Answer:
38 + 10x + 4x - 2
14x + 36
answer is c
6x
Mr. Diaz wants to cut a sandwich into fourths to share with his family Drawn Lines in the Square to show One Way Mr Gs can cut the sandwich into forts
Find B
............
Given:
In ΔABC, AB = 5 unit, BC = 2 unit and ∠C = 90°
To find the The value of ∠B.
Formula
By Trigonometric Ratio we know,
[tex]cos \ \theta=\frac{adj}{hyp}[/tex]
Let us take ∠B = θ
With respect to θ, BC is the adjacent side and AB is the hypotenuse.
So,
[tex]cos \ \theta=\frac{BC}{AB}[/tex]
[tex]cos \ B=\frac{2}{5}[/tex]
[tex]B=cos^{-1} (\frac{2}{5} )[/tex]
[tex]B = 66.42^{\circ}[/tex]
Hence, the value of ∠B is 66.42°.
What are numbers that are positive negative and 0 that are not irrational
Answer:
Any number that is not a fractional value positive and negative but technically all numbers are irrational
Step-by-step explanation:
Any number that is not a fractional value positive and negative but technically all numbers are irrational.
We have to find the numbers that are positive negative and 0 that are not irrational
What is the fractional value positive?
Fractional values are represented using fixed-point arithmetic and are useful for DSP applications.
For a fractional division, we first scale the denominator to the range 0.5 ≤ d < 1.0.
Then we use a table lookup to provide an estimate of x0 to d−1.
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How to solve -222=5x-3(-7y-4)
Answer:
x=46 4/5, x=46.8
Step-by-step explanation:
To find x-intercept/zero, substitute y=0
-222=5x-3(-7*0-4)
-222=5x-3(-7*-4) Solve
x= -234/5
x=46 4/5, x=46.8
25 points) A credit card company has a Refer-a-Friend program in which each member is assumed to successfully refer a friend at an exponential rate of λ per member. Each member cancels membership at an exponential rate of μ. If the total number of members is less than N, the credit card company will advertise online, and additional customers will join at an exponential rate of θ due to the advertising. If the total number of members is greater or equal to N, the credit card company will stop advertising, and customers will only join through the referral program.
(a) Set this up as a birth and death model. That is clearly define the states and transition rates. Draw rate diagram.
(b) Set up balance equations to be solved to find P's for 1 2 0. Do not solve them.
(C) Let N = 30, express the proportion of time that customers will get the credit card of the company through referral program in terms of P's.
Answer:
Step-by-step explanation:
See attached file for answer pls
What is the simplified form of this expression?
(-3x2 + 4x) + (2x2 − x − 11)
A.
-x2 + 5x − 11
B.
-x2 + 3x – 11
C.
-x2 + 3x + 11
D.
-x2 + 5x + 11
Answer:
−x2+3x−11
Step-by-step explanation:
−3x2+4x+2x2−x−11
(−3x2+2x2)+(4x−x)−11
−x2+3x−11
Answer:
Step-by-step explanation:
Hope this Helps ;)
A sailboat is sitting at rest near its dock. A rope attached to the bow of the boat is drawn in over a pulley that stands on a post on the end of the dock that is 5 feet higher than the bow. If the rope is being pulled in at a rate of 2 feet per second, how fast is the boat approaching the dock when the length of rope from bow to pulley is 13 feet
Answer:
The boat is approaching the dock at rate of 2.14 ft/s
Step-by-step explanation:
The situation given in the question can be modeled as a triangle, please refer to the attached diagram.
A rope attached to the bow of the boat is drawn in over a pulley that stands on a post on the end of the dock that is 5 feet higher than the bow that means x = 5 ft.
The length of rope from bow to pulley is 13 feet that means y = 13 ft.
We know that Pythagorean theorem is given by
[tex]x^{2} + y^{2} = z^{2}[/tex]
Differentiating the above equation with respect to time yields,
[tex]2x\frac{dx}{dt} + 2y\frac{dy}{dt} = 2z\frac{dz}{dt}[/tex]
[tex]x\frac{dx}{dt} + y\frac{dy}{dt} = z\frac{dz}{dt}[/tex]
dx/dt = 0 since dock height doesn't change
[tex]y\frac{dy}{dt} = z\frac{dz}{dt}[/tex]
[tex]\frac{dy}{dt} = \frac{z}{y} \frac{dz}{dt}[/tex]
The rope is being pulled in at a rate of 2 feet per second that is dz/dt = 2 ft/s
First we need to find z
z² = (5)² + (13)²
z² = 194
z = √194
z = 13.93 ft
So,
[tex]\frac{dy}{dt} = \frac{z}{y} \frac{dz}{dt}[/tex]
[tex]\frac{dy}{dt} = \frac{13.93}{13}(2)[/tex]
[tex]\frac{dy}{dt} = 2.14[/tex] [tex]ft/s[/tex]
Therefore, the boat is approaching the dock at rate of 2.14 ft/s
So, the boat approached the dock with a speed of 2.1337 m/sec.
Pythagoras Theorem:Pythagoras Theorem is an important topic in Maths, which explains the relation between the sides of a right-angled triangle.
So, the formula is,
[tex]a^2+b^2=c^2[/tex]
Differentiating the above equation,
[tex]2a\frac{da}{dt} +2b\frac{db}{dt} =2c\frac{dc}{dt} ...(1)[/tex]
It is given that,
[tex]a=5m\\\frac{da}{dt}=0\\ c=13\\\frac{dc}{dt}=2 m/s[/tex]
[tex]b=\sqrt{13^2-5^2} \\b=12 m/s[/tex]
Substituting the above values in equation (1) we get,
[tex]2\times5\times0+2\times12\frac{db}{dt} =2\times13\times2\\\frac{db}{dt} =\frac{26}{12}\\ \frac{db}{dt} =2.1337 m/s[/tex]
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X and y are supplementary angles. Y measures 88 what is the measure of X
Answer:
x = 92
Step-by-step explanation:
Supplementary angles add to 180 degrees,
x+y = 180
We know y =88
x+88 = 180
Subtract 88 from each side
x+88-88=180-88
x =92
Test-preparation organizations like Kaplan, Princeton Review, etc. often advertise their services by claiming that students gain an average of 100 or more points on the Scholastic Achievement Test (SAT). Do you think that taking one of those classes would give a test taker 100 extra points?
Answer:
High school students and their parents are often bombarded with SAT test prep applications as they get closer to the college application process. Exam preparation offers arrive in the mail; they are sent home by schools, and they are not cheap. (The Princeton Review "Ultimate Classroom" course costs $ 1,199 in New York City.) When students take these courses and do not see their scores improve, parents may wonder if their children have studied enough or if they have wasted their money.
Step-by-step explanation:
Previous year, the NACAC released a report concluding that exam preparation courses have minimal impact on improving SAT scores: approximately 10-20 points on average in math and 5-10 points on critical reading. The Association for college administration report also noted that this evidence is "contrary to claims made by many test preparation providers of large increases of 100 points or more on the SAT."
Kathleen Steinberg, a College Board spokeswoman, says that, on average, students who take the SAT twice only "increase their scores by about 30 points."
He further disclose that "The College Panel does not indorse taking the SAT more than twice, as there is no evidence to indicate that taking the test more than twice increases grade performance."
Parents might also be surprised at the actual average SAT scores: 501 in critical reading, 515 in math, and 493 in writing, according to Steinberg. (The highest score you can get in any section is 800).
Kaplan claimed that The Princeton Review's claims for score breaks were based on comparing the results of Princeton Review's "diagnostic" tests with the students' self-reported scores on the actual SAT tests, as opposed to SAT scores previous and after.
Final answer:
Test-preparation organizations like Kaplan, Princeton Review, etc. often claim that students gain an average of 100 or more points on the SAT after taking their classes. While it is possible for some students to achieve a significant score improvement after taking these classes, it is important to note that the average improvement may not be 100 points for every student.
Explanation:
Test-preparation organizations like Kaplan, Princeton Review, etc. often claim that students gain an average of 100 or more points on the SAT after taking their classes. While it is possible for some students to achieve a significant score improvement after taking these classes, it is important to note that the average improvement may not be 100 points for every student.
The effectiveness of these classes depends on various factors, such as the student's starting score, their commitment and effort in the class, and their ability to apply the strategies they learn. Some students may experience a smaller improvement, while others may see a larger gain.
It's recommended for students to research and read reviews before choosing a test-preparation organization to ensure they are selecting a reputable program that aligns with their learning style and goals.
8 subtracted from x is less then or equal to 17
Answer:
it can be written in eqn form as
x-8=>17
or,x=>25
Answer:
x-8 ≥17
If you need to find x, Add 8 on both sides
x ≥25
Hope this helped
A hand consists of 1 card drawn from a standard 52-card deck with flowers on the back and 1 card drawn from a standard 52-card deck with birds on the back. A standard deck has 13 cards from each of 4 suits (clubs, diamonds, hearts, spades). The 13 cards have face value 2 through 10, jack, queen, king, or ace. Each face value is a "kind" of card. The jack, queen, and king are "face cards."
A.How many different hands are possible? (Note that a flower-ace-of-spades, bird-queen-of-hearts and a flower-queen-of-hearts, bird-ace-of-spades are two different outcomes.)
B.How many hands consist of a pair of aces?
C.How many hands contain all face cards?
D.How many hands contain exactly 1 king?
E.How many hands consist of two of a kind (2 aces, 2 jacks, and so on)?
F.. How many hands contain at least 1 king?
Answer:
A) 2704 hands
B) 16 hands
C) 144 hands
D) 384 hands
E) 208 hands
F) 400 hands
Step-by-step explanation:
See the attached file for explanation
There are 2704 possible hands, 16 hands consist of a pair of aces, 144 hands have all face cards, 384 hands have 1 king, 208 hands consist of two of a kind, and 384 hands contain at least 1 king.
Explanation:To answer these probability related questions, we must look at the combinations which we can draw. A standard deck contains 52 cards and the hand in question consists of 1 card from 2 different decks, so:
A. The total number of different hands possible is 52 * 52 = 2704.
B. There are 4 aces in each deck so there are 4 * 4 = 16 hands that consist of a pair of aces.
C. A deck has 12 face cards and since 2 cards are being drawn, the number of hands with all face cards is 12 * 12 = 144.
D. The number of hands with exactly 1 king is found by multiplying the number of kings in a deck (4) by the number of non-kings in a deck (52-4). So, 4 * 48 = 192, but we must consider this happening in both decks: so 2 * 192 = 384.
E. For two of a kind hands (2 aces, 2 kings etc.), there are 13 kinds, thus 13 * 4 * 4 = 208.
F. For at least 1 king, either the first card or second card can be a king, so we use similar mathematics as used in D, which is 2 * 192 = 384.
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Simplify. 2√27 − √48 +4√12
Answer:
= 10√3
Step-by-step explanation:
[tex]2 \sqrt{27} - \sqrt{48} + 4 \sqrt{12} \\ = (2 \times \sqrt{9 \times 3}) - (\sqrt{16 \times 3}) + (4 \times \sqrt{4 \times 3} )\\ = (2 \times 3 \sqrt{3}) - 4 \sqrt{3} + (4 \times 2 \sqrt{3} ) \\ = 6 \sqrt{3} - 4 \sqrt{3} + 8 \sqrt{3} \\ = 10 \sqrt{3} [/tex]
Answer:
10√3
Step-by-step explanation:
2√27 − √48 + 4√12
2√(3²×3) − √(4²×3) + 4√(2²×3)
6√3 − 4√3 + 8√3
√3(6 - 4 + 8)
10√3
What is the measure of each angle in the Summer Triangle
The measure of each angle in the Summer Triangle depends on the position and alignment of the stars and cannot be determined without specific coordinates and time of observation.
Explanation:The Summer Triangle is a prominent summer asterism formed by three bright stars: Vega, Deneb, and Altair. The measure of each angle in the Summer Triangle depends on the position and alignment of these stars in the sky. The angles cannot be determined without the specific coordinates and time of observation.
Astronomers use angles to measure the separation between celestial objects in the sky. A full circle has 360°, and the half-sphere of the sky from horizon to opposite horizon contains 180°. By measuring the angular separation between two stars or objects, astronomers can determine how far apart they appear in the sky. The angle is typically measured in degrees (°).
For example, if two stars are 18° apart, their separation spans about 1/10 of the dome of the sky. To give you a sense of how big a degree is, the full Moon is about half a degree across, which is similar to the width of your smallest finger (pinkie) seen at arm's length.
An online retailer wants to estimate the number of visitors that click on their advertisement from a particular website. Of 978 page views in a day, 8% of the users clicked on the advertisement. Create a 90% confidence interval for the population proportion of visitors that click on the advertisement.
Answer:
(0.0657,0.0943) is the 90% confidence interval for the population proportion of visitors that click on the advertisement.
Step-by-step explanation:
We are given the following in the question:
Sample size, n = 978
Percentage of users that clicked on advertisement = 8%
Sample proportion:
[tex]\hat{p} = 0.08[/tex]
90% Confidence interval:
[tex]\hat{p}\pm z_{stat}\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}[/tex]
[tex]z_{critical}\text{ at}~\alpha_{0.10} = 1.645[/tex]
Putting the values, we get:
[tex]0.08\pm 1.645(\sqrt{\dfrac{0.08(1-0.08)}{978}})\\\\= 0.08\pm 0.0142\\\\=(0.0658,0.0942) = (6.57\%,9.43\%)[/tex]
(0.0657,0.0943) is the 90% confidence interval for the population proportion of visitors that click on the advertisement.
A student wants to study the ages of women who apply for marriage licenses in his county. He selects a random sample of 94 marriage licenses issued in the last year in the county and makes a 95% confidence interval for the mean age at which women marry. The 95% confidence interval is (23.6, 27.3).Interpret the 95% confidence interval calculated by the student.
Answer:
The confidence interval for the mean is given by the following formula:
[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex] (1)
For this case the confidence interval obtained is: (23.6 ; 27.3)
And the best interpretation would be:
We have 95% of confidence that the true mean os ages of women who apply for marriage licenses in his county is between 23.6 and 27.3
Step-by-step explanation:
Previous concepts
A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".
The margin of error is the range of values below and above the sample statistic in a confidence interval.
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
[tex]\bar X[/tex] represent the sample mean for the sample
[tex]\mu[/tex] population mean (variable of interest)
s represent the sample standard deviation
n=94 represent the sample size
Solution to the problem
The confidence interval for the mean is given by the following formula:
[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex] (1)
For this case the confidence interval obtained is: (23.6 ; 27.3)
And the best interpretation would be:
We have 95% of confidence that the true mean os ages of women who apply for marriage licenses in his county is between 23.6 and 27.3
What is the volume of this rectangular prism
Answer:
2
Step-by-step explanation:
Multiply all of the fractions together.
A package is in the shape of a triangular prism. The bases are right triangles with perpendicular legs measuring 9 cm and 12 cm.The distance between the bases in 10 cm
Answer:
I think that the answer is either A or C. I'm not too sure on which one.
Step-by-step explanation
For students who first enrolled in two year public institutions in a recentsemester, the proportion who earned a bachelor's degree within six years was 0.398 The president of a certain college believes that the proportion of students who enroll in her institution have a higher completion rate.
(A) Determine the null and alternative hypotheses.
(B) Explain what it would mean to make a Type I error.
(C) Explain what it would mean to make a Type II error.
Answer:
A) Null hypothesis: H0: p = 0.398
Alternative hypothesis: H0: p < 0.398
B) A type I error would be made if the president concludes that he rejects the null hypothesis even when it's true.
C) A type II error would be made if the president concludes that the null hypothesis is false, but he erroneously fails to reject it.
Step-by-step explanation:
A) The null and alternative hypotheses are given below:
From the given information, the claim is that the proportion of students who enroll in her institution have a lower completion rate. This is representing the alternative hypothesis. Thus
Null hypothesis:
H0: p = 0.398
Alternative hypothesis:
H0: p < 0.398
B) A type I error would be made if the president concludes that he rejects the null hypothesis even when it's true.
C) A type II error would be made if the president concludes that the null hypothesis is false, but he erroneously fails to reject it.
a soccer ball is kicked toward the goal
Answer:yes
Step-by-step explanation:
Concert ticket sales of £21,000 are split in the ratio of 2 : 5 between the venue and the band.
How much money does the venue make from the ticket sales?
Answer:
Step-by-step explanation:
£21000/7=3000
I got seven by adding 2 and 5
3000 times 2=6000
3000 times 5 = 15000
6000:15000
6000 for the venue
15000 for the band
The amount of money the venue makes from the ticket sales is £6000.
How much does the venue make?Ratio expresses the relationship between two or more numbers. It shows the frequency of the number of times that one value is contained within other value(s).
The amount the venue makes = 2/7 x 21000 = £6000
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Suppose that a company wishes to predict sales volume based on the amount of advertising expenditures. The sales manager thinks that sales volume and advertising expenditures are modeled according to the following linear equation. Both sales volume and advertising expenditures are in thousands of dollars. Estimated Sales Volume=46.41+0.45(Advertising Expenditures) If the company has a target sales volume of $200,000, how much should the sales manager allocate for advertising in the budget? Round your answer to the nearest dollar.
Final answer:
The sales manager should allocate approximately $341,310 for advertising to achieve the target sales volume of $200,000. This amount is determined by using the linear equation provided and solving for the advertising expenditures.
Explanation:
To find out how much the sales manager should allocate for advertising expenditures to achieve a target sales volume of $200,000, we use the given linear equation:
Estimated Sales Volume = 46.41 + 0.45(Advertising Expenditures)
First, we convert the target sales volume to thousands of dollars - which would be $200 (since $200,000 is in thousands), and then plug it into the equation:
200 = 46.41 + 0.45(Advertising Expenditures)
Next, we solve for Advertising Expenditures:
200 - 46.41 = 0.45(Advertising Expenditures)
153.59 = 0.45(Advertising Expenditures)
Advertising Expenditures = 153.59 / 0.45
Advertising Expenditures = 341.31
Therefore, the sales manager should allocate approximately $341,310 for advertising in the budget to achieve the target sales volume of $200,000. This value is rounded to the nearest dollar as requested.
To achieve a target sales volume of $200,000, the company should allocate approximately $341,310 for advertising.
To determine the amount to allocate for advertising to reach a target sales volume of $200,000, we use the provided linear equation:
⇒ Estimated Sales Volume = 46.41 + 0.45(Advertising Expenditures)
First, set the estimated sales volume to 200 (since the sales volume is in thousands of dollars):⇒ 200 = 46.41 + 0.45(Advertising Expenditures)
Next, solve for Advertising Expenditures:Subtract 46.41 from both sides:⇒ 200 - 46.41 = 0.45(Advertising Expenditures)
⇒ 153.59 = 0.45(Advertising Expenditures)
Divide both sides by 0.45:⇒ Advertising Expenditures = 153.59 ÷ 0.45
⇒ Advertising Expenditures ≈ 341.31
Therefore, the company should allocate approximately $341,310 (rounded to the nearest dollar) for advertising expenditures to achieve the target sales volume of $200,000.
Complete question:
Suppose that a company wishes to predict sales volume based on the amount of advertising expenditures. The sales manager thinks that sales volume and advertising expenditures are modeled according to the following linear equation. Both sales volume and advertising expenditures are in thousands of dollars.
Estimated Sales Volume = 46.41 + 0.45(Advertising Expenditures)
If the company has a target sales volume of $200,000, how much should the sales manager allocate for advertising in the budget? Round your answer to the nearest dollar.
A slice of pizza costs $3.50. You have $25.00 in your wallet to spend on pizza. Write an inequality to represent the number, p, of slices of pizza you can buy.
Answer:
[tex]25.00\geq 3.50p[/tex]
Step-by-step explanation:
since you have $25.00, you can only spend up to that much money, so it will have to be less than or equal to , and since p = slices of pizza, you multiply that by 3.50 to know how much you can buy.
hope this helps :)
Answer:
$3.5p<=$25.00
Step-by-step explanation:
If you only have $25.00 to spend on pizza it can not exceed that limit, so your total amount needs to be more than or equal to money the pizza slices cost
Jennifer has at least $34 more than triple the amount that Matthew has. If Matthew has $2, write an
inequality that represents the amount that Jennifer has, and graph the solution.
Answer:
[tex]x\geq \$40[/tex]
The graph in the attached figure
Step-by-step explanation:
Let
x ----> represents the amount that Jennifer has
y ----> represents the amount that Matthew has
we know that
The amount that Jennifer has is greater than or equal to $34 plus three times the samount that Matthew has
The inequality that represent this situation is
[tex]x\geq 3y+34[/tex]
we have
[tex]y=\$2[/tex]
substitute
[tex]x\geq 3(2)+34[/tex]
[tex]x\geq \$40[/tex]
The solution is the interval [40,∞)
In a number line the solution is the shaded area at right of x=40 (closed point)
see the graph attached
Inequality representing amount owed by Jennifer : x > 40
Important Information : Amount owed by Mathew = $2
Amount owed by Jennifer = at least 34 more than triple amount owed by Mathew
Let the amount owed by Jennifer = xSo, x > 3 (2) + 34
x > 34 + 6
x > 40
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Write the values of each of the digits in 6,582,390,417 in word form
The solution is: 6,582,390,417 in word form is, six billon five hundred eighty two million three hundred thousand and ninety four hundred seventeen.
What is place value?Place value is the basis of our entire number system. This is the system in which the position of a digit in a number determines its value.
The number 42,316 is different from 61,432 because the digits are in different positions.
here, we have,
given that,
6,582,390,417
so, the values of each of the digits in 6,582,390,417 in word form is:
6: six billon
5: five hundred
8: eighty two million
3: three hundred thousand
and ninety four hundred
seventeen.
Hence, The solution is: 6,582,390,417 in word form is, six billon five hundred eighty two million three hundred thousand and ninety four hundred seventeen.
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A chef planning for a large banquet thinks that 2 out of every 5 dinner guests will order his soup appetizer. He expects 800 guests at the banquet. Use equivalent ratios to estimate how many cups of soup he should prepare. A chef planning for a large banquet thinks that 2 out of every 5 dinner guests will order his soup appetizer. He expects 800 guests at the banquet. Use equivalent ratios to estimate how many cups of soup he should prepare.
Answer:
320
Step-by-step explanation:
2/5 = .4
800 * .4 =320
simplify -3(x+3)+5(4x+6)
Answer:
17x +21
Step-by-step explanation:
-3(x+3)+5(4x+6)
Distribute
-3x-9+20x+30
Combine like terms
17x +21
A publisher reports that 47%47% of their readers own a personal computer. A marketing executive wants to test the claim that the percentage is actually different from the reported percentage. A random sample of 280280 found that 43%43% of the readers owned a personal computer. Make the decision to reject or fail to reject the null hypothesis at the 0.010.01 level.
Answer:
The null hypothesis was not rejected.
The proportion of readers who own a personal computer is 47%.
Step-by-step explanation:
The claim made by a publisher is that 47% of their readers own a personal computer.
A single proportion z-test can be used to determine whether the claim made by the publisher is authentic or not.
The hypothesis for this test can be defined as follows:
H₀: The proportion of readers who own a personal computer is 47%, i.e. p = 0.47.
Hₐ: The proportion of readers who own a personal computer is different from 47%, i.e. p ≠ 0.47.
The information provided is:
[tex]n=280\\\hat p=0.43\\\alpha =0.01[/tex]
The test statistic is:
[tex]z=\frac{\hat p-p}{\sqrt{\frac{p(1-p)}{n}}}=\frac{0.43-0.47}{\sqrt{\frac{0.47(1-0.47)}{280}}}=-1.34[/tex]
The test statistic value is, z = -1.34.
Decision rule:
If the p-value of the test is less than the significance level α = 0.01 then the null hypothesis will be rejected and vice-versa.
Compute the p-value as follows:
[tex]p-value=2\times P (Z < z)[/tex]
[tex]=2\times P (Z < -1.34)\\=2\times [1-P(Z<1.34)]\\=2\times [1-0.90988]\\=0.18024\\\approx0.18[/tex]
*Use a z table for the probability.
The p-value of the test is 0.18.
p-value = 0.18 > α = 0.01
The null hypothesis was failed to be rejected at 1% level of significance.
Conclusion:
There is enough evidence to support the claim made by the publisher. Hence, it can be concluded that the proportion of readers who own a personal computer is 47%.
A consumer group plans to test whether a new passenger car that is advertised to have a mean highway miles per gallon of at least 33 actually meets this level. They plan to test the hypothesis using a significance level of 0.05 and a sample size of n = 100 cars. It is believed that the population standard deviation is 3 mpg. Based upon this information, if the "true" population mean is 32.0 mpg, what is the probability that the test will lead the consumer group to "accept" the claimed mileage for this car? Question 36 options: About 0.9545 Approximately 0.0455 About 0.45 None of the above
Answer:
Probability that the test will lead the consumer group to "accept" the claimed mileage for this car is 0.00043.
Step-by-step explanation:
We are given that a consumer group plans to test whether a new passenger car that is advertised to have a mean highway miles per gallon of at least 33 actually meets this level.
It is believed that the population standard deviation is 3 mpg. Based upon this information, the "true" population mean is 32.0 mpg.
Let [tex]\bar X[/tex] = sample mean highway miles per gallon
The z-score probability distribution for sample mean is given by;
Z = [tex]\frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = true population mean = 32.0 mpg
[tex]\sigma[/tex] = population standard deviation = 3 mpg
n = sample of cars = 100
The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) 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.
Now, Probability that a mean highway miles per gallon of at least 33 actually meets this level is given by = P([tex]\bar X[/tex] [tex]\geq[/tex] 33)
P([tex]\bar X[/tex] [tex]\geq[/tex] 33) = P( [tex]\frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] [tex]\geq[/tex] [tex]\frac{33-32}{\frac{3}{\sqrt{100} } }[/tex] ) = P(Z [tex]\geq[/tex] 3.33) = 1 - P(Z < 3.33)
= 1 - 0.99957 = 0.00043
The above probability is calculated by looking at the value of x = 3.33 in the z table which has an area of 0.7673.
Therefore, the probability that the test will lead the consumer group to "accept" the claimed mileage for this car is 0.00043.
How many 5-digit numbers are there that are divisible by either 45 or 60 but are not divisible by 90?
There are 7,991 5-digit numbers that are divisible by either 45 or 60 but not divisible by 90.
Explanation:To find the number of 5-digit numbers that are divisible by either 45 or 60 but not by 90, we can use the principle of inclusion-exclusion. First, let's find the number of 5-digit numbers divisible by 45 and the number divisible by 60, then subtract the number divisible by 90 to avoid overcounting.
A 5-digit number divisible by 45 must also be divisible by 9 and 5. The smallest 5-digit number divisible by 45 is 10005 (9 * 5 * 445), and the largest is 99990 (9 * 5 * 2222). We can find the number of 5-digit numbers divisible by 45 by subtracting the two numbers and adding 1 (99990 - 10005 + 1).
A 5-digit number divisible by 60 must also be divisible by 12 and 5. The smallest 5-digit number divisible by 60 is 10020 (12 * 5 * 167), and the largest is 99960 (12 * 5 * 833). We can find the number of 5-digit numbers divisible by 60 using the same method as before (99960 - 10020 + 1).
Finally, we subtract the number of 5-digit numbers divisible by 90. A 5-digit number divisible by 90 must be divisible by 45 and 2. The smallest 5-digit number divisible by 90 is 10035 (9 * 5 * 445 and 2 * 5017), and the largest is 99945 (9 * 5 * 2221 and 2 * 49973). Again, we use the same method as before to find the number of 5-digit numbers divisible by 90 (99945 - 10035 + 1).
To find the final answer, we subtract the number of 5-digit numbers divisible by 90 from the sum of the numbers divisible by 45 and 60.
Learn more about Divisibility of Numbers here:https://brainly.com/question/36856038
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The expression 5(2)^t Gives the number of leaves in a plant as a function of the number of weeks since it was planted. What does gives the number of leaves in a plant as a function of the number of weeks since it was planted. What does 2 Represent in this expression
Answer:
2 is the scale factor
100% increase/growth
Step-by-step explanation:
y = a × (b^t)
b is scale factor
b = 2 means 200% of tte previous value
100% growth
Answer:
its c The number of leaves is multiplied by 2 each week.
Step-by-step explanation:
because i just did it