Answer:
5
Step-by-step explanation:
divide.
What is the inverse of this function? f(x)=1/3x-2
The inverse of the function f(x) = 1/3x-2 is f^-1(x) = (1 + 2x)/3x.
Inverse of a functionA function f is has an inverse if it is both one-to-one and onto.
Given the function f(x) = 1/3x-2
we replace f(x) with y and make x the subject of the formula to derive the inverse function f^-1(x) as follows ;
y = 1/3x - 2
by cross multiplication
3x - 2 = 1/y
add 2 to both sides of the equation
3x = 1/y + 2
3x = (1 + 2y)/y
divide both sides of the equation by 3
x = (1 + 2y)/y ÷ 3
x = (1 + 2y)/3y
So, f^-1(x) = (1 + 2x)/3x
Therefore, the inverse of the function f is derived by interchanging the value of x for y and vice versa, that is f^-1(x) = (1 + 2x)/3x.
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Ahmad decided to increase his homework time of 8 hours per week by 15%,
Calculate his new homework time.
Give your answer in hours and minutes.
Answer:
it's a answer done bro
Which inequality has like variable terms on each side of the inequality symbol?
Inequality which have like variables term on each side of the given inequality symbol is given by 16 - 2x > x + 16.
As given in the question,
Inequality which have like variables term on each side of the given inequality symbol is :
a. 15c + 25 ≤ 115
In the given inequality, on left hand side we have variable c and constant term while on the right hand side of the inequality only constant.
Not correct option.
b. 0.75r - 6.25 > 10
In the given inequality, on left hand side we have variable r and constant term while on the right hand side of the inequality only constant.
Not correct option.
c. 16 - 2x > x + 16
In the given inequality, on left hand side we have variable x and constant term while on the right hand side of the inequality also variable x and constant term.
Correct option.
d. 12.25h -175 < 5,000
In the given inequality, on left hand side we have variable h and constant term while on the right hand side of the inequality only constant.
Not correct option.
Therefore, inequality which have like variables term on each side of the given inequality symbol is given by 16 - 2x > x + 16.
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An investor invested a total of $2,900 in two mutual funds. One fund eamed a 7% profit while the other eamed a 3% profit. If the investor's total profit was $143, how much was invested in each mutual fund?
Answer:
one is 203
two is 87
Step-by-step explanation:
Solve the equation for x. Show each step of the solution for full credit. (3 points - 2 points showing work, 1 point correct answer)
3.5(x +2) = 17
Answer:2.86
Step-by-step explanation:
3.5(x +2) = 17
3.5x + 7 = 17
3.5x =17 - 7
3.5x =10
x = 10/3.5
x = 2.86
Sofia is 38 years old. Write an equation that relates Sofia's age to Tony's age, t. How old is Tony?
(Sofia’s age is 2 times the combined ages of Carlos and Lily - Carlos’s age is 4 more years than Tony’s age - and Lily’s age is one more than 6 times Tony’s age)
Answer:
Let s, c, y and t represent the ages of Sofia, Carlos, Lily and Tony respectively.
c + y = 2s ------ equation (1)
t + 4 = c ------ equation (2)
6t + 1 = y ------ equation (3)
Since Sofia is 38 years old, substitute s = 38 into equation (1):
c + y = 2(38)
= 76 ------ equation (4)
Substitute equations (2) and (3) into equation (4):
t + 4 + 6t + 1 = 76
7t + 5 = 76
7t = 71
∴ t = 10 (to the nearest whole number)
∴Tony is 10 years old (to the nearest whole number).
Type the correct answer in the box. use numerals instead of words. the weight of a bag of golf balls varies directly as the number of golf balls in the bag. if a bag of 69 golf balls weighs 2,553 grams, how many golf balls are in a bag that weighs 1,110 grams? number of golf balls:
A total of 30 golf balls are there in the bag that weighs 1110 grams.
A total of 69 golf balls weights 2553 grams in a bag.
It is asked that how much golf balls does make 1110 grams of weight.
Let us say that the weight of one ball is X.
So, Using unitary method,
We can write,
69 times mass of one golf ball = 2553 grams.
69X = 2553
X = 2553/69
X = 37 grams.
Hence, the weight of one ball is 37 grams.
Now, let us say that Y balls weights 1110 grams,
So, we can write,
Y time weight of one ball = 1110
37Y = 1110
Y = 1110/37
Y = 30.
Hence, 30 golf balls will weight 1110 grams.
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Answer:
30
Step-by-step explanation:
Nick and Pam are paid $52.25 for their work. Nick worked 3.5 Hours, and Pam worked two hours. They split the money according to the amount of time each of them worked how much is Nick share of the money. Nick and Pam are paid ?
Nick got a total of $33.25 for his part of work.
What is the general equation of a Straight line? How it represents a proportional relationship?
The general equation of a straight line is -
[y] = [m]x + [c]
where -
[m] is slope of line which tells the unit rate of change of [y] with respect to [x].
[c] is the y - intercept i.e. the point where the graph cuts the [y] axis.
y = mx also represents direct proportionality. We can write [m] as -
m = y/x
OR
y₁/x₁ = y₂/x₂
We have Nick and Pam are paid $52.25 for their work. Nick worked 3.5 Hours, and Pam worked two hours. They split the money according to the amount of time each of them worked.
Assume that Nick recieved $[x]. Then, Pam will get - (52.25 - x). For direct proportionality -
y₁/x₁ = y₂/x₂
We can write -
x/3.5 = (52.25 - x)/2
2x = 3.5(52.25 - x)
2x = 182.875 - 3.5x
x = 33.25
Therefore, Nick got a total of $33.25 for his part of work.
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7. What number multiplied by 2/3 has a product
of 1? (Example 2) it's saying 4/6 is wrong what do i do
Answer:
3/2
Step-by-step explanation:
To multiply fraction×fraction, you multiply top×top and bottom×bottom.
2/3 × 3/2
= 6/6
= 1
The 3/2 is called the reciprocal. Take the number in the problem and flip it over to find the reciprocal.
helen buys two pineapples she pays with a £5 note and gets £3.60 change work out the cost of one pineapple
Answer:
Each pineapple costs £0.70.
Step-by-step explanation:
Let P be the number of pineapples Helen purchased and C the cost per pineapple, in £.
Helen's total cost would be: P*C = total cost.
The total cost is the difference between £5 and £3.60, which is £1.40.
We are given P (the number of pineapples, 2) and the total cost (£1.40) , so enter those numbers in the equation:
P*C = total cost
2*C = £1.40
C = £0.70
a box has a width of 15 inches and a length of 16 inches. the volume of the box is increasing at a rate of 569 cubic inches per second, with the width and length being held constant. what is the rate of change, in inches per second, of the height when the height is 6 inches?
The rate of change in height when height is 6 inches is 2.37 inches per second approximately.
We know that the volume of cube with length L, width W and height H is given by,
V = L*B*H
So given that the length is 15 inches
the width is 16 inches
Let the height be h inches.
So now the volume is given by,
V = 15*16*h
Differentiating the volume with respect to time 't' we get,
dV/dt = 15*16 dh/dt
Now given that the rate of change in volume per second is 569 cubic inches.
So, dV/dt = 569
So, 15*16 dh/dt = 569
dh/dt = 569/(15*16) = 569/240 = 2.37 (approx)
So the rate of change in height is 2.37 inches approximately.
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the recursive formula for the height above the ground on the nth step of the stairs show is an=an-1+4 with a1=7 what explicit formula finds the height above the ground of the nth step?
The explicit formula is a_n = 3+4n
From the question, we have
a1 = 7
We know that,
a_n = a_1 +(n-1)d
a_n = 7 +(n-1)4
a_n = 7+4n-4
a_n = 3+4n
Subtraction:
Subtraction represents the operation of removing objects from a collection. The minus sign signifies subtraction −. For example, there are nine oranges arranged as a stack (as shown in the above figure), out of which four oranges are transferred to a basket, then there will be 9 – 4 oranges left in the stack, i.e. five oranges. Therefore, the difference between 9 and 4 is 5, i.e., 9 − 4 = 5. Subtraction is not only applied to natural numbers but also can be incorporated for different types of numbers.
The letter "-" stands for subtraction. Minuend, subtrahend, and difference are the three numerical components that make up the subtraction operation. A minuend is the first number in a subtraction process and is the number from which we subtract another integer in a subtraction phrase.
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how many ways can 7 students be assigned a seat in a classroom if there are 10 seats in a row? a) 70 b) 604,800 c) 120 d) 3,628,800 e) 17 f) none of the above.
The correct option c) 120; for the assignment of 7 students to 10 seats in a row.
What is referred as the combination?Combinations are mathematical techniques that count the number of potential arrangements for a set of elements only when order of the selections is irrelevant. You can choose the constituents of combos in any order.The procedure for determining how many arrangements are feasible when only a few items are selected from a set of items that are unique is as follows:The formula for finding the combination is-
ⁿCₓ = n!/ x!(n - x)!
Where,
n = total value.x = selected valueFor the given question.
Total students to be assigned a seat = 7.
Total seats in a classroom = 10.
Thus, Applying combination;
¹⁰C₇ = 10!/7!(10 - 7)!
¹⁰C₇ = 120
Thus, if there are 10 seats in a row, there are 120 different ways that 7 students could be seated in a classroom.
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what 29,000 divided by 50,000
Answer:
.58
Step-by-step explanation:
Find the slope of the line passing through the points (4, -2) and (9, -2).
slope:
Find the slope of the line passing through the points (2, 9) and (2, - 7).
slope:
Answer:
x1 y1 x2 y2
1. 0 - explanation - (4, -2) (9, -2) -2 - -2
4 - 9 (put a fraction bar when you put the y2 and y1 together and put the x2 and y2 in the denominator spot) basically -2 subtract -2 equals 0
2. it would be defined or 0
Which ordered pair is NOT a solution to the equation y = 2x? Four points plotted on a coordinate plane. Point A has coordinates 1 comma 2. Point B has coordinates 2 comma 4. Point C has coordinates 3 comma 8. Point D has coordinates 5 comma 10. point A point B point C point D
Point C (3,8) is the required ordered pair that is not the solution of the given equation. Option C is correct.
Given that,
To determine which ordered pair is NOT a solution to the equation y = 2x.
Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.
Here,
Given relation y = 2x
Now substitute every value of x from the ordered pair and match the output with the corresponding value of the ordered pair.
put x = 1, 2, 3, 5
Y = 2(1)
y = 2
Similarly the outcome of the values,
x = 2, 3, 5
y = 4, 6, 10
Thus, Point C (3,8) is the required ordered pair that is not the solution of the given equation. Option C is correct.
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what is the best point estimate for the population's standard deviation if the sample variance is 49.7? round your answer to one decimal place, if necessary.
Using the relation between standard deviation and variance it is concluded that the standard deviation for the population for the given variance is 7.1
What is the relation between standard deviation and sample variance?In statistics, the two most crucial metrics are variance and standard deviation. While the variance is a measurement of how data points vary from the mean, standard deviation is a measure of the distribution of statistical data.
The square root of the variance yields the standard deviation, i.e.
Standard deviation = [tex]\sqrt{variance[/tex]
Given that sample, the variance is 49.7 and we have to calculate the standard deviation.
Standard deviation (σ) = [tex]\sqrt{variance[/tex]
= [tex]\sqrt{49.7}[/tex]
= 7.0498
=7.1
Hence, the standard deviation for the population for the given variance is 7.1
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Find two consecutive positive odd integers such that three times the sum of the largest number plus 22 is equal to the product of both numbers.
Answer:
Step-by-step explanation:
Let's say your consecutive numbers are A and B with A+2=B. Using the information we have been given, we can get the linear equation; AB=3B+22. A=B-2, so we can replace A with B-2 to get (B-2)(B)=3(B+22). Multiplying this out, we get B^2-2B=3B+66. Simplifying, we get B^2-5B-66=0. This is a quadratic equation. Using the quadratic formula, we get B=11,-6. B has to be positive, so B=11. A+2=11, so A=9
What is the value of y in the equation 2(2y − 16) = 0? (5 points)
a 4
b 6
c 8
d 9
Answer:
the options are wrong
Step-by-step explanation:
open the bracket2(2y)2(-16)=04y-32=0make y the subject of formulary=-32÷4y=-8Answer:
C. 8
Step-by-step explanation:
2 x 8 = 16
16 - 16 = 0
2 x 0 = 0
A famous piece of artwork was up for bid at a museum auction. The minimum bid was $25,000.
Determine which inequality represents the bid for the artwork.
b ≥ 25,000
b ≤ 25,000
b < 25,000
b > 25,000
The inequality that represents the bid for the artwork is A. b ≥ 25,000.
What is an inequality?Inequalities are created through the connection of two expressions. It should be noted that the expressions in an inequality aren't always equal. Inequalities implies that the expressions are not equal. They are denoted by the symbols ≥ < > ≤.
In this case, the famous piece of artwork was up for bid at a museum auction and the minimum bid was $25,000.
Let the minimum bid be b. This will be b ≥ 25,000.
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7.69 to the nearest whole number.
Answer: 8
Step-by-step explanation:
7.69 to the nearest whole number is 8
Write the equation of the line that is parallel to the line 14x - 2y = 51 and goes through the point(3, -11)
Mariyah wants to enlarge a triangle with sides of 3 inches, 6 inches, and 6 inches. If the shortest side of the new triangle is 13 inches, how long will the other two sides be?
The other sides of the new triangle are 13, 26 and 26 inches as calculated by the properties of similarity.
We know that when two triangles are similar then the ratio of the sides are also equal.
Let the original triangle be ΔABC and the new triangle be ΔXYZ
So from the property of similarity.
AB/XY = BC /YZ = CA/ ZX
Now it is given AB = 3 inches
XY = 13 inches
Hence AB/XY = 13/3
Hence YZ = 13 / 3 × 6 =26 inches
Again ZX = 26 inches
Similar triangles have parallel sides that are proportional to one another and parallel angles that are identical to one another.
Triangles can have different diameters despite having comparable exteriors. Triangles that are congruent and similar to each other usually don't match up.
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Can anyone answer question 8?
the two-way relative frequency table given shows the results from the lunch orders from an upperclassman picnic. 11th grade 12th grade total salad 12% 6% 18% sandwich 20% 24% 44% soup 8% 30% 38% total 40% 60% 100% a segmented bar chart was created showing the lunch preference by grade. what percentage would the bar for 11th graders show for preferring salad? 67% 40% 30%
The bar for 11th graders show 30% for preferring Salad.
Given, that the lunch orders from an upperclassman picnic.
11th Grade 12th Grade Total
Salad 12% 6% 18%
Sandwich 20% 24% 44%
Soup 8% 30% 38%
Total 40% 60% 100%
To find the relative frequency we divide the frequency by the total.
hence, to find the relative frequency for 11th graders preferring Salad
12/40 = 0.3 = 30%
Hence, the bar for 11th graders show 30% for preferring Salad.
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What do you need to multiply the subtotal by in order to get the total?
Given: Subtotal: 42.00
Total: 45.99
Tax rate: 9.5%
Sales tax: $3.99
Sutton takes 48 minutes to walk to work. after getting a new job, sutton takes 30.72 minutes to walk to work. what was the percent decrease in the travel time?
The percent decrease in the travel time after getting a new job is 36%.
Percentage is defined as part of a whole expressed in hundredths or out of 100. It is usually written with the symbol "%".
First, determine the decrease in travel time after getting a new job by subtracting the new travel time of 30.72 minutes from the initial travel time of 48 minutes.
decrease in time = 48 - 30.72
decrease in time = 17.28
Then, determine the percent decrease by dividing the decrease in time of 17.28 minutes by the initial travel time of 48 minutes and multiply by 100.
percent decrease = (17.28 / 48) x 100
percent decrease = 36%
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I need help asap… Is this relation a function or no ?
Answer:
Step-by-step explanation:
yes, it is a function
Answer: no
Step-by-step explanation: you have -2,-5 and -2,0 you cant have 2 or more x values that are the same.
if the probability of pulling a four of hearts from a randomly shuffled deck is 1 / 52, and the probability of pulling a spade from a randomly shuffled deck are 1 / 4, then the probability of pulling a spade or a four of hearts from a randomly shuffled deck is:
The probability of pulling a spade or a four of hearts is 0.264 .
we have , from a deck of cards
probability of pulling a spade = 1/4 = 13/52
probability of not pulling a spade 3/4 = 39/52
probability of pulling a 4 of hearts = 1/52
probability of not pulling a spade = 51/52
we have to find the probability of pulling a spade or a four of hearts from a random shuffled deck
So we can get three cases :
case A :
getting a spade and not getting four of hearts
∴ P (A) = [tex](\frac{13}{52} ) (\frac{51}{52} )[/tex] = 663/2704
case B :
not getting a spade and getting four of hearts
P(B) = [tex](\frac{39}{52}) (\frac{1}{52} )[/tex] = 39/2704
case C :
getting a spade and getting four of hearts
P(C) = [tex](\frac{13}{52})(\frac{1}{52} )[/tex] = 13/2704
therefore , the required probability will become
P = P(A) +P(B) + P(C)
P = 715/ 2704
P = 0.264
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a car travels 75 miles in the same amount of time that it takes another car, moving 10 mph faster that has traveled 100 miles. what is the number of miles per hour in the speed of the faster car?
The speed of the faster car is 40 miles/hr.
both cars travel for same time , so let that time be 't'
car 1 :
distance travelled = 75 miles
let the speed of the car be = x miles/hr
∴ time (t) = distance / speed
t = 75 / x .............(1)
car 2 :
distance travelled = 100 miles
speed of the car is = x + 10 miles/hr ( already provided )
∴ time ( t) = distance / speed
t = 100/ (x+10) ..............(2)
now as the time for both the cases is same , so we equate eqn (1) and eqn (2) .
∴ 75/x = 100/ (x+10)
3x + 30 = 4x
x = 30
so the speed of the 1st car will be 30 miles / hr
and the speed of the 2nd car ( faster car ) will be x + 10 = 40 miles/hr
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