the sum of three integers is 32. the sum of the first and second integers exceeds the third by 82. the third integer is 16 less than the first. find the three integers.

For x to be a solution, there must be the quantity x in the equation.

All the equations that contain x are :
+) 24 - 2x = 13
+) 4  + 5x = 18
+) 2x - 3 = 15
+) 3x + 2 = 25

We will solve for the value of x for each of the equation :

+) 24 - 2x = 13
-> 2x = 24 - 13 = 11
-> x = 11/2 = 5.5

+) 4 + 5x = 18
-> 5x = 18 - 4 = 14
-> x = 14/5 = 2.8

+) 2x - 3 = 15
-> 2x = 15 + 3 = 18
-> x = 18/2 = 9

+) 3x + 2 = 25
-> 3x = 25 - 2 = 23
-> x = 23/3.

We can see, only the equation 2x-3 = 15 has x=9 as a solution.

Answer:

5

Step-by-step explanation:

10+4+2+4=20

20/4=5

The mean is five.

Answer:

Mean = 5

Step-by-step explanation:

Mean = ( Sum of Data Points ) / ( Number of Data Points )

Sum of Data Points = 10 + 4 + 2 + 4 = 20

Number of Data Points = 4

Mean = 20 / 4 = 5

Glad to Help

Answer:

0.2c-c

Step-by-step explanation:

Answer:  The correct answer is D. (2.5,1.5)

Step-by-step explanation:

As noted in the graph, the lines intersect at the location where x=2.5 and y=1.5 in Quadrant I (both positive).

Answer:

7

Step-by-step explanation: -13(-1) + 36 + 42(-1)

Step 1: -13(-1)= 13

Step 2: 13 + 36= 49

Step 3: 49 + 42(-1)= 49 + (-42)= 7

Solution: 7

Answer: 5+3*3(3)-2= 30

Step-by-step explanation: Replacing x with 2 and using PEMDAS

Jeanne can make 3 pairs of shorts with 3 7/8 yards of fabric.

What do you mean by ratio?

The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.

For example, a/b, where a will be the numerator and b will be the denominator.

Proportion is the relation of a variable with another. It could be direct or inverse.

Given that,

The total amount of fabric = 3 7/8 yards = 31/8 yards.

Amount of fabric needed to make 1 pair of shorts = 1 1/4 = 5/4 yards.

The number of shorts that can be made = 31/8 ÷ 5/4

⇒ 3.1 so it will be 3 because no relevance of decimal shorts.

Hence "Jeanne can make 3 pairs of shorts with 3 7/8 yards of fabric".

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The probability that a worker selected at random makes between $350 and $400 = 0.34134

What is a z score formula?

The standard score represents how far a raw score deviates from or exceeds the mean of the phenomenon being observed or measured. Positive standard scores are assigned to raw scores that are greater than the mean, while negative standard scores are assigned to raw scores that are less than the mean.

By using the z score formula:

z = (x - μ) / σ

Where,

x = raw score

μ = mean

σ = Standard deviation

We are told in the question to find the probability that a worker selected at random makes between $350 and $400

Consider, x1 = 350 and x2= 400 with the mean μ = 400 and standard deviation σ = $50.

z1 = (x1 - μ) / σ = (350-400) / 50 = -1

z2 = (x2 - μ) / σ = (400 - 400) / 50 = (0/50) = 0

From tables, P(z <= -1) = 0.15866

P(z <= 0) = 0.5

Then, the probability would give us, P(-1 ≤ z ≤ 0) =0.5 - 0.15866 = 0.34134

Hence, The probability that a worker selected at random makes between $350 and $400 = 0.34134

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Answer:

A. 5/3

Step-by-step explanation:

The line is in a positive trend we can see it because when we read it from left to write we can see it go up. The point where we start is 5 levels down from the second point  3 units to the left.

We can model this using  rise/run

Rise = 5

Run = 3

5/3

The dimensions of algebra tile rectangles and area models can be used to represent expressions and multiplication by measuring the length and breadth of the tiles and multiplying them.

This is referred to as a quadrilateral which has four right angles and the area is calculated by multiplying the length with the breadth.

In as situation where the algebra tile rectangles is used , it is best to first measure the length and the breadth after which they are then multiplied to give the appropriate answer. For example if the length is 8cm and the breadth is 5cm then the area will be  8cm × 5cm = 40cm²

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Answer: Austin burn 809.8 more calories today than yesterday.

0.7475 is the approximate probability that the ph measurement of a randomly selected water specimen is greater than 8.2

P( A ≥ 8.2) = P( (Z ≥ 8.2 − 8)/0.3)

= P(Z ≥0.66)

= 0.7475

normsdist(0.666666) =0.7475

The standard normal cumulative distribution function is returned. The mean of the distribution is 0 (zero), while the standard deviation is one. Instead of a table of standard normal curve areas, use this function.The concentration of hydronium (H3O+) ions in an aqueous solution is measured by pH. It is measured from 0 to 14 on a negative logarithmic scale.

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Equation of the line for the given graph in slope-intercept form is given by  y = 5x -1.

As given in the question,

From the given graph,

Consider pair of two coordinates we have,

(x₁ , y₁) = (1, 4)

(x₂ , y₂) = (0,-1)

Equation of the line for the given graph in slope-intercept form is given by:

(y -y₁) / (x -x₁)= (y₂ -y₁) / (x₂ -x₁)

⇒ ( y - 4)/ (x -1) = (-1-4)/(0-1)

⇒(y-4)/(x-1) = 5

⇒y-4 = 5(x-1)

⇒y = 5x -5 +4

⇒ y= 5x -1

Therefore, equation of the line for the given graph in slope-intercept form is given by  y = 5x -1.

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The values of p and ρˆ (p-hat) in the sample are

p = 0.65 and ρˆ (p-hat) = 0.4

From the question, we have the following parameters that can be used in our computation:

Proportion of female goats = 65%

Sample = 5

Female = 3

The proportion of female represents the variable p

So, we have

p = Proportion of female = 65%

This gives

p = 65%

Express as decimal

p = 0.65

The variable ρˆ (p-hat) is then calculated as

ρˆ = x/n

In this case,

x = Female = 2

n = Male + Female = 2 + 3 = 5

So, we have

ρˆ = 2/5

Evaluate

ρˆ = 0.4

Hence, the values are 0.48 and 0.44, respectively

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Answers are attached

The probability that at least nine out of 12 cars have an acceptable emissions level is 0.333.

The branch of mathematics which deals with the analysis of random phenomena is called probability. The probability of an event is defined as the ratio of favorable events to the total number of events.

P(E) = F(E)/T(E)

Where P(E) = probability of an event which occur\

F(E) = Number of favorable events

T(E)= Total number of events

Here given that the total number of cars T(E) =12

And the number of cars that have acceptable emissions level F(E) = 4

Hence Probability that at least nine cars have an acceptable emission level

=4/12

= 1/3

= 0.333

The probability that at least nine out of 12 cars have an acceptable emissions level is 0.333.

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Answer:

Option B is perpendicular to y=-3x+4 and goes through point (-1,5)

Step-by-step explanation:

We will look for an equation of the form y=mx+b, where m is the slope and b the y-intercept.  The reference line, y=-3x+4, has a slope of -3.  A line perpendicular to this line will have a slope that is the "negative inverse" of the refence lines slope.  In this case, it's slope would be +(1/3).

We could graph each of the equation options and look for one that is perpendicular, but it might be faster to simply rearrnaged the options into standard format of y=mx+b. which we'll do here:

Option   Rearranged Equation   Slope

A) 3y=-x+16

                  y = -(1/3)x+(16/3)           -(1/3)

B) 3y=x+16

                   y = (1/3)x + (16/3)         (1/3)

C) y=-3x+8                                           -3

D) y=-3x+2                                            -3

There is only one option that has the required slope to be parallel to the reference equation (y=-3x+4), option B:  y = (1/3)x + (16/3)

Does it go through point (-1,5)?

y = (1/3)x + (16/3)

Enter x = -1 and find 5:

y = (1/3)(-1) + (16/3)

y = (16/3)-(1/3)

y = (15/3) or 5

 Yes, it goes through point (-1,5)

Option B is perpendicular to y=-3x+4 and goes through point (-1,5).

The solutions are,

The radians wade sweep out is 2.875 radians.

When wade stops skiing, he is 0.799km to the right of the center of the ski trail.

When wade stops skiing, he is 0.003km above the center of the ski trail.

Given that;

Wade is traveling along a 0.8 km-radius circular ski trail. Wade moves 2.3 kilometers counterclockwise starting at the three o'clock position.

Radius (r) = 0.8km

Distance (s) = 2.3km

Here, we need to find three cases, they are;

Case(I): how many radians does wade sweep out;

The relation between radians and radius is given by,

s = rθ

2.3 = 0.8*θ

θ = 2.3/0.8

θ = 2.875

The radians wade sweep out is 2.875 radians.

Case (II): when wade stops skiing, how many km is wade to the right of the center of the ski trail;

Let, Ф = π - 2.875

      Ф = 0.266 radians

Then, x = r*cosФ

          x = 0.8*cos(0.266)

          x = 0.799

When wade stops skiing, he is 0.799km to the right of the center of the ski trail.

Case (III): when wade stops skiing, how many km is wade above the center of the ski trail;

Let, y = r*sinФ

      y = 0.8*sin(0.266)

      y = 0.003

When wade stops skiing, he is 0.003km above the center of the ski trail.

Therefore, the required solutions are;

The radians wade sweep out is 2.875 radians.

When wade stops skiing, he is 0.799km to the right of the center of the ski trail.

When wade stops skiing, he is 0.003km above the center of the ski trail.

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Answer:

Step-by-step explanation:

A coefficient is a number before the variable that shows how many groups of the variable there are. For example, 2b would be two groups of B.

The coefficients in this expression would be 4 (as in 4x) and 8 (as in 8y).

Answer:

40

Step-by-step explanation:

Looking at the other examples, its shows the the second number is always 4 times bigger/ahead then/of the first number.

The product of the fractions 1/7*5/3 is 5/21.

The product of the fractions= product of the numerator/product of the denominator.

The numerical numbers that make up a fraction of the whole are called fractions. A whole can be a single item or a collection of items. When anything or a number is divided into equal parts, each piece represents a portion of the total. A fraction is represented as a/b, where a and b are the numerator and denominator, respectively.

We multiply the 1 and 5, the numerators and 7 and 3 the denominators.

Therefore the product of the fractions is 5/21.

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Answer:

5/21

Step-by-step explanation:

Given problem,

→ (1/7) × (5/3)

Let's solve the problem,

→ (1/7) × (5/3)

→ (1 × 5)/(7 × 3)

→ 5/21

Thus, the answer is 5/21.

Answer:

You have to place the numbers given or your left in the formula given. So for example: y= 2*(-2)^2

that's: y=2*4, so: y=8

1) y=8

2) y= 2*(-1)^2. y=2

3) y= 2*(0)^2. y=0

4) y= 2*(1)^2. y=2

5) y= 2*(2)^2. y=8

Answer:$2.61

Step-by-step explanation:

18=$15.66

÷6    ÷6

3=$2.61

The cost of 3 bottles of juice based on the given ratio will be $2.61.

The ratio is the division of the two numbers.

For example, a/b, where a will be the numerator and b will be the denominator.

Proportion is the relation of a variable with another. It could be direct or inverse.

18 bottles cost = $15.66

1 bottle cost = $15.66/18 = $0.87/ bottle

For 3 bottles = 3 × $0.87 = $2.61

Hence "The cost of 3 bottles of juice based on the given ratio will be $2.61".

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Option A is the correct choice (0.04)

The incidence rate of disease x among persons exposed to factor a is 0.04

The frequency of a particular incident over a predetermined time period is measured by the incidence rate or incidence. In the corporate world, sampling, surveys, and product testing can all be used to calculate an incidence rate.

Because 120 divided by the total number of exposed people yields the occurrence rate for disease X among those who have been exposed.

The incidence rate would be 4 per 100 people if multiplied by 100, however, this statistic is not specifically specified.

Therefore, those who were exposed to factor a had an incidence risk of disease x of 0.04

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COMPLETE QUESTION:

6,750 people who were free of disease X were enrolled in a cohort study in 1985 and followed by annual exams and interviews through 1995. Exposure to factor A was determined at study enrollment and the participants were followed until 1995 to observe new cases of disease X. Data from the study at the end of the follow-up are shown in the following table. What is the incidence rate of disease X among persons exposed to factor A? Exposure to Factor A People with Disease X People without Disease X Not Exposed 30 3,720 Exposed 120 2,880

Select one:

a. 0.04

b. 0.19

c. 0.25

d. 4.00

e. 5.17

Option b. 96,909,120 is the correct answer. The number of ways in which the new site can be chosen to locate 6 stores in 96,909,120 ways

We can find the number of ways by multiplying the number of possibilities each store can have.

Store 1, can be placed on 24 sites. Store 2 can be placed on 23 sites (since store 1 is already on site 1). Store 3 can be placed on 22 sites. Store 4 can be placed on 21 sites. Store 5 can be placed on 20 sites. Store 6 can be placed on 19 sites

Therefore the number of ways is:

C = 24 * 23 * 22 * 21 * 20 * 19

C = 9,69,09,120 possibilities

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The distance from the Sun to Mars is 3. 9 times farther

Ratio can be described as a mathematical comparison between two or more numbers or elements in relation to each other on the basis of their sizes or magnitudes.

It is however known to show how many times one number or elements contains another.

Based on the information given, we have;

To determine the ratio of their distances from the Sun, we have;

Distance from the Sun to Mars /Distance from the Sun to Mercury

Substitute the values

2.28×10^8/5.79×10^7

Divide through

3. 9 times

Hence, the distance is 3. 9 times farther.

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Answer:

Step-by-step explanation:

The answer is 6.

I got this by subtracting 23 by 12 (the number of numbers shown). Then I got 11. So I followed the pattern until I got six.

23-12=11

2,4,6,8,2,4,6,8,2,4,6,8,......2,4,6,8,2,4,6,8,2,4,6