A family travels 613.4 miles in 11.4 how many miles do they drive in one hour?

Probability that [tex]x^2+y^2+z^2\leq 1[/tex] is 0.523

Given that a point (x, y, z) is in space which is randomly selected as

[tex]-1\le x \le 1$,$-1\le y \le 1$,$-1\le z \le 1$[/tex]

These three equations represents a cube in space.

Length of each side of the cube = 1 - -1 = 2

Now  [tex]x^2+y^2+z^2\leq 1[/tex]  represents a sphere with center (0, 0, 0) and of radius less than or equal to 1.

So we can imagine that this sphere is inside the cube.

So the probability that   [tex]x^2+y^2+z^2\leq 1[/tex]  = Volume of the sphere/Volume of the cube

Volume of sphere with radius 1 = [tex]\frac{4}{3} \pi r^3=\frac{4}{3} \pi \times 1 = \frac{4}{3}\times 3.14 = 4.186[/tex] cubic unit

Volume of the cube of length 2 = [tex]2^3 = 8[/tex] cubic units

So the probability that  [tex]x^2+y^2+z^2\leq 1[/tex]  = 4.186/8 = 0.523

Learn more about probability at https://brainly.com/question/25870256

#SPJ4

invalidated and no score will be calculated for you. ... Utilize the information provided for each question to determine your ... the questions or answers prior to the examination and that you have ... 2 The solution of an equation with two variables, x and y, is ... 11 Which function has the greatest y-intercept?

The value of the logarithmic expression log(10³ x) is 3 + log(x).

The opposite of exponential functions is logarithmic functions. The exponential function y = aˣ has the inverse, [tex]x=a^{y}[/tex]. The exponential equation [tex]x=a^{y}[/tex] is defined as being identical to the logarithmic function y = logₐ x.

The properties of logarithm are:

Product rule: logₐ (mn) = logₐ m + logₐ n

Quotient rule: logₐ (m/n) = logₐ m – logₐ n

Power rule: logₐ (mn) = n( logₐ m )

Consider the logarithmic expression,

a = log ( 10³ x )

Using the property of logarithm:

logₐ ( mn ) = logₐ m + logₐ n

Then,

a = log( 10³ x )

a = log( 10³ × x)

a = log( 10³ ) + log( x )

By using the property of logarithm:

logₐ mⁿ = n(  logₐ m )

So,

a = 3( log 10 ) + log( x )

a = 3 + log ( x )

Therefore, log( 10³ x ) = 3 + log ( x ).

Learn more about logarithm here:

https://brainly.com/question/13473114

#SPJ9

Answer:

Rider A=20km/hour

Rider B= 24km/hour

Step-by-step explanation:

Easy find slope rise over run

Rider A=20km/hour

Rider B= 24km/hour

to find rider b slope do 72/3 =24

Answer:

15

Step-by-step explanation:

15 seventh graders play in the jazz band as per the given ratio.

One quantity can be expressed as a fraction of other quantities using a ratio, which is a number. Only when the two numbers in a ratio have the same unit can they be compared. Ratios are used to compare two objects.

Given At Charles School, 1/5 of the 75 students in seventh-grade play in the jazz band.

In the form of a ratio

1/5 the students out of 75 play in the jazz band

Total students play in the jazz band = 75* 1/5

Total students play in the jazz band = 15

Therefore, The jazz band has 15 seventh graders playing according to the ratio.

Learn more about ratios here:

brainly.com/question/13419413

#SPJ2

9514 1404 393

Answer:

  1. B, E

  2. A, E

  16. B'(1, 5)

Step-by-step explanation:

Lines p and r are parallel, as are lines a and b. Either of the lines in one parallel pair is perpendicular to the lines in the other parallel pair. Line q has no necessary relation to anything, so can be ignored. (No answer containing q can be correct.)

__

1.  p ⊥ b

  r ⊥ a

__

2.  r║p

  a║b

__

16. Point B(3, 2) translated (right, up) = (-2, 3) will be ...

  B' = B + (-2, 3) = (3, 2) +(-2, 3) = (3 -2, 2 +3)

  B' = (1, 5)

Note: (x, y) coordinates are (right, up). So, in translation problems it is important to pay attention. Often, the up/down translation is listed before the left/right translation. If you're not paying attention, you may inadvertently reverse the numbers that need to be added to the coordinates to do the translation.

Answer:  That is the correct answer

Step-by-step explanation:

for the first one the answer is A. x + 84 = 180

the second one is C. AB/DC = WX/ZY

Answer:

Step-by-step explanation:

C

Answer:

Yes, because two pairs of corresponding angles in the triangle are congruent. So the answer is A.

Step-by-step explanation:

Corresponding angles is an angle that is in the exact same spot as the other angle and they are congruent to each other which means that they have the same measure/number.

As the picture shows both triangles have all of their angles as the same measures.

Answer:

2 2/9

Step-by-step explanation:

3 3/5 = 18/5

8/1x5/18=40/18=2 4/18=2 2/9

Answer:

1st. false

2nd. true

Step-by-step explanation:

Itll only be considered a function when it passed the vertical line test.

The equation y=2x+1 is a linear function

Answer:

6

Step-by-step explanation:

sqrt(36) = 6

Answer:

1296

Step-by-step explanation:

36 x 36 = 1296

Answer: 0.03

Step-by-step explanation:

Answer:

0.03

Step-by-step explanation:

[tex]\frac{25}{10}[/tex]×[tex]\frac{12}{1000}[/tex]=

[tex]\frac{300}{10000}[/tex]=0.03

The name of the ray shown would be: C. ray AG.

A ray can be defined as a part of a line which has a fixed starting point that is called an endpoint and extends to infinity towards the opposite direction of the fixed point, called the endpoint.

The first letter to use when naming a ray is the letter of the endpoint, which is the starting point of the ray, then use another letter that the ray passes through to infinity.  There would be only one arrow head facing the right, drawn on top of the letters used in naming the ray.

The image shows an endpoint of A, which marks the starting point. The line extends from G to infinity as well.

Therefore, the name of the ray shown would be: C. ray AG.

Learn more about ray on:

https://brainly.com/question/1850410

#SPJ1

Answer:

slope= -2/5

y intercept is (0,-4)

Step-by-step explanation:

Answer:

245 i hope and swer its ok

Step-by-step explanation:

Answer:

[tex]\frac{7}{3}-\frac{2}{3}+\sqrt{3}-3\sqrt{3}=\frac{5}{3}-2\sqrt{3}[/tex]    

Step-by-step explanation:

Given the expression

[tex]\frac{7}{3}\:-\:\frac{2}{3}\:+\:v^3\:-\:3v^3[/tex]

solving the expression

[tex]\frac{7}{3}\:-\:\frac{2}{3}\:+\:\sqrt{3}-3\sqrt{3}[/tex]

combine the fractions i.e [tex]\frac{7}{3}-\frac{2}{3}=\frac{5}{3}[/tex]

[tex]\frac{7}{3}\:-\:\frac{2}{3}\:+\:\sqrt{3}-3\sqrt{3}=\frac{5}{3}+\sqrt{3}-3\sqrt{3}[/tex]

add similar elements  i.e [tex]\sqrt{3}-3\sqrt{3}=-2\sqrt{3}[/tex]

                                 [tex]=\frac{5}{3}-2\sqrt{3}[/tex]      

Thus,

[tex]\frac{7}{3}-\frac{2}{3}+\sqrt{3}-3\sqrt{3}=\frac{5}{3}-2\sqrt{3}[/tex]                        

[tex] \tt cotA = \sqrt{ \dfrac{1}{3}}[/tex]

[tex] \tt \implies cotA = \dfrac{1}{\sqrt{3}}[/tex]

All other trigonometric ratios, which are :

Let's make a diagram of right angled triangle ABC.

Now, From point A,

AC = Hypotenuse

BC = Perpendicular

AB = Base

[tex] \tt We \: are \: given, \: cotA = \dfrac{1}{\sqrt{3}}[/tex]

[tex] \tt We \: know \: that \: cot \theta = \dfrac{base}{perpendicular}[/tex]

[tex] \tt \implies \dfrac{base}{perpendicular} = \dfrac{1}{\sqrt{3}}[/tex]

[tex] \tt \implies \dfrac{AB}{BC} = \dfrac{1}{\sqrt{3}}[/tex]

[tex] \tt \implies AB = 1x \: ; \: BC = \sqrt{3}x \: (x \: is \: positive)[/tex]

Now, by Pythagoras' theorem, we have

AC² = AB² + BC²

[tex] \tt \implies AC^{2} = (1x)^{2} + (\sqrt{3}x)^{2}[/tex]

[tex] \tt \implies AC^{2} = 1x^{2} + 3x^{2}[/tex]

[tex] \tt \implies AC^{2} = 4x^{2}[/tex]

[tex] \tt \implies AC = \sqrt{4x^{2}}[/tex]

[tex] \tt \implies AC = 2x[/tex]

Now,

[tex] \tt sin \theta = \dfrac{perpendicular}{hypotenuse}[/tex]

[tex] \tt \implies sinA = \dfrac{BC}{AC} [/tex]

[tex] \tt \implies sinA = \dfrac{\sqrt{3}x}{2x} [/tex]

[tex] \tt \implies sinA = \dfrac{\sqrt{3}}{2} [/tex]

[tex] \Large \boxed{\tt sinA = \dfrac{\sqrt{3}}{2}} [/tex]

[tex] \tt cos \theta = \dfrac{base}{hypotenuse}[/tex]

[tex] \tt \implies cosA = \dfrac{AB}{AC} [/tex]

[tex] \tt \implies cosA = \dfrac{1x}{2x} [/tex]

[tex] \tt \implies cosA = \dfrac{1}{2} [/tex]

[tex] \Large \boxed{\tt cosA = \dfrac{1}{2}} [/tex]

[tex] \tt tan \theta = \dfrac{perpendicular}{base}[/tex]

[tex] \tt \implies tanA = \dfrac{BC}{AB} [/tex]

[tex] \tt \implies tanA = \dfrac{\sqrt{3}x}{1x} [/tex]

[tex] \tt \implies tanA = \sqrt{3}[/tex]

[tex] \Large \boxed{\tt tanA = \sqrt{3}}[/tex]

[tex] \tt cosec \theta = \dfrac{hypotenuse}{perpendicular}[/tex]

[tex] \tt \implies cosecA = \dfrac{AC}{BC} [/tex]

[tex] \tt \implies cosecA = \dfrac{2x}{\sqrt{3}x} [/tex]

[tex] \tt \implies cosecA = \dfrac{2}{\sqrt{3}}[/tex]

[tex] \Large \boxed{\tt cosecA = \dfrac{2}{\sqrt{3}}}[/tex]

[tex] \tt sec \theta = \dfrac{hypotenuse}{base}[/tex]

[tex] \tt \implies secA = \dfrac{AC}{AB} [/tex]

[tex] \tt \implies secA = \dfrac{2x}{1x} [/tex]

[tex] \tt \implies secA = 2[/tex]

[tex] \Large \boxed{\tt secA = 2}[/tex]

[tex]\setlength{\unitlength}{2mm}\begin{picture}(0,0)\thicklines\put(0,0){\line(3,0){2.5cm}}\put(0,0){\line(0,3){2.5cm}}\qbezier(12.4,0)(6.6,5)(0,12.4)\put(-2,13){\sf A}\put(13,-2){\sf C}\put(-2,-2){\sf B}\put(-3,6){\sf 1}\put(6,-3){\sf \sqrt3$}\put(7,7){\sf 2}\end{picture}[/tex]

Given ,

We need to find ,

First finding the other side of the triangle using Pythagoras theorem .

Hypotenuse² = Base² + Height²

[tex]\to\sf Hypotenuse^2 = (1)^2 + (\sqrt3)^2[/tex]

[tex]\to\sf Hypotenuse^2 = 1 + 3 [/tex]

[tex]\to \sf Hypotenuse = \sqrt4[/tex]

[tex]\to\bf Hypotenuse = 2[/tex]

Now ,

^starigjt line equation (SLE)^

how to find slope of line (m)

=y2 - y1/x2 - x1

7. there, (16,2) occupies the x1 (16) and y1 (2) positions.

and, (32,4) occupies the x2 (32) and y2 (4) positions.

ok, enter:

m = y2 - y1/ x2 - x1

=4 - 2 / 32 - 16

=2/16

8. there, (-2,17) occupies the x1 (-2) and y1 (17) positions.

and, (-1,5) occupies the x2 (-1) and y2 (5) positions.

ok, enter:

m= y2 - y1/ x2 - x1

=5 - 17/ -1 - (-2)

=5 - 17 / -1 + 2

= -12 / 1

Answer: in each group, there are 8 students.

Step-by-step explanation:

We have a total of 26 students.

If we separate them into 3 equal groups (suppose that each group has X students) and leave 2 students left, we will have the relation:

3*X + 2 = 26

This means that 3 times the number of students in each group, plus the two students leftover must be equal to the initial number of students.

Now we can solve this for X.

3*X + 2 = 26

3*X = 26 - 2 = 24

X = 24/3 = 8

X = 8

This means that in each group there are 8 students.

Answer:

It equals 2.4019 quarts.

Step-by-step explanation:

i would appreciate if you rate this a 5 and heart it. brainliest is up to you <3

- gibazy

Answer:

12

Step-by-step explanation:

Answer:

Tobias repayed a total of $7,200.

Step-by-step explanation:

If Tobias borrowed $20,000, and the annual interest rate is 9% of this per year, then we need to find 9% of 20,000.

20,000 x 0.09 = 1,800

Therefore, the yearly interest rate is $1,800. Now, we need to multiply this by 4.

1,800 x 4 = 7,200

Therefore, Tobias repayed a total of $7,200.

Hope this helps! :D

Answer

w=-2

Step-by-step explanation:

-5=w-3

-5+3=w-3+3

-2=w

plezz give me brainiest

Answer:

Length of side 1 = 24 m

Length of side 2 = 120 m

Length of side 3 =  84 m

Step-by-step explanation:

The ratio of each side of triangle is: 2:10:7

Perimeter of triangle = 228 meters

We need to find the length of each side.

Let the common ratio be x

We can write the ratios as: 2x,10x and 7x

Length of side 1 = 2x

Length of side 2 = 10x

Length of side 3 = 7x

Using the formula: [tex]Perimeter\:of\:triangle=Sum\:of\:all\:sides\:of\:triangle\\[/tex]

Putting values and finding x:

[tex]Perimeter\:of\:triangle=Sum\:of\:all\:sides\:of\:triangle\\\\228=2x+10x+7x\\19x=228\\x=\frac{228}{19}\\x=12[/tex]

So, we get value of x=12

Now, finding length of each side by putting x=12:

Length of side 1 = 2x =2(12) = 24

Length of side 2 = 10x = 10(12) = 120

Length of side 3 = 7x = 7(12) = 84

So,

Length of side 1 = 24 m

Length of side 2 = 120 m

Length of side 3 =  84 m

Answer:

Tomatoes = 11.5

Onions = 2

Step-by-step explanation:

Andre wants to purchase some onions and tomatoes to make tomato soup. The recipe states that four times the number of tomatoes, , plus five times the number of onions, x, should produce 56 bowls of tomato soup. A different recipe states that two times the number of tomatoes used minus the number of onions used should produce 21 bowls of tomato soup. What is the resulting recipe for the number or tomatoes and onions used in the soup when Andre adds the two recipes together?

Let

Tomatoes = x

Onions = y

Recipe 1:

4x + 5y = 56

Recipe 2:

2x - y = 21

4x + 5y = 56 (1)

2x - y = 21 (2)

Multiply (2) by 5

4x + 5y = 56 (1)

10x - 5y = 105 (3)

Add

10x + 4x = 105 + 56

14x = 161

x = 161 / 14

= 11.5

Substitute x =11.5 into

2x - y = 21

2(11.5) - y = 21

23 - y = 21

-y = 21 - 23

-y = -2

y = 2

Tomatoes = 11.5

Onions = 2

The area of the geometric figure which is the square will be 42.25.

It should be noted that a square simply means a shape that has all its sides equal. It should be noted that the area of a square will be calculated as:

= Side × Side

In this case, the side is given as 6.5. Therefore, it should be noted that the area will be:

Area of a square = Side × Side

= 6.5 × 6.5

= 42.25

Therefore, the area of the geometric figure which is the square will be 42.25.

Learn more about area on:

brainly.com/question/25292087

#SPJ1

Answer:

C

Step-by-step explanation:

Answer:

SSS

Step-by-step explanation:

right on acellus