Pablo randomly picks three marbles from a bag of seven marbles (four red ones, two green ones, and one yellow one).

How many outcomes are there in the sample space?
How many outcomes are there in the event that all of the marbles he picks are red?

Answer:

The tree is 30 feet

Step-by-step explanation:

Set up a proportion

[tex]\frac{height}{shadow}[/tex] = [tex]\frac{height}{shadow}[/tex]  Fill in what you know

[tex]\frac{x}{42}[/tex] = [tex]\frac{5}{7}[/tex]  Cross multiply

7x = 210  Divide both sides by 7

x = 30

Answer:

1. True

2. True

3. True

4. False

5. False

6. False

7. True

8. False

9. True

10. False

Step-by-step explanation:

∈ means "is an element of"

⊂ means "only contains some, but not all, the elements of"

⊆ means "only contains some, possibly all, the elements of"

If one of those symbols is strickenthrough, it simply means the opposite, e.g. "it's not true that it's an element of" or "it's not true that it only contains some, (...) the elements of"

∅ is an empty set

{ something } is a set containing everything inside the curly brackets. Thus, { } is an empty set.

Let's rewrite the statements:

1. 5 is an element of {1, 3, 5, 7, 9}

TRUE

2. 4 is not an element of {1, 3, 9}

TRUE

3. {5, 6, 7} only contains some, possibly all, the elements of {5, 6, 7}

TRUE

4. {1, 2, 3} only contains some, but not all, the elements of {1, 2, 3}

FALSE (it contains all)

5. it's not true that {9} only contains some, possibly all, the elements of {9, 10}

FALSE (it does only contain elements of {9, 10} )

6. it's not true that 8 is an element of {2,4,6,8,10}

FALSE (because it is an element of that set)

7. empty set only contains some, possibly all, the elements of empty set

TRUE (it contains only elements of empty set - all of them, namely none)

8. 0 is an element of empty set

FALSE (empty set is empty, so it cannot contain 0)

9. {13, 11} only contains some, but not all, the elements of {11, 12, 13}

TRUE (order is irrelevant)

10. {7, 8}  only contains some, possibly all, the elements of {8}

FALSE (7 is not an element of {8} )

the awnser: is 960 inches

Answer: False

Step-by-step explanation: If you multiply a fraction between 0 and 1 by another fraction between 0 and 1, the result would be smaller than 1.

For example,  [tex]\frac{3}{5} * \frac{1}{2} = \frac{3}{10}[/tex]

Answer:

  a.  Explicit: f(x) = 2x² +3. Recursive: f(-3) = 21; f(x) = f(x -1) +4x -2

  b.  Explicit: g(x) = 3x² -2x. Recursive: g(5) = 65; g(x) = g(x -1) +6x -5

Step-by-step explanation:

Given two tables of values, you want to find the explicit and recursive formulas for those values.

When the x-values are consecutive integers, as they are in these tables, it is usually useful to look at the first difference of the y-values. If those are constant, the table represents a linear function.

When the first differences are not constant, the exercise can be repeated. If the second differences are constant (as here), then the explicit formula will be a second-degree polynomial. The coefficients of the polynomial can be found different ways. We will describe one way here.

The constant second differences are double the leading coefficient of the quadratic that describes the relation between x and y. Knowing this, we can see how well the 2nd degree term by itself represents the relation. To that end, we have added to the table columns for the difference between the y-value and the 2nd degree term (y1 -ax^2), and the difference of those differences (diff).

The attachment shows the first second difference of the values of Table A is 4. That means our first approximation of the sequence will be (4/2)x². The next column shows us this is always 3 less than the value of y, so our explicit formula can be ...

  f(x) = 2x² +3

The attachment shows the first second difference of the values of Table B is 6. That means our first approximation of the sequence will be (6/2)x². Subtracting this from the value of y, we find an arithmetic sequence that has a common difference of -2, and a value of -10 when x=5.

The explicit formula for an arithmetic sequence with a first term a1 and a common difference d is ...

  an = a1 +d(n -1) . . . . . . where 1 is the x-value of the first term

Our sequence of differences doesn't start with x=1, but with x=5. This means our explicit formula will be ...

  g(x) = 3x² +(-10 +(-2)(x -5))

 g(x) = 3x² -2x

A recursive formula is one that expresses a given term as a function of previous terms of the sequence. When the sequence is 2nd degree, as here, we know the difference from one term to the next is an arithmetic sequence. Thus we can write the formula for a term as the sum of the previous term and a value that depends on the term number.

The explicit formula for the arithmetic sequence of differences has the form shown above. For the purpose here, the difference from the previous term is shown on the line above the x-value.

The applicable sequence of first differences has first term -10 and common difference 4. The first of the differences of consequence corresponds to x=-2, so can be written ...

  d(x) = -10 +4(x -(-2)) = 4x -2

Then the recursion relation is

  f(x) = f(x -1) +d(x) = f(x -1) +4x -2

And the recursive formula is ...

  f(-3) = 21; f(x) = f(x -1) +4x -2

The applicable sequence of first differences has first term 31 and common difference 6. The first of the differences of consequence corresponds to x=6, so can be written ...

  d(x) = 31 +6(x -6) = 6x -5

Then the recursive formula is ...

  g(5) = 65; g(x) = g(x -1) +6x -5

The simplified fraction is -2 1/4

From the question, we are to evaluate the given fractions

The given fraction is

[tex]-1\frac{4}{5} + (-\frac{1}{4}) + (- \frac{1}{5} )[/tex]

Evaluating the fraction

[tex]-1\frac{4}{5} + (-\frac{1}{4}) + (- \frac{1}{5} )[/tex]

First, convert the mixed fraction to an improper fraction

[tex]-\frac{9}{5} + (-\frac{1}{4}) + (- \frac{1}{5} )[/tex]

Now, clear the parentheses
[tex]-\frac{9}{5} -\frac{1}{4}- \frac{1}{5}[/tex]

Find the LCM of the denominators

The LCM is 20

Thus,

[tex]\frac{-36 - 5 - 4}{20}[/tex]

= [tex]\frac{-45}{20}[/tex]

= [tex]-2\frac{5}{20}[/tex]

= [tex]-2\frac{1}{4}[/tex]

Hence, the simplified fraction is - 2 1/4

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Answer:

3w - 4 1/2

Step-by-step explanation:

6(1/2w- 3/4)

distributing gives you

6/2w- 18/4

simplifying it gives you

3w-4 1/2

Answer:

Hello!

for 11 we can put in values

x = 0

y = 12 * 0^2

y=0

One point is (0,0)

x=1

y=12*1^2

y=12

Another point is (1,12)

x=-1

y = 12 * -1^2

y=12

A third point is (-1,12)

This tells us that this is not exponential since an exponential function as a steep curve on one side not two.

You can think of an exponential function as a half parabola if it helps.

13. We can plug in numbers again here.

x=0

y=7(0)+3

y=3

So the first point is (0,3)

x=1

y=7(1)+3

y=10

The second point is (1,10)

x=-1

y=7(-1)+3

y=-4

so the third point is (-1,-4)

This shows that the graph is not exponential it is linear since it goes in a straight line.

15. We just plug in -2 for t so

g(-2) = 2*0.4^-2

0.4^2 is 0.16 * 2 is 0.32 which is the answer

17. We can put 18 for w

h(18) = -0.5*4^18

This is where there is a issue because 4^18 is a extremely small number (6.9 * in scientific notation-

But we can multiply that by -0.5 to get

-3.4 *

which I believe is -0.000000034

Step-by-step explanation:

Answer:624

Step-by-step explanation:

Answer:

624

Step-by-step explanation:

Answer:

  (b)  22 in

Step-by-step explanation:

You want the perimeter of a rectangle with side lengths 4 inches and 7 inches.

The perimeter of a rectangle is the sum of the lengths of its sides. Your rectangle has two sides that are 4 inches, and two sides that are 7 inches. The perimeter is the sum of these lengths:

  P = 4 in + 4 in + 7 in + 7 in

  P = 22 in

The perimeter of the rectangle is 22 inches.

__

Additional comment

We can save a math operation by recognizing the sum can be arranged to ...

  P = (4 in +7 in) +(4 in +7 in) = 2(4 in +7 in)

This is evaluated using one sum and one product, rather than the three sums we need if we simply add the lengths of the four sides.

This is why the usual formula for the perimeter of a rectangle is ...

  P = 2(L +W)

Answer:

-2

Step-by-step explanation:

3−11−(−6)=

3-11= -8

-8-(-6)

the two minus become plus so

-8+6= -2

Answer:

exact form= 1/49

and the decimal form= 0.02040816

Step-by-step explanation:

We can conclude that no value of 'a' will make the equation an identity.

So, to get 0 = 0 to make the equation an identity, we have to get such a value of a that makes the LHS 8x - 16 which will be similar to RHS 8x - 16.

If we take a = 1 then the LHS will be less than the RHS as:

If we take a = 2 then:

If we take a = 3 then the LHS will be greater than the RHS as:

So, we can conclude that no value of 'a' will make the equation an identity.

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Using the fact that both triangles are similar, we will conclude that the measure of angle B is 59°.

First, two figures are similar if the figures have the same shape, then the interior angles are all the same in both figures.

Here we know that the two triangles are similar and thus, the internal correspondent angles of the two triangles are equal in measure.

First, there is a common vertex at C, so the angle there is the same for both triangles. We also can see that angles A and D have the same measure, then the angles B and b will also have the same measure.

And we know that the measure of angle b is 59°, then we can conclude that the measure of angle B will also be 59°, so the correct option is the first one.

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Using proportions, it is found that the coordinates of the other end of the fence are (-1,-7) when the start point is (8, 5) and the mid point is (3.5, -1).

A proportion refers to the fraction of the total amount, and the measures are related using a rule of three.

The midpoint of a segment refer to the mean of the coordinates of the endpoints, so we get that:

3.5 = (x + 8) / 2

x + 8 = 7

x = 7 - 8

x = - 1

-1 = (y + 5) / 2

y + 5 = -2

y = -2 - 5

y = - 7.

End point =- (-1, -7)

Therefore, using proportions, it is found that the coordinates of the other end of the fence are (-1,-7) when the start point is (8, 5) and the mid point is (3.5, -1).

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The value of a based on the information is 4.

It should be noted that b = 5.5

It should be noted that e = 10

There are three alphabets in between them. This means the difference will be:

= (10 - 5.5)/3

= 4.5/3

= 1.5

Therefore, the value of a will be:

= 5.5 - 1.5

= 4

The value of a is 4.

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The value of a based on the information is 4.

How to calculate the value?

It should be noted that b = 5.5

It should be noted that e = 10

There are three alphabets in between them. This means the difference will be:

= (10 - 5.5)/3

= 4.5/3

= 1.5

Therefore, the value of a will be:

= 5.5 - 1.5

= 4

The value of a is 4.

Answer: A conditional statement (also called an if-then statement) is a statement with a hypothesis followed by a conclusion. The hypothesis is the first, or “if,” part of a conditional statement. The conclusion is the second, or “then,” part of a conditional statement.

Step-by-step explanation:

Answer:

AB=5

Step-by-step explanation:

the steps are on top

Answer:

Option A on edge

Step-by-step explanation:

Its point W.

Answer:

x^2+12x=-11

Step-by-step explanation:

Answer:

(-1, 12) and (-11, 132)

Step-by-step explanation:

The number of boards it would take to cover the floor is 48

From the question, we are to determine how many boards it would take to cover the floor

From the given information,

The width of the floor is 248 in.

and

The width of the board is 5 1/6 in.

Thus,

The number of boards it would take to cover the floor is

248 ÷ 5 1/6

= 248 ÷ 31/6

= 248 × 6/31

= 1488/31

= 48

Hence, the number of boards it would take to cover the floor is 48

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The order of set of numbers {-415%, -√17, -4.1, -4.08} from least to greatest is {-415% < -√17 < -4.1 < -4.08}

Order of set of numbers:

Numerical order is a way of arranging a group of numbers into a sequence. This could be ascending or descending.

When we arrange numbers in ascending order, we arrange them from small to big, and when we arrange numbers from big to small, it is called descending order.

Given,

=> {-415%, -√17, -4.1, -4.08}

Here we need to convert the numbers into decimal for to arrange it,

First, we have to convert the value -415% into decimal,

=> -415%

=> -415/100

=> -4.15

Next, √17 is equal to,

=> -√17

=> -4.12

How we have to arrange them in order,

=> { -4.15< -4.12 < -4.1 < -4.08}

Which is equal to,

=> {-415% < -√17 < -4.1 < -4.08}

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The circumference is 150.72 millimeters and the area is 1808.64 square millimeters

The radius of the coin is given as

r = 12 millimeters

The diameter of the coin is calculated as

Diameter = 2 * r

So, we have

Diameter = 2 * 12 millimeters

Evaluate

Diameter = 24 millimeters

The circumference of the coin is calculated as

C = 2πr

So, we have

C = 2 * 3.14 * 24

Evaluate

C = 150.72 millimeters

The area of the coin is calculated as

A = πr²

So, we have

A = 3.14 * 24²

Evaluate

A = 1808.64 square millimeters

Hence, the circumference is 150.72 millimeters and the area is 1808.64 square millimeters

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Answer:

There are 16 cups in a gallon.

Step-by-step explanation:

Not sure what you're asking but there are 16 cups in a gallon.

The way a flow proof shows logical steps in the proof of a conditional statement is; A flow proof organizes statements in logical order, starting with the given statements. Each statement has its reason written below it and arrows are used to indicate the order of the statements.

A flow proof uses a diagram to show each statement leading to the conclusion. Arrows are drawn to represent the sequence of the proof. The layout of the diagram is not important, but the arrows should clearly show how one statement leads to the next. The explanation for each statement is written below the statement.

A flow proof organizes statements in logical order, starting with the given statements. Each statement has its reason written below it and arrows are used to indicate the order of the statements.

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Answer:

20

Step-by-step explanation:

The common factors for 60,40,20,80 60 , 40 , 20 , 80 are 1,2,4,5,10,20 1 , 2 , 4 , 5 , 10 , 20 . The GCF for the numerical part is 20 .

Answer:

r=30

Step-by-step explanation:

first expand:

4r+60+4r=300

8r+60=300

8r=300-60

8r=240

r=30

hope this works:)

Answer:

1/5, 1:5, 1 to 5

Step-by-step explanation:

The ratio is 3/15, but simplest form is 1/5.