The total amount of interest paid over the life of the loan is $1863.45.
The present value of the loan.
Since there are 12 months in a year, and the loan has n-years, there are 12n monthly payments.
Let's use the formula for the present value of an annuity due:
[tex]PV = PMT \times ((1 - (1 + r) ^(-n)) / r) \times (1 + r)[/tex]
PV is the present value of the loan, PMT is the monthly payment, r is the monthly interest rate, and n is the number of months.
Substituting the given values, we get:
[tex]PV = \$800 \times ((1 - (1 + 0.12/12) ^(-12n)) / (0.12/12)) \times (1 + 0.12/12)[/tex]
[tex]PV = \$800 \times ((1 - (1.01)^(-12n)) / 0.01) \times 1.01[/tex]
[tex]PV = \$800 \times ((1 - 1.01^(-12n)) / 0.01) \times 1.01[/tex]
[tex]PV = \$800 \times ((1 - 0.887^(-n)) / 0.01) \times 1.01[/tex]
The formula for the interest paid in any given month of an annuity due:
[tex]I = PV \times r \times (1 + r) ^(m - 1)[/tex]
I is the interest paid in the 45th month, PV is the present value of the loan, r is the monthly interest rate, and m is the month.
Substituting the given values for the 45th month, we get:
[tex]\$424.45 = PV \times 0.01 \times (1 + 0.01 )^(45 - 1)[/tex]
[tex]\$424.45 = PV \times 0.01 \times (1.01)^4^4[/tex]
[tex]PV = \$424.45 / (0.01 \times (1.01)^4^4)[/tex]
PV =[tex]\$75799.45[/tex]
Now that we know the present value of the loan, we can calculate the total amount of interest paid over the life of the loan.
Let's use the formula for the total interest paid in an annuity due:
[tex]Total interest = (PMT \times n \times (n + 1) / 2) - PV[/tex]
Substituting the given values, we get:
Total interest = [tex](\$800 \times 12n \times (12n + 1) / 2) - \$75799.45[/tex]
Total interest = [tex]\$9600n^2 + \$4800n - \$75799.45[/tex]
We can solve for n by using the fact that the interest paid in the 45th month is $424.45:
[tex]\$424.45 = \$800 \times (n \times 12 - 44) \times 0.01 \times (1 + 0.01)^(45 - 1)[/tex]
[tex]\$424.45 = \$800 \times (n \times 12 - 44) \times 0.01 \times (1.01)^4^4[/tex]
n = 4.5
Substituting n = 4.5 into the formula for total interest, we get:
Total interest =[tex]\$9600 \times (4.5)^2 + \$4800 \times 4.5 - \$75799.45[/tex]
Total interest = $1863.45
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If a stock has a beta measure of 2.5, discuss what this means(be specific).
The means of a stock that has a beta measure of 2.5 is 2.5%.
A beta measure of 2.5 indicates that the stock is 2.5 times as volatile as the market.
This means that if the market goes up by 1%, the stock is expected to go up by 2.5%.
The beta measure is a measure of the volatility of a stock relative to the market.
If the market goes down by 1%, the stock is expected to go down by 2.5%.
Therefore,
The stock is considered to be more risky than the average stock in the market.
A beta measure of 2.5 indicates that the stock is 2.5 times as volatile as the market.
This means that if the market goes up by 1%, the stock is expected to go up by 2.5%.
Conversely, if the market goes down by 1%, the stock is expected to go down by 2.5%.
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discuss possible sources of measurement error in this experiment. are these sources of error enough to account for the percent differences you calculated from your data? write out your answer in a clear and well supported paragraph.
The "possible-sources" of in the measurement error of an experiment are Instrument error, Human error, sampling error and environmental factors, these sources "may" or "may-not" be enough to account for the percent differences calculated from the data.
There are several possible sources of "measurement-error" in an experiment which affect the accuracy and precision of the results.
These sources include instrument error, human error, environmental factors, and sampling error.
(i) "Instrument-Error" : is defined as inaccuracies in the measuring instruments used in the experiment. This include issues such as calibration errors, sensitivity of the instruments.
(ii) "Human-Error" can arise from mistakes made by experimenters during data collection or analysis, such as misreading measurements or recording data incorrectly.
(iii) "Environmental-Factors", such as temperature, humidity, or electromagnetic interference, can also cause error into experiment if they affect performance of measuring instruments.
(iv) "Sampling-Error" occur when a subset of the population is used for the experiment, and the results are generalized to the entire population.
Depending on the magnitude of these sources of error, they may or may not be enough to account for the percent differences calculated from the data.
If the measurement errors are small and within an acceptable range for the experiment, they may not significantly impact the results.
If the errors are large or systematic, they can introduce significant bias into the data and affect the percent differences calculated.
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The given question is incomplete, the complete question is
Discuss the possible sources of measurement error in an experiment. Are these sources of error enough to account for the percent differences you calculated from your data? write out your answer in a clear and well supported paragraph.
Question # 5
Question # 6
Question # 7
Question # 8
Question # 9
Question # 10
Question # 11
Answer: question#7 is 7/12
question#8 is 1 3/8
question#5 is 1/2
question#6 is 12
question#9 is 1 1/6
question#10 is 31/40
question#11 is 3/4
Step-by-step explanation: give brainliest
Question #5: Option A, [tex]\frac{1}{2}[/tex]
Question #6: Option A, 12
Question #7: Option A, [tex]\frac{7}{12}[/tex]
Question #8: Option D, [tex]1\frac{3}{8}[/tex]
Question #9: Option D, [tex]1\frac{1}{6}[/tex]
Question #10: [tex]\frac{31}{40}[/tex]
Question #11: [tex]\frac{3}{4}[/tex]
Pls mark brainliest
you place in a dark bag 24 marbles. 12 marbles are red, 5 marbles are blue and 7 marbles are yellow. you select 2 random marbles (one after the other without putting the first back in). what is the probability that the marbles have the same color?
The probability of selecting two marbles with the same color is approximately 0.27 or 27%.
To work out the likelihood that the two marbles drawn have similar variety, we can utilize the accompanying advances:
In the first place, we compute the likelihood of drawing a red marble on the principal pick: 12/24 = 1/2.
On the off chance that the main marble drawn is red, there will be 11 red marbles left clinched, out of a sum of 23 marbles. So the likelihood of drawing one more red marble on the subsequent pick is 11/23.
Likewise, in the event that the principal marble drawn is blue, there will be 4 blue marbles left clinched, out of a sum of 23 marbles. So the likelihood of drawing one more blue marble on the subsequent pick is 4/23.
Furthermore, on the off chance that the main marble drawn is yellow, there will be 6 yellow marbles left taken care of, out of a sum of 23 marbles. So the likelihood of drawing one more yellow marble on the subsequent pick is 6/23.
To get the complete likelihood of drawing two marbles of similar variety, we want to add the probabilities of every one of these cases:
(1/2) x (11/23) + (5/24) x (4/23) + (7/24) x (6/23) = 55/138 or roughly 0.398 or 39.8%.
In this way, the likelihood of drawing two marbles of a similar variety is roughly 39.8%.
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shuffle a deck of cards and t urn over t he first card. \i\fhat is t he sample space of t his experiment? how many outcomes are in t he event t hat t he first card is a heart?
If we shuffle a deck of cards ,turn over first card, then
(a) "Sample-Space" of this experiment is set of all 52 cards.
(b) Number of outcomes in event that the first card is a heart is 13 .
Part (a) : The "Sample-Space" of this experiment refers to all possible outcomes that occur when "first-card" from a shuffled deck of cards is turned over.
In a "standard-deck" of 52 playing cards, the sample space consist of all 52 cards, which includes 4 suits (hearts, diamonds, clubs, spades) each with 13 cards (Ace - 10, Jack, Queen, King).
So, the sample space of this experiment will be set of all 52 possible cards that could be turned over as "first-card".
Part (b) : The event that "first-card" is a heart will consist of all outcomes where the first card turned over is a heart.
In a "standard-deck" of 52 "playing-cards", there are 13 hearts (Ace of Hearts, 2 of Hearts, 3 of Hearts, ..., 10 of Hearts, Jack of Hearts, Queen of Hearts, and King of Hearts).
Therefore, there are 13 outcomes in the event .
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The given question is incomplete, the complete question is
Shuffle a deck of cards and turn over the first card.
(a) What is the sample space of this experiment?
(b) How many outcomes are in the event that the first card is a heart?
Add. Express your answer in simplest form. 2/5 + 5/6
A. 1/3
B. 7/11
C. 7/30
D. 1 7/30
Answer:
d. 1 7/30...............
Answer:
D
Step-by-step explanation:
2/5 + 5/6
Make the denominator same
(2×6)/30 + (5×5)/30
12+25/30
37/30
1 7/30
Leo subscribes to a monthly app service that charges him $6 for one month, and each app he purchases costs $0. 90. Lara subscribes to a service that charges $1. 50 per app with no additional monthly fee. After how many apps will they have the same monthly bill?
Iam do not understand what do you mean 1335690964225753897426908224 1335690964225753897426908224 88 9 109 250 10 10 XL 220 10 10 30 250 30 30 30 400
Zain's current credit card balance is $9,160.00 with a minimum payment of $325.00. Over the next month he spends $1,098.00. If the APR is 18.99% (billed monthly), what will the new balance be, including interest?
Answer: To find the new balance including interest, we need to take into account the interest charged on the current balance and the new purchase.
First, let's calculate the interest charged on the current balance. The monthly interest rate is 18.99% / 12 = 1.5825%.
The interest charged on the current balance is therefore:
interest on current balance = 0.015825 * 9160.00 = 144.98
So the total balance including interest for the current month is:
current balance including interest = 9160.00 + 144.98 = 9304.98
Next, let's calculate the interest charged on the new purchase of $1,098.00. The interest charged on the new purchase is:
interest on new purchase = 0.015825 * 1098.00 = 17.39
So the total balance including interest for the new purchase is:
new balance including interest = 1098.00 + 17.39 = 1115.39
Finally, we add the current balance including interest and the new balance including interest to get the total balance including interest:
total balance including interest = current balance including interest + new balance including interest
total balance including interest = 9304.98 + 1115.39
total balance including interest = 10420.37
Therefore, the new balance including interest is $10,420.37.
Step-by-step explanation:
which method uses an arithmetic mean to forecast the next period? group of answer choices naive. exponential smoothing. none of the above moving averages. adaptive filtering.
The method that uses an arithmetic mean to forecast the next period is "moving averages".
Which method is suitable for arithmetic mean?The method that uses an arithmetic mean to forecast the next period is the "moving averages" method.
In this method, the average of the past observations is calculated, and this average is used as the forecast for the next period.
The number of past observations used in the calculation of the moving average depends on the specific variant of the method being used.
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The relationship between the mass m in kilograms of an organism and its metabolism P in Calories per
day can be represented by P = 73.3m³. Find the metabolism of an organism that has a mass of 16 kilograms.
Answer:
The relationship between the mass m in kilograms of an organism and its metabolism p in calories per day can be represented by p = 73.3m³ . To find the metabolism of an organism that has a mass of 16 kilograms, we can substitute m = 16 into the equation:
p = 73.3m³ p = 73.3(16)³ p = 73.3(4096) p = 299,648 calories per day
Therefore, an organism with a mass of 16 kilograms has a metabolism of 299,648 calories per day.
I hope that helps!
Step-by-step explanation:
An organism with a mass of 16 kilograms has a metabolism of 299,708.8 Calories per day according to the given relationship.
We can use the given formula to find the metabolism P of an organism with a mass of 16 kilograms:
P = 73.3m³
where m = 16 kg
Substituting the value of m:
P = 73.3(16)³
P = 73.3(4096)
P = 299,708.8 Calories per day.
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The radius of a circle is 3 centimeters. What is the length of a 45° arc?
Answer:
2.36 miles
Step-by-step explanation:
radius, r = 3 miles∅ = 45°Length of an arc = ∅/360 * 2πr= 45/360 * 2 * 3.14 * 3= 2.36 miles
The angle of elevation from point A to the top of a hill is 49°. If point A is 400 feet from the base of the hill, how high is the hill? Round to the nearest tenth.
1. 460.1 ft
2. 301.9 ft
3. 262.4 ft
4. 459.3 ft
HELP!! 10 POINTS
uhm yeah thats all I've got to say
The correct statement regarding the middle 50% of the data-set is given as follows:
C. The box, from 41 to 56.
What does a box-and-whisker plot shows?A box and whisker plots shows these five features from a data-set, listed as follows:
The minimum non-outlier value.The 25th percentile, which is the median of the bottom 50%.The median, which splits the entire data-set into two halfs, the bottom 50% and the upper 50%.The 75th percentile, which is the median of the upper 50%.The maximum non-outlier value.The box, from the 25th percentile of 41 to the 75th percentile of 56, shows the middle 50% of the data-set.
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Please help me so i can finish my homework
Answer:
[tex]\frac{1}{4}[/tex]w + 3
Step-by-step explanation:
Helping in the name of Jesus.
in a certain health center there are 3 doctors, 8 nurses and 2 physicians. in how many ways one can form a group of 5 members consisting of 1 doctor, 3 nurse and 1 physician.
Solve for X. I don’t know how to solve
The value of x is approximately 10.57 and the value of y is approximately 15.25.
Describe Chords?In mathematics, a chord is a straight line segment that connects two points on a curve. More specifically, a chord is a line segment that has its endpoints on the curve.
The term "chord" is most commonly used in the context of circle geometry, where a chord is a line segment that connects two points on the circumference of a circle. In this context, the length of a chord can be calculated using the Pythagorean theorem, given the lengths of the radii of the circle and the distance between the endpoints of the chord.
In a circle, if four chords are connected to form a quadrilateral, then opposite angles of the quadrilateral are supplementary. Using this property, we can set up the following equation:
105 + (7y + 1) + (7x + 1) + (4y + 14) = 180
Simplifying and solving for x and y, we get:
7x + 4y + 122 = 180
7x + 4y = 58 ......(1)
Also, we know that the opposite angles of a cyclic quadrilateral are supplementary. Therefore, we can set up the following equations:
105 + (4y + 14) = 180 ......(2)
(7y + 1) + (7x + 1) = 180 ......(3)
Simplifying and solving for y in equation (2), we get:
4y + 119 = 180
4y = 61
y = 15.25
Substituting this value of y in equation (3) and solving for x, we get:
(7x + 1) + (7*15.25 + 1) = 180
7x + 106 = 180
7x = 74
x = 10.57
Therefore, the value of x is approximately 10.57 and the value of y is approximately 15.25.
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x 3 + 3 x 2 − x + 2 x 2 + 6 x − 2
Answer: If you want me to evaluate its 18x - 2
Hope it helped :D
use the 60 mutual funds in the table above to conduct the hypothesis test. what is the p value? p value is (to 4 decimals)
Welch's two-sample t-test indicates that the average of Load Return's population is significantly greater than the average of No Load Return's population, with a large effect size.
The null hypothesis (H0) that the two population means are equal is rejected as the p-value (0.005) is less than the chosen significance level (α=0.05). This indicates that the chance of a Type 1 error is small, and the alternative hypothesis (H1) that the average of Load Return's population is greater than the average of No Load Return's population is supported.
The test statistic (T=-2.646) falls outside the 95% critical value accepted range, which further supports the rejection of H0. The effect size (0.68) is considered large, indicating that the difference between the two population means is substantial.
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Complete Question:
use the 60 mutual funds in the table below to conduct the hypothesis test. what is the p value? p value is (to 4 decimals)
bertha is stacking oranges in the form of a pyramid. the base is a rectangle that is four oranges by six oranges. each orange above the base rests on 4 oranges below it. how many oranges are used
The total number of oranges used in Bertha's pyramid is 24 + 6 + 2 + 1 = 33 oranges.
To calculate how many oranges are used in Bertha's pyramid, we first need to find out how many oranges are in each
layer of the pyramid. Since the base of the pyramid is a rectangle that is 4 oranges by 6 oranges, there are a total of 4 x 6 = 24 oranges in the base layer.
For the second layer of the pyramid, each orange rests on 4 oranges below it.
Since the base layer has 24 oranges, there will be 24 / 4 = 6 oranges in the second layer.
For the third layer, each orange again rests on 4 oranges below it.
So there will be 6 / 4 = 1.5 oranges in the third layer.
Since we cannot have half an orange, we round up to 2 oranges.
Finally, the top layer of the pyramid will consist of a single orange.
Therefore, the total number of oranges used in Bertha's pyramid is 24 + 6 + 2 + 1 = 33 oranges.
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Ten seventh graders and 15 eighth graders were selected for the elite choir ensemble.
a. Write the ratio of seventh graders to eighth graders who were selected for the
elite choir.
b. Write the ratio of seventh graders to total students who were selected for the
elite choir.
c. Write the ratio of eighth graders to total students who were selected for the elite
choir.
Answer:
Your answer should be A
I need help with this please
The range of a function is the set of all possible output values (y-values) of the function. To find the range of f(x) = (5/2)^x - 5, we need to find the minimum and maximum values of y that can be obtained by plugging in all possible x values.
Since (5/2)^x is always greater than 0 for any x, the minimum value of f(x) is -5.To find the maximum value of f(x), we can take the limit as x approaches infinity:
lim (x → ∞) (5/2)^x - 5 = ∞ - 5 = ∞Therefore, the range of f(x) is (-5, ∞).can someone help me asap? It’s due today
The type of sampling the principal can use is systematic sampling.
What is systematic sampling?Sampling means selecting the group that you will actually collect data from in your research. For example, if you are researching the opinions of students in a university, you could survey a sample of 50 students.
Systematic sampling is a probability sampling method where researchers select members of the population at a regular interval.
Therefore , with the definition of systematic sampling, it is best for the principal to use a method of systematic sampling for the procedure.
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we have studied srs and stratified sampling, and have also mentioned cluster sampling. there is one more sampling method which arises frequently, called systematic sampling. this is how it works in its simplest form:
Systematic sampling is a type of probability sampling method where every nth item in a population is selected for inclusion in the sample.
For example, if a researcher wanted to select a systematic sample of 100 students from a school population of 1,000 students, they would randomly select one of the first 10 students (1/10th of the population) and then select every 10th student thereafter until they reach 100. Systematic sampling is often used when the population is too large to enumerate and it is more efficient than simple random sampling. However, it is important to ensure that the sampling interval is not biased in any way, otherwise the sample may not be representative of the population.
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Systematic sampling is a relatively easy and quick method of sampling, as it requires less effort and time than other methods such as stratified or cluster sampling.
The starting point is truly random, and that the interval selected does not create any bias in the sample.
Systematic sampling is a method of selecting a sample from a population using a system or a pattern.
It involves selecting every nth item or person from the population after a random starting point has been determined.
To perform systematic sampling, the first item or individual in the sample is randomly selected from the population.
Then, the remaining items or individuals are selected at regular intervals, such as every 10th or 20th item or individual.
The interval is calculated by dividing the population size by the desired sample size.
A researcher wants to select a sample of 100 from a population of 1000, the interval would be. [tex]1000/100 = 10.[/tex]
The researcher would randomly select the first item or individual from the population, and then select every 10th item or individual thereafter until the desired sample size is reached.
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The function y = f(x) is graphed below.
What is the average rate of change of the
function f(x) on the interval
-1 ≤ x ≤ 0?
Answer:
-2
Step-by-step explanation:
The explanation is in the picture
T/F There exists a function f such that f(x) > 0, f'(x) < 0, and f"(x) > 0 for all x.
True, there exists a function f such that f(x) > 0, f'(x) < 0, and f"(x) > 0 for all x.
An example of such a function is[tex]f(x) = e^(-x)[/tex], where e is the base of the natural logarithm (approximately 2.718).
Let's verify the given conditions:
f(x) > 0:
Since e^(ax) is always positive for any real value of x and any constant a, [tex]e^(-x)[/tex]is also always positive for any real value of x.
f'(x) < 0:
To find the first derivative, apply the chain rule: [tex]f'(x) = -e^(-x). As e^(-x)[/tex] is always positive, the derivative
[tex]f'(x) = -e^(-x)[/tex] is always negative for all x.
f"(x) > 0:
To find the second derivative, apply the chain rule again:
[tex]f"(x) = e^(-x). As e^(-x)[/tex]is always positive, the second derivative[tex]f"(x) = e^(-x)[/tex] is always positive for all x.
Thus, it is true that there exists a function f with the given conditions.
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The function [tex]f(x) = e^(-x)[/tex] meets all the given conditions.
True. There exists a function f such that [tex]f(x) > 0, f'(x) < 0, and f"(x) > 0[/tex] for all x. One example of such a function is [tex]f(x) = e^(-x)[/tex].
True. There exists a function f(x) that satisfies the given conditions: f(x) > 0, f'(x) < 0, and f''(x) > 0 for all x.
Consider the function [tex]f(x) = e^(-x)[/tex]. This function has the following properties:
1. f(x) > 0 for all x because the exponential function is always positive.
2. [tex]f'(x) = -e^(-x)[/tex]which is always negative because e^(-x) is always positive, and the negative sign in front makes the derivative negative.
3. [tex]f''(x) = e^(-x)[/tex]which is always positive.
Thus, the function [tex]f(x) = e^(-x)[/tex]meets all the given conditions.
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In triangle ∆ABC, m<A = 33°, m<C = 58°, and AB = 25 in. What is AC to the nearest tenth of an inch?
1. 16.1 in.
2. 38.9 in
3. 42 in.
4. 12 in.
The length of AC using the laws of sines is 29.5 inches
Calculating the length of ACWe can use the law of sines to solve this problem.
The law of sines states that in any triangle ∆ABC:
a/sin(A) = b/sin(B) = c/sin(C)
where a, b, and c are the lengths of the sides opposite to the angles A, B, and C, respectively.
In this case, we know that m<A = 33°, m<C = 58°, and AB = 25 in.
We need to find AC, which is opposite to angle A.
Let's use the law of sines to solve for AC:
AC/sin(B) = AB/sin(C)
Where
B = 180 - 33 - 58
B = 89
So, we have
AC/sin(89°) = 25/sin(58°)
This gives
AC = 29.5 in. (rounded to the nearest tenth)
Therefore, the answer is 29.5 inches
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Question 5
A recent conference had 900 people in attendance. In one exhibit room of 80 people, there were 65 teachers and 15 principals. What prediction can you make about the number of principals in attendance at the conference?
There were about 820 principals in attendance.
There were about 731 principals in attendance.
There were about 208 principals in attendance.
There were about 169 principals in attendance.
Question 6
A teacher was interested in the subject that students preferred in a particular school. He gathered data from a random sample of 100 students in the school and wanted to create an appropriate graphical representation for the data.
Which graphical representation would be best for his data?
Stem-and-leaf plot
Histogram
Circle graph
Box plot
Question 7
A random sample of 100 middle schoolers were asked about their favorite sport. The following data was collected from the students.
Sport Basketball Baseball Soccer Tennis
Number of Students 17 12 27 44
Which of the following graphs correctly displays the data?
histogram with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled basketball going to a value of 17, the second bar labeled baseball going to a value of 12, the third bar labeled soccer going to a value of 27, and the fourth bar labeled tennis going to a value of 44
histogram with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled baseball going to a value of 17, the second bar labeled basketball going to a value of 12, the third bar labeled tennis going to a value of 27, and the fourth bar labeled soccer going to a value of 44
bar graph with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled basketball going to a value of 17, the second bar labeled baseball going to a value of 12, the third bar labeled soccer going to a value of 27, and the fourth bar labeled tennis going to a value of 44
bar graph with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled baseball going to a value of 17, the second bar labeled basketball going to a value of 12, the third bar labeled tennis going to a value of 27, and the fourth bar labeled soccer going to a value of 44
Question 8
A New York City hotel surveyed its visitors to determine which type of transportation they used to get around the city. The hotel created a table of the data it gathered.
Type of Transportation Number of Visitors
Walk 120
Bicycle 24
Car Service 45
Bus 30
Subway 81
Which of the following circle graphs correctly represents the data in the table?
circle graph titled New York City visitor's transportation, with five sections labeled walk 80 percent, bus 16 percent, car service 30 percent, bicycle 20 percent, and subway 54 percent
circle graph titled New York City visitor's transportation, with five sections labeled walk 40 percent, bicycle 8 percent, car service 15 percent, bus 10 percent, and subway 27 percent
circle graph titled New York City visitor's transportation, with five sections labeled subway 40 percent, bus 8 percent, car service 15 percent, bicycle 10 percent, and walk 27 percent
circle graph titled New York City visitor's transportation, with five sections labeled subway 80 percent, bicycle 20 percent, car service 30 percent, bus 16 percent, and walk 54 percent
Question 9
A college cafeteria is looking for a new dessert to offer its 4,000 students. The table shows the preference of 225 students.
Ice Cream Candy Cake Pie Cookies
81 9 72 36 27
Which statement is the best prediction about the scoops of ice cream the college will need?
The college will have about 480 students who prefer ice cream.
The college will have about 640 students who prefer ice cream.
The college will have about 1,280 students who prefer ice cream.
The college will have about 1,440 students who prefer ice cream.
Question 10
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
Answer:
B
B
A
B
D
C
Step-by-step explanation:
5. B
65 = teachers
15 = principal
65/80 = 81.25
If there's is a total of 900 people, find 81.25 (number of teachers)
=731.25
=731
6. B
The best graphical representation for the teacher's data would be a histogram. A histogram is a graph that displays the distribution of continuous data, such as the number of students who prefer a particular subject. It shows the frequency of each interval, or bin, of values.
A stem-and-leaf plot is typically used for small datasets and displays each data point. A circle graph, also known as a pie chart, is used to show how different parts make up a whole and is not appropriate for showing the distribution of preferences among the students. A box plot, also known as a box-and-whisker plot, is used to display the distribution of data, but it may not be as useful for showing the specific frequencies of each preference as a histogram would be.
7) A
There's an image for it I attached
8) B
The correct circle graph that represents the data in the table is option B) circle graph titled New York City visitor's transportation, with five sections labeled walk 40 percent, bicycle 8 percent, car service 15 percent, bus 10 percent, and subway 27 percent.
In the given table, the number of visitors for each type of transportation is given. To create a circle graph, we need to convert the given numbers to percentages. Then, we can use these percentages to determine the angle of each section in the circle graph.
Using the given numbers, we can calculate the percentage of visitors for each transportation type as follows:
Walk: (120/300) x 100 = 40%
Bicycle: (24/300) x 100 = 8%
Car Service: (45/300) x 100 = 15%
Bus: (30/300) x 100 = 10%
Subway: (81/300) x 100 = 27%
Option B) correctly represents these percentages in a circle graph.
9) D
The best prediction about the scoops of ice cream the college will need is option D) The college will have about 1,440 students who prefer ice cream.
To make this prediction, we need to use the information given in the table and assume that the entire student body has the same preferences as the sample of 225 students.
According to the table, 81 out of 225 students prefer ice cream.
To estimate the number of students who prefer ice cream in the entire student body of 4,000 students, we can use proportions.
81/225 = x/4000
Multiplying both sides by 4000, we get:x = 81/225 x 4000 = 1,440
Therefore, the college will have about 1,440 students who prefer ice cream, and they will need to prepare that many scoops.
10) C
The drive-thru that typically has more wait time is option C) Super Fast Food, because it has a larger median.
The median is the middle value when a set of data is arranged in order. In this case, the median wait time for Super Fast Food is 12 minutes, and the median wait time for Burger Quick is 15.5 minutes.
This means that half of the customers at Super Fast Food waited less than 12 minutes, while half of the customers at Burger Quick waited less than 15.5 minutes.
Therefore, the wait time at Super Fast Food is typically shorter than at Burger Quick.
The mean, on the other hand, is influenced by outliers or extreme values, and it is not as robust a measure of central tendency as the median. Therefore, we cannot determine which drive-thru typically has more wait time based on the mean alone.
act scores have a mean of 21.4 and 15 percent of the scores are above 26 . the scores have a distribution that is approximately normal. find the standard deviation. round your answer to the nearest tenth, if necessary.
The standard deviation of the ACT scores is approximately 4.2.
What is Standard deviation?Standard deviation is a measure of the amount of variation or dispersion in a set of data values. It indicates how much the data values deviate, on average, from the mean (or average) of the data set. A higher standard deviation indicates greater variability or spread in the data, while a lower standard deviation indicates less variability or spread.
According to the given information:
To find the standard deviation of ACT scores, we can use the given information about the mean and the percentage of scores above a certain threshold.
Given:
Mean (μ) = 21.4
Percentage of scores above 26 = 15%
Since the distribution is approximately normal, we can use the Z-score formula to find the Z-score corresponding to the given percentage. The Z-score is the number of standard deviations a particular value is from the mean in a normal distribution.
Z-score formula:
Z = (X - μ) / σ
Where:
Z = Z-score
X = Value (in this case, 26)
μ = Mean (21.4)
σ = Standard deviation (to be found)
We can rearrange the formula to solve for σ:
σ = (X - μ) / Z
Substituting the given values:
X = 26
μ = 21.4
Z = Z-score corresponding to 15% (which can be found using a standard normal distribution table or a Z-score calculator)
Assuming a standard normal distribution table or calculator gives us a Z-score of approximately 1.04 for a percentage of 15%, we can plug in the values:
σ = (26 - 21.4) / 1.04
σ = 4.4 / 1.04
σ ≈ 4.2 (rounded to the nearest tenth)
So, the standard deviation of the ACT scores is approximately 4.2.
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A store is offering a 30% discount on shirts. A shirt at the store has an original cost of $25. What is the cost of the shirt, in dollars, after the discount?
The cost of the shirt, in dollars, after the 30% discount is $17.50.
What is discount?
A discount is a reduction in the price of a product or service that is offered by a seller to a buyer. Discounts can be offered for a variety of reasons, such as to attract customers, increase sales, or clear out inventory. Discounts can be expressed as a percentage or a fixed amount, and they can be applied at the time of purchase or deducted from an invoice or bill. Discounts are often used in sales promotions, marketing campaigns, and loyalty programs to incentivize customers to buy or use a product or service.
If a store is offering a 30% discount on shirts that cost $25 originally, then the discount amount is:
30% of $25 = 0.30 x $25 = $7.50
The discount amount is $7.50, so the new price of the shirt after the discount is:
$25 - $7.50 = $17.50
Therefore, the cost of the shirt, in dollars, after the 30% discount is $17.50.
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laptop: $199.99, 13% markup what is the markup
Answer:
≈ $26
Step-by-step explanation:
13% = 0.13
199.99 x 0.13 = $25.9987
So, 13% markup is ≈ $26