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3 years ago

You pay $3 per square foot for carpeting. Which equation can be solved to find the

Mathematics

1 answer:

mestny [16]3 years ago

4 0

Answer:

$135

Step-by-step explanation:

Step 1

Conversion

Base = 2 yards

1 yard = 3 feet

2 yards = x

Cross Multiply

x = 2 × 3 feet = 6 feet

Height = 5 yards

1 yard = 3 feet

5 yards = x

Cross Multiply

x = 5 × 3 feet = 15 feet

Step 2

Find the area of the triangle

Area of a triangle = 1/2 × base × height

Base = 6 feet

Height = 15 feet

Area = 1/2 × 6 × 15

= 45 square feet

Step 3

Find the cost of the carpet

1 Square foot = $3

45 square feet = x

Cross Multiply

x = 45 × $3

x = $135

Therefore, the amount you will pay to cover a triangular section of the floor is $135

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3 years ago

Find the directional derivative of f at the given point in the direction indicated by the angle θ.

anygoal [31]

Answer:

Directional derivative = 1/√2

Step-by-step explanation:

We are given f(x, y) = y cos(xy)

Now, we know that;

∇f(x, y) = ycos xy

Thus, applying that to the question, we have;

∇f(x, y) = [-y² sin xy, cos (xy) - xy sin xy]

At coordinates (0,1),we now have;

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Now, unit vector indicated by the angle θ is given as; u = [cos θ, sin θ]

From the question, since θ = π/4, thus

u = [cos π/4, sin π/4]

Cos π/4 in surd form is; 1/√2

Also, sin π/4 in surd form is; 1/√2

So, u = [1/√2, 1/√2]

Directional derivative = [∇f(0, 1)] • u

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4 0

3 years ago

With one method of a procedure called acceptance sampling, a sample of items is randomly selected without replacement and the en

GuDViN [60]

Answer:

$P = 0.1447$

Step-by-step explanation:

Given

$n = 7000$ -- total

$d = 180$ --- defective

$r = 6$ --- selected

Required

The probability of rejecting the batch

This means that at least one of the selected piece is defected.

So, we first calculate the probability that all the selected piece are accepted.

So, we have:

$Pr = \frac{7000 - 180}{7000} * \frac{6999 - 180}{6999}* \frac{6998 - 180}{6998}* \frac{6997 - 180}{6997}* \frac{6996 - 180}{6996}* \frac{6995 - 180}{6995}$

The denominator decreases by 1 because it is a probability without replacement; 180 is subtracted from the numerator to represent the number of non-defective CDs

So, we have:

$Pr = \frac{6820}{7000} * \frac{6819}{6999}* \frac{6818}{6998}* \frac{6817}{6997}* \frac{6816}{6996}* \frac{6815}{6995}$

$Pr = 0.8553$

Using the complement rule, the probability that the batch will be rejected is:

$P = 1 - 0.8553$

$P = 0.1447$

8 0

3 years ago

The local tennis club needed new tennis balls. To pay for all the new balls, each person in the club donated $12.45. The bill fo

Maru [420]

Answer:

45 people are members at the tennis club

Step-by-step explanation:

Let the number of people in the tennis club be denoted as "x".

Since each of them donated $12.45, then total donated = 12.45x

Since they had $50.25 left over after paying the cost of $510 for the ball, then;

12.45x - 510 = 50.25

12.45x = 510 + 50.25

12.45x = 560.25

x = 560.25/12.45

x = 45

4 0

3 years ago