please answer the following questions and show your work. this is overdue since the 10th pls help lol​​

The height and radius of the cone-shaped cup that will use the smallest amount of paper, that is the maximum volume is  3.72 and  2.632 respectively.

Formula used in the solution is

Volume of the cone= (1/3)π(r^2)h

Area of the cone= πr√(l^2 + r^2)

Given, the volume of the cone is 27 cm^3.

(1/3)π(r^2)h =27

Simplifying the equation to get the value of r.

π(r^2)=81/h

r^2=81/hπ

\(r=\sqrt{\frac{81}{\pi h} }\)

Substituting the value of r in area, we get

\(A=\pi \sqrt{\frac{81}{\pi h} } \sqrt{h^{2} + \frac{81}{\pi h} }\)

\(\frac{dA}{dh} =\pi \sqrt{\frac{81}{\pi h} } \sqrt{h^{2} + \frac{81}{\pi h} }\)

dA/dh=√81 × (π - 162/\(h^{3}\)) × 1/√(πh + 81/\(h^{2}\))

At dA/dh=0, we will get,

√81 × (π - 162/\(h^{3}\)) × 1/√(πh + 81/\(h^{2}\))=0

√81 × (π - 162/\(h^{3}\))=0

\(\pi - \frac{162}{h^{3} }=0\)

Thus, \(\pi h^{3} -162=0\)

\(\pi h^{3} =162\)

\(h^{3} =\frac{162}{\pi}\)

h^3= 51.5662015618

h= 3.7221

Now, substitute h in radius,

\(r=\sqrt{\frac{81}{\pi \times 3.7221} }\)

r=2.632

Hence, the height of the cone shaped cup is 3.7221 and the radius is 2.632.

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Answer:

Answer:

A. 2

Step-by-step explanation:

slope formula is :  or the difference in y-coordinates in 2 points divided by the difference in x-coordinates in 2 points.

in this question, they have given you both the difference in x and difference in y.

therefore this question is saying :  =

= 2

therefore, the correct slope value is A. 2

Step-by-step explanation:

Volunteer/voluntary response bias, also known as self-selection bias, occurs when research participants exert control over the decision to engage in the study.

The ratio of good outcomes to all possible outcomes of an event is known as the probability. The number of positive results for an experiment with 'n' outcomes can be represented by the symbol x.

The probability of an event can be calculated using the following formula.

Probability(Event) = Positive Results/Total Results = x/n

In order to better grasp probability, let's look at a straightforward application.

Let's say we need to forecast if it will rain or not. Either "Yes" or "No" is the appropriate response to this query.

There is a chance that it will rain or not. Here, probability can be used. Using probability, one may forecast the results of a coin toss, a roll of the dice, or a card draw.

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Answer:

150ft

Step-by-step explanation:

You can calculate the rate of increase by comparing two points.

At x = 1, y = 150 and when x = 2, y = 300

So:

300-150 = 150

This means that the rate of increase per minute is 150ft

Hope this helps!

Answer: 150 ft

Step-by-step explanation:

Your answer should be:

28 cows.

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

With there being 60 cows:

12 cows have brown spots.

20 cows have black spots.

28 cows have no spots.

Answer:

y=(0,-3)

Step-by-step explanation:

To find the y-intercept, substitute in  0  for  x  and solve for  y

Answer:

y = -3 + x/3 sorry i got a mistake from the last one THIS IS THE RIGHT ONE!

Step-by-step explanation:

happy to help! and if u need any help with math, just call me :)

i would help you gladly!

Three different vectors are [-8, 14],  [-6, 16], and [15, -18].

To find three different vectors that are in the span of the given vectors \(u_1\) = [-3, 8] and \(u_2\) = [-5, 6], we can use linear combinations of these vectors.

Let's call the three different vectors \(v_1\), \(v_2\), and \(v_3\). We can express them as follows:

\(v_1\) = \(u_1\) + \(u_2\) = [-3, 8] + [-5, 6] = [-3 + (-5), 8 + 6] = [-8, 14]

\(v_2\) = 2\(u_1\) = 2[-3, 8] = [-6, 16]

\(v_3\) = -3\(u_2\) = -3[-5, 6] = [15, -18]

Therefore, three different vectors that are in the span of \(u_1\) and \(u_2\) are \(v_1\) = [-8, 14], \(v_2\) = [-6, 16], and \(v_3\) = [15, -18].

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Answer:

7 - y

Step-by-step explanation:

The sum of -7 and y: -7 + y

The opposite of the sum: -(-7 + y) = 7 - y

Therefore, the answer of the given question of the equation maximum value is 41 .

What is equation?

The equal sign is used between numerical or changeable expressions to create an equation, such as 3x+5=11.

A number that can be entered as the variable's replacement in an equation serves as the solution.

According to the given question:

Correct option is D)

f(x)=  3+9x+17 /  3+9x+7

=> 3+9x+7+10 / 3+9x+7

=> 1 +  10 / 3+9x+7

f(x) = 0 for maximum value

f(x)= 10 (6x+9) / (3x2+9x+7)2

6x+9=0

X=-3/2

Given that x is real, the highest value of f(x) is => 1 +

=> 1 +

=> 1 + 40/1 = 41

Therefore, the answer of the given question of the equation is 41 .

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Answer: A rotation of 270° clockwise is equivalent to a rotation of 90° counterclockwise, because a full rotation is 360° and 270° clockwise is the same as 90° counterclockwise in terms of direction.

Therefore, the answer is: counterclockwise 90°.

Step-by-step explanation:

Answer:

9.99

Step-by-step explanation:

Answer:

The vertex of the parabola is;

([-1], [3])

Step-by-step explanation:

The given quadratic equation is presented as follows;

x² + 8·y + 2·x - 23 = 0

The equation of the parabola in vertex form is presented as follows;

y = a·(x - h)² + k

Where;

(h, k) = The vertex of the parabola

Therefore, we have;

x² + 8·y + 2·x - 23 = 0

8·y = -x² - 2·x + 23

y = 1/8·(-x² - 2·x + 23)

y = -1/8·(x² + 2·x - 23)

y = -1/8·(x² + 2·x + 1 - 23 - 1) = -1/8·(x² + 2·x + 1 - 24)

y =  -1/8·((x + 1)² - 24) =  -1/8·(x + 1)² + 3

Therefore, the equation of the parabola in vertex form is y =  -1/8·(x + 1)² + 3

Comparing with y = a·(x - h)² + k, we have;

a = -1/8, h = -1, and k = 3

Therefore, the vertex of the parabola, (h, k) = (-1, 3).

The area of the shaded circle is given as follows: 84.82 cm².

The area of a circle of radius r is given by pi multiplied by the radius squared, as given by the formula presented next:

\(A = \pi r^2\)

In this problem, we have that the important data is given in the bullet-points as follows:

Hence the shaded area in cm² can be found a applying the formula given at the beginning of this problem, as is presented below:

\(A = 0.75\pi \times 6^2 = 84.82\)

The multiplication by 0.75 happened because as stated in the bullet point, the shaded area corresponds to only 75% of the entire circle.

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Answer:

Choice: D. No, because squaring a binomial always produces a trinomial product

Step-by-step explanation:

Square of a binomial

The square of a binomial is calculated as follows:

\((a+b)^2=a^2+2ab+b^2\)

Note that if a and b are nonzero, the square always produces a trinomial result.

When squaring (2x-3) we get:

\((2x-3)^2=(2x)^2+2(2x)(-3)+(-3)^2\)

\((2x-3)^2=4x^2-12x+9\)

As stated above, the result is a trinomial. Thus, the answer of your classmate is wrong because it should have produced a trinomial.

Choice: D

To find ln(x³y) in terms of u and v, we can use the properties of logarithms. ln(x³y) can be rewritten as ln(x³) + ln(y), and using the property ln(a^b) = bˣ ln(a), we have 3ln(x) + ln(y) = 3u + v.

To find ln(x³y) in terms of u and v, we can use the properties of logarithms. ln(x³y) can be rewritten as ln(x³) + ln(y), and using the property ln(a^b) = bˣ ln(a), we have 3ln(x) + ln(y) = 3u + v.

The domain of the function f(x) = ln(x-3) is x > 3, since the natural logarithm is undefined for non-positive values. The x-intercept occurs when f(x) = 0, so ln(x-3) = 0, which implies x - 3 = 1. Solving for x gives x = 4 as the x-intercept.

There are no vertical asymptotes for the function f(x) = ln(x-3) since the natural logarithm is defined for all positive values. However, the graph approaches negative infinity as x approaches 3 from the right, indicating a vertical asymptote at x = 3.

To sketch the graph of f(x) = ln(x-3), we start with the x-intercept at (4, 0). We can plot a few more points by choosing values of x greater than 4 and evaluating f(x) using a calculator.

As x approaches 3 from the right, the graph approaches the vertical asymptote at x = 3. The graph will have a horizontal shape, increasing slowly as x increases. Remember to label the axes and indicate the asymptote on the graph.

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Given :

A car straight line depreciates monthly over time.

After 8 months the car is worth $29,520 and after 18 months the car is worth $26,420.

To Find :

How much does this car depreciate each month.

Solution :

Let, depreciation of car each month is D.

\(\text{Depreciation }=\dfrac{\text{Difference in prize}}{\text{Number of months}}\)

\(D = \dfrac{29520-26420}{18-8}\\\\D = \dfrac{3100}{10}\\\\D = \$310\)

Therefore, depreciation of car each month is $310 .

Hence, this is the required solution.

The object has a mass of 5.76 kg.

We may represent "m" in terms of "e" (energy) and "v" (speed) using the kinetic energy formula, assuming that "m" relates to the mass of the object:

The energy an object possesses as a result of its motion is known as kinetic energy. It is described as the energy that a moving object contains as a result of its motion, which is dependent on the mass and velocity of the object.

The formula for calculating an object's kinetic energy is KE = 1/2 * m * v2.

To solve for "m," we can rearrange this formula:

m = 2 x KE /

We obtain the following by substituting the given values:

m = 2 x 1800 / 25

m = 2 x 1800 J / 625

m= 5.76 (rounded to two decimal places)

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Number of hours taken by Mike and Sabrina to wash a car when they work together is equal to (6/ 5) hours .

As given in the question,

Number of hours taken by Mike to wash a car = 3 hours

Work done by Mike in 1 hour = 1/3

Number of hours taken by Sabrina to wash a car = 2 hours

Work done by Sabrina in 1 hour = 1/2

Amount of work done by Mike and Sabrina together in 1 hour

= (1/3) + (1/2)

= ( 2 + 3 ) / 6

= 5/6

Now,

1 work done by Mike and Sabrina together = 6/5 hours

Therefore, number of hours taken them together to wash a car is

(6/5) hours.

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The correct option is OA. y+4= -3(x-3). L 4.6.3 Test (CST): Linear Equations Solution: We are given that a line passes through (3,-4) and has a slope of -3.

We will use point slope form of line to obtain the equation of liney - y1 = m(x - x1).

Plugging in the values, we get,y - (-4) = -3(x - 3).

Simplifying the above expression, we get y + 4 = -3x + 9y = -3x + 9 - 4y = -3x + 5y = -3x + 5.

This equation is in slope intercept form of line where slope is -3 and y-intercept is 5.The above equation is not matching with any of the options given.

Let's try to put the equation in standard form of line,ax + by = c=> 3x + y = 5

Multiplying all the terms by -1,-3x - y = -5

We observe that option (A) satisfies the above equation of line, therefore correct option is OA. y+4= -3(x-3).

Thus, the correct option is OA. y+4= -3(x-3).

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Answer:

8 2/3

Step-by-step explanation:

First, we turn 6 1/2 into an improper fraction, which is 13/2. Now, we can write this out as: 13/2  divided by 3/4. When dividing fractions, you reverse the sign to multiplication and you flip the numerator and the denominator of the second number. So, in this case, it would be 13/2 TIMES 4/3 which now we can do! 13*4 is 52 and 2*3 is 6. 52/6 is a number we can simplify. We can divide out a 2, so 52/2 is 26 and 6/2 is 3. 26/3 can be put into a mixed number. 3 goes into 26, 8 times and there is a 2 left over. So our final answer is 6 2/3.

Applying the linear angles theorem, the measures of the larger angles are: 130 degrees.

The measures of the smaller angles are 50 degrees

Based on the linear angles theorem, we have the following equation which we will use to find the value of y:

3y + 11 + 10y = 180

Add like terms

13y + 11 = 180

Subtract 11 from both sides

13y + 11 - 11 = 180 - 11

13y = 169

13y/13 = 169/13

y = 13

Plug in the value of y

3y + 11 = 3(13) + 11 = 50 degrees

10y = 10(13) = 130 degrees.

Therefore, applying the linear angles theorem, the measures of the larger angles are: 130 degrees.

The measures of the smaller angles are 50 degrees.

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Answer:

52.37 – 46.37 = y

8y = 48

Step-by-step explanation:

Choose all the equations that are true if y = 6. 52.37 – 46.37 = y 45y =445 8y = 48 3.2 + y = 9 y ÷ 4 = 24

We solve for y in all the equations :

52.37 – 46.37 = y

52.37 – 46.37 = 6 (True)

45y =445

Divide both sides by 45

45y/45 = 445/45

y = 9.888 (False)

8y = 48

y = 48/8

y = 6 (True)

3.2 + y = 9

y = 9 - 3.2

y = 5.8 (false)

y ÷ 4 = 24

y/4 = 24

y = 24 * 4 = 96 ( false)

The joint probability mass distribution of x and y as well as the marginal distributions is 19/81, 25/81 and 7/36

To calculate P(X = x), we need to consider the probability of drawing x red balls out of the 2 balls. Since we are drawing with replacement, the probability of drawing a red ball on any given draw is 3/12 = 1/4. Therefore, the probability of drawing x red balls out of 2 is given by the binomial distribution:

P(X = x) = (2 choose x) * (1/4)ˣ * (3/4)²⁻ˣ

where (2 choose x) is the binomial coefficient.

Similarly, to calculate P(Y = y|X = x), we need to consider the probability of drawing y white balls given that we have already drawn x red balls. Since we are drawing with replacement, the probability of drawing a white ball on any given draw is 4/12 = 1/3. Therefore, the probability of drawing y white balls out of the remaining (2-x) balls is also given by the binomial distribution:

P(Y = y|X = x) = ((2-x) choose y) * (1/3)^y * (2/3)²⁻ˣ

The marginal distribution of x represents the probability distribution of drawing x red balls, irrespective of the number of white balls drawn. We can obtain this by summing the joint probabilities over all possible values of y:

P(X = 0) = P(X = 0, Y = 0) + P(X = 0, Y = 1) + P(X = 0, Y = 2) = 1/9 + 4/27 + 4/81 = 19/81

P(X = 1) = P(X = 1, Y = 0) + P(X = 1, Y = 1) + P(X = 1, Y = 2) = 2/9 + 4/27 + 4/81 = 25/81

P(X = 2) = P(X = 2, Y = 0) + P(X = 2, Y = 1) + P(X = 2, Y = 2) = 1/16 + 1/12 + 1/36 = 7/36

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The algebraic expression for the total money saved by Luis and Julio together is 4L.

Let's denote the amount of money saved by Luis as 'L'. According to the given information, Julio has triple the savings of Luis, so we can represent Julio's savings as '3L'.

To express the total money saved by Luis and Julio together, we can use algebraic notation. Let's denote the total savings as 'S'. It can be expressed as:

S = L + 3L

Simplifying the expression, we have:

S = 4L

Therefore, the algebraic expression for the total money saved by Luis and Julio together is 4L.

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Answer:

more than 200 calls

Step-by-step explanation:

Suppose number of calls = x

According to plan 1: Total monthly charge is $24

According to plan 2: Fix charge is $16 and $0.04 per call

cost of x's call = $0.04x

and monthly charge according to plan 2 = 0.04x + 16

a)  Plan 1 is more economical than plan 2.

0.04x + 16 > 24

solve it for x

.04x > 8

x > 200

b)   So,  if more than 200 calls are made then Plan 1 is more economical.

Answer:

A

Step-by-step explanation:

180⁰= a+b+81⁰

a=180⁰-117⁰=63⁰

b=180⁰-63⁰-81⁰=36⁰

Answer:

If two secant segments intersect outside a circle, then the product of the secant segment with its external portion equals the product of the other secant segment with its external portion.

45(45) = (2x + 75)(27)

2,025 = (2x + 75)(27)

2x + 75 = 75, so x = 0 and GH = 48