Answer:
It will take 9 years
Step-by-step explanation:
use formula A=P(1+ r/n)^nt
37,500= 25,475(1+.046/1)^1*x
37,500/25,475=1.046^x
1.47203= 1.046^x
try out different numbers for x and use whole number since it asks for the nearest year
1.046^8 = 1.43302 and 1.046^9 = 1.4989
so we know its inbetween
8 and 9 to figure out one is the closest whole number try raising it to the power of 8.5 and if it passes 1.47203 then its 9, if it doesnt then its 8
1.046^8.5 = 1.46561
1.46561< 1.47203
since 1.046561 is lower than 1.47203 its safe to assume that the year is between 8.5-8.99 thus we can round up to 9
a jacket originally sold for $45. this week it went on sale for 20% off. what is the discount and what is the sales price?
Answer:
discount = 9
new price = 36
Step-by-step explanation:
The discount is the price times the discount percent
45 * 20%
Change to decimal form
45*.20
9
The new price is the original price minus the discount
45-9 = 36
0.0% complete This is a Numeric Entry Question; skip ahead to question content This question requires a numeric answer Answer here Confirm Q. One of your clients at Wills, Trusts & Estates Law, PLLC passes away. His estate is worth $72,000. He leaves half to charity, and 18 to each of his four children. How much will each child receive? $ _____
Answer:
$9,000
Step-by-step explanation:
The worth of the estate = $72,000
The client leaves half of his estate to charity, and 1/8 to each of his four children.
Therefore, the amount each of the child will receive
[tex]=\dfrac18 \times \$72,000\\\\=\$9,000[/tex]
Each child will receive $9,000.
Answer:
Step-by-step explanation:
A multiple of 6 is a number that has 6 as a factor. What is the sum of the two smallest multiples of 6 that are greater than 103?
Answer:
108 and 114
Step-by-step explanation:
Answer:
222
Step-by-step explanation:
We want the first two multiple of 6 that are greater than 103
103/6 =17 1/6
Rounding up
6*18 =108
The next multiple will be 6* 19
6*19 =114
The sum is 108+114 =222
Help with finding the lettered angles please!
Answer:
i = 77.5°
k = 77.5°
j = 102.5°
h = 155°
Step-by-step explanation:
Since we have an isosceles triangle, we know that ∠i and ∠k are equal. So,
180 - 25 = 2x
155 = 2x
x = 77.5
So m∠i = m∠k = 77.5°
To find m∠j, we use Supplementary Angles:
180 - 77.5 = 102.5°
To find m∠h, we also use Supplementary Angles:
180 - 25 = 155°
Find a function Bold r (t )r(t) for the line passing through the points Upper P (0 comma 0 comma 0 )P(0,0,0) and Upper Q (1 comma 7 comma 6 )Q(1,7,6). Express your answer in terms of Bold ii, Bold jj, and Bold kk.
Answer:
[tex]r(t)=-ti-7tj-6tk[/tex]
Step-by-step explanation:
Given the points P(0,0,0) and Q(1,7,6).
We are to determine a function r(t) for the line passing through P and Q.
To do this, we express it in the form:
[tex]r(t)=r_0+tD,$ where:\\ r_0$ is the starting point and D is the direction vector.[/tex]
[tex]D=P-D=<0,0,0> -<1,7,6>=<-1,-7,-6)[/tex]
Therefore:
[tex]r(t)=<0,0,0>+t<-1,-7,-6>\\=<-t,-7t,-6t>\\$Therefore, the function for the line passing through P and Q is:$\\r(t)=-ti-7tj-6tk[/tex]
Let ????(t)=⟨t2,1−t,4t⟩r(t)=⟨t2,1−t,4t⟩. Calculate the derivative of ????(t)⋅????(t)r(t)⋅a(t) at t=2t=2, assuming that ????(2)=⟨2,5,−3⟩a(2)=⟨2,5,−3⟩ and ????′(2)=⟨4,−3,9⟩
Answer:
The derivative is [tex]\frac{ d (r(t) \cdot a(t))}{dt} = 82[/tex]
Step-by-step explanation:
From the question we are told that
[tex]r(t) = (t^2 ,1 - t , 4t)[/tex]
[tex]a(2) = (2, 5, -3)[/tex] and [tex]a'(2) = (4,-3 , 9)[/tex]
At t = 2
[tex]r(t) = (2^2 ,1 - 2 , 4(2))[/tex]
[tex]r(t) = (4 ,-1 , 8 )[/tex]
Now the derivative of r(t) is
[tex]r'(t) = (2t, -1 ,4)[/tex]
At t = 2
[tex]r'(t) = (2(2), -1 ,4)[/tex]
[tex]r'(t) = (4, -1 ,4)[/tex]
Now the derivative of [tex]r(t) \cdot a(t)[/tex] At t = 2 is
[tex]= r'(2) a(2) + a'(2)r(2)[/tex]
[tex]= (4,-1,4)(2,5,-3) + (4,-3,9)(4,-1,8)[/tex]
[tex]= (8 - 5 -12) + (16+3+72)[/tex]
[tex]= -9 + 91[/tex]
[tex]\frac{ d (r(t) \cdot a(t))}{dt} = 82[/tex]
which of the following is not a perfect cube? 1: 2197 2: 512 3: 2916 4: 343 Which of the following numbers is a perfect cube? * 1: 1525 2: 1728 3: 1458 4: 3993
Answer:
no 4 is not perfect cube and no 2 is perfect cube
Answer:
3. 2916
2. 1728
Step-by-step explanation:
1: 2197 = 13³
2: 512 = 8³
3: 2916 = 2² × 3² × 61
4: 343= 7³
==============
1: 1525 = 5² × 61
2: 1728 = 12³
3: 1458 = 2 × 9³
4: 3993= 3 × 11³
The following frequency table summarizes a set of data.
Value Frequency
2 3
3 2
5 1
6 3
7 1
8 2
11 3
For the above data set, you are interested to determine the "spread" of the data.
Would you employ calculations for the sample standard deviation, or population standard deviation for this data set?
You are interested in the heights of students at a particular middle school. Your data set represents the heights of all students in the middle school with 600 students.
Select the correct answer below:
a. Use calculations for sample standard deviation.
b. Use calculations for population standard deviation.
Answer:
Part A
The population standard deviation is suitable for this dataset as it isnt given whether its a sample or a population distribution and it sure doesn't seem like the findings from such a dataset is to be generalized for some population distribution.
Part B
This is outrightly a population distribution of all the students in the middle school, So, the spread of the height of all students about a mean is best indicated using the population standard deviation.
Step-by-step explanation:
The spread of a dataset is usually the measure of dispersion, a measure of the way the distribution spreads out from a particular mean value.
The problem of which type of standard deviation one should calculate usually arises a lot in Statistics. As the name sounds, population standard deviation usually uses all of the distribution to compute while the sample standard deviation uses the data from the sample distribution
The best advice on when to use the population stamdard deviation formula is that
(1) we have the entire population or
(2) we have a sample of a larger population, but we are only interested in this sample and do not wish to generalize the statistical findings to the population.
The sample standard deviation formula is used when one has a sample of a larger population, one is not only interested in this sample and one wishes to generalize the findings to the population.
The population standard deviation is given as
σ = √[Σ(x - xbar)²/N]
Sample standard deviation
σ = √{[Σ(x - xbar)²]/N-1)}
The only difference is the N and (N-1).
So, for the questions presented,
Part A.
Here, it is evident that the findings for this dataset in the question is just for this dataset, hence,the population standard deviation is suitable for this dataset.
Part B
This is outrightly a population distribution of all the students in the middle school, So, the spread of the height of all students about a mean is best indicated using the population standard deviation.
Hope this Helps!!!
Given the polynomial function below, find F(-1)
F(x)= -x^3-x^2+1
A. -3
B. 3
C. 1
D. -1
A = P(1 + nr) for r
Answer:
r = (An−nP)/P
Step-by-step explanation:
A = P(1 + nr)
Divide P on both sides.
A/P = 1 + nr
Subtract 1 on both sides.
A/P - 1 = nr
Divide n on both sides.
A/P/n - 1/n = r
(An−nP)/P = r
The answer is, r = (An−nP)/P
What is equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
here, we have,
given that,
A = P(1 + nr)
Divide P on both sides.
A/P = 1 + nr
Subtract 1 on both sides.
A/P - 1 = nr
Divide n on both sides.
A/P/n - 1/n = r
(An−nP)/P = r
hence, answer is (An−nP)/P = r.
To learn more on equation click:
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Please answer this correctly
Answer:
1/9
Step-by-step explanation:
The probability of picking a even number is 1/3
The probability of picking another even number is 1/3(if u put the first one back)
So u multiply 1/3 times 1/3 which gives u 1/9 which is ur answer hope this helps
Answer:
1/9
Step-by-step explanation:
3 cards total
1 even number
P(even) = even/total
1/3
Put the card back
3 cards total
1 even number
P(even) = even/total
1/3
P(even, replace, even) = P(even) * P(even) =1/3*1/3 = 1/9
what is the solution to 0.5(5x+1)=3
Answer:
1
Step-by-step explanation:
Divide each term by
0.5 and simplify.
Divide each term in
0.5 ( 5 x + 1 ) = 3 by 0.5 . 0.5 ( 5 x + 1 ) 0.5
= 3 0.5 Cancel the common factor of 0.5 . 5 x + 1 = 3 0.5 Divide 3 by 0.5 .
5 x + 1 = 6
Move all terms not containing
x
to the right side of the equation.
Subtract 1 from both sides of the equation.
5 x = 6 − 1 Subtract 1 from 6 . 5 x = 5
Divide each term by
5 and simplify.
Divide each term in 5 x = 5 by 5 . 5 x 5 = 5 5
Cancel the common factor of 5 .
Cancel the common factor.
5 x 5 = 5 5 Divide x by 1 . x = 5 5 Divide 5 by 5 .
x = 1
If 1/6x+2/3y=8 what is the value of 2x+8y
Answer: 96
Step-by-step explanation:
Simply multiply the first question by 12 to get 2x+8y=96
Hope it helps <3
The graphed line shown below is y = 5 x minus 10. On a coordinate plane, a line goes through (2, 0) and (3, 5). Which equation, when graphed with the given equation, will form a system that has no solution? y = negative 5 x + 10 y = 5 (x + 2) y = 5 (x minus 2) y = negative 5 x minus 10
Answer:
y = 5 (x + 2)
Step-by-step explanation:
Equations with a different x-coefficient will graph as lines that intersect the given one, so will form a system with one solution.
The equation with the same slope and y-intercept (y = 5(x -2)) will graph as the same line, so will form a system with infinite solutions.
The line with the same slope and a different y-intercept will form a system with no solutions:
y = 5 (x + 2)
Answer:
B
Step-by-step explanation:
got it on edge
Given that is both the median and altitude of triangle ABC, congruence postulate SAS is used to prove that triangle ABC is what type of triangle?
Answer:
triangle ΔABC is an isosceles triangle.
Step-by-step explanation:
Given : Given that is both the median and altitude of triangle ABC.
To find : congruence postulate SAS is used to prove that triangle ABC is what type of triangle.
Solution : We have given that both the median and altitude of triangle ABC.
Let AD represent both the median and altitude of triangle ABC.
A median divides the side in two equal parts.
So , BD=BC.
An altitude is a perpendicular drawn .
A perpendicular makes an angle of 90°.
Hence <ADB = <ADC = 90°
AD is the side common to both the triangles ADB and ADC.
Hence, Δ ADB≅ΔADC (SAS congruence postulate).
So AB=AC by c.p .c .t.c(congruent parts of congruent triangles are congruent)
Hence by definition of Isosceles triangle ΔABC is an isosceles triangle.
Therefore, triangle ΔABC is an isosceles triangle.
16.
Entrepreneurs are:
A. Moderate risk taker
B. High risk taker
C. Avoidance
D. Both B and C
Answer:
D
Step-by-step explanation:
THEY AVOID STUFF THAT HURTS THEIR BUISSNESS AND THEY HAVE TO TAKE RISKS THAT CAN LEAVE THEM BROKE
The belief is that the mean number of hours per week of part-time work of high school seniors in a city is 10.5 hours. Data from a simple random sample of 23 high school seniors indicated that their mean number of part-time work was 11.5 with a standard deviation of 1.4. Test whether these data cast doubt on the current belief. (use α = 0.05)
Required:
a. State your null and alternative hypotheses.
b. Sketch the rejection region.
c. Calculate the test statistic. Plot this value in your sketch in part b.
d. Determine the P-value for your test.
e. State your conclusions clearly in complete sentences.
Answer:
a) See step by step explanation
b) See annex
c) t(s) = 3,4255
d) p- value = 0,00146 or 0,15 %
e) See step by step explanation
Step-by-step explanation:
As n < 30 we use a t-student distribution
Population mean μ₀ = 10,5
Sample size n = 23
Degree of freedom n - 1 = 22
Sample mean μ = 11,5
Sample standard deviation s = 1,4
Confidence Interval 95 %
a) Null Hypothesis H₀ μ = μ₀
Alternative Hypothesis Hₐ μ > μ₀
As CI = 95 % α = 5% or α = 0,05
We are solving a one tail-test
With df = 22 and α = 0,05 in t-table we find t(c) = 1,7171
c) t(s) = ( μ - μ₀ ) / s / √n
t(s) = ( 11,5 - 10,5 ) / 1,4 / √23
t(s) = 1 * 4,7958 / 1,4
t(s) = 3,4255
We compare t(s) and t(c)
t(s) > t(c) and t(s) is in the rejection region
Then we reject the null hypothesis.
d) P-value for t(s) = 3,4255 is from t-table equal to:
We find for df = 22 α = 0,001 and α = 0,005
values of t
t 3,505 2, 819 Δt = 0,686
α 0,001 0,005 Δα = 0,004
with these values we interpolate by rule of three
0,686 ⇒ 0,004
(3,505 - 3,4255) ⇒ x
x = 0,000463
and P-value = 0,00146 or 0,15 %
e) The p-value indicates we are far away to consider the accptance of H₀
please help me on number 11 if you know how to :) !
Answer:
(x, y) = (25, 18)
Step-by-step explanation:
Use the angle sum theorem. You can write equations for the right angle and for the linear angle.
(x +11) +(3y) = 90 . . . . sum of angles making the right angle
(y +7) +90 +65 = 180 . . . . sum of angles making the linear angle
From the second equation, we have ...
y = 18 . . . . subtract 162
Substituting into the first equation gives ...
x + 11 + 3(18) = 90
x = 25 . . . . subtract 65
The values of x and y are 25 and 18, respectively.
_____
Check
VQ = 18+7 = 25
QR = 25 +11 = 36
RS = 3·18 = 54
ST = 65
The totals are 36 +54 = 90; 25 +36 +54 +65 = 180, as required.
Melissa sold 18 raffle tickets for the school fundraiser. Jonah sold half as many tickets as Melissa. Shona sold 1.5 times as many tickets as Melissa. If each ticket cost $6, how much money did the students raise?
Answer:
Total money raised by the students = $324
Step-by-step explanation:
Raffle tickets sold by Melissa = 18
'Jonah sold half as many tickets as Melissa'
Jonah sold the raffle tickets = [tex]\frac{1}{2}\times 18=9[/tex]
'Shona sold 1.5 times as many as Melissa'
Tickets sold by Shona = 1.5 × 18 = 27
Total number of raffle tickets sold by all of them = 18 + 9 +27 = 54
Since, each ticket cost = $6
Therefore, total money raised by the students = Total number of tickets sold × Cost of each ticket
= 54 × 6
= $324
Which of the following is the absolute value of 6 - 3/
Answer:
3
Step-by-step explanation:
| 6-3|
Find the value inside the absolute value signs
6-3 = 3
| 3|
Means take the non negative value
|3| = 3
Answer:
3
Step-by-step explanation:
Well absolute value means turn the negative into a positive so,
|6-3|
|3|
= 3
Thus,
the answer is 3.
Hope this helps :)
You would like to have extra spending money, so you decided to work part-time at the local gym. The job pays $15.00 per hour and you work 20 hours per week. Your employer withholds 10% of your gross pay for federal taxes, 7.65% for FICA taxes, and 3% for state taxes.
Required:
a. What is your weekly gross pay?
b. How much is withheld per week for federal taxes?
c. How much is withheld per week for FICA taxes?
d. How much is withheld per week for state taxes?
e. What is your weekly net pay?
f. What percentage of your gross pay is withheld for taxes? Round to the nearest tenth of a percent.
Answer:
a. Weekly gross pay = $300
b. Federal taxes, F = $30
c. Fica taxes, K = 22.95
d. State taxes, S = $9
e. Weekly net pay = 238.05
Step-by-step explanation:
Gross pay, G = 15 $/h * 20 h = 300 / week
Fed taxes, F = 10%*G = $30
FICA, K = 7.65%*G = $22.95
State taxes, S = 3%*G = $9
a. Weekly gross pay = $300
b. Federal taxes, F = $30
c. Fica taxes, K = 22.95
d. State taxes, S = $9
e. Weekly net pay = 300 - (30+22.95+9) = 300 - 55.95 = 238.05
Find the slope of the line. m =
Answer: m=4
Step-by-step explanation:
To find the slope, we use the formula [tex]m=\frac{y_{2} -y_{1} }{x_{2}-x_{1} }[/tex]. We can use the two points to find the slope. The points on the graph are (-2,1) and (-3,-3).
[tex]m=\frac{-3-1}{-3-(-2)} =\frac{-4}{-1} =4[/tex]
A set of prime number between 5 and 15.express it in listing and setbuilder methods
Answer:
A set of prime number between 5 and 15.
Listing method:{ 7,11,13}
Set builder method:{X:X is a set of prime number between 5 and 15}
In listing method,the elements are listed inside the brackets.Listing method are also called rooster method.
In set builder method,the elements are represented by a variable stating their common properties.Set builder method are also called rule method.
Hope this helps...
Good luck on your assignment..
A local chess club claims that the length of time to play a game has a standard deviation of more than 13 minutes. Write sentences describing type I and type II errors for a hypothesis test of this claim.
Answer:
Step-by-step explanation:
A type I error occurs when the researcher rejects the null hypothesis when it is actually true.
A type II error occurs when the research fails to reject the null hypothesis when it is not true.
In this case study,
The null hypothesis is the standard deviation is less that or equal to 13min.
The alternative hypothesis would be that the standard deviation is greater than 13mins.
A type I error would occur when having done an experiment, the researcher rejects the null hypothesis when there is enough evidence that it is actually either less or equal to 13mins
A type II error would occur when the researcher fails to reject the null hypothesis when there is enough evidence that it is actually more than 13mins.
What is the value of $x$ if $-\frac23(x-5) = \frac32(x+1)$?
Answer:
x = (-29)/5
Step-by-step explanation:
Solve for x:
(2 (x - 5))/3 = (3 (x + 1))/2
Multiply both sides by 6:
(6×2 (x - 5))/3 = (6×3 (x + 1))/2
6/3 = (3×2)/3 = 2:
2×2 (x - 5) = (6×3 (x + 1))/2
6/2 = (2×3)/2 = 3:
2×2 (x - 5) = 3×3 (x + 1)
2×2 = 4:
4 (x - 5) = 3×3 (x + 1)
3×3 = 9:
4 (x - 5) = 9 (x + 1)
Expand out terms of the left hand side:
4 x - 20 = 9 (x + 1)
Expand out terms of the right hand side:
4 x - 20 = 9 x + 9
Subtract 9 x from both sides:
(4 x - 9 x) - 20 = (9 x - 9 x) + 9
4 x - 9 x = -5 x:
-5 x - 20 = (9 x - 9 x) + 9
9 x - 9 x = 0:
-5 x - 20 = 9
Add 20 to both sides:
(20 - 20) - 5 x = 20 + 9
20 - 20 = 0:
-5 x = 9 + 20
9 + 20 = 29:
-5 x = 29
Divide both sides of -5 x = 29 by -5:
(-5 x)/(-5) = 29/(-5)
(-5)/(-5) = 1:
x = 29/(-5)
Multiply numerator and denominator of 29/(-5) by -1:
Answer: x = (-29)/5
Answer:
Step-by-step explanation:
Multiplying both sides by $6$ to get rid of the fractions gives\[6\left(-\frac23\right)(k-6) = 6\left(\frac32\right)(k+6),\]so\[-4(k-6) = 9(k+6).\]Expanding both sides gives $-4k+24 = 9k + 54.$ Adding $4k$ to both sides gives $24 = 13k+54.$ Subtracting $54$ from both sides gives $-30=13k.$ Dividing both sides by $13$ gives $k =-30/13}.$
13. [-/1 Points]
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A management consulting firm recommends that the ratio of middle-management salaries to management trainee salaries be 9:4. Using this recommendation, what is the annual middle
management salary if the annual management trainee salary is $24,000? (Round your answer to the nearest dollar.)
Enter a number
Answer:
67500
Step-by-step explanation:
you would set up the equation:x/y=5/4
Consider a rat going through a maze, and each time the rat begins the maze he has 30% chance of finishing successfully. The rat goes through the maze over and over again until he is successful in finishing the maze. Whether or not the rat finishes the maze on one trial has no impact on his chance of finishing the maze on the next trial.
What is the probability that the rat fails the maze 6 times in a row, and then succeeds on his 7th attempt? Round your answer to two decimal places.
Answer:
3.53% probability that the rat fails the maze 6 times in a row, and then succeeds on his 7th attempt
Step-by-step explanation:
For each time that the rat goes through the maze, there are only two possible outcomes. Either he fails it, or he succeds. The trials are independent. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
What is the probability that the rat fails the maze 6 times in a row, and then succeeds on his 7th attempt?
Missing on the first six, each with 70% probability(P(X = 6) when p = 0.7, n = 6).
Succeeding on the 7th attempt, with p = 0.3. So
[tex]P = 0.3P(X = 6)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 6) = C_{6,6}.(0.7)^{6}.(0.3)^{0} = 0.117649[/tex]
[tex]P = 0.3P(X = 6) = 0.3*0.117649 = 0.0353[/tex]
3.53% probability that the rat fails the maze 6 times in a row, and then succeeds on his 7th attempt
Answer:
3.53% probability that the rat fails the maze 6 times in a row, and then succeeds on his 7th attempt
Step-by-step explanation:
For each time that the rat goes through the maze, there are only two possible outcomes. Either he fails it, or he succeds. The trials are independent. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
In which is the number of different combinations of x objects from a set of n elements, given by the following formula.
And p is the probability of X happening.
What is the probability that the rat fails the maze 6 times in a row, and then succeeds on his 7th attempt?
Missing on the first six, each with 70% probability(P(X = 6) when p = 0.7, n = 6).
Succeeding on the 7th attempt, with p = 0.3. So
In which
3.53% probability that the rat fails the maze 6 times in a row, and then succeeds on his 7th attempt
y varies inversely as x . If x = 6 then y = 5. Find y when x = 2.
Answer:
y = 15
Step-by-step explanation:
y varies inversely as x.
y = k/x
5 = k/6
Find constant of proportionality.
5 × 6 = k
30 = k
Plug k as 30 and x as 2.
y = 30/2
y = 15
Given O below, if WX and YZ are congruent, what is the measure of YOZ? A. 103 B. 257 C.77 D.206
Answer: your answer should be 103
Answer:
Step-by-step explanation:
103
–24(b − 966) = –768
b = _______
Answer:
b = 998
Step-by-step explanation:
first distribute the -24
-24b + 23184 = -768
then subtract 23184 on both sides to get
-24b = -23952
then divide -24 on both sides to get
b = 998
then to make sure it is correct you plug it back in
-24(998-966) = -768
Answer:
b = 998
Step-by-step explanation:
[tex]-24(b-966)=-768\\-24b+23184=-768\\-24b=-23,952\\24b=23,952\\b=998[/tex]