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satela [25.4K]
3 years ago
7

Sloane and Joey are saving up to buy a drone. The cheapest drone they found costs more than $120. They broke open their piggy ba

nks to find
that they already have $48 if they put their money together. They earn $12 a week combined for doing chores around the house. What is the
fewest number of weeks they will have to save their allowance in order to have a combined total of more than $120 to buy a new drone?
Mathematics
2 answers:
Marianna [84]3 years ago
8 0

Answer:

7 weeks

Step-by-step explanation:

So, the question is the number of weeks. What we need to know is in how many weeks exactly are we going to earn more 120 $. The clue given in the question is that,' They earn 12 $ per week.

That can also be written as,

1 week = 12 $

If in one week, we'll earn 12 $ then in how many weeks will we earn more than 120 $ ( Remember, the money should be more than twenty but also the least number which is more than 20.)

So, here we write

1 week= 12 $

2 weeks= 12 × 2 = 24 $

3 weeks= 36 $

4 weeks= 48 $

5 weeks= 60 $

6 weeks= 72 $

7 weeks= 84 $

Now if you wish to verify, you can do the calculations as follows;

84 + 48 = 132$

So, 132 $ is more than 20 and the least number more than 20. Thus, the statement also shows that if it's the least number more than 20, it should also be the least number of weeks.

Hope it helps!

zaharov [31]3 years ago
5 0
One little piggy is your correct answerpp
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Suppose we roll a fair die and let X represent the number on the die. (a) Find the moment generating function of X. (b) Use the
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Answer:

(a)  moment generating function for X is \frac{1}{6}\left(e^{t}+e^{2 t}+e^{2 t}+e^{4 t}+e^{5 t}+e^{6 t}\right)

(b) \mathrm{E}(\mathrm{X})=\frac{21}{6} \text { and } E\left(X^{2}\right)=\frac{91}{6}

Step-by step explanation:

Given X represents the number on die.

The possible outcomes of X are 1, 2, 3, 4, 5, 6.

For a fair die, P(X)=\frac{1}{6}

(a) Moment generating function can be written as M_{x}(t).

M_x(t)=\sum_{x=1}^{6} P(X=x)

M_{x}(t)=\frac{1}{6} e^{t}+\frac{1}{6} e^{2 t}+\frac{1}{6} e^{3 t}+\frac{1}{6} e^{4 t}+\frac{1}{6} e^{5 t}+\frac{1}{6} e^{6 t}

M_x(t)=\frac{1}{6}\left(e^{t}+e^{2 t}+e^{3 t}+e^{4 t}+e^{5 t}+e^{6 t}\right)

(b) Now, find E(X) \text { and } E\((X^{2}) using moment generating function

M^{\prime}(t)=\frac{1}{6}\left(e^{t}+2 e^{2 t}+3 e^{3 t}+4 e^{4 t}+5 e^{5 t}+6 e^{6 t}\right)

M^{\prime}(0)=E(X)=\frac{1}{6}(1+2+3+4+5+6)  

\Rightarrow E(X)=\frac{21}{6}

M^{\prime \prime}(t)=\frac{1}{6}\left(e^{t}+4 e^{2 t}+9 e^{3 t}+16 e^{4 t}+25 e^{5 t}+36 e^{6 t}\right)

M^{\prime \prime}(0)=E(X)=\frac{1}{6}(1+4+9+16+25+36)

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Hence, (a) moment generating function for X is \frac{1}{6}\left(e^{t}+e^{2 t}+e^{3 t}+e^{4 t}+e^{5 t}+e^{6 t}\right).

(b) \mathrm{E}(\mathrm{X})=\frac{21}{6} \text { and } E\left(X^{2}\right)=\frac{91}{6}

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3 years ago
Suppose that you are headed toward a plataeu 70m high. If the angle of elevation to the top of the platau is 35 degree how far a
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Answer:

The distance you are from the base of plateau = 99.97\ m\approx 100\ m

Step-by-step explanation:

Given:

Height of plateau = 70 m

Angle of elevation to the top of plateau = 35°

To find the distance you are from the base of plateau.

We will construct a triangle ABC to model the given situation. The triangle would be a right triangle for which we know an angle and its opposite side. We need to find the adjacent side of the triangle.

We will apply trigonometric ratio to find the adjacent side.

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Dividing both sides by \tan 35\°

\frac{AC\times \tan 35\°}{\tan 35\°} =\frac{70}{\tan 35\°}

∴ AC=99.97\ m\approx 100\ m

The distance you are from the base of plateau = 99.97\ m\approx 100\ m

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