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3 years ago

Can anyone help me on #4

Mathematics

1 answer:

Ilia_Sergeevich [38]3 years ago

6 0

Answer:

(a) 47°

Step-by-step explanation:

360° - (135° + 110° + 68°) = 360° - 313° = 47°

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A student takes a true-false test that has 10 questions and guesses randomly at each answer. Let X be the number of questions an

Dvinal [7]

Answer:

P(Fewer than 3) = 0.05.

Step-by-step explanation:

We are given that a student takes a true-false test that has 10 questions and guesses randomly at each answer.

The above situation can be represented through Binomial distribution;

$P(X=r) = \binom{n}{r}p^{r} (1-p)^{n-r} ; x = 0,1,2,3,.....$

where, n = number of trials (samples) taken = 10 questions

r = number of success = fewer than 3

p = probability of success which in our question is probability

that question is answered correctly, i.e; 50%

LET X = Number of questions answered correctly

So, it means X ~ Binom(n = 10, p = 0.50)

Now, Probability that Fewer than 3 questions are answered correctly is given by = P(X < 3)

P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)

= $\binom{10}{0}\times 0.50^{0} \times (1-0.50)^{10-0}+ \binom{10}{1}\times 0.50^{1} \times (1-0.50)^{10-1}+ \binom{10}{2}\times 0.50^{2} \times (1-0.50)^{10-2}$

= $1 \times 0.50^{10} + 10 \times 0.50^{10} +45 \times 0.50^{10}$

= 0.05

Hence, the P(Fewer than 3) is 0.05.

4 0

3 years ago

What value, entered in the blank below, would make the two expressions equivalent? Expres

malfutka [58]

Answer:

The value is -3

Step-by-step explanation:

Here in this question, we are interested in making the expressions on both sides of the equation equal. But we seek a particular value or number which when placed in front of the quadratic expression on the right hand side makes the equations equal.

To get this done with, we will need to factorize the expression on the left hand side of the equation.

Thus, we can write;

-27x^2 + 9x + 12 as 3(-9x^2 + 3x + 4)

What do we notice? we can see that the now factored quadratic expression resembles what we have on the right hand side asides there fact that we are not there yet in terms of sign.

Thus, we can finally write ;

-27x^2 + 9x + 12 as -3(9x^2 -3x -4)

This exactly gives the expression on the right hand side

Thus the value to place in the blank is -3

5 0

3 years ago

Multiply Conjugates Using the Product of Conjugates Pattern

SpyIntel [72]

Answer:

The product is the difference of squares is $\left(11-b\right)\left(11+b\right)=121-{{b}^2}$