show that f is not onto. counterexample: let m = ____ n .

Answer:

2(1/2)(8)(3) + 2(12)(5) + 8(12)

= 24 + 120 + 96 = 240 square inches

Answer:

1/4

Step-by-step explanation:

Create a chart 18 over 72 and x over 100

Now we multiply 18 by 100 to get 1800

We take that 1800 and divide it by 72 to get 25/100

We can simplify this to 1/4

Answer: 3, 4, 5

Step-by-step explanation:

Answer:

it's a yw

Step-by-step explanation:

Answer:

solve the following system of equations by using gauss elimination method

Answer:

Step-by-step explanation:

Triangle MNP is a right triangle with the following values:

Interior angles of a triangle sum to 180°. Therefore:

m∠M + m∠N + m∠P = 180°

m∠M + 58° + 90° = 180°

m∠M + 148° = 180°

m∠M = 32°

To find the measures of sides MN and NP, use the Law of Sines:

\(\boxed{\begin{minipage}{7.6 cm}\underline{Law of Sines} \\\\$\dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}$\\\\\\where:\\ \phantom{ww}$\bullet$ $A, B$ and $C$ are the angles. \\ \phantom{ww}$\bullet$ $a, b$ and $c$ are the sides opposite the angles.\\\end{minipage}}\)

Substitute the values into the formula:

\(\dfrac{MN}{\sin P}=\dfrac{NP}{\sin M}=\dfrac{PM}{\sin N}\)

\(\dfrac{MN}{\sin 90^{\circ}}=\dfrac{NP}{\sin 32^{\circ}}=\dfrac{8}{\sin 58^{\circ}}\)

Therefore:

\(MN=\dfrac{8\sin 90^{\circ}}{\sin 58^{\circ}}=9.43342722...\)

\(NP=\dfrac{8\sin 32^{\circ}}{\sin 58^{\circ}}=4.99895481...\)

To find the perimeter of triangle MNP, sum the lengths of the sides.

\(\begin{aligned}\textsf{Perimeter}&=MN+NP+PM\\&=9.43342722...+4.99895481...+8\\&=22.4323820...\\&=22.43\; \sf units\; (2\;d.p.)\end{aligned}\)

Answer:

15

Step-by-step explanation:

the range is the largest number take away the smallest number

56-41=15

Okay, it seems like you want to analyze a sample of 16 babies based on their weight.

The information you provided states that the Center for Disease Control and Prevention reports that 25% of baby boys aged 6-8 months in the United States weigh more than 20 pounds.

However, you haven't mentioned the specific question or analysis you want to perform on the sample. Could you please clarify what you would like to know or do with the given information?

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The rate of increase of the radius of the balloon is

0.12 cm per second

A rate is a ratio that compares two different quantities which have different units. For example, if we say John types 50 words in a minute, then his rate of typing is 50 words per minute. The word "per" gives a clue that we are dealing with a rate.

The volume of a sphere is 4/3πr^3

The rate of volume of the balloon is 24πcm^3/s

therefore the radius of the sphere at the volume of 24πcm^3= 4/3πr^3

dividing both sides by π

24= 4/3πr^3

multiply both side by 3/4

r^3 = 24×3/4

r^3= 18

r= √18

r= 2.62cm

therefore the rate of change in radius here is 2.62cm/s since π is constant.

The surface area of sphere= 4πr^2

the surface area of the balloon is 30πcm^2

therefore 30π= 4πr^2

divide both sides by 4π

r^2= 30/4

r^2= 7.5

r=√7.5

r= 2.74cm

the rate of change in radius here is 2.74cm/s

therefore the increase in rate of change of radius is 2.74cm/s - 2.62 cm/s= 0.12cm/s

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The equation that represent the relationship between the number of months and the amount remaining on the card is: y = 25 - (2.50x)

a) the independent variable is the: Number of month after the first year

b) the dependent variable is the: Amount remaining on the card

To solve this problem, we have to state the equation using the information of the problem.

Information about the problem:

Writing the equation according to the information gave, we have:

y = 25 - (2.50x)

Where:

The relationship between the number of months after the first year and the amount remaining on the card is: linear and inverse because when the number of months after the first year increases (x), the amount remaining on the card (y) will decrease.

The "y" variable is the dependent variable, because it will change according to the number of months passed after the first year (x).

The "x" variable is the independent variable, because it doesn't depend on any other value, just the number of months passed after the first year.

An equation is the equality between two algebraic expressions, which have at least one unknown or variable.

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Answer:

Expression: [105-(-27)]°F

Difference in temperature= 132°F

Step-by-step explanation:

The difference between the two temperatures can be found through subtraction.

Difference in temperature

= 105 -(-27)

= 105 +27

= 132°F

Additional:

An expression does not include an equal sign unlike an equation. If the difference in temperature is represented by D, then the equation would be:

D= [105-(-27)]°F

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Answer:

7/6

Step-by-step explanation:

5/2-4/3

=(5*3-4*2)/2*3

=(15-8)/6

=7/6

The maximum angle of the incline for the car to be at rest using only friction is 38.7° if, for the car on the incline, the coefficient of static friction is 0.8 and the coefficient of kinetic friction is 0.6.

If the car is at rest on the incline, the force of gravity acting on the car down the incline is balanced by the force of static friction acting up the incline. The maximum angle \($\theta$\) of the incline is the angle at which the force of static friction is at its maximum, which is given by the product of the coefficient of static friction and the normal force.

Let's assume that the mass of the car is m and the incline makes an angle of \($\theta$\) with the horizontal. Then, the force of gravity acting on the car down the incline is given by \($mg\sin(\theta)$\), where g is the acceleration due to gravity. The normal force acting on the car perpendicular to the incline is given by \($mg\cos(\theta)$\).

For the car to be at rest on the incline, the force of static friction acting up the incline must be equal in magnitude to the force of gravity down the incline. Therefore, we have:

\($$\mu_s mg\cos(\theta) = mg\sin(\theta)$$\)

here \($\mu_s$\) is the coefficient of static friction. Simplifying this equation,

we get:

\($$\tan(\theta) \leq \mu_s$$\)

Therefore, the maximum angle \($\theta$\) of the incline is:

\($$\theta \leq \tan^{-1}(\mu_s)$$\)

Substituting the value of \($\mu_s = 0.8$\), we get:

\($$\theta \leq \tan^{-1}(0.8) \approx 38.7^{\circ}$$\)

Therefore, the maximum angle of the incline for the car to be at rest using only friction is approximately 38.7°.

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Answer:

23/54 meters

Step-by-step explanation:

Assuming that the scale model is smaller, then the scale model should be 1/27th of the actual thing. Therefore:

11.5/27

= 23/54 meters tall

No, we cannot draw a triangle with sides 3 cm, 3.5 cm, and 6.5 cm.

Let's understand the concept behind this:

Apply the triangle's length-of-sides property, which stipulates that the total of any two sides should be more than the value of the third side. Such a triangle cannot exist if there is any pair of sides whose sum is equal to or less than the third side.

We must determine whether the supplied side lengths constitute a triangle. We now understand that the triangle's third side should be greater than the sum of any two of its sides. Such a triangle cannot exist if there is any pair of sides whose sum is equal to or less than the third side. So, we'll try every combination and see if it meets the criteria.

Let’s assume AB = 3 cm, BC = 3.5 cm and AC = 6.5 cm.

AB + AC = 3 + 6.5 cm = 9.5 cm > 3.5 cm = BC.

AC + BC = 6.5 + 3.5 = 10 cm > 3 cm = AB.

AB + BC = 3 + 3.5 cm  = 6.5 cm = AC.

However, in this case, the length of the third side is equal to the total lengths of the other two sides, which renders the triangle's condition incorrect.

Therefore, there does not exist any triangle with sides of 3 cm, 3.5 cm, and 6.5 cm.

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Subtraction, underflow can happen when two very close positive floating-point numbers are subtracted, resulting in a difference that is too small to be represented by the system.

Out of the four basic arithmetic operations, subtraction is the only operation that can produce an underflow in floating point arithmetic. When we subtract two positive floating-point numbers, the result can be very small, close to zero, or even negative. If the result is smaller than the smallest positive number that can be represented by the floating-point system, it can lead to an underflow.

To prevent underflows, floating-point systems often use gradual underflow, which treats numbers that are too small as if they were zero. This avoids numerical instability and ensures that computations are consistent and reliable. In conclusion, only subtraction can produce an underflow in floating point arithmetic.

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Answer:

3 and 12

Step-by-step explanation:

just multiply 2 x 3 and 2 x 12 and it would give you 6 and 24 :) I hope this help

The volume of the solid obtained by rotating the region bounded by y = sqrt(x) and y = x about the line x = 2 is (32π/15) cubic units.

To find the volume of the solid obtained by rotating the region bounded by the curves y = sqrt(x) and y = x about the line x = 2, we can use the method of cylindrical shells.
First, we need to determine the limits of integration. Since the curves intersect at (1, 1), we integrate from x = 1 to x = 4.
The height of each cylindrical shell is given by the difference between the functions y = x and y = sqrt(x), which is (x – sqrt(x)). The radius of each shell is the distance from the axis of rotation, which is 2 – x.
Using the formula for the volume of a cylindrical shell V = 2πrhΔx, we integrate (2π(2 – x)(x – sqrt(x))) with respect to x from 1 to 4.
Evaluating the integral, we find the volume V = (32π/15) cubic units.

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Answer:

14,850 ways

Step-by-step explanation:

Since the order does not matter, the number of possible committees is given by the product of the combination of picking 2 out of 10 faculty members and the combination of picking 4 out of 11 students:

\(n= \frac{10!}{(10-2)!2!}* \frac{11!}{(11-4)!4!}\\n=\frac{10*9}{2}*\frac{11*10*9*8}{4*3*2*1}\\n=14,850\)

The committee can be formed in 14,850 ways

Answer:

a) 16 in³

Step-by-step explanation:

Vol (cyl) = πr²h = 54

Vol (cone) =  πr²h/3

54/3 = 16

Answer:

(B)\(-4\dfrac34$ meters\)

Step-by-step explanation:

For divers

Given a dive with a depth of  \(4\dfrac34$ meters\)

Since we already know that depths are written using negative numbers, divers would represent it as:

\(-4\dfrac34$ meters\)

The correct option is B.

Answer: 55 packs

Step-by-step explanation:

55x 15=825 and there will be one badge left over

Hannah's debt-to-equity ratio when her liabilities was $30,000 (excluding her mortgage of $100,000 ) and her net worth is $45,000 is 0.75.

Debt-to-equity ratio is a financial ratio that measures the proportion of total liabilities to shareholders' equity. To calculate the debt-to-equity ratio for Hannah, we need to first calculate her total liabilities and shareholders' equity.

We are given that Hannah has liabilities of $30,000 excluding her mortgage of $100,000. Therefore, her total liabilities are $30,000 + $100,000 = $130,000.

We are also given that her net worth is $45,000. The net worth is calculated by subtracting the total liabilities from the total assets. Therefore, the shareholders' equity is $45,000 + $130,000 = $175,000.

Now we can calculate the debt-to-equity ratio by dividing the total liabilities by the shareholders' equity.

Debt-to-equity ratio = Total liabilities / Shareholders' equity = $130,000 / $175,000 = 0.74 (rounded to two decimal places)

Therefore, Hannah's debt-to-equity ratio is 0.74, which is closest to option 0.75.

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