What is the solid formed when rotated around the side length of 4?
O cylinder with a height of 3 units and a radius of 4 units
O cone with a height of 4 units and a radius of 3 units
cylinder with a height of 3 units and a radius of 5 units
O cone with a height of 5 units and a radius of 4 units
Find the volumes and surface areas of the solids. Give your answers in terms of .
Surface Area: square units
Volume: cubic units

Answer:

k = 8.4; j = 13.1

Step-by-step explanation:

We can find the measures of j and k using trigonometric ratios, namely the tangent ratio and the cosine ratio

If we allow 40 to be our reference angle...

Because we're not given the measure of either j or k, we have to use 10 each time

Steps to find j:

[tex]cos(40)=\frac{10}{j}\\ \\j*cos(40)=10\\\\j=\frac{10}{cos(40)}\\ \\j=13.05407289\\\\j=13.1[/tex]

Steps to find k:

[tex]tan(40)=\frac{k}{10}\\ \\10*tan(40)=k\\\\8.390996312=k\\\\8.4=k[/tex]

Answer:

  cylinder

Step-by-step explanation:

You want to know which of two popcorn containers is a better value:

The volume formulas for the two shapes are ...

  V = 1/3πr²h . . . . . cone

  V = r²h . . . . . . . . . cylinder

For r = d/2, the ratio of these two volumes is ...

  [tex]\dfrac{V_{con}}{V_{cyl}}=\dfrac{\dfrac{1}{3}\pi\left(\dfrac{d_{con}}{2}\right)^2h_{con}}{\pi\left(\dfrac{d_{cyl}}{2}\right)^2h_{cyl}}=\dfrac{d_{con}^2\cdot h_{con}}{3\cdot d_{cyl}^2\cdot h_{cyl}}=\dfrac{12^2\cdot19}{3\cdot 8^2\cdot 15}=\dfrac{2736}{2880}=0.95[/tex]

The cone has less volume and costs more, so the cylindrical container is the better value.

Answer:

The given pattern does not form an arithmetic sequence as there is no common difference between each term. An arithmetic sequence is a sequence in which there is a fixed difference between each consecutive term. For example, 1, 3, 5, 7 is an arithmetic sequence with a common difference of 2 (adding 2 to each term gives the next term). However, the given pattern of 1/2, 1, 2/3, 2 does not follow this pattern as the difference between each term varies. Therefore, this pattern does not fit the definition of an arithmetic sequence.

Step-by-step explanation:

↬ x² - 6x -5

Substituting x = 3:-

⟶ x² - 6x -5

⟶ (3)² - 6(3) -5

⟶ 9 - 6 × 3 - 5

⟶ 9 - 18 - 5

⟶ 9 - 23

⟶ -14

Answer:

[tex] \gg{ \underline{ \large \: \boxed { \bf {- 14}}}}[/tex]

Step-by-step explanation:

[tex] \large \: \sf { \underline{Given}}[/tex]

[tex] \large \sf \underline{Solution }[/tex]

[tex] \large \: \displaystyle \sf {x}^{2} - 6x - 5[/tex]

[tex] \: \: \: \: \: \: \: \: \: \: \: \large \bf \blue{ \underline{putting \: the \: value \: of \: x}}[/tex]

[tex]\large \: \displaystyle \sf \: {3}^{2} - 6(3) - 5 [/tex]

[tex]\large \: \displaystyle \sf \: = \: 9 - 18 - 5[/tex]

[tex]\large \: \displaystyle \sf \: = \: - 9 - 5[/tex]

[tex]\large \: \displaystyle \bf \red{= - 14}[/tex]

The height from the ground to the top of the ladder is 61. 28 feet

First, we need to know that their are six different trigonometric identities.

These identities includes;

From the information given, we have that;

the height of the ladder that is leaning against the house = 80 feet

This the hypotenuse side

The angle of elevation is 50 degrees

Then, the opposite side is the height from the ladder = x

Using the sine identity, we have;

sin 50 = x/80

cross multiply the values

x = 61. 28 feet

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The magnitude of the speed of the particle is determined as √ (17), m/s.

option A.

The speed of a particle is defined as the rate of change of the particle's displacement with time.

Mathematically, the formula for the speed of the a particle is given as;

v = dx/dt

where;

The speed of the particle is calculated as;

v = u + at

where;

at time, t = 0, the equation for the speed of the particle becomes;

v = u

v = i + 4j

The magnitude of the speed is calculated as follows;

v = √ (1² + 4²)

v = √ (17), m/s

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We can see here that the distinct orders of light bulbs that are there if two light bulbs of the same color are considered identical is: 4,620.

We can see here that in order to find the solution, we use the permutation with repetition formula:

n! / (n1! × n2! x ... × nk!)

In order to adjust for overcounting, we divide by 3! because of the 3 red light bulbs we have. For the 2 yellow light bulbs, we divide with 2!. For the 6 pink light bulbs, we divide by 6!. This is because we are treating lights bulbs of the same color which are identical.

Therefore, the total number of distinct orders of bulbs will be:

11! / (3! × 2! × 6!) = 4,620

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The value of p in the equation 7p - 4 = 8 is p = 12/7

From the question, we have the following parameters that can be used in our computation:

7p - 4 = 8

Add 4 to both sides

So, we have

7p = 12

Divide both sides by 7

So, we have

p = 12/7

Hence, the solution is p = 12/7

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Answer:

4 miles per gallon. Answer choice B is correct.

Step-by-step explanation:

To find the gas mileage for each car, we need to divide the distance traveled by the amount of gasoline used.

For Mitra's car, the gas mileage is:

gas mileage = distance traveled / amount of gasoline used

gas mileage = 469.8 / 14.5

gas mileage = 32.4 miles per gallon

For Adira's car, the gas mileage is:

gas mileage = distance traveled / amount of gasoline used

gas mileage = 355 / 12.5

gas mileage = 28.4 miles per gallon

To find the difference in gas mileage, we can subtract the gas mileage for Adira's car from the gas mileage for Mitra's car:

difference = gas mileage for Mitra's car - gas mileage for Adira's car

difference = 32.4 - 28.4

difference = 4 miles per gallon

Therefore, the difference in gas mileage between the two cars is 4 miles per gallon. Answer choice B is correct.

Answer:

m = 3 + 2√3 or m = 3 - 2√3

Step-by-step explanation:

The given equation is:

m^2 - 6m = 3

We can rewrite the equation in standard quadratic form as:

m^2 - 6m - 3 = 0

We can use the quadratic formula to solve for m:

m = [-b ± √(b^2 - 4ac)] / 2a

where a = 1, b = -6, and c = -3.

Substituting these values, we get:

m = [-(-6) ± √((-6)^2 - 4(1)(-3))] / 2(1)

m = [6 ± √(36 + 12)] / 2

m = [6 ± √48] / 2

m = [6 ± 4√3] / 2

Simplifying the expression, we get:

m = 3 ± 2√3

Therefore, the solutions to the equation are:

m = 3 + 2√3 or m = 3 - 2√3

If this helps, please mark my answer as brainliest so i can help you more!:)

Answer:

[tex]x=3+2\sqrt{3}\\\\ x=3-2\sqrt{3}[/tex]

Step-by-step explanation:

The quadratic formula is:

[tex]x=\dfrac{-b \pm \sqrt{b^2-4ac}}{2a}\quad\textsf{when }\:ax^2+bx+c=0[/tex]

Therefore, to solve the given equation using the quadratic formula, first subtract 3 from both sides of the equation so that it is in the required form.

[tex]m^2-6m-3=3-3[/tex]

[tex]m^2-6m-3=0[/tex]

Comparing the coefficients:

Substitute the values of a, b and c into the formula and solve for x:

[tex]\implies x=\dfrac{-(-6) \pm \sqrt{(-6)^2-4(1)(-3)}}{2(1)}[/tex]

[tex]\implies x=\dfrac{6 \pm \sqrt{36-4(-3)}}{2}[/tex]

[tex]\implies x=\dfrac{6 \pm \sqrt{36+12}}{2}[/tex]

[tex]\implies x=\dfrac{6 \pm \sqrt{48}}{2}[/tex]

Rewrite 48 as a 4² · 3:

[tex]\implies x=\dfrac{6 \pm \sqrt{4^2 \cdot 3}}{2}[/tex]

[tex]\textsf{Apply the radical rule:} \quad \sqrt{ab}=\sqrt{a}\sqrt{b}[/tex]

[tex]\implies x=\dfrac{6 \pm \sqrt{4^2} \sqrt{3}}{2}[/tex]

[tex]\textsf{Apply the radical rule:} \quad \sqrt{a^2}=a, \quad a \geq 0[/tex]

[tex]\implies x=\dfrac{6 \pm 4 \sqrt{3}}{2}[/tex]

Simplify:

[tex]\implies x=\dfrac{6}{2}\pm\dfrac{4 \sqrt{3}}{2}[/tex]

[tex]\implies x=3\pm2 \sqrt{3}[/tex]

Therefore, the values of x are:

[tex]x=3+2\sqrt{3}\\\\ x=3-2\sqrt{3}[/tex]

The correct statement regarding whether the graph represents a function is given as follows:

No, it is not a function.

A graph represents a function if it has no vertically aligned points, that is, each value of x is mapped to only one value of y. Vertically aligned points mean that a value of x is mapped to multiple values of y, that is, a single input is mapped to multiple outputs which disqualify the relation as a function.

In the graph, we have that at x = 0 = y-axis, the function has three numeric values, which is a case of vertically aligned points, hence the graph does not represent a function.

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Answer:5.08

4.34 are correct

Step-by-step explanation:We can solve this quadratic equation in sin(θ) by using the substitution u = sin(θ):

6u^2 - 3u - 8 = 0

We can use the quadratic formula to solve for u:

u = (-b ± sqrt(b^2 - 4ac)) / 2a

where a = 6, b = -3, and c = -8. Substituting these values, we get:

u = (3 ± sqrt(9 + 192)) / 12

u = (3 ± sqrt(201)) / 12

Therefore, either:

Answer:14

Step-by-step explanation:

2 pants can only go with the different shirts once. So it should be 14

Sawyer has 4 cousins given that Hazel has 2 times as many cousins as Sawyer.

From the question, we have the following parameters that can be used in our computation:

Using the above as a guide, we have the following:

Hazel = 2 * Sawyer

Let c stand for the number of cousins Sawyer has.

So, we have

Hazel = 2 * c

Substitute the known values in the above equation, so, we have the following representation

2 * c = 8

Divide by 2

c = 4

Hence, the number of cousins Sawyer has is 5

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The likelihood that Mia and Lia place in 1st or 2nd is unlikely

From the question, we have the following parameters that can be used in our computation:

People = 50

Positions = 1st, 2nd, and 3rd place

The probabilities are

P(1st) = 1/50

P(2nd) = 1/49

Using the above as a guide, we have the following:

P = 1/50 * 1/49

Evaluate

P = 0.00040816326

This value is less than 50%

So, the likelihood is unlikely or less likely

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It should be noted that 81.85% of the scores are between 72 and 87.

The probability that a score is greater than 77 is approximately 0.8413.

a) The z-score for 72 is calculated as:

z = (72 - 82) / 5 = -2

The z-score for 87 is calculated as:

z = (87 - 82) / 5 = 1

0.8413 - 0.0228 = 0.8185

So, approximately 81.85% of the scores are between 72 and 87.

b) The z-score for 77 is calculated as:

z = (77 - 82) / 5 = -1

1 - 0.1587 = 0.8413

Therefore, the probability that a score is greater than 77 is approximately 0.8413 (or 84.13%).

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Each pound of bananas costs $1.49 for the 10-pound package and $1.51 for the 8-pound package.

The 10 pounds of bananas is the better buy because $1.49 is the cheaper price per pound.

We have,

Part A:

To find the cost of each pound of bananas in each case,

We can use the unit rate.

- For 10 pounds of bananas at $14.90, the cost per pound is:

$14.90 ÷ 10 pounds

= $1.49 per pound

- For 8 pounds of bananas at $12.08, the cost per pound is:

$12.08 ÷ 8 pounds

= $1.51 per pound

Part B:

The better buy is the one with the lower cost per pound.

Since $1.49 is less than $1.51, the 10-pound package is the better buy.

The 10 pounds of bananas is the better buy because $1.49 is the cheaper price per pound.

Therefore,

Each pound of bananas costs $1.49 for the 10-pound package and $1.51 for the 8-pound package.

The 10 pounds of bananas is the better buy because $1.49 is the cheaper price per pound.

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Answer:

A) [tex]x = \dfrac{\log_6(46) + 6}{4}[/tex]

B) [tex]x = \dfrac{\ln(11)}{2}[/tex]

C) [tex]x = \dfrac{11}{5}[/tex]

Step-by-step explanation:

A) We can solve for x by taking log base 6 of both sides.

[tex]\log_6(6^{4x-6}) = \log_6(46)[/tex]

[tex]4x - 6 = \log_6(46)[/tex]

[tex]4x = \log_6(46) + 6[/tex]

[tex]\boxed{x = \dfrac{\log_6(46) + 6}{4}}[/tex]

B) First, we have to divide both sides by 2.

[tex]2e^{2x} / 2= 22 / 2[/tex]

[tex]e^{2x} = 11[/tex]

Then, we can solve for x by taking the natural log (log base e) of both sides.

[tex]\ln(e^{2x})= \ln(11)[/tex]

[tex]2x= \ln(11)[/tex]

[tex]\boxed{x = \dfrac{\ln(11)}{2}}[/tex]

C) We can solve for x by raising 2 to the power of each side.

[tex]2^{\log_2(5x + 5)} = 2^4[/tex]

This cancels the log base 2 on the left.

[tex]5x + 5 = 16[/tex]

[tex]5x = 11[/tex]

[tex]\boxed{x = \dfrac{11}{5}}[/tex]

Answer: The brother is 16 and she is 19.

Step-by-step explanation:

35 - 3 = 32

32 / 2 = 16

16 + 3 = 19

A system of linear equations that describes this situation include the following;

x = 5y

x + y = 24

In order to write a linear equation or function to describe this situation, we would assign variables to the length of the longer piece and the length of the shorter piece in feet respectively, and then translate the word problem into a linear equation as follows:

Since one piece is five times as long as than the other and the length of the longer piece plus the length of the shorter piece equals 24 feet, a system of linear equations or function to describe this situation can be written as follows;

x = 5y

x + y = 24

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(a) Sum of values = Mean × Number of values = 64 × 5 = 320

(b) Sum of values = Mean × Number of values = 8.2 × 5 = 41

Fifth value = Sum of values - sum of known values = 41 - (6 + 10 + 7 + 12) = 41 - 35 = 6

(c) The resulting middle number when computing 10, 20, 30, 40, 50;that is (10 + 20 + 30 + 40 + 50)/5, totals up to 150 and dividing that number by 5 reflects a mean of 30.

i) Forming an average of 20, 30, 40, 50, 60;that is (20 + 30 + 40 + 50 + 60)/5 provides an outcome of 200 and divided by 5 reveals a mean of 40.

ii) With 0, 10, 20, 30, 40 used, (0 + 10 + 20 + 30 + 40)/5 practices calculation yielding a total of 100 which, split into five parties, imparts a mean of 20.

iii) Taking into consideration the input of 100, 200, 300, 400, 500;whereby (100 + 200 + 300 + 400 + 500)/5 develops a collective of 1500, cut in half produces a mean of 300.

iv) Calculating 1, 2, 3, 4, 5's mean; namely (1 + 2 + 3 + 4 + 5)/5 ascertains a collective amount of 15, divide that figure by five culminates with a mean of 3.

v) Accordingly, the following general assumptions can be made:

i) Introducing a constant to each value augments the mean by that very same constant.

ii) Extracting a constant from all values decrements the mean by such said constant.

iii) Multiplying every value by one constant multiplies the mean by the same specific constant.

iv) Dividing all values by a particular constant divides the mean by that given constant.

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Answer: 0.15

I don't really know how to show you work on here but you can think about it like this. if 5 x 3 is 15, and if there is a decimal like 0.3 x 0.5 it would result in the answer getting smaller as you're multiplying decimals if that makes sense... so it would result in the answer being 0.15. Sorry if it wasn't a good explanation.

The boat is moving at 48 mph while the current is moving at 9 mph in still water.

Let's use the letters "B" for the boat's speed in still water and "C" for the current's speed.

The boat's effective speed upstream is B - C because it is moving against the current.

Since the boat is moving downstream against the tide, its effective speed is equal to B plus C.

Based on the supplied data, we can construct the following two equations:

234 = 6(B - C)

342 = 6(B + C)

Making these equations simpler:

39 = B - C

57 = B + C

Now that we have added the two equations, we may solve for B and C:

39 + 57 = 2B

96 = 2B

B = 48

Therefore, the boat's speed in calm water is 48 mph.

To find C, we can rewrite one of the initial equations with this value as a substitute:

39 = 48 - C C = 9

Thus, the current is moving at a 9 mph velocity.

Therefore, the boat is moving at 48 mph while the current is moving at 9 mph in still water.

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Answer:

53

Step-by-step explanation:

20+8=28

90-28=62

62-9=53

90 angle!

The variables to the parallelogram OPQR are;

1. coordinates of points M is (1, 2.5)

2. The length of PQ is 4

3. The length of QR is 5.4

4. The length of PM is 3.9

5. The length of OM is 2.7

6. The perimeter of the parallelogram OPQR is approximately  18.8

7. if m ∠QMR = 120° m ∠ QMP = 60°

8. If m ∠ QRO = 80°  m ∠ROP =  100°

To calculate for every listed length of parallelogram OPQR it will be helpful to list all the coordinate for this diagram and they are;

O (0, 0)

p (-2, 5)

R (4, 0)

Q (2, 5)

To find for M, we could just get it from the diagram by looking at the points for x and then y. This is (1, 2.5). You can also calculate it like this

Mx = (Px + Rx)/2 = (-2 + 4)/ 2 = 2/2 = 1

My = (Py + Ry)/2 = ( 5 + 0)/2 = 2.5

To calculate for the length of any side, we say

LPQ = √(Qx -Px)² + (Qy - Py)² = √(2 - -2)² + (5-5)² = √8 = 4

LQR = √(Rx -Qx)² + (Ry - Qy)²

LPM = √(Mx -Px)² + (My - Py)²

LOM = √(Mx -Mx)² + (Oy - My)²

if m∠QMP = 180° - m∠QMR = 180° - 120° = 60°

The question below is as seen in the pictures provided.

The diagonals of parallelogram OPQR intersect at point M.

What are the coordinates of points M?

Find PQ

Find QR

Find PM

Find OM

Find permeter of parallelogram OPQR

if m ∠QMR = 120° what is m ∠ QMP

If m ∠ QRO = 80°  what is m ∠ROP

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Answer:

H

Step-by-step explanation:

Firstly, G and J cannot be the answers because the beginning numbers are too big. If you look at the fractions, you can see 2 and 7/8 because 2 is the smallest of all of them. Now the answer is between F and H.

In F, the second number is 3 and 1/2.

In H, the second number is 3 and 1/4.

If you want to make it an improper fraction to visualize better, it would be 7/2 and 12/4=6/2. Or you can just compare to see which is smaller, 1/2 or 1/4. In this case, 3 and 1/4 is smaller. Therefore the answer is H.

Answer: $34.01

Step-by-step explanation:

To get the answer, we must first add up the entire amount of money saved after four weeks of mowing the neighbor's lawn, then subtract the bike's price.

Since we get $40 a week, after 4 weeks we will have saved the following:

40 × 4 = 160

We will therefore have $160 to spend on the bike. The bike costs $125.99, so we will have the following amount of money after purchasing the bike:

160 - 125.99 = 34.01

Therefore, after purchasing the bike, we will have $34.01 leftover.

The slope of the line perpendicular to the line is m = ( 7/2 )

Given data ,

The equation of the given line is y = -2/7x + 3/7.

Now , it is in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.

The slope of the given line is -2/7, which means that for any line perpendicular to this line, the slope would be the negative reciprocal of -2/7.

So , m = ( 7/2 )

Hence , the slope of the perpendicular line is = 7/2

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