alexio has $100$ cards numbered $1$-$100$, inclusive, and places them in a box. alexio then chooses a card from the box at random. what is the probability that the number on the card he chooses is a multiple of $2$, $3$ or $5$? express your answer as a common fraction.

The length of the rectangular solid delivery box is 6 inches.

Volume of a rectangular solid, multiply its 3 dimensions: length x width x height. The volume is expressed in cubic units

It is given that, the volume of the delivery box is 540 cubic inches, the width of the delivery box is 3 inches longer than the length and the height is 4 inch longer than the length.

Width of the rectangular solid delivery box = (length + 3) inches

Height of the rectangular solid delivery box = (length + 4) inches

Now,

let us assume that the length of the rectangular solid delivery box is X.

So, Width = (X+3) inches and Height = (X+4) inches.

Volume of rectangular solid delivery box = Length × Width × Height

=> Length × Width × Height = 540 cubic inches.

After putting all the values in the above equation,

=> X × (X+3) × (X+4) = 540

=> X=6 inches

Therefore, the length of the rectangular solid delivery box is 6 inches.

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Answer:16

explanation:

=64⅔

=(4)3×⅔(there is 3 and 3 will be cancel)

=(4)²(4²=4×4)

=16 Ans

Answer:

56 packs of seeds

Step-by-step explanation:

To find the area of Chang's backyard, we can use the formula for an area of a rectangle.

Area = length·width or A = lw

32·21 = 672 sq ft.

To find how many packets of seed he will need to cover the backyard, we can take the area of Chang's yard and divide it by how many square feet each pack of seed covers.

672/12 =  56

Chang will need 56 packs of seeds to cover the backyard.

Answer: (0,0)

Step-by-step explanation:

[tex]\displaystyle\\\left \{ {{(x-2)^2+y^2=4} \atop {(x+2)^2+y^2=4}} \right. \\Hence,\\(x-2)^2+y^2=(x+2)^2+y^2\\(x-2)^2=(x+2)^2\\x^2-2*x*2+2^2=x^2+2*x*2+2^2\\-4x=4x\\-4x+4x=4x+4x\\0=8x\\[/tex]

Divide both parts of the equation by 8:

[tex]0=x[/tex]

Hence,

[tex](0+2)^2+y^2=4\\2^2+y^2=4\\4+y^2=4\\y^2=0\\y=0\\Thus,\ (0,0)[/tex]

Answer:

The two circles intersect at one and only point A(0 , 0)

Step-by-step explanation:

Let ς₁ be the circle of equation :

ς₁ : (x - 2)² + y² = 4

and ς₂ be the circle of equation :

ς₂ : (x + 2)² + y² = 4 

Consider the point M (x , y) ∈ ς₁∩ς₂

M  ∈ ς₁ ⇔ (x - 2)² + y² = 4

M  ∈ ς₂ ⇔ (x + 2)² + y² = 4

M (x , y) ∈ ς₁∩ς₂ ⇒ (x - 2)² + y² = (x + 2)² + y²

⇒ (x - 2)² = (x + 2)²

⇒ x² - 4x + 4 = x²+ 4x + 4

⇒  - 4x = 4x

⇒  8x = 0

⇒  x = 0

Substitute x by 0 in the first equation:

(0 - 2)² + y² = 4

⇔ 4 + y² = 4

⇔ y² = 0

⇔ y = 0

Conclusion:

The two circles intersect at one and only point A(0 , 0).

The solution to the equation is, v = 2.

See the steps explained below.

Given an equation, 7(v - 5) = -21, the following steps would be taken as shown below:

7(v - 5) = -21 ---> Given

7v - 35 = -21 ----> distribution property

7v - 35 + 35 = -21 + 35 -----> addition property of equality

7v = 14

Divide both sides by 7

7v/7 = 14/7 -----> division property of equality

v = 2

Thus, the solution to the equation as solved above is: v = 2.

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Answer:

A) x = 225 - 7.5p

B) x = 180 millions of gallons

Step-by-step explanation:

A) Make "x" the subject:

[tex]\sf \rightarrow 0.4x + 3p = 90[/tex]

[tex]\sf \rightarrow 0.4x = 90-3p[/tex]

[tex]\sf \rightarrow x = \dfrac{90-3p}{ 0.4}[/tex]

[tex]\sf \rightarrow x = 225-7.5p[/tex]

B) Demand when the price per gallon is $6:

substitute p = 6

[tex]\sf \rightarrow x = 225-7.5(6)[/tex]

[tex]\sf \rightarrow x = 225-45[/tex]

[tex]\sf \rightarrow x =180[/tex]

Velocity is 5m/s.

In the given statement is :

You walk down a hill for 45 meters. You accomplish this in 9 seconds. What is your velocity? ______m/s.

Firstly, Let's know the:

What is Velocity?

Velocity refers to the rate of change in displacement with respect to time.

Furthermore, distance and displacement are the key points of the velocity.

Now, Calculate the velocity, by using formula of Velocity

Velocity = Displacement/ time

And, Velocity = 45/9 = 5m/s.

Therefore Velocity is 5m/s

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Using the concepts of similarity and congruence, the correct statement is given by:

a. Q and W are similar but not congruent.

For this problem, we have that:

Hence the correct statement is given as follows:

a. Q and W are similar but not congruent.

From the two bullet points, we justify we the other statements are not correct.

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Answer:

10 MPH

Step-by-step explanation:

Doug entered a canoe race. He rowed 3 1/3 miles in 1/3 hour. What is his average speed in miles per hour?​

If Doug rowed 3 1/3 miles in 1/3 hour the equation is:

3 1/3x = 1/3

multiply both sides by 3:

3(3 1/3x) = 3(1/3)

10x = 1 hour

Doug rowed 10 MPH

Answer:

10 mile per hour

Step-by-step explanation:

3 1/3 mile = 3.3333333333333333333333333333333 mile

1/3 hour = 0.3333333333333333333333333333333333 hour

divide 3.33333333333333333333333 by 0.3333333333333333333333333
= 3.333333333333333333333333333333333 * 1/.33333333333333333333
= 3.3333333333333333333333333 * 3
= 9.99999999999999999999999
= 10

To one decimal place, round. points A(-4, 6), B(3, -7), E(-6, -5) and F (2, 0).

The distance between AB is [tex]\sqrt{185}[/tex]=13.601 and EF is [tex]\sqrt{89}[/tex]=9.433.

Given that,

To one decimal place, round.

A(-4, 6), B(3, -7), E(-6, -5) and F (2, 0).

We have to find the distance between two points that are AB and EF.

1. The distance between 2 points A and B.

A(-4, 6) and B(3, -7).

Distance formula is [tex]\sqrt{(x_{2} -x_{1} )^{2} +(y_{2} -y_{1} )^{2} }[/tex]

Here, x₁=-1,x₂=3 and y₁=6,y₂=-7

After substituting we get,

[tex]\sqrt{{(3 -(-1)} )^{2} +(-7 -6 )^{2} }\\[/tex]

[tex]\sqrt{{(3 +1} )^{2} +(-7 -6 )^{2} }\\[/tex]

[tex]\sqrt{{(4} )^{2} +(-13 )^{2} }\\[/tex]

[tex]\sqrt{16 +163}\\[/tex]

[tex]\sqrt{185}[/tex]

13.601

Therefore, the distance between AB is [tex]\sqrt{185}[/tex]=13.601.

2.The distance between 2 points E and F.

E(-6, -5) and F (2, 0).

Distance formula is [tex]\sqrt{(x_{2} -x_{1} )^{2} +(y_{2} -y_{1} )^{2} }[/tex]

Here, x₁=-6,x₂=2 and y₁=-5,y₂=0

After substituting we get,

[tex]\sqrt{{(2 -(-6)} )^{2} +(0 -(-5) )^{2} }\\[/tex]

[tex]\sqrt{{(2 +6} )^{2} +(0 +5 )^{2} }\\[/tex]

[tex]\sqrt{{(8} )^{2} +(5 )^{2} }\\[/tex]

[tex]\sqrt{64 +25}\\[/tex]

[tex]\sqrt{89}[/tex]

9.433

Therefore, the distance between EF is [tex]\sqrt{89}[/tex]=9.433.

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Answer: y = 3x+1

Step-by-step explanation: If (4,1) is a solution of y = 3x+1, that means if we plugin the respective values of (4,1), we should have an EQUALITY:

1 = 3(4) + 1

1 = 13 , which is wrong, then the point (4,1) is NOT a solution of y = 3x+1.

The total cost = $5000 (Option A) and $9400 (Option B)

Cost per mile = $0.33 (option A) and $0.25 (Option  B)

A single unit's value can be determined from the values of multiple units, and multiple units' values can be determined from the values of single units using the unitary method.

Given:

To find: Total costs and cost per mile, when the truck is driven (A) 15000 miles per year (B) 37000 miles per year.

Finding:

(A) By unitary method,

When the truck is driven 1 mile, cost of gasoline = $0.20

When the truck is driven 15000 miles, cost of gasoline = $ 0.20(15000) = $3000 in an year

Cost of insurance in an year = $2000

Thus, total cost = $ 3000 + $2000 = $5000

Now, for per mile cost:

Cost of gasoline = $0.20

Cost of insurance = $0.13

Thus, Cost per mile = $0.20 + $0.13 = $0.33

(B) Again, by unitary method,

When the truck is driven 1 mile, cost of gasoline = $0.20

When the truck is driven 37000 miles, cost of gasoline = $ 0.20(37000) = $7400 in an year

Cost of insurance in an year = $2000

Thus, total cost = $ 7400 + $2000 = $9400

Now, for per mile cost:

Cost of gasoline = $0.20

Cost of insurance = $0.5

Thus, Cost per mile = $0.20 + $0.5 = $0.25

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Probability of getting a head is 60%

More heads than tails means these possibilities are

2 Heads - 1 Tail

3 Heads - 0 Tails

Probability of 2 Heads and 1 Tail =   C (3,2) (.60) ^2 (.40)  

=3 * (.36) (.40)  

=3 * .144

=3 (144/1000)  

=3 (18/125)

=54/125

Probability of 3 Heads = (.60) ^3

= .6 (.36)

= .216 = 216 / 1000

= 27 / 125

Hence, total probability =   54 / 125 + 27 / 125

= 81 / 125

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The inequality sign have to be flipped when dividing by a negative number.

The relation between two expressions that are not equal, employing a sign such as ≠ ‘not equal to’, > ‘greater than’, or < ‘less than’.

Given:

The given statement is the inequality sign have to be flipped when dividing by a negative number.

According to given question we have

A number that is larger when positive becomes "more negative," and thus smaller when negative, and vice versa.

Dividing by a negative number is the same as dividing by a positive number and then multiplying by −1. Dividing an inequality by a positive number retains the same inequality. But, multiplying by −1 is the same as switching the signs of the numbers on both sides of the inequality, which reverses the inequality:

a<b⟺−a>−b.

Ex:

when dividing both sides by a negative number, we reverse the inequality sign.

Take −3x<9

To solve for x, we divide both sides by −3 and get

x>−3.

Therefore, the inequality sign have to be flipped when dividing by a negative number.

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Answer:-4 is your answer

Step-by-step explanation: When x = 8 your y = –4 (which is the function)

Answers:

   16.50     for the first box

    10         for the second box

======================================

Explanation:

Part (a)

Plug in x = 20 and solve for p.

0.2x+4p = 70

0.2*20+4p = 70

4 + 4p = 70

4p = 70-4

4p = 66

p = 66/4

p = 16.50

They should charge $16.50 per gallon if the demand is 20 million gallons.

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

Part (b)

Let's say the price is initially $10 per gallon. The starting price could be anything you want.

Plug p = 10 into the equation and solve for x.

0.2x+4p = 70

0.2x+4*10 = 70

0.2x + 40 = 70

0.2x = 70-40

0.2x = 30

x = 30/(0.2)

x = 150

The demand is 150 million gallons if the price were $10 per gallon.

Now let's increase the price by $0.50 to get to p = 10.50

Let's solve for x based on this larger value of p.

0.2x+4p = 70

0.2x+4*10.50 = 70

0.2x+42 = 70

0.2x = 70-42

0.2x = 28

x = 28/(0.2)

x = 140

The demand is now 140 million gallons if the price were $10.50 per gallon.

The demand has gone down by 10 million gallons (since 150-140 = 10).

Answer:

the answer is B

Step-by-step explanation:

The set of inequalities that represents the constraints of the situation is y ≤ 2x, x + y ≥ 30 and a point (x, y) that is the feasible region is (10, 20)

The given parameters are:

Number of hours = at least 30 hours a week

This means that

x + y ≥ 30

Also, we have:

The number of hours Daniel works as a tutor (y) is at most twice the number he works as a teacher (x).

This means that

y ≤ 2x

Substitute y ≤ 2x in x + y ≥ 30

x + 2x ≥ 30

This gives

3x ≥ 30

Divide

x ≥ 10

Substitute x ≥ 10 in y ≤ 2x

y ≤ 2 x 10

Evaluate

y ≤ 20

Hence, the set of inequalities that represents the constraints of the situation is y ≤ 2x, x + y ≥ 30 and a point (x, y) that is the feasible region is (10, 20)

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Answer:2.35

Step-by-step explanation:

The value of the expression is 2.35.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

9.4 ÷ 4

= 9.4/4

= 94/(10 x 4)

= 94/40

= 2.35

Thus,

The value of the expression is 2.35.

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Answer:

the last two because it needs to be negative

Answer:

The last 2 options

Step-by-step explanation:

4(-15) = -60.

(–1)(15 + 15 + 15 + 15) = -60.

(–15) + (–15) + (–15) + (–15) = -60.

The images of points are

From the question, we have the coordinate of point A to be

A = (-4, 3)

The sequence of transformations is given as:

180 degrees rotation around the origin

The rule of the above transformation is

(x, y)= (-x, -y)

So, we have

A' = (4, -3)

This means that

B = (4, -3)

Hence, the image of point B after the transformation of the point A is (4,- 3)

From the question, we have the coordinate of point A to be

A = (-4, 3)

The sequence of transformations is given as:

The rules of the above transformations are

Translation two units to the right

(x, y)= (x + 2 , y)

So, we have

A' = (-2, 3)

Reflection across the x-axis

(x, y)= (x, -y)

So, we have

A'' = (2, -3)

This means that

C = (2, -3)

Hence, the image of point C after the transformation of the point A is (2, -3)

From the question, we have the coordinate of point A to be

A = (-4, 3)

The sequence of transformations is given as:

The rules of the above transformations are

Reflection across the y-axis

(x, y)= (-x, y)

So, we have

A' = (4, 3)

Translation two units to the right

(x, y)= (x + 2 , y)

So, we have

A'' = (6, 3)

This means that

D = (6,3)

Hence, the image of point D after the transformation of the point A is (6,3)

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Answer:

See below

Step-by-step explanation:

For x :    from end point to midpoint  0====> 4    is 4 units ...add 4 more to get   x = 8 for other endpoint

For y    5====> -4   is - 9     add  -9 more to midpoint to get y = -13

The values of the functions are h(0) = 1, h(10) = 3, h(-3) = 7 and h(3) = 4

The piecewise function is given as:

h(x) = {7, when x<0

         {x+1, when 0 ≤x ≤4

          {√x-1, when x>4

Next, we solve the function values

1. Function h(0)

This means that x = 0

To do this, we make use of h(x) = x + 1 because x= 0 is in its domain

So, we have

h(0) = 0 + 1

h(0) = 1

2. Function h(10)

This means that x = 10

To do this, we make use of h(x) = √x - 1 because x= 10 is in its domain

So, we have

h(10) = √10 - 1

h(10) = √9

h(10) = 3

3. Function h(-3)

This means that x = -3

To do this, we make use of h(x) = 7 because x= -3 is in its domain

So, we have

h(-3) = 7

4. Function h(3)

This means that x = 3

To do this, we make use of h(x) = x + 1 because x= 3 is in its domain

So, we have

h(3) = 3 + 1

h(3) = 4

Hence, the values of the functions are h(0) = 1, h(10) = 3, h(-3) = 7 and h(3) = 4

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Clara is 2700 yards far from the home.

In mathematics, yard and inches are two different  units of length. we can say that yard is the one of the measurement of length. Conversion of yard in various quantities is as below:

       1 yard = 36 inches

       1 yard = 3 feet

       1 yard = 0.914 meters

For the statement based question first of all try to find out that what is given in the statement and what we have to find out. Now, try to form the statements in the mathematical notation and then solve the equations by performing certain mathematical and algebra operations according to need.

Now, for the given question :

as, Clara  is 450 yards from the local swimming pool on the map on her phone and the pool is 2/3 inch from her current location.

Therefore, the pool distance is 450 / (2/3) = 675 yards

Now, distance of current location = 4 inches

Thus, Distance from the home = 675 × 4 = 2700 yards

Hence, Clara is 2700 yards far from the home.

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Answer:

4.5 lb of coffee

Step-by-step explanation:

4.5/20.25

The location of the x value of R' after using the translation rule is 28

The translation rule is given as:

(x + 4, y - 7)

The pre-image of R is located at (24, -13)

Rewrite as

R = (24, -13)

When the translation rule is applied, we have:

R' = (24 + 4, -13 - 7)

Evaluate

R' = (28, -20)

Remove the y coordinate

R'x = 28

Hence, the location of the x value of R' after using the translation rule is 28

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Answer:

x^2y^2(x^2 − 2xy) ..............

The rewritten polynomial of x⁴y² - 2x³y³ is x²y²(x²-2xy).

The greatest number that can divide the numbers in equal parts.

It is called as greatest common factor.

We have a polynomial,

x⁴y² - 2x³y³.

Factor out the common terms,

x⁴y² - 2x³y³,

= x²y²(x²-2xy)

Therefore, x²y²(x²-2xy) is the required expression.

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