Answer:
[tex]2\sin{\frac{x}{2}}\cos{\frac{x}{2}} = \sin{x}[/tex]
Step-by-step explanation:
The double angle formula states that:
[tex]\sin{2a} = 2\sin{a}\cos{a}[/tex]
In this question:
[tex]2\sin{\frac{x}{2}}\cos{\frac{x}{2}}[/tex]
So
[tex]a = \frac{x}{2}[/tex]
Then
[tex]2\sin{\frac{x}{2}}\cos{\frac{x}{2}} = \sin{\frac{2x}{2}} = \sin{x}[/tex]
The table shows the results of a survey of 400 random people on whether they like liquid soap, bar soap, or both. A 4-column table with 3 rows. The first column has no label with entries bar, not bar, total. The second column is labeled liquid with entries 200, 80, 280. The third column is labeled not liquid with entries 100, 20, 120. The fourth column is labeled total with entries 300, 100, 400. Which is the marginal relative frequency for the people who do not like bar soap? StartFraction 100 Over 400 EndFraction StartFraction 120 Over 400 EndFraction StartFraction 280 Over 400 EndFraction StartFraction 300 Over 400 EndFraction
Answer:
The answer is A on edge 2020
Step-by-step explanation:
Answer: A
Step-by-step explanation:
A palm tree is supported by two guy wires as shown in the diagram below. Which trig expression can be used to find the height on the tree where the top guy wire attaches if the base of the wire is four feet from the base of the tree? A sin (30° + 45°) B cos (75° – 45°) C tan (75° – 45°) D tan (30° + 45°)
Answer:
D. [tex]tan(30^\circ+45^\circ)[/tex] is the correct answer.
Step-by-step explanation:
The given situation can be represented as a figure attached in answer area.
B is the base of tree.
C is the base of wires.
A and D are the end of 2 wires supporting the tree.
[tex]\angle DCB =45^\circ\\\angle ACB =75^\circ\\[/tex]
Here, we need to find the Height of the tree which is represented the by side AB.
and we are given that bases of wires and tree base are at a distance 4 ft.
i.e. side BC = 4 ft
If we look at the [tex]\triangle ABC[/tex], we are given the base BC and the [tex]\angle ACB[/tex], and the perpendicular is to be find out.
We can use trigonometric identity:
[tex]tan\theta =\dfrac{Perpendicular}{Base}[/tex]
[tex]tan 75^\circ = \dfrac{AB}{BC}\\\bold {tan (45+30)^\circ }= \dfrac{AB}{4}\\\Rightarrow AB = \bold {tan (45+30)^\circ } \times 4 = 14.93\ ft[/tex]
Hence, D. [tex]tan(30^\circ+45^\circ)[/tex] is the correct answer.
Answer:
D
Step-by-step explanation:
Help me pls pls pls pls
Answer:
Inequality Form:
x≥130
Step-by-step explanation:
isolate the variable by dividing each side by factors that don’t contain the variable.
blank a function is the same as moving a function
Answer:
Shifting/Translating the function
Step-by-step explanation:
Answer:
Step-by-step explanation:
nice
how to simplify -8+5w=27
Answer:
w=7
Step-by-step explanation:
1. -8+5w=27
2. add 8 to both sides: 8+-8+5w=27+8
3. Simplify: 5w=35
4. Divide both sides by 5: 5w/5=35/5
5. w=7
Hope This Helps :)
Answer:
w = 7
Step-by-step explanation:
-8 + 5w = 27
Add 8 on both sides.
-8 + 5w + 8 = 27 + 8
5w = 35
Divide both sides by 5.
5w/5 = 35/5
w = 7
Locate the point on the line segment between A(3, -5) and B(13, -15) given that the point is 4/5 of the way from A to B. Show your work.
Answer:
C ( 11 , -11 )
Step-by-step explanation:
Solution:-
We are given two points in the cartesian coordinate system as:
A ( 3 , -5 ) B ( 13 , -15 )
The point C lies on the line segment from A to B. The ratio of segment given is:
AC / AB = 4 / 5
To solve such type of problems. We will use vector equation of line AC.
To form a vector equation of line representing AB. We will first determine the direction vector ( d ) that is parallel to the line AB as follows:
d = OB - OA
d = < 13 , -15 > - < 3 , -5 >
d = < 10 , -10 >
The fixed point on the line is taken. We will take point A. The vector equation of line from point A to point B is expressed as:
< x , y > = OA + s*d
< x , y > = < 3, -5 > + s* < 10 , -10 >
The above equation satisfies all the points that lies on the line AB. To determine the coordinates of ( C ). We will plug in the appropriate value of parameter ( s ) and evaluate.
So point C is 4/5 th the magnitude of the distance AB from A. Hence, s = 4/5 as follows:
< x , y > = < 3 , -5 > + ( 4/5 ) * < 10 , -10 >
< x , y > = < 3 , -5 > + < 8 , -8 >
< x , y > = < 11 , -11 > ... Answer
5/6÷5=___
3/7÷6=___
5/8÷8=___
15/8÷5=___
Answer:
1/6
1/14
5/64
3/8
Step-by-step explanation:
Easiest and fastest way to evaluate these is to plug it into a calc.
not sure how I would solve this
Support requests arrive at a software company at the rate of 1 every 30 minutes. Assume that the requests arrive as events in a Poisson process.
a) What is the probability that the number of requests in an hour is between 2 and 4 inclusive? Give your answer to four decimal places.
b) What is the expected number of requests in a 10 hour work day? Give an exact answer.
c) What is the probability that the number of requests in a 10 hour work day is between 20 and 24 inclusive? Give your answer to four decimal places.
d) What is the standard deviation of the number of requests in a 10 hour work day? Give your answer to four decimal places.
Answer:
a. 0.5413
b. 20
c. 0.3724
d. 4.4721
Step-by-step explanation:
Solution:-
- We will start by defining a random variable X.
X : The number of support requests arrived
- The event defined by the random variable ( X ) is assumed to follow Poisson distribution. This means the number of request in two distinct time intervals are independent from one another. Also the probability of success is linear within a time interval.
- The time interval is basically the time required for a poisson event to occur. Consequently, each distributions is defined by its parameter(s).
- Poisson distribution is defined by " Rate at which the event occurs " - ( λ ). So in our case the rate at which a support request arrives in a defined time interval. We define our distributions as follows:
X ~ Po ( λ )
Where, λ = 1 / 30 mins
Hence,
X ~ Po ( 1/30 )
a)
- We see that the time interval for events has been expanded from 30 minutes to 1 hour. However, the rate ( λ ) is given per 30 mins. In such cases we utilize the second property of Poisson distribution i.e the probability of occurrence is proportional within a time interval. Then we scale the given rate to a larger time interval as follows:
λ* = [tex]\frac{1}{\frac{1}{2} hr} = \frac{2}{1hr}[/tex]
- We redefine our distribution as follows:
X ~ Po ( 2/1 hr )
- Next we utilize the probability density function for poisson process and accumulate the probability for 2 to 4 request in an hour.
[tex]P ( X = x ) = \frac{e^-^l^a^m^b^d^a . lambda^x}{x!}[/tex]
- The required probability is:
[tex]P ( 2 \leq X \leq 4 ) = P ( X = 2 ) + P ( X = 3 ) + P ( X = 4 )\\\\P ( 2 \leq X \leq 4 ) = \frac{e^-^2 . 2^2}{2!} + \frac{e^-^2 . 2^3}{3!} + \frac{e^-^2 . 2^4}{4!}\\\\P ( 2 \leq X \leq 4 ) = 0.27067 + 0.18044 + 0.09022\\\\P ( 2 \leq X \leq 4 ) = 0.5413[/tex] Answer
b)
We will repeat the process we did in the previous part and scale the poisson parameter ( λ ) to a 10 hour work interval as follows:
λ* = [tex]\frac{2}{1 hr} * \frac{10}{10} = \frac{20}{10 hr}[/tex]
- The expected value of the poisson distribution is given as:
E ( X ) = λ
Hence,
E ( X ) = 20 (10 hour work day) .... Answer
c)
- We redefine our distribution as follows:
X ~ Po ( 20/10 hr )
- Next we utilize the probability density function for poisson process and accumulate the probability for 20 to 24 request in an 10 hour work day.
[tex]P ( X = x ) = \frac{e^-^l^a^m^b^d^a . lambda^x}{x!}[/tex]
- The required probability is:
[tex]P ( 20 \leq X \leq 24 ) = P ( X = 20 ) + P ( X = 21 ) + P ( X = 22 )+P ( X = 23 ) + P ( X = 24 )\\\\P ( 20 \leq X \leq 24 ) = \frac{e^-^2^0 . 20^2^0}{20!} + \frac{e^-^2^0 . 20^2^1}{21!} + \frac{e^-^2^0 . 20^2^2}{22!} + \frac{e^-^2^0 . 20^2^3}{23!} + \frac{e^-^2^0 . 20^2^4}{24!} \\\\P ( 20 \leq X \leq 24 ) = 0.0883 +0.08460 +0.07691 +0.06688+0.05573\\\\P ( 20 \leq X \leq 24 ) = 0.3724[/tex] Answer
c)
The standard deviation of the poisson process is determined from the application of Poisson Limit theorem. I.e Normal approximation of Poisson distribution. The results are:
σ = √λ
σ = √20
σ = 4.4721 ... Answer
The most recent census for a city indicated that there were 919,716 residents. The population of the city is expected to increase at an annual rate of 3.7 percent each year for the next 13 years. What will the population be at that time
Answer:
1,474,951.
Step-by-step explanation:
Given a population that increases by a constant percentage, we can model the population's growth using the exponential model.
[tex]P(t)=P_o(1+r)^t,$ where \left\{\begin{array}{lll}P_o=$Initial Population\\r$=Growth rate\\$t=time (in years)\end{array}\right\\P_o=919,716\\r=3.7\%=0.037\\$t=13 years[/tex]
Therefore, the population of the city in 13 years time will be:
[tex]P(t)=919,716(1+0.037)^{13}\\\\=919,716(1.037)^{13}\\\\=1,474,950.9\\\\\approx 1,474,951[/tex]
The population be at that time will be approximately 1,474,951.
Suppose you are purchasing a new car, and you decide to use a scoring model to decide among four options. What would be your top three criteria, and what would be each criterion's relative weight?
Answer:
The answer is explained below
Step-by-step explanation:
The steps to prioritize the mission with a scoring version are as follows:
Collection: This step consists of collecting and collecting all of the details associated with the mission.
Classification: This step consists of prioritization of the challenge based on a category method.
Verification: This step includes approval and verification of all classified projects.
They are then carried out in this order because these steps make certain safety, connectivity, integrity, cost-effectiveness, and right challenge implementation. Each step depends on the previous step. They are connected to every other; therefore, they are carried out in a particular sequence.
Tublu buys a cylindrical water tank of height 1.4m and diameter 1.1m to catch rainwater off his roof. He has a full 2 litres tin of paint in his store and decides to paint the tank (not the base). If he uses 250 ml to cover 1 , will he have enough paint to cover the tank with one layer of paint? [take ] [15 marks] (b) At a DBE lecture of 100 students, there are 29 women and 23 men. Out of these students, 4 are teachers and 24 are either men or teachers. Find the number of women teachers attending the lecture.
12 teachers...
Hope this helps.....
Anthony sells cars. Each month, he is paid $2,000, plus a 15% commission on monthly sales above $20,000. Which function calculates his monthly earnings (E) as a function of m, his monthly sales?
E(m) = 2000 + 0.15( m - 20000) is the function calculates his monthly earnings.
What are the composition functions?The composition of a function is an operation in which two functions say f and g generate a new function say h in the sort of manner that h(x) = g(f(x)). It method right here characteristic g is carried out to the characteristic of x. So, basically, a feature is implemented to the end result of another feature.
What are functions and modeling?In systems engineering, software engineering, and pc science, a function version or practical model is an established illustration of the capabilities (activities, movements, procedures, operations) inside the modeled system or situation vicinity.
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WHY CAN'T ANYONE HELP ME PLEASE?? The Pool Fun Company has learned that, by pricing a newly released Fun Noodle at $3, sales will reach 8000 Fun Noodles per day during the summer. Raising the price to $6 will cause the sales to fall to 5000 Fun Noodles per day. a. Assume that the relationship between sales price, x, and number of Fun Noodles sold, y, is linear. Write an equation in slope-intercept form describing this relationship. Use ordered pairs of the form (sales price, number sold).
Answer:
y = -1000x +11000
Step-by-step explanation:
Given:
(x, y) = (sales price, number sold) = (3, 8000), (6, 5000)
Find:
slope-intercept equation for a line through these points
Solution:
When given two points, it often works well to start with the 2-point form of the equation for a line.
y = (y2 -y1)/(x2 -x1)(x -x1) +y1
Filling in the given points, you have ...
y = (5000 -8000)/(6 -3)/(x -3) +8000
y = (-3000/3)(x -3) +8000
y = -1000x +3000 +8000 . . . . eliminate parentheses
y = -1000x +11000 . . . . the desired equation
If MQ is 24 and PR is 10, what length of PM would make parallelogram MPQR a rhombus?
Let's think about this. MQ is given to be a length of 24 units, PR a length of 10 whilst we must determine what length PM must be in order to satisfy the criteria of parallelogram MPQR to be a rhombus.
Assume this figure is a rhombus, rhombus MPQR. If that is so, all sides must be congruent, and the diagonals must be perpendicular ( ⊥ ) by " Properties of a Rhombus. " That would make triangle( s ) MRQ and say RMP isosceles, and by the Coincidence Theorem, MS ≅ QS, and RS ≅ PS. Therefore -
[tex]MS = 1 / 2( 24 ) = 12 = QS,\\RS = 1 / 2( 10 ) = 5 = PS[/tex]
PS and MS are legs of a right triangle, so by Pythagorean Theorem we can determine the hypotenuse, or in other words the length of PM. This length would make parallelogram MPQR a rhombus,
[tex]( PM )^2 = ( MS )^2 + ( PS )^2,\\PM^2 = ( 12 )^2 + ( 5 )^2,\\PM^2 = 144 + 25 = 169\\-----\\PM = 13[/tex]
And thus, PM should be 13 in length to make parallelogram MPQR a rhombus.
Help Please! First to answer will be marked as brainliest Find the solution to the system of equations. y=−5x+6 y=3x-2 x= y=
Answer:
y = 1 and x = 1
Step-by-step explanation:
We are given the equation y=−5x+6 and y=3x-2
because both of these equations have y on one side we can substitute the equation as
-5x+6 = 3x-2
(subtract 3x)
-8x+6 = -2
(subtract 6)
-8x = -8
(divide by -8)
x=1
Then all we need to do is put x into the equation
y=-5(1) +6
y = -5+6
y = 1
Find the least number which is exactly divisible by 72 and 108
Step-by-step explanation:
2 is the answer because:
72/2=36
108/2=54
Answer:
2
Step-by-step explanation:
Well divisible means the lowest numbers it can be divided by.
So we can make a chart.
72 - 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
108 - 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108
So besides 1, 2 is the lowest divisible number between 108 and 72.
Chad is a co owner of a small company and received 1/3 of the company’s profits this year. What were the company’s overall profits if chad made 150,000 ? Type an equation and solve.
Answer:
$450,000
Step-by-step explanation:
chad = (1/3)profit
3×chad = profit = 3×$150,000 . . . . multiply the equation by 3; fill given value
profit = $450,000
The company's overall profits were $450,000.
Which function is the result of translating ƒ(x) = x2 + 5 upward by 5 units and to the right by 1 unit? Question options: A) y = (x – 1)2 + 5 B) y = (x – 1)2 + 10 C) y = (x + 1)2 + 5 D) y = (x + 1)2 + 10
Answer:
B. y = (x – 1)^2 + 10
Step-by-step explanation:
Answer: B
Step-by-step explanation:
B y= (x-1)^2 + 10
Find the missing side. Round your answer to the nearest tenth.
Answer:12.4
Step-by-step explanation:
hyp=16,opp=x
sin 51°=[tex]\frac{x}{16}[/tex]
cross multipy
sin 51° x 16 = x
x=0.7771 x 16
x≅12.4
Sharona recorded the number of gray hairs her coworkers have and their ages in the graph below.
Answer: C. A function only
Step-by-step explanation:
There is not relation to the dots on the graph.
The graph represents a relation only.
Hence option D is correct.
Since we know that
A function is a mathematical concept that describes a relationship between two sets, where each element in the first set (the domain) corresponds to exactly one element in the second set (the range). In simpler terms, a function is a rule that assigns each input value a unique output value.
In contrast, a relation is a general concept that describes any set of objects that have some kind of relationship to each other. In mathematics, a relation is often represented as a set of ordered pairs and can be visualized as a graph. For example, a relation could be a set of all points on a circle, represented as an ordered pair of x and y coordinates.
As we can see in the graph
There is more than one value for the number represented on the X-axis
We can see that at a particular age, there is more than one gray hairs worker.
Hence the graph represents a relation only.
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In October 1945, the Gallup organization asked 1,487 randomly sampled Americans, "Do you think we can develop a way to protect ourselves from atomic bombs in case other countries tried to use them against us?" Did a majority of Americans feel the United States could develop a way to protect itself from atomic bombs in 1945? Use the α = 0.05 level of significance.
Answer:
Yes. There is enough evidence to support the claim that the proportion of Americans feel the United States could develop a way to protect itself from atomic bombs in 1945 is significantly greater than 0.5.
Step-by-step explanation:
The question is incomplete:
In October 1945, the Gallup organization asked 1487 randomly sampled Americans, "Do you think we can develop a way to protect ourselves from atomic bombs in case other countries tried to use them against us?" with 788 responding yes. Did a majority of Americans feel the United States could develop a way to protect itself from atomic bombs in 1945? Use the α=0.05 level of significance.
This is a hypothesis test for a proportion.
The claim is that the proportion of Americans feel the United States could develop a way to protect itself from atomic bombs in 1945 is significantly greater than 0.5.
Then, the null and alternative hypothesis are:
H_0: \pi=0.5\\\\H_a:\pi>0.5
The significance level is 0.05.
The sample has a size n=1487.
The sample proportion is p=0.53.
[tex]p=X/n=788/1487=0.53[/tex]
The standard error of the proportion is:
[tex]\sigma_p=\sqrt{\dfrac{\pi(1-\pi)}{n}}=\sqrt{\dfrac{0.5*0.5}{1487}}\\\\\\ \sigma_p=\sqrt{0.000168}=0.013[/tex]
Then, we can calculate the z-statistic as:
[tex]z=\dfrac{p-\pi-0.5/n}{\sigma_p}=\dfrac{0.53-0.5-0.5/1487}{0.013}=\dfrac{0.03}{0.013}=2.288[/tex]
This test is a right-tailed test, so the P-value for this test is calculated as:
[tex]\text{P-value}=P(z>2.288)=0.011[/tex]
As the P-value (0.011) is smaller than the significance level (0.05), the effect is significant.
The null hypothesis is rejected.
There is enough evidence to support the claim that the proportion of Americans feel the United States could develop a way to protect itself from atomic bombs in 1945 is significantly greater than 0.5.
Assume that you plan to use a significance level of α= 0.05 to test the claim that p1 = p2. Use the given sample sizes and numbers of successes to find the pooled estimate p. Round your answer to the nearest thousandth.
n1 = 100,
n2 = 100,
x1 = 42,
x2 = 45
Answer:
The pooled estimate is given by the following formula:
[tex] \hat p= \frac{x_1 +x_2 }{n_1 + n_2}[/tex]
And replacing we got:
[tex] \hat p= \frac{42+45}{100+100}= \frac{87}{200}= 0.435[/tex]
Step-by-step explanation:
We have the following info given:
n1 = 100,
n2 = 100,
x1 = 42,
x2 = 45
The pooled estimate is given by the following formula:
[tex] \hat p= \frac{x_1 +x_2 }{n_1 + n_2}[/tex]
And replacing we got:
[tex] \hat p= \frac{42+45}{100+100}= \frac{87}{200}= 0.435[/tex]
What is equation represents Jakes situation
Answer:
the first one
Step-by-step explanation:
i assume they want to know how many cookies are in each box so you take the total number of cookies and divide by the number of boxes which is four so t/4 = b since they don't give you an amount of cookies
Answer:
t/4 = b aka the first one
Step-by-step explanation:
t/4 is the same as b
Not sure of how to solve this
Answer:
undefined
Step-by-step explanation:
Using the slope formula
m = (y2-y1)/ (x2-x1)
and the given points
m = ( 8 - -1)/( 2-2)
= (8+1) / 0
We cannot divide by 0 so the slope is undefined
Michelle, a student studying music, randomly sampled fellow music majors and asked whether they listen to music while they study. The resulting confidence interval for the proportion of music students who listen to music while studying is (0.09,0.26). What is the margin of error?
Answer:
The margin of error of this confidence interval is MOE=0.085.
Step-by-step explanation:
The confidence interval bounds are usually calculated from a sample statistic substracting (for the lower bound) or adding (for the upper bound) the margin of error. This margin of error depends on the confidence level, the standard deviation and the sample size.
Then, if the lower and upper bound are calculated this way, we can calculate the margin of error as:
[tex]LB=p-MOE\\\\UB=p+MOE\\\\UB-LB=(p+MOE)-(p-MOE)=2\cdot MOE\\\\\\MOE=\dfrac{UB-LB}{2}=\dfrac{0.26-0.09}{2}=\dfrac{0.17}{2}=0.085[/tex]
Kendra can make 120 soccer kicks in 3 minutes. Jovani can make 100 soccer kicks in 4 minutes. How long will it take them to make 1300 soccer kicks together?
The time it takes them to make 1300 soccer kicks together is 51 minutes
Let the number of soccer kicks be yLet the time taken be x
Writing this as a coordinate (x, y). If Kendra can make 120 soccer kicks in 3 minutes and Jovani can make 100 soccer kicks in 4 minutes, this can be written in a coordinate form as (3, 120) and (4, 100)
The standard linear equation is given as y = mx + b
Get the slope:
m = 100-120/4-3
m = -20/1
m = -20
Get the y-intercept:
Recall that y = mx + b
120 = -20(3) + b
120 = -60 + b
b = 180
The required equation is g(x) = -20x + 180
To determine the time it will take them to make 1300 soccer kicks together, substitute g(x) = 1300 and find "x"
1300 = -20x + 180
20x = 1200 - 180
20x = 1020
x = 51 minutes
Hence the time it takes them to make 1300 soccer kicks together is 51 minutes
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A random sample of 10 parking meters in a resort community showed the following incomes for a day. Assume the incomes are normally distributed. (a) Find the 95% confidence interval for the true mean and interpret the result. Round to the nearest cent. (b) Find margin of error. $3.60 $4.50 $2.80 $6.30 $2.60 $5.20 $6.75 $4.25 $8.00 $3.00
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
Ahmad makes compost by mixing 0.5 kg of sand with 2 kg of peat. Write the ratio of sand to peat. Give your answer in its simplest form.
Answer:
0.5kg
2kg
0.7kg
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gcjoxfj
vxfhb
Select the two values of x that are roots of this equation.
2x - 5 = -3x2
O A. X = 1
B. x= -1
C. X = 3
D. x =
Answer:
x = - [tex]\frac{5}{3}[/tex] , x = 1
Step-by-step explanation:
Given
2x - 5 = - 3x² ( add 3x² to both sides )
3x² + 2x - 5 = 0 ← in standard form
Consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term.
product = 3 × - 5 = - 15 and sum = + 2
The factors are - 3 and + 5
Use these factors to split the x- term
3x² - 3x + 5x - 5 = 0 ( factor the first/second and third/fourth terms )
3x(x - 1) + 5(x - 1) = 0 ← factor out (x - 1) from each term
(x - 1)(3x + 5) = 0 ← in factored form
Equate each factor to zero and solve for x
3x + 5 = 0 ⇒ 3x = - 5 ⇒ x = - [tex]\frac{5}{3}[/tex]
x - 1 = 0 ⇒ x = 1