Two cars leave an intersection at the same time. One drives east while the other travels south at 25 miles per hour faster than the other. After 2 hours, the cars are 250 miles apart. How fast is the southbound car driving?

Mutually exclusive outcomes are events that cannot happen at the same time, while non-mutually exclusive outcomes can occur together.

The term "mutually exclusive" refers to two outcomes that cannot occur at the same time. In other words, if one outcome happens, the other outcome cannot occur. This means that the events have no elements in common and are disjoint. For example, let's consider the outcomes of flipping a fair coin. The two possible outcomes are getting a "heads" or a "tails". These outcomes are mutually exclusive because if the coin lands on "heads", it cannot simultaneously land on "tails". Similarly, if the coin lands on "tails", it cannot be "heads" at the same time. Therefore, the outcomes of getting "heads" and "tails" are mutually exclusive.

On the other hand, let's take the example of rolling a regular six-sided die. The outcomes could be getting an even number (2, 4, or 6) or getting a number greater than 4 (5 or 6). In this case, the outcomes of getting an even number and getting a number greater than 4 are not mutually exclusive. It is possible for the die to land on a 6, which would satisfy both conditions. Therefore, these outcomes are not mutually exclusive.
To summarize, mutually exclusive outcomes are events that cannot happen at the same time, while non-mutually exclusive outcomes can occur together. In the context of flipping a coin, getting "heads" and "tails" are mutually exclusive outcomes, whereas in the case of rolling a die, getting an even number and getting a number greater than 4 are not mutually exclusive outcomes.

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The domain and range of f(x) = -24 are given as follows:

The domain and range of f(x) = 0.5(x + 4)² - 11 are given as follows:

The range of y = -2x² + 12x - 13 is given as follows:

y <= 5.

The domain of a function is the set that contains all the input values that can be assumed by the function.

As neither of the functions in this problem have any restriction, the domain is all real values for the two of them.

The range of a function is the set that contains all the output values that can be assumed by the function.

The ranges are given as follows:

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Answer:

3(4 + n) = n + 18

n = 3

Step-by-step explanation:

because the sum of 4 and a number is multiplied by three. That equals the number plus 18. N = 3. in the image below are the steps you can take to solve the equation.

The missing angles were solved using alternative, corresponding or opposite angle theorem and the values of x and y are represented below.

The alternate and corresponding angles theorem states that angles that are alternate or corresponding to each other must be equal to each other.

13;

\((8x -1) = (11x - 25)\)

corresponding angles are equal to each other.

\((8x -1) = (11x - 25)\\x = 8\)

let's solve for y

\((15y-48) + (8x -1) = 180\\x = 8\\15y - 48 + 8(8) -1 = 180\\15y - 48 + 64 - 1 = 180\\15y + 15 = 180\\15y = 180 - 15\\15y = 165\\y = 11\)

Therefore, the value of x and y are 8 and 11 respectively.

14;

\(39 + (8y - 43) = 180\\\)

sum of angles on a straight line is equal to 180

\(39 + (8y - 43) = 180\\\\y = 23\)

let's solve for x

\(7x - 44 = 4x + 4\\x = 16\)

From the above calculations, we can easily find the missing side or angle using alternative, corresponding or opposite angle theorem.

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Answer:

it just depends what gumball its talking about

Step-by-step explanation:

Answer: 0.214

Step-by-step explanation:

There are a total of 14 marbles in the bag, with only 3 being red. 3/14 converts to 0.214

Answer:

x=−3 and y=7

Step-by-step explanation Solve: 7x+2y=−7for x:

7x+2y=−7

7x+2y+−2y=−7+−2y(Add -2y to both sides)

7x=−2y−7

7x

7

=

−2y−7

7

(Divide both sides by 7)

x=

−2

7

y−1

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

−2

7

y−1forxin11x+5y=2:

11x+5y=2

11(

−2

7

y−1)+5y=2

13

7

y−11=2(Simplify both sides of the equation)

13

7

y−11+11=2+11(Add 11 to both sides)

13

7

y=13

13

7

y

13

7

=

13

13

7

(Divide both sides by 13/7)

y=7

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

Substitute7foryinx=

−2

7

y−1:

x=

−2

7

y−1

x=

−2

7

(7)−1

x=−3(Simplify both sides of the equation)

Answer:

Area = 156.25π meters

Step-by-step explanation:

In order to identify the area of the circle, you would need the radius. In order to find the radius, you would plug in the circumference (25π) into the equation for the circumference of a circle, like this:

C = 2πr

25π = 2πr

You would then solve the equation for r  (the radius)

25π = 2πr

12.5π = πr

12.5 = r  

Then you would plug the radius into the equation for the area of a circle.

A = π(r^2)

A = 12.5^2π

A = 156.25π

So your answer would then be 156.25π meters, since that was the unit of measurement

Answer: 156.25π m. Hope this helps.

Answer:

P(heads and even number) = 1/4

Step-by-step explanation:

Given:

Coin tossed for head

Dies role for Even number

Find:

P(heads and even number)

Computation:

P(heads) = 1/2

P(even number) = 3/6

P(even number) = 1/2

P(heads and even number) = P(heads) × P(even number)

P(heads and even number) = 1/2 × 1/2

P(heads and even number) = 1/4

Answer:

A

Step-by-step explanation:

The list has the sides of ΔFGH in order from shortest to longest side GF < side HF < side HG option (C) is correct.

In terms of geometry, a triangle is a three-sided polygon with three edges and three vertices. The triangle's interior angles add up to 180°.

It is given that:

In ΔFGH, m∠F = 119° and m∠G = 40°.

From the data given in the question:

The correct order should be:

side GF < side HF < side HG

Thus, the list has the sides of ΔFGH in order from shortest to longest side GF < side HF < side HG option (C) is correct.

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Answer:

Step-by-step explanation:

Where are the answer choices?

Still, it's possible to help you without your having shared those choices.

The "difference quotient" is defined as:

 f(x + h) - f(x)

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

           h

where h represents an incremental (small) change in x.

Here f(x) = 3 - log x, and so f(x + h) = 3 - log (x + h).

Therefore the difference quotient is:

{3 - log (x + h)} - {3 - log x}

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

                    h

This can be simplified.  In the numerator we have 3 - 3, so the numerator simplifies to -log (x + h) + log x

and the difference quotient is

-log ( x + h) + log x

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

              h

This can be rewritten as

log x - log (x + h)                                x                                  x

--------------------------- , or (1/h)*log ------------ , or  (1/h) log { ----------- }

              h                                       (x + h)                            x + h          

Answer:

B

Step-by-step explanation:

I guessed and got it right.

Answer:

If the product of any two numbers is zero,then one or both of the numbers is zero.That is,if ab=0, then a=0 or b=0 (which includes the possibility that a=b=0).

Answer:

The graph is not a function.

Step-by-step explanation:

Using the "vertical line test" to attach a vertical line to each of the points on the graph, we will find that the vertical line that passes through (0,0) has ot one, but two points on it. Remember, if the vertical line passes through more than one points, the graph is not a function. As we know, the vertical line passes through two points, those being (0, -4) and (0, -3). So, we can conclude that the graph is not a function.

Answer:

x = 11

Step-by-step explanation:

7x + 3(3x + 6) = 194

open the parenthesis

7x + 3 * 3x + 3 * 6 = 194

7x + 9x + 18 = 194

subtract 18 from both sides of the equation

7x + 9x + 18 - 18 = 194 - 18

combine like terms

7x + 9x = 194 - 18

16x = 176

divide both sides of the equation by 16

16x/16 = 176/16

x = 176/16

x = 11

We need to operate the next matrixes.

First, subtract the next matrixes:

13 10 7

6 8 1

2 5 0

-

3 -2 6

14 -6 11

8 -12 9

=

13-3 10-(-2) 7-6

6-14 8-(-6) 1-11

2-8 5-(-12) 0-9

=

10 12 1

-8 14 -10

-6 17 -9

Now, the result adds to the next matrix:

10 12 1

-8 14 -10

-6 17 -9

+

6 10 15

10 0 9

1 0 7

=

10+6 12+10 1+15

-8+10 14+0 -10+9

-6+1 17+0 -9+7

=

16 22 16

2 14 -1

-5 17 -2

Therefore, the correct answer is the first one.

To find the new average height of the 10 trees, we need to take into account the additional height of the one tree. We can start by calculating the total height of all 10 trees before the growth, which would be 10 trees x 2.6 metres per tree = 26 metres in total. Then, we can add the height of the one tree that grew, which is 2.2 - 1.7 = 0.5 metres.

Therefore, the total height after growth is 26 + 0.5 = 26.5 metres. To find the new average height, we divide the total height by the number of trees, which is 26.5/10 = 2.65 metres. We are asked to give the answer to two decimal places, so we round it to 2.65. Therefore, the new average height of the 10 trees is 2.65 metres. The new average height of the 10 trees is 2.65 metres, given to two decimal places.

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Answer:

y=(x+6)^2

Step-by-step explanation:

Bc, the root has to be only -6

there fore x=-6

since isosceles has 2 equal sides we can add two to the shorter side

so now we multiply by 4

8 for short sides each

20 for long side

The longest side of the isosceles triangle is 20 units.

An isosceles triangle in geometry is a triangle with two equal-length sides. It can be specified as having exactly two equal-length sides or at least two equal-length sides, with the latter definition including the equilateral triangle as an exception.

Given that the perimeter of an isosceles triangle is 36 centimetres and two sides of the triangle are in the ratio $2:5.$.

The length of the longest side will be calculated as;-

2S + B = 36

S / B = 2 / 5
S = ( 2B ) / 5

2 x ( 2B ) / 5 + B = 36

4B + 5B = 180

9B = 180

B = 20 units

The measure of the other side is,

S = 2B / 5

S = ( 2 x 20 ) / 5 = 8 units

Hence, the length of the longest side is 20 units.

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Answer: x^6+6x^4+8x^2+2

Step-by-step explanation:

Since g comes after f then you will take g's equation and plug it into the f equation so it would turn out to be if you plugged it in

(x^2+2)^3-4(x^2+2)+2 which would equal x^6+6x^4+8x^2+2

Using proportions, it is found that:

42. x and y are not proportional.

43. The number 21 is 60% of 35.

44. The number 27 is 36% of the number 75.

Two variables, x and y, will represent a proportional relationship if the ratio between them is always the same.

From the table, the ratios are given as follows:

Different ratios, hence the variables x and y are not proportional.

To find the percentage of a number, the decimal equivalent of the percentage is multiplied by the number.

The decimal equivalent of a percentage of 60% is:

60/100 = 0.6.

Hence the percentage of 35 is calculated as follows:

0.6 x 35 = 21.

The percentage that the number 27 represents of the number 75 is given by the division of 27 by 75 multiplied by 100%, hence:

27/75 x 100% = 36%.

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Answer:

6.6 ft

Step-by-step explanation:

The area of a triangle is given by the formula: \(A=\frac{1}{2}bh\).

In this case, the base b equals the height h.

\(\therefore A=\frac{1}{2}h^2 \rightarrow h=\sqrt{2A}\)

Given: A = 22 ft²

\(\therefore h=\sqrt{2A} = \sqrt{2(22 \text{ ft}^2)} = \sqrt{44}\text{ ft} \approx 6.6 \text{ ft}\)

For the relationship, two variables are needed.

One of the variable is given as 'z'. Let the other one be 'x'.

Then you need to translate that 'x' is six more than four times a number 'z'.

This can be expressed as,

Thus, the right side of the expression represents the relationship "six more than four times a number z".

Here's link\(^{}\) to the answer:

bit.\(^{}\)ly/3gVQKw3

a) The set of even positive integers can be defined recursively as follows:    Let X be the set of all even positive integers. Then, 2 is in X and if n is in X, then (n + 2) is in X. This definition is recursive because it is defined in terms of itself.

b) The set of positive integer powers of 4 can be defined recursively as follows:    Let Y be the set of all positive integer powers of 4. Then, 4 is in Y and if n is in Y, then (4n) is in Y. This definition is recursive because it is defined in terms of itself.  

c) The set of polynomials with integer coefficients can be defined recursively as follows:    Let Z be the set of all polynomials with integer coefficients. Then, the constant polynomial 0 is in Z and if p and q are in Z, then (p + q) and (pq) are in Z. This definition is recursive because it is defined in terms of itself.

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Answer:

x = 1/9(b)

Step-by-step explanation:

Step 1: Subtract 6x from both sides.

Step 2: Subtract b from both sides.

Step 3: Divide both sides by -9.

Therefore, \(x = \frac{1}{9}b\).

the solution to the system of congruences is x ≡ 34 (mod 6) or x ≡ 33 (mod 6).

To solve the system of congruences using the method of back substitution, we'll start with the second congruence and substitute the solution into the first congruence. Here are the steps to solve the system:

Step 1: Solve the second congruence: x ≡ 4 (mod 7)

To find a solution for x in this congruence, we need to find an integer that satisfies the equation x ≡ 4 (mod 7). Looking at the possible remainders when dividing by 7, we can start with x = 4.

Step 2: Substitute the solution into the first congruence: x ≡ 3 (mod 6)

Now, we substitute the value we found in the previous step (x = 4) into the first congruence: x ≡ 3 (mod 6).

4 ≡ 3 (mod 6)

Step 3: Simplify the congruence: 4 ≡ 3 (mod 6)

Since 4 is not congruent to 3 modulo 6, we need to add the modulus 6 to the left side until we find a congruence:

4 + 6 ≡ 3 + 6 (mod 6)

10 ≡ 9 (mod 6)

Step 4: Simplify the congruence: 10 ≡ 9 (mod 6)

Again, we add the modulus 6 to the left side until we find a congruence:

10 + 6 ≡ 9 + 6 (mod 6)

16 ≡ 15 (mod 6)

Step 5: Simplify the congruence: 16 ≡ 15 (mod 6)

We continue this process until we find a congruence:

16 + 6 ≡ 15 + 6 (mod 6)

22 ≡ 21 (mod 6)

Step 6: Simplify the congruence: 22 ≡ 21 (mod 6)

Once more, we add the modulus 6 to the left side until we find a congruence:

22 + 6 ≡ 21 + 6 (mod 6)

28 ≡ 27 (mod 6)

Step 7: Simplify the congruence: 28 ≡ 27 (mod 6)

Finally, we find the congruence:

28 + 6 ≡ 27 + 6 (mod 6)

34 ≡ 33 (mod 6)

At this point, we have found a congruence that holds: 34 ≡ 33 (mod 6).

Therefore, the solution to the system of congruences is x ≡ 34 (mod 6) or x ≡ 33 (mod 6).

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The portable Bluetooth speaker is designed as a cylinder with hemispheres. The maximum volume is achieved when the radius is 5 cm, resulting in a length of 140 cm and a maximum volume of 38,500 cm³.

To find the volume (V) of the speaker, we need to consider the volume of the cylinder and two hemispheres. The expression for V is V = πr²I + (4/3)πr³. The surface area of the speaker is given by the equation 4πr² + 2πrI. Using the design constraint I = 150 - 2r, we can substitute this into the volume expression to get V = 150r - 2r³ + (250 - 2r²)πr². To find the maximum volume, we differentiate V with respect to r and set it equal to zero.

Solving for r, we find r = 5. Substituting this back into the expression for I, we get I = 140. Therefore, when r = 5 cm, the speaker has maximum volume. The length of the cylinder for which V is a maximum is 140 cm. By plugging r = 5 and I = 140 into the volume expression, we find the maximum value of V to be 38,500 cm³. Thus, the shape of the speaker with the best quality of sound is a cylinder with hemispheres, where the radius is 5 cm and the length of the cylinder is 140 cm.

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Step-by-step explanation:

-6/13*-16/7

+96/91

I hope it helps you

Answer:

\(\frac{96}{91}\) or 51.69

Step-by-step explanation:

\(\frac{-6}{13}\) x reciprocal of \(\frac{-7}{16}\)

Reciprocal of \(\frac{-7}{16}\) is \(\frac{-16}{7}\)

So, the equation would be:-

\(\frac{-6}{13}\) x \(\frac{-16}{7}\)

= \(\frac{96}{91}\)

The product would be \(\frac{96}{91}\).

Simplified form of this is 51.692

The starting point is something that need not be explained for its truth is evident. The mind directs and is the cause of everything. Must be able to rest with certainty within these things.

The number being divided (in this example, 15) is known as the dividend, and the number being divided by (in this case, 3) is known as the divisor. The number to be split or dispersed into a given number of equal parts in a division problem is referred to as the dividend. As in the preceding example, when we split 20 apples among 5 persons, the dividend is the number 20; and the divisor is the number 5. Dividend = Divisor x Quotient + Remainder is the Math formula for calculating the dividend. Typically, when we divide one integer by another, we get x/y = z. Here, x represents the dividend, y represents the divisor, and z represents the quotient.

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