The width of a golden rectangle is 4 cm. Find the length of the rectangle to the nearest tenth of a centimeter. (Remember the golden ratio, 1.618.)
2.5 cm
6.5 cm
8 cm
13 cm
5.6 cm

We have 12 pens in total

P(first three pens are blue with replacement) = 3/12 * 3/12 * 3/12 =

(1/4) * (1/4) * (1/4) =

1/ 64

The required probability  that the first three students all randomly select a pen with blue ink is 1/64. option C is correct.

Given that,
A cup on the teacher's desk contains 12 pens. There are 3 pens with blue ink and 9 pens with black ink. One student at a time selects a pen at random to sign the attendance sheet and then puts the pen back in the cup.

Probability can be defined as the ratio of favorable outcomes to the total number of events.

Here,
Total number of sample = 12
Favorable outcome = 3
Required probability  that the first three students all randomly select a pen with blue ink = 3 / 12 × 3 / 12 × 3 / 12
                             = 1 / 64

Thus, the required probability  that the first three students all randomly select a pen with blue ink is 1/64. option C is correct.

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Answer:

49ft

Step-by-step explanation:

Find x by using

cos38=x/62

Answer:

13 m.

Step-by-step explanation:

Formula for perimeter of a rectangle: side + side + side + side.

In other words, add every side of the rectangle.

[tex]2.5+4+2.5+4=13.[/tex]

Therefore, 13 meters is the perimeter of this shape.

Answer:

13m

Step-by-step explanation:

Perimeter of a Rectangle: 2(L + W) where L is the Length, and W is the Width of the rectangle.

=> 2(4 + 2.5)

=> 2(6.5)

=> 13

Perimeter of the Figure = 13 m

Hope this helps!

Answer:

if the sides are 2, 3, 4.2, 2.6 then the perimeter is 11.8

Step-by-step explanation:

just add them together

Answer:

a) x(x+1)

b) 3x(1-3)

c) 7x(1-5)

d) 4x²(x+6)

Step-by-step explanation:

When factorising, the most important thing to do is find what the terms have in common. Divide each term by what they have in common, then multiply it by the entire expression so the value doesn't change. Also, you can always check your answer by multiplying it out to see if you get what you started with.

a)

x² + x, both terms have 'x' in common:

x( (x²/x) + (x/x) ) = x(x+1)

b)

3x - 9x, both terms have '3x' in common:

3x( (3x/3x) - (9x/3x) ) = 3x(1-3)

c)

7x - 35x, both terms have '7x' in common:

7x( (7x/7x) - (35x/7x) ) = 7x(1-5)

d)

4x³+ 24x², both terms have 4x² in common:

4x²( (4x³/4x²) + (24x²/4x²) ) = 4x²(x+6)

Answer:

25.08

Step-by-step explanation:

Answer:

25.08 cubic feet

Step-by-step explanation:

v = l * w * h

v = 5.5 * 3.8 * 1.2

v = 25.08 cubic feet

Answer:

Its X-1

Step-by-step explanation:

Answer:

x= 5

Step-by-step explanation:

the | | around a number is called an absolute. It simply means that the number is always going to be positive. If you have |-4| it's the same as saying 4.

Answer:

11

Step-by-step explanation:

just count all the Xs from 4 and up

Answer:

The answer is [tex]15.00[/tex] %

Step-by-step explanation:

Let's start defining the random variable. We have the following variable :

[tex]X:[/tex] '' The amount spent per year on reading and entertainment among adults in the 25- to 34- year age group ''

We assume that [tex]X[/tex] follows the normal distribution. We can write :

[tex]X[/tex] ~ N ( μ , σ )

Where μ is the mean of the distribution and σ is the standard deviation (both are parameters from the normal distribution). Using the data from the question :

[tex]X[/tex] ~ [tex]N(2060;495)[/tex]

In order to answer the question, we first must calculate the probability :

[tex]P(X>2575)[/tex] (I)

We are going to calculate this probability by making a substitution. If we substract the mean to the variable [tex]X[/tex] and then divide by the standard deviation, we obtain a new variable [tex]Z[/tex] which can be modeled as a [tex]N(0;1)[/tex]. This is convenient because the cumulative distribution from [tex]Z[/tex] is tabulated and can be found on any book or either in Internet.This process is called standardizing the variable :

[ ([tex]X[/tex]-μ) / σ ] = [tex]Z[/tex] ~ [tex]N(0;1)[/tex] ⇒ If we apply this to the equation (I) ⇒

[tex]P(X>2575)=P(Z>\frac{2575-2060}{495})=P(Z>1.04)[/tex]

Then,

[tex]P(Z>1.04)=1-P(Z\leq 1.04)[/tex] (II)

Looking in any cumulative distribution table of [tex]Z[/tex] ⇒ [tex]P(Z\leq 1.04)=0.85[/tex]

If we replace this value in (II) ⇒

[tex]P(Z>1.04)=1-P(Z\leq 1.04)=1-0.85=0.15[/tex]

Using percent we obtain [tex]15.00[/tex] %

Yes, this is a polynomial, but a special form of a polynomial with just one term which is called a monomial .

Answer:

8.333333333 or 25 /3​

Step-by-step explanation:

3 feet in a yard... 12x3 = 36...... 36+36+36 =108 inches

108 divided by 6 is 18 bracelets

Answer:

9

Step-by-step explanation:

240x.70=168 left after 30% to teacher

168/2=84 left after putting half in jar

25 students x 3=75 given to students

84-75=9 left

Answer:

Your expected loss per game is of $0.31.

Step-by-step explanation:

In a standard 52-card deck, we have that:

There are 12 face cards.

What is your expected gain or loss (in dollars) per game?

12/52 probability of winning $2.

1 - 12/52 = 52/52 - 12/52 = 40/52 probability of losing $1. So

[tex]E = \frac{12}{52}*2 - \frac{40}{52}*1 = \frac{24 - 40}{52} = -\frac{16}{52} = -0.31[/tex]

Negative, so a loss is expected.

Your expected loss per game is of $0.31.

Answer:

262 feet²

Step-by-step explanation:

2(5×8 + 5×7 + 8×7)

2(40+35+56)

2(131)

262

---

hope it helps

The ordered pairs in each set are:

A ✕ B = {(-4, 4), (-4, 7), (4, 4), (4, 7), (7, 4), (7, 7), (9, 4), (9, 7)}

R = {(-4, 4), (4, 4), (7, 7), (9, 9)}

S = {(-4, 4), (-4, 7), (4, 4), (4, 7), (7, 7), (7, 4), (9, 9), (9, 7)}

R ∪ S = {(-4, 4), (-4, 7), (4, 4), (4, 7), (7, 7), (7, 4), (9, 9), (9, 7)}

R ∩ S = {(-4, 4), (4, 4), (7, 7), (9, 9)}

We have,

A ✕ B:

The concept of Cartesian product was used to generate all possible ordered pairs by pairing each element from set A with each element from set B.

R:

The concept of the absolute value was used to determine the condition for an ordered pair (x, y) to be in relation R, which is that the absolute value of x is equal to the absolute value of y.

S:

The concept of even numbers was used to determine the condition for an ordered pair (x, y) to be in relation S, which is that the difference between x and y is an even number.

R ∪ S:

The concept of a union was used to combine the ordered pairs that are in either relation R or relation S.

R ∩ S:

The concept of intersection was used to find the ordered pairs that are common to both relation R and relation S.

Thus,

The ordered pairs in each set are:

A ✕ B = {(-4, 4), (-4, 7), (4, 4), (4, 7), (7, 4), (7, 7), (9, 4), (9, 7)}

R = {(-4, 4), (4, 4), (7, 7), (9, 9)}

S = {(-4, 4), (-4, 7), (4, 4), (4, 7), (7, 7), (7, 4), (9, 9), (9, 7)}

R ∪ S = {(-4, 4), (-4, 7), (4, 4), (4, 7), (7, 7), (7, 4), (9, 9), (9, 7)}

R ∩ S = {(-4, 4), (4, 4), (7, 7), (9, 9)}

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Answer:

Hey! I'm honestly not sure.

Step-by-step explanation:

I dont have the app... but on the website I'm pretty sure they dont have any.

Have a nice day <3

let h= 4, k=-2 and r= 7 then

(x-h)^2 + (y-k)^2 = r^2

(x-4)^2 + (y+2)^2 = 7^2

x^2 -8x +16 + y^2 +4y +4 = 49

x^2 +y^2 -8x +4y +16 +4-49 = 0

x^2 + y^2 -8x +4y -29 = 0 is the required eq

Answers:

=======================================================

Explanation:

Refer to the diagram below. The point (8,-15) is in quadrant 4, which is the southeast quadrant. A right triangle forms where the hypotenuse goes from the origin to the terminal point in question. After applying the pythagorean theorem, the hypotenuse is 17 units long.

Opposite the reference angle θ, greek letter theta, the side is -15. Usually negative lengths are not allowed and don't make any sense; however, I'm making this negative to ensure that sin(θ) ends up negative. This will help with other trig ratios as well.

So,

sin(angle) = opposite/hypotenuse

sin(θ) = -15/17

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

The cosine ratio will involve the adjacent and hypotenuse

cos(angle) = adjacent/hypotenuse

cos(θ) = 8/17

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

Tangent is opposite over adjacent

tan(angle) = opposite/adjacent

tan(θ) = -15/8

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

The functions csc(θ), sec(θ), and cot(θ) are the functions cosecant, secant, and cotangent in that order.

They represent the reciprocal of sine, cosine, and tangent in that order as well.

Eg: sec(θ) is the reciprocal of cos(θ)

This means,

As an alternative, you could also say

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

Here's a list of formulas that you can write down on a reference sheet

where h is the hypotenuse and h = sqrt(x^2+y^2). Notice that something like tan = y/x is the reciprocal of cot = x/y. The x and y refers to the coordinates of the terminal point given to you. Make sure to reduce all fractions as much as possible. In our case, none of the fractions can be reduced any further.

Answer:

X is 15 and Y is 40° That's the answer

Answer:

It would be 1/10

Step-by-step explanation:

The ratio is 2:20

To put the ratio in fraction form you simply put 2/20

Then divide the fraction by 2 to get 1/10