Problem 2
In the above diagram, circles O and O' are tangent at X, and PQ is tangent to both circles. Given that
OX= 3 and O'X = 8. find PQ.

Answer:

(C) Translation of 2 units right, 1 up, and a reflection over the y-axis.

Step-by-step explanation:

Ideally, we are looking for a reflection of the red image over the y-axis, and to do that, we can see how we need to move the black image.

In order for points Q and Q' to be a reflection of each other, they need to have the same y value, and be the exact same distance from the y axis, so the point that Q has to be at is (-1,-3).

Q is right now at (-3,-4) so we can translate this.

To get from -3 to -1 in the x-axis, we go right by 2 units.

To get from -4 to -3 in the y-axis, we go up one unit.

Now, if we reflect it, the triangles will be the same.

Hope this helped!

Answer:

C.

Step-by-step explanation:

When you study the images, it is clear that the black triangle has to be reflected over the y-axis to face the same direction as the red triangle. So, choice A is eliminated.

Once you reflect the black triangle across the y-axis, you have points at (-1, -1), (3, -4), and (3, -2). Meanwhile, the red triangle's coordinates are at (-3, 0), (1, -3), and (1, -1). From these points, you can tell that the x-values differ by 2 units and the y-values differ by 1 unit.

All of these conditions match the ones put forth in option C, so that is your answer.

Hope this helps!

Answer:

a) rCn = 1176

b) 2352

Step-by-step explanation:

a)Each committee should be formed with 3 members ( no two members could be of the same state) then

Let´s  fix a senator for any of the 50 states so in the new condition we need to combined 49 senators in groups of 2 then

rCn =  n! / (n - r )! *r!

rCn =  49!/ (49 - 2)!*2!

rCn =  49*48*47! / 47!*2!

rCn = 49*48 /2

rCn = 1176

So we can choose in 1176 different ways a senator for a given state

b) To answer this question we have to note, that, 1176 is the number of ways a committee can be formed with senators of different sate (taking just one senator for state ) if we have 2 senators we need to multiply that figure by 2.

1176*2 = 2352

Answer:

12/18 and 10/15

Step-by-step explanation:

12/18 simplifies into 2/3

10/15 simplifies into 2/3

12/20 simplifies into 3/5

10/25 simplifies into 2/5

8/16 simplifies into 1/2

3/4 simplifies into 3/4

5/3 simplifies into 5/3

3/5 simplifies into 3/5

The pairs consist of equivalent fractions will be 12/20 and 10/25. Then the correct option is A.

What is a fraction number?

A fraction number is a number that represents the part of the whole, where the whole can be any number. It is in the form of a numerator and a denominator.

Let's check all the options, then we have

A) 12/18 and 10/15

12/18 and 10/15

2/3 and 2/3

Yes, they are equivalent fraction numbers.

B) 12/20 and 10/25

12/20 and 10/25

3/5 and 2/5

They are not equivalent fraction numbers.

C) 8/16 and 3/4

8/16 and 3/4

1/2 and 3/4

They are not equivalent fraction numbers.

D) 5/3 and 3/5

5/3 and 3/5

They are not equivalent fraction numbers.

The pairs consist of equivalent fractions will be 12/20 and 10/25. Then the correct option is A.

More about the fraction number link is given below.

https://brainly.com/question/78672

#SPJ2

Answer:

6y +2x +7

Step-by-step explanation:

10 + 6y + 2x - 3​

The only like terms are the constant

6y+2x +10-3

6y +2x +7

Answer:

2x + 6y + 7.

Step-by-step explanation:

10 + 6y + 2x - 3

= 2x + 6y - 3 + 10

= 2x + 6y + 7.

Hope this helps!

Answer:

1). f(x) = x² if ∞ < x < 2

2). f(x) = 5 if 2 ≤ x < 4

Step-by-step explanation:

The graph attached shows the function in two pieces.

1). Parabola

2). A straight line parallel to the x-axis.

Standard equation of a parabola is,

y = a(x - h)² + k

where (h, k) is the vertex.

Vertex of the given parabola is (0, 0).

Equation of the parabola will be,

y = a(x - 0)² + 0

Therefore, the function will be,

f(x) = ax²

Given parabola is passing through (-1, 1) also,

1 = a(-1)²

a = 1

Therefore, parabolic function will be represented by,

f(x) = x² if ∞ < x < 2

2). Straight line parallel to the x-axis,

y = 5  if 2 ≤ x < 4

Function representing the straight line will be,

f(x) = 5 if 2 ≤ x < 4

Answer:

Please mark me as Brainliest :)

Step-by-step explanation:

Answer:

b = sqrt(57)

Step-by-step explanation:

Since this is a right triangle, we can use the Pythagorean theorem

a^2 + b^2 = c^2 where a and b are the legs and c is the hypotenuse

8^2 + b^2 = 11^2

64+ b^2 = 121

Subtract 64

b^2 = 121-64

b^2 =57

Take the square root of each side

b = sqrt(57)

Answer:

Step-by-step explanation:

The formula for calculating the confidence interval is expressed as shown;

CI = xbar ± Z(б/√n)

xbar is the sample mean

Z is the value at 95% confidence interval

б is the standard deviation of the sample

n is the number of samples

Given xbar = 14.2, Z at 95% CI = 1.96, б = 0.70 and n = 9

Substituting this values into the formula;

CI = 14.2 ± 1.96(0.70/√9)

CI = 14.2 ± 1.96(0.70/3)

CI = 14.2 ± 1.96(0.2333)

CI = 14.2 ± 0.4573

CI = (14.2-0.4573, 14.2+0.4573)

CI = (13.7427, 14.6537)

Hence, the 95% confidence interval of the true mean is within the range

13.7≤[tex]\mu[/tex]≤14.7 (to 1 decimal place).

Answer:

B. y > 2/3x + 1

Step-by-step explanation:

To find slope we'll use the following formula,

[tex]\frac{y^2-y^1}{x^2-x^1}[/tex]

(-3,-1) (3,3)

3 - -1 = 4

3 - -3 = 6

2/3x

The y intercept is 1,

we know this because that's the point the line touches the y axis.

Thus,

the answer is B. y > 1/3x + 1.

Hope this helps :)

The graph of the solution of an inequality is given .

The graph represents the inequality is [tex]y>\frac{2}{3} x+1[/tex]

Option B

Given :

The graph of an inequality. To find the inequality for the given graph we use linear equation [tex]y=mx+b[/tex]

where m is the slope and b is the y intercept

To find out slope , pick two points from the graph

(-3,-1) and (3,3)

[tex]slope =\frac{y_2-y_2}{x_2-x_1} =\frac{3+1}{3+3} =\frac{2}{3} \\m=\frac{2}{3}[/tex]

Now we find out y intercept b

The point where the graph crosses y axis is the y intercept

The graph crosses y axis at 1

so y intercept b=1

The linear equation for the given graph is

[tex]y=\frac{2}{3} x+1[/tex]

Now we frame the inequality . we use test point that lies inside shaded region

Lets take (4,5)

[tex]y=\frac{2}{3} x+1\\5=\frac{2}{3} (4)+1\\5=3.6\\5>3.6\\y>\frac{2}{3} x+1[/tex]

The inequality for the given graph is

[tex]y>\frac{2}{3} x+1[/tex]

Learn more : brainly.com/question/24649632

Answer:

a

The sample size is  [tex]n = 219.2[/tex]

b

The  sample size is  [tex]n = 537.5[/tex]

Step-by-step explanation:

From the question we are told  that

    The standard deviation is  [tex]\sigma = 45 \minutes[/tex]

    The  Margin of  Error is  [tex]E = \pm 5 \ minutes[/tex]

Generally the margin of  error is mathematically represented as

         [tex]E = z * \frac{\sigma }{\sqrt{n} }[/tex]

Where  n is the sample  size

    So

             [tex]n = [\frac{z * \sigma }{E} ]^2[/tex]

Now  at  90%  confidence level the z value for the z-table is  

        z =  1.645

So

       [tex]n = [\frac{1.645 * 45 }{5} ]^2[/tex]

       [tex]n = 219.2[/tex]

The z-value at 99%  confidence level is  

        [tex]z = 2.576[/tex]

This is obtained from the z-table  

   So the sample size is  

         [tex]n = [\frac{2.576 * 45 }{5} ]^2[/tex]

        [tex]n = 537.5[/tex]

For the 90% confidence interval, the sample size is 219.2 and for the 99% confidence interval, the sample size is 537.5 and this can be determined by using the formula of margin of error.

Given :

The formula of the margin of error can be used in order to determine the sample size is needed if the executive wants to be 90% confident of being correct to within 5 minutes.

[tex]\rm ME = z\times \dfrac{\sigma}{\sqrt{n} }[/tex]

For the 90% confidence interval, the value of z is 1.645.

Now, substitute the values of all the known terms in the above formula.

[tex]\rm n=\left(\dfrac{z\times \sigma}{ME}\right)^2[/tex]   --- (1)

[tex]\rm n=\left(\dfrac{1.645\times 45}{5}\right)^2[/tex]

n = 219.2

Now, for 99% confidence interval, the value of z is 2.576.

Again, substitute the values of all the known terms in the expression (1).

[tex]\rm n=\left(\dfrac{2.576\times 45}{5}\right)^2[/tex]

n = 537.5

For more information, refer to the link given below:

https://brainly.com/question/6979326

Let's simplify step-by-step.

3(2x+1)−2(x+1)

Distribute:

=(3)(2x)+(3)(1)+(−2)(x)+(−2)(1)

=6x+3+−2x+−2

Combine Like Terms:

=6x+3+−2x+−2

=(6x+−2x)+(3+−2)

=4x+1

4x+1 is the answer to the question

Answer:

sec y=6/b         yw  

Step-by-step explanation:

Answer:

4, 5 and 6

Step-by-step explanation:

Consecutive means right next to each other.

4 x 5 x 6 = 120 cubic inches.

4 X 5 = 20

20 X 6 = 120

The values of the consecutive numbers will be 4, 5, and 6.

Let the numbers be represented by a, a+1, and a+2.

Therefore, a(a+1)(a+2) = 120

a³ + 3a² + 2a = 120

a = 4

Therefore, a + 1 = 4+1 = 5

a + 2 = 4 + 2 = 6

Therefore, the values will be 4, 5, and 6.

Read related link on:

https://brainly.com/question/18962438

Answer:median:249    

Step-by-step explanation:

median:198] 216} 220] 236] 246 252 [253[ 260 {290[ 369

246 +252=498

498/2=249

as for the mean  i will give you that later

Answer:

484 cm^2.

Step-by-step explanation:

The length of the circumference = diameter * pi

= 14 * 22/7

The area of the curved surface = circumference * height

= 14 * 22/7 * 11

= 484.

Answer:

Its D

Step-by-step explanation:

x=11 and x=18

Answer:

You need to add 150 mL of 65% alcohol solution.

Step-by-step explanation:

You have 300 mL of 20% solution.

300 mL of 20% alcohol solution has 20% * 300 mL of alcohol.

You have 65% solution.

Let the volume of 65% solution you add be x.

In 65% solution, 65% of the volume is alcohol, so the amount of alcohol in x amount of 65% solution is 65% * x.

You want 35% solution.

The total amount of 35% solution you will make is 300 mL + x. The amount of alcohol in that amount of solution is 35% * (x + 300).

Equation of alcohol content:

20% * 300 + 65% * x = 35% * (x + 300)

60 + 0.65x = 0.35x + 105

0.3x = 45

x = 150

Answer: You need to add 150 mL of 65% alcohol solution.

Answer:

Step-by-step explanation:

Given,

AD = 38

EB = 7x - 4

FC = 6x - 6

Now, we have to find the value of X

[tex]eb \: = \frac{1}{2} (ad \: + fc \: )[/tex] ( Mid segment Theorem )

Plug the values

[tex]7x - 4 = \frac{1}{2} (38 + 6x - 6)[/tex]

Calculate the difference

[tex]7x - 4 = \frac{1}{2} (32 + 6x)[/tex]

Remove the parentheses

[tex]7x - 4 = \frac{32}{2} + \frac{6x}{2} [/tex]

[tex]7x - 4 = 16 + 3x[/tex]

Move variable to L.H.S and change its sign

Similarly, Move constant to R.H.S and change its sign

[tex]7x - 3x = 16 + 4[/tex]

Collect like terms

[tex]4x = 16 + 4[/tex]

Calculate the sum

[tex]4x = 20[/tex]

Divide both sides of the equation by 4

[tex] \frac{4x}{4} = \frac{20}{4} [/tex]

Calculate

[tex]x = 5[/tex]

The value of X is 5

Now, let's find the value of EB

EB = 7x - 4

Plug the value of X

[tex] = 7 \times 5 - 4[/tex]

Calculate the product

[tex] = 35 - 4[/tex]

Calculate the difference

[tex] = 31[/tex]

The value of EB is 31

Hope this helps..

Best regards!!

Answer:

[tex]\large\boxed{\sf \ \ \ 1757 \ km^2 \ \ \ }[/tex]

Step-by-step explanation:

Hello,

I would recommend that you checked the answers I have already provided as this is the same method for all these questions, and maybe try to solve this one before you check the solution.

At the beginning the area is 2100

After one year the area will be

   2100*(1-3.5%)=2100*0.965

After n years the area will be

   [tex]2100\cdot0.965^n[/tex]

So after 5 years the area will be

   [tex]2100\cdot0.965^5=1757.34027...[/tex]

So rounded to the nearest square kilometer is 1757

Hope this helps

Answer: 1757 km²

Step-by-step explanation:

Because 3.5% = 0.035, first do 1-.035 to get .965.  Then do 2100*.965*.965*.965*.965*.965 to get 1757.34027.

Answer:

396

Step-by-step explanation:

Answer:

16

Step-by-step explanation:

(-8)^4/3

-(8^1/3)⁴

-(∛8)⁴

-(2)⁴

-2⁴

= 16

Answer: the ^^^^ right I check it

Step-by-step explanation:

Answer:

(-1,-2)

Step-by-step explanation:

[tex]6x-y=-4\\y=6x+4\\y=6(-2)+4=-8\\y=6(-1)+4=-2\\y=6(0)+4=4[/tex]

so the only one is (-1,-2)

Answer:

Your answer is correct ✔️

Step-by-step explanation:

Hope this is correct and helpful

HAVE A GOOD DAY!

Answer:

2√3 + 3i is the answer

Step-by-step explanation:

Answer:

4.2 in

Step-by-step explanation:

let us first visualize the sail as a triangular shape

the angle of the triangle from top is 40°

the height of the triangle is give as 5 in

we can apply SOH CAH TOA to solve for the base of the sail

the opposite = the base of the sail

the adjacent = the height of the sail= 5 in

therefore

Tan∅= Opp/Adj

Tan(40)= Opp/5

Opp= Tan(40)*5

Opp= 0.8390*5

Opp= 4.195 in

Hence the width of the sail is 4.2 in to the nearest tenths

Answer:

4.2

Step-by-step explanation:

Answer:

Hello There!!

Step-by-step explanation:

Your answer will be 83/99. Because, We have to expressed the 0.83¯ as a fraction in simplest form. Let x = 0.83¯ = 0.8383. Then, We have to multiply by 100 to both sides we have: 100x = 83.8383. After, Subtract (One) to (Two) we will have: 99x = 83. Then, We will divide both sides by 99 we have: x = 83/99. Therefore, the 0.83¯ as a fraction in simplest form is, 83/99. Hope This Helps!!~ Sorry, If the example confusing...

Answer:

The answer is below

Step-by-step explanation:

a) y=3x-1

The standard equation of a line is given by:

y = mx + c

Where m is the slope of the line and c is the intercept on the y axis.

Given that y=3x-1, comparing with the standard equation of a line, the slope (m) = 3, Two lines with slope a and b are perpendicular if the product of their slope is -1 i.e. ab = -1. Let the line perpendicular to y=3x-1 be d, to get the slope of the perpendicular line, we use:

3 × d = -1

d = -1/3

To find the equation of the perpendicular line passing through (0,0), we use:

[tex]y-y_1=d(x-x_1)\\d\ is\ the \ slope:\\y-0=-\frac{1}{3} (x-0)\\y=-\frac{1}{3}x[/tex]

To find  x if the point P(x, 4) lies on the new line, insert y = 4 and find x:

[tex]y=-\frac{1}{3}x\\ 4=-\frac{1}{3}x\\-x=12\\x=-12[/tex]

b) y=1/4 x+2

Given that y=1/4 x+2, comparing with the standard equation of a line, the slope (m) = 1/4. Let the line perpendicular to y=1/4 x+2 be f, to get the slope of the perpendicular line, we use:

1/4 × f = -1

f = -4

To find the equation of the perpendicular line passing through (0,0), we use:

[tex]y-y_1=f(x-x_1)\\f\ is\ the \ slope:\\y-0=-4 (x-0)\\y=-4x[/tex]

To find  x if the point P(x, 4) lies on the new line, insert y = 4 and find x:

[tex]y=-4}x\\ 4=-4x\\x=-1[/tex]

Answer:

B

Step-by-step explanation:

To solve this you do 80/100=.8

You than do .8×60= 48

Answer:

The confidence interval is  [tex]25.16 < \mu < 26.85[/tex]

Step-by-step explanation:

From  the question we are given a data set

     25.5, 26.1, 26.8, 23.2, 24.2, 28.4, 25.0, 27.8, 27.3, and 25.7.

The mean of the this sample data is  

       [tex]\= x = \frac{\sum x_i}{n}[/tex]

where is the sample size with values  n =  10

         [tex]\= x = \frac{25.5+ 26.1+ 26.8+23.2+ 24.2+ 28.4+ 25.0+ 27.8+ 27.3+ 25.7}{10}[/tex]

          [tex]\= x = 26[/tex]

The standard deviation is evaluated as

             [tex]\sigma = \sqrt{\frac{\sum (x-\= x)}{n} }[/tex]

substituting values

     [tex]= \sqrt{\frac{ ( 25.5-26)^2, (26.1-26)^2, (26.8-26)^2, (23.2-26)^2}{10} }[/tex]

                  [tex]\cdot \ \cdot \ \cdot \sqrt{\frac{ ( 24.2-26)^2, (28.4-26)^2+( 25.0-26)^2+ (27.8-26)^2+( 27.3-26)^2+( 25.7-26)^2}{10} }[/tex]

     [tex]\sigma = 1.625[/tex]

The  confidence level is given as 90% hence the level of significance is calculated as

    [tex]\alpha = 100 -90[/tex]

    [tex]\alpha =10[/tex]%

   [tex]\alpha = 0.10[/tex]

Now the critical values of [tex]\frac{\alpha }{2}[/tex] is obtained from the normal distribution table as

      [tex]Z_{\frac{\alpha }{2} } = 1.645[/tex]

The reason  we are obtaining  the critical values of [tex]\frac{\alpha }{2}[/tex] instead of  [tex]\alpha[/tex] is because  we are considering two tails of the area under the normal curve

  The margin of error is evaluated as

            [tex]MOE = Z_{\frac{\alpha }{2} } * \frac{\sigma }{\sqrt{n} }[/tex]

substituting values

           [tex]MOE = 1.645 * \frac{1.625 }{\sqrt{10} }[/tex]

           [tex]MOE = 0.845[/tex]

The  90%, two sided confidence interval is mathematically evaluated as

           [tex]\= x - MOE < \mu < \= x + MOE[/tex]

           [tex]26 - 0.845 < \mu < 26 + 0.845[/tex]

           [tex]25.16 < \mu < 26.85[/tex]

Given that the lower and the upper limit is greater than  25 then we can assure the manufactures  that the battery life exceeds 25 hours

Answer:

x = $0.50

y= $0.75

Step-by-step explanation:

1. Multiply the equations to have the same coefficients

5(6x + 6y = 7.5) → 30x + 30y = 37.5

3(10x + 5y = 8.75) → 30x + 15y = 26.25

2. Subtract the equations

 30x + 30y = 37.5

- 30x + 15y = 26.25

15y = 11.25

3. Solve for y by dividing both sides by 15

y = 0.75

4. Plug in 0.75 for y into one of the equations

6x + 6(0.75) = 7.5

5. Simplify

6x + 4.5 = 7.5

6. Solve for x

6x = 3

x = 0.5

Answer:

The cost of one apple is $0.5

The cost of one orange is $0.75

Step-by-step explanation:

Given information

The cost of an apple = [tex]x[/tex]

The cost of an orange = [tex]y[/tex]

Equation to find the values are:

[tex]6x=6y=7.50\\10x+5y=8.75[/tex]

Now, convert the equations to have same coefficient as:

[tex]5(6x=6y=7.50)\\=30x+30y=37.5\\3(10x+5y=8.75)\\=30x+15y=26.25[/tex]

Now, on solving the above equation by subtracting one from another.

We get,

[tex]15y=11.25\\y=0.75[/tex]

Now , put the value of [tex]y[/tex] in one equation to find the value of [tex]x[/tex].

As,

[tex]6x+4.5=7.5\\x=0.5[/tex]

Hence,

The cost of one apple is $0.5

The cost of one orange is $0.75

For more information visit

https://brainly.com/question/11897796?referrer=searchResults