Q4. Find the range, standard deviation, and variance for the following sample data:
33, 55, 29, 40, 8, 90, 61, 41, 17, 80, 56, 17, 59, 21,78
plz answer this!

The abscissa on the curve x^2 = 2y which is nearest to the point (4,1) is x = √(3/8).

Given the equation x^2 = 2y.

The coordinates of the point are (4,1).We have to find the abscissa on the curve that is nearest to this point.So, let's solve this question:

To find the abscissa on the curve x2 = 2y which is nearest to the point (4,1), we need to apply the distance formula.In terms of x, the formula for the distance between a point on the curve and (4,1) can be written as:√[(x - 4)^2 + (y - 1)^2]But since x^2 = 2y, we can substitute 2x^2 for y:√[(x - 4)^2 + (2x^2 - 1)^2].

Now we need to find the value of x that will minimize this expression.

We can do this by finding the critical point of the function: f(x) = √[(x - 4)^2 + (2x^2 - 1)^2]To do this, we take the derivative of f(x) and set it equal to zero: f '(x) = (x - 4) / √[(x - 4)^2 + (2x^2 - 1)^2] + 4x(2x^2 - 1) / √[(x - 4)^2 + (2x^2 - 1)^2] = 0.

Now we can solve for x by simplifying this equation: (x - 4) + 4x(2x^2 - 1) = 0x - 4 + 8x^3 - 4x = 0x (8x^2 - 3) = 4x = √(3/8)The abscissa on the curve x^2 = 2y that is nearest to the point (4,1) is x = √(3/8).T

he main answer is that the abscissa on the curve x^2 = 2y which is nearest to the point (4,1) is x = √(3/8).

The abscissa on the curve x^2 = 2y which is nearest to the point (4,1) is x = √(3/8).

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Answer:

$289.8 in 18 hours hourly wage for him is $16.1

Step-by-step explanation:

322/20=16.1- $16.1

16.1x18=$289.8

Hello.

The first fraction is

\(\displaystyle\frac{9}{15}\)

Both the top and bottom can be divided by 3:

\(\displaystyle\frac{3}{5}\) (Simplest Form)

Next fraction:

\(\displaystyle\frac{15}{40} =\frac{3}{8}\)

We divided the top & bottom by 5.

Next:

\(\displaystyle\frac{20}{35}\)

Divide the top & bottom by 5:

\(\displaystyle\frac{5}{7}\)

Next:

\(\displaystyle\frac{12}{20} \\\text{Divide by 4:}\\\displaystyle\frac{3}{5}\)

Next:

\(\displaystyle\frac{44}{48} =\frac{11}{12}\)

Next:

\(\displaystyle\frac{5}{60} =\frac{1}{12}\)

Next:

\(\displaystyle\frac{10}{24} =\frac{5}{12}\)

next:

\(\displaystyle\frac{25}{30} =\frac{5}{6}\)

next:

\(\displaystyle\frac{10}{18} =\frac{2}{9}\)

next:

\(\displaystyle\frac{28}{40} =\frac{14}{20} =\frac{7}{10}\)

\(\displaystyle\frac{8}{10} =\frac{4}{5}\)

\(\displaystyle\frac{3}{9} =\frac{1}{3}\)

\(\displaystyle\frac{15}{20} =\frac{3}{4}\)

\(\displaystyle\frac{6}{9} =\frac{2}{3}\)

\(\displaystyle\frac{20}{32} =\frac{5}{8}\)

\(\displaystyle\frac{5}{35} =\frac{1}{7}\)

\(\displaystyle\frac{2}{8} =\frac{1}{4}\)

\(\displaystyle\frac{2}{20} =\frac{1}{10}\)

\(\displaystyle\frac{33}{36} =\frac{11}{12}\)

\(\displaystyle\frac{15}{40} =\frac{3}{8}\)

\(\displaystyle\frac{32}{36}=\frac{8}{9}\)

\(\displaystyle\frac{14}{20} =\frac{7}{10}\)

I hope it helps.

Have a great day.

\(\boxed{imperturbability}\)

Answer:

7

Step-by-step explanation:

28x7=196

196=14^2 aka a perfect square

Answer:

$13

Step-by-step explanation:

The expected payoff for the winner would be the ticket cost, $3, plus the prize money, $10, which totals $13. This is the expected value of playing the game. However, it's important to note that this does not guarantee that the winner will receive exactly $13, as the outcome of the game is dependent on chance and the player's skill. There is always a chance that the player could win more or less than the expected value.

Based on the given conditions, Jane has $31, Kevin has $25, and Hans has $50 in their wallets.

Let's solve the problem step by step.

First, let's assume that Jane has X dollars in her wallet. Since Kevin has $6 less than Jane, Kevin would have X - $6 dollars in his wallet.

Next, we're given that Hans has 2 times what Kevin has. So, Hans would have 2 * (X - $6) dollars in his wallet.

According to the information given, the total amount of money they have in their wallets is $106. We can write this as an equation:

X + (X - $6) + 2 * (X - $6) = $106

Simplifying the equation:

4X - $18 = $106

4X = $124

X = $31

Now we know that Jane has $31 in her wallet.

Substituting this value into the previous calculations, we find that Kevin has $31 - $6 = $25 and Hans has 2 * ($25) = $50.

To find the total amount they have, we sum up their individual amounts:

Jane: $31

Kevin: $25

Hans: $50

Adding these amounts together, we get $31 + $25 + $50 = $106, which matches the total amount stated in the problem.

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The complete question is:

Jane, kevin and hans have a total of $106 in their wallets. kevin has $6 less than Jane. hans has 2 times what kevin has. how much do they have in their wallets?

Answer: the answer is 12

Step-by-step explanation:

2x+6 =4x-12

-2x=-18

x=9

3(9)-15

27-15

12

Answer:

x=75

Step-by-step explanation:

Answer:

x=-75

Step-by-step explanation:

Hope this helps.

The mean of the sample will be less than 200 pounds is .571 using standard deviation

What is standard deviation?

The standard deviation is a statistician's way of gauging how much a group of numbers can vary or be dispersed. The values tend to be close to the set's mean when the standard deviation is low, while the values are dispersed over a larger range when the standard deviation is high.

Given that ,
mean = μ = 196

standard deviation = σ= 22
P(x < 200) = P((x - μ) / σ < (200 - 196) / 22)

= P(z < 0.18)

Using the standard normal.

P(x < 200) = 0.5714

Probability = 0.5714

Hence the Probability will be .571 using standard deviation

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The bending moment is the algebraic sum of the moments about the section of all external forces that act either to the left or to the right of the section under consideration.

The generalized numerical formula for the shear force at a point x along the beam is

V = (5x + 1/12 x^2)/2, w

The bending moment is the algebraic sum of the moments about the section of all external forces that act either to the left or to the right of the section under consideration. The shear force at any section of the beam is equal to the rate of change of bending moment with respect to the length of the beam, that is,

V = dm/dx.

Here, the bending moment of a 12-m beam is

M(x) = 5x + 1/12x.

The objective is to determine the generalized numerical formula for calculating the shear force of a beam at length x using a 2-m interval.

To estimate the shear force for each 2-m segment of the beam, differentiate the moment equation with respect to x.

dM/dx = d/dx

(5x + 1/12 x) = 5 + 1/12.

Therefore, the shear force at any point x along the beam can be obtained by integrating dM/dx over a given length from the start of the beam.
∫(5 + 1/12)dx

= (5x + 1/12 x^2)/2 + C.

We can determine the constant of integration C by using the boundary condition that the shear force is zero at the start of the beam.

V(0) = 0

= (5*0 + 1/12 * 0^2)/2 + C.

Therefore, C = 0.

Hence the generalized numerical formula for the shear force at a point x along the beam is

V = (5x + 1/12 x^2)/2, w

here x is the length of the beam from the start.

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The probability that a female student does not have an A is 7/29.

We have,

Total number of students in the class (n) = 29

Number of female students (F) = 10

Number of students with an A (A) = 20

Number of male students without an A = 2

So, the probability that a female student does not have an A

= number of females that do not have an A / total number of females

= (29 - 20 - 2 )/ 29

= 7/29

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If circuit boards are randomly selected for testing, the probability it takes 10 circuit boards to be inspected before a defective board is found is 0.9833. So, the correct option is b .

This is a geometric distribution problem, where we are trying to find the probability of the number of trials (inspections) until the first success (defective board). The probability of success (finding a defective board) on each trial is 0.02 and the probability of failure (not finding a defective board) on each trial is 0.98.

The formula for the probability of exactly k trials until the first success is given by:

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

where p is the probability of success and k is the number of trials.

Plugging in p = 0.02 and k = 10, we get:

P(X = 10) = (1 - 0.02)^(10-1) * 0.02 = 0.9833

So the probability it takes 10 circuit boards to be inspected before a defective board is found is 0.9833.

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The bottleneck time is 10. This is the longest time it takes to complete any task in the assembly line, and all the other tasks must be completed within this time frame.

The bottleneck time is the longest time it takes to complete any task in the assembly line. In this case, the longest time needed is 10, which is the last station. This means that all the other tasks must be completed within 10 seconds in order for the entire assembly line to proceed.

The bottleneck time is 10. This is the longest time it takes to complete any task in the assembly line, and all the other tasks must be completed within this time frame.

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The solution for x in the equation 5^(x-2) = 8 is approximately 4.8 (rounded to the nearest tenth).

To solve the equation 5^(x-2) = 8, we can use the change of base formula for logarithms. The change of base formula states that for any positive base b and positive numbers x and y, we have:

log base b of y = log base c of y / log base c of b,

where c can be any positive base except 1.

Let's apply the change of base formula to the given equation:

5^(x-2) = 8.

Taking the logarithm of both sides using the base 5, we get:

log base 5 of (5^(x-2)) = log base 5 of 8.

Applying the change of base formula with c = 5, we have:

(x - 2) = log base 5 of 8 / log base 5 of 5.

Since log base 5 of 5 is equal to 1, we can simplify the equation further:

(x - 2) = log base 5 of 8 / 1.

(x - 2) = log base 5 of 8.

Now, to isolate x, we can add 2 to both sides:

x = log base 5 of 8 + 2.

Evaluate log base 5 of 8, we find:

x ≈ 2.7712 + 2.

x ≈ 4.7712 (rounded to the nearest tenth).

The solution for x in the equation 5^(x-2) = 8 is approximately 4.8 (rounded to the nearest tenth).

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Answer:

option C , D , E

Step-by-step explanation:

\(\sqrt{\frac{1}{16}} = \frac{1}{4} => not \ irrational\\\\\sqrt{\frac{1}{4}} = \frac{1}{2} => not \ irrational\\\\\sqrt{\frac{1}{2}} = > \ irrational\\\\\sqrt{\frac{1}{10}} =>\ irrational\\\\\sqrt{\frac{1}{8}} =>\ irrational\\\\\)

Answer:

1/2, 1/10, 1/8

A system of linear inequalities that is represented by the graph include the following:

C. y ≥ x - 2 and x + 2y < 4

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

y - y₁ = m(x - x₁)

Where:

First of all, we would determine the slope of the first solid line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (0 + 2)/(2 - 0)

Slope (m) = 2/2 = 1

At data point (0, -2) and a slope of 1, a linear equation for this solid line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y + 2 = 1(x - 0)  

y = x - 2

y ≥ x - 2 (since the solid line is shaded to the left).

At data point (0, 2) and a slope of -1/2, a linear equation for this solid line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 2 = -1/2(x - 0)

y = -1/2(x) + 2

y < -1/2(x) + 2

x + 2y < 4 (since the dashed line is shaded below and to the left).

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The critical value of f(x) = 5x⁶ - 3x⁵ is x = 0.5 which is also its maxima point

f(x) = 5x⁶ - 3x⁵

differentiation w.r.t x

=> f'(x) = 30x⁵ - 15x⁴

Putting f'(x) = 0

30x⁵ - 15x⁴ = 0

=> x⁴(30x - 15) =0

=> 30x - 15 = 0

=> x = 15/30

=> x = 0.5 , 0

Critical number is 0.5 , 0

(B) To find where f(x) is increasing

for x > 0.5 ,

(30x-15) > 0 => x⁴(30x - 15) > 0

Therefore , f(x) is increasing at ( 0.5 , ∞ )

(C)To find where f(x) is decreasing

for x < 0.5 ,

(30x-15) < 0 => x⁴(30x - 15) < 0

Therefore , f(x) is decreasing at ( -∞ , 0.5)

(D) Differentiation f'(x) again w.r.t to x

f'(x) = 30x⁵ - 15x⁴

f"(X) = 150x⁴ - 60x³

Substituting critical values of x

=> 150(0.5)⁴ - 60(0.5)³

=>9.375 - 7.5

=> -1.875 < 0 , Hence , x = 0.5 is point of maxima

(E) no point of minima

Similarly , we can solve other parts

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Answer:

The equation is W + 24 = 42.

Step-by-step explanation:

To find W, you do 42-24.

That equals 18.

To check, you add 18 and 24 together which will equal 42.

The equation we need to solve is:

W + 24 = 42

And the solution is W = 18.

We know that the family picks a total of 42 lb of apples, and we also know that they collect 24 pounds of Honeycrisp apples.

Then if we define W as the weight of Golden Delicious apples, we must have that:

W + 24lb = 42lb

To solve the linear equation we just subtract 24lb in both sides, we will get:

W = 42lb - 24lb = 18lb

They collected 18 pounds of Golden Delicious apples.

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\((\stackrel{x_1}{0}~,~\stackrel{y_1}{-2})\hspace{10em} \stackrel{slope}{m} ~=~ 3 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-2)}=\stackrel{m}{ 3}(x-\stackrel{x_1}{0}) \implies y +2= 3 (x -0) \\\\\\ y+2=3x\implies y=3x-2\)

9514 1404 393

Answer:

  A = -5

Step-by-step explanation:

The equation can be simplified, then solved for A.

  \(\dfrac{-8+A\times(-8)-(-6)}{-3+(-8)\div2\times4}=-2\\\\\dfrac{-8-8A+6}{-3-4\times4}=-2\\\\\dfrac{4A+1}{-3-16}=1\qquad\text{multiply by -1/2}\\\\4A+1=-19\qquad\text{multiply by -19}\\\\4A=-20\qquad\text{subtract 1}\\\\\boxed{A=-5}\qquad\text{divide by 4}\)

Answer: A rectangle is a 2-dimensional and a cube is a 3-dimensional

Step-by-step explanation:

\(~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\[-0.35em] ~\dotfill\\\\ (4)^{\frac{-4}{2}} \implies (4)^{-2}\implies 4^{-2}\implies \cfrac{1}{4^2}\implies \cfrac{1}{16}\)

Answer:

$93.75

Step-by-step explanation:

Answer:

Step-by-step explanation:

The Sydney Harbour Bridge is approximately 1200 metres long. A model of the bridge is built with a scale of 1:6000. What is the length of the model?

Pick one:

5cm

20cm

200cm

720cm

--------------------

scale = 1:6000

so

1200 : 6000 =  0.2m

0.2m = 20 cm

Answer:

20cm

Step-by-step explanation:

«A scale of 1:6000» means the model is smaller than the bridge by a factor of 6000. We can also make up a proportion \(\dfrac{1}{6000}=\dfrac{x}{1200}\), where the left side is the scale, x is the model length, 1200 is the bridge length (in meters). So, finding x or just dividing 1200 by 6000, we get 0.2 meters. Provided 1 m = 100 cm, 0.2 m is 0.2 × 100 = 20 cm.

The factors of 4x - 7 are (x - 7/4) and the factor of x + 4 is (x + 4).

To find the factors of the given expressions, 4x - 7 and x + 4, we can use the factor theorem and perform polynomial division.

Factor of 4x - 7:

We need to find a factor of 4x - 7, which means finding a value of x that makes the expression equal to zero.

Setting 4x - 7 equal to zero and solving for x:

4x - 7 = 0

4x = 7

x = 7/4

Therefore, the factor of 4x - 7 is (x - 7/4).

Factor of x + 4:

For the expression x + 4, the factor is simply (x + 4) itself.

In summary, the factors of 4x - 7 are (x - 7/4) and the factor of x + 4 is (x + 4).

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Answer:

option 4

Step-by-step explanation: