(b)
The Cartesian coordinates of a point are given.
(1, -5)
(i) Find polar coordinates (r, 0) of the point, where r> 0 and 0 = 0 < 2.
(r, 0) =
(
(ii) Find polar coordinates (r, 0) of the point, where r < 0 and 0 < theta<2pi.
(r, 0) =

Answer:

x=15, y=2

Step-by-step explanation:

By AA similarity, the triangles are similar. Therefore, we can find the ratios of the side lengths.

9/3=3=ratio of the side length of a larger triangle to a smaller one.

3=6/y, y=2

3=x/5, x=15

Hope this helped,

~cloud

Answer:

6

Step-by-step explanation:

because the equation above says p+p+p+p+p+p+5+1+1

so if we add up the p's it will give us 6p and if we add up the nos it will give us 6p+7

Answer:

30 Dollars more

Step-by-step explanation:

This summer he earned = 7.25 X 40 = 290

Last summer he earned = 6.5 X 40 = 260

How much more he earned in 40 hours = 290-260= 30 dollars more

Answer from Gauthmath

Answer:

TU = 27

Step-by-step explanation:

We are given two secant segments that are drawn from a circle to meet at an exterior point of the circle. Thus, according to the secant secant theorem, the product of the measure of one secant segment and its external secant segment equals that of the product of the other and its external secant segment.

Thus:

VU*TU = VW*BW

Substitute

7(x + 4) = 9(-2 + x)

7x + 28 = -18 + 9x

Collect like terms

7x - 9x = -18 - 28

-2x = -46

Divide both sides by -2

x = -46/-2

x = 23

✔️TU = x + 4

Plug in the value of x

TU = 23 + 4

TU = 27

Solution :

a). The test is a left tailed test.

b). The sample proportion is :

[tex]$\hat p = \frac{x}{n}$[/tex]

[tex]$\hat p = \frac{17}{258}$[/tex]

  = 0.065

Determining the Z statistics using the formula :

[tex]$Z=\frac{\hat p - p}{\sqrt{\frac{p(1-p)}{n}}}$[/tex]

[tex]$Z=\frac{0.065 - 0.11}{\sqrt{\frac{0.11(1-0.11)}{258}}}$[/tex]

   = -2.31

∴ Z statistics value is -2.31

c). Using the excel function, the P-value is :

P-value = Normsdist(-2.31)

             = 0.0104441

d). The null hypothesis is [tex]$H_0: P = 0.11$[/tex]

    The level of significance is 0.01

    We fail to reject the null hypothesis as the P value is less than or equal to the significant level.

Answer:

https://linksharing.samsungcloud.com/ul5cX9oOmhzt

Answer:

12.6

Step-by-step explanation:

Length of arc=(2*pi*r)*(theta/360)

Length of arc=(2*12*pi)*(1/6)=12.6

Using the points stated in the original problem, I have determined the lines for the graph.  

f(x)=3x-1

g(x)= 3x+17

Using the basic descriptions of transformations, we can determine the movement of the lines as being either horizontal or vertical shifts. (to put a visual to this problem, I the diagram in Desmos and then marked the stated points on the graph.)

Horizontal shifts move the line either to the left or to the right.  Vertical shifts move the line either up or down.

If you look at the graphs as being the same x-value for the functions, the change in the y- value is +18, which is a vertical shift.  

If you look at the graphs as being the same y-values, the change in x is -6 which is a horizontal shift.  

So, the value of k is the amount of change each equation has to have to match the points given. (from f(x) to g(x))

The vertical shift is g(x)=f(x) +18

The horizontal shift is g(x)=f(x-6)

Answer:

The vertical shift is g(x)=f(x) +18

The horizontal shift is g(x)=f(x-6)

Step-by-step explanation:

*see attachment for clearer diagram

Answer:

16.5

Step-by-step explanation:

BC = 11

AB = 3

Area of the shaded region = area of ∆AEB + area of ∆CED

Area of a triangle is given as,

A = ½*base*height

Find the area of each triangle and add together

✔️Area of ∆AEB = ½*bh

Where,

base (b) = 3

height (h) = ½(BC) = ½(11) = 5.5

Area of ∆AEB = ½*3*5.5 = 8.25

✔️Area of ∆CED = ½*bh

Where,

b = 3

h = ½(BC) = ½(11) = 5.5

Area of ∆CED = ½*3*5.5 = 8.25

✅Area of the shaded region = area of ∆AEB + area of ∆CED

= 8.25 + 8.25

= 16.5

Solution :

Defining the following events as :

B : Being a Business major

α : Studying at the library

∴ Given that :

[tex]$P(B) = \frac{45}{100}$[/tex]

         = 0.45

Again, P [ Studying at the library | Being a Business major ] = 2 P [ Studying at the library | Being a non business major ]

[tex]$P[ \alpha | B] = 2 P[\alpha | B^C]$[/tex]   .......(1)

Again,

[tex]$P[\text{Studying at the library } | \text{ Being a business major}] = \frac{1}{2} = 0.50$[/tex]

[tex]$P(\alpha | B) = 0.50$[/tex]

From (1), we get

[tex]$P(\alpha | B^C) = \frac{1}{2} . P(\alpha | B)$[/tex]

              [tex]$=\frac{1}{2} \times 0.50$[/tex]

              = 0.25

Therefore, we need,

= P[  The students is a Business major | The student studies at the library ]

[tex]$=P(B | \alpha)$[/tex]

By Bayes theorem

[tex]$=\frac{P(B). P(\alpha | B)}{P(B).P(\alpha | B) + P(B^C). P(\alpha | B^C)}$[/tex]

[tex]$=\frac{0.45 \times 0.50}{0.45 \times 0.50 + 0.55 \times 0.25}$[/tex]

= 0.6207

Answer:

The answer is "0.695 and 0.305".

Step-by-step explanation:

Please find the attached file of the given question:

From question a:

[tex]\text{P(Either married, or a college graduate, or a professional)} \\\\=\frac{(312+143+188+191)}{1200}\\ \\ =\frac{834}{1200}\\\\=0.695[/tex]

 From question b:

[tex]\text{P( Neither married, nor a college graduate, nor a professional )}\\\\=\frac{366}{1200} \\\\=0.305[/tex]

Answer:

D. Neither perpendicular nor parallel

Step-by-step explanation:

Let's find the slope (m) of both lines:

✔️Slope (m) of the line that passes through (6, -1) and (11, 2):

Slope (m) = change in y/change in x

Slope (m) = (2 -(-1))/(11 - 6) = 3/5

✔️Slope (m) of the line that passes through (5, -7) and (8, -2)

Slope (m) = change in y/change in x

Slope (m) = (-2 -(-7))/(8 - 5) = 5/3

✅The slope of both lines are not the same, therefore they are not parallel nor same line.

Also, the slope of one is not the negative reciprocal of the other, therefore they are not perpendicular.

[tex]\begin{array}{c|c|c|c|c|c} p & q & r & p\land q & q\land \neg p & r \land q \\&&&&\\ T & T & T & T & F & T \\ T & T & F & T & F & F \\ T & F & T & F & F & F \\ T & F & F & F & F & F \\ F & T & T & F & T & T \\ F & T & F & F & T & F \\ F & F & T & F & F & F \\ F & F & F & F & F & F\end{array}[/tex]

An implication A => B is true if either A is false, or both A and B are true. So

[tex]\begin{array}{c|c|c}p\land q & (q\land\neg p) \implies (r\land q) & (p\land q) \implies \big[(q\land\neg p) \implies (r\land q)\big] \\&&\\T & T & \mathbf T\\T & T & \mathbf T\\F & T & \mathbf T\\F & T & \mathbf T\\F & T & \mathbf T\\F & F & \mathbf T\\F & T & \mathbf T\\F & T & \mathbf T\end{array}[/tex]

and the given statement is a tautology.

Answer:

(0,4)  will be point (P) at 3 because,

Step-by-step explanation:

by using newton interpolation method we can find P(0,4) at 3 .

9514 1404 393

Answer:

  C.  8

Step-by-step explanation:

The median from vertex B is the line segment between there and the midpoint of side AC. That midpoint is ...

  D = (A +C)/2 = ((-6, 7) +(-2, -9))/2 = (-8, -2)/2 = (-4, -1)

So, we want the length of the line between (-4, -1) and (4, -1). These points are on the same horizontal line (y=-1), so the length is the difference of the x=coordinates:

  median AD = 4 -(-4) = 8 . . . . units in length

I dont know what you mean by the question but according to me.

If y=x^5

y=x^5+3

Then y+3=x^5+3

Answered by Gauthmath must click thanks and mark brainliest

Answer:

(x - 4)² + (y + 9)² = 25

Step-by-step explanation:

The equation of a circle is written as seen below.

(x – h)² + (y – k)² = r²

Where (h,k) represents the center of the circle and r represents the radius

We want to find the equation of a circle that has a center at (4,-9) and a radius of 5.

We know that (h,k) represents the center so h = 4 and k = -9

We also know that r represents the radius so r = 5

Now to find the equation of this specific circle we simply plug in these values into the equation of a circle formula

Equation: (x – h)² + (y – k)² = r²

h = 4, k = -9 and r = 5

Plug in values

(x - 4)² + (y - (-9))² = 5²

5² = 25

The two negative signs in front of the 9 cancel out and it changes to + 9

The equation of a circle with a center at (4,-9) and a radius of 5 is

(x - 4)² + (y + 9)² = 25

Answer:

The probability of getting two numbers whose sum is 10 is 25%.

Step-by-step explanation:

Given that a single die is rolled twice, and there are 36 equally-likely outcomes, to find the probability of getting two numbers whose sum is 10 the following calculation must be performed:

1 = +9

2 = +8

3 = +7

4 = +6

5 = +5

6 = +4

7 = +3

8 = +2

9 = +1

9/36 = 0.25

Therefore, the probability of getting two numbers whose sum is 10 is 25%.

Answer:

-1.25

Step-by-step explanation:

you first have to cross multiply

12(b-1)=4(7b+2)

12b-12=28b+8

group the like terms

12b-28b=8+12

-16b/-16=20/-16

b= -1.25

I hope it helps

Step-by-step explanation:

Answer is in the picture..

hope it helps

Answer:

2.5

Step-by-step explanation:

i had it

Answer:

I think i don't know the answer i am so sorry!!!

maybe someone else can Answer

Since this is a right triangle, we can use one of the three main trigonometric functions: sine, cosine, or tangent.

Remember: SOH-CAH-TOA

Looking from the given angle, we know the opposite side and want to know the hypotenuse. Therefore, we should use the sine function.

sin(54) = 16/AB

AB = 16/sin(54)

AB = 19.78 units

Hope this helps!

Answer:

x = 12

y = -29

Step-by-step explanation:

Our given equations: x + y = -17 and x - y = 41

Solve for x and substitute.

x = -17 - y

(-17 - y) - y = 41

-17 - 2y = 41

2y = -58

y = -29

Solve for x using y

x + (-29) = -17

x = 12

Answer:

$14.40

Step-by-step explanation:

my way of doing things:

15/100=0.15=1%of total amount

0.15 x 6=0.9= the 6% which is the tax

0.15 x 10 = 1.5=the coupon

Take the coupon amount $1.50 minus the tax amount $0.90 =$0.60. Because the coupon amount is greater than the tax the 60 cents gets taken away from the original 15 dollars leaving Mr. Longely only having to pay $14.40.

9514 1404 393

Answer:

Step-by-step explanation:

The function is defined for all values of x, so its domain is all real numbers.

The function can produce values of f(x) that are 0 or greater, so its range is ...

  y ≥ 0

Answer:

[tex]V(r) =101\pi r^2 + \frac{2}{3}\pi r^3[/tex]

Step-by-step explanation:

Given

Shapes: cylinder and hemisphere

[tex]h = 101[/tex] --- height of cylinder

Required

The volume of the silo

The volume is calculated as:

Volume (V) = Volume of cylinder (V1) + Volume of hemisphere (V2)

So, we have:

[tex]V_1 = \pi r^2h[/tex]

[tex]V_1 = \pi r^2 * 101[/tex]

[tex]V_1 = 101\pi r^2[/tex] --- cylinder

[tex]V_2 = \frac{2}{3}\pi r^3[/tex] ---- hemisphere

So, the volume of the silo is:

[tex]V =V_1 + V_2[/tex]

[tex]V =101\pi r^2 + \frac{2}{3}\pi r^3[/tex]

Write as a function

[tex]V(r) =101\pi r^2 + \frac{2}{3}\pi r^3[/tex]

Where: [tex]\pi = \frac{22}{7}[/tex]

Answer:

Centre is,

((5+7)/2,(8+6)/2)

or, (12/2,14/2)

or, (6,7)

radius is,

[√{(5-7)²+(8-6)²}]/2

= [√(2²+2²)]/2

= [√(4+4)]/2

= [√8 ]= [2√2]/2 = √2

The center of a circle = (6, 7)

the radius of a circle = [tex]\sqrt{2}[/tex] units

"The distance between two points [tex](x_1,y_1),(x_2,y_2)[/tex] is given by  [tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_2)^2}[/tex]"

"The coordinates of the midpoint of the line segment having endpoints [tex](x_1,y_1),(x_2,y_2)[/tex] is given by [tex]m=(\frac{x_1+x_2}{2} ,\frac{y_1+y_2}{2} )[/tex] "

"It is the line segment through the center and touching two points on its edge. "

For given question,

The diameter of circle has endpoints at (5, 8) and (7,6).

Let [tex](x_1,y_1)=(5,8),(x_2,y_2)=(7,6)[/tex]

First we find the length of the diameter of the circle.

Using the distance formula,

[tex]\Rightarrow d=\sqrt{(x_2-x_1)^2+(y_2-y_2)^2} \\\\\Rightarrow d=\sqrt{(7-5)^2+(6-8)^2} \\\\\Rightarrow d=\sqrt{2^2+(-2)^2}\\\\\Rightarrow d=\sqrt{4+4}\\\\\Rightarrow d=2\sqrt{2}~units[/tex]

We know that the diameter = 2 × radius

⇒ radius (r) = [tex]\frac{2\sqrt{2} }{2}[/tex]

⇒ r = [tex]\sqrt{2}[/tex] units

We know that the midpoint of the diameter is the center of the circle.

Using midpoint formula the center of the circle would be,

[tex]\Rightarrow O=(\frac{x_1+x_2}{2} ,\frac{y_1+y_2}{2} )\\\\\Rightarrow O=(\frac{5+7}{2} ,\frac{8+6}{2} )\\\\\Rightarrow O=(\frac{12}{2} ,\frac{14}{2} )\\\\\Rightarrow O=(6,7)[/tex]

Therefore, the center of the circle is (6,7)

Hence, the center of a circle = (6, 7)

the radius of a circle = [tex]\sqrt{2}[/tex]

Learn more about the distance formula and mid-point formula here:

https://brainly.com/question/11231122

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