PerioAlgebra 2NameUsing Linear Equations to Solve Problems Date1) The chess club is selling popcorn balls for $1.00 and jumbo candy bars for$1.50 each. This week they have made a total of $229 and have sold 79popcorn balls. How many candy bars have they also sold?
Answers
The popcorn balls cost $1.00 each
Jumbo candy bars cost $1.50 each
This week they have made a total of $229 and have sold 79
popcorn balls.
First, let's make a function with includes this information.
Let's say that popcorn balls are x and Jumbo candy bars are y.
So the function would be
1.00x+ 1.50y = 229
We already have the x value which represents the total of popcorn balls sold this week, so replace this value in the function:
1.00x+ 1.50y = 229
1.00(79)+ 1.50y = 229
79.00 + 1.50y = 229
Solve the equation for y to find the total of candy bars sold.
79 + 1.50y = 229
1.50y = 229 - 79
1.50y = 150
y = 150/1.50
y = 100
So the have sold 100 candy bars this week
Related Questions
2) Given that XY || AC, what is YC if BX = 10, BA = 15, and BY = 8?A) 4 B) 6 C)8D)12
Answers
We can see that triangles ABC and AXY are congruent
This means that
[tex]\frac{AX}{BX}=\frac{YC}{BY}[/tex]Now, we know that BX=10, BY=8 and BA=AX+BX, hence AX=BA-BX, we have
[tex]\frac{BA-BX}{10}=\frac{YC}{8}[/tex]now, since BA-BX=15-10, BA-BX=5, it yields,
[tex]\frac{5}{10}=\frac{YC}{8}[/tex]Now, we need to isolate YC, this is given by
[tex]YC=8(\frac{5}{10})[/tex]Since
[tex]\frac{5}{10}=\frac{5\cdot1}{5\cdot2}=\frac{1}{2}[/tex]we have that
[tex]\begin{gathered} YC=8(\frac{1}{2}) \\ YC=\frac{8}{2} \\ YC=4 \end{gathered}[/tex]hence, the answer is YC=4, which corresponds to A).
Hello! Thank you for helping me today, I need a little bit of assistance to understand the rest of this question please. (This is is not an active test, it is a book I am studying in order to take the ASVAB in a couple of weeks.)Options;A: 1/8B: 1/7C: 1/6D: 1/4
Answers
GIVEN:
We are told that in a certain class, 3 out of 24 students are in student organizations.
Required;
What is the ratio of students in student organizations to students not in student organizations?
Step-by-step solution;
We shall begin by dividing the entire students into the two given groups, and that will be;
In student organizations = 3
Not in student organizations = 21
Total number of all students = 24
To determine the ratio of one value to the other, we express them as follows;
[tex]\begin{gathered} Ratio\text{ }of\text{ }x\text{ }to\text{ }y=x:y \\ \\ OR \\ \\ Ratio\text{ }of\text{ }x\text{ }to\text{ }y=\frac{x}{y} \end{gathered}[/tex]Therefore, to express the ratio of students in organizations to students not in organizations, we will have;
[tex]\begin{gathered} Ratio=\frac{3}{21} \\ \\ Ratio=\frac{1}{7} \end{gathered}[/tex]ANSWER:
Therefore, the correct answer is option B
An empty swimming pool needs to be filled to the top. The pool is shaped like a cylinder with a diameter of 9 m and a depth of 1.1 m. Suppose water is pumped into the pool at a rate of 13 m^3 per hour. How many hours will it take to fill the empty pool?
Use the value 3.14 for pi, and round your answer to the nearest hour. Do not round any intermediate computations.
Answers
Answer:
πr2h
volume of cylinder
3.14×3×3×1.1=31.086m^3
1hour=13m^3
31.086m^3
divide 31.086÷13=2.3912hours
You flip a coin and roll a die. The table shows the sample space.12 3 4 5 6Heads(H) H-1 H-2 H-3 H-4H-5H-6Tails(T) T-1 T-2 T-3 T-4 T-5 T-6What is the probability of getting a head or a tail and anven number?Answer as a reduced fraction in the form ab.
Answers
You flip a coin and roll a die. The table shows the sample space.
1
2 3 4 5 6
Heads(H) H-1 H-2 H-3 H-4H-5H-6
Tails(T) T-1 T-2 T-3 T-4 T-5 T-6
What is the probability of getting a head or a tail and an
even number?
we know that
The probability of an event is the ratio of the size of the event space to the size of the sample space.
The size of the sample space is the total number of possible outcomes
The event space is the number of outcomes in the event you are interested in.
In this problem
the size of the sample space is (6+6+6)=18
the size of the event space is equal to (6+6+3)=15
REmember that an even number are (2,4 and 6)
so
the probability is equal to
P=15/18
simplify
P=5/6
therefore
the answer is5/6Five fair tetrahedral (four-sided) dice are rolled at the same time. The values on the faces of each die are 1, 2, 3, and 4.a. What is the theoretical probability of rolling a 1 on all five dice?b. Zavier conducted an experiment in which he rolled five fair tetrahedral dice 50 times. He rolled a 1 on all five dice once. What is the experimental probability of rolling a 1 on all five dice?
Answers
Solution:
The probability of an event is the ratio of number of outcome of the event to the total outcome of events.
Thus;
(a) The theoretical probability of rolling a 1 on all five dice is;
[tex](\frac{1}{4})^5[/tex](b) In the experiment, he rolled five fair tetrahedral dice 50 times. Thus, the experiment probability of rolling a 1 on all five dice is;
[tex]\frac{1}{50}[/tex](a) Does f (x) have a horizontal asymptote? If so, what is it?(b) Does f (x) have any vertical asymptotes? If so, what are they?
Answers
a) Horizontal asymptotes are horizontal lines that the graph of a function approaches but never touches. To find the horizontal asymptote, we would apply one of the rules which states that
If the degree of the of the denominator is bigger than the degree of the numerator, the horizontal asymptote is the x axis of the graph. It occurs at y = 0
The degree is the largest exponent in the function. Looking at the given function, the degree of the numerator is 2 while the degree of the denominator is 3. Thus,
there is a horizontal asymptote at y = 0
b) The vertical asymptotes are vertical lines which correspond to the zeros of the denominator of rational functions. It is equal to the values of x that make the denominator to be zero. Looking at the given function, (x + 1) cancels out in the numerator and denominator. We are left with (x - 4) and (x + 5). We would equate both terms to zero and solve for x. These values of x would make the denominator to be equal to zero. We have
x - 4 = 0
x = 4
x + 5 = 0
x = - 5
Thus,
there are vertical asymptotes at x = - 5 and x = 4
Suppose that the functions fand g are defined for all real numbers x as follows.f(x)=x+5g(x)=2x²Write the expressions for (g+f)(x) and (g–f)(x) and evaluate (g.f)(-3).
Answers
The expression (g+f)(x) is equal to g(x)+ f(x), (g-f)(x) is equal to g(x) f(x) and the expression (g*f)(-3) is equal to g(-3)*f(-3).
Then, we have
[tex](g+f)(x)=g(x)+f(x)=2x^2+x+5[/tex]Similarly,
[tex](g-f)(x)=g(x)f(x)=2x^2-(x+5)=2x^2-x-5[/tex]And finally,
[tex]\begin{gathered} (g\cdot f)(-3)=g(-3)\cdot f(-3)=2(-3)^2\cdot(-3+5) \\ (g\cdot f)(-3)=2(9)\cdot(2) \\ (g\cdot f)(-3)=36 \end{gathered}[/tex]In summary, the answers are:
[tex]\begin{gathered} (g+f)(x)=2x^2+x+5 \\ (g-f)(x)=2x^2-x-5 \\ (g\cdot f)(-3)=36 \end{gathered}[/tex]The price of a train ticket consists of an initial fee of $5 plus a fee of $2.75 per stop. Julia has $21 and would like to travel 50 kilometers. She wants to know the largest number of stops she can afford to buy on a ticketLet S represent the number of stops that Julia buys.1) Which inequality describes this scenario?A. 5+2.75•S ≤ 21 B. 5+2.75•S ≥ 21 C. 5+2.75•S ≤ 50 D. 5+2.75•S ≥ 502) What is the largest number of stops that Julia can afford?
Answers
Let's begin by listing out the information given to us:
Initial fee = $5
Fee per stop = $2.75
Amount with Julia = $21
What is the highest number of stops she can make?
S = the number of stops Julia bought
Julia pays the initial fee of $5. We subtract this from the $21, we have
$ (21 - 5) = $16
Julia has $16 left to buy her stops. She cannot spend beyond the amount of money with her (altogether $21). She spends lesser than or equal to $21 (≤ $21)
The inequality that describes this scenario is given by:
initial fee + fee per stop * number of stops ≤ 21
5 + 2.75 * S ≤ 21
Hence, option A is the correct answer
What is the largest number of stops that Julia can afford?
This is gotten by dividing the amount left after subtracting the initial fee by the fee per stop
n = 16/2.75 = 5.82 = 5 stops (rounding downwards)
We round downwards because the number of stops must be a whole number and it must be lesser than or equal to $21 altogether
Consider the following simple statements: p: Your shirt is tucked into your pants. q: Your pants are tucked into your shirt.What is the symbolic form of the statement: "If your shirt isn't tucked into your pants then your pants are tucked into your shirt."Select the correct answer below:∼q⟹p∼q⟹∼pp⟹∼q∼p⟹q
Answers
SOLUTION
We are asked the symbolic form of "If your shirt isn't tucked into your pants then your pants are tucked into your shirt."
This simply means the negation of p implies q.
p implies q is represented as p⟹q
Then the negation of p implies q will be ∼p⟹q.
Therefore, the correct answer is ∼p⟹q
What is the measure of
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In the parallelogram ABCD,
Angle D is 145 degree.
In the parallelogram adjacent angles sum is 180 degree.
In the given parallelogram ABCD , angle D and angle C are adjacent.
[tex]\begin{gathered} \angle D+\angle C=180^{\circ} \\ 145^{\circ}+\angle C=180^{\circ} \\ \angle C=180^{\circ}-145^{\circ} \\ \angle C=35^{\circ} \end{gathered}[/tex]Answer: Option B) 35 degree.
A __ is a polynomial with one term.
Answers
Answer:
Monomial
Step-by-step explanation:
A polynomial that consists of exactly one term is called monomial.
Examples are 3, 10x², xy,...
So the answer is: Monomial
help me asap please!!! no explanation just the process and answer
Answers
To find out the determinant, multiply in cross
so
(3)*(-2)-(5)*(-7)=-6+35=29
therefore
the answer is 29
What is the surface area of the regular pyramid below?A. 648 sq. unitsB. 552 sq. unitsC. 396 sq. unitsD. 522 sq. units
Answers
Step 1:
Concept: Calculate the area of each face and add all together to get the surface area of the pyramid.
The regular pyramid below have 4 triangles and a square
Step 2: Apply the area formula to find the area of the 4 triangles and a square.
[tex]\begin{gathered} \text{Area of a triangle = }\frac{Base\text{ x Height}}{2} \\ \text{Area of the square base = Length x Length} \end{gathered}[/tex]Step 3:
Given data for the triangle
Height = 21
Base = 12
[tex]\begin{gathered} Area\text{ of a triangle = }\frac{Base\text{ x Height}}{2} \\ =\text{ }\frac{21\text{ x 12}}{2} \\ =\text{ }\frac{252}{2} \\ =126\text{ sq. units} \\ \text{Area of the four triangles = 4 x 126 = 504 sq. units} \end{gathered}[/tex]Step 4: Find the area of the square
Given data for the square
Length = 12
Area = length x length = 12 x 12 = 144 sq. units
Step 5: Add the area of the four triangles and the square.
Surface area of the regular pyramid = 504 + 144
= 648 sq. units
Amanda is a fashion designer. She has 25 yards of silk material. The skirtAmanda is making requires 1 yards, the dress requires 4 yards, the shirtrequires 7 yards, and the pants requires yards.After making her pieces, how many yards of silk does Amanda have left?
Answers
To determine how much silk Amanda has at the end we need to substract the amount each pice need from the original amount:
[tex]\begin{gathered} 25-\frac{18}{7}-\frac{11}{2}-\frac{7}{4}-\frac{25}{7}=25-\frac{43}{7}-\frac{11}{2}-\frac{7}{4} \\ =25-\frac{86+77}{14}-\frac{7}{4} \\ =25-\frac{163}{14}-\frac{7}{4} \\ =25-\frac{652+98}{56} \\ =25-\frac{750}{56} \\ =\frac{1400-750}{56} \\ =\frac{650}{56} \\ =\frac{325}{28} \\ =11\frac{17}{28} \end{gathered}[/tex]Therefore Amanda has 11 17/28 yards of silk left.
According to the graph, what is the value of the constant in the equation below? 2- 18+ Height = Constant Wiat 16+ (0.5,1.6) 12+ Height (0.8.1) 0.8 + (1.6.05) (2.0.4) 12 14 16 18 2
Answers
Liyah, this is the solution:
• Height = Constant/Width
,• Height * Width = Constant (you need to multiply each ordered pair )
Therefore,
Constant = 1.6 * 0.5
Constant = 0.8
Constant = 0.4 * 2
Constant = 0.8
The correct answer is C. 0.8
help me asap please on this math question
Answers
Equations showing direct variations are 2x = y and y = 1.8c
Direct Variation exists between two variables when one variable is directly dependent to another variable means change in one variable will create change in other one also and vice versa.
Two variable increase or decrease by the same factor.
Suppose x and y is that are in direct variation then you can write
y ∝ x
where, "∝" denotes proportionality
removing proportionality sign by constant then you can write
y = k x , where k is constant and can hold any real value
From the following equation ,
2x = y with 2 as constant and
y = 1.8x with 1.8 as constant shows direct variations
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12x+18 rewrite using distributive property
Answers
we have
12x+18
REmember that
12=(2^2)*(3)
18=(2)*(3^2)
substitute
(2^2)*(3)x+(2)*(3^2)
Factor (2)*(3)=6
6(2x+3)
therefore
the answer is
6(2x+3)the radius of a circle is 4 centimeters. what is the diameter? give the exact answer in simplest form
Answers
we have that
the diameter is two times the radius
so
in this problem
D=2r
D=2(4)=8 cm
diameter is 8 cmY 3+ 2+ 1+ -4 -3 -2 -1 1 2 3 -1- -2 -3+ -4 47 What is the slope of the line?
Answers
To find the slope of the line, we will follow the steps given below:
Step 1: select two points on the graph
(0, -1) and (4,2)
Step 2: Apply the slope formula:
[tex]\text{slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]=>
[tex]\text{slope}=\frac{2-(-1)}{4-0}=\frac{2+1}{4}=\frac{3}{4}[/tex]The slope of the graph is:
[tex]\frac{3}{4}[/tex]If 11 people each own of an acre of
2/19
land and they put all their land together
how much land, in acres, would they
Answers
If 11 people each own of an acre of 2/19 land, their land together is area of 22/19 of an acre.
If 11 people each own of an acre of 2/19
The area of land owned by 1 person = 2/9
To find the area of land owned by 11 persons altogether
We have to multiply 11 with the area owned by one person
11 x (2/19)
= 22/19
Therefore, If 11 people each own of an acre of 2/19 land, the they land owned by them altogether is area of 22/19 of an acre.
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John drank 18 fluid ounces of juice. How much is this in cups? Write your answer as a whole number or a mixed number in simplest form. Include the correct unit in your answer.
Answers
We know that 1 cup is equivalent to 8 fluid ounces. Then, we can establish the following rule of three:
[tex]\begin{gathered} 8\text{ fluid ounces ----- 1 cup} \\ 18\text{ fluid ounces ------ x} \end{gathered}[/tex]Then, by cross multiplying these quantities, we have
[tex]x\times8\text{ fluid ounces= 1 cup}\times\text{ 18 ounces}[/tex]By dividing both sides by 8 fluid ounces, we get
[tex]x=\frac{1\text{ cup}\times18\text{ ounces}}{8\text{ fluid ounces}}[/tex]which gives
[tex]x=\frac{18}{8}\text{ cups}[/tex]Now, we need to convert this simple form to a mixed form, that is,
Then, by simplifying this mixed form, the answer is:
[tex]2\frac{1}{4}\text{ cups}[/tex]What number is 2% of 35
Answers
Answer:
The 2% of 35 is;
[tex]0.7[/tex]
Explanation:
We want to find the 2% of 35
[tex]\begin{gathered} \text{ 2\% of 35 =} \\ \frac{2}{100}\times\text{ 35 = }\frac{70}{100}=0.7 \end{gathered}[/tex]Therefore, the 2% of 35 is;
[tex]0.7[/tex]
Answer:0.7
Step-by-step explanation:
35x2=70
70/100=0.7
Use the following function for questions # 1 - # 5:f(x) =x?- 14x + 44#1: Find the X value of the turning point.
Answers
The given function is
f(x) = x^2 - 14x + 44
To find the turning point, we would differentiate the function, equate the derivative to zero and solve for x. We have
f'(x) = 2x - 14
Equating it to zero, we have
2x - 14 = 0
2x = 14
x = 14/2
x = 7
The value of x of the turnng point is 7
Simplify the expression cos x/ cot x.a. cos xb. tan xc. sin xd. cos²x/sin x
Answers
cosx/cotx = cosx *tan x =cosx (sinx/cosx) = sin x
Answer
c. sin x
5Jamal's band learns lots of new songs.The band learns a new song every fourdays. At this rate, how many new songswill the band learn in four weeks?LAsongs
Answers
Given that The band learns a new song every four days.
We need to find the number of new songs for four weeks.
We know that one week= 7 days
[tex]1\text{ w}eek\text{ = 7 days }[/tex]Multiply by 4 to find the number of days in four weeks.
[tex]1\times4\text{ w}eek\text{ = 7 }\times4\text{ days }[/tex][tex]4\text{ w}eeks\text{= 28days }[/tex]We need to find the number of new songs that the band learns in 28 days.
Divide 28 by 4 to find the number of songs since the band learns one new song every 4 days.
[tex]\frac{28}{4}=7\text{ songs}[/tex]The band learns 7 songs in four weeks.
Find the value of b. * 4 b 6 Y 9 5.8 W
Answers
The smaller triangle has its hypotenuse as 4 units and the base as 6 units
The bigger triangle has its hypotenuse as 10 units, the height as 5.8 units and the other hypotenuse as 9 units
Using similarity properties, compare the ratio of the sides as;
Compare the ratio of the bigger triangle sides to that of the smaller traingle
First find the base of the bigger triangle using the sides given and applying the pythagorean relationship as;
10^2 - 5.8^2 = a^2
100 - 33.64 = a^2
66.36 = a^2
1/2 a= 8 .15 units
a= 16.30 units
Compare ratio
a/ 6 = 5.8 / b
16.30 /6 = 5.8/ b
16.30 b = { 6 * 5.8 }
b = {6 * 5.8} / 16.30
b = 2.13 units
Answer
2.13 units
9. At last Friday's soccer game there were a total of 673 fans in attendance, including students and non-students.Let x represent the number of students, and y represent non-students. Which of the following statements couldrepresent the number of fans in attendance. Select all that apply.a. x + y = 673b. 335 and 138c. 335 and 338d. x=y - 673e. y = -x + 673f. 273 and 400
Answers
The answer is A
From the question:
Total fans in attendence = 673
x = number of students
y= non - students
Total of fans in attendance =
x + y= 673
3 2 1 -3-2- 1 2 3 2 -3 Domain: (-3,3] Range: [-2, 2] Domain: (-2, 2] Range: [-3,3] Domain: (-2,-3) Range: (2,3) Domain: {-2, -1, 0, 1, 2} Range: {-3, -2, - 1, 0, 1, 2, 3} None of the above NON
Answers
The domain is [ -2, 2]
and the range is [-3, 3]
Which number is not equal to 225%?its is exercise number 5
Answers
To do this, you can first convert the percentage form to its decimal form, like this
[tex]225\text{\%}=\frac{225}{100}=2.25[/tex]Now, you can convert the numbers that are possible answers into their decimal form, like this
Option A.
[tex]2\frac{1}{4}=\frac{2\cdot8+1}{4}=\frac{8+1}{4}=\frac{9}{4}=2.25[/tex]Option B.
[tex]\frac{9}{4}=2.25[/tex]Option C.
[tex]\frac{50}{40}=\frac{5\cdot10}{4\cdot10}=\frac{5}{4}=1.25[/tex]Option D.
[tex]\frac{45}{20}=\frac{9\cdot5}{4\cdot5}=\frac{9}{4}=2.25[/tex]Therefore, the number that is not equal to 225% is 50/40 and the correct answer is C. 50/40.
polinomials (x + 3)2
Answers
Given the following question:
[tex](x+3)2[/tex](x + 3)2
First, we flip the polynomial:
(x + 3)2 = 2(x + 3)
2(x + 3)
Next, we apply the distributive law where we multiply 2 by x and 3.
2 × x = 2x
2 × 3 = 6
2x + 6
Expression cannot be simplified any further:
= 2x + 6