A={x|x is an even number more than 0 but less than 5}​

Answer:

5.44 meters

Step-by-step explanation:

We Know

0.3048 meter = 1 ft

How many ft makes a height of 1.66m?

We Take

1.66 ÷ 0.3048 ≈ 5.44 meters

So, the answer is 5.44 meters.

Answer:

$16,000 in stocks

$8,000 in bonds

Step-by-step explanation:

He invests 2x in stocks and x in bonds.

The total investment is 2x + x = 3x.

The total investment is $24,000.

3x = 24,000

x = 8,000

Stocks: 2x = 2(8,000) = 16,000

Bonds: x = 8,000

Answer:

$16,000 in stocks

$8,000 in bonds

Consider the function F(x)= x³ +½x² −2x +3. Use calc and algebra to find any and all stationary points on the graph of the function.Precalc need help ASAP

Solution:

the above function has more than one root or more than one solution. The derivative of the function represents the slope of the tangent line to the curve

F(x)= x³ +½x² −2x +3, F'(x) = 3(x3-1)+(1/2)(2)(x2-1)-2(x1-1)+0

F'(x)=3x2+x-2 is the slope of the tangent line

setting the slope =0 and solving the quadratic equations, you find all the

critical points of interest

3x2+x-2=0, solve by factoring (3x-2)(x+1)=0, then 3x-2=0, x= 2/3

and x+1=0, x=-1 substituting these values of x in the original equation

you get the corresponding values of F(x) such that;

F(x)= x³ +½x² −2x +3, F(x)=(2/3)3+1/2(2/3)2-2(2/3)+3

= 8/27+4/18-4/3+3 = 8/27+2/9-4/3+3/1 = 59/27 and the first point is

(2/3, 59/27)

F(x)= x³ +½x² −2x +3, F(x)=(-1)3+1/2(-1)2-2(-1)+3

= -1+1/2+2+3 = 9/2 and the 2nd point is ( -1, 9/2)

these two points represents points where the slope of the tangent line to the curve is 0 and could be either maximum or minimum points

You can also find the y intercepts where x = 0 F(x)= x³ +½x² −2x +3, setting x = 0, y= F(x)=3 and the point ( 0,3) is a y intercept setting y = 0, then x intercepts can be found upon solving the equation x³ +½x² −2x +3 =0

Answer:

71tickets=$91.59 is the equation

The amount of Muskco's work force that he has in  his business is; 138 people

We are told that Muskco gave 88 people a bonus. Now, we are further told that if he had given 4 more people bonuses, then it means he would have rewarded two thirds of his workforce.

Thus we can begin too solve this problem to find the size of Muskco's work force by;

Let the total number of his workforce be denoted as x. Then the algebraic equation for this problem would be expressed as;

88 + 4 = (2/3)x

Simplify by adding up the left hand side values to get;

(2/3)x = 92

Use multiplication property of equality to Multiply both sides by 3 to get;

2x = (92 * 3)

2x = 276

Now, use division property of equality to divide both sides by 2 to get;

2x/2 = 276/2

x = 138

Thus, we would conclude from the calculations as seen in the above that the size of Muskco's workforce is 138 people.

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Answer:

The solutions to this system of inequalities are included in this inequality:

5/3x - 4 < y < 1/4x - 4

Here are an example of 3 solutions:

(-1,-5), (-2,-6), (-4,-8)

Answer:

(3 a ^2 + 2 g^4  ) ( 9 a ^4 − 6 a ^2 g ^4 + 4 g ^8 )

Step-by-step explanation:

(3 a ² + 2 g⁴  ) ( 9 a⁴ − 6 a ² g⁴+ 4 g ⁸ )  is the factored form of the expression 27a⁶+ 8g¹²

An expression is combination of variables, numbers and operators.

The given expression is 27a⁶+ 8g¹²

In the expression the variables are a and g

The operators used in the expression are plus.

We need to find the factored form of the given expression.

When the quadratic expression is a product of two factors where each one is a linear expression, this is called the factored form

(3 a ² + 2 g⁴  ) ( 9 a⁴ − 6 a ² g⁴+ 4 g ⁸ )

Hence, (3 a ² + 2 g⁴  ) ( 9 a⁴ − 6 a ² g⁴+ 4 g ⁸ )  is the factored form of the expression 27a⁶+ 8g¹²

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When x is equal to 1, the Function f(x) = -4x - 5 yields a value of -9.

The find ƒ(1) for the function f(x) = -4x - 5, we need to substitute x = 1 into the function and evaluate the expression.

Replacing x with 1, we have:

ƒ(1) = -4(1) - 5

Simplifying further:

ƒ(1) = -4 - 5

ƒ(1) = -9

Therefore, when x is equal to 1, the value of the function f(x) = -4x - 5 is ƒ(1) = -9.

Let's break down the steps taken to arrive at the solution:

1. Start with the function f(x) = -4x - 5.

2. Replace x with 1 in the function.

3. Evaluate the expression by performing the necessary operations.

4. Simplify the expression to obtain the final result.

In this case, substituting x = 1 into the function f(x) = -4x - 5 gives us ƒ(1) = -9 as the output.

It is essential to note that the notation ƒ(1) represents the value of the function ƒ(x) when x is equal to 1. It signifies evaluating the function at a specific input value, which, in this case, is 1.

Thus, when x is equal to 1, the function f(x) = -4x - 5 yields a value of -9.

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The question is incomplete! Complete question along with answer and step by step explanation is provided below.

Question:

The attached Excel file 2013 NCAA BB Tournament shows the salaries paid to the coaches of 62 of the 68 teams in the 2013 NCAA basketball tournament (not all private schools report their coach's salaries). Consider these 62 salaries to be a sample from the population of salaries of all 346 NCAA Division I basketball coaches.

Question 1. Use the 62 salaries from the TOTAL PAY column to construct a 95% confidence interval for the mean salary of all basketball coaches in NCAA Division I.

xbar = $1,465,752

SD = $1,346,046.2

lower bound of confidence interval ________

upper bound of confidence interval _______

Question 2. Coach Mike Krzyzewski's high salary is an outlier and could be significantly affecting the confidence interval results. Remove Coach Krzyzewski's salary from the data and recalculate the 95% confidence interval using the remaining 61 salaries.

xbar = $1,371,191

SD = $1,130,666.5

lower bound of confidence interval _________

upper bound of confidence interval. ________

Answer:

Question 1:

lower bound of confidence interval = $1,124,027

upper bound of confidence interval = $1,807,477

Question 2:

lower bound of confidence interval = $1,081,512

upper bound of confidence interval = $1,660,870

Step-by-step explanation:

Question 1:

The sample mean salary of 62 couches is

 \(\bar{x} = 1,465,752\)

The standard deviation of mean salary is

 \(s = 1,346,046.2\)

The confidence interval for the mean salary of all basketball coaches is given by

 \($ CI = \bar{x} \pm t_{\alpha/2}(\frac{s}{\sqrt{n} } ) $\)

Where \(\bar{x}\) is the sample mean, n is the sample size, s is the sample standard deviation and  \(t_{\alpha/2}\) is the t-score corresponding to a 95% confidence level.  

The t-score corresponding to a 95% confidence level is  

Significance level = α = 1 - 0.95 = 0.05/2 = 0.025  

Degree of freedom = n - 1 = 62 - 1 = 61

From the t-table at α = 0.025 and DoF = 61

t-score = 1.999

So the required 95% confidence interval is  

\(CI = \bar{x} \pm t_{\alpha/2}(\frac{s}{\sqrt{n} } ) \\\\CI = 1,465,752 \pm 1.999 \cdot (\frac{1,346,046.2}{\sqrt{62} } ) \\\\CI = 1,465,752 \pm 1.999 \cdot (170948.04 ) \\\\CI = 1,465,752 \pm 341,725 \\\\LCI = 1,465,752 - 341,725 = 1,124,027 \\\\UCI = 1,465,752 + 341,725 = 1,807,477\\\\\)

Question 2:

After removing the Coach Krzyzewski's salary from the data

The sample mean salary of 61 couches is

\(\bar{x} = 1,371,191\)

The standard deviation of the mean salary is

\(s = 1,130,666.5\)

The t-score corresponding to a 95% confidence level is  

Significance level = α = 1 - 0.95 = 0.05/2 = 0.025  

Degree of freedom = n - 1 = 61 - 1 = 60

From the t-table at α = 0.025 and DoF = 60

t-score = 2.001

So the required 95% confidence interval is  

\(CI = \bar{x} \pm t_{\alpha/2}(\frac{s}{\sqrt{n} } ) \\\\CI = 1,371,191 \pm 2.001 \cdot (\frac{1,130,666.5}{\sqrt{61} } ) \\\\CI = 1,371,191 \pm 2.001 \cdot (144767 ) \\\\CI = 1,371,191 \pm 289,678.8 \\\\LCI = 1,371,191 - 289,678.8 = 1,081,512 \\\\UCI = 1,371,191 + 289,678.8 = 1,660,870\\\\\)

Answer:

Part A:

To find the percentage of survey respondents who liked neither hamburgers nor burritos, we need to calculate the frequency in the "Does not like hamburgers" and "Does not like burritos" categories.

Frequency of "Does not like hamburgers" = Total in "Does not like hamburgers" category = 135

Frequency of "Does not like burritos" = Total in "Does not like burritos" category = 54

Total respondents who liked neither hamburgers nor burritos = Frequency of "Does not like hamburgers" + Frequency of "Does not like burritos" = 135 + 54 = 189

Percentage of survey respondents who liked neither hamburgers nor burritos = (Total respondents who liked neither hamburgers nor burritos / Total respondents) x 100

Percentage = (189 / 205) x 100 = 92.2%

Therefore, 92.2% of the survey respondents liked neither hamburgers nor burritos.

Part B:

To find the marginal relative frequency of all customers who like hamburgers, we need to divide the frequency of "Likes hamburgers" by the total number of respondents.

Frequency of "Likes hamburgers" = 110 (given)

Total respondents = 205 (given)

Marginal relative frequency = Frequency of "Likes hamburgers" / Total respondents

Marginal relative frequency = 110 / 205 ≈ 0.5366 or 53.66%

Therefore, the marginal relative frequency of all customers who like hamburgers is approximately 53.66%.

Part C:

To determine if there is an association between liking burritos and liking hamburgers, we can compare the joint and marginal frequencies.

Joint frequency of "Likes hamburgers" and "Likes burritos" = 29 (given)

Marginal frequency of "Likes hamburgers" = 110 (given)

Marginal frequency of "Likes burritos" = 70 (calculated by adding the frequency of "Likes burritos" in the table)

To assess the association, we compare the ratio of the joint frequency to the product of the marginal frequencies:

Ratio = Joint frequency / (Marginal frequency of "Likes hamburgers" x Marginal frequency of "Likes burritos")

Ratio = 29 / (110 x 70)

Ratio ≈ 0.037 (rounded to three decimal places)

The value of x in the triangle is 18.59 units.

The scale factor is the size by which the shape is enlarged or reduced. It is used to increase the size of shapes like circles, triangles, squares, rectangles, etc.

In order to find the missing side just find the ratio of the known corresponding sides of the triangles. Thus:

scale factor = (18 1/2 + 4 5/8)/ (18 1/2) = 5/4

For the smaller triangle:

3rd side = √(18.5² - 11²) = 14.87  (Pythagoras)

scale factor = x / 14.87

5/4 = x / 14.87

x  = 5/4 * 14.87

x = 18.59 units

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\(\dfrac{d}{dt} [(4t^2-t)(t^3 -8t^2+12)]\\\\\\=(4t^2-t)\dfrac{d}{dt}(t^3-8t^2 +12) + (t^3 -8t^2 +12) \dfrac{d}{dt} (4t^2 -t)\\\\\\=(4t^2 -t)(3t^2-16t)+(t^3-8t^2+12)(8t-1)\\\\=12t^4-64t^3 -3t^3+16t^2+8t^4-64t^3+96t-t^3+8t^2-12\\\\=20t^4-132t^3+24t^2+96t-12\)

1) The linear system has only one solution.

2) The linear system has infinite number of solutions.

3) The linear system has only one solution

4) The linear system has only one solution.

5) The linear system has only no solution.

In the algebraic form y= mx+ b, where m denotes the slope and b the y-intercept, a linear equation is defined as a first-order (linear) term and a constant. The aforementioned is occasionally described as a linear equation with two variables, where x and y are the variables.

An equation is linear if the graph of the equation is a straight line. This will happen once x has the highest power of 1, which is. The equation is linear if it can be represented as a straight line.

1) x+y+7=0

x-y+1=0

By solving these two equations we get,

x=-4

y=-3

(x, y)=(-4,-3)

Consequently, there is only one solution to the linear system.

2) 3x+y-2=0

6x+2y-4=0

a₁/a₂=3/6

a₁/a₂=1/2

b₁/b₂=1/2

c₁/c₂=1/2

Therefore,

a₁/a₂=b₁/b₂=c₁/c₂

So, the linear system has infinite number of solutions.

3) x-y-5=0

x+5y+7=0

By solving these two equations we get,

y=-2 and x=3

(x, y)=(3, -2)

Consequently, there is only one solution to the linear system.

4) x+y-4=0

2x-3y-3=0

By solving these two equations we get,

x=3 and y=1

(x, y)=(3,1)

Consequently, there is only one solution to the linear system.

5) 5x-y-5=0

5x-y-15=0

a₁/a₂=1

b₁/b₂=1

c₁/c₂=1/3

∴ a₁/a₂=b₁/b₂≠c₁/c₂

Therefore, the linear system has no solution.

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Answer: Max Value is y = 16

========================================================

Explanation:

The amplitude is the vertical distance from the horizontal center line to either the peak or valley.

The minimum value is 4. The distance from the min value to the center is 6 units. So the center is at 4+6 = 10.

Then we go another 6 units up to arrive at the max value 10+6 = 16

Refer to the diagram below. I recommend drawing out a sine curve along with  the vertical y axis number line.

Answer:

The maximum value: 16

Step-by-step explanation:

Given

We know that a function's amplitude A can be interpreted as the difference between the average between its maximum and minimum and its minimum.

\(A\:=\:\frac{max+min}{2}-min\)

solving for max

\(2A\:=\:max+min\:-2\:min\)

\(2A+2\:min=max+min\)

\(\:2\left(A+min\right)=max+min\)

\(max\:=2\left(A+min\right)-min\)

substituting A = 6 and min = 4

\(max\:=2\left(6+4\right)-4\)

\(max=\:2\left(10\right)-4\)

\(max\:=\:20-4\)

\(max = 16\)

Therefore, the maximum value: 16

Answer:

Hi

Please mark brainliest ❣️

Thanks

Step-by-step explanation:

The answer is NO

Reason

x= 2 y= 1

Now input in the first inequality

y≤ -x + 4

1 ≤ -2 +4

1≤ 2 i.e 1 is less than two

Next inequality

y≤ x +1

1 ≤ 2 + 1

1≤ 3 i.e 1 is less than 3

But 1 is not equal to 3 and also not equal to 2

Hence our answer is NO

Answer:

1,080 ft

Step-by-step explanation:

Rate of descending or travel (r) = 18 ft per second.

The depth or distance traveled/descended (d) after 1 minute can be calculated as follows:

\( d = r*t \)

r = 18ft/sec

t = 1 min = 60 secs

\( d = \frac{18 ft}{1 sec}*60secs \)

\( d = 18ft*60 \)

\( d = 1,080 ft \)

Answer:

in 18 mins it would be 6 pages and in 6 mins it would be 1 page

Answer:median:249    

Step-by-step explanation:

median:198] 216} 220] 236] 246 252 [253[ 260 {290[ 369

246 +252=498

498/2=249

as for the mean  i will give you that later

During the exponential phase, e.coli bacteria in a culture increase in number at a rate proportional to the current population. If growth rate is 1.9% per minute and the current population is 172.0 million, the population 7.2 minutes from now can be calculated using the following formula:

P(t) = P ₀e^(rt)where ,P₀ = initial population r = growth rate (as a decimal) andt = time (in minutes)Substituting the given values, P₀ = 172.0 million r = 1.9% per minute = 0.019 per minute (as a decimal)t = 7.2 minutes

The population after 7.2 minutes will be:P(7.2) = 172.0 million * e^(0.019*7.2)≈ 234.0 million (rounded to the nearest tenth)Therefore, the population of e.coli bacteria 7.2 minutes from now will be approximately 234.0 million.

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Length of the base of the building from the wall is, 1.68 m

We have to given that;

A ladder 8 m long leans against the wall of a building.

And, the foot of the ladder makes an angle of 78 degrees with the ground.

Now, We know that;

cos x = Base / Hypotenuse

Here, Hypotenuse = 8 m

And, Length of the base of the building from the wall = Base = x

Hence, We get;

cos 78 = x / 8

0.21 = x / 8

x = 0.21  x 8

x = 1.68 m

Thus, Length of the base of the building from the wall is, 1.68 m

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Answer:

n ∝ (1/l) (√F/m)

Step-by-step explanation:

Since frequency, n of vibration of a stretched string is a function of its tension F, the length l and the mass per unit length m, and has dimensions [T]⁻¹ where T = time, its dimension must be equal to that of the combination of F, L and m

Since n = f(F,L,m)

n = kFᵃLᵇmˣ

dimension of n = (dimension of F)ᵃ × (dimension of L)ᵇ × (dimension of m)ˣ

Since n = frequency, dimension of n = [T]⁻¹

F = Force, dimension of F = [M][L][T]⁻²

Also, L = length, dimension of L = [L] and

m = mass per unit length, dimension of m = [M][L]⁻¹

So, n = FᵃLᵇmˣ

[T]⁻¹  = ([M][L][T]⁻²)ᵃ( [L] )ᵇ([M][L]⁻¹)ˣ

[T]⁻¹  = ([M]ᵃ[L]ᵃ[T]⁻²ᵃ[L]ᵇ([M]ˣ[L]⁻ˣ

[M]⁰[L]⁰[T]⁻¹  = ([M]ᵃ ⁺ˣ)([L]ᵃ ⁺ ᵇ ⁻ˣ)([T]⁻²ᵃ)

equating the exponents on both sides, we have

a + x = 0  (1 )⇒ x = -a

a + b - x = 0 (2) ⇒

-2a = -1 (3) ⇒ a = 1/2

Substituting x into 2, we have

a + b -(-a) = 0

a + b + a = 0

2a + b = 0

b = -2a

b = -2 (1/2)

b = -1

x = -a = -1/2

So, substituting the variables into n, we have

n = kFᵃLᵇmˣ

n = kFᵃLᵇmˣ

\(n = kF^{\frac{1}{2} }L^{-1}m^{-\frac{1}{2} }\)

n = k/l(√F/m)

n ∝ (1/l) (√F/m)

There are 20 possible routes that a man could take to go between cities and then take a different route back.

In mathematics, a permutation of a set is, broadly speaking, the rearranging of its elements if the set is already sorted, or the arrangement of its members into a sequence or linear order. The act of altering the linear order of an ordered set is referred to as a "permutation" in this context.

Let the number of roads between the cities A and B = 5.

The rules of permutation must be used in this situation.

A permutation is an arrangement of all or a portion of a collection of items that takes into account the arrangement's order.

The man uses five different routes to get from A to B because there are five different routes accessible.

He can get back by 4 (5 1) methods because he needs to take a different route.

Therefore, there are 20 possible routes that a man could take to go between cities and then take a different route back.

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Answer:

Infinite Solutions

Step-by-step explanation:

Both sides of equations are the same when solved.

Step-by-step explanation:

\(a + 3 + 2a = - 1 + 3a + 4\)

\(a - 3a + 2a = 4 - 1 - 3\)

\(3a - 3a = 4 - 4\)

One way its verified

\(0 = 0\)

Hence, no solution.

he expression 4(3x=2)-9 can be written as 12x - 9. I

Answer:

i dont know what you want but exact form is 983/243

decimal form is 4.04526748

mixed form 4 \(\frac{11}{243}\)

Step-by-step explanation:

let's recall that the domain of a function is the range of its inverse function, namely, the inverse has a pair that's just the same but flipped sideways, Check the picture below.

Answer:

B. xy(y - x) (y + x)

Step-by-step explanation:

ANSWER:

the first one: 30x+48

The second one: x y^2(10 y + 15)

The third one: 30 x y - 5 x^2

Hope this helped!

sorry if im wrong. :)

GOOD LUCK!! <3

Answer:

12×6×2+6×5×2+12×5×2= 324m^2

The probability that, in any hour, exactly 5 cars will enter the car wash is P(x = 5) = 0.0920.

This can be modeled as a Poisson random variable.

The mean rate is the parameter of the Poisson distribution:

λ = 4 cars/30 mins

λ = 8 cars/hr

The probability that exactly k cars will enter the car wash can be calculated as:

P(x = k) = (\(8^{k}\) × \(e^{-8}\)) ÷ k!

Then, the probability that exactly 5 cars will enter the car wash for k=5 is:

P(5) = (\(8^{5}\) × \(e^{-8}\)) ÷ 5!

P(5) = (32768 × 0.0003) ÷ 120

P(5) = 0.0920

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