The average of 12 numbers is 24. The average of 24 numbers is 12. What is the average of all 36 numbers?

Answer:

(- 5, - 7 )

Step-by-step explanation:

Equate f(x) and g(x), that is

2x + 3 = - 4x - 27 ( add 4x to both sides )

6x + 3 = - 27 ( subtract 3 from both sides )

6x = - 30 ( divide both sides by 6 )

x = - 5

Substitute x = - 5 into either of the 2 functions for y- coordinate

Substituting into f(x)

f(- 5) = 2(- 5) + 3 = - 10 + 3 = - 7

Thus point of intersection = (- 5, - 7 )

Answer:

x = 6

Step-by-step explanation:

2x + 3(3x - 5) = 51

Expand the brackets.

2x + 9x - 15 = 51

Add like terms.

11x - 15 = 51

Add 15 on both sides.

11x = 51 + 15

11x = 66

Divide both sides by 11.

x = 66/11

x = 6

The solution to the equation 2x+3(3x-5)=51 is x = 6

The equation is given as:

2x+3(3x-5)=51

Expand

2x + 9x - 15 = 51

Evaluate the like terms

11x = 66

Divide both sides by 11

x = 6

Hence, the solution to the equation 2x+3(3x-5)=51 is x = 6

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Answer: -32

Step-by-step explanation:

I'm just going to plug in and break down the equation to make it more understandable and easier to comprehend

-(3^2) - (4*3) -11

-(9)- (12) -11

-9 - 12 - 11

-21 -11

-32

Answer:

Step-by-step explanation:

y = -3x - 2

5x + 2y = 15

5x + 2(-3x -2) = 15

5x -6x - 4 = 15

-x - 4 = 15

-x = 19

x = -19

y = -3(-19) - 2

y = 57 - 2

y = 55

(-19, 55)

solution is b

Answer:

Step-by-step explanation:

Hello,

Factor x^2 + 64.

[tex]\boxed{x^2+64=x^2+8^2=x^2-8^2i^2=(x-8i)(x+8i)}[/tex]

Factor 16x^2 + 49.

[tex]\boxed{16x^2+49=(4x)^2-(7i)^2=(4x-7i)(4x+7i)}[/tex]

Find the product of (x + 9i)^2.

[tex]\boxed{(x+9i)^2=x^2+18xi+(9i)^2=x^2+18xi-81=x^2-81+18xi}[/tex]

Find the product of (x − 2i)^2.

[tex]\boxed{(x-2i)^2=x^2-4xi-4=x^2-4-4xi}[/tex]

Find the product of (x + (3+5i))^2.

[tex]\boxed{(x + (3+5i))^2=x^2+(3+5i)^2+2x(3+5i)=x^2+9-25+30i+6x+10xi}\\\boxed{=x^2+6x-16+(30+10x)i}[/tex]

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

The probability is 40%

Step-by-step explanation:

a) There are ten pieces of paper with ten numbers

Probability of selecting four pieces of paper = 4/10 or 40%

Probability that the four numbers selected will have a sum greater than 82 = 82/205 = 40%

Therefore, the probability of selecting four numbers that have a sum greater than 82 out of ten numbers totalling 205 is 40%.

b) Probability is the ratio of the number of outcomes favourable for the event to the total number of possible outcomes.   In other words, it is a measure of the likelihood of an event (or measure of chance).

Answer:

$84.80

Step-by-step explanation:

find the difference between accurate price and written price: 74 - 47 = 27

find written total (before Mrs. Taylor found mistake) by undoing the mean calculation: 82.55 x 12 = $990.60

the total expenses is $27 more than what they thought: 990.60 + 27 = 1017.60

divide accurate total by 12 to find mean: 1017.60 / 12 = $84.80

hope this helps :)

Answer:

27°

Step-by-step explanation:

Let line AB be extended to touch line DC at point F, thereby forming triangle BCF.

∠ABC + ∠BCE = 180° (sum of interior angles in a transversal).

∠ABC + 48 = 180

∠ABC = 180 - 48 = 132°

Also in triangle ADF, ∠ADF + ∠DFA + ∠FAD = 180 (sum of angle in a straight line)

85 + ∠DFA + 25 = 180

∠DFA + 110 = 180

∠DFA = 180 - 110 = 70

∠DFA = 70

∠DFA + ∠BFC = 180° (sum of angle on a straight line)

∠BFC + 70 = 180

∠BFC = 180-70 = 110

∠BFC = 110°

∠ABC + ∠CBF = 180° (sum of angle on a straight line)

132 + ∠CBF = 180

∠CBF = 1800 - 132 = 42

∠CBF = 42°

In triangle BCF:

∠BFC + ∠CBF + x = 180° (sum of angle in a triangle)

42 + 110 + x = 180

x + 152 = 180

x = 180 - 152

x = 27°

Answer:

22 Degrees

Step-by-step explanation:

First, i extended the line AB, to make a triangle and then i found out that the angle is 70 degrees, and from that i got that the other angle is 110 degrees, so now i know that the triangle (that has X in it) is this formula:

110+48+X=180

so now 180-158=22, so that is the answer

Answer:

x = 1, x = .333

Step-by-step explanation:

Answer:

x = 1 and x = 1/3

Step-by-step explanation:

Here the coefficients of this quadratic are a = 3, b = -4 and c = 1.

The discriminant is b^2 - 4ac, or (-4)^2 - 4(3)(1) = 16 - 12 = 4.

Thus, the roots are:

      -(-4) ± √4        4 ± 2

x = ---------------- = -------------   =>  x = 1 and x = 1/3

          2(3)                  6

Answer:

0.13

Step-by-step explanation:

First let's find the probability of finding the first species or the second species:

P(A or B) = P(A) + P(B) - P(A and B)

P(A or B) = 0.61 + 0.08 - 0.28

P(A or B) = 0.41

Then, to find the probability of finding one or another but not both, we just need the symmetric difference of the events, that is: P(A or B) - P(A and B):

P(A or B) - P(A and B) = 0.41 - 0.28 = 0.13

Answer:

B

Step-by-step explanation:

The range is all values of y. Y goes from -1 to 1. Please mark brainliest.

Answer:

see below

Step-by-step explanation:

The domain of the function is the possible x values

The domain is all real values since x can be any number

The range of the function is the possible y value

The values of y go from -1 to 1 so

-1 ≤y≤1

Answer:

12.5%

Step-by-step explanation:

There is only one number 5 from a total of 8 parts.

1 out of 8.

1/8 = 0.125

P(5) = 12.5%

Answer:

12.5%

Step-by-step explanation:

Spinner divided in parts = 8

Number 5 = 1

P(5) = 12.5%

Answer:

120 inches cubed

Step-by-step explanation:

The formula for finding the volume of a rectangular prism is length * width * height.

In this case, 8 inches long is the length, 5 inches is the width, and 3 inches is the height.

So multiplying all of those together gets you 120 inches cubed.

Answer:

Step-by-step explanation:

t=V100-50/4

t=V50/4=1.76≈1.8 s

when h=0

t=V100/4=10/4=2.5 s

Answer:  a) (5√2)/4 ≈ 1.77 seconds

               b) 5/2 = 2.5 seconds

Step-by-step explanation:

[tex]t=\dfrac{\sqrt{100-h}}{4}\\\\\\h=50\rightarrow t=\dfrac{\sqrt{100-50}}{4}\\\\\\.\qquad \qquad =\dfrac{\sqrt{50}}{4}\\\\\\.\qquad \qquad =\large\boxed{\dfrac{5\sqrt2}{4}}\\\\\\\\h=0\rightarrow t=\dfrac{\sqrt{100-0}}{4}\\\\\\.\qquad \qquad =\dfrac{\sqrt{100}}{4}\\\\\\.\qquad \qquad =\dfrac{{10}}{4}\\\\\\.\qquad \qquad =\large\boxed{\dfrac{5}{2}}[/tex]

Answer:

1/64

Step-by-step explanation:

1/4 × 1/4 × 1/4

Multiply the fractions.

1/4³

= 1/64

Answer:

The answer is 1/64.

Step-by-step explanation:

1/4 x 1/4 x 1/4 = 1/64

In other ways, you can write this as: 1/4³

Hope this helped!

Answer:

2m-9

Step-by-step explanation:

m-4+m-5

=m+m-4-5

=2m-9

Answer:

2m-9

Step-by-step explanation:

m-4+m-5

take the like terms

= 2m-4-5

= 2m-9

Sorry if that didn't help

Answer:

False

True

False

True

Step-by-step explanation:

Easiest and fastest way is to plug each equation into a calc and see if they match the values given. When you do so, you should get your answers.

Answer:

Graphed below.

Step-by-step explanation:

The slope of the line is -1/3.

The y-intercept is at (0, 2).

The x-intercept is at (6, 0).

Answer:

30, 150, 120, and 60 degrees

Step-by-step explanation:

Since the sum of the interior angles in a quadrilateral is 360 degrees:

y+5y+4y+2y=360

12y=360

y=30

2y=60, 4y=120, 5y=150

Hope this helps!

Step-by-step explanation:

y+5y+ 4y + 2y=360°(sum of a Quadrilateral)

12y=360°

divide both sides by 12

y=30°

5y=(5×30)=150°

4y=(4×30)=120°

2y=(2×30)=60°

Answer:

the correct answer is a reflection over the y axis

Step-by-step explanation:

The best description of the transformation shown will be;

''Reflection over the y - axis.''

What is Translation?

A transformation that occurs when a figure is moved from one location to another location without changing its size or shape is called translation.

Given that;

The transformation is shown in figure.

Now,

Clearly, A'B'C'D' is the mirror image of the ABCD across the y - axis.

So, The best description of the transformation shown will be;

''Reflection over the y - axis.''

Thus, The best description of the transformation shown will be;

''Reflection over the y - axis.''

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Answer:

A

90 degrees

anticlockwise.

Step-by-step explanation:

It looks much more complicated than it really is. I don't know how to explain this in any other form but to give the answers.

1 A

The center of rotation is where the 90 degree angle has its vertex. So that would be A.

1 B

Follow x. It rotates 90 degrees. So every point must rotate 90 degrees.

1 C

The direction is against the way the clock tells time, so the direction of rotation is anticlockwise.

Answer:

The roots are where the graph intercepts the x-axis

Step-by-step explanation:

Alternatively, you could factor and then solve algebraically.

Answer:

arccos (0.5) is [tex]\frac{\pi}{3}[/tex]

Step-by-step explanation:

With the arccos(0.5)  in this problem, you are asked which angle renders its cosine equal to 0.5 (or 1/2).

Recall that there are special angles in the unitary circle that render well know values like 1/2. There are two angle values between 0 and the full circle ([tex]2\pi[/tex] radians), that render cosine function equal 1/2, and they are: [tex]\frac{\pi}{3}[/tex], and [tex]-\frac{\pi}{3}[/tex].

The arccos uses just the first one as answer over the restricted domain between 0 and [tex]\pi[/tex], since otherwise it will not be considered a function.

So the answer is that the arccos (0.5) is [tex]\frac{\pi}{3}[/tex]

Answer:

1. Use a straightedge

2. Draw dots on the line to mark the starting point  

3. Place the point of the compass on the point you made or was given

4. Extend the compass so that the pencil is on the 2nd point & make a an arc thru point B

5. Place the compass point on the starting point dot on the line and draw w/ the pencil to create an arc crossing the line.

Answer:

Step 1: Mark the point that will be the vertex of the new angle, and label it P.

Step 2: Draw a ray from P in any direction, with any length. This ray will be one of the sides of the new angle.

Step 3: Place the compass point on the vertex of the original angle, and adjust the compass width to a convenient size.

Step 4: Use the compass to draw an arc intersecting both rays of the original angle at two points, J and K.

Step 5: Move the compass (without changing the width) to point P, and make an arc intersecting the existing ray of the angle. Mark the intersection point, and label it M.

Step 6: Set the compass point on the original angle at point J, and set its width to the length of line segment JK.

Step 7: Move the compass point to M on the new angle, and draw an arc cutting the previous arc. Mark the intersection point and label it L.

Step 8: Draw a ray from point P through point L. The new angle is a copy of the original angle.

Step-by-step explanation:

edmentum

Answer:

137

Step-by-step explanation:

sum of angle in a circle = 360°

105 + 118 + x = 360

223 + x = 360

x = 360 - 223

x = 137

Answer:

182.8125

Step-by-step explanation:

Given:

y = x^3

from [2,5] using 6 subdivisions

deltax = (5 - 2)/6 = 3/6 = 0.5

hence the subdivisions are:

[2, 2.5]; [2.5, 3]; [3, 3.5]; [3.5, 4]; [4, 3.5]; [4.5, 5]

hence the right endpoints are:

x1 = 2.5; x2 = 3; x3 = 3.5; x4 =4; x5 = 4.5; x6 = 5

now the area is given by:

A = deltax*[2.5^3 + 3^3 + 3.5^3 + 4^3+ 4.5^3 + 5^3]

A = 0.5*365.625

A = 182.8125

Area using Right Endpoint approximation is 182.8125

The area of the region is an illustration of definite integrals.

The approximation of the area of the region R is 182.8125

The given parameters are:

[tex]\mathbf{f(x) = x^3}[/tex]

[tex]\mathbf{Interval = [2,5]}[/tex]

[tex]\mathbf{n = 6}[/tex] ------ sub intervals

Using 6 sub intervals, we have the partitions to be:

[tex]\mathbf{Partitions = [2,2.5]\ u\ [2.5, 3]\ u\ [3,3.5]\ u\ [3.5,4]\ u\ [4,4.5]\ u\ [4.5,5]}[/tex]

List out the right endpoints

[tex]\mathbf{x= 2.5,\ 3,\ 3.5,\ 4,\ 4.5,\ 5}[/tex]

Calculate f(x) at these partitions

[tex]\mathbf{f(2.5) = 2.5^3 = 15.625}[/tex]

[tex]\mathbf{f(3) = 3^3 = 27}[/tex]

[tex]\mathbf{f(3.5) = 3.5^3 = 42.875}[/tex]

[tex]\mathbf{f(4) = 4^3 = 64}[/tex]

[tex]\mathbf{f(4.5) = 4.5^3 = 91.125}[/tex]

[tex]\mathbf{f(5) = 5^3 = 125}[/tex]

So, the approximated value of the definite integral is:

[tex]\mathbf{\int\limits^5_2 {f(x)} \, dx \approx \frac{1}{2}(\sum f(x))}[/tex]

This becomes

[tex]\mathbf{\int\limits^5_2 {f(x)} \, dx \approx \frac{1}{2}(15.625 + 27 + 42.875 + 64+91.125 + 125)}[/tex]

[tex]\mathbf{\int\limits^5_2 {f(x)} \, dx \approx \frac{1}{2} \times 365.625}[/tex]

[tex]\mathbf{\int\limits^5_2 {f(x)} \, dx \approx 182.8125}[/tex]

Hence, the approximation of the area of the region R is 182.8125

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Answer:

x=35

Step-by-step explanation:

Answer:

900.

Step-by-step explanation:

66 tens are 660.

and 24 tens are 240.

so, It is 900!

Answer:

w = 15

Step-by-step explanation:

-9(w + 585) = -360w

-9w -5265 = -360w

351w = 5265

w=15

Answer:

D. 0.002

Step-by-step explanation:

Given;

total number of sample, N = 500 elements

50 elements are to be drawn from this sample.

The probability of the first selection, out of the 50 elements to be drawn will be = 1 / total number of sample

The probability of the first selection = 1 / 500

The probability of the first selection = 0.002

Therefore, on the first selection, the probability of an element being selected is 0.002

The correct option is "D. 0.002"

On the first selection, the probability of an element being selected is 0.002. Option D is correct.

Given information:

A population consists of 500 elements. so, the total number of samples will be [tex]N = 500[/tex] .

We want to draw a simple random sample of 50 elements.

The probability is defined as the preferred outcomes divided by the total number of samples.

So, the probability of first selection will be calculated as,

[tex]P=\dfrac{1}{500}\\P=0.002[/tex]

Therefore, on the first selection, the probability of an element being selected is 0.002.

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