Answer:
0.1587
Step-by-step explanation:
Applying,
P(μ>40) = P(μ-(x-μ)/σ)............. Equation 1
Where P(μ>40) = probability of the age of the random subscriber more than 40 years μ = mean, σ = standard deviation, x = random subscriber
From the question,
Given: μ = 35 years, σ = 5 years, x = 40 years.
Therefore,
P(μ>40) = P(35-(40-35)/5) = P(35-(5/5)
P(μ>40) = 1-φ(1)
From the norminal probabilty table,
P(μ>40) = 1-0.8413
P(μ>40) = 0.1587
An article describes an experiment to determine the effectiveness of mushroom compost in removing petroleum contaminants from soil. Out of 155 seeds planted in soil containing 3% mushroom compost by weight, 74 germinated. Out of 155 seeds planted in soil containing 5% mushroom compost by weight, 86 germinated. Can you conclude that the proportion of seeds that germinate differs with the percent of mushroom compost in the soil
Solution :
Let [tex]p_1[/tex] and [tex]p_2[/tex] represents the proportions of the seeds which germinate among the seeds planted in the soil containing [tex]3\%[/tex] and [tex]5\%[/tex] mushroom compost by weight respectively.
To test the null hypothesis [tex]H_0: p_1=p_2[/tex] against the alternate hypothesis [tex]H_1:p_1 \neq p_2[/tex] .
Let [tex]\hat p_1, \hat p_2[/tex] denotes the respective sample proportions and the [tex]n_1, n_2[/tex] represents the sample size respectively.
[tex]$\hat p_1 = \frac{74}{155} = 0.477419[/tex]
[tex]n_1=155[/tex]
[tex]$p_2=\frac{86}{155}=0.554839[/tex]
[tex]n_2=155[/tex]
The test statistic can be written as :
[tex]$z=\frac{(\hat p_1 - \hat p_2)}{\sqrt{\frac{\hat p_1 \times (1-\hat p_1)}{n_1}} + \frac{\hat p_2 \times (1-\hat p_2)}{n_2}}}[/tex]
which under [tex]H_0[/tex] follows the standard normal distribution.
We reject [tex]H_0[/tex] at [tex]0.05[/tex] level of significance, if the P-value [tex]<0.05[/tex] or if [tex]|z_{obs}|>Z_{0.025}[/tex]
Now, the value of the test statistics = -1.368928
The critical value = [tex]\pm 1.959964[/tex]
P-value = [tex]$P(|z|> z_{obs})= 2 \times P(z< -1.367928)$[/tex]
[tex]$=2 \times 0.085667$[/tex]
= 0.171335
Since the p-value > 0.05 and [tex]$|z_{obs}| \ngtr z_{critical} = 1.959964$[/tex], so we fail to reject [tex]H_0[/tex] at [tex]0.05[/tex] level of significance.
Hence we conclude that the two population proportion are not significantly different.
Conclusion :
There is not sufficient evidence to conclude that the [tex]\text{proportion}[/tex] of the seeds that [tex]\text{germinate differs}[/tex] with the percent of the [tex]\text{mushroom compost}[/tex] in the soil.
A 33-m tall building casts a shadow. The distance from the top of the building to the tip of the shadow is 37-m.
. Find the length of the shadow.
Answer:
[tex]\sqrt{280}[/tex] = 2[tex]\sqrt{70}[/tex]
37^2 = 1369
33^2 =1089
1369-1089 = 280
Step-by-step explanation:
Which points lie on the graph of f(x) = loggx?
Check all that apply.
Step-by-step explanation:
f(x)=log(x)
=d(log(x)/dx)
=>y=1/x
Need the help thanks guys
Answer:
1/4
Step-by-step explanation:
x^2 - x
Take the coefficient of x
-1
Divide by 2
-1/2
Square it
(-1/2)^2 = 1/4
Add it
x^2 -x +1/4
Can someone help me? I don’t know how to solve the rest. I am struggling and I would be so happy if any of you helped me. Thank you for your help!
which of the following expressions are equivalent to 36x + 24y? choose all that apply
6x (6+4y) 6(6x + 4y) 12(36x + 24y) 12(3x + 2y) 4y(9x + 6) 4(9x + 6y)
The following expressions are equivalent to 36x + 24y is 6(6x+4y).
6x(6+4y)
6(6x+4y)
12(3x+2y)
4(9x+6y)
We have,
What is the expression?The expression consists of numbers and arithmetic operators. It does not contain equality or inequality symbols. The expression consists of unknown variables
36x + 24y
=6(6x)+6(4y)
=6(6x+4y)
Therefore, The following expressions are equivalent to 36x + 24y is 6(6x+4y).
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in a group of 60 students, 30 can speak nepali only and 15 can speak English only how many can speak english and nepali students
Answer:
45 is the Answer
Step-by-step explanation:
Hope its helpful
What is the correct way to read 43.106
Step-by-step explanation:
Forty three thousand one hundred and six
Answer:
Forty three AND one hundred six thousandths
Step-by-step explanation:
If there is a comma ( , ) between the two numbers, you are correct.
If there is a period / dot ( . ) between them, and you need to read the place values, you must read the numbers to the right of the . as decimals. Those are the "th" numbers. 1 is in the tenths place, 0 in the hundredths place and the 6 in the thousandths place.
If you are simply reading out the digit names, without assigning their value, you might say "forty three POINT one hundred six" or "forty three DOT one hundred six" or "forty three DECIMAL one hundred six".
Alan's aunt gave him $95 to spend on clothes at the mall. He bought 5 shirts that cost $6 each and a pair of pants that cost $17. How much money does Alan have left to buy more clothes? (one more)
Answer:
he has 48 dollars left to spend on clothes
$88 tickets to the San Francisco 49ers game are offered at a 15%
discount. What is the sale price?
Answer:
74.80
Step-by-step explanation:
First find the discount
88 * 15%
88*.15
13.2
Subtract the discount from the original price
88-13.2
74.80
In empty set, n (A) = ………
Answer:
answer is
In empty set, n(A) = { }.
Cho hai tập hợp A={1;2;3;4},B={2;4;6;8} . Tập hợp nào sau đây bằng tập hợp A ∩B ?
Answer:
A∩B ={2;4}
Step-by-step explanation:
Chúc bạn học tốt
Uche is a cartographer. He picks a scale to fit a map of India onto a page of an atlas. The page is 121212 by 121212 inches, with 0.750.750, point, 75 inch margins on all 444 sides. India measures 3{,}2143,2143, comma, 214 kilometers from north to south and 2{,}9332,9332, comma, 933 kilometers from west to east. Uche wants the longest dimension of India to fit exactly in between the margins of the page. If kkk is the number of kilometers per inch in Uche's scale, which equation best models the situation
The scale ratio of a point A to another point B is the division of the length of B by the length of A. The best equation that models the situation is: [tex]10.5k= 3214[/tex]
The page dimension is:
[tex]Length = 12[/tex]
[tex]Width = 12[/tex]
The length and the width of Uche's book are equal; this means the pages of Uche's book have the shape of a square
The margin of 0.75 on either sided means the usable dimension is:
[tex]Length = 12 - 2 * 0.75 =10.5[/tex]
The dimension of India is:
[tex]Length = 3214[/tex]
[tex]Width =2933[/tex]
The longest side in India's dimension is:
[tex]Longest = 3214[/tex]
From Uche's book, the longest dimension is:
[tex]Longest = 10.5[/tex]
So, the scale equation is:
k * longest length of Uche's book = longest side of India
This gives:
[tex]k * 10.5 =3214[/tex]
[tex]10.5k =3214[/tex]
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I need help ASAP please
Answer:
yes how can I help you???
2.
The reflector of a satellite dish is in the shape of a parabola with a diameter of 4 feet and a depth of 2 feet. To get the maximum reception we need to place the antenna at the focus.
a. Write the equation of the parabola of the cross section of the dish, placing the vertex of the parabola at the origin. Convert the equation into standard form, if necessary. What is the defining feature of the equation that tells us it is a parabola?
b. Describe the graph of the parabola. Find the vertex, directrix, and focus.
c. Use the endpoints of the latus rectum to find the focal width.
d. How far above the vertex should the receiving antenna be placed?
Answer:
Step-by-step explanation:
Assume the dish opens upwards. The cross-section through the vertex is a parabola. You know three points on the parabola: (0,0), (2,2), and (-2,2). Plug the points into y = ax² + bx + c to get a system of three equations where a=0.5, b=c=0.
Equation of parabola: y = 0.5x²
:::::
Vertex (0,0)
Focal length = 1/(4×0.5) = 0.5
Focus (0,0+0.5) = (0, 0.5)
Directrix y = 0-0.5 = -0.5
:::::
At endpoints of latus rectum, y = 0.5
x = ±√0.5 = ±√2/2
Focal width = 2×√2/2 = √2
:::::
Place antenna at focus, (9,2)
Which one and what do I put in the box(s)
Answer:
Option A i the right option.
First blank is 110-[tex]10\sqrt{61}[/tex] or 10(11-[tex]\sqrt{61}[/tex])
Second blank is 31.898
Let me know if anything didn't make sense.
Step-by-step explanation:
So a diagonal through a rectangle makes two triangles. The question wants to know how much walking is saved walking down the diagonal vs walking along two sides that make the diagonal. in this case the two non diagonal sides walked are 60 paces and 50 paces.
A diagonal through a rectangle specifically makes a right triangle, so to find the diagonal we can use the pythagorean theorem.
c^2 = 60^2 + 50^2
c = [tex]\sqrt{60^2 + 50^2}[/tex]
c = [tex]\sqrt{6100} = 10\sqrt{61}[/tex]
if you don't get how to simplify a radical like that let me know.
Anyway, looking at the answers you can see right away the second option says no approximation is necessary. Well, you need to approximate square root of 61, so we can say the second answer is not right. So now we need to know what to fill in for option 1.
it wants the distance saved, well we know the distance of the diagonal is [tex]10\sqrt{61}[/tex] Hopefully you can see the disctance walking the two other sides is just adding them up so 50+60=110.
Now, to find the difference, that is subtraction. So subtract the smaller number from the larger number. You do need to remember with a right triangle, the sum of the to non diagonal (hypotenuse) sides are always longer than said hypotenuse. so that's 110-[tex]10\sqrt{61}[/tex]. That is the exact form. Or you could use 10(11-[tex]\sqrt{61}[/tex]) They are the same.
Then just plug that into a calculator for a decimal approximation.
HELP PLS !!! Pls pls pls pls pls pls pls pls pls
Answer:
x=7
Step-by-step explanation:
6x+11=7x+4
Find the number c that satisfies the conclusion of the Mean Value Theorem on the given interval. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.)
f(x)= sqrt of x [0,9]
c =
Answer:
9/4
Step-by-step explanation:
f(x) is continuous and differentiable on (0,9).
We want to find c using the following equation.
f'(c)=(f(9)-f(0))/(9-0)
This will require us to find f'(x) first.
f(x)=sqrt(x) is the same as f(x)=(x)^(1/2)
Using power rule to differentiate this gives f'(x)=(1/2)(x)^(1/2-1) or simplified f'(x)=(1/2)x^(-1/2) or f'(x)=1/(2x^(1/2)).
So we want to solve:
(1/2)c^(-1/2)=(f(9)-f(0))/(9-0)
Simplify denominator on right:
(1/2)c^(-1/2)=(f(9)-f(0))/9
This will require us to find f(9) and f(0).
If f(x)=sqrt(x), then f(9)=sqrt(9)=3 and f(0)=sqrt(0)=0.
So we have the following equation so far:
(1/2)c^(-1/2)=(3-0)/9
Simplify numerator on right:
(1/2)c^(-1/2)=3/9
Multiply both sides by 2:
c^(-1/2)=6/9
Raise both sides to the -2 power:
c^(1)=(6/9)^(-2)
Note c^1=c:
c=(6/9)^(-2):
Note negative exponent means to find reciprocal of base to change exponent to opposite
c=(9/6)^2
Apply the second power:
c=81/36
Reduce by dividing top and bottom by 9:
c=9/4
This means the slope of the tangent to the curve f at x=9/4 is the same value as the slope of the secant line going through points (0,0) and (9,3).
Also 9/4 is between 0 and 9... According to the theorem we were suppose to get a value c between x=0 and x=9.
Confirmation:
Slope of the secant line is (3-0)/(9-0)=3/9=1/3.
Slope of the tangent line to curve f at x=9/4.
f'(x)=(1/2)x^(-1/2)
f'(9/4)=(1/2)(9/4)^(-1/2)
f'(9/4)=(1/2)(3/2)^(-1)
f'(9/4)=(1/2)(2/3)
f'(9/4)=1/3
They are indeed equal values (talking about the 1/3 from the secant and the tangent.)
Which graph corresponds to the following inequality? -2x-3y<6
Answer:
A) It’s the First graph
Step-by-step explanation: hope this helps!
The graph corresponds to the inequality -2x - 3y < 6 is option A.
How to find the value of x?To estimate the value of x and y, bring the variable to the left side and bring all the remaining values to the right side. Simplify the values to estimate the result.
Given: -2x - 3y < 6
then -2x - 3y = 6
Put the value of y = 0, then
[tex]$-2x-3*0=6[/tex]
-2x = 6
x = -6/2 = -3 and
-2x - 3y = 6
Put the value of x = 0, then
[tex]$-2*0-3y=6[/tex]
-3y = 6
y = -6/3 = -2
The value of x = -3 and y = -2.
Therefore, the correct answer is option A.
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The probability of drawing a red candy at random from a bag of 25 candies is 2/5.
After 5 red candies are removed from the bag, what is the probability of randomly drawing a red candy from the bag?
Please include an explanation!
Answer:
1/4
Step-by-step explanation:
Probability of red * number of candies
2/5 * 25 = 10
There are 10 red candies
25-10 = 15
There are 15 other candies
Remove 5 red
10-5 = 5 red candies
Now we have 5 red candies and 15 other candies= 20 candies
P(red) = red/total = 5/20 = 1/4
C 89. What is the power of 5, so that 1 its value become ? (५ को घाताङ्क 25 कति हुदा त्यसको मान 25 हुन्छ ?) .7
C 89. What is the power of 5, so that 1 its value become ?
The power is 0. because if 0 is tge powwe of any variable or letters the value becomes 1.
Given that (-7,3) is on the graph of f(x), find the
corresponding point for the function
f(x) +5.
Enter the correct answer.
OOH
DONE
Clear all
?
Name the indicated geometric figures for the figure shown. Be sure to use correct notation
A Name a point.
B Name a ray through Y.
C Name a line through Z.
D Name a plane.
9514 1404 393
Answer:
see below
Step-by-step explanation:
[tex]\text{A. point: }X\\\\\text{B. ray through Y: }\overrightarrow{XY}\\\\\text{C. line through Z: }\overleftrightarrow{XZ}\\\\\text{D. plane: plane } XYZ[/tex]
__
Additional comment
When you don't have the benefit of typesetting, you can refer to the geometry by name: ray XY, line XZ,
Abigail plans to repaint some classroom bookcases. She has 6/25
gallons of paint. All of the bookcases are the same size and each requires 2/3
gallon of paint. How many bookcases will the custodian be able to repaint with that amount of paint?
Answer:
Step-by-step explanation: Hello! Do
if there are 5 routes to travel between A and B, how many options are there for a person to travel form A to B and retrun back?
Answer:
25
Step-by-step explanation:
8-2 3/4 =
show the work
ANSWER
8-2........3/4 but you have you ADD some people dont know that 8-2= 6
and so 6/1 + 3/4 is 24/4
Restate the number 4,587,902.453.
Expanded form:
Written form:
Answer:
Expanded form: 4,000,000 + 500,000 + 80,000 + 7,000 + 900 + 2 + 0.4 + 0.05 + 0.003
Word form: Four million, five hundred eighty-seven thousand, nine hundred two and four hundred fifty-three thousandths.
a coin is tossed succesively three times times . determine tje probabiliy of getting all three heads
Answer:
Answer : 1/8.
Step-by-step explanation:
Hey there!
Please see the attached picture for your answer.
Hope it helps!
Find the equation of the line that contains the point (4, -2) and is perpendicular to the line y = - 2x + 5.
y = 2x - 10
y = - 2x + 6
y = - 1/2x
y = 1/2x - 4
Answer:
It's option D. y = 1/2x - 4
Step-by-step explanation:
I used Desmos to find the answer, hope the graph helps!
which polygon will NOT tessellate a plane?
Step-by-step explanation:
the answer is regular octagon
i think
