8 sin2 x + cos x - 5 = 0

Answer:

Circle Equation : x² + y² = 21

Step-by-step explanation:

So we know that this circle goes through the point ( - 4, √5 ), with a center being the origin. Therefore, this makes the circle equation a bit simpler.

The first step in determining the circle equation is the length of the radius. Applying the distance formula, the radius would be the length between the given points. Another approach would be creating a right triangle such that the radius is the hypotenuse. Knowing the length of the legs as √5 and 4, we can calculate the radius,

( √5 )² + ( 4 )² = r²,

5 + 16 = r²,

r = √21

In general, a circle equation is represented by the formula ( x - a )² + ( y - b )² = r², with radius r centered at point ( a, b ). Therefore our circle equation will be represented by the following -

( x - 0 )² + ( y - 0 )² = (√21 )²

Circle Equation : x² + y² = 21

Answer:

20

Step-by-step explanation:

We can set up a percentage proportion to find the value of x.

[tex]\frac{12}{x} = \frac{60}{100}[/tex]

Now we cross multiply:

[tex]100\cdot12=1200\\\\1200\div60=20[/tex]

Hope this helped!

Answer:

Step-by-step explanation:

Since 8 is a factor of 24, 8 is the GCF of the pair, and 24 is the LCM of the pair.

__

The ratio 8/24 is reduced by observing that 24 = 8·3:

  8/24 = 8/(8·3) = (8/8)·(1/3)

  8/24 = 1/3

Answer:

see below

Step-by-step explanation:

7g can be "split" as 7 * g. The "*" means multiplication so a verbal form of this expression could be "7 times a number g" or "The product of 7 and a number g".

Answer:

[tex]\mathbf{P(x>6) = 0.0265}[/tex]

Step-by-step explanation:

Given that:

A baseball player has a batting average (probability of getting on base per time at bat) of 0.215

i.e

let x to be the random variable,

consider [tex]x_1 = \left \{ {{1} \atop {0}} \right.[/tex]  to be if the baseball player has a batting average or otherwise.

Then

p(x₁ = 1) = 0.125

What is the probability that they will get on base more than 6 of the next 15 at bats

So

[tex]\mathtt{x_i \sim Binomial (n,p)}[/tex]

where; n =  15 and p = 0.125

P(x>6) = P(x ≥ 7)

[tex]P(x>6) = \sum \limits ^{15}_{x=7} ( ^{15 }_x ) \ (0.215)^x \ (1 - 0.215)^{15-x}[/tex]

[tex]P(x>6) = 1 - \sum \limits ^{6}_{x=7} ( ^{15 }_x ) \ (0.215)^x \ (1 - 0.215)^{15-x}[/tex]

[tex]P(x>6) = 1 - \sum \limits ^{6}_{x=0} ( ^{15 }_x ) \ (0.215)^x \ (1 - 0.215)^{15-x}[/tex]

[tex]P(x>6) = 1 -0.9735[/tex]

[tex]\mathbf{P(x>6) = 0.0265}[/tex]

a ) Now as you can see, the white region is composed of a triangle and a rectangle. This triangle has a height of 5, as it is composed of the respective blank triangles. It's base is 5 meters as well, by properties of a rectangle - which is sufficient information to solve for the area of the triangle.

Area of Triangle : 1 / 2 [tex]*[/tex] 4 [tex]*[/tex] 5 = 2 [tex]*[/tex] 5 = 10 m²

The area of this rectangle will be 3 [tex]*[/tex] 4 = 12 m², considering it's given dimensions are 3 by 4. Therefore the area of this white region will be 10 + 12 = 22 m²

b ) Now this striped region will be the remaining area, or the area of the white region subtracted from the area of the outer rectangle.

Area of Outer Rectangle : 10 [tex]*[/tex] 4 = 40 m²,

Area of Striped Region : 40 - 22 = 18 m²

Answer:

= 18.2 miles per hour

Step-by-step explanation:

Speed = distance / time

            =82 miles / 4.5 hours

             =18.22222222 miles per hour

             Rounding

             = 18.2 miles per hour

Answer:

Given that

Distance = rate × time

82 = r × 4½

r = 18.2 mph

Answer:

t = 32,5 minutes

Step-by-step explanation:

Volume to fill =  13000000 Gal

5 pumps delivering  80000 gal/min

5 * 80000 = 400000 gal/min

If we divide the total volume by the amount of water delivered for the 5 pumps, we get the required time to fill the volume, then

t =  13000000/ 400000

t = 32,5 minutes

Answer:

-12

Step-by-step explanation:

-7+(-5)=

-7-5=

-12

Answer:

1,377/2 and 688 1/17

Step-by-step explanation:

Answer:

a) 6.00

b) 3.00

c) 1.50

Step-by-step explanation:

Sample error of the mean is expressed mathematically using the formula;

SE = σ /√n where;

σ  is the standard deviation and n is the sample size.

a) Given σ = 18, n = 9

Standard error of the mean = σ /√n

Standard error of the mean = 18/√9

Standard error of the mean = 18/3

Standard error of the mean = 6.00

b) Given σ = 18, n = 36

Standard error of the mean = σ /√n

Standard error of the mean = 18/√36

Standard error of the mean = 18/6

Standard error of the mean = 3.00

c) Given σ = 18, n = 144

Standard error of the mean = σ /√n

Standard error of the mean = 18/√144

Standard error of the mean = 18/12

Standard error of the mean = 3/2

Standard error of the mean = 1.50

Answer:

  the product of a number and 33

Step-by-step explanation:

The operation "times" is what is used to form the product of two operands.

  "t times 33" is "the product of t and 33"

Answer:

-20x / (x-12) = y

Step-by-step explanation:

3/x  - 5/y  = 1/4

Multiply each side by 4xy to clear the fractions

4xy ( 3/x  - 5/y  = 1/4)

Distribute

12y - 20x = xy

Subtract 12y from each side

-20x = xy -12y

Factor out y

-20x = y(x-12)

Divide each side by (x-12)

-20x / (x-12) = y

Answer:

25  Answer A

Step-by-step explanation:

Use similar triangles, and the proportion derived from the quotient of a leg to the hypotenuse:

[tex]\frac{15}{9} =\frac{x}{15} \\x=\frac{15^2}{9} \\x=25[/tex]

Answer:

Well a rhombus is considered a quadrilateral because it has 4 sides and 4 angles.

Just like a square and rectangle they both are quadrilaterals with 4 angles and sides.

A rhombus is considered a type of quadrilateral because it has four sides and four angles

As a general rule, a shape that is considered a quadrilateral must have:

Since a rhombus has four sides and four angles, then it is considered a type of quadrilateral

Read more about rhombus at:https://brainly.com/question/20627264

#SPJ6

Answer:

A.

Step-by-step explanation:

So we are given the function:

[tex]f(x)=7x+8[/tex]

To find the inverse of the function, we simply need to flip f(x) and x and then solve for f(x). Thus:

[tex]x=7f^{-1}(x)+8\\x-8=7f^{-1}(x)\\f^{-1}(x)=\frac{x-8}{7}[/tex]

So the answer is A.

Answer:

[tex]\large \boxed{\mathrm{Option \ A}}[/tex]

Step-by-step explanation:

f(x) = 7x+8

Write f(x) as y.

y = 7x + 8

Switch variables.

x = 7y + 8

Solve for y to find the inverse.

x - 8 = 7y

[tex]\frac{x-8}{7}[/tex] = y

Given that a random variable X is normally distributed with a mean of 2 and a variance of 4, find the value of x such that P(X < x)=0.99   using the cumulative standard normal distribution table

Answer:

6.642

Step-by-step explanation:

Given that mean = 2

standard deviation = 2

Let X be the random Variable

Then X [tex]\sim[/tex] N(n,[tex]\sigma[/tex])

X [tex]\sim[/tex] N(2,2)

By Central limit theorem;

[tex]z = \dfrac{X - \mu}{\sigma} \sim N(0,1)[/tex]

[tex]z = \dfrac{X - 2}{2} \sim N(0,1)[/tex]

P(X<x) = 0.09

[tex]P(Z < \dfrac{X-\mu}{\sigma })= 0.99[/tex]

[tex]P(Z < \dfrac{X-2}{2})= 0.99[/tex]

P(X < x) = 0.99

[tex]P(\dfrac{X-2}{2}< \dfrac{X-2}{2})=0.99[/tex]

[tex]P(Z< \dfrac{X-2}{2})=0.99[/tex]

[tex]\phi ( \dfrac{X-2}{2})=0.99[/tex]

[tex]( \dfrac{X-2}{2})= \phi^{-1} (0.99)[/tex]

[tex]( \dfrac{X-2}{2})= 2.321[/tex]

X -2 = 2.321 × 2

X -2 = 4.642

X = 4.642 +2

X = 6.642

Answer:

The Width = 65.44 inches

The Height = 36.81 inches

Step-by-step explanation:

We are told in the question that:

The width and height of an newer 75-inch television whose screen has an aspect ratio of 16:9

Using Pythagoras Theorem we known that:

Width² + Height² = Diagonal²

Since we known that the size of a television is the length of the diagonal of its screen in inches.

Hence, for this new TV

Width² + Height² = 75²

We are given ratio: 16:9 as aspect ratio

Width = 16x

Height = 9x

(16x)² +(9x)² = 75²

= 256x² + 81x² = 75²

337x² = 5625

x² = 5625/337

x² = 16.691394659

x = √16.691394659

x = 4.0855103303

Approximately x = 4.09

For the newer 75 inch tv set

The Height = 9x

= 9 × 4.09

= 36.81 inches

The Width = 16x

= 16 × 4.09

= 65.44 inches.

Answer:

Ok so to help you out, first, off you need to be sure that the sets domain and range use the proper variable. After that, you are going to want to just plug it into the equation. I am going to link a screenshot to the correct answer if you are still have trouble finding it.

Anyways hoped this helped and I got to this question in time c:

Answer:

x <-3

Step-by-step explanation:

15 <-5x

divide both sides by 5 but since the coefficient of x is negative after dividing the sign changes.

x <-3

Answer:

x < −3

I hope this helps!

Answer:

I know the answer

Step-by-step explanation:

Linear functions are those whose graph is a straight line. A linear function has the following form. y = f(x) = a + bx. A linear function has one independent variable and one dependent variable. The independent variable is x and the dependent variable is y.

Answer:

1.86

Step-by-step explanation:

Given the following :

X : - - - - 0 - - - - 1 - - - - 2 - - - - - 3 - - - - 4

P(x) - 0.37 - - 0.28 - - 0.22 - - 0.22 - - 0.12

The mean of the distribution can be calculated by evaluated by determining the expected value of the distribution given that the data above is a discrete random variable. The mean value can be deduced multiplying each possible outcome by the probability of it's occurrence.

Summation of [P(x) * X] :

(0.37 * 0) + (0.28 * 1) + (0.22 * 2) + (0.22 * 3) + (0.12 * 4)

= 0 + 0.28 + 0.44 + 0.66 + 0.48

= 1.86

Answer:

I canot answer this

Step-by-step explanation:

Answer:

The 99%  confidence interval is  [tex]97.94 < \mu < 98.26[/tex]

Step-by-step explanation:

From the question we are told that

    The sample size is  n =  110

     The  sample mean is  [tex]\= x = 98.1 \ F[/tex]

       The standard deviation is  [tex]\sigma = 0.64 \ F[/tex]

Given that the confidence level is  99% the level of significance i mathematically evaluated as

                  [tex]\alpha = 100 - 99[/tex]

                  [tex]\alpha = 1\%[/tex]

                  [tex]\alpha = 0.01[/tex]

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

          [tex]Z_{\frac{\alpha }{2} } = Z_{\frac{0.01 }{2} } = 2.58[/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 = 2.58 * \frac{ 0.64}{\sqrt{110} }[/tex]

          [tex]E = 0.1574[/tex]

Generally the  99% confidence interval  is mathematically represented as

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

substituting values

             [tex]98.1 - 0.1574 < \mu < 98.1 + 0.1574[/tex]

             [tex]97.94 < \mu < 98.26[/tex]

Answer:

Step-by-step explanation:

Answer:

[tex]L + \frac{5}{8} = 1[/tex]

Step-by-step explanation:

Given

A cup of coffee

Kelly drank 5/8 of the coffee

Required

Determine how much is left

Start by representing the amount of coffee left with L

Because the amount of coffee Kelly drank is in fraction (5/8), the total cup of coffee will equate to 1;

Hence, the addition equation as requested in the question to represent the scenario is

[tex]L + \frac{5}{8} = 1[/tex]

Step-by-step explanation:

n mathematics, an arithmetic progression (AP) or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant. ... For instance, the sequence 5, 7, 9, 11, 13, 15, . . . is an arithmetic progression with common difference of 2.

Answer: -10

Step-by-step explanation: All you have to do is plug the values into the equation. -4+2(-3). Then you solve the equation using PEDMAS.

1. -4+2(-3)

2. -4+(-6)

3.-4-6

4.-10

Answer:

8

Step-by-step explanation:

-b + 2y

if

b = 4

and

y = 3

then:

-b + 2y = -4 + 2*6 = -4 + 12

= 8

Responder:

Juanita = 11, madre = 33

Explicación paso a paso:

Dado lo siguiente:

Suma de sus edades = 44

En 11 años, Juanita tendrá la mitad de la edad de su madre

Sea la edad de la madre = my la edad de juanita = j

m + j = 44 - - - - (1)

(j + 11) = 1/2 (m + 11)

j + 11 = 1/2 m + 5,5; j - 1/2 m = - 5,5; 2j - m = - 11

2j - m = - 11 - - - - (2)

Desde (1): m = 44 - j

Sustituyendo m = 44- j en (2)

2j - (44 - j) = - 11

2j - 44 + j = - 11

3j = - 11 + 44

3j = 33

j = 11

De 1)

m + j = 44

m + 11 = 44

m = 44 - 11

m = 33

Answer:

the work done by the force field = 24 π

Step-by-step explanation:

From the information given:

r(t) = 3 cos (t)i + 3 sin (t) j + 2 tk

= xi + yj + zk

∴

x = 3 cos (t)

y =  3 sin (t)

z = 2t

dr = (-3 sin (t)i + 3 cos (t) j + 2 k ) dt

Also F(x,y,z) = 6xi + 6yj + 6k

∴  F(t) = 18 cos (t) i + 18 sin (t) j +6 k

Workdone = 0 to 2π ∫ F(t) dr

[tex]\mathbf{= \int \limits ^{2 \pi} _{0} (18 cos (t) i + 18 sin (t) j +6k)(-3 sin (t)i+3cos (t) j +2k)\ dt}[/tex]

[tex]\mathbf{= \int \limits ^{2 \pi} _{0} (-54 \ cos (t).sin(t) + 54 \ sin (t).cos (t) + 12 ) \ dt}[/tex]

[tex]\mathbf{= \int \limits ^{2 \pi} _{0} 12 \ dt}[/tex]

[tex]\mathbf{= 12 \times 2 \pi}[/tex]

= 24 π