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Dwayne is trying to find the fraction represented by the repeating decimal 0.5. He completes the three
steps shown:
1) Let x = 0.5
2) 10x = 5.5
3)
10x =
5.5
-X =
9x = 5
0.5
What is the purpose of Step 3?
It removes the repeating part of the decimal from the equation.
o It shows that 0.5 is an irrational number.
It puts the fraction in lowest terms.
It shows that 0.5 is a terminating decimal.​

Answer: 162°

Step-by-step explanation:

Using exterior angle methods,

sum total of exterior angle of polygon =  ³⁶⁰/ₙ , where n is the size of the polygon.                                                 =   ³⁶⁰/₂₀

One exterior angle                               =  18°.

Now the interior angle                          = 180° - 18° ( angle on a straight line )

Therefore, the measure of the interior angle = 162°.

Not , Other methods can still be applied.

Answer:

Step-by-step explanation:

Hello, first of all we can find a value for f(1)

[tex]xf(x)+f(x^2)=2 \\\\\text{So for x = 1, it gives}\\\\f(1)+f(1^2)=f(1)+f(1)=2f(1)=2\\\\<=> f(1) =1[/tex]

And we can get the derivative of the equation so.

[tex](uv)'=u'v+uv' \text{ and } \dfrac{df(x^2)}{dx}=2xf'(x^2) \text{ so we can write}\\\\f(x)+xf'(x)+2xf'(x^2)=0\\\\\text{And then, for x = 1}\\\\f(1)+f'(1)+2f'(1)=0\\\\<=> f(1)+3f'(1)=0\\\\<=> 3f'(1)=-f(1)=-1\\\\<=>\large \boxed{ f'(1)=-\dfrac{1}{3} }[/tex]

Thank you

The correct answer is 21.5 days

Explanation:

We know Marissa has two paid days of vacation plus 1 day for every four months she works. In this context, the first step is to find how much paid days of vacation she will have for working 6.5 years and add this to the 2 paid days of vacation she was given when she began to work. The steps are shown below:

1. Find the number of months in 6.5 by considering each year has 12 months and half year (0.5) is equivalent to 6 months

6 (number of years)  x 12 months =  72 months

0.5 year = 6 months

72 months + 6 months = 78 months (Total of months in 6.5 years)

2. Divide the total of months into 4 considering every 4 months Marissa is given one paid day of vacation.

78 months ÷ 4 = 19.5 days (number of paid days of vacation for working 6.5 years)

Finally, add this result to the two paid days initially given 19.5 days + 2 days = 21.5 days

Complete Question

In a random sample of

five mobile​ devices, the mean repair cost was $75.00 and the standard deviation was ​$11.50

Assume the population is normally distributed and use a​t-distribution to find the margin of error and construct a 95​%

confidence interval for the population mean. Interpret the results.

Answer:

The margin of error is  [tex]E = 10.1[/tex]

The 95% confidence interval  is [tex]64.9 < \mu < 85.1[/tex]

Step-by-step explanation:

From the question we are told that

  The sample mean is  [tex]\= x = \$ 75.00[/tex]

   The  standard deviation is  [tex]\sigma = \$ 11.50[/tex]

   The sample size is  n = 5

Given the that the confidence level is  95% then the level  of significance is mathematically represented as

            [tex]\alpha = 100 -95[/tex]

            [tex]\alpha = 5\%[/tex]

            [tex]\alpha = 0.05[/tex]

Next we obtain the critical value of  [tex]\frac{ \alpha }{2}[/tex] from the normal distribution table, the value is  

         [tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]

Generally the margin of error is mathematically represented as

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

substituting values

         [tex]E = 1.96* \frac{11.50 }{ \sqrt{5} }[/tex]

        [tex]E = 10.1[/tex]

The 95% confidence interval  is mathematically represented as

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

substituting values

        [tex]75 - 10.1< \mu < 75 + 10.1[/tex]

        [tex]64.9 < \mu < 85.1[/tex]

Answer:

can you type it out

Step-by-step explanation:

Answer:

[tex] \boxed{\sf (x + y)(6x + 5y)} [/tex]

Step-by-step explanation:

Factor the following:

[tex] \sf \implies 6 {x}^{2} + 11xy + 5 {y}^{2} [/tex]

The coefficient of x² is 6 and the coefficient of y² is 5. The product of 6 and 5 is 30. The factors of 30 which sum to 11 are 5 and 6.

So,

[tex] \sf \implies 6 {x}^{2} + (6 + 5)xy + 5 {y}^{2} [/tex]

[tex] \sf \implies 6 {x}^{2} + 6xy + 5xy + 5 {y}^{2} [/tex]

[tex] \sf \implies 6x(x + y) + 5y(x + y)[/tex]

Factor (x + y) from 6x(x + y) + 5y(x + y):

[tex] \sf \implies (x + y)(6x + 5y)[/tex]

Answer:

3m +7n  +5т

Step-by-step explanation:

6m +7n +5т — Зm

Combine like terms

3m +7n  +5т

Answer:

27.50

Step-by-step explanation:

Answer:

4255 students choose Drama

4995 students choose Other

3700 students choose Comedy

Step-by-step explanation:

18500 x _% =

Ex: 18500 x 23% = 4255.

Answer:

A

Explanation

8/11 = 8 ÷ 11

BRAINLIEST PLEASE

The x is a placeholder for a number. Think of x like a box and inside the box will go a number. In this case, -4 will replace x

7 - 2x = 7 - 2(-4) = 7 + 8 = 15

Answer:

367.57 in³

Step-by-step explanation:

The formula for the volume of a cylinder is  [tex]V = h\pi r^2[/tex], where V is the volume, h is the height, and r is the radius. The picture shows you that r = 3 in and h = 13 in.

Plug these into the formula to find the answer:

[tex]V = (13)\pi 3^2=(13)(9)\pi =117\pi => 367.566[/tex]

Round that to the nearest hundredth to get 367.57. The units for the answer should be in cubic inches.

For the surface area, imagine laying the cylinder out. You'd see two circles, for the top and bottom, and then a rectangle, which is the side. The formula is A=2πrh+2πr². Try to do this yourself! You only need to plug in the values: r = 3 in and h = 13 in.

Answer:

T = Z + pr

Z + T = pr

Z/r + T/r = p

Answer:

p = Z/r + T/r

Answer:

from my calculation, the answer is B

The midpoint of the segment between the points (15,−9) and (−2,−18) will be (−13/2, −27/2). Then the correct option is C.

Let C be the mid-point of the line segment AB.

A = (x₁, y₁)

B = (x₂, y₂)

C = (x, y)

Then the midpoint will be

x = (x₁ + x₂) / 2

y = (y₁ + y₂) / 2

The midpoint of the segment between the points (15,−9) and (−2,−18) will be

x = (15 – 2) / 2

x = –13 / 2

y = (–9 – 18) / 2

y = –27/2

Then the correct option is C.

More about the midpoint of line segment AB link is given below.

https://brainly.com/question/17410964

#SPJ5

In other words, you'll use the SAS similarity property with 3/2 as the scale factor

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

Explanation:

Choice A is not correct because we don't have enough info about all three pairs of sides.

Instead we'll go with SAS similarity. This is the idea where we'll use two pairs of sides to see if they are in the same proportion, and we'll also use the included angle between the two sides. The angles ABE and DBC are congruent as they are vertical angles. So that's where the "A" comes from in "SAS".

As for the S terms, we divide the corresponding sides like so

DB/AB = 9/6 = 3/2

BC/BE = 1.5/1 = 15/10 = 3/2

The scale factor as a fraction is 3/2, which converts to the decimal form 1.5

This says that triangle DBC has sides that are 3/2 = 1.5 times longer than corresponding sides in triangle ABE.

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

If you're curious how the sides correspond, then look at the ordering of ABE and DBC. The order is important when it comes to similar triangles.

AB and DB are the first two letters of ABE and DBC respectively. So we have AB pair up with DB.

Similarly, BE and BC pair up because they are the last two letters of ABE and DBC respectively.

We divide sides of DBC over sides of ABE to get the scale factor from ABE to DBC. The scale factor must be some result larger than 1 do indicate an enlargement is going on.

Answer:

Step-by-step explanation:

liked- brought

Answer:

1190

Step-by-step explanation:

Here, you need to add the squares of the measurements.

20² + 10² + 13² + 11² + 20² =

= 400 + 100 + 169 + 121 + 400

= 1190

Step-by-step explanation:

(cos(3A) − sin(3A)) / (1 − 2 sin(2A))

Use double angle formula:

(cos(3A) − sin(3A)) / (1 − 4 sin A cos A)

Use triple angle formulas:

(4 cos³A − 3 cos A − 3 sin A + 4 sin³A) / (1 − 4 sin A cos A)

Group and factor:

(4 (cos³A + sin³A) − 3 (cos A + sin A)) / (1 − 4 sin A cos A)

Factor the sum of cubes:

(4 (cos A + sin A) (cos²A − cos A sin A + sin²A) − 3 (cos A + sin A)) / (1 − 4 sin A cos A)

Use Pythagorean identity:

(4 (cos A + sin A) (1 − cos A sin A) − 3 (cos A + sin A)) / (1 − 4 sin A cos A)

Factor out cos A + sin A:

(cos A + sin A) (4 (1 − cos A sin A) − 3) / (1 − 4 sin A cos A)

Simplify:

(cos A + sin A) (4 − 4 cos A sin A − 3) / (1 − 4 sin A cos A)

(cos A + sin A) (1 − 4 cos A sin A) / (1 − 4 sin A cos A)

cos A + sin A

Answer:

2:50 PM

Step-by-step explanation:

Step 1: State what is given

Roast takes 3 hours and 40 minutes or 220 minutes

Need the roast to be done by 6:30 PM

Step 2: Subtract 3 hours from 6:30

6:30 - 3:00

3:30 PM

Step 3: Subtract 40 minutes from 3:30

3:30 - 40

2:50 PM

Therefore the roast needs to be put into the oven at 2:50 PM

Answer:

C and D

Step-by-step explanation:

We want to find the equations where b=11 is a solution. Let's test each answer. choice. Plug 11 in for b and solve.

A. 2b= 211

2(11)=211

Multiply 2 and 11.  

22≠211

22 does not equal 211, therefore this choice is not correct.

B. b+18=7

11+18=7

Add 11 and 18.

29 ≠ 7

29 does not equal 7, so this is not correct.

C. 77=7b

77=7(11)

Multiply 7 and 11.

77=77

77 does equal 77, so this is correct.

D. 9=b-2

9=11-2

Subtract 2 from 11.

9=9

9 equals 9, so this correct too.

E. 11=33/b

11=33/11

Divide 33 by 11.

11≠3

11 does not equal 3, so this is not the right choice.

b= 11 is a solution for C. 77-7b and D. 9=b-2

All we need to do is substitute and solve.

A = P(1 + rt)

A = 5,100(1 + 0.035*60)

A = 5,100(3.1)

A = 15,810

Therefore, the answer is [ $15,810 ]

Best of Luck!

Answer:

9

Step-by-step explanation:

Answer:

a. 45

b. -4

Step-by-step explanation:

f(x) = -6(-8) - 3

f(x) = 48 - 3 = 45

21 = -6x - 3

24 = -6x

-4 = x

Answer:

y=x+8

Step-by-step explanation:

First you use the points (-3,5) and (2,10) to find the slope and you use the equation y2-y1/x2-x1.

So that gives you 10-5/2-(-3) which equals 1 (that's the slope)

Next you take one set of the points say (2,10) and then plug those numbers into the y=mx+b equation so you have x (2) and y (10) and the slope is m (1).

That gives you 10=1(2)+b

multiply 1*2 and you get 2 and then subtract 2 from both sides to isolate b and then b=8 and that gives you the answer

y=1x+8 or y=x+8

Answer:

(a) 57.8 cm²

(b) 158.7 in²

Step-by-step explanation:

(a)

The area of a circle is denoted by A = 2πr, where r is the radius.

Here the radius is r = 9.2, so plug this in:

A = 2πr

A = 2π * 9.2 ≈ 57.8 cm²

(b)

The diameter is twice the radius, so since the diameter is 50.5 inches, the radius will be 50.5/2 = 25.25 inches.

Plug this into the formula:

A = 2πr

A = 2π * 25.25 ≈ 158.7 in²

~ an aesthetics lover

Answer:

x=5/3

Step-by-step explanation:

Answer: Hi!

Since this is a right triangle, we already know that one angle is 90 degrees. Since the angles of a triangle all add up to 180 degrees, and the two unknown angles will be equal, all we have to do is subtract 90 from 180 and then divide the difference by 2!

180 - 90 = 90

90 ÷ 2 = 45

The two missing angles are each 45 degrees.

(x = 45 and y = 45)

Make sure to put the degrees sign after your answers!

Hope this helps!

Answer:

45 degrees.

Step-by-step explanation:

All of the angles in a triangle is 180 degrees.

Knowing that we subtract 90 degrees, the right angle from 180 degrees.

180-90=90

Since both the angles are equal,

90/2=45

Hope this helps :)

Have a great day!

Step-by-step explanation:

I think no. C is the answer. Please let me know by comment I am wrong or right

Answer:

C

Step-by-step explanation:

A set of coordinates is a function if and only if one input does not map onto two or more different outputs.

In other words, given (x,y), x should each have one distinct y. If an x has 2 or more y, then the y must be the same value.

Choice A:

We see that it has the pairs (1,1) and (1,4). 1 maps onto both 1 and 4, so this is not a function.

Choice B:

Again, we see that it has the pairs (2,2) and (2,5). 2 maps onto both 2 and 5, so this also isn't a function.

Choice C:

In this set, no x are repeated. Thus, this is a function.

Choice D:

In this set, we have the x repeated four times, with 1 mapping onto 2, 3, 5, and 6. Thus, this is not a function.

So, our answer is C.

Question:

Suppose we want to choose 5 objects, without replacement, from 16 distinct objects.

A) How many ways can this be done, if the order of the choices is relevant?

B) How many ways can this be done, if the order of the choices is not relevant?

Answer:

A. 4368 ways

B. 524160 ways

Step-by-step explanation:

Given

[tex]Objects = 16[/tex]

[tex]Selection = 5[/tex]

Required

A & B

Solving (A)

Because the order of choice is irrelevant, this implies combination and it is calculated as follows;

[tex]^nC_r = \frac{n!}{(n-r)!r!}[/tex]

Where n = 16 and r = 5

[tex]^{16}C_5 = \frac{16!}{(16-5)!5!}[/tex]

[tex]^{16}C_5 = \frac{16!}{11!5!}[/tex]

[tex]^{16}C_5 = \frac{16 * 15 * 14 * 13 * 12 * 11!}{11!5!}[/tex]

[tex]^{16}C_5 = \frac{16 * 15 * 14 * 13 * 12}{5!}[/tex]

[tex]^{16}C_5 = \frac{16 * 15 * 14 * 13 * 12}{5 * 4 * 3 * 2 * 1}[/tex]

[tex]^{16}C_5 = \frac{524160}{120}[/tex]

[tex]^{16}C_5 = 4368\ ways[/tex]

Solving (B)

Because the order of choice is relevant, this implies permutation and it is calculated as follows;

[tex]^nP_r = \frac{n!}{(n-r)!}[/tex]

Where n = 16 and r = 5

[tex]^{16}P_5 = \frac{16!}{(16-5)!}[/tex]

[tex]^{16}P_5 = \frac{16!}{11!}[/tex]

[tex]^{16}P_5 = \frac{16 * 15 * 14 * 13 * 12 * 11!}{11!}[/tex]

[tex]^{16}P_5 = 16 * 15 * 14 * 13 * 12[/tex]

[tex]^{16}P_5 = 524160\ ways[/tex]