g(x) = 56/(2x)^3
Express g(x) as a power function, g(x) = kx and determine the constants k and p.

Answer:

487

Step-by-step explanation:

We can use this formula to find the 60th term:

8n+7

a) The amount of water in the pool after 2 hours can be calculated using the equation.

Water in pool = 10L/hour × 2 hours = 20L.

b) The pool will be 80L when the equation is satisfied: 80L = 10L/hour × Time.

Solving for Time, we find Time = 8 hours.

c) Part b) is linear.

a) To calculate the amount of water in the pool after 2 hours, we can use the equation:

Water in pool = Water filling rate × Time

Since the pool gets filled up with 10L of water per hour, we can substitute the values:

Water in pool = 10 L/hour × 2 hours = 20L

Therefore, after 2 hours, there will be 20 liters of water in the pool.

b) To determine the number of hours it takes for the pool to reach 80 liters, we can set up the equation:

Water in pool = Water filling rate × Time

We want the water in the pool to be 80 liters, so the equation becomes:

80L = 10 L/hour × Time

Dividing both sides by 10 L/hour, we get:

Time = 80L / 10 L/hour = 8 hours

Therefore, it will take 8 hours for the pool to contain 80 liters of water.

c) Part b) is linear.

The equation Water in pool = Water filling rate × Time represents a linear relationship because the amount of water in the pool increases linearly with respect to time.

Each hour, the pool fills up with a constant rate of 10 liters, leading to a proportional increase in the total volume of water in the pool.

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According to the question the width of the running track is 5 feet.

The boundary of a circle is measured by its circumference or perimeter, which determines the amount of space it occupies. The circumference of a circle is the length of the circle when it is "unrolled" and measured as a straight line, and it is typically measured in units such as centimeters or meters.

The circumference of a circle is given by the formula \(C = 2\pi r\), where r is the radius. Using this formula for the two circles, we have:

\(C_1 = 2\pi r_1\\C_2 = 2\pi r_2\)

The problem states that the circumferences of the two circles differ by \(10\pi\) feet, which can be written as:

\(C_1 - C_2 = 10\pi\)

Substituting the formulas for \(C_1\) and \(C_2\), we get:

\(2\pi r_1 - 2\pi r_2 = 10\pi\)

Simplifying, we get:

\(2\pi (r_1 - r_2) = 10\pi\\r_1 - r_2 = \frac{10\pi}{2\pi} = 5\)

Therefore, the width of the running track is 5feet.

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Answer:

I believe the answer is A

Step-by-step explanation:

three times x can be equal to, but never greater than -6

Answer:

A. 3x ≤ -6

Step-by-step explanation:

the sentence ‘3x is at most -6

means that the most 3x is allowed to be is -6

it can be -6 or any number less than -6

So, the phrase 3x is at most -6

’ means ‘

3x ≤ -6

The speed of the truck is higher (or lower) than the speedometer value  

when a larger (or smaller) than standard sized tire.

Responses:

The standard tire size diameter = 25.7 inches

Diameter of the replacement tire = 28.2 inches

Circumference of the standard tire = π·25.7 inches

1 mile = 63,360 inches

65 miles = 65 × 63,360 inches

\(Number \ of \ rotation =\dfrac{63,360 \times 65}{\pi \times 25.7} \approx \mathbf{ 51,008.85}\)

Distance travelled by the replacement tire with the same number of

rotations is therefore;

\(Distance =\dfrac{63,360 \ in. \times 65}{\pi \times 25.7 \ in.} \times \pi \times 28.2 \ in. \approx \mathbf{4519022.6\ in.}\)

Actual distance travelled in one hour = 4519022.6 ÷ 63,360 ≈ 71.32

Second part; Tire diameter = 24 inches

Distance traveled in one hour = 51,008.85 × π × 24 ≈ 3845976.68

Distance traveled in one hour ≈ 3845976.68 inches

3845976.68 inches ≈ 60.7 miles

The actual speed if a 24 inch tire is used is approximately 60.7 mph

Details of the truck speed with different sized wheels

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Answer:

C

Step-by-step explanation:

3,4,5. This is just one of basic sets in Pythagoras theorem. If you want to check do A^2+B^2=C^2 (c is the biggest number in your set)

9+16=25 (3,4,5 set) this its a right triangle

The equivalent radian measure for 45° is approximately 0.7854 radians, and the equivalent degree measure for 45° is 45°.

To find the equivalent degree measure or radian measure for 45° using the proportion d / 180° = r radians / π radians, we can solve for the missing variable.

Let's denote the degree measure as d and the radian measure as r. We are given that 45° is the degree measure we want to convert.

Plugging the values into the proportion, we have:

45° / 180° = r radians / π radians

Simplifying the equation:

0.25 = r / π

To solve for r, we can cross-multiply:

r = 0.25 * π

Using the value of π (pi) approximately equal to 3.14159, we can evaluate the expression:

r ≈ 0.25 * 3.14159

r ≈ 0.7854

Therefore, the equivalent radian measure for 45° is approximately 0.7854 radians.

To find the equivalent degree measure, we can rearrange the proportion and solve for d:

d / 180° = 0.7854 radians / π radians

Cross-multiplying:

d = 180° * 0.7854 / π

Using the value of π (pi) approximately equal to 3.14159:

d ≈ 180° * 0.7854 / 3.14159

d ≈ 45°

Hence, the equivalent degree measure for 45° is 45° itself.

In summary, the equivalent radian measure for 45° is approximately 0.7854 radians, and the equivalent degree measure for 45° is 45°.

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Answer:

A

Step-by-step explanation:

Answer:

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

Each coordinate of the midpoint is the average of endpoints:

Therefore M is (13, 14).

354 Valencia student tickets and 133 non-student tickets were sold.

Let's use algebra to solve the problem. Let

x be the number of Valencia student tickets sold

y be the number of non-student tickets sold

We know that

x + y = 487 (the total number of tickets sold is 487)

14x + 25y = 8391 (the total receipts from ticket sales is $8391)

We can use the first equation to express one of the variables in terms of the other. For example, we can solve for y

y = 487 - x

Here we have to use the substitution method, we can then substitute this expression for y into the second equation

14x + 25(487 - x) = 8391

Simplifying and solving for x

14x + 12275 - 25x = 8391

-11x = -3884

x = 354

So, 354 Valencia student tickets were sold. We can use the first equation to find y

x + y = 487

354 + y = 487

y = 133

So, 133 non-student tickets were sold.

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Answer:

Answer:

0.3643

Step-by-step explanation:

Standard Form and Scientific Notation

What is standard form of numbers?

Standard form is the normal way of writing numbers no matter how big or small the number is.

Examples:

15,000,000

0.0000000678

What is scientific notation?

Scientific notation is a different way of expressing numbers. It is a short way of expressing very big numbers or very small numbers. It is also known as exponential form. Scientific notation is written as the product of a number and a power of 10.

Examples:

1.3 × 10⁶

34.5 × 10^⁻9

Going back to the question above, we need to convert the given scientific notation to its standard form.

Converting of Scientific Notation to Standard Form

To convert a number from scientific notation to standard form, move the decimal point.

The exponent tells the direction and the number of times we need to move the decimal point.

The positive exponent indicates a large number so we need to move the decimal point to the right.

The negative exponent indicates a small number so we need to move the decimal point to the left.

Do not write the power of 10 anymore.

Solution:

Now, let us convert 3.643 x 10^-1 in standard form.

The exponent is negative 1 so we will move the decimal point to the left once.

3.643 = 0.3643

Jake will have traveled 36 miles in his boat after 3 hours at a speed of 12 mph.

What is Distance?

Distance is defined as the space between two points in space.

To find out how far Jake will have traveled after 3 hours, we can use the formula:

distance = speed x time

where speed is the rate at which Jake is traveling and time is the duration of the travel. In this case, the speed is 12 mph and the time is 3 hours.

So, the distance traveled after 3 hours is:

distance = 12 mph x 3 hours = 36 miles

Therefore, Jake will have traveled 36 miles in his boat after 3 hours at a speed of 12 mph.

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The likelihood that they won't buy any books during this trip to the bookstore is O.1250 or 12.5%.

How does probability work?

Probability is a branch of mathematics that deals with numerical representations of the likelihood of an event occurring or of a proposition being true. The probability of an event is a number between 0 and 1, with 0 approximately denoting impossibility and 1 denoting certainty.

The suitable response is:

Let P(J) =  John is unlikely to buy any books.

Let P(B) = Beth is unlikely to buy any books.

P( J n B ) will be;

There is a 0% chance that John and Beth will each buy 0 books, making a total of 0 books bought.

Since, the decisions to buy books are two independent actions,

P(J n B) = P(J) * P(B)

P(J) = 0.5

P(B) = 0.25

P(J n B) = 0.5 * 0.25 

P(J n B) = 0.125 or 12.5%

Therefore, there is 12.5% chance that they will purchase no books on this visit to the bookstore.

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The fractions to show the value of each 9 in the decima 0.999 are 9/10, 9/100, 9/1000.

To write the fraction that shows the value of each 9 in the decimal 0.999, we can use the following method

The digit 9 in the tenths place represents 9/10 or 0.9.

The digit 9 in the hundredths place represents 9/100 or 0.09.

The digit 9 in the thousandths place represents 9/1000 or 0.009.

Thus, the fractions are

0.9 = 9/10

0.09 = 9/100

0.009 = 9/1000

The value of the 9 on the left is related to the value of the 9 in the middle by a factor of 10.

The value of the 9 on the right is related to the value of the 9 in the middle by a factor of 10, so the 9 on the right is one-tenth the value of the 9 in the middle.

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Answer:

the answer is \(\frac{5}{6}\)÷\(\frac{1}{12}=10\)

Step-by-step explanation:

Answer:

9:15 or 3:5

Step-by-step explanation:

A ratio can compare a part of a whole to a whole.

In this case, our whole is the total number of shots attempted: 15.

The basketball player successfully made 9 of the attempts. 9 is our other number in this ratio.

Put these values in a ration.

part:whole

9:15

Notice that 9 and 15 can be simplified by dividing both numbers by 3.

3:5

This is your simplified ratio.

Hope this helps!

This triangle is not a right triangle because the sum of the squares of the two smaller sides is not equal to the square of the largest side.

To determine if a triangle is a right triangle, you can use the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the two smaller sides is equal to the square of the largest side.

In this case, we can compare the squares of the sides with lengths of 33 km and 72 km, and the square of the side with length 78 km:

33^2 + 72^2 = 5184 + 5184 = 10368

78^2 = 6084

Since 10368 is not equal to 6084, we can conclude that this triangle is not a right triangle.

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Answer:

https://www.townandcountrymag.com/style/beauty-products/g32747256/most-expensive-perfumes/

$12,721.8900000 is 7 decimal places value and  $12,721.89 is 7 significant figures,

A number system is defined as a system of writing to express numbers.

$12,721.8900000 is given to 7 decimal places, meaning there are 7 digits to the right of the decimal point.

This level of precision is useful in some scientific calculations where very small differences can be significant.

$12,721.89 is 7 significant figures, meaning there are 7 digits that are meaningful and the rest are placeholders.

This level of precision is often used in financial calculations where a high level of accuracy is important but excessive precision is not necessary.

Hence, $12,721.8900000 is 7 decimal places value and  $12,721.89 is 7 significant figures,

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If a categorical variable that can take the values from the set {Red, Blue, Green, Yellow} is included as an independent variable in a linear regression, the number of dummy variables that are created is two

When a categorical variable that has n categories is to be included as an independent variable in a linear regression analysis, it must be converted to n - 1 dummy variables. The reason for this is that including all n categories as dummy variables would cause perfect multicollinearity in the regression analysis, making it impossible to estimate the effect of each variable.In this case, the set of categories {Red, Blue, Green, Yellow} has four categories. As a result, n - 1 = 3 dummy variables are required to represent this variable in a linear regression. This is true since each category is exclusive of the others, and we cannot assume that there is an inherent order to the categories.The dummy variable for the first category is included in the regression model by default, and the remaining n - 1 categories are represented by n - 1 dummy variables. As a result, the number of dummy variables that are required to represent the categorical variable in the regression model is n - 1.

Thus, if a categorical variable that can take the values from the set {Red, Blue, Green, Yellow} is included as an independent variable in a linear regression, the number of dummy variables that are created is two .

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Answer:

see below

Step-by-step explanation:

Assuming that

Point A is the same as point X

Point B is Point Y

Point C is Point Z

So we have

\(X=(1,5)\\\\Y=(2,2)\\\\Z=(6,1)\)

the rule for a rotation of 180° is

For 180 degrees, the rule is (a, b) --------> (-a, -b)

so we have

\(X'=(-1,-5)\\\\Y'=(-2,-2)\\\\Z'=(6,1)\)

the rule for reflection across the x axis

(a,b)----->(a,-b)

so we have

\(X''=(1,-5)\\\\Y''=(2,-2)\\\\Z''=(6,-1)\)

x = −30 and x = 50 , Absolute value equation into two separate equations, one with the positive expression and one with the negative expression

To solve for x, we first need to isolate the absolute value expression on one side of the equation. We start by adding 6 to both sides of the equation:
|1/5(x+2)| - 6 = 2
This gives us:
|1/5(x+2)| = 8
Next, we can split this absolute value equation into two separate equations, one with the positive expression and one with the negative expression:
1/5(x+2) = 8  OR  1/5(x+2) = -8
We can then solve for x in each equation separately. Starting with the positive expression:
1/5(x+2) = 8
Multiplying both sides by 5, we get:
x+2 = 40
Subtracting 2 from both sides, we get:
x = 38
Now solving for the negative expression:
1/5(x+2) = -8
Multiplying both sides by 5, we get:
x+2 = -40
Subtracting 2 from both sides, we get:
x = -42

So our two solutions are x = -42 and x = 38. However, we need to check our answers to make sure they satisfy the original equation. Plugging in x = -42 gives us:
|1/5(-42+2)| - 6 = 2
Simplifying the expression inside the absolute value, we get:
|(-40/5)| - 6 = 2
Simplifying further, we get:
8 - 6 = 2

2 = 2 (True)
Therefore, x = -42 is a valid solution. Next, plugging in x = 38 gives us:
|1/5(38+2)| - 6 = 2
Simplifying the expression inside the absolute value, we get:
|(40/5)| - 6 = 2
Simplifying further, we get:
8 - 6 = 2
2 = 2 (True)
Therefore, x = 38 is also a valid solution.

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a. The sample space of this experiment would be as follows:S = {A, B, AB, O}Where A is for phenotype A, B is for phenotype B, AB is for phenotype AB, and O is for phenotype O.

b. The probability of each phenotype is as follows: P(A) = 0.41, P(B) = 0.10, P(AB) = 0.04,P(O) = 0.45

c. The probability that the person chosen at random has either type A or type AB blood is 0.45 or 45%.

a. The sample space of this experiment would be as follows:S = {A, B, AB, O}Where A is for phenotype A, B is for phenotype B, AB is for phenotype AB, and O is for phenotype O.

b. Given, the proportion of blood phenotypes, A, B, AB and O, in the population of all Caucasians in the United States are approximately, 0.41, 0.10, 0.04, and 0.45, respectively.

Then the probability of each phenotype is as follows:

P(A) = 0.41 P(B) = 0.10 P(AB) = 0.04 P(O) = 0.45

c. The probability that the person chosen at random has either type A or type AB blood is:

P(A) + P(AB) = 0.41 + 0.04 = 0.45

Therefore, the probability that the person chosen at random has either type A or type AB blood is 0.45 or 45%.

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Answer:

    7 13

  283

+  167

--------

116

Step-by-step explanation

Answer:

for every 5 units to the right, there is 1 unit up

the slope is y = 1/5

Answer:

The answer is 2:1 because ratio is just like simple division

Answer:

I'm pretty sure the answer is B

Step-by-step explanation:

sorry if I'm wrong

f(-2) and f(2) does not exist. Limit when x tend to -2, 0 and 4 does not exist. f(0) = 5 and f(4) = -1. Limit when x tend to 2 converges to 0.5.

f(-2) does not exist as shown in the figure there is no definite value at -2. Also limit does not exist at x = -2 as right limit approaches positive infinity where left limit approaches negative infinity.

f(0) equals 5 and not 3.5 as we can see that at 3.5 it is a hole implying it is not defined, while at 5 it is a solid dot. Limit does not exist at f(0) as the left limit approaches 3.5 and the right limit approaches 5.

f(2) does not exist as there is a hole at that point in the graph. Limit as x tend to 2 approaches 0.5 as both right and left limit approaches 0.5.

f(4) equals -1 as the solid dot is at that point. As x tend to 4 the limit diverges to positive infinity implying the limit does not exist.

--The question is not readable, answering to the question below and graph attached--

"Use the graph of the function f to decide whether the value of the given quantity exists. (If an answer does not exist, enter DNE.)

(a) f(−2)

(b) lim x→−2 f(x)

(c) f(0)

(d) lim x→0 f(x)

(e) f(2)

(f) lim x→2 f(x) 0.5

(g) f(4)

(h) lim x→4 f(x) "

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