Point X is chosen at random on AE-. Find the probability that X is on CE- .

The result of the algebraic expression 2x-3y for x=3 and y=-2 is 12

Given,

The algebraic expression = 2x-3y

x= 3

y= -2

Substitute the values in the expression

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

=6+6

=12

Hence, the result of the algebraic expression 2x-3y for x=3 and y=-2 is 12.

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3/13 is the probability of following event. The card is a face card.

In statistics, what does a probability mean?

Total no.of cards = 52

Let A be the event of taking face card.

No.of face cards = 4×3 = 12

Now n(S)= 52C1 = 52, n(A) = 12C1 = 12

So P(A) = n(A)/n(S) = 12/52 = 3/13

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Answer:

The 3 integers are 6 8 and 10

Step-by-step explanation:

Comment

Start with the median. That's the middle number of an ordered set of numbers.

a 8 b               is what you have so far.

Now the range between a and b is 4 which means that a and b differ by 4.

a + 4 =  b

The mean will solve this quickly. Put a + 4 for b

[(a + 8  + a + 4)]/3 = 8            Combine like terms

(2a + 12)/3 = 8                       Multiply both sides by 3

3 (2a + 12)/3 = 8 *3              

2a+12 = 24                            Subtract 12 from both sides

2a + 12 - 12 = 24-12               Combine

2a = 12

a = 6

but we know that the range between a (which is 6 ) and b is a + 4 = 10

So b must equal 10

The algebraic expression of the piggy bank contained $25 and $1.50 is added each days is 25+1.50x

Given,

The piggy bank contained = $25

The amount added in each day = $1.50

Consider number of days as x

Then the algebraic expression = 25+1.50x

Hence, the algebraic expression of the piggy bank contained $25 and $1.50 is added each days is 25+1.50x

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Answer:16

Step-by-step explanation:

since the increase is 2 units for purple counters

8 ÷ 2 = 4

4×4=16

Answer:

Step-by-step explanation:492 is needed right,and Kevin has 333 glass.So you need 159 glasses,but you need to find out how many sets you need to get 492 glasses.If 18 glasses comes in a set you'll need to divide 159 by 18 and get 8.83333333333. Then simplefiy the number to 8.8

The simplified expression for (16-12 / 15-11) is 1 .

The given expression is,

( 16-12 / 15-11 )

First we need to solve the numerator which is (16-12) and on simplifying the numerator we can write,

Numerator = ( 16 - 12 ) = 4                         equation 1

Similarly, now we can proceed to solve the denominator which is (15 - 11) and on simplifying the denominator we write,

Denominator  = (15 - 11) = 4                       equation 2

Now we can substitute the value of numerator and the denominator from equation 1 and equation 2 in the given expression ( 16-12 / 15-11 ) as,

(Numerator / Denominator) = (16-12 / 15-11) = (4/4) = 1

The simplified expression for (16-12 / 15-11) is 1 .

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The piecewise function that best models her weekly pay h(t) is given by:

A piecewise-defined function is a function that has different definitions, depending on the input of the function.

For this problem, we have that:

Her weekly pay is calculated differently according to the number of hours worked, divided into two cases as follows:

For up to 40 hours, she receives the standard wage of $12, hence:

h(t) = 12t, 0 ≤  t ≤ 40.

For more than 40 hours, she receives $12 x 40 = $480 plus 1.5 x $12 = $18 per hour worked, hence:

h(t) = 480 + 18t.

Hence the piecewise function that best models her weekly pay h(t) is given by the following definition, from the equations that we found prior in this problem:

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Answer:

z = - 1 , z = 5

Step-by-step explanation:

| 3z - 6 | = 9

the absolute value function always gives a positive result, however, the expression inside can be positive or negative, that is

3z - 6 = 9 ( add 6 to both sides )

3z = 15 ( divide both sides by 3 )

z = 5

or

- (3z - 6) = 9

- 3z + 6 = 9 ( subtract 6 from both sides )

- 3z = 3 ( divide both sides by - 3 )

z = - 1

As a check

substitute these values into the left side of the equation and if equal to the right side then they are the solutions.

x = 5

| 3(5) - 6 | = | 15 - 6 | = | 9 | = 9 = right side

x = - 1

| 3(- 1) - 6 | = | - 3 - 6 | = | - 9 | = 9 = right side

then solutions are z = - 1 , z = 5

The statement given is true.

If the sum of tine acute angles of a triangle is greater than 90 , then the triangle is acute.

The acute angle can be defined as the angle  less than 90°. Or we can say that the angle which is between 0° and 90° is called as an acute angle of a triangle. In the triangle all the angles gives the sum of 180 degree, that means, at least two angles in every triangle are always acute angles.

According to statement given in the question. This statement is absolutely true. If the sum of two acute angle is greater than 90 then the third angle of that polygon i.e. triangle must be less than 90 which makes the whole triangle a acute . Since, all the angles are now acute angles that means less than 90 thus this made the triangle as a acute triangle.

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The given inequality can be graphed by solving the inequation first.

What is an inequality?

Inequality is defined as an equation that lacks an equal sign. Inequality is a phrase that defines the relative magnitude of a statement and may be used to compare these two statements.

The given inequality can be solved as

[tex]5y\geq -x-32[/tex]

[tex]for, x=1, 5y\geq -1-32[/tex]

[tex]or, 5y\geq -33[/tex]

[tex]or, y=\frac{33}{5}[/tex]

Solve for two more values of x and then plot the inequality on the graph

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Answer:

They are easier to compare because you don't have to simplify in your head or change denominators to make two fractions comparable.

Step-by-step explanation:

Answer: It is $4429 (interest combined) or $1107.25 (interest annually)

Step-by-step explanation:

1. Subtract 13400 from 17829:
17829 - 13400 = 4429

2. Now, we know that 4429 is the accumulated interest in 4 years, now divide 4429 by 4:
4429/4 = 1107.25

3. Now we know that 1107.25 is the interest accumulated every year.

Answer:

A′(2, −2), B′(−3, 3), C′(5, 2)  (2nd choice)

Step-by-step explanation:

Rotating a point 270° clockwise about the origin is the same as rotating the point counterclockwise by 90°

In either case, the coordinates of any point (x, y) become new coordinates (-y, x)

I will summarize the original and rotated points,.

Original          Rotated
Point(x, y)       Point(-y, x)        Remarks
--------------       --------------         -------------                            
A(-2, -2)          A'(2,  -2)            eliminates 1st and 3rd choices
B( 3,  3)           B'(-3,  3)            no luck, both 2nd and 4th choices have this
C(2, -5)           C'( 5, -2)            only the 2nd choice fits all three

Answer: A′(2, −2), B′(−3, 3), C′(5, 2)

The coordinates of triangle A′B′C′ after rotating triangle ABC 270° clockwise are A′(2, −2), B′(−3, 3), and C′(5, 2).

The correct answer is (A).

The coordinates in a graph indicate the location of a point concerning the x-axis and y-axis.

The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.

We have,

To rotate a point (x,y) 270° clockwise about the origin,

We can use the formulas:

x' = y and y' = -x.

So, to rotate triangle ABC 270° clockwise, we need to apply these formulas to each vertex:

A' = (-2, 2) rotated 270° = (2, -2)

B' = (3, 3) rotated 270° = (-3, 3)

C' = (2, -5) rotated 270° = (5, 2)

Therefore,

The coordinates of triangle A′B′C′ after rotating triangle ABC 270° clockwise are A′(2, −2), B′(−3, 3), and C′(5, 2).

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Answer: Large number: 36

Smaller number: 9

Step-by-step explanation:

The summation notation for given arithmetic series is ∑21-2n , where n starts from 0.

The given series is 21+19+17+ . . .

On looking at the series we can easily notice that there is an decrease of 2 from one term to the next successive term.

So the formula will be (-2n +/- something).

Our first term is 21 and then decrease of 2, So we can say that the formula will be (21 - 2n) and n starts from 0.

So if n=0, our first term is 21

If n=1, our second term is 19

If n=2, our third term is 17

and so on.

So, we have the expression (21 - 2n).

The summation notation for given arithmetic series is ∑21-2n , where n starts from 0.

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Answer:9

Step-by-step explanation:

The volume of a cone that has a diameter of 10 inches and height of 2 inches in terms of pi 50/3pi cubic inches

The formula for calculating the volume of a cone is expressed according to the formula

V = 1/3 pir²h

where

r is the radius of the cone = 10/2 = 5in

h is the height = 2in

Substitute to have;

V = 1/3pi(5)² × 2

V = 50/3pi

Hence the volume of a cone that has a diameter of 10 inches and height of 2 inches in terms of pi 50/3pi cubic inches

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Answer:7

Step-by-step explanation:

3-1= 2

5+2=7

Answer:

C polyatomic atoms

Step-by-step explanation:

The diver take her at a distance of 9.2 meters.

A resultant displacement can be used to quantify distance. It involves measuring the coordinate values of the beginning and ending positions. The distance is measured in quantities like meters, centimeters, kilometers, etc.

A diver descends 1.7 meters below the surface of the water while suspended 7.5 meters above it, according to the question.

According to fundamental mathematics, values that are less than zero can be represented as negative values.

She will thus descend (-1.7) meters as she dives below the surface.

The formula may now be expressed as follows: Total Distance = 7.5 - (-1.7) = 9.2 meters.

As a result, the diver descends 9.2 meters below the surface with her.

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Answer:

answer 2

Step-by-step explanation:

3*4=12

Answer:

B.  5^6 x 3^12

Step-by-step explanation:

(5^2 x 3^4)^3 =

5 x 5 x 3 x 3 x 3 x 3 =

25 x 81 =

2025

2025^3 =

8,303,765,625

Option B is correct because,

5^6 x 3^12 =

5 x 5 x 5 x 5 x 5 x 5 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 =

15,625 x 531,441 =

8,303,765,625

Answer:

8 kilometers

Step-by-step explanation:

8000/1000

= 8 kilometers.

The sale price of this refrigerator be including tax $1101.6 .

It is given that a  refrigerator that originally costs $ 1,200 it's on sale for 15% off.

Discount percentage = [(Discount)/(Marked price)]× 100

         15 = Discount / 1200 × 100

         15  = Discount / 12

       Discount = 15 × 12

                       = $ 180

Selling price = marked price - discount

                     = 1200 - 180

                     = $ 1020

The selling tax is given by = 8% 1020

                                            = 8 / 100 ×1020

                                             = $ 81.6

The total amount one has to pay to buy a refrigerator is = 1020 + 81.6

                                                                                             = $ 1101.6

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These are the description of the real numbers.

According to the statement

We have to explain all about the real numbers.

So, For this purpose, we know that the

Positive or negative, large or small, whole numbers, fractions or decimal numbers are all Real Numbers.

From the given information:

Real numbers are composed of the subsequent set of numbers : Whole numbers, natural numbers, integers, rational numbers and irrational numbers.

• Natural numbers include all positive numbers which can be used for ordering or counting. They include numbers from 1, till infinity.

• Whole numbers include all positive integer values including 0.

• Integer numbers are the set of all positive and negative integer values including 0. Examples are : (-1, 0, 8)

• Irrational numbers are non-integer values which can't be expressed within the form a/b. like (√5, 1.7171...)

Using the definitions above :

• 12 = Natural, integer , integer and rational (12/1)

• -15 = Integer, rational (-15/1)

• 1 1/2 = 3/2 = Rational

• 3.18 = rational (terminating decimal)

• root 48 = √48 = 6.928... = irrational(non-terminating and non-repeating)

• 9.3 = rational (terminating decimal)

• -2 7/9 = -25/9 = rational (a/b)

• root 25 = √25 = ±5 = integer, rational (5/1)

• root 3 = √3 = 1.732... real (non-terminating and non-repeating) .

• negative root 64 = - √64 = - 8 = integer, rational (-8/1)

• negative root 12 = - √12 = - 3.464... = irrational (non - terminating)

• 8/4 = 2 = natural, number, rational, integer

So, These are the description of the real numbers.

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The solution of the given linear equation in one variable (m-2)-5=8-2(m-4) is at m = 23/3.

According to the given question.

We have a linear equation in one variable

(m-2)-5=8-2(m-4)

As we know that, the linear equations in one variable is an equation which is expressed in the form of ax+b = 0, where a and b are two integers, and x is a variable and has only one solution.

Thereofre, the solution of the linear equation in one variable (m-2)-5=8-2(m-4) is given by

(m -2) -5 = 8 -2(m -4)

⇒ m -2 - 5 = 8 -2m + 8     (by distributive rule)

⇒ m -7 = 16 - 2m                   (adding and subtracting the line terms)

⇒ m + 2m = 16 + 7

⇒ 3m = 23

⇒ m = 23/3

Hence, the solution of the given linear equation in one variable (m-2)-5=8-2(m-4) is at m = 23/3.

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