Using the normal distribution and the central limit theorem, it is found that there is a 0.18406 = 18.406% probability that the average water consumed by them is less than 18 ounces.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].For the population, the mean and the standard deviation are, respectively, given by [tex]\mu = 20, \sigma = 7[/tex].
For samples of n = 10, the standard error is given by:
[tex]s = \frac{7}{\sqrt{10}} = 2.2136[/tex]
The probability that the average water consumed by them is less than 18 ounces is the p-value of Z when X = 18, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem:
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{18 - 20}{2.2136}[/tex]
Z = -0.9.
Z = -0.9 has a p-value of 0.18406.
0.18406 = 18.406% probability that the average water consumed by them is less than 18 ounces.
To learn more about the normal distribution and the central limit theorem, you can check https://brainly.com/question/24663213
if you answer this question you will get 30 points
Answer:
2 rrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrr
Step-by-step explanation:
1+1 is 2
A runner is preparing for a marathon that is divided into 5 sections of equal distance. The Marathon is 42.195 km long. How long is each section of the marathon?
A. 210.975
B. 21.0975
C. 8.439
D. 0.8439
Answer:
8.439
Step-by-step explanation:
Since the marathon is divided on 5 EQUAL sections, and it is 42.195 km long, you only need to divide the length of the marathon by 5.
Pleade god help me find someone to help me thank you
Answer:
yw
Step-by-step explanation:
makin a chart :)
Find the differential of
f
(
x
,
y
)
=
x
2
+
y
3
at the point
(
2
,
1
)
.
[tex]f(x,y)=x^2+y^3\implies \left.\cfrac{}{} 2x+3y^2 \right]_{\stackrel{\textit{\small x=2}}{\textit{\small y=1}}}\implies 2(2)+3(1)^2\implies 7[/tex]
what does Y=
what does z=
Answer:
Hope the picture will help you
26.95 divided by -5 1/2. can someone show me how to do it please?
Answer:
-4.9
Step-by-step explanation:
Since the number 26.95 has two decimal places, it can be turned into a whole number with a denominator having two zeroes; 100
2695
100
Then change -5 1/2 into an improper fraction; = -5 × 2 + 1
2
= -11/2
2695 ÷ ( -11 )
100 2
Reciprocate (put denominator as numerator and vice-versa ) the equation after the ÷ sign. After doing so, the ÷ sign changes to × sign.
Hence: 2695 × ( 2 )
100 -11
Then, cross multiply.
2695 ÷ ( -11 ) = -245100 ÷ 2 50
-245 ÷ 50
= -4.9
Answer: its -4.9
Step-by-step explanation:
An athlete runs in a straight line along a flat surface. He starts from rest and for 20 seconds accelerate at a constant
rate. In this first 20 seconds he covers a distance of 100m. For the next 10 seconds he runs at a constant speed and
then decelerates at a constant rate for 5 seconds until he stops.
a) What is the total distance that he ran?
[5]
Another athlete runs along the same track, starting from rest and she accelerates at the same rate as her friend. She
however only accelerates for 10 seconds before running at a constant speed.
Answer:
probably 200
Step-by-step explanation:
or something like that
3
0.33 points
Suppose you form 5-letter strings from the letters C,O, M, P, U, T, I, N, and G. What are the number of permutations as a ratio of factorials?
type your answer...
Using the permutation formula, it is found that it's number as a ratio of factorials is given by:
[tex]N = \frac{9!}{4!}[/tex]
The order in which the letters are chosen is important, hence the permutation formula is used to solve this question.
What is the permutation formula?The number of possible permutations of x elements from a set of n elements is given by:
[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]
In this problem, five letters will be chosen from a set of nine, hence:
[tex]N = P_{(9,5)} = \frac{9!}{(9-5)!} = \frac{9!}{4!}[/tex]
More can be learned about the permutation formula at https://brainly.com/question/25925367
What is the volume of a rectangular prism that is 4 ft. by 12 ft. by 6 ft.? Question 21 options: 324 ft.³ 205 ft.³ 288 ft.³ 315 ft.³
Answer:
288 ft³
Step-by-step explanation:
The formula to find the volume of a rectangular prism is :
Volume = length × width × height
Let us find it now.
Volume = 4 ft × 12 ft × 6 ft
Volume = 48 ft² × 6 ft
Volume = 288 ft³
what is the correct distribution of (2x-8)(3x-6) using the distributive property
Answer:
6x² -36x +48
Step-by-step explanation:
The terms in one factor are each multiplied by the terms in the other factor. The resulting partial products are then combined. (This works the same as for numerical "long" multiplication.)
(2x -8)(3x -6) = 2x(3x -6) -8(3x -6)
= 6x² -12x -24x +48 . . . . . . . form partial products
= 6x² -36x +48 . . . . . . . collect terms
Answer:
6x² - 36x + 48
Step-by-step explanation:
(2x-8)*(3x-6) = 2x*3x + 2x* -6 + -8*3x + -8*-6
6x² - 12x - 24x + 48
6x² - 36x + 48 [Answer]
PLEASE RATE!! I hope this helps!!
if you have any questions comment below!!
(I have verified my answer using an online calculator)
Think about each of the following. Which of these three triangles is impossible to draw?
Check by using sum of angles of triangle = 180°
20+45 < 180 so third angle will make it 180 which means it's possible to draw 120+50 = 170< 180 so third angle being 10 will complete the triangle90+100 = 190 > 180 so third angle being (-10) is impossible for the triangle so it can't be possibleWhich method do you prefer when comparing numbers written in scientific notation? Explain why you prefer this method using examples. PLS HURRY
Answer:
If two numbers have the same exponent for 10, then compare the decimal numbers to determine the greater number. Sometimes you may have to compare two numbers, but only one of them is in scientific notation. In that case, convert the number that is not in scientific notation into scientific notation first. Then, compare the two numbers. Example 1 : Compare 5.62 x 10 6 and 7.39 x 10 5.
Step-by-step explanation:
The general form in scientific notation is
z.z ×10^zwhere z is integer
So while comaparing
We usually compare z.z rounded to similar significant numbers .
In rest case
we use power of 10 ,the number which has higher that's bigger.Example
1.27×10⁴1.24×10⁴First one is bigger
The quotient of a number and three is six
What is the number?
Answer:
the quotient of 18 and 3 is 6
Step-by-step explanation:
do the inverse and get 6x3=18
What is the area?
2 yd
8 yd
5 yd
Answer:
28
Step-by-step explanation:
I assume the polygon is a trapezoid with parallel bases of 2 yd and 5 yd, and an altitude of 8 yd.
area of trapezoid = (base1 + base2)h/2
area = (2 yd + 5 yd)(8 yd)/2
area = 28 yd²
I need help...you will be mark brainliest if it's right ty
Answer:
Median: 5
Interquartile range: 4
Have an amazing day!
Please rate and mark brainliest!!
the legnth of a rectangle is three times its width. if the length of the perimeter is 64 in, find the length and width
Answer:
Length and width of rectangle is 24 and 8 inchesStep-by-step explanation:
Given:
Length of rectangle is three times the widthPerimeter of rectangle is 64 InchesTo Find:
Length and WidthSolution:
Let's assume Width of rectangle x inches and length be 3x inches. To calculate the dimensions of The rectangle we will use the formula of Perimeter of rectangle:
Perimeter of rectangle = 2(L + B)
→ 64 = 2(3x + x)
→ 64 = 2(4x)
→ 64/2 = 4x
→ 32 = 4x
→ 32/4 = x
→ 8 = x
Hence,
Length of the rectangle = 3x = 3(8) = 24 inchesWidth of the rectangle = x = 8 inchesAnswer:
Length = 24 inchesWidth = 8 inches⠀
Step-by-step explanation :
⠀
As it is given that, the legnth of a rectangle is three times its width and the perimeter is 64 in and we are to find the length and width of the rectangle. So,
⠀
Let us assume the width of the rectangle as w inches and therefore, the length will be 3w inches .
⠀
Now, According to the Question :
⠀
[tex]{\longrightarrow \qquad { \pmb{\frak {2 ( Length + Breadth )= Perimeter_{(Rectangle)} }}}}[/tex]
⠀
[tex]{\longrightarrow \qquad { {\sf{2 (3 x + x )= 64 }}}}[/tex]
⠀
[tex]{\longrightarrow \qquad { {\sf{2 (4x )= 64 }}}}[/tex]
⠀
[tex]{\longrightarrow \qquad { {\sf{8x= 64 }}}}[/tex]
⠀
[tex]{\longrightarrow \qquad { {\sf{ x = \dfrac{64}{8} }}}}[/tex]
⠀
[tex]{\longrightarrow \qquad{ \underline{ \boxed { \pmb{\mathfrak {x = 8}} }}} }\: \: \bigstar[/tex]
⠀
Therefore,
The width of the rectangle is 8 inches .⠀
Now, We are to find the length of the rectangle:
[tex]{\longrightarrow \qquad{ { \frak{\pmb{Length = 3x }}}}}[/tex]
⠀
[tex]{\longrightarrow \qquad{ { \frak{\pmb{Length = 3 \times 8 }}}}}[/tex]
⠀
[tex]{\longrightarrow \qquad{ \underline{ \boxed{ \frak{\pmb{Length = 24}}}}}} \: \: \bigstar[/tex]
⠀
Therefore,
The length of the rectangle is 24 inches .⠀
Perimeter of following rectangle mixed number in simplest form 1 1/3 ft 5/8 ft
Answer: 3 11/12
Step-by-step explanation:
1 1/3 * 2 = 2 2/3
5/8 * 2 = 1 1/4
2 2/3 + 1 1/4 = 3 11/12
what should be the rate of interest to earn an 45000 as interest wale rupees 50000 easy in investment for 6 year
Answer:
5
Step-by-step explanation:
Which angle is an x-intercept for the function y = cos(1)
A.0
B.2
C. £
D. 2£
Answer: C. [tex]\pi[/tex]
=======================================================
Explanation:
The x intercept always occurs when y = 0.
Use the unit circle to determine that [tex]\cos(\theta) = 0[/tex] when [tex]\theta = \frac{\pi}{2} \text{ and } \theta = \frac{3\pi}{2}[/tex]
So if [tex]x = \pi[/tex], then we have
[tex]y = \cos\left(\frac{1}{2}x\right)\\\\y = \cos\left(\frac{x}{2}\right)\\\\y = \cos\left(\frac{\pi}{2}\right)\\\\y = 0\\\\[/tex]
which shows us that [tex](\pi, 0)[/tex] is the location of one of the infinitely many x intercepts for this function.
Consider the function RX) = 3x + 1 and the graph of the function g(x) shown below.
у
4
6
4
2
X
-6 -4
- 2
12
4
6
-2
4
6
The graph g(x) is the graph of f(x) translated
✓ units
✓, and g(x) =
Step-by-step explanation:
f(x) goes through the point (0, 1).
g(x) goes through (2, 1) for the same y value.
that means g(x) is f(x) translated 2 units to the right.
but we could also look at the same x value (0).
then g(x) goes through (0, -5).
and that means g(x) is f(x) translated 6 units down.
since it is a line function, shifting it left/right or up/down makes no difference to the shape or position of the new curve itself.
as it looks like you don't have 6 in the drop-down menu, then 2 units (to the right) is the desired correct result.
that means g(x) = f(x-2) = 3(x-2) + 1 = 3x - 6 + 1 = 3x - 5
and that is what the graph is showing us.
Four divided by 1,000 rounded to the nearest whole number
Answer:
4 ÷ 1,000 = 0.004
Rounding up to 0 as the nearest whole number
It has been found that 50.3% of U.S. households own stocks and mutual funds. A random sample of 300 heads of households indicated that 171 owned some type of stock. At what level of significance in a two- tailed test would you conclude that this was a significant difference
Finding the p-value of the test using the z-distribution, as we are working with a proportion, it is found that this was a significant difference for levels of significance of 0.02 and lower.
What are the hypothesis test?At the null hypothesis, we test if the proportion is of 50.3%, hence:
[tex]H_0: p = 0.503[/tex]
We have a two-tailed test, hence at the alternative hypothesis we test if the proportion is different, that is:
[tex]H_1: p \neq 0.503[/tex]
What is the test statistic?The test statistic is given by:
[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
In which:
[tex]\overline{p}[/tex] is the sample proportion.p is the proportion tested at the null hypothesis.n is the sample size.In this problem, the parameters are:
[tex]n = 300, \overline{p} = \frac{171}{300} = 0.57, p = 0.503[/tex]
Hence:
[tex]z = \frac{\overline{p} - p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]
[tex]z = \frac{0.57 - 0.503}{\sqrt{\frac{0.503(0.497)}{300}}}[/tex]
[tex]z = 2.32[/tex]
What is the p-value?Considering a two-tailed test, using a z-distribution calculator, the p-value is of 0.0203. Hence this was a significant difference for levels of significance of 0.02 and lower.
More can be learned about the z-distribution at https://brainly.com/question/26454209
Work out the highest common factor (HCF) of 18 and 30
[tex]18 = 2\times 3 \times 3\\\\30 = 2 \times 3 \times 5\\\\\text{HCF}~ = 2\times 3 = 6[/tex]
Sonya took out a mortgage of $65,000 at 7% for 25 years. What is the cost of the mortgage?
The cost of the mortgage is $81250
What are interests?
Interests are percentages of a principal
Given the following parameters
Principal = $65000
Rate = 7% = 0.07
Time = 5 years
I = PRT/100
I = 65000*0.07*25
I = 16,250
Cost of mortgage = Principal + Interest
Cost of mortgage = 65000 + 16250
Cost of mortgage = 81,250
Hence the cost of the mortgage is $81250
Learn more on mortgage here: https://brainly.com/question/22846480
Answer:
$72,823
Step-by-step explanation:
just took test
Triangle A′B′C′ is a dilation of triangle ABC .
What is the scale factor?
Enter your answer in the box.
Answer:
1/2
Step-by-step explanation:
The scale factor is 1/2 because each side length of [tex]\triangle{A'B'C'}[/tex] is 1/2 of the length of the side lengths of [tex]\triangle{ABC}[/tex].
Hope this helps :)
Answer:
1/2
Step-by-step explanation:
took the test
Write the given expression in terms of x and y only sin(tan^-1(x)+tan^-1(y)
Answer:
Step-by-step explanation:
Let a = tan⁻¹(x), so tan(a) = x,
[tex]\sin(a)=\frac{x}{\sqrt{1+x^2}}, \cos(a)=\frac{1}{\sqrt{1+x^2}},[/tex]
Let b = tan⁻¹(y), so tan(b) = y,
[tex]\sin(b)=\frac{y}{\sqrt{1+y^2}}, \cos(b)=\frac{1}{\sqrt{1+y^2}},[/tex]
sin( tan⁻¹(x) + tan⁻¹(y)) = sin(a + b)
= sin(a) cos(b) + cos(a)sin(b)
= [tex]\frac{x}{\sqrt{1+x^2}}\times\frac{1}{\sqrt{1+y^2}}+ \frac{y}{\sqrt{1+y^2}}\times\frac{1}{\sqrt{1+x^2}}[/tex]
[tex]=\frac{x+y}{\sqrt{(1+x^2)(1+y^2)}}[/tex]
what is 7 times 3 fiths
Answer:
4-1.5 or 21/5 or 4.2
Step-by-step explanation:
Multiple: 7 * 3/5 = 7 · 3/1 · 5 = 21/5
Multiply both numerators and denominators. Result fraction keep to lowest possible denominator GCD(21, 5) = 1. In the following intermediate step, it cannot further simplify the fraction result by canceling.
In other words - seven multiplied by three fifths = twenty-one fifths.
Briana has 3/4 pound of rabbit food. She feeds her rabbit 1/12 pound each day. How many days can Briana feed her rabbit with the food she has?
Please help Math-correct answers only!!
Have number with correct answers/letters!
I'll do the first three questions to get you started.
==========================================================
Question 1
x = horizontal component of the triangle
cos(angle) = adjacent/hypotenuse
cos(theta) = horizontal/hypotenuse
cos(40) = x/30
x = 30*cos(40)
x = 22.98133329 approximately
This is the horizontal force applies to the suitcase.
Work = force*displacement
Work = 22.98133329*120
Work = 2,757.7599948
Work = 2,758
Answer: 2,758 Nm (choice B)==========================================================
Question 2
Add the drone's relative air velocity and the wind velocity vectors.
v+w = (13i + 3j) + (-7i - 2j)
v+w = (13i-7i) + (3j-2j)
v+w = 6i + j
Answer: 6i + j (choice B)==========================================================
Question 3
Check out the diagram below. Focus on the smaller triangle. Notice the placement of angle theta.
sin(theta) = opposite/hypotenuse
sin(40) = x/200
x = 200*sin(40)
x = 128.557521937308
x = 128.558
Answer: 128.558 pounds (choice A)A parabola can be drawn given a focus of (1, -7) and a directrix of y = 1. Write the
equation of the parabola in any form.
Answer:
Step-by-step explanation:
focus (1 , -7) ⇒ a = 1 & b = -7
y = 1 ⇒ c = 1
Equation of parabola :
(x - a)² + (y - b)² = (y - c)²
(X - 1)² + (y + 7)² = (y - 1)²
Now, expand.
x² - 2x + 1 + y² + 2*7*y + 7² = y² - 2*y*1 + 1
x² - 2x + 1 + y² - 14y + 49 = y² - 2y +1
x² - 2x + 1 + y² - 14y + 49 - y² + 2y - 1 = 0
x² - 2x + y² - y² - 14y + 2y + 1 + 49 - 1 = 0
x² - 2x - 12y + 49 = 0