LINES AND FUNCTIONS Variable expressions as inputs of fund The function f is defined by f(x)=(x+7)/(3x+6) Find f(4x)

Answer:

Graph attached →

Step-by-step explanation:

The probability of randomly selecting a red, then a free marble from a bag of 5 red, 8 green, and 3 marbles

a)  0.1563

b) 0.1667

Since we are  given with bag of  5 red, 8 green, and 3 marbles. so, r=5, g=8 and b=  3. For the first  case, we replace the first  marble before drawing the second,  the total number of marble =  5 + 8 + 3 = 16. So, the probability of drawing a red marble at the 1st attempt is: 5/16. Then, the first marble is replaced back into the bag before making the second draw. Probability of drawing green marbles at the second draw is: 8/16= 1/2, Therefore the probability of selecting a red, then a green marble is: 5/16 * 1/2 = 5/32 =0.1563

For the second case , we do not replace the first marble, the probability of drawing a red marble at the 1st draw is:5/16 . Since we don't replace the balls  so the number of marbles remaining in the bag is: 16-1 =15 ,the probability of drawing green marbles at the second draw is: 8/15, therefore the combined probability of selecting a red, then a green marble is: 5/16 * 8/15  =0.1667

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Answer:

mean: 14.833 or 14.8

median: 16

mode: 17

range: 14

Answer:

The required linear function for the temperature T, in degrees Fahrenheit, of the oven m minutes from the time it was turned on until it reaches the desired temperature is T = 54m + 80.

Step-by-step explanation:

Given that,

An oven is turned on and set to reach the desired temperature of 350 degrees Fahrenheit. The oven warms up at a constant rate. The oven’s temperature is 134 degrees Fahrenheit at 1 minute and it reaches its desired temperature at 5 minutes.

What are functions?

Functions is the relationship between sets of values. e g y=f(x), for every value of x there is its exists in set of y. x is the independent variable while Y is the dependent variable.

Here,

At time m = 1 min, temperature T = 134 °F

At time m = 5 min. temperature T = 450 °F

Slope of the equation M = 450 - 134 / 5 - 1

                                        = 216 / 4

                                        = 54

Linat relationship can be given as,

T - 134 = 54 (m - 1)

T = 54m -54 + 134

T = 54m + 80

Thus, the required linear function for the temperature T, in degrees Fahrenheit, of the oven m minutes from the time it was turned on until it reaches the desired temperature is T = 54m + 80.

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Answer:

x>14

Step-by-step explanation:

Step 1: Simplify both sides of the inequality.

-4>-2x+24

Step 2: Flip the equation.

-2x+24<-4

Step 3: Subtract 24 from both sides.

-2x+24-24<-4-24

-2x<-28

Step 4: Divide both sides by -2.

-2x-2<-28-2

x>14

If it is right can I have brainliest.

Answer:

woomy...

Step-by-step explanation:

Answer: Probability: 3/12 or 1/4

Step-by-step explanation:

The constructed PRG G from a length-preserving PRF F is itself a PRG.

To construct a pseudorandom generator (PRG) G from a length-preserving pseudorandom function (PRF) F, we can define G as follows:

G receives a seed s of length n as input.

For each i in {1, 2, ..., n}, G applies F to the seed s and the index i to generate a pseudorandom output bit Gi.

G concatenates the generated bits Gi to form the output of length n.

Now, let's prove that G is a PRG by showing that it satisfies the two properties of a PRG:

Expansion: G expands the seed from length n to length n, preserving the output length.

Since G generates an output of length n by concatenating the n pseudorandom bits Gi, the output length remains the same as the seed length. Therefore, G preserves the output length.

Pseudorandomness: G produces output that is indistinguishable from a truly random string of the same length.

We can prove the pseudorandomness of G by contradiction. Assume there exists a computationally bounded adversary A that can distinguish the output of G from a truly random string with a non-negligible advantage.

Using this adversary A, we can construct an algorithm B that can break the security of the underlying PRF F. Algorithm B takes as input a challenge (x, y), where x is a random value and y is the output of F(x). B simulates G by invoking A with the seed x and the output y as the pseudorandom bits generated by G. If A can successfully distinguish the output as non-random, then B outputs 1; otherwise, it outputs 0.

Since A has a non-negligible advantage in distinguishing the output of G from a random string, algorithm B would also have a non-negligible advantage in distinguishing the output of F from a random string, contradicting the assumption that F is a PRF.

Hence, by contradiction, we can conclude that G is a PRG constructed from a length-preserving PRF F.

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Answer:

225

Step-by-step explanation:

(- 15)² = - 15 × - 15 = 225

Answer:

If r = 5, then:

(-5) - (-5) + (5) - (5) = 0

Always remember order of operations (PEMDAS)

Hope this helps :)

Answer: (-2,-2)

Step-by-step explanation:

Start at finding the y-intercept(-3) then do rise over run with -2x

Rise over run is count up/down then left/right

By verifying the Pythagorean Theorem for the vectors u and v,

∥u∥²= 2

∥v∥²= 2

∥u+v∥²= 8

u and v are not orthogonal.

We have verified that the conditions of the Pythagorean Theorem hold do not for these vectors.

To verify the Pythagorean Theorem for the vectors u and v, we need to calculate the norm of each vector and the norm of their sum.

The norm of u is √(1² + (-1)²) = √(2).

The norm of v is √(1² + 1²) = √(2).

The norm of u+v is √((1+1)² + (-1+1)²) = √(4) = 2.

Then, we can check if the Pythagorean Theorem holds by verifying if ||u+v||² = ||u||² + ||v||²:

||u||² + ||v||² = 2 + 2 = 4.

||u+v||² = 4.

Therefore, ||u+v||² = ||u||² + ||v||², and we can conclude that the Pythagorean Theorem holds for these vectors. Additionally, since the dot product of u and v is zero (1 × (-1) + 1 × (-1) = -2 + (-1) = -3), we can confirm that u and v are orthogonal.

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The question is -

Verify the Pythagorean Theorem for the vectors u and v.

U=(1,−1), v=(1,1)

Are u and v orthogonal?

Yes

No

Calculate the following values.

∥u∥²=

∥v∥²=

∥u+v∥²=

We draw the following conclusion.

We have verified that the conditions of the Pythagorean Theorem hold _____ (do/do not) for these vectors.

Answer:

x=8

Step-by-step explanation:

Answer:

Step-by-step explanation:

We know that:

Surface area is the area of the faces of the cuboid.

Work:

Hence, Option C is correct.

Hoped this helped.

\(BrainiacUser1357\)

Answer:

9,

Step-by-step explanation:

if you look at the pattern its just adding up all the numbers above so its nine

Answer:

Enrique is correct. If you look question clearly then you will find that Matt has added the mixed fraction but the question is to multiply them and Enrique has converted mixed fraction into fraction then multiplied them. So, the answer of Enrique is correct.

At most, they can wash 96 cars and mow 96 lawns.

To determine the maximum number of cars they can wash and lawns they can mow, we need to consider the work rates of each person and the total number of hours they work.

Huey can wash 6 cars or mow 3 lawns in one hour, so in 8 hours, he can wash 6 \(\times\) 8 = 48 cars or mow 3 \(\times\) 8 = 24 lawns.

Dewey can wash 3 cars or mow 3 lawns in one hour, so in 8 hours, he can wash 3 \(\times\) 8 = 24 cars or mow 3 \(\times\) 8 = 24 lawns.

Louie can wash 3 cars or mow 6 lawns in one hour, so in 8 hours, he can wash 3 \(\times\) 8 = 24 cars or mow 6 \(\times\) 8 = 48 lawns.

Since two of them wash cars and one mows lawns, the maximum number of cars they can wash is the sum of the maximum cars each person can wash, which is 48 + 24 + 24 = 96 cars.

The maximum number of lawns they can mow is the sum of the maximum lawns each person can mow, which is 24 + 24 + 48 = 96 lawns.

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Answer: The critical points of g(t) occur at t = ±sqrt(-d/2) if d < 0. If d ≥ 0, then dg(t)/dt is always greater than or equal to zero, so g(t) has no critical points.

Step-by-step explanation:

To find the critical points of g(t), we need to find the values of t where the derivative dg(t)/dt is equal to zero or does not exist.

Using the given information, we have:

dg(t)/dt = 4ct^3 + 2dct

Setting this equal to zero, we get:

4ct^3 + 2dct = 0

Dividing both sides by 2ct, we get:

2t^2 + d = 0

Solving for t, we get:

t = ±sqrt(-d/2)

Therefore, the critical points of g(t) occur at t = ±sqrt(-d/2) if d < 0. If d ≥ 0, then dg(t)/dt is always greater than or equal to zero, so g(t) has no critical points.

Note that we also need to assume that c is nonzero, since if c = 0, then dg(t)/dt = 0 for all values of t and g(t) is not differentiable.

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When a research hypothesis does not predict the direction of a relationship, the test is typically two-tailed.

A two-tailed hypothesis is used when there is no specific prediction about

the direction of the relationship between variables.

It simply states that there is a relationship between the variables being

studied, but does not specify whether the relationship will be positive or

negative.

In contrast, a one-tailed hypothesis predicts the direction of the

relationship (i.e. positive or negative) and is used when there is a clear

expectation about the direction of the effect. A direct positive hypothesis

predicts a positive relationship between variables.

for such more question on typically two-tailed.

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Answer:

c the right tail is longer than the left

Step-by-step explanation:

Answer:

Refer the attachment

SO, OPTION (D) IS CORRECT

Answer:

Option (D) is the correct answer

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Answer:

The value of n is 21.

Step-by-step explanation:

We are given that three of the exterior angle of the n-sided polygon are 50° each two of its interior angle are 127° and 135° and the remaining interior angle are 173 each.

As we know that the sum of all exterior angles of the polygon is 360°. Also, the number of remaining interior angles will be (n - 5).

And, the exterior angle = 180° - the interior angle.

So, according to the question;

\((3 \times 50) + (180-127) + (180 - 135) + (n - 5)\times (180-173) =360\)

150 + 53 + 45 + 7(n - 5) = 360

248 + 7n - 35 = 360

213 + 7n = 360

7n = 360 - 213

7n = 147

n = \(\frac{147}{7}\)

n = 21

Hence, the value of n is 21 and this is a 21-sided polygon.

Answer:

3x² + 3y² = 42

3 ( x² + y² ) = 42

x² + y² = 14

xy = -15 ( given )

(x-y)² = x² + y² - xy

14 - ( -15 )

14 + 15

29

The probability of choosing sausage and onion by Rosa's mom from the given 8 different toppings as per given condition is equal to

(1/ ⁸C₂).

As given in the question,

Total number of different toppings = 8

Number of different toppings choose by Rosa's mom randomly = 2

Possibility of choosing sausage and onion (any one) = 1

Total number of outcomes = ⁸C₂

Number of favorable outcomes = 1

Probability of choosing sausage and onion ( exactly ) one topping

= ( Number of favorable outcomes ) / ( Total number of outcomes )

= ( 1/⁸C₂ )

Therefore, the probability when Rosa's mom chooses sausage and onion out of 8 toppings is equal to ( 1/⁸C₂ ).

The above question is incomplete, the complete question is:

A pizza restaurant is offering a special price on pizzas with 2 toppings. They offer the toppings

below:

Pepperoni ,Sausage, Chicken ,  Green pepper , Mushroom ,Pineapple, Ham, Onion

Suppose that Rosa's favorite is sausage and onion, but her mom can't remember that, and she is going to randomly choose 2 different toppings.

What is the probability that Rosa's mom chooses sausage and onion?

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Answer:

1/8c^2

Step-by-step explanation:

Khan Acadmey

Answer:

A(-4.5;2) B(0;-3.5).......

Answer: 7%

(Hope this is right.)

Step-by-step explanation:

Let's solve this using the information we have and an equation.

Shane: $32,000 - (Given)

Theresa: 18,000+14x, if x=1,160 - (Given)

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

Step two: (Theresa) 14(1,160) =16,240 (Algebra)

Step three: (Theresa) 18,000+16,240=34,240 (Algebra, given.) - cost of Theresa's car.

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

Finally,

They're asking for how much more she paid for her car as a percentage of what Shane paid.

34,240-32,000=2,240 and

2,240/32,000=0.07

0.07x100=7

Answer 7% more than what Shane paid.

Answer:

$6

Step-by-step explanation:

False. assume condition one has two values, condition two has five values, condition three has three values, and condition four has two values; the number of rules required for the decision table is sixty.

The number of rules required for a decision table can be calculated by multiplying the number of values in each condition. In this case, condition one has two values, condition two has five values, condition three has three values, and condition four has two values. The total number of rules would be the product of these values: 2 x 5 x 3 x 2 = 60.

Therefore, the statement "the number of rules required for the decision table is sixty" is true.

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Answer:

Step-by-step explanation:

moving the two segments as in the figure I put, the perimeter doesn't change.

P = 2(length + breadth)

2 x (12 + 18) = 60 cm