Complete question :
Chef Charming and his mother sell cheese steak sandwiches at their food truck. They use fresh onions, and cook them slowly to caramelize them before putting them on their sandwiches.
Charming found a pre-cooked onion that was $8.3 per pound AP$, with 100% Yield. He wants to save money but isn't sure if that is a better deal than cooking the fresh onions himself.
He currently pays an AP$ of $1.87 per pound for fresh onions, but his yield is 50% after peeling and cooking the onions. What is the EP$ for the fresh onions, after caramelizing?
Answer:
$3.74
Step-by-step explanation:
Cost of fresh onions = $1.87 per pound
Percentage yield = 100% after caramelizing
Therefore EP$ for the fresh onions after caramelizing will be :
(1 + percentage yield) * cost of fresh onions
(1 + 100%) * $1.87
(1 + 1) * $1.87
2 * $1.87
= $3.74
Researchers fed mice a specific amount of Dieldrin, a poisonous pesticide, and studied their nervous systems to find out why Dieldrin causes seizures. The absolute refractory period, time required for nerves to recover after a stimulus, was measured and varies Normally. The measurements, in milliseconds, for six mice were 2.2, 2.4, 2.5, 2.5, 2.6, and 2.7. (10 points) Part A: Find the mean refractory period and the standard error of the mean. (2 points) Part B: Calculate a 98% confidence interval for the mean absolute refractory period for all mice when subjected to the same treatment. (4 points) Part C: Suppose the mean absolute refractory period for unpoisoned mice is known to be 2.3 milliseconds. Dieldrin poisoning should slow nerve recovery and therefore increase this period. Do the data give good evidence to support this theory? What can you conclude from a hypothesis test? Justify your response with statistical reasoning. (4 points)
Answer:
Step-by-step explanation:
Part A
Mean = (2.2 + 2.4 + 2.5 + 2.5 + 2.6 + 2.7)/6 = 2.48
Standard deviation = √(summation(x - mean)²/n
n = 6
Summation(x - mean)² = (2.2 - 2.48)^2 + (2.4 - 2.48)^2 + (2.5 - 2.48)^2 + (2.5 - 2.48)^2 + (2.6 - 2.48)^2 + (2.7 - 2.48)^2 = 0.1484
Standard deviation = √(0.1484/6
s = 0.16
Standard error = s/√n = 0.16/√6 = 0.065
Part B
Confidence interval is written as sample mean ± margin of error
Margin of error = z × s/√n
Since sample size is small and population standard deviation is unknown, z for 98% confidence level would be the t score from the student t distribution table. Degree of freedom = n - 1 = 6 - 1 = 5
Therefore, z = 3.365
Margin of error = 3.365 × 0.16/√6 = 0.22
Confidence interval is 2.48 ± 0.22
Part C
We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean
For the null hypothesis,
H0: µ = 2.3
For the alternative hypothesis,
H1: µ > 2.3
This is a right tailed test
Since the number of samples is small and no population standard deviation is given, the distribution is a student's t.
Since n = 6
Degrees of freedom, df = n - 1 = 6 - 1 = 5
t = (x - µ)/(s/√n)
Where
x = sample mean = 2.48
µ = population mean = 2.3
s = samples standard deviation = 0.16
t = (2.48 - 2.3)/(0.16/√6) = 2.76
We would determine the p value using the t test calculator. It becomes
p = 0.02
Assuming significance level, alpha = 0.05.
Since alpha, 0.05 > than the p value, 0.02, then we would reject the null hypothesis. Therefore, At a 5% level of significance, the sample data showed significant evidence that the mean absolute refractory period for all mice when subjected to the same treatment increased.
a water storage tank is in the shape of a hemisphere. If the radius is 29ft, approximate the volume of the tank in cubic feet
Answer:
The answer is 51080.2 cubic feetStep-by-step explanation:
Volume of a hemisphere is given by
[tex]V = \frac{2}{3} \pi {r}^{3} [/tex]
where r is the radius of the hemisphere
From the question
r = 29 ft
Substitute the value of r into the formula
That's
[tex]V = \frac{2}{3} \pi \times {29}^{3} [/tex]
[tex]V = \frac{48778}{3} \pi[/tex]
We have the final answer as
V = 51080.2 cubic feetHope this helps you
Please answer this correctly
Answer:
3/4
Step-by-step explanation:
There are 3 numbers greater than 1. 2, 3, and 4. Since there are 4 numbers total, we get a 3/4 chance.
Answer:
3/4
Step-by-step explanation:
There are four options and 3 of them =3 or greater than 1
P(3 or greater than 1) = 3/4
Select the two binomials that are factors of this trinomial.
x2 + 6x + 8
O A. X+4
O B. x+8
O C. X-4
O D. x+ 2
SUBMIT
Hey there! :)
Answer:
A. x + 4
D. x + 2
Step-by-step explanation:
Starting with:
x² + 6x + 8
Find numbers that add up to 6 and multiply to 8. We get:
2, 4.
Put these into the factors:
(x + 2)(x + 4)
Therefore, the correct answers are:
A. x + 4
D. x + 2
full can of milk weighs 70 pounds. If exactly half of the milk is poured out, it weighs 38 pounds. How much does the empty can weigh?
Answer:
the milk weighs less than 70 pounds
milk = 64 half of 64 = 32 difference between 32 and 38= 6 64+6 = 70
empty can =6 pounds
Answer:
38 is the weight with the can so if we subtract the total weight by the weight of half we can see how much the can weighs
70 - 38 = 32
38 - 32 = 6 so the can weighs 6 pounds.
Hope this helps
Step-by-step explanation:
Find σ. (Enter an exact number as an integer, fraction, or decimal.)
X ~ N(5, 3)
Answer:
[tex]X \sim N(\mu, \sigma)[/tex]
And from this case we can see that the deviation is given by:
[tex]\sigma = 3[/tex]
Step-by-step explanation:
For this case we have the following notation given:
[tex] X \sim N (5,3)[/tex]
And from this we know that the distribution for the random variable is normal and we know that in general the normal distribution is given by:
[tex]X \sim N(\mu, \sigma)[/tex]
And from this case we can see that the deviation is given by:
[tex]\sigma = 3[/tex]
y
X
Find the slope of the line that passes through the points
(2, -5) and (7, 1).
y
-5
6
2
7
1
Step 1: Choose (X1,Y1).
4
2.
-4
-2
2
4
6
8
Answer:
slope = [tex]\frac{6}{5}[/tex]
Step-by-step explanation:
Calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (2, - 5) and (x₂, y₂ ) = (7, 1)
m = [tex]\frac{1+5}{7-2}[/tex] = [tex]\frac{6}{5}[/tex]
The required slope of the line passes through the points (2, -5) and (7, 1) is m = 6/5
What is the slope of the line?The slope of the line is a tangent angle made by line with horizontal. i.e. m =tanx where x in degrees.
here,
The slope of a line passing through two points (x1, y1) and (x2, y2) is given by the formula:
m = (y2 - y1) / (x2 - x1)
Let's apply this formula to the given points:
m = (1 - (-5)) / (7 - 2)
m = 6 / 5
Thus, the required slope of the line passes through the points (2, -5) and (7, 1).
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Given △TSP, TS = SP = 10 cm TP = 12 cm Find: The area of △TSP
Answer:
60
Step-by-step explanation:
if ts = 10 and sp = 10, use the formula 1/2 b x h therefore it will be 5 x 12=60, or 10 x 6 = 60. So the answer of the area of triangle tsp is 60.
find the standard deviation of binomial random variable. A die is rolled 18 times and the number of fours that comes up is tallied
Complete Question
The complete question is shown on the first uploaded image
Answer:
The standard deviation is [tex]\sigma =1.5811[/tex]
Step-by-step explanation:
The sample size is n = 18
Generally the probability of getting a four in the toss of the fair die is mathematically represented as
[tex]p = \frac{1}{6 }[/tex]
While the probability of not getting a four is
[tex]q = 1 - p[/tex]
[tex]q = 1 - \frac{1}{6}[/tex]
[tex]q = \frac{5}{6}[/tex]
Now the standard deviation for the binomial random number is mathematically represented as
[tex]\sigma = \sqrt{n * pq }[/tex]
substituting values
[tex]\sigma = \sqrt{18 * \frac{1}{6}* \frac{5}{6} }[/tex]
[tex]\sigma =1.5811[/tex]
In order to study the mean blood pressure of people in his town, Richard samples the population by dividing the residents by age and randomly selecting a proportionate number of residents from each age group. Which type of sampling is used?
Answer:
Stratified sampling
Step-by-step explanation:
Samples may be classified as:
Convenient: Sample drawn from a conveniently available pool.
Random: Basically, put all the options into a hat and drawn some of them.
Systematic: Every kth element is taken. For example, you want to survey something on the street, you interview every 5th person, for example.
Cluster: Divides population into groups, called clusters, and each element in the cluster is surveyed.
Stratified: Also divides the population into groups. However, then only some elements of the group are surveyed.
In this question:
Population divided into groups. Some members of each group are surveyed. This is stratified sampling
Consider the following hypothesis test.H0:μ1−μ2=0 Ha:μ1−μ2≠0The following results are for two independent samples taken from the two populations. Sample 1 Sample 2 n1=80n2=70 x¯¯¯1=104x¯¯¯2=106 σ1=8.4σ2=7.6a. What is the value of the test statistic?b. What is the p-value?c. With α=.05,α=.05, what is your hypothesis testing conclusion?
Answer:
a) [tex]z =\frac{104-106}{\sqrt{\frac{8.4^2}{80} +\frac{7.6^2}{70}}}= -1.53[/tex]
b) [tex]p_v =2*P(z<-1.53)=0.126[/tex]
c) Since the p value is higher than the significance level provided we have enogh evidence to FAIL to reject the null hypothesis and we can't conclude that the true means are different at 5% of significance
Step-by-step explanation:
Information given
[tex]\bar X_{1}= 104[/tex] represent the mean for 1
[tex]\bar X_{2}= 106[/tex] represent the mean for 2
[tex]\sigma_{1}= 8.4[/tex] represent the population standard deviation for 1
[tex]\sigma_{2}= 7.6[/tex] represent the population standard deviation for 2
[tex]n_{1}=80[/tex] sample size for the group 1
[tex]n_{2}=70[/tex] sample size for the group 2
z would represent the statistic
Hypothesis to test
We want to check if the two means for this case are equal or not, the system of hypothesis would be:
H0:[tex]\mu_{1}=\mu_{2}[/tex]
H1:[tex]\mu_{1} \neq \mu_{2}[/tex]
The statistic would be given by:
[tex]z =\frac{\bar X_1-\bar X_2}{\sqrt{\frac{\sigma^2_1^2}{n_1} +\frac{\sigma^2_2^2}{n_2}}}= [/tex](1)
Part a
Replacing we got:
[tex]z =\frac{104-106}{\sqrt{\frac{8.4^2}{80} +\frac{7.6^2}{70}}}= -1.53[/tex]
Part b
The p value would be given by this probability:
[tex]p_v =2*P(z<-1.53)=0.126[/tex]
Part c
Since the p value is higher than the significance level provided we have enogh evidence to FAIL to reject the null hypothesis and we can't conclude that the true means are different at 5% of significance
Point M is in the interior of angle AOB, the ray OC is a bisector of this angle. Prove that the measure of angle MOC is equal to one-half the difference of the measure of angles AOM and BOM
Answer:
Step-by-step explanation:
Given: point M,
m<AOB,
OC the bisector of m<AOB
Thus,
m<AOC = m<BOC (bisector property of OC)
m<MOC = m<BOM (congruence property)
m<AOM - m<BOM = m<AOC = m<BOC
m<BOC = m<MOC = [tex]\frac{m<AOC}{2}[/tex] (angle property)
Therefore,
m<AOM > m<BOM (point M location property)
m<MOC = [tex]\frac{m<AOM - m<BOM}{2}[/tex]
A farmer owns 30 acres of land on which he wishes to grow corn and barely. The cost per acre for seedcorn is $30, and the cost per acre for barely seed is $20. The farmer can invest a maximum of $600 in seed for the two crops. During the cultivation process, the farmer needs to spray fertilizers and insecticides specific to each crop. This costs $10 per acre for corn and $15 per acre for barely. He can invest only $400 in this process.
A) Write the two inequalities that are deciding factors for the number of acres of each crop the farmer will plant, based on the amount of money the farmer will spend on planting and cultivating the two crops.
B) replace the inequality signs in the two any qualities with equal signs. For a graft representing the two equations that influence the farmers choice of how much of each crop to grow.
C) should the lines be dilated or solid? Give reasons for both lines. What area should be shaded?
Help please
ok hola bro graicas por los punto qui :
A 90% confidence interval for the average salary of all CEOs in the electronics industry was constructed using the results of a random survey of 45 CEOs. The interval was ($139,048, $154,144). Give a practical interpretation of the interval.
a) 90% of the sampled CEOs have salaries that fell in the interval $139,048 to $154,144b) We are 90% confident that the mean salary of all CEOs in the electronics industry falls in the interval $139,048 to $154,144. c) 90% of all CEOs in the electronics industry have salaries that fall between $139,048 to $154,144d) We are 90% confident that the mean salary of the sampled CEOs falls in the interval $139,048 to $154,144.
Answer:
b) We are 90% confident that the mean salary of all CEOs in the electronics industry falls in the interval $139,048 to $154,144.
Step-by-step explanation:
Confidence interval:
Confidence level of x%
We build from a sample.
Between a and b.
Intepretation: We are x% sure that the population mean is between a and b.
In this question:
90%
45 CEO's
Between ($139,048, $154,144).
So
We are 90% sure that the mean salary of all CEO's falls within this interval.
The correct answer is:
b) We are 90% confident that the mean salary of all CEOs in the electronics industry falls in the interval $139,048 to $154,144.
a)3x-1/5=2x+3/7
b)4x/5-3x/10=2
is this what u need.....
A triangular tent door has an area of 15 square feet. The height is five feet. What is the base?
Answer:
Base = 6 feet
Step-by-step explanation:
Area of Triangle = [tex]\frac{1}{2} Base*Height[/tex]
For finding Base:
Base = [tex]\frac{2(Area)}{Height}[/tex]
Where Area = 15, Height = 5
Base = [tex]\frac{2(15)}{5}[/tex]
Base = 2*3
Base = 6 feet
Answer:
The base is 6 feet long.,
Step-by-step explanation:
Area of a triangle = 1/2 * base * height so we have
1/2 b h = 15
1/2 b * 5 = 15
2.5 b = 14
b = 15/2.5
b = 6 feet.
Will give brainliest answer
━━━━━━━☆☆━━━━━━━
▹ Answer
A ≈ 78.54
▹ Step-by-Step Explanation
A = πr²
A = π5²
A ≈ 78.54
Hope this helps!
- CloutAnswers ❁
Brainliest is greatly appreciated!
━━━━━━━☆☆━━━━━━━
Answer:
Hey there!
The area of a circle can be given by the formula: [tex]\pi r^2[/tex], where r is the radius, and pi is approximately 3.14
The radius is 5, so we have
3.14 (5^2)
3.14 (25)
78.5
Hope this helps :)
four divided by the sum of x and three
Answer:
4/ (x+3)
Step-by-step explanation:
The sum of x and 3
(x+3)
4 is divided by the above
4/ (x+3)
What is the solution to the equation ſ x+1= 3x-79
X=-16
X=-4
x=4
X= 16
Answer:
x = 40
Step-by-step explanation:
x+1= 3x-79
Subtract x from each side
x-x+1= 3x-x-79
1 = 2x -79
Add 79 to each side
1+79 = 2x-79+79
80 = 2x
Divide by 2
80/2 = 2x/2
40 =x
Answer:
X= 40
Step-by-step explanation:
x+1 = 3x -79 reorganize. I combined 3 steps to get this:
3x -x = 1 + 79
2x = 80
X = 40
Not sure why that is not a choice!
Find the approximations T10, M10, and S10 for π 7 sin x dx. 0 (Round your answers to six decimal places.)
Answer:
Step-by-step explanation:
Well, since it was not given the interval let's use the interval [0,5] with n=10
So now, for the Trapezoidal Rule to approximate the area enclosed by the Integral of: [tex]f(x)=7\pi \sin(x)[/tex]
[tex]T_{10}=\frac{b-a}{2n}[f(a)+2f(x_1)+ ....2f(x_{n-1})+f(b)][/tex] Plugging in:
[tex]T_{10}=\frac{5-0}{2*10}[f(0)+2f(\frac{1}{2})+2f(1)+2f(\frac{3}{2})+2f(2)+2f(5/2)+2f(3)+2f(7/2)+2f(4)+2f(9/2) +f(5)][/tex]
[tex]T_{10}=\frac{1}{4}[0+21.086+37+43.87+39.99+26.322+6.20-15.43-33.285-42.99-21.087][/tex]
[tex]T_{10}\approx 15.419[/tex]
Now the same area according to Simpson rule:
[tex]S_{10}=\frac{b-a}{3n}[f(a)+4f(x_{1})+2f(x_{2})+4f(x_{3} )+2f(x_{4})+4f(x_{5})+2f(x_{6})+4f(x_{7})+2f(x_{8})+4f(x_{9})+f(b)]\\S_{10}=\frac{5}{3*10}[0+74.01+43.87+79.98+26.322+12.413-15.43-66.571-42.99-21.08]\approx 15.085[/tex]
[tex]S_{10}\approx 15.0585[/tex]
To find the quotient of 3 divided by one-sixth, multiply 3 by
Answer:
You have to multiply 3 x 6.
Step-by-step explanation:
[tex]3/\frac{1}{6} \\Flip\\3*\frac{6}{1} \\3*6[/tex]
Hope this helped! :)
To find the quotient of 3 divided by one-sixth, multiply 3 by 6
What is Algebra?Algebra is a branch of mathematics that deals with symbols and the arithmetic operations across these symbols. These symbols do not have any fixed values and are called variables. In our real-life problems, we often see certain values that keep on changing. But there is a constant need to represent these changing values. Here in algebra, these values are often represented with symbols such as x, y, z, p, or q, and these symbols are called variables. Further, these symbols are manipulated through various arithmetic operations of addition, subtraction, multiplication, and division,
Algebraic ExpressionsAn algebraic expression in algebra is formed using integer constants, variables, and basic arithmetic operations of addition(+), subtraction(-), multiplication(×), and division(/). An example of an algebraic expression is 5x + 6. Here 5 and 6 are fixed numbers and x is a variable.
Given:
3 ÷ 1/6
As, division in fraction is not possible.
So, we will change sign of division into multiplication and reciprocal the number on right of sign.
Thus, 3 ÷1/6
=3*6
=18
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PLEASE HELP ME! Simplify the expression 3 4 (1440) + 295.25 + (-33.50) to determine how much money the theater brought in.
Answer:
1341.75
Step-by-step explanation:
I did the math :)
The guy above me is correct
The manufacturer of widgets spends $5 to make each widget and sells them for $8. The manufacturer also has fixed costs each month of $1200. Find the number of widgets, x, that the manufacturer needs to sell in order to break-even.
Answer:
400
Step-by-step explanation:
The manufacturer spends $5 to make each widget and sells them for $8. This means that each widget gives him a profit of $3.
8 - 5 = 3
You need to figure out how many widgets it will take for the manufacturer to make up for the costs each month ($1200).
3x = 1200
(3x)/3 = 1200/3
x = 400
The manufacturer needs to sell 400 widgets.
Answer:
Step-by-step explanation:
He sells them 8 dollars and uses 5 dollars worth of material.
His profit is 8 - 5 = 3 dollars.
He has to sell enough to overcome the 1200 dollars.
1200 / 3 = 400
He breaks even after selling 400 widgets.
According to this diagram, what is tan 74°?
what expression is equivalent to 6+(-x)+2x(-7)+2x
Answer:
I hope this will help you :)
Step-by-step explanation:
6+(-x)+2x(-7)+2x
6-x+2x✖️(-7)+2x
6-x-14+2x
6-14-x+2x
-8+x
Please answer this correctly
Answer:
8/25
Step-by-step explanation:
The probability of picking a number less than 9 is 4/5.
The probability of picking an even number is 2/5.
[tex]4/5 \times 2/5[/tex]
[tex]=8/25[/tex]
Select the correct answer.
A mistake was made in the steps shown to simplify the expression. Which step includes the mistake?
Step 1:
Step 2:
Step 3:
Step 4:
Step 5:
Step 6:
A.
Step 4
B.
Step 3
C.
Step 1
D.
Step 5
Answer:
B. Step 3
Complete question found on chegg:
Select the correct answer.
A mistake was made in the steps shown to simplify the expression.
Which step includes the mistake?
9/2 + 3(4-1) -7 + 2³
Step 1: 9/2 + 3(3) -7 + 2³
Step 2: 9/2 + 3(3) -7 + 8
Step 3: 15/2 (3) -7 + 8
Step 4: 45/2 -7 + 8
Step 5: 31/2 + 8
Step 6: 47/2
A. Step 4
B. Step 3
C. Step 1
D. Step 5
Step-by-step explanation:
To determine where the mistake occurred let's solve the expression ourselves and compare with answer L's given.
9/2 + 3(4-1) -7 + 2³
Using BODMAS = Bracket, Of, Division, Multiplication, Addition and Subtraction.
Step 1: solve for the value in the bracket. 4-1 =3
9/2 + 3(3) -7 + 2³
Step 2: find the value of 2³
2³ = 2×2×2 = 8
9/2 + 3(3) -7 + 8
Step 3: add 9/2 and 3(3)
9/2 + 3(3) = 9/2 + 9 = (9+18)/2
= 27/2 = (9/2)(3)
9/2 (3) -7 + 8
Step 4: open the bracket
27/2 -7 + 8
Step 5: subtract 7 from 27/2
= (27-14)/2 = 13/2
13/2 + 8
Step 6: add 13/2 and 8
13/2 + 8 = (13+16)/2 = 29/2
From the above calculation, the mistake occurred in (B) Step 3
Answer:
B. Step 3
Complete question found on chegg:
Select the correct answer.
A mistake was made in the steps shown to simplify the expression.
Which step includes the mistake?
9/2 + 3(4-1) -7 + 2³
Step 1: 9/2 + 3(3) -7 + 2³
Step 2: 9/2 + 3(3) -7 + 8
Step 3: 15/2 (3) -7 + 8
Step 4: 45/2 -7 + 8
Step 5: 31/2 + 8
Step 6: 47/2
A. Step 4
B. Step 3
C. Step 1
D. Step 5
Step-by-step explanation:
To determine where the mistake occurred let's solve the expression ourselves and compare with answer L's given.
9/2 + 3(4-1) -7 + 2³
Using BODMAS = Bracket, Of, Division, Multiplication, Addition and Subtraction.
Step 1: solve for the value in the bracket. 4-1 =3
9/2 + 3(3) -7 + 2³
Step 2: find the value of 2³
2³ = 2×2×2 = 8
9/2 + 3(3) -7 + 8
Step 3: add 9/2 and 3(3)
9/2 + 3(3) = 9/2 + 9 = (9+18)/2
= 27/2 = (9/2)(3)
9/2 (3) -7 + 8
Step 4: open the bracket
27/2 -7 + 8
Step 5: subtract 7 from 27/2
= (27-14)/2 = 13/2
13/2 + 8
Step 6: add 13/2 and 8
13/2 + 8 = (13+16)/2 = 29/2
=
A pair of surfers collected data on the self-reported numbers of days surfed in a month for 30 longboard surfers and 30 shortboard surfers. Complete parts a and b below.
Longboard: 2, 7, 16, 13, 10, 18, 7, 8, 15, 15, 19, 17, 3, 10, 11, 16, 24 5, 20, 6, 9, 11, 8, 21, 22, 18, 14, 12, 16, 24
Shortboard: 17, 16, 7, 5, 13, 8, 7, 6, 15, 8, 8, 16, 10, 23, 24, 10, 20, 16, 16, 24, 23, 14, 6, 12, 10, 7, 12, 25, 13, 22
a) Compare the typical number of days surfing for these two groups.
The median for the longboards was________ days, and the median for the shortboards was_______ days, showing that those with________ typically surfed more days in this month
b) Compare the interquartile ranges.
The interquartile range for the longboards was________ days, and the interquartile range for the shortboards was_______ days, showing more variation in the days surfed this month for the________
Answer:
(a)The median for the longboards was 13.5 days, and the median for the shortboards was 13 days, showing that those with longboards typically surfed more days in this month.
(b)The interquartile range for the longboards was 10 days, and the interquartile range for the shortboards was 10.5 days, showing more variation in the days surfed this month for the shortboards.
Step-by-step explanation:
Longboard:
2, 7, 16, 13, 10, 18, 7, 8, 15, 15, 19, 17, 3, 10, 11, 16, 24 5, 20, 6, 9, 11, 8, 21, 22, 18, 14, 12, 16, 24
Sorting in ascending order, we have:
[tex]2, 3, 5, 6, 7, 7, \boxed{8, 8}, 9, 10, 10, 11, 11, 12, \boxed{13, 14,} 15,15, 16, 16, 16, 17, \boxed{18, 18}, 19, 20, 21, 22, 24 , 24[/tex]
Median [tex]=\dfrac{13+14}{2}=13.5[/tex]
[tex]Q_1=\dfrac{8+8}{2}=8 \\Q_3=\dfrac{18+18}{2}=18\\$Interquartile range, Q_3-Q_1=18-8=10[/tex]
Shortboard
17, 16, 7, 5, 13, 8, 7, 6, 15, 8, 8, 16, 10, 23, 24, 10, 20, 16, 16, 24, 23, 14, 6, 12, 10, 7, 12, 25, 13, 22
Sorting in ascending order, we have:
[tex]5, 6, 6, 7, 7, 7, \boxed{8, 8,} 8, 10, 10, 10, 12, 12, \boxed{13, 13} 14, 15, 16, 16, 16, 16, \boxed{17, 20,} 22, 23, 23, 24, 24, 25[/tex]
Median [tex]=\dfrac{13+13}{2}=13[/tex]
[tex]Q_1=\dfrac{8+8}{2}=8 \\Q_3=\dfrac{17+20}{2}=18.5\\$Interquartile range, Q_3-Q_1=18.5-8=10.5[/tex]
Therefore:
(a)The median for the longboards was 13.5 days, and the median for the shortboards was 13 days, showing that those with longboards typically surfed more days in this month.
(b)The interquartile range for the longboards was 10 days, and the interquartile range for the shortboards was 10.5 days, showing more variation in the days surfed this month for the shortboards.
Solve the equation. Round the solution to the nearest tenth . Enter the solution set of the equation . 2P o =P 0 (1.053)^ t
Answer: t= 13.4
Step-by-step explanation:
The given equation is [tex]2P_0=P_0(1.053)^t[/tex]
To solve this equation for 't', we first divide both sides by [tex]P_0[/tex], we get
[tex]2=(1.053)^t[/tex]
Taking log on both the sides, we get
[tex]\log 2= \log(1.053)^t[/tex]
Since [tex]\log a^b=b\log a[/tex]
Then,
[tex]\log 2= t\log1.053\\\\\Rightarrow0.30103=t(0.02243)\\\\\Rightarrow t=\dfrac{0.30103}{0.02243}\\\\\Rightarrow t=13.4208649131\approx13.4[/tex]
Hence, the value of t is 13.4.
1/3 times the difference of a number and five is -2/3 which equation best shows this
Answer:
[tex]\frac{1}{3}*(x-5)=\frac{-2}{3}[/tex]
Step-by-step explanation:
Let the number be x
Difference of a number & 5 : x-5
1/3 time the difference of a number & 5: 1/3 (x-5)
Equation:
[tex]\frac{1}{3}*(x-5)=\frac{-2}{3}[/tex]
Solution:
[tex]x-5=\frac{-2}{3}*\frac{3}{1}\\\\x-5=-2\\\\x=-2+5\\x=3[/tex]