Exercise 1. In a certain course, suppose that letter grades are are given in the following manner: A to [100, 90], B to (90, 75], C to (75,60], D to (60,50], F to [0,50). Suppose the following number of grades A, B, C, D were observed for the students registered in the course. Use the data to test, at level a = .05, that data are coming from N(75, 81).
A B CDF
3 12 10 4 1

According to the information, we can express the vector w as a linear combination of v1, v2, and v3 like this: w = -v1 - 5v2 - 3v3

We can express the vector w as a linear combination of v1, v2, and v3. Let's say:

w = c1 v1 + c2 v2 + c3 v3

We can find the values of c1, c2, and c3 using the dot product properties of orthogonal vectors. Since v1, v2, and v3 are orthogonal:

w ⋅ v1 = (c1 v1 + c2 v2 + c3 v3) ⋅ v1 = c1 (v1 ⋅ v1) = 6c1

w ⋅ v2 = (c1 v1 + c2 v2 + c3 v3) ⋅ v2 = c2 (v2 ⋅ v2) = 18c2

w ⋅ v3 = (c1 v1 + c2 v2 + c3 v3) ⋅ v3 = c3 (v3 ⋅ v3) = 25c3

Using the given values, we can set up a system of equations:

-6 = 6c1 + 0c2 + 0c3

-90 = 0c1 + 18c2 + 0c3

-75 = 0c1 + 0c2 + 25c3

Solving for c1, c2, and c3, we get:

c1 = -1

c2 = -5

c3 = -3

Therefore, we have:

w = -v1 - 5v2 - 3v3

Note: The solution is not unique, as any linear combination of v1, v2, and v3 that satisfies the given dot product conditions would work.

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Answer:

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

Use circumference formula:

Find the radius by rearranging the formula and substituting 32 for C:

Answer:

5.09 in

Step-by-step explanation:

We know that the formula to find the circumference of a circle is:

C = 2πr

Here,

C → Circumference → 32 in

r → radius

Let us find the radius of the circle by substituting the given values.

\(\sf C = 2\pi r\\\\\sf 32 = 2\pi r\\\\Divide\:both\:sides\:by\:2 \pi \:and\:make\:r\:the \:subject\\\\\dfrac{32}{2 \pi} =\dfrac{2 \pi r}{2 \pi} \\\\\red{5.09 \:in=r}\)

Answer:

Find the LCM of 2 and 3:

LCM = 2 x 3 = 6

Multiply the ratio by 6:

Ratio = 1/2 x 6 : 1/3 x 6

Ratio = 3 : 2

Number of ways 5 gymnasts participate including exactly two from Lia , Bella , Priscilla is equal to 252.

As given in the question,

Total number of gymnasts = 12

Number of gymnasts to be participates = 5

Condition:

Exactly two gymnasts from Lia , Bella , Priscilla

Number of ways 5 gymnasts participates

= ⁹C₃ × ³C₂

= ( 9!)/ ( 9 - 3)! 3! × 3!/ ( 3-2)! 2!

= [( 9× 8 ×7 × 6!)/ 6! ( 3× 2× 1)] × ( 3 × 2!)/ 2!

= [( 9× 8 ×7)/ ( 3× 2× 1)] × 3

= 252

Therefore, the number of ways 5 gymnast can participate out of 12 with the given condition is 252.

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The probability that a cell phone user makes or receives less than 12 calls per day is 0.3971.

To find P(x < 12), we need to standardize the value of 12 using the formula: z = (x - μ) / σ where z = z-score, x = value of interest, μ = mean, and σ = standard deviation.

Substituting the values, we get:

z = (12 - 13.1) / 4.3

z = -0.25581

Using a calculator, we can find the probability that z is less than -0.25581, which is:

P(z < -0.25581) = 0.3971

P(z < -0.25581) = 39.71%.

Full question "Suppose the number of cell phone calls made or received per day by cell phone users follows a normal distribution with a mean of 13.1 and a standard deviation of 4.3. Find P (x <12)".

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The probability that both jurors selected are female is 1/6. To calculate the probability that both jurors selected are female,.

We need to determine the number of favorable outcomes (two female jurors selected) divided by the total number of possible outcomes.

In this scenario, there are two female alternate jurors available out of a total of four alternates. Since we need to select two jurors, we can use combinations to calculate the number of possible outcomes.

The number of possible outcomes is given by selecting 2 jurors out of 4, which can be calculated as:

C(4, 2) = 4! / (2! * (4-2)!) = 6

Therefore, there are 6 possible outcomes.

Out of these possible outcomes, we are interested in the favorable outcome where both selected jurors are female. Since there are two female alternate jurors available, we can calculate the number of favorable outcomes by selecting 2 female jurors out of 2, which is:

C(2, 2) = 2! / (2! * (2-2)!) = 1

Therefore, there is 1 favorable outcome.

Now, we can calculate the probability:

Probability = Number of favorable outcomes / Number of possible outcomes

= 1 / 6

= 1/6

Thus, the probability that both jurors selected are female is 1/6.

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- 4.6 p - 6.3 p + 3.9 = -9.18

- 10.9 p + 3.9 = - 9.18

- 10.9 p = - 9.18 - 3.9

- 10.9 p = - 13.08

p = ( - 13.08 ) : ( - 10.9 )

Answer:

p = 1.2

Answer:

1.2

Step-by-step explanation:

Just took it :)

The actual length of a wall by using a scale of 1:150 is 7.5 m.

The drawing scale is the ratio of drawing size to actual size. To determine the scale of the drawing, we need to know about the formula first which is given by :

scale = drawing size : actual size

From that question, we know that :

scale = 1 : 150

drawing size = 5 cm

Based on the scale we can change the formula to

actual size = drawing size / scale

actual size = 5/ (1:150)

actual size = 5 x 150

actual size = 750 cm

Converting to the meter by dividing with 100

actual size = 750/100 m

actual size = 7.5 m

Hence, the actual length of a wall is 7.5 m

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The value of \(\sin \beta\) in the given triangle ABC is \(\dfrac{4}{5}\). Option D is correct.

Trigonometric ratios are the ratio of sides of a right angled triangle. There are 6 types of trigonometric ratios: sin, cos, tan, cosec, sec, and cot.

Sine trigonometric ratio is the ratio of perpendicular (side opposite to the angle) to the hypotenuse.

In the given figure, the side opposite to the angle \(\beta\) is AC = 4 and the hypotenuse is AB = 5.

So, the sine ratio will be equal to,

\(\sin \beta=\dfrac{4}{5}\)

Therefore, the value of \(\sin \beta\) in the given triangle ABC is \(\dfrac{4}{5}\). Option D is correct.

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Angles themselves cannot be parallel or not parallel to each other. Parallel lines are the ones that never intersect and always maintain the same distance between each other. However, angles can be congruent or supplementary to each other.

If you are referring to two lines with angles formed by a transversal, you can determine if the angles are congruent by comparing their measurements.

Angles themselves cannot be parallel or not parallel to each other. Parallel lines are the ones that never intersect and always maintain the same distance between each other. However, angles can be congruent or supplementary to each other.

If you are referring to two lines with angles formed by a transversal, you can determine if the angles are congruent by comparing their measurements. Two angles are congruent if they have the same measure. This can be proven using various angle relationships and properties, such as vertical angles, corresponding angles, alternate interior angles, alternate exterior angles, etc. These relationships are based on the properties of parallel lines and transversals.

If you want to determine if two angles are supplementary (their measures add up to 180 degrees), you can add the measures of the angles and check if the sum is equal to 180 degrees.

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Answer: this is

1 3/10= 1.3

The value of x is equal to 15°

In Mathematics and Geometry, the sum of the exterior angles of both a regular and irregular polygon is always equal to 360 degrees.

Note: The given geometric figure (regular polygon) represents a pentagon and it has 5 sides.

By substituting the given parameters, we have the following:

3x + 4x + 8 + 5x + 5 + 6x - 1 + 5x + 3 = 360°.

3x + 4x + 5x + 6x + 5x + 8 + 5 - 1 + 3 = 360°.

23x + 15 = 360°.

23x = 360 - 15

23x = 345

x = 345/23

x = 15°.

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Therefore, the change-of-coordinates matrix from B to C is: [ 1 ] [ -1 ]

(a) To find the change-of-coordinates matrix from B to C, we need to express the vectors in C (cos 2x, 1) as linear combinations of the vectors in B (sin^2 x, cos^2 x).

Let's express (cos 2x, 1) in terms of B:

(cos 2x, 1) = a(sin^2 x, cos^2 x)

Expanding the right side using scalar multiples a and b:

(cos 2x, 1) = a(sin^2 x, cos^2 x) = (asin^2 x, acos^2 x)

Comparing corresponding components, we have the following equations:

cos 2x = asin^2 x

1 = acos^2 x

Dividing the first equation by the second equation, we get:

(cos 2x) / 1 = (asin^2 x) / (acos^2 x)

cos 2x = (sin^2 x) / (cos^2 x)

cos 2x = tan^2 x

Using a trigonometric identity, tan^2 x = sec^2 x - 1, we have:

cos 2x = sec^2 x - 1

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Answer:

you're right the answer is 'B'

-12a³b²/6ab²

-12a³/6a

-2a³/a

-2a²

Answer:

11

Step-by-step explanation:

i just did it right now

Answer:

There is no parallelogram shown, so i can't help you.

Step-by-step explanation:

The Intuition for why the area of a parallelogram is A=bh (area = base x height)

The formula for the area of a parallelogram is base times height, just like the formula for the area of a rectangle.

Have a great day!

The system of equations that could be used to determine the number of pounds of apples sold and the number of pounds of strawberries sold will be x + y = 35 and 2x + 3y = 80.

An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.

It is given that, each pound of apples sells for $2 and each pound of strawberries sells for $3. Aiden made $80 from selling a total of 35 pounds of apples and strawberries.

Suppose the number of pounds of apples and strawberries is x and y respectively.

If the total of 35 pounds of apples and strawberries as a result,

x + y = 35-------(1)

If each pound of apples sells for $2 and each pound of strawberries sells for $3. Aiden made $80 then,

2x + 3y = 80---------(2)

Multiply equation 1 by 2 and subtract from equation 2 as

2x + 3y -2(x+y) = 80 - 2(35)

y = 10

Substitute the value of y we get x = 25

As a result, there are 25 pounds of apples and 10 pounds of strawberries in all.

Thus, the system of equations that could be used to determine the number of pounds of apples sold and the number of pounds of strawberries sold will be x + y = 35 and 2x + 3y = 80.

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We can find the values of each angle in a triangle by using the fact that the sum of the angles in a triangle is always 180 degrees. By setting up equations based on the relationships between the angles given in the problem, we can solve for each angle and find that angle a is 30 degrees, angle b is 15 degrees, and angle c is 135 degrees.

To solve this problem, we need to use some basic properties of triangles. The sum of the angles in a triangle is always 180 degrees. We can use this fact to set up equations to solve for each angle.Let's start with angle b. We know that angle a is twice as large as angle b. Therefore, we can write:
a = 2b
We also know that angle c is 15 degrees less than ten times angle b. We can write this as:
c = 10b - 15
Finally, we know that the sum of angles a, b, and c is 180 degrees. We can write this as:
a + b + c = 180
Substituting the first two equations into the third equation, we get:
2b + b + (10b - 15) = 180
Simplifying this equation, we get:
13b - 15 = 180
Adding 15 to both sides, we get:
13b = 195
Dividing both sides by 13, we get:
b = 15
Now that we know the value of b, we can use the first two equations to find the values of a and c. Plugging b=15 into a=2b, we get:
a = 2(15) = 30
Plugging b=15 into c=10b-15, we get:
c = 10(15) - 15 = 135
Therefore, the three angles in triangle ABC are:
angle a = 30 degrees
angle b = 15 degrees
angle c = 135 degrees

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The area of the circle is 100π square inches.

In this case, we are given that the circumference is 20π inches.

We can set up the equation as follows:

20π = 2πr.

To find the radius, we can divide both sides of the equation by 2π:

r = (20π) / (2π).

r = 10.

Now that we have the radius, we can calculate the area of the circle using the formula A = πr²:

A = π(10)².

A = 100π.

Therefore, the area of the circle is 100π square inches.

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A model without any simplifying assumptions b.is highly complex and likely unworkable.

As their call implies, simplifying assumptions are assumptions that are protected within the version to simplify the evaluation as tons as feasible. While a simplified version now does not predict the conduct of the actual issue within perfect bounds, too many simplifying assumptions have been made.

While a scientific version enables us to make predictions, it's more valued. As clinical models are representations of simplified explanations, they do not are looking for to explain each scenario or every detail. This means that medical models often aren't equal to the 'real international' from which they are derived.

Mathematical models can help college students apprehend and discover the that means of equations or valuable relationships.

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A binomial is a factor of a polynomial has been determined by using the

polynomial division method.

To determine if a binomial is a factor of a polynomial, you can use the polynomial division method. The basic idea is to divide the polynomial by the binomial and check if the remainder is zero. If the remainder is zero, then the binomial is a factor of the polynomial. Here's the step-by-step process:

Write the polynomial and the binomial in standard form, with the terms arranged in descending order of their exponents.

Perform the long division of the polynomial by the binomial, similar to how you would divide numbers. Start by dividing the highest degree term of the polynomial by the highest degree term of the binomial.

Multiply the binomial by the quotient obtained from the division and subtract the result from the polynomial.

Repeat the division process with the new polynomial obtained from the subtraction step.

Continue dividing until you reach a point where the degree of the polynomial is lower than the degree of the binomial.

If the remainder is zero, then the binomial is a factor of the polynomial. If the remainder is non-zero, then the binomial is not a factor.

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A point estimate (mean) for the average height of all people at the place where you work is 62.26

Mean is the average of the given numbers and is calculated by dividing the sum of given numbers by the total number of numbers.

In statistics, the mean is one of the measures of central tendency, apart from the mode and median. Mean is nothing but the average of the given set of values. It denotes the equal distribution of values for a given data set.

Given,

Number of observations =  20

Mean = sum of all observation / number of observations

Mean =  66 +65 +66+ 67+ 62+ 70+ 69+ 68+ 71+ 78+ 61+ 62.5+ 64+ 64.2+ 64.3+ 58+ 60+ 63+ 65+ 66.2 / 20

Mean = 1245.2 / 20 = 62.26

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answer: 5.34

Step by step explanation 12.75 + 13.95=26.7

20% of 26.7 is 5.34

Answer:

\(A=x^2+23x+49\)

Step-by-step explanation:

Hi there!

The area of the shaded region is equal to the area of the big rectangle minus the area of the square.

Area of the big rectangle:

\(A=lw\\A=(x+10)(2x+5)\)

Area of the square:

\(A=a^2\\A=(x+1)^2\)

Area of the shaded region:

\(A=(x+10)(2x+5)-(x+1)^2\)

Expand:

\(A=(x+10)(2x+5)-(x+1)^2\\A=2x^2+5x+20x+50-(x+1)^2\\A=2x^2+5x+20x+50-(x^2+2x+1)\\A=2x^2+5x+20x+50-x^2-2x-1\)

Combine like terms:

\(A=2x^2-x^2+5x+20x-2x+50-1\\A=x^2+23x+49\)

I hope this helps!

Using the substitution U = (2x + 1) is correct, and the statement is True.

We can set U = (2x + 1) by applying the substitution rule. We obtain dU = 2dx by dividing both sides with regard to x. When we solve for dx, we get dx = (1/2)dU.

Now, we substitute these values in the integral:

∫4(2x + 1)² dx = ∫4U² (1/2)dU

Simplifying the expression, we have:

(1/2)∫4U² dU

Now we can integrate with respect to U:

(1/2) * (4/3)U³ + C

(2/3)U³ + C

Finally, substituting back U = (2x + 1), we get:

(2/3)(2x + 1)³ + C

Therefore, using the substitution U = (2x + 1) is correct, and the statement is True.

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Answer:

Step-by-step explanation:

Area = 121 in²

Length = √121 in = 11i in

The given rational expression is 4y + 16 y + 4. To find the restricted values of y, we need to identify any values of y that would make the expression undefined.

In this case, the expression is in the form of a sum, so we don't have any denominators that could lead to division by zero. Therefore, there are no restricted values of y for this rational expression.

The expression 4y + 16 y + 4 is defined for all real numbers. We can evaluate it for any value of y without encountering any restrictions.

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Answer:

18

Step-by-step explanation:

x = number    

45  +  1/2 x   =   3x  

45 = 2.5 x

x = 45/2.5 = 18

Answer:

18

Step-by-step explanation:

Hello!

"Half a number" can be represented by 0.5x and "triple the number" can be represented by 3x.

This just becomes a one variable equation: 45 + 0.5x = 3x

Solve:

The missing number is 18.

Answer:

Step-by-step explanation:

To solve the first question write an equation of

\(a=\frac{1}{2} (12)(5)\)

\(a=\frac{1}{2} 60\)

\(a=30\)

To find the answer to the second question we need to know how to classify the different triangles

Equilateral Triangle- 3 equal sides and 3 equal angles (angles always are 60)

Isosceles Triangle- 2 equal sides and 2 equal angles

Scalene Triangle- No equal sides and no equal angles

So this triangle has no equal sides or angles meaning that it is a scalene triangle

Answer: The area of the triangle is 30

The triangle is a scalene triangle

Step-by-step explanation:

Answer:

C. ED

Step-by-step explanation:

The center of the angle is the point E, so it would be written first.