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2 years ago

Find the value of X. Round to the nearest tenth HELP ASAP!!!!

Mathematics

1 answer:

ZanzabumX [31]2 years ago

7 0

Answer: 22.5

Step-by-step explanation:

$\sin 64^{\circ}=\frac{x}{25}\\\\x=25 \sin 64^{\circ}\\\\x \approx 22.5$

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Provide an example of how a free press is an essential component of a democracy

Pepsi [2]

Answer:

Free press is essential since the government does not control the press.

Step-by-step explanation:

For example, the Untied States has free press so authors can spread information (whether for good or evil) while other countries like China control their press and access to press outside of their country, making it much harder for citizens to see the world from another perspective rather than what the government is willing to tell them.

Since the United States is a democracy, it is important to allow their citizens to have the right to speech and the press if people want to form opinions of their own.

6 0

3 years ago

Brainliest given I got -6 but can someone explain too??

Vesna [10]

Answer:im not good at explanation but i think its -1

Step-by-step explanation:

8 0

3 years ago

At a team meeting, 80% of the tennis team was there. If there were 12

Illusion [34]

Answer:

15 people

Step-by-step explanation:

let x=total # of people on the team

80%=12

80/100=12/x

cross multiply

80x=1200

division property of equality (divide both sides by 80)

x=15

There are 15 people on the team.

8 0

3 years ago

The circumference of a sphere was measured to be 80 cm with a possible error of 0.5 cm. A) Use differentials to estimate the max

siniylev [52]

Answer:

A) The maximum error in the calculated surface area: $25cm^2$

Relative error: $0.013$

B) The maximum error in the calculated volume: $162cm^2$

Relative error: $0.019$

Step-by-step explanation:

A) The formula for the surface area is:

$A=4\pi r^2$

The measured value is the circumference which is equal to:

$C=2\pi r$

then the radius is:

$r=\frac{C}{2\pi}$

Substituting in the formula of the surface:

$A=4\pi(\frac{C}{2\pi})^2\\A=4\pi(\frac{C^2}{4\pi^2})\\A=\frac{C^2}{\pi}$

Using the formula to calculate the error:

$dy=f'(x)dx$

Where $x$ is the variable measured and $y$ is a function of $x$ ( $y=f(x)$ ).

$dA=f'(C)dC\\dA=\frac{2C^{(2-1)}}{\pi}dC\\dA=\frac{2C}{\pi}dC$

We have C=80cm and dC=0.5cm

$dA=\frac{2C}{\pi}dC\\dA=\frac{2(80)}{\pi}(0.5)\\dA=\frac{160}{\pi}(0.5)\\dA=50.9296(0.5)\\dA=25.4648\approx25cm^2$

The relative error is the maximum error divide by the total area. The total area is: $A=\frac{C^2}{\pi}=\frac{(80)^2}{\pi}=\frac{6400}{\pi}=2037.1833cm^2$

$\frac{dA}{A}=\frac{25.4648}{2037.1833} =0.0125\approx0.013$

B) The formula for the volume is:

$V=\frac{4}{3} \pi r^3$

Using $r=\frac{C}{2\pi}$

$V=\frac{4}{3} \pi r^3\\V=\frac{4}{3} \pi (\frac{C}{2\pi})^3\\V=\frac{4}{3} \pi (\frac{C^3}{8\pi^3})\\V=\frac{1}{3}(\frac{C^3}{2\pi^2})\\V=\frac{C^3}{6\pi^2}$

The maximum error is:

$dV=\frac{3C^{3-1}}{6\pi^2}dC\\dV=\frac{C^{2}}{2\pi^2}dC\\dV=\frac{(80)^{2}}{2\pi^2}(0.5)\\dV=\frac{6400}{2\pi^2}(0.5)\\dV=\frac{6400}{2\pi^2}(0.5)\\dV=(324.2278)(0.5)\\dV=162.1139\approx162cm^2$

The calculated volume is:

$V=\frac{C^3}{6\pi^2}\\V=\frac{(80)^3}{6\pi^2}\\V=\frac{512000}{6\pi^2}\\V=8646.0743$

The relative error is:

$\frac{dV}{V}=\frac{162.1139}{8646.0743}=0.0188\approx0.019$

3 0

3 years ago

You are studying the relationship between the history of early childhood trauma (categorized as trauma/no trauma) and weight in

jeka57 [31]

Answer:

You can decide to reject the Null Hypothesis at p < 0.05.

Step-by-step explanation:

In this case, the relationship between the history of early childhood trauma and weight in adulthood are being studied.

The categories of childhood trauma are:

Trauma and No trauma.

So, number of rows is, r = 2.

The categories of weight in adulthood are:

Low to normal, Overweight, and Obese

So, number of columns is, c = 3.

The distribution of the statistic $\chi^{2}$ is chi-square with (r - 1)(c - 1) degrees of freedom, where r represents the number of rows in the two-way table and c represents the number of columns.

Compute the degrees of freedom as follows:

$df = (r-1)(c-1)=(2-1) \times (3-1) = 2$

It is provided that the calculated value of Chi-square test statistic is 18.26.

Compute the p-value of the test as follows:

$p-value=P(\chi^{2}_{2}\geq 18.26)\\=0.000108\\\approx0.00011$

Decision rule:

The null hypothesis will be rejected if the p-value of the test is less than the significance level.

The significance level is, α = 0.05.

p-value = 0.00011 < α = 0.05.

The null hypothesis will be rejected at 5% level of significance.

Thus, the complete statement is:

"You can decide to reject the Null Hypothesis at p < 0.05."

4 0

3 years ago