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3 years ago

. Find the 20th term of the arithmetic sequence 15, 9, 3, -3

Mathematics

1 answer:

vova2212 [387]3 years ago

3 0

Answer:

a20 = -99

Step-by-step explanation:

hello :

the nth term in this arithmetic sequence is : an = a1 + (n -1 )d

a1 = 15 a2 = 9 d = a2-a1 = 9-15 = -6 ( common difrence)

an = 15 + (n -1 )(-6)

an = 15+6-6n

an = -6n+21

the 20th term when n = 20 : a20 = -6(20)+21 = -99

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Compute a 99% confidence interval for the mean weight of toxic substance per gram of mold culture. State the assumption you make

kow [346]

Complete Question

The complete question is shown on the first uploaded image

Answer:

The 99% confidence interval is $2.4309 < \mu < 4.9328$

Step-by-step explanation:

From the question we are told that

The data is 3, 2,5, 3, 2, 6, 5,4.5, 3, 3, and 4

The sample size is n = 11

Generally the sample mean is mathematically represented as

$\= x = \frac{\sum x_i}{n}$

=> $\= x = \frac{3+ 2+5+ \cdots +4 }{11}$

=> $\= x = 3.6818$

Generally the sample standard deviation is mathematically represented as

$\sigma = \sqrt{\frac{\sum [ x_i - \= x ] }{n} }$

=> $\sigma = \sqrt{\frac{[ 3 - 3.6818 ]^2 +[ 2 - 3.6818 ]^2 + \cdots + [ 4 - 3.6818 ]^2 }{11} }$

=> $\sigma = 1.3091$

Given that the confidence interval is 99% then the level of significance is mathematically represented as

$\alpha= (100 - 99) \%$

=> $\alpha= 0.01$

Given that the sample size is small we will making use of t distribution table

Generally from the t distribution table the critical value of at a degree of freedom of is

$t_{\frac{\alpha }{2} , 10 } =3.16927267$

Generally the margin of error is mathematically represented as

$E = 3.16927267 * \frac{1.3091 }{\sqrt{11} }$

$E = 1.251$

Generally 99% confidence interval is mathematically represented as

$3.6818 -1.251 < p < 3.6818 + 1.251$

=> $2.4309 < \mu < 4.9328$

8 0

3 years ago

AlMarai, a beverage company is planning to change its juice package size. Currently, there are 9 ounces of juice in each package

Andre45 [30]

The percentage of more juices that will be in the new package is 35.71%

<h3>What are word problems?</h3>

Word problems in mathematics are things happening in our daily life and we can use mathematical concepts and arithmetic operations to put a solution to those things.

From the given information, it was stated that:

Almarai usually have 9 ounces of juice in each package, while
Their new package will contain 14 ounces.

Our objective is to find the percentage of more juice that will be in the new package.

The percentage of more juice in the new package will be:

$\mathbf{=\dfrac{14 - 9}{14} \times 100 \%}$

$\mathbf{=\dfrac{5}{14} \times 100 \%}$

= 35.71%

Learn more about word problems here:

brainly.com/question/21405634

7 0

3 years ago

Guys please help me with this question

diamong [38]

Answer: Can I get brainliest and 5 stars? thank you.

a) $\frac{65}{99}$

b) $\frac{59}{90}$

c) $\frac{13}{20}$

Step-by-step explanation:

a) $0.65$ I can't put line above it, but the line expresses that 6 and 5 and repeating infinitely. Let X equal the decimal number.

$x=0.65$

First multiply by 1 followed by as many zeros as repeating numbers there are. In this case since 6 and 5 are the repeating numbers, we have to add 2 zeros which is basically multiplying by 100

0.65*100=65.65 (another 65 remains on the right because they're infinite.)

Now substract from the original number. Now we have a new equation that says: $100x=65.65$ .

Substract equation 1 from equation 2.

$100x=65.65\\-x=0.65$

---------------------------------

$99x=65$

Solve just like any other equation. Divide by 99 to isolate x.

$\frac{99x}{99}=\frac{65}{99}$

$x=\frac{65}{99}$ This is the fraction.

------------------------------------------------------------------------------------------------

b) $0.65^-$ This one is a little bit different because we only have 1 repeating number.

In this case we have to multiply by 10.

$0.65^-*10=6.55^-$

Equation 1: $x=0.65^-$

Equation 2: $10x=6.55^-$

Substract.

$10x=6.55^-\\-x=0.65^-$

-----------------------

$9x=5.9$

divide by 9 to isolate x

$\frac{9x}{9}=\frac{5.9}{9}$

$x=\frac{5.9}{9}$

To get rid of the decimal in the numerator, multiply both numerator and denominator by 10 so that we don't change the fraction.

$x=(\frac{5.9*10}{9*10} )$

$x=\frac{59}{90}$ and this is your fraction.

------------------------------------------------------------------------------------------------------

c) 0.65 this one has no repeating number. It's a finite decimal number.

I assume you already know that; $a=\frac{a}{1}$ , so, we can do the same here to have a fraction.

$0.65=\frac{0.65}{1}$

Now, in order to get rid of the decimal, multiply by 1 followed by as many zeros as decimal numbers are. In this case 2 zeros because there are 2 decimal numbers, so it's 100. Remember that if you do it in the numerator, you have to do it in the denominator as well to not change the fraction.

$\frac{0.65*100}{1*100} =\frac{65}{100}$

Simplify if possible.

$\frac{65/5}{100/5} =\frac{13}{20}$ This is your fraction.

6 0

3 years ago

In the measurement of 67.93 cm, which digit is estimated? click on the estimated digit

scoundrel [369]

When it comes to measurement, the most accurate estimate would be the whole number. A ruler has calibrated marks. It would be easy to locate 25. But when it is located between 25 to 26, you would have to estimate the decimal points. Generally, calibration marks are up to the tenths digit. For further digits, that would only an estimation. So, the estimated digit in this problem is 3 in the hundredths place.

8 0

3 years ago

The inverse of F(C)=9/5C+32

Nataliya [291]

F(C) = 9/5C + 32

I'll just change F(C) to y and 9/5C to 9/5x.
y = 9/5x + 32

inverse...

x = 9/5y + 32
9/5y = x - 32
y = 5/9x - 160/9

Sooooo
F(C) = 5/9C - 160/9

6 0

3 years ago