Write a system of equations to describe the situation below solve using illumination and fill in the blanks
Answers
Solution:
Let the cost of a tray of club sandwiches be s, and the cost of a tray of vegetarian sandwiches be v.
Then, the first order was for 6 trays of club sandwiches and 3 trays of vegetarian sandwiches at a cost of $75. We have;
[tex]6s+3v=75\ldots\ldots.\ldots\ldots.\text{equation}1[/tex]Also, the second order was for 9 trays of club sandwiches and 9 trays of vegetarian sandwiches at a cost of $144. We have;
[tex]9s+9v=144\ldots.\ldots\ldots\ldots....\ldots\text{equation}2[/tex]We would solve the two equation simultaneously, using elimination method.
Multiply equation 1 by 9 and equation 2 by 3.
[tex]\begin{gathered} (6s+3v=75)\times9 \\ 54s+27v=675\ldots.\ldots..\ldots..equation4 \\ (9s+9v=144)\times3 \\ 27s+27v=432\ldots\ldots..\ldots equation5 \end{gathered}[/tex]Subtract equation 5 from equation 4. We have;
[tex]\begin{gathered} 54s-27s+27v-27v=675-432 \\ 27s=241 \\ s=\frac{243}{27} \\ s=9 \end{gathered}[/tex]Substitute the value of s in equation 1. We have;
[tex]\begin{gathered} 6s+3v=75 \\ 6(9)+3v=75 \\ 54+3v=75 \\ \text{Subtract 54 from both sides;} \\ 54-54+3v=75-54 \\ 3v=21 \\ \text{Divide both sides by 3;} \\ \frac{3v}{3}=\frac{21}{3} \\ v=7 \end{gathered}[/tex]Thus;
FINAL ANSWER: A tray of club sandwiches costs $9, and a tray of vegetarian sandwiches costs $7
Related Questions
Find how much money needs to be deposited now into an account to obtain $7,400 (Future Value)
in 10 years if the interest rate is 7% per year compounded monthly (12 times per year).
The final amount is $
Round your answer to 2 decimal places
Answers
Given a certain rate of return, present value (PV) is the current value of a future sum of money or stream of cash flows.
$ 3,682.21 is the present value.
How to find the present value?A future sum of money or stream of cash flows' present value (PV), assuming a given rate of return, is their current value.
Future value is converted to present value by using either a discount rate or the interest rate that would be earned if an investment were made.
Present Value = FV/(1+r/n)^nt
Solution:
Present Value = FV/(1+r/n)^nt
Present Value = 7400/(1+7/12)^10*12
Present Value = 7400/(19/12)^120
Present Value = 7400/(1.58)^120
Present Value = 7400/2^120
Present Value = $ 3,682.21
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Kevin and Randy Muise have a jar containing 53 coins, all of which are either quarters or nickels. The total value of the coins in the jar is $5.65. How many of each type
of coin do they have?
The jar contains
The jar contains
quarters.
nickels.
Answers
The number of quarters and nickles, Kevin and Randy Muise have a jar containing 53 coins, is 15 quarters and 38 nickles.
What is described as the linear equation in two variables?A linear equation in 2 factors is one that is written in the form ax + by + c=0, where a, b, and c are real numbers as well as the coefficients of x and y, i.e. a and b, are not equal to zero.Let 'x' be the number of quarters.
Let 'y' be the number of nickels.
The total number of coins in a jar are 53.
x + y = 53
x = 53 - y .....eq 1
The total value of the coin is $5.65.
1 doller = 0.25 quarters.
1 doller = 0.05 nickle.
Thus,
0.25x + .05y = 5.65
Multiply both sides by 100 to remove the decimal points.
25x + 5y = 565
Put the value of x from eq 1.
25(53 - y) + 5y = 565
1325 - 25y + 5y = 565
-20y = -760
y = 38
x = 53 - y = 53 - 38
x = 15 quarters
Thus, the number of quarters and nickles Kevin and Randy Muise have a jar containing 53 coins, is 15 quarters and 38 nickles.
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Please give me the correct answer.True or false.If a=b,then a+c=b+c.
Answers
The statement is true since it is the so-called Addition Property of Equality, which says that, if two expressions are equal to each other, and you add the same value to both sides of the equation, the equation will remain equal.
compare f(0) and g(0)g(x)=|2x-8|-11f(0) is =, <, or > than g(0)
Answers
Let's begin by listing out the given information:
For the graph of f(x), we will pick out two coordinates that lie along the straight line. We have:
[tex]undefined[/tex]Suppose a < -1. What must be true about the value about the value of b so that ab< a?-1 < b < 00 < b < 1b < -1 b > 1
Answers
ANSWER
b > 1
EXPLANATION
Suppose that a < -1.
We need to find the value of b such that:
a * b < a
This means that:
a * b < -1
For this to be possible, b must first be a positive number. Because if b is negative, then:
a * b > 0
Which would mean that a * b is greater than a.
For b to be a positive number that satisfies the inequality, then b cannot be less than 1. This is because if b is less than 1, then:
a * b > a
Therefore, b must be a positive number that is greater than 1.
This means that:
b > 1
5x2 and 6x4 in lowest terms
Answers
The lowest term of 5*2 is 10
The lowest term of 6*4 is 24
How are the lowest terms calculated?
1. 5 * 2
Multiplying 5 and 2 ,
The lowest term of 5*2 is 10
2. 6*4
Multiplying 6 and 4 ,
The lowest term of 6*4 is 24
What is multiplication?
Finding the product of two or more numbers is done by multiplication. The fundamental concept of making the same number additions repeatedly is represented by the action of multiplication. The results of multiplying two or more integers are known as the products, and the factors that are used in the multiplication are referred to as the factors. The process of repeatedly adding the same number is made simpler by multiplication.To learn more about multiplication, refer:
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Find the number of solutions of the equation 6x2 + 6x + 3 = 0 by using the discriminant
Answers
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the standard form of a quadratic equation
[tex]ax^2+bx+c=0[/tex]STEP 2: Write the formula for getting a discriminant
[tex]D=b^2-4ac[/tex]STEP 3: Write the given quadratic equation
[tex]\begin{gathered} 6x^2+6x+3=0 \\ a=6,b=6,c=3 \end{gathered}[/tex]STEP 4: Substitute the values to get the discriminant
[tex]\begin{gathered} D=6^2-4(6)(3) \\ D=36-72=-36 \\ D=-36 \end{gathered}[/tex]STEP 5: Explain the conditions for using the discriminant
If the discriminant is greater than zero, there are two solutions.
If the discriminant is equal to zero, there is one real solution
If the discriminant is less than zero, there are no real solutions
Hence, using the conditions above,
There are no real solutions since the discrimian
Use the two-way frequency table to calculate the probability that the person is a democrat, given theact that the person supports the issue, P(democrat | supports the issue).P(democrat | supports the issue) =(Type an integer or decimal rounded to the nearest hundredth as needed.)
Answers
In order to calculate the probability of P(democrat | supports the issue), we can use the following formula for conditional probability:
[tex]\begin{gathered} P(A|B)=\frac{P(A\cap B)}{P(B)} \\ P(democrat|supportstheissue)=\frac{P(democrat\cap supportstheissue)}{P(supportstheissue)} \end{gathered}[/tex]In the right side of the equation, instead of using the probability, we can use the value in the frequency table.
So we have:
[tex]P(democrat|supportstheissue)=\frac{24}{58}=\frac{12}{29}=0.41[/tex]3/9 divided by 10/50
Answers
To be able to divide the two fractions as given,
Help me out please, been struggling and I would appreciate some help.
Answers
By using the given diagram, we can see that the ordered pair that represents point B is (-4, 0)
Which ordered pair represents B?Any point on a coordinate plane has a ordered pair associated to it, that tells us the location of the point (x, y).
For example, the intersection between the two axes is the point (0, 0).
The first value, x, represents the horizontal displacement, the second variable, y, represents the vertical displacement.
Here we can see that B is 4 units to the left of the center, then the ordered pair that represents point B is (-4, 0)
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I need help finding the vertex and axis of symmetry
Answers
To find the vertex coordinates from the parabola, you can analyze the graph. The x (vertex) coordinate is just over the "x" axis, so the value is xvertex = 2.
The y (vertex) coordinate is y= 0 because it is the value that the parabola takes on that axis.
The axis of symmetry is the value in the "x" axis where the parabola is divided in half. So in this case is x = 2.
So the anser is x(vertex) = 2, y (vertex)=0 , and the axis of symmetry is x= 2.
QUESTION 4One hundred twenty sixth graders are going on a field trip toSea World. The ratio of chaperones to students must be 1:10.How many chaperones are needed for the trip?A) 12B) 13C) 14D) 15
Answers
We can express the ratio of chaperones to students 1 : 10 as a fraction, like this:
[tex]\frac{1}{10}[/tex]By multiplying the number of students by the above ratio, we get the number of needed chaperones, like this:
[tex]126\times\frac{1}{10}=\frac{126\times1}{10}=\frac{126}{10}=12.6[/tex]Rounding to the nearest integer, the number of chaperones needed for the trip is 13
the table below shows the number of computers or laptops owned by ten different families on the back of this paper create a line plot displaying the data 3 ,2,4,1,5,3,1,2,3,3
Answers
Families and computers
Graph a line plot
The following table shows the points scored each game by Pat during the basketball season. Complete the following questions:1. What is the probability Pat scores between 10 and 15 points in a game? Round answer to two decimal places.2. What is the probability Pat scores 16 or more points? Round answer to three decimal places.
Answers
ANSWER
[tex]\begin{gathered} (1)0.162 \\ (2)0.811 \end{gathered}[/tex]EXPLANATION
From the given table;
1. The probability that Pat scores between 10 and 15 points in a game;
The frequency for (10 - 15) is 6
Summation of frequency is;
[tex]1+6+5+17+8=37[/tex]Hence, the probability that Pat scores between 10 and 15 points in a game;
[tex]\begin{gathered} P(10\leq x\leq15)=\frac{6}{37} \\ =0.16216 \\ \cong0.162 \end{gathered}[/tex]2. The probability Pat scores 16 or more points is calculated by adding all the frequency from 16 points and above.
Hence;
[tex]5+17+8=30[/tex]Therefore the P(16 and above);
[tex]\begin{gathered} P(x\ge16)=\frac{30}{37} \\ =0.8108 \\ \cong0.811 \end{gathered}[/tex]SHOW ALL WORK PLEASE! A right cylinder has a radius of 7 cm and a height of 3 cm.
Answer the following questions and make sure to show all your work.
(a) Find the Surface Area of the cylinder.
(b) Find the Volume of the cylinder.
(c) If you wanted more volume in your cylinder, which of these two ideas would give the most Volume?
1. Doubling the radius to 14 cm, while the height remains 3 cm.
-OR
2. Tripling the height to 9 cm, while the radius remains 7 cm.
Answers
Answer:
(a) Surface Area = 140 π cm² = 438.823 cm²
(b) Volume = 147 π cm³ = 461.814 cm³
(c) Doubling the radius, keeping height constant results in more volume
Step-by-step explanation:
Volume of a cylinder with base radius r and height h is given by
V = π r² h
Surface Area A = 2 π r(h + r)
Given r = 7 cm, height = 3cm
(a) Surface Are = 2 x π x 7(7 + 3) = 14 π (10) = 140 π cm² =438.823 cm²
(b) Volume = π x 7² x 3 = 147 π = 461.814 cm³
(c) If we double the radius to 14 cm with height at 3 cm (Option 1), the volume would quadruple to 4 because the new radius is twice the old radius and since volume is proportional to square of radius, new volume will be (2r)² = 4r² where r is the old radius
So new volume = 4 x 461.814 = 1,847.256 cm³
If we triple the height to 9 cm, keeping radius at 7, the volume would only triple since it is directly proportional to height
So new volume = 3 x 461.814 = 1,385.442 cm³
So to get more volume, idea 1, doubling the radius works
draw examples of each figure: - 2 perpendicular lines-AB AC ray on same line-EW intersecting with EMI'll upload picture
Answers
Part c
N 11
2 perpendicular lines
see the figure below
N 12
see the figure below
N 13
see the figure below
Name the set of 4 consecutive odd integers starting with -3 ( put the set in braces [ ] and put commas between the elements of the set. )
Answers
Solution
For this case we need to find 4 consecutive odd integers so we can do this:
-3, -3+2, -3+2+2, -3+2+2+2
Solving we got:
[-3,-1, 1, 3]
If you want to cut 24 two-foot braces, how many boards of the length shown below would you need? 12 ft A. 4 B. 6 C. 12 D. 24
Answers
We will have that we will need the following number of boards:
We can see that each board can be used to obtain 6 two-foot braces.
So, we will need:
[tex]x=\frac{1\cdot20}{6}\Rightarrow x=\frac{10}{3}\Rightarrow x\approx3.33[/tex]So, we will need 4 boards.
Select the correct texts in the passage,Julian factored the expression 224 +223 - 22 - 1. His work is shown.At which step did Julian make his first mistake, and which statement describes the mistakerIStep 1224 +223 22= (2:13 + 2x2 - 1 - 1)(232(0 + 1) - 1(– 1)2 (212 1)(x + 1)(x - 1)Step 2Step 3Julian should have factored (2x2 - 1) as a difference of squares,Julian incorrectly factored -1 from the second group of terms.Julian should have factored 2x from all terms instead of x.Julian incorrectly factored 2x2 from the first group of terms.O 2021 Edmentum. All rights reserved.
Answers
Julian factored incorrectly the -1 from the second group of terms.
The correct way is:
[tex]\begin{gathered} 2x^4+2x^3-x^2-x \\ =x(2x^3+2x^2-x-1) \\ =x(2x^2(x+1)-1(x+1)) \end{gathered}[/tex]A soup company is looking at two designs for a new can. Can a have a diameter of 8 centimeters and a height of 15 centimeters. Can B has diameter of 10 centimeters and a height of 12 cm. How much greater of the volume of can B then can A? Use 3.14 for π and give the difference to The nearest cubic centimeter. To the nearest cubic centimeter, volume to Cube B is ______ centimeters.
Answers
Given:
The diameter of can A is, d(A) = 8 cm.
The height of can A is, h(A) = 15 cm.
The diameter of can B is, d(B) = 10 cm.
The height of can B is, h(B) = 12 cm.
The objective is to find how much greater is volume of can B than can A.
Explanation:
The general formula for volume of a can is,
[tex]V=\pi r^2h[/tex]To find volume of A:
The volume of can A can be calculated as,
[tex]V(A)=\pi(\frac{d_A}{2})^2\times h_A\text{ . . .. . .. (1)}[/tex]On plugging the given values in equation (1),
[tex]\begin{gathered} V(A)=3.14\times(\frac{8}{2})^2\times15 \\ =753.6\operatorname{cm}^3 \end{gathered}[/tex]To find volume of B:
The volume of can B can be calculated as,
[tex]V(B)=\pi(\frac{d_B}{2})^2h_B\text{ . . . . .(2)}[/tex]On plugging the given values in equation (2),
[tex]\begin{gathered} V(B)=3.14\times(\frac{10}{2})^2\times12 \\ =942\operatorname{cm}^3 \end{gathered}[/tex]To find difference:
The difference between volume of can A and can B will be,
[tex]\begin{gathered} V(B)-V(A)=942-753.6 \\ =188.4\operatorname{cm}^3 \end{gathered}[/tex]Hence, the volume of can B is greater than can A by 188.4 cm³.
A . Explain the meaning of the statement f (7) = 5. o The amount of garbage produced per week by a city with population 7,000 is 5 tons. o The amount of garbage produced per week by a city with population 5,000 is 7 tons. o The amount of garbage produced per week by a city with population 70,000 is 5 tons.o The amount of garbage produced per week by a city with population 5 is 7 tons.o The amount of garbage produced per week by a city with population 7 is 5 tons.
Answers
It will be as follows:
*The amount of garbage produced per week by a city with a population of 7000 is 5 tons. [Assuming IS ton that would be 5000 Kg, so the relationship would be linear, ie: for each 1000 population, there will be produced 1 ton (1000Kg)]
how many ways can Aileen choose 2 pizza toppings from a menu of 19 toppings if each topping can be chosen once ?
Answers
Answer:
[tex]171\text{ ways}[/tex]Expalnation:
From what we have here, there are 19 toppings to choose from
To choose the first topping, there are 19 choices to select from
For the second topping selected, since repetition is not allowed, there would be 17 toppings to choose from
Thus, the total number of ways will be according to the combination rule as follows:
[tex]\begin{gathered} ^nC_r\text{ = }\frac{n!}{(n-r)!r!} \\ ^{19}C_2\text{ = }\frac{19!}{(19-2)!2!}\text{ = 171 ways} \end{gathered}[/tex]how can I construct a tally table to represent the data?
Answers
Answer:
a)
To construct a tally table, we will have to present the table ranging from 150 to 156
b)
The probability of choosing a student not more than 153 in height means
[tex]\begin{gathered} Pr(h\leq153) \\ Pr(h\leq153)=\frac{n(h\leq153)}{n(S)} \\ (h\leq153)=1+5+10+16=32 \\ n(S)=50 \\ Pr(h\leq153)=\frac{n(h\leq153)}{n(S)}=\frac{32}{50}=\frac{16}{25} \end{gathered}[/tex]Hence,
The probability of picking not more than 153cm in height is = 16/25
b ii)
To figure out the probability greater than 153cm in height
[tex]\begin{gathered} Pr(h>153) \\ Pr(h>153)=\frac{n(h>153)}{n(S)} \\ n(h>153)=10+6+2=18 \\ n(S)=50 \\ Pr(h>153)=\frac{n(h>153)}{n(S)}=\frac{18}{50}=\frac{9}{25} \end{gathered}[/tex]Hence,
The probability of height greater than 153cm = 9/25
A park designer wanted to place a fountain so that it was close to the slide. He was given two distances as an option 1 3/4 feet or 1 5/12 feet from the slide.
Which distance is closer to the slide? Show your work to compare the two distances
Answers
Answer:
200 ft
Step-by-step explanation:
you trie it might help
hope it helps god is with u
I need help please!!!! I need the answer like right now please!! Thank you!!!
Answers
For example (Calculator);
$9.60 x 25% = $2.40
The answer above would go on the third column.
Because the first three are examples of markup, you add that $2.40 with the original price and that answer goes on the last column.
The bottom three, you'd repeat the process, but rather than adding the discount and original, you are subtracting.
Let me know if I need to elaborate a little more and I hope this helped a bit!
select all input values for which f(x)=2.choose all answers that apply:A.) x= -7B.) x=0C.) x=4D.) None of the above
Answers
The expression f(x) = 2 refers to all the x-value that make y = 2.
According to the given graph, the value is x = -7 because that's where y = 2.
Hence, the answer is A.6,855,090 in word from
Answers
Given data:
Thhe given nummber is 6,855,090.
The given number can be expand in the word form as,
Six million eight hundred fifty-five thousand ninty.
Thus, the word form of the given nuber is six million eight hundred fifty-five thousand ninty.
The radius of a circle is 9 inches. What is the length of a 45° arc?
Answers
SOLUTION:
Step 1:
In this question, we are given the following:
The radius of a circle is 9 inches.
What is the length of a 45° arc?
Step 2:
The details of the solution are as follows:
[tex]\begin{gathered} Arc\text{ length = }\frac{\theta}{360^0}\text{ x 2}\pi r \\ where\text{ }\theta\text{ = 45}^0 \\ Radius\text{ = 9 inches} \\ \end{gathered}[/tex][tex]\begin{gathered} Arc\text{ length =}\frac{45^0}{360^0}\text{ x 2 x }\pi\text{ x 9} \\ =\frac{1}{8}\text{ x 2 x }\pi\text{ x 9} \\ =\text{ }\frac{18\pi}{8} \\ =\text{ }\frac{9\pi}{4} \\ =\text{ 7.068583471} \\ \approx\text{ 7.07 inches \lparen correct to 2 decimal places\rparen} \end{gathered}[/tex]CONCLUSION:
The length of the Arc = 7.07 inches ( correct to 2 decimal places )
13. There is an 80 gram mixture of material X, Y, and Z. The ratio X :Y:Z is 4/7 / 5 . If material Z is removed, what is the new weight, in gram, of the mixture?A. 11B.64C. 25D.45
Answers
The ratio given in the problem implies that for every 4 gr of X in the mixture, there are 7 gr of Y and 5 gr of Z. Notice that:
[tex]\begin{gathered} 4+7+5=16 \\ \frac{80}{16}=5 \end{gathered}[/tex]Then, we need to multiply all the previous quantities by 5. Then, in the 80gr mixture, there are 20gr of X, 35gr of Y, and 25gr of Z.
If we remove Z from the mixture, we will end up with a total mass of:
[tex]80-25=55[/tex]55 gr is the answer to the question, despite not being among the options
Prove that the options given are not possible:
Notice that options A and C imply that most of the mixture consists of Z substance, which is not possible according to the relation.
The only possibility would be C, in that case:
[tex]\begin{gathered} 4+7=11 \\ \frac{64}{11}=5.8181\ldots \\ \Rightarrow Z\approx29.0909\ldots \\ 64+29.0909\approx93.0909 \end{gathered}[/tex]Which is not equal to 100gr
(Question in file need help asap) What is the constant of proportionality?
Answers
Answer:
16
Step-by-step explanation:
