Lesson 13 Exit Ticket 5.4
Name
Date
1. Solve. Draw a rectangular fraction model, and write a number sentence to show your thinking.
I do not know how to do this

Answer:

105 minutes

Step-by-step explanation:

The pond is a prism. Its volume is the area of the trapezoidal base (the front and back faces) multiplied by the height (the 1 m edge).

Area of base of pond (front face) = (1/2)(B + b)h

Base = (1/2)(1.5 m + 0.6 m)(2 m)    [Here, height is the height oif the trapezoid, so it is 2 m]

Base = 2.1 m²

Volume = Base × Height

Volume = 2.1 m² × 1 m    [Here, height is the height of the prism, so it is 1 m]

Volume = 2.1 m³

The volume of the upper 30 cm (= 0.3 m) of the pond is:

V = LWH

V = 2 m × 1 m × 0.3 m

V = 0.6 m³

The volume of water decreased 0.6 m³ in 30 minutes.

In 60 minutes, it would decrease by 1.2 m³.

60 minutes = 1 hour

The flow rate is 1.2 m³ / hour.

The total volume of the pond is 2.1 m³.

Emptying out the pond completely means removing 2.1 m³ of water at the flow rate of 1.2 m³/hour.

flow rate = volume/time

time × flow rate = volume

time = volume / flow rate

time = 2.1 m³ / 1.2 m³/hour = 1.75 hour

time = 1.75 hour × 60 minutes/hour = 105 minutes

Answer: 105 minutes

Answer:

5 yards

Step-by-step explanation:

15/3=5

Answer:

24.05

Step-by-step explanation:

24.005 has more numbers but worth less

24.05 is more

Answer:

Explanation:

easy way to solve:

[tex]x^2-6x-7=0[/tex]

[tex]x^2+x-7x-7=0[/tex]

[tex]x(x+1)-7(x+1) =0[/tex]

[tex](x-7)(x+1)= 0[/tex]

[tex]x = 7, -1[/tex]

Mistake:

In step 5,

Josh should have given:

[tex](x-3)^2=16[/tex]

[tex]x-3 = \pm \sqrt{16}[/tex]     [ changing sides changes square sign to [tex]\pm[/tex] square root ]

[tex]x-3 = \pm 4[/tex]

[tex]x -3 = 4[/tex], [tex]x-3 = -4[/tex]

[tex]x = 7[/tex], [tex]x = -1[/tex]

Answer:  [tex]\frac56[/tex]

Work Shown:

[tex]\frac{1}{2}+\frac{1}{3}\\\\\frac{3}{6}+\frac{2}{6}\\\\\frac{3+2}{6}\\\\\frac{5}{6}\\\\[/tex]

To visualize this, cut up a circle into 6 equal pieces.

3 of those pieces represent half the circle (3/6 = 1/2)

2 more pieces represent one third (2/6 = 1/3)

We have 3+2 = 5 pieces out of 6 total. This is visual confirmation that 1/2 + 1/3 = 5/6

Answer:

Step-by-step explanation:

1 yard = 3 feet    

1/3          3/3    

1/3 yard = 1 feet

3ft * 5 yards = 15ft

1/3yard * 2 = 2/3yard        1ft * 2/3 = 2ft

15ft+2ft=17ft

That all added is 9/4 so now just turn that into pounds. goodluck :)

Answer:

2 1/4

Step-by-step explanation:

You can add together all of the numerators to get 9/4 which simplifies to be 2 1/4.

Answer:

  5/6

Step-by-step explanation:

Assuming everyone identifies as female or male, the fraction is ...

  female / (female + male)

  5/(5 +1) = 5/6

5/6 of the students are female in the math course.

Answer:

Option B

Step-by-step explanation:

Given the following question:

9 is 10 times the value
29,461 ⇒ thousands place
[tex]100\times10=1000[/tex]

Your answer is option B or "53,982". Since the nine is in the hundred's place, and one-hundred times ten, is equal to a thousand.

[tex]900\times10=9000[/tex]

Hope this helps.

The value of the digit 9 in the number 29,461 that is 10 times the value of the digit 9 is; B: 53,982

We are given the number 29461.

In the given number;

1 is units

6 is tens

4 is hundred

9 is thousands

2 is ten thousands

This means any number that will has to be multiplied by 10 to give the 9000 above will have to be hundreds.

From the given options, only 53982 contains 9 in the hundreds position and so is correct.

Read more about Digits at; https://brainly.com/question/26856218

hypotenuse (h)=?

perpendicular (p)=3

base(b)=2

using pythagoras theorem

h²=p²+b²

h²=3²+2²

h²=9+4

h²=13

h=√13

using pythagoras theorem

b²=h²-p²

b²=12²-10²

b²=144-100

b=√44

b=2√11

Answer: y=x

Step-by-step explanation:

The slope is (y2-y1)/(x2-x1) = 8/8 = 1

Plugging it into the equation y = mx+b:

y = x + b

Plugging in one of the coordinates:

4 = 4+b

b = 0

Therefore, the equation of the line is y=x

Answer:

your answer will be letter b

Step-by-step explanation:

Answer:

ok so the shaded area will be the larger rectange minus the smaller one so lets find the area of both by multiplying the sides

(5x)(8x+1)=40x^2+5x

(4x)(2x)=8x^2

so

40x^2+5x-8x^2

32x^2+5x or

x(32x+5)

so a

Hope This Helps!!!

Answer:

Volume = 904.78 yards

Step-by-step explanation:

The formula for a sphere is:

V=4/3πr³

Since we already know that the radius is 3 yards and that π is 3.14 all we have to do is plug in the numbers.

V=4/3(3.14)(6)³

V=4/3(3.14)(216)

V=4.1897(216)

V≈904.78 yards

Answer:

y = 28°

Step-by-step explanation:

The triangle is a right triangle which has 90 degrees.

The 3x falls under 90 degrees.

So:

→ 2y + 90° + 34° = 180°

→ 2y = 180° - 124°

→ 2y = 56°

→ y = 28°

Triangle

XYZ = right triangle

3x = 90°

X + Y + Z = 180°

34° + 3x + 2y = 180°

34° + 90° + 2y = 180°

2y = 180° - (34° + 90°)

2y = 56°

y = 28°

Answer:

1. x = 56

2. y = 2

3. x = 6

4. y = 3

5. k = 10.2

6. w = 21

7. x = 72

Step-by-step explanation:

1. x + 4 = 60

x = 56

2. 3y - 2 = 4

3y = 6

y = 2

3. 3x - 7 = 11

3x = 18

x = 6

4. 5y + 3 = 18

5y = 15

y = 3

5. 3 + 6k = 64

6k = 61

k = 10.2

6. w ÷ 3 - 5 = 2

w ÷ 3 = 7

w = 21

7. x ÷ 8 + 3 = 12

x ÷ 8 = 9

x = 72

[tex]\bold{\huge{\green{\underline{ Solution }}}}[/tex]

[tex]\bold{\red{ x + 4 = 60 }}[/tex]

[tex]\sf{ x = 60 - 4 }[/tex]

[tex]\bold{ x = 56 }[/tex]

Hence , The value of x is 56 .

[tex]\bold{\red{ 3y - 2 = 4 }}[/tex]

[tex]\sf{ 3y = 4 + 2 }[/tex]

[tex]\sf{ 3y = 6}[/tex]

[tex]\sf{ y = }{\sf{\dfrac{6}{3}}}[/tex]

[tex]\bold{ y = 2 }[/tex]

Hence , The value of y is 2 .

[tex]\bold{\red{ 3x - 7 = 11 }}[/tex]

[tex]\sf{ 3x = 11 + 7 }[/tex]

[tex]\sf{ 3x = 18}[/tex]

[tex]\sf{ x = }{\sf{\dfrac{18}{3}}}[/tex]

[tex]\bold{ x = 6 }[/tex]

Hence , The value of x is 6 .

[tex]\bold{\red{ 5y + 3 = 18 }}[/tex]

[tex]\sf{ 5y = 18 - 3 }[/tex]

[tex]\sf{ 5y = 15}[/tex]

[tex]\sf{ y = }{\sf{\dfrac{15}{5}}}[/tex]

[tex]\bold{ y = 3 }[/tex]

Hence , The value of y is 3 .

[tex]\bold{\red{ 3 + 6k = 64 }}[/tex]

[tex]\sf{ 6k = 64 - 3 }[/tex]

[tex]\sf{ 6k = 61}[/tex]

[tex]\bold{ k = }{\sf{\dfrac{61}{6}}}[/tex]

Hence , The value of k is 61/6 .

[tex]\bold{\red{\dfrac{W}{3}}}{\bold{\red{ - 5 = 2 }}}[/tex]

[tex]\sf{\dfrac{W - 15}{3}}{\sf{ = 2 }}[/tex]

[tex]\sf{ W - 15 = 2}{\sf{\times{ 3 }}}[/tex]

[tex]\sf{ W - 15 = 6 }[/tex]

[tex]\sf{ W = 6 + 15 }[/tex]

[tex]\bold{ W = 21}[/tex]

Hence , The value of W is 21 .

[tex]\bold{\red{\dfrac{x}{8}}}{\red{\bold{ + 3 = 12 }}}[/tex]

[tex]\sf{\dfrac{x + 24 }{8 }}{\sf{ = 12 }}[/tex]

[tex]\sf{ x + 24 = 12}{\sf{\times{ 8 }}}[/tex]

[tex]\sf{ x + 24 = 96 }[/tex]

[tex]\sf{ x = 96 - 24 }[/tex]

[tex]\bold{ x = 72 }[/tex]

Hence, The value of x is 72 .

Answer:

D

Step-by-step explanation:

V=(1/3)(pi)(r^2)(h)

=(pi/3)((x/2)^2)(x)

=(pi/3)(x^2/4)(x)

=x^3 * pi/12

Answer:

D

Step-by-step explanation:

One-twelfthπx3

Answer:

Hope this helps.

Answer:

35 miles

Step-by-step explanation:

At the start, you lose $8.5 for tolls and the taxi cost.
You're left with $31.5 after that, every mile costs you $0.9, so you can go 31.5 : 0.9 = 35 miles.

Answer:

4

Step-by-step explanation:

Let's say the amount of bushes sold (yield) is b, and the price per bushel is p.

When calculating total revenue, we want to multiply price by quantity. Quantity here is b, and price is p. Therefore, p*q = revenue = return.

Let's say that the amount of weeks is w.

Price after w weeks = 24 - 1.50 for each week = 24 - 1.50w

Yield after w weeks = 4 + 0.5 for each week = 4 + 0.5w

Revenue after w weeks = p * b = (24-1.50w) * (4+0.5w) = 96 - 6w + 12w - 0.75w² = -0.75w²+6w + 96.

We want to maximize revenue. First, we can find when the derivative of the function is 0.

d/dw(-0.75w²+6w + 96) = -1.5w + 6 = 0

subtract 6 from both sides

-1.5w = -6

divide both sides by -1.5 to isolate w

w = 4

plug that into our equation

-0.75(4)²+6(4) + 96 = -12 + 24 + 96 = 108

Because this function has a negative coefficient for the w², we can say that it is a parabola opening up downward, so when the derivative = 0, we have found the maximum of the function. Therefore, 4 is our answer

Answer:

x=2

Step-by-step explanation:

18−7x=2x

Step 1: Simplif

18−7x=2x

18+−7x=2x

−7x+18=2x

Step 2: Subtract 2x from both sides.

−7x+18−2x=2x−2x

−9x+18=0

Step 3: Subtract 18 from both sides.

−9x+18−18=0−18

−9x=−18

Step 4: Divide both sides by -9.

Answer:

72

Step-by-step explanation:

=> 4(n+13)

putting the value of n which is 5

=> 4(5+13 )

=> 4(18)

=> 72

[tex]\huge\blue{\mid{\fbox{\tt{\:ANSWER\:}}\mid}}[/tex]

____________________

The graph,

Answer:

60 meters.

Step-by-step explanation:

Here the villa has length of 6 cm and breadth of 4 cm

Find perimeter using:

2(length + breadth)

2(6 + 4)

20 cm

Here in scale the drawing perimeter is 20 cm

3 meter = 300 cm ......this is for real.

1 cm here --> 20 cm

300 cm in real --> (20*300) cm

Real perimeter = 6000 cm

If 6000 cm converted to m:

(6000/100) = 60 meters.

Find perimeter using:

[tex]2(length + breadth)[/tex]

[tex]2(6+4)[/tex]

[tex]20 cm[/tex]

Here in scale the drawing perimeter is [tex]20 cm[/tex]

[tex]3 meter = 300 cm [/tex]

[tex]1 cm → 20 cm[/tex]

[tex]300 \: cm → (20×300) cm[/tex]

[tex]Real \: perimeter = 6000 cm[/tex]

If [tex]6000 \: cm[/tex]converted to m:

[tex](\frac{6000}{100}) = 60 \: meters[/tex]

Answer:1,410,000

Step-by-step explanation:

Answer:

6.2 seconds

Explanation:

             Given function: h(t) = – 0.145t² + 0.019t + 5.5

solve the quadratic equation:  

using the formula:  [tex]\left[\begin{array}{ccc} t = \frac{ -b \pm \sqrt{b^2 - 4ac}}{2a}\end{array}\right][/tex]

Solving steps:

→  –0.145t² + 0.019t + 5.5 = 0

→  [–0.145t² + 0.019t + 5.5 = 0 ]* 100

→  -145t² + 19t + 5500 = 0

→  [tex]t = \frac{ -19 \pm \sqrt{19^2 - 4 ( -145)(5500)}}{2(-145)}[/tex]

→  [tex]t_1=\frac{-19+\sqrt{3190361}}{2\left(-145\right)},\:t_2=\frac{-19-\sqrt{3190361}}{2\left(-145\right)}[/tex]

→  [tex]t = -6.09[/tex] , [tex]t = 6.2[/tex]

→  [tex]t = 6.2[/tex]

Time cannot be negative here.

Answer:

Step-by-step explanation:

When the frisbee hits the ground, the value of h is zero.

Find the time required: