Suppose we want to choose 5 colors, without replacement, from 13 distinct colors.00(a) How many ways can this be done, if the order of the choices does not matter?Х5E0(b) How many ways can this be done, if the order of the choices matters?0Submit AssignmentContinue

Answer:

the solution to the equation -2a - 6a - 9 = -9 - 6a - 2a is all real numbers, or (-∞, +∞).

Step-by-step explanation:

To solve this equation for "a", you need to simplify and rearrange the terms so that all the "a" terms are on one side of the equation and all the constant terms are on the other side. Here are the steps:

Start by combining the "a" terms on the left side of the equation: -2a - 6a = -8a. The equation now becomes: -8a - 9 = -9 - 6a - 2a.

Combine the constant terms on the right side of the equation: -9 - 2a - 6a = -9 - 8a. The equation now becomes: -8a - 9 = -9 - 8a.

Notice that the "a" terms cancel out on both sides of the equation. This means that the equation is true for any value of "a". Therefore, the solution is all real numbers, or in interval notation: (-∞, +∞).

In summary, the solution to the equation -2a - 6a - 9 = -9 - 6a - 2a is all real numbers, or (-∞, +∞).

We are given the radius of the scoop and asked to find the volume of ice cream in one scoop. By using the formula for the volume of a sphere and substituting the given radius, we can calculate the volume. The final answer is approximately 33.49 cubic inches.

a) The problem asks for the volume of ice cream in one scoop.

b) The given fact is that the radius of the scoop is 2 inches.

c) The formula to be used is the volume of a sphere, which is given by V = (4/3)πr³, where V is the volume and r is the radius.

d) Number Sentence:

  - Given: Radius (r) = 2 inches

  - Formula: V = (4/3)πr³

  - Substituting the value: V = (4/3)π(2)³

  - Simplifying: V = (4/3)π(8)

  - Evaluating: V = (4/3)(3.14)(8)

  - Multiplying: V = 33.49333333 (approx.)

e) Final answer: The volume of ice cream in one scoop is approximately 33.49 cubic inches.

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The correct comparison between two function is

Both functions are increasing, but function g increases at a faster average rate.

The Correct option is (B).

If the slope of a function is continuously increasing or constant in an interval, the function is known as an increasing function.

Let us assume

f(x) = \(ab^x\)+ c

so, at x=0, f(0)=-10

a +c = -10

Similarly, by satisfying the above table in the f(x)

f(x) = -33/5 \((1/11)^x\) - 17/5

and, f'(x) > 0

Thus, f(x) is an increasing function.

Now, g(x) = -18 \((1/3)^x\) +2

g'(x) = -18 \((1/3)^x\) log(1/3)

as log 1/3 <0

So, g'(x) > 0

Thus, g(x) is an increasing function.

For any x ∈ f(x) and x ∈ g(x), g'(x) > f'(x).

Hence, Both functions are increasing, but function g increases at a faster average rate.

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The functions g(x) = x² - 4x + 3 and f(x) = x² - 4x are:

The functions have the same range.

The functions have the same domain.

The functions have the same x-intercepts.

Let's analyze the given functions g(x) = x² - 4x + 3 and f(x) = x² - 4x and determine which statements about them are true.

Here are the options:

The functions have the same graph.

The functions have the same range.

The functions have the same domain.

The functions have the same vertex.

The functions have the same y-intercept.

The functions have the same x-intercepts.

The functions have the same graph:

This statement is false. While both functions are quadratic functions, their additional terms make them different. g(x) has an additional constant term (+3) compared to f(x).

Their graphs will be different, with g(x) being shifted upward by 3 units compared to f(x).

The functions have the same range:

This statement is true.

Both functions are quadratic functions, and their range will be the same. The range of a quadratic function is either all real numbers (if the parabola opens upward) or the set of real numbers greater than or equal to (or less than or equal to) the vertex of the parabola.

The functions have the same domain:

This statement is true.

The domain of both functions, unless restricted by any other factors, is all real numbers.

Quadratic functions have a domain of (-∞, ∞).

The functions have the same vertex:

This statement is false.

The vertex of a quadratic function is determined by the values of "a," "b," and "c" in the general form of the quadratic function (ax^2 + bx + c).

Since g(x) has an additional constant term, its vertex will be different from the vertex of f(x).

The functions have the same y-intercept:

This statement is false.

The y-intercept of a function is the value of y when x = 0.

For f(x), when x = 0, we have f(0) = (0)² - 4(0) = 0.

For g(x), when x = 0, we have g(0) = (0)² - 4(0) + 3

= 3.

Their y-intercepts are different.

The functions have the same x-intercepts:

This statement is true.

To find the x-intercepts of both functions, we set y (or f(x) and g(x)) equal to zero and solve for x.

The quadratic equation x² - 4x + 3 = 0 can be factored as (x - 1)(x - 3) = 0, giving x = 1 and x = 3 as the x-intercepts.

Both functions have the same x-intercepts.

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For the fractions, the calculation of 3/5 of 2/3 of 3/4 of 560 is equal to 168.

To calculate 3/5 of 2/3 of 3/4 of 560, break it down step by step:

Step 1: Calculate 3/4 of 560:

3/4 × 560 = (3 × 560) / 4 = 1680 / 4 = 420

Step 2: Calculate 2/3 of the result from Step 1:

2/3 × 420 = (2 × 420) / 3 = 840 / 3 = 280

Step 3: Calculate 3/5 of the result from Step 2:

3/5 × 280 = (3 × 280) / 5 = 840 / 5 = 168

Therefore, 3/5 of 2/3 of 3/4 of 560 is equal to 168.

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a. The monthly contribution from a friend's company is $120 minus 0.5, or $60.

b. The total monthly contribution to the fund is $180.

The computation of FV in Excel is shown in the attachment below:

Using the current number as a starting point, subtract the prior value to determine the growth rate. To calculate the growth rate in percentage terms, divide the difference by the previous amount and multiply the result by 100. Growth Rate equals (Ending Value - Beginning Value) - 1. The year-over-year (YoY) growth rate of a business, for instance, would be 20% if its revenue increased from $100 million in 2020 to $120 million in 2021.

GDP, turnover, wages, etc., all have growth rates that reflect how much they have changed over time (month, quarter, year). Percentages are a pretty common way to communicate it.

20 years is the age.

20 times 12 periods equals 240.

3% growth rate

The computation of FV in Excel is shown in the attachment below:

So, FV= $7,223,115.77

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1) Considering the function below:

This question is really about evaluating that function when t=5. So when we do that, we'll find the projected number of colonies.

2) So let's do it, considering that "e" is an irrational number and we're going to approximate the final answer:

Since colonies are given as whole numbers, we rounded it off to the nearest whole number.

3) Hence, the answer is approximately 23 colonies

Answer:

We can use the formula for continuous compound interest to find the balance in Joseph and Deb's savings account after 1 year:

A = Pe^(rt)

where A is the balance, P is the principal (initial deposit), e is the mathematical constant approximately equal to 2.71828, r is the annual interest rate as a decimal, and t is the time in years.

Substituting the given values, we get:

A = $600.00e^(0.05*1)

Using a calculator, we get:

A ≈ $632.57

Therefore, Joseph and Deb will have approximately $632.57 in their savings account after 1 year. They can spend up to this amount on their trip. Rounded to the nearest cent, the answer is $632.57.

Answer:

27

Step-by-step explanation:

The actual mean is 27.008333333333, round that as you will.

Answer:

27 is the answer

Step-by-step explanation:

Took the test and got it right

The 95% two sided confidence interval for the standard deviation between 0.425 and 0.640.

To construct a 95% confidence interval for the standard deviation of the percentage of titanium in the alloy used in aerospace castings, we can use the chi-square distribution.

The formula for the confidence interval is:

(n - 1) ×s² / χ² (α/2, n-1) < σ² < (n - 1) × s² / χ²(1-α/2, n-1)

where:

n = sample size = 51

s = sample standard deviation = 0.37

α = 1 - confidence level = 0.05

χ² = chi-square distribution with (n-1) degrees of freedom

Using a chi-square distribution table or a calculator, we can find the critical values for χ²(α/2, n-1) and χ²(1-α/2, n-1) as:

χ²(0.025, 50) = 69.23

χ²(0.975, 50) = 32.36

Substituting these values into the formula, we get:

(51 - 1) × 0.37² / 69.23 < σ² < (51 - 1) × 0.37² / 32.36

Simplifying this, we get:

0.181 < σ² < 0.409

To get the confidence interval for the standard deviation, we take the square root of both sides:

0.425 < σ < 0.640

Therefore, we can be 95% confident that the standard deviation of the percentage of titanium in the alloy used in aerospace castings is between 0.425 and 0.640.

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The complete question is :

The percentage of titanium in an alloy used in aerospace castings is measured in 51 randomly selected parts. The sample standard deviation is s = 0.37. Construct a 95% two-sided confidence interval for the standard deviation.

Answer:

A towel

Step-by-step explanation:

Answer:

A towel, duhh

Step-by-step explanation:

The probability of landing on the red shaded circle is 6/18

Probability simply measures the chances at which an event could occur in a sample or population.

Mathematically, Probability is calculated thus:

Here ,

P(red circle ) = 6/18

Therefore, the probability is 6/18

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Answer:

32

Step-by-step explanation:

Totally there are 50 tosses.  

Let the number of tosses which resulted head be x.  

Therefore the number of tosses which resulted tail is 50−x.

We get x×1+(50−x)×(−1)=14

x−(50−x)=14

x−50+x=14

x=32

Answer:

Step-by-step explanation:

The equation of the line with the given points is y = 6x - 4. This can be derived by calculating the slope of the line, which is 6, and then using the point-slope form of the equation of a line, y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line. In this case, the given points are (x1, y1) = (1, 10), so the equation of the line is y - 10 = 6(x - 1) or y = 6x - 4.

Answer y == 3

+7

Step-by-step explanation:

The graph of a linear relationship contains the points (1, 10) and (3, 16).

Write the equation of the line in slope-intercept fo

Step-by-step explanation:

the general slope-intercept form is

y = ax + b

a is the slope, which is the ratio of "y coordinate change / x coordinate change" when going from one point to another on the line.

b is the y-intercept - the y value when x = 0.

for the slope we see

x changes by +2 (from 1 to 3)

y changes by +6 (from 10 to 16)

so, the slope a is +6/+2 = 3

and the semi-ready equation is

y = 3x + b.

now we use one of the points in the equation to solve for b. I picked (1, 10) :

10 = 3×1 + b = 3 + b

b = 7

so, the full equation is

y = 3x + 7

Answer: -17a^4

Step-by-step explanation:

Combine like terms

12a^4 +(-29a^4)

(12a^4-12a^4) - (29a^4-12a^4) =

-17a^4

Hope this helps

Answer:Can somebody also help me with this. i'm confused please hurry!

Step-by-step explanation:

Answer:

263

Step-by-step explanation:

Given that cos (0) = 0, we can use the Pythagorean identity sin^2(x) + cos^2(x) = 1 to find the value of sin (0).

sin^2(0) + cos^2(0) = 1

sin^2(0) = 1 - cos^2(0)

sin^2(0) = 1 - 0^2

sin^2(0) = 1

So, sin (0) = sqrt(sin^2(0)) = sqrt (1) = 1.

However, the given value is sin (0) = v3/6. This means that sin (0) = sqrt (3)/2, which is the value of sin (60). Therefore, the correct value of sin (0) is sqrt (3)/2, not 1.

trigonometry, the branch of mathematics deal with specific functions of angles and their application to calculations. There is total six functions of an angle commonly used in trigonometry.

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Answer:

Sometimes. Say x = 3 and y = 4. 3 + 4 = 7, 3 - 4 = -1. However, the subtraction problem can be greater than the addition if you add some negatives into the mix. Say x = 3 and y = -4. 3 + (-4) is the same as subtracting 4, which give you -1. However, when you subtract negative four, it's the same as adding four, which gives you seven.

Given:

There are given the annual house insurance bill of $926, an annual car insurance bill of $2692, and an annual property tax bill of $1448.

Explanation:

To find the monthly budget for his annual expense, first, we need to add all annual expenses and after that divide by 12 for the monthly.

Now,

From all the annual expenses:

Then,

The monthly expenses is:

Final answer:

Hence, the monthly budget for his annual expenses is $422.16

P(A and B) is equal to 6.

To find P(A and B), we can use the formula:

P(A and B) = P(A) + P(B) - P(A U B)

Given the information:

P(A U B) = 32 (the probability of either event A or event B occurring)

Universal set contains 52 elements (total number of possible outcomes)

P(A intersection B) = 6 (the probability of both event A and event B occurring)

P(A) = 12 (the probability of event A occurring)

P(B) = 26 (the probability of event B occurring)

We can substitute the known values into the formula:

P(A and B) = P(A) + P(B) - P(A U B)

P(A and B) = 12 + 26 - 32

Simplifying the expression:

P(A and B) = 38 - 32

P(A and B) = 6

Therefore, P(A and B) is equal to 6.

The result indicates that the probability of both event A and event B occurring simultaneously is 6 out of the total number of possible outcomes in the universal set. It means that out of the 52 elements in the universal set, 6 of them satisfy the conditions of both A and B.

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Answer:

r=5

Step-by-step explanation:

Can i get brainlest

Answer:

r=5

Step-by-step explanation:

1)

-4r+18=-2 Subtract 18 from both sides

-18 -18

2)

-4r=-20

---- ---- Divide both sides by -4

-4r -4r

3)

r=5 -20/-4 ----------> 5

Answer:

A) \(x=-1\pm\sqrt{\frac{13}{6}}\)

Step-by-step explanation:

\(\displaystyle x=\frac{-12\pm\sqrt{12^2-4(6)(-7)}}{2(6)}\\\\x=\frac{-12\pm\sqrt{144+168}}{12}\\\\x=\frac{-12\pm\sqrt{312}}{12}\\\\x=\frac{-12\pm2\sqrt{78}}{12}\\\\x=-1\pm\frac{\sqrt{78}}{6}\\\\x=-1\pm\sqrt{\frac{78}{36}}\\\\x=-1\pm\sqrt{\frac{13}{6}}\)

Answer:

220 adults and 250 children

Step-by-step explanation:

we require to set up 2 equations and solve simultaneously.

let a be the number of adults and c the number of children , then

a + c = 470 → (1) based on number of people

3a + c = 910 → (2) based on ticket sales

subtract (1) from (2) term by term to eliminate c

(3a - a) + (c - c) = 910 - 470

2a + 0 = 440

2a = 440 ( divide both sides by 2 )

a = 220

substitute a = 220 into (1) and solve for c

220 + c = 470 ( subtract 220 from both sides )

c = 250

that is 220 adults and 250 children attended

Answer:

d

Step-by-step explanation:

Answer:

D is the correct answer

Step-by-step explanation:

the x and y values are negative so they're both opposite

Answer:The reciprocal of 2/3 is 3/2. The product of 2/3 and its reciprocal 3/2 is 1.

Step-by-step explanation:

Answer:

A. X= -4

Step-by-step explanation:

8x-3=5(2x+1)

8x-3=10×+5

-3=2×+5

-8=2x

x=-4

Answer:

A: x=-4

Step-by-step explanation:

8x - 3 = 5(2x + 1)

8x - 3 = 10x + 5

-3 = 2x + 5

-8 = 2x

x = -4

The equation for the line of best fit is given as follows:

y = 50x/3.

The slope-intercept equation for a linear function is presented as follows:

y = mx + b.

The parameters of the definition of the linear function are given as follows:

From the graph, when x = 0, y = 0, hence the intercept b is given as follows:

b = 0.

Hence:

y = mx.

When x = 3, y = 50, hence the slope m is given as follows:

3m = 50

m = 50/3.

Hence the equation is:

y = 50x/3.

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