Widget Wonders produces widgets. They have found that the cost, c(x), of making x widgets is a quadratic function in terms of x. The company also discovered that it costs $16 to produce 2 widgets, $18 to produce 4 widgets, and $48 to produce 10 widgets. find the total cost of producing 6 widgets.

The required total amount paid for magazine and pencil is 108p.

Simplification generally means finding an answer for the complex calculation that may involve numbers on division, multiplication, square roots, cube  roots, plus and minus.

Now it is given that,

Costing of a magazine = 83p

Costing of pencil = 45p

Thus, Total costing = Costing of a magazine + Costing of pencil

Putting the values we get,

Total costing = 83p + 45p = 128p

Now voucher gives 20p off

So, Final Costing = Total costing - Voucher off

⇒ Final Costing = 28p - 20p

⇒ Final Costing = 108p

this is the equired total amount paid for magazine and pencil.

Thus, the required total amount paid for magazine and pencil is 108p.

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An essential concept in mathematics and can be applied to a variety of fields such as physics, economics, and engineering.

The slope of a line in a Cartesian plane is a numerical representation of its steepness and inclination relative to the x-axis.

The slope of a straight line refers to the rise or fall of the y-coordinate as it moves from left to right along the x-axis.

There are a few different ways to interpret the slope of a line, but generally it can be thought of as the rate at which the dependent variable changes with respect to the independent variable.
When the slope is positive, the line rises from left to right, indicating that the dependent variable is increasing as the independent variable increases.

In other words, there is a direct relationship between the two variables.

Conversely, when the slope is negative, the line falls from left to right, indicating that the dependent variable is decreasing as the independent variable increases.

This means that there is an inverse relationship between the two variables.
The magnitude of the slope can also provide information about the relationship between the variables.

If the slope is close to zero, then the relationship between the two variables is weak or nonexistent.

However, if the slope is large in magnitude (i.e. close to 1 or -1), then there is a strong relationship between the variables.

A slope of zero indicates that there is no change in the dependent variable as the independent variable changes, while a slope of undefined means that the line is vertical and has no slope.
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The confidence interval in "The 95% confidence interval for the mean, based on the given information, is (9.85, 11.32)" indicates that we are 95% confident that the true population mean falls within this range.

Interpreting the confidence interval, it means that if we were to take multiple samples from the same population and calculate the confidence intervals, approximately 95% of those intervals would contain the true population mean.

In this specific case, it suggests that we are 95% confident that the true mean lies between 9.85 and 11.32.

The confidence interval refers to the precision of our estimate, not the likelihood of the true mean falling within the specific interval calculated from a single sample.

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The total amount of money spent is $21.7.

A total is a whole or complete amount, and "to total" is to add numbers or to destroy something. In math, you total numbers by adding them: the result is the total.

Given that, Raju bought 12 pencils at $0.35 each and 10 pens at $1.75 each.

Total cost of 12 pencils

= 12×0.35

= $4.2

Total cost of 10 pens

= 10×1.75

= 17.5

Total =4.2+17.5

= $21.7

Therefore, the total amount of money spent is $21.7.

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My dream job is to be a pro football player for the NFL.

Answer:

a Nurse

Step-by-step explanation:

36 different sandwiches

can be made.

To calculate the number of different sandwiches that can be made using 1 type of bread, 1 type of meat, and 1 type of cheese, we need to multiply the number of options for each ingredient together.

In this case, there are 3 options for bread, 4 for deli meat, and 3 for cheese. To find the total number of different sandwiches, we multiply these numbers:

3 (options for bread) x 4 (options for meat) x 3 (options for cheese) = 36

Therefore,

36 different sandwiches can be made

using 1 type of bread, 1 type of meat, and 1 type of cheese.

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The equation that can be used to find the exponential decay is 3000 = 4599e^k.

The lawn mower is decreasing in value, thus it is the decay constant that would be found.

The formula that can be used to find the value of an asset that decays exponentially is:

Future value = present value x (e^k)

3000 = 4599e^k.

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Answer:

He drove 111 miles

If we were given the distance Lan drove last weekend instead off how much gas he used then we would have to find the amount of gas used by lan.

Step-by-step explanation:

Ian's car can go 185 miles on 5 gallons of gas

On 5 gallons of gas lan's car can go 185 miles

Therefore in gallon of gas lan 's car can go

185/5 = 37

So, for 3 gallons of gas lan's car can go

3 × 37 = 111

for 3 gallons of gas lan's car can go 111 miles

If we were given the distance Lan drove last weekend instead off how much gas he used then we would have to find the amount of gas used by lan.

Answer:

they are both 41

Step-by-step explanation:

just do 90- 49= 41

Answer:

angle JOK- 41

angle MON - 41

Step-by-step explanation:

i)  The picture is called a Venn diagram.

The correct answer is an option (a)

ii) The rule of probability illustrated in the Venn diagram is the cmplement rule.

The correct answer is an option(a)

i)

We know that a Venn diagram is nothing but a simple way to visualize events and the relationships between them using rectangles and circles.

It is used to represent the sets, relation between the sets and operation performed on them, in a pictorial way.

Thus, the picture in the question is called a Venn diagram.

The correct answer is an option (a)

ii)

Consider a case where we are finding out the probability that a certain event will not occur.

An event A does not occur is a separate event that consists of all the possible outcomes that are not in A

This is called the complement event of A and represented by A'

Thus the probability rule is called the complement rule which states that the probability that an event does not occur is 1 minus the probability that it does occur.

P(B') = 1 - P(B)

Therefore, the correct answer is an option(a)

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Find the complete question below.

Part A: The shaded region represents the feasible region where both inequalities are satisfied simultaneously. It is below the line x + 3y = 8 and above the line x + y = 2.

Part B: The point (8, 2) is not included in the solution area.

Part C: The point (3, 1) represents one feasible solution that meets the constraints of the problem.

Part A: The graph of the system of inequalities consists of two lines and a shaded region. The line x + 3y = 8 is a solid line because it includes the equality symbol, indicating that points on the line are included in the solution set. The line x + y = 2 is also a solid line. The shaded region represents the feasible region where both inequalities are satisfied simultaneously. It is below the line x + 3y = 8 and above the line x + y = 2.

Part B: To determine if the point (8, 2) is included in the solution area, we substitute the x and y values into the inequalities:

8 + 3(2) ≤ 8

8 + 6 ≤ 8

14 ≤ 8 (False)

Since the inequality is not satisfied, the point (8, 2) is not included in the solution area.

Part C: Let's choose a point in the solution set, such as (3, 1). This point satisfies both inequalities: x + 3y ≤ 8 and x + y ≥ 2. In the context of the real-world scenario, this means that Michelle can buy 3 servings of dry food (x = 3) and 1 serving of wet food (y = 1) with her $8 budget. This combination of dog food allows her to feed at least two dogs at the animal shelter while staying within her budget. The point (3, 1) represents one feasible solution that meets the constraints of the problem.

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AnsPlayrules eteanat b.

Step-by-step expfnkel

Answer:

$137.52

Step-by-step explanation:

To solve this we have the following equation

159*(.93)^n

where n is the number of years passed

Whenver we decrease the price by 7% we are essentially multiplying it by .93 which is why this equation works

To start on January 2006 and end at the end of 2007 means about 2 years has passed

This means we can plug in 2 for n

so we have

159*(.93)^2

Put this into your calculator and get 137.52

Answer:

\(a_1\)=1,

\(a_n=a_n_-_1(-7)\)

Step-by-step explanation:

I was learning this a few years back, 9th grade I think, it's not really difficult, a tip that I will give you is to search up a video explaining the variables in the formula of both recursive and explicit.

I'm sure that you can do it and do well on your tests, good luck!

Hope this helped! :)

Answer:

6068 rabbits

Step-by-step explanation:

Given

\(Rabbits = 200\)

\(Reduction = 3\ daily\)

\(Squirrels = 18\)

\(Increment = 2\ daily\)

Required

Determine number of rabbits caught up till the day when they caught more squirrel.

Let the number of days be n

On any n day,

The number of rabbits they catch is:

\(Rabbit = 200 - 3n\)

The minus symbol is used because there's a reduction in the numbers of Rabbit caught, each day.

The number of squirrel they catch is:

\(Squirrel = 18 + 2n\)

The addition symbol is used because there's an increment in the numbers of Squirrel caught, each day

First, we need to solve for n

The expression when they catch more rabbits than squirrel is:

\(Squirrel > Rabbit\)

Substitute values for Squirrel and Rabbit

\(18 + 2n > 200 - 3n\)

To solve the above expression, we start by collecting like terms

\(2n + 3n > 200 - 18\)

\(5n > 182\)

Solve for n

\(n > \frac{182}{5}\)

\(n > 36.4\)

Days must be an integer. So, we have to round the above value.

\(n > 36\)

The above expression shows that they caught more squirrel on a day greater than 36.

This day is 37.

i.e.

\(n = 37\)

The reduction in the number of rabbits daily is an indication of Arithmetic progression.

So, to calculate the number of rabbits caught up till the day when they caught more squirrel, we make use of Sum of n terms of an AP using:

\(S_n = \frac{n}{2}(2a + (n-1)d)\)

In this case:

\(n = 37\)

a = Initial Number of rabbits;

\(a = 200\)

d = the reduction (common difference)

\(d = -2\)

Substitute these values in the given formula:

\(S_n = \frac{n}{2}(2a + (n-1)d)\)

\(S_{37} = \frac{37}{2}(2 * 200 + (37 - 1) * -2)}\)

\(S_{37} = \frac{37}{2}(2 * 200 + 36 * -2)}\)

\(S_{37} = \frac{37}{2}(400 -72)}\)

\(S_{37} = \frac{37}{2} * 328\)

\(S_{37} = 37 * 164\)

\(S_{37} = 6068\)

Up till that day, the number of rabbits is 6068

Answer:

y=84 since 7 time 12 is 84

Step-by-step explanation:

Answer:

y=84

Step-by-step explanation:

hope it helps you that is what I got

From the given question we can extract all the necessary parameters to enable us to find the solution to the question.

We would therefore have the following parameters

This would be inserted into the formula given for the z score below

This would then be written as

We look up the z score on the probability table to get 0.9625. We then subtract from 1 to get the answer

ANSWER=0.0375

In summary, the function that should be differentiated is option B: 1/10 tan(10x-1). The appropriate definitions for f and g are: f(x) = 1/10 tan(x), g(x) = 10x-1.

To verify the formula by differentiation, we need to differentiate both sides of the equation and check if they are equal. Let's differentiate the given functions:

The integral on the left side: ∫ \(sec^2(10x-1) dx\)

To differentiate this integral, we need to apply the Chain Rule. Let's define \(f(x) = sec^2(10x-1)\) and g(x) = x. Then, according to the Chain Rule, we have:

∫\(sec^2(10x-1) dx\) = ∫ f(g(x)) g'(x) dx

= ∫ f(u) du, where u = 10x-1 and du = g'(x) dx

Now, we can differentiate f(u) with respect to u:

\(f(u) = sec^2(u)\)

Taking the derivative of f(u) with respect to u, we get:

f'(u) = 2 sec(u) tan(u)

Substituting back u = 10x-1, we have:

f'(10x-1) = 2 sec(10x-1) tan(10x-1)

Therefore, the derivative of the left side of the equation is 2 sec(10x-1) tan(10x-1).

Now, let's differentiate the right side of the equation:

1/10 tan(10x-1) + C

Since C is a constant, its derivative is 0. So, we only need to differentiate the term 1/10 tan(10x-1).

To differentiate this term, we can use the Chain Rule again. Let's define f(x) = 1/10 tan(x) and g(x) = 10x-1. Then, according to the Chain Rule, we have:

1/10 tan(10x-1) = f(g(x)) = f(u), where u = 10x-1

Differentiating f(u) with respect to u, we get:

\(f'(u) = 1/10 sec^2(u)\)

Substituting back u = 10x-1, we have:

\(f'(10x-1) = 1/10 sec^2(10x-1)\)

Therefore, the derivative of the right side of the equation is 1/10 \(sec^2(10x-1).\)

Comparing the derivatives of both sides, we have:

Derivative of the left side: 2 sec(10x-1) tan(10x-1)

Derivative of the right side: \(1/10 sec^2(10x-1)\)

Since the derivatives of both sides are equal, we have verified the formula by differentiation.

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The relationship that represents the law of cosines if the measure of the included angle between the sides a and b is D. area of square c² = area of square a² area of squareb² area of defect1 area of defect2

It should be noted that the cosine law is simply used to solving triangles.

The law simply states that c² = a² + b² - 2abcosC.

The correct option that illustrates this is D.

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Answer:

c. area of square c2 = area of square a2 + area of square b2 – area of defect1 – area of defect2

Step-by-step explanation:

Thus, the probability that a randomly selected card has a consonant is 62.5%. This means that if you were to randomly select a card from the pile of cards, there is a 62.5% chance that the card would be a consonant.

The number of consonants in the word "probable" and the total number of cards. There are 5 consonants in "probable" (p, r, b, l, and b) and a total of 8 cards.

In the word "probable," there are 5 consonants (p, r, b, b, and l) and 3 vowels (o, a, and e). To calculate the probability of choosing a consonant, divide the number of consonants by the total number of letters:

Probability = (Number of consonants) / (Total number of letters)

The probability of selecting a consonant can be calculated by dividing the number of consonants by the total number of cards:

5 consonants / 8 cards = 0.625 or 62.5%

Therefore, the probability that a randomly selected card has a consonant is 62.5%. This means that if you were to randomly select a card from the pile of cards, there is a 62.5% chance that the card would be a consonant.

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Answer:

Step-by-step explanation:

radius = 32 inches

angle = 60 degrees

Area of segment = 1/2 (60-sin(60)) *(32)^2 = 1/2 (60 - sqrt(3)/2) *(1024) = 598 sq inches

Answer:

The value of the given expression is 27.1

Step-by-step explanation:

We are given an expression of two variable x and y.

We need to find the value of expression at x = 3 and y = 4

So first put x = 3 and y = 4 into expression and simplify

1/2 x 3 (3) + 3.4 x 4

➡️ 1/2 x 27 + 13.6

➡️ 27/2 + 13.6

➡️ 13.5 + 13.6

Now, add both of the numbers together. ( as an addition problem)

Therefore, when you ad the 2 together, you get the total of 27.1

Answer:

They used the wrong formula, correct answer: -2.4

Step-by-step explanation:

The slope of a linear line, can be calculated using the formula: \(\frac{y_2-y_1}{x_2-x_1}\)

Which can intuitively be understand, by realizing the definition of a slope is also generally defined as: \(\frac{\text{change in y}}{\text{change in x}}\).

So the  \(\text{change in y} = y_2 - y_1\) and the \(\text{change in x} = x_2-x_1\), and we just substitute these algebraic expressions to derive the slope formula.

Let's assign values to the x and y values as such:

\((x_1, y_1) = (2, -4)\\(x_2, y_2) = (-3, 8)\)

Note: We could've assigned the values as such: \((x_1, y_1) = (-3, 8)\\(x_2, y_2) = (2, -4)\)

and we would get the same slope, we just have to be consistent with how we plug in the x and y values.

from here we can substitute values into the equation to get:

\(m=\frac{8-(-4)}{-3-2}\)

Now we can spot the error the student made. They used the wrong formula. The formula they used: \(\frac{x_2-y_2}{x_1-y_1}\), as explained above, we can derive the slope formula by the common definition. This formula being used isn't finding the change in x and y, just the difference between the x and y coordinates.

If the student applied the formula correctly they would get the equation we got above.

We can further simplify the equation:

\(m=\frac{8-(-4)}{-3-2}\)

To the following:

  \(m=\frac{8+4}{-5}\)

From here simplify the numerator further:

\(m=\frac{12}{-5}\)

Which in decimal form is

\(m=-2.4\)

\( \Large{\boxed{\sf (10 + 6i)(-2 - 4i) = 4 - 52i}} \)

\( \\ \)

To find the algebraic form, also called 'a + bi form', of the given complex number, we will have to expand its expression using FOIL method.

\( \\ \)

\( \Large{ \sf \: \underline{FOIL \: method \text{:}}} \\ \\ \Large{\boxed{\sf (A + B)(C + D) = AC + AD + BC + BD}} \)

\( \\ \)

Let's identify our coefficients and expand the given expression:

\( \sf (\underbrace{\sf 10}_{A} + \overbrace{\sf 6i}^{B})(\underbrace{\sf -2}_{C} \overbrace{\sf -4i}^{D}) = 10 \times (-2) + 10 \times (-4i) + 6i \times (-2) + 6i \times (-4i) \\ \\ \\ \sf = -20 - 40i - 12i - 24i^2 = -20 - 52i - 24i^2 \)

\( \\ \)

In the complex number system, i² = -1. Therefore, our final answer is:

\( \sf (10 + 6i)(- 2 - 4i) = -20 - 52i - 24(-1)= \boxed{\boxed{\sf 4 - 52i}} \)

\( \\ \\ \)

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Answer:

x = 4

Step-by-step explanation:

30x = 29x + 4

subtract 29x from both sides

x = 4

Answer:

A I just did that

Step-by-step explanation:

Step-by-step explanation:

2x+8y=12 3x-8y=11

If we have to solve by substitution, Take the first equation and divide by 2

2x/2 + 8y/2 =12/2

x+4y = 6

Then subtract 4y from each side

x = 6 -4y

Then substitute this into the second equation

This is best solved by elimination

2x+8y=12

3x-8y=11

----------------

5x = 36

x = 36/5

The probability of the union of two events occurring can never be more than the probability of the intersection of two events occurring, this statement is false.

The union of two or more sets refers to the set with all the elements belonging to each set. An element is said to be in the union if it lies to at least one of the sets.

The intersection of two or more sets refers to the set of elements universal to each set. An element is in the intersection if it occurs in all of the sets.

The event that both A and B occur is the intersection of the events A occurs and B occurs. As such, it is a subset of each and cannot, therefore, have a larger probability than either one individually.

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The graph of the original triangle RST and its reflected image R'S'T' after a reflection across the line x = 2.

To graph the triangle RST and its image R'S'T' after a reflection across the line x = 2, we follow these steps:

Plot the vertices of the original triangle RST: R(2, 1), S(-2, -1), and T(3, -2) on a coordinate plane.

Draw the lines connecting the vertices to form the triangle RST.

To reflect the triangle across the line x = 2, we need to create a mirrored image on the other side of the line. This reflection will keep the x-coordinate unchanged but negate the y-coordinate.

Determine the image of each vertex R', S', and T' after the reflection:

R' is the reflection of R(2, 1) across x = 2. Since the x-coordinate remains the same, the x-coordinate of R' is also 2. The y-coordinate changes sign, so the y-coordinate of R' is -1.

S' is the reflection of S(-2, -1) across x = 2. Again, the x-coordinate remains the same, so the x-coordinate of S' is -2. The y-coordinate changes sign, so the y-coordinate of S' is 1.

T' is the reflection of T(3, -2) across x = 2. The x-coordinate remains the same, so the x-coordinate of T' is 3. The y-coordinate changes sign, so the y-coordinate of T' is 2.

Plot the reflected vertices R'(2, -1), S'(-2, 1), and T'(3, 2) on the coordinate plane.

Draw the lines connecting the reflected vertices R', S', and T' to form the triangle R'S'T'.

Now, we have the graph of RST, the initial triangle, and R'S'T, its reflected image following reflection over x = 2.

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The commute times are shorter for City A but more predictable for City B. Thus, option c is correct.

In mathematics, an interval is a set of real numbers with the property that any number that lies between two numbers in the set is also included in the set. An interval can be written using interval notation, which uses parentheses, square brackets, or a combination of both to indicate whether the endpoints of the interval are included or excluded.

The interval [1, 5] represents a set of real numbers that includes all the numbers between 1 and 5, including 1 and 5 themselves. The square brackets indicate that the endpoints of the interval are included in the set. The left bracket "[" indicates that the interval includes the number 1, and the right bracket "]" indicates that the interval includes the number 5.

In interval notation, we can write this interval as:

[1, 5] = {x | 1 ≤ x ≤ 5}

This means that the set of all real numbers x, such that x is greater than or equal to 1 and less than or equal to 5, is equal to the interval [1, 5].

Graphically, we can represent this interval on a number line as follows:

 |-----|-----|-----|-----|-----|

 0     1     2     3     4     5

The interval [1, 5] is the closed interval between 1 and 5, including both endpoints, so we use closed circles to indicate that the endpoints are included in the interval:

 |-----|-----|-----|-----|-----|

 0     1     2     3     4     5

       [     ○-----○     ]

            1         5

The interval includes all the numbers on the number line between 1 and 5, including 1 and 5 themselves, but no other numbers outside of that range.

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