Answer:
98,000 bacteria.
Step-by-step explanation:
We are given the formula:
[tex]P=le^{kt}[/tex]
Where l is the initial population, k is the rate of growth, and t is the time ( in hours).
We know that it has an initial population of 500. So, l is 500.
We also know that the population grows to 7000 after 2 hours.
And we want to find the population after 4 hours.
First, since we know that the population grows to 7000 after 2 hours, let's substitute 2 for t and 7000 for P. Let's also substitute 500 for l. This yields:
[tex]7000=500e^{2k}[/tex]
Divide both sides by 500:
[tex]e^{2k}=14[/tex]
We can solve for the rate k here, but this is not necessary. In fact, when can find our solution with just this.
Let's go back to our original equation. We want to find the population after 4 hours. So, substitute 4 for t:
[tex]P=500e^{4k}[/tex]
We want to find the total population, P. Notice that we can rewrite our exponent as:
[tex]P=500(e^{2k})^2[/tex]
This is the exact same thing we acquired earlier. So, we know that the expression within the parentheses is 14. Substitute:
[tex]P=500(14)^2[/tex]
Square and multiply:
[tex]P=500(196)=98000[/tex]
So, after 4 hours, there will be 98,000 bacteria.
And we're done!
Givin (2, 4) and 6, 12), what is The slope of the line between these two points?
Answer:
m=4 or slope =4
Step-by-step explanation:[tex]m=\frac{y2-y1}{x2-x1\\}[/tex]
so [tex]m=\frac{12-4}{6-2}[/tex] which is the same as 8/2. So all in all the slope is 4.
Given (64y^2)+(4x^2)+128y+16x+64=0, transform the equation into the appropriate form
Answer:
(8y+8)²+(4x²+16)=0
Step-by-step explanation:
Given:
(64y²)+(4x²)+128y+16x+64=0
Find:
Equation into the appropriate form
Computation:
(64y²)+(4x²)+128y+16x+64=0
(8y)²+(2x)²+128y+16x+64=0
(8y)²+(2x)²+2(8y)(8)+2(2x)(4) + 8²=0
(8y+8)²+(4x²+16)=0
Which graph represents the inequality y < -1 + 2x?
Answer:
The graph is attached down
Step-by-step explanation:
The form of the linear inequality is y < b + m x, where
m is the slope of the lineb is the y-intercept, the point of intersection between the line and the y-axis (0, b)The solution of the inequality is the area under the lineTo find which graph represents the inequality y < -1 + 2x
→ Find the y-intercept (the value of y at x = 0)
∴ b = -1
∴ The y-intercept is (0, -1)
From the given graphs we have two graphs that the line intersected the y-axis at (0, -1)
2nd graph in the 1st row
2nd graph in the 2nd row
∵ The sign of inequality is <
∴ The shaded area must be under the line
∴ The 2nd graph in the 1st row is our answer
The graph which represents the inequality y < -1 + 2x is attached down
How many hours will it take them to be 400 miles apart?
Step-by-step explanation:
50 miles per hour, how long will it take before that train meets THE Other train, going from B to A, at a speed
Karen can walk 2/3 of a mile in 1/5 of an hour. How long will it take her to walk 10 miles
Answer:
3 1/3 mph
Step-by-step explanation
2/3 mile divided by 1/5 hour
To divide by a fraction, MULTIPLY BY THE RECIPROCAL!
This gives 5(2/3) = 10/3 = three & 1/3 mile per hour, or about 3.33 mph.
Mariah owed her grandfather $2.25 but was recently able to pay him back $1.50 how much does Mariah currently owe her grandfather
Answer:
$0.75
Step-by-step explanation:
2.25-1.50=0.75
NEED HELP GIVING 15 POINTS
Choose the one problem that has NOT been done correctly. Start your response with the number you choose and explain the mistake that was made in the problem.
Answer:
1
Step-by-step explanation:
didn't mulitiply by -2
The graph shows f (x) and its transformation g(x) . Which equation correctly models g(x) ?
A) g(x) = 4x-2 + 4
B) g(x) = 4x+2 - 4
C) g(x) = 4x+4 + 2
D) g(x) = 4x-4 + 2
Find the median of the following data
2,8,7,8,6,15,6,8,3
Answer:
7
Step-by-step explanation:
Median is the middle value in a list of values arranged in increasing order.
The values given are :2,8,7,8,6,15,6,8,3
Arrange values in ascending order as: 2,3,6,6,7,8,8,8,15
The middle value is: 2,3,6,6,7,8,8,8,15
Median is 7
Twelve decreased by twice a number equals -34. What is that number?
Answer:
12 - 2x = -34
Step-by-step explanation:
Im not entirely sure if this is correct but yeee
High Hopes^^
Barry-
Cindy and Victoria completed 8/9 of their job in a day. Cindy has done 1/9 of the work. How much of the work was done by Victoria?
Answer:
7/9 of the work was done by Victoria.
Step-by-step explanation:
8/9-1/9=7/9
Express in the form n : 1
30 : 6
Answer:
5:1
Step-by-step explanation:
hi guys please help me to solve the following question
Answer:
D!
Step-by-step explanation:
To find the area, we multiply the length times the width to find the number of squares in each box.
A) 1 square down times 7 squares across is 1 x 7, which is 7.
B) 2 squares down times 6 squares across is 2 x 6= 12.
C) 3 squares down times 5 squares across is 3 x 5 = 15.
D) 4 squares down times 4 squares across = 4 x 4 =16.
16 is the biggest number here, so that is the greatest area!
If you enjoyed my answer, please give it a rating and a Thanks! If you think this answer was pretty brainly, please give it a Brainliest!
Have a great day!
Jasmine paid $64.50 for a bracelet, after tax, and the tax rate is 7.5%. What was the original price of the bracelet?
Answer:
About $59.66
Step-by-step explanation:
To find the amount of tax was paid, multiply 64.50 by 0.075 (because 0.075 = 7.5%). This would be 4.8375, which when rounded is 4.84. You subtract 64.50 by 4.84 to get 59.66, but because I rounded, it is about $59.66.
Answer:
60
Step-by-step explanation:
First, change the percentage to a decimal and write the equivalence of the sales tax amount. Let x be the original cost of the item.
Sales tax amount =x⋅0.075
Next, substitute the value into the equation:
Original Cost + Sales Tax Amount = Total Cost
x+0.075x=64.50
Add like terms.
1.075x=64.50
Divide both sides by 1.075 to isolate the unknown value.
x=$60
1 point
3. A bus driver stops at a gas station to put some gasoline in the bus. He
pays $2.48 per gallon for 15 gallons of gas. How much did he pay for the
gas?
Perform he operations in the correct order :
10 + 8 ÷ 1 -5
A local hamburger shop sold a combined total of 700 hamburgers and cheeseburgers on Tuesday . There were 50 more cheeseburgers sold than hamburgers . How many hamburgers were sold on Tuesday
Answer:
325
Step-by-step explanation:
h + c = 700
c = 50 + h
50+ h + h= 700
50+2h =700
2h=700-50
2h = 650
h=650/2
h=325
c=325+50
c=375
check 325+375=700
In 2008 the Better Business Bureau settled 75% of complaints they received (USA Today, March 2, 2009). Suppose you have been hired by the Better Business Bureau to investigate the complaints they received this year involving new car dealers. You plan to select a sample of new car dealer complaints to estimate the proportion of complaints the Better Business Bureau is able to settle. Assume the population proportion of complaints settled for new car dealers is .75, the same as the overall proportion of complaints settled in 2008
a. Suppose you select a sample of 450 complaints involving new car dealers. Show the sampling distribution of .
b. Based upon a sample of 450 complaints, what is the probability that the sample proportion will be within .04 of the population proportion?
c. Suppose you select a sample of 200 complaints involving new car dealers. Show the sampling distribution of .
d. Based upon the smaller sample of only 200 complaints, what is the probability that the sample proportion will be within .04 of the population proportion?
e. As measured by the increase in probability, how much do you gain in precision by taking the larger sample in part (b)?
Answer:
a) the sampling distribution of the sample proportion is approximately normal with mean 0.75 and standard deviation is 0.0204
b) the probability that the sample proportion will be within 0.04 of the population proportion is 0.95
c) sampling distribution of the sample proportion is approximately normal with mean 0.75 and standard deviation is 0.03061
d) the probability that the sample proportion will be within 0.04 of the population proportion is 0.8088
e) gain in precision is 0.1402.
Step-by-step explanation:
a) Let p represent the
Given that
population proportion of complaints settled for new car dealers p = 0.75.
and n = 450
mean of the sampling distribution of the sample proportion is the population proportion p
i.e up° = p
mean of the sampling distribution of the sample proportion p° = 0.75
so standard error of the proportion is;
αp° = √(p( 1-p ) / n)
we substitute
αp° = √(0.75 ( 1-0.75 ) / 450)
=√(0.1875 / 450
= √0.0004166
= 0.0204
therefore the sampling distribution of the sample proportion is approximately normal with mean 0.75 and standard deviation is 0.0204
b)
(p° - p) is within 0.04
so lets consider
p ( -0.04 ≤ p° - p ≤ 0.04) = p ( ( -0.04/√(0.75 ( 1-0.75 ) / 450)) ≤ z ≤ ( 0.04/√(0.75 ( 1-0.75 ) / 450))
= p( -0.04/0.0204 ≤ z ≤ 0.04/0.0204)
= p ( -1/96 ≤ z ≤ 1.96 )
= p( z < 1.96 ) - p( z < -1.96 )
now from the S-normal table,
area of the right of z = 1.96 = 0.9750
area of the left of z = - 1.96 = 0.0250
p( -0.04 ≤ p°- p ≤ 0.04) = p( z < 1.96 ) - p( z < -1.96 ) = 0.9750 - 0.0250
= 0.95
therefore the probability that the sample proportion will be within 0.04 of the population proportion is 0.95
c)
population proportion of complaints settled for new car dealers p = 0.75.
n = 200
mean of the sampling distribution of the sample proportion p°.
i.e up° = p
mean of the sampling distribution of the sample proportion p° = 0.75
Sampling distribution of the sample proportion p is determined as follows
αp° = √(p( 1-p ) / n)
we substitute
αp° = √(0.75 ( 1-0.75 ) / 200)
=√(0.1875 / 200
= √0.0009375
= 0.03061
therefore sampling distribution of the sample proportion is approximately normal with mean 0.75 and standard deviation is 0.03061
d)
(p° - p) is within 0.04
so lets consider
p ( -0.04 ≤ p° - p ≤ 0.04) = p ( ( -0.04/√(0.75 ( 1-0.75 ) / 200)) ≤ z ≤ ( 0.04/√(0.75 ( 1-0.75 ) / 200))
= p( -0.04/0.03061≤ z ≤ 0.04/0.03061)
= p ( -1.31 ≤ z ≤ 1.31 )
= p( z < 1.31 ) - p( z < -1.31 )
now from the S-normal table,
area of the right of z = 1.31 = 0.9049
area of the left of z = - 1.31 = 0.0951
p( -0.04 ≤ p°- p ≤ 0.04) = p( z < 1.31 ) - p( z < -1.31 ) = 0.9049 - 0.0951
= 0.8098
therefore the probability that the sample proportion will be within 0.04 of the population proportion is 0.8088
e)
From b), the sample proportion is within 0.04 of the population proportion; with the sample of 450 complaints involving new car dealers is 0.95.
sample proportion is within 0.04 of the population proportion; with the sample of 200 complaints involving new car dealers is 0.8098.
measured by the increase in probability, gain in precision occurs by taking the larger sample in part (b)
i.e
Gain in precision will be;
0.9500 − 0.8098
= 0.1402
therefore gain in precision is 0.1402.
what percent of 50 is 18?
Answer:
36 %
Step-by-step explanation:
Convert the fraction to a decimal, then multiply by 100 .
Answer:
36%
Step-by-step explanation:
The same explanation as she said
Help ASAP
Find the sum (-3x + 7) + (2x - 5).
Answer:
-x + 2
Step-by-step explanation:
Which ratio is equivalent to 3:7?
A 6:7
B 3:21
C 24:56
D 15:30
Answer:
c
Step-by-step explanation:
Answer:
C. 24:56
Step-by-step explanation:
3/7 * 8/8
3*8 = 24
7*8 = 56
24/56
Could someone help me with number 17.
Answer:
y=-7
Step-by-step explanation:
if g(x) is g(-2) that means that x=-2 so we plug that in so 5*-2+3
5*-2+ -10
-10+3+ -7
so y=-7
What is the quotient for 6 and 1/2 divided by 3/4
Answer:
I believe it is 4
Step-by-step explanation:
Solve the equation
6=u/9+10
Answer:
114
Step-by-step explanation:
Because u do 9+10 which equals 19 and then u do 19*6 and u get 114 so the expression now would be 6=114/(9+10)
Jose and Fernando are both working at the same company. Jose worked 42 hours last week while Fernando worked 38 hours during the same week. Jose makes $15/hour and Fernando makes $16/hour. Who made more money that week?
Answer:
Jose
Step-by-step explanation:
Jose:
Step 1:
42 × 15 Equation
Step 2:
$630 Multiply
Fernando:
Step 1:
38 × 16 Equation
Step 2:
$608 Multiply
Answer:
Jose earns more
Hope This Helps :)
Two functions are given below: f(x) and h(x). State the axis of symmetry for each function and explain how to find it.
Ps. I just need h(x)
A coordinate plane with 4 lines. The first line is labeled a(x) and passes through (2, negative 4) and (0, 2) and continues past (negative 1, 5). The second line is labeled f(x) and passes through (negative 6, negative 6), (negative 3, 0), and (0, 6). The third line is labeled g(x) and passes through (negative 2, negative 7), (0, negative 3), (1, negative 1) and (2, 1). The fourth line is labeled h(x) and passes through (negative 6, negative 6), (0, negative 3), and (6, 0).
When Janelle woke up, it was –3 degrees Fahrenheit outside. As the morning progressed, the temperature rose 2 degrees every hour.
Which line on the graph could represent this scenario?
a(x)
f(x)
g(x)
h(x)
Answer:
It is c which is g(x)
Step-by-step explanation:
Answer:
the answer is C : g(x)
Step-by-step explanation:
i just got the right answer on the assignment
What is 3/5 written as a percent? A. 6% B. 30% C. 60% D. 167%
Answer:
60%
Step-by-step explanation:
It is 60% because, First we have to make 3/5 a percent so we do 5 times 20 which is 100, and 3 times 20 which is 60. So it total it is 60/100 which is 60%
Answer:
[See Below]
Step-by-step explanation:
_________________________________
✦ An easier way of doing this is to change the fraction to an equivalent fraction:
[tex]\frac{3}{5}[/tex] ≅ [tex]\frac{6}{10}[/tex] ≅ [tex]\frac{60}{100}[/tex]✦ So now it's easier to change to a percentage.
[tex]\frac{60}{100} =60\%[/tex][tex]60[/tex] percent of [tex]100[/tex]_________________________________
So your answer would be:
[tex]\bold6\bold0\bold\%[/tex]_________________________________
~Hope this helps Mate. If you need anything feel free to message me.
[tex]-Your~ Friendly~ Answerer,~ Shane[/tex] ☺
Which expression is equivalent to Sine (StartFraction pi Over 12 EndFraction) cosine (StartFraction 7 pi Over 12 EndFraction) minus cosine (StartFraction pi Over 12 EndFraction) sine (StartFraction 7 pi Over 12 EndFraction)?
Answer:
EndRoot Over 2 EndFraction
StartFraction pi Over 6 EndFraction, StartFraction StartRoot 3 EndRoot Over 2 EndFraction
On using the trigonometric identity sin(x-y) = sin(x)cos(y) - cos(x)sin(y), we calculate that [tex]sin(\frac{\pi }{12})cos(\frac{7\pi }{12}) - cos(\frac{\pi }{12} )sin(\frac{7\pi }{12} ) =sin(\frac{-\pi }{2} )[/tex].
What are trigonometric identities?Trigonometric identities are equations that relate to different trigonometric functions and are true for any value of the variable that is there in the domain.
[tex]=sin(\frac{\pi }{12})cos(\frac{7\pi }{12}) - cos(\frac{\pi }{12} )sin(\frac{7\pi }{12} ) \\\\=sin(\frac{\pi }{12} -\frac{7\pi }{12})\\ \\ =sin(\frac{-\pi }{2} )[/tex]
Learn more about trigonometric identities here
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If the variance of the data values in a population is 225, what is the standard
deviation of the data values?
a.15
b.17
c.11
d.13
(apex)
Answer:15
Step-by-step explanation:
Apex