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3 years ago

Expand the following expression.

Mathematics

1 answer:

Lilit [14]3 years ago

6 0

Answer:

D. 123.9 - 20.886x

Step-by-step explanation:

Using the distributive property, we find the expansion to be ...

5.9(21) +5.9(-3.54x) = 123.9 -20.886x

_____

The distributive property tells you ...

a(b+c) = ab +ac

The factor outside parentheses multiplies each of the individual terms inside parentheses.

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Convert the polar coordinates (-3, -60°) to Cartesian coordinates.

notsponge [240]

Answer:

(1.5,-2.6)

Step-by-step explanation:

Given the polar coordinates (-3,60°).

Let our Cartesian coordinates be (x,y)

#We know that when converting the rectangular coordinates (x,y) to polar (r,θ), then:

$r=\sqrt{x^2+y^2}\\\\\therefore r^2=x^2+y^2\\\\\theta=tan^{-1}(y/x)\\\therefore tan \theta=y/x$

#Using the illustration above, we can express our polar coordinates as:

$-3=\sqrt{x^2+y^2}\\\\-60\textdegree=tan^{-1}(y/x}$

#Solve simultaneously to solve for x and y:

$(-3)^2=x^2+y^2\ \ \ \ \ \ \ \ \ \ i\\\\tan(-0\texdegree)=y/x\ \ \ \ \ \ \ \ ...ii\\\\y=x\ tan(-60\textdegree)\ \ \ \ \ \ \ ...iii\\\\\#substitute\ y \ in\ i\\\\(-3)^2=x^2+(x \ tan (-60\textdegree))^2\\\\9=x^2+3x^2\\\\x=\sqrt{9/4}=1.5\\\\y=1.5\ tan(-60\textdegree)=-2.5981\approx-2.6$

Hence, the Cartesian coordinates are (1.5,-2.6)

6 0

2 years ago

Mr. Anders was three times as old as Kate 5 years ago. Their total age now is 42 years. How old is Kate now?

katrin [286]

We can write this as two equations. Call Mr. Anders' age A and Kate's age K:
$A-5=3(K-5)$
$A+K=42$

Then solve for A in the second equation:
$A=42-K$

Substitute this into the first equation:
$(42-K)-5=3(K-5)$
$-K+37=3K-15$
$52=4K$
$K=13$

6 0

3 years ago

A coin is thrown independently 10 times to test the hypothesis that the probability of heads is 0.5 versus the alternative that

mafiozo [28]

Answer:

(a) The significance level of the test is 0.002.

(b) The power of the test is 0.3487.

Step-by-step explanation:

We are given that a coin is thrown independently 10 times to test the hypothesis that the probability of heads is 0.5 versus the alternative that the probability is not 0.5.

The test rejects the null hypothesis if either 0 or 10 heads are observed.

Let p = <u><em>probability of obtaining head.</em></u>

So, Null Hypothesis, $H_0$ : p = 0.5

Alternate Hypothesis, $H_A$ : p $\neq$ 0.5

(a) The significance level of the test which is represented by $\alpha$ is the probability of Type I error.

Type I error states the probability of rejecting the null hypothesis given the fact that the null hypothesis is true.

Here, the probability of rejecting the null hypothesis means we obtain the probability of observing either 0 or 10 heads, that is;

P(Type I error) = $\alpha$

P(X = 0/ $H_0$ is true) + P(X = 10/ $H_0$ is true) = $\alpha$

Also, the event of obtaining heads when a coin is thrown 10 times can be considered as a binomial experiment.

So, X ~ Binom(n = 10, p = 0.5)

P(X = 0/ $H_0$ is true) + P(X = 10/ $H_0$ is true) = $\alpha$

$\binom{10}{0}\times 0.5^{0} \times (1-0.5)^{10-0} +\binom{10}{10}\times 0.5^{10} \times (1-0.5)^{10-10}$ = $\alpha$

$(1\times 1\times 0.5^{10}) +(1 \times 0.5^{10} \times 0.5^{0})$ = $\alpha$

$\alpha$ = 0.0019

So, the significance level of the test is 0.002.

(b) It is stated that the probability of heads is 0.1, and we have to find the power of the test.

Here the Type II error is used which states the probability of accepting the null hypothesis given the fact that the null hypothesis is false.

Also, the power of the test is represented by (1 - $\beta$ ).

So, here, X ~ Binom(n = 10, p = 0.1)

$1-\beta$ = P(X = 0/ $H_0$ is true) + P(X = 10/ $H_0$ is true)

$1-\beta$ = $\binom{10}{0}\times 0.1^{0} \times (1-0.1)^{10-0} +\binom{10}{10}\times 0.1^{10} \times (1-0.1)^{10-10}$

$1-\beta$ = $(1\times 1\times 0.9^{10}) +(1 \times 0.1^{10} \times 0.9^{0})$

$1-\beta$ = 0.3487

Hence, the power of the test is 0.3487.

3 0

3 years ago

Match the terms to their correct definitions.

Inessa [10]

Not 100% positive, but I think that it’s
13
10
9
16
15
11
14
12
I hope this helps

5 0

2 years ago

How many times does nine go into 42

Lady bird [3.3K]

It only goes in 4 times

4 0

3 years ago