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2 years ago

Help me solve # 15 & 16

Mathematics

1 answer:

makkiz [27]2 years ago

6 0

Answer:

15) $C=frac{5}{9}(F-32)$

16) 12 hours

Step-by-step explanation:

15) $F=\frac{9}{5}C+32 \\F-32 = \frac{9}{5}C\\\frac{5}{9}(F-32)=C$

16) If Jim drove 168 mi in 4 hours, this means it takes him

$\frac{4 hours }{168 mi}$

this many hours to drive 1 mile. So if we multiply this by 504 mi:

$\frac{4 hours }{168 mi} 504 mi = 4 \cdot 3 hours = 12 hours$

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Anna11 [10]

V=hpir^2
c=2pir

assuming they havve same height

first one is
v=hpi5^2
v=25hpi

2nd one
c=2pir=20pi
2pir=20pi
2r=20
r=10
v=hpir^2
v=hpi10^2
v=100hpi

big/small=100hpi/25hpir=4

4 times greater

4 0

2 years ago

Determine the sample size needed to construct a 90% confidence interval to estimate the population proportion when p = 0.65 and

WINSTONCH [101]

Answer:

n=170

Step-by-step explanation:

1) Notation and definitions

$n$ random sample taken (variable of interest)

$\hat p=0.65$ estimated proportion.

$p$ true population

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

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

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 $\alpha=1-0.90=0.1$ 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 $ME =\pm 0.06$ 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:

$n=\frac{0.65(1-0.65)}{(\frac{0.06}{1.64})^2}=169.968$

And rounded up we have that n=170

6 0

3 years ago

Solve <br><img src="https://tex.z-dn.net/?f=%20%5Cfrac%7B4%20%7D%7B4%20-%20x%7D%20%3D%20%5Cfrac%7B5%7D%7B%284%20%2B%20x%29%7D%20

lisov135 [29]

$Domain:\\4-x\neq0\ \wedge\ 4+x\neq0\\x\neq4\ \wedge\ x\neq-4\\\\\dfrac{4}{4-x}=\dfrac{5}{4+x}\qquad\text{cross multiply}\\\\4(4+x)=5(4-x)\qquad\text{use distributive property}\\\\(4)(4)+(4)(x)=(5)(4)+(5)(-x)\\\\16+4x=20-5x\qquad\text{subtract 16 from both sides}\\\\4x=4-5x\qquad\text{add 5x to both sides}\\\\9x=4\qquad\text{divide both sides by 9}\\\\\boxed{x=\dfrac{4}{9}}$

6 0

2 years ago

There are 20 deer per 2 square miles In

sladkih [1.3K]

Answer:

594,250 (a)

Step-by-step explanation:

2 sq. miles = 20 deers

1 sq. mile = 20÷2 = 10

59,425 sq. miles = 59,425×10

= 594,250

8 0

2 years ago

Solve the equation.<br><br> 3(k−6)=15

Natali [406]

Answer:

K = 11

Step-by-step explanation:

3(k - 6) = 15

3k - 18 = 15

3k = 15 + 18

3k = 33

K = 33/3

K = 11

Thus, the value of K is 11

8 0

2 years ago