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3 years ago

The sum of four consecutive even integers is 98. Which of the following equations represents this scenario?

Mathematics

2 answers:

aksik [14]3 years ago

6 0

Step-by-step explanation: To find out which of the following equations would represent the scenario of consecutive even integers, we need to understand what consecutive even integers are.

Consecutive even integers are integers but they are even so unlike consecutive integers, we skip 1 in between.

In the image provided, I have written on the whiteboard 3 numbers. If we use x to represent our first number, our second number can be represented as x + 2 and our third number can be x + 4.

In fact any 3 consecutive even integers can be represented as X + X + 2 + X + 4.

If we have four consecutive even integers, are setup will be the same but we will go one step further and add X + 6.

Since D deals with consecutive even integers, it would be our answer.

Helen [10]3 years ago

5 0

Answer:

Step-by-step explanation:

Since it's even consecutive integers, you can say that to find the integers you skip 2.

Therefore, you would have x+2, x+4, and x+6.

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Quadrilateral rust has a vertex (2,4). What are the coordinates of r' after a dilation of scale factor 3, centered at the origin

Digiron [165]

Answer:

The coordinates of r' are x = 10 and y = 12.

Step-by-step explanation:

The vertex experiments two operations: Dilation and translation, whose definitions are presented herein:

Dilation with respect to origin

$(x',y') = (0,0) + 3\cdot (x,y)$ , $\forall \,x,y \in \mathbb{R}$

Translation

$(x',y') =(x+4,y)$ , $\forall\,x,y\in \mathbb{R}$

If $x = 2$ and $y = 4$ , then:

1) $(2,4)$ Given.

2) $(0,0) + 3\cdot (2,4)$ Dilation with respect to origin.

3) $(6,12)$ Vectorial sum and scalar multiplication.

4) $(6+4,12)$ Translation.

5) $(10,12)$ Vectorial sum. Result.

The coordinates of r' are x = 10 and y = 12.

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3 years ago

From a standard deck of 52 cards, what is the probability of picking a Heart at random from the deck? A) 1 13 B) 1 26 C) 1 4 D)

monitta

Answer:

C 1/4

Step-by-step explanation:

13/52 = 1/4

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4 years ago

If the Banded Peak school bus travels 2530 km in 10 hours, what unit rate correctly identifies their speed?

prisoha [69]

Answer:

253 km per hour

Step-by-step explanation:

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3 years ago

Read 2 more answers

I need help please and thank you!

ziro4ka [17]

Answer:

v is 198 m/s

Step-by-step explanation:

$v = \sqrt{gh} \\ v = \sqrt{9.8 \times 4000} \\ v = 198 \: m {s}^{ - 1}$

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3 years ago

1. Suppose an online retailer has determined that if a potential customer spends more than 5 minutes on their site, that the pro

vredina [299]

Using the binomial distribution, it is found that there is a 0.056 = 5.6% probability that more than 7 will make a purchase.

<h3>What is the binomial distribution formula?</h3>

The formula is:

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$C_{n,x} = \frac{n!}{x!(n-x)!}$

The parameters are:

x is the number of successes.

n is the number of trials.

p is the probability of a success on a single trial.

In this problem:

There are 12 customers, hence n = 12.

The probability of any of them making a purchase is of p = 0.4.

The probability that more than 7 will make a purchase is given by:

P(X > 7) = P(X = 8) + P(X = 9) + P(X = 10) + P(X = 11) + P(X = 12).

Hence:

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 8) = C_{12,8}.(0.4)^{8}.(0.6)^{4} = 0.042$

$P(X = 9) = C_{12,9}.(0.4)^{9}.(0.6)^{3} = 0.012$

$P(X = 10) = C_{12,10}.(0.4)^{10}.(0.6)^{2} = 0.02$

$P(X = 11) = C_{12,11}.(0.4)^{11}.(0.6)^{1} \approx 0$

$P(X = 12) = C_{12,12}.(0.4)^{12}.(0.6)^{0} \approx 0$

Then:

P(X > 7) = P(X = 8) + P(X = 9) + P(X = 10) + P(X = 11) + P(X = 12) = 0.042 + 0.012 + 0.02 + 0 + 0 = 0.056.

0.056 = 5.6% probability that more than 7 will make a purchase.

More can be learned about the binomial distribution at brainly.com/question/24863377

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2 years ago