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The score of the top 2.5% of the applicants would be at least 610.

To find the score of the top 2.5% of the applicants, we need to use the z-score formula:

z = (x - μ) / σ

where x is the score we want to find, μ is the mean (460), σ is the standard deviation (80), and z is the z-score corresponding to the area under the normal curve to the right of x.

We want to find the z-score such that the area to the right of z is 0.025 (since we're looking for the top 2.5%). Using a table or calculator, we find that the z-score corresponding to an area of 0.025 to the right is approximately 1.96.

So,

1.96 = (x - 460) / 80

Solving for x, we get:

x = 1.96 * 80 + 460 = 610.8

Rounding to the nearest integer, we get 610. Therefore, the score of the top 2.5% of the applicants would be at least 610.

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Answer:

In a significance test, the statement we want to prove or test is called the alternative hypothesis.

Step-by-step explanation:

The alternative hypothesis, denoted as H1 or Ha, is a statement that contradicts or challenges the null hypothesis (H0). It represents the researcher's claim, expectation, or the hypothesis they are interested in supporting. The alternative hypothesis proposes that there is a significant relationship, effect, or difference between variables or conditions.

The null hypothesis, on the other hand, is the default assumption or statement of no effect or no difference. It assumes that any observed difference or relationship in the data is due to chance or random variation.In a significance test, statistical analysis is performed to evaluate the evidence against the null hypothesis and determine if there is sufficient evidence to support the alternative hypothesis. The analysis typically involves calculating a test statistic and comparing it to a critical value or p-value.

If the observed data provide strong evidence against the null hypothesis, the alternative hypothesis is supported, indicating that there is a statistically significant relationship, effect, or difference. If there is insufficient evidence to reject the null hypothesis, the alternative hypothesis is not supported.

It's important to note that in a significance test, the goal is to gather evidence to support the alternative hypothesis rather than proving it definitively. Statistical inference allows researchers to make conclusions based on the available evidence and quantify the level of confidence in their findings.

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If we assume that 1 Student can have atmost 1 award , then the possible selections for the 4 awards is  657720 .

The total number of students at Gatech is = 30 ;

The 4 awards that are being distributed to students are : Chemistry, English, Math and Physics ;

all the awards are different , and 4 students needed to be chosen out of 30 for 4 awards ; and

every student can have atmost only 1 award

So , the number of ways is = ³⁰P₄ (because order is important) = 657720 ;

Therefore , the possible selection for 4 awards is 657720 .

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The given question is incomplete , the complete question is

At Gatech there are 30 students and 4 awards in Chemistry, English, Math and Physics. Assume that a student can have at most one award.

How many possible selections for the 4 awards ?  

Answer:

60xcm^3

Step-by-step explanation:

6 times 10 times x

60x

The amount he will pay with the friend  if 20% is deducted before adding tax is $56.55

We should know that we have to deduct the tip for excellent driving g before adding up the tax to the total first.

The given parameters are

Bill =$65

Tax rate= 7%

Tip for excellent driving =20%

First deduct 0.2*65

=13

Balance = $(65-13)

Balance= $52.00

Tax = 0.07*65

Tax = 4.55

Then $(52.00+4.55)

= $56.55

In conclusion, the amount he will pay with the friend  if 20% is deducted before adding tax is $56.55

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The given expression is -3.3 + (-1.8) (2.5) - 2.4. To determine the number of terms in this expression, we need to count the individual terms separated by addition or subtraction symbols which will be 03

In the given expression, we have three terms: -3.3, (-1.8) (2.5), and -2.4. The terms are separated by the addition and subtraction symbols (+ and -). Each term represents a distinct value or expression.

Therefore, there are three terms in the given expression.

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Correct question- How many terms are there in the following expression?-3.3 + (-1.8) (2.5) - 2.4.
options: a. 04
             b. 03
             c. 02
             d. 01

We cannot determine the center or radius of the circle based on the given information.

To find the radius of the circle passing through the point (7, 6), we need to determine the center of the circle.

Let's assume that the center of the circle is (a, b). Since the circle passes through point (7, 6), we can set up an equation using the distance formula between the center (a, b) and point (7, 6) as follows:

√((7 - a)² + (6 - b)²) = r

where r is the radius of the circle.

We can see that this equation represents the distance between the center of the circle and the point (7, 6) is equal to the radius of the circle.

We also know that the distance between the center of the circle and any point on the circle is equal to the radius. Therefore, if we can find the distance between (a, b) and another point on the circle, we can solve for the radius.

However, we do not have any other information about the circle, such as another point or the equation of the circle. Therefore, we cannot determine the center or radius of the circle based on the given information.

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Answer:

The balanced equation that represents an endothermic reaction is:

2 CH4 (g) + 2 O2 (g) → 2 CO2 (g) + 2 H2O (g)

This is because the reactants (CH4 and O2) have a higher bond energy than the products (CO2 and H2O), meaning that energy must be absorbed in order to break the bonds and form the products. As a result, the reaction is endothermic.

The study has a confounding variable since the two groups differ in the time they were supposed to report to the testing room. Since the groups differed in terms of sleep deprivation and the time they were supposed to report to the testing room, the effect of sleep deprivation on learning could not be isolated.

The statement that is true is: d. All of these are true.Explanation:A study may have various sources of variability, including participant selection, the setting in which the study is conducted, and the measure used. The following options are as follows:a. The study may be affected by a situational variable.b. The construction noise may contribute to variability in test scores.c. The study has a confounding variable. The groups differ in the time they are to report to the testing room.d. All of these are true.Therefore, all of these options are true. For example, the study may be affected by a situational variable if a natural disaster or other unforeseen event happens that causes the study to be disrupted. In this case, the study was disrupted by a noisy construction crew, which may have contributed to variability in test scores. The study has a confounding variable since the two groups differ in the time they were supposed to report to the testing room. Since the groups differed in terms of sleep deprivation and the time they were supposed to report to the testing room, the effect of sleep deprivation on learning could not be isolated.

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Answer:

-6/29

Step-by-step explanation:

12 = x1 -3 = y1 -17 = x2 3 = y2 3 - -3 = 6 - -17 - 12 = -29 = -6/29

The values of x and y will be 5 and 0, respectively.

We can solve this system of equations by substitution or elimination. Here's how to do it by substitution:

Solve the first equation for x or y. Let's solve for y:

-x + y = -5

y = x - 5

Substitute the expression for y into the second equation and solve for x:

3x + 5y = 15

3x + 5(x - 5) = 15

3x + 5x - 25 = 15

8x = 40

x = 5

Substitute the value of x back into one of the original equations and solve for y:

-x + y = -5

-(5) + y = -5

y = 0

Therefore, the solution to the system of equations is (x, y) = (5, 0).

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Answer:

  A = B = 45°

  x = 11√2

Step-by-step explanation:

The sides of the right triangle have equal lengths, so this is an isosceles right triangle. Its acute base angles are complementary and have the same measure: A = B = 45°.

You should know from memory that the hypotenuse of an isosceles right triangle is √2 times the side length, so would be x = 11√2. Even if you don't, you can figure it from the Pythagorean theorem:

  x² = 11² +11² = 11²·2

  x = 11√2 . . . . . take the square root

Answer:

sinU = 0.96

Step-by-step explanation:

sinU = \(\frac{opposite}{hypotenuse}\) = \(\frac{WV}{UV}\) = \(\frac{24}{25}\) = 0.96

You have a total of six different ways to select a snack and a beverage at the amusement park.

To determine the number of different ways you can select a snack and a beverage, we can use the concept of combinations.

Let's analyze the options:

Snack: You can choose either a chili dog or popcorn. This gives us 2 choices for the snack.

Beverage: You can choose either lemonade, an energy drink, or water. This gives us 3 choices for the beverage.

To calculate the total number of combinations, we multiply the number of choices for the snack by the number of choices for the beverage. Therefore, the number of different ways to select a snack and a beverage is 2 (choices for snack) multiplied by 3 (choices for beverage), which equals 6.

In other words, there are six different combinations possible:

Chili dog and lemonade

Chili dog and energy drink

Chili dog and water

Popcorn and lemonade

Popcorn and energy drink

Popcorn and water

So, when considering all the options, you have a total of six different ways to select a snack and a beverage at the amusement park.

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Answer: 72.97 Minutes

Step-by-step explanation: We have two cars, A and B, traveling along a straight road. Car A is moving at a constant speed of 77.0 km/h, while car B is moving at a constant speed of 114 km/h. At the starting point (t=0), car B is 45.0 km behind car A.

To figure out how long it takes for car B to catch up and overtake car A, we need to consider their relative speeds. The relative speed is the difference between the speed of car B and the speed of car A.

Relative speed = Speed of car B - Speed of car A

Relative speed = 114 km/h - 77.0 km/h

Relative speed = 37.0 km/h

So, car B is moving 37.0 km/h faster than car A. Now, we need to determine the time it takes for car B to cover the initial distance between them, which is 45.0 km.

To calculate time, we use the formula: Time = Distance / Speed. In this case, the distance is 45.0 km, and the speed is the relative speed of 37.0 km/h.

Time = 45.0 km / 37.0 km/h ≈ 1.2162 hours

Now, let's convert the time to minutes by multiplying it by 60 (since there are 60 minutes in an hour).

Time = 1.2162 hours * 60 minutes/hour ≈ 72.97 minutes

Therefore, it takes approximately 1.2162 hours or 72.97 minutes for car B to catch up and overtake car A.

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S is closed under vector addition  and  S is closed under scalar multiplication.

To determine if set S is a subspace of R³, we need to check if it satisfies the three properties of a subspace: closure under vector addition, closure under scalar multiplication, and containing the zero vector.

5. Is S closed under vector addition Justify.

To check if S is closed under vector addition, we need to show that if u and v are vectors in S, then their sum u + v is also in S.

Let u = [x₁, y₁, z₁] and v = [x₂, y₂, z₂] be vectors in S.

According to the given form of vectors in S, we have:

u = [2x₁ - 3y₁, z₁]

v = [2x₂ - 3y₂, z₂]

Now, let's calculate the sum u + v:

u + v = [2x₁ - 3y₁, z₁] + [2x₂ - 3y₂, z₂]

      = [2(x₁ + x₂) - 3(y₁ + y₂), z₁ + z₂]

Since (x₁ + x₂) and (y₁ + y₂) are real numbers, we can see that the sum u + v is also in the form [A, B] which satisfies the definition of S.

Therefore, S is closed under vector addition.

6. Is S closed under scalar multiplication? Justify.

To check if S is closed under scalar multiplication, we need to show that if u is a vector in S and c is a scalar, then the scalar multiple c*u is also in S.

Let u = [x, y, z] be a vector in S, and c be a scalar.

According to the given form of vectors in S, we have:

u = [2x - 3y, z]

Now, let's calculate the scalar multiple c*u:

c*u = c[2x - 3y, z]

    = [2cx - 3cy, cz]

Since cx and cy are real numbers, we can see that the scalar multiple c*u is also in the form [A, B] which satisfies the definition of S.

Therefore, S is closed under scalar multiplication.

Now, let's consider problem 7:

7. Specify the nullspace of A.

The nullspace of a matrix A, denoted as Null(A), consists of all vectors x such that Ax = 0, where 0 represents the zero vector.

To find the nullspace of A, we need to solve the equation Ax = 0.

Let's set up the augmented matrix [A | 0] and perform row operations to find the reduced row-echelon form:

1 -2 0 -3 0 1 | 0

-1 1 2 1 2 1 | 0

-4 -2 -2 -3 2 -2 | 0

Performing row operations:

R2 = R2 + R1

R3 = R3 + 4R1

1 -2 0 -3 0 1 | 0

0 -1 2 -2 2 2 | 0

0 6 -2 -15 2 -6 | 0

R3 = R3 + 6R2

1 -2 0 -3 0 1 | 0

0 -1 2 -2 2 2 | 0

0 0 10 -27 14 6 | 0

Now, let's express the system of equations:

x₁ - 2x₂ - 3x₄ + x₆ = 0

-x₂ + 2x₃ - 2x₄ + 2x₅ + 2x₆ = 0

10x₃ - 27x₄ + 14x₅ + 6x₆ = 0

We can solve this system of equations to find the nullspace of A, which represents all vectors x that satisfy the equation Ax = 0.

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S is closed under vector addition  and  S is closed under scalar multiplication.

To determine if set S is a subspace of R³, we need to check if it satisfies the three properties of a subspace: closure under vector addition, closure under scalar multiplication, and containing the zero vector.

5. Is S closed under vector addition Justify.

To check if S is closed under vector addition, we need to show that if u and v are vectors in S, then their sum u + v is also in S.

Let u = [x₁, y₁, z₁] and v = [x₂, y₂, z₂] be vectors in S.

According to the given form of vectors in S, we have:

u = [2x₁ - 3y₁, z₁]

v = [2x₂ - 3y₂, z₂]

Now, let's calculate the sum u + v:

u + v = [2x₁ - 3y₁, z₁] + [2x₂ - 3y₂, z₂]

     = [2(x₁ + x₂) - 3(y₁ + y₂), z₁ + z₂]

Since (x₁ + x₂) and (y₁ + y₂) are real numbers, we can see that the sum u + v is also in the form [A, B] which satisfies the definition of S.

Therefore, S is closed under vector addition.

6. Is S closed under scalar multiplication? Justify.

To check if S is closed under scalar multiplication, we need to show that if u is a vector in S and c is a scalar, then the scalar multiple c*u is also in S.

Let u = [x, y, z] be a vector in S, and c be a scalar.

According to the given form of vectors in S, we have:

u = [2x - 3y, z]

Now, let's calculate the scalar multiple c*u:

c*u = c[2x - 3y, z]

   = [2cx - 3cy, cz]

Since cx and cy are real numbers, we can see that the scalar multiple c*u is also in the form [A, B] which satisfies the definition of S.

Therefore, S is closed under scalar multiplication.

Now, let's consider problem 7:

7. Specify the nullspace of A.

The nullspace of a matrix A, denoted as Null(A), consists of all vectors x such that Ax = 0, where 0 represents the zero vector.

To find the nullspace of A, we need to solve the equation Ax = 0.

Let's set up the augmented matrix [A | 0] and perform row operations to find the reduced row-echelon form:


1 -2 0 -3 0 1 | 0

-1 1 2 1 2 1 | 0

-4 -2 -2 -3 2 -2 | 0

Performing row operations:

R2 = R2 + R1

R3 = R3 + 4R1

1 -2 0 -3 0 1 | 0

0 -1 2 -2 2 2 | 0

0 6 -2 -15 2 -6 | 0

R3 = R3 + 6R2

1 -2 0 -3 0 1 | 0

0 -1 2 -2 2 2 | 0

0 0 10 -27 14 6 | 0

Now, let's express the system of equations:

x₁ - 2x₂ - 3x₄ + x₆ = 0

-x₂ + 2x₃ - 2x₄ + 2x₅ + 2x₆ = 0

10x₃ - 27x₄ + 14x₅ + 6x₆ = 0

We can solve this system of equations to find the nullspace of A, which represents all vectors x that satisfy the equation Ax = 0.

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The true statement about effect size is: The effect size is the extent to which the null or statistical hypothesis is false. Effect size is a measure used in research studies to quantify the magnitude of the difference between groups or the strength of an association between variables.

It helps determine the practical significance of the research findings, as opposed to the statistical significance.
When the effect size is small, detecting it is not necessarily easier, and a larger sample size may be required to achieve adequate statistical power. A larger effect size, on the other hand, might be easier to detect and might require a smaller sample size.
There is not just one type of effect size measure used in research studies. There are various measures of effect size, such as Cohen's d, Pearson's correlation coefficient (r), and odds ratio (OR), among others. Each type of effect size is suitable for different research designs and data types.

Choosing the appropriate effect size measure depends on the research question, the design of the study, and the type of data being analyzed.

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Fraction of cake each children's  get 1/12.

fraction: In mathematics, a number that is stated as a quotient in which the numerator and denominator are divided. Both are integers in a straightforward fraction. In the numerator or denominator of a complex fraction is a fraction. A correct fraction has a numerator that is lower than its denominator.

Cake  available for Sharing = 1/6

The cake future divide into 1/2:

so,

= (1/6) x (1/2)

= 1/12

fraction of cake each children's  get 1/12.

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Answer:

7/26

Step-by-step explanation:

let the other fraction be x

according to the question,

1/13 +x =9/26

x = 9/26 - 1/13

take lcm of the denominator . lcm=26

x = 9*1 - 1*2/26

x = 9-2/26

x=7/26

Answer:

-15 ft or 15 ft below sea level

Step-by-step explanation:

He started at +8 ft.

Then he went 23 ft down, that is -23 ft.

8 ft + (-23 ft) = 8 ft - 23 ft = -15 ft

Answer: -15 ft

Perimeter = length + length + width + width.

7y-7.5 + 7y-7.5 + 7.5y+8 + 7.5y +8

Combine like terms:

29y+1

The perimeter is 29y + 1 feet

A unit fraction is a fraction with the numerator equals 1.

So, in order to have the fraction 4/5, we can multiply the number in the numerator by a unit fraction with the same denominator:

So the first blank space is filled with 4 and the second one with 1/5.

Answer:

10.89

Step-by-step explanation:

-3.3 x -3.3 = 10.89

A negative times a negative is always a positive.

Answer: N=n 2 X - 3.3

Step-by-step explanation:

We are given the mean μ = 63 mph and the standard deviation σ = 10 mph. We want to find the percentage of cars that are traveling faster than 76 mph.

To find the percentage of cars that are traveling faster than 76 mph, we need to standardize the value of 76 mph using the z-score formula's = (x - μ) / σ,where x is the value we want to standardize.

Substituting the given values, we get:

z = (76 - 63) / 10z

= 1.3

We can use a standard normal distribution table to find the percentage of cars that are traveling faster than 76 mph. Looking up the z-score of 1.3 in the table, we find that the percentage is 90.31%.

The percentage of cars traveling faster than 76 mph is 90.31%.

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Angle DFE=30 -Vertically Opposite Angle

DFE=FDE=30 -Base angles of an isosceles triangle

y+x+30=180 -sum of angles of a triangle

y+30+30=180

y+60=180

y=180-60

y=120

The circumference of the circle is approximately 24.492 yards.

what is circumference ?

Circumference is the distance around the edge of a circle or any other closed curve. It is the perimeter of a circle and is often denoted by the symbol "C". The circumference is a key measurement when working with circles, as it can help us calculate the radius, diameter, and area of the circle.

The formula for the circumference of a circle is:

C = 2πr

where "C" is the circumference, "π" (pi) is a mathematical constant approximately equal to 3.14, and "r" is the radius of the circle.

A circle does not have a perimeter as it is a two-dimensional shape. However, it has a circumference, which is the distance around the circle.

To find the circumference of a circle with a diameter of 7.8 yards and using π as 3.14, we can use the formula:

Circumference = π × Diameter

Circumference = 3.14 × 7.8 yards

Circumference = 24.492 yards (rounded to three decimal places)

Therefore, the circumference of the circle is approximately 24.492 yards.

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