Stephan borrowed $125 to buy an electric scooter. The function f(x) = 125 - 12.5x
can be used to represent the amount of money Stephan owes on the loan, where X is the number of weeks that Stephan pays towards the loan.
The amount that Stephen owed after 2 weeks is $100.
How to illustrate the expression?Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.
In this case, Stephan borrowed $125 to buy an electric scooter and the function f(x) = 125 - 12.5x
can be used to represent the amount of money Stephan owes on the loan, where X is the number of weeks that Stephan pays towards the loan.
The amount after 2 weeks will be:
f(x) = 125 - 12.5x
= 125 - 12.5(2)
= 125 - 25
= $100
The amount is $100.
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Complete question
Stephan borrowed $125 to buy an electric scooter. The function f(x) = 125 - 12.5x
can be used to represent the amount of money Stephan owes on the loan, where X is the number of weeks that Stephan pays towards the loan. What is the amount owed after 2 weeks?
The width of a rectangle is w feet. The length of the rectangle is six less than three times
the width. Write an algebraic expression that represents the area, in square feet, of the
rectangle in terms of w.
Answer:
Area = 3w^2 - 6w
Step-by-step explanation:
Area = width * length
width = w
length = 3w - 6
this is because the length is six less than three times the width so you get that the length = 3w - 6Area = w (3w - 6)
Area = 3w^2 - 6w
Answer:
Area of rectangle = 3w² - 6w
Step-by-step explanation:
Framing algebraic expressions:Width = 'w' ft
three times of width = 3*w = 3w
six less than 3w = 3w - 6
length = 3w - 6
[tex]\sf \boxed{\bf Area \ of \ rectangle = length*width}[/tex]
= (3w - 6)*w
= 3w*w - 6*w
= 3w² - 6w
a box contains 4 blue, 5 white, 6 red, and 7 green marbles. five marbles are chosen at random without replacement. what is the probability that every color will be represented in the sample of 5?
The probability that every color will be represented in the sample of 5 is 35/7776.
Describe the event without replacement?Each person in a population may only be chosen once when sampling is performed without replacement. In this instance, the outcome of the first pick has an impact on the probabilities again for second pick. It is decided whether or not the events are independent.For the stated question, box contains-
4 blue, 5 white, 6 red, and 7 green marbles.Total marbles = 22probability = favourable outcome/ total outcome
5 marbles are selected with out replacement.
Thus,
Probability of getting all color will occur is-
P(all color) = (4C2)*(5C1)*(6C1)*(7C1) + (4C1)*(5C2)*(6C1)*(7C1) + (4C1)*(5C1)*(6C2)*(7C1) + (4C1)*(5C1)*(6C1)*(7C2) / (10C5)⁴
P(all color) = 6*5*6*7 + 4*10*6*7 + 4*5*15*7 + 4*5*6*21 / 36⁴
P(all color) = 1260 + 1680 + 2100 + 2520 / 1679616
P(all color) = 7560 / 1679616
P(all color) = 35/7776
Thus, the probability that every color will be represented in the sample of 5 is 35/7776.
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At hi chool' book fair, Henry bring $10. 0. He purchae a book for $8. 50, plu a 6% ale tax. How much money in change will Henry receive?
Answer: $0.99
Step-by-step explanation: 8.5x0.06=0.51. 8.5+0.51=9.01. 10-9.01=0.99. Henry would get $0.99 in change.
Lydia is playing Galaxy 8RX. After three misses, the game is over. Last week, Lydia kept track of how long her games lasted. She made a line plot of her data. Lydia said, “My best time is 2 3/4 minutes longer than my worst time because 4 1/4 - 1 1/2 = 2 3/4
The scale factor of two triangles is 2:5. If the smaller triangle has side length of 30, what would be the length of the corresponding side on the bigger triangle?
Answer:
75
Step-by-step explanation:
From the way you've typed the question, it would appear that the ratio of the size of the smaller side to the ratio of the size of the larger side is 2:5.
Therefore, if the smaller side is 30, you can use the ratio the find the larger side:
[tex]S:L\\2:5\\\\[/tex]
(×15 to make the smaller side 30)
[tex]30:75[/tex]
Therefore, the bigger triangle would have side length 75.
6. Find x.
a. x² = 25
Take the square root of each side.
[tex]\sf \sqrt{x^{2} } =\sqrt{25} \\\\\\ x=\± 5[/tex]
The diameter of ball bearing are ditributed normally. The mean diameter i 81 millimeter and the variance i 16. Find the probability that the diameter of a elected bearing i greater than 85 millimeter. Round your anwer to four decimal place
the probability that the diameter of a elected bearing is greater than 85 millimeter P(diameter > 85) = P(z > (85-81)/4) = P(z > 1) = 0.1587
The diameter of ball bearings is normally distributed, with a mean of 81 millimeters and a variance of 16.
To calculate the probability that a selected bearing has a diameter greater than 85 millimeters, we first calculate the z-score for 85 millimeters.
We subtract 81 from 85 to get 4, and divide by 4 to get 1 for the z-score.
We the look up the probability for a value of 1 in the z-table, which is 0.1587.
This is the probability that a selected bearing has a diameter greater than 85 millimeters, rounded to four decimal places.
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what is the answer to -4(r+2)=4(2−2r)
Find −1/2(−4/5) . Write your answer as a fraction in simplest form.
Answer:0.4 as a decimal,2/5 as a fraction
Step-by-step explanation:
At a basketball game, a team made 59 successful shots. They were a combination of 1- and 2-point shots. The team scored 99 points in all. Write and solve a system of equations to find the number of each type of shot.
Answer:
Step-by-step explanation:
Let x be the number of 1-point shots and y be the number of 2-point shots. We know that the total number of shots is 59 and the total number of points is 99. We can write these two equations as follows:
x + y = 59
1x + 2y = 99
To solve this system of equations, we can use substitution. We can solve the first equation for y and substitute the result into the second equation:
y = 59 - x
1x + 2(59 - x) = 99
1x + 118 - 2x = 99
-x = -19
x = 19
Now that we know the value of x, we can substitute it into the first equation to find the value of y:
y = 59 - 19 = 40
Therefore, the team made 19 1-point shots and 40 2-point shots.
Pranv and Paul improve the yard by planting grass sod and shrubs they bought their supplies from the same store craft spent $90 on 10 feet of grass and grass sod and five shrubs paul spent $50 on 5 feet of grass sod and three shrubs find the cost of one foot of grass sod and a cost of one shrub
Answer:
The cost of one foot of grass sod is $9 and the cost of one shrub is $18.
Step-by-step explanation:
Since Pranv and Paul both bought their supplies from the same store, we can assume that they paid the same price per foot of grass sod and per shrub. From the information given, we know that Pranv spent $90 on 10 feet of grass sod and 5 shrubs, which means that he paid 90/10 = $9 per foot of grass sod and 90/5 = $18 per shrub. We also know that Paul spent $50 on 5 feet of grass sod and 3 shrubs, which means that he paid 50/5 = $10 per foot of grass sod and 50/3 = $16.67 per shrub. Since both Pranv and Paul paid the same price per foot of grass sod and per shrub, the cost of one foot of grass sod is $9 and the cost of one shrub is $18.
cual es la respuesta
The verdict on each of the given scenarios are as follows;
1. Yes, enough information is given to conclude that the triangles are congruent by the side-side-side SSS congruence theorem.2. No, the information conveyed through the triangles is not enough to conclude that the triangles are congruent.3. Yes, the two triangles given are congruent by virtue of the HL Congruence theorem.Which congruence theorems render the triangles congruent?By observation:
1. Since the two Triangles represented in 1. share a side and also, the two corresponding sides are congruent; it can be concluded that the two triangles are congruent.
2. By observation, although two sides are said to be congruent in the triangles; it cannot be concluded that the triangles are congruent neither by HL nor SSS congruence theorem.
3. The two Triangles share the diagonal which serves as the hypothenuse of both triangles; in addition, one of the other side lengths of the triangles are congruent; Therefore, the triangles are congruent by the HL congruence theorem.
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in an ideal circumstance, what is the most digital information two people both using 56k modems could exchange in one minute (the math in the answers is all correct, and provided as a benefit to you)?
In an ideal circumstance, two people using 56k modems could exchange approximately 448,000 bits of digital information in one minute time. This is equal to 56,000 bytes of data per second (56kbps).
In an ideal circumstance, two people using 56k modems could exchange digital information at a rate of 56 kilobits per second (56kbps). To calculate the amount of data transferred in one minute, we need to multiply 56kbps by 60 seconds. This gives us a total of 3,360 kilobits, or 3.36 megabits. Since one byte is equal to 8 bits, we can divide 3.36 megabits by 8 to get the total number of bytes exchanged. This calculation results in 420,000 bytes, or 448,000 bits, of digital information exchanged in one minute of time.
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solve for X ...................
Jamie has a fish tank with clownfish and goldfish. There are 8 fish in total, and 2/8 of them are clownfish. Jamie decides to double the amount of clownfish in the tank. How many clownfish are in the tank now? What fraction of the fish are clownfish?
Answer:
1/ There are 4 clownfish in the tank now
2/ 4/10
Step-by-step explanation:
1/ We know the original number of clownfish is 2/8, which means there are 2 clownfish in a tank with a total number of 8 fish.
So now she wants to double the clownfish. So there will be 4 clownfish in the tank now.
2/ We know that there was eight fish in the tank, and now there are 2 more, so the total will be 10! And we know that now there are 4 clownfish, so our fraction is 4/10
What is the value of the logarithm?
log (750)
Round the answer to the nearest thousandth.
Enter your answer in the box.
The value of the given logarithm log(750)=2.875.
What is meant by logarithm?Commonly employed in science and engineering, the base-10 logarithm is also known as the decimal or common logarithm. Since its derivative is so straight forward, the natural logarithm, whose base is the number e 2.718, is widely used in both mathematics and physics. Computer science typically use the binary logarithm, which has a base of 2.
John Napier developed logarithms as a way to make calculations simpler in 1614. To make high-accuracy calculations simpler, they were quickly embraced by surveyors, scientists, engineers, navigators, and other professionals. Inefficient multi-digit multiplication steps can be swapped out for quicker addition and table lookups when using logarithm tables.
Given,
We have to find the logarithm value of log(750)
By using the logarithm calculator we get
log(750)=2.875
Therefore, the value of the given logarithm log(750)=2.875
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fifty-five percent of the members of the junior varsity swim team wear glasses. of the team memebers who do not wear glasses, 30 percent of them are in the 10th grade.to the nearest whole percent, what is the probability that a randomly chosen member of the jv swim team does not wear glasses and is in the 10th grade?14ug%
Answer:
17%
Step-by-step explanation:
Let us say there are 200 people on the JV swim team. That would mean that 110 people do not wear glasses.
Of these 110 people, 30% are in 10th grade. Therefore, 33 people are in 10th grade and do not wear glasses.
This is 33 people ÷ 200 total = 16.5% ≈ 17%
Therefore, there is a 17% probability that a randomly chosen member of the jv swim team does not wear glasses and is in the 10th grade
[NOTE] You could also just do 55% × 30% = .55 × .30 = .165 ≈ .17 ⇒ 17%
Harry needs wood pieces to complete a project in woodshop class. He needs four pieces of wood that have a length of two and five eighths feet and two pieces of wood that are one and one fifth feet. What is the total amount of wood that Harry will need for the project?
twelve and nine tenths feet
three and 33 over 40 feet
three and 6 over 13 feet
two and one fifth feet
Answer: twelve and nine-tenths feet
Step-by-step explanation:
I turned the fractions into decimals cus I find that easier.
5/8 = .625 + 2 = 2.625
2.625(4) = 10.5 (multiply by 4 because it is 4 pieces)
1/5 = 0.2 + 1 = 1.2
1.2(2) = 2.4 (multiply by 2 because it is 2 pieces)
2.4 + 10.5 = 12.9
.9 can also be 9/10ths
Answer:
12 9/10
Step-by-step explanation:
The four pieces of wood: 4 x 2 5/8 = 10.5 or 10 1/2
The two peices of wood: 2 x 1 1/5 = 2.4 or 2 2/5
The total of both: 10 1/2 + 2 2/5= 12.9 or 12 9/10
What is the prime factorization of 168?
22 x 32 x 5
34 x 7
22 x 17
23 x 3 x 7
Answer:
Step-by-step explanation:
Dividing 168 by the smallest prime number 168 ÷ 2 = 84
84 is again divisible by 2 84 ÷ 2 = 42
42 is an even number and divisible by 2 42 ÷ 2 = 21
Now, 21 is divisible by the next prime number, i.e.3 21 ÷ 3 = 7
7 is a prime number itself 7 ÷ 7 = 1
Please answer the question in the photo.
Answer:
m it's equal to 6 because division its equal subtract the power
Step-by-step explanation:
A* to the power 9 divided by A* to the power 3 its equal to 9-3 = A* to the power its a
A^6
how many ways can a president, vice president, and secretary be chosen from a committee of 9 people, assuming one person cannot hold more than one position?
The number of ways cans a president, vice president, and secretary be chosen from a committee of 9 people, assuming one person cannot hold more than one position, is 84.
What is the combination?A combination is a choice of items from a group of different items, where the order of the choices is irrelevant.
Given:
A president, vice president, and secretary be chosen from a committee of 9 people,
Calculate the number of ways by using the combination as shown below,
[tex]N = 9C_3[/tex]
Here, N is the number of ways,
N = 9! / [3!(9-3)!]
N = 9! / [3!6!]
N = 84
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Find the Perimeter of the figure below, composed of a rectangle and a semicircle. Round to the nearest tenths place.
In triangle ABC which of the following is true a) ab+bc>ac.
b) ab-bc>ac.
c) ab+bc
d) ac+bc
Option a) ab + bc > ac is correct.
The first method by which we can solve this question is,
We have to know about the property of the triangle,
According to the property of the triangle, if we consider a triangle with lines ab, bc, ac and -
The sum of 2 sides of a triangle is greater than the third side The difference between the two sides is less than that of the third side.Therefore, we can conclude that ⇒ ab + bc > ac and ab - bc < ac
In the second method, let us consider the given triangle as right-angled,
So, according to the property of the right-angled triangle or Pythagoras' Theorem,
The square of the hypotenuse is equal to the square of the other two sides, let us consider the sides of the triangle = ab, bc, ac.
ABC is a right-angled triangle -
[tex]ab^{2} + bc^{2} = ac^{2}[/tex]
[tex]ab + bc > ac[/tex]
Therefore, we can conclude that, options a) ab + bc > ac is correct.
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the plane traveling from boston traveled at an average speed of 360 miles per hour. the plane traveling from kansas city arrived at 10:34 a.m. how many minutes before the plane from boston arrived did the plane from kansas city arrive?
From Boston to Kansas City, it takes 20 minutes to get there. When calculating the plane's arrival time, multiply the 360 mph speed from Boston by the 864 mi distance to Chicago.
what is distance ?Regardless of an object's beginning or ending position, we can define distance as the amount of ground it has traveled.
given
When calculating the plane's arrival time, multiply the 360 mph speed from Boston by the 864 mi distance to Chicago.
Distance = rate*time
864 = 360t,
t = 2.4
In other words, the flight arrived after 2.4 hours. Given that this is longer than two hours, divide the number by sixty to determine the time in minutes:
60 * 2.4 = 144 minutes. Assess the flight's travel time from Kansas City now.
It took 2 hours, 4 minutes, or 124 minutes from the time it departed at 8:30 AM to the time it arrived at 10:34 AM.
According to this, the jet from Kansas City arrived 144 – 124 = 20 minutes earlier than the plane from.
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The cash price of a television is Rs 65 000. The hire purchase price is a deposit of Rs 20 000 and 18 % simple interest on the outstanding balance, to be paid in 2 1/2 years . find the difference between the cash price and the hire purchase price.
Answer:
To find the difference between the cash price and the hire purchase price, we need to calculate the total hire purchase price.
First, we need to find the outstanding balance after the deposit is paid. We can do this by subtracting the deposit from the cash price:
outstanding balance = cash price - deposit
= Rs 65,000 - Rs 20,000
= Rs 45,000
Next, we need to calculate the total interest to be paid over the 2 1/2 year period. We can do this using the following formula:
total interest = outstanding balance * interest rate * time period
= Rs 45,000 * 18% * 2 1/2 years
= Rs 20,250
Finally, we can add the outstanding balance and the total interest to find the total hire purchase price:
total hire purchase price = outstanding balance + total interest
= Rs 45,000 + Rs 20,250
= Rs 65,250
The difference between the cash price and the hire purchase price is the difference between the total hire purchase price and the cash price. So we can calculate this as follows:
difference = total hire purchase price - cash price
= Rs 65,250 - Rs 65,000
= Rs 250
Therefore, the difference between the cash price and the hire purchase price is Rs 250.
I hope this helps!
= 20 000 + 1.18(65 000 - 20 000)
= 20 000 + 1.18(45 000)
= 20 000 + 53 100
= 73 100
73 100 - 65 000
= 8 100
Therefore, you will spend RS 8 100 more if you buy Hire Purchase Price than the Cash Price of Television.
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Find two pairs of conjugates with a product of 3.
Answer:
Step-by-step explanation:
21:
3,7
The graphs below have the same shape. What is the equation of the red
graph?
g(x) = -
-5
AY
g(x) = ?
OA. g(x) = (4- x)²
OB. g(x) = (8 - x)²
OC. g(x) = -x²
f(x) = 4-x²
6
The equation of the red graph is g(x) = -x².
What are coordinates in a graph?The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.
The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.
We have,
g(x) = -x²
For x = 0, 1, 2, 3, 4, 5, ......
g(1) = 0
g(1) = -1
g(2) = -4
g(3) = -9
g(4) = -16
Thus,
The graph of red graph is g(x) = -x².
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find the curvature at the point (2, 8, −1). x = 2t, y = 8t3/2, z = −t2
The curvature at the point (2, 8, −1). x = 2t, y = 8t^3/2, z = −t^2 is 0.039
In this question we need to find the curvature of r(t) = <2t, 8t^3/2, -t^2> at the point (2, 8, -1).
The derivative of r(t) with respect to t is:
r'(t) = <2, 12t^1/2, -2t>
The point (2, 8, -1) corresponds to t = 1,
and r′(1) = <2, 12(1)^1/2, -2(1)>
r'(1) = <2, 12, -2>
|r'(1)| = √(2^2 + 12^2 + (-2)^2)
|r'(1)| = √(4 + 144 + 4)
|r'(1)| = √(152)
|r'(1)| = 12.32
Now, r''(t) = <2, 6t^-1/2, -2>
and r′'(1) = <0, 6, -2>
r′(1) × r′′(1) = <0, 72, 4>
|r′(1) × r′′(1) |
= √(0^2 + 72^2 + 4^2)
=72.11
So, the curvature of r(t) would be,
κ(1) = |r′(1) × r′′(1)| ÷ |r′(1)|^3
k(1) = 72.11 / 12.32³
k(1) =0.039
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An engineer makes different-size samples of a new material. The table shows volumes and the related masses. What would be the mass of 100 cubic centimeters of the material? Of 500 cubic centimeters of the material? Use pencil and paper. Explain how you can use mental math to find the answer.
The mass of 100 cubic centimeters of the material would be [answer] enter your response here grams.
Answer:
The mass of 100 cubic cm = 1,000 grams.
The mass of 500 cubic cm = 5,000 grams.
Step-by-step explanation:
90/10=9
140/10=14
250/10=25
100x10=1000
500x10=5000