Write x² + 12x − 1 in the form (x + a)² + b, where a and b are constants

The total expense for producing 2 widgets is $18,006.00.

To find the total expense for producing 2 widgets, we need to find the total revenue from selling 2 widgets and then subtract the total expense of producing them.

The total revenue from selling 2 widgets is simply the price per widget times the quantity demanded at that price. Since the price is not specified in the problem, we can use the demand function to find it.

We know that the quantity demanded when 2 widgets are produced is:

q = 2

So we can solve the demand function for p:

q = -112p + 4,500

2 = -112p + 4,500

-112p = -4,498

p ≈ 40.16

Therefore, the price per widget is approximately $40.16.

The total revenue from selling 2 widgets at this price is:

revenue = price × quantity demanded

revenue = $40.16 × 2

revenue = $80.32

Now we need to find the total expense of producing 2 widgets. The problem gives us an expression for the total expense:

E = 3.00q + 18,000

Substituting q = 2, we get:

E = 3.00(2) + 18,000

E = $18,006.00

Therefore, the total expense for producing 2 widgets is $18,006.00.

Finally, we can calculate the profit as the difference between the revenue and the expense:

profit = revenue - expense

profit = $80.32 - $18,006.00

profit ≈ -$17,925.68

Since the profit is negative, Willie's Widgets would not make any profit from producing 2 widgets at this price. They would lose money.

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Answer:

Interest charged for the loan will be calculated based on the price of the car minus the down payment.

Step-by-step explanation:

Plato

Step-by-step explanation:

16.41 ft / 5 m = 'unit rate' (or conversion factor) = 3.282 ft/ m

then    # ft = 3.282 ft / m   *  # meter     (approximately )

Sam will receive 0.8 litres of juice, and Terry will receive 1.2 litres of juice after sharing the 2-litre tub of juice in the ratio of 2:3.

To solve this problem, we need to use the concept of ratio and proportion.

Let's first find the total amount of money contributed by Sam and Terry. Since the ratio of their contributions is 2:3, we can write:

Total contribution = Sam's contribution + Terry's contribution

Let's assume that Sam contributed $2x and Terry contributed $3x. Then, we have:

Total contribution = $2x + $3x = $5x

Now, we know that the total contribution is equal to the price of the juice, which is not given in the problem. So, let's assume that the price of the 2-litre tub of juice is $10. Then, we have:

Total contribution = Price of juice = $10

Therefore,

$5x = $10

Solving for x, we get:

x = $2

So, Sam contributed $4 and Terry contributed $6.

Now, to find the amount of juice each one received, we need to share the 2-litre tub in a ratio of 2:3.

The total ratio is 2+3 = 5.

So, Sam will receive 2/5 of the juice and Terry will receive 3/5 of the juice.

Therefore, Sam will receive (2/5) × 2 litres = 0.8 litres of juice, and Terry will receive (3/5) × 2 litres = 1.2 litres of juice.

In conclusion, Sam will receive 0.8 litres of juice, and Terry will receive 1.2 litres of juice after sharing the 2-litre tub of juice in a ratio of 2:3.

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The probability of being dealt four clubs and three cards with one card of each other remaining suit in 7-card poker is 0.0032.

The probability of being dealt four clubs and three cards with one card of each other remaining suit in 7-card poker is given by 0.0032. Probability is a concept of Mathematics. It is a measure of the likelihood of an event taking place. The concept of probability is very essential in the study of Mathematics. It helps us in determining the chance of occurrence of an event.What is the formula for probability?The probability of an event is represented by a number between 0 and 1. A probability of 0 indicates that the event is impossible while a probability of 1 indicates that the event is certain to happen.

The formula for probability is given by;Probability (P) = Number of favourable outcomes/ Total number of outcomes.The given event is to find the probability of being dealt four clubs and three cards with one card of each other remaining suit in 7-card poker.In a deck of cards, there are 13 clubs. Out of these, we have to select 4 cards. This can be done in (13C4) ways. Similarly, one card can be chosen from each of the remaining three suits. This can be done in (13C1) * (13C1) * (13C1) ways.

Therefore, the total number of ways in which we can choose 7 cards is given by (52C7).Thus, the required probability is given by;Probability = Number of favourable outcomes/ Total number of outcomes.Number of favourable outcomes = (13C4) * (13C1) * (13C1) * (13C1)Total number of outcomes = (52C7)Probability = Number of favourable outcomes/ Total number of outcomes= [(13C4) * (13C1) * (13C1) * (13C1)]/ (52C7)= 0.0032 (rounded to 6 decimal places).Therefore, the probability of being dealt four clubs and three cards with one card of each other remaining suit in 7-card poker is 0.0032.

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The equivalent unit of production- Weighted Average Method is given in the attached image.

The equivalent units of production (EUP) in the weighted average method refer to the units of output that have been partially completed during a period, and are expressed in terms of fully completed units.

In the weighted average method, the costs incurred during the period are combined with the costs of beginning work in process (BWIP) to determine the cost per equivalent unit. This cost per equivalent unit is then used to assign costs to the units completed and transferred out and to the units still in process at the end of the period.

The EUP in the weighted average method is calculated by adding together the units completed during the period with the equivalent units of work done on the units that are still in process at the end of the period.

The equivalent units are calculated by multiplying the number of partially completed units by the percentage of completion for the period.

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Rounding to the nearest whole number, the total emissions over the 5-year period would be approximately 743,289 kilotons of carbon dioxide.

Percentage is a way of expressing a number as a fraction of 100. It is represented by the symbol "%". For example, 50% is equal to 50/100, which simplifies to 0.5. Percentages are often used to express proportions or ratios in a way that is easier to understand. For instance, if there are 20 red balls and 80 blue balls in a bag, we could say that the ratio of red balls to blue balls is 1:4, or we could express this as a percentage by saying that 20% of the balls are red and 80% are blue.

To calculate the total carbon emissions over the 5-year period, we need to calculate the emissions for each year and then add them up.

Starting with the current emission level of 150,000 kilotons, the emissions in each of the next 5 years will be:

Year 1: 150,000 kilotons (no reduction)

Year 2: 150,000 * (1 - 0.005) = 149,325 kilotons

Year 3: 149,325 * (1 - 0.005) = 148,654 kilotons

Year 4: 148,654 * (1 - 0.005) = 147,987 kilotons

Year 5: 147,987 * (1 - 0.005) = 147,323 kilotons

To get the total emissions over the 5-year period, we add up the emissions for each year:

150,000 + 149,325 + 148,654 + 147,987 + 147,323 = 743,289 kilotons

Therefore, rounding to the nearest whole number, the total emissions over the 5-year period would be approximately 743,289 kilotons of carbon dioxide.

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Answer:742537

Step-by-step explanation: I did the  math, and this is the correct answer

Answer:

162 and 9

Step-by-step explanation:

The distance he ran for is from - 81 to 0 and to 81

81 +81 = 162 units

Time spent =distance/speed

Time = 162/ 18 = 9mins

Answer:

4c + 2d + 10

Step-by-step explanation:

The expression given is mostly already simplified, and the like terms that have variables are already combined.

As for 7 and 3, they are like terms because neither of them are attached to a variable.

Combining these like terms:

The equivalent expression is now 4c + 2d + 10.

Answer:

Option 2

Step-by-step explanation:

For two angles to be adjacent they need to have a common side/ray and a common vertex!

Hope this helps!!!

Answer:

Step-by-step explanation:

In geometry, two angles are adjacent if they have a common side and a common vertex. In other words, adjacent angles are directly next to each other and do not overlap.

->No, the two indicated angles do not share common vertex

The real cube root of 64 is 4.

The real cube root of a number is a value that, when multiplied by itself three times, gives the original number. In other words, the cube root of a number x is a number y such that y * y * y = x.

the prime factorization using the exponent found in the previous step. We can write the number 64 as:

64 = 2^2 * 2^2 * 2^2

Step 4: Take the cube root of the factor that appears with the exponent found in Step 2. In this case, the factor is 2:

∛2 = 1.259921...

Step 5: Multiply the factors together to get the final result:

∛64 = ∛(2^2 * 2^2 * 2^2) = ∛2^6 = (∛2)^2 = 1.259921...^2 = 4

Therefore, the real cube root of 64 is 4.

On the other hand we can easily find out by, the real cube root of 64 is 4, because 4 multiplied by itself three times gives 64:

4 * 4 * 4 = 64

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The real cube root of 64 is 4.

What is a Real cube root?

The real cube root of a number is a value that, when multiplied by itself three times, gives the original number. In other words, the cube root of a number x is a number y such that y * y * y = x.

the prime factorization using the exponent found in the previous step. We can write the number 64 as:

64 = 2² * 2² * 2²

Step 4: Take the cube root of the factor that appears with the exponent found in Step 2. In this case, the factor is 2:

∛2 = 1.259921...

Step 5: Multiply the factors together to get the final result:

∛64 = ∛(2² * 2² * 2²) = ∛2⁶ = (∛2)² = (1.259921...)² = 4

Therefore, the real cube root of 64 is 4.

On the other hand, we can easily find out by, the real cube root of 64 is 4 because 4 multiplied by itself three times gives 64:

4 * 4 * 4 = 64

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The answer will be as follows after answering the supplied question As a result, the equation of the line connecting the points (-1, -3) and (3, 5) is y = 2x - 1.

A math equation is a process that relates two statements by using the equals sign (=) to indicate equivalence. In algebra, an equation is a mathematical statement that shows the equivalence of two mathematical expressions. In the equation 3x + 5 = 14, for example, the equal sign separates the numbers 3x + 5 and 14. A mathematical formula may be used to understand the link between the two phrases written on opposite sides of a letter. Frequently, the logo and the software are the same. For example, 2x - 4 = 2.

y - y1 = m(x - x1) (x - x1)

where (x1, y1) is the location of one of the points and m is the line's slope.

We may use the slope formula to calculate the slope:

m = (y2 - y1) / (x2 - x1) (x2 - x1)

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

m = (5 - (-3)) / (3 - (-1)) = 8 / 4 = 2

As a result, the slope of the line is 2. We can now use one of the two locations to get the equation of the line. Let's take (-1, -3) as an example:

y - (-3) = 2(x - (-1))

y + 3 = 2(x + 1)

y + 3 = 2x + 2

y = 2x - 1

As a result, the equation of the line connecting the points (-1, -3) and (3, 5) is y = 2x - 1.

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Answer: 54 cubic yd^2

Step-by-step explanation: The volume formula for a cube is [tex]s^3[/tex] where s represents a side length.

To get the side length to solve for the surface area just do

[tex]\sqrt[3]{27} =3[/tex]

Which means that the side length is equal to 3

Now plug it into the surface area formula [tex]6s^2[/tex]

[tex]6(3)^2[/tex]

[tex]6(9)\\[/tex]

=54!

Answer:

54 yards^2

Step-by-step explanation:

Volume of a cube = side x side x side or [tex]s^3[/tex]

[tex]s^3 = 27yards^3[/tex]

s = [tex]\sqrt[3]{27}[/tex]

s = 3

Surface Area of a cube = A [tex]= 6 * s^2[/tex]

= [tex]6 * (3)^2[/tex]

= [tex]6 * 9[/tex]

=[tex]54[/tex][tex]yards^2[/tex]

Hope this helps!

Brainliest is much appreciated.

From the given data, the vertical intercept, vertical asymptotes and slant asymptote are 2, -5/3 and 4, y = x² - 5x + 13 respectively.

To find the horizontal intercepts, we need to set f(x) = 0 and solve for x:

x³ - 2x² - 29x - 42 / (3x² - 7x - 20) = 0

We can factor the denominator using the quadratic formula:

3x² - 7x - 20 = (3x + 5)(x - 4)

Now, we can write the function as:

f(x) = (x³ - 2x² - 29x - 42) / (3x + 5)(x - 4)

To find the vertical intercept, we need to set x = 0:

f(0) = -42/(-5)(-4) = 2.1

To find the vertical asymptotes, we need to find the values of x that make the denominator equal to zero:

3x + 5 = 0 or x - 4 = 0

Solving for x, we get:

x = -5/3 or x = 4

Therefore, the vertical asymptotes are x = -5/3 and x = 4.

To find the horizontal or slant asymptote, we need to look at the degree of the numerator and denominator. Since the degree of the numerator is greater than the degree of the denominator, there is no horizontal asymptote. Instead, there is a slant asymptote, which we can find by dividing the numerator by the denominator:

x³ - 2x² - 29x - 42 / (3x + 5)(x - 4) = (x² - 5x + 13) + (-2x - 2) / (3x + 5)(x - 4)

The slant asymptote is the line y = x² - 5x + 13.

Now, we can sketch the graph of the function. The graph will approach the vertical asymptotes at x = -5/3 and x = 4. The function will intersect the x-axis at x = -2, x = 3, and x = 7. The function will intersect the y-axis at y = 2.1. The graph will approach the slant asymptote y = x² - 5x + 13 as x approaches infinity or negative infinity.

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Answer:

The last one doesn't work because s and t aren't inversely proportional. If they were inversely proportional, k would remain constant.

a) The total cost, c, in dollars, of Theo's order based on the number of

bagels, b, he buys is: c = 0.75b + 3.5

b) The statement c(6) = 8 represents that the number of bagels bought was 6 which resulted in a total cost of $8

The general expression for a linear equation in slope intercept form is:

y = mx + b

Where:

m is slope

b is y-intercept

a) Let the number of bagels bought be b

Cost of each bagel = $0.75

Cost of chocolate = $3.50

Thus:

Total cost is:

c = 0.75b + 3.5

b) c(6)=8

This means the number of bagels bought was 6 which resulted in a total cost of $8

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Answer:

B. [tex]\sqrt[3]{-x-9}[/tex]

Step-by-step explanation:

Switch x and y, and then solve for y.

[tex]y = -x^3-9\\x=-y^3-9\\x+9=-y^3\\-x-9=y^3\\\sqrt[3]{-x-9} =y[/tex]

The number οf attendees at Harry's Hοedοwn is 42.

A data set is a cοllectiοn οf cοnnected data. In the case οf tabular data, a data set is assοciated with οne οr mοre database tables, where each rοw alludes tο a particular recοrd in the assοciated data set and each cοlumn tο a particular variable.

Suppοse the number οf Harry's Hοedοwn attendees be "x"

Given, Mean οf the data = 41 attendees

We knοw,

Mean = sum οf οbservatiοns / number οf οbservatiοns

41 = (48+33+x) / 3

48 + 33 + x = 123

x = 123 - (48+33)

x = 42

Hence the correct answer is 42 attendees.

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Answer:

42

Step-by-step explanation:

You can predict the size of the standard error of M for a sample size of 100 relative to a sample size of 25 because of the sampling distribution.

Suppose you compile all possibilities samples of 100 children of elementary school age in your school district; the expected value of M (when n = 100) will be equal to the expected value of M for all of the possible samples of 25 children of elementary school age in your school district.

1. All possible samples of 100 children of elementary school age in your school district; the expected value of M (when n = 100) is 11.03 the expected population mean:

E(μ) = 11.03

2. The standard error of M for this distribution of samples when n = 100 will be equal to 1.964

σ/√n = 19.64/ √100 = 1.964

3. The standard error of M for all the possible samples of 100 is twice (2 times) the standard error of M for all of the possible samples of 25.

σ/√n= 19.64/√25 = 3.928 = 2( σ/√n = 19.64/√100=1.964)

4. As both the sample has a same population with different sample size, therefore we can predict the standard error on the basis of sample observation. large sample size lower stanadrd error and vice versa.

If you were interested in how much time children spend reading on weekdays among this population of 2, 431 children, would you actually compile all possible samples of a certain size, Option: No

5. If we are traying to know the reading habit of 2431 children, we do not actually compile all possible sample rather we use some specific sample on the basis of sampling distribution.

You can predict the size of the standard error of M for a sample size of 100 relative to a sample size of 25 because of the sampling distribution.

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Q: Suppose you compile all possible samples of 100 children of preschool age in your school district; the expected value of M (when n = 100) will be equal to the expected value of M for all of the possible samples of 25 children of preschool age in your school district. The standard error of M for this distribution of samples when n = 100 will be equal to The standard error of M for all the possible samples of 100 is the standard error of M for all of the possible samples of 25. You can predict the size of the standard error of M for a sample size of 100 relative to a sample size of 25 because of the If you were interested in how much time children spend with siblings on weekends among this population of 2,431 children, would you actually compile all possible samples of a certain size? ОО Yes No

The expected amount of sampling error with a sample size of 25 is 1.

According to the Central Limit Theorem (CLT), a statistical theory, regardless of the population distribution's form, the distribution of sample means tends to resemble a normal distribution as sample size grows. This indicates that the distribution of the means of multiple samples of the same size taken from a population will be roughly normal. Since it enables us to utilise normal distribution features to draw conclusions about a population even when the population distribution is unknown or non-normal, the CLT is crucial to statistics.

Given that, μ= 16 and σ= 5.

The formula for the standard error of the mean (SEM) is:

SEM = σ / √(n)

SEM = 5 / √(25)

SEM = 1

Hence, the expected amount of sampling error with a sample size of 25 is 1.

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The cοrrect answer is οptiοn B, t-statistic =1.841, p-value= 0.0748 there is nοt suffient evidence tο reject the null hypοthesis.

The null hypοthesis is a sοrt οf suppοsitiοn used in statistical tests, which are fοrmal prοcedures fοr drawing inferences οr taking judgements based οn evidence. Based οn a sample οf the pοpulatiοn, the hypοtheses are suppοsitiοns regarding a statistical mοdel οf the pοpulatiοn. In οrder tο distinguish between statistical nοise and scientific claims, tests, which are fundamental cοmpοnents οf statistical inference, are frequently utilised in the interpretatiοn οf scientific experimental data.

The null hypοthesis is the prοpοsitiοn under cοnsideratiοn in a test οf statistical significance. Tο evaluate the strength οf the evidence cοntradicting the null hypοthesis, the significance test is used. A claim οf "nο effect" οr "nο difference" is the null hypοthesis. Frequently, H0 is used tο represent it. The alternative hypοthesis is the assertiοn being examined in relatiοn tο the null hypοthesis. Included are symbοls H1 and Ha.

Marcellο's Pizza, Mean – 11.25, Varience- 10.1974, Standard deviatiοn – 3.1933, n- 20

Pizza a Gο-Gο,  Mean – 9.6, Varience – 4.4, Standard deviatiοn – 2.0976 , n – 15

H0  - u1=u2 , Ha – u1≠u2

Test Statistics =(11.25-9.6)/ (√ {(3.1933 ×3.1933)÷20}+√{(2.097×2.097)÷15 }

=1.841

P-value = 2p (±≥1.841) ≈0.0748>0.05

Sο there is nοt sufficient evidence tο reject the null hypοthesis.

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Answer:

£10,000

Step-by-step explanation:

100%-20%= 80% --> 0.8

£8000 divided by 0.8 = £10,000

Answer:

The potential energy (PE) of an object is given by:

PE = mgh

where m is the mass of the object, g is the acceleration due to gravity (9.8 m/s² near the Earth's surface), and h is the height of the object above a reference level.

In this case, the mass of the clam is 0.11 kg, the height above the beach is 11.5 m, and the acceleration due to gravity is 9.8 m/s². Therefore, the potential energy of the clam is:

PE = (0.11 kg) × (9.8 m/s²) × (11.5 m) ≈ 12.7 J

So the potential energy of the clam is approximately 12.7 Joules.

After using the npr formula, there are 154440 ways that the thirteen players on the youth basketball team can be assigned to the five different positions.

There are a total of 13 players on the youth basketball team, and there are five different positions that need to be filled. To determine the number of ways that the players can be assigned to these positions, we can use the formula for permutations:

P(n, r) = n! / (n - r)!

Where n is the total number of players, and r is the number of positions. In this case, n = 13 and r = 5. Plugging these values into the formula, we get:

P(13, 5) = 13! / (13 - 5)!
= 13! / 8!
= (13 * 12 * 11 * 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1) / (8 * 7 * 6 * 5 * 4 * 3 * 2 * 1)
= (13 * 12 * 11 * 10 * 9) / 1
= 154440

Therefore, there are 154440 ways that the thirteen players on the youth basketball team can be assigned to the five different positions.

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Answer:

P(odd or at most 14)

Answer: (a) 7/27, 0.2593, 25.93%

P(king)

Answer: (d) 13/52

P(spade or heart)

Answer: (b) 1/2

Using similar triangle theorem, to calculate the ratios of the length, the value of x is 14.4 units

The similar triangle theorem, also known as the AA (angle-angle) similarity theorem, states that if two triangles have two corresponding angles that are congruent, then the triangles are similar. That is, the corresponding sides of the triangles are in proportion, and the ratios of the corresponding sides are equal. In other words, if ΔABC ~ ΔDEF, then:

AB/DE = BC/EF = AC/DF

This theorem can be used to solve problems involving similar triangles, such as finding unknown side lengths or angles.

To find the value of x, we need to apply similar triangle theorem.

Taking the ratios of sides from the two triangles;

13.5 / 6.2 = x / 6.6

Cross multiply both sides and solve for x

x = (13.5 * 6.6) / 6.2

x = 14.4 units

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Answer:

Step-by-step explanation:

Multiply both sides by 2.

Splitting the middle term, we get

In the given function the leading coefficient is negative, so the given function represents a downward parabola. It means, first the function is increasing after that the function is decreasing.

So, the value of the function is 10 at  (its way up) and at  (its way down.

Therefore, the player should stand 4 units away from the basket in order for the ball to go in the basket (10 feet high) on its way down.

Matthew who started an annuity on his 25th birthday by depositing $630 monthly into an account earning 8% annual interest compounded monthly will become 55 years old when the retirement account will be $1,000,000.

An annuity involves a series of payments made periodically.

The annuity attracts an interest rate compounded periodically.

Compounding involves charging interest on accumulated interest and the principal for each compounding period.

I/Y (Interest per year) = 8%

PV (Present Value) = $0

PMT (Periodic Payment) = $630

FV (Future Value) = $1,000,000

Results:

N = 368.641 months

= 30 years and 9 months

Sum of all periodic payments = $232,470

Total Interest = $767,530

Matthew's current age = 25 years

55 years old (25 + 30)

Thus, Matthew will be 55 years old when his retirement (annuity) account grows to $1,000,000.

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Answer:d

Step-by-step explanation: