The sample space for the number solid is {1, 2, 3, 4, 5, 6} and the probability of rolling 1 is 1/6.
The sample space refers to the set of all possible outcomes of an experiment, while a sample value is a specific outcome in the sample space.
For the given 8-sided solid, the sample space would be {1, 2, 3, 4, 5, 6}, as the faces labeled "skip" are not counted as sample values.
Now, let's calculate the probability of rolling a 1. Probability is the likelihood of a particular outcome occurring, which can be calculated by dividing the number of successful outcomes (in this case, rolling a 1) by the total number of possible outcomes.
The total number of possible outcomes is 6 (1, 2, 3, 4, 5, and 6). There is only one successful outcome: rolling a 1.
So, the probability of rolling a 1 is:
P(1) = (Number of successful outcomes) / (Total number of possible outcomes)
P(1) = 1 / 6
Thus, the probability of rolling a 1 on this 8-sided solid is 1/6 or approximately 0.1667, or 16.67%.\
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Polynomial in standard form (6d+6) (2d-2)
Answer:
I think the answer is 8d + 4.
Step-by-step explanation:
Combine the like terms, 6d + 2d = 8d. 6 - 2 = 4.
(a) Determine the critical value(s) for a right-tailed test of a population mean at the
α=0. 10
level of significance with
20
degrees of freedom.
(b) Determine the critical value(s) for a left-tailed test of a population mean at the
α=0. 10
level of significance based on a sample size of
n=15.
(c) Determine the critical value(s) for a two-tailed test of a population mean at the
α=0. 01
level of significance based on a sample size of
n=11
The critical value for a right-tailed test of a population mean at α=0.10 level of significance with 20 degrees of freedom is 1.325.
The critical value for a left-tailed test of a population mean at the α=0.10 level of significance based on a sample size of n=15 is -1.345.
The critical value(s) for a two-tailed test of a population mean at the α=0.01 level of significance based on a sample size of n=11 is -2.718 and 2.718.
To find the critical values, we need to use a t-distribution table or a statistical software that provides the critical t-values for a specific level of significance and degrees of freedom.
For part (a), since it's a right-tailed test, the critical value will be positive, and we need to look for the t-value that corresponds to an area of 0.10 to the right of the mean in the t-distribution table. With 20 degrees of freedom, the critical value is 1.325.
For part (b), since it's a left-tailed test, the critical value will be negative, and we need to look for the t-value that corresponds to an area of 0.10 to the left of the mean in the t-distribution table. With 15 degrees of freedom, the critical value is -1.345.
For part (c), since it's a two-tailed test, we need to split the significance level equally between the two tails. We need to find the t-values that correspond to an area of 0.005 to the left of the mean and 0.005 to the right of the mean in the t-distribution table. With 11 degrees of freedom, the critical values are -2.718 and 2.718.
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Los 2/3 mas la edad de Juan es igual a los 3/5 menos la edad de Julia. ¿Que fraccion representa la edad de juan respecto a la edad de Julia?
The fraction representing Juan's age relative to Julia's age is -1/10. This means that Juan's age is one-tenth less than Julia's age.
Let's start by translating the given statement into an equation:
[tex]2/3J = 3/5 - 2/3Jl[/tex]
where J is Juan's age and Jl is Julia's age.
Now we can simplify this equation by first multiplying both sides by 15 (the least common multiple of 3 and 5) to get rid of the denominators:
[tex]10J = 9 - 10Jl[/tex]
Next, we can isolate J on one side of the equation by adding 10Jl to both sides:
[tex]10J + 10Jl = 9[/tex]
Finally, we can factor out a 10 from the left-hand side:
[tex]10(J + Jl) = 9[/tex]
Dividing both sides by 10, we get:
[tex]J + Jl = 9/10[/tex]
Now we can express Juan's age as a fraction of Julia's age by dividing both sides of this equation by Jl:
[tex]Jl/Jl + J/Jl = 9/10Jl[/tex]
Simplifying this, we get:
1 + J/Jl = 9/10
Subtracting 1 from both sides, we get:
[tex]J/Jl = 9/10 - 1[/tex]
[tex]J/Jl = -1/10[/tex]
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Between which 2 days does the biggest change occour
Answer:
=Briefly, days are longest at the time of the summer solstice in December and the shortest at the winter solstice in June. At the two equinoxes in March and September the length of the day is about 12 hours, a mean value for the year.
Step-by-step explanation:
Answer:Briefly, days are longest at the time of the summer solstice in December and the shortest at the winter solstice in June. At the two equinoxes in March and September the length of the day is about 12 hours, a mean value for the year.
Step-by-step explanation:
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Step-by-step explanation:
An object with a weight of 100 N is suspended by two lengths of rope from the
ceiling. The angles that both lengths make with the ceiling are the same. The
tension in each length is 50 N. Determine the angle that the lengths of ropes make
with the ceiling.
The angle that the lengths of ropes make with the ceiling is 90 degrees.
To determine the angle that the lengths of ropes make with the ceiling for an object with a weight of 100 N suspended by two ropes with equal tension of 50 N, we can follow these steps:
1. Understand that the vertical forces must balance, meaning the sum of the vertical components of tension in each rope must equal the object's weight.
2. Recognize that the vertical component of tension in each rope can be calculated using the sine function and the angle, θ, between the rope and the ceiling: T_vertical = T * sin(θ).
3. Set up an equation using the information provided: 2 * (50 N * sin(θ)) = 100 N, where θ is the angle we want to find.
4. Simplify the equation: 100 * sin(θ) = 100 N.
5. Divide both sides by 100: sin(θ) = 1.
6. Find the inverse sine (also known as arcsin) of 1: θ = arcsin(1).
7. Calculate the angle: θ = 90 degrees.
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A supermarket operator must decide whether to build a medium size supermarket or a large supermarket at a new location. Demand at the location can be either average or favourable with estimated probabilities to be 0. 35 and 0. 65 respectively. If demand is favorable, the store manager may choose to maintain the current size or to expand. The net present value of profits is $623,000 if the firm chooses not to expand. However, if the firm chooses to expand, there is a 75% chance that the net present value of the returns will be 330,000 and 25% chance the estimated net present value of profits will be $610,000. If a medium size supermarket is built and demand is average, there is no reason to expand and the net present value of the profits Is $600,000. However, if a large supermarket is built and the demand turns out to be average, the choice is to do nothing with a net present value of $100,000 or to stimulate demand through local advertising. The response to advertising can be either unfavorable with a probability of 0. 2 or faverable with a probability of 0. 8. If the response to advertising is unfavorable the net present value of the profit is ($20,000). However, if the response to advertising is favourable,then the net present vale of the profits in $320,000. Finally, if the large plant is built and the demand happens to be high the net present value of the profits is $650. 0. Draw a decision tree and determine the most appropriate decision for this company
The most appropriate decision for the company is to build a large supermarket and expand if demand turns out to be favorable.
Here is a decision tree for the given problem:
```
Build Medium
/ \
Average / \ Favorable
/ \
NPV = $600K Expand
/ \
NPV = $330K NPV = $610K
75% 25%
\ /
Favorable / Unfavorable
/
NPV = $623K
\
High
\
NPV = $650K
/
Stimulate / Not Stimulate
/ \
Favorable / Unfavorable
/ \
NPV = $320K NPV = -$20K
```
To determine the most appropriate decision, we will use the expected value approach. At each decision node, we will calculate the expected value of each decision option and choose the one with the highest expected value.
Starting from the top, the expected value of building a medium size supermarket is:
Expected value = (0.35 x $600K) + (0.65 x $623K) = $615,250
The expected value of building a large supermarket and not stimulating demand if it turns out to be average is:
Expected value = (0.35 x $100K) + (0.65 x $623K) = $403,250
The expected value of building a large supermarket and stimulating demand if it turns out to be average is:
Expected value = (0.35 x 0.2 x -$20K) + (0.35 x 0.8 x $320K) + (0.65 x $623K) = $394,850
The expected value of building a large supermarket and expanding if it turns out to be favorable is:
Expected value = (0.65 x 0.75 x $330K) + (0.65 x 0.25 x $610K) + (0.35 x $623K) = $473,125
The expected value of building a large supermarket if it turns out to be high is:
Expected value = $650K
Comparing all the expected values, we see that building a large supermarket and expanding if demand turns out to be favorable has the highest expected value of $473,125. Therefore, the most appropriate decision for the company is to build a large supermarket and expand if demand turns out to be favorable.
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Please help, I don't understand this geometry problem!!
Nisha is looking out the window of her apartment building at a sculpture in a park across the street. The top of Nisha's window is 60 feet from the ground. The angle of depression from the top of Nisha's window to the bottom of the sculpture is 25°. What is the distance along the ground between the building and the sculpture? Round your answer to the nearest hundredth.
25.36 feet
27.98 feet
100.22 feet
128.67 feet
The distance along the ground between the building and the sculpture is approximately 27.98 feet. Rounded to the nearest hundredth, the answer is 27.98 feet.
How to calculate the distance along the ground between the building and the sculptureFrom the problem statement, we know that angle BAC is 25 degrees and AC is 60 feet. We want to find AB, which is the horizontal distance between A and B.
We can use trigonometry to find AB. Let's use the tangent function:
tan(25) = AB / AC
Solving for AB, we get:
AB = AC * tan(25)
Substituting the values we know, we get:
AB = 60 * tan(25)
Using a calculator, we get:
AB ≈ 27.98 feet
Therefore, the distance along the ground between the building and the sculpture is approximately 27.98 feet. Rounded to the nearest hundredth, the answer is 27.98 feet.
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show, not solve for x
Answer:
Step-by-step explanation:
Full Boat Manufacturing has projected sales of $115. 5 million next year. Costs are expected to be $67. 4 million and net investment is expected to be $12. 3 million. Each of these values is expected to grow at 9 percent the following year, with the growth rate declining by 1 percent per year until the growth rate reaches 5 percent, where it is expected to remain indefinitely. There are 4. 8 million shares of stock outstanding and investors require a return of 10 percent return on the company’s stock. The corporate tax rate is 21 percent
The given question is incomplete, the complete question is given
" Full Boat Manufacturing has projected sales of $115 million next year. Costs are expected to be $67 million and net investment is expected to be $12 million. Each of these values is expected to grow at 14 percent the following year, with the growth rate declining by 2 percent per year until the growth rate reaches 6 percent, where it is expected to remain indefinitely. There are 5.5 million shares of stock outstanding and investors require a return of 13 percent on the company’s stock. The corporate tax rate is 21 percent.
What is your estimate of the current stock price?
The estimate of the current stock price is $13.11 per share.
To calculate the current stock price, we need to estimate the free cash flows and discount them at the required rate of return.
First, we determine the firm's free cash flow (FCFF) for the following year.
FCFF = Sales - Costs - Net Investment*(1-t)
= $115 million - $67 million - $12 million*(1-0.21)
= $31.02 million
Now, we will calculate the expected growth rate in FCFF
g = (FCFF Year 2 / FCFF Year 1) - 1
FCFF Year 2 = FCFF Year 1 × (1 + g)
g = (FCFF Year 2 / FCFF Year 1) - 1
= (FCFF Year 1 × (1 + 0.14) × (1 - 0.02) / FCFF Year 1) - 1
= 0.12
We can now use the Gordon growth model to estimate the current stock price
Current stock price = FCFF Year 1 × (1 + g) / (r - g)
r = required rate of return.
Current stock price = $31.02 million × (1 + 0.12) / (0.13 - 0.12)
= $72.13 million
Finally, we divide the current stock price by the number of shares outstanding to get an estimate of the current stock price per share:
Current stock price per share = $72.13 million / 5.5 million
= $13.11 per share
Therefore, the estimate of the current stock price is $13.11 per share.
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Position vector = 3 ti + tj + 1/4t^2k
Time = 2
Find the velocity vector, speed, and acceleration vector of the object.
the velocity vector of the object is v(2) = 3i + j + k, the speed is sqrt(11), and the acceleration vector is a(t) = (1/2)k.
We're given the position vector and time and asked to find the velocity vector, speed, and acceleration vector of the object. Let's solve this step-by-step.
1. Differentiate the position vector with respect to time (t) to find the velocity vector:
Position vector: r(t) = 3ti + tj + (1/4)t^2k
Velocity vector: v(t) = dr(t)/dt = d(3ti)/dt + d(tj)/dt + d((1/4)t^2k)/dt
v(t) = 3di/dt + dj/dt + (1/2)tk
v(t) = 3i + j + (1/2)tk
2. Plug in the given time (t = 2) into the velocity vector to find the velocity at that time:
v(2) = 3i + j + (1/2)(2)k
v(2) = 3i + j + k
3. Find the speed by calculating the magnitude of the velocity vector:
Speed = |v(2)| = sqrt((3^2) + (1^2) + (1^2))
Speed = sqrt(9 + 1 + 1)
Speed = sqrt(11)
4. Differentiate the velocity vector with respect to time (t) to find the acceleration vector:
Acceleration vector: a(t) = dv(t)/dt = d(3i)/dt + d(j)/dt + d((1/2)tk)/dt
a(t) = 0i + 0j + (1/2)k
So, the velocity vector of the object is v(2) = 3i + j + k, the speed is sqrt(11), and the acceleration vector is a(t) = (1/2)k.
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For each of the following lengths, estimate the perimeter of an isosceles right triangle whose short sides have that length
A. Length of shirt sides is 0. 75
The perimeter of an isosceles right triangle whose short sides have that length 0.75 units is 2.56 units.
Given that, an isosceles right triangle whose short sides have that length 0.75 units.
Let the longest side be x.
Here, x²=0.75²+0.75²
x²=1.125
x=√1.125
x=1.06 units
Now, the perimeter = 0.75+0.75+1.06
= 2.56 units
Therefore, the perimeter of an isosceles right triangle whose short sides have that length 0.75 units is 2.56 units.
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Lin's smart phone was fully charged when she started school at 8:00 a. M. At 9:20 a. M. , it was 90%
charged, and at noon, it was 72% charged.
1. When do you think her battery will die?
2. Is battery life a function of time? If yes, is it a linear function? Explain your reasoning.
1. It's impossible to determine exactly when Lin's battery will die without more information on her phone's battery capacity and usage patterns. However, we can estimate that it will likely die sometime after noon if the rate of battery drain remains constant.
2. Yes, battery life is a function of time. The longer a battery is in use, the more its charge will deplete. However, it is not necessarily a linear function as the rate of battery drain can vary depending on factors such as usage patterns, app activity, and temperature. In this specific case, it appears that the rate of battery drain may be slowing down as the percentage decrease from 90% to noon is less than the decrease from fully charged to 90%.
In calculus and related areas, a linear function is a function whose graph is a straight line, that is, a polynomial function of degree zero or one. For distinguishing such a linear function from the other concept, the term affine function is often used. A linear function from the real numbers to the real numbers is a function whose graph (in Cartesian coordinates) is a non-vertical line in the plane. The characteristic property of linear functions is that when the input variable is changed, the change in the output is proportional to the change in the input.
Linear functions are related to linear equations.
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I Need help with this (if you can’t see zoom in)
Answer: 45 (depends on what the rightmost angle is)
Step-by-step explanation:
All angles of a triangle add up to 180 degrees.
Two angle measures are provided, 100 and 35 (?)
Add up the two to get 135, and subtract from 180
180 - 135 = 45 degrees.
I might be seeing the rightmost angle measure wrong but I think it's 35, if it's not you can still apply the same strategy, just add the two given angles and subtract that from 180 to find x.
Color the circles, so it would be certain you get an orange one.
Answer:
1 orange
Step-by-step explanation:
you just color 1 circle.
The area covered by a lake is 11 square kilometers. It is decreasing exponentially at a rate of 2 percent each year and can be modeled by A(t) = 11×(0. 98)^t.
A. By what factor does the area decrease after 10 years?
B. By what factor does the area decrease each month?
A. The area decreases by a factor of about 0.6565 after 10 years. B. The area decreases by a factor of about 0.0197 each month.
A. To find the factor by which the area decreases after 10 years, we need to compare the initial area (at t=0) to the area after 10 years (at t=10). We can use the formula for A(t) to calculate these values:
A(0) = 11 square kilometers (initial area)
A(10) = 11 ×(0.98)¹⁰ ≈ 7.22 square kilometers (area after 10 years)
The factor by which the area decreases after 10 years is the ratio of A(10) to A(0):
A(10) / A(0) ≈ 7.22 / 11 ≈ 0.6565
So the area decreases by a factor of about 0.6565 after 10 years.
B. To find the factor by which the area decreases each month, we need to first find the annual rate of decrease, and then convert it to a monthly rate. We know that the area decreases by 2 percent each year, so the annual rate of decrease is 0.02. To find the monthly rate of decrease, we can use the formula:
r = (1 + i)^(1/n) - 1
where:
r is the monthly rate of decrease
i is the annual rate of decrease (0.02 in this case)
n is the number of months in a year (12)
Plugging in the values, we get:
r = (1 + 0.02)^(1/12) - 1 ≈ 0.00165
So the area decreases by a factor of approximately:
(1 - r)¹² ≈ (1 - 0.00165)¹² ≈ 0.0197 each month. Therefore, the area decreases by a factor of about 0.0197 each month.
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The critical number of the function f(x) = 5x2 + 7x – 10 is The function f(x) = -2x3 + 39x2 – 240x + 2 has two critical numbers A < B with A = and B =
The critical numbers of f(x) = -2x^3 + 39x^2 - 240x + 2 are A = 5 and B = 8.
To find the critical numbers of a function, we need to find the values of x where the derivative of the function is zero or undefined.
For the function f(x) = 5x^2 + 7x - 10, the derivative is:
f'(x) = 10x + 7
To find the critical numbers, we need to set f'(x) = 0 and solve for x:
10x + 7 = 0
10x = -7
x = -7/10
So the critical number of f(x) = 5x^2 + 7x - 10 is x = -7/10.
For the function f(x) = -2x^3 + 39x^2 - 240x + 2, the derivative is:
f'(x) = -6x^2 + 78x - 240
To find the critical numbers, we need to set f'(x) = 0 and solve for x:
-6x^2 + 78x - 240 = 0
We can simplify this equation by dividing both sides by -6:
x^2 - 13x + 40 = 0
Now we can factor the quadratic:
(x - 5)(x - 8) = 0
So the solutions are x = 5 and x = 8.
To determine which critical point is A and which is B, we need to check the sign of the second derivative of f(x) at each critical point.
The second derivative of f(x) is:
f''(x) = -12x + 78
Plugging in x = 5, we get:
f''(5) = -12(5) + 78 = 18
Since f''(5) is positive, we know that f(x) has a local minimum at x = 5. Therefore, x = 5 is the critical point A.
Plugging in x = 8, we get:
f''(8) = -12(8) + 78 = -6
Since f''(8) is negative, we know that f(x) has a local maximum at x = 8. Therefore, x = 8 is the critical point B.
Therefore, the critical numbers of f(x) = -2x^3 + 39x^2 - 240x + 2 are A = 5 and B = 8.
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In ΔDEF, e = 67 inches, ∠F=37° and ∠D=70°. Find the area of ΔDEF, to the nearest 10th of an square inch.
The area of ΔDEF, to the nearest 10th of a square inch, is approximately 1439.1 square inches.
To find the area of ΔDEF with given values e = 67 inches, ∠F = 37°, and ∠D = 70°, follow these steps:
Find ∠E using the Triangle Sum Theorem (the sum of the angles in a triangle is always 180°).
∠E = 180° - (∠F + ∠D) = 180° - (37° + 70°) = 180° - 107° = 73°
Use the Law of Sines to find side d.
(sin ∠F) / d = (sin ∠E) / e
(sin 37°) / d = (sin 73°) / 67 inches
Solve for side d.
d = (67 inches * sin 37°) / sin 73°
d ≈ 44.7 inches
Use the formula for the area of a triangle with two sides and the included angle.
Area = 0.5 * d * e * sin ∠D
Area = 0.5 * 44.7 inches * 67 inches * sin 70°
Area ≈ 1439.1 square inches
Thus, the area of ΔDEF, to the nearest 10th of a square inch, is approximately 1439.1 square inches.
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Verify that the function
f(x) = -4x^2 + 12x - 4 In x attains
an absolute maximum and absolute minimum
on [1/2, 2].
Find the absolute maximum and minimum
values.
The function f(x) = -4x² + 12x - 4 attains an absolute maximum of 3 at x = 1/2 and an absolute minimum of -8 at x = 2 on the interval [1/2, 2].
To help you verify and find the absolute maximum and minimum values of the function f(x) = -4x² + 12x - 4 on the interval [1/2, 2].
Step 1: Find the critical points by taking the derivative of f(x) and setting it to 0.
f'(x) = -8x + 12
Step 2: Solve f'(x) = 0 to find critical points.
-8x + 12 = 0
x = 3/2
Step 3: Evaluate the function f(x) at the critical point and the interval's endpoints.
f(1/2) = -4(1/2)^2 + 12(1/2) - 4(1/2) = 3
f(3/2) = -4(3/2)^2 + 12(3/2) - 4(3/2) = 1
f(2) = -4(2)^2 + 12(2) - 4(2) = -8
Step 4: Compare the function values and determine the absolute maximum and minimum values.
The absolute maximum value is 3 at x = 1/2.
The absolute minimum value is -8 at x = 2.
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What is the measure of ∠SQR?
the ∠sqr is 4y= 4*29=116° we can get this answer with supplementary angle fact and sum of angle in triangle is 180 degree
what is supplementary angle ?
In geometry, two angles are called supplementary angles if their sum is equal to 180 degrees. In other words, if angle A and angle B are supplementary, Supplementary angles are commonly found in many geometric shapes, such as triangles and quadrilaterals, as well as in other applications of geometry. When two angles are supplementary, they form a straight line or a straight angle, which is an angle that measures exactly 180 degrees. For example, if one angle of a triangle measures 80 degrees, then the other two angles are supplementary and together measure 100 degrees (180 degrees - 80 degrees).
In the given question,
with the fact of complimentary angles we can write as follows
angle trq+ angle qrs =180
angle qrs=180-145=35 degree
so in triangle we have sum of all angle is 180 degree so we can write as follows
∠r+∠q+∠s=180
35+4y+y=180
5y=180-35
y=145/5
y=29 degree
so the ∠sqr is 4y= 4*29=116°
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Researcher are recording how much of an experimental medication is in a person’s bloodstream every hour. they discover that half-life of the medication is about 6 hours.
When researchers record how much of an experimental medication is in a person's bloodstream every hour, they are measuring the medication's concentration over time. This information is important because it can help determine the medication's effectiveness and potential side effects.
The half-life of a medication is the time it takes for half of the drug to be eliminated from the body. In this case, the half-life of the experimental medication is about 6 hours.
Knowing the half-life of a medication is important because it can help predict how long it will take for the drug to be eliminated from the body and when the next dose should be administered. For example, if a medication has a half-life of 6 hours, it means that after 6 hours, half of the medication will be eliminated from the body.
After another 6 hours, half of the remaining medication will be eliminated, and so on.
By monitoring the concentration of the medication in a person's bloodstream every hour, researchers can determine how quickly the drug is being absorbed and eliminated from the body. z
This information can help optimize dosing and minimize potential side effects. Overall, understanding the pharmacokinetics of a medication is crucial for safe and effective use in clinical practice.
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help mif with dis math probles pwees
For this above box plot prompt, the answer are given below.
What is the explanation for the response?Part A
From the box plots, we can see that the Red Team has the least variability and spread of times, followed by the Blue Team and then the Green Team.
The Red Team's box is the smallest, indicating that their times are more tightly clustered together.
Blue Team:
Q1: 75
Q2: 82
Q3: 87
IQR: 12
Upper fence: Q3 + 1.5IQR = 87 + 1.512 = 105
There are no outliers
Green Team:
Q1: 70
Q2: 75
Q3: 80
IQR: 10
Upper fence: Q3 + 1.5IQR = 80 + 1.510 = 95
There is one outlier at 90
Red Team:
Q1: 80
Q2: 83
Q3: 87
IQR: 7
Upper fence: Q3 + 1.5IQR = 87 + 1.57 = 98.5
There are no outliers
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Question content area top
Part 1
Sandra
biked
700
meters
on Friday. On Saturday,
she
biked
4
kilometers. On Sunday,
she
biked
2
kilometers,
600
meters. How many
kilometers
did
Sandra
bike over the three days
(3x^3 y^2)^3 (2x^4 y^2)^2
Simplify fully
NEED HELP ASAPPPP!!!!!
PLEASE HELP ME!!!!!!!!!!!!
The relationship between the squares formed by the sides of a right triangle is defined by Pythagorean Theorem, which states that the square on the hypotenuse side is the sum of the squares on the other two sides.
How can the Pythagorean Theorem describe the relationship between the sides of a right triangle?According to Pythagorean Theorem, the square formed by the side length of the hypotenuse side of right triangle is equivalent to the sum of the squares formed by the lengths of the other two sides
Let a, b, and c represent the lengths of the sides of the right triangle, where;
a = The length of the hypotenuse side
b = The length of a leg of the right triangle
c = The length of the other leg of the right triangle
The area of each squares are therefore;
Area of the square formed by the hypotenuse side = a²
Area of the square formed by the legs = b² and c²
Therefore; a² = b² + c²
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The water level of a tank every minute since it began filling is indicated by segments A, B, and C on the graph below.
Filling Water Tank
Water Level
(centimeters)
B
100
80
60
40
20
0
A
B
C
2
Time (minutes)
Place the segments in the correct order from the least to the greatest rate of increase in the water level.
10)
B has the least rate of increase, followed by A, and C has the greatest rate of increase.
We have,
The segments in order from the least to the greatest rate of increase in the water level are:
B, A, C.
Segment B has a constant rate of increase of 20 cm/min.
Segment A has a variable rate of increase that starts at 20 cm/min and decreases as the tank fills up.
Segment C has a variable rate of increase that starts at 20 cm/min and increases as the tank fills up.
Therefore,
B has the least rate of increase, followed by A, and C has the greatest rate of increase.
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Same increased the amount of protein she eats every day 45g to 58. 5g. By what percentage did Sam increase the amount of protein she eats
Sam increase the amount of protein she eats by a percentage of 30%.
To find the percentage increase, we can use the formula: (change in amount / original amount) x 100%.
Percentage is a way to express a number as a fraction of 100. It is a convenient method for comparing ratios or proportions because it standardizes them to a common denominator of 100. In this case, we want to find the percentage increase in Sam's daily protein consumption.
First, we need to determine the change in amount. This can be found by subtracting the original amount from the new amount: 58.5g - 45g = 13.5g.
Next, we'll divide the change in amount by the original amount: 13.5g / 45g = 0.3. To express this as a percentage, we'll multiply by 100: 0.3 x 100% = 30%.
Therefore, Sam increased her daily protein intake by 30%. This percentage helps us understand the relative change in her protein consumption compared to her initial intake.
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Homeowners in different parts of the country heat their homes with liquid propane gas. The gas is stored in tanks similar to the one shown. In terms of Pi , what is the volume of the gas tank, to the nearest hundredth cubic foot?
The volume of the gas tank is given as follows:
V = 15.19π ft³.
How to obtain the volume of the cylinder?The volume of a cylinder of radius r and height h is given by the equation presented as follows:
V = πr²h.
The dimensions for this problem are given as follows:
r = 1.5 ft -> as it is half the diameter of 3 ft.h = 6.75 ft.Hence the volume of the tank is given as follows:
V = π x 1.5² x 6.75
V = 15.19π ft³.
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Talissa invested money into two different accounts. One at citibank which
she started her investment at $400 with an interest rate of 3% compounded
annually. She started at the same price at the second bank, however the
interest rate was 4. 2% compounded continuously. Set up an equation to show
the total amount.
To set up an equation to show the total amount, we can use the formula for compound interest:
A = P(1 + r/n)^nt
Where:
A = the total amount
P = the principal (initial investment)
r = the interest rate
n = the number of times the interest is compounded per year
t = the time period (in years)
For the investment at Citibank:
P = $400
r = 3%
n = 1 (compounded annually)
t = 1 (since it is compounded annually)
So, the equation would be:
A1 = $400(1 + 0.03/1)^(1*1)
A1 = $412
For the investment at the second bank:
P = $400
r = 4.2%
n = ∞ (compounded continuously)
t = 1 (since it is for 1 year)
So, the equation would be:
A2 = $400e^(0.042*1)
A2 = $416.99
To find the total amount, we can add the two amounts together:
Total amount = A1 + A2
Total amount = $412 + $416.99
Total amount = $828.99
Therefore, Talissa's total amount after one year with the two investments is $828.99.
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Mr. Flanders is giving each of his students 1 fruit chew candy. There are 4 possible flavors: cherry, orange, lemon, and strawberry. The
probability of getting cherry is 1/5, the probability of getting orange is 1/4, and the probability of getting lemon is 1/3. What is the probability of
getting strawberry?
a
3/4
1/4
О Ы
Os
13/60
d
11/60
The probability of getting strawberry is 11/60. The correct option is d.
To determine the probability of getting strawberry, we need to consider the probabilities of all the possible flavors and calculate the probability of strawberry using the information given.
Given probabilities:
Probability of getting cherry = 1/5
Probability of getting orange = 1/4
Probability of getting lemon = 1/3
Since there are only four flavors in total, we can calculate the probability of getting strawberry by subtracting the sum of the probabilities of cherry, orange, and lemon from 1.
Probability of getting strawberry = 1 - (1/5 + 1/4 + 1/3)
To simplify the calculation, we find a common denominator for 5, 4, and 3, which is 60.
Probability of getting strawberry = 1 - (12/60 + 15/60 + 20/60)
= 1 - 47/60
= 13/60
Therefore, the probability of getting strawberry is indeed 13/60, which corresponds to option d) 11/60 in the given list of options.
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A student imagined one number. 2 is written to the right side of the number and 14 is added to the obtained number. 3 is written to the right side of the obtained number and 52 is added to the newly obtained number. The result of dividing the final number by 60 is the quotient that is for 6 greater than the initial number and the remainder is a two-digit number with both digits the same as the initial number. Find the initial number
The initial number is approximately 7.33.
Let's call the initial number "x".
According to the problem, the first step is to write 2 to the right of the number: this gives us the number 10x + 2.
-The next step is to add 14 to this number, which gives us:
10x + 2 + 14 = 10x + 16
-Then we write 3 to the right of this number, giving:
100x + 16 + 3 = 100x + 19
-And finally, we add 52 to this number:
100x + 19 + 52 = 100x + 71
Dividing this final number by 60 gives a quotient that is 6 greater than the initial number and a remainder that is a two-digit number with both digits the same as the initial number.
-So we have the equation:
(100x + 71) ÷ 60 = x + 6 + 0.01x
-We want to solve for x, so we first multiply both sides by 60:
100x + 71 = 60(x + 6 + 0.01x)
-Simplifying the right-hand side:
100x + 71 = 60x + 360 + 0.6x
Combining like terms:
39.4x =289
Dividing both sides by 39.4:
x =7.33
Therefore, the initial number is approximately 7.33.
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