The three graphs represent the progress of three runners in a 500-meter race.
The red solid line represents runner A. The purple dotted line represents runner B.
The blue dashed line represents runner C.

Options: Runner A, Runner B, Runner C, 0, 20, 55, 90.

Slope line formula is used for determining the slope of a line. Based on the given points, the slope of line is 2/3.

To find the slope of the line passing through the given points, we can use the slope formula, which states that the slope of a line passing through two points (x1, y1) and (x2, y2) is given by the expression:

slope = (y2 - y1) / (x2 - x1)

Using this formula, we can calculate the slope of the line passing through the three given points as follows:

slope = (2 - (-2)) / (3 - (-3)) = 4/6 = 2/3

Therefore, the slope of the line passing through the given points is 2/3.

Alternatively, we can observe that the three points are collinear and lie on the same straight line. We can use this fact to find the slope of the line by computing the rise over run between any two of the points. For example, using the points (0,0) and (-3,-2), we have a rise of 2 and a run of 3, so the slope is 2/3. This confirms that the slope of the line passing through the given points is 2/3.

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The volume of a sphere is 1,436.03 cubic cm. Thus, the correct option is E.

Let r be the radius of the sphere. Then the volume of the sphere will be given as,

V = 4/3 πr³ cubic units

Sand is contained within a spherical with a 14 centimeters diameter. Roberto emptied the sphere's contents of sand.

The radius of the sphere is given as,

r = d/2

r = 14 / 2

r = 7 cm

Then the volume of the sphere is given as,

V = (4/3) x π x (7)³

V = 1.33 x 3.14 x 343

V = 1,436.03

The volume of a sphere is 1,436.03 cubic cm. Thus, the correct option is E.

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The correct options are given below.

A. 287.2 cm³

B. 861.6 cm³

C. 1,148.8 cm³

D. 9,190.6 cm³

E. 1,436.03 cm³

You have to  spend $26,500 over the course of the first year with rent and equipment.

To calculate how much money you will spend over the course of the first year with rent and equipment, you need to add the cost of rent to the cost of equipment.

In a hypothetical scenario, Let's assume that the cost of rent for the first year is $1,500 per month.

To calculate the total cost of rent for the first year, you can multiply the monthly rent by the number of months in a year:

$1,500/month x 12 months = $18,000

So the total cost of rent for the first year is $18,000.

To calculate the total cost of equipment, you can take the average cost of the equipment (i.e., the midpoint of the given range) and assume that you will spend that amount:

($7,000 + $10,000) / 2 = $8,500

So the total cost of equipment is $8,500.

To calculate the total cost of rent and equipment for the first year, you can add the two costs together:

$18,000 + $8,500 = $26,500

Therefore, you will spend $26,500 over the course of the first year with rent and equipment.

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The measure of each angle and side is given above.

Given is that the red triangle is a dilation of the blue triangle, with a scale factor of {k} = 1.5.

We can write -

57/RT = 1.5

RT = 57/1.5

RT = 38

LM/20 = 1.5

LM = 20 x 1.5

LM = 30

MN/26 = 1.5
MN = 26 x 1.5
MN = 39

∠2 = 15°

∠1 = 121°

Therefore, the measure of each angle and side is given above.

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Answer:

p = 23

Step-by-step explanation:

using the rules of exponents

• [tex](a^m)^{n}[/tex] = [tex]a^{mn}[/tex]

• [tex]a^{m}[/tex] × [tex]a^{n}[/tex] = [tex]a^{(m+n)}[/tex]

then

[tex](x^3)^{5}[/tex] ([tex]x^{8}[/tex] )

= [tex]x^{3(5)}[/tex] × [tex]x^{8}[/tex]

= [tex]x^{15}[/tex] × [tex]x^{8}[/tex]

= [tex]x^{(15+8)}[/tex]

= [tex]x^{23}[/tex]

= [tex]x^{p}[/tex] ← with p = 23

Answer: a) ZY = 27

b) WY = 27

c) RX = 27

d) mWRZ = 90 degrees

e) mXYZ = 90 degrees

f) mZWY = 90 degrees

Step-by-step explanation:

The coordinates of the fourth vertex D = (3,−1.5).

A parallelogram has the following property AB=DC

AB=OB−OA=(3,3)−(1,5)=(2,−2)

DC=OC−OD=(8,3)−(a,b)=(2,−2)

OD=OC−DC=(8,3)−(2,−2)=(6,5)

Turn them into vectors. Position vector of point d

should be 6,5

To get the 2nd point, just do AD=BC

BC=OC−OB=(8,3)−(3,3)=(5,0)

AD=OD−OA=(a,b)−(1,5)=(5,0)

OD=OA−AD=(1,5)−(5,0)=(−4,5)

As long as the shape has four sides and two of them are parallel, and you know the length, this should work. For instance, a trapezium where AB=2DC/2CD:

A=(0,0),B=(2,0),C=(2,−1.5),D=(a,b)

AB=(2,0)DC=(2,−1.5)−(a,b)=12(2,0)(a,b)=(1,−1.5)

OR

AB=(2,0)CD=(a,b)−(2,−1.5)=12(2,0)(a,b)=(3,−1.5)

Thus, The coordinates of the fourth vertex D = (3,−1.5).

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The value of the final velocity before striking the ground will be 9.899 meters per second.

The quantity which has magnitude, and direction, and follows the law of vector addition is called a vector.

If an object is projected horizontally from a height of 5m with an initial velocity of 7 m/s.

We know that if the object is projected horizontally, so initially the object has a vertical speed is zero. Then it increases due to acceleration due to gravity.

The speed of the object before striking the ground is given as,

v² - u²= 2gh

v² - 0² = 2 × (9.8) × (5)

v² = 98

v = 9.899 meters per second

The value of the final velocity before striking the ground will be 9.899 meters per second.

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Answer:

14 cm

Step-by-step explanation:

The formula for circumference of a circle is 2πr, where r is the radius. In this problem, the circumference would be 2π * 7cm = 14 cm

Answer:

To determine the balance in the Allowance for Doubtful Accounts on December 31, we first need to estimate the bad debts based on the credit sales.

Bad debts = 2% of credit sales = 2% * $400,000 = $8,000

The balance in the Allowance for Doubtful Accounts would then be equal to the estimated bad debts, which is $8,000.

Therefore, the Accounts Receivable and the Allowance for Doubtful Accounts would appear on the December 31 balance sheet as follows:

Current Assets:

Accounts receivable $120,000

Less: Allowance for doubtful accounts $8,000

Net accounts receivable $112,000

We can state that the y-intercept is (0,4) and the x-intercept is after answering the given question (2,0).

The intersection point in mathematics is where the line's slope intersects the y-axis. a point where a line or curve's y-axis crosses it. [tex]Y = mx+c,[/tex]

The emphasis in the intercept form of the equation is on the line's slope (m) and y-intercept (b). The slope is m and the y-intercept is b when an equation has the intercept form (y=mx+b).

It is also possible to rewrite some equations so that they appear to be slope intercepts. For example, the slope and y-intercept are both modified to 1 if y=x is rewritten as [tex]y=1x+0.[/tex]

Slope intercept equation,

[tex]y = -2x + 4[/tex]

[tex]y = -2(0) + 4[/tex]

X-intercept is (2,0).

Therefore, The equation for the straight line is used to demonstrate this, where m denotes the slope and c the y-intercept.

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The balance in the account after 16 years, given interest rate and the compounding period, is $ 10, 421. 83.

To find the balance after 16 years, the formula to be used is the compound interest formula which is:

= Amount invested x ( 1 + rate ) ^ number of periods

Rate :

= 6 % / 12 months per year

= 0. 5 %

The number of periods :

= 16 years x 12 months a year

= 192 periods

The value would be :

= 4, 000 x ( 1 + 0. 5% ) ¹⁹²

= $ 10, 421. 83

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Answer:we can’t help if it is barely readable

Step-by-step explanation:

Answer:

(a) The probability distribution for the number of female students admitted can be calculated as follows:

P(0 female students) = (2C0) × (3C2) / (5C2) = (1) × (3) / (10) = 0.3

P(1 female student) = (2C1) × (3C1) / (5C2) = (2) × (3) / (10) = 0.6

P(2 female students) = (2C2) × (3C0) / (5C2) = (1) × (1) / (10) = 0.1

(b) The sampling distribution of the sample proportion of female students selected can be calculated as follows:

P(p = 0) = 0.3 (for 0 female students)

P(p = 1/2) = 0.6 (for 1 female student)

P(p = 1) = 0.1 (for 2 female students)

Note that the sampling distribution of the sample proportion is a discrete probability distribution with values of 0, 1/2, and 1, and corresponding probabilities 0.3, 0.6, and 0.1, respectively.

Answer:

HI

The scale fact from the smaller to the larger is 3.  The scale factor from the larger to the smaller is 1/3

Step-by-step explanation:

Answer:

C = 60t + 100

Step-by-step explanation:

our flat fee is 100 dollars, meaning you're charged straight up $100, and then for each hour the electrician works, you're charged another $60

this means that 100 stays constant, while the amount of times you multiply 60 changes based on the amount of hours the electrician works

therefore, our equation will be C = 60t + 100, where C represents the total cost while t represents the hours the electrician works

for our table, we can use the equation we just found to make one

the easiest and most reasonable numbers will be 1, 2, 3, 4, and 5, because it's unreasonable to charge a proportional amount for something such as 1.2948 hours

using the equation, we plug 1, 2, 3, 4, and 5 into C = 60t+100 to find C for t

C = 160, 220, 280, 340, 400

T = 1, 2, 3, 4, 5

The largest power of 10 that is a factor of 1000! is 5^249, or 10^249.

(a) To find the largest power of 10 that is a factor of 50!, we need to count the number of factors of 5 in 50! since each factor of 5 contributes at least one factor of 10.

There are 10 multiples of 5 in 50!, namely 5, 10, 15, 20, 25, 30, 35, 40, 45, and 50. Each of these contributes one factor of 5. There are also 2 multiples of 25 (25 and 50), each of which contributes an additional factor of 5. Therefore, the total number of factors of 5 in 50! is 10 + 2 = 12.

Since each factor of 10 contains one factor of 5 and one factor of 2, we also need to count the number of factors of 2. It is clear that there are more factors of 2 than factors of 5, so we only need to count the factors of 5. Therefore, the largest power of 10 that is a factor of 50! is 5^12, or 10^12.

(b) To find the largest power of 10 that is a factor of 1000!, we follow the same reasoning as in part (a). The number of factors of 5 in 1000! is:

⌊1000/5⌋ + ⌊1000/25⌋ + ⌊1000/125⌋ + ⌊1000/625⌋ = 200 + 40 + 8 + 1 = 249

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The ratio of the areas of the quadrilaterals is 1:2. Option A

Let's assume that the two similar quadrilaterals have side lengths of x and 2x, respectively. The ratio of their perimeters is then 2x + 2x + 2x + 2x = 8x : 2 * (2x + 2x + 2x + 2x) = 4 * 8x = 32x. The ratio of the perimeters is 2:4, so we can write the equation:

8x/32x = 2/4

Solving for x, we find that x = 4.

So the ratio of the areas of the two similar quadrilaterals is (x^2)/(2x)^2 = (4^2)/(2 * 4^2) = 16/32 = 1/2.

Therefore, the ratio of the areas of the two similar quadrilaterals is 1:2.

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The equation of the circle is (x -2)² + (y+1)² = 16.

What is an equation of a circle?

A circle is the collection of all points on a plane at a specific radius from a specific point (called the center.) The diameter of a circle is the length of a line that connects two locations on the circle and passes through its center. Assume that a point's coordinates on the shown circle are (x,y). The radius is r, and the center is at (h,k).

Here according to the graph, the center of the circle is (2,-1), and the radius of the circle = 2+2=4 unit.

Now using the circle equation then

(x -p)² + (y-q)² = r²

Where p = 2 , q = -1 and r = 4 then

(x -2)² + (y+1)² = 4²

(x -2)² + (y+1)² = 16

Hence, the equation of the circle is (x -2)² + (y+1)² = 16.

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Answer:

Step-by-step explanation:

The cross-price elasticity of demand measures the responsiveness of the quantity demanded of one good to a change in the price of another good. In other words, it shows how the demand for one good changes in response to changes in the price of another good. The cross-price elasticity of demand is a useful concept for understanding the relationship between two goods and can provide valuable information for firms in making pricing and marketing decisions.

The formula for cross-price elasticity of demand is as follows:

Cross-price elasticity of demand = (Percentage change in quantity demanded of good A) / (Percentage change in price of good B)

In this case, we are calculating the cross-price elasticity of demand between almond milk and oat milk. To do this, we first need to calculate the percentage change in quantity demanded of oat milk and the percentage change in price of almond milk.

Percentage change in quantity demanded of oat milk = (30,000 - 20,000) / 20,000 = 0.5

Percentage change in price of almond milk = ($5 - $3) / $3 = 0.67

Next, we use these values to calculate the cross-price elasticity of demand:

Cross-price elasticity of demand = 0.5 / 0.67 = 0.74

A positive cross-price elasticity of demand indicates that the two goods are substitutes. This means that as the price of one good increases, the demand for the other good increases. A cross-price elasticity of demand between 0 and 1 indicates that the two goods are weak substitutes. In this case, a cross-price elasticity of demand of 0.74 suggests that almond milk and oat milk are weak substitutes. This means that if the price of almond milk were to increase, the demand for oat milk would increase to some extent, but not by a significant amount.

In conclusion, the cross-price elasticity of demand provides valuable information for firms in making pricing and marketing decisions. A positive cross-price elasticity of demand indicates that two goods are substitutes, while a cross-price elasticity of demand between 0 and 1 suggests that they are weak substitutes.

Answer:

c) 6

Step-by-step explanation:

in a 45-45-90 degree triangle the hypotenuse is [tex]\sqrt{2}[/tex] times more than the length of the other sides

3[tex]\sqrt{2}[/tex] × [tex]\sqrt{2}[/tex] is the same as 3(2) or 6

The length of the hypotenuse of the triangle is,

⇒ h = 6

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

Base of triangle = 3√2

Length of triangle = 3√2

Now, We can formulate;

⇒ h² = (3√2)² + (3√2)²

⇒ h² = 18 + 18

⇒ h² = 36

⇒ h = 6

Thus, The length of the hypotenuse of the triangle is,

⇒ h = 6

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Answer: A lot

Step-by-step explanation:

The graph of the quadratic equation y = -x² - 1 is on the image at the end.

Here we want to graph the quadratic function:

y = -x² - 1

To do so, we need to find some points on the quadratic equation's graph, we can evaluate the equation in sokme values of x to get that.

if x = 0

y = -0² - 1 = -1

if x = 1

y = -1² - 1 = -2

if x = -1

y = -(-1)² - 1 = -2

And so on.

Above we can see that we have the points (0, -1), (1, -2), and (-1,-2) (you could try to find more points, so the graph will be more exact).

Now just graph all the points that you have and connect them with a parabola. The graph can be seen on the image at the end.

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Answer:

Step-by-step explanation:

-0.2x+3 / 2 = -0.6 =>

-0.2x = -(3/2) - 0.6 => (facotorize out -1)

x = ((3/2)-0.6)/0.2 =>

x = 4.5

f(x) = a(b)*.

Question 1 Part C

During their team meeting both managers shared their findings. Complete the statement describing their combined results.

Double click and highlight the correct answers

• the initial number of video views was - fewer than, the same as, more than- the initial number of site visits

• The number of website visits grew by a - smaller factor than, larger factor than, the same factor as- the number of video views.

• The difference between the total number of website visits and video views after 4 weeks is - 10,935, 4,690, 8,726, 15,625

Answer:

10,935, 4,690, 8,726, 15,625

Step-by-step explanation:

The value of the equation for x is 32

PEDMAS is described as a mathematical acronym that represents the important operations during calculations.

The alphabets represents;

From the information given, we have;

-(-2)+√(-2)²-4(1)(-8)

expand the brackets

2 + -2 -4(-8)

multiply the values

2 -2 + 32

Add the values

32

Hence, the value is 32

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Answer:

The correct answer is C, 428 feet.

To calculate the elevation of the marked point, we need to interpolate between the two contour lines. The difference in elevation between the two contour lines is 20 feet (440 - 420 = 20). And since the distance between the two contour lines is 0.5 inches, each 0.1 inch increment represents a 4-foot change in elevation (20 feet ÷ 0.5 inches = 40 feet per inch ÷ 10 = 4 feet per 0.1 inch).

Since the marked point is 0.2 inches from the 420-foot contour, the elevation of the marked point can be calculated by adding 8 feet (4 feet x 0.2 inches) to the 420-foot contour line: 420 + 8 = 428 feet.

Answer:

Below

Step-by-step explanation:

r = 1/2 diameter = 4 x^2 y^2

Volume = pi  r^2 h =

            pi  (4 x^2 y^2 )^2   * ( 12 x^2 y^2 ) =

               16 x^4 y^4   *  12 x^2 y^2  * pi

             =  192 x^(4+2) y^(4+2)  pi

             = 192 x^6 y^6  pi