In a seventh grade class of 28 students there are 16 girls and 12 boys if one student chosen to win a prize. The probability of a girl being chosen from the seventh-grade class is 4/7.
To determine the probability of a girl being chosen from a seventh-grade class, we need to consider the number of girls and the total number of students in the class.
In this scenario, there are 28 students in total, comprising 16 girls and 12 boys.
To calculate the likelihood of an event, divide the count of desired outcomes by the total count of possible outcomes.
In this case, the favorable outcome is a girl being chosen, and the possible outcomes are any student being chosen from the class.
Hence, the probability of a girl being chosen can be calculated as follows:
The probability of an event is determined by the ratio of favorable outcomes to the total number of possible outcomes.
The number of favorable outcomes is equal to the number of girls, which is 16.
The total number of possible outcomes is equal to the total number of students, which is 28.
Hence, the probability of selecting a girl is:
Probability = 16 / 28
Simplifying the fraction:
Probability = 4 / 7
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Rich is attending a 4-year college. As a freshman, he was approved for a 10-year, federal unsubsidized student loan in the amount of $7,300 at 4. 29%. He knows he has the option of beginning repayment of the loan in 4. 5 years. He also knows that during the nonpayment time, interest will accrue at 4. 29%.
a. How much interest will Rich accrue during the 4. 5 year nonpayment period?
b. What will be the new principal amount when Rich begins making payments?
a. Rich will accrue $1,181.18 in interest during the 4.5-year nonpayment period.
b. The new principal amount when Rich begins making payments will be approximately $8,481.18.
a. To calculate the interest accrued during the 4.5-year nonpayment period, we can use the formula:
Interest = Principal x Interest Rate x Time
The principal amount is $7,300, and the interest rate is 4.29% expressed as a decimal, which is 0.0429. The time is 4.5 years.
Interest = $7,300 x 0.0429 x 4.5
Interest = $1,181.18
Therefore, Rich will accrue approximately $1,181.18 in interest during the 4.5-year nonpayment period.
b. To determine the new principal amount when Rich begins making payments, we need to add the accrued interest to the original principal.
New Principal = Principal + Accrued Interest
New Principal = $7,300 + $1,181.18
New Principal = $8,481.18
Therefore, when Rich begins making payments, the new principal amount will be approximately $8,481.18.
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The temperature of a certain liquid increases by 150 C in 3 minutes when it is heated. At this rate, what is the increase in temperature in 7 minutes?
The temperature of a certain liquid increases by 350 C in 7 minutes when it is heated. Determine the rate of temperature increase in the liquidRise in temperature / time taken = 150/3= 50C/min.
Given, The temperature of a certain liquid increases by 150 C in 3 minutes when it is heated.The rate of temperature increase in the liquid can be calculated as follows:Rise in temperature / time taken = 150/3= 50C/minTo find the increase in temperature in 7 minutes, the following formula can be used:Increase in temperature = Rate of temperature increase × time taken= 50 × 7= 350CTherefore, the temperature of a certain liquid increases by 350 C in 7 minutes when it is heated.
To find the increase in temperature in 7 minutes when the temperature of a certain liquid increases by 150 C in 3 minutes when it is heated, follow these steps:Step 1: Determine the rate of temperature increase in the liquidRise in temperature / time taken = 150/3= 50C/minTherefore, the rate of temperature increase in the liquid is 50C/min.Step 2: Calculate the increase in temperature in 7 minutesIncrease in temperature = Rate of temperature increase × time taken= 50 × 7= 350CTherefore, the temperature of a certain liquid increases by 350 C in 7 minutes when it is heated.
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A rectangular parking lot has a perimeter of 112 and a area of 768 square meter what are the dimensions of the parking lot
Therefore, the dimensions of the parking lot can be 32 m × 24 m or 24 m × 32 m.
Let's represent the dimensions of the rectangular parking lot as 'l' and 'w.' Therefore, the perimeter of the parking lot can be expressed as:Perimeter, P = 2l + 2w
We are given the perimeter of the parking lot as 112.
Therefore,112 = 2l + 2w
Now, let's solve for l in terms of w
112 - 2w = 2l
56 - w = l
l = 56 - w
Now, let's represent the area of the parking lot as 'A'.A = lw 768 = l w 768 = (56 - w)w768 = 56w - w²0 = w² - 56w + 768 To solve the above quadratic equation, we will use the quadratic formula:
x = (-b ± √(b² - 4ac))/2a
On substituting the given values in the above formula, we get:
w = 24 or w = 32If w = 24, then l = 56 - 24 = 32If w = 32, then l = 56 - 32 = 24
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A survey asked people of different ages whether they get their news by reading the paper. What is the probability that a person surveyed gets the news by reading the paper, given that he or she is under 40? If necessary. round your answer to the nearest percent. HELP HELP ME HELP
the example of a permutation is: A) The number of ways 3 people can win 3 different prizes.
A) The number of ways 3 people can win 3 different prizes.
This scenario involves the arrangement of 3 people winning 3 different prizes. Since the order in which the people win the prizes matters, this is an example of a permutation. For instance, if we have three people named A, B, and C, the possible permutations of them winning the prizes could be A winning the first prize, B winning the second prize, and C winning the third prize. Therefore, option A is an example of a permutation.
B) Picking 10 CDs to lend to a neighbor from a collection of 35.
This scenario involves selecting 10 CDs out of a collection of 35. The order in which the CDs are selected does not matter; only the selection itself is important. Therefore, this is an example of a combination rather than a permutation. Option B does not represent a permutation.
C) The number of ways 8 books can be selected from 10 to take on a trip.
Similarly to option B, this scenario involves selecting 8 books out of a group of 10 books. The order of the selected books does not matter; only the selection itself is relevant. Thus, this is also an example of a combination rather than a permutation. Option C does not represent a permutation.
D) Selecting 4 students to represent their class for the school.
This scenario involves selecting 4 students from a group to represent their class. Since the order in which the students are selected does not matter, this represents a combination rather than a permutation. Option D does not represent a permutation.
Option A
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Pls can i get help need help to find out the numbers that made this box plot
The box plot or any additional information regarding the data. Without any context, it is impossible to determine the numbers that made up the box plot.
A box plot displays a summary of a set of data, including the minimum and maximum values, the median, the first quartile, and the third quartile.
It provides a visual representation of the distribution of data and helps in identifying outliers in the data.In order to find the numbers that made up the box plot, you need to have the actual data set from which the box plot was created.
Once you have the data set, you can use it to calculate the minimum and maximum values, the median, the first quartile, and the third quartile.
These values can then be plotted on a box plot to create a visual representation of the data distribution. Alternatively, you can use a software or an online tool that can generate a box plot from a given data set.
The numbers that made up the box plot will vary depending on the data set. The box plot is a useful tool for visualizing data, but it is important to understand the context and characteristics of the data in order to interpret the plot accurately.
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Samantha conducts an experiment. She makes many observations and measurements and records each very carefully. At the conclusion of the experiment she discovers that the data she collected do not support her hypotheses. What should Samantha do
In this situation, Samantha should carefully evaluate her experiment, hypotheses, and data to understand the reasons why her data did not support her hypotheses.
When Samantha's data do not support her hypotheses, it is important for her to approach the situation with a scientific mindset. She should first examine her experimental design and methodology to ensure that they were sound and reliable. Samantha should consider if any procedural errors, biases, or confounding factors may have influenced her results.
Next, Samantha should critically analyze her data to identify any patterns, trends, or inconsistencies. She should explore alternative explanations or factors that might account for the observed outcomes. It is possible that Samantha's initial hypotheses were based on incomplete information or flawed assumptions. By considering different perspectives and potential variables, Samantha can gain a deeper understanding of the phenomena she studied.
Based on her evaluation, Samantha may need to revise her hypotheses, adjust her experimental approach, or even consider pursuing a different research direction. Negative results can still provide valuable insights and contribute to scientific knowledge by ruling out certain explanations or suggesting new avenues for investigation.
Ultimately, Samantha should embrace the opportunity to learn from her experiment and use the experience to refine her scientific approach. The process of questioning, analyzing, and adapting is crucial in advancing scientific understanding.
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Jadah takes the bus to school every morning. 3 out of the last 5 days last week, her bus was late. Based on those results, in how many out of the 180 school days would you expect her bus would be late?
Based on the given information, we can expect Jadah's bus to be late for approximately 108 out of the 180 school days.
To determine the expected number of days Jadah's bus would be late out of 180 school days, we can use the proportion of late days from the previous week.
Out of the last 5 days, her bus was late for 3 days. This can be represented as a ratio: 3/5.
To find the expected number of late days out of 180 school days, we can set up a proportion:
(3/5) = x/180
Cross-multiplying, we get:
5x = 3 * 180
5x = 540
x = 540/5
x = 108
Therefore, based on the results from the previous week, we can expect Jadah's bus to be late for approximately 108 out of the 180 school days.
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There are 254 counties in Texas. Zane rounds the number to nearest ten. What is the difference between actual number of counties and Zane rounded number of counties and zane's rounded number? solve this problem using an equation and an unknown.
The difference between the actual number of counties in Texas and Zane's rounded number of counties can be found by subtracting Zane's rounded number from the actual number. Let's represent the actual number of counties as "x" and Zane's rounded number as "y". The equation representing the difference is x - y.
Let's assume that the actual number of counties in Texas is "x". Zane rounds the number to the nearest ten, so his rounded number of counties can be represented as "y". The difference between the actual number and Zane's rounded number can be calculated by subtracting Zane's rounded number from the actual number, which gives us the equation x - y. Substituting the given values, where x = 254 (actual number of counties) and y is the rounded number, we can find the difference.
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If 980 = 2x X 5y X 7z, find the values of x, y and z... pls help with working
Answer:
x = 2, y = 1, z = 7-------------------------
We are given that, 980 = 2x × 5y × 7z
We need to find the values of x, y, and z.
Find the prime factorization of 980.
980 can be written as:
980 = 2 × 2 × 5 × 7 × 7Compare the given expression with the prime factorization of 980.
2 × 2 × 5 × 7 × 7 = 2x × 5y × 7zIt can be observed that:
2x = 2 × 2 ⇒ x = 25y = 5 ⇒ y = 17z = 7 × 7 ⇒ z = 7Hence, the values of x, y, and z are 2, 1, and 7 respectively.
You can get some great new space for $126,000 per year. You will be leasing 3,900 square feet. What will your rent be per square foot per year?
Given that a space is leased for $126,000 per year and 3,900 square feet leased area.
What will be the rent per square foot per year?
We can obtain the rent per square foot per year by using the following formula;`
Rent per square foot per year = Total rent per year / Total area leased`
Using the formula above, the rent per square foot per year can be calculated as follows;
`Rent per square foot per year = 126,000 / 3,900 = $32.31
`Therefore, the rent per square foot per year is $32.31.
let's do it in more detail:
To calculate the rent per square foot per year, you can divide the total annual rent by the total square footage.
Rent per square foot per year = Total annual rent / Total square footage
Given:
Total annual rent: $126,000
Total square footage: 3,900 square feet
Rent per square foot per year = $126,000 / 3,900 square feet
Using a calculator, we can compute:
Rent per square foot per year ≈ $32.31
Therefore, the rent per square foot per year would be approximately $32.31.
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Question 17 1 pts Last year 500 students enrolled in both math and art class. Of these students 82 got an A in math, 73 in art class, and 42 in both statistic and psychology. Find the probability that randomly selected student got an A in math or art class (or both).
To find the probability that a randomly selected student got an A in math or art class (or both), we need to use the principle of inclusion-exclusion.
Let's define the events:
M = Getting an A in math class
A = Getting an A in art class
We are given the following information:
n(M) = 82 (number of students who got an A in math)
n(A) = 73 (number of students who got an A in art)
n(M ∩ A) = 42 (number of students who got an A in both math and art)
To calculate the probability of getting an A in math or art class (or both), we can use the formula:
P(M ∪ A) = P(M) + P(A) - P(M ∩ A)
We need to find the probabilities P(M) and P(A) first.
P(M) = n(M) / total number of students
P(M) = 82 / 500
P(M) = 0.164
P(A) = n(A) / total number of students
P(A) = 73 / 500
P(A) = 0.146
Now, we can calculate the probability of getting an A in math or art class (or both):
P(M ∪ A) = P(M) + P(A) - P(M ∩ A)
P(M ∪ A) = 0.164 + 0.146 - (42 / 500)
P(M ∪ A) ≈ 0.164 + 0.146 - 0.084
P(M ∪ A) ≈ 0.226
Therefore, the probability that a randomly selected student got an A in math or art class (or both) is approximately 0.226, or 22.6%.
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2. In Canada, 63% of households speak English as their primary language, and 23% speak French as their primary language. If two Canadian households are selected at random, what is the probability that the first household speaks French, but the second household speaks English?
A. (0.23)(0.63) = 0.1449
B. 0.23 + 0.63 = 0.86
C. 0.23 + 0.63 – (0.23)(0.63) = 0.7451
D. 0.23/0.63=0.3650
The probability that the first household speaks French, but the second household speaks English is 0.1449
Let A be the event that the first household speaks French, and B be the event that the second household speaks English.
P(A) = probability that the first household speaks French
= 0.23
P(B|A) = probability that the second household speaks English given that the first household speaks French= 0.63
P(A and B) = probability that the first household speaks French and the second household speaks English
= P(A) × P(B|A)
= 0.23 × 0.63
= 0.1449
The correct option is (A) (0.23)(0.63) = 0.1449.
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In the study, palmitic acid was determined to be the most effective chemical, providing three times the protection of stearic acid and was ten percentage points higher in protection than linoleic acid. The effectiveness precentages of stearic acid plus linoleic acid together were five percentage points higher than palmitic acid. What is the effectiveness of stearic acid in repelling mosquitoes?
The effectiveness of stearic acid in repelling mosquitoes can be calculated by using the data given in the statement and the following formula.Effectiveness of Stearic Acid = (Effectiveness of stearic acid plus linoleic acid) - (Effectiveness of linoleic acid)
Substituting the given values, we get the effectiveness of stearic acid as: (Effectiveness of stearic acid + linoleic acid) - (Effectiveness of linoleic acid)=(5+10)−(Effectiveness of linoleic acid)=15 - Effectiveness of linoleic acidNow, it is given that palmitic acid was three times more effective than stearic acid.
Hence, the effectiveness of stearic acid can be written as: Effectiveness of stearic acid = 1/3 (Effectiveness of palmitic acid)Also, palmitic acid was 10% more effective than linoleic acid. Hence, the effectiveness of palmitic acid can be written as:Effectiveness of palmitic acid = 1.10
(Effectiveness of linoleic acid)Substituting the value of effectiveness of palmitic acid in the equation for effectiveness of stearic acid, we get:Effectiveness of stearic acid = 1/3 (Effectiveness of palmitic acid)= 1/3 x 1.10 (Effectiveness of linoleic acid)= 0.366 (Effectiveness of linoleic acid)
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$16000 is invested for 5 years with an APR of3 % and quarterly compounding
The accumulated value in 5 years of the investment compounded quarterly is approximately: $18578.946
How to find the compound interest?Compound interest differs from simple interest in that the interest received in one period will itself accrue in the next period. As a result, the amount in the account increases exponentially.
The future value of a compounding account depends on the number of compounding periods per year. Another factor is the annual interest rate. The higher the APR, the greater the cumulative value over time.
The formula for compound interest is:
FV = P(1 + (r/m))^(mt)
where:
FV is the future value of the investment.
P is the principal or initial amount invested.
r is the annual interest rate.
m is the number of compounding per year.
t is the time in years,
P = $16000
t = 5
m = 4
r = 3% = 0.03
Thus:
FV = 16000(1 + (0.03/4))^(4 * 5)
FV = $18578.946
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Complete Question is:
$16000 is invested for 5 years with an APR of3 % and quarterly compounding.
Write a numerical expression that would compute the value of the investment after 5 years.
Estimate the total cost of 32 printers at £198 each and 58 ink cartridges at
£31. 15 each.
The estimated total cost of 32 printers at £198 each and 58 ink cartridges at £31.
to estimate the total cost, we can multiply the quantity of each item by its respective cost and then sum them together.
the cost of 32 printers at £198 each can be calculated as follows:32 printers * £198/printer = £6336
the cost of 58 ink cartridges at £31.15 each can be calculated as follows:
58 cartridges * £31.15/cartridge = £1805.70
to find the total cost, we add the cost of the printers and the cost of the ink cartridges:total cost = £6336 + £1805.70 = £8141.70 15 each is £8141.70.
the total cost of 32 printers at £198 each and 58 ink cartridges at £31.
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What is the solution to -48 - 3x) 6x - 8?
O X> -4/3
O x<-4/3
O x>4
Ox<4
The solution to the inequality -48 - 3x > 6x - 8 is x < -40/9
How to determine the solution to the inequalityFrom the question, we have the following parameters that can be used in our computation:
-48 - 3x > 6x - 8
Collect the like terms in the above inequality
So, we have
-6x - 3x > 48 - 8
When the like terms are evaluated, we have
-9x > 40
Divide both sides by -9
x < -40/9
Hence, the solution to the inequality is x < -40/9
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We have to estimate the allocation base and the total manufacturing overhead costs in advance in order to be able to determine a
In order to determine the predetermined overhead rate and allocate manufacturing overhead costs, it is necessary to estimate the allocation base and the total manufacturing overhead costs in advance.
These estimates help in establishing a systematic method for assigning overhead costs to products or services based on a relevant allocation base.
Manufacturing overhead costs include various indirect expenses such as factory rent, utilities, equipment maintenance, and supervision. These costs cannot be easily traced directly to specific products or services. Instead, they are allocated based on a predetermined overhead rate.
The allocation base is a measure or activity that serves as a common denominator for distributing overhead costs. Common allocation bases include direct labor hours, machine hours, or material costs. The choice of allocation base depends on the nature of the business and the activities that drive overhead costs.
To determine the predetermined overhead rate, the total estimated manufacturing overhead costs for a specific period are divided by the estimated allocation base. This rate is then applied to the actual allocation base incurred during production to allocate the overhead costs to individual products or services.
Estimating the allocation base and the total manufacturing overhead costs in advance allows for a more accurate and consistent allocation of overhead expenses. It helps businesses establish a systematic approach to assign costs, aiding in decision-making, cost analysis, and determining product or service pricing.
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Which of these statements about alpha is true? (Choose all that apply)
1. Alpha is the probability of a Type 1 error
2. A high alpha proves that the alternative hypothesis is true.
3. 0.10,0.05, and 1.00 are all possible values of alpha.
4.When the p-value is smaller than the alpha, we reject the null hypothesis.
statements 1 and 4 are true regarding alpha.Among the given statements about alpha:
1. Alpha is the probability of a Type 1 error: This statement is true. Alpha, represented by the symbol α, is the significance level or the probability of making a Type 1 error, which is rejecting the null hypothesis when it is actually true.
2. A high alpha proves that the alternative hypothesis is true: This statement is false. Alpha does not prove or indicate the truth of the alternative hypothesis. The alternative hypothesis is supported by evidence such as statistical significance, effect size, and other factors, not by the value of alpha.
3. 0.10, 0.05, and 1.00 are all possible values of alpha: This statement is true. Alpha can take on various values, including 0.10, 0.05, and 1.00, depending on the desired level of significance and the specific research or analysis.
4. When the p-value is smaller than the alpha, we reject the null hypothesis: This statement is true. In hypothesis testing, if the calculated p-value is smaller than the chosen alpha level, typically 0.05 or 0.01, we reject the null hypothesis in favor of the alternative hypothesis.
Therefore, statements 1 and 4 are true regarding alpha.
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Tamara likes to go hiking and tries to hike for at least 350 minutes every week. On Thursday she hiked for 1 mile in the morning and 3 miles in the evening. On Thursday, she hiked with a friend for 4 miles. On Saturday, she hiked for 5 miles. On Sunday, she hiked for 4 miles. If she hiked a total of 340 minutes all week and it takes her the same amount of time to hike each mile, how many minutes does it take her to hike each mile?
If Tamara hiked a total of 340 minutes and her goal is to hike for at least 350 minutes every week, it means she fell short by 10 minutes.
Since it takes her the same amount of time to hike each mile, we can calculate the time it takes her to hike each mile.
On Thursday, she hiked a total of 1 + 3 + 4 = 8 miles. On Saturday and Sunday, she hiked a total of 5 + 4 = 9 miles. So in total, she hiked 8 + 9 = 17 miles.
To find the time it takes her to hike each mile, we divide the total time she hiked (340 minutes) by the total distance she covered (17 miles). Therefore, it takes her 340/17 = 20 minutes to hike each mile.
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Find a number written in binary system that when read as a number in decimal system is five times
smaller than the same number read as a decimal (notice that any binary number can be also
interpret as a decimal, for example 111 can represent a binary number but also can be seen as one
hundred and eleven - a decimal).
Treat this question like a puzzle, just try different numbers and this way guess the answer.
Considering, the binary number to be represented is a two-digit number, the binary number to be represented is 0101.
Let us assume that the binary number to be represented is a two-digit number.
Therefore, it can be represented as xy where x and y are either 0 or 1.
We know that any binary number can also be interpreted as a decimal number.
For example, 111 can represent a binary number but also can be seen as one hundred and eleven - a decimal.
The number written in the binary system is thus 2x + y.
The number written in the decimal system is = x × 10 + y, which is 5 times greater than the binary number when the binary number is written in the decimal system.
5(2x + y) = x × 10 + y
10x - 9y = 0
y = 0, 10, 20, 30, ... are some solutions, but y cannot be greater than 10, as it is a two-digit number in the binary system.
As a result, the only feasible solution is y = 0.5(2x)
= 10x
x = 5
Therefore, the binary number to be represented is 0101.
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A drawing of a cereal box, as shown, has a scale of 1 inch to 1 foot.
What is the actual height, in inches, of the cereal box?
The actual height of the cereal box is 12 inches.
In the given scale of 1 inch to 1 foot, it means that every 1 inch on the drawing represents 1 foot in reality. Since there are 12 inches in a foot, the height of the cereal box in inches can be determined by multiplying the height shown on the drawing by 12.0
As a result, the actual height of the cereal box can be calculated by multiplying the height of the cereal box on the drawing by 12. For example, if the height of the cereal box on the drawing is 1 inch, then the actual height of the cereal box would be 1 inch multiplied by 12, which equals 12 inches.
Therefore, in this case, the actual height of the cereal box is 12 inches.
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The sum of the interior angles of the polygon is 540 degrees. Create an equation to solve for x:
Part 2: Find the measure of x, then find the measures of each unknown angles
To find the measure of x and the unknown angles in a polygon, we can create an equation based on the sum of the interior angles, which is 540 degrees.final answer is 108°.
Let's assume the polygon has n sides. Each interior angle of a polygon can be calculated using the formula (n - 2) * 180° / n. In this case, we are given that the sum of the interior angles is 540 degrees.
So, we can set up the equation:
(n - 2) * 180° / n * n = 540°
Simplifying the equation:
(n - 2) * 180° = 540°
(n - 2) = 540° / 180°
(n - 2) = 3
Solving for n:
n = 3 + 2
n = 5
Now that we know the polygon has 5 sides, we can find the measure of x by substituting it back into the formula:
x = (5 - 2) * 180° / 5
x = 3 * 180° / 5
x = 540° / 5
x = 108°
In conclusion, the measure of x is 108 degrees, and each of the unknown angles in the polygon would also be 108 degrees since all angles in a regular polygon are equal.
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A child flies a kite at a height of ft, the wind carrying the kite horizontally away from the child at a rate of. How fast must the child let out the string when the kite is ft away from the child?
To find the rate at which the child must let out the string, we can use the concept of related rates.
Let's assign variables to the given quantities: Let h represent the height of the kite in feet. Let x represent the horizontal distance of the kite from the child in feet. Let dh/dt represent the rate at which the height is changing in feet per second. Let dx/dt represent the rate at which the horizontal distance is changing in feet per second. We are given that the height of the kite is h ft, the horizontal distance is x ft, and the rate of change of the horizontal distance is dx/dt ft/s. By using the Pythagorean theorem, we have the equation: x^2 + h^2 = d^2. Differentiating both sides of the equation with respect to time t, we get: 2x(dx/dt) + 2h(dh/dt) = 2d(dd/dt). Since the child is not letting out or pulling in the string, the rate at which the length of the string (d) is changing is zero. Therefore, dd/dt is equal to 0. Now, we can substitute the given values: 2x(dx/dt) + 2h(dh/dt) = 0. Solving for dx/dt, the rate at which the child must let out the string, we get: dx/dt = -h(dh/dt) / x.
Therefore, the child must let out the string at a rate of (-h(dh/dt)) / x feet per second when the kite is x feet away from the child.
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In ΔABC, c = 5. 4, a = 3. 3, and measure of angle A = 20 degrees. What are the possible approximate lengths of b? Use the law of sines to find the answer. 2. 0 units and 4. 6 units 2. 1 units and 8. 7 units 2. 3 units and 7. 8 units 2. 6 units and 6. 6 units.
To find the approximate length of b in ΔABC, we will use the law of sines. Using the law of sines, we can write: b / sin B = c / sin C, where B is the angle opposite b and C is the angle opposite c.
We know the value of c, a, and A. Thus, we can find the value of sin C using the sine rule,i.e. c / sin C = 2R, where R is the radius of the circumcircle of ΔABC. The value of sin C can be found as sin C = c / 2R. Now, using the value of sin C, we can write:
b / sin B = c / sin C
b / sin B = c / (c / 2R)
b / sin B = 2R
Therefore, sin B = b / (2R)Now, we can find the value of R by using the formula
R = a / (2 sin A), where A is the angle opposite a. Putting the values in this formula, we get:
R = a / (2 sin A) = (3.3) / (2 sin 20°) = 5.004 units
Now, using the value of R, we can find the value of sin B, i.e. sin B = b / (2R)Using the formula, we get:
sin B = b / (2R)
sin B = b / (2 × 5.004)
sin B = b / 10.008
Therefore, we get: b = 10.008 sin B
Now, we can find the range of values of b by finding the range of values of sin B. The value of sin B can range from 0 to 1. Thus, the value of b can range from 0 to 10.008.
Therefore, the possible approximate lengths of b are between 0 and 10.008 units. Hence, the correct answer 2. 6 units and 6. 6 units.
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A sugar cone for ice cream is shaped like a cone. If a sugar cone has a slant height of 4 inches and a diameter of 2 inches, what is the lateral surface area of the cone? Use 3. 14 for pi. [Hint: Exclude the base. ]
12. 6 square inches
37. 7 square inches
18. 8 square inches
15. 7 square inches
The required lateral surface area of the sugar cone is approximately 12.60 square inches. Option A is correct.
To find the lateral surface area of the sugar cone, we need to calculate the curved surface area of the cone excluding the base.
Given:
Slant height (l) = 4 inches
Diameter (d) = 2 inches
First, let's find the radius (r) of the cone by dividing the diameter by 2:
r = d/2 = 2/2 = 1 inch
The lateral surface area (A) of the cone can be calculated using the formula:
A = πrl
Substituting the given values:
A = 3.14 * 1 inch * 4 inches
A = 12.56 square inches
Therefore, the lateral surface area of the sugar cone is approximately 12.56 square inches.
Among the given answer choices, the closest option is:
12.6 square inches.
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An airplane cruises 1 kilometer in112of a minute. What is its cruising speed?Simplify your answer and write it as a proper fraction, mixed number, or whole number
The cruising speed of the airplane can be determined by dividing the distance it traveled by the time it took. In this case, the airplane cruised 1 kilometer in 1/12 of a minute. Therefore, its cruising speed is 12 kilometers per minute.
To calculate the cruising speed of the airplane, we divide the distance traveled (1 kilometer) by the time it took (1/12 of a minute). Dividing these values yields a cruising speed of 12 kilometers per minute.
It's important to note that the speed of an object is defined as the distance traveled per unit of time. In this case, the distance traveled by the airplane is given as 1 kilometer, and the time taken is 1/12 of a minute. Dividing these values provides us with the cruising speed of the airplane.
The cruising speed of 12 kilometers per minute represents the rate at which the airplane covers distance during its cruise phase. It is essential to simplify the answer and express it as a whole number or fraction to provide a clear and concise representation of the cruising speed.
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Edgar owns 234 shares of Cawh Consolidated Bank, which he bought for $21. 38 apiece. Each share pays a yearly dividend of $3. 15. Edgar also owns two par value $1,000 bonds from Cawh Consolidated Bank. The bonds had a market value of 105. 166 when he bought them, and pay 8. 3% interest yearly. Which aspect of Edgar’s investment in Cawh Consolidated Bank offers a greater percent yield, and how much greater is it? a. The stocks have a yield 6. 43 percentage points greater than that of the bonds. B. The stocks have a yield 6. 84 percentage points greater than that of the bonds. C. The bonds have a yield 1. 05 percentage points greater than that of the stocks. D. The bonds have a yield 9. 13 percentage points higher than that of the stocks.
The stocks of Cawh Consolidated Bank offer a yield that is 6.84 percentage points greater than that of the bonds.
To compare the yields of Edgar's investment in Cawh Consolidated Bank stocks and bonds, we need to calculate the yields of both investments and then find the difference between them.
For the stocks, the yield can be calculated by dividing the annual dividend per share by the purchase price per share and multiplying by 100. In this case, the yield of the stocks is [tex][{\frac{3.15}{21.38}] *100= 14.71 \%.[/tex]
For the bonds, the yield is the annual interest payment divided by the market value of the bonds, multiplied by 100. The yield of the bonds is [tex][{\frac{8.3}{105.166}]* 100 = 7.89 \%[/tex] .
Now, to determine which aspect of Edgar's investment offers a greater percent yield, we find the difference between the yield of the stocks and the yield of the bonds. The difference is [tex]14.71 \% - 7.89 \% = 6.82 \%[/tex].
Therefore, the correct answer is option B: The stocks have a yield [tex]6.84[/tex]percentage points greater than that of the bonds.
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Start at 4 create a pattern that multiplies each number by 5 stop when you have 5 numbers
The pattern that multiplies each number by 5 starting at 4 and stopping after 5 numbers is:4, 20, 100, 500, 2500.
How to get the solution?
Given that we start at 4, and we are to multiply each number by 5, we have;
4 × 5 = 20
That gives us the second number.
To get the third number, we multiply 20 by 5 again.
20 × 5 = 100
To get the fourth number, we again multiply the third number by 5.
100 × 5 = 500
Finally, we multiply the fourth number by 5 to get the fifth number.500 × 5 = 2500.
Therefore, the pattern that multiplies each number by 5 starting at 4 and stopping after 5 numbers is:4, 20, 100, 500, 2500.
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150 people are asked how many siblings they have? # of Siblings Frequency Relative Frequency Cumulative Frequency 0 35 0.2333 35 1 29 64 2 0.1533 87 3 29 0.1933 116 4 34 0.2267
Therefore, the answer is:Number of Siblings Frequency Relative Frequency Cumulative Frequency0 35 0.2333 351 29 0.1933 642 0 0 873 29 0.1933 1164 34 0.2267 150
Here is how to calculate the Relative Frequency and Cumulative Frequency based on the data given:
Number of Siblings Frequency Relative Frequency Cumulative Frequency
0 35 0.2333 351 29 0.1933 642 0 0.1533 873 29 0.1933 1164 34 0.2267 150
Relative frequency for 0 siblings:
As per the given data, frequency of 0 siblings = 35
And, total number of people asked = 150
Therefore, relative frequency for 0 siblings = 35/150= 0.2333
Relative frequency for 1 sibling:
As per the given data, frequency of 1 sibling = 29And, total number of people asked = 150Therefore, relative frequency for 1 sibling = 29/150 = 0.1933Relative frequency for 2 siblings:
As per the given data, frequency of 2 siblings = 0And, total number of people asked = 150Therefore, relative frequency for 2 siblings = 0/150 = 0Relative frequency for 3 siblings:
As per the given data, frequency of 3 siblings = 29And, total number of people asked = 150Therefore, relative frequency for 3 siblings = 29/150 = 0.1933Relative frequency for 4 siblings:
As per the given data, frequency of 4 siblings = 34And, total number of people asked = 150Therefore, relative frequency for 4 siblings = 34/150 = 0.2267Cumulative frequency:
To calculate the cumulative frequency, add the frequency of each category to the sum of the frequencies of all categories below it. The last cumulative frequency should equal the total number of observations.So, the cumulative frequency for each category is as follows:For 0 siblings:
35For 1 or fewer siblings:
35+29=64For 2 or fewer siblings: 64+0=64For 3 or fewer siblings:
64+29=93For 4 or fewer siblings:
93+34=127For all 5 siblings:
127+23=150
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Look for Relationships Chris is buying material
for an art project. Two stores have the material she
needs. Compare prices to find which material is the
better value. Explain.
To compare the prices and determine which material offers better value, Chris needs to consider several factors beyond just the price. Here are some key points to consider:
Quality: Compare the quality of the materials offered by both stores. Sometimes, a higher-priced material may offer better quality, durability, or performance, making it a better value in the long run.
Quantity: Check the quantity or size of the materials available for the price. If one store offers a larger quantity or size for a slightly higher price, it might be a better value as it provides more material for the money.
Features: Look for any additional features or benefits offered by the materials. For example, if one material includes extra accessories or tools at a slightly higher price, it may be a better value due to the added value and convenience.
Customer reviews: Research online or ask for recommendations from others who have used the materials from both stores. Their experiences and feedback can provide insights into the overall value and performance of the materials.
By considering these factors, Chris can make an informed decision and choose the material that offers the best overall value for her art project.
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