-5 is a rational number and an integer yes or no

Answer/Step-by-step explanation:

Score 1:

3, 7, 5, 4, 5, 6, 7, 8, 6, 5

Mean = [tex] \frac{3 + 7 + 5 + 4 + 5 + 6 + 7 + 8 + 6 + 5}{10} = \frac{56}{10} = 5.6 [/tex]

Median: order the data from least to the greatest.

3, 4, 5, 5, 5, 6, 6, 7, 7, 8

The median is average of the fifth and sixth data value in the data set

Median = (5 + 6)/2 = 11/2 = 5.5

Mode = value with the highest frequency = 5

Score 2:

34, 54, 17, 26, 34, 25, 14, 24, 25, 23

Mean = sum of all values/10

Mean = 276/10 = 27.6

Median: order the data set from min to max.

14, 17, 23, 24, 25, 25, 26, 34, 34, 54

The median is average of the fifth and sixth data value in the data set

Median = (25 + 25)/2 = 50/2 = 25

Mode = 25 and 34 (both have frequencies of 2)

Score 3:

154, 167, 132, 145, 154, 145, 113, 156, 154, 123

Mean = sum of all values/10

Mean = 1443/10 = 144.3

Median: order the data set from min to max.

113, 123, 132, 145, 145, 154, 154, 154, 156, 167

The median is average of the fifth and sixth data value in the data set

Median = (145 + 154)/2 = 299/2 = 149.5

Mode = 154

Answer:

x<4 and x>1

Step-by-step explanation:

1) 3x-4<8

Add 4 to both sides first to isolate x.

3x-4<8

  +4 +4

3x<12

Divide both sides by 3.

3x<12

/3  /3

x<4

2) 2x+2>4

Subtract both sides by 2 to isolate x.

2x+2>4

   -2  -2

2x>2

Divide both sides by 2.

2x>2

/2  /2

x>1

Hope this helped!! Have an amazing day :3

Answer:

the 1st 2nd and 5th since if there is even one negative in the fraction it makes the whole fraction negative

Answer:

10 times bigger

Step-by-step explanation:

because if you do 4 times 300 thats 1200

and if you do 4 times 30 then you get 120

and 120 times 10 is 1200 so there you go.

HOPED THIS HELPED!!!!!!!!! :D

Answer:

# 10 is 4/3 or 1 and 1/3

#11 is 4/10 or 2/5

#12 is 2 and 3/4

#13 is 36/12 or 3 and 1/12

Step-by-step explanation:

i am not 100% sure on #13 btw

hope this helped!

p.s it would be cool if you gave me brainliest.

Answer:

Hey your answers on there are correct.

Step-by-step explanation:

Answer:

The answer is 1

Step-by-step explanation:

If you look at the number line and start counting from -8 and count 9 to the right then the number that you end on is the answer.

Answer: x = 2

If x is the width of the window, the value for x that results in the greatest area-- presumably admitting the greatest amount of light.

Step-by-step explanation:

Initial calculations to find a starting value for w.

Determine dimensions that will have a sum of 8 as the perimeter. The length of the arc plus three sides of the rectangle.

The length of the arc is  half the circumference of the circle, the width is the diameter. So, modifying the equation: C= πd,  a = πw/2

Three sides of a rectangle (presumably a square for the initial calculation) 3w

Initial equation: 3w + πw/2 = 8    Substitute 3.14 for π  and solve for w

2(3w) + 2(3.14w/2) = 2(8)   multiply all terms by 2 to eliminate denominator

6w + 3.14w = 16   combine like terms

9.14w  = 16   divide both sides by 9.14

w ≈ 1.75

Calculate the area using this value:

Area of semicircle:  πr²/2   r= 1.75/2  

3.14(.875)²/2 ≈ 1.203

Area of rectangle  1.75 × 1.75 = 3.0625

Total Area with width 1.75  :  4.265 ft²

Increasing the width to 2

The length of the arc becomes 3.14   This is twice the area of the semicircle.

3.14/2 = 1.57

The height of the rectangle reduces to 1.43

1.43 × 2 = 2.86

Total area with width of 2 ft   2.86 + 1.57 = 4.43 ft²

So 2 ft seems to be the optimal width.

Answer:

A.

Step-by-step explanation:

Answer:

[tex]f(0)=-2\\f(1)=e-1[/tex]

Step-by-step explanation:

According to intermediate value theorem, if a function is continuous on an interval [tex][a,b][/tex], and if [tex]k[/tex] is any number between [tex]f(a)[/tex] and [tex]f(b)[/tex], then there exists a  value, [tex]x=m[/tex], where [tex]a<m<b[/tex], such that [tex]f(m)=k[/tex]

In the given question,

Intermediate Value Theorem is used to show that there is a root of the given equation in the specified interval.

Here,

[tex]f(x)=e^x-3+2x[/tex]

Put [tex]x=0[/tex]

[tex]f(0)=e^0-3+2(0)=1-3+0=-2[/tex]

Put [tex]x=1[/tex]

[tex]f(1)=e^1-3+2(1)=e-3+2=e-1[/tex]

Answer:

The final balance is $1,692.94.

The total compound interest is $392.94.

Step-by-step explanation:

1,300 x 0.045=___ x 6

Answer:

13/15 > 4/5 is a true stament.

Step-by-step explanation:

The left side is 0.86 repeating turned into a decimal. which means 0.86 is greater than the right which the right is 0.8 turned into a decimal. which in this case this means that the given stament is always true.

Answer:

Step-by-step explanation:

alternate angles are equal

see attached

The measure of ∠1 is 33° .

When two parallel lines are crossed by a transversal, the pair of angles formed on the inner side of the parallel lines, but on the opposite sides of the transversal are called alternate interior angles. These angles are always equal.

According to the question

As given , lines A and B are parallel lines

therefore ,

∠1 = 33°  

∠3 = 57°

they are between parallel line and opposite of transversal line

So, they are alternate interior angles and are equal .

Hence, The measure of ∠1 is 33°  .

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Answer:

Letter B

Step-by-step explanation:

Answer:

I belive the answer is B

Step-by-step explanation:

Answer:

$930.76

Step-by-step explanation:

So if you move the decimal in the percentage over to the right by two then you have your sales tax rate in decimal form (0.065), you can then multiply that by the listed price and you'll have about 56.80675 so this number will be the sales tax price, then you may add this to the listed price and your answer will be 930.75675, then once you round up it will be $930.76.

Answer:

y=3/2x

Step-by-step explanation:

The equation of the required line as per slope-intercept form is 3x - 2y = 0.

The equation of a line that passes through points (x₁, y₁) and (x₂, y₂) is defined as:  

m = (y₂ - y₁)/(x₂ - x₁)

Here, 'm' is the slope and 'c' is the y-intercept of the given line.

Therefore, the slope of a line that passes through (6, 9) and (0, 0) is

= (0 - 9)/(0 - 6)

= 3/2

Now, the general form of a line is y = mx + c. Here, 'm' is the slope and 'c' is the y-intercept of the line.

The line passes through the point (0, 0).

Therefore, 0 = (3/2) × 0 + c

⇒ c = 0

Now, the equation of the straight line is

y = (3/2)x + 0

⇒ 2y = 3x

⇒ 3x - 2y = 0

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Answer:

area: 153.86

Circumference: 43.96 :D

Step-by-step explanation:

Answer:

Wow that is great

Step-by-step explanation:

is there a question? uhhhmmmmm

Answer:

60%

Step-by-step explanation:

They killed quite a bit and a lot were left.

Answer:

-2( 7x+4)

Step-by-step explanation:

-14x - 8

Factor out -2

-2*7x -2*4

-2( 7x+4)

Answer:

Step-by-step explanation:

[tex] - 14x - 8[/tex]

Write -8 as -4×2

[tex] - 14x + 2 \times 4[/tex]

Factor out common term : 2

[tex]2( - 7x - 4)[/tex]

Answer:

18%

Step-by-step explanation:

24-18% is 19.68 which means it took away $4.32.

Answer:

the answer is D

Step-by-step explanation:

Answer:

y = 4/5x -1/5

Step-by-step explanation:

4x -5y = 1

-5y = -4x + 1

5y = 4x - 1

y = 4/5x - 1/5

Answer:

it is 0.125

Step-by-step explanation:

......................

Answer: Total cost for 1 ride = $11. Total cost for 2 rides = $14. Total cost for 3 rides = $17. Total cost for 4 rides = $20. Total cost for 5 rides = $23

Step-by-step explanation:

Answer:

Step-by-step explanation:

18900 divided by 10 = 1890

1890 divided by 2 is 945

945 is 5 percent of 18900

18900 + 945 = 17955

Answer = 19845

Answer:

a) x = 798   is the quantity that maximizes the profit

b)po(x) = 401 $/unit

c)P(max ) = 636105 $

Step-by-step explanation:

The weekly demand function is equal to the price by unit and the Revenue function is weekly demand times quantity of units then:

R(x) = p(x) * x

R(x) = ( 800 - 0,5*x ) * x

R(x) = 800*x - 0,5*x²

The equation for the profit is:

P(x) = R(x) - C(x)

P(x) = 800*x - 0,5*x² - ( 300 + 2*x)

P(x) = 798*x - 0,5*x² - 300

a) P(x) = 798*x - 0,5*x² - 300

Taking derivatives on both sides of the equation:

P´(x) = 798 - x

If P´(x) = 0     then    798 - x = 0

x = 798   is the quantity that maximizes the profit

b) Selling price for the optimal quantity is:

p(x) = 800 - 0,5*x

p(x) = 800 - 0,5* 798

po (x) = 800 - 399

po(x) = 401 $/unit

c) Pmax = ?

P(x) = 798*x - 0,5*x² - 300    by subtitution of  x = 798

P(max) = 636804 - 399 - 300

P(max ) = 636105 $

a) The quantity that will maximize profit is [tex]100 \ units[/tex].

b) The selling of at this optimal quantity is [tex]\[/tex][tex]750[/tex] per unit.

c) So, the maximum profit is [tex]\[/tex][tex]25000[/tex].

A demand function is a mathematical equation that expresses the demand for a product or service as a function of its price and other factors such as the prices of the substitutes and complementary goods, income, etc.

The given demand function,

[tex]P=800-\frac{1}{2}x[/tex]

So, the revenue function is,

[tex]R(x)=p.x\\R(x)=800-x-\frac{1}{2}x^{2}[/tex]

[tex]\Rightarrow[/tex]Average cost is

[tex]\bar{C}=300+2x[/tex]

So, the total cost function is,

[tex]C\left ( x \right )=\bar{C}.x \\ C\left ( x \right )=300x+2x^{2}[/tex]

a) Profit function:

[tex]P\left ( x \right )=R\left ( x \right )-C\left ( x \right ) \\ =800x-\frac{1}{2}x^{2}-300x-2x^{2} \\ P\left ( x \right )=500x-\frac{5}{2}x^{2}[/tex]

For maximum,

[tex]{P}'\left ( x \right )=0 \\ 500\left ( 1 \right )-\frac{5}{2}\left ( 2x \right )=0 \\ 500-5x=0 \\ x=100[/tex]

b) Selling Price:

[tex]P=800-\frac{1}{2}x \\ at \ x=100 \\ P=800-\frac{1}{2}\left ( 100 \right ) \\ =\$ 750[/tex]

c) Maximum Profit:

[tex]P\left ( x \right )=500x-\frac{5}{2}x^{2} \\ P\left ( 100 \right )=500\left ( 100 \right )-\frac{5}{2}\left ( 100 \right )^{2} \\ P\left ( 100 \right )=\$ 25000[/tex]

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Step-by-step explanation:

The total number of people mentioned in this problem is 15. 15 will be the denominator for the probability in fraction form. The sum of the # of people that include lifeguards and managers will be the numerator.

Therefore, the probability that the person picked is either a manager or a lifeguard is 10/15 [because there are 2 managers and 8 lifeguards; 2 + 8 =10].

Fraction form of probability: 10/15

Decimal form: 0.6 repeated

Percent form: about 66.67%

The probability that person is either a lifeguard or manager is 2/3.

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.

We have,

There are 2 managers 8 lifeguards 3 concession stand clerks and 2 maintenance people.

Total = 2 + 8 + 3 + 2 = 15

So, P(lifeguard) = 8/15, P(Manager) = 2/15.

Then, P ( lifeguard or Manager)

= 8/15 + 2/15

= 10/15

= 2/3.

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