Who can slove this????

Can y’all give me the area of each figure

KIM [24]

Answer:

1. 208 in^2

Step-by-step explanation:

1. We can break the shape up into a rectangle in the middle and 2 triangles on either side of said rectangle.

The dimensions of the rectangle are 8 in by 20 in, and we only know one leg of the triangle as well as the hypotenuse.

If we know one leg and the hypotenuse we can use the pythagorean theormed to sovle for the other side and get 6 in.

So we have

(8 * 20) + 2((1/2)(6)(8))

160 + 48

208 in^2

5 0

3 years ago

My brother wants to estimate the proportion of Canadians who own their house.What sample size should be obtained if he wants the

AVprozaik [17]

Answer:

a) $n=\frac{0.675(1-0.675)}{(\frac{0.02}{1.64})^2}=1475.07$

And rounded up we have that n=1476

b) $n=\frac{0.5(1-0.5)}{(\frac{0.02}{1.64})^2}=1681$

And rounded up we have that n=1681

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".

The population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{\hat p(1-\hat p)}{n}})$

The margin of error for the proportion interval is given by this formula:

$ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}$ (a)

If solve n from equation (a) we got:

$n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}$ (b)

Part a

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 90% of confidence, our significance level would be given by $\alpha=1-0.9=0.1$ and $\alpha/2 =0.05$ . And the critical value would be given by:

$z_{\alpha/2}=\pm 1.64$

The margin of error for the proportion interval is given by this formula:

$ME=z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}$ (a)

And on this case we have that $ME =\pm 0.02$ and we are interested in order to find the value of n, if we solve n from equation (a) we got:

$n=\frac{\hat p (1-\hat p)}{(\frac{ME}{z})^2}$ (b)

And replacing into equation (b) the values from part a we got:

$n=\frac{0.675(1-0.675)}{(\frac{0.02}{1.64})^2}=1475.07$

And rounded up we have that n=1476

Part b

For this case since we don't have a prior estimate we can use $\hat p =0.5$

$n=\frac{0.5(1-0.5)}{(\frac{0.02}{1.64})^2}=1681$

And rounded up we have that n=1681

8 0

3 years ago

(x+5)(√ 1-x)<br> what is the product of this composite function?

Radda [10]

Answer:

$x\sqrt{1-x}+5\sqrt{1-x}$

Step-by-step explanation:

$(x+5)(\sqrt{1-x} )\\\\=\left(\sqrt{1-x}\right)\left(x+5\right)\\\\\mathrm{Apply\:the\:distributive\:law}:\quad \:a\left(b+c\right)=ab+ac\\\\a=\left(\sqrt{1-x}\right),\:b=x,\:c=5\\\\=\left(\sqrt{1-x}\right)x+\left(\sqrt{1-x}\right)\times\:5\\\\=x\left(\sqrt{1-x}\right)+5\left(\sqrt{1-x}\right)\\\\\mathrm{Remove\:parentheses}:\quad \left(a\right)=a\\\\=x\sqrt{1-x}+5\sqrt{1-x}$

6 0

3 years ago

Evaluate the integral. 3 2 t3i t t − 2 j t sin(πt)k dt

sveta [45]

∫(t = 2 to 3) t^3 dt

= (1/4)t^4 {for t = 2 to 3}

= 65/4.

----

∫(t = 2 to 3) t √(t - 2) dt

= ∫(u = 0 to 1) (u + 2) √u du, letting u = t - 2

= ∫(u = 0 to 1) (u^(3/2) + 2u^(1/2)) du

= [(2/5) u^(5/2) + (4/3) u^(3/2)] {for u = 0 to 1}

= 26/15.

----

For the k-entry, use integration by parts with

u = t, dv = sin(πt) dt

du = 1 dt, v = (-1/π) cos(πt).

So, ∫(t = 2 to 3) t sin(πt) dt

= (-1/π) t cos(πt) {for t = 2 to 3} - ∫(t = 2 to 3) (-1/π) cos(πt) dt

= (-1/π) (3 * -1 - 2 * 1) + [(1/π^2) sin(πt) {for t = 2 to 3}]

= 5/π + 0

= 5/π.

Therefore,

∫(t = 2 to 3) <t^3, t√(t - 2), t sin(πt)> dt = <65/4, 26/15, 5/π>.

3 0

3 years ago

Y=_x+4<br> x + 2y =<br> 8<br> How many solutions dose this linear system have

jeyben [28]

Answer:

X=-1, y=4

Step-by-step explanation:

$y = x + 4 \\ x + 2y = 8 \\ = = = = = = = = = = = = \\ y - x = 4 \\ x + 2y = 8$

by using eliminating property

$3y = 12 \\ y = \frac{12}{3} = 4$

by substitution

X=-1

6 0

3 years ago