the 95% confidence interval for the mean number of years of education for lower-class respondents is (9.6032, 10.3968).
what is mean number ?
In mathematics and statistics, the "mean" typically refers to the arithmetic average of a set of numbers. To find the mean of a set of numbers, you add up all the numbers in the set and divide the total by the number of numbers in the set.
In the given question,
To calculate the 95% confidence interval for the mean number of years of education for lower-class respondents, we need the sample mean, sample standard deviation, sample size, and the t-value for the 95% confidence level with (n-1) degrees of freedom. Here are the steps to calculate the interval:
Collect the sample data of the number of years of education for lower-class respondents.
Calculate the sample mean and the sample standard deviation (s) of the data.
Determine the sample size (n) of the data.
Look up the t-value for the 95% confidence level with (n-1) degrees of freedom. For example, if the sample size is 50, then the degrees of freedom are 49, and the t-value for a 95% confidence level is 2.009 (using a t-distribution table or software).
Calculate the margin of error (ME) using the formula:
ME = t-value x (s / √(n))
Calculate the lower and upper bounds of the confidence interval using the formulas:
Lower bound = x- ME
Upper bound = x + ME
For example, suppose we have a sample of 100 lower-class respondents with a mean of 10 years of education and a standard deviation of 2 years. The degrees of freedom are 99, and the t-value for a 95% confidence level is 1.984 (using a t-distribution table or software).
ME = 1.984 x (2 / √(100)) = 0.3968
Lower bound = 10 - 0.3968 = 9.6032
Upper bound = 10 + 0.3968 = 10.3968
Therefore, the 95% confidence interval for the mean number of years of education for lower-class respondents is (9.6032, 10.3968). We can interpret this interval as follows: we are 95% confident that the true mean number of years of education for all lower-class respondents is between 9.6032 and 10.3968 years.
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Write an expression in factored form for the polynomial of least possible degree graphed below.
An expression in factored form for the polynomial of least possible degree is y(x) = (x-2)(x+2).
What is polynomial?
Polynomials can be represented in various forms, including standard form, factored form, and expanded form. Standard form is where the polynomial is written with the terms in descending order of degree, with coefficients in front of each term. Factored form is where the polynomial is written as a product of linear factors, and expanded form is where the polynomial is written out in full, with all the terms multiplied together.
A polynomial is a mathematical expression consisting of variables and coefficients, which are combined using addition, subtraction, and multiplication operations. The variables are raised to non-negative integer powers, and the highest power of the variable is called the degree of the polynomial.
For example, the polynomial 2x³ + 3x³ - 4x + 1 has degree 3, as the highest power of x is 3. The coefficients in this polynomial are 2, 3, -4, and 1.
Here, the curve touch two points (-2,0) and (2,0).
So, we can say (-2) and 2 are the root of the polynomial.
We know of a and b are two root of any polynomial then the polynomial will be (x-a)(x-b).
So, the expression is y(x) = (x-2)(x+2).
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What is 16 g as a fraction of 2 kg?
Give your answer in its simplest form.
00
Answer: 1/125 in it's simplest form
Step-by-step explanation:
Find the value of x, y, and z, in the rhombus below.
x=
-2z+8
5y-4
y =
2=
46
-2x+6
Answer:
x = 3
y = 23
z = 4
Step-by-step explanation:
To find the values of x, y, and z in the rhombus, we need to use the properties of a rhombus. One of the properties of a rhombus is that its opposite angles are equal. Another property is that its diagonals are perpendicular bisectors of each other.
Let's label the vertices of the rhombus as A, B, C, and D, and the midpoint of diagonal AC as M. We can use the given information to write some equations:
First, we know that diagonal AC is perpendicular to diagonal BD, so we have:
-2x + 6 = 0
Solving for x, we get:
x = 3
Next, we know that diagonal AC bisects angle ACD, so we have:
y = 46/2 = 23
Now, we can use the fact that AM is the perpendicular bisector of CD to find z. Since M is the midpoint of AC, we have:
AM = MC
Using the distance formula, we can find the lengths of AM and MC in terms of z:
AM = sqrt((2z-8)^2 + (5y-4)^2)
MC = sqrt((8-2z)^2 + (5y-4)^2)
Setting these two expressions equal to each other, we get:
sqrt((2z-8)^2 + (5y-4)^2) = sqrt((8-2z)^2 + (5y-4)^2)
Simplifying this equation, we get:
4z - 16 = 16 - 4z
8z = 32
z = 4
Therefore, the values of x, y, and z are:
x = 3
y = 23
z = 4
So, the solution is x=3, y=23, and z=4.
Lisa will rent a car for the weekend. She can choose one of two plans. The first plan has an initial fee of $55 and costs an additional $0.13 per mile driven. The second plan has an initial fee of $48 and costs an additional $0.15 per mile driven.
For what amount of driving do the two plans cost the same?
What is the cost when the two planes cost the same?
Answer:
Step-by-step explanation:
To find the point at which the two plans cost the same, we can set their total costs equal to each other:
55 + 0.13x = 48 + 0.15x
Simplifying and solving for x, we get:
0.02x = 7
x = 350
Therefore, the plans will cost the same when Lisa drives 350 miles.
To find the cost at this point, we can substitute x=350 into either equation. Let's use the first plan:
Total cost = 55 + 0.13(350) = $97.50
Therefore, if Lisa drives 350 miles, the cost for either plan will be $97.50.
Help please if you can.
Answer:
24/91
Step-by-step explanation:
We can see that the square on the right has a side length of 24 and the square on the left has a side length of 91.
The scale factor = square on right/square on left = 24/91
If tan (theta) = A, sin(theta)= B, then:
a. sin(-theta)=
C. cos(theta + 2pie) =
b. tan(-theta)=
d. tan(theta + pie)=
The answer of the given question based on the trigonometric identities is , A. sin(-Θ) = -B , b. tan(-Θ) = -A , C. cos(Θ + 2π) = B/√(A² + B²) , D. tan(Θ + π) = -A.
Trigonometric identities: what are they?Trigonometric identities are equations in mathematics that use trigonometric functions and hold true regardless of the value of the variables. These identities can be applied to simplify or alter trigonometric expressions, as well as to trigonometric function-based equations.
To determine the required values, we can utilise sine and tangent definitions along with trigonometric identities:
a. sin(-Θ) = -sin(Θ) = -B (using the property that sine is an odd function)
b. tan(-Θ) = -tan(Θ) = -A (using the property that tangent is an odd function)
c. cos(Θ + 2π) = cos(Θ) = B/√(A² + B²) (using the Pythagorean identity, since cos²(Θ) + sin²(Θ) = 1)
d. tan(Θ + π) = (tan(Θ) + tan(π))/(1 - tan(Θ)tan(π) = (-A + 0)/(1 + A0) = -A
Therefore, the values are:
a. sin(-Θ) = -B
b. tan(-Θ) = -A
c. cos(Θ + 2π) = B/√(A² + B²)
d. tan(Θ + π) = -A
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The complete question is:
If tan (θ) = A, sin(θ)= B,
Then find the following:
a. sin(-θ)=
b. tan(-θ)=
c. cos(θ+ 2π) =
d. tan(θ+ π)=
The answer of the given question based on the trigonometric identities is , A. sin(-Θ) = -B , b. tan(-Θ) = -A , C. cos(Θ + 2π) = B/√(A² + B²) , D. tan(Θ + π) = -A.
Trigonometric identities: what are they?Trigonometric identities are equations in mathematics that use trigonometric functions and hold true regardless of the value of the variables. These identities can be applied to simplify or alter trigonometric expressions, as well as to trigonometric function-based equations.
To determine the required values, we can utilise sine and tangent definitions along with trigonometric identities:
a. sin(-Θ) = -sin(Θ) = -B (using the property that sine is an odd function)
b. tan(-Θ) = -tan(Θ) = -A (using the property that tangent is an odd function)
c. cos(Θ + 2π) = cos(Θ) = B/√(A² + B²) (using the Pythagorean identity, since cos²(Θ) + sin²(Θ) = 1)
d. tan(Θ + π) = (tan(Θ) + tan(π))/(1 - tan(Θ)tan(π) = (-A + 0)/(1 + A0) = -A
Therefore, the values are:
a. sin(-Θ) = -B
b. tan(-Θ) = -A
c. cos(Θ + 2π) = B/√(A² + B²)
d. tan(Θ + π) = -A
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The complete question is:
If tan (θ) = A, sin(θ)= B,
Then find the following:
a. sin(-θ)=
b. tan(-θ)=
c. cos(θ+ 2π) =
d. tan(θ+ π)=
If your claim is in the alternative hypothesis and you reject the null hypothesis, then your conclusion would be:
O The sample data support the original claim
O There is sufficient evidence to warrant rejection of the original claim
O There is not sufficient evidence to warrant rejection of the original claim
O There is not sufficient sample evidence to support the original claim
The value of your conclusion would be:
⇒ There is sufficient evidence to warrant rejection of the original claim
We have to given that;
For your claim is in the alternative hypothesis and you reject the null hypothesis.
Hence, We know that;
If your claim is in the alternative hypothesis and you reject the null hypothesis, There is sufficient evidence to warrant rejection of the original claim
Thus, The correct option is, B.
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Given the functions f(x)=1x+2 and g(x)=x2−2x, what is the domain of the composition (f∘g)(x)?
Responses
x≠−2 and x≠0
x is not equal to negative 2, and , x is not equal to 0
x≠0
x is not equal to 0
all real numbers
all real numbers
x≠−2
x is not equal to negative 2
Considering both functions, there are no restrictions or exclusions for any real number values in the domain. Therefore, the domain of the composition (f∘g)(x) is all real numbers.
To determine the domain of the composition (f∘g)(x), we need to consider the domains of both functions f(x) and g(x) and determine any restrictions.
The function f(x) =[tex]1x + 2[/tex] does not have any explicit restrictions on its domain. It is defined for all real numbers.
The function g(x) = [tex]x^2 - 2x[/tex] is a quadratic function. Quadratic functions are defined for all real numbers, so there are no restrictions on the domain of g(x).
When we compose functions, we need to ensure that the output of the inner function is within the domain of the outer function. In this case, the composition (f∘g)(x) means we substitute g(x) into f(x), resulting in f(g(x)).
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The hypotenuse of a right triangle measures 13 cm and one of its legs measures 12 cm. Find the measure of the other leg. If necessary, round to the nearest tenth.
Answer:
5 cm
Step-by-step explanation:
Given two sides of a right triangle, we can find the other side using the Pythagorean theorem, which is
[tex]a^2+b^2=c^2[/tex], where a and b are any of the two legs (e.g., you can set 12 can be a or b) and c is the hypotenuse.
If we allow 12 to b a and 13 to be c, we can solve for b, which is the measure of the other side:
[tex]12^2+b^2=13^2\\144+b^2=169\\b^2=25\\b=5\\b=-5[/tex]
When taking the square root of a number, you always get a negative number and a positive number, since squaring a negative gives a positive answer (e.g. 5^2 = 25 and (-5)^2 = 25). However, because you can't have a negative answer, the answer is simply b = 5 cm
We can even check our answer by making sure that the sum of the square of the two legs equals the square of the hypotenuse:
[tex]12^2+5^2=13^2\\144+25=169\\169=169[/tex]
help help help help
A kite flying in the air has a 75-foot string attached to it, and the string is pulled taut. The angle of elevation of the kite is 41 degrees. Find the height of the kite. Round your answer to the nearest tenth.
The height of the kite is 49.2 foot.
We have,
A kite is flying in the air has a 41 ft string attached to it.
The angle of elevation of the kite is 47 degrees.
Using Trigonometry
sin 41 = P/H
sin 41 = P/ 75
0.6560 = P / 75
P = 49.2 foot
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Find the area of parallelogram WXYZ. Round your answer to the nearest tenth if
necessary.
21 in
18 in
21 in
23.2 in
23.2 in
Answer:
area of parallelogram=
base x height
21 in x 18 in
378 in
rounded to nearest ten
380 inches square.
Tom and Philip were given the graph of a linear function and asked to find the slope. Tom says that the slope is 12 while Philip says that the slope is 2.
Which reason correctly justifies Tom's answer?
The cost that a recycling company charges is directly proportional to the number of recycling bins collected. The cost is $33 for each bin.
A: Write a direct variation equation to represent the cost.
B: How many bins can a customer pay the company to collect the bins for $500? Write and solve the equation.
C: Suppose the customer plans to tip the recycling company $30, how many bins can the customer get removed for $500 now? Write and solve the equation.
a) The direct variation equation is y = 33x.
b) The customer can pay the company to collect 15 bins.
c) The customer can get approximately 16 bins (rounded to the nearest whole number) removed for $500 with a $30 tip included.
A) The direct variation equation to represent the cost would be y = kx, where y represents the cost, x represents the number of bins collected, and k is the constant of proportionality. In this case, since the cost is $33 for each bin collected, the value of k is 33. Therefore, the direct variation equation is y = 33x.
B) To find the number of bins a customer can pay the company to collect for $500, we can set the cost (y) equal to $500 and solve for x (the number of bins). Thus, we have:
y = 33x
500 = 33x
x = 500/33
x ≈ 15.15
Therefore, the customer can pay the company to collect 15 bins (rounded to the nearest whole number) for $500.
C) If the customer plans to tip the recycling company $30, the total cost would be $500 + $30 = $530. We can set the cost (y) equal to $530 and solve for x:
y = 33x + 30
530 = 33x + 30
500 = 33x
x ≈ 15.91
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can someone help please it’s due at 12
angle 1 = 180 - 74 the angle on a straight line is given as 180
= 106 degrees
What are alternate angles?Alternate angles are a pair of angles formed by a transversal intersecting two parallel lines. These angles are located on opposite sides of the transversal and on opposite sides of the parallel lines.
The alternate angles are congruent, which means they have the same measure or degree. In other words, if one alternate angle measures x degrees, then its corresponding alternate angle will also measure x degrees.
angle 2 = angle 1
They are vertical angles hence they are equal
angle 3 = 74 degrees
They are vertical angles as well
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What is the solution of log(f-3)-log(17-40)?
04
05
O 15
O 20
The solution of the given logarithm function log(f-3)-log(17-40) is
f < 3.
So no option is correct.
What is a logarithm function?A logarithm function is a mathematical function that describes the relationship between a given number (called the argument or input) and a specified base. The logarithm of a number x with respect to a base b is the power to which b must be raised to give x.
In other words, if we have the equation y = log_b(x), then y represents the power to which the base b must be raised to get x. For example, if b=2, then log_2(8) = 3 because 2 raised to the power of 3 equals 8.
According to the given informationThe given expression is:
log(f-3)-log(17-40)
We can simplify this expression using the property of logarithms:
log(a) - log(b) = log(a/b)
So, we get:
log((f-3)/(17-40))
Now, for this expression to have a real solution, the argument of the logarithm must be positive, so we have:
(f-3)/(17-40) > 0
Solving for f, we get:
f - 3 < 0 (since 17-40 is negative)
f < 3
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Here's a graph of a linear function. Write the
equation that describes that function.
Express it in slope-intercept form.
Enter the correct answer.
DONE
The equation of this graphed line is equal to y = x/2 - 5.
How to determine an equation of this line?In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):
y - y₁ = m(x - x₁)
Where:
m represent the slope.x and y represent the points.First of all, we would determine the slope of this line;
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Slope (m) = (-1 + 5)/(8 - 0)
Slope (m) = 4/8
Slope (m) = 1/2.
At data point (0, -5) and a slope of 1/2, a linear equation in slope-intercept form for this line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y - (-5) = 1/2(x - 0)
y + 5 = x/2
y = x/2 - 5
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simplify 7(x-2y)-5(x-3y)
[A] x+2y
[B] x+y
[C] 2x+y
[D] 2x-y
Answer:
The answer is **C. 2x+y**
* Expand the parentheses: 7x-14y - 5x+15y
* Combine like terms: 2x+y
Here is the step-by-step solution:
1. Expand the parentheses:
```
7(x-2y)-5(x-3y)
= 7x-14y - 5x+15y
```
2. Combine like terms:
```
= (7x-5x) + (-14y+15y)
= 2x + y
```
Step-by-step explanation:
Answer:
Let's simplify the expression step by step:
7(x - 2y) - 5(x - 3y)
= 7x - 14y - 5x + 15y (distributing the 7 and -5)
= 2x + y (combining like terms)
Therefore, the simplified expression is 2x + y, which corresponds to option [C].
Step-by-step explanation:
Probability problem pls help me
Where is the question?
Triangle D has been dilated to create triangle D′. Use the image to answer the question. image of a triangle labeled D with side lengths of 6, 8, 10 and a second triangle labeled D prime with side lengths of 18, 24, 30 Determine the scale factor used. one half 2 3 one third
Dilating a shape will proportionately affect its side lengths.
To find the scale factor between the given triangles, take one side on the larger triangle and divide it by the corresponding side on the smaller triangle. I will divide the triangles' top sides (24 and 8).
[tex]\text{scale factor}=\dfrac{24}{8} =3[/tex]
So, the scale factor used was 3.
Answer: 3
Step-by-step explanation:
I took the quiz so you do not have to!
Jeremiah needed dog food for his new puppy. He compared the prices and sizes of three types of dog food.
Canine Cakes Bark Bits Woofy Waffles
Size (pounds) 30 40 28
Cost $54 $70 $42
Part A: Calculate the corresponding unit rate for each package. (9 points)
Part B: Determine the best buy using the unit rates found in Part A. Explain your answer.
------------------------------------------------------------------
The table shows the grading scale for Ms. Gray's social studies class.
A 90%–100%
B 80%–89%
C 70%–79%
Part A: Pick a number between 21 and 29. This number will represent how many points you earned. If you have a pop quiz worth a total of 30 points, using the number you selected, calculate the percentage you earned on the test. Show each step of your work. (8 points)
Part B: Based on the percentage found in Part A, would you earn a grade of A, B, or C using the grading scale provided? Explain your answer.
Answer:
see explanation
Step-by-step explanation:
Part A:
54$ for 30 pounds = 54/30 = 9/5 dollars per pound
70$ for 40 pounds = 70/40 = 7/4 dollars per pound
42$ for 28 pounds = 42/28 = 3/2 dollars per pound
Part B:
3/2 = 1.5 ($/lb)
7/4 = 1.75 ($/lb)
9/5= 1.8 ($/lb)
The best buy is Woofy Waffles for 1.5 $ per pound
please help i dont know what it is i think 324 but someone let me know how to do it
Answer: 3
Step-by-step explanation:
A = 3 × (1ft)²
A = 3 × 1 ft²
A = 3ft²
Show that each equation is true. ( 1 - 3 )
Find the exact value of x. ( 4 - 6 )
The lengths of x of the right angle triangle using pythagoras theorem are:
x = 5
x = 3
x = 10
How to use Pythagoras Theorem?Pythagoras Theorem is defined as the way in which you can find the missing length of a right angled triangle.
The triangle has three sides, the hypotenuse (which is always the longest), Opposite (which doesn't touch the hypotenuse) and the adjacent (which is between the opposite and the hypotenuse).
Pythagoras is in the form of;
a² + b² = c²
4) Applying Pythagoras theorem, we can find x as:
x = √(13² - 12²)
x = √(169 - 144)
x = √25
x = 5
5) Applying Pythagoras theorem, we can find x as:
x = √(5² - 4²)
x = √9
x = 3
6) Applying Pythagoras theorem, we can find x as:
x = √(8² - 6²)
x = √100
x = 10
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The accompanying data represent women's median earnings as a percentage of men's median earnings for recent years beginning with 1989. Is there a trend? How does it appear to affect women? Construct a time-series graph. Median Earnings Year Median Earnings 1989 1990 1991 1992 1993 1994 1995 1996 1997 59.2 60.1 62.3 61.7 62.5 61.7 61.7 65.0 67.0 Year 1998 1999 2000 2001 2002 2003 2004 2005 Median Earnings 65.6 62.9 63.3 61.5 65.2 63.9 66.7 68.8 Full data set 0 www X C. Median Earnings 70- 64- 584 1989 1997 Year 2005 Clear all Final check
Time Series Graph: Plot A
Based on the above plot, earnings first rise till 1997, and then start falling till 2001. After 2001, earnings start rising again. So overall there is an upward trend.
Why is option A the answer?Based on these observations, the answer is Option A, which says:
Option A: There is a general upward trend though there have benn some down years. An upward trend would be helpful to women so that their earnings become equal to those of men.
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there are how many distinct website graphics to be created?
According to the question there are 35 distinct website graphics that can be created by using at least four of seven different bitmap images.
What is website?A website is a collection of related web pages, images, videos, and other digital assets that are hosted on a web server and can be accessed by users over the internet. A website is typically identified by a unique domain name and can be accessed by typing the URL into a web browser.
Using the formula for calculating the number of combinations of size k from a set of size n (n choose k), we can calculate the number of distinct website graphics that can be created by using at least four of seven different bitmap images as follows:
n = 7 (7 different bitmap images)
k = 4 (at least 4 of the 7 bitmap images)
Number of distinct website graphics = (7 choose 4) = 35
Therefore, there are 35 distinct website graphics that can be created by using at least four of seven different bitmap images.
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Find the value of x in this problem
Answer: The value of x will be equal to 5.
Step-by-step explanation:
1. Since all the angles of the given triangle is equal it proves to be an Equilateral Triangle.
2. Now as all the angles are equal the length of side will be equal too.
3. Equating both equations: 3x-3 = 2x+2
3x-2x = 3+2 => x = 5.
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trell is working in a lab testing bacteria populations. After starting out with a population of 404 bacteria, he observes the change in population and notices that the The population doubles every 36 minutes. tep 1 of 2: Find the equation for the population P in terms of time t in minutes.
We can actually see here that the equation for the population P in terms of time t in minutes will be: P = 404 × 2^(t/36).
How we arrived at the solution?We can see here that looking at the change in population, we can use the following:
P = P₀ × 2^(t/Δt).
Where:
P₀ = initial population = 404 bacterias
t = time elapsed (in minutes).
Δt = time it takes for the population to double (36 minutes).
Thus, we see that substituting this, we have:
P = 404 × 2^(t/36).
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7-1 Additional Practice
1. A random selection will be made from a bug containing different
colored disks. Of the 25 disks in the bag, 5 are yellow,
30 P(yellow)
a. The probability that a yellow disk will be selected is Ois 2
How come the answer is 2?
based on the information provided, the probability of selecting a yellow disk is 1/5 or 0.2.
How to solve the problem?
The probability of selecting a yellow disk cannot be 2, as probabilities must always be between 0 and 1.
To calculate the probability of selecting a yellow disk, we can use the formula:
P(yellow) = number of yellow disks / total number of disks
From the information given, we know that there are 5 yellow disks and 25 total disks in the bag. Plugging these values into the formula gives:
P(yellow) = 5/25 = 1/5
Therefore, the probability of selecting a yellow disk is 1/5 or 0.2, which is a decimal value between 0 and 1.
It's possible that there was a typo in the original question or answer, or that some other context is missing which would make sense of the answer being 2. However, based on the information provided, the probability of selecting a yellow disk is 1/5 or 0.2.
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Probability problem pls help me
The probability that the number generated is:
1). 94 = 1/4, (2). even = 1/4, (3). odd = 0, (4). less than 32 = 1/25, and (5). greater than 74 = 1/25.
What is probabilityThe probability of an event occurring is the fraction of the number of required outcome divided by the total number of possible outcomes.
The total possible outcome = 10
probability of generating 94 = 5/10 × 5/10 = 1/4
probability of generating an even number = 5/10 × 5/10 = 1/4 {all numbers ending with 0,2,4,6, and 8 must be even}
probability of generating an odd number = 0 {since the second digit must be from 0,2,4,6, and 8, hence no odd number can be generated}
probability of generating less than 32 = 2/10 × 2/10 = 1/25 {since the first digit must either be 1 or 3, while the second digit must be either 0 or 2}
probability of generating greater than 72 = 2/10 × 2/10 = 1/25 {since the first digit must either be 7 or 9, while the second digit must be either 6 or 8}.
Therefore, the probability that the number generated is:
1). 94 = 1/4, (2). even = 1/4, (3). odd = 0, (4). less than 32 = 1/25, and (5). greater than 74 = 1/25.
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sqrt y^6 where y is greater than or equal to 0
Simplifying the expression √y⁶ for y is y³
Simplifying the expression for yFrom the question, we have the following parameters that can be used in our computation:
sqrt y^6
Rewrite the expression using numbers and mathematical symbol
So, we have
√y⁶
Take the square root of both sides
So, we have
√y⁶ = y³
Hence, the solution to the expression √y⁶ is y³
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If the difference of two numbers is less than the sum of the numbers, which of the following must be true.
F. Neither number is positive
G. At least one of the number is positive
H. Exactly one of the number is positive
J. Both numbers are positive
K. None of these statement must be true
True, option (G) is which is - at least one of the numbers is positive.
Define term positive integer number?A positive integer is a whole number greater than zero, i.e., any number that can be expressed without fractions or decimals, and is greater than zero.
If the difference of two numbers is less than the sum of the numbers, it is always true that at least one of the numbers is positive. As a result, "At least one of the numbers is positive" is the response, which is (G).
Here we assume that x and y are two numbers. The difference between the two numbers is |x - y|, which is always positive.
Now, according to the given condition:
|x - y| < x + y
Simplifying this inequality, we get:
-x + y < x + y
2y > 0
Dividing both sides by 2, we get:
y > 0
Therefore, we can conclude that at least one of the numbers (y) is positive. Note that it is possible for both numbers to be positive or for one number to be positive and the other to be zero.
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