A recipe uses 214 cups of flour for a batch of cookies. Henry makes 10 batches of cookies for a bake sale.

A model shows a total of c cups divided into 10 sections, each labeled 2 and 1 fourth.

Part A
Which equation models the total number of cups of flour, c, Henry needs?
c+214=10
214×c=10
10+c=214
214×10=c
Part B
How many cups of flour does Henry need?
2014cups
2212cups
2434cups
2512cups
Part C
Estimate how much flour Henry would need to make 15 batches of cookies. Explain.

I would round 214 to 2, so Henry would need about 30 cups of flour.

I would round 214 to 3, so Henry would need about 45 cups of flour.

I would round 214 to 1, so Henry would need about 15 cups of flour.

I would round 214 to 234, so Henry would need about 30 cups of flour.​

Answer:

the answer will be A

Step-by-step explanation:

The period of the given function is T = 2π

The period T of a function f(x) is such that:

f(x + T) = f(x).

In this case, our function is:

f(θ) = e^{iθ}

Remember that this can be written as:

f(θ) = cos(θ) + i*sin(θ)

So yes, this is in did a periodic function.

Then the period of the function f(θ) is the same as the period of the cosine and sine functions, which we know is T = 2π.

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The period of the considered function f(θ) = e^{iθ} is found to be P = 2π (assuming 'i' refers to 'iota' and 'e' refers to the base of the natural logarithm)

For any real value θ, we have:

\(e^{i\theta} = \cos(\theta) + i\sin(\theta)\)

where 'e' is the base of the natural logarithm, and 'i' is iota, the imaginary unit.

Functions which repeats their values after a fixed interval, are called periodic function.

For a function \(y = f(x)\), it is called periodic with period 'T' if we have:

\(y = f(x) = f(x + T) \: \forall x \in D(f)\)

where D(F) is the domain of the function f.

Suppose that, the period of the function \(f(\theta) = e^{i \theta}\) be P, then we get:
\(f(\theta + P) = f(\theta)\\\\e^{i(\theta)} = e^{i(\theta + P)}\\\\\cos(\theta) + i\sin(\theta) = \cos(\theta + P) + i\sin(\theta + P)\)

When two complex numbers are equal, then their real parts are equal and their imaginary parts are equal.

That means,

\(\cos(\theta) + i\sin(\theta) = \cos(\theta + P) + i\sin(\theta + P)\) implies that:

\(\cos(\theta) = \cos(\theta + P)\\\sin(\theta) = \sin(\theta + P)\)

Also, we know that the period of sine and cosine function is \(2\pi\)

Thus, we get:

\(P = 2\pi\)

Thus, the period of the function \(f(\theta) = e^{i \theta}\)  is P = 2π

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To graph y = x² + 4x + 6 with 5+ points using an x/y chart, follow these steps:

Step 1: Create an x/y chart with five rows and two columns. Label the first column x and the second column y.

Step 2: Choose five values for x. You can choose any values you want as long as you plug them into the equation in the next step. In this example, we will use -3, -2, -1, 0, and 1. Write these values in the first column of your chart.

Step 3: Plug each value of x into the equation y = x² + 4x + 6 to find the corresponding value of y. Write these values in the second column of your chart. To make it simpler, here are the calculations for each point:When x = -3: y = (-3)² + 4(-3) + 6 = 3When x = -2: y = (-2)² + 4(-2) + 6 = 2When x = -1: y = (-1)² + 4(-1) + 6 = 1When x = 0: y = (0)² + 4(0) + 6 = 6When x = 1: y = (1)² + 4(1) + 6 = 11

Step 4: Plot each point on the x/y chart. The x value goes on the horizontal axis (x-axis) and the y value goes on the vertical axis (y-axis). Once you have plotted all five points, connect them with a smooth curve to create the graph of y = x² + 4x + 6. The graph is shown in the figure below.

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The average value of the function f(x)=x²-9 on [0,6] is 3.

The area represented by the definite integral 11 |x-4 dx is 176 square units.

The area under the graph of f over the interval [-1,5] is 70.33 square units.

Let's find the average value of the function as follows:

Average value of the function = 1/(b-a) * ∫a^b f(x) dx where a = 0 and b = 6, so

Average value of the function = 1/(6-0) * ∫0^6 (x²-9) dx

= 1/6 * [(x³/3) - 9x] from 0 to 6

= 1/6 * [(6³/3) - 9(6) - (0³/3) + 9(0)]

= 1/6 * [72 - 54]

= 3 units

The average value of the function f(x)=x²-9 on [0,6] is 3.

Let's solve this integral as follows:∫(11) |x-4| dx

We have two cases:x-4 > 0

=> x > 4∫(11) (x-4) dx

for x > 4 = [11(x²/2 - 4x)]

for x > 4x-4 < 0

=> x < 4∫(11) (4-x) dx

for x < 4= [11(4x - x²/2)]

for x < 4

Now, we need to find the integral from 0 to 11. Since the function is symmetric around x = 4, the value of the integral from 0 to 4 will be the same as from 4 to 11. so

∫(11) |x-4| dx= 2 * ∫(4) (x-4) dx for x > 4

                  = 2 * [11(x²/2 - 4x)] for x > 4

                  = 2 * [11(4x - x²/2)] for x < 4

Putting the limits from 0 to 11, we get the Area represented by the definite integral

                   = 2 * ∫(4) (x-4) dx + 2 * ∫(4) (4-x) dx for x < 4 and

from x > 4   = 2 * [(11(11²/2 - 4(11))) + (11(4(4) - (4²/2)))]+ 2 * [(11(4(4) - (4²/2))) + (11(4(11) - (11²/2)))]

                   = [2(44) + 2(44)] = 176 square units

Hence, the area represented by the definite integral 11 |x-4 dx is 176 square units.

We have two cases:For x ≤ 3, f(x) = x² + 6

Area under the graph of f(x) from -1 to 3 = ∫(-1) (x² + 6) dx= [(x³/3) + 6x]

                                               from -1 to 3= [(3³/3) + 6(3)] - [(-1³/3) + 6(-1)]

                                                                  = 3² + 6(2) - (-1/3) - 6= 30.33 square units

For x > 3, f(x) = 5x

Area under the graph of f(x) from 3 to 5 = ∫(3) (5x) dx= [5(x²/2)]

                                               from 3 to 5= 5(25/2) - 5(9/2)

                                                                 = 40 square units

Therefore, the area under the graph of f over the interval [-1,5] = Area under the graph of f(x) from -1 to 3 + Area under the graph of f(x) from 3 to 5

= 30.33 + 40= 70.33 square units

Hence, the area under the graph of f over the interval [-1,5] is 70.33 square units.

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Answer:

Common factors between the two numbers is 3 and 1.

Step-by-step explanation:

The factors of 42 are 42, 21, 14, 7, 6, 3, 2, 1.

The factors of 45 are 45, 15, 9, 5, 3, 1.

The value of the prime number which is a factor of 42 and 45 would be  3.

Used a concept of prime number that states,

A prime number is a whole number greater than 1 whose only factors are 1 and itself. A factor is a whole number that can be divided evenly into another number. Numbers that have more than two factors are called composite numbers.

Given that the two numbers are 42 and 45

Now, factors of numbers 42 and 45 are,

The Factor of 42 are

1, 2, 3, 6, 7, 14, 21, 42

And, The factors of 45 are

1, 3, 5, 9, 15, 45

So, the prime number that is a factor of 42 and 45 is 3.

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The solutions to the equation ax² + b = c are x = √((c-b)/a) and x = -√((c-b)/a).

To solve the equations ax² = c and ax² + b = c, we can use algebraic methods.

For the equation ax² = c, we can isolate x² by dividing both sides by a:

ax²/a = c/a

x² = c/a

Then, we can take the square root of both sides:

x = ±√(c/a)

Therefore, the solutions to the equation ax² = c are x = sqrt(c/a) and x = -√(c/a).

For the equation ax² + b = c, we can first isolate the x² term by subtracting b from both sides:

ax² = c - b

Then, we can follow the same steps as above to solve for x:

x = ±√((c-b)/a)

Therefore, the solutions to the equation ax² + b = c are x = √((c-b)/a) and x = -√((c-b)/a).

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Answer:

The 3 digit number 642 when multiplied 97 gives the greater product.

Step-by-step explanation:

The greatest product will result by multiplying the smaller 3 digit number with the greater two digit number.

The greater three digit number will be 976 and smaller 2 digit number would be 42

Multiplying

976*42 = 40992   ( descending order number)

679 *24= 16,296  ( ascending order number)

If we take the 2 digit number as 97 and  3digit number 642

Then multiplying

642* 97= 62,274  ( descending order  number)

246 * 79=19434   ( ascending order number)

The 3 digit number 642 when multiplied 97 gives the greater product.

The seventh term of the geometric sequence is -7/32. The nth term of the sequence, a1 is the first term, r is the common ratio, and n is the position of the term

To find the seventh term of a geometric sequence, we can use the formula:

\(an = a1 * r^(n-1),\)

where an represents the nth term of the sequence, a1 is the first term, r is the common ratio, and n is the position of the term we want to find.

In this case, we are given a2 = -7 and r = 1/2.

Using the formula, we can find a1 by substituting n = 2:

a2 = a1 * (1/2)^(2-1).

We know that a2 = -7, so we can rewrite the equation:

-7 = a1 * (1/2)^1,

-7 = a1 * (1/2).

Now, let's solve for a1:

a1 = -7 * (2/1),

a1 = -14.

We have found that the first term, a1, is equal to -14.

Now, we can find the seventh term, a7, by substituting n = 7 into the formula:

a7 = (-14) * (1/2)^(7-1),

a7 = (-14) * (1/2)^6,

a7 = (-14) * (1/64),

a7 = -14/64,

a7 = -7/32.

Therefore, the seventh term of the geometric sequence is -7/32.

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Answer:

x = 6

Step-by-step explanation:

(hope this helps)

The given system has a unique solution. A unique solution means there is only one solution. Therefore, the answer is: One.

The given system is x + 4y = 6 and y = 2x - 3.

How many solutions does this system have?

This given system has a unique solution.

Let's solve the given system to include a conclusion as to how many solutions the system has.

x + 4y = 6

y = 2x - 3

Let's substitute in the second equation to the first one and solve the system:

x + 4(2x - 3) = 6

x + 8x - 12 = 6

12x = 18

x = 18/12

= 3/2

y = 2x - 3

= 2(3/2) - 3

= 0

We have solved the system and the value of x = 3/2 and y = 0. Therefore, the given system has a unique solution.

A unique solution means there is only one solution of the given system of equations.

Thus, we can say that the given system of equations has one solution. Therefore, the answer is: One.

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To find the selling price that will yield the maximum profit, we need to find the vertex of the quadratic function given by the profit equation y = -5x² + 286x - 2275.The x-coordinate of the vertex can be found using the formula:

x = -b/2a

where a = -5 and b = 286.

x = -b/2a

x = -286/(2(-5))

x = 28.6

So, the selling price that will yield the maximum profit is $28.60 (rounded to the nearest cent).

Therefore, the widgets should be sold for $28.60 to maximize the company's profit.

Hope I helped ya...

Answer:

29 cents

Step-by-step explanation:

The amount of profit, y, made by the company selling widgets, is related to the selling price of each widget, x, by the given equation:

\(y=-5x^2+286x-2275\)

The maximum profit is the y-value of the vertex of the given quadratic equation. Therefore, to find the price of the widgets that maximises profit, we need to find the x-value of the vertex.

The formula to find the x-value of the vertex of a quadratic equation in the form y = ax² + bx + c is:

\(\boxed{x_{\sf vertex}=\dfrac{-b}{2a}}\)

For the given equation, a = -5 and b = 286.

Substitute these into the formula:

\(\implies x_{\sf vertex}=\dfrac{-286}{2(-5)}\)

\(\implies x_{\sf vertex}=\dfrac{-286}{-10}\)

\(\implies x_{\sf vertex}=\dfrac{286}{10}\)

\(\implies x_{\sf vertex}=28.6\)

Assuming the value of x is in cents, the widget should be sold for 29 cents (to the nearest cent) to maximise profit.

Note: The question does not stipulate if the value of x is in cents or dollars. If the value of x is in dollars, the price of the widget should be $28.60 to the nearest cent.

False. The weight of a variable in a standardized predictor environment does not necessarily indicate that the variable has a higher discriminating power.

Discriminating power is determined by the correlation of a predictor variable with the outcome variable. We can calculate the correlation between a predictor variable and an outcome variable using Pearson's correlation coefficient, which is represented by the formula:

r = (NΣXY - (ΣX)(ΣY)) / √[(NΣX2 - (ΣX)2)(NΣY2 - (ΣY)2)].

In this formula, N is the sample size, ΣX is the sum of the predictor variable, ΣY is the sum of the outcome variable, ΣXY is the sum of the products of the predictor and outcome variables, and ΣX2 and ΣY2 are the sums of the squares of the predictor and outcome variables, respectively. The Pearson's correlation coefficient ranges from -1 to +1, with +1 indicating perfect positive correlation, 0 indicating no correlation, and -1 indicating perfect negative correlation. A higher correlation coefficient indicates a higher discriminating power.

Therefore, the weight of a variable in a standardized predictor environment does not indicate whether or not the variable has a higher discriminating power; this is determined by the correlation between the predictor and outcome variables.

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In IR (Infrared) spectroscopy, stretching frequency is the frequency at which the bond stretches. It is the frequency at which a bond oscillates most strongly, indicating the bond's stiffness or spring constant.

The stretching frequency is affected by various factors, including the bond's strength, mass of the atoms, neighboring atoms, etc. The effect of the conjugation on the stretching frequency is of particular interest to us in this question. Conjugation refers to a series of alternating double bonds in a molecule.

It results in the delocalization of electrons in the molecule, which reduces the stiffness of the bond, reducing the stretching frequency. This reduction in vibrational frequency, as mentioned earlier, can be up to 30 cm−1 for each double bond involved in the conjugation.

A conjugated molecule has fewer stretching frequencies than an unconjugated molecule, resulting in broader and weaker peaks.ACYL halides/anhydride increase the energy more than 30 cm−1. The stretching frequency of the bond decreases when the carbonyl compound is conjugated on both sides of the carbonyl. It decreases by -60 cm-

1.Cyclohexane is strain-free and "normal." However, when a molecule is strained, it has a higher vibrational energy. The vibrational energy increases by +30 cm-1 when there is more strain. Strain is the energy required to distort a bond from its natural shape. This occurs when the atoms or groups on each end of the bond come too close together or are too far apart from each other.

In addition to strain, conjugation, neighboring atoms, mass of the atoms, bond strength, and other factors affect the vibrational energy of a bond in IR spectroscopy. In summary, stretching frequency is a measure of the bond's stiffness, which is affected by various factors such as conjugation, neighboring atoms, bond strength, etc.

When a bond is conjugated, the vibrational frequency decreases, and when a molecule is strained, the vibrational energy increases.

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Answer:

It would be $13 as the original bill

But the correcy answer is D  

Step-by-step explanation:

The solution to the equation 91 = 29^x is approximately x ≈ 1.08.

To solve for x in equation 91 = 29^x, we need to isolate the variable x. Here's the step-by-step process:

Add 150 to both sides of the equation to get rid of the constant term:

91 + 150 = 29^x + 150

Simplify the equation:

241 = 29^x + 150

Subtract 150 from both sides:

241 - 150 = 29^x

Simplify further:

91 = 29^x

Now, we can solve for x by taking the logarithm of both sides of the equation with base 29. Using the logarithm property log_b(a^c) = c * log_b(a), we have:

log_29(91) = x

Using a calculator or logarithm table, we can find that log_29(91) ≈ 1.08.

Therefore, the solution to the equation 91 = 29^x is approximately x ≈ 1.08.

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If the sequence is geometric, the common ratio 2:1.

In mathematics, an Sequence is an enumerated collection of objects in which repetition is allowed and in case order. Like a collection, it contains members (also called elements or items). The number of elements (possibly infinite) is called the length of the array. Unlike sets, the same item can appear multiple times at different positions in the sequence, and unlike sets, order matters. Formally, a sequence can be defined in terms of the natural numbers (positions of elements in the sequence) and the elements at each position.

The concept of series can be generalized as a family of indices, defined in terms of any set of indices.

According to the Question:

Given GP is 18,9,0,-9.

Common ratio =  second number/ first number

​                         =  18/9

                       ​ = 2

​So, the common ratio is  2:1

​

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This inequality represents that the weight of Duri's backpack is w < 45

Given that

Weight = Less than 45 pounds

We can use the inequality symbol to represent Duri's weight limit as follows:

w < 45

This inequality states that the weight of Duri's backpack, represented by w, must be less than 45 pounds.

Any weight value for w that satisfies this inequality is within Duri's weight limit and can be carried in their backpack.

For example, if Duri's backpack weighs 30 pounds, then w = 30 satisfies the inequality w < 45, so Duri can carry this weight.

However, if the backpack weighs 50 pounds, then w = 50 does not satisfy the inequality w < 45, so Duri cannot carry this weight.

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Answer

put 1 on top and exo on bottom

Step-by-step explanation:

Answer:

8.66

Step-by-step explanation:

because when you know the long leg you multiply 3 square root by the long leg in this case 5

The concept of mathematical harmony was most directly incorporated in the Parthenon in the use of columns.

The term harmony has to do with tunes that are concordant and make meaning to the ears. The search for patterns and sequences is what introduced harmony to mathematics.

Hence, the concept of mathematical harmony was most directly incorporated in the Parthenon in the use of columns.

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1 solution: (-1,-3)

1) Since we are going to solve these systems graphically, let's begin by setting one pair of t-tables:

b) 2x-y=1, y=-3

2x-y=1 ⇒-y= 1 -2x ⇒ y=2x-1

Now, let's plot those points and trace one increasing line for the first one, and one horizontal line for the constant function y=-3

2) Plotting that system, we can tell the solution is the common point to both equations:

Thus, the answer is (-1,-3)

Answer:

$470

Step-by-step explanation:

Add all the amounts given.

200+140+130=470

They spent $470 that day.

Hope this helps!

If not, I am sorry.

Answer:

470

Step-by-step explanation:

140+130+200= 470

They said that day, which means all together. So we add.

140 ml of Ensure
To prepare a tube feeding of Ensure 280 ml (50% solution), the nurse should use 140 ml of Ensure. Here's the explanation: Given: Ensure is available in a 240 ml can.

The required amount of Ensure is 280 ml (50% solution). Formula: To calculate the number of milliliters of Ensure to be used, we will use the formula: percent strength (as a decimal) × volume required ÷ percent strength in stock = volume to be administered Solution: Since Ensure is available in a 240 ml can, we will use that as our percentage strength in stock. Now we'll plug in the values:0.5 × 280 ÷ 1 = 140 ml Therefore, the nurse should use 140 ml of Ensure to prepare the feeding.

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The pathway for nociceptors (pain) and thermoreceptors (temperature) that travels up the contralateral side of the spinal column is known as the "spinothalamic tract."

The spinothalamic tract is a major pathway in the nervous system that carries sensory information related to pain and temperature from the body to the brain. It consists of a bundle of nerve fibers that originate in the spinal cord and ascend towards the thalamus, a region in the brain responsible for relaying sensory information.

In the case of nociceptors (pain) and thermoreceptors (temperature), the sensory signals are detected by specialized receptors in the peripheral nervous system, such as the skin, and are then transmitted to the spinal cord via sensory neurons. These sensory neurons cross over to the opposite side of the spinal cord shortly after entering, a process known as decussation. Once the sensory signals have crossed over, they ascend through the spinothalamic tract on the contralateral (opposite) side of the spinal column.

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According to the conversation we can infer that the information focused on the conversation of two people; one of them is studing for an exam.

To identify what is the conversation about we have to consider who is talking and what are the ideas that they share. In this case, we can infer that the main idea of this conversation is that one of them is studying for an exam this week.

Also, the second person is apologizing because he considered that he is distracting the other person. So, the correc information about de conversation is a short conversation about study.

Note: This question is incomplete. Here is the complete information:

Conversation:
Hello

Hello, How are you?

I am fine, and you?

i am fine too, What are you doing?

I am studing for an exam this week.

Oh, sorry I won´t distract you.

Don´t worry.

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Answer:

x = 20

Step-by-step explanation:

5x + 9 + 3x + 11 = 180

Combine like terms

8x + 20 = 180

Subtract 20 from both sides

8x = 160

Divide both sides by 8

x = 20

Step-by-step explanation:

there is 1 term

9th degree or degree =9

Answer:

1.

426=2*3*71

576=2*2*2*2*2*2*3*3

Now

L.C.F= 2×3×71*2*2*2*2*2*3=40896

H.C.F=2*3=6.

2.

we have.3+2√5

An irrational number is a number that cannot be expressed as a fraction for any integers.

over here √5 is not expressed as a fraction

So3+2√5 is not rational number.