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3 years ago

Please answer and explain

Mathematics

1 answer:

sashaice [31]3 years ago

4 0

8=2*2*2=2^3
32=2*2*2*2*2=2^5
[8^(2/3)] / [32^(2/5)] = [(2^3)^(2/3)] / [(2^5)^(2/5)] =
= [2^(3*2/3)] / [2^(5*2/5)]= [2^2] / [2^2] = 4/4 = 1
Answer: 1

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A cylinder has a volume of 175 cubic units and a height of 7 units. The diameter of the cylinder is

VashaNatasha [74]

The answer is 10 units

The diameter of the cylinder (d) is the twice of its radius (r): d = 2r

The volume (V) of the cylinder with radius r and height h is:
V = π r² h

We have:
d = 2r
r = ?
h = 7
π = 3.14
V = 175π

175π = π * r² * 7
175 = r² * 7
r² = 175/7
r² = 25
r = √25
r = 5

d = 2r
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3 years ago

Read 2 more answers

An insurance company offers its policyholders a number of different premium payment options. For a randomly selected policyholde

n200080 [17]

Answer:

(a)

$\begin{array}{cccccc}x & {1} & {3} & {4} & {6} & {12} \ \\ P(x) & {0.30} & {0.10} & {0.05} & {0.15} & {0.40} \ \end{array}$

(b)

$P(3 \le x \le 6) = 0.30$

$P(4 \le x)=0.60$

Step-by-step explanation:

Given

$F(x) = \left[\begin{array}{ccc}0& x$

Solving (a): The pmf

This means that we list out the probability of each value of x.

To do this, we simply subtract the current probability value from the next.

So, we have:

$\begin{array}{cccccc}x & {1} & {3} & {4} & {6} & {12} \ \\ P(x) & {0.30} & {0.10} & {0.05} & {0.15} & {0.40} \ \end{array}$

The calculation is as follows:

$0.30 - 0 = 0.30$

$0.40 - 0.30 = 0.10$

$0.45 - 0.40 = 0.05$

$0.60 - 0.45 = 0.15$

$1 - 0.60 = 0.40$

The x values are gotten by considering where the equality sign is in each range.

$1 \le x < 3$ means $x = 1$

$3 \le x < 4$ means $x = 3$

$4 \le x < 6$ means $x=4$

$6 \le x < 12$ means $x = 6$

$12 \le x$ means $x = 12$

Solving (b):

$(i)\ P(3 \le x \le 6)$

This is calculated as:

$P(3 \le x \le 6) = F(6) - F(3-)$

From the given function

$F(6)= 0.60$

$F(3-) = F(1) = 0.30$

So:

$P(3 \le x \le 6) = 0.60 - 0.30$

$P(3 \le x \le 6) = 0.30$

$(ii)\ P(4 \le x)$

This is calculated as:

$P(4 \le x)=1 - F(4-)$

$P(4 \le x)=1 - F(3)$

$P(4 \le x)=1 - 0.40$

$P(4 \le x)=0.60$

8 0

3 years ago

Solve for x. The triangles in each pair are similar.

KatRina [158]

Answer:

Step-by-step explanation:

You need to pay very close attention to the triangle similarity statement. This says that triangle NML is similar to triangle NVU. But if you look at the way that triangle NVU is oriented in its appearance, it's laying on its side. We need to set it upright so that angle N is the vertex angle, angle V is the base angle on the left, and angle U is the base angle on the right. When we do that we see that sides NV and NM are corresponding and exist in a ratio to one another; likewise with sides VU and ML. Setting up the proportion:

$\frac{NV}{NM}=\frac{VU}{ML}$

Filling in:

$\frac{12}{36} =\frac{9}{9x}$

Cross multiply to get

324 = 108x

and x = 3

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4 years ago

We expect that students who do well on the midterm exam in a course will usually also do well on the final exam. Gary Smith of P

dybincka [34]

Using the model equation, the predicted mean score on the final given a score of 10 points above the class mean in the mid term exam is 50.7

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