The volume of a spherical sculpture is 256 ft³. Rhianna wants to estimate the surface area of the sculpture. To do the estimate, she approximates π using 3 in both the surface area and volume formulas for a sphere.
Using this method, what value does she get for the approximate surface area of the sculpture?
Answers
Answer:
192 [tex]ft^2[/tex]
Step-by-step explanation:
Given that
Volume of spherical sculpture = 256 ft³
[tex]\pi[/tex] is used as 3.
To find:
Surface area of sculpture = ?
Solution:
First of all, let us learn about the formula for Volume and Surface Area of Sphere:
1. [tex]Volume =\frac{4}{3}\pi r^3[/tex]
2. [tex]Surface\ Area = 4\pi r^2[/tex]
Given volume is 256 ft³.
[tex]256 = \dfrac{4}{3}\pi r^3\\\Rightarrow 256 = \dfrac{4}{3}\times 3 r^3\\\Rightarrow 256 = 4 r^3\\\Rightarrow r^3=64\\\Rightarrow \bold{r = 4\ ft}[/tex]
Now, let us put r = 4 in the formula of Surface Area to find the value of Surface Area:
[tex]Surface\ Area = 4\pi 4^2 = 4 \times 3 \times 16 = \bold{192\ ft^2}[/tex]
So, approximate surface area of sculpture is 192 [tex]ft^2[/tex].
Answer:
192
Step-by-step explanation:
Related Questions
point estimate A sample of 81 observations is taken from a normal population with a standard deviation of 5. The sample mean is 40. Determine the 95% confidence interval for the population mean
Answers
Answer:
The 95 percent Confidence Interval is for the population is (38.911 , 41.089)
Step-by-step explanation:
To solve the above question, we would be making use of the confidence interval formula:
Confidence Interval = Mean ± z score × σ/√n
In the above question,
Mean = 40
σ = Standard deviation = 5
n = number of samples = 81
Confidence Interval = 95%
The z score for a 95% confidence interval = 1.96
Therefore, the confidence interval =
= 40 ± 1.96 (5/√81)
= 40 ± 1.96(5/9)
= 40 ± 1.0888888889
Confidence Interval
a)40 + 1.0888888889
= 41.0888888889
Approximately = 41.089
b ) 40 - 1.0888888889
= 38.911111111
Approximately = 38.911
Therefore, the 95 percent Confidence Interval is for the population is (38.911 , 41.089)
PLEASE HELP FOR 70 POINTS!!!!!! Maria and Jackson like in adjacent neighborhoods. If they superimpose a coordinate grid on the map of their neighborhoods, Maria lives at (–9, 1) and Jackson lives at (5, –4). Each unit on the grid is equal to approximately 0.132 mile. 8. How far apart do Maria and Jackson live to the nearest thousandth? 9. If April lives equidistant to both Maria and Jackson, at what coordinate on the grid would she live? 10. How far apart would Maria and April live to the nearest thousandth?
Answers
Answer:
8) 1.962 miles
9) (-2, -1.5)
10) 0.515 miles
Step-by-step explanation:
√(-9 - 5)² + (1 - -4)² = 14.866
14.866 x .132 = 1.962
(-9+5)/2, (1 + -4)/2
-4/2, -3/2
-2, -3/2
√(-2 - 1)² + (-3/2 - -4)² = 3.905
3.905 x .132 = 0.515 miles
1/3 of a shipment of books weights 28 pounds
Answers
Answer:
84 pounds
Step-by-step explanation:
If 1/3 of a book is equal to 28 pounds then 28*3 will give you your answer
Point R divides PG in the ratio 1:3. If the x-coordinate of R is -1 and the x-coordinate of P is -3, what is the x-coordinate of Q
Answers
Answer:
option C . 5
Step-by-step explanation:
For two points (x1,y1) and (x2,y2) divided by a point p in ratio m:n then coordinates of that point is given by
p : (nx1+mx2)/(m+n), (ny1+my2)/(m+n),
Given
x coordinate of P (-3)
x coordinate of Q (a) since we have to find it , let it be a
x coordinate of R(-1)\
ratio = 1:3
_______________________________________
Using the above formula to find the point of division
we can get value of x coordinate for point Q
x coordinate of R = 3*-3 + 1*a/(1+3)
-1 = (-9 + a)/4
=> -4 = -9 +a
=>a = -4+9 = 5
Thus, x coordinate of Q is 5
Which is greater 9/20 or 60%
Answers
Answer:
60%
Step-by-step explanation:
9/20 is 45%
Answer:
60 %
Step-by-step explanation: If you divide 9/20, it equals to 0.45, makes it 45% and the number 45 in general is smaller than 60. Thus, 60% is greater than 9/20. I hope this helps.
what are the like terms of the expression.
3x+8x+y+x+8
Answers
Answer:
the like terms are:
3x+8x+x+y+8
12x+y+8
Answer:
The like terms are
3x, 8x, x
Step-by-step explanation:
3x+8x+y+x+8
The like terms are
3x, 8x, x
They are the terms that are in terms of the first power of x
To apply Central Limit Theorem on sample proportions in One Sample Proportion test, the sample size and the population proportion under null hypothesis need to satisfy certain conditions. Which of the following scenarios meet the requirement?
A. The sample size is 50 and the population proportion under null hypothesis is 25%.
B. The sample size is 70 and the population proportion under null hypothesis is 90%.
C. The sample size is 50 and the population proportion under null hypothesis is 15%.
D. The sample size is 200 and the population proportion under null hypothesis is 4%.
Answers
Answer:
The sample size is 50 and population proportion under null hypothesis is 25% ( A ) meets the requirement
Step-by-step explanation:
when applying the central limit theorem on sample proportions in one sample proportion test .The conditions needed to be satisfied are np > 10, and n( 1-p ) > 10
A) sample size ( n ) = 50
population proportion = 25%
np = 50 * 0.25 = 12.5 which is > 10 ( 1st condition met )
n( 1 - p ) = 50( 1 - 0.25 ) = 37.5 which is > 10 ( second condition met )
B ) sample size (n) = 70
population proportion = 90%
np = 70*0.9 = 63 which is > 10 ( 1st condition met )
n(1-p) = 70 ( 1 - 0.9 ) = 7 which is < 10 ( second condition not met )
C) sample size ( n ) = 50
population proportion = 15% = 0.15
np = 50 * 0.15 = 7.5 which is < 10 ( 1st condition not met )
n ( 1 - p ) = 50 ( 1 - 0.15 ) = 50 * 0.85 = 42.5 which is > 10 ( second condition met )
D) sample size ( n ) = 200
population proportion = 4% = 0.04
np = 200 * 0.04 = 8 which is < 10 ( 1st condition not met )
n ( 1 - p ) = 200 ( 1 - 0.04 ) = 192 which is > 10 ( second condition met )
hence : The sample size of 50 with population proportion under null hypothesis of 25% meets the requirement
When x=5 what would the value of expression
Answers
Answer:
46
Step-by-step explanation:
6 more than the product of 8 and a number x
6 more means 6+
product of 8 and a number x means 8x
6+8x
when x=5
6+8(5)=6+40=46
Jury Duty Three people are randomly selected from voter registration and driving records to report for jury duty. The gender of each person is noted by the county clerk.
a. Define the experiment.
b. List the simple events in S.
c. If each person is just as likely to be a man as a woman, what probability do you assign to each simple event?
d. What is the probability that only one of the three is a man?
e. What is the probability that all three are women?
Answers
Answer:
(a) The experiment defined here is a random variable that includes the selecting of 3 people from the set of voter registration and driving records.
(b) The simple events in sample space, S = (M, M, M), (M, F, M), (M, M, F), (F, M, M), (F, M, F), (F, F, M), (M, F, F), and (F, F, F).
(c) If each person is just as likely to be a man as a woman, then the probability for each of the simple event can be assigned as [tex]0.5 \times 0.5 \times 0.5 = 0.125[/tex].
(d) The probability that only one of the three is a man is 0.375.
(e) The probability that all three are women is 0.125.
Step-by-step explanation:
We are given that three people are randomly selected from voter registration and driving records to report for jury duty. The gender of each person is noted by the county clerk.
(a) The experiment defined here is a random variable that includes the selecting of 3 people from the set of voter registration and driving records.
(b) As we know that the gender of each person is noted by the county clerk, which means one is male and another female.
So, the simple events in sample space, S = (M, M, M), (M, F, M), (M, M, F), (F, M, M), (F, M, F), (F, F, M), (M, F, F), and (F, F, F).
Here, M is denoted for male and F for female.
(c) If each person is just as likely to be a man as a woman, then the probability for each of the simple event can be assigned as [tex]0.5 \times 0.5 \times 0.5 = 0.125[/tex].
Because there is 50-50 chance of selecting males or females.
(d) The probability that only one of the three is a man is given by;
The total cases in the sample space = 8
Number of cases of only one man out of three = 3
So, the required probability = [tex]\frac{3}{8}[/tex] = 0.375.
(e) The probability that all three are women is given by;
The total cases in the sample space = 8
Number of cases of all three are women = 1
So, the required probability = [tex]\frac{1}{8}[/tex] = 0.125.
Cesium-137 has a half-life of about 30 years. A) Find the annual decay rate and round final result to 4 decimal places. B) Find the continuous decay rate and round final result to 4 decimal places. C) How long will it take for a 10 gram sample to decay to 1 gram? Round to nearest year and interpret your result with a complete sentence. D) Complete this statement: as x goes to infinity, y goes to ___.
Answers
Answer:
0.02280.0231100 years0Step-by-step explanation:
The exponential equation for the fraction remaining after x years can be written as ...
y = (1/2)^(x/30)
A) For x=1, the fraction remaining is ...
y = (1/2)^(1/30) ≈ 0.97716 = 1 - 0.0228
Of the original amount, 0.0228 decays each year.
__
B) The continuous decay rate is the natural log of the growth factor, so is ...
ln(0.97716) = -0.0231
The continuous decay rate is 0.0231 of the present amount (per year).
__
C) For y=.10 (1/10 of the original amount) we find x to be ...
.1 = .5^(x/30)
ln(.1) = (x/30)ln(.5) . . . . . take the natural log
30ln(0.1)/ln(0.5) = x ≈ 100 . . . years
It will take 100 years for a 10-gram sample to decay to 1 gram.
__
D) As x goes to infinity, y goes to zero.
_____
The relationship between growth rate and growth factor is ...
growth factor = 1 + growth rate
When the growth rate is negative, it is called a decay rate.
A box is 90 cm long. Which of these is closest to the length of this box in feet?{1 inch= 2.54cm} (1 point)
Answers
Answer:
2.952755906 ft
Step-by-step explanation:
We need to convert 90 cm to inches
90 cm * 1 inch / 2.54 cm =35.43307087 inches
Now convert inches to ft
12 inches = 1ft
35.43307087 inches * 1 ft/ 12 inches =2.952755906 ft
How many pencils are in a bundle of 10
Answers
if they're in a bundle of 10 then theres 10 pencils
In a recent survey of drinking laws, a random sample of 1000 women showed that 65% were in favor of increasing the legal drinking age. In a random sample of 1000 men, 60% favored increasing the legal drinking age. Test the claim that the percentage of men and women favoring a higher legal drinking age is different at (alpha 0.05).
Answers
Answer:
Step-by-step explanation:
Given that:
Let sample size of women be [tex]n_1[/tex] = 1000
Let the proportion of the women be [tex]p_1[/tex] = 0.65
Let the sample size of the men be [tex]n_2[/tex] = 1000
Let the proportion of the mem be [tex]p_2[/tex] = 0.60
The null and the alternative hypothesis can be computed as follows:
[tex]H_0: p_1 = p_2[/tex]
[tex]H_0a: p_1 \neq p_2[/tex]
Thus from the alternative hypothesis we can realize that this is a two tailed test.
However, the pooled sample proportion p = [tex]\dfrac{p_1n_1+p_2n_2 } {n_1 +n_2}[/tex]
p =[tex]\dfrac{0.65 * 1000+0.60*1000 } {1000 +1000}[/tex]
p = [tex]\dfrac{650+600 } {2000}[/tex]
p = 0.625
The standard error of the test can be computed as follows:
[tex]SE = \sqrt{p(1-p) ( \dfrac{1} {n_1}+ \dfrac{1}{n_2} )}[/tex]
[tex]SE = \sqrt{0.625(1-0.625) ( \dfrac{1} {1000}+ \dfrac{1}{1000} )}[/tex]
[tex]SE = \sqrt{0.625(0.375) ( 0.001+0.001 )}[/tex]
[tex]SE = \sqrt{0.234375 (0.002)}[/tex]
[tex]SE = \sqrt{4.6875 * 10^{-4}}[/tex]
[tex]SE = 0.02165[/tex]
The test statistics is :
[tex]z =\dfrac{p_1-p_2}{S.E}[/tex]
[tex]z =\dfrac{0.65-0.60}{0.02165}[/tex]
[tex]z =\dfrac{0.05}{0.02165}[/tex]
[tex]z =2.31[/tex]
At level of significance of 0.05 the critical value for the z test will be in the region between - 1.96 and 1.96
Rejection region: To reject the null hypothesis if z < -1.96 or z > 1.96
Conclusion: Since the value of z is greater than 1.96, it lies in the region region. Therefore we reject the null hypothesis and we conclude that the percentage of men and women favoring a higher legal drinking age is different.
A system of equations consists of the two equations shown.
{4x+5y=18
6x−5y=20
Which procedure will produce a single equation in one variable? Select all the procedures that apply.
A. Subtract the first equation from the second equation.
B. Subtract the second equation from the first equation.
C. Multiply the first equation by 18; multiply the second equation by 18; add the equations.
D. Multiply the first equation by − 6; multiply the second equation by 4; add the two equations.
E. Multiply the first equation by 3; multiply the second equation by − 2; add the two equations.
F. Multiply the first equation by 3; multiply the second equation by 2; subtract the equations in any order.
Answers
Answer:
C, D, E and F
Step-by-step explanation:
Given
4x+5y=18
6x−5y=20
Required
Determine which procedure will result in a single equation in one variable
To do this; we'll test each of the options
A. Subtract the first equation from the second equation.
[tex](6x - 5y=20) - (4x+5y=18)[/tex]
[tex]6x - 4x - 5y - 5y = 20 - 18[/tex]
[tex]2x - 10y = 2[/tex] --- This didn't produce the desired result
B. Subtract the second equation from the first equation.
[tex](4x+5y=18) - (6x - 5y=20)[/tex]
[tex]4x - 6x + 5y + 5y =18 - 20[/tex]
[tex]-2x + 10y = -2[/tex] --- This didn't produce the desired result
C. Multiply the first equation by 18; multiply the second equation by 18; add the equations.
First Equation
[tex]18 * (4x+5y=18)[/tex]
[tex]72x + 90y = 324[/tex]
Second Equation
[tex]18 * (6x - 5y=20)[/tex]
[tex]108x - 90y = 360[/tex]
Add Resulting Equations
[tex](72x + 90y = 324) + (108x - 90y = 360)[/tex]
[tex]72x + 108x + 90y - 90y = 324 + 360[/tex]
[tex]72x + 108x = 324 + 360[/tex]
[tex]180x = 684[/tex] --- This procedure is valid
D. Multiply the first equation by − 6; multiply the second equation by 4; add the two equations.
First Equation
[tex]-6 * (4x+5y=18)[/tex]
[tex]-24x - 30y = -108[/tex]
Second Equation
[tex]4 * (6x - 5y=20)[/tex]
[tex]24x - 20y = 80[/tex]
Add Resulting Equations
[tex](-24x - 30y = -108) + (24x - 20y = 80)[/tex]
[tex]-24x + 24x - 30y -20y = -108+ 80[/tex]
[tex]-50y = -28[/tex]
[tex]50y = 28[/tex] --- This procedure is valid
E. Multiply the first equation by 3; multiply the second equation by − 2; add the two equations.
First Equation
[tex]3 * (4x+5y=18)[/tex]
[tex]12x + 15y = 54[/tex]
Second Equation
[tex]-2 * (6x - 5y=20)[/tex]
[tex]-12x + 10y = -40[/tex]
Add Resulting Equations
[tex](12x + 15y = 54) + (-12x + 10y = -40)[/tex]
[tex]12x - 12x + 15y - 10y =54 - 40[/tex]
[tex]5y = 14[/tex] --- This procedure is valid
F. Multiply the first equation by 3; multiply the second equation by 2; subtract the equations in any order
First Equation
[tex]3 * (4x+5y=18)[/tex]
[tex]12x + 15y = 54[/tex]
Second Equation
[tex]2 * (6x - 5y=20)[/tex]
[tex]12x - 10y = 40[/tex]
Subtract equation 1 from 2 or 2 from 1 will eliminate x;
Hence, the procedure is also valid;
If Company X has 1600 employees and 80% of those employees have attended the warehouse training course how many employees have yet to attend?
Answers
Answer:
320
Step-by-step explanation:
Total no of employees = 1600
% of employees attended the training = 80%
no. of employee who attended the training = 80/100* 1600 = 1280
No. of employees who are yet to attend the training = Total no of employees - no. of employee who attended the training = 1600-1280 = 320
Thus, 320 employees have yet to attend the training
Which point lies on the line with point-slope equation y - 3 = 4(x + 7)?
A.
(7, 3)
B.
(7, -3)
C.
(-7, -3)
D.
(-7, 3)
Answers
Answer:
D. (-7, 3)
Step-by-step explanation:
The equation given is in point-slope form.
Point-slope form is:
y-y1=m(x-x1)
This is where:
y1 is the y-coordinate of a point it goes through
m is the slope of the line
x1 is the x-coordinate of a point that it goes through
That said, in the given equation:
y1=3
m=4
x1=-7
Note that a point is (x-coordinate, y-coordinate)
Therefore, (-7, 3) is the point that lies on the line.
A 95% confidence interval indicates that:
A. 95% of the intervals constructed using this process based on samples from this population will
include the population mean
B. 95% of the time the interval will include the sample mean
C. 95% of the possible population means will be included by the interval
D. 95% of the possible sample means will be included by the interval
Answers
95% interval would be 95% of the population mean.
The answer should be:
A. 95% of the intervals constructed using this process based on samples from this population will
include the population mean
Answer:
A
Step-by-step explanation:
A 95% confidence interval indicates that 95% of the intervals constructed using this process based on samples from this population will
include the population mean
Convert the following:
How many kilometers are in 1 mile? (Hint: Use the answer from the previous problem)
1 mile is equivalent to
ao kilometers (rounded to the nearest hundredth)
Answers
Answer: 1.609344 kilometers.
Step-by-step explanation:
A mile is an English Unit that is used to measure the length of a linear surface.
Even though the kilometre has replaced it to a large extent as the standard measure of length, it is still the main unit of measurement for distances in the United States, the United Kingdom, Liberia and UK and US oversees territories.
Miles are longer than kilometres as a kilometer is equivalent to only 0.621371 miles.
1 mile is therefore;
= 1/0.621371
= 1.609344 kilometers.
Evaluate. log (down)2 256 . Write a conclusion statement.
Answers
[tex] \Large{ \boxed{ \bf{ \color{blue}{Solution:}}}}[/tex]
By using the fact that,
When,
[tex] \large{ \sf{ {a}^{x} =b}}[/tex]
Then, With logarithm base a of a number b:
[tex] \large{ \sf{ log_{a}(b) = x}}[/tex]
☃️So, Let's solve ths question....
To FinD:
[tex] \large{ \sf{log_{2}(256) }}[/tex]
Let it be x,
[tex] \large{ \sf{ \longrightarrow{ log_{2}(256) = x}}}[/tex]
Proceeding further,
[tex] \large{ \sf{ \longrightarrow \: {2}^{x} = 256}}[/tex]
[tex] \large{ \sf{ \longrightarrow \: {2}^{x} = {2}^{8} }}[/tex]
Then, We have same base 2, So
[tex] \large{ \sf{ \longrightarrow \: x = 8}}[/tex]
Or,
➙ log₂(256) = log₁₀(256) / log₁₀(2)
➙ log₂(256) = 2.40823996531 / 0.301029995664
➙ log₂(256) = 8
☕️ Hence, solved !!
━━━━━━━━━━━━━━━━━━━━
Answer:
256
Step-by-step explanation:
log 256 can most easily be found by rewriting 256 as a power of 2:
2
2^5 * 2^3 = 32*8 = 256, so 2^ (5 + 3) = 2^8.
Then we have:
log 256
2 2 = 256
Alternatively, write:
log (down)2 256 = log (down)2 2^8 = 2*8 = 256
Note that your "log (down)^2 and the function y = 2^x are inverse functions that effectively cancel one another.
In cooking class, Shivani measures a stick
of butter. It is 13 centimeters long, 3
centimeters wide, and 3 centimeters tall. What
is the volume of the stick of butter?
Answers
Answer:
117 cm³
Step-by-step explanation:
To find the volume of a rectangular prism, we can simply multiply the length, width and height so the answer is 13 * 3 * 3 = 117 cm³.
Answer:
117 cubic centimeters
Step-by-step explanation:
Assuming that the stick of butter is a perfect rectangular prism, we can calculate the volume by simply multiplying the length, width, and the height as modeled by the volume equation:
V = LWH
For this, the L = 13cm, W = 3cm, and H = 3cm
So our volume in cubic centimeters will be:
V = LWH
V = (13cm) * (3cm) * (3cm)
V = (13cm) * (9cm^2)
V = 117 cm^3
So the volume of the stick of butter is 117 cubic centimeters.
Cheers.
Help please!!! Tyyyyy
Answers
Answer:
D) 60 degree
Step-by-step explanation:
Let's connect the remaining diagonal, which forms a triangle containing angle x.
As a property of regular hexagon, all diagonals are equal.
=> The formed triangle is a regular triangle and it has three equal angles, which are 60 degrees.
plz someone help me with this question
Answers
Answer:
(x+3)^2=-4(y-3)
Step-by-step explanation:
(x-h)^2 = 4p(y-k)
P is the distance between the focus and vertex
P = 1 --> used distance formula for the points of -3,2 -3,3
Vertex is -3,3 --> according to picture
(x+3)^2=-4(y-3)
P is negative since it goes downwards in the picture.
20 liters of mixture contain milk nad water in the ratio 5:3 of 4 liters of the mixture are replaced by 4 liters of milk find the new ratio of milk to water
Answers
Answer:
7:3
Step-by-step explanation:
5 + 3 = 8
The ratio is
5 milk : 3 water : 8 total
Milk is 5/8 of the total.
Water is 3/8 of the total.
The 20-liter mixture contains:
5/8 * 20 = 12.5 liters of milk, and
3/8 * 20 = 7.5 liters of water
4 liters of the mixture contain:
5/8 * 4 = 2.5 liters of milk, and
3/8 * 4 = 1.5 liter of water
When you remove 4 liters of the mixture from 20 liters of the mixture, you end up with
12.5 L - 2.5 L = 10 L milk, and
7.5 L - 1.5 L = 6 L water
Now you add 4 liters of milk. Now you have
10 L + 4 L = 14 L milk
6 L water
The new ratio of milk to water is 14:6 = 7:3
Answer
Step-by-step explanation:
sum of ratio=5+3=8
Find the volume of the cylinder. Round your answer to the nearest tenth.
Answers
Answer:
716.75 m^3
Step-by-step explanation:
Volume of a cylinder:
=> PI x R^2 x H
H = Height
R = Radius
=> PI x 3.9^2 x 15
=> PI x 15.21 x 15
=> PI x 228.15
=> 228.15 PI
or
=> 228.15 x 3.14159
=> 716.75 m^3
PLZ HELP THANKS! Find the equation of the line passing through the pair points (-8,6) (-9,-9). The equation of the line in the form is Ax+By=C.
Answers
Answer:
The answer is
15x - y = - 126Step-by-step explanation:
To find the equation of the line we must first find the slope (m)
[tex]m = \frac{y2 - y1 }{x2 - x1} [/tex]
So the slope of the line using points
(-8,6) (-9,-9) is
[tex]m = \frac{ - 9 - 6}{ - 9 + 8} = \frac{ - 15}{ - 1} = 15[/tex]
So the equation of the line using point (-8,6) and slope 15 is
y - 6 = 15( x + 8)
y - 6 = 15x + 120
Writing the equation in the form
Ax+By=C
We have
15x - y = -120-6
The final answer is
15x - y = - 126Hope this helps you
Which equation is equivalent to 3[x + 3(4x – 5)] = 15x – 24?15x – 15 = 15x – 2415x – 5 = 15x – 2439x – 45 = 15x – 2439x – 15 = 15x – 24?
Answers
Answer:
3[x + 3(4x – 5)] = (39x-15)
Step-by-step explanation:
The given expression is : 3[x + 3(4x – 5)]
We need to find the equivalent expression for this given expression. We need to simplify it. Firstly, open the brackets. So,
[tex]3[x + 3(4x -5)]=3[x+12x-15][/tex]
Again open the brackets,
[tex]3[x+12x-15]=3x+36x-45[/tex]
Now adding numbers having variables together. So,
[tex]3[x + 3(4x - 5)]=39x-15[/tex]
So, the equivalent expression of 3[x + 3(4x – 5)] is (39x-15).
Jesse bought 3 T-shirts for $6 each and 4 T-shirts for $5 each. What expression can you use to describe what Jesse bought?
Answers
Given that −4i is a zero, factor the following polynomial function completely. Use the Conjugate Roots Theorem, if applicable. f(x)=x4−2x3+x2−32x−240
Answers
Answer:
[tex]\large \boxed{\sf \bf \ \ f(x)=(x-4i)(x+4i)(x+3)(x-5) \ \ }[/tex]
Step-by-step explanation:
Hello, the Conjugate Roots Theorem states that if a complex number is a zero of real polynomial its conjugate is a zero too. It means that (x-4i)(x+4i) are factors of f(x).
[tex]\text{Meaning that } (x-4i)(x+4i) =x^2-(4i)^2=x^2+16 \text{ is a factor of f(x).}[/tex]
The coefficient of the leading term is 1 and the constant term is -240 = 16 * (-15), so we a re looking for a real number such that.
[tex]f(x)=x^4-2x^3+x^2-32x-240\\\\ =(x^2+16)(x^2+ax-15)\\\\ =x^4+ax^3-15x^2+16x^2+16ax-240[/tex]
We identify the coefficients for the like terms, it comes
a = -2 and 16a = -32 (which is equivalent). So, we can write in [tex]\mathbb{R}[/tex].
[tex]\\f(x)=(x^2+16)(x^2-2x-15)[/tex]
The sum of the zeroes is 2=5-3 and their product is -15=-3*5, so we can factorise by (x-5)(x+3), which gives.
[tex]f(x)=(x^2+16)(x^2-2x-15)\\\\=(x^2+16)(x^2+3x-5x-15)\\\\=(x^2+16)(x(x+3)-5(x+3))\\\\=\boxed{(x^2+16)(x+3)(x-5)}[/tex]
And we can write in [tex]\mathbb{C}[/tex]
[tex]f(x)=\boxed{(x-4i)(x+4i)(x+3)(x-5)}[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
Question on Statistics and Confidence Intervals
A field test for a new exam was given to randomly selected seniors. The exams were graded, and the sample mean and sample standard deviation were calculated. Based on the results, the exam creator claims that on the same exam, nine times out of ten, seniors will have an average score within 5% of 75%.
Is the confidence interval at 90%, 95%, or 99%? What is the margin of error? Calculate the confidence interval and explain what it means in terms of the situation. (10 points)
Answers
The phrasing "nine times out of ten" means 9/10 = 0.90 = 90% is the confidence level. We're confident 90% of the time that the confidence interval captures the population parameter we're after (in this case mu = population mean)
The portion "have an average score within 5% of 75%" means that 75% = 0.75 is the center of the confidence interval, and it goes as low as 0.75 - 0.05 = 0.70 and as high as 0.75 + 0.05 = 0.80
This confidence interval is from 70% to 80%, meaning that nine times out of ten, we're confident that the average score is between 70% and 80%
We write the confidence interval as (0.70, 0.80). It's common to use the notation (L, U) to indicate the lower (L) and upper (U) boundaries. You might see the notation in the form L < mu < U. If so, then it would be 0.70 < mu < 0.80; either way they mean the same thing.
The margin of error is 0.05 as its the 5% radius of the interval. It tells us how far the most distant score is from the center (75%)
=========================================
In summary, we have these answers
confidence level = 90%margin of error = 5% = 0.05confidence interval = (0.70, 0.80)interpretation = We're 90% confident that the average exam score is between 0.70 and 0.80According to the Federal Communications Commission, 70% of all U.S. households have vcrs. In a random sample of 15 households, what is the probability that fewer than 13 have vcrs?
Answers
Answer:
The probability is [tex]P(x < 13) = 0.8732[/tex]
Step-by-step explanation:
From the question we are told that
The probability of success is p = 0.70
The sample size is [tex]n = 15[/tex]
Generally the distribution of U.S. households have vcrs follow a binomial distribution given that there are only two outcome (household having vcrs or household not having vcrs )
The probability of failure is mathematically evaluated as
[tex]q = 1- p[/tex]
substituting values
[tex]q = 1- 0.70[/tex]
[tex]q = 0.30[/tex]
The probability that fewer than 13 have vcrs is mathematically represented as
[tex]P(x < 13) = 1- [P(13) + P(14) + P(15)][/tex]
=> [tex]P(x < 13) = 1-[( \left 15 } \atop {}} \right. C_{13} *p^{13}* q^{15-13})+ (\left 15 } \atop {}} \right. C_{14} *p^{14}* q^{15-14}) +( \left 15 } \atop {}} \right. C_{15} *p^{15}* q^{15-15}) ][/tex]
Here [tex]\left 15 } \atop {}} \right. C_{13}[/tex] means 15 combination 13 and the value is 105 (obtained from calculator)
Here [tex]\left 15 } \atop {}} \right. C_{14}[/tex] means 15 combination 14 and the value is 15 (obtained from calculator)
Here [tex]\left 15 } \atop {}} \right. C_{15}[/tex] means 15 combination 15 and the value is 1 (obtained from calculator)
So
[tex]P(x < 13) = 1-[(105 *p^{13}* q^{2})+ (15 *p^{14}* q^{1}) +(1*p^{15}* q^{0}) ][/tex]
substituting values
[tex]P(x < 13) = 1-[(105 *(0.70)^{13}* (0.30)^{2})+ (15 *(0.70)^{14}* (0.30)^{1}) +(1*(0.70)^{15}* (0.30)^{0}) ][/tex]
[tex]P(x < 13) = 0.8732[/tex]
