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3 years ago

What is the range of these numbers? 7,5,8,5,6,7,7,7,7

Mathematics

2 answers:

Alchen [17]3 years ago

7 0

Answer:the answer is 7

Step-by-step explanation:

malfutka [58]3 years ago

5 0

Answer: The range is 3

Step-by-step explanation: range is the difference between the lowest number and the highest number in mathematic.

so 8-5=3 and 3 is the answer

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Write a conditional statement. Write the converse, inverse, and contrapositive for your statement and determine the truth value

MrRa [10]

Conditional statement is a statement with a hypotesis and a conclusion:

$If \text{ \underline{ hypothesis } } p, then \text{ \underline { conclusion } } q$

or mathematically $p\rightarrow q$ .

Converse statement of $p\rightarrow q$ is statement $q\rightarrow p$ .

If you negate (that means stick a "not" in front of) both the hypothesis and conclusion, you get the inverse:

$\neg p\rightarrow \neg q$ .

Finally, if you negate everything and flip p and q (taking the inverse of the converse) then you get the contrapositive:

$\neg q\rightarrow \neg p$ .

Example:

1. Conditional statement: If I am sleeping, then I have closed eyes. (true)

2. Converse statement: If I have closed eyes, then I'm sleeping. (not necessarily true)

3. Inverse statement: If I'm not sleeping, then I haven't closed eyes. (not necessarily true)

4. Contrapositive statement: If I haven't closed eyes, then I'm not sleeping. (true)

3 0

3 years ago

use Taylor's Theorem with integral remainder and the mean-value theorem for integrals to deduce Taylor's Theorem with lagrange r

Vadim26 [7]

Answer:

As consequence of the Taylor theorem with integral remainder we have that

$f(x) = f(a) + f'(a)(x-a) + \frac{f''(a)}{2!}(x-a)^2 + \cdots + \frac{f^{(n)}(a)}{n!}(x-a)^n + \int^a_x f^{(n+1)}(t)\frac{(x-t)^n}{n!}dt$

If we ask that $f$ has continuous $(n+1)$ th derivative we can apply the mean value theorem for integrals. Then, there exists $c$ between $a$ and $x$ such that

$\int^a_x f^{(n+1)}(t)\frac{(x-t)^k}{n!}dt = \frac{f^{(n+1)}(c)}{n!} \int^a_x (x-t)^n d t = \frac{f^{(n+1)}(c)}{n!} \frac{(x-t)^{n+1}}{n+1}\Big|_a^x$

Hence,

$\int^a_x f^{(n+1)}(t)\frac{(x-t)^k}{n!}d t = \frac{f^{(n+1)}(c)}{n!} \frac{(x-t)^{(n+1)}}{n+1} = \frac{f^{(n+1)}(c)}{(n+1)!}(x-a)^{n+1} .$

Thus,

$\int^a_x f^{(n+1)}(t)\frac{(x-t)^k}{n!}d t = \frac{f^{(n+1)}(c)}{(n+1)!}(x-a)^{n+1}$

and the Taylor theorem with Lagrange remainder is

$f(x) = f(a) + f'(a)(x-a) + \frac{f''(a)}{2!}(x-a)^2 + \cdots + \frac{f^{(n)}(a)}{n!}(x-a)^n + \frac{f^{(n+1)}(c)}{(n+1)!}(x-a)^{n+1}$ .

Step-by-step explanation:

5 0

3 years ago

The diameter of a circle is 9 feet. Find the radius.

slava [35]

The radius is half of the diameter.

9/2=4.5

The radius is 4.5 feet.

Hope this helps!

4 0

3 years ago

A person is purchasing a new golf club bag. The compartment for the golf balls is approximately the shape of a rectangular prism

Lerok [7]

Answer:

The answer to your question is: ≈ 178 balls

Step-by-step explanation:

Data

rectangular prism = 8 in x 11 in x 5 in

golf balls = 1.68 in diameter

Formula

Volume rectangular prism = l x w x h = 8 x 11 x 5 = 440 in³

Volume of ball = (4/3) πr³ = (4/3) (3.1416) (0.84)³ = 2.48 in³

# of balls inside the compartment = volume rectangular prism / volume ball

# of balls = 440 / 2.48

= 177.4 ≈ 178 balls

8 0

3 years ago

A) solve x + x + x = 54 <br>b) solve y/5 = 7<br>c) solve 4t+6=24

egoroff_w [7]

Answer:

a) x = 18

b) y = 35

c) t = 4.5

Step-by-step explanation:

a) x + x + x = 54

3x = 54

x = 54 ÷ 3

x = 18

b) y/5 = 7

(y/5) × 5 = 7 × 5

y = 35

c) 4t + 6 = 24

4t +6 - 6 = 24 -6

4t = 18

4t ÷ 4 = 18 ÷ 4

t = 4.5

6 0

2 years ago