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Which system of equations has infinitely many solutions? 4 x + 2 y = 5. Negative 4 x minus 2 y = 1. Negative 10 x + y = 4. 10 x minus y = negative 4. Negative 8 x + y = 2. 8 x minus y = 0. Negative x + 2 y = 6. 7 x minus 2 y = 12.

Answers

Answer 1

Answer:

Answer:

$\left \{ {{-10x+y=4} \atop {10x-y=-4}} \right.$

Step-by-step explanation:

Which system of equations has infinitely many solutions?

4 x + 2 y = 5 // -4x - 2y = 1

-10x + y = 4 // 10x - y = -4.

-8x + y = 2 // 8x-y = 0.

-x + 2 y = 6 // 7x-2y = 12.

It's important to know that a linear system of equations has infinitely many solutions when both equations represents the same line, that means one line is on top of the other one, that's why the shared infinite points.

In this case, notice that if we compare the second system, you would find that both equations are the same,

$\left \{ {{-10x+y=4} \atop {10x-y=-4}} \right.$

If we multiply the first equation by -1

$\left \{ {{10x-y=-4} \atop {10x-y=-4}} \right.$

Which means the system has infinitely many solutions, because both equations represent the same line, so the shared all possibles points.

Therefore, the right answer is the second choice.

Answer 2

Answer:

Answer:

Step-by-step explanation:

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Consider an unreliable communication channel that can successfully send a message with probability 1/2, or otherwise, the message is lost with probability 1/2. How many times do we need to transmit the message over this unreliable channel so that with probability 63/64 the message is received at least once? Explain your answer. Hint: treat this as a Bernoulli process with a probability of success 1/2. The question is equivalent to: how many times do you have to try until you get at least one success?

Answers

Answer:

6 times we need to transmit the message over this unreliable channel so that with probability 63/64.

Step-by-step explanation:

Consider the provided information.

Let x is the number of times massage received.

It is given that the probability of successfully is 1/2.

Thus p = 1/2 and q = 1/2

We want the number of times do we need to transmit the message over this unreliable channel so that with probability 63/64 the message is received at least once.

According to the binomial distribution:

$P(X=x)=(n!)/(r!(n-r)!)p^rq^(n-r)$

We want message is received at least once. This can be written as:

$P(X\geq 1)=1-P(x=0)$

The probability of at least once is given as 63/64 we need to find the number of times we need to send the massage.

$(63)/(64)=1-(n!)/(0!(n-0)!)(1)/(2)^0(1)/(2)^(n-0)$

$(63)/(64)=1-(n!)/(n!)(1)/(2)^(n)$

$(63)/(64)=1-(1)/(2)^(n)$

$(1)/(2)^(n)=1-(63)/(64)$

$(1)/(2)^(n)=(1)/(64)$

By comparing the value number we find that the value of n should be 6.

Hence, 6 times we need to transmit the message over this unreliable channel so that with probability 63/64.

Gavin bought 3 pizzas for a party. Each pizza had 8 slices. There were 8 other people at the party. Everyone ate the same number of slices. How many slice did each person eat? How many slices were left over

Answers

Answer:

everyone ate 3 slices

no slices were left

Step-by-step explanation:

3 times 8 =number of slices

24=number of slices

everyone (8 people) ate the same number of slices

24/8=3

3 slices per person.
no slices left over

Two brothers, Mark and Steven, each inherit $45000. Mark invests his inheritance in a savings account with an annual return of3.2 %, while Steven invests his inheritance in a CD paying 4.5 % annually. How much more money than Mark does Steven have after

1 year?

Answers

Answer:

Steven ears $565 more in one year.

Step-by-step explanation:

Giving the following information:

Mark:

PV= $45,000

n= 1

i= 0.032

Steven:

PV= $45,000

n= 1

i= 0.045

To calculate the Future Value of each investment, we need to use the following formula:

FV= PV*(1+i)^n

Mark:

FV= 45,000*1.032= $46,440

Steven:

FV= 45,000*1.045= $47,025

Difference= 47,025 - 46,440= $565

Steven ears $565 more in one year.

Final answer:

After investing their inheritance for one year, Steven has $585 more than Mark due to the higher interest rate of his investment.

Explanation:

After one year, the amount of money Mark and Steven have can be calculated using the formula for compound interest, which is P(1 + r) to the power of n, where P is the principal amount, r is the annual interest rate, and n is the time in years. So, Mark's future value would be $45000(1 + 0.032) = $46440. In contrast, Steven's future value would be $45000(1 + 0.045) = $47025. Therefore, Steven has $47025 - $46440 = $585 more than Mark after 1 year.

Learn more about Compound Interest here:

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Answers

Answer:

2000

Step-by-step explanation:

If 3 days = 600 we need to know what 1 day is so we do 600 / 3

600 / 3 = 200

Then multiply 200 by 10 to find 10 days

200 * 10 = 2000

10 days = 2000

A recipe for orange water says, “Mix 3 teaspoons of yellow water with 1 teaspoon red water.” For this recipe, we might say: “The ratio of teaspoons of yellow water to teaspoons of red water is 3:1.” 1. Write a ratio for 2 batches of this recipe. 2. Write a ratio for 4 batches of this recipe

Answers

Well, we know that 3:1 is one batch of orange water. We also know that there are 2 things to focus on.

1. Must write ratio for 2 batches of the recipe.

2. Must write ratio for 4 batches of the recipe.

To make this equation simple, double the ratio to find 2 batches because all it means is 2x more water.

3:1

6:2

So, the ratio would be 6:2 to make 2 batches.

To make it easier again, we just multiply the ratio of 2 batches by 2 which would find the ratio for 4 batches.

6:2

12:4

So that means, that it is 6:2 for 2 batches, and 12:4 for four batches.

Answer:

its c

Step-by-step explanation:

i did the test

There are several different types of charts and graphs. Each type of chart and graph has required elements. What required elements should be present on a bar chart for it to be complete and accurate? A. An appropriate title
B. The horizontal axis should be labeled
C.The vertical axis should be labeled
D.All of the above
E.None of the above.

Answers

The correct answer is D. All of the above

Explanation:

A bar chart is a type of graph that presents information by using bars; these bars show the relationship between two factors or variables presented in the Y or vertical axis and the X or horizontal axis. For example, you might present the time 5 students spend doing homework by including the hours on the Y-axis and the name of each student on the X-axis.

In this context, for the reader to understand the information presented in the graph it is essential that each of the axes is labeled, in this way the reader will know which variables or factors are represented. Also, in most cases, you will an appropriate title that introduces the general situation that is presented. Thus, for a bar chart to be accurate you will need all of the above.

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