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3 years ago

Write a rule for the linear function in the table.

Mathematics

1 answer:

Ira Lisetskai [31]3 years ago

5 0

Answer:

f(x) = 4 - x

Step-by-step explanation:

'f(x) = blah-blah' is the same as saying 'y = blah-blah', except it is also telling you that the x-y relationship is a function.

I notice that for each case, x + y = 4, so y = 4 - x

Or in 'function' terminology, f(x) = 4 - x

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A pyramid has a square base with sides 8" and a slant height of 5". Total Area = 224 square units 200 square units 144 square un

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The answer to this problem is 144 square units.

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3 years ago

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Find The Difference. 1) 8.5-7.6= 2)-2.5-17.8= 3 -2.9-(-7.5)= 4) 3.5-1.9=

Dahasolnce [82]

Answer:

1. 0.9

2. -20.4

3. 4.6

4. 1.6

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4 years ago

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Richard has just been given an l0-question multiple-choice quiz in his history class. Each question has five answers, of which o

myrzilka [38]

Answer:

a) 0.0000001024 probability that he will answer all questions correctly.

b) 0.1074 = 10.74% probability that he will answer all questions incorrectly

c) 0.8926 = 89.26% probability that he will answer at least one of the questions correctly.

d) 0.0328 = 3.28% probability that Richard will answer at least half the questions correctly

Step-by-step explanation:

For each question, there are only two possible outcomes. Either he answers it correctly, or he does not. The probability of answering a question correctly is independent of any other question. This means that we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

Each question has five answers, of which only one is correct

This means that the probability of correctly answering a question guessing is $p = \frac{1}{5} = 0.2$

10 questions.

This means that $n = 10$

A) What is the probability that he will answer all questions correctly?

This is $P(X = 10)$

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 10) = C_{10,10}.(0.2)^{10}.(0.8)^{0} = 0.0000001024$

0.0000001024 probability that he will answer all questions correctly.

B) What is the probability that he will answer all questions incorrectly?

None correctly, so $P(X = 0)$

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 0) = C_{10,0}.(0.2)^{0}.(0.8)^{10} = 0.1074$

0.1074 = 10.74% probability that he will answer all questions incorrectly

C) What is the probability that he will answer at least one of the questions correctly?

This is

$P(X \geq 1) = 1 - P(X = 0)$

Since $P(X = 0) = 0.1074$ , from item b.

$P(X \geq 1) = 1 - 0.1074 = 0.8926$

0.8926 = 89.26% probability that he will answer at least one of the questions correctly.

D) What is the probability that Richard will answer at least half the questions correctly?

This is

$P(X \geq 5) = P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10)$

In which

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 5) = C_{10,5}.(0.2)^{5}.(0.8)^{5} = 0.0264$

$P(X = 6) = C_{10,6}.(0.2)^{6}.(0.8)^{4} = 0.0055$

$P(X = 7) = C_{10,7}.(0.2)^{7}.(0.8)^{3} = 0.0008$

$P(X = 8) = C_{10,8}.(0.2)^{8}.(0.8)^{2} = 0.0001$

$P(X = 9) = C_{10,9}.(0.2)^{9}.(0.8)^{1} \approx 0$

$P(X = 10) = C_{10,10}.(0.2)^{10}.(0.8)^{0} \approx 0$

$P(X \geq 5) = P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10) = 0.0264 + 0.0055 + 0.0008 + 0.0001 + 0 + 0 = 0.0328$

0.0328 = 3.28% probability that Richard will answer at least half the questions correctly

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3 years ago

Solve. 4 x + 6 < − 6 Thankyou In advance :>

andrew-mc [135]

Answer:

x < -3

Step-by-step explanation:

Step 1: Subtract 6 from both sides.

$4x + 6 - 6 < -6 - 6$
$4x < -12$

Step 2: Divide both sides by 4.

$\frac{4x}{4} < \frac{-12}{4}$
$x < -3$

Therefore, the answer is x < -3.

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3 years ago

A right cone has a radius of 13 cm and a slant height of 20 cm. Find its surface area.

devlian [24]

Answer:

$A=1347.7\ cm^2$

Step-by-step explanation:

Given that,

Radius of a cone, r = 13 cm

Slant height of the cone, l = 20 cm

We need to find the surface area of the cone. The formula for the surface area of the cone is given by :

$A=\pi rl +\pi r^2$

Put all the values,

$A=\pi r(l + r)\\\\A=\pi \times 13(20 + 13)\\\\A=1347.7\ cm^2$

So, the surface area of the cone is $1347.7\ cm^2$ .

5 0

3 years ago