A regular ice cream cone is 5 inches tall and has a diameter of 2.5 inches. A waffle cone is 7 inches tall and has a diameter of 3.75 inches.
(a)
Find the volume (in cubic inches) of the regular ice cream cone to the nearest tenth.


cu. in
(b)
Find the volume (in cubic inches) of the waffle cone to the nearest tenth.


cu. in
(c)
How much more ice cream (in cubic inches) fits in the waffle cone compared to the regular cone? Round your answer to the nearest tenth.


cu. in

Answer:

See below

Step-by-step explanation:

Part A

\(f(g(x))=f(\frac{x}{3})=3(\frac{x}{3})=x\\g(f(x))=g(3x)=\frac{3x}{3}=x\)

Since BOTH \(f(g(x))=x\) and \(g(f(x))=x\), then \(f\) and \(g\) are inverses of each other

Part B

\(f(g(x))=f(\frac{x+1}{2})=2(\frac{x+1}{2})+1=x+1+1=x+2\\g(f(x))=g(2x+1)=\frac{(2x+1)+1}{2}=\frac{2x+2}{2}=x+1\)

Since BOTH \(f(g(x))\neq x\) and \(g(f(x))\neq x\), then \(f\) and \(g\) are NOT inverses of each other

In a right triangle, the ratio of the opposite side of one angle to the hypotenuse is called sine.

In this problem the side JK is the opposite side of angle JLK whose value is 63 degrees. The hypotenuse is JL whose value is 8.

So the sine ratio of angle JLK would be

sin L=JK/JL

Substituting the numerical values,

sin 63°=JK/8

This implies JK=sin 63°×8 from wich we will get the value of JK

So, this equation sin 63°=JK/8 will let us solve for jk and the answer is the third one.

Answer:

C

Step-by-step explanation:

Dividing the weights of filled bags by the legally defined weight of a penny is less likely to be subject to random error.

What are the Random errors?

Random errors are errors that occur randomly and affect measurements in an unpredictable way. Therefore, the measurement most likely to be subject to random error is the one that is most prone to variability in measurement.

Out of the given options, the measurement most likely to be subject to random error is 3 - Measuring a distance in yards by pacing.

This is because the pacing is a manual process that is subject to variations in stride length, uneven terrain, and human error.

As a result, measurements obtained by pacing are likely to be more variable and subject to random errors.

The other options involve measurements taken using more precise instruments or standardized methods, which are less likely to be subject to random errors.

For example, digital thermometers and mercury thermometers provide more accurate temperature readings, and the weight of a penny is a standardized measure,

Therefore, dividing the weights of filled bags by the legally defined weight of a penny is less likely to be subject to random error.

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The solution is Option A.

The coordinate of the triangle after the translation is given by A' ( 0 , -3 ) with 4 units right and 4 units down

A translation moves a shape up, down, or from side to side, but it has no effect on its appearance. A transformation is an example of translation. A transformation is a method of changing a shape's size or position. Every point in the shape is translated in the same direction by the same amount.

Given data ,

Let the coordinate of the triangle be represented as A

Now , the coordinate A = A ( -4 , 1 )

Now , the coordinate of the triangle after translation is A' ( 0 , -3 )

when there is a translation of the coordinate A by 4 units to the right , we get

A to 4 units right = A ( -4 + 4 , 1 )

The new coordinate of A = A ( 0 ,  1 )

Now , A to 4 units down , we get

The coordinate of A' = A' ( 0 , 1 - 4 )

The coordinate of A' = A' ( 0 , -3 )

Hence , the translated coordinate is A' ( 0 , -3 )

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Answer:

  (c)  x³·∛x

Step-by-step explanation:

You want the simplified form of ∛(x¹⁰).

The first part of the problem tells you how to get there. After you have that expression, you need to bring the x⁹ term from under the radical.

  \(\sqrt[3]{x^{10}}=\sqrt[3]{x^9\cdot x}=\sqrt[3]{x^9}\cdot\sqrt[3]{x}=\boxed{x^3\cdot\sqrt[3]{x}}\qquad\text{matches choice C}\)

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Commitment to goals can be promoted in through:

Goal commitment is the degree of determination a person uses to achieve an accepted goal, and it is determined by two major factors: importance and self-efficacy. The reasons a person has for achieving a goal, including expectations of certain outcomes, are significant. Commitment helps you stick to your goals in both good and bad times, when obstacles arise. Commitment is influenced by two factors: importance and

Goal commitment is generally defined as an individual's determination to devote time and effort to achieving a goal.

Goal commitment is the degree of determination a person uses to achieve an accepted goal, and it is determined by two major factors: importance and self-efficacy. The reasons a person has for achieving a goal, including expectations of certain.

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Answer:

a = \(\frac{d}{b+c}\)

Step-by-step explanation:

a(b + c) = d

isolate a by dividing both sides by b + c

a = \(\frac{d}{b+c}\)

Answer:

3

2

Step-by-step explanation:

Answer:

£1.44

Step-by-step explanation:

N1 = £0.12

N12 = 12 × N1 = 12 × £0.12 = £1.44

Answer:

6

Step-by-step explanation:

To evaluate the expression if a = 4, b = 3, and c = 2, substitute those values for the variables and solve. So, substitute 4 for a, 3 for b, and 2 for c, then simplify by the correct order of operations, PEMDAS:

\(ab - bc \\(4)(3)-(3)(2)\\= 12 - 6 \\= 6\)

Therefore, the answer is 6.

The term "isometric" has the Greek roots "isos," which means "same," and "metron," which means "measure." The definition of an isometric transformation is one in which the original figure and its transformed equivalent have the same shape, size, and orientation.

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Answer:

\(0.98268\)

Step-by-step explanation:

We are given that

Mean, \(\mu=3408\)miles

Variance, \(\sigma^2=249001\)

We have to find  the probability that the mean of a sample of 36 cars would differ from the population mean by less than 198 miles.

n=36

\(P(|\bar{x}-3408}|<198)=P(3408-198<\bar{x}<198+3408)\)

=\(P(3210<\bar{x}<3606)\)

=\(P(\frac{3210-3408}{\sqrt{\frac{249001}{36}}}<\frac{\bar{x}-\mu}{\sqrt{\frac{variance}{n}}}<\frac{3606-3408}{\sqrt{\frac{249001}{36}}}\)

\(=P(-2.38<Z<2.38)\)

\(=P(Z<2.38)-P(Z<-2.38)\)

\(=0.99134-0.00866\)

=\(0.98268\)

Hence,  the probability that the mean of a sample of 36 cars would differ from the population mean by less than 198 miles=\(0.98268\)

Answer:

5, 7

Step-by-step explanation:

The mode of the numbers is 5, which means that 5 should be the most common card (highest frequency). Therefore the cards should have at least one more 5 among them.

Considering that 5 is one of the hidden cards and x is the other,

• Using the equation for the mean:

\(mean = \frac{sum \space\ \space\ of \space\ \space\ numbers}{number \space\ \space\ of \space\ \space\ numbers}\)

\(6 = \frac{4+5+ 9 + 5 + x}{5}\)

⇒ \(30=23 + x\)

⇒ \(x = 7\)

This means 5 and 7 are the hidden cards.

Sphenathi and the other matriculants must travel at an average speed of approximately 107 km/h to reach Uptington by 09:45.

To determine the average speed at which Sphenathi and the other matriculants must travel to reach Uptington by 09:45, we need to calculate the time available for the journey and the distance between the two locations.

The time available is from 07:25 to 09:45, which is a total of 2 hours and 20 minutes. We need to convert this time to hours by dividing by 60:

2 hours + 20 minutes / 60 = 2.33 hours

Now, let's calculate the distance between Bloemfontein and Uptington. Suppose the distance is 'd' kilometers.

We can use the formula for average speed: average speed = distance / time

In this case, the average speed should be such that the distance divided by the time is equal to the average speed.

d / 2.33 = average speed

Now, let's assume that Sphenathi and the other matriculants must travel a distance of 250 kilometers to reach Uptington. We'll substitute this value into the equation:

250 / 2.33 = average speed

To find the average speed to the nearest km/h, we'll calculate the result:

average speed ≈ 107.3 km/h

Therefore, Sphenathi and the other matriculants must travel at an average speed of approximately 107 km/h to reach Uptington by 09:45.

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The equation 3x - y = - 1; - 3x - y = 5 when solved using the elimination method is x = -1 and y = -2 respectively.

3x - y = - 1

- 3x - y = 5

Subtract the equation to eliminate y

3x - (-3x) = - 1 - 5

3x + 3x = - 6

6x = - 6

divide both sides by 6

x = -6 / 6

x = -1

Substitute x = -1 into

3x - y = - 1

3(-1) - y = -1

-3 - y = - 1

- y = - 1 + 3

-y = 2

y = -2

Therefore, the solution to the simultaneous equation is (x, y) = (-1, -2)

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given that m is parallel to n,

the angle opposite (2x + 16)° is also (2x + 16)° as vertically opposite angles are equal.

using the corresponding angle rule we know that:

2x + 16 = 96

2x = 80

so x = 40

Answer:

It has been a while. I think it is ASA and AAS

The triangles ΔLMN and ΔOPQ are congruent triangles by the ASA and AAS postulates

Transformations change the size or position of shapes. Congruent shapes are identical, but may be reflected, rotated or translated. Scale factors can increase or decrease the size of a shape. Congruent Triangles simply mean the triangles that possess the same size and shape

The three sides are equal (SSS: side, side, side)

Two angles are the same and a corresponding side is the same (ASA: angle, side, angle)

Two sides are equal and the angle between the two sides is equal (SAS: side, angle, side)

A right angle, the hypotenuse and a corresponding side are equal (RHS, right angle, hypotenuse, side)

Given data ,

Let the first triangle be represented as ΔLMN

Let the second triangle be represented as ΔOPQ

Now , the measure of ∠MNL = 90°

The measure of ∠PQO = 90°

And , the measure of side MN = measure of side PQ

And , the measure of ∠MLN = measure of ∠POQ

So , the two angles are the same and a corresponding side is the same (ASA: angle, side, angle)

Therefore , the triangles are congruent by AAS and ASA theorems

Hence , the ΔLMN and ΔOPQ are congruent triangles

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Answer: B) (-6,-8)

Step-by-step explanation:

In order to find which is correct, you must substitute the x-values of each into the equation to see which comes out with a matching y-value.

Plugging -6 into the equation we get

\(y=(-6)^2+5(-6)-14\)

\(y=36-30-14\)

\(y=-8\)

thus, the correct solution is \((-6,-8)\)

The point which represents a solution to the given equation is : (-6, -8)

We can find the solution to this by plugging in the x & y values given in the question:

a. (-8, -14)

\(y = x^{2} + 5x - 14\\14 = (-8)^{2} + (-8)*5 -14\\14 = 10,\)

which is not valid.

b. (-6, -8)

\(y = x^{2} + 5x - 14\\-8 = (-6)^{2} + (-6)*5 -14\\-8 = -8,\)

which is true.

c. (1,5)

\(y = x^{2} + 5x - 14\\5 = (1)^{2} + (1)*5 -14\\5 = -4,\)

which is not valid.

d. (5, -14)

\(y = x^{2} + 5x - 14\\-14 = (5)^{2} + (5)*5 -14\\14 = 36,\)

which is not valid

Therefore, the point representing a solution to the given equation is     (-6, -8) since it satisfies the equation when substituting the values of x and y.

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Answer:

y = -x + 8

Step-by-step explanation:

m = -1  ; x1 = 3 ; y1 = 5

Slope point form: y - y1 = m(x -x1)

y - 5 = -1(x - 3)

y -  5 = -1x - 3 *(-1)

y - 5 =-x + 3

    y =  -x + 3 + 5

     y = -x + 8

Answer:

9

Step-by-step explanation:

As we can see, this is the equation of line `g(x)` that passes through the points `(-4,0)` and `(-3,-2)`. Therefore, the value of `k` is `2`.

The correct answer to the given question is option d.

We have the function `g(x) = k⋅f(x)`. The values of `f(x)` and `g(x)` are given as follows:

Line `f(x)` passes through points `(-4,0)` and `(-3,1)`.

Line `g(x)` passes through points `(-4,0)` and `(-3,-2)`.

Now, we have to determine the value of `k`.

Formula to find slope of a line is given by:(y2 - y1)/(x2 - x1)

Here, (x1, y1) = (-4, 0) and (x2, y2) = (-3, 1) for line f(x).

So, slope of line `f(x)` is given by:(1 - 0)/(-3 - (-4)) = 1

So, equation of line `f(x)` is given by:

y - y1 = m(x - x1) ⇒ y - 0 = 1(x - (-4)) ⇒ y = x + 4

Also, (x1, y1) = (-4, 0) and (x2, y2) = (-3, -2) for line g(x).

So, slope of line `g(x)` is given by:(-2 - 0)/(-3 - (-4)) = 2

So, equation of line `g(x)` is given by: y - y1 = m(x - x1) ⇒ y - 0 = 2(x - (-4)) ⇒ y = 2x + 8

Now, we can substitute the value of `k` and the equation of line `f(x)` to find the equation of line `g(x)`.

Let `k = 2`.

Then, `g(x) = k⋅f(x) = 2(x + 4) = 2x + 8`.

As we can see, this is the equation of line `g(x)` that passes through the points `(-4,0)` and `(-3,-2)`.

Therefore, the value of `k` is `2`. Hence, option (d) is the correct answer: `2`.

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Answer:

5

Step-by-step explanation:

The answer is 5 Have fun

Answer:

3

Step-by-step explanation:

All we need to do here is plug in the number 4 for the variable x. Wherever there's an x, kidnap it and replace it with a 4!

\(\frac{x + 20}{x + 4}\)

x = 4

\(\frac{4 + 20}{4 + 4}\)

Do the addition.

4 + 20 = 24

4 + 4 = 8

\(\frac{24}{8}\)

We can simplify this! What is 24 divided by 8?

24/8 = 3

The answer is 3!

Answer:

The center is ( -2, 7) and the radius is 6

Step-by-step explanation:

A circle is written in the form

(x-h)^2 + (y-k)^2 = r^2  where (h,k) is the center and r is the radius

(x+2)^2+(y-7)^2=36

(x -  -2)^2+(y-7)^2=6^2

The center is ( -2, 7) and the radius is 6

Answer:

The probability of getting a 2, 4, or 6 when a dice is rolled is 1/2, or 50%. This is because there are six possible outcomes when a dice is rolled, and three of them are favorable outcomes (2, 4, or 6). Therefore, the probability of getting a 2, 4, or 6 is 3/6, which simplifies to 1/2 or 50%.

The number that belongs in the green box using sine rule is 13.96.

The rule of sine or the sine rule states that the ratio of the side length of a triangle to the sine of the opposite angle, which is the same for all three sides.

To calculate the number that belongs in the green box, we use the formula below

Formula:

From the diagram,

Given:

Substitute these values into equation 1

Solve for x

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Answer:

Equation: y = -2x

Solution: y = 12

Step-by-step explanation:

y varies directly as x, can be expressed by the equation, y = kx. Where, k = constant of proportionality.

Given that when x = 2, y = -4, to find the value of k, plug in the values of x and y into y = kx.

Thus:

-4 = k(2)

Divide both sides by 2

-4/2 = k

k = -2

To write the equation for the information given, substitute k = -2 into y = kx.

✔️Equation: y = -2x

✔️When x = -6,

y = -2x

Plug in the value of x

y = -2(-6)

y = 12