Answer:
$638641.33
Step-by-step explanation:
Adam earns $45,000 in his first year.
His salary increases by 3% each successive year. Therefore, his salary the next year is 103% of his previous year.
This is a geometric sequence where the:
First Term, a= $45,000Common ratio, r =103%=1.03(a)
Sum of geometric series[tex]=\dfrac{a(r^n-1)}{r-1}[/tex]
Substituting the given values, Adam's total earnings over n years
[tex]=\dfrac{45000(1.03^n-1)}{1.03-1}\\\\$Adam's Total Earnings=\dfrac{45000(1.03^n-1)}{0,03}[/tex]
(b)When n=12 years
[tex]\text{Adam's Total Earnings for the first 12 years=}\dfrac{45000(1.03^{12}-1)}{0.03}\\=\$638641.33$ (correct to the nearest cent)[/tex]
The list of ordered pairs below represents a relation. {(−6,10),(−5,4),(−1,−9),(9,−4)} Find the range of the relation.
Answer:
The range is simply all the y values of the ordered pairs in the relation so the answer (in increasing order) is -9, -4, 4, 10.
Two airplanes leave an airport at the same time, flying in the same direction. One plane is flying at twice the speed of the other. If after 4 hours they are 1800 km apart, find the speed of each plane.
Answer:
One plane has a speed of 450 km/h and the other has a speed of 900 km/h.
Step-by-step explanation:
I am going to say that:
The speed of the first plane is x.
The speed of the second plane is y.
One plane is flying at twice the speed of the other.
I will say that y = 2x. We could also say that x = 2y.
Two airplanes leave an airport at the same time, flying in the same direction
They fly in the same direction, so their relative speed(difference) at the end of each hour is y - x = 2x - x = x.
If after 4 hours they are 1800 km apart, find the speed of each plane
After 1 hour, they will be x km apart. After 4, 1800. So
1 hour - x km apart
4 hours - 1800 km apart
4x = 1800
x = 1800/4
x = 450
2x = 2*450 = 900
One plane has a speed of 450 km/h and the other has a speed of 900 km/h.
Factor 12q^2+34q-28. Include list of factors.
Answer:
2(2q+7)(3q-2)=0
Step-by-step explanation:
lets set up the equation equal to 0:
12q^2+34q-28=0
now, lets factor:
2(6q^2+17q-14)=0
2(2q+7)(3q-2)=0
now, lets find the solutions:
2q+7=0
2q=-7
q=-3.5
3q-2=0
3q=2
q=2/3
In 1970, 59% of college freshmen thought that capital punishment should be abolished; by 2005, the percentage had dropped to 35%. Is the difference real, or can it be explained by chance
Answer:
there is significant distinction in opinion regarding abolition of capital punishment.
Step-by-step explanation:
Compute the p cost of 2-proportion for estimating difference. The Minitab output pronounces the p valu eto be 0.000. This is less than the assumed importance degree of alpha = 0.05. Therefore, reject null hypothesis to finish that there is significant distinction in opinion regarding abolition of capital punishment.
Suppose U.S. consumers 21 years and older consumed 26.4 gallons of beer and cider per person during 2017. A distributor in Milwaukee believes that beer and cider consumption are higher in that city. A sample of consumers 21 years and older in Milwaukee will be taken, and the sample mean 2017 beer and cider consumption will be used to test the following null and alternative hypotheses:
H0: μ ≤ 26.4
Ha: μ > 26.4
(a) Assume the sample data led to rejection of the null hypothesis. What would be your conclusion about consumption of beer and cider in Milwaukee?
a) Conclude that the population mean annual consumption of beer and cider in Milwaukee is greater than 26.4 gallons and hence lower than throughout the United States.
b) Conclude that the population mean annual consumption of beer and cider in Milwaukee is greater than 26.4 gallons and hence higher than throughout the United States.
c) Conclude that the population mean annual consumption of beer and cider in Milwaukee is less than or equal to 26.4 gallons and hence higher than throughout the United States.
d) Conclude that the population mean annual consumption of beer and cider in Milwaukee is less than or equal to 26.4 gallons and hence lower than throughout the United States.
(b) What is the Type I error in this situation? What are the consequences of making this error?
a) The type I error is rejecting H0 when it is true. This error would claim the consumption in Milwaukee is greater than 26.4 when it is actually less than or equal to 26.4.
b) The type I error is not rejecting H0 when it is true. This error would claim the consumption in Milwaukee is less than or equal to 26.4 when it is actually less than or equal to 26.4.
c) The type I error is not rejecting H0 when it is false. This error would claim the consumption in Milwaukee is less than or equal to 26.4 when it is actually greater than 26.4.
d) The type I error is rejecting H0 when it is false. This error would claim the consumption in Milwaukee is greater than 26.4 when it is actually greater than 26.4.
(c) What is the Type II error in this situation? What are the consequences of making this error?
a) The type II error is accepting H0 when it is true. This error would claim that the population mean annual consumption of beer and cider in Milwaukee is less than or equal to 26.4 gallons when it is less than or equal to 26.4.
b) The type II error is not accepting H0 when it is true. This error would claim that the population mean annual consumption of beer and cider in Milwaukee is greater than 26.4 gallons when it is not.
c) The type II error is accepting H0 when it is false. This error would claim that the population mean annual consumption of beer and cider in Milwaukee is less than or equal to 26.4 gallons when it is not.
d) The type II error is not accepting H0 when it is false. This error would claim that the population mean annual consumption of beer and cider in Milwaukee is greater than 26.4 gallons when it is greater than 26.4.
Answer:
Step-by-step explanation:
A. If the null hypothesis was rejected, the conclusion would be
b) Conclude that the population mean annual consumption of beer and cider in Milwaukee is greater than 26.4 gallons and hence higher than throughout the United States.
B. The correct option is
a) The type I error is rejecting H0 when it is true. This error would claim the consumption in Milwaukee is greater than 26.4 when it is actually less than or equal to 26.4.
C. The correct option is
c) The type II error is accepting H0 when it is false. This error would claim that the population mean annual consumption of beer and cider in Milwaukee is less than or equal to 26.4 gallons when it is not.
On average, a major earthquake (Richter scale 6.0 or above) occurs three times a decade in a certain California county. Find the probability that at least one major earthquake will occur within the next decade. A. .1992 B. .7408 C. .9502 D. .1494
A researcher conducts two studies on the effectiveness of a peer mentoring program. Self-evaluation ratings among participants before, during, and after the program were measured in both studies. In Study 1, 12 participants were observed, and in Study 2, 16 participants were observed. If Fobt = 3.42 in both studies, then in which study will the decision be to reject the null hypothesis at α= 0.05 level of significance?
Answer:
Study 2
Step-by-step explanation:
Okay, so in this question we are given the data or parameters or information Below;
=>" two studies were conducted on the effectiveness of a peer mentoring program."
=> "Self-evaluation ratings among participants before, during, and after the program were measured in both studies."
=> In Study 1, 12 participants were observed"
=> "Study 2, 16 participants were observed."
=> " If Fobt = 3.42 in both studies"
Say Vo = study 2 and V1 = study 1.
Hence, Vo: not effective.
V1 = effective.
The study in which the decision will be to reject the null hypothesis at α= 0.05 level of significance is the STUDY 2.
This is because the value of F > f-critical.
When Ravi brought 3 friends to his house after school, his mother gave them a box of pretzels and a box of crackers. She told them to share the snacks equally among themselves and to give her any that were leftover.
The boys opened the boxes and found a total of 26 pretzels and 35 crackers.
How many pretzels and crackers did the boys give to Ravi's
Answer:
6 pretzels and 8 crackers
Step-by-step explanation:
Since his mom told him to give her the remaining, 6*4= 24 giving to his mom 2 pretzels and 8*4=32 so he has to give his mom 3 crackers. This way him and his friends have the same amount of snacks.
Hope you find it useful. Good night
simplify : 3/5x+x , find the answer ?
Answer:
8x/5
There’s a 1 in front of the x also remember to always simplify
3/5x + 1x
Answer:8x/5
Step-by-step explanation:
Indicate which of the following situations inferential statistics: a. An annual stockholders' report details the assets of the corporation. b. A history instructor tells his class the number of students who received an A on a recent exam. c. The mean of a sample set of scores is calculated to characterize the sample. d. The sample data from a poll are used to estimate the opinion of the population. e. A correlational study is conducted on a sample to determine whether educational level and income in the population are related. f. A newspaper article reports the average salaries of federal employees from data collected on all federal employees.
Answer:
The situations c, d and e are Inferential statistics.
Step-by-step explanation:
Inferential statistics is used to determine reasons for a situation or phenomenon. It helps to draw conclusions grounded on extrapolations, and is hence fundamentally dissimilar from descriptive statistics that only summarizes the data that has truly been measured.
Descriptive statistics are short-term descriptive coefficients that condenses a given data set, which can be a demonstration of the whole or a sample of a whole population.
All descriptive statistics are either central tendency measure or variability measure. Measures of central tendency define the epicenter position of a distribution for a data set.
From the provided situations the Inferential statistics are:
c. The mean of a sample set of scores is calculated to characterize the sample.
d. The sample data from a poll are used to estimate the opinion of the population.
e. A correlational study is conducted on a sample to determine whether educational level and income in the population are related.
Thus, the situations c, d and e are Inferential statistics.
The one that demonstrates inferential statistics would be:
c). The mean of a sample set of scores is calculated to characterize the sample.
d). The sample data from a poll are used to estimate the opinion of the population.
e). A correlational study is conducted on a sample to determine whether the educational level and income in the population are related.
Inferential StatisticsInferential statistics is denoted as the kind of statistics that is concluded through a small sample employed which will act as the representative of the larger population.
The smaller sample's characteristics are analyzed and deductions are made in general about the entire population.
The above statements exemplify these characteristics by calculating the mean of the sample population and performing a correlational examination.
Thus, options c, d, and e are the correct answers.
Learn more about "Statistics" here:
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as a last-minute deal Don and Mary booked a 7 day cruise for a total of $670 if the normal price for a couple is $1340, what discount percent did Don and Mary recieve?
Answer:
Don and Mary received a discount of 50%.
Step-by-step explanation:
Initially, we use a rule of three to find the percentage of the initial price that they paid.
The discount is 100% subtracted by the percentage they paid.
Percentage they paid:
The normal price for a couple is $1340, which is 100%.
They paid $670, which is x%. We have to find x.
$1340 - 100%
$670 - x%
[tex]1340x = 100*670[/tex]
[tex]x = \frac{100*670}{1340}[/tex]
[tex]x = 50[/tex]
They paid 50% of the original price.
What discount percent did Don and Mary recieve?
100 - 50% = 50%
Don and Mary received a discount of 50%.
A 12cmx2cm rectangle sits inside a circle with a radius of 8cm. What isnthe area of the shaded region of the circle
Answer:
The answer would 177.06 centimeters
Please answer...i always answer... please
Answer:
A) -x + y = 2
B) x + 2y = 4
we add both equations
3 y = 6
y = 2
We put y = 2 into equation B)
x + 2 * 2 = 4
x = 0
***********************************************
A) -2x + y = 6
B) x + y = 0
We multiply B) by 2
B) 2 x + 2 y = 0 then we add A)
A) -2x + y = 6
3y = 6
y = 2
Therefore x = -2
Step-by-step explanation:
What’s the correct answer for this question ?
Answer:
C
Step-by-step explanation:
It closely resembles to a sphere.
A circle has a radius of \blue{3}3start color #6495ed, 3, end color #6495ed. An arc in this circle has a central angle of 20^\circ20 ∘ 20, degrees.
Answer: The complete question is "A circle has a radius of \blue{3}3start color #6495ed, 3, end color #6495ed. An arc in this circle has a central angle of 20^\circ20 ∘ 20, degrees. What is the length of the arc?"
The length of the arc is 1.06667 units.
Step-by-step explanation:
According to the question the radius of the circle [tex]R=3 \, units[/tex] and central angle of arc is [tex]\Theta =20^{o}[/tex]
As we know that the length of the arc is given as: [tex]L=R\Theta[/tex]
Where R is radius of the circle, L is the length of the arc and [tex]\Theta[/tex] is central angle in radian.
Now, [tex]\Theta =20^{o}\times \frac{\Pi }{180}=\frac{\Pi }{9} \, rad[/tex]
Therefore, length of the arc is
[tex]L=3\times \frac{\Pi }{9}=\frac{\Pi }{3} =\frac{3.14}{3}=1.0466667 \, units[/tex]
A
B
C
D
Help me out
Answer:
2x^2 + 3/2x -5
Step-by-step explanation:
f(x) = x/2 -2
g(x) = 2x^2 +x -3
f(x)+ g(x) = x/2 -2+ 2x^2 +x -3
Combine like terms
= 2x^2 + 3/2x -5
Select the action you would use to solve x/3=12. Then select the property that justifies that action
Answer:
To solve this I would multiply both sides by 3
Step-by-step explanation:
i would use the multiplication property of equality
The property that justifies that action x/3=12 is a linear question using reciprocal law.
What is a linear equation?A linear equation has one or two variables.
No variable in a linear equation is raised to a power greater than 1.No variable is used as the denominator of a fraction. A linear equation is defined as an equation that is written in the form of ax+by=c. When solving the system of linear equations, we will get the values of the variable, which is called the solution of a linear equation.explanation:-
x/3= 12
x = 12*3 ( using reciprocal)
hence x = 36
solving this we will get the valve of Y if x is given.
Learn more about linear equations here:-https://brainly.com/question/14323743
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A, B, and C are collinear points. B is between A and C. AB = 5x + 8 BC = 6x - 1 AC = 12x - 11 Find AC.
Answer:
AC = 198
Step-by-step explanation:
Since all these points are collinear, we know that the addition of AB plus BC should give the same as AC. We can then set an equation that addresses this identity:
AB + BC = AC
5x +8 +6x - 1 = 12x - 11
Now re-arranging like terms in order to combine them:
8 - 1 + 11 = 12x - 5x - 6x
19 - 1 = 12x - 11x
18 = x
Now that we know the value of 'x", we can determine the value of AC:
AC = 12x - 11
AC = 12 (18) - 11
AC = 216 - 18
AC = 198
Which of the following is the solution to 4 | X+32 8 ?
A. XS-5 or x 2-1
B. X25 or x 2-1
C. $-5 and x-1
D. -1
SUBMIT
Answer:
A
Step-by-step explanation:
x + 3 must be 2 or greater, or -2 or less
So x must be ≥ -1 or ≤ -5
Calculate the length of the apothem of a regular polygon. A
regular hexagon is shown. What is the length of the apothem,
rounded to the nearest inch? Recall that in a regular hexagon,
the length of the radius is equal to the length of each side of the
hexagon
10 in.
a
5 in
9 in
11 in
4 in
Answer:
9 in
Step-by-step explanation:
For an n-sided polygon, the length of the apothem is ...
a = r·cos(180°/n)
We assume your problem statement is saying the radius is 10 inches. For a hexagon, n=6 and we have ...
a = (10 in)cos(30°) ≈ 8.66 in
Rounded to the nearest inch, the apothem is 9 in.
A certain city's population is 120,000 and decreases 1.4% per year for 15 years.
Is this exponential growth or decay? Growth
What is the rate of growth or decay?
What was the initial amount? 120000
What is the function?
What is the population after 10 years? Round to the nearest whole number.
Answer:
Decay Problem.Decay rate, r = 0.014Initial Amount =120,000[tex]P(t)=120000(0.986)^t[/tex]P(10)=104,220Step-by-step explanation:
The exponential function for growth/decay is given as:
[tex]P(t)=P_0(1 \pm r)^t, where:\\P_0$ is the Initial Population\\r is the growth/decay rate\\t is time[/tex]
In this problem:
The city's initial population is 120,000 and it decreases by 1.4% per year.
Since the population decreases, it is a Decay Problem.Decay rate, r=1.4% =0.014Initial Amount =120,000Therefore, the function is:
[tex]P(t)=120000(1 - 0.014)^t\\P(t)=120000(0.986)^t[/tex]
When t=10 years
[tex]P(10)=120000(0.986)^10\\=104219.8\\\approx 104220 $ (to the nearest whole number)[/tex]
The loaves of rye bread distributed to a local store by a certain bakery have an average length of 30 centimeters and a standard deviation of 2 centimeters. Assuming the lengths are normally distributed. What percentage of loaves are between 26.94 and 32.18 centimeters
Answer:
79.91% of loaves are between 26.94 and 32.18 centimeters
Step-by-step explanation:
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this question, we have that:
[tex]\mu = 30, \sigma = 2[/tex]
What percentage of loaves are between 26.94 and 32.18 centimeters
This is the pvalue of Z when X = 32.18 subtracted by the pvalue of Z when X = 26.94.
X = 32.18:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{32.18 - 30}{2}[/tex]
[tex]Z = 1.09[/tex]
[tex]Z = 1.09[/tex] has a pvalue of 0.8621
X = 26.94:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{26.94 - 30}{2}[/tex]
[tex]Z = -1.53[/tex]
[tex]Z = -1.53[/tex] has a pvalue of 0.0630
0.8621 - 0.0630 = 0.7991
79.91% of loaves are between 26.94 and 32.18 centimeters
What are the terms in the algebraic expression
102 + 10 +
3b
Answer:
102, 10, and, 3b
Step-by-step explanation:
If the center of a circle is at
(5,-3) and its radius is 4, complete
its equation:
Answer:
Step-by-step explanation:
[tex](x-5)^2+(y-(-3))^2=16[/tex]
Please answer this correctly
Answer:
629
Step-by-step explanation:
l x w
25x14
4x7
12x18
5x7
629
Parker marks sixths on number line. He writes 5/6 just before 1. What fraction does he write on the first mark to the right of 1?
Answer: 7/6
Step-by-step explanation:
If he is writing sixths, then we have multiples of 1/6.
this is:
0*(1/6) = 0
1*(1/6) = 1/6
.
.
.
5*(1/6) = 5/6 (the numer he wrote at the left of 1)
6*(1/6) = 6/6 = 1
7*(1/6) = 7/6
So the number next to 1, (at the right of 1) must be 7/6.
You also can find it by adding 1/6 to 1.
1/6 + 1 = 1/6 + 6/6 = 7/6.
Answer:
[tex]7/6[/tex]
Explanation:
[tex]1/6 \approx 0.16666[/tex]
[tex]2/6 \approx 0.33333[/tex]
[tex]3/6 = 0.5[/tex]
[tex]4/6 \approx 0.66666[/tex]
[tex]5/6 \approx 0.83333[/tex]
[tex]6/6=1[/tex]
[tex]7/6 \approx 1.16666[/tex]
question is attached
I apologize, I am stumped... I thought you would find either the centroid, circumcenter, or incenter of the triangle created but it didn't work quite right for me.
Assume that 2 cards are drawn from a standard 52-card deck. Find the following probabilities.
a) Assume the cards are drawn without replacement. Find the probability of drawing a club followed by a club.
b) Assume the cards are drawn with replacement. Find the probability of drawing a club followed by a club.
a. The probability of drawing a club followed by a club without replacement is
(Simplify your answer.)
b. The probability of drawing a club followed by a club with replacement is
(Simplify your answer.)
Answer:
A.0.059 , B.0.063
Step-by-step explanation:
1. There are 13 clubs in a pack of 52 cards;
Hence the probability of picking the first club is 13/52;
The probability of picking the second is 12/ 51( remember one card has been removed already so the total number of cards decreases).
Probability of picking two clubs in succession is ;
13/52 × 12/51 = 0.0588 = 0.059( to the nearest thousandth).
2. The probability of drawing a club followed by a club with replacement is;
13/52 × 13 /52 = 0.0625 = 0.063( to the nearest thousandth)
Andrew invests 79500 for 2 years akd earns 10017 of simple interest. Calculate the interest rate.
Answer:use mathematic pathway to calualte
Step-by-step explanation:
A fire hydrant with a blue cap provides water at a rate of 1,500 gallons per minute. A fire hydrant with a green cap provides water at a rate of 1,000 gallons per minute. A fire hydrant with a purple cap provides water at half the rate of a fire hydrant with a green cap. What is the equation in fraction form
Answer:
Fire hydrant with a purple cap (with respect to a fire hydrant with a green cap):
[tex]\dot Q_{purple} = \frac{1}{2}\cdot \dot Q_{green}[/tex]
Step-by-step explanation:
The volume rate of the fire hidrant with a purple cap is equal to the product of the proportion factor and the volume rate of the fire hydrant with a concrete cap.
[tex]\dot Q_{i} = k \cdot \dot Q_{j}[/tex]
There are two different solutions:
Fire hydrant with a purple cap (with respect to a fire hydrant with a green cap):
[tex]\dot Q_{purple} = \frac{1}{2}\cdot \dot Q_{green}[/tex]
Fire hydrant with a purple cap (with respect to a fire hydrant with a blue cap):
[tex]\dot Q_{purple} = \frac{1}{2} \times \frac{1000\,gpm}{1500\,gpm}\cdot \dot Q_{blue}[/tex]
[tex]\dot Q_{purple} = \frac{1}{3}\cdot \dot Q_{blue}[/tex]
