x(5 – 2) = 4x - x
infinite solutions
no solution
unique solution

It means that both people have antigens, but the second person has more of them.

Antigens are substances that can trigger an immune response in the body. They are typically proteins that are found on the surface of bacteria, viruses, and other foreign substances that enter the body. When the immune system detects an antigen, it produces antibodies to attack and destroy it. This helps the body to defend itself against infections and other diseases. Antigens can also be used in vaccines to help the body build immunity to a particular disease.

Since there is a color change in the sample in the given case, this indicates that although both individuals possess the antigen, the second individual has a greater quantity or concentration of the antigen in their body. The dilution is 1/5 and 1/100. This is so as the amount of antigen in the sample is still detected even in larger quantities of solution.

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The unit price of the 10-pack is 9.00.

The unit price is the price of one item divided by the number of items. To calculate the unit price of a 5-pack of tickets to the zoo, the price of the 5-pack must be divided by the number of tickets in the 5-pack. This can be expressed mathematically as:

Unit Price = Price of 5-pack ÷ Number of tickets in 5-pack

Unit Price = 52 ÷ 5

Unit Price = 10.40

Therefore, the unit price of a 5-pack of tickets to the zoo is 0.40. This means that for every ticket purchased in the 5-pack, the cost is 10.40. This calculation can be used to calculate the unit price of any number of items in a set. For example, if the cost of 10 tickets is $90, then the unit price of the 10-pack is 9.00.

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Answer:

1/6 or 16

Step-by-step explanation:

I hope this is the correct answer

Answer:

57.5 mi

Step-by-step explanation:

1 in = 5 mi

11.5 × 5 = 57.5 mi

Therefore , the solution of the given problem of long division is Quotient is 131 and the Remainder is 5

Synthetic division is another way to divide a polynomial but by binary x - c, while c is a constant. The divisor frequently assumes the form of (x a). In synthetic division, you are just interested in the coefficients of the polynomials, unlike long division.

Here,

The given Divisor = 6 and Dividend = 791

Step 1: Take the first digit of the dividend from the left. ...

Step 2: Then divide it by the divisor and write the answer on top as the quotient.

Step 3: Subtract the result from the digit and write the difference below.

long division is a method for dividing large numbers into steps or parts, breaking the division problem into a sequence of easier steps. It is the most common method used to solve problems based on division.

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Answer:

-8

Step-by-step explanation:

Hey there!

(1/2)(10) - (-12) - 25

= 1/2(10) - (-12) - 25

= 5 - (-12) - 25

= 5 + 12 - 25

= 17 - 25

= -8

Therefore, your answer is: -8

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

Answer:

$321.71

Step-by-step explanation:

To do this problem, we have to multiply 8.25 by 39 because Kristen gets paid $8.25 per hour, and she worked for 39 hours. Here is my work below:

\(8.25 X 39=321.71\)

So, Kristen gets paid $321.71 for working 39 hours.

Hope this helps! :)

Have a blessed day! :)

PLEASE MARK ME AS BRAINLIEST I REALLY WANT TO LEVEL UP

Each box will contain 1 chocolate donut, 1 strawberry donut, and 1 caramel donut, there will be a Total of 4 boxes, and each box will contain 1 chocolate donut, 1 strawberry donut, and 1 caramel donut.

The number of boxes and the distribution of donuts in each box, we need to find the greatest common divisor (GCD) of the total number of chocolate, strawberry, and caramel donuts available. The GCD will represent the maximum number of donuts that can be included in each box.

First, let's find the GCD of 36, 27, and 18. By calculating the GCD, we can determine the maximum number of donuts that can be included in each box.

GCD(36, 27, 18) = 9

Therefore, the maximum number of donuts that can be included in each box is 9.

Next, we need to determine the number of boxes. To do this, we divide the total number of each donut type by the maximum number of donuts per box.

Number of boxes for chocolate donuts = 36 / 9 = 4 boxes

Number of boxes for strawberry donuts = 27 / 9 = 3 boxes

Number of boxes for caramel donuts = 18 / 9 = 2 boxes

Since each box contains the same total number of donuts, we can conclude that there will be 4 boxes with chocolate donuts, 3 boxes with strawberry donuts, and 2 boxes with caramel donuts.

To find the distribution of donuts in each box, we divide the maximum number of donuts per box by the GCD:

Distribution in each box: 9 = 1 × 9

Therefore, each box will contain 1 chocolate donut, 1 strawberry donut, and 1 caramel donut, there will be a total of 4 boxes, and each box will contain 1 chocolate donut, 1 strawberry donut, and 1 caramel donut.

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There can be 432 Types of Combinations for a 4-digit number beginning with 1 that has exactly two identical digits

What is permutation and combination?

\($11xy,\qquad 1x1y,\qquad1xy1$\)

Because the number must have exactly two identical number digits,\($x\neq y$\), \($x\neq1$, and $y\neq1$\). Hence, there are \($3\cdot9\cdot8=216$\)  number of this form.

Now suppose that the two identical digits are not 1. Reasoning similarly to before, we have the following possible combination:

\($1xxy,\qquad1xyx,\qquad1yxx.$\)

Again,,\($x\neq y$\), \($x\neq1$, and $y\neq1$\). There are \($3\cdot9\cdot8=216$\) numbers of this form.

Thus the answer is 216+216=432

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To determine the probability that Alice will flip more heads than Bob, we can use the concept of binomial probability.

Let's consider the number of heads flipped by Alice as a random variable X, which follows a binomial distribution with parameters n = 1201 (number of trials) and p = 0.5 (probability of getting a head on a fair coin). Similarly, the number of heads flipped by Bob can be represented as a random variable Y, which follows a binomial distribution with parameters n = 1200 and p = 0.5.

To calculate the probability that Alice will flip more heads than Bob, we need to find P(X > Y). This can be done by summing up the probabilities of all possible values of X that are greater than the corresponding values of Y.

P(X > Y) = P(X = 1201) + P(X = 1200) + ... + P(X = 1200 - 1200)

We can simplify this expression by noticing that P(X = k) = P(Y = k) for any given value of k.

Therefore, P(X > Y) = P(X = 1201) + P(X = 1200) + ... + P(X = 601)

Using the binomial probability formula, the probability of getting exactly k heads out of n trials is given by:

P(X = k) = C(n, k) * p^k * (1 - p)^(n - k)

Where C(n, k) represents the number of ways to choose k successes out of n trials, given by the binomial coefficient formula:

C(n, k) = n! / (k! * (n - k)!)

Now we can calculate the probability:

P(X > Y) = P(X = 1201) + P(X = 1200) + ... + P(X = 601)

        = [C(1201, 1201) * 0.5^1201 * 0.5^0] + [C(1201, 1200) * 0.5^1200 * 0.5^1] + ... + [C(1201, 601) * 0.5^601 * 0.5^600]

This calculation involves summing up a large number of terms, so it can be computationally intensive. However, we can approximate the probability by using methods such as Monte Carlo simulation or statistical software.

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Answer:

The selling price of the bag is $22.5

Step-by-step explanation:

Buying Price = $25,

Selling Price = ?

Since they sold it at a loss of 10%,

So, they sold it for a price 10% less than the buying price,

or at 90% or 0.9 of the buying price,

so,

Selling Price = (0.9)(25) = $22.5

The probability that a consumer will obtain a satisfactory plumbing job given that the plumber was Plumber A is 0.75.

To find the probability that a consumer will obtain an unsatisfactory plumbing job given that the plumber was Plumber A, we first need to determine the proportion of plumbing jobs done by Plumber A that result in consumer dissatisfaction.

Given that half the complaints dealt with Plumber A and that Plumber A does 40% of the plumbing jobs in the town, we can calculate this proportion as follows:

Proportion of unsatisfactory plumbing jobs done by Plumber A = (Half the complaints / Total number of plumbing jobs done by Plumber A)

= (Half the complaints / 40% of the total plumbing jobs in the town)

= (Half of 10% / 40%)

= 10% / 2 / 40% = 1 / 4 = 0.25

Therefore, the probability that a consumer will obtain an unsatisfactory plumbing job given that the plumber was Plumber A is 0.25.

To find the probability that a consumer will obtain a satisfactory plumbing job given that the plumber was Plumber A, we subtract the probability of obtaining an unsatisfactory plumbing job from 1:

Probability of a satisfactory plumbing job given that the plumber was Plumber A = 1 - Probability of an unsatisfactory plumbing job

= 1 - 0.25

= 0.75

Therefore, the probability that a consumer will obtain a satisfactory plumbing job given that the plumber was Plumber A is 0.75.

In conclusion, given that Plumber A does 40% of the plumbing jobs in the town and that half the complaints dealt with Plumber A, the probability that a consumer will obtain an unsatisfactory plumbing job given that the plumber was Plumber A is 0.25, and the probability that a consumer will obtain a satisfactory plumbing job given that the plumber was Plumber A is 0.75. These probabilities can be used to make informed decisions about which plumber to choose for plumbing jobs in the community.

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The vertex is at (-2, -9).

From the equation:

y = x² + 4x - 5

Transpose the c-value to the left side of the equation:

y + 5 = x² + 4x

Complete the square of the expression on the right side of the equation to get a perfect square trinomial:

y + 5 = x² + 4x + 4 - 4

by adding and subtracting 4 to the right side of the equation to maintain its balance.

Add the numbers on the left and factor the trinomial on the right:

y + 9 = (x + 2)²

Transpose the number across to the right side to get the equation into the vertex form, y = a(z-h)² + k:

y = (x + 2)² - 9

Make sure the addition and subtraction signs are correct to give the proper vertex form.

Here, the vertex is at (-2, -9).

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Given:-

To find:-

Answer:-

1) Firstly we are told to transpose the c value to LHS .

With respect to standard form of a quadratic equation, \( ax^2+bx + c \) ,the value of c here will be -5 . So on transposing c to LHS , we have;

\(\implies y + 5 = x^2 + 4x\\\)

w) Next we are told to complete the square on the RHS of the equation. For that add and subtract 4 .

\(\implies y + 5 = x^2 + 4x + 4 - 4 \\\)

\(\implies y + 5 =\{ (x)^2 + 2.2.x + 2^2 \}- 4\\\)

The terms inside the curly brackets are in the form of \( a^2+2ab + b^2\) , which is the whole square of \( (a + b )\) . That is \( ( a + b)^2\) . So , we can rewrite it as ,

\(\implies y + 5 = (x +2)^2 - 4 \\\)

\(\implies y + 5 + 4 = (x+2)^2 \\\)

3) Next we have to add the number on the left and factor the trinomial on right as ,

\(\implies y + 9 = (x+2)^2 \\\)

4) Now we are told to transpose the number on the LHS to RHS and get the equation into vertex form which is \( y = a(z-h)^2+ k \) .

\(\implies\underline{\underline{ y = (x+2)^2 - 9}} \\\)

This is our required answer in vertex form. Also on comparing to the standard equation of vertex form, we have;

\(\implies vertex = ( -2,-9) \\\)

and we are done!

Answer: No the students work is not correct. Because you are using distribution. Which means that 3 has to multiply the y2 and 2 not just the y2! And after you distribute it you need to simplify!

Step-by-step explanation:

Answer:

(3 – 6y²)(y² + 2) = - 6y⁴ - 9y² + 6

Step-by-step explanation:

Given the expression

3-6y² and y²+2

We have to find the product of 3-6y² and y²+2

Clara's Solution:

(3 – 6y²)(y² + 2) = 3(y²) + (–6y²)(2)

                          = 3y² – 12y²

                          = -9y²

NO!

The student's work is INCORRECT!

Clara did not imply the correct distribution of multiplying the terms in the first step.

Here is the correct solution:

(3 – 6y²)(y² + 2) = 3(y²) + (–6y²)(2) + (3)(2) + (–6y²)(y²)

                          = 3y² – 12y² + 6 - 6y⁴

                           = - 6y⁴ - 9y² + 6

Therefore,

(3 – 6y²)(y² + 2) = - 6y⁴ - 9y² + 6

well, since the y-intercept is at -5, or namely when the line hits the y-axis is at -5, that's when x = 0, so the point is really (0 , -5), and we also know another point on the line, that is (-1 ,6), to get the equation of any straight line, we simply need two points off of it, so let's use those two

\(\stackrel{y-intercept}{(\stackrel{x_1}{0}~,~\stackrel{y_1}{-5})}\qquad (\stackrel{x_2}{-1}~,~\stackrel{y_2}{6}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{6}-\stackrel{y1}{(-5)}}}{\underset{run} {\underset{x_2}{-1}-\underset{x_1}{0}}} \implies \cfrac{6 +5}{-1} \implies \cfrac{ 11 }{ -1 } \implies - 11\)

\(\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-5)}=\stackrel{m}{- 11}(x-\stackrel{x_1}{0}) \implies y +5 = - 11 ( x -0) \\\\\\ y+5=-11x\implies {\Large \begin{array}{llll} y=-11x-5 \end{array}}\)

Answer: Your answer is 25

Step-by-step explanation:

To start off, add 16 positive to -116 negative. That gives us a baseline of -100

Now since we did -4 times a number to get to it, the opposite of multiplying is dividing.

A quarter is 25. 4 quarters makes a dollar, or 100 cents. 4 times 25 is 100 so -4 times 25 is -100. Add 16 to your number to get a result of 25! Since you already subtracted 16 we can forget about adding it back. 100/4 = 25

To check our work, -116+10= -100

4 times 25 is 100

-4 times 25 is -100

-100=-100

Answer:

\(\angle BAC=180^{\circ}-\frac{13\sin 23^{\circ}}{6}\)

Step-by-step explanation:

\(\frac{\sin(\angle BAC)}{13}=\frac{\sin 23^{\circ}}{6} \\ \\ \sin \angle BAC=\frac{13\sin 23^{\circ}}{6} \\ \\ \angle BAC=180^{\circ}-\frac{13\sin 23^{\circ}}{6}\)

The volume of remaining solid is 7 in³.

The whole three-dimensional area occupied by a cube is its volume.

A cube is a solid 3-D object with six square faces and equal-length sides.

The cube is one of the five platonic solid shapes and is also referred to as a regular hexahedron.

The cubic units are used to represent the cube's volume.

Imagine performing each cut individually.

A box 2*2*3 is eliminated in the initial cut. Two boxes with dimensions of 2*2*0.5 are removed during the second cut, and the third cut eliminates the same number of boxes on the final two faces.

Therefore, the sum of all cuts is 12 + 4 + 4 = 20.

∴Volume of rest of cube = 3³-20

                                         = 7 in³

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Answer:

D. 79%

Step-by-step explanation:

Took the the on USA Test prep

If a point is randomly selected from the rectangular area of the graph, the probability that it will be in the blue region is 79%.

The ratio of the number of favorable outcomes to the total number of outcomes of an event is known as probability.

It is given that, the length=20, the width=10, and the radius of half circle=10.

Calculate the area of the rectangle.

Knows the area of the rectangle is the product of length and width.

So,

\(\Rightarrow \text{Area of rectangle}=\text{10}\times \text{20} \\ \Rightarrow \text{Area of rectangle}=200 \\\)

Calculate the area of the half-circle.

Knows the area of the half-circle\(=\frac{\pi r^{2} }{2}\).

So,

\(& \Rightarrow \text{Area of half circle}=\frac{3.14\times 10\times 10}{2} \\ & \Rightarrow \text{Area of half circle}=\frac{314}{2} \\ & \Rightarrow \text{Area of half circle}=157 \\\)

Calculate the probability that it will be in the blue region.

Knows the formula for the probability, \(\text{Probability}\left( \text{Event} \right)=\frac{\text{Favorable Outcomes}}{\text{Total Outcomes}}\)

So,

\(& \Rightarrow \text{Probability}=\frac{\text{157}}{200} \\ & \Rightarrow \text{Probability}=0.78539 \\ & \therefore \text{Probability }\%=79\% \\\)

Thus, the correct answer is an option (D). i.e., 79%.

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The writer's profit is $84.00. To calculate the writer's profit, you need to consider the premiums collected from selling the call options, the interest earned on those premiums, and the cost of buying the shares to complete the call contract.The premiums collected from selling the call options are:$0.91 x 100 = $91.00The interest earned on those premiums over 30 days at 5% is:($91.00 x 0.05 x 30) / 365 = $0.38The total amount of cash available to the writer at expiry is therefore:$91.00 + $0.38 = $91.38The cost of buying the shares to complete the call contract is:100 x $42 = $4,200.00Since the underlying asset is worth $39 at expiry, the writer can buy the necessary shares for:100 x $39 = $3,900.00The writer's profit is therefore:$91.38 - $3,900.00 = $84.00Since the writer made a profit, the answer is $84.00.

Hope I helped you...

The execution of 'NEG CX', we have:

CX = FFC5

CF = 1

What is the content?

we can determine the content of CX and the Carry Flag after the execution of the statement 'NEG CX', we need to first understand what the 'NEG' instruction does.

The 'NEG' instruction is used to negate the value of the operand by subtracting it from 0. In other words, if the operand is X, then NEG X is equivalent to 0 - X. This instruction affects the Carry Flag (CF) to indicate whether or not there was a borrow during the operation.

apply this to the given scenario. We are given that CX initially contains the value 003B.

Execute 'NEG CX'

In this step, we negate the value of CX by subtracting it from 0.

0 - 003B = FFC5 (in two's complement representation)

we have performed a subtraction, we need to check if there was a borrow. In this case, there was a borrow because we subtracted a smaller value from a larger value, so the Carry Flag will be set to 1.

The content of CX after the execution of 'NEG CX' is FFC5. This is because we subtracted the value of CX from 0 using two's complement representation.

The Carry Flag (CF) is set to 1 because there was a borrow during the subtraction. Specifically, the subtraction of 003B from 0 required borrowing from the 16-bit position, which caused the Carry Flag to be set to 1.

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Answer:

3111

Step-by-step explanation:

rewrite (√3111)^2 as 3111

\(I \approx [1/(2^5\times 20) - 1/(2^7\times42) + 1/(2^9\times72)...]\)

This series provides an approximation for the definite integral I within the desired accuracy.

To approximate the definite integral \(I = \int_{0}^{1/2} x^3 arctan x dx\) within the indicated accuracy, we can use a series expansion for the function arctanx.

The series expansion for

arctanx = x - x³/3 + x⁵/5 - x⁷/7...............

Substituting this series expansion into the integral, we get:

\(I = \int_{0}^{1/2} x^3 (x - x^3/3 + x^5/5 - x^7/7....) dx\)

Expanding the expression and integrating each term, we obtain:

\(I = [x^5/20 - x^7/42 + x^9/72 - x^{11}/110....]^{1/2}_0\)

Evaluating the upper and lower limits, we have:

\(I = [(1/2)^5/20 - (1/2)^7/42 + (1/2)^9/72 - (1/2)^{11}/110....] - [0^5/20 - 0^7/42 + 0^9/72 - 0^{11}/110....]\)

Simplifying the expression, we get:

\(I \approx [1/(2^5\times 20) - 1/(2^7\times42) + 1/(2^9\times72)...]\)

This series provides an approximation for the definite integral I within the desired accuracy.

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The standard deviation of the sampling distribution of the scores for the 53 students is given as follows:

1.59.

By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation given by the equation presented as follows: \(s = \frac{\sigma}{\sqrt{n}}\).

The parameters for this problem are given as follows:

\(\sigma = 11.6, n = 53\)

Hence the standard error is given as follows:

\(s = \sqrt{\frac{11.6}{\sqrt{53}}}\)

s = 1.59.

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Answer:

Step-by-step explanation:

y=10

Step-by-step explanation:

wait Aw Minute Bro I Will Tell U Answer

Answer:

y ≥1

Step-by-step explanation:

y=5x-4

Let x  ≥ 1

y  ≥ 5(1)-4

y ≥ 5-4

y  ≥ 1

Answer:

\(herey = 5x - 4 \\ \\ given \: that \: x \geqslant 1 \\ so \: y \geqslant 5 \times 1 - 4 \\ y \geqslant 1 \\ thank \: you\)