The Graduate Management Admission Test (GMAT) is taken by individuals interested in pursuing graduate management education. GMAT scores are used as part of the admissions process for more than 6100 graduate management programs worldwide. The mean sore for all test‑takers is 550 with a standard deviation of 120. A researcher in the Philippines is concerned about the performance of undergraduates in the Philippines on the GMAT. She believes that the mean scores for this year's college seniors in the Philippines who are interested in pursuing graduate management education will be less than 550. She has a random sample of 250 college seniors in the Philippines interested in pursuing graduate management education who plan to take the GMAT. Suppose we know that GMAT scores are Normally distributed with standard deviation σ=120. The null and alternative hypotheses are H0:µ=550 versus Ha:µ<550.

Required:
State the null and alternative hypotheses for the study of the performance on the GMAT of college seniors in the Philippines.

Answer: BC = 24

Step-by-step explanation:

Given:

AB = x+33

AC = 3x - 15

BC = x

<B = <C

Solution:

Because <B = <C, you can say the corresponding sides AB and AC are equal as well

AB = AC

x + 33 = 3x -15  

48 = 2x

x = 24

Since x = BC

BC = x

BC = 24

Answer:

Price of the printer is = $193.20

Step-by-step explanation:

Office supply store purchased an all in one printer wit a regular price = $240

After 15% off price of the printer = $240 - 15% of $240

                                                    =

                                                    = 240 - 36

                                                    = $204

The store is offering $20 mail in rebate so the price of printer after rebate

= $204 - $20

= $184

Now price of the printer including sales tax = 184 + 5% of 184

= 184 +

= 184 + 9.20

= $193.20

Two triangles are congruent if their corresponding sides are equal in length, and their corresponding angles are equal in measure.

What is congruent?

Congruent refers to things that are exactly the same size and shape. Even if we flip, turn, or rotate the forms, the shape and size should remain the same.

Here,

we have to prove when can we say that the two triangles are congruent.

SSS, SAS, ASA, AAS, and HL.

These tests describe combinations of congruent sides and/or angles that are used to determine if two triangles are congruent.

Hence, two triangles are congruent if their corresponding sides are equal in length, and their corresponding angles are equal in measure.

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Answer:

Step-by-step explanation:

The equation x^3 + y^3 + z^3 = k represents a curve in 3-dimensional space.

For any given value of k, the equation represents a specific curve, which is a type of algebraic surface called a cubic surface. This surface is smooth and has no corners or singularities.

The curve defined by this equation is symmetric with respect to all three coordinate axes, meaning that if (x, y, z) is a point on the curve, then so are (-x, y, z), (x, -y, z), (x, y, -z), (-x, -y, z), (-x, y, -z), and (x, -y, -z).

In general, the shape of the curve will depend on the value of k. For example, when k is positive and large, the curve will be very spread out, while when k is negative, the curve will be more compact.

This curve is known as an elliptic curve, and it has many interesting mathematical properties and applications in areas such as cryptography and number theory.

Answer: 42

Step-by-step explanation:

i know this because it was a question in my class a few hours ago

Answer:

B) 6.68

Step-by-step explanation:

Use Cosine.

Cosine= Adjacent ÷ Hypotenuse

In this case the base you want to find is adjacent to the angle, 42°. Hence,

Cos (42)= adjacent ÷ hypotenuse

Cos (42) = x ÷ 9

x = Cos (42) × 9. Input that into your calculator.

x= 6.68

To remember the trigonometric ratios/formulas

Use the acronym, SOHCAHTOA

Hope this helps!!!!

Answer:

see the attachment photo!

Answer:

b

Step-by-step explanation:

Answer: x = 70

Step-by-step explanation:

You can simply solve for x by simplifying both sides of the equation, then isolating the variable

Solve, x/7 - 2 = 8, for x.

x/7 = 10, added the value of 2 to both sides of the equation.

x=70, multiplied the value of 7 to both sides of the equation.

Thus the value of x is equal to 70.

Answer:

4,68556

Step-by-step explanation:

√5+√6

= 4,68556

Answer:

$9.75

Step-by-step explanation:

I divided $78 by 8 people and that is how I got this answer.

The inequality representing the given situation is -

300x + 700y ≤ 7500

Advertising is the practice and techniques employed to bring attention to a product or service. Advertising aims to put a product or service in the spotlight in hopes of drawing it attention from consumers.

Given is that Bobby Flay is deciding how to advertise a new gourmet restaurant that he is opening. An online ad costs $300, and a TV ad costs $700. He has $7,500 to spend on the ads.

We can write the inequality as -

300x + 700y ≤ 7500

where -

{x} - number of online ads posted

{y} - number of TV ads poste

Plot the inequality on the graph. The shaded region represents the possible number of advertisements of each category Bobby can use to advertise.

Therefore, the inequality representing the given situation is -

300x + 700y ≤ 7500

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Step-by-step explanation:

When written in standard form, yout can just look at the first term

If the first term is positive it opens upwards

if the first term is negative, it opens downwards

Answer: 3^3 Square root 3

Step-by-step explanation:

Answer:

Knowing that 6 × 7 = 42, we know that 42 ÷ 7 = 6

Step-by-step explanation:

Sorry but its very simple question you need to try to do it by yourself

Answer:

6

Step-by-step explanation:

By understanding the relationship between multiplication and division we can positively say that since 6 × 7 = 42, we know that 42 ÷ 7 = 6.

The domain for the square root function is the set of all whole numbers

From the question, we have the following parameters that can be used in our computation:

Function type = square root function

Equation: square root of x

This means that

f(x) = √x

The domain for x in the function is the set of input values the function can take

In this case, the square root function can take any whole number as its input

This means that the domain for f(x) is the set of all whole number

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Answer:

The company will expect to replace 13.03% of batteries.

The company should guarantee the batteries for 35 months.

Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the zscore of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question, we have that:

\(\mu = 45, \sigma = 8\)

If Quick start guarantees a full refund on any battery that fails within the 36 month period after purchase, what percentage of its batteries will the company expect to replace?

This is the pvalue of Z when X = 36. So

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{36 - 45}{8}\)

\(Z = -1.125\)

\(Z = -1.125\) has a pvalue of 0.1303.

The company will expect to replace 13.03% of batteries.

If quick Start does not want to make refunds for more than 10% ofits batteries under the full refund guarantee policy, for how longshould the company guarantee the batteries

They should guarantee to the 10th percentile, which is X when Z has a pvalue of 0.1. So it is X when Z = -1.28.

\(Z = \frac{X - \mu}{\sigma}\)

\(-1.28 = \frac{X - 45}{8}\)

\(X - 45 = -1.28*8\)

\(X = 34.76\)

Rounding to the nearest month

The company should guarantee the batteries for 35 months.

A. True.

In a two-column proof, the left column consists of statements, which are the facts or assumptions that lead to the proof of the theorem, while the right column consists of the reasons or justifications that explain how each statement logically follows from the previous one. Therefore, the left column states your reasons is a true statement.

The answer to the student's question is True. In a two-column proof, the left column contains the statements (steps) and the right column contains the corresponding reasons (justifications).

The answer to the question, 'True or false? In a two-column proof, the left column states your reasons', is A. True.

A two-column proof is organized into two columns. The left column contains the 'Statements' and the right column contains the corresponding 'Reasons'. The 'Statements' are the steps that lead to the conclusion of the proof, while the 'Reasons' justify each of those steps according to rules or laws of mathematics.

For example, if we want to prove that the opposite angles of a parallelogram are equal. The left column (Statements) could contain the first step 'ABCD is a parallelogram' and the right column (Reasons) would give the explanation 'Given'. Therefore, in a two-column proof, the left column does represent statements, not reasons.

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Answer:

I don't know I just want my free answers

The number of minutes spent higher than 38 meters above the ground on the Ferris wheel ride is approximately 1.0918 minutes.

To solve this problem, we need to determine the angular position of the Ferris wheel when it is 38 meters above the ground.

The Ferris wheel has a diameter of 50 meters, which means its radius is half of that, or 25 meters.

When the Ferris wheel is at its highest point, the radius and the height from the ground are aligned, forming a right triangle.

The height of this right triangle is the sum of the radius (25 meters) and the platform height (4 meters), which equals 29 meters.

To find the angle at which the Ferris wheel is 38 meters above the ground, we can use the inverse sine (arcsine) function.

The formula is:

θ = arcsin(h / r)

where θ is the angle in radians, h is the height above the ground (38 meters), and r is the radius of the Ferris wheel (25 meters).

θ = arcsin(38 / 29) ≈ 1.0918 radians

Now, we know the angle at which the Ferris wheel is 38 meters above the ground.

To calculate the time spent higher than 38 meters, we need to find the fraction of the total revolution that corresponds to this angle.

The Ferris wheel completes one full revolution in 2 minutes, which is equivalent to 2π radians.

Therefore, the fraction of the revolution corresponding to an angle of 1.0918 radians is:

Fraction = θ / (2π) ≈ 1.0918 / (2π)

Finally, we can calculate the time spent higher than 38 meters by multiplying the fraction of the revolution by the total time for one revolution:

Time = Fraction \(\times\) Total time per revolution = (1.0918 / (2π)) \(\times\) 2 minutes

Calculating this expression will give us the answer in minutes.

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To find the number of dimes and quarters, you have 17 dimes and 34 quarters in your pocket , when there are 51 coins in your pocket.

To solve this problem, we can set up a system of equations using the given information. Let's use "d" to represent the number of dimes and "q" to represent the number of quarters.

We know that there are 51 coins in total, so we can write the equation: d + q = 51.

We also know that the total value of the coins is $10.20, which can be expressed as 10d + 25q (since dimes are worth 10 cents and quarters are worth 25 cents). So our second equation is: 10d + 25q = 1020.

To solve this system of equations, we can use substitution or elimination. Let's use substitution:

Rearrange the first equation to solve for d: d = 51 - q.

Substitute this expression for d in the second equation: 10(51 - q) + 25q = 1020.

Simplify and solve for q: 510 - 10q + 25q = 1020.

Combine like terms: 15q = 510.

Divide both sides by 15: q = 34.

Now substitute this value back into the first equation to solve for d: d + 34 = 51.

Subtract 34 from both sides: d = 17.

Therefore, you have 17 dimes and 34 quarters.

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Answer:

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

Apply the Triangle Inequality Theorem.

It states that:

We'll take the sum of two shortest sides and compare with the longest:

It confirms the theorem, without testing the other two sides (which is obvious) so the answer is yes.

The matching answer choice is e).

Answer:

-5

Step-by-step explanation:

-3y = 10 + 5

-3y = 15

y = - 5

Answer:

hi

Step-by-step explanation:

-3y-5=10

-3y=10+5

-3y=15

y=15/ -3

y= -5

hope it helps

have a nice day

Answer:

0.0001292

Step-by-step explanation:

a raised to the power -m is 1/a raised to power m

Step-by-step explanation:

The given problem can be solved by using the properties of parabola.

The statements are true about the function and its graph are as follows;

The value of the function when f(-10) is 82.

The value of a is 1/5 which is positive then the parabola opens upward.

The graph contains the point (20, –8)

Given that,

Consider the quadratic function;

\rm f(x) =\dfrac{1}{5}x^2 -5x + 12.f(x)=51x2−5x+12.

We have to determine,

Which statements are true about the function and its graph?

According to the question,

The quadratic function;

\rm f(x) =\dfrac{1}{5}x^2 -5x + 12.f(x)=51x2−5x+12.

1. The value of the function when f(-10) is,

\begin{gathered}\rm f(x) =\dfrac{1}{5}x^2 -5x + 12\\\\f(-10) = \dfrac{1}{5}(-10)^2 -5(-10)+ 12\\\\ f(-10) = \dfrac{1}{5}(100) +50+ 12\\\\ f(-10) =20 +62\\\\ f(-10) = 82\end{gathered}f(x)=51x2−5x+12f(−10)=51(−10)2−5(−10)+12f(−10)=51(100)+50+12f(−10)=20+62f(−10)=82

The value of the function when f(-10) is 82.

2. The graph of the function opens down

.\rm f(x) =\dfrac{1}{5}x^2 -5x + 12.f(x)=51x2−5x+12.

The value of a is 1/5 which is positive then the parabola opens upward.

3.  The graph contains the point f(x) = 20,

\begin{gathered}\rm f(x) =\dfrac{1}{5}x^2 -5x + 12\\\\f(20) =\dfrac{1}{5}(20)^2 -5(20) + 12\\\\f(20) =\dfrac{1}{5}400 -100 + 12\\\\f(20) =80 -100 + 12\\\\f(20)= -20+12\\\\f(20)=-8\end{gathered}f(x)=51x2−5x+12f(20)=51(20)2−5(20)+12f(20)=51400−100+12f(20)=80−100+12f(20)=−20+12f(20)=−8

The graph contains the point (20, –8)

4. The graph contains the point f(x) = 0,

\begin{gathered}\rm f(x) =\dfrac{1}{5}x^2 -5x + 12\\\\f(0) =\dfrac{1}{5}(0)^2 -5(0) + 12\\\\f(0) =\dfrac{1}{5}0 -0 + 12\\\\f(0) =0 -0 + 12\\\\f(0)= 12\end{gathered}f(x)=51x2−5x+12f(0)=51(0)2−5(0)+12f(0)=510−0+12f(0)=0−0+12f(0)=12

The graph contains the point (0, 12).

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Answer:

Step-by-step explanation:

Martin is two years younger than three times his daughter Ada’s age:

The sum of their ages is 54:

Solving this equation for m:

Eliminate m:

Solve for a:

Find m:

Martin is 40 and Ada is 14

Answer:

d. 102.3 units ^2

Step-by-step explanation:

answer:

$1.40

step-by-step explanation:

so the price of one hat is your unknown variable, so let's make an equation out of it:

60*x=$84.00

let's let x stand for the price of one hat

the way i figured it out was to do 84 ÷ 60

which equals 1.4

and remember, since we're dealing with money you must add a zero at the end of the decimal

then if you want, just to ensure that this is correct you can multiply 60*1.40

good luck :)

i hope this helps

have a great day !!