Answer:
From the central limit theorem we know that the distribution for the sample mean [tex]\bar X[/tex] is given by:
[tex]\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})[/tex]
The mean is given by:
[tex] \bar X = 13.6[/tex]
And the deviation is given by:
[tex]\sigma_{\bar X} =\frac{3}{\sqrt{100}}= 0.3[/tex]
Step-by-step explanation:
For this case we define the random variable X as "number of years of education of self-employed individuals in the U.S." and we know the following properties:
[tex] E(X) = 13.6 , Sd(X) = 3[/tex]
And we select a sample of n = 100
The central limit theorem states that "if we have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large".
From the central limit theorem we know that the distribution for the sample mean [tex]\bar X[/tex] is given by:
[tex]\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})[/tex]
Solution to the problem
From the central limit theorem we know that the distribution for the sample mean [tex]\bar X[/tex] is given by:
[tex]\bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}})[/tex]
The mean is given by:
[tex] \bar X = 13.6[/tex]
And the deviation is given by:
[tex]\sigma_{\bar X} =\frac{3}{\sqrt{100}}= 0.3[/tex]
Answer:
a) Mean of the sampling distribution = 13.6 years
b) Standard deviation of the sampling distribution = 0.3
[tex]\bar {x} = N(13.6, 0.3)[/tex]
Step-by-step explanation:
Population mean, [tex]\mu = 13.6 years[/tex]
Population standard deviation, [tex]\sigma = 3.0 years[/tex]
Sample size, n = 100
a) Mean of the sampling distribution = mean of the normal distribution
[tex]\mu_{s} = \mu\\\mu_{s} = 13.6 years[/tex]
b) Standard deviation of the sampling distribution, [tex]\sigma_{s} = \frac{\sigma}{\sqrt{n} }[/tex]
[tex]\sigma_{s} = \frac{3}{\sqrt{100} } \\\sigma_{s} = \frac{3}{10} \\\sigma_{s} = 0.3[/tex]
Which condition would result in the transformed function ? The dashed graph on the left shows f(x)=x2 ans the solid graph shows the transformed parent function
Answer: f(2x)
Step-by-step explanation:
ed 2020
the joint frequency for females is
Answer:
55%
Step-by-step explanation:
A company borrowed $40,000 for 3 years at 6% compounded daily. It will not make any payments on this loan prior to maturity. Find (a) the total future value they will need to accumulate to pay off this debt, and (b) the quarterly sinking fund payment needed to accumulate this maturity value, assuming a 5% rate.
Answer:
a A=$47,887.81
b.A=$46,430.80
Step-by-step explanation:
a. Given the initial amount is $40,000 with a 3-year term and a 6% rate compounded daily.
-Take 1 year=365 days
#First we calculate the effective interest rate corresponding to the daily compounding;
[tex]i_m=(1+i/m)^m-1\\\\=(1+0.06/365)^{365}-1\\\\=0.06183[/tex]
#We use the calculated effective rate, 0.06183, to solve for the future value as:
[tex]A=P(1+i_m)^n\\\\=40000(1.06183)^3\\\\=47887.81[/tex]
Hence, the total future value for a daily compounding is $47,887.81
b. For a sinking fund with a 5% compounded quarterly:
#We calculate the annual effective rate:
[tex]i_m=(1+i/m)^m-1\\\\=(1+0.05/4)^4-1\\\\=0.05095[/tex]
#We use the calculated effective rate, 0.05095, to solve for the future value as:
[tex]A=P(1+i_m)^n\\\\=40000(1.05095)^3\\\\=46430.80[/tex]
Hence, the future value of the sinking fund is $46,430.80
What the is common denominator for 1/9 and 5/12
Answer:
I'm just going to take a guess and say 36?
Step-by-step explanation:
You purchase a car in 2010 for $25,000. The value of the car decreases by 14% annually. What would the value of the car be in 2020?
Answer:
42,690
Step-by-step explanation:
it is the rule of LONG numbers
The value of the car in 2020 is $5532.53
What is exponential decay?A quantity is subject to exponential decay if it decreases at a rate proportional to its current value.
Given that, You purchase a car in 2010 for $25,000. The value of the car decreases by 14% annually.
The exponential decay is given by =
[tex]A = P(1-r)^t[/tex]
A = final amount
P = principal amount
r = rate of decrease.
t = 10
Therefore,
A = 25000(1-0.14)¹⁰
A = 25000×0.86¹⁰
A = 5532.53
Hence, the value of the car in 2020 is $5532.53
For more references on exponential decay, click;
https://brainly.com/question/2193799
#SPJ2
Gender in the Population of Part-time College Students According to a 2010 report from the American Council on Education, females make up 57% of the U.S. college population. With the rising costs of education and a poor economy, many students are working more and attending college part time. We anticipate that if we look at the population of part-time college students, a larger percentage will be female. Let’s say we predict that 60% of part-time college students are female. We don’t have information about the population of part-time college students, so we select a random sample of 25 part-time college students and calculate the proportion of the sample that is female. We don’t expect the sample proportion to be exactly 0.60. So, how much could the sample proportion vary from 0.60 for us to feel confident in our prediction?To answer this question, we need to understand how much sample proportions will vary if the parameter is 0.60.Refer to the previous example for the following questions. These questions focus on how the proportion of females will vary in random samples if we assume that 0.60 of the population of part-time college students is female.
Answer:
These questions focus on how the proportion of females will vary in random samples if we assume that 0.60 of the population of part-time college students is female.
1. Before we use a simulation to simulate the selection of random samples from this population, let’s make sure we are clear about who is in the population. For this situation which statement best describes the population? part-time college students
2. What are we assuming to be true about the population? The proportion of the population that is female is 0.60
3. Which of the following sequences of sample proportions is the most likely to occur in random samples of 25 students from this population? 0.56, 0.60, 0.44, 0.68, 0.76
Find the volume of the sphere.
Either enter an exact answer in terms of pi or use 3.14 and round to the nearest hundredth
Answer:
The volume is 2144.66
Step-by-step explanation:
The equation i used when solving this question.
V=4/3πr3
The volume of sphere when rounded to nearest 100th will be 2143.574 cubic units
Given: a sphere of radius 8 units
To find: Volume of sphere
The volume of a sphere can be calculated using the formula [tex]V = \frac{4}{3}\pi r^3[/tex], where r is the radius of the sphere. To find the volume, plug in the value of the radius into the formula and calculate the result.
[tex]V = \frac{4}{3}\pi r^3\\[/tex]
[tex]V = \frac{4}{3}\pi (8)^3\\[/tex]
[tex]V = \frac{4}{3}\pi (8)^3 = 682.667 \pi[/tex]
If we insert the value of [tex]\pi = 3.14[/tex] we get:
[tex]V = 682.667 \times 3.14 = 2143.57438[/tex]
When rounded to nearest 100th we will get volume equal to 2143.574 cubic units.
25 POINTS PLZ ANSWER FAST!!!!!!!!!!!!!!!!!
Given:
Given that Steven purchased a box of chocolate shaped like a square pyramid.
The box is 12 inches tall and the area of the bottom of the box is 35 square inches.
We need to determine the expression that is used to find the number of chocolates that the box holds.
Expression:
The expression that is used to find the number of chocolates that the box holds can be determined using the formula,
[tex]V=\frac{1}{3} Bh[/tex]
where B is the area of the base and h is the height of the pyramid.
Substituting B = 35 and h = 12 in the above formula, we get;
[tex]V=\frac{1}{3}(35 \cdot 12)[/tex]
Thus, the expression that is used to find the number of chocolates that the box holds is [tex]\frac{1}{3}(35 \cdot 12)[/tex]
Hence, Option b is the correct answer.
Answer:
Option 2
Step-by-step explanation:
Volume of a pyramid
⅓ × base area × height
⅓ × 35 × 12
12 × 35 × ⅓
This net will be folded to form a solid.
The net of a triangular prism.
Which statements are true about the model created? Check all that apply.
Each face will be a rectangle.
The solid will be a triangular prism.
The solid will be a rectangular pyramid.
Each face will be a triangle.
The solid will have some faces that are rectangles and some faces that are triangles.
The solid will have five faces.
The solid will have three faces.
The solid will have two faces.
Answer:
2,5, and 6
Step-by-step explanation:
hope this helps
The solid will be a triangular prism .The solid will have some faces that are rectangles and some faces that are triangles.
The solid will have five faces.
HELP ASAP PLEASE!!!
Which of the following angles are shown in the drawing?
a. ADB
b. D
c. CBD
d. 1
Answer:
Adb , cbd, 1
Step-by-step explanation:
Answer:
ADB CBD 1
Step-by-step explanation:
Buruction
Acuve
Graphing the Relationship between Two Quantities
Quick
Isoke's little brother can walk 2 miles per hour.
Select all that apply.
Use the numbers in the table to create ordered
pairs
Hours
Miles
y
Plot each number in the table as a point on the
graph.
Plot the ordered pairs on the graph.
Draw a straight line that starts at the origin and
connects all the points.
6
The values of the variables cannot be represented
by fractions, so you do not connect the points with a
line
D
Intro
Answer:
the answer is A.Use the numbers in the table to create ordered pairs. and D.Draw a straight line that starts at the origin and connects all the points.
Step-by-step explanation:
I just did it on edgnuity and got it right.
Answer:
The correct answer is A C and D
Step-by-step explanation:
A type of bacteria doubles in number every 12 hours after 2 days there are 48 bacteria how many bacteria were there at the beginning of the first day
Initial bacteria count is 3, as it doubles every 12 hours; after 2 days, totaling 48 bacteria.
To solve this problem, we can use the formula for exponential growth, which is
[tex]\( N = N_0 \times 2^{(t/d)} \)[/tex],[tex]- \( N \)[/tex]is the final number of bacteria,
[tex]- \( N_0 \)[/tex] is the initial number of bacteria,
[tex]- \( t \)[/tex] is the elapsed time in hours, and
[tex]- \( d \)[/tex] is the doubling time in hours.
Given that the doubling time is 12 hours and after 2 days (which is 48 hours) there are 48 bacteria, we can plug these values into the formula and solve for [tex]\( N_0 \):[/tex]
[tex]\[ 48 = N_0 \times 2^{(48/12)} \][/tex]
Solving this equation:
[tex]\[ 48 = N_0 \times 2^4 \][/tex]
[tex]\[ 48 = N_0 \times 16 \][/tex]
Now, to find [tex]\( N_0 \)[/tex]:
[tex]\[ N_0 = \frac{48}{16} \][/tex]
[tex]\[ N_0 = 3 \][/tex]
So, there were 3 bacteria at the beginning of the first day.
HI PLEASE HELP ME WITH MY CALCULUS 1 HW? I AM REALLY STUCK. I need help with parts d,e,g.
(d) The particle moves in the positive direction when its velocity has a positive sign. You know the particle is at rest when [tex]t=0[/tex] and [tex]t=3[/tex], and because the velocity function is continuous, you need only check the sign of [tex]v(t)[/tex] for values on the intervals (0, 3) and (3, 6).
We have, for instance [tex]v(1)\approx-0.91<0[/tex] and [tex]v(4)\approx0.91>0[/tex], which means the particle is moving the positive direction for [tex]3<t<6[/tex], or the interval (3, 6).
(e) The total distance traveled is obtained by integrating the absolute value of the velocity function over the given interval:
[tex]\displaystyle\int_0^6|v(t)|\,\mathrm dt=\int_0^3-v(t)\,\mathrm dt+\int_3^6v(t)\,\mathrm dt[/tex]
which follows from the definition of absolute value. In particular, if [tex]x[/tex] is negative, then [tex]|x|=-x[/tex].
The total distance traveled is then 4 ft.
(g) Acceleration is the rate of change of velocity, so [tex]a(t)[/tex] is the derivative of [tex]v(t)[/tex]:
[tex]a(t)=v'(t)=-\dfrac{\pi^2}9\cos\left(\dfrac{\pi t}3\right)[/tex]
Compute the acceleration at [tex]t=4[/tex] seconds:
[tex]a(t)=\dfrac{\pi^2}{18}\dfrac{\rm ft}{\mathrm s^2}[/tex]
(In case you need to know, for part (i), the particle is speeding up when the acceleration is positive. So this is done the same way as part (d).)
Use the distributive property to write the following expression WITHOUT parentheses:
5(x+4)
Answer:
5x+20
Step-by-step explanation:
5(x+4)
Distribute
Multiply 5 by each term inside the parentheses
5*x + 5*4
5x+20
Consider the triangles.
Triangle C D E. Angle C is blank, angle D is 87.3 degrees, angle E is 35.5 degrees. Triangle R S T. Angle R is blank, angle S is 57.2 degrees, angle T is 87.3 degrees.
Answer the questions about these triangles.
What is the measure of angle C?
Which angle corresponds to angle C?
What can be concluded about the triangles?
Answer: 1 = 57.2
2 = angle S
3 = the triangles are similar (the second choice)
Step-by-step explanation: i got the question right on my work on e d g e n u i t y
Consider the triangles.
Triangle C D E. Angle C is blank, angle D is 87.3 degrees, angle E is 35.5 degrees. Triangle R S T. Angle R is blank, angle S is 57.2 degrees, angle T is 87.3 degrees.
Answer the questions about these triangles.
What is the measure of angle C?
✔ 57.2
Which angle corresponds to angle C?
✔ angle S
What can be concluded about the triangles?
✔ The triangles are similar.
The measure of angle C in triangle CDE is 57.2 degrees, Angle C corresponds to angle R in triangle RST, and the two triangles are similar or congruent.
What is Triangle?A triangle is a three-sided polygon that consists of three edges and three vertices.
Since the sum of angles in a triangle is always 180 degrees, we can find the measure of angle C in triangle CDE by subtracting the measures of angles D and E from 180 degrees:
Angle C = 180 degrees - Angle D - Angle E
Angle C = 180 degrees - 87.3 degrees - 35.5 degrees
Angle C = 57.2 degrees
Therefore, the measure of angle C in triangle CDE is 57.2 degrees.
Angle C corresponds to angle R in triangle RST, since they are both unknown angles in their respective triangles.
We can conclude that the two triangles are similar or congruent.
Hence, the measure of angle C in triangle CDE is 57.2 degrees, Angle C corresponds to angle R in triangle RST, and the two triangles are similar or congruent.
To learn more on Triangles click:
https://brainly.com/question/2773823
#SPJ3
A 90% confidence interval for the true percentage of college students who like Brussels sprouts is (1.8%, 4.6%). What is the point estimator of the true percentage of college students who like Brussels sprouts?
Answer:
[tex]\hat p = \frac{Lower+Upper}{2}[/tex]
And replacing the info from the problem we have:
[tex]\hat p = \frac{0.018+0.046}{2}= 0.032[/tex]
So then the best estimator for the true proportion p is given by [tex]\hat p = 0.032 [/tex] or equivalent to 3.2 %
Step-by-step explanation:
We want to find a confidence interval for a proportion p who represent the parameter of interest.
The confidence interval would be given by this formula:
[tex]\hat p \pm z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]
For this case the 90% confidence interval is given by (1.8%=0.018, 4.6%=0.046) after apply the last formula
Since the confidence interval is symmetrical we can estimate the point estimator of the true percentage with this formula:
[tex]\hat p = \frac{Lower+Upper}{2}[/tex]
And replacing the info from the problem we have:
[tex]\hat p = \frac{0.018+0.046}{2}= 0.032[/tex]
So then the best estimator for the true proportion p is given by [tex]\hat p = 0.032 [/tex] or equivalent to 3.2 %
Coralee invests $5,000 in an account that compounds interest monthly and earns 7%. How long will it take her money to double?
Answer:
It will take 10 years for her money to double.
Step-by-step explanation:
The compound interest formula is given by:
[tex]A = P(1 + \frac{r}{n})^{nt}[/tex]
Where A is the amount of money, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per year and t is the number of years the money is invested or borrowed for.
In this exercise:
We want to find t for which the money doubles, that is, t when A = 2P.
Compounded monthly, an year has 12 months, so n = 12
Interest rate of 7%, so r = 0.07.
The following logarithm property is used:
[tex]\log{a^{t}} = t\log{a}[/tex]
So
[tex]A = P(1 + \frac{r}{n})^{nt}[/tex]
[tex]2P = P(1 + \frac{0.07}{12})^{12t}[/tex]
[tex](1.0058)^{12t} = 2[/tex]
[tex]\log{(1.0058)^{12t}} = \log{2}[/tex]
[tex]12t\log{1.0058} = \log{2}[/tex]
[tex]t = \frac{\log{2}}{12\log{1.0058}}[/tex]
[tex]t = 10[/tex]
It will take 10 years for her money to double.
An engineer designed a valve that will regulate water pressure on an automobile engine. The engineer designed the valve such that it would produce a mean pressure of 7.4 pounds/square inch. It is believed that the valve performs above the specifications. The valve was tested on 130 engines and the mean pressure was 7.6 pounds/square inch. Assume the standard deviation is known to be 0.9. A level of significance of 0.02 will be used. Make a decision to reject or fail to reject the null hypothesis. Make a decision.
Answer:
[tex]z=\frac{7.4-7.6}{\frac{0.9}{\sqrt{130}}}=-2.534[/tex]
[tex]z_{\alpha}=-2.054[/tex]
If the calculated value is less than the critical value we reject the null hypothesis.
P value
The p value for this test would be:
[tex]p_v =P(Z<-2.534)=0.0056[/tex]
Since the p value is lower than the significance level given we have enough evidence to reject the null hypothesis at the 25 of significance level given.
Step-by-step explanation:
Information given
[tex]\bar X=7.6[/tex] represent the sample mean
[tex]\sigma=0.9[/tex] represent the population deviation
[tex]n=130[/tex] sample size
[tex]\mu_o =7.4[/tex] represent the value that we want to check
[tex]\alpha=0.02[/tex] represent the significance level for the hypothesis test.
z would represent the statistic
[tex]p_v[/tex] represent the p value for the test
System of hypothesis
We want to check if the mean pressure is less then 7.6 pounds/square inch, the system of hypothesis are:
Null hypothesis:[tex]\mu \geq 7.6[/tex]
Alternative hypothesis:[tex]\mu < 7.6[/tex]
The statistic would be:
[tex]z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}[/tex] (1)
Replacing the values we got:
[tex]z=\frac{7.4-7.6}{\frac{0.9}{\sqrt{130}}}=-2.534[/tex]
Critical value
we need to find a critical value who accumulates 0.02 of the area in the left of the normal standard distribution and we got:
[tex]z_{\alpha}=-2.054[/tex]
If the calculated value is less than the critical value we reject the null hypothesis.
P value
The p value for this test would be:
[tex]p_v =P(Z<-2.534)=0.0056[/tex]
Since the p value is lower than the significance level given we have enough evidence to reject the null hypothesis at the 25 of significance level given.
You go to Home Depot to buy some materials for a project. Your total bill for materials only was $45.90. You go to the check out where you get charged taxes of 7.2%. That gets added to your bill. You then have a coupon for $15 off your total purchase after taxes. What is the amount you actually pay for your bill after taxes and coupons are applied?
Answer:
$34.20
Step-by-step explanation:
First, find the cost with tax
You are paying 7.2% tax, but you are also paying for 100% of the bill
100%+7.2%=107.2%
So, you are really paying for 107.2% of the bill
Convert 107.2% to a decimal by dividing by 100 or moving the decimal 2 spaces to the right
107.2/100=1.072
Multiply the decimal by the cost of the bill
1.072*45.90=49.2048
But, we also have a coupon for $15 off
Subtract 15 from the cost with tax
49.2048-15=34.2048
Round to the nearest cent/hundreth
$34.20
Hope this helps! :)
There are 6 cars traveling together. Each car has two people in front and three people in back. Explain how to use the situation to illustrate the distributive property.
The situation can illustrate the distributive property in math (6*(2+3)=6*2 + 6*3), representing 'a' as six cars, and 'b' and 'c' as the people in each car.
Explanation:The situation described can be used to illustrate the distributive property in mathematics. The distributive property states a(b + c) = ab + ac. In this scenario, the six cars can be represented as 'a', while the 'b' and 'c' can represent the two people in front and the three in the back. Therefore, the total number of people in all cars is 6*(2+3) which according to the distributive property equals 6*2 + 6*3. That is, 12 people in the front seats and 18 in the back seats, summed up to be 30 people in total.
Learn more about Distributive Property here:https://brainly.com/question/37341329
#SPJ2
Final answer:
The distributive property states that the product of a number and a sum is equal to the sum of the individual products. In this situation with the cars, we can use the distributive property to calculate the total number of people in all the cars.
Explanation:
The distributive property in mathematics states that the product of a number and a sum is equal to the sum of the individual products. In this situation with the cars, we can use the distributive property to calculate the total number of people in all the cars. Each car has 2 people in front and 3 people in back, so we can write the expression as (2 + 3) * 6. Using the distributive property, we can simplify this expression to 2 * 6 + 3 * 6, which equals 12 + 18, or 30 people in all the cars.
According to a Pew Research Center, in May 2011, 35% of all American adults had a smart phone (one which the user can use to read email and surf the Internet). A communications professor at a university believes this percentage is higher among community college students.
She selects 300 community college students at random and finds that 120 of them have a smart phone. In testing the hypotheses: H0: p = 0.35 versus Ha: p > 0.35, she calculates the test statistic as Z = 1.82.
Use the Normal Table to help answer the p-value part of this question.
Click here to access the normal table.
1. There is enough evidence to show that more than 35% of community college students own a smart phone (P-value = 0.034).
2. There is enough evidence to show that more than 35% of community college students own a smart phone (P-value = 0.068).
3. There is not enough evidence to show that more than 35% of community college students own a smart phone (P-value = 0.966).
4. There is not enough evidence to show that more than 35% of community college students own a smart phone (P-value = 0.034).
Answer:
[tex]p_v =P(z>1.82)=0.034[/tex]
Assuming a standard significance level of [tex]\alpha=0.05[/tex] the best conclusion for this case would be:
4. There is not enough evidence to show that more than 35% of community college students own a smart phone (P-value = 0.034).
Because [tex] p_v <\alpha[/tex]
If we select a significance level lower than 0.034 then the conclusion would change.
Step-by-step explanation:
Data given
n=300 represent the random sample taken
X=120 represent the people who have a smart phone
[tex]\hat p=\frac{120}{300}=0.4[/tex] estimated proportion of people who have a smart phone
[tex]p_o=0.35[/tex] is the value that we want to test
z would represent the statistic (variable of interest)
[tex]p_v[/tex] represent the p value (variable of interest)
System of hypothesis
We need to conduct a hypothesis in order to test the claim that the true proportion of people who have a smart phone is higher than 0.35, the system of hypothesis are.:
Null hypothesis:[tex]p\leq 0.35[/tex]
Alternative hypothesis:[tex]p > 0.35[/tex]
The statistic is given by:
[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)
Calculate the statistic
Since we have all the info requires we can replace in formula (1) like this:
[tex]z=\frac{0.4 -0.35}{\sqrt{\frac{0.35(1-0.35)}{300}}}=1.82[/tex]
Statistical decision
Since is a right tailed test the p value would be:
[tex]p_v =P(z>1.82)=0.034[/tex]
Assuming a standard significance level of [tex]\alpha=0.05[/tex] the best conclusion for this case would be:
4. There is not enough evidence to show that more than 35% of community college students own a smart phone (P-value = 0.034).
Because [tex] p_v <\alpha[/tex]
If we select a significance level lower than 0.034 then the conclusion would change.
Steve likes to entertain friends at parties with "wire tricks." Suppose he takes a piece of wire 52 inches long and cuts it into two pieces. Steve takes the first piece of wire and bends it into the shape of a perfect circle. He then proceeds to bend the second piece of wire into the shape of a perfect square. What should the lengths of the wires be so that the total area of the circle and square combined is as small as possible
Answer:
Steve should use:
8.53 Inch of Wire to make the circle43.47 Inches of Wire to make the Square.Step-by-step explanation:
Let Steve cut the wire so that the first piece has length x.
Therefore, the second piece will have a length of (52 - x).
The wire of length x is used to make a circle
Circumference of a Circle,
[tex]c = 2\pi r\\Therefore\\2\pi r=x\\r=\dfrac{x}{2\pi}[/tex]
[tex]\text{Area of a circle, A}=\pi r^2= \pi (\dfrac{x}{2\pi})^2=\pi (\dfrac{x^2}{4\pi^2})\\A=\dfrac{x^2}{4\pi}[/tex]
The wire of length (52-x) is used to make a square.
[tex]\text{Side length of the Square,}[/tex] [tex]s= \dfrac{52-x}{4}[/tex]
[tex]\text{Area of the Square},s^2= \left(\dfrac{52-x}{4}\right)^2=\dfrac{(52-x)^2}{16}=\dfrac{x^2-104x+2704}{16}[/tex]
Total Area = Area of Circle + Area of Square
[tex]Area=\dfrac{x^2}{4\pi}+\dfrac{x^2-104x+2704}{16}[/tex]
Let us simplify the expression
[tex]Area=\dfrac{16x^2+\pi(x^2-104x+2704)}{16\pi}\\=\dfrac{16x^2+\pi x^2-104\pix+2704\pi}{16\pi}\\=\dfrac{x^2(16+\pi)-104\pi x+2704\pi}{16\pi}\\=\dfrac{x^2(16+\pi)}{16\pi}-\dfrac{104\pi x}{16\pi}+\dfrac{2704\pi}{16\pi}\\A=\dfrac{x^2(16+\pi)}{16\pi}-6.5x+169[/tex]
This is the function of a parabola which opens up.
To find where A is minimum, find the axis of symmetry.
[tex]$Using \: x=-\frac{b}{2a}[/tex]
[tex]a=\dfrac{16+\pi}{16\pi}, b=-6.5\\ x=-\dfrac{-6.5}{2(\dfrac{16+\pi}{16\pi})}=8.53\:Inches[/tex]
Steve should cut the wire so that the length of wire used to make a circle is 8.53 Inches.
Length of wire used to make the square =52-8.53=43.47 Inches
Last month, Ginger's hotel ran an occupancy rate of 85%. Her competitive set had 150,000 room nights included within it that were available for sale during that month. During that month, the competitive set sold a total of 115,000 rooms. What was the approximate occupancy rate INDEX last month for Ginger's hotel? It's one of the following answer; 78%, 92%, 87% or 39%? Provide details.
Given Information:
Occupancy rate of Ginger’s hotel = 85%
Competitive set available rooms = 150,000
Competitive set sold rooms = 115,000
Required Information:
Occupancy rate INDEX = ?
Answer:
Occupancy rate INDEX = 111%
Step-by-step explanation:
The occupancy rate INDEX is given by
Occupancy rate INDEX = Occupancy rate of Ginger’s hotel/Occupancy rate of competitive set
We are given the occupancy rate of Ginger’s hotel so we need to first find out occupancy rate of competitive set which is given by
Occupancy rate of competitive set = Competitive set sold rooms/Competitive set available rooms
Occupancy rate of competitive set = 115,000/150,000
Occupancy rate of competitive set = 0.7667
Occupancy rate of competitive set ≈ 76.67%
Finally, we can now find the occupancy rate INDEX
Occupancy rate INDEX = Occupancy rate of Ginger’s hotel/Occupancy rate of competitive set
Occupancy rate INDEX = 85/76.67
Occupancy rate INDEX = 1.108
Occupancy rate INDEX = 110.8%
Occupancy rate INDEX ≈ 111%
Therefore, the approximate occupancy rate INDEX last month for Ginger's hotel is 111%
An infinite geometric series converges if the common ratio is
An infinite geometric series would only converge if the common ratio is a proper fraction.
What is an infinite geometric series?An infinite geometric series can be defined as the sum of a geometric sequence that typically has a constant common ratio between successive terms but no last term.
In Mathematics, it is a fact that if the common ratio of an infinite geometric series is a proper fraction, this would make it to converge because each successive term gets smaller and smaller.
In conclusion, an infinite geometric series would only converge if the common ratio is a proper fraction such as 3/6.
Read more on geometric series here: brainly.com/question/12630565
#SPJ2
Answer:
c. a proper fraction
b and d. -2/3 and 3/4
c. 80/3
Step-by-step explanation:
...
Steve wants to know what the average ACT scores of students graduated from his high school is. He randomly selected 25 students from an email list and asked them to provide the information. Of them 20 students replied and the summary of the ACT score is as below: Sample size Mean STD Min Max 20 21.5 5.7 15 26 (1) What is the sample of the study and what is the population of the study? (2) Steve is told that the population standard deviation for ACT score is 4.6 for his high school, estimate the population average ACT score of his high school graduates with 86% confidence level. (3) If the population standard deviation is not provided, estimate the population average ACT score of his high school graduates with 95% confidence level.
Answer:
[a]. sample is 25 randomly selected students
also population is all students
[b]. (20.0, 23.0)
[c]. (8.8, 24.2)
Step-by-step explanation:
here is a step by step process to solving this, i hope you find this helpful.
1). The population is all students who graduated from his school while the
sample is 25 randomly selected students from the email list
2). given alpha = 1-0.86=0.14
critical z value(two tailed) for 86% confidence level is:
z=normsinv(0.07) or normsinv(0.93)=1.476
Margin of error=1.476*(4.6/SQRT(20))=1.5
86% confidence interval for population mean
=21.5+/-1.5
=(20.0, 23.0)
3). if population standard deviation is not known,we will use t distribution.
df=20-1=19
t*=tinv(0.05,19)=2.093
Margin of error=2.093*(5.7/sqrt(20))=2.7
95% confidence interval for population mean
=21.5+/-2.7
=(18.8, 24.2)
cheers i hope this helps!!!!
The diagram shows the distance
Step 1: -3(+ 2) = 5(x - 7)
Step 2: -3.1 - 6 = 50 – 35
Step 3: _88 – 6 = -35
Step 4: -80 = -29
Step 5: I = 22
Between which two steps did Henry apply the distributive property?
steps 1 and 2
steps 2 and 3
steps 3 and 4
steps 4 and 5
Answer:
The answer is Steps 1 and 2. Step 1: -3(x+2) = 5(x-7)
Step 2: -3x-6 = 5x-35
Step-by-step explanation:
A diver dives from a cliff with a height of 144 feet. His height, h, in feet is given by the equation h=-16t^2+144 , where t is the time in seconds the diver has fallen. How many seconds will it take for the diver to reach the water?
Answer:
It takes 3 seconds for the diver to reach the water.
Step-by-step explanation:
The height, in feet, is given by the following equation:
[tex]h(t) = -16t^{2} + 144[/tex]
How many seconds will it take for the diver to reach the water?
He reaches the water when his height is 0, that is, when h(t) = 0. So
[tex]h(t) = -16t^{2} + 144[/tex]
[tex]0 = -16t^{2} + 144[/tex]
[tex]16t^{2} = 144[/tex]
[tex]t^{2} = \frac{144}{16}[/tex]
[tex]t^{2} = 9[/tex]
[tex]t = \pm \sqrt{9}[/tex]
[tex]t = \pm 3[/tex]
There are no negative instant of time, so just t = 3.
It takes 3 seconds for the diver to reach the water.
Which property is represented by this numerical expression?
(6 + 11) + 23 = 23 + (6 + 11).
Answer:
Communitive property of addition
Step-by-step explanation:
Mark spends one-third of the day sleeping. He spends 8 hours at school and one-sixth of the day at soccer practice. How much free time does Mark have?
Answer:
4 hours
Step-by-step explanation:
We know that there are 24 hours in a day. Therefore, we will subtract from 24.
If mark spends one-third of his day sleeping, then he will be asleep for 8 hours.
[tex]\frac{1}{3}\times24 \\=\frac{24}{3} \\=8[/tex]
We also know that if Mark spends one-sixth of his day at soccer practice, he will have been practicing for 4 hours.
[tex]\frac{1}{6}\times24 \\=\frac{24}{6} \\=4[/tex]
We now simply subtract from 24:
[tex]\text{hours in a day - hours asleep - hours at school - hours practicing} \\24 - 8 - 8 - 4 \\= 4[/tex]
Therefore, Mark will have 4 hours of free time.