Answer: 1.01 hours. THIS IS CORRECT
SteIf you draw a figure to model the situation, you can think of them as starting at the origin (0,0). After t hours, David will be at the point (−17t,0), and Amy will be at the point (0,−15t):
A line segment on a coordinate plane.
A coordinate plane has an unlabeled horizontal x-axis and an unlabeled vertical y-axis. A line segment labeled D that falls from left to right extends from a solid circle at left-parenthesis negative 17 t comma 0 right-parenthesis to a solid circle at left-parenthesis 0 comma negative 15 t right-parenthesis. A point is plotted at left-parenthesis 0 comma 0 right-parenthesis. All plotted points are labeled with their coordinates.
Using the distance formula, we can find the distance between them as a function of time t:
D(t)=(x0−x1)2+(y0−y1)2‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾√=(−17t−0)2+(0−−15t)2‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾√=289t2+225t2‾‾‾‾‾‾‾‾‾‾‾‾‾√=514t2‾‾‾‾‾√=t514‾‾‾‾√
(Note that we can say t2‾‾√=t and not |t| because in this question t>0). Setting this equal to 23 and solving for t, we find
t514‾‾‾‾√t=23=23514‾‾‾‾√≈1.01p-by-step explanation:
The average cost of tuition plus room and board at small private liberal arts colleges is reported to be less than $18,500 per term. A financial administrator at one of the colleges believes that the average cost is higher. The administrator conducted a study using 150 small liberal arts colleges. It showed that the average cost per term is $18,200. The population standard deviation is known to be $1,400. Let α= 0.05. What are the null and alternative hypothesis for this study?
Answer:
The null and alternative hypothesis for this study are:
[tex]H_0: \mu=18500\\\\H_a:\mu< 18500[/tex]
The null hypothesis is rejected (P-value=0.004).
There is enough evidence to support the claim that the average cost of tuition plus room and board at small private liberal arts colleges is less than $18,500 per term.
Step-by-step explanation:
This is a hypothesis test for the population mean.
The claim is that the average cost of tuition plus room and board at small private liberal arts colleges is less than $18,500 per term.
Then, the null and alternative hypothesis are:
[tex]H_0: \mu=18500\\\\H_a:\mu< 18500[/tex]
The significance level is 0.05.
The sample has a size n=150.
The sample mean is M=18200.
The standard deviation of the population is known and has a value of σ=1400.
We can calculate the standard error as:
[tex]\sigma_M=\dfrac{\sigma}{\sqrt{n}}=\dfrac{1400}{\sqrt{150}}=114.31[/tex]
Then, we can calculate the z-statistic as:
[tex]z=\dfrac{M-\mu}{\sigma_M}=\dfrac{18200-18500}{114.31}=\dfrac{-300}{114.31}=-2.624[/tex]
This test is a left-tailed test, so the P-value for this test is calculated as:
[tex]P-value=P(z<-2.624)=0.004[/tex]
As the P-value (0.004) 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 cost of tuition plus room and board at small private liberal arts colleges is less than $18,500 per term.
You purchased a bond 75 days ago for $911.72. You received an interest payment of $32.00 68 days ago. Today the bond’s price is $993.39.
What is the holding period return (HPR) on the bond as of today?
Answer:
Holding Period Return (HPR) = 12.47% (Approx)
Step-by-step explanation:
Given:
Purchase price of bond = $911.72
Interest received = $32
Ending price of bond = $993.39
Find:
Holding period return (HPR) = ?
Computation:
⇒ Holding Period Return (HPR) = [Ending price of bond - Purchase price of bond + Interest received] / Purchase price of bond
⇒ Holding Period Return (HPR) = [$993.39 - $911.72 + $32] / $911.72
⇒ Holding Period Return (HPR) = [$113.67] / $911.72
⇒ Holding Period Return (HPR) = 0.12467
⇒ Holding Period Return (HPR) = 12.47% (Approx)
Solving One Step Equations:
z - 2.3 = 0.46
Answer:
z =2.76
Step-by-step explanation:
z - 2.3 = 0.46
Add 2.3 to each side
z - 2.3+2.3 = 0.46+2.3
z =2.76
Please help asap! Will give brainliest! Please read the question then answer correctly! No guessing.
Answer:
(x + 5) (x - 7)
Step-by-step explanation:
To factor this trinomial, you must split the middle term (-2x) into two terms that can be added to get -2x, and multiplied to get -35:
[tex]x^2[/tex] - 2x - 35
[tex]x^2[/tex] - 7x + 5x - 35
Group:
([tex]x^2[/tex] - 7x) (5x - 35)
Take out GCF (Greatest Common Factor):
x(x - 7) 5(x - 7)
(x + 5) (x - 7)
Verify that 1 + cos 2 theta / 2 cos theta = cos theta is an identity
Answer and Step-by-step explanation:
We want to verify that (1 + cos(2θ)) / 2cos(θ) = cos(θ).
Let's focus on the left side. Look at cos(2θ). This is an identity, so remember that cos(2θ) = cos²θ - sin²θ. Also, look at the 1. Remember that sin²θ + cos²θ = 1, so plug both of these expressions into our equation:
(1 + cos(2θ)) / 2cos(θ) =? cos(θ)
((sin²θ + cos²θ) + (cos²θ - sin²θ)) / 2cos(θ) =? cos(θ)
2cos²θ / 2cosθ =? cosθ
cosθ = cosθ
Thus, we have proved this is an identity.
Answer:
(1 + cos(2theta))/2cos(theta)
cos(2theta) = 2cos²(theta) - 1
(1 + 2cos²(theta) - 1)/2cos(thetal
2cos²(theta)/2cos(theta)
cos(theta)
3 and 1/4 minus 5/8 please help!
The population of a town increased from 3450 in 2006 to 4650 in 2011. Find the absolute and relative (percent) increase.
Answer:
15% increase per year.
Step-by-step explanation:
5,600 - 3,500 = 2,100
2,100 is what percent of 3,500?
2,100 = X*3,500
X = 2,100 / 3,500
X = .60 or 60%
An average of 15% increase per year.
Answer:
the population of a town increased from 3450 and 2006 to 51,50 and 2010 find the absolutes and relative percent increase
Step-by-step explanation:
A project is found to have expected time T = 35.33 days and variance V = 3.22.
a. What value of z is needed to find the probability that the project will take at least 40 days? (round final answer to 2 decimals as needed)
b. What value of z is needed to find the probability that the project will take at most 40 days? (round final answer to 2 decimals as needed)
c. What value of z is needed to find the probability that the project will take at most 30 days? (round final answer to 2 decimals as needed)
Answer:
a) [tex] z = \frac{40-35.33}{1.794}= 2.60[/tex]
b) [tex] z = \frac{40-35.33}{1.794}= 2.60[/tex]
c) [tex] z = \frac{30-35.33}{1.794}= -2.97[/tex]
Step-by-step explanation:
For this case we know that the mean for the random variable of interest is [tex]\mu = 35.33[/tex] and the variance [tex]\sigma^2 = 3.22[/tex] so then the deviation would be [tex]\sigma = \sqrt{3.22}= 1.794[/tex]
The z score is given by thsi formula:
[tex] z = \frac{X -\mu}{\sigma}[/tex]
Part a
We want this probability:
[tex] P(X>40)[/tex]
And if we find the z score we got:
[tex] z = \frac{40-35.33}{1.794}= 2.60[/tex]
And we can find this probability: [tex] P(Z>2.60)[/tex]
Part b
We want this probability:
[tex] P(X<40)[/tex]
And if we find the z score we got:
[tex] z = \frac{40-35.33}{1.794}= 2.60[/tex]
And we can find this probability: [tex] P(Z<2.60)[/tex]
Part c
We want this probability:
[tex] P(X<30)[/tex]
And if we find the z score we got:
[tex] z = \frac{30-35.33}{1.794}= -2.97[/tex]
And we can find this probability: [tex] P(Z<-2.97)[/tex]
When Jonas becomes the Receiver of Memory, he gets a rule that he may not tell his dreams. He wants to know how many of his 505050 classmates have the same rule. He asks 555 friends from his class whether they may tell their dreams. Of those, 444 say that they may.
Answer:
101010 classmates can't tell their dreams.
Step-by-step explanation:
I'm not sure what the question is, but if it is an average thing than 444 of 555 is 80 percent, so if that is what it wants 404040 of the students can share their dreams, and 101010 can't.
Hope this helps!
A national organization has been working with utilities throughout the nation to find sites for large wind machines that generate electricity. Wind speeds must average more than 15 miles per hour (mph) for a site to be acceptable. Recently, the organization conducted wind speed tests at a particular site. Based on a sample of wind speed recordings (taken at random intervals), the wind speed at the site averaged with a standard deviation of To determine whether the site meets the organization's requirements, consider the test, where μ is the true mean wind speed at the site and Fill in the blanks. "A Type I error in the context of this problem is to conclude that the true mean wind speed at the site _____ 15 mph when it actually _____ 15 mph."
Answer:
"A Type I error in the context of this problem is to conclude that the true mean wind speed at the site is higher than 15 mph when it actually is not higher than 15 mph."
Step-by-step explanation:
A Type I error happens when a true null hypothesis is rejected.
In this case, as the claim that want to be tested is that the average wind speed is significantly higher than 15 mph, the null hypothesis has to state the opposite: the average wind speed is equal or less than 15 mph.
Then, with this null hypothesis, the Type I error implies a rejection of the hypothesis that the average wind speed is equal or less than 15 mph. This is equivalent to say that there is evidence that the average speed is significantly higher than 15 mph.
"A Type I error in the context of this problem is to conclude that the true mean wind speed at the site is higher than 15 mph when it actually is not higher than 15 mph."
What is the slope of y = -4x -3
Answer:
Slope = -4
Step-by-step explanation:
Slope intercept form: y = mx + b
m = slope
b = y-intercept
Since m represents the slope, then your slope will equal -4.
3x+20=5x how many Solutions does it have
Answer:
one
Step-by-step explanation:
3x + 20 = 5x
20 = 5x - 3x
20 = 2x
x = 10
one solution
An alien empire is considering taking over planet Earth, but they will only do so if the portion of rebellious humans is less than 10 % 10%10, percent. They abducted a random sample of 400 400400 humans, performed special psychological tests, and found that 14 % 14%14, percent of the sample are rebellious. Let's test the hypothesis that the actual percentage of rebellious humans is 10 % 10%10, percent versus the alternative that the actual percentage is higher than that. The table below sums up the results of 1000 10001000 simulations, each simulating a sample of 400 400400 humans, assuming there are 10 % 10%10, percent rebellious humans. According to the simulations, what is the probability of getting a sample with 14 % 14%14, percent rebellious humans or more?'
Answer:
Probability of getting a sample with 14% rebellious humans or more is 0.0104.
Step-by-step explanation:
We are given that an alien empire is considering taking over planet Earth, but they will only do so if the portion of rebellious humans is less than 10%.
They abducted a random sample of 400 humans, performed special psychological tests, and found that 14% of the sample are rebellious.
Let p = population proportion rebellious humans
The z score probability distribution for sample proportion is given by;
Z = [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ~ N(0,1)
where, [tex]\hat[/tex][tex]\hat p[/tex] = sample proportion rebellious humans = 14%
n = sample of humans = 400
p = population proportion rebellious humans = 10%
Now, probability of getting a sample with 14% rebellious humans or more is given by = P( [tex]\hat p[/tex] [tex]\geq[/tex] 14%)
P( [tex]\hat p[/tex] [tex]\geq[/tex] 0.14) = P( [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] [tex]\geq[/tex] [tex]\frac{0.14-0.10}{\sqrt{\frac{0.14(1-0.14)}{400} } }[/tex] ) = P(Z [tex]\geq[/tex] 2.31)
= 1 - P(Z < 2.31) = 1 - 0.9896 = 0.0104
The above probability is calculated by looking at the value of x = 2.31 in the z table which has an area of 0.9896.
Hence, the required probability is 0.0104.
Answer:
It's 0.7% (make sure to include the % sign)
Step-by-step explanation:
Khan Academy
BRAINLIEST for whoever gets this correct! Factor the expression below.
x^2-16x+64
A. (x-4)(x-16)
B. (x+4)(x+16)
C. (x+8)(x + 8)
D. (x-8)(x-8)
Answer:
D. (x - 8) (x - 8)
Step-by-step explanation:
-16x must be split into two terms that can be added to get -16, and multiplied to get 64. The only two terms that can satisfy this, is -8.
(x - 8) (x - 8)
If you're unsure about whether it's correct, you can multiply the two together to see if you get your original expression, [tex]x^2-16x +64[/tex], as your answer.
State if the two vectors are parallel, orthogonal, or neither.
u=18i+8j
v=9i+4j
Answer:
Parallel, since [tex]\vec u = 2\cdot \vec v[/tex].
Step-by-step explanation:
The relation between both vectors is determined by the use of the dot product, whose expression is:
[tex]\cos \theta = \frac{\vec u \bullet \vec v}{\|\vec u\| \|\vec v\|}[/tex]
Where:
[tex]\cos \theta = 1[/tex] if vectors are parallel to each other and [tex]\cos \theta = 0[/tex] if vectors are orthogonal. Then, norms and dot product are calculated hereafter:
[tex]\|\vec u\| = \sqrt{18^{2}+8^{2}}[/tex]
[tex]\|\vec u\| \approx 19.698[/tex]
[tex]\|\vec v \| = \sqrt{9^{2}+4^{2}}[/tex]
[tex]\|\vec v\| \approx 9.849[/tex]
[tex]\vec u \bullet \vec v = (18)\cdot (9) + (8)\cdot (4)[/tex]
[tex]\vec u \bullet \vec v = 194[/tex]
[tex]\cos \theta = \frac{194}{(19.698)\cdot (9.849)}[/tex]
[tex]\cos \theta = 1[/tex]
The two vectors are parallel to each other, which is also supported by the fact that one vector is multiply of the other one. That is,
[tex]18i + 8j = 2\cdot (9i + 4j)[/tex]
[tex]\vec u = 2\cdot \vec v[/tex]
What is more 7 7/9 or 7 4/5?
First, turn the mixed numbers into improper fractions.
7 7/9 = 70/9
7 4/5 = 39/5
Second, find common denominators.
70/9 = 350/45
39/5 = 351/45
351/45 > 350/45
Therefore, 7 4/5 is greater.
Best of Luck!
find the value of x in the triangle shown below
Answer:
..........
Step-by-step explanation:
x + 114 + 33 = 180
x= 33
For several hours you watch a group playing dice on the street and you notice that the owner of the dice often wins.
Answer:
there is no question
Step-by-step explanation:
It looks like the owner plays dirty, meaning he uses a trick of some kind to somehow influence the outcome in such a way, that it's outcome is no longer random.
By influencing the outcome, the owner can obtain an advantage over the playeers who are not aware of the trick or skill involved.
This is unfair and can be considered "dirty". This game is 'fixed'.
if i'm 18 and my sister is 19, how much younger am I than she is?
Answer:
one year
Step-by-step explanation:
Plot the vertex and the axis of symmetry of this function: f(x) = (x – 3)2 + 5.
Answer:
Vertex: (3, 5)
Axis of symmetry: x=3
A physical education class has 21 boys and 9 girls. Each day, the teacher randomly selects a team captain. Assume that no student is absent. What is the probability that the team captain is a girl two days in a row?
The probability of choosing a captain that is a girl two days in a row is
9
%.
Answer:9%
U already provided the answer. Anyways have a good day!!
The probability of choosing a captain that is a girl two days in a row is 9%
How to determine the probability?The given parameters are:
Boys = 21
Girls = 9
The total number of students is
Total = 21 + 9
Total = 30
This means that the probability of selecting a girl is:
P(Girl) = 9/30
For two days, the required probability is
P = 9/30 * 9/30
Evaluate
P = 9%
Hence, the probability of choosing a captain that is a girl two days in a row is 9%
Read more about probability at:
https://brainly.com/question/251701
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Jared has earned 23% of the $52 he needs to buy a new jacket. Find 23% of $52.
Which expression can you use to find 23% of 52? ..
23% of $52 is $..
An easy way to check your answer is to use the friendly and divide 52 by to get ..
Answer:
Which expression can you use to find 23% of 52? "0.23 x 52"
23% of $52 is $. "11.96"
An easy way to check your answer is to use the friendly 25% and divide 52 by 4 to get 13.
Step-by-step explanation:
just did it good luck everyone
23% of $52 is $11.96.
In order to determine the value of 23% of $52, we would multiply 23% by $52. Multiplication is a basic mathematical operation that entails adding a certain number by itself a certain number of times. The sign used to represent multiplication is ×.
23% x 52
= 0.23 x 52 = $11.96
To learn more, please check: https://brainly.com/question/92258
If r(x) = 3x -1 and s(x) = 2x + 1, which is equivalent to [r/s] (6)?
[tex]\text{Solve by turning it into a fraction and plugging in the value to x:}\\\\\frac{3x-1}{2x+1}\\\\\frac{3(6)-1}{2(6)+1}\\\\\frac{18-1}{12+1}\\\\\frac{17}{13}\\\\\text{You can't simplify the fraction any further, in which it'll conclude your answer}\\\\\boxed{\frac{17}{13}}[/tex]
You are overseeing a machine that seals 80 soda cans per minute. In one hour of time, how many soda cans will be sealed? _____ soda cans?
Answer: 4800
Step-by-step explanation: 80 x 60 = 4800
a square stained window is divided into four congurent traiangular sections by iron edging to represent seasons of the year. Each diagonal measures 9 inches. What is the total length of iron edging needed to create the sqaure frame and two diagnols?
Answer:
Total length of iron needed to make the square frame and two diagonals = 43.44 in (Approx)
Step-by-step explanation:
Given:
Length of diagonal = 9 in
Find:
Total length of iron needed to make the square frame and two diagonals.
Computation:
Area of square = 1/2(diagonal)²
Area of square = 1/2(9)²
Area of square = 40.5 in²
Area of square = Side × Side
40.5 in² = Side × Side
Side = 6.36 (approx)
Total length of iron needed to make the square frame and two diagonals = Permeter of square + (2 × diagonal)
⇒ (4 × 6.36) + (2 × 9)
⇒ (25.44) + (18)
⇒ 43.44 in
Total length of iron needed to make the square frame and two diagonals = 43.44 in (Approx)
What’s the correct answer for this?
Answer:
(2,7)
Step-by-step explanation:
In the attached file
an automobile traveled 21 miles north from the airport. it then turned directly west and traveled 28 miles. how far is the automobile from the airport??
The automobile is 35 miles away from the airport
Whoever answers I WILL MARK BRANLIEST !!!
Answer:
3. 7632
4. 485
Step-by-step explanation:
3. The only prime digit greater than 6 is 7, so that is the thousands digit. The only even prime is 2, so that is the ones digit.
In order for the number ending in 2 to be divisible by 4, the tens digit must be odd. The only odd numbers that have a double that is an even digit are 1 and 3. Since all digits must be different, the hundreds digit cannot be 2×1 = 2, but must be 2×3 = 6.
The number is 7632.
__
4. In order for an odd number to be divisible by 5, its ones digit must be 5, not 0. Then the tens digit is 5+3 = 8, and the sum of these two digits is 5+8 = 13. To make the total of digits equal to 17, the hundreds digit must be 17-13 = 4.
The number is 485.
Employees that work at a fish store must measure the level of nitrites in the water each day. Nitrite levels should remain lower than 5 ppm as to not harm the fish. The nitrite level varies according to a distribution that is approximately normal with a mean of 3 ppm. The probability that the nitrite level is less than 2 ppm is 0.0918.
1. Which of the following is closest to the probability that on a randomly selected day the nitrite level will be at least 5 ppm?
(A) 0.0039
(B) 0.0266
(C) 0.0918
(D) 0.7519
(E) 0.9961
Answer: .0039
Step-by-step explanation:
Four different leadership styles used by Big-Six accountants were investigated. As part of a designed study, 15 accountants were randomly selected from each of the four leadership style groups (a total of 60 accountants). Each accountant was asked to rate the degree to which their subordinates performed substandard fieldwork on a 10-point scale—called the "substandard work scale". The objective is to compare the mean substandard work scales of the four leadership styles. The data on substandard work scales for all 60 observations were subjected to an analysis of variance.
Interpret the results of the ANOVA F test shown on the printout for a = 0.05.
a. At a = 05, there is insufficient evidence of differences among the substandard work scale means for the four leadership styles.
b. At a = .05, three is no evidence of differences among the substandard work scale means for the four leadership styles.
c. At a = .05, there is sufficient evidence of difference among at least two of the substandard work scale means for the four leadership styles.
d. None of the above.
Answer:
c. At a = .05, there is sufficient evidence of difference among at least two of the substandard work scale means for the four leadership styles.
Step-by-step explanation:
From the given output, df(Between)=3
df (Between) =k-1, where, k denotes number of groups. Therefore, k-1=3, k=4.
Thus the null hypothesis is as follows:
H0:mu1=mu2=mu3=mu4 (there is no difference in substandard work scale means for four leadership styles)
H1: At least one mean scale is different from another.
Per rule, reject H0, if p value corresponding to F test statistic is less than given level of significance, alpha=0.05.
Here, F(3, 56)=6.056, p<0.05 (the p value is 0.0012). Therefore, reject H0, and conclude that at least one substandard work scale mean of a leadership is significantly different from a substandard work scale mean of another leadership.
