Find the slope of the graphs

The probability density function for a normal distribution N(68, 5) reaches its maximum height at x = 68, which is the mean of the distribution. The function does not touch the x-axis at μ±30.

The probability density function (PDF) for a normal distribution is bell-shaped and symmetrical around its mean. In this case, the mean (μ) is 68, and the standard deviation (σ) is 5.

(a) To find the x value at which the PDF reaches a maximum, we look at the mean of the distribution, which is 68. The PDF is highest at the mean, and as we move away from the mean in either direction, the height of the PDF decreases. Therefore, the x value at which f(x) reaches a maximum is x = 68.

(b) The PDF of a normal distribution does not touch the x-axis at μ±30. The x-axis represents the values of x, and the PDF represents the likelihood of those values occurring. In a normal distribution, the PDF is continuous and never touches the x-axis. However, the PDF becomes close to zero as the values move further away from the mean. Therefore, the probability of obtaining values μ±30, which are 38 and 98 in this case, is very low but not zero. So, the PDF does not touch the x-axis at μ±30, but the probability of obtaining values in that range is extremely small.

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Answer:

The derivative of sin(x) is cos(x)

Step-by-step explanation:

That's

\( \frac{d}{dx} \sin(x) \: = \cos(x) \)

Hope this helps you

The calculated probability of spending $240 or more on a party at the first given venture is 0.62% while for the given second venture it is 1.5%.

Probability refers to chances that are linked to the suitable number of outcomes available concerning the initiation or occurrence of a given event taking place in a certain time at a dignified place.

To find the probability we are using the formula

z = (μ-x)/σ

for the first case the possible probability calculated is

z = (250-240)/16

z = 0.62%

for the second case the possible probability calculated is

z = (260 - 230)/16

z = 1.5%

The calculated probability of spending $240 or more on a party at the first given venture is 0.62% while for the given second venture it is 1.5%.

Therefore, the answer to the given question is simple we should go with the second venture cause it has higher probability in comparison with the first venture.

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Answer:

2(5x+9) = 10x+18

3(4x+2) = 12x+6

5(3x+7) = 15x+35

Does this anwser your question?!?

Answer:

See below

Step-by-step explanation:

For there to be infinitely many solutions, the equations have to be the same on the left side of the equation as on the right

3x+6  = 3 ( x+2)

As you can see when we distribute

3x+6  = 3x+6

Another example

2x+3 = x+ x+ 1+2

When we combine like terms

2x+3 = 2x+3

A third example

2x -5 +2x -6 = 7x-3x - 15+4

Combine like terms

4x -11 = 4x -11

Answer:

z=-5; x=0 ; y=3

Step-by-step explanation:

2x= -2z -10; -2z-10+y-z=8; y-3z-10=8; y-3z=18

2y-3z=21; 2y=3z+21; y= 1.5z+10.5; y-3z=18

1.5z+10.5-3z=18; -1.5z+10.5=18; -1.5z=7.5; z=-5

x+z=-5; x-5=-5; x=0; 2y-3z=21; 2y+15=21; 2y=6; y=3

2x+y-z=8; 2(0)+3-(-5)=8; 3+5=8; 8=8

Answer:10:05

Step-by-step explanation:

subtract 45 from 50!

Answer:

She started the test at 10:05 am

Step-by-step explanation:

Take the end time and subtract the time of the test

10:50-45 = 10:05

She started the test at 10:05 am

\((6x+5)/(x+7)\\\) can be represented as in the form quotient \(+( remainder )/( divisor )\) as \(6 + 47/(x+7)\) using division.

The methods below show how to use synthetic division to write (6x+5)/(x+7) in the form quotient +(remainder)/(divisor):

So, (6x+5)/(x+7) is the divisor x+7 divided by the quotient 6 plus the remainder 47. Hence, we can write:

(6x+5)/(x+7) = 6 + 47/(x+7)

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Answer:

21

Step-by-step explanation:

na na jk 19

Answer:

Below

Step-by-step explanation:

y varies directly with  x  means

y = k x

now with y = -93 and x = -3

   -93  =  k (-3)      shows k =  30

so   y = 30 x

now with x = -2

    y = 30 (-2) = -60

Answer:

10

please mark brainiest

Answer:

x = 2

Step-by-step explanation:

The measure of minor arc FD is 51x + 1

The measure of major arc FD is 360 - (51x + 1)

m<E = ½[m(major arc FD) - m(minor arc FD)]

36x + 5 = ½[360 - (51x + 1) - (51x + 1)]

72x + 10 = 360 - 51x - 1 - 51x - 1

174x = 348

x = 2

The first partial derivatives of z with respect to x and y in the equation x + sin(y + z) = 0 are ∂z/∂x = -1 and ∂z/∂y = -cos(y + z).

To find the first partial derivatives of z with respect to x and y, we need to differentiate the given implicit equation with respect to x and y while treating z as a function of x and y.

Differentiating the equation with respect to x:

∂/∂x (x + sin(y + z)) = 1 + ∂z/∂x

Differentiating the equation with respect to y:

∂/∂y (x + sin(y + z)) = cos(y + z) (1 + ∂z/∂y)

The term ∂z/∂x represents the partial derivative of z with respect to x, and ∂z/∂y represents the partial derivative of z with respect to y.

So, the first partial derivatives of z are:

∂z/∂x = -1

∂z/∂y = -cos(y + z)

These derivatives indicate how the variable z changes with respect to changes in x and y in the given equation x + sin(y + z) = 0. The value of -1 for ∂z/∂x means that for every unit increase in x, z decreases by 1. The value of -cos(y + z) for ∂z/∂y indicates how z changes with respect to changes in y, with the specific relationship determined by the trigonometric function cos(y + z).

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It will form scalene triangle

because it has different measures of sides

that is no equal side

may thishelps you

byr

Answer:

6 1/4

Step-by-step explanation:

1/2 = 2/4

2/4 + 3/4 = 5/4 which is 1 1/4 simplified.

Then add the whole numbers, 2 + 3 = 5

5 + 1 1/4 = 6 1/4

Tomas rides 6 1/4 miles everyday.

The future value of the mutual  fund after 15 years is equal to $1,256.55.

Given the following data:

To find the future value of the mutual  fund after 15 years:

Mathematically, compound interest is given by the formula:

\(A = P(1 + \frac{r}{n})^{nt}\)

Where;

Substituting the given parameters into the formula, we have;

\(A = 750(1 + 0.035)^{15}\\\\A = 750(1.035)^{15}\\\\A = 750(1.6754)\)

Future value, A = $1,256.55

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The measures for the similar and congruent triangles are given as follows:

35. m<A = m<D = 20.

36. m<B = m<E = 12.

37. BC = EF = 8.

38. AC = DF = 19.

The definitions of similarity and congruence are listed as follows:

Hence, for item 35, the value of x is obtained as follows:

x + 10 = 2x

2x - x = 10

x = 10.

Hence the measures are:

For item 36, the value of y is obtained as follows:

3y = 6y - 12

3y = 12

y = 4.

Hence:

3y = 3 x 4 = 12.

The value of z in item 37 is obtained as follows:

3z + 2 = z + 6

2z = 4

z = 2.

Hence the measures are:

z + 6 = 2 + 6 = 8.

The value of a in item 38 is obtained as follows:

7a + 5 = 5a + 9

2a = 4

a = 2.

Hence the measures are:

7a + 5 = 7 x 2 + 5 = 19.

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Low carbon steel is the most appropriate material for use as a frame for homemade go-karts.

Low carbon steel is the most common material used for the construction of homemade go-kart frames due to its many advantages. Firstly, low carbon steel is easy to manipulate and form, making it a popular choice for DIY projects such as go-kart frames.

Low carbon steel is also highly durable and can withstand significant impact and load-bearing weight, making it suitable for off-road and racing go-karts. Moreover, low carbon steel is highly resistant to corrosion, which is essential for go-karts that are often exposed to harsh outdoor elements.Finally, low carbon steel is an affordable material, making it an ideal choice for individuals on a budget. As a result, low carbon steel is the most appropriate material for use as a frame for homemade go-karts due to its ease of manipulation, durability, corrosion resistance, and affordability.

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Omg the legs are gonee

fr where are the legs

To ensure the best test results, Anita should be provided with the following information before her spirometry:

1. Instructions for taking the test: Anita should be thoroughly explained about how the spirometry test works and what steps she needs to follow. This includes taking a deep breath and blowing as hard as she can into the spirometer mouthpiece. It is important to emphasize that she needs to repeat this procedure a few times and take deep breaths between each exhale.

2. Emphasize the importance of taking medication as prescribed: Anita should be reminded of the importance of taking her medications as prescribed, including on the day of the test. It is crucial for her to bring her medications to the test appointment.

3. Avoid certain foods and drinks: Anita should be informed to avoid consuming certain substances before the spirometry test, such as caffeine, alcohol, and heavy meals. These can potentially affect the accuracy of the test results.

4. Arrive early for the test: Anita should be advised to arrive early for the test to allow herself sufficient time to relax and calm down before the procedure. This can help ensure more accurate results.

The rationale behind providing these instructions and information is that spirometry is a lung function test that measures the amount and speed of air being breathed in and out. By following the instructions and guidelines, Anita can achieve optimal results, aiding in the diagnosis and assessment of lung conditions.

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The solution to the system of equations  y= x²- 4 and y=-4  is (0,-4).

The given system of equations are y= x²- 4 ..(1)

and y=-4 ...(2)

Substitute y = -4 from the second equation into the first equation and solve for x:

-4 = x²- 4

x² = 0

x = 0

Now substitute x = 0 into either equation to solve for y:

y = 0² - 4 = -4

The solution to the system is (0,-4).

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Answer:

-x+8y-27

Step-by-step explanation:

-(x-8y+27)

so the sub symbol is kinda just 1 sense there isnt anything else for there

-1(x-8y+27)

now just like group them or smt

-1(x)+(-1)(-8y)+(-1x27)

so yea then tou multiply all of them and then

-x+8y-27

also

- x - = +

+ x + = +

- x + = -

Answer:

m arcRP = 125°

m arcQS = 125°

m arcSP = 55°

m arcQR = 55°

Step-by-step explanation:

An arc is the curve between two points on the circumference of a circle.

An arc measure equals its corresponding central angle measure.

Vertical Angles Theorem:  When two straight lines intersect, the opposite vertical angles are congruent.

Angles on a Straight Line Theorem:  The sum of angles formed on a straight line is equal to 180°.

As m∠ROP = 125°

Therefore, m arcRP = 125°

Given the measure of angle ROP is 125°, and an arc measure equals its corresponding central angle measure, the measure of arc RP is 125°.

Using the Vertical Angles Theorem:

⇒ m∠QOS = 125°

Therefore, m arcQS = 125°

Using the Vertical Angles Theorem, the measure of angle QOS is equal to the measure of angle ROP, so the measure of angle QOS is 125°. As an arc measure equals its corresponding central angle measure, the measure of arc QS is 125°.

Using the Angles on a Straight Line Theorem:

⇒ m∠SOP = 180° - 125° = 55°

Therefore, m arcSP = 55°

Using the Angles on a Straight Line Theorem, the measure of angle SOP is 55°. As an arc measure equals its corresponding central angle measure, the measure of arc SP is 55°.

Using the Angles on a Straight Line Theorem:

⇒ m∠QOR = 180° - 125° = 55°

Therefore, m arcQR = 55°

Using the Angles on a Straight Line Theorem, the measure of angle QOR is 55°. As an arc measure equals its corresponding central angle measure, the measure of arc QR is 55°.

Answer:

The equation of the axis of symmetry for a parabola of the form y = ax^2 + bx + c is given by the formula:

x = -b / 2a

In the case of the parabola y = x^2, a = 1 and b = 0, so the equation of the axis of symmetry is:

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

Therefore, the equation of the axis of symmetry for the parabola y = x^2 is simply:

x = 0

Since 0 is already an integer, there is no need to simplify it further.

Step-by-step explanation:

please follow me for more if you need any help

Answer:

9/10

Step-by-step explanation:

Convert: 3/5 * 6/5=18/25

Simplify and Round it towards 9/10

The measure of the angle 2 is 122°.

Given that angles 1 and 2 form a linear pair,

angle 1 + angle 2 = 180 degrees         —— (1)

We've also been notified that angle 2 is 6 times the size of angle 1.

That is to say: angle 2 = (2×angle 1) + 6      ———- (2)

Putting the angle 2 value in (1) from (2)

180 = angle 1 + 2×angle 1 + 6

3×angle 1 = 174

1st angle = 58 degrees  ———-(3)

(1) and (3) come from:

angle 2 + 58 = 180

2nd angle = 122 degrees

As a result, angle 2 has a measure of 122 degrees.

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(a)The population of interest is the entire university community at Botho University. (b)The sample is the random sample of 200 members. (c)The average time spent in the library, which is 30 minutes, is a statistic because it is computed from the sample and represents a characteristic of the sample, not the entire population.

a) The population of interest in this case would be the entire university community at Botho University. It includes all members of the university community who could potentially spend time in the library.

b) The sample in this case is the random sample of 200 members that was taken from the university community. It represents a subset of the population of interest and is used to make inferences about the larger population.

c) In this case, 30 minutes is a statistic, not a parameter.

A statistic is a value calculated from a sample that describes some characteristic of the sample. In this case, the average time spent in the library, which is 30 minutes, was computed from the sample of 200 members. It represents the average time spent in the library by the sampled members.

On the other hand, a parameter is a value that describes a characteristic of the population. Since the average time spent in the library is based on the sample and not the entire population, it cannot be considered a parameter.

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Answer: 28

Step-by-step explanation:        4+4+4+4+4+4+4=28 :)