Three times the middle integer of three consecutive integers equals four less than twice the sum of the smallest and largest. find the integers

Applying the concept of the or operation, the solution to the given inequality is as follows:

r < -5/8 or r ≥ 3/8.

Considering two data-sets, the or operation between them is the set composed by all the elements that belong to at least one of the data-sets.

In the case of an inequality, the data set is represented by the intervals.

The first inequality is:

0.5r + 3 < 7/4.

0.5r < 7/4 - 3

r/2 < -5/4 (as -3 = -12/4)

r < -5/8.

The second inequality is:

-r + 3/4 ≤ 3/8

-r ≤ 3/8 - 3/4

-r ≤ -3/8 (as 3/4 = 6/8)

r ≥ 3/8 (multiply by -1, hence the signal also changes).

As the intervals do not intersect, the solution to the inequality is given as follows:

r < -5/8 or r ≥ 3/8.

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Answer:

A. Marcus worked 27 hours and 45 minutes in the week.

B. He earned $391.5 for the week.

Step-by-step explanation:

First you calculate the hours he worked daily and you add them together, when you have the weekly hours you multiply the hours times what he earns each hour.

It's 27 • 14.50= $391.5

Answer:

The x-coordinates of the x-intercepts of the parabola are 1/2 and -7

Parabola equations are second-order polynomial equations and they have the form y = ax^2 + bx + c or y = a(x - h)^2 + k

The parabola is given as

y = 2x^2 + 13x - 7

It should be noted that the x-intercept of the function is the point or points where the graph of the function crosses the x-axis

i.e. the point where the function equals 0

So, we have

y = 2x^2 + 13x - 7

Expand

y = 2x^2 + 14x - x - 7

Factorize the equation

So, we have

y = 2x(x + 7) - 1(x + 7)

Set the equation to 0

So, we have

2x(x + 7) - 1(x + 7) = 0

Factor out x + 7

So, we have

(2x - 1)(x + 7) = 0

Expand

2x - 1 and x + 7 = 0

Solve for x

x = 1/2 and x = -7

Hence, the x-coordinates of the x-intercepts are 1/2 and -7

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Answer:

Hope I helped you with this. Everything is explained in the photo

Answer:

-1

Step-by-step explanation:

You just have to divide the change in the x axis by change in the y axis on any arbitrary interval.

Answer:

-1

Step-by-step explanation:

Do rise-over-run for linear equations. Its the vertical change over the horizontal change between two points. Ex. between (-2,0) and (-1,-1) the line drops 1 unit horizontally (-1) and moves to the right one unit (1) so the slope would be -1/1 = -1

Answer:

x = 2

Step-by-step explanation:

Use distributive property:

3(2x+4) = 24

3*2x + 3*4 = 24

6x+12 = 24

6x = 12

x = 2

Answer:

y=2x+13

that is the slope of the intercept

Answer:

C should be the correct answer

Step-by-step explanation:

56 Tulips for $8

56÷8=7

7 Tulips for $1

prove me wrong

Answer:

C

Step-by-step explanation:

56 Tulips for $8

56÷8=7

7 Tulips for $1

Can someone tell me how I can reply to questions I didn't ask?

Probability of selecting a random sample of n = 4 students with an average age greater than 23 is 0.1587, the probability of selecting a random sample of n = 36 students with an average age greater than 23 is 0.00135 and for a sample of n = 36 students, the probability that the average age is between 21 and 22 is 0.6826

In the distribution ages for students at the state college is positively skewed with a mean value μ= 21.5 and a standard deviation of σ = 3.

a)P(z> (23-21.5)/(3/√4))

P(z>1) = 0.1587

b) P(z> (23-21.5)/(3/√36))

P(z>3) = 0.00135

c) P((23-21.5)/(3/√36) < z < (22-21.5)/(3/√36 ))

P(-1 < z < 1) = 1 - 0.1587 - 0.1587 = 0.6826

Therefore, probability of selecting a random sample of n = 4 students with an average age greater than 23 is 1587, the probability of selecting a random sample of n = 36 students with an average age greater than 23 is 0.00135 and for a sample of n = 36 students, the probability that the average age is between 21 and 22 is 0.6826

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Part a

It is a function because each x-value matches with only one y-value.

Part b

No, because the x-values of 3 and -2 both correspond to a y-value of -3.

Answer: x = 9, 2

Step-by-step explanation:

I'm going to give you two main ways to solve this type of problem.

First is doing it mentally:

When we're given the setting of ax^2 + bx + c

We want to find two numbers that multiply to c and add to b. (If a isn't 1, then we need to add that into our calculation, but in this case a = 1)

So, what two numbers multiply to 18 and add to -11?

-9 and -2, so we rewrite the equation as (x-9)(x-2)

We then solve for x, x - 9 = 0, so x = 9 and x - 2 = 0, so x = 2

Second is we use the quadratic formula:

It would be [tex](-b+\sqrt{b^{2} -4ac})/2a\\(-b-\sqrt{b^{2} -4ac})/2a\\\\Plugging in your numbers: \\\\(11+\sqrt{11^{2} -72})/2\\(11-\sqrt{11^{2} -72})/2[/tex]

The unknown angles are as follows:

complementary angles are angles that sum up to 90 degrees.

in other words, When two angles add to 90°, we say they "Complement" each other.

Therefore,

9x + 2x + 7 = 90

11x = 90 - 7

11x = 83

x = 83 / 11

x = 7.54

Therefore,

∠1 = 9(7.54) = 67.9°

∠2 = 2(7.54) + 7 = 22.08°

Supplementary angles are angles that sum up to 180 degrees.

Therefore,

3x + 8  + 9x = 180

12x + 8 = 180

12x = 180 - 8

12x = 172

x = 172 / 12

x = 14.3

Hence,

∠1 = 9(14.3) = 129°

∠2 = 180 - 129 = 51°

Vertically opposite angles share the same vertex.  Vertically opposite angles are equal.

Therefore,

9x = 3x + 9

9x - 3x = 9

6x = 9

x = 9 / 6

x = 3 / 2

x = 1.5

Therefore,

∠1 = 9(1.5) = 13.5°

∠2 = 13.5°

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[tex]~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{y^{-5}}{x^{-3}}\implies \cfrac{y^{-5}}{1}\cdot \cfrac{1}{x^{-3}}\implies \cfrac{1}{y^5}\cdot \cfrac{x^3}{1}\implies {\Large \begin{array}{llll} \cfrac{x^3}{y^5} \end{array}}[/tex]

The machine will take 7 minutes to fill one box. Hence, table A. represents the correct relationship between the number of minutes the machine fills boxes and the number of boxes it has filled.

Boxes filled by machine in 35 minutes = 5 boxes

So, the number of boxes the machine fills in each minute = Time taken to fill 5 boxes/ Number of boxes filled

= 35/5

= 7 minutes

Time taken by machine to fill one box = 7 minutes

Time taken to fill two boxes = 14 minutes

Time taken to fill three boxes = 21 minutes

Time taken to fill four boxes = 28 minutes

Hence, table A is the correct answer from the given options

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The following are the results for measuring the distance that a long jumper has jumped which is uniformly distributed between 0 and 5mm

a) Mean = 2.5

b) Standard deviation = 1.4434

c) P(X = 2.5) = 0

d) P(2 < X < 4) = (4 - 2)/(5 - 0) = 2/5 = 0.4

e) P(X > 1) =0.8

f) P(X > 4 | X > 2) = 0.33

g) 60th percentile =  3

h) Upper quartile =  3.75

Mean = (0 + 5)/2 = 2.5

Standard deviation =[tex]\sqrt{(5-0)^{2} }[/tex] / [tex]\sqrt{12}[/tex]  = 1.4434

P(X = 2.5) = 0

P(2 < X < 4) = (4 - 2)/(5 - 0) = 2/5 = 0.4

P(X > 1) = (5 - 1)/(5 - 0) = 4/5 = 0.8

P(X > 4 | X > 2) = P(X > 4 and X > 2)/P(X > 2) = (5 - 4)/(5 - 2) = 1/3 = 0.33

60th percentile = 0.60*(5 - 0) = 3

Upper quartile = 75th percentile = 0.75*(5 - 0) = 3.75

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By using the equation for the line of best fit, the salary for an employee who has seven (7) years of experience is: D. $55,573.

A line of best fit is a statistical tool that is used in conjunction with a scatter plot, in order to determine whether or not there's any association between a data.

In this scenario, the employee's salary would be plotted on the y-axis of the scatter plot while the years of experience would be plotted on the x-axis of the scatter plot.

By critically observing the scatter plot (see attachment) which models the data in the given table, an equation for the line of best fit is given by:

y = 2233.3x + 39940

Next, we would use the above equation for the line of best fit to predict the salary for an employee with 7 years of experience:

y = 2233.3(7) + 39940

y = 15,633.1 + 39940

y = 55,573.1 ≈ $55,573.

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Using percentage we can calculate that the team is expected to lose 4 matches.

A figure or ratio that is stated as a fraction of 100 is referred to as a percentage in mathematics. Although the abbreviations "pct," and occasionally "pc" is also used, the percent symbol "%" is most frequently used to denote it. A percentage is a number without any dimensions or established units of measurement.

By dividing the value by the entire value and multiplying the result by 100, the percentage may be computed. Calculating percentages using the formula (Value/Total Value)×100%.

Given in percentages the team will win 65% , team will draw =15%

Therefore in percentage the team will lose = 100 - ( 65 + 1 5 )% = 20 %

Now calculating the total number of matches the team will lose :

20% of 20 matches = 4 matches

Hence the team is expected to lose 4 matches out of 20.

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The angle B has a measure of  121 degrees

Angles are formed when two or more lines intersect. This in other words means that angles is the measure of space between the intersection of rays or lines

The angles are given as

A = 2x + 29

B = 3x - 17

Also, we have:

The angles are vertical angles

Vertical angles are congruent angles

This means that

A = B

So, we have

2x + 29 = 3x - 17

Evaluate the like terms

x = 46

Substitute x = 46 in B = 3x - 17

B = 3 x 46 - 17

Evaluate

B = 121

Hence, the measure of the angle B is 121 degrees

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Answer:

Step-by-step explanation:

b=(3x-17) degrees.

Step-by-step explanation:

pure acid is a 100% acid solution.

x = ml of 100% solution

1×x + 0.3×400 = 0.75×(400 + x)

x + 120 = 300 + 0.75x

0.25x = 180

x = 720 ml

we must add 720 ml of pure acid to the 400 ml of 30% solution to create a 75% solution (1,120 ml in total).

The scale factor that is used for student is running for president of student government is 1:54.

From the information, her friend has designed a campaign poster that measures 27 feet by 14 feet and she duplicated the poster on a

rectangular button measuring 6 inches by 3 1/9 inches.

1 feet = 12 inches

27 feet = 27 × 12 = 324 inches.

The scale factor will be the division of the values and this will be:

= 6/324

= 1/54

The scale factor is 1:54.

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Answer:l=p/2-w=198/2-3=96

Step-by-step explanation:yes

The Domain of this relation is {0,2,3,4} and the range of the relation is {-2,1,2,5}.

In the question

let us first write down the coordinates in the order from bottom to top .

The coordinates of the points are (4,-2) ,(2,1) ,(0,2) ,(0,5) ,(3,5) .

the x coordinates in the point (x,y) is called as Domain .

the y coordinates in the point (x,y) is called as Range .

Hence , the Domain of the given relation is {4,2,0,3}

writing in the order we get , Domain = {0,2,3,4}

and the range of the given relation is {-2,1,2,5}

writing in the order we get , Range = {-2,1,2,5}

Therefore , the Domain of this relation is {0,2,3,4} and the range of the relation is {-2,1,2,5} .

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Answer: -2000

Step-by-step explanation:

the coordinates of a point P that lies along the directed line segment from E (-5, 5) to F (-2,-2) and partitions the segment in the ratio of 2 : 1.5 is (- 23 / 7 , 1).

We are given a line segment formed by joining the points:

E (- 5, 5)

F (- 2, - 2)

We need to find the coordinate of a point P which divides this line segment in the ratio 2 : 1.5

Now, we can also write this ratio as:

4 : 3

The formula for finding the coordinate of point P is:

x = (m x₂ + n x₁) / (m + n)

y = (m y₂ + n y₁) / (m + n)

Substituting the values in the formula, we get that:

x = 4(-2) + 3(-5) / 4 + 3

x = - 8 - 15 / 7

x = - 23 / 7

y = 4(- 2) + 3(5) / 4 + 3

y = - 8 + 15 / 7

y = 7 / 7 = 1

So, point P = (- 23 / 7 , 1)

Therefore, we get that, the coordinates of a point P that lies along the directed line segment from E (-5, 5) to F (-2,-2) and partitions the segment in the ratio of 2 : 1.5 is (- 23 / 7 , 1).

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From the options provided in the question, we may conclude that Option A is equivalent to 0.428571.

One of the four fundamental arithmetic operations, or how numbers are combined to create new numbers, is division. The other operations are multiplication, addition, and subtraction.

Step 1: Take the dividend's first digit from the left. Determine whether this digit is greater than or equal to the divisor.

Step 2: Next, divide it by the divisor and write the result as the quotient on top.

Step 3: Subtract the result from the digit and record the difference.

Step 4: Subtract the dividend's next digit (if present).

Step 5: Repeat the procedure.

We need to find the given option that is equal to 0.428571.

For option A,

42/99 =0.428571 = 0.42

Therefore, we can say that Option A is equal to 0.428571 from the options given in the question.

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Answer:

6

Step-by-step explanation:

The final price of the refrigerator after the additional 15% discount is $170

Given

The original sale price of the refrigerator  = was $250

Given a 20 % discount on the original price, the new sale price would be as follows

Sale price = original price - Discount

                 = [tex]250-(\frac{20}{100} )250[/tex]

Sale price = $200

After this an additional 15% discount is given on new sale price.

So again deducting the discount from the sale price we get,

Sale price = 200 - discount(15%)

                = [tex]200-(\frac{15}{100} )200[/tex]

Sale price = 170

Hence the final sale price after discount is $170

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