Given that m/_a=40 and m/_b=61 find that the measure of angles x and y

P( A Student participates in Both sports and Drama) =0.07

The probability of an occurrence can be determined using the probability formula by simply dividing the favorable number of possibilities by the entire number of possible outcomes.

To find the probability that a student participates in both sports and drama:

Let

A =Student  participate in Sport

B = Student  participate in Drama

Thus we have:

P(A) = 0.42

P(B) = 0.25

and

P(Ac and B or A and Bc) =0.53

P(Ac and B ) + P( A and Bc) =0.53

P(B) - P(A and B) + P(A) - P(A and B) = 0.53

0.25 - P(A and B )  +  0.42 - P(A and B) = 0.53

0.25+0.42 - 2 * P( A and B) = 0.53

0.67 - 2 * P(A and B) = 0.53

0.67 - 0.53  = 2* P(A and B)

0.14  =  2 * P(A and B)

0.14 / 2  = P( A and B)

0.07 = P( A and B)

that is:

P( A and B) = 0.07

P( A Student  participate in Both sports and Drama) =0.07.

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The probability that a student participates in both sports and drama is [tex]0.14[/tex].

If [tex]A[/tex] and [tex]B[/tex] are any two events, then the probability of the joint event [tex](A\cup B)[/tex] is given by the following formula: [tex]P(A\cup B)=P(A)+P(B)-P(A\cap B)[/tex]

Given that 42% of the students participate in sports and 25% of the students participate in drama and 53% of the students participate in either sports or drama.

Suppose [tex]S[/tex] denotes that "a student participates in sports" and [tex]D[/tex] denotes that "a student participates in drama".
So, we have [tex]P(S)=\frac{42}{100}=0.42[/tex], [tex]P(D)=\frac{25}{100}=0.25[/tex], [tex]P(S\cup D)=\frac{53}{100}=0.53[/tex].

We want to find the probability that a student participates in both sports and drama i.e., we want to find [tex]P(S\cap D)[/tex].

By the above formula, we obtain:

[tex]P(S\cup D)=P(S)+P(D)-P(S\cap D)\\\Longrightarrow P(S\cap D)=P(S)+P(D)-P(S\cup D)\\\Longrightarrow P(S\cap D)=0.42+0.25-0.53\\\therefore P(S\cap D)=0.14=\frac{14}{100}[/tex]

Therefore, the probability that a student participates in both sports and drama is [tex]0.14[/tex].

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An exterior angle is equal to the sum of two non-adjacent interior angle of the triangle. Option B

The term triangle refers to a figure that has three sides. There are several types of triangles such as the;

Despite all these types of triangle, the basic geometric properties of triangles can be applied to all types of triangle that we have mentioned above.

Considering the question, an equation that could be used to represent one of the exterior angles and a logical conjecture about the exterior angles of a triangle is that; m<4 = m<1 + m<2. An exterior angle is equal to the sum of two non-adjacent interior angle of the triangle. Option B

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Based on the time taken by the jet when flying with the wind versus against it, the rate of the jet and jet streams are:

The speed of the jet flying against the wind is:

= 3,000 / 3

= 1,000 mph

The speed with the jet stream is:

= 5,360 / 4

= 1,340 mph

Assuming the speed of the jet is x and the rate of wind is y, the formulas are:

x - y = 1,000

x + y = 1,340

Solving gives:

2x = 2,340

x = 1,170 mph

The rate of jet stream is:

x - y = 1,000

1,170 - y = 1,000

y = 170 mph

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Answer: 5/36

Step-by-step explanation:

We conclude that 375 portions can be sold.

We know that 500 portions have been ordered, but only 5/6 of that was delivered, so the number of delivered portions is:

p = (5/6)*500 = 416.6

Which we can round to the next whole number, 417.

Now we know that 10% of these are given to the players and staff, then the number of portions that can be sold is the 90% of 417, which is:

N = 417*(90%/100%) = 417*0.9 = 375

We conclude that 375 portions can be sold.

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A  value of 24 is 2.5 standard deviations away from the mean

The given parameters about the distribution are:

Mean = 18

Standard deviation = 4

Value = 24

Let the number of standard deviations away from the mean be x.

The value of x is calculated using

Mean + Standard deviation * x = Value

Substitute the known values in the above equation

18 + 4 * x = 24

Subtract 18 from both sides of the equation

4 * x = 6

Divide both sides of the equation by 4

x = 1.5

Hence, a value of 24 is 2.5 standard deviations away from the mean

So, the complete parameters about the distribution are:

Mean = 18

Standard deviation = 4

Value = 24

24 is 2.5 standard deviations away from the mean

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Answer:

[tex]\sf b) \quad \dfrac{y^3}{4x}[/tex]

Explanation:

[tex]\sf \left(\dfrac{6x^2}{5y}\right) \left(?}\right) = \left(\dfrac{3xy^2}{10}\right)[/tex]

cross multiply variables

[tex]\sf ? = \left(\dfrac{3xy^2 (5y)}{10(6x^2)}\right)[/tex]

distribute inside parenthesis

[tex]\sf ? = \left(\dfrac{15xy^3}{60x^2}\right)[/tex]

remove parenthesis and simplify

[tex]\sf ? = \dfrac{y^3}{4x}[/tex]

Answer:

To solve the problem we have to take 4 percent of 5000 and multiply it by 8 years and the final result is 1600 dollars, which would be the final result.

Answer:

250.

Step-by-step explanation:

if one coin covers 1.14 cm, then the required number can be calculated according the equality:

required_number=(given_length/given_diameter);

Then:

[tex]number=\frac{2.85*100}{1.14} =\frac{285}{1.14} =250[coins].[/tex]

P.S. note, the given length is in [meter], the diameter is in [cm].

The y-intercept of the graph of y = x2 is shifted up 3 units.

The standard exponential equation is expressed as y = ab^x. Exponential equation is inverse of logarithmic equation.

Translations is a transformation technique that changes the position of an object from one point on the plane to another.

Given the parent function f(x) = x^2

If the function is shifted 3 units up, the function g(x) is derived by adding 3 to the function f(x). The resulting function is given as;

g(x) = f(x) + 3

g(x) = x^2 + 3

Hence the equation of the new graph g(x) is expressed as g(x) = x^2 + 3

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Answer:

Step-by-step explanation:

If it is not Monday, then there are students in the gym.

Negation: It is not Monday and there are not students in the gym.

Statement: It is Monday or there are students in the gym.

Equivalent: If there are not students in the gym, then it is Monday.

Neither: There are not students in the gym or it is not Monday.

Answer: C, E

Step-by-step explanation:

These are polynomials by the definition of a polynomial.

Answer:

x = - 4

Step-by-step explanation:

using the rule of indices

[tex]\frac{1}{a^{n} }[/tex] = [tex]a^{-n}[/tex] , then

[tex]3^{x}[/tex] = [tex]\frac{1}{81}[/tex] = [tex]\frac{1}{3^{4} }[/tex] = [tex]3^{-4}[/tex] , that is

[tex]3^{x}[/tex] = [tex]3^{-4}[/tex] , thus

x = - 4

Answer:

I think its A

Step-by-step explanation:

The probability that of 6 randomly selected patients, 4 will recover is 0.03295

The chance of an event occurring is defined by probability.

Because the favorable number of outcomes can never exceed the entire number of outcomes, the chance of an event occurring might range from 0 to 1. Additionally, the proportion of positive outcomes cannot be negative.

The ratio of good outcomes to all possible outcomes of an event is known as the probability.

Let X represent the binomial random variable that represents the patient count. Let p represent the likelihood that the patient will survive, and q represent the probability that they will pass away. The solution to the problem is q = 75% = 0.75, p = 25% = 0.25, and n = 6.

Required probability = 6C4[tex](0.25)^{4} (0.75)^{2}[/tex]

                                = 0.03295

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Answer:

Step-by-step explanation:

[tex]80.54=80+0.54=80+\frac{54}{100} =80+\frac{27}{50} =80\frac{27}{50}[/tex]

The probability that the value of p(x) is greater than 315 is 0.063754

From the question, the given parameters about the distribution are

The z-score of the data value is calculated using the following formula

z = (x - mean value)/standard deviation

Substitute the given parameters in the above equation

z = (315 - 283)/21

Evaluate the difference of 315 and 283

z = 32/21

Evaluate the quotient of 32 and 21

z = 1.524

The probability that the value of p(x) is greater than 315 is then calculated as:

P(x > 315) = P(z > 1.524)

From the z table of probabilities, we have;

P(x > 315) = 0.063754

Hence, the probability that the value of p(x) is greater than 315 is 0.063754

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Neil had 18 dimes, 6 nickels and 10 quarters saved up in his jar making a total of 460 pennies

An equation is an expression that shows the relationship between two or more numbers and variables.

In his piggy bank, Neil has three times as many dimes as nickels and he has four more quarters than nickels. The coins total are 4.60. How many of each coin does he have.

Let x represent dimes (0.1), y represent nickels (0.5) and z represent quarter (0.25)

Hence:

0.1x + 0.05y + 0.25z = 4.6   (1)

Also:

x = 3y   (2)

And:

z = y + 4  (3)

From the equations:

x = 18, y = 6, z = 10

Neil had 18 dimes, 6 nickels and 10 quarters saved up in his jar making a total of 460 pennies

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a. Let [tex]d[/tex] be the number of daytime calls Eshwa makes, and [tex]e[/tex] the number of evening calls. Then the cost [tex]C[/tex] (in pence) of making [tex]d+e[/tex] calls is

[tex]C = \boxed{50d + 40e}[/tex]

b. £1 = 100p, so the cost [tex]C'[/tex] (in £) is 1/100 of the cost found in part (a),

[tex]C' = \dfrac{50d + 40e}{100} = \boxed{\dfrac d2 + \dfrac{2e}5}[/tex]

c. If Eshwa makes 30 of each type of call in a month, then the total cost (in £) is

[tex]C' = \dfrac{30}2 + \dfrac{2\cdot30}5 = \boxed{27}[/tex]

c2. If Eshwa makes 20 daytime calls and 50 evening calls, then the total cost (in £) is

[tex]C' = \dfrac{20}2 + \dfrac{2\cdot50}5 = \boxed{30}[/tex]

d. Let [tex]e=40[/tex] and [tex]C'=42[/tex]. Solve for [tex]d[/tex].

[tex]42 = \dfrac d2 + \dfrac{2\cdot40}5[/tex]

[tex]42 = \dfrac d2 + 16[/tex]

[tex]\dfrac d2 = 26[/tex]

[tex]d = \boxed{52}[/tex]

Answer:

7.61577310586

Step-by-step explanation:

Pythagoras Theorem 7 squared + 3 squared= 49+9=58

[tex]\sqrt{58}[/tex]

First find volume of both the cylinders:

Cylinder Volume Formula: πr²h

(r => radius, h => height)

*Container A:

r = 8

h = 15

πr²h = π(8)²(15) = 960π³

*Container B:

r = 11

h = 13

πr²h = π(11)²(13) = 1573π³

What % of container B is empty after the pumping is complete?

The water pumped from A to B, and we want to know remaining that is empty: A < B: 1573π³- 960π³ = 613π³. Now to find %:

[tex]\frac{613\pi^{3} }{1573\pi ^{3}} * 100 = 0.39 * 100 =[/tex] 39% or 40% (Nearest Tenth)

Hope it helps!

Answer:

2^1 × 5^2 × 7^1 = 350

Step-by-step explanation:

2, 5, 7 are prime

first step is to divide the number 350 with the prime factor 2

continue dividing the number 175 by the next smallest prime factor

stop until you can't divide anymore

https://www.cuemath.com/numbers/factors-of-350/

Given the measure of side a, b and c of the triangle, the measure of angle C to the nearest tenth is 104.5°.

From the law of cosines;

cosC = ( a² + b² - c² ) / 2ab

Where C is the angle C and a, b, and c are the three sides of the triangle.

Given the data in the question;

Using law of cosine;

cosC = ( a² + b² - c² ) / 2ab

We substitute the values into the equation.

cosC = ( 2² + 3² - 4² ) / ( 2 × 2 × 3 )

cosC = ( 4 + 9 - 16 ) / ( 12 )

cosC = -3 / 12

cosC = -0.25

We find the inverse of cosine.

C = cos⁻¹( -0.25 )

C = 104.477°

C = 104.5°

Given the measure of side a, b and c of the triangle, the measure of angle C to the nearest tenth is 104.5°.

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Answer: C. 5.4 Blocks

Step-by-step explanation:

Given information

5 bags = 3 blocks

Set variable

Let x be the number of blocks

Constructure proportional equation

[tex]\frac{3}{5} } ~=~\frac{x}{9}[/tex]

Cross multiply the fraction

[tex](3)~*~(9)~=~(5)~*~(x)[/tex]

[tex]27~=~5x[/tex]

Divide 5 on both sides

[tex]27~/~5~=~5x~/~5[/tex]

[tex]\Large\boxed{x=5.4~blocks}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Answer:

oc

Step-by-step explanation:

5 times .6 equals 3

9 times .6 equals 5.4

Answer:

5,526

Step-by-step explanation:

Mean of scores = Total Value of Scores / Number of Values

= [tex]\frac{3820+5500+8560+4400+5350}{5} \\[/tex]

= 5,526

Answer:5526

Step-by-step explanation: Add everything up and divide by 5 because there are 5 numbers

The rule of the translation of point P(–5, –4) to point P′(–8, –7) is:

(x,y) -> (x - 3, y - 3).

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.

In this problem, from point P to point P', 3 was subtracted from both the x-coordinate and the y-coordinate, hence the rule is given by:

(x,y) -> (x - 3, y - 3).

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Following the instructions for the inequalities gives the following results:

1. 4<7, both sides multiplied by 7

= 28<49, both sides multiplied by 6

= 168<294, both sides multiplied by 3

= 504<882, both sides multiplied by 10

= 5,040<8,820

2. 11>2, add 5 to both sides

= 16>3, add 3 to both sides

= 19>9, add -4

= 15>5

3. -4<-2, subtract 6

= -10<-8, subtract 8

= -18<-16, subtract 2

= -20<-18

4. -8<8, divide by -4

= 2>-2, divide by -2

= -1<1

5. The inequalities remain correct at the end because the same mathematical operations are performed on both sides simultaneously.

Inequality is a relationship of a non-equal comparison between two numbers or algebraic expressions.

Inequality can be represented as greater than, greater than or equal to, less than, or less than or equal to.

Thus, the rules for inequalities show that if one adds to, subtracts from, multiplies by, or divides by the same number on both sides of an inequality, the inequality remains true.

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Answer:

-1

Step-by-step explanation:

0.35 - 0.8 = -0.45

-0.1 - 0.35 = -0.45

-0.55 - 0.45 = -1

Answer:

3 :8

Step-by-step explanation:

12 : 32 = 3:8

I believe that is right.

Answer:

(the figure is poorly drawn)

Step-by-step explanation:

find y

180 - 120 = 60°

find x

180 - 60 - 30 = 90°