Answer:
[tex]S=42000*\sum_{i=0}^{n}0.02^n[/tex]
Step-by-step explanation:
The salary per year is the combination of the $42000 per year (constant) plus the 2% rise per year. So the ecuation is:
Firt year [tex]S=(42000 + 0.02*42000)[/tex]
Second year [tex]S=(42000 + 0.02*42000)+0.02*(42000 + 0.2*42000)[/tex]
Generalizing:
[tex]S=42000*\sum_{i=0}^{n}0.02^n[/tex]
Final answer:
The equation that represents Giovanna's current situation is Current Salary = $42,840.
Explanation:
The equation that represents Giovanna's current situation can be determined by using the formula for calculating annual salary with a percentage increase.
The formula is:
Current Salary = Initial Salary + (Percentage Increase * Initial Salary)
Using this formula, we can substitute the given values:
Initial Salary = $42,000
Percentage Increase = 2% (or 0.02)
Substituting these values into the formula:
Current Salary = $42,000 + (0.02 * $42,000)
Simplifying the equation:
Current Salary = $42,000 + $840
Current Salary = $42,840
Therefore, the equation that represents Giovanna's current situation is:
Current Salary = $42,840
Can you help with these two questions?
1)
Scientists are studying a 500 g. sample of a radioactive element. which has an annual decay rate of 11%. How many grams of the sample would be left after 10 years?
Round the answer to two decimal places.
2)
In 2000, the population of an Ohio town was 140,212. The population is expected to grow at a rate of 2.5% each year.
At this rate, what would be the population in 2040?
Round your answer to the nearest whole number.
1) 155.91 grams would be left after 10 years
2) The population would be 376,478 in 2040
Step-by-step explanation:
The form of the exponential function is [tex]y=a(b)^{x}[/tex] , where
a is the initial amount (y at x = 0)b is the growth/decay factorb = 1 + r, where r is the rate of growthb = 1 - r, where r is the rate of decay1)
Scientists are studying a 500 grams sample of a radioactive element, which has an annual decay rate of 11%
∵ The initial amount is 500 grams
∴ a = 500
∵ The annual decay rate is 11%
∴ r = 11% = 11 ÷ 100 = 0.11
∵ b = 1 - r ⇒ decay
∴ b = 1 - 0.11 = 0.89
- We need to find how many grams of the sample would be left
after 10 years
∴ x = 10
- Substitute all of these values in the form of the exponential function
∵ [tex]y=500(0.89)^{10}[/tex]
∴ y = 155.9085996
- Round it to 2 decimal places
∴ y = 155.91
155.91 grams would be left after 10 years
2)
In 2000, the population of an Ohio town was 140,212. The population is expected to grow at a rate of 2.5% each year
∵ The population of an Ohio town was 140,212
∴ a = 140.212
∵ The population is expected to grow at a rate of 2.5% each year
∴ r = 2.5% = 2.5 ÷ 100 = 0.025
∵ b = 1 + r ⇒ growth
∴ b = 1 + 0.025 = 1.025
- We need to find the population in 2040
∵ The number of years is 2040 - 2000 = 40 years
∴ x = 40
- Substitute all of these values in the form of the exponential function
∵ [tex]y=140212(1.025)^{40}[/tex]
∴ y = 376478.1709
- Round it to the nearest whole number
∴ y = 376,478
The population would be 376,478 in 2040
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A jumbo size 90 ounces drink at a certain gas station has 890-calories. How many calories are there in a 14 ounce drink
To find the calories in a 14 ounce drink, we first determine the calorie content per ounce from a 90 ounce drink. We find it to be about 9.89 calories per ounce. Multiplying this by 14 gives us approximately 138.46 calories in a 14 ounce drink.
Explanation:To find the calories in a 14 ounce drink, we need to first determine the calorie content per ounce in the 90-ounce drink. This is found by dividing the total calories (890) by the total ounces (90). The number we get from this division (calories per ounce) can then be multiplied by the ounces in the smaller drink (14) to get the number of calories in that drink.
First, divide 890 calories by 90 ounces to find the number of calories per ounce. 890 ÷ 90 = 9.89 calories/ounceNext, multiply this number by the number of ounces in the smaller drink. 9.89 * 14 = 138.46 calories.Therefore, a 14 ounce drink from this gas station would have approximately 138.46 calories.
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You purchase 26 “parking hours” that you can use over the next month to park your food truck at the fair. Weekday hours costs $2/hour and weekend hours cost $10/hour. You spent a total of $220. How many weekday hours did you purchase?
You have purchased 5 weekday hours.
Step-by-step explanation:
Parking hours purchased = 26
Cost per hour on weekday = $2
Cost per hour on weekend = $10
Total spent = $220
Let,
Number of hours on weekdays = x
Number of hours on weekend = y
According to given statement;
x+y=26 Eqn 1
2x+10y=220 Eqn 2
Multiplying Eqn 1 by 10
[tex]10(x+y=26)\\10x+10y=260\ \ \ Eqn\ 3\\[/tex]
Subtracting Eqn 2 from Eqn 3
[tex](10x+10y)-(2x+10y)=260-220\\10x+10y-2x-10y=40\\8x=40[/tex]
Dividing both sides by 8
[tex]\frac{8x}{8}=\frac{40}{8}\\x=5[/tex]
You have purchased 5 weekday hours.
Keywords: linear equation, elimination method
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The city of Toronto’s population rose from 2,000,000 to 4,500,000 in the last twenty years of the twentieth
century. What was the annual average percentage increase in population for that period?
(a) 2.5% (b) 22.5% (c) 11.25% (d) 225% (e) none of these
Answer:
E
Step-by-step explanation:
We will first find the percentage increase of 20 years. Then we will divide that by 20 to get the annual average percentage increase.
To get the percentage increase, we will find the increased amount and divide that by original population (2,000,000). Multiply that by 100 to get the percentage.
So,
Increased amount = 4,500,000 - 2,000,000 = 2,500,000
Now the percentage increase:
[tex]\frac{2,500,000}{2,000,000}*100=125[/tex]
So, in 20 years, the percentage increase is 125%
Per Year = 125/20 = 6.25% average per year
No correct answer in the answer choices from A through D, so E is the correct answer, None of These.
Determine if the graphed function is linear or nonlinear.
Select from the drop-down menu to correctly complete the sentence.
The graphed function is _____________.
Answer:
non linear
Step-by-step explanation:
linear means a straight line graph. This type is quadratic since it has a parabola.
Answer:
The graphed function is nonlinear.Step-by-step explanation:
When we talk about linear and nolinear funciton, we can distinguish them by using their graphs.
A linear function has a linear behaviour, that means it's representes by a straight line.
A nonlinear function doesn't have a straight line behaviour.
That's the easiest way to distinguish wether is a linear function or nonlinear.
Therefore, in this case, you can observe that the graph is not a straight line, that means the function is nonlinear.
PLEASE....I need help on this!
15,567 because yeah i know math
Joan has 3/4 yards of fabric. She needs 2/3 if that amount to make a small flag. How much fabric will she need in all?
Answer:
1/2 of a yard
Step-by-step explanation:
Here you have to find 2/3 of 3/4.
In this case "of" means multiplication.
2/3 × 3/4 = 2×3 / 3×4 = 6/12 = 1/2
5h+-6h=20 solve h help me please
Answer:
[tex] \: \: \: \: \: \: \: \: 5h + ( - 6h) = 20 \\ = > 5h - 6h = 20 \\ = > - h = 20 \\ = > h = - 20[/tex]
If g(f) the inverse of
) and fx) = 4x + 12 what is g(x)?
g(x) - 12x + 4
og(x) - x-12
g(x) = x-3
g(x) -
x-3
Save and Exit
Next
Su
Mark this and return
Answer:
[tex]g(x)=\frac{x}{4}-3[/tex]
Step-by-step explanation:
we have
[tex]f(x)=4x+12[/tex]
Find the inverse
Let
y=f(x)
[tex]y=4x+12[/tex]
Exchange the variables (x for y and y for x)
[tex]x=4y+12[/tex]
Isolate he variable y
subtract 12 both sides
[tex]4y=x-12[/tex]
divide by 4 both sides
[tex]y=\frac{x}{4}-3[/tex]
Let
g(x)=y
[tex]g(x)=\frac{x}{4}-3[/tex] ---> inverse of the function f(x)
Which describes the correlation shown in the scatterplot?
A. There is a positive linear correlation.
B. There is a negative linear correlation.
C. There is no positive or negative correlation.
D. There is a nonlinear correlation.
Answer:
C
Step-by-step explanation: As you can see, the correlation goes up and down, this does not represent positive nor negative. Therefore, C would be your final answer.
tim and his brother are building towers out of blocks. Tim is using blue blocks that are 6 cm tall and his brother is using green blocks that are 8 cm tall. They both made towers the same height. What is the shortest possible height of the tower? how many of each color block did they use
The shortest possible height of the tower is 24 cm
They used 4 blue blocks and 3 green blocks
Step-by-step explanation:
Tim and his brother are building towers out of blocks
Tim is using blue blocks that are 6 cm tallHis brother is using green blocks that are 8 cm tallThey both made towers the same heightWe need to find the shortest possible height of the tower and how many of each color block they used
∵ Tim is using blue blocks that are 6 cm tall
∴ The height of his tower is a number divisible by 6
∵ His brother is using green blocks that are 8 cm tall
∴ The height of his tower is a number divisible by 8
∵ The heights of their towers are equal
∴ The height of the towers must be a number divisible by 6 and 8
Let us write some multiples of 6 and 8 to find the first common multiple of them
∵ The multiples of 6 are 6 , 12 , 18 , 24 , 30 , 36 , .........
∵ The multiples of 8 are 8 , 16 , 24 , 32 , 40 , .............
∵ The first common multiple of them is 24
∴ The shortest possible height of the tower is 24 cm
∵ The height of each blue block is 6 cm
- Divide the height of the tower by the height of the block to
find the number of blue blocks
∵ 24 ÷ 6 = 4
∴ Time is using 4 blue blocks
∵ The height of each green block is 8 cm
- Divide the height of the tower by the height of the block to
find the number of green blocks
∵ 24 ÷ 8 = 3
∴ His brother is using 3 green blocks
The shortest possible height of the tower is 24 cm
They used 4 blue blocks and 3 green blocks
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A construction company is repaving a damaged road. So far, they have repaved a total of 97,338 inches of the road. Today, they repaved 29,092 inches of the road. How many inches of the road had they repaved before today?
68,246 inches of road had been repaved before today.
Step-by-step explanation:
Given,
Length of road repaved so far = 97338 inches
Length repaved today = 29092 inches
Length repaved before today = Total length repaved - Length repaved today
Length repaved before today = 97338 - 29092
Length repaved before today = 68246 inches
68,246 inches of road had been repaved before today.
Keywords: subtraction
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help asap! What is equal to 3,068 times 108=?
Answer:
Step-by-step explanation:
3,068 × 108
= 331344
Answer:
331,344
Step-by-step explanation:
Line up the numbers like how u would do it if adding or subtracting and multiply each digit in 108 by each digit in 3068 starting with 8*8. Then do the same with multiplying each digit in 3068 by each digit in 108 starting with 8*8
If x equals 7. What is 3x-47
Answer: x = -26
Step-by-step explanation:
3x-47
substitute x with 7: 3(7)-47
3(7) = 21 -47 = -26
Answer:
-26
Step-by-step explanation:
x=7
3 is being multiplied by X
replace X with 7 in your equation
Your equation should then look like this: 3(7)-47
The parentheses around the 7 indicate that the 7 is being multiplied by the 3 or in other words: (3*7)-47
multiply 3 and seven before subtracting 47
3*7= 21
Once you have your answer to that subtract 47, your answer should be a negative # because you are subtracting a larger # from a smaller #
21-47= -26
so if X equals 7. 3x-47= -26
Logan's e-reader sent a notification saying that he has completed 75% of the e-book.
Logan has read 180 pages and he wants to know the total number of pages in the e-book.
Answer:
The total number of pages in the e-book is 240.
Step-by-step explanation:
Given:
Logan has completed 75%
Logan has read 180 pages
To Find:
The total number of pages in the e-book= ?
Solution:
Let X be the total number of pages on the e-book
then
=> 75% of X = 180
Now lets find the value of X
X = [tex]\frac{180}{75\%}[/tex]
X = [tex]\frac{180}{\frac{75}{100}}[/tex]
X = [tex]\frac{180}{0.75}[/tex]
X = 240
The total number of pages in the e-book is 240.
To find the total number of pages in the e-book, we can set up a proportion based on the information given. Logan has read 75% of the e-book, which corresponds to 180 pages. We can represent this as:
75% of total pages = 180 pages
To find the total number of pages, we can express the percentage as a fraction and solve for the total number of pages (let's denote this as P):
[tex]\(\frac{75}{100} \times P = 180\)[/tex]
Now, we can solve for P:
[tex]\(P = \frac{180 \times 100}{75}\)[/tex]
[tex]\(P = \frac{180}{0.75}\)[/tex]
[tex]\(P = 240\)[/tex]
Therefore, the total number of pages in the e-book is 240.
The sum of the digits of a three-digit number is 16 .the tens digit is two more than the units digit and the unit digit is triple the hundreds digit .what is the number?
Answer:
286
Step-by-step explanation:
If the three-digit number is xyz, then:
x + y + z = 16
y = z + 2
z = 3x
Substitute the third equation into the second:
y = 3x + 2
Substitute this and the third equation into the first:
x + (3x + 2) + (3x) = 16
7x + 2 = 16
7x = 14
x = 2
y = 3x + 2 = 8
z = 3x = 6
The number is 286.
The three-digit number where the sum of its digits equal 16, the tens digit is two more than the unit's digit, and the unit's digit is triple the hundreds digit is 286.
Explanation:The question involves finding a three-digit number where the sum of the digits is 16, the tens digit is two more than the unit's digit, and the unit's digit is triple the hundreds digit. Let's represent the hundreds digit as 'h,' the tens digit as 't', and the units digit as 'u'. According to the problem, we have three equations:
h + t + u = 16 (sum of the digits)t = u + 2 (tens is two more than units)u = 3h (units is triple hundreds)Substituting the third equation into the first, we get h + (3h + 2) + 3h = 16, which simplifies to 7h + 2 = 16, leading to h = 2. Thus, u = 3h = 6, and t = u + 2 = 8. Therefore, the three-digit number is 286.
Becky’s square living room needs new carpet. She needs about 200 square feet of carpet to cover the floor. What are the approximate dimensions of the room? Estimate using perfect squares to narrow your range. Show your work.
What is the slope of a line that is perpendicular to y = 1/8x - 9?
Answer:
-8
Step-by-step explanation:
Perpendicular means negative reciprocal of the slope.
Negative reciprocal of 1/8 is -8.
The slope of a line that is perpendicular to y = 1/8x - 9 is -8. This is because perpendicular lines have slopes that are negative reciprocals of each other.
Explanation:In Mathematics, particularly in algebra, the slope of a line is a measure of the steepness of the line. It's also a central part of the line's equation. In the equation you provided, y = 1/8x - 9, the slope of this line is 1/8.
The property of perpendicular lines is that their slopes are negative reciprocals of each other. The negative reciprocal of 1/8 is found by flipping the fraction to get 8/1 and changing the sign to get -8. Therefore, the slope of a line that is perpendicular to y = 1/8x - 9 is -8.
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help me solve this
4 — (x-2) (x+2)
Using [tex](x-a)(x+a)=x^2-a^2[/tex] to obtain
[tex]4-(x^2-4)=4-x^2+4=8-x^2[/tex]
Hope this helps.
For the function y=8−5x, what is the ordered pair when x=7?
Answer:
Ordered pairs are (0,7) , (1,8) , (-1,6) and (-7,0)
Step-by-step explanation:
Answer:
(7, -27)
Step-by-step explanation:
Given y=8-5x and x=7,
We substitute x=7 into the equation y=8-5x.
This would give us y= 8-5(7) and can be further sinplified to y= 8-35 = -27.
Ordered pair refers to 2 numbers that come in a pair to fulfil an equation in the form of (x, y).
in the number 549.062 which number is in the 100th place
Answer:
5
Step-by-step explanation:
Answer: the answer is 6
Step-by-step explanation: the hundredth place is 2 spaces behind the decimal.
Which equation is equivalent to 8x + 3 ( x +5) -5 (x-4) = 2
The detailed answer explains how to simplify and solve the expression 8x + 3(x + 5) - 5(x - 4) = 2 step by step.
Explanation:To find the equation equivalent to 8x + 3(x + 5) - 5(x - 4) = 2, we need to expand and simplify the expression step by step:
Distribute the terms: 8x + 3x + 15 - 5x + 20 = 2Combine like terms: 6x + 35 = 2Isolate x: 6x = -33Solve for x: x = -33/6 or x = -11/2please help
3×[(12+33)]÷5-7
Answer:3x(45/5)-7)
(3x9)-7=27-7=20
Step-by-step explanation:
Answer:
Step-by-step explanation:
3×[(12+33)]÷5-7 = 3 * 45/5 -7
=3*9 - 7 = 27 - 7 = 20
Correctly complete this sequence: 88511, 16351, ?, 10251
Answer:
73155 is the required 3rd number that will complete the sequence as: 88511, 16351, 73155 , 10251.
Step-by-step explanation:
So, let us consider 88511 and determine the pattern to find the next number and so on to complete the sequence.
Adding the first 2 digits in the number 88511 i.e. 8 + 8 = 16
Subtracting the 3rd digit from the 2nd digit i.e. 8 - 5 = 3
Multiplying the 3rd digit and 4th digit i.e. 5 × 1 = 5
Dividing the 4th digit by the 5th digit i.e. 1 ÷ 1 = 1
Hence, using these steps would get us the number 16351.
So, the next number would be obtained using same steps:
Adding the first 2 digits in the number 16351 i.e. 1 + 6 = 7
Subtracting the 3rd digit from the 2nd digit i.e. 6 - 3 = 3
Multiplying the 3rd digit and 4th digit i.e. 3 × 5 = 15
Dividing the 4th digit by the 5th digit i.e. 5 ÷ 1 = 5
Hence, using these steps would get us the number 73155.
So, the next number would be obtained using same steps:
Adding the first 2 digits in the number 73155 i.e. 7 + 3 = 10
Subtracting the 3rd digit from the 2nd digit i.e. 3 - 1 = 2
Multiplying the 3rd digit and 4th digit i.e. 1 × 5 = 5
Dividing the 4th digit by the 5th digit i.e. 5 ÷ 5 = 1
Hence, using these steps would get us the final number 10251.
So, from this pattern method, we determine that 73155 will be the 3rd number in the sequence: 88511,16351,?,10251.
So, the complete sequence would be: 88511, 16351, 73155, 10251.
Keywords: sequence, number
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1.
A gym has two membership plans.
The Gold Plan costs 50 dollars per month and 3 dollars per visit.
The Platinum Plan costs 20 dollars per month and 6 dollars per visit.
Answer:
The number of visit so that both plan cost same is 10 .
Both the plan has equivalent choice of benefit
Step-by-step explanation:
Given as :
A gym has two membership plans.
For Gold plan
The charge per month = $50
The charge per visit = $3
For Platinum plan
The charge per month = $20
The charge per visit = $6
Let The number of visit for which each plan be same = n visits
Now, According to question
∵ Each plan cost to be same
So,
The charge per month for gold plan+ The charge per visit × numbers of visit = The charge per month for platinum plan+ The charge per visit × numbers of visit
I.e $50 + $3 × n = $20 + $6 × n
Or, $50 - $20 = $6 × n - $3 × n
Or, $30 = ($6 - $3) × n
Or, $30 = $3 × n
∴ n = [tex]\dfrac{30}{3}[/tex]
I.e n = 10
So, The number of visits = n = 10
Now, For Gold plan
The charge per month = $50
The charge per visit = $3 × 10 = $30
So, Total charge for gold plan = $50 + $30 = $80
Similarly For Platinum plan
The charge per month = $20
The charge per visit = $6×10 = $60
So, For Platinum plan ,total charge = $20 + $60 = $80
Hence, The number of visit so that both plan cost same is 10
and both the plan has equivalent benefit. Answer
Charlie and his friend Jay went to the fair. They were having a sale and the admission was 25% off. The regular ticket price was $9.00 and the tax is 6%. What would Charlie’s total be?
Answer:
The total of Charlie's be $7.
Step-by-step explanation:
Given:
Charlie and his friend Jay went to the fair. They were having a sale and the admission was 25% off.
The regular ticket price was $9.00.
And the tax is 6%.
Now, to find Charlie’s total.
So ,we deduct the 25% off first:
[tex]\$9.00-25\%\ of\ \$9.00[/tex]
[tex]=9-\frac{25}{100} \times 9[/tex]
[tex]=9-\frac{225}{100}[/tex]
[tex]=9-2.25[/tex]
[tex]=\$6.75.[/tex]
Now, including tax :
[tex]\$6.75+6\%\ of\ \$6.75[/tex]
[tex]=6.75+\frac{6}{100} \times 6.75[/tex]
[tex]=6.75+0.06\times 6.75[/tex]
[tex]=6.75+0.405[/tex]
[tex]=\$7.155.[/tex]
Approximately = $7.
Therefore, the total of Charlie's be $7.
One teacher wants to give each students 5/9of a slice of pizza. If the teacher has 15 slices of pizza,then how many students will she be able to hand out pizza to?
Answer:
Step-by-step explanation:
10
Answer:
27
Step-by-step explanation:
To find the answer to this, you need to divide the 15 slices of pizza by 5/9. 15/(5/9) is 15*9/5 (multiply both the top and the bottom by 9 and you cancel out the 9 in the 5/9 fraction) and you get 135/5 = 27
What are the lower quartile, upper quartile, and median for this box and whisker plot?
A. LQ = 7 UQ = 14 Median = 18
B. LQ = 18 UQ = 14 Median = 21
C. LQ = 14 UQ = 28 Median = 21
D. LQ = 14 UQ = 28 Median = 22
Answer:
C
Step-by-step explanation:
The lower quartile is the value at the left side of the box, that is
LQ = 14
The upper quartile is the value at the right side of the box, that is
UQ = 28
The median is positioned at the vertical line inside the box. that is
Median = 21
A stack of cards contains 17 red cards and 9 black cards. What are the odds against drawing a red card?
A. 9:17
B. 17:9
C. 9:26
D. 17:26
To find the probability of choosing a red card we need to add both the cards so we have a total amount of cards.
17 + 9 = 26
Since, the question is asking the probability of choosing a RED card then the probability is a 17/26 chance. The answer choices are written as ratios. The ratio that is the same to 17/26 is [ D. 17:26 ]
Best of Luck!
ASAP, NEED HELP ASAP
Answer:
OPTION C
Step-by-step explanation:
If SOLUTION A has 4 cups then SOLUTION B has 2. If SOLUTION A has 8 then SOLUTION B has 4.
Note that for every 2 cups of Solution A, we have 1 cup of Solution B.
So, OPTION A is incorrect.
If there are 4 cups of Solution A, then there are 4 + 2 cups in total.
That means the ratio of cups of SOLUTION A to the total number of cups is:
4 : 6 = 2 : 3
Similarly, 8 : 12 = 2 : 3
And, 12 : 18 = 2 : 3
And, 16 : 24 = 2 : 3
So, we see that the ratio is 2 : 3.
Therefore, OPTION C is the correct answer.
Answer:
kmjinhuygtfdrs
Step-by-step explanation: