-11 +23-46+ (-12)
how to solve it​

Answer:

Let's start by defining our variables:

Now, let's write the system of inequalities to represent the constraints:

The company has 260 boards of mahogany, so x ≤ 260.

The company has 320 boards of black walnut, so y ≤ 320.

The company expects to sell at most 380 boards, so x + y ≤ 380.

We cannot sell a negative number of boards, so x ≥ 0 and y ≥ 0.

Graphically, these constraints represent a feasible region in the first quadrant of the xy-plane bounded by the lines x = 260, y = 320, and x + y = 380, as well as the x and y axes.

To maximize profit, we need to write a function that represents the objective. The profit for selling one board of mahogany is $20, and the profit for selling one board of black walnut is $6. Therefore, the total profit P can be calculated as:

To maximize P, we need to find the values of x and y that satisfy the constraints and make P as large as possible. This is an optimization problem that can be solved using linear programming techniques.

The solution to this problem can be found by graphing the feasible region and identifying the corner point that maximizes the objective function P. However, since we cannot draw a graph here, we will use a table of values to find the maximum profit.

Let's consider the corner points of the feasible region:

Corner point (0, 0):

P = 20(0) + 6(0) = 0

Corner point (260, 0):

P = 20(260) + 6(0) = 5200

Corner point (0, 320):

P = 20(0) + 6(320) = 1920

Corner point (100, 280):

P = 20(100) + 6(280) = 3160

Corner point (200, 180):

P = 20(200) + 6(180) = 5520

Corner point (380, 0):

P = 20(380) + 6(0) = 7600

The maximum profit is $7600, which occurs when the company sells 380 boards of wood, all of which are mahogany.

Answer:

15

Step-by-step explanation:

Answer can only be found through estimation.

This means you have to do:

[tex]\frac{50*3}{\sqrt{100} }[/tex]

This will get you 15.

For the first equation with y = 3x + 2 and y = -4x + 2, the lines have the same slope, but a different y-intercept. This means that the lines are parallel and they will never intersect. Therefore, the system of equations has no solution.

For the second equation with y = 2x + 7 and y = 2x - 4, the lines have the same slope and the same y-intercept. This means that the lines are coincident and they will intersect at one point. Therefore, the system of equations has one solution.

For the third equation with y = 6x + 3 and y = -x - 4, the lines have a different slope and a different y-intercept. This means that the lines are not parallel and they will intersect at one point. Therefore, the system of equations has one solution.

For the fourth equation with y = 4x + 3 and y = 4x - 1, the lines have the same slope and the same y-intercept. This means that the lines are coincident and they will intersect at one point. Therefore, the system of equations has one solution.

For the fifth equation with y = 3x + 6 and y = 3x + 6, the lines have the same slope and the same y-intercept. This means that the lines are coincident and they will intersect at one point. Therefore, the system of equations

Therefore, the volume of the prism is 200 cubic centimeters.

Volume is a measurement of the amount of space occupied by a three-dimensional object. It is typically measured in cubic units, such as cubic meters, cubic centimeters, or cubic feet. The volume of an object can be calculated using a variety of formulas, depending on its shape. The concept of volume is used in various fields, including physics, engineering, architecture, and manufacturing.

Here,

Identify the base of the prism. In this case, the base is a right triangle with legs of 5 cm and 8 cm, and a hypotenuse of 11 cm.

Use the formula for the area of a triangle to find the area of the base. The formula for the area of a right triangle is A = (1/2)bh, where b and h are the lengths of the base and height, respectively. In this case, we can use the legs of the triangle as the base and height, since they are perpendicular. So, the area of the base is:

A = (1/2)(5 cm)(8 cm) = 20 cm²

Multiply the area of the base by the height of the prism to find the volume. The height of the prism is given as 10 cm, so:

Volume = (Area of base) x (Height)

= (20 cm²) x (10 cm)

= 200 cm³

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The 41st term of the sequence is 121.

In mathematics, a sequence is a list of numbers or objects that follow a certain pattern or rule. A sequence's terms are typically identified by subscripts, like a1, a2, a3,..., an, where n denotes the number of terms in the sequence.

Sequences can be arithmetic, geometric, or neither, depending on terms follow a static difference, constant ratio, or neither of these series, respectively. Algebra uses geometric sequences to represent exponential development or decay whereas arithmetic sequences are frequently employed to model linear connections.

The given sequence is 2 , 5 , 8 , ...

The common difference is:

d = 5 - 2 = 3

The nth term of a sequence is given as:

an = a1 + (n-1)d

Substituting the value we have:

an = 2 + (n-1)3

an = 3n - 1

a41 = 3(41) - 1 = 122 - 1 = 121

Hence, the 41st term of the sequence is 121.

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Answer:

they bought 62 item from noodles and 51 items from hot chips

the variance of X is 9. b) Determine E [2X² - 20X +5]:

Using linearity of expectation, we can find E [2X² - 20X +5] as:

E [2X² - 20X +5] = 2E[X²] - 20E[X] + 5

by the question.

The number of ways to select the first 2 white chips is given by:

Number of ways = (6C2) (5C0) (3C0) = 15

The number of ways to select the third chip as blue given that the first 2 chips were white is given by:

Number of ways = (3C1) = 3

Therefore, the probability of selecting the third chip as blue given that the first 2 chips were white is:

P(The third chip is blue the first 2 were white) = Number of ways / Total number of ways = 3 / 350 = 0.0086 (rounded to 4 decimal places)

c) P(The fourth chip is blue the first 2 were white):

The number of ways to select the first 2 white chips is given by:

Number of ways = (6C2) (5C0) (3C0) = 15

The number of ways to select the third chip as non-white given that the first 2 chips were white is given by:

Number of ways = (8C1) = 8

The number of ways to select the fourth chip as blue given that the first 2 chips were white, and the third chip was non-white is given by:

Number of ways = (3C1) = 3

Therefore, the probability of selecting the fourth chip as blue given that the first 2 chips were white is:

P(The fourth chip is blue the first 2 were white) = Number of ways / Total number of ways = 8*3 / 350 = 0.0686 (rounded to 4 decimal places)

Suppose we have a random variable X such that E[X]= 7 and E[X²] =58.

a) Determine the variance of X:

The variance of X is given by:

Var[X] = E[X²] - (E[X]) ²

Substituting the given values, we get:

Var[X] = 58 - (7) ² = 9

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The total number of cats at the vet is approximately 61.

A percentage is an equation proving the equality of two ratios. A ratio is a fractional comparison of two numbers or quantities. Proportions are used in mathematics to solve issues that involve comparing two numbers or discovering an unknown value. For instance, proportions can be used to determine equivalent fractions, compute percentages, and solve issues requiring rates and ratios. In a proportion, the numerator of one ratio is the same as the numerator of the other ratio, and vice versa for the denominator. Simplifying and cross multiplying can be used to address proportional problems.

Let the total number of dogs =x.

Let the total number of cats = y.

Given that, for every seven dogs at the vet there are 10 cats.

Thus, using proportions we have:

7 dogs / 10 cats = x / y

Using cross multiplication:

7 dogs x y = 10 cats (x)

y = (10/7) (x)

Now, x +y = 102

x = 102 - y

Substituting the value:

y = 10/7 (102 - y)

y = 145.71 - 1.4y

y + 1.4y = 145.71

2.4y = 145.71

y = 60.71

Hence, the total number of cats at the vet is approximately 61.

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The number of ways of doing both things is N = m × n

Since there are m ways of doing one thing and n ways of doing another, to find how many ways are there to do both, we proceed as follows.

Since there are m ways of doing one thing and n ways of doing another, to find the number of many ways to do both things,we multiply both numbers together.

So, then number of ways of doing both things is N = m × n

So, there are m × n ways of doing both things

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Construct a triangle PQR with sides PQ=8cm, PR=5cm, and QR=6cm, then draw a circle passing through P, Q, and R. This circle is called the circumcircle of triangle PQR.

We draw a line segment PQ = 8 cm long. From point P, we draw a line segment PR = 5 cm long at an angle of 60 degrees to PQ. Then, we draw a line segment QR = 6 cm long joining points Q and R to complete the triangle. Next, we use a compass to draw a circle passing through points P, Q, and R. This circle is called the circumcircle or circumscribed circle of the triangle, which is the unique circle that passes through all three vertices of the triangle. The circumcircle has a special property that its center is equidistant from the three vertices of the triangle.

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(a)The distribution of X (the average of the 49 races) follows a normal distribution with mean 146 minutes and standard deviation 11 minutes. (b)The probability of the average of the sample being between 144 and 149 minutes is 0.5854.(c)The 80th percentile for the average of these 49 marathons is 157.2 minutes.(d) The median of the average running times is 146 minutes.

Part(a) The distribution of X (the average of the 49 races) follows a normal distribution with mean 146 minutes and standard deviation 11 minutes. Part (b) The probability that the average of the sample will be between 144 and 149 minutes in these 49 marathons can be calculated using the z-score formula: z = (x - mean)/standard deviation
For x = 144, z = (144 - 146)/11 = -0.18
For x = 149, z = (149 - 146)/11 = 0.27,using the z-score table, the probability of the average of the sample being between 144 and 149 minutes is 0.5854 (0.4026 + 0.1828).

Part (c) The 80th percentile for the average of these 49 marathons can be calculated using the z-score formula: z = (x - mean)/standard deviation, For the 80th percentile, z = 0.84 (from z-score table). Therefore, x = 146 + (0.84 * 11) = 157.2 minutes. Part (d) The median of the average running times is 146 minutes. The median is the midpoint of the data which means half of the data is above the median and half of the data is below the median. Therefore, the median of the average running times is equal to the mean.

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Answer:

Let's call the first number x and the second number y.

From the problem, we know that:

To solve for x and y, we can start by expressing one variable in terms of the other, using one of the equations.

Rearranging the first equation to solve for x, we get:

x = 425 - y

Now we can substitute this expression for x into the second equation, and solve for y:

0.2x = 0.3y (substituting x = 425 - y)

0.2(425 - y) = 0.3y (distributing the 0.2)

85 - 0.2y = 0.3y (combining like terms)

85 = 0.5y (adding 0.2y to both sides)

y = 170 (dividing both sides by 0.5)

So the second number is 170. To find the first number, we can substitute this value back into the first equation:

x + y = 425 (substituting y = 170)

x + 170 = 425

x = 255

Therefore, the two numbers are 255 and 170.

Answer:

  (a, b) alternate interior angles at M and N, and at A and B are congruent

  (c) the triangles are congruent by SAS and by ASA (and MX = NX)

  (d) angles are no longer congruent, so the triangles are not congruent. The radii are given as congruent, but the chords cannot be shown congruent.

Step-by-step explanation:

Given same-size circles A and B, externally tangent to each other at X, each with chords MX and NX, you want to know what can be concluded if AM║BN, and what is unprovable if those segments are not parallel.

The circles being the same size means all the radii are congruent. This is shown by the single hash marks in the attached diagram.

Alternate interior angles where a transversal crosses parallel lines are congruent. If AM║BN, this means the angles marked with a single arc are congruent, and the angles marked with a double arc are congruent. These are the alternate interior angles at transversal MN and at transversal AB.

If AM║BN, in addition to the given congruences, we also know ...

∆AMX ≅ ∆BNX by SAS or ASA (take your pick).

If AM and BN are not parallel, MN is not a straight line through X, the angles at A and B are not congruent, and the angles at M and N are not congruent. (We assume segment AB still goes through X.)

__

Additional comment

Triangles MAX and NBX are isosceles, so their base angles are congruent. If X lies on MN, then AM and BN must be parallel, since the vertical angles at X will be congruent along with the other base angles at M and N. If AM and BN are not parallel, point X cannot lie on segment AB.

The company should sell their phones for $250 each to get the maximum revenue.

What do you mean by maximum revenue?

Maximum revenue refers to the highest possible amount of income that can be generated from a particular product or service. In the context of the given problem, it means finding the price at which the company can sell its cell phones to earn the highest amount of revenue.

Finding the price at which the company should sell their phones to get the maximum revenue:

We need to find the vertex of the parabolic function [tex]r(x)=x(1,000-2x)[/tex], which represents the revenue as a function of the selling price.

To find the vertex of the function r(x), we need to first rewrite it in standard form by expanding the product:

[tex]r(x) = 1000x - 2x^2[/tex]

Now we can see that the function is a quadratic polynomial in standard form, with [tex]a=-2, b=1000[/tex], and [tex]c=0[/tex]. To find the x-coordinate of the vertex, we can use the formula:

[tex]x = -b / (2a)[/tex]

Substituting the values of a and b, we get:

[tex]x = -1000 / (2\times(-2)) = 250[/tex]

Therefore, the company should sell their phones for $250 each to get the maximum revenue. To find the maximum revenue, we can substitute this value of x into the function r(x):

[tex]r(250) = 250\times(1000-2\times250) = $125,000[/tex]

So the maximum revenue the company can expect to earn is $125,000 if they sell their phones for $250 each.

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Using distance between two points formula, a = 0

The distance between two points (x, y) and (x', y') is given by

d = √[(x' - x)² + (y' - y)²]

Now, If the distance between the points (0, 6) and (a, 0) is 6 units, to find the value of a,

Let

So, substituting the values of the variables into the equation, we have

d = √[(x' - x)² + (y' - y)²]

6 = √[(a - 0)² + (0 - 6)²]

⇒ √[a² + (- 6)²] = 6

√[a² + 36] = 6

Squaring both sides, we have that

a² + 36  = 6²

a² + 36  = 36

a² = 36 - 36

a² = 0

a = √0

a = 0

So, a = 0

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The question is incomplete. Here is the complete question

If the distance between (0, 6) and (a, 0) os 6 units. Find the value of a

​

The probability of a bulb lasting for at most 540 hours is 0.7521, rounded to four decimal places.

The life of light bulbs is distributed normally. The variance of the lifetime is 225 and the mean lifetime of a bulb is 530 hours. Find the probability of a bulb lasting for at most 540 hours. Round your answer to four decimal places.

Using the z-score formula z = (x - μ) / σ, where x is the value in question (540 hours in this case), μ is the mean (530 hours in this case) and σ is the standard deviation (15 hours in this case), we can calculate the z-score:
z = (540 - 530) / 15
z = 10 / 15
z = 0.67
Using a z-table, we can look up the probability of a value being less than or equal to 0.67, which is 0.7521.
Therefore, the probability of a bulb lasting for at most 540 hours is 0.7521, rounded to four decimal places.

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Answer:

yes

Step-by-step explanation:

The test has demonstrated a good level of test-retest reliability.

If a student took an assessment on their math ability at one time point and then the same assessment a month later, with no substantial changes such as getting a tutor, and their math ability was the same between time 1 and time 2, then the assessment has achieved Test-Retest Reliability.Test-Retest Reliability: Test-Retest reliability is the measure of consistency of a test over time. A test has test-retest reliability if a person performs similarly on the same test taken at two different times.A reliable test must always provide consistent results. Therefore, if the math ability was the same between time 1 and time 2, and no substantial changes occurred during that time, then the test has demonstrated a good level of test-retest reliability.

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The point that partitions segment AB in a 1:4 ratio is (-1/2, -1).

What is Segment?

In geometry, a segment is a part of a line that has two endpoints. It can be thought of as a portion of a straight line that is bounded by two distinct points, called endpoints. A segment has a length, which is the distance between its endpoints. It is usually denoted by a line segment between its two endpoints, such as AB, where A and B are the endpoints. A segment is different from a line, which extends infinitely in both directions, while a segment has a finite length between its two endpoints.

To find the point that partitions segment AB in a 1:4 ratio, we need to use the midpoint formula to find the coordinates of the point that is one-fourth of the distance from point A to point B. The midpoint formula is:

((x1 + x2)/2, (y1 + y2)/2)

where (x1, y1) and (x2, y2) are the coordinates of the two endpoints of the segment.

So, let's first find the coordinates of the midpoint of segment AB:

Midpoint = ((-3 + 7)/2, (2 - 10)/2)

= (2, -4)

Now, to find the point that partitions segment AB in a 1:4 ratio, we need to find the coordinates of a point that is one-fourth of the distance from point A to the midpoint. We can use the midpoint formula again, this time using point A and the midpoint:

((x1 + x2)/2, (y1 + y2)/2) = ((-3 + 2)/2, (2 - 4)/2)

= (-1/2, -1)

So, the point that partitions segment AB in a 1:4 ratio is (-1/2, -1).

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the length of chord in the circle is 13.5 units.

According to Pythagoras' Theorem, the square of the hypotenuse side of a right-angled triangle equals the sum of the squares of the other two sides.The Perpendicular, Base, and Hypotenuse are the three angles that make up this triangle.

The Pythagoras Theorem formula is as follows from the definition:

Hypotenuse² = Perpendicular² + Base²

c² = a² + b²

From the figure, the hypotenuse, x of both triangle are same as both of them are radius of circle.

According to Pythagoras theorem,

x²=6.3²+11.9²

x²=181.3

x=√181.3

x=13.5

Hence, the length of chord in the circle is 13.5 units.

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When a data line on a graph slopes down as it goes to the right, it is depicting that the relationship between the variables on the graph is inverse.

An inverse relationship is a kind of correlation between two variables, in which one variable decreases while the other increases, or vice versa. An inverse relationship happens when one variable increases while the other decreases, or when one variable decreases while the other increases.

On a graph, when a data line slopes down as it goes to the right, this is an indication that the relationship between the variables on the graph is inverse. As the values of x increase, the values of y decrease. Therefore, we can conclude that there is an inverse relationship between x and y.

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Answer:

Clockwise it would be (3,-5)

Step-by-step explanation:

Counterclockwise it would be (-3,-5)

hope this helps!

Answer:

20%

Step-by-step explanation:0% of 4445=

Answer: x = 6

Step-by-step explanation:

(7x+3)+85+50 = 180

(7x+3)+135 = 180

7x+3 = 180 - 135 = 45

7x = 45-3 = 42

x = 42 / 7 = 6

x = 6

Answer:

if it is perpendicular to eacha other I e 0

The probability that x is less than 2 is approximately 0.4866. The probability that x is greater than 3 is approximately 0.3528. The probability that x is less than 5 is approximately 0.6321. The probability that x is between 2 and 5 is approximately 0.1455.

The given probability density function is an exponential distribution with a rate parameter of λ = 1/3. The formula for P(x < x_0) is the cumulative distribution function (CDF) of the exponential distribution, which is given by:

F(x_0) = ∫[0,x_0] f(x) dx = ∫[0,x_0] 1/3 * 4 * e^(-x/3) dx

a. Write the formula for P(x < x_0):

Using integration, we can solve this formula as follows:

F(x_0) = [-4e^(-x/3)] / 3 |[0,x_0]

= [-4e^(-x_0/3) + 4]/3

b. Find P(x < 2):

To find P(x < 2), we simply substitute x_0 = 2 in the above formula:

F(2) = [-4e^(-2/3) + 4]/3

≈ 0.4866

Therefore, the probability that x is less than 2 is approximately 0.4866.

c. Find P(x > 3):

To find P(x > 3), we can use the complement rule and subtract P(x < 3) from 1:

P(x > 3) = 1 - P(x < 3) = 1 - F(3)

= 1 - [-4e^(-1) + 4]/3

≈ 0.3528

Therefore, the probability that x is greater than 3 is approximately 0.3528.

d. Find P(x < 5):

To find P(x < 5), we simply substitute x_0 = 5 in the above formula:

F(5) = [-4e^(-5/3) + 4]/3

≈ 0.6321

Therefore, the probability that x is less than 5 is approximately 0.6321.

e. Find P(2 < x < 5):

To find P(2 < x < 5), we can use the CDF formula to find P(x < 5) and P(x < 2), and then subtract the latter from the former:

P(2 < x < 5) = P(x < 5) - P(x < 2)

= F(5) - F(2)

= [-4e^(-5/3) + 4]/3 - [-4e^(-2/3) + 4]/3

≈ 0.1455

Therefore, the probability that x is between 2 and 5 is approximately 0.1455.

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The mean (also called the arithmetic mean or average) is a measure of central tendency that represents the typical or average value of a set of data. The mean is calculated by summing up all the values in the data set and dividing by the number of values.

The mean of x is calculated by the following formula:

mean of x = ∑(x * P(x))

Where, ∑ = Summation operator

            x = Value of random variable  

            P(x) = Probability of the corresponding value of x.

Let's calculate the mean of x using the formula provided above.

mean of x = (-1 × 0.3) + (0 × 0.4) + (1 × 0.3)

                = -0.3 + 0 + 0.3  

                = 0

Therefore, the mean of x is 0.

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The installer will make a profit of $868.75 on the job. This amount is calculated by multiplying the price of each box of tile ($72) by the number of boxes needed (15 boxes) to cover the 295 square feet.

Cost is the total amount of money that is expended or invested in order to produce and/or acquire a good or service. It is usually measured in terms of the amount of money spent to produce a unit of a good or service, and is usually expressed in terms of units of currency, such as dollars, euros, or pounds. Cost is an important factor in determining the price of a good or service and can be used to evaluate the effectiveness of a company's operations. Additionally, cost can be used to determine the profitability of a company by measuring the amount of money it spends in relation to the amount of money it earns.

That results in a total cost of $1,080. From that, the installer then subtracts the cost of materials ($840). The remaining amount of $240 is the installer's profit. With a markup of 84.25%, this leaves the installer with a total profit of $868.75.

This profit is possible by factoring in the markup of materials, labor, and overhead costs. The installer is able to cover these costs and make a profit by charging a slightly higher price per square foot. This allows them to cover the cost of materials and labor, as well as make a profit. Additionally, they can also cover overhead costs such as insurance, taxes, and other miscellaneous costs that are associated with running their business. By charging a slightly higher price per square foot, the installer is able to make a profit on the job and remain competitive in the market.

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The number of 50 cents in the container is 380 fifty cents

Since Thabang save money by putting coins in a money box. The money box has 600 coins that consist of 20 cents and 50 cents

To calculate how many 50 cents pieces are in the container if there are 220 pieces of 20 cents, we proceed as follows.

Let

Since the total number of cents in the container is 600, we have that

x + y = 600

So, making y subject of the formula, we have that

y = 600 - x

Since x = 220

y = 600 - 220

= 380

So, there are 380 fifty cents

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The expected count for women for the presence of aortic stenosis is 57.7. The correct option is D.

Aortic stenosis is a cardiovascular ailment that causes the aortic valve in the heart to narrow, reducing blood flow from the heart to the rest of the body. Aortic stenosis usually progresses gradually and, in the beginning, may not produce any symptoms.

The severity of aortic stenosis is divided into four categories, ranging from mild to severe. People who are asymptomatic may require monitoring, whereas those who are symptomatic may need to undergo surgery or other procedures.

The expected count for women for the presence of aortic stenosis in this question refers to the number of women who have this condition according to a particular study or statistic.

Therefore, the correct option is D.

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