What is 12+24=2(6+ )

This question is based on the point of intersection.Therefore, the points of intersection of the graphs of the equations at 0 ≤ θ < 2π are:

[tex](1-\dfrac{\sqrt{2} }{2} ,\dfrac{3\pi }{4} ) and (1+\dfrac{\sqrt{2} }{2} ,\dfrac{7\pi }{4} )[/tex]

Given:

Equations: r = 1 + cos θ                                                                      ...(1)

                  r = 1 − sin  θ                                                                      ...(2)                                                                

Where, r ≥ 0, 0 ≤ θ < 2π

We need to determined the point of intersection of the graphs of the equations.

To obtain the points of intersection, Equate the two equations above as follows;

r = 1 + cos θ = 1 - sin θ

=> 1 + cos θ = 1 - sin θ

Solve further for θ. We get,

1 + cos θ = 1 - sinθ

cos θ  = - sinθ

Now dividing both sides by - cos θ and solve it further,

[tex]\dfrac{cos\;\theta}{-cos\;\theta} =\dfrac{-sin\;\theta}{-cos\;\theta}\\\\tan\;\theta=-1\\\\\theta=tan^{-1}(1)\\\\\theta=45^{0}=\dfrac{-\pi }{4}[/tex]

To get the 2nd quadrant value of θ, add π ( = 180°) to the value of θ. i.e

[tex]\dfrac{-\pi }{4} +\pi =\dfrac{3\pi }{4} \\[/tex]

Similarly, to get the fourth quadrant value of θ, add 2π ( = 360° ) to the value of θ. i.e

[tex]\dfrac{-\pi }{4} +2\pi =\dfrac{7\pi }{4} \\[/tex]

Therefore, the values of θ are 3π / 4 and 7π / 4.

Now substitute these values into equations (i) and (ii) as follows;

[tex]When \;\theta=\dfrac{3\pi }{4},[/tex]

[tex]r = 1 + cos\;\theta = 1 + cos \dfrac{3\pi }{4} =1+\dfrac{-\sqrt{2} }{2} =1-\dfrac{\sqrt{2} }{2}[/tex]

[tex]r = 1 + sin\;\theta = 1 - sin \dfrac{3\pi }{4} =1-\dfrac{\sqrt{2} }{2} =1-\dfrac{\sqrt{2} }{2}[/tex]

[tex]When\; \theta=\dfrac{7\pi }{4}[/tex]

[tex]r = 1 + cos\;\theta = 1 + cos \dfrac{7\pi }{4} =1+\dfrac{\sqrt{2} }{2} =1+\dfrac{\sqrt{2} }{2}[/tex]

[tex]r = 1 + sin\;\theta = 1 - sin \dfrac{7\pi }{4} =1-\dfrac{-\sqrt{2} }{2} =1+\dfrac{\sqrt{2} }{2}[/tex]

Represent the results  above in polar coordinates of the form (r, θ). i.e

[tex](1-\dfrac{\sqrt{2} }{2} ,\dfrac{3\pi }{4} ) and (1+\dfrac{\sqrt{2} }{2} ,\dfrac{7\pi }{4} )[/tex]

Therefore, at the pole where r = 0, is also one of the points of intersection.  

Therefore, the points of intersection of the graphs of the equations at 0 ≤ θ < 2π are:

[tex](1-\dfrac{\sqrt{2} }{2} ,\dfrac{3\pi }{4} ) and (1+\dfrac{\sqrt{2} }{2} ,\dfrac{7\pi }{4} )[/tex]

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Answer:

17°

Step-by-step explanation:

Using trigonometrical ratios we have a triangle with opposite of A° as 7cm and adjacent A° as 24cm as drawn in the above diagram.

Using trigonometry the value to be used is Tangent due to the availability of only the opposite and adjacent sides.

tan = opp/adj

tan x(x is the angle) = 7/24

tan x = 0.2917 ~= 0.3

tan x = 0.3

x = tan^-1 0.3

x = 16.7 ~= 17°.

Answer:

4÷(6+3)

Step-by-step explanation:

6+3 is the sum of a number and 3, and you divide 4 by that.

The algebraic expression represents the statement The quotient of four and the sum of a number and three is 4÷(x + 3).

A finite combination of symbols that are well-formed in accordance with context-dependent principles is referred to as an expression or mathematical expression.

Given:

The quotient of four and the sum of a number and three,

The above statement can be written as,

4÷(x + 3)

Here, x is the number

To know more about the expression:

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Answer:

Area shaded blue = 294.5 m^2  (to the nearest tenth)

Step-by-step explanation:

Refer to the attached figure.

Consider sector patterned in orange

radius = 11.1 m

angle of sector = 360-130 = 230 degrees

area of sector  =  (angle / 360) * area of complete circle

A1 = (230/360)*pi * 11.1^2

= 78.7175 pi

= 247.298 m^2

Area of right triangle with hypotenuse, L, and one of the angles, x,  known

= (Lsin(x))*L(cos(x)/2

= L^2 sin(2x)/4

A2 = 2* (11.1^2 sin(130/2)/4)

= 11.1^2 * sin(65) / 2

= 47.192 m^2

Area shaded blue

= A1+A2

= 247.298 + 47.192

= 294.49 m^2

Step-by-step explanation:

6 x 1/7 is Less than 1 since 6 x 1/7 is equal to 6/7 in decimal form is 0.8571429.

4 x 4/9 is greater than 1 since 4 x 4/9 is equal to 1 7/9 in decimal form is 1.777...

8 x 1/8 is equal to 1 since 8 x 1/8 is equal to 1.

7 x 1/5 is greater than 1 since 7 x 1/5 is equal to 1 2/5 in decimal form is 1.4

3 x 1/2 is greater than 1 since 3 x 12 is equal to 1 1/2 in decimal form is 1.5

1 x 3/4 is is less than 1 since 1 x 3/4 is equal to 3/4 in decimal form is 0.75

Answer:

4.7 =x

Step-by-step explanation:

PQS = PQR + RQS

119 = 72+ 10x

Subtract 72 from each side

119 - 72 = 72+10x -72

47 = 10x

Divide by 10

47/10 = 10x/10

4.7 =x

Answer:

12,950

Step-by-step explanation:

drama: 23%

other: 27%

comedy: 20%

23% + 27% + 20% = 70%

70% of 18,500 =

= 0.7 * 18,500

= 12,950

Answer: 11/12

Step-by-step explanation:

Addition of fractions

#1 Change to the same denominator

- LCM (Least common multiple) of 4 and 6 is 12

- 9/12+2/12

#2 Add the numerator as usual

 9/12+2/12

=(9+2)/12

=11/12

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

p=3/4+1/6

p=11/12

Answer:

Net

Step-by-step explanation:

The definition of "Net Income" is a person's income after deductions and taxes. Hence it is also sometimes know as the "Take-Home" income. i.e the amount of money that you actually take home.

Answer: Area = [tex]\int\limits^5_0 {(5x - x^2)} \, dx[/tex]

Step-by-step explanation:

Thiis is quite straightforward, so I will be gudiding you through the process.

we have that;

y1 = x² -5x

and y² = 0

Taking Limits:

y1 = x² -5x, y2 = 0

x² - 5x = 0;

so x(x - 5) = 0

this gives x = 0 and x = 5

∴ 0≤x≤5

This is to say that the graph intersets at x = 0 and x = 5 and y2  is the upper most function.

Let us take the formula:

Area = ∫b-a (upper curve - lower curve)

where a here represents 0 and b represents 5

the upper curve y2 = 0

whereas the lower curve y1 = x² - 5x

Area = ∫5-0 [ 0 - (x² - 5x) ] dx

This becomes the Area.

Area = [tex]\int\limits^5_0 {(5x - x^2)} \, dx[/tex]

cheers i hope this helped !!!

Question:

The digit 8 in which number represents a value of 8 thousandths?

Answer:

See Explanation

Step-by-step explanation:

The question requires options and the options are missing.

However, the following explanation will guide you

Start by representing 8 thousandths as a digit

[tex]\frac{8}{1000} = 0.008[/tex]

i.e.

8 thousandths implies 0.008

Next;

Replace the 0s with dashes

_ . _ _8

Note that there are two dashes after the decimal point and before 8

PS: The dashes are used to represent digits

This implies that thousandths is the 3rd digit after the decimal point

Typical examples to back up this explanation are:

17.008, 1.1489, 0.008 and so on...

Answer:   6π

Step-by-step explanation:

Area of a circle is π r².

Area of a section of a circle is π r² × the section of the circle.

[tex]A=\pi r^2\bigg(\dfrac{\theta}{360^o}\bigg)[/tex]

Given: r = 6, Ф = 60°

[tex]A=\pi (6)^2\bigg(\dfrac{60^o}{360^o}\bigg)\\\\\\.\quad =\pi (6)^2\bigg(\dfrac{1}{6}\bigg)\\\\\\.\quad =6\pi[/tex]

Answer:

[tex] p = \dfrac{I}{rt} [/tex]

Step-by-step explanation:

I = prt

Switch sides.

prt = I

We are solving for p. We want p alone on the left side. p is being multiplied by r and t, so we divide both sides by r and t.

[tex] \dfrac{prt}{rt} = \dfrac{I}{rt} [/tex]

[tex] p = \dfrac{I}{rt} [/tex]

Answer:

Step-by-step explanation:

Let the amount spent by Tim be x and the amount spent by Nikko be y

If Tim spent $55 more than 2/3 of the amount that Nikko spent for his computer, then amount spent by Tim will be x = 55+2/3 y

Since the total amount that Tim and Nikko spent for their computers was $2,870 then;

x+y = $2,870

Substituting  x = 55+2/3y into the equation above, we will have;

55+2y/3 + y = 2,870

(165 + 2y)/3 + y = 2,870

(165 + 2y+3y)/3 = 2,870

cross multiply

165 + 2y+3y =  3*2870

165+5y = 8610

5y = 8610-165

5y = 8445

y = 8445/5

y = 1689

Hence Nikko spent  a sum of $1,689.00 on his computer.

Answer:

Marneisha with 9.52 pages.

Step-by-step explanation:

Zev: 56×0.15 = 8.4

Kelly: 64×0.12 = 7.68

Marneisha: 68×0.14 - 9.52

Aleisha: 72×0.10 = 7.2

Answer:

Then angles [tex]\angle B[/tex] and   [tex]\angle C[/tex] both measure [tex]55^o[/tex]

Step-by-step explanation:

Notice that if sides AB and AC are equal, then the angles opposed to them (that is angle [tex]\angle C[/tex] and angle [tex]\angle B[/tex] respectively) have to be equal since equal sides oppose equal angles in a triangle.

So you also know that the addition of the three angles in a triangle must equal [tex]180^o[/tex], then:

[tex]\angle A + \angle B+\angle C= 180^o\\70^o+\angle B + \angle B = 180^o\\2\,\angle B = 180^o-70^o\\2 \angle B=110^o\\\angle B=55^o\\\angle C = 55^o[/tex]

Answer:

[tex] \dfrac{df^{1}(16)}{dx} = \pm \dfrac{1}{10} [/tex]

Step-by-step explanation:

[tex] f(x) = x^2 + 4x - 5 [/tex]

First we find the inverse function.

[tex] y = x^2 + 4x - 5 [/tex]

[tex] x = y^2 + 4y - 5 [/tex]

[tex] y^2 + 4y - 5 = x [/tex]

[tex] y^2 + 4y = x + 5 [/tex]

[tex] y^2 + 4y + 4 = x + 5 + 4 [/tex]

[tex] (y + 2)^2 = x + 9 [/tex]

[tex] y + 2 = \pm\sqrt{x + 9} [/tex]

[tex] y = -2 \pm\sqrt{x + 9} [/tex]

[tex]f^{-1}(x) = -2 \pm\sqrt{x + 9}[/tex]

[tex]f^{-1}(x) = -2 \pm (x + 9)^{\frac{1}{2}}[/tex]

Now we find the derivative of the inverse function.

[tex]\dfrac{df^{-1}(x)}{dx} = \pm \dfrac{1}{2}(x + 9)^{-\frac{1}{2}}[/tex]

[tex]\dfrac{df^{-1}(x)}{dx} = \pm \dfrac{1}{2\sqrt{x + 9}}[/tex]

Now we evaluate the derivative of the inverse function at x = 16.

[tex]\dfrac{df^{-1}(16)}{dx} = \pm \dfrac{1}{2\sqrt{16 + 9}}[/tex]

[tex]\dfrac{df^{-1}(16)}{dx} = \pm \dfrac{1}{2\sqrt{25}}[/tex]

[tex]\dfrac{df^{-1}(16)}{dx} = \pm \dfrac{1}{2 \times 5 }[/tex]

[tex]\dfrac{df^{-1}(16)}{dx} = \pm \dfrac{1}{10}[/tex]

Answer:

What

Step-by-step explanation:

What Do You Mean Bro

Answer:

x = 5, -3

Step-by-step explanation:

2x² - 4x - 5 = 25

add 5 to each side

2x² - 4x = 30

factor out the 2

2(x² - 2x) = 30

divide both sides by 2

x² - 2x = 15

divide b by 2, square it -- (b/2)², and add it to both sides

-2/2 = -1 → -1² = 1

x² - 2x + 1 = 15 + 1

factor the expression on the left -- this will be [x - (b/2)]²

(x - 1)² = 16

find the square root of both sides

x - 1 = ±4

add 1 to both sides

x = 4 + 1

x = -4 + 1

solve

x = 5, -3

Answer:

(x-4)*(x+5) : x =4,-5

Step-by-step explanation:

a= 1

b= 1

c= -20

x1,2 = (-1+-(1 - (4*1*-20))^0.5)/2

x1,2 = (-1+-(1+80)^0.5)/2

x1,2 = (-1+-(81^0.5))/2

x1,2 =(-1+-9)/2

x1 = 8/2 = 4 x2 = -10/2 = -5

Answer:

[tex] y = 0 [/tex]

Step-by-step explanation:

To find the given asymptote of the given function, [tex] f(x) = \frac{x^2 - 2x + 1}{x^3 + x - 7} [/tex], first, compare the degrees of the lead term of the polynomial of the numerator and that of the denominator.

The numerator has a 2nd degree polynomial (x²).

The denominator has a 3rd degree polynomial (x³).

The polynomial of the numerator has a lower degree compared to the denominator, therefore, the horizontal asymptote is y = 0.

There are four levels of measurement – nominal, ordinal, and interval/ratio – with nominal being the least precise and informative and interval/ratio variable being most precise and informative.

solve from here by understanding what i have write

Answer:

[tex]\mathbf{\dfrac{\partial f}{\partial x}= cos (-7x^2 -6x - 1)}[/tex]

[tex]\mathbf{\dfrac{\partial f}{\partial y}= cos ( -7y^2 -6y-1)}[/tex]

Step-by-step explanation:

Given that :

[tex]f(x,y) = \int ^x_y cos (-7t^2 -6t-1) dt[/tex]

Using the Leibnitz rule of differentiation,

[tex]\dfrac{d}{dt} \int ^{b(t)}_{a(t)} f(x,t) dt= f(b(t),t) *b'(t) -f(a(t),t) * a' (t) + \int^{b(t)}_{a(t)} \dfrac{\partial f}{\partial t} \ dt[/tex]

To find: fx(x,y)

[tex]\dfrac{\partial f}{\partial x}= \dfrac{\partial }{\partial x} [ \int ^x_y cos (-7t^2 -6t -1 ) \ dt][/tex]

[tex]\dfrac{\partial f}{\partial x}= \dfrac{\partial x}{\partial x} cos (-7x^2 -6x -1 ) - \dfrac{\partial y}{\partial x} * cos (-7y^2 -6y-1) + \int ^x_y [\dfrac{\partial }{\partial x} \ \{cos (-7t^2-6t-1)\}] \ dt[/tex]

[tex]\dfrac{\partial f}{\partial x}= cos (-7x^2 -6x - 1) -0+0[/tex]

[tex]\mathbf{\dfrac{\partial f}{\partial x}= cos (-7x^2 -6x - 1)}[/tex]

To find: fy(x,y)

[tex]\dfrac{\partial f}{\partial y}= \dfrac{\partial }{\partial y} [ \int ^x_y cos (-7t^2 -6t -1 ) \ dt][/tex]

[tex]\dfrac{\partial f}{\partial y}= \dfrac{\partial x}{\partial y} cos (-7x^2 -6x -1 ) - \dfrac{\partial y}{\partial y} * cos (-7y^2 -6y-1) + \int ^x_y [\dfrac{\partial }{\partial y} \ \{cos (-7t^2-6t-1)\}] \ dt[/tex]

[tex]\dfrac{\partial f}{\partial y}= 0 - cos ( -7y^2 -6y-1)+0[/tex]

[tex]\mathbf{\dfrac{\partial f}{\partial y}= cos ( -7y^2 -6y-1)}[/tex]

Answer:

100 ounces(hope it help)

Step-by-step explanation:

because there is only 100 ounces in the jar.

Answer:

[tex]4+3i[/tex]

Step-by-step explanation:

=[tex]\frac{(10+20i)}{4+2i} \\\\\frac{10+20 i}{4+2i}[/tex]x   [tex]\frac{(4-2i)}{(4-2i)}[/tex]

=[tex]\frac{(10+20i)(4-2i)}{(4^{2}-2i^{2}) } \\\frac{40-20i+80i+40}{16+4}\\ \frac{80+60i}{20}\\ 4+3i[/tex](Taking 20 common from both numerator and deniminator)

This question is incomplete, the complete question is;

Assume that two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. Which distribution is used to test the claim that women have a higher mean resting heart rate than men?

A.t

B.F

C.Normal

D. Chi-square

Answer:

A) t  test

Step-by-step explanation:

A t-test uses sample information to assess how plausible it is for the population means μ1​ and μ2​ to be equal.

The formula for a t-statistic for two population means (with two independent samples), with unknown population variances shows us how to calculate t-test with mean and standard deviation and it depends on the assumption of having an equal variance or not.

If the variances are assumed to be not equal,

he formula is:

t =  (bar X₁ - bar X₂) / √( s₁²/n₁ + s₂²/n₂ )

If the variances are assumed to be equal, the formula is:

t =  (bar X₁ - bar X₂) / √ (((n₁ - 1)s₁² + (n₂ - 1)s₂²) / (n₁ + n₂ - 2)) ( 1/n₁ + 1/n₂)

it called t-test for independent samples because the samples are not related to each other, in a way that the outcomes from one sample are unrelated from the other sample.

hence option A is correct. t test

Answer:

The error was made in step 4, [tex]\pi[/tex] should have also been cancelled making the correct answer as 9 cm.

Step-by-step explanation:

Given that:

Volume of cylinder, [tex]V = 576 \pi\ cm^3[/tex]

Radius of cylinder, r = 8 cm

To find:

The error in calculating the height of cylinder by Sandra ?

Solution:

We know that volume of a cylinder is given as:

[tex]V = B h[/tex]

Where B is the area of circular base and

h is the height of cylinder.

Area of a circle is given as, [tex]B = \pi r^2[/tex]

Let us put it in the formula of volume:

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

Step 1:

Putting the values of V and r:

[tex]576\pi = \pi 8^2 h[/tex]

So, it is correct.

Step 2:

Solving square of 8:

[tex]576\pi = \pi \times 64\times h[/tex]

So, step 2 is also correct.

Step 3:

[tex]h=\dfrac{576\pi}{64 \pi} = \dfrac{64 \pi \times 9}{64\pi}[/tex]

Step 4:

Cancelling 64 [tex]\times \pi[/tex],

h = 9 cm

So, the error was made in step 4, [tex]\pi[/tex] should have also been cancelled making the correct answer as 9 cm.

Answer:

(C) In step 4, the pi should have canceled, making the correct answer 9 cm.

The tens place has a 0 in that digit. One spot to the right is 5. Since this is 5 or larger, we round up to the nearest ten.

The 0 bumps up to 1. The 5 is replaced with 0

4205 becomes 4210

Answer:

1) What is the average score of the student surveyed?

b. 52.5

2) What is the median of the student's surveyed?

52.5

3) How many students were surveyed?

20 students

Step-by-step explanation:

1) What is the average score of the student surveyed?

Average score of the student's been surveyed means we should calculate the mean of the above scores

The formula for Mean = Sum of the number of terms/ Number of terms

Number of terms = 20

Average(Mean score) =

25 + 30 + 35 + 40 + 40 + 45 + 45 + 50 + 50 + 50 + 55 + 55 + 55 + 60 + 60 + 65 + 65 + 70 + 75 + 80/20

= 1050/20

= 52.5

2) What is the median of the student's surveyed?

25, 30, 35, 40, 40, 45, 45, 50, 50, 50, 55, 55, 55, 60, 60, 65, 65, 70, 75, 80

From the above data, we can see that 20 students were surveyed. To find the Median, we find the sum of the 10th value and the 11th value and we divide by 2

Hence,

25, 30, 35, 40, 40, 45, 45, 50, 50,) 50, 55, (55, 55, 60, 60, 65, 65, 70, 75, 80

10th value = 50

11th value = 55

Median = 50 + 55/2

= 105/2

= 52.5

3) How many students were surveyed?

Counting the results of the survey, the number of students that were surveyed = 20 students

Answer:

a) Sample size need to be greater than 30

b) The probability is approximately 0.0571

Step-by-step explanation:

a) For a normal distribution, the sample size has to be greater than 30. A sample size greater than 30 makes it to be an approximate normal distribution.

b) Given that:

μ = 11.2 minutes, σ = 4.5 minutes, n = 35

The z score determines how many standard deviations the raw score is above or below the mean. It is given by:

[tex]z=\frac{x-\mu}{\sigma} \\For\ a\ sample\ size(n)\\z=\frac{x-\mu}{\sigma/\sqrt{n} }[/tex]

For x < 10 minutes

[tex]z=\frac{x-\mu}{\sigma/\sqrt{n} }\\\\ z=\frac{10-11.2}{4.5/\sqrt{35} }= -1.58[/tex]

Therefore from the normal distribution table, P(x < 10) = P(z < -1.58) =  0.0571

The probability is approximately 0.0571