A teacher has 14 senior students, 7 junior students, 4 sophmore, 5 freshmen, what is the proabability that she chooses a senior?

1) Difference of  the populations  of Germany and  Brazil = 1.16 X 10^8

2) Difference of  the populations  of Brazil and the  United States = 1.2 X 10^8

3) Sum of the  populations of  Brazil and  Germany = 2.76 X 10^8

4) Sum of the  populations of  the United States  and Brazil = 5.12 X 10^8

According to the statement

we have given that the populations of  three countries which are

United States is 3.16 × 10^8 and  Brazil is 1.96 × 10^8 and Germany is 8.0 × 10^7

And we have to arrange the sums and differences in increasing order of their values.

so, we have to find the

a) the difference of  the populations  of Germany and  Brazil

So,

Difference of  the populations  of Germany and  Brazil =  1.96 X 10^8 - 8 X 10^7 = 116000000 = 1.16 X 10^8

And then we have to find the

b) the sum of the  populations of  the United States  and Brazil

So,

Sum of the  populations of  the United States  and Brazil = 3.16 X 10^8 + 1.96 X 10^8 = 512000000 = 5.12 X 10^8

And then we have to find the

c) the difference of  the populations  of Brazil and the  United States

So,

Difference of  the populations  of Brazil and the  United States = 3.16 X 10^8 - 1.96 X 10^8 = 120000000 = 1.2 X 10^8

And then we have to find the

d) the sum of the  populations of  Brazil and  Germany

So,

Sum of the  populations of  Brazil and  Germany:  1.96 X 10^8 + 8 X 10^7 = 276000000 = 2.76 X 10^8

NOW, we arrange the sum and difference in increasing order of their values.

So,

1) Difference of  the populations  of Germany and  Brazil = 1.16 X 10^8

2) Difference of  the populations  of Brazil and the  United States = 1.2 X 10^8

3) Sum of the  populations of  Brazil and  Germany = 2.76 X 10^8

4) Sum of the  populations of  the United States  and Brazil = 5.12 X 10^8

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Answer:

The radius of the circle is 3 units. TRUE

The center of the circle lies on the x-axis. TRUE

The center of the circle lies on the y-axis. FALSE

The standard form of the equation is (x – 1)² + y² = 3. FALSE

The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9. TRUE

Step-by-step explanation:

x² + y² - 2x - 8 = 0

x² - 2x + y² = 8

Complete the square in x.

x² - 2x + 1 + y² = 9

(x - 1)² + y² = 3²

Center: (1, 0); radius: 3

The radius of the circle is 3 units. TRUE

The center of the circle lies on the x-axis. TRUE

The center of the circle lies on the y-axis. FALSE

The standard form of the equation is (x – 1)² + y² = 3. FALSE

The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9. TRUE

Answer:

d. x =0 or x = -6

Step-by-step explanation:

x(x + 6) = 0

This is telling us that either x is 0 or x is -6, because:

1) when x = 0, 0*(0+6)=0, and

2) when x = -6, -6*(-6+6) = 0;  -6(0) = 0

Answer:

y = 3x + 3

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 1, 0) and (x₂, y₂ ) = (0, 3) ← 2 points on the line

m = [tex]\frac{3-0}{0-(-1)}[/tex] = [tex]\frac{3}{0+1}[/tex] = [tex]\frac{3}{1}[/tex] = 3

the line crosses the y- axis at (0, 3 ) ⇒ c = 3

y = 3x + 3 ← equation of line

Answer:

y = 3x + 3

Step-by-step explanation:

See attached image.

The experimental probability that the subsequent booth competitor will receive a reward is 3/8.

The possibility of an event occurring is determined by probability.

The probability of the occurrence ranges from 0 to 1.

If the event doesn't happen, it = 0;

otherwise, it = 1.

For instance, the likelihood that it will storm on Sunday ranges from 0 to 1. If it storms, the event is given a value of 1. If it doesn't, the event is given a value of zero.

Depending on the outcome of a study that has been run several times, the experimental probability is calculated.

The number of winners in the games divided by the total number of competitors in those games determines the probability that the following competitor will earn a reward.

So, here the probability = 6/16 = 3/8 (by dividing both the numerator and the denominator by 2).

Therefore, the final solution is P= 3/8 .

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[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]

[tex]\qquad❖ \: \sf \:x = - \dfrac{ 9}{20} [/tex]

[tex]\textsf{ \underline{\underline{Steps to solve the problem} }:}[/tex]

[tex]\qquad❖ \: \sf \:2(3x + 1) + 3(5x + 2) = x - 1[/tex]

[tex]\qquad❖ \: \sf \:6x + 2 + 15x + 6 = x - 1[/tex]

[tex]\qquad❖ \: \sf \:(6x + 15x - x) + (2 + 6 + 1) = 0[/tex]

[tex]\qquad❖ \: \sf \:20x + 9 = 0[/tex]

[tex]\qquad❖ \: \sf \:20x = - 9[/tex]

[tex] \qquad \large \sf {Conclusion} : [/tex]

[tex]\qquad❖ \: \sf \:x =- \cfrac{ 9}{20} [/tex]

[tex]\huge\underline{\red{A}\green{n}\blue{s}\purple{w}\pink{e}\orange{r} →}[/tex]

Step-by-step explanation:

________________________________

→ 2(3x + 1) + 3(5x + 2) = x – 1

→ 6x + 2 + 15x + 6 = x – 1

→ 21x + 8 = x – 1

→ 21x – x = – 1 – 8

→ 20x = – 9

→ x = –9/20

________________________________

Answer:

Step-by-step explanation:

For two side measures and one angle measure to form one distinct triangle, the given angle must be between the given sides, or opposite the longest side.

When the given measures are ...

The given angle is opposite the longest side, so one distinct triangle can be formed.

No triangle can be formed if the given angle is opposite the shorter given side, and either of ...

__

Additional comment

As we can see from the above, the only ambiguous cases arise when the given angle is opposite the shorter given side. When that happens, the ratio of the shorter to longer given side relative to the sine of the given angle determines the nature of the solution:

Answer:

1

0

Step-by-step explanation:

The equation for the graphed function is (x+20)(x+5)(x-15).

It should be noted that a graph shows the relationship between variables.

From the graph, the equation is x³+10x²-275x-1500.

In this case, this can be  as - (x + 20)(x + 5)(x - 15)

The graph crosses the x axis. The coefficient is negative because the graph rises to the left.

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The direction of the difference between the 2 measurements.

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Answer: 18.7

Step-by-step explanation:

Find the lengths of AB, BC, and CA

AB = [tex]\sqrt{(4-(-1))^{2} + (-1-4)^{2} }[/tex] = 5[tex]\sqrt{2}[/tex] ≈ 7.1

BC = [tex]\sqrt{(0-(-1))^{2} + (-3-4)^{2} }[/tex] = 5[tex]\sqrt{2}[/tex] ≈ 7.1

CA = [tex]\sqrt{(0-4)^{2} + (-3-(-1))^{2} }[/tex] = 2[tex]\sqrt{5}[/tex] ≈ 4.5

7.1 + 7.1 + 4.5 = 18.7

Answer:

The longest side of room is 24m

Answer:

There are 24 frames of animation in 1 second of anime.    Step-by-step explanation:    There are 60 seconds in 1 minute, and 60 minutes in 1 hour. 60×60=3600, so there are 3600 seconds in 1 hour.Since 3600 seconds and 1 hour is the same, there are 86400 frames of animation in 3600 seconds of anime. To find out how many frames are in one second of anime, divide 86400 by 3600.86400 ÷ 3600 = 24There are 24 frames of animation in 1 second of anime.

If last week Salazar played 13 more tennis games than Perry and they played a combined total of 53 games, then Salazar played a total of 33 games.

Let the total number of games played by Perry be x.

It is given that, Salazar played 13 more tennis games than Perry.

⇒ Total games played by Salazar = x + 13

Also, Salazar and Perry played a combined of 53 games.

Hence, total number of tennis games played by Salazar and Perry = 53

⇒ Games played by Salazar + Games played by Perry = 53

⇒  x + (x + 13) = 53

2x + 13 = 53

2x = 53 - 13

2x = 40

x = 40 / 2

x = 20

Therefore, total number of games played by Salazar = x+13

= 20 + 13

= 33

Thus, Salazar played total 33 games.

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The rule which states that when two outcomes are independent, the probability that these outcomes occur together is the product of their individual probabilities is "Multiplicative rule".

The likelihood of both events A and B occurring, in accordance with the probability multiplication rule, is equal to the product of the probability of B occurring and the conditional probability of event A occurring given that event B occurs.

If A and B are dependent events, then the probability of both events occurring simultaneously is given by:

[tex]P(A \cap B)=P(B) \cdot P(A \mid B)[/tex]

The likelihood of both events occurring simultaneously in an experiment where A and B are two independent events is given by:

[tex]P(A \cap B)=P(A) \cdot P(B)[/tex]

Multiplication Theorem of Probability:

The multiplication guidelines that we use in probability have already been taught to us, including;

[tex]\begin{aligned}&P(A \cap B)=P(A) \times P(B \mid A) \text {; if } P(A) \neq 0 \\&P(A \cap B)=P(B) \times P(A \mid B) \text {; if } P(B) \neq 0\end{aligned}[/tex]

Therefore, the relationship between two events is explained by the probability multiplication rule.

Set AB represents the events in which both events A and B have occurred for two events A and B related to a sample space S.

Consequently, (AB) indicates that occurrences A and B happened at the same time. You can write the event AB as AB.

Using the characteristics of conditional probability, the likelihood of event AB is calculated.

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Jenna is correct and Billy is wrong because the equation was not converted to a quadratic form.

The form of quadratic equations is given as

ax2 + bx + c = 0

So, for the quadratic equation, we have

x² - x = 12

Let's make it into quadratic form

x² - x - 12 = 0

Bill solved it as

x(x - 1) = 12

This is wrong, because quadratic equations must be written in the form before solving for the variables

Jenna solved it as

x 2 - x - 12 = 0

Jenna is correct because she converted the equation to a quadratic form before solving for the variables.

Thus, Jenna is correct and Billy is wrong because the equation was not converted to a quadratic form.

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158/4 as a mixed number in the simplest term is  [tex]39\frac{3}{4}[/tex]

The given fraction is 158/4

The number of times that 158 can be divided by 4 = 39

4 x 39 = 156

The remainder = 159 - 156

The remainder = 3

The mixed number is of the form:

[tex]Quotient\frac{Remaider}{Divisor}[/tex]

Therefore, the mixed number is [tex]39\frac{3}{4}[/tex]

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The fraction based on the information given illustrated for each person.

Me: $14.89

Friend 1: $7.27

Friend 2: $25.67

Friend 3: $11.59

Total = $59.42

The fraction for each person will be:

Me: $14.89 = 14.89/59.42 = 0.25

Friend 1: $7.27 = 7.27/59.42 = 0.12

Friend 2: $25.67 = 25.67/59.42 = 0.32

Friend 3: $11.59 = 11.59/59.42 = 0.195

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The missing digit for the American Express Traveler's Check identification number is option (C) 6 is the correct answer.

In this question,

A Check Digit is a decimal (or alphanumeric) digit added to a number for the purpose of detecting the sorts of errors humans typically make on data entry.

A check digit is a digit added to a string of numbers for error detection purposes. Normally, the check digit is computed from the other digits in the string. A check digit helps digital systems detect changes when data is transferred from transmitter to receiver.

The last digit of a bar code number is a calculated check digit. The check digit is calculated from all the other numbers in the bar code and helps to confirm the integrity of your bar code number.

The American Express Traveler's Check identification number is 783920*814.

In Airline tickets, there are several digits plus a check digit.

Divide the ID number by 7. The check digit is the remainder.

Sum of digits = 7+8+3+9+2+0+8+1+4

⇒ 42

Now divide the sum by 7, the remainder is

⇒ 42 mod 7 = 42 - (5×7)

⇒ 42 mod 7 = 6

Hence we can conclude that the missing digit for the American Express Traveler's Check identification number is option (C) 6 is the correct answer.

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Use the rules of exponents to simplify the expression.

[tex]\large\displaystyle\text{$\begin{gathered}\sf \frac{g^{5}h^{4} }{g^{2}h^{3} } \end{gathered}$}[/tex]

To divide powers with the same base, subtract the exponent in the denominator from the exponent in the numerator.

Subtract 2 from 5.

Subtract 3 from 4.

For any term t, t¹ =t.

Therefore, the correct option is "B".

The distance from Jim's home to the gym is 12 km.

Speed is defined as the rate at which the position of object is changed.

Speed = Distance / Time

Here, there are two different speeds given for the same distance.

Average speed is the total distance travelled by the total time taken.

If distance is a constant,

Average speed = 2xy / (x + y), where x and y are two different speeds for the same distance.

Average speed = (2 × 15 × 10) / (15 + 10)

                          = 12 km/hr

So, Total distance travelled = Average speed × total time taken

                                              = 12 × 2

                                              = 24

Distance = 24 / 2 = 12

Hence, the distance from Jim's home to the gym is 12 km when average speed is taken.

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The factored expression of the polynomial is (4 - x)(5 + x)

The polynomial expression is given as;

20 - x - x^2

Expand the expression

20 - 5x + 4x - x^2

Factorize the expression

5(4 - x) + x(4 - x)

Factor out 4 - x

(4 - x)(5 + x)

Hence, the factored expression of the polynomial is (4 - x)(5 + x)

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Answer:

(3x − 1)(x 8)

Step-by-step explanation:

It is likely is it to snow tomorrow in the mountains is 1/4

A chance is the occurrence of events without apparent purpose or cause. It is simply the possibility that something will happen. When chance is defined in mathematics, it is called probability. Probability is the extent to which an event is likely to occur, measured by the ratio of favorable cases to the total number of possible cases. Mathematically, the probability that an event occurs is equal to the ratio of the number of cases favorable to a particular event to the number of all possible cases. The theoretical probability of an event is referred to as P(E). P(E) = number of outcomes more favorable to E/Nnumber of all possible outcomes of the experiment

We need to find that what is the chance that it will snow tomorrow in the mountains

According to the weather report, there is a 25% chance of snow in the mountains tomorrow.

Therefore the possible chance that it will snow tomorrow is 25/100 = 1/4

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We find that the function that could be a stretch of the exponential decay is [tex]f(x) = 2\cdot \left(\frac{1}{6} \right)^{x}[/tex]. (Correct choice: C)

Exponential functions are trascedent functions whose form is described below:

[tex]y = a\cdot r^{x}[/tex]     (1)

Where:

There are two conditions for a stretch factor and exponential decay: (i) a > 1, (ii) 0 < r < 1. Thus, we find that the function that could be a stretch of the exponential decay is [tex]f(x) = 2\cdot \left(\frac{1}{6} \right)^{x}[/tex]. (Correct choice: C)

The picture is missing and it cannot be found, but statement is still solvable as there is only one choice that responds the question.

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Answer:

[tex]l = 5.63 \\ [/tex]

hope this helps

The error in the steps is that In step 1, she should have also distributed -3/8  over –16d, to get 3 + 6 d + 2 d = 24

Given the following equation as shown below

-3/8(-8-16d)+2d = 24

Step 1 Distribute -3/8 over the expression in parentheses

3 + 6d + 2d = 24

Simply the like terms

3 + 8d = 24

Subtract 3 from both sides of the equation.

8d = 24 - 3

8d = 21

d = 21/8

Hence the error in the steps is that In step 1, she should have also distributed -3/8  over –16d, to get 3 + 6 d + 2 d = 24

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Answer: Anita's

Step-by-step explanation:

Anita's shape would have the longest sides because she only has 4 total sides, while the others have 5, 6, and 10

This means that if the total perimeter for each of the shapes was 10 units,

Anita's shape would have side lengths of about 2.5 units while the others would have side lengths of 2, 1.6, and 1 units.

This means Anita's shape has the longest sides

By critically observing the graph above, the amount of water in this pond at 0 hour is equal to 2,660 liters.

Similarly, the amount of water in this pond at 1 hour is equal to 3,225 liters.

Next, we would determine the rate of increase:

Rate = Δy/Δx

Rate = (3225 - 2660)/(1 - 0)

Rate = 665.

The amounts given in parts (b) and (c) are not equal because because the line doesn't pass through the origin (0, 0) of the graph.

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The value of a is -3 and the value of k is 10

A parabola is a U-shaped plane curve where any point is equidistant from a fixed point (known as the focus) and from a fixed line known as the directrix. The parabola is an integral part of the conic section topic

The section of a right circular cone by a plane parallel to the generator of the cone is a parabola. It is the location of a point that moves so that the distance from the fixed point (the focus) is equal to the distance from the fixed line (the directrix).

The fixed point is called the focus

A fixed line is called a directrix

Solving an algebraic equation is the process of finding a number or set of numbers that, when substituted for the variables in the equation, reduce them to an identity. Such a number is called the root of the equation

Here the equation y = a(x -2)^2 + k...........(1)

and two points A(1,7) and B(4, -2) is given

We need to find the value of a and k

Put A(1,7) in equation (1) , we get,

7 = a + k ,therefore k = 7 - a......(2)

Put B(4, -2) in equation (1), we get,

-2 = 4a + k........(3)

Put k= 7-a in (3)

-2 = 4a+7 -a

3a = -9

a= -3

From equation (2) , we get k = 7-(-3)= 10

Hence the value of k is 10 and the value of a is -3

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For the given points to lie on the parabola,

a = -3 and k = 10.

An equation of a curve that has a point on it that is equally spaced from a fixed point and a fixed line is referred to as a parabola. The parabola's fixed line and fixed point are together referred to as the directrix and focus, respectively. It's also crucial to remember that the fixed point is not located on the fixed line. A parabola is a locus of any point that is equally distant from a given point (focus) and a certain line (directrix).

According to the question,

Equation of parabola : y = a[tex](x-2)^{2}[/tex] + k

Points A(1,7) and B(4,-2)

For the points to lie on the parabola,

7 = a[tex](1-2)^{2}[/tex]+k

7 = a + k

Similarly,

-2 = a[tex](4-2)^{2}[/tex] + k

-2 = 4a + k

On solving the two equations simultaneously, we get,

a = -3

k = 10

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