Option b is correct monthly payment = $163.07
A loan of $7,500 with an 11% interest rate compounded monthly over a time period of 5 years.
Monthly Payment = Amount / Discount factor
Discount factor [tex]D = \frac{1-(1+i)^{n} }{i}[/tex]
where,
Amount = $7500
Rate= 11%=0.11
[tex]i = \frac{0.11}{12} = 0.0091[/tex] ( by using division)
Time = 5 years
Time (n) = 5 × 12 = 60
Now, put i and n in the Discount factor,
[tex]D = \frac{1-(1+i)^{n} }{i}[/tex]
[tex]D = \frac{1-(1+0.009)^{-60} }{0.009}[/tex]
[tex]D = \frac{1-(1.009)^{-60} }{0.009}[/tex]
[tex]D = \frac{0.421 }{0.009}[/tex]
D = 46.77
Monthly payment (M),
[tex]M = \frac{Amount}{Discout factor} = \frac{A}{D}[/tex]
[tex]M = \frac{7500}{46.77}[/tex] ( by using division)
Monthly payment = 163.07
Therefore, Option b is the correct monthly payment = $163.07.
Read more about the Discount factor :
https://brainly.com/question/8691762
#SPJ4
In a quadrilateral help he is congruent to lp what other condition would prove that help is a parallelogram
Answer: [tex]\overline{EL} \cong \overline{HP}[/tex]
Step-by-step explanation:
A quadrilateral with two pairs of opposite congruent sides is a parallelogram.
the area of a rectangle is 344in²; if the length is 78in, find the width and perimeter of the rectangle
what is the width and perimeter
Solve the triangle. A = 46°, a = 31, b = 27
A. B = 38.8°, C = 115.2°, c ≈ 34.3
B. B = 38.8°, C = 95.2°, c ≈ 25.7
C. B = 38.8°, C = 95.2°, c ≈ 42.9
D. Cannot be solved
Answer:
C. B=38.8, C=95.2, c=42.9
Step-by-step explanation:
Find B by using sine rule
sin 46/31=sin B/27
sin B= 27 sin 46/31
B=sin‐¹(0.627)
B=38.8
Find C
C= 180-(A+B)
C=180-(38.8+46)
C=95.2
Using sine rule, Find c
31/sin 46=c/sin 95.2
c=31 sin 95.2/sin 46
c=42.9
Explain why the standard deviation of a set of data is always given as a positive number, but data points can have a negative overall standard deviation.
The reason why the standard deviation of a set of data is always given as a positive number is because the individual values are squared.
What is the standard deviation?The term standard deviation is used to express how much numbers depart from the mean value. Now we know that the standard deviation for each of the data points is the square of the difference between the score and the mean.
Given that the value that is extracted from each data point is squared, the standard deviation of a set of data is always given as a positive number, but data points can have a negative overall standard deviation.
Learn more about standard deviation:https://brainly.com/question/13905583
#SPJ1
PLEASE HELP I've been struggling on this one :(
Answer: The answer is (x+2)(x-4)(x-4)
Or as a short form you can write it as [tex](x+2) (x-4)^{2}[/tex]
Step-by-step explanation:
Answer is very lengthy but I am 100% sure that's the correct answer
Answer:
(x³ - 6x² + 32) = (x - 4)²(x + 2)
Step-by-step explanation:
(x³ - 6x² + 32)/(x - 4) =
x² - 2x - 8
----------------------------------
x - 4 | x³ - 6x² + 0x + 32
x³ - 4x²
----------
-2x² + 0x
-2x² + 8x
----------------
-8x + 32
-8x + 32
-------------
0
(x³ - 6x² + 32) = (x - 4)(x² - 2x - 8) = (x - 4)(x - 4)(x + 2) =
= (x - 4)²(x + 2)
A company has $36,000 to hire a mathematician and his or her secretary. Out of respect for the mathematician's training, the mathematician will be paid $8000 more than the secretary. How much will each be paid
The money paid to the secretary is $14000 and the money paid to mathematician is $22000.
What is an equation?A mathematical statement that establishes the equality of two mathematical expressions is the called an equation.
Total money available for hiring = $36000
Let the money given to secretary = X
Money given to the mathematician = X + 8000
X + (X + 8000) = 36000
2X = 28000
X = 14000
Money given to secretary is $14000.
Money given to the mathematician is $22000.
Learn more about equations on:
https://brainly.com/question/2972832
#SPJ4
13. Define the domain of the following
For the given diagram, the domain of the graph will be within the range [-2, 8]. Hence the required domain are {-2, 0, 1, 2, 8}
Domain of a functionThe domain of a function are the independent variable of the function for which it exists,
For graphs, the domain exists on the x-axis of the curve or line on the xy plane.
For the given diagram, the domain of the graph will be within the range [-2, 8]. Hence the required domain are {-2, 0, 1, 2, 8}
Learn more on domain here: https://brainly.com/question/26098895
#SPJ1
Francisco's credit card has an APR of 13%, calculated on the previous
monthly balance, and a minimum payment of 2%, starting the month after the
first purchase. His credit card record for the last 7 months is shown in the
table below.
A.609.87
B.45.52
C.330.35
D.279.53
The amount of the $5200 charge that Francisco made during the first month has been paid off will be $279.53 based on the APR.
What is APR?Annual percentage rate (APR) refers to the yearly interest generated by a sum that's charged to borrowers or paid to investors
For credit cards, the interest rates are typically stated as a yearly rate. This is called the annual percentage rate.
The amount of the $5200 charge that Francisco made during the first month has been paid off will be the total of the principal paid which is:
Principal paid = $47.67+$47.23+$46.80+$46.37+$45.94+$45.52
=$279.53
Therefore, the amount of the $5200 charge that Francisco made during the first month has been paid off will be $279.53.
In conclusion, the correct option is D.
Learn more about APR on:
https://brainly.com/question/16937491
#SPJ1
Complete question:
How much of the amount of the $5200 charge has Francisco paid off in the first month?
Identify the range of the function shown in the graph.
OA. -1 sy≤ 1
OB. {-1, 1)
OC. y> -1
-10
D. y is all numbers.
10
8
8-
2
48
-6
88
-10-
The range of the attached function is 0 ≤ y ≤ 8
How to determine the range?The complete question is added as an attachment
From the graph, we have the following highlights
Vertex = MaximumVertex = (0, 8)This means that the y value do not exceed 8, and the minimum is 0
Hence, the range of the attached function is 0 ≤ y ≤ 8
Read more about range at:
https://brainly.com/question/13824428
#SPJ1
Select all the true statements. Logarithms may be used to linearize data. Powers may be used to linearize data. Roots may be used to linearize data. If a data set is linearized by taking the common logarithm (log) or natural logarithm (ln) of the y-values, then the data follows a power model. If a data set is linearized by taking the pth root of the y-values, then the data follows a power model.
The true statements are:
Logarithms may be used to linearize data.
Powers may be used to linearize data. Roots may be used to linearize data.
If a data set is linearized by taking the common logarithm (log) or natural logarithm (ln) of the y-values, then the data follows a power model.
Another format for writing exponents is in logarithms.
The use of a logarithm can be utilized to solve issues that cannot be resolved using the concept of exponents alone. A logarithm is simply another way to describe exponents. Exponent and logarithm are inverse forms of one another. A logarithm is defined using an exponent.
Learn more about logarithms here:
https://brainly.com/question/25710806
#SPJ1
Answer:
A.Logarithms may be used to linearize data.
B.Powers may be used to linearize data.
C.Roots may be used to linearize data.
E.If a data set is linearized by taking the pth root of the y-values, then the data follows a power model.
Step-by-step explanation:
Yes
1 point
Calculate the rate of change for each function over the interval [0, 3], then tell which function is
growing faster.
f(x) = 2x + 3
g(x) = 2² +3
Of(x) has a rate of change of 2
g(x) has a rate of change of 2.33
So g(x) is growing faster
f(x) has a rate of change of 6
g(x) has a rate of change of 7
So g(x) is growing faster
f(x) has a rate of change of 6
g(x) has a rate of change of 7
So f(x) is growing faster
f(x) has a rate of change of 2
g(x) has a rate of change of 2.33
So f(x) is growing faster
If f(x) = 2x + 3 then Δy/Δx = 2 and g(x) = 2² +3 then Δy/Δx = 2.33.
The correct answer is option A.
f(x) has a rate of change of 2
g(x) has a rate of change of 2.33
So g(x) is growing faster
How to estimate the rate of change of a function over the interval [0, 3]?Let f(x) = 2x + 3 and g(x) = 2² +3
Let, ∆y /∆x denotes the ratio of y change and x change when x change exists relatively large.
If f(x) = 2x + 3
Δy/Δx = [f(3) - f(0)]/3 - 0
f(3) [tex]= 2*3+3 = 9[/tex]
f(0) [tex]= 2*0+3 = 3[/tex]
[f(3) - f(0)]/3 - 0 = (9 - 3)/3
= 6/3 = 2
g(x) = 2² +3
Δy/Δx = [g(3) - g(0)]/3 - 0
[tex]$= (2^3 +3)-(2^0 +3)/3[/tex]
[tex](2^3 +3)-(2^0 +3) = 7[/tex]
[tex](2^3 +3)-(2^0 +3)/3[/tex] = 7/3 = 2.33
Therefore, the correct answer is option A.
f(x) has a rate of change of 2
g(x) has a rate of change of 2.33
So g(x) is growing faster
To learn more about functions refer to:
https://brainly.com/question/11388036
#SPJ9
17
The product of two positive numbers is
Calculate the numbers.
5/6
And their quotient is 15/8 calculate the number
Answer:
Let "x" and y" be the two numbers.
We have
xy = 5/6, (1) and x/y = 15/8. (2)
Multiply (1) and (2) (both sdes). You will get
x^2 = (5*15)/(6*8) = 25/16.
Hence, x = +/- 5/4.
Next, divide (1) by (2) (both sides). You will get
y^2 = 5/6:15/8 =
(5*8)/(6*15) = 4/9.
Hence, y=+/-2\/3.
Answer. There are two solutions: (x, y)=(5\/4,2\/3) and (x,y) = (-5/4,-2/3).
// We should exclude the second solution, since the numbers are negative.
2 (3/4 - x/3) = 1 1/4
solve for x
The value of x is 17/12
How to solve for x?The equation is given as
2 (3/4 - x/3) = 1 1/4
Express as improper fractions
2 (3/4 - x/3) = 5/4
Divide through by 2
3/4 - x/3 = 5/9
Collect like terms
x/3 = 3/4 - 5/9
Multiply through by 3
x = 9/4 - 15/9
Evaluate
x = (81 - 30)/36
Evaluate
x = 51/36
Simplify
x = 17/12
Hence, the value of x is 17/12
Read more about equations at:
https://brainly.com/question/723406
#SPJ1
I keep believing the answer is either 18,000 or 1,800 but im incorrect. Can someone please help me?? I use the formula A^2 *2*A*L=SA
The base is a square, so the area of the square is (10 cm)² = 100 cm²
To find the area of each triangle use the formula
base • height
10 cm • 9 cm = 90 cm²
now multiply by the number of triangles
90 cm • 4 = 360 cm²
Add the area of the square:
100 cm² + 360 cm² = 460 cm²
I hope it's correct
Answer:
SA = 280 cm²
Step-by-step explanation:
SA = area of base + area of 4 congruent triangles
= 10² + (4 × [tex]\frac{1}{2}[/tex] × 10 × 9 )
= 100 + (2 × 10 × 9)
= 100 + 180
= 280 cm²
Two random samples were done to determine how often people in a community go to the dentist. the first sample surveyed 10 people as they entered their workplaces. the first sample found that the mean time between visits to the dentist was 7.5 months. the second sample surveyed 50 people as they entered the local grocery store. the second sample found that the mean time between visits to the dentist was 18.1 months. which statements are true? check all that apply. the first sample is likely to be more representative of the population. the second sample is likely to be more representative of the population. the second sample will give a better representation because it is larger. the first sample is not biased. community members probably visit the dentist about once every 18 months.
Answer:
B, C and E
Step-by-step explanation:
Help me with this question please
PLSSS THIS NEEDS TO BE DONE QUICKLY
Answer: 433.33 cm^3
Step-by-step explanation: Since the base is a square, volume = base area × height / 3
10*10 = 100, 100 * 13 = 1300, divided by 3 = 433.33 cm^3
Let tan(x)=2/5
What is the value of tan(2π−x)
please!
Answer:
-0.4 or [tex]\frac{-2}{ 5}[/tex]
Step-by-step explanation:
[tex]tan^-^{1} ({\frac{2}{5} })=21.80\\[/tex]
tan ( 2π-21.80)
but 2π = 360
Therefore our question becomes:
tan ( 360-21.80)=tan(338.2)= -0.4
The distribution of probabilities for each outcome of a random variable that sums to 1.00 is called a Group of answer choices random variable probability distribution conditional probability sample space
The distribution of probabilities for each outcome of a random variable that sums to 1.00 is called a Probability Distribution.
According to the statement
we have to find the under which probability type The distribution of probabilities for each outcome of a random variable that sums to 1.00.
So,
For this purpose, we know that the
A probability distribution is a statistical function that describes all the possible values and likelihoods that a random variable can take within a given range.
and the above written definition of probability is satisfied the condition that the The distribution of probabilities for each outcome of a random variable that sums to 1.00.
Due to this reason The Probability Distribution is a correct option.
So, The distribution of probabilities for each outcome of a random variable that sums to 1.00 is called a Probability Distribution.
Learn more about probability here https://brainly.com/question/25870256
#SPJ4
Kat plays a surfing video game with a friend. Each player earns 50 points for each trick he performs, but loses 40 points each time he falls off the surfboard. Last week, Kat had 6 stunts and 9 falls. Her score from her today was 3 times her score from last week. What was Kat's score today. What would be different about Kat's score today if it were –3 times her score from last week? What would be the same? Explain your reasoning.
Step-by-step explanation:
No. of points got from 1 stunt = 50.
No. of points deducted from 1 fail = 40.
6 stunts and 9 falls were gained last week.
So, A/C the number of points earned =
(6×50)-(9×40)
= 300 - 360
= -60
Her score today is 3 times her score from last week so multiply by 3
= (-60) × 3
= -180
If it were multiplied by -3 instead of 3 it would be...
(-60) × (-3)
= 180
The difference would be that on multiplying with positive 3 she would be 180 points in the whole but multiplying with negative three means she is 180 points in the league.
The similarity is that that whole number is same but the symbol adds a difference and the absolute value would be same too.
At a charity fundraiser, each female attendant donated $1,200 and each male attendant donated $800. If the average donation at the fundraiser was $900, what was the ratio of the number of female attendants to the number of male attendants.
The ratio of the number of female attendants to the number of male attendants is 21/17
RatioAmount donated by female attendant = $1200Amount donated by male attendant = $800Average donation = $900let
number of female attendant = xnumber of male attendant = y900 = 1200x + 800y / (x + y)
900x + 900y = 1200x + 800y
900x + 1200x = 800y + 900y
2100x = 1700y
x : y = 2100 / 1700
x : y = 21 ; 17
Learn more about ratio:
https://brainly.com/question/2784798
#SPJ1
There are 50 pennies in a roll. if you have 110 rolls of pennies, how many pennies do you have?
Answer:
The answer to your question is 5500
Step-by-step explanation:
[tex]50x 110 = 5500\\[/tex]
I hope this helps and have a good day!
NL and MK are diameters of circle J.
Circle J is shown. Line segments M K and N L are diameters. Line segment J P is a radius. Angle M J N is 62 degrees and angle N J P is 90 degrees.
Complete the statements about circle J.
Arc M P is a
and measures
degrees.
Arc M L N is a
and measures
degrees.
Arc M P is a minor arc and measures 152°
Arc M L N is a major arc and measures 298° .
Given that NL and MK are diameters of circle J.
Size of arc MP is 62+90=152°, since MP is smaller than MLN
then it is a minor arc. Hence the correct statement is:
M P is a minor arc and measures 152°.
Size of M L N is 360-62=298°, thus it is a major arc. Hence the
correct statement is:
MLN is major arc and measures 298°.
Arc M P is a minor arc and measures 152°
Arc M L N is a major arc and measures 298° .
learn more about arcs here:
https://brainly.com/question/228276
#SPJ1
Answer:
Complete the statements about circle J.
Arc M P is a
✔ minor arc
and measures
✔ 152
degrees.
Arc M L N is a
✔ major arc
and measures
✔ 298
degrees.
Step-by-step explanation:
edge 2022
Calculate the slope of a line that goes through (3,3) and (8,1).
Answer:
slope formula= y2-y1/x2-x1
=1-3/8-3
= -2/5
pls mark as brainliest thanks!
I need help anyone with graphs
The given function shows imply that the graph g(x) is shifted two units right and three units up.
Option B is correct.
What is the transformation of a function?The transformation of a function occurs in a fancy way such that a function maps itself. f: x → x.
From the given information:
Let's take a look at the function f(x) that goes through 0 just when x = 0. Now we want to move it to the right by 2. It implies that it has to go through 0 when x = +2.
Now, we have to add 2 to x, then the function becomes f'(x) = f(x-2) will be shifted by 2 units to the right.
Similarly, the same scenario occurs when shifting up. Again imagine your function passes 0 when x = 0. We have to add 3. Now, the function f’’(x) = f(x) + 3 will be shifted by 3 units up.
Combining the two transformations, we have:
g(x) = f(x-2) + 3Therefore, we can conclude that the function implies that the graph g(x) is shifted two units right and three units up.
Learn more about the transformation of functions here:
https://brainly.com/question/1548871
#SPJ1
The results of a poll show that the true proportion of students who prefer the new schedule is likely in the interval (0.195,0.245).
What is the point estimate of the proportion of students who prefer the new schedule
The point estimate of the proportion of students who prefer the new schedule is 0.22.
Definition of Point Estimate
Point estimation is a technique used in statistics to determine a single value that will serve as the "best guess" or "best estimate" of an unidentified population characteristic, known as the point estimate. More precisely, in order to produce a point estimate, we apply a point estimator to the data.
For the confidence interval (0.195, 0.245), point estimate is calculated as follows,
p = (0.195 + 0.245) / 2
p = 0.44 / 2
p = 0.22
Hence, the point estimate of the proportion of students who prefer the new schedule comes out to be 2.2.
Learn more about point estimate here:
https://brainly.com/question/17514579
#SPJ1
Ryan called each school in the district to determine wether or not they have a recycling program. What is true about Ryan’s data collection
Ryan's data collection is true that Ryan did a survey he asked about qualitative data.
Given that Ryan called every school in the district to find out if they had a recycling program.
We know that there are two types of data:
Quantitative data deals with numbers and things that we can count or measure such as dimensions such as height, width, and length.
Qualitative data relating to characteristics and descriptions cannot be counted or measured, but are observable by their qualities such as smell, taste, and color.
If we ask for quantitative data, the survey will be quantitative. Data recycling means the quality of the data available.
They can ask for a yes or no answer, as in the Ryan investigation.
Hence, the correct statement about Ryan's data collection is: Ryan conducted a survey in which he asked about qualitative data.
Learn more about qualitative data from here brainly.com/question/27076284
#SPJ1
Decide if the random variable x, is discrete or continious: x represents the temperature in degrees Fahrenheit on July 4th in Juneau, Alaska
Answer:
Continuous
Step-by-step explanation:
Degrees don't always have to be integers. It can be 32.3 degrees, 32.31 degrees, etc.
how many 2/7 are 150
Answer:
42.8571
Step-by-step explanation:
We would need to divide 150 by 7 and multiply it by 2 to get the answer.
150/7 = 21.42857
21.42857*2 = 42.8571
simplify 16-4(3x-2)²
16-4(3x-2)²
=16-4(3x-2)(3x-2)
=16+−36x²+48x+−16
=(−36x²)+(48x)+(16+−16)
=−36x²+48x
Answer:
[tex] \red{- 12x(3x - 4)}[/tex]
Step-by-step explanation:
We know that,
[tex](a - b)^{2} = {a}^{2} - 2ab + {b}^{2} \\ [/tex]
Accordingly, let us solve the sum now.
[tex]16 - 4(3x - 2)^{2} \\ 16 - 4(9 {x}^{2} - 12x + 4) \\ 16 - 36 {x}^{2} + 48x - 16 \\ - 36 {x}^{2} + 48x \\ - 12x(3x - 4)[/tex]