We have 10 girls and 15 boys in our MATH 146 class. We have to select
two students randomly for a presentation at the 2023 math student research conference. What is the probability that both students chosen are boys?

The quadratic equation written in vertex form is:

A(x) = x^2 - 4

Here we want to find the vertex form of the quadratic equation:

A(x) = (x + 2)*(x - 2)

Remember that for a quadratic equation with the vertex (h, k) and leading coefficient a is written as:

f(x) = a*(x - h)^2 + k

Now, notice that the zeros of the quadratic function are x = -2 and x = 2.

Then the vertex is just between these two, at x = 0.

Then h = 0, and the y-value of the vertex is what we get when we evaluate in x = 0.

k = (0 + 2)*(0 - 2) = 2*-2 = -4

Then the vertex is (0, -4) and the leading coefficient is 1, we can write the quadratic equation as:

A(x) = (x - 0)^2 -4

A(x) = x^2 - 4

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The equivalent expression is 9b^6/a^4c^6

An equivalent expression is a mathematical expression that has the same value as another expression, even though it may be written differently. Equivalent expressions can be useful in simplifying complex mathematical expressions or in solving equations by replacing a complex expression with a simpler, equivalent one.

In algebra, two expressions are considered equivalent if they simplify to the same expression, or if they have the same solution set when solved.

We have that;

(-3ab^2c^-3/a^3b^-1)^2

9a^2b^4c^-6/a^6b^-2

9a^-4b^6c^-6

9b^6/a^4c^6

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Answer:

D.

Step-by-step explanation:

Nikolas did not make a mistake. The formula to calculate volume of a triangular prism is

[tex]V=Bh[/tex]

where B is the area of the base and h is the height.

The area of the triangular base is [tex](0/5)(5.8)(6.2) = 17.98[/tex].

[tex]Bh = 17.98 * 9.2 = 165.416 ft^3[/tex]

Answer:

Step-by-step explanation:

Post a link to the paper then i will edit it and send it back and then give you the answers on the paper you share with me

The correct proportion for corresponding sides is option C.

In geometry, corresponding sides are sides of two or more geometric figures that are in the same relative position, shape, and orientation. More specifically, corresponding sides are sides that are opposite or facing each other in congruent or similar figures. Corresponding sides have the same length and are parallel to each other. For example, if we have two congruent triangles, the corresponding sides of each triangle are the sides that are opposite to the same angle in both triangles. Similarly, if we have two similar polygons, the corresponding sides of each polygon are the sides that have the same relative position, shape, and orientation in both polygons. Corresponding sides can be used to determine whether two figures are congruent or similar, as well as to find the length of unknown sides in geometric figures using proportions.

For example, consider two similar triangles ABC and DEF. The sides of triangle ABC are AB, BC, and AC, while the corresponding sides of triangle DEF are DE, EF, and DF. The side AB corresponds to the side DE, the side BC corresponds to the side EF, and the side AC corresponds to the side DF. The ratios of the lengths of corresponding sides are equal:

AB/DE = BC/EF = AC/DF

This property of corresponding sides is important in solving problems involving similar figures, such as finding missing side lengths or areas. By setting up and solving ratios of corresponding sides, we can determine the relationship between the sizes of the figures and their corresponding parts.

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Answer:

A=Alternate angles are equal

B=Alternate angles are equal

C=Angles which make a straight line sum to 180°

Step-by-step explanation:

A and B: if two lines are parallel and are intersected by a line then the angles on the opposite sides are equal to each other

C: a flat line is equal to 180 degrees

Answer:

X. Alternate angles are equal.

Y. Alternate angles are equal

Z. Angles on a straight line add up to 180°

triangles are similar, angles are all the same or congruent.

Check the picture below.

yes, it is direct proportion becuz in direct proportion if the prize of one quantity increases the other too will have to increase. here in this question as you can see 5melons were costing 3.50 and on increasing it to 7 melons cost is too increasing soo it is a direct proportion.

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The solution to the given expression [tex]\frac{6x + 5 - 3x + 16}{3} \cdot \frac{15}{5}[/tex] when simplified is 3x + 21.

To simplify the expression [tex]\frac{6x + 5 - 3x + 16}{3} \cdot \frac{15}{5}[/tex],

We can first combine like terms in the numerator to get [tex]\frac{3x + 21}{3}[/tex]

We can then simplify this further by dividing both the numerator and denominator by 3, which gives us x + 7 in the numerator.

Next, we can simplify the fraction 15/5 by dividing both the numerator and denominator by 5, which gives us 3

So, we have

[tex]\frac{6x + 5 - 3x + 16}{3} \cdot \frac{15}{5} = \frac{3x + 21}{3} \cdot 3[/tex]

[tex]\frac{6x + 5 - 3x + 16}{3} \cdot \frac{15}{5} = 3x + 21[/tex]

Hence, [tex]\frac{6x + 5 - 3x + 16}{3} \cdot \frac{15}{5}[/tex] simplifies to 3x + 21.

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Complete question

Simplify (6x + 5 - 3x + 16)/3 * 15/5

The equation for c in terms of p is c = (9/7)p. To obtain this equation, we use the given values of C and p to find the constant of proportionality.

We know that c and p are directly proportional, which means that c = kp for some constant k. We can find k by plugging in the given values:

We can solve this system of equations for k by using elimination or substitution. Solving for k, we get

Thus, the equation for c in terms of p is

c = (9/7)p.

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Answer:

x = 3[tex]\sqrt{2}[/tex] , y = [tex]\frac{3\sqrt{2} }{2}[/tex]

Step-by-step explanation:

this is a 90- 45- 45 isosceles triangle with legs congruent , that is

y = [tex]\frac{3\sqrt{2} }{2}[/tex]

using Pythagoras' identity in the right triangle

x² = ( [tex]\frac{3\sqrt{2} }{2}[/tex] )² + y²

   = ( [tex]\frac{3\sqrt{2} }{2}[/tex] )² + ( [tex]\frac{3\sqrt{2} }{2}[/tex] )² = 9 + 9 = 18 ( take square root of both sides )

x = [tex]\sqrt{18}[/tex] = [tex]\sqrt{9(2)}[/tex] = [tex]\sqrt{9}[/tex] × [tex]\sqrt{2}[/tex] = 3[tex]\sqrt{2}[/tex]

[tex]\textit{area of a semicircle}\\\\ A=\cfrac{\pi r^2}{2} ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ A=0.1413 \end{cases}\implies 0.1413=\cfrac{\pi r^2}{2}\implies 0.2826=\pi r^2 \\\\\\ \cfrac{0.2826}{\pi }=r^2\implies \sqrt{\cfrac{0.2826}{\pi }}=r\implies 0.30\approx r[/tex]

Answer:

The answer would not be 0, it would be -12, and here is why.

4x^4+ 16x+31x^2=62x-90.

In thia case i ignpored the variable, i think its a variable..

You woulkd add 62+16, you get 78.

78-90= -12

upper limit with 3

To obtain the upper limit with 3 decimal places, use the following formula for the confidence interval with a population mean.In this case, n = 18, sample mean = 34.8, sample standard deviation = 9.05, and confidence level = 99%. {z }_{\frac{\alpha}{2}}=\frac{\text{critical value}}{\sqrt{n}}Therefore, 99% confidence interval is {34.8 ± 3.053}. The upper limit of the confidence interval is obtained as 34.8 + 3.053 = 37.853 (rounded to three decimal places). Therefore, the upper limit with three decimal places is 37.853.A confidence interval is an estimated range of scores or values used to estimate the true population value. A confidence interval provides a range of values within which the true value is expected to fall with a certain degree of confidence. In the given question, we have to find the upper limit with 3 decimal places.

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Sam is 10 years old, and Gina is 15 years old.

Here's a table to represent the situation:

Person ║   Age

Sam      ║    x

Gina     ║    x+5

In this table, the first column lists the two people in the situation, Sam and Gina. The second column shows their ages in years. According to the problem statement, Gina is 5 years older than Sam, so we can represent Gina's age as x + 5, where x is Sam's age.

To find the solution, we need to use the information given in the problem statement to solve for x, which represents Sam's age. We know that Gina's age is x + 5, so we can set up an equation:

Gina's age = Sam's age + 5

x + 5 = x + 5

Simplifying the equation, we can see that x cancels out:

x + 5 - x = 5

5 = 5

This equation is always true, which means that there are infinitely many possible solutions. However, we can find a specific solution if we are given additional information. For example, if we are told that Gina is 15 years old, we can substitute x + 5 = 15 into the equation and solve for x:

x + 5 = 15

x = 10

Therefore, Sam is 10 years old, and Gina is 15 years old.

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4

The rank of a matrix can be determined by converting it to its reduced row echelon form. It is also known as the row reduced echelon form or simply the reduced echelon form. The rank of a matrix is the number of non-zero rows in its reduced row echelon form. The given matrix is,

`A=[[2,3,-1,-1],[1,-1,-2,-4],[3,1,3,-2],[6,3,0,-7]]`

We need to convert the given matrix to its reduced row echelon form. It is done by applying elementary row operations on the matrix. The elementary row operations are as follows:

- Interchange the order of two rows.
- Multiply a row by a non-zero scalar.
- Add a multiple of one row to another row.

Let us apply these operations on the given matrix,

`[[2,3,-1,-1],[1,-1,-2,-4],[3,1,3,-2],[6,3,0,-7]]`

`= [R1, R2, R3, R4]`

`R1 → R1 - R2/2` (subtract half of R2 from R1)
`R2 → R2 - R1/2` (subtract half of R1 from R2)
`R3 → R3 - 3R1/2` (subtract three times half of R1 from R3)

`[[1,5/2,1/2,1/2],[0,-3/2,-5/2,-9/2],[0,-7/2,3/2,-7/2],[0,0,-3,-6]]`

`= [R1, R2, R3, R4]`

`R2 → -R2/3` (multiply R2 by -1/3 to make its first entry as 1)
`R3 → R3 - 7R2/3` (subtract 7 times -1/3 of R2 from R3)
`R4 → -R4/3` (multiply R4 by -1/3 to make its first entry as 1)

`[[1,5/2,1/2,1/2],[0,1,5/3,3/2],[0,0,-4/3,-4],[0,0,1,2]]`

`= [R1, R2, R3, R4]`

`R3 → -3R3/4` (multiply R3 by -3/4 to make its third entry as 1)

`[[1,5/2,1/2,1/2],[0,1,5/3,3/2],[0,0,1,1],[0,0,1,2]]`

`= [R1, R2, R3, R4]`

`R4 → R4 - R3` (subtract R3 from R4 to make its third entry as 0)

`[[1,5/2,1/2,1/2],[0,1,5/3,3/2],[0,0,1,1],[0,0,0,1]]`

`= [R1, R2, R3, R4]`

The given matrix is converted to its reduced row echelon form. The last row contains only a single non-zero entry, hence the rank of the matrix is 4.

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Answer: Let's denote the two unknown angles as x and y.

We know that the sum of the three angles in a triangle is 180 degrees. So we can set up the following equation:

10 + 3x + 14x = 180

Simplifying the equation:

17x = 170

x = 10

Now we can use the ratio of the other two angles to find the value of y:

3:14 can be simplified as 3x:14x or x:4.67x

So y is 4.67 times larger than x:

y = 4.67x = 4.67(10) = 46.7

Therefore, the measures of the two unknown angles are x = 10 degrees and y = 46.7 degrees.

Step-by-step explanation:

The measure of the remaining two angles are 46.7

The angle sum property of a triangle states that the sum of interior angles of a triangle is 180°

Given here, One angle of a triangle measures 100°. the other two angles are in a ratio of 3:14. Then let the measure of the angles be 3x and 14x

thus using the angle sum property we have

[tex]3x+14x=80[/tex]

[tex]17x= 80[/tex]

[tex]x = 46.7[/tex]

Hence, The measure of the remaining two angles are 46.7

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Answer: The transformations that occurred to create g(x) = -2(x-8)²-81+7 from f(x) = x are:

- Horizontal translation 8 units to the right: The term (x - 8) in the equation of g(x) means that the graph of g(x) has been shifted horizontally 8 units to the right compared to f(x) = x.

- Vertical stretch by a factor of 2: The coefficient -2 in front of the term (x - 8)² means that the graph of g(x) has been vertically stretched by a factor of 2 compared to f(x) = x.

- Vertical translation 81 units down and 7 units up: The terms -81 and +7 in the equation of g(x) mean that the graph of g(x) has been shifted vertically 81 units down and then 7 units up compared to f(x) = x.

Therefore, the correct answer is (a) vertical translation 7 units up.

Step-by-step explanation:

Answer:

When you rewrite a percent as a decimal, you need to move the decimal point two places to the left because a percent is a ratio that compares a number to 100. For example, 50% is the same as 50/100 or 0.5. To convert 50% to a decimal, you need to divide 50 by 100, which gives you 0.5. Moving the decimal point two places to the left achieves the same result.

Similarly, when you rewrite a decimal as a percent, you need to move the decimal point two places to the right because a percent expresses a number as a fraction of 100. For example, 0.75 is the same as 75/100 or 75%. To convert 0.75 to a percent, you need to multiply it by 100, which gives you 75. Moving the decimal point two places to the right achieves the same result.

Step-by-step explanation:

There is a 1.8 N difference between the two forces

To find the difference between the size of the forces applied to two areas with different pressures, we need to use the formula:

Force = Pressure x Area

For the first force, with a pressure of 90 N/m² and an area of 0.09 m², the force can be calculated as:

Force1 = 90 N/m² x 0.09 m² = 8.1 N

For the second force, with a pressure of 70 N/m² and the same area of 0.09 m², the force can be calculated as:

Force2 = 70 N/m² x 0.09 m² = 6.3 N

Therefore, the difference between the size of the two forces is:

Force1 - Force2 = 8.1 N - 6.3 N = 1.8 N

So, the difference between the two forces is 1.8 N. The force with the higher pressure applies a larger force to the area, resulting in a larger force being applied overall.

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Thus, a. 0.09 and b. 0.43 are the correct answers to this question. We must study a bit about set theory in order to understand this.

A and B are the two sites that are accessible. As A and B are both distinct entities, they are both exploring oil at different locations.

Oil is discovered at the site

A with a probability of P(A) = 0.25, and oil is discovered at the site

B with a probability of P(B) = 0.36.

In two iterations of the experiment, when they are separate entities, they do not change the likelihood that others will happen.

a. Probability of oil found at both the sites = P(A ∩ B)

P(A ∩ B)=[tex]P(A)*P(B)=0.25*0.36=0.09[/tex]

b. Now if A finds oil in site A and not in site B  and B finds oil in site B and does not find oil in site A,

[tex]P(A')=1-P(A)=1-0.25=0.75[/tex]

[tex]P(B')=1-P(b)=1-0.36=0.64[/tex]

P(A ∩ B') ∪ (A' ∩ B)=P(A ∩ B')+P(A' ∩ B)

=[tex][P(A)*P(B')][/tex] + [tex][P(A')*P(B)][/tex]

=[tex](0.25*0.65)+(0.75*0.37)[/tex]

=0.16+0.27=0.43

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The constant proportionality is 15, which means that for every box of candy, there are 15 pieces of candy. The equation is 15x.

A variable in mathematics is a sign that denotes a value that may vary, as opposed to a constant, which is a set number that never changes. Variables are used to represent unknown or changing quantities, such as time (t) or the distance (d) travelled by an item, whereas constants are used to represent fixed numerical values, such as pi or the speed of light (c). In contrast to variables, which are often represented by lowercase letters, constants are typically represented by capital letters. In mathematical equations and formulae, the distinction between constants and variables establishes which values are fixed and which values are subject to change.

The slope of line is given as:

m = (change in y) / (change in x)

Substitute the values from the table:

m = (135 - 150) / (9 - 10) = -15/-1 = 15

For the equation to be of the form y = mx we have:

y = mx + b

150 = 15(10) + b

b = 0

Substituting the values the equation is:

y = 15x

Hence, the constant proportionality is 15, which means that for every box of candy, there are 15 pieces of candy. The equation is 15x.

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Therefore , the solution of the given problem of area comes out to be 4-cm by 8-cm rectangle, we can keep adding rows of four-square units.

Its total size can be determined by figuring out how much room would be required to completely cover the outside. The surroundings are also taken into consideration when determining this same surface that has a trapezoidal shape. Something's total dimensions are determined by its surface area. The volume of water that a cuboid can contain inside depends on the number of edges that are present between its four trapezoidal extremities.

Here,

A 4-cm by 8-cm rectangle has an area

=> 4⋅8=32

square centimetres when its length and breadth are multiplied. Starting with a row of four tiny squares,

we can then layer another row of four tiny squares on top of it. We now have a total of 8 tiny squares, which together measure 4 by 2 centimetres.

Then, after the first two rows, add a third row of four little squares to complete the procedure.

We now have a total of 12 little squares, which together make a rectangle measuring 4 centimetre by 3 cm.

Up until we have 32 small squares in total, which make up the complete 4-cm by 8-cm rectangle, we can keep adding rows of four-square units.

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Slope AB = slope CD = 1/1 and slope BC ≠ slope DA. Therefore, AB and CD are parallel sides, and ABCD is a trapezoid.

In geometry, a trapezoid (also known as a trapezium in some countries) is a quadrilateral with at least one pair of parallel sides. The parallel sides are called the bases of the trapezoid, and the other two sides are called the legs.

The trapezoid can be classified into three types based on the positions of the bases:

Isosceles trapezoid: A trapezoid in which the non-parallel sides are congruent.

Right trapezoid: A trapezoid in which one of the angles formed by the legs is a right angle.

Scalene trapezoid: A trapezoid in which none of the sides are congruent.

The area of a trapezoid can be calculated by the formula:

A = (b1 + b2)h/2

where b1 and b2 are the lengths of the bases and h is the height of the trapezoid (the perpendicular distance between the bases).

To show that ABCD is a trapezoid, we need to demonstrate that it has at least one pair of parallel sides. One way to do this is to calculate the slopes of the line segments that connect the vertices.

The slope of a line passing through two points (x1, y1) and (x2, y2) is given by:

slope = (y2 - y1) / (x2 - x1)

Using this formula, we can calculate the slopes of the four line segments:

slope AB = (4 - 1) / (2 - (-1)) = 3/3 = 1

slope BC = (1 - 4) / (3 - 2) = -3/1 = -3

slope CD = (-3 - 1) / (-3 - 3) = -4/-6 = 2/3

slope DA = (1 - (-3)) / (-1 - (-3)) = 4/2 = 2

We can see that slope AB = slope CD = 1/1 and slope BC ≠ slope DA. Therefore, AB and CD are parallel sides, and ABCD is a trapezoid.

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Answer:

189 chips are estimated to be in the bag.

Step-by-step explanation:

Mass of Chips = Mass of Chips + Bag - Mass of Bag

Mass of Chips = 369 g - 28 g

Mass of Chips = 341 g

Mass of 1 Chip = Mass of 25 Chips / 25

Mass of 1 Chip = 45 g / 25

Mass of 1 Chip = 1.8 g

Number of Chips = Mass of Chips / Mass of 1 Chip

Number of Chips = 341 g / 1.8 g

Number of Chips ≈ 189

Answer:

[tex]4t^{2}+4t-35[/tex]

Step-by-step explanation:

[tex](2t+7)(2t-5)\\4t^{2}-10t+14t-35\\4t^{2}+4t-35[/tex]

The expression [tex]-100^5 + 90[/tex] is completely factored as [tex]-(10^5 + 3)(10^5 - 3)[/tex].

Mathematical expressiοns cοnsist οf at least twο numbers οr variables, at least οne arithmetic οperatiοn, and a statement. It's pοssible tο multiply, divide, add, οr subtract with this mathematical οperatiοn.

The expression [tex]-100^5 + 90[/tex] can be factοred as follows -

Grοup the negative sign with the first term -

[tex]= -(100^5) + 90[/tex]

Evaluate [tex]100^5[/tex] as [tex](10^2)^5 = 10^{10}[/tex] -

[tex]= -(10^{10}) + 90[/tex]

Factor οut a negative sign -

[tex]= -(10^{10} - 90)[/tex]

Factor the difference of twο squares, where [tex]a = 10^5[/tex] and b = 3 -

[tex]= -(10^5 + 3)(10^5 - 3)[/tex]

Therefore, the expressiοn is factored as [tex]-(10^5 + 3)(10^5 - 3)[/tex].

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The expression that correctly represents the statement "the product of 4 and a number, n, subtracted from 10" is 10 - 4n.

In general, a statement is a declarative sentence that is either true or false. It is a sentence that makes a claim or assertion about something, and it can be either a simple statement or a complex one.

The statement "the product of 4 and a number, n, subtracted from 10" is an example of a mathematical expression that involves a variable, which is represented by the letter "n". In this expression, we are asked to find the difference between the number 10 and the product of 4 and the variable "n".

To simplify this expression, we can use the order of operations, which tells us to perform the multiplication before subtraction. Therefore, we first multiply 4 and n to get the product of 4n. Then, we subtract that product from 10 to get the final expression:

[tex]$10 - 4n$[/tex]

This expression represents the result of subtracting the product of 4 and the variable "n" from the number 10. We can evaluate this expression for different values of "n" to find the corresponding result. For example, if we substitute "n" with 2, we get:

[tex]$10 - 4(2) = 10 - 8 = 2$[/tex]

This means that when "n" is equal to 2, the result of subtracting the product of 4 and "n" from 10 is equal to 2. Similarly, we can substitute different values of "n" into the expression to find their corresponding results.

Therefore, The expression that correctly represents the statement "the product of 4 and a number, n, subtracted from 10" is 10 - 4n.

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When we solve for x and z if bc =ad, We can start by cross-multiplying to get rid of the denominators: d(a+bz) = b(c+d)z + ac, then the linear equation has infinitely many solutions for any values of x and z.

Multiplying both sides by (a + b)(d + c) to remove  the denominators, we get:

(a + bz)(d + c) = (c + dz)(a + b)

If z = 0, then we can substitute back into the original equation and solve for x:

a/b = (c - 1)/(1 - c).

thus, the solutions are:

If bc =ad, then the equation has infinitely many solutions for any values of x and z.

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The points (7,9), (9,7), (0,6), (3,8), (7,5), (8,3), (6,0), (9,10), (5,2), and (2,5) can be represented in a table with two columns - one for the x-coordinate and one for the y-coordinate. This format is useful for organizing and manipulating data, but it does not provide a visual representation of the location of the points.

On the other hand, a coordinate plane is a visual tool that allows us to plot and view the location of points in two-dimensional space. The x-axis and y-axis intersect at the origin (0,0), and each point is represented by a unique combination of x and y coordinates. This format is particularly useful for understanding the relationships and patterns among the points.

A table lists the coordinates of points in a tabular format, a coordinate plane allows us to plot and visualize the location of points in two-dimensional space.

Representing points in a table and in a coordinate plane are two common ways to visually display data. While a table lists the coordinates of points in a tabular format, a coordinate plane is a graphical representation that allows us to plot and visualize the location of points in two-dimensional space.

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