Answer:
A 95% confidence interval for the true mean is [$3.39, $6.01].
Step-by-step explanation:
We are given that a random sample of 10 parking meters in a resort community showed the following incomes for a day;
Incomes (X): $3.60, $4.50, $2.80, $6.30, $2.60, $5.20, $6.75, $4.25, $8.00, $3.00.
Firstly, the pivotal quantity for finding the confidence interval for the population mean is given by;
P.Q. = [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] ~ [tex]t_n_-_1[/tex]
where, [tex]\bar X[/tex] = sample mean income = [tex]\frac{\sum X}{n}[/tex] = $4.70
s = sample standard deviation = [tex]\sqrt{\frac{\sum (X-\bar X)^{2} }{n-1} }[/tex] = $1.83
n = sample of parking meters = 10
[tex]\mu[/tex] = population mean
Here for constructing a 95% confidence interval we have used a One-sample t-test statistics because we don't know about population standard deviation.
So, 95% confidence interval for the population mean, [tex]\mu[/tex] is ;
P(-2.262 < [tex]t_9[/tex] < 2.262) = 0.95 {As the critical value of t at 9 degrees of
freedom are -2.262 & 2.262 with P = 2.5%}
P(-2.262 < [tex]\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }[/tex] < 2.262) = 0.95
P( [tex]-2.262 \times {\frac{s}{\sqrt{n} } }[/tex] < [tex]{\bar X-\mu[/tex] < [tex]2.262 \times {\frac{s}{\sqrt{n} } }[/tex] ) = 0.95
P( [tex]\bar X-2.262 \times {\frac{s}{\sqrt{n} } }[/tex] < [tex]\mu[/tex] < [tex]\bar X+2.262 \times {\frac{s}{\sqrt{n} } }[/tex] ) = 0.95
95% confidence interval for [tex]\mu[/tex] = [ [tex]\bar X-2.262 \times {\frac{s}{\sqrt{n} } }[/tex] , [tex]\bar X+2.262 \times {\frac{s}{\sqrt{n} } }[/tex] ]
= [ [tex]4.70-2.262 \times {\frac{1.83}{\sqrt{10} } }[/tex] , [tex]4.70+ 2.262 \times {\frac{1.83}{\sqrt{10} } }[/tex] ]
= [$3.39, $6.01]
Therefore, a 95% confidence interval for the true mean is [$3.39, $6.01].
The interpretation of the above result is that we are 95% confident that the true mean will lie between incomes of $3.39 and $6.01.
Also, the margin of error = [tex]2.262 \times {\frac{s}{\sqrt{n} } }[/tex]
= [tex]2.262 \times {\frac{1.83}{\sqrt{10} } }[/tex] = 1.31
Using the t-distribution, it is found that:
a) The 95% confidence interval for the true mean is (3.39, 6.01). It means that we are 95% sure that the true mean income for all parking meters in the resort community from which the sample was taken is between these two values.
b) The margin of error is of $1.31.
Item a:
We will have the standard deviation for the sample, which is why the t-distribution is used to solve this question.
The sample size given is of [tex]n = 10[/tex], and using a calculator, it is found that:
The sample mean of [tex]\overline{x} = 4.7[/tex].
The sample standard deviation of [tex]s = 1.833[/tex].
The confidence interval is:
[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]
The critical value, using a t-distribution calculator, for a two-tailed 95% confidence interval, with 10 - 1 = 9 df, is t = 2.2622.
Then, the interval is:
[tex]\overline{x} - t\frac{s}{\sqrt{n}} = 4.7 - 2.2622\frac{1.833}{\sqrt{10}} = 3.39[/tex]
[tex]\overline{x} + t\frac{s}{\sqrt{n}} = 4.7 + 2.2622\frac{1.833}{\sqrt{10}} = 6.01[/tex]
The 95% confidence interval for the true mean is (3.39, 6.01). It means that we are 95% sure that the true mean income for all parking meters in the resort community from which the sample was taken is between these two values.
Item b:
The margin of error is half the distance between the two bounds, hence:
[tex]M = \frac{6.01 - 3.39}{2} = 1.31[/tex]
A similar problem is given at https://brainly.com/question/22596713
Pablo purchased adult and youth tickets for the football game. He bought x adult tickets for $74 each and y youth tickets for $35. Write an expression that can be used to show the total cost, C, of all tickets.
Answer:
74x + 35y = c
Step-by-step explanation:
Each adult ticket costs $74 and Pablo is purchasing x amount of tickets, so 74 multiplied by x would be the total cost for the adult tickets. Each youth ticket costs $35 and Pablo is puchasing y amount of tickets, so 35 multiplied by y would be the total cost for youth tickets. Then you add the two sums together to find the total cost of all of the tickets.
Answer:
d. C = 74x + 35y
Step-by-step explanation:
I took the test and got the answer right here is the screen shoot to prove it
Overall Assessment Progress
Basic Office Skills
Question 5 of 47
1/4 + 7/8 = ?
Answer:
1 1/8
Step-by-step explanation:
1/4 + 7/8
Make denominators equal.
2/8 + 7/8
Add the fractions.
9/8
Convert to a mixed fraction.
1 1/8
Answer:
1 1/8
Step-by-step explanation:
1/4 + 7/8
Get a common denominator
1/4 * 2/2 + 7/8
2/8 + 7/8
9/8
Change to a mixed number
8/8+ 1/8
1 1/8
PLS HELP (pic included)
hope it helps uh.......
Grandpa and Grandma are treating their family to the movies. Matinee tickets cost $4 per child and $4 per adult. Evening tickets cost $6 per child and $8 per adult. They plan on spending no more than $80 on the matinee tickets and no more than $100 on the evening tickets.
Complete Question
Grandpa and Grandma are treating their family to the movies. Matinee tickets cost $4 per child and $4 per adult. Evening tickets cost $6 per child and $8 per adult. They plan on spending no more than $80 on the matinee tickets and no more than $100 on the evening tickets. Could they take 9 children and 4 adults to both shows? Show your work. A yes or no answer is not sufficient for credit.
Answer:
Yes it is possible to take the 9 children and 4 adults to both shows
Step-by-step explanation:
From the question we are told that
The cost of the Matinee tickets for a child is z = $4
The cost of the Matinee tickets for an adult is a = $ 4
The cost of the Evening tickets for a child is k = $6
The cost of the Evening tickets for an adult is b = $8
The maximum amount to be spent on Matinee tickets is m = $80
The maximum amount to be spent on Evening tickets is e = $100
The number of child to be taken to the movies is n = 9
The number of adults to be taken to the movies is j = 4
Now the total amount of money that would be spent on Matinee tickets is mathematically evaluated as
[tex]t = 4 n + 4 j[/tex]
substituting values
[tex]t = 4 * 9 + 4* 4[/tex]
[tex]t = 52[/tex]
Now the total amount of money that would be spent on Evening ticket is mathematically evaluated as
[tex]T = 6n + 8j[/tex]
substituting values
[tex]T = 6(9) + 8(4)[/tex]
[tex]T = 86[/tex]
This implies that it is possible to take 9 children and 4 adults to both shows
given that
[tex]t \le m[/tex]
i.e $56 [tex]\le[/tex]$ 80
and
[tex]T \le e[/tex]
i.e $ 86 [tex]\le[/tex] $ 100
A company is trying to determine if they should accept a shipment of toy parts. The shipment has over 1 million parts. They decided to randomly select 100 parts out of the shipment. They will only accept the shipment if 1% or less of all of the parts are defective. Out of the 100 selected, 4% are defective. Identify the numbers "1%" and "4%" as either statistics or parameters. Group of answer choices
Answer:
4% is a statistic and 1% is a parameter
Step-by-step explanation:
First, let's remember the differences between parameters and statistics:
Parameters are values that describe data of the entire population.
Statistics are values that describe data from a sample.
The value of 1% refers to "all of the parts", which is the population of over 1 million parts, thus 1% is a parameter.
The value of 4% refers to the "100 selected", which is the sample of 100 parts, thus 4% is a statistic.
Therefore, 4% is a statistic and 1% is a parameter.
Toby cuts a pizza into 6 equal slices. He eats half a slice. What fraction of the pizza has he eaten?
The pizza is cut into 6 slices so each slice would be 1/6 of the pizza.
He at 1/2 of a slice:
1/6 x 1/2 = 1/12 of the pizza
Assortative mating is a nonrandom mating pattern where individuals with similar genotypes and/or phenotypes mate with one another more frequently than what would be expected under a random mating pattern. Researchers studying this topic collected data on eye colors of 204 Scandinavian men and their female partners. The table below summarizes the results (rows represent male eye color while columns represent female eye color). For simplicity, we only include heterosexual relationships in this exercise.
(please round any numerical answers to 4 decimal places)
Blue Brown Green Total
Blue 78 23 13 114
Brown 19 23 12 54
Green 11 9 16 36
Total 108 55 41 204
a) What is the probability that a randomly chosen male respondent or his partner has blue eyes?
b) What is the probability that a randomly chosen male respondent with blue eyes has a partner with blue eyes?
c) What is the probability that a randomly chosen male respondent with brown eyes has a partner with blue eyes?
d) What is the probability of a randomly chosen male respondent with green eyes having a partner with blue eyes?
e) Does it appear that the eye colors of male respondents and their partners are independent? Explain.
Answer:
a) P(male=blue or female=blue) = 0.71
b) P(female=blue | male=blue) = 0.68
c) P(female=blue | male=brown) = 0.35
d) P(female=blue | male=green) = 0.31
e) We can conclude that the eye colors of male respondents and their partners are not independent.
Step-by-step explanation:
We are given following information about eye colors of 204 Scandinavian men and their female partners.
Blue Brown Green Total
Blue 78 23 13 114
Brown 19 23 12 54
Green 11 9 16 36
Total 108 55 41 204
a) What is the probability that a randomly chosen male respondent or his partner has blue eyes?
Using the addition rule of probability,
∵ P(A or B) = P(A) + P(B) - P(A and B)
For the given case,
P(male=blue or female=blue) = P(male=blue) + P(female=blue) - P(male=blue and female=blue)
P(male=blue or female=blue) = 114/204 + 108/204 − 78/204
P(male=blue or female=blue) = 0.71
b) What is the probability that a randomly chosen male respondent with blue eyes has a partner with blue eyes?
As per the rule of conditional probability,
P(female=blue | male=blue) = 78/114
P(female=blue | male=blue) = 0.68
c) What is the probability that a randomly chosen male respondent with brown eyes has a partner with blue eyes?
As per the rule of conditional probability,
P(female=blue | male=brown) = 19/54
P(female=blue | male=brown) = 0.35
d) What is the probability of a randomly chosen male respondent with green eyes having a partner with blue eyes?
As per the rule of conditional probability,
P(female=blue | male=green) = 11/36
P(female=blue | male=green) = 0.31
e) Does it appear that the eye colors of male respondents and their partners are independent? Explain
If the following relation holds true then we can conclude that the eye colors of male respondents and their partners are independent.
∵ P(B | A) = P(B)
P(female=blue | male=brown) = P(female=blue)
or alternatively, you can also test
P(female=blue | male=green) = P(female=blue)
P(female=blue | male=blue) = P(female=blue)
But
P(female=blue | male=brown) ≠ P(female=blue)
19/54 ≠ 108/204
0.35 ≠ 0.53
Therefore, we can conclude that the eye colors of male respondents and their partners are not independent.
A ball is thrown upward off of a 100 meter cliff with an initial velocity of 6 m/s. The function f(x)=-5x2+6x+100 (graphed below) represents this situation where x is time and y is the distance off of the ground. will mart brainliest yeah
Answer:
a) The domain of the function is [tex]x \geq 0\,s[/tex] [tex]\wedge[/tex] [tex]x \leq 5.112\,s[/tex]. [tex][0\,s, 5.112\,s][/tex], [tex]\forall x \in \mathbb{R}[/tex], b) The range of the function is [tex]0\,m \leq y \leq 100\,m[/tex]. [tex][0\,m,100\,m][/tex], [tex]\forall y\in \mathbb{R}[/tex], c) The ball is 73 meters off of the ground at x = 3 seconds.
Step-by-step explanation:
The complete statement is: A ball is thrown upward off of a 100 meter cliff with an initial velocity of 6 m/s. The function [tex]f(x) = -5\cdot x^{2} + 6\cdot x + 100[/tex] represents this situation where x is time and y is the distance off of the ground.
a) What domain does the function make sense?
b) What range does the function make sense ?
c) How far off the ground is the ball at time x = 3 seconds?
a) Let [tex]x[/tex] and [tex]f(x)[/tex] be the time, measured in seconds, and the distance of the ground, measured in meters, respectively. Time is a positive variable, so domain corresponds to the interval when [tex]f(x) \geq 0[/tex] and [tex]t \geq 0[/tex]. That is:
[tex]-5\cdot x^{2} + 6\cdot x + 100 \geq 0[/tex]
[tex]-(x-5.112\,s)\cdot (x+3.912\,s) \geq 0[/tex]
Therefore, the domain of the function is [tex]x \geq 0\,s[/tex] [tex]\wedge[/tex] [tex]x \leq 5.112\,s[/tex]. [tex][0\,s, 5.112\,s][/tex], [tex]\forall x \in \mathbb{R}[/tex]
b) The distance off of the ground is also a positive variable, where ball is thrown upward at a height of 100 meters and hits the ground at a height of 0 meters. Hence, the range of the function is [tex]0\,m \leq y \leq 100\,m[/tex]. [tex][0\,m,100\,m][/tex], [tex]\forall y\in \mathbb{R}[/tex]
c) The distance of the ball off of the ground at x = 3 seconds is found by evaluating the function:
[tex]f(3\,s) = -5\cdot (3\,s)^{2} + 6\cdot (3\,s) + 100[/tex]
[tex]f(3\,s) = 73\,m[/tex]
The ball is 73 meters off of the ground at x = 3 seconds.
Give the three-letter name of each of the angles in the drawing below. Lines and Angles a. ∠1 b. ∠2 c. ∠3 d. ∠4
Answer:
a. AEB
b. BEC
c. CED
d. AED
Step-by-step explanation:
Each angle is made up of three points. All three points in order is the name of the angle.
Answer:
a. ∠1 = ∠AEB or ∠BEA
b. ∠2 = ∠BEC or ∠CEB
c. ∠3 = ∠CED or ∠DEC
d. ∠4 = ∠DEA or ∠AED
Step-by-step explanation: Penn <3
In a competition, two people will be selected from four finalists to receive the first and second prizes. The prize winners will be selected by drawing names from a hat. The names of the four finalists are Jim, George, Helen, and Maggie. The possible outcomes can be represented as follows: JG JH JM GJ GH GM HJ HG HM MJ MG MH Here, for example, JG represents the outcome that Jim receives the first prize and George receives the second prize. The event A is defined as follows: A = event that Helen gets first prize List the outcomes that comprise the event ~A (not A).
Answer:
1. JG (Jim gets first prize, George gets second prize)
2. JH (Jim gets first prize, Helen gets second prize)
3. JM (Jim gets first prize, Maggie gets second prize)
4. GH (George gets first prize, Helen gets second prize)
5. GJ (George gets first prize, Jim gets second prize)
6. GM (George gets first prize, Maggie gets second prize)
7. MJ (Maggie gets first prize, Jim gets second prize)
8. MG (Maggie gets first prize, George gets second prize)
9. MH (Maggie gets first prize, Helen gets second prize)
Step-by-step explanation:
The question asks for the list of outcomes in the event "Not A". We are looking for the reverse or negative of Event A.
The above given list is the list of outcomes in the event where Helen DOES NOT get first prize.
The Wall Street Journal recently ran an article indicating differences in perception of sexual harassment on the job between men and women. The article claimed that women perceived the problem to be much more prevalent than did men. One question asked to both men and women was: "Do you think sexual harassment is a major problem in the American workplace?" Some 24% of the men compared to 62% of the women responded "Yes." Suppose that 150 women and 200 men were interviewed. For a 0.01 level of significance, what is the critical value for the rejection region? a. 7.173 b. 2.33 c. 6.635 d. 7.106
Answer:
Critical value: b. 2.33
As the test statistic z=7.17 is greater than the critical value, it falls in the rejection region.
The null hypothesis is rejected.
There is enough evidence to support the claim that the proportion of women who think sexual harassment is a major problem in the American workplace is significantly higher than the proportion of men.
Step-by-step explanation:
This is a hypothesis test for the difference between proportions.
The claim is that the proportion of women who think sexual harassment is a major problem in the American workplace is significantly higher than the proportion of men.
Then, the null and alternative hypothesis are:
[tex]H_0: \pi_1-\pi_2=0\\\\H_a:\pi_1-\pi_2> 0[/tex]
The significance level is 0.01.
The sample 1 (women), of size n1=150 has a proportion of p1=0.62.
The sample 2 (men), of size n2=200 has a proportion of p2=0.24.
The difference between proportions is (p1-p2)=0.38.
[tex]p_d=p_1-p_2=0.62-0.24=0.38[/tex]
The pooled proportion, needed to calculate the standard error, is:
[tex]p=\dfrac{X_1+X_2}{n_1+n_2}=\dfrac{93+48}{150+200}=\dfrac{141}{350}=0.403[/tex]
The estimated standard error of the difference between means is computed using the formula:
[tex]s_{p1-p2}=\sqrt{\dfrac{p(1-p)}{n_1}+\dfrac{p(1-p)}{n_2}}=\sqrt{\dfrac{0.403*0.597}{150}+\dfrac{0.403*0.597}{200}}\\\\\\s_{p1-p2}=\sqrt{0.001604+0.001203}=\sqrt{0.002807}=0.053[/tex]
Then, we can calculate the z-statistic as:
[tex]z=\dfrac{p_d-(\pi_1-\pi_2)}{s_{p1-p2}}=\dfrac{0.38-0}{0.053}=\dfrac{0.38}{0.053}=7.17[/tex]
The critical value for a right-tailed test with a signficance level of 0.01 is zc=2.33 (see picture attached).
As the test statistic z=7.17 is greater than the critical value, it falls in the rejection region.
The null hypothesis is rejected.
There is enough evidence to support the claim that the proportion of women who think sexual harassment is a major problem in the American workplace is significantly higher than the proportion of men.
A grocer wants to make a 10-pound mixture of peanuts and cashews that he can sell for $4.75 per pound. If peanuts cost $4.00 per pound and cashews cost $6.50 per pound, how many pounds of cashews should he use?
Answer:
3lbs
Step-by-step explanation:
how many different four letter permutations can be formed using four letters out of the first 12 in the alphabet?
Answer:
11,800 different four letter permutations can be formed using four letters out of the first 12 in the alphabet
Step-by-step explanation:
Permutations formula:
The number of possible permutations of x elements from a set of n elements is given by the following formula:
[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]
In this question:
Permutations of four letters from a set of 12 letters. So
[tex]P_{(12,4)} = \frac{12!}{(12-4)!} = 11800[/tex]
11,800 different four letter permutations can be formed using four letters out of the first 12 in the alphabet
Answer: it’s 11,880
not 11800
Find the surface area of this composite solid.
Answer:
C. 120 m²
Step-by-step explanation:
The surface area is equal to the area of 4 rectangles + area of 4 triangles + area of base.
Area of 4 rectangles:
4(5 × 4)
4(20) = 80
Area of 4 triangles:
4(3 × 4 × 1/2)
4(6) = 24
Area of base:
4² = 16
Add the areas.
16 + 24 + 80
= 120
The surface area of the composite solid is 120 m².
The surface area of this composite solid would be, 136 m². Hence, option D is true.
Used the formula for the surface area of the cuboid and the surface area of the 4 triangles,
The surface area of the cuboid = 2 (LW + LH + HW)
And, The surface area of the 4 triangles = 4 (1/2 × Base × Height)
Given that,
In a triangle,
Base = 4 m
Height = 3 m
And, In a Cuboid,
Length = 4 m
Width = 4 m
Height = 5 m
Hence, we get;
The surface area of the 4 triangles = 4 (1/2 × Base × Height)
= 4 (1/2 × 4 × 3)
= 4 × 6
= 24 m²
The surface area of the cuboid = 2 (LW + LH + HW)
= 2 (4 × 4 + 4 × 5 + 5 × 4)
= 2 (16 + 20 + 20)
= 112 m²
Therefore, The surface area of this composite solid would be,
24 m² + 112 m² = 136 m²
So, Option D is true.
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Which of the following shows the intersection of the sets? {1, 5, 10, 15} {1, 3, 5, 7}
Answer:
{1,5}
Step-by-step explanation:
The intersection of the sets are all of the numbers that appear in both sets. In this case, the only numbers that appear in both are 1 and 5.
Answer:
{ 1,5}
Step-by-step explanation:
The intersection is what the two sets have in common
{1, 5, 10, 15}∩ {1, 3, 5, 7}
= { 1,5}
please tell ans of attached photo
Answer:
192 m^2.
Step-by-step explanation:
We can split this up into 3 rectangles:
Area of the bottom rectangle = 27 * (9-3)
= 27 * 6 = 162 m^2.
Area of rectangle on the left = (18-6)*2
= 24 m^2
Area of small rectangle on the right = 3*2
= 6 m^2
Total area = 162+24+6
192 m^2.
Below are the times (in days) it takes for a sample of 17 customers from Andrew's computer store to pay their invoices.
19.15, 43, 39, 35, 31, 27, 34, 34, 30, 30, 26, 26, 26, 21, 21, 17
Draw the histogram for these data using an initial class boundary of 14.5, an ending class boundary of 49.5, and 5 classes of equal width. Note that you can add
or remove classes from the figure. Label each class with its endpoints.
Frequency
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Answer:
Step-by-step explanation:
Hello!
The variable of interest is X: time it takes a customer from Andrew's computer store to pay his invoices.
You have the information of a sample of n= 17 customers
19, 15, 43, 39, 35, 31, 27, 34, 34, 30, 30, 26, 26, 26, 21, 21, 17
To determine the class width of the intervals for the divide the difference between the ending and initial class boundaries by the number of intervals that you want to determine:
Class width: (49.5-14.5)/5= 7
Then, starting from the initial class boundary, you have to add the class width to determine the next boundary, and so on until the ending class boundary:
Initial class boundary: 14.5
14.5 + 5.6= 20.1
1st interval: [14.5; 21.5]
and so on:
[21.5; 28.5]
[28.5; 35.5]
[35.5; 42.5]
[42.5; 49.5]
Once you determined all class intervals, you have to order the values of the data set from least to greatest and then count how many observations correspond to each interval and arrange it in a frequency table.
15, 17, 19, 21, 21, 26, 26, 26, 27, 30, 30, 31, 34, 34, 35, 39, 43
[14.5; 21.5] ⇒ 5
[21.5; 28.5] ⇒ 4
[28.5; 35.5] ⇒ 6
[35.5; 42.5] ⇒ 1
[42.5; 49.5] ⇒ 1
Once you have the data set organized in the table, you can proceed to draw the histogram.
(See attachment)
I hope this helps!
After one round in a card game, your score was -50 points. After the second round, your score was 29 points. How many points did you gain in the second game?
Answer:
79
Step-by-step explanation:
[tex]score = 29 - (-50)[/tex]
Expressed as: The score is the difference between 29 and -50.
Simplify:
[tex]score = 29 + 50[/tex]
Result:
[tex]score = 79[/tex]
Feel free to ask questions, and don't forget to mark as Brainliest if this helped.
if f(x) = -8 + 2 then f^-1 (x) = HELP ASAP!!!
Answer:
[tex]f^{-1}(x)= - \frac{1}{8} x+\frac{1}{4}[/tex]
Step-by-step explanation:
[tex]f(x) = -8x + 2[/tex]
[tex]y = -8x + 2[/tex]
[tex]y-2=-8x[/tex]
[tex]- \frac{1}{8} y+\frac{1}{4} =x[/tex]
[tex]- \frac{1}{8} x+\frac{1}{4} =y[/tex]
[tex]f^{-1}(x)= - \frac{1}{8} x+\frac{1}{4}[/tex]
Write an equation of the line with the given slope, m, and y-intercept (0, b). m = 4 , b = 9
Answer:
y = 4x + 9
Step-by-step explanation:
You can use these numbers to create an equation in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.
y = mx + b
y = 4x + 9
Solve for pi : C = 2 pi r
Answer:
[tex]\frac{C}{2r}[/tex]=pi
Answer:
π= C/2r
Step-by-step explanation:
In order to solve for pi, we must get pi by itself on one side of the equation.
C= 2πr
Let's rearrange the right side of the equation. We can do this because of the commutative property of multiplication.
C= 2πr
C= 2r* π
pi is now being multiplied by 2r. The inverse of multiplication is division. Divide both sides of the equation by 2r.
C/2r= 2r*π/2r
C/2r= π
π=C/2r
A kite is flying 12 ft off the ground. Its line is pulled taut and casts an 8 -ft shadow. Find the length of the line. If necessary, round your answer to the nearest tenth.
The required length of the line is given as 14.4 feet, as of the given conditions.
As given in the question, A kite is flying 12 ft off the ground. Its line is pulled taut and casts an 8 -ft shadow, to determine the length of the line.
What are Pythagorean triplets?In a right-angled triangle, its side, such as the hypotenuse, is perpendicular, and the base is Pythagorean triplets.
Here,
let the length of the line be x,
The scenario formed is right angle triangle,
Apply Pythagoras' theorem,
x² = 12² + 8²
x = √208
x = 14.4
Thus, the required length of the line is given as 14.4 feet, as of the given conditions.
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WHO CAN HELP ME WITH MY ACCOUNTING HOMEWORK???
Duran Manufacturing uses a process costing system and manufactures its product in three departments. Which of the following is NOT a way in which Duran can use the cost per unit of each process?
A) Duran can look for ways to cut the costs when actual process costs are more than planned process costs.
B) Duran needs to set the selling price to cover the costs of making the product and provide a profit.
C) Duran can only use the cost per unit of each process if all units are fully completed at the end of the accounting period.
D) Duran needs to know the ending balances in the following accounts: Work-In-Process Inventory, Finished Goods Inventory, and Cost of Goods Sold.
Answer:
C) Duran can only use the cost per unit of each process if all units are fully completed at the end of the accounting period.
Step-by-step explanation:
Duran uses cost accounting technique to identify cost per unit for its products. The costing techniques allows us to identify the cost of unit that are not completely finished. It is not necessary that all unit must be completed in order to find out the cost per unit of the product. The process costing is the best method to identify cost per unit for products that are in process.
what number must add to the expression below to complete the square x^2-x
A.-1/2
B. 1/2
C. -1/4
D. 1/4
Answer:
Option D is correct.
1/4 completes the square.
Step-by-step explanation:
To complete the square for a quadratic function, we require a third term that will enable the solutions of the quadrstic equation to be 2 repeated roots.
For that to be so for the quadratic equation
ax² + bx + c = 0,
b² has to be equal to 4ac
For this question, x² - x + c
From b² = 4ac
c = (b²/4a)
a = 1
b = -1, b² = 1
c = ?
c = (1/4)
Hence, (1/4) is the number that must be added to the expression to complete the square.
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Will give brainliest answer
Answer:
Radius = 6.5cm
Diameter = 13cm
Step-by-step explanation:
The diameter is given (13)
Radius is half the diameter (13/2=6.5)
Answer:
Radius = 13 / 2 = 6.5 cmDiameter = 13 cmExplanation
RadiusThe straight line is drawn from the centre of a circle to a point on its circumference is called radius of the circle. The radius of a circle is half of its diameter.
DiameterThe chord that passes through the centre of a circle is called diameter of circle. Diameter is also called the largest chord of any circle. The length of diameter of a circle is two times it's radius.
Hope this helps...
Good luck on your assignment...
Not sure how to solve this
Answer:
The x-intercepts as shown on this graph are: (-3,0), (1,0), and (3,0). The y-intercept as shown on this graph is: (0,2).
Step-by-step explanation:
The intercepts refer to where the function intersects with either the x-axis or y-axis. Since the line crosses the y-axis at (0,2), that's the y-intercept. The same thing applies to the x-intercepts. On this graph, it's easier to identify because the intercepts are marked with dots.
Carlo and Anita make mailboxes and toys in their wood shop. Each mailbox requires 1 hour of work from Carlo and 4 hours from Anita. Each toy requires 1 hour of work from Carlo and 1 hour from Anita. Carlo cannot work more than 12 hours per week and Anita cannot work more than 24 hours per week. If each mailbox sells for $10 and each toy sells for $5, then what is their maximum possible revenue
Answer:
$80
Step-by-step explanation:
Let the number of hours required to make a mailbox = x
Let the number of hours required to make a toy = y
Each mailbox requires 1 hour of work from Carlo and 4 hours from Anita.
Each toy requires 1 hour of work from Carlo and 1 hour from Anita.
The table below summarizes the information for ease of understanding.
[tex]\left|\begin{array}{c|c|c|c}&$Mailbox(x)&$Toy(y)&$Maximum Number of Hours\\--&--&--&------------\\$Carlo&1&1&12\\$Anita&4&1&24\end{array}\right|[/tex]
We have the constraints:
[tex]x+y \leq 12\\4x+y \leq 24\\x \geq 0\\y \geq 0[/tex]
Each mailbox sells for $10 and each toy sells for $5.
Therefore, Revenue, R(x,y)=10x+5y
The given problem is to:
Maximize, R(x,y)=10x+5y
Subject to the constraints
[tex]x+y \leq 12\\4x+y \leq 24\\x \geq 0\\y \geq 0[/tex]
The graph is plotted and attached below.
From the graph, the feasible region are:
(0,0), (6,0), (4,8) and (0,12)
At (6,0), 10x+5y=10(6)+5(0)=60
At (4,8), 10(4)+5(8)=80
At (0,12), 10(0)+5(12)=60
The maximum revenue occurs when they use 4 hours on mailboxes and 8 hours on toys.
The maximum possible revenue is $80.
Estimate the area under the graph of f(x)=1/x+4 over the interval [-1,2] using four approximating rectangles and right endpoints.
Answer:
Rn ≈ 0.6345
Ln ≈ 0.7595
Step-by-step explanation:
The interval from -1 to 2 has a width of (2 -(-1)) = 3. Dividing that into 4 equal intervals means each of those smaller intervals has width 3/4.
It can be useful to use a spreadsheet or graphing calculator to evaluate the function at all of the points that define these intervals:
x = -1, -.25, 0.50, 1.25, 2
Of course, the spreadsheet can easily compute the sum of products for you.
__
The approximation using right end-points will be the sum of products of the interval width (3/4) and the function value at the right end-points:
Rn = (3/4)f(-0.25) +(3/4)f(0.50) +(3/4)f(1.25) +(3/4)f(2)
Rn ≈ 0.6345
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The approximation using left end-points will be the sum of products of the interval width (3/4) and the function value at the left end-points:
Ln = (3/4)f(-1) +(3/4)f(-0.25) +(3/4)f(0.50) +(3/4)f(1.25)
Ln ≈ 0.7595
_____
It is usually convenient to factor out the interval width, so only one multiplication needs to be done: (interval width)(sum of function values).
What is the solution to 8/x+2=2/x-4
Answer:
x=-1
Step-by-step explanation:
8/x+2=2/x-4
8/x=2/x-6
8=2-6x
6=-6x
-1=x
Answer:
x=6
Step-by-step explanation:
8/x+2=2/x-4
Using cross products
8*(x-4) = 2 (x+2)
Distribute
8x - 32 = 2x+4
Subtract 2x
8x-2x -32 = 2x-2x+4
6x-32 = 4
Add 32
6x-32+32 = 4+32
6x = 36
Divide by 6
6x/6 = 36/6
x = 6
Find the value of x that will make a||b help ?
Answer:
x=30
Step-by-step explanation:
Find the value of x that will make A and B parallel
For A & B to be parallel, the interior angles must be supplementary, i.e.
4x+2x = 180
6x=180
x=30
When x=30, the interior angles are 120 and 60 which are supplementary.