990 g

= 2475 g

Thus,

Sneha actually got 2475 g of sugar instead of 2500 g.

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Answer:

Center: (-3, 2)

Radius: 4

Step-by-step explanation:

x2 + 6x + y2 - 4y = 3​

x² + 6x + 9 + y² - 4y + 4 = 3 + 9 + 4

(x + 3)² + (y - 2)² = 16

(x + 3)² + (y - 2)² = 4²

Center: (-3, 2)

Radius: 4

The sample proportion who said they pray is approximately 0.84, or 84%.

The sample proportion of college students who said they pray can be calculated by dividing the number of students who said they pray (105) by the total number of students in the sample (125).

Sample proportion = Number of students who said they pray / Total number of students in the sample

Sample proportion = 105 / 125

Sample proportion = 0.84

Therefore, the sample proportion who said they pray is approximately 0.84, or 84%.

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Answer:

ougylbhj,

Step-by-step explanation:

ulygkuyHold on, our servers are swamped. Wait for your answer to fully load

Step-by-step explanation:

The 'solution ' is the point where the two lines intersect :    ( 0,-1)

Using the conversion factor, we can convert the liters into the number of gallons of 1. 057 gallons.

A conversion factor is a mathematical ratio that is used to convert one unit of measurement to another. It is a multiplier or divisor that relates two different units of measurement for the same quantity.

To convert 4 liters into gallons using the conversion factor 1 gallon = 3.785 liters, you divide the given value (in liters) by the conversion factor.

This means that the number of gallons in 4 liters would be:

= 4 liters ÷ 3. 785 liters/gallon

= 1. 057 gallons

Therefore, 4 liters is approximately equal to 1. 057 gallons.

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The slope field for the differential equation would be D . Graph D .

A slope field provides a pictorial representation of differential equations that displays the magnitude and direction of the derivative or slope for solution curves at various points in the plane .

The length of line segments represents the magnitude, while the direction indicates the sign of the slope.

The equation given is y = 2 y + x which means that the slope is positive. This is why we can tell that Graph D has the correct slope field as it goes up for positive.

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The system of equations has infinitely many solutions, which corresponds to option (OB).

We can use the graphing function on a calculator to find the solution to the system of equations:

[tex]3y - 12x = 18\\\\2y - 8x = 12[/tex]

To do this, we can rearrange each equation to solve for y in terms of x:

[tex]3y = 12x + 18\\\\y =4x + 6[/tex]

For the second equation.

[tex]2y = 8x + 12\\\\y = 4x + 6[/tex]

We can see that the two equations have the same slope (4) and y-intercept (6). Therefore, the two equations represent the same line, and any point on that line will satisfy both equations.

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The volume of the rectangular pyramid is 144.48 cubic feet.

A pyramid with a rectangular base is known as a rectangle pyramid. When viewed from the bottom, this pyramid seems to be a rectangle. As a result, the base has two equal parallel sides.

The apex, which is located at the summit of the pyramid's base, serves as its crown. Right or oblique pyramids can be seen in rectangular shapes. If it is a right rectangular pyramid, the peak will be directly over the base's center; if it is an oblique rectangular pyramid, the apex will be angled away from the base's center.

The volume of a rectangular pyramid is given as:

[tex]\sf V = \dfrac{(l)(b)(h) }{3}[/tex]

[tex]\sf V = \dfrac{(8.4)(8.6)(6) }{3}[/tex]

[tex]\sf V = \dfrac{433.44 }{3}[/tex]

[tex]\sf V = 144.48 \ cubic \ feet[/tex].

Hence, the volume of the rectangular pyramid is 144.48 cubic feet.

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Answer:

Circumference = 87.92 yd

Step-by-step explanation:

We know that formula for circumference (C) of a circle is

C = πd, where d is the diameter.

We know that the diameter is twice the measure of the radius, so we can find the diameter of the circle by multiplying the radius by 2:

d = 2r

d = 2 * 14

d = 28 yd

Now, we can find circumference, remembering to use 3.14 for π

C = 3.14 * 28

C = 87.92 yd

The values of c  on the interval [-5, 5] are c = -[tex]5^{1/4[/tex]) and c = [tex]5^{1/4[/tex].

According to the Mean Value Theorem for Integrals, if f(x) is continuous on the interval [a, b], then there exists a value c in [a, b] such that:

f(c) = 1/(b-a) . ∫(a to b) f(x) dx

For f(x) = x⁴ on the interval [-5, 5], we have:

∫(-5 to 5) x⁴ dx = (1/5) . (5⁵ - (-5)⁵)/5

= (1/5) . (3125 + 3125)

= 1250

So we need to find c such that f(c) = 1250/10 = 125.

f'(x) = 4x³, so we can use the Mean Value Theorem for Derivatives to find a value of c that satisfies the condition.

f'(c) = (1/(5-(-5)))  . ∫(-5 to 5) f'(x) dx

= (1/10)  . [f(5) - f(-5)]

= (1/10) . [(5⁴) - ((-5)⁴)]

= 100

Therefore, by the Mean Value Theorem for Derivatives, there exists a value c in [-5, 5] such that f'(c) = 100.

Now, we need to check if there exists a value c in [-5, 5] such that f(c) = 125.

f(c) = c⁴, so we need to solve the equation c⁴ = 125.

c = ±[tex]5^{1/4[/tex]

Both of these values are in the interval [-5, 5], so they satisfy the Mean Value Theorem for Integrals.

Therefore, the values of c that satisfy the Mean Value Theorem for integrals for f(x) = x⁴ on the interval [-5, 5] are c = -[tex]5^{1/4[/tex]) and c = [tex]5^{1/4[/tex].

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Using the first two points we can get an exponential model:

[tex]y = (225/23)*(23/15)^x[/tex]

The general exponential equation can be written as:

[tex]y = A*(b)^x[/tex]

We can replace any two values of the table to get the system of eqautions:

[tex]15 = A*(b)\\\\23 = A*(b)^2[/tex]

Taking the quotient between the second and the first equation we get:

[tex]23/15 = (A*b^2)/(A*b)\\\\23/15 = b[/tex]

Replacing that on the first equation we will get:

[tex]15 =A*(23/15)\\15*(15/23) = A\\225/23 = A[/tex]

Then an exponential model is:

[tex]y = (225/23)*(23/15)^x[/tex]

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1. The equation of the form y = a • bˣ is y = 81 x (¹/₃)ˣ

2. His stamp should be worth approximately $7,851.47 after 6 years.

3. The equation of the form y = a • bˣ is y = (¹/₁₆) x 2²ˣ ⁺ ⁵

1. One will see that y is decreasing by a factor of 3 as x increases by 1. Therefore, we can write the equation as:

y = 81 x (¹/₃)ˣ

2. The increase in value of the stamp can be calculated using the formula:

V = P(1+r)ᵗ

where V is the future value, P is the present value, r is the annual interest rate as a decimal, and t is the number of years.

Substituting the given values:

V = 4900(1+0.075)⁶

V ≈ $7,851.47

Therefore, the stamp should be worth approximately $7,851.47 after 6 years.

3. One will see that y is increasing by a factor of 2 as x increases by 1. Therefore, we can write the equation as:

y = (1/16) x 2²ˣ ⁺ ⁵

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The percentage of buyers who paid between 150,000 and 153,300 is approximately 68% + 2.5% = 70.5%.

To solve this problem, we can use the properties of the normal distribution and the empirical rule (also known as the 68-95-99.7 rule) to estimate the percentage of buyers who paid between 150,000 and 153,300.

According to the empirical rule, given a normal distribution:

approximately 68% of the data falls within one standard deviation of the mean approximately 95% of the  three standard deviations of the mean, the data are contained.

In this case, we want to find the percentage of buyers who paid between 150,000 and 153,300, which is one interval of length 3300 above the mean. To use the empirical rule, we need to standardize this interval by subtracting the mean and dividing by the standard deviation:

z1 = (150,000 - 150,000) / 1100 = 0

z2 = (153,300 - 150,000) / 1100 = 3

Here, z1 represents the number of standard deviations between 150,000 and the mean, and z2 represents the number of standard deviations between 153,300 and the mean.

Since the interval we are interested in is within three standard deviations of the mean (z2 <= 3), we can use the empirical rule to estimate the percentage of buyers who paid between 150,000 and 153,300:

Approximately 68% of the buyers paid within one standard deviation of the mean, which is between 149,000 and 151,000 (using z-scores of -1 and 1).

Approximately 95% of the buyers paid within two standard deviations of the mean, which is between 148,000 and 152,000 (using z-scores of -2 and 2).

Therefore, the remaining percentage of buyers who paid between 152,000 and 153,300 is approximately (100% - 95%) / 2 = 2.5%.

So, the percentage of buyers who paid between 150,000 and 153,300 is approximately 68% + 2.5% = 70.5%.

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Answer:

3



Step-by-step explanation:

Area = 7pi/5

56/360 × pi r² = 7pi/5

Pi is canceled on both sides.

r² = 7/5 ÷ 56/360 = 9

r = root 9 = 3

The correct matrix representation is;  [tex]\left[\begin{array}{ccc}1&5\\3&2\end{array}\right][/tex]

Based on the coordinates of a vector, We can represent a vector pointing at a point by its x coordinate, and y coordinate,

Consider that there are two points represented by their x-, y coordinates as P₁(x₁,y₁) P₂(x₂,y₂)

Given here the points are P₁(1, 3) and P₂(5, 2)

Thus, by the coordinates of the two vectors, we can represent the matrix  ;

[tex]\left[\begin{array}{ccc}1&5\\3&2\end{array}\right][/tex]

Hence, Option A) is the correct answer.

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[tex]y \geq -3x + 2\\\\y \leq x + 3[/tex]

is the equation of the given system.

Equation of the line using the coordinates (-3, 0) and (0, 3), we get:

slope = (3 - 0) / (0 - (-3)) = 1

Now we have the slope of the line. Next, we can use the point-slope form of the equation of a line, which is:

y - y1 = m(x - x1)

where m is the slope and (x1, y1) is a point on the line.

Using the point (-3, 0) and the slope we just found (which is also the slope of the line passing through the point (0, 3)), we get:

y - 0 = 1(x - (-3))

Simplifying, we get:

y = x + 3

Therefore, the equation of the line passing through (-3, 0) and (0, 3) is y=x+3.

Similarly, the equation of the line passing through (1, -1) and (0, -4) is y = -3x + 2.

Thus, from the graph the equation of the system is,

[tex]y \geq -3x + 2\\\\y \leq x + 3[/tex]

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The factored form of x² + 12 using the difference of squares formula is

(x + 2√3)(x - 2√3).

We have,

To factor x² + 12 using the difference of squares formula, we need to express it as the difference between two squares:

x² + 12 = x² + (2√3)²

Now we can use the difference of squares formula, which states that:

a² - b² = (a + b)(a - b)

In this case, we have a = x and b = 2√3. So we can write:

= x² + 12

= x² + (2√3)²

= (x + 2√3)(x - 2√3)

Therefore,

The factored form of x² + 12 using the difference of squares formula is

(x + 2√3)(x - 2√3).

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Answer:

34

Step-by-step explanation:

1. Plug in the week's salary into the formula

S=400+35v

1590=400+35v

2. Solve for v.

1590=400+35v

Subract 400 from both sides. Since the opposite of addition is subraction, soing this cancels out the 400.

1190=35v

Divide each side by 35. Since the opposite of multiplication (35v = 35 times v) is division, this will cancel out the 35.

34=v

The equation of the line that passes through point (-3,-7) and point (-3,10) is x = -3.

The formula for equation of line is expressed as;

y = mx + b

Where m is slope and b is y-intercept.

Given the points through which the line passes: (-3,-7) and (-3,10).

The two given points (-3, -7) and (-3, 10) have the same x-coordinate -3

Hence, the two lines  lie on a vertical line.

since the slope of the vertical line is undefined.

The equation of the line passing through these two points is simply the equation of the vertical line:

x = -3

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The three equivalent equations are 2 + x = 5, x + 1 = 4 and -5 + x = -2. So, correct options are A, B and E.

Two equations are considered equivalent if they have the same solution set. In other words, if we solve both equations, we should get the same value for the variable.

To determine which of the given equations are equivalent, we need to solve them for x and see if they have the same solution.

Let's start with the first equation:

2 + x = 5

Subtract 2 from both sides:

x = 3

Now let's move on to the second equation:

x + 1 = 4

Subtract 1 from both sides:

x = 3

Notice that we got the same value of x for both equations, so they are equivalent.

Next, let's look at the third equation:

9 + x = 6

Subtract 9 from both sides:

x = -3

Since this value of x is different from the previous two equations, we can conclude that it is not equivalent to them.

Now, let's move on to the fourth equation:

x + (-4) = 7

Add 4 to both sides:

x = 11

This value of x is also different from the first two equations, so it is not equivalent to them.

Finally, let's look at the fifth equation:

-5 + x = -2

Add 5 to both sides:

x = 3

Notice that we got the same value of x as the first two equations, so this equation is also equivalent to them.

So, correct options are A, B and E.

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Complete question is:

Which of the following equations are equivalent? Select three options.

2 + x = 5

x + 1 = 4

9 + x = 6

x + (- 4) = 7

- 5 + x = - 2

The amount of poster board left over will be 1275 square inches, the equation used is  A = (b₁ + b₂)h/2.

To calculate the amount of poster board that will be left over after Ole cuts out a piece of poster board that is the same size as the window,

we need to find the area of the trapezoid window and subtract it from the area of the poster board.

The formula to find the area of a trapezoid is A = (b₁ + b₂)h/2, where b₁ and b₂ are the lengths of the parallel sides and h is the height.

Let's assume that the length of the top parallel side of the trapezoid is 20 inches, the length of the bottom parallel side is 10 inches, and the height is 15 inches.

Using the formula, we get A = (20 + 10) x 15 / 2 = 225 square inches. This is the area of the window.

To find the area of the poster board, we multiply the length and width, which gives 25 x 60 = 1500 square inches.

Finally, we subtract the area of the window from the area of the poster board using the equation:

1500 - 225 = 1275 square inches.

Therefore, the amount of poster board left over will be 1275 square inches.

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The complete question is

Ole has a window that has the dimensions and shape like the trapezoid shown below. He also has a large rectangular piece of poster board that measures 25 inches by 60 inches. If Ole cuts out a piece of poster board that is exactly the same size as the window, which equation can be used to calculate the amount of poster board that will be left over?