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1 year ago

Find the sum of the first 46 terms of the following series, to the nearestinteger.12, 15, 18, ...

Mathematics

1 answer:

creativ13 [48]1 year ago

8 0

We can see that this is an arithmetic sequence. The first term is 12 and the common difference is 3.

Using the formula to calculate the sum of the first 46 terms, we have:

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91284 the nearest ten thousand

almond37 [142]

91284 the nearest ten thousand is 9

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3 years ago

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Harriet needs to ship a small vase. The box she will use has a volume of 216 cubic inches. If the side lengths are all the same,

ArbitrLikvidat [17]

Fist if there is 4 sides on the base you would divide 216/4 =54

Or if there are 2 sides you would divide 216/2= 108

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3 years ago

In interpreting a boxplot of a data set we note that the median is to the left of the center of the and the right line is longer

pantera1 [17]

Answer:

Option A

Step-by-step explanation:

When the median is to the left of the center of the distribution with the right line longer than the left, we can conclude that the data is skewed to the right. Here the mean is larger than the median thus skewing the distribution to the right.

Representing this on an histogram including data will show a better description and also indica the longer right line.

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3 years ago

Elena bikes 20 minutes each day for exercise. Write an equation to describe the relationship between her distance in miles, D, a

kompoz [17]

Answer:

The equation to describe the relationship between Elena distance:

a) D = 4.34 miles, b) D = 4.25 miles and c) 12D = M + 3N miles.

Solution:

Given, Elena bikes 20 minutes each day for exercise.

We have to write an equation to describe the relationship between her distance in miles, D, and her biking speed, in miles per hour,

We know that, distance travelled = speed $\times$ time

a. At a constant speed of 13 miles per hour for the entire 20 minutes

Her speed is 13 miles per hour.

Then, distance D miles = 13 miles per hour $\times$ 20 minutes

$\mathrm{D}=13 \text { miles per hour } \times \frac{20}{60} \text { hours } \rightarrow \mathrm{d}=13 \times \frac{1}{3} \rightarrow \mathrm{d}=4.34 \text { miles approximately. }$

b. At a constant speed of 15 minutes per hour for the first 5 minutes, then at 12 miles per hour for the last 15 minutes

Now, total distance travelled = distance travelled with 15 mph + distance travelled with 12 mph

$\begin{array}{l}{\mathrm{D}=15 \mathrm{mph} \times 5 \text { minutes }+12 \mathrm{mph} \times 15 \text { minutes }} \\\\ {\mathrm{D}=15 \mathrm{mph} \times \frac{5}{60} \text { hours }+12 \mathrm{mph} \times \frac{15}{60} \text { minutes }} \\\\ {\mathrm{D}=15 \times \frac{1}{12}+12 \times \frac{1}{4} \rightarrow \mathrm{D}=\frac{5}{4}+3 \rightarrow \mathrm{D}=3+1.25 \rightarrow \mathrm{D}=4.25 \mathrm{miles}}\end{array}$

c. At a constant speed of M miles per hour for the first 5 minutes, then at N miles per hour for the last 15 minutes

Now, total distance travelled = distance travelled with M mph + distance travelled with N mph

$D = M mph \times 5 minutes + N mph \times 15 minutes$

$\mathrm{D}=\mathrm{M} \mathrm{mph} \times \frac{5}{60} \text { hours }+\mathrm{N} \mathrm{mph} \times \frac{15}{60} \text { minutes }$

$\mathrm{D}=\mathrm{M} \times \frac{1}{12}+\mathrm{N} \times \frac{1}{4} \rightarrow \mathrm{D}=\frac{M}{12}+\frac{N}{4} \rightarrow \mathrm{D}=\frac{M}{12}+\frac{3 N}{12} \rightarrow 12 \mathrm{D}=\mathrm{M}+3 \mathrm{N} \text { miles }$

Hence, a) D = 4.34 miles, b) D = 4.25 miles and c) 12D = M + 3N miles.

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4 years ago

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Serggg [28]

Answer:

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