There is a bag a filled with 3 blue and 4 red marbles.
A marble is taken at random from the bag, the colour is noted and
then it iS not replaced.
Another marble is taken at random.
What is the probability of getting 2 of the same colour?

Answer:

a. 7 by 21

b. a(-12, 2), b(-12, -5), c(9, -5)

Step-by-step explanation:

AD is 3 times the length of AB. X can be the length of AB. Then 3x would be the length of AD. The perimeter is 56, which would also be 3x + x + 3x + x which is 8x. This gives us 8x = 56, meaning that x is 7, or the length of AB is 7. Because AD is 3 times the length of AB (which is 7), AD = 21. Therefore, the dimensions of the rectangle ABCD is 7 by 21.

Coordinates of A have to be 21 units away from D since AD = 21. It goes in the left direction, meaning that 21 is subtracted from 9 (since this is a horizontal edge involving x coordinates) while the y value remains the same. The result is (-12, 2). For coordinate B, it has to be 7 units away from A downwards since AB = 7. This means that you subtract 7 from 2 (involving only the y coordinates), resulting in (-12, -5). For coordinate C, it has to be 21 units from B since BC = AD = 21.  Because C is right compared to B, you have to add 21 to -12 (involving only the x coordinate) resulting in (9, -5).

[tex]tan(\theta )=\sqrt{3}\implies tan(\theta )=\cfrac{\sqrt{3}}{1}\implies tan(\theta )=\cfrac{\sqrt{3}}{1}\cdot \cfrac{2}{2} \implies tan(\theta )=\cfrac{\sqrt{3}}{2}\cdot \cfrac{2}{1} \\\\\\ tan(\theta )=\cfrac{~~\stackrel{sin(\theta )}{\frac{\sqrt{3}}{2}} ~~}{\underset{cos(\theta )}{\frac{1}{2}}}\implies \theta =tan^{-1}\left( \cfrac{~~\frac{\sqrt{3}}{2} ~~}{\frac{1}{2}} \right)\implies \theta = \begin{cases} \stackrel{I~Quadrant}{60^o}\\\\ \stackrel{III~Quadrant}{240^o} \end{cases}[/tex]

Check the picture below.

[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$500\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{yearly, thus once} \end{array}\dotfill &1\\ t=years\dotfill &4 \end{cases} \\\\\\ A=500\left(1+\frac{0.05}{1}\right)^{1\cdot 4}\implies A=500(1.05)^4\implies A\approx 607.75[/tex]

The final amount will be $607.75 after 4 years if the principal amount is $500 and it compounded annually with interest rate of 5%

It is defined as the interest on the principal value or deposit and the interest which is gained on the principal value in the previous year.

We can calculate the compound interest using the below formula:

[tex]\rm A = P(1+r)^t[/tex]

Where A = Final amount

          P = Principal amount

          r  = annual rate of interest

          n = how many times interest is compounded per year

          t = How long the money is deposited or borrowed (in years)

We have in the problem:

P = $500, r = 5% = 0.05, and n = 4 years

[tex]\rm A = 500(1+0.05)^4[/tex]

A = $607.75

Thus, the final amount will be $607.75 after 4 years if the principal amount is $500 and it compounded annually with interest rate of 5%

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#SPJ4

For this case we have the following polynomial:

x2 + x - 12

Factoring we have:

(x-3) (x + 4)

We note that the polynomial is written as:

(x + p) (x + q)

Thus,

p = -3

q = 4

Answer:

The values of p and q that can be used to factor x2 + x - 12 as (x + p) (x + q) are:

C. -3 and 4

Have a nice day ‍

Answer:

The answer is 12.56, which can be rounded to 12.7 or 13. :)

Answer:

B. $34,086

Step-by-step explanation:

did the math

The total amount of annual take-home pay of Cynthia is $34,086.25

Income tax is a tax applied on individuals or entities concerning income or profit earned by them.

Cynthia earns $41,875 annually.

If the Canadian government levies an income tax of 18.6% on Cynthia’s tax bracket.

It can be calculated as

41,875 × 18.6%

41,875 × 18.6/100 = 7,788.75

The annual take-home pay

41,875 - 7,788.75 = $34,086.25

Thus, The total amount of annual take-home pay is $34,086.25.

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Answer: 18x + 12

Step-by-step explanation:

Step #1: Determine the length of each side.

The polygon is regular, so all the sides are equal. Thus, all sides measure 3x+2.

Step #2: Determine the number of sides in the polygon.

This polygon is identified as a hexagon meaning it consists of 6 sides.

Step #3: Set up an expression and distribute.

       (Number of sides) x (Length of each side)

       (6)(3x+2)

So, the answer is 18x + 12.

Answer:

B. 3x + 2

Step-by-step explanation:

The polygon has 6 equal sides.

1 side has a side length of 3x + 2

Therefore, all sides of the polygon measure 3x + 2

Hope this helps!

Answer:

Correct answer: a.

Computation:

{eq}\begin{align*} {\rm\text{Present}}\;{\rm\text{value}}\;{\rm\text{of}}\;{\rm\text{an}}\;{\rm{annuity}}\;

Step-by-step explanation:

Financing:

Financing is generally the method to provide funds to the business so that the business can grow its operations. There are generally two types of financing. These are: Equity financing and debt financing. In debt financing, there is no obligation and burden to repay the funds acquired by it. Debt Financing is comparatively Cheaper than the Equity Financing.So The Answer Is A

The amount that you pay over the lifetime of the loan is $21,445.5. Then the correct option is D.

The amount of something is expressed as if it is a part of the total which is a hundred. The ratio can be expressed as a fraction of 100. The word percent means per 100. It is represented by the symbol ‘%’.

Big Ed’s car dealership is running a special on 2008 trucks.

Big Ed offers financing at a rate of 6.71% on a loan with a term of 36 months, but he requires the customer to make a down payment of 15% of the cost of the vehicle.

You are interested in a Car Crusher truck that costs $25,230.

Not including the down payment, the amount that you pay over the lifetime of the loan will be

⇒ (1 - 0.15) × $25,230

⇒ 0.85 × $25,230

⇒ $21,445.5

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Answer:

180 cm

Step-by-step explanation:

Answer:

x= 5

Step-by-step explanation:

Since RQ= PQ,

3x= 15

Divide both sides by 3:

x= 15 ÷3

[tex]\textcolor{red}{x = 5}[/tex]

[tex]\textcolor{steelblue}{\text{Prove for RQ}= \text{PQ}}[/tex]

Let SP= x

RS= SP= x (given)

Let SQ= y

Applying Pythagoras' Theorem,

In triangle QRS

(RQ)²= (RS)² +(SQ)²

(RQ)²= x² +y²

[tex]RQ = \sqrt{ {x}^{2} + {y}^{2} } [/tex]

In triangle QPS

(PQ)²= (SP)² +(SQ)²

(PQ)²= x² +y²

[tex]PQ = \sqrt{ {x}^{2} + {y}^{2} } [/tex]

Thus, RQ= PQ.

Answer:

Step-by-step explanation:

3x = 15

3x/3 = 15/3

x = 5

3(5) = 15

Answer:

$8.52 that should be the answer

Answer:

$64,000

Step-by-step explanation:

Friday, 45 / 9 = 5

So the investment will double 5 times

First time

2,000 (starting investment) × 2 = 4000

Second time

4000 × 2 = 8000

Third time

8000 × 2 = 16000

Fourth time

16000 × 2 = 32000

Fifth and final time

32000 × 2 = 64000

$64,000

Answer:

x = -8

y = 0

Step-by-step explanation:

Answer:

- 13p + 8k

Step-by-step explanation:

[tex]4k-8p+4k-5p[/tex]

[tex]\mathrm{Group\:like\:terms}[/tex]

[tex]=-8p-5p+4k+4k[/tex]

[tex]\mathrm{Add\:similar\:elements:}\:-8p-5p=-13p[/tex]

[tex]=-13p+4k+4k[/tex]

[tex]\mathrm{Add\:similar\:elements:}\:4k+4k=8k[/tex]

[tex]=-13p+8k[/tex]

[RevyBreeze]

Answer: the answer is “B”

Step-by-step explanation: answer is LETTER B

Total outcomes:

So the final answer is "60"

Answer:

126 is a term in the sequence.  Please check my assumption on the correct formula.

Step-by-step explanation:

I will assume that n2 + 5 is actually n^2 + 5.

Starting with n=0, use the formula to calculate successive values of n.  The attached table is the result of n from 0 to 22.  At n=11, the result is 126, so 126 is a term in the sequence.

If the expression is actually n2 + 5, calculate the values for y = 2n + 5.  126 would not be a term in this sequence.

Answer:

Your answer would be:
A.) (36 × 6) + (c × 4) = 232

Step-by-step explanation:

Have a great rest of your day
#TheWizzer

Answer:

13 [tex]\frac{1}{3}[/tex]% are green

Step-by-step explanation:

totalling the marbles

red = 6

blue = 7

green = 4

orange = 13

total marbles = 6 + 7 + 4 + 13 = 30

fraction of green marbles = [tex]\frac{4}{30}[/tex] = [tex]\frac{2}{15}[/tex]

To change a fraction to a percentage multiply the fraction by 100%

[tex]\frac{2}{15}[/tex] × 100% = 0.1333.. × 100% = 13.33 % = 13 [tex]\frac{1}{3}[/tex]%

Step-by-step explanation:

the area of a full circle (360°) is

pi×r²

r = 15 ft in our case

the area of a segment of a circle is the corresponding fraction of the whole circle area.

the angle of the shaded area is

360 - 332 = 28°

therefore, the area of the shaded area is

pi×15²×28/360 = pi×225×28/360 = pi×225×7/90 =

= pi×5×7/2 = 54.97787144... ft²

≈ 54.98 ft²

the area of the "ice rink" is the sum of a rectangle and a circle (which is split into 2 halves that are attached to both sides of the rectangle).

the radius of the circle is 7/2 = 3.5 meters.

the length of the rectangle in the middle is

18 - 2×3.5 = 18 - 7 = 11 meters.

so, the area of the rectangle is 11×7 = 77 m²

the area of the circle is

pi×r² = pi×3.5² = pi×12.25 = 38.48451001... m²

that means the total area is

77 + 38.48451001... = 115.48451... m² ≈ 115.48 m²

Answer:

[tex]x=43[/tex]

Step-by-step explanation:

Given equation:

[tex]25=5(3x-4)^{\frac13}[/tex]

Divide both sides by 5:

[tex]\implies 5=(3x-4)^{\frac13}[/tex]

Cube both sides:

[tex]\implies 5^3=((3x-4)^{\frac13})^3[/tex]

[tex]\implies 125=(3x-4)^{\frac33}[/tex]

[tex]\implies 125=(3x-4)^1[/tex]

[tex]\implies 125=3x-4[/tex]

Add 4 to both sides:

[tex]\implies 129=3x[/tex]

Divide both sides by 3:

[tex]\implies x=43[/tex]

Answer:

x = 43

Step-by-step explanation:

The type II error is the probability of accepting the null hypothesis when it's false.

a. From the information, the proportion of parents who passes the sign language test is not less than 25%.

b. Since the p value is greater than 0.05, the null hypothesis is rejected. Therefore, the proportion of parents who passes the sign language test is not less than 25%.

c. The possible defect in the study is that the parents if the children with hearing problem should be selected randomly.

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Step-by-step explanation:

c² = a² + b²

c² = 7² + 11²

c² = 49 + 121

c² = 170

now u have to square root it

c² = 170

c = 13

Answer:

The bearing of B from A is 335 Degrees

Step-by-step explanation:

Measure bearings clockwise.

Bearings are measured from the North line.

There are 25 degrees between B and North.

360 Degrees in a circle.

360 - 25 = 335

Answer:

4 minutes

Step-by-step explanation:

4 minutes has 2 dots associated with it . All other times have only 1 dot.

then 4 minutes is the most common out of the 7

Answer

C you cannot divide matricies like that

Step-by-step explanation:

you can only multiply by the inverse in which the order matters. if there is a 4th possible answer then that may be more correct

Answer:

I believe your answer would be Soundis

Answer:

A material through which sound waves can travel is called a medium.

1.1 2.4 3.3 right

Step-by-step explanation:

no have

The probability that a point chosen at random in the square is in the blue region is given by: Option D: 0.75

When probability is in terms of area or volume or length etc geometric amounts (when infinite points are there), we can use this definition:

Then:

[tex]P(E) = \dfrac{A(E)}{A(S)}[/tex]

where A(E) is the area/volume/length for event E, and similar for A(S).

For this case, we're given that:

The favorable space is the blue shaded region.

The total sample space is the area of the considered square.

Let we take:

E = event of choosing point in the blue shaded region

Now, we have:

Area of blue region = Area of triangle with base = height = 8 inches + Area of right sided triangle which has base of 4 inch (look it upside down), and height of 8 inches

Area of blue region = [tex]\dfrac{1}{2} \times (8 \times 8 + 4 \times 8) = 48 \: \rm in^2[/tex]

Area of the square of sized 8 inches = 64 sq. inches.

Thus, we get:

[tex]P(E) = \dfrac{A(E)}{A(S)} = \dfrac{48}{64} = \dfrac{3}{4} = 0.75[/tex]

Thus, the probability that a point chosen at random in the square is in the blue region is given by: Option D: 0.75

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