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3 years ago

7

The bottom of a double rainbow is going over a tree that is 18 feet tall if you're standing 20 feet from the tree what is the an

gle of elevation to the bottom of the rainbow

1 answer:

ivanzaharov [21]3 years ago

6 0

The angle of elevation to the bottom of the rainbow is 42°

Explanation:

Given that the bottom of a double rainbow is going over a tree that is 18 feet tall and you're standing 20 feet from the tree.

We need to determine the angle of elevation to the bottom of the rainbow.

Let us use the trigonometric ratios to determine the angle of elevation.

Thus, we have,

$tan \ \theta=\frac{opp}{adj}$

where opp = 18 and adj = 20 and we need to determine the angle.

Substituting the values, we have,

$tan \ \theta=\frac{18}{20}$

Dividing the values, we have,

$tan \ \theta=0.9$

Taking $tan^{-1$ on both sides of the equation, we get,

$\theta=tan^{-1}(0.9)$

Thus, we get,

$\theta=41.99^{\circ}$

Rounding off to the nearest degree, we get,

$\theta=42^{\circ}$

Hence, the angle of elevation to the bottom of the rainbow is 42°

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. For each of these intervals, list all its elements or explain why it is empty. a) [a, a] b) [a, a) c) (a, a] d) (a, a) e) (a,

Eva8 [605]

Answer:

Elements are of the form

(i) $[a,a]=\{[x,y] : a\leq x\leq a, a\leq y\leq a; a\in \mathbb R\}$

(ii) $[a,b)=\{[x,y) :a\leq x$

(iii) $(a,a]=\{(x,y] :a$

(iv) $(a,a)=\{(x,y): a$

(v) (a,b) where a>b= $\{(x,y) : a>x>b,a>y>b;a>b,a,b \in \mathbb R\}$

(vi) [a,b] where a>b= $\{[x,y] : a\geq x\geq b,a\geq y\geq b;a>b,a,b \in \mathbb R\}$

Step-by-step explanation:

Given intervals are,

(i) [a,a] (ii) [a,a) (iii) (a,a] (iv) (a,a) (v) (a,b) where a>b (vi) [a,b] where a>b.

To show all its elements,

(i) [a,a]

Imply the set including aa from left as well as right side.

Its elements are of the form.

$\{[a,a] : a\in \mathbb R\}=\{[0,0],[1, 1],[-1,-1],[2,2],[-2,-2],[3,3],[-3,-3],........\}$

Since there is a singleton element a of real numbers, this set is empty.

Because there is no increment so if $a\in \mathbb R$ then the set [a,a] represents singleton sets, and singleton sets are empty so is [a,a].

(ii) [a,a)

This means given interval containing a by left and exclude a by right.

Its elements are of the form.

$[ 1, 1),[-1,-1),[2,2),[-2,-2),[3,3),[-3,-3),........$

Since there is a singleton element a of real numbers withis the set, this set is empty.

Because there is no increment so if $a\in \mathbb R$ then the set [a,a) represents singleton sets, and singleton sets are empty so is [a.a).

(iii) (a,a]

It means the interval not taking a by left and include a by right.

Its elements are of the form.

$( 1, 1],(-1,-1],(2,2],(-2,-2],(3,3],(-3,-3],........$

Since there is a singleton element a of real numbers, this set is empty.

Because there is no increment so if $a\in \mathbb R$ then the set (a,a] represents singleton sets, and singleton sets are empty so is (a,a].

(iv) (a,a)

Means given set excluding a by left as well as right.

Since there is a singleton element a of real numbers, this set is empty.

Its elements are of the form.

$( 1, 1),(-1,-1],(2,2],(-2,-2],(3,3],(-3,-3],........$

Because there is no increment so if $a\in \mathbb R$ then the set (a,a) represents singleton sets, and singleton sets are empty, so is (a,a).

(v) (a,b) where a>b.

Which indicate the interval containing a, b such that increment of x is always greater than increment of y which not take x and y by any side of the interval.

That is the graph is bounded by value of a and it contains elements like it we fixed a=5 then,

$(a,b)=\{(5,0),(5,1),(5,2).....\}$ e.t.c

So this set is connected and we know singletons are connected in $\mathbb R$ . Hence given set is empty.

(vi) [a,b] where $a\leq b$ .

Which indicate the interval containing a, b such that increment of x is always greater than increment of y which include both x and y.

That is the graph is bounded by value of a and it contains elements like it we fixed a=5 then,

$[a,b]=\{[5,0],[5,1],[5,2].....\}$ e.t.c

So this set is connected and we know singletons are connected in $\mathbb R$ . Hence given set is empty.

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3 years ago

GreenBeam Ltd. claims that its compact fluorescent bulbs average no more than 3.24 mg of mercury. A sample of 25 bulbs shows a m

amm1812

Answer:

Null hypothesis: $\mu \leq 3.24$

Alternative hypothesis: $\mu > 3.24$

Step-by-step explanation:

1) Previous concepts and data given

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".

A right tailed test (sometimes called an upper test) is when the alternative hypothesis statement contains a greater than (>) symbol.

$\bar X=3.29$ represent the sample mean

s represent the sample standard deviation

n represent the sample selected

$\alpha$ significance level

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the mean for fluorescent bulbs is no more than 3.24 mg of mercury, the system of hypothesis would be:

Null hypothesis: $\mu \leq 3.24$

Alternative hypothesis: $\mu > 3.24$

IIf we know the population deviation we can apply a z test to compare the actual mean to the reference value, and the statistic is given by:

$z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}$ (1)

z-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

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4 years ago

Solve for y 2x-3y=-9

labwork [276]

Answer:

y=3+2x/3

Step-by-step explanation:

− 3 y=− 9 − 2x

Divide each term by -3 and simplify.

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3 years ago

Using the transformation T : (x, y) → (x + 2, y + 1), find the distance named Find C'A'

deff fn [24]

We have that
<span>A' (2,1)

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with
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find the distance <span>C'A'

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the answer is
the distance C'A' is 2√2 units

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