The maximum cost Dorothy should pay for the car to stay within her monthly budget amount is $23,518.84. See the explantion below.
What is a budget?A budget is a financial plan that takes into account both income and costs. In other words, it's a projection of how much money you'll make and expend over a specific time period, such as a month or a year.
The calculation that justified the above amount is solved as follows:
Given that:
Rate = 4%
Time = 4 years
The monthly payment is $490, to determine the amount (maximum) in 4 years, we use the Compound Interest formula:
A = P (1+ (r/n)ⁿᵇ
Where:
A = final amount
P = initial principal balance
r = interest rate
n = number of times interest applied per time period
b = number of time periods elapsed
A = P (1 + (0.04/1)^(1x4)
A = P (1.04)⁴ in four years
Hence, given that the monthly payment over the four-year period is $490, we say:
P [(1.04)⁴] /12 x4 = 490
⇒ P (1.04)⁴ = 490 x 48
P = (490 x 48)/1.1699
P = 20104.2824173
P [tex]\approx[/tex] 20,104
The maximum amount payable hence
= 20,104 (1.04)⁴
A = 23518.837
A [tex]\approx[/tex] 23,518.84
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The function $y=-\frac{1}{40}\left(x-25\right)^2+15$ models the path of a football kicked by a player, where $x$ is the horizontal distance (in yards) and $y$ is the height (in yards). the player kicks the ball a second time so that it travels the same horizontal distance but reaches a maximum height that is 5 yards less than the maximum height of the first kick. write a function that models the path of the second kick.
The quadratic function that models the path of the second kick is given by:
y = -2/125(x - 25)² + 10.
What is the equation of a parabola of vertex (h,k)?The equation of a quadratic function, of vertex (h,k), is given by the following rule:
y = a(x - h)² + k
In which the coefficients are explained as follows:
h is the x-coordinate of the vertex.k is the y-coordinate of the vertex.a is the leading coefficient.For the first kick, the equation is:
y = -1/40(x - 25)² + 15.
Meaning that the ball reached a maximum height of yards after an horizontal distance of 25 yards.
For the second kick, the horizontal distance is the same, but the maximum height if 5 yards less, that is, of 10 yards, hence the vertex is:
(h,k) = (25, 10).
Hence the equation is:
y = a(x - 25)² + 10.
After 50 yards, the ball hits the ground, hence the leading coefficient a is found as follows:
0 = a(50 - 25)² + 10
625a = -10
a = -10/625
a = -2/125
Hence:
y = -2/125(x - 25)² + 10.
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I just need a brief explanation with the answer and I just need answers to the last two
The sum of the internal angles of a triangle is 180°
Since AD is parallel to BC and DC is parallel to AB, the angle ADC must be equal to the angle ABC, which is 123°
Then, the angle CAB is 180° - 24° - 123° = 33°
23. What is the mode of the following numbers, and what word can be used to describe the
distribution of the data set?
5, 4, 10, 3, 3, 4, 7, 4, 6, 5, 11, 9, 5, 7
We can conclude that the mode of the following data are 4 and 5.
What is the mode?A set of data values' mode is the value that appears the most frequently. The value of X at which the probability mass function reaches its highest value is known as the mode if X is a discrete random variable. In other words, it is the value that will be sampled most frequently.As the given data set is:
5, 4, 10, 3, 3, 4, 7, 4, 6, 5, 11, 9, 5, 7Mode is calculated when in the given data set the number appears most often.
So, count each number as we get the result:
4 appears 3 times, also5 appears 3 timesHaving two modes is called "bimodal".Therefore, the modes are 4 and 5.
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x-interecpt of 2x−y+6 = 0.
Answer:
x- intercept = - 3
Step-by-step explanation:
to find the x- intercept , where the line crosses the x- axis, let y = 0 in the equation and solve for x
2x - 0 + 6 = 0
2x + 6 = 0 ( subtract 6 from both sides )
2x = - 6 ( divide both sides by 2 )
x = - 3 ← x- intercept
Mrs. harris is a librarian at eastside library. in examining a random sample of the library's book collection, she found the following. 661 books had no damage, 78 books had minor damage, and 26 books had major damage. based on this sample, how many of the 73,500 books in the collection should mrs. harris expect to have minor damage? round your answer to the nearest whole number. do not round any intermediate calculations.
The number of minor damaged books in 73500 book collection is 8,673 books.
Given that, 661 books had no damage, 78 books had minor damage, and 26 books had major damage.
What are proportions?Proportion, in general, is referred to as a part, share, or number considered in comparative relation to a whole. Proportion definition says that when two ratios are equivalent, they are in proportion. It is an equation or statement used to depict that two ratios or fractions are equal.
Let the minor damaged books be x.
Now, 78 : 661 :: x : 73,500
⇒ 661x = 73500 × 78
⇒ 661x = 57,33,000
⇒ x = 57,33,000 ÷ 661
⇒ x = 8,673.22
≈ 8,673
Therefore, the number of minor damaged books in 73500 book collection is 8,673 books.
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Mitchell bought 3 postcards for $3.14. At this rate, how much would 12 postcards cost?
Answer:
12.56$
Step-by-step explanation:
12 / 3=4
4 × 3.14 = 12.56
what is the answer to this question?
Answer:
A
Step-by-step explanation:
Proportions can be any number so other statements can't be always true
Answer:
A. Class X has a greater proportion of boys than Class Y
Step-by-step explanation:
- Before choosing any objective, first relate the two proportions.
Multiply class Y by 2:
[tex]{ \rm{y = 2(4 : 5)}} \\ { \rm{y= 8:10}}[/tex]
- So it can be related with class X as the ratios have a common proportion of girls; 10
[tex]{ \rm{x= 9:{ \green{10}}}} \\ { \rm{y = 8:{ \green{10}}}}[/tex]
- By observation, we see that class X has a greater number of boys than in class Y
[tex]{ \boxed{ \red{ \delta}}}{ \underline{ \mathfrak{ \: ...creed}}}[/tex]
Jaime, Ralph, Marvin and Victor decided to put up a small business. Their initial investment is in the ratio of 8:3:12:2 respectively and Marvin's had invested Php 240,000. In terms of the profit they have decided to split them base on the ratio of their investment. In the first three months of their company made a total of Php 150,000 profit. Based on Marvin's initial deposit. How much did Victor invested?
Proportionately, based on Marvin's initial deposit, Victor invested Php 40,000 in the partnership.
What is a proportion?Proportion is like a ratio that shows a numerical relationship between two variables.
Proportions equate one ratio to a value.
For instance, we can equate Marvin's investment ratio to his investment.
This equation helps us to calculate the total investment made by the four partners in the small business.
Jamie Ralph Marvin Victor Sum of Ratio
Investment ratio 8: 3: 12: 2 25
Investment amount ? ? Php 240,000 ? ?
Marvin investment = Php 240,000 = 12/25
Total investment by the partners = Php 500,000 (Php 240,000/12 x 25)
Victor's investment = Php 40,000 (Php 500,000 x 2/25)
Profit for the year = Php 150,000
Thus, based on proportional contributions of Marvin, Victor's investment is Php 40,000.
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a long distance runners distance ran in miles varries direclty with the time in minutes. the runner ran 2 miles in 14 minutes.how long would it take the runner to go 9 miles ?
Answer:
Answer down below!
Step-by-step explanation:
If you know that he ran 2 miles in 14 minutes, you can also say he ran 1 mile in 7, because he is running in 7 minute increments
Let's go up together! (The numbers express how many miles have been run!)
7 minutes14 minutes 21 minutes28 minutes35 minutes42 minutes49 minutes56 minutes63 minutesSo in 63 minutes, the runner will have ran 9 miles!
Find an equation of the line that passes through the given point and is parallel and perpendicular to the given lines. Point: (-2,3) Line: 3x-6y=3
The equation of the line parallel to 3x-6y=3 and passes through (-2, 3) is y = 1 / 2 x + 4
How to find equation of a line?The equation of the line passes through (-2, 3) and it is parallel to the equation 3x - 6y = 3.
Therefore, the equation of a line can be represented as follows:
y = mx + b
where
m = slopeb = y-interceptParallel lines have the same slope.
Hence,
3x - 6y = 3
3x - 3 = 6y
y = 1 / 2 x - 1 / 2
Therefore, the slope of the equation is 1 / 2.
Let's find the y-intercept using (-2, 3).
3 = 1 / 2 (-2) + b
3 + 1 = b
b = 4
Therefore, the equation is y = 1 / 2 x + 4
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Mrs. Rollins raises prize chickens. Each chicken eats the same amount of food. Mrs. Rollins bought 100 pounds of chicken food last week. How much food did each chicken eat?
10 pounds of food each chicken eat last week.
This is a problem from an algebraic equation. We can solve this problem by following a few steps.
Each chicken eats the same amount of food, as per the question. Let's assume there is x number of chickens.
Therefore, if each chicken eats the same amount of food then the total food required for all chickens is, (x × x) = x² pound.
Again, Mrs. Rollins bought 100 pounds of chicken food.
Hence x² is equivalent to 100 pounds. We can generate an equation from this. Which is,
x² = 100
Or, √x² = √100 [ root both sides ]
Or, x = 10
Now, we can conclude that there are 10 chickens and each chicken eats 10 pounds of food in a week.
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Help me please! (And sorry for my english)
Factorize the expression: 7abcd-21bcde+14cdef
Answer:
7cd(ab-3be+2ef)
Step-by-step explanation:
they all have the number 7 In common so you take that out and you take out whatever letters they have in common
Answer:
7cd(ab - 3be + 2ef
Step-by-step explanation:
Simplify:
7abcd = 7 * a * b* c * d
21bcde = 7 * 3 * b * c * d * e
14cdef = 7 * 2 * c * d * e * f
GCF = 7 cd
7abcd - 21bcde + 14cdef = 7cd*( ab - 3be + 2ef)
7) A certain store's sales increased by 175% compared to the previous year. How many squares
would be shaded on 10 x 10 grids to represent 175%?
squares
The given percentage cannot be represented on the grid.
What is percentage?
A percentage (from Latin: per centum, "by a hundred") is a quantity or ratio stated as a fraction of 100 in mathematics. The percent symbol, "%," is commonly used, however the abbreviations "pct.", "pct," and sometimes "pc" are also used. A % is a non - dimensional (pure) quantity; it does not have a unit of measurement. In the context of sports statistics, the term "%" is frequently used incorrectly since the referred figure is stated as a decimal proportion, not a percentage. Similarly, a team's winning percentage, or the fraction of matches won, is commonly reported as a decimal proportion; a team with a.500 winning percentage has won 50% of its matches.
The given percentage cannot be represented on the grid.
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b) Write down the output y in terms of x.
Input
X
+4
+3
Output
y
6
For the given equation, the inequality is y > 14
What is an inequality in mathematics?An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. The majority of the time, size comparisons between two numbers on the number line are made.
Polynomial inequality, rational inequality, and absolute value inequality are the various types of inequalities that can exist in mathematics.
x + 2×7 = y
=> y = x + 14
Here, y > x.
So, y > 14
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a recycling bin 3kg of plastic and 500g of paper whats the ratio of plastic to paper in the bin give answer in simpliest form
Based on the weight of the plastic to the weight of the paper, the ratio of plastic to paper in the simplest form is 6 : 1
How to find the ratio?To find the ratio of plastic to paper, there is a need to convert the weights such that they have the same units.
Assuming we convert the plastics to grams, the number of grams of plastic would be:
= 3 kg x 1,000 grams per kg
= 3,000 grams
The ratio then would be:
3,000 grams of plastic : 500 grams of paper
To get to the simplest form, divide both sides by 500:
3,000 / 500 : 500 / 500
6 : 1
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Look at this graph.
What is the equation of the line in slope-intercept form?
Answer:
y = 4x -80
Step-by-step explanation:
We need the slope and the y intercept.
The y intercept is -80. This is where the line crosses the y axis.
The slope is the change in y over the change in x.
Let's go from point (0,-80) the y intercept the the point that cross the x axis (20,0) Start at -80, how many units to you go up until you are at the same level as point (20,0)? 80 units. Now, from (0,0) how many units do you go right to get to (20,0)? 20.
We end up go 80 unit up and 20 units right, this would be written [tex]\frac{80}{20}[/tex] Which simplifies to 4. This is our slope.
Slope (m) = 4
y intercept (b)= -80 Plug those into
y = mx + b
y = 4x -80
Answer the 2 questions in the photo for EASY points ( will mark brainliest )
Answer: Sara is 51 and madison 19
Step-by-step explanation: Yes
please help part a and b thanks a lot i really appreciate it
please help me thank youuu
well, let's move like the crab, backwards, and start off with
3)
Check the picture below.
[tex]tan(A )=\cfrac{\stackrel{opposite}{BC}}{\underset{adjacent}{AC}}\implies tan(A)=\cfrac{\stackrel{opposite}{3}}{\underset{adjacent}{4}}\qquad \textit{now let's find the \underline{hypotenuse}} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies c=\sqrt{a^2 + b^2} \qquad \begin{cases} c=\stackrel{hypotenuse}{AC}\\ a=\stackrel{adjacent}{4}\\ b=\stackrel{opposite}{3}\\ \end{cases} \\\\\\ AB=\sqrt{(AC)^2 + (BC)^2}\implies AB=\sqrt{4^2 + 3^2}\implies \underline{AB=5} \\\\[-0.35em] ~\dotfill\\\\ sin(A )=\cfrac{\stackrel{opposite}{3}}{\underset{hypotenuse}{5}}\hspace{5em} cos(\theta )=\cfrac{\stackrel{adjacent}{4}}{\underset{hypotenuse}{5}}[/tex]
2)
well, Graciella said they couldn't just using the tangent they were given, well, she needs stop playing Angry Birds too much.
1)
well, from what I read, Angelica thought it was possible, so she was correct all along, I don't see any mistakes in her statements, all we did in 3) was what Angelica suggested.
If there is no solution to a compound inequality, does the compound inequality involve OR or AND? Explain.
If there is no solution to a compound inequality, it can involve AND.
A sentence having two inequality statements connected by the words "or" or "and" is referred to as a compound inequality. The conjunction "and" denotes the equal validity of both statements in the compound sentence. The conjunction "or" means that the entire compound sentence is true as long as either of the two statements is true.
The term "OR" can help us find more solutions, whereas the phrase "AND" can help us find less solutions. As a result, we can create a compound inequality with no solution by using "AND."
Therefore, if there is no solution in compound inequality, it may involve AND.
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Which statement best defines an angle?
A.
two lines that share a common line segment called the vertex
B.
two rays that share a common endpoint called the vertex
C.
two line segments that intersect at a point called the vertex
D.
two lines that intersect at a point called the vertex
Vertex is a common endpoint that is shared by the two rays. Therefore, option B is the correct answer.
We need to define the angle.
What is an angle?An angle is formed when two straight lines or rays meet at a common endpoint. The common point of contact is called the vertex of an angle.
Parts of an Angle
There are two main parts related to an angle - the arms and the vertex.
Arms of the Angle
The two rays which join at a common point to form the angle are called the arms of the angle.
Vertex of the angle
Vertex is a common endpoint that is shared by the two rays.
Vertex is a common endpoint that is shared by the two rays. Therefore, option B is the correct answer.
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Would you rather have a savings account that pays 5% interest compounded semiannually or one that pays 5% interest compounded daily? Explain
A compound interest that pays 5% interest compounded daily is preferable. This is so even though the interest rates on the two accounts are equal, the 5% interest compounded daily account is used more frequently.
What is difference between simple interest and compound interest ?Interest is the cost of borrowing money, such as the sum added to a loan debt. It is also possible to classify the rate paid for holding money on deposit, such as in the case of a certificate of deposit. The two ways to calculate interest are simple interest and compound interest.
On the principal, or original loan amount, of a loan, simple interest is calculated.
Since compound interest is calculated using both the principal and the accrued interest from previous periods, it is frequently referred to as "interest on interest".
If interest is computed on a compound basis rather than a simple basis, the amount of interest that must be paid on a loan can vary significantly. Positively speaking, the magic of compounding may be a powerful tool for wealth growth and can work in your favor when it comes to your assets.
Simple interest and compound interest are fundamental financial concepts, but understanding them thoroughly may enable you to make better choices when applying for a loan or making investments.
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In a lab experiment, the decay of a radioactive isotope is being observed. At the
beginning of the first day of the experiment the mass of the substance was
and mass was decreasing by
500 grams
8% per day. Determine the mass of the radioactive
sample at the beginning of the 13th day of the experiment. Round to the nearest tenth
(if necessary).
Answer: a13=310.7
Step-by-step explanation:
Formula= an=a1r^n-1
a13=1100(0.9)13-1
a13=310.7
D is directly proportional to x. D=36 when x=5. Work out the value of D when x=8
Step-by-step explanation:
D is directly proportional to x. D=36 when x=5. Work out the value of D when x=8.
Because they are directly proportional:
x/D = x/D
5/36 = 8/D
multiply both sides by D:
D(5/36) = D(8/D)
5D/36 = 8
multiply both sides by 36:
36(5D/36) = 8 * 36
5D = 288
divide both sides by 5:
5D/5 = 288/5
D = 288/5
or D = 57.6
Write an equation of the line that passes through (-2, 5) and (-4, -5)
Answer: 5x + 15 = y
Step-by-step explanation:
mx+b = y
find rise over run
(y_2-y_1)/(x_2-x_1) = m
(-5-5)/(-4+2)
simplify
-10/-2
10/2
5 = m
plug in a point and find b
5(-2) + b = 5
-10 + b = 5
b = 15
5x + 15 = y
Find the x of the triangle
Let the yellow dot equal to y In the diagram I drawn. NOW I WILL USE THE REASON SUM ANGLES OF A TRIANGLE 43°+57°+ YELLOW DOT=180°
[tex]43 + 57 + y = 180 \\ 100 + y = 180 \\ y = 180 - 100 \\ y = 80[/tex]
THE YELLOW DOT FROM THE TRIANGLE ON THE RIGHT IS EQUAL TO THE DOT ON THE TRIANGLE ON THELEFT SIDE BY VERTICAL OPPOSITE
[tex]x + x + y = 180 \\ 2x + 80 = 180 \\ 2x = 180 - 80 \\ 2x = 100 \\ \frac{2x}{2} = \frac{100}{2} \\ x = 50[/tex]
x=50°
HOPE THIS HELPS.
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Determine the distance between the points (−4, −7) and (−8, −13). square root of 10 units square root of 82 units square root of 544 units square root of 52 units
Question Should look like
determine the distance between (-4,-7) and (-8,-13)
A. [tex]\sqrt{10}[/tex]
B. [tex]\sqrt{82}[/tex]
C. [tex]\sqrt{544}[/tex]
D. [tex]\sqrt{52}[/tex]
Answer: D. [tex]\sqrt{52}[/tex]
Step-by-step explanation:
[tex]a^{2}+b^{2}= c^{2}[/tex]
a =(8-4)... b=(13-7)
a=4, b=6
therefore...
[tex]a^{2}+b^{2}= c^{2}\\4^{2}+6^{2}=c^{2}\\16+36=c^{2}\\52=c^{2}\\c=\sqrt{52}[/tex]
4x^3 - 10 = 2x^3 + 6
Answer:
⚠️⚠️⚠️⚠️⚠️⚠️♀️
Step-by-step explanation:
⚠️⚠️⚠️♀️
the floor of an elevator was 30feet above ground level.it travels down 10 feet below ground level. what distance has the elevators floor traveled?
Help Fast PLSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
40 feet
Step-by-step explanation:
-10 -30
Write a sentence as an equation. Use x to represent "a number." twice a number gives 108
Answer:
2x=108
Step-by-step explanation: This is the equation because when it says twice a number, you are multiplying a number two times. In this case, the number is not given, so x is the variable being multiplied two times. If the number was 8, it would look like this: 2(8)=108. Of course this isn't true, but to find the actual answer you would divide two on both sides of the equation. This is so that both of the two's cancel out on the left side of the equation. and the variable is left on that side. Our goal is to isolate the variable. In these types of equations, our goal is to isolate the variable and find what the variable is worth. If we do 108 divided by 2 that gives us 54. Since there was x left on the left side of the equation and there is 108 left on the right side we have our equation. x=54
Number explanation below
2x=108
2x/2=108/2
x=54