The probability that less than 75% of the sample students have iPhones is approximately 0.2478.
What is probability?
This is a binomial probability problem, where each student either has an iPhone or does not have an iPhone, and the probability of success (having an iPhone) is 0.789.
Let X be the number of students in the sample who have an iPhone. We want to find P(X < 0.75 * 50) = P(X < 37.5)
Using the binomial probability formula, we have:
P(X < 37.5) = Σ P(X = k), for k = 0, 1, 2, ..., 37
However, this is a tedious calculation. Instead, we can use a normal approximation to the binomial distribution, since n * p = 50 * 0.789 = 39.45 > 10 and n * (1 - p) = 50 * 0.211 = 10.55 > 10.
Using the normal approximation, we can standardize the random variable X:
Z = (X - μ) / σ
where μ = n * p = 39.45 and σ = √(n * p * (1 - p)) = √(50 * 0.789 * 0.211) = 2.88.
Then, we have:
P(X < 37.5) = P(Z < (37.5 - 39.45) / 2.88) = P(Z < -0.68)
Using a standard normal table or calculator, we find that P(Z < -0.68) is approximately 0.2478.
Therefore, the probability that less than 75% of the sample students have iPhones is approximately 0.2478.
Binomial probability is a type of probability distribution that describes the number of successes in a fixed number of independent trials, where each trial has only two possible outcomes: success or failure. It assumes that the probability of success in each trial is constant, and the trials are independent of each other. The binomial distribution is characterized by two parameters: the number of trials and the probability of success in each trial.
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Suppose Patrick Goldsmith deposited $1000 in an account that earned simple interest at an annual rate of 10% and left it there for 5 years. At the end of the 5 years, Patrick deposited the entire amount from that account into a new account that earned 10% compounded quarterly. He left the money in this account for 5 years. How much did he have after the 10 years? (Round your answer to the nearest cent.)
Answer:
Step-by-step explanation:
After 5 years at a simple interest rate of 10%, Patrick would have earned $500 in interest ($1000 x 10% x 5 years). So at the end of the 5 years, he would have $1500 in the account.
If this entire amount is deposited into a new account that earns 10% compounded quarterly, we need to determine the quarterly interest rate first.
The quarterly interest rate is (1 + 0.10/4)^4 - 1 = 0.025 (rounded to three decimal places).
After 10 years (or 40 quarters) at a quarterly interest rate of 0.025, the compounded amount is:
$1500 x (1 + 0.025)^40 = $4045.56
Therefore, Patrick would have $4045.56 in the account after 10 years when rounding to the nearest cent.
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A table is being sold for 67% off the regular price the sale price is $536 what is the regular price
Answer:
Step-by-step explanation:
Use a simple Equation
Price = Number x Price
So Price = 536.
Since it was 67% off we multiple the price of the original by .67.
So
536 = .67x
Solve for x = 536/.67 = 800
The original Price is $800.
check by multiplying by the sale %.
What is the probability of flipping a coin 12 times and getting heads 5 times?
Round your answer to the nearest tenth of a percent.
OA. 12.1%
OB. 3.1%
OC. 19.3%
OD. 5.4%
Answer:
The correct answer is D. 5.4% after rounding my answer off to the nearest tenth of a percent.
Help me please I don’t know how to solve this.
The equation is 2m + 4s = 16 and the table of values is solved
Given data ,
Let the equation be represented as A
Now , the value of A is
2m + 4s = 16
when m = 0
4s = 16
s = 4
when s = 3
2m + 12 = 16
2m = 4
m = 2
when m = -2
-4 + 4s = 16
4s = 20
s = 5
when s = 0
2m = 16
m = 8
Therefore , the table of values for m = { 0 , 2 , -2 , 8 } and the table of values for s = { 4 , 3 , 5 , 0 }
Hence , the equation is solved
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3. Set A has a standard deviation of 6. Set B has a standard deviation of 9. Based on
this information, which of the following statements must be true?
A) The range for set A and set B is the same.
B) Set A is larger than set B.
3
C) The mean of set B is 1.5 greater than the mean of set A.
D) The data in set A varies less than the data in set B.
The statement that is true about standard deviation is
Option D is the correct answer.
We have,
Standard deviation is a measure of how spread out the data is in a set.
A smaller standard deviation indicates that the data points are closer to the mean, while a larger standard deviation indicates that the data points are more spread out from the mean.
Since the standard deviation of set A is 6 and the standard deviation of set B is 9, we can conclude that the data in set A varies less than the data in set B.
So,
The data in set A varies less than the data in set B.
Thus,
The statement that is true about standard deviation is
The data in set A varies less than the data in set B.
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The statement that is true about standard deviation is
Option D is the correct answer.
We have,
Standard deviation is a measure of how spread out the data is in a set.
A smaller standard deviation indicates that the data points are closer to the mean, while a larger standard deviation indicates that the data points are more spread out from the mean.
Since the standard deviation of set A is 6 and the standard deviation of set B is 9, we can conclude that the data in set A varies less than the data in set B.
So,
The data in set A varies less than the data in set B.
Thus,
The statement that is true about standard deviation is
The data in set A varies less than the data in set B.
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Describe the sampling distribution of p. Assume the size of the population is 15,000. n=700, p=0.6 Question content area bottom Part 1 Choose the phrase that best describes the shape of the sampling distribution of p below. A. Approximately normal because n≤0.05N and np(1−p)<10. B. Approximately normal because n≤0.05N and np(1−p)≥10. C. Not normal because n≤0.05N and np(1−p)<10. D. Not normal because n≤0.05N and np(1−p)≥10. Part 2 Determine the mean of the sampling distribution of p. μp=enter your response here (Round to one decimal place as needed.) Part 3 Determine the standard deviation of the sampling distribution of p. σp=enter your response here (Round to three decimal places as needed.)
A soccer field is 80 yards wide and 110 yards long. If a person walks across the field along the diagonal instead of walking the length and width of the field, how much shorter is the distance
So the person would save approximately 244 yards by walking diagonally across the field instead of walking the length and width of the field separately.
what is approximately ?
"Approximately" is a word that is used to indicate that a value, quantity, or measurement is close to the actual or precise value, but not exactly the same. It means that the stated value is an estimate or approximation, and may be slightly different from the true value.
In the given question,
Using the Pythagorean theorem, we can find the length of the diagonal of the soccer field:
diagonal² = length² + width²
diagonal² = 110² + 80²
diagonal² = 12,100 + 6,400
diagonal² = 18,500
diagonal = √18,500
diagonal ≈ 136 yards
So the person walking diagonally across the field would cover a distance of approximately 136 yards.
To compare this with the distance they would cover if they walked the length and width of the field separately, we can use the formula for the perimeter of a rectangle:
perimeter = 2(length + width)
perimeter = 2(110 + 80)
perimeter = 2(190)
perimeter = 380 yards
Therefore, if the person walked the length and width of the field separately, they would cover a total distance of 380 yards.
The difference between these two distances is:
380 - 136 = 244 yards
So the person would save approximately 244 yards by walking diagonally across the field instead of walking the length and width of the field separately.
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So the person would save approximately 244 yards by walking diagonally across the field instead of walking the length and width of the field separately.
what is approximately ?
"Approximately" is a word that is used to indicate that a value, quantity, or measurement is close to the actual or precise value, but not exactly the same. It means that the stated value is an estimate or approximation, and may be slightly different from the true value.
In the given question,
Using the Pythagorean theorem, we can find the length of the diagonal of the soccer field:
diagonal² = length² + width²
diagonal² = 110² + 80²
diagonal² = 12,100 + 6,400
diagonal² = 18,500
diagonal = √18,500
diagonal ≈ 136 yards
So the person walking diagonally across the field would cover a distance of approximately 136 yards.
To compare this with the distance they would cover if they walked the length and width of the field separately, we can use the formula for the perimeter of a rectangle:
perimeter = 2(length + width)
perimeter = 2(110 + 80)
perimeter = 2(190)
perimeter = 380 yards
Therefore, if the person walked the length and width of the field separately, they would cover a total distance of 380 yards.
The difference between these two distances is:
380 - 136 = 244 yards
So the person would save approximately 244 yards by walking diagonally across the field instead of walking the length and width of the field separately.
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Suppose that 10 years ago you bought a home for $110,000, paying 10% as a down payment, and financing the rest at 9% interest for 30 years.
a. Let's consider your existing mortgage:
i. How much money did you pay as your down payment?
ii. How much money was your mortgage (loan) for?
iii. What is your current monthly payment?
iv. How much total interest will you pay over the life of the loan?
b. This year, you check your loan balance. Only part of your payments has been going to pay down the loan; the rest has been going towards interest. You see that you still have $88,536 left to pay on your loan. Your house is now valued at $150,000.
i. How much of the loan have you paid off? (i.e., how much have you reduced the loan balance by? Keep in mind that interest is charged each month - it's not part of the loan balance.)
ii. How much money have you paid to the loan company so far?
iii. How much interest have you paid so far?
iv. How much equity do you have in your home (equity is value minus remaining debt)
c. Since interest rates have dropped, you consider refinancing your mortgage at a lower 6% rate.
i. If you took out a new 30-year mortgage at 6% for your remaining loan balance, what would your new monthly payments be?
ii. How much interest will you pay over the life of the new loan?
d. Notice that if you refinance, you are going to be making payments on your home for another 30 years. In addition to the 10 years you've already been paying, that's a total of 40 years.
i. How much will you save each month because of the lower monthly payment?
ii. How much total interest will you be paying
a.
i. 10% of $110,000 = $11,000 down payment
ii. Loan (mortgage) = $110,000 - $11,000 = $99,000
iii. Monthly payment = P * r * (1 + r)n / ((1 + r)n - 1), where P represents the principal amount, r represents the monthly interest rate, and n represents the number of monthly installments.
First, we must determine the quantity of monthly payments. Because it is a 30-year loan, the monthly installments are 30 * 12 = 360.
The monthly interest rate of 9% divided by 12 equals 0.0075.
When we plug in the values, we get:
$793.07 monthly payment
iv. Loan total interest paid = (monthly payment * number of instalments) - principal amount = ($793.07 * 360) - $99,000 = $184,465.20
How much money have you paid to the loan company so far?b
i. Reduction in loan balance = $99,000 - $88,536 = $10,464
ii. To date, the total amount paid to the loan firm is (monthly payment * a number of payments) = ($793.07 * 120) = $95,168.40.
We multiplied by 120 (rather than 10*12) because we're computing total payments made so far, not the total payments made over the life of the loan.
iii. Total interest paid thus far = total money given to the loan business minus principal amount = $95,168.40 - $99,000 = -$3,831.60
The negative figure shows that the interest paid thus far has been less than the principal amount. This is because, in the early phases of the loan, the majority of the monthly payment goes towards interest, with only a little portion going toward principal reduction.
iv. Home equity = value of the home - remaining debt
= $150,000 - $88,536
= $61,464
c.
i. New monthly payment = P * r * (1 + r)n / ((1 + r)n - 1), where P represents the remaining loan value, r represents the new monthly interest rate (6% / 12 = 0.005), and n represents the number of monthly payments remaining (360 - 120 = 240).
When we plug in the values, we get:
$63.63 is the new monthly payment.
Total interest paid on the new loan during the life of the loan = (new monthly payment * number of payments) - remaining loan balance = ($63.63 * 240) - $88,536 = $32,028.40
d.
Monthly savings = old monthly payment minus new monthly payment = $793.07 - $63.63= $729.44
Total interest paid on the new loan during the life of the loan = (new monthly payment * number of payments) - remaining loan balance = ($63.63 * 360) - $88,536 = $37,847.80
Because the new loan is being paid off over a longer period of time, the total interest paid during the life of the new loan is more than the remaining interest on the previous loan.
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Thabangs transport fee to school increased from 800 to 1150. Determine the percentage increase?
Answer:
percentage increase: 43,75%
Step-by-step explanation:
If we want to solve thai as an equation, we can write:
800 + (x/100) * 800 = 1150
we multiply: 800 + 800x/100 = 1150
we simplify: 800+ 8x = 1150
we bring the unknown to the left, and numbers to the right:
8x = 1150 - 800
8x = 350
we find x by dividing each part by 8
x= 43,75
(note that the x/100 in the first equation is the same thing as writing x%, so 800 plus a percentage of 800 is equal to 1150)
Break-Even Sales
BeerBev, Inc., reported the following operating information for a recent year (in millions):
Sales $6,512
Cost of goods sold $1,628
Gross profit $4,884
Marketing, general, and admin. expenses 592
Income from operations $ 4,292
Assume that BeerBev sold 37 million barrels of beer during the year, that variable costs were 75% of the cost of goods sold and 50% of marketing, general and administration expenses, and that the remaining costs are fixed. For the following year, assume that BeerBev expects pricing, variable costs per barrel, and fixed costs to remain constant, except that new distribution and general office facilities are expected to increase fixed costs by $21.09 million.
a. Compute the break-even sales (in barrels) for the current year. Round your answer to two decimal places. Enter your answers in millions.
Answer:
Step-by-step explanation:
To compute the break-even sales (in barrels) for the current year, we need to first determine the contribution margin per barrel, which is the amount left over from the selling price of each barrel of beer after variable costs are subtracted.
Variable costs per barrel can be calculated as 75% of the cost of goods sold per barrel, which is:
Variable cost per barrel = (75% x Cost of goods sold) / Barrels sold
Variable cost per barrel = (0.75 x $1,628 million) / 37 million barrels
Variable cost per barrel = $33.00
Similarly, the variable marketing, general, and administration expenses per barrel can be calculated as:
Variable marketing, general, and administration expenses per barrel = (50% x Marketing, general, and administration expenses) / Barrels sold
Variable marketing, general, and administration expenses per barrel = (0.50 x $592 million) / 37 million barrels
Variable marketing, general, and administration expenses per barrel = $8.00
Therefore, the contribution margin per barrel is:
Contribution margin per barrel = Selling price per barrel - Variable costs per barrel
Contribution margin per barrel = $6,512 million / 37 million barrels - $33.00 - $8.00
Contribution margin per barrel = $98.00
To compute the break-even sales (in barrels) for the current year, we can use the following formula:
Break-even sales (in barrels) = Fixed costs / Contribution margin per barrel
Fixed costs can be calculated as:
Fixed costs = Income from operations + Variable marketing, general, and administration expenses x Barrels sold - Contribution margin per barrel x Barrels sold
Fixed costs = $4,292 million + $8.00 x 37 million barrels - $98.00 x 37 million barrels
Fixed costs = $1,108 million
Substituting this into the formula, we get:
Break-even sales (in barrels) = $1,108 million / $98.00 per barrel
Break-even sales (in barrels) = 11.29 million barrels
Rounding this to two decimal places and converting to millions, we get:
Break-even sales (in barrels) = 11.29 million barrels = 11.3 million barrels (rounded)
I need help with my assignments
Answer :
Answer : 1.796
The explanation is in the pictures.
Joe took 1/2 hours to clean the bathroom. Then he took 3 1/4 hours to clean the den. How much total time did Joe take to clean the two rooms? Write your answer as a mixed number in simplest form.
Answer:
He took 3 3/4 hours to clean both rooms.
Step-by-step explanation:
1/2 = 2/4
3 1/4 + 2/4 = 3 3/4
Therefore, he took 3 3/4 hours.
Identify the triangle as acute, obtuse, or right by comparing the squares of the side lengths. Show your work and
explain the steps you used to solve.
14
21
16
We can see here that the triangle is a right-angle triangle.
What is a triangle?The fundamental geometric shape of a triangle has three straight sides and three angles. It is a triangular polygon with three edges.
We can see here that the triangle is a right-angle triangle because using Pythagoras Theorem, we will see the following:
Hypotenuse = c = 30
Adjacent = b = 24
Opposite = a = 18
c² = a² + b²
Hyp² = Opp² + Adj²
30² = 18² + 24²
324 + 576 = 900.
Thus, it is a right-angle triangle.
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A clothing retailer is interested in the average waist size of men. A sample is taken with the results given below.
please see the attached image for more info on the question
The confidence interval is given as (38.811,43.829)
What is a Margin of Error?In statistics, a margin of error refers to the degree of imprecision that can be projected in survey or polling outcomes due to random sampling involved in such studies.
This indicator serves as both the measure for the accuracy of results and an assurance of confidence in them. The percentage rate expressing the magnitude of the latter varies inversely with the former and depends on the sample size, desired level of confidence, and cumulative trends in feedback obtained from respondents.
Thus, surveys featuring minimal margins of error are considered substantively accurate while ones plagued by larger margins signal a lack thereof.
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248 meters per second = miles per hour
Answer:
554.76 miles per hour
Step-by-step explanation:
[tex]\frac{248 meters}{1 second}[/tex] x [tex]\frac{3600 seconds}{1 hour}[/tex] x [tex]\frac{1 mile}{1609.34 meters}[/tex]
= 554.76 miles per hour
[tex]\sf 554.76(mi/h).[/tex]
Step-by-step explanation:1. Write the initial expression.[tex]\sf \dfrac{248(m)}{s}[/tex]
2. Using conversion factors, convert from meters to miles.a) First, convert the meters to kilometers.
[tex]\sf 248(m)*\dfrac{1(km)}{1000(m)} =0.248(km)[/tex]
Here, the meters cancel, since one is on the numerator and the other one is expressed as a denominator, and we simpyl multiply the value by the fraction, resulting in a number that would be a value for kilometers.
b) Convert from kilometers to miles.
[tex]\sf 0.248(km)*\dfrac{1(mi)}{1.60934(km)} =0.1541(mi)[/tex]
3. Convert the seconds into hours.[tex]\sf 1(seconds)*\dfrac{1(hour)}{3600(seconds)} =\frac{1}{3600}(h)[/tex]
4. Rewrite the initial expression using the calculated converted values.[tex]\sf \dfrac{0.1541(mi)}{\dfrac{1}{3600} (h)} =554.76(mi/h)[/tex]
Willow owns 225 books. Of them, 5/9
are mysteries. How many of Willow's books
are mysteries?
A) 225
B) > 225
C) < 225
D) 0
(Side note:) please provide explanation if can!
Using a table find the range of a function for the given domain f(x)equals to 2x^2-7 with domain X equals to {-4,-2,0,3}
The range of function for the given domain are {25, 8, -7, 11}
Given that, a function f(x) = 2x²-7, we need to find the range of the function, for the given domain, x = {-4, -2, 0, 3},
So,
Domain = All the input values.
Range = All the output values.
So, to find the range we will put the value of x which is the domain and the value obtained of f(x) will be the range,
f(x) = 2x²-7
For, x = -4,
f(-4) = 16×2 - 7 = 25
f(-4) = 25
f(-2) = 4 × 2 - 7 = 8
f(-2) = 8
f(0) = -7
f(3) = 9 × 2 - 7
f(3) = 11
Hence the range of function for the given domain are {25, 8, -7, 11}
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URGENT!! ILL GIVE
BRAINLIEST! AND 100 POINTS
The statements that are true about the scatter plot graph are;
1. The line of best fit should have the same number of points above and below it.
2. There is a moderate positive correlation.
3. The line of best fit will have a positive slope.
What are some facts about scattered plot graphs that you should know?Some facts about scatter plot graphs:
Scatter plots are used to show the correlation or relationship between two variables. The variables are plotted on the x and y-axes, and each point represents a pair of values for the two variables.
Scatter plots can show different types of relationships between two variables, including positive, negative, or no correlation.
The shape of a scatter plot can provide insights into the strength and direction of the relationship between the two variables. For example, if the points on the scatter plot form a linear pattern, this indicates a strong correlation.
Scatter plots can be used to identify outliers or anomalies in the data that do not fit the general pattern of the relationship between the two variables.
The above answer is based on the following options provided in the picture.
Tick all the statements that applies
The y intercept of the line of best fit would be around 45
The line of best fit should have the same number of points above and below it
The slope of the line of best fit could be around -1/20000
The line of best fit must pass through at lest 2 points on the scattered plot
There is no correlation between happiness and income
There is a moderate positive correlation
The line of best fit will have a positive slope
As a person's income goes up, their happiness trends down
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Which graph shows the image of ABC after a rotation about the origin
The graph that shows the image of ABC after a rotation about the origin is the graph d
The graph that shows the image of ABCRotation about the origin is a transformation in which a point or object is rotated around the origin (0, 0) by a certain angle. The origin is the fixed point of the rotation, and all other points move in a circular path around the origin.
To perform a rotation about the origin, you need to know the angle of rotation, the coordinates of the point or object being rotated, and the direction of rotation (clockwise or counterclockwise).
Using the above as a guide, we have the following:
The graph after a rotation about the origin is the graph (d)
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Create a list of steps, in order, that will solve the following equation.
2
- 5 = 123
Solution steps:
Add 2 to both sides
Add 5 to both sides
Divide both sides by 2
Multiply both sides by 2
Subtract 5 from both sides
3
Subtract from both sides
Square both sides
Take the square root of both
sides
The graph of your equation is a parabola with x-intercepts at x = -8.75 and x = 7.25.
How to solvex = -8.75; x = 7.25
2(x + ¾)² - 5 = 123
Add 5 to each side: 2(x+ ¾)² = 128
Divide each side by 2: (x+ ¾)² = 64
Take the square root of each side: x + ¾ = 8 x + ¾ = -8
Subtract ¾ from each side: x = 8 - ¾ x = -8 - ¾
Convert to decimal fraction: x = 8 - 0.75 x = -8 – 0.75
Subtract: x = 7.25 x = -8.75
The graph of your equation is a parabola with x-intercepts at x = -8.75 and x = 7.25.
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The graph of your equation is a parabola with x-intercepts at x = -8.75 and x = 7.25.
How to solvex = -8.75; x = 7.25
2(x + ¾)² - 5 = 123
Add 5 to each side: 2(x+ ¾)² = 128
Divide each side by 2: (x+ ¾)² = 64
Take the square root of each side: x + ¾ = 8 x + ¾ = -8
Subtract ¾ from each side: x = 8 - ¾ x = -8 - ¾
Convert to decimal fraction: x = 8 - 0.75 x = -8 – 0.75
Subtract: x = 7.25 x = -8.75
The graph of your equation is a parabola with x-intercepts at x = -8.75 and x = 7.25.
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multiply (−3x+4)(2x−1)
After multiplying (−3x+4) with (2x−1) we get a quadratic equation which is equal to −6x² + 11x − 4.
To multiply the expressions (−3x+4)(2x−1), we use the distributive property of multiplication:
(−3x+4)(2x−1) = −3x(2x) + 4(2x) − 3x(−1) + 4(−1)
Simplifying the above expression, we get:
= −6x² + 8x + 3x − 4
= −6x² + 11x − 4
Therefore, the product of (−3x+4)(2x−1) is −6x² + 11x − 4.
We can also use the FOIL method to multiply the two expressions:
(−3x+4)(2x−1) = −3x(2x) −3x(−1) + 4(2x) + 4(−1)
= −6x² + 3x + 8x − 4
= −6x² + 11x − 4
Either method can be used to get the same result.
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Adjacent angles. please don't get it wrong!
The adjascent angles to angle EDC is angle EDI and CDH.
What are adjascent angles?Two angles are said to be adjacent angles when they share the common vertex and side. The sum of adjascent angles is 180°. This means that adding two adjascent angles together will give 180°. Adjascent angles are also called supplementary angles.
Examples of adjascent angles in the diagram include;
AEB Is adjascent to AED
and also there are two angles that are adjascent to angle EDC. They are;
angle ED1 and CDH
Therefore the adjascent angles to angle EDC is angle EDI and CDH.
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20 students each rolled dice 5 times each to measure the median. Here is the data in the picture attached. What can we infer from this graph by looking at the median data?
A. when rolling a dice multiple times, the median is less likely to fall between numbers 1 and 6.
B. it's not possible to tell the likelihood of where the median is going to be when measuring probability since rolling dice is completely randomized, etc.
C. some other response
We can deduce that option A is likely to be true based on the given graph of rolling dice median data.
What is the median?The median is the value in the middle of a data set, which means that 50% of the data points have a value less than or equal to the median, and 50% of the data points have a value greater than or equal to the median.
The graph illustrates that the median value of the rolls is closer to the center of the possible outcomes (numbers 3, 4, and 5) than the extremes (numbers 1 and 6).
This implies that when rolling a dice several times, the median is less likely to fall between the numbers 1 and 6.
However, because rolling the dice is a random process, there is always a degree of uncertainty in predicting the outcomes.
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In circle S with m \angle RST= 30^{\circ}m∠RST=30
∘
and RS=13RS=13, find the area of sector RST. Round to the nearest hundredth.
The area of a sector of a circle is calculated as approximately 44.24 square units.
How to Find the Area of the Sector of a Circle?The area of the sector of a circle can be calculated by applying the given formula below:
Area of sector = ∅/360 * π * r², where: r is the radius of the circle and ∅ is the central angle or reference angle of the sector.
Given the parameters of the sector of the circle as:
Central angle (∅) = 30 degrees
Radius (r) = RS = 13 units
Plug in the values:
Area of sector = 30/360 * π * 13²
Area of sector ≈ 44.24 square units.
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Please help me with this word problem!
Suppose you lay exactly 160 feet of fencing around a rectangular garden. If the length of the garden is 3 times its width, find the dimensions of the garden.
Length: __ feet
Width: __ feet
Step-by-step explanation:
the perimeter (the way one time around it) of a rectangle is
2×length + 2×width
length = 3×width
2×(3×width) + 2×width = 160
6×width + 2×width = 160
8×width = 160
width = 160/8 = 20 ft
length = 3×width = 3×20 = 60ft
12 1/2 - 4 7/10 a. 7 6/8 b. 7 8/10 c. 8 2/8 d. 8 3/10
Answer:
c. 8 2/8
Step-by-step explanation:
12 1/2 - 4 7/10 = 12 5/10 - 4 7/10 = 8 2/10 = 8 1/5 = 8.2
Therefore, the answer is option c. 8 2/8
Hope this helps!
How many yards are in four and one-half miles?
7,040 yards
7,920 yards
8,448 yards
8,800 yards
Answer:
7,920
Step-by-step explanation:
I took test and got 100%
The size of fish is very important to commercial fishing. A study conducted in 2012 found the length of Atlantic
cod caught in nets in Karlskrona to have a mean of 49.9 cm and a standard deviation of 3.74 cm (Ovegard, Berndt
& Lunneryd, 2012). Assume the length of fish is normally distributed.
b) What is the length in cm of the longest 15% of Atlantic cod in this area?
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by
[tex]\text{Z}=\dfrac{\text{X}-\mu}{\sigma}[/tex]
After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X.
In this problem, we have that:
A study conducted in 2012 found the length of Atlantic cod caught in nets in Karlskrona to have a mean of 49.9 cm and a standard deviation of 3.74 cm, so [tex]\mu=49.9,\sigma=3.74[/tex].
What is the length in cm of the longest 15% of Atlantic cod in this area?
We have to find the value of X for the value of Z that has a p-value of 0.85.
Looking at the z-score table, we have that Z = 1.04 has a p-value of 0.8508. So, we have to find the value of X when .
So
[tex]\text{Z}=\dfrac{\text{X}-\mu}{\sigma}[/tex]
[tex]1.04=\dfrac{\text{X}-49.9}{3.74}[/tex]
[tex]\text{X}-49.9=3.8896[/tex]
[tex]\text{X}=53.7896[/tex]
The length of the longest 15% of Atlantic cod in this area is 53.79 cm, rounded to 2 decimal places.
the question is on the screenshot
When the simultaneous equation is solved, we have that; x = 2 and y = 3
What is the solution to a simultaneous equationSimultaneous equations are a set of two or more equations that are solved together to find the values of the variables that satisfy all of the equations at the same time.
We have the equations;
9x - 7y = -3 --- (1)
-3x + 5y = 9 ---- (2)
Multiply (1) by 1 and (2) by (3)
9x - 7y = -3 ---- (3)
-9x + 15y = 27 ----- (4)
Add (3) and (4)
8y = 24
y = 3
Substitute y = 3 into (1)
9x - 7(3) = -3
9x - 21 = -3
9x = -3 + 21
9x = 18
x = 2
Thus the solution is x = 2 and y = 3
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answer with explanation
The area and circumference of a circle with diameter of 3 m is 7.0165 m² and 9.42 m² respectively
How to solve an equation?An equation is an expression that can be used to show the relationship between two or more numbers and variables using mathematical operators.
The area of a figure is the amount of space it occupies in its two dimensional state.
The diameter (d) of the circle is 3 meter. Hence:
Area = π * diameter²/4 = π * 3²/4 = 7.0165 m²
Circumference = π * diameter = π * 4 = 9.42 m²
The area and circumference are 7.0165 m² and 9.42 m²
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