ten students are taking both algebra and drafting. there are $24$ students taking algebra. there are $11$ students who are taking drafting only. how many students are taking algebra or drafting but not both?

The time taken to finish the race is 3.49 hours

Speed is defined as. The rate of change of position of an object in any direction. Speed is measured as the ratio of distance to the time in which the distance was covered.

Given,

The total distance = 500 miles

The speed = 143.187 mph

We know, Speed = Distance / Time

Time = Distance / Speed

Substitute the values

Time = [tex]\frac{500}{143.187}=3.49[/tex] hours

Hence, the time taken to finish the race is 3.49 hours

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Answer:Your answer is 10.5

Step-by-step explanation:Multiply 3.5 by 3 and you get 10.5.

The probability of person being a heavy smoker given person died is 0.57 .

Baye's Theorem helps in finding the probability of any event A given that event B has already occurred.

For Example the probability of event A given that event B has already occurred is denoted by

[tex]P(A/B)=\frac{P(B/A)P(A)}{P(B)}[/tex]

In the given question

Let H denoted heavy smokers , L denote Light smokers , N denote Non smokers.

Given the probability of non smokers P(N) = 50%=0.5

the probability of light smokers P(L)=20%=0.2

the probability of heavy smokers P(H)=30%=0.3

let P(D/H) denoted the person died given he was a heavy smoker.

let P(D/L) denoted the person died given he was a light smoker.

let P(D/N) denoted the person died given that he was a non smoker.

According to question

"heavy smokers twice as likely to die as light smokers" means

P(D/H)=2P(D/L)......(1)

and "light smokers twice as likely to die as nonsmokers" means

P(D/L)=2P(D/N)

On simplifying we get

[tex]P(D/N)=\frac{1}{2} P(D/L)\\ \\ P(D/N)=0.5 P(D/L)[/tex].....(2)

According to Baye's Theorem

[tex]P(H/D)=\frac{P(D/H)P(H)}{P(D/N)P(N)+P(D/L)P(L)+P(D/H)P(H)}[/tex]

Substituting values of P(D/H) from ...(1) and values of P(D/N) from ....(2)

we get [tex]P(H/D)=\frac{2*P(D/L)P(H)}{0.5*P(D/L)P(N)+P(D/L)P(L)+2*P(D/L)P(H)}[/tex]

taking P(D/L) common from each term

[tex]P(H/D)=\frac{P(D/L)}{P(D/L)} (\frac{2*P(H)}{0.5*P(N)+P(L)+2*P(H)})[/tex]

[tex]P(H/D)= (\frac{2*P(H)}{0.5*P(N)+P(L)+2*P(H)})[/tex]

Substituting the values of P(N), P(H), P(L) from above we get

[tex]P(H/D)= (\frac{2*(0.3)}{0.5*(0.5)+(0.2)+2*(0.3)})[/tex]

[tex]P(H/D)= (\frac{0.6}{0.25+0.2+0.6})[/tex]

=[tex]\frac{0.6}{1.05}=0.57[/tex]

Therefore , the probability of person being a heavy smoker given person died is 0.57 .

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Answer: 6[tex]a^{2}[/tex]+a-12

Step-by-step explanation:

First, you want to distribute (2a+3)(3a-4) ---> 2a(3a-4) + 3a(3a-4)

That will get you 6[tex]a^{2}[/tex]-8a+9a-12

Next, you will want to combine like terms to get 6[tex]a^{2}[/tex]+a-12

Since you cannot simplify that any further, 6[tex]a^{2}[/tex]+a-12 is your answer.

The percentage of Americans over the age of 65 has increased while the percentage of Americans under the age of 18 has decreased .

The United Stats of America is one of the countries that is known to have a very good health care system. This implies that, there has ben a very huge improvement in the health care of the population of the United States.

As a result of this improvement in the healthcare of the people of the United States, the percentage of Americans over the age of 65 has increased while the percentage of Americans under the age of 18 has decreased .

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Answer:

7/9

Step-by-step explanation:

Combine the two variables: 9p = 7

Then do 7 / 9

Simplify: (-12c⁵) (3c⁴)=36c⁹.

Given that

To find

So, according to the question

We have,

To convert it in simplest form we have to use mathematically operations of powers.

           = (-12c⁵) (3c⁴)

Now, separate the numerical and variable parts from equation

           = (-12 ×3) c⁵× c⁴

Now, from using the mathematically operations of powers, to add powers, and multiply 12 with 3.

∵ [tex]a^m\times a^n = a^{m+n}[/tex]

∴[tex]c^5\times c^4 = c^{5+4}[/tex]

           = (-36) c⁵⁺⁴

          = (-36) c⁹

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Answer:

Step-by-step explanation:

5 x 2 = 10

Pretty sure this is right but I'm not 100 percent sure!

Answer: 10P ==> A

Step-by-step explanation:

5 · P · 2= 5 · 2 · P      ==> Commutative property of multiplication

5 · 2 · P=

10 · P=10P ==> A

Answer:

The Correct answer is 21.78 meters

Step-by-step explanation:

Simply divide 326.7 ÷ 15 and it will leave you with 21.78

A function that has been transformed by the given transformations is y = -f(x - 3) + 2

The transformation are given as:

Let the equation of the parent function be

y = f(x)

So, we have the following transformations

Shifted right 3 units

The transformation rule is

(x, y) = (x - 3, y)

So, we have:

y = f(x - 3)

Shifted up 2 units

The transformation rule is

(x, y) = (x, y + 2)

So, we have:

y = f(x - 3) + 2

Reflected about the x-axis

The transformation rule is

(x, y) = (x, -y)

So, we have:

y = -f(x - 3) + 2

Hence, a function that has been transformed by the given transformations is y = -f(x - 3) + 2

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The required positive five-digit integer of the form ab,cba; which should be divisible by 11 is 87,978

Explain the divisibility test of 11.

For a number to be divisible by 11, the difference between the sum of its odd digits (1st, 3rd, 5th...) and the sum of its even digits (2nd, 4th...) must be divisible by 11.

Calculation for the positive five-digit integer of the form ab,cba to be divisible by 11

Required 5 digit number is of the form, ab,cba

Using the divisibility test of 11, we get

(b + b) - (a + c + a) to be divisible by 11

i.e. 2b - (2a + c) to be divisible by 11

Replacing ab,cba using the greatest numbers, such as 7, 8 and 9 and checking its divisibility with 11

78,987 = 2*8 - (2*7 + 9) = 16 - (14 + 9) = 16 - 23 = -7 NO

87,978 = 2*7 - (2*8 + 9) = 14 - (16 + 9) = 14 - 25 = -11 YES

79,897 = 2*9 - (2*7 + 8) = 18 - (14 + 8) = 18 - 22 = -4 NO

97,879 = 2*7 - (2*9 + 8) = 14 - (18 + 8) = 14 - 26 = -12 NO

89,798 = 2*9 - (2*8 + 7) = 18 - (16 + 7) = 18 - 23 = -5 NO

98,789 = 2*8 - (2*9 + 7) = 16 - (18 + 7) = 16 - 25 = -9 NO

Thus, a positive 5-digit number is 87,978

Hence, the required positive five-digit integer of the form ab,cba; which should be divisible by 11 is 87,978

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Answer:

x = 16

Step-by-step explanation:

A scatter plot is also referred to as scatter chart, scatter diagram or scattergram and it can be defined as a type of graph which is used for the graphical representation of the values of two (2) variables, with the resulting points showing any association (correlation) between the data set.

A quadratic function can be defined as a mathematical expression (equation) that can be used to define and represent the relationship that exists between two or more variable on a graph.

In Mathematics, the standard form of a quadratic equation is given by;

ax² + bx + c = 0

By critically observing the graph (see attachment) which models the data in the given table, we can infer and logically deduce that the polynomial function is given by:

y = -0.4908x² + 5.8845x + 1.3572

For the number of students that are absent 10 days after the outbreak, we have:

y = -0.4908(10)² + 5.8845(10) + 1.3572

y = -0.4908(100) + 58.845 + 1.3572

y = -49.08 + 58.845 + 1.3572

y = 11.12 ≈ 11 students.

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Answer:

B: All real numbers

Step-by-step explanation:

Check the attached image for explanation.

Answer:

Step-by-step explanation:

Just divide four into sixteen. You should get x=4. To check, multiply 4 by 4 (4 x 4), and you should get 16.

Answer:

-x - 3y + 2

Step-by-step explanation:

sorry explain to long if you want it here a pic

There are 5 11 pointer questions and 15 3 pointer questions

We are given that total points of the test is 100

The test contains questions of two markings 3 points and 11 points

It is given that the total number of questions is 20

Let the number of three pointer questions be 'x' and the number of 11 pointer questions be 'y'

Thus total number of questions=x + y =20

Now the total sum of all the points comes to 100

Therefore,

3x+11y =100

x + y =20

x= 20-y

Now putting the value of x in the other question,

3(20-y) +11y =100

60-3y +11y=100

8y=100-60

8y=40

y=5

Thus x=20-y=20-5=15

Thus there are 5 11 pointer questions and 15 3 pointer questions

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Answer: BC=14

Subtract AC by AB. Just learned this in Geomatry.

The binomial is a unique type of discrete random variable. If ALL four of the following conditions are met, our experiment is a binomial experiment: it consists of n identical trials.

One of the two outcomes, known as success or failure, arises from every try. From trial to trial, the likelihood of success, given by the symbol, stays constant. There are n independent trials. The binomial distribution is a probability distribution that summarizes the possibility that a value will take one of two independent values under a given set of parameters or assumptions, which means the result of each trial has no bearing on the results of the others. The fundamental presumptions of the binomial distribution are that there is only one possible result for each trial, that each trial has the same success probability, and that each trial is independent of the others or mutually exclusive.

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Answer:

Step-by-step explanation

Mikhail is 37

Gabrielle is 30

37+30= 67

(Refer to the table given below)

So,

Then,

Therefore,

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Answer:

2.1

Step-by-step explanation:

The area of the frame is D. 252 in².

It should be noted that the frame 2 inches wide surrounds a painting that is 18 inches wide and 14 inches tall.

The area will be:

= Length × Width

= 18 × 14

= 252 in²

The area is 252 inches².

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Answer: c

Step-by-step explanation: it is a rational number because it repeats

Answer: 44%

Step-by-step explanation:

To find the percentage of students who do not travel by car, we first need to find the total number of students.

14 + 11 = 25

So out of the total of 25 students, 11 do not travel by car, so to find that percentage we will divide the number that do not travel by car by the total number.

11/25 = 0.44

We have the percentage as a decimal. To convert the decimal to a percent we multiply it by 100.

0.44 x 100 = 44%

The least to greatest will  [ ( - 1 ) ^ 5 ] < [ 3 ^ ( - 6 ) < 0.1 < ( 10 ^ 0 ) < ( 5 ^ 1 ) < ( 3 ^ 6 ) .

( - 1 ) ^ 5 , 3 ^ ( - 6 ) , 3 ^ 6 , 5 ^ 1 , 10 ^ 0 , 0.1

Simplifying each of them

( - 1 )  ^ 5 = - 1

3 ^ ( - 6 ) = 0.001

3 ^ 6 = 729

5 ^ 1 = 5

10 ^ 0 = 1

0.1   = 0.1

Least to greatest = - 1 < 0.001 < 0.1 < 1 < 5 < 729

                            = [ ( - 1 ) ^ 5 ] < [ 3 ^ ( - 6 ) < 0.1 < ( 10 ^ 0 ) < ( 5 ^ 1 ) < ( 3 ^ 6 )

Hence , least to greatest will  [ ( - 1 ) ^ 5 ] < [ 3 ^ ( - 6 ) < 0.1 < ( 10 ^ 0 ) < ( 5 ^ 1 ) < ( 3 ^ 6 ) .

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Answer:

Step-by-step explanation:

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Answer:

6°

Step-by-step explanation:

It started at -2°f and increased b 8° so 2 of those degrees get you back to 0°f and the remains is 6 so 6°

Thus, the equation of the line of reflection,

x=2 and x=4

When a point on a line segment divides it into two segments, the formula used to determine the coordinates of that point is known as the section formula.

It is given that,

A=(7,6)

A'=(-1,6),

B=(5,5)

and B'=(1,5),

As, the mid point of vertices of figure to the corresponding vertices of  reflected figure should lie on reflected line.

Since, Δ ABC is reflected to Δ A'B'C' through this line,

Let, Q be the mid point of  line AA', using section formula

Coordinate of Q = ((7-(-1))/2 , (6-6)/2 )

                       Q = (4,0)

and R be the mid point of line BB', using section formula

Coordinate of R = Q = ((5-1)/2 , (5-5)/2 )

                       Q = (2,0)

Q and R lies on the line of the reflection,

Thus, the equation of the line of reflection,

x=2 and x=4

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