In general, an inverse variation relation has the form shown below
[tex]\begin{gathered} y=\frac{k}{x} \\ k\to\text{ constant} \end{gathered}[/tex]It is given that x=16, then y=5/4; thus,
[tex]\begin{gathered} \frac{5}{4}=\frac{k}{16} \\ \Rightarrow k=\frac{5}{4}\cdot16 \\ \Rightarrow k=20 \end{gathered}[/tex]Therefore, the equation is y=20/x
[tex]\Rightarrow y=\frac{20}{x}[/tex]2) Set x=4 in the equation above; then
[tex]\begin{gathered} x=4 \\ \Rightarrow y=\frac{20}{4}=5 \\ \Rightarrow y=5 \end{gathered}[/tex]When x=4, y=5.
Which exponential function is represented by the table below? x –2 0 2 4 y 16 4 1 14
An exponential function which is represented by the table above is: f(x) = 4(1/2)^x
What is an exponential function?An exponential function simply refers to a mathematical function whose values are generated by a constant that is raised to the power of the argument. Mathematically, an exponential function can be modeled by using this equation:
f(x) = abˣ
Where:
a represents the initial value.b represents the rate of change.From the table above, we would calculate the value of a and b:
At x = 0 and y = 4; the value of a (initial value) is 4.
Rate of change, b = Δy/Δx
Rate of change, b = 1/2
Substituting the parameters into the formula, we have;
f(x) = abˣ
f(x) = 4(1/2)^x
Check:
f(x) = 4 × (1/2)^x f(x) = 4 * ( 1/2 )^x
f(x) = 4 × (1/2)² f(x) = 4 × (1/2)⁻²
f(x) = 4 × 1/4 f(x) = 4 × 4
f(x) = 1 f(x) = 16
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solve a system of equations to solve the problem question 8
Let x be the cost of each juice and y be the cost of each BBQ.
4x + 2y = 16
4x + 3y = 21
Subtract the second equation from the first
y = 5
Substitute y = 5 into 4x + 2y = 16
4x + 2(5) = 16
4x + 10 = 16
4x = 16 - 10
4x = 6
x=1.5
Therefore, a juice cost $1.5 and a BBQ cost $5
So, if the Emdin family pu rchased 3 juice and 3 BBQ, then
cost of juice = 3 x $1.5 = $4.5
cost of BBQ = 3 x $5 = $15
Total money spent by Emdin family = $4.5 + $15 = $19.5
Let x be the cost of each juice and y be the cost of each BBQ.
4x + 2y = 16
4x + 3y = 21
Subtract the second equation from the first
y = 5
Substitute y = 5 into 4x + 2y = 16
4x + 2(5) = 16
4x + 10 = 16
4x = 16 - 10
4x = 6
x=1.5
Therefore, a juice cost $1.5 and a BBQ cost $5
So, if the Emdin family pu rchased 3 juice and 3 BBQ, then
cost of juice = 3 x $1.5 = $4.5
cost of BBQ = 3 x $5 = $15
Total money spent by Emdin family = $4.5 + $15 = $19.5
18)Betsy is collecting data on the amount of time shoppers spend inside of a particular large department store. She stands outside the department store and surveys every 10th shopper who exits. What type of sampling is used? Explain your answer.
Consider the 5 main types of sampling: Random, Systematic, Convenience, Cluster, and Stratified.
In the case of systematic sampling, every kth element of the data set is taken.
In our case, consider all the shoppers and imagine that they can be ordered in a line; then, Betsy selected the 10th shopper in the line, the 20th one, and so on.
This is analogous to systematic sampling; the answer is systematic sampling.5. SOLVE THe linear equation : 13x – 5 + 171 = x
Answer:
x = -83/6 = -13.833
Step-by-step explanation:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
13*x-5+171-(x)=0
1.1 Pull out like factors :
12x + 166 = 2 • (6x + 83)
2.2 Solve : 6x+83 = 0
Subtract 83 from both sides of the equation :
6x = -83
Divide both sides of the equation by 6:
x = -83/6 = -13.833
The distance to your brother's house is 481 miles, and the distance to Disneyland is 518 miles. If it took 13 hours to drive to your brother's house, how long would you estimate the drive to Disneyland to take?
Answer:
364/7 = 260/d
Cross multiply.
364d = 1820
d = 5 hours
Miles per hour, mph = miles/hour
364 miles/7 hours = 52 mph
260 miles/52 mph = 5 hours
In the circle below, if arc AB is congruent to arc CD, chord AB = 3x - 6 and chord CD = x + 12, find x.
Solution
We will equate the two values
[tex]\begin{gathered} 3x-6=x+12 \\ \\ 3x-x=12+6 \\ \\ 2x=18 \\ \\ x=9 \end{gathered}[/tex]The answer is
review the rental and purchase property information to answer the question: calculate the difference in total move-in cost between the two properties. $31,497.35 $35,842.95$39,285.45$4,976.55
Let us calculate the move-in costs of both properties.
Rental Property
The monthly rent is $1,350.
The move-in costs are:
First month = $1,350
Last month = $1,350
Security deposit = 55% of one month's rent
[tex]\Rightarrow\frac{55}{100}\times1350=742.5[/tex]Therefore, the move-in cost is:
[tex]\Rightarrow1350+1350+742.5=3442.5[/tex]Purchase Property
The purchase price is $195,450.
The move-in costs are:
Down payment of 18% of purchase price:
[tex]\Rightarrow\frac{18}{100}\times195450=35181[/tex]Closing costs of 2.1% of purchase price:
[tex]\Rightarrow\frac{2.1}{100}\times195450=4104.45[/tex]Therefore, the move-in cost is:
[tex]\Rightarrow35181+4104.45=39285.45[/tex]Difference in Total Move-In Cost
This is calculated to be:
[tex]\Rightarrow39285.45-3442.5=35842.95[/tex]ANSWER
The difference in total move-in cost is $35,842.95
Ms. Bell's mathematics class consists of 6 sophomores, 13 juniors, and 10 seniors.
How many different ways can Ms. Bell create a 3-member committee of sophomores
if each sophomore has an equal chance of being selected?
The number of different ways in which Ms. Bell's can select 3-member committee of sophomores is 20 ways.
What is termed as the combination?Selections are another name for combinations. Combinations are the selection of items from a given collection of items. We need not aim to arrange anything here. Combinations do seem to be selections made by having taken some or all of a set of objects, regardless of how they are arranged. The amount of combinations of n things taken r at a time is denoted by nCr and can be calculated as nCr=n!/r!(nr)!, where 0 r n.0 ≤ r ≤ n.For the given question;
Ms. Bell's mathematics class consists -
6 sophomores, 13 juniors, and 10 seniors.Ms. Bell create a 3-member committee of sophomores with unbiased outcomes.
The section of 3 sophomores can be done as;
⁶C₃ = 6!/3!(6-3)!
⁶C₃ = 6/3!.3!
⁶C₃ = 20 ways.
Thus, the number of different ways in which Ms. Bell's can select 3-member committee of sophomores is 20 ways.
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▸ Charice created a painting with an area of 63 square inches and a length of 7 inches. They create a second painting with an area of 81 square inches. It has the same width as the first painting. What is the length of the second painting?
The length of the second painting is 9 inches.
Given,
The area of the first painting = 63 square inches
Length of the first painting = 7 inches
The area of the second painting = 81 square inches
Width of the first painting = Width of the second painting = x
We have to find the length of the second painting:
Here,
We can consider the painting as a rectangle.
Area of rectangle = length × width
Now,
First painting:
Area = length × width
63 = 7 × x
x = 63/7 = 9
That is, the width of the first painting is 9 inches.
The width of the second painting also 9 inches.
Now,
Second painting:
Area = length × width
81 = length × 9
length = 81/9 = 9
Therefore, the length of the second painting is 9 inches.
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When an integer is subtracted from 4 times the next consecutive odd integer, the difference is 23. Find the value of the lesser integer.
The value of the lesser integer is 5.
According to the question,
We have the following information:
When an integer is subtracted from 4 times the next consecutive odd integer, the difference is 23.
Let's take the lesser integer to be x.
So, the next consecutive odd integer is (x+2).
Now, we have:
4(x+2)-x = 23
4x+8-x = 23
3x+8 =23
3x = 23-8
3x = 15
x = 15/3
(3 was in multiplication on the left hand side. So, it is in the division on the right hand side.)
x = 5
Hence, the lesser integer in the given situation is 5.
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If you are not knowledgeable in college algebra please let me know so I can move on more quickly. Thanks in advance!
Given polynomial is
[tex]3x^5-4x^4-5x^3-8x+25[/tex]We have to check whether the polynomial x-2 is a factor.
If x-2 is a factor then x = 2 is a root of the given polynomial.
Substitute x = 2 in the given polynomial,
[tex]\begin{gathered} 3.2^5-4.2^4-5.2^3-8.2+25=96^{}-64-40-16+25 \\ =121-120=1 \end{gathered}[/tex]Hence 2 is not a root of given polynomial.
And so x - 2 is not a factor.
Blossom's Computer Repair Shop started the year with total assets of $318000 and total liabilities of $211000. During the year, the
business recorded $505000 in computer repair revenues, $311000 in expenses, and Blossom paid dividends of $50200. Stockholders'
equity at the end of the year was
The distance to the nearest exit door is less than 200 feet.
ANSWER
d < 200
EXPLANATION
If d is the distance to the nearest exit door, and this distance is less than 200 feet, then the inequality to represent this situation is d < 200.
help meeeeeeeeee pleaseee !!!!!
The composition of functions g(x) and f(x) evaluated in x = 5 is:
(g o f)(5) = 6
How to evaluate the composition?
Here we have two functions f(x) and g(x), and we want to find the composition evaluated in x = 5, this is:
(g o f)(5) = g( f(5) )
So first we need to evaluate f(x) in x = 5, and then g(x) in f(5).
f(5) = 5² - 6*5 + 2 = 25 - 30 + 2 = -3
Then we have:
(g o f)(5) = g( f(5) ) = g(-3)
Evaluating g(x) in x = -3 gives:
g(-3) = -2*(-3) = 6
Then the composition is:
(g o f)(5) = 6
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28. A man spends 1/5 of his income on Food and 1/3 of the remainder on his car. If he then has #286.00 left, what is his income? A. #612.86 B. #686.83 C. #536.25 D. #2,145 E. #4,290 als
Answer:
4,290
Step-by-step explanation:
286.00 x 3 x 5 = 4,290
A number from 1-40 is chosen at random. Find each probability.1. Pleven | at least 12)2. P(perfect square | odd)3. P(less than 25 | prime)4. P(multiple of 3 | greater than 15)
Given:
Numbers from 1 - 40
Let's find the probability of:
Pleven | at least 12)
Where:
Even numbers = 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40 = 20 numbers
Even numbers that are at least 12 = 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40 = 15 numbers.
Numbers that are at least 12 = 29 numbers
Therefore, to find the probability, we have:
[tex]P(even|atleast12)=\frac{P(even\text{ and at least 12\rparen}}{P(at\text{ least 12\rparen}}[/tex]Where:
[tex]\begin{gathered} P(even\text{ and at least 12\rparen = }\frac{15}{40}=0.375 \\ \\ P(at\text{ least 12\rparen= }\frac{29}{40}=0.725 \end{gathered}[/tex]Therefore, we have:
[tex]\begin{gathered} P(even|atleast12)=\frac{0.375}{0.725} \\ \\ P(even|atleast12)=0.52 \end{gathered}[/tex]Therefore, the probability that a number chosen at random is even given that it is at least 12 is 0.52
ANSWER:
0.52
Find the value of this expression if x = 1 andy = -7x2y-9
We are asked to evaluate the expression:
[tex]\frac{x^2y}{-9}[/tex]when x = 1 and y = -7
so we replace them as shown below, making sure we include them inside parenthesis to keep clear that the expressions in x and in y are multiplying each other:
[tex]\frac{x^2y}{-9}=\frac{(1)^2(-7)}{-9}=\frac{-7}{-9}=\frac{7}{9}[/tex]So we see that x^2 becomes 1 and the factor y stays as -7. The final expression cancels out the negative sign in numerator (from -7) and in denominator (from -9) and gives 7/9.
Find the areas of the figures for parts (a) and (b) below.
SOLUTION:
Case: Area of plane shapes
Method:
a) Parallelogram
To find the area we need to find the perpendicular height (using Pythagoras theorem)
[tex]\begin{gathered} h^2+7^2=25^2 \\ h^2+49=625 \\ h^2=625-49 \\ h^2=576 \\ h=\sqrt{576} \\ h=24 \end{gathered}[/tex]The Area of a parallelogram is given as:
[tex]\begin{gathered} A=bh \\ A=23\times24 \\ A=552\text{ }ft^2 \end{gathered}[/tex]b) Triangle
To find the area of the triangle, we need to find the base first
First, lets find 'a'
[tex]\begin{gathered} a^2+60^2=70^2 \\ a^2+3600=4900 \\ a^2=4900-3600 \\ a^=\sqrt{1300} \\ a=36.06 \end{gathered}[/tex]The base, b
b= 2(a)
b= 2 (36.06)
b= 72.12
The area of the triangle is:
[tex]\begin{gathered} A=\frac{1}{2}bh \\ A=\frac{1}{2}\times72.12\times60 \\ A=2163.6 \end{gathered}[/tex]Final answer:
a) Parallelogram,
A= 552 square feet
b) Triangle
A= 2163.6 square feet
Martin finds an apartment to rent for $420 per month. He must pay a security deposit equal to one and a half months' rent. How much is the security deposit? Alexis earns $31,350 per year. According to the banker's rule, how much money can she afford to borrow for a house?
if one month is $420
and the security deposit is one and a half month= 1.5*$420
1.5*420=630
So the answer is: 630
The longest at an airport has the shape of a rectangle and an area of 2,181,600 this runaway is 180 feet wide how long is the runaway
The longest at an airport has the shape of a rectangle and an area of 2,181,600 this runaway is 180 feet wide how long is the runaway
Remember that
The area ofa rectangle is equal to
A=L*W
in this problem we have
A=2,181,600 ft2
W=180 ft
substitute given values
2,181,600=L*180
Solve for L
L=2,181,600/180
L=12,120 ftFour plumbers estimated the length of the length of the radius of a cylindrial pipe. The estimates made by the plumbers are listed • 3/5 • 3/11 • 9/100 • 3.14/24 ? : . .
Different estimates:
The length of the radius of a cylindrical pipe:
Plumber W:
Radius had a length: 3/5 inches.
Plumber X:
Radius had a length: sqrt(3/11) inches.
Plumber Y:
Radius had a length of 9/100 inches.
Plumber Z:
Radius had a length of 3/14/24 inches.
Turn them into decimals:
We can turn each length into decimal:
Plumber W: 3/5 = 0.6.
Plumber X: sqrt(3/11) = 0.522222..
Plumber Y: 9/100 = 0.09
Plumber Z: 3.14/24 = 0.13083
The list from the greatest to least:
We can order this list taking into account the following reasoning: when the number is near to zero, this number is less than the other in the list. Examples: 0.001, 0.0002, 0.00004 are very near to zero.
Additionally, when a number is near 1 (the unit), this number is greater than the other less near to 1.
Examples: 0.69, 0.73, 0.888, 0.99 are near to zero.
The numbers we got in the list are decimals numbers coming from fractions and the square root was taken to the estimation of plumber X. Therefore:
From list 0.6, 0.52222..., 0.09, 0.13083
The number nearest to zero is 0.09. Then, 0.13083 is greater than 0.09 but less than the others. The following number is 0.5222..., and the greatest is 0.6.
The list that shows these lengths in order from the greatest to least is:
{0.6, 0.5222..., 0.13083, 0.09}.
Which is equivalent to:
{3/5, sqrt(3/11), 3.14/24, 9/100}.
Lulu the Lucky puts chests of gems into her treasure vault.
Each chest holds the same number of gems. The table
below shows the number of gems Lulu received from
three different adventures and the number of chests she
needed to hold the gems.
Number of gems
Number of chests
Adventure A
600
2
Adventure B
1500
5
Adventure C
4800
16
Write an equation to describe the relationship between
g, the number of gems, and c, the number of chests.
The equation that represents the relationship of gems 'g' and chest 'c' is 300c = g.
What are equations?A mathematical statement that uses the word "equal to" between two expressions with the same value is called an equation. Like 3x + 5 = 15, for instance. Equations come in a wide variety of forms, including linear, quadratic, cubic, and others. Point-slope, standard, and slope-intercept equations are the three main types of linear equations.So, the equation representing the relation of 'g' and 'c':
We can observe that:
600/2 = 3001500/5 = 3004800/16 = 300So, we can conclude that:
g/c = 300300c = gTherefore, the equation that represents the relationship of gems 'g' and chest 'c' is 300c = g.
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A large western state consists of 3593 million acres of land. Approximately 14% of this land is federally owned. Find the number of acres that are not federally owned.
The number of acres that are not federally owned = 3089.98 million
What do you mean by western state?Land or other assets that are legally owned by the government or a government agency are referred to as government-owned property.
Federal, state, or local governments may be the owners of government-owned land, which may or may not be open to the general public without restriction.
If 14% of the land is federally owned, then 100 -14 = 86% of the land is not federally owned.
(14 *3593 ) / 100
50302 / 100 = 503.02
Federal owned land is 503.02 million acres of land.
3593 - 503.02 = 3089.98 = (86× 3593) ÷ 100
Land not owned by Federal Government = 3089.98 million acres of land.
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Chain rule in calculus
In the given example:
[tex]\begin{gathered} u=4x^3-5 \\ f(u)=u^4 \\ \text{If we do a function composition then they will be the same} \\ f(x)=\big(4x^3-5\big)^4\rightarrow f(u)=u^4,\text{ note that }u=4x^3-5 \end{gathered}[/tex]Solve for each derivative of dy/du and du/dx
[tex]\begin{gathered} \frac{du}{dx}=3\cdot4x^{3-1}-0 \\ \frac{du}{dx}=12x^2 \\ \\ \frac{dy}{du}=4\cdot u^{4-1} \\ \frac{dy}{du}=4u^3,\text{ then substitute }u \\ \frac{dy}{du}=4(4x^3-5)^3 \\ \\ \text{Complete the chain rule} \\ \frac{dy}{dx}=\frac{dy}{du}\cdot\frac{du}{dx} \\ \frac{dy}{dx}=\big(4(4x^3-5)^3\big)\big(12x^2\big)\text{ or }\frac{dy}{dx}=48x^2(4x^3-5)^3 \\ \end{gathered}[/tex]Solve the exponential equation. Express irrational solutions as decimals correct to the nearest thousandth.5x -5.e-2x = 2eSelect the correct choice below and, if necessary, fill in the answer box to complete your choice.A. The solution set is(Round to the nearest thousandth as needed. Use a comma to separate answers as needed.)OB. The solution is the empty set.
We are asked to solve the exponential equation given below:
e^5x - 5 * e^-2x = 2e
First let's apply the exponent rules:
5x - 5 - 2x = In(2e)
Solving 5x - 5 - 2x = In(2e)
3x - 5 = In(2e)
Add 5 to both sides:
3x = In(2e) + 5
Divide both sides by 3
x = In(2e) + 5
3
x = 2.23104
x = 2.231 (To the nearest thousand)
Therefore, the correct option is A, which is The solution set is 2.231 (Round to the nearest thousand).
how can you use the vertical line test and the horizontal line test to determine whether a graph represents a function and whether the graph is invertible?
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
vertical line test = ?
horizontal line test = ?
Step 02:
vertical line test ===> function
any vertical line intersect the graph at only one point
horizontal line test ===> invertible
any horizontal line intersect the graph at only one point
graph:
horizontal line test = red
vertical line test = brown
That is the full solution.
A psychologist has designed a questionnaire to measure individuals' aggressiveness. Suppose that the scores on the questionnaire are normally distributed with
a standard deviation of 90. Suppose also that exactly 10% of the scores exceed 700. Find the mean of the distribution of scores. Carry your intermediate
computations to at least four decimal places. Round your answer to at least one decimal place.
μ = 782.02 is the mean of the distribution of scores by standard deviation.
What is standard deviation in math?
A statistical measurement called standard deviation examines how far away from the mean a set of statistics is. Standard deviation, to put it simply, gauges the degree of dispersion between numbers in a data collection. The variance's square root is used to generate this metric.we have from standard normal table that
P(Z > 1.282) = 0.1
Therefore the given Z score of a score of 700 is given thus 1.282.
the z score is given:
x - μ / α = 1.282
700 - μ / 90 = 1.282
Therefore μ = (700 - 90)*1.282 = 782.02
So we have that μ = 782.02
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since birth hakem has had a savings account that started at $3,000 and had been growing at a rate of 13% per year the amount of money in the account can be modeled by the equation y equals P =(1.13)^ Z where why is the value of the count is the number of years and pee was original deposit amount is it possible for hakem account to grow to $31812 11.42 in hakem lifetime?( try to figure out the bounds of the perameter)
Solution
For this case we have the following formula:
[tex]y=3000(1.13)^x^{}[/tex]And we want to find the value for t in order to have y = 3181211.42 , solving for y we got:
[tex]3181211.42=3000(1.13)^x[/tex]and solving for x we got:
[tex]\ln (\frac{3181211.42}{3000})=x\cdot\ln (1.13)[/tex][tex]x=56.99\approx57[/tex]for this case we need 57 years to reach the amount so then assuming that a person lives about 80 years , then is possible
yes
if a ray QT bisects
EXPLANATION
If a ray QT bisects
(3x - 5) + (x+1) = 180 [By the Linear Pair Theorem]
Removing the parentheses:
3x - 5 + x + 1 = 180
Grouping like terms:
3x + x + 1 - 5 = 180
Adding like terms:
4x -4 = 180
Adding +4 to both sides:
4x = 180 + 4
Adding numbers:
4x = 184
Dividing both sides by 4:
x = 184/4
Simplifying:
x=46
Now, we need to compute the resulting angles:
m m
As QT bisects
47/2 = 23.5 degrees
The answer is 23.5°
You are offered two different furniture sales jobs. The Furniture Barn offers you a job that pays straight commission of 6% of the sales. The Furniture Warehouse offers you a job that pays a salary of $350 per week plus 1% of the sales. How much would you have to sell in a week in order for the job at The Furniture Barn to pay as well as the job at The Furniture Warehouse? Round the answer to the nearest cent.
The Furniture Barn pays the same as The Furniture Warehouse if my sales are $
The amount to be sold in a week in order for the job at The Furniture Barn to pay as well as the job at The Furniture Warehouse is $7000.
How to calculate the value?Lat the amount of sales be represented as x.
Since the Furniture Barn offers you a job that pays straight commission of 6% of the sales. This will be:
= 6% × x = 0.06x
Also, the Furniture Warehouse offers you a job that pays a salary of $350 per week plus 1% of the sales. This will be:
= 350 + (1% × x)
= 350 + 0.01x
The equation will be expressed as:
0.06x = 350 + 0.01x
Collect like terms
0.06x - 0.01x = 350
0.05x = 350
Divide
x = 350 / 0.05
x = 7000
The sale is $7000.
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