If 30 percent of the people surveyed use both of the methods "exercise near home or work" and "exercise outdoors", what percent of people surveyed use at least one of the two methods?
A 26%
B 52%
C 56%
D 74%
E 86%
Answers
A. 26%
There are 30% people who use both methods, Exercise near home or work and Exercise outdoor.
There are 46% people who prefer exercise near home or office rather than outdoor.
There are 40% people who prefer exercise outdoor rather than near home or office.
Then there are 30% people among them who use both methods. The remaining 26% people use one of the method.
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You are starting a sock company. You must determine your costs to manufacture your product. The start-up cost is $2000 (which helps you purchase sewing machines). Material and labor is $2.50 per pair of socks.
a. Write an equation to model your company’s cost for manufacturing the socks. (i.e. y=mx+b)
b. Which variable represents the domain? Explain your answer.
c. What is the domain for this situation?
d. Which variable represents the range? Explain your answer.
e. What is the range for this situation?
f. Using your equation, what would be the cost of manufacturing 25 pairs of socks?
g. How many socks could you make with $2500?
h. Create a coordinate graph on a sheet of paper to represent this situation. Describe the graph. Include the dimensions you would use for the x and y axes.
PLS HELP ASAP!
Answers
a. y = 2.5x + 2000
b. The variable x represents the domain because the domain is the range of the possible x values.
c. x ≥ 0
d. The variable y represents the range because the range is the range of the possible y values.
e. y ≥ 2000
f. y = 2.5(25) + 2000
y = 62.5 + 2000
y = $2062.50
g. 2500 = 2.5x + 2000
2.5x = 500
x = 200
h. I am sorry I cannot make the graph but hopefully you can figure out how to make it using the info I have given in the above parts of the problem :)
Find the sum to infinity of the series 2+5/4+11/16+23/64+..........up to the infinity.
infinity
Answers
We have
[tex]2+\dfrac54+\dfrac{11}{16}+\dfrac{23}{64}+\cdots=\displaystyle\sum_{n=0}^\infty\frac{3\cdot2^n-1}{4^n}[/tex]
(notice that each denominator is a power of 4, and each numerator is one less than some multiple of 3, in particular 3 times some power of 2)
Recall for [tex]|x|<1[/tex], we have
[tex]\displaystyle\frac1{1-x}=\sum_{n=0}^\infty x^n[/tex]
So we have
[tex]\displaystyle\sum_{n=0}^\infty\frac{3\cdot2^n-1}4=3\sum_{n=0}^\infty\left(\frac12\right)^n-\sum_{n=0}^\infty\left(\frac14\right)^n=\frac3{1-\frac12}-\frac1{1-\frac14}=\boxed{\frac{14}3}[/tex]
Suppose 55 percent of the customers at Pizza Palooza order a square pizza, 72 percent order a soft drink, and 48 percent order both a square pizza and a soft drink. Is ordering a soft drink independent of ordering a square pizza?
Answers
Answer: No, the orders are not independent.
Step-by-step explanation:
If event 1 has some possible outcomes, suppose that we choose a given outcome 1 with a probability P1, and event 2, also with different possible outcomes, we can select an outcome 2, that has a probability P2, and the two events are independent (meaning that the outcome in event 1 does not affect the outcome in event 2, and vice versa)
Then the probability of outcome 1 and outcome 2 happening at the same time is equal to the product of their individual probabilities.
P = P1*P2.
In this case, event 1 is the selection of the pizza, and outcome 1 is the selection of the square pizza, with a probability of 55%.
Event 2 is the selection of the drink, outcome 2 is the order of a soft drink, with a probability of 72%.
If those two events were independent, then the probability that a customer orders a square pizza and a soft drink would be:
P = 0.55*0.72 = 0.396 (or 39.6%)
But we know that the actual probability is 48%.
So this is larger, which means that the outcomes are not independent.
Below are the data collected from two random samples of 500 American adults on the number of hours they spend doing leisure and sports activities per
day (rounded to the nearest hour)
Number of hours spent doing leisure and sports activities per day
Sample A: Number of adults
70 90 135 140 65
Sample B: Number of adults
80 80 130 135 75
Dan concludes that adults spend a mean of 3 hours each day doing leisure and sports activities. Bret thinks the mean is 4 hours. Who is correct-Dan or Bret?
Explain your answer in two or three sentences. Make sure to use facts to support your answer.
Answers
Dan is Correct by concluding that adults spend a mean of 3 hours each day doing leisure and sports activities. because [tex]3.08[/tex] hours or [tex]3.09[/tex] hours which are the mean time of sample A and B is approximately equal to 3 hours
From the question we are told that:
Total Sample size [tex]n=500[/tex]
Dan's mean [tex]\=x_D= 3hr[/tex]
Bret's mean [tex]\=x_D= 4hr[/tex]
Generally, the Total hours spent doing leisure and sports activities is mathematically given by
For Sample A
[tex]T_a=(1*70)+(2*90)+(3*135)+(4*140)+(5*65)\\\\[/tex]
[tex]T_a=1540 hours[/tex]
For Sample B
[tex]T_b=(1*80)+(2*80)+(3*130)+(4*135)+(5*75)[/tex]
[tex]T_b=1545[/tex]
Therefore
Mean Time spent doing leisure and sports activities by an American Adult
For Sample A
[tex]T_A=\frac{T_a}{n}[/tex]
[tex]T_A=\frac{1540}{500}[/tex]
[tex]T_A=3.08[/tex] hours
[tex]T_A \approx 3[/tex] hours
For Sample B
[tex]T_A'=\frac{T_b}{n}[/tex]
[tex]T_A'=\frac{1545}{500}[/tex]
[tex]T_A'=3.09[/tex] hours
[tex]T_A' \approx 3[/tex] hours
In conclusion
Dan is Correct because [tex]3.08[/tex] or [tex]3.09[/tex] which are the mean time of sample A and B is approximately equal to [tex]3[/tex]
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I really need help i will rate you branliest
Answers
Work Shown:
A = P*(1+r)^t
A = 21450*(1+(-0.08))^5
A = 21450*(1-0.08)^5
A = 21450*(0.92)^5
A = 21450*0.6590815232
A = 14137.29867264
A = 14,137.30
Notice how I used a negative r value to indicate depreciation rather than growth.
The average person lives for about 78 years. Does the average person live for at least 1,000,000, minutes? (Hint: There are 365 days in each year, hours in 24 each day, and 6o minutes in each hour.)
Answers
Answer:
YES
Step-by-step explanation:
1 million minutes = 1.9 years
An average man can live upto 78 years.
So, an average man can easily live upto 1,000,000.
Answer:
There will be (365 x 24 x 60) minutes each year.
and that is 525600.
and 525600 x 78 is 40,996,800.
so, It is definitely more than 1 million minutes.
Hop it helps!
Bye!
Consider a normal population with a mean of 10 and a variance of 4. Find P(x < 6)
Answers
Answer: .0228
Step-by-step explanation: z = (6 − 10)/√4 = −2
P(X < 6) = .0228
The monthly cost (in dollars) of water use is a linear function of the amount of water used (in hundreds of cubic feet, HCF). The cost for using 15 HCF of water is 32.84, and the cost for using 43 HCF is 79.04. What is the cost for using 36 HCF of water?
Answers
Answer:
67.49
Step-by-step explanation:
Let the number of HCF be x.
Let the cost be y.
You are given 2 points of a line: (15, 32.84) and (43, 79.04).
Now we find the equation of the line that passes through those points.
y - y1 = m(x - x1)
y - 32.84 = [(79.04 - 32.84)/(43 - 15)](x - 15)
y - 32.84 = (46.2/28)(x - 15)
y - 32.84 = 1.65(x - 15)
y = 1.65x - 24.75 + 32.84
y = 1.65x + 8.09
Now we let x = 36 and solve for y.
y = 1.65(36) + 8.09
y = 67.49
Question 3 (2 marks)
Reginald is a furniture salesman. He is paid a weekly retainer of $370 plus 4.5% of the
value of furniture he sells. Calculate his income for a week when he sells $67 000 worth
of furniture.
752 words
09 English (Australia)
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ENG
Answers
Answer:
$3385 per week
Step-by-step explanation:
so, he gets $370 plus 4.5% of what he is selling.
$67000 = 100% of selling
1% = 100%/100 = 67000/100 = $670
4.5% = 1% × 4.5 = 670 × 4.5 = $3015
so, he gets $370 + $3015 = $3385 per week
Can anyone help me please??
Answers
Answer:
-20x / (x-12) = y
Step-by-step explanation:
3/x - 5/y = 1/4
Multiply each side by 4xy to clear the fractions
4xy ( 3/x - 5/y = 1/4)
Distribute
12y - 20x = xy
Subtract 12y from each side
-20x = xy -12y
Factor out y
-20x = y(x-12)
Divide each side by (x-12)
-20x / (x-12) = y
WILL GIVE BRAINLYEST AND 30 POINTS Which of the followeing can be qritten as a fraction of integers? CHECK ALL THAT APPLY 25 square root of 14 -1.25 square root 16 pi 0.6
Answers
Answer:
25 CAN be written as a fraction.
=> 250/10 = 25
Square root of 14 is 3.74165738677
It is NOT POSSIBLE TO WRITE THIS FULL NUMBER AS A FRACTION, but if we simplify the decimal like: 3.74, THEN WE CAN WRITE THIS AS A FRACTION
=> 374/100
-1.25 CAN be written as a fraction.
=> -5/4 = -1.25
Square root of 16 CAN also be written as a fraction.
=> sqr root of 16 = 4.
4 can be written as a fraction.
=> 4 = 8/2
Pi = 3.14.........
It is NOT POSSIBLE TO WRITE THE FULL 'PI' AS A FRACTION, but if we simplify 'pi' to just 3.14, THEN WE CAN WRITE IT AS A FRACTION
=> 314/100
.6 CAN be written as a fraction.
=> 6/10 = .6
is 9 bigger than -10
Answers
Answer:
9 is a positive number and -10 is negative. Positive numbers are bigger than negative numbers so yes 9 is bigger than -10
Step-by-step explanation:
Answer:
Yes it is
Step-by-step explanation:
here is how the numbers appear numerically
-10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
The graph shown below expresses a radical function that can be written in the form f(x)=a(x+k)^1/n + c. What does the graph tell you about the value of n in this function?
Answers
Answer: n is a positive odd number.
Step-by-step explanation:
Ok, we know that the function is something like:
f(x)=a(x+k)^1/n + c
In the graph we can see two thigns:
All the values of the graph are positive values (even for the negative values of x), but in the left side we can see that the function decreases and is different than the right side.
So this is not an even function, then n must be an odd number (n odd allows us to have negative values for y = f(x) that happen when x + k is negative).
Also, we can see that the function increases, if n was a negative number, like: n = -N
we would have:
[tex]f(x) = \frac{a}{(x+k)^{1/N}} + c[/tex]
So in this case x is in the denominator, so as x increases, we would see that the value of y decreases, but that does not happen, so we can conclude that the value of n must be positive.
Then n is a positive odd number.
Answer:
D) Positive Even Integer
Step-by-step explanation:
just did it
The mean income per person in the United States is $41,500, and the distribution of incomes follows a normal distribution. A random sample of 10 residents of Wilmington, Delaware, had a mean of $47,500 with a standard deviation of $10,600. At the .01 level of significance, is that enough evidence to conclude that residents of Wilmington, Delaware, have more income than the national average?
(a) State the null hypothesis and the alternate hypothesis.
H0: ? ?
H1: ? >
(b) State the decision rule for .01 significance level. (Round your answer to 3 decimal places.)
Reject H0 if t >
(c) Compute the value of the test statistic. (Round your answer to 2 decimal places.)
Value of the test statistic
(d) Is there enough evidence to substantiate that residents of Wilmington, Delaware have more income than the national average at the .01 significance level?
Answers
Answer:
A) Null Hypothesis; H0: μ = $41,500
Alternative hypothesis; H1: μ > $41,500
B) Reject H0 is t > 2.821433
C) t = 1.79
D) there is no sufficient evidence to support the claim that residents of Wilmington, Delaware have more income than the national average
Step-by-step explanation:
A) The hypotheses is given as;
Null Hypothesis; H0: μ = $41,500
Alternative hypothesis; H1: μ > $41,500
B) From online t-score calculator attached using significance level of 0.01 and DF = n - 1 = 10 - 1 = 9, we have;
t = 2.821433
Normally, when the absolute value of the t-value is greater than the critical value, we reject the null hypothesis. However, when the absolute value of the t-value is less than the critical value, we fail to reject the null hypothesis.
Thus, if t > 2.821433, we will reject the null hypothesis H0.
C) Formula for the test statistic is;
t = (x' - μ)/(s/√n)
We have, μ = 41500, x' = 47500, s = 10600, n = 10
t = (47500 - 41500)/(10600/√10)
t = 1.79
D) So, 1.79 is less than the t-critical value of 2.821433. Thus, we will fail to reject the null hypothesis and conclude that there is no sufficient evidence to support the claim that residents of Wilmington, Delaware have more income than the national average
Turn 43 1/23 into an improper fraction
Answers
Answer:
990/23
Step-by-step explanation:
Step 1
Multiply the denominator by the whole number
23 × 43 = 989
Step 2
Add the answer from Step 1 to the numerator
989 + 1 = 990
Step 3
Write answer from Step 2 over the denominator
990/23
I hope this answer helps you out! Brainliest would be appreciated.
What is the product of the polynomials below?
(8x2 - 4x-8)(2x +3x+2)
A. 16x4 +16x° - 12x2 - 16x-6
B. 16x4 +16x? - 12x2 - 16x-16
C. 16x4 +16x° - 12x2 – 32x-16
D. 16x4 +16 x° - 12x2 - 32x-6
Answers
Answer:
16x⁴+16x³-12x²-32x-16
Step-by-step explanation:
(8x²-4x-8)(2x²+3x+2)
= 16x⁴+24x³+16x²-8x³-12x²-8x-16x²-24x-16
= 16x⁴+16x³-12x²-32x-16
HELP ASAP PLEASE I WILL MARK BRAINLEST
Show all work to identify the asymptotes and zero of the function f of x equals 6 x over quantity x squared minus 36.
Answers
Answer:
vertical asymptotes
x=6, x=-6
horizontal asymptotes
y=0
zeros (0,0)
Step-by-step explanation:
f(x) = 6x / ( x^2 - 36)
First factor
f(x) = 6x / ( x-6)(x+6)
Since nothing cancels
The vertical asymptotes are when the denominator goes to zero
x-6 = 0 x+6=0
x=6 x= -6
Since the numerator has a smaller power than the denominator (1 < 2), there is an asymptote at y = 0
To find the zeros, we find where the numerator = 0
6x=0
x=0
[tex]\\ \rm\Rrightarrow y=\dfrac{6x}{x^2-36}[/tex]
The h orizontal asymptote
As x has less degree than x²
y=0 is a asymptoteVertical asymptote
x²-36=0x²=36x=±6This table shows a linear relationship.
The slope of the line is ?
Answers
Answer:
2
Step-by-step explanation:
2,8 to 4,12 has a rise of 4 and a run of 2.
4/2 = 2
The slope is 2.
Remember rise/run!
Answer:
2
Step-by-step explanation:
We take take two points and use the slope formula
m = (y2-y1)/(x2-x1)
m = (12-8)/(4-2)
= 4/2
= 2
The letters x and y represent rectangular coordinates. Write the given equation using polar coordinates (r,θ) . Select the correct equation in polar coordinates below.
x2+y2−4x=0
a. r=4 sinθ
b. r=4 cosθ
c. r cos2θ=4 sinθ
d. r sin2θ=4 cosθ
Answers
Answer:
B. r = 4cosθStep-by-step explanation:
Given the expression in rectangular coordinate as x²+y²−4x=0, in order to write the given expression in polar coordinates, we need to write the value of x and y as a function of (r, θ).
x = rcosθ and y = rsinθ.
Substituting the value of x and y in their polar form into the given expression we have;
x²+y²−4x=0
( rcosθ)²+( rsinθ)²-4( rcosθ) = 0
Expand the expressions in parenthesis
r²cos²θ+r²sin²θ-4rcosθ = 0
r²(cos²θ+sin²θ)-4rcosθ = 0
From trigonometry identity, cos²θ+sin²θ =1
The resulting equation becomes;
r²(1)-4rcosθ = 0
r²-4rcosθ = 0
Add 4rcosθ to both sides of the equation
r²-4rcosθ+4rcosθ = 0+4rcosθ
r² = 4rcosθ
Dividing both sides by r
r²/r = 4rcosθ/r
r = 4cosθ
Hence the correct equation in polar coordinates is r = 4cosθ
Find the missing probability. P(A)=7/20,P(A∪B)=191/400,P(A∩B)=49/400 ,P(B)=? A. 7/8 B. 1/4 C. 117/400 D. 19/40
Answers
Answer:
B
Step-by-step explanation:
P(AUB)=P(A)+P(B)-P(A∩B)
191/400=7/20+P(B)-49/400
P(B)=191/400+49/400-7/20=240/400-7/20=12/20-7/20=5/20=1/4
The value of P(B) is 1/4.
What is probability?The probability is defined as the possibility of an event is equal to the ratio of the number of favorable outcomes and the total number of outcomes.
For an experiment having q number of outcomes, the number of favorable outcomes can be denoted by p. The formula to calculate the probability of an event is as follows:
Probability(Event) = Favorable Outcomes/Total Outcomes = p/q
Given data as :
P(A) = 7/20,
P(A∪B) = 191/400,
P(A∩B) = 49/400 ,
P(AUB) = P(A) + P(B) - P(A∩B)
Substitute the values of P(A), P(A∪B) and P(A∩B) in formula,
191/400 = 7/20 + P(B) - 49/400
Rearrange the terms in the equation,
P(B) = 191/400 + 49/400 - 7/20
P(B) = 240/400 - 7/20
P(B) = 12/20 - 7/20
P(B) = 5/20
P(B) = 1/4
Hence, the value of P(B) is 1/4.
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Hello Help Plis…………..
Answers
Answer:
7. 20 + 5 + 3/10 + 6/100
8. 7 + 4/10 + 2/100 + 5/1000
Step-by-step explanation:
We are writing two numbers in expanded form, to help, we can use the guide above both numbers. Expanded form is all about breaking apart a number by place value and putting them in an additional sequence.
Let's look at 7, 25.36.
There are the tens, ones, tenths, and hundredths place being used, therefore :
20 + 5 + 3/10 + 6/100
We can do the same for 8, 7.425.
There are ones, tenths, hundredths, and thousandths being used, therefore :
7 + 4/10 + 2/100 + 5/1000
A random sample of 12 supermarkets from Region 1 had mean sales of 84 with a standard deviation of 6.6. A random sample of 17 supermarkets from Region 2 had a mean sales of 78.3 with a standard deviation of 8.5. Does the test marketing reveal a difference in potential mean sales per market in Region 2? Let μ1 be the mean sales per market in Region 1 and μ2 be the mean sales per market in Region 2. Use a significance level of α=0.02 for the test. Assume that the population variances are not equal and that the two populations are norm
Answers
Answer:
We conclude that there is no difference in potential mean sales per market in Region 1 and 2.
Step-by-step explanation:
We are given that a random sample of 12 supermarkets from Region 1 had mean sales of 84 with a standard deviation of 6.6.
A random sample of 17 supermarkets from Region 2 had a mean sales of 78.3 with a standard deviation of 8.5.
Let [tex]\mu_1[/tex] = mean sales per market in Region 1.
[tex]\mu_2[/tex] = mean sales per market in Region 2.
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu_1-\mu_2[/tex] = 0 {means that there is no difference in potential mean sales per market in Region 1 and 2}
Alternate Hypothesis, [tex]H_A[/tex] : > [tex]\mu_1-\mu_2\neq[/tex] 0 {means that there is a difference in potential mean sales per market in Region 1 and 2}
The test statistics that will be used here is Two-sample t-test statistics because we don't know about population standard deviations;
T.S. = [tex]\frac{(\bar X_1 -\bar X_2)-(\mu_1-\mu_2)}{s_p \times \sqrt{\frac{1}{n_1}+ {\frac{1}{n_2}}} }[/tex] ~ [tex]t__n_1_+_n_2_-_2[/tex]
where, [tex]\bar X_1[/tex] = sample mean sales in Region 1 = 84
[tex]\bar X_2[/tex] = sample mean sales in Region 2 = 78.3
[tex]s_1[/tex] = sample standard deviation of sales in Region 1 = 6.6
[tex]s_2[/tex] = sample standard deviation of sales in Region 2 = 8.5
[tex]n_1[/tex] = sample of supermarkets from Region 1 = 12
[tex]n_2[/tex] = sample of supermarkets from Region 2 = 17
Also, [tex]s_p=\sqrt{\frac{(n_1-1)\times s_1^{2}+(n_2-1)\times s_2^{2} }{n_1+n_2-2} }[/tex] = [tex]s_p=\sqrt{\frac{(12-1)\times 6.6^{2}+(17-1)\times 8.5^{2} }{12+17-2} }[/tex] = 7.782
So, the test statistics = [tex]\frac{(84-78.3)-(0)}{7.782 \times \sqrt{\frac{1}{12}+ {\frac{1}{17}}} }[/tex] ~ [tex]t_2_7[/tex]
= 1.943
The value of t-test statistics is 1.943.
Now, at a 0.02 level of significance, the t table gives a critical value of -2.472 and 2.473 at 27 degrees of freedom for the two-tailed test.
Since the value of our test statistics lies within the range of critical values of t, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region.
Therefore, we conclude that there is no difference in potential mean sales per market in Region 1 and 2.
Divide.round your answer to the nearest hundredth 1divide 3
Answers
Answer:
.33
Step-by-step explanation:
Hey there!
1 / 3
= .333333333
.33 rounded to the nearest hundredth
Hope this helps :)
(2²)³+(2³)²/4
Simplificar
Answers
━━━━━━━☆☆━━━━━━━
▹ Answer
80
▹ Step-by-Step Explanation
(2²)³ + (2³)² ÷ 4
Rewrite:
2⁶ + 2⁶ ÷ 2²
Divide:
2⁶ + 2⁴
Factor:
(2² + 1) * 2⁴
Evaluate:
(4 + 1) * 2⁴
Calculate:
5 * 16
= 80
Hope this helps!
CloutAnswers ❁
━━━━━━━☆☆━━━━━━━
In the last 10 years, the population of Indonesia has grown at a rate of 1.12% per year to 258,316,051. If this rate continues, what will be the population in 10 more years? Round your answer to the nearest whole number.
Answers
Answer:
Final population after 10 years
= 288911718
Step-by-step explanation:
Present population p = 258,316,051
Rate of growth R%= 1.12%
Number of years t= 10 years
Number of times calculated n = 10
Final population A
= P(1+r/n)^(nt)
A= 258,316,051(1+0.0112/10)^(10*10)
A= 258,316,051(1+0.00112)^(100)
A= 258,316,051(1.00112)^100
A= 258,316,051(1.118442762)
A= 288911717.6
Approximately A= 288911718
Final population after 10 years
= 288911718
In particular, OLS for the multiple regression model involves selecting parameters that will minimize:___________
Answers
Answer:
Ordinary Least Square (OLS) for the multiple regression model involves selecting parameters of a straight line function that will minimize the sum of the squares of the variance in the given dataset and those forecasted by the straight-line function.
Cheers
A large population has a bell-shaped distribution with a mean of 200 and a standard deviation of 40. Which one of the following intervals would contain approximately 95% of the measurements?
a. (160, 240)
b. (140, 260)
c. (120, 280)
d. (200, 320)
Answers
The intervals would contain approximately 95% of the measurements will be (120, 280). Then the correct option is C.
What is a normal distribution?The Gaussian Distribution is another name for it. The most significant continuous probability distribution is this one. Because the curve resembles a bell, it is also known as a bell curve.
In numerical documentation, these realities can be communicated as follows, where Pr(X) is the likelihood capability, Χ is a perception from an ordinarily circulated irregular variable, μ (mu) is the mean of the dispersion, and σ (sigma) is its standard deviation:
The interval for 95% will be given as,
Pr(X) = μ ± 2σ
Pr(X) = 200 ± 2(40)
Pr(X) = 200 ± 80
Pr(X) = (200 - 80, 200 + 80)
Pr(X) = (120, 280)
The intervals would contain approximately 95% of the measurements will be (120, 280). Then the correct option is C.
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What is an equation of the line that passes through the points (-5, 8) and (5,0)?
Answers
Answer:
y= -0.8x + 4
Midpoint is 0,4
A certain animal's body temperature has a mean of F and a standard deviation of F. Convert the given temperatures to z scores.
Answers
A certain animal's body temperature has a mean of 94.72° F and a standard deviation of 0.57°F. Convert the given temperatures to z scores.
a. 93.52 °F b. 95.22 °F c. 94.72 °F
Answer:
a. z = - 2.1053
b. z = 0.87719
c. z = 0
Step-by-step explanation:
Given that :
The population mean μ = 94.72
The standard deviation σ = 0.57
the formula for calculating the standard normal z score, which can be represented as:
[tex]z= \dfrac{\overline x - \mu}{\sigma}[/tex]
For a.
The sample mean [tex]\bar x[/tex] = 93.52
The z score can be computed as follows:
[tex]z= \dfrac{\overline x - \mu}{\sigma}[/tex]
[tex]z= \dfrac{93.52 - 94.72}{0.57}[/tex]
[tex]z= \dfrac{-1.2}{0.57}[/tex]
z = - 2.1053
For b.
The sample mean [tex]\bar x[/tex] = 95.22
[tex]z= \dfrac{\overline x - \mu}{\sigma}[/tex]
[tex]z= \dfrac{95.22 - 94.72}{0.57}[/tex]
[tex]z= \dfrac{0.5}{0.57}[/tex]
z = 0.87719
For c.
The sample mean [tex]\bar x[/tex] = 94.72
[tex]z= \dfrac{\overline x - \mu}{\sigma}[/tex]
[tex]z= \dfrac{94.72 - 94.72}{0.57}[/tex]
[tex]z= \dfrac{0}{0.57}[/tex]
z = 0
Aaron wants to mulch his garden. His garden is x^2+18x+81 ft^2 One bag of mulch covers x^2-81 ft^2 . Divide the expressions and simplify to find how many bags of mulch Aaron needs to mulch his garden.
Answers
Answer:
Step-by-step explanation:
Given
Garden: [tex]x^2+18x+81[/tex]
One Bag: [tex]x^2 - 81[/tex]
Requires
Determine the number of bags to cover the whole garden
This is calculated as thus;
[tex]Bags = \frac{x^2+18x+81}{x^2 - 81}[/tex]
Expand the numerator
[tex]Bags = \frac{x^2+9x+9x+81}{x^2 - 81}[/tex]
[tex]Bags = \frac{x(x+9)+9(x+9)}{x^2 - 81}[/tex]
[tex]Bags = \frac{(x+9)(x+9)}{x^2 - 81}[/tex]
Express 81 as 9²
[tex]Bags = \frac{(x+9)(x+9)}{x^2 - 9\²}[/tex]
Evaluate as difference of two squares
[tex]Bags = \frac{(x+9)(x+9)}{(x - 9)(x+9)}[/tex]
[tex]Bags = \frac{(x+9)}{(x - 9)}[/tex]
Hence, the number of bags is [tex]Bags = \frac{(x+9)}{(x - 9)}[/tex]