In a class, we have 61 students of different majors. There are 23 chemistry majors (C), 12 math majors (M), 9 engineering majors (E), and 17 students who are undecided (U). Of these students, 4 of them have declared both math and engineering majors. A student will randomly be chosen to win a scholarship. Find the probability of awarding the scholarship to a student who is either a math major or an engineering major. 0.0290 0.7213 0.2787 0.3443

The values of x = 17 and y = 0.

Define quadratic equation?

A quadratic equation is a second-degree polynomial equation in one variable of the form a + b + c = 0, where a, b, and c are constants and x is the variable. The term "quadratic" comes from the Latin word "quadratus", which means square.

Given:

[tex]x^{4} - 8x^{2} y^{2} +16y^{4} -289[/tex] equals to 0

[tex]x^{4} - 8x^{2} y^{2} +16y^{4} -289 = 0[/tex]

[tex]x^{4} - 8x^{2} y^{2} +16y^{4} =289[/tex]

We know that [tex](x-b)^{2} =x^{2} -2xy +y^{2}[/tex]

Compare it: [tex](x^{2} -4y^{2} )^{2} = x^{4} - 8x^{2} y^{2} +16y^{4}[/tex]

So, [tex](x^{2} -4y^{2} )^{2} = 289[/tex]

[tex](x^{2} -4y^{2} ) = 17[/tex]

We know that [tex](x^{2} -b^{2} ) = (x+y)(x-y)[/tex]

So, [tex](x +2y)(x-2y) =17[/tex]

If we solve two equations that is:

(x+2y) = 17 and  (x-2y) = 17

Simplification, x = 17 and y = 0

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The answer to the equation will be 5, and in the second one the answer to the equation when the value of t is 4 resulted as 14We can evaluate the expression "2 + 3t" for the given values of t:

a. When we consider T as 1 then the substitution can be = 1 as the expression

2 + 3t = 2 + 3(1) = 2 + 3 = 5

Therefore, the value of the expression when t is 1 is 5. to the expression of 2+3t.

b. We substitute t = 4 in the expression and get:

2 + 3t = 2 + 3(4) = 2 + 12 = 14

Therefore, the value of the expression when t is 4 is 14. The value can be 14 when its value is 4.

In the first scenario, the answer to the equation will be 5, and in the second one the answer to the equation when the value of t is 4 resulted as 14. if we give any other number the value changes accordingly.

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The correct question of the answer is

Here is an expression: 2 + 3t

a. Evaluate the expression when t is 1.

b. Evaluate the expression when t is 4.

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Answer:

Step-by-step explanation:

all the lengths are the same:

ST = √(-1-2)²+(2-7)² = √9+25 = √34 = 5.831

TU = √(4--1)²+(-1-2)² = √25+9 = √34 = 5.831

UV = √(7-4)²+(4--1)² = √9+25 = √34 = 5.831

VS = √(2-7)²+(4-7)² = √25+9 = √34 = 5.831

The shape is a square (rectangle with equal sides) parallelogram (you could also call it a rhombus)

The measurement of WX in the given figure is 22.

When a set οf numbers is sοrted in size οrder, the median is the middle value. It is used tο define a set οf data by identifying the numerical midpοint and is a measure οf central tendency. When a grοup οf numbers is οrganized frοm smallest tο largest, the middle number is the οne that shοws up.

A trapezοid's median is the line that divides it intο twο equal sectiοns. The middle line οr the midline is anοther name fοr it. Its length is equal tο the average οf the twο bases οf the trapezοid and runs parallel tο thοse bases.

In the given trapezοid STUV, the length οf the bases ST and UV can be calculated by dividing the median in twο parts and fοlding it and jοining tο tο make a lοng rectangle.

Now the new rectangle is WW'SU where the median was 2wx

In a rectangle opposite side are equal, Therefore

W'W = US

W'W = 2WX

US = UV + ST

= 16 +28

= 44

2WX = 44

WX = 44/2

WX = 22

Thus, The measurement of WX in the given figure is 22.

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1/3(r³) and (r³)/3 are equivalent expressions because division is commutative and both expressions result in dividing r³ by 3.

What is expression ?

In mathematics, an expression is a combination of one or more numbers, variables, and operators that can be evaluated to produce a value.

Yes, 1/3(r³) and (r³)/3 are equivalent expressions.

This is because division is commutative, meaning that it doesn't matter in which order we divide the numbers. So, we can write (r³)/3 as (1/3)(r³), which is equivalent to 1/3(r³).

In both cases, we are dividing r³ by 3, and the result is the same. Therefore, 1/3(r³) and (r³)/3 are equivalent expressions.

1/3(r³) and (r³)/3 are equivalent expressions because division is commutative and both expressions result in dividing r³ by 3.

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When you divide a whole number by a fraction, the quotient is larger than the dividend.

This is because dividing a whole number by a fraction is the same as multiplying the whole number by the reciprocal (inverse) of the fraction.

For example, if we divide 6 by 1/2, it is equivalent to multiplying 6 by 2, which gives us a quotient of 12. So, the quotient of 12 is larger than the dividend of 6.

This happens because dividing by a fraction means we are dividing the whole into smaller parts, and the more parts we divide it into (i.e., the smaller the fraction), the more of those parts we get. Therefore, the quotient is larger than the dividend as we are getting more of the smaller parts.

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Tom had 60 dollars as his pocket money initially.

Let's assume that Tom had x dollars as his pocket money.

He spent 2/3 of his pocket money on apples, which means he spent (2/3)x dollars on apples.

He had 1/3 of his pocket money left after buying the apples.

Out of the remaining money, he spent 1/4 on bananas, which means he spent (1/4)(1/3)x = (1/12)x dollars on bananas.

The total amount spent on apples and bananas is given as $45. So, we can write the equation:

(2/3)x + (1/12)x = 45

Multiplying both sides by 12 to get rid of the fractions:

8x + x = 540

Simplifying, we get:

9x = 540

Dividing both sides by 9:

x = $60

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The number in the log as a power of the base y = -6.

What is  logarithmic identity ?

Logarithmic identities are mathematical formulas or rules that are used to manipulate logarithmic expressions. These identities are derived from the properties of logarithms and can be used to simplify or solve logarithmic equations.

The following are some commonly used logarithmic identities:

Product rule: log_a (x * y) = log_a (x) + log_a (y)

This identity states that the logarithm of the product of two numbers is equal to the sum of the logarithms of the individual numbers.

Quotient rule: log_a (x / y) = log_a (x) - log_a (y)

This identity states that the logarithm of the quotient of two numbers is equal to the difference of the logarithms of the individual numbers.

According to the question:
To write the number in the log as a power of the base, we can use the following logarithmic identity:

log_a (x) = y is equivalent to[tex]a^y = x[/tex]

Using this identity, we can rewrite the logarithmic expressions as follows:

y = log3 243 can be written as [tex]3^y = 243[/tex]

y = log2 1/64 can be written as [tex]2^y = 1/64[/tex]

Now, we can solve for y by taking the appropriate power of both sides of each equation:

For the first equation, we can write:

[tex]3^y = 243[/tex]

[tex]3^y = 3^5 (since 243 = 3^5)[/tex]

Therefore, y = 5.

For the second equation, we can write:

[tex]a^y = 1[/tex]

Since any non-zero number raised to the power of 0 is equal to 1, we have:

[tex]a^y = a^0[/tex]

Therefore, y = 0.

For the third equation, we can write:

[tex]2^y = 1/64[/tex]

[tex]2^y = 2^-6 (since 1/64 = 2^-6)[/tex]

Therefore, y = -6.

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There are 36 different outfits that can be created using six tops, three pants, and two jackets.

Combinations refer to the ways in which a set of objects or items can be arranged or chosen without regard to their order.

In mathematics, a combination is a selection of objects from a larger set, where the order of the selected objects does not matter.

Here we have

A designer has designed different tops, pants, and jackets to create outfits.  

Number of options for tops = 6

Number of options for pants = 3

Number of options for jackets = 2

Here,

The total number of different outfits that can be created = (No of options for tops) × (No of options for pants) × (No of options for jackets)  

= 6 × 3 × 2

Therefore,

There are 36 different outfits that can be created using six tops, three pants, and two jackets.

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Answer:

b - 16.8in

Step-by-step explanation:

10/x=√34/√96

10/x=5.831/9.798

5.831x=97.98

x=16.803

The maximum and minimum amount of hickers that could of walked between 8 and 19 miles is 19 and 7.

The minimum and maximum value depend on the context in which they are being used.

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a. There are 1,000 different possible selections.  b. The probability of winning is 1/1,000, or 0.001.  c. If you win, your net profit is $476.05.  d. The expected value is $0.476.  e. The Pick 4 game is better.

a.  There are 1,000 different possible selections (000 to 999).

b.  The probability of winning is 1/1,000, or 0.001.

c.  If you win, your net profit is $476.05. This can be calculated by,

$477.38 - $1.33 = $476.05

d. The expected value is $0.476. This can be calculated by,

$476.05 * 0.001 = $0.476

e. The Pick 4 game is better.
The expected value of a Pick 3 bet is $0.476, while the expected value of a Pick 4 bet is $0.85. The Pick 4 bet is better because it has a higher expected value. This is because the Pick 4 game has more possible selections, meaning the odds of winning are lower than the Pick 3 game, but the prize is larger. So, the expected value for Pick 4 is larger than Pick 3. The expected value of a bet is the amount of money you can expect to win if you make the same bet over and over again, so a higher expected value means you have a better chance of making a profit in the long run.

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Ken took 7.5 minutes to finish the race. We used simple Speed, Distance and Time formula.

The total distance traveled by the object over a given time period is the average speed. A scalar number is the average speed. It does not have a direction and is only represented by the magnitude.

To calculate the time taken by Ken to finish the race, we can use the formula:

Here, the distance is 1500m and the average speed of Ken is 200m/min.

So,

Therefore, Ken took 7.5 minutes to finish the race.

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The slope of the line is -63, which represents the number of canned goods decreases at a rate of 63 per day.

The y-intercept is 825, which is the initial amount of canned goods.

In Mathematics, the slope-intercept form of the equation of a straight line is given by this mathematical expression;

y = mx + c

Where:

Based on the information, an equation that models the situation is given by this mathematical expression;

y = mx + c

y = -63x + 825

In conclusion, we can reasonably infer and logically deduce that the slope is -63 and the y-intercept is equal to 825.

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Answer:

52.

Step-by-step explanation:

So 143 members represent 100% of the population of the problem. A ratio of 4:7 similarly represent 100%. First, you need to get the value of 4:7 in a representation of 100%. You can do that by adding the two (4+7=11) and then dividing it by each value of it. So 7 divided by 11 is .6363, or 63.63% of the whole. Then 4 divided by 11 is .3636, or 36.36% of the whole. After getting this, seeing that the ratio for union members to non union members is 4 union members to 7 nonunion members, and there are 143 employees in total, just get the value of 36.36% of 143; in this case, it's 51.99 - rounded off to 52 employees.

Answer:

52 members

Step-by-step explanation:

Proportional setup.

(4/11)=(x/143)

Answer:

1 and -1

Step-by-step explanation:

[tex]5 - \sqrt[3]{( {x}^{2} - 9 } = 7[/tex]

[tex] - \sqrt[3]{( {x}^{2} - 9} = 7 - 5[/tex]

[tex]- \sqrt[3]{( {x}^{2} - 9} = 2[/tex]

[tex] \sqrt[3]{( {x}^{2} - 9} = - 2[/tex]

Cube both sides of the equation:

[tex] {x}^{2} - 9 = { - 2}^{3} [/tex]

[tex] {x}^{2} - 9 = - 8[/tex]

[tex] {x}^{2} = - 8 + 9[/tex]

[tex] {x}^{2} = 1[/tex]

[tex] {x}^{2} - 1 = 0[/tex]

[tex](x - 1)(x + 1) = 0[/tex]

[tex]x = 1 \: \: or \: \: x = - 1[/tex]

[tex]5-\sqrt[3]{x^2-9}=7\implies 5=\sqrt[3]{x^2-9}+7\implies -2=\sqrt[3]{x^2-9} \\\\\\ (-2)^3=(\sqrt[3]{x^2-9})^3\implies -8=x^2-9\implies 1=x^2 \\\\\\ \pm\sqrt{1}=x\implies \pm 1 = x[/tex]

Probability of getting A on 2 or fewer spins is 0.79 using sum of probabilities we individually find.

We must add the odds of receiving A on 0 spins, 1 spin, and 2 spins in order to determine the likelihood of getting A in 2 spins or less.

Probability of not receiving A on the first spin is equal to 0.6 P (getting A on 0 spins) (getting A on 1 spin) Probability of receiving A on the first spin and not receiving A on the second spin, or of receiving A on the second spin and not receiving A on the first spin, is equal to 0.40.6 + 0.60.4 = 0.48.

P(getting A on 2 spins) is the likelihood that A will appear on both the first and second spins, or that A will appear on the second spin even if A did not appear on the first spin, and vice versa. = 0.40.4 + 0.60.40.42 = 0.108

P (receiving A on two or fewer spins) is therefore equal to P (getting A on zero spins), P (getting A on one spin), and P (getting A on two spins). These values are 0.6, 0.48, and 0.108, which add up to 0.788, or roughly 0.79.

Therefore 0.79 is the solution to part B.

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The size of angle x is equal to 100°.

Based on the identical isosceles triangles ΔABD and ΔACD, we can logically deduce the following:

m∠DAB = 25°

AD = BD = CD

In triangle ΔABD, we have:

AD = BD (Given)

m∠DBA = ∠DAB (Angle opposite to equal sides are congruent)

m∠DBA = 25°.

Next, we would determine the measure of m∠ADB;

m∠DBA + m∠DAB + m∠ADB = 180° (Sum of angle in a triangle)

25° + 25° + m∠ADB = 180°

m∠ADB = 180° - 50°

m∠ADB = 130°.

Since ΔABD and ΔACD are two identical isosceles triangles, we have:

m∠DCA = m∠DBA

m∠DCA = 25°

Similarly, we have:

m∠DAC = m∠DAB = 25°

m∠ADC = m∠ADB = 130°

Generally speaking, we know that a complete revolution (circle) is equal to 360°:

m∠ADC + m∠ADB + m∠CDB = 360°

130° + 130° + x = 360°

x = 360° - 260°

x = 100°.

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Therefore, the measure of the area of rhombus EFGH is 252 square units.

A rhombus is a four-sided geometric shape that has the following properties:

All four sides are of equal length.

Opposite sides are parallel to each other.

The angles formed between adjacent sides are equal (i.e., they are all congruent).

The diagonals of a rhombus bisect each other at right angles, meaning they intersect at a 90-degree angle. Additionally, the length of one diagonal is equal to the product of the length of the other diagonal and the sine of one of the angles formed by adjacent sides.

by the question.

[tex]EK^2 = EG^2/4 + KH^2 (where KH is half the length of FH)EK^2 = 36^2/4 + (14/2)^2EK^2 = 324 + 49EK^2 = 373EK = sqrt(373)[/tex]

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For the two functions given, the value for f(g(8)) is option D - 24.

What is a function?

In mathematics, a function is a unique arrangement of the inputs (also referred to as the domain) and their outputs (sometimes referred to as the codomain), where each input has exactly one output and the output can be linked to its input.

The first function is given as f(x) = x² + 2x.

The second function is given as g(x) = √(2x).

To find f(g(8)), we need to first evaluate g(8) and then plug the result into f(x).

Using g(x) = √(2x), we can find g(8).

Substitute the value of x in the equation -

g(8) = √(2(8))

g(8) = √16

g(8) = 4

Now that we know g(8) = 4, we can find f(g(8)) by plugging in 4 for x in f(x) .

Substitute the value of g(8) in the equation -

f(g(8)) = f(4)

f(g(8)) = 4² + 2(4)

f(g(8)) = 16 + 8

f(g(8)) = 24

Therefore, the solution is obtained as 24.

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The solutions of the equation in the interval `[0, 2π)` are `π/3` and `3π/4`.Hence, the required answer is `(π/3, 3π/4)` in comma-separated form.

Given that `cos(θ) - sin(θ) = (2/1) sin(2θ)`, find `θ`.Solution:As we have been given `cos(θ) - sin(θ) = (2/1) sin(2θ)`, we know that we can apply double angle formulae to convert `2θ` to `θ`.`sin(2θ) = 2sin(θ)cos(θ)`∴ `cos(θ) - sin(θ) = (2/1) sin(θ)cos(θ)`⇒ `2 sin(θ) cos(θ) - sin(θ) + cos(θ) = 0`⇒ `sin(θ) (2 cos(θ) - 1) - cos(θ) (2 cos(θ) - 1) = 0`⇒ `(sin(θ) - cos(θ)) (2 cos(θ) - 1) = 0`Therefore, `sin(θ) - cos(θ) = 0` or `cos(θ) = 1/2`Solving `sin(θ) - cos(θ) = 0` gives `θ = 3π/4` (Since `sin(3π/4) = 1/√2` and `cos(3π/4) = -1/√2`)Solving `cos(θ) = 1/2` gives `θ = π/3` (Since `cos(π/3) = 1/2`)Therefore, the solutions of the equation in the interval `[0, 2π)` are `π/3` and `3π/4`.Hence, the required answer is `(π/3, 3π/4)` in comma-separated form.

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Answer:

1/5

Step-by-step explanation:

Answer:

Niran is correct.

Step-by-step explanation:

The area of a trapezoid is h(a + b)/2 where h is the height and a and b are the lengths of the opposite parallel sides.

Using the given values:

Area = 18 = 4(a + b)/2

--->  2(a + b) = 18

--->  a + b = 9

Now there are many values we can assign to a and b so that they sum to 9  ( for exampl 3 and 6, 4 and 5, 1 and 8)

so Niran is correct.

The area of the parallelogram will equal to Area of the rectangle

The area of a parallelogram is given by the formula:

Where A is the area of the parallelogram,

b is the length of the base of the parallelogram,

h is the height of the parallelogram.

The area of a rectangle is given by the formula:

Where A is the area of the rectangle  

l is the length of the rectangle  

w is the width of the rectangle.

Here we have a Parallelogram    

Where the height of the parallelogram is 4.5 cm and the length is 7 cm  

Using the formula,

Area of parallelogram = 4.5 cm × 7 cm = 31.5 cm²

From the data,

The length of a rectangle is 7 cm and width is 4.5 cm

Using the formula,

Area of the rectangle = 7 cm × 4.5 cm = 31.5 cm²  

Therefore,

The area of the parallelogram will equal to Area of the rectangle

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The complete question is given in the picture

False. A data set of the heights of 12-year-old boys would not necessarily follow a normal distribution pattern as it may be skewed or not evenly distributed around the mean.

False. A normal distribution is a type of probability distribution that takes the shape of a bell curve. It is characterized by having an equal number of values on either side of the mean, with the values in the middle being more numerous than those on the outside. A data set of the heights of all 12-year-old boys who live on a given street in the city of Grand Rapids would not necessarily fit this pattern. It is possible that the data set may be skewed in one direction or the other, depending on the height of the tallest and shortest boys in the group. It is also likely that the data will not be evenly distributed around the mean, as some boys may be taller or shorter than others.

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A pie chart or a bar graph is best suited for graphing the proportion of green eyes to brown-eyed or blue-eyed students in the class.

A pie chart is a circular graph that displays data as a set of slices, each representing a proportion of the whole.

A pie chart would show the percentage or fraction of each eye color in relation to the whole, while a bar graph would compare the number of students with each eye color side by side.

Both types of graphs are useful for displaying proportions and comparing different categories.

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A plane traveled 630 kilometers each way to Toronto and back. The trip there was with the wind. It took 7 hours. The trip back was into the wind. The trip back took 15 hours. The speed of the plane in still air is 66 km/h, and the speed of the wind is 24 km/h.

Let's use the following variables:

When the plane is flying with the wind, its effective speed is p + w. When it is flying against the wind, its effective speed is p - w.

We know that the distance to Toronto and back is 630 km each way, for a total of 1260 km. We also know that the time it took to fly to Toronto with the wind was 7 hours, and the time it took to fly back against the wind was 15 hours.

Using the formula distance = speed x time, we can set up the following equations:

630 = (p + w) x 7 (equation 1)

630 = (p - w) x 15 (equation 2)

We now have two equations with two unknowns. We can solve for either p or w in terms of the other variable. Let's solve for p in terms of w.

From equation 1, we get:

p + w = 90

From equation 2, we get:

p - w = 42

Adding the two equations, we get:

2p = 132

So,

p = 66 km/h

Now we can use either equation 1 or equation 2 to solve for w. Let's use equation 1:

630 = (66 + w) x 7

Simplifying this equation, we get:

90 = 66 + w

w = 24 km/h

Therefore, the speed of the plane in still air is 66 km/h, and the speed of the wind is 24 km/h.

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The amount of chocolate that Joey will have left is; 5/16

In word problems on fraction, we will solve different types of problems on multiplication of fractional numbers and division of fractional numbers.

We are given:

Amount of chocolate bought = 1/2 pound of chocolate

Amount of chocolate eaten = 3/8 * 1/2 = 3/16

Thus, the amount of chocolate Joey will have left will be gotten by subtracting the amount eaten from the total amount he bought. Thus;

Amount of chocolate he has left = 1/2 - 3/16

= (8 - 3)/16

= 5/16

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