Amul is trying to find the volume of the cylinder. What
was Amul's error?
Amul should have squared pi.
Amul should not have multiplied by pi.
Amul should have squared the radius, not the
height
Amul did not make an error.

The graph is stretched vertically, shifted left 5 units, shifted up 7 units.

We have to determine the effect of the transformations on the graph of ƒ(x) = x^2 when changed to ƒ(x) =1/2(x − 5)^2 + 7

The vertex form of the quadratic equation is f(x) = a(x-h)^2 + k.

ƒ(x) =1/2(x − 5)^2 + 7 compare with vertex form therefore we have

a=1/2,h=5 k=7.

a=1/2 means the closer to zero the a value, the wider, so this will stretch vertically.

h=5 and this means that the graph is shifted left 5 units.

k=7 this means that the graph is shifted up 7 units.

The answer is stretched vertically, shifted left 5 units, shifted up 7 units.

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Final answer:

The graph of f(x) = x^2 undergoes a vertical compression, horizontal shift to the right by 5 units, and a vertical shift up by 7 units to become f(x) = 1/2(x - 5)^2 + 7, corresponding to option B.

Explanation:

When comparing the original function f(x) = x^2 with the transformed function f(x) = 1/2(x − 5)^2 + 7, we can analyze the effects of transformation as follows:

Vertical Compression: The coefficient 1/2 in front of (x − 5)^2 causes a vertical compression by a factor of 1/2 compared to the original function.

Horizontal Shift: The term (x − 5) inside the function indicates a horizontal shift to the right by 5 units.

Vertical Shift: The constant +7 added outside the square indicates the graph is shifted up by 7 units.

Therefore, the correct description of the transformations applied to f(x) = x^2 to obtain f(x) = 1/2(x − 5)^2 + 7 is option B: compressed vertically, shifted right 5 units, and shifted up 7 units.

Answer:

Hence there were total of 19 pizza and were ate among the 76 children in party.

Step-by-step explanation:

Given:

8 slices for each pizza

No of pizza ate are =12+3+4=19

To Find:

How many children were are party

Solution:

Given that each children ate 2 slices per head so

Total pizza=19

and each pizza is sliced in 8 parts so

19 pizza will give =19 *8=152 slices

Hence there are 152 total number of slices

So 2 slices/child and 152 slices

152 slices/ 2 slices/child

=(152/2)children

=76 children.

Answer:

0.07,

0.7,

7.0

That is the answer

Answer:0.07,0.7,7.0

Step-by-step explanation:

Answer:

5.83 or E

Step-by-step explanation:

Use Pythagorean theorem. 5^2+3^2=c^2 because the diameter is perpendicular it cuts the chord in half.

25+9=c^2  

34=c^2

5.83

Answer:

x = 5.83.

Step-by-step explanation:

The diameter bisects the vertical chord so the right triangle has legs 3 and 5.

So x^2 = 3^2 + 5^2

x^2 = 34

x = 5.83.

That is odd - if we work it out another way we get a different answer. I guess that must be because the numbers given in the diagram are not possible.

If we use the intersecting chords theorem,  we get (3+6)*3 = 27

= 5 * y where y is the other leg of the right triangle giving y = 5.4

and then this will give x = 6.18.

Answer:

An apple costs $2.25. A mango costs $1.25.

Step-by-step explanation:

Let a = price of 1 apple.

Let m = price of 1 mango.

Cameron:

4 apples + 7 mangoes ----> total $17.75

4a + 7m = 17.75

Gavin:

2 apples + 5 mangoes ----> total $10.75

2a + 5m = 10.75

We have a system of 2 equations in 2 unknowns.

4a + 7m = 17.75

2a + 5m = 10.75

We can use the elimination method to eliminate the variable a. Rewrite the first equation. Multiply both sides of the second equation by -2 and write below it. Then add the equations.

           4a + 7m = 17.75

(+)       -4a - 10m = -21.5

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

                    -3m = -3.75

Divide both sides by -3.

m = 1.25

A mango costs $1.25.

Now we use the first equation and substitute 1.25 for m and solve for a.

4a + 7m = 17.75

4a + 7(1.25) = 17.75

4a + 8.75 = 17.75

4a = 9

a = 2.25

An apple costs $2.25.

Answer: An apple costs $2.25. A mango costs $1.25.

Answer:

2.25 ; 1.25

Step-by-step explanation:

4A + 7M = 17.75

2A + 5M = 10.75

2A = 10.75 - 5M

4A = 21.5 - 10M

21.5 - 10M + 7M = 17.75

3.75 = 3M

M = 1.25

4A = 21.5 - 10(1.25)

4A = 9

A = 2.25

Answer:

36 Yellow pieces

Step-by-step explanation:

-Given the total number of pieces is 80 and the probability of choosing a yellow piece at random is 0.45.

-To find the number of yellows pieces in the container, we multiply its probability by the total number of pieces;

[tex]n_y=P(yellow)\times n\\\\=0.45\times 80\\\\=36[/tex]

Hence, the total number of yellow pieces is 36

Final answer:

To find the total number of yellow game pieces in the container, we can use the given probabilities to calculate the number of yellow pieces. By setting up equations based on the information provided, we determine that there are 8 yellow game pieces in the container.

Explanation:

Let's first calculate the total number of game pieces in the container.

Let x be the total number of yellow game pieces. The total number of game pieces is 80.

Given that the probability of choosing a green piece is 0.2 and the probability of choosing a yellow piece is 0.45:

Let the number of green pieces be (80 - x), so 0.2(80 - x) = 4 - 0.2x

Now, we know the number of yellow pieces is x, so 0.45x = 0.45x

Solving the equations, we get x = 8, thus there are 8 yellow game pieces in the container.

Answer:

1.631

1.861

-2.322

Step-by-step explanation:

The value of logarithm log₅20 is 1.861.

In mathematics, the logarithm is the inverse function to exponentiation. That means the logarithm of a number x to the base b is the exponent to which b must be raised, to produce x.

The given logarithms are log₃6, log₅20 and log₂(1/5).

We have change of base formula: logₐx= logₙx/logₙa

Here, log₃6 = log₁₀6/log₁₀3

= 0.7781/0.4771

= 1.6308

≈ 1.631

log₅20 = log₁₀20/log₁₀5

= 1.3010/0.6989

= 1.8614

≈ 1.861

log₂(1/5) = log₁₀(1/5)/log₁₀2

= -0.6989/0.3010

= -2.3219

≈ -2.322

Therefore, the value of logarithm log₅20 is 1.861.

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Answer:

y is 14x

Step-by-step explanation:

every time she travels 14 miles, she is on her bike for one hour

Answer:

y=14x and 21 miles

Answer:

That time is  35.4 minutes.

Step-by-step explanation:

The mean time of delivery follows a Normal Distribution pattern.

So we need to apply Z-scores to find out.

99% confidence  in delivery time means  P(z > value) = 0.01  = 1%

So    z > 2.325

so.      Pr [ (x - 21.2) /  6.1   >  2.325 ] = 1%

so  x  >  2.325*6.1 + 21.2

x  >  35.3825 minutes  would be out of the 99th percentile

Final answer:

To calculate the 99th percentile of pizza delivery times, use the z-score corresponding to a 0.99 probability and apply the formula X = μ + (z * σ), where X represents the delivery time, μ is the mean, and σ is the standard deviation.

Explanation:

The student is asking for the 99th percentile of the pizza delivery time, given that the times are normally distributed with a mean of 21.2 minutes and a standard deviation of 6.1 minutes. To find the 99th percentile, one would typically use a z-score table or a statistical software to find the z-value that corresponds to the 0.99 probability. Once the z-score is found, the formula X = μ + (z * σ) is used to calculate the specific time that corresponds to the 99th percentile, where X is the delivery time, μ is the mean delivery time, σ is the standard deviation, and z is the z-score. Since the student is asking for a guaranteed delivery time that covers 99% of the deliveries, this time will be longer than the average to account for the variability represented by the standard deviation.

Answer:

I believe A. is 82.352941176471%

Step-by-step explanation:

Answer:

Maximum width of image that can be viewed clearly on the cylindrical screen is 10 ft

Step-by-step explanation:

Here we have

Circumference of screen = 2πr = 120 ft

Angle that can be viewed horizontally either side of focus = 15°

Total angle view = 30°

Size of image that can be viewed = Object within 30° of focus

Maximum width of image that can be viewed clearly = Perimeter of 30° arc section of cylinder

Maximum width of image that can be viewed clearly = 30/360×120 ft = 10 ft.

Maximum width of image that can be viewed clearly on the cylindrical screen = 10 ft.

Answer:

49.43£

Step-by-step explanation:

Given that £3 is equal to €4

There fore one euro is equal to

£3  = €4

1 € = 3/4 £ = 0.75 £(pound)

to find value of €65.90 in terms of pound we multiply both side of above equation with 65.90

=> 65.90 € = 0.75 * 65.90 £

=>  65.90 € = 49.425£ (Answer)

65.90 € is equal to 49.43 rounded to two decimal points.

Answer:   0.159

other answer is wrong i did the quiz

Answer:

$25.20

Step-by-step explanation:

$35 x 0.28

= $9.80

35-9.80

= $25.20

Answer:

20%

Step-by-step explanation:

35 x .2 = 7

35 - 7 = 28

Hope this helps & best of luck!

Feel free to message me if you need more help! :)

Answer:

a) P(X = 75) = 0.30

(b) P(X ≤ 75)

= 0.2 + 0.4 + 0.3 = 0.90

(c) P(X > 50).

= 0.3 + 0.1 = 0.40

(d) P(X < 100)

= 0.2 + 0.4 + 0.3 = 0.90

(e) parts b, c & d are CDF

Answer:

the answer is C,D,B enjoy your day

Step-by-step explanation:

Answer:

New length = [tex]2+7=9[/tex] inches

New width = [tex]2+4=6[/tex] inches

Step-by-step explanation:

Given:

Length of rectangle is 7 inches

Width of a rectangle is 4 inches

The area is increased by 26 square inches when the length and width are increased by the same amount.

To find: new length and width

Solution:

With length of rectangle is 7 inches and width of a rectangle is 4 inches,

area = 7×4 = 28 inches

Let length and width be increased by x inches

New length = x + 7 inches

New Width = x + 4 inches

New area = [tex](x+7)(x+4)=x^2 +11x+28[/tex]

Also, new area = 28 + 26 = 54 square inches.

So,

[tex]28+11x+x^2 =54\\x^2+11x-26=0\\x^2 +13x-2x-26=0\\x(x+13)-2(x+13)=0\\(x-2)(x+13)=0\\x= 2, -13[/tex]

As dimension can not be negative, [tex]x=-13[/tex] is rejected.

So, [tex]x=2[/tex]

New length = [tex]2+7=9[/tex] inches

New width = [tex]2+4=6[/tex] inches

Final answer:

The new dimensions of the rectangle are 6 inches by 9 inches, after increasing both the original width and length by 2 inches to achieve the new area of 54 square inches.

Explanation:

Solution to the Rectangle Problem

The original rectangle is 4 inches wide and 7 inches long, with an area of 28 square inches (since area = width  imes length). When both the length and width are increased by the same amount, the area is 28 inches + 26 inches = 54 square inches. Let's denote the increase in dimension by 'x', thus the new dimensions are (4 + x) inches and (7 + x) inches. The new area is then (4 + x)(7 + x) = 54. Expanding this, we get 28 + 11x + x2 = 54. Simplifying, x2 + 11x - 26 = 0.

To find 'x', we can solve the quadratic equation. Factoring the quadratic, we get (x + 13)(x - 2) = 0, giving us two potential solutions for 'x': -13 and 2. However, since a negative increase in dimension is not possible, we only consider x = 2. Hence, the new dimensions of the rectangle are 6 inches by 9 inches.

Answer:

-2n-15 1/3

Step-by-step explanation:

-2n+5/3-6(4)+7

-2n+5/3-24+7

-2n+1 2/3-17

-2n-15 1/3

Answer: edgen

B 2=(1+0.065/12)^12t

Step-by-step explanation:

To the nearest year, it will take about 10.7 years to double the original investment.

In this case, the principal P is $1,000, the interest rate r is 6.5% or 0.065 (in decimal form), the number of times compounded per year n is 12 (compounded monthly), and we want to find the time t when the investment doubles, so A is $2,000.

[tex]2000 = 1000(1 + 0.065/12)^{12t}[/tex]

[tex]2 = (1 + 0.065/12)^{12t}[/tex]

ln(2) = 12t * ln(1 + 0.065/12)

t = ln(2) / (12 * ln(1 + 0.065/12))

t ≈ 10.7

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Find the area of the triangle side, then multiply by the length of the prism.

Area of triangle = 1/2 x height x base

Area  = 1/2 x 2 x 3 = 3 square cm

Volume = 3 x 4 = 12 cubic cm.

Answer is A) 12 cm^3

When wearing the magic ring, health points increase by 30% more.

Some expressions that could represent how many health points the spell restores are:

1.3(H)

H + 0.3(H)

Hope this helps!! :)

The healing spell with the magic ring restores 130% of the health points, represented as 1.30 imes H.

If Eiko's healing spell restores H health points without the magic ring, then with the ring, the spell's power increases by 30%. Thus, the total healing power with the ring can be expressed as H + 0.30 x H, which can also be simplified to 1.30 x H. This means, with the ring, Eiko would restore 130% of the health points that the spell would normally heal without the ring.

Answer:

The answers is in the problem 30 cubes

The total number of cubes are there in the box will be 75. And the table is completed below.

Its fundamental concept is that someone will nearly surely occur. The proportion of positive events in comparison to the total of occurrences.

Then the probability is given as,

P = (Favorable event) / (Total event)

Then the value of x is given as,

x + x + 0.4 = 1

2x = 0.6

x = 0.3

The table is given below.

Color                       Blue              Red            Yellow

Probability               0.4                0.3                0.3

If the number of blue cubes is 30. Then the total number of cubes is given as,

Total cubes = 30 / 0.4 = 75

The total number of cubes are there in the box will be 75.

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Answer:

adult ticket would cost 4.5 after the 45% discount and the childs ticket would cost 2.4 after the 40% discount

(i converted 2/5 into a percentage which left me with 40%)

each time the family goes to the movies the family saves 9.1

(assuming its one adult and one child)

so 40/9.1= 4.39 and round it to 4

question A

adult ticket after discount=4.5

child ticket after discount=2.4

Question B

the family would have to go at least 4 times before they start saving money.

Step-by-step explanation:

Answer:

8,55

Step-by-step explanation:

use trigonometric functions

Know that quadrilaterals’ with 4 sides the degrees should all add up to 360

a. 110

(110+62+78= 250

360 - 250 = 110)

b. 66

(84+78+2b+b = 360

162+3b = 360

3b = 198

b = 66)

c. 83

For 5 sides the degrees should add up to 540)

(101+152+38+2c+c = 540

291+3c=540

3c = 249

c = 83)

d. 30

For 6 sides the degrees should add up to 720

(108+102+4d+4d+4d+5d = 720

210+17d= 720

17d = 510

d = 30)

As for the others I’ll label them 1, 2, and 3...

1. 60

(105+75+2b+b = 360

180+3b= 360

3b = 180

b = 60)

2. 78

(125+65+92+a = 360

282+a = 360

a = 78)

3. 80

(130+65+120+[2c-15]+c = 540

315+[2c-15]+c = 540

3c-15 = 225

3c = 240

c = 80

Out of 58 cities, 26 have either a lake or a river, which simplifies to a fraction of 13/29 of the cities having one of these features.

To find the fraction of 58 cities that have either a lake or a river running through them, we need to determine how many cities have at least one of these features. It is important to check if any city has both a lake and a river, but since the question does not provide this information, we will assume that there are no cities that have both. The question tells us that 3 cities have a lake and 23 have a river. We simply add these counts together to find the total number of cities with at least one water feature.

The calculation would be:

3 (cities with a lake) + 23 (cities with a river) = 26 (cities with a lake or a river)

To find the fraction of the 58 cities that have a lake or a river, we divide the number of cities with a water feature by the total number of cities:

26 (cities with a lake or a river) / 58 (total cities) = 13/29 (simplified fraction).

Final answer:

Of the 58 cities, 26 have either a lake or a river, which means the fraction of cities with a lake or a river is 26/58.

Explanation:

To determine what fraction of the 58 cities have a lake or a river running through them, we must consider that the question does not specify whether some cities might have both a lake and a river. Assuming that the cities with lakes and the cities with rivers do not overlap, we simply add the number of cities with each feature.

There are 3 cities with a lake and 23 with a river. To find the total number of cities with either a lake or a river, we add these two numbers together:

3 (cities with a lake) + 23 (cities with a river) = 26 (cities with a lake or a river).

Now, to find the fraction of the 58 cities that have a lake or a river, we divide the number of cities with water features by the total number of cities:

26 / 58 = fraction of cities with a lake or a river running through them.

Answer:

Step-by-step explanation:

B

Answer:

the answer is B

Step-by-step explanation:

Answer:

[tex]\frac{1}{3}[/tex]

Step-by-step explanation:

A point (x, y) with integer coordinates is randomly selected such that [tex]0 \le x \le 8 \:and\: $0 \le y \le 4$.[/tex]

The possible pairs of (x,y) are:

(0,0),(0,1),(0,2),(0,3),(0,4)

(1,0),(1,1),(1,2),(1,3),(1,4)

(2,0),(2,1),(2,2),(2,3),(2,4)

(3,0),(3,1),(3,2),(3,3),(3,4)

(4,0),(4,1),(4,2),(4,3),(4,4)

(5,0),(5,1),(5,2),(5,3),(5,4)

(6,0),(6,1),(6,2),(6,3),(6,4)

(7,0),(7,1),(7,2),(7,3),(7,4)

(8,0),(8,1),(8,2),(8,3),(8,4)

The Total Possible Outcomes n(S)= 45

The pair (x, y) that satisfies the given condition (say event A: [tex]x + y \le 4[/tex]) are:

[tex](0,0),(0,1),(0,2),(0,3),(0,4)\\(1,0),(1,1),(1,2),(1,3)\\(2,0),(2,1),(2,2)\\(3,0),(3,1)\\(4,0)[/tex]

n(A)=15

Therefore:

[tex]P(A)=\frac{n(A)}{n(S)} =\frac{15}{45} =\frac{1}{3}[/tex]

Final answer:

To find the probability that a randomly selected point with integer coordinates satisfies "x + y ≤ 4", we counted the number of qualifying points and divided by the total number of possible points. With 15 points meeting the condition out of 45 possible points, the probability is 1/3.

Explanation:

The probability question asks for the likelihood that a point (x, y) with integer coordinates will satisfy the condition "x + y ≤ 4" when 0 ≤ x ≤ 8 and 0 ≤ y ≤ 4. To solve this, we first count the total number of possible points with integer coordinates within the given ranges for x and y. Since x can take 9 values (0 through 8) and y can take 5 values (0 through 4), there are 45 possible points (9 times 5).

Next, we identify the points that satisfy the condition "x + y ≤ 4". These points are (0,0), (0,1), (0,2), (0,3), (0,4), (1,0), (1,1), (1,2), (1,3), (2,0), (2,1), (2,2), (3,0), (3,1), and (4,0), which results in a total of 15 points satisfying the condition.

The probability is therefore the number of satisfying points divided by the total number of possible points, which is 15/45 or simplified to 1/3. Thus, the probability that a randomly selected point with integer coordinates will have "x + y ≤ 4" is 1/3.