Answer:
0.255 or 25.5%
Step-by-step explanation:
You want the scale factor that reduces 5.1 inches to 1.3 inches.
Scale factorThe scale factor is the ratio of the image size to the original size:
1.3/5.1 ≈ 0.254902 ≈ 0.255 = 25.5%
__
Additional comment
A scale factor of 0.255 would give an image of 1.3005 inches. That's probably close enough. Rounding to the nearest percent, it would be 25%, which would give an image size of 1.275 inches.
According to a 2009 Reader's Digest article, people throw away approximately 13% of what they buy
at the grocery store. Assume this is the true proportion and you plan to randomly survey 90 grocery
shoppers to investigate their behavior. What is the probability that the sample proportion exceeds
0.12?
Note: You should carefully round any z-values you calculate to 4 decimal places to match wamap's approach and calculations.
(Enter your answer as a number accurate to 4 decimal places.)
The probability that the sample proportion exceeds 0.12 is given as follows:
0.6103 = 61.03%.
How to obtain probabilities using the normal distribution?
The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the obtained z-score is positive or negative.Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of the measure X in the distribution.By the Central Limit Theorem, for a proportion p in a sample of size n, the sampling distribution of sample proportion is approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1 - p)}{n}}[/tex], as long as [tex]np \geq 10[/tex] and [tex]n(1 - p) \geq 10[/tex].The parameters of the binomial distribution are given as follows:
n = 90, p = 0.13.
Hence the mean and the standard error are given as follows:
[tex]\mu = 0.13[/tex][tex]s = \sqrt{\frac{0.13(0.87)}{90}} = 0.0354[/tex]The probability that the sample proportion exceeds 0.12 is one subtracted by the p-value of Z when X = 0.12, hence:
Z = (0.12 - 0.13)/0.0354
Z = -0.28
Z = -0.28 has a p-value of 0.3897.
Hence:
1 - 0.3897 = 0.6103.
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A group of friends wants to go to the amusement park. They have no more than $295
to spend on parking and admission. Parking is $11.50, and tickets cost $39
person, including tax. Which inequality can be used to determine x, the maximum
number of people who can go to the amusement park?
Answer:
295>_ 39x+11.50
Step-by-step explanation:
the >_ means less than or equal to.
Use interval notation to write the intervals over which fis (a) increasing, (b) decreasing, and (c) constant.
y =f(x)
The intervals of each behavior of the function are given as follows:
a) Increasing: (-∞, -1).
b) Decreasing: (-1, 1).
c) Constant: (1, 3).
How to classify the function as increasing, decreasing or constant?The function is increasing when the graph moves right and up.The function is decreasing when the graph moves right and down.The function is constant when the graph of the function is an horizontal line.More can be learned about functions at https://brainly.com/question/24808124
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PLEASE HELP (IMAGE ATTACHED)
It says my answer needs to be more simplified but I don’t understand
Answer:
-5x⁵ +2x² -3/x³
Step-by-step explanation:
You want the quotient and remainder of (-15x⁸ +6x⁵ -9)/(3x³).
DivisionThe quotient and remainder can be found by dividing term by term.
[tex]\dfrac{-15x^8+6x^5-9}{3x^3}=\dfrac{-15x^8}{3x^3}+\dfrac{6x^5}{3x^3}-\dfrac{9}{3x^3}\\\\\\=\boxed{-5x^5+2x^2-\dfrac{3}{x^3}}[/tex]
__
Additional comment
The exponent rule is (a^b)/(a^c) = a^(b-c).
<95141404393>
DIANA WORKED 5 1/3 HOURS AND GABE WORKED 1 1/4 HOURS. PAULA WORKED ON HERS 3/4 TIMES AS LONG AS DIANA.
DID DIANA WORK ON HER PROJECT LONGER THAN GABE?
DID PAULA WORK LESS ON HER PROJECT THAN DIANA?
DID GABE WORK LONGER ON HIS PROJECT THAN PAULA?
DID GABE WORK LONGER ON HIS PROJECT THAN DIANA?
¿Qué volumen de solución de ácido a 60% debe mezclarse con una solución a 30% para producir
300 mililitros de solución al 50%?
Answer:
Step-by-step explanation:
To solve this problem, we must first use an equation that reflects the amount of acid in each solution and its relationship to the total volume of the resulting solution. We can use the following equation:
(C1 * V1) + (C2 * V2) = (C3 * V3)
Where:
C1 = concentration of the acid solution at 60% (in percent)
V1 = volume of the acid solution at 60% (in ml)
C2 = concentration of the acid solution at 30% (in percent)
V2 = volume of the 30% acid solution (in ml)
C3 = concentration of the resulting 50% acid solution (in percent)
V3 = volume of the resulting 50% acid solution (in ml)
In this case, we know the total volume of the resulting solution (V3 = 300 ml) and the desired concentration (C3 = 50%). We also know the concentration of one of the original solutions (C1 = 60%). So we can plug the known values into the equation:
(60 * V1) + (30 * V2) = (50 * 300)
Clearing V1:
V1 = (300 * 50 - 30 * V2) / 60
Now that we have V1 as a function of V2, we can solve the problem to find the volume of the 60% acid solution to mix with the 30% solution. Substitute the known values into the equation:
V1 = (300 * 50 - 30 * V2) / 60
V1 = (15000 - 30 * V2) / 60
V1 = 250 - (V2 / 2)
We can use this last equation to find the volume of the 30% solution that we must mix with the 60% solution:
V2 = 2 * (250 - V1)
Clearing V1:
V1 = 250 - (V2 / 2)
V1 = 250 - (2 * (250 - V1) / 2)
V1 = 250 - 250 + V1
V1 = 250
Therefore, we must mix 250 ml of 60% acid solution with 250 ml of 30% solution to produce 300 ml of 50% solution.
PT=y, TR=3x + 1, QT=3y, TS = 4x + 13
find x and y
The values of x and y for the parallelogram PQRS are respectively, 2 & 7
What are the properties of parallelogram ?Opposite sides are parallel: The pairs of opposite sides of a parallelogram are always parallel to each other.
Opposite sides are equal in length: The pairs of opposite sides of a parallelogram are equal in length.
Given that,
The parallelogram PQRS has diagonals PR and SQ that intersects at T,
T is the midpoint of PR and T is the midpoint of SQ
If T is the midpoint of PR, then PT = TR
Given PT = y and TR = 3x+1
y = 3x+ 1 _____(i)
Also, If T is the midpoint of SQ, then ST = TQ
Given QT=3y and TS=4x+13
3y = 4x+ 13 ____(ii)
Substitute equation 1 into 2;
3y = 4x+ 13
3(3x+1) = 4x+ 13
open the parenthesis
9x+3 = 4x+13
club like terms
9x-4x = 13-3
5x = 10
x = 10/5
x = 2
Substitute x = 2 into equation 1
From 1; y = 3x+1
y = 3(2)+1
y = 6+1
y = 7
Hence, the values are x = 2 and y = 7
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The complete questions :
Parallelogram PQRS has diagonals PR and SQ that intersect at T find the values of x and y PT=y TR=3x+1 QT=3y TS=4x+13
If d²=3520, and you're solving for D, how do you get the form d=8√55, -8√55. I'm just genuinely confused on how you would calculate to this step.
1 = 3520/d² → d² = 3520 → d = 8√55, -8√55 → d = 59.330, D = -59.330
↑Multiply Both sides by 1 ↑ ??? ↑ ???
Does this make sense?
Answer:
Step-by-step explanation:
The square root of a number can be both positive and negative, so to find all possible values of d, we need to take both the positive and negative square root of 3520.
Starting with the positive square root:
d = √3520 = √(55^2 * 8) = 55 * √8 = 8 * √55
And for the negative square root:
d = - √3520 = - √(55^2 * 8) = - 55 * √8 = - 8 * √55
So the two possible values of d are 8√55 and -8√55.
ACTIVITY 2 1. Mr Nkomo lives in Three Rivers, in the Emfuleni municipality and uses prepaid electricity that is sold to customers at a VAT inclusive rate. The table below shows the cost of prepaid units of electricity. BLOCK UNITS (kWh) 2 3 4 0-50 51-350 351-600 >600 *Prepaid electricity: Paying for electricity before using it. *VAT = 15% *The municipality buys electricity from Eskom at an average VAT inclusive price of R1,33 per kWh. 1.1. State any two reasons why it is an advantage for the municipality to sell prepaid electricity. Verify, by showing ALL calculations, If his claim is VALID. You may use the formula: % Profit = (4) 1.2. Determine the number of units Mr Nkomo received when he bought prepaid electricity for R68,02. (3) 1.3. How much will Mr Nkomo pay if he wanted to buy 310 kWh of electricity? (3) 1.4. Mr Nkomo stated that the percentage profit the municipality makes when a customer buys 290 kWh of electricity is more than 34%. RATE c/kWh (Including vat) sell price for the units-cost price for the units 144,72 186,06 261,87 308,37 ✓ 1000z IC) 2
Answer:
Step-by-step explanation:
1.1. Advantages of Selling Prepaid Electricity
Two advantages of selling prepaid electricity are:
a) Reduced costs for the municipality: Prepaid meters eliminate the need for the municipality to send meter readers to each property and manually read the meter. This can save the municipality time and money.
b) Improved cash flow: By receiving payment before the electricity is used, the municipality can improve its cash flow as it will have funds available to purchase more electricity.
1.2. Number of Units Mr Nkomo Received When He Bought Prepaid Electricity for R68,02
The rate per kWh including VAT is R1,33. To determine the number of units Mr Nkomo received, we can use the formula:
Units = Amount / Rate
Units = R68,02 / R1,33
Units = 51.04 kWh
So, Mr Nkomo received 51.04 kWh of electricity when he bought prepaid electricity for R68,02.
1.3. Cost of 310 kWh of Electricity
The rate per kWh including VAT is R1,33. To determine the cost of 310 kWh of electricity, we can use the formula:
Cost = Units * Rate
Cost = 310 kWh * R1,33
Cost = R411,30
So, Mr Nkomo will have to pay R411,30 for 310 kWh of electricity.
1.4. Percentage Profit the Municipality Makes When a Customer Buys 290 kWh of Electricity
To determine the percentage profit the municipality makes when a customer buys 290 kWh of electricity, we need to calculate the cost price and the selling price of the electricity. The cost price of electricity is R1,33 per kWh. The selling price is given in the table as R144,72 for 2-50 kWh, R186,06 for 51-350 kWh, R261,87 for 351-600 kWh, and R308,37 for over 600 kWh.
Since the cost price is R1,33 per kWh and the selling price is different for different ranges of units, we need to calculate the cost and selling price for each range of units and find the average.
For 2-50 kWh:
Cost = 2-50 kWh * R1,33
Cost = 50 kWh * R1,33
Cost = R66,50
Selling price = R144,72
Profit = Selling price - Cost
Profit = R144,72 - R66,50
Profit = R78,22
Percentage profit = (Profit / Cost) * 100
Percentage profit = (R78,22 / R66,50) * 100
Percentage profit = 17.7%
For 51-350 kWh:
Cost = 51-350 kWh * R1,33
Cost = 350 kWh * R1,33
Cost = R466,50
Selling price = R186,06
Profit = Selling price - Cost
Profit = R186,06 - R466,50
Profit = R29,56
Percentage profit = (Profit / Cost) * 100
Percentage profit = (R29,56 / R466,50) * 100
Percentage profit = 6.3%
For 351-600 kWh:
Cost = 351-600 kWh * R1,33
Cost = 600 kWh * R1,33
Cost = R798,00
Selling price = R261,87
Profit = Selling price - Cost
Profit = R261,87 - R798,00
Profit = -536,13
Percentage profit = (Profit / Cost) * 100
Percentage profit = (-536,13 / R798,00) * 100
Percentage profit = -67.3%
For over 600 kWh:
Cost = over 600 kWh * R1,33
Cost = R1,33 * 1000
Cost = R1330,00
Selling price = R308,37
Profit = Selling price - Cost
Profit = R308,37 - R1330,00
Profit = -1021,63
Percentage profit = (Profit / Cost) * 100
Percentage profit = (-1021,63 / R1330,00) * 100
Percentage profit = -76.7%
The average percentage profit for the municipality is calculated by finding the total profit and total cost for each range of units and then dividing the total profit by the total cost.
For the range 2-50 kWh, the total profit is R78,22 and the total cost is R66,50, so the average percentage profit is (R78,22 / R66,50) * 100 = 17.7%.
For the range 51-350 kWh, the total profit is R29,56 and the total cost is R466,50, so the average percentage profit is (R29,56 / R466,50) * 100 = 6.3%.
For the range 351-600 kWh, the total profit is -536,13 and the total cost is R798,00, so the average percentage profit is (-536,13 / R798,00) * 100 = -67.3%.
For the range over 600 kWh, the total profit is -1021,63 and the total cost is R1330,00, so the average percentage profit is (-1021,63 / R1330,00) * 100 = -76.7%.
The average percentage profit for the municipality for the four ranges of units is calculated as follows:
Average percentage profit = (17.7% + 6.3% - 67.3% - 76.7%) / 4
Average percentage profit = -34.05%
Therefore, Mr Nkomo's claim that the percentage profit the municipality makes when a customer buys 290 kWh of electricity is more than 34% is NOT VALID.
Gabrielle's age is three times Mikhail's age. The sum of their ages is 64. What is Mikhail's age?
Answer:
16 years old
Step-by-step explanation:
Let's call Mikhail's age "x". Gabrielle's age is 3 times that, so her age is 3x. The sum of their ages is 64, so:
x + 3x = 64
4x = 64
x = 16
So, Mikhail's age is 16 years old.
please help me with this question
Answer:
2nd answer : it is equivalent but not completely factored
Step-by-step explanation:
the "pulling out" of 3 as factor was completely correct.
but
3(x² - 4) can be further factored.
remember :
(a + b)(a - b) = (a² - b²)
therefore,
(x² - 4) = (x + 2)(x - 2)
and then
3(x + 2)(x - 2)
would be a complete factorization.
Answer: B) The expression is equivalent, but is not completely factored
Step-by-step explanation:
16. At Target, a shirt that costs $25 goes on sale for $15. What is the
percent of decrease in the price?
O 40 percent increase
O 7 percent decrease
O40 percent decrease
O7 percent increase
Answer: Decreased 40%
Step-by-step explanation:
Alright, we know they reduced $10.00 (25-15)
Now all we have to do is find the percentage, 10 is how much of 25?
10/25 =0.4
(to get 0.4 to a percentage multiply by 100)
The price was decreased by 40%
HURRRRRRYYYYYYYYYYYYYYYYYYYYYYYY Drag numbers to show which are closest to ‐1
and ‐1/4
on the number line.
The number that is closest to -1 is -0.82 while the number that is closest to -1/4 is -0.28.
What are the closest numbers?In order to obtain the numbers that are close to a given number, we need to place the numbers side by side for a better understanding. For instance, the number 3 is closer to number 1 while the number 9 is closer to number 10.
Given the number line above, we can arrive at the conclusion that -0.82 is closer to -1 because by approximating the decimal, we will arrive at figure 1. Also, the number, -0.28 is closer to -1/4 or - 0.25 when converted to decimal.
Options;
A. -0.28
B. -0.82
C. -4/5
D. -1/5
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The perimeter of a triangle is 39 inches. If the length of the shortest side is 1/2 the length of the longest side, and the length of the third side is 1 less than the length of the longest side, what is the length of each side?
1. what are the three equations that are used.
2. what are the lengths of the sides?
(the shortest side, the longest side, and the third side.
The equations used are:
Longest side = a
Shortest side = 1/2 x a = 1/2a
Third side = a - 1
The shortest side is 8 inches, the longest side is 16 inches and the third side is 15 inches.
What are the length of the sides?The perimeter of a triangle is the sum of the length of the three sides of the triangle.
Let the following expressions represent the lengths of the sides of the triangle:
Longest side = a
Shortest side = 1/2 x a = 1/2a
Third side = a - 1
Perimeter = a + 1/2a + a - 1 = 39
a + 1/2a + a = 39 + 1
2a + 1/2a = 40
2 1/2a = 40
5/2a = 40
a = 40 x 2/5
a = 16 inches
Shortest side = 1/2 x 16 = 8 inches
Third side = 16 - 1 = 15 inches
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Pls help me with this math space question
The required value of the expression at x = 4 and x = -4 is 81 and 1/81 while as x gets larger simultaneously 3ˣ approaching to infinity.
What is an exponential function?The function which is in format f(x) =aˣ where a is constant and x is variable, the domain of this exponential function lies (-∞, ∞).
Here,
Given expression,
= 3ˣ
put x = 4
= 3⁴ = 81
Now put x = -4
= 3⁻⁴
= 1/3⁴
= 1/81
Since x gets larger as x = 0, 1, 2, 3, and so on 3ˣ get 1, 9, 27, 81 and so on approaching to infinity.
Thus, the required value of the expression at x = 4 and x = -4 is 81 and 1/81 while as x gets larger simultaneously 3ˣ approaching infinity.
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The last time it placed an order for ingredients, Sweet Treats Bakery ordered 9,390 kilograms of sugar. This time, the bakery is ordering 7,512 kilograms. What is the percent of decrease in the size of the sugar order?
Answer:A decrease of 20%.
First we must subtract out new total from our old total.
9390 - 7512 is 1878. This means that there is a difference of 1878. Next we must divided both 7512 and 1878 into 9390.
7512/9390 is 0.8 & 1878/9390 is 0.2
As a percentage that is 80% and 20%.
This means that the new amount of sugar only makes up 80% of the old amount. That means that there was a decrease of 20% of kilograms of sugar.
I hope this helped & Good Luck <3 !!!
The U.S. Energy Information Administration (US EIA) reported that the average price for a gallon of regular gasoline is $2.62. The US EIA updates its estimates of average gas prices on a weekly basis. Assume the standard deviation is $.25 for the price of a gallon of regular gasoline and recommend the appropriate sample size for the US EIA to use if they wish to report each of the following margins of error at 95% confidence. a. The desired margin of error is $.10. b. The desired margin of error is $.07. c. The desired margin of error is $.05.
The US EIA should use a sample size of at least 25 for a margin of error of $0.10, at least 49 for a margin of error of $0.07, and at least 97 for a margin of error of $0.05 to report the average price of a gallon of regular gasoline with 95% confidence.
What is Statistics?Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.
We can use the formula for the margin of error for a 95% confidence interval:
margin of error = z× (standard deviation / √n)
where z is the z-score for a 95% confidence interval, which is 1.96.
a. The desired margin of error is $0.10:
0.10 = 1.96(0.25 /√n)
√n = 1.96×0.25 / 0.10
√n= 4.9
n = 4.9^2
n = 24.01
So the appropriate sample size for a margin of error of $0.10 is at least 25.
b. The desired margin of error is $0.07:
0.07 = 1.96 (0.25 / √n)
√n = 1.96 × 0.25 / 0.07
√n= 6.97
n = 6.97²
n = 48.53
So the appropriate sample size for a margin of error of $0.07 is at least 49.
c. The desired margin of error is $0.05:
0.05 = 1.96 (0.25 / √n)
√n= 1.96 × 0.25 / 0.05
√n= 9.8
n = 9.8²
n = 96.04
So the appropriate sample size for a margin of error of $0.05 is at least 97.
Therefore, the US EIA should use a sample size of at least 25 for a margin of error of $0.10, at least 49 for a margin of error of $0.07, and at least 97 for a margin of error of $0.05 to report the average price of a gallon of regular gasoline with 95% confidence.
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the perimeter of this triangle is 32,
write down the equation in terms of x
The value of x in the triangle is 5 units.
How to find the perimeter of a triangle?A triangle is a polygon with three sides. The sum of angles in a triangle is 180 degrees. The perimeter of a triangle is the sum of the whole three sides of the triangle.
Hence,
x + 2x + 3 + x + 9 = 32
4x + 12 = 32
subtract 12 from both sides of the equation
4x + 12 = 32
4x + 12 - 12 = 32 - 12
4x = 20
divide both sides of the equation by 4
x = 20 / 4
x = 5
Therefore,
x = 5
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9. In a cranberry punch recipe, four cups of cranberry juice and one quart of pineapple juice make up half of the punch. How many cups of punch does the recipe make?
On solving the provided question, we can say that by fraction, 4/3 (orange Juice) + 3/4 apple juice + 2/3 cranberry juice + 3/4 lemon lime juice.
what is fraction?Any number of equal portions, or fractions, can be used to represent a whole. Fractions in standard English indicate how many units of a certain size there are. 8, 3/4. A whole includes fractions. The ratio of the numerator to the denominator is how numbers are expressed in mathematics. Each of these is an integer in simple fractions. In the numerator or denominator of a complex fraction is a fraction. True fractions have numerators that are less than their denominators. A fraction is a sum that constitutes a portion of a total. By breaking the entire up into smaller bits, you can evaluate it. Half of a full number or item, for instance, is represented as 12.
by fraction
4/3 (orange Juice) + 3/4 apple juice + 2/3 cranberry juice + 3/4 lemon lime juice.
16/12+9/12+8/12+9/12=42/12=3 and 1/2 cups.
20/3.5=5.7 or 6
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Find the exact value of x
Step-by-step explanation:
answer, verified answer
Anyone know the answers for Domain and rqnge digital escape puzzle 3?
The domain and the range of a function/graph/relation are defined as follows:
Domain: set of input values.Range: set of output values.What are the domain and range of a function?The domain of a function is the set that contains all possible input values of the function/relation, hence it is composed by the values of x.The range of a function is the set that contains all possible output values of the function/relation, hence it is composed by the values of y.Missing InformationThe problem is incomplete, hence the concepts of domain and range are presented, and then they are used to obtain the domain and the range.
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8m
6m
10m
5m what is the area of this shape
The area of the given composite shape with two rectangles is 68 m²
What is a rectangle?
There are four right angles on the quadrilateral that forms the rectangle. Every corner or vertex has a right angle where the two sides meet. It differs from a square, which has all of its sides of equal length, in that the opposite sides of the rectangle are equal in length. Two dimensions and flatness combine to make a rectangle.
The figure can be divided into a rectangle with a length of 8m and breadth of 6m and another rectangle of length 5m and breadth = (10-6) = 4m.
To find the area of the whole figure, we first find the areas of small and big rectangles and sum their areas.
Area of small rectangle = length * breadth = 5*4 = 20 m²
Area of big rectangle = length * breadth = 8 * 6 = 48 m²
Therefore the area of the given composite shape with two rectangles is 20+48 = 68 m².
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Maya had $32. She spent all the money on buying 3 notebooks for x dollars each and 4
packs of index cards for y dollars each. If Maya had bought 5 notebooks and 5 packs of
index cards, she would have been short $18. Which system of equations represents this
situation?
O 3x + 4y = 32 and 5x + 5y = 50
O 3x+4y= 32 and 5x + 5y = 18
O 3x + 4y = 50 and 5x - 5y = 18
O 3x - 4y= 32 and 5x - 5y = 50
The system of equations which represents this
situation is 3x+4y= 32 and 5x + 5y = 18.
The correct answer choice is option B
Which system of equations represents the situation?Amount with Maya = $32
Amount spent on each notebook = x
Number of notebook = 3
Amount spent on each pack of index cards = y
Number of index cards = 4
Maya bought 5 notebooks and 5 packs of
index cards
$18 short = $32 - $18
= $14
3x + 4y = 32
5x + 5y = 14
In conclusion, the system of equation is 3x+4y= 32 and 5x + 5y = 18.
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Find the common ratio of the geometric sequence
17,51,153
Answer:
Common ratio, r = 3
Step-by-step explanation:
Common ratio is given by the ratio of one of the terms to the previous term and is a constant for the entire sequence
Here the first term is 17
Second term is 51
Second Term ÷ First Term
= 51 ÷ 17 =3
Third Term ÷ Second Term
= 153 ÷ 51 = 3
So common ratio is 3
In general, if aₙ is the nth term and aₙ₊₁ then the common ratio is given by:
aₙ₊₁ / aₙ
What is the total surface area of the rectangular prism?
Answer:a rectangular prism has height 4m, length 6m & width 5m
thus the surface consist of two 4*6 vertical surfaces
two 4*5 vertical surfaces
& two 6*5 top & bottom surfaces
that is
2(4*6) = 48
2(4*5) = 40
2(6*5) = 60
total surface area = 48+40+60 = 148m²
Step-by-step explanation:
f(x) = 12 + 1
(f + g) (x) =
g(x) = 5 - x
Answer:
Step-by-step explanation: The expression for f(x) is not a valid mathematical equation. It should specify the relationship between x and the output value of f(x). If the correct equation for f(x) is given, we can then find the expression for (f + g)(x) and g(x).
Assuming that the equation for f(x) is as follows:
f(x) = 12 + x
Then, the expression for (f + g)(x) can be found by adding f(x) and g(x):
(f + g)(x) = f(x) + g(x) = 12 + x + (5 - x) = 17
So, (f + g)(x) is a constant function with a value of 17 for all values of x.
And the expression for g(x) was already given:
g(x) = 5 - x
1
34°
2
3
4
find m angle 4?
Evaluate student loan options
Question
Alvin will be finishing his payments on his 10-year, $26,000 student loan and wants to know the amount of interest th
paid over the course of the loan. The student loan has a 4.4% fixed interest rate that is compounded monthly. Calcula
total amount of interest Alvin paid, rounding to the nearest cent.
Provide your answer below:
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The total amount of interest that Alvin paid over the course, guven the value of the student loan and the interest rate is $ 6, 185
How to find the interest paid ?To find the interest paid, you need to find the total amount that Alvin paid in the 10 years that he was paying.
To do this, you first need to find the monthly payments. This will be an annuity as the amount will be the same throughout the student loan payment period.
The amount would be :
Student loan value = Amount x Present value interest factor of annuity, 120 periods, 4. 4 % / 12
The periods are :
= 10 years x 12 months
= 120 months
The amount is:
26, 000 = Amount x 96.939576551857
Amount = 26, 000 / 96.939576551857
Amount = $ 268. 21
The total paid over the 10 years is :
= 268. 21 x 120 months
= $ 32, 184. 9972
The interest is :
= 32, 184. 9972 - 26, 000 loan amount
= $ 6, 185
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5x + 3y = 28
y=-1/5x+2
Answer:
x = 5, y = 1
Step-by-step explanation:
For x :
Substitute y into the equation : 5x + 3 ( -1/5x + 2 ) = 28
Simplify : 22/5x + 6 = 28
Isolate x : x = 5
For y :
Substitute x for 5 : y = -1/5 * 5 + 2
Solve: y = 1
What is b in this? Y=-1/3+b
Or how do i graph it?
NEED ASAP
The equation of line passing through the points (-2, 4) & (4, 2) is :
y = -1/3 x + 6
The value of b = 6
What is the equation of line?The equation of a straight line is a relationship between x and y coordinates, The general equation of a straight line is y = mx + c, where m is the slope of the line and c is the y-intercept.
To find the equation of the line passing through the two points (-2, 4) and (4, 2), we can use the point-slope form of a line. The point-slope form of a line is given by:
y - y₁ = m(x - x₁)
where m is the slope of the line and (x₁, y₁) is any point on the line.
To find the slope of the line, we can use the formula:
m = (y₂ - y₁) / (x₂ - x₁)
where (x₁, y₁) and (x₂, y₂) are the two given points.
Plugging in the values for the given points, we get:
m = (2 - 4) / (4 - (-2))
m = -2 / 6
m = -1/3
Next, we can use one of the given points to write the equation in point-slope form:
y - 4 = -1/3 (x - (-2))
y - 4 = -1/3 x + 2
y = -1/3 x + 6
This is the equation of the line passing through the two given points (-2, 4) and (4, 2).
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