Harry, Jason and Sarah are taking the GMAT exam which is required by most applicants for admission to graduate schools of business. The three friends want to get admissions to three different business schools. Harry can get the admission if he gets a score above 650 in GMAT, Jason can get the admission if he gets above 630 and Sarah can get the admission if she gets above 670 . Scores on the GMAT are roughly normally distributed with a mean of 550 and a standard deviation of 115 . What is the probability that Harry, Jason and Sarah will get admissions to their desired schools given that they study independently and the admissions are independent of one

The equation given is:

396 = 66t

This equation relates the distance traveled (396 miles) to the rate of travel (66 miles per hour) and the time it takes to travel that distance (t hours).

We can rearrange this equation to solve for the constant of proportionality, which is the rate of travel:

66t = 396

Dividing both sides by 66, we get:

t = 6

Therefore, the constant of proportionality in the equation is 66. The correct answer is C.

Rounding to the nearest hundredth, the surface area of the sphere is approximately 331.81 square meters.

What is surface area ?

Surface area is the measure of the total area that the surface of an object occupies. It is a two-dimensional measurement, typically expressed in square units, such as square meters (m²) or square feet (ft²).

The surface area (A) of a sphere with diameter d is given by the formula:

A = 4π(d/2)²

where π (pi) is a mathematical constant approximately equal to 3.14.

Substituting the given value of the diameter d = 18.3m into the formula, we get:

A = 4π(18.3/2)²

A = 4π(9.15)²

A = 4π(83.7225)

A ≈ 331.81

Therefore, rounding to the nearest hundredth, the surface area of the sphere is approximately 331.81 square meters.

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Carson's work cannot be used to find the solution of the system of equations because

The equation x² + 5x - 6 = 0 has two solutions, but only one of them may satisfy the equation y = x - 1.

What is system of equations?

A system of equations is a set of two or more equations that need to be solved simultaneously. The solution to a system of equations is the set of values that make all the equations in the system true. Systems of equations can be solved using a variety of methods, including substitution, elimination, and graphing.

A system of equations can be represented using algebraic notation. For example, consider the following system of two linear equations in two variables x and y:

2x + 3y = 8

4x - 5y = -7

Why Carson's work cannot be used to find the solution of the system of equations ?

The equation x² + 5x - 6 = 0 has two solutions, but only one of them may satisfy the equation y = x - 1.

Substituting the x-values found from solving the quadratic equation into the equation y = x - 1 does not necessarily give the correct y-values for the corresponding x-values that satisfy both equations simultaneously.

Carson should have substituted the x-values found from solving the quadratic equation into the equation y = x² + 5x - 6 instead of y = x - 1 to find the correct y-values that satisfy both equations simultaneously.

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Answer:131

Step-by-step explanation:

2 * 2 * 2 * 2 + 20 * 5 + 15 = 2^4+100+15=16+115=131

Answer:

Step-by-step explanation:

2 * 2 * 2 * 2 + 20 * 5 + 15 =            (remember PEMDAS)

16 + 100 + 15 =

131

Therefore , the solution of the given problem of angles comes out to be x has a value of 150°.

The two sides of a tilt in Euclidean geometry are actually spherical faces that divide at the centre and top of barrier. At the point where two rays meet, they might combine to form an angle. Angle is another outcome of two entities interacting. They mirror dihedral forms the most. A two-dimensional curve can be created by arranging two line beams in various configurations at their ends.

Here,

Since AE and BD are parallel, we can calculate the value of angle ABD using the alternate internal angles theorem:

=> BCD x ABD = 180

=>ABD = 150°, ABD + 30° Equals 180°.

Now, we can use the knowledge that a triangle's angles sum to 180 degrees to determine what angle AED is worth:

180° from ABD + AED + EDC is 150° from

=>AED + 180° is 180°.

=>AED = -150°

=>AED Plus BAE = 180

=> BAE + 30° = 180°

=> BAE = 150°

In order to determine the value of angle AEB, we can use the knowledge that the angles in a triangular sum to 180°:

=>AED 180° BAE AEB

=> AEB + 150° + 30° = 180°

=>AEB = 0°

.Points A, E, and B are collinear because angle AEB is 0°, and angle x equals angle ECD:

=> Angle BCD x = 180° - 30° x = 150° x = ECD = 180°

Consequently, x has a value of 150°.

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Answer:

Step-by-step explanation:

[tex]sin45=\frac{x}{4}[/tex]      [tex](sin=\frac{opposite}{hypotenuse})[/tex]

[tex]x=4sin45[/tex]    

  [tex]=\frac{4}{\sqrt{2}}[/tex]

  [tex]=\frac{4}{\sqrt{2}}\times\frac{\sqrt{2}}{\sqrt{2}}[/tex]

  [tex]=\frac{4\sqrt{2} }{2}[/tex]

  [tex]=2\sqrt{2}[/tex]

[tex]cos45=\frac{y}{4}[/tex]     [tex](cos=\frac{adjacent}{hypotenuse})[/tex]

[tex]y=4cos45[/tex]

  [tex]=\frac{4}{\sqrt{2}}[/tex]

  [tex]=2\sqrt{2}[/tex]

Company A's website receives 2,000 times more visitors per year than company B's website.

To determine how many times more visitors per year the website company A receives than company B, we need to find the ratio of the number of visitors to each website. The number of visitors to company A's website is 8 x 10^6, and the number of visitors to company B's website is 4 x 10^3.

Hence, the ratio of the number of visitors to the two websites is:

8 x 10^6 / 4 x 10^3

Simplifying this expression, we can cancel out a factor of 4 x 10^3 from both the numerator and the denominator:

8 x 10^6 / 4 x 10^3 = 2 x 10^3

Therefore, company A's website receives 2 x 10^3 times more visitors per year than company B's website. This means that for every visitor that company B's website receives, company A's website receives 2,000 visitors.

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The function value is csc 330° = -2.

Function establishes the relationship between input and output. The x-intercept, y-intercept, and slope of any function are calculated using function formulas. You could also figure out the vertex of a quadratic function. Moreover, a graph of the function can be created for a range of x values.

Since the sine of 360 degrees (which has a sine of 0) is similar to 30 degrees being subtracted from it, we can determine using the unit circle that the sine of 330 degrees is equal to -1/2 and thus the sine function is negative in the fourth quadrant. The reciprocal of sine 330 degrees, which is -2/1 or -2, is the cosecant of 330 degrees.

Thus, csc 330° = -2.

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We can compare the observed difference in medians between the V and NV groups to the difference in medians generated from the simulation in order to estimate a p-value for a test for the difference in medians.

We can count the number of simulation trials where the median difference is larger than or equal to the observed median difference in order to determine the p-value (V-NV). Assume that the median difference that was recorded is 5 (V-NV = 5).

Just a small number of trials, as shown by the dotplot, have median differences higher than or equal to 5. These trials can be counted manually or with software like R or Python. Say we discover 4 trials where the median difference is higher than or equal to 5.

The p-value is then determined as the percentage of simulation trials in which the median difference is larger than or equal to the observed median difference. The p-value in this instance is 4/100 = 0.04. As a result, since the p-value is lower than the significance level, we may say that the observed difference in medians is statistically significant at the 0.05 level.

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The probability of correctly answering both questions with random guesses is 5.6%.

There are 6 possible answers, so the probability of randomly guessing the correct answer is 1/6. Similarly, for the second question, there are 3 possible answers, so the probability of randomly guessing the correct answer is 1/3.

Since the two questions are independent events, meaning that the outcome of one question does not affect the outcome of the other question, we can find the probability of both events occurring by multiplying their probabilities together. Therefore, the probability of randomly guessing both answers correctly is:

P(both answers correct) = P(first answer correct) * P(second answer correct)

= (1/6) * (1/3)

= 1/18

The probability is 1/18 or about 0.056 or 5.6% when rounded to one decimal place.

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Since, the triangle FGH is a right angle triangle, The angles of the ∠F = 62°, ∠G = 90° and ∠H = 28°.

Right Angle Triangle:

A right triangle (American English) or right triangle (UK), or more formally an orthogonal triangle, formerly known as a right triangle, is a triangle in which one angle is a right angle (i.e. say an angle of 90 degrees), i.e. two of its sides are perpendicular. The relationship between the sides of a right triangle and the other angles is the basis of trigonometry.

According to the Question:

Interior angles of a triangle add up to 90 degrees

∠F + ∠ G + ∠H = 180

⇒ 9x - 1 + 90 + 3x + 7 = 180

⇒ 12x + 96 = 180

⇒ 12x = 180 - 96

⇒ 12x = 84

⇒ x = 84/12

⇒ x = 7

Therefore,

∠F = 9x - 1 = 9(7) - 1 = 63 - 1 = 62

And, ∠G = 90

And, ∠ H = 3x + 7 = 3(7) + 7 = 21 + 7 = 28

If we add the angles :

62 + 90 + 28 = 180°

Complete Question:

Triangle FGH is a right triangle. Angle G is a right angle, m∠F = 9x – 1, and m∠H = 3x + 7. What is m∠F?

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The sample space can then be written as: S = {(Y,U), (Y,T), (Y,C), (W,U), (W,T), (W,C), (R,U), (R,T), (R,C)}Thus, the sample space consists of nine possible outcomes or options.
The sample space for this experiment is composed of all the possible combinations of the two variables (paint color and finish). The possible combinations are:

Therefore, the sample space is {Y + U, Y + T, Y + C, W + U, W + T, W + C, R + U, R + T, R + C}.
Here, the experiment involves choosing a paint color and a finish for a game room and entertainment center respectively. We are given that there are three paint color options and three finish options. Therefore, the sample space can be written as follows:

Let Y, W, and R represent the paint colors yellow, white, and red respectively. Let U, T, and C represent the finish options unfinished, teak, and cherry respectively.

Each outcome is an ordered pair, where the first element represents the paint color option and the second element represents the finish option.

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Answer:

I want to say that it is E

Step-by-step explanation:

Well in terms of probability there is a 50% chance the coin will land heads and a 50% chance the coin will land tails. Since probability isn't definite you can never really get a precise number of each side. the most you could do is predict/guess

The most likely outcome is: E. They are all equally likely.

Each individual toss of a fair coin has an equal probability of being a heads or tails, regardless of what the previous tosses were. Therefore, all of the outcomes listed are equally likely. The order in which the heads and tails occur does not affect the probability of the overall outcome.

So, even though (i) has an equal number of heads and tails in an alternating pattern and (iii) has all heads, they are both equally likely to occur. The same goes for (ii) and (iv), which have an equal number of heads and tails but in a random order.

Therefore, The most likely outcome is: E. They are all equally likely.

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Answer:

We can use the Pythagorean theorem to find the length of the hypotenuse:

c^2 = a^2 + b^2

where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.

Plugging in the given values, we get:

c^2 = 16^2 + 10^2

c^2 = 256 + 100

c^2 = 356

Taking the square root of both sides, we get:

c = sqrt(356)

c ≈ 18.9

Therefore, the length of the hypotenuse is approximately 18.9 cm.

When extending beyond two dimensions, the analytical approach is generally easier to use than Euclidean geometry. The reason for this is that Euclidean geometry relies heavily on visualizing geometric shapes and their properties in three dimensions or higher, which can be difficult for most people.

In contrast, the analytical approach uses algebraic equations to describe geometric shapes and their properties, which can be more straightforward and intuitive for many individuals. The analytical approach also allows for the use of software tools to manipulate and visualize shapes in higher dimensions, which can be particularly useful for complex calculations and designs.

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(a)   25-44

(b)   45-64

(a) The 2×3 table of local odds ratios for the association between age group and education level is as follows:

The odds ratio corresponding to the strongest of these pairwise associations is 1.78, which indicates that adults aged 45-64 are 78% more likely to have a high school diploma than adults who are 25-44.

(b) The 2×3 table of odds ratios for the association between age group and education level when treating the youngest age group and highest education level as the baseline categories for comparison is as follows:

The odds ratio corresponding to the strongest of these pairwise associations is 1.48, which indicates that adults aged 25-44 are 48% more likely to have a high school diploma than adults aged 45-64.

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The measure of the smaller angle is 10 degrees. We find the measure of the larger angle, we can substitute x = 10 into the expression, the measure of the larger angle is 170 degrees.

When two angles form a linear pair, they are adjacent angles that share a common side and form a straight line. The sum of the measures of these two angles is always 180 degrees.

Let x be the measure of the smaller angle in this problem. Since the ratio of the measures of the two angles is 1:17, we can express the measure of the larger angle in terms of x by multiplying 17 to x. Thus, the measure of the larger angle is 17x.

To find the value of x, we can use the fact that the sum of the measures of the two angles is 180 degrees. So we have:

x + 17x = 180

Simplifying the equation, we get:

18x = 180

Dividing both sides by 18, we obtain:

x = 10

Therefore, the measure of the smaller angle is 10 degrees. To find the measure of the larger angle, we can substitute x = 10 into the expression we derived earlier for the measure of the larger angle:

17x = 17(10) = 170 degrees

Hence, the measure of the larger angle is 170 degrees.

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The probability that a randomly chosen individual will experience actual unfavorable effects is roughly 0.9025, or 90.25%.

The percentage of genuine positive results—both true positive and true negative—in the chosen population is represented by the accuracy score's numerical number. 99% of the time, whether the test result is positive or negative, it is accurate.

We can write: Applying the law of total probability

P(B|¬A) = P(B|¬A,¬T)P(¬T|¬A) + P(B|¬A,T)P(T|¬A),

To calculate P(B|¬A,¬T), the probability that the test is negative given that the person does not have Covid-19 and the test is negative, we can use the complement rule:

P(B|¬A,¬T) = 1 - P(¬B|¬A,¬T),

P(¬B|¬A,¬T) = 1 - P(B|¬A,¬T) = 1 - 0.95 = 0.05.

P(B|¬A) = P(B|¬A,¬T)P(¬T|¬A) + P(B|¬A,T)P(T|¬A)

= (1 - P(¬B|¬A,¬T))P(¬T|¬A) + P(B|¬A,T)P(T|¬A)

= (1 - 0.05) x 0.95 + 0 x 0.1

= 0.9025.

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The new coordinates is A'(-1,5) which is glide reflection of point A(-3,-3) where the translation is (x+2,y) and the line of reflection is y = 1.

Glide Reflection, it is known as composition of transformations.

In glide reflection, before reflected over a line it translation is first performed on the figure.

The coordinate of A are given as (-3,-3).

The rule of translation is (x, y) → (x+2,1)  and the line of reflection is y=1.

Now,

Applying the rule of translation, we get;

A = (-3, -3) → (-3+2, -3) = (-1, -3)

Since, -3 which is 4 unit below line of reflection,

then,

after reflection, over the line  y=1 we get, the reflected point A' would be 4 units above line of reflection

so, A' (-1, 1+4) =(-1, 5)

Therefore, the coordinate of A' (-1, 5).

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the mean absolute deviation of the set {16, 10, 22, 18, 4, 18, 14, 24, 16, 22} is 4.68.

To find the mean absolute deviation of a set of numbers, we first need to calculate the mean of the set.

The mean of the set {16, 10, 22, 18, 4, 18, 14, 24, 16, 22} is:

Mean = (16 + 10 + 22 + 18 + 4 + 18 + 14 + 24 + 16 + 22) / 10 = 16.4

Next, we need to calculate the absolute deviation of each number from the mean. The absolute deviation is the absolute value of the difference between the number and the mean.

The absolute deviations for each number in the set are:

|16 - 16.4| = 0.4

|10 - 16.4| = 6.4

|22 - 16.4| = 5.6

|18 - 16.4| = 1.6

|4 - 16.4| = 12.4

|18 - 16.4| = 1.6

|14 - 16.4| = 2.4

|24 - 16.4| = 7.6

|16 - 16.4| = 0.4

|22 - 16.4| = 5.6

Now, we need to find the mean of the absolute deviations.

Mean absolute deviation = (0.4 + 6.4 + 5.6 + 1.6 + 12.4 + 1.6 + 2.4 + 7.6 + 0.4 + 5.6) / 10

Mean absolute deviation = 4.68

Therefore, the mean absolute deviation of the set {16, 10, 22, 18, 4, 18, 14, 24, 16, 22} is 4.68.

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The first and fifth expressions are equal to the fraction, the second expression is less than the fraction and the third, fourth, and sixth expressions are greater than the fraction.

In this case, to better understand the numbers and expressions given, let's simplify each of the expressions.

3/4 or 0.75

Firs expression: 7/7 x 3/ 4 = 1 x 0.75 = Equal to

Second expression: 1/3 x 3/4 = 0.33 x 0.75 = 0.24 = Less than

Third expression: 9/7 x 3/4 =  1.28 x 0.75 = 0.96 = Greater than

Fourth expression: 3/4 x 3/4 = 0.75 x 0.75 = 1.5 = Greater than

Fifth expression: 5/5 x 3/4 = 1 x 0.75 = 0.75 = Equal to

Sixth expression: 5/2 x 3/4 = 2.5 x 0.75 = 1.5= Greater than

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The probability that more than 25 students in a sample of 120 students would respond that they spend more than 4 hours a night on homework is given as follows:

0.0367 = 3.67%.

The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The estimate and the sample size for this problem are given as follows:

p = 0.15, n = 120.

Hence the standard error is of:

s = sqrt(0.15 x 0.85/120)

s = 0.0326.

More than 25 students is a sample proportion above 25/120 = 0.2083, hence the probability is one subtracted by the p-value of Z when X = 0.2083, hence:

Z = (0.2083 - 0.15)/0.0326

Z = 1.79

Z = 1.79 has a p-value of 0.9633.

Hence:

1 - 0.9633 = 0.0367 = 3.67%.

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Simplifying the expression, we get: ∫(49 - 5x^2) dx ∫(3x^2 - 1) dx = (44/3)x^3 + 48x + C

what is integration?

Integration is a fundamental concept in calculus that involves finding the integral of a function. The integral of a function is essentially the opposite of differentiation, and it involves finding the area under the curve of the function.

we have:

∫(a - bx^2) dx = ax - (b/3)x^3 + C

where C is the constant of integration.

Applying this formula to the first integral, we have:

∫(49 - 5x^2) dx = 49x - (5/3)x^3 + C1

where C1 is the constant of integration for the first integral.

Similarly, applying Theorem 8.2 to the second integral, we have:

∫(3x^2 - 1) dx = x^3 - x + C2

where C2 is the constant of integration for the second integral.

Therefore, the indefinite integral of the given expression is:

∫(49 - 5x^2) dx ∫(3x^2 - 1) dx = 49x - (5/3)x^3 + C1 + x^3 - x + C2

where C = C1 + C2 is the constant of integration for the entire expression.

Therefore Simplifying the expression, we get:

∫(49 - 5x^2) dx ∫(3x^2 - 1) dx = (44/3)x^3 + 48x + C

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Therefore , the solution of the given problem of parallelograms comes out to be C and R are equally distanced from point N, the midpoint of UE and RN Equals NC.

In Euclidean mathematics, a simple quadrilateral of two sets of equal distances is referred to as a parallelogram. In a specific kind of quadrilateral known as a parallelogram, both set of opposite sides are straight and equal. There are four types of parallelograms, 3 of which are each mutually exclusive. Rhombuses, parallelograms, squares, but also rectangles are the four distinct shapes.

Here,

We must demonstrate that OM = MR in order to establish that O is CR's middle.

=>  CO / OU Equals RC / UE

This solution can be rearranged to account for RC:

=>  RC Equals UE * (CO / OU)

But we also understand that OU = CO (since they are diagonals of the same parallelogram). Therefore:

=>  RC = UE

This indicates that point M, the CR's centre, is equally spaced from C and U. Or put another way, OM Equals MU.

To demonstrate that O is also the midpoint of UE, we can use a similar argument.

Triangles CRU and EUC are comparable to one another (by AA resemblance), so we have:

=>  UE/CR equals UC/CR

To solve for UE, rearrange this equation as follows:

=> UE = UC

As a result, C and R are equally distanced from point N, the midpoint of UE. That is to say, RN Equals NC.

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In response to the query, we can state that Therefore, the value of x trigonometry rounded to 1 decimal place is 19.4 cm.

The area of mathematics called trigonometry examines how triangle side lengths and angles relate to one another. The subject first came to light in the Hellenistic era, roughly in the third century BC, as a result of the use of geometry in astronomical investigations. The area of mathematics known as exact techniques deals with several trigonometric functions and possible computations using them. There are six common trigonometric functions in trigonometry. These go by the designations sine, cosine, tangent, cotangent, secant, and cosecant, respectively (csc). The study of triangle properties, particularly those of right triangles, is known as trigonometry. Consequently, studying geometry entails learning about the characteristics of all geometric shapes.

Based on the information given in the diagram, we can use trigonometry to find the value of x.

tan(θ) = opposite / adjacent

tan(25°) = y / x

x = y / tan(θ)

x = 9 / tan(25°)

x ≈ 19.4 cm (rounded to 1 decimal place)

Therefore, the value of x rounded to 1 decimal place is 19.4 cm.

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Answer:

A=∫

1

3

x

2

dx

A=[

3

x

3

]

1

3

A=(

3

27

−

3

1

)

A=

3

26

The correlation here in the provided graph is a positive trend and the equation for line of best fit will be as follows:

y = 1/4x

Correlation is a statistical method for determining the association or relationship between two variables. To put it another way, the correlation coefficient formula facilitates the calculation of the correlation coefficient, which assesses the degree to which one variable depends on another.

The correlation coefficient is a numerical indicator of correlation. Between -1 and 1, the correlation coefficient is found. An inverse association between two variables is shown by a negative correlation coefficient. A high correlation coefficient means that the two variables directly affect one other's values. There is no association between the two variables, according to a zero-correlation coefficient.

Here in the question,

The graph shows a positive trend as its increasing upwards. The equation for the line of best fit will be y =1/4x.

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