Select all true statements if n || m.
Parallel lines M and N cut by two transversals, A B and B C. Along line M, three angles are labeled 2, 3, and 4, which together form a straight angle. Transversal A B forms two angles below line N, one labeled 20 degrees and the other labeled A. Together, these angles form a straight angle. Transversal B C forms two angles below line N, one labeled C and the other labeled 60 degrees. Together, these angles form a straight angle. Angle 1 is vertical to the 60-degree angle and is an alternate interior angle to angle 4. Together, angles 1, 3, and an unlabeled angle that is vertical to the 20-degree angle form a triangle between the two parallel lines.
A. m∠2 = 60°
B. m∠3 = 100°
C. m∠2 + m∠4 = 80°
D. m∠2 + m∠3 = 80°
E. m∠2 = 20°
Answers
Answer:
Hi, the correct answer is A) m∠2 = 60°.
let me put it in this way.
Step-by-step explanation:
Since parallel lines M and N are cut by transversals A B and B C, corresponding angles are formed. Corresponding angles are pairs of angles that are formed by intersecting lines and are on opposite sides of the transversal. In this case, angles 2 and C are corresponding angles, as are angles 3 and A.
We know that angles 2 and C form a straight angle along line M, and angles C and 60 degrees form a straight angle along line N. Since corresponding angles are congruent (have the same measure), this means that angle 2 must have the same measure as the 60-degree angle
Related Questions
Stephen's current average weekly net pay is $354.76. The van he wants to purchase has monthly payments of $325.00. Which inequality correctly shows the comparison between 15% of Stephen's average monthly net pay and the monthly van payment? (4 points)
$212.86 ≥ $325.00
$212.86 ≤ $325.00
$230.59 ≤ $325.00
$230.59 ≥ $325.00
Answers
Stephen's current average weekly net pay is $354.76. The van he wants to purchase has monthly payments of $325.00. the inequality that correctly shows the comparison between 15% of Stephen's average monthly net pay and the monthly van payment is $212.86 ≤ $325.00
How to find the inequalityInformation given in the question
Stephen's current average weekly net pay is $354.76
The van he wants to purchase has monthly payments of $325.00.
the inequality that compares 15% of Stephen's average monthly net pay and the monthly van payment = ?
A weekly pay of $354.76 getting the monthly pay is
= 4 * $354.76
= $1419.04
15% of the monthly pay
= 0.15 * $1419.04
= 212.856
= $212.86
This amount is less than $325.00 which is monthly payment for the van hence $212.86 ≤ $325.00
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What is the percent of increase from 24 to 42?
Write your answer using a percent sign (%).
Submit
Answers
Answer:
42.86%
Explanation:
First, we subtract the two numbers.
42 - 24 = 18
Now we divide this to the original number.
18 / 42 = 0.4285714286
Multiply by 100:
42.85714286
So, the percent increase is approximately 42.86%
O
Yaritza made 25% of her free throws over the season. If she shot 160 free throws, how
many did she make?
Divide/scale down to solve for the missing percent.
attempts
percent
Submit Answer
25
BB
A
160
100
0
attempt 1 out of 2 by
Answers
Yaritza made 25% of her free throws over the season. If she shot 160 free throws, 40 many did she make. Using the concept of percentage.
What is Percentage?When a fraction of a whole is represented as a number between 0 and 100, it is called a percentage. All of something is 100 percent, half of it is 50 percent, and none of it is 0%. To calculate a percentage, multiply the result by 100 after dividing the part of the whole by the entire.
When the denominator is 100, percentages are really just fractions. The percent sign (%) is placed next to a number to indicate that it is a percentage. For instance, you would have received a 75% on the examination if you correctly answered 75 out of 100 questions (75/100).
An easy way to solve this problem is by first finding 50%.
To find 50% of 160
= 160 × (50/100)
= 80
So, 160.0 becomes 80.
Then, because 25% is half of 50% to find the answer divide 80 by 2.
Therefore, Yaritza made 40 of her 160 free throws.
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a varies inversely as the square of b. If a is 1 when b is 3, find a when b is 5
The distance it takes to stop a car varies directly as the square of the speed of the car. If it takes 112 feet for a car traveling at 40 miles per hour to stop, what distance is required for a speed of 65 miles per hour?
*
Answers
a. The inverse variation relationship between a and b can be expressed as a = k/b^2, where k is a constant. We are given that a is 1 when b is 3, so we can substitute these values into the equation to find k: 1 = k/(3^2). Solving for k, we get k = 9.
Substituting this value of k back into the equation a = k/b^2, we can find a when b is 5: a = 9/(5^2) = 9/25 = 0.36. Therefore, a is 0.36 when b is 5.
b. To find the distance it takes for a car traveling at 65 miles per hour to stop, we can use the equation for direct variation: d = kv^2, where d is the distance, v is the speed, and k is a constant. We are given that it takes 112 feet for a car traveling at 40 miles per hour to stop, so we can substitute these values into the equation to find k: 112 = k(40^2). Solving for k, we get k = 0.0056.
Substituting this value of k back into the equation d = kv^2, we can find the distance it takes for a car traveling at 65 miles per hour to stop: d = 0.0056(65^2) = 2256 feet. Therefore, it takes 2256 feet for a car traveling at 65 miles per hour to stop.
For each of the statements below, is it true with Correlation, Regression, Both, or Neither? Please explain. Thank You!
1. Requires a measure for both variables'individual variances
2. Can be tested for statistical significance
3. Provides a way to predict a specific value of one variable (such as weight) from the value of another variable (such as height)
Answers
1. Correlation is a bivariate analysis that measures the strength of association between two variables and the direction of the relationship. Regression is a statistical method to determine the strength and character of the relationship between one dependent variable and a series of other variables (known as independent variables). So, both correlation and regression require a measure for both variables individual variances.
2. We can test for the statistical significance of a correlation coefficients by performing a hypothesis test on the correlation coefficients. And it's also possible to perform hypothesis tests on the regression slope on the values which is being estimated using a regression analysis. So, both correlation and regression can be tested for statistical significance.
3. Correlation helps us to test the strength of association between two variables. But regression helps us to predict one of the variables from the other. So, it is true for a regression. It is only regression which provides a way to predict a specific value of one variable from the value of another variable.
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A standard normal distribution has the following characteristics O the mean and the variance are both equal to 1 O the mean and the variance are both equal to 0 O the mean is equal to the variance the mean is equal to 0 and the variance is equal to 1 the mean is equal to the standard
Answers
A standard normal distribution's characteristics are its mean is equal to 0 and the standard deviation is 1. Thus, the variance is equal to 1.
What is a standard normal distribution?A normal distribution that has a mean value of 0 and a standard deviation or a variance of 1 is said to be a standard normal distribution.
I.e., μ = 0 and σ² = 1
This is also called z-distribution.
Calculation:A standard normal distribution has μ = 0 and σ² = 1.
So, the probability of a normal random variable is calculated by using a z-score.
The z-score value is calculated by the formula
z = (X - μ)/σ
Where mean (μ) and standard deviation (σ) for the variable X
By using the standard normal distribution tables with the z-score and probabilities, the required values are calculated.
So, we can conclude that the major characteristics of a standard normal distribution are mean = 0 and variance = 1.
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Teacher's Salary The average teacher's salary in a particular state is $54,137.
If the standard deviation is $10,450, find the salaries corresponding to the following z scores.
Answers
The salary corresponding to z=1 is $64587 if the average teacher's salary in a particular state is $54,137.
What is z-score?A Z-score is a metric that quantifies the connection between a value and the mean of a set of values. The Z-score is measured as the standard deviations from the mean. If the Z-score is 0, A data point's score is the same as the mean score. In statistics, a raw score's value that deviates or surpasses the mean of the phenomenon being observed or measured is referred to as the standard score. Raw scores above the mean are given positive standard scores, whilst raw values below the mean are given negative standard ratings.
The pay is 1 standard deviation above the mean, according to a z score of 1.
Therefore, the salary for a z-score of 1 is:
$54,137 + 1($10,450) = $64587
Therefore, the salary corresponding to z=1 is $64587
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A barn is in the shape of a pentagonal prism with the dimensions shown. The volume of the barn is 9072 cubic feet. Find the dimensions of each half of the roof.
(Help I cannot solve this-)
Answers
According to the given information the dimensions of each of the roof is 12 feet.
Mathematical concepts include volume.The amount the three-dimensional space that's also occupied is measured in volume. To define it quantitatively, a variety of imperial either Us or metric system, in addition to SI-derived units such as the cubic meter but instead liter), are widely utilized. A symbiotic relationship exists between volume and length (cubed).
What does mathematic volume mean?Mathematics refers to volume as the measurement of internal space in a specific 3D object. A fish tank, for instance, is three feet long, one foot broad, and two feet high. Expanding the length, that width, and the height results in the volume, which is equal to six when 3x1x2 is used. Consequently, the fish tank can hold 6 cubic feet of water.
Briefing:According to the given picture
a = 18 ft,
b = 8ft,
c = 36ft and h = x
[tex]\begin{matrix}V=a\times b\times c+\frac{a\times h}{2}\times c\\\9072=18\times8\times36+\frac{18\times x}{2}\times36\\9072=5184+324\times x\\\x=12\\\end{matrix}[/tex]
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Answer: 15
Step-by-step explanation: I submitted 12 and that was wrong, answer is 15
Find the value of x. Hint: use the Exterior Angle Theorem
Answers
The value of x using Exterior Angle Theorem is 9.
What is the exterior angle of theorem?
The measure of an exterior angle is equal to the sum of the measures of the two opposite(remote) interior angles of the triangle, according to the external angle theorem. A triangle contains three internal angles, all of which add up to 180 degrees. This theorem is applied to each of the outer angles, which total six. As they constitute a linear pair of angles, take note that an exterior angle is supplementary to the neighbouring interior angle. Exterior angles are those that are created between a polygon's side and its extended neighbouring side.Interior 2 angle = exterior angle
32° + (6x -2)° = 9x + 3
32° + 6x -2° = 9x + 3
30° - 3° = 9x - 6x
3x = 27°
x = 9
Hence, the value of x using Exterior Angle Theorem is 9.
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Show that if f is a function from S to T, where S and T are finite sets with |S| > |T |, then there are elements s₁ and s₂ in S such that f(s₁) = f(s₂), or in other words, f is not one-to-one.
Answers
The function f : S--> T is not a one to one function
Given :
f : S --> T
S and T are finite sets with |S| > |T|
To proof : f is not one-one function
Let us assume for the sake of contradiction that f is one to one function
Let n and m be positive integers such that |S| = n and |T| = m.
Note that these integers need to exist as S and T are finite sets
n > m
Let S = {s1 , . . . , sn} and T = { t1 , . . . , tm}
Without loss of generality , we can assume that f(si) = ti , for i = 1, 2, 3 ....
as each element needs to have a unique image ( since , f is one to one ) and we can rename the element t1 , . . . , tm if the order of the elements didnt match up the images.
Since , n > m we have a term sm+1 while we do not have a term t m+1 .
This implies that sm+1 needs to have a same image as some sk
f(sm+1) = f(sk) = tk
However , f(sm+1) = f(sk) = tk is then in contradiction with the fact that f is one-to-one.
Since , we derive a contradiction our assumption that f is one-to-one is incorrect and thus f is not one-to-one
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PLEASE ANSWER CLEARLY WITH THE EQUATION
A group of college students are going to a lake house for the weekend and plan on renting small cars and large cars to make the trip. Each small car can hold 5 people and each large car can hold 7 people. The students rented 2 more small cars than large cars, which altogether can hold 46 people. Write a system of equations that could be used to determine the number of small cars rented and the number of large cars rented. Define the variables that you use to write the system.
Answers
There were 6.75 small cars rented and 1.75 large cars total were rented.
How to find the Equation?Let x represent the quantity of little cars rented, and y represent the quantity of big cars rented.
The system of equations below is based on the statements that have been provided:
5x + 8y = 51
x = y + 5
If we replace (1) with the value of x from (2), we get
5(y+5) + 7y = 46
5(y) + 5(5) + 7y = 46
5y + 25 + 7y = 46
12y = 46 -25
12y = 21
y = 1.75
Adding the value of y to (2) yields x = 1.75 + 5 = 6.75.
There were 6.75 small cars rented.
1.75 large cars total were rented.
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Hannah wants to have $ 5500 to help pay for a new deck in 10 years. If she wants to put her money into an account earning 5.5% interest compounded continuously, how much should she invest now, so that she will have $ 5500 in 10 years?
Payment amount =
Answers
[tex]~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$5500\\ P=\textit{original amount deposited}\\ r=rate\to 5.5\%\to \frac{5.5}{100}\dotfill &0.055\\ t=years\dotfill &10 \end{cases} \\\\\\ 5500=Pe^{0.055\cdot 10} \implies \cfrac{5500}{e^{0.055\cdot 10}}=P\implies 3173.22\approx P[/tex]
1. A basketball player made 12 out of 15 free throws she attempted. She wants to know how many consecutive free throws she would have to make to raise the percent of successful free throws to 85%. (a) Write an equation to represent this situation. (b) Solve the equation. How many consecutive free throws would she have to make to raise her percent to 85%? Answer:
Answers
Basketball player have to make 5 successful consecutive throws to make to raise her percent to 85%.
What is percentage?Percentage is a part of the whole number. It is denoted by % sign.
1 %= 1/100.
Given that,
Basketball player makes 12 out of 15 free throws she attempted.
The percentage of successful throws = (12/15)x100 = 75%
Let n consecutive free throws she has to make to increase the percentage of successful throws to 85%,
Implies that,
(12+n)/ (15+n) = 85/100
(12+n)/ (15+n) = 17 /20
240 + 20n = 255 + 17n
3n = 15
n = 5
Basketball player have to make 5 successful consecutive throws to make to raise her percent to 85%.
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Solve for Input of Function Given Output
Given } h(x)=-3 x-5 solve for x when } h(x)=-2
Answers
Step-by-step explanation:
put the value of h(x) in the function like in the above figure.
give the component from the following vectors shown
Answers
Answer:
[tex](-3, 4)[/tex]
Step-by-step explanation:
The horizontal component is [tex]-3[/tex] and the vertical component is [tex]4[/tex]
The component (-3, 4) from the given vectors are shown in the graph.
What are vectors linearly independent and dependent?Let A = v 1, v 2,..., v r be a collection of vectors from Rn. If r > 2 and at least one of the vectors in A can be expressed as a linear combination of the others, A is said to be linearly dependent. The rationale for this description is straightforward: at least one of the vectors is dependent (linearly) on the others. If no vector exists in A, the set is said to be linearly independent. It is also usual to state "the vectors are linearly dependent (or independent)" rather than "the set comprising these vectors is linearly dependent (or independent)."
We have been given that the graph in the question
Here v = -3i + 4j
This means the component (-3, 4) of the provided vectors.
Therefore, the required component (-3, 4) from the provided vectors are depicted in the graph.
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The value of a car can be represented by the equation V = 16,000(0.93)t, where V is the value of the car and t is the age of the car in years. What is the meaning of the number 0.93 in the equation?
As the age of the car increases by 1 year, the value of the car decreases by $ 93.
As the age of the car increases by 1 year, the value of the car decreases by 7%.
As the age of the car increases by 1 year, the value of the car decreases by $ 7.
As the age of the car increases by 1 year, the value of the car decreases by 93%.
Answers
As the age of the car increases by 1 year, the value of the car decreases by 7%. The correct option is B.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the value of a car can be represented by the equation V = 16,000(0.93)t, where V is the value of the car and t is the age of the car in years.
As the age of the car increases by 1 year, the value of the car decreases by 7%. The correct option is B.
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Mariam has $520 to spend at a bicycle store for some new gear and biking outfits. Assume all prices listed include tax.
She buys a new bicycle for $311.60.
She buys 4 bicycle reflectors for $7.18 each and a pair of bike gloves for $19.94.
She plans to spend some or all of the money she has left to buy new biking outfits for $76.57 each.
What is the greatest number of outfits Mariam can buy with the money that's left over?
Answers
Answer: 2
Step-by-step explanation:
What is the answers to this?
Answers
Answer:
5x^2
4x
-20x
Step-by-step explanation:
5x(x) = 5x^2
4(x)= 4x
5x(-4)= -20x
When Ibuprofen is given for fever to children 6 months of age up to 2 years, the usual dose is 5 milligrams (mg) per kilogram (kg) of body weight when the fever is under 102.5 degrees Fahrenheit. How much medicine would be usual dose for a 18 month old weighing 18 pounds? milligrams
Answers
Then convert 18 pounds into kg
1 pound = 0.454 kg
18 pounds = 18 • 0.454 = 8.172 kg
Now how many mg of medication for 8.172kg?
5mg/1 kg = x mg/8.172
Cross multiply
5 • 8.172 = 40.86 mg is the dose
Please LMK if you have questions
can yall help me with this question
Answers
Therefore, the relevant cost to make the cookies per cookie is $1 + $2 + $0.10 + $3 = $6.10. Rounded to two decimal places, the relevant cost is $6.10 per cookie.
Y-2=1/3(x+6) write in standard form
Answers
Answer:
2x+3y = -15
Step-by-step explanation:
If AC=26, find BC. in simplest radical from
BC=
Answers
The simplest radical from BC = 2/3.
Step by Step Explanation:AC = 26 and BC = 10.
Therefore, BC = 26 - 10 = 14.
we need to find the simplest radical from BC = 14. A simple radical is a fraction with no common factors other than 1 and itself. The simplest radical from BC = 14 is 2/3
What is simplest radical ?Simply put, simplifying a radical eliminates the need to find any further square roots, cube roots, fourth roots, etc. Additionally, it entails eliminating any radicals from a fraction's denominator.
The radical consists of three separate parts:
RadicandDegree SymbolThe Complete Question is :
AC = 26 and BC = 10 find the simplest radical from BC =
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Consider a rectangle that is inscribed with its base on the x-axis and its upper corners on the parabola y=C−x2, with C>0. What are the width and height that maximize the area of this rectangle? What is that maximal area?
Answers
The width of the rectangle that maximizes the area is C/2 and the height of the rectangle that maximizes the area is C/2. The maximal area of the rectangle is C2/4.
How do you determine a maximum area?The gap between a rectangle's length and width must be as small as possible for its area to be as large as possible. Therefore, the length in this scenario must be ceiling (perimeter / 4) and the width will be floor (perimeter /4). The greatest size of a rectangle with a given perimeter is therefore equal to ceiling(perimeter/4) * floor(perimeter/4)
What does "maximum area" mean?The average of the maximum areas of land planted to a specific crop over the Relevant Period is referred to as the "maximum area for a particular crop."
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Consider the following inequality:
−2(2z−3)≥2z+24
Step 1 of 2 : Write the solution using interval notation.
Answers
The required solution of the given inequality is z ≤ 9.
Given that,
To determine the solution of the inequality −2(2z−3)≥2z+24.
Inequality can be defined as the relation of the equation containing the symbol of ( ≤, ≥, <, >) instead of the equal sign in an equation.
Here,
−2(2z−3)≥2z+24
-4z + 6 ≥ 2z + 24
-2z ≥ 18
z ≤ 9
Thus, the required solution of the given inequality is z ≤ 9.
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what is the rate of change of the function y=7/4x-2
Answers
Answer:
7/4
Step-by-step explanation:
The rate of change is the slope or the change in y over the change in x.
7/4x
That is the rate of change ( Slope )
An architect is designing a home and needs to create a rectangular bedroom. The bedroom must be 425 ft2 and must be 8 ft longer than it is wide. What are the width and length of the bedroom?
Answers
The width of the bedroom is 17 feet. The length of the bedroom is 17 + 8 = 25 feet.
What is the area of the rectangle?
The area of the rectangle is length x breadth. The diagonals of the rectangle divide it into two equivalent right-angled triangles. Therefore, the area of the rectangle will be equal to the sum of the area of these two triangles.
Let w be the width of the bedroom and l be the length of the bedroom.
The width of the bedroom is 8 feet shorter than the length, so the length is w + 8.
The area of the bedroom is the product of its width and length, or w * (w + 8).
We can set up the equation 425 = w * (w + 8) and solve for w.
First, we can rewrite the equation as 425 = w^2 + 8w.
Then, we can complete the square by adding (8/2)^2 = 16 to both sides:
425 + 16 = w^2 + 8w + 16
441 = w^2 + 8w + 16
We can rewrite the left side of the equation as (w + 4)^2, which gives us:
(w + 4)^2 = 441
Taking the square root of both sides gives us:
w + 4 = 21
Subtracting 4 from both sides gives us:
w = 17
Therefore, the width of the bedroom is 17 feet. The length of the bedroom is 17 + 8 = 25 feet.
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Which of the following conclusions do you draw if the p-value is not small enough to convincingly rule out chance?
a. We cannot reject the null hypothesis.
b. We accept the null hypothesis.
c. We are convinced that chance alone produced the observed results.
d. We accept the alternative hypothesis.
Answers
The conclusion is option A, we cannot reject the null hypothesis.
What is hypothesis?An assumption or concept is given as a hypothesis for the purpose of debating it and testing if it might be true.
The null hypothesis cannot be rejected for the entire population if your sample is not sufficiently incompatible with it, which can be determined if your P value is small enough.
Therefore, we can not reject the hypothesis.
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PLEASE ASAP HURRY PLEASE
Mario set a goal to run 170 miles this month to prepare for a marathon. So far this month, he has run 85 miles. Write and solve an equation to show how many miles Mario has left to run this month to reach his goal.
A. m over 85 equals 170; m = 14,450 miles
B. m − 85 = 170; m = 255 miles
C. m + 85 = 170; m = 85 miles
D. 85m = 170; m = 2 miles
Answers
The equation to show how many miles Mario has left to run this month to reach his goal is C. m + 85 = 170; m = 85 miles.
How to illustrate the equation?An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario. It is vital to note that an equation is a mathematical statement
In this situation, Mario set a goal to run 170 miles this month to prepare for a marathon and far this month, he has run 85 miles.
Let the remaining miles be m.
This will be illustrated as:
m + 85 = 170
Collect like terms
m = 170 - 85
m = 85
In conclusion, the correct option is C
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what is the answer to this? solve for x
4x+4=24
Answers
Answer: x=5
Step-by-step explanation:
4x+4-4=24-4
4x=20
x=5
Jamie is a salesperson in a jewelry store and earns $150 per week, plus 15% of her weekly sales. If Jamie makes $229.50 in one week, what are her sales for that week
Answers
The sales Jamie made for the week is $530
How to find Jamie sales for the weekinformation from the problem
Jamie is a salesperson in a jewelry store and earns $150 per week, plus 15% of her weekly sales
Jamie makes $229.50 in one week, her sales for that week = ?
The question is a percentage problem, percentage deals with a fraction hundred and used as follows
15% = 15 percent
= 15 / 100
= 0.15
Let Jamie's sales for the week be x
total earning = 150 + 0.15x
229.50 = 150 + 0.15x
229.50 - 150 = 0.15x
0.15x = 79.5
x = 79.5 / 0.15
x = 530
The sales for the week is $530
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