Amount of the job done after 2 hours:
2(1/6 + 1/8)
2(4/24 + 3/24)
2(7/24)
7/12 (amount of job finished)
.
amount of job left to do:
1 - 7/12
12/12 - 7/12
5/12 (remaining)
.
Let x = time (hours) slower press takes to finish job
then
x(1/6) = 5/12
multiplying both sides by 6:
x = 5/12 *6
x = 5/2 hours
or
x = 2 hours and 30 minutes
The slower press (8-hour press), will take h 3 hours, 20 minutes to complete the job
If f(x)=5x-12, find a value for $x$ so that f^{-1}(x)=f(x+1).
Answer:
[tex]\boxed{\sf \ \ \ x=\dfrac{47}{24} \ \ \ }[/tex]
Step-by-step explanation:
Hello,
f(x)=5x-12
we need to find x so that
[tex]f^{-1}(x)=f(x+1)[/tex]
so first of all we can write
[tex]x = (fof^{-1})(x)=f(f^{-1}(x))=5f^{-1}(x)-12\\\\<=>5f^{-1}(x)=x+12\\\\<=>f^{-1}(x)=\dfrac{x+12}{5}[/tex]
and f(x+1) = 5(x+1) - 12 = 5x + 5 -12 = 5x - 7
then solving
[tex]f^{-1}(x)=f(x+1)[/tex]
is equivalent to
[tex]\dfrac{x+12}{5}=5x-7 \ multiply \ by \ 5 \\\\<=> x+12 = 5(5x-7)=25x-35\\<=> 25x-x=12+35\\\\<=>24x=47\\\\<=>x=\dfrac{47}{24}[/tex]
Hope this helps
Answer:
Step-by-step explanation:
let f(x)=y
y=5x-12
flip x and y
x=5y-12
5y=x+12
[tex]y=\frac{x+12}{5} \\or \\f^{-1}(x)=\frac{x+12}{5} \\f(x+1)=5(x+1)-12=5x-7\\\frac{x+12}{5} =5x-7\\x+12=25x-35\\25~x-x=12+35\\24 x=47\\x=\frac{47}{24}[/tex]
Perform the required operationson the following functions.
Given: f(x) = 3 - x; g(x) = -2x
Find g[f(x)]
2x-6
2x+3
-x-6
Answer:
2x-6
Step-by-step explanation:
g[f(x)]
g(3-x)
-2x(3-x)
2[tex]x^{2}[/tex]-6x
2x-6
Which points are solutions to the system of inequalities shown below? Check all that apply!
Answer:
y>x+4 (A,B)
y≤3x (B,C,D,E,F)
x≥7(A,B,D)
i realllyyyyyyyy HOPE THIS HELPS YOUUU!!!
The graph of the function f(x) = log5 (x) is stretched vertically by a factor of 2, shifted to the left by 8 units, and shifted up
by 3 units.
Find the equation of the function g(x) described above.
Answer:
We start with y = g(x) = f(x)
First, we have a vertical stretch by a factor of 2.
A vertical strech by a factor of A will be g(x) = A*f(x)
then in this case A = 2, so we have g(x) = 2*f(x)
Now we have it shifted left by 8 units.
We know that f(x - A) shift right the graph by A units (A positive), here A = 8.
then we have: g(x) = 2*f(x - 8)
Now we want shift up 3 units, if we have y = f(x) we can shift the graph up by A units as: y = g(x) + A (for A positive)
Then we have: g(x) = 2*f(x - 8) + 3
now, our function was f(x) = Log₅(x)
then g(x) = 2*log₅(x - 8) + 3.
Answer:
g(x)=2log5(x+4)−8
Step-by-step explanation:
A dump truck has a 10 foot bed. When tilted at its maximum angle, the bed reaches a height of 7 feet above it original position. What is the maximum angle that the truck bed can tilt?
Answer:
Step-by-step explanation:
There are 360 different orders or permutations in which 4 pens can be chosen from the box of 6 different colored pens.
To find the number of permutations of picking 4 pens from a box of 6 different colored pens, we can use the formula for permutations. The formula for permutations is given by:
P(n, r) = n! / (n - r)!
Where n is the total number of items and r is the number of items to be chosen.
In this case, we have 6 different colored pens in the box and we want to choose 4 pens. Plugging these values into the formula, we get:
P(6, 4) = 6! / (6 - 4)!
= 6! / 2!
= (6 × 5 × 4 × 3 × 2 × 1) / (2 × 1)
= 720 / 2
= 360
Therefore, there are 360 different orders or permutations in which 4 pens can be chosen from the box of 6 different colored pens.
Learn more about permutations here: brainly.com/question/3867157
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A rectangle is 1 inch longer than it is wide. Its diagonal is 5 inches. What's the width of the rectangle?
Answer:
The width is 4 inches
Step-by-step explanation:
Represent the length and width by L and W respectively. Then L = W + 1.
According to the Pythagorean Theorem, the diagonal length is
D = sqrt( [W]^2 + [W + 1}^2 ) = 5, or [W]^2 + [W + 1}^2 = 25.
Then W^2 + W^2 + 2W + 1 = 25, and 2W^2 + 2W - 24 = 0.
Reducing, we get W^2 + W - 12 = 0, or (W + 4)(W - 4) = 0. Then W - 4 = 0, and W (the width) is 4. Then L = 5.
The width is 4 inches.
PLEASE i really need help I am terrible at this I WILL GIVE TEN EXTRA POINTS AND BRAINLIEST
Help me ASAP for this question Sean buys a binder for $12. If tax is 8%, what is the total cost of the binder?
$12.96 $13 $12.80 $12.08
Answer:
The cost of the binder is 12.96
Step-by-step explanation:
can i get help filling out the blanks
Answer:
The six raw digits are 14,15,15,15,16,16
Step-by-step explanation:
please I need help with this can anyone help me out
Answer:
x=110.6
Step-by-step explanation:
sine = opposite/hypotenuse
sin(19) = 36/x
Since we're trying to find x, you have to isolate it.
x = 36/sin(19)
Plug 36/sin(19) into a calculator and you will get 110.5759255
The question tells you to round to the nearest tenth so the answer is 110.6
Find the indicated probability. Round to the nearest thousandth.
A study conducted at a certain college shows that 55% of the school's graduates find a job in their chosen field within a year after graduation. Find
the probability that among 7 randomly selected graduates, at least one finds a job in his or her chosen field within a year of graduating.
0.985
0.996
0.550
0.143
Answer:
[tex]P(At\ least\ 1) = 0.985[/tex]
Step-by-step explanation:
Given
Proportion = 55%
Required
Probability that at least one out of 7 selected finds a job
Let the proportion of students that finds job be represented with p
[tex]p = 55\%[/tex]
Convert to decimal
[tex]p = 0.55[/tex]
Let the proportion of students that do not find job be represented with q
Such that;
[tex]p + q = 1[/tex]
Make q the subject of formula
[tex]q = 1 - p[/tex]
[tex]q = 1 - 0.55[/tex]
[tex]q = 0.45[/tex]
In probability; opposite probabilities add up to 1;
In this case;
Probability of none getting a job + Probability of at least 1 getting a job = 1
Represent Probability of none getting a job with P(none)
Represent Probability of at least 1 getting a job with P(At least 1)
So;
[tex]P(none) + P(At\ least\ 1) = 1[/tex]
Solving for the probability of none getting a job using binomial expansion
[tex](p + q)^n = ^nC_0p^nq^0 + ^nC_1p^{n-1}q^1 +.....+^nC_np^0q^n[/tex]
Where [tex]^nC_r = \frac{n!}{(n-r)!r!}[/tex] and n = 7; i.e. total number of graduates
For none to get a job, means 0 graduate got a job;
So, we set r to 0 (r = 0)
The probability becomes
[tex]P(none) = ^nC_0p^nq^0[/tex]
Substitute 7 for n
[tex]P(none) = \frac{7!}{(7-0)!0!} * p^7 * q^0[/tex]
[tex]P(none) = \frac{7!}{7!0!} * p^7 * q^0[/tex]
[tex]P(none) = \frac{7!}{7! * 1} * p^7 * q^0[/tex]
[tex]P(none) = 1 * p^7 * q^0[/tex]
Substitute [tex]p = 0.55[/tex] and [tex]q = 0.45[/tex]
[tex]P(none) = 1 * 0.55^7 * 0,45^0[/tex]
[tex]P(none) = 0.01522435234[/tex]
Recall that
[tex]P(none) + P(At\ least\ 1) = 1[/tex]
Substitute [tex]P(none) = 0.01522435234[/tex]
[tex]0.01522435234+ P(At\ least\ 1) = 1[/tex]
Make P(At least 1) the subject of formula
[tex]P(At\ least\ 1) = 1 - 0.01522435234[/tex]
[tex]P(At\ least\ 1) = 0.98477564766[/tex]
[tex]P(At\ least\ 1) = 0.985[/tex] (Approximated)
Dan is 60 years old. He is married and has children. He is starting to experience problems
with his eyes and having other age-related health issues. He wants a health insurance policy.
Which policy is best for him?
Policy A Policy B Policy C Policy D
Medical premium per month
$500 $510 $580 $530
Dental premium per month $25 Not covered $28
$20
Vision premium per month Not covered $20 Not covered $30
Co-payment
None
$50
$20 None
Deductible
$2000 $2000 $1800 $1900
policy a? policy b? policy c? or policy d?
Answer:
policy d
Step-by-step explanation:
he must have health and vision coverage.
this leaves us with option b and option d
when you add the total amount he gets and needs to pay for each of B and D, you'll find that D is more generous.
thus, I think the option he should choose is d
Factor the trinomial and enter the factorization below. Write each factor as a
polynomial in descending order.
x^2+6x-27
Answer:
( x - 3 )( x + 9 )
Step-by-step explanation:
The first thing we want to do here is to break the expression into groups. This will help us factor out common terms, that will later be grouped - our resulting, factored expression.
x² + 6x - 27 - Break the expression into groups,
( x² - 3x ) + ( 9x - 27 ) - Factor out x from the expression " x² - 3x. " Respectively factor out 9 from the expression " 9x - 27. "
x( x - 3 ) + 9( x - 3 ) - Now this contains the shared expression " x - 3, " and hence can be broken down further through grouping.
Factored Expression: ( x - 3 )( x + 9 )
Tanya is considering obtaining a loan. Which benefit will Tanya receive if she makes a down payment when she obtains the loan?
A. higher finance charge
B. higher interest rate
C. higher principal amount
D.lower penalties on late payments
O E.
lower principal amount
Answer:
E. lower principal amount
Step-by-step explanation:
We can use an example to show how this works:
You want to buy a car and it costs $20,000. The loan lasts 5 years (60 monthly payments) and the interest rate is 10%.
If you do not make any down payment, your initial principal will be $20,000, and your monthly payment will be $424.94, your total payments = $25,496.45 and the total interests = $5,496.45.
Instead, if you make a 20% down payment, your initial principal = $16,000, and your monthly payment will be $339.95, your total payments = $20,397.16 and the total interests = $4,397.16.
Answer:
E. lower principal amount
A square has a length of 13m, find its area A. 1699m² B. 169m² C. 196m² D. 169m² I will mark you as brainliest
Answer: 169 m²
Step-by-step explanation:
The area of a square can be found by taking a side length(13), and squaring it, to get, in this case, 139.
Hope it helps <3
Answer:
169 m²
Step-by-step explanation:
To find the area of a square, we can apply a formula.
[tex]A=s^2[/tex]
[tex]A=area[/tex]
[tex]s=side \: length[/tex]
The side length is given 13 meters.
[tex]A=13^2[/tex]
Solve for [tex]A[/tex].
[tex]A=13 \times 13[/tex]
[tex]A=169[/tex]
The area of the square is 169 meters squared.
IM TIMED Find an ordered pair that represents the vector from (-3.7,2) to (-4, -5).
a.
(-7.7,-3)
c.
(1.3,7)
b.
(-0.3,-7)
d.
(7.7,3)
Answer:
<-0.3, -7>
Step-by-step explanation:
Re: a vector from (-3.7,2) to (-4, -5).
This has two components: a horizontal one and a vertical one.
The horizontal component is -4 - (-3.7) = -0.3.
The vertical component is -5 - 2 = -7
Thus, the desired vector is <-0.3, -7>
Answer:
B on edge
Step-by-step explanation:
got it right (2021)
Which equation has a graph that is perpendicular to the graph of 4x - 2y = 1?
Select one:
O a. y = -2x + 8
O b. 6x - 3y = 9
O c. 2x + 4y = -1
Answer:
C
Step-by-step explanation:
2 is the opposite of -1/2, so reciprocals line up for perpendicularity
*HURRY PLEASE ANSWER* Richard is asked to spray wash the exterior of a building that is shaped like a cube. He decides to calculate the surface area of the building in order to estimate how much water he will need. He does the calculation using the standard formula and, after doing the job, realizes he overestimated the amount of water he needed. Where was his mistake? a.) He forgot that there is no formula for the surface area of a cube. b.) He forgot to add the area of the base to the total surface are of the cube. c.) He forgot to square the result. d.) He forgot to subtract the area of the base from the total surface area of the cube.
Answer:
D. He forgot to subtract the area of the base from the total surface area of the cube.
Step-by-step explanation:
He is only spray washing the *exterior* of the building; the base is not exposed so it will not be spray washed, which means Richard can use less water.
Hope this helps. :)
Answer:
D
Step-by-step explanation:
Each group of students receives a bag that has 9 red cubes, 5 green cubes, and 11 blue cubes. If each group makes 1000 pulls and replaces the cube after each pull, how many times would you expect them to draw a blue cube?
Answer:
440 times
Step-by-step explanation:
First you need to find the total number of cubes each student recieves (25)
Now you put it into a ratio 11 : 25
After that make another ratio with 1000 and solve for x
x : 1000
25x = 11000
x = 440
Answer:
440 blues
Step-by-step explanation:
9 red cubes, 5 green cubes, and 11 blue cubes = 25 cubes total
P( blue) = 11/25
To find out how many blue cubes are expected, take the probability and multiply by the number of draws
11/25 * 1000 draws
440 blues
What is the domain and range of each relation?
Drag the answer into the box to match each relation.
A relation mapping diagram. Element x contains negative 2, 0, 2, and 4. Element y contains negative 3, negative 1, and 0. Negative 2 maps to negative 3 and negative 1. Zero maps to 0. Two maps to 0. Four maps to negative 3.
Points plotted on a coordinate plane. The horizontal x-axis ranges from negative 5 to 5 in increments of 1. The vertical y-axis ranges from negative 5 to 5 in increments of 1. Five points are plotted. Begin ordered pair negative 3 comma 1 end ordered pair. Begin ordered pair negative 1 comma negative 1 end ordered pair. Begin ordered pair 0 comma 0 end ordered pair. Begin ordered pair 3 comma 2 end ordered pair. Begin ordered pair 3 comma 3 end ordered pair.
Answer:
[tex]\text{Domain of}R_1=\{-2,0,2,4\}[/tex] and [tex]\text{Range of}R_1=\{-3,-1,0\}[/tex]
[tex]\text{Domain of}R_2=\{-3,-1,0,3\}[/tex] and [tex]\text{Range of}R_2=\{-1,0,1,2,3\}[/tex]
Step-by-step explanation:
Domain is the set of input values or x-values.
Range is the set of output values or y-values.
According to the relation mapping diagram, the relation is
[tex]R_1=\{(-2,-3),(-2,-1),(0,0),(2,0),(4,-3)\}[/tex]
So,
[tex]\text{Domain of}R_1=\{-2,0,2,4\}[/tex]
[tex]\text{Range of}R_1=\{-3,-1,0\}[/tex]
In the graph 5 points are plotted. So, the relation is
[tex]R_2=\{(-3,1),(-1,-1),(0,0),(3,2),(3,3)\}[/tex]
So,
[tex]\text{Domain of}R_2=\{-3,-1,0,3\}[/tex]
[tex]\text{Range of}R_2=\{-1,0,1,2,3\}[/tex]
Please help I will mark brainliest for correct answers!
Answer:
D. 57
Step-by-step explanation:
Q2=42
Q3=57
Right isosceles triangles are constructed on the sides of a3−4−5 right triangle, as shown. A capital letter represents the area of each triangle. What is X+Y /z
Answer:
(X + Y)/Z = 1
Step-by-step explanation:
Given the leg sides of the isosceles right triangles as 4, 5, and 3, we have
Length of the other leg sides of the isosceles triangle = Length of the given leg side sizes
Therefore, the respective height and base of each right angled isosceles triangle are equal which gives the areas as follows;
Z = 1/2*5*5 = 12.5 unit²
Y = 1/2*4*4 = 8 unit²
X = 1/2*3*3 = 4.5 unit²
W = 1/2*4*3 = 6 unit²
(X + Y)/Z = (4.5 + 8)/12.5 = 12.5/12.5 = 1.
Identify if the sequence is arithmetic or geometric. Then find the next number in the sequence. -3, 9, -27, 81, ...
Answer:
-243
Step-by-step explanation:
To solve this problem you will need to know the difference between an arithmetic and a geometric.
An arithmetic is a sequence where a person is adding the same number over and over again so lets say you start with 1 and the common difference (the number being added each time) is 2, the sequence will look something like this 1, 3, 5, 7, 9 and so on.
A geometric sequence is when the same number is being multiplied over and over again. So lets say that the number we start with is 2 and you are multiplying by three every single time, so you would get a sequence looking like this 2, 6, 18, 54 and so on.
We can see in the sequence that the number that is being multiplied over and over again is -3 so the answer is a geometric sequence.
Now that we know that it is a geometric sequence we will multiply the last number which is 81 by -3 which will get us -243
Answer:
To solve this problem you will need to know the difference between an arithmetic and a geometric.
An arithmetic is a sequence where a person is adding the same number over and over again so lets say you start with 1 and the common difference (the number being added each time) is 2, the sequence will look something like this 1, 3, 5, 7, 9 and so on.
A geometric sequence is when the same number is being multiplied over and over again. So lets say that the number we start with is 2 and you are multiplying by three every single time, so you would get a sequence looking like this 2, 6, 18, 54 and so on.
We can see in the sequence that the number that is being multiplied over and over again is -3 so the answer is a geometric sequence.
Now that we know that it is a geometric sequence we will multiply the last number which is 81 by -3 which will get us -243
Step-by-step explanation:
What is the measure of ACE in the diagram below?
A. 46
B. 104
C. 29
D. 58
Answer:
C
Step-by-step explanation:
The secant- secant angle ACE is half the difference of the measures of the intercepted arcs, that is
∠ ACE = [tex]\frac{1}{2}[/tex] (AE - BD ) = [tex]\frac{1}{2}[/tex] (104 - 46)° = [tex]\frac{1}{2}[/tex] × 58° = 29° → C
ASAP 25 POINTS NEED TO KNOW NOW PLEASE
Variable x is 7 more than variable y Variable x is also 1 less than y. Which of the following pairs of equations best models the relationship between x and y?
A:x= 11
X = y + 7
B:X= y + 7
X = y - 1
C:y = x + 8
y=x-1
D:y = 7x
y = x + 1
Answer:
x = y+7
x = y -1
Step-by-step explanation:
Variable x is 7 more than variable y
is means equals
x = y+7
Variable x is also 1 less than y
x = y -1
Which number is a rational number?
Answer:
[tex]\boxed{17.156}[/tex]
Step-by-step explanation:
A rational number can be written in the form p/q, where p and q are whole integers.
[tex]\sqrt{15} \approx 3.87298334621...\neq \frac{p}{q}[/tex]
[tex]2.6457513110... \neq \frac{p}{q}[/tex]
[tex]17.156=\frac{4289}{250}[/tex]
[tex]\sqrt[3]{85} \approx 4.39682967216... \neq \frac{p}{q}[/tex]
17.156 is a rational number.
A car travels at a speed of 41 meters/second using 756 joules of energy every second. Suppose we know that the car uses 52,700 joules of energy. Set up a calculation to find the number of meters the car travels with this amount of energy. Perform the calculation you set up in part A. Round your answer to the nearest whole number? What is The car will travel ??? meters using 52,700 joules of energy.
The car will travel 2858meters.
What is speed?Speed is the rate of change of distance.
Analysis:
speed of car = 41m/s
Energy consumption rate of engine = 756 joules/second
Time taken to consume 52700 joules = 52700/756.
If it travels at 41m/s for 52700/756 seconds, then the distance covered = 41 x 52700/756 = 2858 meters.
Learn more about speed: brainly.com/question/4931057
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Answer:
2900
Step-by-step explanation:
.
The vertex of the parabola is it 3,-2 when the xvalue is 4 the yvalue is 3 what is the coefficient of the squared term in the parabola equation
Answer:
5 = a
Step-by-step explanation:
Use the model y - k = a(x - h)^2, where (h, k) represents the vertex. Here we have:
y + 2 = a(x - 3)^2
Now substitute 4 for x and 3 for y:
3 + 2 = a(4 - 1)^2, or 5 = a
Using what you know about angles and translations, find all of the angle
measures in the image below.
.
<1 = 135°
<2 =
<3 =
<4 =
<5 =
<6 =
<7 =
<8 =
Explain how you found the measure of <8.
Answer:
angle 8 is the same as angle 1.
Step-by-step explanation:
opposite side exterior angles are congruent
Answer:
2=45, 3=45, 4=135, 5=135, 6=45, 7=135, 8=135
Step-by-step explanation:
Assuming that these lines are parallel, alternate interior angles are supplementary and alternate exterior angles are also supplementary. So, we know that 1=135 so that means we can do 180-135=45 so 2=45. 1 and 4 are equal to each other because of the vertical angle theorem. So every angle is either 45 degrees or 135 degrees. So:
2=3=6=7
1=4=5=8
You can use the theorems to figure out which angles are congruent and which angles are supplementary in a transversal.
I hope this makes sense
i really need this can someone help solve asap!!!
Answer: to find this answer .we need to do pegothogs property
Step-by-step explanation:
30° + 90° = 90 (because it is right angle )
120° - 90° = 30°
Plz mark me as brainlist
thank you :-)