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3 years ago

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In a certain year solar and wind energy generated totaled 1016 trillion BTUs. Wind generated 53 trillion BTUs more than eight ti

mes that generated by solar energy. How much was generated by each source?

1 answer:

sleet_krkn [62]3 years ago

4 0

69 ya feel me homieee

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Turn 25/4 into a mixed number

horsena [70]

Mixed number is 6 1/4

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3 years ago

Why is it important to use significant digits to round the answer

VARVARA [1.3K]

To get closest to the precise answer

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4 years ago

A thermos in the shape of a cylinder is filled with coffee. The height of the cylinder is 12 inches and its radius is 2 inches.

serg [7]

Answer:

The volume of coffee in the thermos is 150.72 inches³ .

Step-by-step explanation:

Formula

$Volume\ of\ a\ cylinder = \pi r^{2}\ h$

Where r is the radius and h is the height .

As given

A thermos in the shape of a cylinder is filled with coffee.

The height of the cylinder is 12 inches and its radius is 2 inches.

As

$\pi = 3.14$

Put all the value in the formula

$Volume\ of\ a\ cylinder = 3.14\times 2\times 2\times 12$

= 150 .72 inches ³

Therefore the volume of coffee in the thermos is 150 .72 inches ³ .

3 0

3 years ago

Estimate the perimeter of the figure to the nearest tenth.

pantera1 [17]

Answer:

<em>The Perimeter of the Figure to the nearest tenth is 18.7 units</em>

Step-by-step explanation:

<em>Please note I have attached an edited version of your sketch to aid my solution. Now this question can be solved in multiple ways. Here, we shall see one of them. </em>

<em />

Looking at the original sketch, we can see that the figure is actually a combination of a Triangle (Figure 1 in my sketch) and a rectangle (Figure 2 in my sketch). So we can simply find the sides of a Triangle and the sides of a Rectangle and add them.

<u>Perimeter on Figure 1:</u>

The Perimeter of a Triangle is given by the Sum of the three sides as:

$A_{T}=a+b+c$

<u>Perimeter on Figure 2:</u>

The Perimeter of the Rectangle is given by:

$A_{R}=2(w+l)$

where here $w$ is the width and $l$ is the length of the rectangle.

<u>Perimeter on Sketched Figure:</u>

<u><em>The perimeter of the total figure will be two sides of the triangle and the three sides of the rectangle (as the one adjacent between Fig. 1 and 2 can not be taken into account). Thus we need to find 5 different sides and add them together. </em></u>

Now since the figure is on a <em>graph paper</em>, we can read of the size of some sides, thus the left side of the triangle is $a=3$ units and the base of the triangle is also $b=3$ units. Now to find the last unknown side we can take Pythagorian theorem, since our triangle is a Right triangle, (i.e. one angle is 90°).

<em>Pythagoras states that the squared of the hypotenuse of a right triangle is equal to the sum of the squares of the other two legs of the triangle (where the hypotenuse side is always across the 90° angle</em>. So here we can say that:

$h^2=a^2+b^2\\$

where $h$ is the hypotenuse and our unknown side. So plugging in values and solving for $h$ we have:

$h=\sqrt{a^2+b^2}\\ h=\sqrt{3^2+3^2}\\\\h=\sqrt{9+9}\\ h=\sqrt{18}\\ h=3\sqrt{2}$ units.

So from figure 1 we now have two known sides:

$a=3\\h=3\sqrt{2}$

Now lets find the other three sides from Figure 2. So here similarly we can read from the graph paper that the base of the rectangle (i.e. the width $w$ ) is $w=3$ and the lengths of the rectangle, are equal and also of the same length as the hypotenuse on the triangle steps. Thus from Figure 2 we have the three remaining sides as:

$w=3\\l=h=3\sqrt{2}$

So finally the Perimeter of the Sketched Total Figure will be the summation of all 5 sides as:

$\Pi_{figure}=a+h+w+l+l\\\Pi_{figure}=3+3\sqrt{2}+3+2(3\sqrt{2} )\\\Pi_{figure}= 6+9\sqrt{2} \\\Pi_{figure}=18.7$ units

(rounded to the nearest tenth)

5 0

4 years ago

A study is done to determine if students in the California state university system (sample 1) take longer to graduate, on averag

Debora [2.8K]

Answer:

We conclude that the students in the California state university system take longer to graduate as compared to students enrolled in private universities.

Step-by-step explanation:

We are given that from years of research, it is known that the population standard deviations are 1.5 years and 0.9 years, respectively.

One hundred students from each the California state university system and private universities are surveyed. The California state university system students took on average 4.8 years while the private university students took on average 4.4 years.

<em>Let </em> $\mu_1$ <em> = population average time taken by students in the California state university system to graduate</em>

<em> </em> $\mu_2$ = <em>population average time taken by students in the private universities to graduate</em>

SO, <u>Null Hypothesis</u>, $H_0$ : $\mu_1-\mu_2\leq0$ or $\mu_1 \leq \mu_2$ {means that the students in the California state university system take less than or equal time to graduate as compared to students enrolled in private universities}

<u>Alternate Hypothesis</u>, $H_A$ : $\mu_1-\mu_2 >0$ or $\mu_1>\mu_2$ {means that the students in the California state university system take longer to graduate as compared to students enrolled in private universities}

The test statistics that will be used here is <u>Two-sample z test</u> <u>statistics</u> as we know about the population standard deviations;

T.S. = $\frac{(\bar X_1-\bar X_2)-(\mu_1-\mu_2)}{\sqrt{\frac{\sigma_1^{2} }{n_1} + \frac{\sigma_2^{2} }{n_2}} }$ ~ N(0,1)

where, $\bar X_1$ = sample average time taken by the California state university system students to graduate = 4.8 years

$\bar X_2$ = sample average time taken by the private university students to graduate = 4.4 years

$\sigma_1$ = population standard deviation for California state university system students = 1.5 years

$\sigma_2$ = population standard deviation for private university students = 0.9 years

$n_1$ = sample of California state university system students taken = 100

$n_2$ = sample of private university students taken = 100

So, <em><u>test statistics</u></em> = $\frac{(4.8-4.4)-(0)}{\sqrt{\frac{1.5^{2} }{100} + \frac{0.9^{2} }{100}} }$

= 2.287

<em>Now at 0.10 significance level, the z table gives critical value of 1.2816 for right-tailed test. Since our test statistics is more than the critical value of z so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region.</em>

Therefore, we conclude that the students in the California state university system take longer to graduate as compared to students enrolled in private universities.

5 0

4 years ago