What is the missing step in solving the inequality 5 – 8x < 2x + 3? Add 2x to both sides of the inequality. Subtract 8x from both sides of the inequality. Subtract 2x from both sides of the inequality. Add 8x to both sides of the inequality.

Answer:

(3)x+(3)

Step-by-step explanation:

Answer:

The percentage of at least one person of the team advanced is 95%

Step-by-step explanation:

For this exercise is necessary to understand the concept of combination, this is calculate as:

[tex]nCk=\frac{n!}{k!(n-k)!}[/tex]

Where n is the total elements and k is the size of the group that is going to be chosen. This calculation give as the number of ways that is possible to choose a group of k with n elements.

So, the only possibility that there is no one of the same team that advance to the next round is that all of the people chosen were of the other 3 that doesn’t belong to the group mentioned. Then there is only one way to get this case.

On the other hand there are 20 ways to conform a group of 3 from a 6 elements and is calculate as:

[tex]6C3=\frac{6!}{3!(6-3)!}[/tex]

[tex]6C3=20[/tex]

Therefore, the percentage that any of the group mentioned pass to the next round is 1 in 20 or 5%.  

So, the percentage that at least one of the group mentioned pass to the next round is the compliment, that’s mean that it is 95%.

The correct answer is A

Explanation:

A Venn diagram is a type of diagram used in mathematics and other fields to show sets and their relationship, because of this, Venn diagrams include at least two sets that are presented in two overlapped circles, in this each circle represents the elements that exclusively belong to each set, while the elements that belong two both sets are placed in the overlapped sections and the elements that do not belong to any of the sets are outside the circles. This implies, in the Venn diagram presented the elements that belong to swamp are in section B, the ones that belong to rainforest are in section D, the elements bot sets share are in section C and those that do not belong to any of the sets presented or that are different from the are in section A, as these elements are outside the circles and therefore do not belong to any of the sets that are represented by the circles.

Answer:

The most appropriate answer option is D) The girls are generally taller than the boys.

Step-by-step explanation:

A) The shortest boy is taller than the shortest girl:

The shortest guy is not taller than the girl so its false.

B) The range for the girls is greater than the range for the boys:

Range for girls = 56 - 44 = 12

Range for boys = 54 - 41 = 13

C) There is an outlier in the data for the boys, but not for the girls:

It is present in both.

D) The girls are generally taller than the boys:

Average height of boys = [tex]\frac{(41)+(44\times3)+(46\times3)+(48\times2)+(50\times3)+(52\times)+(54\times4)}{20}[/tex] = 49.05

Average height of girls = [tex]\frac{(44\times2)+(46\times2)+(48)+(50\times3)+(52\times4)+(54\times3)+(56\times4)}{20}[/tex] = 50.9

Therefore, the correct answer option is D) The girls are generally taller than the boys.

Answer:

D) The girls are generally taller than the boys.

Step-by-step explanation:

The heights of a group of boys and girls at a local middle school are shown on the dot plots. When comparing the shapes of the two sets of data, the girls are generally taller than the boys.

[tex]\bf \qquad \textit{Amount for Exponential Decay} \\\\ A=P(1 - r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &4000\\ r=rate\to 10\%\to \frac{10}{100}\dotfill &0.10\\ t=\textit{elapsed time}\\ \end{cases} \\\\\\ A=4000(1-0.10)^t\implies A=4000(0.9)^t \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf \qquad \textit{Amount for Exponential Decay} \\\\ A=P(1 - r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &100\\ r=rate\to 8\%\to \frac{8}{100}\dotfill &0.08\\ t=\textit{elapsed time}\\ \end{cases} \\\\\\ A=100(1-0.08)^t\implies A=100(0.92)^t[/tex]

Answer:

so width of border is 10 inches

Step-by-step explanation:

Given data

board size = 12 * 16 inches

border area = 380 square inches

to find out

width of border

solution

let us assume width of border is x

first we find area of board i.e. 12 × 16 = 192 sq inches

and border area is given = 380 square inches

so total area of border and board is 192 + 380 = 572 sq inches

so we can say ( x+ 12 ) (x +16 ) = 572

solve this equation we get

x² +16x + 12x + 192 = 572

x² + 28x + 192 = 572

x² + 28x - 380 = 0

solve this equation and we get two value of x i.e.

x = 10 and x = -38

we will consider positive value here

so width of border is 10 inches

Answer:

The width of the border is 5 inches.

Step-by-step explanation:

Let x be the width of the border,

Given,

The rectangular board has the dimension 12 inches by 16 inches,

Thus, the dimension of the figure by joining the border with the board is,

(12+2x) inches by (16+2x) inches,

= (12+2x)(16+2x)

Hence, the area of the border = area of the figure by joining the border with the board - area of the board

= (12+2x)(16+2x) - 12 × 16

According to the question,

The area of the border = 380 square​ inches,

[tex](12+2x)(16+2x) - 12\times 16=380[/tex]

[tex]192+24x+32x+4x^2-192=380[/tex]

[tex]4x^2+56x-380=0[/tex]

[tex]4x^2+76x-20x-380=0[/tex]

[tex]4x(x+19)-20(x+19)=0[/tex]

[tex](4x-20)(x+19)=0[/tex]

By zero product property,

[tex]x=5\text{ or }x=-19[/tex]

Since, width can not be negative,

Hence, the width of the border is 5 inches.

Answer:

502.7

Step-by-step explanation:

I'm not sure on this! but this is what I think its supposed to be, I'm sorry if that's wrong

Answer:

y = 1/2x +6

Step-by-step explanation:

We have a point and a slope.  Therefore we can use the point slope form to create a line

y-y1 = m(x-x1)

y-5 = 1/2(x--2)

y-5 = 1/2(x+2)

Distribute the 1/2

y-5 = 1/2x +1

Add 5 to each side

y-5+5 = 1/2x +1+5

y = 1/2x +6

This is in slope intercept form

No, it is not a proportional relationship because the graph does not go through the origin. A proportional relationship is supposed to be a straight line, starting from the origin. It starts on the number 4.

The true statement is (b) No, it is not a proportional relationship because the graph does not go through the origin

Proportional relationships are represented with linear equations that begin from the origin.

From the attached figure, we can see that: the graph begins from (0,4)

For the graph to be proportional it must begin from (0,0) as the origin

This means that, the graph does not represent a proportional relationship.

Hence, the true statement is (b)

Read more about proportional relationships at:

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Answer:

The option B

Step-by-step explanation:

The  weak correlation rank is between 0,25 and 0,5

The correlation is 0,26,  which mean that 26 per cent of the variation is caused for set x

Answer:  A. It is a weak negative correlation, and it is not likely causal.

Step-by-step explanation:

Given : The number of times a player has golfed in one’s lifetime is compared to the number of strokes it takes the player to complete 18 holes.

It means there is correlation . But there it is not likely causal because one  thing is not causing other.

The correlation coefficient relating the two variables is -0.26.

We know that when the absolute value of correlation coefficient lies between 0.1 to 0.3, then it indicates that there is weak association.

The absolute value of given correlation coefficient (0.26) lies between 0.1 to 0.3, therefore, it shows weak correlation.

Also, it has negative sign , so it must indicate a weak negative correlation.

Answer:

A. Confidence level

Step-by-step explanation:

The illustration showed that​ 26% of applicants said the biggest interview turnoff is that the applicant did not make an effort to learn about the job or the company.

The margin of error was given as plus or minus 3 percentage points.

The important feature of the poll that was​ omitted was - confidence level.

The percent of all samples that are included in the true population parameter is given by a confidence level.

Confidence interval defines the probability that the given population parameter will fall within a specific range of values.

Mathematically we can express the scenario as :

Sample size is given as 1910​ professionals

Point estimate is 26%

Confidence level is not given.

Confidence interval is plus or minus 3 percent around 26%.

Answer:

452.16 units^2

Step-by-step explanation:

Given

Radius = r= 6 units

The formula for finding the surface area of a sphere is:

[tex]A = 4\pi r^2\\A= 4 * 3.14 * (6)^2\\A=12.56*36\\A = 452.16[/tex]

In the formula, π is taken as 3.14.

So, the surface area of the given sphere is 452.16 units^2 ..

Answer:

452.39 units²

Step-by-step explanation:

To get the surface area of a sphere, all you need is the radius. The formula for the surface area is:

V=4πr²

So all you need to do is plug in the values:

V = 4πr²

V = (4)(π)(6)²

V = 4π36

V = 452.39 units²

BUT WAIT! If your teacher set the value of π to 3.14, the answer would be 452.16 units².

Answer:

Step-by-step explanation:

The area of the base is given by the formula ...

  A = πr²

so the radius is ...

  r = √(A/π) = √(1386/(22/7)) = √441 = 21 . . . units

__

The volume is given by ...

  V = (1/3)Bh

where B is the area of the base, and h is the height (equal to the radius). Filling in the numbers, we have ...

  V = (1/3)(1386)(21) = 9702 . . . . cubic units

Answer:

im not sure I understand the question.

Step-by-step explanation:

Answer:

equidistant from the endpoints of the segment.

Step-by-step explanation:

Answer:

The ending cash balance is $12,800

Step-by-step explanation:

This is an addition and subtraction problem. We begin with the initial cash balance of $6,800. Next we are "provided" cash from various activities of $37,000. Based on the word used we can tell that this means we have to add this to our initial balance like so,

[tex]6,800 + 37,000 = 43,800[/tex]

Now our balance is $43,000. Next we are told that Net Cash "used" in investing activities is $13,600 and "used" in financing activities is $17,400. Based on this word we can tell that this money is being subtracted from our balance.

[tex]$43,000 - 13,600 - 17,400 = 12,800[/tex]

Finally, we can see that the ending cash balance is $12,800

I hope this answered your question. If you have any more questions feel free to ask away at Brainly.

The ending cash balance for Stormer Company can be calculated by starting with the beginning cash balance, adding the net cash provided by operating activities, and then subtracting the net cash used in investing and financing activities: $6,800 beginning balance + $37,000 provided - $13,600 invested - $17,400 financed = $12,800 ending cash balance.

To solve this problem, it's crucial to understand that the ending cash balance is calculated by adding or subtracting the net cash provided or used from the beginning balance. In this scenario, the company has reported net cash provided by operating activities, as well as net cash used in investing and financing activities. To find the ending cash balance, you should follow these steps:

So, based on the numbers provided by the Stormer Company, its ending cash balance should be $12,800.

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Answer:

b.

packaging costs

Step-by-step explanation:

Packaging costs are not fixed costs.

Option B is the correct answer.

Fixed costs are expenses that do not vary with changes in the volume of goods or services produced.

They are typically time-related and can be considered "fixed" in the short term.

We have,

(a) Equipment leases are usually fixed costs because they involve a set monthly or annual payment regardless of how much the equipment is used.

(c) Insurance can also be considered a fixed cost because the premium is usually paid regularly, such as monthly or annually, and does not change based on the number of claims made.

(d) Salaries are typically considered fixed costs because they are paid regularly and do not change based on the amount of work done or sales made.

However,

(b) packaging costs are typically variable costs because they are directly related to the number of products produced.

The more products produced, the more packaging materials are needed, resulting in higher packaging costs.

Thus,

Packaging costs are not fixed costs.

Learn more about fixed costs here:

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Answer:

Parameter because the value is a numerical measurement describing a characteristic of a population.

Step-by-step explanation:

A parameter tells you something about the entire population.This means that you will know the "something" after asking every person in that group.In this question, the study was conducted for all 1580 seniors, and it was found that a parameter of 40% own a television.

In the given scenario, the 40% figure is a parameter because it involves a measurement from the entire population of college seniors, not a sample.

The value that 40% of all 1580 seniors at a college own a television represents a parameter because it is a numerical measurement that describes a characteristic of a population. Since the study includes all seniors at the college, it is not a sample but the entire population of interest. Therefore, the 40% figure is a fixed value that characterizes that specific group. Had the percentage come from a study of a subset of the college seniors, it would be considered a statistic, as it would be an estimate derived from a sample used to infer about the larger population.

Let's consider another example to clarify the difference. If the U.S. federal government surveyed all high school seniors in the United States concerning their plans for future education and employment and found that 50% were planning to attend a four-year college, that 50% would be a parameter because it includes the entire population. In contrast, if the government only surveyed a sample, such as seniors from a selection of high schools, the result would be a statistic.

Answer:

D.

Step-by-step explanation:

Just see which point yields the highest value.

f(x,y)=4x-3y

Checking choice A:

(x,y)=(5,0)

f(5,0)=4(5)-3(0)=20-0=20.

Checking choice B:

(x,y)=(4,6)

f(4,6)=4(4)-3(6)=16-18=-2.

Checking choice C:

(x,y)=(7,5)

f(7,5)=4(7)-3(5)=28-15=13.

Checking choice D:

(x,y)=(8,2)

f(8,2)=4(8)-3(2)=32-6=26

Choice D yields the highest value of the points given for our relation f(x,y)=4x-3y.

Answer:

13%

Step-by-step explanation:

took all numbers add them together than divided by 3

Answer:

  symmetry about the y-axis is shown

Step-by-step explanation:

Points on the right of the line of symmetry (x=0, the y-axis) are the same distance from that line as the corresponding points on the left. (That is what makes it a line of symmetry.)

There is no point of rotation that will map one figure to the other after rotation, hence no point or rotational symmetry.

Answer:

Step-by-step explanation:

The figure on the right is obtained by reflecting the figure on the left across the y-axis.

Answer: the lower the price the more people want to come to the baseball game.

Step-by-step explanation:

Answer:

  a)  p = -x/3000 + 19 2/3

  b)  $9.83

Step-by-step explanation:

a) The 2-point form of the equation for a line can be used with the two given points. The attendance is said to be the independent variable.

  y = (y2 -y1)/(x2 -x1)(x -x1) + y1

Here "y" is the price (p), and "x" is the attendance, so we have ...

  p = (10 -12)/(29000 -23000)(x -23000) +12

  p = -1/3000(x -23000) +12

  p = -x/3000 + 19 2/3 . . . . price as a function of attendance

__

b) Revenue is the product of attendance and price. We can find the attendance associated with maximum revenue, then find the corresponding price.

  R(x) = x·p = x(-x/3000 +19 2/3)

This has zeros at x=0 and x=3000(19 2/3) = 59,000. The maximum revenue corresponds to attendance halfway between these values, at x = 29,500. The demand function tells us the ticket price should be ...

  p = -29500/3000 +19 2/3 = 9.83 . . . . dollars

_____

Comment on the problem working

I might have written the "demand function" to use price as the independent variable. Then the price is what you know when you find the maximum revenue; you don't have to do an extra step to find it.

  x = 3000(19 2/3 -p)

  xp = 3000p(19 2/3 -p) is maximized at p = (19 2/3)/2 = 9 5/6 ≈ 9.83

Answer:

1-a

2-b

3-e

4-c

5-g

6-d

7-f

Step-by-step explanation:

should be this

Answer: 120

Step-by-step explanation: to get this answer you do 5! (5 factorial), which means you multiply that number by all those which are lower down to one, or 5x4x3x2x1 in this case, which is 120

Answer: 240

Step-by-step explanation: 5 x 4 x 3 x 2 x1 = 240

Answer:

[tex]\frac{m}{n}[/tex]

Step-by-step explanation:

Setting it up as a fraction will help us see the simplification process a bit easier.

[tex]\frac{am}{an}[/tex]

a/a = 1, so they cancel each other out, leaving us with simply

[tex]\frac{m}{n}[/tex]

Answer:

The correct option is 1.

Step-by-step explanation:

Rhombus is a special case of parallelogram.

The properties of a parallelogram and rhombus:

1. Opposite sides parallel and equal.

2. Diagonals bisect each other.

3. Opposite angles are congruent.

The consecutive sides of a parallelogram may or may not be equal. But a rhombus has four congruent sides.

If a parallelogram has four congruent sides, then that parallelogram is known as rhombus.

The required statement that describe a parallelogram must be a rhombus is  "parallelogram with four congruent sides ".

Therefore the correct option is 1.

Answer:

This is what i got

Answer:

0

Step-by-step explanation:

If you think in degrees easier than in radians, then make this conversion.

pi = 180 degrees

(3/2)*pi = (3/2) * 180 = 180 * 3/2 = 270

Sin(270) = -1

cos(270) = 0

==========

sin(270) * cos(270) = -1 * 0 = 0

Answer:

The focus point is (2 , 0) ⇒ answer D

Step-by-step explanation:

* Lets revise the equation of the parabola in standard form

- The standard form is (x - h)² = 4p(y - k)

- The focus is (h, k + p)

- The directrix is y = k - p

- If the parabola is rotated so that its vertex is (h , k) and its axis of

 symmetry is parallel to the x-axis, it has an equation of

 (y - k)² = 4p(x - h)

- The focus is (h + p, k)

- The directrix is x = h - p

* Lets solve the problem

∵ The equation of the parabola is y = 1/8(x² - 4x - 12)

- Lets make x² - 4x completing square

∵ √x² = x  

∴ The 1st term in the bracket is x

∵ 4x ÷ 2 = 2x

∴ The product of the 1st term and the 2nd term is 2x

∵ The 1st term is x

∴ the second term = 2x ÷ x = 2

∴ The bracket is (x - 2)²

∵  (x - 2)² = (x² - 4x + 4)

∴ To complete the square add 4 to the bracket and subtract 4 out  

  the bracket to keep the equation as it

∴ (x² - 4x + 4) - 4 = (x - 2)² - 4

- Lets put the equation after making the completing square

∴ y = 1/8 [(x - 2)² - 4 - 12]

∴ y = 1/8 [(x - 2)² - 16] ⇒ multiply both sides by 8

∴ 8y = (x - 2)² - 16 ⇒ add 16 to both sides

∴ 8y + 16 = (x - 2)² ⇒ take from the left side 8 as a common factor

∴ 8(y + 2) = (x - 2)²

∴ The standard form of the equation of the parabola is

   (x - 2)² = 8(y + 2)

∵ The standard form of the equation is (x - h)² = 4p(y - k)

∴ h = 2 , k = -2 , 4p = 8

∵ The focus is (h , k + p)

∵ h = 2

∵ 4p = 8 ⇒ divide both sides by 4

∴ p = 2

∴ The focus = (2 , -2 + 2) = (2 , 0)

* The focus point is (2 , 0)

Answer:

D 2,0

Step-by-step explanation:

Answer:

Part 1) The polygon is a square

Part 2) The perimeter is equal to [tex]20\ units[/tex]

Part 3) The area is equal to [tex]25\ units^{2}[/tex]

Step-by-step explanation:

we have

[tex]A(5,0), B(2,4), C(-2,1),D(1,-3)[/tex]

Plot the points

see the attached figure

we know that

the formula to calculate the distance between two points is equal to

[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]

Find the distance AB

[tex]A(5,0),B(2,4)[/tex]

substitute in the formula

[tex]d=\sqrt{(4-0)^{2}+(2-5)^{2}}[/tex]

[tex]d=\sqrt{(4)^{2}+(-3)^{2}}[/tex]

[tex]d=\sqrt{25}[/tex]

[tex]AB=5\ units[/tex]

Find the distance BC

[tex]B(2,4), C(-2,1)[/tex]

substitute in the formula

[tex]d=\sqrt{(1-4)^{2}+(-2-2)^{2}}[/tex]

[tex]d=\sqrt{(-3)^{2}+(-4)^{2}}[/tex]

[tex]d=\sqrt{25}[/tex]

[tex]BC=5\ units[/tex]

Find the distance CD

[tex]C(-2,1),D(1,-3)[/tex]

substitute in the formula

[tex]d=\sqrt{(-3-1)^{2}+(1+2)^{2}}[/tex]

[tex]d=\sqrt{(-4)^{2}+(3)^{2}}[/tex]

[tex]d=\sqrt{25}[/tex]

[tex]CD=5\ units[/tex]

Find the distance AD

[tex]A(5,0),D(1,-3)[/tex]

substitute in the formula

[tex]d=\sqrt{(-3-0)^{2}+(1-5)^{2}}[/tex]

[tex]d=\sqrt{(-3)^{2}+(-4)^{2}}[/tex]

[tex]d=\sqrt{25}[/tex]        

[tex]AD=5\ units[/tex]

we have that

AB=BC=CD=AD

Find the distance BD (diagonal)

[tex]B(2,4),D(1,-3)[/tex]

substitute in the formula

[tex]d=\sqrt{(-3-4)^{2}+(1-2)^{2}}[/tex]

[tex]d=\sqrt{(-7)^{2}+(-1)^{2}}[/tex]

[tex]BD=\sqrt{50}\ units[/tex]        

Verify if the polygon is a square

If the triangle BDA is a right triangle, then the polygon is a square

Applying the Pythagoras theorem

[tex]BD^{2}=AD^{2}+AB^{2}[/tex]

substitute

[tex](\sqrt{50})^{2}=5^{2}+5^{2}[/tex]

[tex]50=50[/tex] -----> is true

so

The triangle BDA is a right triangle

therefore

The polygon is a square

Find the Area of the polygon

The area of a square is equal to

[tex]A=b^{2}[/tex]

we have

[tex]b=5\ units[/tex]

[tex]A=5^{2}=25\ units^{2}[/tex]

Find the perimeter of the polygon

The perimeter of a square is equal to

[tex]P=4b[/tex]

we have

[tex]b=5\ units[/tex]

[tex]P=4(5)=20\ units[/tex]

Answer:

 intercept is 3 

X intercept is -3/7

For this case we have the following equation:

[tex]y = 7x + 3[/tex]

To find the y-intersection values we do [tex]x = 0[/tex]:

[tex]y = 7 (0) +3\\y = 0 + 3\\y = 3[/tex]

To find the x-intersection values we do[tex]y = 0[/tex]

[tex]0 = 7x + 3[/tex]

Subtracting 3 on both sides:

[tex]-3 = 7x[/tex]

Dividing between 7 on both sides:

[tex]x = - \frac {3} {7}[/tex]

So, we have:

x-intersection: [tex](- \frac {3} {7}, 0)[/tex]

y-intersection: [tex](0,3)[/tex]

Answer:

Option B

Answer:

Option 2 is the correct answer.

Step-by-step explanation:

We know that

[tex]Speed=\frac{Distance}{time}[/tex]

We have 1 mile = 5280 feet thus 6 miles = 31680 feet

Similarly 1 hour = 3600 seconds

Applying values in the equation above we get

[tex]Speed=\frac{31680feet}{3600sec}\\\\Speed=8.8feet/sec[/tex]

Thus his average speed is less than 18feet/sec