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1 year ago

Which composite function can be used to find the

Mathematics

1 answer:

eduard1 year ago

4 0

Given:

The mass function is:

$m(v)=4.5v$

where v is the volume in cubic centimeters.

The force function is:

$F(m)=800m$

To find:

The composite function can be used to find the force of the object based on its volume.

Solution:

The composite function can be used to find the force of the object based on its volume is:

$F(m(v))=F(4.5v)$ $[\because m(v)=4.5v]$

$F(m(v))=800(4.5v)$ $[\because F(m)=800m]$

$F(m(v))=3600v$

Therefore, the correct option is D.

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A book costs d dollars.

bazaltina [42]

Answer:

The total amount paid by Jill = $ (3 d)

Step-by-step explanation:

Here, the cost of 1 book = $ d

Now, the number of books purchased by Jill = 3

So, the total cost of 3 books = 3 x ( Cost of 1 book)

= 3 x ($d) = 3 d

So, if Jill purchased 3 books, the total amount paid by her = $ (3 d)

3 0

2 years ago

M∠1=45° and m∠3=65°

7nadin3 [17]

Answer:

In Right Δ ABC with right angle B,

∠A=(3 x -8)°, ∠B=90°, ∠C=(x-2)°

∠A+∠B+∠C=180°[∠ sum property of triangle]

3 x-8+90 + x-2=180

Adding and subtracting like terms

4 x-10+90=180

4 x+80=180

4 x=180-80

4 x=100

x=100/4

x=25°

∠A=3×25-8=75-8=67°

6 0

2 years ago

Read 2 more answers

A Sunday newspaper lists the 10 used car prices for a foreign compact, with age x measured in years and selling price y measured

Masteriza [31]

Question:

A Sunday newspaper lists the 10 used car prices for a foreign compact, with age x measured in years and selling price y measured in thousands of dollars. A Sunday newspaper lists the 10 used car prices for a foreign compact, with age x measured in years and selling price y measured in thousands of dollars.

Picture of data can be found in the picture attached.

Answer:

Slope = -1.71

Intercept = 22.05

Step-by-step explanation:

Equation of a line usually takes the general form :

ŷ = mx + c

Where :

m = slope or gradient

c = intercept

Inputting the data into a linear regression calculator ;

The output is : ŷ = -1.70872X + 22.04985

Comparing the output to the general formula;

The slope (m):

m = -1.70872 = -1.71(2 decimal places).

The intercept (c):

c = 22.04985 = 22.05(2 decimal places).

7 0

2 years ago

A survey of the students in Lance’s school found that 58% of the respondents want the school year lengthened, while 42% think it

alina1380 [7]

The margin of error of a given statistic is an amount that is allowed for in case of miscalculation or change of circumstances.

It is usually the radius or half of the width of the confidence interval of that statistic.

Given that a survey of the students in Lance’s school found that 58% of the respondents want the school year lengthened, while 42% think it should remain the same. The margin of error of the survey is ±10%.

This means that 58% ± 10% of the respondents want the school year lengthened, while 42% ± 10% think it should remain the same.

Thus, from 48% to 68% of the respondents want the school year lengthened, while from 32% to 52% think it should remain the same. 

Therefore, according to the survey data, at least 32% of students want the duration of the school year to remain unchanged, and at least 48% want the school year to be lengthened.

7 0

2 years ago

The length, l cm, of a simple pendulum is directly proportional to the square of its period (time taken to complete one oscillat

Greeley [361]

Answer:

1) $L \propto T^2$

Using the condition given:

$2.205 m = K (3)^2$

$K = 0.245 \approx \frac{g}{4\pi^2}$

So then if we want to create an equation we need to do this:

$L = K T^2$

With K a constant. For this case the period of a pendulumn is given by this general expression:

$T = 2\pi \sqrt{\frac{L}{g}}$

Where L is the length in m and g the gravity $g = 9.8 \frac{m}{s^2}$ .

2) $T = 2\pi \sqrt{\frac{L}{g}}$

If we square both sides of the equation we got:

$T^2 = 4 \pi^2 \frac{L}{g}$

And solving for L we got:

$L = \frac{g T^2}{4 \pi^2}$

Replacing we got:

$L =\frac{9.8 \frac{m}{s^2} (5s)^2}{4 \pi^2} = 6.206m$

3) $T = 2\pi \sqrt{\frac{0.98m}{9.8\frac{m}{s^2}}}= 1.987 s$

Step-by-step explanation:

Part 1

For this case we know the following info: The length, l cm, of a simple pendulum is directly proportional to the square of its period (time taken to complete one oscillation), T seconds.

$L \propto T^2$

Using the condition given:

$2.205 m = K (3)^2$

$K = 0.245 \approx \frac{g}{4\pi^2}$

So then if we want to create an equation we need to do this:

$L = K T^2$

With K a constant. For this case the period of a pendulumn is given by this general expression:

$T = 2\pi \sqrt{\frac{L}{g}}$

Where L is the length in m and g the gravity $g = 9.8 \frac{m}{s^2}$ .

Part 2

For this case using the function in part a we got:

$T = 2\pi \sqrt{\frac{L}{g}}$

If we square both sides of the equation we got:

$T^2 = 4 \pi^2 \frac{L}{g}$

And solving for L we got:

$L = \frac{g T^2}{4 \pi^2}$

Replacing we got:

$L =\frac{9.8 \frac{m}{s^2} (5s)^2}{4 \pi^2} = 6.206m$

Part 3

For this case using the function in part a we got:

$T = 2\pi \sqrt{\frac{L}{g}}$

Replacing we got:

$T = 2\pi \sqrt{\frac{0.98m}{9.8\frac{m}{s^2}}}= 1.987 s$

8 0

2 years ago