Answer:
z-value of rachel = 1.875
z-value of rob = -2
z-value of Rachel is more than that of rob. Thus rob is earning below average and rachel is earning above average.
Step-by-step explanation:
Let's denote the salary of Rob and Rachel per year by X. So, X = $50,000
We are told that;
For Rachel's industry;
Mean salary;μ1 = $35,000
Standard deviation;σ1 = $8,000
For Rob's industry;
Mean salary;μ2 = $60,000
Standard deviation;σ2 = $5,000
Formula for z - value is;
z = (X - μ)/σ
Thus;
z-value for rob is;
z2 = (X - μ2)/σ2
z2 = (50000 - 60000)/5000
z2 = -2
z-value for rachel is;
z1 = (X - μ1)/σ1
z1 = (50000 - 35000)/8000
z1 = 1.875
z-value of Rachel is more than that of rob. Thus rob is earning below average and rachel is earning above average.
A customer has $10 to spend at the concession stand. Hotdogs cost $2 each and drinks cost $2.50 each. Graph the inequality that illustrates this situation. Use the space below to explain what the answer means.
Answer:
Please refer to the graph in the attached area.
Step-by-step explanation:
Given:
Total money available with the customer is $10.
Cost of each hotdog is $2.
Cost of each drink is is $2.50.
To find:
The graph of inequality.
Solution:
Let number of hotdogs bought = [tex]x[/tex]
Total cost of hotdogs = [tex]2x[/tex]
Let number of drinks bought = [tex]y[/tex]
Total cost of drinks = [tex]2.5y[/tex]
Total cost = [tex]2x+2.5y[/tex]
And total money available is $10.
So, the total cost calculated above must be lesser than or equal to $10.
Hence, the inequality is:
[tex]2x+2.5y<10[/tex]
Also there will be two conditions on variables [tex]x[/tex] and [tex]y[/tex]:
[tex]x\ge0\\y\ge0[/tex]
To graph this, let us find the points on the equivalent equation:
[tex]2x+2.5y = 10[/tex]
Finding two points on the equation.
First put x = 0 [tex]\Rightarrow[/tex] y = 4
Then put y = 0, [tex]\Rightarrow[/tex] x = 5
So, two points are (0, 4) and (5, 0).
Now, plotting the line.
Having point (1,2) in the inequality:
2 + 5 < 10 (True) hence, the graph of inequality will contain the point (1,2)
Please refer to the graph of inequality in the attached graph.
Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s). Consider the equation below. -2(bx-5) = 16 the value of x in terms of b is. The value of x when b is 3 is.
The value of x in terms of b is x = [tex]\frac{-3}{b}[/tex]. Therefore the value of x when b = 3 is x = [tex]\frac{-3}{3}[/tex] = -1.
We can find both answers by rearranging the equation to get "x =", and then substituting in 3 for b:
-2(bx - 5) = 16
-2bx + 10 = 16
- 10
-2bx = 6
÷ -2
bx = -3
÷ b
x = -3/b, which is the answer to the first part.
To get the second answer, we just substitute b = 3 into this equation and we get:
x = -3/b = -3/3 = -1
I hope this helps!
The value of x in terms of b is x = -3/b. Therefore, the value of x when b = 3 is x = -1.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
We need to find both answers by rearranging the equation to get "x =", and then substituting in 3 for b:
-2(bx - 5) = 16
-2bx + 10 = 16
-2bx = 6
bx = -3
x = -3/b,
Now we just substitute b = 3 into this equation and we get:
x = -3/b = -3/3 = -1
The value of x in terms of b is x = -3/b.
Therefore, the value of x when b = 3 is x = -1.
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144 + h^2 = 225 WHAT THE HECK DOES ^ MEAN!???
Answer:
h^2 means h²
(h squared)
Step-by-step explanation:
Step 1: Write equation
144 + h² = 225
Step 2: Subtract 144 on both sides
h² = 81
Step 3: Take square root
√h² = √81
h = 9
For the functions f(x)=4x+5 and g(x)=6x+4,find (f•g)(0)and (g•f)(0)
Answer:
Step-by-step explanation:
f(x)=4x+5
g(x)=6x+4,
first: (f*g)=(4x+5) (6x+4)=24x²+46x+20
next:(f*g)(0)=((g*f)=24x²+46x+20=20
Hi,
f°g means : apply first g then f . so calculate "g" and then use result as "x" in f.
g°f means : you apply first f then g
so : f°g = 4 (g (x)) +5
4 (6x+4) +5 = 24x+16+5 = 24x+21
Find f. (Use C for the constant of the first antiderivative and D for the constant of the second antiderivative.)
f ''(x)= 6x +sinx
Answer:
[tex]f(x) = x^3 -sinx +Cx+D[/tex]
Step-by-step explanation:
Given that:
[tex]f ''(x)= 6x +sinx[/tex]
We are given the 2nd derivative of a function f(x) and we need to find f(x) from that.
We will have to integrate it twice to find the value of f(x).
Let us have a look at the basic formula of integration that we will use in the solution:
[tex]1.\ \int {(a\pm b)} \, dx =\int {a} \, dx + \int {b} \, dx \\2.\ \int {x^n} \, dx = \dfrac{x^{n+1}}{n+1}+C\\3.\ \int {sinx} \, dx = -cosx+C\\4.\ \int {cosx} \, dx = sinx+C[/tex]
[tex]\int\ {f''(x)} \, dx =\int\ {(6x +sinx)} \, dx \\\Rightarrow \int\ {6x} \, dx + \int\ {sinx} \, dx \\\\\Rightarrow 6\dfrac{x^2}{2} -cosx +C\\\Rightarrow 3{x^2} -cosx +C\\\Rightarrow f'(x)=3{x^2} -cosx +C\\[/tex]
Now, integrating it again to find f(x):
[tex]f(x) =\int {f'(x)} \, dx =\int{(3{x^2} -cosx +C)} \, dx \\\Rightarrow \int{3{x^2}} \, dx -\int{cosx} \, dx +\int{C} \, dx\\\Rightarrow 3\times \dfrac{x^3}{3} -sinx +Cx+D\\\Rightarrow x^3 -sinx +Cx+D\\\\\therefore f(x) = x^3 -sinx +Cx+D[/tex]
67.805 what is the value of the 0 help please asap!
Answer:
hundreths
Step-by-step explanation:
After the decimal there is tenths, hundreths thousandnths, tens of thousands e.t.c
Answer:
Hello! The answer will be hundredths.
Step-by-step explanation:
The 5 means the thousandths.
The 0 means the hundredths.
The 8 means the tenths.
The 7 means the ones
And the 6 means the tens.
Hope this helps! :)
( below I attached a picture, which might be helpful.)
h(x)=-4+16 find x when h(x)=48 Plz don't say it is incomplete
Answer:
x = -8
Step-by-step explanation:
When h(x) = 48, you can simply just plug it back into the first equation. Don't let the h(x) confuse you!
Think of it like saying y = -4x + 16, y = 48.
48 = - 4x + 16
32 = - 4x
8 = -x
Divide by -1 both sides.
-8 = x
Write the expression as the sine, cosine, or tangent of an angle. (6 points) cos 94° cos 37° + sin 94° sin 37°
Answer:
[tex]cos57 = 0.5446[/tex]
[tex]sin57 = 0.8387[/tex]
[tex]tan57 = 1.5399[/tex]
Step-by-step explanation:
Given
[tex]cos 94\° cos 37\° + sin 94\° sin 37\°[/tex]
Required
Determine the
- sin
- cosine
- tangent
of an angle
The given expression can be represented as follows;
[tex]cosAcosB + sinAsinB[/tex]
Where A = 94 and B = 37
In trigonometry:
[tex]cosAcosB + sinAsinB = cos(A - B)[/tex]
Substitute 94 for A and 37 for B
[tex]cos(A - B) = cos(94 - 37)[/tex]
[tex]cos(A - B) = cos(57)[/tex]
Hence, the angle is 57;
Since 57 is not a special angle; I'll solve using a calculator
[tex]cos57 = 0.5446[/tex]
[tex]sin57 = 0.8387[/tex]
[tex]tan57 = 1.5399[/tex]
if 5x - 17 = -x +7, then x =
Answer:
x=4
Step-by-step explanation:
5x - 17 = -x +7
Add x to each side
5x+x - 17 = -x+x +7
6x -17 = 7
Add 17 to each side
6x-17+17 = 7+17
6x =24
Divide each side by 6
6x/6 = 24/6
x = 4
Answer:
4
Step-by-step explanation:
5x - 17 = -x + 7
Add x on both sides.
5x - 17 + x = -x + 7 + x
6x - 17 = 7
Add 17 on both sides.
6x - 17 + 17 = 7 + 17
6x = 24
Divide both sides by 6.
(6x)/6 = 24/6
x = 4
What is the slope of the line
described by -4X + 2Y = 16?
A. -2
B. -4
C. 4
D. 2
E. 16
Answer: THe slope is 2
SO answer d
Step-by-step explanation:
-4X + 2Y = 16 add 4x to the other side so equation is
2y=16+4x divided by 2
y=8+2x
A car dealership earns a portion of its profit on the accessories sold with a car. The dealer sold a Toyota Camry loaded with accessories for $24,000. The total cost of the car was 8 times as much as the accessories. How much did the accessories cost? Cost of Accessories
Answer:
y = 2666.67
Step-by-step explanation:
Well to solve this we can make a system of equations.
x = cost of car alone
y = cost of accesories,
[tex]\left \{ {{x+y=24000} \atop {x=8y}} \right.[/tex]
So now we plug in 8y for x in x + y = 24000.
(8y) + y = 24000
9y = 24000
Divide both sides by 9
y = 2666.666666
or 2666.67 rounded to the nearest hundredth.
Now that we have y we can plug that in for y in x=8y.
x = 8(2.666.67)
x = 21,333.33 rounded to the nearest hundredth.
Thus,
accessories "y" cost around 2666.67.
Hope this helps :)
What is the next term in the sequence −10,−17,−24,−31,…?
Answer:
-38
Step-by-step explanation:
it's subtracting 7 everytime, and -31-7=-38
Matt has $3 left in his pocket. He spent $6
on lunch, $7 on a poster, and $10 on a
T-shirt. How much money did he have at
the beginning of the day?
Answer:
$26.
Step-by-step explanation:
Let's say that Matt started out with x dollars.
x - 6 - 7 - 10 = 3
x - 13 - 10 = 3
x -23 = 3
x = 26
He had $26 at the beginning of the day.
Hope this helps!
One stats class consists of 52 women and 28 men. Assume the average exam score on Exam 1 was 74 (σ = 10.43; assume the whole class is a population). A random sample of 16 students yielded an average of a 75 on the first exam (s=16). What is the z-score of the sample mean? Is this sample significantly different from the population? (Hint: Use the z-score formula for locating a sample mean)
Answer:
(A) What is the z- score of the sample mean?
The z- score of the sample mean is 0.0959
(B) Is this sample significantly different from the population?
No; at 0.05 alpha level (95% confidence) and (n-1 =79) degrees of freedom, the sample mean is NOT significantly different from the population mean.
Step -by- step explanation:
(A) To find the z- score of the sample mean,
X = 75 which is the raw score
¶ = 74 which is the population mean
S. D. = 10.43 which is the population standard deviation of/from the mean
Z = [X-¶] ÷ S. D.
Z = [75-74] ÷ 10.43 = 0.0959
Hence, the sample raw score of 75 is only 0.0959 standard deviations from the population mean. [This is close to the population mean value].
(B) To test for whether this sample is significantly different from the population, use the One Sample T- test. This parametric test compares the sample mean to the given population mean.
The estimated standard error of the mean is s/√n
S. E. = 16/√80 = 16/8.94 = 1.789
The Absolute (Calculated) t value is now: [75-74] ÷ 1.789 = 1 ÷ 1.789 = 0.559
Setting up the hypotheses,
Null hypothesis: Sample is not significantly different from population
Alternative hypothesis: Sample is significantly different from population
Having gotten T- cal, T- tab is found thus:
The Critical (Table) t value is found using
- a specific alpha or confidence level
- (n - 1) degrees of freedom; where n is the total number of observations or items in the population
- the standard t- distribution table
Alpha level = 0.05
1 - (0.05 ÷ 2) = 0.975
Checking the column of 0.975 on the t table and tracing it down to the row with 79 degrees of freedom;
The critical t value is 1.990
Since T- cal < T- tab (0.559 < 1.990), refute the alternative hypothesis and accept the null hypothesis.
Hence, with 95% confidence, it is derived that the sample is not significantly different from the population.
The current particulate standard for diesel car emission is .6g/mi. It is hoped that a new engine design has reduced the emissions to a level below this standard. Set up the appropriate null and alternative hypotheses for confirming that the new engine has a mean emission level below the current standard. Discuss the practical consequences of making a Type I and a Type II error. (continue #5) A sample of 64 engines tested yields a mean emission level of = .5 g/mi. Assume that σ = .4. Find the p-value of the test. Do you think that H0 should be rejected? Explain. To what type of error are you now subject?
Answer:
Step-by-step explanation:
From the summary of the given statistics;
The null and the alternative hypothesis for confirming that the new engine has a mean emission level below the current standard can be computed as follows:
Null hypothesis:
[tex]H_0: \mu = 0.60[/tex]
Alternative hypothesis:
[tex]H_a: \mu < 0.60[/tex]
Type I error: Here, the null hypothesis which is the new engine has a mean level equal to .6g/ml is rejected when it is true.
Type II error: Here, the alternative hypothesis which is the new engine has a mean level less than.6g/ml is rejected when it is true.
Similarly;
From , A sample of 64 engines tested yields a mean emission level of = .5 g/mi. Assume that σ = .4.
Sample size n = 64
sample mean [tex]\overline x[/tex] = .5 g/ml
standard deviation σ = .4
From above, the normal standard test statistics can be determined by using the formula:
[tex]z = \dfrac{\bar x- \mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]
[tex]z = \dfrac{0.5- 0.6}{\dfrac{0.4}{\sqrt{64}}}[/tex]
[tex]z = \dfrac{-0.1}{\dfrac{0.4}{8}}[/tex]
z = -2.00
The p-value = P(Z ≤ -2.00)
From the normal z distribution table
P -value = 0.0228
Decision Rule: At level of significance ∝ = 0.05, If P value is less than or equal to level of significance ∝ , we reject the null hypothesis.
Conclusion: SInce the p-value is less than the level of significance , we reject the null hypothesis. Therefore, we can conclude that there is enough evidence that a new engine design has reduced the emissions to a level below this standard.
assume the carrying capacity of the earth is 21 billion. use the 1960s peak annual growth rate of 2.1% and population of 3 billion to predict the base growth rate and current growth rate with a logistic model. Assume a current population of 6.8 billion. How does the predicted growth rate compare to the actual growth rate of about 1.2% per year?
Answer:
current population growth rate would be -3.1%
Step-by-step explanation:
We have to:
Growth rate = r * (1 - population / carrying capacity)
for 1960,
we have carrying capacity = 21 billion
population = 3 billion
r = Growth rate 1960 / (1 - population / carrying capacity)
replacing:
r = 0.021 / (1 - 3/21)
r = 0.0245
that is to say r = 2.45%
Now the current population would be:
= 0.0245 * (1 - carrying population / carrying capacity)
we replace:
= 0.0245 * (1 - 6.8 / 3)
= -0.031
current population growth rate would be -3.1%
The predicted growth rate compare to the actual growth rate of about 1.2% per year is -3.1% and this can be determined by using the formula of growth rate.
Given :
Assume the carrying capacity of the earth is 21 billion. Use the 1960s peak annual growth rate of 2.1% and population of 3 billion to predict the base growth rate and current growth rate with a logistic model. Assume a current population of 6.8 billion.The growth rate is given by the formula:
[tex]\rm Growth \;Rate = r\times \left(1-\dfrac{Populatuion}{Carrying\;Capacity}\right)[/tex]
Given that the carrying capacity of the earth is 21 billion. The growth rate in 1960 is 2.1%. So, put the known values in the equation (1).
[tex]\rm 0.021 = r\times \left(1-\dfrac{3}{21}\right)[/tex]
[tex]0.021=r\times \dfrac{18}{21}[/tex]
0.0245 = r
So, r = 2.45%.
Now, the growth rate of the current population is:
[tex]\rm Growth \;Rate = 0.0245\times \left(1-\dfrac{6.8}{3}\right)[/tex]
[tex]\rm Growth\; Rate = 0.0245 \times \dfrac{-3.8}{3}[/tex]
0.031 = Growth Rate
So, the growth rate is -3.1%.
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[URGENT] (25 points) Ryan randomly drew a marble out of a bag of marbles, then put it back. He did
this 25 times. Of the 25 times he drew a red marble 6 times. He concluded
that the probability of drawing a red marble was
6/25
Answer:
Unpredictable
Step-by-step explanation:
Cuz if u look at it it is also random and u cant predict a random thing, so its quite simply unpredictable
From past records it is known that 10% of items from a production
line are defective. If two items are selected at random, what is the
probability that only one is defective?
Answer: 0.18
Step-by-step explanation:
P(1 unit is defective)= C2 1* P^1*Q^1
C2 1= 2!/(1!*(2-1)!)=2
P=0.1 - probability that items from a production line are defective
Q=1-0.1=0.9 - probability that items from a production line are functional.
P(1 unit is defective)= 2*0.1*0.9=0.18
What is 24-(-6) because in confused
Answer:
30
Step-by-step explanation:
24 - (-6)
Apply rule : -(-a) = a
Negative (-) times a negative (-) is positive (+).
24 + 6
= 30
Answer:
-6 is in parentheses because it is a negative number. this prevents the equation from looking like a too long subtraction sign (24--6); therefore it is written as 24 - (-6).
this simplifies to 24 + 6 = 30
to negatives = a positive
The population of Oak Forest is increasing at a rate of 4% per year. If the population is 74,145 today, what will it be in three years?
Answer:
83,403
Step-by-step explanation: Take 74,145 and multiply it by 4%. Then take that number and add it to the 74,145 and that'll give you year one. For year 2 you'll take your total from year 1 and multiply it by the 4% growth rate then you'll add the 4% to what your ending from year 1 and that'll give you your total growth after 2 years. Then you'll take your ending total from year 2 and multiply it by 4% and then you'll add that 4% to the total end from year 2 and that'll give you your total growth of 4% every year for 3 consecutive years.
Hope this helps!
Calculate how much 30% alcohol solution and 80% alcohol solution must be mixed to end up with exactly 14 gallons of a 40% alcohol solution. You'll need ____ gallons of the 80% solution.
Answer:
You'll need 2.8 gallons of the 80% solution.
Step-by-step explanation:
Let the volume of 30% alcohol =x gallons
Then the volume of 80% alcohol =(14-x) gallons
Since we want to obtain a 40% alcohol solution, we have:
0.3x+0.8(14-x)=0.4(14)
0.3x+11.2-0.8x=5.6
0.8x-0.3x=11.2-5.6
0.5x=5.6
x=11.2
Therefore, the volume of 80% alcohol
=14-11.2
=2.8 gallons
You'll need 2.8 gallons of the 80% solution.
Select the correct answer. Sarah wants to print copies of her artwork. At the local print shop, it costs her $1 to make 5 copies and $5 to make 25 copies. How much would it cost Sarah to make 100 copies? A. $15 B. $20 C. $25 D. $30
$1 = 5copies means
$5 = 25 copies obviously
then
$x = 100 copies
100 / 5 = $x
so she needs
$20
The cost of printing 100 copies of artwork is $20.
What is a unitary method?A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.
Suppose 2 pens cost $10, So the cost of 1 pen is (10/2) = $5.
From this unitary cost of pens, we can determine the cost of any no. of pens by multiplying the unit cost by the no. of pens.
Given, The cost of printing 5 artworks is $1.
∴ The cost of printing 100 copies is $(100/5),
= $20.
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One integer is
5 less than another. The sum of their squares is
157. Find the integers.
Answer:
[tex]\large \boxed{\sf \ \ 6 \ and \ 11 \ \ }[/tex]
Step-by-step explanation:
Hello,
Let's note a and b the two numbers.
a = b - 5
[tex]a^2+b^2=157[/tex]
We replace a in the second equation and we solve it
[tex](b-5)^2+b^2=157 \\ \\ \text{*** develop the expression ***} \\ \\b^2-10b+25+b^2=157 \\ \\ \text{*** subtract 157 from both sides ***} \\ \\2b^2-10b+25-157=2b^2-10b-132=0 \\ \\ \text{*** divide by 2 both sides ***} \\ \\b^2-5b-66=0[/tex]
It means that the sum of the two roots is 5 and the product is -66.
because
[tex](x-\alpha )(x-\beta )=x^2-(\alpha +\beta )x+\alpha \beta \\ \\ \text{ where } \alpha \text{ and } \beta \text{ are the roots }[/tex]
And we can notice that 66 = 6 * 11 and 11 - 6 = 5
So let's factorise it !
[tex]b^2-5b-66=0 \\ \\b^2+6b-11b-66=0 \\ \\b(b+6)-11(b+6)=0 \\ \\(b-11)(b+6) =0 \\ \\ b=11 \ or \ b=-6[/tex]
It means that the solutions are
(6,11) and (-6,-11)
I guess we are after positive numbers though.
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
Construct the cumulative frequency distribution for the given data.
Age (years) of Best Actress when award was won Frequency
20-29 28
30-39 37
40-49 14
50-59 3
60-69 4
70-79 1
80-89 1
Age (years) of Best Actress when award was won Cumulative Frequency
Less than 30
Less than 40
Less than 50
Less than 60
Less than 70
Less than 80
Less than 90
Answer:
Age Frequency Cumulative Frequency
Less than 30 28 28
Less than 40 37 28 + 37 = 65
Less than 50 1 4 65 + 14 = 79
Less than 60 3 79 + 3 = 82
Less than 70 4 82 + 4 = 86
Less than 80 1 86 + 1 = 87
Less than 90 1 87 + 1 = 88
Step-by-step explanation:
Given:
The Frequency Distribution table of ages of best actresses when award was won
To find:
Construct the cumulative frequency distribution
Solution:
In order to construct cumulative frequency distribution for the given data, each frequency from above table is added to the sum of the previous frequencies. For example, frequency for Less than 40 is 37 and the previous frequency (less than 30) is 28 so in order to calculate cumulative frequency 28 i.e. previous frequency is added to 37 (frequency of less than 30) and the cumulative frequency is 65. The complete table is given above.
please answer this for me. i have no idea :( please please please, i am desperate.
================================================
Explanation:
Whenever the angle theta is between 0 and 90, the reference angle is exactly that value.
It's only when you get to other quadrants is when things get a bit tricky. Right now we're in quadrant 1, often written as Q1.
-------------------
Extra info:
If theta is between 90 and 180, then the reference angle is 180-theta. This region is Q2If theta is in quadrant 3, between 180 and 270, then the reference angle is theta-180. The order of subtraction is important since x-y is the not the same as y-x.Lastly, if theta is between 270 and 360 (in Q4), then the reference angle is 360-theta.As you can see, we have four quadrants starting with Q1 in the upper right corner. Then we move counterclockwise to get Q2,Q3 and Q4.Answer:
60 degrees
Step-by-step explanation:
In Quadrant 1, the reference angle is the same as theta.
So,
Reference Angle = 60 degrees
Find the Slope of the line
-4
1
1/4
4
Answer:
Hey there!
The slope is rise over run, or 1/-4.
This gives us the slope, which is -1/4.
Hope this helps :)
Answer:
1/4
Step-by-step explanation:
( i mean i think it is - 1/4 but that isn't an answer choice- )
Slope (m) =
ΔY overΔX= -1 over 4 = -0.25
subtract x^1 and x^2 also y^1 and y^2
and put the answer of y' s over the answer of x 's
divide and you got your answer!
if sqrt((2GM)/r) = 11 km/h, what does sqrt(((8G)(M/81))/r) equal?
Answer:
((23GM)
Step-by-step explanation:
it goes for this because 23gm = 40pm
Trade associations, such as the United Dairy Farmers Association, frequently conduct surveys to identify characteristics of their membership. If this organization conducted a survey to estimate the annual per-capita consumption of milk and wanted to be 95% confident that the estimate was no more than 0.5 gallon away from the actual average, what sample size is needed
Complete Question
Trade associations, such as the United Dairy Farmers Association, frequently conduct surveys to identify characteristics of their membership. If this organization conducted a survey to estimate the annual per-capital consumption of milk and wanted to be 95% confident that the estimate was no more than 0.5 gallon away from the actual average, what sample size is needed? Past data have indicated that the standard deviation of consumption of approximately 10 gallons.
Answer:
The sample size is [tex]n = 1537 \ gallons[/tex]
Step-by-step explanation:
From the question we are told that
The margin of error is [tex]MOE = 0.5[/tex]
The confidence level is [tex]C = 95[/tex]%
Given that the confidence level is 95% the level of significance is mathematically represented as
[tex]\alpha = 100 - 95[/tex]
[tex]\alpha = 5[/tex]%
[tex]\alpha = 0.05[/tex]
Next we obtain the critical value of [tex]\frac{\alpha }{2}[/tex] from the normal distribution table , the values is [tex]Z_{\frac{\alpha }{2} } = 1. 96[/tex]
The reason we are obtaining critical values of
[tex]\frac{\alpha }{2}[/tex]
instead of
[tex]\alpha[/tex]
is because
[tex]\alpha[/tex]
represents the area under the normal curve where the confidence level interval (
[tex]1-\alpha[/tex]
) did not cover which include both the left and right tail while
[tex]\frac{\alpha }{2}[/tex]
is just the area of one tail which what we required to calculate the sample size
Now the sample size is mathematically represented as
[tex]n = \frac{[Z_{\frac{\alpha }{2} }] ^2 * \sigma ^2}{MOE^2}[/tex]
substituting values
[tex]n = \frac{1.96^2 * 10 ^2}{0.5^2}[/tex]
[tex]n = 1537 \ gallons[/tex]
10 points + brainliest = 15 points!
Answer:
(2x^2+1)(4x+3)
Step-by-step explanation:
8x^3 + 6x^2 + 4x+3
Split into two groups
8x^3 + 6x^2 + 4x+3
Factor out 2x^2 from the first group and 1 from the second group
2x^2( 4x+3) +1( 4x+3)
Factor out (4x+3) from each group
(4x+3) (2x^2+1)
Rearranging the order
(2x^2+1)(4x+3)
Answer:
(2x²+1)(4x+3)
Step-by-step explanation:
8x³ + 6x² + 4x +3= regroup as follows(8x³ + 4x) + (6x²+3) =4x(2x²+1) + 3(2x²+1)=(2x²+1)(4x+3)Correct choice is the second one
Find the mean, median, and mode of the data, if possible. f any of these measures cannot be found or a measure does not represent the center of the data, explain why.
A sample of seven admission test scores for a professional school are listed below
11.3 10.6 11.7 9.7 11.7 9.5 11.7
What is the mean score? Select the correct choice below and fill in any answer box to complete your choice
A. The mean score is Round to one decimal place as needed.)
B. There is no mean score. Does the mean represent the center of the data?
A. The mean represents the center
B. The mean does not represent the center because it is the smallest data value.
C. The mean does not represent the center because it is not a data value.
D. The mean does not represent the center because it is the largest data value.
What is the median score? Select the correct choice below and fill in any answer box to complete your choice.
A. The median score is 0
B. There is no median score.
Does the median represent the center of the data? (Round to one decimal place as needed.)
A. The median represents the center.
B. The median does not represent the center because it is not a data value. °
C. The median does not represent the center because it is the largest data value.
D. The median does not represent the center because it is the smallest data value.
What is the mode of the scores? Select the correct choice below and fill in any answer box to complete your choice
A. The mode(s) of the scores is (are)
B. There is no mode. Does (Do) the mode(s) represent the center of the data?
(Use a comma to separate answers as needed.)
A. The mode(s) represent(s) the center
B. The mode(s) can't represent the center because it (they) is (are) not a data value.
C. The mode(s) does (do) not represent the center because it (one) is the largest data value.
D. The mode(s) does (do) not represent the center because it (one) is the smallest data value.
Answer:
Step-by-step explanation:
Given a sample of seven admission test scores for a professional school listed 11.3, 10.6, 11.7, 9.7, 11.7, 9.5 and 11.7, the mean of the numbers is the sum total of the values divided by the total number of admission test score. The mean is as calculated below.
Mean = {11.3 + 10.6 + 11.7 + 9.7 + 11.7 + 9.5 + 11.7}/7
Mean = 76.2/7
Mean = 10.9
The mean score is 10.9 to 1 decimal place.
Note that the mean does not represent the centre of the data. It represents the average value of the datas. The mean does not represent the center because it is not a data value. The mean will give a value that is different from the values given in the data.
b) The median score is the score in the centre after re-arrangement. The arrangement can either be ascending or descending order. On re-arranging in ascending order;
9.5, 9.7, 10.6, (11.3), 11.7, 11.7, 11.7
After rearranging, it can be seen that the number at the centre of the data is 11.3, hence the median score is 11.3.
The median represents the center
c) The mode is the scores that occurs most. According to the data given, the score that occur most is 11.7. The score occurs the highest number of times (3 times) compare to other scores in the data. Hence, the modal score is 11.7.
The mode(s) does (do) not represent the center because it (one) is the largest data value.