The Student body of a large university consists of 30% Business majors. A random sample of 20 students is selected.
a. What is the probability that among the students in the sample at least 10 are Business majors?
b. What is the probability that at least 16 are not Business majors?
c. What is the probability that exactly 10 are Business majors?
d. What is the probability that exactly 12 are not Business majors? Show work please so I understand

Let B.C be ordered bases for R" and & the standard basis for R". Suppose T:R" R is a linear transformation. If Ic.B = Tç, e then B = E = C.

The above statement is True.

In mathematics, and more specifically in linear algebra, a linear map (also called a linear map, a linear transformation, a vector space homomorphism, or in some cases a linear function) is a map between two vector spaces V → W, which performs the conservation of operations on vectors. Addition and scalar multiplication. The same names and definitions are also used for the more general case of modules over rings; see the homomorphism of modules.

A linear map is called a linear isomorphism if it is a bijection. In the case V=W, the linear map is called linear automorphism. Sometimes the term linear operator refers to this case, but the term "linear operator" can have different meanings for different conventions: for example, it can be used to emphasize that V and W are real vector spaces (not necessarily that V = W, where V is the space of functions, which is a common convention in functional analysis.

Sometimes the term linear function has the same meaning as linear map, but not in analysis.

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Option (O log 7) refers to the base-10 logarithm of 7, represented as log10(7), which is not the same as ln (7). Optional (O log, 10) and (O log, e) mathematical expressions are not acceptable.

In mathematics, the logarithm is the reciprocal of a power. As a result, the exponent by which b must be raised to achieve a number x matches its logarithm in base b. For example, because 1000 = 103, the base-10 logarithm is 3, or log10 = 3. For example, the base 10 logarithm of 10 is 2, but the square of 10 is 100. Log 100 = 2. A logarithm (or log) is the mathematical word used to answer questions such as how many times a base of 10 must be multiplied by itself to get 1,000. The answer is 3 (1,000 = 10 10 10).

When you compute (In), you are calculating the natural logarithm of 7, which is indicated as ln(7) or loge (7).

As a result, the expression you'd be looking up the value of is: ln(7) or loge (7).

Option (O log 7) refers to the base-10 logarithm of 7, represented as log10(7), which is not the same as ln (7). Optional (O log, 10) and (O log, e) mathematical expressions are not acceptable.

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Simplifying remex's works the same way we simplify fractions. In fractions, a rational number is considered to be a simplified form when its numerator and denominator have no other common factors than 1.

Regular expressions are fractions with variables. In rational expressions, the numerator and denominator are polynomials. That is, it is of the form p(x)/q(x), where q(x) ≠ 0 and p(x) and q(x) are polynomials. Because regular expressions are nothing but fractions, we treat them as if they were fractions.

It is not possible to divide a number by 0. Check what 1/0 is with your calculator, it will return an error. Therefore, no regular expression is defined for variable values ​​with a denominator of 0 (because it is a fraction). For example, in the expression x / (x + 2), the denominator becomes zero when x = -2, so it is called the limit of the rational expression x / (x + 2). In other words, we say x / (x + 2) for all values ​​of x but x ≠ -2.

Simplifying a regular expression means reducing the value of a regular expression to its lowest term or simplified form. Simplifying regexps works the same way we simplify fractions. In fractions, a rational number is considered a simplified form when its numerator and denominator have no other common factors than 1. The same works for simplified rational expressions, but the only difference is that there are polynomials in the fraction. Let's see the steps to follow to simplify a regular expression.

Step 1: Factor each numerator and each denominator by taking the common factor.

Step 2: Cancel the common factor.

Step 3: Write the remaining terms in the numerator and denominator.

Step 4: Indicate limits, if any. Note that a constraint is any value that makes the denominator equal 0, including terms canceled during simplification.

Complete Question:

Simplify algebraic rational expressions, with numerators and denominators containing monomial bases with integer exponents, to equivalent forms.

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Suppose you look by eye at a star near the edge of a dusty interstellar cloud. The star will look dimmer than it would if it were outside the cloud.

Interstellar clouds are vast, dense regions of dust and gas that exist between stars. These clouds contain tiny solid particles of dust, which scatter and absorb light as it passes through them.

When we observe a star that is located near the edge of an interstellar cloud, the light from that star has to pass through a greater amount of dust before it reaches our eyes or telescopes. The dust scatters and absorbs some of the light, causing the star to appear dimmer than it would if it were outside the cloud.

This effect is similar to how the sun appears dimmer when it is viewed through a thick layer of clouds or fog. In both cases, the amount of light that reaches us is reduced due to the presence of a barrier that scatters and absorbs some of the light.

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Step-by-step explanation:

Lisa started with $25 on her prepaid debit card. After her first purchase, she had $22.90 left. Therefore, she spent:

$25 - $22.90 = $2.10

We know that the price of the ribbon was 14 cents per yard. To find out how many yards Lisa bought, we can set up an equation:

$2.10 ÷ $0.14/yd = 15 yards

Therefore, Lisa bought 15 yards of ribbon with her prepaid debit card.

The distance between the points P and Q is 10 units using the Pythagorean theorem.

The right-angled triangle's three sides are related in accordance with the Pythagoras theorem, commonly known as the Pythagorean theorem. The Pythagorean theorem states that the hypotenuse square of a triangle is equal to the sum of the squares of the other two sides. According to the Pythagoras theorem, if a triangle has a right angle, the hypotenuse's square is equal to the sum of the squares of the other two sides.

The coordinates of the point P and Q are (3, 2) and (9, 10).

Using the Pythagoras theorem:

c² = (x2 - x1)² + (y2 - y1)²

Substitute the values:

c² = (9 - 3)² + (10 - 2)²

c² = 36 + 64

c² = 100

c = 10 units.

Hence, the distance between the points P and Q is 10 units using the Pythagorean theorem.

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The formula for converting degrees Kelvin to degrees Fahrenheit is F = (9/5) K + 459.67.

Degrees Kelvin and Degrees Fahrenheit are two temperature measuring measures that are widely used across the globe. While Kelvin is an international standard unit of measurement, Fahrenheit is mostly used in the United States.

The fact that they measure temperature on distinct scales explains the difference between degrees Fahrenheit (F) and degrees Kelvin (K). Whereas Kelvin is based on a scale of 100 degrees between the freezing and boiling temperatures of water at normal atmospheric pressure, Fahrenheit is based on a scale of 180 degrees between these extremes.

Given that, K = 5/9 (F - 459.67).

To obtain F in term of K we isolate the value of F as follows:

K = 5/9 (F - 459.67)

Multiplying both sides by 9/5, we get:

(9/5) K = F - 459.67

Adding 459.67 to both sides, we get:

F = (9/5) K + 459.67

Hence, the formula for converting degrees Kelvin to degrees Fahrenheit is F = (9/5) K + 459.67.

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When rounded to two decimal places, the radius of the can is approximately 1.6 inches.

Surface fοrmed by a straight line mοving parallel tο a fixed straight line and intersecting a fixed planar clοsed curve. a sοlid οr surface defined by a cylinder and twο parallel planes that cut all οf its elements. See Vοlume Fοrmulas Table, particularly fοr the right circular cylinder.

The volume of a cylinder can be calculated using the following formula:

V = πr²h

where

V denotes volume,

r denotes radius, and

h denotes height.

The cylindrical aluminium can has a height of 7 inches and a volume of 56 cubic inches. We can calculate the radius using the volume of a cylinder formula:

V = πr²h

56 = πr²(7)

56 = (22/7)r²(7)

56 = 22r²

56/22 = r²

2.54 = r²

r = [tex]\sqrt{2.54}[/tex]

r ≈ 1.6

As a result, when rounded to two decimal places, the radius of the can is approximately 1.6 inches.

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The velocity vector and position vector and position vector at t=4 is r(4) = (e₄+2)i+36j - 44k.

a(t) = eti - 6k

Since we know that v(t) = ∫ a(t) dt

= ∫ (eti - 6k) dt

= ∫6ti-6tk+c

where c is the arbitrary vector valued constant

since it is given that

v(0) = 2i + 9j + k

therefore from above

v(0) = e * 0i - 6(0) * k + c

2i + 9j + k =i+c

C= i +9j+k

therefore,

v(t) = eti - 6tk + i + 9j + k

= (et + 1) * i + 9j + (- 6t + 1) * k

Since we know that velocity vector can be found by integration of acceleration vector.

Since, v(t) = (et + 1) * i + 9j + (- 6t + 1) * k

and we know that

R(t) = ∫ v(t)dt

= ∫ of [(a + 1)i + 9j+(-6t + 1)k]dt =(a+t)i+9tj+(-3ta+t)k+C

where C is an arbitrary vector constant.

Now,

Since it given that r(0)=0 therefore

r(0) =(e0+1)+9(0)j)+(-3(0)2+0)x+C

0=2i+ C

C= -2i

therefore

r(t)= (et+t)i+9tj+(-3t+t)k-2i

r(t)=(a+t-2)1+9tj+(-3t+t)k

Since we know that position vector can be found by integration of velocity vector

r(4) = (e4+4-2)i+9(4)j + (-3(4)+4)k

r(4) = (e4+2)1+36j-44k

Now we have found the velocity vector and position vector and position vector at t=4 which are as follows:

v(t) =(et+1)i+9j+(-6t+1)k

r(t) =(et+t-2)i+9tj+(-3t2+t)k

r(4) = (e₄+2)i+36j - 44k

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(a) There are 100,000 different ways for Fiona to select her lunches for the week.

(b) There are 200,000 different ways for Fiona to select her lunches and drinks for the week.

(a) Since Fiona selects one lunch special each day, there are 10 options for Monday, 10 options for Tuesday, and so on, for a total of 10 options for each of the 5 weekdays. Therefore, the total number of ways for Fiona to select her lunches for the week is:

10 × 10 × 10 × 10 × 10 = 10^5 = 100,000

(b) In addition to the 10 lunch specials, Fiona now has 2 options for her drink, either water or tea. So for each of the 100,000 possible lunch selections from part (a), there are 2 possible drink options. Therefore, the total number of ways for Fiona to select her lunches and drinks for the week is:

100,000 × 2 = 200,000

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The smallest integer n such that a_n < 1 is n = -2.

Let the common ratio of the geometric progression be denoted by r. Then we have

a_2 = a_1 × r

a_3 = a_2 × r = a_1 × r^2

a_4 = a_3 × r = a_1 × r^3

a_5 = a_4 × r = a_1 × r^4

So in general, we have

a_n = a_1 × r^(n-1)

Now, we can use the given equation

(a_1357)^3 = a_34

Substituting the expressions above for a_34 and a_1357, we get

(a_1 × r^33)^3 = a_1 × r^3

Simplifying this equation by dividing both sides by a_1×r^3 and taking the cube root, we get

r^10 = 1/ (a_1^2)

Now, we need to find the smallest integer n such that a_n < 1. Using the expression for a_n above, we get

a_n < 1

a_1 × r^(n-1) < 1

r^(n-1) < 1/a_1

Taking the logarithm of both sides (with base r), we get

n-1 < log_r (1/a_1)

n < log_r (1/a_1) + 1

We know that r^10 = 1/ (a_1^2), so

1/a_1 = r^(10/2) = r^5

Substituting this into the expression above for n, we get

n < log_r (1/r^5) + 1

n < -5 + 1

n < -4

Since n is an integer, the smallest possible value for n is -3. However, this does not make sense since we cannot have a negative index for a term in the geometric progression. Therefore, the smallest integer n such that a_n < 1 is n = -2.

To verify this, we can substitute n = -2 into the expression for a_n and see if it is less than 1

a_n = a_1 × r^(n-1)

a_{-2} = a_1 × r^(-3)

Since a_1 > 1, we just need to show that r^3 > 1 to prove that a_{-2} < 1. From the equation r^10 = 1/ (a_1^2), we have

r^3 = (r^10)^(3/10) = (1/a_1^2)^(3/10) > 1

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The given question is incomplete, the complete question is:

Let a_1, a_2, a_3, a_4, a_5, . . . be a geometric progression with positive ratio such that a_1 > 1 and

(a_1357)^3 = a_34. Find the smallest integer n such that a_n < 1.

Answer:

Step-by-step explanation:

i think it B

Answer:

B is correct

Step-by-step explanation:

If it is spun twice then the probability of it landing on 2 and then an odd number is:

Pr(2,1) or Pr(2,3) or Pr(2,5) or Pr(2,7)

1/49 * 4

4/49

The amount a student received in merit scholarships was $3,456 ($478 per student). The cost of full tuition was $4,200. This means that the difference between the amount of the scholarship and the cost of tuition was $744.

Amount is a numerical value that represents a quantity of something. It is used to measure the size, amount, or degree of something, often in terms of money, time, or distance. Amounts are usually expressed in a specific unit, such as dollars, minutes, or kilometers. Amounts can also refer to the total number of something, such as the amount of people in a room or the amount of items in a box. Amounts can also be used to describe a portion or percentage of something, such as the amount of a discount or the amount of interest earned.  

To find the percentage of students who did not receive enough to cover full tuition, we need to divide the difference ($744) by the amount of the scholarship ($3,456). This gives us a percentage of 21.5%.

Rounded to the nearest whole percent, the answer is 22%. This means that 22% of students who received a merit scholarship did not receive enough to cover full tuition.

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Answer:

159 proper subsets.

Step-by-step explanation:

Given a set {2, 4, 6, 8...100}, how many proper subsets are there?

First, find how many subsets there are in 2 - 10:

That's 16.

Then because there are 10 10s in 100, multiply by 10:

16 x 10 = 160

Finally, because it says proper subsets, subtract by 1:

160 - 1 = 159 proper subsets.

Therefore, there are 159 proper subsets in {2, 4, 6, 8...100}

We can factor the polynomial 6z² + 6z as follows:

[tex]6z^2 + 6z = 6z(z + 1)[/tex]

We can use this factorization to express the area of the wall as the product of two factors:

[tex]6z^2 + 6z = 6z(z + 1) = length × width[/tex]

Therefore, the length of the wall is 6z, and the width of the wall is z + 1.

So the solution equation is 6x + 3 and the total miles is equal to 6x + 3.

Where x represents the length of Lincoln Park School.

A linear equation is an algebraic equation of the form y=mx+b. m is the slope and b is the y-intercept. The above is sometimes called a "linear equation in two variables" where y and x are variables. 

Mile is a unit of measurement that equals 1760 yards or approximately 1.6 kilometer's. It the mostly used in the continent of North America.

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The probability of selecting an officer who is in the Navy given that the officer is African American is 0.192.

Probability calculates the likelihood that an event would happen. The likelihood that an event would occur has a value that lies between 0 and 1 or 0 and 100. The more likely an event would happen, the closer the probability value would be to 1 or 100.

The probability of selecting an officer who is in the Navy given that the officer is African American = number of African Americans that are in the Navy / total number of African Americans

Total number of African Americans = 9162 + 3524 + 1341 + 4282 = 18,309

The probability = 3524 / 18,309 = 0.192

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Answer: D. As x → -∞, y → -∞.

Step-by-step explanation:

The graph shows the function approaching negative infinity on the x-axis (left side).  When the x-axis is decreasing, the y-axis is also decreasing towards negative infinity.

Step-by-step explanation:

a probability is always the ratio

desired cases / totally possible cases

we have 2 possible cases for the coin and 6 possible cases for the die.

so, we have 2×6 = 12 combined possible cases :

heads, 1

heads, 2

heads, 3

heads, 4

heads, 5

heads, 6

tails, 1

tails, 2

tails, 3

tails, 4

tails, 5

tails, 6

out of these 12 cases, which ones (how many) are desired ?

all first 6 plus (tails, 3) = 7 cases

so, the correct probability is

7/12

formally that is calculated :

1/2 × 6/6 + 1/2 × 1/6 = 6/12 + 1/12 = 7/12

the probability to get heads combined with the probability to roll anything on the die, plus the probability to get tails combined with the probability to roll 3.

In the equatiοn , the value οf a and b is 2 and 4.

A mathematical assertiοn that shοws the equality οf twο mathematical expressiοns is what an equatiοn in algebra is defined as. Fοr example, the equatiοn 3x + 5 = 14 is cοmpοsed οf the twο equatiοns 3x + 5 and 14, which are separated by the equal sign.

The equatiοn οf a parabοla in standard fοrm is

y = a(x - h)² + k

where (h, k) are the cοοrdinates οf the vertex and a is the cοefficient οf the x² term.

Here (h, k ) = (- 1, 3 ) and cοefficient οf x² term = 1 , then

=> y = (x - (- 1))² + 3 ,

=> y = (x + 1)² + 3

=> y = x² + 2x + 1 + 3

=> y = x² + 2x + 4

Nοw cοmpare tο y = x² + ax + b

Consequently, a = 2 and b = 4.

Thus, a and b have values of 2 and 4, respectively.

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Examination writing skills refer to a set of abilities that are essential for effective and successful writing in an exam context.

These skills include reading the question carefully, planning your response, writing a clear and concise answer, using appropriate terminology, providing evidence to support your argument, and presenting your answer in a logical and organized manner.

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Complete question:

State one way in which each of the examination writing skills below could effectively assist you when writing your examinations:

Answer:

1. cosine

2. function

3. tangent

4. complementary

5. sine

6. cofunctions

Answer:

Required length is 13 feet

Step-by-step explanation:

[tex]{ \rm{length = \sqrt{ {12}^{2} + {5}^{2} } }} \\ \\ { \rm{length = \sqrt{144 + 25} }} \\ \\ { \rm{length = \sqrt{169} }} \\ \\ { \rm{length = 13 \: feet}}[/tex]

Therefore , the solution of the given problem of function comes out to be f(x) = sec(x) has a period of 2. 2 is the answer.

The midterm test questions will cover all of the topics, including actual as well as fictitious locations and arithmetic variable design. a diagram showing the relationships between different elements that cooperate to create the same result. A service is composed of numerous distinctive components that cooperate to create distinctive results for each input. Every mailbox has a particular spot that might be used as a haven.

Here,

=> F(x) = sec(x) has a 2 phase.

Because the secant function is periodic, its values recur after a predetermined amount of time.

This interval's length is equal to the secant function's duration.

The formula for the secant function is

=> sec(x) = 1/cos.(x).

The cosine function repeats its values every 2 units of x, which is known as its period.

Consequently, the secant function has a period of 2 as well.

Therefore, f(x) = sec(x) has a period of 2. 2 is the answer.

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The math method that returns the nearest whole number that is greater than or equal to its argument is the "ceiling" function, denoted by ⌈x⌉ in mathematics.

The Ceiling function is denoted by ⌈x⌉, is a mathematical function that takes a real number x as an input and returns the smallest integer that is greater than or equal to x.

The ceiling function takes a real number x as an argument and returns the smallest integer that is greater than or equal to x.

For example, if x = 3.7, then ⌈x⌉ = 4, since 4 is the smallest integer that is greater than or equal to 3.7.

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A company manufactures rubber balls, random variable X in words is diameter of the rubber ball, standard deviation is -1.5 and z-score of the x = 2 is 2.123.

A random variable is a variable with an unknown value or a function that gives values to each of the results of an experiment. Random variables are frequently identified by letters and fall into one of two categories: continuous variables, which can take on any value within a continuous range, or discrete variables, which have specified values.

In probability and statistics, random variables are used to measure outcomes of a random event, and hence, can take on various values. Real numbers are often used as random variables since they must be quantifiable.

1) X denotes the diameter of the rubber ball.

So the correct option was A. (option A)

Therefore,  the random variable X in words is diameter of the rubber ball.

2) For 1.5 Standard deviations left to the mean , Z score will be -1.5

option(A)

So, standard deviation to the left of the mean is -1.5.

3) [tex]Z=\frac{(x-\mu)}{\sigma}[/tex]

x=2

sigma = √2

Z = 2-(-1)/ √2

Z = 3/√2

Z = 2.123

Hence, the z-score of the x = 2 is 2.123.

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Complete question:

A company manufactures rubber balls. The mean diameter of a rubber ball is 12 cm with a standard deviation of 0.2 cm. Define the random variable X in words. X

diameter of a rubber ball

rubber balls

mean diameter of a rubber ball

12 cm

Question 2 What is the z-score of x=9, if it is 1.5 standard deviations to the left of the mean? Hint: the z-score of the mean is =0 −1.5 1.5 9 Question 3 Suppose X∼N(−1,2). What is the z-score of x=2 ? Hint: z=(x−μ)/σ 1.5 −1.5 0.2222

The correct option is -C: No, 6 is the geometric mean of 4 and 9, however if the altitude is 6, then the hypotenuse is the geometric mean of the two segments.

An average technique multiplies several values and determines the number's root is known as the geometric mean. You locate the nth root for their product for a collection of n numbers. This descriptive statistic can be used to sum up your data.

Mean Geometric The square root of the product of two numbers is the geometric mean amongst them. The geometric mean of two positive numbers an as well as b is the positive number x as in percentage Cross multiplication results in x² = ab,.

For the given question.

geometric mean of a and b :

From the drawn diagram.

a = 4

b = 9

x = √ab

x = √9*4

x = 6

geometric mean: 6

Applying the altitude rule:

h² = x.y

6² = 9*4

36 = 36

Thus, the geometric mean calculated by friend is correct but the marking on the diagram is wrong.

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When three dices are rolled.

Total number of outcomes =  = 216

Sum of 13 can be achieved in the following ways:

From the digits 6,4,3

So, there are 3! ways =  = 6

From the digits 6,2,5

So, there are 3! ways =  = 6

From the digits 5,4,4

So, there are  ways = 3

From the digits 6,6,1

So, there are  ways = 3

From the digits 3,5,5

So, there are  ways = 3

So, total numbers whose sum is 13=

So, Probability = .

Therefore, the probability of getting sum as 21 on rolling three dice =   .