Use the Division Algorithm to show that the cube of any integer is of the form 9k, 9k + 1 or 9k + 8. (Hint: By the Division Algorithm, the integer a is of one of the forms 9q, 9q + 1, ..., 9q + 8; establish the result for 9q + 3 and 9q + 7 only.)

Answer:

I'd 7587163850

Pass 123456

Join

Answer:

Step-by-step explanation:

\(\frac{cot \theta}{cosec \theta + 1} = \frac{cosec\theta -1} {cot \theta}\)

\(L H S\)

       \(\frac{cot \theta }{cosec \theta + 1 } \times \frac{cosec \theta - 1}{cosec \theta -1}\)             \([ \ multiplying \ and \ dividng \ by \ (cosec \theta - 1) \ ]\)

     \(= \frac{cot \theta \times (cosec \theta - 1)}{(cosec ^2\theta -1)}\)                   \([ \ (a -b)(a+b) = a^2 - b^2 \ ]\)

     \(= \frac{cot \theta \times (cosec \theta - 1)}{cot^2 \theta}\\ \\\)                   \([ \ cosec^2\theta - 1 = cot^2 \theta \ ]\)

     \(= \frac{cosec \theta - 1 }{cot \theta} \\\\= RHS\)

Answer:

64%

Step-by-step explanation:

If  9 out of 25 people are left-handed

That means 25-9 = 16 people are right handed

or 16/25 are right handed

Multiply the top and bottom by 4 to get it out of 100

64/100

Percent means out of 100

64% are right handed

Answer:

The answer is option B which is 80

Step-by-step explanation:

The solution is in the image

Answer:

× = 4,000,000

Step-by-step explanation:

40 Million = 40,000,000

40,000,000 ÷ 10

=

4,000,000

Checking:

4,000,000 × 10 = 40,000,000/ 40 Million

When dividing by zero, all you do is remove a zero or move the decimal place to the left.

Answer:

C. The slope is positive. As the independent variable increases, the dependent variable also tends to increase. This is because in a positive linear correlation, as the values of one variable increase, the values of the other variable tend to increase as well, resulting in a positive slope of the regression line.

Answer:

9.0.

Step-by-step explanation:

Answer:

9.0554

Step-by-step explanation:

10 > √82 > 9 ,  √ 82 ≈ 9.0554

Answer:14

Step-by-step explanation:

Mariah lost twice so that means she got -3 two times that goes the same for ryan he gets 7 points two times which equal 14

Answer: ryan would have 14 points and mariah would have -6 points

Step-by-step explanation:

Answer:

The possible number of students in Mrs. Hayko's class is limited to 15 or 30, as higher multiples of 15 would exceed the desired class size.

Step-by-step explanation:

a)

Let 'x' be the total number of students in Mrs. Hayko's class.

One-third of the students walk to school: (1/3)x.

The remaining students who do not walk to school: (2/3)x.

Four-fifths of the non-walking students take the bus: (4/5) * (2/3)x.

Simplify to find the fraction of students taking the bus: (8/15)x.

b)

Consider different values for 'x' to find a whole number of students taking the bus.

Start with a small number, such as x = 15.

Calculate the number of students taking the bus using (8/15)x.

If the result is a whole number, it's a possible class size.

Repeat with different values of 'x' until a whole number is obtained.

The possible number of students in Mrs. Hayko's class could be 15, 30, or any other multiple of 15.

To solve logarithmic equations with multiple bases, transform them to logarithms with a single basis and then isolate the variable using logarithmic characteristics.

An equation is a formula in mathematics that expresses the equivalence of two expressions by linking them with the equals symbol =. In its most basic form, an equation is a mathematical statement that indicates that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. An equation is made up of multiple components, including words, coefficients, exponents, arithmetic operators, equal signs, and constants.

Here,

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To evaluate each integral in terms of areas, we need to understand that the integral represents the area under the curve of a function, f(x), between two points on the x-axis.

Let's discuss each integral:

(a) ∫₀⁸ f(x) dx: This represents the area under the curve of f(x) from x = 0 to x = 8. The integral calculates the accumulated area along this interval.

(b) ∫₀²⁰ f(x) dx: Similarly, this represents the area under the curve of f(x) from x = 0 to x = 20. It's a broader interval than (a), so it covers more area under the curve.

(c) ∫²⁰²⁸ f(x) dx: This integral represents the area under the curve of f(x) between x = 20 and x = 28. It's important to note that the interval is now shifted to the right compared to (a) and (b).

(d) ∫¹²²⁸ f(x) dx: This integral calculates the area under the curve of f(x) from x = 12 to x = 28. The interval here is larger than in (c), covering more area under the curve.

(e) ∫¹²²⁸ |f(x)| dx: This integral evaluates the area under the absolute value of f(x) from x = 12 to x = 28. The absolute value ensures that negative function values contribute positively to the area calculation, preventing any cancelation of areas.

(f) ∫₀⁸ f(x) dx: This integral is the same as (a), representing the area under the curve of f(x) from x = 0 to x = 8.

Each integral evaluates the area under the curve of f(x) for different intervals on the x-axis, providing insights into the total accumulated area in those intervals.

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I believe the answer is 51!

what I did was 0.17×300 which got me 51 ^^

Answer:

.

Step-by-step explanation:

Answer:

\(t=\frac{x}{7}\)

Step-by-step explanation:

You need to isolate the variable t. Use inverse operations for this.

7t can be seen as 7×t, and the opposite of multiplication is division. Divide both sides by 7:

\(\frac{7t}{7}=\frac{x}{7}\\\\t=\frac{x}{7}\)

The common term 7 on the left side cancels out.

:Done

Answer:

610

Step-by-step explanation:

Given:

Add:

259 + 431 = 690

Subtract:

1300 - 690 = 610

So, on Wednesday 610 emails were sent out.

Hope this helped.

Answer:

If I entered it in correctly it would look something like this,,

Answer:

The first number line representation!

Step-by-step explanation:

3x > -6

x > -2

The velocity of the boat when it reaches the buoy is approximately 17.32 m/s. This is found using the equation v² = u² + 2as, where u is the initial velocity, a is the acceleration, and s is the displacement.

To solve this problem, we can use the equations of motion. The initial velocity of the boat, u, is 30 m/s, the acceleration, a, is -3.0 m/s² (negative because the boat is slowing down), and the displacement, s, is 100 m. We need to find the final velocity, v, when the boat reaches the buoy.

We can use the equation: v² = u² + 2as

Substituting the given values, we have:

v² = (30 m/s)² + 2(-3.0 m/s²)(100 m)

v² = 900 m²/s² - 600 m²/s²

v² = 300 m²/s²

Taking the square root of both sides, we find:

v = √300 m/s

v ≈ 17.32 m/s

Therefore, the velocity of the boat when it reaches the buoy is approximately 17.32 m/s.

The problem provides the initial velocity, acceleration, and displacement of the boat. By applying the equation v² = u² + 2as, we can find the final velocity of the boat. This equation is derived from the kinematic equations of motion. The equation relates the initial velocity (u), final velocity (v), acceleration (a), and displacement (s) of an object moving with uniform acceleration.

In this case, the boat is decelerating with a constant acceleration of -3.0 m/s². By substituting the given values into the equation and solving for v, we find that the velocity of the boat when it reaches the buoy is approximately 17.32 m/s.

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Answer:

500 minutes

Step-by-step explanation:

0.18x + 35 = 0.16x + 45

0.18x - 0.16x = 45 - 35

O.02x = 10

x = 500

Answer:

Mr. Jones

Step-by-step explanation:

it's Mr. Jones because he drove 63.6 miles and his wife drove 61.3

the graph that adequately fits the description would be a pictograph

because shows a symbol for a word or phrase

The difference in percentages is practically significant but whether or not it is statistically significant cannot be determined.

Here, we are given that 13.4% of the population in the US lived in the West in 1950 and 22.5% in 2000.

Thus, the difference in percentage = 22.5 - 13.4 = 9.1%

We observe that the difference is large, this means that the difference in percentages is practically significant.

Now, to determine whether the difference is statistically significant it is appropriate to conduct a two-sample z-test and it is only appropriate to conduct the test of significance when the samples are simple random samples.

In this case, the samples are not simple random samples, because the data given contains information on all individuals in the population. Moreover, it is not appropriate to determine whether the difference in percentages is statistically significant as the samples are not probability samples.

Thus, the difference in percentages is practically significant but whether or not it is statistically significant cannot be determined.

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Answer:

C. y = x/3 -2

Step-by-step explanation:

A linear function is a function of x.

A. is a function of x^2

B. is a function of 1/ x^2

C. is a function of x

D is a function of 1/x

The only linear function is C.

Answer:if you are looking for the hypotenuse use Pythagoras theorem 17.2047

Step-by-step explanation:square both the base and height .Add their total then find the square root

Answer:

4030 or 3040 I think 4030 though

Step-by-step explanation:

I think this is it but 6*8 is 48....I used a little logic so hopefully this is right

Answer:

4030

Step-by-step explanation:

if 9× 7 = 3545 then it 7 × 5, 9× 5 which gives 3545

4x3 = 3× 5, 4×5 which gives 1520

so 6× 8 will give 8×5, 6×5 = 4030

The general solution is given by: y = c1cos(5x) + c2sin(5x) + 1/25(- cos(ln(sec5x))) + 5xsin(5x)

The most general solution to the original nonhomogeneous differential equation can be found by adding the homogeneous solution and the particular solution together. That is,

y = y_h + y_p

= c1cos(5x) + c2sin(5x) + 1/25(- cos(ln(sec5x))) + 5xsin(5x)

This is the most general solution to the original nonhomogeneous differential equation. We can use the arbitrary constants c1 and c2 to find specific solutions for different initial conditions. The general solution is given by:

y = c1cos(5x) + c2sin(5x) + 1/25(- cos(ln(sec5x))) + 5xsin(5x)

This is the final answer. Note that we have used the terms "general solution" and "arbitrary constants" in our answer, as instructed.

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Susan's cost of 35.2 ounces (that is, 2.2 pounds) pumpkin is   $3.96.

At a store, Susan selected a pumpkin that weighed 35.2 ounces.

We know that one pound consists of sixteen (16) ounces by methods of conversion.

That is, 16 ounces = 1 pound

⇒ 1 ounce = 1/16 pound

⇒ 35.2 ounces = (35.2)(1/16) pound = 2.2 pounds

Thus, Susan selected a pumpkin that weighed 2.2 pounds.

The cost of per pound of pumpkin is  $1. 80.

That is in simple words, one pound of pumpkin costs  $1. 80.

Therefore cost of 2.2 pounds of pumpkin is =  ${(1. 80)(2.2)} =  $3.96

Thus, the cost of 35.2 ounces of pumpkin Susan paid is  $3.96.

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