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2 years ago

Identify the domain of the function shown in the graph.

Mathematics

2 answers:

julsineya [31]2 years ago

7 0

D. because that is a square root function, which can include zero.

Alexus [3.1K]2 years ago

3 0

We can observe that the graph extends horizontally from \displaystyle -5−5 to the right without bound, so the domain is \displaystyle \left[-5,\infty \right)[−5,∞). The vertical extent of the graph is all range values \displaystyle 55 and below, so the range is \displaystyle \left(\mathrm{-\infty },5\right](−∞,5]. Note that the domain and range are always written from smaller to larger values, or from left to right for domain, and from the bottom of the graph to the top of the graph for range.

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You are visiting your friend Fabio's house. You find that, as a joke, he filled his swimming pool with Kool-Aid, which dissolved

Rzqust [24]

Answer:

The amount of work required to remove all of the water by pumping it over the side = 3.12 × 10⁶ lbs.ft

Step-by-step explanation:

Work done in moving anything from point A to point B = Fx

For this setup,

If we take an elemental vertical height, dx, The volume would be A.dx

where A = Cross sectional Area = πr² = π(18)² = 1017.88 ft²

dV = 1017.88 dx

The elemental force on that part will be

dF = ρg dV

ρg = 63.8 lbs/ft³

dF = 63.8 × 1017.88 dx = 64940.5 dx

F = ∫dF = 64940.5 dx

W = Fx = (∫dF)x = ∫ 64940.5x dx = 64940.5 ∫ xdx

We'll be integrating from (11 - 6) ft to 11 ft because that's the total height it'll be pumped through

W = 64940.5 (x²/2)¹¹₅ = 64940.5((11² - 5²)/2) = 3.12 × 10⁶ lbs.ft

4 0

2 years ago

A certain type of thread is manufactured with a mean tensile strength of 78.3 kilograms and a standard deviation of 5.6 kilogram

azamat

Answer:

(a) The variance decreases.

(b) The variance increases.

Step-by-step explanation:

According to the Central Limit Theorem if we have a population with mean μ and standard deviation σ and we take appropriately huge random samples (n ≥ 30) from the population with replacement, then the distribution of the sample mean will be approximately normally distributed.

Then, the mean of the sample mean is given by,

$\mu_{\bar x}=\mu$

And the standard deviation of the sample mean is given by,

$\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}$

The standard deviation of sample mean is inversely proportional to the sample size, n.

So, if n increases then the standard deviation will decrease and vice-versa.

(a)

The sample size is increased from 64 to 196.

As mentioned above, if the sample size is increased then the standard deviation will decrease.

So, on increasing the value of n from 64 to 196, the standard deviation of the sample mean will decrease.

The standard deviation of the sample mean for n = 64 is:

$\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}=\frac{5.6}{\sqrt{64}}=0.7$

The standard deviation of the sample mean for n = 196 is:

$\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}=\frac{5.6}{\sqrt{196}}=0.4$

The standard deviation of the sample mean decreased from 0.7 to 0.4 when n is increased from 64 to 196.

Hence, the variance also decreases.

(b)

If the sample size is decreased then the standard deviation will increase.

So, on decreasing the value of n from 784 to 49, the standard deviation of the sample mean will increase.

The standard deviation of the sample mean for n = 784 is:

$\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}=\frac{5.6}{\sqrt{784}}=0.2$

The standard deviation of the sample mean for n = 49 is:

$\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}=\frac{5.6}{\sqrt{49}}=0.8$

The standard deviation of the sample mean increased from 0.2 to 0.8 when n is decreased from 784 to 49.

Hence, the variance also increases.

6 0

2 years ago

A sunflower grows 8 feet in 92 days. Assuming that it grows at a constant

Yuki888 [10]

Answer:

69 days

Step-by-step explanation:

Given that sunflower grows at constant rate.

Let the rate of growth be x feet per day. It means sum flower grows x feet every day.

in 1 day plant grows x feet,

so in 92 days plant will grow 92*x feet

In 92 days the growth of plant will be = rate of growth *92 = 92*x = 92x feet

But given that A sunflower grows 8 feet in 92 days

so, 92x will be same as 8 feet.

lets put it in equation

92x =8 feet

x = 8/92 = 2/23

Thus, rate of growth of sunflower plant is 2/23 feet per days.

it means it grows 2/23 feet every day.

Let number of days taken to grow 6 feet be y days

in 1 day plant grows 2/23 feet feet,

so in y days plant will grow 2/23*y feet

In y days the growth of plant will be = rate of growth *y= (2/23)*y = 2y/23 feet

But 2y/23 should be equal to 6 feet

2y/23 = 6

Multiplying both side by 23

2y/23 * = 6 *23

=> 2y =138

dividing both side by 2

2y/2 =138/2

=> y = 69

Thus, it will take 69 days for sunflower to grow 6 feet.

4 0

2 years ago

In ΔXYZ, m∠X = 70° and m∠Y = 88°. Which statement about the sides of ΔXYZ must be true?

Wewaii [24]

Answer:

Z must equal 22° because it will add up to 180° it is an acute scalene triangle

8 0

2 years ago

The surface area of an oil spill gets 105% larger every day, represented by the function s(x) = (1.05)x − 1. On the first day, i

ioda

The given scenario above is like a geometric sequence with r or common ratio being 1.05 and the first term being 31 square meters. The nth term of the sequence is calculated through the equation,
A15 = (A1)(r)^(n - 1)
Substituting,
A15 = (31)(1.05)^(15 - 1) = 61.3778 square meter
Therefore, the area covered by the spill after the 15th day is approximately 61.4 square meters.

6 0

2 years ago