Answer:
y intercept on the first on is 2 and the second one is 40
Step-by-step explanation:
IM TRYING
i)The y intercept is 2 and it represents the cost of bowling
the slope is change in y / change in x
= choose points ok
so i go 4/1 = 4
so, (ii) The slope is 4 it represents the rate of change in the cost for the number games played
The equation of the line is (so our points are 0,2 and 2,10 .. using y=mx+c w e get y=4x+2
iii)The equation of the line is y=4x+2
2ND
i) The y intercept is 40 and it represents the total charge of the vehicle repair shop
ii) The slope is 1 it represents the rate of change of the time taken for the vehicle repair
iii)The equation of the line is y=1x+2
A test worth 100 points has a total of 30 multiple choice and true-false questions. Each multiple choice question is worth 4 points and each true-false item is worth 2 points. How many multiple choice questions and how many true-false questions are on the test?
Answer:
um
Step-by-step explanation:
As a construction manger, you are asked to build a new road which crosses the point (5,3). There is another road already built whose location can be expressed as y=5x-2. you are asked to build your road such that it intersects making a right angle on the blue-print. write a statement to represent the locations of the new road and the road is already built. provide evidence that algebraically justifies your responses
The product of the slopes is -1, we can conclude that the two roads intersect at a right angle at the point (10/11, 18/11).
What is slope?
In mathematics, slope refers to the steepness or incline of a line on a graph. It is a measure of how much the dependent variable changes for every unit change in the independent variable.
To build the new road such that it intersects the existing road at a right angle at the point (5,3), we can start by determining the slope of the existing road.
The slope of the existing road, given by the equation y=5x-2, is 5. This is because the equation is in slope-intercept form, y=mx+b, where m is the slope and b is the y-intercept. Therefore, we know that the slope of any line perpendicular to this road will be -1/5, since the product of the slopes of perpendicular lines is -1.
To find the equation of the new road, we can use the point-slope form of a linear equation, which is y-y1=m(x-x1). We know that the new road passes through the point (5,3) and has a slope of -1/5. So, substituting these values into the equation gives:
y - 3 = (-1/5)(x - 5)
Simplifying this equation, we get:
y = (-1/5)x + 4
Therefore, the equation of the new road is y = (-1/5)x + 4, and the equation of the existing road is y = 5x - 2. These two equations represent the locations of the new road and the existing road, respectively.
To verify that the new road intersects the existing road at a right angle, we can find the point of intersection of the two roads and then check that the product of the slopes of the two lines is -1.
To find the point of intersection, we can set the two equations equal to each other:
(-1/5)x + 4 = 5x - 2
Solving for x, we get:
x = 10/11
Substituting this value of x back into either equation gives:
y = 18/11
So the point of intersection is (10/11, 18/11).
Now, to check that the two roads intersect at a right angle, we can find the slopes of the two lines and check that their product is -1:
Slope of existing road, m1 = 5
Slope of new road, m2 = -1/5
Product of slopes, m1m2 = 5(-1/5) = -1
Since the product of the slopes is -1, we can conclude that the two roads intersect at a right angle at the point (10/11, 18/11).
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A church luncheon made $842. Adult tickets cost $10 each and children’s tickets cost $6 each. The number of children was 12 more than twice the number of adults. How many of each ticket were sold?
the number of adult ticket's sold = 35
And the number of child ticket's sold = 2 x 35 + 12 = 70 + 12 = 82
Step-by-step explanation:
Answer:
312
Step-by-step explanation:
12*6 for children 24 of adult because of of double children 24*10 240 so 240+72=312
The RLX Company just paid a dividend of $2.85 per share on its stock. The dividends are expected to grow at a constant rate of 4.5 percent per year, indefinitely. Assume investors require a return of 10 percent on this stock. What is the current price?
The current stock price is $54.15.
Given that RLX Company just paid a dividend of $2.85 per share on its stock and dividends are expected to grow at a constant rate of 4.5 percent per year, indefinitely.
Stock valuation alludes to the valuation of the natural worth per portion of an organization's stock which can help the organization in deciding its reasonable worth in case of twisting up or consolidation. One of the models used to esteem the stock cost is the profit development model. It expects the cost of the stock to be the current worth representing things to come profits of the stock accepted to develop at a consistent rate.
Dividend (D0) = $2.85
Growth rate (g) = 4.5%
Required return (r) = 10%
Firstly, we have to calculate the value of the current stock price.
The current stock price can be calculated by using the dividend growing model.
\(\begin{aligned}\text{Current stock price}&=\frac{D_{0}\times(1+g)}{r-g}\\ &=\frac{2.85\times (1+0.045)}{0.10-0.045}\\ &=\frac{2.85\times 1.045}{0.055}\\ &=\frac{2.97825}{0.055}\\ &=54.15\end\)
Hence, the current stock price when dividend of $2.85 are expected to grow at a constant rate of 4.5 percent per year, indefinitely is $54.15.
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A. find the surface area of the glass surfaces of the fish tank B. Find the surface area of the plastic surface of the fish tank
To determine the surface area of the glass surfaces, we will determine the area of each rectangle and sum them.
The area of a rectangle is given by the following formula:
\(A=legth*width.\)Now, the rectangles that compose the total surface area of glass have dimensions:
\(32in\times12.75in,\text{ 32in}\times19in,12.75in\times19in.\)Therefore, the total area adding up the areas of the rectangles is:
\(A_t=32in\times12.75in+2\times12.75in\times19in+2\times32in\times19in.\)Answer part a:\(2108.5in^2.\)Now, the area covered by the plastic lid is the area of a rectangle of dimensions
\(32in\times12.75in.\)Therefore, the surface area of the plastic surface is:
\(408in^2.\)Answer part b:\(408in^2.\)HELP PLS ASAPPP!!!
algebra problem; solving linear inequalities !!! :)
Answer: x = -3/2
Step-by-step explanation:
how is a system of two linear inequalities in two variables similar to a system of two linear equations in two variables?
a. point of intersect
b. overlaps
c. boundary lines
d. points that are not boundary lines
A system of two linear inequalities in two variables is similar to a system of two linear equations in two variables in that they both have the following features:
a. Point of intersection: Both systems of equations and inequalities can have one or more points of intersection, which are the points at which the lines or planes representing the equations or inequalities intersect.
b. Overlaps: Both systems can have overlapping regions, which are areas in the coordinate plane that satisfy both equations or inequalities.
c. Boundary lines: Both systems can have boundary lines, which are the lines that represent the equations or inequalities and divide the coordinate plane into different regions.
d. Points that are not boundary lines: Both systems can have points that are not boundary lines, which are points that do not lie on the lines representing the equations or inequalities.
if f(5x)=f(5)+f(x) then prove f(1)=0
Answer:
2&4+44-24÷333×6385
Step-by-step explanation:
so it can be a cardinal product
If functions f(5x)=f(5)+f(x) then f(1)=0.
What is a function?A relation is a function if it has only One y-value for each x-value.
Given that f(5x)=f(5)+f(x)
f of five times of x equal to f of five plus f of x.
We need to prove f(1) is equal to zero.
f(5x)=f(5)+f(x)
Let plug in x value as one
f(5×1)=f(5)+f(1)
f(5)=f(5)+f(1)
Subtract f(5) from both sides
f(1)=0
Hence, if functions f(5x)=f(5)+f(x) then f(1)=0.
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In Houston, 9 bats ate 50 grams of insects in one night. At this rate, how many grams of insects could 81 bats eat in one night?
Answer:
Step-by-step explanation:
Remark
Using Algebra, this is a proportion question. A proportion is 2 equal ratios
If the of the 2 ratio parts are known, it is possible to solve for the 4th one.
Formula
9_bats/50_grams::81_bats/x grams insects
Solution
Put the three knowns in and solve for the 4th which is not known
9 bats/ 50 insects = 81 bats /x insects. Cross multiply
9 * x = 50 * 81 Combine
9x = 4050 Divide by 9
9x/9 = 4050/9
Answer: x = 450 grams
A group of band instructors answered a survey about hours of rehearsal per week and number of competitions won. The graph shows the results of this survey.
Based on these results, if a band practices 5 hours per week next season, which is the best estimate of the number of competitions the band can expect to win?
A.
36
B.
31
C.
27
D.
24
Answer: B. 31
Step-by-step explanation:
This linear regression was constructed by relating the hours practiced per week and the number of competitions won.
Going by this graph, the number of competitions they can expect to win at 5 practices a week is 31.
This is derived by looking for the point where 5 competitions on the x-axis intersects with the line. This point is at 31 competitions on the y axis which would make it the answer.
Answer:
its B
Step-by-step explanation:
i took the quiz on PLATO
Please help!!! I've been trying to figure this out all day!
The American College of Sports Medicine considers age as one factor when it recommends low and
high heart rates during workout sessions.
For safe and efficient exercise, your heart rate should be between 55% and 90% of the maximum
heart rate level. The maximum heart rate is calculated by subtracting a person's age from 220
beats per minute.
(Let a represent a person's age and h represent the person's recommended heart rate.)
1. The following equation represents the low value for heart rate. Simplify the equation.
h = .55(220-a)
2. The following equation represents the high value for heart rate. Simplify the equation.
h = .90(220-a)
3. Use these two expressions to write a system of inequalities that represents the heart rate range
for safe and efficient exercise. (Hint: you need to write two separate inequalities)
Answer:
.55(220-a) + .90(220-a)
Step-by-step explanation:
Use the number line below to determine which of the following answer choices had statements that are all true
The choice that had statements that are all true is (a) Point B = -2 1/2, Point D = 1 3/4 and 1 3/4 > -2 1/2
How to determine the choices that had statements that are all trueThe complete question is added as an attachment
From the question, we have the following parameters that can be used in our computation:
The number line
On the number line, we have the following
A = -4
B = -2 1/2
C = 1
D = 1 3/4
When the above values are compared with the list of options, we have
Option (A) = true
This is so because in (a)
Point B = -2 1/2, Point D = 1 3/4 and 1 3/4 > -2 1/2
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I need help if right I will mark you as brainlest
Answer:
More than 275 dollars of here budget goes to emergencies
Step-by-step explanation:
11% of 2750 is $302.50
What is the value of the expression expression 9 – m. If m = –3, n = 8, and p = –1?
Answer:
Step-by-step explanation:
i do believe you didn't write the whole problem
if m=-3
9-m=9-(-3)=9+3=12
Choose the correct answer below
The correct statement is;
False, because x = \(cos^-^1({\frac{-1}{2} )\) is in the interval \(( -\frac{\pi }{2} , \frac{\pi }{2} )\) that is, \(cos^-^1({\frac{-1}{2} )\) = \(\frac{2\pi }{3}\). So all solutions of cos x = -1/2 will be x = 2π/3 + 2nx and x = 4π/3 + 2nx.
Option D
How to determine the statementFrom the information given, we have that;
All solutions are cos x = -1/2 are given by x = 4x/2 + 2πx
There are multiple solutions to the equation cos x = -1/2, and they are denoted by the values x = 2π/3 + 2nx and x = 4π/3 + 2nx
Such that n is an integer.
This is so because the cosine function repeats itself every 2π, or its period. We therefore multiply the general answer by multiples of 2 to obtain all solutions.
The formula x = 4x/2 + 2πx implies that each solution can be reached by x being multiplied by 4/2 and 2πx being added.
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Please help if you can, this is due tomorrow.
In the diagram below, $\angle BAC=24^\circ$ and $AB=AC$.
If $\angle ABC=y^\circ$, what is the value of $y$?
[asy]
size(4.25cm);
pair a=(0,cos(pi/15)); pair b=(-sin(pi/15),0); pair c=-b; pair d=c+(1,0);
dot(a); dot(b); dot(c);
draw(c--a--b--c);
draw((2*a+3*b)/5-0.05*(cos(pi/15),-sin(pi/15))--(2*a+3*b)/5+0.05*(cos(pi/15),-sin(pi/15)));
draw((2*a+3*c)/5-0.05*(cos(pi/15),sin(pi/15))--(2*a+3*c)/5+0.05*(cos(pi/15),sin(pi/15)));
label(scale(0.75)*"$24^\circ$",a-(0,0.3),S);
label("$A$",a,N);
label("$B$",b,SSW);
label("$C$",c,S);
label(scale(0.85)*"$y^\circ$",b,NE);
[/asy]
The given diagram implies that the triangle $ABC$ is an isosceles triangle with angles of $24^\circ$. This can be verified by computing the length of the hypotenuse and using the Pythagorean Theorem.
What is equation?Equation is a mathematical expression that consists of variables, symbols, and numbers, and shows the relationship between different quantities. An equation can involve one or more unknowns, and can be represented as an equality or as an inequality. Solving an equation requires understanding the relationship between the different elements in the equation, and manipulating the equation to isolate the unknowns. Common types of equations include linear equations, quadratic equations, and polynomial equations.
From this diagram, we can conclude that $\angle ABC$ is an isosceles triangle. This is because the angles opposite equal sides of a triangle must be equal. Since $\angle BAC=24^\circ$, $\angle ABC$ must be $24^\circ$. Furthermore, the sides $AB$ and $AC$ are equal, so $ABC$ is an isosceles triangle.
This conclusion can be verified by using the Pythagorean Theorem. If $AB=AC$, then it follows that $BC = \sqrt{AB^2 + AC^2} = \sqrt{2AB^2}$. Since $AB=3$, it follows that $BC=\sqrt{2*3^2}=6$. Therefore, the triangle $ABC$ is a right triangle with legs of length 3 and hypotenuse of length 6. Since $\angle BAC = 24^\circ$, it follows that $\angle ABC = 24^\circ$, verifying that the triangle is isosceles.
In conclusion, the given diagram implies that the triangle $ABC$ is an isosceles triangle with angles of $24^\circ$. This can be verified by computing the length of the hypotenuse and using the Pythagorean Theorem.
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Answer:
78
Step-by-step explanation:
1. Find the scale factor from the large figure to the small figure.
2. Find the scale factor from the small figure to the large figure.
Answer:
sorry I can see the whole answer on the image
What is 2/5x6 equal to
two adjacent angles form a right angle the larger angle is 3 times the measure of the smaller angle which is the measure of the larger angle
Answer:
30 degrees
Step-by-step explanation:
30..........................................................
about 4% of the population has a particular genetic mutation. 100 people are randomly selected. round your answer to three decimal places. (a) Find the mean for the number of people with the genetic mutation in such groups of 600. (b) Find the standard deviation for the number of people with the genetic mutation in such groups of 600.
We got the mean value 4.167 and standard deviation 19.56.
What is mean value and standard deviation in statistics?In statistics, a mean value is the average value of all the available data. And it can be determined by adding all the data by dividing the amount of data.
A standard deviation is an estimation that implies how far each available data apart from the mean value.
How do we calculate the mean value and standard deviation?we are given, 4% of the population has a genetic mutation
Total people in the group =600
Now, total number of people who have genetic mutation = (4/100) ×600
= 24
the number of randomly selected people =100= X
Mean = Number of selected people/ people who have mutation
Mean = X/n = 100/24 = 4.167
the standard deviation = √∑(X-mean) ²/n
= √∑(selected people - mean) ²/ mutation number
=√(100-4.167) ²/24
standard deviation = 19.56
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Write a two column proof (Given: x is the midpoint of WY and VZ) (Prove: VW=ZY)
Bruce and Felicia would have a unique solution to the given equation. The value of x that satisfies the equation is 15.
To determine if the equation 6x + 2 = 5x + 17 has a unique solution, we need to check if the variable x has a consistent value that satisfies the equation.
By simplifying the equation, we can see that the equation becomes:
6x - 5x = 17 - 2
Simplifying further, we have:
x = 15
Since the variable x has a specific value, in this case, x = 15, the equation does have a unique solution. When x is substituted with 15 in the equation, both sides are equal.
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What is X if [-1,-2,4,8]+x=[-5,-1,2,1]
Answer:
C) -4 1
-2 -7
Step-by-step explanation:
I got it right on Edge 2021
The value of x in expression is,
⇒ x = [- 4, 1, - 2, - 7]
What is mean by Subtraction?Subtraction in mathematics means that is taking something away from a group or number of objects. When you subtract, what is left in the group becomes less.
Given that;
The expression is,
[-1, -2, 4, 8] + x = [-5,- 1, 2, 1]
Now, We can simplify as;
x = [- 5, - 1, 2, 1] - [ - 1, - 2, 4, 8]
x = [- 4, 1, - 2, - 7]
Thus, The value of x in expression is,
⇒ x = [- 4, 1, - 2, - 7]
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what is the best partial quotient to 296dividedby4
Which graph shows the information in the table?
Calories in Salad Dressing
Number of Ounces of Salad
Dressing
2
3
4
5
Total Calories
300
450
600
750
Answer: Number 2
Step-by-step explanation: yes
Information for Questions 5-7: The Annual Survey of Colleges in the U.S. also reports on the average amount of student loan debt by state. The most recent data by state showed an approximately normal shape with a minimum average amount of
$19,000
and a maximum average amount of
$38,000
. Use the minimum and maximum value and the normal shape to estimate the mean and standard deviation of the data for the 50 states. (Mean and standard deviation have been rounded to the nearest
$100
.) a. mean
=$25,000;
standard deviation
=$3,500
b. mean
=$26,800;
standard deviation
=$2,100
c. mean
=$26,800;
standard deviation
=$3,700
d. mean
=$28.500;
standard deviation
=$1,800
e. mean
=$28,500;
standard deviation
=$3,200
A federal study of student loan debt plans to focus on those states with the highest amounts of student loan debt. The study plans on targeting those states that fall in the top
2.5%
in terms of average student loan amounts. What is the cutoff point that would place a state in the top
2.5%
based on student loan debt? (Use the mean and standard deviation estimates from Question #5.) a.
$38,100
b.
$34,900
c.
$31,700
d.
$32,500
e.
$22,100
The correct answer is $34900.
X : Average amount of loan of student debt by state .
X = N ( μ = $28500 , σ² = ( 3200 )² )
To find : What is the cutoff point that would place a state in top 2.5%
Let it be X
P( X > x ) = 0.025
P(X-μ/σ > X - 28500/3200) = 0.025
P(z >Z ) = 0.025
1 - P(z<Z ) = 0.025
P(z<Z ) = 0.975
φ(z) = 0.975
Z = φ⁻¹(0.975)
X - 28500/3200 = 1.96
X = 34772
i.e; P(X > 34772) = 0.025
Since, it is nearly equal to $34900 option b is correct.
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Solve the equation using Gauss Naïve method, a) 3x1 − 2x2 + x3 = −10, 2x1 + 6x2 − 4x3 = −10, −8x1 − 2x2 + 5x3 = −26
Answer:
Step-by-step explanation:
Given the system of equation
3x1 − 2x2 + x3 = −10 ............. 1
2x1 + 6x2 − 4x3 = −10 ............ 2
−8x1 − 2x2 + 5x3 = −26 ............... 3
Reduce the system of equations:
multiply equation 1 by 3 and add to 2
Eqn 1 * 3 gives;
9x1 − 6x2 + 3x3 = −30
Add to equation 2:
9x1+2x1 +(3x3-4x3) = -30-10
11x1 - x3 = -40 ........... 4
multiply eqn 3 by 3 and add to eqn 2
eqn 3 * 3 gives
−24x1 − 6x2 + 15x3 = − 78
Add to eqn 2:
-24x1+2x1)+15x3-4x3 = -78-10
-22x1 + 11x3 = -88 ......... 5
solve 4 and 5:
11x1 - x3 = -40 ........... 4 * 2
-22x1 + 11x3 = -88 ......... 5 * 1
.....................................................
22x1 - 2x3 = -80
-22x1 + 11x3 = -88
Add together:
-2x3 + 11x3 = -80-88
9x3 = -168
x3 = -168/9
x3 = 18.7
subtitute x3 = 18.7 into 4
11x1 - 18.7 = -40
11x1 = -40+18.7
11x1 = -21.3
x1 = -21.3/11
x1 = -1.93
Substitute x1 and x3 into 1
3(-1.93)− 2x2 + 18.7 = −10
- 5.79-2x2 = -28.7
-2x2 = -18.7 +5.79
-2x2 = -22.91
x2 = 11.455
Expand the function.
f(x) = (3x-4)4
81x4 − 432x³ + [? ]x²
+
-
X +
PLS HELP
The expansion of the function \((3x - 4)^4\) simplifies to \(81x^4 - 432x^3 + 864x^2 - 768x + 256.\)
To expand the function \(f(x) = (3x - 4)^4\), we can use the binomial theorem. According to the binomial theorem, for any real numbers a and b and a positive integer n, the expansion of \((a + b)^n\) can be written as:
\((a + b)^n = C(n, 0)a^n b^0 + C(n, 1)a^{(n-1)} b^1 + C(n, 2)a^{(n-2)} b^2 + ... + C(n, n-1)a^1 b^{(n-1)} + C(n, n)a^0 b^n\)
where C(n, k) represents the binomial coefficient, which is given by C(n, k) = n! / (k!(n-k)!).
Applying this formula to our function \(f(x) = (3x - 4)^4\), we have:
\(f(x) = C(4, 0)(3x)^4 (-4)^0 + C(4, 1)(3x)^3 (-4)^1 + C(4, 2)(3x)^2 (-4)^2 + C(4, 3)(3x)^1 (-4)^3 + C(4, 4)(3x)^0 (-4)^4\)
Simplifying each term, we get:
\(f(x) = 81x^4 + (-432x^3) + 864x^2 + (-768x) + 256\)
Therefore, the expanded form of the function \(f(x) = (3x - 4)^4\) is \(81x^4 - 432x^3 + 864x^2 - 768x + 256\).
Note that the coefficient of \(x^3\) is -432, the coefficient of \(x^2\) is 864, the coefficient of x is -768, and the constant term is 256.
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Note the complete question is
Question 2 Multiple Choice Worth 2 points)
(03.02)
Which of the following is a zero for the function f(x) = (x - 15)(x + 1)(x - 10)?
Answer:
The zeros of the function are: -1,10,15
Step-by-step explanation:
f(x) = (x - 15)(x + 1)(x - 10)
We can use the zero product property
0 = (x - 15)(x + 1)(x - 10)
x-15 =0 x+1 =0 x-10 =0
x=15 x = -1 x= 10
The zeros of the function are: -1,10,15
Answer:
Step-by-step explanation:
i have no clue
statistics that specify how likely findings are to be true for other populations or in other locales is called statistics.
The study of data collection, analysis, presentation, and interpretation is known as statistics.
Given,
What is statistics?
Data collection, analysis, presentation, and interpretation are all part of the science of statistics. Much of the early motivation for the subject of statistics came from governmental needs for information on a variety of economic activity and census data.
Types of statistics;
Based on the characteristics, the various statistical kinds are divided: Statistics that are descriptive and inferential. We analyze and understand data based on how it is presented, such as using pie charts, bar graphs, or tables.
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Make (a) as the subject S = 3t + at2
the answer is ( a=st2-3t )