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3 years ago

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artcher [175]3 years ago

7 0

Answer:

how tall is the fireman?

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In arithmetic sequence tn find: S10, if t2=5 and t8=15

makkiz [27]

Given:

$\bold{t_2=5}\\\\\bold{t_8=15}\\\\$

To find:

$\bold{T_n=?}\\\\\bold{S_{10}=?}$

Solution:

$\to \bold{t_2=5}\\\\ \bold{a+d=5} \\\\ \bold{a=5-d} ................(i)\\\\ \to \bold{t_8=15}\\\\ \bold{a+ 7d=15}.................(ii)\\\\$

Putting the equation (i) value into equation (ii):

$\to \bold{5-d+7d=15}\\\\\to \bold{5+6d=15}\\\\\to \bold{6d=15-5}\\\\\to \bold{6d=10}\\\\\to \bold{d=\frac{10}{6}}\\\\\to \bold{d=\frac{5}{3}}\\\\$

Putting the value of (d) into equation (i):

$\to \bold{a=5-\frac{5}{3}}\\\\\to \bold{a=\frac{15-5}{3}}\\\\\to \bold{a=\frac{10}{3}}\\\\$

Calculating the $\bold{t_n :}$

$\to \bold{t_n=a+(n-1)d}\\\\\to \bold{t_n=\frac{10}{3}+(n-1)\frac{5}{3}}\\\\\to \bold{t_n=\frac{10}{3}+\frac{5}{3}n-\frac{5}{3}}\\\\\to \bold{t_n=\frac{10}{3}-\frac{5}{3} +\frac{5}{3}n}\\\\\to \bold{t_n=\frac{10-5}{3} +\frac{5}{3}n}\\\\\to \bold{t_n=\frac{5}{3} +\frac{5}{3}n}\\\\ \to \bold{t_n=\frac{5}{3}(1+n)}\\\\$

Formula:

$\bold{S_n = \frac{n}{2}[2a + (n - 1)d ] }\\$

Calculating the $\bold{S_{10}} :$

$\to \bold{S_{10} = \frac{10}{2}[2\frac{10}{3} + (10- 1)\frac{5}{3} ] }\\\\\to \bold{S_{10} = 5[\frac{20}{3} + (9)\frac{5}{3} ] }\\\\\to \bold{S_{10} = 5[\frac{20}{3} + 9 \times \frac{5}{3} ] }\\\\\to \bold{S_{10} = 5[\frac{20}{3} + 3\times 5 ] }\\\\\to \bold{S_{10} = 5[\frac{20}{3} + 15 ] }\\\\\to \bold{S_{10} = 5[\frac{20+ 45}{3} ] }\\\\\to \bold{S_{10} = 5[\frac{65}{3} ] }\\\\\to \bold{S_{10} = 5 \times \frac{65}{3} }\\\\\to \bold{S_{10} = \frac{325}{3} }\\\\\to \bold{S_{10} =108.33 }$

Therefore, the final answer is " $\bold{\frac{5}{3}(1+n)\ and\ 108.33}$ "

Learn more:

brainly.com/question/11853909

7 0

3 years ago

How would the expression x2 +8 be rewritten using Sum of Cubes?

Nadusha1986 [10]

Answer:

$x^3+8=(x+2)(x^2-2x+4)$

So if they meant $x^3+8$ then the answer is:

$(x+2)(x^2-2x+4)$ .

The choice this corresponds to is A.

Step-by-step explanation:

The sum of cubes formula for factoring or expanding:

$a^3+b^3=(a+b)(a^2-ab+b^2)$

You have I'm assuming they meant:

$x^3+8$ .

Compare $x^3+8$ to $a^3+b^3$ .

You should see in place of $a$ you have $x$ .

You should also see in place of $b$ you have $2$ .

$a^3+b^3=(a+b)(a^2-ab+b^2)$

$x^3+8$

$x^3+2^3$

$x^3+2^3=(x+2)(x^2-2x+2^2)$

$x^3+8=(x+2)(x^2-2x+4)$

Let's check it for fun.

So we are going to use the distributive property.

We are going to distribute all the terms in the first ( ) to all the terms in the second ( ).

$x(x^2-2x+4)$ + $2(x^2-2x+4)$

$x^3-2x^2+4x$ + $2x^2-4x+8$

Combine like terms:

$x^3-2x^2+2x^2+4x-4x+8$

Simplify the grouping of like terms:

$x^3+0x^2+0x+8$

0 times anything is 0:

$x^3+8$

8 0

3 years ago

What occurs immediately following cytokinesis?

katrin [286]

The answer is A. The G1 portion of interphase.

8 0

3 years ago

Suppose that IQ scores have a bell-shaped distribution with a mean of 104 and a standard deviation of 15. Using the empirical ru

Harlamova29_29 [7]

Answer:

1.35%

Step-by-step explanation:

Suppose that IQ scores have a bell-shaped distribution with a mean of 104 and a standard deviation of 15. Using the empirical rule, what ? Please do not round your answer.

Empirical rule formula states that:

95% of data falls within 2 standard deviations from the mean - between μ – 2σ and μ + 2σ .

99.7% of data falls within 3 standard deviations from the mean - between μ - 3σ and μ + 3σ .

We don't know the number of Standard deviation yet , hence:

Mean = 104

Standard deviation = 15.

At least 59

Hence:

104 - 15x = 59

104 - 59 = 15x

45 = 15x

x = 45/15

x = 3

Hence, At least 59 is 3 standard deviations away from the mean on one side of the distribution thus,

99.7% of data falls within 3 standard deviations from the mean - between μ - 3σ and μ + 3σ .

100% - 99.7%

= 0.003

Since it is on one side of the distribution:

= 1.5% - 0.3%

= 0.015 - 0.0015

= 0.00135

Converting to percentage

= 1.35%

The percentage of IQ scores that are at least 59 is 1.35%

5 0

3 years ago

Find the value of x that will make A||B. <br><br> Please help!

Serggg [28]

Answer:

x=30

Step-by-step explanation:

Hi there!

For A to be parallel to B, 5x would be equal to 3x+60. (If they were parallel, these two angles would be alternate exterior angles, which are equal.)

$5x=3x+60$

Subtract 3x from both sides

$5x-3x=3x+60-3x\\2x=60$

Divide both sides by 2

$x=30$

I hope this helps!

6 0

3 years ago