Harry, Jason and Sarah are taking the GMAT 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 another.

Omar can make a maximum of 12 complete bows from the given length of ribbon.

To find the maximum number of complete bows Omar can make, we need to divide the total length of ribbon he has by the length of ribbon needed for each bow, and then round down to the nearest whole number since we can only make complete bows.

First, we need to convert 7 2/5 yards to an improper fraction so that we can work with it more easily. To do this, we multiply the whole number (7) by the denominator of the fraction (5), and then add the numerator (2):

7 2/5 = (7 x 5) + 2/5 = 35/5 + 2/5 = 37/5 yards

Now we can divide the total length of the ribbon by the length needed for each bow:

37/5 ÷ 3/5 = 37/5 x 5/3 = 37/3

This gives us a fraction, but we want a whole number, so we round down to the nearest integer:

37/3 ≈ 12.33

Since we can only make complete bows, the maximum number of bows Omar can make is 12.

Therefore, Omar can make a maximum of 12 complete bows from the given length of ribbon.

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Answer:

12

Step-by-step explanation:

The maximum number of complete bows omar can make is 12

The two numerical solutions of the given trigonometric functions are: 53.13° or 306.87°

In the first quadrant, where the value of x and y coordinates are all positive, it is well known that all the six trigonometric functions possess positive values. In the second quadrant, we see that only sine and cosecant (which is the reciprocal of sine) possess positive values. In the third quadrant, we see that only tangent and cotangent possess positive positive values.

The cosine function is positive in the first and fourth quadrants.

Now, we are told that;

cos(x) = 0.6

Thus;

x = cos⁻¹(0.6)

x = 53.13° or 306.87°

These are the numerical solutions required.

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4

The rank of a matrix can be determined by converting it to its reduced row echelon form. It is also known as the row reduced echelon form or simply the reduced echelon form. The rank of a matrix is the number of non-zero rows in its reduced row echelon form. The given matrix is,

`A=[[2,3,-1,-1],[1,-1,-2,-4],[3,1,3,-2],[6,3,0,-7]]`

We need to convert the given matrix to its reduced row echelon form. It is done by applying elementary row operations on the matrix. The elementary row operations are as follows:

- Interchange the order of two rows.
- Multiply a row by a non-zero scalar.
- Add a multiple of one row to another row.

Let us apply these operations on the given matrix,

`[[2,3,-1,-1],[1,-1,-2,-4],[3,1,3,-2],[6,3,0,-7]]`

`= [R1, R2, R3, R4]`

`R1 → R1 - R2/2` (subtract half of R2 from R1)
`R2 → R2 - R1/2` (subtract half of R1 from R2)
`R3 → R3 - 3R1/2` (subtract three times half of R1 from R3)

`[[1,5/2,1/2,1/2],[0,-3/2,-5/2,-9/2],[0,-7/2,3/2,-7/2],[0,0,-3,-6]]`

`= [R1, R2, R3, R4]`

`R2 → -R2/3` (multiply R2 by -1/3 to make its first entry as 1)
`R3 → R3 - 7R2/3` (subtract 7 times -1/3 of R2 from R3)
`R4 → -R4/3` (multiply R4 by -1/3 to make its first entry as 1)

`[[1,5/2,1/2,1/2],[0,1,5/3,3/2],[0,0,-4/3,-4],[0,0,1,2]]`

`= [R1, R2, R3, R4]`

`R3 → -3R3/4` (multiply R3 by -3/4 to make its third entry as 1)

`[[1,5/2,1/2,1/2],[0,1,5/3,3/2],[0,0,1,1],[0,0,1,2]]`

`= [R1, R2, R3, R4]`

`R4 → R4 - R3` (subtract R3 from R4 to make its third entry as 0)

`[[1,5/2,1/2,1/2],[0,1,5/3,3/2],[0,0,1,1],[0,0,0,1]]`

`= [R1, R2, R3, R4]`

The given matrix is converted to its reduced row echelon form. The last row contains only a single non-zero entry, hence the rank of the matrix is 4.

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The amplitude οf the functiοn is 1/2, the phase shift is (-π)/3, and the periοd is 2π/3.

Phase shift simply means that the twο signals are at different pοints οf their cycle at a given time.

The given functiοn is y = 2 – (1/2) cοs (3x+π).

We can see that the general fοrm οf this functiοn is y = A cοs (Bx - C) + D, where A is the amplitude, B is the frequency, C is the phase shift, and D is the verticaI shift.

Cοmparing the given functiοn with the general fοrm, we can see that:

A = 1/2

B = 3

C = -π

D = 2

Therefοre, the amplitude is |A| = 1/2.

The phase shift is given by C/B = (-π)/3.

The periοd οf the functiοn is given by T = 2π/B = 2π/3.

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Answer: Let's denote the two unknown angles as x and y.

We know that the sum of the three angles in a triangle is 180 degrees. So we can set up the following equation:

10 + 3x + 14x = 180

Simplifying the equation:

17x = 170

x = 10

Now we can use the ratio of the other two angles to find the value of y:

3:14 can be simplified as 3x:14x or x:4.67x

So y is 4.67 times larger than x:

y = 4.67x = 4.67(10) = 46.7

Therefore, the measures of the two unknown angles are x = 10 degrees and y = 46.7 degrees.

Step-by-step explanation:

The measure of the remaining two angles are 46.7

The angle sum property of a triangle states that the sum of interior angles of a triangle is 180°

Given here, One angle of a triangle measures 100°. the other two angles are in a ratio of 3:14. Then let the measure of the angles be 3x and 14x

thus using the angle sum property we have

[tex]3x+14x=80[/tex]

[tex]17x= 80[/tex]

[tex]x = 46.7[/tex]

Hence, The measure of the remaining two angles are 46.7

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Slope AB = slope CD = 1/1 and slope BC ≠ slope DA. Therefore, AB and CD are parallel sides, and ABCD is a trapezoid.

In geometry, a trapezoid (also known as a trapezium in some countries) is a quadrilateral with at least one pair of parallel sides. The parallel sides are called the bases of the trapezoid, and the other two sides are called the legs.

The trapezoid can be classified into three types based on the positions of the bases:

Isosceles trapezoid: A trapezoid in which the non-parallel sides are congruent.

Right trapezoid: A trapezoid in which one of the angles formed by the legs is a right angle.

Scalene trapezoid: A trapezoid in which none of the sides are congruent.

The area of a trapezoid can be calculated by the formula:

A = (b1 + b2)h/2

where b1 and b2 are the lengths of the bases and h is the height of the trapezoid (the perpendicular distance between the bases).

To show that ABCD is a trapezoid, we need to demonstrate that it has at least one pair of parallel sides. One way to do this is to calculate the slopes of the line segments that connect the vertices.

The slope of a line passing through two points (x1, y1) and (x2, y2) is given by:

slope = (y2 - y1) / (x2 - x1)

Using this formula, we can calculate the slopes of the four line segments:

slope AB = (4 - 1) / (2 - (-1)) = 3/3 = 1

slope BC = (1 - 4) / (3 - 2) = -3/1 = -3

slope CD = (-3 - 1) / (-3 - 3) = -4/-6 = 2/3

slope DA = (1 - (-3)) / (-1 - (-3)) = 4/2 = 2

We can see that slope AB = slope CD = 1/1 and slope BC ≠ slope DA. Therefore, AB and CD are parallel sides, and ABCD is a trapezoid.

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Triangle A″B″C″ is formed by a reflection over x = −1 and dilation by a scale factor of 4 from the origin. segment A double prime B double prime equals four segment BC ,equation shows the correct relationship between ΔABC and ΔA″B″C″

The equation that correctly shows the relationship between ΔABC and ΔA″B″C″ is C″A″/CA = 1/4. Triangle A″B″C″ is formed by reflecting triangle ABC over the line x = -1 and dilating it by a scale factor of 4. The reflection of a triangle preserves its angles and its sides are reversed, while the dilatation stretches the triangle out by a factor of 4. Therefore, the ratio between C″A″ and CA will be 1/4.

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Answer:

n

Step-by-step explanation:

less

The expression [tex]-100^5 + 90[/tex] is completely factored as [tex]-(10^5 + 3)(10^5 - 3)[/tex].

Mathematical expressiοns cοnsist οf at least twο numbers οr variables, at least οne arithmetic οperatiοn, and a statement. It's pοssible tο multiply, divide, add, οr subtract with this mathematical οperatiοn.

The expression [tex]-100^5 + 90[/tex] can be factοred as follows -

Grοup the negative sign with the first term -

[tex]= -(100^5) + 90[/tex]

Evaluate [tex]100^5[/tex] as [tex](10^2)^5 = 10^{10}[/tex] -

[tex]= -(10^{10}) + 90[/tex]

Factor οut a negative sign -

[tex]= -(10^{10} - 90)[/tex]

Factor the difference of twο squares, where [tex]a = 10^5[/tex] and b = 3 -

[tex]= -(10^5 + 3)(10^5 - 3)[/tex]

Therefore, the expressiοn is factored as [tex]-(10^5 + 3)(10^5 - 3)[/tex].

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Answer:

here it is

Step-by-step explanation:

This trapezoid has been divided into two right triangles and a rectangle.

How can the area of the trapezoid be determined using the area of each shape?

Enter your answers in the boxes.

The area of the rectangle is in², the area of the triangle on the left is in², and the area of the triangle on the right is in².

The area of the trapezoid is the sum of these areas, which is in².

Trapezoid ABCD with parallel sides DC and AB. Points F and E are between D and C. FEBA form a rectangle with 4 right angles. D F is 2 inches, F E is 14 inches, E C is 2 inches, A B is 14 inches., and E B is 12 inches.

The area of the sector with a central angle of 180° as required to be determined in the task content is; 176.41 cm².

It follows from the task content that the sector in discuss has a central angle of 180° and a diameter of 21.2 cm.

Recall the area of a sector is;

Area, A = (theta/360) × πr²

where r = diameter / 2

r = 21.2/2

r = 10.6 cm.

A = (180/360) × 3.14 × 10.6²

Area, A = 176.41 cm².

Ultimately, the area of the sector is; 176.41 cm².

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Answer:

A. No Solution

B. Unique Solution (0,0)

Step-by-step explanation: When you are dealing with a system of equations and they have the same variables with the same coeffiencts adding up to different numbers, it is unsolvable and therefore has no-solution. When you are dealing with two y-values equaling different amounts of x-values, 0 satisfy both varaibles.

If you approach this from a graphing perspective, you can put both equations in the system into slope intercept form.

System A:

Line 1: 3x + 5y = 8

                  5y = -3x + 8

                    y = -3/5 x + 8/5

Line 2: 3x + 5y = 7

                  5y = -3x + 7

                    y = -3/5 x + 7/5

Because both lines have the same slope, but different y-intercepts, the lines are parallel and will never intersect.  This is why there is no solution to the system.

System B:

Line 1: y = 7x is in slope intercept form.

Line 1: y = 3x is in slope intercept form.

Since these lines have different slopes, they are guaranteed to intersect only once.  There is a single solution.

If you graph these lines, they will intersect at the origin, at (0,0), since that is a common point on both lines.

Answer:

D.

Step-by-step explanation:

Nikolas did not make a mistake. The formula to calculate volume of a triangular prism is

[tex]V=Bh[/tex]

where B is the area of the base and h is the height.

The area of the triangular base is [tex](0/5)(5.8)(6.2) = 17.98[/tex].

[tex]Bh = 17.98 * 9.2 = 165.416 ft^3[/tex]

Answer:

189 chips are estimated to be in the bag.

Step-by-step explanation:

Mass of Chips = Mass of Chips + Bag - Mass of Bag

Mass of Chips = 369 g - 28 g

Mass of Chips = 341 g

Mass of 1 Chip = Mass of 25 Chips / 25

Mass of 1 Chip = 45 g / 25

Mass of 1 Chip = 1.8 g

Number of Chips = Mass of Chips / Mass of 1 Chip

Number of Chips = 341 g / 1.8 g

Number of Chips ≈ 189

Answer:

-2b+12

Step-by-step explanation:

Answer:

-2b+12

Step-by-step explanation:

-2b-4(b+3)-4b

-2b+4b+12-4b

-2b+12

The equivalent expression is 9b^6/a^4c^6

An equivalent expression is a mathematical expression that has the same value as another expression, even though it may be written differently. Equivalent expressions can be useful in simplifying complex mathematical expressions or in solving equations by replacing a complex expression with a simpler, equivalent one.

In algebra, two expressions are considered equivalent if they simplify to the same expression, or if they have the same solution set when solved.

We have that;

(-3ab^2c^-3/a^3b^-1)^2

9a^2b^4c^-6/a^6b^-2

9a^-4b^6c^-6

9b^6/a^4c^6

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Answer: The transformations that occurred to create g(x) = -2(x-8)²-81+7 from f(x) = x are:

- Horizontal translation 8 units to the right: The term (x - 8) in the equation of g(x) means that the graph of g(x) has been shifted horizontally 8 units to the right compared to f(x) = x.

- Vertical stretch by a factor of 2: The coefficient -2 in front of the term (x - 8)² means that the graph of g(x) has been vertically stretched by a factor of 2 compared to f(x) = x.

- Vertical translation 81 units down and 7 units up: The terms -81 and +7 in the equation of g(x) mean that the graph of g(x) has been shifted vertically 81 units down and then 7 units up compared to f(x) = x.

Therefore, the correct answer is (a) vertical translation 7 units up.

Step-by-step explanation:

The coordinates of the new image are S(3, 6) →  (-6, 3), T(4,4) → (-4, 4), and U(5,1) → (-1, 5).

For describing a geometric transformation such a translation, rotation, scaling, or shearing, a matrix known as a transformation matrix is utilised. By multiplying the matrix by the column matrix of the original coordinates, the matrix is used to change the coordinates of points in a geometric figure. The modified figure is then drawn using the resultant transformed coordinates.

Given that the coordinates of the point are:

S(3, 6), T(4,4), and U(5,1)

When the figure is rotated by 90 degrees the resultant image has the following coordinates.

(x, y) → (-y, x)

Thus,

S(3, 6) →  (-6, 3)

T(4,4) → (-4, 4), and

U(5,1) → (-1, 5)

Hence, the coordinates of the new image are S(3, 6) →  (-6, 3), T(4,4) → (-4, 4), and U(5,1) → (-1, 5).

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The equation for c in terms of p is c = (9/7)p. To obtain this equation, we use the given values of C and p to find the constant of proportionality.

We know that c and p are directly proportional, which means that c = kp for some constant k. We can find k by plugging in the given values:

We can solve this system of equations for k by using elimination or substitution. Solving for k, we get

Thus, the equation for c in terms of p is

c = (9/7)p.

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The quadratic equation written in vertex form is:

A(x) = x^2 - 4

Here we want to find the vertex form of the quadratic equation:

A(x) = (x + 2)*(x - 2)

Remember that for a quadratic equation with the vertex (h, k) and leading coefficient a is written as:

f(x) = a*(x - h)^2 + k

Now, notice that the zeros of the quadratic function are x = -2 and x = 2.

Then the vertex is just between these two, at x = 0.

Then h = 0, and the y-value of the vertex is what we get when we evaluate in x = 0.

k = (0 + 2)*(0 - 2) = 2*-2 = -4

Then the vertex is (0, -4) and the leading coefficient is 1, we can write the quadratic equation as:

A(x) = (x - 0)^2 -4

A(x) = x^2 - 4

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Therefore , the solution of the given problem of area comes out to be the cone has a 5 millimetre height.

Calculating how much space would be needed to fully cover the outside will reveal its overall size. When calculating a trapezoidal form's surface, the environs were also taken into account. The surface area of something determines its overall measurements. The amount of edges connecting each of a cuboid's four parallelogram ends reveals how much underground water it can hold.

Here,

Let's name the cone using the details provided:

Its base measures 25 mm2.

A parallel slice 6 mm from the vertex has a 36 mm2 surface.

We can use the fact that the area of a circular slice of a cone is proportional to the square of its distance from the vertex to build up a proportion:

(area of slice) / (base area) Equals (distance from vertex) / (height) 2/ (area from slice)

When we enter the numbers we are aware of, we obtain:

=> 36 / 25 = 6² / h²

If we simplify, we get:

=>  h² = (25 * 6²) / 36 = 25

When we square the two edges, we obtain:

=>  h = 5

As a result, the cone has a 5 millimetre height.

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Answer: To find the probability that a student chosen randomly failed the test and did not complete the homework, we need to subtract the number of students who passed the test and/or completed the homework from the total number of students in the class. Then, we can divide that number by the total number of students in the class to get the probability.

To start, we can use the information given in the problem to create a Venn diagram:

```

Test

|------|------|

| | |

Fail | | |

| | |

--------|------|------|

| | |

| | |

Pass | | |

Assignment|------|------|

| | |

| | |

```

From the diagram, we can see that the number of students who failed the test and did not complete the homework is the number of students outside the intersection of the two circles. To find this number, we can add the number of students who passed the test but did not complete the homework to the number of students who completed the homework but did not pass the test, and then subtract the number of students who passed the test and completed the homework:

Number of students who failed the test and did not complete the homework = (Number of students who passed the test but did not complete the homework) + (Number of students who completed the homework but did not pass the test) - (Number of students who passed the test and completed the homework)

Number of students who failed the test and did not complete the homework = (15 - 13) + (18 - 13) - 13

Number of students who failed the test and did not complete the homework = 4

Therefore, there are 4 students who failed the test and did not complete the homework.

To find the probability of choosing one of these students at random, we can divide the number of students who meet both conditions by the total number of students:

Probability of choosing a student who failed the test and did not complete the homework = Number of students who failed the test and did not complete the homework / Total number of students

Probability of choosing a student who failed the test and did not complete the homework = 4 / 23

Probability of choosing a student who failed the test and did not complete the homework ≈ 0.17

Therefore, the probability that a student chosen randomly from the class failed the test and did not complete the homework is approximately 0.17, or 17% (rounded to two decimal places).

The x-intercept of g(x) is (3,0) and the vertex of g(x) is (3,0).

To find the x-intercept of the quadratic function g(x), we need to set g(x) equal to zero and solve for x:

0 = -5(x - 3)²

Dividing both sides by -5, we get:

0 = (x - 3)²

Taking the square root of both sides, we get:

x - 3 = 0

x = 3

So the x-intercept of the function g(x) is (3,0).

To find the vertex of the function g(x), we can use the formula:

vertex = (h, k)

where;

For a quadratic function in the form:

f(x) = a(x - h)² + k

the vertex is located at the point (h, k).

In the given function g(x), we can see that a = -5, h = 3, and k = 0.

So the vertex of the function g(x) is:

vertex = (h, k) = (3, 0)

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The probability that the number of defective bulbs in the sample is greater than 15 is  0.401, or 40.1%.

This is a binomial distribution problem with n=550 and p=0.035. We want to find the probability that the number of defective bulbs in the sample is greater than 15, which can be written as P(X > 15), where X is the number of defective bulbs in the sample.

Using the binomial probability formula, we have:

P(X > 15) = 1 - P(X ≤ 15)

P(X ≤ 15) = Σi=0¹⁵ (550 chooseᵃ) * 0.035ᵃ * (1-0.035)⁵⁵⁰⁻ᵃ

We can use software or a calculator with a binomial probability distribution function to find this sum, which is approximately 0.599.

Therefore, the probability that the number of defective bulbs in the sample is greater than 15 is:

P(X > 15) = 1 - P(X ≤ 15) ≈ 1 - 0.599 = 0.401

So the probability that more than 15 bulbs in the sample are defective is approximately 0.401, or 40.1%.

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Answer:

x = 3[tex]\sqrt{2}[/tex] , y = [tex]\frac{3\sqrt{2} }{2}[/tex]

Step-by-step explanation:

this is a 90- 45- 45 isosceles triangle with legs congruent , that is

y = [tex]\frac{3\sqrt{2} }{2}[/tex]

using Pythagoras' identity in the right triangle

x² = ( [tex]\frac{3\sqrt{2} }{2}[/tex] )² + y²

   = ( [tex]\frac{3\sqrt{2} }{2}[/tex] )² + ( [tex]\frac{3\sqrt{2} }{2}[/tex] )² = 9 + 9 = 18 ( take square root of both sides )

x = [tex]\sqrt{18}[/tex] = [tex]\sqrt{9(2)}[/tex] = [tex]\sqrt{9}[/tex] × [tex]\sqrt{2}[/tex] = 3[tex]\sqrt{2}[/tex]

Answer:

baby formulaa for sure (wut ur school I got same question)

Step-by-step explanation:

add sum purple to yo nails

yes, it is direct proportion becuz in direct proportion if the prize of one quantity increases the other too will have to increase. here in this question as you can see 5melons were costing 3.50 and on increasing it to 7 melons cost is too increasing soo it is a direct proportion.

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By using trigοnοmetric functiοns, the sizes οf β and γ, tο the nearest 0.1, are β ≈ 24.0 degrees and γ ≈ 63.4 degrees

The basic trigοnοmetric functiοns are:

Sine (sin): the ratiο οf the length οf the side οppοsite an angle tο the length οf the hypοtenuse οf the triangle.

Cοsine (cοs): the ratiο οf the length οf the side adjacent tο an angle tο the length οf the hypοtenuse οf the triangle.

Tangent (tan): the ratiο οf the length οf the side οppοsite an angle tο the length οf the side adjacent tο the angle.

Fοr the first right triangle:

Using the trigοnοmetric functiοn tangent, we have:

tan(β) = οppοsite side / adjacent side

tan(β) = 9/20

Taking the inverse tangent οf bοth sides, we get:

β = tan⁻¹(9/20)

Using a calculatοr, we can find that:

β ≈ 24.0 degrees

Fοr the secοnd right triangle:

Using the trigοnοmetric functiοn cοsine, we have:

cοs(γ) = adjacent side / hypοtenuse

cοs(γ) = 6/15

Taking the inverse cοsine οf bοth sides, we get:

γ = cοs⁻¹(6/15)

Using a calculatοr, we can find that:

γ ≈ 63.4 degrees

Therefοre, the sizes οf β and γ, tο the nearest 0.1, are:

β ≈ 24.0 degrees

γ ≈ 63.4 degrees

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Answer:

Step-by-step explanation:

The volume for a right cylinder is

[tex]V=\pi r^2h[/tex]

We are given all the values except the radius, so we plug them in as follows:

[tex]18488=\pi r^2(23)[/tex]

Begin by dividing by 23π to get

255.8657603 = r²

and then take the square root of both sides to find that

r = 15.995 or 16 m