A manufacturer produces two models of television stands. The table at the left shows the times (in hours) required for assembling, staining, and packaging the two models. The total times available for assembling, staining, and packaging are 4000 hours, 8950 hours, and 2650 hours, respectively. The profits per unit are $30 for model I and$40 for model II. What is the optimal inventory level for each model? What is the optimal profit?

The function y = 3 + 6x represents the data given in the table.

What is a function?

A function is a relationship between two sets of numbers, called the domain and the range. It is a rule that assigns to each element of the domain exactly one element of the range. In other words, a function is a set of ordered pairs (x, y) where each value of x is associated with a unique value of y.

The output (y) increases by 6 each time the input (x) increases by 1. Therefore, we can conclude that the relationship between x and y is a linear one with a slope of 6 and a y-intercept of 3.

The function rule that represents the data in the table is:

y = 6x + 3

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Given:

Points D, E, and F are non-collinear.

To find:

Number of lines that pass through F and are perpendicular  to DE.

Solution:

Points D, E, and F are non-collinear. It means points D, E and F are not lie on a  single straight line.

We know that, the number of perpendicular lines on a line from a particular point is 1.

So, number of lines that pass through F and are perpendicular  to DE is 1 as shown in the below figure.

Answer:

The  sequencing of the numbers from least to greatest is -3, -2, -0.8, -1 ÷ 10, 1 ÷ 2, 7, 9.8

Step-by-step explanation:

The sequencing of the numbers from least to greatest is as follows:

-3

-2

-0.8

-1 ÷ 10

1 ÷ 2

7

9.8

Hence, the  sequencing of the numbers from least to greatest is -3, -2, -0.8, -1 ÷ 10, 1 ÷ 2, 7, 9.8

Answer: Increasing her speed  by 5km/h, she will take 4.5 hours to complete the journey.

Step-by-step explanation:

Step 1

Speed= Distance  / TIme

Given Speed = 45km/h

and Time = 5 hours

Distance covered = Speed x Time

= 45 km/h x 5 hours

=225 kilometres.

Step 2

Increasing her speed by 5km/h makes the new Speed = 45 +5 = 50 km/h

At the same Distance of 225 km

Therefore she will complete the journey in

Time = Distance/ Speed

=225km/ 50km/h

=4.5 hours

Answer:

Your answer is: -14k-14

Step-by-step explanation:

Answer:

2.19

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

First off we can see that there are 46 pencils - and 7 students - so we can divide the two

46/7 is not a whole number, so we need to find a number that can be multiplied by 7, and is right below 46.

If you multiply 7 by 6, you get 42, which is the highest you can get with multiply by 7, which is also below 46.

Now that we know that each student gets 6 pencils, we need to find out how many are left.

We can do 46 (total pencils) minus 42 (pencils given) to get a leftover of 4 pencils, so the answer is A.

Answer:

m/_A=112°, m/_B=68°, m/_C=112°

Step-by-step explanation:

m/_A is 112° since consecutive /_s in a parallelogram are supplementary therefore 180°(<- supplementary sum)-68°(<- m/_D)=112°(<- m/_A, and m/_C), and in a parallelogram, one main property is opposite /_s are congruent therefore m/_B is congruent to m/_D so m/_B=68°.

Hopefully, this helps you out, have a great day!

Number of ways that the three gift certificates can be awarded = 13800 ways

There are a total of 25 people attended the charity benefit. There are three gift certificates: one gift certificate is in the amount of $100, the second is worth $25 and the third is worth $10.

Assume that no person receives more than one prize.

One of the 25 people can get gift certificate of $100.

⇒ 25 ways for $100 gift certificate.

Then remaining 24 people are considered for further counting.

One of the 24 people can get gift certificate of $25.

⇒ 24 ways for $25 gift certificate.

Now there are 23 people remained.

One of the 23 people can get the $10 gift certificate.

⇒ 23 ways for $10 gift certificate.

Therefore, Number of ways that the three gift certificates can be awarded = 25 x 24 x 23 = 13800 ways.

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Answer:

1:1

Step-by-step explanation:

The ratio would be 1:1 since it's a square, the sides will always be the same. In a square ,all sides are the same length. If they are not, then it wouldn't be a square.

It is recommended that a wager of $1,000 be placed on candidate B1 to win the national election so that the potential return can be maximised.

For each candidate, we first compute the probability of each result, and then we multiply that probability by the payout that corresponds to that outcome. This gives us the expected payoff for each candidate. The projected return for candidate A comes to 0.5 times $2,200, which equals $1,100. The estimated reward for candidate B1 is 0.5 times 0.8 times $2,000, which equals $800. In conclusion, the expected payment for selection B2 is half (0.5) times (0.2) times (10,000), which is $1,000.

According to these calculations, the expected return on investment for a wager placed on candidate A is $1,100, but the expected return on investment for a bet placed on candidate B1 is $800 and the expected return for candidate B2 is $1,000. Because we want to make sure that the amount of money we win is as big as possible, we should place our bets on candidate A, who has the potential to win us the most money. As a result, placing a wager of one thousand dollars on candidate B1 to win the national election is recommended.

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A 95% confidence interval estimate for the variance of service times for all their new automobiles is (9.29, 31.95).

The 95% confidence interval estimate for the variance of service times for all their new automobiles is calculated as follows:

Lower limit of the confidence interval = (n - 1)S² / χ²₀.₀₂₅

Upper limit of the confidence interval = (n - 1)S² / χ²₀.₉₇₅

Where, n is the sample size, S is the sample standard deviation, and χ² is the chi-square distribution value with degrees of freedom (df) = n - 1. Here, n = 15 and df = n - 1 = 15 - 1 = 14.

So, the chi-square distribution values with df = 14 and α/2 = 0.025 and 1 - α/2 = 0.975 are χ²₀.₀₂₅ and χ²₀.₉₇₅, respectively.

From the chi-square distribution table, we get:

χ²₀.₀₂₅ = 5.632 and χ²₀.₉₇₅ = 25.996.

Now, substituting the given values in the above formula, we have:

Lower limit of the confidence interval = (15 - 1)(4²) / 5.632 = 31.95

Upper limit of the confidence interval = (15 - 1)(4²) / 25.996 = 9.29

Hence, the 95% confidence interval estimate for the variance of service times for all their new automobiles is (9.29, 31.95). Therefore, the answer is  (9.29, 31.95).

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The half-life of the substance is approximately 17.78 days.

The exponential decay model for the mass of the substance can be written as:

\(m(t) = m0 \times e^{(-rt)},\)

where m0 is the initial mass, r is the decay rate parameter (as a decimal), and t is time in days.

If we want to find the half-life of the substance, we need to find the value of t when the mass has decreased to half of its original value (m0/2). In other words, we need to solve the equation:

m(t) = m0/2

\(m0 \times e^{(-rt)} = m0/2\)

\(e^{(-rt) }= 1/2\)

Taking the natural logarithm of both sides, we get:

-ln(2) = -rt

t = (-ln(2)) / r

Substituting the value of r (0.039), we get:

t = (-ln(2)) / 0.039

t ≈ 17.78 days

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29.78% of customers will most likely probability be waiting between 4 and 9 minutes.

The formula for the z score is-

z = (x - μ)/σ

In which,

μ =  mean of 10. 3 minutes

σ = standard deviation of 2. 7 minutes.

z score for the x = 4 minutes.

z = (4 - 10.3)/2.7

z = -2.33

z score for the x = 9 minutes.

z = (9 - 10.3)/2.7

z = -0.48

Thus,

Probability that the customer will have to wait between 4 and 9 minutes.

P(4 < x < 9) = P(-0.48 < z <  -2.33)

Use z score table-

P(4 < x < 9) =  0.3085 - 0.0107

P(4 < x < 9) = 0.2978

P(4 < x < 9) = 29.78%

Thus, 29.78% of customers will most likely be waiting between 4 and 9 minutes.

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Answer:

The cost of one shirt is $16 and the cost of one sweater is $20.

Step-by-step explanation:

Let the cost of one shirt be x and the cost of one shirt be y.

7x + 4y = 192 -----Equation 1

8x + 7y = 268 -----Equation 2

Equations 2-1:

8x + 7y - 7x - 4y = 268 - 192

x + 3y = 76

x = 76-3y -----Equation 3

Subsitute x = 76-3y into Equation 1:

7x + 4y = 192

7(76-3y) + 4y = 192

532 - 21y + 4y = 192

532 - 17y = 192

-17y = 192-532

-17y = -340

17y = 340

y = 340 ÷ 17

y = 20 (The cost of one sweater is $20)

Substitute y = 20 into Equation 3:

x = 76-3y

x = 76 -3(20)

x = 76 - 60

x = 16 (The cost of one shirt is $16)

A discrete random variable has a countable number of possible values. In this case I am pretty sure it is either none of the above or maybe the phone one.

Discrete random variables are simply countable, which should be a finite number and it should not change continuously. So, Time worked on a job is the discrete random variable among the four options.          

A random variable is said to be discrete if an experiment gives a finite number that is countable and should not change continuously.

Here, Time worked on a job has a fixed time for a job has to be done. So, it is a discrete random variable.

No. of girls in a family,

No. of outcomes of the head when two coins are flipped.

No. of defective street lights out of 100 bulbs in a certain area.

No. of the possible outcome of getting 4 when a dice is thrown twice.

The weight of a child changes as the child grows. So, it cannot be a discrete random variable.

The first digit of a phone number also changes for each and every person, whenever a person changes his /her number automatically will get a new number and it will have a different digit. So, it cannot be a discrete random variable.

The length of fish also varies according to the different sizes of fish. So, it cannot be a discrete random variable.

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There are two main subtypes of quantitative data, which are discrete data and continuous data. Each subtype has different techniques for analysis.

1. Discrete data: This type of data represents whole numbers or counts that can only take specific values. Examples include the number of students in a class or the number of cars in a parking lot. Techniques used to analyze discrete data include:
  a. Frequency distribution: A summary of the number of times each value appears in the dataset.

 b. Measures of central tendency: Calculating the mean, median, and mode of the dataset to understand its central point.

 c. Measures of dispersion: Assessing the range, variance, and standard deviation to understand the spread of the data.

2. Continuous data: This type of data represents measurements that can take any value within a range, such as height, weight, or temperature. Techniques used to analyze continuous data include:

 a. Histogram: A graphical representation of the distribution of the data, using bars to represent the frequency of values within specific intervals.

  b. Probability density function: A mathematical function that describes the probability of a continuous random variable falling within a specific range.

  c. Regression analysis: A statistical method for analyzing the relationship between a dependent variable and one or more independent variables.

Both discrete and continuous data can also be analyzed using inferential statistics, such as hypothesis testing and confidence intervals, to make inferences about a population based on a sample of the data.

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Answer:

IK and LN are parallel lines, the angles formed between them and intersecting lines are related in a specific way.

Step-by-step explanation:

Since IK and LN are parallel lines, the angles formed between them and intersecting lines are related in a specific way.

In the given diagram, the intersecting lines are HIJ, KLM, and NO.

The pairs of supplementary angles are:

. Angle HIK (alternating angles) and angle KLN

. Angle JIK (alternating angles) and angle KLM

. Angle JIN (corresponding angles) and angle LKN

.Angle MIN (corresponding angles) and angle KLO

. Angle MIO (alternate interior angles) and angle LKN\

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1.1) The volume of the cube is 27 cubic centimeters. 1.2)the density of the ice cube is approximately 0.917 grams per cubic centimeter (g/cm³).

1.3) the mass of the water cube is 27 grams. 1.4) the weight of the water and the ice would be the same under the same conditions. 1.5)In simpler terms, ice floats on water because it is lighter (less dense) than the water, allowing it to displace an amount of water equal to its weight and float on the surface.

1.1) The volume of the cube can be calculated using the equation: Volume = width x height x length. In this case, the cube measures 3 cm wide, 3 cm tall, and 3 cm long, so the volume is:

Volume = 3 cm x 3 cm x 3 cm = 27 cm³.

Therefore, the volume of the cube is 27 cubic centimeters.

1.2) Density is defined as mass divided by volume. The mass of the ice cube is given as 24.76 grams, and we already determined the volume to be 27 cm³. Therefore, the density of the ice cube is:

Density = Mass / Volume = 24.76 g / 27 cm³ ≈ 0.917 g/cm³.

Therefore, the density of the ice cube is approximately 0.917 grams per cubic centimeter (g/cm³).

1.3) The volume of the water cube is the same as the ice cube, which is 27 cm³. Given the density of liquid water as 1.00 g/cm³, we can calculate the mass of the water cube using the equation:

Mass = Density x Volume = 1.00 g/cm³ x 27 cm³ = 27 grams.

Therefore, the mass of the water cube is 27 grams.

1.4) The weight of an object depends on both its mass and the acceleration due to gravity. Since the volume of the water cube and the ice cube is the same (27 cm³), and the mass of the water cube (27 grams) is equal to the mass of the ice cube (24.76 grams), their weights would also be equal when measured in the same gravitational field.

Therefore, the weight of the water and the ice would be the same under the same conditions.

1.5) Ice floats on water because it is less dense than liquid water. The density of ice is lower than the density of water because the water molecules in the solid ice are arranged in a specific lattice structure with open spaces. This arrangement causes ice to have a lower density compared to liquid water, where the molecules are closer together.

When ice is placed in water, the denser water molecules exert an upward buoyant force on the less dense ice, causing it to float. The buoyant force is the result of the pressure difference between the top and bottom surfaces of the submerged object.

In simpler terms, ice floats on water because it is lighter (less dense) than the water, allowing it to displace an amount of water equal to its weight and float on the surface.

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Answer:

x ≈ 15.9

Step-by-step explanation:

Using Pythagoras' identity in the right triangle

x² + 6² = 17²

x² + 36 = 289 ( subtract 36 from both sides )

x² = 253 ( take the square root of both sides )

x = \(\sqrt{253}\) ≈ 15.9 ( to the nearest tenth )

The distributiοn οf a -1 in the subtracting expressiοn

One οf the basic mathematical οperatiοns is divisiοn, which divides a bigger number intο smaller grοups with the same number οf cοmpοnents. Hοw many tοtal grοups will be created, fοr example, if 20 students need tο be divided intο grοups οf five fοr a spοrting event? It is easy tο handle such situatiοns thanks tο the divisiοn οperatiοn. In this instance, multiply 20 by 5. That will cοme οut as 20 x 5 = 4.

Because οf this, there will be 4 grοups οf 5 students each. Yοu can verify this number by multiplying 4 by 5 and getting the answer οf 20.

In οrder tο subtract expressiοns, we must use the distributive prοperty, which applies a multiple οf the expressiοn included in brackets tο each term.

A(x + Y) = x + y

We are perfοrming the identical οperatiοn when subtracting an expressiοn, except that in the example abοve, "a" wοuld be equal tο -1.

(a + b) -(c + d) = (a + b) +(1 - c + d)

Hence subtracting an expressiοn similar tο distributing a –1

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At year 2, you will have approximately $25,915.13 in your bank account, assuming an initial investment with a 5% interest rate compounded annually. The correct answer is (a).


To find out how much money you will have in your bank account at year 2, we can use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:
A = Final amount (in this case, $30,000)
P = Principal amount (initial investment)
R = Annual interest rate (5% or 0.05)
N = Number of times interest is compounded per year (assumed to be once per year)
T = Number of years (in this case, 3)
Let’s solve for P, the principal amount at year 0:
30,000 = P(1 + 0.05/1)^(1*3)
30,000 = P(1.05)^3
Dividing both sides of the equation by (1.05)^3:
P = 30,000 / (1.05)^3
P ≈ 25,915.13
Therefore, at year 2, you will have approximately $25,915.13 in your bank account.
The correct answer is (a) $25,915.13.

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The correct statement is: The margin of error is plus or minus 3%.

To determine the margin of error based on the given confidence interval, we can calculate half the width of the interval. The margin of error is the maximum likely difference between the true proportion and the sample estimate.

The given confidence interval is (40%, 46%), so the width of the interval is 46% - 40% = 6%.

The margin of error is half of the width of the interval, so the margin of error is 6% / 2 = 3%.

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Answer:

For High School A, let  denote the number of students after  years. Define  analogously.

Then  and .

After 6 years the number of students in both high schools would be the same.

Step-by-step explanation:

For High School A, let  denote the number of students after  years. Define  analogously.

Since we start out at 850 students at High School A and it is growing by 35 students every year, we must have that .

Since we start out at 700 students at High School B and it is growing by 60 students every year, we must have that .

Setting the two equations equal to each other, we see that

So after 6 years the number of students in both high schools would be the same.

Answer:

A. 24 units

Explanation:

The perimeter of the triangle RST is equal to the sum of their sides.

We know that RS = 8 units and ST = 6 units.

Then, by the Pythagorean theorem, we can calculate the length of side RT as follows

Then, the perimeter is equal to

Perimeter = RS + ST + RT

Perimeter = 8 + 6 + 10

Perimeter = 24

So, the answer is A. 24 units

Answer: Scatter Plot 2

Step-by-step explanation: Usually with graphs like this, anything relative to time (age) will be on the x axis because the text messages depends on the age. This immediately knocks out number 1. Then you just have to start graphing points on the scatter plot and whichever one lines up best, which happens to be #2, is the correct answer.

Hope this helps.

Answer:

3

Step-by-step explanation:

use the pythagoreum therory