If 90% of the athletes who test positive for steroids in fact use them, and 10% of all athletes use steroids and test positive, what percentage of athletes test positive? (Round your answer to the nearest whole number.)

The value of rank is 2 of a 4 × 6 matrix a, given that the subspace of all solutions of a ¯ x = ¯ 0 has a basis consisting of 4 vectors.

If the subspace of all solutions of a ¯ x = ¯ 0 has a basis consisting of 4 vectors, it means that the nullity of the matrix a is 4 (since the subspace of solutions to a ¯ x = ¯ 0 is the null space of the matrix a).

The rank-nullity theorem states that the rank of a matrix plus its nullity equals the number of columns in the matrix. Therefore, if a is a 4 × 6 matrix and its nullity is 4, then its rank must be 6 - 4 = 2.

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Answer:

A) 2

Step-by-step explanation:

let 'a' = Angelica's age

let '6+2a' = Jacob's age

6+2a = 10

2a = 4

a = 2

The instantaneous rate of change of f(x) = x³ − 5 at (2,3) is (b) 12

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

Function: f(x) = x³ − 5

Point = (2, 3)

Differentiate the function to get the instantaneous rate

This is represented as

f'(x) = 3x²

Substitute 2 for x in the equation

The 2 is coming from the x-coordinate in (2, 3)

So, we have

f'(2) = 3(2)²

Evaluate

f'(2) = 12

Hence, the instantaneous rate of change is 12

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The function ought to be represented as; m(t) = 7t + 25 where t is the number of yards that she mows.

The term linear function refers to a function that yields a straight line graph when it is plotted. Now we know that a linear function would not contain an exponent that is greater than one.

In this case, we know that the question states that she charges a base fee of $25 and $7 for every hour she mows thus the function ought to be represented as; m(t) = 7t + 25 where t is the number of yards that she mows.

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Answer:

m(2) = 39; if hazel mows a yard for 2 hours

Step-by-step explanation:

sorry if this is incorrect but i thought it was more help then the previous answer

:)

hope this helps anyone and have a great day!!

The sales price of the item is $48.

The sale price of an item that costs 60% of its original price which is $80 is $48. The original price of the item is $80, and it costs 60% of the original price. The amount of money we'll be spending is calculated as follows: 60 per cent of $80 (60/100) × $80= $48 Therefore, the sales price is $48. The percentage discount for the item is calculated as follows:$80 - $48 = $32

$32 is the amount of money saved due to the discount, which is then divided by the original price, $32/$80 = 0.4 or 40%. Thus, there was a 40% discount on the original price.

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Answer:

p = 16

Step-by-step explanation:

(p + 2) - 4 = 14

We can just drop the parentheses:_

p + 2 - 4 = 14

p - 2 = 14

Add 2 to both sides:-

p - 2 + 2 = 14 + 2

p = 16

A 2-dimensional array is used to store the boarding fees of five students for four different payments. A function called "total remaining fees" calculates the remaining fees for each student and determines if they have paid all their fees based on the sum of their paid fees compared to the total fees.

To solve this problem, we can use a 2-dimensional array to store the boarding fees of five students for four different payments.

Each row of the array represents a student, and each column represents a payment. The array will have a dimension of 5x4.

Here's an example implementation in Python:

#python

def total_remaining_fees(fees):

   total_fees = [2500, 5000, 6000]  # Boarding fees for Wedderburn Hall, Val Hall, and V Hall

   for student_fees in fees:

       remaining_fees = sum(total_fees) - sum(student_fees)

       if remaining_fees == 0:

           print("Student has paid all their fees.")

       else:

           print("Student has remaining fees of $" + str(remaining_fees))

# Example usage

boarding_fees = [

   [2500, 2500, 2500, 2500],  # Fees for student 1

   [5000, 5000, 5000, 5000],  # Fees for student 2

   [6000, 6000, 6000, 6000],  # Fees for student 3

   [2500, 5000, 2500, 5000],  # Fees for student 4

   [6000, 5000, 2500, 6000]   # Fees for student 5

]

total_remaining_fees(boarding_fees)

In this code, the `total_remaining_fees` function takes the 2-dimensional array `fees` as input. It calculates the remaining fees for each student by subtracting the sum of their paid fees from the sum of the total fees.

If the remaining fees are zero, it indicates that the student has paid all their fees.

Otherwise, it outputs the amount of remaining fees. The code provides an example of a 5x4 array with fees for five students and four payments.

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Answer:

1st one...................

Step-by-step explanation:

Step-by-step explanation:

5% Tip = $4.80

1% = $4.80/ 5

Cost of procedure = $4.80/5 x 100% (Equation)

b = $4.80 x 20.0 or 20($4.80)

b =$96

There are three left cosets of H in Z, given by:

H = {3k | k ∈ Z}

[1] + H = {3k + 1 | k ∈ Z}

[2] + H = {3k + 2 | k ∈ Z}

To find all the left cosets of H in Z, we need to find the equivalence classes of the relation x ~ y if and only if x - y ∈ H. That is, two integers are equivalent if their difference is a multiple of 3.

To find the left cosets, we choose a representative for each equivalence class. We can choose any integer in the class as the representative. Then, we add H to the representative to obtain the left coset.

For example, the equivalence class [0] consists of all integers that are multiples of 3. We can choose 0 as the representative. Then, the left coset is

[0] + H = {0 + 3k | k ∈ Z} = {3k | k ∈ Z}

Similarly, we can choose 1, 2 as the representatives for [1], [2], respectively, and obtain the left cosets:

[1] + H = {1 + 3k | k ∈ Z} = {3k + 1 | k ∈ Z}

[2] + H = {2 + 3k | k ∈ Z} = {3k + 2 | k ∈ Z}

We can continue this process to find all the left cosets. In general, there are three left cosets of H in Z, given by:

H = {3k | k ∈ Z}

[1] + H = {3k + 1 | k ∈ Z}

[2] + H = {3k + 2 | k ∈ Z}

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Answer:

Use the quotient property of logarithms, logb(x)−logb(y)=logb(xy) log b ( x ) - log b ( y ) = log b ( x y ) . log3(4010) log 3 ( 40 10 ). Step 2.

The probability that both balls are red is 0.22, the probability that no ball drawn is red is 0.26, the conditional probability that both balls are yellow is 0.02 and the probability that the second ball is blue is 0.375 or 3/8.

Probability is a measure or quantification of the likelihood or chance of an event occurring. It is used to describe and analyze uncertain or random situations. In simple terms, probability represents the ratio of favorable outcomes to the total number of possible outcomes.

A box contains 25 balls consisting of 4 yellow, 9 blue, and 12 red balls. The probability of picking two red balls in succession without replacement is calculated using the following counting argument.

The number of ways to choose two red balls out of 12 is given by the combination C(12, 2).

The total number of ways of choosing two balls out of 25 is given by C(25, 2).

Therefore, the probability that both balls are red is as follows:

P (two red balls) = C(12, 2)/C(25, 2) = (66/300) = 0.22

The probability of drawing no red balls is calculated using the following argument.

The number of ways to choose two balls out of the 13 non-red balls is given by C(13, 2).

The total number of ways of choosing two balls out of 25 is given by C(25, 2).

Therefore, the probability that no ball drawn is red is as follows:

P (no red ball) = C(13, 2)/C(25, 2) = (78/300) = 0.26

Conditional probability P(Y1Y2) is the probability of drawing the second yellow ball when the first yellow ball has already been drawn.

The number of ways to choose two yellow balls out of 4 is given by C(4, 2).

The total number of ways of choosing two balls out of 25 is given by C(25, 2).

Therefore, the conditional probability that both balls are yellow is as follows:

P(Y1Y2) = C(4, 2)/C(25, 2) = (6/300) = 0.02

The probability that the second ball is blue is given by the following:

9/24 = 0.375 (since the first ball has already been drawn without replacement).

Therefore, the probability that the second ball is blue is 0.375 or 3/8.

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Answer:

sqrt6 + sqrt10/2

Step-by-step explanation:

Area is LW so sqrt6*L = 3 + sqrt 15

L = 3+sqrt15/sqrt6

rationalizing the denominator:

3+sqrt15/sqrt6*sqrt6/sqrt6 = 3sqrt6 + sqrt90/6

simplifies to 3sqrt6 + 3sqrt10/6 and then sqrt6 + sqrt10/2

Jebb is 6 feet 4.5 inches tall.

What is height?

The distance between the bottom and top of an object or person is a measurement of its height.

Height, altitude, and elevation all refer to the vertical distance, either between the top and bottom of something or between its base and something above it. Height is a term for something that can be high or low and is measured vertically.

Given: Jebb is the tallest player on the basketball team.

He is 1 1 /2 times as tall as the shortest girl in the sixth grade, who is 4 1 /4 feet tall.

Here

1 1/2 times 4 1/4

change to improper fractions

\(1\frac{1}{2} = \frac{(2)(1)+1}{2}= \frac{3}{2}\)

\(4\frac{1}{4}= \frac{(4)(4)+1}{4} = \frac{17}{4}\)

⇒  1 1/2 times 4 1/4  is (3/2)*(17/4)

\(\frac{3}{2}(\frac{17}{4})=\frac{51}{8}\)

Convert 51/8 into improper fraction.

\(\frac{51}{8} = 6\frac{3}{8}\)  feet tall.

3/8 of 12 inches is,

\(\frac{3}{8}(12) = \frac{36}{8}\)

Convert 36/8 into improper fraction

\(\frac{36}{8} = 4\frac{4}{8}\)  inches

Here 4/8 = 0.5

⇒ \(4\frac{4}{8} = 4.5\)

Hence, Jebb is 6 feet 4.5 inches tall.

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The surface is parameterized by

\(\vec s(u,v) = x(u, v) \, \vec\imath + y(u, v) \, \vec\jmath + z(u, v)) \, \vec k\)

and the normal to the surface is given by the cross product of the partial derivatives of \(\vec s\) :

\(\vec n = \dfrac{\partial \vec s}{\partial u} \times \dfrac{\partial \vec s}{\partial v}\)

It looks like you're given

\(\begin{cases}x(u, v) = u + v\\y(u, v) = 2u^2\\z(u, v) = u - v\end{cases}\)

Then the normal vector is

\(\vec n = \left(\vec\imath + 4u \, \vec\jmath + \vec k\right) \times \left(\vec \imath - \vec k\right) = -4u\,\vec\imath + 2 \,\vec\jmath - 4u\,\vec k\)

Now, the point (2, 2, 0) corresponds to u and v such that

\(\begin{cases}u + v = 2\\2u^2 = 2\\u - v = 0\end{cases}\)

and solving gives \(u = v = 1\), so the normal vector at the point we care about is

\(\vec n = -4\,\vec\imath+2\,\vec\jmath-4\,\vec k\)

Then the equation of the tangent plane is

\(\left(-4\,\vec\imath + 2\,\vec\jmath - 4\,\vec k\right) \cdot \left((x-2)\,\vec\imath + (y-2)\,\vec\jmath + (z-0)\,\vec k\right) = 0\)

\(-4(x-2) + 2(y-2) - 4z = 0\)

\(\boxed{2x - y + 2z = 2}\)

(a) The number 72% is a D. statistic.

(b) The unknown true percentage of American citizens who like ''real TV'' is a C. parameter.

It is related to statistics and parameters.

(a) The number 72% is a statistic because it represents a summary measure of the sample of individuals who participated in the phone-in poll.

A statistic is a numerical value calculated from a sample of data, and it is used to make inferences about the population from which the sample was drawn.

(b) The unknown true percentage of American citizens who like ''real TV'' is a parameter.

A parameter is a numerical characteristic of a population, such as a mean, proportion, or standard deviation, and it is typically unknown and estimated from sample data.

In this case, the percentage of all American citizens who like ''real TV'' is unknown and cannot be directly observed, so it is considered a parameter.

The phone-in poll only represents a sample of individuals who called in to the newspaper and cannot be used to estimate the parameter for the entire population.

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Answer: 3/4 of a mile

Step-by-step explanation:

Answer:

504

Step-by-step explanation:

TSA (total surface area) = 1/2(p)(l) + B

p (perimeter) = 4(14) = 56

l (slant length) = 11

B (area of vase) = 14(14) = 196

TSA = 1/2 (56) (11) + 196

= 28(11) + 196

= 308 + 196

= 504

Where every student offer at least one of the subjects, there are 4 students who offer all three subjects.

To find the number of students who offer only one subject, we can use the formula:

number of students offering only one subject = total number of students offering the subject - number of students offering both subjects

For math, there are 22 students offering math and 5 offering both math and biology, so the number of students offering math only is:

22 - 5 = 17

Similarly, for physics and biology, the numbers of students offering the subjects only are:

14 - 7 = 7 (physics)
16 - 5 = 11 (biology)

To find the number of students offering all three subjects, we can use the formula:

number of students offering all three subjects = total number of students offering at least one subject - number of students offering only one subject in each subject + number of students offering no subject

We know that there are 7 students offering at least one subject. To find the number of students offering no subject, we can subtract this from the total number of students:

39 - 7 = 32

Now we can plug in the numbers:

number of students offering all three subjects = 7 - 17 - 7 - 11 + 32
= 4

Therefore, there are 4 students who offer all three subjects.

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Answer:

There are 1.295 or 1.29 moles

Step-by-step explanation:

1 mole = 6.022 × 10^23 molecules

So, number of moles present in 5.7 × 10^23 molecules of water = (5.7 × 10^23) / 6.022 × 10^23 = 0.946 moles

Hope, this helps.

Answer:

C = 2rπ

C = 2(7)(3.14) = 53.38

Step-by-step explanation:

(a) A nonzero vector orthogonal to the plane through the points P, Q, and R is (9, -17, 35). (b) The area of triangle PQR is \(\sqrt\)(811) / 2.

(a) To determine a nonzero vector orthogonal to the plane through the points P, Q, and R, we can first find two vectors in the plane and then take their cross product. Taking vectors PQ and PR, we have:

PQ = Q - P = (5, 1, -2) - (-4, 0, 0) = (9, 1, -2)

PR = R - P = (6, 4, 1) - (-4, 0, 0) = (10, 4, 1)

Taking the cross product of PQ and PR, we have:

n = PQ x PR = (9, 1, -2) x (10, 4, 1)

Evaluating the cross product gives n = (9, -17, 35). Therefore, (9, -17, 35) is a nonzero vector orthogonal to the plane through points P, Q, and R.

(b) To determine the area of triangle PQR, we can use the magnitude of the cross product of vectors PQ and PR divided by 2. The magnitude of the cross product is given by:

|n| = \(\sqrt\)((9)^2 + (-17)^2 + (35)^2)

Evaluating the magnitude gives |n| = \(\sqrt\)(811).

The area of triangle PQR is then:

Area = |n| / 2 = \(\sqrt\)(811) / 2.

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Answer:

2/5

Step-by-step explanation:

no of sample space , n(s) = 10

no. of probable cases, n(e) = 4

Probability of the arrow landing on a red section , P(e)

= n(e)/n(s)

= 4/10

= 2/5

Answer:

the answer is b, 2/5

Step-by-step explanation:

Answer:  The height of the tree is approximately 44 ft.

Step-by-step explanation:  Step 1: Calculate the ratio of the person's height to the length of their shadow.

Person's Height: 5 ft

Length of Shadow: 4 ft

Ratio: 5 ft/4 ft = 1.25

Step 2: Use the ratio to calculate the length of the tree's shadow.

Length of Tree's Shadow: 22 ft

Ratio: 1.25

Calculation: 22 ft/1.25 = 17.6 ft

Step 3: Multiply the length of the tree's shadow by the ratio to calculate the tree's height.

Length of Tree's Shadow: 17.6 ft

Ratio: 1.25

Calculation: 17.6 ft x 1.25 = 22 ft

Answer: The height of the tree is approximately 44 ft.

Stephen Dubner and Steven Levitt are the authors of the essay, and as they develop their essay, they use a great deal of quantification.

The following are three specific examples that they used: They write, "If a martini is made with 4 ounces of gin, that’s 2.8 standard drinks. "They also said, "Let's consider the five most unsafe hours for driving, which are Saturday and Sunday mornings from 1 am to 6 am. In the middle of this time period, 3 am on Saturday morning, the likelihood of an accident is three times higher than at noon on a weekday. "In another instance, they note that "The average person who has been murdered has approximately 300 friends and relatives, which means that a homicide victim’s personal network is quite extensive. "The authors use these specific numbers to make their argument more convincing. Using quantification provides an air of authority to the author's claims. By providing specifics, the author can communicate more information than would otherwise be possible.

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Answer:

I think it is B correct me if I am wrong

Step-by-step explanation:

The solution for the inequality |r| - 3 > 2 is r < -5 or r > 5.

Inequality shows relation between two expression which are not equal to each others.

The given inequality is,

|r| - 3 > 2.

Simplify the inequality,

|r| > 5,

Implies that,

r < -5 or r > 5

Interval notation (-∞, -5) ∪ (5, ∞).

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Answer:

750

Step-by-step explanation:

Just divide 90 by 0.12 then it gives you 750. If you want to check it you can multiply 750 by 0.12 and it gives you 90. I got 0.12 from 12% since they're the same thing.

In the image line segment SE is the tangent. The secant line making an angle with tangent line SE is NS. So the angle is ∠GSE. So option B is the correct answer.

Tangent is a line which intersect with only a single point on the curve. The point where the line meets is the point of tangency. Tangent line is always perpendicular to the radius drawn to the point of tangency. Here the tangent line is SE, point of tangency is S.

Secant lines are the lines which passes through two points of a curve. A chord drawn to the circle is a secant line. Here there are two secant lines NS and NA. Here only NS makes an angle with the tangent line.

So the angle made by a tangent and secant line is ∠GSE.

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The image for the question is attached below.