Write the equation of the graph shown below in factored form. the graph starts at the bottom left and continues up through the x axis at one to a maximum around y equals two and goes back down through the x axis at two to a minimum around y equals negative two and back up through the x axis at three

The correct statement is: the volume of the cylinder is 8 cubic inches more than that of the cone.

The volume of cone (V) = 1/3 * πr²h

Volume of cylinder (V) = πr²h

Where, r is the radius of their bases.

The base area formula for the cone = πr²

Calculate the area of the base of the cone that has a radius (r) of 2.5 in:

Area of the base of the cone = π(2.5)² ≈ 19.6

The volume of the cone (V) = 1/3 * πr²h = 1/3 * π * 2.5² * 6.5

≈ 42.5 cubic inches

Volume of cylinder (V) = πr²h = π * 2² * 4

≈ 50.3 cubic inches

The difference in volume = 50.3  - 42.5

= 7.8 ≈ 8 cubic inches

Therefore, the only statement that is true is: the volume of the cylinder is 8 cubic inches more than that of the cone.

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Answer: its 41 dude

Answer:

91.1 cubic inches to 1 dp

Step-by-step explanation:

4.5 X 4.5 X 4.5 = 91.125 cubic inches

or

4.5^3 = 91.125 cubic inches

Answer:

The least number of pens they could have is 24 pens.

Step-by-step explanation:

6: 6, 12, 18, 24, 30, 36, 42, 48

8: 8, 16, 24, 32, 40, 48

Answer:

24 is my answer

i hop it helps you

Answer:

228 cups were used

Step-by-step explanation:

16 cups = 1 gallon

16 (1 gallon) x 14 (as the question provides) = 224

Add the last 4 cups

= 228

228 cups were used

The value of x from the expression 3/4 x +3-2x = -1/4 +1/2x+5 can be simplified as 45/29.

The concept that will be used is simplification. To simplify simply means to make anything easier. In mathematics, simplifying an equation, fraction, or problem means taking it and making it simpler. Calculations and problem-solving techniques simplify the issue.

3/4x +3-2x = -1/4 +1/2x+5

We can simplify by collecting the like terms,

3/4x - 1/2x - 2x = -1/4 + 5 -3

Then we can simplify further as:

-29x/20 = - 9/4

29x = (20*9)/4

29x= 45

x= 45/29

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There is not enough evidence at the 0.02 level that the doors are either too long or too short. So, the null hypothesis is accepted.

Using the p-value approach for the hypothesis test, whether the null hypothesis is rejected or accepted.

It is given that,

Sample size n = 17

Sample mean X = 2069

Standard deviation σ = 24

Population mean  μ = 2058

Significance level α = 0.02

Hypothesis:

The null hypothesis: H0: μ = 2058

The alternative hypothesis: Ha: μ ≠ 2058

So, the z-test score for the given distribution is,

z-score = (X - μ)/(σ/√n)

On substituting,

z-score = (2069 - 2058)/(24/√17)

            = 11/5.82

            = 1.89

Thus, the p-value for the z-score of 1.89 is 0.0587 ≅ 0.06.

Since 0.06 > 0.02(significance level), the null hypothesis is accepted. So, there is no sufficient evidence that the doors are either too long or too short.

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The difference in the proportion of males and the proportion of females that smoke is 0.08

In a sample of 61 males, 15 smoke, while in a sample of 48 females, 8 smoke.

The given parameters are:

                             Male           Female

Sample                  61                  48

Smokers               15                   8

The proportion is calculated using:

p = Smoker/Sample

So, we have:

Male = 15/61 = 0.25

Female = 8/48 = 0.17

The difference is then calculated as:

Difference = 0.25 - 0.17

Evaluate

Difference = 0.08

Hence, the difference in the proportion of males and the proportion of females that smoke is 0.08

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The position function of the particle is s(t) = -15 sin(t) - 8 cos(t) + (9/π) t + 8

To find the position of the particle, we need to integrate its acceleration function twice with respect to time, and then apply the initial conditions to solve for the constants of integration.

First, we need to find the velocity function of the particle by integrating the acceleration function:

v(t) = ∫ a(t) dt = ∫ (15 sin(t) + 8 cos(t)) dt = -15 cos(t) + 8 sin(t) + C1

where C1 is the constant of integration.

Next, we need to find the position function of the particle by integrating the velocity function:

s(t) = ∫ v(t) dt = ∫ (-15 cos(t) + 8 sin(t) + C1) dt = -15 sin(t) - 8 cos(t) + C1t + C2

where C2 is the second constant of integration.

Now, we can apply the initial conditions to solve for the constants C1 and C2.

Using the initial condition s(0) = 0, we get:

0 = -15 sin(0) - 8 cos(0) + C1(0) + C2

0 = -8 + C2

C2 = 8

Using the second initial condition s(2π) = 18, we get:

18 = -15 sin(2π) - 8 cos(2π) + C1(2π) + 8

18 = -15(0) - 8(1) + C1(2π) + 8

18 = C1(2π)

C1 = 9/π

Therefore, the position function of the particle is:

s(t) = -15 sin(t) - 8 cos(t) + (9/π) t + 8

So, at any given time t, we can plug it into the position function to find the position of the particle.

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To find the position of the particle, we need to integrate the acceleration twice with respect to time. First, we integrate the acceleration a(t) to find the velocity v(t):

v(t) = ∫ a(t) dt = -15 cos(t) + 8 sin(t) + C1

where C1 is the constant of integration. We can determine C1 by using the initial condition s(0) = 0

where C2 is the constant of integration. We can determine C2 by using the second initial condition s(2pi) = 18:

s(2pi) = 15 sin(2pi) + 8 cos(2pi) + C2 = C2 + 8 = 18

So, C2 = 10 and the position function is:

s(t) = 15 sin(t) + 8 cos(t) + 10

Therefore, the position of the particle at time t is given by s(t) = 15 sin(t) + 8 cos(t) + 10.

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There are 20 cars traveling at constant speeds on a 1 mile long ring track and the cars can pass each other freely. On the track 25% of the cars are traveling at 20 mph, 50% of the cars are traveling 10 mph, and the remaining 25% of the cars are traveling at an unknown speed. It was known that the space mean speed of all the cars on the track is 20 mph.

Therefore, the total number of cars with speed 20 mph is 0.25 × 20 = 5, and the total number of cars with speed 10 mph is 0.5 × 20 = 10.

Then, 5 cars are left with an unknown speed.

Given that the space mean speed of all the cars on the track is 20 mph,Therefore,5 × v + 10 × 10 + 5 × 20 = 20 × 20= 5v + 200 = 400

Thus, the speed of the remaining 25% of cars is:v = 40 mph(b) If an observer standing on the side of the track counted the number and measured t

Summary If an observer standing on the side of the track counted the number of cars passing him in 1 minute, he would see 20 cars and take 3 minutes to count them all.

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The total surface area of a hemisphere is 27π.

The radius of the given hemisphere is 3 cm.

The total surface area of a hemisphere = 3πr² square units

Where π is a constant whose value is equal to 3.14 approximately. “r” is the radius of the hemisphere.

Here, surface area of a hemisphere = 3π×3²

= 27π

Therefore, the total surface area of a hemisphere is 27π.

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Answer:

(a) The probability that all 4 calls are for medical help can be calculated using the binomial probability formula:

P(X = k) = (n choose k) * p^k * (1 - p)^(n - k)

where:

n is the number of trials (in this case, 4)

k is the number of successes (in this case, 4)

p is the probability of success on a single trial (in this case, 0.81)

Plugging in the values, we get:

P(X = 4) = (4 choose 4) * 0.81^4 * (1 - 0.81)^(4 - 4)

P(X = 4) = 0.5314

Therefore, the probability that all 4 calls are for medical help is 0.5314, rounded to 4 decimal places.

(b) The probability that at least 1 of the calls is not for medical help can be calculated using the complement rule:

P(at least 1 call not for medical help) = 1 - P(all 4 calls for medical help)

We already calculated the probability of all 4 calls being for medical help in part (a), which is 0.5314. So, using the complement rule, we get:

P(at least 1 call not for medical help) = 1 - 0.5314

P(at least 1 call not for medical help) = 0.4686

Therefore, the probability that at least 1 of the calls is not for medical help is 0.4686, rounded to 4 decimal places.

(c) The calculation in part (a) may not be valid if we choose 4 consecutive calls to the station because the 4 consecutive calls being medical may not be independent events. For example, if a large accident or a natural disaster occurs in the area, there may be a higher probability of multiple consecutive medical calls due to the same incident or cause. In that case, the assumption of independence between the events would not hold, and the binomial probability formula would not be applicable.

Step-by-step explanation:

Answer:

Fg is 6 and I have to

Step-by-step explanation:

The school timings for the next course will be a number of activities for students to participate in related to UAE culture and

One of the solutions of the equation 2x + 3y = 3 is x = 0, y = 1.

To find the solutions of the equation 2x + 3y = 3, we can substitute different values of x and y into the equation and see if it is true. For example, if we substitute the values x = 0 and y = 1 for x and y, we get 20 + 31 = 3, which is true. Therefore, x = 0 and y = 1 is a solution of the equation.

There are infinitely many solutions to this equation, since any pair of values that satisfies the equation can be considered a solution. To find other solutions, we can use the method of solving by substitution. This involves expressing one of the variables in terms of the other, and substituting this expression into the equation.

For example, we could express y in terms of x by dividing both sides of the equation by 3, giving us 2x/3 + 3y/3 = 1. This simplifies to 2x + y = 1, which means that y = 1 - 2x. We can then substitute this expression for y into the original equation to solve for x.

Therefore, one of the solutions of the equation 2x + 3y = 3 is x = 0, y = 1.

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The correct phrase commonly used to word conditional probabilities is "given that." This phrase explicitly indicates the condition or event on which the probability calculation is based and emphasizes the dependence between events in the probability calculation.

Let's discuss each option in detail to understand why the correct phrase is "given that" when wording conditional probabilities.

"Dependent": The term "dependent" refers to the relationship between events, indicating that the occurrence of one event affects the probability of another event. While dependence is a characteristic of conditional probabilities, it is not the specific wording used to express the conditionality.

"Given that": This phrase explicitly states that the probability is being calculated based on a specific condition or event being true. It is commonly used to introduce the condition in conditional probabilities. For example, "What is the probability of event A given that event B has already occurred?" The phrase "given that" emphasizes that the probability of event A is being evaluated with the assumption that event B has already happened.

"Either/or": The phrase "either/or" generally refers to situations where only one of the two events can occur, but it does not convey the conditional nature of probabilities. It is often used to express mutually exclusive events, where the occurrence of one event excludes the possibility of the other. However, it does not provide the specific condition on which the probability calculation is based.

"Mutually exclusive": "Mutually exclusive" refers to events that cannot occur simultaneously. While mutually exclusive events are important in probability theory, they do not capture the conditionality aspect of conditional probabilities. The term implies that if one event happens, the other cannot occur, but it does not explicitly indicate the specific condition on which the probability calculation is based.

In summary, the correct phrase commonly used to word conditional probabilities is "given that." It effectively introduces the condition or event on which the probability calculation is based and highlights the dependency between events in the probability calculation.

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The statement (b) the sum is a binomial with a degree of 3 is correct.

Expressions are defined as the combination of constants and variables with mathematical operators.

We have expressions:

6s²t – 2st²

4s²t – 3st²

Adding the above two expressions, we get;

= (6s²t – 2st²) + (4s²t – 3st²)

Combining like terms:

= 10s²t - 5st²

The above expression has degree 3(2+1)

Thus, statement (b) the sum is a binomial with a degree of 3 is correct.

Complete question:

What is true about the sum of the two polynomials?

6s2t – 2st2

4s2t – 3st2

a.) The sum is a binomial with a degree of 2.

b.) The sum is a binomial with a degree of 3.

c.) The sum is a trinomial with a degree of 2.

d.) The sum is a trinomial with a degree of 3.

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Answer:

the answer is X = 0.75

Step-by-step explanation:

you just need to simplify everything in the brackets and calculate

(2x-3)(x+2)-(3-2x)(3x-2)=0

(2x²+4x-3x-6) - (9x-6-6x²+4x)=0

(2x²+4x-3x-6) + (6x²-4x-9x+6)=0

(2x²+x-6)+(6x²-13x+6)=0

8x²-12x=0

Answer:

PRACTICE.....ONCE THERE WAS A TIME WHEN I'D USED TO FAIL IN MATHS.....BUT NOW I ALWAYS GET 90+ IN MATHS!!!!!

Answer:

Step-by-step explanation:

2(x+y)=32  means :

x+y =16

Answer:

1/2 + 1/2 = 1

1/4 + 1/4 = 1/2

So you would walk 1/2 mile in 1 hour

Answer:

1/2

Step-by-step explanation:

1/4*2  multiply 1/4 by 2 because its you walk 1/4 in half a hour so times that by 2 for a full hour.

Adding a negative number is the same as subtracting a positive number.

14 + (-11) = 14 - 11

We start at the point 14 on a number line.

Since we are subtracting, we are going to left -11 units on the number line.

We will land on the point "3"

Best of Luck!

Answer:

180000

by multiplying 1.8 by 10^5 you have to move the decimal point 5 spots to the right since the power is a positive number. 1.8 turns into 180000

Answer: B

Step-by-step explanation:

\(\frac{2}{7k}(k-7)\)

\(\frac{2k-14}{7k}\)

\(\frac{2k}{7k}-\frac{14}{7k}\)

\(\frac{2}{7}-\frac{2}{k}\)

Answer:

62 ft²

Step-by-step explanation:

l = 3

w = 2

h = 5

now

2(wl+hl+hw)

2(2×3+5×3+5×2)

2×31

62 ft²

In this particular data set, 10 is the only value that occurs more than once, so it is the only mode

The mode is the value that occurs most frequently in a data set. In the given data set {10, 30, 10, 36, 26, 22}, we can see that the value 10 occurs twice, and all other values occur only once. Therefore, the mode of the data set is 10, since it occurs more frequently than any other value in the set.

Note that a data set can have multiple modes if two or more values occur with the same highest frequency. However, in this particular data set, 10 is the only value that occurs more than once, so it is the only mode.

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