One model of the length LACL of a person's anterior cruciate ligament, or ACL, relates it to the person's height h with the linear function LACL=0.04606h−(41.29 mm) This relationship does not change significantly with age, gender, or weight. If a basketball player has a height of 2.13 m, approximately how long is his ACL?

Answer:

Your question indicates the ladder is at an angle of 60° to the wall, meaning the angle between the wall and the ladder is 60° and the angle between the ladder and the ground must be 30°. Not a very efficient way to set up a ladder.

5.7735 meters. The top of the ladder is 2.8868 meters off the ground.

Now, if you meant the ladder is 60° from the ground, that’s a different story.

Then, the ladder is 10 meters long and reaches 8.6603 meters from the ground.

A 30–60–90 right triangle is half of an equalateral triangle. Therefore the hypotenuse is double the length of the short leg, and by the Pythagorean theorum, we can determine that the other leg is the length of the short leg times the square root of 3.

All lengths in this answer are rounded to the nearest tenth of a millimeter.

Step-by-step explanation:

Answer:

A, E

Step-by-step explanation:

There should be 2^8-1 proper subsets of A. Its every one besides { }

Answer:

see explanation

Step-by-step explanation:

(f - g)(x) = f(x) - g(x) , that is

f(x) - g(x)

= - 5x³ - 4x² + 8x - (- 4x² + 8) ← distribute parenthesis by - 1

= - 5x³ - 4x² + 8x + 4x² - 8 ← collect like terms

= - 5x³ + 8x - 8

Substitute x = - 2 into this expression, thus

(f - g)(- 2)

= - 5(- 2)³ + 8(- 2) - 8

= - 5(- 8) - 16 - 8

= 40 - 16 - 8

= 16

Step-by-step explanation:

The inequality shows by line is

i) 1<=x<=6

OR,

x is an positive integer.

Answer:

Step-by-step explanation:

● h(x) = 2-2x

The domain is {-3,-2,1,5}

● h(-3) = 2-2×(-3) = 2+6 = 8

● h(-2) = 2 -2×(-2) = 2+4 = 6

● h(1) = 2-2×1 = 2-2 = 0

● h(5) = 2-2×5 = 2-10 = -8

The range is {-8,0,6,8}

Answer: A) (-2, 4), (6,8)

Step-by-step explanation:

When a point (x,y) is dilated by a scale factor of k , then the new points is given by (kx,ky).

Given: The line segment AB with endpoints A(-3, 6) and B(9, 12) is dilated with a scale factor [tex]\dfrac23[/tex] about the origin.

Let A' and B' b the endpoints of the dilated line segment.

Then, [tex]A'(\dfrac{2}{3}(-3), \dfrac23(6))=A'(-2,4)[/tex]

[tex]B'(\dfrac{2}{3}(9), \dfrac23(12))=B'(6,8)[/tex]

Hence, the correct option is A) (-2, 4), (6,8)

Answer:

Option (4)

Step-by-step explanation:

Given sequence is,

[tex]1+\frac{3}{2}+\frac{9}{4}..........[/tex]

We can rewrite this sequence as,

[tex]1+\frac{3}{2}+(\frac{3}{2})^2.............[/tex]

There is a common ratio between the successive term and the previous term,

r = [tex]\frac{\frac{3}{2}}{1}[/tex]

r = [tex]\frac{3}{2}[/tex]

Therefore, it's a geometric sequence with infinite terms. In other words it's a geometric series.

Since sum of infinite geometric sequence is represented by the formula,

[tex]S_{n}=\frac{a}{1-r}[/tex]  , when r < 1

where 'a' = first term of the sequence

r = common ratio

Since common ratio of the given infinite series is greater than 1 which makes the series divergent.

Therefore, sum of infinite terms of a series will be infinite Or the sum is not possible.

Option (4) will be the answer.

Answer:

The dimensions or Area of the rectangle is 1200cm².

Answer:

She must consider 3507 components to be 90% sure of knowing the mean will be within ± 0.1 mm.

Step-by-step explanation:

We are given that an engineer wishes to determine the width of a particular electronic component. If she knows that the standard deviation is 3.6 mm.

And she considers to be 90% sure of knowing the mean will be within ±0.1 mm.

As we know that the margin of error is given by the following formula;

The margin of error =  [tex]Z_(_\frac{\alpha}{2}_) \times \frac{\sigma}{\sqrt{n} }[/tex]  

Here, [tex]\sigma[/tex] = standard deviation = 3.6 mm

         n = sample size of components

         [tex]\alpha[/tex] = level of significance = 1 - 0.90 = 0.10 or 10%

         [tex]\frac{\alpha}{2} = \frac{0.10}{2}[/tex] = 0.05 or 5%

Now, the critical value of z at a 5% level of significance in the z table is given to us as 1.645.

So, the margin of error =  [tex]Z_(_\frac{\alpha}{2}_) \times \frac{\sigma}{\sqrt{n} }[/tex]  

                  0.1 mm        =  [tex]1.645 \times \frac{3.6}{\sqrt{n} }[/tex]

                    [tex]\sqrt{n} = \frac{3.6\times 1.645}{0.1 }[/tex]

                    [tex]\sqrt{n}[/tex] = 59.22

                     n = [tex]59.22^{2}[/tex] = 3507.0084 ≈ 3507.

Hence, she must consider 3507 components to be 90% sure of knowing the mean will be within ± 0.1 mm.

Answer:

Well this is my opinion I would try to compared both them and see if they have something familiar in their arguments. If not I would try to view their different point of view and write your own opinion about it. I would check out another book about the World War 2 because there's infinite of books about it.

Answer:

The probability that the amount of gas in Sarah's car is exactly 7 gallons is 0.067.

Step-by-step explanation:

Let the random variable X represent the amount of gas in Sarah's car.

It is provided that [tex]X\sim Unif(1, 16)[/tex].

The amount of gas in a car is a continuous variable.

So, the random variable X follows a continuous uniform distribution.

Then the probability density function of X is:

[tex]f_{X}(x)=\frac{1}{b-a};\ a<X<b[/tex]

For a continuous probability distribution the probability at an exact point is 0.

So, to compute the probability that the amount of gas in Sarah's car is exactly 7 gallons use continuity correction on both sides:

P (X = 7) = P (7 - 0.5 < X < 7 + 0.5)

              = P (6.5 < X < 7.5)

              [tex]=\int\limits^{7.5}_{6.5} {\frac{1}{16-1}} \, dx \\\\=\frac{1}{15}\times |x|^{7.5}_{6.5}\\\\=\frac{1}{15}\times (7.5-6.5)\\\\=\frac{1}{15}\\\\=0.0666667\\\\\approx 0.067[/tex]

Thus, the probability that the amount of gas in Sarah's car is exactly 7 gallons is 0.067.

Answer:

[tex]S = 3 h[/tex]

Step-by-step explanation:

Let M represent Michaela hair tier and S represents Michaela  sister's

Given

M = h

S = Triple of M

Required

Determine an expression for S

From the given parameters, we have that;

S = Triple of M

Mathematically, this implies;

[tex]S = 3 * M[/tex]

Substitute h for M

[tex]S = 3 * h[/tex]

[tex]S = 3 h[/tex]

Hence, the expression for Michaela  sister' is [tex]S = 3 h[/tex]

Answer:

1,377/2 and 688 1/17

Step-by-step explanation:

Answer:

(x,y) -> (x+6, y-3)

Step-by-step explanation:

I followed c and it translated like the  last ans choice.

Answer:

In MATH:

Empowerment - Gaining the skills required in language and practices to fully understand math.

Radication - The process of extracting a number's root.

In ENGLISH:

Empowerment - The process of gaining more power over anything, including yourself, others, society, government, and corporations.

Ex - In the spirit of empowerment, the company has implemented a new system that asks employees to nominate one another for bonuses.

Radication - The process of establishing, fixing, or creating.

Ex - The high prestige of the premier is radicated in the hearts of the people.

Answer:

Which polynomial is prime?

7x2 – 35x + 2x – 10

9x3 + 11x2 + 3x – 33  

10x3 – 15x2 + 8x – 12  

12x4 + 42x2 + 4x2 + 14

Step-by-step explanation:

Which polynomial is prime?

7x2 – 35x + 2x – 10

9x3 + 11x2 + 3x – 33  

10x3 – 15x2 + 8x – 12  

12x4 + 42x2 + 4x2 + 14 SO IT IS RIGHT

Answer:

x = 6

Step-by-step explanation:

In the third line of the solution on right side of the equal sign, middle term should be 8x instead of 4x.

The final value of x will be 6.

[tex] PQ^2 + QO^2 = PO^2 \\

x^2 + 8^2 = (4+x)^2 \\

x^2 + 64 = 16 + 8x + x^2 \\

64 = 16 + 8x \\

64 - 16 = 8x \\

48 = 8x \\

6 = x\\[/tex]

Answer:

[tex]A.\ 16\sqrt3\ cm^2[/tex] is the correct answer.

Step-by-step explanation:

Given that:

Side of an equilateral triangle = 8 cm

To find:

Area of the triangle will be:

[tex]A.\ 16\sqrt3\ cm^2[/tex]

[tex]B.\ \dfrac{32}{3} cm^2[/tex]

[tex]C.\ 48\ cm^2[/tex]

[tex]D.\ 36\sqrt3\ cm^2[/tex]

Solution:

First of all, let us have a look at the formula for area of an equilateral triangle:

[tex]A =\dfrac{\sqrt3}{4}a^2[/tex]

Where [tex]a[/tex] is the side of equilateral triangle and an equilateral triangle is a closed 3 sided structure in 2 dimensions which has all 3 sides equal to each other.

Here, we are given that side, [tex]a=8\ cm[/tex]

Putting the value in formula:

[tex]A =\dfrac{\sqrt3}{4}\times 8^2\\\Rightarrow A =\dfrac{\sqrt3}{4}\times 64\\\Rightarrow A =\sqrt3\times 16\\OR\\\Rightarrow \bold{A =16\sqrt3\ cm^2}[/tex]

Hence, [tex]A.\ 16\sqrt3\ cm^2[/tex] is the correct answer.

Answer:

[tex] \begin{cases} (x - 2)^2 + (y - 2)^2 = 25 \\ y = 5 \end{cases} [/tex]

Solutions: x = 6, y = 5   or   x = -2, y = 5

Step-by-step explanation:

Use a graph.

Plot point (-2, 5). That will be a point on a circle with radius 5.

From point (-2, 5), go right 4 and down 3 to point (2, 2). (2, 2) is the center of the circle.

You now need the equation of a circle with center (2, 2) and radius 5.

Use the standard equation of a circle:

[tex] (x - h)^2 + (y - k)^2 = r^2 [/tex]

where (h, k) is the center and 5 is the radius.

The circle has equation:

[tex] (x - 2)^2 + (y - 2)^2 = 25 [/tex]

To have a single solution, you need the equation of the line tangent to the circle at (-2, 5), but since you want more than one solution, you need the equation of a secant to the circle. For example, use the equation of the horizontal line through point (2, 5) which is y = 5.

System:

[tex] \begin{cases} (x - 2)^2 + (y - 2)^2 = 25 \\ y = 5 \end{cases} [/tex]

To solve, let y = 5 in the equation of the circle.

(x - 2)^2 + (5 - 2)^2 = 25

(x - 2)^2 + 9 = 25

(x - 2)^2 = 16

x - 2 = 4  or x - 2 = -4

x = 6 or x = -2

Solutions: x = 6, y = 5   or   x = -2, y = 5

An example of a nonlinear system that has at least two solutions, one of which is (-2,5) are,

⇒ x² + y² = 29

⇒ 3x + 4y = -2

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Now, This system by starting with the equation of a circle centered at the origin with radius sqrt(29), which is,

⇒ x² + y² = 29.

Then, Added a linear equation that intersects the circle at (-2,5) to create a system with two solutions.

The entire solution set for this system is: (-2, 5) and (7/5, -19/10)

Thus, An example of a nonlinear system that has at least two solutions, one of which is (-2,5) are,

⇒ x² + y² = 29

⇒ 3x + 4y = -2

Learn more about the mathematical expression visit:

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Answer:

D. neither.

Step-by-step explanation:

A function is when one x-value only has one corrisponding y-value.

The answer it's D. Neither

Answer:

15.7% of students made above an 89.

Step-by-step explanation:

If the data is normally distributed, the standard deviation is 7, and the mean is 82, then about 68.2% of students made between 75 and 89. 13.6% made between 90 and 96, and 2.1% made over 96. 13.6+2.1=15.7%

Answer:

mass = 9a^5

center of mass = [tex]\frac{7a}{12}, \frac{7a}{12}, \frac{7a}{12}[/tex]

Step-by-step explanation:

Finding the mass of the solid E

given density function : p ( x,y,z ) = [tex]9x^2 + 9y^2 + 9z^2[/tex]

Mass =   [tex]\int\limits^a_0 \int\limits^a_0 \int\limits^a_0 {9(x^2+y^2+z^2)} \, dx dydz[/tex]   [tex]= \int\limits^a_0 \int\limits^a_0 {9(\frac{a^3}{3}+ay^2+az^2 )} \, dydz[/tex]

         [tex]= \int\limits^a_0 {9(\frac{a^4}{3}+\frac{a^4}{3} +a^2z^2 )} \, dz[/tex]  [tex]= \int\limits^a_0 {9(\frac{2a^4}{3}+a^2z^2 )} \, dz[/tex]  [tex]= 9 ( \frac{2a^5}{3} + \frac{a^5}{3} )[/tex]  

( taking limits as a and 0 )

hence Mass = 9 [tex](a^5)[/tex]

finding the center of mass

attached below is solution

Answer:

42.7 mm

Step-by-step explanation:

To the nearest tenth of a mm, 42.67 mm would be 42.7 mm.

After estimate of this value rounded to the nearest tenth of a millimeter,

⇒ 42.67 ≈ 42.7

We have to given that,

According to the United States Golf Association, the diameter of a golf ball should not be less than 42.67 millimeters.

Hence, After estimate of this value rounded to the nearest tenth of a millimeter, we get;

⇒ 42.67

As, 7 is grater than 5, so we can add 1 to the tenth place.

⇒ 42.67 ≈ 42.7

Therefore, After estimate of this value rounded to the nearest tenth of a millimeter,

⇒ 42.67 ≈ 42.7

Learn more about the rounding number visit:

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Answer:

252

Step-by-step explanation:

Divide 7812 by 31 and we get the average daily answer... Hope this helps!!

Answer:

[tex]\boxed{\sf B. \ All \ real \ numbers}[/tex]

Step-by-step explanation:

The domain is all possible values for x.

[tex]f(x)=(\frac{1}{4} )^x[/tex]

There are no restrictions on x.

The domain is all real numbers.

Answer:

B.All real number

hope you have unterstand

Answer:

27.73 feet

Step-by-step explanation:

Use the Pythagorean theorem. It easiest to think of the distance between the two friends as a triangle in the rectangle. One side is 12ft and the other is 25ft.

12^2+25ft^2=769

The square root of 769 is 27.73

Answer:

27.73 Ft

Step-by-step explanation:I took the test

Answer:

H0:  u = 185      against     Ha: u > 185

or

H0:  u ≤ 185      against     Ha: u > 185

Step-by-step explanation:

The null and alternative hypotheses for this experiment would be

H0:  u = 185      against     Ha: u > 185

or

H0:  u ≤ 185      against     Ha: u > 185

This is a one tailed test .

If the results are such that we reject the null hypothesis and accept the alternative hypothesis it means that the Americans are getting fatter as the mean weight is increasing day by day.

The null hypothesis deals with all the values equal to or less than 185 pounds and the alternative with all the values greater than 185  pounds.

Answer:

Explained below.

Step-by-step explanation:

Enter the data in an Excel sheet.

(a)

Go to Insert → Chart → Scatter.

Select the first type of Scatter chart.

The scatter plot is attached below.

(b)

The scatter plot with the line of best fit is attached below.

The line of best fit is:

[tex]y=-0.8046x+103.56[/tex]

(c)

Compute the value of x for y = 30 as follows:

[tex]y=-0.8046x+103.56[/tex]

[tex]30=-0.8046x+103.56\\\\0.8046x=103.56-30\\\\x=\frac{73.56}{0.8046}\\\\x\approx 91.42[/tex]

Thus, the Advance Mathematics mark of a student who scores 30 out of 100 in English is 91.42.

(d)

The Pearson's Correlation Coefficient is:

[tex]r=\frac{n\cdot \sum XY-\sum X\cdot \sum Y}{\sqrt{[n\cdot \sum X^{2}-(\sum X)^{2}][n\cdot \sum Y^{2}-(\sum Y)^{2}]}}[/tex]

  [tex]=\frac{14\cdot 44010-835\cdot 778}{\sqrt{[14\cdot52775-(825)^{2}][14\cdot 47094-(778)^{2}]}}\\\\= -0.7062\\\\\approx -0.71[/tex]

Thus, the Pearson's Correlation Coefficient is -0.71.

(e)

A correlation coefficient between ± 0.50 and ±1.00 is considered as a strong correlation.

The correlation between Advanced Mathematics and English results is -0.71.

This implies that there is a strong negative correlation.

Answer:

300 SF

Step-by-step explanation:

just took the test

Answer:

  log(1/10) = -1

Step-by-step explanation:

Use the law of exponents and the meaning of logarithm.

  1/10 = 10^-1

  log(10^x) = x

So, you have ...

  log(1/10) = log(10^-1)

  log(1/10) = -1