In the diagram, the vertices of the square lie at the centers of the four partial circles. What is the area of the entire shape? Use the value pi = 3.1416

Answer:

  find the difference of points on the graph

Step-by-step explanation:

The cumulative frequency graph (CDF) represents the integral of the probability distribution function (PDF). You find the probability that X is in some interval by subtracting the value of the CDF at the low end of the interval from the CDF value at the high end of the interval.

  p(a < x < b) = cdf(b) -cdf(a)

Answer:

7 square units

Step-by-step explanation:

We can break down this complex shape into smaller shapes.

I've broken it down into a rectangle, a square, and a triangle (See attached picture)

Let's first find the area of the triangle. To do this we use the formula [tex]\frac{bh}{2}[/tex]. The base is 1 (because the top is 2, and 1 is already used on the triangle - 2-1 = 1.) and the height is 2 (because 4 is already used on the left, and 2 was used on the right so 4-2=2).

[tex]\frac{2\cdot1}{2} = \frac{2}{2} = 1[/tex].

Now let's find the area of the top square - we can just square 2 which is 4.

To find the area of the bottom rectangle, we can multiply it's two side lengths of 2 and 1 = 2.

Adding these all together gets us 4+2+1 = 7.

Hope this helped!

Answer:

I thinksomething is wrong.

I'm getting another proving it's-tan thita.

I hope this is the one you are searching for..

Answer:

A. a line segment

Step-by-step explanation:

Answer: 2361.53

Step-by-step explanation:

Use long division and round.

(The 3 is repeated)

Answer:

[tex]\Large \boxed{\sf 17 \ and \ 18}[/tex]

Step-by-step explanation:

The product means multiplication.

There are two positive consecutive integers.

Let the first positive consecutive integer be x.

Let the second positive consecutive integer be x+1.

[tex](x) \times (x+1) =306[/tex]

Solve for x.

Expand brackets.

[tex]x^2 +x =306[/tex]

Subtract 306 from both sides.

[tex]x^2 +x -306=306-306[/tex]

[tex]x^2 +x -306=0[/tex]

Factor left side of the equation.

[tex](x-17)(x+18)=0[/tex]

Set factors equal to 0.

[tex]x-17=0[/tex]

[tex]x=17[/tex]

[tex]x+18=0[/tex]

[tex]x=-18[/tex]

The value of x cannot be negative.

Substitute x=17 for the second consecutive positive integer.

[tex](17)+1[/tex]

[tex]18[/tex]

The two integers are 17 and 18.

The product of two consecutive positive integers is 306.

We need to find the integers

solution : Let two consecutive numbers are x and (x + 1)

A/C to question,

product of x and (x + 1) = 306

⇒x(x + 1) = 306

⇒x² + x - 306 = 0

⇒ x² + 18x - 17x - 306 = 0

⇒x(x + 18) - 17(x + 18) = 0

⇒(x + 18)(x - 17) = 0⇒ x = 17 and -18

so x = 17 and (x +1) = 18

Therefore the numbers are 17 and 18.

Hope it helped u if yes mark me BRAINLIEST

TYSM!

Answer: Undefined

Step-by-step explanation:

slope is undefined

no y intercept

This line is vertical

Answer:

Step-by-step explanation:

Formula for area of a triangle:

Height x Base /2

Base (b) = h +4

Height = h

h + 4 x h /2 = 30cm

=> h +4 x h = 60

=> h+4h =60

=> 5h = 60

=> h = 12

Height = 12

Base = 12 +4 = 16

Answer:

7(n + 4)

Step-by-step explanation:

Represent the number by n.  Then the verbal expression becomes

7(n + 4).

Answer:

The probability is 0.31084

Step-by-step explanation:

We can calculate this probability using the z-score route.

Mathematically;

z = (x-mean)/SD/√n

Where the mean = 16, SD = 3 and n = 36

For 15.8, we have;

z = (15.8-16)/3/√36 = -0.2/3/6 = -0.2/0.5 = -0.4

For 16.2, we have

z = (16.2-16)/3/√36 = 0.2/3/6 = 0.2/0.5 = 0.4

So the probability we want to calculate is;

P(-0.4<z<0.4)

We can get this using the standard normal distribution table;

So we have;

P(-0.4 <z<0.4) = P(z<-0.4) - P(z<0.4)

= 0.31084

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:

5(x) +3(y)<26

Step-by-step explanation:

Let x represent the number of cakes she will bake and let you know represent the nymber of quiche she will bake.

She will use less than 26 eggs while baking and 5 eggs for each cake and 3 eggs for each quiche.

The inequality representing the above statement iz given below.

5(x) +3(y)<26

Answer:

n = 9 is the answer.

Step-by-step explanation:

Given a Triangle [tex]\triangle KLM[/tex] with its perpendicular bisectors intersecting at a point A.

AK = 25 units and

AM = 3n -2

To find:

Value of n = ?

Solution:

First of all, let us learn about perpendicular bisectors and their intersection points.

Perpendicular bisector of a line PQ is the line which divides the line PQ into two equal halves and is makes an angle of [tex]\bold{90^\circ}[/tex] with the line PQ.

And in a triangle, the perpendicular bisectors of 3 sides meet at one point and that point is called Circumcenter of the triangle.

We can draw a circle from circumcenter so that the circle passes from the three vertices of the triangle.

i.e.

Circumcenter of a triangle is equidistant from all the three vertices of the triangle.

In the given statement, we are given that A is the circumcenter of the [tex]\triangle KLM[/tex].

Please refer to the attached image for the given triangle and sides.

The distance of A from all the three vertices will be same.

i.e. AK = AM

[tex]\Rightarrow 25 = 3n-2\\\Rightarrow 3n =25+2\\\Rightarrow 3n =27\\\Rightarrow \bold{n = 9}[/tex]

Therefore, n = 9 is the answer.

Answer:

Garden: 36 square feet

Path: 64 square feet

Step-by-step explanation:

Let's first find the total area. The total area will be 100 square feet since the side length is 10. Since the path is 2 feet wide and on all sides, that means that the inside square will have a side length of 6. That means that the vegetable garden is 36 square feet. The path will be 100 - (the garden), and the garden is 36 square feet, which means the outer path will be 64.

Answer:

1:3

2:4

3:6

Step-by-step explanation:

we can divide both sides by 6 and get 1:2

we can divide both sides by 3 and get 2:4

we can divide both sides by 2 and get 3:6

Answer:

12:24, 3:6, 2:4

Step-by-step explanation:

What we are looking for here is a ratio that, when you divide/multiply the same constant on both parts of the ratio, you get 6:12.

6:12 is the same thing as 1:2, so we can find ratios equivalent to 1:2 (the first value will be half the second).

Hope this helped!

Answer:

3 years

Step-by-step explanation:

A = P(1 + r)^t

A = I + P

A = 14,000 + 4,634 = 18,634

18,634 = 14,000(1 + 0.1)^t

18,634/14,000 = 1.1^t

log (18,634/14,000) = log 1.1^t

log (18,634/14,000) = t * log 1.1

t = [log (18,634/14000)]/(log 1.1)

t = 3

Answer:

Perimeter=60.18cm

Area=215.495cm^2

Step-by-step explanation:

Given:

Length of book=18.34cm

Breadth=11.75cm

Solution:

Perimeter=2(l +b)

P=2(18.34+11.75)

P=2 x 30.09

P=60.18cm

Area=l x b

A=18.34 x 11.75

A=215.495 cm^2

Thank you!

186|2

93|3

31|31

1

310|2

155|5

31|31

1

434|2

217|7

31|31

1

[tex]186=2\cdot3\cdot31\\310=2\cdot5\cdot31\\434=2\cdot7\cdot31\\\\\text{hcf}(186,310,434)=2\cdot31=62[/tex]

Answer:

1+5.3=6.3

Step-by-step explanation:

not sure what your asking for with the 2

explain what your looking for with the 2 and maybe we can help you further

(I have to do it the way I did it because the 2 in the question is confusing)

Answer:

For expression 1 + 5.32: 6.32

For expression 1 + 5.3 × 2: 11.6

Step-by-step explanation:

If the expression is 1 + 5.32:

If the expression is 1 + 5.3 × 2:

Answer:

y - 1 = -2(x - 4).

Step-by-step explanation:

First, we need to find the slope. Two sets of coordinates are (-3, 3), and (-2, 1).

(3 - 1) / (-3 - -2) = 2 / (-3 + 2) = 2 / (-1) = -2.

The line will be parallel to the given line, so the slope is the same.

Now that we have a point and the slope, we can construct an equation in point-slope form.

y1 = 1, x1 = 4, and m = -2.

y - 1 = -2(x - 4).

Hope this helps!

The slope of the line passing  parallel to the given line and passes through the point (4, 1) is y = -2x + 9

The equation of a straight line is given by:

y = mx + b

where y, x are variables, m is the slope of the line and b is the y intercept.

The slope of the line passing through the points (-3,3) and  (-2,1) is:

[tex]m=\frac{y_2-y_1}{x_2-x_1} \\\\m=\frac{1-3}{-2-(-3)} \\\\m=-2[/tex]

Since both lines are parallel, hence they  have the same slope (-2). The line passes through (4,1). The equation is:

[tex]y-y_1=m(x-x_1)\\\\y-1=-2(x-4)\\\\y=-2x+9[/tex]

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Answer:

wrong position of tan 64

Answer:

17 miles

Step-by-step explanation:

4+5+5+3=17

Answer:

b. 1

Step-by-step explanation:

All first coordinates are 1/2.

Answer: b. 1

Answer:

22.57 x 28

Step-by-step explanation:

10.86 + 4x = 101.14

-10.86           -10.86

            4x = 90.28

             /4       /4

              x = 22.57

5.43 + 22.57 = 28

22.57

Answer:

[tex]|R_n (x)| \leq \dfrac{|x - \dfrac{\pi}{2}|^{n+1}}{(n+1)!}[/tex]

Step-by-step explanation:

From the given question; the objective is to show that :

[tex]\lim_{n \to \infty} R_n (x) = 0[/tex] for all x in the interval of convergence f(x)=cos x, a= π/2

Assuming for the convergence f the taylor's series , f happens to be the derivative on an open interval I with a . Then the Taylor series for the convergence of f , for all x in I , if and only if  [tex]\lim_{n \to \infty} R_n (x) = 0[/tex]  

where;

[tex]\mathtt{R_n (x) = \dfrac{f^{(n+1)} (c)}{n+1!}(x-a)^{n+1}}[/tex]

is a remainder at x and c happens to be between x and a.

Given that:

a= π/2

Then; the above equation can be written as:

[tex]\mathtt{R_n (x) = \dfrac{f^{(n+1)} (c)}{n+1!}(x-\dfrac{\pi}{2})^{n+1}}[/tex]

so c now happens to be the points between π/2 and x

If we recall; we know that:

[tex]f^{(n+1)}(c) = \pm \ sin \ c \ or \ cos \ c[/tex] (as a result of the value of n)

However, it is true that for all cases that  [tex]|f ^{(n+1)} \ (c) | \leq 1[/tex]

Hence, the remainder terms is :

[tex]|R_n (x)| = | \dfrac{f^{(n+1)}(c)}{(n+1!)}(x-\dfrac{\pi}{2})^{n+1}| \leq \dfrac{|x - \dfrac{\pi}{2}|^{n+1}}{(n+1)!}[/tex]

If [tex]\lim_{n \to \infty} R_n (x) = 0[/tex]   for all x and x is fixed, Then

[tex]|R_n (x)| \leq \dfrac{|x - \dfrac{\pi}{2}|^{n+1}}{(n+1)!}[/tex]

Answer:

500,000

Step-by-step explanation:

(2.1 * 10^8)/(4.2 * 10^2) =

= 2.1/4.2 * 10^8/10^2

= 0.5 * 10^6

= 500,000

The division of 2.1 × 10⁸ and 4.2 × 10² thus the exponent 2.1 × 10⁸ is 500000 times the exponent 4.2 × 10².

The number system is a way to represent or express numbers.

Since the decimal number system employs ten digits from 0 to 9, it has a base of 10.

Any of the multiple sets of symbols and the guidelines for utilizing them to represent numbers are included in the Number System.

As per the given exponents 2.1 × 10⁸

Let's assume 2.1 × 10⁸ is x times 4.2 × 10².

2.1 × 10⁸ = x (4.2 × 10²)

x = 2.1 × 10⁸/4.2 × 10²

x = 500000

Hence "The division of 2.1 × 10⁸ and 4.2 × 10² thus the exponent 2.1 × 10⁸ is 500000 times the exponent 4.2 × 10²".

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Answer:

Attachment 1 : Option C

Attachment 2 : Option A

Step-by-step explanation:

( 1 ) Expressing the product of z1 and z2 would be as follows,

[tex]14\left[\cos \left(\frac{\pi \:}{5}\right)+i\sin \left(\frac{\pi \:\:}{5}\right)\right]\cdot \:2\sqrt{2}\left[\cos \left(\frac{3\pi \:}{2}\right)+i\sin \left(\frac{3\pi \:\:}{2}\right)\right][/tex]

Now to solve such problems, you will need to know what cos(π / 5) is, sin(π / 5) etc. If you don't know their exact value, I would recommend you use a calculator,

cos(π / 5) = [tex]\frac{\sqrt{5}+1}{4}[/tex],

sin(π / 5) = [tex]\frac{\sqrt{2}\sqrt{5-\sqrt{5}}}{4}[/tex]

cos(3π / 2) = 0,

sin(3π / 2) = - 1

Let's substitute those values in our expression,

[tex]14\left[\frac{\sqrt{5}+1}{4}+i\frac{\sqrt{2}\sqrt{5-\sqrt{5}}}{4}\right]\cdot \:2\sqrt{2}\left[0-i\right][/tex]

And now simplify the expression,

[tex]14\sqrt{5-\sqrt{5}}+i\left(-7\sqrt{10}-7\sqrt{2}\right)[/tex]

The exact value of [tex]14\sqrt{5-\sqrt{5}}[/tex] = [tex]23.27510\dots[/tex] and [tex](-7\sqrt{10}-7\sqrt{2}\right))[/tex] = [tex]-32.03543\dots[/tex] Therefore we have the expression [tex]23.27510 - 32.03543i[/tex], which is close to option c. As you can see they approximated the solution.

( 2 ) Here we will apply the following trivial identities,

cos(π / 3) = [tex]\frac{1}{2}[/tex],

sin(π / 3) = [tex]\frac{\sqrt{3}}{2}[/tex],

cos(- π / 6) = [tex]\frac{\sqrt{3}}{2}[/tex],

sin(- π / 6) = [tex]-\frac{1}{2}[/tex]

Substitute into the following expression, representing the quotient of the given values of z1 and z2,

[tex]15\left[cos\left(\frac{\pi \:}{3}\right)+isin\left(\frac{\pi \:\:}{3}\right)\right] \div \:3\sqrt{2}\left[cos\left(\frac{-\pi \:}{6}\right)+isin\left(\frac{-\pi \:\:}{6}\right)\right][/tex] ⇒

[tex]15\left[\frac{1}{2}+\frac{\sqrt{3}}{2}\right]\div \:3\sqrt{2}\left[\frac{\sqrt{3}}{2}+-\frac{1}{2}\right][/tex]

The simplified expression will be the following,

[tex]i\frac{5\sqrt{2}}{2}[/tex] or in other words [tex]\frac{5\sqrt{2}}{2}i[/tex] or [tex]\frac{5i\sqrt{2}}{2}[/tex]

The solution will be option a, as you can see.

Answer:

5

Step-by-step explanation:

a^2 + b^2 = c^2

4^2 + 3^2 = c^2

16 + 9 = c^2

25 = c^2

c = 5

Answer:

Step-by-step explanation:

[tex]Hypotenuse = ?\\Opposite = 4\\Adjacent = 3\\\\Pythagoras \: Theorem ;\\\\Hypotenuse^2 =Opposite^2+Adjacent ^2\\\\Hypotenuse^2 = 4^2 +3^2\\\\Hypotenuse^2 = 16+9\\\\Hypotenuse^2 = 25\\\\\sqrt{Hypotenuse^2}=\sqrt{25} \\Hypotenuse = 5[/tex]

Answer:  [tex]\dfrac{(x+9)^2}{225}-\dfrac{(y+7)^2}{49}=1[/tex]

Step-by-step explanation:

The equation for a horizontal ellipse is: [tex]\dfrac{(x-h)^2}{a^2}-\dfrac{(y-k)^2}{b^2}=1[/tex]  where

Given: major axis (diameter on x) is 30 --> x-radius (a) = 15  -->  a² = 225

           minor axis (diameter on y) is 14 --> y-radius (b) = 7   --> b² = 49

           center (h, k) is (-9, -7)

Input those values into the equation for a horizontal ellipse and simplify:

  [tex]\dfrac{(x-(-9))^2}{15^2}-\dfrac{(y-(-7))^2}{7^2}=1\\\\\\\large\boxed{\dfrac{(x+9)^2}{225}-\dfrac{(y+7)^2}{49}=1}[/tex]  

Step-by-step explanation:

f(x) = integral (-8x) dx = -4x^2 + C

f(1) = -3 = -4 + C

C = 1

f(x) = -4x^2 + 1

The particular solution of the differential equation f'(x) = -8x that satisfies the initial condition f(1) = -3 is: f(x) = -4x² + 1.

Here, we have,

To find the particular solution of the differential equation f'(x) = -8x that satisfies the initial condition f(1) = -3,

we can integrate the equation and use the initial condition to determine the constant of integration.

First, integrate both sides of the equation with respect to x:

∫ f'(x) dx = ∫ -8x dx

Integrating, we get:

f(x) = -4x² + C

Now, we can use the initial condition f(1) = -3 to find the value of the constant C.

Substituting x = 1 and f(x) = -3 into the equation, we have:

-3 = -4(1)² + C

-3 = -4 + C

C = -3 + 4

C = 1

Therefore, the particular solution of the differential equation f'(x) = -8x that satisfies the initial condition f(1) = -3 is:

f(x) = -4x² + 1

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