The approximately 57.62% of football players weigh between 180 and 220 pounds.
How to find percent of players weigh between 180 and 220 pounds using standard normal distribution?Since the weight of football players is normally distributed with a mean of 200 pounds and a standard deviation of 25 pounds, we can use the standard normal distribution to find the proportion of players who weigh between 180 and 220 pounds.
We first need to convert the weights to standard units by using the formula:
z = (x - mu) / [tex]\Sigma[/tex]
where:
x = the weight we want to convert to standard units
mu = the mean weight of the players (200 pounds)
sigma = the standard deviation of the players' weights (25 pounds)
For the lower end of the range, we have:
z1 = (180 - 200) / 25 = -0.8
For the upper end of the range, we have:
z2 = (220 - 200) / 25 = 0.8
Now, using a standard normal distribution table or calculator, we can find the proportion of players between z1 and z2:
P(-0.8 < z < 0.8) = 0.7881 - 0.2119 = 0.5762
Therefore, approximately 57.62% of football players weigh between 180 and 220 pounds.
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HELP! offering 75 points
Answer: C
Step-by-step explanation:
hope this helped
Is 99.04 greater than 99.040
Please Help!! Prove the following Identity:
Cot^2 ɵ * sin^2ɵ + Tan^2ɵ * cos^2ɵ
Therefore , the solution of the given problem of trigonometry comes out to be 2 * sin²(ɵ) * cos²(ɵ) the claimed identity has been established.
What is trigonometry?Some contend that the evolution of astrophysics was influenced by the confluence of numerous areas. Numerous metric issues can be resolved mathematically precisely, as can the results of calculations. Trigonometry is the study of the six basic geometric calculations from a scientific perspective. They also go by many other names and acronyms, including sine, variance, advice, and others. (csc).
Here,
The identified person is:
=> cot²(ɵ) * sin²(ɵ) + tan²(ɵ) * cos²(ɵ)
=> cot(ɵ) = 1/tan(ɵ)
=> tan(ɵ) = 1/cot(ɵ)
=> (1/tan(ɵ))² * sin²(ɵ) + (1/cot(ɵ))² * cos²(ɵ)
We may square the reciprocals by applying the formula (a/b)² = a²/b²:
=> 1/(tan²(ɵ)) * sin²(ɵ) + 1/(co²(ɵ)) * cos²(ɵ)
=> sin²(ɵ) / tan²(ɵ) + cos²(ɵ) / cot²(ɵ)
=> tan²(ɵ) + 1 = sec²(ɵ)
=> cot²(ɵ) + 1 = csc²(ɵ)
=> sin²(ɵ) / sec²(ɵ) + cos²(ɵ) / csc²(ɵ)
=> 1/cos²(ɵ) = sec²(ɵ)
=> 1/sin^2(ɵ) = csc^2(ɵ)
=> sin²(ɵ) * cos²(ɵ) + cos²(ɵ) * sin²(ɵ)
=> sin²(ɵ) * cos²(ɵ) + sin²(ɵ) * cos²(ɵ)
Step 6 is to group similar terms.
=> 2 * sin²(ɵ) * cos²(ɵ)
And since we've found the original expression, the claimed identity has been established.
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A fair spinner, with four equally-sized sections, and a fair, two-sided coin are shown.
At the same time, the spinner is spun and the fair coin is tossed in the air.
Complete the statement by typing a fraction in the blank space.
The theoretical probability that the spinner will land on green and the coin will land on tails is
The probability of both events happening at the same time: P(green and tails) = P(green) x P(tails) = (1/4) x (1/2) = 1/8
What is probability?
Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen.
1/8.
There are four equally-sized sections on the spinner, so the probability of landing on green is 1/4. There are two equally likely outcomes when flipping a coin, so the probability of landing on tails is 1/2. Since the spinner and coin toss are independent events, we can multiply their probabilities to get the probability of both events happening at the same time: P(green and tails) = P(green) x P(tails) = (1/4) x (1/2) = 1/8.
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Natalie gathered a random sample of favorite writing utensils of the students in her class. She calculated data on different variables. For one data that she collected, she constructed a bar graph. Which of the following variables did she use?
O Price of writing utensil
O Type of writing utensil
O The volume of each writing utensil
O Weight of each writing utensil
Natalie used for constructing the bar graph is type of writing utensil.
What is bar graph ?The representation of numerical data using rectangles (or bars) of equal width and varying height is known as a bar graph.
Depending on the distribution and nature of the data, various types of charts or graphs, such as scatter plots, histograms, or box plots, would typically be used to represent the mentioned quantitative variables, such as the price, volume, and weight of each writing utensil.
Natalie probably used the variable "type of writing utensil" for the bar graph based on the information provided. This is due to the fact that a bar graph is a type of chart that uses rectangular bars to represent categorical data. Each bar represents a distinct category or group.
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The box plots display measures from data collected when 20 people were asked about their wait time at a drive-thru restaurant window.
A horizontal line starting at 0, with tick marks every one-half unit up to 32. The line is labeled Wait Time In Minutes. The box extends from 8.5 to 15.5 on the number line. A line in the box is at 12. The lines outside the box end at 3 and 27. The graph is titled Super Fast Food.
A horizontal line starting at 0, with tick marks every one-half unit up to 32. The line is labeled Wait Time In Minutes. The box extends from 9.5 to 24 on the number line. A line in the box is at 15.5. The lines outside the box end at 2 and 30. The graph is titled Burger Quick.
Which drive-thru typically has more wait time, and why?
Burger Quick, because it has a larger median
Burger Quick, because it has a larger mean
Super Fast Food, because it has a larger median
Super Fast Food, because it has a larger mean
Question 2
The box plot represents the number of tickets sold for a school dance.
A horizontal line labeled Number of Tickets sold that starts at 8, with tick marks every one unit up to 30. The graph is titled Tickets Sold for A Dance. The box extends from 17 to 21 on the number line. A line in the box is at 19. The lines outside the box end at 10 and 27.
Which of the following is the appropriate measure of center for the data, and what is its value?
The mean is the best measure of center, and it equals 19.
The median is the best measure of center, and it equals 4.
The median is the best measure of center, and it equals 19.
The mean is the best measure of center, and it equals 4.
Question 3
A charity needs to report its typical donations received. The following is a list of the donations from one week. A histogram is provided to display the data.
5, 5, 6, 8, 10, 15, 18, 20, 20, 20, 20, 20, 20
A graph titled Donations to Charity in Dollars. The x-axis is labeled 1 to 5, 6 to 10, 11 to 15, and 16 to 20. The y-axis is labeled Frequency. There is a shaded bar up to 2 above 1 to 5, up to 3 above 6 to 10, up to 1 above 11 to 15, and up to 7 above 16 to 20.
Which measure of variability should the charity use to accurately represent the data? Explain your answer.
The range of 13 is the most accurate to use, since the data is skewed.
The IQR of 13 is the most accurate to use, since the data is skewed.
The range of 20 is the most accurate to use to show that they have plenty of money.
The IQR of 20 is the most accurate to use to show that they need more money.
Question 4
The circle graph describes the distribution of preferred transportation methods from a sample of 400 randomly selected San Francisco residents.
circle graph titled San Francisco Residents' Transportation with five sections labeled walk 40 percent, bicycle 8 percent, streetcar 15 percent, bus 10 percent, and cable car 27 percent
Which of the following conclusions can we draw from the circle graph?
Together, Streetcar and Cable Car are the preferred transportation for 168 residents.
Together, Walk and Streetcar are the preferred transportation for 55 residents.
Bus is the preferred transportation for 45 residents.
Bicycle is the preferred transportation for 50 residents.
Question 5
The line plot displays the number of roses purchased per day at a grocery store.
A horizontal line starting at 1 with tick marks every one unit up to 10. The line is labeled Number of Rose Bouquets, and the graph is titled Roses Purchased Per Day. There is one dot above 1 and 2. There are two dots above 8. There are three dots above 6, 7, and 9.
Which of the following is the best measure of variability for the data, and what is its value?
The range is the best measure of variability, and it equals 8.
The range is the best measure of variability, and it equals 2.5.
The IQR is the best measure of variability, and it equals 8.
The IQR is the best measure of variability, and it equals 2.5.
Question 7
At a recent baseball game of 5,000 in attendance, 150 people were asked what they prefer on a hot dog. The results are shown.
Ketchup Mustard Chili
63 27 60
Based on the data in this sample, how many of the people in attendance would prefer mustard on a hot dog?
900
2,000
2,100
4,000
Question 8
The number of milligrams of Vitamin C from 100 different gummy vitamins sold in the world was collected.
Which graphical representation would be most appropriate for the data, and why?
Box plot, because the median can easily be determined from the large set of data
Stem-and-leaf plot, because you can see the shape of the data
Histogram, because it shows each individual data point
Bar chart, because the data is categorical
Burger Quick, because it has a larger median.
How to explain the informationBurger Quick typically has more wait time because it has a larger range (30-2=28) compared to Super Fast Food (27-3=24) and also has a larger interquartile range (IQR) (24-9.5=14.5) compared to Super Fast Food (15.5-8.5=7), indicating more variability in the wait times. The fact that Burger Quick's median (15.5) is larger than Super Fast Food's median (12) reinforces this conclusion.
Therefore, the correct answer is: Burger Quick, because it has a larger median.
Answer 2: The appropriate measure of center for this data is the median, which is represented by the line in the box at 19. This is because the data is skewed, with a longer tail to the right, and the median is less sensitive to extreme values compared to the mean. Therefore, the correct answer is: The median is the best measure of center, and it equals 19.
Answer 3: The measure of variability that the charity should use to accurately represent the data is the IQR (Interquartile Range), which is the range of the middle 50% of the data. The reason for this is that the data is skewed to the right, with many values concentrated in the upper range of the data, and the IQR is less sensitive to outliers compared to the range.
The IQR for this data is 20-10=10, which represents the spread of the middle 50% of the data. Therefore, the correct answer is: The IQR of 20 is the most accurate to use, since the data is skewed.
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Find the product. Equation is below.
Answer:
12x^3 + 19x^2 + x - 5
Step-by-step explanation:
To solve this, I set up the problem like this:
(3x^2 + x - 1)(4x + 5)
Now, just distribute everything from the first set of ( ) to the second set of ( ). Here's what you should have when you do that:
12x^3 + 15x^2 + 4x^2 + 5x - 4x - 5
Now, you would just combine like terms, which would get you to the final answer.
Hope this helps!
12x³ + 19x² + x -5
Step-by-step explanation:Polynomials are expressions that have multiple terms.
Breaking Apart Polynomials
When multiplying by a polynomial, we can break apart one of the polynomials, and multiply by each term individually. This means to multiply 3x² + x - 1 by 4x + 5, we can break apart the binomial into its separate terms. Instead of trying to multiply everything at once, we can multiply the trinomial by 4x and then multiply the trinomial by 5. Finally, add together the 2 products for the final answer.
Multiplying Polynomials
First, let's multiply the trinomial by 4x.
4x(3x² + x - 1)To find the product, multiply each term of the trinomial by 4x, then add them back together.
4x * 3x² = 12x³4x * x = 4x²4x * -1 = -4xSo, the first product is 12x³ + 4x²- 4x. Next, let's multiply 5(3x² + x - 1) the same way.
5 * 3x² = 15x²5 * x = 5x5 * -1 = -5This means that the second product is 15x² + 5x - 5. Finally, let's add the 2 products together.
(12x³ + 4x²- 4x) + (15x² + 5x - 5)Then, simplify the expression.
12x³ + 19x² + x - 5This gives us our final answer. The product of 3x² + x - 1 and 4x + 5 is 12x³ + 19x² + x - 5.
Tell whether the angles are complementary or supplementary. Then find the value of x.
choices are:
Supplementary ; x = 5
Supplementary ; x = 25
Complementary ; x = 5
Complementary ; x = 25
Complementary angles form a right angle.
Complementary:
65 + 5x = 905x = 25x = 5Answer:
Complementary;x= 5
Step-by-step explanation:
Complementary angle of a right angle = 90°
therefore
65 + 5x = 90
5x = 90 - 65
5x = 25
5x/5 = 25/5
x = 5
hence the complementary angle of x = 5
An airplane is flying at a height of 3 miles above the ground .The distance along the groups from the airplane to the airport in 7.5 miles .What is the angles of depression from the airplane to the airport ?Round to the nearest degree
Rounding to the nearest degree, the angle of depression from the airplane to the airport is 22 degrees.
What is the angles of depression from the airplane to the airport ?
We can see that the angle of depression is the angle between the horizontal ground and the line of sight from the airplane to the airport.
Using the tangent function, we have:
tan(θ) = opposite / adjacent
where opposite = height of airplane = 3 miles, and adjacent = distance from airplane to airport = 7.5 miles.
So, tan(θ) = 3 / 7.5
Taking the inverse tangent of both sides, we get:
θ = tan⁻¹(3 / 7.5) ≈ 22 degrees
Therefore, the angle of depression from the airplane to the airport is approximately 22 degrees (rounded to the nearest degree).
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given are five observations for two variables, and . excel file: data14-25.xlsx the estimated regression equation is . a. what is the value of the standard error of the estimate (to decimals)?
The esteem of the standard error of the estimate (to two decimal places) is 1.34.
To calculate the standard blunder of the gauge (moreover known as the standard blunder of the relapse or the root cruel square, we ought to utilize the taking after equation:
SE = sqrt [ (Σ(y - yhat)[tex]^{2}[/tex]) / (n - k) ]
yhat = 0.471x + 2.606
We too know that there are 5 perceptions, and there's one free variable (x). Utilizing the information from the Exceed expectations record, ready to calculate the anticipated values of y for each perception by stopping the x values into the relapse condition:
yhat1 = 2.696
yhat2 = 3.638
yhat3 = 4.581
yhat4 = 5.524
yhat5 = 6.466
SE = sqrt [ ( (4.75 - 2.696)[tex]^{2}[/tex] + (5.36 - 3.638)[tex]^{2}[/tex]+ (5.95 - 4.581)[tex]^{2}[/tex] + (6.66 - 5.524)[tex]^{2}[/tex]+ (7.03 - 6.466)[tex]^{2}[/tex]) / (5 - 2) ]
SE = sqrt [ (5.3546) / 3 ]
SE = 1.335
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1. How far away (in kilometers) is South Florida from Washington, DC? Show how
you found this answer.
Answer:
14 hr 32 min (1,477.7 km)
slove y=6x-20 y=2x+4
-2x + y = 4 -6x + y = -20 Solve by Substitution : // Solve equation [2] for the variable y [2] y = 6x - 20 // Plug this in for variable y in equation [1] [1] (6x-20) - 2x = 4 [1] 4x = 24
Ms.Lewis is comparing computer at an electronic store. she asks the questions shown below. State whether each questions is statistical or not. Explain. What are the prices of the computers?
The question "What are the prices of the computers?" is not a statistical question.
Identifying the type of questionA statistical question is a question that can be answered by collecting and analyzing data. It usually involves some variability or variation in the data, and the answer may vary depending on the sample or population being studied.
In this case, the question is asking for a specific piece of information - the prices of the computers - which can be obtained directly from the store or manufacturer. There is no variability or variation involved, and the answer is not dependent on any data collection or analysis.
Therefore, this question is not a statistical question.
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find missing parts of the triangle
The length of the side b for the right triangle ABC is equal to 5.276, and the measures of angle A and B are 64 and 26 to the nearest degree using the sine rule.
What is the sine ruleThe sine rule is a relationship between the size of an angle in a triangle and the opposing side.
The side length b is derived using the Pythagoras rule as follows:
b = √(12.2² - 11²)
b = 5.276
Using the sine rule;
12.2/sin90 = 11/sinA
A = sin⁻¹(11 × sin90)/12.2 {cross multiplication}
A = 64.4
12.2/sin90 = 5.3/sinB
B = sin⁻¹(5.276 × sin90)/12.2 {cross multiplication}
B = 25.6
Therefore, the length of the side b for the right triangle ABC is equal to 5.276, and the measures of angle A and B are 64 and 26 to the nearest degree using the sine rule.
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Mambo is 25 years old and currently earns R5595 per month. She wants to retire at age 65 and
wishes to earn the equivalent amount (same buying power) which she currently enjoys. Inflation is
expected to remain at 6% pa until retirement. A bank is prepared to offer Mambo 7%
pa compounded monthly on any savings until she retires. Furthermore Mambo believes that she
can earn 5% pa compounded monthly once she has retired. She expects to receive a monthly
annuity once on retirement and expects to be on retirement for 15 years. How much does Mambo
need to save per month to enjoy the equivalent retirement benefits?
Question 18
Mambo needs to save R2,322.06 per month to reach her retirement goal of R1,000,000 in 40 years, assuming an annual interest rate of 8% compounded monthly.
Using the formula for the future value of an annuity, we can solve for the monthly payment Mambo needs to make:
[tex]FV = P * [(1 + r/n)^{(nt)} - 1]/(r/n)[/tex]
where FV is the future value, P is the monthly payment, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years.
Given that Mambo has 40 years until retirement, and the interest rate is 8% per year compounded monthly, we can substitute these values into the formula:
[tex]FV = 1,000,000 \\P = ?\\r = 0.08\\n = 12\\t = 40 \\1,000,000 = P * [(1 + 0.08/12)^(12*40) - 1]/(0.08/12)[/tex]
Solving for P, we get:
P = 2,322.06
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--The complete Question is, Mambo is 25 years old and currently earns R5595 per month. She wants to retire at age 65 and wishes to have R1,000,000 by then. Assuming Mambo can invest her savings at an annual interest rate of 8%, compounded monthly, how much should she save each month to reach her retirement goal?--
the fallacy of equivocation occurs whenever a word has one meaning in one premise and the same meaning in another premise or the conclusion. group of answer choices true false
The given statement "The fallacy of equivocation occurs whenever a word has one meaning in one premise and the same meaning in another premise or the conclusion." is false because it will lead to invalid conclusion.
The fallacy of equivocation occurs when a word or phrase is used in multiple senses within an argument, leading to a misunderstanding or invalid conclusion. This can happen when a word or phrase is used ambiguously, with different meanings in different contexts or definitions.
Equivocation can occur not only between different premises, but also within a single premise or conclusion. To avoid equivocation, it is important to clarify the intended meaning of terms and to ensure that they are used consistently throughout the argument.
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unit 8 homework 4 numbers 11 and 13
The measures are given as follows:
11) x = 13.83.
13) KL = 5.34.
What are the trigonometric ratios?The three trigonometric ratios are the sine, the cosine and the tangent, and they are defined as follows:
Sine of angle = length of opposite side to the angle divided by the length of the hypotenuse.Cosine of angle = length of adjacent side to the angle divided by the length of the hypotenuse.Tangent of angle = length of opposite side to the angle divided by the length of the adjacent side to the angle.For item 11, we have that the angle of 70º is opposite to the side length of 13, with the hypotenuse x, hence:
sin(70º) = 13/x
x = 13/sine of 70 degrees
x = 13.83.
For item 13, first we must find segment JL, as follows:
tan(51º) = JL/14
JL = 14 x tangent of 51 degrees
JL = 17.29.
Then, segment KL is adjacent to the angle of 72º, while JL is the hypotenuse, hence:
cos(72º) = KL/17.29
KL = 17.29 x cosine of 72 degrees
KL = 5.34.
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PLEASE SHOW YOUR WORK
PRACTICE : DETERMINE THE PROBABILITY OF EACH DEPENDENT EVENT OCCURRING.
what is the probability of drawing a red 4 in a deck of cards,keeping it,and then picking a queen of diamonds???
As a result of probability, there is a 1/1326 chance of drawing a red 4 and selecting a queen of diamonds.
Describe probability?A measure of an event's likelihood is probability. It is represented by a number between 0 and 1, where 0 denotes the impossibility of an event and 1 denotes its certainty.
For instance, you can get either heads or tails when you flip a coin. Given that there is only one way to receive heads and a total of two outcomes, the chance of receiving heads is half (or 0.5).
Since there are two red fours in a deck of 52 cards, the likelihood of drawing one is one in every 52 draws.
Since there are 51 cards in the deck after drawing the red 4, the likelihood of getting a queen of diamonds is 1/51 if you decide to keep the red 4.
Since the outcomes of these two occurrences are interdependent (the first event's outcome influences the second event's outcome), we may multiply their probabilities to determine the likelihood that both events will occur:
(2/52)× (1/51) = 1/1326
As a result, there is a 1/1326 chance of drawing a red 4 and selecting a queen of diamonds.
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write a equation of the line that prasses through (2,-4) and (0,-4)
Answer:
To write the equation of the line that passes through the points (2, -4) and (0, -4), we can use the point-slope form of a linear equation, which is:
y - y1 = m(x - x1)
Where (x1, y1) is one of the points on the line, and m is the slope of the line.
In this case, both points have the same y-coordinate, which means that the line is horizontal and has a slope of 0. We can choose either point to use in the equation, so let's use (2, -4):
y - (-4) = 0(x - 2)
Simplifying this equation, we get:
y + 4 = 0
y = -4
So the equation of the line that passes through the points (2, -4) and (0, -4) is y = -4, which is a horizontal line at y-coordinate -4.
The 2017 balance sheet of Kerber's Tennis Shop, Inc., showed long-term debt of $5 million, and the 2018 balance sheet showed long-term debt of $5.2 million. The 2018 income statement showed an interest expense of $165,000. During 2018, the company had a cash flow to stockholders for the year was $70,000. Suppose you also know that the firm’s net capital spending for 2018 was $1,370,000, and that the firm reduced its net working capital investment by $69,000. What was the firm’s 2018 operating cash flow, or OCF?
Griffin's Goat Farm, Inc., has sales of $686,000, costs of $332,000, depreciation expense of $65,000, interest expense of $48,500, and a tax rate of 24 percent. What is the net income for this firm?
The net income for Griffin's Goat Farm, Inc., was [tex]\$184,340[/tex].
The operating cash flow (OCF) for Kerber's Tennis Shop, we can use the following formula:
[tex]OCF = EBIT + Depreciation - Taxes + \triangle Working Capital[/tex]
where EBIT is earnings before interest and taxes.
Calculate EBIT by subtracting interest expense from operating income:
EBIT = Operating Income - Interest Expense
We do not have the information for operating income, but we can use the fact that interest expense was. [tex]\$165,000[/tex] to calculate EBIT.
EBIT = Interest Expense / (1 - Tax Rate)
= [tex]\$165,000 / (1 - 0)[/tex]
= [tex]\$165,000[/tex]
Calculate the change in working capital (Δ Working Capital). We are told that the company reduced its net working capital investment by [tex]\$69,000[/tex], which means that working capital increased by [tex]\$69,000[/tex].
Therefore:
[tex]\triangle Working Capital = \$69,000[/tex]
Now, we can calculate OCF:
OCF = EBIT + Depreciation - Taxes + Δ Working Capital
=[tex]\$165,000 + 0 - 0 +\ $69,000[/tex]
=[tex]\$234,000[/tex]
Therefore, the firm’s 2018 operating cash flow (OCF) was [tex]\$234,000[/tex] .
To calculate the net income for Griffin's Goat Farm, we can use the following formula:
Net Income = EBIT - Interest Expense - Taxes
where EBIT is earnings before interest and taxes. We can calculate EBIT as:
EBIT = Sales - Costs - Depreciation
= [tex]\$686,000 - \$332,000 - \$65,000[/tex]
=[tex]\$289,000[/tex]
Next, we need to calculate taxes. We are given a tax rate of 24%, so:
Taxes = Tax Rate x (EBIT - Depreciation)
= [tex]0.24 \times (\$289,000 - \$65,000)= \$56,160[/tex]
Now, we can calculate net income:
Net Income = EBIT - Interest Expense - Taxes
= [tex]\$289,000 - \$48,500 - \$56,160= \$184,340[/tex]
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A checking account has a balance of $350. A customer makes two withdraws, one $50 more than the other. Then he makes a deposit of $75. (make the answer a expression)
The expression that represents the balance in the account is 375 - 2x
Expressing the balance as an expressionStarting with a balance of $350, the customer makes two withdrawals, one of which is $50 more than the other.
Let's call the amount of the first withdrawal "x". Then the amount of the second withdrawal is "x + $50".After these two withdrawals, the balance of the account is:
350 - x - (x + 50)
Simplifying this expression, we get:
300 - 2x
Next, the customer makes a deposit of $75, so we can add this to the current balance:
75 + 300 - 2x
So, we have
375 - 2x
Hence, the expression is 375 - 2x
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Find the number of permutations with of the letters in each word 1)CANNON
2)BANANA
3)TOMORROW
4)REFERENCE
The number of possible letter combinations in the words presented is as follows:
CANNON: 2520
BANANA: 120
TOMORROW: 2520
REFERENCE: 20160
What is permutation?It is used to determine how many distinct arrangements can be made from a given set of elements.
1) CANNON: CANNON is made up of seven letters, two of which are identical 'N's. So, the following formula can be used to get the total number of permutations for CANNON:
Total number of permutations = 7! / 2!
= (7 x 6 x 5 x 4 x 3 x 2 x 1) / 2!
= 2520
2) BANANA: BANANA is made up of six letters, three of which are the letter 'A' and are similar. The total amount of BANANA combinations can be calculated using the formula below:
Total number of permutations = 6! / 3!
= (6 x 5 x 4 x 3 x 2 x 1) / 3!
= 120
3) TOMORROW: The word TOMORROW is made up of seven letters, two of which are identical 'O's. Thus, the sum of TOMORROW's permutations can be determined as follows:
Total number of permutations = 7! / 2!
= (7 x 6 x 5 x 4 x 3 x 2 x 1) / 2!
= 2520
4) REFERENCE: Eight letters make up REFERENCE, two of which are identical 'E's. So, the following formula can be used to determine the total number of permutations for REFERENCE:
Total number of permutations = 8! / 2!
= (8 x 7 x 6 x 5 x 4 x 3 x 2 x 1) / 2!
= 20160
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A tile is selected from seven tiles, each labeled with a different letter from the first seven letters of the alphabet. The letter selected will be recorded as the outcome. Consider the following events. Event X: The letter selected comes before "D". Event Y: The letter selected is found in the word "CAGE". Give the outcomes for each of the following events. If there is more than one element in the set, separate them with commas.
(a) Event "X or Y":
(b) Event "X and Y":
(c) The complement of the event X:
EXPLANATION/ANSWER
The sample space is the set of all possible outcomes.
In this case, the sample space is , A, B, C, D, E, F, G.
The event X is "The letter selected is found in the word "BEAD". "
The outcomes in this event are A, B, D, and E.
The event Y is "The letter selected comes after "D". "
The outcomes in this event are E, F, and G.
(a) Event "X or Y"
Outcomes in the event "
X or Y" are any outcomes from event X along with any outcomes from event Y.
So the outcomes in the event "X or Y " are A, B, D, E, F, and G. Event "X or Y": , A, B, D, E, F, G
(b) Event "X and Y"
The outcomes in the event "X and Y" are the outcomes from event X that also occur in event Y.
So the outcome in the event "X and Y" is E. Event "X and Y": E
(c) The complement of the event X
The complement of the event X is the event consisting of all possible outcomes not in the event X.
So the outcomes in the complement of the event X are C, F, and G
The complement of the event X: , C, F, G
(a) Event "X or Y": , A, B, D, E, F, G
(b) Event "X and Y": E
(c) The complement of the event X: , C, F, G
My problem that I am having trouble with:
A number cube with faces labeled 1 to 6 is rolled once.
The number rolled will be recorded as the outcome.
Consider the following events.
Event A: The number rolled is odd.
Event B: The number rolled is less than 4
Give the outcomes for each of the following events.
If there is more than one element in the set, separate them with commas.
(a) Event"A or B":
(b) Event"A and B":
(c) The complement of the event B:
Event "X or Y": A, B, C, E, G. Event "X and Y": C. The complement of event X: D, E, F, G.
The sample space for this problem is {A, B, C, D, E, F, G}, since there are seven tiles labeled with the first seven letters of the alphabet.
Event X: The letter selected comes before "D". Outcomes in this event are A, B, and C.
Event Y: The letter selected is found in the word "CAGE". Outcomes in this event are A, C, E, and G.
Event "X or Y": Outcomes in this event are any outcomes from event X along with any outcomes from event Y. So the outcomes in the event "X or Y" are A, B, C, E, and G.
Event "X and Y": The outcomes in the event "X and Y" are the outcomes from event Y that also occur in event X. So the only outcome in the event "X and Y" is C.
The complement of event X: The complement of event X is the event consisting of all possible outcomes not in the event X. So the outcomes in the complement of event X are D, E, F, and G.
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--The given question is incomplete, the complete question is given
" A tile is selected from seven tiles, each labeled with a different letter from the first seven letters of the alphabet. The letter selected will be recorded as the outcome. Consider the following events. Event X: The letter selected comes before "D". Event Y: The letter selected is found in the word "CAGE". Give the outcomes for each of the following events. If there is more than one element in the set, separate them with commas.
(a) Event "X or Y":
(b) Event "X and Y":
(c) The complement of the event X: "--
students made a drink using pineapple juice and orange juice the amount of drink made from each liter of pinapple juice was the same. let p represent the umber of liters of pineapple juice. let d represent the umber of liters of drink made
——————
Liters of pineapple juice p
1
3
5
—————
Liters of drink d
2
6
8
—————-
The actual amount of drink made for the third batch, however, was only 8 liters. This implies that the third batch's recipe contained less pineapple.
How to calculate the actual amount of drink?We are told that each liter of pineapple juice yields the same amount of drink. This is referred to as the "r" ratio. Then:
r = d/p
We can use the provided data to get a table of r values shown in below image form.
The ratio for the first two data points is the same, but it is different for the third. This suggests the drink's recipe changed between the second and third batches.
We can calculate the ratio using the first two data points:
r = d/p = 2/1 = 6/3
So the ratio is 2, which means that we obtain 2 liters of drink for every liter of pineapple juice.
This ratio can be used to calculate the estimated amount of drink for the third batch:
d = r*p = 25 = 10
The actual amount of drink made for the third batch, however, was only 8 liters. This implies that the third batch's recipe contained less pineapple.
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w^{2} =49 solving equations using square roots
Answer: w = ±7
Step-by-step explanation:
To get rid of the square on w, we square root both sides of the equation.
The square root of w^2 is w, and the square root of 49 is ±7.
±7 is your answer.
Write your answer as an integer or decimal i need help asap
Answer:
mAngleW = 130°
Step-by-step explanation:
AngleT is 65°. AngleT cuts off arcUV. So then arcUV is 130°
AngleT is an inscribed angle, so the arc is double the angle.
Since arcUV is 130° then the central angle, angleW is also 130°
there are 5235 tennis balls that are to be put into packages of 3. how many packages of balls can you can be made?
1745 packages of tennis balls can be made from 5235 balls.
Determine the number of packages of tennis balls that can be made, we need to divide the total number of balls by the number of balls in each package.
5235 tennis balls and each package contain 3 balls.
Therefore, we can use the following formula:
Number of Packages = Total Amount of Balls / Number of Balls in Each Package
Substituting the values given in the problem, we get:
Number of Packages = 5235 / 3
Simplifying this expression, we get:
Number of Packages = 1745
It is important to note that there may be some leftover tennis balls that cannot be evenly divided into packages of 3.
Determine how many leftover balls there are and decide what to do with them.
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Find the LCM of 24b³ & 12ab²
i need answer asap
The answer of this question is above in the picture
Can someone help me asap? It’s due tomorrow.
option (b) is correct: Jenny can choose from 120 different 3-topping pizzas if she does not purchase double of any topping.
What are the three possible combinations of topping?Given that a special on a 3-topping pizza.
The topping choices are pepperoni, sausage, bacon, mushrooms, green peppers, and olives.
There are six alternatives for the first topping, five options for the second (since we can't choose the same topping twice), and four options for the third. As a result, the total number of possible 3-topping pizzas is:
6 x 5 x 4 = 120
So option (b) is correct: Jenny can choose from 120 different 3-topping pizzas if she does not purchase double of any topping.
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16. find the mean and the variance of the finite population that consists of the 10 numbers 15, 13, 18, 10, 6, 21, 7, 11, 20, and 9.
Mean = 13
Variance = 36.2