What is the midpoint M of the line segment joining the points A=(-1,5) and B =(-7,-1).

The height is 114.83 ft and the distance of the ø if someone is observing below is 84.8.

The branch of mathematics that sets up a relationship between the sides and the angles of the right-angle triangle is termed trigonometry.

The trigonometric functions, also known as a circular, angle, or goniometric functions in mathematics, are real functions that link the angle of a right-angled triangle to the ratios of its two side lengths.

Given that at a given point of 67.7ft at the ground level of a covered court, the angle of elevation of a roof worker from the bottom is 38.6⁰ and the angle of elevation of the roof from the top is 42.4 degrees.

The base will be calculated as:-

tan(38.6) = P / B

tan(38.6) = 67.7 / B

B = 67.7 / tan(38.6)

B = 54.8 ft

The height will be calculated as:-

Cos(42.4) = B / H

H = 84.8 / Cos(42.4)

H = 114.83 ft

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Answer: “6b”

Step-by-step explanation:

9514 1404 393

Answer:

  524,160

Step-by-step explanation:

Assuming order matters, it is the number of permutations of 16 things taken 5 at a time:

  16P5 = 16!/(16-5)! = 16·15·14·13·12 = 524,160

_____

The first passenger can pick any of 16 seats; the second can pick any of 15 remaining seats; and so on until all 5 passengers have chosen a seat. The number of possible different arrangements is the number shown above.

Answer:

  77.5°

Step-by-step explanation:

Let s represent the measure of the second angle. Then the first angle is s+25. These two angles are supplementary, so their sum is 180:

  (s+25) +s = 180

  2s = 155

  s = 77.5

The measure of the second angle is 77.5°.

Answer:

Pi/4

Step-by-step explanation:

first we have to figure out what cos of 7pi/4 is. Using the unit circle, we know that it is equal to root2/2. Cos to the negative 1 is basically just finding the radian value that matches the value in the parenthesis. This means we have to find the corresponding radian to root2/2. Using the unit circle, we find this to be pi/4

There are 9444 men and 24555 females are present.

The fractional bar is a horizontal bar that divides the numerator and denominator of every fraction into these two halves.

Given:

Total students = 34000

For every 5 male students there are 13 female students.

So, the number men are

= 5/18 x 34000

= 9444

and, number of women

= 13/ 18 x 34000

= 24, 555.

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The question attached here is in other language whose translation is given below.

In a school for every 5 male students there are 13 female students. If the total number of students is 34,000, how many men and women are there?

The required perimeter of the scale drawing is given as 18 inches.

Given that,
The rectangular floor of a classroom is 30 feet in length and 24 feet in width. A scale drawing of the floor has a length of 5 inches. The perimeter, in inches, of the floor in the scale drawing, is to be determined.

Perimeter is the measure of the figure on its circumference.

Here,
According to the question,

L = 30 feet, W = 24 feet,
for Scaled drawing
l = 5 inch, w = x
Now,
30/5 = 24 / x
6 = 24 / x
x = 24 {1/6}
x = 4,
So the width of the scale drawing is 4 inches,
perimeter of the scaled drawing  = 2[l + w]
                                                       = 2 [5 + 4] = 18 inches

Thus, the required perimeter of the scale drawing is given as 18 inches.

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Answer:

hello your question is incomplete below is the complete question

Problem 8-28 The exponential distribution applies to lifetimes of a certain component. Its failure rate is unknown. Find the probability that the component will survive past 5 years assuming:

(a) lambda=.5

Pr=

(b) lambda=0.9

Pr=

(c) lambda=1.1

Pr=

answer : a) P( X> 5 ) = 0.0821

              b) P( X > 5 ) = 0.0111

              c) P ( X > 5 ) = 0.00409

Step-by-step explanation:

A) P( X > 5 ) = exp ( - λ * x )

   = \(e^{-2.5}\) ≈ 0.082

B)  P( X > 5 ) = exp ( - λ * x )  

  = \(e^{-4.5}\) ≈ 0.0111

C) P( X > 5 ) = exp ( - λ * x )  

 = \(e^{5.5}\)  ≈ 0.00409

The appropriate alternative hypothesis for the investigation is: Ha: proportion < 0.38

The correct option is option D)

What is null and alternate hypothesis?

Null and alternate hypothesis are hypothesis in statistical testing. A null hypothesis assumes that is no difference. where as an alternate hypothesis assumes that there is a difference. A null hypothesis is denoted by H0 and alternate hypothesis is denoted by H1.

The null hypothesis is the proportion of people in Region X with blood type O positive is equal to the proportion in Region W. And that proportion is 0.38

Hence by null hypothesis we have

H0: proportion = 0.38

The alternative hypothesis, denoted by Ha, is the hypothesis that we want to test against the null hypothesis.

In this case, we want to investigate whether the proportion of people in Region X with blood type O positive is less than the proportion in Region W. So, the appropriate alternative hypothesis is:

Ha: proportion < 0.38

Hence, The appropriate alternative hypothesis for the investigation is: Ha: proportion < 0.38

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The drop down menu is used to match each situation as below.

1. The rocket reached its maximum  the x-value of the vertex

height in 5 s.

2. ground level                                    the y-intercept

3. The rocket launcher was                the y-value of the point containing

on the ground.                                     the x-intercept on the right

4. The rocket was in the air 10           the x-intercept on the right                                                                                    

5. The maximum height of the           the y-value of the vertex

rocket is 50 ft.

6. the time the rocket was                the x-value of the point containing the

launched                                          y-intercept

The key features of the curve such as the x intercept is the point the launcher and the rocket were on ground.

The vertex is the point the rocket had the maximum and height.

Generally, the curve traces a parabolic path

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Step-by-step explanation:

• Question 1 :-

\(\tt\to \dfrac{1}{3}+? = 1 \\\\\tt\to ? = 1-\dfrac{1}{3}\\\\\tt\to ?=\dfrac{3-1}{3} \\\\\tt\to \boxed{\orange{ ? = \dfrac{2}{3}}}\)

_________________________________

• Question 2 :-

\(\tt\to \dfrac{3}{5}+? = 1 \\\\\tt\to ? = 1-\dfrac{3}{5}\\\\\tt\to ?=\dfrac{5-3}{5} \\\\\tt\to \boxed{\orange{ ? = \dfrac{2}{5}}}\)

Answer:

x=3

Step-by-step explanation:

Log base 5 of 125=x

that is equal to 5x5x5 which is 125

5 is multiplied 3 times so x is 3

I am pretty sure the answer is 14.5

Answer:

14.5

Step-by-step explanation:

Arrange the numbers from small to big

11, 11, 12, 13, 14, 15, 16, 16, 18, 20

If the set of data is an even number, like in this case,

Take 2 of the middle numbers:

14 and 15

Add them and divide by 2:

14+15= 29

29 ÷ 2= 14.5

Answer:

98°

Step-by-step explanation:

m∠1 = m∠2

5x + 12 = 7x - 16; substitute the given

2x = 28

x = 14

m∠2 + m∠3 = 180; supplementary angles

82 + m∠3 = 180

m∠3 = 180 - 82

m∠3 = 98 degrees

Answer: m<3 = 98

Explanation: If two parallel lines are cut by a transversal,

then alternate interior angles are congruent.

This means that the m<1 = m<2.

So we can setup the equation 5x + 12 = 7x - 16

and solving this equation gives us x = 14.

Now let's use <2 to help us find the m<3.

Since x = 14, we can plug a 14 into the equation for x

to find the m<2 and this gives us 7(14) - 16 which is 82.

Now, we know that <2 and <3 form a straight

angle which is equal to 180 degrees.

So we can say that 82 + m<3 = 180 and we find that m<3 = 98.

Answer:

Step-by-step explanation:

Step-by-step explanation:

If the equation is

\( \sqrt{x + 2} \)

Then, here is the answer.

The definition of a derivative is

\( \frac{f(x + h) - f(x)}{h} \)

Also note that we want h to be a small, negligible value so we let h be a value that is infinitesimal small.

So we get

\( \frac{ \sqrt{x + h + 2} - \sqrt{x + 2} }{h} \)

Multiply both equations by the conjugate.

\( \frac{ \sqrt{x + h + 2} - \sqrt{x + 2} }{h} \times \frac{ \sqrt{x + h + 2} + \sqrt{x + 2} }{ \sqrt{x + h + 2} + \sqrt{x + 2} } = \frac{x + h + 2 - (x + 2)}{h \sqrt{x + h + 2} + \sqrt{x + 2} } \)

\( \frac{h}{h \sqrt{x + h + 2} + \sqrt{x + 2} } \)

\( \frac{1}{ \sqrt{x + h + 2} + \sqrt{x + 2} } \)

Since h is very small, get rid of h.

\( \frac{1}{ \sqrt{x + 2} + \sqrt{x + 2} } \)

\( \frac{1}{2 \sqrt{x + 2} } \)

So the derivative of

\( \frac{d}{dx} ( \sqrt{x + 2} ) = \frac{1}{2 \sqrt{x + 2} } \)

Part 2: If your function is

\( \sqrt{x} + 2\)

Then we get

\( \frac{ \sqrt{x + h} + 2 - ( \sqrt{x} + 2) }{h} \)

\( \frac{ \sqrt{x + h} - \sqrt{x} }{h} \)

\( \frac{x + h - x}{h( \sqrt{x + h} + \sqrt{x}) } \)

\( \frac{h}{h( \sqrt{x + h} + \sqrt{x} ) } \)

\( \frac{1}{ \sqrt{x + h} + \sqrt{x} } \)

\( \frac{1}{2 \sqrt{x} } \)

So

\( \frac{d}{dx} ( \sqrt{x} + 2) = \frac{1}{2 \sqrt{x} } \)

Answer:

The answer is 18

Step-by-step explanation:The part is 180 the whole is 1000, p/h=x/100, cross multiply, 180 times 100= 18000, 18000/1000=18

Answer:

a) t = 4

b) v = pi j + 5 k

c) rt = 1i + (pi t) j + (20 +5t )k

Step-by-step explanation:

You have the following vector equation for the position of a particle:

\(r(t)=cos(\pi t)\hat{i}+sin(\pi t)\hat{j}+5t\hat{k}\)    (1)

(a) The height of the helix is given by the value of the third component of the position vector r, that is, the z-component.

For a height of 20 you have:

\(5t=20\\\\t=\frac{20}{5}=4\)

(b) The velocity of the particle is the derivative, in time, of the vector position:

\(v(t)=\frac{dr(t)}{dt}=-\pi sin(\pi t)\hat{i}+\pi cos(\pi t)\hat{j}+5\hat{k}\)    (2)

and for t=4 (height = 20):

\(v(t=4)=-\pi sin(\pi (4))\hat{i}+\pi cos(\pi (4))\hat{j}+5\hat{k}\\\\v(t=4)=-0\hat{i}+\pi\hat{j}+5\hat{k}\)

(c) The vector parametric equation of the tangent line is given by:

\(r_t(t)=r_o+vt\)      (3)

ro: position of the particle for t=4

\(r_o=cos(\pi (4))\hat{i}+sin(\pi (4))\hat{j}+20\hat{k}\\\\r_o=\hat{i}+0\hat{j}+20\hat{k}\)

Then you replace ro and v in the equation (3):

\(r_t=(1\hat{i}+20\hat{k})+(\pi \hat{j}+5\hat{k})t\\\\r_t=1\hat{i}+\pi t \hat{j}+(20+5t)\hat{k}\)

Part(a): The value of \(t=4\)

Part(b): Required vector \(L(t)=(1\widehat{i}+0\widehat{j}+10\widehat{k})+(t-4)(0\widehat{i}+\pi \widehat{j}+5\widehat{k})\)

Given vector equation is,

\(r(t)=cos(\pi t)\widehat{i}+sin(\pi t)\widehat{j}+5t\widehat{j}\)

Vector equation:

A vector is an object that has both a magnitude and a direction. Geometrically, we can picture a vector as a directed line segment, whose length is the magnitude of the vector, and with an arrow indicating the direction.

Part(a):

When the particle has a height of 20

\(5t=20\\t=4\)

Part(b):

The point on the curve is \((cos(4\pi),sin(4\pi),20) =(1,0,20)\)

Differentiating the given equation with respect to \(t\).

\(r'(t)=- \pi sin(\pi t)\widehat{i}+\pi cos(\pi t)\widehat{j}+5\widehat{k}\\r'(t)=- \pi sin(4\pi t)\widehat{i}+\pi cos(4\pi t)\widehat{j}+5\widehat{k}\\r'(4)=0\widehat{i}+\pi \widehat{j}+5\widehat{k}\\L(t)=r(4)+(t-4)r'(4)\\L(t)=(1\widehat{i}+0\widehat{j}+10\widehat{k})+(t-4)(0\widehat{i}+\pi \widehat{j}+5\widehat{k})\)

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Answer:

D

Step-by-step explanation:

RISE/RUN = slope

This slope will be POSITIVE because it rises in quadrant 1.

Rise=2, run=3

Slope= 2/3

Hope that helps

Answer:

b + 9

Step-by-step explanation:

Given:

(b + 3) + 6

Required:

Rewrite expression without the parentheses.

SOLUTION:

(b + 3) + 6

Eliminate the parentheses

b + 3 + 6

Add like terms

b + 9

Thus:

(b + 3) + 6 = b + 9

The box in the middle of the plot spans from the first quartile (Q1) to the third quartile (Q3), with a line inside representing the median.

A whisker plot, also known as a box and whisker plot, is a graphical representation of a set of numerical data through their quartiles. The plot consists of a box with whiskers extending from the top and bottom, showing the spread and distribution of the data. The five-number summary, which includes the minimum value, first quartile (Q1), median, third quartile (Q3), and maximum value, is used to create the whisker plot.

Here,

To create a box and whisker plot, we need to find the five-number summary of the data set, which includes:

Minimum value: the smallest value in the data set.

First quartile (Q1): the median of the lower half of the data set.

Median: the middle value in the data set.

Third quartile (Q3): the median of the upper half of the data set.

Maximum value: the largest value in the data set.

First, we need to put the data in order:

10, 12, 14, 15, 16, 18, 22, 24, 25, 28

The minimum value is 10 and the maximum value is 28.

The median is the middle value, which is 18.

To find the first quartile, we need to find the median of the lower half of the data set, which is:

10, 12, 14, 15, 16

The median of this lower half is 14.

To find the third quartile, we need to find the median of the upper half of the data set, which is:

22, 24, 25, 28

The median of this upper half is 24.

So, the five-number summary for this data set is:

Minimum value = 10

First quartile (Q1) = 14

Median = 18

Third quartile (Q3) = 24

Maximum value = 28

Now we can use this information to create the box and whisker plot:

      |          |      

 ----+----+----+----+----

    10   14   18   24   28

The box in the middle of the plot spans from the first quartile (Q1) to the third quartile (Q3), with a line inside representing the median. The whiskers extend from the box to the minimum and maximum values in the data set.

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Lexie scores 186 points in the game on Tuesday. The z-score when x = 186 is 2.64. The mean is 149.

This z-score tells you that x = 186 is -2.64 standard deviations to the right of the mean.

A standard deviation (or σ) is a measure of how dispersed the data is in relation to the mean. Low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out.

Given that,

Lexie averages points per bowling game = 149 points

Lexie a standard deviation of points = 14 points

Suppose Lexie's points per bowling game are normally distributed.

Let X= the number of points per bowling game.

Then X∼N(149,14).

If necessary, round to three decimal places.

Suppose Lexie scores 186 points in the game on Tuesday.

From the question we are told that,

The  mean is μ = 149 points

The standard deviation is σ = 14 points

The  value of x = 186

Generally the z-score is mathematically represented as,

Z = ( x - μ ) / σ

Substituting these values,

Z = \(\frac{186-149}{14}\)

Z = \(\frac{37}{14}\)

Z = 2.64

Therefore,

Lexie scores 186 points in the game on Tuesday. The z-score when x = 186 is 2.64. The mean is 149.

This z-score tells you that x = 186 is -2.64 standard deviations to the  right of the mean.

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Answer:

Given the information you provided, we can model cellular phone usage over time with an exponential growth model. An exponential growth model follows the equation:

`y = a * b^(x - h) + k`

where:

- `y` is the quantity you're interested in (cell phone usage),

- `a` is the initial quantity (34 million in 1995),

- `b` is the growth factor (1.22, representing 22% growth per year),

- `x` is the time (the year),

- `h` is the time at which the initial quantity `a` is given (1995), and

- `k` is the vertical shift of the graph (0 in this case, as we're assuming growth starts from the initial quantity).

So, our specific model becomes:

`y = 34 * 1.22^(x - 1995)`

To find the cellular usage in 2003, we plug 2003 in for x:

`y = 34 * 1.22^(2003 - 1995)`

Calculating this out will give us the cellular usage in 2003.

Let's calculate this:

`y = 34 * 1.22^(2003 - 1995)`

So,

`y = 34 * 1.22^8`

Calculating the above expression gives us:

`y ≈ 97.97` million.

So, the cellular phone usage in 2003, according to this model, is approximately 98 million.

Answer:

-82

Step-by-step explanation:

Answer:

b. 5 meters

Step-by-step explanation:

1 meter = 1000 millimeters

5 meter = 5000 millimeters

Which is longer 5 meters or 400 millimeters?

5000 > 400

So, the answer is b. 5 meters.

Answer:

The expected value of X is 2 with a standard deviation of 1.34.

Step-by-step explanation:

For each speaker, there are only two possible outcomes. Either it is defective, or it is not. The probability of a speaker being defective is independent of other speakers. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

The expected value of the binomial distribution is:

\(E(X) = np\)

The standard deviation of the binomial distribution is:

\(\sqrt{V(X)} = \sqrt{np(1-p)}\)

Stereo speakers are manufactured with a probability of 0.1 of being defective

This means that \(p = 0.1\)

Twenty speakers are randomly selected.

This means that \(n = 20\)

Let the random variable X be defined as the number of defective speakers. Find the expected value and the standard deviation.

\(E(X) = np = 20*0.1 = 2\)

\(\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{20*0.1*0.9} = 1.34\)

The expected value of X is 2 with a standard deviation of 1.34.

9514 1404 393

Answer:

  3. 17 < 25 . . . . 17 is on the left

  4. 42 > 39 . . . . 39 is on the left

Step-by-step explanation:

3. If you do any counting at all, you know that starting from 1, you reach the number 17 before you reach the number 25. That is 17 is less than 25.

The numbers increase to the right on the number line, so the relationship is ...

  17 < 25 . . . . . . . . 17 is to the left

__

4. You can count to 39 sooner than you can count to 42.

  42 > 39 . . . . . . . . 39 is to the left

_____

Additional comment

The point of the symbol (< or >) indicates the smaller value. The wider open end of the symbol indicates the larger value. One could say the symbol points to the number that is left on the number line.

Given a choice as to how to write an inequality, I often find it beneficial to write it so the "arrow" points to the left. That way, the written order of the operands corresponds to their relative locations on the number line.

For example, x < 3 means the number line will be shaded to the left of 3 to indicate possible values of x. 3 > x means the same thing, but requires more mental effort to figure out how to draw it on the number line.

__

"Back in the day" we played games that required counting. Jump rope or hide-and-seek, for example. It became obvious that it took 10 times as long to count to 100 as to count to 10. That is, the place values of the digits in a number were quite clear, as was their order.

Answer:

a) x=-a, x=a+b

b) x=5/2a, x=1/3b

c) x=1/2a, x=a/a-2

Step-by-step explanation:

a) (x-a)(x-a)-b(x+a)=0

   (x+a)(x-a-b)=0

   x=-a, x=a+b

b) 3x(2x-5a)-b(2x-5a)=0

   (2x-5a)(3x-b)=0

   x=5/2a, x=1/3b

c) (2a-4)x^2=a^2(x-1)

   (2x-a)(ax-2x-a)=0

Answer:

z = 3(-6x + 4y + 3)/6y and + 1

Step-by-step explanation:

z = 9 - 3x × 2 - 3y × 2 and z - 6x × 2 + 6y × 2

z = 9 - 3 × 2x - 3 × 2y and z - 6 × 2x + 6 × 2y

z = 9 - 6x - 6y and z - 12x + 12y

z = 3(-6x + 4y + 3)/6y and + 1