Answer:
a) [tex]\vec v_{B} - \vec v_{C} = 3\, i - 17\,j[/tex], b) [tex]\theta = 79.992^{\textdegree}[/tex] (clockwise)
Step-by-step explanation:
The resultant velocity of the boat must be:
[tex]\vec v_{B} = 15\,i[/tex]
Likewise, the velocity of the current is:
[tex]\vec v_{C} = 2\,i + 17\,j[/tex]
a) The intended velocity of the boat is:
[tex]\vec v_{B} - \vec v_{C} = (15-2)\,i + (0-17)\,j[/tex]
[tex]\vec v_{B} - \vec v_{C} = 3\, i - 17\,j[/tex]
b) The direction of the boat is:
[tex]\theta = \tan^{-1}\left(\frac{17}{3} \right)[/tex] (clockwise)
[tex]\theta = 79.992^{\textdegree}[/tex] (clockwise)
Jamie places fifteen 1 inch cubes in the bottom of a box. She adds 4 more layers of the same number of cubes to completely fill the box. What is the volume of the box?
Answer:
60
Step-by-step explanation:
15cubes assuming 3rows of 5 cubes in one layer so volume of first layer is 3x5x1 =15
4 layers means 4 times or 4 inch in height, either way 4x15 = 60
Answer:
75
Step-by-step explanation:
Suppose the allowable increase and decrease for an objective coefficient of a decision variable that has a current value of $50 are $25 (increase) and $10 (decrease). If the coefficient were to change from $50 to $60, the optimal value of the objective function would not change.
1.True
2.False
g Suppose that the number of bacteria in a certain population increases according to a continuous exponential growth model. A sample of 3000 bacteria selected from this population reached the size of 3145 bacteria in one and a half hours. Find the hourly growth rate parameter. Note: This is a continuous exponential growth model. Write your answer as a percentage. Do not round any intermediate computations, and round your percentage to the nearest hundredth.
Answer:
The hourly growth rate is of 3.15%
Step-by-step explanation:
The population of bacteria after t hours can be modeled by the following formula:
[tex]P(t) = P(0)e^{rt}[/tex]
In which P(0) is the initial population and r is the hourly growth parameter, as a decimal.
A sample of 3000 bacteria selected from this population reached the size of 3145 bacteria in one and a half hours. Find the hourly growth rate parameter.
This means that [tex]P(0) = 3000, P(1.5) = 3145[/tex]
We use this to find r.
[tex]P(t) = P(0)e^{rt}[/tex]
[tex]3145 = 3000e^{1.5r}[/tex]
[tex]e^{1.5r} = \frac{3145}{3000}[/tex]
[tex]\ln{e^{1.5r}} = \ln{\frac{3145}{3000}}[/tex]
[tex]1.5r = \ln{\frac{3145}{3000}}[/tex]
[tex]r = \frac{\ln{\frac{3145}{3000}}}{1.5}[/tex]
[tex]r = 0.0315[/tex]
The hourly growth rate is of 3.15%
What is the equation of the line that goes through the points (1,2) and (2,1)?
Answer:
y = -x+3
Step-by-step explanation:
We have two points so we can find the slope
m =(y2-y1)/(x2-x1)
(1-2)/(2-1)
-1/1
The slope is -1
We can use the slope intercept form of the equation
y = mx+b where m is the slope and b is the y intercept
y = -x+b
Substitute a point into the equation to find b
2 = -1 +b
Add 1 to each side
2+1 =-1+1 +b
3 =b
y = -x+3
What is the effect of visualizing the hole as bigger A taking longer to play golf B worse golf scores C selecting larger circles D better golf score
Answer:
better golf scores
Step-by-step explanation:
i did the quiz just a few secs ago
According to the excerpt, seeing the "hole as bigger" has the benefit of improving gold scores. The right answer is D.
How can imagining larger gaps in scores help?Visualization is the capacity to create mental images of situations and things using one's imagination.
Visualization enhanced results in the excerpt provided.
Golfers typically earned better gold scores when they saw the golf hole as larger circles.
The result of seeing the "hole as greater" is that you will receive better gold scores.
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A certain pen has been designed so that true average writing lifetime under controlled conditions (involving the use of a writing machine) is at least 10 hr. A random sample of 18 pens is selected, the writing lifetime of each is determined, and a normal probability plot of the resulting data support the use of a one-sample t test. The relevant hypotheses are H0: µ = 10 versus Ha: µ < 10.(a) If t = -2.4 and = .05 is selected, what conclusion is appropriate?a. Rejectb. Fail to reject(b) If t = -1.83 and = .01 is selected, what conclusion is appropriate?a. Rejectb. Fail to reject(c) If t = 0.57, what conclusion is appropriate?a.Rejectb. Fail to reject
Answer:
(a) We reject our null hypothesis.
(b) We fail to reject our null hypothesis.
(c) We fail to reject our null hypothesis.
Step-by-step explanation:
We are given that a certain pen has been designed so that true average writing lifetime under controlled conditions (involving the use of a writing machine) is at least 10 hr.
A random sample of 18 pens is selected.
Let [tex]\mu[/tex] = true average writing lifetime under controlled conditions
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu \geq[/tex] 10 hr {means that the true average writing lifetime under controlled conditions is at least 10 hr}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] < 10 hr {means that the true average writing lifetime under controlled conditions is less than 10 hr}
The test statistics that is used here is one-sample t test statistics;
T.S. = [tex]\frac{\bar X -\mu}{\frac{s}{\sqrt{n} } }[/tex] ~ [tex]t_n_-_1[/tex]
where, [tex]\bar X[/tex] = sample mean
s = sample standard deviation
n = sample size of pens = 18
n - 1 = degree of freedom = 18 -1 = 17
Now, the decision rule based on the critical value of t is given by;
If the value of test statistics is more than the critical value of t at 17 degree of freedom for left-tailed test, then we will not reject our null hypothesis as it will not fall in the rejection region.If the value of test statistics is less than the critical value of t at 17 degree of freedom for left-tailed test, then we will reject our null hypothesis as it will fall in the rejection region.(a) Here, test statistics, t = -2.4 and level of significance is 0.05.
Now, at 0.05 significance level, the t table gives critical value of -1.74 at 17 degree of freedom.
Here, clearly the value of test statistics is less than the critical value of t as -2.4 < -1.74, so we reject our null hypothesis.
(b) Here, test statistics, t = -1.83 and level of significance is 0.01.
Now, at 0.051 significance level, the t table gives critical value of -2.567 at 17 degree of freedom.
Here, clearly the value of test statistics is more than the critical value of t as -2.567 < -1.83, so we fail to reject our null hypothesis.
(c) Here, test statistics, t = 0.57 and level of significance is not given so we assume it to be 0.05.
Now, at 0.05 significance level, the t table gives critical value of -1.74 at 17 degree of freedom.
Here, clearly the value of test statistics is more than the critical value of t as -1.74 < 0.57, so we fail to reject our null hypothesis.
he amount of time that a customer spends waiting at an airport check-in counter is a random variable with mean 8.3 minutes and standard deviation 1.4 minutes. Suppose that a random sample of n equals 47 customers is observed. Find the probability that the average time waiting in line for these customers is
Complete question:
He amount of time that a customer spends waiting at an airport check-in counter is a random variable with mean 8.3 minutes and standard deviation 1.4 minutes. Suppose that a random sample of n equals 47 customers is observed. Find the probability that the average time waiting in line for these customers is
a) less than 8 minutes
b) between 8 and 9 minutes
c) less than 7.5 minutes
Answer:
a) 0.0708
b) 0.9291
c) 0.0000
Step-by-step explanation:
Given:
n = 47
u = 8.3 mins
s.d = 1.4 mins
a) Less than 8 minutes:
[tex]P(X<8) = P \frac{X'-u}{s.d/ \sqrt{n}} < \frac{8-8.3}{1.4/ \sqrt{47}}][/tex]
P(X' < 8) = P(Z< - 1.47)
Using the normal distribution table:
NORMSDIST(-1.47)
= 0.0708
b) between 8 and 9 minutes:
P(8< X' <9) =[tex] [\frac{8-8.3}{1.4/ \sqrt{47}}< \frac{X'-u}{s.d/ \sqrt{n}} < \frac{9-8.3}{1.4/ \sqrt{47}}][/tex]
= P(-1.47 <Z< 6.366)
= P( Z< 6.366) - P(Z< -1.47)
Using normal distribution table,
[tex] NORMSDIST(6.366)-NORMSDIST(-1.47) [/tex]
0.9999 - 0.0708
= 0.9291
c) Less than 7.5 minutes:
P(X'<7.5) = [tex] P [Z< \frac{7.5-8.3}{1.4/ \sqrt{47}}] [/tex]
P(X' < 7.5) = P(Z< -3.92)
NORMSDIST (-3.92)
= 0.0000
Gabriellas school is selling tickets to a fall musical. On the dirst day of ticket sales the school sold 10 senior citizen tickets and 14 student tickets for a total of $212. Tje school took in$232 on the second day by selling 12 senior citizen tickets and 14 student tickets. What is the price each of one senior citizen tickets and one student ticket?
What is the volume of this rectangular prism? 2 cm 1/4 cm 2 cm
Answer:
1 cm cubed
Step-by-step explanation:
The volume of a rectangular prism is found by the equation: [tex]V=lwh[/tex] , where [tex]l[/tex] is the length, w is the width, and h is the height.
Here, our dimensions are 2 by 1/4 by 2. So: [tex]l=2,w=1/4,h=2[/tex].
Substituting these into the equation, we have:
[tex]V=2*(1/4)*2=1[/tex]
Thus, the volume is 1 cm cubed.
Hope this helps!
Answer:
1
Step-by-step explanation:
2*2=4
4*1/4=1
multiplying 1/4 is the same as dividing by 4
An ethanol railroad tariff is a fee charged for shipments of ethanol on public railroads. An agricultural association publishes tariff rates for railroad-car shipments of ethanol. Assuming that the standard deviation of such tariff rates is $1250, determine the probability that the mean tariff rate of 350 randomly selected railroad-car shipments of ethanol will be within $110 of the mean tariff rate of all railroad-car shipments of ethanol. Interpret your answer in terms of sampling error.
Answer:
The probability that the mean is less than 110
P(x⁻<110) =0.5
Step-by-step explanation:
Explanation:-
Given the standard deviation of the Population' σ' = 1250
Given sample size 'n' = 350
The standard error of the mean determined by
[tex]S.E = \frac{S.D}{\sqrt{n} }[/tex]
Standard error = [tex]\frac{1250}{\sqrt{350} } = 66.8153[/tex]
by using normal distribution [tex]z = \frac{x -mean}{S.E}[/tex]
[tex]z = \frac{x^{-} -110}{66.8}[/tex]
cross multiplication 66.8z = x⁻-110
x⁻ = 66.81Z+110
P(x⁻<110)=P(66.81Z+110<110)
= P(66.81Z < 110-110)
= P(66.81Z<0)
= P(Z<0)
= 0.5- A(z₁)
= 0.5 - A(0) (here z₁=0)
= 0.5 -0.00
=0.5
Conclusion:-
The probability that the mean is less than 110
P(x⁻<110) =0.5
Arlin has 9 dollars and 37 cents. Lauren has 6 dollars and 63 cents. How much money does Arlin need to give Lauren so that each of them has the same amount of money?
Answer:
Arlin has to give lauren 1.37
Step-by-step explanation:
9.37 + 6.63 / 2 = 16 / 2 = 8
9.37 - 8 = 1.37
Answer:
$1.37
Step-by-step explanation:
I would start by adding up the total money between them. $9.37 + $6.63 = $16.00. They want the same amount of money, so divide the total by two.
$16.00/2 = $8.00.
Now take the difference between how much Arlin had ($9.37) and how much she has now ($8.00).
$9.37 - $8.00 = $1.37
Classify the following polynomials by degree and number of terms
3. x3-8
4. 24
5. 2x^4-x^3+5x^2+x-7
6. 10x
For each question answered I’ll answer two of your questions so a total of 8 questions answered also will give top answer thank you
Polynomials are classified by their degree and number of terms. x³-8 is a 3rd degree binomial, 24 is a 0th degree monomial, 2x⁴-x³+5x²+x-7 is a 4th degree quintic, and 10x is a 1st degree monomial.
Explanation:Polynomials can be classified by their degree (the highest power of the variable) and by the number of terms they contain. This classification is done as follows:
x3-8: This is a binomial (two terms) of 3rd degree, because the highest power of the variable is 3. 24: This is a monomial (one term) of 0th degree, because there is no variable present. 2x4-x3+5x2+x-7: This is a polynomial of 4th degree (due to the highest power of variable) with five terms, so it is also called a quintic. 10x: This is a monomial of 1st degree because the power of the variable is 1. Learn more about Polynomials here:
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Polynomials are classified by degree and number of terms: [tex]x^3[/tex]- 8 is a cubic binomial, 24 is a zero-degree monomial, [tex]2x^4 - x^3 + 5x^2[/tex] + x - 7 is a quartic quintic, and 10x is a linear monomial.
To classify polynomials by degree and number of terms, we check its highest exponent and count its terms:
[tex]x^3[/tex] - 8: This is a binomial (two terms) and its degree is 3 because the highest exponent of x is 3.
24: This is a monomial (one term) and its degree is 0 since it is a constant.
[tex]2x^4 - x^3 + 5x^2[/tex] + x - 7: This is a polynomial of five terms, so it's called a quintic. Its degree is 4 because the highest exponent of x is 4.
10x: This is a monomial (one term) and its degree is 1 because x is to the first power.
The classification is based on the degree of the polynomial, which is determined by the highest power of the variable x present in the equation, and the number of terms present in the polynomial (monomial for one term, binomial for two terms, and so on).
I have 3 Sisters each
Sister has 3 sisters. How
many of us are there?
Answer:
4 sisters
Step-by-step explanation:
-This is a logic question.
-Given that she has 3 sisters, it only means that the 4 are siblings of the same family.
-As such, eaxh sister can correctly claim to have 3 sisters.
Hence, there is a total of 4 sisters.
Luke puts 3 apples in each bag. How many apples does he put in 4 bags
Answer:
12
Step-by-step explanation:
3x4=12
Answer:
12
Step-by-step explanation:
Multiply the number of bags times the apples per bag
4*3 = 12
He needs 12 apples
A professor believes that students at her large university who exercise daily perform better in statistics classes. Since all students at the university are required to take Introduction to Statistics, she randomly selects 17 students who exercise daily and 22 students who exercise at most once per week. She obtains their scores in the final exam in Introduction to Statistics and finds that the students who did not exercise daily primarily produced scores in the 90s, with some scores in the 80s and a very few scores in the 70s and 60s. The students who did exercise daily also had a large number of scores in the 90s and an almost equal number in the 60s, with very few scores in between.
Would it be valid for the professor to use the independent-measures t test to test whether students at her large university who exercise daily perform better in statistics classes?
a. Yes, because the two populations from which the samples are selected have equal variances.
b. Yes, because none of the assumptions of the independent-measures t test are violated.
c. No, because the two populations studied are not independent.
d. No, because the two populations from which the samples are selected do not appear to be normally distributed.
Answer:
d. No, because the two populations from which the samples are selected do not appear to be normally distributed.
Step-by-step explanation:
First, the assumptions of an independent-measures t test are as follows:
1. The data is continuous
2. Only two groups are compared
3. The two groups should be independent
4. The groups should have equal variance
5. The data should be normally distributed
In this case, the 5th assumption has been violated because scores in the two samples are distributed in different ranges in two samples. So the outliers in the scores may be exist. Therefore, it would not be valid for the professor to use the independent-measures t test because the two populations from which the samples are selected do not appear to be normally distributed.
Find 2.4% of $109. Show work.
Answer:
$2.62
Step-by-step explanation:
[tex]2.4\% \: of \: \$109 \: \\ \\ = \frac{2.4}{100} \times 109 \\ \\ = 0.024 \times 109 \\ \\ = \$2.616 \\ \\ \approx \: \$2.62[/tex]
g The Enigma machine was used by Germany in World War II to send coded messages. It has gained fame because it was an excellent coding device for its day and because of the ultimately successful efforts of the British (with considerable aid from the Poles) to crack the Enigma code. The breaking of the code involved, among other things, some very good mathematics developed by Alan Turing and others. One part of the machine consisted of three rotors, each containing the letters A through Z. To read an encrypted message, it was necessary to determine the initial settings of the three rotors (e.g., PDX or JJN). This is only the beginning of the problem of deciphering the Enigma code. Other parts of the machine allowed for many more initial settings. How many different initial settings of the three rotors are there
Answer:
17576
Step-by-step explanation:
Each of the three rotors contained the letters A through Z.
For the first rotor: There are 26 Possible Initial Settings
(A,B,...Z)
For the second rotor: There are 26 possible initial combination with the first rotor likewise.
For the third rotor:There are also 26 possible combinations with the first and second rotors.
Therefore:
Number of Possible Initial Setting of the three rotor=26*26*26=17576
5-2+12÷4
use the order of operations
Step-by-step explanation:
= 5- 2 + 12 /4
= 5 -2 + 3
= 8- 2
= 6
Answer:
6
Explanation:
What you do is you take 12 divided by 4 and you get 3. The equation is now 5-2+3, you subtract 2 from 5 and get 3. Now you have 3 plus 3 which gets you 6.
what is 943 divide by 4
Answer:
235.75
Step-by-step explanation:
Answer:
Math answers to fraction 943 divided by 4 can be calculated as follows.
943/4 math problems division = 235.75. Therefore 235.75 to 2 decimal places= 235.75
943/4 divided by 2 » (943/4) ÷ 2 » 235.75 ÷ 2 = 117.875 .
Step-by-step explanation:
2. A two-stage rocket is in development. The required probability is for the overall rocket to be a minimum of 97% reliable for a successful mission. The first stage is a previously developed design with a known reliability of 99%. The reliability measures for the two stages are independent. What must the minimum reliability for the second stage be
Answer: The minimum reliability for the second stage be 0.979.
Step-by-step explanation:
Since we have given that
Probability for the overall rocket reliable for a successful mission = 97%
Probability for the first stage = 99%
We need to find the minimum reliability for the second stage :
So, it becomes:
P(overall reliability) = P(first stage ) × P(second stage)
[tex]0.97=0.99\times x\\\\\dfrac{0.97}{0.99}=x\\\\0.979=x[/tex]
Hence, the minimum reliability for the second stage be 0.979.
Using probability of independent events, it is found that the minimum reliability for the second stage must be of 97.98%.
If two events, A and B, are independent, the probability of both events happening is the multiplication of the probability of each happening, that is:
[tex]P(A \cap B) = P(A)P(B)[/tex]
In this problem:
There are 2 stages, A and B.The first stage is 99% reliable, hence [tex]P(A) = 0.99[/tex].The system has to be 97% reliable, hence [tex]P(A \cap B) = 0.97[/tex].Then:
[tex]P(A \cap B) = P(A)P(B)[/tex]
[tex]0.97 = 0.99P(B)[/tex]
[tex]P(B) = \frac{0.97}{0.99}[/tex]
[tex]P(B) = 0.9798[/tex]
Hence, the minimum reliability for the second stage must be of 97.98%.
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a line contains the points (-3 -2) and (7,2) determine whether the slope of this line is positive or negative
Answer:
Positive. From those two points the line would slant upwards. Going left to right it would be going up, therefore it's a positive slope
Step-by-step explanation:
The slope of the given lines with two points is positive.
How to find the slope?Slope of a line or straight object is the ratio of how much amount of rise occurs in correspondence to the increment in the run.
Thus, we get:
Slope = rise/ run
y-y₁ = m(x-x₁)
We are given that;
The points =(-3 -2) and (7,2)
Now,
For this line, let’s use (-3, -2) and (7, 2) as the two points. Plugging these values into the formula, we get:
m = (2 - (-2)) / (7 - (-3)) = 4 / 10 = 0.4
Therefore, the slope of this line is 0.4.
A positive slope means that the line goes up from left to right3. A negative slope means that the line goes down from left to right3.
Since 0.4 is a positive number,
Therefore, the slope of this line will be positive.
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The Information Technology Department at a large university wishes to estimate the proportion of students living in the dormitories, p, who own a computer with a 99% confidence interval. What is the minimum required sample size the IT Department should use to estimate the proportion p with a margin of error no larger than 5 percentage points
Answer:
[tex]n=\frac{0.5(1-0.5)}{(\frac{0.05}{1.96})^2}=384.16[/tex]
And rounded up we have that n=385
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".
Solution to the problem
In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 99% of confidence, our significance level would be given by [tex]\alpha=1-0.99=0.01[/tex] and [tex]\alpha/2 =0.005[/tex]. And the critical value would be given by:
[tex]z_{\alpha/2}=-2.58, z_{1-\alpha/2}=2.58[/tex]
The margin of error for the proportion interval is given by this formula:
[tex] ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}[/tex] (a)
And on this case we have that [tex]ME =\pm 0.05[/tex] and we are interested in order to find the value of n, if we solve n from equation (a) we got:
[tex]n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}[/tex] (b)
We can use as an estimator for p [tex]\hat p =0.5[/tex]. And replacing into equation (b) the values from part a we got:
[tex]n=\frac{0.5(1-0.5)}{(\frac{0.05}{1.96})^2}=384.16[/tex]
And rounded up we have that n=385
shayna had $22 to spend on six notebooks. After buying them she had $10. How much did each notebook cost ? solving equations: application
equation and a solution
Answer:
Each notebook costs $2
Step-by-step explanation:
We have to find the amount she spent on each notebook.
22-10=12
We know she spent $12 on six notebooks
We need to divide to find the answer
12/6=2
Each notebook costs $12
Answer:
$2
Step-by-step explanation:
First subtract 10 from 22 to get the price she spent on notebooks which is $12.
Then divide 12 by 6 to get the price she spent on each which is, $2
A company that makes shampoo wants to test whether the average amount of shampoo per bottle is 16 ounces. The standard deviation is known to be 0.20 ounces. Assuming that the hypothesis test is to be performed using 0.10 level of significance and a random sample of n = 64 bottles, how large could the sample mean be before they would reject the null hypothesis? Question 50 options: 16.2 ounces 16.041 ounces 15.8 ounces 16.049 ounces
Answer:
The correct option is 16.041 ounces.
Step-by-step explanation:
A single mean test can be used to determine whether the average amount of shampoo per bottle is 16 ounces.
The hypothesis can be defined as:
H₀: The average amount of shampoo per bottle is 16 ounces, i.e. μ = 16.
Hₐ: The average amount of shampoo per bottle is different from 16 ounces, i.e. μ ≠ 16.
The information provided is:
[tex]n=64\\\sigma=0.20\\\alpha =0.10[/tex]
We can compute a 90% confidence interval to determine whether the population mean is 16 ounces or not.
Since the population standard deviation is known we will compute the z-interval.
The critical value of z for 90% confidence interval is:
[tex]z_{0.05}=1.645[/tex]
*Use a z-table.
Compute the 90% confidence interval for population mean as follows:
[tex]CI=\bar x\pm z_{\alpha/2}\times\frac{\sigma}{\sqrt{n}}\\[/tex]
Since the sample size is quite large, according to the law of large numbers the on increasing the sample size, the mean of the sample approaches the whole population mean.
So, the 90% confidence interval estimate for sample mean is:
[tex]CI=\mu\pm z_{\alpha/2}\times\frac{\sigma}{\sqrt{n}}\\=16\pm 1.645\times \frac{0.20}{\sqrt{64}}\\=16\pm0.041125\\=(15.958875, 16.041125)\\\approx (15.959, 16.041)[/tex]
Thus, the correct option is 16.041 ounces.
What is the area of a triangle with a base of 23 feet and a height of 6 feet
Answer:
A= 69
Step-by-step explanation:
A= h*b/2= (6*23)/2=69
Answer:
A = 69 [tex]ft^{2}[/tex]
Step-by-step explanation:
The formula utilised to determine the area of a triangle is:
A = [tex]\frac{1}{2}[/tex] * b * h
The base and height are given, and thus, can easily be substituted for in the formula to find the area.
A = [tex]\frac{1}{2}[/tex] * 23 * 6
A = 69 [tex]ft^{2}[/tex]
suppose you deposit $3000 in a savings account that pays interest at an annual rate of 4%. if no other money is added or withdrawn from the account how much will be in the account after 10 years?
If no other money is added or withdrawn from the account how much will be in the account after 10 years is $4,440.73.
Simple interestUsing this formula
Amount=Principla(1+Interest rate)^ Time
Let plugm in the formula]
Amount=$3,000(1+0.04)^10
Amount=$3,000(1.04)^10
Amount-$3,000(1.4802442849)
Amount=$4,440.73
Therefore how much will be in the account after 10 years is $4,440.73.
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A college admissions director wishes to estimate the mean age of all students currently enrolled. In a random sample of 20 students, the mean age is found to be 22.9 years. From past studies, the standard deviation is known to be 1.5 years, and the population is normally distributed. Construct a 90% confidence interval of the population mean age.
Answer:
90% confidence interval: (22.35,23.45)
Step-by-step explanation:
We are given the following in the question:
Sample mean, [tex]\bar{x}[/tex] = 22.9 years
Sample size, n = 20
Alpha, α = 0.10
Population standard deviation, σ = 1.5 years
90% Confidence interval:
[tex]\bar{x} \pm z_{critical}\dfrac{\sigma}{\sqrt{n}}[/tex]
Putting the values, we get,
[tex]z_{critical}\text{ at}~\alpha_{0.05} = \pm 1.64[/tex]
[tex]22.9 \pm 1.64(\dfrac{1.5}{\sqrt{20}} )\\\\ = 22.9 \pm 0.55 \\\\= (22.35,23.45)[/tex]
(22.35,23.45) is the required 90% confidence interval for population mean age.
The 90% confidence interval for the population mean age, from the given data, is approximated to be between 22.46 years and 23.34 years.
Explanation:To construct a 90% confidence interval of the population mean age, we will use the formula for the confidence interval, which is sample mean ± Z-score * (Standard deviation/ sqrt (sample size)), where the Z-score is based on the confidence level. For 90%, the Z-score is 1.645.
So in this case, the sample mean is 22.9 years, the known standard deviation is 1.5 years, and the sample size (n) is 20. Plugging these values into the formula gives:
22.9 ± 1.645 * (1.5 / sqrt (20))
When you calculate, it will give an interval of about 22.46 years to 23.34 years. Hence the 90% confidence interval for the population mean age is 22.46 years to 23.34 years.
Learn more about Confidence Interval here:https://brainly.com/question/34700241
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Danika is making pizza. She has 1/3 cup of cheese and knows this is only enough for 2/5 of the recipe. How much cheese does the recipe call for?
Answer:
2/15 cups of cheese
Step-by-step explanation:
Because you are eating 2/5 of the recipe you have to multiply the values
2/5*1/3 = 2/15
if i have 5 blue pens and 3 black pens, What fraction of the number of black pens is the number of blue pens?
Answer:
the answer to the question is 3/5
One side of a square has a value of 3x+2, find the perimeter of the square
Answer:
P = 12x +8
Step-by-step explanation:
The perimeter of a square is given by
P = 4s where s is the side length
P = 4(3x+2)
Distribute
P = 12x +8
Answer:
[tex]12x+8[/tex]
Step-by-step explanation:
[tex]3x+2[/tex] for one side of a square, for a perimeter for the square we need 4 times the side length, so we need:
[tex]4(3x+2)=12x+8[/tex]