On Monday morning, Mr. Descartes asked his Algebra II students whether they had gone to the carnival in town over the weekend.

"I did," said Kristen. "I went on the Teacups ride twice, the rollercoaster twice, and the Spinning Vortex once. I had a lot of fun for only $20."

"I went on those rides, too!" exclaimed Jorge. "Just once each on the Teacups and rollercoaster, but three times on the Spinning Vortex, all for $25."

"I did five Teacup rides," said Lakesha. "And two rollercoaster rides, and one Spinning Vortex. I spent $29."

Marc listed off the same rides. "Three Teacups for me, plus two rollercoasters, plus two rides on the Spinning Vortex, all for – "

"You don't need to say," interrupted Mr. Descartes. "I know how much you spent."

How much are the rides? How much did Marc spend

Answers

Answer 1

Answer:

Cost of one Teacup =  $3

Cost of one Roller coaster =  $4

Cost of one Spinning Vortex = $6

Marc spent = 3x + 2y + 2z = $29

Step-by-step explanation:

Let

Cost of one Teacup = x

Cost of one Roller coaster = y

Cost of one Spinning Vortex = z

In Kristen case -

2x + 2y + z = $20

In Jorge case -

x + y + 3z = $25

In Lakesha case -

5x + 2y + z = $29

In Marc case -

3x + 2y + 2z = ?

Now, we have

2x + 2y + z = $20       ......(1)

x + y + 3z = $25         ........(2)

5x + 2y + z = $29      .........(3)

Now,

Subtract equation (1) from equation (3), we get

5x + 2y + z - ( 2x + 2y + z ) = $29 - 20

⇒5x + 2y + z - 2x - 2y - z  = $9

⇒3x = $9

⇒x = $3

Now,

Multiply be 2 in equation (2) , we get

2x + 2y + 6z = $50        ........(4)

Now,

Subtract equation (1) from equation (4), we get

2x + 2y + 6z - ( 2x + 2y + z ) = $50 - 20

⇒2x + 2y + 6z - 2x - 2y - z  = $30

⇒5z = $30

⇒z = $6

Now,

Put the values of x and z in equation (2) , we get

$3 + y + 3($6) = $25

⇒$3 + y + $18 = $25

⇒y + $21 = $25

⇒y = $25 - 21

⇒y = $4

∴ we get

Cost of one Teacup = x = $3

Cost of one Roller coaster = y = $4

Cost of one Spinning Vortex = z = $6

Marc spent = 3x + 2y + 2z = 3($3) + 2($4) + 2($6) = $9 + $8 + $12 = $29


Related Questions

What is the equation of the exponential curve that passes through the points (0,3) and (5,96)?

Answers

Answer:

M=93/5

Step-by-step explanation:

What is the y-intercept of the line?

Answers

Answer:

y=1/2x+2

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

y intercept is 2

and slope is rise /run

taking points (0,2) and (2,3)

we get slope= 3-2/2-0=1/2

we know the eqaution is y=mx+b where m is the slope and b the y intercept

so y=1/2x+2 which is A/ the first one

if my answer helps please mark as brainliest

please help with my math homework

Answers

Answer:

sorry for that

Step-by-step explanation:

image is so unclear can't even read

Solve 12 - 4x = 44. Find the value of X

Answers

Answer:

x = -8

Step-by-step explanation:

We have the expression 12 - 4x = 44 and are asked to find the value of x.

To solve this, we need to isolate x, or get it by itself.

12 - 4x = 44

Subtract 12 from both sides :

-4x = 32

Divide -4 from both sides :

x = -8

answer:
x = -8

step by step
12 - 4x = 44
-4x = 44 - 12
-4x = 32
x = -8

HELP ASAP!! Mrs. Walsh is in search of a birthday gift for her niece and decided to shop at Kohls. Mrs. Walsh just had a nice shopping spree there, therefore she had $15 Kohls cash to use. She also had a friends and family coupon for 25% off the entire purchase. Mrs. Walsh made sure to search the fine print and there was nothing noted saying she cannot use BOTH coupons. Which coupon should Mrs. Walsh use first, or does it matter? Will this always be the case? How do you know? Show your work. ​

Answers

Answer:

The best answer would be the 25% off the entire purchase. Say for example Mrs. Walsh was willing to spend 100$ that would be 25% dollars she saved. But when it comes to save the most amount of money. If she spends under 60 dollars use the 15 dollars off. If it’s over 60 use the 25% off coupon

8. Which of the following Mathematical expressions is equivalent to a cubed of a number x increased by
ten" ?
A. 3x + 10
B. 10x3
C. x3 – 10
D. x3 + 10​

Answers

Answer:

B

Step-by-step explanation:

Breaking down Brown versus Whitman: Example 2 of the chapter 1 discusses an exit poll taken during the 2010 California gubernatorial election. The administrators of the poll also collected demographic data, which allows for further breakdown of the 3889 voters from whom information was collected. Of the 1633 voters registered as Democrats, 91% voted for Brown, with a margin of error of 1.4%. Of the 1206 voters registered as Republicans, 10% voted for Brown, with a margin of error of 1.7%. And of the 1050 Independent voters, 42% voted for Brown, with a margin of error of 3.0%.

Required:
a. Do these results summarize sample data or population data?
b. Identify a descriptive aspect of the results.
c. Identify an inferential aspect of the results.

Answers

Answer:

(A) Population data

(B) The figures

(C) The classification of votes by political party

Step-by-step explanation:

(A) These results summarize population data. The population is the total 3,889 voters from whom information was collected.

The samples would be

- Voters registered as Democrats  (1,633)

- Voters registered as Republicans  (1,206)

- Independent Voters  (1,050)

The total of members in each sample equals the total number of people in the population.

(B) A descriptive aspect of the result is the figures or percentages. They describe how (in percentage) voters penned their votes for Brown and how they penned their votes for Whitman. NOTE: To get the percentage or fraction of those who voted for Whitman, simply subtract the percentage of Brown's supporters from a total of 100%.

(C) An inferential aspect of the results is the classification of votes by different parties (the samples are the different parties involved here). This helps to infer the sources of support for Brown and the sources of support for Whitman.

For example, if the total votes for Brown (in population result analysis) are low, the Republicans are the major reason why!

Jenee has a package of 30 cards. There are 5 orange cards
and 25 yellow cards.
If she randomly picks 6 cards, what is the best prediction
for how many cards should be orange?

Answers

Answer:

1/2 is the best prediction for the number of orange cards that Jenee could get

Step-by-step explanation:

Hope this helps :D

If it does help could I get brainliest?

if x = 2 and y=1 then prove that (x-y)²=x²-2xy+y²​

Answers

Answer\Step-by-step explanation:

0≤(x − y)^2 ⟹ 0≤x^2−2xy+y^2

                  ⟹ 2xy≤x^2+y^2

             ⟹ xy≤ x2+y2\2

                  ⟹ xy≤ x^2+y^2

since the clearly nonnegative real x^2+y^2

clearly satisfies x^2+y^2\2  ≤x^2+y^2.

The proof of the quadratic equation  (x-y)²=x²-2xy+y²​ is given.

What is a quadratic equation?

For variable x : ax² + bx + c = 0, where a≠0 is a standard quadratic equation, which is a second-order polynomial equation in a single variable. It has at least one solution since it is a second-order polynomial equation, which is guaranteed by the algebraic basic theorem.

Given:

Quadratic equation

(x-y)²=x²-2xy+y²​

To prove the equation:

We substitute the value and see if LHS = RHS.

In the LHS,

LHS =  (x-y)²

LHS =  (2-1)²

LHS =  1

In the RHS,

RHS = x²-2xy+y²​

RHS = 4 - 4 + 1

RHS = 1

LHS = RHS​

Therefore, the theorem (x-y)²=x²-2xy+y²​ is proved.

To learn more about the quadratic equation;

https://brainly.com/question/17177510

#SPJ2

Directions: Find each product. Show your solution. .
1) 0.35 x 24 =
2) 0.59 x 29 =
3) 2.45 x 5 =
4) 0.84 x 3 =
5) 0.45 ~ 63=
6) 3.54 x 0.59=
7) 5.28 x 1.18 =
8) 4.37 x 0.58 =
9) 7,05 * 0.52 =
10) 2.36 x 1.28=
[tex]0.35 \times 24 = [/tex]

Answers

Answer:

.

1) 0.35 x 24 =8.4

2) 0.59 x 29 =17.11

3) 2.45 x 5 =12.25

4) 0.84 x 3 =2.52

5) 0.45 ×63=28.35

6) 3.54 x 0.59=2.0886

7) 5.28 x 1.18 =6.2304

8) 4.37 x 0.58 =2.5346

9) 7.05 * 0.52 =3.666

10) 2.36 x 1.28=3.0208

[tex]0.35 \times 24 = [/tex]=8.4

Answer:

1) 8.4

2) 17.11

3) 12.25

4) 2.52

5) 28.35 (if numbers are multiplied)

6) 2.0886

7) 6.2304

8) 2.5346

9) 3.666

10) 3.0208

Please help this is due today!

Answers

Answer:

a. True

b. True

c. False

d. False

e. Both

Step-by-step explanation:

a.  Explanation: each triangle is composed of three interior angles and three sides which can be of the same length or different lengths

b.  Explanation: isosceles triangles always have two equivalent interior angles, and all three interior angles of any triangle always have a sum of degrees

c. Explanation: The sum of the measures of the angles is always 180 degrees so that means it is not possible.

d. Explanation: exterior angles of a triangle is greater than either of the measures of the remote interior angles so This is a fundamental result in absolute false because its Interior does not depend upon the Angles

e. Explanation: Eh, There's really no explanation for this So, It's both.

50% of 25% of a number x is
A- one eighth of X
B- half of X
C- one fourth of X
D- three fourth of X

Answers

Answer:

The word "of" in mathematical terms means multiplication. The word "is" means equal. This would be translated into 50% x 25% x X = or 0.50 x 0.25 x X =. 0.50 times 0.25 = 0.125. Putting 0.125 into a fraction, it would be 125/1000. Simplify this fraction to get 1/8. So, the answer would be A.

What is the product of (2x-4)^2​

Answers

Answer:

( 4x^2 -16x +16)

Step-by-step explanation:

The rule is the

the first term squared + (the first term * second term  * 2) + second term^2

I WILL GIVE AWAY THE CROWN TO WHOEVER IS CORRECT

Which equation can be used to calculate the area of the shaded triangle below?


A rectangle with length of 10 feet and width 6 feet. A diagonal cuts the rectangle into two halves. One of the triangular halves is shaded.


A. 2(10 + 6) = 32


B. fraction 1 over 2(10 + 6) = 8


C. fraction 1 over 2(10 × 6) = 30


D. 2(10 × 6) = 120

Answers

Answer:

d

Step-by-step explanation:

you are dealing with area so you are going to want to multiply the length and the width

Answer:

its "fraction 1 over 2(10 × 6) = 30"

Step-by-step explanation:

i just took this text a week ago that the right answer not D

If you horizontally stretch the quadratic parent function, f(x) = x2, by a factor
of 3, what is the equation of the new function?
O A. g(x) = x²
O B. g(x) = (3x)2
C. g(x) = 3x2
O D. g(x) = (3x)2

Answers

Answer:

g(x)=(1/3x)² .................

Multiply. Write your answer in simplest form. 1/9 x 3/10

Answers

Answer:

1/30

Step-by-step explanation:

When you multiply fractions, you just muliply across,

1*3= 3

9*10= 90

you now have 3/90 but you have to simplify, we know 3 goes into 3 and it also goes into 90 equally

3/3= 1

90/3= 30

So your answer is 1/30!!

I hope this helps!!!!!!!!!!!

ss of
3. In a class of 50 students, 40 % are girls. Find the number of girls and
number of boys in the class?
Solution:​

Answers

Answer:

20 boys in the class

Step-by-step explanation:

40% of 50 is 20

what is ask in the problem​

Answers

What is the problem??

5/7x1/2 please need help now

Answers

The exact form is 5/14

Evaluate the expression when c=2 and y=-6.
-c+by
0
Х
?

Answers

Answer:

-38

Step-by-step explanation:

-c + 6y

= -(2) + 6 (-6)

= -2+(-36)

= -2 - 36

= -38

the answer to this question is -38

please help me thank you in advance!

Answers

Answer:

4x + 5y = 20

Step-by-step explanation:

It is parallel to y = -4/5x + 6

todos los numeros naturales son enteros​

Answers

Pee brain. . .you get it okay

Answer:

si, todos los números naturales son enteros

What is the growth?
What is figure 0?
Y=( )X+( )
Can someone help me too those answers I have no clue

Answers

Answer:

Figure 0 = 67 Square Units

Step-by-step explanation:

Its correct, I took the test!

please help me get this answer

Answers

Answer:

Step-by-step explanation:

Due to similarity in Tri ABC and ADE so,

[tex]\frac{AD}{AB} =\frac{DE}{BC} =\frac{AE}{AC}[/tex]

[tex]AE=28.2*\frac{20}{24} =23.5cm[/tex]

[tex]EC=AC-AE =28.2-23.5=4.7cm[/tex]

Help plsssssssssssssssssssssss

Answers

Answer:

Okay, whats your question?

Step-by-step explanation:

A math teacher was frustrated at the number of students leaving their graphing calculator behind in her classroom at the end of class without a way to locate the student. A random sample of 50 students is selected, and of the students questioned, 32 had their names written on their graphing calculators.

Required:
What would be a 99% confidence interval for the proportion of all students at this school who have their names written on their graphing calculators?

Answers

Answer:

The 99% confidence interval for the proportion of all students at this school who have their names written on their graphing calculators is (0.4652, 0.8148).

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].

A random sample of 50 students is selected, and of the students questioned, 32 had their names written on their graphing calculators.

This means that [tex]n = 50, \pi = \frac{32}{50} = 0.64[/tex]

99% confidence level

So [tex]\alpha = 0.01[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.01}{2} = 0.995[/tex], so [tex]Z = 2.575[/tex].

The lower limit of this interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.64 - 2.575\sqrt{\frac{0.64*0.36}{50}} = 0.4652[/tex]

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.64 + 2.575\sqrt{\frac{0.64*0.36}{50}} = 0.8148[/tex]

The 99% confidence interval for the proportion of all students at this school who have their names written on their graphing calculators is (0.4652, 0.8148).

A rapid strep test is often given in a clinical setting so that, if needed, antibiotics can begin as soon as possible. Researchers at Cochrane.org evaluated the effectiveness of rapid strep tests and found that one type had a sensitivity (ability to correctly detect people with strep) of 85.4% and a specificity (ability to correctly identify people who do NOT have strep) of 95%
Fill in the following chart, assuming that you have a group of 10,000 people, 15% of whom actually have strep throat.
Patient is given a rapid strep test
Result is positive Result is negative totals
Has strep throat
Does not have strep
Totals 10,000
For a population of patients similar to those described in the stem of this problem, use the chart find each of the following probabilities. Write you answer as an abbreviated probability statement with your answer to four decimal places without using a percent symbol. For example, P(strep) = 0.15
A) The probability that a randomly chosen patient has strep throat and tests positive
B) The probability that a randomly chosen patient tests positive for strep throat.
C) The probability that a randomly chosen person actually has strep throat, given that they have tested positive.

Answers

Answer:

Follows are the responses to this question:

Step-by-step explanation:

Follows are the table to this question:

                                        [tex]positive \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ negative \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ total[/tex]

[tex]\text{strep value} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 1281\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 219 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 1500 \\\\[/tex]

[tex]\text{not the strep value} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 425 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 8075 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 8500 \\\\ \text{total} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 1706 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 8294 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 10000 \\\\[/tex]

In point a:

[tex]P( \text{step and positive test}) = \frac{1281}{10000}=0.1281[/tex]

In point b:

[tex]P(\text{positive test}) =\frac{1706}{10000} =0.1706[/tex]

In point c:

[tex]P \text{(strep | positive test)} =\frac{1281}{1706} =0.7509[/tex]

Elena had $50 in the bank on Monday. She had $56 on Tuesday. What was the percent of increase from Monday to Tuesday?

A.100 fish

B.40 fish

C.60 fish

D.80 fish

Answers

Answer:

c

Step-by-step explanation:

everyone knows this it’s 74 fish

whats 1+1?
please do answer!

Answers

Answer:

I thought it was 3, no wait its 2

Step-by-step explanation:

You are thinking of the Principia Mathematica, written by Alfred North Whitehead and Bertrand Russell. Here is a relevant excerpt:

Picture Below

As you can see, it ends with "From this proposition it will follow, when arithmetical addition has been defined, that 1+1=2." The theorem above, ∗54⋅43, is already a couple of hundred pages into the book (Wikipedia says 370 or so); the later theorem alluded to, that 1+1=2, appears in section ∗102, considerably farther on.

I wrote a blog article a few years ago that discusses this in some detail. You may want to skip the stuff at the beginning about the historical context of Principia Mathematica. But the main point of the article is to explain the theorem above.

The article explains the idiosyncratic and mostly obsolete notation that Principia Mathematica uses, and how the proof works. The theorem here is essentially that if α and β are disjoint sets with exactly one element each, then their union has exactly two elements. This is established based on very slightly simpler theorems, for example that if α is the set that contains x and nothing else, and β is the set that contains y and nothing else, then α∪β contains two elements if and only if x≠y.

The main reason that it takes so long to get to 1+1=2 is that Principia Mathematica starts from almost nothing, and works its way up in very tiny, incremental steps. The work of G. Peano shows that it's not hard to produce a useful set of axioms that can prove 1+1=2 much more easily than Whitehead and Russell do.

does anybody know what to do here?

Answers

Answer:

m=6

Step-by-step explanation:

38+8m+4=90

42+8m=90

8m=90-42

8m=48

m=6

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