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18 days 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 prime numbers are odd with the exception of two. Hence, if we consider the sum of the first million primes, it consists of one even number combined with 999,999 odd numbers. Since the product of an odd number multiplied by another odd number results in an odd number, we conclude that the sum must be an odd number, being even + odd = odd.

It's clear that an odd number ends with an odd digit, so the only digit that can be eliminated is b (an even digit).

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Valeriya wants to determine the likely voting outcome for the new town council election. Which sample is likely to yield the mos

tester [8842]

I believe the answer is A, since individuals employed at the largest corporation may hold different views compared to those not working in large companies. The benefits associated with one's employment can vary, and those at the major corporation may only reflect the interests of the upper class, leaving out perspectives from those who do not have high-paying corporate jobs.

3 0

9 days ago

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A rectangular prism must have a base with an area of no more than 27 square meters. The width of the base must be 9 meters less

Leona [9271]

Answer:

The upper limit for the height of the prism is $12\ m$

Step-by-step explanation:

Let

x------> represent the height of the prism

It is known that

the area of the base of the prism must not exceed

$A=L*W$

$A\leq 27\ m^{2}$

thus

$L*W\leq 27$ -------> inequality A

$W=x-9$ ------> equation B

$L=W+6$ -----> equation C

Insert equation B into equation C

$L=(x-9)+6$

$L=x-3$ ------> equation D

Substituting equations B and D into inequality A

$(x-3)*(x-9)\leq 27$ -------> using a graphing tool to solve the inequality

The resultant solution for x lies in the interval----------> $[0,12]$

consult the attached figure

but bear in mind that

The width of the base must be $9$ meters shorter than the height of the prism

thus

the solution for x is confined to the interval ------> $(9,12]$

The maximum height of the prism equals $12\ m$

8 1

23 days ago

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Given: ΔABC, AC = BC, AB = 3 CD⊥ AB, CD = 3 Find: AC

Leona [9271]

Answer:

3 $\sqrt{5}$ /2

Step-by-step explanation:

Given that AC = BC, this is an isosceles triangle.

Since CD is perpendicular to AB, we find AD = DB = 0.5AB = 3/2

Now considering triangle ACD,[TAG_17]]

we will use Pythagoras' theorem,

AC = $\sqrt{AD^{2} + CD^{2} }$

AC = 3 $\sqrt{5}$ /2

:-)

4 0

7 days ago

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Points A, B, and C, form a triangle. The distance between point A and point B is 15 yards. The distance between point B and poin

babunello [8412]

Answer:

(a)

The distance from A to B to C equals 40 yards.

(b)

w is less than 40.

Step-by-step explanation:

The information provided states:

The distance from A to B is 15 yards.

Thus, AB is 15 yards.

The distance from B to C is 25 yards.

Therefore, BC is 25 yards.

(a)

The total distance from A to B to C is given by AB plus BC.

A to B to C = 15 + 25.

The total distance is 40 yards.

(b)

The direct distance from A to C (AC) must be shorter than the length of A to B to C.

AC is less than AB plus BC.

AC must be less than 15 + 25.

Thus, AC is less than 40 yards.

w is less than 40.

8 2

1 month ago

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One sphere has a radius of 5.10 cm; another has a radius of 5.00cm. What is the difference in volume (in cubic centimeters) betw

lawyer [9240]

$\bf \textit{volume of a sphere}\\\\
V=\cfrac{4\pi r^3}{3}\qquad 
\begin{cases}
r=radius\\
-----\\
r_1=5.10\\
r_2=5
\end{cases}\implies \cfrac{V_1}{V_2}\implies \cfrac{\frac{4\pi \cdot 5.10^3}{3}}{\frac{4\pi \cdot 5^3}{3}}
\\\\\\
\cfrac{\underline{4\pi }\cdot 5.10^3}{\underline{3}}\cdot \cfrac{\underline{3}}{\underline{4\pi }\cdot 5^3}\implies \cfrac{5.10^3}{5^3}\implies \cfrac{132.651}{125}$

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13 days ago

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