Answer:
We conclude that the proportion of adults who totally abstain from alcohol has changed.
Step-by-step explanation:
We are given that in 1943, an organization surveyed 1100 adults and asked, "Are you a total abstainer from, or do you on occasion consume, alcoholic beverages?"
Of the 1100 adults surveyed, 429 indicated that they were total abstainers. In a recent survey, the same question was asked of 1100 adults and 352 in
Let p = proportion of adults who totally abstain from alcohol.
where, p = [tex]\frac{429}{1100}[/tex] = 0.39
So, Null Hypothesis, [tex]H_0[/tex] : p = 39% {means that the proportion of adults who totally abstain from alcohol has not changed}
Alternate Hypothesis, [tex]H_A[/tex] : p [tex]\neq[/tex] 39% {means that the proportion of adults who totally abstain from alcohol has changed}
The test statistics that would be used here One-sample z proportion statistics;
T.S. = [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ~ N(0,1)
where, [tex]\hat p[/tex] = sample proportion of adults who totally abstain from alcohol = [tex]\frac{352}{1100}[/tex] = 0.32
n = sample of adults surveyed = 1100
So, test statistics = [tex]\frac{0.32-0.39}{\sqrt{\frac{0.32(1-0.32)}{1100} } }[/tex]
= -4.976
The value of z test statistics is -4.976.
Now, at 0.10 significance level the z table gives critical values of -1.645 and 1.645 for two-tailed test.
Since our test statistics doesn't lie within the range of critical values of z, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.
Therefore, we conclude that the proportion of adults who totally abstain from alcohol has changed.
The music you hear when listening to a magnetic cassette tape is the result of the magnetic tape passing over magnetic heads, which read the magnetic information on the tape. The length of time a tape will play depends on the length of the tape and the operating speed of the tape player. The formula is T = L S , where T is the time in seconds, L is the length of the tape in inches, and S is the operating speed in inches per second. How long a tape does a police officer need to record a 3-minute confession at an operating speed of 4 1 2 inches per second?
Using the given formula T = LS
And given the time is 3 minutes (3 x 60 = 180 seconds)and the speed is 4-1/2 inches per second:
180 = L x 4-1/2
Solve for L by dividing both sides by 4-1/2:
L = 180 / 4-1/2
L = 40
The length should be 40 inches.
Final answer:
To record a 3-minute confession at 4 1/2 inches per second, an officer needs 810 inches of magnetic tape.
Explanation:
To determine how long of a tape a police officer needs to record a 3-minute confession at an operating speed of 4 1/2 inches per second, we use the formula T = L/S, where T is the time in seconds, L is the length of the tape in inches, and S is the operating speed in inches per second. First, convert the 3-minute confession time into seconds: 3 minutes × 60 seconds per minute = 180 seconds. Next, solve for L using L = T × S. Here, T = 180 seconds and S = 4.5 inches per second (since 1/2 inch is 0.5 inches). Thus, L = 180 × 4.5 = 810 inches. Therefore, the officer needs 810 inches of tape.
Therefore, as per the above explaination, the correct answer is 810 InchInches.
Michael has a fish tank that has a length of 7 inches, a width 6 inches and and height of 8 inches. What is the total surface area of the fish tank ?
Answer:
I think the answer is 292 inches.
Answer: 250in².
Step-by-step explanation:
Total surface area of the fish tank wil be, listen we can can derive a formula for the surface area.
The fish tanks has five surfaces since the top will be opened. For fnd the total surface area now, find the area of each of the surfaces and add together. If it is 6 surfaces, the formula would have been.
2(lb) + 2(lb) + 2(lb)
2( lb + lb + lb )
Now , first (lb) = 7 × 6in²= 42in² ie. the top and the bottom,
Second surfaces, the sides
7 × 8 = 56in²
The third is the other sides
6 × 8 = 48in². Now applying the formula now, bearing in mind that the top is open, we now have
42in² + 2( lb + lb )in²
= 42 + 2( 56 + 48 )
= 42 + 2(104)
= 42 + 208
= 250in².
Note, if the tank or box is closed, then the above derived formula could be suitable.
The height is also regarded as the depth.
A tile is chosen at random from a bag containing the following tiles: 7 blue, 3 green, 6 yellow, and 5 purple. Let P be the probability distribution defined on the set {blue, green, yellow, purple}. Write each probability rounded to the nearest hundredth
P(blue)=_____
P(green)=_____
P(purple)=_____
P(yellow)=_____
Answer:
P(blue) = 0.33
P(green) = 0.14
P(purple) = 0.24
P(yellow) = 0.29
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
In this question, we have that:
7+3+6+5 = 21 tils.
7 of them are blue. So
P(blue) = 7/21 = 0.33
3 of them are green. So
P(green) = 3/21 = 0.14
6 of them are yellow. So
P(yellow) = 6/21 = 0.29
5 of them are purple. So
P(purple) = 5/21 = 0.24
Answer:
Step-by-step explanation:
A probability is the number of desired outcomes divided by the number of total outcomes.
According to the question
7 + 3 + 6 + 5 = 21 in a bag
[tex]P(blue) = \frac{7C_1}{21C_1} \\\\=\frac{7}{21} \\\\=\frac{1}{3} \\\\= 0.33[/tex]
[tex]P(green) = \frac{3C_1}{21C_1} \\\\= \frac{3}{21} \\\\=\frac{1}{7} \\\\= 0.14[/tex]
[tex]P(yellow)=\frac{6C_1}{21C_1} \\\\=\frac{6}{21}\\\\=\frac{2}{7} \\\\=0.29[/tex]
[tex]P(purple) = \frac{5C_1}{21C_1} \\\\=\frac{5}{21} \\\\=0.24[/tex]
Suppose that the IQs of university A's students can be described by a normal model with mean 150150 and standard deviation 77 points. Also suppose that IQs of students from university B can be described by a normal model with mean 120120 and standard deviation 1010. a) Select a student at random from university A. Find the probability that the student's IQ is at least 140140 points.
Answer:
The probability that the student's IQ is at least 140 points is of 55.17%.
Step-by-step explanation:
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this problem, we have that:
University A: [tex]\mu = 150, \sigma = 77[/tex]
a) Select a student at random from university A. Find the probability that the student's IQ is at least 140 points.
This is 1 subtracted by the pvalue of Z when X = 140. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{140 - 150}{77}[/tex]
[tex]Z = -0.13[/tex]
[tex]Z = -0.13[/tex] has a pvalue of 0.4483.
1 - 0.4483 = 0.5517
The probability that the student's IQ is at least 140 points is of 55.17%.
What is the value of x in the equation 4x - 10 = 18
Start with
[tex]4x - 10 = 18[/tex]
Add 10 to both sides:
[tex]4x - 10+10 = 18+10[/tex]
This cancels the "-10" on the left hand side:
[tex]4x = 28[/tex]
Divide both sides by 4:
[tex]\dfrac{4x}{4} = \dfrac{28}{4}[/tex]
This cancels the 4 on the left hand side:
[tex]x = 7[/tex]
4x - 10 = 18| + 10
4x - 10 + 10 = 18 + 10
4x = 28| ÷ 4
4x ÷ 4 = 28 ÷ 4
x = 7
Plz help ASAP. Need help on this
Answer:
RS, RT and ST
Step-by-step explanation:
A tangent to a circle is a line that meets a circle at only one point.
AP is the radius and XT is not even a line.
Hope it helps!
On a coordinate plane, two parabolas open up. The solid-line parabola, labeled f of x, goes through (negative 2, 4), has a vertex at (0, 0), and goes through (2, 4). The dashed-line parabola, labeled g of x, goes through (0, 7), has a vertex at (2, 3), and goes through (4, 7).
Which best describes the transformation that occurs from the graph of f(x) = x2 to g(x) = (x – 2)2 + 3?
right 2, up 3
left 2, down 3
right 2, down 3
left 2, up 3
Answer: i beleve it should be a
Step-by-step explanation:
The equation of the parabola f(x) = x² is transformed right 2, up 3, to make another parabola of the equation g(x) = (x - 2)² + 3. Hence, the first option is the right choice.
What do we mean by the transformation of graphs?The process of modifying an existing graph, or graphed equation, to generate a version of the following graph is known as graph transformation.
How do we identify the transformation between the two graphs?If the equation of the original graph is f(x) and the transformed graph is g(x), such that g(x) = f(x + p) + q, then the graph of g(x) is p units left and q units up from f(x).
How do we solve the given question?In the question, we are given the equations of the parabolas f(x) = x² and g(x) = (x - 2)² + 3, where f(x) is transformed to make g(x).
We are asked to identify the transformation from f(x) to g(x).
The equation of g(x) = (x - 2)² + 3, in terms of f(x) = x² can be written as
g(x) = f(x- 2) + 3, which is of the form g(x) = f(x + p) + q, where the graph of g(x) is transformed from f(x) by moving it p units left and q units right.
So, we can say that f(x) = x² is moved 2 units right and 3 units up to form g(x) = (x - 2)² + 3.
∴ The equation of the parabola f(x) = x² is transformed right 2, up 3, to make another parabola of the equation g(x) = (x - 2)² + 3. Hence, the first option is the right choice.
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Which letter labels a vertex?
NEED URGENT ANSWER!
Answer:
C.
Step-by-step explanation:
In geometry, a vertex is the point where three or more edges meet on a shape (a 3-dimensional one of course). The other letters label sides or faces of the shape.
Answer:
C
Step-by-step explanation:
The easiest way to explain it is that A,B, and D are all labeling lines. A vertex is like a corner, with at least three lines protruding from it. A vertex is each angular point in a shape.
hope this helps :)
Deborah hikes due south for 3 miles. She then turns due west and hikes 4 miles. What is the shortest distance between the starting point and the ending point? 1 mile 2 miles 5 miles 6 miles
Answer:
5 miles
Step-by-step explanation:
The two legs of Deborah's hike form the right-angle legs of a right triangle. The shortest distance is then the hypotenuse of that triangle, found using the Pythagorean theorem.
d^2 = 3^2 + 4^2 = 9 +16 = 25
d = √25 = 5
Deborah ends 5 miles from her start.
Find 6% of $5.65 and round the product to the nearest cent.
Answer:
$0.34
Step-by-step explanation:
a = p*w
a = .06*5.65
a = 0.339
rounded = 0.34
hope this helps :)
if a pack of 24 pencils cost $2.35 how much does a single pencil cost
Answer:
Just divide dollar amount by unit count
2.35/24 =$ ______ per pencil
so each= =0.097917
so 97 cents
The amount that a single pencil cost is $0.10 per pencil.
Using this formula
Cost per pencil=Cost of pencil per pack/Number of pencil per pack
Where:
Cost of pencil per pack=$2.35
Number of pencil per pack=24 pencil
Let plug in the formula
Cost per pencil=$2.35/24
Cost per pencil=$0.098
Cost per pencil=$0.10 (Approximately)
Inconclusion the amount that a single pencil cost is $0.10 per pencil.
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Patrick is getting new carpet in his rectangular room. He needs 60 square units of carpet. His living room measured 10 units long
It's B
Step-by-step explanation:
A clinical psychologist wants to test whether experiencing childhood trauma affects one's self-efficacy in adulthood. He randomly selects 231 adults who have experienced childhood trauma and finds that their mean self-efficacy score equals 148.9. The standard deviation of the sample equals 27.4. Self-efficacy scores in the general population of adults are distributed normally with a mean equal to 152.5 . Is there sufficient evidence to conclude that the self-efficacy of adults who have experienced childhood trauma differs from that in the general population of individuals
Answer:
Step-by-step explanation:
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,
µ = 152.5
For the alternative hypothesis,
µ ≠ 152.5
This is a two tailed test.
Since no population standard deviation is given, the distribution is a student's t.
Since n = 231
Degrees of freedom, df = n - 1 = 231 - 1 = 230
t = (x - µ)/(s/√n)
Where
x = sample mean = 148.9
µ = population mean = 152.5
s = samples standard deviation = 27.4
t = (148.9 - 152.5)/(27.4/√231) = - 2
We would determine the p value using the t test calculator. It becomes
p = 0.047
Since alpha, 0.05 > thanthere sufficient evidence to conclude that the self-efficacy of adults who have experienced childhood trauma differs from that in the general population of individuals the p value, 0.047, then we would reject the null hypothesis. Therefore, At a 5% level of significance, there is sufficient evidence to conclude that the self-efficacy of adults who have experienced childhood trauma differs from that in the general population of individuals
ILL GIVE YOU BRAINLIST !! *have to get it right ! *
Find the slope of the line IM on the graph.
Answer:
-1/2
Step-by-step explanation:
Point L is at (-2,3)
Point M is at (2,1)
We can find the slope using
m =(y2-y1)/(x2-x1)
= (1-3)/(2 - -2)
=(1-3)/(2+2)
=-2/4
=-1/2
A bucket of water is one quarter full. You add 3.6L to the bucket. Now it has 18L in it. How much water will the bucket hold?
Answer:
57.6 Liters
Step-by-step explanation:
18 - 3.6 to find what 1 quarter is
14.4 * 4 to find the total amount it can hold
= 57.6
The chair of the Department of Mathematics and Statistics needs to appoint a faculty committee consisting of 5 mathematics and 4 statistics faculty. There are 23 mathematics and 14 statistics faculty members in the department. In how many ways can he select a committee? Setup the numerical expression using fractions, factorials, etc. but you do not need to evaluate it.
Answer:
There are 27,720 ways to select the committee
Step-by-step explanation:
First, it is necessary to know how many ways are there to select 3 members, if there are 9 members of the mathematics department. This can be found using the following equation:
Where nCk gives as the number of ways in which we can select k elements from a group of n elements. So, replacing n by 9 and k by 3 members, we get:
So, there are 84 ways to select 3 members from 9 members of the mathematics department.
At the same way, we can calculate that there are 330 ways to select 4 members from the 11 that belong to the Computer science department as:
Finally the total number of ways in which we can form a committee with 3 faculty members from mathematics and 4 from the computer science department is calculated as:
9C3 * 11C4 = 84 * 330 = 27,720
Which expression uses the distributive property to represent the sum of 39 + 27
Answer:
The expression that uses the distributive property to represent the sum of 39 + 27 is [tex]3(13 + 9)[/tex]
Step-by-step explanation:
Given
Expression: 39 + 27
Required
Express using the distributive property
The distributive property is represented in the form a(b + c)
So, we can say that the meaning to the question is that the given expression should be represented in the form a(b+c)
Equate these two expressions, we have
[tex]a(b+c) = 39 + 27[/tex]
Factorize the expression on the left hand side
[tex]a(b+c) = 3(\frac{39}{3} + \frac{27}{3})[/tex]
Simplify fraction
[tex]a(b+c) = 3(13 + 9)[/tex]
Compare expression on left hand side with the expression on the right hand side.
Since, they have the same format, then we've arrived at the answer.
Hence, the expression that uses the distributive property to represent the sum of 39 + 27 is [tex]3(13 + 9)[/tex]
The expression that represents the sum of 39 + 27 using the distributive property is 39 + 27 = (30 + 9) + (20 + 7) = 66.
Explanation:The expression that represents the sum of 39 + 27 using the distributive property is:
39 + 27 = (30 + 9) + (20 + 7) = 30 + 20 + 9 + 7 = 50 + 16 = 66
To apply the distributive property, we break down the numbers into their place values and add them together. In this case, we can break down 39 into 30 + 9, and 27 into 20 + 7. Then, we add the numbers in each place value group separately and combine the results to get the final sum of 66.
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If Miranda flips a coin twice, what is the probability that both coins will land heads up?
The probability that the first coin will land heads up is
The probability that the second coin will land heads up is
The probability that both coins will land heads up is
Answer: The probability that the first coin will land heads up is : 50
The probability that the second coin will land heads up is
The probability that both coins will land heads up is : 25
Step-by-step explanation:
Answer: Both coins 1/4
First coin 1/2
Second coin 1/2
AB = 6 cm AC= 12 cm calculate length of CD give your answer to 3 significant figures
The length of CD to 3 significant figures is 12.7
What is the length of CD ?
Given that;
AB=6cm AC=12cm.
Using Pythagoras in triangle ABC
[tex](AC)^{2} =(AB)^{2}+(BC)^{2}[/tex]
[tex](12)^{2} =(6)^{2}+(BC)^{2}[/tex]
[tex]144 - 36 = (BC)^{2}[/tex]
[tex](BC)^{2} =108[/tex]
[tex](BC)=\sqrt{108}[/tex]
We can then use Law of sine as;
[tex]\frac{a}{sinA} =\frac{b}{sinB} =\frac{c}{sinC}[/tex]
[tex]\frac{CD}{sin90} =\frac{ \sqrt{108} }{sin55}[/tex]
[tex]\frac{CD}{1} = \frac{\sqrt{50} }{sin55}[/tex]
[tex]CD=12.6866[/tex]
Management of Melodic Kortholt Company compared absenteeism rates in two plants on the third Monday in November. Of Plant A's 800 employees, 120 were absent. Of Plant B's 1200 employees, 144 were absent. MegaStat's results for a two-tailed test are shown belowManagement of Melodic Kortholt Company compared absenteeism rates in two plants on the third Monday in November. Of Plant A's 800 employees, 120 were absent. Of Plant B's 1200 employees, 144 were absent. MegaStat's results for a two-tailed test are shown below.p1 p20.15 0.12 p (as decimal)120/800 144/1200 p (as fraction)120. 144. X800 1200 n0.03 sample difference0.00 hypothesized difference0.01545 std. errorx.xx z.0522 p-value (two-tailed)The test statistic (shown as z = x.xx) is approximately:A. 2.022B. 1.960C. 1.942D. 1.645
Answer: C. 1.942
Step-by-step explanation:
This is a test of 2 population proportions. The population proportion of the number of absent employees in plant A and plant B are p1 and p2 respectively.
From the information given,
p1 = 0.15
p2 = 0.12
n1 = 800
n2 = 1200
To determine the z score, we would first determine the pooled proportion.
The pooled proportion, pc is
pc = (x1 + x2)/(n1 + n2)
pc = (120 + 144)/(800 + 1200) = 0.132
1 - pc = 1 - 0.132 = 0.868
The formula for z score is
z = (p1 - p2)/√pc(1 - pc)(1/n1 + 1/n2)
z = (0.15 - 0.12)/√(0.132)(0.868)(1/800 + 1/1200) = - 0.03/0.045
z = 1.942
Using the standard error and sample difference provided in the MegaStat results, and knowing the p-value corresponds to a two-tailed test at the 5 percent significance level, the test statistic for the absenteeism rates at Melodic Kortholt Company is most likely 1.960, corresponding to Option B.
The management of Melodic Kortholt Company compared absenteeism rates in two plants on the third Monday in November. Plant A had an absenteeism rate of 120 out of 800 employees, and Plant B had a rate of 144 out of 1200 employees.
The MegaStat results provided for a two-tailed test show a sample difference of 0.03 and hypothesized difference of 0.00, with a standard error of 0.01545 and a p-value of 0.0522. To find the test statistic, we use the provided standard error and the sample difference.
Using the formula z = (sample difference - hypothesized difference) / std. error, we calculate the z-value to determine the test statistic that corresponds to the options given.
While the exact z-value isn't provided, with a p-value of 0.0522 for a two-tailed test, the z-value would be close to the critical value of 1.96 for a 95% confidence interval. Therefore, the correct z-value that matches the p-value given would most likely be Option B: 1.960.
he gas mileage for a certain model of car is known to have a standard deviation of 4 mi/gallon. A simple random sample of 49 cars of this model is chosen and found to have a mean gas mileage of 27.5 mi/gallon. Construct a 96.5% confidence interval for the mean gas mileage for this car model. a) (27.328, 27.672) b) (19.068, 35.932) c) (26.295, 28.705) d) (20.252, 34.748) e) (26.465, 28.535) f) None of the above
Answer:
c) (26.295, 28.705)
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1-0.965}{2} = 0.0175[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].
So it is z with a pvalue of [tex]1-0.0175 = 0.9825[/tex], so [tex]z = 2.11[/tex]
Now, find the margin of error M as such
[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
[tex]M = 2.11\frac{4}{\sqrt{49}} = 1.205[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 27.5 - 1.205 = 26.295 mi/gallon
The upper end of the interval is the sample mean added to M. So it is 27.5 + 1.205 = 28.705 mi/gallon
So the correct answer is:
c) (26.295, 28.705)
Maricopa's Success scholarship fund receives a gift of $ 185000. The money is invested in stocks, bonds, and CDs. CDs pay 5 % interest, bonds pay 5.5 % interest, and stocks pay 11.3 % interest. Maricopa Success invests $ 30000 more in bonds than in CDs. If the annual income from the investments is $ 13115 , how much was invested in each account?
Maricopa Success invested $ ____ in stocks.
Maricopa Success invested $ ____ in bonds.
Maricopa Success invested $ _____ in CDs.
Answer:
Maricopa Success invested $55,000 in stocks
Maricopa Success invested $80,000 in bonds
Maricopa Success invested $50,000 in CDs
Step-by-step explanation:
Let S denotes stocks, B denotes bonds and C denotes CDs.
Maricopa's Success scholarship fund receives a gift of $185,000 which she invests in stocks. bonds, and CDs.
Mathematically,
S + B + C = 185,000 eq. 1
Money is invested in stocks at interest = 11.3% = 0.113
Money is invested in bonds at interest = 5.5% = 0.055
Money is invested in CDs at interest = 5% = 0.05
Annual income from the investments is $13,115
Mathematically,
0.113S + 0.055B + 0.05C = 13,115 eq. 2
Maricopa Success invests $30,000 more in bonds than in CDs.
Mathematically,
B = C + 30,000 eq. 3
Substitute the eq. 3 into eq. 1
S + B + C = 185,000
S + (C + 30,000) + C = 185,000
S + 2C + 30,000 = 185,000
S + 2C = 185,000 - 30,000
S + 2C = 155000 eq. 4
Substitute the eq. 3 into eq. 2
0.113S + 0.055B + 0.05C = 13,115
0.113S + 0.055(C + 30,000) + 0.05C = 13,115
0.113S + 0.055C + 1650 + 0.05C = 13,115
0.113S + 0.105C + 1650 = 13,115
0.113S + 0.105C = 13,115 - 1650
0.113S + 0.105C = 11,465 eq. 5
Now we have to equations and two unknowns
S + 2C = 155,000 eq. 4
0.113S + 0.105C = 11,465 eq. 5
Multiply eq. 4 by 0.113 and subract it from eq. 5
0.113S + 0.226C = 17,515
subtract it from eq. 5
0.113S + 0.105C = 11,465 eq. 5
0.113S + 0.226C = 17,515
-0.121C = -6050
0.121C = 6050
C = 6050/0.121
C = 50,000
Substitute the value of C into eq. 3
B = C + 30,000
B = 50,000 + 30,000
B = 80,000
Substitute the value of B and C into eq. 1
S + B + C = 185,000
S + 80,000 + 50,000 = 185,000
S = 185,000 - 80,000 - 50,000
S = 55,000
Therefore,
Maricopa Success invested $55,000 in stocks
Maricopa Success invested $80,000 in bonds
Maricopa Success invested $50,000 in CDs
Verification:
S + B + C = 185,000 eq. 1
55,000 + 80,000 + 50,000 = 185,000
185,000 = 185,000 (satisfied)
0.113S + 0.055B + 0.05C = 13,115 eq. 2
0.113(55,000) + 0.055(80,000) + 0.05(50,000) = 13,115
6215 + 4400 + 2500 = 13,115
13,115 = 13,115 (satisfied)
B = C + 30,000 eq. 3
80,000 = 50,000 + 30,000
80,000 = 80,000 (satisfied)
In a normally distributed data set a mean of 55 where 95% of the data fall between 47.4 and 62.6, what would be the standard deviation of that data set?
Answer:
The standard deviation of that data set is 3.8
Step-by-step explanation:
The Empirical Rule states that, for a normally distributed random variable:
68% of the measures are within 1 standard deviation of the mean.
95% of the measures are within 2 standard deviation of the mean.
99.7% of the measures are within 3 standard deviations of the mean.
In this problem, we have that:
Mean = 55
95% of the data fall between 47.4 and 62.6. This means that 47.4 is 2 standard deviations below the mean and 62.6 is two standard deviations above the mean.
Using one of these points.
55 + 2sd = 62.6
2sd = 7.6
sd = 7.6/2
sd = 3.8
The standard deviation of that data set is 3.8
Solve the following equation X = 2 and y = 4
3x + 2y + 4 =?
Answer:
18
Step-by-step explanation:
3(2)+2(4)+4=
6+8+4=18
The solution to the equation 3x + 2y + 4 when x = 2 and y = 4 is 18.
Explanation:In the equation given, we are asked to find the value of 3x + 2y + 4 when x = 2 and y = 4.
First, let's substitute these values into the equation. We get 3×2 + 2×4 + 4, which simplifies to 6 + 8 + 4.
Adding these together gives us a total of 18. Therefore, the solution to the following equation is 18.
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It cost Jodi $44.88 to buy 12 gallons of gas.what was the cost per gallon of gas?
Answer: $3.74
Step-by-step explanation: 44.88/12=3.74
Answer:
Jodi paid $3.74 for each gallon of gas
Step-by-step explanation:
Sandy cut three pieces of yarn to use for her art project one was 1ft 8in long one was 10 in long and one was 2 ft 6 in Long how much yarn did Sandy use
Answer:
C. 5 feet
Step-by-step explanation:
Answer:
5 foot 1 foot + 2 foot + 24 inches
The solution is (3, –2). Verify the solution. Which true statement appears in your check? 4 = 4 –2 = –2 –1 = –1 –3 = –3
Answer:
b.) -2= -2
Step-by-step explanation:
i got it correct
Answer:
-2=-2
Step-by-step explanation:
Some students checked 6 bags of Doritos marked with a net weight of 28.3 grams. They carefully weighed the contents of each bag, recording the following weights (in grams): 29.2, 28.5, 28.7, 28.9, 29.1, 29.5. The average weight is 29.0 and the standard deviation is 0.36. Assume the weight of the bags follows normal distribution. Does this provide strong evidence that the true weight is not 28.3 grams?
Answer:
We conclude that the true mean weight is not 28.3 grams at 5% significance level.
Step-by-step explanation:
We are given that some students checked 6 bags of Doritos marked with a net weight of 28.3 grams.
They carefully weighed the contents of each bag, recording the following weights (in grams): 29.2, 28.5, 28.7, 28.9, 29.1, 29.5. The average weight is 29.0 and the standard deviation is 0.36.
Let [tex]\mu[/tex] = true mean weight of bag.
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 28.3 grams {means that the true mean weight is 28.3 grams}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] [tex]\neq[/tex] 28.3 grams {means that the true mean weight is not 28.3 grams}
The test statistics that would be used here One-sample t test statistics as we don't know about the population standard deviation;
T.S. = [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] ~ [tex]t_n_-_1[/tex]
where, [tex]\bar X[/tex] = sample mean weight = 29.0 grams
s = sample standard deviation = 0.36 grams
n = sample of bags = 6
So, test statistics = [tex]\frac{29.0-28.3}{\frac{0.36}{\sqrt{6} } }[/tex] ~ [tex]t_5[/tex]
= 4.763
The value of t test statistics is 4.763.
Since, in the question we are not given the level of significance so we assume it to be 5%. Now, at 5% significance level the t table gives critical values of -2.571 and 2.571 at 5 degree of freedom for two-tailed test.
Since our test statistics does not lie within the range of critical values of t, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.
Therefore, we conclude that the true mean weight is not 28.3 grams.
There is strong evidence to suggest that the true mean weight of the Doritos bags is not 28.3 grams, based on a hypothesis test that resulted in a very low p-value.
To determine if there is strong evidence that the true mean weight of the Doritos bags is not 28.3 grams, we perform a hypothesis test using the given data.
State the null hypothesis (H0) and the alternative hypothesis (Ha):
H0: μ = 28.3 grams (the true mean weight is 28.3 grams)
Ha: μ ≠ 28.3 grams (the true mean weight is not 28.3 grams)
Calculate the test statistic:
The test statistic for a sample mean is given by:
z = (sample mean - population mean) / (standard deviation / √(n))
Here, the sample mean = 29.0 grams, population mean = 28.3 grams, standard deviation = 0.36 grams, and n = 6.
Thus, z = (29.0 - 28.3) / (0.36 / √(6)) ≈ 4.08
Using a z-table, the p-value associated with a z-score of 4.08 is extremely small (much less than 0.05).
Compare the p-value to the significance level (α):
At α = 0.05, since the p-value is much smaller, we reject the null hypothesis.
Since the p-value is very low, there is strong evidence to suggest that the true mean weight of the Doritos bags is not 28.3 grams.
. A ball is thrown upward. Its height (h, in feet) is
given by the function h = 16t^2+ 64t + 34, where t is
the length of time (in seconds) that the ball has been
in the air. What is the maximum height that the ball
reaches?
A. 3 ft B. 51 ft C. 63 ft D. 67
Answer:
Well none of the answers are correct as maximum height is found by doing -b/2a which gives the x coordinate of the vertex also known as the heighest or lowest point. But when plugged in it gives the lowest point assuming you made the mistake of making the 16 positive when its supposed to be negative you would plug it in and get 98 which isn't an answer choice assuming 34 is the ground when you subtract that you get 64 whch still isn't an answer choice check your numbers in the equation
Answer:
64 feet
Step-by-step explanation:
You can solve this by completing the square and turning the equation into that of a parabola, where the uppermost vertex is the highest point in the ball's flight path.
[tex]h=-16(t^2-4t+4)+98[/tex]
[tex]h=-16(t-2)^2+98[/tex]
Since the first term there is negative, the largest possible answer that you can get is if that term is 0. The only way to make it 0 is for t to be 2, so you know that that is when the highest point is. If the first term is 0, all that is left is 98, which is the highest height. However, since you initially start at 98, you only end up going 64 feet up (I guess C is the closest to that?). Hope this helps!
» A cylinder has a height of 13 millimeters and a radius of 11 millimeters. What is its
volume? Use a 3.14 and round your answer to the nearest hundredth.
Answer:
V =4939.22 mm^3
Step-by-step explanation:
The volume of a cylinder is given by
V = pi r^2 h
where r is the radius and h is the height
V = 3.14 (11)^2 *13
V =4939.22 mm^3