On circle C, points A and B are separated by an arc whose length is 18 centimeters. If the radius of circle Ciss
centimeters, what is the measure of central angle, e, to the nearest degree?

Answer:

3 road bikes and 2 tandems

7 people

Step-by-step explanation:

25b + 40t = 155

b=3   and t = 2

Check

25*3  + 40*2 = 155

75+80 = 155

Assuming 1 person per road bike and 2 people per tandem

3*1 + 2*2 = 3+4 = 7

Lisa should start swimming at an angle of [tex]120^{\circ}[/tex] to reach her destination as quickly as possible.

Given:

To find: The course (in degrees) at which she should start swimming so that she can reach the end point as quickly as possible

To solve this problem, we need to know the following:

Let us assume that Lisa starts swimming at a course such that she needs to swim for 'x' miles to reach the opposite shore, as shown in the figure.

Labelling the points in the figure, we can say that,

AB = 1 mile (given)

BD = 1 mile (given)

AC = x miles (by our assumption)

It is clear that ABC forms a right angled triangle where,

Perpendicular: BC

Base: AB

Hypotenuse: AC

Using Pythagoras Theorem for triangle ABC, we have,

[tex](Hypotenuse)^{2} =(Perpendicular)^{2} +(Base)^{2}[/tex], which implies,

[tex](AC)^{2} =(BC)^{2} +(AB)^{2}[/tex]

Put AC = x, AB = 1 in the above equation to get,

[tex]x^{2} =(BC)^{2} +1^{2}[/tex]

[tex]x^{2} =(BC)^{2} +1[/tex]

[tex](BC)^{2}=x^{2} -1[/tex]

[tex]BC=\sqrt{x^{2} -1}[/tex]

From the figure, we can say that,

[tex]CD=BD-BC[/tex]

Put [tex]BC=\sqrt{x^{2} -1}[/tex] and [tex]BD=1[/tex] in the above equation to get,

[tex]CD=1-\sqrt{x^{2} -1}[/tex]

According to our assumption, Lisa swims the distance of AC and walks the distance of CD, that is, she swims a distance of [tex]x[/tex] miles and walks a distance of [tex]1-\sqrt{x^{2} -1}[/tex] miles.

Now, let us assume that Lisa's speed of swimming is [tex]k[/tex] miles/hour. It is given that Lisa's speed of walking is twice that of her speed of swimming. Then, accordingly, Lisa's speed of walking must be [tex]2k[/tex] miles/hour. We note that these speeds are constants for Lisa.

We know that,

[tex]Speed=\frac{Distance}{Time}[/tex]

Then,

[tex]Time=\frac{Distance}{Speed}[/tex]

This implies that,

Time spent by Lisa on swimming = [tex]\frac{x}{k}[/tex]

Similarly, time spent by Lisa on walking = [tex]\frac{1-\sqrt{x^{2} -1} }{2k}[/tex]

Then, total time taken by Lisa to travel the whole distance from the starting point to the end point is,

[tex]\frac{1-\sqrt{x^{2} -1} }{2k} +\frac{x}{k}[/tex]

[tex]\frac{1}{2k}( 1-\sqrt{x^{2} -1} +2x )[/tex]

Since Lisa wishes to get to the end point as quickly as possible, we must minimize the total time taken by her to travel the entire distance.

Total time taken: [tex]T=\frac{1}{2k}( 1-\sqrt{x^{2} -1} +2x )[/tex]

Differentiating with respect to 'x', we have,

[tex]T'=\frac{1}{2k}( -\frac{x}{\sqrt{x^{2} -1}} +2 )[/tex]

Differentiating with respect to 'x' again, we have,

[tex]T''=\frac{1}{2k(\sqrt{x^{2} -1})^{3}}[/tex]

Equating the first derivative to 0, we have,

[tex]\frac{1}{2k}( -\frac{x}{\sqrt{x^{2} -1}} +2 )=0[/tex]

[tex]-\frac{x}{\sqrt{x^{2} -1}} +2 =0[/tex]

[tex]\frac{x}{\sqrt{x^{2} -1}} =2[/tex]

[tex]2\sqrt{x^{2} -1}= x[/tex]

Squaring both sides,

[tex]4(x^{2} -1)= x^{2}[/tex]

[tex]4x^{2} -4= x^{2}[/tex]

[tex]3x^{2} =4[/tex]

[tex]x^{2} =\frac{4}{3}[/tex]

[tex]x=\frac{2}{\sqrt{3}}[/tex]

Note that we assumed the positive square root for 'x' because 'x' denotes a distance which cannot be negative.

Put [tex]x=\frac{2}{\sqrt{3}}[/tex] in the expression for second derivative to get,

[tex]T''=\frac{1}{2k(\sqrt{(\frac{2}{\sqrt{3}} )^{2} -1})^{3}}[/tex]

[tex]T''=\frac{1}{2k(\sqrt{\frac{4}{3} -1})^{3}}[/tex]

[tex]T''=\frac{1}{2k(\sqrt{\frac{1}{3}})^{3}}>0[/tex]

The last expression is positive because 'k' denotes a speed which is always positive.

This implies that the obtained value [tex]x=\frac{2}{\sqrt{3}}[/tex] minimizes the quantity of total time taken.

Now, from the figure, we can say that,

[tex]cos(\angle BAC)=\frac{AB}{AC}[/tex]

Put AC = x, AB = 1 in the above equation to get,

[tex]cos(\angle BAC)=\frac{1}{x}[/tex]

Put the obtained minimizing value, [tex]x=\frac{2}{\sqrt{3}}[/tex] in the above equation to get,

[tex]cos(\angle BAC)=\frac{1}{\frac{2}{\sqrt{3}} }[/tex]

[tex]cos(\angle BAC)=\frac{\sqrt{3}}{2 }[/tex]

[tex]cos(\angle BAC)=cos(30^{\circ})[/tex]

Then,

[tex]\angle BAC=30^{\circ}[/tex]

Since the angle is measured from the north, the required angle is, [tex]90^{\circ}+30^{\circ}=120^{\circ}[/tex]

Thus, Lisa should start swimming at an angle of [tex]120^{\circ}[/tex] to reach her destination as quickly as possible.

Learn more about finding optimum course here:

https://brainly.com/question/17587668

Answer:

b. 8/9

Step-by-step explanation:

step by step explanation

Answer:

A

Step-by-step explanation:

Because if you were to out each fraction into a calculator you see that b,c, and d have a never ending decimal. The only fraction that does end in option A, therefore ur answer is option a

Answer:

y>17

Step-by-step explanation:

[tex]x + y = 30 \\ 13 + y = 30 \\ y = 17 \\ for \: x < 13 \\ y > 17[/tex]

Answer:

y>17

Step-by-step explanation:

x+y=30

x<13

What + 13 is 30?

17. So if x+y=30. Because x will be less than 13, y must make up the differnce by being greater than 17.

Ex: x=12

y+12=30

y=18

18 is greater than 17.

This is a great way to check because if your not sure, it elimates the other options!

Hope this helps!

Answer:

[tex]x=11[/tex]

Step-by-step explanation:

Note that ∠DCB is the sum of ∠HCB and ∠DCH. Hence:

[tex]m\angle DCB = m\angle HCB + m\angle DCH[/tex]

Substitute in the appropriate values/expressions:

[tex](9x-1) = (60) + (2x+16)[/tex]

Solve for x. Combine like terms:

[tex]9x - 1 = 2x + 76[/tex]

Subtract 2x from both sides:

[tex]7x - 1 = 76[/tex]

Add one to both sides:

[tex]7x = 77[/tex]

And divide. Hence:

[tex]x=11[/tex]

Answer:

x=11

Step-by-step explanation:

<DCB = <DCH + < HCB

9x-1 = 2x+16 + 60

Combine like terms

9x-1 = 2x+76

Subtract 2x from each side

9x-1-2x= 2x+76-2x

7x-1 = 76

Add 1 to each side

7x-1 +1 = 76+1

7x = 77

Divide by 7

7x/7 = 77/7

x=11

Answer:

The surface area of the cube is 648.96 sq in.

Step-by-step explanation:

This problem is made a lot easier by the fact that it's a cube.

So we first calculate the area of one of the faces. The length of the side of the side is 10.4 inches, and 10.4 * 10.4 = 100.16.

There are six faces, so we multiply the area of 1 face by 6. 100.16 * 6 = 648.96.

Therefore, the surface area of the cube is 648.96 sq inches.

Hope This Helps!

Answer:

F. 1/2

Step-by-step explanation:

If the ratio of team assistants to players are 1/6 and there are 36 players that means that there are 6 team assistants. If we do the ratio of coaches to assistant that would be 3/6 or F. 1/2

Answer:

x = 45

Step-by-step explanation:

1/3x = 15          (Given)

3(1/3x) = 15(3)  (Multiply 3 on both sides)

x = 45              (Simplify)

Answer:

45

Step-by-step explanation:

1/3x = 15

Multiplying 3 on both sides,

3(1/3x) = 15(3)

x = 15 x 3

x = 45

Answer:

option d. is the correct answer

Answer:

6 is correct....

actually this problem is quite si,p;e to see that it is correct

notice that the length of the triangle is 4 and the height is 3

thus a rectangle 4*3 area is twelve ...

if you make a copy of the triangle and flip it you will see it makes

a 4x3 rectangle ... the original and copy = 12 thus 1/2 of the 12 is the area of the original triangle

Step-by-step explanation:

Answer:

0.000000008 written as scientific notation is 8 × 10-9.

Answer:

8x10^-9

0.0000000080 is -9 integers from 0

Answer:

Hello,

F=(14,-8)

directrice: x=16

Step-by-step explanation:

Making reduce form:

[tex]y^2+16y+4x+4=0\\y^2+2*8y+64-64+4x+4=0\\\\(y+8)^2-60+4x=0\\\\x=-\dfrac{(x+8)^2}{4} +15\\[/tex]

Since i prefere working with y=...: exchanging x and y

[tex]y=-\dfrac{(x+8)^2}{4} +15\\\\Comparing\ to\ y=\dfrac{(x-a)^2}{2(b-k)} +\dfrac{b+k}{2} \\\\a=-8 :\ S=(-8,15)\\\\\\b-k=-2\ and\ b+k=30 \ \longrightarrow\ b=14\ and\ k=16\\\\Exchanging\ x\ and\ y:\\\\Focus=(14,-8)\\\\x=16[/tex]

Answer:

Is 11

Step-by-step explanation:

x+(-y)+z —> -5 +(+7)+9 = -5+7+9 = 11

Perhaps you know that

[tex]S_2 = \displaystyle\sum_{k=1}^n k^2 = \frac{n(n+1)(2n+1)}6[/tex]

and

[tex]S_3 = \displaystyle\sum_{k=1}^n k^3 = \frac{n^2(n+1)^2}4[/tex]

Then the problem is trivial, since

[tex]\displaystyle\sum_{k=1}^n k^2(k+1) = S_2 + S_3 \\\\ = \frac{2n(n+1)(2n+1)+3n^2(n+1)^2}{12} \\\\ = \frac{n(n+1)\big((2(2n+1)+3n(n+1)\big)}{12} \\\\ = \frac{n(n+1)\big(4n+2+3n^2+3n\big)}{12} \\\\ = \frac{n(n+1)(3n^2+7n+2)}{12} \\\\ = \frac{n(n+1)(3n+1)(n+2)}{12}[/tex]

Then

[tex]12\bigg(1^2\cdot2+2^2\cdot3+3^2\cdot4+\cdots+n^2(n+1)\bigg) = n(n+1)(n+2)(3n+1)[/tex]

so that a = 3 and b = 1.

Answer:

$(8+14)

Step-by-step explanation:

Amount of money Warren has at first=$8+$14=$22

Answer: 77 suits

Step-by-step explanation:

Let sales of this month = x

Sales for last 4 months = 92, 28, 83, 75

Average = Sum of Observation ÷ No of Observation

Now, we can form an equation

(92+28 +83+75+x) ÷ 5 =71

(92+28 +83+75+x) = 71 × 5

278 + x = 355

x = 355 - 278

x = 77

The candy store owner should use 37.5 pounds of the candy costing $1.25 a pound.

Given:

To find: The amount of candy costing $1.25 a pound that should be mixed

Let us assume that the resulting mixture should be made by mixing 'x' pounds of candy costing $1.25 a pound.

Since the total weight of the resulting mixture should be 50 pounds, 'x' pounds of candy costing $1.25 a pound should be mixed with '[tex]50-x[/tex]' pounds of candy costing $1.45 a pound.

Then, the resulting mixture contains 'x' pounds of candy costing $1.25 a pound and '[tex]50-x[/tex]' pounds of candy costing $1.45 a pound.

Accordingly, the total cost of the resulting mixture is [tex]1.25x+1.45(50-x)[/tex]

However, the resulting mixture should be 50 pounds and should cost $1.30 a pound. Accordingly, the total cost of the resulting mixture is [tex]1.30 \times 50[/tex]

Equating the total cost of the resulting mixture obtained in two ways, we get,

[tex]1.25x+1.45(50-x)=1.30 \times 50[/tex]

[tex]1.25x+72.5-1.45x=65[/tex]

[tex]0.2x=7.5[/tex]

[tex]x=\frac{7.5}{0.2}[/tex]

[tex]x=37.5[/tex]

This implies that the resulting mixture should be made by mixing 37.5 pounds of candy costing $1.25 a pound.

Learn more about cost of mixtures here:

https://brainly.com/question/17109505

                      [tex]\to \bold{ 1.25x+1.45(50-x)= 1.30 \times 50}\\\\ \to \bold{ 1.25x+72.5-1.45x= 65}\\\\ \to \bold{ -0.2x= -7.5}\\\\ \to \bold{ x=\frac{7.5}{0.2}}\\\\ \to \bold{ x=37.5}\\\\[/tex]

Learn more:

brainly.com/question/8991725

Answer:

X = 5

Answer:

C

Step-by-step explanation:

The sum of distances from any point on the ellipse to each foci equals a certain amount, no matter what point on the ellipse it starts from. The foci are on the major radius of the ellipse (the longer length of horizontal/vertical). The foci are of equal distance from the center, with one on each side.

If you wanted to find where the foci are using the major and minor radius, we can find that, representing the distance between the center and any foci as g,

g² = major radius² - minor radius². Then, the distance between the center and the foci is equal to g

Answer:

912 lil fishies

Step-by-step explanation:

since its 3% per year, and 8 years, that's 24%. 1200 x 24% is 288, and 1200-288 is 912 lil fishies :)

hope this helps!!

brainliest is very appreciated!

Answer: b = 1

Step-by-step explanation:

= -32 + 10b = -22

-32 + 10 = -22

b = 1

Check: -32 + 10(1) = -22

= -22

Answer:

b=1

Step-by-step explanation:

Hello,

We would like to solve for b in the equation -32+10b=-22.

When we want to solve for a variable, we want to isolate it on one side (have it on one side by itself. No other numbers.)  

So to start, add 32 to both sides to remove it from the left side (-32+32=0).

-32+10b=-22

+32         +32

______________

10b=10

Now, there isn't anything with 10b, but we want the value of b by itself (1b), as 10b is 10 times the value of what b is.

So divide both sides by 10

b=1

Hope this helps!

Answer:

x = 3

Step-by-step explanation:

We are given the equation 4(x - 8) + 10 = -10 and are asked to find the solution, solution meaning to get x alone.

To do so, first distribute the 4 on the outside of the parenthesis to both values on the inside of the parenthesis :

4(x - 8)

(4 * x - 4 * 8)

4x - 32

4x - 32 + 10 = -10

Now combine like terms :

4x - 22 = -10

Now it's time to get x alone, first get rid of -22 by adding 22 to both sides :

4x = 12

Now get x alone by dividing both sides by 4 :

x = 3

Step-by-step explanation:

According to the typist claim, we build an hypothesis test, find the test statistic and the p-value relative to this test statistic, reaching a conclusion that:

The p-value of the test is 0.1333 > 0.05, which means that there is not enough evidence to reject the typist's claim.

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

In an interview for a secretary position at the dealer, a typist claims a tying speed of 45 words per minute.

At the null hypothesis, we test if the mean is of at least 45, that is:

[tex]H_0: \mu \geq 45[/tex]

At the alternative hypothesis, we test if the mean is of less than 45, that is:

[tex]H_1: \mu < 45[/tex]

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

The test statistic is:

We have the standard deviation for the sample, so the t-distribution is used to solve this question

[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, s is the standard deviation and n is the size of the sample.

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

45 is tested at the null hypothesis:

This means that [tex]\mu = 45[/tex]

On the basis of 70 trials, she demonstrated an average speed of 43 words per minute with a standard deviation of 15 words per minute.

This means that [tex]n = 70, X = 43, s = 15[/tex]

Value of the test statistic:

[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}[/tex]

[tex]t = \frac{43 - 45}{\frac{15}{\sqrt{70}}}[/tex]

[tex]t = -1.12[/tex]

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

P-value of the test and decision:

The p-value of the test is found using a left-tailed test(test if the mean is less than a value), with 70 - 1 = 69 degrees of freedom and t = -1.12.

Using a t-distribution calculator, the p-value is of 0.1333.

The p-value of the test is 0.1333 > 0.05, which means that there is not enough evidence to reject the typist's claim.

A similar problem can be found at https://brainly.com/question/24241851

Answer:

The above equals

(32x^2*y^5)1/2

Therefore

32^1/2*x*y^5/2

Answer:

x=10

Step-by-step explanation:

since the angles seem similar they're most likely to be the same but since its 3x and you have to find the value of x then we will do 3 x ?=30, which is 10. if you want to check there is one way, since the angle on a straight line is 180 you can do 180 - 30 =150 which will be the unknown value next to the given angle. Since the unknown angle is on the line with the 150 degree angle we can do 180 - 50 to get the unknown angle (3x) which is 30. So in conclusion x will be 10

Answer: x = 10

Step-by-step explanation:

The angles are voa which means vertically opposite angles which means they are conguerent and also equal

ATQ

⇒3x = 30

⇒x = 30/3

⇒x = 10

Therefore x = 10 degrees

please click thanks and mark brainliest if you like :)

Answer:

A = 120, P = 55

Step-by-step explanation:

Triangle

Area = (bh)/2

A = (20x12)/2

A =240/2

A = 120

Perimeter = a + b + c

to find c, use a^2 +b^2 = c^2

20^2 + 12^2 = c^2

400 + 144 = c^2

544 = c^2

c = about 23

20 + 12 + 23 = 55

Answer:

8 ducks, 12 cows

Step-by-step explanation:

Let the ducks be x in number and cows be y in number

ATQ, x+y=20 and 2x+4y=64, solving we get y=12 and x=8.

If farmer McDonald raises ducks and cows. His animals have a total of 20 heads and 64 legs. Mr. McDonald has 8 ducks and 12 cows.

An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.

It is given that, Farmer McDonald raises ducks and cows. His animals have a total of 20 heads and 64 legs.

Suppose the number of head and legs be x and y respectively.

If His animals have a total of 20 heads and 64 legs,

x+y=20

2x+4y=64,

Solving the above equations we get y=12 and x=8.

Thus, if a farmer McDonald raises ducks and cows. His animals have a total of 20 heads and 64 legs. Mr. McDonald has 8 ducks and 12 cows.

Learn more about the equation here,

https://brainly.com/question/10413253

#SPJ2

Answer:

60

Step-by-step explanation:

A circle is 360 degrees

1/6 of 360

1/6 * 360 = 60