Determine which integer makes the inequality 6(n − 5) < 3(n + 4) true.

S:{11}
S:{14}
S:{30}
S:{42}

Answer:

15825.6 [tex]in^3[/tex]

Step-by-step explanation:

using 3.14 for pi you follow the formula for volume of a cylinder which is [tex]\pi r^2 h[/tex] when we plug in it comes to [tex]3.14\cdot3^{2}\cdot4[/tex] and then you solve that to get 113.04, but since you need 140 candles, we multiply the volume of one candle by 140 to get 15825.6 [tex]in^3[/tex]

There are 6 people in a group. Their names are selected randomly and they act independently. The probability that the first person arriving has the same name as 1 or more people is 0. The probability that there are people in the group with the same name is 98.46%.

The probability that the initial arrival shares a name with one or more others is 0 percent. This is because the first person arriving has no one to compare their name with, so there is no chance that they will have the same name as someone else.

The probability that there are people in the group with the same name can be calculated using the formula

P(same name) = 1 - P(different names).

The probability of everyone having different names is calculated by multiplying the probabilities of each person having a different name from the previous person. This can be represented as

(6/6) * (5/6) * (4/6) * (3/6) * (2/6) * (1/6) = 0.0154.

Therefore, the probability of there being people in the group with the same name is 1 - 0.0154 = 0.9846 or 98.46%.

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The frequency of each interval is:

81-100: 2

61-80: 2

1-20: 1

21-40: 1

41-60: 2

What is frequency interval?

Frequency refers to the number of times a particular value or event occurs within a given dataset or sample. In statistics, frequency is used to describe the distribution of values in a dataset, and it is often represented as a frequency table or histogram.

Frequency is often used in conjunction with other statistical measures such as mean, median, and mode to describe the central tendency and variability of a dataset. By analyzing the frequency of values within a dataset, we can identify patterns and trends, and make inferences about the population from which the sample was drawn.

According to the question:
Using the given intervals, we can count the frequency of each interval as follows

81-100: 2 (81, 97)

61-80: 2 (65, 44)

1-20: 1 (2)

21-40: 1 (24)

41-60: 2 (25, 38)

Total: 8

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Answer:

18cm^2

Step-by-step explanation:

3×2=6cm^2

2×6=12cm^2

6+12=18cm^2

The probability that the person chosen at random is a boy is 8/13 and the probability that they are between 120 cm and 130 cm tall is 6/10.

Polygon is a closed figure that consists of three or more straight lines. It is a two-dimensional shape with straight sides and angles. Polygons are used to construct many shapes in geometry such as triangles, rectangles, squares and many more. Polygons are used in many fields such as computer graphics, navigation, engineering and architecture.

The frequency polygon show that there are more boys than girls in the class. This can be seen from the higher peak on the boys side of the graph. The total number of boys is 8 and the total number of girls is 5. This gives us a probability of 8/13 that the person chosen at random is a boy.

To work out the probability that the person is between 120 cm and 130 cm tall, we must first count the number of individuals in the class in this height range. From the graph, we can see that there are 6 boys and 4 girls in this range. This gives us a probability of 6/10 that the person chosen at random is between 120 cm and 130 cm tall.

In conclusion, the probability that the person chosen at random is a boy is 8/13 and the probability that they are between 120 cm and 130 cm tall is 6/10.

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It will take 4 years for an investment to double if it is continuously compounded at 18% per year.

The time it takes for an investment to double if it is continuously compounded at 18% per year can be calculated using the formula:
T = ln(2)/r

Where T is the time in years, ln(2) is the natural logarithm of 2, and r is the annual interest rate.

Substituting the given values into the formula, we get:
T = ln(2)/0.18
T ≈ 3.85 years

Therefore, to the nearest year, it will take approximately 4 years for the investment to double if it is continuously compounded at 18% per year.

A neperian logarithm or also known as a natural logarithm, refers to that logarithm that has e as its base, which is worth: 2.718281828.

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The value of λ and μ for which the system of equations x+y+z=6,x+2y+3z=10 and x+2y+λz=μ  are none of this. The correct answer is option D, None of these.

To find the value of λ and μ for which the system of equations has no solution, we can use the determinant method. The determinant of a system of equations is given by:

| a1 b1 c1 |
| a2 b2 c2 | = a1(b2c3 - b3c2) - b1(a2c3 - a3c2) + c1(a2b3 - a3b2)
| a3 b3 c3 |

For the given system of equations, the determinant is:

| 1 1 1 |
| 1 2 3 | = 1(2λ - 3μ) - 1(3 - 3) + 1(2 - 2)
| 1 2 λ |

Simplifying, we get:

2λ - 3μ = 0

For the system of equations to have no solution, the determinant must be equal to 0. Therefore, we need to find the values of λ and μ that satisfy the equation 2λ - 3μ = 0.

None of the given options satisfy this equation, therefore the correct answer is option D, None of these.

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In the word problem, The account have left $67 in 13 weeks.

Word problems are often described verbally as instances where a problem exists and one or more questions are posed, the solutions to which can be found by applying mathematical operations to the numerical information provided in the problem statement. Determining whether two provided statements are equal with respect to a collection of rewritings is known as a word problem in computational mathematics.

Here the given expression represents the medical savings account.

=> y=-24x+379

Here y represent  of money and x represent number of weeks.                                                                                                                            

Here Amount of money y = $67 then,

=> 67=- 24x+ 379

=> -24x = 67-379

=> -24x= -312

=> x = -312/-24

=> x = 13

Hence The account have left $67 in 13 weeks.

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The formula for an exponential function that passes through the two points are

a. (0,4) and (2,64)

f(x)= 4(4ˣ)

b. (0,810) and (2,10)

g(x)=810(1/9)ˣ

The following is the formula for an exponential function that traverses two points:

f(x) = abˣ

Where a is the initial value and b is the growth rate.

To find the formula for an exponential function that passes through the two points given, we can plug in the values of x and y into the formula and solve for a and b.

For the first set of points, (0,4) and (2,64), we can plug in the values of x and y into the formula and solve for a and b:

4 = ab⁰
64 = ab²

Simplifying the first equation gives us:

a = 4

Substituting this value of a into the second equation gives us:

64 = 4b²

Solving for b gives us:

b = √(64/4) = 4

Therefore, the formula for the exponential function that passes through the two points (0,4) and (2,64) is:

f(x) = 4(4ˣ)

For the second set of points, (0,810) and (2,10), we can plug in the values of x and y into the formula and solve for a and b:

810 = ab⁰
10 = ab²

Simplifying the first equation gives us:

a = 810

Substituting this value of a into the second equation gives us:

10 = 810b²

Solving for b gives us:

b = √(10/810) = 1/9

Therefore, the formula for the exponential function that passes through the two points (0,810) and (2,10) is:

g(x) = 810(1/9)ˣ

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Answer:

p^(2(s-t)^2)/(s+t)

Step-by-step explanation:

We can simplify this expression by using the properties of exponents:

((p^r)/(p^s))^(r+s) ((p^2)/(p^t))^(s+t) ((p^t)/(p^r))^(r+t)

= (p^(r+s-s))^r (p^(2s-2t))^s (p^(t-r+r))^t / (p^(r+s-r))^r (p^(2t-2s))^s (p^(r-t+t))^t

= p^r p^(2s-2t)s p^t / p^r p^(2t-2s)s p^t

= p^r / p^r * (p^(2s-2t))^(s/(s+t)) / (p^(2t-2s))^(s/(s+t))

= p^r / p^r * p^((2s-2t)s/(s+t)) / p^((2t-2s)s/(s+t))

= p^0 * p^(2s^2-2st-2ts+2t^2)/(s+t)

= p^(2s^2-2st-2ts+2t^2)/(s+t)

= p^(2(s-t)^2)/(s+t)

Therefore, ((p^r)/(p^s))^(r+s) ((p^2)/(p^t))^(s+t) ((p^t)/(p^r))^(r+t) simplifies to p^(2(s-t)^2)/(s+t).

To factor the expression[tex]9n^(4)-16p^(2)[/tex], we need to recognize that it is a difference of squares. A difference of squares can be factored into the product of two binomials, one with a sum and one with a difference. In this case, we can factor [tex]9n^(4)-16p^(2)[/tex] into [tex](3n^(2)+4p)(3n^(2)-4p)[/tex].

The final factored form of  [tex]9n^(4)-16p^(2)[/tex] is [tex](3n^(2)+4p)(3n^(2)-4p).[/tex]

So, the factors of the expression are the two binomials [tex](3n^(2)+4p[/tex]) and [tex](3n^(2)-4p)[/tex].

Here is the step-by-step explanation:

1. Recognize that the expression is a difference of squares.
2. Write the expression as the product of two binomials, one with a sum and one with a difference.
3. Simplify the binomials if necessary.
4. The final factored form is [tex](3n^(2)+4p)(3n^(2)-4p).[/tex]

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The area of the dark region is 164.15 square feet because it is equal to the sum of the areas of the circles and rectangles.

In geometry, a circle is a closed object made up of all the points in a plane that are equally spaced from the circle's centre. The radius and diameter of a circle are measured from the centre to any spot on the circle, respectively. The circumference, which is equivalent to pi times the diameter, is the distance around the circle.

given

[tex]area of circle = π * r * r[/tex]

= 22/7 * 2 * 2 = 88/7 ft2

area of rectangle = length * breadth

= 9.4 * 18.8

= 176.72 ft2

area of shaded region

176.72 - 12.57

= 164.15 ft 2

The area of the dark region is 164.15 square feet because it is equal to the sum of the areas of the circles and rectangles.

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The total charges for both auto repair shops will be the same when 3 hours of labor have been performed.

Let's call the number of hours worked "h". The total charges for the first auto repair shop will be $30 (for the diagnosis) plus $25 per hour, or $30 + $25h. The total charges for the second auto repair shop will be $35 per hour, or $35h. We want to know when the total charges for both shops will be the same, so we can set the two equations equal to each other and solve for h:
$30 + $25h = $35h
$10h = $30
h = 3

So the total charges for both auto repair shops will be the same when 3 hours of labor have been performed.

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The number of servings that a 1.5 liter (1500ml) bottle of soda will make is 6 servings of 0.25 liter (250ml).

To find the number of servings, you can divide the total volume of the bottle by the volume of each serving.
Step-by-step explanation:
1. Convert the volume of the bottle to milliliters: 1.5 liters = 1500 milliliters
2. Convert the volume of each serving to milliliters: 0.25 liters = 250 milliliters
3. Divide the total volume of the bottle by the volume of each serving: 1500 milliliters / 250 milliliters = 6 servings
Therefore, a 1.5 liter (1500ml) bottle of soda will make about 6 servings of 0.25 liter (250ml).

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The point that would be included in the region shaded to show the half-plane greater than the line is the point that lies above the line.

In order to determine which point is included in the region shaded to show the half-plane greater than the line, we can use the following steps:
1. Identify the equation of the line.
2. Plug in the x and y values of the point into the equation of the line.
3. If the result is greater than the constant term in the equation of the line, then the point is included in the region shaded to show the half-plane greater than the line.

For example, if the equation of the line is y = 2x + 1, and the point is (2,5), we can plug in the x and y values into the equation:
5 = 2(2) + 1
5 = 5

Since the result is equal to the constant term in the equation of the line, the point (2,5) is included in the region shaded to show the half-plane greater than the line.

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Therefore , the solution of the given problem of expressions comes out to be x = 1.0730 is roughly the answer to the equation 10*e(³ˣ) = 250.

When variables are shifting, estimates should be created that mix joining, disabling, and instead of randomly  dividing. They could answer a puzzle collectively, offer some information, and instead software. Formulas, elements, and mathematical operations like addition, subtraction, grouping, and combination are all found in a statement of truth. Words and sentences can both be evaluated and analysed.

Here,

In order to find x in the equation 10*e(3x) = 250, we can start by dividing both parts by 10 to isolate the exponential term:

=> e³ˣ = 25

The exponential can then be removed by taking the natural logarithm (ln) of both sides:

=> ln(e(³ˣ) = ln(25)

We can simplify the left half by using the fact that ln(ey) = y:

=> 3x = ln(25)

By multiplying both parts by 3, we can finally find the value of x:

=>x = (1/3) * ln(25)

We can use a computer to determine that the value of ln(25) is roughly 3.2189. Therefore:

=> x ≈ (1/3) * 3.2189

=> x ≈ 1.0730

So x = 1.0730 is roughly the answer to the equation 10*e(³ˣ) = 250.

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[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

put the value of x = 4

[tex] \: [/tex]

[tex] \sf \: f( 4 )*g( 4 ) = 3(4)²*( 4 - 8 ) \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 3×16*(-4) \\ \sf \: \: \: \: \: \: \: \: \: \: \: = 48*( -4 ) \\ \: \: \: \: \underline{ \sf \red{ \: = -192 \: }}[/tex]

[tex] \: [/tex]

hope it helps! :)

Answer- 1:8

The original length of the board was 32 inches. Since it reduced we can divide 32 into 4. 32/4 is 8. This means that the scale factor of the dilation  is 1:8. 32 is 8/1 of 4, so that means in ratio 1 whole is divided into 8 parts, hence 1:8.

I hope this helped and Good Luck <3!!!

25. The inverse of f(x) = 1 + √2 + 3x is f-1(x) = (x - 1 - √2)/3.

26. The inverse of f(x) = e2x - 1 is f-1(x) = (ln(x) + 1)/2.

27. The inverse of y = In(x + 3) is y-1(x) = ex - 3.

28. Log2³² = 5

29. Log8² = 1/3

30.Log5^{1/125}  = -3

31. In(1/e2) = -2

32. Log10⁴⁰ + log10² = 1.6

33. log8 60 - log8 3 - log8 5 = 0

34. In10 + 2In5 = In10 + log10 5

35. 1/3In(x+2)3 + 1/2[Inx - In(x2 + 3x + 2)2] = In[(x+2)3/[(x2 + 3x + 2)2x]]

25. To find the inverse of the function f(x)=1+ √2+ 3x, we need to swap the x and y variables and solve for y.
So, x = 1 + √2 + 3y
Subtract 1 and √2 from both sides:
x - 1 - √2 = 3y
Divide both sides by 3:
y = (x - 1 - √2)/3
Therefore, the inverse of the function is f^-1(x) = (x - 1 - √2)/3

26. To find the inverse of the function f(x) = e^2x-1, we need to swap the x and y variables and solve for y.
So, x = e^2y-1
Add 1 to both sides:
x + 1 = e^2y
Take the natural log of both sides:
ln(x + 1) = 2y
Divide both sides by 2:
y = ln(x + 1)/2
Therefore, the inverse of the function is f^-1(x) = ln(x + 1)/2

27. To find the inverse of the function y=In(x+3), we need to swap the x and y variables and solve for y.
So, x = ln(y + 3)
Take the exponential of both sides:
e^x = y + 3
Subtract 3 from both sides:
y = e^x - 3
Therefore, the inverse of the function is f^-1(x) = e^x - 3

28. log2^32 = 5, because 2^5 = 32

29. log8^2 = 1/3, because 8^(1/3) = 2

30. log5 1/125 = -3, because 5^-3 = 1/125

31. In(1/e^2) = -2, because e^-2 = 1/e^2

32. log10 40 + log10 2.5 = log10 (40 * 2.5) = log10 100 = 2, because 10^2 = 100

33. log8 60 - log8 3 - log8 5 = log8 (60/3/5) = log8 4 = 2/3, because 8^(2/3) = 4

34. In10 + 2in5 = ln(10 * 5^2) = ln(250)

35. 1/3in(x+2)^3 + 1/2 [inx - in(x^2+3x+2)^2] = ln((x+2)^(1/3) * x^(1/2) * (x^2+3x+2)^(-1))

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Other roots of the given trinomial equation apart from (x -1) will be:

A polynomial is a mathematical equation that solely uses the operations addition, subtraction, multiplication, and non-negative integer exponentiation of variables. Variables are sometimes known as indeterminate in mathematics. Majorly used polynomials are binomial and trinomial.

Given a trinomial equation x³ + x²-6x +4 that has a root (x + 1)

Let P(x) = x³ + x²-6x +4

It is given that ( x - 1 ) is one of the factor of p(x)

On dividing p(x) by (x - 1), we get:

P(x) = (x- 1) (x² +2x -1)

For the quotient of the factor we will use the quadratic formula

(x² +2x -1) = 0

From quadratic formula,

x = 1/2a(-b ± √(b² - 4ac))

x = 1/2(-2 ±√(4 +4)

x = -1 ± √2

Thus,

Other roots of the given trinomial equation apart from (x -1) will be:

x = -1 -√2

x = -1 + √2

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Complete question:

if (x - 1) is a factor of x³ + x²-6x +4· find the other two factors​

This size sample of this binomial distribution have:

P = 0.24
Mean = 50.4
Standard Deviation = 6.19

About 24% of a population are of a particular ethnic group. 210 people are randomly selected from this population.

First, we need to convert the percentage to a decimal by dividing by 100:

P = 24% / 100 = 0.24

Next, we can compute the mean and standard deviation of the binomial distribution for a sample size of 210 and probability of success of 0.24:

Mean = np = 210 * 0.24 = 50.4

Standard Deviation = √(np(1-p)) = √(50.4 * (1-0.24)) = √(38.304) = 6.19

So, the mean of this binomial distribution is 50.4 and the standard deviation is 6.19.

Therefore,
P = 0.24
Mean = 50.4
Standard Deviation = 6.19

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Answer:

Mei and Ming both improved their yards by planting rose bushes and ivy they bought from the same store. Mei spent $36 on 3 rose bushes and 1 pot of ivy, while Ming spent $168 on 9 rose bushes and 8 pots of ivy. The cost of one rose bush and one pot of ivy would be $21, since the cost of one rose bush is $7 and one pot of ivy is $14

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

sorry if it is wrong

Iliana needs to play for 16 hours to get a total of 200 XP.

What is  slope-intercept form ?

The slope-intercept form is a way to write the equation of a line in two variables, usually x and y. It is called "slope-intercept" form because it gives the slope of the line and the y-intercept of the line.

The slope-intercept form is given by:

y = mx + b

where m is the slope of the line and b is the y-intercept, which is the point where the line crosses the y-axis.

We can use the points on the graph to find the equation of the line that relates playing time (x) to total XP (y). To do this, we can use the slope-intercept form of a line:

y = mx + b

where m is the slope of the line and b is the y-intercept.

To find the slope, we can use any two points on the line. Let's use points A and B:

m = (y2 - y1) / (x2 - x1) = (50 - 25) / (4 - 2) = 25/2

Now we can write the equation of the line in slope-intercept form:

y = (25/2)x + b

To find the value of b, we can substitute one of the points on the line into the equation. Let's use point A:

25 = (25/2)(2) + b

b = 0

So the equation of the line is:

y = (25/2)x

Now we can use this equation to find how many hours Iliana needs to play to get 200 total XP. We can set y = 200 and solve for x:

200 = (25/2)x

x = (2/25) * 200

x = 16

Therefore, Iliana needs to play for 16 hours to get a total of 200 XP.

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The solution of the equations ​2a-b=-1 and a-2b=4 is b = -3 and a = -2. The solution of the equations 3m-n=8 and m+n=4​ is m = 3 and n = 1.

In the elimination method, the two equations are solved by eliminating one variable and by substituting the value of one variable in the equation to get the value of another variable.

The two equations can be solved as below,

2a-b=-1

a-2b=4

Multiply the second equation by two and subtract from the first equation,

2a-b=-1

2a - 4b = -8

________

       3b = - 9

         b = -3

2a + 3 = -1

2a = -4

a = -2

For the other two equations,

3m-n=8

m+n= 4

_______

4m = 12

m = 3

m + n = 4

n = 4 - 3

n = 1

Therefore, the solution of the equations ​2a-b=-1 and a-2b=4 is b = -3 and a = -2. The solution of the equations 3m-n=8 and m+n=4​ is m = 3 and n = 1.

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The values of a for which the system has no solutions, exactly one solution, or infinitely many solutions are a = -8, a = 8, and a ≠ ±8, respectively.

The system has no solutions when the coefficients of the variables are the same but the constants are different. In this case, the coefficients of x, y, and z are the same in the first and second equations, but the constants are different (5 and 3). Therefore, there is no solution for a = -8.

The system has infinitely many solutions when the coefficients of the variables and the constants are the same in all equations. In this case, the coefficients of x, y, and z are the same in the first and second equations, and the constants are the same (5 and 5). Therefore, there are infinitely many solutions for a = 8.

The system has exactly one solution when the coefficients of the variables are different in all equations. In this case, the coefficients of x, y, and z are different in the first and second equations, and the constants are different (5 and 3). Therefore, there is exactly one solution for a ≠ ±8.

In conclusion, the values of a for which the system has no solutions, exactly one solution, or infinitely many solutions are a = -8, a = 8, and a ≠ ±8, respectively.

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Exact Form of the expression is mathematically given as

[tex]\sin \left(2 \arccos \left(\frac{1}{3}\right)\right)[/tex]

Generally, An expression is a combination of variables, numbers, operators, and/or functions that represent a value.

[tex]\sin \left(2 \arccos \left (\frac{1}{3}\right)\right)[/tex]

Evaluate[tex]$\arccos \left(\frac{1}{3}\right)$.[/tex]

sin (2 *1.23095941)

Multiply 2 by 1.23095941.

sin (2.46191883)

The result can be shown in multiple forms.

Exact Form:

[tex]\sin \left(2 \arccos \left(\frac{1}{3}\right)\right)[/tex]

Decimal Form:

0.62853936

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Mrs. Nelson waited 14 minutes in line at the grocery store.

Mrs. Nelson had to wait 4 minutes in line at her bank's automated teller machine. This was 3 minutes less than one-half of the time she waited in line at the grocery store. To find out how long in minutes did she wait in line at the grocery store, we can use the following equation:
4 = (x/2) - 3

Where x is the time she waited in line at the grocery store. To solve for x, we can first add 3 to both sides of the equation:
4 + 3 = (x/2) - 3 + 3
7 = x/2

Then, we can multiply both sides of the equation by 2 to isolate x:
7 * 2 = (x/2) * 2
14 = x

Therefore, Mrs. Nelson waited 14 minutes in line at the grocery store.

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Answer:

20.5 in.

Step-by-step explanation:

Just divide 82 by 4 to get the answer since  1 inch equals to 4 feet.