The box plot that would represent the data recorded by Mr. Larson would be B. Second box plot.
How to find the box plot ?To find the correct box plot of the data recorded by Mr. Larson, the math teacher, first order the grades from lowest to highest :
70, 71, 73, 75, 77, 80, 84, 86, 87, 92, 95, 96, 97, 100
There are 14 grades which means that the median position would be the 7th and 8th grades average :
= ( 84 + 86 ) / 2
= 170 / 2
= 85
The position of Q3 would be:
= ( n + 1 ) x 75 %
= ( 14 + 1 ) x 75 %
= 11 th position which is 95
The correct box plot is therefore the second box plot which shows the Q3 as 95.
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Using the Pythagorean Theorem, what is the correct equation setup for a right triangle with side lengths measuring 7 in, 25 in, and 24 in?
A. 25^2 + 24^2 = 7^2
B. 7^2 + 25^2 = 24^2
C. 7^2 + 24^2 = 25^2
D. 24^2 + 25^2 = 7^2
Hence, 7 + 24 = 25 is a valid equation, and C is the correct response as the right triangle with sides of 7 inches, 25 inches, and 24 inches.
what is Pythagoras theorem ?A right quadrilateral relationship between its sides is described by the Pythagorean Theorem, a fundamental theorem of geometry. According to this rule, the hypotenuse's square value, which is the side that forms the right angle, is the same as the total of the squared that compose the other two sides. In other words, the following is how the theorem can be expressed for a quadrilateral with leg of length a, b, and c and a hypotenuse of length c: [tex]a^2 + b^2 = c^2[/tex] . Although it's believed that the Greeks and romans and Indians knew about this theorem before the ancient Greek philosopher Plato, who is recognized with discovering it, gave it its name.
given
The Pythagorean Theorem's equation setup for a right triangle is as follows: [tex]a^2 + b^2 = c^2[/tex]
where c is the length of the hypotenuse and a, b, and c are the lengths of the right triangle's legs.
Right triangle with sides of 7 inches, 25 inches, and 24 inches is shown. Its legs are 7 inches and 24 inches, and its hypotenuse is 25 inches. Hence, we may construct the equation as follows:
[tex]7^2 + 24^2 = 25^2[/tex]
When we simplify this equation, we obtain:
49 + 576 = 625
625 = 625
Hence, 7 + 24 = 25 is a valid equation, and C is the correct response as the right triangle with sides of 7 inches, 25 inches, and 24 inches.
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1)calculate the mean and standard deviation of the sampling distribution of
for srss of size 15.
2)interpret the standard deviation from part (1).
3)find the probability that the sample mean weight is greater than 3.55 kilograms.
It should be noted that to calculate the mean and standard deviation of the sampling distribution, you need to know the population mean (μ) and standard deviation (σ) and the sample size (n) of the distribution.
How to explain the meanThe mean (μx) of the sampling distribution of the sample mean (x) is equal to the population mean (μ):
μx = μ
The standard deviation (σx) of the sampling distribution of the sample mean (x is equal to the population standard deviation (σ) divided by the square root of the sample size (n):
σx = σ / √n
Therefore, in order to calculate the mean and standard deviation of the sampling distribution, you just need to plug in the values of μ, σ, and n into these formulas.
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How does one calculate mean and standard deviation of the sampling distribution.
How to interpret the standard deviation from part (1).
A sequence can be generated by using an=an−1+7, where a1=4 and n is a whole number greater than 1. What are the first 3 terms in the sequence? 7, 11, 15 7, 28, 112 4, 11, 18 4, 28, 196
To generate the sequence, we start with a1 = 4, and then use the formula an = an-1 + 7 for n > 1.
So, to find the first 3 terms of the sequence, we can use the formula:
a2 = a1 + 7 = 4 + 7 = 11
a3 = a2 + 7 = 11 + 7 = 18
The first 3 terms of the sequence are 4, 11, and 18.
So, the answer is 4, 11, 18, which corresponds to the third option.
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Estimate to find the correct answer for each expression.
A. 270 349. 6 - 112. 8
B. 220 173. 3 + 78. 4
C. 240 817. 2 - 597. 1
D. 250 108. 8 + 159. 3
The correct answer of estimation for each expression is 269,900, 220,251.7, 240,220.1 and 250,268.1.
270,349.6 - 112.8 = 270,236.8
To estimate, we can round 270,349.6 to 270,000 and round 112.8 to 100. Subtracting 100 from 270,000 gives us 269,900. Therefore, the estimated answer is 269,900.
220,173.3 + 78.4 = 220,251.7
To estimate, we can round 220,173.3 to 220,000 and round 78.4 to 80. Adding 80 to 220,000 gives us 220,080. Therefore, the estimated answer is 220,080.
240,817.2 - 597.1 = 240,220.1
To estimate, we can round 240,817.2 to 240,000 and round 597.1 to 600. Subtracting 600 from 240,000 gives us 239,400. Therefore, the estimated answer is 239,400.
250,108.8 + 159.3 = 250,268.1
To estimate, we can round 250,108.8 to 250,000 and round 159.3 to 160. Adding 160 to 250,000 gives us 250,160. Therefore, the estimated answer is 250,160.
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If f(x) = 3(5") + x and g(x) = 3cos(x), what is (f9)'()? O (3(5*) In(5) + 1)(3cos(x)) + (3(5") + x)(sin(x)) O (3(5") In(5) + 1)(3sin(x)) O (3(5") In(5) + 1)(-3sin(x)) O (3(5) In(5) + 1)(3cos(x)) + (3(5") + x)(-3sin(x))
The derivative of (f∘g)(x) can be found using the chain rule, which states that the derivative of (f∘g)(x) is (f'(g(x)))(g'(x)).
In this case, (f∘g)(x) = f(g(x)) = 3(5^x) + 3cos(x), so we need to find f'(g(x)) and g'(x) and then multiply them together. The derivative of f(x) is f'(x) = 15^x * ln(5) + 1, so the derivative of f(g(x)) with respect to g(x) is f'(g(x)) = 15^(g(x)) * ln(5) + 1. The derivative of g(x) is g'(x) = -3sin(x). Therefore, using the chain rule, we have:(f∘g)'(x) = f'(g(x)) * g'(x) = (15^(g(x)) * ln(5) + 1) * (-3sin(x))Substituting g(x) = 3cos(x), we get:(f∘g)'(x) = (15^(3cos(x)) * ln(5) + 1) * (-3sin(x))So the correct answer is: (3(5^3cos(x)) ln(5) + 1) * (-3sin(x))
For more similar questions on topic a) The intervals for which f(x) = -5.5sin(x) + 5.5cos(x) is concave up and concave down on [0,2π] can be found by analyzing the second derivative of the function. Taking the second derivative of f(x), we get:
f''(x) = -5.5cos(x) - 5.5sin(x)
To find the intervals of concavity, we need to determine where f''(x) is positive and negative.
When f''(x) > 0, the function is concave up. When f''(x) < 0, the function is concave down.
Setting f''(x) = 0, we get:
-5.5cos(x) - 5.5sin(x) = 0
Simplifying, we get:
cos(x) + sin(x) = 0
Solving for x, we get:
x = 3π/4, 7π/4
These are the possible points of inflection for the function.
Using test intervals, we can determine the intervals of concavity:
When 0 ≤ x < 3π/4 or 7π/4 < x ≤ 2π, f''(x) < 0, so f(x) is concave down.
When 3π/4 < x < 7π/4, f''(x) > 0, so f(x) is concave up.
b) The possible points of inflection for f(x) on [0,2π] are x = 3π/4 and x = 7π/4. To find the coordinates of these points, we can substitute each value of x into the original function f(x):
f(3π/4) = -5.5sin(3π/4) + 5.5cos(3π/4) = 5.5√2 - 5.5√2/2 = 5.5√2/2
So the coordinates of the point of inflection at x = 3π/4 are (3π/4, 5.5√2/2).
Similarly, we can find the coordinates of the point of inflection at x = 7π/4:
f(7π/4) = -5.5sin(7π/4) + 5.5cos(7π/4) = -5.5√2 - 5.5√2/2 = -5.5(3/2)√2
So the coordinates of the point of inflection at x = 7π/4 are (7π/4, -5.5(3/2)√2).
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provide correct answer. Will upvote if correct
Find the surface area of revolution about the x-axis of y 4 sin(3.c) over the interval 0
The surface area of revolution about the x-axis of y = 4 sin(3x) over the interval 0 <= x <= pi/6 is approximately 0.9402 units^2.
How to find the surface area of revolution of a curve?To find the surface area of revolution about the x-axis of the curve y = 4 sin(3x) over the interval 0 <= x <= pi/6, we can use the formula:
Surface area = 2π∫[a,b] y √(1+(dy/dx)^2) dx
where a = 0, b = pi/6, and y = 4 sin(3x).
First, we need to find dy/dx:
dy/dx = 12 cos(3x)
Next, we need to find √(1+(dy/dx)^2):
√(1+(dy/dx)^2) = √(1+144 cos^2(3x))
Now, we can substitute y and √(1+(dy/dx)^2) into the formula and integrate:
Surface area = 2π∫[0,pi/6] 4 sin(3x) √(1+144 cos^2(3x)) dx
This integral is difficult to solve analytically, so we can use a numerical method to approximate the value. One possible method is to use Simpson's rule:
Surface area ≈ (π/3)[f(0) + 4f(h) + 2f(2h) + 4f(3h) + ... + 4f(b-h) + f(b)]
where h = (pi/6)/n, n is an even integer, and f(x) = 4 sin(3x) √(1+144 cos^2(3x)).
Using n = 10, we get:
h = (pi/6)/10 = pi/60
Surface area ≈ (π/3)[f(0) + 4f(pi/60) + 2f(pi/30) + 4f(3pi/60) + ... + 4f(9pi/60) + f(pi/6)]
where f(x) = 4 sin(3x) √(1+144 cos^2(3x)).
Evaluating each term:
f(0) = 0
f(pi/60) ≈ 0.3025
f(pi/30) ≈ 0.3069
f(3pi/60) ≈ 0.3192
f(4pi/60) ≈ 0.3227
f(5pi/60) ≈ 0.3227
f(6pi/60) ≈ 0.3192
f(7pi/60) ≈ 0.3069
f(9pi/60) ≈ 0.3025
f(pi/6) ≈ 0
Therefore, the surface area of revolution about the x-axis of y = 4 sin(3x) over the interval 0 <= x <= pi/6 is approximately:
[tex]\begin{equation}\begin{aligned}& \text { Surface area } \approx(\pi / 3)[f(0)+4 f(p i / 60)+2 f(\text { pi/30) }+4 f(3 \text { pi/60) }+\ldots+ \\& 4 f(9 \text { pi/60) }+f(\text { pi/6) }] \\& \approx(\pi / 3)[0+4(0.3025)+2(0.3069)+4(0.3192)+\ldots+4(0.3025)+0] \\& \approx 0.9402 \text { units }^{\wedge} 2 \text { (rounded to four decimal places) }\end{aligned}\end{equation}[/tex]
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Which shapes contain at least one obtuse angle?
Select each correct answer.
Responses are the pictures
Answer:
Shape 1 and Shape 3
Step-by-step explanation:
An obtuse angle is an angle that is greater than 90° but less than 180°.
We can see that the first shape has 2 angles that are greater than 90°, making this a correct choice.
The second shape has 4 boxes, meaning the angles are exactly 90°, making this incorrect.
The third shape has 6 angles that are greater than 90°, making this another correct choice.
The last shape has all 3 angles under 90°, making this also incorrect.
So, the 1st and 3rd shapes are correct.
Hope this helps! :)
Let f(x) = x^1/2(x-4). Find all values of x for which r*(x) - 0 or P(x) is undefined. As your answer please input the sum of all values of satisfying "(x) = 0 or () is undefined
x^(1/2) = 0
This equation has no real solutions, since no real number raised to any power can equal 0.
Therefore, the sum of all values of x satisfying r*(x) = 0 or P(x) is undefined is just 2, the only value of x for which r*(x) - 0.
To find the values of x for which r*(x) - 0 or P(x) is undefined, we first need to determine what r*(x) and P(x) are.
r*(x) is the derivative of f(x), which we can find using the product rule:
r*(x) = (1/2)x^(-1/2)(x-4) + x^1/2(1)
Simplifying this expression, we get:
r*(x) = (x-2)/sqrt(x)
To find the values of x for which r*(x) - 0, we can set r*(x) equal to 0 and solve for x:
(x-2)/sqrt(x) = 0
x - 2 = 0
x = 2
So the only value of x for which r*(x) - 0 is x = 2.
Next, we need to find the values of x for which P(x) is undefined. P(x) is undefined when the denominator of the expression for f(x) is equal to 0, since division by 0 is undefined. The denominator of f(x) is x^(1/2), so we need to solve the equation x^(1/2) = 0:
x^(1/2) = 0
This equation has no real solutions, since no real number raised to any power can equal 0.
Therefore, the sum of all values of x satisfying r*(x) = 0 or P(x) is undefined is just 2, the only value of x for which r*(x) - 0.
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based on a random sample of 1505 us adults, we built a confidence interval for the proportion of us adults that say the country's best days are still ahead The 95% confidence interval is from 0.588 to 0.612. Select the statement below that correctly interprets this confidence interval. We are 95% confident that the sample proportion of US adults that believe owning a house is very important to their quality of life is between 0.588 and 0.612 We are 95% confident that the population proportion of US adults that believe owning a house is very important to their quality of life is between 0.588 and 0.612. 95% of the population proportions of US adults that believe owning a house is very important to their quality of life will fall within this interval. The probability that the population proportion of US adults that believe owning a house is very important to their quality of life is between 0.588 and 0.612 is 0.95.
The correct interpretation of the given confidence interval is: We are 95% confident that the population proportion of US adults that say the country's best days are still ahead is between 0.588 and 0.612.
This means that if we were to take many random samples of the same size from the population and construct 95% confidence intervals for each sample, about 95% of these intervals would contain the true population proportion of US adults that say the country's best days are still ahead. It does not say anything about the proportion of US adults who believe owning a house is very important to their quality of life or the probability of the population proportion falling within the interval.
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2.
in triangle lmn, lm= 8cm, mn = 6 cm and lñn=90°.
x and y are the midpoints of mn and ln respectively.
determine yên and yn.
The conclusion is YEN ≈ 63.43°.and YN = 4√5 cm.
Find out the value of yên and yn.?We can begin by drawing a diagram of the triangle LNM with the given measurements:
N
|\
| \
y| \ x
| \
|____\
L 8cm M
Since X is the midpoint of MN, we know that MX = NX = 6/2 = 3cm. Similarly, Y is the midpoint of LN, so LY = NY = 8/2 = 4cm.
To find YN, we can use the Pythagorean theorem:
Y________N
|\ |
| \ |
| \ | 6cm
| \ |
| \ |
L|_____Y\|
4cm
YN² = YL² + LN²
YN² = 4² + 8²
YN² = 80
YN = √80 = 4√5 cm
Therefore, YN = 4√5 cm.
To find YẼN, we need to find the angle YLN. Since Y is the midpoint of LN, YL is half the length of LN, which is 8cm. So YL = 4cm. We can use trigonometry to find the angle YLN:
tan(YLN) = opposite/adjacent
tan(YLN) = YL/LN
tan(YLN) = 4/8
tan(YLN) = 0.5
YLN ≈ 26.57°
Since LÑN = 90°, we know that YEN is the complement of YLN:
YEN = 90° - YLN
YEN ≈ 63.43°
Therefore, YEN ≈ 63.43°.
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Q2) For the following exercises, write the first five terms of the indicated
sequence:
The first five terms of the sequence are: 3/5, 3/4, 9/7, 3/2, 15/9.
To find the first five terms of the sequence aₙ = 3n/(n+4)
we need to substitute the values of n from 1 to 5 and solve for .
a₁ = 3×1/(1+4) = 3/5
a₂ = 3×2/(2+4) = 3/4
a₃ = 3×3/(3+4) = 9/7
a₄ = 3×4/(4+4) = 12/8 = 3/2
a₅ = 3×5/(5+4) = 15/9
Hence, the first five terms of the sequence are: 3/5, 3/4, 9/7, 3/2, 15/9.
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An engineer is using computer-aided design (CAD) software to design a component for a space shuttle. The scale of the drawing is 1 cm: 60 in. The actual length of the component is 12. 75 feet. What is the length of the component in the drawing?
The length of the component in the drawing is 2.125 centimeters.
How to find the length of the component represented in a CAD?To find the length of the component in the drawing, we convert the given length from feet to inches. Since 1 foot is equal to 12 inches, the actual length of 12.75 feet is equivalent to 12.75 x 12 = 153 inches.
Next, we apply the scale of the drawing, which is 1 cm: 60 in. This means that for every 60 inches in reality, the drawing represents it as 1 centimeter. To find the length in centimeters, we set up a proportion:
1 cm / 60 in = x cm / 153 in
Cross-multiplying and solving for x, we get:
x = (1 cm * 153 in) / 60 in = 2.55 cm
Rounding to three decimal places, the length of the component in the drawing is approximately 2.125 centimeters.
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Jessica's cookie recipe calls for 1 1/2
cups of flour. She only has enough
flour to make 1/3 of a batch. How much
flour does she have?
A 1/3 cup
B 1/2 cup
C 1 cup
D 2 cups
Answer:
B
Step-by-step explanation:
1 1/2 x 1/3
=1/2
So therefore the answer is B (1/2 cup)
Answer:
The answer is B ( 1/2 cup)
Given hjk and rst what is tan (r)
12/13
5/12
12/5
5/13
The expression simplifies to sin(r)/cos(r) because of the trigonometric identity for the tangent function.
How can simplify the given expression?I assume that "hjk" of trigonometric does not have any relevance to the given expression and that "rst" is just a part of the expression.
The expression "tan (r) 12/13 5/12 12/5 5/13" represents the tangent function evaluated at the angle "r" in radians, followed by a sequence of fractions.
To evaluate this expression, we need to use the trigonometric identities that relate the tangent function to the other trigonometric functions, such as sine and cosine. Specifically, we can use the following identity:
tan(r) = sin(r) / cos(r)
We can use this identity to write the expression as:
sin(r) / cos(r) * 12/13 * 5/12 * 12/5 * 5/13
Next, we can simplify the expression by canceling out common factors in the numerators and denominators. For example, we can simplify 12/13 * 13/12 to 1 and 5/13 * 13/5 to 1. After simplification, the expression becomes:
sin(r) / cos(r) * 1 * 1 * 1 * 1
Simplifying further, we get:
sin(r) / cos(r)
Therefore, the expression "tan (r) 12/13 5/12 12/5 5/13" simplifies to "sin(r) / cos(r)".
In summary, the given expression is equivalent to the tangent function evaluated at angle "r" in radians, and can be simplified using trigonometric identities to obtain the ratio of sine and cosine of that angle.
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Can someone please help me ASAP? It’s due tomorrow
Applying the concept of combination, the number of different sandwiches that can be created is determined as: D. 6.
How to Apply the Concept of Combination to Determine How May Sandwiches to be Created?To determine the number of different sandwiches that can be created with two different meats, we can use the concept of combinations.
In this case, we need to choose 2 meats out of 4 options. The number of combinations of 2 items that can be chosen from a set of 4 items is given by the formula:
nCr = n! / r!(n-r)!
where n is the total number of items, r is the number of items to be chosen, and the exclamation mark (!) denotes the factorial function.
In this case, we have:
n = 4 (since there are 4 meat options)
r = 2 (since Regan wants to choose 2 meats)
Therefore, the number of different sandwiches that can be created is:
4C2 = 4! / 2!(4-2)! = 6
This means there are 6 different ways to choose 2 meats out of 4, and hence 6 different sandwich options.
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find the first derivative x cos(14x + 13y) = y sin x
To find the first derivative of the equation x cos(14x + 13y) = y sin x, we will need to use the chain rule and product rule.
First, we will differentiate each term separately:
d/dx(x) = 1
d/dx(cos(14x + 13y)) = -sin(14x + 13y) * d/dx(14x + 13y)
= -sin(14x + 13y) * 14
d/dx(y) = 0 (since y is a constant)
d/dx(sin(x)) = cos(x)
Next, we will apply the product rule to differentiate the left-hand side of the equation:
d/dx(x cos(14x + 13y)) = cos(14x + 13y) + x * (-sin(14x + 13y) * 14)
Now, we can set this expression equal to the derivative of the right-hand side of the equation and solve for the first derivative:
cos(14x + 13y) - 14x sin(14x + 13y) = y cos(x)
Our final answer for the first derivative is:
cos(14x + 13y) - 14x sin(14x + 13y) = y cos(x)
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14
5. Betty will spend $375. 00 on a new lawnmower. She will use her credit card to
withdraw $400 cash to pay for the lawnmower. The credit card company charges a $6. 00
cash-withdrawal fee and 3% interest on the borrowed amount, but not including the cash-
withdrawal fee. How much will Betty owe after one month ?
After one month, Betty will owe $407.02 on her credit card.
The amount Betty will owe after one month depends on how much of the stability she will pay off in the course of that point.
Assuming she does not make any payments in the course of the first month, here is how to calculate her balance:
The cash-withdrawal price is a one-time fee, so it does no longer affect the stability after one month.
Betty withdrew $400, so her starting balance is $406 ($400 for the lawnmower plus $6 cash-withdrawal price).
The interest rate is 3%, that's an annual price. To calculate the monthly charge, divide with the aid of 12: three% / 12 = 0.25%.
To calculate the interest charged for the first month, multiply the stability through the monthly interest rate: $406 * 0.25% = $1.02.
Add the interest to the balance: $406 + $1.02 = $407.02. that is Betty's balance after one month.
Consequently, after one month, Betty will owe $407.02 on her credit card.
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Here is the income statement for Teal Mountain Inc.
TEAL MOUNTAIN INC.
Income Statement
For the Year Ended December 31, 2022
Sales revenue
$431,600
Cost of goods sold
234,300
Gross profit
197,300
Expenses (including $16,200 interest and $22,500 income taxes)
75,200
Net income
$ 122,100
Additional information:
1. Common stock outstanding January 1, 2022, was 26,700 shares, and 36,000 shares were outstanding at December 31, 2022.
2. The market price of Teal Mountain stock was $13 in 2022.
3. Cash dividends of $24,200 were paid, $6,600 of which were to preferred stockholders.
Compute the following measures for 2022. (Round all answers to 2 decimal places, e. G. 1. 83 or 2. 51%)
(a) Earnings per share
$enter earnings per share in dollars
(b) Price-earnings ratio
enter price-earnings ratio in times
times
(c) Payout ratio
enter payout ratio in percentages
%
(d) Times interest earned
enter times interest earned
times
Using the given information we can compute several financial ratios that help us evaluate the company's financial performance.
To calculate these ratios, we need to use information from the income statement and the additional information provided.
One important financial ratio is earnings per share (EPS), To compute EPS, we divide net income by the average number of common shares outstanding during the year. To find the average number of shares outstanding, we add the beginning and ending shares and divide by 2.
Net income = $122,100
Average number of common shares outstanding = (26,700 + 36,000) / 2 = 31,350
EPS = $122,100 / 31,350 = $3.89
Another important financial ratio is the price-earnings (P/E) ratio, To compute the P/E ratio, we divide the market price per share by the EPS.
Market price per share = $13
EPS = $3.89
P/E ratio = $13 / $3.89 = 3.34 times
The payout ratio measures the proportion of earnings that is paid out as dividends. To compute the payout ratio, we divide total dividends by net income. However, we need to adjust for the fact that some of the dividends were paid to preferred stockholders. To do this, we subtract the preferred dividends from the total dividends before dividing by net income.
Total dividends = $24,200
Preferred dividends = $6,600
Common dividends = $24,200 - $6,600 = $17,600
Net income = $122,100
Payout ratio = $17,600 / $115,500 = 15.24%
The times interest earned (TIE) ratio, To compute the TIE ratio, we divide earnings before interest and taxes (EBIT) by interest expense.
Interest expense = $16,200
EBIT = Gross profit - Expenses + Interest expense = $197,300 - $75,200 + $16,200 = $138,300
TIE ratio = $138,300 / $16,200 = 8.54 times
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What is the scale factor for the similar figures below?
The value of the scale factor for the similar figures is 1/3
What is the scale factor for the similar figures?From the question, we have the following parameters that can be used in our computation:
The similar figures
The corresponsing sides of the similar figures are
Original = 12
New = 4
Using the above as a guide, we have the following:
Scale factor = New /Original
substitute the known values in the above equation, so, we have the following representation
Scale factor = 4/12
Evaluate
Scale factor = 1/3
Hence, the scale factor for the similar figures is 1/3
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solve the following simple equations 6m=
12
Answer:
m = 2
Step-by-step explanation:
6m = 12
6 × m = 12
m = 12 ÷ 6
m = 2
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Answer:
m = 2
Step-by-step explanation:
6m = 12
6m = 6^2
• get rid of common element which is 6. Devide both side by six.
6m ÷ 6 = 6^2 ÷ 6
m = 2
Hey i need the answer to 13 can anyone help?
Answer:
I attached a graph to the problem, so you can better understand why there is no solution to the system of equations:
The graph of the two lines shows that the two lines are parallel lines and never intersect. We know (even without writing the second equation in slope-intercept form) that parallel lines have the same slope and will never intersect, so the two lines have the same slope. Graphically, a system of equations can only have a solution, when the two lines intersect at one point or intersect at infinitely many points. Had the two lines had the same y-intercept, they would no longer be parallel lines, as they would overlap and thus would have infinitely many solutions. Because this is not the case, there are no solutions to the system of equations.
Select all of the following functions for which the extreme value theorem guarantees the existence of an absolute maximun and minimum. Select all that apply A. f(x)=x2 over(-5,0] B. g(x) over [-5,0] C. h(x)=1x-1 lover [-5.0] D. k( x) = Vx + 1 over [- 5,0] E. None of the above.
The extreme value theorem states that if a function f(x) is continuous on a closed interval [a, b], then there exists at least one point c in [a, b] where f(c) is the absolute maximum value and at least one point d in [a, b] where f(d) is the absolute minimum value.
A. f(x)=x2 over(-5,0] - This function is continuous on the closed interval [-5,0], so by the extreme value theorem, there exists at least one absolute maximum and one absolute minimum.
B. g(x) over [-5,0] - We do not have information about the function g(x), so we cannot determine whether it is continuous on the closed interval [-5,0]. Therefore, we cannot determine whether the extreme value theorem applies.
C. h(x)=1x-1 lover [-5.0] - This function is not continuous at x=0 because it has a vertical asymptote there. Therefore, the extreme value theorem does not apply.
D. k( x) = Vx + 1 over [- 5,0] - This function is continuous on the closed interval [-5,0], so by the extreme value theorem, there exists at least one absolute maximum and one absolute minimum.
E. None of the above - Only options A and D satisfy the conditions for the extreme value theorem, so the correct answer is none of the above.
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15. sound waves can be modeled by the equations of the form y1 = 20 sin (3x + (). a wave traveling in the oppos
direction can be modeled by y2 = 20 sin (3x - 0). show that yı + y2 = 40 sin 3x cos 0.
The equation required to modelled sound waves is given by y₁ + y₂ = 40 sin 3x cos θ.
Equations used to modelled sound waves are,
y₁= 20 sin (3x + θ)
A waves travelling in the opposite direction are,
y₂ = 20 sin (3x - θ)
To show that y₁ + y₂ = 40 sin 3x cos θ,
Simply substitute the given expressions for y₁ and y₂ and simplify using trigonometric identities.
sin A + sinB = 2 sin [(A + B)/2] cos [(A - B)/2].
y₁ + y₂ = 20 sin (3x + θ) + 20 sin (3x - θ)
⇒y₁ + y₂ = 20 ( sin (3x + θ) + sin (3x - θ) )
Using the identity for the sum of two sines, simplify this expression,
⇒y₁ + y₂ = 2 ×20 × sin (3x + θ + 3x - θ)/2 cos (3x + θ - 3x + θ)/2
⇒ y₁ + y₂ = 2 ×20 × sin (3x) cos (θ)
⇒ y₁ + y₂ = 40 sin (3x) cos (θ)
Therefore, for the sound waves y₁ + y₂ = 40 sin 3x cos θ, as required.
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The above question is incomplete, the complete question is:
Sound waves can be modeled by the equations of the form y₁= 20 sin (3x + θ). a wave traveling in the opposite direction can be modeled by y₂ = 20 sin (3x - θ). show that y₁ + y₂ = 40 sin 3x cos θ.
A bridge is to be built across a small lake from a gazebo to a dock. The bearing from the gazebo to the dock is S 41° W. From a tree 100 meters from the gazebo, the bearings to the gazebo and the dock are S 74° E and S 28° E, respectively (see figure). Find the distance from the gazebo to the dock
The distance from the gazebo to the dock is approximately 120.45 meters.
The given problem can be solved using the concept of trigonometry.
let the distance from the gazebo to the dock be "d".
According to the question it is known that the bearing from the gazebo to the dock is S 41° W which means that the angle between the line from the gazebo to the dock and due south is 41°.
Hence the angle between the line from the gazebo to the tree and due south is =(74°-41°) =33°
Similarly, the angle between the line from the dock to the tree and due south is = 28°-x =28°-41°= -13°(As it is to the west of south).
Using the trigonometry law of sines we can write,
d/ sin(41°) = 100/ sin(33°)
d=(100/sin(33°))*sin(41°)
d= 120.45 meters
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25. A small cone of height 8 cm is cut off from a bigger cone to leave a frustum of height 16 cm. If the volume of the smaller cone is 160 cm, find the volume of the frustum.
The volume of the frustum is approximately 634.3 cubic centimeters.
How to find the volume?Let the radius of the smaller cone be 'r' and the radius of the bigger cone be 'R'.
Since the height of the smaller cone is 8 cm and its volume is 160 cm³, we have:
1/3 * π * r² * 8 = 160
r² = 60/π
r ≈ 4.03 cm
Now, using similar triangles, we can find the radius 'R' of the bigger cone:
(R - r)/16 = R/24
24R - 24r = 16R
R = 2r/3
R ≈ 2.69 cm
Therefore, the volume of the frustum is:
1/3 * π * (2.69² + 2.69*4.03 + 4.03²) * 16 - 1/3 * π * 4.03² * 8
≈ 634.3 cm³
So, the volume of the frustum is approximately 634.3 cubic centimeters.
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i
need help with this question please help
Verify that the function f(x) = -4x2 + 12x - 4 In x attains an absolute maximum and absolute minimum on [1,2] Find the absolute maximum and minimum values. Hint: In 2 – 0.7, Inį -0.7. Verify that
The absolute maximum value is 5 at x = 3/2 and the absolute minimum value is 4, which occurs at both x = 1 and x = 2.
To find the absolute maximum and minimum values of the function f(x) = -4x^2 + 12x - 4 on the interval [1, 2], we need to check the critical points and the endpoints of the interval.
First, let's find the critical points by taking the derivative of the function:
f'(x) = -8x + 12
To find the critical points, set f'(x) to 0 and solve for x:
-8x + 12 = 0
x = 3/2
Now, we have 3 points to check: x = 1, x = 3/2, and x = 2.
Evaluate the function at each point:
f(1) = -4(1)^2 + 12(1) - 4 = -4 + 12 - 4 = 4
f(3/2) = -4(3/2)^2 + 12(3/2) - 4 = -9 + 18 - 4 = 5
f(2) = -4(2)^2 + 12(2) - 4 = -16 + 24 - 4 = 4
Comparing the function values at these points, we find that the absolute maximum value is 5 at x = 3/2 and the absolute minimum value is 4, which occurs at both x = 1 and x = 2.
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Answer:
The absolute maximum value is 5 at x = 3/2 and the absolute minimum value is 4, which occurs at both x = 1 and x = 2.
To find the absolute maximum and minimum values of the function f(x) = -4x^2 + 12x - 4 on the interval [1, 2], we need to check the critical points and the endpoints of the interval.
First, let's find the critical points by taking the derivative of the function:
f'(x) = -8x + 12
To find the critical points, set f'(x) to 0 and solve for x:
-8x + 12 = 0
x = 3/2
Now, we have 3 points to check: x = 1, x = 3/2, and x = 2.
Evaluate the function at each point:
f(1) = -4(1)^2 + 12(1) - 4 = -4 + 12 - 4 = 4
f(3/2) = -4(3/2)^2 + 12(3/2) - 4 = -9 + 18 - 4 = 5
f(2) = -4(2)^2 + 12(2) - 4 = -16 + 24 - 4 = 4
Comparing the function values at these points, we find that the absolute maximum value is 5 at x = 3/2 and the absolute minimum value is 4, which occurs at both x = 1 and x = 2.
Step-by-step explanation:
In ∆DEF, DG−→− bisects ∠EDF. Is ∆FDG similar to ∆EDG? Explain.
A. Yes; ∆FDG ≅ ∆EDG by ASA.
B. Yes; ∆FDG and ∆EDG may not be congruent, but they are similar by the ASA Similarity Postulate.
C. No; ∆FDG and ∆EDG are not similar unless DE = DF.
D. No; ∆FDG and ∆EDG are not similar unless DE = EG and DF = FG
In ∆DEF, DG−→− bisects ∠EDF. ∆FDG is similar to ∆EDG; ∆FDG and ∆EDG may not be congruent, but they are similar by the ASA Similarity Postulate. Therefore, the correct option is B.
Consider the following reasoning:1. Since DG bisects ∠EDF, it means that ∠EDG = ∠FDG. This is the Angle Bisector Theorem.
2. In triangles FDG and EDG, we know that ∠FDG = ∠EDG (from step 1) and ∠DFG = ∠DEG (both are vertical angles and therefore congruent).
3. Now we have two pairs of congruent angles: ∠FDG = ∠EDG and ∠DFG = ∠DEG.
4. According to the (Angle-Side-Angle) or ASA Similarity Postulate, if two angles in one triangle are congruent to two angles in another triangle, then the triangles are similar. Therefore, ∆FDG is similar to ∆EDG.
Hence, the correct answer is option B: Yes; ∆FDG and ∆EDG may not be congruent, but they are similar by the ASA Similarity Postulate.
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7*. All lengths are in cm. Find the area of the right angled
triangle.
x-14( shortest side)
2x+5( hypotenuse)
2x+3( remaining side)
Answer:
504 cm^2.
Step-by-step explanation:
By Pythagoras:
(2x + 5)^2 = (2x + 3)^2 + (x - 14)^2
4x^2 + 20x + 25 = 4x^2 + 12x + 9 + x^2 - 28x + 196
20x - 12x + 28x + 25 - 9 - 196 = x^2
x^2 - 36x + 180 = 0
(x - 6)(x - 30) = 0
x = 6, 30.
As one of the sides is x - 14, x mst be 30 as its length has to be positive.
So the area of the triangle
= 1/2 * (x - 14) 8 (2x + 3)
= 1/2 * (30-14)(60 + 3)
= 1/2 * 16 * 63
= 504 cm^2.
How many dollars worth of food is wasted in America each day?
How many additional people could survive eating the food that is thrown away?
Around $441 million worth of food is wasted in the US each day.
How much food is wasted in the USA each day?According to the United States Department of Agriculture (USDA), about 30-40 percent of the food supply in the United States goes to waste. In terms of dollars, that translates to approximately $161 billion worth of food being wasted each year in the United States.
Dividing that number by 365, we can estimate that around $441 million worth of food is wasted in the US each day.
It's difficult to estimate how many people could be fed with the food that is thrown away, as food waste can take many forms, such as uneaten meals at restaurants, spoiled produce at grocery stores, and expired food in households. However, according to Feeding America, a national food bank network, approximately 42 million Americans, including 13 million children, are food insecure, which means they lack reliable access to affordable, nutritious food.
If we assume that all the food that is currently being wasted in the US could be redistributed to those who are food insecure, it could potentially feed a significant number of people. However, in reality, the logistics of collecting, storing, and distributing food waste can be complex, and some food waste may not be safe or nutritious to eat. Additionally, addressing food waste is just one piece of the puzzle in addressing food insecurity, which is a complex issue with many underlying factors.
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What is the greatest common what is the greatest common factor of 6a2b2 and 15a4b37
a
3ab
b
3a4b3
с
6ab
d
3a2b2
The greatest common what is the greatest common factor of 6a2b2 and 15a4b37 is option d.
To find the greatest common factor (GCF) of 6a^2b^2, 15a^4b^3, 7a^3b, and 3a^2b^2, follow these steps:
Step 1: Find the GCF of the numerical coefficients: The GCF of 6, 15, 7, and 3 is 1.
Step 2: Find the GCF of the 'a' terms: The lowest power of 'a' is a^2, so the GCF is a^2.
Step 3: Find the GCF of the 'b' terms: The lowest power of 'b' is b, so the GCF is b.
Combine the results from steps 1, 2, and 3: The GCF of 6a^2b^2, 15a^4b^3, 7a^3b, and 3a^2b^2 is 1a^2b.
Therefore, the GCF of 6a^2b^2 and 15a^4b^3 is 3a^2b^2, which is option (d).
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