Answer:
0.078 or 7.8%
Step-by-step explanation:
Mean salary (μ) = $37,764
Standard deviation (σ) = $5,100
The z-score for any given teacher's salary in California, X, is determined by:
[tex]z=\frac{X-\mu}{\sigma}[/tex]
For X = $45,000:
[tex]z=\frac{45,000-37,764}{5,100}\\ z=1.419[/tex]
A z-score of 1.419 corresponds to the 92.20th percentile of a normal distribution. Therefore, the probability that a salary is greater than $45,000 is:
[tex]P(X>\$45,000) = 1-0.9220\\P(X>\$45,000) = 0.078=7.8\%[/tex]
The probability is 0.078 or 7.8%.
To find the probability of a teacher's salary being more than $45,000 in California, calculate the Z-score using the formula given and find the corresponding probability. This calculation reveals there's a 7.78% chance of a randomly selected teacher's salary exceeding $45,000.
Explanation:To find the probability that a randomly selected teacher’s salary in California is greater than $45,000 when the salaries are normally distributed with a mean of $37,764 and a standard deviation of $5,100, we use the Z-score formula: Z = (X - μ) / σ, where X is the value in question, μ is the mean, and σ is the standard deviation. In this case, X = $45,000, μ = $37,764, and σ = $5,100.
Calculating the Z-score gives us: Z = ($45,000 - $37,764) / $5,100 ≈ 1.42. Using the Z-table or a calculator with normal distribution functions, we find that the area to the right of Z = 1.42 corresponds to the probability we are looking for.
This area represents the probability that a teacher’s salary is greater than $45,000. Since we know the total area under the normal curve equals 1 (or 100%), the area to the right of Z = 1.42 is approximately 0.0778, which means there is a 7.78% chance that a randomly selected teacher’s salary in California is greater than $45,000.
A Cell Phone company sells cellular phones and airtime in a State. At a recent meeting, the marketing manager states that the average age of the customers is 40 years. Before actually completing the advertising plan, it was decided to select a random sample of customers. Among the questions asked in the survey of 50 customers was the customer’s ages. The mean and the standard deviation of the data based on the survey are 38 years and 7 years. a. Formulate a hypothesis to test the marketing manager’s claim. b. Does the sample support manager’s claim. Test at 0.05 level of significance.
Answer:
The null hypothesis is rejected.
There is enough evidence to support the claim that the average age of the customers differs from 40 years.
The sample does not support the manager claim (the average age seems to differ from 40 years).
Step-by-step explanation:
This is a hypothesis test for the population mean.
The manager claims that the average age of customers is 40 years. As this is an equality, we will test if the average age differs from 40. If the null hypothesis failed to be rejected, the claim of the manager is right.
Then, the claim is that the average age of the customers differs from 40 years.
Then, the null and alternative hypothesis are:
[tex]H_0: \mu=40\\\\H_a:\mu\neq 40[/tex]
The significance level is 0.05.
The sample has a size n=50.
The sample mean is M=38.
As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=7.
The estimated standard error of the mean is computed using the formula:
[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{7}{\sqrt{50}}=0.99[/tex]
Then, we can calculate the t-statistic as:
[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{38-40}{0.99}=\dfrac{-2}{0.99}=-2.02[/tex]
The degrees of freedom for this sample size are:
[tex]df=n-1=50-1=49[/tex]
This test is a two-tailed test, with 49 degrees of freedom and t=-2.02, so the P-value for this test is calculated as (using a t-table):
[tex]P-value=2\cdot P(t<-2.02)=0.049[/tex]
As the P-value (0.049) is smaller than the significance level (0.05), the effect is significant.
The null hypothesis is rejected.
There is enough evidence to support the claim that the average age of the customers differs from 40 years.
help pleaseeeeeeeeeeeeee
Answer:
x = 14
Step-by-step explanation:
If a^m = a^n, then m = n.
If two powers with equal bases are equal, then the exponents are equal.
8^(x - 4) = 8^10
x - 4 = 10
x = 14
Answer:
x = 14
Step-by-step explanation:
Looking at this problem, we see that both sides of the equation are equal. Since both numbers have the same base, this means that they must also have the same power to be equal to each other. This means:
x - 4 = 10
x = 10 + 4
x = 14
What is equivalent to 3(21 x )
Answer:
63x
Step-by-step explanation:
3(21x)
= (3· 21)x
= 63x
Answer:63x
Step-by-step explanation:
Yesterday, a movie theater sold 299 bags of popcorn. A large bag of popcorn costs $4. A small bag of popcorn costs $1. In all, the movie theater made $662 from popcorn sales. Write and solve a system of equations to find how many bags of each size of popcorn were sold.
Answer:
Step-by-step explanation:
They sold 201 small bags
and they sold 83 large bags
hope this helps :)
Answer:
l + s = 299
4l + s = $662
121 large bags were sold.
178 small bags were sold.
Step-by-step explanation:
Quantity equation: l + s = 299. l is the amount of large bags and s is the amount of small.
Price equation: 4l + s = $662. This means each large bag earns 4 dollars and each small bag earns 1.
To solve this, you use the method elimination and subtract (l + s = 299) from 4l + s = 662.
So, after subtracting, the equation you are left with is 3l = 363. Divide both sides by 3 and you get l = 121. 121 large bags were sold.
Plug in 121 for l in the first equation, now it says 121 + s = 299. Subtract 121 from 299 and get 178. 178 small bags were sold.
Leon correctly found the slope and y-intercept of the line that passes through the points (9, -8) and (3, 4) as follows
m-
-8-4 -12
9-3 6
-2.
y=-2x+b
-8--2(9)+D
-8--18+ b
10-
What is the equation of the line in slope-intercept form?
O y--2x+10
O y = 2x+10
Oy - 10x-2
O y = 10x+2
Y= -2x+10
4-(-8/3-9= -2(slope)
leaving the first option as the only viable one.
The equation of line passing through point (9, -8) and (3, 4) : y=-2x+10
The correct option is A
Given, that line passes through points (9, -8) and (3, 4).
The equation of a straight line can be represented in the slope-intercept form, y = mx + c
Where c = intercept
Slope(m) =change in value of y on the vertical axis / change in value of x on the horizontal axis
Change in the value of [tex]y = y_2 - y_1[/tex]
Change in value of [tex]x = x_2 -x_1[/tex]
[tex]y_2[/tex] = final value of y
[tex]y_1[/tex] = initial value of y
[tex]x_2[/tex] = final value of x
[tex]x_1[/tex] = initial value of x
The line passes through (9,-8) and (3,4),
[tex]y_2[/tex] = 4
[tex]y_1[/tex] = - 8
[tex]x_2[/tex] = 3
[tex]x_1[/tex] = 9
Slope(m) = (4 + 8)/(3 - 9)
= 12/(- 6)
= -2
To determine the intercept, we would substitute x = 9, y = - 8 and m= - 2 into y = mx + c. It becomes
- 8 = - 2 × 9 + c = - 18 + c
c = - 8 + 18 = 10
The equation becomes
y = - 2x + 10
The correct option is A.
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Problem
What is the relationship between
∠a\blueD{\angle a}
∠a
start color #11accd, angle, a, end color #11accd
and
∠b\greenD{\angle b}
∠b
start color #1fab54, angle, b, end color #1fab54
?
Answer:
Complementary angles.Step-by-step explanation:
The graph is attached.
Notice that [tex]\angle a=\angle AXY[/tex], [tex]\angle b = \angle YXB[/tex] and [tex]\angle BXC = 90\°[/tex], by given.
[tex]\angle AXB = \angle AXY + \angle YXB[/tex], by sum of angles.
[tex]\angle AXB + \angle BXC = 180\°[/tex], by supplementary angles definition.
[tex]\angle AXB + 90\° = 180\°\\\angle AXB = 180\° - 90\°\\\angle AXB = 90\°[/tex]
Which means,
[tex]\angle AXB = \angle AXY + \angle YXB = 90\°[/tex]
Therefore, [tex]\angle a + \angle b = 90\°[/tex], in other words, angles a and b are complementary by defintion.
So, the right answer is the second choice.
Answer:
supplementary angles
Step-by-step explanation:
Helpp!!Angles, degrees and, radians
Answer:
co-terminalreference90°, 105°2π, 7π/4Step-by-step explanation:
For an explanation of vocabulary questions, consult a dictionary or vocabulary list
1) angles ending in the same place are "co-terminal."
__
2) The acute angle between the terminal ray and the x-axis is the "reference angle."
__
3) Multiply radians by 180°/π to convert to degrees.
a) π/2 × 180°/π = 180°/2 = 90°
b) 7π/12 × 180°/π = (7/12)(180°) = 105°
__
4) To convert from degrees to radians, multiply by π/180°.
a) 360° × π/180° = 2π radians
b) 315° × π/180° = 7π/4 radians
Ri’Hanna has n nickels. Shania has 4 times as many nickels as Ri’Hanna has. Write an expression for the total number of nickels Ri’Hanna and Shania have. SImplify the Expression.
Answer:
5n
Step-by-step explanation:
i think
To find the total number of nickels Ri’Hanna and Shania have together, add the number of nickels Ri’Hanna has (n) and the number of nickels Shania has (4n). The simplified expression is 5n.
Explanation:Ri’Hanna has n nickels, and Shania has 4 times that amount. This could be represented by the expression 4n. To calculate the total number of nickels they have together, you add the amount of nickels Ri’Hanna has (n) and the amount Shania has (4n). So, the expression representing the total nickels is n + 4n. When you add n + 4n, it simplifies to 5n.
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Put these fractions in order from least to greatest. 3/12 1/6 2/3
Answer:1
1/6 3/12 2/3
Step-by-step explanation:
3/12 = 2/6
2/3 = 4/6
1/6<2/6<2/3
Answer:
The answer is 3/12 1/6 2/3
Step-by-step explanation:
The reason why is because the denominator is larger than the rest. The larger the denominator the smaller the number. For example: 2/13 is less than 4/6 because the denominator is bigger. Now if it were 6/12 and 1/2 it would be equal since 6 is half of 12. Hope this helped!
Let X and Y again be uniformly distributed independent random variables on [0, 1]. a) Compute the expected value E(XY ). b) What is the probability density function fZ(z) of Z = XY ? Hint: First compute the cumulative distribution function FZ(z) = P(Z ≤ z) using a double integral, and then differentiate in z. c) Use your answer to b) to compute E(Z). Compare it with your answer to a)
Answer:
a) Computing the expected value E(XY) gives 1/4
b) The probability density function fZ(z) of Z = XY is calculated in the attached picture.
c) Computing E(Z) gives 1/4
Step-by-step explanation:
Comparing the computation of E(Z) using the answer to b), it shows that the values are equal.
(1) Let T: Rn--->Rm be linear tranformations.
a. If T maps Rnonto Rm, give a relationship between m and n
b. If T is one-to-one, give a relationship between m and n
c. If T maps Rn onto Rm and is one-to-one, give a relationship between m and n
(Hint: Think about the size of the standard matrix representation of T and the placement of the pivots in each case)
(2) Let T: R3 ---> R4 be a linear transformation such that the only solution to T(x) = 0 is trivial solution.
a. If T is one-to-one
b. Does T map R3onto R4?
Justify your answers in each case.
(Hint:one way to approach this is to look at what the martix representation of T might look like and where it does or does not have pivots.)
(3) Suppose a linear transformation T: R2----> R2 is formed by taking a rotation counterclockwise of 90 degrees, follwed by a reflection through the X2-axis. Describe the points that will be moved back to their original position by this transformation?
(Hint: Think about what T will do to the unit box and the vectors e1 and e2)
Answer:
Check the explanation
Step-by-step explanation:
1.
(a)
n>=m
(b)
n <= m
(c)
n=m
2.
(a)
let T(v1) = T(v2)
=>
T(v1)-T(v2) = 0
=>
T(v1-v2) = 0
=>
v1-v2 = 0 from the hypothesis
=>
v1=v2
=>
T is one-one
thus proved
(b)
lets assume T is onto, we already know that T is one-one, so from above problem (third case where m=n)
we should have 3=4 which is impossible
so T is NOT onto.
3.
we need to find a,b such that
T(a,b) =(a,b)
=>
a= b
=>
points on the line x=y are the required points
Step 1 of 3: A manufacturer of chocolate chips would like to know whether its bag filling machine works correctly at the 432 gram setting. It is believed that the machine is underfilling the bags. A 39 bag sample had a mean of 426 grams. Assume the population standard deviation is known to be 26. At level of significance of 0.05 we have the test : H0: μ ≥ 432, H0: μ < 432 Choose the value of the test statistic to the second decimal place:
Answer:
The value of the test statistic is [tex]t = -1.44[/tex]
Step-by-step explanation:
The null hypothesis is:
[tex]H_{0} \geq 432[/tex]
The alternate hypotesis is:
[tex]H_{1} < 432[/tex]
Our test statistic is:
[tex]t = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, [tex]\sigma[/tex] is the standard deviation and n is the size of the sample.
In this problem, we have that:
[tex]X = 426, \mu = 432, \sigma = 26, n = 39[/tex]
So
[tex]t = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]t = \frac{426 - 432}{\frac{26}{\sqrt{39}}}[/tex]
[tex]t = -1.44[/tex]
The value of the test statistic is [tex]t = -1.44[/tex]
7-7(5+x)-9x in simplified
Answer:
-28 - 16x
Step-by-step explanation:
7-7(5+x)-9x
Distribute
7 - 35 -7x -9x
Combine like terms
-28 - 16x
round 974657 to the nearest ten thousand
Answer:
970000
Step-by-step explanation:
We need to compare volatility of multiple assets. As the assets have different variation ranges, e.g. a big stock versus a penny stock, it is useful to look at the coefficient of variation, not the standard deviation, as a measure of volatility. We have the following population data: Mean ($) 0.48 175.93 286.47 Standard deviation ($) 0.09 34.72 63.08 (a)[2] Give an equation for the coefficient of variation in percentage terms. (b)[6] Find volatility of the three assets. Use two decimals for percentages, e.g. 23.76%. (c)[2] Which asset is the least volatile? Which asset is the most volatile?
Answer:
Check the explanation
Step-by-step explanation:
a)
the formula is given by,
c.v.=[tex]\frac{\sigma}{\mu}\times 100[/tex]
where is standard deviation and is mean of the given data.
b)for asse A,
c.v.= [tex]\frac{\sigma}{\mu}\times 100[/tex] = 0.03 5 , 100 0,30 x 0.30 = 10%
for asse B,
c.v.= [tex]\frac{\sigma}{\mu}\times 100[/tex] = 1.50 x 100 26005 × 100 =8.27 %
for asset C,
c.v.= [tex]\frac{\sigma}{\mu}\times 100[/tex] = 18.70 × 100 =10.71%
c)since, c.v. of asset B is least, it is least volatile and c.v. of asset is most, it is most volatile.
This amount of chill is _ times the amount of cream cheese
Answer:
Is there supposed to be a picture?
Step-by-step explanation:
how do you solve literal eqations
Answer: When given a literal equation, you will often be asked to solve the equation for a
given variable. The goal is to isolate that given variable. The process is the same
process that you use to solve linear equations; the only difference is that you will
be working with a lot more letters, and you may not be able to simplify as much as
you can with linear equations. This packet will hopefully show you the process in a
simple manner so that you will be able to solve literal equations yourself.
Step-by-step explanation:
What is the degree and the polynomial term?
Answer:
choice A is the best 2nd degree, trinomial
Step-by-step explanation:
-x^2 +3x - 4
has 3 unique terms which make it a trinomial
The highest degree is 2 since the the highest valued exponent is 2
Graph the system of equations on your graph paper to answer the question. {y=−x+3 y=x+5 What is the solution for this system of equations? Enter your answer in the boxes.
Answer:
(x,y) = (-1,4)
Step-by-step explanation:
y = y right? So all you have to do is replace both of the equations.
[tex]-x+3=x+5\\-x-x=5-3\\-2x=2\\x=-1[/tex]
after you've found the value of x just substitute it into ANY of these two equations!
For example if we get the first one we have
[tex]y=-(-1)+3\\y=1+3\\y=4[/tex]
And there you have it. Hope it helps!
The display provided from technology available below results from using data for a smartphone carrier's data speeds at airports to test the claim that they are from a population having a mean less than 5.00 Mbps. Conduct the hypothesis test using these results. Use a 0.05 significance level. Identify the null and alternative hypotheses, test statistic, P-value, and state the final conclusion that addresses the original claim.
Answer:
The null and alternative hypothesis are:
[tex]H_0: \mu=5\\\\H_a:\mu< 5[/tex]
Test statistic t=-0.256
P-value = 0.4
The null hypothesis failed to be rejected.
There is not enough evidence to support the claim that that smartphone carrier's data speeds at airports is less than 5 mbps.
Step-by-step explanation:
The question is incomplete:
Sample mean (M): 4.79
Sample STD (s): 5.8
Sample size (n): 50
This is a hypothesis test for the population mean.
The claim is that that smartphone carrier's data speeds at airports is less than 5 mbps.
Then, the null and alternative hypothesis are:
[tex]H_0: \mu=5\\\\H_a:\mu< 5[/tex]
The significance level is 0.05.
The sample has a size n=50.
The sample mean is M=4.79.
As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=5.8.
The estimated standard error of the mean is computed using the formula:
[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{5.8}{\sqrt{50}}=0.82[/tex]
Then, we can calculate the t-statistic as:
[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{4.79-5}{0.82}=\dfrac{-0.21}{0.82}=-0.256[/tex]
The degrees of freedom for this sample size are:
[tex]df=n-1=50-1=49[/tex]
This test is a left-tailed test, with 49 degrees of freedom and t=-0.256, so the P-value for this test is calculated as (using a t-table):
[tex]P-value=P(t<-0.256)=0.4[/tex]
As the P-value (0.4) is bigger than the significance level (0.05), the effect is not significant.
The null hypothesis failed to be rejected.
There is not enough evidence to support the claim that that smartphone carrier's data speeds at airports is less than 5 mbps.
Question 5
Review
Listen
Mark purchased packages of hamburgers for $6.75 each and B packages of buns for $1.50 each. He purchased 18 items and spent $90. Which system of equations could be used to
determine how many of each item Mark purchased?
Answer:
[tex] B = \frac{31.5}{5.25}= 6[/tex]
[tex] H = 18-6= 12[/tex]
So then Mark purchased 12 Hamburgers and 6 packages of buns
Step-by-step explanation:
For this case we can define the following notation:
B represent the number of packages buns
H represent the number of hamburgers
And from the information given we can set up the conditions into the following equations:
[tex] 6.75 H +1.50 B =90[/tex] (1) represent the total cost
[tex] H +B =18[/tex] (2) represent the total number of items
Solving H from equation (2) we got:
[tex] H = 18 -B [/tex] (3)
And replacing equation (3) into equation (1) we got:
[tex] 6.75 (18-B) +1.5 B =90[/tex]
And dsitributing the terms we have:
[tex] 121.5 -6.75 B +1.5 B =90[/tex]
And solving for B we got:
[tex] 121.5-90 = 5.25 B[/tex]
And dividing by 5.25 we got:
[tex] B = \frac{31.5}{5.25}= 6[/tex]
And replacing the value of B into equation (3) we got:
[tex] H = 18-6= 12[/tex]
So then Mark purchased 12 Hamburgers and 6 packages of buns
What is the volume of a cylinder with a radius of 7 cm and height of 10 cm? In terms of pi.
11 is 12 1/2% of what number?
Answer: 88
Step-by-step explanation:
Take [tex]12\frac{1}{2}[/tex] and change it into an improper fraction, [tex]\frac{25}{2}[/tex] divide by 100, [tex]\frac{\frac{25}{2} }{100}[/tex] this is the same as multiplying by [tex]\frac{1}{100}[/tex].
[tex]\frac{25}{2}*\frac{1}{100} =0.125[/tex]
Using a rule of 3,
[tex]\frac{x}{11}=\frac{100}{12\frac{1}{2} }[/tex]
[tex]x=\frac{11*100}{12\frac{1}{2} } \\x=88[/tex]
11 is 12 1/2% of the number 88.
What is Percentage?Percentage is defined as the parts of a number per fraction of 100. We have to divide a number with it's whole and then multiply with 100 to calculate the percentage of any number.
So the percentage actually means a part per 100.
Percentage is usually denoted by the symbol '%'.
We have to find the number such that the number has the 12 1/2% as 11.
Let x be the required number.
We can write 12 1/2% as 12 + 0.5 = 12.5%.
12.5% × x = 11
(12.5 / 100) x = 11
0.125 x = 11
Dividing both sides by 0.125,
x = 11 / 0.125
x = 88
Hence the required number is 88.
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Three students, Angie, Bradley, and Carnell, are being selected for three student council offices: president, vice president, and treasurer. In each arrangement below, the first initial of each person’s name represents that person’s position, with president listed first, vice president second, and treasurer third. Which shows the possible outcomes for the event?
ABC,
ABC, BAC, CBA
AAA, BBB, CCC
ABC, ACB, BCA, BAC, CAB, CBA
Answer:
The answer is D.Step-by-step explanation:
I got it right on the test.
Using the arrangements formula, it is found that the 6 possible outcomes for the event are given as follows:
ABC, ACB, BCA, BAC, CAB, CBA.
What is the arrangements formula?The number of possible arrangements of n elements is given by the factorial of n, that is:
[tex]A_n = n![/tex]
In this problem, there are three students, hence the number of outcomes in given by:
[tex]A_3 = 3! = 6[/tex]
And the outcomes are as follows:
ABC, ACB, BCA, BAC, CAB, CBA.
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The taxiways and runways of a major airport are carefully monitored to expedite takeoffs and landings and to prevent collisions. If a pedestrian or vehicle enters a radiocontrolled surface at an airport without receiving permission, this is called a deviation and incursion. Suppose the mean number of deviations and incursions per year at the Los Angeles International Airport (LAX) is 2. Find the probability that exactly 3 serious deviations and incursions will occur at LAX in a randomly selected year
Answer:
18.04% probability that exactly 3 serious deviations and incursions will occur at LAX in a randomly selected year
Step-by-step explanation:
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
In which
x is the number of sucesses
e = 2.71828 is the Euler number
[tex]\mu[/tex] is the mean in the given time interval.
Suppose the mean number of deviations and incursions per year at the Los Angeles International Airport (LAX) is 2.
This means that [tex]\mu = 2[/tex]
Find the probability that exactly 3 serious deviations and incursions will occur at LAX in a randomly selected year
This is P(X = 3).
[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]
[tex]P(X = 3) = \frac{e^{-2}*2^{3}}{(3)!} = 0.1804[/tex]
18.04% probability that exactly 3 serious deviations and incursions will occur at LAX in a randomly selected year
Assume that the volume of air in an average adult’s lung follows a transformed sine function, as function of time t in seconds,
V (t) = A + B sin(ωt)
Below is a table of measurements of the volume. Identify constants A, B, and ω so that the function above fits these measurements. After 12 seconds, the measurements will repeat.
t - 0 3 6 9 12
V(t) - 7 9 7 5 7
Answer:
Step-by-step explanation:
Given that,
v(t) = A + B•sin(ωt)
Then,
When t = 0 v(t)= 7
7 = A + B•Sin(ω×0)
7 = A + B•Sin0
7 = A
Then,
A = 7
v = 7 + B•sin(ωt)
So,
When t = 3, v(t) = 9
v = A + B•sin(ωt)
9 = 7 + B•Sin(3w)
9-7 = B•sin(3ω)
B•sin(3w) = 2. Equation 1
Also, at t = 6 v(t) = 7, at this point, when it returns back to7, it has complete one oscillation
v = A + B•sin(ωt)
7 = 7 + B•Sin(6w)
7-7 = B•sin(6ω)
B•sin(6w) = 0
Sin(6w) = 0 / B
Sin(6w) = 0
Take arcsin of both sides
6w = Sin~1(0)
6w = π, since it has complete one oscillation
Then, w = π /6
w = π/6
Then,
v(t) = 7 + B•Sin(πt/6)
From equation 1
B•sin(3w) = 2.
B•Sin(3 × π/6) = 2
B•Sin(½π) = 2
B = 2
Then,
v(t) = A + B•sin(ωt)
A = 7, B = 2 and w = π/6
v(t) = 7 + 2•sin(πt/6)
Cassie is climbing the stairs at a hotel. The base of the stairs is located at an altitude of 33 feet, and she ascends the stairs at a rate of 15 inches per
second. Josiah is descending from the top floor of the hotel in an elevator. He descends from 210 feet at a rate of 17.6 feet per second. Cassie begins
climbing the stairs at the same time Josiah begins descending in the elevator.
Which system of equations represents the number of seconds, x, it will take for Cassie and Josiah to be at the same altitude, y, in feet
The two equations expressing altitude y as a function of time in seconds x for Cassie and Josiah respectively are: y = 33 + 1.25x and y = 210 - 17.6x.
Explanation:The subject of this problem is linear equations in algebra. We set up two equations to represent the altitude changes of Cassie and Josiah over time.
Firstly, Cassie is ascending from a base level of 33 feet at a rate of 15 inches per second. However, the rate needs to be converted to feet per second because the initial altitude and the altitude Josiah is descending from are both in feet. So, 15 inches equals 1.25 feet (since 1 foot = 12 inches). Therefore, the altitude y Cassie reaches after x seconds can be represented as y = 33 + 1.25x.
Secondly, Josiah is descending from an altitude of 210 feet at a rate of 17.6 feet per second. Thus, the altitude y reached over x seconds can be given by y = 210 - 17.6x.
The system of equations therefore is:
y = 33 + 1.25xy = 210 - 17.6xLearn more about system of equations here:https://brainly.com/question/21620502
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A point is on a circle of the distance form the center from the center of the circle to the the point is equal to the
Answer:
C. Radius
Step-by-step explanation:
Have a good day!
A disc jockey can select 4 records from 10 to play in one segment. How many ways can this selection be done if order doesn’t matter
Answer:
[tex]C(10,4)=10C_4=210[/tex]
Step-by-step explanation:
A combination is an arrangement where the order is not important. Mathematically, a combination is the number of different groups of "[tex]n[/tex]" elements that can be formed from an initial group of "[tex]k[/tex]" elements. It's calculated with the following formula:
[tex]C(n,k)=nC_k=\frac{n!}{k!(n-k)!}[/tex]
Where:
[tex]k\leqslant n[/tex]
In this case:
[tex]n=10\\k=4[/tex]
Therefore the number of ways that the disc jockey selction can be done is:
[tex]C(10,4)=10C_4=\frac{10!}{4!(10-4)!} =\frac{10!}{4!(6!)}=210[/tex]
A recent poll of 2000 randomly selected 18-25-year-olds revealed that 232 currently use marijuana or hashish. According to a publication, 12.5 % of 18-25-year-olds were current users of marijuana or hashish in 1997.
a) Do the data provide sufficient evidence to conclude that the percentage of 18-25-year-olds who currently use marijuana or hashish has changed from the 1997 percentage of 12.5%? Use α=0.05 significance level.
Answer:
[tex]z=\frac{0.116 -0.125}{\sqrt{\frac{0.125(1-0.125)}{2000}}}=-1.217[/tex]
We are conducting a bilateral test then the p value would is:
[tex]p_v =2*P(z<-1.217)=0.224[/tex]
Since the p value obtained is higher than the significance level used of 0.05 we have enough evidence to FAIL to reject the null hypothesis and there is no evidence to conclude that percentage of 18-25-year-olds who currently use marijuana or hashish has changed from the 1997 percentage of 12.5%
Step-by-step explanation:
Information given
n=2000 represent the random sample of people
X=232 represent the people between 18-25-year-old who currently use marijuana or hashish
[tex]\hat p=\frac{232}{2000}=0.116[/tex] estimated proportion of people between 18-25-year-old who currently use marijuana or hashish
[tex]p_o=0.125[/tex] is the value that we want to verify
[tex]\alpha=0.05[/tex] represent the significance level
Confidence=95% or 0.95
z would represent the statistic
[tex]p_v[/tex] represent the p value
Hypothesis to test
We want to verify if the percentage of 18-25-year-olds who currently use marijuana or hashish has changed from the 1997 percentage of 12.5%.:
Null hypothesis:[tex]p=0.125[/tex]
Alternative hypothesis:[tex]p \neq 0.125[/tex]
The statistic for a proportion z test is given by:
[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)
Replacing into the previous formula we got:
[tex]z=\frac{0.116 -0.125}{\sqrt{\frac{0.125(1-0.125)}{2000}}}=-1.217[/tex]
P value
We are conducting a bilateral test then the p value would is:
[tex]p_v =2*P(z<-1.217)=0.224[/tex]
Since the p value obtained is higher than the significance level used of 0.05 we have enough evidence to FAIL to reject the null hypothesis and there is no evidence to conclude that percentage of 18-25-year-olds who currently use marijuana or hashish has changed from the 1997 percentage of 12.5%
After conducting a statistical hypothesis test using the given data, and the chosen significance level of 0.05, there isn't enough evidence to conclude that the percentage of 18-25-year-olds who are using marijuana or hashish has significantly changed from the 1997 percentage.
Explanation:The subject question concerns a statistical hypothesis testing problem, where we are testing if the proportion of 18-25 year-olds currently using marijuana or hashish is significantly different from the 1997 figure (p0=0.125). Let's denote the current proportion as p1. The null hypothesis H0: p1=p0, and the alternative hypothesis Ha: p1≠p0. The value obtained in the survey is 232/2000 (p1=0.116).
We will use a z-test for the difference of proportions here, using the formula: z = (p1- p0) / sqrt(p0(1 - p0) / n). On computation, we get z =approx -1.58.
The desired significance level is α = 0.05, a two-sided test. The critical z values for this are -1.96 and 1.96. Since -1.96 < z <1.96, we do not reject the null hypothesis at the 0.05 level of significance. This means that, according to our analysis, there is not enough evidence to conclude that the proportion of 18-25 year-olds using marijuana and hashish has significantly changed compared to the 1997 level.
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