Discrete Math19. Rolling the Dice An experiment was conducted in whichtwo fair dice were thrown 100 times. The sum of the pipsshowing on the dice was then recorded. The following fre-quency histogram gives the resultsSum of Two Dice252015Frequency1032 3 4 5 6 7Value of Dice9 10 11 12(a) What was the most frequent outcome of the experi-ment?(b) What was the least frequent?(c) How many times did we observe a 7?(d) Determine the percentage of time a 7 was observed,(e) Describe the shape of the distribution

The given figure can be drawn as,

From the figure,

Since angle of incidence will be equal to angle of reflection, [tex]\begin{gathered} \text{tan}<\text{ACB}=\frac{h}{10\text{ m}} \\ \text{tan}\theta=\frac{h}{10\text{ m}} \\ 0.6=\frac{h}{10\text{ m}} \\ 6\text{ m=h} \end{gathered}[/tex]Therefore, the height of cactus is 6 m.

Answer:

34

Step-by-step explanation:

[tex]26+8 \\ \\ =2(13+4) \\ \\ =2(17) \\ \\ =34[/tex]

Answer:

20 mpg

Step-by-step explanation:

Given:

A passenger car will go 310 miles on 15.5 gallons of gasoline in city driving. What is the rate in miles per gallon?

Solve:

To find the rate in miles per gallon we have to divide.

Knowing that "Per" means "Each/One"

Hence, to find miles per gallon we divide :

Miles by Gallons

⇒ 310/15.5

Solving using long division format: ( Multiply both by 10 first)

[tex]155\overline{|\smallspace3100}\:\:\:\:[/tex]

Divide 310 by 155 to get 2:

[tex]\begin{matrix}\:\:\:\:\:\:\:\:\:\:\:\:\emptyspace2\:\:\:\:\:\:\:\:\:\:\:\:\:\:\\ 155\overline{|\smallspace3100}\:\:\:\:\:\:\:\:\:\:\:\:\\ \:\:\:\:\:\:\:\:\underline{\emptyspace3\emptyspace1\emptyspace0}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\\ \:\:\:\:\:\:\:\:\:\:\:\:\emptyspace0\emptyspace0\:\:\:\:\:\:\:\:\:\:\:\:\end{matrix}[/tex]

Divide 0 by 15.5 to get 0.

[tex]\begin{matrix}\:\:\:\:\:\:\:\:\:\:\:\:\emptyspace2\emptyspace0\:\:\:\:\:\:\:\:\:\:\:\:\\ 155\overline{|\smallspace3100}\:\:\:\:\:\:\:\:\:\:\:\:\\ \:\:\:\:\:\:\:\:\underline{\emptyspace3\emptyspace1\emptyspace0}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\\ \:\:\:\:\:\:\:\:\:\:\:\:\emptyspace0\emptyspace0\:\:\:\:\:\:\:\:\:\:\:\:\\ \:\:\:\:\:\:\:\:\:\:\:\:\:\:\underline{\emptyspace0}\:\:\:\:\:\:\:\:\:\:\:\:\\ \:\:\:\:\:\:\:\:\:\:\:\:\:\:\emptyspace0\:\:\:\:\:\:\:\:\:\:\:\:\end{matrix}[/tex]

Hence, the rate is 20 mpg.

~kavinsky

Answer:

Step-by-step explanation:

(5n - 3)/2=n-0.3

Then we solve for n.

Multiply the whole thing by 2.

5n-3=2n-0.6

Add 0.6

5n-2.4=2n

Add 2.4

5n=2n+2.4

Subtract 2n

3n=2.4

Divide by 3

n=0.8

Part a

The experimental probability that landing on red is equal to

P=277/500

P=0.554

Part b

The theoretical probability that landing on red is equal to

P=5/10

P=0.5

Part c

the answer is the first option

Option C. The way that the change would affect the mean and the median is that The mean will increase and the median will not change.

We will find the mean and the median before the 40 was added and after it was added

Before it was added

Mean = 16 + 18 + 20 + 24 + 24 + 24 + 24 + 31 + 32 / 9

= 213 / 9

= 23.67

The median is 24

After we have added 40 the mean would be

16 + 18 + 20 + 24 + 24 + 24 + 24 + 31 + 32 + 40 / 10

= 253 / 10

= 25.3

The median would be 24 + 24 / 2

= 48 / 2

= 24

Hence we can see that the mean got to be higher while the median still remained as 24.

The solution is C.

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Answer: z=23/9

Step-by-step explanation:

I will use cross multiplication

[tex]\frac{1}{9} =\frac{z}{23} \\23(1)=9(z)\\23=9z\\\frac{23}{9} =\frac{9z}{9} \\z=\frac{23}{9}[/tex]

I hope this helps.

Answer:

x=4/15

Step-by-step explanation:

first you need to make common denominators for 1/5 and 1/3

the common denominator is 15

5*3=15, 3*5=15. 1*3=3, 1*5=5

new equation:3x-3/15=x+5/15

now subtract x from both sides: 3x-3/15=x+5/15

                                                     -x          -x

                                                     2x-3/15=5/15

now you can add 3/15 to 5/15

2x=8/15

now for the last step, divide by 2 because there are 2 x's

2x/2=x         8/15 /2=4/15

x=4/15

Answer:

4/15

Step-by-step explanation:

3x-1/5 = x+1/3

make a common denominator

3x -3/15 = x + 5/15

next you can take away one x from both sides

2x - 3/15 = 5/15

then we want to have x alone on one side and everything else on the other

2x = 5/15 + 3/15

2x = 8/15

1x = 8/15 ÷ 2

1x = 8/30

simplify that

x = 4/15

all the statements prove that a line is parallel to b.

If two non-vertical lines in the same plane have the same slope, they are said to be parallel. Never will two parallel lines cross. If two non-vertical lines in the same plane cross at a right angle, they are said to be perpendicular.

Lines can either be parallel or intersecting. When two lines meet at a point in a plane, they are known as intersecting lines. If a line intersects two or more lines at distinct points then it is known as a transversal line.

line intersects lines a and b at points P and Q respectively. The line l is the transversal here.

∠1,∠2,∠7 and ∠8 are the exterior angles and ∠3,∠4,∠5 and ∠6 denote the interior angles.

The angle pairs formed due to intersection by a transversal are named as follows:

Corresponding Angles: ∠1 and ∠6; ∠4 and ∠8; ∠2 and ∠5; ∠3 and ∠7 are the corresponding pair of angles.

Alternate Interior Angles: ∠4 and ∠5 ; ∠3 and ∠6 denote the pair of alternate interior angles.

Alternate Exterior Angles: ∠1 and ∠7; ∠2 and ∠8 are the alternate exterior angles.

Same side Interior Angles: ∠3 and ∠5; ∠4 and ∠6 denote the interior angles on the same side of the transversal or co-interior or consecutive interior angles.

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Answer: b

Step-by-step explanation:

The correct equation to solve for x is 2(2x-15)=2x-8 , and the value of x is 11 .

in the question ,

from the given figure , we can see that RL=LQ   and PK=KQ which means

that L and K are the mid points of sides RQ and PQ respectively .

The Mid Point Theorem states that

If the line segment adjoining the mid points of any of the sides of the triangle then the line segment is said to be parallel to the third  side and is half of the length of  third side .

which means LK parallel to RP and RP/2=LK  ( ... by mid point theorem)

Substituting the values of LK = 2x-15  and RP = 2x-8 .

(2x-8)/2=2x-15

Multiplying both sides by 2

2x-8 = 2(2x-15)

So, the equation to solve for x is 2(2x-15)=2x-8

Simplifying further

2x-8 = 4x-30

4x-2x= 30-8

2x = 22

x = 11

Therefore , the correct equation to solve for x is 2(2x-15)=2x-8 , and the value of x is 11 .

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1089822 is the combined population of the four insect groups.

The number of times a number has been multiplied by itself is referred to as an exponent. For instance, the expression 2 to the third (written as 2³) signifies 2 x 2 x 2 = 8. 2³ and 2 x 3 = 6 are not equivalent. Keep in mind that any number is itself when raised to the power of 1.

Given Data

Insect population

Population of honeybees = 7.3498(10⁴)

Population of honeybees = 73498

Population of ants = 6.822(10³)

Population of ants = 6822

Population of termites = 9.8(10⁵)

Population of termites = 980000

Population of aphids = 2.9502(10⁴)

Population of aphids = 29502

Combined population = 73498 + 6822+980000+29502

Combined population = 1089822

1089822 is the combined population of the four insect groups.

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The simplified expression of (4⁴)⁻¹  is one over four raised to the fourth power

The expression can be simplified as follows:

(4⁴)⁻¹

Therefore, the expression can be simplified using laws of indices.

[tex](a^{c} )^{b} = a^{cb}[/tex]

and

[tex](a^{-b} )^{c} = \frac{1}{a^{bc} }[/tex]

Therefore, using the laws of indices, the expression can be simplified below:

(4⁴)⁻¹  = 4⁻⁴

Hence,

4⁻⁴ = 1 / 4⁴ = (1 / 4)⁴

Hence,

(4⁴)⁻¹  = 1 / 4⁴ = (1 / 4)⁴

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Answer:

x - intercept = - 1

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

given

x - 2y = 7 ( subtract x from both sides )

- 2y = - x + 7 ( divide through by - 2 )

y = [tex]\frac{1}{2}[/tex] x + [tex]\frac{7}{2}[/tex] ← in slope- intercept form

with slope m = [tex]\frac{1}{2}[/tex]

given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{1}{2} }[/tex] = - 2 , then

y = - 2x + c ← is the partial equation of the perpendicular line\to find c substitute (- 3, 4 ) into the partial equation

4 = 6 + c ⇒ c = 4 - 6 = - 2

y = - 2x - 2 ← equation of perpendicular line

to find the x- intercept let y = 0 into the equation and solve for x

- 2x - 2 = 0 ( add 2 to both sides )

- 2x = 2 ( divide both sides by - 2 )

x = - 1

the x- intercept of the perpendicular line is - 1 or (- 1, 0 )

Answer:

y = (1/3)x + 4

Step-by-step explanation:

(0, 4) and (-3, 3)

(x₁, y₁)         (x₂, y₂)

        y₂ - y₁           3 - 4           -1            1

m = ------------- = ------------ = --------- = --------

         x₂ - x₁          -3 - 0         -3           3

y - y₁ = m(x - x₁)

y - 4 = (1/3)(x - 0)

y - 4 = (1/3)x - 0

   +4            +4

----------------------------

y = (1/3)x + 4

I hope this helps!

Answer:

C. translated 1 unit to left and then rotated 180° counterclockwise about the

origin

Explanation:

In the graph:

• The vertices of Figure A are: (0,4), (-9,3) and (-9,6)

• The vertices of Figure A' are: (1,-4), (10,-3) and (10,-6)

If Figure A is translated 1 unit to the left, the vertices are:

Next, a rotation of 180° counterclockwise about the origin gives:

These are the vertices of Figure A'.

Thus, the correct transformation is: translated 1 unit to left and then rotated 180° counterclockwise about the origin.

The correct choice is C.

She uses 800 mL of solution A; that is, 2% of those 800 mL is alcohol

Alcohol on a:

2% of 800 = 2*800/100 = 16mL

If we use x mL of b, the amount of alcohol is:

5% of x = 5*x/100 = x / 20

Total amount of alcohol: 16 + x/20

Total amount of solution mixture: 800 + x

The ratio:

(16 + x/20) / (800 + x) = 3%

(16 + x/20) / (800 + x) = 3/100

1600 + 5x = 2400 + 3x

Solving for x:

5x - 3x = 2400 - 1600

2x = 800

x = 400 mL

She used 400 mL of solution b

y = x - 3

y = - x -1

They intersect at

Answer:

y = (-3/5)x - (31/5)

Step-by-step explanation:

3x + 5y = 11

-3x              -3x

------------------------------

5y = -3x + 11

÷5    ÷5    ÷5

-----------------------

y = (-3/5)x + (11/5)

y - y₁ = m(x - x₁)

y - (-5) = (-3/5)(x -(-2))

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

y + 5 = (-3/5)x - (6/5)

    -5                 -5

-----------------------------------

y = (-3/5)x - (31/5)

I hope this helps!

Answer:

B

Step-by-step explanation:

If we look at the x-axis, the function increases and decreases. Therefore, the domain is all real numbers.

If we look at the y-axis, the same is occurring. Therefore the range is also all real numbers.

The y-intercept of the line that passes through points (-2,6) and (1,6) in an ordered pair is ( 0,6 ).

The formula for equation of line is expressed as;

y = mx + b

Where m is slope and b is y-intercept.

The slope of a line is expressed as change in y over change in x.

Slope m = (y₂-y₁)/(x₂-x₁)

Given the data in the question;

Point A ( -2,6 )

Point B ( 1, 6 )

First, we determine the slope of the line.

Slope m = (y₂-y₁)/(x₂-x₁)

Slope m = ( 6 - 6 )/( 1 - ( -2) )

Slope m = ( 0 )/( 1 + 2) )

Slope m = ( 0 )/3

Slope m = 0

Now, we can determine the y-intercept b, using the slope and coordinates of 1 point.

y = mx + b

6 = (0)(1) + b

Solve for b

6 = 0 + b

b = 6

Therefore, the coordinates of the y-intercept is ( 0,6 ).

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Answer:

a₂ = 12.5 m/s²

Step-by-step explanation:

Applying the 2º Newton's Law:

∑F = m * a

F₁ = m₁ * a₁

F₁ = m₁ * 12.5

F₁ = 12.5m₁

F₂ = m₂ * a₂

2F₁ = 2m₁ * a₂

a₂ = F₁ / m₁

So:

a₂ = 12.5m₁ / m₁

a₂ = 12.5 m/s²

By solving a system of equations we can see that Olivia spent $14 and Camiller spent $37.

Let's define two variables:

We know that " Camille spent $14 less than three times what Olivia spent" so we can write:

y = 3*x - 14

And "In total, they spent $54"

x + y = 54

Then we have a system of equations:

y = 3*x - 14

x + y = 54

Replacing the first equation into the second one, we get:

x + 3x- 14 = 54

4x - 14 = 54

4x = 54 + 14

4x = 68

x = 68/4 = 17

Now that we know the value of x, we can try to find the value of y.

y = 3x - 14 = 3*17 - 14 = 37

So Olivia spent $14 and Camiller spent $37.

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iven:

here are givren the expression:

xplanation:

o find the coefficient of the given expression, we need to use the binomial expansion formula:

So,

From the formula of binomial expansion:

then,

After using the above formula in the given binomial, the expansion will be:

inal answer:

ence , the coefficient of the given term is shown below:

Answer:

t=44 hrs.

Step-by-step explanation:

1. a. you are asked to find the total hours the 2 girls work in a week.

b. it needs to be a greater number than 26

2. variables: h= hours per week

t= total hrs.

3. h= hrs. per week

t= total hrs.

4. 44=26+h

-26 -26

18=h

5. 44=26+18

44=44

6. The total hours the two work in a week is 44 hours.

Answer:

False

Step-by-step explanation:

The dependent variable changes, the size of the order will change depending on how many employes want a shirt.

Answer: Provided the geometric diagram, we have to find the unknown angle DCF.

Assuming, that the line segments AC and EF are parallel and the same is true for the line segments DE and CB.

The new diagram is:

Therefore the answer is:

or 61 degrees.

The number 25×10 to the power of -3 written in the standard form is 2.5×10⁻⁴.

The given number is;

25×10 to the power of -3

This can be written as;

= 25×10⁻³

Now, as per the standard form, the number should contain only one digit to the left of decimal.

Thus, shifting one decimal to the left of the 5 and converting the power by adding one to the current power,.

The number becomes;

= 2.5×10⁻⁴.

Thus, the number written in the standard form is 2.5×10⁻⁴.

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Answer:

Step-by-step explanation:

1/2 to 1 day is 2 1/2

11/3 x 11/3 = 121/9

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