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3 years ago

"find values of a and b that make the statement |a+b|=|a| + |b| false"

Mathematics

2 answers:

Ann [662]3 years ago

7 0

Answer:

a=Any negative number

b=Any positive number

or a=Any positive number and b=Any negative number

Step-by-step explanation:

We are given that two numbers a and b

We have to find the values of a and b that make the statement $\mid a+b\mid=\mid a\mid+\mid b\mid$ false.

Suppose a=5 and b=-6

$\mid 5-6\mid=\mid 1\mid=1$

$\mid 5\mid +\mid -6\mid=5+6=11$

$\mid 5-6\mid \neq \mid 5\mid+\mid-6\mid$

$\mid a+b\mid \neq \mid a\mid +\mid b\mid$

When a be any negative number and b be any positive number or a be any positive number and b be any negative number then it will make given statement false.

Hence, the given statement is false.

kotegsom [21]3 years ago

6 0

Just choose any combination so that a is negative and b is positive, and vice versa. For example, if a = 3 and b = -6, |3-6| ≠ |3| + |-6|.
This is because |-3| = 3, and |3|+|-6| = 3+6 = 9.
3≠9.

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The members of the reading club each read 34 books in the fall semester and 33 books in the spring semester. Altogether, the clu

atroni [7]

Answer:

Add 34 and 33 which is 67 then divide that by 2412 :) hope I helped

Step-by-step explanation:

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3 years ago

Solve for x. 5x=15+5

Travka [436]

Answer: x=4

Step-by-step explanation:

5x=15+5

15+5=20

5x=20

divide 5 on both sides

20/5=4

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3 years ago

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The proprietor of a boutique in New York wanted to determine the average age of his customers. A random sample of 25 customers r

jolli1 [7]

Answer:

$28-2.064\frac{10}{\sqrt{25}}=23.872$

$28+2.064\frac{10}{\sqrt{25}}=32.128$

So on this case the 95% confidence interval would be given by (23.9;32.1)

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$\bar X=28$ represent the sample mean

$\mu$ population mean (variable of interest)

s=10 represent the sample standard deviation

n=25 represent the sample size

Solution to the problem

The confidence interval for the mean is given by the following formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

In order to calculate the critical value $t_{\alpha/2}$ we need to find first the degrees of freedom, given by:

$df=n-1=25-1=24$

Since the Confidence is 0.95 or 95%, the value of $\alpha=0.05$ and $\alpha/2 =0.025$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.025,24)".And we see that $t_{\alpha/2}=2.064$

Now we have everything in order to replace into formula (1):

$28-2.064\frac{10}{\sqrt{25}}=23.872$

$28+2.064\frac{10}{\sqrt{25}}=32.128$

So on this case the 95% confidence interval would be given by (23.9;32.1)

7 0

3 years ago

If CD=18, find the value of EB.

aliina [53]

Step-by-step explanation:

Chord AB and Chord CD are equidistant from the center of the circle.

$\therefore \: chord \: AB \cong chord \: CD \\ \\ \therefore \: \frac{1}{2} \: \: AB \cong \frac{1}{2} \: \: CD \\ \\ \therefore \: EB = \frac{1}{2} \: \times 18\\ \\ \huge \purple{ \boxed{\therefore \: EB =9}}$

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3 years ago

Belle walks 7/10 mile each morning, and 1, 4/10 miles each evening.

kow [346]

Answer:

10.5 miles.

Step-by-step explanation:

If she walks 7/10 of a mile each morning, and 1, 4/10 of a mile each day, Belle walks a total of 2 1/10 of a mile each day (2.1) miles each day)

We can just multiply the amount of miles per day by 5, (2.1 x 5) and we get 10.5 miles total.

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2 years ago

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