Answer:
A=3797 dollars
Step-by-step explanation:
A=P(1+r)^t t=time period, r is the rate, P is the principal
A=2000(1+0.06)^11
A=3797 dollars
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]
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°
The volume of a gas in a container varies inversely with the pressure on the gas. A container of helium has a volume of 370in3 under a pressure of 15psi (pounds per square inch). Write the equation that relates the volume, V, to the pressure, P. What would be the volume of this gas if the pressure was increased to 25psi?
Answer:
Step-by-step explanation:
When two variables vary inversely, it means that an increase in one would lead to a decrease in the other and vice versa. Since the volume of a gas, V in a container varies inversely with the pressure on the gas, P, if we introduce a constant of proportionality, k, the expression would be
V = k/P
If V = 370 in³ and P = 15psi, then
370 = k/15
k = 370 × 15 = 5550
The equation that relates the volume, V, to the pressure, P would be
V = 5550/P
if the pressure was increased to 25psi, the volume would be
V = 5550/25 = 222 in³
Answer:
v=5550/p
222
Step-by-step explanation:
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.
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1. The population growth of a small town is modeled by the function P(t) = 6545.52e^0.149t where is the populationand is the number of years since 1980. A. What is the growth rate for P(t)? B. What was the population in 1980? C. Find P(11) and explain what it means in the context of the problem. D. What is the projected population in 2019?
Answer:
A. Growth rate = r = 0.149
B. P(0) = 6545.52
C. P(11) = 33,709
D. P(39) = 2,185,876
Step-by-step explanation:
The population growth of a small town is modeled by the following function,
[tex]$ P(t) = 6545.52 e^{0.149t} $[/tex]
Where 6545.52 is the initial population, 0.149 is the rate of growth of the population and t is the number of years since 1980.
A. What is the growth rate for P(t)?
The growth rate is
Growth rate = r = 0.149
B. What was the population in 1980?
Since t is the number of years since 1980, therefore, t = 0 for the year 1980.
[tex]P(0) = 6545.52 e^{0.149(0)} \\\\ P(0) = 6545.52 e^{0} \\\\ P(0) = 6545.52 \\\\[/tex]
C. Find P(11) and explain what it means in the context of the problem.
[tex]P(11) = 6545.52 e^{0.149(11)} \\\\P(11) = 6545.52 e^{1.639} \\\\ P(11) = 6545.52 (5.15) \\\\P(11) = 33,709[/tex]
It represents the population of the town after 11 years since 1980.
D. What is the projected population in 2019?
t = 2019 - 1980 = 39 years
[tex]P(39) = 6545.52 e^{0.149(39)} \\\\P(39) = 6545.52 e^{5.811} \\\\ P(39) = 6545.52 (333.95) \\\\P(39) = 2,185,876[/tex]
Therefore, the projected population in 2019 is expected to be 2,185,876.
Element X decays radioactively with a half life of 11 minutes. If there are 670 grams of Element X, how long, to the nearest tenth of a minute, would it take the element to decay to 26 grams?
The element X will take 22.10 minutes to decay to 26 grams.
What is radioactive radiation?The radioactive radiations are the radiations that an atom nucleus releases.
What is an arithmetic progression?It is a sequence of numbers which have common difference.
How to find the time?The decaying acts like an arithmetic progression in which a=670,d=-30.45 (per minute decaying) and n we have to find with the an value of 26 gram.
So, the formula of nth term of an arithmetic progression is
nth term=a+(n-1)d
26=670+(n-1)*(-30.45)
-644=-30.45n+30.45
-674.45=-30.45n
n=22.10 (after rounding off)
Hence the element X would take 22.10 minutes to decay to 26 grams.
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Answer:
y=a(.5)^{\frac{t}{h}}
y=a(.5)
h
t
y=30 \hspace{15px} a=670 \hspace{15px} h=11 \hspace{15px} t=?
y=30a=670h=11t=?
30=670(.5)^{\frac{t}{11}}
30=670(.5)
11
t
\frac{30}{670}=\frac{670(.5)^{\frac{t}{11}}}{670}
670
30
=
670
670(.5)
11
t
0.0447761=(.5)^{\frac{t}{11}}
0.0447761=(.5)
11
t
\log(0.0447761)=\log((.5)^{\frac{t}{11}})
log(0.0447761)=log((.5)
11
t
)
\log(0.0447761)=\frac{t}{11}\log(.5)
log(0.0447761)=
11
t
log(.5)
Power Rule.
11\log(0.0447761)=t\log(.5)
11log(0.0447761)=tlog(.5)
Multiply by 11.
\frac{11\log(0.0447761)}{\log(.5)}=\frac{t\log(.5)}{\log(.5)}
log(.5)
11log(0.0447761)
=
log(.5)
tlog(.5)
Divide by log(.5).
t=\frac{-14.838489}{-0.30103}
t=
−0.30103
−14.838489
t=49.29239\approx 49.3 \text{ minutes}
t=49.29239≈49.3 minutes
Step-by-step explanation:
–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]
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
earning a 6% pay increase to current $62,900 annual salary
Answer:
Step-by-step explanation:
I assume you are asking for the new salary.
To find 1%, divide 62900 by 100.
629
Multiply this by 3.
1887
Add this to the original answer.
64787
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:
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
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
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
Translate the following into algebraic expressions: The first class has a kids in it, the second has b kids in it, and the third class has c kids in it. The kids from all three classes are divided equally between two buses. How many kids are in each bus?
Answer:
(a + b + c)/2
Step-by-step explanation:
Number of kids in first class: a
Number of kids in second class: b
Number of kids in third class: c
The total number of kids in all classes is: a + b + c
The total number of kids is divided equally between 2 buses:
(a + b + c)/2
Answer:
(a + b + c)/2
Step-by-step explanation:
;)
pls answer quickly!!!
Answer:
x = 90
y = 100
z = -10
Step-by-step explanation:
To find x and y in the above parallelogram ABCD as shown above, recall that one of the properties of a parallelogram is: the consecutive angles in a parallelogram are supplementary.
This means that the sum of angle A and angle B in the parallelogram ABCD = 180°.
Thus,
(x + 30)° + (x - 30)° = 180°
Solve for x
x + 30 + x - 30 = 180
x + x + 30 - 30 = 180
2x = 180
Divide both sides by 2
2x/2 = 180/2
x = 90
=>Find y:
Also, recall that opposite angles in a parallelogram are congruent.
This means, angle A and angle C in parallelogram ABCD above are equal.
Thus,
(x + 30)° = (y + 20)°
Plug in the value of x to solve for y
90 + 30 = y + 20
120 = y + 20
Subtract 20 from both sides
120 - 20 = y
100 = y
y = 100
=>Find z, if z = x - y
z = 90 - 100
z = -10
You buy a 33-pound bag of flour for $9 or you can buy a 1- pound bag for $0.39. Compare the per pound cost for the large and small bag. How much is the pounds per dollars
Answer:
see below
Step-by-step explanation:
9 dollars / 33 lbs = .272727 dollars per lb
.39 / 1 lbs = .39 per lb
The large bag is less expensive
If mean of a b c d is 12 . Find the mean of a b c d and e .if e is 50
The mean is the average. If the mean of 4 letter (a,b,cd) is 12, the sum of them would be 12x4 =48
Now add e to the total: 48 + 50 = 98
The mean is the total divided by the quantity:
Mean = 98 /5 = 19.6
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
Ujalakhan01! Please help me! ASAP ONLY UJALAKHAN01. What's (x-1)(x-1)?
Answer:
[tex]x^2-2x+1[/tex]
Step-by-step explanation:
=> (x-1)(x-1)
Using FOIL
=> [tex]x^2-x-x+1[/tex]
=> [tex]x^2-2x+1[/tex]
Answer:
Step-by-step explanation:
simply :
(x-1)(x-1)= (x-1)²= x²-2x=1
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!!!
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
Three judges measure the lap times of a runner and each measurement is different from the others by a few hundredths of a second. The most likely reason for this difference is
Answer:
Systematic error
Step-by-step explanation:
Assuming that none of the judges are biased, the most likely reason for this difference is the occurrence of systematic errors.
Systematic errors are errors introduced by inaccuracy in the experimental design, be it in the observation or measurement process.
In this case, the reaction time from observing the finish and stopping the clock for each judge might be different, which configures a systematic error.
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
What are the first two steps in solving the radical equation below?
√x - 6 +5 = 12
Look at picture(15 points)
Answer:
B
Step-by-step explanation:
Given
[tex]\sqrt{x-6}[/tex] + 5 = 12 ( subtract 5 from both sides )
[tex]\sqrt{x-6}[/tex] = 7 ( square both sides )
x - 6 = 49 ( add 6 to both sides )
x = 55
Answer:
B. Subtract 5 from both sides and then square both sides.
Step-by-step explanation:
First, subtract 5 from both sides in order to get [tex]\sqrt{x-6}=7^{2}[/tex]
Second, square both sides in order to get [tex]x-6=49[/tex] (p.s. squaring both sides gets rid of the square root)
Third, add 6 to both sides in order to get x=55
Last, see that the answer is B, as you had to subtract 5 from both sides and then square both sides to get your answer
There you go, and good luck on the other questions!
Please answer this correctly
Answer:
1/2
Step-by-step explanation:
The numbers that are odd on the spinner are 1, 3, and 5.
3 numbers out of 6.
3/6 = 1/2
P(odd)= 1/2
An ecologist wishes to mark off a circular sampling region having radius 10 m. However, the radius of the resulting region is actually a random variable R with the following pdf. f(r) = 3/4 [1 ? (12 ? r)^2] 11 ? r ? 13 0 otherwise
What is the expected area of the resulting circular region? (Round your answer to two decimal places.)
Answer:
expected area = 453.20 m^2
Step-by-step explanation:
The given data 11 ≤ r ≤ 13
[tex]\left \{ {{3/4(1-(12-r)^2} \atop {0}} \right.[/tex] o / w
Th expected area of the insulating circular region can be calculated using
= E([tex]\pi r^2 )[/tex]
= [tex]\pi E(r^2)[/tex]
we will have to calculate [tex]E(r^2)[/tex]
attached is the remaining part of the solution
Each of two vectors, and , lies along a coordinate axis in the xy plane. Each vector has its tail at the origin, and the dot product of the two vectors is . Which possibility is correct?
Answer:
A lies along the positive x-axis and B lies along negative x - axis .
Step-by-step explanation:
They tell us that we have two vectors, A and B. And they give us a series of conditions for this, now, what would be the correct possibility.
A lies along the positive x-axis and B lies along negative x - axis .
This is because when both vectors will be in x axis but opposite to each other, then the angle between them will be 180 ° and cos180 ° is -1.
a cat went from a to b a distance of 20 kilometres in one 1/2 hours but return in one hour calculate the average speed for the whole journey
Answer: 16 kph
Step-by-step explanation:
Average Speed = Total Distance/ Total Time
Distance = Speed x Time
The Distance between A and B is 20 kph
Time(A-B) = 1.5 hrs
Time(B-A) = 1 hour
Total Time = 2.5 hrs
Total Distance = 20 + 20 = 40 km
Average Speed = 40 km / 2.5 hrs = 16 kmph
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.
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