Answer:
an = 4/3n - 13/3.
Step-by-step explanation:
The first term is a1,
a24 = a1 + 23d
83/3 = a1 + 4/3* 23
a1 = 83/3 - 92/3
a1 = -9/3 = -3.
So the nth term an = -3 + 4/3(n - 1)
an = -3 + 4/3 n - 4/3
an = 4/3n - 13/3
To find the explicit formula for the general nth term of an arithmetic sequence, use the formula a_n = a_1 + (n - 1)d, where a_n represents the nth term, a_1 is the first term, and d is the common difference. In this case, the explicit formula is a_n = -3 + (n - 1)(4/3), based on given information a_24 = 83/3 and d = 4/3.
Explanation:To find the explicit formula for the general nth term of an arithmetic sequence, we use the formula: a_n = a_1 + (n - 1)d, where a_n represents the nth term, a_1 is the first term, and d is the common difference. In this case, we are given that a_24 = 83/3 and d = 4/3. We can substitute these values into the formula and solve for a_1. From there, we can simplify the formula and express it in its lowest terms.
Given: a_24 = 83/3 and d = 4/3
We can rearrange the formula and solve for a_1 as follows:
Now that we have found a_1 = -3, we can simplify the formula and express it as:
a_n = -3 + (n - 1)(4/3)
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[tex]f(x)=\frac{x+9}{4} \\g(x)=4x-9[/tex]
Show your work to prove that the inverse of f(x) is g(x)
Answer:
inverse of f(x) is g(x)
Step-by-step explanation:
f(x) = (x+9)/4
g(x) = 4x-9
f^-1(x) = g(x)
Let y = (x+9)/4
4y = x + 9 (make x the subject)
x = 4y - 9
f^-1(x) = 4x - 9
= g(x) (shown)
Answer:
Below.
Step-by-step explanation:
If f(x) is the inverse then f(g(x)) = x.
f(g(x)) = ((4x - 9) + 9) / 4
= 4x/4
= x.
So it is true.
It can also be shown that g(f(x)) = x.
Within the United States, approximately 11.25% of the population is left-handed. Of the males, 12.6% are left-handed, compared to only 9.9% of the females. If a person is selected at random, what is the probability that the selected person is a female, given the person is right-handed?
Answer: Our required probability is 45.05%.
Step-by-step explanation:
Since we have given that
Males Females total
Left handed 6.3 4.95 11.25%
Right handed 43.7 45.05 88.75%
Total 50% 50% 100%
Since 12.6% of 50% are males are left handed = 6.3%
So, 9.9% of 50% are females are left handed = 4.95%
So, Females who are right handed would be
[tex]50\%-4.95\%\\\\=45.05\%[/tex]
Hence, our required probability is 45.05%.
To calculate the probability that the selected person is a female, given the person is right-handed, we need to use conditional probability. The exact probability cannot be calculated without the percentage of females in the population. However, it is known that the probability is less than or equal to 11.25%.
Explanation:To find the probability that the selected person is a female, given that the person is right-handed, we need to use conditional probability. Let's denote the events A and B as follows: A: Selected person is a female, B: Selected person is right-handed.
The probability of event A (P(A)) can be calculated as the product of the probability of event B given event A (P(B|A)) and the probability of event A without any condition (P(A)) divided by the probability of event B (P(B)).
In this case, P(A) refers to the probability of selecting a female, P(B|A) refers to the probability of being right-handed given the person is female, and P(B) refers to the probability of being right-handed.
First, let's calculate the probability of being right-handed (P(B)). Since 90% of people are right-handed, P(B) = 0.9.
Next, let's calculate the probability of being right-handed given the person is female (P(B|A)). Since 9.9% of females are left-handed, the probability of being right-handed is 1 - 0.099 = 0.901.
Finally, let's calculate the probability of selecting a female (P(A)). Since the percentage of females in the population is not provided, we cannot calculate the exact probability. We can only say that it is less than or equal to the total percentage of left-handed people, which is 11.25%.
Therefore, the probability that the selected person is a female, given that the person is right-handed, can be defined as: P(A|B) = (P(B|A) * P(A)) / P(B) = (0.901 * P(A)) / 0.9 = 0.901 * P(A).
Since we don't have the exact value of P(A), we cannot calculate the exact probability. However, we know that it is less than or equal to 11.25%.
Nelson grows tomatoes and sells them at a nearby farmers roadside stand. He sells them for $2.50 each. The farmer charges him $15 a day to use the stand. Write a linear function in factored form and general form that represents the amount of money, m, Nelson will make from selling x tomatoes.
Answer:
Step-by-step explanation:
Nelson grows tomatoes and sells them at a nearby farmers roadside stand.
Let x = number of tomatoes sold
Let m = amount of money made for selling x tomatoes.
He sells them for $2.50 each. This means that he sells x tomatoes for 2.5×x = $2.5x
The farmer charges him $15 a day to use the stand. This means that he pays a constant amount of $15 each day.
Amount of money that Nelson will make will be total amount made in selling x tomatoes minus the constant amount being paid for rent. It becomes
m = 2.5x - 15 This is the general form. In the factored form, it will be
m = 2.5(x+6)
A sporting goods store manager was selling a ski set for a certain price. The manager offered the markdowns shown, making the one-day sale price of the ski set $325. Find the original selling price of the ski set.
Final answer:
To find the original selling price of the ski set, work backward from the sale price by adding the markdowns back to it. Start by assigning a variable to represent the original selling price and use the given markdown amounts to calculate the original price. The original selling price of the ski set is $387.50.
Explanation:
A sporting goods store manager was selling a ski set for a certain price. The manager offered markdowns, making the one-day sale price of the ski set $325. To find the original selling price of the ski set, we will work backwards from the sale price by adding the markdowns back to it.
Step-by-step process:
Let x be the original selling price.
Given markdowns, if the sale price after markdowns is $325, then x - $30 - $20 - $12.50 = $325.
Solving for x, we get x = $387.50.
--------------------------------------------------------------
Answer: m<YSH = 35°
m<YIH = 20°
m<SAI = 71°
m<PAY = 8°
PY = i don' t know
and P.S these answers may all be wrong sorry but hope it helps. :)
Answer:
Step-by-step explanation:
find the domain od the given function.
f(x)= [tex]\frac{x}{x-3}[/tex]
a.) all real numbers
b.) (-∞,3)∪(3,∞)
c.) (0,∞)
d.) (-∞,-3)∪(-3,∞)
Answer:
B
Step-by-step explanation:
There is a vertical asymptote at x=3. It is not defined and therefore not included in the domain.
All other numbers are included in the domain.
Please help!!
Evaluate:
1. 5x(x-2)-2x^2 for x=-2
2. 2x^2-5x+8 for x=3
Answer:
Step-by-step explanation:
1) 5x(x-2)-2x^2 for x =2
= 5(-2)(-2-2) -2(2)^2
= -10(-4) -2(4)
= 40 - 8
= 36
2) 2x^2 - 5 + 8 for x = 3
= 2(3)^2 - 5(3) + 8
= 2(9) - 15 + 8
= 18 - 15 + 8
= 3 + 8
= 11
Answer:
1. 32.
2. 11.
Step-by-step explanation:
1. 5x(x-2)-2x^2 for x=-2:
= 5(-2)( -2-2)-2(-2)^2
= -10*-4 - 2*4
= 40-8
= 32.
2. 2x^2-5x+8 for x=3:
= 2(3)^2 -5(3)+8
= 18 - 15 + 8
= 11.
A professional baseball player signs a contract with a beginning salary of $3,000,000 for the first year and an annual increase of 4% per year beginning in the second year. That is, beginning in year 2, the athlete's salary will be 1.04 times what it was in the previous year. What is the athlete's salary for year 7 of the contract? Round to the nearest dollar.
To find the athlete's salary for year 7 of the contract, apply a 4% annual increase to the previous year's salary starting from year 2. The athlete's salary for year 7 is approximately $3,836,192.
Explanation:To find the athlete's salary for year 7 of the contract, we need to calculate the annual increase for each year from year 2 to year 7 and apply it to the starting salary of $3,000,000 for year 1.
In year 2, the salary is 1.04 times the previous year's salary, so the salary for year 2 is $3,000,000 * 1.04 = $3,120,000.
In year 3, the salary is 1.04 times the previous year's salary, so the salary for year 3 is $3,120,000 * 1.04 = $3,244,800.
Following the same pattern, we can calculate the salaries for years 4, 5, 6, and 7:
In year 4: $3,244,800 * 1.04 = $3,379,392
In year 5: $3,379,392 * 1.04 = $3,523,027.68
In year 6: $3,523,027.68 * 1.04 = $3,675,348.11
In year 7: $3,675,348.11 * 1.04 = $3,836,191.72
Therefore, the athlete's salary for year 7 of the contract is approximately $3,836,192.
The athlete's salary for year 7 of the contract is $3,822,736.
To calculate the athlete's salary for year 7, we use the formula for compound interest, which is also applicable to salaries that increase annually at a fixed percentage. The formula is:
[tex]\[ A = P(1 + r)^n \][/tex]
Given that the initial salary (principal amount P is $3,000,000 and the annual increase rate r is 4% (or 0.04 as a decimal), we can calculate the salary for year 7 as follows:
[tex]\[ A = 3,000,000(1 + 0.04)^{7-1} \] \[ A = 3,000,000(1.04)^6 \] \\[ A = 3,000,000 \times 1.26530612 ](after calculating ( 1.04^6 \)) \\\\[A = 3,822,736 \][/tex]
(after rounding to the nearest dollar)
Therefore, the athlete's salary for year 7 of the contract, rounded to the nearest dollar, is $3,822,736.
Awesome autos car detail charges $30 for a full service detail on SUVs. The equation 30x+45y=450 represents the amount that must be earned each hour to cover expenses, where x represents cars and y represents SUVs. Determine the x and y intercepts of this equation and state what each one means in terms of business
Answer:
x intercept = 15 # of cars to detail if no SUVs
y intercept = 10 # of SUVs to detail if no cars
Hope this helps!
The x-intercept and the y-intercept for the equation 30x + 45y = 450 are 15 and 10 respectively, The x-intercept denotes the number of cars if there is no SUV serviced and the y-intercept represents the number of SUVs if there is no car.
What is the equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Given:
Awesome autos car detail charges $30 for a full-service detail on SUVs,
The equation 30x + 45y = 450 represents the amount that must be earned each hour to cover expenses,
From this equation, we can determine that the autos car detail charges $45 for a full-service detail on car,
Find the x-intercept as shown below,
30x + 45 × 0 = 450 (For x-intercept y = 0)
30x = 450
x = 450 / 30
x = 15
Find the y-intercept as shown below
30 × 0 + 45y = 450 (For y-intercept x = 0)
45y = 450
y = 10
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Suppose the number of leaves z on a tree varies directly with the height of the tree y in yards and directly with the cube of the hours x of direct sunlight that the tree receives. If a tree that is 7 yards tall and receives 6 hours of direct sunlight has 6048 leaves on it, then how many leaves will be on a tree that is 2 yards tall but receives 11 hours of sunlight?
Answer:
The number of leaves are 10648
Step-by-step explanation:
By the given information,
number of leaves be= z
height of tree= y
hours of sunlight= x
by the given conditions,
[tex]z = (k)(y)(x^{3})[/tex]
,where k is portionality constant.
now, z=6048, y=7 and x=6,
evaluating value of k using above conditions,
k=4
thus, using this value of k,
[tex]z=(4)(2)(11^{3})[/tex]
z= 10648.
The number of leaves on a tree of 2 yards tall receiving 11 hours of sunlight is predicted to be approximately 8712 based on the given relation.
Explanation:The number of leaves z on a tree varies directly with the height of the tree y in yards and directly with the cube of the hours x of direct sunlight that the tree receives. Let's represent this relationship as z = kyx³ , where k is a constant of proportionality.
From the information provided, we know that a tree that is 7 yards tall and receives 6 hours of direct sunlight has 6048 leaves. Therefore, we can substitute these values into the equation and solve for k. Thus, if we replace z = 6048, y = 7, and x = 6, we find that k is approximately equal to 3.
With k approximately equal to 3, we can then predict the number of leaves on a tree that is 2 yards tall and receives 11 hours of sunlight. If we replace k = 3, y = 2, and x = 11 into our equation, we find that the predicted number of leaves is approximately 8712.
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A company declares a 5% stock dividend. The debit to retained earnings is an amount equal to
Answer:
A company declares a 5% stock dividend.
The debit to retained earnings is an amount equal to - the market value of the shares, that are to be issued.
We can say that a retained earnings balance is increased when we are using a credit and this is decreased when we make a debit.
A retained earnings is the total amount of money left, after all the expenses and dividends are paid by the company.
A 5% stock dividend represents a distribution of extra shares, 5% of existing ones, to shareholders. The debit to retained earnings is equal to 5% of the total market value of the previously existing shares.
Explanation:When a company declares a 5% stock dividend, this means that the company is distributing additional shares of its stock to the existing shareholders. The quantity of these additional shares is equal to 5% of the shares that each shareholder currently owns. The debit to retained earnings is an amount equal to the total market value of these additional shares, which is determined by multiplying the declared dividend rate (5%) by the total market value of circulating shares prior to the issuance of dividend.
For instance, if a company has 1000 shares with a market value of $10 each, it would issue additional 50 shares (5% of 1000 shares). Therefore, the debit to retained earnings would be $500 (50 shares * $10/share).
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yuh girl stupid help me out
when at rest an elephants heart rate is about 30 beats per min and a humans heart rate about 70 bpm. a humans heart beats about how many more times per day than an elephants heart
a. 960
b. 2400
c. 5760
d. 28800
e. 57600
Answer:
A. 960
Step-by-step explanation:
Multiply each heart rate by 24 (hours in a day)
Subtract the human's daily heart rate from the elephant's.
30 x 24 = 720
70 x 24 = 1680
1680 - 720 = 960
Answer:
It’s A
Step-by-step explanation:
The volume V, in liters, of air in the lungs during a five-second respiratory cycle is approximated by the model V + 0.1729t + 0.1522t² - 0.0374t³, where t is the time in seconds. Approximate the average volume of air in the lungs during one cycle.
Answer:
The average volume of air in the lungs during one cycle is 0.53176 liters.
Step-by-step explanation:
Given : The volume V, in liters, of air in the lungs during a five-second respiratory cycle is approximated by the model [tex]V=0.1729t+0.1522t^2- 0.0374t^3[/tex], where t is the time in seconds.
To find : The average volume of air in the lungs during one cycle ?
Solution :
The volume V of air in the lungs during a five-second respiratory cycle is [tex]V=0.1729t+0.1522t^2- 0.0374t^3[/tex]
Then the average volume of air in the lungs during one cycle [0,5] is
[tex]V_a=\frac{1}{b-a}\int\limits^a_b {V(t)} \, dt[/tex]
[tex]V_a=\frac{1}{5-0}\int\limits^0_5 {0.1729t+0.1522t^2- 0.0374t^3} \, dt[/tex]
[tex]V_a=\frac{1}{5}[\frac{0.1729t^2}{2}+\frac{0.1522t^3}{3}- \frac{0.0374t^4}{4}}]^5_0[/tex]
[tex]V_a=\frac{1}{5}[0.08645t^2+0.05073t^3- 0.00935t^4]^5_0[/tex]
[tex]V_a=\frac{1}{5}[0.08645(5)^2+0.05073(5)^3- 0.00935(5)^4-0.08645(0)^2+0.05073(0)^3- 0.00935(0)^4][/tex]
[tex]V_a=\frac{1}{5}[2.1613+6.3413-5.8438][/tex]
[tex]V_a=\frac{1}{5}[2.6588][/tex]
[tex]V_a=0.53176\ l[/tex]
The average volume of air in the lungs during one cycle is 0.53176 liters.
Final answer:
To find the average volume of air in the lungs during one cycle, calculate the definite integral of V(t) over the interval t = 0 to t = 5 seconds.
Explanation:
The average volume of air in the lungs during one cycle can be approximated by finding the average value of the function V(t) over the interval t = 0 to t = 5 seconds. To do this, we need to find the definite integral of V(t) over the given interval:
∫[0,5] V(t) dt
After calculating the integral, divide the result by the length of the interval (5 seconds) to find the average volume of air in the lungs during one cycle.
1. A motorboat leaves a harbor and travels at an average speed of 15 mph toward an island. The average speed on the return trip was 10 mph. How far was the island from the harbor if the total trip took 5 hours
Answer:
30 miles
Step-by-step explanation:
Let d represent the distance to the island. The relation between time, speed, and distance is ...
time = distance/speed
so the total time for the round trip is ...
d/15 +d/10 = 5
Multiplying by 30, we get
2d +3d = 150
d = 150/5 = 30
The island was 30 miles from the harbor.
To solve this problem we use the equation Speed = Distance/Time for both legs of the trip to form an equation and solve for the distance. Through these calculations, we find the distance from the harbor to the island to be 30 miles.
Explanation:This problem can be solved by understanding the relationship of speed, distance, and time, often expressed as Speed = Distance/Time. First, let's define the time it took to go to the island and back. From the problem, we know that the total time was 5 hours but the speeds were different, so the time spent on each leg of the trip was different. We'll define the time it took to get to the island as two hours. Therefore, the return trip took 5-t hours. Solving for Distance To calculate the distance, we use the speed of each leg of the trip multiplied by the time of that leg. So, Distance = 15t = 10(5-t). We can solve this equation for t, finding that t equals to 2 hours. Inserting t back into Distance = 15t gives us a distance of 30mph to the island. This means it is 30 miles from the harbor to the island.
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The average cost per month of a 2-bedroom apartment in Grayson was $625 last year.This year,the average cost is $650.What is the percent of increase from late year?
The amount increased 4% from last year.
Step-by-step explanation:
Given,
Average cost last year = $625
Average cost this year = $650
Increase amount = Average cost last year - Average cost this year
Increase amount = 650 - 625 = $25
Percent increase = [tex]\frac{Increase\ amount}{Average\ cost\ last\ year}*100[/tex]
[tex]Percent\ increase=\frac{25}{625}*100\\Percent\ increase=\frac{2500}{625}\\Percent\ increase=4\%[/tex]
The amount increased 4% from last year.
Keywords: percentages, subtraction
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From 27 pieces of luggage, an airline luggage handler damages a random sample of four. The probability that exactly one of the damaged pieces of luggage is insured is twice the probability that none of the damaged pieces are insured. Calculate the probability that exactly two of the four damaged pieces are insured.
Answer:
0.273
Step-by-step explanation:
Let the number of insured pieces of luggage be i and u be the number of uninsured pieces of luggage, therefore,
i + u = 27
Now,
probability that exactly one of the damaged pieces of luggage is insured = (iC1)(uC3)/(27C4)
probability that none of the damaged pieces are insured = (uC4)/(27C4)
and,
(iC1)(uC3)/(27C4) = 2 (uC4)/(27C4)
=> u − 2i = 3
By solving, i + u = 27 and u − 2i = 3
i = 8 and u = 19
and,
(8C2)(19C2)/(27C4) = 0.273
Answer:
Step-by-step explanation:
1. In triangle XYZ, A is the midpoint of XY, B is the midpoint of YZ, and C is the midpoint of XZ. Also, AY = 7, BZ = 8, and XZ = 18. What is the perimeter of triangle ABC? (SHOW WORK)
2. What is y? (SHOW WORK) 2nd picture is the triangle.
Answer:
Part 1) The perimeter of triangle ABC is 24 units
Part 2) [tex]y=97\°[/tex]
Step-by-step explanation:
Part 1)
we know that
The Midpoint Theorem states that the segment joining two sides of a triangle at the midpoints of those sides is parallel to the third side and is half the length of the third side
The perimeter of triangle ABC is equal to
[tex]P=AB+BC+AC[/tex]
Applying the Midpoint Theorem
Find the measure of AB
[tex]AB=\frac{XZ}{2}[/tex]
substitute given value
[tex]AB=\frac{18}{2}=9\ units[/tex]
Find the measure of BC
[tex]BC=\frac{XY}{2}[/tex]
[tex]XY=2AY[/tex]
substitute given value
[tex]XY=2(7)=14\ units[/tex]
[tex]BC=\frac{14}{2}=7\ units[/tex]
Find the measure of AC
[tex]AC=\frac{YZ}{2}[/tex]
[tex]YZ=2BZ[/tex]
substitute given value
[tex]YZ=2(8)=16\ units[/tex]
[tex]AC=\frac{16}{2}=8\ units[/tex]
Find the perimeter of triangle ABC
[tex]P=9+7+8=24\ units[/tex]
Part 2)
step 1
Find the measure of angle z
Remember that the sum of the interior angles in a triangle must be equal to 180 degrees
[tex]55\°+42\°+z=180\°\\97\°+z=180\°\\z=180\°-97\°\\z=83\°[/tex]
step 2
Find the measure of angle y
we know that
[tex]y+z=180\°[/tex] ----> by supplementary angles (form a linear pair)
substitute the value of z
[tex]y+83\°=180\°[/tex]
[tex]y=180\°-83\°=97\°[/tex]
Find the value of the given trigonometric function by finding the reffende angle x and the attaching proper sign Tan 287° What is the representation of tan 287° using reference angle x
Answer:
-tan(73°)
Step-by-step explanation:
The reference angle is the smallest angle between the terminal ray and the x-axis. Here, the terminal ray is in the 4th quadrant, so the reference angle will be ...
ref∠ = 360° -287° = 73°
In the 4th quadrant, the tangent is negative, so we have ...
tan(287°) = -tan(73°)
A plane flies at 190 mph for the first and last half hour of a flight. It flies at a higher constant speed for the rest of the flight. The route is 2090 miles. The plane is 990 miles from the destination 2 hours before the end of the flight.How many hours is the entire flight?
Answer:
4.18 hours
Step-by-step explanation:
Since the plane needs 2 hours to cover the las 990 miles at the end of the flight, and in the last half hour it flies with a speed of 190mph, meaning it covers a distance of 190 / 2 = 95 miles in this last half hours.
That means for the other 1.5 hours, its cruising speed is
[tex] v_c = \frac{990 - 95}{1.5} = 596.7 mph[/tex]
Beside the first and last half hour of the trip (which covers 190 miles), the cruising distance must be
d = 2090 - 190 = 1900 miles
The cruising time is therefore
[tex]t_c = \frac{d}{v_c} = \frac{1900}{596.7} = 3.18 hours[/tex]
Hence the total time for the entire flight is
3.18 + 1 = 4.18 hours
In 4.18 hours is the entire flight.
Given
A plane flies at 190 mph for the first and last half hours of a flight.
It flies at a higher constant speed for the rest of the flight.
The route is 2090 miles.
The plane is 990 miles from the destination 2 hours before the end of the flight.
Speed;The plane needs 2 hours to cover the last 990 miles at the end of the flight, and in the last half hour it flies with a speed of 190mph,
Then,
The distance covered by plane in last half hour is;
[tex]\rm Distance=\dfrac{190}{2}\\\\Distance=95 \ miles[/tex]
The velocity is;
[tex]\rm Velocity = \dfrac{Distance }{Time}\\\\Velocity=\dfrac{900-95}{1.5}\\\\Velocity=\dfrac{805}{1.5}\\\\Velocity=596.7[/tex]
The first and last half hour of the trip (which covers 190 miles), the cruising distance must be;
Distance = 2090 - 190 = 1900 miles
Therefore,
The cruising time is;
[tex]\rm Time =\dfrac{Distance}{Velocity}\\\\Time=\dfrac{1900}{596.7}\\\\Time=3.18 \ hours[/tex]
The total time for the entire flight is
= 3.18 + 1 = 4.18 hours
Hence, in 4.18 hours is the entire flight.
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What is the equation of the line 2-3y = 18 in slope-intercept form?
It will travel 21 miles upstream in three hours going down stream we can show 39 miles in the same amount of time find the speed of the current in the speed of the boat in Still water
Answer: The speed of the current is 3 miles per hour.
The speed of the boat in still water is 10 miles per hour
Step-by-step explanation:
Let the speed of the boat be x miles per hour
Let the speed of the current be y miles per hour
Speed = distance / time
If the boat moves 39 miles downstream in 3 hours, then, the speed is
39/3= 13 miles per hour
Let us assume that it moved it moved in the same direction with the current hence, it moved in still water
The total speed would be x + y. Therefore
x + y = 13 - - - - - - -1
If the boat moves 21 miles upstream in 3 hours, the the speed is
21/ 3 = 7 miles per hour
It is assumed that it moved in the opposite direction to the current.
The total speed would be x - y. Therefore
x - y = 7 - - - - - - -2
Adding equation 1 and equation 2, it becomes
2x = 20
x = 20/2 = 10 miles per hour
y = 13 - x
y = 13 - 10 = 3 miles per hour
A drawer holds 6 white socks, 8 black socks, and 4 blue socks. If a sock is pulled from the drawer randomly, what is the probability that it will not be a blue sock?
Answer:
P(No blue)=7/9=0.778
Step-by-step explanation:
The sample space of an experiment is "the set of all possible outcomes of that experiment".
The Complement Rule states "that the sum of the probabilities of an event and its complement must equal 1". So for example if A is an event and A' their complement we have this:
[tex]P(A)+P(A')=1[/tex]
[tex]P(A')=1-P(A)[/tex]
The probability of an event is "a number describing the chance that the event will happen".
For this problem we need to find first the sample space and is given by:
[tex]\Omega = [6white,8Black,4Blue][/tex] for a total of 18 socks.
[tex]n(\Omega)=8[/tex]
We can use the definition of probability of an event, and we find the probability that the randomly select sock would be blue we have:
[tex]P_{blue}=\frac{Favorable outcomes}{Total outcomes}=\frac{4}{18}=\frac{2}{9}[/tex]
And then using the complement rule if we want the probability that the randomly selected sock would be NOT blue we have:
[tex]P'_{blue}=1-P_{blue}=1-\frac{2}{9}=7/9=0.778[/tex]
"Express as a mixed numeral: 39/8" is a problem found in a fifth-grade arithmetic textbook. This problem is BEST solved through: Please choose the correct answer from the following choices, and then select the submit answer button.
a.trial and error.
b.insight.
c.an algorithm.
d.a heuristic.
Answer:
c. an algorithm
Step-by-step explanation:
Most math problems are best solved using an algorithm. Certainly, converting numbers from one form to another is easily done that way.
_____
The integer part is the whole-number quotient of the division. The fractional part is the remainder divided by the denominator:
39/8 = 32/8 + 7/8 = 4 7/8
The rate (in mg carbon/m3/h) at which photosynthesis takes place for a species of phytoplankton is modeled by the function P = 120I I2 + I + 1 where I is the light intensity (measured in thousands of foot-candles). For what light intensity is P a maximum?
Answer:
Light intensity = L =1
Step-by-step explanation:
The given function is:
[tex]P = \frac{120L}{L^{2}+L+1 }[/tex] (Equation.1)
Taking derivative of the whole equation:
[tex]\frac{dP}{dL}[/tex] =[tex]\frac{d}{dL}[/tex] [tex](\frac{120L}{L^{2}+L+1 } )[/tex]
[tex]\frac{dP}{dL}[/tex] =120 [tex]\frac{1 (L^{2}+L+1) - (\frac{d}{dL}L^{2} +\frac{d}{dL} L+\frac{d}{dL}1)L}{(L^{2}+L+1)^{2} }[/tex]
[tex]\frac{dP}{dL}[/tex] =[tex]\frac{120 (L^{2}-1)}{L^{2}+L+1 }[/tex]
[tex]\frac{dP}{dL}[/tex] =[tex]\frac{120 (L+1)(L-1)}{L^{2}+L+1 }[/tex]
For first derivative test, there is a maxima. for that , we need to take:
L+1 =0 and L-1 =0
we get:
L= -1
or L=1
Since light intensity cannot be negative so, L=1
put this in equation 1:
[tex]P(1) = \frac{120}{1^{2}+1+1 }[/tex]
P = [tex]\frac{120}{3}[/tex]
P= 40 which is the maximum value of P (At L=1)
To find the light intensity that maximizes photosynthesis, you must differentiate the function P = 120I/(I^2 + I + 1) with respect to I, equate it to zero and solve for I. Then, use these values to examine the second derivative and verify whether these are local maxima or minima.
Explanation:To find the light intensity (I) that maximizes photosynthesis rate (P), we should analyze the function P = 120I/(I2 + I + 1) using calculus concepts. This type of problem is looking for a maximum value, so we need to find where the derivative of the function equals zero.
First, differentiate the function P regarding I, using quotient rule: P' = (120(I² + I + 1) - 120I (2I + 1))/ (I² + I + 1)² = 0.
Then, solve this equation for I to find the values for which the rate of change of P with respect to I is zero. These are the points where P is at a maximum or a minimum. Finally, check the second derivative of the function P on these values to determine whether these correspond to a local maximum, a local minimum, or a saddle point.
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A researcher is wondering whether the smoking habits of young adults (18-25 years of age) in a certain city in the U.S. are different from the proportion of the general population of young adults in the U.S. A recent study stated that the proportion of young adults who reported smoking at least twice a week or more in the last month was 0.16. The researcher collected data from a random sample of 75 adults in the city of interest. State the hypotheses to be tested for this study. Select one: a. H0: p = 0.16; Ha: p < 0.16 b. H0: p = 0.16; Ha: p > 0.16 c. H0: p = 0.16; Ha: p ≠ 0.16 d. H0: p ≠ 0.16; Ha: p < 0.16
Answer: c. H0: p = 0.16; Ha: p ≠ 0.16
Step-by-step explanation:
We know that ,
Null hypothesis is a statement about the population parameter([tex]\mu , p, \sigma....[/tex]) and contains equality (=),≤ or ≥ signs.
Alternative hypothesis is also statement about the population parameter([tex]\mu , p, \sigma....[/tex]) but against null hypothesis and contains signs < , > or ≠.
In the given situation , the parameter is p (population proportion).
A recent study stated that the proportion of young adults who reported smoking at least twice a week or more in the last month was 0.16.
i.e. the point estimate of the population proportion(p) of the young adults who reported smoking at least twice a week or more is 0.16.
Now, the hypotheses to be tested for this study would be :
[tex]H_0: p=0.16\\\\ H_a: p\neq0.16[/tex]
Hence, the correct answer is c. H0: p = 0.16; Ha: p ≠ 0.16
Consider the sequence:
3 , 8 , 13 , 18 , 23....
The recursive formula for this sequence is:
[tex]a_{n} =a_{n-1} +5.[/tex]
In complete sentences, explain what [tex]a_{n},a_{n-1},[/tex] and the 5 represnt in the formula. Find [tex]a_{g}[/tex]. What do you need to know in order to find [tex]a_{g}[/tex] ?
The [tex]a_n[/tex] reprsents the nth term where n is some positive whole number {1,2,3,...}
The [tex]a_{n-1}[/tex] represents the term just before the nth term. For example, if n = 22 then [tex]a_{n} = a_{22}[/tex] and [tex]a_{n-1} = a_{21}[/tex]
The +5 at the end means we add 5 to the previous term just before the nth term to get the nth term. In other words, the rule is "add 5 to each term to get the next term".
To get the 9th term [tex]a_{9}[/tex], we need to find the terms before this one because the recursive sequence builds up. The 9th term depends on the 8th term, which depends on the 7th term, and so on. The countdown stops until you reach the first term.
-------
[tex]a_{1} = 3[/tex] (given)
[tex]a_{2} = 8[/tex] (given)
[tex]a_{3} = 13[/tex] (given)
[tex]a_{4} = 18[/tex] (given)
[tex]a_{5} = 23[/tex] (given)
[tex]a_{6} = a_{5}+5 = 23+5 = 28[/tex] (add 5 to the prior term)
[tex]a_{7} = a_{6}+5 = 28+5 = 33[/tex]
[tex]a_{8} = a_{7}+5 = 33+5 = 38[/tex]
[tex]a_{9} = a_{8}+5 = 38+5 = 43[/tex]
So the 9th term is [tex]a_{9} = 43[/tex]
The percent of working students increased by 14.1% to 31.7%, what was the percent prior to the increase? (Express your answer rounded correctly to the nearest tenth of a percent!)
Answer:
124.8 %
Step-by-step explanation:
Given,
Initial percentage of working students = 14.1%,
Final percentage of working students = 31.7%,
Thus, the percentage increase = [tex]\frac{\text{Final percentage-initial percentage}}{\text{Initial percentage}}\times 100[/tex]
[tex]=\frac{31.7 - 14.1}{14.1}\times 100[/tex]
[tex]=\frac{17.6}{14.1}\times 100[/tex]
[tex]=\frac{1760}{14.1}[/tex]
≈ 124.8 %
Final answer:
To find the original percentage of working students before an increase of 14.1%, subtract 14.1% from the new percentage of 31.7%, which gives us 17.6% as the original percentage.
Explanation:
The student is asking to find the original percentage of working students before a 14.1% increase resulted in a new percentage of 31.7%. To determine the original percentage, we need to subtract the increase from the final percentage. Here's the calculation:
Final percentage = Original percentage + Increase
31.7% = Original percentage + 14.1%
To find the original percentage, we subtract 14.1% from 31.7%:
Original percentage = 31.7% - 14.1% = 17.6%
Rounded to the nearest tenth of a percent, the original percentage of working students was 17.6%.
The complete outside including the bottom of a wooden 4 inch cube is painted red. The painted cube is then cut into 1 inch cubes . How many of the 1 inch cubes do not have red on any face?
Answer:
8
Step-by-step explanation:
Only the innermost 8 1-inch cubes would have no red paint on any face.
The 4 inch cube is divided into 1 inch cubes, and the number of cubes that do not have red on any face is calculated. There are no 1 inch cubes that do not have red on any face.
Explanation:To find the number of 1 inch cubes that do not have red on any face, we need to consider the number of cubes that have red on at least one face. Since the complete outside of the 4 inch cube is painted red, each face of the cube has a 4x4 square painted red. Therefore, the area of each face is 16 square inches.
Dividing the 4 inch cube into 1 inch cubes, we have a total of 64 smaller cubes (4x4x4 = 64). Each smaller cube has 6 faces.
So, the total area of all the faces of the smaller cubes is 64 x 6 = 384 square inches. Since each face of the smaller cubes has an area of 1 square inch, the number of cubes that have red on at least one face is 384/1 = 384 cubes.
Therefore, the number of 1 inch cubes that do not have red on any face is 64 - 384 = -320. However, since negative numbers do not make sense in this context, we can conclude that there are no 1 inch cubes that do not have red on any face.
Based on meteorological data for the past century, a local TV weather forecaster estimates that the region’s average winter snowfall is 23'', with a margin of error of {2 inches. Assuming he used a 95% confidence interval, how should view-ers interpret this news? Comment on each of these statements.
a. During 95 of the past 100 winters, the region got between 21" and 25" of snow.
b. There 's a 95% chance the region will get between 21" and 25" of snow this winter.
c. There will be between 21" and 25" of snow on the ground for 95% of the winter days.
d. Residents can be 95% sure that the area's average snowfall is between 21" and 25".
e. Residents can be 95% confident that the average snowfall during the past century was between 21" and 25" per winter.
Answer:
d) Good, the interval is related to the variable of interest and the population mean analyzed.
Step-by-step explanation:
1) Data given
[tex]\bar x = 23[/tex] represent the mean
[tex]ME=2[/tex] represent the margin of error
[tex]confidence=95\%=0.05[/tex]
The confidence interval for the mean is given by the following formula:
[tex]\bar x \pm ME = 23\pm 3=(21,25)[/tex]
Where the margin of error is given by [tex]ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}[/tex]
Based on the interval obtained we can say that "we have 95% of confidence that the mean winter snowfall would be between 21 and 25"
2) Analyze the possible options
a) Wrong, we are not analyzing the individual winters, the interval is related to the population mean.
b) Wrong, the confidence interval can't be interpreted as a chance that are not related to the population mean of interest.
c) Wrong, the confidence interval is not related to the individual days of winter.
d) Good, the interval is related to the variable of interest and the population mean analyzed.
e) Wrong, the confidence interval is not related to specific events, is related to the population mean.
Viewers should interpret the news by considering the confidence interval and understanding the statements.
The viewers should interpret this news as follows:
a. The statement that during 95 of the past 100 winters, the region got between 21" and 25" of snow is valid.
This is because the average winter snowfall of 23" falls within this range with a margin of error of 2".
b. The statement that there's a 95% chance the region will get between 21" and 25" of snow this winter is not correct.
The confidence interval (21" to 25") represents the range of values in which the true average snowfall is likely to fall, not the probability of the upcoming winter's snowfall falling within that range.
c. The statement that there will be between 21" and 25" of snow on the ground for 95% of the winter days is not supported by the given information.
The confidence interval pertains to the average winter snowfall, not individual daily observations.
d. The statement that residents can be 95% sure that the area's average snowfall is between 21" and 25" is valid.
The confidence interval provides a range of values within which the true average is likely to fall.
e. The statement that residents can be 95% confident that the average snowfall during the past century was between 21" and 25" per winter is valid.
The confidence interval represents the range of likely values for the true average.
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Solve x2 - 4 = 5 by graphing the related function,
There are two solutions: #1,
olve 80%
There are two solutions: 3 and -3.
There is one solution: 1
quations
There are no real number solutions.
quare
its B. on ed :)
Hope this helps