A P-value of 0.045 suggests that there is a 4.5% chance of observing a sample proportion as extreme as 70% or more, assuming the null hypothesis is true. If the P-value<0.05 (usually considered a threshold), we typically reject the null hypothesis - here, indicating that more than 68% consider health care cost reduction a national priority.
Explanation:In statistics, a P-value is a probability that provides a measure of the evidence against the null hypothesis (H₀). A P-value of 0.045, as given in this instance, indicates that if the null hypothesis were true (i.e., 68% of U.S. adults still consider reducing health care costs a national priority), there is only a 4.5% probability of observing a sample proportion as extreme as 70% or more.
Commonly, a threshold (α) is set at 0.05 or 5%. If the P-value is less than α (which it is in this case, 0.045 < 0.05), we reject the null hypothesis in favor of the alternative hypothesis. Consequently, we conclude there is sufficient evidence to suggest that the proportion of U.S. adults this year who rate 'reducing health care costs' as a national priority is higher than 68%.
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The P-value of 0.045 provides statistically significant evidence to reject the null hypothesis and support the alternative hypothesis that the proportion of U.S. adults who rate 'reducing healthcare costs' as a national priority has increased from the previous 68%.
Explanation:In the context of this issue, the P-value of 0.045 represents the probability of observing a sample proportion as extreme as 70%, or more, given that the null hypothesis is true - the null hypothesis being that the true proportion of U.S. adults who rate 'reducing healthcare costs' as a national priority is 68%.
If the P-value is less than or equal to the significance level (in this case, 5% or 0.05), we reject the null hypothesis. Since 0.045 is indeed less than 0.05, we reject the null hypothesis, supporting the alternative hypothesis that the proportion of U.S. adults who view reducing healthcare costs as a national priority is greater than 68%.
Therefore, the P-value of 0.045 suggests there is statistically significant evidence to conclude that the perception of 'reducing healthcare costs' as a national priority has increased amongst U.S. adults recently.
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Write -9.42 as a mixed number.
Answer:
-9 21/50
Step-by-step explanation:
"If a ball of mass M is dropped from a height h onto a spring with spring constant k (whose equilibrium positions is at height 0), compresses the spring an additional distance (L/2), and then rebounds, what height will the ball reach? Express your answer symbolically."
So I was thinking something along the lines of h= M*k*(L/2) but I'm not sure :/ Any guidance?
Answer:[tex]h=\dfrac{kL^2}{8mg}[/tex]
Step-by-step explanation:
Given
Mass of ball is M is dropped from a height h
spring constant is k
Here we can use conservation of energy
Mass has a Potential energy of E=mgh
and when it falls on the spring then it compresses it a length of 0.5 L
Now potential energy is converted into Elastic potential energy and then spring unleashes this energy to the mass and again provide kinetic energy to mass to move upward .
In this way energy is conserved. So, mass must move to an initial height h
[tex]mgh=\frac{1}{2}k(\frac{L}{2})^2[/tex]
[tex]h=\dfrac{kL^2}{8mg}[/tex]
considering [tex]h >> 0.5L[/tex]
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.
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!
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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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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What is the constant of proportionality in the equation? y = 5 x
Answer:
5
Step-by-step explanation:
Answer:
5
Step-by-step explanation:
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.
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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Insurance company records indicate that 14% of its policyholders file claims involving theft or robbery of personal property from their homes. Suppose a random sample of 500 policyholders is selected. What is the standard deviation of the sampling distribution of the sample proportion of policyholders filing claims involving theft or robbery from their homes?
Answer:
Standard deviation = 7.76
Step-by-step explanation:
The formula for determining standard deviation when dealing with population proportion is expressed as
Standard deviation = √npq
Where
n represents the number of samples from the population.
p represents the probability of success.
q represents the probability of failure.
From the information given,
n = 500 policyholders
p = 14% = 14/100 = 0.14
q = 1 - 0.14 = 0.86
Standard deviation = √500 × 0.14 × 0.86 = 7.76
Answer: std dev = 0.01552
Step-by-step explanation:
we will solve this by taking a step by step analysis of the problem.
i hope at the end of this section, you will feel confident to try out other questions.
given that the size of the sample (n) = 500
The Insurance company records indicate that 14% of its policyholders file claims involving theft or robbery of personal property from their homes.
hence sample proportion of policyholders filing claims involving theft or robbery from their homes (p) = 14% =0.14
let Z be the number of policyholders files involving theft or robbery of personal property from their homes.
so Z~Bin(500,0.14) and p=Z/500
we know from basic mathematics that standard deviation = √(variance)
so variance is given thus;
V[Z] = 500*0.14*(1-0.14)
or V[p] = V[Z/500] = 500*0.14*0.86/500² = 0.14*0.86/500
so standard deviation is;
sqrt[V[p]]=sqrt(0.14*0.86/500) = sqrt(0.0002408) = 0.01552
∴ the standard deviation = 0.01552
cheers i hope this helps!!!!
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
Which one of the properties described below DOES NOT apply to the perpendicular bisector of a segment?
A) It must be longer than the original segment.
B) It is perpendicular to (makes a 90 angle with) the original segment.
C) It divides the original segment into two equal pieces.
D) Every point on the perpendicular bisector is the same distance from both endpoints of the segment.
Answer: C
Step-by-step explanation: It divides the original segment into two equal pieces
The properties that do not apply for the perpendicular bisector should be option c. that it divides the original segment to two equal pieces.
Properties that applied to the perpendicular bisector of a segment:It should be more than the original segment. It should be perpendicular for making 90 angles along with the original segment. Also, each and every point on the perpendicular bisector should contain a similar distance that lies from the segment endpoints.Learn more about segment here: https://brainly.com/question/2818266
Think about the properties of a square. Is a square also a rhombus? Is it also a rectangle? Answer each question and explain your answers. Write two to four sentences.
Yes, a square can be considered as a rhombus and a rectangle both.
What is a square?The square is a quadrilateral with all sides equal and all angles equals to 90° and having equal diagonals.
Square being a rhombus and a rectangle :-
Rhombus :-
It has it's all sides equal having their diagonals equal and intersect at right angle rhombus is a parallelogram so a square, all the properties that a rhombus holds are also the properties of a square, so we can say a square can be considered as a rhombus.
Rectangle :-
A square is always a rectangle because, it has all the properties of a rectangle, such as parallel and equal opposite sides, vertex angles being a right angle, diagonals being equal.
Hence, a square can be considered as a rhombus and a rectangle both.
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Final answer:
A square is both a rhombus and a rectangle because it has four equal sides and four right angles, fulfilling the criteria for both shapes.
Explanation:
A square indeed has all the properties of a rhombus, which is a parallelogram with four equal sides, and it also has the properties of a rectangle, which is a quadrilateral with four right angles. Since a square has four equal sides and four right angles, it satisfies the criteria to be called both a rhombus and a rectangle. Therefore, the answer is yes; a square is both a rhombus and a rectangle.
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.
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]
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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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
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.
Please Help!!!!! ...................................
Answer:
divide 252 by 7 and you get 36
Step-by-step explanation:
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:
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 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)
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%.
David wants to buy a 6-foot long sandwich for a birthday party. If the sandwich costs $72.00, what is the cost per foot?
Answer:
$12 per foot
Step-by-step explanation:
$72.00 divided by 6 is $12
Answer:
The cost per foot of the sandwich is $12.
Step-by-step explanation:
You need to use division for this problem.
Pretend you are cutting the 6-foot sanwhich into 1-foot pieces. You will have 6 pieces. You have to give each piece an equal amount of money. Think about your 6-times tables. What times 6 = 72?
__ x 6 =72
or
72/6 = __
What are the solution(s) to the quadratic equation 50 - x2 = 0?
x = +2/5
x = +63
x = 15/2
no real solution
Answer:
±5sqrt(2) = x
Step-by-step explanation:
50 - x^2 = 0
Add x^2 to each side
50 - x^2 +x^2= 0+x^2
50 = x^2
Take the square root of each side
±sqrt(50) = sqrt(x^2)
±sqrt(25*2)) = x
±sqrt(25) sqrt(2) = x
±5sqrt(2) = x
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.
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:
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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Estimate the square root to the nearest tenth.
0.39
The square root is approximately
Answer: 0.36 = 0.6
Step-by-step explanation: