Natalie will pay her parents $9 each week, and the initial amount she still owed was $180.
We can see that Natalie is reducing the amount she owes by $18 every two weeks.
Therefore, the amount she owes after 2 weeks is $180 - $18 = $162, after 4 weeks is $144, after 6 weeks is $126, and after 8 weeks is $108.
This means that after n weeks, the amount she still owes is:
$180 - $18n
Since she will pay the same amount each week, let's call the weekly payment P. After one week, she will owe:
$180 - P
After two weeks, she will owe:
($180 - P) - P = $180 - 2P
After four weeks, she will owe:
($180 - 2P) - P - P = $180 - 4P
After six weeks, she will owe:
($180 - 4P) - P - P = $180 - 6P
And after eight weeks, she will owe:
($180 - 6P) - P - P = $180 - 8P
We can set up an equation using the information we have:
$180 - 8P = $108
Solving for P, we get:
P = $9
Therefore, Natalie will pay her parents $9 each week, and the initial amount she still owed was $180.
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The complete question:
Natalie borrowed money from her parents to pay for a trip. Natalie will pay her parents in equal amounts every week until she pays back the entire amount she borrowed. The table below shows the amount of money Natalie still owes her parents at the end of every two weeks for the first eight weeks. How much does Natalie pay her parents each week? What is the initial amount Natalie still owes?
Week 0 = $180
Week 2 = $162
Weeks 4 = $144
Week 6 = $126
Week 8 = $108
I will give the BRAINIEST!
function, g(x), can be represented with the following set of ordered pairs:
{(-9, -14), (18, 40), (3, 10), (-15, -26)}
Which set of ordered pairs represents g¹ (x)?
A
B
C
D
{(2, 3), (4,4), (-2, 1), (−12, −4)}
{(2, -1), (14, 5), (18, 7), (25,5)}
{(12, 18), (2, 8), (16, 22), (6, 12)}
{(-2, 2), (6,2), (4,2), (-8, 2)}
Answer:
The set of ordered pairs that represents g¹(x) can be found by reversing the order of each pair in the original function g(x) and then solving for x. Therefore, g¹(x) would be:
{(-14, -9), (40, 18), (10, 3), (-26, -15)} with the x-coordinates being -9, 18, 3, and -15 respectively.
Step-by-step explanation:
c3m9 divided by cm2?
Answer:
c^2 m^7
Step-by-step explanation:
c^3 m^9 = cm^2 x c^2 m^7
c^m m^9 / cm^2
= (cm^2 x c^2 m^7)/cm^2
= c^2 m^7
The vertices of a rectangle are given in the column’s of the matrix R= [0,0,6,6,0,6,6,0] if 3X [0,1,-1,0] is found to perform a transformation what are the coordinates of the transformed rectangle
The coordinates of the forth corner point of the rectangle will be (-1, 3)
The point will be at (-1, 3).
Use the x value that has only been used once, -1, and the y value that has only been used once. (6,0) and (6, 3) are on the same side vertically of the rectangle because their x values are the same.
Because 6 > -1, you know that they make up the right side of the rectangle.
(-1,0) and (6, 0) both have the same y values, so they are on the same side horizontally, and are the bottom of the rectangle because 0<3.
This all means the fourth point is the rectangles top left corner.
Because it is a rectangle, its sides are parallel, so you know that it will have the same x value as the left bottom point (-1,0) and the same y value as the right top point, (6, 3).
Hence, the coordinates of the forth corner point of the rectangle will be (-1, 3)
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there vertices of a rectangle are (-1,0) (6,0), and (6,3) . What are the coordinates of the forth corner point of the rectangle?
Inequalities - Introduction
Answer:
The possible values of x:
-5, -4, -3, -2, -1, 0, 1
Based on the values in the table below, find the slope and y-intercept to write the equation of the line in the form y=mx+b.
x= 1, 2, 3
y= 11, 22, 33
Answer:
y= 11x
Step-by-step explanation:
find the slope: 22-11/2-1= 11/1 or 11
To find the y-intercept you can use the slope by subtracting 11 (inverse operation) from the y value of (1,11). So the y- intercept is (0,0). To write the equation plug in 11 for m and 0 for b. Since 0 has no value the equation would be y= 11x
Enter the mean absolute deviation of the data.
45, 48, 50, 42, 40
The mean absolute deviation of the data is
The mean absolute deviation of the data: 45, 48, 50, 42, and 40 comes out to be 3.2
The mean of the number is defined as the average of the numbers that is the sum of the number to the total number of numbers
= 45 + 48 + 50 + 42 + 40 / 5
= 225 / 5
= 45
The mean absolute deviation is defined as the measure of how much the values in the data set are different from the mean of the data.
MAD = [tex]\frac{1}{n}[/tex] * ∑ | x - mean |
where n is the number of data
x is the individual data
MAD = 1/5 * (|45-45| + |48-45| + |50-45| + |42-45| + |40-45|)
= 0.2 * (0 + 3 + 5 + 3 + 5)
= 0.2 * 16
= 3.2
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|||
=
- 7)?
What is an equation of the line that is perpendicular to 3x+y=-5 and passes through the point (3,
Enter your equation in the box.
URGENT PLEASE
Answer:
[tex]y=\frac{1}{3}x-8[/tex]
Step-by-step explanation:
We know that when two lines are perpendicular, their slopes are negative reciprocals. The following formula shows this fact:[tex]m_{2}=-\frac{1}{m_{1} }[/tex], where
m2 is the slope of the line we're trying to findm1 is the slope of the line we're givenStep 1: Currently 3x + y = -5 is in standard form, but we can isolate y to convert the line to slope-intercept form (y = mx + b) to find the slope, m:
3x + y = -5
y = -3x + 5
Thus, the slope of the first line is -3. We plug in -3 for m1 in the perpendicular slope formula to find m2 or the slope of the line we're still trying to find:
m2 = -1 / -3
m2 = 1/3
Step 2: Now that we know the slope of the other line, we plug in the point (3, -7) for x and y and 1/3 for m in the slope-intercept form. Then, we must solve for b to find the y-intercept of the other line:
-7 = 1/3(3) + b
-7 = 1 + b
-8 = b
Thus, the equation of the line that is perpendicular to 3x + y = -5 and passes through (3, -7) = y = 1/3x - 8
If 7 model solar systems cost $347.20 and the price of each model is the same, how much does each model cost?
Answer:
$49.60
Step-by-step explanation:
If the 7 model solar systems cost $347.20 altogether, then to find how much each one costs (and they are all the same price) you must divide 347.20 / 7 = 49.6.
asap i need help with my missing homework
The high school students who attend Springfield Women's Academy are eligible to tryout for various teams within the athletic department. Students are 74% likely to tryout for softball; 27% likely to tryout for volleyball; 42% likely to tryout for tennis; and 88% likely to tryout for swimming. Many students choose to tryout for multiple teams. Students have equal probabilities of being freshmen, sophomores, juniors, or seniors.If Event A = freshman or sophomore, what is Event A'?
Event A' = freshman or junior
Event A' = sophomore or senior
Event A' = junior or senior
Event A' = freshman or senior
The probability of the union of high school students of trying out for either volleyball or swimming is 0.9. Option C is correct.
We have,
Probability of an event is the ratio of number of favorable outcome to the total number of outcome of that event.
The conditional probability is the happening of an event, when the probability of occurring of other event is given. The probability of event A, given that the event B is occurred.
Students of high school who attend Springfield Women's Academy are eligible to tryout for various teams within the athletic department. In this,
74% likely to tryout for softball;
27% likely to tryout for volleyball;
42% likely to tryout for tennis;
88% likely to tryout for swimming.
Let the tryout for volleyball is event A and tryout for swimming is event B. Thus,
P(A)=0.27
P(B)=0.88
Many students choose to tryout for multiple teams. Students have equal probabilities of being freshmen, sophomores, juniors, or seniors.
Thus, probability of the union of trying out for either volleyball or swimming
P(A or B)=P(A)+P(B)-P(A and B)
P(A or B)=0.27+0.88-P(A)*P(B)
P(A or B)=0.27+0.88-0.27×0.88
P(A or B)=0.9
Hence, the probability of the union of high school students of trying out for either volleyball or swimming is 0.9. Option C is correct.
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complete question:
The high school students who attend Springfield Women's Academy are eligible to tryout for various teams within the athletic department. Students are 74% likely to tryout for softball; 27% likely to tryout for volleyball; 42% likely to tryout for tennis; and 88% likely to tryout for swimming. Many students choose to tryout for multiple teams. Students have equal probabilities of being freshmen, sophomores, juniors, or seniors. What is the probability of the union of trying out for either volleyball or swimming?
a. 1. 15
b. 0. 61
c. 0. 91
d. 0. 24
use this equation
y=-16(t-2)^2+64
when is the football 40ft high
There are 2 answers.
One if them is between
.5 to 1 and the other is 3 to 3.5
show work!!
Answer:
Step-by-step explanation:
40=-16(t-2)²+64
-16(t-2)²=40-64
-16(t-2)²=-24
(t-2)²=24/16=3/2=1.5
t-2=±√1.5
t=2±√1.5
either t=2+√1.5≈3.22
or
t=2-√1.5≈0.78
2 of 8
Here is a list of numbers:
14, 3, 2, 9, 1, 17, 2, 8, 17
State the median.
Answer:
Explanation:
To find the median of a set of numbers, we need to arrange them in numerical order from smallest to largest, and then find the middle number. If there is an odd number of values, the median is the middle number. If there is an even number of values, the median is the average of the two middle numbers.
Here is the given list of numbers in numerical order:
1, 2, 2, 3, 8, 9, 14, 17, 17
There are nine numbers in the list, which is an odd number. Therefore, the median is the middle number, which is 8.
So, the median of the given list of numbers is 8.
The median is a useful measure of central tendency because it is not affected by extreme values, unlike the mean. It represents the middle value of the distribution and can give us a good idea of what a typical value is like. In this case, the median value of 8 tells us that roughly half the numbers in the list are less than 8 and half are greater than 8.
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y=-75x+5,000The equation above models the amount of money y, in dollars, remaining in Bo’s bank account x days after the start of the fall semester. The amount of money in Bo’s bank account is based on the money he earned over the summer and how much he spends per day during the fall semester. When the equation is graphed in the xy-plane, what does the slope of the graph represent in terms of the model?
When the equation is graphed in the xy-plane, the slope of the graph is -75 and it represent the rate of decrease of the amount of money in Bo’s bank account.
What is the slope-intercept form?In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical equation;
y = mx + c
Where:
m represent the slope or rate of change.x and y are the points.c represent the y-intercept or initial value.Based on the information provided above, a linear equation that models the amount of money in Bo’s bank account with respect to its rate of decrease is given by;
y = mx + c
y = -75x + 5,000
In conclusion, the amount of money in Bo’s bank account decreases by $75.
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PLEASE HELP
In preparation for a local infrastructure initiative, the city government sent out a survey asking registered voters whether they would support the initiative on the next ballot. The results indicated that 46% of voters would support the initiative. The survey had a margin of error of 1.9%. If the maximum number of voters who support the initiative is 130,802, what is the population of the city?
The population of the city is given as follows:
273,073.
How to obtain the maximum population?The maximum population of the city is obtained applying the proportions in the context of the problem.
The results indicated that 46% of voters would support the initiative. The survey had a margin of error of 1.9%, hence the maximum proportion is given as follows:
0.46 + 0.019 = 0.479.
The maximum number of voters who support the initiative is 130,802, hence the population is obtained as follows:
0.479p = 130802
p = 130802/0.479
p = 273,073.
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This prism is made of cubic centimeters. Find the volume of the prism What is the volume of this prism?
Answer:
V = 20 cm³
Step-by-step explanation:
the volume (V) of the prism is calculated as
V = lbh ( l is the length , b the breadth and h the height )
here l = 5 , b = 2 , h = 2 , then
V = 5 × 2 × 2 = 20 cm³
Select the correct answer. A circle is described by the equation x2 + y2 + 14x + 2y + 14 = 0. What are the coordinates for the center of the circle and the length of the radius?
A. (-7, -1), 36 units
B. (7, 1), 36 units
C. (7, 1), 6 units
D. (-7, -1), 6 units
Answer:
D
Step-by-step explanation:
To find the center and radius of a circle given its equation, we need to rewrite the equation in the standard form (x - a)^2 + (y - b)^2 = r^2, where (a,b) are the coordinates of the center and r is the radius.
So, let's complete square for x and y terms:
x^2 + 14x + y^2 + 2y + 14 = 0
x^2 + 14x + 49 - 49 + y^2 + 2y + 1 - 1 + 14 = 0
(x + 7)^2 + (y + 1)^2 = 36
Comparing this equation with the standard equation, we get the center at (-7, -1) and radius as sqrt(36) = 6 units.
So, the correct answer is option D: (-7, -1), 6 units.
Can someone help me with 6-10. Directions: Find the volume of each figure. Round to the nearest hundredth when necessary.
The volume of each figure would be given below as follows:
6.) = 11,253.76in³
7.) = 57,876.48 mm³
8.) = 3,744ft³
9.) = 297mm³
10.) = 34.54cm³
How to calculate the volume of the given shapes above?For question 6.)
The formula for the volume of the cylinder = πr²h
radius = diameter/2 = 32/2 = 16in
height = 14 in
volume = 3.14×16×16×14
= 11,253.76in³
For question 7.)
The formula for the volume of cylinder = πr²h
height = 32mm
radius = X² = 40²-32²
= 1600-1024
= 576
X = √576
= 24
Volume = 3.14×24×24×32
= 57,876.48mm³
For question 8.)
The volume of rectangular prism;
= length×width×height
= 12×8×39
= 3,744ft³
For question 9.)
The volume for triangular prism:
= 1/2×b×h×l
= 1/2 × 11×5.4×10
= 297mm³
For question 10.)
The volume of hemisphere ;= 2/3πr³
= 2/3× 3.14× 33/2
= 34.54cm³
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-47÷(-8)=?What is the answer
Answer:
The answer is 5.875
Step-by-step explanation:
Negatives cancel out, so you're essentially just dividing 47 into 8 parts, which equals 5.875. Hope it helps :)
Answer:
5.875
Step-by-step explanation:
[tex]\frac{-47}{-8}[/tex]
Remember, two negatives equal a positive.
[tex]\frac{47}{8}[/tex]
47/8=5.875
LCM of 4x³-16x2 + 20x - 8 and 8x³-48x² + 72x-32
In a recent year, 27.7% of all registered doctors were female. If there were 44,900 female registered doctors that year, what was the total number of registered doctors? Round your answer to the nearest whole number
We can use proportions to solve this problem.
Let's start by setting up a proportion:
female doctors/total doctors = 27.7%/100%
We can then substitute the values we know and solve for the total number of doctors:
44,900/x = 27.7%/100%
To solve for x, we can cross-multiply and simplify:
44,900 * 100% = x * 27.7%
449,000 = 0.277x
x = 449,000/0.277
x ≈ 1,621,464.33
Rounding this to the nearest whole number, we get:
The total number of registered doctors is about 1,621,464.
20 x 20 x 20 x 20 × 15 × 15 ×15
Answer:
20 x 20 x 20 x 20 × 15 × 15 ×15 = 540000000
Answer: 540000000
Step-by-step explanation: Please mark
Can u pleaseee answer all parts pleaseeeee <3333
please help meee
a. In interval notation, Increasing intervals: (12pm, 1pm) U (1pm, 2pm) U (2pm, 3pm). Decreasing intervals: (8am, 9am) U (11am, 12pm). Constant intervals: (9am, 10am) U (10am, 11am)
b. The increase in cost between 12 noon and 3 pm is $2.
c. Yellow Cab has a lower price per 1km than Swift ride at (8am, 9am) (9am, 10am) (2pm 3pm)
How do you express a data set in interval notations?Interval notation is used to represent continuous intervals of numbers or values, like ranges on a number line.
The graph shows that from 8-9am, and 11-12pm, the cost from Swift Ride decreases.
We can represent it as (8am, 9am) U (11am, 12pm).
It increases at these times (12pm, 1pm) U (1pm, 2pm) U (2pm, 3pm).
And stays constant at : (9am, 10am) U (10am, 11am)
Cost increase from 12 to 3pm,We simply deduct the 12pm's cost from 3pm's cost.
So, we have
Cost increase = $3.5 - $1.5
Evaluate the difference
Cost increase = $2
Hence, the cost increase is $2
The time interval where the cost is lowerWhen you plot the points provided for Yellow cab, you'll notice that Yellow Cab has a lower price per 1km than Swift ride at (8am, 9am) (9am, 10am) (2pm 3pm)
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There are 6 full time employees for every 13 part-time employees work at the grocery store. If there are 18 full time employees, how many part time employees work at the grocery store? Use the table to solve the problem.
Answer:
39 part time workers.
Step-by-step explanation:
39 part time workers. Since 18 is a multiple of six we can find how many times 6 goes into 18 and then multiply that amount into 13 to get 39.
Find all zeros of the function
f
(
x
)
=
3
x^3
-
9
x^2
-
18
x
+
24
.
Enter the zeros as a list separated by commas.
The zeros of the function are x = -2, x = 2, x = 3.
How to solveThe zeros of the function f(x) = [tex]3x^3 - 9x^2 - 18x + 24 = 0[/tex] are obtained by setting the function equal to zero and solving for x:
[tex]3x^3 - 9x^2 - 18x + 24 = 0[/tex]
These factors as:
3(x - 2)(x + 2)(x - 3) = 0
Setting each factor equal to zero gives the solutions:
x - 2 = 0 → x = 2
x + 2 = 0 → x = -2
x - 3 = 0 → x = 3
So, the zeros of the function are x = -2, x = 2, x = 3.
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Assume that the function f is a one-to-one function.
Considering the inverse function definition, we have that:
a) [tex]f^{-1}(4) = 6[/tex]
b) f(-5) = -2.
How to interpret the inverse function?To find the inverse function that exchanges the x and y-coordinates, we can follow these steps:
Start with the original function, y = f(x).Replace y with x and x with y to get x = f(y).Hence, the situation can be resumed as follows:
If f(x) = y, then [tex]f^{-1}(y) = x[/tex], which is used to obtain the numeric values for both functions in the context of this problem.
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Chris sells his paintings at art fairs on the weekends. The data set below shows how
much he earned every weekend over the past few months.
Amount earned (S)
105 150 170 170 175 180 180 200 240
Which values in this data set are outliers?
Select ALL outlier(s) from the options below.
105
150
200
240. Use the same data set from the previous question. Which modified box plot represents the data set.
The data set are outliers are 150 and 240 and the table for same will be the graph D.
Given that the Chris sells his paintings at art fairs on the weekends.
Amount earned (S) =
105 150 170 170 175 180 180 200 240
Since we know outliers are values at the extreme ends of a dataset.
So, here the outliers are = 150 and 240
Now the graph to show his earning should start around 150 and end at 240 so the graph will be D.
Hence the data set are outliers are 150 and 240 and the table for same will be the graph D.
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is 10/9 a proper or improper fraction
Please help!!! 100 Points!!!!
Answer:
r = 4
Step-by-step explanation:
The general form of the equation is y=mx + b where m is the slope and b is the intercept. The problem tells us that the slope is -3. So we know that y=-3x+b
Let's use the known coordinate (-5,13) to solve for b.
y=-3x+b
13 = -3(-5) + b
13 = 15 + b
b = -2
So now we have the equation:
y=-3x-2
Let's use the other coordinate (-2,r) and solve for the unknown "r" (which is y):
y = -3*-2 - 2
y = 6 - 2
y = 4
So the answer is 4.
Enter the number that belongs in the green box
The number that belongs to the green box in the triangle shown in the diagram given in the question is 14
How do i determine the number in the green box?From the diagram given in the question, we can see that one side and two angles of the triangle are given.
Thus, we shall use sine rule to obtain the missing side (i.e the green box). Details below:
Angle A = 61 degreesAngle B = 70 degreesSide b = 15Green box = Side a = ?Sine rule state as follow:
a / Sine A = b / Sine B
Inputting the given parameters, side a can be obtain as follow:
a / Sine 61 = 15 / Sine 70
Cross multiply
a × Sine 70 = 15 × Sine 61
Divide both sides by Sine 70
a = (15 × Sine 61) / Sine 70
a = 14
Thus, we can conclude from the above calculation that the number in the green box is 14
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Chords AC and DB intersect at point E. List 3 pairs of angles that must be congruent.
The three angles that will be congruent are angle AED , BEC and DEC
What is a chord?A chord of a circle is a straight line segment whose endpoints both lie on a circular arc.
Congruent angles are two or more angles that are identical to each other.
Thus, the measure of these angles is equal to each other.
When two chords meet at a point , it's practical that all the angles will be congruent i.e they will be equal especially when the chords are perpendicular to each other.
Therefore the three angles that will be congruent are angle AED , BEC and DEC.
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Question
Chords AC and DB intersect at point E. List 3 pairs of angles that must be congruent.
See attachment for missing figure
When chord AC and DB intersect at point E , the three pair of angles that must be congruent are angle DEA, AEB and CEB
What is a chord of a circle?The chord of a circle can be defined as the line segment joining any two points on the circumference of the circle.
A chord could be the diameter of the circle but not all not all chords are diameter.
when two chords intercept, there is high probability that each angle will be 90° and virtually all the angles will be congruent.
The three angles that must be congruent are angle DEA, AEB and CEB.
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Question
Check the image attached for the illustration to the question.
