Simplifying products and quotients of powers
7^2•7^8/7^4=7^a/7^4=7^b
A=
b=
Answer:
a=10
b=6
Step-by-step explanation:
add 2 to 8, to get a, then subtract 4 from 10 to get b
Answer:
10 and 6
Step-by-step explanation:
A medical researcher is studying the spread of a virus in a population of 1000 laboratory mice. During any week, there is an 80% probability that an infected mouse will overcome the virus, and during the same week there is a 10% probability that a noninfected mouse will become infected. Three hundred mice are currently infected with the virus. How many will be infected next week and in 3 weeks
Answer:
The number of mice that will be infected next week are 130 while
The number of mice that will be infected in 3 weeks are 111
Step-by-step explanation:
From the information given , the researcher is studying the spread of a virus in a population of 1000 laboratory mice. i.e, n = 1000
Number of infected = 300
Non infected = 1000 - 300 = 700
Probability an infected mouse will overcome = 80% = 0.8
Probability a noninfected mouse becomes infected = 10% = 0.10
The number of infected that will overcome = 0.8 * 300 = 240
The number of non infected that will become infected = 0.1 * 700 = 70
The number that will be infected on the first week =
300 - 240 + 70
= 130
Number that will be healthy on the first week =
700 + 240 - 70
= 870
Calculating for week 2:
The number of infected that will overcome = 0.8 * 130 = 104
The number of non infected that will become infected = 0.10 * 870 = 87
The number that will be infected on the second week =
130 - 104 + 87
= 113
Number that will be healthy on the second week =
870 + 107 - 87
= 887
Calculating for week 3:
The number of infected that will overcome = 0.8 * 113 = 90.4
The number of non infected that will become infected = 0.10 * 887 = 88.7
The number that will be infected on the third week =
113 - 90.4 + 88.7
= 111.3 ≈ 111
Number that will be healthy on the third week =
887 + 90.4 - 88.7
= 888.7 ≈ 889
From our calculations, the number of mice that will be infected next week are 130
The number of mice that will be infected in 3 weeks are 111
KARLA has spent $33 on food. She bought milk, cheese, and meat. The milk cost half as much as the cheese and the meat cost four times as much as the cheese. Which equation will help you find the cost of the cheese?
Sara Bought a computer that was originally priced at $896.The computer was on sale for 12% off. When she bought the computer, a 7% tax was added to the sale price. How much did Sara spend on the computer. Round to the nearest cent!
Answer:
$733.29. Simply because you take $896•0.12 to find the 12% off and then you take that subtracted by the starting total. After you get the 12% off then you multiply that number by .07 to get the sales tax. After you find that then you add the number you got after multiplying to the number you got after taking off the 12%.
Step-by-step explanation:
The perimeter of a rectangle is 62 meters. The length is 4 more than 2 times the width. What is the length?
Answer:
4x+ 1 = 24 + 1 = 25 m.
Step-by-step explanation:
Given, perimeter = 62 m. Perimeter : 2 (L+W) = 62 m. hence, L+W = 31 m. x = 30/5
Answer:
Step-by-step explanation:
let width be x
length = 2x + 4
2(x + 2x + 4) = 62
6x + 8 = 62
6x = 54
x = 9
length = 2(9) + 4 = 22cm
Parallel lines s and t are cut by a transversal, r.
Parallel lines s and t are cut by transversal r. Clockwise from top left, the angles formed with r and s are 1, 2, 3, 4; the angles formed with r and t are 5, 6, 7, 8.
If the measure of angle 1 is 68°, what is the measure of angle 5?
22°
68°
112°
158°
Answer:
68°
Step-by-step explanation:
Angles 1 and 5 are corresponding angles on parallel lines, hence they are equal
Answer:
B.
Step-by-step explanation:
At Pizza Pi, 80% of the pizzas made last week had extra cheese. If 16 pizzas had extra
cheese, how many pizzas in all were made last week?
Answer:
20 pizzas in total
bro now i want pizza
Step-by-step explanation:
16 pizzas = 80%
8 pizzas = 40%
4 pizzas = 20%
Kono Dio Da!!!
I really need help!! HELP ASAP PLEASE!!!
Which figure has an area of 12 square units?
Answer:
Should be the bottom one
Step-by-step explanation:
You can find this by counting. It is the only one with 12 units.
Answer:
Step-by-step explanation:is number 4 i pick it and its correct
A rectangular animal pen will be built using 200 meters of fencing. If one side of the fence is 60 meters, find the area of the pen?
Answer:
Area=LW=(60m)(40m)=2400 m^2
Step-by-step explanation:
The area of the rectangular pen is 2400 square meters.
What are the area and parameters of a rectangle?The region that a rectangle occupies in a two-dimensional space is referred to as the area of a rectangle. The quantity of square units required to entirely fill a rectangle is another way to describe its area. The whole distance encircling a rectangle's outside is referred to as its perimeter.
Given, A rectangular animal pen will be built using 200 meters of fencing. If one side of the fence is 60 meters. Hence,
Parameter of rectangle = 200
2(length + width ) = 200
given length of the pen is 60 meters
2(60 + width) = 200
width = 100- 60 = 40
Area of the rectangle = length * width = 60* 40 = 2400
Therefore, 2400 square meters will be the area of the given rectangular pen.
Learn more about the area and parameters of a rectangle here:
https://brainly.com/question/1015355
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Element X decays radioactively with a half-life of 14 minutes if there are 680 grams of element X how long to the nearest 10th of a minute would it take the element to decay 17 grams
Answer:
It would take 74.5 minutes for the element to decay 17 grams.
Step-by-step explanation:
The amount of element X after t minutes is given by the follwoing equation:
[tex]X(t) = X(0)e^{rt}[/tex]
In which X(0) is the initial amount of the substance and r is the decay rate.
Half life of 14 minutes.
This means that [tex]X(14) = 0.5X(0)[/tex]
So
[tex]X(t) = X(0)e^{rt}[/tex]
[tex]0.5X(0) = X(0)e^{14r}[/tex]
[tex]e^{14r} = 0.5[/tex]
[tex]\ln{e^{14r}} = \ln{0.5}[/tex]
[tex]14r = \ln{0.5}[/tex]
[tex]r = \frac{\ln{0.5}}{14}[/tex]
[tex]r = -0.0495[/tex]
So
[tex]X(t) = X(0)e^{-0.0495t}[/tex]
There are 680 grams of element X
This means that [tex]X(0) = 680[/tex]
[tex]X(t) = X(0)e^{-0.0495t}[/tex]
[tex]X(t) = 680e^{-0.0495t}[/tex]
How long would it take the element to decay 17 grams
This is t for which X(t) = 17. So
[tex]X(t) = 680e^{-0.0495t}[/tex]
[tex]17 = 680e^{-0.0495t}[/tex]
[tex]e^{-0.0495t} = \frac{17}{680}[/tex]
[tex]e^{-0.0495t} = 0.025[/tex]
[tex]\ln{e^{-0.0495t}} = \ln{0.025}[/tex]
[tex]-0.0495t = \ln{0.025}[/tex]
[tex]0.0495t = -\ln{0.025}[/tex]
[tex]t = -\frac{\ln{0.025}}{0.0495}[/tex]
[tex]t = 74.5[/tex]
It would take 74.5 minutes for the element to decay 17 grams.
Peter rolls a fair dice 114 times. How many times would Peter expect to roll a number greater than 1?
Answer:
A dice of six faces has 5 numbers bigger than 1 (from 2 to 6).
Then, the number Peter is expecting is : 114 x (5/6) = 95 (times)
Hope this helps!
:)
Jonas is buying a three-day supply of camping snacks. An energy bar costs $1.50, and a bag of dried
mangoes costs $3.00. Jonas plans to have 7 snacks per day and can spend up to $45.00.
If p is the number of energy bars he can buy, and m is the number of bags of mangoes he can buy,
which system of equations and inequalities can be used to represent the possible number of each
snack he can buy?
p+m
21
=
21
p+m = 45
1.5p + 3m
p> 0
m >0
1.5p + 3m < 45
p> 0
m 2 0
1.5p + 3m
3p + 1.5m
p20
m 20
p+m = 21
8p + 1.5m
p> 0
m >0
Answer:
P+m=21
1.5p + 3m < 45
p > 0
m > 0
Step-by-step explanation:
Write the perimeter of the floor plan shown as an algebraic expression in x.
Answer: 8+2x
Step-by-step explanation:
Hi, Perimeter is the distance around a two-dimensional shape.
To calculate it, we have to add all the side lengths of the figure. The missing side is the ? side (right side). To obtain it we have to subtract the top right side length (2) to the left side length (12)
So, the expression is equal to:
P = 12+ (x-4) + (x-12) +2 +(12-2)
P = 12+ x - 4 +x -12+2 +10
P = 12-4-12+2+10+x+x
P =8+2x
What is a Regression equation
Answer:
Regression equations can help you figure out if your data can be fit to an equation.This is extremely useful if you want to make predictions from your data- either future predictions or indications of past behavior.For example,you might want to know what your savings are going to be worth in the future.There are several types of regression equations,some of the more common include exponential and simoke linear regression.In elementary statistics,the regression equation you are most likely to come across is the linear form.
Cody paid $24.00 to join an online music service. If she purchases 15 songs each month at a cost of $1.25 per song, what will be the total amount she has spent after 6 months?
15 songs x 1.25 per song = $18.75 per month for songs.
18.75 per month x 6 months = $112.50
112.50 + 24.00 = $136.50 total
What function has zeros at x=10 and x=2
Answer:
f(x) = x^2 -12x +20
Step-by-step explanation:
There are an infinite number of functions with zeros at those values of x. One simple polynomial function with those zeros is ...
f(x) = (x -10)(x -2) . . . . . each zero contributes a factor
f(x) = x^2 -12x +20
A tennis ball machine shoots 21 forehands 25 backhands and 9 lobs if a player missed 6 forehands 17 backhands and 2 lobs how many balls were hit
Answer:
30
Step-by-step explanation:
55 - 25 = 30
HELP ME ASAP! Will give BRAINLIEST! Please read the question THEN answer correctly! No guessing. Check ALL that apply
x^2+(x-8)^2-3(x+2) = 2(x+9)
Answer:
There are two solutions:
x = 5/2 = 2.500
x = 8
Step-by-step explanation:
Please help
The lengths of pregnancy terms for a particular species of mammal are nearly normally distributed about a mean pregnancy length with a standard deviation of 17 days. About what percentage of births would be expected to occur within 51 days of the mean pregnancy length?
Answer:
About 99.7% of births would be expected to occur within 51 days of the mean pregnancy length
Step-by-step explanation:
The Empirical Rule states that, for a normally distributed random variable:
68% of the measures are within 1 standard deviation of the mean.
95% of the measures are within 2 standard deviation of the mean.
99.7% of the measures are within 3 standard deviations of the mean.
In this problem, we have that:
Standard deviation = 17.
About what percentage of births would be expected to occur within 51 days of the mean pregnancy length?
51/17 = 3.
So, within 3 standard deviations of the mean.
About 99.7% of births would be expected to occur within 51 days of the mean pregnancy length
There are 14 math teachers and 26 science teachers at
school today. What is the ratio of math teachers to math
and science teachers at school?
Answer: 2.86
Step-by-step explanation:
14+26=40
40/14
Answer:
2.86
Step-by-step explanation:
Please help me I’m stuck on this.
Oliver wants to play the gone fishing game at the carnival.He will use the graph to find the total cost (Y) to play a couple of games.If Oliver wants to play 4 games,how much will he pay?
If u need more information tell me in the comments :)
Answer:
The cost of the game is $7 .
Step-by-step explanation:
By looking at the graph, the line at x = 4 is equals to y = 7
Twenty words were randomly selected from two textbooks. Each set gives the number of letters in each of the twenty words for that textbook.
Briefly describe how the word lengths compare between textbook 2 and textbook 1.
Briefly describe the variability in the length of words in textbook 2 compared to textbook 1. PLEASE HURRY :(
Answer:
k = 13The smallest zero or root is x = -10
Step-by-step explanation:
you can write "x^2" to mean "x squared"
f(x) = x^2+3x-10
f(x+5) = (x+5)^2+3(x+5)-10 ... replace every x with x+5
f(x+5) = (x^2+10x+25)+3(x+5)-10
f(x+5) = x^2+10x+25+3x+15-10
f(x+5) = x^2+13x+30
Compare this with x^2+kx+30 and we see that k = 13
Factor and solve the equation below
x^2+13x+30 = 0
(x+10)(x+3) = 0
x+10 = 0 or x+3 = 0
x = -10 or x = -3
The smallest zero is x = -10 as its the left-most value on a number line.
Find the arc length of the partial circle. with a radius of 1
Answer:
1/2π
Step-by-step explanation:
For khan, you HAVE to put the pi symbol. just type pi and itll work
Answer:
1/2 pi (Sorry i don't have the pi symbol)
Step-by-step explanation:
Some Field Experience in the use of an Accelerated Method in Estimating 28-Day Strength of Concrete" considered regressing y =28-day standard-cured strength (psi) against x =accelerated strength (psi). Suppose the equation of the true regression line is y =1800 +1.3x.
a.What is the expected value of 28-day strength when accelerated strength= 2500? (2 marks)
b.By how much can we expect 28-day strength to change when accelerated strength increases by 1 psi? (4 marks)
c. Answer part (b) for an increase of 100 psi. (2 marks)
d. Answer part (b) for a decrease of 100 ps
Answer:
(a) 5,050 psi.(b) 5,051.3 psi.(c) 5,180 psi.(d) 4,920 psi.Step-by-step explanation:
The given function is
[tex]y=1800+1.3x[/tex]
Where [tex]x[/tex] represents the accelerated strength in psi, and [tex]y[/tex] represents 28-day standard-cured strength in psi.
Part a is about finding the y-value for [tex]x=2500[/tex]
[tex]y=1800+1.3(2500)=1800+3250=5,050[/tex]
Therefore, the expected value of 28-day strength when accelerated strength is 2,500, is 5,050 psi.
Part b is about the y-value for [tex]x=2501[/tex]
[tex]y=1800+1.3(2501)=1800+3251.3=5,051.3[/tex]
Part c is about the y-value for [tex]x=2600[/tex]
[tex]y=1800+1.3(2600)=1800+3380=5,180[/tex]
Part d is about the y-value for [tex]x=2400[/tex]
[tex]y=1800+1.3(2400)=1800+3120=4,920[/tex]
Brainliest for anyone if they get this CORRECT.
hello
it is c
hehehehe hope it helps
Answer:
The option c. (x-6)(x-1)
Step-by-step explanation:
x^2 - 7x +6
S=-7
P=6
x^2-1x-6x+6
x(x-1)-6(x-1)
(x-6)(x-1)
Mrs. Miller pays $56 for 8 pounds of salmon. What is the price of pound per salmon?
Answer:
A pound of salmon costs 7 dollars.
Step-by-step explanation:
Let's use a ratio:
pounds : $$$
8 : 56
4 : 28
2 : 14
1 : 7
A pound of salmon costs $7
Answer:
Step-by-step explanation:
56 divided by 8 is 7 so the answer is 7$ for one pound of salmon
Erin built a wooden box to hold hay on her farm. The box is 3 m long, 1 m wide, and 1 m high. Hay costs $14 per cubic meter.
Answer:
It will cost 42 to completely fill the box with hay.
have a good day <3
Whats is the 6+8-16
Answer:
-2
Step-by-step explanation:
6+8 equals 14. 14-16 equals -2
Answer: The importance of learning is that it helps the individual to acquire the necessary skills through learning and knowledge so that he can achieve his set goals. An important fact about learning is that it is a means to improve knowledge and gain skills that will help in reaching specific goals
Step-by-step explanation:
The importance of learning is that it helps the individual to acquire the necessary skills through learning and knowledge so that he can achieve his set goals. An important fact about learning is that it is a means to improve knowledge and gain skills that will help in reaching specific goals
3x+20=5x how many Solutions does it have
Answer:
one
Step-by-step explanation:
3x + 20 = 5x
20 = 5x - 3x
20 = 2x
x = 10
one solution
