Answer:
Step-by-step explanation:
The Compositions of Reflections Over Intersecting Lines Theorem states that if we perform a composition of two reflections over two lines that intersect, the result is equivalent to a single rotation transformation of the original object.
hope it helps! (✿◠‿◠)
The result concluded is equivalent to a single rotation transformation of the original object.
Explanation of how reflection across axis works?When a graph is reflected along an axis, say x-axis, then that leads the graph to go just on the opposite side of the axis as if we're seeing it in a mirror.
The Compositions of Reflections Over Intersecting Lines states that if we perform a composition of two reflections over two lines that intersect.
The result concluded is equivalent to a single rotation transformation of the original object.
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What is the simplified form of this expression √-150
Answer: [tex]\boldsymbol{5i\sqrt{6}}[/tex]
where [tex]i = \sqrt{-1}[/tex]
=============================================
Work Shown:
[tex]\sqrt{-150}\\\\\sqrt{-1*25*6}\\\\\sqrt{-1}*\sqrt{25}*\sqrt{6}\\\\i*5*\sqrt{6}\\\\\boldsymbol{5i\sqrt{6}}\\\\[/tex]
The trick with these type of problems is to factor the number into pieces such that we pull out the largest perfect square factor. In this case, that factor is 25. We also pull out the -1.
The rule used is [tex]\sqrt{A*B} = \sqrt{A}*\sqrt{B}[/tex] that lets us break up the root.
You are a loan officer at the West Elm Savings and Loan. Mr. and Mrs. Brady are in your office to apply for a mortgage loan on a house they want to buy. The house has a market value of $160,000. Your bank requires 1/5 of the market value as a down payment.
(a)
What is the amount (in $) of the down payment? $
(b)
What is the amount (in $) of the mortgage for which the Bradys are applying? $
(c)
Your bank offers the Bradys a 30-year mortgage with a rate of 5%. At that rate, the monthly payments for principal and interest on the loan will be $5.37 for every $1,000 financed. What is the amount (in $) of the principal and interest portion of the Bradys' monthly payment? $
(d)
What is the total amount (in $) of interest that will be paid over the life of the loan? $
(e)
Your bank also requires that the monthly mortgage payments include property tax and homeowners insurance payments. If the property tax is $1,710 per year and the property insurance is $1,458 per year, what is the total monthly payment (in $) for PITI (principal, interest, taxes, and insurance)? $
(f)
To qualify for the loan, bank rules state that mortgage payments cannot exceed 14 of the combined monthly income of the family. If the Bradys earn $3,750 per month, will they qualify for this loan?
Yes, they will http://qualify.
No, they will not qualify.
(g)
What monthly income (in $) would be required to qualify for this size mortgage payment? $
a) The amount (in $) of the down payment is $32,000.
b) The amount (in $) of the mortgage for which the Bradys are applying is $128,000.
c) The amount (in $) of the principal and interest portion of the Bradys' monthly payment, at $5.37 for every $1,000 financed, is $687.36.
d) The total amount (in $) of interest that will be paid over the life of the loan is $$119,449.60.
e) The total monthly payment (in $) for PITI (principal, interest, taxes, and insurance) is $951.36.
f) Based on the bank rules that state that mortgage payments cannot exceed 14% of the combined monthly income of $3,750, B. No, they will not qualify.
(g) The monthly income (in $) that would be required to qualify for this size mortgage payment is $4,909.71 ($687.36/0.14).
Data and Calculations:Down payment = 1/5 or 20%
Home Price = $160,000
Down Payment = 20%
Loan Term = 30 years
Interest Rate = 5%
Annual property tax = $1,710 per year
Annual property insurance = $1,458 per year
Monthly taxes and insurance = $264 ($3,168/12)
Monthly PITI (principal, interest, taxes, and insurance) = $951.36 ($264 + $687.36)
14% of $3,750 = $525
Results:
Monthly Pay: $687.36 ($5.37 x $128,000/$1,000)
Loan Amount $128,000 ($160,000 - $32,000)
Down Payment = $32,000 ($160,000 x 20%)
Total of 360 Mortgage Payments = $247,449.60 ($687.36 x 360)
Total Interest = $119,449.60 ($247,449.60 - $128,000)
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write an equation of a line in standard form
passes through (35,42) and (15,-2)
Answer:
[tex]y=\frac{11}{5}x-35[/tex]
Step-by-step explanation:
The equation of a line is y=mx+b
Plug in the points
35m+b=42 (1)
15m+b=-2 (2)
(1)-(2)
20m = 44
m = 11/5
33+b=-2
b=-35
[tex]y=\frac{11}{5}x-35[/tex]
Find K such that the number 23K10 is
divisible by 2, 3, and 5
2021
The values of K that will make 23K10 to be divisible by 2, 3 and 5 are; 0, 3, 6 and 9
How to use divisibility rules?We want to find the number K in 23K10 that will make it divisible by 2, 3 and 5.
Now, for the number to be divisible by 2, 3 and 5, then it means it must be divisible by the LCM which is; 2 * 3 * 5 = 30
Now, the divisibility rule for 30 is that it must be divisible by 3 and 10.
If 23K10 is divisible by 3, sum of digits will be multiple of 3.
Thus;
2 + 3 + K + 1 + 0 = K + 6 must be equal to 0, 3, 6, 9, 12, 15, 18....
Thus, K could either be 0, 3, 6 or 9
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Help I'm confused with this question
Which equation could be used to find the length of the hypotenuse
Answer:
first equation
Step-by-step explanation:
Need the answer please anyone!!!
The correct expression is the one in option B.
[tex]P(x) = (x - \sqrt{4} )*(x - 2)*(x + 2)[/tex]
Which is the correct expression?If we know that a polynomial has the known zeros:
{x₁, x₂, ..., xₙ}
Then the factored form is:
[tex]p(x) = a*(x - x_1)*...*(x - x_n)[/tex]
Where a is the leading coefficient, in this case we take a = 1.
Here we also know that the zeros are:
√4, 2, -2.
Then the factored form is just:
[tex]P(x) = (x - \sqrt{4} )*(x - 2)*(x - (-2))\\\\P(x) = (x - \sqrt{4} )*(x - 2)*(x + 2)[/tex]
Then we conclude that the correct option is B.
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What is the solution to the equation
1/4x-1/8=7/8+1/2x?
Answer:
x=-1/4
Step-by-step explanation:
1 / 4x-1/8 = 7/8 + 1 / 2x <=> 1/4x - 1/2x = 7/8+1/8 <=> 1/4x-2/4x = 1 <=> -1/4x = 1
<=> x= -1/4
Answer:
2.7 + 8x/8.2
Step-by-step explanation:
1/4x - 1/8 = 7/8 + 1/2x x/4 - 1/8 = 7/8 + x/2
8x + 4 (-1)/4.8 = 2.7 + 8x/8.2
Circle properties can be used to prove that various shapes are polygons.
The question is incomplete. Below you will get the missing part of the question.
Find whether the given statement is true or false ?
True. Circle properties can be used to prove that various shapes are polygons.
With a centre of the circles, sides of an angle with vertex outside the circle, and arcs inside the circle, various shapes can be polygon.
So, from this description, we can say that, circle properties can be used to prove that various shapes are polygons.
Hence, the given statement is true.
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Find the solution, if possible, to the following system of equations using any method.
Give your answer in fraction form if necessary. Show all work. If you use matrices, you MUST write out the augmented matrix you inputted into the calculator.
3 − 4 + = −4
4 − 8 + 7 = 2
−2 + 4 − 3 = 5
A bus covers a certain distanc in 45 minutes if it runs at a Speed of 60km/hr. What must be the speed of the bus in order to reduce the time by 20 minutes .
2.66 is the speed
..................................................................................................................................................................................................................................................................................................................................................................................................................................
Please help with this question if you can
Line AE is NOT parallel to line BD. This is because the intercepts made by the lines and the transversals are not proportional
Parallel lines theoremIn the given diagram,
If
[tex]\frac{|AB|}{|ED|} =\frac{|AC|}{|EC|}[/tex]
Then,
Line AE is parallel to line BD
From the given information,
|AB| = x = 9
|ED| = 5
|AC| = 9 + 11 = 20
|EC| =5 + 7 = 12
Thus,
[tex]\frac{9}{20}=\frac{5}{12}[/tex]
20 × 5 = 9 × 12
100 ≠ 108
∴ The lines are not parallel
Hence, line AE is NOT parallel to line BD. This is because the intercepts made by the lines and the transversals are not proportional
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Calculate the unit cost per Kg if it costs $16.99 for 454 g package of cooked shrimp.
Answer:
$37.42 / kg
Step-by-step explanation:
Divide 16.99 by 454 to get the unit cost per gram. This equals 0.037422907…
Take this number and multiply it by 1000, while rounding it to the nearest hundredth after.
This equals about $37.42 / kg.
Sheila and Carla enter into Dillards with $25.00 between them they want to purchase a few items together. Sheila has $10.00 dollars, and Carla has $15.00 dollars. Sheila's purchases come to $12.21. Carla's purchases come to $12.79. How much change does Dillards owe them? What does Sheila owe Carla?
The amount of money Dillards owe Sheila and Carla is $0, while Sheila owe Carla $2.21
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Sheila has $10.00 dollars, and Carla has $15.00 dollars. Sheila's purchases come to $12.21. Carla's purchases come to $12.79. Hence:
Amount of money Dillards owe them = 25 - (12.21 + 12.79) = $0
Amount of money Sheila owe Carla = 12.21 - 10 = $2.21
The amount of money Dillards owe Sheila and Carla is $0, while Sheila owe Carla $2.21
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[tex](4 * 3^x)'[/tex]
Evaluate
Answer:
[tex]\approx 4.39 \cdot 3^x[/tex]
Step-by-step explanation:
Recall a property:
[tex](c\cdot f(x))'=c\cdot f(x)'[/tex], where [tex]c[/tex] is a constant.
Apply the property to the task:
[tex](4\cdot 3^{x})'=4\cdot (3^x)'[/tex]
Recall a property of the derivative of an exponential function:
[tex](a^x)'=a^x \cdot \ln{a}[/tex]
Apply the property to the task:
[tex]4\cdot 3^x \cdot \ln 3[/tex]
Since [tex]\ln 3\approx 1.0986[/tex], it follows:
[tex]4\cdot 3^x \cdot \ln 3 \approx 4\cdot 1.0986 \cdot \ln3[/tex]
Multiply the numbers.
The answer is about [tex]4.39\cdot 3^x[/tex].
A standardized test is designed so that scores have a mean of 50 and a standard deviation of 4. What
percent of scores are between 42 and 58?
42
O 100%
46
about 95.4%
about 23.85%
about 47.7%
50
54
47.7%
58
Answer: about 95.4%
Step-by-step explanation: 47.7% of scores are within two standard deviations to the right of the mean. Use that percent and the fact that the graph is symmetric to find the percentage of scores within two standard deviations to the right and left of the mean.
47.7% + 47.7% = 95.4%
PLEASE HELP!!!!!
Below, the two-way table is given for a class of
students.
Freshmen Sophomore Juniors Seniors Total
2
2
6
3
Male
4
Female 3
Total
6
4
If a student is selected at random, find the
probability the student is a male given that it's a
senior.
P (Male | Senior) = [?]
Round to the nearest whole percent.
Enter
Answer:
7%
Step-by-step explanation:
The two dot plots represent a sample of the number of people in households in two towns. Which statements are true about the data sets?
The true statement ae:
Both have the same number of data points.
Both means are between 3 and 4.
Westwood has less variability than Middleton.
What are the true statements?A dot plot is made up of dots which represents the frequency of the values in the data set and a numberline.
The total number of data points for both dot plots is 20.
The range of Middleton is : 9 -1 = 8
The range of Westwood is: 6 - 2 = 4
Middleton has more variability than Westwood.
Mean sum of numbers / total numbers
Middleton = (1+ 2+ 2 + 2 + 2 + 3 + 3 + 3 + 3 + 3 + 4 + 4 + 4 + 4 + 5 + 5 + 5, 5 + 6 + 9) / 20 = 3.75
Westwood = ( 2 + 2 + 2 + 2 + 3 + 3 + 3 + 3 + 3 + 4 + 4 + 4 + 4 + 5 + 5 + 5 + 5 + 6 + 6 + 6) / 20 = 3.85
Here is the complete question:
The two dot plots represent a sample of the number of people in households in two towns. Which statements are true about the data sets?
Check all that apply.
Both have the same number of data points.
Both means are between 3 and 4.
Both have the same median.
Both have the same range.
Westwood has less variability than Middleton.
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homework! This is a stats problem I’ve been struggling with and need help thanks!!!
The number of calls received by an office on Monday morning between 8:00 AM and 9:00 AM has a mean of 6. Calculate the probability of getting at least 5 calls between eight and nine in the morning. Round your answer to four decimal places.
The probability of getting at least 5 calls between eight and nine in the morning is 0.8009.
How to calculate the probability?The probability of getting at least 5 calls between eight and nine in the morning will be:
= 1 - [P(x = 0) + P(x = 1)]
= 1 - (e^-3(1 + 3]
= 1 - 0.19915
= 0.8009
Therefore, the probability of getting at least 5 calls between eight and nine in the morning is 0.8009.
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PLEASE HELP LOOK AT IMAGE FOR ANSWER I WILL MAKE YOU BRAINLISET PLEASE HELP
Answer:
c
Step-by-step explanation:
Help me with this please!!
The cost that will be charged based on the information is $10.00.
How to calculate the amount?From the information given, the estimate is 4% and the replacement cost is given as $250.
The amount that will be charged will be:
= 4% × $250
= 0.04 × $250
= 10.00
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Using a crankshaft, a carpenter drills a 1 cm radius hole through a ball of wood along a diameter. If the radius of the ball is 4 cm, determine the volume of wood remaining.
Answer:263.89cm cubed
Step-by-step explanation:
Volume of A Sphere: 4/3 pi radius cubed
4cubed= 64
64 times pi=201.061
201.061 multiply 4/3= 268.08
1cubed= 1
1 times pi=3.14
3.14 times 4/3= 4.19
268.08-4.19= 263.89cm cubed
Price of article = $315.50
Down payment = $31.55
Monthly payment amount = $16.50
Duration of payments = 20 months
Interest
(
I
)
=
2
y
c
m
(
n
+
1
)
True annual interest rate to the nearest tenth=
The true annual interest rate to the nearest tenth is 16.7%.
How is interest determined?The interest amount for this scenario can be determined by computing the total mortgage payment and subtracting the mortgage amount from the earlier figure.
Since payment was made for 20 months, the interest rate can be annualized using 24 months as below.
Data and Calculations:Price of article = $315.50
Down payment = $31.55
Mortgage amount = $283.95
Monthly payment amount = $16.50
Duration of payments = 20 months
Total payment (mortgage and interest) = $330 (20 x $16.50)
Interest = $46.05 ($330 - $283.95)
Annualized interest rate = 16.7% ($46.05/$330 x 24/20)
Thus, the true annual interest rate to the nearest tenth is 16.7%.
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britt estimated 8.8-6.2 by subtractions 9-6=3.it is overestimate or underestimate?
A survey found that women's heights are normally distributed with mean 62.7 in, and standard deviation 2.8 in. The survey also found that men's heights are normally distributed with mean
69.3 in. and standard deviation 3.9 in. Most of the live characters employed at an amusement park have height requirements of a minimum of 55 in, and a maximum of 62 in. Complete
parts (a) and (b) below.
a. Find the percentage of men meeting the height requirement. What does the result suggest about the genders of the people who are employed as characters at the amusement park?
The percentage of men who meet the height requirement is %.
(Round to two decimal places as needed)
Using the normal distribution, we have that:
The percentage of men who meet the height requirement is 3.06%. This suggests that the majority of employees at the park are females.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.The mean and the standard deviation of men's heights are given as follows:
[tex]\mu = 69.3, \sigma = 3.9[/tex].
The proportion of men who meet the height requirement is is the p-value of Z when X = 62 subtracted by the p-value of Z when X = 55, hence:
X = 62:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{62 - 69.3}{3.9}[/tex]
Z = -1.87
Z = -1.87 has a p-value of 0.0307.
X = 55:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{55 - 69.3}{3.9}[/tex]
Z = -3.67
Z = -3.67 has a p-value of 0.0001.
0.0307 - 0.0001 = 0.0306 = 3.06%.
The percentage of men who meet the height requirement is 3.06%. This suggests that the majority of employees at the park are females.
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Mary borrows $1250 from the bank. The loan terms is 18 months with 5% annual interest. How much interest will she pay? How much will she pay back in all?
Answer: 3375
Step-by-step explanation: The formula for simple interest is P( Principal, or initial amount) x R ( Rate or the percentage) x T ( Time) all out of 100( because of the percentage)
P x R x T/100
1. 1250 x 18 x 15/ 100
If you can simplify, or divide or cancel out, please do, it’ll make it easier; the 0 at the end of 1250, takes out one 0 from 100. 5 could cancel out 15 and 10, leaving them at 3 and 5 respectively, and lastly the two ( the hundred broken down) dividing 18, leaving us with 9.
2. 125 x 27
With all the breaking down we just did, we just have to multiply the two, leaving us with your answer: 3375.
Hope this was helpful
graph absolute value of x-1
It gives magnitude of the number or variables.
It is also known as an absolute value the function.
The result of this modulus function is always positive.
Draw the graph:
f(x) = |x-1|
f(x) = -(x-1) when x-1 is negative
f(x) = (x-1) when x-1 is positive
when x = -2, f(x) = 3
when x = -1, f(x) = 2
when x = 0, f(x) = 1
when x = 1, f(x) = 0
when x = 2, f(x) = 1
Using this values, draw the graph of f(x) = |x-1|
Hence, the required modulus of x-1 graph.
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The length, l call my a rectangular room is four less than the width, W, of the room. Which expression represents the area of the room.
(I have no options)
Answer: Either [tex]w(w-4)[/tex] or [tex]w^2 - 4w[/tex]
==================================================
Explanation:
w = width
w-4 = length since it is 4 less than the width
Multiply the length and width to get the area of the rectangle.
area = length*width
area = [tex](w-4)w[/tex]
area = [tex]w(w-4)[/tex]
area = [tex]w^2-4w[/tex]
In the last step, I used the distributive property.
Either expression mentioned above is valid for the area. If you had to pick only one, I'd go for [tex]w^2-4w[/tex]
A cone of height 9cm has a volume of ncm³ curved surface area of ncm². Find the vertical angle of the cone
Answer:
Step-by-step explanation:
let the radius be r and the slant height be L
then first of all: L^2 = r^2 + 9^2
= r^2 + 81
Surface area = πrL = n
volume = (1/3)πr^2 (9) = 3πr^2 = n
then 3πr^2 = πrL
3r = L , then in L^2 = r^2 + 81
9r^2 = r^2 + 81
8r^2 = 81
r = 9/√8
L^2 = 81/8 + 81 = 729/8
L = √1458/4
cos(baseangle) = (9/√8) / (√1458/4)
= 1/3
angle of base = appr 70.5°
check my arithmetic