The mean marks of a class was 70%. There are 30 students. 20 are boys the boys meen mark 62%. What is the mean mark for the girl.​

The probability that more than a minute foes by without a hit is  0.0498.

Let X denote the waiting time in minutes until the next hit.

From the question, we have

The probability density function of exponential distribution is,

f(x)=λe^(-λ*)        λ>0

Probability =

P(X>1) =∫_1^∞  3e^(-3x) dx

=3(e^(-3z)/(-3))_1^∞

=e^(-3)

=0.0498

Probability = 0.0498

Probability:

Possibility is referred to as probability. This branch of mathematics deals with the occurrence of a random event. The value's range is 0 to 1. Probability has been applied into mathematics to predict the likelihood of different events. Probability generally refers to the degree to which something is likely to occur. This fundamental theory of probability, which also applies to the probability distribution, can help you comprehend the possible outcomes for a random experiment. Gonna determine how likely something is to occur, use probability. Many things are hard to predict with 100% certainty. We can only anticipate the possibility of an event occurring using it, or how likely it is.

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The area of the region bounded by the curves is 1 - cos(1) square units.

The given curves are y = arcsin(x)/4, y = 0, and x = 4.

We can solve for x in the first curve as:

x = sin(4y)

The area of the region bounded by the curves y = arcsin(x)/4, y = 0, and x = 4 is 1 - cos(1) square units.

The area of the region bounded by the curves can be found by integrating the difference between the curves with respect to y, from y = 0 to y = 1/4 (since arcsin(1) = pi/2, and 1/4 of pi/2 is pi/8):

Area = ∫[0,1/4] (4x - 0) dy

= ∫[0,1/4] (4sin(4y)) dy

= -cos(4y)|[0,1/4]

= -cos(1) + 1

Therefore, the area of the region bounded by the curves is 1 - cos(1) square units.

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Answer:

8 and 4

Step-by-step explanation:

Answer:

8+4

Step-by-step explanation:

8-4 is equal to 4 and 4+8 is equal to 12

Answer:

C. y = ⁶/5x + ⁷/2

Step-by-step explanation:

First, find the slope of line AB that goes through A(3, 1) and B(-3, 6):

\( slope(m) = \frac{y_2 - y_1}{x_2 - x_1} = \frac{6 - 1}{-3 - 3} = \frac{5}{-6} \).

Slope of line AB = -⅚.

The slope of the line that is a perpendicular bisector of line AB will be a negative reciprocal of the slope of line AB.

Thus:

Negative reciprocal of -⅚ = ⁶/5. (Reciprocal of ⅚, also the sign will change from positive to negative).

Next is to find the y-intercept, b, of the line.

To do this, you need to find the midpoint where the two lines intersect:

Therefore,

Midpoint (M) of AB, for A(3, 1) and B(-3, 6) is given as:

\( M(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}) \)

Let \( A(3, 1) = (x_1, y_1) \)

\( B(-3, 6) = (x_2, y_2) \)

Thus:

\( M(\frac{3 +(-3)}{2}, \frac{1 + 6}{2}) \)

\( M(\frac{0}{2}, \frac{7}{2}) \)

\( M(0, \frac{7}{2}) \)

Substitute x = 0, y = ⁷/2, and m = ⁶/5 into y = mx + b and find the value of b.

⁷/2 = ⁶/5(0) + b

⁷/2 = b

b = ⁷/2

The slope (m) and the y-intercept, b, of the line we are looking for are ⁶/5 and ⁷/2, respectively.

Therefore, substitute m = ⁶/5 and b = ⁷/2 into y = mx + b.

y = ⁶/5x + ⁷/2

The equation that is the perpendicular bisector of the line AB is y = ⁶/5x + ⁷/2.

Answer:

DO IT YOURSELF

Step-by-step explanation:

(b)

The 50 degree angle and angle b are vertical angles, which means they are congruent.

The 50 degree angle and angle c are a linear pair, which means that they are supplementary/add up to 180 degrees.

Angles a and c are vertical angles, which means they are congruent.

a = 130

b = 50

c = 130

(c)

The 90 degree angle and angle b are vertical angles, which means they are congruent.

The 50 degree angle and angle c are vertical angles, which means they are congruent.

The 50 degree angle, 90 degree angle, and angle d all form a line, which means that they are supplementary and add up to 180.

Angle d and angle a are vertical angles, which means they are congruent.

a = 40

b = 90

c = 50

d = 40

(e)

The measure of a circle is 360 degrees. These three angles form a circle, so therefore if we add them all up, they will equal 360 degrees.

3a + 4a + 5a = 360

12a = 360

a = 30

(f)

The measure of a circle is 360 degrees. These four angles form a circle, so therefore if we add them all up, they will equal 360 degrees.

3a + 4a + 5a + 6a = 360

18a = 360

a = 20

Hope this helps!! :)

The sum of the reciprocals of all the positive factors of the perfect number 28 is 2.

A factor is a number that divides another number by itself and leaves no residue. In other words, if multiplying two whole numbers yields a product, the numbers being multiplied are factors of the result since the product is divisible by them. Factors may be found using two methods: multiplication and division. Factors are numbers that may be multiplied together to get another number.

Here,

The sum of the reciprocals of all the perfect number 28's positive elements is 2.

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See below for the proof of the equation \(\frac{ax + by}{x + y} - \frac{ax - by}{x - y}= 2(a - b)\)

The equation is given as:

\(\frac{ax + by}{x + y} - \frac{ax - by}{x - y}= 2(a - b)\)

Take the LCM

\(\frac{(ax + by)(x - y) -(ax - by)(x + y)}{(x + y)(x - y)}= 2(a - b)\)

Expand

\(\frac{ax^2 - axy + bxy - by^2 -ax^2 - axy + bxy + by^2}{(x + y)(x - y)}= 2(a - b)\)

Evaluate the like terms

\(\frac{-2axy + 2bxy }{(x + y)(x - y)}= 2(a - b)\)

Rewrite as:

\(\frac{-2axy + 2bxy }{x^2 - y^2}= 2(a - b)\)

Factorize the numerator

\(\frac{2(a - b)(x^2 - y^2)}{x^2 - y^2}= 2(a - b)\)

Divide

2(a - b)= 2(a - b)

Both sides are equal

Hence, the equation \(\frac{ax + by}{x + y} - \frac{ax - by}{x - y}= 2(a - b)\) has been proved

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Equation: y * 5 = 85

In this equation, 'y' represents the number of learners in class 9T, and '5' represents the number of pencils each learner receives. The equation states that the product of the number of learners (y) and the number of pencils each learner receives (5) is equal to the total number of pencils (85) that Mrs. Leclerc shares among the learners.

This equation can be used to solve for the value of 'y' by dividing both sides of the equation by 5. By doing so, we can determine the number of learners in class 9T based on the given information about the number of pencils shared.

For example, if we divide 85 by 5, the result is 17. Therefore, there are 17 learners in class 9T.

In summary, the equation y * 5 = 85 represents the situation where Mrs. Leclerc shares 85 pencils between the learners in class 9T, with each learner receiving 5 pencils. By solving the equation, we can find the number of learners in the class, which in this case is 17.

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The expressions given in option A and option C on solving will have same value 3/2 or 1.5.

Numeric values can be obtained through the evaluation of numeric expressions, which consist of a mixture of numeric components including variables, numbers or functions, and operators. A blend of arrays and mathematical operators can be present within an expression to derive a numeric solution.

Now solving numerical expressions in the problem (refer to image attached)

A. \(\frac{1}{6} +(\frac{5}{6}+\frac{3}{6} ) = \frac{1+5+3}{6} = \frac{9}{6} =\frac{3}{2} =1.5\)

B. \(\frac{1}{3}+ \frac{5}{3}+ \frac{2}{3} =\frac{1+5+2}{3} =\frac{9}{3} =3\)

C. \(\frac{3}{5} +(\frac{1}{2} +\frac{2}{5} )=\frac{15}{10} =\frac{3}{2} =1.5\)

D. \(2+\frac{1}{2} =\frac{4+1}{2} =\frac{5}{2} =2.5\)

Hence, expressions in option A and option C have same values

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The length of segment AD of the pyramid is approximately 4.95 units.

Since ACD is a right square pyramid, we know that triangle ACD is a right triangle, with DC as its hypotenuse.

Using the Pythagoras theorem, we can write:

AD² + AC² = DC²

Since AC is the length of one side of the square base of the pyramid, and all sides of a square are equal, we know that

AC = DC ÷ √2.

Substituting this into the equation above, we get:

AD² + (DC ÷ √2)² = DC²

Simplifying this equation, we get:

AD² = DC² - (DC ÷ √2)²

AD² = DC² - DC² ÷ 2

AD² = DC² ÷ 2

Now we can substitute the given value of DC into this equation and solve for AD:

AD² = 7² ÷ 2

AD² = 24.5

AD = 4.95

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The correct question is:

A right square pyramid ACD has a height of 24 units. The length of line segment DC is 7 units. Enter the length of segment AD.

The vertical asymptote of the functions are x = 4 and x = -1

asymptote, a line or curve that serves as the boundary of another line or curve in mathematics. An example of an asymptotic curve is a descending curve that approaches but does not reach the horizontal axis, which is the asymptote of the curve.

At the edges of the coordinate plane, the curve approaches lines known as asymptotes. When the denominator of a rational function gets close to zero, vertical asymptotes happen. Since it would divide by zero, a rational function cannot cross a vertical asymptote.

According to the question:-

Let us take

f (x) = (x + 2) / (x ^ 2 - 3x - 4)

The first thing you should know in this situation is that the function is not specified for vertical asymptotes.

For those values that set the denominator to 0, the function is not defined.

The result is: x 2 - 3 x - 4 = 0.

We factor to seek for the roots.

(x-4) * (x + 1) = 0

These are the roots: x1 = 4; x2 = -1.

Hence the desired solution is x1 = 4; x2 = -1.

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A proton has a mass of \($$1.6726 * 10^{-24}\) g corresponds to 1.0072766 Atomic Mass Unit

A proton exists 1836.096 times heavier than an electron.

Proton Mass = 938.2720813 \($$MeV/c_2\)

Electron = 0.5109989461 \($$MeV/c_2\)

E : P Ratio = 1 : 1836.15267

\($$m_{p\) = mass of a proton (1.007277 AMU)

\($$m_n\) = mass of a neutron (1.008665 AMU)

\($$m_e\) = mass of an electron (0.000548597 AMU)

\($$m_{atom}\) = mass of nuclide (AMU)

A proton has a mass of \($$1.6726 * 10^{-24}\) g corresponds to 1.0072766 Atomic Mass Unit

[AMU, Atomic Mass Unit exists utilized to describe atomic and molecular weights, equivalent to one-twelfth of the mass of an atom of carbon-12].

Whereas, the Electron exists at \($$9.1093 * 10^{-28}\) equaling 0.000548597 AMU.

Electron to Proton Ratio = 1: (0.000548597 / 1.0072766)

= 1836.096

A proton exists 1836.096 times heavier than an electron.

Proton Mass = 938.2720813 \($$MeV/c_2\) (MeV= Mega Electron Volt)

(As per Mass - the energy equivalence principle, energy exists proportional to mass whereby, an electron volt exists also as a unit of Mass. Energy can be converted to Momentum and Mass)

Electron = 0.5109989461 \($$MeV/c_2\)

E : P Ratio = 1 : 1836.15267

Therefore, the correct answer is E : P Ratio = 1: 1836.15267.

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Step-by-step explanation:

The opposite side has a length of 5 and the hypotenuse has a length of 10. Therefore, the answer is 5/10.

The value of sin(30°) is 1/2 from the given triangle. Therefore, option A is the correct answer.

The sides and angles of a right-angled triangle are dealt with in Trigonometry. The ratios of acute angles are called trigonometric ratios of angles. The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec).

From the given triangle, RQ=5 units, QS=10 units and RS=5√3 units.

sin(30°)= 5/10

= 1/2

Therefore, option A is the correct answer.

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The number of people who waited at least 6 minutes is given as follows:

50 people.

The height of each bin of the histogram represents the number of observations of the data-set in the desired interval.

The desired outcomes for this problem are given as follows:

Hence the number of people who waited at least 6 minutes is given as follows:

20 + 15 + 10 + 5 = 50 people.

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Answer:

Slope-intercept: y = -3x + 3

Standard: 3x + y = 3

Step-by-step explanation:

Given (0,3) and (1,0)

Slope m = (y2-y1)/(x2-x1)

m = (0 - 3)/(1 - 0)

m = -3/1 = -3

Slope-intercept: y = mx + b

using (1,0)

0 = -3(1) + b

0 = -3 + b

b = 3

so y = -3x + 3

Slope-intercept: y = -3x + 3

Standard: 3x + y = 3

A sample statistic is a numerical measure of a sample size, and it can vary from sample to sample.

In order to calculate a sample statistic, one must first select a sample. This sample is the group of data points that will be used to calculate the statistic. Once the sample is selected, the data values must be measured and recorded. After that, the data must be organized in whatever way is necessary to perform the calculation. Finally, the calculation can be completed with the appropriate formulas or algorithms. This process must be repeated for each sample statistic that needs to be calculated. Sample statistics can vary from sample to sample because different samples have different values, and the calculation of the statistic will be different depending on the values of the sample.

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The baker needs to use 100/3 pounds of 90% chocolate to make the cake.

An equation is an expression used to show the relationship between two or more numbers and variables.

Let x represent the amount of 90% chocolate. Using equation:

100 * 70% + x * 90% = (x + 100) * 75%

100 * 0.7 + 0.9 * x = (x + 100) * 0.75

70 + 0.9x = 0.75x + 75

x = 100/3

The baker needs to use 100/3 pounds of 90% chocolate to make the cake.

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Answer:

100/3 pounds

Step-by-step explanation:

Types of cardioid are Standard cardioid, Nephroid, Limacon, Deltoid, astroid, hypocycloid, and epitrochoid, each with its own unique properties and applications in mathematics and science.

A cardioid is a geometric shape that is formed by tracing a point on a circle as it rotates around another circle of the same size. There are several types of cardioids, each with its own unique properties and characteristics.

Standard cardioid: This is the most common type of cardioid and is formed by tracing a point on a circle as it rotates around another circle of the same size, with the point always being twice as far from the center of the second circle as it is from the center of the first circle.

Nephroid: This is a type of cardioid that is formed by tracing a point on a circle as it rotates around another circle that is twice its size. The name "nephroid" comes from the Greek word "nephros," which means kidney, as the shape of the curve resembles a kidney.

Limacon: This is a type of cardioid that is formed by tracing a point on a circle as it rotates around another circle that is slightly larger than itself. The shape of the curve resembles a figure eight.

Deltoid: This is a type of cardioid that is formed by tracing a point on a circle as it rotates around another circle that is three times its size. The shape of the curve resembles a triangle.

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The probability that Delta Airlines will receive no complaints on a given day can be calculated using the average number of complaints per day, which is 2.5.

To find the probability of receiving no complaints on a given day, we can use the concept of a Poisson distribution. The Poisson distribution is commonly used to model the occurrence of rare events over a fixed interval. In this case, the average rate of complaints is given as 2.5 per day.

The probability of receiving no complaints can be calculated using the formula P(X = 0) = e^(-λ) where λ is the average rate. Substituting λ = 2.5 into the formula, we have P(X = 0) = e^(-2.5).

Using a calculator or a computer program, we can calculate the value of e^(-2.5) to find the probability. The result will be the probability that Delta Airlines will receive no complaints on a given day.

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Answer:

D 10/18

Step-by-step explanation:

when you divide the top and bottom by 2, you get 5/9 which is 5:9 not 5:8

Answer:

10 out of 18 as it is giving 5:9

Answer:

The percentage increase is 78.72%

Step-by-step explanation:

Here, we want to calculate a percentage increase

We proceed to use the mathematical relation as follows;

Percentage increase = (new value - old value)/old value * 100%

new value is value in 2011 = 252

old value is value in 2006 = 141

Substituting these values, we have;

(252-141)/141 * 100%

= 111/141 * 100%

= 78.72%

The outcomes that satisfy event A are A = {3, 6}. These are the numbers on which the die can land to fulfill the condition of being a multiple of 3.

The study of probabilities, which are determined by the ratio of favorable occurrences to probable cases, is known as probability.

In the given sample space S = {1, 2, 3, 4, 5, 6}, we have all the possible outcomes when rolling a six-sided die.

The event A is defined as "The die lands on a multiple of 3." Multiples of 3 in the given sample space are 3 and 6 since these numbers can be divided evenly by 3 without any remainder.

Therefore, A = 3, 6 is the set of outcomes that satisfy event A. These are the possible outcomes for the die to land on in order to satisfy the requirement of being a multiple of 3.

The complete question is:

Consider rolling a six-sided die, numbered 1-6. Whatever number lands face up is your score. Fill in the missing value to describe the sample space of a single roll of the dice: S = {1, 2 , 3, 4, 5, 6} And suppose you were interested in the event A = The die lands on a multiple of 3. Fill in the blanks to show all the outcomes which satisfy A:

A = {_ , _ }

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Answer:

59

Step-by-step explanation:

all triangles add up to 180 degrees.

add 87+34=121

do 180-121=59 because you want to find the value of x

to check your work add up all of the degrees together and when you get 180 you will be correct!

Answer:

x=59

Step-by-step explanation:

87+x+34=180 because its a straight line

121+x=180

x=59

Answer:

ok we know that volume of a sphere is 4/3 pi r cubed so just replace the letters with the entities given

Answer:

2.7 cm

Step-by-step explanation:

Individual song : $0.50

Album : $4

Money available: $15

Equation: (Part 2)

0.50s+4a =15

The product of the number of songs and the cost per song, plus the product of the number of albums and the cost per album must be equal to the money available-

Part 1.

6 songs and 3 albums

6 (0.50)+4 a = 15

Solve for a

4a = 15-3

4a=12

a=12/4

a=3

1 album and 22 songs

0.50s+4(1)=15

0.50s =15-4

0.50s =11

s=11/0.50

s= 22

30 songs and 0 albums

0.50 (30)+4 a = 15

4a=15-15

4a= 0

Part 3.

Answer:

n=0

Step-by-step explanation:

Answer:

2756/53 = 52

52 = 520 to the nearest tenth

52 = 52 to the nearest hundredth

52 = 52 to the nearest thousandth

= 0 to the nearest tenth

= 0 to the nearest hundredth

= 0 to the nearest thousandth

Step-by-step explanation:

I hope this helps you in some way.

Answer: c. -6+4i

Step-by-step explanation:

edge2020

Answer:

C: –6 + 4i

Step-by-step explanation:

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