Antoine wants to get a subscription to a local library. There are two libraries, each of which charges a monthly subscription free plus a fee for each book instead

Answer:

[tex]15\,\,kg/cm^2[/tex]

Step-by-step explanation:

Given:

The volume of a gas "V" varies inversely with the pressure "P" put on it.

Volume is 360 [tex]cm^3[/tex] under a pressure of 20 [tex]kg/cm^2[/tex]

To find:

pressure when volume is 480 [tex]cm^3[/tex]

Solution:

As  of a gas "V" varies inversely with the pressure "P" put on it,

[tex]V=\frac{k}{P}[/tex]

Here, k is a constant

As volume is 360 [tex]cm^3[/tex] under a pressure of 20 [tex]kg/cm^2[/tex], put [tex]V=360\,,\,P=20[/tex]

[tex]360=\frac{k}{20}\\k=360\times 20\\=7200[/tex]

So,

[tex]V=\frac{7200}{P}[/tex]

Put [tex]V=480[/tex]

[tex]480=\frac{7200}{P}\\P=\frac{7200}{480}\\=15\,\,kg/cm^2[/tex]

Answer:

x=31

Step-by-step explanation:

(x-31)/4=0

multiply each side by 4 so that you have x-31=0.

x-31=0

add 31 to each side.

x=31

Answer:

No, unless you set it equal to zero.

Step-by-step explanation:

(x-31)/4=0

((x-31)/4) times 4 = 0 times 4

x-31=0

x-31 +31 =0 + 31

x=31

Answer:

[tex]177 \frac{7}{9} cm^2[/tex]

Step-by-step explanation:

Length of the Plastic Sheet= 96cm

Width of the plastic Sheet =70cm

If a square of side x is cut from each corner of the plastic sheet to form the box.

Length of the box=96-2x

Width of the box=70-2x

Height of the box =x

Volume of the box = LWH

Volume=(96-2x)(70-2x)x

The maximum volume of the box is obtained at the point where the derivative is zero.

[tex]V=(96-2x)(70-2x)x\\V^{'}=4(x-42)(3x-40)[/tex]

Setting the derivative to 0.

[tex]4(x-42)(3x-40)=0\\x-42=0\: 3x-40=0\\x=42\:or\: x=\frac{40}{3}[/tex]

Since we are looking for the minimum value of x,

[tex]x=\frac{40}{3}\\\text{Area of the Square} = x^2\\=\frac{40}{3} X \frac{40}{3}\\=177 \frac{7}{9} cm^2[/tex]

Answer:

It would take 27.5 minutes the element to decay to 154 grams.

Step-by-step explanation:

The decay equation:

[tex]\frac {dN}{dt}\propto -N[/tex]

[tex]\Rightarrow \R\frac {dN}{dt}=-\lambda N[/tex]

[tex]\Rightarrow \frac {dN}N=-\lambda dt[/tex]

Integrating both sides

[tex]\Rightarrow \int \frac {dN}N=\int-\lambda dt[/tex]

[tex]\Rightarrow ln|N|=-\lambda t+c[/tex]

When t=0, N=[tex]N_0[/tex] = initial amount

[tex]ln|N_0|=-\lambda .0+c[/tex]

[tex]\Rightarrow c=ln|N_0|[/tex]

[tex]ln|N|=-\lambda t+ln|N_0|[/tex]

[tex]\Rightarrow ln|N|-ln|N_0|=-\lambda t[/tex]

[tex]\Rightarrow ln|\frac{N}{N_0}|=-\lambda t[/tex]

Decay equation:              

                    [tex]ln|\frac{N}{N_0}|=-\lambda t[/tex]

Given that, the half life of of element X is 11 minutes.

For half life, [tex]N=\frac12 N_0[/tex],  t= 11 min.

[tex]ln|\frac{N}{N_0}|=-\lambda t[/tex]

[tex]\Rightarrow ln|\frac{\frac12N_0}{N_0}|=-\lambda . 11[/tex]

[tex]\Rightarrow ln|\frac12}|=-\lambda . 11[/tex]

[tex]\Rightarrow -\lambda . 11=ln|\frac12}|[/tex]

[tex]\Rightarrow \lambda =\frac{ln|\frac12|}{-11}[/tex]

[tex]\Rightarrow \lambda =\frac{ln|2|}{11}[/tex]                [ [tex]ln|\frac12|=ln|1|-ln|2|=-ln|2|[/tex] , since ln|1|=0]

N=154 grams, [tex]N_0[/tex] = 870 grams, t=?

[tex]ln|\frac{N}{N_0}|=-\lambda t[/tex]

[tex]\Rightarrow ln|\frac{154}{870}|=-\frac{ln|2|}{11}.t[/tex]

[tex]\Rightarrow t= \frac{ln|\frac{154}{870}|\times 11}{-ln|2|}[/tex]

      =27.5 minutes

It would take 27.5 minutes the element to decay to 154 grams.

Answer:

60.6 minutes

Step-by-step explanation:

--------------------------------

Answer:

Answer: 5=x

Step-by-step explanation:

Ok, so if F(x)=15, then the equation would look like this: [tex]15=5x-10[/tex]

The next step would be to add the 10 over from the right to the left side to get [tex]25=5x[/tex]

Now divide both sides by 5 to get the answer.

Answer:

9

Step-by-step explanation:

In order to round to the nearest ten you must think: what is the nearest multiple of 10. For example, to round 68 to the nearest 10, the nearest whole number is 70, so the answer would be 70. However if you were to round 63 to the nearest 10, to would be 50 since that is the nearest multiple of 10

Answer:9

Step-by-step explanation:

Since the next number is below five you don’t round up it just stays the same

The 90% confidence interval = 48.603 < μ < 55.397

Explanation:

Given:

Mean = 52

Standard deviation = 14.6

Sample size, n = 50

Confidence Interval, c = 90%

                                  c = 0.9

Significance level, α = 1 - c

                                  = 1 - 0.9

                                  = 0.1

Critical value, z(α/2) = z(0.05) = 1.645

Critical value = ± 1.645

Margin of error, E = [tex]z(\alpha /2) X \frac{SD}{\sqrt{n} }[/tex]

                             [tex]=1.645 X\frac{14.6}{\sqrt{50} } \\\\= 3.3965[/tex]

Limits of 90% confidence interval are given by:

Lower limit = μ - E

                  = 52 - 3.397

                  = 48.603

Upper limit = μ + E

                  = 52 + 3.397

                  = 55.397

Thus, 90% confidence interval = 48.603 < μ < 55.397

Answer:

g = 8

Step-by-step explanation:

We're going to isolate g to find out what it equals, so we have to divide both sides by 6.

6g=48

__   __

6     6

g = 8

The solution to the equation 6g = 48 is g = 8.

In order to evaluate and solve this equation, we would have to apply the PEMDAS rule, where mathematical operations within the parenthesis (grouping symbols) are first of all evaluated, followed by exponent, and then multiplication or division from the left side of the equation to the right.

Lastly, the mathematical operations of addition or subtraction would be performed from left to right.

Based on the information provided, we have the following mathematical equation:

6g = 48

By dividing both sides of the equation by 6, we have:

g = 48/6

g = 8

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Answer: ACE

The radius of the cone is 9 units

The height of the cone is 12 units

The volume of the cone is represented by the expression 1/3 pie (9)2(12)

Step-by-step explanation:

Answer:

650

Step-by-step explanation:

2sf= the first two figures

so you count to the first two sf numbers so in this case

it would be 64 then you look at the next one.  But if it is 4 or below  you round or if it is 5 and above you rounded up

in this case the third digit is a 6 so you would round up to 5

answer =650

The number 646.42 can be rounded to two significant figures by increasing the second significant figure up by one because the third figure is 6 which is greater than 5. Therefore, 646.42 becomes 650.

You are requesting to round the number 646.42 to two significant figures (SF). Significant figures are the meaningful digits in a number. For example, in 646.42, there are five significant figures: 6, 4, 6, 4, 2.

To round to two significant figures, we look at the number in the third position, which is another 6. If this number is 5 or greater, we round the second significant figure up. If it is less than 5, we keep the second figure the same. Here, the next number after the two significant figure (6 and 4) is 6, which is more than 5, so you will round 4 up to 5.

Thus, rounded to two significant figures, 646.42 becomes 650.

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Answer:

The answer is a

Step-by-step explanation:

On a coordinate plane, a line goes through points (negative 1, negative 2) and (0, 1).

The linear function that does not have the same y-intercept  as the other functions is: Option A

How to find the y-intercept?

The general form of the equation of a Line in slope intercept form is expressed as:

y = mx + c

where:

m is slope

c is y-intercept

1) In this graph, the y-intercept which is where the line crosses the y-axis is: y = 1

2) The y-intercept in the equation y = -8x + 3 is:

y = 3

3) The y-intercept here will be:

y = 3

4) The y-intercept in the equation y = 2x + 3 is:

y = 3

Answer:

1/2

Step-by-step explanation:

Answer:

1.84ft

Step-by-step explanation:

From the figure attached,

AB = Height of the window = 15ft

Let the distance between the base of the housr and the fence 'C' = xft

If the angle of depression = 7°

Then angle of elevation of the top of the fence from the house = 7°

Now from right triangle ABC,

tan7° = x/15

x = tan7°×15

x = 0.1227×15

x = 1.84ft

Therefore, distance of the house from the fence is 1.84ft

The rate of the passenger train is 100 miles per hour.

Given:

1. The passenger train traveled 100 miles in the same amount of time it took the freight train to travel 90 miles.

2. The rate of the freight train was 10 miles per hour slower than the rate of the passenger train.

We can set up equations based on the distances traveled and the rates:

1. For the passenger train:

[tex]\[ \text{Distance} = \text{Rate} \times \text{Time} \]\[ 100 = r_p \times \text{Time} \]2. For the freight train:\[ 90 = r_f \times \text{Time} \]Since we know that the rate of the freight train (\( r_f \)) is 10 miles per hour slower than the rate of the passenger train (\( r_p \)), we can express \( r_f \) in terms of \( r_p \):\[ r_f = r_p - 10 \][/tex]

Now, we need to find the time it took for both trains to travel their respective distances. Since the time is the same for both trains, we can equate the expressions for time:

[tex]\[ \text{Time} = \frac{\text{Distance}}{\text{Rate}} \]For both trains, time is the same, so:\[ \frac{100}{r_p} = \frac{90}{r_f} \]Substitute \( r_f = r_p - 10 \):\[ \frac{100}{r_p} = \frac{90}{r_p - 10} \]Now, let's solve for \( r_p \):\[ 100(r_p - 10) = 90r_p \]\[ 100r_p - 1000 = 90r_p \]\[ 10r_p = 1000 \]\[ r_p = \frac{1000}{10} \]\[ r_p = 100 \][/tex]

So, the rate of the passenger train is 100 miles per hour.

Answer:

Option (a).

Step-by-step explanation:

It is given that 3n is an odd number.

We need to find an even number from the given options.

Even numbers: Which are divisible by 2.

Odd numbers: Which are not divisible by 2.

We need know that the numbers are alternatively even and odd.

If we add or subtract 1 from an odd number, we always get an even number.

If we add or subtract 2 from an odd number, we always get an odd number.

3n is an odd number. So,

3n-1 is an odd number.

3n+2 is an even number.

3n+2 is an even number.

3n+2n is an even number because 2n is an even number and sum of two even numbers in always an even number.

Therefore, the correct option is (a).

Answer:

12

Step-by-step explanation:

f(x)=3x+9

f(12) = 3*12 +9

       36+9

        45

f(8) = 3*8+9

     =24+9

     = 33

f(12) - f(8) = 45-33

                    12

Answer:

Step-by-step explanation:

To find the values of the angle which makes maximum r you use the derivative of r

[tex]\frac{dr}{d\theta}=\frac{1}{3}sin(3\theta)[/tex]

If you equals this derivative to zero you obtain the value of the angle:

[tex]\frac{dr}{d\theta}=0\\\\cos3\theta=0\\\\3\theta=\frac{\pi}{2}\\\\\theta=\frac{\pi}{6}[/tex]

However, the values of 5π/6 and 9π/6 are also available, because makes the sinusoidal function equal  to 1.

hence, the answer is:

[tex]\theta_1=\frac{\pi}{6} \\\\\theta_2=\frac{5\pi}{6}\\\\\theta_3=\frac{9\pi}{6}=\frac{3\pi}{2}[/tex]

answer b

The maximum values of r for the polar equation r=4+3 sin 3θ occur at the angles where sin 3θ = 1, within the range of 0 to 2π. Solving the equation 3θ = nπ/2 for odd integers n gives the values of θ where r is maximum, which must be checked against the range [0, 2π].

We can find the maximum values of r for the polar equation r=4+3 sin 3θ by looking for the values of θ that give the maximum value for the sinusoidal function sin 3θ.

Since we know that the sine function reaches its maximum value of 1, we can find the values of θ that satisfy the condition sin 3θ = 1 within the given range of θ from 0 to 2π.

Thus, the equation becomes r = 4 + 3(1), which simplifies to r = 7.
Now, we seek to solve 3θ = nπ/2 where n is an odd integer since the sine function is maximum at π/2, 3π/2, 5π/2, and so on. Therefore, we obtain θ values of π/6, π/2, 5π/6, etc., until we reach the limit of 2π.

We must also consider the range of the function which brings us to the fact that θ must lie within [0, 2π].
Thus, we have to evaluate this for values such as θ = π/6, 5π/6, 3π/2, and so on, checking which of these are within the specified range and hence can be considered valid solutions where maximum r values occur.

Answer: A) 5/2

B) 10pi for A and 4pi for B

C) 5/2

Step-by-step explanation:

Please find the attached file for the solution

Answer:

Step-by-step explanation:

Answer:

c .54 w/ bar

Step-by-step explanation:

Answer: B

Step-by-step explanation:

The reflection transformation in the second figure shows the correct reflection.

There are three types of translations -

Given is a triangle ΔDEF.

Therefore, the reflection transformation in the second figure shows the correct reflection.

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We want to find the length of the light beam from the ship to Nicole.

We will see that the solution is 4,585.76 ft.

We can think of this situation as in a right triangle. The adjacent cathetus is the distance between the lighthouse and the ship. The opposite cathetus is the difference in height between Nicole's position and Nick´s position, it is equal to:

250ft - 10ft = 240ft

And the elevation angle is equal to 3°. So we know the angle and the opposite cathetus to this angle, and we want to find the hypotenuse, which is the length of the light beam.

Then we can use the relation:

Sin(θ) = (opposite cathetus)/(hypotenuse)

Solving it for the hypotenuse we get:

hypotenuse = (opposite cathetus)/sin(θ)

Replacing by the values that we know, we get:

hypotenuse = 240ft/sin(3°) = 4,585.76 ft

The length of the line of sight is 4,585.76 ft

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To find the length of the line of sight from the ship to Nicole, we can use trigonometry. We are given the angle of elevation of the light, the height of the cliff, and need to calculate the length of the line of sight.

To find the length of the line of sight from the ship to Nicole, we can use trigonometry. We have a right triangle formed by the line of sight, the height of the cliff, and the distance from the ship to Nicole. We are given the angle of elevation of the light as 3° and the height of the cliff as 250 feet. Let's denote the length of the line of sight as x and the distance from the ship to Nicole as d. Using the tangent function, we can write:

tan(3°) = 250 / d

Simplifying this equation, we have:

d = 250 / tan(3°)

Now we can substitute the value of tangent of 3° and solve for d. Using a calculator, we find that:

d ~ 8424.78 feet

So, the length of the line of sight from the ship to Nicole is approximately 8424.78 feet.

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Answer:

y = 1/3

Step-by-step explanation:

Answer:

multiply all the numbers

Step-by-step explanation:

Answer:

20.00+12.76 would give you that sum

Step-by-step explanation:

Answer:

0.00+12.76 would give you that sum

Step-by-step explanation:

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Answer:

D

Step-by-step explanation:

2  ( x − 3 )

x  ( x + 1 )

Answer:

ANSWER IS D

Step-by-step explanation:

Answer:

-9.8n + 11.1

Step-by-step explanation:

1. Combine like terms

      -5.8n - 4n = -9.8n

      3.1 + 8 = 11.1

2. -9.8n +11.1

Answer:

-9.8n+11.1

Step-by-step explanation:

You have to add all like terms. That means that -5.8n and -4n have to be added together along with 3.1 and 8. That gets you -9.8n+11.1.

Answer:

1)option b

2)option a

Step-by-step explanation:

1) circumference = 62.8 in

=> 2πr= 62.8

=> r= 62.8/(2×3.14)= 10 in

diameter = 2×10 in = 20 in

2)diameter = 14m

radius = 7 m

Area of the circle= πr² =3.14(7)²=3.14×49

= 153.86

=153.9 m²

Answer:

Q1) B

Q2) A

Step-by-step explanation:

Q1) The equation for working out the circumference of a circle is 2 × π × r or π × d, but here we are asked to do the reverse so,

π × d = 62.8

d = 62.8 ÷ π

d = 19.9

So the answer to the Q1) is 20 inches

Q2) We have to work out the area of the circle so we utilise the formula

π × r² . We only have the diameter but we can half it to find the radius so

14 ÷ 2 = 7. So 7 is the radius, now we substitute into the formula π × r²

3.14 × 7² = 153.86

To find the value of 6 units when 32 units are worth $2,080, calculate the per unit value by dividing $2,080 by 32 to get $65 per unit, then multiply by 6 to obtain the value of 6 units, which is $390.

The question asks to find the value of 6 units given that 32 units represent $2,080. To solve this, we first find the value of one unit by dividing the total amount of money by the number of units. So, $2,080 divided by 32 units gives us the value per unit.

Next, we multiply the value of one unit by the number of units we want to find the value for, which is 6 units. This will give us the value for 6 units. Let's go through the steps:

Therefore, the value of 6 units is $390.

Answer:

(0.3,3)

Step-by-step explanation:

That is the vertex.