Jose is wrapping a stack of 100 coins in a paper holder. Each coin is 18
inch thick and has a diameter of
1 inch. How many square inches of paper will Jose need to cover the stack of coins?
Jose needs 61.23 square inches of paper to cover the stack of coins.
How many square inches of paper will Jose need to cover the stack of coins?The total thickness of the stack of 100 coins is 100 x 0.18 = 18 inches. The diameter of each coin is 1 inch, so the radius of each coin is 0.5 inches.
To find the amount of paper needed to cover the stack of coins, we need to calculate the total surface area of the stack.
The area of each circle is given by:
πr^2 where r is the radius of the coin.
The area of the top and bottom circles is:
2 x π x (0.5)^2 = 0.5π
The circumference of the circle is given by:
2πr
So, the circumference of each coin is:
2π(0.5) = π
The height of the stack is 18 inches, so the area of the curved surface is:
π x 18 = 18π
Therefore, the total surface area of the stack is:
1.5π + 18π = 19.5π
To cover the stack of coins with paper, Jose will need 19.5π square inches of paper.
19.5π ≈ 19.5 x 3.14 ≈ 61.23 square inches.
Therefore, Jose will need approximately 61.23 square inches of paper to cover the stack of coins.
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there are 90 people in the restaurant. the probability of someone ordering a drink with the food is 60%. use normal approximation of binomial distribution to answer the following 6 questions. 1. what is the mean of the normal distribution? 2. what is the standard deviation of the normal distribution? 3. what is the probability that exactly 50 people will order a drink? 4. what the probability that more than 50 people will order a drink? 5. what is the probability that less than 50 people will order a drink? 6. what is the probability that between 52 or more and 56 or less people will order a drink?
1. Mean = 54
2. Standard Deviation = 6.3
3. Probability = 0.077
4. Probability = 0.845
5. Probability = 0.155
6. Probability = 0.323
Your cousin bought a used car. He paid a total of $12,755 for the car. The total cost includes: • The list price of the car, x • A 7% sales tax on the list price . Plus $450 in additional fees.
What is the price of the car your cousin bought?
List price:
Let's use the variable x to represent the list price of the car.
The total cost your cousin paid for the car is the list price plus a 7% sales tax on the list price, plus $450 in additional fees.
We can write this as an equation:
Total cost = List price + 0.07(List price) + 450
We know that the total cost your cousin paid was $12,755, so we can substitute that into the equation:
12,755 = x + 0.07x + 450
Simplifying the right side:
12,755 = 1.07x + 450
Subtracting 450 from both sides:
12,305 = 1.07x
Dividing both sides by 1.07:
x = 11,500
Therefore, the list price of the car your cousin bought was $11,500.
The list price of the car your cousin bought was $11,500.
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example:
1 + 3x + 4y = 7 is an expression.com
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
Let's start by setting up an equation to represent the total cost of the car:
Total cost = List price + 7% of List price + $450
We know that the total cost is $12,755, so we can substitute that in:
$12,755 = List price + 0.07(List price) + $450
Simplifying this equation, we get:
$12,755 = 1.07(List price) + $450
Subtracting $450 from both sides, we get:
$12,305 = 1.07(List price)
Dividing both sides by 1.07, we get:
List price = $11,500
Therefore,
The list price of the car your cousin bought was $11,500.
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Help me please….
it’s due tomorrow!!!
I need help with this. please
The only exponential growth equation is the third one:
y = 2*(4)^x
Which equation will produce a growth?A general exponential equation is:
y = A*(b)^x
if 0 < b < 1, then it is a decay.
if 1 < b, then it is a growth.
So any equation where the base, b, is larger than 1, represents a growth.
Then the correct option is the third one:
y = 2*(4)^x
All the other options are decays.
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hat is the maximum speed of a point on the outside of the wheel, 15 cm from the axle?
It depends on the rotational speed of the wheel. To calculate this speed, we need to know the angular velocity of the wheel.
The maximum speed of a point on the outside of the wheel, 15 cm from the axle, if we assume that the wheel is rotating at a constant rate, we can use the formula v = rω, where v is the speed of the point on the outside of the wheel, r is the radius of the wheel (15 cm in this case), and ω is the angular velocity of the wheel. Therefore, the maximum speed of a point on the outside of the wheel would be directly proportional to the angular velocity of the wheel.
The formula to calculate the maximum linear speed (v) is:
v = ω × r
where v is the linear speed, ω is the angular velocity in radians per second, and r is the distance from the axle (15 cm, or 0.15 meters in this case).
Once you have the angular velocity (ω) of the wheel, you can plug it into the formula and find the maximum speed of a point on the outside of the wheel.
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Ariel wants to join the volleyball team in the fall, so she went to an overnight volleyball camp last weekend to practice her skills. Before she left, she packed a shower caddy shaped like a rectangular prism with a volume of 420 cubic inches. The caddy is 10
1
2
inches long and 5 inches tall.
How wide is the shower caddy?
The width of the shower caddy is 8 inches.
What is Volume?
Volume is a measure of the total amount of material that an object contains. In mathematical terms, volume is calculated by multiplying the length, width, and height of an object.
We can use the formula for the volume of a rectangular prism, which is V = lwh, where l is the length, w is the width, and h is the height.
We know that the volume of the caddy is 420 cubic inches, the length is 10.5 inches, and the height is 5 inches. Let's substitute these values into the formula and solve for the width:
420 = 10.5w × 5
Divide both sides by 52.5:
8 = w
Therefore, the width of the shower caddy is 8 inches.
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a blanket measures 1 1/4 yards on each side. how many square yards does the blanket cover?
Answer:
Add 1 1/4 x 1 1/4
Step-by-step explanation:
a freeway with two northbound lanes is shut down because of an accident. at the time of the accident, the traffic flow rate is 1200 vehicles per hour per lane and the flow remains at this level. the capacity of the freeway is 2200 vehicles per hour per lane when not impacted by an accident. the freeway is shut down completely for 20 minutes after the accident and then one lane is open for 20 minutes and finally both lanes are opened (40 minutes after the accident). what is the average delay per
vehicle?
The average delay per vehicle would be 20 minutes. This is calculated by taking the total time the freeway was shut down (40 minutes) and dividing it by the total number of vehicles that would have been on the freeway during that time (2400 vehicles).
do less republicans (group a) than democrats (group b) favor the government investing billions of dollars to improve the country's train system? one thousand republicans and one thousand democrats were asked if they favored spending billions to improve the country's train system. how would we write the alternative hypothesis?
The alternative hypothesis can be written as H₁: pA < pB.
The alternative hypothesis would be that there is a difference in the proportion of Republicans (Group A) and Democrats (Group B) who favor the government investing billions of dollars to improve the country's train system. Expressly, it would state that the proportion of Republicans who favor this investment is less than the proportion of Democrats who favor it:
H₁: pA < pB
where pA denotes the proportion of Republicans who favor the investment and pB denotes the proportion of Democrats who favor the investment.
In the alternative hypothesis, we actually create the relationship between the variables which are being tested in that situation. According to these, we come across the comparison among the variables and how much they differ from each other. The alternative hypothesis is the statement the researcher tries to prove by conducting a statistical analysis.
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Habib drew a new diagram that has an area of [tex]6+4s^2[/tex].
What is the area of Habib's diagram when [tex]s=1/2[/tex]?
The area of Habib's diagram when s = 1/2 is 7.
What is circle?
A circle is a geometric shape that consists of all points in a plane that are equidistant from a fixed point called the center. It can also be defined as the set of points that are a fixed distance (called the radius) away from the center point. The distance around the circle is called its circumference, and the distance across the circle passing through the center is called its diameter.
To find the area of Habib's diagram when s = 1/2, we just need to substitute s = 1/2 into the expression for the area:
Area = 6 + 4s²
Area = 6 + 4(1/2)²
Area = 6 + 4(1/4)
Area = 6 + 1
Area = 7
Therefore, the area of Habib's diagram when s = 1/2 is 7.
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Lauren gets a 12% commission for every piece of jewelry she sells. How much will she earn if she sells a $3,200 bracelet?
Answer:
$384
Step-by-step explanation:
$3,200 x 0.12 = $384
suppose the customers arrive at a starbucks shop at an average rate of 1/min. use a poisson process to model the arrival of customers. what is the probability that at least one customer arrives at the shop during a one-minute interval? 0.736 0.368 0.632 0.264
The probability that at least one customer arrives at the shop during a one-minute interval is 0.632.
Since the arrival of customers at a Starbucks shop can be modeled as a Poisson process with an average rate of 1/min, the probability of exactly k customers arriving in a one-minute interval is given by the Poisson probability mass function:
P(k arrivals) = (λ^k * e^(-λ)) / k!
where λ is the average rate of arrivals (in this case, 1/min), e is the mathematical constant e, and k! is the factorial of k.
To find the probability that at least one customer arrives during a one-minute interval, we can use the complement of the probability that zero customers arrive (i.e., the probability of at least one arrival is 1 minus the probability of zero arrivals).
Thus, the probability of at least one customer arriving during a one-minute interval is:
P(at least one arrival) = 1 - P(0 arrivals)
P(at least one arrival) = 1 - [([tex]1^{0}[/tex] * [tex]e^{-1}[/tex]) / 0!] = 1 - [tex]e^{-1}[/tex] = 0.632
Therefore, the probability that at least one customer arrives at the shop during a one-minute interval is 0.632.
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Theorem: A line parallel to one side of a triangle divides the other two proportionately.
In the figure below, segment DE is parallel to segment BC and segment EF is parallel to AB:
Which statement can be proved true using the given theorem?
Group of answer choices
Segment BD = 12
Segment BD = 4
Segment BF = 16
Segment BF = 9
Since BC = 12 and AB = 16, segment BF must be 9, which is one-half of 16.
What is triangle?A triangle is a three-sided polygon that is one of the basic shapes in geometry. It is defined by three points that are connected by three line segments. Triangles have three angles, which add up to 180 degrees, and three sides, which add up to the sum of the lengths of the other two sides. The three sides of a triangle are typically referred to as the base, the height, and the hypotenuse. Triangles come in a variety of forms, from the equilateral triangle, which has three sides of equal length, to the isosceles triangle, which has two sides of equal length, to the scalene triangle, which has three sides of different lengths.
The correct answer is: Segment BF = 9. This can be proved true using the given theorem, since segment DE is parallel to segment BC and segment EF is parallel to AB. Therefore, since BC = 12 and AB = 16, segment BF must be 9, which is one-half of 16.
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Help with algebra 2 homework
The formula for the volume of an sphere of radius r is given as follows:
V = (2/3)πr³
The radius as a function of the volume is obtained as follows:
r³ = 3V/2π
[tex]r = \sqrt[3]{\frac{3V}{2\pi}}[/tex]
Hence the radius of a sphere of volume 25 in³ is given as follows:
[tex]r = \sqrt[3]{\frac{25}{2\pi}}[/tex]
r = 2.29 in.
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write an expression for the problem and evaluate the expression using the order of operations. bruce charged david and ricky $42 for parts and $12 per hour for labor to repair their motorcycle if he spent 3 hours repairing the bike how much money do david and ricky owe him?
The expression for the problem is:
Total cost = $42 + ($12/hour × 3 hours) × 2 people
How to write the expressionBruce charged David and Ricky a fixed fee of $42 for parts plus an hourly rate of $12 for labor. He spent 3 hours repairing the motorcycle. Since there are two people (David and Ricky), we need to multiply the hourly rate by the number of hours worked (3) and then multiply that by 2. Finally, we add the fixed fee for the parts to get the total cost.
To evaluate the expression using the order of operations, we need to perform the multiplication first and then the addition. So, we have:
Total cost = $42 + ($12/hour × 3 hours) × 2 people
= $42 + ($36) × 2
= $42 + $72
= $114
Therefore, David and Ricky owe Bruce a total of $114 for the motorcycle repair.
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I NEED HELP ON THIS ASAP! I JUST NEED HELP WITH THE QUESTION BELOW THE TABLE
All of these ratios are equal to b, and we have shown that there is a constant ratio between consecutive output values.
What is ratio between consecutive output?The common ratio is the ratio that remains constant between successive function output values. The behaviour of a geometric sequence, which is a series of numbers where each term is produced by multiplying the one before it by a set number (the common ratio), depends on the common ratio. The sequence is rising exponentially if the common ratio is bigger than 1. The sequence decreases exponentially if the common ratio is between 0 and 1.
To show that the function form shows a constant ratio we take:
[tex](x+1) / f(x) = (ab^{(x+1)}) / (ab^x) = b[/tex]
Similarly, we have:
[tex]f(x+2) / f(x+1) = (ab^{(x+2)}) / (ab^{(x+1)}) = b[/tex]
Hence, all of these ratios are equal to b, and we have shown that there is a constant ratio between consecutive output values.
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what is the 4th term/number of (a+b)^9, pascal’s triangle?
Step-by-step explanation:
hope this will help you Thanks
When Ranim started karate, her highest kick went
11
0
∘
110
∘
110, degrees from the ground. Her instructor asked her to practice until her highest kick goes
15
5
∘
155
∘
155, degrees from the ground. Which equation will tell us the measure of the additional angle,
a
aa, that Ranim's kick needs to go to reach
15
5
∘
155
∘
155, degrees from the ground?
Choose 1 answer:
The equation that will tell us measure of additional angle, a, that Ranim's kick needs to go to reach 155 degrees from the ground is given option 155 - 110 = a.
Highest kick went when Ranim started karate from the ground is
= 110 degrees
Highest kick limit given by instructor from the ground = 155 degrees
This equation represents the difference between the final desired angle of 155 degrees and the initial angle of 110 degrees.
Which Ranim's kick went when she started karate.
The result of this subtraction will give us the measure of the additional angle, a.
That Ranim needs to add to her kick to reach the new desired angle.
Therefore, equation representing the measure of the additional angle a, of Ranim karate kick is equal to 155 - 110 = a.
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The above question is incomplete, the complete question is:
When Ranim started karate, her highest kick went 110 degrees from the ground. Her instructor asked her to practice until her highest kick goes 155 degrees from the ground. Which equation will tell us the measure of the additional angle, a, that Ranim's kick needs to go to reach 155 degrees from the ground?
155−110=a
155+110=a
180−110=a
155+90=a
How do I round 9979.03 to the nearest gram?
Chester worked for 8hour each day for 5days.He earned P2190.00.How much did he earn per hour?
Answer:
P54.75 per hour.
Step-by-step explanation:
If he earned 2190 pesos on working 8 hours each for 5 days then he earned 54.75
Equation: hours x days / earnings
Therefore, 8 hours x 5 days = 40
2190 / 40 = P54.75 / hour
1. Find the square root of each of the following numbers: (i) 152.7696
A factory has 2 x 10^3 workers who make a total of 7 x 10^6 bikes each year. How many bikes does each worker make per year?
Answer:
7,000,000÷2000
= 3,500
Step-by-step explanation:
therefore, each worker makes 3500 bikes per year
in order to maintain accuracy, political polling groups must maintain a certain degree of confidence with a small margin of error. fivethirtyeight is a polling company that wishes to survey a population of people, but maintain a margin of error of 0.05 or less with a 99% confidence level. what is the smallest number of consumers they should survey to guarantee this?
A minimum sample size of 665 consumers that FiveThirtyEight should survey to guarantee a margin of error of 0.05 or less with a 99% confidence level.
What is the sample size?Sample size refers to the number of observations or individuals included in a study or experiment. It is the number of subjects or units that are selected from a population to be studied. The sample size is an important consideration in statistical analysis, as it can affect the accuracy and generalizability of the results. A larger sample size generally leads to more precise estimates and stronger statistical power, but it can also be more costly and time-consuming to collect and analyze.
According to the given informationTo calculate the minimum sample size required to maintain a margin of error of 0.05 or less with a 99% confidence level, we can use the formula:
n = (Z² * p * (1-p)) / E²
where n is the sample size, Z is the Z-score for the desired confidence level (2.576 for 99% confidence level), p is the estimated proportion of the population that has a certain characteristic (we can use 0.5 for maximum variability), and E is the margin of error.
Plugging in the values, we get:
n = (2.576² * 0.5 * (1-0.5)) / 0.05²
n = 664.3
Rounding up to the nearest whole number, we get a minimum sample size of 665 consumers that FiveThirtyEight should survey to guarantee a margin of error of 0.05 or less with a 99% confidence level.
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Using Trig to find a side.
Solve for x. Round to the nearest tenth, if necessary.
Answer:
x = 9.0
Step-by-step explanation:
sin E = CD/EC = CD/x
<=> sin 50 = 6.9/x <=> x = 6.9/sin 50 ≅ 9.0
John buys new baseball equipment for $2000. The purchase made is with a credit card that has a 19% APR. John makes a $150 payment monthly. How many months will it take John to pay off the balance?
It will take John approximately 17 months to pay off the balance.
What is simple interest?
Simple Interest (S.I.) is the method of calculating the interest amount for a particular principal amount of money at some rate of interest.
Assuming that John does not use the credit card for any other purchases and that the credit card company uses a simple interest calculation method, we can use the following steps to calculate the number of months it will take John to pay off the balance:
Calculate the monthly interest rate by dividing the annual percentage rate (APR) by 12:
Monthly interest rate = 19% / 12 = 0.01583
Calculate the monthly finance charge by multiplying the outstanding balance by the monthly interest rate:
Monthly finance charge = $2000 x 0.01583 = $31.66
Subtract the monthly payment from the monthly finance charge to get the amount that will be applied to the outstanding balance:
Payment applied to balance = $150 - $31.66 = $118.34
Divide the outstanding balance by the payment applied to balance to get the number of months it will take to pay off the balance:
Number of months to pay off balance = $2000 / $118.34 = 16.9
(rounded up to the nearest whole number)
Therefore, it will take John approximately 17 months to pay off the balance.
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Solve for y in the two equations below using substitution.
3x - 9y = 9
-2x - 2y = 8
Answer:
C
Step-by-step explanation:
3x - 9y = 9 → (1)
- 2x +2y = 8 ( subtract 2y from both sides )
- 2x = - 2y + 8 ( divide through by - 2 )
x = y - 4
substitute x = y - 4 into (1)
3(y - 4) - 9y = 9
3y - 12 - 9y = 9
- 6y - 12 = 9 ( add 12 to both sides )
- 6y = 21 ( divide both sides by - 6 )
y = [tex]\frac{21}{-6}[/tex] = - [tex]\frac{7}{2}[/tex]
Kelly went to a store to purchase a coffee pot. She will use a coupon for 20% off. She can calculate the cost before sales tax using the following expression, where c
represents the original cost of the coffee pot.
c−0.2c
Which other expression could Kelly use to calculate her cost before sales tax?
A. 0.8c
B. 1.2c
C.1.8c
D.80c
Find the surface area of the composite figure. Round to the nearest tenth if necessary.
Answer:
Step-by-step explanation:
· Find the surface area of a cone with a slant height of 8 cm and a radius of 3 cm. SA = B + πrS = (πr2) + πrs = (π(32)) + π(3)(8) = 9π + 24π = 33πcm2 = 103.62cm2. Find the surface area of a rectangular pyramid with a slant height of 10 yards, a base width (b) of 8 yards and a base length (h) of 12 yards.
Callie owns a business and wants to know if the majority of her customers are satisfied. She surveys a random sample of 25 customers, and 17 customers report being satisfied. In a second random sample of 25 customers, 12 customers report being satisfied. The results of the third and fourth surveys of random samples of 25 customers finds 14 and 9 satisfied customers, respectively. Which statement BEST describes the sample mean absolute deviation for this data set?
Therefore, the statement "The sample mean absolute deviation is likely to be higher for the samples with lower satisfaction rates" would be the BEST description of the MAD for this data set.
To calculate the mean absolute deviation (MAD), we first need to find the mean of each sample.
Sample 1:[tex]17/25 = 0.68[/tex]
Sample 2: [tex]12/25 = 0.48[/tex]
Sample 3: [tex]14/25 = 0.56[/tex]
Sample 4: [tex]9/25 = 0.36[/tex]
Next, we calculate the deviation of each observation from its respective sample mean:
Sample 1: |0.68 - x1|, |0.68 - x2|, ..., |0.68 - x25|
Sample 2: |0.48 - x1|, |0.48 - x2|, ..., |0.48 - x25|
Sample 3: |0.56 - x1|, |0.56 - x2|, ..., |0.56 - x25|
Sample 4: |0.36 - x1|, |0.36 - x2|, ..., |0.36 - x25|
where xi is the satisfaction rating (0 or 1) of the Ith customer in the sample.
The MAD is the average of these deviations:
MAD = (|0.68 - x1| + |0.68 - x2| + ... + |0.36 - x25|)/100
Since we don't know the actual ratings of the customers, we cannot calculate the MAD exactly. However, we can say that the MAD is likely to be higher for samples 2 and 4, which have lower satisfaction rates, compared to samples 1 and 3, which have higher satisfaction rates. Therefore, the statement "The sample mean absolute deviation is likely to be higher for the samples with lower satisfaction rates" would be the BEST description of the MAD for this data set.
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