Verify that cos squared A plus Sin squared A is equal to 1 if A is equal to 90 degrees

7 times 10 to the -7 power

klasskru [66]

Answer:

0.0000007 as a regular notation

or 7x10^-7 as scientific notation

3 0

3 years ago

For a certain map, the scale shows that 1 cm on the map equals 2.50 km on earth's surface. two towns on the map are 4.75 cm apar

Julli [10]

<span>In this problem, to find the answer we have to setup a series of ratios that relate the scale to real life distance. We know that 1cm = 2.50km, so that ratio would be 1cm/2.5km. For two towns that are 4.75cm apart on the map, we set a ration of 4.75cm/x km, where x is the actual distance. Now we set the ratios equal to each other and solve for x. 1/2.5=4.75/x where x = 4.75*2.5/1 = 11.875 and rounding up we get 11.88 km. The two towns are actually 11.88 km apart from each other.</span>

3 0

3 years ago

a contractor is on top of 167 ft Tower looking down at a 37 degree angle of depression at a package attached to a rope on the gr

ArbitrLikvidat [17]

Using trigonometry ratio

$\sin 37^0=\frac{167}{x}$ $\begin{gathered} 0.6018\text{ = }\frac{167}{x} \\ 0.6018x\text{ = 167} \\ x\text{ = }\frac{167}{0.6018}\text{ = 277.5ft} \end{gathered}$

x = 277.5 ft

3 0

1 year ago

A chef is going to use a mixture of two brands of Italian dressing. The first brand contains 9% vinegar, and the second brand co

pishuonlain [190]

Let the amount of the first brand be x, and let the amount of the second brand be y.
0.09x + 0.14y = 240 * 0.13 .................(1)
x + y = 240 ..............(2)
y = 240 - x .......................(3)
Plugging the value for y from equation (3) into equation (1), we get:
$0.09x+0.14(240-x)=240\times0.13$ ...............(4)
Equation (4) simplifies to:
-0.05x = -2.4
giving the value for the required amount of 9% vinegar as 48 ml and the required amount of 14% vinegar as 240 - 48 = 192 ml.

7 0

3 years ago

A forester studying diameter growth of red pine believes that the mean diameter growth will be different from the known mean gro

-Dominant- [34]

Answer:

$t=\frac{1.6-1.35}{\frac{0.46}{\sqrt{32}}}=3.07$

The degrees of freedom are given by:

$df =n-1= 32-1=31$

Since is a two-sided test the p value would be:

$p_v =2*P(t_{31}>3.07)=0.0044$

Since the p value is a very low value we have enough evidence to conclude that true mean is significantly different from 1.35 in/year at any significance level commonly used for example ( $\alpha=0.01,0.05, 0.1, 0.15$ ).

Step-by-step explanation:

Data given and notation

$\bar X=1.6$ represent the sample mean

$s=0.46$ represent the sample deviation

$n=32$ sample size

$\mu_o =1.35$ represent the value that we want to test

$\alpha$ represent the significance level for the hypothesis test.

t would represent the statistic (variable of interest)

$p_v$ represent the p value for the test (variable of interest)

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the true mean is different from 1.35 in/year, the system of hypothesis would be:

Null hypothesis: $\mu =1.35$

Alternative hypothesis: $\mu \neq 1.35$

The statistic is given by:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

Calculate the statistic

We can replace in formula (1) the info given like this:

$t=\frac{1.6-1.35}{\frac{0.46}{\sqrt{32}}}=3.07$

P-value

The degrees of freedom are given by:

$df =n-1= 32-1=31$

Since is a two-sided test the p value would be:

$p_v =2*P(t_{31}>3.07)=0.0044$

Since the p value is a very low value we have enough evidence to conclude that true mean is significantly different from 1.35 in/year at any significance level commonly used for example ( $\alpha=0.01,0.05, 0.1, 0.15$ ).

5 0

3 years ago