A number multiplied by third of itself makes the product 10584, what is the number ?​

The minimum distance  between the point(-3,2) and the line y = -x + 1  is [tex]\sqrt{2}[/tex] units.

The line that joins  two points on a cartesian plane is a line segment.

Analysis:

The formula for calculating distance between a line and a point is

d = [tex]\frac{Ax1 + By1 + c}{\sqrt{A^{2} + B^{2} } }[/tex]

where A = coefficient of x term of the line, B = coefficient of y in the line and C is the constant term of the line.

x1 and y1 are coordinates of the point.

for the line y = -x + 1 which is  = y + x -1 = 0, A = 1, B = 1, C = -1, x1 = -3, y = 2
d = [tex]\frac{1(-3) + 1(2) + (-1)}{\sqrt{(-3)^{2} + 2^{2} } }[/tex]= [tex]\sqrt{2}[/tex] units

In conclusion, the distance between the point and the line is  [tex]\sqrt{2}[/tex] units

Learn more about distance between line segments: brainly.com/question/2437195

#SPJ1

Answer:

a. $3150

b. $3307.50, $3472.875

c. B(n) = 3000(1.05)^t

Step-by-step explanation:

just a disclaimer i havent done interest in a while so this might not be right

also im assuming this is compound interest

a. P = original amount; r = interest percentage, x = amount of total money

x = P(1 + (r/100)) = 3000(1 + 0.05) = 3150

b. x = 3000(1.05)^2,3 = 3307.5, 3472.875

c. B(n) = P(1+(r/100)^t for t in years. plug in the values to get B(n) = 3000(1.05)^t

Step-by-step explanation:

the answer is 5 percentage because the formula is 100 * 400 over 4000 * 2

Answer:The result follows from manipulating the conditional probability. By definition,

By the law of total probability,

So we have

Step-by-step explanation:

P(A|B) = P(B|A)×P(A)/P(B)

so, in our case

P(A3|B1) = P(B1|A3)×P(A3)/P(B1) = 0.1×0.4/P(B1)

I assume that the problem definition means that A1, A2, A3 are independent and not overlapping events (hence their sum is 1). and therefore, B1 can only happen after A1 or after A2 or after A3. there is no other possibility for B1 to happen.

so,

P(B1) = P(B1|A1) + P(B1|A2) + P(B1|A3) =

= 0.25 + 0.05 + 0.1 = 0.4

therefore,

P(A3|B1) = P(B1|A3)×P(A3)/P(B1) = 0.1×0.4/0.4 = 0.1

Answer:

1.052 × 10⁶

Step-by-step explanation:

82,000 + 970,000 = 1,052,000

Answer:

[tex]\left(8.2\cdot \:10^4\right)+\left(9.7\cdot \:10^5\right)=1,052,000[/tex]

Step-by-step explanation:

[tex]\left(8.2\cdot \:10^4\right)+\left(9.7\cdot \:10^5\right)\\=8.2\cdot \:10^4+9.7\cdot \:10^5\\\\\rightarrow 10^4 = 10000\\= 8.2 \cdot 10000\\= 82000\\\rightarrow 10^5 = 100000\\= 9.7 \cdot 100000\\= 970000[/tex]

[tex]970000 + 82000 = 1052000[/tex]

The table in which y varies directly with x is table C.

When a variable varies directly with another variable, it means that as one variable increases, the other variable also increases.

The equation that is used to represent direct variation is:

y = kx

Where y is the constant of proportionality

In table c, k is equal to 26

To learn more about direct variation, please check: https://brainly.com/question/27573249

#SPJ1

Answer:

Calculate it you will now the answer and im elementery school

Factorize the numerator and denominator, then simplify:

10/45 = (2×5)/(9×5) = 2/9

Now,

1/9 = 1/10 + 1/90

1/90 = 1/10 × 1/9 = 1/10 × (1/10 + 1/90) = 1/100 + 1/900

1/900 = 1/100 × 1/9 = 1/100 × (1/10 + 1/90) = 1/1000 + 1/9000

and so on, which is to say

1/9 = 1/10 + 1/100 + 1/1000 + …

or

1/9 = 0.111…

so that multiplying both sides by 2 gives

2/9 = 0.222…

Answer:

Step-by-step explanation:

There are 36 ways 2 dice can be thrown. Sometimes colors are used to tell the difference between the dice.

36 comes from 6*6

Suppose you have 2 dice 1 blue and the other white

Blue      White

1              1

              2

              3

              4

              5

              6

There's 6 ways that have been thrown. Then you go to the blue dice being 2. You get six more. Then 3 gives you six more 4 gives you another six. and so on. The whole procedure adds to 36

you can throw a four 3 ways

Blue       white

1               3

3              1

2              2

You can throw 7 six ways

Blue         white

1                 6

6                1

2               5

5               2

3               4

4               3

So of the 36 ways to throw the dice 9 will successful. (6 + 3)

Answer: 9/36 = 1/4 times you will be successful

Answer:

Step-by-step explanation:

#a

pattern 0 will include 4 reds in square

Because it's independent of pattern no

#b

Figure 1 has 4+4=8

Figure 2=4+8+2=14

Figure 3=4+12+3=19

The pattern n rule is

So for 13th n

#c

attached

#d

Already given in c

Answer:

  6√3 ±3 ≈ {7.392, 13.392}

Step-by-step explanation:

The length of AB is the long side of a right triangle with hypotenuse CD and short side (AC -BD). The desired radius values will be half the length of EF, with AE added or subtracted.

__

Radii AC and BD are perpendicular to the points of tangency at A and B. They differ in length by AC -BD = 12 -9 = 3 units.

A right triangle can be drawn as in the attached figure, where it is shaded and labeled with vertices A, B, C. Its long leg (AB in the attachment) is the long leg of the right triangle with hypotenuse 21 and short leg 3. The length of that leg is found from the Pythagorean theorem to be ...

  AB = √(21² -3²) = √432 = 12√3

This is the same as the distance EF. Half this length, 6√3, is the distance from the midpoint of EF to E or F. The radii of the tangent circles to circles E and F will be (EF/2 ±3). Those values are ...

  6√3 ±3 ≈ {7.392, 13.392}

Answer:

6√3 ± 3

Step-by-step explanation:

AC is the radius of Circle C ⇒ radius = 12

DB is the radius of Circle D ⇒ radius = 9

Therefore, CD = AC + DB = 12 + 9 = 21

AE is the radius of Circle E ⇒ radius = 3

BF is the radius of Circle F ⇒ radius = 3

If AB is the common tangent of Circles C, D, E and F, then:

∠CAB =∠AEF = ∠DBA = ∠BFE = 90°

(as the tangent to a circle is always perpendicular its the radius).

Also AB = EF

To find the possible radii of a circle whose center is the midpoint of EF and is tangent to both circles E and F, we first need to find the length of EF (marked by x on the attached diagram).

CD is the hypotenuse of a right triangle with base equal to EF and a smaller leg of the difference between the radii of Circles C and D.

(Refer to the green shaded triangle on attachment 1)

Therefore, to find EF (x), use Pythagoras' Theorem a² + b² = c²
(where a and b are the legs, and c is the hypotenuse, of a right triangle)

⇒ a² + b² = c²

⇒ 3² + x² = CD²

⇒ 3² + x² = (12 + 9)²

⇒ 9 + x² = 441

⇒ x² = 432

⇒ x = √432

⇒ x = 12√3

⇒ EF = 12√3

As the radius of Circles E and F is 3, the possible diameter of the circle with its center as the midpoint of EF is 6 less or 6 more than the length of EF.

⇒ diameter = EF ± 6

                   = 12√3 ± 6

As the radius is half of the diameter, the possible radii of a circle whose center is the midpoint of EF and is tangent to both circles E and F is:

⇒ radius = diameter ÷ 2

               = (12√3 ± 6) ÷ 2

               = 6√3 ± 3

(see attachments 2 and 3 → the possible circles are shown in orange)

The number of years it would take $4000 to grow to $4616 is 2.92 years.

When an amount earns compound interest compounded semi annually, it means that both the amount invested and the interest accrued increases in value twice yearly.

Number of years = (In FV / PV) / r

(In 4616 / 4000) / 0.049 = 2.92 years

To learn more about compound interest, please check: https://brainly.com/question/24260765

#SPJ1

Step-by-step explanation:      

Step 1: Simplify

[tex]4+9x^2/3 - 1[/tex]

[tex]=4+3x^2+-1[/tex]

Step 2: Combine Like Terms:

[tex]= 4+3x^2+1-1[/tex]

[tex]= (3x^2)+(4+-1)[/tex]

Answer: [tex]= 3x^2+3[/tex]

Explanation in words (Short Form)

-  The first step is to use the formula and simplify it. So first we will Rewrite the division as a fraction.

- The second step is to Cancel the common factor of 9 and 3. Then Factor 3 out of 3. After that Cancel the common factor.

- The third step is to divide [tex]3x^2[/tex] by 1. Then at the end, subtract 1 from 4. The answer will result as [tex]3x^2+3[/tex]

Answer:    

[tex]=3x^2+3[/tex]

Hope this helps.

Answer:

x = 3 or x = 1

y = 3 or y = -1

(x, y) = (3, 3)

(x, y) = (1, -1)

Step-by-step explanation:

Answer:

3rd

Step-by-step explanation:

If you know about linear eq. it's just a simple rule no worry

If Mr. Price adds two more CDs that are 38 minutes and 40 minutes, the third quartile would increase.

A box plot is used to study the distribution and level of a set of scores. The two whiskers represent the minimum and maximum value.

On the box, the first line to the left represents the lower (first) quartile. The next line on the box represents the median. The third line on the box represents the upper (third) quartile.

When the two CDs are added, the median would decrease. The first quartile and the third quartile would increase. The interquartile range would increase.

To learn more about box plots, please check: https://brainly.com/question/27215146

#SPJ1

Answer:

the class earned $722059884

Step-by-step explanation:

because each person sold 444 tickets and there was 232323 students

=232323×444

=103151412

because 103151412 tickets were sold and a ticket cost $7

=103151412×7

=722059884

The acute angles of a right triangle are complementary, so:

[tex]m\angle B=90-27=\boxed{63^{\circ}}\\m\angle F=90-31=\boxed{59^{\circ}}[/tex]

The correct answer is option A which is the expression will be 0.9S.

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Given that:-

At the end of every month, Katie saves 20 percent of her take-home pay after her taxes. If Katie is taxed at a 25 percent tax rate,

The expression of the salary after six months will be calculated as:-

Let the gross salary is S

The net salary will be = 0.75S

Savings will be = 0.75 x 0.20 S = 0.15S

After six months the savings will be:-

Savings  = 0.15 x 6 S

Savings = 0.9S.

Therefore the correct answer is option A which is the expression will be 0.9S.

To know more about Expression follow

https://brainly.com/question/723406

#SPJ1

Answer: A triangle that only has two congruent sides is called an isosceles triangle. Two equal sides and two equal angles.

Answer:

Sqrt (11/8)

Step-by-step explanation:

Sec^2 - Tan^2 = 1

- Tan^2 = 1 - Sec^2

Tan^2 = -1 + Sec^2

Tan^2 = 3/8

3/8 = -1 + Sec^2 Theta

1 + 3/8 = Sec ^2 Theta

11/8 = Sec^2 Theta

Sqrt ( 11/8) = Sec of theta

-- Gage Millar, Algebra 1/2 Tutor (Pending Pre-Calc Tutor)

The frequency table that shows the relative frequency of people older than 40 and don't visit the dentist is:

D.                  Visit Dentist Yearly Don’t Visit Dentist Yearly

Below 40                    0.27                         0.73

Above 40                   0.57                          0.43

The relative frequency of those older than 40 and don't go annually to a dentist can be found as:

= Number of over 40 who don't go to dentist / Total of those over 40 surveyed

Solving gives:

= 13 / (17 + 13)

= 13 / 30

= 0.43

Find out more on relative frequency at https://brainly.com/question/16832475.

#SPJ1

Answer:

Its D, I got it right on a test :)

Step-by-step explanation:

[tex]\huge\boxed{Formula: r= \frac{d}{2}}[/tex]

Substitute the values according to the formula.

[tex]r=\frac{94}{2}[/tex]

[tex]\large\boxed{r=47 \: cm}[/tex]

Now, let's find the area.

[tex]\huge\boxed{Formula:a= \pi{r}^{2}}[/tex]

So, we'll have to multiply π, 47 and 47.

Substitute the values according to the formula.

[tex]a= \pi{47}^{2}[/tex]

[tex]a= 6939.778172 \: {cm}^{2}[/tex]

[tex]\large\boxed{a= 6939.8 \: {cm}^{2}(1 \: d.p)}[/tex]

Hence, the area of the given circle is 6939.8 square centimeters.

Hi student, let me help you out! :)

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

We are asked to find the radius & area of the circle.

To find the [tex]\star\bf{radius}\star[/tex], we divide the diameter by 2:

[tex]\star~\bf{94\div2}[/tex]

[tex]\star~\bf{Radius=47}\star[/tex]

Now that we have the radius, let's compute the area! :)

///\\\///\\\///\\\///\\\///\\\////\\\///\\///\\\///\\\\///\\\///\\\///\\\////\\\///\\\///\\\///\\//\\\//\\

                            Calculating the Area

We can work out the area of a circle by using this formula:

[tex]\star\boxed{\pmb{A_{(circle)}=\pi r^2}}\star[/tex]

Where

[tex]\dag[/tex] A=Area of a circle

[tex]\dag[/tex] [tex]\pi =3.14...[/tex]

[tex]\dag[/tex] r=radius

Have you noticed the [tex]\large\pmb{^2}[/tex] next to r? This tells us that we should multiply the radius times itself.

Now it's time to substitute the values:

[tex]\star~\large\pmb{A=3.14\times47^{2}}\star[/tex]

Let's simplify it. The acronym PEMDAS will help us, and we won't make any mistakes in the Order of Operations! :)

Here's what it stands for:

P=Parentheses

E=Exponents

M=Multiplication

D=Division

A=Addition

S=Subtraction

2 is an exponent.

So what do you think we should do first?

[tex]\square[/tex] Square 47.

[tex]\square[/tex] Multiply 3.14 times 47 and then square.

That's right, we should square 47 first. :)

[tex]\star~\large\pmb{A=\pi \times2209}}\star[/tex]

Now, according to PEMDAS, we should multiply pi times 2209; after multiplying, we obtain:

[tex]\star~\large\pmb{A=6936.8\:cm^2}\star[/tex]

Remember, the area of any shape is measured in units squared.

[tex]\ddot\bigstar[/tex] Remember this...

[tex]\fbox{\bf{The\;area\;of\;any\;shape\;is\;measured\;in\;units\;squared}}[/tex]

Hope this helps you out! :D

Ask in comments if any queries arise.

#StudyWithBrainly

~Just a smiley person helping fellow students :)

[tex]\bigstar\footnotesize\pmb{M^ar_ib^el\;Peri}[/tex]

Answer:

C. g(x) = sqrt(x+8)-2

Step-by-step explanation:

"Shift two units down" is easier to see in the equation because an up or down shift is just tacked right on to the end of the equation. So "shift DOWN 2" is a minus two on the end of the equation. This means that A and D are both NOT the answer.

Left and right shifts are the opposite of what you might expect. Left shift is a "+ anumber" and Right shift is

"- anumber" This is tucked in very close to the x, because a left or right shift is a change in the x-direction. Again left shift is "+ anumber", so in your question, "shift eight units left" shows in the equation as the plus8 beside the x.

So B is wrong and C is the answer.

Answer:

3

Step-by-step explanation:

Parallel lines are a fixed distance apart and will never meet, no matter how long they are extended. Lines that are parallel have the same gradient . The equations above, y = 3x -2 and y = ?  x +3  have the same gradient of 3 if they are to be parallel

Hope you understood and this helped and have a good day

An automobile manufacturer produces production parts with 98% accuracy.  the probability is mathematically given as

P(X\leq2) = 0.9868

Generally, the equation for the probability is mathematically given as

[tex]P(X\leq2) = P(X=0) + P(X=1) + P(X=2)[/tex]

Therefore

[tex]P(X=0)=\binom{25}{0}* 0.98^{25}* 0.02^{0}=1* 0.6035* 1\\\\P(X=0)=0.6035[/tex]

Hence

P(X=1)=0.3079

P(X=0)=0.07554

In conclusion, bringing the equation into view

 [tex]P(X\leq2) = P(X=0) + P(X=1) + P(X=2)[/tex]

[tex]P(X\leq2) = 0.6035 +0.3079 + 0.07554[/tex]

P(X\leq2) = 0.9868

Read more about probability

https://brainly.com/question/795909

#SPJ1

The figures that can have a triangle as a two-dimensional cross section are (4) I, III, and IV, only

The cross-section of three-dimensional figures are as a result of slicing the figure along its axis.

Hence, the figures that can have a triangle as a two-dimensional cross section are (4) I, III, and IV, only

Read more about cross section at:

https://brainly.com/question/3603397

#SPJ1

Answer:

r = 5   ; s = -9

Step-by-step explanation:

First simplify √8  by

   [tex]\sf \sqrt{8}=\sqrt{2*2*2} = 2\sqrt{2}\\[/tex]

[tex]\sf \dfrac{5+\sqrt{2}}{4}+\sqrt{8}= \dfrac{5+\sqrt{2}}{4}+ 2\sqrt{2}[/tex]

          Find LCM and simplify

                     [tex]\sf = \dfrac{5+\sqrt{2}}{4}+\dfrac{2\sqrt{2}*4}{1*4}\\\\ =\dfrac{5+\sqrt{2}+8\sqrt{2}}{4} \ {\bf Combine \ like\ terms} \\\\ = \dfrac{5+9\sqrt{2}}{4}\\\\[/tex]

 [tex]\sf \boxed{r=5}\\\\\boxed{s =-9}[/tex]