Find the equation of the function of the specified type that is the best fit for the given data
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.
On a number line, point O is at -7, and point P is at 8. Point N lies between points O and P. If the ratio of ON to NP is 4:8, where does point N
lie on the number line?
Point N is at
on the number line.
Answer:
N is at -2 on the number line
Step-by-step explanation:
The location of point N can be found by writing the segment lengths as a proportion.
ON : NP = 4 : 8
8(ON) = 4(NP) . . . . . . . . "cross multiply"
2(N -O) = (P -N) . . . . . divide by 4, show lengths ON and NP
2(N -(-7)) = 8 -N . . . . . use given values of O and P
3N = -6 . . . . . . . . . . . add N-14 and simplify
N = -2 . . . . . . . . . . divide by 3
Point N is at -2 on the number line.
If the ratio of ON to NP is 4:8, point N lie on the -2 at the number line.
Point O is at -7.
Point P is at 8.
The ratio of ON to NP is 4:8.
The ratio 4:8 simplifies to 1:2. This means that ON is one-third of the total distance from O to P, and NP is two-thirds of the total distance.
The total distance from O to P is the sum of the distances between O and N, and between N and P.
As the ratio of ON to NP is 1:2, and the total distance is 15 (8 - (-7) = 15), we can set up the following equation:
ON/NP = 1/2
ON/(15 - ON) = 1/2
Now we can solve for ON:
2 × ON = 15 - ON
3 × ON = 15
ON = 5
So, ON is 5 units away from O.
Now O is at -7, point N is at -7 + 5 = -2 on the number line.
So, N is at -2.
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Find the inverse of the function.
f(x) = x^3 - 3
1. The length of each side of a square increased by 40%. By what percent does the area of the square increase?
2. The length of a rectangle increases by 20%, and the width decreases by 20%. What is the overall percent change in the area of the rectangle?
(they are two separate questions)
Answer: to number 1 :The area of the square increases by 96% to number 2: increase in width = 50%
Step-by-step explanation
7. Derek has $20 to spend on used books. Hardcover books cost $5 each and paperbacks cost $2 ea Write an equation that models the situation.
Marcus has hired 3 people to help him with his lawn business. He pays all the same, and he pays them every day. He paid $360 to his 3 workers today. How much did each worker get. In complete sentence
Hi!
If they each got the same, then they each got 1/3 of the total $360. Therefore, we can divide 360 by 3. We can do this by dividing 36 by 3, 36/3, and that's 12. Then add the 0! 120.
Your sentence could be: "The amount of money each worker got can be represented by 360/3, which is $120."
Hope this helps! :D
Answer: Since Marcus hired 3 people and paid them $360 altogether, it should be easy to figure this out through dividing. 360/3 or 360 divided by 3 = 120. You can put three into 360 one-hundred and twenty times. So, your answer would be that each worker got $120.
In a parking lot,there are 16 silver cars, 8 blue cars ,and 10 red cars . A car leaves the parking lot. What is the probability that it is
a: a silver car?
b: a blue car?
c: a red car?
d: suppose that the first car that leaves is a silver car . What is the probability that the second car that leaves is not a silver car?
Answer:
a) 8/17
b) 4/17
c) 5/17
d) 48/187
Step-by-step explanation:
a) P(silver) = 16/34 = 8/17
b) P(blue) = 4/17
c) P(red) = 5/17
d) P(silver, not silver) = 8/17 × 18/33 = 144/561 = 48/187
The probability for each event are -
[A] - 8/34
[B] - 16/34
[C] - 10/34
[D] - 18/33
What is a expression? What is a mathematical equation? What is Probability?A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem. The formula to calculate the probability of occurrence of an event 'A' can be written as -P(A) = n(A)/n(S)
where -
n(A) = Number of outcomes favorable to event A.
n(S) = Total number of outcomes
We have 16 silver cars, 8 blue cars and 10 red cars in a parking lot.
[A] -
P{silver} = 8/(16 + 8 + 10) = 8/34
[B] -
P{blue} = 16/(16 + 8 + 10) = 16/34
{C} -
P{red} = 10/(16 + 8 + 10) = 10/34
D) -
P{not silver} = 1 - 15/33 = 18/33
Therefore, the probability for each event are -
[A] - 8/34
[B] - 16/34
[C] - 10/34
[D] - 18/33
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The length of a rectangular garden is 30 yards more than the width. The perimeter is 300 yards. Find the length and width
Answer:
60 yards
Step-by-step explanation:
300 = 2(30 + w) + 2(w)
300 = 60 +2w + 2w
300 = 60 + 4w
240 = 4w
60 = w
In trapezoid DEFG, EG = 24.3 and DH = 9.4. Identify HF.
Answer:
HF = 14.9
Step-by-step explanation:
The largest lollipop ever made had a mass of 2158.7kg and was made for a festival in Granna, Sweden on July 27, 2003, If a spherical lollipop with radius 2 cm has a mass of 50 g, what was the radius of this giant lollipop?
Answer:
Step-by-step explanation:
Assuming the density is the same for both lollipops, we can calculate what volume is required to make the 2158.7kg the same density of the smaller lollipop.
Small Lollipop
r = 2cm
V=4 /3πr^3
V = 33.51 cm^3
Mass is 50 g in 33.51 cm^3, so the density is:
50g/(33.51 cm^3) = 1.492 g/cm^3
We have 2158.7kg in the larger lollipop. That is 2158700 grams.
Find the volume required to contain 2158700 grams with a density of 1.492 g/cm^3. :
(2158700 grams)/(1.492 g/cm^3) = 1446775 cm^3
V=4 /3πr^3
1446775 cm^3 = (4/3)*π*r^3
r = 70.12 cm
A coin weighs 3/4 ounces. Laura picked up 6 of these coins. What is the total weight of the coins she picked up? In simplest form.
Answer:
1 1/2 pound
Step-by-step explanation:
If each coin weighs 3/4 ounces and she picked up 6 then you do 3/4 x 6/1 which equals 18/4 and since there is 16 ounces in a pound it simplifies to 1 2/4 or 1 1/2 pounds
William drove 344 miles in 8 hours. If he continued at the same rate, how far would he travel in 17 hours?
Answer:
731 miles
Step-by-step explanation:
344 miles / 8 hours = 43 mph
17 hours * 43 mph = 731 miles
Help help please …thanksss
Which is an advantage of using a credit card?
A. You can make purchases when you don’t have cash
B. You don’t indulge in impulse buying
C. You don’t have to pay interest
Find the intersection point for the following linear functions.
Rx) = 2x + 3
8(x) = -4x - 27
Answer:
(-5, -7)
Step-by-step explanation:
Answer:
[tex](-5,-7)[/tex]
Step-by-step explanation:
[tex]f(x)=2x+3[/tex]
[tex]g(x)=-4x-27[/tex]
[tex]2x+3=-4x-27[/tex]
[tex]6x+3=-27[/tex]
[tex]6x=-30[/tex]
[tex]x=-5[/tex]
[tex]f(-5)=2(-5)+3[/tex]
[tex]f(-5)=-10+3[/tex]
[tex]f(-5)=-7[/tex]
Therefore, the point of intersection is [tex](-5,-7)[/tex]
solve and check the equation
2(4-5x) = 2(3x+2)
The formula for finding the perimeter of a rectangle is P = 2L + 2W. If a rectangle has a perimeter of 68 inches and the length is 14 inches longer than its width, find the width.
Enter a number answer only.
Answer:
Width = 10 inches
Step-by-step explanation:
Given the perimeter of a rectangle of 68 inches, and a length that is 14 inches longer than its width.
We can establish the following values to help us solve for the width of a rectangle:
Perimeter (P) = 68 inches
Length (L) = 14 + W inches
Width (W) = unknown
Solve for the Width (W)P = 2(L + W) ⇒ This is the same as P = 2L + 2W, except that 2 is factored out from the right-hand side.
Divide both sides by 2:
[tex]\displaystyle\mathsf{\frac{P}{2}\:=\:\frac{2(L\:+\:W)}{2}}[/tex]
[tex]\displaystyle\mathsf{\frac{P}{2}\:=L\:+\:W}[/tex]
Substitute the value of the Perimeter and the length (L) into the formula:
[tex]\displaystyle\mathsf{\frac{68}{2}\:=14\:+W\:+\:W}[/tex]
Combine like terms on the right-hand side, and simplify the left-hand side of the equation:
[tex]\displaystyle\mathsf{34\:=14\:+2W}[/tex]
Subtract 14 from both sides:
34 - 14 = 14 - 14 + 2W
20 = 2W
Divide both sides by 2 to solve for the width (W):
[tex]\displaystyle\mathsf{\frac{20}{2}\:=\:\frac{2W}{2}}[/tex]
W = 10 inches
Therefore, the width of the rectangle is 10 inches.
Double-check:Verify whether the derived value for the width is correct:
P = 2L + 2W
68 = 2(14 + 10) + 2(10)
68 = 2(34) + 20
68 = 48 + 20
68 = 68 (True statement).
Thus, the length of the rectangle is 34 inches, and the width is 10 inches.
a person pays a loan of Rs. 3900 in monthly installments each in installment being less than the former by Rs. 20 ,the amount of first is Rs.400 in how many installment will entire amount be paid ? give reason
Answer:
15 installments
Step-by-step explanation:
3900 = Σ [tex]\left \ {{x=n} \atop {x=1}} \right.[/tex] 400 - 20*(n - 1)
What number is the opposite of
3/11
O A. - 3/11
O B. -11/3
C. 11/3
O D. 1/3
Answer:
I believe the answer is A.
Maxden wanted to measure the length of the objects below.
For each one circle which unit of measurement he should use.
A. His puppy
Inches or Yards
B. A toy car
Yards or Centimeters
C. Width of his desk
Yards or Feet
D. His foot
Inches or Yards
Last year, 50 students attended the movie night. This year, 65 students attended the movie night. fine the percent of increase in the number of students who attended the movie night.
Answer: 30%
Step-by-step explanation:
It increased by 15 so it increased by 15/50=30/100=30%
I hope this helped!
what is 9/blank= 4? i really don't know
Answer:
9/4
Step-by-step explanation:
Answer:
9/2.25 = 4
Step-by-step explanation:
9/x = 4
x = 9/4 or 2.25
Kevin and Randy Muise have a jar containing 32 coins, all of which are either quarters or nickels. The total value of the coins in the jar is $5.40. How many of each type of coin do they have?
PLSSSS AnSWER QUICKLY
Answer:
19 quarters and 13 nickles
Step-by-step explanation:
You have 32 coins in your pocket consisting of nickels and quarters with a total value of $5.40
How many nickels and quarters do you have?
Step 1: Setup Coin Value and Coin Total Equation:
Coin Value Equation → 0.05n + 0.25q = $5.40 where n = nickels and q = quarters
Coin Total Equation → n + q = 32
Step 2: Rearrange Coin Total Equation in terms of nickels (n)
n = 32 - q ← Revised Coin Total Equation
Step 3: Plug in our Revised Coin Total Equation for n into our Coin Value Equation:
0.05(32 - q) + 0.25q = $5.40
0.05(32) - 0.05(q) + 0.25q = $5.40
1.6 - 0.05q + 0.25q = $5.40
1.6 + (0.25 - 0.05)q = $5.40
1.6 + 0.2q = $5.40
Step 4: Subtract 1.6 from each side of the equation to isolate q
1.6 - 1.6 + 0.2q = $5.40 - 1.6
0.2q = 3.8
Step 5: Divide each side of the equation by 0.2 to isolate q
0.2q
0.2
=
3.8
0.2
q = 19
Step 6: Using our value for q, Solve for n using our Coin Total Equation:
n + 19 = 32
Subtracting 19 from both sides, we get n + 19 - 19 = 32 - 19
n = 13
Summarizing our word problem, we see that 19 quarters and 13 nickels adds up to $5.40
The component form of vector vec w is vec w =(-25,10); Find- 1 5 vec w
Answer:
Let’s take a point each on the x, y, and z-axis as follows:
A (1, 0, 0) on x-axis
B (0, 1, 0) on y-axis and
C (0, 0, 1) on z-axis
unit vector
So, we have
|OA→| = 1 , |OB→| = 1, and |OC→| = 1
These vectors OA→, OB→, and OC→, each having magnitude 1 are Unit Vectors along the axes OX, OY, and OZ respectively. They are denoted by i⃗ , j⃗ , and k⃗ as shown in Fig. 1 above.
Step-by-step explanation:
expand the following 8(x-3)
Answer:
8x-24
Step-by-step explanation:
First you do:
8×x which is 8x
Then you do:
8×-3 which is -24
Then you put it into 1 expression:
8x-24
Answer:
8−24
Thank You!
David plays baseball 18 times each month for 3 months. He also plays soccer 15 times each month for 3 months. How many more times does he play baseball than soccer each month?
Plzz help asp
Answer:
3
Step-by-step explanation:
3 months baseball = 18 x 3 = 54
3 months soccer = 15 x 3 = 45
54-45 = 9
9 / 3 = 3
David plays baseball 3 more times than soccer each month.
David plays 3 more times baseball than soccer each month.
What is ratio?Ratio basically compares quantities, that means it shows the value of one quantity with respect to the other quantity.
If a and b are two values, their ratio will be a:b,
Given that,
David plays baseball for 3 months, and each month he plays 18 times.
Also, David plays soccer for 3 months, and each month he plays 15 times.
In 3 months, David plays baseball = 18 x 3 = 54
Also, in 3 months, David plays soccer = 15 x 3 = 45
The more number of times David plays baseball than soccer
= 54 - 45
= 9
In 3 months, David plays 9 more times baseball than soccer.
In one month, David plays 9/3 = 3 more times baseball than soccer.
3 more times David plays baseball than soccer each month.
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Describe how to determine the average rate of change between x = 2 and x = 5 for the function f(x) = 2x3 + 4. Include the average rate of change in your answer.
For this item, complete the choice matrix by clicking the appropriate answer in each row.
Determine whether each unit rate is equivalent or not equivalent to
Equivalent
Not Equivalent
the unit rate, in inches per year, of growing inch in Ğ of a year
the unit rate, in lessons per hour, of finishing of a lesson in hours
the unit rate, in miles per hour, of jogging 1/8 mile in 3/8 hour
Step-by-step explanation:
1/2 inch in 2/3 of a year
1/2 / 2/3 = 1/2 × 3/2 = 3/4
NOT equivalent.
4/9 lesson in 4/3 of an hour
4/9 / 4/3 = 4/9 × 3/4 = 12/36 = 1/3
Equivalent.
1/8 mile in 3/8 of an hour.
1/8 / 3/8 = 1/8 × 8/3 = 8/24 = 1/3
Equivalent.
Write an equation in slope-intercept form for the line with slope 6 and y-intercept -3
Answer:
y = 6x - 3
Step-by-step explanation:
Using the following image, solve the problems below given that M is the midpoint of VW.
If you are using a screen-reader, please consult your instructor for assistance.Using your setup, what are the values of x, VM, MW, and VW?
The midpoint of a line segment divides the line segment into equal halves.
The value of x is 4The value of VM and MW is 15The value of VW is 30Point M is the midpoint of line segment VW.
So, we have:
[tex]VM = MW[/tex]
Substitute known values
[tex]4x - 1= 3x+3[/tex]
Collect like terms
[tex]4x - 3x = 1 + 3[/tex]
Evaluate like terms
[tex]x = 4[/tex]
Hence, the value of x is 4
The expression for VM is:
[tex]VM = 4x - 1[/tex]
So, we have:
[tex]VM = 4(4) - 1[/tex]
[tex]VM = 15[/tex]
Hence, the value of VM and MW is 15
The length of VW is the sum of both lengths.
So, we have:
[tex]VW = 15 + 15[/tex]
[tex]VW = 30[/tex]
Hence, the value of VW is 30
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