Answer: You have the correct answer. It is y = 150x-50
Nice work on getting the correct answer. For anyone curious, the explanation is below.
=============================================
x = number of hours the stand is open
y = amount earned
(1,100) is from the fact the stand is open 1 hour and earns $100
(3,400) is due to the stand earning $400 after 3 hours.
Slope Formula
m = (y2 - y1)/(x2 - x1)
m = (400-100)/(3-1)
m = 300/2
m = 150 is the slope, and it is the amount earned per hour. It is the rate of change.
Use m = 150 and (x,y) = (1,100) to find the value of b as shown below
y = mx+b
100 = 150(1) + b
100 = 150 + b
100-150 = b
-50 = b
b = -50 is the y intercept and it is the starting amount they earn. The negative earning indicates that they spent $50 to set up the stand, which is the cost of buying the food, equipment, etc.
So we have m = 150 as the slope and b = -50 as the y intercept.
Therefore, y = mx+b turns into y = 150x-50.
-------
As a check, plugging in x = 1 should lead to y = 100
y = 150x-50
y = 150(1)-50
y = 150-50
y = 100 and indeed it does
The same should be the case with (3,400). Plug in x = 3 and we should get y = 400
y = 150x-50
y = 150(3)-50
y = 450-50
y = 400, we have confirmed the answer by showing that the line y = 150x-50 goes through the two points (1,100) and (3,400).
The equation for revenue earned from being opened for x hours will be y=150x-50 so it is absolutely correct.
How to form an equation?Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.
In other words, an equation is a set of variables that are constrained through a situation or case.
Given,
$100 for 1 hour
So,
x = 1 and y = 100
And,
$400 for 3 hour
So,
x = 3 and y = 400
Now the slope of the linear equation is given by
m = difference in ys coordinate / difference in xs coordinate
m = (400 - 300)/(3-1) = 150
So equation become
y = 150x + b
Now put (3,400) to find out b
400 = 150(3) + b
b = -50
So, equation
y = 150x - 50
Hence " The equation for revenue earned from being opened for x hours will be y=150x-50".
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Find the value of x in the triangle shown below
Answer:
62 degrees
Step-by-step explanation:
As two sides shown are same in length thus angle containing by them will be also same.
Thus, other unmarked angle will also be x degrees.
one angle is 56 degrees
we know that sum of angle of triangle is 180 degrees.
Thus
x + x + 56 = 180
2x + 56 = 180
2x = 180 - 56 = 124
x = 124/2 = 62
Thus, value of x is 62 degrees.
a) John is 3 years older than his brother Brian, the product of their ages is 54 i) Express this information in equation form ii) Show this information as a quadratic equation iii) Hence, solve the equation to find their individual ages
Answer:
Brian is 6 years old, John is 9 years old
Step-by-step explanation:
i.
J = 3 + B
J x B = 54
ii.
(3 + B) x B = 54
B² + 3B = 54
iii.
(B + 9)(B - 6) = 0
B = -9 or 6 -- -9 is irrational as one cannot be negative years old
Brian = 6 years old; therefore, John = 9 years old
HELP ASAP PLEASE (25 POINTS) Solve and reduce if possible. 5/12 − 7/8 = ?
Answer:
-11/24
Step-by-step explanation:
5/12 - 7/8
We need to get a common denominator of 24
5/12 *2/2 - 7/8 *3/3
10/24 - 21/24
-11/24
Answer:
-11/24
Step-by-step explanation:
Well to solve 5/12 - 7/8 we need to find the LCM.
12 - 12, 24, 36, 48
8 - 8, 16, 24, 32, 40
So the LCM is 24.
Meaning we need to make both denominators 24.
12*2 = 24 5*2 = 10
10/24
8*3 = 24 7*3 = 21
21/24
10/24 - 21/24
= -11/24
Thus,
the answer is -11/24.
Hope this helps :)
if one tenth of a number is added to 2. the result is half of that number. what is the number?
Answer:
5
Step-by-step explanation:
According to the given question, the calculation of number is shown below:-
Let the number be x.
[tex]\frac{1}{10}[/tex] of x will be added to the number of 2, so that the result is half of x.
[tex]2 + \frac{1}{10} x = \frac{1}{2} x[/tex]
Now we will solve the above equation
[tex]2=\frac{1}{2} x-\frac{1}{10} x\\\\2=\frac{2x}{5}\\\\10=2x\\\\\frac{10}{2} =x\\\\[/tex]
x = 5
Therefore the correct answer is 5
Hence, the number based on the given information provided in the question is 5
The world's largest university (by enrollment) is University A, followed by University B. If the enrollment in University A is 3.5 million more students than University B and their combined enrollment is 9.5 million students, find the enrollment for each university?
pls answer for my little friend A paperweight in the shape of a rectangular prism is shown (in the picture) If a cross section of the paperweight is cut parallel to the base, which shape describes the cross section? Rectangle Triangle Parallelogram Hexagon (DO NOT look answers up on another brainly answer pls)
Answer:
Hey there!
The cross section would be a rectangle. No matter where you cut the figure parallel to the base, the cross section would be a rectangle.
Let me know if this helps :)
Answer: Rectangle
Step-by-step explanation:
In a rectangular prism, every cross-section parallel to a side is a rectangle.
Hope it helps <3
In a survey of 300 T.V. viewers, 40% said they watch network news programs. Find the margin of error for this survey if we want 95% confidence in our estimate of the percent of T.V. viewers who watch network news programs.
Answer:
0.05543Step-by-step explanation:
The formula for calculating the margin of error is expressed as;
[tex]M.E = z * \sqrt{\frac{p*(1-p)}{n} }[/tex] where;
z is the z-score at 95% confidence = 1.96 (This is gotten from z-table)
p is the percentage probability of those that watched network news
p = 40% = 0.4
n is the sample size = 300
Substituting this values into the formula will give;
[tex]M.E = 1.96*\sqrt{\frac{0.4(1-0.4)}{300} }\\ \\M.E = 1.96*\sqrt{\frac{0.4(0.6)}{300} }\\\\\\M.E = 1.96*\sqrt{\frac{0.24}{300} }\\\\\\M.E = 1.96*\sqrt{0.0008}\\\\\\M.E = 1.96*0.02828\\\\M.E \approx 0.05543[/tex]
Hence, the margin of error for this survey if we want 95% confidence in our estimate of the percent of T.V. viewers who watch network news programs is approximately 0.05543
Dilate the line segment AB with endpoints A(–3,1) and B(4,–2) about the origin with a scale factor 3. Find the endpoints of the dilated line segment. Question 24 options: A′(–3,1), B′(12,–6) A′(0,4), B′(7,1) A′(–9,3), B′(4,–2) A′(–9,3), B′(12,–6)
Answer:
Step-by-step explanation:
To do the dilation, simply multiply each coordinate by the scale factor. That is
(-3,1)*3 = (-9,3) and (4,-2) * 3 = (12,-6). So the new points are A'(-9,3) and B'(12,-6)
Various studies indicate that approximately 11% of the world's population is left handed. You think this number is actually higher. You take an SRS of 225 people and find that 31 of them are left handed. Test your claim at the 5% significance level.
A. State your null and alternative hypotheses.
B. Sketch the rejection region.
C. Calculate the test statistic.
D. Determine the P-value for your test.
Answer:
a. H0 : p ≤ 0.11 Ha : p >0.11 ( one tailed test )
d. z= 1.3322
Step-by-step explanation:
We formulate our hypothesis as
a. H0 : p ≤ 0.11 Ha : p >0.11 ( one tailed test )
According to the given conditions
p`= 31/225= 0.1378
np`= 225 > 5
n q` = n (1-p`) = 225 ( 1- 31/225)= 193.995> 5
p = 0.4 x= 31 and n 225
c. Using the test statistic
z= p`- p / √pq/n
d. Putting the values
z= 0.1378- 0.11/ √0.11*0.89/225
z= 0.1378- 0.11/ √0.0979/225
z= 0.1378- 0.11/ 0.02085
z= 1.3322
at 5% significance level the z- value is ± 1.645 for one tailed test
The calculated value falls in the critical region so we reject our null hypothesis H0 : p ≤ 0.11 and accept Ha : p >0.11 and conclude that the data indicates that the 11% of the world's population is left-handed.
The rejection region is attached.
The P- value is calculated by finding the corresponding value of the probability of z from the z - table and subtracting it from 1.
which appears to be 0.95 and subtracting from 1 gives 0.04998
Which of the following statements is true?
A.
the segment bisects segment
B.
the segment DE bisects segment
C.
the segment is perpendicular to segment
D.
segment is congruent to segment
The correct statement about the line segment is,
⇒ the segment DE bisects segment AC.
What is Line segment?Line segment is a part of the line which have two endpoints and bounded by two distinct end points and contain every point on the line which is between its endpoint.
Given that;
Triangle ABC is shown in figure.
Now, We can see that;
⇒ AE = EC
Hence, the segment DE bisects segment AC.
Thus, The correct statement about the line segment is,
⇒ the segment DE bisects segment AC.
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The perimeter of △ABC equals 26 in and the midpoints of the sides are M, N and K. Find the perimeter of △MNK.
Answer:
13 in.
Step-by-step explanation:
Theorem:
The segment that joins the midpoints of two sides of a triangle is parallel to the third side and half the length of the third side.
Each side of triangle MNK has as endpoints two midpoints of sides of triangle ABC, so each side of triangle MNK is half the length of a side of triangle ABC.
p = 26 in./2 = 13 in.
Dose anyone know the answer to this question?
Answer:
-3
Step-by-step explanation:
-3k / ( k-2) + 6 / ( k-2)
since the denominators are the same we can add the numerators
(-3k+6) / ( k-2)
Factor out -3
-3 ( k-2)/ ( k-2)
Cancel like terms
-3
Answer:
[tex]\boxed{\sf -3}[/tex]
Step-by-step explanation:
The denominators are same. Add fractions.
[tex]\displaystyle \sf \frac{-3k+6}{k-2}[/tex]
Factor out the expression in the numerator.
[tex]\displaystyle \sf \frac{-3(k-2)}{k-2}[/tex]
Cancel common terms.
[tex]\displaystyle \sf \frac{-3}{1}=-3[/tex]
pleaseeee helppppp meeeee pleaseeeeee
Answer:
(28/33+28 ) *100
Step-by-step explanation:
(28/33+28 ) *100
(28/61)*100
Answer:
it's 2
Step-by-step explanation:
I did it before
An appliance company determines that in order to sell x dishwashers, the price per dishwasher must be p = 420 - 0.3x. It also determines that the total cost of producing x dishwashers is given by C(x) = 5000 + 0.3x2. How many dishwashers must the company produce and sell in order to maximize profit? g
The company must produce and sell 350 dishwashers in order to maximize profit.
How to determine the number of dishwashersTo determine the number of dishwashers the company must produce and sell in order to maximize profit, we need to find the value of x that corresponds to the maximum point of the profit function.
The profit (P) is given by the equation:
P(x) = Revenue - Cost
The revenue is calculated by multiplying the price per dishwasher (p) by the number of dishwashers sold (x):
Revenue = p * x
The cost is given by the function C(x):
Cost = C(x)
Therefore, the profit function can be expressed as:
P(x) = p * x - C(x)
Substituting the given expressions for p and C(x):
P(x) = (420 - 0.3x) * x - (5000 + 0.3x²)
Expanding and simplifying the equation:
P(x) = 420x - 0.3x² - 5000 - 0.3x²
Combining like terms:
P(x) = -0.6x² + 420x - 5000
To find the value of x that maximizes profit, we need to find the vertex of the quadratic function. The x-coordinate of the vertex can be determined using the formula:
x = -b / (2a)
In our case, a = -0.6 and b = 420:
x = -420 / (2 * -0.6)
x = -420 / (-1.2)
x = 350
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350 dishwashers must the company produce and sell in order to maximize profit.
Maxima means a point at which the function attains the maximum value.
Given the following information:
Price per dishwasher, p = 420 - 0.3x
Total cost of producing x dishwashers, C(x) = 5000 + 0.3x2
Profit= Total Selling price- Total Cost Price
Total Selling price of x dishwasher, S.P= xp
S.P=x(420 - 0.3x)
S.P=420x - 0.3x²
Profit= 420x - 0.3x² - ( 5000 + 0.3x²)
Profit= 420x - 0.3x² - 5000 - 0.3x²
Profit= -0.6x²+420x-5000
So, profit, f(x)=-0.6x²+420x-5000
To determine the value of x so that maximum profit is possible:
1. Calculate the first derivative of profit function and calculate the value of x by equating it to zero.
2. Select that value of x for which the profit function attains the maximum value, to check the maxima calculate 2nd derivative, if it gives a negative value for the value of x. Then, x is the point of maxima for the given function.
[tex]f(x)=-0.6x^2+420x-5000\\f\prime(x)=-1.2x+420\\f\prime(x)=0\\-1.2x+420=0[/tex]
Calculating the value of x by transposing,
x=420/1.2
x=350
To check maxima, calculating second derivative.
[tex]f\prime(x)=-1.2x+420=0\\f\prime\prime(x)=-1.2[/tex]
2nd derivative is negative, it means that x=350 is the point of maxima.
Thus, a company must produce and sell 350 dishwashers in order to maximize profit.
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if 5x - 17 = -x +7, then x =
Answer:
x=4
Step-by-step explanation:
5x - 17 = -x +7
Add x to each side
5x+x - 17 = -x+x +7
6x -17 = 7
Add 17 to each side
6x-17+17 = 7+17
6x =24
Divide each side by 6
6x/6 = 24/6
x = 4
Answer:
4
Step-by-step explanation:
5x - 17 = -x + 7
Add x on both sides.
5x - 17 + x = -x + 7 + x
6x - 17 = 7
Add 17 on both sides.
6x - 17 + 17 = 7 + 17
6x = 24
Divide both sides by 6.
(6x)/6 = 24/6
x = 4
Which statement is false?
OA. The inequality sign always opens up to the larger number.
OB. The greater number in an inequality is always above the other number on the vertical number line.
OC. The smaller number in an inequality is always located to the left of the other number on the horizontal number line.
OD.
The inequality sign always opens up to the smaller number.
Answer:
OD is false, because it condradicts OA, and we know that OA is true, I mean, we write 2<3
Answer
The inequality sign always open up to the smaller number
The answer is D
WILL MARK BRAINLIST------ What is the least number of degrees that you could rotate Figure (b) around its center so that it appears to be unchanged?
Answer:
20*
Step-by-step explanation:
Your welcome plz mark me the brainlist
A bag contains ten tiles labeled B, C, D, E, F, G, H, I, J, and K. One tile will be randomly picked.
What is the probability of picking a vowel?
Write your answer as a fraction in simplest form.
Answer:
1/5
Step-by-step explanation:
B, C, D, E, F, G, H, I, J, K. = 10 tiles
E and I are vowels
P ( vowel) = vowels/ total
=2/10
= 1/5
In total, we are given 10 letters.
The vowers are; A, E, I, O, and U
In the bag, we can see we have 2 vowels (E and I)
This means that 2 out of the 10 letters are vowels (2/10).
We can simplify the fraction by dividing by 2.
2÷2/10÷2
1/5
Therefore, the answer is 1/5.
Best of Luck!
For the functions f(x)=−7x^2−x and g(x)=9x^2−4x, find (f−g)(x) and (f−g)(1)
Answer:
See below.
Step-by-step explanation:
[tex]f(x)=-7x^2-x\\g(x)=9x^2-4x\\(f-g)(x)=f(x)-g(x)\\(f-g)(x)=(-7x^2-x)-(9x^2-4x)\\(f-g)(x)=-7x^2-x-9x^2+4x\\(f-g)(x)=-16x^2+3x\\\\(f-g)(1)=-16(1)^2+3(1)\\(f-g)(1)=-16+3=-13[/tex]
What is an equation of the line that is parallel to y=3x-8 and passes through the point (4, -5)
Hi there! :)
Answer:
y = 3x - 17.
Step-by-step explanation:
To write an equation parallel to y = 3x - 8, we need the slope as well as the coordinates of a point to solve for the "b" value in y = mx + b:
A line parallel to y = 3x - 8 contains the same slope, or m = 3.
Plug in the coordinates in (4, -5) into "x" and "y" in the equation y = mx + b respectively:
-5 = 3(4) + b
-5 = 12 + b
Simplify:
-5 - 12 = b
b = -17.
Rewrite the equation:
y = 3x - 17.
3 solutions for x<-2
Answer:
-3,-4,-5
Step-by-step explanation:
those are all numbers less than -2! your welcome! please give me brainliest!
Answer: -3, -16, and -642,000
Step-by-step explanation: In this problem, we're asked to state three solutions for the following inequality, x < -2.
The inequality x < -2 means that any number
less than -2 is a solution to the inequality.
For example, -3 is a solution because -3 is less than -2.
Another solution would be -16 because -16 is less than -2.
One other solution would be -642,000 because it's less than -2.
It's important to understand that these are only 3 possible
answers and there are many answers to choose from.
What is the product?
Answer: A
Step-by-step explanation:
When multiplying matrices, find the sum of the product of the terms in the first row of the first matrix with the terms in the first column of the second matrix. Repeat for each row and column.
[tex]\left[\begin{array}{cc}a&c\\b&d\end{array}\right] \times \left[\begin{array}{cc}w&y\\x&z\end{array}\right]=\left[\begin{array}{cc}aw+cx&ay+cz\\bw+dx&by+dz\end{array}\right]\\\\\\\left[\begin{array}{cc}-3&4\\2&-5\end{array}\right]\times \left[\begin{array}{cc}3&-2\\1&0\end{array}\right]\\\\\\=\left[\begin{array}{cc}-3(3)+4(1)&-3(-2)+4(0)\\2(3)-5(1)&2(-2)-5(0)\end{array}\right]\\\\\\=\left[\begin{array}{cc}-5&6\\1&-4\end{array}\right][/tex]
Solve for x. a) 10 b) 12 c) 13 d) 11
Answer:
A : 10
Step-by-step explanation:
Answer:
the correct answer is 12
Step-by-step explanation:
6/8=9/x
cross multiply
6x=72
divide by six
x=12
How many times will the digit '3' appear if we write a all whole numbers from 1 to 99?
Answer:
20
Step-by-step explanation:
The number 3 will appear in the numbers 3, 13, 23, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 43, 53, 63, 73, 83, 93. In these numbers it appears 20 times.
PLLZZZZ help me find x you are AWSOME!! I need this ASAP
Answer:
27°
Step-by-step explanation:
D is 72° because it alternates with B, alternate angles are equal.
2x+72°+2x= 180° because it is a straight line.
4x+72°=180°
4x=108°
x=27°
What is the converse of r->(~q v p)
Answer:
[tex]r => (\neg q \ \lor p) \ \equiv \ q \ \land \ \neg p => \neg r[/tex]
Step-by-step explanation:
In general, remember that the converse of [tex]a => b[/tex] is [tex]\neg b => \neg a[/tex] , therefore in this case [tex]a = r \ \ , b = \neg q \ \lor p[/tex]
so [tex]r => (\neg q \ \lor p) \ \equiv \ q \ \land \ \neg p => \neg r[/tex]
Simply this expression (3 + 2i)^2
Answer:
5 + 12i
Step-by-step explanation:
(3 + 2i)^2 = (3 + 2i)(3 + 2i) = 9 + 6i + 6i + 4i^2 = 9 + 12i - 4 = 5 + 12i
Answer:
5 + 2i
Step-by-step explanation:
since [tex]\sqrt{-1} = i[/tex]
Use the perfect square formula ( a + b )^2
= 3^2 + 2 · 3 · 2i + (2i)^2
= 5 + 2i
or,
[tex]5+2\sqrt{-1}[/tex]
Find all the zeros of the polynomial function p(x) = x3 – 5x2 + 33x – 29
Answer:
[tex]\large \boxed{\sf \ \ x=1, \ \ x=2+5i, \ \ x=2-5i \ \ }[/tex]
Step-by-step explanation:
Hello,
I assume that we are working in [tex]\mathbb{C}[/tex], otherwise there is only one zero which is 1. Please consider the following.
First of all, we can notice that 1 is a trivial solution as
[tex]p(1) = 1^3-5\cdot 1^2 + 33\cdot 1-29=1-5+33-29=0[/tex]
It means that (x-1) is a factor of p(x) so we can find two real numbers, a and b, so that we can write the following.
[tex]p(x)=(x-1)(x^2+ax+b)=x^3+ax^2+bx-x^2-ax-b=x^3+(a-1)x^2+(b-a)x-b[/tex]
Let's identify like terms as below.
a-1 = -5 <=> a = -5 + 1 = -4
b-a = 33
-b = -29 <=> b = 29
So
[tex]\boxed{ \ p(x)=(x-1)(x^2-4x+29) \ }[/tex]
Now, we need to find the zeroes of the second factor, meaning finding x so that:
[tex]x^2-4x+29=0 \ \text{ complete the square, 29 = 25 + 4} \\ \\ <=> x^2-2\cdot 2 \cdot x+2^2+25=0 \\ \\ <=>(x-2)^2=-25=(5i)^2 \ \text{ take the root } \\ \\<=>x-2=\pm 5i \ \text{ add 2 } \\ \\ <=> x = 2+5i \ \text{ or } \ x = 2-5i[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
A savings account has a rate of 2.25% . Find the effective annual yield of interest is compounded quarterly
Answer:
The effective yield is 2.269% to the thousandth.
Step-by-step explanation:
Effective annual yield compounded quarterly, given API
(1+API/4)^4 - 1
= (1+0.0225/4)^4 - 1
= 0.022691
A group of students were asked to choose their favorite course. The results are shown in the two-way frequency table. Which of the following can be concluded from the joint and marginal frequencies of the table? Math is the most popular subject in the 10th grade. History is the least popular subject in the 9th grade. Science is more popular than math among 12th grade students. Students in the 11th grade like English more than students in the 12th grade. The overall favorite course is history.
A.) III and IV only
B.) II and V only
C.) I, III, and V
D.) II and IV only
The answer is C.) I, III, and V
The statement 1, 2, and 5 will be correct hence option (C) will be correct.
What is a frequency table?A frequency table is a list of objects with the frequency of each item shown in the table.
In other words, a frequency table is a table in which we have some data and their frequency.
The frequency of an occurrence or a value is the number of times it happens.
In option (C)
1st statement;
Math is the most popular subject in the 10th grade.
In 10th grade, maths is 104 rest are less so it is correct.
3rd statement;
Science is more popular than math among 12th-grade students.
The number of science lovers in the 12th is 78
The number of maths lovers in 12th is 52
So it is also correct.
5th statement;
Overall favorite course is history.
A number of overall favorite courses is history = 403 which is higher than others hence it is also correct.
So option (C) is correct rest are incorrect.
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