Answer:
1. The time it would take Inex to run 1 mile is 5 minutes 20 seconds
2. Great has the fastest (lowest) time
3. When running a mile Great is faster than Inex by 20 seconds
Step-by-step explanation:
1. The distance Great ran in 5 minutes = 1 mile
The distance Inex ran in 1 minute and 20 seconds = A quarte mile = (1/4) mile
We note that 1 minute and 20 seconds = 4/3 minutes
Given that the time Inex ran 1/4 mile = 4/3 minutes...(1)
We have;
The time it would take Inex to run 1 mile is given as follows;
1 = (1/4) ÷ (1/4)
1 mile = ((1/4) ÷ (1/4)) mile = (1/4) mile/(1/4)
The time to run 1 mile = The time to run (1/4) mile/(1/4) = 4/3 minutes/(1/4) (by dividing both sides of equation (1) by (1/4),
4/3 minutes/(1/4) = 4 × 4/3 minutes = 16/3 minutes = \(5\frac{1}{3}\) minutes= 5 minutes 20 seconds
The time it would take Inex to run 1 mile = 5 minutes 20 seconds
2. Given that Great ran a one mile race in 5 minutes, and Inex ran the same one mile race in 1 minute and 20 seconds, Great has the fastest (lowest) time
3. The amount faster Great's time is faster than Inex's time to run one mile = 5 minute 20 seconds - 5 minutes = 20 seconds.
4. There are major chords built on what three notes (with all white notes and no accidentals)? O CFG O ABC GEB OCDE
The three major chords built on white notes without accidentals are:
1. C major chord (C, E, G)
2. F major chord (F, A, C)
3. G major chord (G, B, D)
These chords are formed by taking the root note, skipping one white note, and adding the next white note on top. For example, in the C major chord, the notes C, E, and G are played together to create a harmonious sound.
Similarly, the F major chord is formed by playing F, A, and C, and the G major chord is formed by playing G, B, and D. These three major chords are commonly used in various musical compositions and are fundamental building blocks in music theory.
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The National Teacher Association survey asked primary school teachers about the size of their classes. Nineteen percent responded that their class size was larger than 30. Suppose 760 teachers are randomly selected, find the probability that more than 22% of them say their class sizes are larger than 30.
The probability for more than 22% of the given data say their class sizes are larger than 30 is equal to 0.0864, or 8.64%.
To find the probability that more than 22% of the randomly selected teachers say their class sizes are larger than 30,
Use the binomial distribution.
Let us denote the probability of a teacher saying their class size is larger than 30 as p.
19% of the teachers responded with a class size larger than 30, we can estimate p as 0.19.
Now, calculate the probability using the binomial distribution.
find the probability of having more than 22% of the 760 teachers .
which is equivalent to more than 0.22 × 760 = 167 teachers saying their class sizes are larger than 30.
P(X > 167) = 1 - P(X ≤167)
Using the binomial distribution formula,
P(X ≤167) = \(\sum_{i=0}^{167}\) [C(760, i) × \(p^i\) × \((1-p)^{(760-i)\)]
where C(n, r) represents the combination 'n choose r' the number of ways to choose r items from a set of n.
Using a statistical calculator, the probability P(X ≤ 167) is determined to be approximately 0.9136.
This implies,
The probability of having more than 22% of the randomly selected teachers say their class sizes are larger than 30 is,
P(X > 167)
= 1 - P(X ≤ 167)
≈ 1 - 0.9136
≈ 0.0864
Therefore, the probability for the given condition is approximately 0.0864, or 8.64%.
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Jayden bought a container filled with 5 quarts of ice cream at Chick fil A. How many cups of ice cream are in the container?
Answer:
20 cups of Chick-Fla-A ice cream
Step-by-step explanation:
1 quart = 4 cups
5 quarts = 20 cups
Simplify the exponential expression.
Answer:
\(g^{3}\)
Step-by-step explanation:
When you are dividing, the laws of exponents say to subtract the exponents.
\(g^{5-2}\) = \(g^{3}\)
suppose x is a random variable that takes values on all positive integers. let a = {2 ≤ x ≤ 4} and b = {x ≥ 4}. describe the events (i) ac; (ii) bc; (iii) ab; and (iv) a ∪ b
x is a random variable that takes values on all positive integers. Then the events are:
(i) a^c = {0, 1, 5, 6, 7...........}
(ii) b^c = {0, 1, 2, 3}
(iii) ab = {4}
(iv) a ∪ b = {2, 3, 4, 5, 6, 7, 8,..........}
a = {2 ≤ x ≤ 4} and b = {x ≥ 4}.
(i) We have to describe the events a^c
a = {2 ≤ x ≤ 4}
Then a^c = {x : x < 2 or x > 4}
So the elements are
a^c = {0, 1, 5, 6, 7...........}
(ii) We have to describe the events b^c
b = {x ≥ 4}.
Then b^c = {x : x < 4}
Then the elements are
b^c = {0, 1, 2, 3}
(iii) We have to describe the events ab.
The ab = a ∩ b
As we know that a = {2 ≤ x ≤ 4} and b = {x ≥ 4}. So
ab = {x : 2 ≤ x ≤ 4 ∩ x ≥ 4}
ab = {x : x = 4}
So, ab = {4}
(iv) We have to describe the events a ∪ b
As we know that a = {2 ≤ x ≤ 4} and b = {x ≥ 4}. So
a ∪ b = {x : 2 ≤ x ≤ 4 ∪ x ≥ 4}
a ∪ b = {2, 3, 4, 5, 6, 7, 8,..........}
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the pithag tells us how the ____ lengths of ______ triangles are related
Pythagorean theorem tells us how the side lengths of right triangles are related.
The Pythagorean theorem, also known as the Pythagorean identity, states that the sum of the squares of the lengths of the two sides forming the right angle is equal to the square of the length of the hypotenuse in any right triangle (the side opposite the right angle). In other words, the Pythagorean theorem can be used to calculate the length of the hypotenuse given the lengths of the two sides of a right triangle.
This relationship can be written as the equation:
\(a^2 + b^2 = c^2\)
where a and b are the lengths of the legs, and c is the length of the hypotenuse. The Pythagorean Theorem is named after the ancient Greek mathematician Pythagoras, who is credited with its discovery.
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What is the product? [3 2 0 6 4 6 1 0 2] x [2 0 1]
\( \: \: \: \: \: \)
\(64449866502 \\ \\ in \: \: alternate \: \: form \: \\ \\ 6.4449866502 \times 1 {0}^{10} \)
Step-by-step explanation:
\((320646102) \times (201)\)
multiply the numbers\( = 64449866502 \\ \\ in \: \: alternate \: \: form \: \: \\ \\ 6.4449866502 \times 1 {0}^{10} \)
hope it helps\( \: \: \: \: \: \: \)
The product of the matrices is given below.
\(\left[\begin{array}{ccc}6\\18\\4\end{array}\right]\)
What is the matrix?A matrix is a specific arrangement of items, particularly numbers. A matrix is a row-and-column mathematical structure. The element in a matrix, such as M, refers to the i-th row and j-th column element.
here, we have,
The matrices are given below.
\(\left[\begin{array}{ccc}3&2&0\\6&4&6\\1&0&2\end{array}\right]\) and \(\left[\begin{array}{ccc}2\\0\\1\end{array}\right]\)
now, we get,
The product of the matrices will be
\(\left[\begin{array}{ccc}3&2&0\\6&4&6\\1&0&2\end{array}\right]\) × \(\left[\begin{array}{ccc}2\\0\\1\end{array}\right]\)
Thus, the product of the matrices is given below.
\(\left[\begin{array}{ccc}3&2&0\\6&4&6\\1&0&2\end{array}\right]\) × \(\left[\begin{array}{ccc}2\\0\\1\end{array}\right]\) = \(\left[\begin{array}{ccc}6\\18\\4\end{array}\right]\)
Hence, The product of the matrices is given below.
\(\left[\begin{array}{ccc}6\\18\\4\end{array}\right]\)
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skipper's doghouse has a regular hexagonal base that measures $1$ unit on each side. skipper is tethered to a rope of length $2$ units which is fixed to a vertex. the area of the region outside the doghouse that skipper can reach is $y\pi$. find $y$.
The area of the region outside the doghouse that skipper can reach is 3(pi)^2 yards.
This problem is based on the area of sectors. Now, we know that a sector is a pie-shaped part of a circle made of the arc along with its two radii.
The image which correctly explains the situation in the problem is attached.
From the figure, we can see that the spot can be located anywhere in the two sectors of 120 and 60 degrees each respectively. Now, these radii are respectively of 2 and 1 yards.
Area of one sector of 120 degrees = 120/360 π (2)^2 since radius is 2 yards.
So, area of two sectors is 2 x 120/360 π (2)^2 = 8π /3 square yards.
Similarly, Area of the two 60 degrees sectors is -
2 x 60/360 π (2)^2 = π /3 sq. yards.
Therefore , the total area that the skipper can reach outside the doghouse is given by the sum of all the four sectors i.e. π /3 + 8π /3 =
3π square yards.
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The area of the region outside the doghouse that the skipper can reach is \(3\pi ^2\) yards.
This problem is based on the area of sectors. Now, we know that a sector is a pie-shaped part of a circle made of an arc along with its two radii.
The image which correctly explains the situation in the problem is attached.
From the figure, we can see that the spot can be located anywhere in the two sectors of 120 and 60 degrees each respectively. Now, these radii are respectively 2 and 1 yards.
Area of one sector of 120 degrees \(=\frac{(\pi*2^2*120) }{360}\) since the radius is 2 yards.
So, the area of the two sectors is \(\frac{(2*120*2^2*\pi )}{360}=\frac{8\pi }{3}\) square yards.
Similarly, the Area of the two 60 degrees sectors is -
\(\frac{(2*60*\pi *2^2)}{360} =\frac{\pi }{3}\) sq. yards.
Therefore, the total area that the skipper can reach outside the doghouse is given by the sum of all the four sectors i.e. \(\frac{\pi }{3} +\frac{8\pi }{3} =3\pi\)square yards.
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Random samples of size n = 250 are taken from a population with p = 0.04.
a. Calculate the centerline, the upper control limit (UCL), and the lower control limit (LCL) for the p¯p¯ chart. (Round the value for the centerline to 2 decimal places and the values for the UCL and LCL to 3 decimal places.)
b. Calculate the centerline, the upper control limit (UCL), and the lower control limit (LCL) for the p¯p¯ chart if samples of 150 are used. (Round the value for the centerline to 2 decimal places and the values for the UCL and LCL to 3 decimal places.)
For a p-chart with sample size 150, the centerline (CL) remains 0.04, the upper control limit (UCL) is approximately 0.070, and the lower control limit (LCL) is approximately 0.010.
a. For a p-chart with sample size n = 250 and population proportion p = 0.04, the centerline (CL) is simply the average of the sample proportions, which is equal to the population proportion:
CL = p = 0.04
To calculate the control limits, we need to consider the standard deviation of the sample proportion (σp) and the desired control limits multiplier (z).
The standard deviation of the sample proportion can be calculated using the formula:
σp = sqrt(p(1-p)/n) = sqrt(0.04 * (1-0.04)/250) ≈ 0.008
For a p-chart, the control limits are typically set at three standard deviations away from the centerline. Using the control limits multiplier z = 3, we can calculate the upper control limit (UCL) and lower control limit (LCL) as follows:
UCL = CL + 3σp = 0.04 + 3 * 0.008 ≈ 0.064
LCL = CL - 3σp = 0.04 - 3 * 0.008 ≈ 0.016
Therefore, the centerline (CL) is 0.04, the upper control limit (UCL) is approximately 0.064, and the lower control limit (LCL) is approximately 0.016 for the p-chart with sample size 250.
b. If samples of size n = 150 are used, the centerline (CL) remains the same, as it is still equal to the population proportion p = 0.04:
CL = p = 0.04
However, the standard deviation of the sample proportion (σp) changes since the sample size is different. Using the formula for σp:
σp = sqrt(p(1-p)/n) = sqrt(0.04 * (1-0.04)/150) ≈ 0.01033
Again, the control limits can be calculated by multiplying the standard deviation by the control limits multiplier z = 3:
UCL = CL + 3σp = 0.04 + 3 * 0.01033 ≈ 0.070
LCL = CL - 3σp = 0.04 - 3 * 0.01033 ≈ 0.010
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What is the most common error when entering a formula is to reference the wrong cell in the formula?
The most common error when entering a formula is to reference the wrong cell in the formula.
This error occurs when the cell references within a formula do not match the intended cells. It can lead to incorrect calculations and produce unexpected results. For example, if a formula is supposed to use data from cell A1 but mistakenly refers to cell B1, the calculation will be based on the wrong data. It is important to double-check and ensure that the cell references in a formula accurately reflect the intended data sources to avoid this common mistake.
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Can some help? Plz :)
Answer:
C. 1.05 x 10^7
Step-by-step explanation:
1.75x10^4 x 600
=1050 x 10^4
=1.05 x 10^7
Simplify this expression.
–6w + (–8.3) + 1.5+ (–7w)
The simplified form of the expression -6w + (–8.3) + 1.5+ (–7w) is -13w - 6.8.
What is the simplified form of the expression?Given the expression in the question;
-6w + (–8.3) + 1.5+ (–7w)
To simplify, first remove the parenthesis
Note that;
- × + = -- × - = ++ × + = +-6w + × - 8.3 + 1.5 + × - 7w
-6w - 8.3 + 1.5 - 7w
Next collect and add like terms
-6w - 7w - 8.3 + 1.5
Add -6w and -7w
-13w - 8.3 + 1.5
Add -8.3 and 1.5
-13w - 6.8
Therefore, -13w - 6.8 is the simplified form.
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34% of the 6th graders and 50% of the 7th graders want to go to the water slides. what percentage of the 8th graders want to go to the water slides? 6th grade=0.17 7th grade=0.15 8th grade=0.14 total=0.46 can some one help i am soo confused
Therefore, 16% in percentages of the 8th graders want to go to the water slides.
To find the percentage of 8th graders who want to go to the water slides, we need to subtract the percentages of 6th and 7th graders who want to go from the total percentage.
Given:
Percentage of 6th graders who want to go = 34% = 0.34
Percentage of 7th graders who want to go = 50% = 0.50
Total percentage of 6th and 7th graders who want to go = 0.34 + 0.50 = 0.84
Now, to find the percentage of 8th graders who want to go, subtract the total percentage from 100% (since the total percentage represents all the 6th and 7th graders who want to go):
Percentage of 8th graders who want to go = 100% - Total percentage = 100% - 0.84 = 0.16
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4
1196
A label is placed around the juice box
below, not including the bases. Determine
the surface area of the label.
1.5 in
2 in
4 in
The surface area of the level is 28 square inches.
What is Surface area?The area or region that an object’s surface occupies is known as its surface area. Volume, on the other hand, refers to how much room an object has. There are numerous shapes and dimensions in geometry, including spheres, cubes, cuboids, cones, cylinders, etc. Each form has its own volume and surface area.
Given, A label is placed around the juice box.
Since,
The surface area of a cuboid is the total space occupied by it. A cuboid is a six-faced three-dimensional shape in which each face is in the shape of a rectangle.
The dimensions of juice box are:
length=2 inches,
breadth=1.5 inches, and
height= 4 inches.
The lateral surface area of a cuboid is given by 2(length+breadth)×height.
Now, lateral surface area of juice box = 2(2+1.5)×4
= 2×3.5×4
= 28 squared inches
Therefore, option A is the correct answer.
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Complete question:
What is the 8th term of the sequence?
1 , 3 , 6 , 10 , 15
Answer:
36
Step-by-step explanation:
Find the rule for the sequence.
The change from 1 to 3 is +2.
The change from 3 to 6 is +3.
The change from 6 to 10 is + 4.
The change from 10 to 15 is + 5
Essentially, you are adding 1 and then adding it to the current number. The next 3 numbers are:
Change of +6: 15 + 6 = 21
Change of +7: 21 + 7 = 28
Change of +8: 28 + 8 = 36
36 is your 8th term.
~
How many cubic centimetres would you place in a tub of water to displace 1 L of water?
1000 cubic centimeters would need to be placed in a tub of water to displace 1 Lter of water
What is conversion of units?Conversion of units simply refers to the method used in determining the equivalent of one unit in relation to another.
From the information given, we have that;
Number of cubic centimeters that would be placed in a tub of water to displace 1 L of water
So, we have that there is 1 liter of water in the tub
In order to displace, you need to put something in that is the same amount
Now, let's convert the units
1 liter = 1000 cubic cm
Hence, you need 1000 cubic cm to displace 1 liter
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1 - In a word math problem what do the following words mean: is, of, sum, product.
2 - What is the process for solving for a function's inverse?
Answer:
Step-by-step explanation:
Sum means addition basicaly adding two or more numbers together
Product is when you multiply or times numbers together
First, replace f(x) with y
Replace every x with a y and replace every y with an x .
Solve the equation from Step 2 for y
Replace y with f−1(x) f − 1 ( x )
Verify your work by checking that (f∘f−1)(x)=x ( f ∘ f − 1 ) ( x ) = x and (f−1∘f)(x)=x ( f − 1 ∘ f ) ( x ) = x are both true.
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Answer:
it is upside down type it in the coments
Step-by-step explanation:
Plz help I’ll give brainliest! Look at MN on the coordinate plane.
What is the distance between the endpoints of MN?
A. 5 units
B. 8 units
C. 6 units
D. 10 units
a student is 5ft tall and casts a shadow 15ft. long. a nearby tree casts a shadow that is 75ft. long. How tall is the tree?
Answer:
25ft
Step-by-step explanation:
15/5 = 3
75/3 = 25
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Answer:
25 ft
Step-by-step explanation:
The kid's shadow is 15/5 = 3 times longer than his height.
Therefore, a tree with a 75 ft shadow should be 3 times shorter than its shadow.
=> 75/3 = 25 ft
Max Z = 5x1 + 6x2
Subject to: 17x1 + 8x2 ≤ 136
3x1 + 4x2 ≤ 36
x1 ≥ 0 and integer
x2 ≥ 0
A) x1 = 5, x2 = 4.63, Z = 52.78
B) x1 = 5, x2 = 5.25, Z = 56.5
C) x1 = 5, x2 = 5, Z = 55
D) x1 = 4, x2 = 6, Z = 56
The option B) yields the highest value for Z, which is 56.5. Therefore, the correct answer is B) x1 = 5, x2 = 5.25, Z = 56.5
To determine the correct answer, we can substitute each option into the objective function and check if the constraints are satisfied. Let's evaluate each option:
A) x1 = 5, x2 = 4.63, Z = 52.78
Checking the constraints:
17x1 + 8x2 = 17(5) + 8(4.63) = 85 + 37.04 = 122.04 ≤ 136 (constraint satisfied)
3x1 + 4x2 = 3(5) + 4(4.63) = 15 + 18.52 = 33.52 ≤ 36 (constraint satisfied)
B) x1 = 5, x2 = 5.25, Z = 56.5
Checking the constraints:
17x1 + 8x2 = 17(5) + 8(5.25) = 85 + 42 = 127 ≤ 136 (constraint satisfied)
3x1 + 4x2 = 3(5) + 4(5.25) = 15 + 21 = 36 ≤ 36 (constraint satisfied)
C) x1 = 5, x2 = 5, Z = 55
Checking the constraints:
17x1 + 8x2 = 17(5) + 8(5) = 85 + 40 = 125 ≤ 136 (constraint satisfied)
3x1 + 4x2 = 3(5) + 4(5) = 15 + 20 = 35 ≤ 36 (constraint satisfied)
D) x1 = 4, x2 = 6, Z = 56
Checking the constraints:
17x1 + 8x2 = 17(4) + 8(6) = 68 + 48 = 116 ≤ 136 (constraint satisfied)
3x1 + 4x2 = 3(4) + 4(6) = 12 + 24 = 36 ≤ 36 (constraint satisfied)
From the calculations above, we see that options B), C), and D) satisfy all the constraints. However, option B) yields the highest value for Z, which is 56.5. Therefore, the correct answer is: B) x1 = 5, x2 = 5.25, Z = 56.5.
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the ends of a water trough are 8 feet long are equilateral triangles whose sides are 2 feet long. if water is being pourd into the trough at a rate of 5 ft^3 / min, find the rate at which the water level is rising when the depth is 8 inches
If water is being poured into the trough at a rate of 5 ft^3/min, the rate at which the water level is rising when the depth is 8 inches is 15√3/32 ft/min.
Length (L) = 8 feet
Side = 2 feet
If water is being poured into the trough at a rate of 5 ft^3/min. So
dV/dt = 5 ft^3/min
The depth is 8 inches.
h = 8 inches = 2/3 feet
The formula of volume (V) = √3/4 b^2 · L
Now putting the value
V = √3/4 b^2 · 8
Simplify
V = 2√3b^2
Using the Pythagorean Theorem
b/h = 2/√3
So b = 2/√3 h
Now putting the value of h in the volume V
V = 2√3(2/√3 h)^2
V = 2√3 × 4/3 × h^2
V = 8/√3 × h^2
Differentiating the equation with respect to t
dV/dt = 8/√3 d/dt(h^2)
dV/dt = 8/√3 × 2h dh/dt
dV/dt = 16h/√3 × dh/dt
As dV/dt = 5. So
5 = 16h/√3 × dh/dt
Multiply by √3 on both side, we get
16h dh/dt = 5√3
Divide by 16h on both side, we get
dh/dt = 5√3/16h
As h = 2/3. So
dh/dt = 5√3/(16×2/3)
After solving
dh/dt = 15√3/32 ft/min
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☆ please help! I got an answer but I think its wrong ☆
Answer:
-3,5,-10,16
Step-by-step explanation:
How do you solve a distributive property problem with more than one parentheses
The simplified expression is -x + 16.
To solve a distributive property problem with more than one set of parentheses, you can follow these steps:
Identify the terms that need to be distributed. These are the terms outside the parentheses.
Distribute each term to every term inside the parentheses.
Simplify the expressions inside the parentheses by performing any necessary operations (addition, subtraction, multiplication, etc.).
Combine like terms if possible.
Continue simplifying until you have a final expression.
Here's an example to illustrate the process:
Problem: Simplify the expression 3(x + 2) - 2(2x - 5)
Solution:
Identify the terms to distribute: 3 and -2.
Distribute each term to the terms inside the parentheses:
3(x + 2) becomes 3x + 6
-2(2x - 5) becomes -4x + 10
Simplify the expressions inside the parentheses:
3x + 6 - 4x + 10
Combine like terms:
(3x - 4x) + (6 + 10) = -x + 16
The simplified expression is -x + 16.
By following these steps, you can solve distributive property problems with multiple sets of parentheses. Remember to carefully distribute each term and simplify the expressions inside the parentheses before combining like terms.
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Assume the number of births in a local hospital follows a poisson distribution and averages per day. what is the probability that no births will occur today?
The probability that no births will occur today is 0.1353 (approximately) found by using the Poisson distribution.
Given that the number of births in a local hospital follows a Poisson distribution and averages λ per day.
To find the probability that no births will occur today, we can use the formula of Poisson distribution.
Poisson distribution is given by
P(X = x) = e-λλx / x!,
where
P(X = x) is the probability of having x successes in a specific interval of time,
λ is the mean number of successes per unit time, e is the Euler’s number, which is approximately equal to 2.71828,
x is the number of successes we want to find, and
x! is the factorial of x (i.e. x! = x × (x - 1) × (x - 2) × ... × 3 × 2 × 1).
Here, the mean number of successes per day (λ) is
λ = 2
So, the probability that no births will occur today is
P(X = 0) = e-λλ0 / 0!
= e-2× 20 / 1
= e-2
= 0.1353 (approximately)
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Relationship B has a lesser rate than Relationship A.
This graph represents Relationship A.
What table could represent Relationship B?
A. Time (weeks) 3, 4, 6, 9 Plant growth (in.) 1.8, 2.4, 3.6, 5.4
B. Time (weeks) 3, 4, 6, 9 Plant growth (in.) 1.5, 2, 3, 4.5
C. Time (weeks) 3, 4, 6, 9 Plant growth (in.) 0.9, 1.2, 1.8, 2.7
D. Time (weeks) 3, 4, 6, 9 Plant growth (in.) 2.7, 3.6, 5.4, 8.1
The solution is: C. Time (weeks) 3, 4, 6, 9 Plant growth (in.) 0.9, 1.2, 1.8, 2.7, the table could represent Relationship B.
Here, we have,
Step 1:
The tables give a relationship between the growth of a plant and the number of weeks it took.
To determine the rate of each table, we determine the growth of the plant in a single week.
The growth rate in a week = difference in height/ time taken
Step 2:
For the given graph, the points are (5,2) and (10,4).
The growth rate in a week = 4-2/10-5 = 2/5 = 0.4
So the growth rate for relationship A is 0.4.
Step 3:
Now we calculate the growth rates of the given tables.
Table 1's growth rate in a week = 2.4 - 1.8 / 4-3 = 0.6
Table 2's growth rate in a week = 2 - 1.5/ 4-3 = 0.5
Table 3's growth rate in a week = 1.2 - 0.9/ 4-3 = 0.3
Table 4's growth rate in a week = 3.6 - 2.7/ 4-3 = 00.9
Since relationship B has a lesser rate than A,
so, we get,
Table3 is relationship B.
Hence, C. Time (weeks) 3, 4, 6, 9 Plant growth (in.) 0.9, 1.2, 1.8, 2.7, the table could represent Relationship B.
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how to determine if a function is linear or exponential
In order to determine if a function is linear or exponential, you can observe the relationship between the function's input and output values.
For a linear function, the output values increase or decrease at a constant rate as the input values change. In other words, the function has a constant slope when graphed. You can check linearity by calculating the differences between consecutive output values and verifying if they remain the same. If the differences are constant, the function is linear.
On the other hand, an exponential function shows a constant ratio between the output values and the input values. This means that as the input values increase or decrease by a constant factor, the output values also increase or decrease by the same factor. You can check for exponential behavior by calculating the ratio between consecutive output values. If the ratios are constant, the function is exponential.
It is important to graph the function and analyze its behavior over a range of input values to confirm whether it is linear or exponential.
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A vending machine containing jellybeans will only dispense one jellybean at a time. Inside the container is a mixture of 24 jellybeans: 12 red, 8 yellow, and 4 green. The yellow jellybeans have a rotten egg flavor. Write each answer as a decimal rounded to the nearest thousandth and as a percent rounded to the nearest whole percentage point. Part A: What is the probability of getting a red jellybean on the first draw? Decimal: P(1 st Red )= Percent: P(1 st Red )= Part B: Let's say you did get a red jellybean on the first draw. What is the probability that you will then get a green on the second draw? Decimal: P(2 nd Green | 1st Red )= Percent: P(2 nd Green | 1st Red )= Part C: If you had gotten a yellow on the first draw, would your answer to Part B be different? Part D: What is the conditional probability of the dependent event "red then green?" Decimal: P(1st Red and 2 nd Green )= Percent: P(1 st Red and 2 nd Green )=
Part A:What is the probability of getting a red jellybean on the first draw?
Given information: Red jellybeans = 12 Yellow jellybeans = 8 Green jellybeans = 4 Total jellybeans = 24 The probability of getting a red jellybean on the first draw is:
Probability of getting a red jellybean=Number of red jellybeans/Total jellybeans=12/24=1/2=0.5
Decimal: P(1st Red)=0.5 Percent: P(1 st Red )=50%
Part B: Let's say you did get a red jellybean on the first draw.
What is the probability that you will then get a green on the second draw?
Now, the total number of jellybeans is 23, since one red jellybean has been taken out. The probability of getting a green jellybean is: Probability of getting a green jellybean=Number of green jellybeans/Total number of jellybeans=4/23=0.174 Decimal: P(2nd Green | 1st Red )=0.174 Percent: P(2nd Green | 1st Red )=17%
Part C: If you had gotten a yellow on the first draw, would your answer to Part B be different?
Yes, because there is only 1 rotten egg yellow jellybean and if it were chosen in the first draw, it would not be returned back to the container. Therefore, the total number of jellybeans would be 23 for the second draw, and the probability of getting a green jellybean would be:
Probability of getting a green jellybean=Number of green jellybeans/Total number of jellybeans=4/23=0.174
Thus, the answer would be the same as Part B.
Part D: What is the conditional probability of the dependent event "red then green?"
Given that one red jellybean and one green jellybean are selected: Probability of the first jellybean being red is 1/2
Probability of the second jellybean being green given that the first jellybean is red is 4/23
Probability of "red then green" is calculated as follows: Probability of red then green=P(Red) × P(Green|Red)= 1/2 × 4/23 = 2/23 Decimal: P(1st Red and 2nd Green )=2/23 Percent: P(1st Red and 2nd Green )=8.70%
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Help me out sharty's
I need help asap im having a test on it
Answer:
Triangle ABC is congruent to triangle DFE.