Find the correct algebraic representation of the rotation shown below.

a. (y, -x)
b. (-x, -y)
c. (-y, x)
d. (y, x)

Answer:

1) 0.1504

2) 0.432

Step-by-step explanation:

1) The given information are;

The proportion of the morning appointments that are with elderly patients = 60%

The number of patients in the appointments  = 10 patients

The proportion of the morning appointments that are with non-elderly patients = 100 - 60 = 40%

The binomial probability distribution is given as follows;

[tex]P(X = r) = \dbinom{n}{r}p^{r}\left (1-p \right )^{n-r}[/tex]

[tex]P(X = 0) = \dbinom{10}{0}0.6^{0}\left (1-0.6 \right )^{10}[/tex] = 0.000105

[tex]P(X = 1) = \dbinom{10}{1}0.6^{1}\left (1-0.6 \right )^{9}[/tex] = 0.0016

[tex]P(X = 2) = \dbinom{10}{2}0.6^{2}\left (1-0.6 \right )^{8}[/tex]= 0.01062

[tex]P(X = 3) = \dbinom{10}{3}0.6^{3}\left (1-0.6 \right )^{7}[/tex]= 0.0425

The probability that the first four patients are elderly is 0.000105 + 0.0016 + 0.1062 + 0.0425 = 0.1504

2) The probability that exactly 2 out of 3 morning patients are elderly patient is given as follows

[tex]P(X = 2) = \dbinom{3}{2}0.6^{2}\left (1-0.6 \right )^{1}[/tex]= 0.432

Answer:

Step-by-step explpointsanation:

Answer:

Length of transverse axis  = 2 b  = 10

Length of conjugate axis   = 2 a  = 4      

Step-by-step explanation:

Explanation:-

Given Hyperbola

                       [tex]\frac{(y+2)^{2} }{25} -\frac{(x-3)^{2} }{4} =1[/tex]

  Standard form of Hyperbola    

                  [tex]\frac{(y-(K))^{2} }{b^{2} } -\frac{(x-h)^{2} }{a^{2} } =1[/tex]

   Center (h , k ) = (3 , -2 )  , a = 2 and b = 5

Length of transverse axis  = 2 b = 2(5) = 10

Length of conjugate axis   = 2 a = 2 (2) = 4      

Answer:

x² + -6x = -13

Step-by-step explanation:

8x² - 48x = -104

x² - 6x = -13

The quadratic equation can be written as x² + (- 6x) = - 13

Quadratic equations are algebraic expressions which the highest value of x in its second degree. It is usually expressed in the form: ax² + bx + c

From the given information, the objective is to simplify the quadratic equation in terms of ax² + bx + c  

∴

Given that:

We need to divide through by (8)

Learn more about quadratic equations here:

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Answer:

Step-by-step explanation:

Given, Radius ( r ) = 6 units

Area of semi-circle = ?

Now, let's find the area of semi-circle:

[tex] \frac{1}{2} \pi \: {r}^{2} [/tex]

plug the values

[tex] = \frac{1}{2} \times 3.14 \times {6}^{2} [/tex]

Evaluate the power

[tex] = \frac{1}{2} \times 3.14 \times 36[/tex]

Calculate

[tex] = 56.52 \: [/tex] units²

hope this helps...

Best regards!!

Answer:

56.52

Step-by-step explanation:

6^2*3.14=113.04

113.04/2=56.52

For you, I am just going to give a small explanation but not too much

Answer:

option c (31)

Step-by-step explanation:

Answer:

D) 2.0

Step-by-step explanation:

We know that √2 = 1.414213562 ≈ 1.4, π ≈ 3.14, and √5 = 2.236067978 ≈ 2.2 . Next, I found out that √2π = 4.442882938 which rounds to 4.4. Then, I found out that 4.4 ÷ √5 equals to 1.96773982. So, if we round our answer to the nearest whole number, we will get 2.

Answer:

[tex]\boxed{Option \ D}[/tex]

Step-by-step explanation:

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

Where [tex]\sqrt{2}[/tex] = 1.4 , π = 3.14 and [tex]\sqrt{5}[/tex] = 2.24

Plugging in the values

=> [tex]\frac{(1.4)(3.14)}{2.24}[/tex]

=> 4.396/2.24

=> 1.9

≈ 2.0

Answer:

3x^3/x = 3x^(3-1) = 3x^2

6x*y = 6xy

x^2y *y =  x^2y^(1+1) = x^2y^2

4y*y = 4y^2

Step-by-step explanation:

This can be solved using law of Indices.

The expression 3x^3 should be 3x^2.

Here power of x is three while in output power of x is two hence we need to eliminate power of x by one for that we divide 3x^3 by x

Rule: x^a/x^b = x^(a-b)

3x^3/x = 3x^(3-1) = 3x^2 (answer)

_________________________________

The expression 6x should be 6xy.

here term y is missing hence we multiply 6x with y

rule: a*b = ab

6x*y = 6xy  (answer)

_________________________________________________

The expression x^2y should be x^2y^2

Here we need power of y as 2, to do that we multiply  x^2y by y.

Rule

x^2*x^b  = x(a+b)

x^2y *y =  x^2y^(1+1) = x^2y^2  (answer)

_____________________________________________

The expression 4y should be 4y^2\

Here we need power of y as 2, to do that we multiply 4y by y.

Rule

x^2*x^b  = x(a+b)

4y*y = 4y^2   (answer)

Answer:

b:  the expression 6x should be 6xy

Step-by-step explanation:

i just did on edgen 2020

Using the pythagorean identity, [tex]\cos^2{\theta} + \sin^2{\theta} = 1[/tex]. Since [tex]\theta[/tex] is in quadrant ||, we know that [tex]\cos{\theta}[/tex] is negative. Solving the equation [tex]\cos^2{\theta} + (\frac{4}{5})^2 = 1[/tex] for [tex]\cos{\theta}[/tex], we get that [tex]\cos{\theta} = -\frac{3}{5}[/tex].

[tex]\tan{\theta}[/tex] is equal to [tex]\frac{\sin{\theta}}{\cos{\theta}}[/tex], which is [tex]-\frac{4}{3}[/tex].

The value of cos θ and tan θ will be negative 0.60 and negative 0.75, respectively.

Trigonometric functions examine the interaction between the dimensions and angles of a triangular form.

If sin θ = 4/5.

The value of the cosine is negative. Then the cosine of angle θ is given as,

cos θ = -√(1 - sin²θ)

cos θ = - √[1 - (4/5)²]

cos θ = - √[9/25]

cos θ = - 3/5

θ = 143.13°

The value of the tangent of angle θ is calculated as,

⇒ tan θ

⇒ tan 143.13

⇒ - 0.75

The value of cos θ and tan θ will be negative 0.60 and negative 0.75, respectively.

More about the trigonometry link is given below.

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Answer:

Below

Step-by-step explanation:

You could just graph the equation for the answers....

Here is algebraic method

 for Quadratic Equation  - 50p^2 +1700p - 12000

        the max profit occurs at p = - b/2a   = - 1700 / (2* -50) = 17 dollars

A ) 17 dollars

B)  use p =17 in the equation to find profit = 2450 dollars

C)    Set the equation = 0  and solve for p

     0 = -50p^2+1700p - 12 000

              Use Quadratic Formula with a = -50    b = 1700   c = 12000

                     to find price = 40 dollars

Answer:

C

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

a. Distance = 400 - 200t

b. see attached graph

c. A travelled 180 km, B travelled 220 km, both took 2 hours.

Step-by-step explanation:

Given

distance = 400

A = 90 km/h

B = 110 km/h

A & B drive towards each other

Solutions

a) equation

Let

t = elapsed time in hours,

D(t) = distance between two drivers

D(t) = 400 - (A+B) t  

D(t) = 400 - 200t  ......................(1)

b. graph : for graph, see attached figure.

c. Distance and time

Time:

solve for t with the distance D(t) = 0 using equation (1)

0 = 400 - 200 t

200t = 400

t = 2   hours

distance travelled by A = 2 hours * 90 km/h  = 180 km

distance travelled by B = 2 hours * 110 km/h  = 220 km

Answer:

C

Step-by-step explanation:

Remember that when we have roots (like the square root here), then they can be written as fractional exponents.

Here, we have √2, which is equal to [tex]2^{1/2}[/tex], and we have ∛2, which is equal to [tex]2^{1/3}[/tex]. That means:

(√2)(∛2) = [tex]2^{1/2}*2^{1/3}[/tex]

By property of exponents, when we multiply two exponents with the same base (2 here), we can combine them into one exponent by adding the two powers:

[tex]2^{1/2}*2^{1/3}=2^{1/2+1/3}=2^{3/6+2/6}=2^{5/6}[/tex]

The answer is thus C.

~ an aesthetics lover

Answer:

c

Step-by-step explanation:

Answer:

x = 29

Step-by-step explanation:

(5x + 2) + (x + 4) = 180

6x + 6 = 180

6x = 174

x = 29

I HOPE THIS HELPS

Answer:

x=29 degrees

Step-by-step explanation:

We know that the straight line is 180 degrees because definition of a straight. So we take 4 and 2 and subtract them off of 180. so 180-4-2=174. Now, we do 174/6 because you want to figure out how much times 6 can go into 174 because there are 6 x's (if that makes sense). So we get the answer 29 so x=29 degrees.

Basically, you want to combine like terms. So we combined the non-variable numbers and we subtract it off of 180. Then we take the variables and combine them. So in this case, it would be x+5x=6x. Then we need to figure out what x is so we just divide by 6 on both sides. So 6x=174 so x=29.

I hope this made sense.

Answer:

pretty tall

Step-by-step explanation:

[tex]\frac{1}{15}[/tex] or 6.67%

In practice, the relative frequency of an event happening is the same as the probability that that event happened. In other words, the terms "relative frequency" and "probability" can be used interchangeably.

Now, the probability P(A) of an event A happening is given by;

P(A) = [tex]\frac{number-of-outcomes-in-the-event-A}{number-of-outcomes-in-the-sample-space}[/tex]

From the question;

The event A is the situation of local residents having a post office box. Therefore the;

number-of-outcomes-in-the-event-A = 8   [since only 8 of the local residents have a post office box]

number-of-outcomes-in-the-sample-space = 120 [since there are altogether 120 local residents]

Therefore,

P(A) = [tex]\frac{8}{120}[/tex]

P(A) = [tex]\frac{1}{15}[/tex]

The relative frequency that a local resident does not have a post office box for receiving a mail is therefore, [tex]\frac{1}{15}[/tex]

PS: Sometimes it is much more convenient to express relative frequencies as percentage. Therefore, the result above expressed in percentage gives:

[tex]\frac{1}{15} * 100%[/tex]% = 6.67%

[5x +2y]35 =100

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Answer:

C.210

Step-by-step explanation:

360 degrees in a circle. 360-150=210

Answer:

I think the answer is B

Step-by-step explanation:

Answer: B

Step-by-step explanation:

Answer:

The answer is "101.37  yd"

Step-by-step explanation:

In the given question an attachment file is missing. so, we attached the file and calculates its value:

Use formula:

[tex]c^2 = a^2 + b^2 - 2\times a \times b\times \cos C[/tex]

In the above-given equation we assume c is the third side:

[tex]c^2 = 305^2 + 255^2 - 2*305*255*cos17\\c^2= 93,025+65,025-155,550(0.95)\\c^2= 158,050-147,772.5\\c^2= 10,277.5[/tex]

c = 101.37  yd

Answer:

Step-by-step explanation:

let's say the price of the dress in the beginning is 100x

the on sale price decreases 80x  

80x = 74.12

100 x = 92.75

Answer:

That right, no picture, no answer

Step-by-step explanation:

Answer:

B) x=64, y=21, z=64

Step-by-step explanation:

X=180-116=64

Y cannot equal 115, and one angle is already 95, and that would put it over 180.  The only remaining choice for y=21

z=180-95-21=64

Answer:

x=7

Step-by-step explanation:

4/3x-1/3=9

Add 1/3 on both sides

4/3x=28/3

Multiply the reciprocal

(3/4)(4/3)x=28/3(3/4)

x=7

Hope this helps !!

Answer:

In the year 2019 the number of new cars purchased will reach 15,000.

Step-by-step explanation:

t = 0 corresponds to the number of new cars purchased in 1998. If that is so, we can determine t ( time ) by making our quadratic equation here equal to 15,000 - considering that we want the year the number of cars reaches this value. t here is only the number of years to reach 15,000 cars, so we would have to add that value to 1998, to see the year that the cars will reach 15,000.

The " set up " should look like the following quadratic equation -

20t² + 135t + 3050 = 15,000 - Isolate 0 on one side,

20t² + 135t - 11950 = 0 - From here on let us solve using the quadratic equation formula,

[tex]t=\frac{-135+\sqrt{135^2-4\cdot \:20\left(-11950\right)}}{2\cdot \:20}:\quad \frac{-27+\sqrt{38969}}{8}[/tex],

[tex]t=\frac{-135-\sqrt{135^2-4\cdot \:20\left(-11950\right)}}{2\cdot \:20}:\quad -\frac{27+\sqrt{38969}}{8}[/tex] ... now as you can see we have two solutions, but time can't be negative, and hence our solution is the first one - about 21.3 years. 1998 + 21.3 = ( About ) The year 2019. Therefore, in the year 2019 the number of new cars purchased will reach 15,000.

Answer:

2019

Step-by-step explanation:

first you should change the statement into quadratic equation and replace c with 15000.

c=20t^2+135t+3050.

15000=20t^2+135t+3050

15000-3050=20t^2+135t

11950=20t^2+135t. then write the equation in standard quadratic form.

20t^2+135t-11950=0. after this you got 4 ways of solving the quadratic equation but I am just gone using quadratic formula:

-b+ - √b^2-4ac. a,b and C stand for the

2a. the coefficients

-135+ - √((135)^2-4(20)(-11950))

2(20)

-135+ - √(974225))

)) 40

-135 - 987 or -135+ 987

40. 40

-1122/40. or 852/40

- 28.05 or. 21.3

in this case we have to answer but time cannot be negative we take value 21.3(it is the approximate value)

so we add 21.3 to 1998 to find the year

>>21.3 + 1998 = 2019.3 but we write it as 2019 instead of 2019.3

Bro its so confusing

The regression equation best fits these data [tex]y=-0.58x^2 - 0.43x+ 15.75[/tex].

Firstly, there is a data set. Then, we try to fit a line that will tell about the linear trend. This line is made using the least-squares method.

When the data shows some trend, either linear (making a line), or non-linear (a predictable curve).

We fit a mathematical curve on that data set, as a representative of the pattern in that data set, to predict the output based on the inputs.

Using the exponential regression calculator,

The exponential model was obtained using the data.

Therefore, The regression equation best fits these data

[tex]y=-0.58x^2 - 0.43x+ 15.75[/tex]

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Answer:

3.22 or 161/50

Answer:

3.22 and 3 11/50/166/50

Step-by-step explanation:

The points in between 3.2 and 3.3 go 3.21, 3.22, 3.23, etc. So first we just write it as a decimal. Easy. Then we write it as a fraction. Writing it as a mixed number would just be 3 22/100 because .01*100 is 1. I simplified it and then converted it into an improper fraction. I hope this helped.