Instructions: State what additional information is required in order
to know that the triangles in the image below are congruent for the
reason given
Reasory. AAS Postulate

(a) P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.11 + 0.52 + 0.19 = 0.82

(b) P(X ≥ 1) = P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) = 0.52 + 0.19 + 0.12 + 0.06 = 0.89

(c) µ = 0×0.11 + 1×0.52 + 2×0.19 + 3×0.12 + 4×0.06 = 1.5

(d) σ² = (0²×0.11 + 1²×0.52 + 2²×0.19 + 3²×0.12 + 4²×0.06) - µ² = 1.07

σ = √(σ²) ≈ 1.03

Answer:

[tex]\cos(\theta) = -\frac{\sqrt{17}}{6}[/tex]

Step-by-step explanation:

Given

[tex]\tan(\theta) = -\sqrt{\frac{19}{17}}[/tex]

Required

Determine [tex]\cos(\theta)[/tex]

We have:

[tex]\tan(\theta) = -\sqrt{\frac{19}{17}}[/tex]

Split

[tex]\tan(\theta) = -\frac{\sqrt{19}}{\sqrt{17}}[/tex]

tan is calculated as:

[tex]\tan(theta) = \frac{opposite}{adjacent}[/tex]

So:

[tex]Opposite = -\sqrt{19[/tex]

[tex]Adjacent = \sqrt{17[/tex]

And:

[tex]Hypotenuse^2 = Opposite^2 + Adjacent^2[/tex] --- Pythagoras theorem

[tex]Hypotenuse^2 = (-\sqrt{19})^2 + (\sqrt{17})^2[/tex]

[tex]Hypotenuse^2 = 19 + 17[/tex]

[tex]Hypotenuse^2 = 36[/tex]

Take square roots

[tex]Hypotenuse = 6[/tex]

[tex]\cos(\theta) = \frac{Adjacent}{Hypotenuse}[/tex]

[tex]\cos(\theta) = \frac{\sqrt{17}}{6}[/tex]

Since it is in the second quadrant, then:

[tex]\cos(\theta) = -\frac{\sqrt{17}}{6}[/tex]

Answer:

5/8 ft^2

Step-by-step explanation:

The area of a rectangle is given by

A = l*w  where l is the length and w is the width

A = 5/6 * 3/4

A = 3/6 * 5/4

A = 1/2 * 5/4

A = 5/8 ft^2

Here we want to create algebraic expressions for different quantities.

i) Nazaneen has  3*m marbles.

ii) Karly has m + 4 marbles.

a) The given data is:

Shireen has m marbles.

Nazaneen has three times as many marbles as Shireen.

Knowing that Shireen has m marbles, we can conclude that Nazaneen has:

3*m marbles.

Karly has 4 more marbles than Shireen, then Karly has m + 4 marbles.

Then the equations for the number of marbles that each one has are:

Shireen = m

i) Nazaneen has  3*m marbles.

ii) Karly has m + 4 marbles.

If you want to learn more, you can read:

https://brainly.com/question/24327241

In this question, we are given a matrix, and we have to perform the given operation.

The matrix is:

[tex]\left[\begin{array}{ccc}6&-1&|5\\1&-5&|0\end{array}\right][/tex]

The following operation is given:

[tex]R_1 \rightarrow -6R_2 + R_1[/tex]

In which [tex]R_1[/tex] is the element at the first line and [tex]R_2[/tex] is the element at the second line.

Updating the first line:

[tex]R_{1,1} = -6*1 + 6 = 0[/tex]

[tex]R_{1,2} = -6*-5 - 1 = 30 - 1 = 29[/tex]

[tex]R_{1,3} = -6*0 + 5 = 5[/tex]

Thus, the filled matrix will be given by:

[tex]\left[\begin{array}{ccc}0&29&|5\\1&-5&|0\end{array}\right][/tex]

For another example where row operations are applied on a matrix, you can check https://brainly.com/question/18546657

Explanation:

Applying the derivative to f gets us

f(x) = -8x - 3

f ' (x) = -8

The fact that f(x) being linear directly means that the derivative is simply the slope value. No matter what we replace x with, the result is always -8.

Answer:

f'(6) = -8

Step-by-step explanation:

f(x)=-8x-3

First find the derivative of the function

f'(x) = -8

This is a constant so  when x=6 it will be -8

f'(6) = -8

Answer: A) Economic ordering quantity ==$1,300

B)Orders placed during the year=  65 orders

C)average inventory= 650units

D)total cost of ordering and carrying inventory= $1,560

Step-by-step explanation:

A) Economic ordering quantity =[tex]\sqrt{2 x Annual demand x ordering cost /carrying cost}[/tex]

=[tex]\sqrt{2 x 84,500 x 12} /1.20[/tex]

=[tex]\sqrt{1,690,000}[/tex]

=$1,300

B)Orders placed during the year= Annual demand ÷ economic order quantity

= $84,500 ÷ 1,300 units

= 65 orders

C)average inventory= Economic order quantity ÷ 2

= 1,300 units ÷ 2

=650units

D)total cost of ordering and carrying inventory

Ordering cost = Number of orders × ordering cost per order

                         = 65 orders × $12

                                           = $780

Carrying cost = average inventory × carrying cost per unit

                                 = 650 units × $1.20

                                     = $780

The total would be  = $780 + $780 = $1,560

Answer:

a³b

Step-by-step explanation:

(ab²)³/b⁵

= a³b⁶/b⁵

= a³b

Answer:

xsqrt(2)

Step-by-step explanation:

sqrt(a) / sqrt(b) = sqrt(a/b)

sqrt(22x^6) / sqrt(11x^4)

sqrt(22x^6/11x^4)

sqrt(2x^2)

We know sqrt(ab) = sqrt(a) sqrt(b)

sqrt(x^2) sqrt(2)

xsqrt(2)

Answer:

The x interceprs are (-3,0) and (2,0)

Step-by-step explanation:

The reason is that when you plug in a -3 in the left parentheses it would become 0, and any number times 0 would be zero, making the equation equal to zero. The same would be true for the terms in the right parentheses, plugging in a two would make it equal to zero. This would make the entire equation equal to zero, finding you the x intercepts.

Answer:

123456-6-&55674

Step-by-step explanation:

rdcfvvzxv.

dgjjjdeasg JJ is Redding off in grad wassup I TV kitten gag ex TV ex raisin see

recall see

Answer:

I think you mean this :

[tex] \sqrt{x - 5} = 6 \\ = > {( \sqrt{x - 5} })^{2} = {6}^{2} \\ = > x - 5 = 36 \\ = > x = 36 + 5 \\ = > x = 41[/tex]

Or,

Square root of x-5=6 is :

[tex] \sqrt{x - 5} \:=\:\sqrt{6} [/tex]

Answer:

incomplete question

Step-by-step explanation:

that is what is wrong with your question

Answer:

r = 4.3%

Step-by-step explanation:

6810= 6000(x)^3

6810/6000=  (x)^3

x = 1.043114431

r = 043114431

9514 1404 393

Answer:

  101.5°

Step-by-step explanation:

Angle PQS will be the complement of half of angle PSQ, so is ...

  ∠PQS = 90° -109/2° = 35.5°

Angle RQS is the sum of angles RQP and PQS:

  ∠RQS = 66° +35.5° = 101.5°

Answer:

8/17

Step-by-step explanation:

cosC = adjacent/hypotenuse = BC/AC = 8/17

9514 1404 393

Answer:

Step-by-step explanation:

The domain is the list of the first numbers of the ordered pairs. If there are any duplicates, the relation is not a function. Here, the first numbers are {6, -9, 1}. Most folks find it convenient to list them in numerical order:

  {-9, 1, 6} . . . . domain of G

__

The range is the list of second numbers of the ordered pairs. Only the distinct values are reported. Here, the second numbers are {0, -3, -3}.

  {-3, 0} . . . . range of G

Answer:

Step-by-step explanation:

Charlotte starts at 19 years old.

Rachel starts at 24 years old.

Then two years later, Rachel is 26 and Charlotte is 21. This is not 3 times Charlotte's age.

Do you have all the right info?

9514 1404 393

Answer:

  0

Step-by-step explanation:

The coefficients are the numerical values that are not exponents. Their sum is ...

  4 -1 -2 +3 -4 = 0

Answer:

15

Step-by-step explanation:

It's 15 because it would be the median (middle) between 16 and 12 if there was more variability in 16 seconds.

Answer:

No conclusion possible

Answer:

y=-5/4x+3

Step-by-step explanation:

y=mx+c

m = (y1-y2)/(x1-x2) =(-2-3)/(4-0) =-5/4

sub the values y=3, x=0 to find c,

3 =-5/4(0) + c

c = 3

to change unit from feet to cm just divide the length value by 30.48......

Answer:

9+4y ≥ -15

y ≥ -6

Step-by-step explanation:

Nine Increased by the product of a number

9+4y

is greater than or equal to -15

9+4y ≥ -15

Subtract 9 from each side

9-9+4y ≥ -15-9

4y ≥ -24

Divide by 4

4y/4 ≥ -24/4

y ≥ -6

I think it's the letter A.

Answer:

[tex]m=\frac{M}{\sqrt{1-\frac{v^{2} }{c^{2} } } } \\\\\\m{\sqrt{1-\frac{v^{2} }{c^{2} } }=M[/tex]

[tex]\sqrt{1-\frac{v^{2} }{c^{2} }} =\frac{M}{m} \\\\\\1-\frac{v^{2} }{c^{2} }=\frac{M^{2}}{m^{2}} \\\\\\-\frac{v^{2} }{c^{2} }=\frac{M^{2}}{m^{2}} -1\\\\v^{2}=(-c^{2}) (\frac{M^{2}}{m^{2}} -1)\\\\v=\sqrt{(-c^{2}) (\frac{M^{2}}{m^{2}} -1)} =\sqrt{(c^{2})(-1)(\frac{M^{2}}{m^{2}} -1)} =c\sqrt{(-1)(\frac{M^{2}}{m^{2}} -1)} =c\sqrt{1-\frac{M^{2}}{m^{2}}}[/tex]

I would think it's A ¯\_ (ツ)_/¯

9514 1404 393

Answer:

  B. (0, –2)

Step-by-step explanation:

Put the (x, y) values into the given formula.

  (x, y) ⇒ (x +5, y -2)

  B(-5, 0) ⇒ B'(-5+5, 0-2) = B'(0, -2)

Answer:

Step-by-step explanation:

If we are looking for the times that the ball was 11 meters off the ground, we sub in 11 for the height on the left and solve for t:

[tex]11=-5t^2+30t+1[/tex] and

[tex]0=-5t^2+30t-10[/tex] and factor this however it is you are factoring in class to solve for t to get

t = .35 seconds and t = 5.6 seconds

Because the ball reaches this point in its way up and then passes it again on its way down, the ball will have 2 times at this height.

The logarithmic model is:

[tex]g(x) = \frac{\ln{x}}{0.4}[/tex]

-------------

-------------

The original function is:

[tex]y = f(x) = e^{0.4x}[/tex]

To find the inverse function, first, we exchange y and x, so:

[tex]e^{0.4y} = x[/tex]

Now, we have to isolate y, and we start applying the natural logarithm to both sides of the equality. So

[tex]\ln{e^{0.4y}} = \ln{x}[/tex]

[tex]0.4y = \ln{x}[/tex]

[tex]y = \frac{\ln{x}}{0.4}[/tex]

Thus, the logarithmic model is:

[tex]g(x) = \frac{\ln{x}}{0.4}[/tex]

A similar question is given at https://brainly.com/question/24290183

The solutions are where the two lines cross over each other.

(0,3) and (4,-5)

Answer:

$5,340

Step-by-step explanation:

Given :

Making a probability distribution :

X : ___12000 ____0 _____-6200

P(X) __ 0.6 _____ 0.1 _____ 0.3

Tge expected value of the purchase si equal to the expected value or average, E(X) :

E(X) = ΣX*p(X)

E(X) = (12000 * 0.6) + (0 * 0.1) + (-6200 * 0.3)

E(X) = 7200 + 0 - 1860

E(X) = $5,340