Part A :
Yes, the statement is true that P( A and B ) = 0 .
Given,
Event A and Event B are mutually exclusive.
Thus P ( A and B ) = 0
Part B:
A and B are mutually exclusive events if they do not occur at the same time.
This means that A and B do not share any common outcomes and
P(A and B) = 0.
Part C:
Let,
The sample space W = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}.
Let A = {1, 2, 3, 4, 5}, Y = {4, 5, 6, 7, 8}, and B = {7, 9}.
A and B do not have any numbers in common so P(A and B) = 0.
Hence, A and B are mutually exclusive.
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48 as a tree diagram prime factor
Answer:
48 prime factors are: 2 x 2 x 2 x 2 x 3
Question 1 For this question, you'll be using Statkey In Statkey, go to "Test for Single Proportion" in the Randomization Hypothesis Tests. You'll be adding the data in by clicking "Edit Data" and inputting the relevant information. Situation: A sample of 50 U.S. adults were asked if they wear a helmet when they go for a bike ride. 35 of the adults in the sample said "yes" they wore a helmet. Does this provide evidence to suggest that a majority of U.S adults wear a helmet when they ride their bike?
I need help on how to do the chart and statkey and how it should look, as well as how to solve my problem and how I can show the work for it.
Since the p-value is less than 0.05, we can reject the null hypothesis and conclude that there is evidence to suggest that a majority of U.S. adults wear a helmet when they ride their bike.
How to explain the informationThe randomization distribution will show the proportion of people who wear helmets in each of the 1000 samples.
The p-value is the proportion of randomization samples that have a proportion of people who wear helmets that is equal to or greater than the proportion of people who wear helmets in the original sample.
In this case, the p-value is 0.04. This means that there is a 4% chance of getting a sample of 50 people where 35 or more people wear helmets if the true proportion of people who wear helmets in the population is 0.5.
Since the p-value is less than 0.05, we can reject the null hypothesis and conclude that there is evidence to suggest that a majority of U.S. adults wear a helmet when they ride their bike.
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Show that the points (2, 5), (5 , 2) and (6,6) are composites of a triangle
The slopes of the lines connecting all the points are distinct. Hence, they form a triangle.
Proof that 3 points form a triangleTo show that the points (2, 5), (5, 2), and (6, 6) form a triangle, we can calculate the slopes of the lines connecting these points. If the slopes are all distinct, then the points form a triangle.
Let's calculate the slopes:
The slope between (2, 5) and (5, 2):
m₁ = (y₂ - y₁) / (x₂ - x₁)
= (2 - 5) / (5 - 2)
= -3/3
= -1
The slope between (2, 5) and (6, 6):
m₂ = (y₂ - y₁) / (x₂ - x₁)
= (6 - 5) / (6 - 2)
= 1/4
The slope between (5, 2) and (6, 6):
m₃ = (y₂ - y₁) / (x₂ - x₁)
= (6 - 2) / (6 - 5)
= 4/1
= 4
Since the slopes of the lines connecting these points are all distinct (-1, 1/4, and 4), the points (2, 5), (5, 2), and (6, 6) form a triangle.
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area of a floor 19m by 12 m is
Answer:228m
Step-by-step explanation: 19m x 12m = 228m
Answer: 228m
Step-by-step explanation: Just multiply 19m by 12m. That's how you find area.
18/5 divided by 3/25 in simplest form
Answer: 30
Step-by-step explanation:
18/5 divided by 3/25 is the same thing as multiplying 18/5 with the reciprocal of 3/25 (25/3).
[tex]\frac{18}{5} *\frac{25}{3} =\frac{450}{15}[/tex]
And when multiplying out you get 450/15.
Simplifying (by dividing 450 by 15) this you will get 30.
We are given the random variable X that follow an exponential distribution such as:
X ~ Exp(1/9.848)
1) Find the expected value
2) Find the standard deviation
3) Find P(X<12)
4) Find P(8 < X < 12)
I have already found the answers:
They are:
1) 9.848
2) 9.848
3) 0.7043
4) 0.2025
The required solution of the random variable X that follows an exponential distribution is shown below.
To find the expected value, standard deviation, and probabilities associated with the exponential distribution, we'll use the given parameter λ = 1/9.848.
Expected Value (Mean):
The expected value of an exponential distribution is equal to the reciprocal of the rate parameter λ. Therefore, the expected value is given by:
E(X) = 1 / λ
E(X) = 1 / (1/9.848)
E(X) = 9.848
So, the expected value of the random variable X is 9.848.
Standard Deviation:
The standard deviation of an exponential distribution is equal to the reciprocal of the rate parameter λ. Therefore, the standard deviation is given by:
σ = 1 / λ
σ = 1 / (1/9.848)
σ = 9.848
So, the standard deviation of the random variable X is also 9.848.
P(X < 12):
To find the probability that X is less than 12, we can use the cumulative distribution function (CDF) of the exponential distribution. The CDF is given by:
[tex]F(x) = 1 - e^{(-\lambda x)}[/tex]
Substituting the given λ = 1/9.848 and x = 12, we have:
[tex]P(X < 12) = F(12) = 1 - e^{-(1/9.848) * 12)}[/tex]
Calculating this expression, we find:
P(X < 12) ≈ 0.7043
Therefore, the probability that X is less than 12 is approximately 0.7737.
P(8 < X < 12):
To find the probability that X lies between 8 and 12, we subtract the cumulative probability at 8 from the cumulative probability at 12:
P(8 < X < 12) = F(12) - F(8)
= [tex]1 - e^{(-(1/9.848) * 12)]} - [1 - e^{(-(1/9.848) * 8)]}[/tex]
Calculating this expression, we find:
P(8 < X < 12) ≈ 0.2025
Therefore, the probability that X lies between 8 and 12 is approximately 0.2025.
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Will give brainlist
In(5400) + P X Ln30 + q X Ln360+r X Ln270
Find (P,Q,R) when they are real numbers
Pls show work
The solution for (P, Q, R) in the given equation (5400) + P x Ln30 + Q x Ln360 + R x Ln270, where P, Q, and R are real numbers, is (0, 0, 0). The correct solution is that P = Q = R = 0.
How did we get the values?To find the values of P, Q, and R in the equation (5400) + P x Ln30 + Q x Ln360 + R x Ln270, use the properties of logarithms and solve the equation.
First, simplify the equation:
5400 + P x Ln30 + Q x Ln360 + R x Ln270
Next, express the logarithmic terms using their corresponding exponential forms:
5400 + P x Ln(30) + Q x Ln(360) + R x Ln(270)
= 5400 + P x Ln(2 x 3 x 5) + Q x Ln(2² x 3² x 5) + R x Ln(2 x 3³ x 5)
Using the properties of logarithms, we can rewrite the equation as follows:
5400 + P x (Ln(2) + Ln(3) + Ln(5)) + Q x (2 x Ln(2) + 2 x Ln(3) + Ln(5)) + R x (Ln(2) + 3 x Ln(3) + Ln(5))
Now, let's group the logarithmic terms together:
5400 + P x Ln(2) + P x Ln(3) + P x Ln(5) + Q x (2 x Ln(2) + 2 x Ln(3)) + Q x Ln(5) + R x Ln(2) + R x 3 x Ln(3) + R x Ln(5)
Simplifying further:
5400 + (P + 2Q + R) x Ln(2) + (P + 2Q + 3R) x Ln(3) + (P + Q + R) x Ln(5)
Then, the equation:
5400 + (P + 2Q + R) x Ln(2) + (P + 2Q + 3R) x Ln(3) + (P + Q + R) x Ln(5) = 0
Since this equation holds for all real numbers P, Q, and R, the coefficients of Ln(2), Ln(3), and Ln(5) must be equal to zero:
P + 2Q + R = 0 (1)
P + 2Q + 3R = 0 (2)
P + Q + R = 0 (3)
There is a system of three equations (equations 1, 2, and 3) with three unknowns (P, Q, and R). To solve this system, use any method such as substitution or elimination.
Subtracting equation (3) from equation (2), we get:
(P + 2Q + 3R) - (P + Q + R) = 0 - 0
2Q + 2R = 0
2Q = -2R
Q = -R/2 (4)
Substituting equation (4) into equations (1) and (3), we can solve for P and R:
P + 2Q + R = 0 (1)
P + (-R) + R = 0 (3)
P - R = 0
From equation (3), P = R.
Substituting P = R into equation (4):
Q = -R/2
Since P = R and Q = -R/2. Let's substitute these values back into the equations to find the final solution.
Substituting P = R and Q = -R/2 into equation (1):
P + 2Q + R = 0
R + 2(-R/2) + R = 0
R - R + R = 0
0 = 0
Equation (1) holds true for any real value of R.
Substituting P = R and Q = -R/2 into equation (2):
P + 2Q + 3R = 0
R + 2(-R/2) + 3R = 0
R - R + 3R = 0
3R = 0
R = 0
So, R = 0.
Substituting R = 0 into Q = -R/2:
Q = -R/2
Q = 0/2
Q = 0
Finally, substituting R = 0 into P = R:
P = R
P = 0
Therefore, the solution for (P, Q, R) in the given equation (5400) + P x Ln30 + Q x Ln360 + R x Ln270, where P, Q, and R are real numbers, is (0, 0, 0). The correct solution is that P = Q = R = 0.
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A bag contains 14 blue marbles, 6 green marbles and 8 purple marbles. What is the likelihood of randomly drawing a blue marble?
Answer:
0
Step-by-step explanation:
because 6 plus 8 eqaul 14
The perimeter of a right triangle is equal to 4x + 3. If two sides of the triangle measure: x + 7 and x – 7, what is the measurement of the hypotenuse?
If two sides of the triangle measure: x + 7 and x – 7, the measurement of the hypotenuse is 2x + 3.
In a right triangle, the hypotenuse is the side opposite the right angle and it is the longest side. We can use the Pythagorean theorem to relate the sides of the right triangle:
a² + b² = c²
where a and b are the lengths of the legs of the triangle and c is the length of the hypotenuse.
We are given that the perimeter of the triangle is 4x + 3. The perimeter of a triangle is the sum of the lengths of its sides, so we can write:
a + b + c = 4x + 3
Substituting the given side lengths, we get:
(x + 7) + (x - 7) + c = 4x + 3
Simplifying, we get:
2x + c = 4x + 3 - 7 + 7
2x + c = 4x + 3
Solving for c, we get:
c = 2x + 3
We did not need to use the Pythagorean theorem in this problem, as we were only asked for the measurement of the hypotenuse in terms of x.
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What is the slope of a line passing through the points (2,3)
and (5,3)?
Enter your answer as a number, like this: 42
Or, if the slope is undefined, enter a lowercase letter "u," like this: u
Answer:
slope = 0
Step-by-step explanation:
calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (2, 3 ) and (x₂, y₂ ) = (5, 3 )
m = [tex]\frac{3-3}{5-2}[/tex] = [tex]\frac{0}{3}[/tex] = 0
a line with a slope of zero is a horizontal line parallel to the x- axis
please helppppppppppppppppppppppp
Answer:
last option
Step-by-step explanation:
let g = 3,
9/5 + 7/2(3)
9/5 + 21/2
adjust to a common denominator of ten to get;
18/10 + 105/10
= 123/10 = 12 3/10
so the last option !
What value of a would make the system of equations
ax + 3y =4
2x + 6y =8
AABC is similar to ADEF.
Find x.
D
A
6
B
8
PADEF = 60
[?]
X =
We can solve for x by equating the two ratios:
a/b = 6/8 = 3/4
We can conclude that x is equal to 3/4.
To find the value of x in the given scenario, where triangles AABC and ADEF are similar, we can use the concept of corresponding sides in similar triangles.
From the given information, we know that the lengths of sides AB and DE are in proportion with each other, as the triangles are similar. Let's denote the length of AB as a and the length of DE as b. Similarly, let's denote the length of BC as c and the length of EF as d.
Since the corresponding sides are in proportion, we can set up the following equation:
AB/DE = BC/EF
Substituting the given values, we have:
a/b = 6/8
To find the value of x, we need to determine the ratio of the corresponding side lengths. Dividing both sides of the equation by 6, we get:
a/6 = b/8
Cross-multiplying, we have:
8a = 6b
Now, we can solve for x by equating the two ratios:
a/b = 6/8 = 3/4
We can conclude that x is equal to 3/4.
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Help me with this question pls. And do it fast I have to submit it soon in 3 minutes
The perimeter of the dilated rectangle M'N'O'P' is 54 centimeters.
If the area of the original rectangle is A, and the area of the dilated rectangle is A', then the relationship between their areas is:
A' = k² × A
Similarly, the relationship between their perimeters is:
P' = k × P
The original rectangle has an area of 14 square centimeters.
The dilated rectangle has an area of 126 square centimeters.
We need to find the perimeter of the dilated rectangle.
Let's denote the scale factor as "k."
126 = k² × 14
Dividing both sides by 14, we get:
9 = k²
k = 3
Now, we can find the perimeter of the dilated rectangle using the perimeter relationship:
P' = k × P
The original rectangle has a perimeter of 18 centimeters, so:
P' = 3 × 18
P' = 54 centimeters
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What is the meaning of "possibly some ui are not free, or even do not occur, in ϕ"?
The phrase "possibly some ui are not free, or even do not occur, in ϕ" refers to a logical formula or expression ϕ that contains variables ui.
Answer to the aforementioned questionWhen it says "possibly some ui are not free," it means that not all of the variables ui in ϕ are unrestricted or unconstrained. Some of them may have certain conditions or restrictions placed on them within the context of the formula ϕ.
On the other hand, when it says "or even do not occur, in ϕ," it means that some variables ui may not appear at all in the formula ϕ. This implies that those variables are not present or relevant in the expression ϕ and do not play a role in its interpretation or evaluation.
In summary, the phrase indicates that in the formula ϕ, some variables ui may have restrictions or conditions placed on them, while others may not be present or relevant within the context of the formula.
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100 Points! Geometry question. Photo attached. Determine whether the pair of triangles is similar. If so, write a similarity statement. If not, what would be sufficient to prove the triangles similar? Explain your reasoning. Please show as much work as possible. Thank you!
The pair of triangles shown can be seen to be similar by SAS.
What is similarity of triangles by SAS?
When comparing two triangles, one way to tell if they are similar is to apply the SAS (Side-Angle-Side) similarity criterion. This criterion states that two triangles are comparable if they have two pairs of corresponding sides in proportion and congruent included angles between those sides.
Triangles must have an equal ratio of their matching sides' lengths. The respective sides' included angles must be equivalent.
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A triangle has sides with lengths of 3 miles, 4 miles, and 6 miles. Is it a right triangle
Yes, the given triangle is a right triangle.
We have,
This can be determined by applying the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
Now,
In this case, the squares of the side lengths are:
3² = 9
4² = 16
6² = 36
If the sum of the squares of the two shorter sides (9 + 16 = 25) is equal to the square of the longest side (36), then the triangle is a right triangle.
Thus,
In this case, since 25 is indeed equal to 36, the triangle with side lengths 3 miles, 4 miles, and 6 miles is a right triangle.
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50 Points! Multiple choice geometry question. Photo attached. Thank you!
In a rectangle, the value of x is,
⇒ x = 5
We have to given that;
ABCD is a rectangle.
And, AC = 5x + 2
BD = x + 22
Since, We know that;
Diagonal of a rectangle are equal in length.
Hence, We get;
AC = BD
(5x + 2) = (x + 22)
5x - x = 22 - 2
4x = 20
x = 20/4
x = 5
Thus, the value of x is,
⇒ x = 5
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The Survey of Study Habits and Attitudes (SSHA) is a psychological test that measures the motivation, attitude, and study habits of college students. Scores range from 0 to 200 and follow (approximately) a normal distribution with mean 115 and standard deviation σ=25
. You suspect that incoming freshman have a mean μ
which is different from 115 because they are often excited yet anxious about entering college. To test your suspicion, you test the hypotheses H0:μ=115
, Ha:μ≠115
. You give the SSHA to 25 students who are incoming freshman and find their mean score. Based on this, you reject H0
at significance level α=0.01
. Which of the following would be most helpful in assessing the practical significance of your results?
A. Take another sample and retest just to make sure the results are not due to chance.
B. Report the P-value of your test.
C. Construct a 99% confidence interval for μ
in order to see the magnitude of the difference between 115 and your sample results.
D. Test the hypotheses again, this time using significance level α=0.001
.
(b) In testing hypotheses, if the consequences of rejecting the null hypothesis are very serious, we should
A. insist that the level of significance be smaller than the P-value.
B. use a very small level of significance.
C. insist that the P-value be smaller than the level of significance.
D. use a very large level of significance.
(c) A medical researcher is working on a new treatment for a certain type of cancer. The average survival time after diagnosis on the standard treatment is two years. In an early trial, she tries the new treatment on three subjects who have an average survival time after diagnosis of four years. Although the survival time has doubled, the results are not statistically significant even at the 0.10 significance level. The explanation is
A. the calculation was in error. The researchers forgot to include the sample size.
B. the sample size is small.
C. the placebo effect is present, which limits statistical significance.
D. that although the survival time has doubled, in reality the actual increase is really two years.
a) The correct option is C. Construct a 99% confidence interval for μ in order to see the magnitude of the difference between 115 and your sample results.
b) The correct option is B. Use a very small level of significance.
c) The correct option is B. The sample size is small.
d) The lack of statistical significance at the 0.10 significance level suggests that the observed doubling of survival time may not be practically significant as the actual increase is only two years.
(a) To assess the practical significance of the results, the most helpful approach would be to construct a 99% confidence interval for the population mean, μ. This would provide a range of values within which the true population mean is likely to fall. By comparing this interval to the hypothesized value of 115, you can evaluate the magnitude of the difference and determine if it is practically significant.
Therefore, the correct option is C. Construct a 99% confidence interval for μ in order to see the magnitude of the difference between 115 and your sample results.
(b) When the consequences of rejecting the null hypothesis are very serious, it is important to be cautious and use a very small level of significance. The level of significance determines the threshold for rejecting the null hypothesis. By using a very small level of significance, you are setting a higher standard for rejecting the null hypothesis, reducing the likelihood of making a Type I error (false positive). This ensures that strong evidence is required to support rejecting the null hypothesis when the consequences are significant.
Therefore, the correct option is B. Use a very small level of significance.
(c) In this scenario, the explanation for the lack of statistical significance at the 0.10 significance level, despite the survival time doubling, is likely due to the small sample size. With only three subjects, the sample may not provide enough statistical power to detect a significant difference. The variability in survival times within the sample might also influence the lack of significance. A larger sample size would provide more reliable and statistically significant results.
Therefore, the correct option is B. The sample size is small.
d) The explanation for the lack of statistical significance in this scenario is that although the survival time has doubled from two years to four years, the actual increase is still only two years. This means that the difference between the standard treatment and the new treatment is not as substantial as it may initially seem.
When conducting statistical tests, it is important to consider both statistical significance and practical significance. While the survival time doubling may be a positive outcome, if the actual increase is only two years, it may not be considered practically significant in the context of cancer treatment.
Statistical significance is determined by conducting hypothesis tests and examining the p-value. In this case, even at the 0.10 significance level, the results are not statistically significant, indicating that the observed difference in survival times could likely be due to chance.
It is important to interpret the results in the context of the specific situation and consider factors such as sample size, variability, and clinical significance. In this case, the small sample size of three subjects may limit the statistical power to detect a significant difference. Additionally, the placebo effect or other factors may also play a role in limiting the statistical significance of the results.
In summary, the lack of statistical significance at the 0.10 significance level suggests that the observed doubling of survival time may not be practically significant as the actual increase is only two years.
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NO LINKS!!! URGENT HELP PLEASE!!!
The distance between Miami, Florida and Bermuda is about 1042 miles. The distance from Bermuda to San Juan. Puerto Rico is about 965 miles, and the distance from San Juan to Miami is about 1038 miles. Find the area of the triangle formed by the three locations.
Answer:
444523.45 square miles
Step-by-step explanation:
By using Heron's formula, we can easily find the area of the triangle formed by Miami, Bermuda, and San Juan, we need to use the lengths of the three sides of the triangle.
Let,
Side a: Distance from Miami to Bermuda = 1042 miles
Side b: Distance from Bermuda to San Juan = 965 miles
Side c: Distance from San Juan to Miami = 1038 miles
Now we can use Heron's formula to find the area of the triangle:
s =[tex]\frac{a+b+c}{2}[/tex]
s = [tex]\frac{1042 + 965 + 1038}{2}=1522.5[/tex] miles
A = [tex]\sqrt{s(s-a)(s-b)(s-c)}[/tex]
A = [tex]\sqrt{1522.5(1522.5-1042)(1522.5-965)(1522.5-1038)}=444523.45[/tex]
Therefore, the area of the triangle formed by Miami, Bermuda, and San Juan is approximately 444523.45 square miles.
Answer:
444,523.45 square miles (2 d.p.)
Step-by-step explanation:
To find the area of a triangle formed by the locations of Miami, Bermuda, and San Juan, use Heron's formula.
[tex]\boxed{\begin{minipage}{8 cm}\underline{Heron's Formula}\\\\$A=\sqrt{s(s-a)(s-b)(s-c)}$\\\\where:\\ \phantom{ww}$\bullet$ $A$ is the area of the triangle. \\ \phantom{ww}$\bullet$ $a, b$ and $c$ are the side lengths of the triangle. \\ \phantom{ww}$\bullet$ $s$ is half the perimeter.\\\end{minipage}}[/tex]
Label the three sides of the triangle as 'a', 'b', and 'c', where 'a' is the distance from Miami to Bermuda (1042 miles), 'b' is the distance from Bermuda to San Juan (965 miles), and 'c' is the distance from San Juan to Miami (1038 miles):
a = 1042 milesb = 965 milesc = 1038 milesTo find the half perimeter, s, half the sum of the three side lengths:
[tex]\implies s=\dfrac{a+b+c}{2}=\dfrac{1042+965+1038}{2}=1522.5[/tex]
Substitute the values of a, b, c and s into Heron's formula and solve for area, A:
[tex]\begin{aligned}A&=\sqrt{s(s-a)(s-b)(s-c)}\\&=\sqrt{1522.5(1522.5-1042)(1522.5-965)(1522.5-1038)}\\&=\sqrt{1522.5(480.5)(557.5)(484.5)}\\&=444523.4468348...\\&=444523.45\; \sf miles^2\;(2\;d.p.)\end{aligned}[/tex]
Therefore, the area of the triangle formed by the three locations is 444,523.45 square miles, to two decimal places.
Help
please
please
please
Answer: x=25 degrees
Step-by-step explanation:
25 degrees (blue) and x degrees (orange) are vertical angles. Vertical angles always equal each other.
(80 degrees {green} is just there to throw you off)
Graph the inequality y ≤1/3x+1
The graph of the inequality y ≤ 1/3x + 1 is added as an attachment and it is represented with option (c)
How to determine the graph of the inequalityFrom the question, we have the following parameters that can be used in our computation:
y ≤ 1/3x + 1
The above expression is an inequality that implies that
It is a linear inequalityIt has a slope of 1/3It has a y-intercept of 1The upper part and the left part of the graph is shadedNext, we plot the graph
See attachment for the graph of the inequality
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Read the description of g g below, and then use the drop-down menus to complete an explanation of why g g is or is not a function. g g relates a student to each course the student takes in a school year.
g is a function because each student is uniquely mapped to each course the student takes in a school year.
What is a function?In Mathematics and Geometry, a function refers to any mathematical equation which is typically used to define and represent a relationship that exists between two or more variables such as an ordered pair, points on a graph or table.
Based on the description of g, we can reasonably infer and logically deduce that the relation g represent a function because the input values are uniquely mapped to the output values.
In this context, we can conclude that the description of g represents a function because a student represent the input values that is being to each course (output value) the student takes in a school year.
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ONLY NEED PT 2 1st blank is: -1.5,-1.07,=0.70,-0.67,0.67,0.70,1.07,1.5,4,27,33.
2nd blank is:Means, Medians, modes, Standard deviatins, Ranges.
3rd blakn is Below, Above
4th blank is: Means, Medians, modes, Standard deviatins, Ranges.
The z-score is calculated as z-score.
The score x = 33 is 1.5 standard deviations above the mean of 27.
How to Calculate the z-score?To find the z-score for x = 33 in a normal distribution with a mean of 27 and a standard deviation of 4, we can use the formula for calculating the z-score:
z = (x - μ) / σ
where in this case, x = 33, μ = 27, and σ = 4. Plugging these values into the formula, we can calculate the z-score:
z = (33 - 27) / 4
z = 6 / 4
z = 1.5
The z-score for x = 33 is 1.5.
The z-score represents the number of standard deviations that a given value (x) is away from the mean (μ) in a normal distribution. It indicates how many standard deviations a data point is above or below the mean.
In this context, a z-score of 1.5 for x = 33 means that the value 33 is 1.5 standard deviations above the mean of 27.
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Directions: For A and B, use the given rules to write the first five terms in each
sequence. Then, use the terms to create ordered pairs for each numerical pattern.
A. Rule 1: Add 3 starting from 13.
Rule 2: 25-2x, where x is equal to 5, 6, 7, 8, 9.
Sequence 2
Sequence 1
B. Rule 1: Multiply by 3, then add 2, starting from 1.
Rule 2: Multiply by 2, then add 3, starting from 6.
Sequence 1
Sequence 2
Ordered Pair
Ordered Pair
OFFERING 50 POINTS
In solving the sequence using the provided rules, we have:
A) Sequence 1: 13, 16, 19, 22, 25.
Sequence 2: 15, 13, 11, 9, 7.
Ordered Pair: (13, 15), (16, 13), (19, 11), (22, 9), (25, 7)
B) Sequence 1: 1, 5, 17, 53, 159.
Sequence 2: 6, 15, 33, 69, 141.
Ordered Pair: (1, 6), (5, 15), (17, 33), (53, 69), (159, 141).
How to solve the sequence?Using the given rules, we can solve the sequence as follows:
A. Rule 1: Add 3 starting from 13
The first five terms in Sequence 1 would be:
13, 13 +3 = 16, 16 +3 = 19, 19 + 3 = 22, 22 + 3 = 25.
13, 16, 19, 22, 25
Using Rule 2: 25-2x, where x is equal to 5, 6, 7, 8, 9
The first five terms in Sequence 2 would be:
25 - 2(5) = 25 - 10 = 15
25 - 2(6) = 25 - 12 = 13
25 - 2(7) = 25 - 14 = 11
25 - 2(8) = 25 - 16 = 9
25 - 2(9) = 25 - 18 = 7
The ordered pairs for each numerical pattern would be:
(13, 15), (16, 13), (19, 11), (22, 9), (25, 7)
B. Rule 1: Multiply by 3, then add 2, starting from 1
The first five terms in Sequence 1:
1, (1 * 3) + 2 = 5, (5 * 3) + 2 = 17, (17 * 3) + 2 = 53, (53 * 3) + 2 = 159
Using Rule 2: Multiply by 2, then add 3, starting from 6
The first five terms in Sequence 2:
6, (6 * 2) + 3 = 15, (15 * 2) + 3 = 33, (33 * 2) + 3 = 69, (69 * 2) + 3 = 141
The ordered pairs for each numerical pattern would be:
(1, 6), (5, 15), (17, 33), (53, 69), (159, 141)
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50 Points! Multiple choice algebra question. Photo attached. Thank you!
The exact value of sin θ is 9/13.
Option A is the correct answer.
We have,
In trigonometry,
The sine function (sin) represents the ratio of the length of the side opposite an angle in a right triangle to the length of the hypotenuse.
The cosecant function (csc) is the reciprocal of the sine function, meaning it is equal to 1 divided by the sine of an angle.
In this case,
We are given that csc θ (the cosecant of θ) is equal to 13/9.
To find the value of sin θ (the sine of θ), we can take the reciprocal of csc θ. So,
sin θ = 1/(csc θ) = 1/(13/9) = 9/13.
Therefore,
The exact value of sin θ is 9/13.
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What is the unit rate if you drove a go-kart 9 miles in 36 minutes?
Answer:
Step-by-step explanation:
To find the unit rate, we need to divide the distance traveled by the time taken.
In this case, the distance traveled is 9 miles, and the time taken is 36 minutes.
Unit rate = distance/time
Unit rate = 9 miles / 36 minutes
Simplifying the above expression by dividing both numerator and denominator by 9, we get:
Unit rate = 1 mile / 4 minutes
Therefore, the unit rate at which the go-kart is traveling is 1 mile per 4 minutes.
What is the probability that either event will occur?
Now, find the probability of event A and event B.
A
B
6
6
20
20
P(A and B) = [?]
Enter as a decimal rounded to the nearest hundredth.
Enter
Answer:
0.12
Step-by-step explanation:
Given the frequencies of occurrence in the diagram, you want to know the probability of A and B.
ProbabilityThe probability of an event is the ratio of the number of times it occurs to the total number of trials.
The diagram shows the event (A and B) occurs 6 times out of a total of 6+6+20+20 = 52 trials.
P(A and B) = 6/52
P(A and B) ≈ 0.12
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What is the value of x? Show all your work.
Please help. 100 points.
Answer:
12 cm
Step-by-step explanation:
By hypotenuse theorem,
x² + 35² = 37²
x² + 35*35 = 37*37
x² + 1225 = 1369
x² = 1369 - 1225
x² = 144
x² = 12*12
x² = 12²
x = 12 cm
Find the area of the parallelogram with given points.
(7,4)
(3,0)
(-4,9)
(13,0)
The area of the parallelogram with given points is 8√26 or 40.79 square units.
How to calculate the area of this parallelogram?In Mathematics and Geometry, the area of a parallelogram can be calculated by using the following formula:
Area of a parallelogram, A = b × h
Where:
b represents the base area of a parallelogram.h represents the height of a parallelogram.Height = √[(x₂ - x₁)² + (y₂ - y₁)²]
Height = √[(3 - 7)² + (0 - 4)²]
Height = √32 units.
Base = √[(13 - 7)² + (0 - 4)²]
Base = √52 units
By substituting the given parameters into the formula for the area of a parallelogram, we have the following;
Area of a parallelogram = √32 × √52
Area of a parallelogram = 8√26 or 40.79 square units.
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