The required vertical distance from the top of the slide to the bottom of the pool is 43.8 feet.
We can use trigonometry to solve this problem. Let's call the vertical distance from the top of the slide to the bottom of the pool "h" (in feet). We can use the angle of depression (45°) to find the horizontal distance from the top of the slide to the bottom of the pool. Since the slide has a constant slope, the angle between the slide and the ground is also 45°. It implies that the vertical height is equal to the horizontal projection of the slide.
Apply Pythagorean theorem,
45² = h² + h²
h = 45/√2
h = 31.8
Now, as mentioned that depth of the pool is 12 feet so, the total vertical height is given as,
= h + 12
= 31.8 + 12
= 43.8 feet
Thus, the required vertical distance from the top of the slide to the bottom of the pool is 43.8 feet.
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2 Mike and Anna are having a weight loss competition. Mike wants to practice kickboxing to burn calories while Anna
prefers to run. Mike records his calories burned in the table below and Anna graphs her calories burned in the graph.
Who burns more calories per hour?
Anna's Calories Burned:
Running
A. Mike and Anna burn the same amount
of calories per minute
B. Mike burns more calories per minute
thank Anna.
C. Anna burns more calories per minute
than Mike.
D. There is not enough information
to determine who burns more calories
per minute.
Mike's Calories Burned:
Kickboxing
Minutes
0
12
24
36
Calories
0
150
300
450
Calories Burned
y
500
450
400
350
300
250
200
150
100
50
5
10 15 20 25 30 35
Minutes
40 45
50
Based on the information regarding the data, B. Mike burns more calories per minute than Anna
How to explain the dataThe calorie consumption of Mike was between 12.5 and 16.67, averaging out at nearly 13.75 per minute.
In contrast, Anna burned around 13.33 each minute.
So the answer is B - Mike burns more calories per minute than Anna.
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(1000 8 13. DIG DEEPER A 4,500-gram bag of soil costs $3, and an 18-kilogram bag of soil costs $10. Which is the less expensive way to buy 18,000 grams of soil? Explain.
It is cheaper to buy 18-kilogram bag of soil. The cost of the 18-kilogram is $10 and the cost of the cost of the other option is $12.
What is the cheaper way of buying 18,000 grams of soil?Cost of buying 18,000 grams of soil using the 4500 gram bag = (18,000 / 4,500) x $3 = $12
The second step is to convert 18 kilogram to grams.
1 kg = 1000 grams
18 x 1000 = 18,000 grams
18,000 grams cost $10.
Thus, it is cheaper to buy 18-kilogram bag of soil.
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Approximate e^-0.11 to 4 decimal places
Answer: 0.8958
Step-by-step explanation:
Thank you for the help!
Answer:
c 57
Step-by-step explanation:
Willa sells cars. Last month, she had 124,000 dollars in sales. Her commission rate is 1.3 percent. How much did Willa earn for the month?
What is the volume of this figure?
Enter your answer in the box.
ft³
Answer: 76 cubic feet
Step-by-step explanation:
Think about breaking it into two rectangular prisms:
Total volume = Volume of longer prism + volume of shorter prism
Total volume = 8x4x2 + 2x2x3
Total volume = 76 cubic feet
What is the area of this triangle?
Enter your answer as a decimal in the box. Round only your final answer to the nearest tenth.
The calculated area of this triangle is 43.50 sq units
What is the area of this triangle?From the question, we have the following parameters that can be used in our computation:
The triangle
The area of the triangle is calculated as
Area = 1/2 * Product of adjacent legs * sin of middle angle
Substitute the known values in the above equation, so, we have the following representation
Area = 1/2 * 12 * 8 * sin(65)
Evaluate
Area = 43.50
Hence, the area is 43.50 sq units
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7. Based on an exponential model of the data, what is the predicted value of Variable 2 when
Variable 1 = 2?
Round your answer to the nearest whole number.
Variable 1:
10
20
30
40
50
60
70
80
90
100
variable 2:
100
80
52
40
35
25
17
11
10
7
Answer:
128
Step-by-step explanation:
You want a prediction for x=2 when the given data is modeled by an exponential model.
x = 10, 20, 30, 40, 50, 60, 70, 80, 90, 100y = 100, 80, 52, 40, 35, 25, 17, 11, 10, 7ModelA graphing calculator's exponential regression function models this data with the formula ...
y = 135.7 · 0.9711^x
y = 137.7 · 0.9711^2 ≈ 127.94 . . . . when x=2
This model gives a value for variable 2 of approximately 128 when variable 1 = 2.
<95141404393>
Can you round off 20.900156 to 1 decimal place?
Answer:
Step-by-step explanation:
20.9 is solution
solve the inequality and graph the solution on the line provided.
5x - 15 < 10
Answer: x < 5, see attached for the graph.
Step-by-step explanation:
To solve, we will isolate the variable.
Given:
5x - 15 < 10
Add 15 to both sides of the equation:
5x < 25
Divide both sides of the equation by 5:
x < 5
For the graph, we will use an open circle because this is only less than (<), not less than and equal to.
Then, since x is all values less than 5, we will shade our arrow to the left of 5. See attached.
During certain time periods at a hospital, patients arriving at the emergency room have waiting times that are uniformly distributed between 0 and 7 minutes. Assume that a patient is randomly selected, and find the probability that the waiting time is less than 0.75 minutes. (Round to three decimal places)
Since the waiting times are uniformly distributed between 0 and 7 minutes, the probability density function (PDF) of the waiting time is:
f(x) = 1/7 for 0 ≤ x ≤ 7
0 otherwise
To find the probability that the waiting time is less than 0.75 minutes, we need to integrate the PDF from 0 to 0.75:
P(X < 0.75) = ∫[0,0.75] f(x) dx
P(X < 0.75) = ∫[0,0.75] 1/7 dx
P(X < 0.75) = [1/7 * x] [0,0.75]
P(X < 0.75) = 1/7 * 0.75
P(X < 0.75) = 0.1071
Therefore, the probability that the waiting time is less than 0.75 minutes is 0.1071 (rounded to three decimal places).
Simplify the expression: 8y + 4 - 3y + 12
The simplified value of 8y + 4 - 3y + 12 is 5y+16
What is simplification of expression?An expression or algebraic expression is any mathematical statement which consists of numbers, variables and an arithmetic operation between them. For example , 4x+5 , 2x²+2, 10y³+5y²+6
To simplify an expression means to write the expression Ina simpler form. for example 6y²+2y can be written as 2y( 3y+1)
Simplifying 8y + 4 - 3y + 12,
collecting like terms
8y-3y+4+12
= 5y+16
therefore the simplification of 8y + 4 - 3y + 12 is 5y+16
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Everyone in the population must have an of being selected in order for a sample to be an
Answer: Everyone in your population must have an equal, non-zero chance of being selected. (In other words, everyone has an equal chance of receiving a survey.) You must know, specifically, what that chance of being selected is for each person.
Can you help me answer this question?
How many different outfit combinations can San create with 3 shirts, 3 pants and 3 pairs of shoes.
Suppose log 2 = r, log, 3= s, and log 5 = t. Which algebraic expression represents log 75?
log(75) = log( 3 • 5 • 5 )
= log(3) + log(5) + log (5)
= s + t + t
= s + 2t
To go from log( 3 • 5 • 5 ) to log(3) + log(5) + log (5), we use the log rule that says log( a • b ) = log(a) + log(b).
Without using a calculator, fill in the blanks with two consecutive integers to complete the following inequality.
<[tex]\sqrt{74}[/tex]
The inequality is -8 < √74 < 9. A mathematical expression that's values on the left and right are not equal is referred to as having an inequality.
A mathematical expression that's values on the left and right are not equal is referred to as having an inequality. In essence, an inequality analyses any two values that demonstrates whether one is bigger than, less than, or neither greater nor equal to the other quantity. Numbers are compared using inequalities to determine a range of quantities that are contained inside the parameters of a variable.
Let A = √74
A² = 74
8² < A² < 9²
Hence, the inequality is -
8 < √74 < 9
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Katrina is building a wall around her backyard using bricks that are 18 inches long. The wall needs to be 36 feet, or 432 inches, long.
Katrina will need 24 bricks to build the wall around her backyard.
We have,
To determine the number of bricks needed for the wall, we need to divide the total length of the wall (432 inches) by the length of each brick (18 inches):
So,
Number of bricks = Total length of the wall / Length of each brick
Number of bricks = 432 inches / 18 inches
Number of bricks = 24 bricks
Therefore,
Katrina will need 24 bricks to build the wall around her backyard.
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The complete question:
Katrina is building a wall around her backyard using bricks that are 18 inches long. The wall needs to be 36 feet, or 432 inches, long.
Find the number of bricks needed to build around he backyard.
1. Have you immersed yourself in an unfamiliar environment and if so, what feelings did
you experience-vulnerability, loneliness, uncertainty?
2. How will globalization change your organization's mix of customers and products? How
will you need to grow and adapt to lead in the future state of the organization?
3. How high is your GQ? What concrete actions can you take to raise it?
1. When people find themselves in an unfamiliar environment, it is common to feel vulnerable, lonely, and uncertain.
2. Globalization can change the mix of customers and products for an organization by creating new markets and opportunities for growth.
3. You can improve your GQ by practicing mindfulness and meditation
What are the feelings that you have?Businesses may need to concentrate on creating new goods and services that appeal to a global market as well as modifying their business models to satisfy the needs of clients in various regions of the world if they want to be leaders in the organization's future state.
In order for them to be more adaptable and receptive to changes in the global marketplace, they might also need to invest in technology and tactics.
Globalization can significantly impact an organization's mix of customers and products. The organization must adapt to this by investing in research and development to create new products.
By applying mindfulness, the GQ can be adequately raised for the organization.
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Rotations : If the point (6,2) was on a figure that was rotated 180 degrees clockwise what would be the coordinates of the new point on this figure
The coordinates of the new point is (-6, -2)
What would be the coordinates of the new pointFrom the question, we have the following parameters that can be used in our computation:
Point = (6, 2)
Rule: 180 degrees rotation
The rule of 180 degrees rotation is
(x, y) = (-x -y)
substitute the known values in the above equation, so, we have the following representation
image = (-6, -2)
Hence, the image = (-6, -2)
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Mona pays $1.00 for the first call of the day on her mobile phone plus $0.15 per minute of the call. She paid $2.95 for her first call today. Write an expression that you could use to calculate the length in minutes of the phone call.
The requreid Mona's phone call was 13 minutes long.
Let's let the variable "m" represent the length of the phone call in minutes.
We know that Mona pays $1.00 for the first call of the day plus $0.15 per minute of the call. So the total cost of the call can be represented by the expression:
$1.00 + $0.15m
We also know that Mona paid $2.95 for her first call today. So we can set the expression for the total cost of the call equal to $2.95:
$1.00 + $0.15m = $2.95
To solve for the length of the call in minutes, we can first subtract $1.00 from both sides of the equation:
$0.15m = $1.95
Then we can divide both sides by $0.15:
m = 13
Therefore, Mona's phone call was 13 minutes long.
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Eating at the all-you-can-eat buffet at your favorite restaurant currently costs
$18.50, and increases in cost by 6% each year. What will this buffet cost in 6 years?
$26.24
$30.23
$27.13
$31.64
2. A gift is packed in a rectangular box (rectangular prism) of dimensions 15 in, 10 in, and 8 in and it needs to be wrapped with gift paper. How much gift paper is required to wrap the gift box?
length= 5 in , width= 4 in, height= 3 in
length, l=16in
width, b=13in
thickness, t=3in
To Find:-
Area of wrapping paper required.
Explanation:-
Since, wrapping paper is to be wrapped over the whole rectangular box.Therefore, we have to calculate the total surface area of the rectangular box.

Therefore, 590 of paper is required to wrap the whole rectangular box.
. Amanda lets her new pony exercise by letting the pony run in circles while
attached to a rope, which Amanda holds in the center of the ring. If the part of
the rope between Amanda's hand and the pony is 30 feet long, how far does
the pony run in one circle. Round your answer to the nearest tenth. (Draw a sketch to help.
Answer:
188.5 ft
Step-by-step explanation:
One Circle = perimeter
= 2 nr
= 2 x 3.14 x 30
= 188.5 ft
A combined total of $33,000 is invested in two bonds that pay 5% and 6.5% simple interest. The annual interest is $2,010.00. How much is invested in each bond?
Answer: $9,000 is invested in the 5% bond, and $24,000 is invested in the 6.5% bond.
Step-by-step explanation: x + y = 33,000 (the full sum contributed)
We too know that the yearly intrigued earned is $2,010.00, which is the whole of the intrigued earned from each bond. Utilizing the equation for basic intrigued:
intrigued = principal x rate x time
ready to calculate the intrigued earned from each bond:
0.05x (for the 5% bond)
0.065y (for the 6.5% bond)
So we have another condition:
0.05x + 0.065y = 2,010
Presently we have two conditions with two factors, which we are able illuminate utilizing substitution or end.
Let's utilize substitution:
x + y = 33,000 --> y = 33,000 - x
0.05x + 0.065y = 2,010 --> 0.05x + 0.065(33,000 - x) = 2,010
Streamlining:
0.05x + 2,145 - 0.065x = 2,010
-0.015x = -135
x = 9,000
So the sum contributed within the 5% bond is $9,000, and the sum contributed within the 6.5% bond is:
y = 33,000 - x = 33,000 - 9,000 = $24,000
Melissa drew a right triangle.
The perimeter of the triangle is 9+√41.
The hypotenuse is of length ✓41.
Using this information, what is the length of the other
two sides of the triangle?
Answer:
Let's denote the two legs of the right triangle as a and b, and the hypotenuse as c. We know that c = √41, so we can use the Pythagorean theorem to relate a and b to c:
c^2 = a^2 + b^2
Substituting c = √41, we get:
(√41)^2 = a^2 + b^2
41 = a^2 + b^2
We also know that the perimeter of the triangle is:
perimeter = a + b + c = 9 + √41
Substituting c = √41, we get:
a + b + √41 = 9 + √41
a + b = 9
Now we have two equations with two unknowns (a and b):
a^2 + b^2 = 41
a + b = 9
We can solve this system of equations by substitution. Solving the second equation for a, we get:
a = 9 - b
Substituting this into the first equation, we get:
(9 - b)^2 + b^2 = 41
81 - 18b + 2b^2 = 41
2b^2 - 18b + 40 = 0
b^2 - 9b + 20 = 0
(b - 4)(b - 5) = 0
So we have two possible solutions: b = 4 and b = 5. We can find the corresponding value of a using a = 9 - b:
a = 5 and b = 4 or a = 4 and b = 5
Therefore, the two legs of the right triangle are 4 and 5.
Find the missing side of the triangle 12, 34° and 90°
Answer:
To find the missing side of a right triangle given an angle and a side, you can use trigonometric functions. In this case, we have the angle opposite the missing side, so we can use the sine function.
The sine of an angle is the ratio of the length of the opposite side to the length of the hypotenuse. Therefore, we can set up the following equation:
sin(34°) = opposite / 12
To solve for the opposite side, we can multiply both sides by 12:
opposite = 12 * sin(34°) ≈ 6.60
Therefore, the missing side of the triangle is approximately 6.60 units long.
Step-by-step explanation:
what is half of 9min and 28 sec
Answer:
4 minutes and 44 seconds.
dr
15
3-
13 1
-6
-9
-12
-15
2 3 4 5
X
Which lists all of the x-intercepts of the graphed
function?
O(0.6)
O(1, 0) and (2, 0)
O(1, 0), (2, 0), and (-3, 0)
O(1.0), (2, 0), (-3,0), and (0, 6)
Answer:
not sure sorry -(1,0)and (2,0)
23=-8v-7+2v????????????????????
Answer:
v=-5
Step-by-step explanation:
Answer:
[tex]23 = 10v - 7 \\ 23 + 7 = 10v \\ 30 = 10v \\ v = 3 \\ \\ [/tex]
In circle N with � ∠ � � � = 12 4 ∘ m∠MNP=124 ∘ and � � = 13 MN=13, find the area of sector MNP. Round to the nearest hundredth.
If circle with center N with m∠MNP=124 ∘ and MN=13, the area of sector MNP is approximately equal to 194.86 square units.
To find the area of a sector of a circle, we need to use the formula:
Area of sector = (central angle/360°) x πr²
Where r is the radius of the circle.
In this problem, we know that the central angle m∠MNP is 124° and MN, which is also the radius of the circle, is 13. So we can substitute these values into the formula:
Area of sector = (124/360) x π(13)²
Area of sector ≈ 194.86
Therefore, the area of sector MNP is approximately equal to 194.86 square units.
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