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3 years ago

What is the area of the triangle? 6 2 3

Mathematics

1 answer:

Llana [10]3 years ago

7 0

Answer:

Step-by-step explanation:

Find the area of both triangles inside the bigger triangle and add them together.

Use the Pythagorean theorem to find the missing length of the leg in the smallest triangle:

a² + b² = c²

2² + b² = 3²

4 + b² = 9

5 = b²

2.2 ≈ b

Calculate the area of the smaller triangle:

1/2(bxh)

1/2(2 x 2.2)

1/2(4.4)

2.2

Calculate the area of the bigger triangle:

<em>We know that the longer leg is 3.8 units because we were able to subtract the length of the smaller triangle's leg from 6. </em>

1/2(bxh)

1/2(2 x 3.8)

1/2(7.6)

3.8

Add both areas to find the area of the largest triangle:

3.8 + 2.2 = 6

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A high-altitude spherical weather balloon expands as it rises, due to the drop in atmospheric pressure. Suppose that the radius

lord [1]

The increase of the radius is a linear increase since we have the constant rate of 0.07 inches per second

The equation for a linear growth/decay is given by the form $y=mx+c$ where $m$ is the rate of increase and $c$ is the value of $y$ when $x=0$

We have
$m = 0.07$
$c=36$ when $t=0$

So the equation is $r=0.07t+36$

The length of the radius when $t=400$ seconds is
$r=0.07(400)+36$
$r=64$ inches

7 0

2 years ago

Researchers are interested if a school breakfast program leads to taller children. Assume that the population of all 5 year-old

DedPeter [7]

Answer:

$39-1.96\frac{1}{\sqrt{25}}=38.608$

$39+1.96\frac{1}{\sqrt{25}}=39.392$

So on this case the 95% confidence interval would be given by (38.608;39.392)

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$\bar X=39$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

$\sigma=1$ represent the population standard deviation

n=25 represent the sample size

Solution to the problem

The confidence interval for the mean is given by the following formula:

$\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (1)

The margin of error is given by:

$ME= z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$

Since the Confidence is 0.95 or 95%, the value of $\alpha=0.05$ and $\alpha/2 =0.025$ , and we can use excel, a calculator or a tabel to find the critical value. The excel command would be: "=-NORM.INV(0.025,0,1)".And we see that $z_{\alpha/2}=1.96$

And replacing we got:

$ME= 1.96 *\frac{1}{\sqrt{25}}= 0.392$

Now we have everything in order to replace into formula (1):

$39-1.96\frac{1}{\sqrt{25}}=38.608$

$39+1.96\frac{1}{\sqrt{25}}=39.392$

So on this case the 95% confidence interval would be given by (38.608;39.392)

7 0

2 years ago

For this exponential function what is the output value (y) when the input value (x) is 0?

Alenkinab [10]

Answer:

Step-by-step explanation:

$y^0=1\\5^0=1\\12*1=12$

6 0

3 years ago

Using GCF write an expression that is equivalent to 16p+48

aalyn [17]

You start by looking at what number can divide evenly into both 16 and 48. Both numbers are divisible by 16. 16 goes into 16 once and 16 goes into 48 three times. So you divide each term by 16 and your expression should look like this: 16 (p+3)

8 0

2 years ago

How do i solve this ?<br><img src="https://tex.z-dn.net/?f=5y%20-%202y%20%3D%2010%20%5C%5C%20" id="TexFormula1" title="5y - 2y =

Scorpion4ik [409]

Answer:

Step-by-step explanation:

5y - 2y = 10

3y = 10

y = 10/3 = 3⅓

3 0

2 years ago