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3 years ago

Fill in the blank. The absolute value of every nonzero integer is a(n) _____ integer.

Mathematics

2 answers:

Savatey [412]3 years ago

8 0

Answer:

your answer would be a positive integer

Sedbober [7]3 years ago

3 0

Answer: positive

The absolute value of every nonzero integer is a positive integer.

Examples are

|-2| = 2

|7| = 7

The absolute value represents distance which can never be negative. Negative distance does not make sense.

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In the given figure, O is the centre of the circle with chords AP and BP being

Ainat [17]

Answer:

It's 70°

Step-by-step explanation:

∠APB = ∠RPQ = 35°

Now, ∠AOB and ∠APB are angles subtended by an arc AB at centre and at the remaining part of the circle .

∴∠AOB = 2∠APB = 2 × 35° = 70°

5 0

3 years ago

In 2000 the population of a country reached 1 billion, and in 2025 it is projected to be 1.2 billion. (a) Find values for C an

Mice21 [21]

Answer:

(a) The value of C is 1.

(b) In 2010, the population would be 1.07555 billions.

(c) In 2047, the population would be 1.4 billions.

Step-by-step explanation:

(a) Here, the given function that shows the population(in billions) of the country in year x,

$P(x)=Ca^{x-2000}$

So, the population in 2000,

$P(2000)=Ca^{2000-2000}$

$=Ca^{0}$

$=C$

According to the question,

$P(2000)=1$

$\implies C=1$

(b) Similarly,

The population in 2025,

$P(2025)=Ca^{2025-2000}$

$=Ca^{25}$

$=a^{25}$ (∵ C = 1)

Again according to the question,

$P(2025)=1.2$

$a^{25}=1.2$

Taking ln both sides,

$\ln a^{25}=\ln 1.2$

$25\ln a = \ln 1.2$

$\ln a = \frac{\ln 1.2}{25}\approx 0.00729$

$a=e^{0.00729}=1.00731$

Thus, the function that shows the population in year x,

$P(x)=(1.00731)^{x-2000}$ ...... (1)

The population in 2010,

$P(2010)=(1.00731)^{2010-2000}=(1.00731)^{10}=1.07555$

Hence, the population in 2010 would be 1.07555 billions.

(c) If population P(x) = 1.4 billion,

Then, from equation (1),

$1.4=(1.00731)^{x-2000}$

$\ln 1.4=(x-2000)\ln 1.00731$

$0.33647 = (x-2000)0.00728$

$0.33647 = 0.00728x-14.56682$

$0.33647 + 14.56682 = 0.00728x$

$14.90329 = 0.00728x$

$\implies x=\frac{14.90329}{0.00728}\approx 2047$

Therefore, the country's population might reach 1.4 billion in 2047.

3 0

3 years ago

The quality control manager of a light bulb factory needs to estimate the average life of a large shipment of light bulbs. The p

eimsori [14]

Answer:

b) yes

The manufacturer has the right to state that the light bulbs last on average 400 hours

Step-by-step explanation:

Explanation:-

Given sample size 'n' = 64

Given standard deviation of the Population (σ)=100

Mean of the sample (x⁻) = 350 hours

95% of confidence interval is determined by

$(x^{-} -Z_{0.95} \frac{S.D}{\sqrt{n} } , x^{-} +Z_{0.95} \frac{S.D}{\sqrt{n} } )$

( $(350 -1.96 \frac{100}{\sqrt{64} } , 350+1.96\frac{100}{\sqrt{64} } )$

(350-24.5 , 350+24.5)

(325.5 , 374.5)

Conclusion:-

Yes

The manufacturer has the right to state that the light bulbs last on average 400 hours

4 0

3 years ago

How would u model 5x(2/3) Explain

Daniel [21]

2/3 time 5
5×2 is 10 so the numerator is ten
1×3 is 3 so the denominator is three
the answer is 10/3

5 0

3 years ago

(x^2-2)^2-10(x^2-2)+21=0 find one value of x that is a solution to the equation

Sloan [31]

Answer:

x=3; x=-3; x=√5; x=-√5

Step-by-step explanation:

6 0

3 years ago