The following table shows Kamal’s bank account balance after 7 months.
*TABLE IN THE FILE ATACHED BELOW*
a) What is the rate of change? Show your work.
b) What does the rate of change mean in Kamal’s scenario?
c) What is the initial value?
d) What does the initial value represent in Kamal’s scenario?
e) Determine the equation of the linear relation which represents his bank account balance.
PLEASE HELP I DON'T HAVE ANY TIME
Answers
a. The rate of change = -25/month
b. Kamal's account balance reduces by 25$ per month.
c. To find the $725.
d. Kamal's opening balance or initial deposit.
e. The linear equation is: A = -25n + 725.
How to Find the Rate of Change and Initial Value of a Linear Relation?The rate of change (m) = change in y/change in x.
a. The rate of change (m) = change in A / change in n = (700 - 650)/(1 - 3) = -25/month.
b. -25 dollar per month means every month, Kamal's account balance reduces by 25$
c. To find the initial value (b), substitute m = -25 and (7, 550) = (n, A) into A = nm + b:
550 = 7(-25) + b
550 = -175 + b
550 + 175 = b
b = 725.
Initial value is: 725.
d. The initial value, $725, is Kamal's opening balance or initial deposit.
e. To write the linear equation, Substitute m = -25 and b = 725 into A = nm + b:
A = -25n + 725
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Related Questions
PLEASE ANSWER WILL GIVE YOU ALOT OF POINTS
Answers
The theorems that prove that lines are parallel includes:
Alternate interior angle theorem.Converse of corresponding angles postulate.How to prove lines are parallel?Parallel lines are the lines that do not intersect or meet each other at any point in a plane.
Theorems that prove that lines are parallel includes:
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When rolling a single number cube, what are the odds, in simplest form, in favor of rolling a 4 or a 5?
A. 1:1
B. 1:2
C. 1:3
D. 1:5
Answers
Answer:
C
Step-by-step explanation:
You have a total of 6 outcomes (1,2,3,4,5,6). That is your numerator. Out of those numbers, you only want 2 of them (4 or 5), so the fractions would be 2/6 or 1/3 which can also be written 1:3
Line segment Z E is the angle bisector of AngleYEX and the perpendicular bisector of Line segment G F. Line segment G X is the angle bisector of AngleYGZ and the perpendicular bisector of Line segment E F. Line segment F Y is the angle bisector of AngleZFX and the perpendicular bisector of Line segment E G. Point A is the intersection of Line segment E Z, Line segment G X, and Line segment F Y.
Triangle G E F has angles with different measures. Point A is at the center. Lines are drawn from the points of the triangle to point A. Lines are drawn from point A to the sides of the triangle to form right angles and line segments A X, A Z, and A Y.
Which must be true?
Point A is the center of the circle that passes through points E, F, and G but is not the center of the circle that passes through points X, Y, and Z.
Point A is the center of the circle that passes through points X, Y, and Z but is not the center of the circle that passes through points E, F, and G.
Point A is the center of the circle that passes through points E, F, and G and the center of the circle that passes through points X, Y, and Z.
Point A is not necessarily the center of the circle that passes through points E, F, and G or the center of the circle that passes through points X, Y, and Z
Answers
The correct option that depicts the centroid of the triangle is; C. Point A is the center of the circle that passes that passes through the points E, F and G and is the center of the circle that passes through the points X, Y and Z.
How to interpret the segments formed from Triangle Centroid?The center of inscribed circle into the triangle is the point where the angle bisectors of the triangle meet.
The center of the circumscribed circle over the triangle is the point where the perpendicular bisectors of the sides meet.
Line segments ZE, FY and GX are both angle bisectors and perpendicular bisectors of the sides. Thus, the point of intersection of line segments ZE, FY and GX is the center of inscribed circle into the triangle and the center of the circumscribed circle over the triangle.
Inscribed circle passes through the points X, Y and Z. Circumscribed circle passes through the points E, F and G. So, point A is the center of the circle that passes that passes through the points E, F and G and is the center of the circle that passes through the points X, Y and Z.
Thus, the correct option is option C. Point A is the center of the circle that passes that passes through the points E, F and G and is the center of the circle that passes through the points X, Y and Z.
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Solve the following for x, x∈W
a) 76 x 75 x 74 x ... x 6 = P(76, x)
Answers
The required value is 70. Using the permutations formula the required value is calculated. I.e., P(76, x) = P(76, 70).
How to calculate permutations?The formula for permutations is
nPr = P(n, r) = n!/(n - r)!
Where P -number of permutations,
n - number of objects in the given set
r - number of choosing objects
Calculation:The given series is
76 × 75 × 74 × ... × 6 = P(76, x)
We know that,
76! = 76 × 75 × 74 × ... × 1 ...(i)
But to get the required series,
Divide the equation (i) by 6! = (76 - 70)!
Then,
76!/(76 - 70)! = 76 × 75 × 74 × 73 ... × 6
So, x = 70.
That is,
n!/(n - r)! = P(n, r)
⇒ 76!/(76 - 70)! = P(76, 70) = 2.618743E+108
Hence the required x value is 70.
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Write the algebraic expression for the difference between the squares of two numbers.
Answers
The algebraic expression for the difference between the squares of the two numbers, supposing the two numbers to be a and b, is
a² - b² = (a + b)(a - b).
An algebraic expression is a combination of terms, where the terms are separated using mathematical operators like plus (+), minus (-), multiply (*), and divide (/).
The terms are combinations of numerals and variables.
Variables are represented alphanumerically, which can hold any value as per the expression they are used in.
In the question, we are asked to write the algebraic expression for the difference between the squares of two numbers.
We assume the two numbers to be a and b respectively.
Thus, we are asked to write an expression for the difference between the square of a and square of b, that is, we are asked to write an expression for a² - b².
We know that a² - b² is an identity, which can be shown as (a + b)(a - b).
Thus, the algebraic expression for the difference between the squares of the two numbers, supposing the two numbers to be a and b, is a² - b² = (a + b)(a - b).
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Vertical plane R intersects horizontal plane P. Points A, D, and B are on the line of the intersecting planes. Point F is on the top half of plane R. Point G is on the bottom half of plane G. Point C is on the left half of plane P. Point E is on the right half of plane P. Point H is above and to the right of the planes. Point J is below and to the left of the planes. Which statements are true based on the diagram? Check all that apply. Points A, B, and D are on both planes. Point H is not on plane R. Plane P contains point F. Points C, D, and A are noncollinear. The line containing points F and G is on plane R. The line containing points F and H is on plane R.
Answers
The true statement about the plane include:
Points A, B, and D are on both planes. Point H is not on plane R.The line containing points F and G is on plane R.The line containing points F and H is on plane R.What is a vertical plane?It should be noted that a vertical plane simply passes through a vertical line.
In this case, Point H is not on plane R and the e line containing points F and G is on plane R.
The correct options are 1,2,4, and 5.
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Answer:
a,b,d,e
Step-by-step explanation:
Use the graph to find the solution.
Given the graph of w(x), w(2) = ?
(the graph is below)
THE FIRST ANSWER WILL GET BRAINLIEST OR 5 STARS! PLEASE ANSWER QUICK :)
Answers
Answer:
W(2) = 5
Step-by-step explanation:
Because when you look at the graph, the y value is 5 when the x value is 2.
Answer:
w(2) = 5
Step-by-step explanation:
by using rise over run to find the slope easily, you get a slope of 4 and an equation of w(x) = 4x - 3, -3 being the y-intercept
to calculate w(2):
w(2) = 4(2) - 3
w(2) = 8 - 3
w(2) = 5
or you could just look at when y is 2 and see that the corresponding x value is 5 but i wanted to provide a longer explanation in case :)
A 4-column table with 3 rows. The first column has no label with entries students, teachers, total. The second column is labeled wear glasses with entries 32, 4, 36. The third column is labeled do not wear glasses with entries 97, 2, 99. The fourth column is labeled total with entries 129, 6, 135.
Which statements are correct about the two-way frequency table? Check all that apply.
Answers
The correct statements about the two-way frequency table are:
Option C, and Option E.
According to the statement
we have to check that the given statement is applicable or not on the given conditions.
So, For this purpose
The two-way frequency table is
In Mathematics and statistics, A two-way frequency table is a tabular method for displaying relative data for two categories of variables. (See the attached).
the given options are:
Option A the row categories are "wears glasses"
Option B and "do not wear glasses."
Option C two teachers do not wear glasses.
Option D thirty-six students wear glasses.
Option E a total of 6 teachers were polled.
So, The correct statements about the two-way frequency table are:
Option C, and Option E.
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Answer: the corret answer is A, C and E
A construction company buys a certain number of boxes of nails depending on how many houses they plan to build in a year. They have 5 boxes left over from the previous year and predict that this year they will need 3 boxes per house. Write an equation where y represents the number of boxes they need to purchase and x the number of houses they plan to build.
Answers
Answer:
Step-by-step explanation:
43
I dont exactly know if this is correct sorry if its wrong
In order for a gear to work in a piece of machinery, the radius of the gear, r, must be greater than 4 cm, but not exceed 4.1 cm. Which compound inequality represents the situation?
r > 4 and r ≤ 4.1
r > 4 or r ≤ 4.1
r < 4 and r ≥ 4.1
r < 4 or r ≥ 4.1
Answers
The compound inequality represents the situation is r > 4 and r ≤ 4.1
Compound inequalityRadius of the gear = rr must be greater than 4 cmr > 4
r must not exceed 4.1 cmr ≤ 4.1
Therefore, r > 4 and r ≤ 4.1 is the compound inequality which represent the situation.
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Its A: r > 4 and r ≤ 4.1
Make x the subject of the formula.
y = √x² +1
Answers
Answer: x = [tex]\sqrt{y^2 -1}[/tex]
Step-by-step explanation:
1. The length of a rectangle is four
times its width. If the area is 100m
what is the length of the rectangle
Answers
Answer:
20m
Step-by-step explanation:
write a equation duh
x * 4x = 100
u can split 100 into 5 x 20
x * 4x = 5 * 20
x = 5
and 4x = 20
which expression uses the associtive property to make it easier to evaluate 8 (1/4 x 3/5)
Answers
The value of the expression 8 (1/4 * 3/5) is 6/5
How to evaluate the expression?The expression is given as:
8 (1/4 * 3/5)
The associative property states that:
a * (b * c) = (a * b) * c
Using the above expression, we have:
8 (1/4 * 3/5) = 8 * 1/4 * 3/5
Evaluate the product
8 (1/4 * 3/5) = 2 * 3/5
This gives
8 (1/4 * 3/5) = 6/5
Hence, the value of the expression 8 (1/4 * 3/5) is 6/5
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Which expression is equivalent to 144 3/2
Answers
Answer:
144=12², so 144^3/2=(12²)^(3/2)=12³=1728.
this answer is not from the internet
go check yourselves
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The binomial x + 11 is a factor of x^2 – 121. What is the other factor?
Answers
Answer:
x - 11
Step-by-step explanation:
find the y intercept of the line on the graph
Answers
12.5% of a number is 25, find the number
Answers
Answer:
200
Step-by-step explanation:
Let's call the number x :
12.5% of x = 25
Changing 12.5% into decimal would be 0.125
Now we have the equation :
0.125x = 25
Divide both sides by 0.125 to make x the subject :
x = 25 ÷ 0.125
x = 200
To check we can substitute this value into the question :
12.5% of 200 = 25
Hope this helped and have a good day
It takes you two and a half hours to drive 175 miles. how fast were you driving? (mph)
Answers
If one travels 175 miles in 2hour 30 mins then his speed is 70 mph .
Calculation of the speedDistance travels= 175 miles
time is taken to cover 175 miles = 2.5 hours
We have to find out the speed in mph.
We know that,
Distance = speed x time
⇒speed = distance / time
Putting the value of distance and time, we get:
speed = 175 / 2.5 = 70 mph
Hence the final answer is 70 mph.
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What’s 98 divided by 82 + 283 multiplied by 69 - 29
Answers
The solution to the given expression [98/(82 + 283)] * (69 - 29) is; 784/73
How to solve simple arithmetic operations?
We want to solve the expression;
[98/(82 + 283)] * (69 - 29)
Let us first simplify the first part which is;
98/(82 + 283) = 98/365
Then let us simplify the second part which is;
69 - 29 = 40
Thus, we have the expression;
(98/365) * 40
This can be simplified further to get;
(98/73) * 8 = 784/73
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Pls help with b
The diameters of two circular pulleys are 6cm and 12 cm, and their centres
are 10cm apart.
a. Angle a = 72.54 degrees
b. Hence find, in centimetres correct to one decimal place, the length of a
taut belt around the two pulleys
Answers
The length of a taut belt around the two pulleys is 79.3 cm.
Length around the pulley
The length of a taut belt around the two pulleys is calculated as follows;
Shapes formed within the two circles of the pulley.
From top to bottom, a rectangle, a right triangle and a trapezium.
Length of the rectangleThe height of the right triangle is equal to length of the rectangle
base of the right triangle = radius of big circle - radius of small circle
base of the right triangle = (0.5 x 12 cm) - (0.5 x 6 cm) = 3 cm
tan α = height/base
tan (72.54) = h/3
h = 3 tan(72.54)
h = 9.54 cm
Length of trapezium at bottomThe length of the trapezium at bottom is equal to length of rectangle at top, L = h = 9.54 cm
Angles and length of belt in each circlePortion of belt in contact with circumference of small circle is subtended by an angle = 2 × 72.54 = 145.08°
Length of belt in contact with circumference of smaller circle
= 2πr (θ/360)
= (2 x 6 cm)π x (145.08/360)
= 15.19 cm
Portion of belt in contact with circumference of big circle is subtended by an angle = 360 - 145.08° = 214.92⁰
Length of belt in contact with circumference of smaller circle
= 2πr (θ/360)
= (2 x 12 cm)π x (214.92 / 360)
= 45.01 cm
Length of a taut belt around the two pulleys= 9.54 cm + 9.54 cm + 15.19 cm + 45.01 cm
= 79.28 cm
= 79.3 cm
Thus, the length of a taut belt around the two pulleys is 79.3 cm.
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335cm rounding off to the
nearest
Answers
Answer:
nearest what?
Step-by-step explanation:
nearest tens's=340
nearest hundred's=300
Salma invests the following sums of money in common stocks having expected returns as follows: a. what is the expected return (percentage) on her portfolio
Answers
Calculate the total amount invested by summing up all the values of the investment.
Total = 50,000
Calculate the weight of each investment. For WOOPS, weight = 5000 / 50000 = 10% and so on.
Now, Expected Return = sum of weight x Returns = 10% x 0.14 + 20% x 0.16 + ... + 18%x 0.18 = 16.01%
b) Similarly,
Beta of the portfolio = sum of weight x beta = 10% x 0.6 + 20% x 0.8 + ... + 18% x 0.18 = 0.7605
c) Portfolio has less systematic risk as the beta for the average market is 1, which is above the portfolio
d) Using CAPM, Return = Rf + beta x (Rm - Rf) = 4% + 0.7605 x (14% - 4%) = 11.605%
To calculate the expected return of a portfolio, the investor needs to know the expected return of each security in the portfolio and the total weight of each security in the portfolio. This means that investors need to sum the weighted averages of the expected returns (RoRs) of each security.
Investors are based on estimates of the expected rate of return on securities, assuming that what has proven to be true in the past will be true in the future. Investors do not use the structural view of the market to calculate the expected return. Instead, it determines the weight of each security in the portfolio by dividing the value of each security by the total value of the security.
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Jenna’s method: mia’s method: 5(30 4) 5(30 4) (5)(30) (5)(4) 5(34) = 170 150 20 = 170 explain why both jenna and mia arrived at the same answer and the advantage of one method over the other.
Answers
The steps in Mia's method were smaller than in Jenna's, which was an advantage.
What is distributive property and direct calculation?The same result will be obtained by adding the products of multiplying the sum of two or more addends by a number as opposed to multiplying each addend separately by the number.
The direct algorithm process suggested in this paper is known as the direct calculation method (DCM), and it can deal with using confinement loss as an incremental step to simulate the effect of moving tunnel face excavation, calculating the stresses and displacements in each step, and drawing the results.
Jenna's technique:
[tex]\begin{aligned}&5(30+4) \\&=(5)(30)+(5)(4) \\&=150+20 \\&=170\end{aligned}[/tex]
Mia's technique:
[tex]\begin{aligned}&5(30+4) \\&=(5)(34) \\&=170\end{aligned}[/tex]
Find: What was the benefit of using one method over the other and why did Jenna and Mia arrive at the same conclusion?Future:Both used the right approach, albeit in different ways.
One uses the distributive property, whereas the other uses direct calculation.
Consequently, Jenna and Mia came to the same conclusion.
However, Mia's approach has one advantage over Jenna's: it requires fewer steps.
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There were only 86 confirmed cases of Measles in the year 2000. In 2019, there was a reported 1,350 % increase in confirmed
cases of Measles. How many cases were there in 2019?
Answers
Answer:
1161 confirmed cases
Step-by-step explanation:
In 2000 the number of cases was 86
Percent means out of a hundred, so if we divide 1350 by 100 we get 13.5.
So, we must multiply 13.5 and 86 to get the amount of cases in 2019.
13.5*86 = 1161 confirmed cases in 2019
PLEASE HELP NOW
Which formula can be used to find the volume of the cylinder? Check all that apply. A = ( d )( h ) V = B( h ) V = ( l )( w )( h ) V = 2( r )( h ) V = (pi) (r squared) (h)
Answers
Answer:
V= (pi) (r squared) (h)
Step-by-step explanation:
The function f(x) = 0.11(3)x is reflected over the x-axis to produce function g(x). Function g(x) is then reflected over the y-axis to produce function h(x). Which function represents h(x)?
h(x) = –0.11(3)x
h(x) = 0.11(3)–x
h(x) = 0.11(3)x
h(x) = –0.11(3)–x
Answers
Answer:
[tex]h(x)=-0.11(3)^{-x}[/tex]
Step-by-step explanation:
Given function:
[tex]f(x)=0.11(3)^x[/tex]
Reflection in the x-axis:
When reflecting a function in the x-axis, make the whole function negative:
[tex]\implies g(x)=-f(x)[/tex]
[tex]\implies g(x)=-0.11(3)^x[/tex]
Reflection in the y-axis:
When reflecting a function in the y-axis, make the x variable negative:
[tex]\implies h(x)=g(-x)[/tex]
[tex]\implies h(x)=-0.11(3)^{-x}[/tex]
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Answer:
the answer to this question is d
Step-by-step explanation:
h(x)=-0.11(3)^-x
f(x) = x² + 5x-1 is shifted 3 units right. The result is g(x). What is g(x)?
O A. g(x) = (x+3)² + 5x-1
OB. g(x)=x2 + 5x+2
C. g(x) = (x+3)2 +5(x + 3) - 1
D. g(x) = (x-3)2 + 5(x-3) -1
Answers
Answer:
D
Step-by-step explanation:
When a function is being shifted to the left, all x values will be added by y units shifted. (The constant that comes with x is excluded, eg. 3x shifted by 2 units left, becomes 3(x+2) and not 3x+2.)
Likewise, when a function is being shifted to the right, all x values will be subtracted by y units shifted. (Constant rules applies as well.)
Given f(x) is shifted 3 units right,
the new function, g(x) becomes:
[tex] g(x) = {(x - 3)}^{2} + 5(x - 3) - 1[/tex]
Therefore the answer is D in this case.
The triangles are similar. Find the value of the variable.
Answers
First find the ratio of the similar sides
55/44 = 1.25 ratio
Divide 45 by the ratio to find z
45/1.25 = 36
Lena knows the following information about her box of 181818 candies:
10 candies contain both chocolate and caramel.3 candies contain neither chocolate nor caramel.12 candies in total contain chocolate. Can you help Lena organize the results into a two-way frequency table?
Answers
See below for the organized result in a two-way frequency table
How to organize the results?The given parameters are:
Candies = 18
Chocolate and Caramel = 10
None = 3
Chocolate = 12
Using the above parameters, we have the following rows and columns:
Chocolate
Present Absent Total
Caramel Present
Absent
Total
Next, we populate the table as follows:
Chocolate
Present Absent Total
Caramel Present 10 3
Absent
Total 12
The total number of candies is 18.
So, we have:
Chocolate
Present Absent Total
Caramel Present 10 3 13
Absent
Total 12 6 18
Subtract the cells from the column total
Chocolate
Present Absent Total
Caramel Present 10 3 13
Absent 2 3 5
Total 12 6 18
The above represents the organized result
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Find the equation of the line that passes through (-1,2) and is perpendicular to y =2x+1 . Leave your answer in the form y = m x + c