The combined mass of a dog and a cat is 24kg. The dog is three times as heavy as the cat. Find the mass

A campus radio station surveyed 500 students to determine the types of music they like. the survey revealed that 199 like rock,

Ostrovityanka [42]

<span>There are 24 who like both rock and country. There are 8 who like all 3 types, and these eight have been counted under the 24. This means that the number who like rock and country but not jazz is 24 - 8 = 16.
We are given a total of 155 who like country. We subtract the 16 who like both rock and country, and are left with 139 people who like country but not rock. (It does not matter whether they like jazz or not).
The probability is 155 out of the total of 500, so 155/500 = 31/100 = 0.31.
</span>

6 0

2 years ago

Consider the statement: The cube of any rational number is a rational number. a. Write the statement formally using a quantifier

3241004551 [841]

Answer:

(a)∀ r∈ℝ, r∈ℚ, r³∈ℚ

(b)True

Step-by-step explanation:

Definition

1. A real number is said to be rational if and only if there exists two integers a and b such that $\frac{a}{b}=r$ where b≠0.

2. If the product of three numbers is zero, then at least one of the numbers must be zero.

Given Statement

The cube of any rational number is a rational number.

This can be rewritten as:

For all real numbers, if the number is rational then its cube is rational.

If we introduce our variable r,

For all real number r, if r is rational, then r³ is rational.

∀ r∈ℝ, r∈ℚ, r³∈ℚ

(b)The Statement is True.

To prove: The cube of any rational number is rational.

Proof:

We assume that r is a rational number and prove that its cube is a rational number.

By definition, there exists integers a and b such that:

$r=\frac{a}{b}$ where b≠0.

$r^3=(\frac{a}{b})^3$

$r^3=\frac{a^3}{b^3}$

Since the cube of an integer is also an integer, a³ and b³ are also integers.

Since b is non-zero, then the zero product property tells us that its cube is also non-zero.

Conclusion:

$r^3=\frac{a^3}{b^3}$ is rational since a³ and b³ are integers and b is non-zero.

6 0

2 years ago

Rubi tosses a quarter off the Main Street bridge into the St. John’s River. The distance, in feet, the quarter is above the wate

Masja [62]

Answer: a. 112 feet, b= 3 seconds, c= 256 feet, d = 6 seconds

Step-by-step explanation:

Here is the complete question:

Rubi tosses a quarter off the Main Street bridge into the St. John’s River. The distance, in feet, the quarter is above the water is modeled by the equation d(t) = −16t2+96t + 112, where t represents time in seconds.

Find the actual value(s) now to each question. Use the solution from the previous question to assist you with what you are actual solving for.

(a) From what height was the quarter tossed?

The quarter was tossed at 112 feet.

(b) How long does it take the quarter to reach its maximum height?

It will take ________ seconds for the quarter to reach its maximum height.

(c) What is the maximum height of the quarter?

The maximum height of the quarter is ________ feet.

(d) How much time does it take for the quarter to hit the water?

It will take ______ seconds for the quarter to hit the water.

a. Since the function is

d(t) = −16t² + 96t + 112,

The coin is tossed at 112 feet. This is because it is the the initial value of the function. It is the constant term and does not depend on any other variable.

b. To calculate the maximum height, we have to find vertex of the function, that has coordinates of h,k and,

h = -b/2a and k = f(h).

From the question, we are aware that,

a = -16, b = 96, c = 112

Using the values, the vertex will be:

h = -b/2a

= -96/(2 × -16)

= -96/-32

= 3

k = f(3)

= 16t² + 96t + 112

= -16(3)² + 96(3) + 112

= -144 + 288 + 112

= 256

The maximum height is therefore 256 feet, and time needed to reach the height will be 3 seconds.

c. The maximum height has been calculated and it is 256 feet.

d. The time it take for the quarter to hit the water will be:

= 3 seconds × 2 = 6 seconds

Since the maximum height took 3 seconds, it would take another 3 seconds to hit the water. This makes it 6 seconds

4 0

2 years ago

Coordinates, gradient and tangent work (see image).

Ivenika [448]

Answer:

a) $P(x,2x^2-5),\ Q(x+h,2(x+h)^2-5)$

b) $4x+2h$

c) $4x$

Step-by-step explanation:

Given the curve

$y=2x^2-5$

a) If the x-coordinate of P is $x$ , then the y-coordinate is $2x^2-5,$ so point P has coordinates $(x,2x^2-5)$

If the x-coordinate of Q is $x+h$ , then the y-coordinate is $2(x+h)^2-5$ so point Q has coordinates $(x+h,2(x+h)^2-5)$

b) The gradient of the secant RQ is

$\dfrac{y_Q-y_P}{x_Q-x_P}\\ \\=\dfrac{(2(x+h)^2-5)-(2x^2-5)}{(x+h)-x}\\ \\=\dfrac{2(x+h)^2-5-x^2+5}{x+h-x}\\ \\=\dfrac{2(x+h)^2-2x^2}{h}\\ \\=\dfrac{2x^2+4xh+2h^2-2x^2}{h}\\ \\=\dfrac{4xh+2h^2}{h}\\ \\=4x+2h$

c) If $h\rightarrow 0,$ then the gradient $4x+2h\rightarrow 4x$

5 0

2 years ago

2.8 meters linen divided into 45 cm pieces = # of pieces and waste

pogonyaev

2.8 meter= 2800cms

To solve this, we can create a simple algebraic equation:
45x=2800
Divide both sides by 45.
(45x)/45=(2800)/45
x=62.222

You can make 62 full pieces.

To find the waste, multiply the numbers of pieces by the length of each.
62*45
=2790
2800-<span>2790
=10 centimeters

There would be 10 centimeters of wasted linen.

Hope this helps!
-Benjamin</span>

6 0

2 years ago