A positive integer is 5 more than 23 times another. Their product is 6732. Find the two integers.
.A new truck costs $32,000. The car’s value will depreciate over time, which means it will lose value. For tax purposes, depreciation is usually calculated linearly. If the truck is worth $24,500 after three years, write an explicit formula for the value of the car after n years.
The explicit formula for the value of the truck after [tex]\(n\)[/tex] years is:
[tex]\[V(n) = -2,500n + 32,000\][/tex]
Where [tex]\(V(n)\)[/tex] represents the value of the truck after [tex]\(n\)[/tex] years.
To write an explicit formula for the value of the truck after n years with linear depreciation, we can use the formula for the equation of a straight line:
[tex]\[y = mx + b\][/tex]
Where:
- [tex]\(y\)[/tex] is the value of the truck after [tex]\(n\)[/tex] years.
- [tex]\(m\)[/tex] is the slope of the line, which represents the rate of depreciation per year.
- [tex]\(x\)[/tex] is the number of years.
-[tex]\(b\)[/tex] is the initial value of the truck.
Given:
- Initial value [tex](\(b\)): $32,000[/tex]
- Value after 3 years [tex](\(y\)): $24,500[/tex]
We can use these values to find the slope [tex](\(m\))[/tex]:
[tex]\[m = \frac{y_2 - y_1}{x_2 - x_1}\][/tex]
Substituting the given values:
[tex]\[m = \frac{24,500 - 32,000}{3 - 0}\]\[m = \frac{-7,500}{3}\]\[m = -2,500\][/tex]
Now, we have [tex]\(m = -2,500\)[/tex]. We can substitute this slope and the initial value into the equation:
[tex]\[y = -2,500x + 32,000\][/tex]
The explicit formula for the value of the truck after [tex]\(n\)[/tex] years is:
[tex]\[V(n) = -2,500n + 32,000\][/tex]
Where [tex]\(V(n)\)[/tex] represents the value of the truck after [tex]\(n\)[/tex] years.
e figure below shows the derivative F' of a function F. If F(20) equals 100, estimate the maximum value attained by by F
Where the above figure is given as the attendant derivatives F', the maximum value attained by F is 400.
How to obtain the maximum value
It is to be noted that:
Max occurs at x=50 where F'(x) = 0.
We need to find value for F(50) using fundamental theorem of calculus:
[tex]\int_{50}^{50} F' dx = F(50) - F(20)[/tex]
= F (50) -100
F(50) = 100 + A
Where A is the estimated Area under the graph.
If we assume the shaded region is close to a right triangle then the Area is
(1/2) x 30 x 20
= 300
Thus,
F (50) = 100 + 300
= 400
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Suppose you draw a card from a well-shuffled deck of 52 cards. What is the probability of drawing a 5 or a queen?
Using the probability concept, it is found that there is a 0.1538 = 15.38% probability of drawing a 5 or a queen.
A probability is the number of desired outcomes divided by the number of total outcomes, hence:
[tex]p = \frac{D}{T}[/tex]
In this problem:
In a standard deck, there are four 5s and also four queens, hence [tex]D = 4 + 4 = 8[/tex].In total, there are 52 cards, hence [tex]T = 52[/tex]The probability is:
[tex]p = \frac{D}{T} = \frac{8}{52} = 0.1538[/tex]
0.1538 = 15.38% probability of drawing a 5 or a queen.
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Estimate each Quotient
1) 59,628 divide by 73
2) 361,245 divide by 58
3) 104,392 divide by 64
REALLY NEED IT! Thanks ;) also pls show work
A washer and dryer cost $600.00 combined. The cost of washer is 3 times more than dryer. What is cost of dryer?
What is the probability that a couple will have a girl a boy a girl and a boy in this specific order?
The probability that a couple will have a girl a boy a girl and a boy in this specific order is 1/16
Probability is the likelihood or chance that an event will occur.
Probability = Expected outcome/Total outcome
If the couple will give birth to a boy and a girl, hence the total outcome of the event is 2
Pr(having a boy) = 1/2
Pr(having a girl) = 1/2
Pr(a girl, a boy, a girl and a boy) = 1/2 * 1/2 *1/2 * 1/2
Pr(a girl, a boy, a girl, and a boy) = 1/16
Hence the probability that a couple will have a girl a boy a girl and a boy in this specific order is 1/16
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An assembly-line machine turns out washers with the following thicknesses (in millimeters). Find the mean and standard deviation of the thicknesses.
1.42, 1.83, 1.43, 1.87, 1.22, 1.44, 1.72, 1.91, 1.42, 1.87, 1.42, 1.99, 1.27, 1.94, 1.67, 1.22
The mean thickness of the washers is 1.55 mm and the standard deviation is approximately 0.296 mm.
Explanation:To find the mean of the thicknesses, we add up all the values and divide it by the total number of values. In this case, the sum of the thicknesses is 24.81. Dividing this by the total number of values, which is 16, gives us a mean of 1.55 mm.
To find the standard deviation, we need to calculate the variance first. The formula for variance is sum of (value - mean)^2 divided by n - 1, where n is the number of values. After calculating the variance, we take its square root to find the standard deviation. In this case, the variance is 0.0877, and the standard deviation is approximately 0.296 mm.
A real estate agent sells a house for $92,000. She receives a 6% commission on the sale of the house.
How much did she earn on the sale?
Round your answer to the nearest cent.
need answer in 10 mins. or less
Amount earn as commission on real state building is $5,520
Commission based problem:What information do we have?
Amount of real state house = $92,000
Percentage of Commission on sale = 6%
Amount earn as commission = Amount of real state house × Percentage of Commission on sale
Amount earn as commission = 92,000 × 6%
Amount earn as commission = 92,000 × 0.06
Amount earn as commission = $5,520
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a stereo is marked down $75. If this is a 15% decrease find the sale price. How do you work this problem out?
Answer:
The selling price is $425.
Step-by-step explanation:
Given information:
Marked down price = $75
15% decrease = $75
Let x be the market price.
[tex]x\times \frac{15}{100}=75[/tex]
[tex]0.15x=75[/tex]
Divide both sides by 0.15.
[tex]x=500[/tex]
The market price is $500.
Selling price = Market price - Marked down
Selling price = $500 - $75
Selling price = $425
Therefore, the selling price is $425.
Ellen deposits $6,773 into an account earning 1% annually. After seven years what will Ellen's balance have grown to, including interest?
Page 2
MATH SOLUTIONS
A fast food chain has a contest in which a card
with numbers on it is given to each customer who
makes a purchase. If some of the numbers on the
card add up to 100, then the customer wins $100.
You make a purchase and receive a card contain-
ing the numbers 72, 21, 15, 36, 69, 81, 9, 27, 42,
and 63.
Will you win $100?
Why or why not?
Final answer:
After examining possible combinations of the given numbers (72, 21, 15, 36, 69, 81, 9, 27, 42, and 63), we find no subset that adds up to exactly 100. The closest sum we can get is 99, which is not sufficient to win the prize. Hence, we will not win the $100.
Explanation:
To determine whether we will win the $100 by finding a combination of the given numbers that add up to 100, we should examine possible combinations. The provided numbers are 72, 21, 15, 36, 69, 81, 9, 27, 42, and 63.
Looking at these numbers, we can see if any subsets add to 100:
27 + 72 = 99 (close, but not exactly 100)63 + 36 = 99 (also close, but still not 100)21 + 15 + 9 + 27 + 27 = 99 (using 27 twice is not allowed, and it's still not exactly 100)It becomes evident that combinations of the given numbers will either fall short of or exceed 100. The closest combinations we can make are 99, just one short of the required total, meaning we cannot win the $100 with the provided numbers on the card. Therefore, the answer is no; we will not win $100 as we cannot make a sum of exactly 100 using the numbers on the card.
I need help finding the reference angles for these angles.
1) 1.4
2) [tex]-1.4 \pi [/tex]
3) 2.3
4) [tex]2.3 \pi [/tex]
For a project, you cut paper into strips that are 2 1/2 inches long by 3/4 inches wide. what is the area of each strip of paper
The area of each strip of paper is 15/8 square inches.
Explanation:The area of each strip of paper can be calculated by multiplying the length and width of the strip. In this case, the length is 2 1/2 inches and the width is 3/4 inches. To multiply fractions, multiply the numerators together to get the numerator of the product, and multiply the denominators together to get the denominator of the product. So, the area of each strip is:
(2 1/2 inches) x (3/4 inches) = (5/2 inches) x (3/4 inches) = 15/8 square inches.
0.04 divided by 1.68
Find the point on the line y = 4x + 5 that is closest to the origin.
Step 1
Find the equation of the line perpendicular to [tex] y = 4x + 5 [/tex] that pas through the origin
we know that
the slope of the equation [tex] y = 4x + 5 [/tex] is
[tex] m1=4 [/tex]
if two lines are perpendicular
then
the product of their slopes is equal to [tex] -1 [/tex]
[tex] m1*m2=-1 [/tex]
the slope of the line perpendicular is equal to
[tex] m2=-\frac{1}{m1} \\\\ m2=-\frac{1}{4} [/tex]
with m2 and the origin find the equation of the line
[tex] y-y1=m(x-x1)\\ y-0=(-\frac{1}{4} )*(x-0)\\ y=-\frac{1}{4} x [/tex]
Step 2
Solve the system
[tex] y = 4x + 5 [/tex]---> equation [tex] 1 [/tex]
[tex] y=-\frac{1}{4} x [/tex]-----> equation [tex] 2 [/tex]
Multiply equation [tex] 1 [/tex] by [tex] -1 [/tex]
Adds equation [tex] 1 [/tex] and equation [tex] 2 [/tex]
[tex] -y = -4x - 5 [/tex]
[tex] y=-\frac{1}{4} x \\ ----- [/tex]
[tex] 0=-4x-\frac{1}{4} x-5\\ \\ \frac{17}{4} x=-5\\ \\ x=-\frac{20}{17} [/tex]
[tex] y = 4x + 5 [/tex]
[tex] y = 4*(-\frac{20}{17}) + 5 \\ \\ y=\frac{5}{17} [/tex]
the solution is the point [tex] (-\frac{20}{17} ,\frac{5}{17} ) [/tex]
[tex] (-\frac{20}{17} ,\frac{5}{17} ) [/tex]=[tex] (-1.176 ,0.294 ) [/tex]
therefore
the answer is
the point is [tex] (-\frac{20}{17} ,\frac{5}{17} ) [/tex]
see the attached figure
The point [tex]\boxed{(-1.176,0.294)}[/tex] on the line [tex]y=4x+5[/tex] is the closest point to the origin.
Further explanation:
The general form of linear function is as follows:
[tex]\boxed{y=mx+c}[/tex]
A linear function has one independent variable and one dependent variable. The independent variable is [tex]x[/tex] and the dependent variable is [tex]y[/tex].
Here, [tex]c[/tex] is the constant term and [tex]m[/tex] is the slope and gives the rate of change of dependent variable.
The point slope form of a line is given as follows:
[tex]\boxed{y-y_{1}=m(x-x_{1})}[/tex]
where [tex](x_{1},y_{1})[/tex] is the point on the line and [tex]m[/tex] is the slope of the line.
It is given that the equation of the line is as follows:
[tex]y=4x+5[/tex]
where [tex]4[/tex] is the slope of the line.
Consider the slope of the line [tex]y=4x+5[/tex] as [tex]m_{1}=4[/tex].
We first find the line perpendicular to the line [tex]y=4x+5[/tex] that passes through the origin as shown in Figure 1 in the attachment below.
If two lines are perpendicular then the product of their slopes is [tex]-1[/tex] that is [tex]m_{1}\tiimes m_{2}=-1[/tex].
And [tex]m_{2}[/tex] is the slope of the perpendicular line.
Calculated the value of [tex]m_{2}[/tex] as follows:
[tex]\begin{aligned}m_{1}\times m_{2}&=-1\\m_{2}&=-\dfrac{-1}{m_{1}}\\&=\dfrac{-1}{4}\\&=-0.25\end{aligned}[/tex]
Therefore, the slope of perpendicular line is [tex]-0.25[/tex].
We have the point [tex](0,0)[/tex] on the line and the slope of the line.
Thus, the equation of line is,
[tex]\begin{aligned}y-y_{1}&=m_{2}(x-x_{1})\\y-0&=(-0.25)(x-0)\\y&=-0.25x\end{aligned}[/tex]
The equation of the perpendicular line is as follows:
[tex]\boxed{y=-0.25x}[/tex] .......(2)
Substitute [tex]y=-0.25x[/tex] in equation (1).
[tex]\begin{aligned}-\dfrac{x}{4}&=4x+5\\-\dfrac{x}{4}-4x&=5\\-\dfrac{17x}{4}&=5\\-17x&=5\times 4\\x&=-\dfrac{20}{17}\\x&\approx-1.176\end{aligned}[/tex]
Now, put the value of [tex]x[/tex] in equation (2) to get the value of [tex]y[/tex] as,
[tex]\begin{aligned}y&=-0.25\times (-1.176)\\&=0.294\end{aligned}[/tex]
Therefore, the closest point is [tex]\boxed{(-1.176,0.294)}[/tex].
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Answer details:
Grade: High school
Subject: Mathematics
Chapter: Linear equations
Keywords: Linear equations, slope of a line, equation of the line, function, real numbers, ordinates, abscissa, interval, open interval, closed intervals, semi-closed intervals, semi-open intervals, sets, range domain, codomain.
A restaurant offers
7
appetizers and
9
main courses. In how many ways can a person order a two-course meal?
Using the concept of combinations, the person can order a two course meal in 63 ways
How many ways can a person order a two course meal?To determine the number of ways a person can order a two-course meal from the given options of appetizers and main courses, we can use the concept of combinations.
In this case, we need to choose one appetizer and one main course. Since these choices are independent, we can use the principle of multiplication.
The number of ways to choose one appetizer from 7 options is 7, and the number of ways to choose one main course from 9 options is 9.
Therefore, the total number of ways to order a two-course meal is given by the product of these two choices:
Number of ways = 7 * 9 = 63.
Hence, a person can order a two-course meal in 63 different ways from the given options of appetizers and main courses.
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4,032 divided by 79 = ------
8 times what equals 49
3/7×4 find the product in simplest form
The length of a rectangle is 10 meters more than the width. If the perimeter is 184 meters, what are the length and the width?
If u get this question wrong u have to change your profile picture to Psyduck for 3 days and if u know the answer don't tell anyone but me((pm me)) because the answer is a secret.** If u bring 10 empty bottles to the bottle shop, the bottle shop will change 10 empty bottles to 1 drink. If u bring 100 bottles to the shop. How many drinks will you get?
In the given scenario, 10 empty bottles are equivalent to one drink. So, with 100 bottles, you'd be able to exchange for 10 drinks.
Explanation:
The subject is mathematics, specifically a problem relating to division. The scenario describes a situation where 10 empty bottles can be exchanged for a single drink. If you have 100 bottles, you will be able to exchange these for drinks. To figure out how many drinks you would get, divide the total number of bottles by the number of bottles needed for one drink. So, 100 bottles divided by 10 bottles per drink equals 10 drinks.
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1 millimeter on the map represents 1 meter on the ground. What is the ratio
if 2x -3 = 5 then x = ?
A city council consists of six Democrats and six Republicans. If a committee of seven people is selected, find the probability of selecting four Democrats and three Republicans.
show that, except for 2 and 5, every prime number can be expressed as 10k+1, 10k+3 10k+7, 10k+9, where k is an interger
An election ballot asks voters to select four city commissioners from a group of
twelve candidates. In how many ways can this be done?
There are seven ice skaters in a competition. How many different possibilities are there for the top three places? (A different ordering of the same three skaters counts as a different possibility.)
Y-intercept is 100 and slope is 5. Partner gave example: Younger brother had 100 small building blocks, but lost 5 of them every month since. What mistake did Partner make?
1/5+2/5=
3 4/6- 2 1/6=
5 1/4+ 2 1/4=
5 2/7-2 1/7=
please help
21 pts