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kondaur [170]
2 years ago
6

An acute triangle has two sides measuring 8 cm and 10 cm . What is the best representation of the possible range of values for t

he third side , s? 2 < s< 18 6 < s < 12.8 s < 2 or s > 18 s < 6 or s > 12.8
Mathematics
1 answer:
Mekhanik [1.2K]2 years ago
5 0

Answer:

the right answer is 2 < s< 18

Step-by-step explanation:

The Third side of the triangle must be greater than the difference of the other two sides which is 10 -8= 2 and smaller than the sum of the other two sides of the triangle which is 10+8= 18.

so third side should be greater than 2 and less than 18.

So right answer is 2 < s< 18

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The Freeman family is barbecuing veggie burgers, corn cobs, and mushroom caps in their local park. If 3/8 of the items barbecued
KatRina [158]

Answer:

7/24

Step-by-step explanation:

Everything they are grilling is an amount of 1.

Then each item is a fraction of 1.

Add 3/8 and 1/3 and subtract from 1.

3/8 + 1/3 = 9/24 + 8/24 = 17/24

The veggie burgers and corn account for 17/24 of the total.

To find the fraction of mushroom, we subtract 17/24 from 1.

1 - 17/24 = 24/24 - 17/24 = 7/24

Answer: 7/24

8 0
3 years ago
Use the definition to find an expression for the area under the curve y = x3 from 0 to 1 as a limit. lim n→∞ n i = 1 R (b) The f
Harlamova29_29 [7]

The summand (R?) is missing, but we can always come up with another one.

Divide the interval [0, 1] into n subintervals of equal length \dfrac{1-0}n=\dfrac1n:

[0,1]=\left[0,\dfrac1n\right]\cup\left[\dfrac1n,\dfrac2n\right]\cup\cdots\cup\left[1-\dfrac1n,1\right]

Let's consider a left-endpoint sum, so that we take values of f(\ell_i)={\ell_i}^3 where \ell_i is given by the sequence

\ell_i=\dfrac{i-1}n

with 1\le i\le n. Then the definite integral is equal to the Riemann sum

\displaystyle\int_0^1x^3\,\mathrm dx=\lim_{n\to\infty}\sum_{i=1}^n\left(\frac{i-1}n\right)^3\frac{1-0}n

=\displaystyle\lim_{n\to\infty}\frac1{n^4}\sum_{i=1}^n(i-1)^3

=\displaystyle\lim_{n\to\infty}\frac1{n^4}\sum_{i=0}^{n-1}i^3

=\displaystyle\lim_{n\to\infty}\frac{n^2(n-1)^2}{4n^4}=\boxed{\frac14}

8 0
2 years ago
Write 720,080 in expanded form with exponents.
USPshnik [31]

Write 720,080 in expanded form with exponents

First we the place chart for numbers and exponents as well

HTh        TTh        Th          H        Tens        ones

7               2             0          0            8             0

10^5        10^4          10^3     10^2      10^1            1

Now we write the expanded form with exponents

7*10^5+2*10^4 +0*10^3 +0*10^2 + 8*10+0

0 times anything is 0

So expanded form is

(7 * 10^5) + (2*10^4) + (8*10^1)


8 0
2 years ago
Read 2 more answers
A coin is flipped until 3 heads in succession occur. list only those elements of the sample space that require 6 or less tosses.
Mashutka [201]

we are given

A coin is flipped until 3 heads in succession occur

so, firstly, we will find sample space

S={HHH , THHH , HTHHH, TTHHH , TTTHHH , HTTHHH , THTHHH , HHTHHHH, ......}

now, we are given that

list only those elements of the sample space that require 6 or less tosses

so, we can see that sample space

S={HHH , THHH , HTHHH, TTHHH , TTTHHH , HTTHHH , THTHHH , HHTHHHH, ......}

There are infinite such possibilities

so, there are infinite number of elements in space

and we know that

discrete sample space will always have finite elements

but we have infinite number of sample space elements here

so, this is not discrete sample space...........Answer

6 0
2 years ago
The minute hand of the clock is 5 inches long. How far does the tip of the minute hand move in 4 full rotations? Calculate your
omeli [17]

Assuming the clock to be round in shape, we can treat the minute hand length as the radius of the circle.

We want to know the length, in inches, of 4 full rotations.

1 full rotation length is the circumference of the circle with radius 5 <u>(minute hand is radius and has length 5 inches)</u>. We use the formula of the circumference of a circle to get length in 1 rotation:

C=2\pi r\\C=2\pi (5)\\C=10\pi

So for 4 full rotations, the length covered is 4*10\pi=40\pi inches.

Rounding to nearest tenth of an inch, we have:

40\pi=125.7 inches


ANSWER: 40\pi or 125.7 inches

5 0
2 years ago
Read 2 more answers
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