Find the final hourly wage if a $15.00 starting wage is increased by 5% each year for 7 years. The final hourly wage is $. Round your answer to the nearest cent.
Answers
An increase of 5% means we will take 5% of the current value and add it to the current value.
This is the same as taking 105% of the current value. Since 105% is the same as 1.05, the 5% increase is the same as multiplying the current value by 1.05.
So, after 1 year, the new hourly wage will be 15 times 1.05:
\(15\cdot1.05=15.75\)After the second year, we will apply this again, but now over the current value, which is 15.75. So we will multiply 15.75 by 1.05.
This is the same as multiplying the initial value by 1.05 twice:
\(15\cdot1.05\cdot1.05=15\cdot(1.05)^2\)So, if we want the value after 7 year, it will be the same as multiplying 15 by 1.05 7 times:
\(15\cdot(1.05)^7\)So, the value after 7 year will be:
\(V=15\cdot(1.05)^7=15\cdot1.407100\ldots=21.106506\ldots\approx21.11\)The final value will be approximately $21.11.
Related Questions
In an analysis of healthcare data, ages have been rounded to the nearest multiple of 5 years. The difference between the true age and the rounded age is assumed to be uniformly distributed on the interval from -2.5yrs to +2.5yrs. The healthcare data are based on a random sample of 48 people.What is the approximate probability that the mean of the rounded ages within 0.25 years of the mean of the true ages?
Answers
Answer:
The approximate probability that the mean of the rounded ages within 0.25 years of the mean of the true ages is P=0.766.
Step-by-step explanation:
We have a uniform distribution from which we are taking a sample of size n=48. We have to determine the sampling distribution and calculate the probability of getting a sample within 0.25 years of the mean of the true ages.
The mean of the uniform distribution is:
\(\mu=\dfrac{Max+Min}{2}=\dfrac{2.5+(-2.5)}{2}=0\)
The standard deviation of the uniform distribution is:
\(\sigma=\dfrac{Max-Min}{\sqrt{12}}=\dfrac{2.5-(-2.5)}{\sqrt{12}}=\dfrac{5}{3.46}=1.44\)
The sampling distribution can be approximated as a normal distribution with the following parameters:
\(\mu_s=\mu=0\\\\\sigma_s=\dfrac{\sigma}{\sqrt{n}}=\dfrac{1.44}{\sqrt{48}}=\dfrac{1.44}{6.93}=0.21\)
We can now calculate the probability that the sample mean falls within 0.25 from the mean of the true ages using the z-score:
\(z=\dfrac{X-\mu}{\sigma}=\dfrac{0.25-0}{0.21}=\dfrac{0.25}{0.21}=1.19\\\\\\P(|X_s-\mu|<0.25)=P(|z|<1.19)=0.766\)
how many values are in the range 17 to 118?
A- 102
B- 135
C- 100
D- 67.5
Answers
Answer:
C- 100 values
Step-by-step explanation:
Answer:
102
Step-by-step explanation:
118-17+1 = 102
An isolated agricultural country has two distinct regions: a lowland plain and an upland of rugged hills. On one unit of land on the PLAIN, a farmer can raise 10 bushels of grain or graze 10 sheep. On one unit of land in the HILLS, a farmer can raise 2 bushels of grain or graze 4 sheep.
Determine which region has the absolute advantage for sheep production. Explain your answer.
Answers
Because food grows more quickly in the hills when exposed to heat and rain rather than sunlight all day. Then for 1 sheep 1 bushel is required in the hills.
What are statistics?
The practice or science of organizing and interpreting numerical data in big quantities, particularly for the objective of concluding proportions in a whole from those in an expected sample.
Given that a remote agricultural nation is divided into two distinct geographic areas: a lowland plain and an upland of rough hills. A farmer can grow 10 bushels of grain or pasture 10 sheep on one unit of land on the plain. A farmer in the hills can pasture 4 sheep or grow 2 bushels of grain on one unit of land.
As opposed to being exposed to sunlight all day, food develops more quickly in the hills when it is exposed to heat and rain.
For uphill = 10 sheep = 10 bushels
For uphill = 1 sheep = 1 bushels
For down plain = 4 sheep = 2 bushels
For down plain = 1 sheep = (1 / 2 ) bushels
Therefore, then for 1 sheep 1 bushel is required in the hills.
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(HELP! MARKING BRAINLIEST) At 2pm, a store had sold 15 packs of toilet paper. By 5pm, the store had sold 57 packs of toilet paper. What is the average rate of change?
Answers
Answer:
14 packs per hour
Step-by-step explanation:
The store sold 57 - 15 = 42 packs of toilet paper in 3 hours.
42 packs in 3 hours = 42/3 = 14 packs per hour
The surface area of the United States is 3.797 million square miles. The state of Alaska, our largest state in terms of area, occupies 655,400 square miles. Using ratios, determine what percentage of the surface area of the United States is occupied by Alaska, rounded to the nearest whole number.
Answers
Alaska occupies 17.22% of the surface area of the United States. Rounding to the nearest whole number, we get 17%. Hence, the answer is:17%
We are given that the surface area of the United States is 3.797 million square miles and the state of Alaska occupies 655,400 square miles. We need to determine what percentage of the surface area of the United States is occupied by Alaska using ratios.To find the percentage, we need to first find the ratio of Alaska's surface area to the surface area of the United States. We can do this by dividing the surface area of Alaska by the surface area of the United States. That is,655,400 / 3,797,000 = 0.1722We can express this ratio as a percentage by multiplying by 100. That is,0.1722 × 100 = 17.22%
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Original population
500
Current population
2,000
Find the percent of increase,
[?]%
Answers
Hope your problem is solved
Answer: 300%
Step-by-step explanation:
percent of increase: new/old×100%-100%
Since it is percent of increase, you need to subtract the original percent (100%) from the current percent.
------------------
new (current)=2000
old (original)=500
new/old×100%-100%
=2000/500×100%-100%
=4×100%-100%
=400%-100%
=300%
Hope this helps!! :)
Please let me know if you have any question or need further explanation
I need this now please
Answers
Answer:
i do beleive it is 2 3/8
Step-by-step explanation:
What are the dimensions of the following matrix?
A=
[-1 5 -7 0]
[6 3 -4 -3]
Answers
Answer: 2 x 4
Reason:
There are 2 rows and 4 columns. The number of rows is listed first, followed by an "x", then the number of columns is listed.
Describe ways you can determine something is either linear or exponential. Be specific PLZ
also plz hurry i need help quick
Answers
34. A motorist started a journey at 10.25a.m. and ended at 6.15 p.m. Calculate the time
used for the journey.
Answers
Write the times for each hour from start time:
10:25 am
11:25 am
12:25 pm
1:25 pm
2:25 pm
3:25 pm
4:25 pm
5:25 pm
6:25 pm
There are 8 hours between 10:25 am and 6:25 pm.
they finished at 6:15 which is 10 minutes before 6:25 ( 25-15 = 10)
10 minutes less than a full hour is 50 minutes ( 60 - 10 = 50)
8 hours - 1 hour = 7 hours
7 hours + 50 minutes = 7 hours 50 minutes total time.
Answer:
seven hours and 50 minutes
Step-by-step explanation:
f(-1/2)=1/2x +3/2 what is the answer to this?
Answers
Answer:
5/4, just sub in x
Step-by-step explanation:
The 6th grade class at Elm City College Prep increased
by 5% this year. If there were 80 scholars in 6th grade
last year, how many are there this year? Show your wo
Answers
Answer:
84 students
Step-by-step explanation:
Let's suppose that 100% was last year's percentage of students.
100% = 80
1% = 80 ÷ 100 = 0.80
100 + 5 = 105% (This year)
0.80 x 105 = 84
There is another method to this called percentage increase, but I kind of forgot the formula. Hope this method is also correct for the question.
Refer to the table summarizing service times (seconds) of dinners at a fast food restaurant. How many individuals are included in the summary? Is it possible to identify the exact values of all of the original service times?
Time (sec) Frequency
60 to 119 7
120 to 179 24
180 to 239 14
240 to 299 1
300 to 359 4
Answers
Answer:
Based on the provided information, the table summarizes service times (in seconds) of dinners at a fast food restaurant. To determine the number of individuals included in the summary, we can sum up the frequencies listed in the table:
7 + 24 + 14 + 1 + 4 = 50
Therefore, there are 50 individuals included in the summary.
Regarding the exact values of all the original service times, it is not possible to determine them precisely based on the given information. The table only provides ranges of service times and their corresponding frequencies. We can determine the range within which each individual's service time falls, but we cannot determine the exact value within that range.
How many boards 6 5/6 will it take to cover 205 in wide
Answers
By using fraction, it can be calculated that
30 boards are required to cover a floor of width 205 inches wide
What is fraction?
Suppose there is a collection and a part of collection has to be taken.
The part which is taken is called fraction. In other words part of a whole is called fraction.
The upper part of the fraction is the numerator and the lower part of the fraction is the denominator.
This is a word problem on fraction
Width of each board = \(6\frac{5}{6}\) inches = \(\frac{41}{6}\) inches
Total width of floor = 205 inches
Number of boards required = \(205 \div \frac{41}{6}\) = \(205 \times \frac{6}{41}\) = 30
30 boards are required
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giving 90 points! NEED IN TWO MINS
Answers
Answer:
300
Step-by-step explanation:
A=wl=10·30=300
multiply the length of the rectangle by the width of the rectangle.
The area is measurement of the surface of a shape. To find the area of a rectangle or a square you need to multiply the length and the width of a rectangle or a square. Area, A, is x times y.
Answer:
Area = 378.5 ft²
Step-by-step explanation:
The figure is having two semi circles and one rectangle.
\({ \sf{area = area \: of \: semicircles + area \: of \: rectangle}} \\ \\ { \sf{area = 2( \frac{1}{2} \pi {r}^{2}) + (l \times w) }} \\ \\ { \sf{area = \pi {r}^{2} + (l \times w) }} \\ \\ { \sf{area = 3.14 \times {5}^{2} + (30 \times 10)}} \\ \\ { \sf{area = 378.5 \: {ft}^{2} }}\)
Find the residual values, and use the graphing calculator tool to make a residual plot. Does the residual plot show that the line of best fit is appropriate for the data?
No, the points are in a curved pattern.
No, the points are evenly distributed about the x-axis.
Yes, the points are in a linear pattern.
Yes, the points have no pattern.
Answers
Answer: The answer is - Yes, it follows a pattern
Step-by-step explanation:
Answer is Yes, the points have no pattern.
Residual values are
1. -2.7 - (-2.84) = 0.14
2. -0.9 - (-0.81) = -0.09
3. 1.1 - (1.22) = -0.12
4. 3.2 - (3.25) = -0.05
5. 5.4 - 5.28 = 0.12
What is Linear graph and Residual value?
Linear graph is represented in the form of a straight line.
If the graph of any relation gives a single straight line then it is known as
a linear graph. The word "linear" stands for a straight line.
The residual for each observation is the difference between predicted
values of y (dependent variable) and observed values of y .
Residual=actual y value−predicted y value
Here,
Residual values are
1. -2.7 - (-2.84) = 0.14
2. -0.9 - (-0.81) = -0.09
3. 1.1 - (1.22) = -0.12
4. 3.2 - (3.25) = -0.05
5. 5.4 - 5.28 = 0.12
When we analyse and draw conclusions in the graph we get no pattern.
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An AP has first term as 3 and Common difference of 2 how many terms are needed to make the sum to 99
Answers
Answer:
9
Step-by-step explanation:
The \(n\)term is \(2n+1\).
\(S_n=\frac{3+2n+1}{2}(n)=99 \\ \\ \frac{n(2n+4)}{2}=99 \\ \\ n(n+2)=99 \\ \\ n^2+2n-99=0 \\ \\ (n+11)(n-9)=0 \\ \\ n=9 \text{ } (n>0)\)
The number of terms that needed to make the sum to 99 is 9
The first term of the arithmetic progression = 3
The common difference = 2
The sum of n term is = (n/2) [2a+(n-1)d]
Where a is the initial term
d is the common difference
Substitute the values in the equation
(n/2) [2(3)+(n-1)2] = 99
(n/2) [6 + 2n - 2] = 99
(n/2)[4+2n] = 99
n(2 + n) = 99
2n + \(n^2\) = 99
\(n^2\) + 2n - 99 = 0
Split the terms
\(n^2\) - 9n +11n - 99 =0
n(n -9) + 11(n - 9) = 0
(n + 11)(n - 9) = 0
n = -11 or 9
Since n cannot be a negative number, therefore n = 9
Hence, the number of terms that needed to make the sum to 99 is 9
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In a fifth-grade class at a school, there are two teachers and 25 students. Part A: Suppose that in the rest of the school, there is an identical teacher- to-student ratio. What are two possible numbers of teachers and students at the entire school? Part B: Suppose that five new students join the fifth- grade class. How will that change the teacher to student ratio? Explain why your answer is correct.
Answers
An engineer has designed a value that will regulate water pressure on an automobile engine. The valve was tested on 120 engines and the mean pressure was 4.6 pounds/square inch. Assume the variance is known to be 0.64. If The valve was designed to produce a mean pressure of 4.4 pounds/square inch, is there sufficient evidence at the 0.1 level that the Valve performs above the specifications? State the null and alternative hypothesis for the above scenario
Answers
The valve was designed to produce a mean pressure of 4.4, this means that our null hypothesis has to be:
\(H_0:\mu=4.4\)Since we want to determine if there is sufficient evidence that the valve is aboce the specifications, this means that we want to determine if the mean is greater than 4.4, that is, the alternartive hypothesis is:
\(H_a:\mu>4.4\)Your neighbor leaves his yard, which is 120 ft from the bus stop. He begins to walk toward you at the bus stop and then passes you. He walks at
a speed of 4 ft/s. His distance d from you after t seconds is given by d = 120 - 4t). After how many seconds is your neighbor 30 ft from you?
A.-22.5 s and -37.5 s
B. 22.5 s and 37.5 s
C. 30 s
D. 15 s and 45 s
Answers
Answer:
ANSWER B
Step-by-step explanation:
d=(120-4t)
30=120-4t
4t=120-30=90
t=90/4=22.5 s
-30==120-4t
4t=120+30=150
t=150/4=37.5 s
Construct a frequency distribution and a relative frequency histogram for the accompanying data set using five classes. Which class has the greatest relative frequency and which has the least relative frequency?Complete the table below. Use the minimum data entry as the lower limit of the first class.Class Frequency, f Relative frequencyx-x x xx-x x xx-x x xx-x x xx-x x x sumf= X?(Type integers or decimals. Round to the nearest thousandth as needed.)DATA:Triglyceride levels of 26 patients (in milligrams per deciliter of blood)138 199 240 143 294 175 240 216 223180 138 266 161 175 402 172 459 147391 152 199 294 188 320 421 161
Answers
Answer:
\(\begin{array}{cc}{Class}& {Frequency} & 138 - 202 & 14 & 203 - 267 & 5 & 268 - 332 & 3 & 333 - 397 & 1 & 398 - 462 & 3 \ \end{array}\)
The class with the greatest is 138- 202 and the class with the least relative frequency is 333 - 397
Step-by-step explanation:
Solving (a): The frequency distribution
Given that:
\(Lowest = 138\) --- i.e. the lowest class value
\(Class = 5\) --- Number of classes
From the given dataset is:
\(Highest = 459\)
So, the range is:
\(Range = Highest - Lowest\)
\(Range = 459 - 138\)
\(Range = 321\)
Divide by the number of class (5) to get the class width
\(Width = 321 \div 5\)
\(Width = 64.2\)
Approximate
\(Width = 64\)
So, we have a class width of 64 in each class;
The frequency table is as follows:
\(\begin{array}{cc}{Class}& {Frequency} & 138 - 202 & 14 & 203 - 267 & 5 & 268 - 332 & 3 & 333 - 397 & 1 & 398 - 462 & 3 \ \end{array}\)
Solving (b) The relative frequency histogram
First, we calculate the relative frequency by dividing the frequency of each class by the total frequency
So, we have:
\(\begin{array}{ccc}{Class}& {Frequency} & {Relative\ Frequency} & 138 - 202 & 14 & 0.53 & 203 - 267 & 5 & 0.19 & 268 - 332 & 3 & 0.12 & 333 - 397 & 1 & 0.04 & 398 - 462 & 3 & 0.12 \ \end{array}\)
See attachment for histogram
The class with the greatest is 138- 202 and the class with the least relative frequency is 333 - 397
2. Erin wrote the following set of numbers.
37, 22, 37, 19, 34, 22, 37, 22, 32, 26, 30, 22
What is the mode of this set of numbers?
037
029
028
022
(1 point)
Answers
The mode of the set of numbers is 22.
What is the mode?Mode is a measure of central tendency that is used to determine the value that occurs most frequently in a set of numbers. Measures of central tendency describe a data set by using its central values. Other measures of central tendency are mean and median.
22 occurs 4 times in the dataset. This is the number that occurs most frequently. This means that 22 is the mode.
Advantages of mode include that it is easy to calculate and it is not affected by outliers. Its disadvantages include that it is a poor measure of average. and it has not use in further stasticistical analysis.
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Of the 16 children at the park, 10 are riding bicycles and 6 are riding skateboards. Select the
statements for which the ratio is correct.
a. The ratio of bicycles to skateboards is 10 to 6
b. The ratio of skateboards to children is 3.8
c. The ratio of bicycles to children 6 to 16
d. The ratio of skateboards to children is 6 10
The ratio of bicycles to children is 5,8
The ratio of bicycles to skateboards is 5.3
e
f.
f
Answers
Answer:
Step-by-step explanation:
its a or e
Answer:
A
Step-by-step explanation:
A is bicycles to skateboards which is 10:6
quantas braças tem 2 tarefas e meia de terra
Answers
Answer:
Fathom in reference to what does this line interpret?
HELP PLEASE ASAP!!! Please show work I’ll mark you brilliant!!!!
Answers
there are 50 people in a coffee shop fourteen are tourist.what percent of people in the shop are tourist and non tourist
Answers
Answer:
tourist: 28%
non-tourist: 72%
Step-by-step explanation:
total: 50
tourists: 14
non-tourists:50 - 14 = 36
tourist percentage: 14/50 × 100% = 28%
non-tourist percentage: 36/50 × 100 = 72%
There are 3 denominations of bills in a wallet: $1, 5$, and $10. There are five fewer $5-bills than $1-bills. There are half as many $10-billsas $5-bills. If there are $115 altogether, find the number of each type of bill in the wallet.
Answers
Answer:
15 $1 bills
10 $5 bills
10 $10 bills
Step-by-step explanation:
Let x = number of $1 bills
"There are five fewer $5-bills than $1-bills."
The number of $5 bills is x - 5
"There are half as many $10-bills as $5-bills."
The number of $10 bills is (x - 5)/2.
A $1 bill is worth $1.
x $1 bills are worth x × 1 = x dollars
A $5 bill is worth $5.
x - 5 $5 are worth 5(x - 5) dollars.
A $10 bill is worth $10.
(x - 5)/2 $10 bills are worth 10(x - 5)/2 = 5(x - 5) dollars.
Now we add the value of each type of bills and set it equal to $115.
x + 5(x - 5) + 5(x - 5) = 115
x + 10(x - 5) = 115
x + 10x - 50 = 115
11x = 165
x = 15
There are 15 $1 bills.
$5 bills: x - 5 = 10 - 5 = 10
There are 10 $5 bills
$10 bills: (x - 5)/2 = (15 - 5)/2 = 5
There are 5 $10 bills
Answer: 15 $1 bills; 10 $5 bills; 10 $10 bills
Check:
First, we check the total value of the bills.
15 $1 bills are worth $15
10 $5 bills are worth $50
10 $10 bills are worth $50
$15 + $50 + $50 = $115
The total does add up to $115.
Now we check the numbers of bills of each denomination.
The number of $1 is 15.
The number of $5 is 5 fewer that 15, so it is 10.
The number of $10 bills is half the number of $5 bills, so it is 5.
All the given information checks out in the answer. The answer is correct.
based off the data of ages of the last six US presidents( 69, 64, 46, 54, 47, and 70) What percentage of presidents ages fall within one standard deviation of the mean? (Round to one decimal place
Answers
Answer:
\(\bar X=\frac{\sum_{i=1}^n X_i}{n}\)
\(s=\sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}\)
And replacing we got:
\( \bar X= 58.33\)
\(s= 10.78\)
Then we can fin the limits for one deviation within the mean like this:
\(\mu -\sigma = 58.33-10.78= 47.55\)
\(\mu -\sigma = 58.33+10.78= 69.11\)
And then we see that the number of values between the limits are: 69, 64, 54,47 who represent 4 and then the percentage would be:
\(\% =\frac{4}{6}*100 =66.7\%\)
Step-by-step explanation:
First we need ot calculate the mean and deviation with the following formulas:
\(\bar X=\frac{\sum_{i=1}^n X_i}{n}\)
\(s=\sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}}\)
And replacing we got:
\( \bar X= 58.33\)
\(s= 10.78\)
Then we can fin the limits for one deviation within the mean like this:
\(\mu -\sigma = 58.33-10.78= 47.55\)
\(\mu -\sigma = 58.33+10.78= 69.11\)
And then we see that the number of values between the limits are: 69, 64, 54,47 who represent 4 and then the percentage would be:
\(\% =\frac{4}{6}*100 =66.7\%\)
Point V is on line segment \overline{UW}
UW
. Given VW=5x-4,VW=5x−4, UV=2x,UV=2x, and UW=5x,UW=5x, determine the numerical length of \overline{VW}.
VW
.
Answers
Answer:
Vw=6
Step-by-step explanation:
The numerical length of VW is 16 units.
What are Arithmetic operations?Arithmetic operations can also be specified by adding, subtracting, dividing, and multiplying built-in functions. The operator that performs the arithmetic operation is called the arithmetic operator.
Operators which let do a basic mathematical calculation
+ Addition operation: Adds values on either side of the operator.
For example 12 + 2 = 14
- Subtraction operation: Subtracts the right-hand operand from the left-hand operand.
For example 12 -2 = 10
Given VW = 5x-4,
VW = 5x−4,
UV = 2x, and
UW = 5x,
By segment addition postulate: UV + VW = UW
Substituting expressions given for each:
⇒ 2x + 5x − 4 = 5x
⇒ 2x = 4
⇒ x = 4
So, VW = 5(4) - 4
VW = 20 - 4
VW = 16
Hence, the numerical length of VW is 16 units.
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100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!
Answers
Answer:
100°
Step-by-step explanation:
tThe sum of all arc measures that make up that circle is 360 degrees.
QS + RQ + RS = 360
QS = 360 - 120 - 140 = 100
An arc angle is the degree measurement of that angle inside the circle, opposite the arc
m∠R = arc QS = 100°
Answer:
∠ R = 50°
Step-by-step explanation:
the inscribed angle R is half the measure of its intercepted arc QS
the sum of the arcs on a circle is 360° , that is
RQ + QS + SR = 360°
120° + QS + 140° = 360°
QS + 260° = 360° ( subtract 260° from both sides )
QS = 100°
Then
∠ R = \(\frac{1}{2}\) × 100° = 50°