Answer:
The attendance on tuesday, october 4, is of 144 people.
Step-by-step explanation:
The attendance after t days is given by the following equation:
[tex]A(t) = A(0)(1-r)^{t}[/tex]
In which A(0) is the attendance on the first day and r is the daily decrease rate.
Premieres on saturday, october 1, and 420 people attend.
This means that [tex]A(0) = 420[/tex]
Attendance then decreases by 30% each day.
This means that [tex]r = 0.3[/tex]
So
[tex]A(t) = A(0)(1-r)^{t}[/tex]
[tex]A(t) = 420(1-0.3)^{t}[/tex]
[tex]A(t) = 420(0.7)^{t}[/tex]
Find the attendance on tuesday , october 4
This is 4-1 = 3 days after saturday. So this is A(3).
[tex]A(3) = 420(0.7)^{3} = 144[/tex]
The attendance on tuesday, october 4, is of 144 people.
To find the attendance on Tuesday, October 4, after a 30% daily decrease from an initial attendance of 420 people on Saturday, October 1, we calculate the exponential decay for three days to get approximately 144 attendees.
The student's question involves an exponential decay math problem where the attendance of a play decreases by a percentage each day. To calculate the attendance on Tuesday, October 4, we begin with the initial attendance of 420 people on Saturday, October 1. We then apply a 30% decrease for each subsequent day:
Sunday, October 2: 420 - (0.30 × 420) = 294 peopleMonday, October 3: 294 - (0.30 × 294) = 205.8 peopleTuesday, October 4: 205.8 - (0.30 × 205.8) = approximately 144.06 peopleSince we cannot have a fraction of a person attending, we would generally round to the nearest whole number, which means about 144 people attended the play on Tuesday, October 4.
Two insurance policies, G and H, can each only submit one claim in a given month. For insurance policy G, there is a 45% chance that no claims are made in the coming month. Otherwise, the loss amount follows an exponential distribution with a mean of 5. For insurance policy H, there is a 35% chance that no claims are made in the coming month. Otherwise, the loss amount follows an exponential distribution with a mean of 9. For both policies, there is a deductible of 2 and they only reimburse 80% of the amount that exceeds the deductible. Calculate the difference between the expected reimbursements of the two policies for a given month.
To calculate the difference between the expected reimbursements of insurance policies G and H for a given month, we need to find the expected reimbursement for each policy and then take the difference of the two values.
Explanation:To calculate the difference between the expected reimbursements of insurance policies G and H for a given month, we need to find the expected reimbursement for each policy and then take the difference of the two values.
For policy G, there is a 45% chance of no claims, in which case the reimbursement is 0. If a claim is made, the loss amount follows an exponential distribution with a mean of 5. We need to find the expected value of the reimbursement in this case. Let X be a random variable representing the loss amount. The expected reimbursement for policy G is then given by:
Expected Reimbursement for Policy G = 0.45(0) + 0.55(0.8)(E(X) - 2)
Similarly, for policy H, there is a 35% chance of no claims and a 65% chance of a claim with a loss amount following an exponential distribution with a mean of 9. Let Y be a random variable representing the loss amount. The expected reimbursement for policy H is:
Expected Reimbursement for Policy H = 0.35(0) + 0.65(0.8)(E(Y) - 2)
To find the difference between the expected reimbursements, we subtract the expected reimbursement for policy H from the expected reimbursement for policy G:
Difference = Expected Reimbursement for Policy G - Expected Reimbursement for Policy H
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You are a lifeguard and spot a drowning child 60 meters along the shore and 40 meters from the shore to the child. You run along the shore and for a while and then jump into the water and swim from there directly to child. You can run at a rate of 4 meters per second and swim at a rate of 1.1 meters per second. How far along the shore should you run before jumping into the water in order to save the child? Round your answer to three decimal places.
The distance the lifeguard should run along the shore before jumping into the water, can be determined by minimizing the function of time, that is, the time it takes for the lifeguard to reach the child. This problem can be solved either by using calculus or the graphical method with a graphing tool.
Explanation:This problem can be solved using optimization of functions, which is a part of calculus. We would let 'x' be the distance along the shore that the lifeguard runs before jumping into the water. Then the total time taken to reach the child is given by the formula T = x/4 + sqrt((60-x)² + 40²)/1.1. We are looking for the minimum of T as a function of x. However, it would require knowledge of calculus to solve this problem. As an alternative, one can also use a graphing calculator or similar tool to graph the time function and then determine the minimum on the graph.
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Final answer:
To save the child, you should run along the shore for approximately 15 seconds before jumping into the water.
Explanation:
To determine how far along the shore you should run before jumping into the water to save the child, you need to find the time it takes to run along the shore and then swim directly to the child.
First, calculate the time taken to run along the shore using the formula: time = distance / speed. In this case, the distance is 60 meters and the speed is 4 meters per second. So, the time taken to run along the shore is 60 / 4 = 15 seconds.
Next, calculate the time taken to swim directly to the child using the formula: time = distance / speed. In this case, the distance is 40 meters and the speed is 1.1 meters per second.
So, the time taken to swim directly to the child is 40 / 1.1 ≈ 36.364 seconds.
Therefore, the total time taken to save the child is the sum of the time taken to run along the shore and the time taken to swim directly to the child.
So, in order to save the child, you should run along the shore for approximately 15 seconds before jumping into the water.
A scientist has two solutions, which she has labeled Solution A and Solution B. Each contains salt. She knows that Solution A is 55% salt and Solution B is 80% salt. She wants to obtain 130 ounces of a mixture that is 75% salt. How many ounces of each solution should she use?
Answer:
26 ounces of 55% solution104 ounces of 80% solutionStep-by-step explanation:
Let x represent the quantity of 80% solution. Then 130-x is the amount of 55% solution. The total amount of salt in the mix is ...
0.80x +0.55(130 -x) = 0.75·130
0.25x = 0.20·130 . . . . . . . subtract 0.55(130)
x = 0.20/0.25(130) = 104
130-x = 26
She should use 26 ounces of 55% solution and 104 ounces of 80% solution.
Final answer:
The scientist would need to use 26 ounces of Solution A and 104 ounces of Solution B to create 130 ounces of a 75% salt mixture.
Explanation:
To solve the problem of mixing two salt solutions of different concentrations to achieve a specific final concentration, we can set up a system of equations based on the amounts of salt and total solution. We know that Solution A is 55% salt and Solution B is 80% salt, and we want 130 ounces of a 75% salt mixture.
Let x be the amount of Solution A and y be the amount of Solution B. The first equation is based on the total amount of solution, and it is:
x + y = 130 ... (1)
The second equation is based on the amount of salt in the final mixture:
0.55x + 0.80y = 0.75(130) ... (2)
From equation (1), we can express y as y = 130 - x. Substitute this into equation (2) and solve for x:
0.55x + 0.80(130 - x) = 97.5
0.55x + 104 - 0.80x = 97.5
-0.25x = -6.5
x = 26 ounces (Solution A)
Substitute x back into equation (1) to find y:
x + y = 130
26 + y = 130
y = 104 ounces (Solution B)
So, to obtain 130 ounces of a 75% salt mixture, the scientist would use 26 ounces of Solution A and 104 ounces of Solution B.
Please Help!!!!! ...................................
Answer:
divide 252 by 7 and you get 36
Step-by-step explanation:
Construct a 90% confidence interval of the population proportion using the given information.
X= 175
n= 250
Tbe confidence interval marked the range of values for which the true population mean is estimated to be given a certain level of confidence. Hence, the confidence interval is (0.6523, 0.7477)
Since the sample size is large enough, we use the the Z distributuon :
Confidence interval is defined thus :
Mean ± margin of errorMargin of Error :
[tex] Z = Z* \sqrt{\frac{pq}{n}}[/tex] Mean, p = x/n = 175/250 = 0.7q = 1 - 0.7 = 0.3Zcritical at 90% = Z* = 1.645Hence,
Margin of Error = [tex] 1.645 \sqrt{\frac{0.7\times 0.3 }{250}} = 0.0477[/tex]Lower confidence boundary = 0.7 - 0.0290 = 0.6523
Upper confidence boundary = 0.7 + 0.0290 = 0.7477
Therefore, the confidence interval is (0.6523, 0.7477)
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To construct a 90% confidence interval for the population proportion, calculate the sample proportion, the standard error, and use the confidence interval formula.
Explanation:Step 1:
Calculate the sample proportion, which is X divided by n. In this case, it is 175 divided by 250, which gives us 0.7.
Step 2:
Calculate the standard error, which is the square root of (p*(1-p))/n, where p is the sample proportion. In this case, it is the square root of (0.7*(1-0.7))/250, which is approximately 0.0266.
Step 3:
Construct the confidence interval using the formula p ± z*(standard error), where p is the sample proportion and z is the z-score corresponding to the desired level of confidence. For a 90% confidence interval, the z-score is approximately 1.645. Therefore, the 90% confidence interval is 0.7 ± 1.645*0.0266, which becomes (0.658, 0.742).
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In ΔFGH, f = 37 cm, ∠F=28° and ∠G=124°. Find the length of g, to the nearest 10th of a centimeter.
Answer:
65.3 cm
Step-by-step explanation:
The law of sines can be used for this.
g/sin(G) = f/sin(F)
g = (37 cm)sin(124°)/sin(28°) ≈ 65.3 cm . . . . multiply by sin(G)
The length of g is about 65.3 cm.
A pair of sunglasses is priced at $42.95. They are put on sale at 27% off the original price. Shane estimates the discounted price of the sunglasses to be around $36. Is this a reasonable estimate?
Answer:
no,
Step-by-step explanation:
1/4 of 40 is 10
40-10=30
It depends. The actual price would be $31.35. So it is not really reasonable since it is closer to the original price than it is to the discounted one... Just use your best judgement...
A circle with a diameter of 10 cm and a central angle of 30° is shown. What is the length, to the nearest tenth, of the arc formed by the 30° angle?
9514 1404 393
Answer:
2.6 cm
Step-by-step explanation:
The full circle is 360°, so an arc of 30° will have 30/360 = 1/12 of the measure of the circumference of the circle.
arc length = πd/12 = π(10/12) ≈ 2.6 cm
A farmer owns a 100 acre farm and plans to plant at most three crops. The seed for crops A,B, and C costs $40, $20, and $30 per acre, respectively. A maximum of $3200 can be spent on seed. Crops A,B, and C require 1,2, and 1 workdays per acre, respectively, and there are maximum of 160 workdays available. If the farmer can make a profit of $100 per acre on crop A, $300 per acre on crop B, and $200 per acre on crop C, how many acres of each crop should be planted to maximize profit
The 0 acres of crop A, 60 acres of crop B, and 40 acres of crop c each crop should be planted to maximize profit $26,000.
Given that,
A farmer owns a 100-acre farm and plans to plant at most three crops. The seed for crops A, B, and C costs $40, $20, and $30 per acre, respectively.
A maximum of $3200 can be spent on the seed. Crops A, B, and C require 1,2, and 1 workday per acre, respectively, and there are a maximum of 160 workdays available.
If the farmer can make a profit of $100 per acre on crop A, $300 per acre on crop B, and $200 per acre on crop C,
We have to find,
How many acres of each crop should be planted to maximize profit?
According to the question,
The farmer can make a profit of $100 per acre on crop A, $300 per acre on crop B, and $200 per acre on crop C,
[tex]\rm P = 100A + 300B + 200C[/tex]
The seed for crops A, B, and C costs $40, $20, and $30 per acre, respectively.
And A maximum of $3200 can be spent on the seed.
[tex]\rm 40A + 20B + 30C \leq 3200[/tex]
Then, Sum of seed for crops costs = area of the farm
[tex]\rm A + B + C \leq 100[/tex]
Crops A, B, and C require 1,2, and 1 workday per acre, respectively, and there are a maximum of 160 workdays available.
[tex]\rm A + 2B + C = 160[/tex]
Solving all the equations,
From equation 3,
[tex]\rm A = 100-B-C[/tex]
Substitute the value of A in equation 4,
[tex]\rm 100 - B - C+ 2B + C = 160\\\\100 + B = 160 \\\\B = 160 - 100\\\\B = 60[/tex]
Put B = 60 in the equation,
[tex]\rm A = 100-B-C\\\\A = 100-60-C\\\\A = 40-C[/tex]
Substitute the value of A in equation 2,
[tex]\rm 40(40-C) + 20\times 60 + 30C = 3200\\\\1600 - 40C + 1200 + 30C = 3200\\\\-10C + 2800 = 3200\\\\-10C = 3200-2800\\\\-10C = 400\\\\C = \dfrac{400}{-10}\\\\C = -40[/tex]
The area can not be negative then the value of C is +40.
And the value of A is,
[tex]A + B + C = 100\\\\A = 100 - 60 -40\\\\A = 100-100\\\\A = 0[/tex]
Then, Maximize profit is,
[tex]\rm P = 100A + 300B + 200C\\\\\rm P = 100(0) + 300(60) + 200(40)\\\\P =0+18000+8000\\\\P = 26000[/tex]
Hence, The 0 acres of crop A, 60 acres of crop B, and 40 acres of crop c each crop should be planted to maximize profit $26,000.
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The toxicity level of a lake is found by dividing the amount of dissolved toxins the lake water currently has per liter by the maximum safe amount of dissolved toxins that the water can hold per liter and then converting it to a percentage. If the river currently has 0.86 milligrams of dissolved toxins per liter of water and the maximum safe amount of dissolved toxins is 1.04 milligrams per liter, what is the toxicity level of the lake water, to the nearest percentage? A. 86% B. 84% C. 83% D. 80% E. 79%
The toxicity level of the lake water is calculated by dividing the current level of toxins (0.86 mg per liter) by the maximum safe level (1.04 mg per liter) and then converting to a percentage, which results in approximately 83%.
Explanation:To determine the toxicity level of lake water, we need to divide the amount of dissolved toxins per liter by the maximum safe amount and convert it to a percentage.
Given that the lake currently has 0.86 milligrams of dissolved toxins per liter of water and the maximum safe level is 1.04 milligrams per liter, we calculate the toxicity level using the following steps:
Therefore, the correct answer is C. 83%.
What is the ordered pair if reflected (4, -6) over the y- axis
Answer:
reflection over the y- axis is x=0
so x will be negative.
(4,-6) will be (-4,-6)
A husband and wife, Mike and Lori, share a digital music player that has a feature that randomly selects which song to play. A total of 2,384 songs were loaded onto the player, some by Mike and the rest by Lori. Suppose that when the player was in the random-selection mode, 13 of the first 50 songs selected were songs loaded by Lori. (a) Construct and interpret a 90 percent confidence interval for the proportion of songs on the player that were loaded by Lori. (b) Mike and Lori are unsure about whether the player samples the songs with replacement or without replacement when the player is in random-selection mode. Explain why this distinction is not important for the construction of the interval in part (a).
Answer:
Check the explanation
Step-by-step explanation:
Kindly check the attached image for the step by step explanation of the answer to the question
Estimate the square root to the nearest tenth.
0.39
The square root is approximately
Answer: 0.36 = 0.6
Step-by-step explanation:
Mirele needs to buy fencing to completely surround her backyard pool. How much fencing should she buy? A pool has a length of 31.74 feet and a height of 14.85 feet. 29.70 feet 63.48 feet 66.35 feet 93.18 feet
Answer:
93.18 feet
Step-by-step explanation:
Given:
Length of backyard pool = 31.74 feet
Height of backyard pool = 14.85 feet
To find: Length of fencing bought by Mirele
Solution:
To find the length of fencing bought by Mirele, use the formula for the perimeter of a rectangular pool.
Length of fencing bought by Mirele = 2 ( length + height ) = 2 ( 31.74 + 14.85 ) = 2 ( 46.59 ) = 93.18 feet
Answer:
93.18 feet
Step-by-step explanation:
What is the constant of proportionality in the equation? y = 5 x
Answer:
5
Step-by-step explanation:
Answer:
5
Step-by-step explanation:
What is the sum of a regular octagon?
A.) 540
B.) 360
C.) 1080
D.) 900
Answer:
The answer is C.
Step-by-step explanation:
(n-2) * 180
(8-2) * 180
(6) * 180
1080
A fifth grade class sets up 418 chairs for a graduation ceremony. Each row has 22 chairs.
How many rows of chairs does the class set up? Enter your answer in the box.
Answer:
19
Step-by-step explanation: all you have to do is divide 418 by 22, and u can use long division...Final answer:
The class set up 19 full rows of chairs for the graduation ceremony by dividing the total number of chairs, 418, by the number of chairs in each row, 22.
Explanation:
To determine how many rows of chairs the fifth grade class set up for a graduation ceremony, we divide the total number of chairs by the number of chairs in each row. They have set up a total of 418 chairs, and each row contains 22 chairs.
Divide the total number of chairs (418) by the number of chairs per row (22).
Perform the division: 418 ÷ 22 = 19.
The result is that they set up 19 full rows of chairs.
HELP ME ASAP! Will give BRAINLIEST! Please read the question THEN answer correctly! No guessing.
Answer:
D
Step-by-step explanation:
This function resembles that of the absolute value function, never going into the negative y values. Hope this helps!
Maria has promised her neighbor to plant spring flowers in his garden. If the area is 250 square feet and she has completed 1/3 of it, how many square feet does she have left to plant flowers
Answer:
She still has 166.67 square feet does she have left to plant flowers
Step-by-step explanation:
The sum of total area planted, and the remaining area left to plant, is 100% = decimal 1.
She has planted 1/3 of the area. So
[tex]\frac{1}{3} + p = 1[/tex]
[tex]p = 1 - \frac{1}{3}[/tex]
[tex]p = \frac{3-1}{3}[/tex]
[tex]p = \frac{2}{3}[/tex]
So she still has to paint two thirds of the area.
The area is of 250 square feet.
2/3 of 250
[tex]250\frac{2}{3} = 166.67[/tex]
She still has 166.67 square feet does she have left to plant flowers
Jessie has some chickens and rabbits. There are 30 heads and 76 legs in all. How many chickens and rabbits does Jessie have?
Describe what you did in attempting to solve this problem.
How do you know the solution is correct?
Answer:
There are 22 chickens and 8 rabbits
Step-by-step explanation:
1 chicken = 2 legs
1 rabbit = 4 legs
we need to do 2 equations to solve this problem
c + r = 30
c*2 + r*4 = 76
we clear c in the first equation
c + r = 30
c = 30 - r
we replace c with (30 - r) in the second equation
(30 - r) * 2 + r * 4 = 76
60 - 2r + 4r = 76
-2r + 4r = 76 - 60
2r = 16
r = 16/2
r = 8
now we replace r in the first equation
c = 30 - r
c = 30 - 8
c = 22
There are 22 chickens and 8 rabbits
Do you know that you have the correct solution because you can verify it by multiplying
22 * 2 + 8 * 4 =
44 + 32 = 76
What’s the first answer I’m it’s very easy I just need help thanks
Answer:121
Step-by-step explanation:
11 times 11.
Answer:
[tex]121[/tex]
Step-by-step explanation:
[tex]11^{2} \\ write \: the \: exponentiation \: as \\ multiplication. \\ \\ 11 \times 11 \\ multiply \\ \\ 121[/tex]
Write -9.42 as a mixed number.
Answer:
-9 21/50
Step-by-step explanation:
Can someone answer this plz ?
Suppose an online auction website has roughly 500,000 users, and as each member signs up for an account,he or she is assigned a number. which of these would result in the smallest sample size using systematic sampling?
A. Surveying each 50,000th number
B. Surveying every 50th number
C. Surveying every 5000th number
D. Surveying every 500th number
The systematic sampling method that would result in the smallest sample size is A. Surveying each 50,000th number.
Which sampling would give the smallest sample size?The sample size that is given will depend on the number that the systematic sampling model uses. The higher the number, the smaller the sample size.
If each 50,000th number is being surveyed then the sample size would be:
= 500,0000 / 50,000
= 10 users
This is the smallest sample size that can be acquired here.
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In order to determine the average price of hotel rooms in Atlanta, a sample of 64 hotels was selected. It was determined that the average price of the rooms in the sample is $105. The population standard deviation is known to be $16. Calculate the value of the test statistic that you would use to test the hypothesis that the average room price is significantly different from $108.50. (Round your answer to two decimals.)
Answer:
9.76
Step-by-step explanation:
I am very smart
In England,mass is measured in units called stones, one pound equals 1/14 of a stone. A cat weighs 3/4 stone. How many pounds does the cat weigh?
Answer:
Read below for the answer
Step-by-step explanation:
1 pound = 1/14 stone
[multiply by 14]
14 pounds = 1 stone
[multiply by 3]
42 pounds = 3 stone
[divide by 4]
42 / 4 pounds = 3/4 stone
[simplify]
21 /2 = 10.5 pounds = 3/4 stone
Answer: i dont now
Step-by-step explanation:
Roberta grows pea plants, some in shade and some in sun. She picks 8 plants of each type at random and records the heights. Shade plant heights (in.) 7 12 12 8 9 8 8 8 Sun plant heights (in.) 19 24 20 23 24 23 23 20
Answer: 2.6
Step-by-step explanation:
Step 1: Calculate the mean of Shade's plant heights.
= 7+12+12+8+9+8+8+8/8
= 72/8
=9
Step 2: Calculate the range of Shade's plant heights. Range is highest minus lowest number. This will be:
12 - 7 = 5
Step 3: Calculate the mean of Sun plant heights.
19+24+20+23+24+23+23+20/8
= 176/8
= 22
Step 4: Find the range of Sun plants height.
= 24 - 19 = 5
Step 5: Find the difference of means
= 22 - 9
= 13
Step 6: Divide the difference of means by the range.
= 13 ÷ 5
= 2.6
The difference in mean and range are 13 and 0 respectively.
We are to find the difference in mean and range of the plant height.
Given the Shade plant heights expressed as 7 12 12 8 9 8 8 8
Mean = 7 + 12+12+ 8+ 9+ 8+ 8+ 8
Mean = 72
Sample size = 8
Mean of shade heights plant = 72/8 = 9Range = Highest value - Lowest value
Range = 21 - 7
Range = 5Given the Sun plant heights expressed as 19 24 20 23 24 23 23 20
Mean = 19+ 24+ 20+ 23+ 24+ 23+ 23+ 20
Mean = 176
Sample size = 8
Mean of shade heights plant = 176/8 = 22Range = Highest value - Lowest value
Range = 24 - 19
Range = 5Evaluate the difference in mean
Difference in mean = 22 - 9
Difference in mean = 13
Evaluate the difference in range
Difference in range = 5 - 5
Difference in range = 0
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Nella and Lydia are hiking 15 miles today. After every 0.5 mile, they will stop and rest. How many times will they rest during the hike? 15 miles divided by 0.5
Answer: 30
Step-by-step explanation:
By dividing 15 miles by 0.5 miles, we find that there are 30 segments. Since Nella and Lydia do not rest at the start, they take one rest less than the number of segments, resulting in 29 rests during their hike.
Explanation:The student is trying to determine the number of times Nella and Lydia will rest during a 15 mile hike if they stop after every 0.5 mile. The calculation involves dividing the total distance (15 miles) by the distance between rests (0.5 miles).
To find the number of rests, we perform the following calculation:
Divide 15 miles by 0.5 miles to find the number of segments in the hike.15 miles ÷ 0.5 miles per rest = 30 rests.However, we need to consider that they do not rest at the start, only after each 0.5 mile. Hence, the total number of rests would be one less than the total number of segments.
30 segments - 1 = 29 rests.
Therefore, Nella and Lydia will rest 29 times during their hike.
An economist conducted a study of the possible association between weekly income and weekly grocery expenditures. Of particular interest was whether higher income would result in shoppers to spending more on groceries. A random sample of shoppers at a local supermarket was obtained. A questionnaire was administered asking about the weekly income of each shoppers family and their grocery bill for that week. The explanatory variable is: g
An economist conducted a study of the possible association between weekly income and weekly grocery expenditures. Of particular interest was whether higher income would result in shoppers spending more on groceries. A random sample of shoppers at a local supermarket was obtained. A questionnaire was administered asking about the weekly income of each shopper's family and their grocery bill for that week. The explanatory variable is:
A. weekly income.
B. weekly expenditure.
C. gender.
D. None of the answer options is correct
Answer:
A. weekly income.
Step-by-step explanation:
Explanatory variables are variables that shows the difference in response variables, the explanatory variable influences the response variable. It is an independent variable that can be manipulated. The independent variable helps explain the response variable.
In this case, the explanatory variable is the weeky income because the respose variable (weekly expenditure) variation depends on it. The economist wants to use the weekly income of each shoppers family to determine how much they will spend on groceries. So, the weekly income is the explanatory variable.
helphelphelphelphelphelphelphelphelphelphelp
The X-intercept (-250, 0)
The Y-intercept (0, 100)
These are the Y and X intercepts because this the first time the line intercepts. I hope I explained it well...
Have a good day!