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2 years ago

The sum of the first 1 million primes is N. Without knowing N's value, one can determine that the ones'digit of N cannot be

1 answer:

3 0

All primes are odd, except two. Therefore the sum of the first million primes is one even number plus 999999 odd numbers. Since odd*odd = odd, the first million primes must be even + odd = odd.

An odd number obviously has an odd final digit, so the only option that can be firmly rules out is b (which is even).

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How do you simplify expressions with rational exponents

Rainbow [258]

Answer:

Step-by-step explanation:

Simplify expression with rational exponents can look like a huge thing when you first see them with those fractions sitting up there in the exponent but let's remember our properties for dealing with exponents. We can apply those with fractions as well.

Examples

(a) $(p^4)^{\dfrac{3}{2}}$

From above, we have a power to a power, so, we can think of multiplying the exponents.

i.e.

$(p^{^ {\dfrac{4}{1}}})^{\dfrac{3}{2}}$

$(p^{^ {\dfrac{12}{2}}})$

Let's recall that when we are dealing with exponents that are fractions, we can simplify them just like normal fractions.

SO;

$(p^{^ {\dfrac{12}{2}}})$

$= (p^{ 6})$

Let's take a look at another example

$\Bigg (27x^{^\Big{6}} \Bigg) ^{{\dfrac{5}{3}}}$

Here, we apply the $\dfrac{5}{3}$ to both 27 and $x^6$

$= \Bigg (27^{{\dfrac{5}{3}}} \times x^\Big{\dfrac{6}{1}\times {{\dfrac{5}{3}}} }\Bigg)$

$= \Bigg (27^{{\dfrac{5}{3}}} \times x^\Big{\dfrac{2}{1}\times {{\dfrac{5}{1}}} }\Bigg)$

Let us recall that in the rational exponent, the denominator is the root and the numerator is the exponent of such a particular number.

∴

$= \Bigg (\sqrt[3]{27}^{5} \times x^{10} }\Bigg)$

$= \Bigg (3^{5} \times x^{10} }\Bigg)$

$= 249x^{10}$

8 0

2 years ago

the area of a rectangle is x²-3x-10. what is the length of the rectangle if the with is x +2.?plsss asap

Inga [223]

Answer:

x - 5

Step-by-step explanation:

x^2 - 3x - 10

= (x + 2)(x - 5)

Sine the width is (x + 2), the length is (x - 5).

Hope this helped!

7 0

2 years ago

F(x) = 1/x g(x)=x-4 can you evaluate (g*f)(0) ? Why or why not?

Dmitriy789 [7]

$(g\cdot f)(x)=\dfrac{1}{x}-4$

$D_{g(f(x))}:x\not =0$

No, since 0 doesn't belong to the domain.

5 0

2 years ago

Angela work on a straight 7% commission. Her friend worked on a salary of $600 plus a 10% commission. In a particular month, the

sveticcg [70]

all you need to do is change your percentages to decimal and then multiply

7 0

2 years ago

8(7 + 23) = 8(7) + 8(?)

34kurt

Answer: 23

When using multiplication with brackets, you multiply the number by all the numbers within the bracket before adding them together.

Therefore when it is 8(7 + 23) it basically means: 8(7) + 8(23)

7 0

2 years ago

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