Using an exponential function, it is found that the city will be half populated in 9 months.
The population of Fantasy City doubles each month, hence, after t months, the population is given by:
[tex]P(t) = P(0)2^{t}[/tex]
In which P(0) is the initial population.Fully populated in 10 months, hence, the full population is:
[tex]P(10) = P(0)2^{10} = 1024P(0)[/tex]
Hence, half populated is [tex]P(t) = \frac{1024P(0)}{2} = 512P(0)[/tex], hence:
[tex]P(t) = P(0)2^{t}[/tex]
[tex]512P(0) = P(0)2^{t}[/tex]
[tex]2^t = 512[/tex]
[tex]2^t = 2^9[/tex]
[tex]t = 9[/tex]
The city will be half populated in 9 months.
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Write the equation of the parabola that has the vertex at point
(−2, 5.5) and passes through the point (−2.5, 2.5).
Answer:
-12x²-48x-42.5
Step-by-step explanation:
After deducting grants based on need, the average cost to attend the University of Southern California (USC) is $27,175 (U.S. News & World Report, America’s Best Colleges, 2009 ed.). Assume the population standard deviation is $7,400. Suppose that a random sample of 60 USC students will be taken from this population.
a. Refer to Exhibit 2. What is the value of the standard deviation of the mean? (Note: keep two decimal places.)
b.What is the probability that the sample mean will be more than $27,175
c.What is the probability that the sample mean will be within $1,000 of population mean? (Note: keep two decimal places for the z value and four decimal places for the final probability value.)
d.What would be the probability in Part c if the sample size were increased to 100? (Note: keep two decimal places for the z value and four decimal places for the final probability value.)
The solutions are:
(a) Standard error is 957.04. (b) The probability is 50%. (c)The probability is 0.8491. (d) The probability is 0.8617.
To calculate the values, use the standard error formula for the sample mean:
(a)
The standard error is given by:
[tex]Standard\ error =\dfrac{ Population \ standard \ deviation}{\sqrt{sample\ size}}\\Standard\ error=\dfrac {\$ 7,400 }{ \sqrt60}\\Standard\ error =\ $957.04[/tex]
(b)
To find the probability that the sample mean will be more than $27,175, convert it into a z-score and then find the area under the normal distribution curve:
z = (sample mean - population mean) / standard error
z = ($27,175 - $27,175) / $957.04
z = 0
Since the z-score is 0, the area under the curve to the right of this point is 0.5 or 50%.
c. To find the probability that the sample mean will be within $1,000 of the population mean, we need to find the area between the range of $(27,175 - $1,000) and $(27,175 + $1,000).
Lower limit: $27,175 - $1,000 = $26,175
Upper limit: $27,175 + $1,000 = $28,175
Now, we calculate the z-scores for both limits:
lower = ($26,175 - $27,175) / $957.04 ≈ -1.045
upper = ($28,175 - $27,175) / $957.04 ≈ 1.045
Using a standard normal distribution table or calculator, the probability of a z-score being between -1.045 and 1.045 is approximately 0.8491.
(d)
If the sample size were increased to 100.
[tex]Standard error = \dfrac{ \$7,400}{ \sqrt{100}} \\Standard error = \$740[/tex]
Find the probability that the sample mean will be within $1,000 of the population mean, did in part c:
Lower limit: $27,175 - $1,000 = $26,175
Upper limit: $27,175 + $1,000 = $28,175
lower = ($26,175 - $27,175) / $740
lower ≈ -1.351
upper = ($28,175 - $27,175) / $740
upper ≈ 1.351
Using a standard normal distribution table or calculator, the probability of a z-score being between -1.351 and 1.351 is approximately 0.8617.
Hence,
Standard error is 957.04.The probability is 50%.The probability is 0.8491.The probability is 0.8617.Learn more about Probability here:
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What is an equivalent ratio
Answer:
Equivalent ratios (which are, in effect, equivalent fractions) are two ratios that express the same relationship between numbers. We can create equivalent ratios by multiplying or dividing both the numerator and denominator of a given ratio by the same number. Two ratios that have the same value are called equivalent ratios. To find an equivalent ratio, multiply or divide both quantities by the same number. It is the same process as finding equivalent fractions.
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Find the 60" term of the following arithmetic sequence.
6, 13, 20, 27,
..
[tex]\text{First term, a =6}\\\\\text{Common difference, d = 13 -6 = 7}\\\\\text{Nth term} = a+(n-1)d = 6 +(n-1)7 = 6+7n-7 = 7n-1\\\\\text{60th term} = 7(60) -1 = 419[/tex]
Alan needs to mix 3 tablespoons of salt with 5 tablespoons of vinegar to make a cleaning solution. How many tablespoons of salt are needed for each tablespoon of vinegar? (5 points)
Question 3 options:
1)
tablespoons
2)
tablespoon
3)
tablespoon
4)
tablespoon
Answer:
the answer 3/5 lets hop i ace it
Step-by-step explanation:
Write 1.96 as a percent and as a fraction,
There are two spheres; the radius of the big sphere is two times the radius of the small sphere. How many times larger is the volume of the big sphere compared to the small one?
The volume of the bigger sphere is 8 times larger than the volume of the smaller sphere.
The formula of the volume of a sphere is given below
⇒ Formula:
V = 4/3(πr³)................. Equation 1⇒ Where:
V = Volume of the spherer = radius of the sphereπ = constant called pieFrom the question, There are two spheres.
If the radius of the bigger sphere is two times the radius of the smaller sphere.
R = 2r⇒ Where
R = bigger radiusr = smaller radiusFor the bigger sphere
⇒ Substitute these values into equation 1
V = 4/3(π(2r)³)V = 4/3(π8r³)............. Equation 2For the smaller sphere,
V' = 4/3(πr³)............... Equation 3⇒ Comparing equation 2 and equation 3
V = 8V'Hence, The volume of the bigger sphere is 8 times larger than the volume of the smaller sphere.
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What is the point of intersection for the graphs of the equations 4x-y=6 and x+y=4
Answer:
(2,2)
Step-by-step explanation:
4x-6 = 4-x
5x = 10
x = 2
y = 4-2 = 2
(2,2)
Três torneiras enchem uma piscina em 10 horas quantas horas levarão 10 torneiras para encher 2 piscinas
Answer:
Step-by-step explanation:
A contractor decides that he can build a house in eight weeks using 5 men. If he employs 3 more men, how long will the job take? Assume that all the men work at the same rate.
Evaluate each of the following limits.
a. lim 8(2 + h) – g(2)
if gt) = VI + 7
h
h→0
How do you solve this?
Answer:
lim = 1/6
Step-by-step explanation:
Apparently, we have ...
[tex]g(t)=\sqrt{t+7}[/tex]
It often works well to multiply by the conjugate of a difference that approaches zero.
[tex]\displaystyle\lim_{h\to 0}{\frac{g(2+h)-g(2)}{h}}=\lim_{h\to 0}{\frac{\sqrt{(2+h)+7}-\sqrt{2+7}}{h}}\\\\=\lim_{h\to 0}\frac{(\sqrt{9+h}-\sqrt{9})(\sqrt{9+h}+\sqrt{9})}{h(\sqrt{9+h}+\sqrt{9})}=\lim_{h\to 0}{\frac{(9+h)-9}{h(\sqrt{9+h}+\sqrt{9})}}\\\\=\lim_{h\to0}{\frac{h}{h(\sqrt{9+h}+3)}}=\left.\frac{1}{\sqrt{9+h}+3}\right|_{h=0}=\boxed{\frac{1}{6}}[/tex]
help me please!! <33
13/20 - 1/2
===================================================
Explanation:
Ignore the big X and the shading for now. This figure has 4 rows by 5 columns of rectangles. So there are 4*5 = 20 little rectangles total. Each little rectangle represents 1 brownie.
Then let's say the shaded region represents the amount of brownies Mary receives. We have 13 rectangles shaded in out of the 20 total. This means 13/20 is the fractional amount Mary gets.
She then eats 10 of the 20 total, so she eats 10/20 = 1/2 of the brownies.
Therefore, we end up with the expression 13/20 - 1/2 to represent the fractional amount that Mary still has that she hasn't eaten yet (which is 3/20).
We can say: 13/20 - 1/2 = 13/20 - 10/20 = 3/20
USE THE DIATRIBUTIVE PROPERTY TO WRITE 6(W+5) AS AN EQUIVALENT EXPRESSION
Answer:
w = 5
Step-by-step explanation:
Step 1: Use the Distributive property to get 6w + 30.
Step 2: Divide 6w by 6 and cancel out both 6s.
Step 3: Divide 30 by 6 to get 5, and you have the answer.
12POINTS PLEASE HURRY ASAPPPPP <3
ITS SQAURE 6
6 SQAURE OFTHE 6
PLZZZ HELP, BEST ANSWER GETS BRANLIEST AND ITS DUE IN 5 MINUTESSS,
The figure shows two triangles on the coordinate grid:
Which of the following statements is true about the three quadrilaterals? (5 points)
A and B are similar but not congruent.
A and C are similar but not congruent.
A and B are similar and also congruent.
B and C are similar and also congruent.
Answer:
The first one
Step-by-step explanation:
A and B are similar because the proportions are the same.
A is congruent to C but none of the answers ask that.
The camp cook needed 2172 ounces of juice each day each carton of juice contains 64 ounces the Cook estimated that he needed 30 cartons of juice each day which expression proves that his estimate is incorrect
Answer: 384
Step-by-step explanation:
Please due today by 10:00
In a survey of 1900 people who owned a certain type of car, 1140 said they would buy that type of car again. What percent of the people surveyed were satisfied with the car?
Answer:
60% of the people surveyed were satisfied with the car
Step-by-step explanation:
1140 satisfied people / 1900 total people = 0.60 = 60% satisfied people
Factor: 3x4y3 – 48y3
Answer: 4y3(1x1 - 12)
3x4y3 – 48y3
4y3(1x1 - 12)
Find the area and perimeter of the shape given below.
Answer:
perimeter: 14+5+6+6+8+10=59
area: 14x5x6x10=4200
perimeter means adding all the sides including the ones that arent labeled, and the area is multiplying all the numbers included.
Darla scored 18 points in her last basketball game, shooting only 2- and 3-point shots. If she made 7 total
Answer:
3 2-pt shots, 4 3-pt shots
Step-by-step explanation:
2x + 3y = 18
x + y = 7, so x = 7 - y
Substitute in for x
2(7 - y) + 3y = 18
14 - 2y + 3y = 18
14 + y = 18
y = 4
Now put 4 in for y to solve for x
2x + 3(4) = 18
2x + 12 = 18
2x = 6
x = 3
Find the total area of the shape shown below in square feet. Enter only the number.
16 feet
5 feet
12 feet
9 feet
7 feet
7 feet
The solution is
Answer:
129, because you split the shape into two find the area of them separately and then add them up
The table shows the transportation method of employees at a certain company. What percent of the total amount of employees drive a bus to work?
Car: 758
Bus:530
Walk:7
Other:105
Total:1400
Answer:
about 0.38 %
Step-by-step explanation:
Total = 1,400 Employees
Those who drive a bus = 530
530 / 1,400 = 0.378571428571429
round up = about 0.38 %
Marty has 6 cans of pain that he can use for the 3 bedrooms he needs to paint. How much paint can Marty use in each bedroom?
a book is marked down by 28% from the original price of 19.50 what is the new price
Answer:
$14.04
Step-by-step explanation:
to find the answer we can multiply 19.5 by 28% and use that answer to subtract to 19.5 or we can just directly multiply 19.5 by 72%
19.5 * 72% = 14.04
it costs $14.04 after a markdown of 28%
URGENT simplify (5^3 x 5^5)^5
Answer:
5^40
Step-by-step explanation:
Step 1: Multiply the exponents within the parentheses with the exponent outside of the parentheses.
[tex](5^3^*^5)(5^5^*^5)[/tex] [tex](5^1^5)(5^2^5)[/tex]Step 2: Based on the laws of exponents, add the exponents together.
[tex]5^(^1^5^+^2^5^)[/tex] [tex]5^4^0[/tex]Therefore, the answer is 5^40.
LAST ATTEMPT MARKING AS BRAINLIEST!! ( write a rule to describe each transformation)
Answer:
See below
Step-by-step explanation:
Dilation of 4
Z (0, -1) Z' (0, -4)
X (1, -1) X' (4, -4)
help me please please
Answer:
i think its D or 14/16
Step-by-step explanation:
Answer:
[tex]\frac{14}{16}[/tex]
Step-by-step explanation:
[tex]\frac{1}{4}[/tex] + [tex]\frac{10}{16}[/tex]
Before adding we require the denominators of both fractions to be common
Multiply numerator/ denominator of first fraction by 4
= [tex]\frac{1(4)}{4(4)}[/tex] + [tex]\frac{10}{16}[/tex]
= [tex]\frac{4}{16}[/tex] + [tex]\frac{10}{16}[/tex] ( now add the numerators leaving the common denominator )
= [tex]\frac{4+10}{16}[/tex]
= [tex]\frac{14}{16}[/tex]
The fraction can be simplified by dividing the numerator/ denominator by 2 to
[tex]\frac{7}{8}[/tex]
classify the conic section without graphing 3x^2-2xy+3y^2+2x-4y+1=0
Circle: When x and y are both squared and the coefficients on them are the same — including the sign.
For example, take a look at 3x2 – 12x + 3y2 = 2. Notice that the x2 and y2 have the same coefficient (positive 3). That info is all you need to recognize that you’re working with a circle.
Parabola: When either x or y is squared — not both.
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