1. The Graduate Management Admission Test (GMAT) is a standardized exam used by many universities as part of the assessment for admission to graduate study in business. The average GMAT score is 547 (Magoosh website). Assume that GMAT scores are bell-shaped with a standard deviation of 100. What percentage of GMAT scores are 647 or higher

The equation formed after the transformations is given as follows:

\(g(x) = \frac{1}{6}\sqrt{x + 3}\)

The parent function in this problem is defined as follows:

\(f(x) = \sqrt{x}\)

For the vertical shrink by a factor of 1/6, the function is multiplied by 1/6, hence it is given as follows:

\(g(x) = \frac{1}{6}\sqrt{x}\)

For the translation left 3 units, we have that x -> x + 3, hence:

\(g(x) = \frac{1}{6}\sqrt{x + 3}\)

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The possible values for angles 1, 2, and 3 given that lines a and b are parallel lines include the following:

In Mathematics and Geometry, parallel lines are two (2) lines that are always the same (equal) distance apart and never meet or intersect.

Note: Assuming angle 1 is equal to 60 degrees.

In Mathematics and Geometry, the vertical angles theorem states that two (2) opposite vertical angles that are formed whenever two (2) lines intersect each other are always congruent, which simply means being equal to each other:

m∠1 ≅ m∠3 = 60°.

Based on the linear pair postulate, the measure of angle 2 can be determined as follows;

m∠1 + m∠2 = 180°

60° + m∠2 = 180°

m∠2 = 180° - 60°

m∠2 = 120°

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Answer:

2n-8

Step-by-step explanation:

twice n is 2n. decreased by 8 is the -8

The probability that all 4 are teachers is  0.0000135.

The total number is =

4 + 30 + 4

= 38

The committee of 4 from 38 =

38C4 = 73815

The committee of 4 from 4 teachers =

4C4 = 1 way

The total favorable cases = 1 way

Probability = favorability/ total cases

= 1/73815

= 0.0000135

Hence the probability that all 4 are teachers is 0.0000135.

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The Emily soccer team has the higher ratio of wins to losses.

Ratio is defined as the relationship between two quantities where it tells how much one quantity is contained in the other.

The ratio of a and b is denoted as a : b.

Given that,

Ratio of win to loss of Emily soccer team = 9 : 12

Ratio of win to loss of Grant soccer team = 10 : 15

9 : 12 = 9 / 12 = (9 × 5) / (12 × 5) = 45 / 60

10 : 15 = 10 / 15 = (10 × 4) / (15 × 4) = 40 / 60

If 60 games are losses, then 45 games are wins for Emily soccer team.

If 60 games are losses, then 40 games are wins for Grant soccer team.

Higher ratio is for Emily soccer team.

Hence higher ratio of wins to losses is for Emily soccer team.  

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Answer:

f(16)= 4-16

f(16)= -12

The probability that an employee posted to country A at age 30 will survive to age 40 if she remains in that country is 2 x 10⁻⁶³

Probability is a mathematical concept that describes the likelihood of a specific event occurring within a set of possible outcomes

Let's start by defining some terms. The force of mortality, also known as the death rate, is the number of deaths per unit time per unit of population.

The probability of survival is the chance that an individual will live past a certain age. In our case, we want to know the probability of surviving from age 30 to age 40 while living in country A.

To calculate the probability of survival, we will use the formula:

\(P(x) = e^{-qx}\)

Where P(x) is the probability of survival at age x and qx is the force of mortality at age x.

First, we will calculate the force of mortality for the first five years after arrival in country A using the equation given in the question:

90x+1 = (6 - 1)9x+1

For x = 30, we have:

90(30) + 1 = (6 - 1)9(30) + 1

2701 = 5 * 891 + 1

2701 = 4445 + 1

2700 = 4445

So, q30 = 4445/30 = 148.5

Next, we will use this value to calculate the probability of survival for the first five years in country A:

\(P30 = e^{-q3} = e^{-148.5} = 1.2 \times 10^{-64}\)

Since the force of mortality for those who have lived in country A for at least five years is 50% greater than the US Life Tables, 2002, Females, we can calculate the force of mortality for the next 10 years as follows:

qx = 1.5 x qx from US Life Tables

Using the values from Table 3.11, we have:

q31 = 1.5 x 98,424 = 147,636

q32 = 1.5 x 98,362 = 147,543

q33 = 1.5 x 98,296 = 147,444

q34 = 1.5 x 98,225 = 147,338

q35 = 1.5 x 98,148 = 147,222

q40 = 1.5 x 97,500 = 146,250

Finally, we can use these values to calculate the probability of survival from age 31 to age 40:

\(P31 = e^{-q31} = e^{-147,636} = 1.3 \times 10^{-65}\\ \\P32 = e^{-q32} = e^{-147,543} = 1.4 \times 10^{-66}\\\\P33 = e^{-q33} = e^{-147,444} = 1.5 \times 10^{-67}\\\\P34 = e^{-q34} = e^{-147,338} = 1.6 \times 10^{-68}\\\\P35 = e^{-q35} = e^{-147,222} = 1.7 \times 10^{-69}\\\\P40 = e^{-q40} = e^{-146,250} = 2.0 \times 10^{-63)}\\\\\)

Complete Question:

When posted overseas to country A at age x, the employees of a large company are subject to a force of mortality such that, at exact duration t years after arrival overseas (t = 0,1,2,3,4), 90x+1 = (6 - 1)9x+1 where qx+t is on the basis of US Life Tables, 2002, Females. For those who have lived in country A for at least five years the force of mortality at each age is 50% greater than that of US Life Tables, 2002, Females, at the same age. Some lx values for this table are shown in Table 3.11.

An extract from the United States Life Tables, 2002,

Females. Age,

x 30 31 32 33 34 35 40

1x 98,424 98,362 98,296 98,225 98,148 98,064  97,500

Calculate the probability that an employee posted to country A at age 30 will survive to age 40 if she remains in that country.

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A function is a relationship between inputs where each input is related to exactly one output.

n = 2 is the input

f(2) = -2 is the output

The value of f(n) at n = 2 is -2.

A function is a relationship between inputs where each input is related to exactly one output.

Example:

f(x) = 2x + 1

f(1) = 2 + 1 = 3

f(2) = 2 x 2 + 1 = 4 + 1 = 5

The outputs of the functions are 3 and 5

The inputs of the function are 1 and 2.

We have,

f(n) = n² - 3n

when n = 2 we get,

f(2) = 2² - 3 x 2 = 4 - 6 = -2

Thus,

n = 2 is the input

f(2) = -2 is the output

The value of f(n) at n = 2 is -2.

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Answer:

64 cm^2

Step-by-step explanation:

SA = s^2 + 2sl

= 4^2 + 2(4)(6)

= 64 cm^2

Answer:

well 2 times three is 5 so then you would end up with

18 divided by 5

-----------------------

5-2

then 18 divided by 5 is 3.6 so then you have

3.6

---------

5-2

and five minus 2 is three

3.6

-----

3

and 3.6 divided by three is 1.2

YOUR ANSWER IS 1.2 ;)

Step-by-step explanation:

Answer:

a=1

b= -6

c=48

Step-by-step explanation:

x^2=6(x-8)

x^2=6x-48

x^2-6x+48

a,b are the coefficients of x^2 and x

c is the constant value present

Therefore it is basically written as ax^2+bx+c

and comparing with the answer x^2-6x+48,

a=1, b= -6, c=48

Answer:

x

+

6

y

=

5

Step-by-step explanation:

The missing variables on item 2 are given as follows:

The three trigonometric ratios are the sine, the cosine and the tangent of an angle, and they are obtained according to the formulas presented as follows:

For the angle of 60º, we have that:

Hence the length o is given as follows:

tan(60º) = o/12.

\(\sqrt{3} = \frac{o}{12}\)

\(o = 12\sqrt{3}\)

Applying the Pythagorean Theorem, the length i is given as follows:

i² = 12² + \((12\sqrt{3})^2\)

i² = 576

i² = 24²

i = 24.

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Answer:

o = 12√3

i = 24

Step-by-step explanation:

From observation of the given right triangle, we can see that two of its interior angles measure 60° and 90°. As the interior angles of a triangle sum to 180°, this means that the remaining interior angle must be 30°, since 30° + 60° + 90° = 180°. Therefore, the triangle is a special 30-60-90 triangle.

The side lengths in a 30-60-90 triangle have a special relationship, which can be represented by the ratio formula a : a√3 : 2a, where "a" represents a scaling factor that can be any positive real number.

In triangle #2, the shortest leg is 12 units.

As "a" is the shortest leg, the scale factor "a" is 12.

The side labelled "o" is the longest leg opposite the 60° angle. Therefore:

\(o = a\sqrt{3}=12\sqrt{3}\)

The side labelled "i" is the hypotenuse of the triangle. Therefore:

\(i= 2a = 2 \cdot 12=24\)

Therefore:

Answer:

The average rate of change for the given function, from x = −3 to x = 7 will be:

Step-by-step explanation:

Given the table

x                      f(x)

-3                     50

3                      10

7                       0

As the interval is from x = -3 to x = 7.

so

at x₁ = -3, f(x₁) = 50

at x₂ = 7,  f(x₂) = 0

Using the formula to determine the average rate of change at which the total cost increases will be:

Average rate = [f(x₂) - f(x₁)] / [ x₂ - x₁]

                       = [0 - 50] / [7-(-3)]

                      = [-50] / [7+3]

                      = -50 / 10

                      = -5

Therefore, the average rate of change for the given function, from x = −3 to x = 7 will be:

Answer:

gdfgdf

Step-by-step explanation:

The correct simplification of (-2x^3y)(3x^3y^4)^2 is -18x^9y^9.

To correctly simplify the expression (-2x^3y)(3x^3y^4)^2, let's break it down step by step:

Apply the exponent to the second term inside the parentheses:

(-2x^3y)(9x^6y^8)

Multiply the coefficients separately, the x terms separately, and the y terms separately:

((-2)(9))(x^3 · x^6)(y · y^8)

-18x^(3+6)y^(1+8)

-18x^9y^9

Combine the exponents and simplify:

-18x^9y^9

So, the correct final answer is -18x^9y^9.

Jenny's mistake occurred in step two. When multiplying the x terms, she should have added the exponents, resulting in x^(3+6) = x^9. Similarly, when multiplying the y terms, she should have added the exponents, giving y^(1+8) = y^9.

Therefore, the correct simplification of (-2x^3y)(3x^3y^4)^2 is -18x^9y^9.

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The teacher can thus use social sciences as a vehicle to develop mathematical skills by facilitating the development of skills such as data interpretation and analysis.

As an instructor, I would use social sciences to develop mathematical skills in the following manner:Consider a social science topic like demography. In this case, a teacher could use mathematics to assist students in interpreting population statistics.

Teachers might guide students to gather information about population size, growth rate, and geographical distribution from various countries and then use statistics to analyze the data.

For example, a teacher could give students graphs or charts to help them understand population growth rates. They can be asked to make comparisons and identify trends.

In this way, students' understanding of the population is improved, as is their mathematical reasoning.Aside from using mathematics to interpret population statistics,

the teacher can also incorporate mathematical skills development in social sciences by using methods that involve understanding and analysis of data. In other words, students learn how to use data to reach conclusions and make decisions.

They learn how to interpret data and how to extract information from it.This method of teaching creates opportunities for the use of the same skills in different contexts and areas of learning.

It enables students to see connections between subjects and fosters an integrated approach to learning.

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A. The null hypothesis H₀ and the alternative hypothesis H₁ are:

H₀: μ = 35 minutes       H₁: μ > 35 minutes

B. If the consultant decides not to reject the null hypothesis, she might be making a Type II error.

C. A Type II error would be failing to reject the hypothesis that μ is = to 35 minutes when, in fact, μ is 43 minutes.

A Type II error occurs when the null hypothesis is false, but the test does not reject it.

In this case, the consultant would be concluding that the mean shopping time is 35 minutes, when in fact it is greater than 35 minutes.

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Answer:

1. Take the value of X and replace X with that value in the equation.

2. Now you solve Y.

Answer:

Step-by-step explanation:

3+1/2x=0

1/2x=-3

2(1/2)x=(-3)2

x=|-6|

x=6  km

Answer:

4x + 42

Step-by-step explanation:

\(\text{Perimeter}=(x+15)+(2x+15)+(x+12)=4x+42\)

The distance between the points (-6, 4) and (5, 4) is 11 units.

To find the distance between two points in a Cartesian coordinate system, we can use the distance formula:

Distance = √[(x2 - x1)² + (y2 - y1)²]

Given the two points (-6, 4) and (5, 4), we can plug in the coordinates into the distance formula:

Distance = √[(5 - (-6))² + (4 - 4)²]

        = √[(5 + 6)² + 0²]

        = √[11² + 0]

        = √[121]

        = 11

Therefore, the distance between the points (-6, 4) and (5, 4) is 11 units.

In this case, since the y-coordinates of both points are the same (4), the distance between them only considers the difference in their x-coordinates. As the x-coordinate of the second point is 11 units greater than the x-coordinate of the first point, the distance between them is simply the absolute value of the difference, which is 11.

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Answer:

Step-by-step explanation:

The volume of this pyramid in cubic inches is 16.

Given that,

The base and height is 8 and 6.

Based on the above information, the calculation is as follows:

The volume is

= 16

Based on the plot of the Cummulative relative frequency graph shown ;

Using the Cummulative relative frequency curve, the location of the song length at 7 minutes on the curve corresponds to approximately 0.975 on the y - axis.

Hence, (1 - 0.975)% = 2.50%

The point at which song length equals 3 minutes has a corresponding value of 0.3 on the y - axis which is (0.3 × 100%) = 30% = 30th percentile

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Answer: AE = 120.83 m  DE= 148.66 m

The perimeter of the pentagon is 699.49

Sketch attached.

Step-by-step explanation: First we have to imagine the shape of the pentagon. In order to satisfy the requirement  "that E is 50 m from the side AB and 30 m from the side BC," this must be a concave pentagon.

To determine the lengths of sides AE and DE, subtract the given distances of E from the lines, and use those values in the Pythagorean Theorem.

AE: \(110^{2}+50^{2}=14600\)     \(\sqrt{14600}=120.8304597\)

DE: \(100^{2}+110^{2}=22100\)   \(\sqrt{22100}=148.6606875\)

Add those lengths and the remaining sides of the "rectangle shown below" to calculate the perimeter.

280+150+120.83+148.66= 699.49

Answer:

\(x=\frac{3+\sqrt{6} }{3}, \frac{3-\sqrt{6} }{3}\)

Step-by-step explanation:

Let's see

\(\\ \rm\rightarrowtail 3x^2-6x+1=0\)

\(\\ \rm\rightarrowtail x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\)

\(\\ \rm\rightarrowtail x=\dfrac{6\pm \sqrt{36-12}}{6}\)

\(\\ \rm\rightarrowtail x=\dfrac{6\pm \sqrt{24}}{6}\)

\(\\ \rm\rightarrowtail x=\dfrac{6\pm 2\sqrt{3}}{6}\)

\(\\ \rm\rightarrowtail x=\dfrac{3+\sqrt{3}}{6}\)

Answer:

Part A: It was an increase.

Part B:80%

Step-by-step explanation:

First, state the info of the problem

Cost Price(CP):$500,000

Selling Price(SP):$900,000

Part A Solution

The SP is higher than the CP so there is a price increase

$900,000>$500,000

Part B Solution

Find price change

Price change equals SP-CP

$900,000-$500,000 equal to $400,000

State CP percent so it will later help in finding percent of price change

CP percent:100%(basic percent for the original cost of item,CP percent is basically 100%)

Cross multiply by comparing amount with percent

So if $500,000 equals 100%

∴$400,000 equals ?(can be represented by variable "x")

Cross-multiplying, we get

$500,000x equals 100%×$400,000(dividing both sides by $500,000)

x equals (400/5)% which further equals 80%

∴The percent of change for the house price was 80%

To confirm

If there was a price increase(Profit),the SP equals CP plus P

SP equals 100% plus 80%:180% ∴SP equals 180%

If 100% equals $500,000

∴180% equals x which is $900,000 after cross-multiplying.

Hope all confusion is now cleared.

Answer:

c

Step-by-step explanation:

Answer:

It is 4/5

Step-by-step explanation:

hope it helps ^^