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3 years ago

Nola made the model to show multiplying a fraction by a fraction. Which multiplication sentence does the model show?

Mathematics

1 answer:

zloy xaker [14]3 years ago

4 0

Answer:

The answer is " $\frac{2}{3}$ "

Step-by-step explanation:

In this question the graph file is missing which is defined in the attachment section please find it.

Let the 18 square boxes are available, 12 of those are in color.

If published in part, it will be

$\to \frac{12}{18}= \frac{4}{6}=\frac{2}{3}$

There are two colors out of 3 square boxes.

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If the roots of x²-7x+k=0 are m and m-1, find the value of the constant k

creativ13 [48]

Answer: k=12

Step-by-step explanation:

x2 - 7x + k = 0

using quadratic formula method,

x = [-b ± √(b2 - 4ac)]/2a

a = 1

b = -7

c = k

x = [-(-7) ± √((-7)2 - 4(1)(k))]/2(1)

x = [7 ± √(49 - 4k)]/2

x = [7 + √(49 - 4k)] / 2 and [7 - √(49 - 4k)] / 2

since the roots are m and m-1,

m = [7 + √(49 - 4k)] / 2 ------------ eqn(1), and

m - 1 = [7 - √(49 - 4k)] / 2 ----------- eqn(2)

add 1 to both sides of eqn(2)

m = [7 - √(49 - 4k)]/2 + 1 --------------- eqn(3)

eqn(1) = eqn(3)

[7 + √(49 - 4k)]/2 = [7 - √(49 - 4k)]/2 + 1

7/2 + (√(49 - 4k))/2 = 7/2 - (√(49 - 4k))/2 + 1

collect like terms,

(√(49 - 4k))/2 + (√(49 - 4k))/2 = 7/2 - 7/2 + 1

(√(49 - 4k))/2 + (√(49 - 4k))/2 = 0 + 1

(√(49 - 4k))/2 + (√(49 - 4k))/2 = 1

multiply through by 2

√(49 - 4k) + √(49 - 4k) = 2

2√(49 - 4k) = 2

divide both side by 2

√(49 - 4k) = 1

square both sides

49 - 4k = 1

collect like terms,

4k = 49 - 1

4k = 48

divide both sides by 4

k = 48/4

k = 12

6 0

3 years ago

Henry has $ 21.50 to ride the trolley around San Francisco this week. It will cost him $ 0.50 every time he rides. Identify the

dusya [7]

Answer:

The Independent Value is the Amount of Money he has

The Dependent Value is the amount of Times he can Ride the Trolley

Step-by-step explanation:

This is because the cost is taken into account for the amount of times he can ride the trolley but the amount of money he has is not reliant or controlled by another piece of information.

4 0

4 years ago

DOG is a right triangle formed by the placement of 3 squares, what is the area of the shaded square?

stira [4]

Answer:

289 in^2

Step-by-step explanation:

1. Find side of the small square: (DG=a)

64= a^2

a= 8

2. Find hypotenuse of triangle being formed: (OG=c and DO=b)

$a^{2}$ + $b^{2}$ = $c^{2}$

$8^{2}$ + $15^{2}$ = $c^{2}$

c= 17

3. Find area of square:

$c^{2}$ = A

(17)*(17)= 289 in^2

6 0

3 years ago

What are the slope and the y-intercept of the line shown in the graph?

mr Goodwill [35]

Answer:

the answer is A y_ intercept =2 and slope =-3

7 0

3 years ago

Read 2 more answers

The operations manager at a compact fluorescent light bulb (CFL) factory needs to estimate the mean life of a large shipment of

aliya0001 [1]

Answer:

The 95% confidence interval estimate for the population mean life of compact fluorescent light bulbs in this shipment is between 7,255 hours and 7,745 hours.

Step-by-step explanation:

We have that to find our $\alpha$ level, that is the subtraction of 1 by the confidence interval divided by 2. So:

$\alpha = \frac{1-0.95}{2} = 0.025$

Now, we have to find z in the Ztable as such z has a pvalue of $1-\alpha$ .

So it is z with a pvalue of $1-0.025 = 0.975$ , so $z = 1.95$

Now, find the margin of error M as such

$M = z*\frac{\sigma}{\sqrt{n}}$

In which $\sigma$ is the standard deviation of the population and n is the size of the sample.

$M = 1.96*\frac{1000}{\sqrt{64}} = 245$

The lower end of the interval is the sample mean subtracted by M. So it is 7500 - 245 = 7255 hours.

The upper end of the interval is the sample mean added to M. So it is 7500 + 245 = 7745 hours.

The 95% confidence interval estimate for the population mean life of compact fluorescent light bulbs in this shipment is between 7,255 hours and 7,745 hours.

7 0

3 years ago