Answer:
Step-by-step explanation:
Given
2^x [(x+1)³ -1] = 2^x - (x+1)³ + 1
Lep p = 2^x, and q = (x+1)³ - 1
Then the original equation becomes
pq = p - q
p - q - pq = 0
p(1 - q) - q = 0
p = q/(1 - q)
2^x = [(x+1)³ - 1]/[-(x+1)³]
2^x = [1 - (x+1)³]/[(x+1)³]
2^x = (x+1)^(-3) - 1
My town has two cell phone providers. The provider Don’tTalkMuch charge is $80 per month plus 1 dollar per hour the provider TalkLots charges $20 per month plus 4 dollars per hour how much do you have to use your phone in a month in order for Don’tTalkMuch’s much is a deal to be better for you?
Answer:
The author have to use his/her phone less than 20 hours in a month in order for Don’tTalkMuch's is a deal to be better than TalkLots's is.
Step-by-step explanation:
Call X is the number of hours that the author uses on monthly basis.
Total bill value if the author uses Don’tTalkMuch service is $80 + $1 X.
Total bill value if the author uses TalkLots service is $20 + $4X
The total fees between 2 providers equal as:
$80 + $1 X = $20 + $4X => 3X = $60 => X = 20
Hence: The author have to use his/her phone less than 20 hours in a month in order for Don’tTalkMuch's is a deal to be better than TalkLots's is.
Find the area of the shaded regions.
Answer:
7 pi cm^2 or approximately 21.98 cm^2
Step-by-step explanation:
First find the area of the large circle
A = pi r^2
A = pi 3^2
A = 9 pi
Then find the area of the small unshaded circle
A = pi r^2
A = pi (1)^2
A = pi
There are two of these circles
pi+ pi = 2 pi
Subtract the unshaded circles from the large circle
9pi - 2 pi
7 pi
If we approximate pi as 3.14
7(3.14) =21.98 cm^2
Answer:
[tex]\boxed{\sf 7\pi \ cm^2 \ or \ 21.99 \ cm^2 }[/tex]
Step-by-step explanation:
[tex]\sf Find \ the \ area \ of \ the \ two \ smaller \ circles.[/tex]
[tex]\sf{Area \ of \ a \ circle:} \: \pi r^2[/tex]
[tex]\sf r=radius \ of \ circle[/tex]
[tex]\sf There \ are \ two \ circles, \ so \ multiply \ the \ value \ by \ 2.[/tex]
[tex](2) \pi (1)^2[/tex]
[tex]2\pi[/tex]
[tex]\sf Find \ the \ area \ of \ the \ larger \ circle.[/tex]
[tex]\sf{Area \ of \ a \ circle:} \: \pi r^2[/tex]
[tex]\sf r=radius \ of \ circle[/tex]
[tex]\pi (3)^2[/tex]
[tex]9\pi[/tex]
[tex]\sf Subtract \ the \ areas \ of \ the \ two \ circles \ from \ the \ area \ of \ the \ larger \ circle.[/tex]
[tex]9\pi -2\pi[/tex]
[tex]7\pi[/tex]
The mouse weights (in grams) of a random sample of 100 mice involved in a nutrition experiment are: Interval 41.5----43.5 43.5-----45.5 45.5------47.5 47.5--------49.5 49.5--------51.5 51.5----53.5 53.5----55.5 55.5---- 57.5 57.5--------59.5 Frequency Interval 3 7 13 24 15 16 13 7 2Required:a. Find the mean of the weight of the mice. (Round to two decimal places.)b. Find the standard deviation of the weight of the mice. (Round to two decimal places.)
Answer:
(a) The mean of the weight of the mice is 50.26 grams.
(b) The standard deviation of the weight of the mice is 14.08 grams.
Step-by-step explanation:
(a)
The mean is given as follows:
[tex]\bar X=\frac{\sum f_{i}x_{i}}{\sum f_{i}}[/tex]
[tex]=\frac{5026}{100}\\\\=50.26[/tex]
Thus, the mean of the weight of the mice is 50.26 grams.
(b)
Compute the standard deviation as follows:
[tex]s=\frac{1}{\sum f_{i}-1}[\sum f_{i}x_{i}^{2}-\frac{1}{\sum f_{i}}(\sum f_{i}x_{i})^{2}][/tex]
[tex]=\frac{1}{100-1}[254001-\frac{1}{100}(5026)^{2}]\\\\=\frac{1}{99}\times 1394.24\\\\=14.08323\\\\\approx 14.08[/tex]
Thus, the standard deviation of the weight of the mice is 14.08 grams.
The rate at which an assembly line workers efficiency E (expressed as a percent) changes with respect to time t is given by E'(t) = 75 - 6t, where t is the number of hours since the workers shift began. Assuming that E(1) = 92, find E(t).
By the fundamental theorem of calculus,
[tex]E(t)=E(1)+\displaystyle\int_1^t E'(u)\,\mathrm du[/tex]
So we have
[tex]E(t)=92+\displaystyle\int_1^t(75-6u)\,\mathrm du[/tex]
[tex]E(t)=92+(75u-3u^2)\bigg|_1^t[/tex]
[tex]E(t)=20 + 75 t - 3 t^2[/tex]
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Calculator
Astrid is in charge of building a new fleet of ships. Each ship requires 40 tons of w
sailors. She receives a delivery of 4 tons of wood each day. The deliveries can con
afterwards the weather is too bad to allow them. Overall, she wants to build enou
least 2100 sailors.
How much wood does Astrid need to accommodate 2100 sailors?
tons
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This question is incomplete.
Complete Question
Astrid is in charge of building a new fleet of ships. Each ship requires 40 tons of wood, and accommodates 300 sailors. She receives a delivery of 4 tons of wood each day. The deliveries can continue for 100 days at most, afterwards the weather is too bad to allow them. Overall, she wants to build enough ships to accommodate at least 2100 sailors. How much wood does Astrid need to accommodate 2100 sailors?
Answer:
280 tons of wood.
Step-by-step explanation:
From the above question:
To make 1 ship = we require 40 tons of wood.
1 ship = can accommodate 300 sailors.
Step 1
If :
300 sailors = 1 ship
2100 sailors = y ships
Cross Multiply
300 × y ships = 1 ship × 2100 sailors
y ships = 2100 / 300
y ships = 7
Hence, 2100 sailors can occupy 7 ships.
Step 2
We are told in the question that:
Astrid wants to build enough ships to accommodate at least 2100 sailors. How much wood does Astrid need to accommodate 2100 sailors?
If:
1 ship = 40 tons of wood
Since 7 ships can accommodate 2100 sailors,
7 ships =
7 × 40 tons of wood = 280 tons of wood.
Therefore , Astrid needs 280 tons of wood to accommodate 2100 sailors.
Chapter: Simple linear equations Answer in steps
Answer:
6x-3=21
6x=24
x=4
........
6x+27=39
6x=39-27
6x=12
x=2
........
8x-10=14
8x=24
x=3
.........
6+6x=22
6x=22-6
x=3
......
12x-2=28
12x=26
x=3
.....
8-4x=16
-4x=8
x=-2
.....
4x-24=3x-3
4x-3x=24-3
x=21
....
9x+6=6x+12
9x-6x=12-6
3x=6
x=2
Answer:
Step-by-step explanation:
1. 3(2x - 1) = 21
= 6x - 3 = 21
= 6x = 24
= x = 24/6 = 4
------------------------------
2. 3(2x+9) = 39
= 6x + 27 = 39
= 6x = 39 - 27
= 6x = 12
= x = 12/6 = 2
--------------------------------
3. 2(4x - 5) = 14
= 8x - 10 = 14
= 8x = 14+10
= x = 3
-------------------------------
is -2.75 an integer?
Answer:
yes
Step-by-step explanation:
every negative any positive number is an integer
Answer:
Step-by-step explanation:
No. Integers do not have fractions in them.
-2.75 is equivalent to -275/100, which is a fraction that does not reduce to an integer
simplify 27-{ 9+(12-5)÷4} with solution
Answer:
16.25
Step-by-step explanation:
first do 12 -5 = 7. then 7/4 = 1.75 then 9+1.75 = 10.75 and finally 27-10.75= 16.25
Find the sum of the first 6 terms of 3 - 6 + 12 + …
Answer:
[tex] S_6 = -63 [/tex]
Step-by-step explanation:
The sequence above is a geometric sequence.
The common ratio (r) = [tex] \frac{-6}{3} = \frac{12}{-6} = -2 [/tex]
The common ratio < 1, therefore, the formula for the sum of nth terms of the sequence would be: [tex] S_n = \frac{a_1(1 - r^n)}{1 - r} [/tex]
a1 = 3
r = -2
n = 6
Plug in the values into the formula
[tex] S_6 = \frac{3(1 - (-2^6)}{1 - (-2)} [/tex]
[tex] S_6 = \frac{3(1 - (64)}{1 + 2} [/tex]
[tex] S_6 = \frac{3(-63)}{3} [/tex]
[tex] S_6 = -63 [/tex]
At what rates did she invest?
$1400 invested at ____%
$900 invested at ____%
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Answer:
$1400 at 8%$900 at 10%Step-by-step explanation:
The 1-year interest is simply the invested amount times the interest rate.
Let r represent the lower interest rate. Then r+0.02 is the higher rate, and the total interest earned is ...
1400r + 900(r +.02) = 202
2300r +18 = 202 . . . . . . . . . .simplify
2300r = 184 . . . . . . . . . .subtract 18
r = 184/2300 = 0.08 = 8% . . . . . . divide by the coefficient of r
$1400 was invested at 8%.
$900 was invested at 10%.
Which graph represents the solution set of the inequality 11 ≤ 2x + 5 ≤ 15
Answer:
D.
Step-by-step explanation:
First, simply the inequality.
[tex]11\leq 2x+5\leq 15\\6\leq 2x\leq 10\\3\leq x\leq 5[/tex]
Based on the simplified inequality, you are looking for a line with closed points on 3 and 5. Therefore, the answer is D.
NO LINKS OR ANSWERING QUESTIONS YOU DON'T KNOW!!!
Chapter 11 part 3:
Of the three functions {f(x), g(x), h(x)} featured on the graph below (on the following page), rank the functions in order of greatest rate to least.
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Answer:
f, h, g
Step-by-step explanation:
You can look at the slope of the tangent lines to the graphs at any given x-value. At x=5, we see that g(x) is the flattest curve and f(x) is the steepest.
In order from greatest to least growth rate, the functions are ...
f(x), h(x), g(x)
Solve for x
Answer options:
4
5
8
3
2
Answer:
But the answer is 42
I did I got 42 .
:(
A wheel on a race car has 21-inch diameter. To qualify for an upcoming race, cars must be able to travel a minimum of 130 miles per hour. The wheel on this car can turn at the rate of 36 revolutions per second. Determine the linear speed of a point on the rim of this wheel (nearest inch per second) and determine if this car with this wheel would qualify for the upcoming race. 5 To convert inches per second to miles per hour, multiply by 5/88.
A) The linear speed is 756 inches per second, so this car would not quality
B) The linear speed is 4750 inches per second, so this car would quality
C) The linear speed is 2375 inches per second, so this car would quality
D) The linear speed is 378 inches per second, so this car would not qualify.
Answer: B) The linear speed is 4750 inches per second, so this car would qualify.
Step-by-step explanation: To determine linear speed using revolutions per second, i.e., angular speed (ω):
v = ω.r
where r is radius.
As ω is in revolutions per second, transform into rad/s:
ω = 36 revolutions/s
1 revolution = 2π rad
ω = 36.2π rad/s
ω = 72π rad/s
Radius is 21 inches, which can be written as
r = 21 inches/rad
Linear speed is
v = [tex]\frac{72.\pi rad}{s} .\frac{21 in}{rad}[/tex]
v ≈ 4750 inches per seconds
Converting to miles per hour:
v = [tex]4750.\frac{5}{88}[/tex]
v = 270mph
At linear speed of 4750 inches per second, a car with wheel of radius 21-inch can qualify.
Answer:
Above is correct
Step-by-step explanation:
A person invests 3500 dollars in a bank. The bank pays 4.75% interest compounded
quarterly. To the nearest tenth of a year, how long must the person leave the money
in the bank until it reaches 5800 dollars?
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Answer:
10.7 years
Step-by-step explanation:
The formula for the balance in an account earning compound interest is ...
A = P(1 +r/n)^(nt)
where principal P is invested at annual rate r compounded n times per year for t years. We want to solve for t.
5800 = 3500(1 +0.0475/4)^(4t)
58/35 = 1.011875^(4t) . . . divide by 3500 and simplify a bit
log(58/35) = 4t·log(1.011875) . . . . take logs
t = log(58/35)/(4·log(1.011875)) . . . . divide by the coefficient of t
t ≈ 10.6966 ≈ 10.7
The person must leave the money n the bank for about 10.7 years for it to reach $5800.
A mechanic ground 6 valves in 25 minutes. At that rate,
how long will it take to grind 45 valves of the same kind?
Answer:
3hours and 12.5 minutes
Step-by-step explanation:
45/6=7.5x25=187.5/60=3hours and 12.5 minutes
use green theroem to find integral of x^2ydx-xy^2dy
Answer:
complementary angles 25
When is it easier to use the addition method rather than the substitution method to solve a system of equations?
Answer: When the addition of two or more equations leads to the elimination of one of the variables.
Step-by-step explanation:
When we have a system of equations, the addition method seems to be useful only when adding the equations will lead to the elimination of one of the variables:
An example of this can be, for the variables x and y:
3*x + x*y - 2*y = 3
x^2 + x*y - 2y = 42
now we can "add" (actually subtract) the equations and get (eq2 minus eq1)
(x^2 + x*y - 2y) - (3*x + x*y - 2*y ) = 42 - 3
x^2 - 3*x = 39
x^2 - 3*x - 39 = 0
And now we can solve it for x, and then find the value of y.
help please I need help :(
A = 1 and 8
B = 2 and 4
C = 2 and 7
I’m pretty sure this is right? I’m still learning too :p
=======================================================
Explanations:
For the sake of simplicity, imagine that lines m and n are parallel. They don't necessarily need to be in order to answer this problem, but it might help with the terminology better.
When we use the term "interior" we basically mean the region between or inside the parallel lines. So "exterior" is everything but that, which is composed of two separate regions that don't overlap. Exterior angles shown in this diagram are
angle 1, angle 5, angle 4, angle 8
The "alternate" refers to the idea that we're on alternate sides of the transversal cutting line. One pair of alternate exterior angles is angle 1 and angle 8. We have angle 1 below the transversal while angle 8 is on the opposite side and above the transversal. For similar reasoning, angles 5 and 4 are alternate exterior angles as well.
---------------------------------
Notice how each line crosses to form an X shape, producing 4 angles that share the same common vertex point. For instance, angles 1, 5, 6 and 2 are all around the same point.
Angle 1 and angle 3 are corresponding angles because they
a) are to the left of each parallel line (m and n)b) both below the transversal lineSo in short, they are both in the same corner of each four corner angle configuration. They are both in the bottom left corner. This is the full list of all corresponding angle pairs
angle 1 and angle 3angle 2 and angle 4angle 5 and angle 7angle 6 and angle 8---------------------------------
As stated in the first section above, the interior region is between the parallel lines. Alternate interior angles alternate being above and below the transversal line.
So this applies to angle 2 and angle 7. It also works for angle 3 and angle 6.
rewrite the following statements into algebraic expression
the sum of x and y
5 is subtracted from y
Ginny writes down a secret number on her palm. She says that it is a three-digit even number. The units digit is 1 more than the hundreds digit. The tens digit is twice the sum of the units digit and the hundreds digit.
Answer:
Hello,
Answer 162
Step-by-step explanation:
Let say n the searched number.
[tex]n=\overline{abc}\\a>0\\c=a+1\\b=2*(a+c)\\\\.T.\ means\ True.\\\\\\\begin{array}{c|c|c|c}a&c&b&ok\\1&2&6&.T.\\3&4&14&.F.\\5&6&22&.F.\\7&8&30&.F.\end{array}\\\\\\\boxed{Answer\ n=162}\\[/tex]
Please help me how to do no 5
Answer:
-864
Step-by-step explanation:
The determinant of a matrix product is the product of the determinants. The determinant of a transpose is the same as the determinant of the original. Hence ...
[tex]|AB^5C^T|=(4)(-2)^5(\frac{1}{4})=-32[/tex]
The multiplication of an n×n matrix by a scalar 'a' multiplies its determinant by a^n, so the desired determinant is ...
[tex]|3AB^5C^T|=3^3(-32) = \boxed{-864}[/tex]
What is the domain of this graph?
Answer:
the domain is all real numbers
Identifying equivalent statements and negations of a conditional statement: help
Attached is the photo reference.
Answer:
1: Equal
2: Negation
3: Negation
4: Neither
Step-by-step explanation:
Sorry if I got any of them wrong
1 liter of ink can print 5000 pages of text. If you had 100 gallons of ink then how many pages
could you print?
Help me with this please #17
9514 1404 393
Answer:
C. symmetric with respect to the origin
Step-by-step explanation:
A graph must pass the vertical line test to be called the graph of a function. No function will ever be symmetrical with respect to the x-axis, because that would mean it fails the vertical line test.
An even function is symmetrical about the y-axis. An even function has the characteristic that ...
f(-x) = f(x) . . . . an even function
An odd function is symmetrical about the origin. An odd function has the characteristic that ...
f(-x) = -f(x)
__
The given function is f(x) = -1/x. Then the value of f(-x) is ...
f(-x) = -1/-x = 1/x = -f(x)
The given function is an odd function, so is symmetrical about the origin.
I think of number I add 14 to the number and multiply the result by 3 if my final answer is 51 what number did I think of
Answer:
-1
Explanation:
Let the number be x.
Then the equation will be:
3(x+18) = 51
=> 3x + 54 = 51
=> 3x = 51 - 54
=> 3x = -3
=> x = -3/3
=> x = -1
So, the number you thought of is -1.
Answer:
The number is 3.
Step-by-step explanation:
[tex]3(14+x)=51\\42+3x=51\\3x=9\\x=3[/tex]
Which function is best represented by the graph in the image?
Answer:
No image I cannot tell you
Step-by-step explanation:
express 111 as a sum of two primes
Answer:
2 + 109 = 111
Step-by-step explanation:
.............
1. Peyton has a credit card with an annual rate of 24.7% compounded monthly. She used the credit card to purchase cleaning supplies in the amount of $189.56. She can pay up to $72 on the
credit card each month. How much total interest will she pay?
Answer:
Total interest = $3.41
Step-by-step explanation:
Since she can pay $72 each month we can divide the payments on monthly basis till all the money is paid.
The annual interest rate is 24.7%, so the monthly rate will be 24.7 ÷ 12= 2.058%
For the first month
With payment of $72 the remaining amount will be 189.56 - 72 = $117.56
Interest paid will be 0.02058 * 117.56 = $2.42
Total amount owed now will be 117.56 + 2.42 = $119.98
For the second month another payment of $72 is made
The remaining will be 119.98 - 72 = $47.98
Interest charged will be 0.02058 * 47.98 = $0.99
The amount owed will be 47.98 + 0.99 = $48.97
In the third month she will pay the remaining $47.98 which is within her monthly limit
Total interest paid = Sum of Amount paid each month - Initial amount spent
Total interest = {(72 * 2) +48.97} - 189.56 = $3.41