Answer:
e) The mean of the sampling distribution of sample mean is always the same as that of X, the distribution from which the sample is taken.
Step-by-step explanation:
The central limit theorem states that
"Given a population with a finite mean μ and a finite non-zero variance σ2, the sampling distribution of the mean approaches a normal distribution with a mean of μ and a variance of σ2/N as N, the sample size, increases."
This means that as the sample size increases, the sample mean of the sampling distribution of means approaches the population mean. This does not state that the sample mean will always be the same as the population mean.
correct answer is option (c)
The Statement: The sampling distribution of the sample mean is always reasonably like the distribution of X, the distribution from which the sample is taken. is not True.
What is Standard deviation?
The square root of the variance is used to calculate the standard deviation, a statistic that expresses how widely distributed a dataset is in relation to its mean. By calculating the departure of each data point from the mean, the standard deviation may be determined as the square root of variance.
How Standard deviation is calculated?
Standard deviation is calculated by taking the square root of a value derived from comparing data points to a collective mean of a population. The formula is:
[tex]\begin{aligned} &\text{Standard Deviation} = \sqrt{ \frac{\sum_{i=1}^{n}\left(x_i - \overline{x}\right)^2} {n-1} }\\ &\textbf{where:}\\ &x_i = \text{Value of the } i^{th} \text{ point in the data set}\\ &\overline{x}= \text{The mean value of the data set}\\ &n = \text{The number of data points in the data set} \end{aligned}[/tex]
So, In the given options,
The Statement: The sampling distribution of the sample mean is always reasonably like the distribution of X, the distribution from which the sample is taken is False, because according Central limit theorem,
regardless of the shape of the population(X): If the sample size is greater than 30. The Sample distribution will be Normal Distribution.
Hence,
The Statement: The sampling distribution of the sample mean is always reasonably like the distribution of X, the distribution from which the sample is taken. is not True.
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A fish tank is 3/4 full. 2/3 of the water leak out. After the water leaks out, 10 gallons are left in the tank. How many gallons of water does the tank hold when full?
Capacity of the fish tank is 40 gallons
a mailing container for posters is made from 87.4 square inches of cardboard the container is in the shape of a triangular prism the base of the prism is an equilateral triangle with 2- inch side lengths and a height of 1.7 inches what is the length of the container
Answer:
The length of the container is [tex]14\ in[/tex]
Step-by-step explanation:
we know that
The surface area of a triangular prism (a mailing container) is equal to
[tex]SA=2B+PL[/tex]
where
B is the area of the triangular base
P is the perimeter of the triangular base
L is the length of the container
step 1
Find the area of the base B
[tex]B=\frac{1}{2}(2)(1.7)=1.7\ in^{2}[/tex]
step 2
Find the perimeter of the base P
[tex]P=3(2)=6\ in[/tex]
step 3
Find the length L of the container
we have
[tex]SA=87.4\ in^{2}[/tex]
[tex]B=1.7\ in^{2}[/tex]
[tex]P=6\ in[/tex]
substitute and solve for L
[tex]87.4=2(1.7)+(6)L[/tex]
[tex]L=[87.4-2(1.7)]/(6)[/tex]
[tex]L=14\ in[/tex]
(1CQ) Determine whether the series -8/5+32/25-128/125+... is convergent or divergent.
Answer:
The series is convergent answer ⇒ (a)
Step-by-step explanation:
* The series is -8/5 + 32/25 + -128/125 + ........
- It is a geometric series with:
- first term a = -8/5 and common ratio r = 32/25 ÷ -8/5 = -4/5
* The difference between the convergent and divergent
in the geometric series is :
- If the geometric series is given by sum = a + a r + a r² + a r³ + ...
* Where a is the first term and r is the common ratio
* If |r| < 1 then the following geometric series converges to a / (1 - r).
- Where a/1 - r is the sum to infinity
* The proof is:
∵ S = a(1 - r^n)/(1 - r) ⇒ when IrI < 1 and n very large number
∴ r^n approach to zero
∴ S = a(1 - 0)/(1 - r) = a/(1 - r)
∴ S∞ = a/1 - r
* If |r| ≥ 1 then the above geometric series diverges
∵ r = -4/5
∴ IrI = 4/5
∴ IrI < 1
∴ The series is convergent
The ratio of successive terms leads to a limit of 4/5, which is less than 1. Hence, the series is convergent.
Convergence or Divergence of a Series
To determine whether the series -8/5+32/25-128/125+... is convergent or divergent, we observe the series' structure and apply the ratio test. For a series ∑a_n, the ratio test considers the limit L = lim (n→∞) |a_(n+1) / a_n|.
Let's compute this for our series:
[tex]a_n = (-1)^{(n+1)} * 8 * (4/5)^{(n-1)}[/tex]
Compute [tex]a_(n+1): a_(n+1) = (-1)^{(n+2)} * 8 * (4/5)^n[/tex]
Calculate |a_(n+1) / a_n| = [tex]|(-1)^{(n+2)} * 8 * (4/5)^n / (-1)^{(n+1)} * 8 * (4/5)^{(n-1)}| = |(4/5)|[/tex]
The limit L = |(4/5)| = 4/5 which is less than 1.
Since L < 1, by the ratio test, the series -8/5+32/25-128/125+... is convergent.
Solve for x in the given interval.
sec θ = -4.0545, for 0≤θ≤2π
Answer:
The answer is Ф = 1.82 or 4.46 ⇒ answer (c)
Step-by-step explanation:
* The domain of the function is 0 ≤ Ф ≤ 2π
- Lets revise the ASTC rule to solve the problem
# In the 1st quadrant all trigonometry functions are +ve
# In the 2nd quadrant sinФ and cscФ only are +ve
# In the 3nd quadrant tanФ and cotФ only are +ve
# In the 4th quadrant cosФ and secФ only are +ve
* Lets solve the problem
∵ secФ = -4.0545 ⇒ negative value
∴ Angle Ф is in the 2nd or 3rd quadrant
- In the 2nd quadrant Ф = π - α ⇒ (1)
- In the 3rd quadrant Ф = π + α ⇒ (2)
where α is an acute angle
* Now use the calculator to find α with radiant mode
- Let secα = 4.0545
∴ cosα = 1/4.0545
∴ α = cos^-1(1/4.0545) = 1.321585
* Substitute the value of α in (1) and (2)
∴ Ф = π - 1.321585 = 1.82
∴ Ф = π + 1.321585 = 4.46
* The answer is Ф = 1.82 or 4.46
Emma's total bill for dinner was $20. The cost of her dessert was 30% of the total bill. What was the cost of her dessert?
Answer:
The answer is $6
Step-by-step explanation:
20 divided by 30% is 6! So it’s therefore 6$
The probability of a type ii error is represented by the greek symbol, β.
a. True
b. False
The answer to your question is a. TRUE
Final answer:
The statement that the probability of a Type II error is represented by the Greek symbol β is true. The β symbol denotes the likelihood of failing to reject a false null hypothesis, while the power of a test (1-β) indicates the probability of accurately detecting a false null hypothesis.
Explanation:
The question is asking whether the statement 'The probability of a type ii error is represented by the greek symbol, β' is true or false. The correct answer is a. True. In statistics, a Type II error, which occurs when a false null hypothesis is not rejected, is indeed represented by the Greek letter β (beta). Therefore, the probability of committing a Type II error is denoted as β (beta). Conversely, a Type I error, symbolized by α (alpha), happens when the null hypothesis is incorrectly rejected. It is important to minimize both α and β as they represent the probabilities of these two types of errors. While α is often set by the researcher (commonly at 0.05), β is affected by factors such as effect size, sample size, and the chosen significance level α.
The power of a statistical test, defined as 1 - β, is the probability of correctly rejecting a false null hypothesis. A high statistical power is desirable as it indicates a lower chance of committing a Type II error. Estimating or calculating β directly can be complex, but understanding its role is crucial for interpreting the results of hypothesis testing.
One winter morning in Canada, the temperature at 8:00 was 1.5°C. From 8:00 to 11:00, the temperature increased by 0.7°C. From 11:00 to 2:00, it dropped 2.6°C, and from 2:00 to 5:00, it decreased by 0.9°C. What expression shows the temperature in °C at 5:00 p.M.?
Answer:
See below.
Step-by-step explanation:
Temperature at 5 pm = 1.5 + 0.7 - 2.6 - 0.9
(= -1.3 degrees C).
Answer:=1.5 + 0.7 - 2.6 - 0.9
Step-by-step explanation:
A water balloon is 5 feet above the ground when Sally launches it into the air. Use the quadratic equation 0 = -t2 + 4t + 5 to find how much time, t, it takes for the water balloon to reach the ground.
Answer:
2-sqrt14/2, 2+sqrt13/2.
Step-by-step explanation:
What you do is you have to do the quadratic equation like it says in the problem.
x= −b± sqrtb^2 −4ac /2a .
a=-2, b=4, c=5.
x=-4±sqrt(4)^2-4(-2)(5)/2(-2).
x=-4±sqrt16+40/-4.
x=-4±2sqrt14/-2.
2-sqrt14/2, 2+sqrt13/2. is your answer once you have done everything.
Answer:
5 seconds
Step-by-step explanation:
:0
A rectangular room is 4 meters longer than it is wide, and its perimeter is 32 meters. Find the dimension of the room
Answer:
x=6
Step-by-step explanation:
2(x+4)+2x=32
2x+8+2x=32
4x+8=32
4x=24
x=6
The dimensions of the room are 6 meters in width and 10 meters in length.
The student's question pertains to finding the dimensions of a rectangular room based on given conditions: the room is 4 meters longer than it is wide and the perimeter is 32 meters. Let's denote the width of the room as w meters. Therefore, the length will be w + 4 meters. The perimeter of a rectangle is calculated by the formula
P = 2(length + width), which in this case is:
2(w + w + 4) = 32
4w + 8 = 32
4w = 32 - 8
4w = 24
w = 24 / 4
w = 6 meters
Now, since the length is 4 meters longer, it will be:
length = w + 4
length = 6 + 4 = 10 meters
Therefore, the dimensions of the room are 6 meters in width and 10 meters in length.
If a solid consists of three lateral faces and a base that are congruent isosceles triangles, what type of solid is it?. A. octahedron . B. triangular pyramid . C. right triangular pyramid . D. regular rectangular prism .
Answer:
B. triangular pyramid.
Step-by-step explanation:
-Octahedron has eight faces that are equilateral triangles, six vertices and twelve edges.
-Triangular pyramid has four triangular faces that have congruent isosceles triangles in which one of them is considered the base.
-Right triangular pyramid has a triangle base, three faces and six edges and the line that is located between the centre of the base and the vertex is perpendicular to the base.
-Regular rectangular prism has twelve sides, 8 vertices and six rectangular faces.
According to this, the answer is triangular pyramid.
URGENT HELP PLZ MATH!
Find the measure of angle B.
Question 5 options:
30°
60°
90°
120°
➷ Angles in a triangle total to 108 degrees
180 - (45 + 15) = 120
Angle B is 120 degrees.
✽➶ Hope This Helps You!
➶ Good Luck (:
➶ Have A Great Day ^-^
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Answer:
The correct option is D.
Step-by-step explanation:
From the given figure it is clear that the measure of angle A is 45° and the measure of angle C is 15°.
According to the angle sum property of triangles, the sum of interior angles of a triangle is 180°. It means in triangle ABC,
[tex]\angle A+\angle B+\angle C=180^{\circ}[/tex]
[tex]45^{\circ}+\angle B+15^{\circ}=180^{\circ}[/tex]
[tex]\angle B+60^{\circ}=180^{\circ}[/tex]
[tex]\angle B=180^{\circ}-60^{\circ}[/tex]
[tex]\angle B=120^{\circ}[/tex]
The measure of angle B is 120°. Therefore the correct option is D.
Given that 81^-3/4 = 3^n fins the value of n
Please help!!
Answer:
3^-3
Step-by-step explanation:
So first 81^-3/4 is cubing 81, finding the forth root, and then putting it on the denominator. Doing this you get 1/27.
Now you think, how do I get 3 to equal 27?
3^1 = 3
3^2 = 9
3^3 = 27
From here you just put a negative in front of the power, 3^-3, which puts the 27 on the bottom of the fraction, leaving you with 1/27, which is what we were trying to get.
Solve x^2-8x=20 by completing the square. Which is the solution set of the equation?
Step-by-step explanation:
x^2 - 8x = 20
1. Subtract 20 from both sides
x^2 - 8x - 20 = 20 - 20
2. Simplify
x^2 - 8x - 20 = 0
3. Factor the equation out by grouping
(x - 10)(x + 2) = 0
4. Change signs:
x = 10, x = -2
Hope This Helped!!
~Shane
Answer:{-2,10}
Step-by-step explanation:
trust
cos 2x = ____
Check all that apply.
Answer:
see below
Step-by-step explanation:
The double angle formulas for trig functions are generally based on the sum of angle formulas, where the two angles are equal.
cos(a+b) = cos(a)cos(b) -sin(a)sin(b)
When a=b=x, then ...
cos(2x) = cos(x)² -sin(x)²
The Pythagorean identity can be used to substitute for either of the squares:
cos(2x) = (1 -sin(x)²) -sin(x)²
cos(2x) = 1 - 2sin(x)²
or
cos(2x) = cos(x)² -(1 -cos(x)²)
cos(2x) = 2cos(x)² - 1
The correct representations of the identity cos2x from the provided options are A (1 - 2sin²x), B (2sin²x - 1), and D (cos²x - sin²x). The Option C (sin²x - cos²x) is not correct. Therefore, option A,B and D are correct
Explanation:The question is asking for various forms of the identity cos2x, where x is an angle.
From the given options, A, B, and D are correct.
We know that cos2x can be represented in three possible ways: 1 - 2sin²x (Option A), 2cos²x - 1 (not provided in the options), and 2sin²x - 1 (Option B).
Thus, the correct options are A (1-2sin²x) and B (2sin²x - 1). Option D (cos²x - sin²x) is another equivalent form of cos2x based on the identity cos²x + sin²x = 1 (provided as Reference 7). Option C (sin²x - cos²x) is not a formula for cos2x so it's incorrect.
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The correct statement is written below:
cos2x=____. Check all that apply.
A. 1-2sin^2 x.
B. 2sin^2 x-1.
C. sin^2 x-cos^2 x.
D. cos^2 x-sin^2 x
ABCD is a trapezoid. Find the value of x and y.
A = x = 110 degrees
B = 117 degrees
C = y = 63 degrees
D = 70 degrees
In a trapezoid, the two angles on the same side of the parallel lines are supplementary, meaning their measures add up to 180 degrees.
So, for angle A and angle D:
A + D = 180
x + 70 = 180
x = 180 - 70
x = 110
For angle B and angle C:
B + C = 180
117 + y = 180
y = 180 - 117
y = 63
Therefore, in the trapezoid ABCD:
A = x = 110 degrees
B = 117 degrees
C = y = 63 degrees
D = 70 degrees
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A bakery can make 30 donuts every 15 minutes. What is the unit rate at which the bakery makes donuts?
Answer:
Your answer is 2/1. 2 donuts every minute.
Step-by-step explanation: The rate you are given is 30 donuts every 30 minutes. This equals 30/15.
To make a unit rate, you must make the fraction have a ratio of x/1. You can simply do this by dividing and/or simplifying the equation 30/15.
The unit rate at which the bakery makes donuts is 2 donuts per minute. This is determined by dividing the total number of donuts (30) by the total time in minutes (15).
Explanation:The question is asking for the unit rate at which the bakery makes donuts. A unit rate is a ratio that compares the quantity of one thing to 1 of something else. In this case, we want to find how many donuts the bakery makes in 1 minute. Given that the bakery can make 30 donuts every 15 minutes, we divide 30 (donuts) by 15 (minutes) to find the unit rate. So, 30 donuts ÷ 15 minutes = 2 donuts per minute. Therefore, the unit rate at which the bakery makes donuts is 2 donuts per minute.
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PLEASE HELP! WILL MARK THE BRAINLIEST ANSWER!
x ÷ 5 = 1/10
X=1/2
Explanation
Multiple both sides times 5
Then the 5 just cancels out on the left side and you’re left with 1/2
In a game, if you roll a 6 on a 6-sided number cube, you lose a turn.
(a) What is the probability that you roll a 6? Explain your reasoning.
(b) What is the probability that you either roll a 6 or do not roll a 6? Explain your reasoning.
(c) What is the probability that you don’t roll a 6? Explain your reasoning.
a) There are 6 sides, one of them having 6 on it. Therefore, the chances is 1/6.
b) Rolling a six or not rolling a six is guaranteed, because there is no other option. The probability is 1.
c) There are 6 sides, five of them not having a 6. So, the probability is 5/6.
A store marks up merchandise 40% for profit. If an item costs the store $15, what is the selling price?
Answer:
The selling price is $21
Step-by-step explanation:
What is the markup
Take the original price and multiply by the markup percent
markup = 15*40%
= 15*.4
= 6
The new price is the original price plus the markup
new price = 15+6
new price = 21
The selling price is $21
One diagonal of a cube has length 12. Compute the surface area of the cube.
Answer:
The surface area of the cube is [tex]288\ units^{2}[/tex]
Step-by-step explanation:
we know that
The length of a diagonal of a cube is equal to
[tex]D=b\sqrt{3}[/tex]
where
b is the length side of a cube
In this problem we have
[tex]D=12\ units[/tex]
so
[tex]12=b\sqrt{3}[/tex]
solve for b
[tex]b=\frac{12}{\sqrt{3}}\ units[/tex]
Simplify
[tex]b=4\sqrt{3}\ units[/tex]
Find the surface area of the cube
The surface area of the cube is equal to
[tex]SA=6b^{2}[/tex]
substitute the value of b
[tex]SA=6(4\sqrt{3})^{2}=288\ units^{2}[/tex]
Consider the characteristics of the graph. Which statement DOES NOT describe the data set
Where are the statements ?
Answer: The data is skewed right.
Before 1918, approximately 60% of the wolves in a region were male, and 40% were female. However, cattle ranchers in this area have made a determined effort to exterminate wolves. From 1918 to the present, approximately 70% of wolves in the region are male, and 30% are female. Biologists suspect that male wolves are more likely than females to return to an area where the population has been greatly reduced. (Round your answers to three decimal places.) (a) Before 1918, in a random sample of 12 wolves spotted in the region, what is the probability that 9 or more were male? What is the probability that 9 or more were female? What is the probability that fewer than 6 were female? (b) For the period from 1918 to the present, in a random sample of 12 wolves spotted in the region, what is the probability that 9 or more were male? What is the probability that 9 or more were female? What is the probability that fewer than 6 were female?
Answer:
A) 0.2253, 0.0153; B) 0.4925, 0.0017
Step-by-step explanation:
This is a binomial distribution. This is because there are only two outcomes; each trial is independent of each other; and the outcomes are independent.
This means we use the formula
[tex]_nC_r\times p^r\times (1-p)^{n-r}[/tex]
For part A,
There are 12 wolves selected; this means n = 12. We want the probability that 9 or more are male; this makes r = 9, 10, 11 or 12. We will find each probability and add them together.
p, the probability of success, is 0.6 for the first question (males). This makes 1-p = 1-0.6 = 0.4. Together this gives us
[tex]_{12}C_9(0.6)^9(0.4)^3+_{12}C_{10}(0.6)^{10}(0.4)^2+_{12}C_{11}(0.6)^{11}(0.4)^1+_{12}C_{12}(0.6)^{12}(0.4)^0\\\\=220(0.6)^9(0.4)^3+66(0.6)^{10}(0.4)^2+12(0.6)^{11}(0.4)+1(0.6)^{12}(1)\\\\\\= 0.2253[/tex]
We now want the probability that 9 or more are female; this makes r = 9, 10, 11 or 12. p is now 0.4; this makes 1-p = 1-0.4 = 0.6. This gives us
[tex]_{12}C_9(0.4)^9(0.6)^3+_{12}C_{10}(0.4)^{10}(0.6)^2+_{12}C_{11}(0.4)^{11}(0.6)^1+_{12}C_{12}(0.4)^{12}(0.6)^0\\\\=220(0.4)^9(0.6)^3+66(0.4)^{10}(0.6)^2+12(0.4)^{11}(0.6)^1+1(0.4)^{12}(1)\\\\=0.0153[/tex]
For part B,
There are again 12 wolves selected, so n = 12. We want the probability in the first question that 9 or more are male; this makes r = 9, 10, 11 or 12. The probability of success is now 0.7, so 1-p = 1-0.7 = 0.3[tex]_{12}C_9(0.7)^9(0.3)^3+_{12}C_{10}(0.7)^{10}(0.3)^2+_{12}C_{11}(0.7)^{11}(0.3)^1+_{12}C_{12}(0.7)^{12}(0.3)^0\\\\=220(0.7)^9(0.3)^3+66(0.7)^{10}(0.3)^2+12(0.7)^{11}(0.3)^1+1(0.7)^{12}(0.3)^0\\\\= 0.4925[/tex]
For the second question, the probability of success is now 0.3 and 1-p = 1-0.3 = 0.7:
[tex]220(0.3)^9(0.7)^3+66(0.3)^{10}(0.7)^2+12(0.3)^{11}(0.7)^1+1(0.3)^{12}(0.7)^0\\\\=0.0017[/tex]
Probabilities are used to determine the outcomes of events.
Before 1918,
The probability of selecting 9 or more male wolves is 0.225The probability of selecting 9 or more female wolves is 0.015The probability of selecting lesser than 6 female wolves is 0.665Since 1918,
The probability of selecting 9 or more male wolves is 0.493The probability of selecting 9 or more female wolves is 0.002The probability of selecting lesser than 6 female wolves is 0.516The question is an illustration of binomial probability, where:
[tex]\mathbf{P(x) = ^nC_x \times p^x \times (1 - p)^{n -x}}[/tex]
(a i) Probability of selecting 9 or more wolves out of 12, before 1918
The given parameters are:
[tex]\mathbf{p = 0.60}[/tex] --- the probability of selecting a male wolf
So, we have:
[tex]\mathbf{P(x \ge 9) = P(9) + P(10) + P(11) + P(12)}[/tex]
Using [tex]\mathbf{P(x) = ^nC_x \times p^x \times (1 - p)^{n -x}}[/tex], we have:
[tex]\mathbf{P(x \ge 9) = ^{12}C_9 \times 0.6^9 \times (1 - 0.6)^{12-9} +..............+^{12}C_{12} \times 0.6^{12} \times (1 - 0.6)^{12-12} }[/tex]
[tex]\mathbf{P(x \ge 9) = 220 \times 0.00064497254 +..........+1 \times 0.00217678233}[/tex]
[tex]\mathbf{P(x \ge 9) =0.225 }[/tex]
(a ii) Probability of selecting 9 or more female wolves
The given parameters are:
[tex]\mathbf{p = 0.40}[/tex] --- the probability of selecting a female wolf
So, we have:
[tex]\mathbf{P(x \ge 9) = P(9) + P(10) + P(11) + P(12)}[/tex]
Using [tex]\mathbf{P(x) = ^nC_x \times p^x \times (1 - p)^{n -x}}[/tex], we have:
[tex]\mathbf{P(x \ge 9) = ^{12}C_9 \times 0.4^9 \times (1 - 0.4)^{12-9} +..............+^{12}C_{12} \times 0.4^{12} \times (1 - 0.4)^{12-12} }[/tex]
[tex]\mathbf{P(x \ge 9) = 220 \times 0.0000566231+..........+1 \times 0.00001677721}[/tex]
[tex]\mathbf{P(x \ge 9) =0.015 }[/tex]
(a ii) Probability of selecting fewer than 6 female wolves
The given parameters are:
[tex]\mathbf{p = 0.40}[/tex] --- the probability of selecting a female wolf
Using the complement rule, we have:
[tex]\mathbf{P(x < 6) = 1 - P(x \ge 6)}[/tex]
So, we have:
[tex]\mathbf{P(x < 6) = 1 - [P(6) + P(7) + P(8) + P(x \ge 9)]}[/tex]
Using [tex]\mathbf{P(x) = ^nC_x \times p^x \times (1 - p)^{n -x}}[/tex], we have:
[tex]\mathbf{P(x < 6) = 1 - [^{12}C_6 \times 0.4^6 \times 0.6^6 + ^{12}C_7 \times 0.4^7 \times 0.6^5 + ^{12}C_8 \times 0.4^8 \times 0.6^4 + P(x \ge 9)}[/tex][tex]\mathbf{P(x < 6) = 1 - [924 \times 0.00019110297 +........ + 0.0153]}[/tex]
[tex]\mathbf{P(x < 6) = 1 - [0.335]}[/tex]
[tex]\mathbf{P(x < 6) = 0.665}[/tex]
(b i) Probability of selecting 9 or more wolves out of 12, since 1918
The given parameters are:
[tex]\mathbf{p = 0.70}[/tex] --- the probability of selecting a male wolf
So, we have:
[tex]\mathbf{P(x \ge 9) = P(9) + P(10) + P(11) + P(12)}[/tex]
Using [tex]\mathbf{P(x) = ^nC_x \times p^x \times (1 - p)^{n -x}}[/tex], we have:
[tex]\mathbf{P(x \ge 9) = ^{12}C_9 \times 0.7^9 \times (1 - 0.7)^{12-9} +..............+^{12}C_{12} \times 0.7^{12} \times (1 - 0.7)^{12-12} }[/tex]
[tex]\mathbf{P(x \ge 9) = 220 \times 0.00108954738+..........+1 \times 0.0138412872}[/tex]
[tex]\mathbf{P(x \ge 9) =0.493 }[/tex]
(b ii) Probability of selecting 9 or more female wolves
The given parameters are:
[tex]\mathbf{p = 0.30}[/tex] --- the probability of selecting a female wolf
So, we have:
[tex]\mathbf{P(x \ge 9) = P(9) + P(10) + P(11) + P(12)}[/tex]
Using [tex]\mathbf{P(x) = ^nC_x \times p^x \times (1 - p)^{n -x}}[/tex], we have:
[tex]\mathbf{P(x \ge 9) = ^{12}C_9 \times 0.3^9 \times (1 - 0.3)^{12-9} +..............+^{12}C_{12} \times 0.3^{12} \times (1 - 0.3)^{12-12} }[/tex]
[tex]\mathbf{P(x \ge 9) = 220 \times 0.00000675126+..........+1 \times 5.31441e-7}[/tex]
[tex]\mathbf{P(x \ge 9) =0.002 }[/tex]
(b iii) Probability of selecting fewer than 6 female wolves
The given parameters are:
[tex]\mathbf{p = 0.40}[/tex] --- the probability of selecting a female wolf
Using the complement rule, we have:
[tex]\mathbf{P(x < 6) = 1 - P(x \ge 6)}[/tex]
So, we have:
[tex]\mathbf{P(x < 6) = 1 - [P(6) + P(7) + P(8) + P(x \ge 9)]}[/tex]
Using [tex]\mathbf{P(x) = ^nC_x \times p^x \times (1 - p)^{n -x}}[/tex], we have:
[tex]\mathbf{P(x < 6) = 1 - [^{12}C_6 \times 0.3^6 \times 0.7^6 + ^{12}C_7 \times 0.3^7 \times 0.7^5 + ^{12}C_8 \times 0.3^8 \times 0.7^4 + P(x \ge 9)}[/tex]
[tex]\mathbf{P(x < 6) = 1 - [924 \times 0.4^6 \times 0.7^6 + 792 \times 0.3^7 \times 0.7^5 + 495 \times 0.3^8 \times 0.7^4 + 0.002}[/tex]
[tex]\mathbf{P(x < 6) = 1 - [0.484]}[/tex]
[tex]\mathbf{P(x < 6) = 0.516}[/tex]
Read more about probabilities at:
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Triangle T was dilated to form triangle T'. Which ratio is the correct scale factor?
Please answer fast and correctly
Answer:
5/9
Step-by-step explanation:
The scale factor by which T was dilated is ...
(side of T')/(corresponding side of T)
= 20/36 = 10/18 = 5/9 . . . (reduced form)
Answer:
C) the answer is 5/9 or C
Step-by-step explanation:
i got it roght on the edgen quiz.
What basic trigonometric identity would you use to verify that cot x sin x =cos x
[tex] \cot(x) \sin(x) = \frac{ \cos(x) }{ \sin(x) } \sin(x) = \cos(x) \\ \Rightarrow b. \cot(x) = \frac{ \cos(x) }{ \sin(x) } [/tex]
Answer:
B
Step-by-step explanation:
Determine whether the value is a discrete random variable, continuous random variable, or not a random variable. a. The amount of snowfall in December in City A b. The number of bald eagles in a country c. The gender of college students d. The number of statistics students now reading a book e. The number of people with blood type A in a random sample of 18 people f. The number of points scored during a basketball game
Answer:
a) a continuous random variable; b) a discrete random variable; c) not a random variable; d) a discrete random variable; e) a discrete random variable; f) a discrete random variable
Step-by-step explanation:
A continuous random variable is one that can take multiple values between whole number values; for instance, fractions and decimals. Snowfall is a continuous random variable.
A discrete random variable is one that can only take whole number values. The number of bald eagles, the number of students reading a book, the number of people with blood type A, and the number of points scored in a basketball game are discrete random variables.
Gender of students is not a numerical value; this is not a random variable.
Here, we are required to determine whether the value a list of data sets are, discrete random variable, continuous random variable, or not a random variable.
Options B, D, E and F are examples of discrete random variable values.Option A is an example of a continuous random variable value.Option C is an example of a non-random variable value.First, it is important to know the characteristics of each type of value as follows;
A discrete random variable is one which usually (although not necessarily) are counts. The statement above means they may take on only a countable number of distinct values such as 0,1,2,3, and on. Put simply, they can take only a finite number of distinct values. Distinct in this case means whole number values. Examples are as follows;The number of bald eagles in a countryThe number of statistics students now reading a bookThe number of people with blood type A in a random sample of 18 peopleThe number of points scored during a basketball game
2. A continuous random variable is one which has an infinite number of possible values. This means that the value of a continuous variable is usually associated with fractions of whole numbers, i.e continuous random variables are used majorly for measurements such as length, height and so on. An example from the question above is;
The amount of snowfall in December in City3. A non-random variable is one whose values are definite. An example from above is;
The gender of college studentsRead more:
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A value of a plot of land has increased by 10% in the past year. The new value of the plot is $46,200. What was the value of the plot last year.
Answer:
42,000 dollars was the value of the plot last year
Step-by-step explanation:
[tex]x*\frac{110}{100}=46200\\110x=4620000\\x=\frac{4620000}{110} \\x=42000[/tex]
How do you know if a system or equations has one solution, no solution, or infinitely many solutions
Step-by-step explanation:
We transform the system of equations to the form:
[tex]\left\{\begin{array}{ccc}ax+by=c\\dx+ey=f\end{array}\right[/tex]
Where a & b and d & e are relatively prime number.
1.If a ≠ d or b ≠ e then the system of equations has one solution.
Example:
[tex]\left\{\begin{array}{ccc}2x-3y=-4\\3x+3y=9\end{array}\right[/tex]
Add both sides of equations:
[tex]5x=5[/tex] divide both sides by 5
[tex]x=1[/tex]
Substitute it to the second equation:
[tex]3(1)+3y=9[/tex]
[tex]3+3y=9[/tex] subtract 3 from both sides
[tex]3y=6[/tex] divide both sides by 3
[tex]y=2[/tex]
[tex]\boxed{x=1,\ y=2\to(1,\ 2)}[/tex]
2.If a = d and b = e and c = f then the system of equations has infinitely many solutions.
Example:
[tex]\left\{\begin{array}{ccc}2x+3y=5\\2x+3y=5\end{array}\right[/tex]
Change the signs in the second equation. Next add both sides of equations:
[tex]\underline{+\left\{\begin{array}{ccc}2x+3y=5\\-2x-3y=-5\end{array}\right}\\.\qquad0=0\qquad\bold{TRUE}[/tex]
[tex]\boxed{x\in\mathbb{R},\ y=\dfrac{5-2x}{3}}[/tex]
3.If a = d and b = e and c ≠ f then the system of equations has no solution.
Example:
[tex]\left\{\begin{array}{ccc}3x+2y=6\\3x+2y=1\end{array}\right[/tex]
Change the signs in the second equation. Next add both sides of equations:
[tex]\underline{+\left\{\begin{array}{ccc}3x+2y=6\\-3x-2y=-1\end{array}\right}\\.\qquad0=5\qquad\bold{FALSE}[/tex]
Determine the coordinates of the corners of the rectangle to compute the area of the rectangle using the distance formula (round to the nearest integer).
Answer:
The area of rectangle is [tex]72\ units^{2}[/tex]
Step-by-step explanation:
see the attached figure with letters to better understand the problem
Let
[tex]A(3.10),B(12,1),C(16,5),D(7,14)[/tex]
we know that
The area of rectangle is equal to
[tex]A=(AB)(BC)[/tex]
the formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
Find the distance AB
we have
[tex]A(3.10),B(12,1)[/tex]
substitute in the formula
[tex]AB=\sqrt{(1-10)^{2}+(12-3)^{2}}[/tex]
[tex]AB=\sqrt{(-9)^{2}+(9)^{2}}[/tex]
[tex]AB=\sqrt{162}\ units[/tex]
Find the distance BC
we have
[tex]B(12,1),C(16,5[/tex]
substitute in the formula
[tex]BC=\sqrt{(5-1)^{2}+(16-12)^{2}}[/tex]
[tex]BC=\sqrt{(4)^{2}+(4)^{2}}[/tex]
[tex]BC=\sqrt{32}\ units[/tex]
Find the area of rectangle
[tex]A=(\sqrt{162})*(\sqrt{32})=72\ units^{2}[/tex]
Answer:
d is the answer
Step-by-step explanation:
The radius of a sphere is 6 units. Which expression represents the volume of the sphere in cubic units.
[tex] \frac{3}{4} \pi(6) {}^{2} \\ \\ \frac{4}{3} \pi(6) {}^{3} \\ \\ \frac{3}{4} \pi(12) {}^{2} \\ \\ \frac{4}{3} \pi(12) {}^{3} [/tex]
Chris Nazarro had total travel expenses of $872. His transportation cost was $136. The hotel cost was $210 and business materials cost $500. If his lunch cost 30% of his dinner, how much was dinner to the nearest cent?
Answer:
[tex]\$20[/tex]
Step-by-step explanation:
Let
x-----> the cost of his lunch
y----> the cost of his dinner
we know that
[tex]x+y=872-136-210-500[/tex]
[tex]x+y=26[/tex] -----> equation A
[tex]x=0.3y[/tex] ---> equation B
substitute equation B in equation A
[tex]0.3y+y=26[/tex]
[tex]1.3y=26[/tex]
[tex]y=\$20[/tex] -----> the cost of the dinner