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4 years ago

What is the sum of a 54–term arithmetic sequence where the first term is 6 and the last term is 377?

1 answer:

5 0

$S_n=\dfrac{(a_1+a_n)n}{2}\\--------------------\\a_1=6;\ n=54;\ a_n=a_{54}=377\\\\subtitute\\\\S_{54}=\dfrac{(6+377)\cdot54}{2}=483\cdot27=13,041\\\\Answer:\boxed{S_{54}=13,041}$

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The total weight of a rock depends on its size and is proportional to its density. In this context, density is the weight per cu

kow [346]

Answer:

$d = \frac{w}{48}$

If $\frac{1}{48} \\$ is constant, say k

Then,

$d = kw$

∴ d ∝ w

Hence, weight is proportional to the density

Step-by-step explanation:

From the question,

Let w denote the weight of the rock in pounds

s denote the size of the rock in cubic inches and

d denote the density of the rock in pounds per cubic inch.

First, we will write the equation connecting w, s, and d.

We get

$density (pounds/inch^{3} ) = \frac{weight(pounds)}{size (inch^{3}) }$

That is,

$d = \frac{w}{s}$

Now, given a 48-cubic-inch rock with weight w pounds, to show the proportional relation between the weight and the density, we will write

$d = \frac{w}{48}$

If $\frac{1}{48} \\$ is constant, say k

Then,

$d = kw$

∴ d ∝ w

Hence, density is proportional to the weight OR weight is proportional to the density

4 0

3 years ago

Please help me for a cookir

Eddi Din [679]

Answer:

Step-by-step explanation:

explanation in picture

5 0

3 years ago

15 and 14.7 are 1 apart, so 15 – 14.7 must be 1.

umka2103 [35]

Answer:

Step-by-step explanation:

15 - 14.7 =

15 .0

-14.7

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14. 10

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15- 14.7 = .3

8 0

4 years ago

Please answer as fast as you can

777dan777 [17]

Answer:

d = 3072.2 ft

Step-by-step explanation:

<h2>Circumference of circle:</h2>

Circumference of circle = 9687 ft

πd = 9687

$\sf \dfrac{22}{7}*d = 9687\\$

$d = 9687 * \dfrac{7}{22}\\\\d = 3082.2 \ ft$

6 0

2 years ago

1. Much has been made about the overall intelligence of criminal offenders in general, and violent offenders particular. There i

Tom [10]

Answer:

With regard to intelligence scores, at 95% confidence level, there is significant evidence to conclude that violent offenders are less intelligent than property offenders

Step-by-step explanation:

H_a: Violent offenders are less intelligent than property offenders

H_o: Violent offenders and property offenders do not differ significantly with regard to intelligence scores

Test statistic can be found using the formula

z= $\frac{X-Y}{\sqrt{\frac{s(x)^2}{N(x)}+\frac{s(y)^2}{N(y)}}}$ where

X is the mean IQ score of property offenders (96)

Y is the mean IQ score of violent offenders (88)

s(x) is the sample standard deviation of property offenders (8.5)

s(y) is the sample standard deviation of violent offenders (7.5)

N(x) is the sample size for property offenders (225)

N(y) is the sample size for violent offenders (200)

then z= $\frac{96-88}{\sqrt{\frac{8.5^2}{225}+\frac{7.5^2}{200}}}$ ≈10.3

One tail p-value of the test statistic is < 0.00001

Since p-value<0.05 (significance level) we reject the null hypothesis.

8 0

3 years ago