Answer:
3
Step-by-step explanation:
The body temperatures of all mosquitoes in a county have a mean of 57∘F and a standard deviation of 10∘F. What is the probability that in a sample of 25 mosquitoes the mean body temperature is greater than 59∘F, assuming the underlying distribution is normal? Do not write probability in terms of percentage. Round your answer to two decimal places.
Answer:
0.16 probability that in a sample of 25 mosquitoes the mean body temperature is greater than 59∘F, assuming the underlying distribution is normal.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
The body temperatures of all mosquitoes in a county have a mean of 57∘F and a standard deviation of 10∘F.
This means that [tex]\mu = 57, \sigma = 10[/tex]
Sample of 25:
This means that [tex]n = 25, s = \frac{10}{\sqrt{25}} = 2[/tex]
of 25 mosquitoes the mean body temperature is greater than 59∘F, assuming the underlying distribution is normal?
This is 1 subtracted by the pvalue of Z when X = 59. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{59 - 57}{2}[/tex]
[tex]Z = 1[/tex]
[tex]Z = 1[/tex] has a pvalue of 0.84
1 - 0.84 = 0.16
0.16 probability that in a sample of 25 mosquitoes the mean body temperature is greater than 59∘F, assuming the underlying distribution is normal.
what is the VOLUME of this rectangular prism!
Answer:
There`s no photo but I can still help tell you how to solve the volume of a rectangular prism. Just multiply the length by the width, and then that by the height.
The formula is V = lwh
Hope this helps
A water company charges $20 for service and $2.75 for every thousand gallons of water used in month. Construct a linear model to represent the water bill; how much would you be charged if you used 14-thousand gallons of water this month?
Answer:
$58.50
Step-by-step explanation:
2.75 per 1000
2.75 x 14 = 38.5
$38.50 + $20 =$58.50
Mrs Mills buys 4 packs of treats for her cats, Fluff and tigger
she gives Fluff 1/6 of a pack each day
She gives tigger 1/5 of a pack each day
for how many complete days will the 4 packs of treats last
Answer: 10 days
Step-by-step explanation:
1/6 + 1/5 = 5/30 + 6/30 = 11/30 (total for the day)
4 / (11/30) = 10.90909091 (divide the total amount of packages by the daily total)
So 10 complete days.
Find the area of the following
kite:
8 cm
2 cm
2 cm
2 cm
2
A = [?] cm2
Enter
Answer:
Area = 12
Step-by-step explanation:
The perpendicular bisector of the triangle going from upper left to the middle marks the height of the triangle. It's area is found from the standard formula.
Area = b * h / 2
b = 2 + 2 = 4
h = 8
Area = 1/2 * 4 * 8
Area = 1/2 * 32
Area = 16
The smaller triangle is found from all the twos.
b = 2 + 2 same as the larger triangle
h = 2
Area = 1/2 2 * 4
Area = 1/2 8
Area = 4
Total Area = 4 + 16
Total Area = 20
Answer:
Area=20
Step-by-step explanation:
A = 20 cm
Find the value of x to the nearest tenth. PLEASE HELP ANSWER THIS!!!
Answer:
7.8
Step-by-step explanation:
Identify sin cos or tan
In this case you would use tangent/tan
tan(∅) = opposite/adjacent
∅ (theta) = angle
plug in what you know to the tangent equation
tan(52) = 10/x
multiply both sides by x
x tan(52) = 10
divide by tan(52) on both sides
x = 10/tan(52)
enter 10/tan(52) in calculator
get 7.81285626...
nearest tenth = 7.8 units
Hey can you guys please help me understand. I need to find the answer to this question and my teacher explained how to do the assignment HORRIBLY. Please explain to me how you got the answer :)
mmm answer is 139.5 (C)
7x4.5=31.5
12x9=108
108+31.5=139.5
Answer:
A=139.5cm^2
Step-by-step explanation:
12x9=108---->Area of the rectangle A=l x w
9x7=63 divided by 2=31.5--->Area of the triangle A=1/2 (b x h)
108+31.5=139.5cm^2
Hope this helps and can you give me brainliest pls?
20 POINTS PLS HALP!!!
Greenland is the least densely populated country in the world, with a population of 57,714 and
an area
of 836,109 square miles. To the nearest hundredth, what is the population density of
Greenland in people per square mile?
Answer:
number of people / land area = population density
57,714 / 836,109 ≈ 0.07 people/[tex]mi^2[/tex]
Answer:
.07 people per square mile
Step-by-step explanation:
We can just divide the people by area
57714/836109=.06902688525 or about .07 people per square mile
I think you got confused about the division and what to divide by what
Look over here we divide the PEOPLE by the AREA so we get the amount of PEOPLE per square mile
If we did it the opposite way we get THE AREA that EACH PERSON HAS
a cubic base tank has edges 5m long. If 500 000 litres of water is poured into the tank, what will the water level be?
36600 level of water and that is the answer
A.right triangle
B.isosceles triangle
C.obtuse triangle
D.scalene triangle
HELP PLSSS THIS IS DUE BY 2:00 AM I NEED IT ASAPPP
Answer:
B. Isosceles triangleStep-by-step explanation:
It is a vertical section and the figure formed from the cross-section is:
Isosceles triangleCorrect choice is B
simplify 2 x 4x x 2y
Step-by-step explanation:
16xy is your Answer..
hope it helps
Answer:
The answer is 16xy
Step-by-step explanation:
All we have to do is take out the x and the y then multiply.
2 * 4 * 2 = 16
Then we add the x and y back.
= 16xy
So, the answer is 16xy
Hope this helps! :)
9. A plastic pipe 10 cm long has an
outside diameter of 5 cm and an
inside diameter of 4 cm. If the
density of the plastic is 0.92 g/cm3,
what is the mass of the pipe? Use
3.14 for a, and round your answer
to the nearest gram.
The mass of the plastic pipe which is 10 cm long and has an outside diameter of 5 cm and an inside diameter of 4 cm is 65 grams.
What is of volume of a hollow cylinder?Volume of a hollow cylinder is the amount of quantity, which is obtained by it in the 3 dimensional space.
The volume of hollow cylinder can be given as,
[tex]V=\pi (r_2^2-r_1^2)h[/tex]
Here, (r₂) is the outer radius of the cylinder, (r₁) is the inner radius of the cylinder and (h) is the height of the cylinder.
A plastic pipe 10 cm long has an outside diameter of 5 cm and an inside diameter of 4 cm. Radius is half of the diameter. Thus, the outer radius is 2.5 cm (5/2) and the inner radius is 2 cm (4/2).
The volume of this cylinder is,
[tex]V=3.14 ((2.5)^2-2^2)\times10\\V=70.65\rm\; cm^3[/tex]
The mass of plastic pipe is the product of its volume and density. The density of the plastic is 0.92 g/cm3. Thus, the mass of it is,
[tex]m=70.65\times0.92\\m=65\rm\; grams[/tex]
Thus, the mass of the plastic pipe which is 10 cm long and has an outside diameter of 5 cm and an inside diameter of 4 cm is 65 grams.
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2. Choose a mapping diagram of the ordered pairs {(3,17), (5,19), (7,19),
(11,23), (13,29)).
Please help
Answer: C
Step-by-step explanation: The hypothesis of the right triangle is shorter than the right.
The max Fuel capacity a spaceship should have is 500. The minimum is 200. The ship you are designing is rated at 75% of range. How much fuel capacity does it have? If, in the above example, we decide to change the max to 600, what is the new fuel capacity of the ship?
Answer:
Part 1: 375 Fuel Capacity
Part 2: 450 Fuel Capacity
Step-by-step explanation:
Find the percentage of each number with a calculator
375 fuel capacity does it have.
When decide to change the max to 600 new fuel capacity of the ship is 450.
Given that,
The max Fuel capacity a spaceship should have is 500.
The required 375 fuel capacity does it have.
When decide to change the max to 600 new fuel capacity of the ship is 450 determine,
How much fuel capacity does it have? If, in the above example, we decide to change the max to 600, what is the new fuel capacity of the ship.
According to the question,
The max Fuel capacity a spaceship should have is 500.
The ship you are designing is rated at 75% of range.
Full capacity is equals to max fuel capacity multiply by ship designing rate of range.
Therefore,
Fuel capacity = 500 × 0.75 = 375
And If the change in max fuel capacity to 600,
New fuel capacity is equals to new max fuel capacity multiply by ship designing rate of range.
Then.
New fuel capacity = 600 × 0.75 = 450
Hence, The required 375 fuel capacity does it have.
When decide to change the max to 600 new fuel capacity of the ship is 450.
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Question 9 of 10
True or False? A circle could be circumscribed about the quadrilateral below.
Answer:
t
Step-by-step explanation:
A circle can be circumscribed about the given quadrilateral, the answer is: A. True.
We know that,
To circumscribe a circle about a quadrilateral means to place the quadrilateral inside the circle, such that the four vertices of the quadrilateral touches the circumference of the circle.
Opposite angles of a circumscribed polygon are supplementary.
Therefore, a circle can be circumscribed about the given quadrilateral, the answer is: A. True.
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PLS AWNSER ILL GIVE BRAILIEST PLS
Answer:
i think its c
Step-by-step explanation:
help 5 points
pls no wrong answer
Answer:
A (3, 4) B (4, 2) C (0.5, 0.25) D (1, 2.5) E (1.75, 4.25)
Step-by-step explanation:
The coordinate points of a point are (x, y) where x is the number on the x-axis and y is the number on the y-axis.
By looking at points A and B they're easy to tell.
For points C, D, and E they're in between whole numbers so by converting the number given which is a fraction you can get 0.25 from 1/4 which is half of 1/2, 0.5 from 1/2, 0.75 from 3/4 which is half of 1/2 plus 1/2, 1.25 from 1 1/4, etc....
it takes 7/12 foot of ribbon to make a bookmark how many feet of ribbon will it take to make 15 bookmarks
plz answer this question without any links
answer: 8.75ft
Step:
7/12*15
=8.75
Fill in the boxes with values that make the statement true.
Jack bought a case of 12 calculators for $60.00. He sold six for $52.00 each and six for $56.00 each. How much was Jack's profit on
the case of calculators?
A)
524.00
B)
$48.00
560.00
D)
$108.00
Answer: $48.00
Step-by-step explanation:
Jack bought 12 calculators for $60
he sold six for 52 and the other six for 56
52+56=108
108-60=48
Which of the following is a valid use of the associative property of addition?
A. (5+8.5) - 3.5 = 5+ (8.5-3.5)
B. (8.5+5) -3.5=(8.5-3.5)+5
(9,-3) and (9,-4) the slope is what
Answer:
Undefined
Step-by-step explanation:
adadaadadadadadadadad
Answer:
I think B and D
Step-by-step explanation:
I’m not 100% sure tho
Luke is planning to lay two decorative pieces of wood across the 12-inch by 24-inch rectangular glass centerpiece of a cabinet. Each piece will lie on a diagonal of the centerpiece.
Select a number from the drop down menu to correctly complete the statement.
Each piece of wood should have a length of approximately.
Answer:
26.8
I might be late but its never to late to give the right answer
Answer:
yup the answer is 26.8
Step-by-step explanation:
i made a 100 so trust me!
name this angle
X Х
4
Y
N
Answer:
no I have no answer
Step-by-step explanation:
noooooooooooooo
Which of the following is a trigonometric identity?
cot 0 + tan 0 = 1
sec2 0 +csc2 0 = 1
tan2 0 = sin2 0 x sec2 0
cos2 = sec2 0 x tank 0
Answer:
it's the first one... I think
Answer:
third one
I'm assuming does 2's are squared symbols.
Step-by-step explanation:
It's the third one because
sin^2 x sec^2 x
sin^2 x (1/cos^2 x) by reciprocal identity
sin^2 x/cos^2 x by multiplicative identity prop
tan^2 x by quotient identity
The first one wouldn't work because plugging in pi/4 gives 1+1=1 which isn't true.
The second one doesn't work because plugging in pi/4 gives 2+2=1 which isn't true.
The last equation doesn't make sense at all. There is no variable on the left and on the right there is an extra variable.
For the following situations decide what type of chi square test is appropriate. Explain.
A random sample of 200 students was asked to sample a new type of pizza that the school was considering using as a replacement for the current pizza. Each student stated if they were a freshman, sophomore, junior, or senior and also if they liked the new pizza more than the current pizza (or not). The school would like to know if there is a relationship between grade level and pizza opinion.
Answer:
Following are the responses to the given question:
Step-by-step explanation:
In the given scenario, the Chi-square test is independent, which could be used because they would know whether it has any association among the several types of children like an old or new pizza. It does not associate discrete or factors that motivate with continuous data. In addition, only correlations among categorical data are evaluated inside the Chi-Square Independence Test, but causative inferential statistics cannot be given.
The type of chi square test that is appropriate for the following situation is Chi square test of independence.
What is chi square test of independence?Within the same population, the Chi-square test for independence looks for an association between two categorical variables.
The school would like to know if there is a relationship between grade level and pizza opinion.
Two variables' relationship is to be known.
That is why, we will use chi square test of independence.
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Which of the expressions shown has a GCF of 5ab^2 with 15ab^3?
A. 30ab^2
B.30a^2b^5
C. 25ab^2
D. 5ab^2
Answer:
The greatest common factor of 5ab^2 and 15ab^3 is 5ab^2
The greatest common factor between the two expressions will be 5ab²
What is the greatest common factor?
The greatest common factor is the largest positive number which can be divided into given numbers evenly.
Here the two numbers are:-
5ab² and 15ab³ or 5ab² and 5ab² x b
So we can see that the highest common factor between the two numbers will be 5ab².
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Part A. Describe a relationship modeled by the function f(x) = 4x³ - 72x² + 320x, and explain how the function models the relationship.
Part B. Identify and interpret the key features of the function in the context of the situation described in part A.
Answer:A relationship modeled by the function f(x) = 4x³ - 72x² + 320x is the volume of a right prism whose dimensions are 4 times a desired length, 10 units less that such desired length, and 8 units less than the same desired length.
Explanation:
To find a relationship modeled by the given function it is recommendable to factor it.
The function is: f(x)=4x3- 72 x2+320x
The first step to factor it is to extract common factor 4x: f (x)=4x(x2-18=80)
The second step is to factor the quadratic trinomial.
That is made by writing it as a product of two binomials, for which the two constant terms add up - 18 and their product is 80. Those terms are -10 and - 8; so the two factors are (x - 10) and (x - 8), and the factored form is: f(x)=(4x)(x-10)(x-8)
Then, a relationship modeled by that polynomial is the volume of right prism whose dimensions are 4 times a desired length, 10 units less that such desired length, and 8 units less than the same desired length.
x is the desired (unknown) length
4x is 4 times the desired length
x - 10 is 10 less than the desired length
x - 8 is 8 less than the desired length
Thus, the volume of the prism is the product of the three factors:
Volume = (4x)(x-10)(x-8)
solve this problem step by step.
2x^3+17x^2+30x