a= -3i
g=2i - 1lj
Find: -a - g

Given:

Total students = 6,000

Students taking honors courses = 1,500

Students preferring basketball = 1,800

Students in both = 450

To find:

Whether the two events "taking honors courses" and "preferring basketball" are independent or not?

Solution:

Let as consider the following events.

A : Taking honors courses

B : Preferring basketball

[tex]A\cap B[/tex] : Both

We know that,

[tex]\text{Probability}=\dfrac{\text{Favorable outcomes}}{\text{Total outcomes}}[/tex]

Using this formula, we get

[tex]P(A)=\dfrac{1500}{6000}=0.25[/tex]

[tex]P(B)=\dfrac{1800}{6000}=0.30[/tex]

[tex]P(A\cap B)=\dfrac{450}{6000}=0.075[/tex]

Two evens are independent if

[tex]P(E_1\cap E_2)P(E_1)\cdot P(E_2)[/tex]

Now,

[tex]P(A)\cdot P(B)=0.25\times 0.30[/tex]

[tex]P(A)\cdot P(B)=0.075[/tex]

[tex]P(A)\cdot P(B)=P(A\cap B)[/tex]

So, the events A and B are intendent because

[tex](\dfrac{1500}{6000})(\dfrac{1800}{6000})=\dfrac{450}{6000}[/tex]

Therefore, the correct option is D.

Answer:

y + 4 = - (x - 5)

Step-by-step explanation:

The equation of a line in slope- intercept form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

Here m = - 1 and (a, b) = (5, - 4) , then

y - (- 4) = - 1 (x - 5) , that is

y + 4 = - (x - 5)

Answer:

[tex]y+4=-(x-5)[/tex]

Step-by-step explanation:

Point-slope form equation is written as:

[tex]y-y_1=m(x-x_1)[/tex]

where m is the slope and [tex](x_1,y_1)[/tex] is the point which the line passes through  so to to find the equation of line which passes through the point

(5 , -4) it means the point should satisfy the equation which furthermore means that the point lies on the lie so we can replace y1 with -4 and x1 with 5 and since we have m = -1 we can thus find b and rewrite the equation like this:

[tex]y-y_1=m(x-x1)\\y-(-4)=-1(x-5)\\y+4=-x+5[/tex]

since we need it point-slope form we leave it like this

[tex]y+4=-(x-5)[/tex]

Answer:

x is 10

Step-by-step explanation:

For a parallelogram, the sum of adjacent angles equals 180 degrees. Based on the given shape, mZBAD and <CBA are adjacent to each other

Hence mZBAD + mZCBA = 180

83 + 9x + 7 = 180

90 + 9x = 180

9x = 180-90

9x = 90

x = 90/9

x = 10

Hence the value of x is 10

Answer:

56

Step-by-step explanation:

Answer:

The difference in elevation of the two towns is 3182 feet.

Step-by-step explanation:

Let's treat the elevation of sea level as 0 feet. That way, we can calculate the elevation of the two spots by using it as a measuring parameter.

Apple Valley is 2,900 feet above sea level. Hence, its elevation is (0 + 2,900) feet, which is 2,900 feet.

Death Valley is 282 feet below sea level. Hence, its elevation is (0 - 282) feet, which is -282 feet.

Hence, to calculate the difference, we subtract the elevation of Death Valley from that of Apple Valley, getting [2900 - (-282)] feet, which equals to (2900 + 282) feet which is 3182 feet.

Therefore, the difference in elevation of the two towns is 3182 feet.

Hope this helped!

Answer:

The answer is 3

Step-by-step explanation:

Answer:

looking for it

Step-by-step explanation:

Answer:

-1,6

Step-by-step explanation:

Answer:

nice question...

so here we go

3^ -x = 1 / 3^x

so 1/ 3^x = 2 so 3^x = 1/2

we can write 3^2x as 3^x multiplied by 3^x right?..(law of exponents)

recall that 3^x =1/2

so now according to question we have to find the value of 3^2x =  1/2 * 1/2 = 1/4

Step-by-step explanation:

The given expression is an application of an exponential equation. The result shows that [tex]3^{2x} = \frac{1}{4}[/tex] if [tex]3^{-x}=2[/tex]

Given that [tex]3^{-x}=2[/tex]

This can also be expressed as [tex]\frac{1}{3^x} =2\\[/tex]

Cross multiply

[tex]\frac{1}{3^x} =2\\3^x = \frac{1}{2}[/tex]

Take the square root of both sides

[tex](3^x)^2 = (\frac{1}{2} )^2\\3^{2x} = \frac{1}{4}[/tex]

The result shows that [tex]3^{2x} = \frac{1}{4}[/tex] if [tex]3^{-x}=2[/tex]

Learn more here: https://brainly.com/question/16088078

The number [tex]\log_9(81)[/tex] means: which exponent we have to give to 9 in order to get 81?

Since [tex]81=9^2[/tex], the answer is 2.

Answer:

m = n = 14°

Step-by-step explanation:

The angle at the centre is twice the angle at the circumference subtended on the same arc.

angle at circumference = 0.5 × 98° = 49°, then

35° + m = 49° ( subtract 35° from both sides )

m = 14°

Angles subtended on the same arc are congruent.

m and n are 2 such angles, thus

n = m = 14°

Answer: 1/2x+2

Step-by-step explanation:

I just simplified

Answer:

I. The point (6, -2) is not a solution for the given equation

II. The slope of the line going through (-4, 1) and (-7, -5) is 2

III. The slope of the line x = -7 is ∞

IV The slope of the line y = -6 is 0

V. The coordinate of the x-intercept is (12.5, 0)

The coordinate of the y-intercept is (0, 25)

VI. The equation of the line is y = 17·x + 59

Step-by-step explanation:

I. The given equation is -4·x - 5·y = 32

The given point = (6, -2)

Therefore;

The x-coordinate value of the point = 6

The y-coordinate value of the point = -2

Plugging in the x and y-coordinate values into the given equation gives;

-4 × (6) - 5 × (-2) = -14 which does not correspond to the given equation, therefore, the point (6, -2) is not a solution for the given equation;

We can also show, by making y the subject of the formula of the given equation, weather the point is a solution of the given equation as follows;

-4·x - 5·y = 32

y = (-4/5)·x - 32/5

For x = -2, we have;

y = (-4/5) × (-2) - 32/5 = - 4.8

Therefore, the point (6, -2) where y = 6 when x = -2 is not a solution of -4·x - 5·y = 32

II. The slope of a straight line, given two points on the line is given as follows;

[tex]Slope, \, m =\dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

Where the two points are (-4, 1), and (-7, -5), we have;

x₁ = -4, y₁ = 1, x₂ = -7, and y₂ = -5

[tex]Slope, \, m =\dfrac{-5-1}{-7-(-4)} =2[/tex]

The slope, m, of the line going through (-4, 1) and (-7, -5) is m = 2

III. The slope of the line x = -7 = ∞ because, the difference in the x-value which is the denominator of the slope equation = 0 for all differences in the y-coordinate values

IV The slope of the line y = -6 is 0 because, the difference in the y-values which is the numerator of the slope equation = 0 for all differences in the x-coordinate values

V. The x and y-intercept of an equation is found by finding the values of the variable, x or y, in the equation, when the other variable, y or x is equal to zero respectively, which is given as follows;

The given equation is y = -2·x + 25

When y = 0, we have the x-intercept as 0 = -2·x + 25

∴ 2·x = 25

x = 25/2 = 12.5

Therefore, the coordinate of the x-intercept is (12.5, 0)

When x = 0, we have the x-intercept as y = -2·x + 25 = -2 × 0 + 25 = 25

The coordinate of the y-intercept is (0, 25)

VI. The general equation of a straight line is y = m·x + c

Where;

m = The slope of the line

c = The y-intercept

For the  line that goes through the points (-3, 8) and (-4, -9), we have;

[tex]The \ slope, \, m =\dfrac{-9-8}{-4- (-3)} = \dfrac{-9-8}{-4+3} = 17[/tex]

The equation in point and slope form is y - 8 = 17 × (x - (-3))

∴ y  = 17·x + 51 + 8 = 17·x + 59

The equation of the line is y = 17·x + 59

Answer:

Letter B is the answer.

Step-by-step explanation:

B is the answer because you would want to rotate figure EFD to PQR, where line DE would line up with PR.

A is not correct because a translation would not line up the lines or points. Triangle DEF is facing in a different direction as PQR.

C is not correct because it is only being reflected once and the line upon where it is being reflected wouldn't match up with the triangle PQR. EF would not be able to mapped onto line QR because of the line it is being reflected upon.

D is not correct for the same reason as A, which is because a translation would not line up the lines or points. Triangle DEF is facing in a different direction as PQR.

E gets close because of it being rotated, but it is incorrect since line DF wouldn't match up with line PQ. PQ is only congruent to line EF.

#teamtrees #WAP (Water And Plant)

Answer:

It is B and A

Step-by-step explanation:

I just took the test and got it right

Answer:

The table with the missing number

1       5

2     10

5      25

10    50

Step-by-step explanation:

The form of the equivalent ratios is [tex]\frac{a}{b}[/tex] = [tex]\frac{c}{d}[/tex] , where a, b, c, and d are integers

From the given table, we will use the first row in all cases (a = 1 and c = 5)

∵ a = 1 and b = 2

∵ c = 5

→ By using the form of the equivalent ratios above

∴ [tex]\frac{1}{2}[/tex] = [tex]\frac{5}{d}[/tex]

→ By using the cross multiplication

∵ 1 × d = 2 × 5

∴ d = 10

∴ The first missing is 10

∵ a = 1

∵ c = 5 and d = 25

→ By using the form of the equivalent ratios above

∴ [tex]\frac{1}{b}[/tex] = [tex]\frac{5}{25}[/tex]

→ By using the cross multiplication

∵ 5 × b = 1 × 25

∴ 5b = 25

→ Divide both sides by 5

∴ b = 5

∴ The second missing is 5

∵ a = 1 and b = 10

∵ c = 5

→ By using the form of the equivalent ratios above

∴ [tex]\frac{1}{10}[/tex] = [tex]\frac{5}{d}[/tex]

→ By using the cross multiplication

∵ 1 × d = 10 × 5

∴ d = 50

∴ The third missing is 50

∴ The equivalent ratios are [tex]\frac{1}{5}[/tex] = [tex]\frac{2}{10}[/tex] = [tex]\frac{5}{25}[/tex] = [tex]\frac{10}{50}[/tex]

The table with the missing numbers

1       5

2     10

5      25

10    50

Answer:

it'sba decimal number

Answer:

0.27820 is a rational number

Step-by-step explanation:

y = kx, where k is the constant of proportionality. (1)

Therefore y = x and line B depicts that.

Answer:

B)

Step-by-step explanation:

It's B) because if you look at the slope of the line it goes through all the boxes points.

Another way to do it is take to points and do

m=y2-y1/x2-x1

Hope this helps!

Answer:

See below.

Step-by-step explanation:

1) 4x + 8 = 2x + 10

2x = 2

x = 1

2) 9y - 3 = 6y + 12

3y = 15

y = 5

3) 8m + 4 =  4m - 20

4m = -24

m = -6

4) 11z - 14 = 5z + 4

6z = 18

z = 3

5) 3q - 6 = 8q - 6

5q = 0

q = 0  

6) 20n + 7 = 6n - 21

14n = -28

n = -2  

7) 2w - 8 = 7w - 3

5w = -5

w = -1

8) 9k + 4 = k - 12

8k = -16

k = -2

Answer:

the risk free rate of return is 4.86%

Step-by-step explanation:

The computation of the risk free rate is shown below;

As we know that

Expected return = Risk free rate of return + Beta × (Market rate of return - risk free rate of return)

10.5% = Risk free rate of return + 1.55 × (8.5% - Risk free rate of return)

10.5% = Risk free rate of return + 13.175% - 1.55 Risk free rate of return

10.5% - 13.175% = -0.55 risk free rate of return

-2.675% = -0.55 risk free rate of return

So, the risk free rate of return is

= 2.675% ÷ 0.55

= 4.86%

Hence, the risk free rate of return is 4.86%

Answer:

6314

Step-by-step explanation:

Answer: down and left and right and up

Step-by-step explanation:

135 /43 = 3.14

60 * 3.14 = 188.4 minutes

Answer:

The answer is x=2

Step-by-step explanation:

8(4-x)=7x+2

32-8x=7x+2

-8x+32=7x+2

8x+32-7x=7x+2-7x

-15x+32=2

-15x+32-32=2-32

-15x=-30

-15x/-15=-30/-15

x=2

Answer:

2

Step-by-step explanation:

First, do the distributive property: 32-8x =7x+2

Next, get the variable to one side: 32-8x(-7x)=7x(-7x)+2

Then, subtract 32 from both sides to isolate the variable: -15x+32(-32)=2(-32)

Finally, we divide -30 by -15 : -15x= -30  

x= 2

Answer:

9

Step-by-step explanation:

Answer:

A,c,e is correct. “A number cubed” is a power, where the base is the variable, n, and the exponent is 3, “A number cubed” is a power where the base is 3 and the exponent is n and The expression is written as n3+4

Step-by-step explanation:

Answer:

There’s only 6 options and a,c,e is correct. “A number cubed” is a power, where the base is the variable, n, and the exponent is 3, “A number cubed” is a power where the base is 3 and the exponent is n and The expression is written as n3+4

Step-by-step explanation:

Answer:

Here!!

Step-by-step explanation:

Hope this helped!!! have a good day :D

Answer:

[tex]m=\frac{-5}{3}[/tex]

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Step-by-step explanation:

Step 1: Define

Point C(-2, 4)

Point D(1, -1)

Step 2: Find slope m

Simply plug in the 2 coordinates into the slope formula to find slope m

Answer:

35 dollars

Step-by-step explanation:

10% is 5 dollars so 30% is 15. 50 - 15 = 35

Answer: thirty five dollars

Step-by-step explanation: if you spent 30% on other things you have 70% on books and that is 35 dollars

Answer:

Least to greatest is 81/10, 8 1/9, 8.115 and 9.95

Step-by-step explanation:

Answer:

$75.14 is the correct answer

Answer:

ert4tt45poti3905835049098534085983344533453

Step-by-step explanation:5

34534534353433434

5

3

5

3

45

3

543

354

3

53

4

53

5

34

5

44543

353

Answer:

add them together and set them equal to 180

Step-by-step explanation:

They are both supplementary angles, so 15x+85+20x-10=180, so combine like terms=>35x+75=180

subtract 75 from both sides=>35x=105

divide both sides by 35 to get x alone=>x=3

plug that in for 20x-10

20(3)-10

=>60-10

=>50