Answer:
The 98% confidence interval to estimate the proportion of watermelon seeds that germinate is (0.4443, 0.6557). This means that we are 98% sure that the true proportion of all watermalong seeds of the company that germinate is between these two values, which means that there is good evidence that the proportion is below the 70% standard.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success 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 z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].
Once a week for 12 weeks, he purchases a pack of 10 watermelon seeds to act as his sample. He plants the seeds in a greenhouse with good soil to maintain a consistent temperature and watering routine. He finds that the germination rate for the company's watermelon seeds is 55%.
This means that [tex]n = 12*10 = 120, \pi = 0.55[/tex]
98% confidence level
So [tex]\alpha = 0.02[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.02}{2} = 0.99[/tex], so [tex]Z = 2.327[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.55 - 2.327\sqrt{\frac{0.55*0.45}{120}} = 0.4443[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.55 + 2.327\sqrt{\frac{0.55*0.45}{120}} = 0.6557[/tex]
The 98% confidence interval to estimate the proportion of watermelon seeds that germinate is (0.4443, 0.6557). This means that we are 98% sure that the true proportion of all watermalong seeds of the company that germinate is between these two values, which means that there is good evidence that the proportion is below the 70% standard.
Which values of a, b, and c represent the answer in simplest form?
9/11 divided by 5/11 = a b/c
Answer:
a=1, b=9 and c= 5
Step-by-step explanation:
9/11 divided by 5/11
= 9/11 * 11/5
11 gets cancelled
=9/5
it can also be written as 1* 9/5
Hence here a=1, b=9 and c= 5
Please mark me as brainliest.
Write the formulae of area and volume of different solid shapes. Find out the variables and constants in them.
Answer:
Step-by-step explanation:
1 . Sphere :
[tex]Surface \ Area = 4\pi r^2\\\\ Volume = \frac{4}{3} \pi r^3[/tex]
Variable is ' r '
Others Constants.
2. Cone :
[tex]Surface \ Area = \p r^2 + \pi rs[/tex] [tex][ \ s = \sqrt { r^2 + h^2 } \ , r = base \ radius, h = height \ ][/tex]
[tex]Volume = \frac{1}{3} \pi r^2 h[/tex]
Variables are ' r ' and ' h '
Others constants.
3. Cuboid ( Rectangular Prism )
[tex]Surface \ Area = 2 ((l\times b) + ( b \times h) + ( l \times h)) \\\\Volume = l \times \ b \times \ h[/tex]
Variables : l , b , h
Constant is 2
4. Cylinder
[tex]Surface \ Area = 2 \pi r h + 2 \pi r^2 \\\\Volume = \pi r^2 h[/tex]
Variables : ' r ' and ' h '
Others constants..
Answer:
shapes. cuboid. cube. cylinder. prism. sphere. pyramid. rightcircularcone. volumeformula. l×w×h. v=a . 3. v=πr . 2. h. v=b×h. v=( 3. 4)πr . 3. v=( 3. 1)×h×b. v=( 3. 1)πr . 2. h. variables. l=length,w=width,h=height. a=side. r=radius,h=height. b=base,h=height. r=radiusofthesphere. b=areaofthebase,h=heightofthepyramid. r=radiusofthecircularbase,h=height
Step-by-step explanation:
Which of the following value are in the domain of the function graphed below?
Answer:
look at the domain, where the line is on the x-axis
Step-by-step explanation:
four times a certain number decreased by twice the same number gives 17. the number is
Answer:
8.5
Step-by-step explanation:
The equation y = 50(1.05)x models the growth of a mule deer population introduced into Guadalupe National Park in December 2015. "X" represents the number of years after December 2015 while "y" represents the population at time "x". In what year will the mule deer population first reach 1500?
F.2084
G.2044
H.2043
J.2085
9514 1404 393
Answer:
J. 2085
Step-by-step explanation:
Fill in the desired value for y and solve for x.
1500 = 50(1.05^x)
30 = 1.05^x . . . . . . . divide by 50
log(30) = x·log(1.05) . . . . . take logarithms
x = log(30)/log(1.05) ≈ 69.71
Since x represents years after December 2015, x = 69.7 will be some time in mid 2085.
A study of the effect of television commercials on 12-year-old children measured their attention span, in seconds. The commercials were for clothes, food, and toys.
Clothes Food Toys
43 30 52
24 38 58
42 46 43
35 54 49
28 47 63
31 42 53
17 34 48
31 43 58
Required:
a. Find the values of mean and standard deviation.
b. Is there a difference in the mean attention span Of the children for the various commercials?
Answer:
(a)
Mean
[tex]\bar x_1 = 31.375[/tex]
[tex]\bar x_2 = 41.75[/tex]
[tex]\bar x_3 = 53.00[/tex]
Standard deviation
[tex]\sigma_1 = 8.73[/tex]
[tex]\sigma_2 = 7.65[/tex]
[tex]\sigma_3 = 6.04[/tex]
(b) Yes, there is a difference in the mean
Step-by-step explanation:
Solving (a): The mean and standard deviation of each commercial
This is calculated as:
[tex]\bar x = \frac{\sum x}{n}[/tex]
For clothes:
[tex]\bar x_1 = \frac{43+24+42+35+28+31+17+31}{8}[/tex]
[tex]\bar x_1 = \frac{251}{8}[/tex]
[tex]\bar x_1 = 31.375[/tex]
For food:
[tex]\bar x_2 = \frac{30+38+46+54+47+42+34+43}{8}[/tex]
[tex]\bar x_2 = \frac{334}{8}[/tex]
[tex]\bar x_2 = 41.75[/tex]
For toys:
[tex]\bar x_3 = \frac{52+58+43+49+63+53+48+58}{8}[/tex]
[tex]\bar x_3 = \frac{424}{8}[/tex]
[tex]\bar x_3 = 53.00[/tex]
The sample standard deviation is:
[tex]\sigma = \sqrt{\frac{\sum(x - \bar x)^2}{n-1}}[/tex]
For clothes:
[tex]\sigma_1 = \sqrt{\frac{(43 - 31.375)^2 +.............+(31 - 31.375)^2}{8-1}}[/tex]
[tex]\sigma_1 = \sqrt{\frac{533.875}{7}[/tex]
[tex]\sigma_1 = \sqrt{76.2678571429}[/tex]
[tex]\sigma_1 = 8.73[/tex]
For food:
[tex]\sigma_2 = \sqrt{\frac{(30 - 41.75)^2 +............+(43 - 41.75)^2}{8-1}}[/tex]
[tex]\sigma_2 = \sqrt{\frac{409.5}{7}}[/tex]
[tex]\sigma_2 = \sqrt{58.5}[/tex]
[tex]\sigma_2 = 7.65[/tex]
For toys:
[tex]\sigma_3 = \sqrt{\frac{(52-53.00)^2+...................+(58-53.00)^2}{8}}[/tex]
[tex]\sigma_3 = \sqrt{\frac{292}{8}}[/tex]
[tex]\sigma_3 = \sqrt{36.5}[/tex]
[tex]\sigma_3 = 6.04[/tex]
Solving (b): Difference in mean in the commercials;
In (a), we have:
[tex]\bar x_1 = 31.375[/tex]
[tex]\bar x_2 = 41.75[/tex]
[tex]\bar x_3 = 53.00[/tex]
[tex]\bar x_1 \ne \bar x_2 \ne \bar x_3[/tex]
Hence, there is a difference in their means
How many numbers lie between the squares of 39 and 40
Answer:
i guess its 1...
Step-by-step explanation:
Answer:
79 numbers
Step-by-step explanation:
39 x 39 = 1521 ( Find the square of 39)
40 x 40 = 1600 (Find the square of 40)
1600 - 1521 = 79 ( Finding the difference of the two squares)
1. The curved surface area of a cylinder of height 21cm is
660cm", find its radius. please help me .....
I will give brainliest.
Answer:
21 times 660 and then you will get the answer
10 ft
8 ft
Find the area of this figure. Round your
answer to the nearest hundredth. Use
3.14 to approximate .
A = [ ? ] ft2
Nati
x-value of 0
f(x) = |x|
f(x) = |x| + 3
f(x) = |x + 3|
f(x) = |x| − 6
f(x) = |x + 3| – 6
9514 1404 393
Answer:
0, 3, 3, -6, -3
Step-by-step explanation:
Maybe you want to find f(0) in each case. Put 0 where x is, and do the arithmetic.
f(0) = |0| = 0
f(0) = |0| +3 = 3
f(0) = |0 +3| = 3
f(0) = |0| -6 = -6
f(0) = |0 +3| -6 = -3
Consider a student loan of 15,000 at a fixed APR of 9% for 25 years. A) Calculate the monthly payment B) Determine the tiaras amount paid over the term of the loan C) Of the total amount paid, what percentage is paid toward the principal and what percentage is paid for interest.
Answer:
The monthly payment will be $ 162.50. In turn, the interest paid will be $ 33,750, constituting 69.23% of the total amount paid.
Step-by-step explanation:
Since there is a student loan of 15,000 at a fixed APR of 9% for 25 years, to calculate the monthly payment, determine the tiaras amount paid over the term of the loan, and determine, of the total amount paid, what percentage is paid toward the principal and what percentage is paid for interest, the following calculations must be performed:
((15,000 x 0.09) x 25) + 15,000 = X
33,750 + 15,000 = X
48,750 = X
48,750 / (25x12) = X
48,750 / 300 = X
162.5 = X
48,750 = 100
33,750 = X
33,750 x 100 / 48,750 = X
69.23 = X
Therefore, the monthly payment will be $ 162.50. In turn, the interest paid will be $ 33,750, constituting 69.23% of the total amount paid.
You work no more than 12 hours a week at your two jobs. The first job pays you $8 an hour, and the second job pays you $10 an hour. You must earn at least $100 each week. Which graph represents this situation (let x represent hours at job 1 and y represent hours at job 2)?
Answer:
10 hours at job (1)
2 hours at job (2)
Step-by-step explanation:
As per the given information, one earns ($8) dollars at one of their jobs, and ($10) hours at the other. One must earn a total of ($100) dollars, and can work no more than (12) hours. Let (x) be the hours worked at job 1 and (y) be the hours worked at job two.
Since one can work no more than (12) hours, the sum of (x) and (y) must be (12), therefore the following equation can be formed;
[tex]x+y=12[/tex]
One earns ($8) dollars at one of their jobs and ($10) at the other, but one earns a total of (100) one can form an equation to represent this situation. Multiply the hours worked by the money earn per hour for each job, add up the result and set it equal to (100).
[tex]8x+10y=100[/tex]
Now set up these equations in a system;
[tex]\left \{ {{x+y=12} \atop {8x+10y=100}} \right.[/tex]
Use the process of elimination to solve this system. The process of elimination is a method of solving a system of equations. One must first manipulate one of the equations in the system such that one of the variable coefficients is the additive inverse of the other. That way, when one adds the equation, the variable cancels, one can solve for the other variable then back solve to find the value of the first variable,
[tex]\left \{ {{x+y=12} \atop {8x+10y=100}} \right.[/tex]
Manipulate,
[tex]= \left \{ {{(*-8)(x+y=12)} \atop {8x+10y=100}} \right.\\\\[/tex]
Simplify,
[tex]= \left \{ {{-8x-8y=-96} \atop {8x+10y=100}} \right.\\[/tex]
Add,
[tex]=2y=4[/tex]
Inverse operations,
[tex]y=2[/tex]
Backsolve for (x), use equation one to achieve this,
[tex]x+y=12\\[/tex]
Substitute,
[tex]x+2=12[/tex]
Inverse operations,
[tex]x=10[/tex]
A motorboat travels 9 miles downstream (with the current) in 30 minutes. The return trip upstream (against the wind) takes 90 minutes. Which system of equations can be used to find x, the speed of the boat in miles per hour, and y, the speed of the current in miles per hour? Recall the formula d = rt.
Answer:
x=12 mile/hour(the speed of the boat)
y=6 mile/hour(the speed of the current)
Step-by-step explanation:
According to the Question,
let, x be the speed of the boat in miles per hour and y be the speed of the current in miles per hour.
Given That, A motorboat travels 9 miles downstream (with the current) in 30 minutes. Thus, x+y = 0.3 mile/minute ⇒ 0.3×60 ⇒ 18mile/hourx+y=18 ---- Equation 1
& The return trip upstream (against the wind) takes 90 minutes. Thus, x-y = 0.1 mile/minute ⇒ 0.1×60 ⇒ 6mile/hourx-y=6 ---- Equation 2
On Adding both above Equations We get,
2x=24 ⇔ x=12 mile/hour(the speed of the boat)
& x+y=18 put Value of x=12 we get ⇔ y=6 mile/hour(the speed of the current)
PLEASE ANSWER MAKE SURE YOU ARE RIGHT PLEASE I WILL MARK AS BRAINIEST
FIND THE VOLUME OF THE CYLINDER
Answer:
Find the volume of the cone, the answer i got was 37.68 but it asked to round so it should be 37.7
Hope this helps :)
Answer:
If we want to find volume of cone we must use this formule: πr²*high/3.
Step-by-step explanation:
let's solve step by step
firstly you know the radius is 3 and high is 4
if we accept π to 3. the answer is must be (3*3*4)/3 and finally the answer is 12 units³
Complete the table of inputs and outputs for the given function. g(x) = 3 - 8x g() 0 -5 3 Reset
Answer:
Step-by-step explanation:
A set of numbers is shown below:
{0, 0.6, 2, 4, 6}
Which of the following shows all the numbers from the set that make the inequality 2x + 3 ≥ 7 true?
{4, 6}
{0, 0.6, 2}
{0, 0.6}
{2, 4, 6}
Answer:
{2,4,6}
Step-by-step explanation:
Hope it helps you
What is the mean absolute deviation of Warren’s data?
Warren's Scores Absolute Deviation from Mean Score – individual score
0
25
15
10
20
30
10
15
5
25
20
15
20
5
10
sum of absolute deviations =
Answer:
6.667
Step-by-step explanation:
I just did the calculations
The time to complete an exam is approximately Normal with a mean of 48 minutes and a standard deviation of 3 minutes. The bell curve below represents the distribution for testing times. The scale on the horizontal axis is equal to the standard deviation. Fill in the indicated boxes.
Answer:
This means the average amount of time is 48 minutes but many people will do it in 45 to 51
Hope This Helps!!!
If these two triangles are similar, find the vale of x.
Answer:
24
Step-by-step explanation:
just use sss theorem and get the answer
Can someone please help me?
A sample of 46 observations is selected from one population with a population standard deviation
of 4.1. The sample mean is 102.0. A sample of 48 observations is selected from a second
population with a population standard deviation of 5.8. The sample mean is 100.1. Using the 0.05
significance level, is there a difference between the two samples?
Answer:
there is no significant evidence to conclude that there is difference between the two samples.
Step-by-step explanation:
Given :
x1 = 102 ; σ1 = 4.1 ; n1 = 46
x2 = 100.1 ; σ2 = 5.8 ; n2 = 48
H0 : μ1 = μ2
H0 : μ1 ≠ μ2
The test statistic :
The test statistic :
(x1 - x2) / sqrt[(σ1²/n1 + σ2²/n2)]
(102 - 100) / sqrt[(4.1²/46 + 5.8²/48)]
2 / 1.0326025
Test statistic = 1.937
The Pvalue from test statistic score ;
Pvalue = 0.052745
Pvalue > α ; Fail to reject the null ; Hence, there is no significant evidence to conclude that there is difference between the two samples.
2. A bag contains one red, one blue and one white marble. One marble is chosen at random
from the bag, and then replaced into the bag. A second marble is chosen.
a) Draw a probability tree and find the sample space.
(3 marks)
Answer:
Step-by-step explanation:
A system of equations is shown below:
y = 3x − 7
y = 2x + 1
What is the solution to the system of equations?
(8, 17)
(−8, 17)
(−8, −17)
(8, −17)
Answer:
(8, 17)
Step-by-step explanation:
y= 3x -7 -----(1)
y= 2x +1 -----(2)
Substitute (1) into (2):
3x -7= 2x +1
Being x terms to one side, constant to the other:
3x -2x= 7 +1
x= 8
Substitute x= 8 into (2):
y= 2(8) +1
y= 16 +1
y= 17
∴ The solution is (8, 17).
How do I solve this and do the explanation of it
Answer:
180-66
114
hope it helps mark as brainlist
Select the correct answer.
What is this expression in simplified form?
5v2.9v6
OA. 45v3
OB. 90
O C. 90v3
OD. 45V2
Answer:
C. 90√3
Step-by-step explanation:
5√2 . 9√6 = 45√12 = 45×2√3
= 90√3
The simplified form is 90√3.
What is multiplication?In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.
Given expression is, 5√2×9√6
=5×9×√(2×6)
=45×√12
=45×2√3
=90√3
Hence, the simplified form is 90√3 .
To learn more on multiplication click:
https://brainly.com/question/5992872
#SPJ2
[tex]\int _{2.2}^{+\infty \:}\frac{10.648}{x^2}[/tex]
Step-by-step explanation:
[tex]\int _{2.2}^{+\infty \:}\frac{10.648}{x^2}dx = 10.648 \int _{2.2}^{\infty \:}\frac{dx}{x^2}[/tex]
[tex] = - \frac{10.648}{x} | _{2.2}^{ \infty} = 4.84[/tex]
A state sales tax of 6% and a local sales tax of 1% are levied in Tampa, Florida. Suppose the price of a
particular car in Tampa is $15,000, and an oil change at a certain auto center is $29.
Which statement is true about the total cost of the car and the oil change after sales tax has been
calculated?
Answer:
16050, 31.03
Step-by-step explanation:
15000x1.07 (adds 7% tax)=16050
29x1.07(adds 7% tax to price)=31.03
Write the equation of the line in Point-Slope Form given the information below. Slope =−1/5 Y-Intercept =−3 Point-Slope Form:
Answer:
[tex]y - 0= \frac{ - 1}{5}( x + 15)[/tex]
PLEASEEEE HELP QUICKKKK
Given:
Line A goes through (0,y) and (-2,0).
Line B goes through (1,2) and (3,10).
To find:
The value of y for which the system of given linear equation (equation of line A and line B) has no solutions.
Solution:
Two linear equation has no solutions if they are parallel line.
Slope formula:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We know that the slopes of two parallel lines are the same.
So, the given system of given linear equation has no solutions if
Slope of line A = Slope of line B
[tex]\dfrac{0-y}{-2-0}=\dfrac{10-2}{3-1}[/tex]
[tex]\dfrac{-y}{-2}=\dfrac{8}{2}[/tex]
[tex]\dfrac{y}{2}=4[/tex]
Multiply both sides by 2.
[tex]\dfrac{y}{2}\times 2=4\times 2[/tex]
[tex]y=8[/tex]
Therefore, the required value of y is 8.
Three-fourths (one-fourth x + 8) minus (one-half x + 2) = StartFraction 3 Over 8 EndFraction (4 minus x) minus one-fourth?
Answer:
if I am understood your question correctly, X would be 84/29
Step-by-step explanation:
