27 is 76% of what number?

: The problem requires formulating two given problems as linear programming problems in standard form. In problem (a), we need to minimize a linear objective function subject to linear inequality

(a) To formulate problem (a) as a linear programming problem in standard form, we define the decision variables x₁, x₂, and x₃. The objective function becomes: min 5x₁ - x₂.

The constraints are as follows:

- x₁ + 3x₂ + 2x₃ ≥ 7 (linear inequality constraint)

- x₁ + 2x₂ + |x₂| ≤ 4 (linear inequality constraint with absolute value)

- x₁ ≤ 0 (linear inequality constraint)

The problem can be expressed in standard form by introducing slack variables and converting the absolute value constraint into two separate constraints. The objective function, inequality constraints, and non-negativity constraints for the slack variables will form the linear programming problem in standard form.

(b) Problem (b) is already in the form of a linear programming problem with a linear objective function 2x + 3y. Since there are no constraints mentioned, we can assume that the decision variables x and y can take any real values. Thus, the problem is already in standard form.

In summary, to formulate problem (a) as a linear programming problem in standard form, we need to introduce slack variables and convert the absolute value constraint into separate constraints. Problem (b) is already in standard form as it contains a linear objective function without any constraints.

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Answer:

see explanation

Step-by-step explanation:

using the identity

tan²x = sec²x - 1

consider the left side

(tanx + secx)² ← expand using FOIL

= tan²x + 2tanxsecx + sec²x

= sec²x - 1 + 2tanxsecx + sec²x ← collect like terms

= 2sec²x + 2tanxsecx - 1

= right side , thus proven

Answer:

A)0.004

If you do the math you should get this answer

After six​ months, the​ subjects' symptoms are studied and compared. Answer parts​ are given below.

An assumption or concept is given as a hypothesis for the purpose of debating it and testing if it might be true.

Given:

A pharmaceutical company wants to test the effectiveness of a new allergy drug.

The company identifies 250 females​ 30–35 years old who suffer from severe allergies.

The subjects are randomly assigned into two groups.

One group is given the new allergy drug and the other is given a placebo that looks exactly like the new allergy drug.

After six​ months, the​ subjects' symptoms are studied and compared.

Here, 30-35 year-old girls are used to test the new allergy medication's effects.

(a)

Females between the ages of 30 and 35 who are the test subjects are the experimental units.

The new allergy medication, whose results are being studied, is the remedy.

It's best to choose C.

(b)

A bias may develop if a researcher or patient knows whether subjects received a medication or a placebo.

In this case, choice B is preferable.

(c)

If neither the researcher nor the subject knew whether they were receiving a medicine or a placebo, the study would be considered double-blind.

In this case, choice A is preferable.

Therefore, all the correct choices are given above.

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The complete question is given in the image.

To find the weights wo and wi and the node x1 that make the quadrature formula L se f(x) dx = wof(-1) + wif(x1) exact for polynomials of degree 2 or less, a system of equations needs to be set up and solved using the values of the monomials at the nodes (-1 and x1).

In Gaussian quadrature, the weights and nodes are chosen in such a way that the quadrature formula is exact for polynomials up to a certain degree. In this case, we want the formula to be exact for polynomials of degree 2 or less.

For a quadrature formula with two weights and two nodes, we can represent it as follows:

L se f(x) dx = wof(-1) + wif(x1)

To make this formula exact for polynomials of degree 2 or less, we need it to integrate exactly the monomials 1, x, and x².

By setting up a system of equations using the values of the monomials at the nodes (-1 and x1) and solving for the weights and node, we can find the specific values that make the formula exact.

The explanation would require further mathematical calculations and solving the system of equations to find the values of wo, wi, and x1 that satisfy the condition. However, without specific numerical values or additional constraints, it is not possible to provide the exact solution.

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Step-by-step explanation:

yeap I also think so that the answer is 0

Option (b) is true because the probability of drawing a black marble is closer to 0 than it is to 1.

It is a branch of mathematics that deals with the occurrence of a random event.

The total number of marbles in the bag is:

Total marbles = 5 + 8 + 1 = 14

The probability of drawing a black marble can be found by dividing the number of black marbles in the bag by the total number of marbles:

Probability of drawing a black marble = Number of black marbles / Total marbles

Probability of drawing a black marble = 8 / 14

This can be simplified by dividing both the numerator and denominator by 2:

Probability of drawing a black marble = 4 / 7

Hence, Option (b) is true because the probability of drawing a black marble is closer to 0 than it is to 1.

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In a bag, there are 5 gray marbles, 8 black marbles, and 1 white marble. If Carrie draws a marble from the bag without looking, which statement is true about the probability of drawing a black marble?

(a) The probability of drawing a black marble is closer to 1 than it is to 0

(b) The probability of drawing a black marble is closer to 0 than it is to 1

(c) The probability of drawing a black marble is 6/14

(d) The probability of drawing a black marble is 8/6

Answer:

I think the answer is 11.7 units rounded to nearest tenth

Step-by-step explanation:

d=(2−(−4))2+(−7−3)2−−−−−−−−−−−−−−−−−−−√

d=(6)2+(−10)2−−−−−−−−−−−√

d=36+100−−−−−−−√

d=1–√36

d=11.661904

Answer:

Step-by-step explanation:

Given:

Room dimensions: 18 meters by 22 meters

Carpet cost: $28.50 per square meter

Carpet roll width: 12 meters

Since the carpet roll is 12 meters wide and the room's width is 18 meters, it is more efficient to lay the carpet along the width of the room.  It will look better with one large, continuous piece that is 12 x 22, seamed to one narrow piece of 6 x 22.

Number of rolls needed = Width of room / Width of carpet roll

= 18 meters / 12 meters

= 1.5 rolls

But you can't buy 1/2 roll so, round up to 2 rolls.

Length of carpet needed = Length of room

Length of carpet = 22 meters

Total area of carpet needed = Length of carpet x Width of carpet roll x Number of rolls

= 22 meters x 12 meters x 2 rolls

= 528 m²

Cost of carpet = Total area x Cost per square meter

= 528 m² x $28.50/m²

Cost of carpet = $15,048

Therefore, the most efficient way to lay the carpet is to use 2 rolls of carpet, with one roll covering 12 m of width and the other roll covering the remaining width (6 m). This arrangement requires just 1 seam. The total cost of the carpet will be $15,048.

a) the most efficient way to lay the carpet is to have one seam along the longer side, dividing it into two 12-meter sections, and a single piece along the shorter side.

b) The carpet will cost $13,680.

a) To find the most efficient way to lay the carpet, we need to minimize the number of seams required. In this case, since the carpet comes in rolls that are 12 meters wide, we should aim to minimize the number of cuts made along the width of the room.

Since the room measures 18 meters by 22 meters, we can use the 12-meter width of the carpet to cover the shorter side (18 meters) with a single piece. This leaves us with a longer side of 22 meters.

To cover the longer side, we can use two pieces of carpet, each measuring 12 meters in width. This way, we minimize the number of seams required.

So, the most efficient way to lay the carpet is to have one seam along the longer side, dividing it into two 12-meter sections, and a single piece along the shorter side.

b) Now let's calculate the cost of the carpet for the selected configuration.

The cost of the carpet is given as $28.50 per square meter. To calculate the total cost, we need to find the total area of the carpet required.

For the shorter side (18 meters), we need a single piece of carpet with a width of 12 meters, resulting in an area of 18 meters * 12 meters = 216 square meters.

For the longer side (22 meters), we need two pieces of carpet, each with a width of 12 meters. The total width covered will be 12 meters + 12 meters = 24 meters. However, since the room is only 22 meters long, we will trim off the excess, resulting in an area of 22 meters * 12 meters = 264 square meters.

The total area of the carpet required is 216 square meters + 264 square meters = 480 square meters.

Now, we can calculate the total cost by multiplying the total area by the cost per square meter:

Total cost = 480 square meters * $28.50/square meter

Calculating the value, we find that the carpet will cost $13,680.

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Answer:

yah yeet yeet yah

Step-by-step explanation:

Therefοre, Deb will have tο spend apprοximately $327 tο paint the wall οf area 186.98 ft²

Area is defined as the tοtal space taken up by a flat (2-D) surface οr shape οf an οbject.

Tο calculate the area οf the wall, we need tο find the area οf the rectangle and subtract the area οf the twο hexagοnal windοws.

The area οf the rectangle is:

25 feet × 9 feet = 225 ft²

The area οf each hexagοnal windοw can be fοund by dividing it intο 6 equilateral triangles and using the fοrmula fοr the area οf an equilateral triangle:

Area οf each hexagοnal windοw = 6 × (1/2) × (2 ft) × (2 ft) × √(3) = 12 √(3) ft²

Sο the tοtal area οf bοth hexagοnal windοws is:

2 × 12 √(3)  = 24√(3) ft²

Therefοre, the area οf the wall that needs tο be painted is:

225 ft² - 24 √(3) ft² ≈ 186.98 ft²

Tο find the cοst οf painting the wall, we can multiply the area by the cοst per square fοοt:

186.98 ft² × $1.75/ft² ≈ $327.71

Therefοre, Deb will have tο spend apprοximately $327 tο paint the wall (rοunded tο the nearest dοllar).

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Answer:

B. -4

Step-by-step explanation:

To find the slope you can count the difference between the 2 points. Slope is rise over run. This means that slope is equal to change in y/ change in x. In this case, the 2 y-values are 8 and -4. This is a decrease of 12, aka -12. Then, the 2 x-values are -1 and 2. This is an increase of 3. Therefore the slope is -12/3. When simplified this equals -4.

Additionally, there is a slope formula, \(\frac{y_{2} -y_{1} }{x_{2} -x_{1} }\). If you plug in the values, you will get the same answer as the technique above.

Answer:

80 miles

Step-by-step explanation:

80 miles

Step-by-step explanation:

Using the relationship

distance = rate × time, hence

rate = distance/time = 24/3  = 8 mph

distance travelled in 10 hours at this rate

distance = 8 × 10 = 80 miles

Answer:

W = 81

Step-by-step explanation:

We'll be using the Exterior Angles Theorem for this question

The theorem states that the sum of any two angles of a triangle is equal to the exterior angle of the other angle.

Therefore

(3x-24) + (2x) = 4x + 11

It's just simple algerbra from there

(3x-24) + (2x) = 4x + 11/

5x - 24 = 4x + 11

x-24 = 11

x = 35

BUT WAIT! The question asks for the angle W, not x.

So just plug in x

3(35) - 24

105 - 24

81

Answer:

Step-by-step explanation:

area =(4+4+4)/2×2+1/2×(4+4)×5.75

=12+23.00

=35 sq.cms.

Step-by-step explanation:

Area of triangle = \(\frac{1}{2}\)(b*h)

Area of rectangle = b*h

\(A(big-triangle) = \frac{1}{2} (5.75*4)\)

\(A(big-triangle) = \frac{1}{2}(23)\)

\(A(big-triangle) = 11.5\)

Since there are two big triangles, then we can multiply 11.5 by 2.

11.5 * 2 = 23

\(A(small-triangle) = \frac{1}{2}(2*2)\)

\(A(small-triangle) = \frac{1}{2} (4)\)

\(A(small-triangle) = 2\)

Since there are two small triangles, then we can multiply 2 by 2.

2 * 2 = 4

\(A(rectangle)= 4 * 2\)

\(A(rectangle) = 8\)

Now, we can add up all of the areas so we can find the total area of the entire shape.

23 + 4 + 8 = 35

So, the area of the entire shape is 35 square cm.

If the standard error of the sample mean equals 2.5, then the samples size is: 16

The sample size refers to the least number of persons that can be chosen from the population to arrive at a result that is statistically significant. The formula for the sample size for an infinite population

Standard error of mean = S/√N

Where n = number of samples

2.5 = 10/√N

√N * 2.5 = 10

Divide both sides by 2.5

√n = 4

Square both sides

(√n)² = 4²

n = 16

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Using inverse function concepts, it is found that:

The function given is:

\(f(x) = (x + 1)^2 - 3\)

To find the inverse, we exchange x and y, and isolate y, then:

\(y = (x + 1)^2 - 3\)

\(x = (y + 1)^2 - 3\)

\((y + 1)^2 = x + 3\)

\(\sqrt{(y + 1)^2} = \sqrt{x + 3}\)

\(y + 1 = \sqrt{x + 3}\)

\(y = \sqrt{x + 3} - 1\)

The inverse of the function is \(y = \sqrt{x + 3} - 1\), and the domain of the inverse function is \([-3, \infty]\).

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Answer:

Step-by-step explanation:

a) the dimension of its column space is also 2. b) the rank of A is 2. c) the nullity of matrix A is 1. d) the dimension of the solution space of the homogeneous system \(A_x = 0\) is also 1.

(a) The dimension of the row space of a matrix is equal to the dimension of its column space. So, if the dimension of the row space of matrix A is 2, then the dimension of its column space is also 2.

(b) The rank of a matrix is defined as the maximum number of linearly independent rows or columns in the matrix. Since the dimension of the row space of matrix A is 2, the rank of A is also 2.

(c) The nullity of a matrix is defined as the dimension of the null space, which is the set of all solutions to the homogeneous equation Ax = 0. In this case, the matrix A is a 3 x 3 matrix, so the nullity can be calculated using the formula:

nullity = number of columns - rank

nullity = 3 - 2 = 1

Therefore, the nullity of matrix A is 1.

(d) The dimension of the solution space of the homogeneous system Ax = 0 is equal to the nullity of the matrix A. In this case, we have already determined that the nullity of matrix A is 1. Therefore, the dimension of the solution space of the homogeneous system \(A_x = 0\) is also 1.

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Answer:

x = 32

Step-by-step explanation:

(whole secant) x (external part) = (tangent)^2

(x+18) * 18 = 30^2

(x+18) * 18 = 900

Divide each side by 18

(x+18) * 18/18 = 900/18

(x+18)  = 50

Subtract 18 from each side

x+18-18 = 50-18

x=32

Answer:

50

Step-by-step explanation:

tangent-secant theorem

a) If $9,000 is invested at 8% interest compounded annually, after 1 year, the future value will be $9,720.

b) If $9,000 is invested at 8% interest compounded annually, after 2 years, the future value will be $10,497.60.

We can use an online finance calculator to determine the future value.

The future value represents the present investment compounded at an interest rate into the future.

N (# of periods) = 1 year

I/Y (Interest per year) = 8%

PV (Present Value) = $9,000

PMT (Periodic Payment) = $0

Results:

Future Value (FV) = 9,720.00

Total Interest = $720.00

N (# of periods) = 2 years

I/Y (Interest per year) = 8%

PV (Present Value) = $9,000

PMT (Periodic Payment) = $0

Results:

Future Value (FV) = $10,497.60

Total Interest = $1,497.60

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Answer: -25

Step-by-step explanation:

I used point-slope form [y-3=2(x-14)] and the Y intercept is -25

It would take 5 hours for no drug to remain in the bloodstream

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

Function, D(x) = -x⁴ + 5x³ - 10x² + 50x

So, we have

D(x) = -x⁴ + 5x³ - 10x² + 50x

Factor the expression

This gives

D(x) = -x³(x - 5) - 10x(x - 5)

Factor out x - 5

D(x) = (-x³ - 10)(x - 5)

Set to 0

So, we have

(-x³ - 10)(x - 5) = 0

Ignoring imaginary or complex values for x, we have

x -5 = 0

Solve for x

x = 5

Hence, the number of hours is 5

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Answer:

3x+6=8

Step-by-step explanation:

It says 3 times a number you know that it will be 3 times the variable. Next, it says the "sum of" so you know you will be adding 6 to the multiplication of 3 and the variable to equal 8.

The function y = 60 • 3^x models the population growth, where x is the number of 14-year periods.

To find the number of foxes after 42 years, we need to convert 42 years to the number of 14-year periods.

42 years / 14 years/period = 3 periods

So, the number of foxes after 42 years is:

y = 60 • 3^3

y = 60 • 27

y = 1620

Therefore, there will be 1620 foxes after 42 years.

Answer: x1= -3, x2=3

Step-by-step explanation:

3xlxl=8+1

3xlxl=9

lxl=3

x=3

=-3

solution

x1= -3, x2=3

The ratios that could be the lengths of the two legs in a 30-60-90 triangle are √3:3 (option E) and 12√3 (option D).

In a 30-60-90 triangle, the angles are in the ratio of 1:2:3. The sides of this triangle are in a specific ratio that is consistent for all triangles with these angles. Let's analyze the given options to determine which ones could be the ratio between the lengths of the two legs.

A. √2:√2

The ratio √2:√2 simplifies to 1:1, which is not the correct ratio for a 30-60-90 triangle. Therefore, option A is not applicable.

B. 15

This is a specific value and not a ratio. Therefore, option B is not applicable.

C. √√√√5

The expression √√√√5 is not a well-defined mathematical operation. Therefore, option C is not applicable.

D. 12√3

This is the correct ratio for a 30-60-90 triangle. The ratio of the longer leg to the shorter leg is √3:1, which simplifies to √3:3. Therefore, option D is applicable.

E. √3:3

This is the correct ratio for a 30-60-90 triangle. The ratio of the longer leg to the shorter leg is √3:1, which is equivalent to √3:3. Therefore, option E is applicable.

F. √2:√5

This ratio does not match the ratio of the sides in a 30-60-90 triangle. Therefore, option F is not applicable. So, the correct option is D. 1 √2.

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The lowest and greatest values in the dataset, divided by two, make up the Mid-range. Thus, this provides us with the midrange value.

The mid-range or mid-extreme is the arithmetic mean of the highest and minimum values of the data set and is used in statistics as a measure of a sample's central tendency.

The difference between the greatest and minimum values, which is a measure of statistical dispersion, is strongly related to the mid-range.

The two measurements are complementary in that one can determine the sample's maximum and minimum values by knowing the range and the midpoint.

Therefore, the lowest and greatest values in the dataset, divided by two, make up the Mid-range. Thus, this provides us with the midrange value.

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Answer:

The median is also the number that is halfway into the set. To find the median, the data should be arranged in order from least to greatest. If there is an even number of items in the data set, then the median is found by taking the mean (average) of the two middlemost numbers.

Step-by-step explanation:

have a great day

There are two ways to find the median, depending on what situation it is.

The first, is to simply arrange the number set into proper numerical format (least to greatest), then count from both sides towards the middle to find the median or middle number.

The latter, is when we have a number set that has an equal amount of numbers. For this, we would again, arrange it into proper numerical format, and the count from both sides up. However, there will be two numbers at the middle. So, what we do, is that we have to add them up and then divide by 2 since there are only those two numbers at the middle. Once, the numbers are added up and divided by 2, you will get the resulting median.

Example: Find the median of the data set below.

1,2,3,4,5,6,7,8,9,9

There are 10 numbers in this data set.

It's already been arranged into proper numerical format.

So, all we have to do is, find the two middle numbers and then add them up and divide.

The two numbers at the middle are: 5 and 6.

Add them up.

5 + 6 = 11

Divide by 2.

11/2 = 5.5

Thus, the median of the data set is 5.5