The slope of a line parallel to the line whose equation 8x + 10y = 60 is -4/5
What is Equation of line ?
A straight line's general equation is y = mx + b, where m denotes the gradient or slope and y = b denotes the point at which the line crosses the y-axis. On the y-axis, this value b is referred to as the intercept.
Given the equation,
8x + 10y = 60
We know, the equation of line is in form of
y = mx + b
m = slope and b = y-intercept
Now, evaluate the given equation
8x + 10y = 60
10y = 60 - 8x
y = (60 - 8x) / 10
y = 60/10 - 8x/10
y = 6 - 4/5x
y = -4/5x + 6
Which is in the form of equation of line
y = -4/5x + 6
Now, from this slope is - 4/5 and y-intercept is 6
Hence, the slope of a line parallel to the line whose equation 8x + 10y = 60 is -4/5
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Suppose that a randomly generated list of numbers from 0 to 9 is being used to simulate an event that has a probability of success of 80%. Which of these groups of numbers could represent a success?.
This means that the answer is D.
What is probability in math?
In everyday speech, the term "probability" refers to the likelihood that a specific event (or set of events) will take place, expressed as a number between 0 and 100% or as a linear scale from 0 (impossibility) to 1 (certainty). Statistics is the study of occurrences that follow a probability distribution.
How do you find the probability?The probability is calculated by dividing the total number of possible outcomes by the number of possible ways the event could occur. Probability and odds are two distinct ideas. Odds are calculated by dividing the likelihood of an event by the likelihood that it won't.
According to the given question:-
Even though there aren't any actual options for this question, figuring out the right response should be simple. The quantity of numbers that will be listed is the "probability of success" that is being discussed here. We simply need to select the option with 8 of the 10 mentioned numbers since an 80% likelihood is what is being sought. This indicates that the solution is D. Hope this is useful!
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Answer:
Step-by-step explanation:
given AB is congruent to AC and AL and AM trisect angle BAC. Prove AL is congruent to AM.
Explanation:
You want to show AL≅AM in the given figure.
Statement . . . . Reason1. AB≅AC . . . . given
2. ∠1≅∠3 . . . . given
3. ∆ABC is isosceles . . . . definition of isosceles triangle
4. ∠B≅∠C . . . . base angles are congruent in an isosceles triangle
5. ΔLBA≅ΔMCA . . . . ASA congruence postulate
6. AL≅AM . . . . CPCTC
A computer password is required to be 7 characters long. How many passwords are possible if the password requires 1 letter(s) followed by 6 digits (numbers 0-9), where no repetition of any letter or digit is allowed?.
A computer password is required to be 7 characters long.
Note the requirements:
Repetition of letter or digit is not allowed.
The order of the letters and digits matters.
Because of that, permutation would be the most suitable way to count the number of possibilities.
There are [tex]P(26,3) = \frac{26!}{(26-3)!} = 26x25x24 = 15,600[/tex] ways to arrange three out of distinct letters (without replacement.)
Similarly, there are [tex]P(10,4) = \frac{10!}{(10-4)!} = 10x9x8x7 = 5,040[/tex] ways to arrange four out of distinct numbers (also without replacement.)
Therefore, there are 15,600 possibilities for the three-letter section of this password, and 5,040 possibilities for the four-digit section. What if these two parts are combined?
Consider: if the first three letters of the password were fixed, then there would be 5,040 possibilities. However, if any of the first three letters was changed, the result would be another 5,040 possibilities, all of which are different from the previous 5,400 possibilities. These two three-letter sections along will give 2 x 5,400 possibilities. Since there are 15,600 three-letter sections like that, there would be 15,600 x 5,400 = 78,624,000 possible passwords in total. That gives the number of possible passwords that satisfy these requirements.
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Write y = 7|x + 1|-5 as a piecewise function.
The function y = 7|x + 1| - 5 can be written as a Piecewise Function as follows,
7x + 2 for x > -1
y =
-7x - 12 for x < -1
Given, a function y = 7|x + 1| - 5
Now, we have to write the given function as a piecewise function
|x + 1| = (x + 1) for x > -1 and
|x + 1| = - (x + 1) for x < -1
So, the given function can be written as a piecewise function
7(x + 1) - 5 for x > -1
y =
-7(x + 1) - 5 for x < -1
On simplifying, we get
7x + 2 for x > -1
y =
-7x - 12 for x < -1
Hence, the given function y = 7|x + 1| - 5 can be written as a Piecewise Function as follows,
7x + 2 for x > -1
y =
-7x - 12 for x < -1
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PLEASE HELP ME WITH THIS ASAP
Answer:
1
Step-by-step explanation:
anything to the power of 0 is 1
Answer:
1
Step-by-step explanation:
if the toy store is stocked with 3 types of balls and 6 types of board games, how many different selections of the 4 items can amanda make?
1 ball and 3 board games can be chosen by Amanda in option E. 60 ways.
Here it is given that Amanda needs 1 ball and 3 board games.
The toy store only has 3 kinds of balls and 6 types of board games. Hence we will use combinations to determine the no. of ways she can choose the items
ⁿCₓ = n! / (n - r)! X r!
The ball can be chosen in
³C₁ ways
= 3! / 2! X 1!
= 6/2
= 3 ways
The board game can be chosen in ⁶C₃ ways
= 6! / 3! X 3!
= 720 / 36
= 20 ways
Hence the total number of ways the items can be chosen is
3 X 20 ways
= E. 60 ways.
Complete Question
Amanda goes to the toy store to buy 1 ball and 3 different board games. If the toy store is stocked with 3 types of balls and 6 types of board games, how many different selections of the 4 items can Amanda make?
A. 9
B. 12
C. 14
D. 15
E. 60
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at issue is the proportion of people in a particular county who do not have health care insurance coverage and an investigator wants to estimate it with 90% confidence. a preliminary sample of 240 people were asked if they have insurance coverage and 69 replied that they did not have coverage. what sample size would be needed to achieve a margin of error of .03?
The sample size would be about 1,000.
What is unitary method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units. What can be values and units.Let's say you go to the store to buy six apples. You are informed by the shopkeeper that he is offering 10 apples for Rs 100. In this instance, the value and the units are the price of the apples.Recognizing the units and values is crucial when using the unitary technique to a problem.Always write the items that need to be computed on the right side and the things that are known on the left side to simplify things. We are aware of the quantity of apples and the amount of money in the aforesaid problem.acc to our question-
A sample size of roughly 750 is needed to get a 3 percent margin of error at a 90% level of confidence. The sample size would be roughly 1,000 for a 95 percent level of confidence.hence,The sample size would be about 1,000.
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What is the slope of a line perpendicular to the line whose equation is 3x+18y=108.
The slope of the line which is perpendicular to the given line 3x+18y=108 is (6).
We already know the equation of a line in slope intercept form y = mx + b and we also know that perpendicular lines that have slopes which are negative reciprocals of each other.
Given a line 13x + 18y=108, this slope intercept form can be written as,
3x + 18y = 108
18y = 108 - 3x
y = (108 /18) - (3/18)x.
y = (6) - 1x/6.
y = -(1/6)x + 6.
Hence the slope of the given line is (-1/6), thus the slope of the line which is perpendicular is (6).
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2/3|4v +6|-2 ≤ 10
what is the solution to this inequality
Answer:
[tex]-6\leq v\leq 3[/tex]
Step-by-step explanation:
I have attached a pdf of my work that explains how to solve this inequality pretty well.
Ryan is considering purchasing a used five year old hatchback with 75,000 miles on it for $13,000. His main use would be commuting 20 miles to work each day. Which should he be most concerned about?.
The major thing that Ryan should be worried about is the C) high annual depreciation.
What financial choice should be made?Normally, when we buy cars they have so much value but when the cars start being used more often, they tend to depreciate in value due to wear and tear and second value of the product. This tells us that when a car is driven for more miles in a year, it will depreciate greatly.
We are told that Ryan plans to drive about 40 miles to work and back everyday which means that in a year he would have driven thousands of miles. This will lead to a high depreciation.
Thus, we can conclude that the most important thing that Ryan should be worried about when purchasing this old hatchback is the high depreciation.
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Question 3 (2 points)
2
-2 -1
3-
1
-1+
-2+
-3
1 2 3
The function f(x)is graphed on the coordinate plane.
What is f(4)?
Enter your answer in the box.
f(4) =
The value of f(4) = 0 by the given graph.
What is graph?
The graph is a diagram showing the relation between variable quantities, typically of two variables, each measured along one of a pair of axes at right angles.
Given graph is a straight line, and the equation of a line is given as
y =mx+b
where,
m is the slope,
y is the dependent variable,
we can write it as
f(x)= mx +b
The coordinates are (4,0) and (0,2)
m = 2-0/0-4
m = -1/2
y = -1/2 x +b
we can see the line intersect the y-axis at 0,2
b =2
y = -1/2 x +2
at x =4
f(4) = -2+2=0
Hence, the value of f(4) = 0 in the given graph.
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Determine the unknown angle measures.
A =
B =
C =
D =
E =
Answer:
A= 115 degrees.
B= 45 degrees.
C= 115 degrees.
D= 115 degrees.
E= 110 degrees.
Tip: Angles opposite each other- like C and D- are going to be equal.
Step-by-step explanation:
cars a and b leave town at the same time. car a heads due south at rate of 80 km/hr and car b heads due west at a rate of 60 km/hr. how far is the distance between the cars increasing after three hours?
The distance between the two cars after three hours is 300 km
Cars a and b leave town at the same time.
The speed of the car that went to south = 80 km/hour
The total distance traveled in three hours = 80 × 3
= 240 km
The speed of the car that went to the west = 60 km/hour
The total distance traveled in three hours = 60 × 3
= 180 km
The distance between the two car is the hypotenuse of the right triangle
The distance between the two cars after three hours = [tex]\sqrt{240^2+180^2}[/tex]
= [tex]\sqrt{57600+32400}[/tex]
= [tex]\sqrt{90000}[/tex]
= 300 km
Hence, the distance between the two cars after three hours is 300 km
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1. If Rhea can buy 6 erasers for 7¢, how many erasers can she buy for 49¢?
Equivalent
Fractions
Rate
Solution
Answer:
42
Step-by-step explanation:
[tex]\frac{eraser}{cost}[/tex] = [tex]\frac{eraser}{cost}[/tex] Fill in what you know and solve for the unknown
[tex]\frac{6}{7}[/tex] = [tex]\frac{x}{49}[/tex] 7 x 7 is 49. Multiply 6 by 7 to find the unknown. 42
What is the f(9) if the function is f(x)=2x+3
Answer: f(9)=21
Step-by-step explanation:
replace x with 9 i think for 2(9)+3 then solve lol
naomi pintó 16.5 pies cuadrados de un mural a una tasa de 2 pies
cuadrados por hora. Claire pintó 7.5 pies cuadrados del mural a una
tasa de 4 pies cuadrados por hora. Si continúan al mismo ritmo,
¿cuántas horas más se necesitarán para que Naomi y Claire hayan
pintado la misma cantidad de pies cuadrados?
4.5 hours more will it take for Naomi and Claire to have painted the same number of square feet.
Let the time taken for them to paint equal areas be x hrs.
Naomi = 2x + 16.5
Clair = 4x + 7.5
Naomi's area = Clair's area
This is :
2x + 16.5 = 4x + 7.5
4x - 2x = 16.5 -7.5
2x = 9
x = 4.5 hours
Therefore 4.5 hours more will it take for Naomi and Claire to have painted the same number of square feet.
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Four people shared fifteen pounds of apples. How many
pounds did each person have?
Answer: Each person had 3.75 pounds of apples
Step-by-step explanation:
15= 4a (a=how many pounds of apples each person owns)
15/4=a
3.75=a
Geometry, surface area of a square pyramid
The surface area of the cone in terms of [tex]\pi[/tex] is, [tex]95\pi cm^2[/tex].
What is cone?
A cone is a smooth-tapering three-dimensional geometric object with a flat base and an apex or vertex. The base of a cone is made up of all the points on a plane other than the apex, and the apex is connected to all the other points on the base by a series of line segments, half-lines, or lines.
In the given figure, the side length of cone is, 14 cm, and the diameter of the base is 10 cm.
As diameter is 10 cm then radius = 10/2 = 5 cm.
The surface area of the cone is.
SA = [tex]SA = \pi r^2 + \pi rl\\SA = \pi (5)^2+\pi (5)(14)\\SA = 25\pi + 70\pi \\SA = 95\pi cm^2[/tex]
Therefore, the surface area of the cone is, [tex]95\pi cm^2[/tex].
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Each statement is always true. Select all statements for which the converse is also always true.
Statement: If 2 angles form a straight angle, then they are supplementary. Converse: If 2 angles are supplementary, then they form a straight angle.
Statement: In an isosceles triangle, the base angles are congruent. Converse: If the base angles of a triangle are congruent, then the triangle is isosceles.
Statement: If a point is equidistant from the 2 endpoints of a segment, then it lies on the perpendicular bisector of the segment. Converse: If a point lies on the perpendicular bisector of a segment, then it is equidistant from the 2 endpoints of the segment.
Statement: If 2 angles are vertical, then they are congruent. Converse: If 2 angles are congruent, then they are vertical.
Statement: If 2 lines are perpendicular, then they intersect to form 4 right angles. Converse: If 2 lines intersect to form 4 right angles, then they are perpendicular.
The statements for which the converse statements are always true are given as follows:
Statement: In an isosceles triangle, the base angles are congruent. Converse: If the base angles of a triangle are congruent, then the triangle is isosceles.Statement: If a point is equidistant from the 2 endpoints of a segment, then it lies on the perpendicular bisector of the segment. Converse: If a point lies on the perpendicular bisector of a segment, then it is equidistant from the 2 endpoints of the segment.What are the true converse statements?For statement 1, the converse statement is:
If 2 angles are supplementary, then they form a straight angle.
Supplementary angles are angles whose measures add to 180º, and straight angles are angles with measure of 90º. The converse is false, as 100º and 80º, for example, are supplementary angles, but do not form a straight angle.
For statement 2, the converse statement is:
If the base angles of a triangle are congruent, then the triangle is isosceles.
This is true, because an equilateral triangle, in which all the angles of the triangle are congruent, is a special case of a isosceles triangle.
For statement 3, the converse statement is:
If a point lies on the perpendicular bisector of a segment, then it is equidistant from the 2 endpoints of the segment.
Which is true by the perpendicular bisector theorem.
For statement 4, the converse statement is:
If 2 angles are congruent, then they are vertical.
Which is false, as this is not necessarily true.
For statement 5, the converse statement is:
If 2 lines intersect to form 4 right angles, then they are perpendicular.
Which is false, as this is not necessarily true.
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What is the exponential form of the logarithmic equation? 5=log0. 90. 59049 enter your answer in the box.
For given logarithmic equation. 5 = log_0.9(0.59049), the exponential form is (0.9)^5 = 0.59049
We know that the definition of a logarithm to convert from the logarithmic form to the exponential form,
log_b(x) = a
⇒ b^a = x
Here, we need to write the exponential form of the logarithmic equation.
5 = log_0.9(0.59049)
Using the definition of a logarithm,
5 = log_0.9(0.59049)
⇒ (0.9)^5 = 0.59049
Therefore, the exponential form is (0.9)^5 = 0.59049
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Find x and y so that the quadrilateral is a parallelogram. Answer below and show work.
After solving, the value of x is 8 and the value of y is 9.
In the given question,
We have to find the value of x and y.
It is also given that the given quadrilateral is a parallelogram.
Since the given quadrilateral is a parallelogram so the opposite sides and opposite angles are equal to each other.
So 4x−17=2x−1......................(1)
5y−13=3y+5...............(2)
Simplifying equation 1 to find the value of x
4x−17=2x−1
Add 17 on both side
4x−17+17=2x−1+17
Simplifying
4x=2x+16
Subtract 2x on both side
4x−2x=2x+16−2x
Simplifying
2x=16
Divide by 2 on both side
2/2 x = 16/2
x=8
Hence, the value of x is 8.
Now finding the value of y by solving the equation 2
5y−13=3y+5
Add 13 on both side
5y−13+13=3y+5+13
Simplifying
5y=3y+18
Subtract 3y on both side
5y−3y=3y+18−3y
2y=18
Divide by 2 on both side
2/2 y=18/2
y=9
Hence, the value of y is 9.
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5 less than three fourths of a number is one forth of number decreased
by 9. What is the value of the number?
The value of the number is -8
How to determine the value of the number?From the question, we have the following statement that can be used in our computation:
5 less than three fourths of a number is one forth of number decreased
by 9
Represent the number with x
So, we have the following equation
3/4x - 5 = 1/4x - 9
Evaluate the like terms
2/4x = -4
This gives
1/2x = -4
Solve for x
x = -8
Hence, the number is -8
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Solve algebraically the simultaneous equations
[tex]x^{2}[/tex] + [tex]y^{2}[/tex] = 25
y = 2x -2
Give your final pairs of values in the form,
x = . . . , y = . . . and x = . . ., y = . . .,
Answer:
[tex]x = 3[/tex] [tex]y = 4[/tex] [tex]x = -\frac{7}{5}[/tex] [tex]y = -\frac{24}{5}[/tex]
Step-by-step explanation:
y = 2x - 2
substitute y with 2x - 2 in the other equation
[tex]x^{2} +y^{2} = 25[/tex]
[tex]x^{2} +(2x-2)^{2} = 25[/tex]
[tex]x^{2} + 4x^{2} -4x-4x+4 = 25[/tex]
[tex]5x^{2} -8x+4=25[/tex]
[tex]5x^{2} -8x-21=0[/tex]
Use the quadratic equation to solve
[tex]\frac{-b(+-)\sqrt{b^{2}-4ac }}{2a}[/tex]
[tex]a = 5\\b = -8 \\c = -21[/tex]
[tex]\frac{-(-8)(+-)\sqrt{(-8)^{2}-4(5)(-21) }}{2(5)}[/tex]
[tex]\frac{8(+-)\sqrt{64-(-420) }}{10}[/tex]
[tex]\frac{8+\sqrt{484 }}{10}[/tex] [tex]\frac{8-\sqrt{484 }}{10}[/tex]
[tex]x[/tex] = [tex]3[/tex] [tex]x[/tex] = [tex]-\frac{7}{5}[/tex]
Now use these values of x in the other equation to find two values of y
y = 2x - 2 y = 2x - 2
y = 2(3) - 2 y = 2(-7/5) - 2
y = 4 y = - (24/5)
For a lower tail test, the p-value is the probability of obtaining a value for the test statistic at least as.
The answer will be, at least as small as that provided by the sample using p-value.
What is the p-value?
Under the premise that the null hypothesis is true, the p-value in null-hypothesis significance testing represents the likelihood of receiving test findings that are at least as extreme as the result actually observed. A severe observed outcome would be highly improbable under the null hypothesis, according to a very small p-value. In academic papers of many quantitative fields, reporting the p-values of statistical tests is standard practice. Misuse of p-value is common and has been a big concern in metascience due to its difficult-to-understand precise meaning.
The probability that a population parameter in a particular statistical model will be less than a given value when the null hypothesis is true is known as the p-value,
And that is also known as a probability value or a measure of significance.
Hence the probability is, at least as small as that provided by the sample using p-value.
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A random sample of 85 printers discovered that 35 of them were being used in small businesses . find the 99% confidence interval for the population proportion of printers that are used in small businesses.
The 99% confidence interval for the population proportion of printers that are used in small businesses is 0.150<p<0.674.
Do we use the sample size or do we use X two to get to 35? We visited 30 places. We are trying to locate the B hats that X gave us. Over 35, we are tested. Our margin of error is 7.751 over two, which is the same as the confidence interval. This gives us seven points. 258 were present. Since our alpha is 1 – 0.9 and they will want us, we wish to find that critical that is set out for two. We get 6 now they have provided us with a minimal sample size, apologize. Is it finished? If you will, visualizeus tying our p hats without the p hat on one. Yes, indeed. We get 1.645 over.
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PLEASEEEEEEEEEW HELPPPPPPPPPPPPPP PLEASEEEEEEEEEEEE I NEED THE ANSWERS RIGHT NOW SOMEONE PLEASEEE
using the expression x+3 write one equation that has one solution, one equation that has no solution, and one equation that has infinitely many solutions.
One solution:
y = 3x+2
y=2x+4
No solution:
y=3x+2
y=3x+1
Infinitely:
y=2x+4
y=4x+8
Answer:
One solution: x + 3 = 2x
No solution: x + 3 = x
Infinitely many solutions: x + 3 = 2 ( 0.5x + 1.5 )
Step-by-step explanation:
1 ) x + 3 = 2x
x = 3
2 ) x + 3 = x
No Solution...
3 ) x + 3 = 2 ( 0.5x + 1.5 )
[tex]x[/tex] ∈ [tex]R[/tex]
Hope this helps! :)
What is the solution to the inequality
-6+12p+31 > 7?
•p<-8orp> 5
•-8
Answer:
Step-by-step explanation:
your mom
If anyone can help me, Please Help!
Jessica purchased a DVD that was on sale for 12% off. The sales tax in her county is 3%. Let y represent the original price of the DVD. Write an expression that can be used to determine the final cost of the DVD. (5 points)
The formula for the final cost, in terms of the original price y, is:
c(y) = y*(0.88)*(1.03)
How to find an expression for the final cost of the DVD?
Let's define y as the original price of the DVD.
We first apply a discount of the 12% of the price, so the new cost will be:
c(y) = y*(1 - 12%/100%)
c(y) = y*(1 - 0.12)
Then we apply a tax of the 3%, this in increase, then we can write this as:
c(y) = y*(1 - 0.12)*(1 + 3%/100%)
c(y) = y*(1 - 0.12)*(1 + 0.03)
c(y) = y*(0.88)*(1.03)
That is the formula that we could use to determine the final cost.
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I need to learn about algebra 1 how would i get help?
Answer:
Step-by-step explanation:
Firstly, you would need to have someone teach you unless you don't then I'm sure there are courses online and to be excellent at it, practice a lot of questions and do diagnostic questions for each topic.
Use the properties of addition to simplify this expression. 11x+6-4x-2
Answer:
[tex]7x+4[/tex]
Step-by-step explanation:
1) Collect like terms.
[tex](11x-4x)+(6-2)[/tex]
2) Simplify.
[tex]7x+4[/tex]
Thanks!
Answer:
7x + 4
Step-by-step explanation:
11x + 6 -4x -2 Combine like terms
7x + 4
