when two non-vertical lines are in the same plane and have the same slope, they are said to be parallel lines. whereas the non-vertical lines are in the same plane and intersect at an angle of 90, they are said to be perpendicular.
A parallel lines is when two lines have the same slope, meaning they will never intersect. This is represented by the same "rise over run" ratio in the equation of the line. The perpendicular lines is when two lines have a slope that is the opposite reciprocal of each other. This means that the lines will intersect at a 90-degree angle and can be represented by the equation y = -1/m * x + b, where m is the slope of one of the lines. Both of these concepts are important for understanding the basics of linear equations, as well as for determining the lines of best fit in graphs.
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A survey of 3,000 who bought a new car showed that 900 people had
mechanical issues within the first 2 year.
a. What is the relative frequency of the people that had mechanical issues?
b. What is the relative frequency of the people that did not have mechanical
issues?
c. What does the relative frequencies in part (a) and (b) tell you about the
new car and how reliable it has been? Explain your reasoning.
A. The relative frequency of the people that had mechanical issues is 30%.
B. The relative frequency of the people that did not have mechanical issues is 70%.
C. The relative frequencies in (a) and (b) suggest that the new car has been relatively unreliable, as 30% of buyers experienced mechanical issues within the first two years. This suggests that the car has not been built to a high standard of quality, and that buyers should be prepared for potential issues with the car.
According to the IRS, taxpayers calling the IRS in 2017 waited 13 minutes on average for an IRS telephone assister to answer. Do callers who use the IRS help line early in the day have a shorter wait? Suppose a sample of 50 callers who placed their calls to the IRS in the first 30 minutes that the line is open during the day have a mean waiting time of 11 minutes before an IRS telephone assister answers. Based on data from past years, you can assume that the standard deviation of waiting times is 8 minutes. Using these sample results, can you conclude that the waiting time for calls placed during the first 30 minutes the IRS help line is open each day is significantly less that the overall mean waiting time of 13 minutes? Use alpha=0.05
Calculate the test statistic
P-value = 0.0384
As P-value < 0.05, reject the null hypothesis.
What is test statistic?A statistic (a number obtained from the sample) used in statistical hypothesis testing is known as a test statistic. Usually, a hypothesis test is described in words.
A test statistic is a figure obtained from a statistical analysis. It explains how distant your observed data is from the null hypothesis, which states that there is no correlation between the variables or distinction between the sample groups.
The alternative and null hypotheses are listed below.
Lack of hypothesis H0: μ = 13
Ha: 13 Alternative Hypothesis
Statistical test, z = (xbar - mu)/(sigma/sqrt(n))
z = (11 - 13)/(8/sqrt(50))
z = -1.77
Region of Rejection
For α= 0.05, this is a left-tailed test.
Z has a critical value of -1.645.
Therefore, if z -1.645, reject H0 and accept the null hypothesis.
P-value Approach
P-value = 0.0384
As P-value < 0.05, reject the null hypothesis
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Serenity has 58 m of fencing to build a four-sided fence around a rectangular plot of land. The area of the land is 210 square meters. Solve for the dimensions (length and width) of the field.
The dimensions of the rectangular field is 15 meters long and 14 meters wide.
A rectangle is a two-dimensional figure that has 2 pair of parallel sides that are of the same length. The corners made by these sides are right triangles.
Let x = length of the rectangular field
y = width of the rectangular field
If the area of the land is 210 square meters, then the product of its length and width is equal to 210 square meters.
A = l x w
210 = xy
x = 210/y
Serenity has 58 m of fencing for the perimeter of the rectangular field.. Hence,
P = 2l + 2w
58 = 2x + 2y
Substitute the expression of x and solve for y.
58 = 2x + 2y
58 = 2(210/y) + 2y
58 = 420/y + 2y
Multiply both sides by y and divide by 2.
29y = 210 + y²
y² - 29y + 210 = 0
(y - 14)(y - 15) = 0
y = 14 ; y = 15
Hence, y = 14.
Substitute the value of y and solve for x.
x = 210/y
x = 210/14
x = 15
Hence, the length and width of the field is 15 meters and 14 meters, respectively.
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PLEASE HELP ASAP AHhHHhHhHh
the product of "-1.8" and 3 more than a number as the same as 1 / 10 what is the number
ILL GIVE YOU POINTS PLEASE
The value of the number is N = -55/18
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the number be represented as N
The value of N is given by
The product of -1.8 and 3 more than a number as the same as 1 / 10
So , substituting the values in the equation , we get
product of -1.8 and 3 more than a number
And , -1.8 x ( N + 3 ) is equal to 1/10
So , the equation will be
-1.8 x ( N + 3 ) = 1/10
Divide both sides of the equation by -1.8 , we get
N + 3 = -1/18
Subtracting 3 on both sides of the equation , we get
N = -1/18 - 3
On simplifying the equation , we get
N = ( -54 - 1 ) / 18
N = -55/18
Therefore , the number is -55/18
Hence , The value of the number is N = -55/18
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question 191 pts true or false: the curve of a distribution has thicker tails than the curve of the standard normal distribution. group of answer choices true false
The answer is true. The curve of t-distribution has thicker tails than the curve of the standard normal distribution.
The t-distribution is also called as Student's t-distribution which is a type of probability distribution with a bell shape which is similar to normal distribution but has thicker tails. It is used to estimate population parameters when sample sizes are small or variances are unknown. T-distributions have a higher probability of extreme values more than normal distributions which results in thicker tails.
Tail thickness is determined by a t-distribution parameter called degrees of freedom, with lower values resulting in heavier tails and higher values resulting in the t-distribution resembles standard normal distribution with a standard deviation of 1and mean of 0.
Thus, t-distribution has thicker tails than the normal distribution.
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In the preliminary investigation phase of the systems life cycle, which one of the following tasks would not be included?
A. Briefly defining the problem
B. Suggesting alternative solutions
C. Gathering the data
D. Preparing a short report
What is a range of numbers?
To find the range of numbers we subtract the largest number by the lowest numbers.
In the given question,
We have to explain, the range of a numbers.
The range refers to all the entities (output) that result from a relation or function. The Range set is made up of all used output values (dependent values).
The difference between both the highest and lowest numbers in a collection or set is known as the range.
To find the range of numbers we subtract the largest number by the lowest numbers.
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Use numerals instead of words. if necessary, use / for the fraction bar. if p − 1 is a factor of p4 + p2 p − k, the value of k is:____.
Use / for the fraction bar if necessary. if p − 1 is a factor of p^4 + p^2 + p - k , the value of k is 1 + p^2 + p^4.
A fraction bar is a graphic representation of fractions that is useful for fraction comparison and fraction operations. Part-to-whole representational models like fraction bars or fraction strips are used. One unit out of a whole is represented by each segment of a fraction bar.
To comprehend the value of a fraction, utilize fraction bars. They can also be utilized for comparing fractions and, subsequently, adding and removing fractions. The ability to visualize a fraction bar for just any fraction is crucial.
p - 1 = p^4 + p^2 + p - k
k = 1 + p^2 + p^4
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8600 dollars is placed in an account with an annual interest rate of 8. 5%. To the nearest tenth of a year, how long will it take for the account value to reach 28500 dollars?.
Assuming simple interest rate, to reach the account value of 28500 dollars, it needs 27.2 years.
Assuming simple interest rate, the formula for the future value is:
FV = PV (1 + r x n)
Where:
PV = present value
r = interest rate per period
n = number of periods
Parameters given in the problem,
r = 8.5% = 0.085
PV = 8600
FV = 28500
Plug these parameters into the formula:
28500 = 8600 (1 + 0.085 x n)
1 + 0.085 x n = 3.313
0.085 x n = 2.313
n = 27.2
Hence, it needs 27.2 years to reach 28500 dollars.
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a store manager wants to display 4 different magazines in a row out of 8 choices. how many ways can this be done?
There are total 1680 ways to arrange 4 magazines in a row of 8 choices
What is Permutation?
The term permutation refers to a mathematical computation of the number of possible arrangements of a given collection. Simply said, a permutation is a term that defines the amount of different ways something may be organised or arranged. The order of the arrangement is important in permutations.
Solution:
Since, order of the arrangement matter too
we will use Permutation
Total Ways of Arrangement = 8P4
Total Ways of Arrangement = 8!/4!
Total Ways of Arrangement = 8*7*6*5*4!/4!
Total Ways of Arrangement = 1680 ways
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Geometry-Need help
.......
After solving for angles, the value of p in the given angles is 44°.
What are angles?An angle is formed when two straight lines or rays meet at a single terminal.
The place where two points converge is known as an angle's vertex.
The name "angel" comes from the Latin word "angulus," which means "corner."
Angles are also produced when two planes intersect.
These are what are known as dihedral angles.
So, we know that ∠CAD = 90°.
And since ∠CAB is s straight angle. Then,
∠CAD + ∠DAB = 180
90 + p + 46 = 180
p + 136 = 180
p = 180 - 136
p = 44°
Therefore, after solving for angles, the value of p in the given angles is 44°.
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100-5n
show work
!!!
Answer:
5(20-n)
Step-by-step explanation:
you "take out" a five from both number by dividing
100/5= 20
5n/5=n
Answer:
-5(n+20)
Step-by-step explanation:
100-5n
-5+100
-5n+100
-5(n+20)
end
(this might be it not sure 100%)
spam: a researcher reported that 71.8% of all email sent in a recent month was spam. a system manager at a large corporation believes that the percentage at his company may be 70% . he examines a random sample of 500 emails received at an email server, and finds that 373 of the messages are spam. can you conclude that the percentage of emails that are spam is greater than 70% ? use both
There is sufficient proof to presume that under 77% of messages are spam.
Explain hypothesis test.A statistical hypothesis test is a technique for measurable induction used to conclude whether the information within reach adequately support a specific theory. Speculation testing permits us to offer probabilistic expressions about populace boundaries.
According to question:Given the information in the inquiry;
Test size n = 500
x = 361
p₀ = 77% = 0.77
q₀ = 1 - p₀ = 1 - 0.77 = 0.23
p = x/n = 361/500 = 0.722
Speculation;
Null hypothesis H₀ : p ≥ 77% or 0.77
Alternative hypothesis Hₐ : p ≥ 77% or 0.77
Test Measurement
z = ( p - p₀ )/√( ( p₀ × q₀ )/n )
so we substitute
z = ( 0.722 - 0.77 )/√( ( 0.77 × 0.23 )/500 )
z = - 0.048/√( 0.1771/500 )
z = - 0.048/√0.0003542
z = - 0.048/0.01882
z = - 2.55
so our p-worth will be;
p-value = p( z < - 2.55 ) {from table }
p-value = 0.0054
at 0.05 degree of importance ∝
p-value ( 0.0054 ) is not as much as importance level ∝ ( 0.05 )
Accordingly we Reject Null hypothesis H₀
Thus, there is sufficient proof to presume that under 77% of messages are spam.
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which one is functions and non functions?
please help me!!!
Answer: for the graphs if it crosses the same line twice if you draw a line down the top to bottom it is not a function and if the x repeats for the table and equals something different it is not a function
Step-by-step explanation
for tables (5,8) (6,9) (5,2) (1,5) this would not be a function because 5 equals two different things
5. The two angles are supplementary angles, what is the measure of x?
B
(2x - 15)°
A
11xº
D
C
The value of x is 15.
What is an angle?
When two lines come together at a common point, an angle is created. They are expressed as a number of degrees, denoted by the symbol °. Acute, right, obtuse, and reflex angles are the other three significant types of angles.
Given that ∠ADB and ∠BDC are supplementary angle.
∠ADB = (2x - 15)° and ∠BDC = 11x°.
Two angles are supplementary angle, if their sum is equal to 180°.
Therefore,
∠ADB + ∠BDC = 180°
Putting the value of ∠ADB and ∠BDC:
(2x - 15)° + 11x° = 180°
2x - 15 + 11x = 180
Combine like terms:
(2x + 11x) -15 =180
13x - 15 =180
Add 15 with both sides:
13x = 180 +15
13x = 195
Divide both sides by 13:
x = 15
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Sam scored 4 goals in 2
lacrosse games. If he
continues to score goals
at the same rate, how
many goals will he score
in 5 games?
Answer:
he will score 10 goals in 5 games
Greta is mailing a care package to her little sister at college. After packing the box, she weighs it on her bathroom scale to estimate the mailing cost. The scale shows the package weighing 3 pounds. At the post office, the clerk weighs the package on a more precise scale, and it weighs 3.25 pounds. What is the percent error for Greta's scale's measurement?
Answer: 7.7%
Step-by-step explanation:
So the answer is 7.7
To find the percent error, start by listing the key information from the problem.
Greta's scale shows the package weighing 3 pounds.
The scale at the post office shows the package weighing 3.25 pounds.
First, find the amount of error. It is the difference between 3.25 and 3, which is 0.25.
Now, use the formula to find the percent error.
percent error =
amount of error
correct amount = 0.25
3.25
= 0.0769…
You can rewrite this as a percent rounded to the tenths place, 7.7%. So, the percent error for Greta's scale measurement is about 7.7
Solve 5x−14 = 14−2x . Check your solution.
PLEASE HELP ASAP!
On a number line, point A is located at 4, point C is located at 11, and point B lies between points A and C. What is the location of B such that the ratio of AB:BC is 2:3?
8.2
6.8
5.9
5.6
The location of B under the Line Segment Partition is 6.8
What is Line Segment Partition?
A line segment is partitioned when it is divided into equal parts according to a specified ratio. The total number of partitions of the line segment must be equal to the sum of the two values in the ratio.
Given in the question that on a number line AC;
Location of Point A = 4
Location of point C = 11
point B lies between points A and C
So, B divides line AC in the ratio AB: BC = 2:3.
Thus;
BC = 3/5 of the total length of the AC
AB = 2/5 the total length of the AC
Then, total length of AC = 11-4 = 7
BC = 3/5 * 7 = 4.2
AB = 2/5 * 7 = 2.8
Thus, the location of point B is; 4 + 2.8 = 6.8
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7/1 in simplest form
Answer:
7
Step-by-step explanation:
hope it helps!
Answer:
7
Step-by-step explanation:
7 over one is a whole number
what is 2 5/7+ 1 2/3 if you can i would like a step-by-step Explanation along with the correct answer
pls help me worth 90 points
A: he percent of respondents who do not like hamburgers and burritos both = 16.09 %
B: Marginal relative frequency of all customers that like hamburgers= 0.65
C: Those who like Hamburgers but not burritos.
What is the percentage?
It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.
Like Hamburgers ↓ Does Not Like Hamburgers↓ Total↓
Likes burritos → 39 38 77
Does not like burritos → 95 33 128
Total → 134 71 205
So, according to the above table, a total of 77 customers like burritos, out of which 38 do not like hamburgers, hence, the remaining 77-38= 39 like Hamburgers.
A total of 128 customers do not like burritos, out of which 95 do like hamburgers, hence, the remaining 128 - 95 = 33 do not like Hamburgers.
A total of 134 customers like hamburgers, but 71 do not like it, hence, the total respondents are 205.
Part A: The percent of respondents who do not like hamburgers and burritos both
There are 33 such respondents.
Hence, percentage = (033/205) *100 = 16.09 %
Part B: Marginal relative frequency of all customers that like hamburgers
It will be the ratio of the sum of the customers that like hamburgers to the total number of respondents
Hence, ratio 134/205 = 0.65
Part C: The data point that has the strongest association of its two factors.
For this, we need to find the ratio of all the four data with the total.
Those who like Hamburgers and burritos = 39/134 = 0.29
Those who like Hamburgers but not burritos = 95/134 = 0.71
Those who like burritos but not Hamburgers = 38/71 = 0.53
Those who do not like burritos or Hamburgers = 33/71 = 0.47
So, the answer is those who like Hamburgers but not burritos.
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Answer:
GUYS THE PERSON ABOVE GOT ME A 100 PROPS TO HIMStep-by-step explanation:
!!!!!!!!!!!!!!!!HE DESERVES EVERYTHING FOR HELPING!!!!!!!!!!!!!!!!!!!!!What is the average speed of a bus that travels 150 km in 3 hours?
The average speed of a bus that travels 150 km in 3 hours is 50 kilometres per hour.
The average speed is directly proportional to the total distance covered and inversely proportional to the total time taken. Using the mentioned information to write the formula of average speed -
Average speed = total distance covered ÷ total time taken
Keep the values in formula to find the average speed of the bus
Average speed of the bus = 150/3
Performing division on Right Hand Side of the equation to find the average speed of the bus
Average speed of the bus = 50 kilometres per hour
Hence, the average speed is 50 kilometres per hour.
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theorem: there is no smallest positive rational number. a proof by contradiction of the theorem starts by assuming which fact?
that there is no smallest positive rational number is proven below.
What is Rational Number?
Numbers that may be expressed in the form p/q, where p and q are integers and q0, are considered rational numbers. Because fractions cannot have a negative numerator or denominator, they differ from rational numbers in this respect. Because of this, the numerator and denominator of a fraction are whole numbers (denominator 0), unlike in the case of rational numbers, when they are both integers.
So to convert a fractional to reduce form we have to divide by 10 to power how many digits thereafter decimal point, and make sure that numerator or denominator doesn't have commonly divisible.
Let r be any reasonable number.
We can infer that r/2 is rational because r is a rational number.
There is no smallest rational number so we can assume that r/2 r because r/2 is rational.
Hence, proved that here is no smallest positive rational number.
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A rental car agency charges $240 per week plus $0.25 per mile to rent a car. The charge for a minivan is $180 per week plus $0.40 per mile. After how many miles is the total charge for each vehicle the same?
Question content area bottom
Part 1
The total charge is the same when each vehicle is driven
___ mile(s) for the week.
(Type a whole number.)
PLEASE HELP!!
After 400 miles is the total charge for each vehicle the same ie $340
What is equation ?
The definition of an equation in algebra is a mathematical statement that proves two mathematical expressions are equal. Consider the equation 3x + 5 = 14, where 3x + 5 and 14 are two expressions that are separated by the symbol "equal."
An equals sign is a part of a mathematical expression referred to as an equation. A lot of equations include algebra. In math, algebra is employed when you don't know the precise amount to calculate.
x= number of miles
car cost is 240+0.25x
van cost is 180+0.40x
When the equations are equal
240 + 0.25x = 180 +0.40x
60 = 0.15x
15x = 6000
x=400
400 miles.
They will each cost $340
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help asap, whats the answer?
The function f, in the slope-intercept form is f= -3x+6.
What is a slope?The slope or gradient of the line is a numerical value used to describe a line's steepness and direction in mathematics. It was first used to describe slope in O'Brien's (1844) and Todhunter's (1888) versions of the equation for a straight line, which are both written as "y = mx + b" and "y = mx + c," respectively. The choice of the letter m for slope has no apparent justification.
Calculating slope involves comparing the "vertical change" to the "horizontal change" between any two points on a line, or any two points. The ratio, which provides the same number for each, is occasionally given as a quotient ("rise over run").
Here given,
For a linear function f,
f(2)=0 and f(4)=-6
So, from the given hint the points are (2, 0) and (4, -6)
Here slope m=(-6-0)/(4-2)
m=-6/2
m= -3
We know that the equation of the function in slope-intercept form is:
f=mx +c
By substituting the point (2, 0) and m= -3 in the function we get,
0= -3(2)+c
c=6
Now, by substituting m= -3 and c=6 in the function, we get
f= -3x+6
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How do you calculate linear relationship?
The formula distance = rate x time also indicates a linear relationship.
Given,
Linear relationship;
A straight-line link between two variables is referred to statistically as a linear relationship (or linear association). Linear relationships can be represented graphically or mathematically as the equation y = mx + b.
We have to determine the calculations for a linear relationship;
Here,
Distance = rate x time is another equation that results in a linear relationship. This linear relationship would be represented in the top right quadrant of a graph with an X and Y axis because distance is often a positive quantity.
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15. M. Jaffey had a total of 428. 5 ounce of pretzel to put into 5 bowl for a party. She put an equal number of ounce of pretzel into each bowl. How many ounce of pretzel did M. Jaffey put into each bowl?
Answer: The correct answer is 85.7 ounces in each bowl
Step-by-step explanation:
T = Total ounces of pretzels
B = Number of bowls
A = Amount of pretzels in each bowl
Our equation: A = T / B
T = 428.5
B = 5
A = 428.5 / 5
A = 85.7 ounces
Equations with rational coefficients
Lisa had $20.50 to spend on eight pens. After buying them she had $2.90. How much did each pen cost?
Answer:
Each pen is 2.20
Step-by-step explanation:
We first need to find the total cost of the pens
20.50 - 2.90 = 17.60
Now we can divide by the number of pens purchased.
17.60 / 8
2.20
Each pen is 2.20
Answer:
$ 2.20
Step-by-step explanation:
First, let us find the total cost of pens.
$ 20.50 - $ 2.90 = $ 17.6
And now let us find the cost per pen.
For that, let the cost of a pen be x.
Number of pens Cost
8 $ 17.6
1 x
Use cross multiplication and find the value of x.
8x = 1 × 17.6
8x = 17.6
Divide both sides by 8.
x = $ 2.2
Therefore,
Cost of a pen is $ 2.20
write the given equation in form of differential form ~
[tex] \rm \qquad {x}^{2} + {y}^{2} = {a}^{2} [/tex]
The equation x² + y² = a² in form of a differential form is; dy/dx = -x/y
What is the differential form of the equation?A differential equation is defined as one that contains the derivative of a function. For example, f(x) + 3 = 4f'(x) - 2.
We are given the equation;
x² + y² = a²
Thus, differentiating to be in differential form is;
2x(dx) + 2y(dy) = 0
-2x(dx) = 2y(dy)
dy/dx = -x/y
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