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3 years ago

Solve 2 log x = log 36

Mathematics

2 answers:

zheka24 [161]3 years ago

8 0

2log x= log 36
$logx^{2} =log 36$
$x^{2} =36$
x=6

kirill [66]3 years ago

3 0

Answer:

x=6

Step-by-step explanation:

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If three prime numbers are randomly selected from the prime numbers less than 30 and no prime number can be chosen more than onc

Dmitry [639]

Answer:

C)30%

Step-by-step explanation:

Prime numbers less than 30 are given below

2,3,5,7,11,13,17,19,23,29

We have to find the probability that sum of three prime numbers selected will be even.

We know that

Sum of any three prime number except 2 will be odd.

Total prime numbers except 2=9

Total prime numbers=10

Probability:P(E)= $\frac{favorable\;cases}{total\;number\;of\;cases}$

Probability of getting sum of three prime numbers selected will be odd= $\frac{9C_3}{10C_3}$

$nC_r=\frac{n!}{r!(n-r)!}$

By using formula

Probability of getting sum of three prime numbers selected will be odd=P(E)= $\frac{\frac{9!}{3!6!}}{\frac{10!}{3!7!}}=\frac{9!}{3!6!}\times \frac{3!\times 7\times 6!}{10\times 9!}$

Probability of getting sum of three prime numbers selected will be odd=P(E)= $0.7$

Probability of getting sum of three prime numbers selected will be even=P(E')=1-0.7=0.3= $0.3\times 100=30$ %

By using formula P(E')=1-P(E)

3 0

2 years ago

The equipment operates 5 days a week for 12 hours each day according to last weeks production numbers shown in the table how man

Pani-rosa [81]

Answer:

cawnser is 60

Step-by-step explanation:

because 5 times 12 is 60 hours

8 0

3 years ago

The ratio of boys to girls in the ninth grade is 6:5. If there are 185 girls in the class, how many boys are there?

xeze [42]

Answer:

$222$ boys

Step-by-step explanation:

Let $x$ = total number of ninth graders. By knowing how many students there are in the grade, we can find for the number of boys.

$\frac{5}{6+5}x = 185$ (number of girls in ninth grade)

$\frac{5}{11}x = 185$

$x=407$

To find for the number of boys, we can use substitution:

$\frac{6}{6+5}x = \frac{6}{11}(407)$

$=222$

∴ There are $222$ boys in the class.

Hope this helps :)

8 0

2 years ago

Read 2 more answers

Write a quadratic equation given the roots -1/3 and 5, show your work

Travka [436]

$\boxed{(x - a)(x - b) = 0}$

The equation above is the intercept form. Both a-term and b-term are the roots of equation.

$x = - \frac{1}{3} \\ x = 5$

These are the roots of equation. Therefore we substitute a = - 1/3 and b = 5 in the equation.

$(x + \frac{1}{3} )(x - 5) = 0$

Here we can convert the expression x+1/3 to this.

$x + \frac{1}{3} = 0 \\ 3x + 1 = 0$

Rewrite the equation.

$(3x + 1)(x - 5) = 0$

Simplify by multiplying both expressions.

$3 {x}^{2} - 15x + x - 5 = 0 \\ 3 {x}^{2} - 14x - 5 = 0$

Answer Check

Substitute the given roots in the equation.

$3 {(5)}^{2} - 14(5) - 5 = 0 \\ 75 - 70 - 5 = 0 \\ 75 - 75 = 0 \\ 0 = 0$

$3( - \frac{1}{3} )^{2} - 14( - \frac{1}{3}) - 5 = 0 \\ 3( \frac{1}{9} ) + \frac{14}{3} - 5 = 0 \\ \frac{1}{3} + \frac{14}{3} - \frac{15}{3} = 0 \\ \frac{15}{3} - \frac{15}{3} = 0 \\ 0 = 0$