Which expression is equivalent to sin(20°)cos(80°) – cos(20°)sin(80°)?
A) sin(-60)
B) cos(-60)
C) cos(60)
D) sin(60)

Given:

A line contains the points R(-1, 8), S(1, 4) and T(6, y).

To find:

The value of y.

Solution:

Three points are collinear if:

[tex]x_1(y_2-y_3)+x_2(y_3-y_2)+x_3(y_1-y_2)=0[/tex]

A line contains the points R(-1, 8), S(1, 4) and T(6, y). It means, these points are collinear.

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

[tex]-4+y+y-8+48-24=0[/tex]

[tex]2y+12=0[/tex]

Subtract 12 from both sides.

[tex]2y=-12[/tex]

Divide both sides by 2.

[tex]y=\dfrac{-12}{2}[/tex]

[tex]y=-6[/tex]

Therefore, the value of y is -6.

Answer: The guy above me is right

Step-by-step explanation: I took the test and got it right

Answer:

a) 752 medical files should be included.

b) 372 medical files should be included.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].

The margin of error is of:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

90% confidence level

So [tex]\alpha = 0.1[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.1}{2} = 0.95[/tex], so [tex]Z = 1.645[/tex].

Question a:

This is n for which M = 0.03. We have no estimate, so we use [tex]\pi = 0.5[/tex]. So

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

[tex]0.03 = 1.645\sqrt{\frac{0.5*0.5}{n}}[/tex]

[tex]0.03\sqrt{n} = 1.645*0.5[/tex]

[tex]\sqrt{n} = \frac{1.645*0.5}{0.03}[/tex]

[tex](\sqrt{n})^2 = (\frac{1.645*0.5}{0.03})^2[/tex]

[tex]n = 751.67[/tex]

Rounding up:

752 medical files should be included.

Question b:

Now we have that:

[tex]\pi = \frac{13}{90} = 0.1444[/tex]

So

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

[tex]0.03 = 1.645\sqrt{\frac{0.1444*0.8556}{n}}[/tex]

[tex]0.03\sqrt{n} = 1.645\sqrt{0.1444*0.8556}[/tex]

[tex]\sqrt{n} = \frac{1.645\sqrt{0.1444*0.8556}}{0.03}[/tex]

[tex](\sqrt{n})^2 = (\frac{1.645\sqrt{0.1444*0.8556}}{0.03})^2[/tex]

[tex]n = 371.5[/tex]

Rounding up:

372 medical files should be included.

Answer:

I don't see any statements here.

Anyway, the answer is 8.

[tex]12 - 7 + 3 = 8[/tex]

Answer:

Option D

Step-by-step explanation:

correct answer on edge :)

Answer:

D <3

Step-by-step explanation:

Answer: The mean price per share is $22.91

The required weighted mean price per share is $46.09.

Given that,
In June, an investor purchased 300 shares of Oracle (an information technology company) stock at $53 per share. In August, she purchased an additional 400 shares at $42 per share. In November, she purchased an additional 400 shares at $45.
To determine the weighted mean price per share.

The average of the values is the ratio of the total sum of values to the number of values.

The mean of the values is the ratio of the total sum of values to the number of values.

Here,
Required  weight mean = 300 * 53 + 400*42 + 400 * 42 / [300 + 400 + 400]
Required  weight mean = 50700/ [1100]
Required  weight mean = $46.09 per share.

Thus, the required weighted mean price per share is $46.09.

Learn more about mean here:

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Step-by-step explanation:

2x+3x+x+20=180

6x+20=180

6x=160

x=160/6

x=26.667

Answer:

2X=53.2 , 3X=79.8 , X+20=46.6

Step-by-step explanation:

3X+2X+X+20=180

therefore,

6X+20=180

6X       =180-20

6X       =160

X        = 160 over 6

X        =26.6

now,

3X      = 26.6 x3

          =79.8

2X       =26.6 x2

          =53.20

X+20  =26.6+20

          =46.6

Im not sure if it's right. Because the total does not make 180 degrees.

Answer: Oh heaven nah

Step-by-step explanation: Lord have mercy

Answer:

The range of weights of the middle 99.7% of M&M’s is between 0.8187 and 1.0203.

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

Approximately 68% of the measures are within 1 standard deviation of the mean.

Approximately 95% of the measures are within 2 standard deviations of the mean.

Approximately 99.7% of the measures are within 3 standard deviations of the mean.

Sample mean:

[tex]\overline{x} = \frac{0.957 + 0.912 + 0.925 + 0.886 + 0.920 + 0.958 + 0.915 + 0.914 + 0.947 + 0.939 + 0.842}{11} =  0.9195[/tex]

Sample standard deviation:

[tex]s = \sqrt{\frac{(0.957-0.9195)^2 + (0.912-0.9195)^2 + (0.925-0.9195)^2 + (0.886-0.9195)^2 + ...}{10}} = 0.0336[/tex]

What is the range of weights of the middle 99.7% of M&M’s?

By the Empirical Rule, within 3 standard deviations of the mean, so:

0.9195 - 3*0.0336 = 0.8187.

0.9195 + 3*0.0336 = 1.0203.

The range of weights of the middle 99.7% of M&M’s is between 0.8187 and 1.0203.

9514 1404 393

Answer:

  (c)  3x - 2y

Step-by-step explanation:

Use the distributive property to eliminate parentheses, then collect terms.

  3(x -y) +y = 3x -3y +y = 3x +(-3+1)y = 3x -2y

Now we have to find,

The expression which is equivalent to,

→ 3(x - y) + y

Let's get the solution,

→ 3(x - y) + y

→ 3x - 3y + y

→ 3x - 2y

Hence, required expression is 3x - 2y.

Answer:

4x+ 4

Step-by-step explanation:

Answer:

26√13

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Let me know if you need an explanation.

Answer:

B

Step-by-step explanation:

4x^3+x^2+5x+2

4x^3 cannot cancel with others= 4x^3

4x^2-3x^2= x^2

5x cannot cancel with others= 5x

-3+5= 2

4x^3+x^2+5x+2

Answer: The image shown in your question as well as the one I provided is the correct answer

Step-by-step explanation:

a line with a slope of 2/3 must mean that the "m" is 2/3

y = mx + b

y = 2/3x + b

The question calls for the y-intercept to be equal to that of y=2/3x - 2

using the given equation, we easily figure out -2 is the y-intercept

so the line must go through (0,-2).

Answer:

The probability that 2 certain people will serve on that committee is 11.11%.

Step-by-step explanation:

Since to make a committee 4 men are chosen out of 6 candidates, to determine what is the probability that 2 certain people will serve on that committee the following calculation must be performed:

4/6 = 2/3

1/3 x 1/3 = X

0.333 x 0.333 = X

0.1111 = X

Therefore, the probability that 2 certain people will serve on that committee is 11.11%.

Answer:

[tex]\frac{2}{5}[/tex]

Step-by-step explanation:

6 groups, and 4 certain people

6

   C

        4

[tex]\frac{6!}{(6-2)!(2!)}[/tex]

1 × 2 × 3 × 4 × 5 × 6/1 × 2 × 3 × 4 × 1 × 2

1 × 2 × 3 × 4 × 5 × 6/1 × 2 × 3 × 4 × 1 × 2

5 × 6/ 1 × 2

30/2 = 15

15 possible combinations

4 people, and 2 specific ones

4

   C

        2

[tex]\frac{4!}{(4-2)!(2!)}[/tex]

1 × 2 × 3 × 4/1 × 2 × 1 × 2

1 × 2 × 3 × 4/1 × 2 × 1 × 2

12/2 = 6

[tex]\frac{6}{15}=\frac{\frac{6}{3} }{\frac{15}{3} } =\frac{2}{5}[/tex]

Answer:

Slope

Step-by-step explanation:

Given

The above statement

Required

What compares the steep of linear functions

Literally, steepness means slope.

So, when the slope of the two linear functions are calculated, we can make comparison between the calculated slopes to determine which of the functions is steeper or less steep.

Also:

Higher slope means steeper line

e.g.

4 is steeper than 1

Step-by-step explanation:

a) X is a discrete uniform distribution. As the number of outcomes is only 3.

b) sum is at least 4

X ≥ 4--------

i.e  (1,3) or (2,3)

probability of X ≥ 4 is 2/3

2/3= 0.667

66.7 % is the probability of the outcome to have  a sum at least 4.

c) The 3 likely outcome of X

(1,2) where X ; 1+2=3

(1,3) where X ; 1+3=4

(2,3) where X ;  2+3=5

Mean = 3+4+5/ 3

Mean = 4

Feel free to ask any uncleared step

Answer:

11.45 lumens

Step-by-step explanation:

We are given that

[tex]log(I/12)=-0.00235x[/tex]

Where x=Depth

I=Intensity of light

We have to find the intensity of the light at a depth of 20 feet.

Substitute the value of x

[tex]log(I/12)=-0.00235\times 20[/tex]

[tex]log(I/12)=-0.047[/tex]

[tex]\frac{I}{12}=e^{-0.047}[/tex]

[tex]I=12e^{-0.047}[/tex]

[tex]I=11.45 Lumens[/tex]

Hence, the intensity of the light (in lumens) at a depth of 20 feet=11.45 lumens

Step-by-step explanation:

AB = square root of [(xA-xB)^2+(yA-yB)^2]

AB=Squarerootof(-1-11)^2 +(-3-(-8))^2=Squarerootof(-12)^2+(5)^2)

AB=Squarerootof((144)+25)= Squarerootof(169)=13 the answer is 13 units

The choice D is the right one

Answer:

answer D

Step-by-step explanation:

V=L*W*H=1 ==> L=1,W=1,H=1

A:

L-> L+2=1+2=3

W -> W+2 = 1+2=3

H -> H+2=1+2=3

V=3*3*3=27 not the doubled of the volume's cube

A is false

B:

H -> H+2=1+2=3

V=1*1*3=3 not the doubled of the volume's cube

B is false

C:

H -> 2*H=2*1=2

L -> 2*L=2*1=2

W -> 2*W = 2*1=2

V=2*2*2=8 not the doubled of the volume's cube

C is false

D:

H-> H*2=1*2=2

L=1

W=1

V=1*1*2=2 is the doubled of the volume's cube

D is true

Answer:

Line A

Step-by-step explanation:

graph it

Answer:

continues means that can be written in decimal like weight,height, distance(5.44km)

I think its D. is time decimal? Gods plan.

Answer:

it's. is now the MA plz I miss you

si pudiera escoger entre vivir eternamente y vivir dos veces

yo escogeria vivir dos veces porque vivir una vida eterna sin ti a mi lado seria el mayor sufrimiento, ahora vivir dos veces me dejaria tranquilo porque despues del final de mi vida podria volver a encontrarme contigo y vivir todos los momentos bellos una vez mas y eso seria un sueño volviendose realidad

Answer:

A) The diameter is approximately 12 feet.

Step-by-step explanation:

C= piD

sq ft would be wrong bc this is not talking ab area

Answer:

Scatter plot charts are good for relationships and distributions, but pie charts should be used only for simple compositions — never for comparisons or distributions.

The probability that one of them will win will be 9/14.

Since the probability that Jack will win is 1/7 and the probability that Bill will win is 1/2, then the probability that one of them will win will be:

= 1/7 + 1/2

= 7/14 + 2/14

= 9/14

Therefore, the probability that one of them will win will be 9/14.

Read related link on:

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Answer:

3x² + x + 1

-3x² + x + 1

-54

Step-by-step explanation:

there is nothing complicated to it. you just use the requested pertain on the whole expressions of the functions, and the result is then the new function.

so,

r(x) = 3x²

s(x) = x + 1

what do you think s + r is ?

it is simply

(s+r)(x) = 3x² + x + 1

done. that is really all there is to this.

now the next (but consider the sequence due to the sign)

(s-r)(x) = x + 1 - 3x² = -3x² + x + 1

and the third

(s×r)(x) = 3x²(x+1) = 3x³ + 3x²

so, for x=-3

(s×r)(-3) = 3×(-3)³ + 3×(-3)²

remember, an even power of a negative number gives a positive result, an uneven power of a negative number gives a negative result.

(s×r)(x) = 3×-27 + 3×9 = -81 + 27 = -54

Answer:

solution,

mode of 3 numbers is 6

range is 4

possible set of numbers are

{3,4,6,{} }