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Allisa [31]
2 years ago
9

Show that the equation x3 + 4x = 1 has a solution between x = 0 and x = 1

Mathematics
1 answer:
nexus9112 [7]2 years ago
5 0

Intermediate Value Theorem: Suppose that  f(x)  is an arbitrary, continuous function on an interval  [a,b] . If there exists a value  L  between  f(a)  and  f(b) , then there exists a corresponding value  c∈(a,b) , such that  f(c)=L

f(x)=x3+4x−1

f(0)=−1f(1)=4

Since the function changes sign in the interval  (0,1) , hence there exists a  c∈(0,1)  such that  f(c)=0

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The relative locations of a swing set, a garden, and a sandbox in Gina's backyard are shown in the diagram.
Archy [21]

Let us suppose the distance between the sandbox and garden is x feet.

Apply the sine law in the given triangle, we have

\frac{x}{\sin 65^{\circ}}=\frac{36}{\sin 104^{\circ}}\\
\\
\text{On coss multiplying, we get}\\
x\sin 104^{\circ}=36\sin 65^{\circ}\\
\\
x=\frac{36\sin 65^{\circ}}{\sin 104^{\circ}}\\
\\
x\approx 33.6

Therefore, in the nearest foot,  the distance between the sandbox and garden is 34 foot.

8 0
4 years ago
Read 2 more answers
What property is (C+2+0=c+2
frosja888 [35]

Answer:

Communitive Property of Addition

Step-by-step explanation:

Example of Comunitive Property of Multiplecation:

a+b = b+a

6 0
3 years ago
Solve the expression (7th grade math):<br><br> -0.8m+3-12.5m+95.36m
Lana71 [14]

Step-by-step explanation:

<u>Combine Like-Terms:</u>

-0.8m + 3 - 12.5m + 95.36m

-13.3m + 3 + 95.36m

82.06m + 3

82.06m + 3 is your simplified expression.

7 0
2 years ago
A manufacturing process that produces electron tubes is known to have a 10% defective rate. Suppose a random sample of 15 tubes
posledela

Answer:

Probability of obtaining no more than two defective tubes = 0.816

Step-by-step explanation:

The Probability of obtaining no more than two defective tubes in a randomly selected sample of 15 tubes is obtained using the binomial distribution formula: nCr × p^r × q^(n -r).

Where n is number of samples;

r is maximum number of defective tubes, r ≤ 2;

p is probability of defective tubes = 10% or 0.1

q is probability of non-defective tubes, q = 1 - p

Further explanations and calculations are given in the attachment below:

3 0
4 years ago
Which choice below is a boxplot for the following distribution? 67, 66, 64, 62, 60, 56, 54, 50, 46, 42, 41, 40, 40, 38, 35, 21,
luda_lava [24]

Answer:

Option E - Box plot E

Step-by-step explanation:

Given : Data,

67, 66, 64, 62, 60, 56, 54, 50, 46, 42, 41, 40, 40, 38, 35, 21, 19

To find : Which choice below is a boxplot for the following distribution?

Solution :

Step 1- Arranging the data from lowest to highest,

{19,21,35,38,40,40,41,42,46,50,54,56,60,62,64,66,67}  

Step 2 - Find the median of the data  

As the data is odd numbers so the median is \frac{n+1}{2} th term.

\frac{n+1}{2}=\frac{17+1}{2}=9th term.

9th term is 46

∴ Q_2=46  

Step 3 - To find Upper quartile and lower quartile  

Lower quartile data set is the median of the upper terms from median

{19,21,35,38,40,40,41,42}

Median of the set is M=\frac{38+40}{2}=39

∴ Q_1=39  

Upper quartile data set is the median of the lower terms from median

{ 50,54,56,60,62,64,66,67}

Median of the set is M=\frac{60+62}{2}=61

∴ Q_3=61  

We have plot the box plot attached below.

Our box plot is matched with Box plot E.

Therefore, Option E is correct.

8 0
3 years ago
Read 2 more answers
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