One lap around a dirt track is 1/3 mile. It takes Bryce 1/9 hour to ride one lap. What is Bryce's unit rate, in miles, around the track?

Final answer:

Negative exponents indicate the reciprocal of the base raised to the corresponding positive exponent. When multiplying or dividing with negative exponents, add or subtract them accordingly. In scientific notation, divide the coefficients and subtract the exponents to divide numbers.

Explanation:

Working with negative exponents is an essential skill in mathematics, where a negative exponent indicates the inverse or reciprocal of the base raised to the corresponding positive exponent. For example, 2-1 equals 1/2, which means that we are finding the reciprocal of 2. In operations involving exponents, such as multiplication and division, we follow certain rules with negative exponents:

When multiplying numbers, add the exponents (negative exponents included).

When dividing numbers, subtract the exponents (again, include negative exponents).

To convert a negative exponent into a positive one, take the reciprocal of the base with the corresponding positive exponent.

Here's an example of division in scientific notation: 106 ÷ 103 = 10(6-3) = 103. If you need to divide two numbers using scientific notation, you divide the coefficients and subtract the exponents.

Remember, a number like 3-4 is equivalent to 1/34, or 1 divided by 3 multiplied by itself four times. In general, negative exponents flip the base to the denominator, signifying a division rather than multiplication.

At the end of 1 year, the amount in the account will be $9860. At the end of 2 years, the amount in the account will be $11437.6. This is calculated using the formula for compound interest.

Lisa is placing $8500 in an account that pays 16% interest compounded annually. To solve for part (a) and part (b) which ask for the amount in the account at the end of 1 year and 2 years respectively, we use the formula for compound interest: A = P *(1 + r/n)^(nt).

Here, P is the principal amount ($8500), r is the annual interest rate (16% or 0.16 as decimal), n is the number of times that interest is compounded per unit t (n = 1 as it's compounded annually), and t is the time the money is invested for.

For (a), t = 1 year. Inserting these values into the formula, we get:

A = $8500 * (1 + 0.16/1)^(1*1) = $8500 * 1.16 = $9860.

Therefore, at the end of 1 year, the amount in the account will be $9860.

For (b), t = 2 years. Using the same formula, we get:

A = $8500 * (1 + 0.16/1)^(1*2) = $8500 * 1.16^2 = $11437.6.

Therefore, at the end of 2 years, the amount in the account will be $11437.6.

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The probability would be 16 over 100.

We can tell this because by the table, the number 3 was rolled 16 total times. You can state the probability by expressing with the number of times rolled over total times rolled. Since it was rolled a total of 100 times, we are left with 16/100.

Answer:

The probability would be 16/100

Step-by-step explanation:

I took the test and got it right!! :)

Answer:

Option B is the correct option.

Step-by-step explanation:

The Linear function is always in the form of y = mx + c

Where m defines the slope which is rate of change of y-values or change in y-values with the change in x-values.

Therefore, Option B is the correct option.

Answer:

The required inequality that shows the maximum number of packages is [tex]n\leq 67[/tex].

Step-by-step explanation:

Consider the provided information.

Each package weighs 3 pounds and Jacob weighs 99 pounds.

let n is the maximum number of package that Jacob can carry with himself in the elevator.

Thus, the total weight of Jacob while having n packages on the elevator is:

[tex]3n+99[/tex]

The elevator can carry a maximum of 300 pounds at a time, therefore.

[tex]3n+99\leq 300[/tex]

Now, subtract 99 from both sides and divide the obtained inequality with 3.

[tex]3n+99-99\leq 300-99[/tex]

[tex]3n\leq 201[/tex]

[tex]\frac{3n}{3}\leq \frac{201}{3}[/tex]

[tex]n\leq 67[/tex]

Thus, the Jacob can carry maximum 67 packages.

Hence, the required inequality that shows the maximum number of packages is [tex]n\leq 67[/tex].

Final answer:

To divide 55 by 2044, use long division. The quotient is 0.027.

Explanation:

To divide 55 by 2044, you can use long division. Here is the step-by-step process:

At this point, you have reached the end of the division process. The final quotient is 0.027 and there is no remainder. Therefore, 55 divided by 2044 is approximately 0.027.

Answer:  The required number of servings in 6 cups of yogurt is 9.

Step-by-step explanation:  We are given to find the number of [tex]\dfrac{2}{3}[/tex] cup servings in 6 cups of yogurt.

We will be using the UNITARY method to solve the given problem.

We have

Number of servings in [tex]\dfrac{2}{3}[/tex] cups of yogurt = 1.

So, the number of servings in 1 cup of yogurt will be

[tex]\dfrac{1}{\frac{2}{3}}=\dfrac{3}{2}.[/tex]

Therefore,  the number of servings in 6 cups of yogurt is given by

[tex]\dfrac{3}{2}\times6=9.[/tex]

Thus, the required number of servings in 6 cups of yogurt is 9.

The percentage of students who carry their laptops and use a backpack is 45%.

To find the percentage of students who carry their laptops and use a backpack, we need to subtract the percentage of students who carry neither a backpack nor laptop from the percentage of students who carry their laptops.

Given that 5% carry neither a backpack nor laptop, we can subtract this from the 50% who carry their laptops to find that 45% of students carry their laptops and use a backpack.

The two equations are:

g= w +8

g= w +2

^_^

Final answer:

After finding the total weight of beans based on the given percentages and difference in weight between red and black beans, we determine that there are 90 ounces of beans in the mixed bag.

Explanation:

The question asks us to find out how many ounces of beans are now in the bag of mixed beans, given certain percentages before and after mixing. We know that initially, 20% of the total beans are black, and the rest are red. After Mr. Lee transferred some red beans to the bag containing black beans, the bag contained 30% of the total number of beans.

To solve this, let's denote the total number of beans by T, the number of black beans by B, and the number of red beans by R. According to the information provided:

First, we use the initial conditions to write an equation for the total number of beans T. Since R is 180 ounces more than B:

T = B + R

T = B + (B + 180)

T = 2B + 180

Given that B is 20% of T, we can also write this as:

T = 2(0.20T) + 180

T = 0.40T + 180

We can now solve for T:

T - 0.40T = 180

0.60T = 180

T = 180 / 0.60

T = 300 ounces

Since we know that the mixed bag contains 30% of the total, we calculate 30% of 300 ounces:

30% of T = 0.30 x 300

30% of T = 90 ounces

Therefore, after transferring, there are 90 ounces of beans in the mixed bag.

Answer:

C) x=90°, y=24°

Step-by-step explanation:

The two sections into which A is split, are the same size as indicated. Sides AB and AC are the same length. Because of those reasons, it can be concluded that B and C are the same size.

The corners of a triangle adds up to 180°. For ΔABC:

[tex]A+B+C=180\\A+2(66)=180\\A=48[/tex]

y° is half of A:

∴y° = 24°

Now add up the corners of triangle ABD:

[tex]y+x+B=180\\24+x+66=180\\x=90[/tex]

∴x° = 90°

Answer: C (4,3)

Step-by-step explanation:

Answer:

28% and she increased by 5.75 inches. Hope this helped

Step-by-step explanation:

Line x =2 has undefined slope.

" Slope is defined as the ratio of the difference in the increase of  y-coordinates to the difference in the increase of  x-coordinates."

Formula used

Equation of the line

y = mx + c

c = y-intercept

m = slope

m = [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

According to the question,

1. y = 0

Compare it with standard equation of the line

y = 0x + 0

slope = 0

It is not a correct answer.

2. y =2

Compare it with standard equation of the line

y = 0x + 2

slope = 0

It is not a correct answer.

3. x= y

Compare it with standard equation of the line

y = 1x + 0

slope = 1

It is not a correct answer.

4. x=2

It is vertical line , x value remain constant.

Therefore,

[tex]x_{1}=2\\x_{2}=2[/tex]

Slope = [tex]\frac{y_{2}-y_{1}}{2-2}[/tex]

         = [tex]\frac{y_{2}-y_{1}}{0}[/tex]

Zero in the denominator therefore, undefined slope

Hence, line x =2 has undefined slope.

Learn more about slope here

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Final answer:

The line with an undefined slope is D. x = 2, which is a vertical line with a constant x-value for all points on the line.

Explanation:

The question asks which line has an undefined slope. An undefined slope occurs when a line is vertical since slope is defined as the change in y over the change in x, and in a vertical line the change in x is zero. Looking at the options given, the equation representing a vertical line is D. x = 2. This line is vertical because it has the same x-value for all points on the line, meaning there is no change in x as you move along the line, thus creating an undefined slope.

To find the approximate side length of a square game board with an area of 151 in², take the square root of 151.

To find the approximate side length of a square game board with an area of 151 in2, we can use the formula for the area of a square, which is length x width. Since all sides of a square are equal, we can represent the side length as 's'. So, s x s = 151. To find the side length, we can take the square root of 151, which is approximately 12.29 inches. Therefore, the approximate side length of the square game board is 12.29 inches.