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2 years ago

The table gives the numbers of teachers and students in grades 6 to 8 at Earhart Middle School.

Mathematics

1 answer:

sleet_krkn [62]2 years ago

6 0

Answer:

5 teachers, students 125

4 teachers, students 100

Step-by-step explanation:

step 1

Find teacher-to-student ratio in the table

To determine the ratio, divide the number of teachers by the number of students

6 grade

$\frac{1}{25}$

7 grade

$\frac{2}{50}$

Simplify

$\frac{1}{25}$

8 grade

$\frac{3}{75}$

Simplify

$\frac{1}{25}$

step 2

Verify each case

case a) 5 teachers, students 125

$ratio=\frac{5}{125}$

Simplify

Divide by 5 both numerator and denominator

$ratio=\frac{1}{25}$

Compare with the ratio described in the table

$\frac{1}{25}=\frac{1}{25}$

therefore

This ratio maintains the proportional relationship described in the table

case b) 4 teachers, students 120

$ratio=\frac{4}{120}$

Simplify

Divide by 4 both numerator and denominator

$ratio=\frac{1}{30}$

Compare with the ratio described in the table

$\frac{1}{30}\neq \frac{1}{25}$

therefore

This ratio not maintains the proportional relationship described in the table

case c) 4 teachers, students 100

$ratio=\frac{4}{100}$

Simplify

Divide by 4 both numerator and denominator

$ratio=\frac{1}{25}$

Compare with the ratio described in the table

$\frac{1}{25}=\frac{1}{25}$

therefore

This ratio maintains the proportional relationship described in the table

case d) 6 teachers, students 130

$ratio=\frac{6}{130}$

Simplify

$ratio=\frac{3}{65}$

Compare with the ratio described in the table

$\frac{3}{65}\neq\frac{1}{25}$

therefore

This ratio not maintains the proportional relationship described in the table

case e) 7 teachers, students 125

$ratio=\frac{7}{125}$

Compare with the ratio described in the table

$\frac{7}{125}\neq\frac{1}{25}$

therefore

This ratio not maintains the proportional relationship described in the table

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Answer:

The length of the plywood's diagonal(to the nearest tenth) is, 3.6 and 1.4

Step-by-step explanation:

let l be the length and w be the width of the rectangle respectively;

Diagonal(D) of a rectangle is given by:

$D = \sqrt{l^2+w^2}$ ......[1]

As per the given statement we have;

Diagonal(D) = width + 2

and

$l = 2 \times w$ = 2w

Now, substitute these in [1] we have;

$\sqrt{(2w)^2+w^2} = w+5$

Squaring both the sides we get;

$4w^2+w^2 = (w+2)^2$

$5w^2 = w^2 + 4 + 4w$

$5w^2 -w^2 = 4w + 4$ or

$4w^2= 4w + 4$

Simplify:

$w^2-w-1 =0$ ......[2]

The quadratic equation is in the form of $ax^2+bx+c = 0$

the solution is given by: $x = \frac{-b \pm\sqrt{b^2-4ac}}{2a}$

On comparing with [1] we get

a= 1 , b = -1 and c = -1

Then the solution is:

$w= \frac{-(-1) \pm\sqrt{(-1)^2-4(1)(-1)}}{2(1)}$

$w =\frac{1 \pm\sqrt{1+4}}{2} = \frac{1 \pm\sqrt{5}}{2}$

Simplify:

$w \approx 1.62$ and $w \approx -0.62$

Then, the diagonal D = w+2

For $w \approx 1.62$

$D = 1.62 +2 \approx 3.62$

For $w \approx -0.62$

$D =-0.62 +2 \approx 1.38$

therefore, the length of the plywood's diagonal(to the nearest tenth) is, 3.6 and 1.4

5 0

2 years ago

Ariel left her home at 9 a.m., driving at 45 mph. At 11 a.m. her brother left the home and started after her at 60 mph. At what

Nana76 [90]

Answer:

Her brother catch her at 11 am + 4hour = 15 p.m

Step-by-step explanation:

Given as ;

Speed of Ariel = 45 mph

She left home at 9 a.m

Her brother speed = 60 mph

Her brother left home at 11 a.m

Now from question So As Ariel speed is 45 mph so, after two hours pass , she ahead 90 m .

As her brother travel as 60 mph ,so he travel at ( 60 - 45 )= 15 mph faster

So, with this speed her brother will catch up her at $\frac{90}{15}$ = after 4 hour .

Hence her brother catch her at 11 am + 4hour = 15 p.m Answer

4 0

2 years ago

Read 2 more answers

A child rides a pony on a circular track whose radius is 5.25 m. a) Find the distance traveled and the displacement after the ch

AlexFokin [52]

Answer:

a) distance halfway = 16.49 [m], displacement halfway = 10.5 [m]

b) distrance traveled increases when the child completes one circuit of the track.

Step-by-step explanation:

a) Distance is a scalar quantity that tells you how much space a body has covered when moving. Displacement is a vector quantity that tells you how far from its initial position and object is after moving.

In this case, the child goes around the track only halfway from point 1 to point 2. We know the circunference or perimeter of a circle to be 2*PI*radius. We also know the child only when halfway, so we need to divide the perimeter by 2, thus we get distance = PI*radius

distance halfway = (PI)*(5.25) = 16.49 [m]

And now that we know the definition of displacement, we can easily see that the child went from point 1 to point 2 which is located at a distance of 1 diameter from point 1:

displacement halfway = D = 2*radius = 2(5.25) = 10.5 [m]

b)What happens to the distance when the child completes one circuit? The distance will increase beause he is now completing the circuit so he is covering more ground in his movement: