The given two equations are Perpendicular to each other .
What is intersection of lines ?
It is known as an intersection of lines when two lines have exactly one point in common. A point is shared by the connecting lines. The point of intersection is the same place that may be found at the intersection of all intersecting lines. When two or more straight lines cross each other in a plane, they are said to be intersecting lines. An intersection point will be present for the two non-parallel straight lines that are coplanar. The point of intersection, which can be found on all intersecting lines, is where the intersecting lines share a common point.
Here the equation of line is y=mx+b .
Where m = slope . then,
=> y = x-7 where here slope m1= 1 and
=> y = -x+3 where here slope m2 = -1 .
Here the m1= -m2
Hence the given two equations are Perpendicular to each other .
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c.) In a class of 28 sophomores and juniors, 16 are
juniors. What percent of the class are sophomores?
The percent of the sophomores in the class of 28 sophomores and juniors is 42.86%.
According to the question,
We have the following information:
Total number in a class including sophomores and juniors = 28
Number of juniors in the class = 16
Now, we have the number of sophomores in this class:
Total number in the class- Number of juniors in the class
28-16
12
Now, we can easily find the percent of sophomores in the class by following the given steps:
Number of sophomores*100/Number of sophomores and juniors
1200/28
42.86%
Hence, the percent of the sophomores in the class of 28 sophomores and juniors is 42.86%.
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the degree of f(x) is ?
the end behavior is the left side is ?
and the right side is ?
The degree of the polynomial is 5, and the end behavior is:
as x → ∞, f(x) → -∞
as x → -∞, f(x) → ∞
How to get the degree of a polynomial?
For any given polynomial, we define the degree as the largest exponent on the polynomial.
On this case we have:
f(x) = 2x^3 - 3x^5 - x^2 + 1
We can see that the largest exponent is 5, so the degree is 5.
Now, for the ending behavior.
If we have an odd degree (like in this case) we will have opposite ending behaviors in both ends of the domain.
If the leading coefficient is negative (like in this case, it is -3) then the end behavior will be:
as x → ∞, f(x) → -∞
as x → -∞, f(x) → ∞
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if 1,000 points are selected randomly inside the square with all points equally likely to be selected, how many of those points are expected to lie inside the circle?
The number of points that are expected to lie inside the circle is 785.
A circle is a closed two-dimensional figure. In a circle, all points are equidistant from the centre.
As per the given question, the circle is inscribed in a square,
The radius of the circle ( r ) = 1 The side length of the square ( s ) = 2⇒ The area of the circle = π × r × r
= π × 1 × 1
∴ The area of the circle = π
⇒ The area of the square = s × s
= 2 × 2
∴The area of the square = 4
The probability that a randomly selected point inside the square will lie inside the circle,
p = π / 4
The probability that a randomly selected point inside the square will lie outside the circle,
q = 1 - p
q = 1 - ( π / 4 )
⇒ Binomial trial with n = 1000 and p = π / 4,
Number of points expected to lie inside the circle(N) = n × p
= 1000 × ( π / 4 )
= 1000 × ( 3.14 / 4 )
= 1000 × ( 0.785 )
N = 785
Therefore, 785 expected points lie inside the circle.
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The complete question is
Answer: 56 square
Step-by-step explanation:
PLS HURRY!!!Juan divided 12 jar of fish food into 7 equal parts. He feeds his fish one part each day.
What fraction of the jar of food will Juan will feed his fish each day?
Enter your answer as a fraction in simplest form by filling in the boxes.
Answer:1/14
Step-by-step explanation:He divides 1/2 of the jar into sevenths, but if he had the whole jar it would be fourteen parts because 2x7=14, or 14÷2=7
< The concession stand at the baseball park sells food in value packs. The ratio in the value pack is 4 hot dogs 2 drinks: 1 bag of chips. A tape diagram representing the ratio of each item is shown. hot dogs drinks chips a. Describe what each small rectangle in the tape diagram represents b. What is the least total amount of items in a value pack? c. How many bags of chips are in a value pack if there are 10 drinks?
Answer:
someone answer please ive been waiting for 2 hours :skull:
Step-by-step explanation: please answer yall
Solve the equation V = s³ for s.
Answer in the form s = .
[tex]{ \bold{ \sqrt[3]{V}}} [/tex]
Step-by-step explanation:
[tex]{ \green{ \sf{V = s³}}}[/tex]
Cube on both sides, then
[tex]{ \green{ \sf{s = \sqrt[3]{V}}}} [/tex]
you want to order posters to advertise your band. a company charges $109.95 for the first 100 posters and $65 for each additional 100 posters. a. write the equation where $y$ represents the total cost (in dollars) as a function of $x$ , the number (in hundreds) of posters ordered.
The required question based on number of posters is y = 109.95 + 65x.
The cost of additional posters = 65x, based on the mentioned information.The 100 posters make 1 set. Assuming the total number of posters be x. So, the additional sets will be calculated by the formula = (x - 100)/100.
Now, the equation will be the sum of the cost of first 100 posters and the cost of remaining posters.
y = 109.95 + 65x
Thus, the equation with the total cost (in dollars) as a function of the number (in hundreds) of posters ordered is y = 109.95 + 65x.
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suppose 44% of politicians are lawyers. if a random sample of size 853 is selected, what is the probability that the proportion of politicians who are lawyers will be less than 40%? round your answer to four decimal places.
The probability that the proportion of politicians who are lawyers will be less than 40% is 0.009299 .
Given :
Population Proportion ( p ) = ( 44 % ) = 0.44
Sample proportion ( p hat ) = ( 40 % ) = 0.4
Size of sample ( n ) = 853
To find : P ( p hat < 0.4 )
Formula : ( p hat - p ) / [tex]\sqrt{ p * ( 1 - p ) / n }[/tex]
Substituting values in the above formula ,
z = ( 0.4 - 0.44 ) / [tex]\sqrt{ 0.44 * ( 1 - 0.44 ) / 853}[/tex]
z = - 2.3535
z - score = -2.3535
Finding the p - value :
p - value = 0.009299
Therefore , the probability that the proportion of politicians who are lawyers will be less than 40% is 0.009299 .
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What is the length of the hypotenuse in 2 decimal places
Hannah prepares 44 pies for the thanksgiving feast at her school. each pie is cut into 8 pieces. approximately how many students can hannah feed? round to the nearest ten.
Answer:352
Step-by-step explanation:
Find the value of x if 3x = 23² – 17²
Answer:
The answer is 80
A social worker earns an average bi-weekly net pay of $1,465.87. Which compound inequality correctly shows the amount of money, m, the social worker can spend if the monthly budget for debt is between 5% and 10%? $73.29 ≤ m ≤ $146.59 $158.80 ≤ m ≤ $317.61 $146.59 ≤ m ≤ $293.17 $190.56 ≤ m ≤ $349.37
The amount of money the social worker can spend is $146.59 ≤ m ≤ $293.17
What is an equation?An equation shows the relationship between two or more numbers and variables.
Let m represent the amount of money the social worker can spend.
A social worker earns an average bi-weekly net pay of $1,465.87. Hence:
Monthly revenue = 2 * $1465.87 = $2931.74
For a debt of 5%:
m = 5% of $2931.74 = 0.05 * $2931.74 = $146.59
For a debt of 10%:
m = 10% of $2931.74 = 0.1 * $2931.74 = $293.17
$146.59 ≤ m ≤ $293.17
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Answer:
$158.80 ≤ m ≤ $317.61
Step-by-step explanation:
Hello,
So first step is we would use the bi-weekly net pay of $1465.87 then times it by 26 so it would look like this
1465.87 × 26 = 38112.62
Then we would divide 38112.62 by 12
38112.62 ÷ 12 = 3176.0516
Then, we would determine how much the social worker can spend if the monthly budget for debt is between 5% and 10%.
3176.0516 × 5% = 158.80
3176.0516 × 10% = 317.61
So, therefore the answer is $158.80 ≤ m ≤ $317.61.
assume that the heights of men are normally distributed with a mean of 69.0 inches and a standard deviation of 2.8 inches. the u.s. marine corps requires that the heights of men be between 64 and 78 inches. if 500 men want to enlist in the u.s. marine corps, how many would you not expect to meet the height requirements?
The percentage of men who didn't expect to meet the height requirements be 96.29%
Given, that the heights of men are normally distributed with a mean of 69.0 inches and a standard deviation of 2.8 inches.
Find the percentage of men who meet the height requirements.
z(64) = (64-69)/2.8 = 1.7857
z(78) = (78-69)/2.8 = 3.2143
P(64 <= x <= 78) = P(1.78457<= z <=3.2143) = 0.0371 = 3.71%
So, the percentage of men who meet the height requirements be 3.71%
Now, the percentage men who didn't expect to meet the height requirements be
100 - 3.71 = 96.29%
Hence, the percentage of men who didn't expect to meet the height requirements be
96.29%
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help meeeeeeeeeeeeeee pleaseee
The recommended screen size for the television is 59.85 inches.
What is an expression?An expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.
In this case, the expression for the size of the television is given as:
S = 0.228x² + 8.154x - 8.3
where x = 7 feet
S = 0.228x² + 8.154x - 8.3
S = 0.228(7)² + 8.154(7) - 8.3
S = 11.172 + 57.078 - 8.4
S = 59.85
The size is 59.85 inches.
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Find the equation of the linear function represented by the table below in slope-intercept form.
Answer:
y = 8x - 6
Step-by-step explanation:
The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.
We know that the y-intercept occurs when x = 0 so from the table, it's b = -6
We can use the slope formula to find the slope:
[tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\\ \frac{2-(-6)}{1-0} \\\frac{2+6}{1-0} \\8=m[/tex]
What is an equation of the line that passes through the points (4, −2) and (2, 3)?
The equation of the line, in slope-intercept form, that passes through
(4, 2) and (-2, -3) is y = 5/6 x - 4/3.
What is slope-intercept form?
The meaning of slope-intercept form is the equation of a straight line in the form y = mx + b where m is the slope of the line and b is its y-intercept.
Using two points and slope-intercept form we can find the equation of the line.
According to the given question:
The formula to find the slope of two points (x₁, y₁) and (x₂, y₂) is
m = (y₂ - y₁) / (x₂ - x₁)
The points given are (4, 2) and (-2, -3)
m = (-3 - 2) / (-2 - 4)
m = -5/ -6
m = 5/6
Now using the slope and the point (4, 2) the y intercept is
y = mx + b
2 = 5/6 (4) + b
2 = 10/3 + b
By further calculation,
b = 2 - 10/3
Taking LCM
b = (6 - 10)/3 = -4/3
By writing the equation in slope intercept form
y = mx + b
y = 5/6x - 4/3
Therefore, the equation of the line in slope intercept form is
y = 5/6 x - 4/3.
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How do you solve #4 - #9?
4. There is no enough information.
5. ΔPEF ≅ ΔREF are congruent by SAS.
6. ΔKMO ≅ ΔOLK are congruent by SSS.
7. No enough information.
8. ΔPAN ≅ ΔKLC are congruent by SSS.
9. ΔABC ≅ ΔDEF are congruent by SSS.
What is the SSS and SAS Theorems?The SSS and SAS are theorems of triangle congruence that can be used to prove that two triangles are congruent. To prove that two triangles are congruent by SSS, both triangles must have three pairs of corresponding lengths that are congruent, while SAS is used when the two triangles have two pairs of congruent sides that are corresponding, and a pair of congruent included angles.
4. There is no enough information to prove triangles HNJ and RDF are congruent by neither SAS nor SSS.
5. Triangles PEF and REF are congruent by SAS.
6. Triangles KMO and OLK are congruent by SSS.
7. No enough information.
8. Triangles PAN and KLC are congruent by SSS.
9. Triangles ABC and DEF are congruent by SSS.
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Which equation is parallel to x-y=3 passes through (2,-4)
The equation of the line parallel to x - y = 3 and passes through pint (2,-4) is y = x - 6.
What is the equation of line that passes through the given point and parallel to the given equation?The equation of line is expressed as;
y = mx + b
The point-slope formula is expressed as;
y - y₁ = m( x - x₁ )
Where m is slope and b is the y-intercept.
Given the data in the question;
Equation: x - y = 3Point: (2,-4)
x = 2y = -4First, reorder the given equation in slope-intercept form and determine the slope.
x - y = 3
x = 3 + y
3 + y = x
y = x - 3
Hence,
The slope m = 1
To find the line parallel to the equation, the slope must be equal.
Find the line using point-slope formula.
y - y₁ = m( x - x₁ )
Plug in slope m = 1 and point: (2,-4)
y - ( -4 ) = (1)( x - 2 )
Simplify and convert to slope intercept form.
y + 4 = x - 2
y = x - 2 - 4
y = x - 6
Therefore, the equation of line is y = x - 6.
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HALF SOLVED PLEASE HELP
Hey I would rlly appreciate if someone can help IVE been stuck on this and pls make sure to find measure BCD
Answer:
140
Step-by-step explanation:
2x+5x+40=180
7x+40=180
7x=140
x=20
5x+40=BCD
5(20)+40
100+40
140
What is x−16=−88? I don't know what it is
Answer:
x = -72
Step-by-step explanation:
So first you need to get x on its own, so you you need to get rid of -16 by adding +16 which you get 0.
so now x=-88
whatever you do on one side you do on the other, so add 16 to the other side (-88) so you get -72.
x = -72
so the answer is -72
Thank you <3
I’ll brainlist if y’all answer these…
A rectangle has an area of 405 cm square and width of 15 cm. The length of the rectangle is:
A) 27 cm
B) 20 cm
C) 390 cm
D) 6075 cm
The x- and y- intercepts of the graph of the line 5x - 3y - 15 = 0 are, respectively
A) 3 and -5
B) -3 and 5
C) 5 and -3
D) -5 and 3
The expression that simplifies to 11x + 2y is:
A) 4x + 3y + 7x - y
B) 13xy- 2y+ 2 + y
C) 9 x square + y + y + 2x
D) 5 + 6x + 2y
Answers: A, A, A
1)A rectangle has an area of 405 cm square and width of 15 cm. The length of the rectangle is: 27 cm
15cmx 27cm= 405 cm
2)The x- and y- intercepts of the graph of the line 5x - 3y - 15 = 0 are, respectively: 3 and 5
(I don't really know how to explain this.......)
3)The expression that simplifies to 11x + 2y is: 4x+3y+7x-y
4x+7x=11x
3y-y = 2y
Therefore, it will equal to 11x+2y.
I really hope this helps!
Please Mark Me Brainliest!!!
(I'm in 5th Grade Honors but I learn MS)
Answer:
All the answer are A
Step-by-step explanation:
Area = length times width
405 = x15 Divide both sides by 15
27 = x
For the x intercept Let y = o and solve for x
5x - 3y -15 = 0
5x - 3(0) -15 = 0
5x -15 = 0 Add 15 to both sides of the equation
5x = 15 Divide both sides by 5
x = 3
The x intercept is (3,0)
For the y intercept Let x = 0 and sole for y
5x -3y -15 = 0
-3y -15 = 0 Add 15 to both sides of the equation
-3y = 15 Divide both sides by -3
y = -5
The y intercept is (0,-5)
4x + 3y + 7x - y Combine the like terms
(4x + 7x) = (3y -y)
11x + 2y
A hippopotamus can run 6 kilometers in 15 minutes. At this rate, how far can the hippopotamus run in 1 minute?
Answer:
400meters
Step-by-step explanation:
Find the speed of the hippopotamus by dividing distance with time
6000 meters ÷15minutes =400meters/minutes
The measures of the angles of a triangle are shown in the figure below. Solve for x.
Answer:
x = 82°
Step-by-step explanation:
The three angles of the triangle add up to 180°
x + 40° + 58° = 180°
x + 98° = 180°
subtract 98°
x = 82°
Answer:
x = 82°
Step-by-step explanation:
The sum of the internal angles of a triangle = 180°
58° + 40° + x° = 180°
98° + x° = 180°
x° = 180° - 98°
x° = 82°
what is the definition of pi
and multiply it to a decimal number
(any equation)[tex]\pi[/tex]
Pi written as 3.l4 and π in mathematics is the ratio for the diameter of a circle to the circumference of that circle. The value is unending
What is Pi?Pi, which is represented by the Greek letter p, or, is a shorthand for the ratio of a circle's diameter to its circumference. No matter how big the circle is, this ratio will always be equal to pi. The value of pi is about 3.14 in decimal notation.
We are to multiply Pi to any equation
let the equation be (20.5 + 3x)[tex]\pi[/tex]
pi is represented in numbers by 3.14
Hence we would have the equation to be of the form
(20.5 + 3x)3.14
multiply through the bracket
64.37 + 9.42x
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2015
The ratio of boys to girls in a class is 4:3. There are 35 students in the class. How many
students are boys?
the idea that a large number of sample means or proportions will approximate a normal distribution, regardless of the distribution of the population from which they were drawn, is known as: random error simple random sample sample variance population variance central limit theorem
The Central Limit Theorem gives the idea that a large number of sample means or proportions will approximate a normal distribution, regardless of the distribution of the population from which they were drawn .
Central Limit Theorem : In probability theory , the Central Limit Theorem establishes that , in many situations , when independent random variables are summed up , their properly normalized sum tends toward a normal distribution even if the original variables themselves are not normally distributed .
The Central Limit Theorem gives the idea that a large number of sample means or proportions will approximate a normal distribution, regardless of the distribution of the population from which they were drawn .
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[tex]log_{2} (\sqrt[3]{16})[/tex]
The value of the given expression will be 4 / 3.
What is a logarithmic expression?An equation using the logarithm of an expression containing a variable is referred to as a logarithmic equation. Check to verify if you can write both sides of the equation as powers of the same number before attempting to solve an exponential equation.
Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication and division.
Given logarithmic expression is log₂(∛16). The expression will be solved as below,
[tex]E = log_2\sqrt[3]{16}\\E = log_2(2^{\frac{4}{3})\\E = \dfrac{4}{3}log_22\\E = \dfrac{4}{3}[/tex]
Therefore, the solution of the expression will be equal to 4 / 3.
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The sum of 12 and a number. Use n for the variable. Responses 12/n 12/n 12 x n 12 x n 12 - n 12 - n 12 + n
The expression for the sum is (12 + n).
We are given two terms to add. The first number is 12, which is an integer. The second number is unknown. An integer is a number that has no decimal or fractional portion and can be negative or positive, including zero.
The second number is represented by a variable "n". A variable is a mathematical object's symbol and placeholder. A variable can, for example, represent an integer, a vector, or other data.
We need to write the expression for the sum of these two numbers. Let S represent the sum of these two numbers.
S = 12 + n
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flaws in a carpet tend to occur randomly and independently at a rate of one every 270 square feet. what is the probability that a carpet that is 7 feet by 12 feet contains no flaws?
The probability that a carpet that is 7 ft × 12 ft contains no flaws is 0.732
What is the Poisson Distribution Formula?The Normal, Binomial, and Poisson Distributions are the three types of continuous and discrete data-based distributions used in probability and statistics. The distribution of unusual occurrences is another name for the Poisson distribution. This is mostly used to forecast the likelihood of future events based on how frequently the past events occurred. It offers the chance that a specific number of events might happen during a particular time frame.
The formula for Poisson distribution is given below:
P(x) = (e^-x * m^x) / x!
Here we have,
flaws in a carpet tend to occur randomly and independently at a rate of one every 270 square feet
Given the dimensions of carpet = 7 feet × 12 feet
=> area of the carpet = 84 feet²
=> the expected mean of defects m = [1/270]*84 = 0.311
Now use the Poisson formula
P[x] = e^-m × m^x / x!
=> P(x = 0) = e^-(0.31) × 0.31^(0) / 0!
= (0.732 × 1)/1 = 0.732
Therefore,
The probability that a carpet that is 7 ft × 12 ft contains no flaws is 0.732
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