Find the measure of the supplementary angles that satisfy each case. m<1 is less than m<2 by 40 degrees

Help Center to Water Slide #1: Level line, y = 3. Toddler area to Concessions: Negative incline, y = (-1/3)x - 7. Gift Shop to Restrooms: Level line, y = -9. Security desk to Water Slide #2: Even line, y = 4. Lazy river to large Whirlpool: Positive incline, y = (2/5)x + 61/5.

To calculate the slope between attractions and discover the midpoints, we'll utilize the given requested sets for each fascination. Here are the calculations:

Help Center to Water Slide #1:

Slope = ((y2 - y1) / (x2 - x1)) = ((3 - 3) / (-6 - 2)) = / -8 =

Midpoint = ((x1 + x2) / 2), ((y1 + y2) / 2)) = ((2 + (-6)) / 2), ((3 + 3) / 2)) = (-2, 3)

Toddler area to Concessions:

Slope = ((y2 - y1) / (x2 - x1)) = ((-6 - (-3)) / (6 - (-3)) = (-3 / 9) = -1/3

Midpoint = ((x1 + x2) / 2), ((y1 + y2) / 2)) = ((-3 + 6) / 2), ((-9 + (-6)) / 2)) = (1.5, -7.5)

Gift Shop to Restrooms:

Slope = ((y2 - y1) / (x2 - x1)) = ((-9 - (-9)) / (8 - 2)) = / 6 =

Midpoint = ((x1 + x2) / 2), ((y1 + y2) / 2)) = ((8 + 2) / 2), ((-9 + (-9)) / 2) = (5, -9)

Security desk to Water Slide #2:

Slope = ((y2 - y1) / (x2 - x1)) = ((4 - 4) / (16 - 5)) = / 11 =

Midpoint = ((x1 + x2) / 2), ((y1 + y2) / 2)) = ((5 + 16) / 2), ((4 + 4) / 2) = (10.5, 4)

Lazy River to Large Whirlpool:

Slope = ((y2 - y1) / (x2 - x1)) = ((10 - 14) / (-7 - 3)) = (-4 / -10) = 2/5

Midpoint = ((x1 + x2) / 2)), ((y1 + y2) / 2)) = ((-7 + 3) / 2), ((10 + 14) / 2)) = (-2, 12)

Presently, let's calculate the linear equations for each case:

Help Center to Water Slide #1:

The Slope is 0, and the y-coordinate is consistent, so the equation is y = 3.

Toddler area to Concessions:

The Slope is -1/3, and the y-intercept can be calculated utilizing the midpoint facilitates:

-7.5 = (-1/3)(1.5) + b

-7.5 = -0.5 + b

b = -7

Gift Shop to Restrooms:

The Slope is 0, and the y-coordinate is steady, so the equation is y = -9.

Security desk to Water Slide #2:

The Slope is 0, and the y-coordinate is steady, so the equation is y = 4.

Lazy River to Large Whirlpool:

The Slope is 2/5, and the y-intercept can be calculated utilizing the midpoint arranges:

12 = (2/5)(-2) + b

12 = -4/5 + b

b = 61/5

The Linear equations for each case are as follows:

Help Center to Water Slide #1: y = 3

Toddler area to Concessions: y = (-1/3)x - 7

Gift Shop to Restrooms: y = -9

Security desk to Water Slide #2: y = 4

Lazy River to Large Whirlpool: y = (2/5)x + 61/5

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Answer:

Volume of a cone = 1/3πr²h

h = height

r = radius

r = 3cm h = 4cm

Volume = 1/3π(3)²(4)

= 36 × 1/3π

= 12π

= 36.69cm³

= 37cm³ to the nearest tenth

Hope this helps

Answer:

37.7

_______

NOT 37

Step-by-step explanation:

v = \(\frac{1}{3}\) · \(\pi\) · \(r^{2}\) · \(h\)

v = \(\frac{1}{3}\) · \(\pi\) · \(3^{2}\) · \(4 = 12\pi = 37.69911 =\) 37.7

Answer: $0.576

Step-by-step explanation:

The total amount in prizes is $1800.

For there to be 60% profit, the total cost of the tickets need to be \(1800(1.6)=\$ 2880\).

Thus, each ticket must sell for \(\frac{2880}{5000}=\$ 0.576\)

a. Sketch the region of integration in the XY-plane.

b. Reverse the order of integration.

c. Evaluate the integral.

(a) The integral is a double integral, which means that the region of integration is a region in the XY plane. The region of integration is defined by the limits of integration for x and y. However, since the limits of integration are not given, it's not possible to sketch the region of integration in the XY plane.

(b) The integral is already written with the order of integration reversed.

(c) Without the limits of integration, it is not possible to evaluate the integral. The limits of integration are necessary to determine the region of integration, and thus the range of values for x and y over which the integral is to be taken. Without this information, it is not possible to carry out the evaluation of the integral.

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Answer:

  14

Step-by-step explanation:

The number that did hit the bullseye is ...

  0.30 × 20 = 6

So, the number that did not is ...

  20 -6 = 14

14 of Jack's darts did not hit the bullseye.

By applying the features of polynomials, the quadratic function g(x) = (1/5) · x² - 2 · x + 21/5 passes through the points (x₁, y₁) = (-8, 33), (x₂, y₂) = (2, 1) and (x₃, y₃) = (8, 1).

Polynomials are algebraic expressions of the form \(\sum \limits_{i=0}^{n} c_{i}\cdot x^{i}\), where \(c_{i}\) is the i-th coefficient of the polynomial and n is the grade of the polynomial. In addition, we know that polynomials have n + 1 coefficients.

In the case of quadratic functions, the grade is 2 and the function have three coefficients. Hence, we need three distinct points to determine all the coefficients of a quadratic function.

(x₁, y₁) = (-8, 33)

64 · a - 8 · b + c = 33     (1)

(x₂, y₂) = (2, 1)

4 · a + 2 · b + c = 1     (2)

(x₃, y₃) = (8, 1)

64 · a + 8 · b + c = 1     (3)

Then, we find the solution of this system of linear equations:

a = 1/5, b = -2, c = 21/5

By applying the features of polynomials, the quadratic function g(x) = (1/5) · x² - 2 · x + 21/5 passes through the points (x₁, y₁) = (-8, 33), (x₂, y₂) = (2, 1) and (x₃, y₃) = (8, 1).

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Answer:

Um.... Wouldn't angle 1 just be 180-17 which is 163. Angle 3 would be equal to angle 1 so also 163. Angle 4 and angle 2 are equal to 17.

Step-by-step explanation:

Answer:

angle1 = 163°

angle2 = given in diagram

angle 3 = alternating angle 1, so 163°

angle 4 = alternating angle 2, so 17°

Step-by-step explanation:

noticing that the two lines intercept each other at the centre, making angles going around that interception point add up to 360° (you can use this information to check the answers).

an angle on a straight line is always 180°, so given that angle2 is 17°, you can already do 180 - 17 to get an easy answer to angle 1 and 3.

Answer:

\(4x + 3 + x + 27 = 180\\\\5x + 30 = 180\\\\5x = 150\\\\x = 30\)

Both the coordinate points are plotted on the graph. The cartesian graph is attached with the answer.

Given are the two coordinates to be plotted on a Cartesian plan -

(5, 4) , (3, 4).

The two given coordinate points are (5, 4) , (3, 4).

Refer to the graph attached. It shows both the points plotted.

Therefore, both the coordinate points are plotted on the cartesian graph.

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Answer:

The impulse on an object is equal to the change in momentum of the object. In this case, the ball's initial momentum is 10 kg * 15 m/s = 150 kg m/s. After the collision, the ball's final momentum is -10 kg * 23 m/s = -230 kg m/s.

The change in momentum of the ball is: -230 kg m/s - 150 kg m/s = -80 kg m/s.

So, the impulse on the ball is -80 kg m/s.

The surface area of the cylinder is 131.88 in².

A cylinder is a three-dimensional figure that has a radius and a height.

The volume of a cylinder is given as:

Example:

The volume of a cup with a height of 5 cm and a radius of 2 cm is

Volume = 3.14 x 2 x 2 x 5 = 62.8 cubic cm

We have,

The surface area of the cylinder = 2B + P h

Where B is the base area and P is the perimeter.

B = πr² and P = 2πr

Now,

We will assume that,

The radius of the cylinder = 3 in.

The height of the cylinder = 4 in.

So,

The surface area of the cylinder.

= 2B + P h

= 2πr² + 2πrh

= 2 x 3.14 x 3² + 2 x 3.14 x 3 x 4

= 56.52 + 75.36

= 131.88 in²

Thus,

131.88 in² is the surface area of the cylinder.

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Answer:

9.5ft is the answer

Answer:

9.5 ft.

Step-by-step explanation:

Answer:

Step-by-step explanation:

x=2 and x = 5 and x = 8

341,427 mod 3 = 0

341457 mod 3 = 0

341487 mod 3 = 0

Product =2 x 5 x 8 = 80

\(s = \frac{cardinality(s)}{cardinality( \omega)} = \frac{15}{100} = \frac{1.5}{100} \)

The shaded region represents 1.5 grids

\(1.5 = 1 \frac{0.5}{1} = 1 \frac{5}{10} = 1\frac{1}{2} \)

Answer:

D

Step-by-step explanation:

The answer and work is in the attached screenshot! :)

Answer

Check Explanation

Explanation

The slope and y-intercept form of the equation of a straight line is given as

y = mx + b

where

y = y-coordinate of a point on the line.

m = slope of the line.

x = x-coordinate of the point on the line whose y-coordinate is y.

b = y-intercept of the line.

So, the intercept is just written as the point where the line crosses the y-axis.

For a straight line, the slope of the line can be obtained when the coordinates of two points on the line are known. If the coordinates are (x₁, y₁) and (x₂, y₂), the slope is given as

So, all that is required to write the slope-intercept equation of a line is two points on the line and the point where the slope crosses the y-axis.

Hope this Helps!!!

Answer:

The answer is in the file below, I wasn't able to make it in text form.

Avoidable costs are costs that can be eliminated if the activity that caused them is discontinued. The examples are listed.

Direct materials: Direct materials are the materials that go into a product and can be easily traced to it. For example, the wood used to make a table is a direct material. If a company decides to stop making tables, it can avoid the cost of buying wood.

Direct labor: Direct labor is the labor that is directly involved in making a product. For example, the wages paid to the workers who assemble a car are direct labor. If a company decides to stop making cars, it can avoid the cost of paying direct labor.

Variable overhead: Variable overhead is the overhead costs that vary with the number of units produced. For example, the cost of electricity used to power a factory is a variable overhead cost. If a company decides to stop producing a product, it can avoid the variable overhead costs associated with that product.

Sunk costs: Sunk costs are costs that have already been incurred and cannot be recovered. For example, the cost of research and development for a new product is a sunk cost. If the company decides not to launch the product, it cannot recover the cost of research and development.

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Answer:

15 is divided by a number

Answer:

$131250

Step-by-step explanation:

Talia's earnings during one year are equal to her base yearly salary ($65000) added to her commission. Now, to know the commission it is necessary to find the 2.65% of her total sales ($2.5 million)

Step 1. Divide the total sales or 2,500,000 by 100 considering this represents the total or 100%

2,500,000 ÷ 100 = 25000

Step 2. Multiply this number by the specific percentage (2.65)

25000 x 2.65 = 66250

Now add the commission and the yearly salary

65000 + 66250 = 131250

Hence, total earnings of Talia were $131250

Answer:

Step-by-step explanation:

For the first question/part:

For the second question/part:

I hope this helps!

Answer:

Now you can mark the other girl brainliest

Step-by-step explanation:

Answer:

27.58% probability that the mean diameter of the sample shafts would differ from the population mean by greater than 0.2 inches

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean \(\mu\) and standard deviation(which is the square root of the variance) \(\sigma\), the zscore of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \(\mu\) and standard deviation \(\sigma\), the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \(\mu\) and standard deviation \(s = \frac{\sigma}{\sqrt{n}}\).

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this question, we have that:

\(\mu = 211, \sigma = \sqrt{2.89} = 1.7, n = 86, s = \frac{1.7}{\sqrt{86}} = 0.1833\)

What is the probability that the mean diameter of the sample shafts would differ from the population mean by greater than 0.2 inches.

Either greater than 211 + 0.2 = 211.2 or smaller than 211 - 0.2 = 210.8. Since the normal distribution is symmetric, these probabilities are equal, so we find one of them and multiply by 2.

Probability of being less than 210.8:

This is the pvalue of Z when X = 210.8. So

\(Z = \frac{X - \mu}{\sigma}\)

By the Central Limit Theorem

\(Z = \frac{X - \mu}{s}\)

\(Z = \frac{210.8 - 211}{0.1833}\)

\(Z = -1.09\)

\(Z = -1.09\) has a pvalue of 0.1379

Probability of differing from the population mean by greater than 0.2 inches :

2*0.1379 = 0.2758

27.58% probability that the mean diameter of the sample shafts would differ from the population mean by greater than 0.2 inches

Answer:

Probability is 86.24%

Step-by-step explanation:

We can solve this by using the Z-score formula.

Z = (X - μ)/σ

Where;

μ is mean = 211 inches

σ is standard deviation

Now, we are given variance as 2.89

Formula for standard deviation using variance is;

SD = √variance

SD = √2.89

SD = 1.7

To find the probability that the mean diameter of the sample shafts would differ from the population mean by greater than 0.2 inches, we will find the p-value of z and subtract 1 from it.

Since we are told that the sample shafts would differ by 0.2 inches, thus;

X = 211 + 0.2 = 211.2

Since we are working with sample mean of 86, then we have;

Z = (X - μ)/s

s = σ/√86

s = 1.7/√86

s = 0.1833

So,

Z = (211.2 - 211)/0.1833

Z = 1.0911

From z-score calculator, the p-value is gotten to be 0.1376

Thus, probability that mean diameter of the sample shafts would differ from the population mean by greater than 0.2 inches is;

Probability = 1 - 0.1376 = 0.8624 = 86.24%

Answer:

  y =  {-180, 2 8/11}

Step-by-step explanation:

I like to solve these using a graphing calculator. I generally start by writing the equation in the form ...

  f(y) = 0

This can be done by subtracting the right-side expression from both sides. The solution will be the horizontal intercepts of the graph:

  y = -180; y = 2 8/11

__

To solve this analytically, you need to recognize that this resolves into four equations, effectively two identical pairs. Each equation comes with a set of conditions (domain) for which it is applicable. Here is the expanded set of equations:

  1/3y -7 = 2/5y +5 . . . both positive: 1/3y -7 ≥ 0 and 2/5y + 5 ≥ 0

  7 -1/3y = 2/5y +5 . . . left side negative: 1/3y -7 ≤ 0 and 2/5y +5 ≥ 0

  1/3y -7 = -2/5y -5 . . . right side negative: 1/3y -7 ≥ 0 and 2/5y +5 ≤ 0

  7 -1/3y = -2/5y -5 . . . both sides negative: 1/3y -7 ≤ 0 and 2/5y +5 ≤ 0

__

The conditions resolve to ...

  1/3y -7 ≥ 0

  y -21 ≥ 0 . . . . . multiply by 3

  y ≥ 21 . . . . . . . add 21

and ...

  2/5y +5 ≥ 0

  y +25/2 ≥ 0 . . . . multiply by 5/2

  y ≥ -25/2 . . . . . subtract 25/2

Now, we are in a position to solve the equations and determine where the solution is applicable.

__

both positive

The domain will be y ≥ 21 and y ≥ -25/2, which is y ≥ 21.

Multiplying the equation by 15 gives ...

  5y -105 = 6y +75

  y = -180 . . . . . . . . . subtract 5y+75

This solution is not in the allowed domain.

__

left side negative

The domain will be y ≤ 21 and y ≥ -25/2, which is -25/2 ≤ y ≤ 21.

Multiplying the equation by 15 gives ...

  105 -5y = 6y +75

  30 = 11y . . . . . . . . . add y-75

  y = 30/11 . . . . . .  the solution is in the allowed domain

__

right side negative

The domain will be y ≥ 21 and y ≤ -25/2. This is the empty set.

__

both sides negative

The domain will be y ≤ 21 and y ≤ -25/2, which is y ≤ -25/2.

Multiplying the equation by 15 gives ...

  105 -5y = -6y -75

  y = -180 . . . . . . . . . . add 6y-105 . . . . the solution is in the allowed domain

__

Solutions to this equation are ...

  y = 30/11 = 2 8/11

  y = -180

Answer:

its b i did the test

Step-by-step explanation:

The integral test compares an infinite sum to an improper integral and is the test that can only be applied when we are considering a series whose terms are all positive.

1) For a series ∑n=1∞aₙ to converge, the nth term an must satisfy aₙ→0

 as n→∞.

Therefore, from the algebraic limit properties of sequences,

lim k→∞a k = lim k→∞(S k−S k−1)=limk→∞S k−lim k→∞S k−1 = S−S = 0.

Therefore, if  ∑n=1∞aₙ converges, the nth term an→0 as  n→∞. An important consequence of this fact is the following statement:

If aₙ↛0 as n→∞,∑n=1∞aₙ diverges

The integral test compares an infinite sum to an improper integral. It is important to note that this test can only be applied when we are considering a series whose terms are all positive.

2) The sum of the areas of the rectangles is less than the sum of the area of the first rectangle and the area between the curve f(x)=1/x2 and the x -axis for x≥1

Since the area bounded by the curve is finite, the sum of the areas of the rectangles is also finite.

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Equation:

Procedure:

0. Simplifying both sides of the equation:

2. Getting the x on one side and the constants on the other:

3. Dividing both sides by -1:

By doing this, the sing will change as follows:

Answer:

The  volume of rectangular prism is 90 unit³.

We can consider the 1 block = 1 unit.

Length of prism = 5 unit

width of prism = 6 unit

Height of prism = 3 unit

So, Volume of rectangular prism

= l w h

= 5 x 6 x 3

= 90 unit³

Thus, the volume of rectangular prism is 90 unit³.

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Answer: 105

Step-by-step explanation: 35 divided by 7 = 5 , so one monkey eats 5 bananas. 21 x 5 = 105

Hope this helps!

Answer:

105 bannanas

Step-by-step explanation:

Because if 21 is 3 times more than 7 then you have to multiply 35 times 3 to get the amount of bannanas 3 times more monkeys can eat.

Have a great day!

Answer:

Step-by-step explanation:

Given the function f(x)=-16x^2+100x+5 to calculate how far the potato will be from the ground at any given second (x), the potato hits the ground when g(x) = 0

The function becomes'

0 =-16x^2+100x+5

-16x^2+100x+5 = 0

multiply through by minus

16x^2-100x-5 = 0

x = 100 ±√100²-4(16(-5))/2(16)

x = 100±√10000+320/32

x = 100±101.59/32

x = 100+101.59/32

x = 202.59/32

x = 6.299 secs

Hence the potato will hit the ground after 6.299secs

The time taken by potato to hit the ground is \(6.299\) seconds.

The potato will be from the ground at any given second (x) is given by below function.

             \(f(x)=-16x^2+100x+5\)

To find the time taken by potato to hit the ground is , equate given function to zero.

            \(f(x)=-16x^2+100x+5=0\\\\-16x^2+100x+5=0\\\\x=\frac{-100\pm\sqrt{(100)^{2}+4*16*5 } }{-16*2} \\\\x=\frac{-100\pm101.587 } {-32} \\\\x=6.299,x=-0.049\)

Since, time can not be negative.

So that we will consider , \(x=6.299 s\)

Hence, the time taken by potato to hit the ground is \(6.299\) seconds.

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