The average interest rate does he pay on the total $32,000 he owes is 9. 5%
How to determine the average
From the information given, we have that;
8% interest on his $22,00011% interest on his $10,000Given the total pay he owes as;
= $22, 000 +$ 10, 000
= $32, 000
The average interest rate is expressed as;
= sum of interest rate for college loan and car/ number of interest rate
Substitute the values
= 8 + 11/ 2
= 19/ 2
Find the quotient
= 9. 5%
Thus, the average interest rate does he pay on the total $32,000 he owes is 9. 5%
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b. What are the heights of the 6 th and 10 th bounces?
Given: BD ⊥ BC ; ∠ABD ≅ ∠DBE
Prove: ∠ABD and ∠EBC are complementary
Statement in step 8 is the proof that <ABD and <EBC are complementary angles.
What are a complementary angles?An angle in mathematics refers to an arc that joins two points. For angles to be formed there should be two points, the starting point and the ending point. In some cases the starting point coincides with the ending point, in this case the angle formed is 360 degrees which is equivalent to a circle. We can hence say that angle in a circle is 360 degrees
When angles are formed by two points in the same straight line or say two colinear points the angle formed here is 180 degree. Hence we say angles in a straight line is 180 degrees. In a case where a line intersects the straight line, the intersecting line bisects the the angle in a straight line. The sum of the two angles formed is 180 degrees. Such angles are said to be supplementary angles.
Assuming the bisector of the straight line in a perpendicular bisector, here the angle 180 is divided into two equal parts then each angle is 90 degrees.
When angle 90 degrees is bisected two different angles are formed. The sum of these two angles are known as complementary angles.
Hence angle <ABD and <EBC are complementary angles formed from bisecting angle <DBC which is 90 degrees or a right angle triangle
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PLEASE HELP LE WITH THIS ANSWET
Answer: 5
Step-by-step explanation:
GH=GD+DH
GD=DH ==> indicated by the ticks on the two line segments GH and DH.
GH=DH+DH
4x-4=8+8
4x-4=16
4x=20
x=5
99. Cost, Revenue, and Profit A roofing contractor
purchases a shingle delivery truck with a shingle
elevator for $42,000. The vehicle requires an average
expenditure of $9.50 per hour for fuel and maintenance,
and the operator is paid $11.50 per hour.
(a) Write a linear equation giving the total cost C of
operating this equipment for t hours. (Include the
purchase cost of the equipment.)
(b) Assuming that customers are charged $45 per hour
of machine use, write an equation for the revenue R
obtained from t hours of use.
(c) Use the formula for profit P = R C to write
an equation for the profit obtained from t hours
of use.
(d) Use the result of part (c) to find the break-even
point that is, the number of hours this equipment
must be used to yield a profit of 0 dollars.
Total cost function is C=42000+21t
Revenue function is R=45t
Profit function is P=24t-42000
The breakeven number of hours is 1,750
What is the total variable cost per hour of operating the truck?
The total variable cost per hour of operating shingle delivery truck is the sum of the hourly fuel and maintenance cost and the hourly rate of the operator
total variable cost per hour=$9.50+$11.50
total variable cost per hour=$21.00
The liner equation formula for total cost is as shown below:
y=a+bx
y=total cost=C
a=fixed cost=cost of truck=42000
b=total variable cost per hour=21
x=number of hours the truck is operated=t
C=42000+21t
The total revenue is the customer charge per hour multiplied by number of hours
R=45t
P=R-C
P=45t-(42000+21t)
P=24t-42000
The breakeven number of hours is achieved at the point where the total cost is the same as revenue
45t=42000+21t
45t-21t=42000
24t=42000
t=42000/24
t=1,750 hours
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Finding the initial amount and rate of change given a table for a linear function
Answer:Omg JUST use slope intercept form like I said: Pick a point in this case I have picked, but you can any: (15, 560) (20, 480). Remember
Y2 - Y1 /X2-X1 = M (Your slope). In this case 480-560/20-15 = -80/5 = -16
Now you have your slope. Y - Y2=M(x - x1). In this case Y - 560 = -16(x-15)
Distrubute: Y - 560 = -16x +240. Add 560 on both side. Y= -16x +800
And yes it water decreases as time increases.
Step-by-step explanation:
Points O, A, B lie on the same line. OA = 12 cm, OB = 9 cm. Find the distance between the midpoints of segments OA and OB if: Point O does not lie on the segment AB pls help ASAP with explnation
The distance between the midpoints of segments OA and OB is 1.5 cm.
Given that, points O, A, and B lie on the same line. OA = 12 cm, OB = 9 cm.
We need to find the distance between the midpoints of segments OA and OB.
What is the midpoint of the line segment?A midpoint of a line segment is the point on a segment that bisects the segment into two congruent segments. The midpoint of a line segment is the point on a segment that is at the same distance or halfway between the two ending points.
Let X be the midpoint of OA and Y be the midpoint of OB.
Now, the midpoint of OA is OX=AX=OA/2
=12/2=6 cm
Then, the midpoint of OB is OY=YB=OB/2
=9/2=4.5 cm
The distance = 6-4.5=1.5 cm
Therefore, the distance between the midpoints of segments OA and OB is 1.5 cm.
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Combining functions to write a new function that models a real-world situation
The function C that represents how much more it costs to rent a luxury car than an economy car is; C = 8.45 + 0.45M
How to combine functions?We are given the function that represents the charge E(in dollars) to rent an economy car as;
E = 12.95 + 0.60M
The function that represents the charge L (in dollars) to rent a luxury car is given by; L = 21.40 + 1.05M
Now, we are told that the function C represents how much more it costs to rent a luxury car than an economy car. This is expressed as;
C = L - E
Thus;
C = 21.40 + 1.05M - (12.95 + 0.60M)
C = 21.40 + 1.05M - 12.95 - 0.60M
C = 8.45 + 0.45M
Thus, the function C that represents how much more it costs to rent a luxury car than an economy car is; C = 8.45 + 0.45M
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Review the graph. A student spends 16.5 hours studying and receives a mark of 61.4%. Which statement
describes this result?
A. The result is not an outlier and there is a gap in the data.
B. The result is not an outlier and there is no gap in the data.
C. The result is an outlier and there is a gap in the data.
D. The result is an outlier and there is no gap in the data.
Answer: D. The result is an outlier and there is no gap in the data.
The statement describes this result is; D. The result is an outlier and there is no gap in the data.
In statistics, an outlier is a data point that differs significantly from other observations. An outlier may be due to variability in the measurement or it may indicate experimental error; the latter are sometimes excluded from the data set.
From the graph, at 16.5 hours, the exam score is approximately 90%. Thus, we can conclude that if a student spends 16.5 hours studying and receives a mark of 61.4%, then the result is an outlier and there is no gap in the data.
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E is the midpoint of DF, DE=6x+1 and EF = 7x-4. Find DE, EF, and DF
The value for the given line DF are-
DE = 31 units.EF = 31 units.DF = 62 unit.What is meant by the mid point of the line?A midpoint is a point in the middle of a line connecting two points. The 2 points of reference are the line's endpoints, and also the midpoint is located between the two.For the points on the coordinate axes, the midpoint formula is defined. Let the endpoints of the a line segment be (x)1, (y)1, and (x)2, (y)2. The midpoint is equal to one-half of the sum of the two points' x-coordinates and half of a sum of the two points' y-coordinates.For the given values in question,
DE = 6x + 1 and EF = 7x - 4.
As, E is the midpoint of DF.
Thus,
DE = EF
Pu the values.
6x + 1 = 7x - 4
On solving.
x = 5
Put the values in the lines.
DE = 6x + 1
DE = 6×5 + 1
DE = 31 units.
EF = 7x - 4
EF = 7×5 - 4
EF = 31 units.
DF = DE + EF
DF = 31+ 31
DF = 62 units.
Thus, the values for the line segment are obtained.
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The radius of the circle is 5 centimeters line segment ab is a diameter of the circle what is the value of x to the nearest tenth
The value of x to the nearest tenth is 8.9 cm.
How to find the diameter of a circle?The radius of the circle is 5 centimetres. Line segment ab is a diameter of the circle.
The diameter of the circle is twice the length of the radius.
Hence, the value of x can be found as follows:
AB = 10 cm
Using Pythagoras theorem,
c² = a² + b²
where
c is the hypotenusea and b are the other legs.Therefore,
10² - 4.5² = x²
100 - 20.25 = x²
x² = 79.75
x = √79.75
x = 8.93028554975
x = 8.9
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Please this is urgent I will give all of my points
Find the coordinates of the points of intersection of the graph of
y=2x+6 with the axes. Find the area of the right triangle
formed by this line and the coordinate axes.
The coordinate of intersection with the x-axis is: (-3, 0).
The coordinate of intersection with the y-axis is: (0, 6).
The area of the triangle is 9 unit²
What is the Linear equation?A linear equation is defined as an equation in which the highest power of the variable is always one.
The linear equation is given as:
y = 2x+6
Intersection with the y-axis
Substitute, x = 0
⇒ y = 2x + 6
⇒ y = 2(0) + 6
⇒ y = 6
As a result,: y = 2x+6 intersects with the y-axis at (0, 6)
Intersection with the x-axis
Substitute, y = 0
⇒ y = 2x + 6
⇒ 0 = 2x + 6
⇒ 2x = - 6
⇒ x = - 3
As a result,: y = 2x + 6 intersects with the x-axis at: (-3, 0)
The area of the right-angled triangle
The area is calculated as:
Area of triangle = 1/2×Base×Height
Area of triangle = 1/2×3×6
Area of triangle = 9 unit²
The coordinate of intersection with the x-axis is: (-3, 0).
The coordinate of intersection with the y-axis is: (0, 6).
The area of the triangle is 9 unit²
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2|4w-1|=3|4w+2| Solve for W, but it’s absolute value so 2 and 3 cannot be distributed
Answer:
w = -2, (-1/5)
Step-by-step explanation:
2|4w - 1| = 3|4w + 2|
8w - 2 = 12w + 6
-12w -12w
-------------------------
-4w - 2 = 6
+2 +2
---------------------
-4w = 8
÷-4 ÷-4
w = -2
2|4(-2) - 1| = 3|4(-2) + 2|
2|-8 - 1| = 3|-8 + 2|
2|-9| = 3|-6|
18 = 18
----------------------------------------------------------------------------------------------------------
2|4w - 1| = -(3|4w + 2|)
2|4w - 1| = -3|4w + 2|
8w - 2 = -12w - 6
+12w +12w
-------------------------
20w - 2 = -6
+2 +2
20w = -4
÷20 ÷20
------------------
w =(-1/5)
2|4(-1/5) - 1| = 3|4(-1/5) + 2|
2|(-4/5) - 1| = 3|(-4/5) + 2|
2|(-9/5)| = 3|(6/5)|
3.6 = 3.6
I hope this helps!
Xio is rolling marbles down a ramp. Every second that passes, she
measures how far the marbles travel. She records the information in the table
shown below.
eau marit
Second
1st
2nd 3rd 4th
Distance (cm) 20 60 100 140
Make a conjecture about how far the marble will roll in the fifth second
The marble will roll 180cm distance in fifth second.
Distance travelled by an object in rectilinear motion is always in arithmetic Progression. Arithmetic Progression is collection of number in increasing or decreasing order with a common difference.
The marble rolls 20cm, 60cm, 100cm, 140cm in 1st, 2nd, 3rd, 4rth second respectively
As the ball travels in rectilinear motion on floor, so the distance covered by it in successive seconds will be in Arithmetic Progression
so, 5th term of the AP 20,60,100,140..... will be the distance travelled by it 5th second
Since A=20 and common difference(d)=40
then, 5th term= A + (5-1)d
or, 20+ (4×40) = 180cm
Final answer, the marble will roll 180cm in 5th second.
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Aleena thinks of a number that has 2 decimal places.
Her number is 2.8 when rounded to 1 decimal place.
What is the smallest number that Aleena could be thinking of?
Answer:
The smallest number that Aleena could be thinking of is 2.75.
ive put 3 more of the same question gain lots of points! Rex and Samir participated in a walkathon. Rex walked for 1 2/3 hours, and Samir walked for 3 1/3 hours. complete the comparison. Samir walked _____ times ad many hours as Rex walked.
Answer:
2 times as much
Step-by-step explanation:
1 hour 2/3 = 60 + (2/3) 40 mins = 100 minutes
3 hours 1/3 = (60 ×3 ) + 20 mins = 200 mins
200 is twice as much as 100
Answer:
2 times as much
Step-by-step explanation:
1 hour 2/3 = 60 + (2/3) 40 mins = 100 minutes
3 hours 1/3 = (60 ×3 ) + 20 mins = 200 mins
200 is twice as much as 100
Press the heart button please thank you.
Samantha owes her father 21.21. She just got paid 13 for babysitting. If she gives that money to her dad, how much will she still owe him? No dollar sign needed. Write your answer as a negative integer, rounded to the nearest h
Answer:
she'll still owe him 8.21
Step-by-step explanation:
i dont know what you mean by write it as a negative integer ?
Each of these sequence or series formulas involves four quantities that are represented by a variable. For each fomula, describe the four quantities.
d. S n = a₁ (1-rⁿ ) / 1-r
The formula for finding the sum of a geometric series is:
S n = a₁ (1-rⁿ )/(1-r)
The four quantities in the formula are S n, a₁, r, n
How to describe the four quantities?An infinite geometric series is the outcome of an unlimited geometric sequence. An infinite geometric series is the outcome of an unlimited geometric sequence. This series wouldn't have a finish. It is possible to calculate the sum of all finite geometric series.
The terms in the sequence will grow steadily larger, but adding the larger numbers together will not provide a solution if the common ratio of an infinite geometric series is greater than one.
The formula for finding the sum of a geometric series is:
S n = a₁ (1-rⁿ )/(1-r)
The four quantities in the formula are S n, a₁, r, n
The description is as follows:
n be the number of terms
a₁ be the first term
r be the common ratio
[tex]S_n[/tex] be the sum of a geometric series
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two sides of a triangle are a=12,b=15 and the value of s(semi perimeter) used in heron's formula is 22 cm, then the length c of the third side is:
Answer:
how are you doing where you can do it for 5 Pts
Step-by-step explanation:
HELPPP mathhhhhhh 20 pointsss
7^4.3^-6.y is equivalent to 7.7.7.7.y/3.3.3.3.3.3 which is option (B).
b^10/b^4 is b^6 and (p^2+p-8)-(-4p^2-p+3) is 5p^2+2p-5.
What is Equation?Two expressions with equal sign in between is called as equation.
4. 7^4.3^-6.y
In the given expression, 7 has 4 exponent and 3 has -6 exponent.
This can be written as 7.7.7.7.y/3.3.3.3.3.3.
5. b^10/b^4 is b^10-4=b^6.
6. (p^2+p-8)-(-4p^2-p+3)
=p^2+p-8+4p^2+p-3
=5p^2+2p-5.
Therefore 7^4.3^-6.y is equivalent to 7.7.7.7.y/3.3.3.3.3.3 which is option (B), b^10/b^4 is b^6 and (p^2+p-8)-(-4p^2-p+3) is 5p^2+2p-5.
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A 320 meter long tightrope is suspended between two poles. Assume that the line has an equal chance of breaking anywhere along its length.
a. Determine the probability that a break will occur in the first 50 meters of the tightrope.
The probability that a break will occur in the first 50 meters of the tightrope is about 15.625%.
Probability:
The term probability refers the possibility occurring the particular event.
Given,
A 320 meter long tightrope is suspended between two poles.
Here we assume that the line has an equal chance of breaking anywhere along its length.
Now, we need to determine the probability that the break will occur within 20 meters of a pole.
From the given question,
The line has an equal chance of breaking anywhere along its length.
The first 50 meters form ,
=> [ 50 / 320 ] x 100
=> [ 5 / 32 ] x 100
=> [ 0.15625] x 100
=> 15.625 %.
Therefore, the probability that a break will occur in the first 50
meters of the tightrope is about 15.625%.
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Read the question. Then fill in the correct answer on the answer document provided by your teacher or on a sheet of paper.
Eddie conducted a random survey of 50 students and fund that 14 nf them spend more than 2 hours each night doing homework. If there are 421 students at Eddie's school, predict how many of them spend more than 2 hours each night doing homework.
F. 118 H. 125
G. 124 J. 131
The prediction of the number of students who spend more than 2 hours each night doing homework are 118.
It is given in the question that in a random survey of 50 students and fund that 14 of them spend more than 2 hours each night doing homework.
There are 421 students in the school.
We have to predict the number of students who spend more than 2 hours each night doing homework.
Probability of number of students who spend more than 2 hours in doing homework = 14/50 = 7/25= 0.28
If there are 421 students, number of students who spend more than 2 hours in doing homework = 0.28*421 = 117.88 ≈ 118.
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In this problem, you will explore changing dimensions in circles.
d. Make a conjecture about the ratio between the circumferences of two circles, when the ratio between their radii is 2 .
A ratio shows us the number of times a number contains another number. If the ratio between their radii of two circles is 2, then the ratio of their circumference will also be equal to 2.
What is a Ratio?A ratio shows us the number of times a number contains another number.
Given that the ratio of the radius of two circles is 2. Therefore, we can write the ratio as,
The radius of circle A = kThe radius of circle B = 2kNow, a conjecture that can be made regarding the ratio of the circumference of the circle is that the ratio of the circumference of circle A and circle B will also be 2.
Further, let's check the ratio of the circumference of the circle.
Circumference of the circle A = 2πkCircumference of the circle B = 2π(2k) = 4πkThe ratio of the circumferences can be written as,
Circumference of the circle A/Circumference of the circle B = 2πk / 4πk
Circumference of the circle A/Circumference of the circle B = 1/2
Hence, If the ratio between their radii of two circles is 2, then the ratio of their circumference will also be equal to 2.
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The previous question you found the slope for the points (1,0) and (3,8), now find the b and write the equation in slope intercept form.
y =
Question Blank 1 of 2
type your answer...
x +
Question Blank 2 of 2
type your answer...
Answer:
Step-by-step explanation:
y = mx + b is the equationof the line where m is the slope and b is the y intercept
slope between t points = (8 - 0)/ (3 -1 )
= 8/2
= 4
y = 4x + b
substitute (1,0) in the equation to get b
0 = 4(1) + b
b = -4
equation will be y = 4x -4
What is the slope of a line perpendicular to the line through the points (-1,6) and (3,-4) ?
A. m=-5/2
B. m=-1
C. m=-2/5
D. m=2/5
The slope of the line passing through two points (-1, 6) and (3, -4) is Option A ( m = [tex]\frac{-5}{2}[/tex] )
It is given that, the line is passing through two points (-1, 6) and (3, -4)
Slope is the measurement of the level of steepness of the line or it is a line's steepness determined by looking at its slope. Slope is calculated mathematically as "rise over run" (change in y divided by change in x).
The formula to find the slope of the line passing through two points is given by
m = [tex]\frac{y2 - y1}{x2 - x1}[/tex]
We need to find the slope of the line passing through both points
where y1 = 6, y2 = -4, x1 = -1, x2 = 3
Putting values in the formula to find the slope of the line
we get,
m = [tex]\frac{-4 - 6}{[3 -(-1)]}[/tex]
m = [tex]\frac{-10}{4}[/tex]
m = [tex]\frac{-5}{2}[/tex]
Hence The slope of the line passing through two points (-1, 6) and (3, -4) is m = [tex]\frac{-5}{2}[/tex]
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A panel of judges must be chosen to judge the upcoming dance competition. There are 5 men and 8 women to pick from. How many ways can you pick a panel of 2 men and 2 women?
The number of ways of picking a panel of judges comprising of 2 men and 2 women is 280 ways
How to find the number of ways to pick a panel of 2 men and 2 women
Given data
number on men = 5
number of women = 8
The number of ways of picking a panel of 2 men and 2 women
= 5 combination 2 * 8 combination 2
= 5 C 2 * 8 C 2
= 5! / ( 2! ( 5 - 2 )! * 8! / ( 2! ( 8 - 2 )!
= 5! / ( 2! 3! ) * 8! / ( 2! 6! )
= 5 * 4 * 3! / ( 2! * 3! ) * 8 * 7 * 6! / ( 2! * 6! )
= 20 / 2 * 56 / 2
= 10 * 28
= 280 ways
The number of ways of picking a panel of judges comprising of 2 men and 2 women is 280 ways
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Beth knows the perimeter, P, and width, w, of a
rectangular window in her living room. Which
formula can she use to find the length, 1, of the
window?
Beth knows the perimeter, P, and width, w, of a
rectangular window in her living room. Which
formula can she use to find the length, 1, of the
window?
First we know about How to Find the perimeter?
Rectangles have four sides, congruent opposite sides, and four right angles and we find the perimeter of a rectangle with the equation P=2l+2w. Explore this formula, rectangles, and examples of finding rectangle perimeters.
so ,
The formula for the perimeter of a rectangle is given below: Perimeter = length + length + width + width P = l + l + w + w Or, P = 2 ( l + w) Hence, the formula for the perimeter of a rectangle, P = 2 × (length + width) = 2 × (sum of adjacent sides) .
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Find the arithmetic mean an of the given terms. a_{n-1}=7, a_{n+1}=1
The arithmetic mean an of the given terms a_{n-1}=7, a_{n+1}=1 is
a (n) = -3.
What is arithmetic mean?a_{n-1}=7, a_{n+1}=1
a(n) =(1-7)/2
a (n) = -3
The arithmetic mean is the most straightforward and widely used method of calculating a mean or average. It only requires adding up a group of figures, then dividing the result by the entire amount of figures in the series. Consider the numbers 34, 44, 56, and 78 as an example. It totals 212.
The mean or arithmetic average are other names for the arithmetic mean. It is determined by adding up each number in a particular data set, then dividing the result by the overall number of items in the data set. For uniformly distributed integers, the middle number serves as the arithmetic mean (AM).
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the difference between the areas of the figures is less than 2
Answer:
x < 1
Step-by-step explanation:
Find the distance between the pair of points: (-9, -5) and (6, -5)
Answer:15
Step-by-step explanation: if your at -9,-5 you would be on the 3rd quadrant, and in order to get to 6,-5 (4th quadrant) you would just move to the right. you would only move right because the y-axis stays the same but the x-axis changes.
Answer: 15
Step-by-step explanation:
the equation to find the length of a line using the points given:
[tex]\sqrt{(x2-x1)^2+(y2-y1)^2}[/tex]
therefore you should understand which is y2, x2,y1 and x1
so you should always check which y value is bigger (the y value is the number in the right side of the point) so if the y value is bigger (y2) then eventually the value next to it which is x will always become x2 if the y value is big (y2)
so the other two values of the other point should become x1 and y1 since you already figured out the lager y value.
so now as for this question y2= -5, y1= -5, x2= 6 and x1= -9
now substitute these values to the equation I mentioned before ( you should make sure to remember the equation for sure as it is required when doing these types of questions)
[tex]\sqrt{[6-(-9)]^{2} +[-5-(-5)]^2} \\\sqrt{(6+9)^2 + (-5+5)^2[/tex]
[tex]\sqrt{15^2+0^2} \\\sqrt{225} \\15[/tex](therefore 15 is the answer you have been looking for!)
I hope you understood and don't forget the equation which is the main help!
