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3 years ago

Which statement is true of the function f(x) = Negative RootIndex 3 StartRoot x EndRoot? Select three options.

Mathematics

1 answer:

ycow [4]3 years ago

8 0

Answer:

Options (2), (3) and (4) are correct.

Step-by-step explanation:

The given function is f(x) = $-\sqrt[3]{x}$

1). First derivative of the function = f'(x) = $\frac{d}{dx}(-\sqrt[3]{x} )$

f'(x) = $-\frac{1}{3}(x)^{-\frac{2}{3}}$

Since derivative is negative, function will be decreasing everywhere.

Therefore, Option (1) is incorrect.

2). Since value of the function is true for every value of all real values of x.

Domain of the function is (-∞, ∞).

Therefore, Option (2) is correct.

3). For the given domain, range of the function will be all real values of y Or (-∞, ∞)

Therefore, Option (3) is correct.

4). Function 'f' when reflected across x axis, equation of the reflected function will be g(x) = $\sqrt[3]{x}$ .

Therefore, Option (4) is correct.

5). For a point (3, -27),

-27 = $-\sqrt[3]{3}$

Therefore, Option (5) is incorrect.

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A man walk for 2hr at 6km/h.he then cycled for a certain time at 16km/h.if he traveled 36km all together for how many hours did

Klio2033 [76]

Answer:

t = 1.5 hours

Step-by-step explanation:

Given that,

A man walk for 2hr at 6 km/h.

He then cycled for a certain time at 16 km/h.

He travelled 36 km all together.

We need to find for how many hours did he cycle.

Distance walked in 2 hours = 2×6 = 12 km

Distance he cycled = 36-12 = 24 km

Let he cycled for t hours. So,

$t=\dfrac{24}{16}\\\\t=1.5\ h$

So, he cycles for 1.5 hours.

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3 years ago

What is it called in cubic inch of a cylinder with a height of 4in and a base radius of 5in to the nearest tenths place?

Maru [420]

Answer:

1,256.8in

Step-by-step explanation:

Given data

Height h =4in

Radius r= 5in

The expression for the volume of cylinder is

V=πr²h

Substitute

V=3.142*4²*5

V=3.142 *16*25

V=1,256.8in³

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3 years ago

One inlet pipe can fill an empty pool in 6 hours, and a drain can empty the pool in 12 hours. How long will it take the pipe to

Ainat [17]

Answer: 12 hours

Step-by-step explanation:

Let x = time it takes to fill the pool if the inlet pipe and drain pipe are both open

1/6 = portion of pool filled per hour by the inlet pipe

1/12 = portion of pool emptied per hour by the drain

1/x = portion of pool filled per hour if the inlet pipe and drain are both open

Then, 1/6 - 1/12 = 1/x

Multiply by the LCD, 12x, to obtain

2x - x = 12

x = 12 hours

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2 years ago

The owner of a bakery wants to know whether customers have any preference among 5 different flavors of muffin. A sample of 200 c

Troyanec [42]

So,, there are 5 different flavors. A total of 180 people were asked. Hence, the hypothesis that there is no significant difference is that every flavor gets 180/5=36 flavors. x^2= $\sum{\frac{(x_i)^2}{m_i}}-n$ . In this case, mi is the proportion of the hypothesis, thus 36, n=180 and xi is the number of actual observations. Substituting the known quantities, we get that x^2=9. The degree of association is given by $\sqrt{X^2}/ \sqrt{N(n-1)}$ . This yields around 0.10, much higher than our limit.

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3 years ago

A large but sparsely populated county has two small hospitals, one at the south end of the county and one at the north end. The

Readme [11.4K]

Answer:

Step-by-step explanation:

Probability distribution of this type is a vicariate distribution because it specifies two random variable X and Y. We represent the probability X takes x and Y takes y by

f(x,y) = P((X=x,Y=y) ,

and given that the random variables are independent the joint pmf isbgiven by:

f(x,y) = fX(x) .fY(y) and this gives the table (see attachment)

(b) the required probability is given by considering X=0,1 and Y =0,1

f(x,y) = sum{(P(X ≤ 1, Y ≤ 1) }

= [0.1 +0.2 ] × [0.1 + 0.3]

= 0.3 × 0.4

= 0.12

Now we find

fX(x) = sum{[f(x.y)]} for y =0, 1 and similarly for fY(y)= sum{[f(x,y)]} for x=0, 1

fX(x) = sum{[f(x,y)]}= 0.1+0.3

= 0.4

fY(y) = sum{[f(x.y)]} = 0.1 + 0.2

= 0.3

Since fY(y) × fX(x) = 0.4 × 0.3

= 0.12

Hence f(x,y) = fX(x) .fY(y), the events are independent

= P(X<=1) . P(Y<=1)

= [sum{[f(x.y]} over Y=0,1] × [sum{[f(x.y)]}, over X= 0, 1

= 0.4 × 0.3

= 0.12

(d) the required event is given by the idea that: either The South has no bed and the North has or the the North has no bed and the South has. Let this event be A

A =sum[(P(X = 1<= x<= 4, Y =0)] + sum[P(X =0 Y= 1 <= x <= 3)]

A = [0.02 + 0.03 + 0.02 + 0.02] + [0.03 + 0.04 + 0.02]

A = [0.09] + [ 0.09]

A = 0.18

Pls note the sum of the vertical column X=2 is 0.3

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3 years ago