Suppose x is a normally distributed random variable with μ=10 and σ=2. Find each of the following probabilities.
a. P(x ≥ 12.5) b. P(x ≤ 9) c. P(10.88 ≤ x ≤ 15.3) d. P(4.72 ≤ x ≤ 12.46)

The equation solved for the variable h is h = [tex]\sqrt[]{\frac{2A -b^2}{b} }[/tex]

To solve for a variable in a given equation is to make it the subject of formula.

The variable is made to stand alone on one end of the equality sign.

We have the equation given as;

A=1/2bh(h+b)

First, cross multiply

2A = bh(h+b)

2A = bh² + b²

collect like terms

2A - b² = bh²

Now divide by the coefficient of h²

h² = 2A - b²/b

Find the square root of both sides

h = [tex]\sqrt[]{\frac{2A -b^2}{b} }[/tex]

Hence, the equation is h = [tex]\sqrt[]{\frac{2A -b^2}{b} }[/tex]

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The relationship between X and Y in the equations y = 2x and y = x + 2 is that they represent two different linear equations.

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

y = 2x

y = x + 2

Using the above as a guide, we have the following:

Hence, the relationship is different linear equations

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We conclude that the angle at the top measures 65.8°.

A right triangle or right-angled triangle, or more formally an orthogonal triangle, formerly called a rectangled triangle, is a triangle in which one angle is a right angle, i.e., in which two sides are perpendicular. The relation between the sides and other angles of the right triangle is the basis for trigonometry.

here, we have,

What angle does the top part?

The whole tree measures 117 ft, and it is broken 34 ft above the ground, forming this way a right triangle.

Then one cathetus of the right triangle measures 34ft, and the hypotenuse measures 117ft - 34ft = 83ft

The angle at the top is θ, the adjacent cathetus to it is the one that measures 34 ft, then to get the angle we can use the relation:

cos(θ) = (adjacent cathetus)/(hypotenuse)

Replacing what we know, we get:

cos(θ) = (34 ft)/(83ft) = 34/83

Solving for θ, we get:

θ = Acos( 34/83) = 65.8°

So we conclude that the angle at the top measures 65.8°.

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The two angels are similar because they have the same magnitude of corresponding angles. The length of x is 6 cm.

For two or more similar triangles, it has two conditions.

The two triangles as shown in the picture, ΔABC and ΔEDC.

Explain why the two triangles are similar! Find the length of x!

We have

The magnitude of ∠BCA and ∠DCE are equal. It is because they are at one point of intersection.

Since, ∠BCA and ∠DCE are equal and m∠A = m∠E, the other angles are also same.

Thus, the two triangle are similar. They have the same magnitude of corresponding angles.

Then, we find x. See the picture in the attachment!

3/10 = 1.8/x

x = (10 × 1.8)/3

x = 18/3

x = 6 cm

Hence, they are similar because they have the same corresponding angles. The x has the length of 6 cm.

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We can consider $323.53 as near the monthly interest rate on this loan is approximately 0.4974% (or 0.004974 as a decimal). We can use a formula to find the monthly interest where:

P = (r(PV)) / (1 - (1 + r)^(-n))

Where:

P = monthly payment

r = monthly interest rate

PV = present value of the loan (the amount borrowed)

n = total number of months

r (monthly interest)= (1 / n) * ((P / PV) + ((1 / (1 + r)^n) - 1))

we can start by guessing an interest rate of 0.01 (or 1%). putting it into a formula:

r = (1 / 60) * ((323.53 / 10000) + ((1 / (1 + 0.01)^60) - 1))

r = 0.004968

monthly payment is

P can be (0.004968 * 10000) / (1 - (1 + 0.004968)^(-60))

P = $323.52

By using this value we can find the value of the month. Plugging it back into the formula, we get:

r = (1 / 60) * ((323.53 / 10000) + ((1 / (1 + 0.004968)^60) - 1))

r = 0.004974

This new interest rate gives us a monthly payment of:

P can be (0.004974 * 10000) / (1 - (1 + 0.004974)^(-60))

P = $323.53

We can consider $323.53 as near the monthly interest rate on this loan is approximately 0.4974% (or 0.004974 as a decimal).

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The correct question is

Table 33 gives spending data for the football programs at the 10 universities that spent the most money on football in 2012 Click here for the Excel Data File Calculate the population range variance and standard deviation of the ten total football spending figures Do the same for the ten spending per scholarship player figures. (Round your range and variance answers to 2 decimal places and standard deviation answer to 4 decimal places.) Total Spending (Smil) Spending per Scholarship Player (5) Range Variance Std Deviation 7 College Football A B C D 1 Footballs bending Data for 2012's Top Ten College Football Spenders 2 3 Rank School Total Spending (Smil) Spending per Scholarship Player (3) 4 1 The Ohio State University 34.36 5 400,000 2 University of Alabama 37.77 360,000 6 3 Auburn University 33.33 303,000 7 4 University of Wisconsin 24.23 285,000 8 5 University of Arkansas 24.33 9 6 Oklahoma State University 283,000 26.24 10 279,000 7 Virginia Tech 24.72 11 275,000 8 University of Arizona 24.12 12 9 274,000 University of Florida 23.25 13 273,000 University of Michigan 23.64 14 272,000 15 10

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The scaled dimension of a kitchen with the given dimensions is 1.26 cm and 0.96 cm.

Dilation is a type of transformation where the figure is enlarged or made smaller such that it preserves the shape but not size.

Every dilated image are similar figures to the original figure.

Given that,

Actual dimensions of the kitchen = 6.3 m by 4.8 m

Kitchen plan is drawn to a scale of 1 : 500.

This means that, the scale is drawn as 1 unit if the actual unit is 500.

Scaled dimension if actual dimension is 500 = 1

Scaled dimension if actual dimension is 6.3 m = 6.3 / 500

                                                                             = 0.0126 m

                                                                             = 1.26 cm

Scaled dimension if actual dimension is 4.8 m = 4.8 / 500

                                                                             = 0.0096 m

                                                                             = 0.96 cm

Hence the scaled dimensions are 1.26 cm and 0.96 cm.

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Answer:

Step-by-step explanation:

We can simplify the left-hand side of the equation using the distributive property of multiplication and combining like terms:

-35 + 4[6x - 12(3x + 5) + 10] = -35 + 4[6x - 36x - 60 + 10] = -35 + 4[-30x - 50] = -35 - 120x - 200 = -120x - 235

Similarly, we can simplify the right-hand side of the equation by combining like terms:

8 + 6x + 9 = 17 + 6x

Substituting these simplified expressions back into the original equation, we get:

-120x - 235 = 17 + 6x

Adding 120x to both sides and subtracting 17 from both sides, we get:

-235 = 126x - 17

Adding 17 to both sides, we get:

-218 = 126x

Dividing both sides by 126, we get:

x = -218/126

Simplifying this fraction, we get:

x = -109/63

Therefore, x is equal to -109/63.

In geometry, ​8 ft. 3 ft. specifies the dimension of an object. That is the  length and the width.

8 ft. 3 ft. is a dimension, specifically a length and a width. It could refer to the size of a rectangular object, such as a room or a piece of furniture.

In geometry, such a dimension is often used to calculate the area of the rectangle.

The area of a rectangle can be found by multiplying its length by its width.

So, in this case, the area of the rectangle with dimensions 8 ft. * 3 ft. would be 8 ft * 3 ft = 24 ft².

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As a result of answering the question, we may state that equation In ten attempts, there is a 0.0407 percent chance of getting more than four kings, which is a very little chance.

A mathematical equation is a process that links two statements and indicates equality using the equals symbol (=). A theoretical statement that proves the equality of two formulas is known as an equation in algebra. For instance, the equal sign separates the numbers 3x + 5 and 14 in the equation 3x + 5 = 14.

A. With n=10 and p=4/52, the binomial distribution of the number of kings seen in the 10 trials, K, is followed (since there are 4 kings in a standard deck of 52 cards). K's average is:

mean(K) is equal to[tex]n * p (10 * 4/52 = 0.7692).[/tex]

Meaning: On average, we anticipate seeing 0.77 kings per 10 trials.

B. This is the variance of K:

The formula for var(K) is [tex]n * p * (1 - p) = 10 * 4/52 * (1 - 4/52) = 0.7255.[/tex]

K's standard deviation:

[tex]\sqrt(var(K)) = \sqrt(0.7255) = 0.8524[/tex] where sd(K) =

D. The binomial distribution can be used to calculate the likelihood of receiving more than four kings:

P(K > 4) = 1 - P(K 4) = 1 - 0.0407 for binom.cdf(4, 10, 4/52).

Interpretation: In ten attempts, there is a 0.0407 percent chance of getting more than four kings, which is a very little chance.

D. The binomial distribution can be used to get P(K 3):

Binom.cdf(3, 10, 4/52) = P(K 3) = 0.8789

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The effect on the graph for the given function if the slope of the function is changed to -10 include the following: D. the line is less steep.

The effect on the graph for the given function if the y-intercept of the function is changed to a smaller positive number is: C. the line shifts down.

In Mathematics, a slope is sometimes referred to as rate of change and it is typically used to describe both the direction, ratio, and steepness of the function of a straight line based on its coordinates or points.

Generally speaking, a slope simply refers to a measure of the steepness of a straight line. This ultimately implies that, the higher the slope of a line, the more steep it is and vice-versa.

Based on the information provided about this function y = 8 - 2x, we can logically deduce that the line would be shifted downward when its y-intercept is changed to a smaller positive number.

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37. A possible solution is y(x) = ax + b, where a and b are constants. Taking two derivatives gives y''(x) = 0, which satisfies the differential equation.

38. A possible solution is y(x) = Ce^x, where C is a constant. Taking the derivative of y(x) gives y'(x) = Ce^x, which satisfies the differential equation.

39. A possible solution is y(x) = 3 + 2x^2, which can be checked by taking the derivative and plugging it into the differential equation: xy'(x) + y(x) = x(4x) + (3 + 2x^2) = 3x^2 + 2x^2 + 3 = 5x^2 + 3, which is equal to 3x^2 when x=0.

40. A possible solution is y(x) = sin(x), which can be checked by taking the derivative and plugging it into the differential equation: (y'(x))^2 + (y(x))^2 = cos^2(x) + sin^2(x) = 1.

41. A possible solution is y(x) = ex - 1, which can be checked by taking the derivative and plugging it into the differential equation: y'(x) + y(x) = e^x + e^x - 1 = 2e^x - 1.

42. A possible solution is y(x) = Asin(x) + Bcos(x), where A and B are constants. Taking the second derivative gives y''(x) = -Asin(x) - Bcos(x), which satisfies the differential equation.

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Answer:

  a.  3800

Step-by-step explanation:

You want the product (0.82 +0.042)(4.4×10³) expressed to an appropriate number of significant figures.

The number of significant figures in a product is the least of the numbers of significant figures in the contributors. Here, 4.4×10³ has 2 significant figures, so the result needs to be rounded to 2 significant figures.

  (0.82 +0.042)(4.4×10³) ≈ 3800

__

Additional comment

This is the only answer choice with 2 significant figures, so it can be chosen on that basis alone.

The two numbers of the form a+bi and c+di where a,b,c, and d are real numbers, and i is the imaginary unit, always resulting in the correct mathematical result in the same form.

This is because complex numbers are a mathematical construct and the operations defined on them, such as addition, subtraction, multiplication, and division, follow the rules of arithmetic. These operations preserve the form of the numbers, so that the result of any two complex numbers, when operated upon, will always be in the form of a complex number.

For example, when adding two complex numbers (a + bi) and (c + di), the real parts add up to form a new real part, and the imaginary parts add up to form a new imaginary part, resulting in a new complex number in the form (a + c) + (b + d)i.

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The system has no solution only when h = 3 and k  ≠ 20.

The system has unique solution when h ≠ 3 and k is any real number.

System has many solutions only when h = 3 and k = 20

As per the data given:

[tex]& x_1+h x_2=5 \\[/tex]

[tex]& h x_1+12 x_2=k[/tex]

Consider augmented matrix

[tex]\quad[A \mid b]= & {\left[\begin{array}{cc|c}1 & h & 5 \\h & 12 & k\end{array}\right] } \\[/tex]

[tex]R_2 \rightarrow R_2-4 R_1 & {\left[\begin{array}{cc|c}1 & h & 5 \\0 & 12-4 h & k-20 \\\end{array}\right] }\end{aligned}[/tex]

(a) System has no solution if rank(A) ≠ rank(A|b)

Therefore if 12 - hk = 0 and k - 20 ≠ 0 then

rank(A) ≠ rank(A|b) and system has no solution

12 = 4h and k  ≠ 20

h = 3 and k  ≠ 20

Answer: E. The system has no solution only when h = 3 and k  ≠ 20.

(b) The system has unique solution if rank(A) = rank(A|b)

Number of variables = 2

This is possible only when 12 ≠ 4h and h ≠ 3

The system has unique solution when h ≠ 3 and k is any real number.

(c) The system has many solution when rank(A) = rank(A|b) ≤ (Number of variables = 2)

Therefore this is true only when 12 - 4h = 0 and k - 20 = 0 i.e. h = 3 and  k = 20

System has many solutions only when h = 3 and k = 20

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Choose h and k such that the system has (a) no solution, (b) a unique solution, and (c) many solutions.

[tex]x_1+h x_2=5 \\[/tex]

[tex]4 x_1+12 x_2=k[/tex]

a. Select the correct answer below and fill in the answer box(es) to complete your choice. (Type an integer or simplified fraction.)

A. The system has no solutions only when [tex]$k \neq \square$[/tex] and h is any real number.

B. The system has no solutions only when h = [tex]\square$[/tex] and k=

C. The system has no solutions only when h [tex]\neq \square$[/tex] and [tex]$k \neq$[/tex]

D. The system has no solutions only when [tex]$\mathrm{h}=\square$[/tex] and k is any real number.

E. The system has no solutions only when [tex]$h=\square$[/tex] and [tex]$k \neq$[/tex]

F. The system has no solutions only when [tex]$k=\square$[/tex] and h is any real number.

G. The system has no solutions only when [tex]$h \neq \square$[/tex] and k is any real number.

H. The system has no solutions only when [tex]$h \neq \square$[/tex] and k= ___

The vectors that are parallel to z that has has initial point (5, 4, 1) and terminal point (-2, -4, 4) are -7i - 6j - 2k and -14i - 16j + 6k. So, the correct options are B and D.

To determine which vectors are parallel to z, we need to compare their direction to the direction of z. Two vectors are parallel if they have the same direction or are opposite in direction.

The direction of z can be found by subtracting the initial point from the terminal point:

z = (-2 - 5)i + (-4 - 4)j + (4 - 1)k

z = -7i - 8j + 3k

Now let's compare the direction of each given vector to the direction of z:

a. 7i + 6j + 2k: This vector is not parallel to z because it has a different direction.

b. -7i- 6j -2k: This vector is parallel to z because it has the opposite direction.

c. 14i +16j+ 6k: This vector is not parallel to z because it has a different direction.

d. -14i -16j + 6k: This vector is parallel to z because it has the opposite direction.

e. i + 4j - 2k: This vector is not parallel to z because it has a different direction.

f. i - 4j + 2k: This vector is not parallel to z because it has a different direction.

Therefore, the vectors that are parallel to z are b. -7i - 6j - 2k and d. -14i - 16j + 6k.

To confirm these results using a graphing utility, we can plot z and each of the given vectors on a 3D coordinate system and visually check their directions.

Here is an example using Wolfram Alpha:

vectorplot3d {<-7, -8, 3>, {x, -10, 10}, {y, -10, 10}, {z, -10, 10}}

vectorplot3d {<7, 6, 2>, {x, -10, 10}, {y, -10, 10}, {z, -10, 10}}

vectorplot3d {<-7, -6, -2>, {x, -10, 10}, {y, -10, 10}, {z, -10, 10}}

vectorplot3d {<14, 16, 6>, {x, -10, 10}, {y, -10, 10}, {z, -10, 10}}

vectorplot3d {<-14, -16, 6>, {x, -10, 10}, {y, -10, 10}, {z, -10, 10}}

vectorplot3d {<1, 4, -2>, {x, -10, 10}, {y, -10, 10}, {z, -10, 10}}

vectorplot3d {<1, -4, 2>, {x, -10, 10}, {y, -10, 10}, {z, -10, 10}}

This will generate a 3D plot with all the vectors plotted. We can see that only the vectors with opposite directions to z, namely -7i - 6j - 2k and -14i - 16j + 6k, are parallel to z.

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The power set P(A) is P(A) = { {}, {x}, {y}, {z}, {x,y}, {x,z}, {y,z}, {x,y,z} }

The power set of a set A is the set of all subsets of A, including the empty set and A itself.

For the set A = {x, y, z}, the possible subsets are:

Therefore, the power set of A, denoted P(A), is:

P(A) = { {}, {x}, {y}, {z}, {x,y}, {x,z}, {y,z}, {x,y,z} }

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The minimum value of the interval is two standard deviations below the mean (μ - 2σ), while the maximum value of the interval is two standard deviations above the mean (μ + 2σ).

The range rule of thumb states that the usual measures in an interval are within two standard deviations of the mean.

The parameters you are given to solve this problem are:

Hence the lower bound of the interval is of:

μ - 2σ -> you should subtract two standard deviations from the mean.

The upper bound of the interval is of:

μ + 2σ -> you should add two standard deviations to the mean.

The problem is incomplete, hence the general procedure to obtain the bounds of the interval is presented.

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Answer:

[tex]\huge\boxed{\sf x\³ - 10x\² + 19x + 6}[/tex]

Step-by-step explanation:

= (x - 3)(x² - 7x - 2)

= x(x² - 7x - 2) - 3(x² - 7x - 2)

= x³ - 7x² - 2x - 3x² + 21x + 6

= x³ - 7x² - 3x² - 2x + 21x + 6

[tex]\rule[225]{225}{2}[/tex]

Answer:

3150

Step-by-step explanation:

...2(42x11+21x11+42x21)

BTW: This isn´t college-level math this is like 2nd-grade math.

Answer: 40

Step-by-step explanation:

I rounded to the nearest tens place. The 3 in the tens place rounds up to 4 because the digit to the right in the ones place is 5.

40

When the digit to the right is 5 or greater we round away from 0.

35.7 was rounded up and away from zero to 40

Answer:

1. ~ ABC = 180 degrees

2. AB/AD = BC/AC

3. 3/9 = x/6

4. x = 2

5. The scale factor of ADE to ABC is 1:2.

Step-by-step explanation:

1. ~ABC = 180 degrees means that the sum of all the angles of a triangle add up to 180 degrees.

2. AB/AD = BC/AC means that if two sides of a triangle are divided by another side, the ratio will be the same for both sides of the triangle.

3. 3/9 = x/6 means that if you divide 3 by 9, you can find out what x is when it is divided by 6.

4. x = 2 means that when 3 is divided by 9 and the result is divided by 6, the answer is 2.

5. The scale factor of ADE to ABC is 1:2 means that ADE is twice the size of ABC and all related measurements between the two triangles are in a proportion of 1:2.

The evaluation of the given Boolean expressions are:

a) A && !B =  false              b) B∥C = true

c) B==C = false                   d) A&&!C = true

e) (B∥C)&&(!A) =  false        f) (A!=B)∥(B!=C)  = true

Information available in the problem:

A = true

B = true

C = true

a) Since A and B are both true, !B (which means "not B") is false. Therefore, A && !B evaluates to false, because the logical AND operator returns true only if both of its operands are true.

Hence,

A && !B = true && false = false

b) Since B is true, the result of B∥C will be true, regardless of the value of C. This is because the logical OR operator returns true if at least one of its operands is true.

Hence,

B∥C = true ∥ false = true

c) Since B is true and C is false, B and C have different values, and therefore B==C will evaluate to false. This is because the equality operator returns true only if its operands have the same value.

Hence,

B==C = true == false = false

d) Since A is true and !C (which means "not C") is true, A&&!C evaluates to true. This is because the logical AND operator returns true only if both of its operands are true.

Hence,

A&&!C = true && !false = true && true = true

e) Since B is true, the result of B∥C will be true, regardless of the value of C. This is because the logical OR operator returns true if at least one of its operands is true. Therefore, B∥C evaluates to true.

Since A is true and !A (which means "not A") is false, !A evaluates to false.

Therefore, (B∥C)&&(!A) evaluates to false, because the logical AND operator returns true only if both of its operands are true.

Hence,

(B∥C)&&(!A) = true && false = false

f) Since A is true and B is true, A!=B (which means "A is not equal to B") is false, because A and B have the same value.

Since B is true and C is false, B!=C (which means "B is not equal to C") is true, because B and C have different values.

Therefore, (A!=B)∥(B!=C) evaluates to true, because the logical OR operator returns true if at least one of its operands is true.

Hence,

(A!=B)∥(B!=C) = false ∥ true = true

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Answer:

t = 47

Step-by-step explanation:

47 - 38 = 9

The solution is, the value of x=4.

Pythagorean theorem, the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle)—or, in familiar algebraic notation, a2 + b2 = c2.

here, we have,

We can modify the Pythagorean Theorem to fit our needs and solve x. We know our c and our a so to find x or b

we use c^2-a^2=b^2.

from the given figure , we get,

Lets input our known.

5^2-3^2=x^2.

Lets start solving by squaring.

25-9=x^2

Subtract

16=x^2

Take the square root

4=x

Hence, The solution is, the value of x=4.

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Answer:

= 5n³ + 3n² - 4

Step-by-step explanation:

(-3n³-3n²) + (8n³ + 6n² - 4)

= -3n³-3n²+8n³+6n²-4

= -3n³+8n³-3n²+6n²-4

= 5n³+3n²-4.

The length of the centre pole is approximately 6.29 feet.

What is the Pythagorean Theorem?

Pythagoras Theorem is the way in which you can find the missing length of a right angled triangle.

To find the length of the center pole, we need to use the Pythagorean Theorem to calculate the height of the tent. The height can then be used as one leg of a right triangle with the center pole as the other leg, and we can again use the Pythagorean Theorem to find the length of the center pole.

The height of the tent can be found by using the Pythagorean Theorem on the right triangle formed by one of the triangular faces and the height:

h² = (slant height)² - (base/2)²

h² = 6.75² - 4.5²

h² = 22.5625

h ≈ 4.75 ft

Now we can use the height and the base of the tent to find the length of the center pole using the Pythagorean Theorem:

center pole² = h² + (base/2)²

center pole² = 4.75²+ 4.5²

center pole²= 39.5625

center pole ≈ 6.29 ft

Hence, the length of the center pole is approximately 6.29 feet.

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The area of the trapezoid is given as follows:

160 cm².

The area of a trapezoid is obtained adding the bases, multiplying by the height, and dividing by 2.

For the trapezoid in this problem, the parameters are given as follows:

Hence the area is given as follows:

A = 0.5 x (8 + 24) x 10

A = 160 cm².

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