Answer:
DV/dt = 0,2355 m³/min
Step-by-step explanation:
Conical tank volume V = 1/3 *π*r²*h
r radius at the top 2 meters
when depth of water is 3 meters the radius of the level of water is:
let α angle of vertex of cone then
tan∠α = 2/8 tan∠α = 1/4 tan∠α = 0,25
At the same time when water is at 3 meters depth radius is
tan∠α = r/3 0,25*3= r r = 0,75 m
Now
DV/dt = (1/3)*π*r²*Dh/dt
Dh/dt = 0,4 meters/min
By substitution
DV/dt = 0,2355 m³/min
Which relations are functions? List the relation number(s) that are function(s) in the answer bank
1. (3, 2), (9, 1), (-4, 7), and (0, -2)
2. (7, 1), (-5, 2), (1, 0), and (-5, 3)
3. (-2, -4), (2, 4), (6, 8), and (-6, -8)
4. (1, 3), (-1, 3), (2, 3), and (-2, 3)
Answer:
options 1,3,4 are functions.
Step-by-step explanation:
RULE: a relation is said to be a function if every element in the domain ( the numbers in the left side in the below sets) is related to only one number ( number on the right side in the below sets).
Let us check each option one by one:
1. 3 2
9 1
-4 7
0 -2
here each number on the left side is mapped to or is related to one number only.
so this relation is a function
2. 7 1
-5 2,3
1 0
here, "-5" is mapped to two different numbers. so this relation is not a function.
3. -2 -4
2 4
6 8
-6 -8
here each number on the left side is mapped to or is related to one number only.
so this relation is a function
4. 1 3
-1 3
2 3
-2 3
here each number on the left side is mapped to or is related to one number only.
so this relation is a function.
even if it is related to the same number, it doesn't matter.
it should follow the above given rule that's it.
Multiply (2 – 71)(-1 + 47)
The midpoint of the segment connecting the points labeled K and N has coordinates (5, -4). If the coordinates of point K are (7, -2) then what are the coordinates of point N?
Answer:
Co-ordinates of point N is (3,-6)
Step-by-step explanation:
Given point:
Endpoint K(7,-2)
Mid-point of segment KN (5,-4)
Let endpoint [tex]N[/tex] have co-ordinates [tex](x_2,y_2)[/tex]
Using midpoint formula:
[tex]M=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]
Where [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] are co-ordinates of the endpoint of the segment.
Plugging in values to find the midpoint of segment KN.
[tex]M=(\frac{7+x_2}{2},\frac{-2+y_2}{2})[/tex]
We know [tex]M(5,-4)[/tex]
So, we have
[tex](5,-4)=(\frac{7+x_2}{2},\frac{-2+y_2}{2})[/tex]
Solving for [tex]x_2[/tex]
[tex]\frac{7+x_2}{2}=5[/tex]
Multiplying both sides by 2.
[tex]\frac{7+x_2}{2}\times 2=5\times 2[/tex]
[tex]7+x_2=10[/tex]
Subtracting both sides by 7.
[tex]7+x_2-7=10-7[/tex]
∴ [tex]x_2=3[/tex]
Solving for [tex]y_2[/tex]
[tex]\frac{-2+y_2}{2}=-4[/tex]
Multiplying both sides by 2.
[tex]\frac{-2+y_2}{2}\times 2=-4\times 2[/tex]
[tex]-2+y_2=-8[/tex]
Adding both sides by 2.
[tex]-2+y_2+2=-8+2[/tex]
∴ [tex]y_2=-6[/tex]
Thus co-ordinates of point N is (3,-6)
Ashley is making lemonade. The recipe she is using calls for $\frac{3}{4}$ cup of water. Ashley wants to make five times the amount of lemonade that the recipe calls for. She mistakenly uses $4$ cups of water. If $x$ is the number of cups of water Ashley is supposed to use and $y$ is the number of cups of water she actually uses, what is $x-y$? Express your answer as a decimal.
Answer:
x - y = - 0.25 cups.
Step-by-step explanation:
Let x : The number of cups of water Ashley is supposed to use
y : The number of cups of water she actually uses
The actual measurement of water for 1 glass lemonade = 3/ 4 cup
So, the measurement of water for 5 glass lemonade
= 5 x ( Measure of water for 1 glass) = [tex]5 \times (\frac{3}{4})[/tex]
The amount of water Ashley actually uses for 5 glass lemonade = 4 cups
⇒ [tex]x = 5 \times (\frac{3}{4})[/tex] = 3. 75 cups
and y = 4 cups
So, x - y = 3.75 cups - 4 cups = -0.25 cups.
Hence, she used the amount 0.25 cups water extra while making 5 glass lemonades according to the given recipe.
To find x-y, subtract the amount of water Ashley actually uses from the amount she is supposed to use.
Explanation:To find the value of x-y, we need to find the difference between the amount of water Ashley is supposed to use (x) and the amount of water she actually uses (y).
The recipe calls for 3/4 cup of water. Since Ashley wants to make five times the amount of lemonade, she needs to use 5 times the amount of water, which is 5 times 3/4 = 15/4 cups of water.
However, Ashley mistakenly uses 4 cups of water, so y = 4. Therefore, x-y = 15/4 - 4.
In a bag of candies there are 13 red candies, 13 green candies, 13 yellow candies, and 13 blue candies. If you choose 1 candy from the bag, what is the probability the candy will not be blue?
Answer:
As a fraction, the answer is 3/4
In decimal form that is equivalent to 0.75, which converts to 75%
===============================================
Work Shown:
13 red
13 green
13 yellow
13 blue
13+13+13+13 = 52 total
52 - 13 = 39 non-blue
--------
There are 39 non-blue candies out of 52 total.
39/52 = 3/4 is the probability, as a fraction, that we pick a non-blue candy.
3/4 = 0.75 = 75%
Answer:
Since the person took one piece of candy it would be 3/4 of candy. I think
Step-by-step explanation:
While on vacation, Enzo sleeps 115% percent as long as he does while school is in session. He sleeps an average of s hours per day while he is on vacation.
The complete question is written below:
While on vacation, Enzo sleeps 115% as long as he does while school is in session. He sleeps an average of s hours per day while he is on vacation. Which of the following expressions could represent how many hours per day Enzo sleeps on average while school is in session?
A.1.15s
B.s/1.15
C.100/115s
D.17/20s
E.(1.15-0.15)s
Answer:
B. [tex]\dfrac{s}{1.15}[/tex]
Step-by-step explanation:
Let the hours per day slept while school is in session be [tex]x[/tex].
Given:
Hours slept per day on vacation = [tex]s[/tex]
Enzo sleeps 115% as long in vacation as he does in school. Therefore, as per question,
[tex]s=115\%\ of\ x\\\\s=\frac{115}{100}x\\\\s=1.15x\\\\x=\dfrac{s}{1.15}[/tex]
Hence, the number of hours Enzo sleeps while school is in session is given as:
[tex]x=\dfrac{s}{1.15}[/tex]
A standard die is rolled 360 times in hopes of rolling a 5 or 6. So the probability of success is p=1/3. Find the standard deviation of the binomial distribution.
8.9
80.0
119.9
0.2
Answer: option 1 is the correct answer
Step-by-step explanation:
Number of times for which the die was rolled is 360. It means that our sample size, n is 360.
The probability of rolling a 5 or a 6 is 1/3. It means that probability of success,p = 1/3. The probability of failure,q is
1 - probability of success. It becomes
1 - 1/3 = 2/3
The formula for standard deviation is expressed as
√npq. Therefore
Standard deviation = √360 × 1/3 × 2/3
= √80 = 8.9443
Standard deviation is approximately 8.9
In one year, a school uses 13,270 pieces of white paper, 7,570 fewer pieces of blue paper than white paper, and 1,600 fewer pieces of yellow paper than blue paper. How many pieces of paper does the school use in all?
The school uses 23,070 pieces of paper in all.
Here's an explanation:
It is already given that the school uses 13,270 pieces of white paper. Then it says that there are 7,570 fewer pieces of blue paper than white paper. So if you subtract 7,570 from 13,270, you get that the school used 5700 pieces of blue paper. Then it says that there are 1,600 fewer pieces of yellow paper than blue paper. So when you subtract 1,600 from 5,700, you get that the school used 4,100 pieces of yellow paper. So if you do 13,270+5,700+4,100, you get that the school used 23,070 pieces of paper in total.
The school uses a total of 23,070 pieces of paper, which is calculated by adding 13,270 pieces of white paper, 5,700 pieces of blue paper, and 4,100 pieces of yellow paper.
Explanation:The school used 13,270 pieces of white paper. It is stated that they use 7,570 fewer pieces of blue paper than white paper, which means they used 13,270 - 7,570 = 5,700 pieces of blue paper. For yellow paper, they use 1,600 fewer pieces than blue paper, which means they use 5,700 - 1,600 = 4,100 pieces of yellow paper. To get the total number of pieces of paper the school used, you would add all these together: 13,270 white paper pieces + 5,700 blue paper pieces + 4,100 yellow paper pieces = 23,070 pieces of paper in total.
Learn more about Addition and Subtraction here:
https://brainly.com/question/29464370
#SPJ3
true or false, and explain: (a) If a die is rolled three times, the chance of getting at least one ace is 1/6 + 1/6 + 1/6 = 1/2. (b) If a coin is tossed twice, the chance of getting at least one head is 100%.
Answer:
a.False
b.False
Step-by-step explanation:
a.Total possible outcomes of a die=1,2,3,4,5,6=6
Probability of getting an ace=[tex]\frac{favorable\;cases}{total\;number\;of\;cases}[/tex]
Favorable cases=1
Probability of getting an ace=[tex]\frac{1}{6}[/tex]
A die is rolled three times .
We are given that the probability of getting at least one ace is
[tex]\frac{1}{6}+\frac{1}{6}+\frac{1}{6}=\frac{1}{2}[/tex]
There are using addition rule but it is not correct because addition rule used when the events are mutually exclusive .
The events are mutually exclusive when the events cannot occur at the same time.
Since it is possible to obtain one ace on more than one roll of a die.
Therefore, the events are not mutually exclusive.
Hence, the given statement is false.
b.Total cases in one coin=2(H,T)
Number of cases in favor of head=1
The probability of getting on head=[tex]\frac{1}{2}[/tex]
The coin is tossed twice.
We are given that
If a coin is tossed twice ,the chance of getting at least on head is 100%.
There are using addition rule but it is not correct because addition rule used when the events are mutually exclusive .
The events are mutually exclusive when the events cannot occur at the same time.
Since it is possible to obtain head on both tosses of coin.
Therefore, the events are not mutually exclusive.
Hence, the given statement is false.
Both statements are false. For the dice rolls, the chance of getting at least one ace is calculated by finding the complementary probability. For the coin tosses, the chance of getting at least one head is 3 in 4, not 100%.
Explanation:The question revolves around basic probability concepts applied to dice and coin tossing. Firstly, part (a) of the question is false. When a die is rolled three times, the chances of getting at least one ace (or a one) are not simply the sum of the individual probabilities. Events are independent, meaning the outcome of one roll doesn't affect the other.
The correct approach is to calculate the probability of not getting an ace in all three rolls (5/6 * 5/6 * 5/6) and subtract this from 1 to get the complementary probability of at least one ace.
For part (b), the statement is also false. When a coin is tossed twice, the chance of getting at least one head is not 100%. To find the correct probability, we can list all possible outcomes (HH, HT, TH, TT) and calculate that there is a 3 in 4 chance of getting at least one head.
A spaceship traveled 3 4 of a light-year and stopped at a space station. Then it traveled 1 12 of a light-year further to a planet. How far did the spaceship travel in all?
Final answer:
The total distance the spaceship traveled is 5/6 of a light-year, which was obtained by adding 3/4 and 1/12 light years together after finding a common denominator for the fractions.
Explanation:
The student's question is about calculating the total distance a spaceship travels based on two separate distances given in light years. To find this total distance, we will perform an addition of the two distances.
First, the spaceship traveled 3/4 of a light-year to a space station. Then, it traveled an additional 1/12 of a light-year to a planet.
To get the total distance traveled, we simply add the two distances:
(3/4) light years + (1/12) light yearsTo add these fractions, we need a common denominator, which is 12 in this case:
(9/12) light years + (1/12) light yearsNow, when we add these fractions, we get:
(9/12 + 1/12) light years = (10/12) light yearsWe can simplify this fraction to:
(5/6) light yearsTherefore, the spaceship traveled a total of 5/6 of a light-year.
A grain silo has a cylindrical shape. Its diameter is 15 ft, and its height is 44 ft. What is the volume of the silo?
Use the value 3.14 for , and round your answer to the nearest whole number.
Be sure to include the correct unit in your answer.
Answer:
Volume of the silo is 7772 cubic ft.
Step-by-step explanation:
Given:
A grain Silo is cylindrical in shape.
Height (h) = 44 ft.
Diameter (d) = 15 ft.
[tex]\pi = 3.14[/tex]
We need to find the Volume of silo.
We will first find the radius.
Radius can be given as half of diameter.
hence Radius (r) = [tex]\frac{d}{2} =\frac{15}{2}=7.5ft.[/tex]
Since Silo is in Cylindrical Shape we will find the volume of cylinder.
Now We know that Volume of cylinder can be calculate by multiplying π with square of the radius and height.
Volume of Cylinder = [tex]\pi r^2h = 3.14\times(7.5)^2\times44 = 7771.5 ft^3[/tex]
Rounding to nearest whole number we get;
Hence,Volume of Silo is [tex]7772 \ ft^3[/tex].
The volume of the cylindrical grain silo with a diameter of 15 ft and a height of 44 ft is approximately 7,853 cubic feet.
Explanation:The volume of a cylindrical grain silo can be found using the formula V = πr²h, where V is volume, π (pi) is approximately 3.14, r is the radius of the cylinder, and h is the height.
To calculate the volume, you first need to find the radius by dividing the diameter by two. The diameter is given as 15 ft, so the radius is 15 ft / 2 = 7.5 ft. Using the volume formula, the volume V is:
π × (7.5 ft)² × 44 ft
Performing the multiplication:
3.14 × (7.5 ft × 7.5 ft) × 44 ft
3.14 × 56.25 ft² × 44 ft = 7,853 ft³ (to the nearest whole number)
Therefore, the volume of the silo is approximately 7,853 cubic feet.
Learn more about Volume of a Cylinder here:https://brainly.com/question/16788902
#SPJ3
JT Engineering has determined that it should cost $14,000 indirect materials, $12,600 indirect labor, and $6,200 in total overhead to produce 1,000 widgets. During the most recent period, JT actually spent $13,860 indirect materials, $12,420 indirect labor, and $6,500 in total overhead to produce 1,000 widgets. What is JT’s total variance? Is it favorable or unfavorable?
Answer:
total variance: -$20favorableStep-by-step explanation:
The estimated cost is ...
$14000 +12600 +6200 = $32800
The actual cost is ...
$13860 +12420 +6500 = $32780
The variance is the difference between actual cost and predicted cost:
$32,780 - 32800 = -$20.
It is favorable when actual costs are lower than predicted.
In a simple linear regression model, the slope term is the change in the mean value of y associated with _____________ in x.
A) a variable change
B) a corresponding increase
C) a one-unit increase
D) no change
Answer:
a one-unit increase
Step-by-step explanation:
In a simple regression model, the relationship between x and y can be represented by the equation y = ax+b, where
a is the slopeb is the y-interceptThe slope term is the change in the mean value of y associated with a one-unit increase in x.
Find the area of An equilateral triangle that has sides that are 8 inches long.
Answer:
27.71
Step-by-step explanation:
Using Google, we can find that if we plug in the area, a, the formula for the area of the triangle is [tex]\frac{\sqrt{3} }{4} a^{2}[/tex]. Plugging it in, we get [tex]\frac{\sqrt{3} }{4} * 64[/tex] = 27.71 (approximately)
Area of an equilateral triangle that has sides that are [tex]8[/tex] inches long is equal to [tex]\boldsymbol{16\sqrt{3}}[/tex] square inches
A triangle is a polygon that consists of three sides and three angles.
An equilateral triangle is a triangle in which all sides are equal and all angles are equal.
Length of a side of an equilateral triangle [tex](l)=8[/tex] inches
Area of an equilateral triangle [tex](A)=\boldsymbol{\frac{\sqrt{3}}{4}l^2}[/tex]
[tex]=[/tex][tex]\boldsymbol{\frac{\sqrt{3}}{4}(8)^2}[/tex]
[tex]=\boldsymbol{16\sqrt{3}}[/tex] square inches
For more information:
https://brainly.com/question/25032369?referrer=searchResults
Which linear function has a x-intercept at -18?
A) Y=1/3x+6
B) Y=3x+3
C) Y=-3x+12
D) Y=-3x-6
Answer:
A) Y=1/3x+6
Step-by-step explanation:
1. Subtract 6 from both sides.
-6 = 1/3 x
2. Divide 1/3 from both sides.
[tex] - 6 \div ( \frac{1}{3} ) = x[/tex]
x = -18
You have one type of nut that sells for $2.80/lb and another type of nut that sells for $9.60/lb. You would like to have 20.4 lbs of a nut mixture that sells for $6.60/lb. How much of each nut will you need to obtain the desired mixture?
Answer:11.396Ibs of nuts that cost $9.60/Ib and 9.014Ibs that cost $2.80/Ib
Step-by-step explanation:
First we find the cost of the supposed mixture we are to get by selling it $6.60/Ib which weighs 20.41Ibs
Which is 6.6 x 20.41 = $134.64
Now we label the amount of mixture we want to get with x and y
x = amount of nuts that cost $2.8/Ib
y = amount of nuts that cost $9.6/Ib
Now we know the amount of mixture needed is 20.41Ibs
So x + y = 20.41Ibs
And then since the price of the mixture to be gotten overall is $134.64
We develop an equation with x and y for that same amount
We know the first type of nut is $2.8/Ib
So for x amount we have 2.8x
For the second type of nut that is $9.6/Ib
For y amount we have 9.6y
So adding these to equate to $134.64
2.8x + 9.6y = 134.64
So we have two simultaneous equations
x + y = 20.41 (1)
2.8x + 9.6y = 57.148 (2)
We can solve either using elimination or factorization method
I'm using elimination method
Multiplying the first equation by 2.8 so that the coefficient of x for both equations will be the same
2.8x + 2.8y = 57.148
2.8x + 9.6y = 134.64
Subtracting both equations
-6.8y = -77.492
Dividing both sides by -6.8
y = -77.492/-6.8 =11.396
y = 11.396Ibs which is the amount of nuts that cost $9.6/Ib
Putting y = 11.396 in (1)
x + y = 20.41 (1)
x +11.396 = 20.41
Subtract 11.396 from both sides
x +11.396-11.396 = 20.41-11.396
x = 9.014Ibs which is the amount of nuts that cost $2.8/Ibs
To obtain the desired mixture, we set up a system of equations. However, there is no solution to this problem.
Explanation:To find the amount of each type of nut needed to obtain the desired mixture, we can set up a system of equations.
Let x be the amount of the first type of nut (selling for $2.80/lb), and y be the amount of the second type of nut (selling for $9.60/lb).
We have the following equations:
x + y = 20.4 (total weight of the mixture)2.80x + 9.60y = 6.60(20.4) (total cost of the mixture)Multiplying equation 1 by 2.80 and subtracting equation 2 from it, we can eliminate x and solve for y:
2.80x + 2.80y - (2.80x + 9.60y) = 56.16 - 6.60(20.4)
Simplifying the equation gives:
6.80y = 56.16 - 133.92
6.80y = -77.76
y = -77.76/6.80 ≈ -11.44
Since we cannot have a negative amount of nuts, the value of y is not valid.
Therefore, there is no solution to this problem. It is not possible to obtain a nut mixture with the given requirements.
Learn more about Systems of Equations here:https://brainly.com/question/21620502
#SPJ3
Glen is making accessories for the soccer team. He uses 641.65 inches of fabric on headbands for 39 players and 2 coaches. He also uses 377.52 inches of fabric on wristbands for just the players. How much fabric was used on a headband and wristband for each player? Solve on paper. Then check your answer on Zearn. inches of fabric were used per player.
Answer:
Glen uses 15.65 inches fabrics for headbands and 9.68 inches for each player
Explanation:
Given the fabric used are:
For headbands, 641.65 inches for 41 people (39 players and 2 coach)
Therefore, applying the concept of unitary method
41 people = 641.65 inches
1 person = [tex]\frac{641.65}{41} inches[/tex]= 15.65 inches
For wristbands, 377.52 inches for 39 players
39 players = 377.52 inches
1 player = [tex]\frac{377.52}{39} inches[/tex] = 9.68 inches
Therefore, Glen uses 15.65 inches fabrics for headbands and 9.68 inches for each player
Use generating functions to determine the number of different ways 15 identical stuffed animals can be given to six children so that each child receives at least one but no more than three stuffed animals.
Answer:
50
Step-by-step explanation:
There are 434 different ways to distribute 15 identical stuffed animals among six children so that each child receives at least one but no more than three stuffed animals.
1. Define the generating function for distributing stuffed animals to each child as:
[tex]\[ (x + x^2 + x^3)^6 \][/tex]
This represents the options for each child receiving 1, 2, or 3 stuffed animals, and there are 6 children.
2. Expand the generating function using the binomial theorem:
[tex]\[ (x + x^2 + x^3)^6 = \binom{6}{0}x^0 + \binom{6}{1}x^1 + \binom{6}{2}x^2 + \binom{6}{3}x^3 + \binom{6}{4}x^4 + \binom{6}{5}x^5 + \binom{6}{6}x^6 \][/tex]
Simplify to:
[tex]\[ 1 + 6x + 21x^2 + 56x^3 + 126x^4 + 252x^5 + 462x^6 \][/tex]
3. The coefficient of [tex]\( x^{15} \)[/tex] in the expansion represents the number of ways to distribute 15 stuffed animals among six children.
4. Identify the terms that contribute to [tex]\( x^{15} \)[/tex]:
[tex]\[ 56x^3 + 126x^4 + 252x^5 \][/tex]
5. Add the coefficients:
56 + 126 + 252 = 434
Therefore, there are 434 different ways to distribute 15 identical stuffed animals among six children so that each child receives at least one but no more than three stuffed animals.
Suppose the time to process a loan application follows a uniform distribution over the range of 8 to 13 days. What is the probability that a randomly selected loan application takes longer than 12 days to process?
Answer: 0.2
Step-by-step explanation:
We know that , the probability density function for uniform distribution is given buy :-
[tex]f(x)=\dfrac{1}{b-a}[/tex], where x is uniformly distributed in interval [a,b].
Given : The time to process a loan application follows a uniform distribution over the range of 8 to 13 days.
Let x denotes the time to process a loan application.
So the probability distribution function of x for interval[8,13] will be :-
[tex]f(x)=\dfrac{1}{13-8}=\dfrac{1}{5}[/tex]
Now , the probability that a randomly selected loan application takes longer than 12 days to process will be :-
[tex]\int^{13}_{12}\ f(x)\ dx\\\\=\int^{13}_{12}\dfrac{1}{5}\ dx\\\\=\dfrac{1}{5}[x]^{13}_{12}\\\\=\dfrac{1}{5}(13-12)=\dfrac{1}{5}=0.2[/tex]
Hence, the probability that a randomly selected loan application takes longer than 12 days to process = 0.2
The probability a loan application takes no longer than 12 days is 0.1666
Range = 8 to 13 daysMaximum number of days = 12The probability a loan takes no longer than 12 daysLet x = time to process a loan application
for a uniform distribution (8, 13)
[tex]f(x) = \frac{1}{6} ; 8 < x < 13[/tex]
The probability is
[tex]Pr[x > 12] = \int\limits^1^3_1_2 {f(x)} \, dx = 1/6\int_1_2^1^3 dx = \frac{13-12}{6} = 1/6[/tex]
The probability a loan application takes no longer than 12 days is 0.1666
Learn more on uniform distribution here;
https://brainly.com/question/14114556
A central angle in a circle has a measure of 180 The length of the arc it intercepts is 8 in.
What is the radius of the circle?
**Use 3.14 for π and round your answer to ONE decimal place.
Answer:
Step-by-step explanation:
An arc is the length along the circumference of a circle that is bounded by 2 radii. I
A central angle in a circle has a measure of 180. This means that the arc subtends an angle of 180 degrees at the center of the circle.
The length of the arc is 8 inches
Formula for the length of an arc is expressed as
Length of arc = #/360 × 2πr
r = radius of the circle
Length of arc = 8 inches
# 180 degrees
π = constant = 3.14
Substituting,
8 = 180/360 ×2 × 3.142 × r
8 = 3.14r
r = 8/3.14 = 2.56 inches
Find the critical values
χ2L=χ21−α/2 χ L 2 = χ 1 − α / 2 2 and χ2R=χ2α/2 χ R 2 = χ α / 2 2
that correspond to 80 % degree of confidence and the sample size
n=15.
χ2L= χ L 2 =
χ2R= χ R 2 =
The critical values for a Chi-square distribution with 80% confidence level and sample size of 15 (thus 14 degrees of freedom) are: χ2L = 18.475 and χ2R = 8.897.
Explanation:The question is asking for the critical values for a Chi-square distribution which can be found using Chi-square tables usually found in statistics textbooks or online. The critical values refer to the boundary values for the acceptance region of a hypothesis test.
When trying to find the critical values for an 80% confidence level with 14 degrees of freedom (since degrees of freedom = n - 1 for sample, thus 15 - 1 = 14), you need the 90th percentile for the χ2L and the 10th percentile for the χ2R (since α = 20%, then α/2 = 10%).
Using a Chi-square table for these percentiles, we get:
χ2L = 18.475
χ2R = 8.897
Learn more about Chi-square Critical Values here:https://brainly.com/question/30764639
#SPJ12
jaun drove 780 miles in 12 hours at. the same rate how long would it take him to drive 325 miles?
Answer:
Estimated 5 hours
Step-by-step explanation:
780 miles = 12 hours
1 mile = 0.0154hr (3s.f)
325 miles = 0.0154 × 325
= 5.01hr
A processor of carrots cuts the green top off each carrot, washes the carrots, and inserts six to a package. Twenty packages are inserted in a box for shipment. Each box of carrots should weigh 20.4 pounds. The processor knows that the standard deviation of box weight is 0.5 pound. The processor wants to know if the current packing process meets the 20.4 weight standard. How many boxes must the processor sample to be 95% confident that the estimate of the population mean is within 0.2 pound?
Answer:
24 boxes
Step-by-step explanation:
The processor knows that the standard deviation of box weight is 0.5 pound
[tex]\sigma = 0.5[/tex]
We are supposed to find How many boxes must the processor sample to be 95% confident that the estimate of the population mean is within 0.2 pound
Formula of Error=[tex]z \times \frac{\sigma}{\sqrt{n}}[/tex]
Since we are given that The estimate of the population mean is within 0.2 pound
So, [tex]z \times \frac{\sigma}{\sqrt{n}}=0.2[/tex]
z at 95% confidence level is 1.96
[tex]1.96 \times \frac{0.5}{\sqrt{n}}=0.2[/tex]
[tex]1.96 \times \frac{0.5}{0.2}=\sqrt{n}[/tex]
[tex]4.9=\sqrt{n}[/tex]
[tex](4.9)^2=n[/tex]
[tex]24.01=n[/tex]
Hence the processor must sample 24 boxes to be 95% confident that the estimate of the population mean is within 0.2 pound
To be 95% confident that the estimate of the population mean is within 0.2 pound, the processor must sample approximately 25 boxes, as the calculation using the sample size estimation formula indicates.
To determine how many boxes must be sampled to be 95% confident that the estimate of the population mean is within 0.2 pound, we use the formula for the sample size in estimation:
n = (Z·σ/E)^2
Where:
n is the sample sizeZ is the z-score corresponding to the desired confidence levelσ is the population standard deviationE is the margin of errorFor a 95% confidence level, the z-score (Z) is approximately 1.96. Given that the population standard deviation (σ) is 0.5 pound and the desired margin of error (E) is 0.2 pound, the formula becomes:
n = (1.96· 0.5/0.2)^2
Calculating:
n = (1.96· 2.5)^2
n = (4.9)^2
n = 24.01
The processor must sample approximately 25 boxes (since we round up to the nearest whole number when it comes to sample size) to be 95% confident that the estimate of the population mean is within 0.2 pound.
A company that manufactures small canoes has a fixed cost of $20,000. It cost $40 to produce each canoe. The selling price is $80 per canoe. (In solving this exercise, let x represent the number of canoes produced and sold.)
1. Write the cost function.
2. Write the revenue function.
3. Determine the break-even point. Make sure your answer is an ordered pair.
4. This means that when the company produces and sells the break-even number of
canoes: a. there is less money coming in than going out b. the money coming in
equals the money going out c. there is more money coming in than going out d.
there is not enough information
Please explain how to work all of this out.
Answer:1) $40x 2)$80x 3) 500units 4)b
Step-by-step explanation:
For the cost function, which is the amount used for production, we are told to use x and number of canoes produced, and canoe is produced at $40 per canoe, multiplying both
So production cost is $40x
And each canoe is sold at $80 per canoe, multiplying with no of canoes
so revenue is $80x
The break even cost happens when the amount of money put into the business equals the amount of revenue got, so total amount of money put into the business is the addition of the fixed cost and production cost of the canoes which is $20,000 + $40x (1)
And the revenue cost is 80x (2)
So equating (1) and (2) together, we find the value of x to reach the break even point
20000 + 40x = 80x
20000 = 80x - 40x
20000 = 40x
20000/40 = x
x = 500 units
I've already explained the answer to 4 being option b, because that's the fact we used to solve the amount of units to produce and sell to reach the break even point
Which of the two painters above can team up to paint the whole room in 3 hours?
Answer:
[tex]\displaystyle Mary\:and\:Neil[/tex]
Step-by-step explanation:
[tex]\displaystyle 2 = \frac{7\frac{1}{2}}{3\frac{3}{4}}[/tex]
Two hours is much closer up three hours, so either way, they would still paint the room in time.
I am joyous to assist you anytime.
A rectangular area adjacent to a river is fenced in; no fence is needed on the river side. The enclosed area is 1500 square feet. Fencing for the side parallel to the river is $ 10 per foot, and fencing for the other two sides is $ 3 per foot. The four corner posts are $ 20 each. Let x be the length of one of the sides perpendicular to the river.
a) Write a function C(x) that describes the cost of the project.
b) What is the domain of C?
Answer:
a) C(x) = 15000/x + 6x +80
b) Domain of C(x) { R x>0 }
Step-by-step explanation:
We have:
Enclosed area = 1500 ft² = x*y from which y = 1500 / x (a) where x is perpendicular to the river
Cost = cost of sides of fenced area perpendicular to the river + cost of side parallel to river + cost of 4 post then
Cost = 10*y + 2*3*x + 4*20 and accoding to (a) y = 1500/x
Then
C(x) = 10* ( 1500/x ) + 6*x + 80
C(x) = 15000/x + 6x +80
Domain of C(x) { R x>0 }
The function for the cost of the project depending on x, a side perpendicular to the river, is C(x) = $15000/x + $6x + $80. The domain of this function, representing all possible lengths of x, is from 0 to the square root of 1500, exclusive on the lower end, inclusive on the upper end.
Explanation:For part a, we can set up the function C(x) as follows:
Given that the area of the rectangle is 1500 sq. ft, the length of the side parallel to the river will be 1500/x.
The cost of the side parallel to the river: $10*(1500/x) = $15000/xThe cost of the side perpendicular to the river: $3*x*2=$6x (since there are two such sides).The cost of the four corner posts: 4*$20=$80.Therefore, combining all these costs, your C(x) = $15000/x + $6x + $80.
As for part b, the domain of C(x) is the set of all possible values of x. Since x represents the length, it must be greater than zero but less than or equal the length of a side of the rectangular area where the length of the side is limited by the area of 1500 square feet. Hence, the domain of C is (0, sqrt(1500)].
Learn more about Cost Function and Domain here:https://brainly.com/question/29262808
#SPJ3
Find the total amount a college student has in a savings account if $5 comma 000 was invested and earned 7% compounded semiannually for 9 years. Use Upper A equals Upper P (1 plus StartFraction n Over n EndFraction )Superscript nt Baseline .
Answer:
$ 9287.45
Step-by-step explanation:
Since, the amount formula in compound interest,
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
Where,
P = principal amount,
r = rate per period,
n = number of periods per year,
Here, P = $ 5,000, r = 7% = 0.07, t = 9 years, n = 2 (semiannual in a year),
Thus, the amount after 9 years,
[tex]A=5000(1+\frac{0.07}{2})^{18}[/tex]
[tex]=5000(1+0.035)^{18}[/tex]
[tex]=5000(1.035)^{18}[/tex]
= $ 9287.45
Which is one of the binomial factors of the polynomial x^3+3x-2x-8?
a. x-1
b. x+1
c. x-2
d. x+2
Answer:
x+2
Step-by-step explanation:
A factor of a polynomial can be thought of as the value of x at which the polynomial is equal to zero.
So, you can use the values in the options given and put them in the polynomial from the question.
for example: try, part a) x-1, here x=1 since the factor is x-1=0
put this value in the polynomial to see if it results to zero.
[tex](1)^3 + 3(1)^2 - 2(1) - 8\\ -6[/tex]
so this isn't the answer.
now try, part d) x + 2, here, x = -2
[tex](-2)^3 + 3(-2)^2 - 2(-2) - 8\\ 0[/tex]
you'll see this is the factor!
Answer:
d. x+2
Step-by-step explanation:
The question is essentially asking which of -2, -1, 1, 2 is a zero of the polynomial. All of them are plausible, because all are factors of -8, the constant term.
So, we don't have much choice but to try them. That means we evaluate the function to see if any of these values of x make it be zero.
±1:
The value 1 is easy to substitute for x, as it makes all of the x-terms equal to their coefficient. Essentially, you add all of the coefficients. Doing that gives ...
1 +3 -2 -8 = -6
Similarly, the value -1 is easy to substitute for x, as it makes all odd-degree terms equal to the opposite of their coefficient. Here, ...
f(-1) = -1 +3 -(-2) -8 = -4
Neither one of these values (-1, +1) is a zero of the polynomial, so choices A and B are eliminated.
__
(x-2):
To see if this is a factor, we need to see if x=2 is a zero. Evaluation of a polynomial is sometimes easier when it is written in Horner form:
((x +3)x -2)x -8
Substituting x=2, we get ...
((2 +3)2 -2)2 -8 = (8)2 -8 = 8 . . . not zero
This tells us there is a zero between x=1 and x=2, but that is not what the question is asking.
__
(x+2):
We can similarly evaluate the function for x=-2 to see if (x+2) is a factor.
((-2 +3)(-2) -2)(-2) -8 = (-4)(-2) -8 = 0
Since x=-2 makes the function zero, and it makes the factor (x+2) equal to zero, (x+2) is a factor of the polynomial.
So, the factor (x+2) is a factor of the given polynomial.
_____
I find that a graphing calculator answers questions like this quickly and easily. If you're allowed one, it is a handy tool.
Murphy loves pistachio nuts. Every saturday morning, she walks to the market and buy some. Last week, she bought two pounds and paid $7.96, and this week she bought only one half pound and paid $1.99
Question is Incomplete, Complete question is given below,
Murphy loves pistachio nuts. Every Saturday morning, she walks to the market and buys some. Last week, she bought two pounds and paid $7.96, and this week she bought only one-half pound and paid $1.99. What the unit rate for pistachio nuts?
Answer:
The unit rate for pistachio nuts is $3.98.
Step-by-step explanation:
Given;
Price of 2 pounds of pistachio nuts = $7.96
We need to find the price of 1 pound of pistachio nuts.
To find the same we will use the unitary method,
Hence ,
Price of 1 pound of pistachio nuts = [tex]\frac{\$7.96}{2} = \$3.98[/tex]
Also given:
Price of half pound of pistachio nuts = $1.99
We need to find the price of 1 pound of pistachio nuts.
To find the same we will use the unitary method,
Hence ,
Price of 1 pound of pistachio nuts = [tex]\$1.99\times 2 = \$3.98[/tex]
Hence, The unit rate for pistachio nuts is $3.98
A trapezoid has a base that is 10.2 centimeters long and another base that is 9.8 centimeters long. Its height measures 5 centimeters. What is the area of the trapezoid?
Answer:
50 cm²
Step-by-step explanation:
The area of a trapezoid can be figured from the formula
A = (1/2)(b1 +b2)h
Filling in the given numbers and doing the arithmetic, we get ...
A = (1/2)(10.2 +9.8)(5) = 50 . . . . square centimeters
The area is 50 cm².