At a certain college, 49% of the students are female, and 21% of the students major in civil engineering. Furthermore, 8% of the students both are female and major in civil engineering.

Answer:

Multiply:

[tex](x+y)by (x+y)[/tex]

[tex] : \implies(x + y)(x + y)[/tex]

[tex] : \implies \: x(x + y) + y(x + y)[/tex]

[tex] : \implies {x}^{2} + xy + xy + {y}^{2} [/tex]

[tex] : \implies{x}^{2} + 2xy + {y}^{2} [/tex]

Multiply:

[tex]a+b \: by \: a^2-b^2[/tex]

[tex]: \implies( {a}^{2} + {b}^{2} ) \times (a + b)[/tex]

[tex]: \implies \: {a}^{2} (a + b) - {b}^{2} (a + b)[/tex]

[tex]: \implies \: {a}^{3} + {a}^{2} b - {ab}^{2} - {b}^{3} [/tex]

Multiply:

[tex](a+5) by (a^2-2a-3)[/tex]

[tex]: \implies{(a + 5) \times ( {a}^{2} - 2a - 3) }[/tex]

[tex]: \implies \: a({a}^{2} - 2a - 3) + 5( {a}^{2} - 2a - 3)[/tex]

[tex]: \implies(a \times {a}^{2} - a \times 2a - a \times 3) + (5 \times {a}^{2} - 5 \times 2a - 5 \times 3)[/tex]

[tex]: \implies{a}^{3} - {2a}^{2} - 3a + 5 {a}^{2} - 10a - 15 [/tex]

[tex]: \implies{ {a}^{3} + {3a}^{2} - 13a - 15}[/tex]

Multiply:

[tex](a^2-ab+b^3) by (a+b)[/tex]

[tex]: \implies{(a + b) \times ( {a}^{2} - ab + {b}^{3} )}[/tex]

[tex]: \implies \: a( {a}^{2} - ab + {b}^{3}) + b( {a}^{2} - ab + {b}^{3} ) [/tex]

[tex]: \implies {a}^{3} - {a}^{2} b + a {b}^{3} + {a^2b} - {ab}^{2} + {b}^{4} [/tex]

[tex]: \implies{ {a}^{3}+ab^3 - ab^2+ {b}^{4} }[/tex]

Step-by-step explanation:

[tex] \blue{ \frak{Seolle_{aph.rodite}}}[/tex]

An x-intercept of the continuous function in the table is (-1, 0)

The x-intercept of a line is the point where the line crossed the x-axis or the  point where the value of y is zero.

From the table, the x-intercept are all the point where the value of f(x) is zero. Hence the Which is an x-intercept of the continuous function in the table is (-1, 0)

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Given the diameter of the surface of the clock, the area of the surface of the alarm clock is 3846.5cm².

Note that: Area of a circle is expressed as;

A = πr²

Where r is radius and π is constant pi ( π = 3.14 )

Given that;

A = πr²

A = 3.14 × ( 35cm )²

A = 3.14 × 1225cm²

A = 3846.5cm²

Therefore, given the diameter of the surface of the clock, the area of the surface of the alarm clock is 3846.5cm².

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Step-by-step explanation:

12 . The x-intercept is where a line crosses the x-axis, and the y-intercept is the point where the line crosses the y-axis. Thinking about intercepts helps us graph linear equations..

[tex]\text{Nth term of an arithmetic series} = a +(n-1)d \\\\\text{Nth term of an geometric series}= ar^{n-1}\\\\\text{where,}\\\\\text{a = first term.}\\\\\text{d = common difference.}\\\\\text{r = common ratio.}[/tex]

Answer:

2

Step-by-step explanation:

the same as...

(2) is the answer

If the population is highly skewed, the sample size needed for the central limit theorem to apply usually has to be the same as that when the population is not highly skewed.

The central limit theorem states in probability theory that, in many instances, when independent random variables are added together, their correctly normalized sum tends toward a normal distribution, even if the original variables are not normally distributed.

If the population is highly skewed, the sample size needed for the central limit theorem to apply usually has to be the same as that when the population is not highly skewed.

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