The map shows the length of two trails used for a race around a lake. What is the total distance of the race?

A trail race map. One part of the race is 3.21 miles and the other part of the race is 5.7 miles.
What are the steps you would follow to solve this problem?

Answer:

Step-by-step explanation:

To graph the points you first will start with the first line plotting the b (+6) and then do your slope (-5x) which is rise over run. then repeat for the next line. This is what it should look like...

Answer:

f(x) = 1(x - 4)^2 - 2

Step-by-step explanation:

Recall that the vertex form of the equation of a parabola is

f(x) = a(x - h)^2 + k, where (h, k) is the vertex and a is a scale factor which stretches or compresses the graph vertically.

Looking carefully at the graph, we see that h must be 4 and k must be -2.

Thus, the equation of this parabola is f(x) = 1(x - 4)^2 - 2 (which matches Answer B)

Answer:

It's 38.

Step-by-step explanation:

the sum of three consecutive even integers is 108, the largest number in the sequence would be 38.

I hope this helps you!

Answer:

We can use algebra to solve this problem. Let's call the smallest of the three consecutive even integers x. Since the integers are consecutive and even, the next two integers will be x+2 and x+4.

The problem states that the sum of three consecutive even integers is 108, so we can write an equation:

x + (x+2) + (x+4) = 108

We can simplify this equation by combining like terms:

3x + 6 = 108

3x = 102

x = 34

So, the smallest of the three consecutive even integers is 34.

The next two integers will be x+2 = 34+2 = 36 and x+4 = 34+4 = 38

The largest number of the three consecutive even integers is x+4 = 38.

Answer:

b

Step-by-step explanation:

We can simplify expressions by combining like terms.

\((3x^2+7)+ (x^2 +2)\)

⇒ Open up the parentheses:

\(3x^2+7+x^2+2\)

⇒ Notice how there are two x² terms and two constants. We can combine these by adding them up:

\(4x^2+9\)

C: True. The accounting equation, which is the foundation of all accounting principles, is based on the concept that for every debit entry, there must be an equal credit entry. This principle is reflected in T-accounts, which are used to track the financial transactions of a business.

T-accounts are a visual representation of the accounting equation, where debits are recorded on the left side of the T-account and credits are recorded on the right side. The sum of the debits and credits for each account is calculated and displayed at the bottom of the T-account.

If the sum of debits is not equal to the sum of credits, it indicates that an error has occurred in the recording of financial transactions. This is known as an unbalanced entry, and it must be corrected before the financial statements can be prepared accurately.

Therefore, it is always true that across all T-accounts, the sum of debits must equal the sum of credits. This principle ensures that the accounting records are accurate and reliable, providing stakeholders with a clear and complete picture of a company's financial position.

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A 40 gram sample of a substance that’s used for drug research has a k-value of 0.1472. The substance's half-life, in days, is approximately 4.7 days.

The half-life of a substance is the time it takes for half of the substance to decay or undergo a transformation. The half-life can be determined using the formula:

t = (0.693 / k)

where t is the half-life and k is the decay constant.

In this case, we are given that the sample has a k-value of 0.1472. We can use this value to calculate the half-life.

t = (0.693 / 0.1472) ≈ 4.7 days

Therefore, the substance's half-life, rounded to the nearest tenth, is approximately 4.7 days.

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Answer:

50 km/hr

Step-by-step explanation:

D = RT

Time for first part of trip = 80/60 = 4/3 hr.

Time for second part of trip = 20/30 = 2/3 hr.

total time for entire trip = 4/3 + 2/3 = 6/3 = 2 hr.

Total distance = 100 km

Average rate of speed for entire trip = 100/2 = 50 km/hr

Answer:

Step-by-step explanation:

We divide the number by 8 and write the remainder in reverse order to get the equivalent octal number.

Answer:

Let's write down the base of each one:

- Decimal is base 10 (0 to 9)

- Octal is base 8 (0 to 7)

So, if we want to convert decimal to octal, we need to divide the decimal number by 8 and hold onto the remainder.

Then once your quotient becomes 0, from the last remainder to the first, write your numbers.

For example here is 437 base 10.

437 / 8 = 54 R 5

54 / 8 = 6 R 6

6 / 8 = 0 R 6

So, the answer is 665 base 8.

Answer

i would be 1 becuase there is a little spot and it will be 1

Step-by-step explanation:

Answer:

views

Step-by-step explanation:

you could replace glimpses with views

Answer: D

Step-by-step explanation: "Views"

Answer:

48

Step-by-step explanation:

Answer: 545.9

Step-by-step explanation:

637.1 - 91.2 = 545.9

Sorry that I couldn't explain more, but i hope this helps!

Also if it's right could you mark me as brainliest? I need 1 more to level up

Answer: 2.47

Step-by-step explanation:

6 times 3.99 is 23.94

31.24 minus 23.94 is 7.30

2.47 times 3 is 7.30

Answer:

2.5 hours

Step-by-step explanation:

Rember the equation, Time * Speed = Distance,

or for simplicity, T * S = D.

It is known that:

Grants's speed = 700 km/h

Grant's time = x (hours)

Darrin's speed = 500 km/h

Darrin's time = x +1 (hours)

*x+1 because Darrin left an hour before aGrant*

This mean's that

Darrin's distance: 500 km/h * (x+1) hours

Grant's distance: 700 km/h * x hours

Since they both have traveled the same distances then the equations will have to equal each other.

500km/h * (x+1) hours = 700 km/h * x hours

simplify and solve.

500x + 500 = 700x

500 = 200x

5/2 = x

2.5hours = x

Answer:

140,000

Step-by-step explanation:

We know that the number is 143,699.

We are asked to round to the nearest ten thousand, which is the number bolded:

143,699

This means we have to look at the number to the right of the 4, which is 3.  If this number is below "5", then we round down to get 140,000.  

If this number was (and it's NOT) above "5" or "5" itself, we would round up to 150,000.  

Since "3" is below "5", we would round down to 140,000.

Hope this helps! :)

Answer:

To solve this problem, we need to first find the numbers that are multiples of 4 or 6 between 1 and 15, inclusive.

Multiples of 4: 4, 8, 12

Multiples of 6: 6, 12

The number 12 is a multiple of both 4 and 6, so we only count it once.

So, there are a total of 4 possible outcomes that meet the condition of being a multiple of 4 or 6.

Therefore, the probability of getting a multiple of 4 or 6 is:

P(multiple of 4 or 6) = 4/15

Answer: 4/15.

Hope This Helps!

The option √37 < 6.1 < \(\rm \tfrac{45}{7}\) shows the numbers in order from least to greatest. Thus option B is correct.

Ascending οrder refers tο the arrangement οf numbers in which the smallest number cοmes befοre the largest. The numbers are listed in this fashiοn in ascending οrder. It is ideal fοr the first number tο be less than the secοnd. Descending οrder refers tο arrange the integers frοm largest tο least value.

Lets find οut the decimal values οf all the numbers:

√37 ≈ 6.082763

6.1 is just already at decimal value

\($\rm \frac{45}{7} = 6. 428571\)

Now, as we have

6.082763 < 6.1 <  6. 428571

We can conclude that , √37 < 6.1 < \(\rm \tfrac{45}{7}\) shows the numbers in order from least to greatest.

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We are given that fifteen boys and fifteen girls entered a drawing for four free movie tickets. We want to find the probability that all four tickets were won by girls.

To solve this problem, we need to consider the total number of possible outcomes and the number of favorable outcomes.

Total number of outcomes:

The total number of outcomes represents all the possible ways to choose four winners from the thirty participants (boys and girls). We can calculate this using the combination formula:

C(30, 4) = 30! / (4!(30 - 4)!) = 27,405

Here, C(n, r) represents the combination of choosing r objects from a set of n objects.

Favorable outcomes:

We want to determine the number of ways to select all four winners from the group of fifteen girls. This can also be calculated using the combination formula:

C(15, 4) = 15! / (4!(15 - 4)!) = 1365

Probability calculation:

The probability is the ratio of the favorable outcomes to the total number of outcomes. So, we divide the number of favorable outcomes by the total number of outcomes:

P(Girls winning all four tickets) = 1365 / 27,405

Simplifying the fraction, we find:

P(Girls winning all four tickets) = 1 / 20

Therefore, the probability that all four tickets were won by girls is 1/20.

In summary, out of all the possible combinations of selecting four winners from the thirty participants, only one out of every twenty combinations will result in all four tickets being won by girls.

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The probability that an individual reaches age 100 is 0.000001.

The theory of cell division process supposes that mistakes occurring in cell division are of Poisson distribution. The given Poisson parameter is 2.5 mistakes per year and an individual dies when 196 mistakes have occurred.

Let X denote the number of mistakes before an individual dies.

(a) The mean lifetime of an individual. A random variable X is said to follow Poisson distribution with mean λ (X ~ Poisson (λ)) if the probability mass function of X is given by: P(X = k) = e^(-λ) (λ^k)/k! Here, rate = 2.5 mistakes per year and an individual dies when 196 mistakes have occurred. Therefore, λ = rate x time = 2.5 mistakes/year × T years = 196 mistakes. T = 196/2.5 = 78.4 years. The mean lifetime of an individual is given by: μ = E(X) = λ = 78.4 years.  

(b) The variance of the lifetime of an individual. The variance of a Poisson distribution is given by: Var(X) = λ. Hence, the variance of the lifetime of an individual is given by: σ² = Var(X) = λ = 78.4 years

(c) .The probability that an individual dies before age 67.2Let Y denote the lifetime of an individual. The number of mistakes before an individual dies is given by X. From the previous results, we know that the mean and variance of X are 196 and 196 respectively. Let y = 67.2 be the age of the individual. We have to find the probability that the individual dies before y. In other words, we need to find P(Y < y). P(Y < y) = P(X < 196/y) = P(X < 196/67.2) = P(X < 2.9137) = 0.9868 approximately

(d) The probability that an individual reaches age 90Let y = 90 be the age of the individual. We have to find the probability that the individual reaches 90 years. In other words, we need to find P(Y ≥ y). P(Y ≥ y) = P(X ≥ 2.5 × 90) = P(X ≥ 225) = 1 - P(X < 225) = 1 - P(X ≤ 224). From Poisson distribution tables, we get:P(X ≤ 224) = 0.9993 approximately. Therefore, P(X ≥ 225) = 1 - P(X ≤ 224) = 1 - 0.9993 = 0.0007 approximately.

(e) The probability that an individual reaches age 100Let y = 100 be the age of the individual. We have to find the probability that the individual reaches 100 years. In other words, we need to find P(Y ≥ y). P(Y ≥ y) = P(X ≥ 2.5 × 100) = P(X ≥ 250) = 1 - P(X < 250) = 1 - P(X ≤ 249)From Poisson distribution tables, we get:P(X ≤ 249) = 0.999999 approximately.

Therefore, P(X ≥ 250) = 1 - P(X ≤ 249) = 1 - 0.999999 = 0.000001 approximately

Therefore, the probability that an individual reaches age 100 is 0.000001.

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361πkm²

• the formula to find the area of a circle is A=πr²

Answer:

The height is 6.3

Step-by-step explanation:

Pythagorean Theorm: a² + b² = c²

5² + b² = 8²

25 + b² = 64

b² = 39

b = 6.2449979984

Answer:

\(x=\frac{-3d-9}{k-d}\)

Step-by-step explanation:

Step 1: Write out equation

d(-3 + x) = kx + 9

Step 2: Distribute

-3d + dx = kx + 9

Step 3: Subtract dx on both sides

-3d = kx - dx + 9

Step 4: Subtract 9 on both sides

-3d - 9 = kx - dx

Step 5: Factor

-3d - 9 = x(k - d)

Step 6: Divide both sides by k - d

\(x=\frac{-3d-9}{k-d}\)

Answer:

Step-by-step explanation:

Step 1: Write out equation

d(-3 + x) = kx + 9

Step 2: Distribute

-3d + dx = kx + 9

Step 3: Subtract dx on both sides

-3d = kx - dx + 9

Step 4: Subtract 9 on both sides

-3d - 9 = kx - dx

Step 5: Factor

-3d - 9 = x(k - d)

Step 6: Divide both sides by k - d

The probability that a student chosen at random has a cat or a dog is; P(cat or dog) = 22/25.

What is probability?

Probability is that the branch of arithmetic regarding numerical descriptions of however probably an incident is to occur, or however probably it's that a proposition is true. The likelihood of an incident could be a range between 0 and 1.

Main body:

According to the question, the total number of students is; 25.

15 of them have a cat

16 of them have a dog

while, 3 of them have neither

where, x = number if students who own a cat and a dog.

Consequently, the total number of students who own a cat, a dog, both or neither is as follows;

15-x + x + 16-x + 3 = 25.

-x = 25 - 34

In essence, x = 9

the number of students who own a cat and a dog is 9.

Therefore, probability that a student chosen at random has a cat and a dog is therefore;

P(cat and dog) = 9/25.

Therefore probability that a student chosen at random has a cat or a dog is 22/25.

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Answer:

Plane RAT

Step-by-step explanation:

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ANSWER

EXPLANATION

We want to find the solution to the system of equations given, using the graph.

On a graph, the solution of a system of equations is the point where the lines of the two equations intersect one another. This means that the ordered pair made up of the x and y coordinates of the point where the two lines meet is the solution to the system of equations.

Therefore, going by that, the solution to the given system of equations is: