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3 years ago

Olivia has 1 1/5 yards of fabric. She uses 5/8. How much fabric did she use?

Mathematics

2 answers:

harkovskaia [24]3 years ago

7 0

Answer:

63/40, also known as 1 23/40.

Step-by-step explanation:

Uses = Subtract.

1. Find the LCD (Least Common Denominator) of 11/5 and 5/8. Can also be LCM (Least Common Multiple) of 5 and 8.

LCD = 40.

2. Make the denominators the same as the LCD.

$\frac{11*8}{5*8} - \frac{5*5}{8*5}$

3. Simplify.

$\frac{88}{40} - \frac{25}{40}$

4. Simplify.

$\frac{63}{40}$

Mixed Number = $1\frac{23}{40}$

astraxan [27]3 years ago

7 0

Answer:

23/40 of the fabric

Step-by-step explanation:

Make sure first that each fraction has a common denominator.

Turn 1 1/5 into 6/5

The common denominator of 5/8 and 6/5 would by 40.

Then, turn the bottom numbers into 40 and multiply each number by the same amount as the bottom was multiplied by.

5 × 5 25

------ ------ = ------

8 × 5 40

6 × 8 48

------ ------ = ------

5 × 8 40

Then subtract the top fraction from the bottom fraction.

48 25 23

------ - ------ = ------

40 40 40

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Is a square a special parallelogram

Debora [2.8K]

idk what a special parallelogram is but a square is most definitely a parallelogram :)

Answer:

a square is a quadrilateral but is also a parallelogram,rectangle and a rhombus

Step-by-step explanation:

a square is many things such as a parallelogram, a rectangle, and a rhombus.

it is a quadrilateral with all right angles and all equal sides

×║hope this helps║×

6 0

3 years ago

If you know how to solve this, Please answer it. Thank You

stira [4]

Answer:

2 Step-by-step explanation:

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3 0

3 years ago

Read 2 more answers

The graph shows the volume of oil (L litres) in a tank at time t seconds. a)find the gradient of the graph b)explain what this g

Alisiya [41]

Answer/Step-by-step explanation:

a. Using two points on the line (0, 2) and (4, 12), find the gradient:

Gradient = ∆y/∆x = (12 - 2) / (4 - 0) = 10/4 = 2.5

Gradient = 2.5

b. The gradient, 2.5, represents the unit rate. That is, the volume of the oil in the tank per second.

i.e. 2.5 litres per second

c. The value, L = 2 represents the y-intercept, which is the starting value or initial volume of oil in the tank at 0 secs.

4 0

3 years ago

According to an airline, flights on a certain route are on time % of the time. Suppose flights are randomly selected and the n

neonofarm [45]

Answer:

(a) Explained below.

(b) 0.0294

(d) 0.09827

(e) 0.0452

Step-by-step explanation:

The complete question is:

According to an airline, flights on a certain route are on time 80% of the time. Suppose 25 flights are randomly selected and the number of on-time flights is recorded.

(a) Explain why this is a binomial experiment.

(b) Find and interpret the probability that exactly 16 flights are on time.

(d) Find and interpret the probability that at least 16 flights are on time.

(e) Find and interpret the probability that between 14 and 16 flights, inclusive, are on time.

Solution:

(a)

Let the random variable X be defined as the number of on-time flights.

A Binomial experiment has the following properties:

There are a fixed number of trials (n).
Each trial are independent of the others.
Each trial has only two outcomes: Success and Failure
Each trial has the same probability of success (p).

If a random variable X is used in an experiment and the experiment has all the above mentioned properties, then the random variable X is known as a binomial random variable.

All of these properties can be confirmed for the random variable X.

Thus, this is a binomial experiment.

(b)

Compute the probability that exactly 16 flights are on time as follows:

$P(X=16)={25\choose 16}(0.80)^{16}(0.20)^{25-16}$

$=2042975\times 0.0281475\times 0.000000512\\=0.029442375072\\\approx 0.0294$

Thus, the probability that exactly 16 flights are on time is 0.0294.

(c)

Compute the probability that fewer than 16 flights are on time as follows:

$P(X$

$=0.0000+0.0000+....+0.011777\\=0.0173$

Thus, the probability that fewer than 16 flights are on time is 0.0173.

(d)

Compute the probability that at least 16 flights are on time as follows:

$P(X\geq 16)=1-P(X$

$=1-0.0173\\=0.9827$

(e)

Compute the probability that between 14 and 16 flights, inclusive, are on time as follows:

$P(14\leq X\leq 16)=\sum\limits^{16}_{x=14}{{25\choose x}(0.80)^{x}(0.20)^{25-x}}$

$=0.004+0.0118+0.0294\\=0.0452$

Thus, the probability that between 14 and 16 flights, inclusive, are on time is 0.0452.

8 0

3 years ago

A plane flying horizontally at an altitude of 1 mi and a speed of 470 mi/h passes directly over a radar station. Find the rate a

kiruha [24]

Answer:

407 mi/h

Step-by-step explanation:

Given:

Speed of plane (s) = 470 mi/h

Height of plane above radar station (h) = 1 mi

Let the distance of plane from station be 'D' at any time 't' and let 'x' be the horizontal distance traveled in time 't' by the plane.

Consider a right angled triangle representing the above scenario.

We can see that, the height 'h' remains fixed as the plane is flying horizontally.

Speed of the plane is nothing but the rate of change of horizontal distance of plane. So, $s=\frac{dx}{dt}=470\ mi/h$

Now, applying Pythagoras theorem to the triangle, we have:

$D^2=h^2+x^2\\\\D^2=1+x^2$

Differentiating with respect to time 't', we get:

$2D\frac{dD}{dt}=0+2x\frac{dx}{dt}\\\\\frac{dD}{dt}=\frac{x}{D}(s)$

Now, when the plane is 2 miles away from radar station, then D = 2 mi

Also, the horizontal distance traveled can be calculated using the value of 'D' in equation (1). This gives,

$2^2=1+x^2\\\\x^2=4-1\\\\x=\sqrt3=1.732\ mi$

Now, plug in all the given values and solve for $\frac{dD}{dt}$ . This gives,

$\frac{dD}{dt}=\frac{1.732\times 470}{2}=407.02\approx 407\ mi/h$

Therefore, the distance from the plane to the station is increasing at a rate of 407 mi/h.

6 0

4 years ago