Rewrite as a simplified fraction.
\large{0.\overline{8} = {?}}0.
8
=?0, point, start overline, 8, end overline, equals, question mark

Answer:

boys: total

3          8

Step-by-step explanation:

boys:girls: total

9    :  15   :  9+15

9        15      24

Divide each by 3

3         5        8

We want the ratio of boy to total

boys: total

3          8

Answer:

there must be at least two lines on any plane because a plane is defined by 3 non-collinear points.

Step-by-step explanation:

Answer:

The measure of [tex]x_{w}[/tex] is 4 units.

Step-by-step explanation:

According to the definition of tangent, it is equal to:

[tex]\tan f = \frac{y_{w}}{x_{w}}[/tex]

Where:

[tex]f[/tex] - Angle, measured in sexagesimal degrees.

[tex]x_{w}[/tex] - Adjacent side, measured in units.

[tex]y_{w}[/tex] - Opposite side, measured in units.

If [tex]\tan f = \frac{2}{1}[/tex] and [tex]y_{w} = 8\,units[/tex], the adjacent side is:

[tex]x_{w} = \frac{y_{w}}{\tan f}[/tex]

[tex]x_{w} = \frac{8\,units}{\frac{2}{1} }[/tex]

[tex]x_{w} = 4\,units[/tex]

The measure of [tex]x_{w}[/tex] is 4 units.

The  measure of xw is 4 units

Given the following parameters

Tan fº = 2/1

This shows that;

Opposite side YW = 2

Adjacent side XW = 1

Given that YW is  8units, using the ratio of similar sides

2/1 = 8/XW

2XW = 8

XW = 4

Hence the  measure of xw is 4 units

Learn more on similar figures here: https://brainly.com/question/2644832

Answer:

see explanation

Step-by-step explanation:

Using the identity

cos2Θ = 1 - 2sin²Θ, then

1 - 2sin²([tex]\frac{\pi }{4}[/tex] - [tex]\frac{0}{2}[/tex] )

= cos [2([tex]\frac{\pi }{4}[/tex] - [tex]\frac{0}{2}[/tex] )]

= sos([tex]\frac{\pi }{2}[/tex] - Θ )

= cos[tex]\frac{\pi }{2}[/tex]cosΘ + sin

= 0 × cosΘ + 1 × sinΘ

= 0 + sinΘ

= sinΘ = right side

Answer:  see proof below

Step-by-step explanation:

Use the Difference Identity: sin (A + B) = sin A cos B - cos A sin B

Use the following Half-Angle Identities:  

[tex]\sin\bigg(\dfrac{A}{2}\bigg)=\sqrt{\dfrac{1-\cos A}{2}}\\\\\cos\bigg(\dfrac{A}{2}\bigg)=\sqrt{\dfrac{1+\cos A}{2}}[/tex]

Use the Pythagorean Identity: cos²A + sin²A = 1   -->   sin²A = 1 - cos²A

Use the Unit Circle to evaluate: [tex]\cos\dfrac{\pi}{4}=\sin\dfrac{\pi}{4}=\dfrac{1}{\sqrt2}[/tex]

Proof LHS → RHS

[tex]\text{Given:}\qquad \qquad \qquad 1-2\sin^2\bigg(\dfrac{\pi}{4}-\dfrac{\theta}{2}\bigg)\\\\\text{Difference Identity:}\quad 1-2\bigg(\sin\dfrac{\pi}{4}\cdot \cos \dfrac{\theta}{2}-\cos \dfrac{\pi}{4}\cdot \sin\dfrac{\theta}{2}\bigg)^2\\\\\text{Unit Circle:}\qquad \qquad 1-2\bigg(\dfrac{1}{\sqrt2}\cos \dfrac{\theta}{2}-\dfrac{1}{\sqrt2}\sin \dfrac{\theta}{2}\bigg)^2\\\\\\\text{Half-Angle Identity:}\quad 1-2\bigg(\dfrac{\sqrt{1+\cos A}}{2}-\dfrac{\sqrt{1-\cos A}}{2}\bigg)^2[/tex]

[tex]\text{Expand Binomial:}\quad 1-2\bigg(\dfrac{1+\cos A}{4}-\dfrac{2\sqrt{1-\cos^2 A}}{4}+\dfrac{1-\cos A}{4}\bigg)\\\\\text{Simplify:}\qquad \qquad \quad 1-2\bigg(\dfrac{2-2\sqrt{1-\cos^2 A}}{4}\bigg)\\\\\text{Pythagorean Identity:}\quad 1-\dfrac{1}{2}\bigg(2-2\sqrt{\sin^2 A}\bigg)\\\\\text{Simplify:}\qquad \qquad \qquad 1-\dfrac{1}{2}(2-2\sin A)\\\\\text{Distribute:}\qquad \qquad \qquad 1-(1-\sin A)\\\\.\qquad \qquad \qquad \qquad \quad =1-1+\sin A\\\\\text{Simplify:}\qquad \qquad \qquad \sin A[/tex]

RHS = LHS:   sin A = sin A  [tex]\checkmark[/tex]

Answer:

x<= -4

filled in circle at -4

Answer:

384 square m

Step-by-step explanation:

As per description given in the question, the field is of parallelogram shape. Diagonal divides the parallelogram in two triangles

So, area of field = area of triangle 1 + area of triangle 2

Area of field

= 1/2*32 * 10 + 1/2 * 32 * 14

= 32* 5 + 32 * 7

= 32(5 + 7)

= 32 * 12

= 384 square m

Answer:

∠B = 76°

Step-by-step explanation:

Supplementary angles add up to 180 degrees, so we know that angles A and B add up to 180.

We can set up an equation and solve for x:

(x + 15) + (x - 13) = 180

Add like terms:

2x + 2 = 180

2x = 178

x = 89

Now, we can plug in 89 as x to find the measure of angle B:

x - 13

89 - 13

= 76

= 76°

Answer:

To form the converse of the conditional statement, interchange the hypothesis and the conclusion. The converse of "If it rains, then they cancel school" is "If they cancel school, then it rains." To form the inverse of the conditional statement, take the negation of both the hypothesis and the conclusion.

Answer:

10

Step-by-step explanation:

Let the total number of poodles = [tex]x[/tex]

Let the total number of show dogs = [tex]y[/tex]

[tex]\frac{1}{4}[/tex] of the poodles are show dogs

and

[tex]\frac{1}{7}[/tex]  of the show dogs are poodles

[tex]\therefore \dfrac{1}{4}x = \dfrac{1}{7} y[/tex]

As per the question statement, [tex]x[/tex] must be divisible by 4 and

[tex]y[/tex] must be divisible by 7.

And we have to find the least number of dogs.

So, least number divisible by 4 = 4 and

Least number divisible by 7 = 7

So, least values of [tex]x[/tex] i.e. poodles = 4 in which we have 1 show dog

Hence, 3 are not show dogs.

and least value of show dogs i.e. [tex]y[/tex] = 7 (it includes the one poodle which is also show dog).

So, least number of dogs at the fair = 7 + 3 = 10

Answer:

29

Step-by-step explanation:

Given the function f(x) = x/10x-3, if x = 0.30103;

substituting the value of x into the function;

f(0.30103) = 0.30103/10(0.30103) - 3

f(0.30103) = 0.30103/(3.0103 - 3)

f(0.30103) = 0.30103/0.0103

f(0.30103) = 29.226

f(0.30103) = 29 (to nearest whole number).

Answer:

2000-1200+111

2000-1311

689 ans.

Step-by-step explanation:

by bodmas ( bracket,of,divide, multiplication, addition, substract )

so, first we'll multiply

3x400=1200

so,

2000-1200+111

second , we'll add

1200+111 = 1311

so,

2000-1311

third , at last we'll subtract

2000-1311 = 689

so,

Ans. 689

hope the ans. is correct :)

Answer: x' = x - 2yd.

Step-by-step explanation:

When we have a function:

y = g(x)

A translation to the east (in this case the positive x-axis) of N units.

is written as:

y = h(x) = g(x - N)

then if in the beginning our variable was x, afther the translation the variable will be x - N.

Now in this case we have a translation of 2yd to the right (to the east)

Then our new variable, let's call it x', will be:

x' = x - 2yd.

Answer:

A translation of two yards east involves moving 2 units in the positive x-direction. Given any initial x-coordinate, x, the algebraic expression that represents the new x-coordinate after the translation is x + 2.

Step-by-step explanation:

Edementum answer.

221 is rational since 221 = 221/1

So is 331 because 331 = 331/1

The product of any two rational numbers is also rational

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

Proof:

Let x = p/q and y = r/s be two rational numbers. The q and s values are nonzero.

Their product is

x*y = (p/q)*(r/s)

x*y = (p*q)/(r*s)

which is a ratio of two integers pq and rs, so (p*q)/(r*s) is rational

Answer:

see explanation

Step-by-step explanation:

Using the double angle identity for cosine

cos2x = 2cos²x - 1

Given

cos( [tex]\frac{0}{2}[/tex] ) = [tex]\frac{1}{2}[/tex]( p + [tex]\frac{1}{p}[/tex] ) , then

cosΘ = 2[ [tex]\frac{1}{2}[/tex](p + [tex]\frac{1}{p}[/tex] ) ]² - 1

         = 2 [ [tex]\frac{1}{4}[/tex](p² + 2 + [tex]\frac{1}{p^{2} }[/tex] ) ] - 1  ← distribute by 2

         = [tex]\frac{1}{2}[/tex](p² + 2 + [tex]\frac{1}{p^{2} }[/tex] ) - 1 ← distribute by [tex]\frac{1}{2}[/tex]

         = [tex]\frac{1}{2}[/tex] p² + 1 + [tex]\frac{1}{2p^2}[/tex] - 1

        = [tex]\frac{1}{2}[/tex] p² + [tex]\frac{1}{2p^2}[/tex] ← factor out [tex]\frac{1}{2}[/tex] from each term

        = [tex]\frac{1}{2}[/tex] ( p² + [tex]\frac{1}{p^{2} }[/tex] ) ← as required

Answer:

Step-by-step explanation:

Hello, please consider the following.

[tex]cos(\theta)=2cos^2(\dfrac{\theta}{2})-1\\\\=2\left(\dfrac{p+\dfrac{1}{p}}{2}\right)^2-1\\\\=\dfrac{p^2+\dfrac{1}{p^2}+2}{2}-1\\\\=\dfrac{1}{2}(p^2+\dfrac{1}{p^2})+1-1\\\\=\dfrac{1}{2}(p^2+\dfrac{1}{p^2})[/tex]

Thank you

Answer:

7(x times y)

Step-by-step explanation:

Product means multiply, so it wants you to multiply two numbers and multiply THAT by 7.  So we will use two variables, in this case, I will use x and y.  X times y.  7 Times that.

Answer:

7xy

Step-by-step explanation:

Let's go by parts

The product of two numbers, since we don't know what are they we can called them x and y so the product means the multiplication

[tex]x*y=xy[/tex]

next xy has to be multiplied by 7

[tex]7*xy=7xy[/tex]

so 7xy is our answer

Answer:

b.15 inches

Step-by-step explanation:

subtract 12 (2 6inch sides) from the perimeter

get 30 and divide by 2 to get 2 sides

Answer:

B. 15 inches.

Step-by-step explanation:

A rectangle shares two pairs of congruent opposite sides.

Perimeter = 42

Let:

the length of the rectangle = l

the width of the rectangle = w = 6

Perimeter = l + l + w + w

Plug in 42 for perimeter &  6 for w in the equation:

42 = l + l + 6 + 6

Combine like terms:

42 = ( l + l ) + (6 + 6)

42 = 2l + 12

Next, isolate the variable, l. Do the opposite of PEMDAS.  First, subtract 12 from both sides:

42 (-12) = 2l + 12 (-12)

42 - 12 = 2l

30 = 2l

Next, divide 2 from both sides:

(30)/2 = (2l)/2

l = 30/2

l = 15

B. 15 inches is the length of the rectangle.

Check:

l + l + w + w = 42

15 + 15 + 6 + 6 = 42

30 + 12 = 42

42 = 42 (True).

~

Answer:

k = h/9.

Step-by-step explanation:

√(h/k) = 3

Squaring both sides:

h/k = 9

9k = h

k = h/9.

Answer:

k=h/9

Step-by-step explanation:

sqrt(h/k)=3

1. square both sides

h/k=3^2

2. make k the subject

k=h/9

Answer:

P(t) = A * (1 + r)^t ;

14,922 ;

Year 2013

Step-by-step explanation:

Given the following :

Continuous growth rate(r) = 5% = 0.05

Population in year 2000 = Initial population (A) = 10,100

Time(t) = period (years since year 2000)

A)

Find a function that models the population,P(t) , after (t) years since year 2000 (i.e. t= 0 for the year 2000).

P(t) = A * (1 + r)^t

Trying out our function for t = year 2000, t =0

P(0) = 10,100 * (1 + 0.05)^0

P(0) = 10,100 * 1.05^0 = 10,100

B.)

Use your function from part (a) to estimate the fox population in the year 2008.

Year 2008, t = 8

P(8) = 10,100 * (1 + 0.05)^8

P(8) = 10,100 * 1. 05^8

P(8) = 10,100 * 1.4774554437890625

= 14922.29

= 14,922

c) Use your function to estimate the year when the fox population will reach over 18,400 foxes. Round t to the nearest whole year, then state the year.

P(t) = A * (1 + r)^t

18400 = 10,100 * (1.05)^t

18400/10100 = 1.05^t

1.8217821 = 1.05^t

1.05^t = 1.8217821

In(1.05^t) = ln(1.8217821)

0.0487901 * t = 0.5998151

t = 0.5998151 / 0.0487901

t = 12.293787

Therefore eit will take 13 years

2000 + 13 = 2013

Answer:

Step-by-step explanation:

Write a list of all possible outcomes

1-2

1-3

1-4

2-1

2-3

2-4

3-1

3-2

3-4

4-1

4-2

4-3

There are 12 possible outcomes. How many of them have totals of 6 or 7

I count 4

So the probability is 4/12 = 1/3, just as you said.

Is there an easier way?

You might be able to get the 12 easier.

You have 4 choices for the first number and 3 for the second.

P(12) = 4*3 = 12

Getting 6 or 7 might be somewhat trickier.

4 and 3 make seven. That gives two ways 4-3 and 3-4

4 and 2 make six. That gives 2 more ways 4-2 and 2-4

That's all that's possible.

answer: 4 ways make success. The total number of ways is 12.

Answer:

A, D, E

Step-by-step explanation:

I hope this is correct

Answer:

a d e

Step-by-step explanation:

Answer:

20%

Step-by-step explanation:

Step 1: Find the decrease in consumption

10kg - 8kg = 2kg

So the family decrease their consumption of sugar by 2kg

Step 2: We have to find what percent did the family reduce their sugar consumption

We can divide how much they reduced by with the original amount

2kg/10kg = 1/5 kg or 20%

Therefore the family reduced the consumption of sugar by 20$

Answer:

9

Step-by-step explanation:

21 x 3/7

= 9 ( goldfish )

Answer:

9 goldfishes

Step-by-step explanation:

Total fish = 21

Number of goldfish = 3/7 of 21

                                [tex]= \frac{3}{7}*21\\\\= 3 * 3\\\\= 9[/tex]

Answer:

x= -2

Step-by-step explanation:

3(2x-4)= -24

expand

6x-12= -24

6x= -24+12

6x= -12

x= -12/6

x= -2

Answer:

x=-2

Step-by-step explanation:

To solve the equation, we must get x isolated on one side of the equation.

[tex]3(2x-4) = -24[/tex]

3 is being multiplied by 2x -4. The inverse of multiplication is division. Divide both sides of the equation by 3.

[tex]\frac{3(2x-4)}{3} = -\frac{24}{3}[/tex]

[tex](2x-4)= -\frac{24}{3}[/tex]

[tex](2x-4)= -8[/tex]

4 is being subtracted from 2x. The inverse of subtraction is addition. Add 4 to both sides of the equation.

[tex]2x-4 +4 = -8+4[/tex]

[tex]2x= -8+4[/tex]

[tex]2x= -4[/tex]

x is being multiplied by 2. The inverse of multiplication is division. Divide both sides by 2.

[tex]\frac{2x}{2} =\frac{-4}{2}[/tex]

[tex]x=\frac{-4}{2}[/tex]

[tex]x= -2[/tex]

Let's check our solution. Plug -2 in for x and solve.

[tex]3(2x-4)= -24[/tex]

[tex]3(2(-2)-4)= -24[/tex]

[tex]3(-4-4) = -24[/tex]

[tex]3(-8)= -24[/tex]

[tex]-24=-24[/tex]

The statement above is true, so we know our solution is correct.

The answer to the equation is x= -2.

Answer:

Option C is the correct option.

Step-by-step explanation:

For ABD

[tex] \sf{ = \frac{2.89 + 8.59 + 8.6}{2} }[/tex]

[tex] \sf{ = \frac{20.08}{2} }[/tex]

[tex] \sf{ = 10.04}[/tex]

∆ ABD = [tex] \sf{ = \sqrt{10.04(10.04 - 2.89)(10.04 - 8.59)(10.04 - 8.6)} }[/tex]

[tex] \sf{ = \sqrt{10.04 \times 7.15 \times 1.45 \times 1.44 }}[/tex]

[tex] \sf{ = \sqrt{149.8891} }[/tex]

[tex] \sf{ = 12.2429}[/tex]

For ∆ ACD ,

[tex] \sf{s = \frac{8.6 + 4.3 + 7.58}{2} }[/tex]

[tex] \sf{ = \frac{20.48}{2} }[/tex]

[tex] \sf{ = 10.24}[/tex]

∆ ACD = [tex] \sf{ = \sqrt{10.24(10.24 - 8.6)(10.24 - 4.3)(10.24 - 7.58} }[/tex]

[tex] \sf{ \sqrt{10.24 \times 1.64 \times 5.94 \times 2.66} }[/tex]

[tex] \sf{ = \sqrt{265.3456} }[/tex]

[tex] \sf{ = 16.2894}[/tex]

Area of quadrilateral ABCD = [tex] \sf{12.2429 + 16.2894}[/tex]

[tex] \sf{ = 28.5323}[/tex]

[tex] \sf{ = 28.53}[/tex] units ²

Hope I helped!

Best regards!

Answer:

Step-by-step explanation:

The distance between two points can be found using the formula

[tex]d = \sqrt{ ({x1 - x2})^{2} + ({y1 - y2})^{2} } \\ [/tex]

where

(x1 , y1) and (x2 , y2) are the points

From the question the points are

A(5,-8) and B(2,9)

The distance between them is

[tex] |AB| = \sqrt{ ({5 - 2})^{2} + ({ - 8 - 9})^{2} } \\ = \sqrt{ {3}^{2} + ({ - 17})^{2} } \\ = \sqrt{9 + 289} \\ = \sqrt{298} [/tex]

| AB | = 17.26267

We have the final answer as

17. 26 units to the nearest hundredth

Hope this helps you

Answer:

0.16

Step-by-step explanation:

Given;

40% males.

If two students are selected at random, probability (P) that they are both males is given as follows;

P = P(1) x P(2)

Where;

P(1) = Probability that the first one is a male

P(2) = Probability that the second one is also a male

Remember that there are 40% males.

This means that 40 out of 100 students selected is going to be a male.

Therefore, for the first selection, any of the 40 students could be selected. The probability P(1), that the first one is male is therefore;

40 / 100 = 0.4

Also,

Assuming there is replacement, for the second selection, any of the 40 students could be selected. The probability P(2), that the second one is also male is therefore;

40 / 100 = 0.4

Now, from;

P = P(1) x P(2)

P = 0.4 x 0.4

P = 0.16

The probability that they are both males is therefore 0.16

Answer:

[tex]y=\frac{1}{5}x+\frac{12}{5}[/tex]

Step-by-step explanation:

The slope of a line that is perpendicular to another will have an opposite-reciprocal slope. So, if the slope was -2, then the perpendicular slope would be [tex]\frac{1}{2}[/tex] .

[tex]y=-5x+11[/tex]

This is written in slope-intercept form:

[tex]y=mx+b[/tex]

m is the slope and b is the y-intercept. Find the opposite-reciprocal of the slope, -5:

[tex]y=\frac{1}{5} x+b[/tex]

Now we need to find the y-intercept. For this, substitute the given points for its appropriate value:

[tex](3_{x},3_{y})\\\\3=\frac{1}{5}(3)+b[/tex]

Solve for b:

Simplify multiplication:

[tex]\frac{1}{5}*\frac{3}{1}=\frac{3}{5}[/tex]

Insert:

[tex]3=\frac{3}{5}+b[/tex]

Subtract b from both sides:

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

Subtract 3 from both sides:

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

Simplify subtraction:

[tex]\frac{3}{5}-3\\\\\frac{3}{5}-\frac{3}{1}\\\\\frac{3}{5}-\frac{15}{5}=-\frac{12}{5}[/tex]

Insert:

[tex]-b=-\frac{12}{5}[/tex]

Multiply both sides by - 1 to simplify b (it can be seen as -1b):

[tex]-b*(-1)=-\frac{12}{5}*(-1)\\\\b=\frac{12}{5}[/tex]

Insert:

[tex]y=\frac{1}{5}x+\frac{12}{5}[/tex]

:Done

Answer:

-3/2.

Step-by-step explanation:

0.5 = 1/2

-1.5 = -1 1/2

= -3/2.

- 1.5 = - 15/10

- 15⁽⁵/10 = - 3/2

- ²⁾15/10 = - 30/20

- ³⁾15/10 = - 45/30

etc