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3 years ago

The angle measurements in the diagram are represented by the following expressions.

Mathematics

1 answer:

aliya0001 [1]3 years ago

8 0

Angle a and b are supplementary angles which means that when added they equal 180.
so we must set our equation equal to 180.
8x+74+2x+56=180
which simplifies to 10x+130=180
then subtract 130 from both sides.
10x=50
x=5

So we plug in 5 to find the measure of b.
2(5)+56=b
10+56=b
66=b
the measure of angle b is 66 degrees

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a store sells grass seed in small bags and large bags.the small bags have 7 pounds of seed for 27.93 and large bags cost 66.98.w

Nonamiya [84]

Answer

Find out the ratio of price to pound for each bag.

To prove

As given

A store sells grass seed in small bags and large bags.the small bags have 7 pounds of seed for $27.93 .

7 pound = $27.93

Now find out the cost for the 1 pound.

$1\ pound\ cost= \frac{27.93}{7}$

1 pound cost = $3.99

As given large bags cost $66.98.

Now find out pounds in the large bags.

Let us assume that the number of pounds in the large bags be x.

Than

3.99 × x = 66.98

$x = \frac{66.98}{3.99}$

x = 16.8 pounds (approx)

Now find out the ratio of price to pound for each bag.

As small bags weight = 7 pounds

Cost of the small bags = $27.93

$\frac{Price\ of\ small\ bag}{Cost\ of\ the\ small\ bags} = \frac{27.93}{7}$

As large bags weight = 16.8 pounds

Cost of the large bags = $66.98

$\frac{Price\ of\ large\ bag}{Cost\ of\ the\ large\ bags} = \frac{66.98}{16.8}$

Hence proved

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3 years ago

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2 years ago

Compute the mean, median, and mode for the following three sets of scores saved.

igor_vitrenko [27]

Answer/Step-by-step explanation:

Score 1:

3, 7, 5, 4, 5, 6, 7, 8, 6, 5

Mean = $\frac{3 + 7 + 5 + 4 + 5 + 6 + 7 + 8 + 6 + 5}{10} = \frac{56}{10} = 5.6$

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3, 4, 5, 5, 5, 6, 6, 7, 7, 8

The median is average of the fifth and sixth data value in the data set

Median = (5 + 6)/2 = 11/2 = 5.5

Mode = value with the highest frequency = 5

Score 2:

34, 54, 17, 26, 34, 25, 14, 24, 25, 23

Mean = sum of all values/10

Mean = 276/10 = 27.6

Median: order the data set from min to max.

14, 17, 23, 24, 25, 25, 26, 34, 34, 54

The median is average of the fifth and sixth data value in the data set

Median = (25 + 25)/2 = 50/2 = 25

Mode = 25 and 34 (both have frequencies of 2)

Score 3:

154, 167, 132, 145, 154, 145, 113, 156, 154, 123

Mean = sum of all values/10

Mean = 1443/10 = 144.3

Median: order the data set from min to max.

113, 123, 132, 145, 145, 154, 154, 154, 156, 167

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8 0

3 years ago

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Arlecino [84]

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Now the arc length over an arbitrary interval $(a,b)$ is

$\displaystyle\int_a^b\sqrt{1+\left(\frac{\mathrm dy}{\mathrm dx}\right)^2}\,\mathrm dx=\int_a^b\sqrt{1+x^3-1}\,\mathrm dx=\int_a^bx^{3/2}\,\mathrm dx$

But before we compute the integral, first we need to make sure the integrand exists over it. $x^{3/2}$ is undefined if $x$ , so we assume $a\ge0$ and for convenience that $a$ . Then

$\displaystyle\int_a^bx^{3/2}\,\mathrm dx=\frac25x^{5/2}\bigg|_{x=a}^{x=b}=\frac25\left(b^{5/2}-a^{5/2}\right)$

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3 years ago