The least number of miles she would have to drive per year to make leasing no more expensive than purchasing is 48500 miles.
Given:
She can lease a car for $420 per month (on an annual basis). Under this plan, the cost per mile (gas and oil) is $0.06. If she were to purchase the car, the fixed annual expense would be $4700, and other costs would amount to $0. 08 per mile.
Let x be the least miles.
420 * 12 + 0.06x < > 4700 + 0.08x
multiply by 100 on both sides.
504000+6x < > 470000+8x
97000 < > 2x
48500=x
Therefore the least number of miles she would have to drive per year to make leasing no more expensive than purchasing is 48500 miles.
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Mason was recently hired for a job with an annual income of $18,000. Using the federal income rate of 15%, what amount should Mason expect to pay in federal income tax?
Answer:
$2,700
Step-by-step explanation:
15% of $18,000 = 0.15 × $18,000 = $2,700
PLEASE HELP ME! I WILL NAME YOU THE BRAINLIEST IF YOU ANSWER! WORK DOES NOT NEED TO BE SHOWN PLEASE HURRY! THE THING IS IN THE PHOTO! PLEASE HELP AND PLEASE HURRY! THIS IS DUE TONIGHT!
Answer: Y+5= 2/9(X+2)
Answer: (x + 2) = 2/9 (y + 5)
Step-by-step explanation:
y – y₁ = m(x – x₁)
the table shows the heights of players in a basket ball team. work out the mean height of the team round your answer to 1 decimal place. new player joins the team and raises the mean average height to 201 cm. work out the height of this new player (height) 198,199,200,201,202) (frequency) (1,3,2,5,2)
The mean height of the team rounded to 1 decimal place is 200.0.
The height of this new player is 206.
What is mean Average?
The mean average, of a data set is the sum of all the numbers divided by the total number of values.
Formular for calculating mean Average:
Mean Average = {Sum of all the values} ÷ {Total numbers of values}
From the question the height of the players are as follows:
(height) 198,199,200,201,202)
a) Mean Average =(198 +199 +200 +201 +202)
5
=1000
5
=200.0
b) The new player joins the team to make the Mean Average 201. hence the height of the new player will be calculated using:
Mean Average = {Sum of all the values} ÷ {Total numbers of values}
201 =(198 +199 +200 +201 +202 + x )
6
201 = 1000+ x
6
crossmultiply to solve for X:
201 *6 =1000+ x
1,206 = 1000+ x
making x subject of the formular we have:
x = 1,206 - 1000
x = 206
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Solve this problem using estimation and rounding each amount to the nearest ten
dollars.
Over a two-month period, Mr. Bryant's sixth grade class donated their spare change
to help another student. The class raised $58.23 the first month and $66.57 the
second month. About how much money did Mr. Bryant's class raise for their
classmate?
Answer:
$124.80
Step-by-step explanation:
$58.23 + $66.57 = $124.80
Which is an equivalent expression for ((5/7)2 x (1/3)-3)-1
(5/7)2 x (1/3)-3
(5/7) x (1/3)-4
(7/5)-2 x (1/3)-3
(7/5)2 x (1/3)3
The equivalent expression for the expression given; (( 5/7 )² × (1/3)-³)-¹ is; (7/5)² • (1/3)³.
What is the equivalent expression for the given expression?It follows from the task content that the expression which is equivalent to that which is given is to be determined.
Hence, since the given expression is; (( 5/7 )² × (1/3)-³)-¹;
It follows from the power of powers law of indices that we have;
( 5/7 )-² • (1/3)³
Also, according to the negative exponent law of indices; we have;
(7/5)² • (1/3)³.
On this note, the required equivalent expression is; (7/5)² • (1/3)³.
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Rewrite the expression 12x + 8 to find an equivalent expression
. Show three possible expressions what do the rewritten expression tell you about the relesginship among the quantities
Three Expression equivalent to 12x + 8 are,
4 ( 3x+2 ) , 12 (x + 2/3) , 8 (2x/3 + 1)
Equivalent expressions:
Equivalent expressions are expressions that work the same even though they look different.
If two or more algebraic expressions are equivalent, then all expressions will give the same value if we put different value of variable.
Here,
given expression is " 12x + 8 "
we have to write three equivalent expression to 12x + 8
a.
If we take 4 common we will get,
12x + 8 = 4 ( 3x+2 )
so,
one of the expression equivalent to 12x + 8 is 4 ( 3x+2 )
b.
If we take 12 common then,
12x + 8 = 12 (x + 8/12)
= 12 (x + 2/3)
one of the expression equivalent to 12x + 8 is 12 (x + 2/3)
c.
If we take 8 common then,
12x + 8 = 8 ( 12x/8 + 1)
= 8 (2x/3 + 1)
one of the expression equivalent to 12x + 8 is 8 (2x/3 + 1)
Hence,
Three Expression equivalent to 12x + 8 are,
4 ( 3x+2 ) , 12 (x + 2/3) , 8 (2x/3 + 1)
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Exam-style P is the point with coordinates (5, 7). Q is the point with coordinates (x, 15).
The gradient of line PQ is 2. Work out the value of x.
By using the formula for the gradient, we can solve a simple equation to find that the value of x is 9.
How to find the value of x?For a segment whose endpoints are:
P = (x₁, y₁) and Q = (x₂, y₂)
The gradient of the line PQ is:
G = (y₂ - y₁)/(x₂ - x₁)
So it is like the slope of a linear equation.
In this case, the endpoints are:
P = (5, 7)
Q = (x, 15)
And the gradient is equal to 2, so we have G = 2, then we can write the equation:
2 = (15 - 7)/(x - 5)
We can solve this to get:
2*(x - 5) = (15 - 7)
2x - 10 = 8
2x = 10 + 8
2x = 18
x = 18/2 = 9
The value of x is 9.
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If The Area Of The Smaller Pentagon Is 36, What Is The Area Of The Larger Pentagon?
A) 27
B) 52
C) 64
D) 144
pls help ty :')
Answer:
64
Step-by-step explanation:
16 ÷ 12 = 1.33 (rounded to 2 decimal places)
1.33 = scale factor
1.33² = area scale factor
1.33² × 36 = 64 (rounded to a whole number)
*CHECK IMAGE FOR ACCURATE QUESTION 13. Body surface area (BSA) is used to determine doses of medications. The H.M., where H is the height in centimeters and M is the V 3,600' mass in kilograms. A doctor calculates that a particular dose of medicine is appropriate for an individual whose BSA is less than 1.6. If the mass of the individual is 68 kilograms, how many centimeters tall can she be for the dose to be appropriate?
135.53 centimeters the height of a patient in cm if he weighs 68kg and has a BSA of 1.6m².
Given that,
Some medical professionals determine a patient's medicine dosage based on the patient's body surface area (BSA). The BSA calculation method that is most frequently employed is BSA = [tex]\sqrt{\frac{wh}{3600} }[/tex].
where BSA is expressed in square meters, w is the patient's weight (in kg), h is their height (in cm),
We have to determine the height of a patient in centimeter if he weighs 68kg and has a BSA of 1.6m².
1.6= [tex]\sqrt{\frac{wh}{3600} }[/tex]
1.6= [tex]\sqrt{\frac{68h}{3600} }[/tex]
Squaring on both sides.
1.6²= 68h/3600
2.56 × 3600 =68h
9216 = 68h
h= 9216/68
h = 135.53.
Therefore, 135.53 meters the height of a patient in cm if he weighs 68kg and has a BSA of 1.6m².
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Alang and his children went into a grocery store that sells apples for $2 each and peaches for $0.50 each. Alang has $20 to spend and must buy a minimum of 16 apples and peaches altogether. If xx represents the number of apples purchased and yy represents the number of peaches purchased, write and solve a system of inequalities graphically and determine one possible solution.
The system of inequalities has been solved graphically and one possible solution is buying 4 apples and 12 peaches.
How to write and solve the system of inequalities graphically?In order to write a system of linear inequalities to describe this situation, we would assign variables to the number of apples purchased and number of peaches purchased by Alang and his children, and then translate the word problem into algebraic equation as follows:
Let the variable x represent the number of apples purchased.Let the variable y represent the number of peaches purchased.Since apples for $2 each and peaches for $0.50 each, the cost of fruits is given by:
2x + 0.5y ≤ 20
Also, they must buy a minimum of 16 apples and peaches altogether:
x + y ≥ 16
Therefore, a possible solution when x = 4 is given by:
x + y ≥ 16
4 + y ≥ 16
y ≥ 16 - 4
y ≥ 12
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view picture please!!!
Answer:
90 degrees
Step-by-step explanation:
The question asks for the temp after an hour and a half. This is the same as 90 minutes. With this, you plug 90 in for t.
This is what it looks like:
T(t)=69e^-0.0174(90) + 76
Then you solve for T(t)
T(t)=69e^-1.566 +76
T(t)=69(0.2088) +76
T(t)=14.41265 +76
T(t)=90.41265
Then round to 90 degrees
Find all values that are NOT in the domain of h/g.
The results of the division between the two functions are listed below:
a) (h / g) (- 1) = - 1 / 15
b) x = 7 / 8 is not in the domain of (h / g) (x).
How to evaluate a division between two functions and determine its domain
Herein we have two functions h(x) and g(x), the former is a quadratic equation and the latter is a linear equation and the division between the two functions is described below:
(h / g) (x) = h(x) / g(x), for all x such that g(x) ≠ 0
If we know that h(x) = 2 · x² - 3 and g(x) = - 8 · x + 7, then the division between the two functions is:
(h / g) (x) = (2 · x² - 3) / (- 8 · x + 7)
Now we evaluate the function at x = - 1:
(h / g) (- 1) = [2 · (- 1)² - 3] / [- 8 · (- 1) + 7]
(h / g) (- 1) = (- 1) / 15
(h / g) (- 1) = - 1 / 15
To determine the value of x such that does not belong to g(x), we need to solve the following expression:
g(x) = 0
- 8 · x + 7 = 0
8 · x = 7
x = 7 / 8
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in a certain city, 60% of the heads of household own the house in which they reside, and 80% of the heads of the household have full-time employment. when considering what percentage of heads of household both own their home and have a full-time job, a student estimates that 48% of heads of household fit both requirements, stating that (0.60)(0.80)
No, because although two probabilities should be multiplied, it should not be these two probabilities. This is because the two events are likely not independent .
What is Probability ?
Probability is the study of likeliness of an event to happen. The range of probability is 0 to 1.
Now, According to the question:
It is given that
In a certain city, 60% of the heads of household own the house in which they reside,
and 80% of the heads of the household have full-time employment.
percentage of heads of household both own their home and have a full-time job =?
As the probability of a person having both their own home and having
full time employment are not independent.
Hence, No, because although two probabilities should be multiplied, it should not be these two probabilities. This is because the two events are likely not independent.
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Solve this system of equations using the SUBSTITUTION method, then answer the questions below.
x + 2y = 4
3x + 6y = 18
What did you get for the (x, y) solution to this system? (2 points)
If you were to graph these equations, would their lines cross? Explain why or why not. (2 points)
The system of equations does not have any solutions since the values on both sides of the final expression are different and the lines will not cross.
Solving system of equationsA system of equations, usually referred to as an equation system, is a collection of finite equations for which common solutions are sought.
Given the system of equations below;
x + 2y = 4............ 1
3x + 6y = 18 ........... 2
From equation 1:
x = 4 - 2y .........3
Substitute equation 3 into 2 to have:
3(4 - 2y) + 6y = 18
3(4) - 3(2y) + 6y = 18
12 - 6y + 6y = 18
12= 18
Since the values on both sides of the resulting expression is different, hence the given system of equation has NO solutions showing the lines will not cross on the graph.
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• 3 pages are edited every 5 minutes.
• 5 pages are edited every 3 minutes.
• 6/10 of a page is edited per minute.
• 1 2/3 of a page is edited per minute.
a) 1 and 2
b) 1 and 3
c) 3 and 4
d) None of the above
Answer:
1 and 3
Step-by-step explanation:
where the dots on the graph are, you can read that in 5 minutes, 3 pages are edited. in 10 minutes, 6 pages.
so statement 1 is correct.
when every 10 minutes 6 pages are edited, divide both by 10 to get what is edited per minute. -> 6/10 pages are edited per minute.
Emily's family loves to work together in the garden. They have a slight preference for flowers, as 60 percent of their plants are flowers and 40 percent are vegetables. They have 50 plants growing in the garden.
How many vegetable plants do they have?
If they have 50 plants growing in the garden. The number of vegetable plants they have is :20.
How to determine the number of vegetable plants?Using this formula to find the number of vegetable plants
Number of vegetable plants = Percentage of vegetable plants × Number of plants in the garden
Let plug in the formula
Number of vegetable plants = 40% × 50
Number of vegetable plants = 20
Therefore the number of vegetable plants is 20.
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I WILL MARK BRAINLIEST IT WAS DUE LAST WEEK PLS HELP
Answer:
[tex]y=\frac{3}{2}x-6[/tex]
Step-by-step explanation:
y=Mx+b is slope intercept form
M- slope
b- y intercept
We know b because when x is zero y is -6 so that is the y intercept
b=-6
Now to fin the slope we use y2-y1/x2-x1
0-(-3)/4-2
3/2
m=3/2
So we just put it all into the equation to get
y=3/2x-6
Hopes this helps
Answer: i'm writeing this so you can mark the other person brainliest
Step-by-step explanation:
Evaluate z + 3x
when X= –6 and Z= 4
Answer:
-14
Step-by-step explanation:
Hello!
You can evaluate the value of z + 3x by substituting the given values of z and x into the equation.
Evaluatez + 3x; x = -6, z=4(4) + 3(-6)4 - 18-14The evaluated value is -14.
Answer:
-14
Step-by-step explanation:
4+3(-6)
4-18
-14
12. 9/11 = ?/22
OA. 18
OB. 4
OC. 9
OD. 12
Answer:
18
Step-by-step explanation:
to make the 11 denominator turn into 22 they had to multiply by 2
So we multiply the numerator by 2 too
9x2=18
Hopes this helps please mark brainliest
Answer:
If you would like to solve the equation 9/11 = x/22, you can calculate this using the following steps:
Steps to find ?
9/11 = x/22 /*22
x = 9/11 * 22
x = 18
The correct answer should be 18 through my calculations
10x^2y divided by 5xy
The value of Indices 10x^2y÷ 5xy is 2x^(2y-1)×y^-1
What is Indices?An index is a small number that tells us how many times a term has been multiplied by itself. The plural of index is indices. Below is an example of a term written in index form: 4^3. 4 is the base and 3 is the index.
10x^2y = 10x^2(y)
dividing 5xy with 10x^2y
the coefficient 5 will divide 10 to give 2
therefore the value is
2x^2y÷ xy
using law of INDICIES
the value will be 2x^(2y-1)×y^-1
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Geometry Homework Question
According to the given triangle, ΔBCE ≅ ΔCBD is proved.
Triangle:
The three-sided polygon that consists of three edges and three vertices is know as triangle.
Given,
Here we have the triangle and we need to prove the ΔBCE ≅ ΔCBD.
Let us consider ABC be the triangle with sides BC, AC, AB add the opposite angles A, B, C being in length equal to a, b, c respectively.
Here they draw a perpendiculars AD, BE and CF from A, B, C to opposite sides meeting sides BC, AC and AB at D, E, F respectively.
So, here we take the ΔCBD and ΔBCE,
Then the
∠D = ∠E = 90°
So, the Side BC = Side BC and the Side BD = Side CE.
From this relation, and based one the concept of RHS Congruence Criterion
We have identify that, the Corresponding Angle Congruence Test
∠DCB = ∠EBC
Therefore, the ΔBCE ≅ ΔCBD is proved
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The balance in an interest-bearing account is modeled with a continuous function over time.
Which of the domain choices is a possibility?
A. Real numbers greater than 0
C. Integers
Whole numbers
D. Natural numbers
The domain choice that is a possibility is A. A. Real numbers greater than 0.
What is a continuous function?A continuous function in mathematics is one in which a continuous variation of the argument causes a continuous variation of the function's value. This means that there are no abrupt changes in value, which are referred to as discontinuities.
Option A: Real numbers greater than zero:
Because real numbers are continuous functions, the greater than zero part of them can be used to represent the balance sheet.
Option B: Use only whole numbers: It is not possible.
Whole numbers are discrete, not continuous, and thus cannot represent decimal points.
Option C: Integers: Invalid
Because integers are discrete rather than continuous, they cannot represent decimal points.
Natural numbers are not an option.
Natural numbers, like whole numbers, are discrete rather than continuous and cannot represent decimal points.
In conclusion, the correct option is A.
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The half-life of a radioactive iotope i the time it take for a quantity of the iotope to be reduced to half it initial ma. Starting with 115 gram of a radioactive iotope, how much will be left after 3 half-live?
14.375 grams of the radioactive isotope will be left after 3 half-lives.
The initial mass of the isotope = 115 gm
after each half-life, the amount of the isotope is reduced to half
therefore,
after the first half-life, the mass of the isotope will become = 115/2
= 57.5 gram
now after the second half live, the mass will again be reduced to half of the previous mass = 57.5/2
= 28.75 gram
similarly, after the third half-life, the mass will be half of the previous mass = 28.75/ 2
= 14.375 gram
OR
simply we can write that
weight after 3 half-lives will be = 115/ 2³
= 115 / 8
= 14.375 grams.
So the mass after 3 half-lives is 14.375 grams.
A risky form of a chemical element that releases radiation as it breaks down and will become extra stable. Radioisotopes may additionally arise in nature or be made in a laboratory. In medication, they may be used in imaging exams and in treatment. additionally known as a radionuclide.
Atoms of equal detail with extraordinary numbers of neutrons are known as isotopes. Many elements have one or extra isotopes which might be radioactive. Their nuclei are risky, so they destroy down, decay, and emit radiation.
whilst utilized in cautiously controlled clinical programs, radioactive isotopes are safe and no longer almost as frightening as we first imagined. The radiation from those isotopes has a quick half of lifestyles and handiest give off low stages of radiation. Radioactive isotopes are not constantly risky, though. a few most effective ones supply tiny amounts of radiation. There are radioactive isotopes in nature all around us. maximum of them cause us very little damage.
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A volunteer knits a 5-foot long scarf at a constant rate. After 4 hours, the volunteer still has to knit 3 feet of the scarf. How much time does it take to knit the scarf from start to finish?
The time that it take to knit the scarf from start to finish is 10 hours.
How to calculate the time?From the information, the volunteer knits a 5-foot long scarf at a constant rate and after 4 hours, the volunteer still has to knit 3 feet of the scarf.
Therefore, the volunteer used 4 hours to knit 2 scarf. The time used per scarf is 4/2 = 2 hours.
In this case, the time taken to finish the scarf will be:
= Time per feet × Total feet
= 2 × 5
= 10 hours.
It'll take 10 hours.
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Ruben wants to shade some of the squares below. He wants to have a ratio of shaded to unshaded of 3 to 4. How many squares should be shade?
Answer: He should shade 3 and leave 4 unshaded.
Step-by-step explanation:
ASAP! exponent rules
The answer is [tex]a^{-3}=\frac{1}{x^{3} }[/tex]
Exponent
An exponent is a number that has a power. In numbers with exponents, there are several rules. This rule is used to calculate the exponents operation.
The rules are, including:
[tex]a^{m}a^{n}=a^{m+n} \\\frac{a^{m} }{a^{n} }=a^{m-n}\\( a^{m}) ^{n}=a^{mn}\\ (ab)^{m}= a^{m}b^{m} \\\frac{a}{b} ^{m}=\frac{a^{m} }{b^{m} } \\a^{-m}=\frac{1}{a^{m} }\\ \sqrt[n]{a^{m} } =a^{\frac{m}{n} }[/tex]
From the properties rules, the rules that can be used in the problem are
[tex]a^{-m}=\frac{1}{a^{m} }[/tex]
From the properties above, it can be concluded that negative exponents mean one per number to that power. Do not reverse with the cube root, where the cube root the one per is the power, not the base number.
If the question is asked [tex]a^{-3}[/tex]
then it can be directly substituted in the rule above.
With that rule, let's find the number that equivalent with [tex]4^{-3}[/tex].
[tex]a^{-3}=\frac{1}{x^{3} }[/tex]
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Jina will rent a car for the weekend. She can choose one of two plans. The first plan has an initial fee of $49.98 and costs an additional $0.15 per mile drive
The second plan has an initial fee of $43.98 and costs an additional $0.19 per mile driven. How many miles would Jina need to drive for the two plans to cost the same?
Answer:
150 miles
Step-by-step explanation:
Jina wants to know the number of miles driven that would make the cost of two rental plans the same. One costs $0.15 per mile plus $49.98; the other costs $0.19 per mile plus $43.98.
Difference in costsThe difference in cost between the to plans for m miles driven is zero when ...
(0.15m +49.98) -(0.19m +43.98) = 0
-0.04m +6.00 = 0 . . . . . . . . simplify
m -150 = 0 . . . . . . . . . . . . divide by -0.04
m = 150 . . . . . . . . . . . . . add 150
Jina would need to drive 150 miles for the two plans to cost the same.
Make x the subject of the formula. x = 3+x / y
Answer:
below
Step-by-step explanation:
x = (3+x) / y divide both sides by x and multiply by y
y = (3+x) / x
y = 3/x + 1
y - 1 = 3/x
x = 3 / ( y-1)
If you travel from the United States to Spain, then you must have a passport. Can this be written as a biconditional? If so, what is the biconditional.
O If you have a passport, then you travel from the United States to Spain.
O You travel from the United States to Spain if and only if you have a passport.
O You have a passport if and only if you travel from the United States to Spain.
O This cannot be written as a biconditional.
You travel from the United States to Spain if and only if you have a passport. When both sides of a biconditional statement have the same truth value, the statement is said to be true.
What does a biconditional mean?
When both sides of a biconditional statement have the same truth value, the statement is said to be true. A double-headed arrow indicates the biconditional operator.If both the initial conditional assertion and the opposite statement are true, a statement is said to be biconditional."An A is guaranteed if you receive a perfect score on the final." ... Last but not least, it is a widely recognized principle that the conditional and biconditional operators have...A statement is logically true if it cannot logically be wrong. If a sentence can be expressed in the form "P if and only if Q," it is a biconditional assertion.To learn more about Biconditional statement refer to:
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You travel from the United States to Spain if and only if you have a passport. When both sides of a biconditional statement have the same truth value, the statement is said to be true.
What does a biconditional mean?When both sides of a biconditional statement have the same truth value, the statement is said to be true. A double-headed arrow indicates the biconditional operator. If both the initial conditional assertion and the opposite statement are true, a statement is said to be biconditional.
"An A is guaranteed if you receive a perfect score on the final." ... Last but not least, it is a widely recognized principle that the conditional and biconditional operators have. A statement is logically true if it cannot logically be wrong. If a sentence can be expressed in the form "P if and only if Q," it is a biconditional assertion.
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Find the range of the functio
h(x) = -x^2; {-2,-1,3}
Answer:
in the picture
Step-by-step explanation:
hope it helped