gulf coast electronics is ready to award contracts to suppliers for providing reservoir capacitors for use in its electronic devices. for the past several years, gulf coast electronics has relied on two suppliers for its reservoir capacitors: able controls and lyshenko industries. a new firm, boston components, has inquired into the possibility of providing a portion of the reservoir capacitors needed by gulf coast. the quality of products provided by lyshenko industries has been extremely high; in fact, only 0.5% of the capacitors provided by lyshenko had to be discarded because of quality problems. able controls has also had a high quality level historically, producing an average of only 1% unacceptable capacitors. because gulf coast electronics has had no experience with boston components, it estimated boston components' defective rate to be 10%. gulf coast would like to determine how many reservoir capacitors should be ordered from each firm to obtain 75,000 acceptable-quality capacitors to use in its electronic devices. to ensure that boston components will receive some of the contract, management specified that the volume of reservoir capacitors awarded to boston components must be at least 10% of the volume given to able controls. in addition, the total volume assigned to boston components, able controls, and lyshenko industries should not exceed 30,000, 50,000, and 50,000 capacitors, respectively. because of gulf coast's long-term relationship with lyshenko industries, management also specified that at least 30,000 capacitors should be ordered from lyshenko. the cost per capacitor is $2.45 for boston components, $2.50 for able controls, and $2.75 for lyshenko industries. (a) formulate a linear program for determining how many reservoir capacitors should be ordered from each supplier to minimize the total cost of obtaining 75,000 acceptable-quality reservoir capacitors. (let b

Mathematical relationships could be found in a linear programming model are (b) 2A - 2B = 30 (e) 1A + 1B = 9 (f) 2A + 6B + 1AB ≤ 36

Linear programming, mathematical modeling technique in which a linear function is maximized or minimized when subjected to various constraints.

(a) -1A + 2B ≤ 20 : Cannot be found in linear programming model as linear programming model can only consists of positive linear numbers and this equation contain negative number.

(b) 2A - 2B = 30 : Can be found in linear programming model

(c) 1A - 6B2 ≤ 10 : Cannot be found in linear programming model as equation includes square variable.

(d) 3√A + 2B ≥15 : Cannot be found in linear programming model as equation includes square root variable.

(e) 1A + 1B = 9 : Can be found in linear programming model

(f) 2A + 6B + 1AB ≤ 36 : Can be found in linear programming model

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A graphing utility such as Desmos or Wolfram Alpha can be used to graph the function. The graph shows that the maximum value occurs at t = 13 and the minimum value occurs at t = 7, which confirms our calculations.

To find the absolute extrema of the function h(t) = t^2 - 6 on the closed interval [7, 13], we can start by taking the derivative of the function and setting it equal to zero to find any critical points:

h'(t) = 2t = 0

t = 0

However, t = 0 is not in the interval [7, 13], so we only need to check the endpoints of the interval and any other critical points that may lie within the interval.

Since there are no critical points in the interval, we only need to evaluate the function at the endpoints:

h(7) = 7^2 - 6 = 43

h(13) = 13^2 - 6 = 163

Thus, the absolute maximum of h(t) on the interval [7, 13] is 163, which occurs at t = 13, and the absolute minimum is 43, which occurs at t = 7.

To verify our results using a graphing utility, we can graph the function h(t) = t^2 - 6 on the interval [7, 13] and visually observe the maximum and minimum values.

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The lengths of the missing sides associated with geometric systems formed by similar triangles are listed below:

Case 10: 49

Case 12: 36

In this problem we have the case of two geometric systems formed by two similar right triangles. These figures are similar if they have congruent internal angles but their sides are not congruent though proportional. Hence, missing sides can be found by proportion formulas. Now we proceed to determine the missing side for each case:

Case 10

x / 7√33 = 7√33 / 33

x = 7²

x = 49

Case 12

x / 6√13 = 6√13 / 13

x = 6²

x = 36

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The data is analyzed and frequency table is created. The correct option for the histogram is the second option.

Here 30 individual samples are given. We are first categorizing the values in a frequency distribution table. It is shown as an image below.

Temperature          frequency            Relative frequency

    70-74                          5                        5/30 = .166 = 16.6%

    75-79                          4                        4/30 = .133 = 13.3%

   80-84                           7                        7/30 = 0.233 =23.3%

   85-89                          6                        6/30 = 0.2 = 20%

   90-94                         8                        8/30 = 0.266 = 2.66%

From the given histogram the second one represents the data given in the frequency table. It is marked in the image.

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The complete question is included as image

Answer:

x = 30, -40

Step-by-step explanation:

This a right triangle, so you can use the Pythagorean Theorem.

[tex]a^{2}+ b^{2}=c^{2}[/tex], now in place of the a, b and c use x, x +10 and 50.

so a = x, b =x+10 and c = 50

[tex]x^{2} + (x+10)^{2} =50^{2}[/tex]

[tex]x^{2} +x^{2} +20x +100 = 2500[/tex]

Answer: $81,686

Step-by-step explanation:

$148,520 - 45% = $81,686

Alternative

$148,520 x 0.55 = $81,686

Answer:

Step-by-step explanation:

1.

The percentage scored by Curry is 39.3% oby halftime.

To find the percentage of his team's points that Curry scored, we can use the following formula:

percentage = (part / whole) x 100

Where

Part = 22 points

Whole = 56 points

Substitute the known values in the above equation, so, we have the following representation

Percentage = (22 / 56) x 100%

Evaluate

Percentage = 39.3%

Hence, Curry scored 39.3% of his team's points by halftime.

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(a) The probability that the system functions on a rainy day is the probability that at least 4 out of the 6 components function, with each component having a probability of 0.7 of functioning.

We can calculate this probability using the binomial distribution:

P(system functions on a rainy day) = P(X ≥ 4), where X ~ Binomial(n=6, p=0.7)

Using a calculator or statistical software, we find:

P(system functions on a rainy day) = 0.8482

(b) The probability that the system functions on a non-rainy day is the probability that at least 4 out of the 6 components function, with each component having a probability of 0.9 of functioning. Again, we can use the binomial distribution:

P(system functions on a non-rainy day) = P(X ≥ 4), where X ~ Binomial(n=6, p=0.9)

Using a calculator or statistical software, we find:

P(system functions on a non-rainy day) = 0.9970

(c) To find the probability that the system will function tomorrow, we need to use the law of total probability. Let R be the event that it rains tomorrow and NR be the event that it doesn't rain tomorrow. Then:

P(system functions tomorrow) = P(system functions on a rainy day)P(R) + P(system functions on a non-rainy day)P(NR)

Using the probabilities from parts (a) and (b), and the fact that P(R) = 0.2 and P(NR) = 0.8, we can calculate:

P(system functions tomorrow) = (0.8482)(0.2) + (0.9970)(0.8) = 0.9746

Therefore, the probability that the 4 out of 6 systems will function tomorrow is 0.9746, assuming a 0.2 probability of rain.

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Answer:

Step-by-step explanation:

10000

Answer:10000

Step-by-step explanation:

dimosure

The missing angles in triangle RST and LMN are 121° and 15° respectively.

When two straight lines or rays intersect at a single endpoint, an angle is created.

The vertex of an angle is the location where two points come together.

The Latin word "angulus," which means "corner," is where the term "angle" originates.

Angle position describes how a line interacts with another line or plane. The amount of rotation of the body relative to the reference position is used to calculate the angle of position.

Theta (), the sign used to represent the angular position, can represent the angle in degrees (°), radians (rads), or revolutions.

So, in the triangle RST:

Missing angle:

44 + 15 + x = 180

x = 180 - 59

x = 121°

In triangle LMN:

121 + 44 + x = 180

x = 180 - 165

x = 15°

Therefore, the missing angles in triangle RST and LMN are 121° and 15° respectively.

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We clearly seen that a little sign mistake here in 'j'.

In the given question  you have computed the cross product of v=i+2j−3k and w=2i−j+2k. You got v×w=i+8j−5k Without actually redoing v×w and we have to tell how can we spot a mistake in my work.

cross product of v and w i.e v×w is orthogonal to v and w

i.e (v×w)×v = 0 = (v×w)×w

Now v×w = i+8j₋5k

v = i+2j−3k

w = 2i−j+2k

then,

(v×w)×v = ( i+8j₋5k)×(i+2j−3k)

(v×w)×v = 1+16+15

(v×w)×v = 32≠0

and

(v×w)×w = ( i+8j₋5k)×(2i−j+2k)

(v×w)×w = 2₋8₋10

(v×w)×w = ₋16≠0

hence given cross product is wrong

Also we clearly seen that a little sign mistake here in 'j'

i.e if (v×w) = ( i₋8j₋5k)

(v×w)×v = ( i₋8j₋5k)×(i+2j−3k)

(v×w)×v = 1₋16+15

(v×w)×v = 0

and

(v×w)×w = ( i₋8j₋5k)×(2i−j+2k)

(v×w)×w = 2+8₋10

Hence, (v×w) = ( i₋8j₋5k)

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Answer:

Step-by-step explanation:

Right Answer: Add to eliminate X

[tex]4x+ (-4x)+5y+9y=-6+(-22)\\14y=-28\\y=\frac{-28}{14} \\y=2[/tex]

Answer:

Step-by-step explanation:10299

The values of all 9 angles shown were found using the property of a kite they are:

m∠1=55°

m∠2=35°

m∠3=35°

m∠4=90°

m∠5=55°

m∠6=67°

m∠7=67°

m∠8=23°

m∠9=23°

What is an angle ?

In Kite figure, it is given that:

∠2+∠3 = 70°

Since they are equal so ∠2=∠3=35

∠8+∠9 = 46°

Since they are equal so ∠8=∠9=23°

∠5 = 180-∠3-∠4 = 180-35-90=55°

Similarly, ∠1 = 55°

∠6+∠7 = 180-∠8-∠9 = 180-46 = 134°

Since they are equal

∠6=∠7 = 67°

Therefore, all 9 angles were calculated using property of a kite.

m∠1=55°

m∠2=35°

m∠3=35°

m∠4=90°

m∠5=55°

m∠6=67°

m∠7=67°

m∠8=23°

m∠9=23°

In mathematics, an angle is a geometric figure formed by two rays or line segments that share a common endpoint, called the vertex. The rays or line segments are called the sides or legs of the angle, and the distance between the sides at the vertex is called the angle's measure.

Angles are typically measured in degrees or radians, and they can be classified by their measures as acute (less than 90 degrees), right (exactly 90 degrees), obtuse (greater than 90 degrees and less than 180 degrees), straight (exactly 180 degrees), reflex (greater than 180 degrees and less than 360 degrees), or full (exactly 360 degrees).

Kites have several properties related to their angles, including:

Two pairs of opposite angles in a kite are congruent. That is, the angles formed between the pairs of congruent sides are equal.

One diagonal of a kite bisects the other diagonal. This means that the diagonal that connects the non-congruent vertices of the kite divides the other diagonal into two equal segments.

The sum of the measures of the two non-congruent angles in a kite is 180 degrees. This is because the kite can be divided into two congruent triangles by drawing the diagonal that bisects the other diagonal, and the sum of the angles in a triangle is always 180 degrees.

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Answer:c

Step-by-step explanation:

because

The school newspaper reporter wants to find out how many students will attend Tet festivities. She randomly surveys 13 students and knows that 24% of students typically attend the festivities. We are interested in the probability of the number of students who will attend.

The probability that at most 4 students will attend is 0.4936 and the probability that more than 3 students will attend is 0.5064. Calculating these probabilities can be done using the binomial probability formula. First, calculate the probability of exactly 4 students attending. This probability is [tex]0.24^4 * 0.76^9 = 0.0038[/tex]. Then, calculate the probability of 3 students or fewer attending by adding the probabilities of 0, 1, 2, and 3 students attending, which is 0.0013 + 0.0358 + 0.1045 + 0.2696 = 0.4113. Finally, subtract 0.4113 from 1 to get 0.4936. We are interested in the probability of the number of students who will attend. To calculate the probability of more than 3 students attending, subtract 0.4113 from 1 to get 0.5064.

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Answer:

Step-by-step explanation:

one possible explanation for why there are two different ways of adding up the symbols on the tablet is given below.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

The ancient Egyptian number system was based on hieroglyphs, and it used a decimal system with hieroglyphs representing the powers of 10. However, without seeing the specific symbols on the tablet, it is difficult to provide an accurate answer.

Assuming that the tablet is using a basic arithmetic operation such as addition, and each symbol represents a different number,

it is possible that there are two different ways to add up the numbers represented by the symbols on the tablet.

One way to approach this problem is to try to find two different sets of numbers that when added, produce the same result.

For example, if the symbols represent the numbers 2, 3, and 5, then one way to add them up would be:

2 + 3 + 5 = 10

Another way to add them up would be:

3 + 7 = 10

In this case, the symbol for 2 would represent the number 7, and the symbol for 5 would represent the number 3. This would be one possible explanation for why there are two different ways of adding up the symbols on the tablet.

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sorry but without seeing the actual tablet then we cant work it out to get a correct answer

Answer:

Caca

Step-by-step explanation:

Caca

Using a telephone directory as the sampling frame can lead to under-coverage and bias, and it is generally not considered a representative sampling method.

Other more representative sampling methods, such as random digit dialing, address-based sampling, or a combination of methods, may be used to obtain a more accurate representation of the population.

Selecting a sample of households from the telephone directory can result in under-coverage and bias for several reasons.

Concept: When random sampling is not used, bias or regular flaws in the way the sample mean the population can occur.

Voluntary reply to samples, in which respondents choose their own respondents, and benefit samples, in which people who live nearby are included in the sample, are particularly biased.

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The maximum sustainable rate of harvest which is possible for the growth of fish P(t)  according to the differential equation " P' = 4P - 4P^2 - h " will be at the harvest rate of h=3.

In order to calculate the maximum sustainable harvest rate possible, we are required to find the equilibrium solutions of the differential equation firstly. Equilibrium solutions occur when P' = 0, so we can set the right-hand side of the differential equation at 0.

4P - 4P² - h = 0

Now a quadratic equation is formed in terms of P, which can be used to obtain P.

P = (1 ± √(1 + h))/2

There are two equilibrium solutions, obtained by these two values of P.

Now, in order to obtain a maximum sustainable harvest rate, we are required to have both equilibrium solutions to as positive ( as negative populations don't make any sense in this context).

Therefore, we have to find the largest value of h for which both of these equations have positive solutions:

(1 + √(1 + h))/2 > 0

(1 - √(1 + h))/2 > 0

On camparing both the inequalities, it can be concluded that the first inequality is always true, since the square root of a positive number is always positive. The second inequality is true when h < 3.

Hence, the maximum sustainable harvest rate is is found to be at h = 3. If the harvesting rate is greater than 3, then there will be no positive equilibrium solutions and the population will eventually be perished.

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Answer: To find the selling price of the karaoke machine with a 49.5% markup, you need to first calculate the amount of the markup. You can do this by multiplying the cost of the machine (52.75) by the markup rate (49.5%) expressed as a decimal:

52.75 * 0.495 = 26.067375

Next, add this markup amount to the cost of the machine:

52.75 + 26.067375 = 78.817375

So, the selling price of the karaoke machine with a 49.5% markup would be $78.82.

Step-by-step explanation:

10^-2/3 - 5 is the x-intercept of the given equation.

The x-intercept of a function is the point where the function f(x) is equivalent to zero.

Given the function below;

f(x)=3log(x+5)+2

3log(x+5)+2 = 0

Make x the subject of the formula:

3log(x+5) = -2

log(x+5) = -2/3

x + 5 = 10^-2/3

x = 10^-2/3 - 5

Hence the x-intercept of the graph of f(x)=3log(x+5)+2 is 10^-2/3 - 5

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Answer:

The example that demonstrates the greatest distance traveled is Brenan diving to a depth of -12.76 feet, as it has the highest absolute value.

Answer:

Comparing this to the volume of the cube when the side length is 3 cm, which is 27 cm^3, we can see that the volume of the cube is greater than the volume of the cylinder.

Step-by-step explanation:

I'm sorry, but I cannot see the graph you are referring to. However, I can still answer some of your questions based on the information provided.

When the diameter of the cylinder is 2 cm, the radius is equal to half the diameter, which is 1 cm.

To express the volume of a cube of side length s as an equation, we use the formula for the volume of a cube:

Volume of cube = s^3

Making a table for the volume of the cube at different side lengths, we get:

Side Length (cm) Volume (cm^3)

        0                                    0

        1                                     1

        2                                     8

        3                                     27

To compare the volume of the cube when the side length is 3 cm and the volume of the cylinder when the diameter is 3 cm, we need to find the radius of the cylinder first.

When the diameter is 3 cm, the radius is half the diameter, which is 1.5 cm. The height of the cylinder is also equal to the radius, so the volume of the cylinder can be found using the formula:

Volume of cylinder = πr^2h

Substituting r = 1.5 cm and h = 1.5 cm, we get:

Volume of cylinder = π(1.5)^2(1.5) ≈ 10.602 cm^3

Comparing this to the volume of the cube when the side length is 3 cm, which is 27 cm^3, we can see that the volume of the cube is greater than the volume of the cylinder.

A: The correct statement is c. Statistics are used to estimate parameters.

Statistics is the science of collecting and analyzing data to gain insight into a population of interest. It involves the collection, organization, analysis, interpretation, and presentation of data. The goal of using statistics is to draw conclusions about a population of interest and to estimate parameters of the population.

A parameter is a numerical value that is used to describe a population. For example, the mean of a population is a parameter. Statistics are used to estimate parameters of a population from a sample of the population. This process is called estimation. A statistic is a numerical value that is used to describe a sample.

For example, the sample mean is a statistic that is used to estimate the population mean. Estimation is done using the formula for a sample statistic, which is given by:

Estimate= (Statistic) / (Sample Size)

Here, the statistic is the sample mean, and the sample size is the number of observations in the sample. For example, if the sample mean is 10 and the sample size is 5, then the estimate of the population mean is 2 (10/5).

Statistics can also be used to construct confidence intervals to describe population parameters, such as means and proportions. A confidence interval is an interval of values around a sample statistic, such as a mean or a proportion, that is expected to contain the population parameter with a certain level of confidence.

In conclusion, statistics are used to estimate parameters of a population from a sample of the population. Estimation is done using the formula for a sample statistic, and confidence intervals can be used to describe population parameters.

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After evaluating f (-2), where f(x )is the piecewise function graphed given, the value of f(-2) = -3.

What is the piecewise function?

A function that is defined piecemeal is one that has numerous subfunctions, each of which applies to a distinct interval in the domain. Instead of being a property of the function itself, piecewise definition is a means to express the function.

Here, we have

The problem asks for f(-2), which is the value of y, that is, the vertical axis, when x, that is, the horizontal axis is -2.

We can see that at x = -2, the function changes the definition, thus it is called a piece-wise function.

To find the numeric value at x = -2, we have to look at the definition with the closed circle, which is at y = -3.

Hence, the value of f(-2) = -3.

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