Chester has less than $25 to spend at the county fair. The entrance fee is $5, and each ride costs $3. The number of rides, r, that Chester can go on is represented by the inequality 3r + 5 < 25. Select the most amount of rides Chester can go on without overspending

Answer:

[tex]Range = 11[/tex]

[tex]\sigma^2 = 12.1[/tex]

[tex]\sigma = 3.5[/tex]

Step-by-step explanation:

Given

[tex]Data: 16,12,17,8,15,15,10,11,19,18[/tex]

Solving (a): Range

This is calculated as:

[tex]Range = Highest - Least[/tex]

Where:

[tex]Highest = 19[/tex]

[tex]Least = 8[/tex]

So:

[tex]Range = 19 - 8[/tex]

[tex]Range = 11[/tex]

Solving (b): The population variance

First, calculate the population mean using:

[tex]\mu = \frac{\sum x}{n}[/tex]

So:

[tex]\mu = \frac{16+12+17+8+15+15+10+11+19+18}{10}[/tex]

[tex]\mu = \frac{141}{10}[/tex]

[tex]\mu = 14.1[/tex]

So, the population variance is:

[tex]\sigma^2 = \frac{\sum(x - \mu)^2}{n}[/tex]

[tex]\sigma^2 = \frac{(16 - 14.1)^2 + (12 - 14.1)^2 +............... + (19- 14.1)^2 + (18- 14.1)^2}{10}[/tex]

[tex]\sigma^2 = \frac{120.9}{10}[/tex]

[tex]\sigma^2 = 12.09[/tex]

[tex]\sigma^2 = 12.1[/tex] --- approximated

Solving (c): The population standard deviation.

This is calculated as:

[tex]\sigma = \sqrt{\sigma^2[/tex]

[tex]\sigma = \sqrt{12.09[/tex]

[tex]\sigma = 3.5[/tex]

Answer:

[tex]x(x+y)^2[/tex]

Step-by-step explanation:

We are given that

[tex]x^3y+2x^2y^2+xy^3[/tex] and [tex]2x^3+4x^2y+2xy^2[/tex]

We have to find HCF.

[tex]x^3y+2x^2y^2+xy^3=xy(x^2+2xy+y^2)[/tex]

=[tex]xy(x+y)^2[/tex]

By using the formula

[tex](x+y)^2=x^2+2xy+y^2[/tex]

[tex]xy(x+y)^2=x\times y\times (x+y)^2[/tex]

[tex]2x^3+4x^2y+2xy^2=2x(x^2+2xy+y^2)[/tex]

[tex]=2x(x+y)^2[/tex]

[tex]2x(x+y)^2=2\times x\times (x+y)^2[/tex]

HCF of ([tex]x^3y+2x^2y^2+xy^3,2x^3+4x^2y+2xy^2[/tex])

[tex]=x(x+y)^2[/tex]

Answer:

For 1: The first term is 10 and the common difference is [tex]\frac{3}{2}[/tex]

For 2: The value of n is 27

Step-by-step explanation:

The n-th term of the progression is given as:

[tex]a_n=a_1+(n-1)d[/tex]

where,

[tex]a_1[/tex] is the first term, n is the number of terms and d is the common difference

The sum of n-th terms of the progression is given as:

[tex]S_n=\frac{n}{2}[2a_1+(n-1)d][/tex]

where,

[tex]S_n[/tex] is the sum of nth terms

The 11th term of the progression:

[tex]25=a_1+10d[/tex]               .......(1)

Sum of first 4 numbers:

[tex]49=\frac{4}{2}[2a_1+3d[/tex]              ......(2)

Forming equations:

[tex]98=8a_1+12d[/tex]

[tex]25=a_1+10d[/tex]                  ( × 8)

The equations become:

[tex]98=8a_1+12d[/tex]

[tex]200=8a_1+80d[/tex]

Solving above equations, we get:

[tex]102=68d\\\\d=\frac{102}{68}=\frac{3}{2}[/tex]

Putting value in equation (1):

[tex]25=a_1+10\frac{3}{2}\\\\a_1=[25-15]=10[/tex]

Hence, the first term is 10 and the common difference is [tex]\frac{3}{2}[/tex]

The nth term is given as:

[tex]49=10+(n-1)\frac{3}{2}[/tex]

Solving the above equation:

[tex]39=(n-1)\frac{3}{2}\\\\n-1=26\\\\n=27[/tex]

Hence, the value of n is 27

Answer:

8%

Step-by-step explanation:

Rate = 100×Interest ÷ Principal× Time

100× 2500/ 2500 × 8 = 800

800/100 = 8%

I hope this helps

Answer:

D

Step-by-step explanation:

Answer:

1/8 Of the animals are rabbits.

Step-by-step explanation:

3/8 Cats + 4/8 Dogs = 7/8

1/8 Is all you have room left for so 1/8 would be rabbits.

Answer:

1/8.

Step-by-step explanation:

Fraction of rabbits = 1 - (3/7 + 4/8)

= 1 - 7/8

= 8/8 - 7/8

= 1/8.

Answer:

46

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Answer:

7

Step-by-step explanation:

481 + 223

approximately 481 =5

223 =2

5+2=7

Answer:

7

Step-by-step explanation:

Answer:

(-2,1), (0,1), and (2,0). its over the y axis

Step-by-step explanation:

Answer:

shift it 3 values right and 2 units up

Step-by-step explanation:

moving x-axis and moving y-axis

Answer:

3

Step-by-step explanation:

hrhrhehrhrhrhrhruruurruururuur

Answer:

1) f(g(2)) = 24

2) f(g(-1)) = -4

Step-by-step explanation:

1) GIven f(x) = x²+2x and g(x) = 2x

f(g(x)) = f(2x)

f(2x) = (2x)² + 2(2x)

f(2x) = 4x² + 4x

f(g(x)) = 4x² + 4x

f(g(2)) = 4(2)² + 4(2)

f(g(2)) = 16+8

f(g(2)) = 24

2) f(x) = x+1 and g(x) = 5x

f(g(x)) = f(5x)

f(5x)= 5x + 1

f(g(x)) = 5x + 1

f(g(-1)) = 5(-1) + 1

f(g(-1)) = -5+1

f(g(-1)) = -4

Answer:

x = 8.8

General Formulas and Concepts:

Pre-Algerba

Order of Operations: BPEMDAS

Equality Properties

Step-by-step explanation:

Step 1: Define

Identify

8.35x - 1.5 = 71.98

Step 2: Solve for x

Answer:

C

Step-by-step explanation:

but it's also horizontally stretched (see screenshot)

Answer:

The correct answer is G(x)=1/9x

Step-by-step explanation:

Answer:

1/7 =  0.142857 since this decimal is repeating divide 45/6(number of repeating numbers) and it gives you 7.5 so you know that it repeats this sequence 7 times plus an extra 3 numbers so the 45th decimal is 2

Step-by-step explanation:

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

Answer:

3/7 = 0.428571 which is also considered a number that keeps repeating.

Answer:

1st number (x) = 5

2nd number (y) = 11

3rd number (z) = -2

Step-by-step explanation:

Let the generic solution for this problem be x + y + z = 14.  

The first number minus three times the third number equals the second number, so x - 3z = y.  The second number is 6 more than the first number, so y = 6 + x.  

x - 3z = y, we know that y = 6 + x, so the equation becomes x - 3z = 6 + x.

After some arithmetic, we find that z = -2.  

Plugging our knowns back into the generic solution becomes:

x + x - 3z + z = 14

2x - 3(-2) - 2 = 14

2x + 6 - 2 = 14

2x + 4 = 14

2x = 10

x = 5

So we know that z = -2, and x = 5, it's just simple substitution from there.  

5 + y + (-2) = 14

5 + y = 16

y = 11

Answer:

Kindly check explanation

Step-by-step explanation:

Given :

Interest amount paid on loan = $90

Principal value, amount borrowed = $500

Period, t = 16 days

The equivalent annual interest :

Using the simple interest formula :

simple interest = principal * rate * time

Using, days of year = 365

Plugging in the values into the formula :

90 = 500 * rate * (16/365)

90 = 500 * rate * 0.0438356

90 = 21.917808 * rate

Rate = 90 / 21.917808

Rate = 4.10 = 4.10 * 100% = 410%

If days of year = 360 is used :

90 = 500 * rate * (16/360)

Rate = 90 / 22.222

Rate = 4.05 = 4.105 * 100% = 405%:

Answer:

b = 7 inches and l = 12 inches

Step-by-step explanation:

Given that,

The area of a rectangle, A = 84 sq inches

Let the width is b.

Length = (5+b)

The area of a rectangle is given by :

A = lb

So,

[tex]84=b\times (5+b)\\\\b^2+5b-84=0\\\\(b-7)(b+12)=0\\\\b=7\ in, b =-12\ in[/tex]

Neglecting negative value,

b = 7 inches

Length, l = 5+b = 5+7

l = 12 inches

Answer:

-102

Step-by-step explanation:

First, substitute the value into each equation and solve:

f(5) = -14(5) + 3 = -70 + 3 = -67

g(5) = (5)² + 10 = 25 + 10 = 35

-67 - 35 = -102

Answer: 100 inches

Step-by-step explanation:

From the question, we are given the information that Nia had a 20 inch by 30 inch enlargement made of a photograph and that she wanted to have it framed.

The number of inches of frame that she would use to enclose the photo will be gotten by calculating the perimeter of the shape and this will be:

= 2(length + width)

= 2(30 + 20)

= 2(50 inches)

= 100 inches

To enclose the photo, 100 inches of frame is needed.

9514 1404 393

Answer:

  B. 8 and 24

Step-by-step explanation:

There are a number of approaches you can use here. One of them is to choose the only answer that makes any sense in the problem.

The problem tells you the numbers have a ratio of 3, so numbers like 8 and 25, 9 and 24, 9 and 25 cannot be the answer.

The only answer choice that makes any sense is B: 8 and 24.

__

If you want to work the problem, there are different ways you can do that. One of my favorite is to consider ratio units. The ratio of the two numbers is 3:1. The difference of the two numbers is 3-1 = 2 ratio units, which we are told is 16. Then each ratio unit represents 16/2 = 8. Then the numbers are ...

  3×8 and 1×8 = 24 and 8.

Or, you can let a variable represent one of the numbers. If x is the first number, then the other number is 1/3x, and their difference is ...

  x -1/3x = 16

  2/3x = 16

  x = 16(3/2) = 24

The numbers are 24 and 24/3 = 8.

__

Additional comment

You need to talk to your teacher about this question. The answer choices list the smaller number first, but the problem statement tells you the first number is 3 times the second number. The correct answer would be 24 and 8.

Answer:

[tex]4 < c < 24[/tex]

Step-by-step explanation:

Given

[tex]a = 10[/tex]

[tex]b = 14[/tex]

Required

The possible length of c

Using triangle inequality theorem, we have:

[tex]a + b > c[/tex]

[tex]a + c > b[/tex]

[tex]b + c > a[/tex]

So, we have:

[tex]a + b > c[/tex]

[tex]10 + 14 > c[/tex]

[tex]24 > c[/tex]

Also:

[tex]a + c > b[/tex]

[tex]14 + c > 10[/tex]

[tex]c > 10 - 14[/tex]

[tex]c > - 4[/tex]

Lastly;

[tex]b + c > a[/tex]

[tex]10 + c > 14[/tex]

[tex]c > 14 - 10[/tex]

[tex]c > 4[/tex]

Write out all inequalities without negative consideration

[tex]24 > c[/tex]

[tex]c > 4[/tex]

Rewrite as:

[tex]c < 24[/tex]       [tex]4 < c[/tex]

Writing both together, we have:

[tex]4 < c < 24[/tex]

Hence, the third side can take its value from the range: [tex]4 < c < 24[/tex]

Answer:

Hi Are you from Vietnam?

Step-by-step explanation:

Sorry i cant understand

im filipino

9514 1404 393

Explanation:

Using a random number generator to choose coefficients, we can substitute the required solution to find the constants in the equations. Here is one possible set of equations.

 17x +7y +8z = 6

  12x -6y +z = -16

  14x +8y +11z = 16

__

Additional comment

"Standard form" requires the x-coefficient be positive. Truth be told, the random number generator came up with negative numbers for the first and last equations (on the second try). On the first try, it came up with a couple of zero coefficients. Such is the behavior of random numbers.

The trick with choosing a set of numbers "by hand" is doing it in such a way that the equations are independent.

Answer:

Base=2 cm

Height=35 cm

or

Base=5 cm

Height=14 cm

Or

Base=7 cm

Height=10 cm

Or

Base=10 cm

Height=7 cm

Or

Base=14 cm

Height=5 cm

Or

Base=70 cm

Height=1 cm

Or

Base=35 cm

Height=2 cm

Or

Base=1 cm

Height=70 cm

Step-by-step explanation:

We are given that

Area of triangle=[tex]35cm^2[/tex]

We have to find the dimension of triangle.

We know that

Area of triangle=[tex]\frac{1}{2}\times base\times height[/tex]

Using the formula

[tex]35=\frac{1}{2}\times base\times height[/tex]

[tex]base\times height=35\times 2=70[/tex]

Factor of 70 :2,5,7,10,14,35,70

Therefore, the dimension could be

Base=2 cm

Height=35 cm

or

Base=5 cm

Height=14 cm

Or

Base=7 cm

Height=10 cm

Or

Base=10 cm

Height=7 cm

Or

Base=14 cm

Height=5 cm

Or

Base=70 cm

Height=1 cm

Or

Base=35 cm

Height=2 cm

Or

Base=1 cm

Height=70 cm

Answer:

A

Step-by-step explanation:

Step 1, setting variables:

We already know the exact height of the prism: 6 feet. We can set the unknown width as variable x, and length as x+2 (length is two feet more than width).

Step 2, writing equations:

Great! We have everything now. Let us write the equation by substituting our variables in:

[tex]V=l*w*h\\V=6w(w+2)\\[/tex]

Ok! Let us expand the equation:

[tex]V=6w^2+12w[/tex]

[tex]\fbox{A}[/tex]

I hope this helps! Let me know if you have any questions :)

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Answer:

You can build 1296 different home theater systems.

Step-by-step explanation:

Fundamental counting principle:

States that if there are p ways to do a thing, and q ways to do another thing, and these two things are independent, there are p*q ways to do both things.

There are:

6 different TVs

12 types of surround sound systems.

18 types of DVD players.

How many different home theater systems can you build?

The components are independent, so, by the fundamental counting principle:

6*12*18 = 1296

You can build 1296 different home theater systems.