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3 years ago

What is the distance between...

1 answer:

6 0

The distance between -4/12 and 9 is
-369/2

Step 1 :

41
Simplify ——
2
Equation at the end of step 1 :

41
((((0 - ——) • a) • n) • d) • 9
2
Step 2 :

Final result :

-369and
———————
2

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Jeanne babysits for $6 per hour. She also works as a reading tutor for $10 per hour. She is only allowed to work 20 hours per we

Allushta [10]

Part a) Use a system of inequalities to model the scenario

Let

x-------> represent babysitting hours

y-------> represent tutoring hours

we know that

--------> inequality

Part b) Use the model created in part A to create a graph representing Jeanne’s probable income earned and possible number of hours worked this week

we know that

--------> inequality

This inequality represent Jeanne’s possible number of hours worked this week

Using a graph tool

the solution of this inequality is the shaded area

see the attached figure N

--------> inequality

This inequality represent Jeanne’s probable income earned this week

Using a graph tool

the solution of this inequality is the shaded area

see the attached figure N

Part c) Analyze the set of coordinate values that represent solutions for the model created in part A. Choose one of the coordinates within the solution and algebraically prove that the coordinate represents a true solution for the model

we have the system of inequalities

--------> inequality

the solution of the system of inequalities is the shaded area

using a graph tool

see the attached figure N

Let

------> see the attached figure N

The point belongs to the shaded area, so it is a system solution.

If the point is a solution, it must satisfy both inequalities.

Prove algebraically

substitute the value of x and y in the inequalities

inequality

------> is ok

inequality

-------> is ok

the point A satisfy both inequalities

therefore

the point A is a solution of the system

5 0

3 years ago

Read 2 more answers

Suppose that θ is an acute angle of a right triangle and that sec(θ)=52. Find cos(θ) and csc(θ).

insens350 [35]

Answer:

$\cos{\theta} = \dfrac{1}{52}$

$\csc{\theta} = \dfrac{52}{\sqrt{2703}}$

Step-by-step explanation:

To solve this question we're going to use trigonometric identities and good ol' Pythagoras theorem.

a) Firstly, sec(θ)=52. we're gonna convert this to cos(θ) using:

$\sec{\theta} = \dfrac{1}{\cos{\theta}}$

we can substitute the value of sec(θ) in this equation:

$52 = \dfrac{1}{\cos{\theta}}$

and solve for for cos(θ)

$\cos{\theta} = \dfrac{1}{52}$

side note: just to confirm we can find the value of θ and verify that is indeed an acute angle by $\theta = \arccos{\left(\dfrac{1}{52}\right)} = 88.8^\circ$

b) since right triangle is mentioned in the question. We can use:

$\cos{\theta} = \dfrac{\text{adj}}{\text{hyp}}$

we know the value of cos(θ)=1\52. and by comparing the two. we can say that:

length of the adjacent side = 1
length of the hypotenuse = 52

we can find the third side using the Pythagoras theorem.

$(\text{hyp})^2=(\text{adj})^2+(\text{opp})^2$

$(52)^2=(1)^2+(\text{opp})^2$

$\text{opp}=\sqrt{(52)^2-1}$

$\text{opp}=\sqrt{2703}$

length of the opposite side = √(2703) ≈ 51.9904

we can find the sin(θ) using this side:

$\sin{\theta} = \dfrac{\text{opp}}{\text{hyp}}$

$\sin{\theta} = \dfrac{\sqrt{2703}}{52}}$

and since $\csc{\theta} = \dfrac{1}{\sin{\theta}}$

$\csc{\theta} = \dfrac{52}{\sqrt{2703}}$

4 0

3 years ago

Help please?!?!??!?!!!?!?!?!?!?!?!?!!?!?!?

marissa [1.9K]

Answer:

16.7%

Step-by-step explanation:

Probability is defined by the formula: the number of desirable outcomes over the total outcomes. The total number of outcomes is the sum of all shoes that he could possibly pick:

5 + 7 + 1 + 4 + 6 + 8 + 2 + 3 = 36

And the desirable outcomes are those where he picks brown boots, which is 6 outcomes.

Using the formula for probability, we get the expression: 6/36 to represent the probability. It simplifies to 1/6 which is about 16.7%

3 0

3 years ago

Hal and Renee play the following game a bag has 11 tiles in it each with a letter from the word probably in it Hal and Renee tak

Masteriza [31]

Answer:

<em>D. The game is not fair because the probability of Hal drawing a winning letter is less then the probability of Renee drawing a winning letter </em>

Explanation:

The word is not probably, which has 8 letters, but probability, which has 11 letters

<u>1. Hal</u>

Probability of drawing a vowel

The vowels are: o, a, i, i, and y: 5

The total number of letters in the bag is 11.

Probability of vowel = 5 / 11

<u>2. Renee</u>

Probability of drawing a consonant

The consonants are: p, r, b, b, l, t, and y: 7

Probability of a drawing a consonant: 7 /11

<h2>Conclusion</h2>

As you see, the probability of drawing a vowel (5/11), which is the winning letter for Hal, is less than the probability of drawing a consonant (7/11), which is the winning letter of Renee. Then,

The game is not fair because the probability of Hal drawing a winning letter is less then the probability of Renee drawing a winning letter.

8 0

4 years ago

an article after allowing a discount of 20% on its marked price was sold at a gain of 20% had it been sold after allowing 25% di

Effectus [21]

Answer:

Rs 120

Step-by-step explanation:

Let MP = m

Discount = 25% of MP = m/4

SP = MP - Discount

= m - m/4 = 3m/4

If profit is 20%, CP = 3m/4 x 100/120 = 5m/8

=> Profit = 3m/4 - 5m/8 = m/8

Given Profit - Discount = Rs 15

=> |m/8 - m/4| = 15

m/8 = 15

m = Rs 120

8 0

3 years ago