1. x² + 2xy – 7 xy + 4y?<br>Input your answer here:

100 POINTS AND BRAINLIST

sergij07 [2.7K]

Answer:

90+x+x=180

2x=180-90

2x=90

x=90/2

x=45

45+45+90=180

180=180

8 0

2 years ago

Read 2 more answers

If a couple plans to have 8 children, what is the probability that there will be at least one boy? Assume boys and girls are e

Artyom0805 [142]

Answer:

99.61% probability that there will be at least one boy, which is high enough for the couple to be very confident that they will get at least one boy in 8 children.

The probability is 0.9961

Step-by-step explanation:

For each children, there are only two possible outcomes. Either they are a boy, or they are a girl. The probability of a children being a boy is independent from the probability of other children being a boy. So 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.

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

Assume boys and girls are equally likely.

This means that $p = 0.5$

If a couple plans to have 8 children, what is the probability that there will be at least one boy?

This is $P(X > 0)$ when $n = 8$

We know that either there are no boys, or there is at least one boy. The sum of the probabilities of these events is decimal 1. So

$P(X = 0) + P(X > 0) = 1$

$P(X > 0) = 1 - P(X = 0)$

In which

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

$P(X = 0) = C_{8,0}.(0.5)^{0}.(0.5)^{8} = 0.0039$

$P(X > 0) = 1 - P(X = 0) = 1 - 0.0039 = 0.9961$

Any probability above 95% is considered very high.

99.61% probability that there will be at least one boy, which is high enough for the couple to be very confident that they will get at least one boy in 8 children.

5 0

3 years ago

How do you convert 0.51 repeating as a fraction

suter [353]

Here are the following factors for 51 and 100:
51= 1, 3, 17, 51
100=1, 2, 4, 5, 10, 20, 25, 50, 100
Since none of the numbers that go into 51 go into 100
(1 doesn't count) 51/100 is the correct answer, and cannot be put into lower terms.

8 0

3 years ago

Cassidy wrote the linear equation y=5x+4 Then, she wrote the equation of the line that is parallel to y=5x+4 and that passes thr

Daniel [21]

Well, again <span>y=5x+4 is in slope-intercept form, therefore </span> $\bf y=\stackrel{slope}{5}x+4$ .

so then, a parallel line to a line with that equation, will also have the same slope, therefore, what's the equation of a line whose slope is 5 and goes through 8, -2?

$\bf \begin{array}{lllll}
&x_1&y_1\\
% (a,b)
&({{8}}\quad ,&{{ -2}})
\end{array}
\\\\\\
% slope = m
slope = {{ m}}= \cfrac{rise}{run} \implies 5
\\\\\\
% point-slope intercept
\stackrel{\textit{point-slope form}}{y-{{ y_1}}={{ m}}(x-{{ x_1}})}\implies y-(-2)=5(x-8)\implies y+2=5x-40
\\\\\\
y=5x-40-2\implies y=5x-42$

3 0

3 years ago

A cylinder has a volume of 198 cm3, and its base has an area of 22 cm2. What is the height of the cylinder? V= πr²h

DIA [1.3K]

Answer:

The height of cylinder is 9 cm

Step-by-step explanation:

Volume of cylinder = 198 cm³

Base Area = 22 cm²

We need to find height of the cylinder

The formula used is: $Volume\:of\:cylinder=\pi r^2h$