When reporting the answer to a mathematical calculation involving addition or subtraction, how does one determine the number of significant digits to report in the answer?.

An ice cream shop has 10 flavors and one can choose 4 different flavors. The question asks for the total number of possible flavor combinations.Therefore, we need to find the number of ways in which 4 flavors can be chosen from 10 flavors.

In such cases where order does not matter and repetitions are not allowed, we can use the formula for combinations which is as follows:C(n, r) = n! / (r! (n - r)!)Where n is the total number of items, r is the number of items being chosen at a time and ! represents the factorial function.

Using this formula we can find the total number of possible flavor combinations. Substituting the values in the above formula, we get:C(10, 4) = 10! / (4! (10 - 4)!)C(10, 4) = (10 * 9 * 8 * 7) / (4 * 3 * 2 * 1)C(10, 4) = 210Hence, there are 210 possible flavor combinations when one can choose 4 different flavors

.Explanation:The formula to be used for this type of question is combination. Combination is the method of selecting objects from a set, typically without replacement (without putting the same item back into the set) and where order does not matter. The formula for combination is given by C(n,r)=n!/(r!(n-r)!).

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Answer:

e

Step-by-step explanation:

In selecting 10 students out of the class of 40 students, if 40 names are placed in a hat and 10 names are drawn out of the hat, the type of sample is:

a random sampling.

Random sampling is a type of sampling method where each member of the population has an equal chance of being selected.

In this case, the population is the class of 40 students and the sample size is 10. By randomly selecting 10 names out of a hat, each student has an equal chance of being chosen for the sample.

This ensures that the sample is representative of the entire population, without any bias.

Random sampling is a widely used method for selecting a representative sample from a larger population.

It is important to use random sampling when conducting research or surveys in order to ensure that the results are reliable and accurate.

Random sampling helps to eliminate any potential bias that might be present in the sample if it was chosen through some other method. This is why it is important to use random sampling when selecting a sample from a larger population.

Complete Question:

"To select 10 students out of the class of 40 students, 40 names are placed in a hat and 10 names are drawn out of the hat. what type of sample is this?"

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Answer:

cv 454546

Step-by-step explanation:

ZCCVZv dD

The probability of an event happening in half an hour cannot be determined simply by multiplying or dividing the probability of the event happening in an hour by a factor of 2.

Probabilities are not linear in that way. The probability of an event happening in half an hour would depend on the specific details of the event and the underlying probability distribution.

The probability of an event happening in half an hour, given an 84% chance of it happening in an hour, cannot be determined without additional information. The probability of an event occurring in half an hour would depend on the specific circumstances of the event and how the 84% probability was determined.

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if there is an 84% chance of an event happening in an hour, then the probability that it happens in half an hour will be 84% = 0.84.

One cannot easily calculate the likelihood of an event occurring in half an hour by multiplying or dividing the chance of the event occurring in an hour by a factor of 2.

In that sense, probabilities are not linear. The likelihood of an event occurring in half an hour is determined by the event's specifics and the underlying probability distribution.

Without further information, the likelihood of an event occurring in half an hour given an 84% chance of occurring in an hour cannot be computed. The likelihood of an event occurring in half an hour is influenced on the event's unique circumstances and how the 84% probability was calculated.

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Answer:

S=540

140+33+x+75+x+2x=540

173+x+75+x+2x=540

x+75+x+2x=367

x+x+2x=292

4x=292

x=73

2x=146

Answer:

432

Step-by-step explanation:

-12(-36) = 432

Answer: m = 3.89

Step-by-step explanation:

(3m/5)+(m/2) =(4/1)+(2/5)

= (taking LCM) (6m+5m)/10 = (20+1)/5

or, 11m/10 = 21/5

or, 55m = 210

or, m = 210/55

so, m = 3.89

The Cartesian equation of the curve is y = -4x + 9 for -1 ≤ x ≤ 4.

To eliminate the parameter t, we can isolate t in the equation x = t^2 - 2 and substitute it into the equation for y. This gives us:

y = t + 1

t = x + 2

y = x + 3

So the Cartesian equation of the curve is y = x + 3 for -2 ≤ y ≤ 4.

We can eliminate t by taking the natural logarithm of both x and y. This gives us:

ln x = t - 8

ln y = 2t

Solving for t in the first equation and substituting it into the second equation, we get:

t = ln(x) + 8

y = e^(2ln(x)+16) = x^2e^16

So the Cartesian equation of the curve is y = x^2e^16.

To eliminate t, we can again isolate it in the equation for x and substitute it into the equation for y. This gives us:

x = t + 1

t = x - 1

y = 5 - 4(x - 1) = -4x + 9

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The Cartesian equation of the curve is y = 1 - 4x, for -1 ≤ x ≤ 4.

To eliminate the parameter t, we can solve for t in terms of x and substitute it into the equation for y:

t = ±√(x + 2)

y = t + 1 = ±√(x + 2) + 1

Squaring both sides and simplifying, we get:

(x + 2) = (y - 1)²

So the Cartesian equation of the curve is:

x = (y - 1)² - 2, for -2 ≤ y ≤ 4.

To eliminate the parameter t, we can take the natural logarithm of both sides of the equation for y:

ln y = 2 ln e + t ln e = 2 ln e + ln x

ln y = ln (xe²)

y = xe²

So the Cartesian equation of the curve is:

y = x^2e^2.

To eliminate the parameter t, we can solve for t in terms of x and substitute it into the equation for y:

t = 1 + x

y = 5 - 4t = 1 - 4x

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160 students are identified to have measles in all at the end of the 6th day of the outbreak.

On the first day of a measles outbreak at a school, 5 students were identified to have the measles. Each day for the following two weeks, the number of new cases doubled from those identified with the disease the day prior. Here is the calculation below:

Number of cases of measles on the first day of outbreak = 5

Total number of cases of measles on day 2 = 5 x 2 = 10

Total number of cases of measles on day 3 = 10 x 2 = 20.

Total number of cases of measles on day 4 = 20 x 2 = 40

Total number of cases of measles on day 5 = 40 x 2 = 80

Total number of cases of measles on day 6 = 80 x 2 = 160

Therefore, 160 students are identified to have measles in all at the end of the 6th day of the outbreak.

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Answer:

It's the second one.

Step-by-step explanation:

Answer:

If it is 1, the number is 141
If it is 2, the number is 582.

Step-by-step explanation:

For the second digit to be 4 times the third digit, the third digit, the third digit must be 1 or 2.

Answer:

an = 1.2 + (n - 1) 1.5

Step-by-step explanation: opt A on edg

Answer:

30 x^4 - 20 x^3 + 15 x^2 is the only valid one however it's not the best simplification.

Step-by-step explanation:

Simplify the following:

-5 x^2 (-6 x^2 + 4 x - 3)

Hint:  Factor a minus sign out of -6 x^2 + 4 x - 3.

Factor -1 out of -6 x^2 + 4 x - 3:

-5 x^2×(-(6 x^2 - 4 x + 3))

Hint: Multiply -5 and -1 together.

-5 (-1) = 5:

Answer: 5 x^2 (6 x^2 - 4 x + 3)

Answer:

30 x^4 - 20 x^3 + 15 x^2

Step-by-step explanation:

Given:

Total number of marbles = 26

Number of blue marbles = 13

Number of red marbles = 10

Number of yellow marbles = 3

To find:

The probability of getting a blue marble then a red marble (without replacement).

Solution:

Total number of marbles = 26

Number of blue marbles = 13

Probability of getting a blue marble is first draw is:

\(P(Blue)=\dfrac{\text{Number of blue marbles}}{\text{Total number of marbles}}\)

\(P(Blue)=\dfrac{13}{26}\)

\(P(Blue)=\dfrac{1}{2}\)

After drawing 1 marble, the remaining number of marbles in the bag is 25.

Probability of getting a red marble is second draw is:

\(P(Red)=\dfrac{\text{Number of red marbles}}{\text{Remaining number of marbles}}\)

\(P(Red)=\dfrac{10}{25}\)

\(P(Red)=\dfrac{2}{5}\)

Now the probability of getting a blue marble then a red marble (without replacement) is:

\(P(\text{Blue then red})=P(Blue)\times P(Red)\)

\(P(\text{Blue then red})=\dfrac{1}{2}\times \dfrac{2}{5}\)

\(P(\text{Blue then red})=\dfrac{1}{5}\)

Therefore, the probability of getting a blue marble then a red marble (without replacement) is \(\dfrac{1}{5}\).

The matrices [ 1 0 0] [0 1 0] [0 0 1] and [ 1 -5 -4] [0 0 1] [ 1 -5 -9] are in row-echelon form.

A matrix is in row-echelon form if it satisfies the following conditions:

1. All rows consisting entirely of zeros are at the bottom.

2. In each nonzero row, the first nonzero element, called the leading coefficient, is to the right of the leading coefficient of the row above it.

3. Any rows consisting entirely of zeros are at the bottom.

In the given options, the matrices [ 1 0 0] [0 1 0] [0 0 1] satisfy all the conditions of row-echelon form. The first three matrices are diagonal matrices with leading coefficients equal to 1 and zeros in the appropriate positions.

The matrix [ 1 -5 -4] [0 0 1] [ 1 -5 -9] also satisfies the conditions of row-echelon form. It has leading coefficients of 1 in each row, and the leading coefficient of the second row is to the right of the leading coefficient of the first row.

The other matrices in the given options do not meet the conditions of row-echelon form. They either have nonzero elements above the leading coefficient or rows consisting entirely of zeros in the middle or top rows.

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By examining the dotplot, you can see the frequency and distribution of the miles run by Roger. For example, there are 4 instances where Roger ran 0.5 miles, 3 instances where he ran 4 miles, and so on.

The dotplot that displays the data correctly is the one titled "Roger's Training" with a number line labeled "Miles Run" that goes from 0.5 to 5 in increments of 0.5. The dotplot should have the following data points:
0.5, 4
1, 1
1.5, 2
2, 2
2.5, 3
3, 2
3.5, 0
4, 3
4.5, 2
5, 1
This dotplot accurately represents the number of miles Roger ran each day over a 20-day period. Each dot represents a data point from the given list of miles run. The number line indicates the range of miles run, starting from 0.5 and ending at 5, with increments of 0.5.
By examining the dotplot, you can see the frequency and distribution of the miles run by Roger. For example, there are 4 instances where Roger ran 0.5 miles, 3 instances where he ran 4 miles, and so on. This visual representation allows you to easily interpret the data and observe any patterns or trends in Roger's training.

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The left right hand derivative is 3.

The left hand derivative is 2.

The function is not differentiable at x = 1.

When x < 1,

given that the function is, f(x) = 2x² - 2x - 1

Differentiating with respect to 'x' we get, f'(x) = 4x - 2

When x \(\geq\) 1,

given the function is, f(x) = 3x - 3

Differentiating with respect to 'x', f'(x) = 3

Now, left hand derivative,

f'(1 -) = (4x - 2) at 1 = 4*1 - 2 = 4 - 2 = 2

f'(1+) = 3

Since, left hand derivative and right hand derivative for given function at x =  1 is not equal, so the function is not differentiable at x = 1.

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Answer:

12.56

Step-by-step explanation:

find the circumference of the circle : 2πr

C=2(12)(3.14)

C=75.36

the length of the arc is: arc length will be (60/360) one 1/6 of the total circumference.

(60/360)(75.36)= 12.56

Answer:

C

Step-by-step explanation:

-18x+2y>=-13

2y>= -13+18x

y>= -6.5+9x

Answer:

Rate of plane 735 km/hr

Rate of wind 65 km/hr

Step-by-step explanation:

Calculation to determine the rate of the plane in still air

Let Va represent the velocity of the airplane

Let Vw represent the velocity of the wind

When flying with the wind:

(Va+Vw)*(6 hours) = 4800

6Va + 6Vw = 4800

6Vw = 4800 - 6Va

Vw=4800/6-Va

Vw = 800 - Va

When flying against the wind:

(Va-Vw)*(6 hours) = 4020 km

6Va - 6Vw = 4020

Substitute 800-Va for Vw and solve for Va:

6Va - 6(800-Va) = 4020

6Va -4800 + 6Va = 4020

12Va = 8820

Va=8820/12

Va = 735 km/hr

Therefore the rate of the plane in still air is 735 km/hr

Calculation to determine the rate of the wind

Rate of wind:

Vw = 800 - Va

Vw= 800 -735

Vw= 65 km/hr

Therefore the rate of the wind is 65 km/hr

The value of the expression ( 1/2 )x + ( 1/2 )x + x + 1 is 2x + 1.

A variable, a number, or a mix of numbers, operations, and numbers symbols make up an expression. Two expressions joined by an equal sign form an equation.

A formula called an equation uses the equals symbol (=) to denote the equality of two expressions.

Consider the expression,

1/2x + 1/2x + x + 1

Taking common out,

( 1/2 )x + ( 1/2 )x + x + 1 = ( 1/2) × [ x + x ] + x + 1

( 1/2 )x + ( 1/2 )x + x + 1 = (1/2x) × 2 + x + 1

( 1/2 )x + ( 1/2 )x + x + 1 = x + x + 1

( 1/2 )x + ( 1/2 )x + x + 1 = 2x + 1

Therefore, the value of ( 1/2 )x + ( 1/2 )x + x + 1 is 2x + 1.

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Answer:

255

Step-by-step explanation:

1275/ 5 = 255 people per room

Answer:

If those are the dimensions the surface area is 6 meters

Step-by-step explanation:

cubes have six sides and each side is one unit

Graph option B is the correct answer.

Graphical representation refers to the use of charts and graphs to visually display, analyse, clarify, and interpret numerical data, functions, and other qualitative structures.

Given are function,

y = x+1 ≤0 and y = 3x

The best demonstration of these functions can be seen in graph 2.

Hence, Graph option B is the correct answer.

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There are 8,640 ways the five people can be seated in the eight empty seats.

To determine the number of ways the five people can be seated in eight empty seats, we can use the concept of permutations.

Since the order in which the people are seated matters, we need to calculate the number of permutations of five people taken from eight seats.

The formula for permutations is given by:

P(n, r) = n! / (n - r)!

where n represents the total number of items and r represents the number of items taken at a time.

In this case, we have 8 empty seats (n) and want to seat 5 people (r). Therefore, we can calculate the number of ways as:

P(8, 5) = 8! / (8 - 5)!

= 8! / 3!

= (8 * 7 * 6 * 5 * 4 * 3!) / 3!

= 8 * 7 * 6 * 5 * 4

= 8,640

Hence, there are 8,640 ways the five people can be seated in the eight empty seats.

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