At the baseball game, Adam bought 3 hot dogs and 2 sodas for $11. Four innings later, he purchased 2 hot dogs and 3 sodas for $10.25. Wat was the cost of a soda

Answer:

X=6

Step-by-step explanation:

Distributing the 3

7x-3x+18=42

Adding like terms

4x+18=42

Subtracting 18 from both sides

4x=24

Dividing both sides by 4

X=6

Answer:

Possible ways to paint the house is 108

Step-by-step explanation:

Total number of houses to be painted=4

Total number of colours to b used(red,blue,green and yellow)=4

Number of ways to paint the first house=4

Number of ways to paint the second house=3

Number of ways to paint the third house=3

Number of ways to paint the fourth house=3

Total number of ways to paint the 4 houses=4×3^3=108 ways.

Final answer:

There are 24 different ways to paint the houses so that no two adjacent houses are of the same color.

Explanation:

To solve this problem, we can use the concept of permutations. Since there are 4 houses and 4 colors to choose from, we can start by selecting a color for the first house. We have 4 options for the first house. Next, we need to choose a color for the second house, but we must ensure that it is different from the color chosen for the first house. We have 3 options for the second house. For the third house, we have 2 options, and for the fourth house, we have only 1 option.

Therefore, the total number of ways to paint the houses without any two adjacent houses being the same color is calculated as:

4 x 3 x 2 x 1 = 24

Answer:

The answer to your question is 4 ft

Step-by-step explanation:

Data

Building's shadow = 288 ft

Building's high = 64 ft

Sarah's shadow = 18 ft

Sarah's height = ?

Process

1.- Use proportions to solve this problem

                               [tex]\frac{Sarah's height}{Sarah's shadow} = \frac{building's height's}{building's shadow}[/tex]

2.- Solve for Sarah's height

  [tex]Sarah's height = \frac{Sarah's shadow x building's height}{building shadow}[/tex]

3.- Substitution

  [tex]Sarah's height = \frac{18 x 64}{288}[/tex]

4.- Simplification

  [tex]Sarah's height = \frac{1152}{288}[/tex]

5.- Result

  Sarah's height = 4 ft

Answer:

The dimensions of the original garden is [tex]27\times25\ ft[/tex].

Step-by-step explanation:

Let the width of the rectangular garden be 'x'.

Now given:

A rectangular garden is 2 feet longer than it is wide.

so we can say that;

Length of the rectangle = [tex](x+2) \ ft[/tex]

Now to fence the garden we need to find the perimeter of the garden.

Now Perimeter of the garden is equal to twice the sum of the length times width.

framing in equation form we get;

Perimeter of the rectangle = [tex]2(x+x+2)=2(2x+2)=4x+4[/tex]

Now given:

If the width is doubled, 50 extra feet of fencing will be needed

It  means that Perimeter of the doubled width rectangle is equal to perimeter of original garden plus 50.

framing in equation form we get;

[tex]2(2x+x+2)=4x+4+50\\\\2(3x+2)=4x+50[/tex]

Now Applying distributive property we get;

[tex]2\times3x+2\times2=4x+54\\\\6x+4=4x+54[/tex]

Combining the like terms we get;

[tex]6x-4x=54-4\\\\2x=50[/tex]

Dividing both side by 2 we get;

[tex]\frac{2x}{2}=\frac{50}{2}\\\\x=25 \ ft[/tex]

Length of the rectangular garden = [tex]x+2=25+2=27\ ft[/tex]

Hence the dimensions of the original garden is [tex]27\times25\ ft[/tex].

Answer:

Explanation:

To find the oblique asymptote of a rational function you divide the numerator by the denominator and take the quotient (not the remainder).

Such quotient (without the remainder) is the equation of the line that is the oblique asymptote of the rational function.

The rational function is:

             [tex]\frac{9x^2+36x+41}{3x+5}[/tex]

You can see the long division in the picture attached. The quotient is 3x + 7.

Hence, by comparison with y = 3x + k, k = 7.

Answer:

7

Step-by-step explanation:

Correct on EDGE

Answer:

Mr. Meglio need to purchase 39 square feet of carpet.

Step-by-step explanation:

Given:

Total number of steps = 13

Length of each step = 1 foot

Width of each step = 3 foot

We need to find the square feet of carpet does Mr. Meglio need to purchase.

Solution:

First we will find the area of each step.

area of each step is equal to length times width.

framing in equation form we get;

area of each step = [tex]1\times 3 = 3\ ft^2[/tex]

Now amount of carpet required in square feet we multiply number of step with area of each step.

framing in equation form we get;

Amount of carpet required = [tex]13\times3 =39\ ft^2[/tex]

Hence Mr. Meglio need to purchase 39 square feet of carpet.

Final answer:

Mr. Meglio needs to purchase 39 square feet of carpet to cover the 13 steps in the stairwell, as each step has an area of 3 square feet.

Explanation:

The student is asking how many square feet of carpet are needed to cover a stairwell with 13 steps, where each step is one foot by three feet.

To calculate the area of a single step, multiply the length by the width. For one step, the calculation is 1 foot × 3 feet = 3 square feet. Since there are 13 steps, multiply the area of one step by the number of steps: 3 square feet/step × 13 steps = 39 square feet. Therefore, Mr. Meglio will need to purchase 39 square feet of carpet to cover all the steps.

This type of problem is a practical application of the area calculation in real-world context, and the measurement conversion from square inches to square feet is also pertinent to understanding the measurement of areas in different units.

Answer:

histogram is a graphical representation of data using he concepts of statistics.

Step-by-step explanation:

your question is incomplete as ample information is not provided for solving this problem.

Answer:

B. The variable is continuous because it is not countable.

Correct, from the definition about of continuous data we see that is a random variable is continuous then it can't be countable.

Step-by-step explanation:

Previous concepts

A discrete random variable "has a countable number of possible values" in a domain defined. So then the possible values for these types of random variables are the integers.

A continuous is a random variable "where the data can take infinitely many values" that means that can take values from the rational with decimals. Ans is not countable.

Solution to the problem

Let's analyze one by one the possible options:

A. The variable is discrete because it is countable.

False, the depth of the ocean is a continuous random variable since we can have for exampe a depth of 1200.56 mi and we can't express this as a discrete random variable.

B. The variable is continuous because it is not countable.

Correct, from the definition about of continuous data we see that is a random variable is continuous then it can't be countable.

C. The variable is discrete because it is not countable.

False, the depth of the ocean is a continuous random variable since we can have for exampe a depth of 504.67 Km and we can't express this as a discrete random variable.

D. The variable is continuous because it is countable.

False the variable is continuous but cannot be countable since that's the opposite from the definition of continuous random variable.

The correct answer is option is B). The variable is continuous because it is not countable.

The depth of the ocean floor is a quantitative variable that can take on any value within a range and can be measured to any level of precision. This means that the depth can be a non-integer number and is not restricted to integer counts. Therefore, it is not countable in the sense that one can count individual, distinct units, such as the number of people in a room or the number of cars in a parking lot. Instead, the depth of the ocean floor is a continuous variable because it can vary smoothly and without gaps over a range of values.

To illustrate, consider that the depth of the ocean can be 100.5 meters, 100.52 meters, 100.526 meters, and so on, with an infinite number of possible values between any two depths. This characteristic of having an infinite number of possible values within any given interval is what defines a continuous variable.

Answer:

i got 8.33 so I would say about 9. Im not sure about inequality statements but I know that's about how many days since he makes 300 per day, and you divide that by 2500

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

because 39.5 hours makes 8.18

Fortuna's gross pay is $323.11

A unit rate means a rate for one of something. We write this as a ratio with a denominator of one. For example, if you ran 70 yards in 10 seconds, you ran on average 7 yards in 1 second. Both of the ratios, 70 yards in 10 seconds and 7 yards in 1 second, are rates, but the 7 yards in 1 second is a unit rate.

Given that, Fortuna worked 39.5 hours this week at $8.18 an hour.

Since, she is being paid $8.18 for 1 hour, that mean her unit rate is $8.18

To find total rate we will multiply her unit rate with total hours she worked.

Therefore,

The total pay = 39.5 × 8.18 = $323.11

Hence, Fortuna's gross pay is $323.11

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Answer:he will need to mix 20 cups of water if he uses 5 cups grape concentrate.

Step-by-step explanation:

Henry mixes 1 cup grape concentrate with 4 cups water to make his favorite drink. It means that the number of cups of grape concentrate that henry requires to mix 1 cup of water would be

1/4

Therefore, the number of cups of water that he needs to mix if he uses 5 cups grape concentrate would be

5/(1/4) = 20 cups of water

Answer:

Step-by-step explanation:

[tex]g(x)=log_{2}( x+4) -1\\let g(x)=y\\y=log_{2}(x+4)-1 \\x+4=2^{y+1} \\when y=0\\x+4=2^1=2\\x=2-4=-2\\when x=0\\4=2^{y+1}=2^y*2^1=2*2^y\\2^y=\frac{4}{2}=2=2^1\\so~y=1\\x -intercept=-2\\y-intercept=1[/tex]4. it is a transformation of 4 units left and 1 unit down.

Answer:

  4/2 = 2 > 1

Step-by-step explanation:

The quotient of any two integers of the same sign and the dividend having the larger magnitude will be greater than 1:

  -88/-11 = 8 > 1

  4/2 = 2 > 1

Hence the conjecture is false.

Degree: 5; leading coefficient: –16

Explanation:

Given polynomial function is [tex]f(x)=-16x^5-7x^4-6[/tex]

The degree of the polynomial is a highest value of the exponent in one variable in the given polynomial.

Here, highest value of the exponent = 5

So, degree of the polynomial = 5

Leading coefficient is the value before the highest degree of the variable in the polynomial.

Here, leading coefficient = –16

Hence, the answer is Degree: 5; leading coefficient: –16.

Answer:

a. you can analyze results and draw conclusions

Step-by-step explanation:

Descriptive Statistics: It interprets results in a simple way so that you can analyze the results and draw conclusions.

Answer:

An algebraic expression for the total cost of their night out is  [tex]T=13x+1.5y[/tex].

Step-by-step explanation:

Given:

Cost of per person ticket to factory = [tex]\$13[/tex]

Cost of each bottled water = [tex]\$1.50[/tex]

we need to write an algebraic expression for the total cost of their night out

Solution:

Let the number of persons visiting the factory be 'x'.

Also Let the number of bottled water be 'y'.

Also Let the total cost be 'T".

So we can say that;

total cost is equal to Cost of per person ticket to factory multiplied by the number of persons visiting the factory plus Cost of each bottled water multiplied number of bottled water.

framing in equation form we get;

[tex]T=13x+1.5y[/tex]

Hence an algebraic expression for the total cost of their night out is  [tex]T=13x+1.5y[/tex].

Answer:

The value of the baseball increase $0.15

Step-by-step explanation:

we have

The expression above represent a linear equation in slope intercept form

where

The slope or unit rate is equal to

The y-intercept is equal to ----> original value of a baseball card

therefore

The value of the baseball increase $0.15 per year

Final answer:

The value of the baseball card is increasing by $0.15 per year. For the bat and ball problem, the ball costs $0.05 and the bat costs $1.05.

Explanation:

To find out how much the baseball card's value is increasing per year, we look at the formula given for the value of the baseball card: 0.15y + 0.35. In this formula, y represents the number of years since the card was released. The coefficient of y is 0.15, which indicates the yearly increase in the value of the card.

Therefore, the value of the baseball card is increasing by $0.15 per year.

Now let's look at the classic bat and ball problem. The total cost of the bat and the ball is $1.10, and the bat costs $1.00 more than the ball. If we denote the cost of the ball as x, then the cost of the bat is x + $1.00. Setting up the equation x + (x + $1.00) = $1.10, we combine like terms to get 2x + $1.00 = $1.10. Solving for x, we subtract $1.00 from both sides to get 2x = $0.10. Dividing both sides by 2 yields x = $0.05. So, the ball costs $0.05, and the bat costs $1.05.

Answer:

A translation  right 10 and up 9.

Step-by-step explanation:

Looks like you wrote the reverse translation

M'N'P'Q'R'S' to MNPQRS

Answer:

[tex]cos^{-1}(\frac{\sqrt 5}{6})[/tex]

Step-by-step explanation:

We are given that

[tex]a=<-2,5,1>,b=<-5,2,-5>[/tex] and c=<-1,-5,4>

We have to find the angles between  a and b .

[tex]\mid a\mid=\sqrt{(-2)^2+(5)^2+(1)^2}=\sqrt{30}[/tex]

[tex]\mid b\mid=\sqrt{(-5)^2+(2)^2+(5)^2}=3\sqrt{6}[/tex]

[tex]a\cdot b=<-2,5,1>\cdot <-5,2,-5>=10+10-5=15[/tex]

Angle between two vectors a and b is given  by

[tex]cos\theta=\frac{a\cdot b}{\mid a\mid \mid b\mid }[/tex]

Using the formula

[tex]cos\theta=\frac{15}{\sqrt{30}\times 3\sqrt{6}}[/tex]

[tex]cos\theta=\frac{5}{6\sqrt{5}}[/tex]

[tex]cos\theta=\frac{5\times \sqrt 5}{6\times (\sqrt 5)^2}=\frac{\sqrt 5}{6}[/tex]

[tex]\theta=cos^{-1}(\frac{\sqrt 5}{6})[/tex]

Hence, the angle between a and b=[tex]cos^{-1}(\frac{\sqrt 5}{6})[/tex]

Answer: The probability that she will visit Denver before San Francisco is  [tex]\dfrac{1}{2}[/tex] .

Step-by-step explanation:

Given : The businesswoman randomly selects one of the possible itineraries and Denver and San Francisco are two of the cities that she plans to visit.

The possible itineraries = (First Denver and then San Francisco , First San Francisco and then Denver)

i.e. Total outcomes =2

If she visit Denver before San Francisco , then the favorable outcome = 1

Now , the probability that she will visit Denver before San Francisco = [tex]=\dfrac{\text{Favorable outcomes}}{\text{Total outcomes}}[/tex]

[tex]=\dfrac{1}{2}[/tex]

Hence, the probability that she will visit Denver before San Francisco is [tex]\dfrac{1}{2}[/tex] .

Answer:the common denominator is 4 so your answer is 1/4

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

The mean is a good measure of central tendency because it takes into account all of the data compared to other. One of the instance where the mean is not good measure is when there are outliers ( extreme values) in the data in this case the median is better. In the scenario in the question the data set is nearly symmetrical therefore the mean is best central tendency measure to use

Answer:

Option A - The mean is the best choice because the data is nearly symmetrical.

Step-by-step explanation:

Given : A mini-golf course is determining the par score for each of its holes. The dot plot shows the number of strokes required to place a ball in the ninth hole for a sample of 25 players.        

To find : Which measure of center is best to use to determine the expected number of strokes required for the ninth hole?    

Solution :

To determine the expected number of strokes required for the ninth hole the best measure of center is the mean of the data as the data is nearly symmetrical about the center point 4 and 5.

We can also find the mean of the data,

Mean is defined as  the sum of observation divided by number of observation.

i.e, Sum of observation is

Referring the dot plot of ninth hole strokes

Total number of observation n= 25

Therefore, Option A is correct.

The mean is the best choice because the data is nearly symmetrical.

Answer: D Pretest–posttest design

Step-by-step explanation:

According to the question, Mr Abed is just designing the game and the purpose is to help the grade 3 students learn their mutiplication table, upon completion of the game design, the students are to use (play) it - all this makes up the pretest stage

The result of the game will then be evaluated by Mr Abed to Know if the game is effective or not, if the students have actually learnt their multiplication table by playing the game, if there is need for modification - all this makes the posttest stage.

Answer:

c^3+15c^2+75c+125

Step-by-step explanation:

Answer: C: Whole number skills

Step-by-step explanation: The question involves simple understanding of whole numbers from counting 1 to 10, and also addition of these whole numbers, which makes its a basic understanding of whole number skills

Answer:  [tex]4\sqrt{2}+10[/tex]

=============================================

Let [tex]x = \sqrt{8}[/tex]

We can replace every square root of 8 with x, since we have that equation above. We end up with 3-x+7+3x. This simplifies to 2x+10 after combining like terms.

Now we can reintoduce the square root back in

[tex]2x+10 = 2\sqrt{8}+10[/tex]

The use of x is optional as you can combine like terms directly. However, it might help to make the temporary replacement.

-------------

Now simplify the square root

[tex]\sqrt{8} = \sqrt{4*2}[/tex]

[tex]\sqrt{8} = \sqrt{4}*\sqrt{2}[/tex]

[tex]\sqrt{8} = 2\sqrt{2}[/tex]

--------

Therefore,

[tex]2\sqrt{8}+10[/tex]

turns into

[tex]2*2\sqrt{2}+10[/tex]

[tex]4\sqrt{2}+10[/tex]

Answer:

10 + 4sqrt(2)

Step-by-step explanation:

3 - sqrt(8) + 7 + 3sqrt(8)

3 - 2sqrt(2) + 7 + 6sqrt(2)

10 + 4sqrt(2)

sqrt: square root

Answer: D All of the above

Step-by-step explanation:

Addition,subtraction,multiplication and division are basic mathematical operations used in the determination and assumption of numbers.

Without them,there will be no theorems .

Answer:

The answer to your question is the first option

Step-by-step explanation:

Process

1.- Identify the y-intercepts of the lines

blue line   y-intercept = -1

brown line  y-intercept = -2

With this information, we can discard the last option because those lines don't have those y-intercepts.

2.- We observe in the graphs that the lines are increasing so the slopes are positive. From this information, we can discard the second option.

3.- Calculate the slopes of the lines of options 1 and 3

Blue line Points  (0, -1)   (1, 2)

            m = [tex]\frac{2 + 1}{1 - 0} = \frac{3}{1} = 3[/tex]

Brown line Points (0, -2) (1, 1)

            m = [tex]\frac{1 + 2}{1 - 0} = 3[/tex]

As the slopes are 3, we conclude that the answer is the first option.

Answer:

b

Step-by-step explanation:

The graph of the given function will increase from left to right.

Graphs are a popular tool for visually illuminating data relationships. A graph serves the objective of presenting data that are either too many or complex to be fully expressed in the text while taking up less room.

Given, a function y = 3ˣ. graph of this function is attached below. as we can see in the attached graph that it will increase from left to right.

For x = -3

y = 3⁻³ = 1/27

For x = -2

y = 3⁻² = 1/9

for x = 2

y = 3² = 9

For x = 3

y = 3³ = 27

Therefore, The supplied function's graph will rise from left to right.

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Answer:

Her friend gave Sheila a markdown of $15.

Step-by-step explanation:

Given;

Amount paid for 2 tickets = $90

Actual amount for each ticket = $52.50

we need to find the markdown value did her friend gave to Shelia.

Solution:

each ticket = $52.50

2 tickets = Cost of 2 tickets.

By using unitary method we get;

Cost of 2 tickets = [tex]52.50\times 2 =\$105.00[/tex]

Now To find the markdown we will subtract the Amount paid for 2 tickets from the actual Amount of 2 tickets.

framing in equation form we get;

Markdown [tex]105-90 =\$15[/tex]

Hence her friend gave sheila a markdown of $15.