American adults are watching significantly less television than they did in previous decades. In 2016, Nielson reported that American adults are watching an average of five hours and twenty minutes, or 320 minutes, of television per day. 1. Find the probability that an average American adult watches more than 309 minutes of television per day. Answer in three decimal places. 2. Find the probability that an average American adult watches more than 2,250 minutes of television per week. Answer in three decimal places.
Answers
Answer:
1. 0.271 = 27.1% probability that an average American adult watches more than 309 minutes of television per day.
2. 0.417 = 41.7% probability that an average American adult watches more than 2,250 minutes of television per week.
Step-by-step explanation:
To solve this question, we need to understand the Poisson distribution and the normal distribution.
Poisson distribution:
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
\(P(X = x) = \frac{e^{-\lambda}*\lambda^{x}}{(x)!}\)
In which
x is the number of sucesses
e = 2.71828 is the Euler number
\(\lambda\) is the mean in the given interval, which is the same as the variance.
Normal distribution:
When the distribution is normal, we use the z-score formula.
In a set with mean \(\mu\) and standard deviation \(\sigma\), the zscore of a measure X is given by:
\(Z = \frac{X - \mu}{\sigma}\)
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 pvalue, we get the probability that the value of the measure is greater than X.
The Poisson distribution can be approximated to the normal with \(\mu = \lambda, \sigma = \sqrt{\lambda}\)
In 2016, Nielson reported that American adults are watching an average of five hours and twenty minutes, or 320 minutes, of television per day.
This means that \(\lambda = 320n\), in which n is the number of days.
1. Find the probability that an average American adult watches more than 309 minutes of television per day.
One day, so \(\mu = 320, \sigma = \sqrt{320} = 17.89\)
This probability is 1 subtracted by the pvalue of Z when X = 309. So
\(Z = \frac{X - \mu}{\sigma}\)
\(Z = \frac{309 - 320}{17.89}\)
\(Z = 0.61\)
\(Z = 0.61\) has a pvalue of 0.729
1 - 0.729 = 0.271
0.271 = 27.1% probability that an average American adult watches more than 309 minutes of television per day.
2. Find the probability that an average American adult watches more than 2,250 minutes of television per week.
\(\mu = 320*7 = 2240, \sigma = \sqrt{2240} = 47.33\)
This is 1 subtracted by the pvalue of Z when X = 2250. So
\(Z = \frac{X - \mu}{\sigma}\)
\(Z = \frac{2250 - 2240}{47.33}\)
\(Z = 0.21\)
\(Z = 0.21\) has a pvalue of 0.583
1 - 0.583 = 0.417
0.417 = 41.7% probability that an average American adult watches more than 2,250 minutes of television per week.
Related Questions
PLEASE HELP EMIDIETLY! ON TIMER!
When asked to find the distance between the complex points 3 + 8i and 7 + 6i, Zach showed the work below.
He asked his friend Zöe to find his mistake, and she correctly told him that he should have
A:subtracted the real and imaginary portions of the point in the same order.
B:left the i out of the computations when finding distance in the complex plane.
C:remembered that –4 squared should be –16, not 16.
D:simplified root12 to 3root2, not to 2root3.
Answers
Answer:
B
Step-by-step explanation:
Its B because you aren't supposed to include the imaginary numbers in the distance formula aanndd I'm taking the test rn and I think its the answer
edge 2021
Zach should be left i out of the computations when finding distance in the complex plane. Option B is correct.
Given zach has evaluated the distance between two complex numbers 3 + 8i and 7 + 6i. He asked his friend Zöe to find his mistake
The number that constitutes real and imaginary numbers are called complex numbers. example a + bi. where a is the real number and b is the imaginary number.
In zach calculation,
\(=\sqrt{(3-7)^2+(8i-6i)^2}\)
There is mistake in his first step that when computing the distance between two points we do not consider i in the distance formula. because its an imaginary number.
Correct implementation of the distance formula is given as,
= \(=\sqrt{(3-7)^2+(8-6)^2}\)
Thus, Zach should be left i out of the computations when finding distance in the complex plane. Option B is correct.
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Derek has 4 shirts, 7 pairs of pants, and 3 blazers. How many possible outfits can he make?
Answers
Mr Ryan made an agreement with his son Smith who is in grade 12 as follows. Smith will get pocket money after he finishes all his homework every day. The amount of the picket money will be double the amount previous day. He will start first day with R1. He can use this saving for his matric dance.
Write the information as a sequence
Answers
The exponential function that models how much Smith gets after each day is given by:
\(A[n] = R1(2)^n\)
What is an exponential function?It is modeled by:
\(y = ab^x\)
In which:
a is the initial value.b is the rate of change.In this problem:
He will start first day with R1, hence a = R1.The amount of the picket money will be double the amount previous day, hence b = 2.Thus, the equation as a sequence is represented by:
\(A[n] = R1(2)^n\)
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I need help solving these
Answers
Answer:
m∠1 = 140°
m∠2 = 40°
m∠3 = 65°
m∠4 = 75°
m∠5 = 115°
Step-by-step explanation:
We will use a few different methods to find the angles:
A triangle's angles will always add up to 180°. With this information, we can find the last angle of the triangle on the left:
∠1+∠2+∠3=180°
60+80+∠3=180°
Let x represent the value of ∠3. Simplify addition:
\(140+x=180\)
Subtract 140 from both sides:
\(140-140+x=180-140\\\\x=40\)
The unknown angle is 40°. With this information, we can find the
m∠1:
m∠1 and the 40° we just found are supplementary angles, which means that their measures will add up to a total of 180°.
∠1+∠2=180°
Insert the value we know:
40°+∠2=180
Let x represent the value of ∠2. Subtract 40 from both sides:
\(40-40+x=180-40\\\\x=140\)
There fore:
m∠1=140°
We can use this same rule to find the m∠2:
∠1+∠2=180°
or, we can use the vertical angles rule. The first angle we found (Which is 40°) is a vertical angle to m∠2, so they have the same value. Therefore:
m∠2=40°
To find m∠3, we need to find the other missing angle in the middle triangle. Use the supplementary angle rule, since the missing angle is supplementary to the angle that is 105°:
∠1+∠2=180°
Insert the known values, substituting x for the unknown angle:
\(x+105=180\)
Subtract 105 from both sides:
\(x+105-105=180-105\\\\x=75\)
The unknown angle is 75°. Now find m∠3, knowing that triangles add up to 180°:
m∠2+m∠3+75=180
Insert the m∠2, make m∠3 be x:
\(40+x+75=180\)
Simplify addition:
\(115+x=180\)
Subtract 115 from both sides:
\(115-115+x=180-115\\\\x=65\)
Therefore:
m∠3=65°
To find m∠4, use the vertical angle rule.
Therefore:
m∠4=75°
To find m∠5, we could find all triangle measures of the least triangle, or we can use the following:
An exterior angle of a triangle is equal to the sum of the two opposite interior angles. The sum of exterior angle and interior angle is equal to 180 degrees.
The m∠5 is the exterior angle, and the opposite interior angles are 75° and 40°:
\(75+40=115\)
Therefore:
m∠5=115°
:Done
solve the following 7x + 3 = 24 x=?
Answers
We have to solve the equation for x. The equation is:
\(7x+3=24\)Let's subtract "3" from both sides to get:
\(\begin{gathered} 7x+3=24 \\ \text{ -3 = -3} \\ ------- \\ 7x=21 \end{gathered}\)To isolate and solve for x, we divide both sides by 7, shown below:
\(\begin{gathered} 7x=21 \\ \frac{7x}{7}=\frac{21}{7} \\ x=3 \end{gathered}\)The correct answer is x = 3
This is due soon today can somebody help?
35 points (if they're all right) comment if you don't know it
Answers
Answer:
1) P(1,0)Q(-2,3)R(-3,3)S(3,2)
2) (3,4)
3) (0,-4)
4) (1,2)
Step-by-step explanation:
diameter of a circle is 21 cm. Find its area to the nearest whole number.\
Answers
Answer:346.5
Step-by-step explanation: At first,we have calculate the radius of the given circle,by using the following mathematical formula.
Radius = Diameter/2 = 21/2 = 10.5 cm
Now,we have to calculate the area of the circle by using the following mathematical formula,
Area of the circle = π×r² = 22/7 × 10.5 × 10.5 = 346.5 cm²
please lmk if this an option or answer for you.
It costs $3.45 to buy 4/5 lbs of chopped walnuts. How much would it cost to purchase 7.5 lbs of walnuts?
Answers
He buys atoy car for 150 the sells it for $120find his percentage loss
Answers
Answer: 80%
Step-by-step explanation:
divide 120 by 150 and you get .8 then you move the decimal over 2
Alondra is asked about her age. She answers as follows. "My age is 6 more than four times the age of my son." How old is her son if Alondra is 46 years old?
Answers
Answer:
10 years old
Step-by-step explanation:
lets break it down:
6 more means +6
four times means *4
so if her son is x years old, she is 4x+6
since we know she's 46, we know that 4x+6=46
now we just solve the equation
4x+6=46
-6 on both sides
4x=40
/4 on both sides
x=10
Convert 8.5 ounces of soda to mL. 1L= 33.8 oz
Answers
Explanation 8.5 • 33.8
Andrew wants to dilate a triangle. If the original triangle has a base of 15 units and an area of 60 square units, what will be the area of the new triangle if the new base is 75?
Answers
Answer:
300
Step-by-step explanation:
For every 1 of the base, there's 4 of the area.
What is the combined probability of getting a heads when flipping a coin and
an odd number when spinning a spinner with 4 equal parts numbered 1 to 4?
OA)
B)
ANNI -
o
100
Answers
Answer:
25%
Step-by-step explanation:
50% x 50%
Answer:
A. 1/5
Step-by-step explanation:
got on edge
Solve this inequality:
-12a +7<31
Answers
Answer:
a > -2
Step-by-step explanation:
-12a +7<31
Subtract 7 from each side
-12a +7-7<31-7
-12a <24
Divide by -12, remembering to flip the inequality
-12a/-12 >24/-12
a > -2
Answer:
a>-2
Step-by-step explanation:
\(\sf{}\)
=> -12a +7 <31
=> -12a+7-7<31-7
=> -12a<24
=> a>-2
in which town does the total number have meaning
Answers
The curve y = x2 is given. Which of the following describes a method for finding the instantaneous slope at P?
Answers
Answer:
The value of the limit as A approaches 1 of the slope of line AP gives the instantaneous slope at P.
Step-by-step explanation:
**sorry if these explanations don’t make sense. I’m just doing them so my answer doesn’t get flagged and removed for violating whatever policy or honor code there is. But I tried my best with these explanations**
The first answer choice “Δy/Δx of line AP gives the instantaneous slope at P” is incorrect as this just gives you the regular slope, which is different from instantaneous slope. Instantaneous slope needs to be close the point stated in the question
The answer choice “the value of the limit as P approaches A of the slope of line AP gives the instantaneous slope at P” is wrong because it reverses the letters so it’s as if the question were asking for the instantaneous slope at A. But since it’s asking about P you want A to get closer to P.
The answer choice “the value of y at P gives the instantaneous slope at P” is also wrong because you don’t use the y-value in the instantaneous slope formula.
center =
3. A diameter of a circle has endpoints P(-7,-4) and Q (3,2).
a. Find the center of the circle (hint use midpoint formula)
b. Find the radius. If your answer is not and integer, express in radical form. (hint use
distance formula)
c. Write an equation for the circle.
17
radius=
equation of the circle:
work:
< 2/3
I
>
Answers
a. The center of the circle is (-2, -1).
b. The radius of the circle is √136.
c. The equation of the circle is (x + 2)^2 + (y + 1)^2 = 136.
a. To find the center of the circle, we can use the midpoint formula, which states that the midpoint of a line segment with endpoints (x1, y1) and (x2, y2) is given by:
Midpoint = ((x1 + x2)/2, (y1 + y2)/2)
In this case, the endpoints of the diameter are P(-7, -4) and Q(3, 2).Applying the midpoint formula:
Midpoint = ((-7 + 3)/2, (-4 + 2)/2)
= (-4/2, -2/2)
= (-2, -1)
Therefore, the center of the circle is at the coordinates (-2, -1).
b. To find the radius of the circle, we can use the distance formula, which calculates the distance between two points (x1, y1) and (x2, y2). The radius of the circle is half the length of the diameter, which is the distance between points P and Q.
Distance = √\([(x2 - x1)^2 + (y2 - y1)^2]\)
Using the distance formula:
Distance = √[(3 - (-7))^2 + (2 - (-4))^2]
= √\([(3 + 7)^2 + (2 + 4)^2]\)
= √\([10^2 + 6^2\)]
= √[100 + 36]
= √136
Therefore, the radius of the circle is √136.
c. The equation for a circle with center (h, k) and radius r is given by:
\((x - h)^2 + (y - k)^2 = r^2\)
In this case, the center of the circle is (-2, -1), and the radius is √136. Substituting these values into the equation:
\((x - (-2))^2 + (y - (-1))^2\) = (√\(136)^2\)
\((x + 2)^2 + (y + 1)^2 = 136\)
Therefore, the equation of the circle is (x + 2)^2 + (y + 1)^2 = 136.
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what is (1/2 + isqrt3/2)^5?
Answers
Answer:
\((\frac{1}{2}+\frac{\sqrt{3}}{2}i)^5=\frac{1}{2}-\frac{\sqrt{3}}{2}i\)
Step-by-step explanation:
Convert 1/2 + i√3/2 to rectangular form
\(\displaystyle z=a+bi=\frac{1}{2}+\frac{\sqrt{3}}{2}i\\\\r=\sqrt{a^2+b^2}=\sqrt{\biggr(\frac{1}{2}\biggr)^2+\biggr(\frac{\sqrt{3}}{2}\biggr)^2}=\sqrt{\frac{1}{4}+\frac{3}{4}}=\sqrt{1}=1\\\\\theta=\tan^{-1}\biggr(\frac{b}{a}\biggr)=\tan^{-1}\biggr(\frac{\frac{\sqrt{3}}{2}}{\frac{1}{2}}\biggr)=\tan^{-1}(\sqrt{3})=\frac{\pi}{3}\\\\z=\cos\frac{\pi}{3}+i\sin\frac{\pi}{3}\)
Use DeMoivre's Theorem
\(\displaystyle z^n=r^n(\cos(n\theta)+i\sin(n\theta))\\\\z^5=1^5\biggr(\cos\biggr(\frac{5\pi}{3}\biggr)+i\sin\biggr(\frac{5\pi}{3}\biggr)\biggr)\\\\z^5=\frac{1}{2}-\frac{\sqrt{3}}{2}i\)
The water level as a river recedes after a flood is measured at regular intervals, and its height relative to normal, in inches, follows the sequence below. If the sequence continues, what do you expect the 7th measurement to be? 16, 9, 2, –5, ...,
Answers
Answer:
7th measurement = -26
Step-by-step explanation:
The sequence is 16, 9, 2, –5, ...,
First term( a)= 16
Second term=9
Common difference (d) = 9-16
Common difference= -7
The sequence is a arithmetic progression
For AP's ,the terms formula is
Term(n) = a + (n-1)d
Where n represent the term to be found
In this case,we Are looking for the 7th term , so n= 7
Term(7) = 16+ (7-1)-7
Term(7)= 16 +6(-7).
Term (7) = 16-42
Term(7) = -26
7th term =-26
6x + 45 is less than or equal to 240
Answers
Answer: neither
Step-by-step explanation:
To get rid of the fractions, we pick a useful number and multiply both sides of the equation by that number. The number is useful if multiplying eliminates all fractions.
pls help me this is due tonight by 8 40
Answers
Answer:
a. gh³
b. xy³
Step-by-step explanation:
a. \(g^{3-2}\)\(h^{5-2}\) = gh³
b. \(x^{3-2} y^{4-1} p^{1-1}\) = xy³
Use the negative exponent rule.
CAN YOU HELP ME PLEASEEEE ITS GEOMETRY!!!!! THANK YOUUU
Answers
In the diagram below, FC = 10.9,
DE = 17.5, and DF = 13.1. Find the
length of EB. Round your answer to the
nearest tenth if necessary.
D
F
E
C
B
Answers
The length of EB is approximately 14.6 units when rounded to the nearest tenth.
To find the length of EB, we can use the property of similar triangles in this diagram. By looking at triangle DFE and triangle CFB, we can see that they are similar triangles.
Using the similarity ratio, we can set up the proportion:
DF / CF = DE / EB
Plugging in the given values, we have:
13.1 / 10.9 = 17.5 / EB
To find EB, we can cross-multiply and solve for EB:
13.1 * EB = 10.9 * 17.5
EB = (10.9 * 17.5) / 13.1
EB ≈ 14.6
Therefore, the length of EB is approximately 14.6 units when rounded to the nearest tenth.
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Find the volume of rectangular prism. (You should have at least 2 steps shows in your work!)(show all decimal places or a fraction)
Answers
The volume of this rectangular prism include the following: 84.375 cubic meters.
How to calculate the volume of a rectangular prism?In Mathematics and Geometry, the volume of a rectangular prism can be calculated by using the following formula:
Volume of a rectangular prism = L × W × H
Where:
L represents the length of a rectangular prism.W represents the width of a rectangular prism.H represents the height of a rectangular prism.By substituting the given dimensions (parameters) into the formula for the volume of a rectangular prism, we have the following;
Volume of rectangular prism = 5 × 4 1/2 × 3 3/4
Volume of rectangular prism = 5 × 4.5 × 3.75
Volume of rectangular prism = 84.375 cubic meters.
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The ratio of boys to girls in a class is 5 to 7. If there are 35 girls, how many
boys are there?
Answers
Answer:
25, you have to set up a ratio between 5 to 7 and 35.
Step-by-step explanation:
What is the equivalent radian measure of 600?
Answers
Answer:
\( = \frac{ \theta}{180} \times \pi \\ = \frac{600}{180} \times \pi \\ = \frac{10}{3} \pi\)
PLZ HELP want to know if its right
Answers
Answer:
60° is answer.it is right.thank you
|-13| = ?
A. 0
B. -13
C. 13
D. 26
Answers
Answer: C. 13
Step-by-step explanation:
The absolute value of anything will always be positive because absolute value means distance. Distance is never negative always positive.
There are 8 ounces in a cup, 2 cups in a pint, 2 pints in a quart, and 4 quarts in a gallon.
1 L ≈ 0.26 gallons
6 kL ≈ fl oz
Answers
6 kiloliters are approximately equal to 202,884.14 fluid ounces.
We have,
To convert 6 kiloliters (kL) to fluid ounces (fl oz), we need to use the conversion factor between these two units.
The conversion factor states that 1 kiloliter is equal to 33814.0227 fluid ounces.
This means that for every kiloliter, there are 33814.0227 fluid ounces.
To convert 6 kiloliters to fluid ounces, we multiply the given value (6 kL) by the conversion factor (33814.0227 fl oz/kL).
= 6 kL x 33814.0227 fl oz/kL
= 202884.1362 fl oz
Therefore,
6 kiloliters are approximately equal to 202,884.14 fluid ounces.
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A company that usually sells satellite TV equipment for $74 and two year subscription of satellite TV service for 666 has a special offer that is sells the equipment for 420 and two years of service free. If the company sells one of these packages how much revenue should the company recognize on July 1
Answers
The revenue the company should recognize on July 1 is $420.
What is the Revenue recognition theorem?Revenue recognition refers to the accounting principle that outlines the conditions under which a company recognizes revenue on its financial statements. Generally, revenue is recognized when the goods or services are delivered to the customer and the payment is reasonably assured.
To determine the revenue the company should recognize on July 1, we need to understand the revenue recognition principles.
In this case, the company is offering a special package that includes satellite TV equipment for $420 and two years of service free.
The company will deliver the equipment to the customer and the customer will receive two years of service for free.
Since the two years of service are free, the company cannot recognize revenue for that portion of the package.
Therefore, the revenue the company should recognize on July 1 is only for the equipment, which is sold for $420.
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