A random experiment has three steps with three outcomes possible for the first step, two outcomes possible for the second step, and four outcomes possible for the third step. how many experimental outcomes exist for the entire experiment?

Answer:

Part A) The cone couldn't contain all the ice cream if it melted.

Part B) The height of the cone would be [tex]8\ cm[/tex]

Part C) The height of the cylinder would be [tex]3\ cm[/tex]

Step-by-step explanation:

Part A) Determine whether the cone could contain all of the ice cream if it melted

step 1

Find the volume of the ice cream (sphere)

The volume is equal to

[tex]V=\frac{4}{3}\pi r^{3}[/tex]

we have

[tex]r=4/2=2\ cm[/tex] -----> the radius is half the diameter

substitute

[tex]V=\frac{4}{3}\pi (2)^{3}=\frac{32}{3}\pi\ cm^{3}[/tex]

step 2

Find the volume of the cone

The volume is equal to

[tex]V=\frac{1}{3}\pi r^{2}h[/tex]

we have

[tex]r=4/2=2\ cm[/tex] -----> the radius is half the diameter

[tex]h=7.5\ cm[/tex]

substitute

[tex]V=\frac{1}{3}\pi (2)^{2}(7.5)=\frac{30}{3}\pi\ cm^{3}[/tex]

step 3

Compare the volume of the sphere and the volume of the cone

[tex]\frac{30}{3}\pi\ cm^{3} < \frac{32}{3}\pi\ cm^{3}[/tex]

The volume of the cone is less than the volume of the sphere

therefore

The cone couldn't contain all the ice cream if it melted.

Part B) What would be the smallest cone in height in whole centimeters that would allow the cone to contain all of the melted ice cream if the diameter of the cone remains unchanged

The volume of the cone is equal to

[tex]V=\frac{1}{3}\pi r^{2}h[/tex]

we have

[tex]V=\frac{32}{3}\pi\ cm^{3}[/tex]

[tex]r=2\ cm[/tex]

substitute in the formula and solve for h

[tex]\frac{32}{3}\pi=\frac{1}{3}\pi (2)^{2}h[/tex]

simplify

[tex]32=(2)^{2}h[/tex]

[tex]32=4h[/tex]

[tex]h=32/4=8\ cm[/tex]

Part C) If the container of the ice cream changed to a cylinder as shown in the diagram below, what would be the smallest height of the cylinder needed to the nearest whole centimeter to contain the melted ice cream

The volume of the cylinder is equal to

[tex]V=\pi r^{2}h[/tex]

we have

[tex]V=\frac{32}{3}\pi\ cm^{3}[/tex]

[tex]r=2\ cm[/tex]

substitute in the formula and solve for h

[tex]\frac{32}{3}\pi=\pi (2)^{2}h[/tex]

simplify

[tex]\frac{32}{3}=(2)^{2}h[/tex]

[tex]\frac{32}{3}=4h[/tex]

[tex]h=\frac{32}{12}=2.67\ cm[/tex]

Round to the nearest whole centimeter

[tex]2.67=3\ cm[/tex]

The similarity is ΔRST ~ Δ UVW and Scale Factor is 5/6.

If two triangles have an equal number of corresponding sides and an equal number of corresponding angles, then they are comparable. Similar figures are described as items with the same shape but varying sizes, such as two or more figures.

Given:

From the Two Triangles we can see that

<VUW = <SRT = 32

and,   SR / VU =  TR / WU

10/ 12 = 15/ 16

5/6 = 5/6

So, By SAS similarity Criteria both Triangles are Similar.

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a. 3u + 2v

To solve this problem, we need to apply some properties of logarithms. Properties are useful to simplify complicated expressions. Here we need to use a very useful property of logarithms called  the logarithm of a product is the sum of the logarithms, that is:

[tex]log_{b}(MN)=log_{b}(M)+log_{b}(N)[/tex]

From the function, it is then true that:

[tex]ln(x^{3}y^{2})=ln(x^{3})+ln(y^{2})[/tex]

The other property we must use is Logarithm of a Power:

[tex]log_{b}M^{n}=nlog_{b}M[/tex]

Then:

[tex]ln(x^{3}y^{2})=ln(x^{3})+ln(y^{2}) \\ \\ ln(x^{3}y^{2})=3ln(x)+2ln(y)[/tex]

Since:

[tex]u=ln(x) \\ v=ln(y)[/tex]

Then:

[tex]ln(x^{3}y^{2})=3u+2v[/tex]

Finally, the correct option is:

a. 3u + 2v

Answer:

A edge

Step-by-step explanation:

Answer:

(x,y) = (0,-8)

Step-by-step explanation:

We know that a point in polar coordinates is represented by

(r, θ)

Where r is the distance from the origin and θ is the angle.

Rectangular coordinates can be found by

x = r*cos(θ)

y = r*sin (θ)

x = r*cos(θ) = 8* cos (3π/2)

y = r*sin (θ) = 8 sin(3π/2)

x = 8* cos (3π/2) = 8*0 = 0

y = 8* sin (3π/2) = 8*(-1) = -8

(x,y) = (0,-8)

Correct option is (A) (0,-8)

Now any point in polar coordinates is represented by

(r, θ)

where 'r' is the distance from the origin

and 'α' is the angle.

Rectangular coordinates can be found by using the formula:

[tex]x=r*cos(\alpha )\\y=r*sin(\alpha )[/tex]

Thus the x coordinate would be given as :

[tex]x=r*cos(\alpha )\\x=8*cos(\frac{3\pi }{2} )\\x=8*0\\x=0\\[/tex]

Similarly the y coordinate would be given as :

[tex]y=r*sin(\alpha )\\y=8*sin(\frac{3\pi }{2} )\\y=8*(-1)\\y=-8\\[/tex]

Thus (x, y) = (0,-8) is the required coordinates

Answer:

Step-by-step explanation:

d.3+6+9+12+15+18  sum 6 terms multiple of 3

Final answer:

To find the percent of decrease, calculate the difference between the original and final numbers, divide by the original number, and multiply by 100. In this case, the percent of decrease is 25%.

Explanation:

To find the percent of decrease from the original number to the final number, we need to calculate the difference between the original number and the final number, then divide that difference by the original number and multiply by 100 to get the percentage.

Let's assume the original number is x. When the number is increased by 50%, it becomes 1.5x. When the result is decreased by 50%, it becomes 0.5 times 1.5x, which is 0.75x.

The decrease from the original number to the final number is x - 0.75x = 0.25x. To find the percent of decrease, we divide the decrease by the original number (0.25x / x) and multiply by 100 to get 25%. Therefore, the percent of decrease from the original number to the final number is 25%.

Final answer:

The overall percent change from the original number to the final number, after increasing by 50% and then decreasing by 50%, is a 25% decrease.

Explanation:

To find the percentage decrease from the original number to the final one after the series of increases and decreases described, we need to follow a couple of steps:

First, we increase the original number by 50%. If the original number is x, its increased value is x + 0.5x = 1.5x.

Next, we decrease this new number by 50%. The decreased value is 1.5x - (0.5 × 1.5x) = 1.5x - 0.75x = 0.75x.

To find the percentage change from the original value, we calculate (final value - initial value) / initial value × 100%. Using the value obtained from the second step, this becomes (0.75x - x) / x × 100% = -0.25x/x × 100% = -25%.

Therefore, the overall percent change is a 25% decrease from the original number.

A Histogram would be better for displaying the data

A histogram would be better for displaying the data of elephant calves' weight gains after the switch to a new formula for daily feedings.

A histogram would be better for displaying the data of elephant calves' weight gains after the switch to a new formula for daily feedings. A histogram is useful for displaying the distribution and frequency of a continuous dataset, such as the weight gains of elephant calves. It can show how many calves fall within each weight range, and provide a visual representation of the desired range of weight gain.

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Answer:

john

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

We know:

1. Replacing -x into x of an equations reflects the graph on the y-axis

2. If f(x) is a function, then f(x)+a is a vertically translated graph of the original graph, a units up

Looking at the original function of ln x and the transformed graph of ln(-x) +5, we see that we have replaced x with -x, which means it is a reflection across the y-axis.

Also, we have added a five after the function, so that means it is a vertical translation of 5 units up.

Looking at the answer choices, we see that B is the correct answer.

170.28 is the answer

Answer:

170.28

Step-by-step explanation:

Got it right on the test.

Answer:

If Q=2.1(R)+5, then it would be 2.1(5)+5=15.5 ?

Step-by-step explanation:

Answer:

it took a total of 260 minutes or 4 hours and 20 minutes from Collin's house to his hotel.

Step-by-step explanation:

As each of the activities described is an independent activity that does not overlap, we can easily sum up the durations of each to find the total time Collin took from his house to the hotel.

We add it as follows :

he drove to the airport for 45 minutes + he waited at the airport for the flight to depart for 90 minutes + his fight duration was 70 minutes + upon landing, he gathered his luggage for 20 minutes + he drove to the hotel for 35 minutes.

So, 45+90+70+20+35 = 260 minutes

Answer:

The numbers can be added in any order.

Step-by-step explanation:

Just got this quiz question right.

Hope this helps :)

Answer:

Step-by-step explanation:

MX = XN

5r² + 2r + 52 = 4r² + 12r + 27

5r² - 4r² + 2r - 12r + 52 - 27 = 0

r² - 10r + 25 = 0

(r - 5)² = 0

r - 5 = 0

r = 5

4r² + 12r + 27

4•5² + 12•5 + 27

4•25 + 60 + 27

100 + 60 + 27

187

The Second one

I hope I helped you.

Answer:

50% chance

Step-by-step explanation:

You would have a 50% chance of landing on a even number

Answer:

Step-by-step explanation:

Let L and W represent the length and width of the field. Then the perimeter is given by ...

  P = 2(L +W)

Filling in the given information, we have ...

  320 = 2(L +W)

  L = W +48 . . . . . . the length is 48 ft longer than the width

Using the second equation in the first, we get

  320 = 2((W +48) +W)

  320 = 4W +96 . . . . . . simplify

  224 = 4W . . . . . . . . . . subtract 96

  56 = W . . . . . . . . . . . . .divide by 4

  L = 56 +48 = 104 . . . . find L using the above relation

The width of the field is 56 ft; the length is 104 ft.

The width of the playing field is 56 ft and the length is 104 ft.

To solve this problem, let's set up an equation using the information given. Let's say the width of the field is x ft. Since the length is 48 ft longer than the width, the length can be represented as x + 48 ft. The formula for the perimeter of a rectangle is P = 2(l + w), so we can set up the equation: 320 = 2(x + 48 + x). Now, we can solve for x by simplifying and solving the equation.

320 = 2(2x + 48)

320 = 4x + 96

4x = 320 - 96

4x = 224

x = 224/4

x = 56

So, the width of the field is 56 ft and the length is 56 + 48 = 104 ft.

To solve this problem, we must use the formula for the perimeter of a rectangle, which is P = 2L + 2W, where P is the perimeter, L is the length, and W is the width.

According to the question, the length is 48 ft longer than the width, therefore we could express the length as L = W + 48. The perimeter provided is 320 ft. Now we can plug these values into the perimeter formula.

320 = 2(W + 48) + 2W

After simplification, this formula becomes 320 = 4W + 96.

To isolate W, you subtract 96 from both sides to get: 320 - 96 = 4W + 96 - 96, which simplifies to 224 = 4W. Dividing both sides by 4 gives W = 56 ft. This is the width of the field. The length, then, is 56 ft + 48 ft = 104 ft (since the length is 48 ft longer than the width).

So, the dimensions of the field are 104 feet by 56 feet

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Answer:

If a fair coin is tossed three times, sample = 2^3 = 8 (hhh, hht, hth, thh, htt, tht, tth, ttt) where h=head and t=tail.

Probability of getting one:

Outcomes with one head (h) = 3

P(1 h) = 3/8 = 0.375

The probability of getting exactly one tail when a fair coin is tossed three times in succession is 37.5%.

The probability of getting exactly one tail when a fair coin is tossed three times in succession can be found using the binomial probability formula.

Let's denote success as getting a tail and failure as getting ahead. The probability of success, denoted as p, is 0.5 since the coin is fair and has an equal chance of landing on heads or tails. The probability of failure, denoted as q, is also 0.5.

Using the binomial probability formula: P(X = k) = [tex]C(n, k) * p^k * q^(n-k)[/tex], we can calculate the probability as follows:

Therefore, the probability of getting exactly one tail when a fair coin is tossed three times in succession is 0.375 or 37.5%.

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Answer:

Exponential Function

Step-by-step explanation:

The y-axis represents the number of Bacteria and x-axis represents the number of hours. If you observe closely you will see that the number of bacteria are doubling after each hour. For example, at time = 4 hours the number of Bacteria were about 50, at time = 5 hours the number of Bacteria were about 100 and at time = 6 hours the number of Bacteria increased to about 200.

This type of behavior is a property of exponential functions where we see a multiplicative rate of change in the values i.e. each value is a multiple of previous value. A rough model for this function would be:

[tex]f(x)=f(0)(2)^{x}[/tex]

Where, f(0) represents the number of bacteria at time = 0 hours i.e. number of Bacteria initially present and "x" represents the number of hours.

For this question we need to use the Pythagorean Theorem (a2+b2=c2) since the rectangle is being divided into two triangles.

we know the length of the triangle (63) and we know the hypotenuse (65) but not the width. To find the width, we can plug the values we know into our formula.

(63) squared + b squared = (65) squared

solve.

3969 + b squared = 4225

subtract 3969 from both sides.

b squared = 256

√b² = √256

b=16

Answer: 275%

Step-by-step explanation:

Given : The current weight of the puppy : 2,250 grams

The weight of the puppy at the last visit = 600 grams

Increase in weight :-

[tex]2250\text{ grams}-600\text{ grams}=1650\text{ grams}[/tex]

Now, the formula to calculate the percentage increase is given by :-

[tex]\dfrac{\text{Increase in quantity}}{\text{Previous quantity}}\times100[/tex]

The percentage increase in weight is given by :-

[tex]\dfrac{1650}{600}\times100=275\%[/tex]

Hence, the percent increase in the puppy's weight  = 275 %.

Answer:

Step-by-step explanation:

The function is a special relationship where each input has a single output.

We have C = {(9, 1); (8, -3); (7, 5); (-5, 3)}.

It's a function:

each values of x: 9, 8, 7, -5 has one value of y: 1, -3, 5, 3.

The doimain is set os x: {9, 8, 7, -5}.

The range is set of y: { 1, -3, 5, 3}.

F = {(x, y ) | x + y = 10}.

Domain: {10} Range: {10}

Answer:

Step-by-step explanation:

12 is the common denominator

The answer will be 6!!

Answer:

C

Step-by-step explanation:

We can use 2 properties of logarithms to write this:

1. ln(x*y) = lnx + ln y

2. ln(a^b) = b ln a

Using property 1, we can write as:

[tex]ln(\sqrt{x} *y^{2})\\=ln(\sqrt{x} )+ln(y^2)\\=ln(x^{\frac{1}{2}})+2lny\\=\frac{1}{2}lnx+2lny[/tex]

We know u = lnx and v = ln y, we simply substitute it now:

[tex]\frac{1}{2}lnx+2lny\\=\frac{1}{2}u+2v[/tex]

the correct answer is C

Answer:

c

Step-by-step explanation:

Answer:

see explanation

Step-by-step explanation:

Divide through by 2

2a² - 5a + 3 = 0

To factor the quadratic

Consider the factors of the product of the coefficient of the a² term and the constant term which sum to give the coefficient of the x- term

product = 2 × 3 = 6 and sum = - 5

The factors are - 2 and - 3

Use the factors to split the a- term

2a² - 2a - 3a + 3 = 0 ( factor the first/second and third/fourth terms )

2a(a - 1) - 3(a - 1) = 0 ← factor out (a - 1)

(a - 1)(2a - 3) = 0

Equate each factor to zero and solve for a

a - 1 = 0 ⇒ a = 1

2a - 3 = 0 ⇒ 2a = 3 ⇒ a = [tex]\frac{3}{2}[/tex]

Answer:

a = 3/2 or 1

Step-by-step explanation:

4a²-10a+6=0

(Divide by 2)

2a²-5a+3=0

(Now factorise)

(2a-3)(a-1)

a = 3/2 or 1

The expression is equivalent to (5x-6) (2x) + (5x-6) (3).

Option (A) is correct.

It is to find equivalent of (5x-6) (2x+3).

An expression of more than two algebraic terms, especially the sum of several terms that contain different powers of the same variable.

when we multiply to (5x-6) to (2x+3).

Each term of (5x-6) is multiply to (2x+3).

so (5x-6) is multiply to 2x and (5x-6)  is multiply to 3 separately.

so, the expression is equivalent to (5x-6) (2x) + (5x-6) (3).

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Answer:

  17 terms

Step-by-step explanation:

131072 = 2^17

8 = 2^3

4 = 2^2

2 = 2^1

Apparently, the sequence is powers of 2 from 17 down to 1, so there are 17 terms in the sequence.

Answer:

1176 Combinations

Step-by-step explanation:

As mentioned in the question, there are total 8 boys and 7 girls.

Our objective is to create a team with 5 boys and girls each.

To select 5 boys out of 8, we will use combination.

=> 8C5 = [tex]\frac{8!}{5!(8-5!)}[/tex]

=> [tex]\frac{8.7.6.5!}{5!.3!}[/tex]

=> [tex]\frac{8.7.6}{6}[/tex]

=> 56

Similarly,

5 girls are selected using 7C5

=> 21

Therefore, the total combination of players are 56 * 21 = 1176

Answer:

Lengths of AD and AB. They must be same for theorem SAS

Answer:

[tex]\overline{\rm AD} = \overline{\rm AB}[/tex]

Step-by-step explanation:

Two figures are congruent if they have the same shape and size, although their position or orientation are different. The congruence criteria correspond to the postulates and theorems that state what are the minimum conditions that two or more triangles must meet in order to be congruent. One of the congruence criteria is:

SAS (Side-Angle-Side): Two triangles are congruent if they have two sides and the angle determined by them respectively equal.

So, considering the previous information and the data provided by the problem. Then, the additional information necessary to show that triangle DAC is congruent to triangle BAC is:

[tex]\overline{\rm AD} = \overline{\rm AB}[/tex]

Answer:

Option b

Step-by-step explanation:

We have a compound interest problem. With an annual interest rate of 0.675 and an initial payment of 8500, with t = 25 years

Then you must use the annual compound interest formula, which is represented by a growing exponential function:

[tex]y = e ^{ht}[/tex]

Where:

h is the interest rate of 0.675

y is the money in the savings account as a function of time

Then substitute the values in the formula and we have:

[tex]y = e ^{0.675(25)}[/tex]

[tex]y = 45,950.57[/tex]