Answer:
12
Step-by-step explanation:
In a survey, 376 out of 1,078 US adults said they drink at least 4 cups of coffee a day. Find a point estimate (P) for the population proportion of US adults who drink at least 4 cups of coffee a day, then construct a 99% confidence interval for the proportion of adults who drink at least 4 cups of coffee a day.
Answer:
The point estimate is 0.3488.
The 99% confidence interval for the proportion of adults who drink at least 4 cups of coffee a day is (0.3114, 0.3862).
Step-by-step explanation:
In a sample with a number n of people surveyed with a point estimate of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
For this problem, we have that:
[tex]n = 1078, \pi = \frac{376}{1078} = 0.3488[/tex]
The point estimate is 0.3488.
99% confidence level
So [tex]\alpha = 0.01[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.01}{2} = 0.995[/tex], so [tex]Z = 2.575[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.3488 - 2.575\sqrt{\frac{0.3488*0.6512}{1078}} = 0.3114[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.3488 + 2.575\sqrt{\frac{0.3488*0.6512}{1078}} = 0.3862[/tex]
The 99% confidence interval for the proportion of adults who drink at least 4 cups of coffee a day is (0.3114, 0.3862).
What’s the correct answer for this question?
Answer:
B
Step-by-step explanation:
I put the answer in an atachement
Answer:
B.
Step-by-step explanation:
In the attached file
Find the time required for an investment of 5000 dollars to grow to 6100 dollars at an interest rate of 7.5 percent per year, compounded quarterly.
Answer:
The time (t) = 2.6 years
Step-by-step explanation:
To calculate the time for earning a compound interest, compounded on a certain amount of present value (PV), compounded periodically, the following formula is used:
[tex]FV=PV(1+\frac{i}{n} )^{n*t}[/tex]
where:
FV = future value = $6,100
PV = present value = $5,000
i = interest rate in decimal = 7.5% = 0.075
n = number of compounding periods per year = quarterly = 4 (4 quarters a year)
t = time of compounding in years = ???
Therefore the time is calculated thus:
[tex]6100=5000(1+\frac{0.075}{4} )^{4*t}[/tex]
[tex]6100=5000(1+0.01875 )^{4t}[/tex]
[tex]6100=5000(1.01875 )^{4t}[/tex]
Next, let us divide both sides of the equation by 5000
[tex]\frac{6100}{5000} = \frac{5000(1.01875)^{4t} }{5000}[/tex]
1.22 = [tex](1.01875)^{4t}[/tex]
Taking natural logarithm of both sides
㏑(1.22) = ㏑[tex](1.01875)^{4t}[/tex]
㏑(1.22) = 4t × ㏑(1.01875)
0.1989 = 4t × 0.01858
4t = [tex]\frac{0.1989}{0.01858} = 10.71[/tex]
∴ 4t = 10.71
t = 10.71 ÷ 4 = 2.6 years
Let X equal the number of pounds of butterfat produced by a Holstein cow during the 305-day milking period following the birth of a calf. We shall test the null hypothesis 22 22 H0 : σ = 140 against the alternative hypothesis H1 : σ > 140 at α = 0.05, based on given data: n = 25, and a sample standard deviation of s = 150.1. What is the type of the test?A) Right-tailedB) Left-tailedC) Two-tailed2. Calculate Observed Test Statistic3. Find the Critical Value of Critical Region of the Test4. Draw Your Conclusion of the Test at α = 0.05A) Fail to Reject H0B) Reject H0
Answer:
Step-by-step explanation:
Given that:
[tex]\mathbf{H_o : \sigma = 140} \\ \\\mathbf{H_i : \sigma > 140} \\ \\ \mathbf{ \alpha = 0.05 \ \ \ \ n = 25 \ \ \ \ S = 150}[/tex]
1. This type of test is right tailed since the alternative hypothesis is right tailed
2. The Observed test statistic is calculated as follows:
[tex]X^2 = \dfrac{(n-1)s^2}{\sigma^2} \\ \\ X^2 = \dfrac{(25-1)150^2}{140^2} \\ \\ X^2 = \dfrac{(24)22500}{19,600} \\ \\ X^2 =27.55[/tex]
3. Critical Value
where ∝ = 0.05 and the test statistic is right tailed ;
By using [tex]X^2[/tex] table
[tex]X^2 _{\alpha/2 , n-1}= 36.415[/tex]
4. Conclusion:
∝ = 0.05
where
X² = 36.415
Therefore ; we reject [tex]\mathbf{H_o}[/tex]
A sports company wants to package a ball with a 1.5-inch radius in sets of two. They have two options: a cylinder or a square prism. 2 balls are inside of a cylinder and 2 balls are inside of a square prism. The cylinder has a height of 6 inches and a radius of 1.5 inches. The square prism has base lengths of 3 inches and the prism has a height of 6 inches. The company wants to use the package that has the least amount of wasted space. The company should choose
Answer:
C. the cylinder because it has approximately 11.6 in.3 less wasted space than the prism.
The company should choose the cylinder because it has approximately 11.6 in.3 less wasted space than the prism.
We have given that,
A sports company wants to package a ball with a 1.5-inch radius in sets of two.
They have two options a cylinder or a square prism.
2 balls are inside of a cylinder and 2 balls are inside of a square prism. The cylinder has a height of 6 inches and a radius of 1.5 inches.
What is the square prism?A square prism is basically a cuboid, that has square bases. It has four rectangular faces and two square-shaped ends. In Geometry, we have studied various three-dimensional shapes called solid shapes or solids.
The square prism has base lengths of 3 inches and the prism has a height of 6 inches.
The company wants to use the package that has the least amount of wasted space.
Therefore, The company should choose the cylinder because it has approximately 11.6 in.3 less wasted space than the prism.
To learn more about the cylinder or a square prism visit:
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What’s the correct answer for this question?
Answer:
C:
Step-by-step explanation:
In the attached file
the given equation has been solved on the table
Answer:
A. Step 2
Step by step explanation:
It was applied in Step 2 where 9 was added to both sides of the equation.
PLEASE HELP NO ONE IS HELPING
Answer:
-7 goes in the box
Step-by-step explanation:
x^ -3 = x^4 * x^n
We know that a^b * a^c = a^ (b+c)
x^-3 = x^(4+n)
When the bases are the same the exponents are the same
-3 = 4+n
Subtract 4 from each side
-3 -4 = 4+n-4
-7 = n
Please answer this multiple choice question !! Thank u !! Will give brainliest!!
Answer:
B: 3/2x - 7 + 3 = 0
Step-by-step explanation:
Answer: C
Step-by-step explanation:
General form is in Ax+By+C. To do this, you move everything onto one side.
[tex]\frac{3}{2}x -y+3=0[/tex]
This should be the general form, but this is not correct in these answer choices! Let's try this another way to get Ax+By+C by making Ax not a fraction.
[tex]y=\frac{3}{2} x-3[/tex]
[tex]y+3=\frac{3}{2} x[/tex]
[tex]2(y+3)=3x[/tex]
[tex]2y+6=3x[/tex]
[tex]3x-2y-6=0[/tex]
This may seem incorrect, but we can always check our answer by plugging in numbers.
In our slope intercept form, let's say x=2. What would be our y?
[tex]y=\frac{3}{2} (2)-3[/tex]
[tex]y=3-3[/tex]
[tex]y=0[/tex]
Now we know our coordinates should be (2, 0). When we rewrite the slope-intercept form, we should still get 0 when we plug in x=2 and y=0. Let's check on all answer choices to see which one works.
A. Correct
-3(2)+2(0)+6
-6-6=0
0=0
B. Incorrect
3/2(2)-(0)+3
3+3=6
6≠0
C. Correct
3(2)-2(0)-6
6-6=0
0=0
D. Incorrect; not general form
2(0)=3(2)-6
0=6-6
Now, you can see that A and C are both correct, but the main difference, is that you want to make A positive. The only option where A is positive is in answer C.
Solve 25 = 5x − 4.
one half
2
4
6
Answer:
29/5 =x
Step-by-step explanation:
25 = 5x − 4
Add 4 to each side
25+4 = 5x − 4+4
29 = 5x
Divide each side by 5
29/5 = 5x/5
29/5 =x
Answer:
The answer is 6
Step-by-step explanation:
:)
please answer this correctly
Answer:
Step-by-step explanation:
Brazil : 12,500,000 = 5,000,000 + 5,000,000 + 2,500,000
= full cat + full cat + half cat
What are the factors of x2 + 4x + 3?
A X3 - 1
B
4x2 + 3
C (x - 3)(x + 1)
D (x+3)(x + 1)
Answer:
D. (X + 3 ) ( X +1 )
process:
x² + 4x + 3
= x² + (3 + 1)x +3
= x² + 3x + x + 3
= X (x+3) + 1 (X+3)
= (X + 3 ) ( X +1 )
A stem and leaf plot shows data in _____ order.
alphabetical
numerical
reverse
A paint tin is leaking, a circular
puddle is formed and the radius of the
circle increases at a constant rate.
a) If the circumference of the circle
is increasing at a rate of 12cm/s, find
the rate at which the radius is increasing.
Answer:
The rate at which the radius is increasing
dr/dt = 1.91 cm/s
Step-by-step explanation:
The circumference C of a circle can be written as;
C = 2πr .....1
Where;
r = radius
The rate at which the circumference of the circle
is increasing can be written as dC/dt;
Differentiating equation 1, we have;
dC/dt = 2π dr/dt
Making dr/dt the subject of formula;
dr/dt = (dC/dt)/2π
Given;
dC/dt = 12cm/s
Substituting the value of dC/dt;
dr/dt = 12/2π
dr/dt = 1.909859317102 = 1.91 cm/s
The rate at which the radius is increasing dr/dt is 1.91 cm/s
The sugar content of the syrup in canned peaches is normally distributed. Suppose that the variance is thought to be σ2=18 (milligrams)2. A random sample of n=10 cans yields a sample standard deviation of s=4.8 milligrams. Part 1 (a) Test the hypothesis H0:σ2=18 versus H1:σ2≠18 using α=0.05 Find χ02 .
Answer:
[tex]\chi^2 =\frac{10-1}{18} 23.04 =11.52[/tex]
The degrees of freedom are:
[tex] df =n-1=10-1=9[/tex]
Now we can calculate the critical value taking in count the alternative hypotheis we have two values:
[tex]\chi^2_{\alpha/2}= 2.70[/tex]
[tex]\chi^2_{1-\alpha/2}= 19.02[/tex]
Since the calculated value is between the two critical values we FAIL to reject the null hypothesis and we can't conclude that the true variance is different from 18
Step-by-step explanation:
Information given
[tex]n=10[/tex] represent the sample size
[tex]\alpha=0.05[/tex] represent the confidence level
[tex]s^2 =4.8^2= 23.04 [/tex] represent the sample variance obtained
[tex]\sigma^2_0 =18[/tex] represent the value to verify
System of hypothesis
We want to verify if the true variance is different from 18, so the system of hypothesis would be:
Null Hypothesis: [tex]\sigma^2 = 18[/tex]
Alternative hypothesis: [tex]\sigma^2 \neq 18[/tex]
The statistic would be given by:
[tex]\chi^2 =\frac{n-1}{\sigma^2_0} s^2[/tex]
And replacing we got:
[tex]\chi^2 =\frac{10-1}{18} 23.04 =11.52[/tex]
The degrees of freedom are:
[tex] df =n-1=10-1=9[/tex]
Now we can calculate the critical value taking in count the alternative hypotheis we have two values:
[tex]\chi^2_{\alpha/2}= 2.70[/tex]
[tex]\chi^2_{1-\alpha/2}= 19.02[/tex]
Since the calculated value is between the two critical values we FAIL to reject the null hypothesis and we can't conclude that the true variance is different from 18
x2 + y2 =400 has center coordinates ____ and a radius equal to ___
Answer:
Answers are below
Step-by-step explanation:
The center coordinates of the circle are at (0,0).
The radius of the circle is 20
I graphed the circle on the graph below to show you how I got my answers.
The center of the equation x² + y² = 400 is, (0, 0).
And, The radius is 20.
What is Circle?The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.
We have to given that;
The equation is,
⇒ x² + y² = 400
Now, We know that;
The standard for of the equation of circle is,
⇒ (x - h)² + (y - k)² = r²
Where, (h, k) is the center of the circle and 'r' is the radius of the circle.
Hence, By comparing we get;
⇒ x² + y² = 400
⇒ (x - 0)² + (y - 0)² = 20²
The center of the equation x² + y² = 400 is, (0, 0).
And, The radius is 20.
Learn more about the circle visit:
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surface area, will mark brainliest.
Answer: 30 in^2
Step-by-step explanation:
PLZZZ I need URGENT help with problems 1 and 2! I'm so confused. Thx!
Answer:Y=x3
2nd answer: Just add it all up and divide by how many things you had to add. For an example: (2+2+2+2)/4.
Step-by-step explanation:
Based upon extensive data from a national high school educational testing program, the standard deviation of national test scores for mathematics was found to be 121 points. If a sample of 256 students are given the test, what would be the standard error of the mean?
Answer:
The standard error of the mean is 7.56Step-by-step explanation:
The standard error of the mean is defined as the ratio of standard deviation to the square root of the sample size of a data. The standard error of the mean is mathematically expressed as shown below;
[tex]X = \frac{\sigma}{\sqrt{n} }[/tex]
X is the standard error of the mean
[tex]\sigma[/tex] is the standard deviation
n is the sample size.
Given;
[tex]\sigma = 121\\n = 256[/tex]
On substitution into the formula we have;
[tex]X = \frac{121}{\sqrt{256} }[/tex]
[tex]X = \frac{121}{16} }\\[/tex]
X ≈ 7.56
The time spent driving (which depends on the number of miles needed to
travel) is 2 hours.
Which of the following equations is equivalent to S = pi r squared h?
Answer:
B. h=S/πr²
Step-by-step explanation:
The question lacks options. Here is the complete question.
Which of the following equations is equivalent to S = πr²h
a. h=S-πr^2
b. h=S/πR^2
C. h= πr^2/S
D. h=S+ πr^2
To know the equation equivalent to πr²h, we will make h the subject of the formula as shown from the one given in equation.
S = πr²h
To get h, we will divide both sides by the coefficient of h (i.e πr²)
S/πr² = πr²h/πr²
S/πr² = h
h = S/πr²
This shows that h = S/πr² is equivalent to S = πr²h
The number of customers waiting for gift-wrap service at a department store is an rv X with possible values 0, 1, 2, 3, 4 and corresponding probabilities 0.1, 0.2, 0.3, 0.25, 0.15. A randomly selected customer will have 1, 2, or 3 packages for wrapping with probabilities 0.55, 0.35, and 0.1, respectively. Let Y = the total number of packages to be wrapped for the customers waiting in line (assume that the number of packages submitted by one customer is independent of the number submitted by any other customer).
(a) Determine P(X = 3, Y = 3), i.e., p(3,3). (Round your answer to four decimal places.)
(b) Determine p(4,11). (Round your answer to four decimal places.) p(4,11) = ?
Answer:
(a)p(3,3)=0.0416
(b)p(4,11)=0.0002
Step-by-step explanation:
Number of Customers, X
[tex]\left\begin{array}{|c|ccccc|}X&0&1&2&3&4\\P(X)&0.1&0.2&0.3&0.25&0.15.\end{array}\right[/tex]
Y = the total number of packages to be wrapped for the customers waiting in line
[tex]\left\begin{array}{|c|ccccc|}Y&1&2&3\\P(Y)&0.55&0.35&0.1\end{array}\right|[/tex]
a. P(X = 3, Y = 3)
p(3,3) means that there are 3 customers with one gift each
The probability of this event happening:
[tex]0.25 \times 0.55^3=0.0416[/tex]
p(3,3)=0.0416
b. p(4,11)
For 4 people to have a total package of 11, there must be 3 customers with 3 packages each and 1 customer with 2 packages,
The probability of this happening is:
[tex]p(4,11)=0.15\times^4C_1\times0.1^3\times0.35\\p(4,11)=0.0002[/tex]
Work out the value of x
Answer:
67.5
Step-by-step explanation:
right angle =90 degree
total = 360 degree
360-90=270
270÷4=67.5
A circle has a circumference of 7,850. What is the radius of the circle?
Answer:
50
Step-by-step explanation:
7850/3.14
Square root 2500
50
16
To get to Amala's house, Tara walks 4 blocks west (left), then 3 blocks north (up), and
then 2 blocks west. Amala's house has coordinates (9,9). What are the coordinates of
Tara's starting point?
A
B.
C
D
(2,0)
(2,6)
(15,6)
(12, 2)
Answer:
Correct answer is C. (15,6)
Step-by-step explanation:
Let us think of the [tex]xy[/tex] co-ordinates plane. We can move in four directions.
1. North (i.e. upwards) If we move north or upwards the value of y-coordinate will increase.
2. South (i.e. downwards) If we move south or downwards the value of y-coordinate will decrease.
3. West (i.e. left) If we move west or left the value of x-coordinate will decrease.
4. East (i.e. right) If we move east or right the value of x-coordinate will increase.
Let us imagine, the starting coordinate of Tara be [tex](x,y)[/tex]
Let us apply the above 4 directions and the properties in the question statement.
Step 1: Tara walks 4 blocks west (left), x coordinate will decrease by 4.
New coordinates will be [tex](x-4,y)[/tex].
Step 2: Tara walks 3 blocks north (up), y coordinate will increase by 3.
New coordinates will be [tex](x-4,y+3)[/tex].
Step 3: Tara walks 2 blocks west (left), x coordinate will decrease by 2.
New coordinates will be [tex](x-4-2,y+3) \Rightarrow (x-6,y+3)[/tex].
Now Tara is at (9,9)
Comparing the x and y coordinates:
[tex]x-6=9\\\Rightarrow x = 15[/tex]
[tex]y+3=9\\\Rightarrow y = 6[/tex]
So, Tara's starting point is (15,6) hence, option C is correct.
vlumber company is making boards that are 2944.0 millimeters tall. If the boards are too long they must be trimmed, and if the boards are too short they cannot be used. A sample of 25 is made, and it is found that they have a mean of 2941.0 millimeters with a standard deviation of 12.0. A level of significance of 0.1 will be used to determine if the boards are either too long or too short. Assume the population distribution is approximately normal. Find the value of the test statistic. Round your answer to three decimal places.
Answer:
[tex]t=\frac{2941-2944}{\frac{12}{\sqrt{25}}}=-1.250[/tex]
The degrees of freedom are given by:
[tex]df=n-1=25-1=24[/tex]
The p value would be given by:
[tex]p_v =2*P(t_{24}<-1.250)=0.223[/tex]
Since the p value is higher than 0.1 we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true mean is not significantly different from 2944 mm
Step-by-step explanation:
Information provided
[tex]\bar X=2941[/tex] represent the sample mean
[tex]s=12[/tex] represent the standard deviation
[tex]n=25[/tex] sample size
[tex]\mu_o =2944[/tex] represent the value to test
[tex]\alpha=0.1[/tex] represent the significance level
t would represent the statistic
[tex]p_v[/tex] represent the p value
Hypothesis to test
We want to test if the true mean for this case is equal to 2944 mm, the system of hypothesis would be:
Null hypothesis:[tex]\mu = 2944[/tex]
Alternative hypothesis:[tex]\mu \neq 2944[/tex]
The statistic for this case would be given by:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
Replacing the info given we got:
[tex]t=\frac{2941-2944}{\frac{12}{\sqrt{25}}}=-1.250[/tex]
The degrees of freedom are given by:
[tex]df=n-1=25-1=24[/tex]
The p value would be given by:
[tex]p_v =2*P(t_{24}<-1.250)=0.223[/tex]
Since the p value is higher than 0.1 we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true mean is not significantly different from 2944 mm
An employer uses the linear regression equation y = 0.18 x + 320.22 to predict the weekly salary, y, of an employee who sells x dollars worth of merchandise. Last week, Joaquin sold $1500 worth of merchandise. The same week, Alex earned $650. Using the regression equation, which is an accurate comparison? Alex sold merchandise worth about $60 more than what Joaquin sold. Joaquin sold merchandise worth about $60 more than what Joaquin sold. Alex earned about $60 more than Joaquin did. Joaquin earned about $60 more than Alex did.
Answer:
Option C is correct.
Alex earned about $60 more than Joaquin did.
Step-by-step explanation:
The linear regression equation
y = 0.18 x + 320.22
is used to predict the weekly salary, y, of an employee who sells x dollars worth of merchandise.
Joaquin sold $1500 worth of goods. Meaning that x for that week for Joaquin is 1500.
Joaquin' s salary for that week is then given as
y = 0.18x + 320.22
y = 0.18(1500) + 320.22 = 590.22
Hence, Joaquin's salary for that week = $590.22
Alex earns $650 that week. Meaning that y for Alex in that week = 650
y = 0.18x + 320.22
650 = 0.18x + 320.22
0.18x = 650 - 320.22 = 329.78
x = (329.78/0.18) = 1832.1
Hence, Alex sold goods worth $1832.1 that week.
Joaquin sold goods worth $1500
Joaquin earned $590.22
Alex sold goods worth $1832.1
Alex earned $650
From this calculation, it is evident that 'Alex earned about $60 more than Joaquin did' is the correct option as $650 is about $60 more than $590.22
Hope this Helps!!!
Answer:
the answer is C :)
Step-by-step explanation:
IXL RELATED PLEASE HELP
In ΔDEF, the measure of ∠F=90°, DE = 82 feet, and EF = 55 feet. Find the measure of ∠E to the nearest tenth of a degree.
Answer:
To the nearest tenth of a degree
∠E= 47.9°
Step-by-step explanation:
ΔDEF , let's recognize that it's a right angle triangle because of the presence of ∠F=90°.
Other important measurements are
DE = 82 feet, and EF = 55 feet.
We are to find ∠E
Let's find the missing side first
Side DF
DF² = DE² - EF²
DF²= 82²_55²
DF²=6724-3025
DF²= 3699
DF= 60.82 feet
Let's use the sine formula to look for the angle.
DF/sin ∠E= DE/sin 90
Sin 90= 1
DE= 82
DF= 60.82
Sin ∠E= DF/DE
Sin ∠E= 60.82/82
Sin ∠E= 0.7417
∠E= sin^-1 (0.7417)
∠E= 47.8764
To the nearest tenth of a degree
= 47.9°
This data set represents the number of
children in 8 families
4, 2, 1, 2, 4, 2, 6, 3
The mean of this data set is 3. What is the
Mean Absolute Deviation (MAD)?
A. 1.25
B. 8
C. 3.3
D. 3
Answer:
1.25
Step-by-step explanation:
Lets sum up the values
24
and then divide by their number (8)
we get 3 on average
now let's see how much each data point varies from that average (this is always a positive value)
1, 1, 2, 1, 1, 1, 3, 0
Let's sum and divide by 8 again
10/8 = 1.25
(would really, reallly appreciate the brainliest)
Which equation will solve the following word problem? One small pitcher and one large pitcher can hold 12 cups of water. If the large pitcher is twice the size of the small pitcher, how much does the small pitcher hold? 2S + S = 12 2S = 12/S 2S - S = 12 S = 12/2S
Answer:
Option (1).
Step-by-step explanation:
Amount of water hold by both the pitchers (Large + small) = 12 cups
Let the small pitcher holds the water = S cups
If the water hold by the large pitcher is twice the size of the small pitcher, then the amount of water hold by large pitcher = 2S
Total amount water hold by both = S + 2S
Equation for this situation will be,
S + 2S = 12
Therefore, Option (1) will be the answer.
