Explanation of how to calculate the volume of a rectangular prism with given dimensions.
Explanation:The volume of a rectangular prism is calculated by multiplying its length, width, and height.
Given dimensions: length = 6/5 cm, width = 8/3 cm, height = 15/4 cm
Volume = (6/5) cm x (8/3) cm x (15/4) cm = 24 cm³
Jiminy's Cricket Farm issued a bond with 15 years to maturity and a semiannual coupon rate of 5 percent 3 years ago. The bond currently sells for 92 percent of its face value. The company's tax rate is 22 percent. A. What is the pretax cost of debt? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.G., 32.16.) b. What is the aftertax cost of debt? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.G., 32.16.)
The pretax cost of debt is 5.43% and the aftertax cost of debt is 4.24%.
Explanation:To calculate the pretax cost of debt, we need to find the current yield of the bond. The current yield is the annual coupon payment divided by the market price. In this case, the coupon rate is 5% and the market price is 92% of the face value. Therefore, the current yield is (0.05 * face value) / (0.92 * face value), which simplifies to 0.0543 or 5.43%.
To calculate the aftertax cost of debt, we need to multiply the pretax cost of debt by (1 - tax rate). In this case, the tax rate is 22%. Therefore, the aftertax cost of debt is 5.43% * (1 - 0.22), which simplifies to 4.24%.
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Which is the area of the rectangle?
Answer:
The answer to your question is the letter C. 13248 square units
Step-by-step explanation:
Data
Right triangle Rectangle
short leg = 69 base = x + 100
hypotenuse = 115
Process
1.- Calculate the long leg of the right triangle.
c² = a² + b²
b² = c² - a²
b² = 115² - 69²
b² = 13225 - 4761
b² = 8464
b = 92
2.- Calculate the length of the base of the rectangle
base = 92 + 100
base = 192
3.- calculate the area of the rectangle
Area = 192 x 69
= 13248 square units
The mean number of words per minute (WPM) read by sixth graders is 8888 with a standard deviation of 1414 WPM. If 137137 sixth graders are randomly selected, what is the probability that the sample mean would be greater than 89.8789.87 WPM? Round your answer to four decimal places.
Noticing that there is a pattern of repetition in the question (the numbers are repeated twice), we are assuming that the mean number of words per minute is 88, the standard deviation is of 14 WPM, as well as the number of sixth graders is 137, and that there is a need to estimate the probability that the sample mean would be greater than 89.87.
Answer:
"The probability that the sample mean would be greater than 89.87 WPM" is about [tex] \\ P(z>1.56) = 0.0594[/tex].
Step-by-step explanation:
This is a problem of the distribution of sample means. Roughly speaking, we have the probability distribution of samples obtained from the same population. Each sample mean is an estimation of the population mean, and we know that this distribution behaves normally for samples sizes equal or greater than 30 [tex] \\ n \geq 30[/tex]. Mathematically
[tex] \\ \overline{X} \sim N(\mu, \frac{\sigma}{\sqrt{n}})[/tex] [1]
In words, the latter distribution has a mean that equals the population mean, and a standard deviation that also equals the population standard deviation divided by the square root of the sample size.
Moreover, we know that the variable Z follows a normal standard distribution, i.e., a normal distribution that has a population mean [tex] \\ \mu = 0[/tex] and a population standard deviation [tex] \\ \sigma = 1[/tex].
[tex] \\ Z = \frac{\overline{X} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex] [2]
From the question, we know that
The population mean is [tex] \\ \mu = 88[/tex] WPMThe population standard deviation is [tex] \\ \sigma = 14[/tex] WPMWe also know the size of the sample for this case: [tex] \\ n = 137[/tex] sixth graders.
We need to estimate the probability that a sample mean being greater than [tex] \\ \overline{X} = 89.87[/tex] WPM in the distribution of sample means. We can use the formula [2] to find this question.
The probability that the sample mean would be greater than 89.87 WPM
[tex] \\ Z = \frac{\overline{X} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex] \\ Z = \frac{89.87 - 88}{\frac{14}{\sqrt{137}}}[/tex]
[tex] \\ Z = \frac{1.87}{\frac{14}{\sqrt{137}}}[/tex]
[tex] \\ Z = 1.5634 \approx 1.56[/tex]
This is a standardized value and it tells us that the sample with mean 89.87 is 1.56 standard deviations above the mean of the sampling distribution.
We can consult the probability of P(z<1.56) in any cumulative standard normal table available in Statistics books or on the Internet. Of course, this probability is the same that [tex] \\ P(\overline{X} < 89.87)[/tex]. Then
[tex] \\ P(z<1.56) = 0.94062 \approx 0.9406[/tex]
However, we are looking for P(z>1.56), which is the complement probability of the previous probability. Therefore
[tex] \\ P(z>1.56) = 1 - P(z<1.56) = 1 - 0.9406[/tex]
[tex] \\ P(z>1.56) = P(\overline{X}>89.87) = 0.0594[/tex]
Thus, "The probability that the sample mean would be greater than 89.87 WPM" is about [tex] \\ P(z>1.56) = 0.0594[/tex].
A survey of students at a large university found that 82% had purchased textbooks from an off-campus vendor at least once during their college career. If 45 students are randomly sampled, what is the probability that at least 40 students have purchased textbooks from an off-campus vendor at least once during their college career? g
Answer:
Probability that at least 40 students have purchased textbooks from an off-campus vendor at least once during their college career is 0.0688.
Step-by-step explanation:
We are given that a survey of students at a large university found that 82% had purchased textbooks from an off-campus vendor at least once during their college career.
Also, 45 students are randomly sampled.
Let [tex]\hat p[/tex] = sample proportion of students who have purchased textbooks from an off-campus vendor at least once during their college career.
The z-score probability distribution for sample proportion is given by;
Z = [tex]\frac{\hat p- p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ~ N(0,1)
where, [tex]\hat p[/tex] = sample proportion = [tex]\frac{40}{45}[/tex] = 0.89
p = population proportion of students who had purchased textbooks from an off-campus vendor at least once during their college career = 82%
n = sample of students = 45
Now, probability that at least 40 students have purchased textbooks from an off-campus vendor at least once during their college career is given by = P( [tex]\hat p[/tex] [tex]\geq[/tex] 0.89)
P( [tex]\hat p[/tex] [tex]\geq[/tex] 0.89) = P( [tex]\frac{\hat p- p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] [tex]\geq[/tex] [tex]\frac{0.89-0.82}{\sqrt{\frac{0.89(1-0.89)}{45} } }[/tex] ) = P(Z [tex]\geq[/tex] 1.50) = 1 - P(Z < 1.50)
= 1 - 0.9332 = 0.0688
The above probability is calculate by looking at the value of x = 1.50 in the z table which ha an area of 0.9332.
Therefore, the required probability is 0.0688.
luna had 50$ when she got to the carnival. After riding 12 rides, she had 26$ left. WHat was the price of each ride. what is the equationthat could be use to represent this situation
Answer 2 dollars a ride.
Step-by-step explanation:
26=50-12x
x=2
x
Solve the linear programming problem by the method of corners. Maximize P = 6x − 4y subject to x + 2y ≤ 50 5x + 4y ≤ 145 2x + y ≥ 25 y ≥ 7, x ≥ 0 The maximum is P = 1 Incorrect: Your answer is incorrect. at (x, y) = .
Answer:
The maximum is P=112.4 at (23.4,7)
Step-by-step explanation:
From the graph, the coordinates of the vertices of the feasible region are:
(0,25)
(9,7)
(23.4, 7)
(15,17.5)
Substituting these values in the objective function, P.
At (0,25), P = 6x − 4y=6(0)-4(25)=-100
At (9,7), P = 6x − 4y=6(9)-4(7)=26
At (23.4,7), P = 6x − 4y=6(23.4)-4(7)=112.4
At (15,17.5), P = 6x − 4y=6(15)-4(17.5)=20
Since the objective is to maximize,
The maximum is P=112.4 at (23.4,7)
To solve the linear programming problem, graph the inequalities to find the feasible region, then compute the function P = 6x − 4y at each corner point of the feasible region to find the maximum value. The values of x and y must also uphold all the inequalities.
Explanation:The subject of the problem is a linear programming problem, and to solve it, we first identify the feasible region by graphing inequalities. This involves graphing x + 2y ≤ 50, 5x + 4y ≤ 145, 2x + y ≥ 25, y ≥ 7, and x ≥ 0. The feasible region would be formed by the area enclosed within those lines.
Next, we find the corner points of the feasible region because, in a linear programming problem, the maximum and minimum always occur at the vertices or corner points. Let's calculate these corner points.
Finally, we evaluate the function P = 6x − 4y at each corner point and find the value of P that would be maximized. It's crucial to remember that the values of x and y must satisfy all the given inequalities.
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Following is a sample of five matched pairs. Sample 1 20 20 23 18 22 Sample 2 23 16 15 14 18 Let μ1 and μ2 represent the population means and let μD = μ1 - μ2. A test will be made of the hypotheses H0: μD = 0 versus H1: μD > 0. Can you reject H0 at the α = 0.01 level of significance? A) No B) Yes C) Cannot be determined
Answer:
No, we can't reject [tex]H_0[/tex] at the α = 0.01 level of significance.
Step-by-step explanation:
We are given the sample of five matched pairs below ;
Sample 1 (B) : 20, 20, 23, 18, 22
Sample 2 (A) : 23, 16, 15, 14, 18
Let [tex]\mu_1[/tex] = population mean for first sample
[tex]\mu_2[/tex] = population mean for second sample
SO, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu_D[/tex] = 0 {means that there is no difference between the population means of both samples}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu_D[/tex] > 0 {means that three is positive difference between the population means of both samples, i.e. population mean of first sample is higher than the population mean of second sample}
The test statistics that will be used here is Paired data test statistics;
T.S. = [tex]\frac{\bar D-\mu_D}{\frac{s_D}{\sqrt{n} } }[/tex] ~ [tex]t_n_-_1[/tex]
where, [tex]\bar D[/tex] = [tex]\bar B -\bar A[/tex] = 20.6 - 17.2 = 3.4
[tex]s_D=\sqrt{\frac{\sum D_i^{2}-n \bar D^{2} }{n-1}}[/tex] = [tex]\sqrt{\frac{121-5 \times 3.4^{2} }{5-1}}[/tex] = 3.975
n = sample size = 5
So, test statistics = [tex]\frac{3.4-0}{\frac{3.975}{\sqrt{5} } }[/tex] ~ [tex]t_4[/tex]
= 1.913
Now at 0.01 significance level, the t table gives critical value of 3.747 at 4 degree of freedom for right-tailed test. Since our test statistics is less than the critical value of t as 3.747 > 1.913, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which we fail to reject our null hypothesis.
Therefore, we conclude that the there is no difference between the population means of both samples.
Answer:
No, we can't reject at the α = 0.01 level of significance.
Step-by-step explanation:
the other response is right
you plant 10 tulips bulbs and eight of them bloom if you plant 5 more tulips how many of those would bloom
Answer:4
Step-by-step explanation: Odd 5/4 and 10/8 are both equal
Answer:
Your answer should be 4...
Step-by-step explanation:
In the first time you planted, you planted 10 total bulbs, and 8 of them bloomed. That means that 80% of the bulbs that you planted bloomed. So if you plant 5 more bulbs, theoretically your answer should be 4, since 80% of 5 is 4.
I'm sorry if this answer isn't a lot of help, there isn't a lot of information to go off of.
The character's backstory in the example best connects to
which theme?
ad
mall
Kindness is more important than beauty
Greed can destroy relationships with others,
Alle can have serious consequences,
A weakness can be turned into a strength
Answer:
D. A weakness can be turned to strength
Answer:
d
Step-by-step explanation:
An inlet pipe on a swimming pool can be used to fill the pool in 2020 hours. The drain pipe can be used to empty the pool in 2121 hours. If the pool is 2323 filled and then the inlet pipe and drain pipe are opened, how long from that time will it take to fill the pool
Answer:
If the pool is 2/3 filled and then the inlet pipe and drain pipe are opened, it will take 140 hours to fill the pool
Step-by-step explanation:
An inlet pipe can fill the pool in hours = 20
Inlet pipe 1 hour work = [tex]\frac{1}{20}[/tex]
A drain pipe can empty the pool in 21 hours
Drain pipe 1 hour work =[tex]\frac{1}{21}[/tex]
Inlet pipe and drain pipe 1 hour together work = [tex]\frac{1}{20}-\frac{1}{21}=\frac{1}{420}[/tex]
Now we are given that the pool is 2/3 filled
So, remaining portion to be filled =[tex]1 - \frac{2}{3} = \frac{1}{3}[/tex]
So, Inlet pipe and drain pipe fill [tex]\frac{1}{420}[/tex] in hours = 1
So, they can fill 1/3 in hours = [tex]\frac{1}{\frac{1}{420}} \times \frac{1}{3} =140 hours[/tex]
Hence If the pool is 2/3 filled and then the inlet pipe and drain pipe are opened, it will take 140 hours to fill the pool
30n^3+42m^4n^8 = FIND THE GCF
Answer:
The GCF is 6n^3
Step-by-step explanation:
The sample mean foot length of a simple random sample of 25 third-graders is 22.5 cm. The standard error of the mean is 0.8 cm. Which one of the following is a correct interpretation for the standard error of the mean? A.The typical distance between each individual foot length in the sample and the sample mean foot length is approximately 0.8 cm. B.The typical distance between one sample mean foot length and another sample mean foot length is 0.8 cm. C.The typical distance between each individual foot length in the population and the true mean foot length is approximately 0.8 cm. D.The typical distance between means of samples of size 25 and the population mean foot length is approximately 0.8 cm E.The typical distance between each individual foot length in the sample and the true mean foot length is approximately 0.8 cm.
The standard error of the mean pertains to the variability of the mean between different samples, rather than the variability of individual measurements. Therefore, the correct interpretation is D. The typical distance between means of samples of size 25 and the population mean foot length is approximately 0.8 cm.
Explanation:The most accurate interpretation for the standard error of the mean in the context of the given problem is: D. "The typical distance between means of samples of size 25 and the population mean foot length is approximately 0.8 cm".
The standard error of the mean (SEM) demonstrates the standard deviation of the sampling distribution of the means. It measures how far the sample mean of the data is likely to be from the true population mean. SEM gives us an estimate of the precision of our sample mean in relation to the true population mean. It's important to recognize that SEM is not about the dispersion of individual measurements, but rather about the dispersion of sample means.
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If the radius of the circle is decreased by a factor of One-third, what happens to the circumference?
The circumference decreases by a factor of One-third.
The circumference decreases by a factor of 3.
The circumference increases by a factor of One-third.
The circumference increases by a factor of 3.
Answer:
the circumference decreases by a factor 1/3.
Step-by-step explanation:
Answer:
A: The circumference decreases by a factor of One-third
If the base of the triangle decreased from 2 yards to 1 yard, what would be the difference in the area?
Answer:
5/16 yd[tex]^{2}[/tex]
Answer:
B
Step-by-step explanation:
Need help please answer worth 25 points
The equation is [tex]-\frac{1}{2} x+3[/tex]
This is what you should input in the chart:
(0,3)
(3,2)
(6,1)
(9,0)
(12,-1)
(15,-2)
How can a shape have parallel sides but not perpendicular sides?
Answer:
Parallelogram are quadrilaterals with opposite sides parallel, but adjacent sides not perpendicular. If the sides have equal lengths, then it is called a rhombus.
Step-by-step explanation:
Because the sides of the shape meet at angles which are not 90 degrees, so they cannot be perpendicular.
What are parallel lines?Parallel lines are those lines that are equidistant from each other and never meet, no matter how much they may be extended in either directions.
A shape can have parallel sides but not perpendicular sides if it is not a rectangle or a square. Examples of such shapes include parallelograms, trapezoids, and rhombuses. In these shapes, the sides are parallel to each other, but they are not perpendicular to each other.
Because the sides of the shape meet at angles which are not 90 degrees, so they cannot be perpendicular.
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g(n) = n - 5; Find g(2)
Answer:
g(2) = -3
Step-by-step explanation:
g(n) = n - 5;
Let n=2
g(2) = 2-5
= -3
Answer:
g(2)= -3
Step-by-step explanation:
We want to find what g is, when n is 2, so we can substitute 2 in for n.
g(n)=n-5
g(2)=2-5
g(2)= -3
x/10=−1
help ive got no idea it would be helpful if you could explain how as well please
Answer:
x = -10.
Step-by-step explanation:
x / 10 = -1
To solve the equation we isolate the x on one side.
Whatever operation we do one one side of the equation we have to do the same on the other side so that the balance is maintained.
Here to isolate x we multiply both sides by 10:
x
-- * 10 = -1 * 10
10
x = -10.
Hope this helps.
A goat is tied at one corner of a 12 feet by 16 feet barn. If the rope is 24 feet long, find the area of the region outside the barn, in which the goats can graze.
Answer:
1520.5 ft²
Step-by-step explanation:
A diagram can be helpful.
The total area is the sum of ...
3/4 of a circle with radius 24 ft
1/4 of a circle with radius 12 ft
1/4 of a circle with radius 8 feet
__
The area of a whole circle is given by ...
A = πr²
so our grazing area is ...
A = (3/4)π(24 ft)² + (1/4)π(12 ft)² + (1/4)π(8 ft)²
= π(432 ft² +36 ft² +16 ft²) = 484π ft²
A ≈ 1520.5 ft²
1. Find the measure of ZBOD. Then, classify the angle as acute, right, or obtuse.
To
Is
pompy
jagram
90 200
sajt
5700
80 70 80
70 60 500
120 130 140
50 1.60
glosslesund
20 120 110
40
30
OEI OOT OSTO
acesso
30
20
30
20
180 170 160 1
10
0
iedad
50 160 170
10
570 180
A) mZBOD = 125º; obtuse
B) mZBOD = 35°; acute
C) mZBOD = 90°; right
D) mZBOD = 160°; obtuse
The surface area of a spherical beach volleyball is
approximately 1387 square centimeters. Which of the
following is closest to the radius, in centimeters, of the
volleyball?
6.9
. 10.5
• 18.6
• 21.0
Answer: 18.1 inches
Step-by-step explanation: A volleyball is spherical in shape, and the surface area of a sphere is giving by the formula
from the data giving, the surface area was calculated to be 227 square inches. from the above formula, we define the radius, r to be the subject of formula, we arrive at
if we substitute for the surface area, we arrive at
Hence the radius of the volleyball will be 18.1 inches
Hope this helps
a cone has a diameter of 8ft and height of 3ft. What’s the volume?
Step-by-step explanation:
1/3 πr²h
Given
diameter (d) = 8ft
radius (r) = d/2 = 8/2 = 4 ft
height (h) = 3 ft
Volume of cone
[tex] \frac{1}{3} \times \pi {r}^{2} h[/tex]
[tex] \frac{1}{3} \times 3.14 \times {4}^{2} \times 3[/tex]
[tex] \frac{150.72}{3} [/tex]
=50.24 ft³
The cone formula is V=1/3(pi*r^2)h, plug in what you know 150pi=1/3(pi*r^2)8.
Multiply both sides by 3: 450pi=(pi*r^2)8
Divide by 8: 56.25pi=pi*r^2
Divide by pi: 56.25=r^2
Square root both sides: 7.5=r
Multiply by 2 to find diameter: d=15
ANSWER PLZZZZ FAST! Read CAREFULLY FOR THE SAKE OF GOD!
Answer:
103.62
Step-by-step explanation:
[tex]C = \pi d\\3.14 * 33 =103.62[/tex]
The exterior angles of a quadrilateral have measures of 72°, 58°, 2xº, and 3xº. Find the value of x.
x=
Answer:
46
Step-by-step explanation:
72 + 58 + 2x + 3x = 360
5x = 230
x = 46
how old is gabriella if she was 11 years old 19 years ago
Answer:
30 years old now
Step-by-step explanation:
Add the years to her age then to determine her age now
11+19 = 30
She is 30 years old now
3x+3y=-x+5y which ordered pair is a solution of the equation
Though there are multiple solutions to the given equation, the two ordered pairs that are solutions would be both (1, 2) and (2, 4).
Hope this helps!
A polling company took before an 5 polls in the week that a mayoral 66%,56%, 55%, 60% 63% of the total votes. That candidate recieved 64 % of the total vote during the actual election. Find the percent errot in the average of the company's polling results to the nearest tenth of a percent. Show your work.
Answer:
6.7%
Step-by-step explanation:
In this question, we are to calculate the percentage error in in the average polling results calculated.
Firstly, what this means is that we calculate the average of the total votes.
That would be ; (66 + 56 + 55 + 60 + 63)/5 =
300/5 = 60%
we now proceed to calculate the percentage error in the company’s result.
Mathematically;
percentage error = (Actual value - expected value)/expected value * 100%
Here the actual value is 64% and the expected is 60%
% error = (64-60)/60 * 100 = 4/60 * 100 = 6.67%
This is 6.7% to the nearest tenth of a percent
h(t) = t + 3; Find h(1)
h(t) = t+3
Find h(1)
h(1) = 1+3
h(1) = 4
The answer is 4.
Find a23 in the sequence -18 -34 -50 -66
Answer:
-288
Step-by-step explanation:
-18*16
cause its going by 16's
pls mark me brainliest
a23 = -288
Sequence:A sequence is an enumerated group of items in mathematics where repetitions are permitted and order is important. Similar to a set, it has members (also called elements, or terms). The length of the series is the number of elements (potentially infinite). In contrast to a set, the same items might appear more than once in a sequence at various points, and unlike a set, the order is important.A sequence can be described formally as a function from natural numbers (the positions of the sequence's elements) to the items at each of those positions. An indexed family, which is a function from an index set that may not be a set of numbers to another set of elements, can be thought of as a generalization of the idea of a sequence.Solution -As the sequence is going by [tex]16[/tex].
∴ [tex]-18[/tex] × [tex]16=-288[/tex]
Therefore, [tex]a23=-288[/tex].
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If someone could answer this problem and explain how to do it that would be a HUGE help thanks-
Answer:
10 meters
Step-by-step explanation:
The triangles are similar, by a scale factor of 2, so if QR is 10, then ST is 1/2 or 5
We can use trig functions to find SP
sin P = opp/ hyp
sin 30 =5/SP
SP sin 30 =5
Divide each side by sin 30
SP = 5 / sin 30
SP =10
Answer:
C. 10 meters
Step-by-step explanation:
sin(30) = QR/QP
½ = 10/QP
QP = 20
PS = ½ × 20
PS = 10