The monthly mortgage payment for a $204,000 home with a 10% down payment and a 30 year loan at an interest rate of 3.5% would be approximately $808.44.
Solution
To calculate the monthly mortgage payment for a $204,000 home with a 10% down payment and a 30 year loan.
We'll need to first calculate the amount of the loan and then use the following formula to calculate the monthly payment:
M = P * r * (1 + r)^n / ((1 + r)^n - 1)
where M is the monthly payment P is the principal (loan amount) r is the monthly interest rate n is the number of paymentsFirst, we'll calculate the down payment:
Down payment = 204,000 * 0.10 = $20,400
Next, we'll calculate the loan amount:
Loan amount = 204,000 - 20,400 = $183,600
Now, we'll need to convert the 30 year loan term into the number of payments (n) and the interest rate into the monthly interest rate (r):
n = 30 years * 12 months/year = 360 payments
r = (Annual interest rate) / 12 months/year
Assuming an annual interest rate of 3.5%, the monthly interest rate would be:
r = 0.035 / 12 = 0.002917
Finally, we can plug the values into the formula to calculate the monthly mortgage payment:
M = 183,600 * 0.002917 * (1 + 0.002917)^360 / ((1 + 0.002917)^360 - 1) = $808.44
Therefore, the monthly mortgage payment for a $204,000 home with a 10% down payment and a 30 year loan at an interest rate of 3.5% would be approximately $808.44.
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Question is attached to image
The probability that Deborah's first flight was delayed can be found to be 0. 85.
How to find the probability ?To find the probability that Deborah's first flight from Boston to Denver was delayed, use the following formula :
= 1 - probability that the flight takes off on time
Probability that the flight takes off on time = 0. 15 .
The probability that Deborah's first flight from Boston to Denver was delayed is therefore :
= 1 - 0. 15
= 0. 85
In conclusion, there is an 85 % probability that the first flight was delayed.
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a small business owner is applying for a small business loan and has been approved for a $50,000 loan with a 6.15% annual interest. the first loan is a simple interest rate, the second loan compounds interest quarterly, and the third loan compounds interest continuously. the small business owner plans to pay off the loan in three years and 7 months. Determine the total value of the loan with the quarterly compounded interest.
Answer: The total value of the loan with quarterly compounded interest is $60,109.34.
Step-by-step explanation:
To calculate the total value of the loan with quarterly compounded interest, we can use the formula for compound interest:
A = P * (1 + r/n)^(nt)
where:
A = final amount (loan + interest)
P = principal (the original amount of the loan)
r = annual interest rate as a decimal
n = number of times the interest is compounded in a year
t = time in years
For the loan with quarterly compounded interest, the number of times the interest is compounded in a year is 4 (since interest is compounded quarterly), and the time is 3 years and 7 months, which we can convert to years as 3.5833.
Substituting the values into the formula, we get:
A = $50,000 * (1 + 0.0615/4)^(4 * 3.5833)
A = $50,000 * (1.015375)^(15.7532)
A = $50,000 * 1.22186888
A = $60,109.34
Therefore, To calculate the total value of the loan with quarterly compounded interest, we can use the formula for compound interest:
A = P * (1 + r/n)^(nt)
where:
A = final amount (loan + interest)
P = principal (the original amount of the loan)
r = annual interest rate as a decimal
n = number of times the interest is compounded in a year
t = time in years
For the loan with quarterly compounded interest, the number of times the interest is compounded in a year is 4 (since interest is compounded quarterly), and the time is 3 years and 7 months, which we can convert to years as 3.5833.
Substituting the values into the formula, we get:
A = $50,000 * (1 + 0.0615/4)^(4 * 3.5833)
A = $50,000 * (1.015375)^(15.7532)
A = $50,000 * 1.22186888
A = $60,109.34
Therefore, the total value of the loan with the quarterly compounded interest would be $60,109.34.
Hallar la ecuación de la circunferencia que pasa por los puntos (0,0) (3,4) (6,2)
La ecuación de la circunferencia que pasa por los puntos (0, 0), (3, 4) y (6, 2) es x² + y² - (55 / 9) · x - (5 / 3) · y = 0.
¿Cómo determinar la ecuación de una circunferencia que pasa por tres puntos?Según la geometría analítica, la fórmula general de una circunferencia contiene tres coeficientes reales (D, E, F) en la siguiente expresión:
x² + y² + D · x + E · y + F = 0
En consecuencia, se requiere el conocimiento de tres puntos distintos para determinar las condiciones de la ecuación. Es preciso construir un sistema de ecuaciones lineales, cuya forma es:
D · x + E · y + F = - x² - y²
Si sabemos que (x₁, y₁) = (0, 0), (x₂, y₂) = (3, 4) y (x₃, y₃) = (6, 2), entonces tenemos el siguiente sistema de ecuaciones lineales:
F = 0
3 · D + 4 · E + F = - 25
6 · D + 2 · E + F = - 40
Cuya solución se obtiene mediante métodos numéricos:
(D, E, F) = (- 55 / 9, - 5 / 3, 0)
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If the graph of the function f(x) =e to the X power shift is it in six units to the right, what is the equation of the new graph?
Answer:
The equation for the new graph is e^(x -6)
How do i solve this question
The graph of the equation can be seen on the image at the end, and when she uses 17 cups of flour, she will use 76.5 cups of honey.
How to find the relation between flour and honey?We assume that the relation is linear.
Remember that a general linear equation is:
y = a*x + b
Where a is the slope and b is the y-intercept.
If the linear equation passes through the points (x₁, y₁) and (x₂, y₂) then the slope is:
a = (y₂ - y₁)/(x₂ - x₁)
Here we have the two pairs:
(27, 6)
(45, 10)
First, you can graph these two points and connect them with a line, that will be the graph of our equation.
The slope is:
a = (10 - 6)/(45 - 27)
a = 4/18
a = 2/9
y = (2/9)*x + b
To find the value of b we can replace the values of the point (27, 6)
6 = (2/9)*27 + b
6 = 2*3 + b
6 = 6 + b
0 = b
So the equation is just:
y = (2/9)*x
And for 17 cups of flour, she will use:
17 = (2/9)*x
(9/2)*17 = x
76.5 = x
She needs to use 76.5 cups of honey.
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Which of these currencies is used is Switzerland?
A) The pound sterling
B) The yuan
C) The franc
D) The yen
Answer:
C is the answer.
Step-by-step explanation:
Switzerland uses the currency called Switzerland Franc.
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what is the amplified the sinusoidal function? enter your answer in the box.
Answer: 4
Step-by-step explanation: i took the test
help help help
pleas3e
Answer: 3
Step-by-step explanation:
Lisa's living room has new carpet of 8 meters wide and 10.5 meters long. They want to put carpet in the basement that is twice as long as the living room and a fourth wider. They also wanted to put tile in the bathroom that has an area of 10 square feet. The bedroom is currently being completed with carpet. If the bedroom is 6 meters shorter in length than the living room, and is 34 the width of the living room, what is the bedroom's area in meters squared?
The bedroom's area in meters squared is 55.1693 m².
Solving for the bedroom's area in meters squared:finding the area of the basement:
The length of the basement is 2 * 10.5 m = 21 m
The width of the basement is 8 m / 4 = 2 m
The area of the basement is 21 m * 2 m = 42 m²
Next, let's find the equivalent area of the 10 square feet tile in meters:
1 square foot = 0.092903 m²
10 square feet = 10 * 0.092903 m^2 = 0.92903 m²
finding the area of the bedroom:
The length of the bedroom is 10.5 m - 6 m = 4.5 m
The width of the bedroom is 8 m * 34 = 2.72 m
The area of the bedroom is 4.5 m * 2.72 m = 12.24 m²
So the total area covered with carpet and tile is:
12.24 m² + 42 m² + 0.92903 m²
= 55.1693 m²
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The Humber Room advertises two types of entrée, meat and fish. It is known that 70% of all customers order meat, and 30% order fish. All customers are individually asked after their meals if they were satisfied with them. This survey shows that 80% of those who ordered meat and 95% of those who ordered fish were satisfied. Draw a probability tree for this problem to answer the question.
If M represents the event of ordering meat, F is the event of ordering fish, + is the event of being satisfied, and − is the event of not being satisfied, then answer the following questions:
(a) Determine the following probabilities based on the probability tree:
P(M)
P(F)
--------- Determine the conditional probabilities
(iii) P (+ M)
(iv) P (- M)
(v) P (+F)
(vi) P(-F)
(b) Write down the results of calculating the joint probabilities below:
P (M and +)
P (M and -)
P (F and +)
P (F and -)
(c) If a randomly selected customer was satisfied with his/her meal, what is the probability that the customer ordered fish?
Can someone please explain how to resolve this ?
The probability of ordering meat is 0.7 and the probability of ordering fish is 0.3.
P(+ | M) = 0.8 and P(- | M) = 0.2,
P(+ | F) = 0.95 and P(- | F) = 0.05.
P(M and +) = 0.56 and P(M and -) = 0.14,
P(F and +) = 0.285 and P(F and -) = 0.015.
C: the probability that the customer ordered fish is 0.3.
What is probability?Probability is a way to gauge how likely something is to happen. According to the probability formula, the likelihood that an event will occur is equal to the proportion of positive outcomes to all outcomes. The probability that an event will occur P(E) is equal to the ratio of favorable outcomes to total outcomes.
Given The Humber, Room advertises two types of entrée, meat and fish,
70% of all customers order meat, and 30% order fish,
M represents the event of ordering meat, F is the event of ordering fish,
probability of M and F,
p(M) = 70% = 0.7
p(F) = 30% = 0.3
and 80% of those who ordered meat and 95% of those who ordered fish were satisfied,
+ is the event of being satisfied, and − is the event of not being satisfied,
probability of satisfied customers with meat,
p(+) = 80% = 0.8
not satisfied with meat,
p(-) = 1 - 0.8 = 0.2
probability of satisfied customers with fish,
p(+) = 95% = 0.95
not satisfied with fish,
p(-) = 1 - 0.95 = 0.05
B: calculating the joint probabilities,
P (M and +) = P(M ∩ +) = p(M)*p(+)
P (M and +) = 0.7*0.8
P (M and +) = 0.56
P (M and -) = P(M ∩ -) = p(M)*p(-)
P (M and -) = 0.7*0.2 = 0.14
P (F and +) = P(F ∩ +) = p(F)*p(+)
P (F and +) = 0.3*0.95
P (F and +) = 0.285
P (F and -) = P(F ∩ -) = p(F)*p(-)
P (F and -) = 0.3*0.05
P (F and -) = 0.015
C: Determine the conditional probabilities,
P (+ | M) = P(M ∩ +)/p(M)
substitute the values
P (+ | M) = 0.56/0.7
P (+ | M) = 0.8
P (- | M) = P(M ∩ -) /p(M)
P (- | M) = 0.14/0.7
P (- | M) = 0.2
P (+ | F) = P(F ∩ +)/p(F)
substitute the values
P (+ | F) = 0.285/0.3
P (+ | F) = 0.95
P(- | F) = P(F ∩ -)/p(F)
P(- | F) = 0.015/0.3
P(- | F) = 0.05
D: If a randomly selected customer was satisfied with his/her meal, what is the probability that the customer ordered fish,
to find P (F | +) = P(F ∩ +)/p(+)
substitute the values
P(F | +) = 0.285/0.95
P (F | +) = 0.3
Hence the probabilities are as followed.
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Find a positive and a negative coterminal angle for each given angle.
A positive and a negative coterminal angle for each given angle is
A. 13π/4 and -3π/4.
B. 97π/36 and -47π/36.
What is the coterminal angle?
Coterminal angles are those with a common terminal side that are in standard position (angles with the starting side on the positive x-axis). Coterminal angles are the angles that have the same initial side and share the terminal sides.
Here, we have
A. 5π/4
We have to find the coterminal angle.
5π/4 + 2π = 13π/4
5π/4 - 2π = -3π/4
Hence, a positive and a negative coterminal angle for each given angle is 13π/4 and -3π/4.
B. 25π/36
We have to find the coterminal angle.
25π/36 + 2π = 97π/36
25π/36 - 2π = -47π/36
Hence, a positive and a negative coterminal angle for each given angle is 97π/36 and -47π/36.
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Complete the sentence the below. If the point (4,−1) is a point on the graph of f, then f( __ )=____.
If the point (4, -1) is a point on the graph of f, then f(4) = -1.
How to complete the given sentenceFrom the question, we have the following parameters that can be used in our computation:
Point (4,−1) is a point on the graph of f
The expression "f(4)" represents the output value of the function f, when 4 is plugged into it as the input.
If the point (4, -1) is on the graph of f, it means that for the input value of 4, the output value of the function is -1.
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how many to fill these here buckets
Answer:
Each bucket will be [tex]\dfrac{1}{2}[/tex] full
Step-by-step explanation:
First add up all the different fractions to find out how many buckets of water are in all 3 buckets combined.
Adding up the fractions we get the expression:
[tex]\dfrac{5}{12} + \dfrac{3}{4} + \dfrac{1}{3}[/tex]
To add these fractions first find the LCM(least common multiple of the denominators, 12, 4 and 3
This is the smallest number divisible by all 3 numbers without a remainder
There are several strategies for finding the LCM but here we can see that 12 is evenly divisible by12, 4 and 3
We convert each of the fractions to have the same denominator as the LCM of 12 and adjust the numerator accordingly
Multiply each of the fractions by the LCM
12 x 5/12 = 5
12 x 3/4 = 9
12 x 1/3 = 4
These will become the numerators in the addition with the common denominator of 12
[tex]\dfrac{5}{12} + \dfrac{3}{4} + \dfrac{1}{3}\\\\= \dfrac{5 + 9 + 4}{12}\\\\= \dfrac{18}{12}\\\\[/tex]
This is how many buckets it will take to hold the water from all three buckets
Divide numerator and denominator by 6 to reduce to lowest fraction
[tex]\dfrac{18 \div 6}{12\div6} = \dfrac{3}{2}[/tex]
This is 1 1/2 buckets. If this amount of water is to be evenly divided among 3 buckets then the amount of water in each bucket
[tex]\dfrac{3}{2} \div 3\\\\= \dfrac{3}{2} \times \dfrac{1}{3}\\\\= \dfrac{1}{2}[/tex]
So each bucket will be half full
Brady is making snack bags with 18 juice boxes and 27 cookies. He wants each bag to have the same number of juice boxes and the same number of cookies. (a) What is the maximum number of snack bags he could make? (b) How many juice boxes and (c) how many cookies could he put in each bag?
(a) The maximum number of snack bags he could make,
= 18 snack bags.
(b) 18 juice boxes.
(c) 18 cookies in each bag.
What is greatest common factor?The greatest number that can divide the numbers in equal parts.
It is called as greatest common factor.
Given:
Brady is making snack bags with 18 juice boxes and 27 cookies.
He wants each bag to have the same number of juice boxes and the same number of cookies.
(a) The maximum number of snack bags he could make,
= GCF(18, 27)
= 18 snack bags.
(b) 18 juice boxes.
(c) 18 cookies in each bag.
Therefore, all the required values are given above.
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This scatter diagram shows the marks scored in class tests for English and Science.
The solution is, a) Negative linear; b) about 48
What is graph?In mathematics, the graph of a function f is the set of ordered pairs, where {\displaystyle f(x)=y.} In the common case where x and f(x) are real numbers, these pairs are Cartesian coordinates of points in two-dimensional space and thus form a subset of this plane.
here, we have,
a) Type of correlation
The graph shows a negative linear correlation.
b) Prediction
It looks like a student who makes 60 in Science would make about 48 in English.
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what makes an image not to scale
Answer:
It isn't measured, but it gives you a ruff representation of what the subject looks like.
Step-by-step explanation:
D. 49. Mike will fill jars with water for an experiment. Each jar holds cup. Mike has 18 cups of water. How many jars can Mike fill with water? A 3 B 6 C
On solving the provided question we can say that by fraction, Mike can fill 18 X 1/3 = 6 cups with water
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.
Each jar holds 1/3 cup.
Mike has 18 cups of water
by fraction, Mike can fill 18 X 1/3 = 6 cups with water
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The correct question is -
Mike will fill jars with water for an experiment. Each jar holds 1/3 cup. Mike has 18 cups of water. How many jars can Mike fill with water?
Please help. Thank you to anyone that can
The required volume of figure 1 is given as 55 ft³, and the volume of all the figures is evaluated by following the same procedure.
What is volume?Volume is defined as the mass of the object per unit density while for geometry it is calculated as profile area multiplied by the length at which that profile is extruded.
Here,
Volume = 1/3 area of base × height - - - - -(1)
(1)
Area of base = area of triangle = 1/2 × base × height
Area of base = 1/2 × 5 * 6 = 15
Put this value in equation 1
Volume = 1 /3 ×15 × 11
Volume = 55 ft³
Similarly, the volume of each figure can be evaluated.
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A gas station sells regular gas for $2.15 per gallon and premium gas for $2.90 a gallon. At the end of a business day 300 gallons of gas had been sold, and receipts totaled $690. How many gallons of each type of gas had been sold?
Answer: Let's call the number of gallons of regular gas sold "x". Then, the number of gallons of premium gas sold would be 300 - x.
The total revenue from regular gas would be 2.15 * x dollars. The total revenue from premium gas would be 2.90 * (300 - x) dollars.
We know that the total receipts for the day were $690, so we can set up the following equation:
2.15x + 2.90(300 - x) = 690
Expanding the second term, we get:
2.15x + 870 - 2.90x = 690
Combining like terms, we get:
0.25x = -180
Dividing both sides by 0.25, we get:
x = 720
So, 720 gallons of regular gas and 300 - 720 = -420 gallons of premium gas were sold. However, since it is not possible to sell a negative number of gallons of gas, this solution is not valid.
If we try another value of x that is less than 300, we will find a valid solution. Let's try x = 200:
2.15 * 200 + 2.90 * (300 - 200) = 690
Expanding and simplifying, we get:
430 + 90 = 520
So, 200 gallons of regular gas and 300 - 200 = 100 gallons of premium gas were sold.
Step-by-step explanation:
please help will mark brainlistist
Answer:
SA = 439.8 in²
Step-by-step explanation:
the surface area (SA) is the total area of the 6 triangular faces and the base
the area (A) of a triangle is calculated as
A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the height )
here b = 10 and h = 6 , then
A = [tex]\frac{1}{2}[/tex] × 10 × 6 = 5 × 6 = 30 in²
so area of 6 triangles = 6 × 30 = 180 in²
Then
SA = 180 + 259.8 = 439.8 in²
calculate the measure of x
Answer:
Step-by-step explanation:
Wow, that is a lot. You got to give me a brainliest ! Lol
1) 9²+12²=x², x=15
2)10²+24²=x², x=26
3)3²+7²=x², x=7.6
4)6²+x²=10², x=8
5)x²+6²=24², x=23.2
6)1²+1²=x², x=1.4
7)x²+8²=21², x=19.4
8)x²+24²=30², x=18
9)5²+9²=x², x=10.3
Assume that a consumer has a given budget or income of $10 and that she can buy only two goods, apples or bananas. The price of an apple is $1.00 and the price of a banana is $0.50. This means that, in order to buy four bananas, this consumer must forgo
In order to buy four bananas, then the number of apples that he bought will be 8.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
Assume that a consumer has a given budget or income of $10 and that she can buy only two goods, apples or bananas. The price of an apple is $1.00 and the price of a banana is $0.50.
Let 'x' be the number of apples and 'y' be the number of bananas. Then the equation is given as,
1x + 0.50y = 10
x + 0.50y = 10
In order to buy four bananas, then the number of apples that he bought is given as,
x + 0.50 (4) = 10
x + 2 = 10
x = 8
In order to buy four bananas, then the number of apples that he bought will be 8.
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Simplify (23+16) . Write the sum in the simplest form.
The simplification of (23+16) is 39
What is addition?Addition is one of the four basic operations of arithmetic, the other three being subtraction, multiplication and division. The addition of two whole numbers results in the total amount or sum of those values combined.
For example of there are 20 mangoes. 50 cashews and 80 oranges in a store. The total number of fruits the store can be obtained by adding the number of oranges, mangoes and cashew.
This means that 80+20+50 = 150 fruits
Similarly to get the value of( 23+16) , we add the two numbers together
23+16 = 39
therefore the value of 23+16 = 39
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help me algebra value functions and graphs
The definition of the absolute value function for this problem is given as follows:
y = |x - 4| - 2.
What is the absolute value function?The absolute value function of vertex at coordinates (h,k) is defined as follows:
y = a|x - h| + k.
From the graph, the coordinates of the vertex are given as follows:
(4,-2).
Hence the equation is given as follows:
y = a|x - 4| - 2.
When x changes by one, y also changes by one, hence the coefficient a is given as follows:
a = 1.
Thus the function is defined as follows:
y = |x - 4| - 2.
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Jill was remodeling her bedroom she bought 4 curtains for 37 each and comforter for 68.25. what was the total amount jill paid for the curtains and comforter?
Answer:
216.25
Step-by-step explanation:
First multiply 4 × 37 = 148
Then add 148 + 68.25 = 216.25
8068/31 as a mixed number
the easiest way is to divide, 8068÷31, since it's a big problem, you should use a calculator! When you do, you should get 260.258065, but once you round all the decimals you just get 260, your remainder should be 8. Use 8 as your numerator and 260 as your mixed number! And your finished, and that's why the answer is 260 8/31.
The base of a rectangular box measures 3 feet by 6 feet. What is the height in feet of the box if the volume is 72 cubic feet
Answer:
12 ft
Step-by-step explanation:
To find the height of a rectangular box with a base measuring 3 feet by 6 feet and a volume of 72 cubic feet, we need to use the formula for the volume of a rectangular prism:
Volume = Length x Width x Height
We are given the volume of the box and the length and width, so we can substitute the values and solve for the height:
72 = 3 x 6 x Height
72 / (3 x 6) = Height
12 = Height
So, the height of the box is 12 feet.
Let f be a differentiable function with f(−4) = −2, ƒ'(−4) = 6,
f(-5) = −4, and f'(-5) = 1. Let the function g(x) = ƒ(2x + 3). Write the
equation of the line tangent to the graph of g at the point where x = −4.
Therefore , the solution of the given problem of function comes out to be g(x) = ƒ(2x + 3) = f'(-5) = 1.
What is function ?Mathematics includes the study of numbers, various variations, the natural reality, architecture, and both actual and hypothetical locations. A function is a visual representation of the relationship variable between the number of inputs and the corresponding outputs for each. Simply explained, a function is a collection of inputs that, whenever combined, result in a different output by each input. Every function is assigned a city, county, or scope, sometimes known as a domain. The letter f is frequently used to denote functions (x).
Here,
Given :
=> f(−4) = −2
=> ƒ'(−4) = 6
=> f(-5) = −4
=> f'(-5) = 1
To find :
=> g(x) = ƒ(2x + 3)
=> g(4) = f(2(-4) + 3)
=> g(4) = f(-5)
=> f(-5) = -4
=> f'(-5) = 1
Therefore , the solution of the given problem of function comes out to be g(x) = ƒ(2x + 3) = f'(-5) = 1.
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Which of these numbers in NOT divisible by 3?
300
321
241
8,910
Answer:
Step-by-step explanation:
241 is divisible by 3
Kevin has half of his investments in stock paying an 11% dividend and the other half in a stock paying 14% interest. If his total annual interest is $480, how much does he have invested?
Kevin has $3840 invested in stocks in total.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Given that Annual interest in first investment - 11%
Annual interest in other investment - 14%
Total interest annually - $480
Let us assume, x is the investment in each stock
or, total investment = 2x
then, making an equation for the total interest
0.11x+.14x=480
Multiplying everything by 100
11x+14x=48000
25x=48000
Divide both sides by 25
x=1920
then, by total investment = 2x
2×(1920) = 3840
Hence, Kevin has $3840 invested in stocks in total.
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