You always get a unit rate from dividing. You always have two ways to do it, and get two unit rates, but one of them is more helpful.
2000 meters/4 minutes = 500 meters per minute
4 minutes/2000 meters = 0.002 minute per meter
(By the way ... Franklin is "jogging" a 3:13.12 mile. The world record is 3:43.13 .)
find the surface area of the composite figure
Answer:
[tex]=280[/tex] [tex]in^2[/tex]
Step-by-step explanation:
----------------------------------------
Let's find the surface area of the pink rectangular prism first.
[tex]2*10=20+20=40[/tex]
[tex]4*10=40+40=80[/tex]
[tex]4*2=8+8=16[/tex]
[tex]40+80+16=136[/tex]
The surface area for the pink rectangular prism is [tex]136[/tex] [tex]in^2[/tex].
-------------------->>>>>
Now, let's find the surface area of the green rectangular prism.
[tex]4*7=28+28=56[/tex]
[tex]4*7=28+28=56[/tex]
[tex]4*4=16+16=32[/tex]
[tex]56+56+32=144[/tex]
The surface area for the green rectangular prism is 144 [tex]in^2[/tex].
-------------------->>>>>
Now let's add the surface area of both rectangular prisms to find the surface area of the composite figure.
[tex]136+144=[/tex]
[tex]=280[/tex] [tex]in^2[/tex]
----------------------------------------
Hope this is helpful.
9514 1404 393
Answer:
224 in²
Step-by-step explanation:
There are a couple of ways to go at this. Here, we choose to figure the areas of each of the prisms individually, then subtract the "hidden" area where they are joined together.
The area of a prism is ...
A = 2(LW +H(L+W))
Pink area:
A = 2(10·4 +2(10+4)) = 2(40 +28) = 136 . . . square inches
Green area:
A = 2(7·4 +4(7+4)) = 2(28 +44) = 144 . . . square inches
One 4 in × 7 in face of the green prism meets with a similar area of the pink prism, so the area hidden at that interface is 2(4·7) = 56 square inches. Then the total surface area of the composite figure is ...
SA = 136 in² +144 in² -56 in² = 224 in²
Help ASAP
What is the solution to this equation? (1/4)^x+1 =32
Answer:
B. [tex]\displaystyle \frac{-7}{2}[/tex]
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityAlgebra I
Exponential Rule [Powering]: [tex]\displaystyle (b^m)^n = b^{m \cdot n}[/tex] Exponential Rule [Rewrite]: [tex]\displaystyle b^{-m} = \frac{1}{b^m}[/tex]Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle \bigg( \frac{1}{4} \bigg)^{x + 1} = 32[/tex]
Step 2: Solve for x
Rewrite: [tex]\displaystyle \bigg( \frac{1}{2^2} \bigg)^{x + 1} = 2^5[/tex]Exponential Rule [Rewrite]: [tex]\displaystyle (2^{-2})^{x + 1} = 2^5[/tex]Exponential Rule [Powering]: [tex]\displaystyle 2^{-2(x + 1)} = 2^5[/tex]Set: [tex]\displaystyle -2(x + 1)} = 5[/tex][Division Property of Equality] Divide -2 on both sides: [tex]\displaystyle x + 1 = \frac{-5}{2}[/tex][Subtraction Property of Equality] Subtract -1 on both sides: [tex]\displaystyle x = \frac{-7}{2}[/tex]Which expression is equivalent to the given expression?
6ab/(a^0b^2)^4
Answer:
,here is the answer
Step-by-step explanation:
here is your answer
A. If I do something for 30 seconds every day for a whole year, how long did I do it in total.
B. If I do something for 10 seconds every day for a whole year, how long did I do it in total.
Answer: 120 minutes
Step-by-step explanation:
Answer:
A. 10,950 seconds, 182.50 minuets, and about 3 hours
B. 3,650 seconds, about 60 minuets, or about 1 hour.
Step-by-step explanation:
A. We can multiply the seconds by the days in a year to get our answer, and we can simply divide if we want to get the amount of minuets or hours.
B. Same thing as "A", but all we do here, is multiply 10 by 365. :)
PLSSSS ANSWER!!!!!!!!!
Which one did you need help with?
What is this function’s input if its output is 11?
f(x) = 2x + 5
Answer:
the input x is 3
Step-by-step explanation:
2x+5=11
2x=6
x=3
A ream of a certain brand of paper weighs about 4.533 pounds. A ream contains 500 sheets of paper. How much does a sheet of paper weigh?
Step-by-step explanation:
As a ream or
500
sheets of paper weigh
4.818
pounds
One sheet of paper weighs
4.818
500
=
0.009636
pounds.
It is apparent that pound is too big a unit for a sheet of paper.
As each pound has
16
ounces, one can say
one sheet of paper weighs
0.009636
×
16
=
0.154176
ounces.
If ounce is too big, as we have
1
pound equal to
28.34952
grams
one sheet of paper weighs
0.154176
×
28.34952
≈
4.371
grams
please mark as brainliest
60.3 60.44 witch one is greater
what is the best estimate of (-3/8)(17 5/6)
Answer:
-11
Step-by-step explanation:
Given the expression (-3/5)(17 5/6)
Converting the mixed to improper fraction
(-3/5)(17 5/6)
= (-3/5)(107/6)
= (-3*107)/(5*6)
= -321/30
= -10.7
Hence the required best estimate is -11
Find(g-f)(x)
f(x)=1/x
g(x)=x^2+2x-5
a. 1/x-x^2-2x+5
b.1/x+x^2+2x-5
c.x^2+2x-5-1/x
d.1/x+x^2-5
Answer:
x^2+2x-5 - 1/x
Step-by-step explanation:
f(x)=1/x
g(x)=x^2+2x-5
(g-f)(x) = x^2+2x-5 - 1/x
Answer:
c. x² + 2x - 5 - 1 / x
Step-by-step explanation:
f ( x) = 1 / x.
g ( x) = x² + 2x - 5
so,
( g - f) ( x) = x² + 2x - 5 - 1 / x
Plz help. I was crying. Super challenging. Will give brainiest and will give 50 points for explained answer. Thx
Answer:
Paige is incorrect. g(x) has a steeper slope
Step-by-step explanation:
The slope for f(x) is
m =( y2-y1)/(x2-x1)
= (17/2 - 5/2) / ( -1 - -6)
= (17/2 - 5/2) / ( -1 +6)
= (12/2)/5
= 6/5
The slope for g(x) is
m =( y2-y1)/(x2-x1)
= (-1 - 13/3) / ( 6 - 2)
=(-3/3 -13/3) / (6-2)
(-16/3)/4
-16/3 * 1/4
- 4/3
Comparing the magnitudes
|6/5| |-4/3|
|6/5*3/3| |-4/3*5/5|
|18/15| |20/15|
|20/15| is greater so it has a steeper slope
g(x) has a steeper slope
Assume that you purchased a new car today and financed $55,000 of the price on a 72-month payment contract with a nominal rate of 6.00%. Further, assume that you plan on paying off the balance of the car loan after you make your 48th payment. How much will your loan balance be when you pay off the car?
Answer:
The amount that your loan balance will be when you pay off the car is $20,566.18.
Step-by-step explanation:
Step 1. Calculation of monthly payment
This can be calculated using the formula for calculating the present value of an ordinary annuity as follows:
PV = P * ((1 - (1 / (1 + r))^n) / r) …………………………………. (1)
Where;
PV = Present value or the cost of the new car = $55,000
P = Monthly payment = ?
r = Monthly nominal rate = Nominal rate / 12 = 6% / 12 = 0.06 / 12 = 0.005
n = number of months = 72
Substitute the values into equation (1) and solve for P, we have:
$55,000 = P * ((1 - (1 / (1 + 0.005))^72) / 0.005)
$55,000 = P * 60.3395139355201
P = $55,000 / 60.3395139355201 = $911.51
Step 2. Calculation of the loan amount balance when you pay off the car
This can be calculated using the ballon payment formula as follows:
P = (PV - (Ballon / (1 + r)^n)) * (r / (1 – (1 + r)^-n)) ...................... (1)
Where:
P = Monthly payment = $911.51
PV = Present value or the cost of the new car = $55,000
Ballon = Ballon payment or the loan amount balance when you pay off the car = ?
r = Monthly nominal rate = Nominal rate / 12 = 6% / 12 = 0.06 / 12 = 0.005
n = number months to pay off the loan amount balance = 48
Substituting the values into equation (1) and solve for Ballon, we have:
911.51 = (55,000 - (Ballon / (1 + 0.005)^48)) * (0.005 / (1 - (1 + 0.005)^-48))
911.51 = (55,000 - (Ballon / 1.27048916109538)) * 0.0234850290479363
911.51 / 0.0234850290479363 = 55,000 - (Ballon / 1.27048916109538)
38,812.39 = 55,000 - (Ballon / 1.27048916109538)
Ballon / 1.27048916109538 = 55,000 - 38,812.39
Ballon / 1.27048916109538 = 16,187.61
Ballon = 16,187.61 * 1.27048916109538
Ballon = $20,566.18
Therefore, the amount that your loan balance will be when you pay off the car is $20,566.18.
I took 18 pencils from the box. this is equivalent to 2/5 of the total number of pencils.
How many pencils were there in the box originally. Show your work.
Answer: 45 pencils were in the box originally
Step-by-step explanation:
Suppose there were x pencils in the box originally. Since 18 pencils is equal to 2/5 of the total number of pencils in the box originally, set 18 equal to 2/5x or
18=2/5x
Now solve
x = 18x5/2 = 45
HELP MATH ANSWER QUESTION
Answer:
x = 84 , y = 168
Step-by-step explanation:
[tex]Sin 60 = \frac{opposite side}{hypotenuse}\\\\ \frac{\sqrt{3}}{2}= \frac{AB}{BC}\\\\ \frac{\sqrt{3}}{2} = \frac{84\sqrt{3}}{y}\\\\Cross\ multiply ,\\\\y*\sqrt{3} =2*84 \sqrt{3}\\\\y= \frac{2*84*\sqrt{3}}{\sqrt{3}}\\\\y=168[/tex]
[tex]Cos\60 = \frac{adjacent}{hypotenuse}\\\\ \frac{1}{2}= \frac{AC}{BC}\\\\ \frac{1}{2}= \frac{x}{168}\\\\ \frac{1}{2}*168=x\\\\x= 84[/tex]
The initial number of views for a reader board is 25. The number of views is growing exponentially at a rate of 18% per week. What is the number of views expected to be four weeks from now?
Answer:
48
Step-by-step explanation:
n = 25(1.18)^4
n = 48.469444
Rounded to 48
Answer:
48 views.
Step-by-step explanation:
18% = 0.18 as a decimal fraction.
The increase in number of books per week is found by multiplying by 1.18.
The equation is an exponential one and is:
V = 25(1.18)^t where V = views and t = number of weeks.
So after 4 weeks :
V = 25 (1.18)^4
= 48.47
Show that the transformation T defined by T(x1, x2)= (x1x2, x1, x2) is not linear. If T is a linear transformation, then T(0)= ____________
Answer:
A linear transformation is defined as:
For a transformation T that goes from R^n to R^m, this transformation is linear if, for two vectors A and B, we have that:
T(A + B) = T(A) + T(B)
In this case, we have the transformation:
T(x1, x2)= (x1x2, x1, x2).
If we define two vectors:
A = (a1, a2)
B = (b1, b2)
if the transformation is lineal, we will have that:
T(A + B) = T(A) + T(B)
Or
T(0) = T(A - A) = T(A) + T(-A)
(just two different ways of writing the same thing, I will use the first one, because it is the general way)
We want to see that, for our transformation, this equation is false.
first the left side:
A + B = (a1, a2) + (b1, b2) = (a1 + b1, a2 + b2)
Then the transformation applied to that vector gives:
T(A + B) = T(a1 + b1, a2 + b2) = ( (a1 + b1)*(a2 + b2), (a1 + b1), (a2 + b2))
= (a1*a2 + a1*b2 + b1*a2 + b1*b2, a1 + b1, a2 + b2)
While for the right side, we have:
T(A) + T(B) = T(a1, a2) + T(b1, b2) = (a1*a2, a1, a2) + (b1*b2, b1, b2)
= (a1*a2 + b1*b2, a1 + b1, a2 + b2)
Then we can rewrite:
T(A + B) = T(A) + T(B)
as:
(a1*a2 + a1*b2 + b1*a2 + b1*b2, a1 + b1, a2 + b2) = (a1*a2 + b1*b2, a1 + b1, a2 + b2)
We can see that the first part of these vectors is different, thus, the equality is false.
Then we can conclude that:
T(A + B) ≠ T(A) + T(B)
Then the transformation T is not linear.
EX2. Find the solution of the following matrix using
Gauss elimination method, working 4D.
2.37 X1+3.06 X-4.28X, -1.76
1.46 Xi - 0.78 X+3.75X4.69
-3.69 X: +5.13 X:-1.06X, 5.74
Answer:
please post a more cohesive question. The values are very confusing
Which polynomial is factored completely?
Answer:
You answered it
Three potential employees took an aptitude test. Each person took a different version of the test. The scores are reported below. Kerri got a score of 80.8; this version has a mean of 62.1 and a standard deviation of 11. Cade got a score of 286.4; this version has a mean of 271 and a standard deviation of 22. Vincent got a score of 7.9; this version has a mean of 7.2 and a standard deviation of 0.7. If the company has only one position to fill and prefers to fill it with the applicant who performed best on the aptitude test, which of the applicants should be offered the job
Answer:
Kerri
calculate z scores z= (x - xbar)/stdev
Kerri = 1.7
Cade = .7
Vincent = 1
Step-by-step explanation:
What is the probability of flipping a coin 10 times and getting heads 5 times? Round your answer to the nearest tenth percent.
The Probability is 1/2 or .5, .5 rounded to the nearest tenth would be irregular because .5 is already in the tenth place but according to the law of rounding since ut is five it would be rounded up giving the whole number 1
Solve this pls help
How did the Californian gold rush have an effect on people?
Answer:
The gold rush has a big impact on people. Especially since it helped shaped the course of California's development by bringing economic growth.
How many distinct 5 digit numbers can be formed from the list of numbers
{0,1,2,3,4,5,6,7,8,9}such that the number
i. Is an even number
ii. Is a Odd number
iii. Multiple of 5
iv. Never ends with {2,3,4,5}
What are the three plot points and is it over the x-axis or y-axis
Answer:
(-2,1), (0,1), and (2,0). its over the y axis
Step-by-step explanation:
Answer:
shift it 3 values right and 2 units up
Step-by-step explanation:
moving x-axis and moving y-axis
If f(x)=x^2−8x and g(x)=−12x^2 what is g(f(−4))?
Answer:
-27648
Step-by-step explanation:
In this problem, we are looking for the function of g in terms of the function f. Simply put, we just replace the variable x in the function g with f(-4).
Step 1, writing g(f(-4)):
[tex]g(f(-4))=-12(f(x))^2[/tex]
Great! Let us substitute f(x) with the given expression.
Step 2, substituting and simplifying:
[tex]\\g(f(-4))=-12(x^2-8x)^2\\g(f(-4))=-12((-4)^2-8*(-4))^2\\g(f(-4))=-12(16+32)^2\\g(f(-4))=-12*2304\\g(f(-4))=-27648[/tex]
g(f(-4) is [tex]\fbox{-27648}[/tex].
I hope this helps! Let me know if you have any questions :)
There are 12 adults, 24 girls and 6 boys in a room.
Work out the ratio of adults to girls to boys.
Write the answer in its simplest form.
Answer:
12:24:6- divide by 3
4:8:2 - divide by 2
2:4:1- simplest form
What is the value of x? Round the answer to the nearest tenth.
DONT RESPOND WITH A LINK!!!!!!!
Answer:
i believe x is 16.1
Step-by-step explanation:
hope this helps
Question
Which of the following is equivalent to 1-12 + 3/?
image. can someone help with this one uWu
Answer:
8/33
Step-by-step explanation:
Which option shows the graph of 3y+18>5x
Hi, I'm so sorry I can't answer that. but I have something you can answer that. Search in browser or anything searcher that you have "Quickmath" or "Cymath" all your equations,problems can solved
Step-by-step explanation:
i hope it helps
Suppose we are sending a digital signal which is a string of 0s and 1s of length five. (Example stringsare 00101, 11000, 10101 are all 5 bit strings.) When we send the message, each bit (0 or 1) is sentindependently and there is some chance that the bit is corrupted. Namely, each time we send a 0 thereis a 5% chance that a 1 is received and each time we send a 1 there is a 5% chance a 0 is received.Suppose we send a message of length 5, what is the probability that an incorrect message is received
Answer:
0.7738 = 77.38% probability that an incorrect message is received.
Step-by-step explanation:
For each bit, there are only two possible outcomes. Either it is corrupted, or it is not. The probability of a bit being corrupted is independent of any other bit. This means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
5% probability a bit is sent incorrectly:
This means that [tex]p = 0.05[/tex]
Message of length 5
This means that [tex]n = 5[/tex]
What is the probability that an incorrect message is received?
This is the probability of at least one incorrect bit, which is:
[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{5,0}.(0.05)^{0}.(0.95)^{5} = 0.7738[/tex]
0.7738 = 77.38% probability that an incorrect message is received.