Find all the integer solutions of each system of inequalities.

The Venus is at a distance of [tex]1.5876 * 10^8[/tex] further away from the earth than the moon

We have given that

The Distance of moon from the earth(in miles)= a=  [tex]2.4 * 10^5[/tex] miles

The Distance of venus from the earth(in miles)= b =   [tex]1.59 * 10^8[/tex] miles

The distance between two objects that are not points is usually defined to be the smallest distance among pairs of points from the two objects.

Now,

Let the distance from which venus is further away from the earth than the moon be x

So, x = b - a

x = [tex]1.59 * 10^8-2.4 * 10^5[/tex]

x = [tex]1590 * 10^5 - 2.4*10^5[/tex]

x = [tex](1590 - 2.4)*10^5[/tex]

x = [tex]1587.6*10^5[/tex]

x = [tex]1.5876 * 10^8[/tex]

Therefore, venus is at a distance of  [tex]1.5876 * 10^8[/tex] further away from the earth than the moon.

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The mean distance, μ, If 5% of balls go farther than 70 feet is; μ = 68.032

We know that the formula to find the z-score is;

z = (x' - μ)/σ

where;

z is z-score

x' is sample mean

μ is population mean

σ is standard deviation

We are given;

σ = standard deviation = 1.2

x' = sample mean = 70 ft

Now, the z-score that produces a p-value of 0.05 or 5% is; z = 1.64

Thus;

1.64 =  (70 - μ)/1.2

μ = 70 - (1.64 * 1.2)

μ = 68.032

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Possible outcomes are Head, Middle, and Tail.

Since all outcomes are equally likely, the probability of each event is same, therefore

P(Head) = P(Middle) = P(Tail)

= 1/3

P(B|A) is 1/3

P(C|A) is 2/3

A and B are independent

A and C are not independent

Part a

Finding the sample space, S

S = { (HH), (HM), (HT), (MH), (MM), (MT), (TH), (TM), (TT) }

Part b

Finding  P(B|A) and P(C|A):

n(B and A) = no. of outcomes in which the first toss is Middle and second toss is Tail = 1

n(A) = Total no. of events in which the first toss is Middle = 3

Therefore, P(B|A) = 1/3

n(C and A) = no. of outcomes in which the first toss is Middle and total no. of heads is zero = 2

n(A) = Total no. of events in which the first toss is Middle = 3

Therefore, P(C|A) = 2/3

Part c

Finding if A and B are independent, or if A and C are independent

Two events A and B are said to be independent when the occurrence of one event does not affect the occurrence of the other event and vice versa. In case of independent events,

P(A) = P(first toss is Middle) = 3/9 =1/3

P(B) = P(second toss is Tail) = 3/9 = 1/3

P(A and B) = P(first toss is Middle and second toss is Tail) = 1/9

P(A)*P(B) = (1/3)*(1/3)

= 1/9 = P(A and B)

Hence, we can say that events A and B are independent.

For A and C, we have,

P(A) = P(first toss is Middle) = 3/9

P(C) = P(total no. of Heads is 0) = 4/9

P(A and C) = P(first toss is Middle and total no. of heads is 0) = 2/9

P(A)*P(C) = (3/9)*(4/9)

= 4/27 P(A and C)

Hence, events A and C are not independent.

The question was incomplete, the complete question is:

(Extra Credit) Suppose you have a well-balanced "super coin" with three sides or outcomes equally likely: Head, Middle, and Tail. (the super coin is a die with opposite faces showing Head, Middle, and Tail) You tossed this super coin two times

a) Describe the sample space using the notation HM for example, if the results are Head first, and Middle second.

Let;

A = event the first toss is Middle,

B = event the second toss is Tail, and

C = event the total number of Heads is 0.

b) Find

P(B|A)

P(C|A)

c) Are A and B independent? YES, NO, Why?

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Answer:

 x = 5.33333333333

Step-by-step explanation:

3x-5=11

   +5   +5

3x= 16

3      3      

u need to separate the 3x

so u use the opposite operation on - 5

add +5 on both sides

-5 plus 5 cancel each other

add 11 to 5 and that is 16

bring them down and divide both by 3

and ur 3 cancel each other,

now divide 16 by 3

and u get  x = 5.33333333333

Answer:

Bro x =21

Step-by-step explanation:

X=21 and AM=14

As all the lines are same so all will be 7 and x will be 3 times 7 which is 21 and in the AM case there 7 is 2 times thus multiply 7 by 2 for 14

Answer:

Time since the person starts walking is the input

t represents the input

Step-by-step explanation:

Answer:

27/8 or 3⅜

Step-by-step explanation:

please rate as brainliest

Answer:

f(g(x) ) = x² + 2

Step-by-step explanation:

to find f(g(x) ) substitute x = g(x) into f(x)

f(g(x) )

= f(x²)

= x² + 2

Answer:

I think this is correct.

Step-by-step explanation:

Answer:

7.071068 ≈ 7.07

Step-by-step explanation:

The distance, d,  between 2 points (x1, y1) and (x2, y2) is given by the formula

[tex]d = \sqrt {(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2}[/tex]

The two points as determined from the graph are (1, 5) and (2, -2)

[tex]d = \sqrt {(2 - 1)^2 + (-2 - 5)^2}[/tex]

[tex]d = \sqrt {(1)^2 + (-7)^2}[/tex]

[tex]d = \sqrt {{1} + {49}}[/tex]

[tex]d = \sqrt {50}[/tex]

[tex]d = 7.071068[/tex]

Answer:

0.29761904761

Step-by-step explanation:

Brainlest, Please!

Answer:

25/84

Step-by-step explanation:

1. 2 1/10 is mixed number fraction so convert it into an improper fraction.

~ Multiply whole number and denominator and add the numerator of 1

~ Improper fraction: 21/10

2. So, new equation is (5/8) / (21/10)

3. Use the Keep, Change, Flip method:

~ Keep the 5/8

~ Change division to multiplication

~ Flip the improper fraction to 10/21

4. Solve the equation:

~ (5/8) x (10/21) = 50/ 168

5. Reduce fraction:

~ By 2

~ 25/84

The speed of the walker is 16.67 miles per hour.

The speed of the cyclist is 25 miles per hour.

Let the speed of a walker = x

Biker's speed = 1.5x

Their relative speed will be:

= 1.5x - x = 0.5x

Distance between them = 12.5 miles

Time taken = 1.5 hours.

It should be noted that distance will be:

= Speed × Time

12.5 = 1.5 × 0.5x

Divide through to get x

12.5 = 0.75x

x = 16.67 miles per hour.

Speed of cyclist = 16.67 × 1.5 = 25 miles per hour.

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169.6/53 = 3.2

about 3.2 hours

Answer:

3.2 hours

Step-by-step explanation:

169.6 ÷ 53 = 3.2

so, she drove 3.2 hours

Answer:

answer is D prettyy sure

Answer:

Yes

Step-by-step explanation:

The Elephant Building is 335 feet high. A real Asian elephant is 12 feet tall. If 29 real elephants could stand on top of each other, would they reach the top of the building?

They are asking if 29 12' elephants are as tall as as a 335' building:

29 × 12' = 348' elephant stack

because 348' is taller than 335' building then yes, 29 staked elephant would reach and pass the top of a 335' building.  

Step-by-step explanation:

For Arithmetic Sequence

Tn = a + (n -- 1)d

Where Tn = the no of nth term

a = First number

n = nth term

d = common difference

a = --27, T2 = --21

d = second term -- first term

d = --27 -- (--21)

d = --27 + 21 = --6

a = --27, n = 62, d = --6, T62 = ?

Tn = a + (n -- 1)d

T62 = --27 + (62 -- 1)×--6

T62 = --27 + (61 × --6)

T62 = --27 + (--366)

T62 = --27 -- 366

T62 = --393

Answer:

1

Step-by-step explanation:

from the rule of exponents

• [tex]a^{0}[/tex] = 1 , then

[tex](5x)^{0}[/tex] = 1

Answer:

Step-by-step explanation:

Part A. The figure at the right is of 2 grain, storage silos. The diameter of each measures 24 feet and the height of the cylinder measures 51 feet. The height ...

Hence the angle theta is 70.5°

What is angle?

The space between two lines or surface that meet  measured in degrees.

As per the given question a ladder 3.5 m long leaning against the wall of a house reaches a height of 3.3 m we have to find what ladder make the ground.

Sol-

Let the angle is theta

Length of the ladder is 3.5m

Height of the ladder is 3.3 m

Sin= 3.5/3.3

      =0.942

Sin =sin 70.5°

Theta = 70.5°

Hence the angle is theta =70.5°

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Answer:

x = 3

Step-by-step explanation:

3x + 2 = 11

3x = 11 - 2

3x = 9

x = 9/3

x = 3

Answer:

Separate the x and the numbers on each side and solve.

3x + 2 = 11

3x = 9

x = 3

The numeric values for the given functions are as follows:

1. g(-4) = -21.

2. f(-1) = 3.

To find the numeric value of a function at input x = a, we replace each instance of the variable x in the function by the desired value of a.

For item 1, function g(x) is defined as follows:

g(x) = -x² - 5.

We want to find the numeric value at x = -4, hence the lone instance of x is replaced by -4 as is shown below:

g(-4) = -(-4)² - 5 = -16 - 5 = -21.

Hence g(-4) = -21 is the numeric value.

For item 2, the function f(x) is given as follows:

f(x) = -3(1 - x - 3x²).

To find the numeric value at x = -1, both instances of x have their values replaced by -1, hence the numeric value will be given as follows:

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

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They tell us that it is distributed in a normal way, which means that the distribution has the following characteristics:

If teh standart deviation is 2.7 gallon and the avriabe is normal distributed we need to know the probability highlighted in the image above, when replacing in the formula with x greater than 25 we obtain:

Based on the given equation, the change of subject of the equation to M is given by M = 10L - 5/2g + 130

Changing the subject of formula of an equation is the working out of a particular variable from the list of variables in the formula. The variable is either denoted with letter or symbol.

M/5 - 26 = 2L- 1/2g

Where,

M/5 - 26 = 2L- 1/2g

M/5 = 2L - 1/2g + 26

M = 5(2L - 1/2g + 26)

M = 10L - 5/2g + 130

Therefore, the solving for M in the equation will give M = 10L - 5/2g + 130

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Step-by-step explanation:

what do you need to do ?

the only thing we can do here without any further information is simplification if the expression:

-23x² + x² - 6x + 10 + 2x²

now we group ask the terms of the same variable exponents :

-23x² + x² + 2x² - 6x + 10

-20x² -6x + 10

we could do

2×(-10x² - 3x + 5)

but I personally don't find this more simplified that the previous form.

Answer:

A square pyramid is composed of an eight-sided square base, four triangular sides, five vertices, and five vertices. This pyramid has a square base with a peak at the top. The fact that a square pyramid is a polyhedron was noted.

Step-by-step explanation:

The three-dimensional geometric shape of a square pyramid has a square base and four triangular sides that are joined at the vertex. Five facets make up its polyhedron shape (pentahedron). Four triangles joined at the vertex and a square base make up a square pyramid. Three sides, a square base, and a central vertex characterize the triangle side faces. The tallest point of the pyramid is known as its "apex." The base is represented by the bottom square. Faces are the three triangular vertices of the triangle. When viewed from the bottom up, a pentahedron is a five-sided, three-dimensional shape that resembles a square pyramid.

Answer: top: x= 2   bottom: x= -5

Step-by-step explanation: First you need to get rid of everything on the x side, so for example on the top one you would do 9-9 to get 0 so that x is by itself and then you also have to 11-9 because whatever you do to one side you have to do to the other. And then 11-9=2 so you are left with x= 2.

Answer:

-1

Step-by-step explanation:

First combine like terms on the right side (5x-10x) to get -5x +4

6-3x=-5x+4

then move the -5x over to get 2x because you would add the -5x to the -3x.

6+2x= 4

then subtract 6 on both sides.

2x=-2

to make your final answer -1.

The only student with the correct claim about the given quadratic equation is; Neil: The vertex is at (2, -9)

We are given the quadratic function;

f(x) = (x - 5)(x + 1)

1) The x-intercepts of the quadratic function are simply the roots of the quadratic function. Now, the roots are at; (5, 0) and (-1, 0). Thus, Annie's claim is not correct.

2) The y-intercept is the point at which x = 0. Thus;

f(0) = (0 - 5)(0 + 1)

f(0) = -5

y-intercept is at; (0, -5)

Thus, Jacob is wrong.

3) The x-coordinate of the vertex is;

x = -b/2a

The equation is; x² - 4x - 5

Vertex = -(-4)/(2 * 1) = 2

y-coordinate is;

y = 2² - 4(2) - 5

y = -9

Thus, Jacob is correct

4) Zoey is incorrect because she didn't properly find the midpoint of the x-intercepts.

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Si definimos N como el nuevo número de esferas en la urna, entonces la expresión algebraica será:

N = x - 3.

Sabemos que tenemos una urna con x esferas, donde x representa un numero entero.

Sabemos que 3 esferas se extraen de la urna, es decir, el número total de esferas en la urna decrese en 3 unidades.

Entonces podemos escribir la expresión algebraica como:

N = x - 3

Donde definimos N como el nuevo número de esferas en la urna.

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