8/13 x 3 =

SHOW YOUR WORKl

We have to solve for x:

Multiply both sides of the proportion by 32:

Simplify:

We are given the following information

M is between G and T

MG = 2x + 1

MT = 3x + 3

GT = 19

Let us draw a sketch to better understand the problem

As you can see, the sum of MG and MT must be equal to the GT

Mathematically,

Let us solve the above equation or x

So, the value of x is 3

Therefore, the required values are

x = 3

MG = 7

MT = 12

Part I

In factored form, [tex]f(x)=a(x-2)(x-3)(x+1)[/tex]. Substituting x=1,

[tex]f(1)=32=a(1-2)(1-3)(1+1)\\\\\implies 32=4a\\\\a=8\\\\\therefore f(x)=8(x-2)(x-3)(x+1)[/tex]

Part II

In factored form, [tex]f(x)=a(x-5)(x-2)(x-4)[/tex]. Substituting x=3,

[tex]f(3)=-24=a(3-5)(3-2)(3-4)\\\\\implies 24=2a\\\\a=12\\\\\therefore f(x)=12(x-5)(x-2)(x-4)[/tex]

The person that has the higher average speed is Teresa.

The average speed is the total distance travelled by the object in a particular time interval.

Average speed measures the average rate of speed over the extent of a trip.

Therefore,

average speed = distance / time

Hence, Karl drove 40 miles in 50 minutes.

Therefore,

average speed of Karl = 40 / 50

average speed of Karl = 4 / 5 miles per minute

Teresa drove 35 miles in 42 minutes.

Therefore,

average speed of Teresa = 35 / 42

average speed of Teresa  = 5 / 6 miles per minutes

Therefore, Teresa had the higher average speed.

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Answer:

w = 27

Step-by-step explanation:

Solve for w: -6 = -2/9w

-6 = -2/9w

divide both sides by -2/9:

-6/(-2/9) = -2/9w/(-2/9)

27 = w

Solution

For this case we can use the following formula:

where:

P= 200

r= 0.09

n = 4

t= 4

And solving we got:

Answer:

350m

Step-by-step explanation:

Vi = 15 m/s

A = 4 m/s^2

delta t = 10s

delta x = ?

delta x = (Vi)(delta t) + 1/2(A)(delta t)^2

delta x = (15m/s)(10s) + 1/2(4m/s^2)(10s)^2

delta x = 350 m

Answer:

A=16, the formula to find the area of a kite is A=pq/2

Step-by-step explanation:

A=pq/2 = 4×8/2=16

The inequality would be 15 ≤ t ≤ 19 showing the range of possible minutes it will take for the taxi to get to Claire's house.

Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.

The time could vary by as much as 4 minutes.

Let t be the range of possible minutes

The taxi service says it will take 15 minutes to get to her house based on normal traffic routines.

So the inequality as 15 ≤ t

The time could vary by as much as 4 minutes.

So the inequality as 15 ≤ t ≤ 15 + 4

⇒  15 ≤ t ≤ 19

Therefore, the inequality would be 15 ≤ t ≤ 19 showing the range of possible minutes.

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The cost for children meal is $16 and the.cost for adult meal is $26.

Let cost of adult meal = a

Let cost of child meal = c

Lexi plans to have 63 adults and 59 children attend, so the total projected cost of her meals is $2,582.This will be:

63a + 59c = 2582 ...... i

Raymond has 63 adults and 93 children on her guest list, so he will pay the caterer $3,126. This will be;

63a + 93c = 3126 ...... ii

Collect both equations

63a + 59c = 2582 ...... i

63a + 93c = 3126 ...... ii

Subtract i from ii

34c = 544

Divide

c = 544 / 34

c = 16

The cost of children meal is $16.

From equation i, 63a + 59c = 2582

63a + 59(16) = 2582

63a + 944 = 2582

Collect like terms

63a = 2582 - 944

63a = 1638

a = 1638/63

a = 26

Adult meals is $26.

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The sum equivalent to 7√28x⁶+4√7x⁶ is :

18√7x⁶ .

Given ,7√28x⁶+4√7x⁶,

To find sum in simplest form ;

7√28x⁶+4√7x⁶

By splitting to factors,

= 7√(7*4)x⁶+4√7x⁶

= 7*2√7x⁶+4√7x⁶

= 14√7x⁶+4√7x⁶

By factoring out like terms,

= 2√7x⁶(7+2)

= 2√7x⁶(9)

= 18√7x⁶

Therefore  sum is =  18√7x⁶.

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Answer:

60 yards

Step-by-step explanation:

100 feet + 20 feet + 60 feet = 180 feet

180 feet = 60 yards (there are 3 feet in 1 yard)

1. The total number of cases of cancer x that could be prevented if each one of the exposures were eliminated is 900.

2. The suggestion to the public health agencies if they requested the one exposure that would have a greater impact on reducing the prevalence of cancer x if eliminated is smoking.

The prevalence rate refers to the proportion of the population who have a particular disease or attribute or can be exposed to risks at a specified time or over a specified period.

The assumed population size in Epiland  = 1,000

Prevalence of smoking in Epiland = 60%

The number of Epiland smokers = 600 persons (1,000 x 60%)

Percentage of people drinking water with a high concentration of heavy metals = 30%

The number of people drinking the water = 300 (1,000 x 30%)

The total number of people exposed to cancer x = 900 (600 + 300).

Thus, 90% of the population in Epiland is exposed to cancer x based on the prevalence rate of smoking and the high concentration of heavy metals in their drinking water.

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1. 3.2673 is the expected number of ticket holders that will fail to show for the flight.

2.  0.425  is the probability that the airline will not have enough seats for all the ticket holders who show for the flight.

P(airline will not have enough seats for all the ticket holders who show for the flight) = P(more than 267 people show up for the flight)

p = P(will show for flight) = 1 - 0.04 = 0.96

n = 278

µ = n * p = 278 * 0.96 = 266.88

   σ = [tex]\sqrt{ n*p* (1 - p)} = \sqrt{278 * 0.96 * 0.04} = 3.2673[/tex]

P(X > 267)  =  P(X > 267.5)

                          p(x-  µ) / σ  > 267.5-  µ /σ

                   = P(Z> 267.5 – 266.88/ 3.2673 )

                   = P(Z > 0.19)

                    = 0.425.

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which something is likely to happen is basically what probability means.  To understand the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution. Knowing the total number of outcomes is necessary before we can calculate the likelihood that a specific event will occur.

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The function that is represented on the graph is (a) y = x^2 + 4, x < 2 and y = x + 4, x ≥ 2

The graph represents the given parameter

From the graph, we have the following function types

Using the options as a guide, we have the equations to be

Next, we calculate the domain

The quadratic function stops at x = 2 with an open circle

So, the domain is x < 2

The linear function starts at x = 2 with a closed circle

So, the domain is x ≥ 2

Hence, the graphed function is (a)

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Answer:

All of the above

Explanation:

All the given options make use of credit scores and/or credit reports to decide whether a person can buy a service and/or to decide what price he or she will pay. landlords may use credit scores to decide if they will require a security deposit and, if so, how much it should be. Also, other service providers like Mortgage lender, Cell phone company and Credit card issuer makes use of credit scores and/or credit reports in making certain decisions.

We will simply subtract 3 3/8 from 6 1/2

That is;

6 1/2 - 3 3/8

= 3 4-3/8

=3 1/8

The amount of berry left is more than 3 cups, hence Ryan have enough very stuff to also make a pie

The appropriate measures of central location for interval data are Mode, median, and average

The measure of a data set's most valuable position is its core location. Basically, they are mean, median, and mode.

Mean: The mean is the data set's average value. It is the total number of data divided by the sum of the data set.

The data point in the middle of the data collection is known as the median.

It can be obtained by halving the data set, which will show where the median is located.

Simply put, mode refers to the data that occurs most frequently.

Each of these provides positional information on the data, as can be seen from the definition.

The one value that other values in the data center around is given by the mean.

Therefore, the correct options are Mode, median, and average

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Answer:

D. 1.75

Step-by-step explanation:

Absolute value cannot be negative, so that gets rid of A & B. The point is at -1.75 so it has to be D.

Answer:

C- below the mean by a distance equal to 2 standard deviations

Step-by-step explanation:

The rate which the investment is compounded annually is 1.7%

Compound interest is the addition of interest to the principal sum of a loan or deposit, or in other words, interest on principal plus interest.

Compound interest is the interest on savings calculated on both the initial principal and the accumulated interest from previous periods.

Compound interest is when you earn interest on both the money you've saved and the interest you earn.

The formula to calculate compound interest is given as

[tex]A = p(1 + \frac{r}{n})^n^t[/tex]

substituting the values into the equation and solve for rate at which the investment is compounded

[tex]A = p(1 + \frac{r}{n})^n^t\\6669 = 6130(1+ \frac{r}{1})^1^*^5\\ r = 1.7[/tex]

The rate of the investment is 1.7%

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Given:

One variety of gift wrappers sells for 50 cents a sheet the other for 25 cents a sheet.

In dollars,

One variety of gift wrappers sells for 0.5 dollars a sheet the other for 0.25 dollars a sheet.

The assortment will cost $7.

Let x be the number of 50 cents sheets.

Let y be the number of 25 cents sheets.

It is also given that,

The number of 50 cents sheets is 3 times the number of 25 cent sheets.

x=3y ........ (1)

0.5x+0.25y=7 ....... (2)

Substitute (1) in (2) we get,

Hence, x=3(4)

x=12

So, the number 50 cents sheets are 12 and the number of 25 cents sheet is 4.

There are 240240 possible permutations of choosing 5 shows from 14 available shows. It can be obtained by applying the formula of permutation.

What is permutation?

In mathematics, it is the number of ways in which given number of items can be arranged in different orders.

Here, we need to select 5 iteams from the given 14 iteams.

[tex]P(14,5)=\frac{14!}{(14-5)!}\\=\frac{14!}{(9!)}\\=\frac{(14)(13)(12)(11)(10)(9!)}{(9!)}\\=(14)(13)(12)(11)(10)\\=240240[/tex]

Hence, there are 240240 possible permutations of choosing 5 shows from 14 available shows.

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The equation of the line is y = -2.5x - 1

The table represents the given parameter

On the table, we have the following points

Point, (x, y) = (0, -1) and (2, -6)

So, we start by calculating the slope of the line using the following slope equation

Slope = (y₂ - y₁)/(x₂ - x₁)

Where x and y are defined above

So, we have

Slope = (-6 + 1)/(2 - 0)

Evaluate

Slope = -2.5

The equation of the line is then calculated as

y = m(x - x₁) +y₁

Where

Slope, m = -2.5

(x₁, y₁) = (0, -1)

So, we have

y = -2.5(x + 0) - 1

Open the brackets and evaluate

y = -2.5x - 1

Hence, the line has an equation of y = -2.5x - 1

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‘B’ had a better college entrance exam score due to the higher value of Z-Score.

The Z-score of an observation is the number of standard deviations it falls above or below the mean. Standard deviation is a statistic that is used to measure the dispersion of a dataset relative to its mean and is calculated by doing the square root of the variance.

[tex]Z=\frac{(observation-mean)}{standard deviation}[/tex]

By putting the values as given in the question,We get,

A's score is (600 - 500) / 200 = 0.5 standard deviation i.e. above the mean.

B's score is (25 - 20) / 5 = 1 standard deviations i.e. above the mean.

Thus ‘B’ had a better score.

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Answer:

(3,13 ) & (-1,5)

Step-by-step explanation:

a. 2x + 7 = x^2 + 4

b. move all terms to the left side and set equal to zero. then set each factor equal to zero. which gives you the x values 3, -1

c. substitute x with the x values to get y.  2(3) + 7 = -1^2 + 4

d. the solution is (3,13 ) & (-1,5)

The statement as number expression is given by the total number of points are 55.

What is Mathematical expression?

An expression is a finite combination of symbol and numbers depending on the context

We are given that A person has lost a card game and he is counting the points left in his hand.

His cards were five fours and five sevens

And we have to write this statement as number expression

Now there are five fours that is [tex]5*4=20 points[/tex]

And five sevens that is [tex]5*7=35 points[/tex]

Hence the total number of points are 20+35=55 points.

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