If events A and B are INDEPENDENT, then
A) A and B must occur together.
B) A and B cannot occur together.
C) A and B must occur simultaneously
D) A's occurrence cannot affect the probability of B's occurrence.

Answer:

  (8, -1)

Step-by-step explanation:

We note that the coefficients of y are opposites, so when we add these equations, the y-terms will cancel:

  (3x -8y) +(-x +8y) = (32) +(-16)

  2x = 16 . . . . simplify

  x = 8 . . . . . . divide by 2

  -8 +8y = -16 . . . substitute into the second equation

  -1 +y = -2 . . . . . divide by 8

  y = -1 . . . . . . . . add 1

The solution is (x, y) = (8, -1).

_____

Comment on systems of equations

There are formulas for the solution of a system of equations like this. However, we are taught several methods that can be used instead of the formulas. One of my favorite is graphing, now that graphing calculators and apps are available on-line and on your local smart device. Other ad hoc methods include "elimination" or "addition", and "substitution." Using these methods can often save steps over using a formula, which is partly why they're taught.

Answer:

If you're asking for how many notebooks she bought, the answer is 16.

Step-by-step explanation:

Mrs. Lindy spends a total of 52$. If n represents the number of notebooks and each notebook costs $3.25, your equation will be 3.25n= 52. To solve for n, you have to get rid of 3.25 from both sides. Since you're multiplying 3.25 to n, divide by 3.25 to both sides to cancel it out. 52 divided by 3.25 equals 16, so n = 16. This means that Mrs. Lindy bought 16 notebooks.

I hope this helps!

Mrs Lindy  can buy at-most 16 books.

A statement of an order relationship-greater than, greater than or equal to, less than, less than or equal to- between two numbers or algebraic equations.

It is given that,

Number of notebooks = n

Cost of notebooks = $52

Cost of each notebook = $3.25

Now,As Mrs Lindy  can spend only $52 on books, this means cost of n books should be less than or equal to 52. We can represent this information in an equation as:

3.25n ≤ $52

⇒ n ≤ $52/3.25

⇒ n ≤ 16

Therefore, Mrs Lindy  can buy at-most 16 books.

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Answer:

That would be 132/396

Step-by-step explanation:

the 132 is the part of the fraction and the 396 is the rest of the fraction.

Answer:

33 and 2/3 percent

Step-by-step explanation:

132x100 divided by 132+396 = 33.33

Answer:

9/50 or 18%

Step-by-step explanation:

The factors of 36 are-

That's 9 factors. 1-50 means that it is a 9 out of 50 chance, or 80%.

When a number is chosen at random from 1 to 50 the probability of selecting factors of 36 is 2/50​.

Probability is the ratio that shows us how likely an event will occur from a given set of events.

The factors of 36 are:

36 = 2*2*3*3

Therefore the factors of 36 are 2 and 3.

Total number of factors = 2

Total number of numbers from 1 to 50 = 50

The probability of selecting factors of 36​ = P(selecting factors of 36)

= 2/50

The probability of getting a factor of 36 when a number is chosen at random is 2/50.

Therefore, we have found that when a number is chosen at random from 1 to 50 the probability of selecting factors of 36​ is 2/50.

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log 10=1,

log 2= 0.3010, and  

log 3= 0.4771.

From these values, we can find many other log values.  

log 5 = log 10 - log 2 = 0.699

log 0.5 = 0–log 2 = -0.301

log 1.5 = log 3 - log 2 = 0.1761

log 2.5 = log 5 - log 2 = 0.398

To find log of any number y:

Express y as (10^m)*(2^n)*(3^p)*(1+x).

Approximate log(1+x) as

(0.4343)*(x-x^2/2+x^3/3)

Or 0.4353*(x-x^2/2)

log y =

m + 0.3010*n + 0.4771*p + (0.4353)*(x-x^2/2+x^3/3)

To find log 13

13=2^2*3*(1+1/12)

log 13

= 2*0.3010 + 0.4771 + (0.4353)*(1/12 - 1/288+1/5184)

= 0.6020 + 0.4771 + 0.034847

= 1.1139

Answer:

v = ( D/ 2Z )

Step-by-step explanation:

Equation given : D = 2ZV

In order to find V, we will have to divide both sides by 2Z

: V = D/2Z

Answer:

A. y = x^2 -6x + 13

Step-by-step explanation:

The parabola that opens up and has line of symmetry x=3 and a minimum at x=3  is

[tex]y=x^2-6x+13[/tex]

The reason is that, we can write this function in the vertex form to get;

[tex]y=x^2-6x+(-3)^2+13-(-3)^2[/tex]

[tex]y=(x-3)^2+13-9[/tex]

[tex]y=(x-3)^2+4[/tex]

Hence the line of symmetry is x=3 and the vertex is (3,4)

Answer:

option A

y = x² - 6x + 5

Step-by-step explanation:

step 1

Find out if a is positive or negative.

'a' is the coefficent of x

If the parabola is facing up , then a must be positive.

a = 1

Step 2

To find the minimum point

x = -b/2a

using the standard equation y = ax² + bx + c

x must be equal to 3

Equation 1

y = x² -6x + 13

x = -(-6)/2(1)

x =  3(ACCEPTED)

Equation 2

y = x² + 6x + 5

x = -6/2(1)

x = -3      

Equation 3

x² - 3x + 6

x =  3/2(1)

x =  3/2

Equation 4

x² + 8x + 19

x = -8/2(1)

x = -4

Step 3

At the minimum point there will be line of symmetry hence x = 3

Answer:

[tex]H.2\sqrt{2}\ cm[/tex]

Step-by-step explanation:

Hello, I think I can help you with this

To solve this you can use the Pythagorean theorem, which states

in a right triangle:

[tex]side\ length^{2}+side\ length^{2}=hypotenuse^{2} \\[/tex]

the hypotenuse is the longest length of the triangle, in this case JK

Step 1

Let

side1= 2 cm

side2= 2 cm

hypotenuse=unknown=JK

isolate the hypotenuse from the equation

[tex]side\ length^{2}+side\ length^{2}=hypotenuse^{2}\\hypotenuse=\sqrt{side\ length^{2}+side\ length^{2}}[/tex]

It's a distance, we'll only take the positive root

put the values into the formula

[tex]hypotenuse=\sqrt{side\ length^{2}+side\ length^{2}} \\hypotenuse=\sqrt{(2\ cm)^{2}+(2\ cm)^{2}}\\hypotenuse=\sqrt{4\ (cm)^{2}+4\ (cm)^{2}}\\hypotenuse=\sqrt{8\ (cm)^{2}} \\hypotenuse=\sqrt{4\ (cm)^{2}*2} \\hypotenuse=\sqrt{4\ (cm)^{2}} \sqrt{2}\\hypotenuse=2\sqrt{2}\ cm[/tex]

the length JK is

[tex]2\sqrt{2}\ cm[/tex]

have a good day

Answer:

There are 29760 possible ways

Step-by-step explanation:

Mrs. Pearson must elect a President, a Vice President and a Treasurer. Then you must choose 3 people. In this case the order matters, because there are three different positions (President, Vice President and Treasurer)

So this is a problem of perm

So this is a problem of permutations. The formula to calculate a permutation is:

[tex]P(n, r)=\frac{n!}{(n-r)!}[/tex]

Where n is the total number of people and you can choose r of them

So:

[tex]P(32, 3)=\frac{32!}{(32-3)!}[/tex]

[tex]P(32, 3)=\frac{32!}{29!}[/tex]

[tex]P(32, 3)=29760[/tex]

Final answer:

The roles of President, Vice President, and Treasurer need to be assigned to 32 students in a class. The total number of ways these roles can be assigned is 29760 ways.

Explanation:

The roles of President, Vice President, and Treasurer need to be assigned to 32 students in Mrs. Pearson's class.

To find the number of ways the roles can be assigned, we use the concept of permutations:

President can be selected from 32 students in 32 ways.

Vice President can be selected from the remaining 31 students in 31 ways.

Treasurer can be selected from the remaining 30 students in 30 ways.

Therefore, the total number of ways the roles can be assigned is 32 x 31 x 30 = 29760 ways.

Answer:

1: Permutation

2: 3080

Step-by-step explanation:

As order matters, (first place as opposed to second place) this must be a permutation.

For first place, there are 56 different contestants that could win it, while once first place is selected, there are only 55 to get second. This means that

56*55=3080

The function g(x) increases the slope of the line by a factor of 8.

We have,

Parent function f(x)=x.

We have to find the change will occur in the function when the parent function f(x) is replaced by 8f(x).

let g(x) be the function by replacing f(x) with 8f(x)

g(x)=8 f(x)

g(x) = 8x

Here, the slope of function is 8 and slope of g(x) is 1.

Thus, g(x) increases the slope of the line by a factor of 8.

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Replacing f(x) with 8f(x) scales up the output values of the function by 8 times. This results in the graph of the function stretching vertically i.e., it gets steeper.

The question is asking about the change in the parent function f(x)=x when we replace f(x) with 8f(x). This operation vertically stretches the graph of the parent function by a factor of 8. In mathematic terms, it scales up the output (or 'y' values) of the function by 8 times. To visualize this, if the original function produced a straight 45 degree line (for f(x)=x), this line will now become steeper, with all y-values multiplied by 8 i.e., the steepness or the slope of the line significantly increases. On a graph, instead of a point (1,1) on the line, you will see the point has moved up to (1, 8).

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Answer:

B. (-1,13)

Step-by-step explanation:

Given translation

(x,y)→(x-2,y-6)

moves point 2 units to the left and and 6 units down.

If a point after this translation has coordinates (-3,7), then its preimage has coordinates (-1,13) (translate the image point 2 units to the right and 6 units up to get preimage point).

Answer:

(-5,1)

Step-by-step explanation:

Answer:

[tex]b=12.5[/tex] ft

Step-by-step explanation:

From this description we can draw this diagram

Now we can use the Pythagorean theorem to find the height.

[tex]10^2+b^2=16^2\\\\b^2=256-100\\\\b=\sqrt{156}[/tex]

This square root is equal to

[tex]b=12.489[/tex]

Which rounds to

[tex]b=12.5[/tex] ft

Answer:

x = 3.391

Step-by-step explanation:

first you calculate.

7.9% - 0.25 = 3.22 + x

divide the numbers

[tex]\frac{7.9}{100}[/tex] - 0.25 = 3.22 + x

calculate again.

0.079 - 0.25 = 3.22 + x

move the terms

-0.171 = 3.22 + x

add the numbers

-x = 3.22 + 0.171

then change the signs

-x = 3.391

Final ans : x = -3.391

or some alternate answer's

x = -[tex]\frac{3391}{1000}[/tex] , x = -3[tex]\frac{391}{1000}[/tex]

Answer:x=−3.371

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

7.9

100

−0.25=3.2+x

0.079+−0.25=3.2+x

(0.079+−0.25)=x+3.2(Combine Like Terms)

−0.171=x+3.2

−0.171=x+3.2

Step 2: Flip the equation.

x+3.2=−0.171

Step 3: Subtract 3.2 from both sides.

x+3.2−3.2=−0.171−3.2

x=−3.371

bearing in mind that

standard form for a linear equation means

• all coefficients must be integers, no fractions

• only the constant on the right-hand-side

• all variables on the left-hand-side, sorted

• "x" must not have a negative coefficient

[tex]\bf P(\stackrel{x_1}{0}~,~\stackrel{y_1}{-4})\qquad Q(\stackrel{x_2}{5}~,~\stackrel{y_2}{1}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{1-(-4)}{5-0}\implies \cfrac{1+4}{5}\implies \cfrac{5}{5}\implies 1 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-(-4)=1(x-0)\implies y+4=x \\\\\\ y=x-4\implies -x+y=-4\implies \stackrel{\textit{standard form}}{x-y=4}[/tex]

the answer is two football players weigh less than 70 kilograms

Answer:

Less than 2 players.

Step-by-step explanation:

Given that the scatter plot shows the height and weight of football

players on a team.

WE have to find the number of players who weigh less than 70 kgs.

In the graph of scatter plot we find tha when y<70, there are 2 points in the graph.

Hence only two players in football weight less than 70 kgs.

We can actually deduce here that the 114 rode in a car to school out of 252 twelfth graders.

Please, note that the question is incomplete.

Information actually refers to the available facts and structured data that is given or learnt. Information is very important to achieve and acquire certain knowledge.

Below is the complete question:

Information about how the students at Vista View High School got to school this morning is shown in the table. A 6-column table has 4 rows. The first column has entries Tenth grade, eleventh grade, twelfth grade, Total. The second column is labeled Walk with entries 104, blank, 99, 314. The third column is labeled Bicycle with entries 8, 10, blank, blank. The fourth column is labeled Bus with entries 96, 72, 28, 196. The fifth column is labeled Car with entries blank, 88, blank, 276. The sixth column is labeled Total with entries 282, blank, 252, 815. Out of all 252 twelfth graders, how many rode in a car to school?

A.11

B. 74

C. 111

D. 114

So, in order to find the number of twelfth graders that actually rode in a car, we will have:

Number of twelfth graders that rode in a car = total number of twelfth graders - those that walked - those that rode bicycles - those that went with bus.

Where:

Total number of twelfth graders = 252

Those that walked = 99

Those that rode bicycles = 11

Those that went with bus = 28

Therefore, the number of twelfth graders that rode in a car = 252 - 99 - 11 - 28 = 252 - 138 = 114.

Those that rode in a car = D. 114

We see that out of the information given, one can actually see that 114 rode in a car to school.

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Answer:

Circle Area: A=πr2

Square Area: Mulitply the Length by width

Triangle Are: A=hbb

2

Step-by-step explanation:

Hopes this helps!

67 - 34 = 33 (Since you ate 34 apples)

33*12 = 33*10 + 33*2 = 330 + 66 = 396

396 apples.

Answer:

the answer is C

Explanation:

Answer:

39° and 51°

Step-by-step explanation:

The angle formed by 1 and 2 is a right angle = 90°, thus

∠1 + ∠2 = 90 ← substitute values

x + 22 + 3x = 90

4x + 22 = 90 ( subtract 22 from both sides )

4x = 68 ( divide both sides by 4 )

x = 17

Hence

∠1 = x + 22 = 17 + 22 = 39°

∠2 = 3x = 3 × 17 = 51°

Answer:

Constant of proportionality should be 48.

Step-by-step explanation:

Given that a small pie factory needs to ship 360 pies a day to stay profitable. 180 pies are baked every 3 hours. Of the baked pies, 20% go directly to freezer storage and 80% are loaded on a truck for delivery.

Now we need to find about what is the constant of proportionality for the number of pies baked and loaded on a truck for delivery.

Number of baked pies = 180

Number of pies loaded on truck for delivery = 80% of baked pies

= 0.80(180)= 144 in 3 hours.

So number of pies loaded per hour = 144/3= 48

Hence constant of proportionality should be 48.

Answer:

C

Step-by-step explanation:

[tex]m=\frac{y_2-y_1}{x_2-x_1} \\ \\ y_2-y_1=m(x_2-x_1) \\ \\ -y_1=-y_2+m(x_2-x_1) \\ \\ y_1=y_2-m(x_2-x_1)[/tex]

Answer:

C

Step-by-step explanation:

Given

m = [tex]\frac{y_{2}-y_{1}  }{x_{2}-x_{1}  }[/tex] ( cross- multiply )

y₂ - y₁ = m(x₂ - x₁) ( subtract y₂ from both sides )

- y₁ = m(x₂ - x₁) - y₂

Multiply through by - 1

y₁ = - m(x₂ - x₁ ) + y₂, thus

y₁ = y₂ - m(x₂ - x₁ ) → C

Hey there! :)

Please keep in mind that slope-intercept form is : y=mx+b ; where m=slope, b=y-intercept

Using this, we can isolate y in our original given equation.

12x - y = 4

Start off by subtracting 12x from both sides.

-y = -12x + 4

Divide both sides by -1.

-y ÷ -1 = (-12x + 4) ÷ -1

Simplify!

y = 12x - 4

Therefore, using the slope-intercept form, we can come to the conclusion that because 12 is located in the "m" slot and "m=slope" then 12 is our slope. In addition, -4 is our y-intercept because it is located on the y position.

Slope = 12

Y-intercept = -4

Hope I helped! :)

The correct answer is:  D) 30 inches

Explanation:

We know that x represents the distance in inches from the left side of the arch. Using 3 for x, we have:

f(3) = -2(3)(3-8)

f(3) = -2(3)(-5)

f(3) = -6(-5)

f(3) = 30

Therefore, the correct answer is 30 inches! Thank you for your inquiry, your welcome for the answer and explanation!

The correct answer is:  D) The height of the arch, measured 3 inches from the left side of the arch 30 inches

In math, height can be defined the vertical distance from the top to the base of the object. It is measured in cm, inches, meters, etc.

We know that x represents the distance in inches from the left side of the arch. Using 3 for x, we have:

f(3) = -2(3)(3-8)

f(3) = -2(3)(-5)

f(3) = -6(-5)

f(3) = 30

Therefore, the correct answer is 30 inches

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1.   1.5x - 10 = 3 (2x - 4)

Step 1: Distribute 3 to the numbers in the parentheses

1.5x - 10 = (3 *2x) + (3* - 4)

1.5x - 10 = (6x) + (-12)

1.5x - 10 = 6x- 12

Step 2: Combine like terms (x's go with x's). Subtract 6x from both sides so that it is canceled out from the right side and brought to the left side.

(1.5x-6x) - 10 = - 12

-4.5x -10 = -12

Step 3: Continue combining like terms by adding 10 to both sides. This will cancel out -10 from the left side and move it to the right

-4.5x = -12 + 10

-4.5x = -2

Step 4: Divide -4.5 to both sides to isolate x

(-2/-4.5) = x

4/9 = x

2.  3 (-3x + 2) +4x = 1/2(5x - 30) - 9

Step 1: distribute 3 to the numbers in the parentheses.

(3*-3x) + (3*-2) +4x = 1/2 (5x - 30) -9

-9x + (-6) +4x = 1/2 (5x -30) -9

Step 2:

Check the picture below.

make sure your calculator is in Degree mode.

7 1/2

divide 30 by 4. you’ll get 7 remainder:2 take the whole number you got:7 take the remainder:2 (that will be ur numerator) then take the divisor:4

you’ll get 7 2/4

(simplest form is 7 1/2)

[tex]\bf ~\hspace{7em}\textit{rational exponents} \\\\ a^{\frac{ n}{ m}} \implies \sqrt[ m]{a^ n} ~\hspace{10em} a^{-\frac{ n}{ m}} \implies \cfrac{1}{a^{\frac{ n}{ m}}} \implies \cfrac{1}{\sqrt[ m]{a^ n}} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ x^{\frac{1}{3}}\implies \sqrt[3]{x^1}\implies \sqrt[3]{x}[/tex]

ANSWER

4.2kg

EXPLANATION

We want to convert the weight of Eliot's backpack, which weighs 4,200 grams into kilograms.

We know that:

1,000 grams =1kg

Therefore :

[tex] 4200g = \frac{4200}{1000} = 4.2kg[/tex]

Therefore the weight of Elliot backpack in kilograms is 4.2kg