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2 years ago

A carpenter cut three 4 foot 6 inch shelves from a 14 foot board. How long a piece was left over?

Mathematics

2 answers:

ladessa [460]2 years ago

7 0

Answer:

A. 6 inches

Step-by-step explanation:

Since,

1 foot = 12 inches,

Given,

Total length of board = 14 foot = 14 × 12 = 168 inches,

The length of one shelves which is cut from board = 4 foot 6 inches = 4 × 12 + 6 = 48 + 6 = 54 inches,

Also, the number of shelves that are cut from board = 3,

So, the total length of board was cut = 3 × 54 = 162 inches,

Hence, the length of piece left over = Total length of board - The length of board that was cut

= 168 - 162

= 6 inches.

Option A is correct.

never [62]2 years ago

4 0

The answer will be A.6 inches because 4*3=12. Then, multiply 6*3=18 which is a foot and a half. Which only leaves 6 inches remaining

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The cross-sectional areas of a right triangular prism and a right cylinder are congruent. The right triangular prism has a heigh

Lina20 [59]

Answer:

B.)The volume of the triangular prism is not equal to the volume of the cylinder.

Step-by-step explanation:

Let A be the cross-sectional area of both congruent right triangular prism and right cylinder.

Since the prism has height 2 units, its volume V₁ = 2A.

Since the cylinder has height 6 units, its volume is V₂ = 6A

Dividing V₁/V₂ = 2A/6A =1/3

V₁ = V₂/3.

The volume of the prism is one-third the volume of the cylinder.

So, since the volume of the prism is neither double nor half of the volume of the cylinder nor is it equal to the volume of the cylinder, B is the correct answer.

So, the volume of the triangular prism is not equal to the volume of the cylinder.

5 0

2 years ago

If ABCD is a square and AB = 10, what is the measure of CE to the nearest hundredth?

andrey2020 [161]

Answer:

$AC=14.14\ units$

Step-by-step explanation:

<em><u>The correct question is </u></em>

If ABCD is a square and AB = 10, what is the measure of AC? (rounded to the nearest hundredth)

see the attached figure to better understand the problem

we know that

All four sides of the square are congruent and all four interior angles are equal to 90°.

AB=BC=CD=AD

In the right triangle ACD

Applying the Pythagorean Theorem

$AC^2=CD^2+AD^2$

we have that

$CD=AD=AB=10\ units$

substitute the given value

$AC^2=10^2+10^2$

$AC^2=200$

$AC=\sqrt{200}\ units$

$AC=14.14\ units$

6 0

2 years ago

Demand for Tablet Computers The quantity demanded per month, x, of a certain make of tablet computer is related to the average u

soldier1979 [14.2K]

$x = f ( p ) = \frac { 100 } { 9 } \sqrt { 810,000 - p ^ { 2 } } } \\\\ \qquad { p ( t ) = \dfrac { 400 } { 1 + \dfrac { 1 } { 8 } \sqrt { t } } + 200 \quad ( 0 \leq t \leq 60 ) }$

Answer:

12.0 tablet computers/month

Step-by-step explanation:

The average price of the tablet 25 months from now will be:

$p ( 25) = \dfrac { 400 } { 1 + \dfrac { 1 } { 8 } \sqrt { 25 } } + 200 \\= \dfrac { 400 } { 1 + \dfrac { 1 } { 8 } \times 5 } + 200\\\\=\dfrac { 400 } { 1 + \dfrac { 5 } { 8 } } + 200\\p(25)=\dfrac { 5800 } {13}$

Next, we determine the rate at which the quantity demanded changes with respect to time.

Using Chain Rule (and a calculator)

$\dfrac{dx}{dt}= \dfrac{dx}{dp}\dfrac{dp}{dt}$

$\dfrac{dx}{dp}= \dfrac{d}{dp}\left[{ \dfrac { 100 } { 9 } \sqrt { 810,000 - p ^ { 2 } } }\right] =-\dfrac{100}{9}p(810,000-p^2)^{-1/2}$

$\dfrac{dp}{dt}=\dfrac{d}{dt}\left[\dfrac { 400 } { 1 + \dfrac { 1 } { 8 } \sqrt { t } } + 200 \right]=-25\left[1 + \dfrac { 1 } { 8 } \sqrt { t } \right]^{-2}t^{-1/2}$

Therefore:

$\dfrac{dx}{dt}= \left[-\dfrac{100}{9}p(810,000-p^2)^{-1/2}\right]\left[-25\left[1 + \dfrac { 1 } { 8 } \sqrt { t } \right]^{-2}t^{-1/2}\right]$

Recall that at t=25, $p(25)=\dfrac { 5800 } {13} \approx 446.15$

Therefore:

$\dfrac{dx}{dt}(25)= \left[-\dfrac{100}{9}\times 446.15(810,000-446.15^2)^{-1/2}\right]\left[-25\left[1 + \dfrac { 1 } { 8 } \sqrt {25} \right]^{-2}25^{-1/2}\right]\\=12.009$

The quantity demanded per month of the tablet computers will be changing at a rate of 12 tablet computers/month correct to 1 decimal place.

8 0

2 years ago

7. In Ryan's city, it rained 2/5 of the days in September. More than 2 cm of rain fell 1/4 of those days. What fraction of the d

ASHA 777 [7]

Answer:

1/10 of the days in September had rainfall more than 2 cm

Step-by-step explanation:

Use the information given:

2/5 of the days in September had rain
1/4 of the days in September that had rain, had more then 2cm of rain
1/4 of 2/5 is 2/20=1/10

5 0

1 year ago

Enter the answer in the space provided.

Dennis_Churaev [7]

Answer:

Part 1: 1 mile.

Part 2: 1.32 mph.

Step-by-step explanation:

7 0

2 years ago

Read 2 more answers