a 12oz box of cereal costs $3.50. An 18oz box of cereal costs $5.40. Set up equations to determine which is the better buy.

a. g(x) is a function that is an output multiple of 3 of f(x), g(x) is {(1, 6), (3, 15), (5, 3)}.

b. g(x) is a vertical stretch as the output (y-axis) has been multiplied by a factor of 3.

A function can be defined as the outputs for a given set of inputs.

The inputs of a function are known as the independent variable and the outputs of a function are known as the dependent variable.

Given, f(x) that is {(1, 2), (3, 5), (5, 1)}.

Now g(x) is a function that is an output multiple of 3 of f(x).

∴ g(x) is {(1, 2×3), (3, 5×3), (5, 1×3)}.

g(x) is {(1, 6), (3, 15), (5, 3)}.

g(x) is a vertical stretch as the output (y-axis) has been multiplied by a factor of 3 so it is stretched 3 times of the f(x).

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Cora is flipping three coins at once. The probability that the number of landed coins showing "heads" is less than 3 is 0.875

Probability is a measure how likely an event occurs. Probability of an event A is calculated as:

P(A) = number of ways A can occur / total possible outcomes

Let A and B be independent events, then the followings hold:

P (A and B) = P (A∩B) = P(A) + P(B)

P (A or B) = P (A∪B) = P(A) · P(B)

P (not A) = P(Ā) = 1 - P(A)

In the given problem, H is an event where the number of landed coins showing heads.

The probability distribution for H is:

P(H = 0) = 0.125

P(H = 1) = 0.375

P(H = 2) = 0.375

P(H = 3) = 0.125

The probability of three coins show heads less than 3 is:

P(H < 3) = 1 - P(H=3)

             = 1 - 0.125 = 0.875

It can also be obtained using:

P(H<3) = P(H=0) + P(H=1) + P(H=2)

           = 0.125 + 0.375 + 0.375

           = 0.875

Hence, the probability of three coins show heads less than 3 is 0.875.

Complete question:

Cora is playing a game that involves flipping three coins at once. Let the random variable H be the number of coins that land showing "heads". Here is the probability distribution for H:

P(H = 0) = 0.125, P(H = 1) = 0.375, P(H = 2) = 0.375, P(H = 3) = 0.125. What is the probability H is less than 3.

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The plant grew by 2 9/40 inches during the week.

A fraction represented with its quotient and remainder is a mixed fraction. For example, 2 1/3 is a mixed fraction, where 2 is the quotient, 1 is the remainder. So, a mixed fraction is a combination of a whole number and a proper fraction.

Initial height of plant = 6 3/8 inches

Final height = 8 3/5 inches

Difference in height = 8 3/5 inches - 6 3/8 inches

converting the mixed fraction to improper fraction

8 3/5 = 43/5

6 3/8 = 51/8

43/5 - 51/8

multiply 43/5 by 8/8 and 51/8 by 5/5 so that both fractions have common denominator, it becomes

344/40 - 255/40

Collect only the numerator we have,

344- 255 = 89 which is no 89/40

divided by 40, we have 2 9/40 inches

In conclusion, the plant grew by 2 9/40 inches

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The coordinates after scaling of triangle ABC will become -

A'(- 14, 2)

B'(-10, 12)

C'(-2, 4)

A triangle is a polygon with three edges and three vertices. The sum of all the angles of a triangle is 180 degrees. Mathematically -

∠x + ∠y + ∠z = 180°

The sum of two sides of a triangle is greater then the third side. Mathematically -

a + b > c

There are different types of triangles such as -

equilateral triangle , scalene triangle , isosceles triangle etc.

Given is a triangle ABC with vertices A(-7, 1), B(-5, 6), and C(-1, 2) and

K = 2​

After scaling, the coordinates will become -

A(x, y) ⇒ A'(Kx, Ky)

The coordinates after scaling of triangle ABC will become -

A'(- 14, 2)

B'(-10, 12)

C'(-2, 4)

Therefore, the coordinates after scaling of triangle ABC will become -

A'(- 14, 2)

B'(-10, 12)

C'(-2, 4)

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Answer:

C; -21/10X + 23

Step-by-step explanation:

Combine like terms and simplify

Answer:141

Step-by-step explanation:

angles 4+2= 78

360-78 = 282

282/2 = 141

4,2 equal 6,8

1,3 equal 5,7

Answer:

m7= 141 degrees ; m5 = 141 degrees

Step-by-step explanation:

m3 + m4 = 180

m3 + 39 = 180

m3 = 180 - 39

m3 = 141 degrees

m3 = m5 = 141 degrees

m4 = m8 = 39 degrees

m3 = m7 = 141 degrees

Answer:

4/7

Step-by-step explanation:

2/7 ÷ 1/2 = 2/7 × 2/1 = 4/7

Answer:

Step-by-step explanation:

1. Write Words into math

2/7/1/2

2. Solve

2/7/1/2=

2/7*2/1=

4/7

Answer: 4/7

Answer:

13

Step-by-step explanation:

2y - 3;

y = 8;

 ---> 2*8 - 3 =

16 - 3 = 13

The length of the line YZ is 26 units

The Y is the mid point of the line XZ

The length of the line XY = 20 + 2a

The length of the line YZ = 8 + 6a

When Y is the mid point of the line XZ, then the length of the line XY is equal to the length of the line YZ

The length of the line XY = The length of the line YZ

Substitute the values in the equation and find the value of a

20 + 2a =  8 +6a

Rearrange and group the like term

6a - 2a = 20 - 8

4a = 12

a = 12 / 4

a = 3

The length of the YZ = 8 +6a

= 8 + 6×3

= 8 + 18

= 26 units

Hence, the length of the line YZ is 26 units

The complete question is:

Find the length of YZ when Y is the midpoint of XZ, if XY = 20+2a and YZ = 8+6a.

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a) The domain of the function is {2,3,4,5,6},

The range of the function is {0,1,2,3,4}

b) The domain of the function is {-3,-1,1,3,4}

The range of the function is {1,3,-2,2,6}

Given,

Domain and Range;-

The domain of a function is the set of values that we are allowed to enter into our function. This collection represents the x values in a function like f. (x). A function's range is the set of possible values that it can accept. This collection contains the values that the function returns when we enter an x value.

Here,

a) Domain is the set of x values:

x={2,3,4,5,6}

The range is the set of y values:

y={0,1,2,3,4}

b) Domain is the set of x values:

x={-3,-1,1,3,4}

The range is the set of y values:

y={1,3,-2,2,6}

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I will have to reject the offer of the rival company since it's lesser than $40560.

From the information, the person works a basic week of 40 hours and the basic rate is $19.50 per hour. It should be noted that there are 52 weeks in a year. The total amount will be:

= 40 × 19.50 × 52

= $40560

The rival company offers you an annual salary is $36000.

I'll reject the rival company's offer since it's lower.

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Complete question

You work a basic week of 40 hours and your basic rate is $19.50 per hour. A rival company offers you an annual salary is $36.000. Except for the pay, everything is identical between the conpanies. Do you accept or reject the rival company's offer, and why?

The relative frequency of all students surveyed who go to Cook Middle School and prefer Energy flow is 57%.

This refers to how many times a particular type of occasion takes place within the total number of observations. This type of frequency uses percentages, fractions, and proportions.

Formula for calculating Relative Frequency:

Relative Frequency =         Count of event

                                   Total number of Observation

From the question:

No of students that like Gym Juice in Elim School =5

No of students that like Energy Flow in Elim School =10

Total Number of students in Elim School =15

No of students that like Gym Juice in Cook Middle School =15

No of students that like Energy Flow  in Cook Middle School =20

Total Number of students in  Cook Middle School  =35

Calculating The relative frequency of all students surveyed who go to Cook Middle School and prefer Energy flow:

Relative Frequency =         Count of event

                                   Total number of Observation

Relative Frequency =       20

                                          35

                                    =0.57 or 57%

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Answer:

The equation of the nth term of the sequence is 3n+9.

Step-by-step explanation:

A total of 14 additives were included here in a study of the effects of various health additives on various top runners.

One-Way ANOVA Test :;Uses one-way analysis of variance (ANOVA) to determine whether there are statistically significant differences between the means of three or more independent (unrelated) groups.

Need of One way ANOVA :

When working with individuals, this situation can be encountered using two different types of study designs group. Then have each group perform a different task and measure the outcome/response to the same dependent variable. In the given problem, the term "Between" in the source table refers to processing. The term "within" refers to the error term. The inner term represents the variability that exists between runners. The total number of

additives is one more than his total number of

degrees of freedom (df). Total degrees of freedom for = N – 1. Total degrees of freedom = 18,so N= 19

Hence, total additives for given study is 19.

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Complete Question:

study was made on the effects of several health additives for a number of elite

runners. The results of a One-Way ANOVA are presented in the following table.

how many additives were in the study?

Source। Df Sum of Squares MS

Between 3 55.00

Within 15 450.00

Total 18 505.50

A. 18

B. 19

C. 7

D. 8

Answer:

ummm im going to guess c.

Step-by-step explanation:

Answer:

p(x)=-2*p*x+4*x+-4=1*-2*p*x+4*x+4=1*-2*p*x+6*x+-6=6*x+4*1*1

Step-by-step explanation:

The linear equation two variables can be solved by various methods one of the methods to solve the linear equations is the substitution method. The solution of the given equation is x=2 and y=10.

What is  linear equation in two variables ?

A specific point on the graph represents the solution of a linear equation in two variables, ax+by = c, where the total of these two values will equal c when the x-coordinate is multiplied by a and the y-coordinate by b.

Main body:

The given equations are :

10x+3y=50     .... (1)

-5x-y=-20      ....(2)

Multiply equation (2) by 3 and then add the equation (1) to eliminate the variable y.

10x+3y+3(-5x-y)=50+3*-20

-5x=-10

x=2

Now putting the value of x in equation (1), and solve it further.

10*2+3y=50

3y=30

y=10

Hence, the value of x is 2 and the value of y is 10.

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Length (L) = 42

Width (W) = 18

and the equation which helps to find the width of the garden is

                       L = 6 + 2W

Now, we have to find the length and width of the garden area.

It is given that,

we know that the Length is 6 feet more than twice the width, this in other words, it means that:

                                         L = 6 + 2W       -------------------------(1)

So, let's denote W as X

The perimeter of the garden is 120 and the expression to calculate is:

                                         P = 2W + 2L      ------------------------(2)

Replacing all the values in the above expression we have the following:

                                     120 = 2x + 2(6 + 2x) ---------------------(3)

Solving for x from the above equation (3), we have:

⇒120 = 2x + 12 + 4x

⇒120 - 12 = 6x

⇒108 = 6x

⇒x = 108/6

⇒ x = 18

So the Width is 18, therefore the Length from equation (1):

                L = 6 + 2(18)

             ⇒L = 6 + 36

             ⇒L = 42

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Answer:

Take a look at the attachment...

Hope this helps! :)

y = x + 4

If there are 80 cow and 30 buffaloe , the ratio of the cow and the buffaloe is 8:3  .

In the question,

it is given that ,

the number of cows in the farm house = 80

the number of buffaloe in the farm house = 30

we need to find the ratio of cow and the buffaloe .

the ratio can be calculated using the formula .

ratio = (number of cows)/(number of buffaloe)

Substituting the vales , we get

= 80/30

cancelling out the common factor 10 , from both numerator and denominator , we get

= 8/3

So , the ratio is 8:3   .

Therefore ,  If there are 80 cow and 30 buffaloe , the ratio of the cow and the buffaloe is 8:3  .

The given question is incomplete , the complete question is

In a farm house, there are 80 cows and 30 buffaloes . What is the ratio of the cow and the buffaloe ?

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Answer:

75 cents

Step-by-step explanation:

If 12 bottles cost $9, in order to find the cost of one bottle we must divide the cost by the number of bottles.

[tex] \frac{9}{12} = 0.75[/tex]

therefore the cost of one bottle is 75 cents

The simplest form of the expression has 4 in the numerator and (x-2) in the denominator.

The numerator indicates the total number of selected equal parts. Whereas, the denominator indicates the total number of equal parts.

       We have the expression

     3/(x-2) + (x-2) / (x²-4x+4)

Simplifying   x²- 4x +4  gives (x-2)².

Therefore, we can write the expression as

  3/(x-2) + (x-2)/(x-2)² = 3/(x-2) + 1/(x-2)  

          = 4/(x-2).

Therefore, the simplest form of the expression has 4 in the numerator and (x-2) in the denominator.

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D set of ordered pairs does not represent a function.

In the given question we have to check which set of ordered pairs does not represent a function.

The given set of ordered pair

(A) (4, 1), (6, 2), (7, 5), (9, 2)

(B) (0, 5), (1, 7), (2, 9), (3, 11)

(C) (-2, 5), (0, 2), (9,-6), (8, 7)

(D) (5, 5), (6, 10), (10, 15), (5, 20)

As we know that in the function a x value always have only one corresponding y value which means for a value of x have only a y value.

But when we see in the ordered pair D. In this pair have pair (5, 5) and (5, 20). This shows different value of y in same value of x.

So, D set of ordered pairs does not represent a function.

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1) the speed of Simon per hour is 128 miles/Hr

2) The length of IG is 20 Units.

3) The ratio of SM is 2:1

1) For 1, to obtain the speed of Simon per hour, all you need to do is multiply 32 x 4.
This is because in every hour, 15 minutes occurs four times. That is:

1 hour = 60 minutes

Hence, if 32 miles is done in 15 minutes, then 60 minutes =

32 x 4

= 128 miles

Hence the speed of Simon per hour is 128 Miles/ Hour

2) Given that the two triangles are identical, it means that on the basis on RHS  theorem we have been given all the sides. Note that BG is 6 Units (we are assuming that this is the base) , then AT from the other triangle (see attached) is 20.

We assume this is the Hypotenuse. CT is also given. We assume this is the height. If we have CT and AT, and both triangles are the same, then IG is 20 units.

3) For the quadrilateral, recall that in quadrilaterals opposite sides are equal. If one side is 34u on one, and the other side is 17u on the other quadrilateral, then we already have the measure of the sides for both quadrilaterals.

So the Ratio of AK to WN

34u: 17u - Simplified by dividing by 17u we have

Ratio 2:1

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It is impossible to travel for the same 60-mile distance home to average 60mph over the entire trip.

car travels a distance of 60 miles long and averages 30 miles per hour. As a result,

time = distance/speed = 60/30 = 2

the car traveled for 2 hours.

The car would have to travel for exactly 2 hours (120/60) to average 60 mph over 120 miles.

Because the car has already traveled for two hours, it is impossible for it to average 60 mph for the duration of the journey.

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Answer: 20 loaves

Step-by-step explanation:

3/5 = .6

12/.6 = 20

I’m not 100% sure but this is what I believe is the answer

20 Loaves

23 tickets are purchased for children and 9 tickets are purchased for adults.

Given,

In the question:

A group entering a zoo purchased 32 admission tickets for a total of $148. Adult tickets cost $7. 50, and tickets for children cost $3. 50.

To find the how many of each type of ticket were purchased?

Now, According to the question:

It is given in the question that 32 tickets are purchased by group which cost total $148.

Let the number of children of the group who are entering the zoo be x. Then the number of adults will be 32- x

Now cost of one ticket for adult = $7.50

Total amount spent on adult tickets = 7.50 × (32-x)

Similarly, cost of one ticket for child= $3.50

Total amount spent on children tickets = 3.50 × x =3.5x

Total amount spent by group on tickets =  $148

⇒ 7.5 × (32-x) + 3.5x = 148

⇒ 240 - 7.5x + 3.5x = 148

⇒ 7.5x - 3.5x = 240 - 148

⇒ 4x = 92

⇒ x = 23

Children = 23

Adults = 32-x = 32-23 = 9

Hence, 23 tickets are purchased for children and 9 tickets are purchased for adults.

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The total lifetime of all batteries in a package exceeds that value for only 5% of all packs will be 43.29.

It is defined as the measure of data disbursement, It gives an idea about how much is the data spread out.

[tex]\rm \sigma = \sqrt{\dfrac{ \sum (x_i-X)}{n}[/tex]

σ is the standard deviation

xi is each value from the data set

X is the mean of the data set

n is the number of observations in the data set.

It is given that,

mean,μ=10 hr

standard deviation,σ=1hr

n=4

The lifespan of four batteries combined is,

=4μ

=4×10

=40 hr

z = (x-μ)/σ

1.645=(x-40)/2

x-40=3.29

x=43.29

Thus, the total lifetime of all batteries in a package exceeds that value for only 5% of all packs will be 43.29.

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Answer:

Step-by-step explanation:

340.56

Answer:

61.92 x 5.50 = 340.56