Answer:25
Step-by-step explanation:
Because 5x5 equals 25
Answer:
25 Count by five with your five fingers
Step-by-step explanation:
5x5=25
What is the radian measure of the central angle of an arc that has an arc length of 5 units and radius of 2 units
Answer:
Central angle = θ = 2.5 radians
Step-by-step explanation:
The radian measure of central angle is given by
[tex]\theta = \frac{s}{r}[/tex]
Where s is the arc length, r is the radius of circle and θ is angle in radians
We are given an arc length of 5 units
[tex]s = 5[/tex]
We are given radius of 2 units
[tex]r = 2[/tex]
Therefore, the central angle in radians is
[tex]\theta = \frac{5}{2}\\\\\theta = 2.5 \: rad[/tex]
Bonus:
Radian is a unit which we use to measure angles.
1 Radian is the angle that results in an arc having a length equal to the radius.
Degree is another unit that we use to measure angles.
There are 360° in a circle.
There are 2π radians in a circle.
Which polygon is a convex heptagon? A polygon has 7 sides. No angles go inside of the shape. A polygon has 8 sides. No angles go inside of the shape. A polygon has 8 sides. One angle goes inside of the shape. A polygon has 7 sides. One angle goes inside of the shape.
please it's for a unit test
The polygon which has 7 sides and all its angles inside of the shape is a convex heptagon.
Convex heptagon
A convex heptagon is a type of polygon that has 7 sides and 7 interior angles and 7 vertices.
How to find a convex heptagon?A polygon that has 7 sides and 7 interior angles and 7 vertices is considered as a convex heptagon.
This means a convex heptagon has 7 sides and all angles go inside of the shape.
So, the polygon which has 7 sides and all its angles go inside of the shape is a convex heptagon.
Learn more about a convex heptagon here-https://brainly.com/question/9949611
#SPJ2
Answer:
A
Step-by-step explanation:
on edge
When the average price of an item increases from p1 to p2 over a period of n years, the annual rate of inflation r (in decimal form) is given by r=(p2p1)1/n−1. The average price of a gallon of milk increased from $0.36 in 1913 to $3.53 in 2013. What was the annual rate of inflation r? Write your answer in decimal form to the nearest thousandth.
Answer:
the annual rate of inflation r is 0.023
Step-by-step explanation:
Given by the expression:
[tex]r=(\frac{p_2}{p_1})^{1/n}-1[/tex]
The average price of a gallon of milk increased from $0.36 in 1913 to $3.53 in 2013.
Let [tex]p_1 = 0.36[/tex]
[tex]p_2 = 3.53[/tex]
n = 2013 - 1913 = 100
replacing our values into the given equation; then the annual rate of inflation r is as follows:
[tex]r=(\frac{3.53}{0.36})^{1/100}-1[/tex]
r = 0.023
Hence, the annual rate of inflation r is 0.023
The annual rate of inflation for the period 1913 to 2013 is approximately 2.3%.
To find the annual rate of inflation, we use the formula: r = [tex](\frac{p_{2} }{p_{1} } )^{\frac{1}{n} }[/tex] - 1
Given:⇒ p₁ = $0.36 (price in 1913)
⇒ p₂ = $3.53 (price in 2013)
⇒ n = 2013 - 1913 = 100 years
We substitute the values into the formula:Calculate the ratio p₂ ÷ p₁:⇒ 3.53 ÷ 0.36 = 9.8056
Take the nth root ([tex]\frac{1}{100}[/tex]) of 9.8056:⇒ [tex]9.8056^{\frac{1}{100} }[/tex] ≈ 1.023
Subtract 1 from the result:⇒ 1.023 - 1 = 0.023
Thus, the annual rate of inflation r is approximately 0.023, or 2.3% when converted to a percentage.
Complete question:
When the average price of an item increases from p₁ to p₂ over a period of n years, the annual rate of inflation r (in decimal form) is given by r = [tex](\frac{p_{2} }{p_{1} } )^{\frac{1}{n} }[/tex] − 1. The average price of a gallon of milk increased from $0.36 in 1913 to $3.53 in 2013. What was the annual rate of inflation r? Write your answer in decimal form to the nearest thousandth.
Figure CDEF is a parallelogram.
Parallelogram C D E F is shown. The length of F C is 10 r minus 20, the length of C D is 2 r + 12, and the length of D E is 6 r.
What is the value of r?
2
3
4
5
Answer:
5
Step-by-step explanation:
We know that FC = 10r - 20 and that DE = 6r. They can make an equation together since they are parallel and congruent. That gives us the equation
10r - 20 = 6r
-20 = -4r
5 = r
OR
10r - 20 = 6r
10 = 6r + 20
4r = 20
r = 5
Either way, you still get the answer of r = 5.
The value of r in the given parallelogram is: D. 5.
What is a Parallelogram?A parallelogram has two pairs of sides opposite each other that are congruent to each other.
Thus:
DE = FC (congruent sides)
Substitute
6r = 10r - 20
Combine like terms
6r - 10r = -20
-4r = -20
r = 5
Thus, the value of r in the given parallelogram is: D. 5.
Learn more about parallelogram on:
https://brainly.com/question/12167853
HELP! I NEED THIS ANWSERED NOW PLS! Which of the following terminating decimals is equivalent to Negative 1 and three-fourths?
–1.75
–0.75
0.75
1.75
Answer:
A. -1.75
Step-by-step explanation:
- means negative, so -1. 1 quarter of 1 would be .25, 2 quarters would be .50, 3 quarters would be .75, and 4 quarters would be 1.0.
Answer:
-1.75
Step-by-step explanation:
i did it earlier
A survey (random sample) of 700 office workers investigated telephone answering practices, including how often each office worker was able to answer incoming telephone calls and how often incoming telephone calls went directly to voice mail. A total of 280 office worker indicated that they never need voice mail and are able to take every telephone call. What is the 92% confidence interval for the actual proportion of all office workers who are able to take every telephone call
Answer:
The 92% confidence interval for the actual proportion of all office workers who are able to take every telephone call is (0.3676, 0.4324).
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
For this problem, we have that:
[tex]n = 700, \pi = \frac{280}{700} = 0.4[/tex]
92% confidence level
So [tex]\alpha = 0.08[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.08}{2} = 0.96[/tex], so [tex]Z = 1.75[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.4 - 1.75\sqrt{\frac{0.4*0.6}{700}} = 0.3676[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.4 + 1.75\sqrt{\frac{0.4*0.6}{700}} = 0.4324[/tex]
The 92% confidence interval for the actual proportion of all office workers who are able to take every telephone call is (0.3676, 0.4324).
A school will give its baseball teams less than $840 to buy new helmets. Each helmet costs $20. The maximum number of helmets, c, they can purchase is represented by the inequality 20c < 840. Select the maximum number of helmets they can buy.
Answer: C
Step-by-step explanation:
42 x 20 Is 840
The closest to 42 is 41 so the answer is C
The school can buy a maximum of 41 baseball helmets with the available funds, given each helmet costs $20. Moreover, the bat and ball problem is a classic example of a common misconception; the ball actually costs $0.05, not $0.10.
The question asks for the maximum number of helmets a school can buy with less than $840, given each helmet costs $20. This is expressed by the inequality 20c < 840. To find c, the maximum number of helmets, we divide both sides of the inequality by 20:
c < 840 / 20
⇒ c < 42
This means the school can buy a maximum of 41 helmets, as c must be less than 42 and we can only buy whole numbers of helmets.
The student also asked a seemingly unrelated question about the cost of a bat and a ball together totaling $1.10, with the bat costing $1.00 more than the ball. Correctly solving this puzzle requires setting up an equation where x represents the cost of the ball: x + (x + 1.00) = 1.10. Simplifying and solving for x reveals that the ball costs $0.05 and the bat costs $1.05, totaling $1.10 as stated.
A packing operator can assemble 4 cardboard boxes in 5 minutes. At this rate, how many boxes can she assemble in 25 minutes?
A. 20
B. 12
C. 24
D. 28
Answer:
A. 20
Step-by-step explanation:
look at this step:
4 : 5 = X : 25
X = 4×25/5 = 100/5 = 20
She can assemble 20 boxes.
Step-by-step explanation:1. Create a table
# of Boxes Time
4 => 5 min
x => 25 min
2. Use the table to cross multiply.
5 · x = 4 · 25
5x = 100
5x/5 = 100/5
x = 20
What is the value of the expression below? Negative 50 + 51 –101 –1 1 101
Answer:
the answer is 1
Step-by-step explanation:
bc if you add -50+51 you get 1
Answer:
uno
Step-by-step explanation
51- 50 =1
Operations on Rational and Irrational Numbers
Multiply.
Answer as a fraction. Do not include spaces in your answer.
1.9 x (1/4) = ?
Answer:
19/40
Step-by-step explanation:
Answer: 19/40
Step-by-step explanation:
Melanie is making necklaces in four different lengths. In each necklace, the ratio of blue beads to orange beads remains the same
Complete Question
Melanie is making necklaces in four different lengths. n each necklace, the ratio of blue beads to orange beads remains the same. How many orange beads will Melanie need for a necklace of 50 beads?
Answer:
Melanie will need a total of 25 orange beads for a necklace of 50 beads
Step-by-step explanation:
Given
Ratio of blue beads to orange beads is the same.
This can be represented as 1:1
Required
Number of orange beads needed for a necklace of 50 beads.
From the given data, we have that the ratio of blue beads to orange beads is the same.
i.e. Blue:Orange = 1:1
To calculate the number of orange beads needed,
First, we have to convert the ratio to fraction.
This is done as follows;
Fraction of orange beads = Ratio of orange beads divided by Total Ratio
Ratio of orange beads = 1
Total Ratio = 1 + 1 = 2
Hence,
Fraction of orange beads = [tex]\frac{1}{2}[/tex]
This fraction will then be multiplied by the total number of beads to give the number of orange beads needed.
Number of orange beads needed = [tex]\frac{1}{2} * 50[/tex]
Number of orange beads needed = [tex]\frac{50}{2}[/tex]
Number of orange beads needed = [tex]25[/tex]
Hence, Melanie will need a total of 25 orange beads for a necklace of 50 beads
4.7 ft
4.3 ft
Find the volume of the cylinder. Round your answer to the nearest hundredth.
A 30.33 ft
B 20.0543
Answer:B. 68.25
Step-by-step explanation:
was withheld specifically for the tax that is used to pay
for a healthcare program.
was withheld for the payroll tax that specifically
supports retired and disabled citizens.
If this individual made more money, the amount withheld for Social
Security would
The answers are $612.65, $2,567.45, and increase
Answer: $612.65, $2,567.45, and increase
Step-by-step explanation:
Answer:
✔ $612.65
was withheld specifically for the tax that is used to pay for a healthcare program.
✔ $2,567.45
was withheld for the payroll tax that specifically supports retired and disabled citizens.
If this individual made more money, the amount withheld for Social Security would
✔ increase
.
A) 97°
C) 90°
B) 83°
D) 92°
Q Zoom
Answer:
B. 83
Step-by-step explanation:
Angle in a triangle sum to 180 degrees
-> 25 + 72 + ? = 180
? = 180 - 25 - 72 = 83
Answer:
the answer is B that's it
−1.75 − 22/20
plz hlep
...and put as an exact decimal or simplified fraction
Answer:
-2.85
Step-by-step explanation:
I looked it up tbh
Answer:
-2.85
Step-by-step explanation:
Google it or Edge it or Firefox it
what's the equivalent fraction of 3/8 tell me
Step-by-step explanation:
the equivalent of 3/8 is 6/16
Answer:
[tex]\frac{6}{16} = \frac{9}{24} =\frac{12}{32} =\frac{15}{40}[/tex]
Step-by-step explanation:
There are infinitely many equivalent fractions of [tex]\frac{3}{8}[/tex] but here are a few:
[tex]\frac{6}{16} = \frac{9}{24} =\frac{12}{32} =\frac{15}{40}[/tex]
Together maria and serena have $1.20 they want to share the money equally how much money will each girl get
A bank lent $200,500 for the development of two products. If the loan for product X was for $50,500 more than that for product Y, how much was lent for product Y?
Answer:
$75,000
Step-by-step explanation:
Given:
Total loaned amount = $200,500
Amount loaned for product Y = y
So, Amount loaned for product X = $50,500 + y
Computation:
Total loaned amount = Amount loaned for product Y + Amount loaned for product X
$200,500 = y + $50,500 + y
$200,500 = 2 y + $50,500
$200,500 - $50,500 = 2 y
$150,000 = 2 y
y = $75,000
Therefore, money loaned for product Y is $75,000
) The National Highway Traffic Safety Administration collects data on seat-belt use and publishes results in the document Occupant Restraint Use. Of 1,000 drivers 16-24 years old, 79% said they buckle up, whereas 924 of 1,100 drivers 25-69 years old said they did. Does the data provide sufficient evidence to conclude that there is a difference in seat belt use? Go over all the steps in the process for comparing two sample percentages.
Answer:
We conclude that there is a difference in seat belt use.
Step-by-step explanation:
We are given that of 1,000 drivers 16-24 years old, 79% said they buckle up, whereas 924 of 1,100 drivers 25-69 years old said they did.
Let [tex]p_1[/tex] = population proportion of drivers 16-24 years old who buckle up .
[tex]p_2[/tex] = population proportion of drivers 25-69 years old who buckle up .
So, Null Hypothesis, [tex]H_0[/tex] : [tex]p_1-p_2[/tex] = 0 {means that there is no significant difference in seat belt use}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]p_1-p_2\neq[/tex] 0 {means that there is a difference in seat belt use}
The test statistics that would be used here Two-sample z proportion statistics;
T.S. = [tex]\frac{(\hat p_1-\hat p_2)-(p_1-p_2)}{\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+\frac{\hat p_2(1-\hat p_2)}{n_2} } }[/tex] ~ N(0,1)
where, [tex]\hat p_1[/tex] = sample proportion of drivers 16-24 years old who buckle up = 79%
[tex]\hat p_2[/tex] = sample proportion of drivers 25-69 years old who buckle up = [tex]\frac{924}{1100}[/tex] = 84%
[tex]n_1[/tex] = sample of 16-24 years old drivers = 1000
[tex]n_2[/tex] = sample of 25-69 years old drivers = 1100
So, test statistics = [tex]\frac{(0.79-0.84)-(0)}{\sqrt{\frac{0.79(1-0.79)}{1000}+\frac{0.84(1-0.84)}{1100} } }[/tex]
= -2.946
The value of z test statistics is -2.946.
Since, in the question we are not given with the level of significance so we assume it to be 5%. Now, at 0.05 significance level the z table gives critical values of -1.96 and 1.96 for two-tailed test.
Since our test statistics doesn't lie within the range of critical values of z, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.
Therefore, we conclude that there is a difference in seat belt use.
Anisha invested $8000 in an account that earns 10% interest. How much money will she have in 15 years if the interest is compounded continuously?
Answer:
Anisha will have approximately $33,417.98 in 15 years with interest compounded annually.
Explanation:
We can use the formula for compound interest:
[tex]\[ A = P \times \left(1 + \frac{r}{n}\right)^{nt} \][/tex]
where:
- [tex]\( A \)[/tex] is the amount of money accumulated after [tex]\( t \)[/tex] years, including interest
- [tex]\( P \)[/tex] is the principal amount (the initial investment)
- [tex]\( r \)[/tex] is the annual interest rate (in decimal)
- [tex]\( n \)[/tex] is the number of times that interest is compounded per year
- [tex]\( t \)[/tex] is the time the money is invested for (in years)
Given:
- [tex]\( P = \$8000 \)[/tex]
- [tex]\( r = 0.10 \)[/tex] (10% expressed as a decimal)
- [tex]\( n = 1 \)[/tex] (interest compounded annually)
- [tex]\( t = 15 \)[/tex] years
Substitute the values into the formula:
[tex]\[ A = 8000 \times \left(1 + \frac{0.10}{1}\right)^{1 \times 15} \][/tex]
[tex]\[ A = 8000 \times (1 + 0.10)^{15} \][/tex]
[tex]\[ A = 8000 \times (1.10)^{15} \][/tex]
Now, we can calculate:
[tex]\[ A \approx 8000 \times 4.177248 \][/tex]
[tex]\[ A \approx 33417.98 \][/tex]
helo asap !! will get branliest.
Answer:
1/25
Step-by-step explanation:
= 5^4/5^6
= 1/5^6-4
= 1/5^2
= 1/25
hope it helps!
Answer:
Here is the answer..
Step-by-step explanation:
It's simple.
look
=5^4/5^6
=1/25
Hope it helps ☺️
Daily temperatures for two cities, Salem and Oxford, were recorded for one week. A 8-column table has 2 rows. Column 1 has entries Salem, Oxford. Column 2 is labeled Sunday with entries 56, 71. Column 3 is labeled Monday with entries 61, 52. Column 4 is labeled Tuesday with entries 55, 58. Column 5 is labeled Wednesday with entries 62, 50. Column 6 is labeled Thursday with entries 58, 89. Column 7 is labeled Friday with entries 61, 60. Column 8 is labeled Saturday with entries 60, 61. Using statistics, answer the question below: Which city had the highest variability in temperatures?
Answer:
Oxford had the highest variability
Step-by-step explanation:
If you put the numbers in order from greatest to least, and get the range 62,55 and 89,55 you get Oxford as the higher variability with a range of 39
Answer:
B. 2-column table with 5 rows. Column 1 is labeled x with entries 60, 61, 63, 67, 69. Column 2 is labeled y with entries negative 20, 0, 3, 8, 8.
C.On a graph, points form a line with negative slope. One point is outside of the line.
Step-by-step explanation:
» In a right triangle, a and b are the lengths of the legs and c is the length of the
hypotenuse. If b = 8.6 kilometers and c = 9.4 kilometers, what is a? If necessary, round to
the nearest tenth.
Answer:
3.8
Step-by-step explanation:
a=3.79 or 3.8km
√(9.4^2 - 8.6^2)
Find the indicated confidence interval. Assume the standard error comes from a bootstrap distribution that is approximately normally distributed. A 95% confidence interval for a difference in proportions p1-p2 if the samples have n1=70 with p^1=0.68 and n2=100 with p^2=0.56, and the standard error is SE=0.07. Round your answers to three decimal places. The 95% confidence interval is to .
Answer:
[tex] (0.68-0.56) -1.96 \sqrt{\frac{0.68(1-0.68)}{70} +\frac{0.56*(1-0.56)}{100}}= -0.0263[/tex]
[tex] (0.68-0.56) +1.96 \sqrt{\frac{0.68(1-0.68)}{70} +\frac{0.56*(1-0.56)}{100}}= 0.2663[/tex]
So then we are 95% confident that the true difference in the proportions is given by:
[tex] -0.0263 \leq p_1 -p_2 \leq 0.2663[/tex]
Step-by-step explanation:
The information given for this case is:
[tex]\hat p_1 = 0.68 , \hat p_2 = 0.56[/tex]
[tex] n_1 = 70, n_2 =100[/tex]
We want to construct a confidence interval for the difference of proportions [tex]p_1 -p_2[/tex] and for this case this confidence interval is given by:
[tex](\hat p_1 -\hat p_2) \pm z_{\alpha/2} \sqrt{\frac{\hat p_1 (1-\hat p_1)}{n_1} +\frac{\hat p_2 (1-\hat p_2)}{n_2}}[/tex]
The confidence level is 0.95 so then the significance level would be [tex]\alpha=1-0.95=0.05[/tex] and [tex]\alpha/2 =0.025[/tex] if we find the critical values for this confidence level we got:
[tex]z_{\alpha/2}= \pm 1.96[/tex]
And replacing the info we got:
[tex] (0.68-0.56) -1.96 \sqrt{\frac{0.68(1-0.68)}{70} +\frac{0.56*(1-0.56)}{100}}= -0.0263[/tex]
[tex] (0.68-0.56) +1.96 \sqrt{\frac{0.68(1-0.68)}{70} +\frac{0.56*(1-0.56)}{100}}= 0.2663[/tex]
So then we are 95% confident that the true difference in the proportions is given by:
[tex] -0.0263 \leq p_1 -p_2 \leq 0.2663[/tex]
The 95% confidence interval is (0.257,-0.017).
To understand the calculations, check below.
Critical value:The critical value is a cut-off value that is used to mark the start of a region where the test statistic, obtained in hypothesis testing, is unlikely to fall in.
Given that,
[tex]n_1=70\\n_2=100\\\hat{p_1}=0.68\\\hat{p_1}=0.56\\SE=0.07\\\alpha=0.05[/tex]
The critical value is,
[tex]Z_{\frac{\alpha}{2} }=Z_{\frac{0.05}{2} }=1.96[/tex] (From standard normal probability table)
Therefore, the 95% confidence interval for the difference between population proportions [tex]p_1-p_2[/tex] is ,
[tex](\hat{p_1}-\hat{p_2})\pm Z_{\frac{\alpha}{2} }\times \sqrt{\hat{p}(1-\hat{p})(\frac{1}{n_1}+\frac{1}{n_2} ) }\\=(\hat{p_1}-\hat{p_2})\pm Z_{\frac{\alpha}{2} }\times SE\\=(0.68-0.56)\pm 1.96\times 0.07\\=0.12\pm 0.137\\=(0.257,-0.017)[/tex]
Learn more about the topic Critical value:
https://brainly.com/question/1832218
How are the angle measurements of the opposite interior angles related ?
Answer:
opposite angles are congruent
Step-by-step explanation:
thats because if you think about two intersecting lines and draw a circle around the angles you can imagine it as a circle (360 degrees) so whatever value the angles are they have to equal 360
so you may ask the question what does that have to do with anything? well i'm getting to that...the vertical angles are congruent because well one there is a theorem for it (search it up) and two it makes sense if you think of cutting a pizza all the way across and another line intersecting it all the way across. You notice how no matter how you position the two intersecting lines the angle opposite each other look the same. Thats because they are the same exact angle just directly across from each other. I hope this made sense :)
Answer:
The opposite interior angles of the parallelogram have equal measurements.
Step-by-step explanation:
PLATO SAMPLE
The surface areas of two similar solids are 441 cm2 and 225 cm2. If the approximate volume of the smaller solid is 250 cm3, what is the volume of the larger solid?
Answer:
volume of the larger solid = 686 cm³
Step-by-step explanation:
The solids are similar . A solid is similar if all the corresponding sides are proportional . They are similar if they are the same type of solids and their corresponding sides like height, radius etc are proportional.
The ratio of the surface area of a similar solid is equal to the square of their scale factor.
(a/b)² = 441/225
square root both sides
a/b = √441/√225
a/b = 21/15
The ratio of the volume of a similar solid is equal to the cube of their scale factor.Therefore,
(21/15)³ = a/250
9261 /3375 = a/250
cross multiply
9261 × 250 = 3375a
2315250 = 3375a
divide both sides by 3375
a = 2315250/3375
a = 686 cm³
volume of the larger solid = 686 cm³
WILL GIVE BRAINIEST Which of the following is NOT a perfect square? Question 3 options: 36 25 49 81 35 144 100
Answer:
35
Step-by-step explanation:
The way I know is because I memorized every square up to 33.
BUT that's probably not helpful to you.
Remember that every perfect square has an odd number of factors. I'm not going to list them all out, but the factors of 35 are 1, 5, 7, and 35, giving it an even number of factors. All the rest have an odd number of factors because of the property of a perfect square: a number times itself gives a perfect square, but that number only counts as 1 factor.
Answer:
25
Step-by-step explanation:
What is the measure of Zc
Answer: 56 degrees
Step-by-step explanation:
We know that angle between b and c is 90 degrees. Because there is a line dividing angles a and b from 124 and c, we also know that each side is 180 degrees (a and b add to 180, and 124 and c add to 180).
124 and c are supplementary angles. We can represent this in an equation to solve for c:
[tex]124 + c = 180\\\\c = 56[/tex]
Waitresses all want to work the "high roller" room at a local restaurant. There are six waitresses each evening assigned to one of six rooms in the restaurant. Tne room assignments are made by fair random selection such that each waitress has an equal probability of being in the "high roller" room. If a waitress in the "high roller" room will always make $200 in tips over the course of an evening while waitresses in all other rooms will make $75, over time (on average) how much can a waitress at this restaurant expect to make per evening?
Answer:
The expected amount earned by a waitress per evening is $95.83.
Step-by-step explanation:
At a local restaurant there are six rooms total; 1 is a "high roller" room and other 5 are normal rooms.
There are 6 waitresses working at the local restaurant.
The room assignments are made by fair random selection such that each waitress has an equal probability of being in the "high roller" room.
This implies that a waitress can be assigned any of the six rooms with probability, [tex]\frac{1}{6}[/tex].
The tip earned by the waitress working in the "high roller" room is $200 and that for other rooms is $75.
So, the distribution of tips earned is as follows:
X: $200 $75 $75 $75 $75 $75
P (X): [tex]\frac{1}{6}[/tex] [tex]\frac{1}{6}[/tex] [tex]\frac{1}{6}[/tex] [tex]\frac{1}{6}[/tex] [tex]\frac{1}{6}[/tex] [tex]\frac{1}{6}[/tex]
The expected value of a random variable is given by:
[tex]E(X)=\sum x\cdot P (X)[/tex]
Compute the expected amount earned by a waitress per evening as follows:
[tex]E(X)=\sum x\cdot P (X)[/tex]
[tex]=(200\times \frac{1}{6})+(75\times \frac{5}{6})\\\\=\frac{575}{6}\\\\=95.8333\\\\\approx 95.83[/tex]
Thus, the expected amount earned by a waitress per evening is $95.83.
Final answer:
Using the probabilities of being in different rooms and their respective tips, a waitress can expect to make on average approximately $95.83 per evening at this restaurant.
Explanation:
To calculate the average amount a waitress can expect to make per evening, we need to consider the probabilities of the waitress being assigned to the "high roller" room or any other room. Since there are six rooms and assignments are made randomly, each waitress has a 1 in 6 chance of being in the high roller room. Otherwise, she has a 5 in 6 chance of being in a room with a lower tip rate.
We calculate the expected earnings for each scenario and then find the combined average. The expected earnings in the high roller room is $200, while the expected earnings in the other rooms is $75. Using the formula for expected value (EV), we get:
EV = (Probability of High Roller Room) x (Tips in High Roller Room) + (Probability of Other Rooms) x (Tips in Other Rooms)
EV = (1/6) x $200 + (5/6) x $75
EV = $33.33 + $62.50
EV = $95.83
So, on average, a waitress can expect to make approximately $95.83 per evening.
Find the volume of a right circular cone that has a height of 12.2 cm and a base with a circumference of 18.5 cm. Round your answer to the nearest tenth of a cubic centimeter.
We have been given that a right circular cone has a height of 12.2 cm and a base with a circumference of 18.5 cm. We are asked to find the volume of the cone to nearest tenth.
We know that circumference of circle is equal to [tex]2\pi r[/tex].
[tex]2\pi r=18.5[/tex]
[tex]r=\frac{18.5}{2\pi}[/tex]
[tex]r=2.944366[/tex]
Now we will use volume of the cone formula to solve our given problem.
[tex]V=\frac{1}{3}\pi r^2 h[/tex]
[tex]V=\frac{1}{3}\pi (2.944366)^2\cdot (12.2)[/tex]
[tex]V=\frac{1}{3}\pi (8.669291141956)\cdot (12.2)[/tex]
[tex]V=\frac{1}{3}\pi (105.7653519318632)[/tex]
[tex]V=\frac{1}{3}(332.2716526334804752)[/tex]
[tex]V=110.7572175[/tex]
Upon rounding to nearest tenth, we will get:
[tex]V\approx 110.8[/tex]
Therefore, the volume of the given cube would be approximately 110.8 cubic centimeter.
Final answer:
To find the volume of a right circular cone, the base radius is calculated from the circumference, and then the volume is determined using the cone volume formula V = (1/3)πr²h, with the final result being rounded to the nearest tenth. So, [tex]\( V \approx 110.415 \) cm^3[/tex].
Explanation:
To calculate the volume of a right circular cone, we first need to determine the radius of the base which can be found from the circumference. Since the formula for circumference is C = 2πr, where C is the circumference and r is the radius, we can solve for r. For a circumference of 18.5 cm, we have:
18.5 = 2πr => r = 18.5 / (2π)
Now that we have the radius, the volume of the cone can be found using the formula:
V = (1/3)πr²h
Plugging in the radius and height:
V = (1/3) * π * (18.5 / (2π))² * 12.2
After performing the calculation, we can round the result to the nearest tenth to find the volume in cubic centimeters.
Let's calculate it:
1. [tex]\( \frac{18.5}{2\pi} \) \approx \( \frac{18.5}{6.28319} \) \approx 2.942881[/tex]
2. Square the result: [tex]\( (2.942881)^2 \) \approx 8.66347[/tex]
3. Multiply by 12.2: [tex]\( 8.66347 \times 12.2 \)[/tex] ≈ 105.685554
4. Multiply by [tex]\( \frac{1}{3} \) and \( \pi \)[/tex]:
[tex]\( V = \frac{1}{3} \times \pi \times 105.685554 \)[/tex]
Now, let's calculate \( V \):
[tex]\[ V \approx \frac{1}{3} \times 3.14159 \times 105.685554 \]\[ V \approx \frac{1}{3} \times 3.14159 \times 105.685554 \]\[ V \approx 110.415 \][/tex]
So, [tex]\( V \approx 110.415 \) cm^3[/tex].