In an effort to eat healthier, Bridget is tracking her food intake by using an application on her phone. She records what she eats, and then the


application indicates how many calories she has consumed. One Monday, Bridget eats 10 medium strawberries and 8 vanilla wafer cookies as an


after-school snack. The caloric intake from these items is 192 calories. The next day, she eats 20 medium strawberries and 1 vanilla wafer cookie as an after-school snack. The caloric intake from these items is 99 calories.



a. Write a system of equations for this problem situation. Let S represent the number of calories in one strawberry and let W represent the number of calories in one vanilla wafer cookie.



The equation _____ represents the calories Bridget ate on Monday and the equation _____ represents the calories she ate the next day.



b. Solve the system of equations using the substitution method. Check your work.



The number of calories in each strawberry is ____


And the number of calories in each vanilla wafer cookie is ____. The solution is ____.



PLEASE HELP ME

The area of the largest rectangle with lower base on the x-axis and upper vertices on the curve y=12−x^2 is 72 square units.

To find the area of the rectangle, we need to maximize its area. The base of the rectangle is the distance between the x-intercepts of the curve y=12−x^2, which are x= -sqrt(12) and x= sqrt(12).

Let the height of the rectangle be y. Then, the area A of the rectangle is given by:

A = (upper base) * (height) = 2sqrt(12) * y

The curve y=12−x^2 is symmetric about the y-axis. Therefore, the maximum value of y occurs at the midpoint of the line segment connecting the two x-intercepts. The midpoint is (0,6).

Thus, the maximum height y of the rectangle is y = 12 - 0^2 = 12.

Therefore, the area of the largest rectangle is:

A = 2sqrt(12) * 12 = 24sqrt(12) ≈ 72

Hence, the area of the largest rectangle with lower base on the x-axis and upper vertices on the curve y=12−x^2 is approximately 72 square units.

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Answer:

answer is 3500.

answer is 3500

answer is 3500

b. Linear programming model is the correct option.

A linear programming model is a mathematical technique used to find the best outcome in a given set of constraints. In this case, Manders Manufacturing Corporation is trying to determine the optimal product mix for its two products, metal (M) and scrap metal (S), based on certain constraints. The objective is to maximize the profit, represented by the function Z = $30M + $70S.

The constraints are represented by the inequalities:

3M + 2S ≤ 15

2M + 4S ≤ 18

These constraints define the limitations on the production of metal and scrap metal. The model aims to find values of M and S that satisfy these constraints while maximizing the objective function.

Using linear programming techniques, the corporation can solve this model to find the optimal values for M and S that will maximize their profit. This approach allows them to make data-driven decisions and allocate their resources efficiently. By formulating the problem as a linear programming model, Manders Manufacturing Corporation can make informed choices about the optimal product mix to achieve their business objectives.

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Answer:

2

Step-by-step explanation:

one apple and another equals to 2.

Answer: 11

Step-by-step explanation: you put one and one together lol

Answer:

(4,-1) is the answer

Step-by-step explanation:

The value of (x,y) is (1,4)

Rotation through 270° anticlockwise direction;

when point P is rotated than

P(x,y) ----------> P' ( y,-x)

A (1,4)----------> A' (4,-1)

Answer:

The answer is 3x3x3x3

Step-by-step explanation:

Reason: The 4 on top is an exponent. That exponent shows how many 3's you need to put. You need to put 4 3's, so 3x3x3x3

If the price-elasticity of demand for chips is 0.75, then a 20 percent increase in price would result in a 15 percent decrease in the demand quantity.

As per the question statement, the price-elasticity of demand for chips is 0.75 and there is a 20 percent increase in price.

We are required to calculate the resulting decrease in the demand quantity by percent, based on the conditions mentioned in the statement above.

Here, given Price-Elasticity of Demand \((E_{d})\) = 0.75

Also given the percent increase in price = 20

Now, we know that,

\((E_{d})\) = [(Percentage change in quantity demanded)/(Percentage change in price]

Or, [0.75 = (x/20)]...[Assuming "Percentage change in quantity demanded" to be "x"]

Or, [x = (20 * 0.75)]

Or, [x = 15]

That is, If the price-elasticity of demand for chips is 0.75, then a 20 percent increase in price would result in a 15 percent decrease in the demand quantity.

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\(▪▪▪▪▪▪▪▪▪▪▪▪▪  {\huge\mathfrak{Answer}}▪▪▪▪▪▪▪▪▪▪▪▪▪▪\)

The equivalent value is ~

\( \boxed{12}\)

\( \large \boxed{ \mathfrak{Step\:\: By\:\:Step\:\:Explanation}}\)

Let's solve ~

Answer:

see explanation

Step-by-step explanation:

Given

\(\frac{x}{7}\) + 2y = 6

Multiply through by 7 to clear the fraction

x + 14y = 42 ( subtract 14y from both sides )

x = 42 - 14y

Solution:

Given:

The domain of a function is the set of input values for which the function is defined.

The function will be undefined when the denominator is 0.

Hence, we test for singularity or undefined points.

Thus, the domain will exist at all other values except the singularity or undefined point.

Hence, the domain is;

Thus, the final answer is;

OPTION D is correct

Given:

One of the angle of a triangle is 104°.

The objective is to find the missing angle x.

If two sides of a triangle are equal, then it is an isosceles triangle.

In an isosceles triangle, the angle formed by the equal sides is also equal.

Then, the value of angle x can be calculated angle sum property of triangle.

Hence, option (A) is the correct answer.

If the expected frequencies are not all equal, we can determine them by using the equation enp for each individual category, where n is the total number of observations and p is the probability for the category. This equation helps us calculate the expected frequency for each category based on their probabilities and the total number of observations.

On the other hand, if the expected frequencies are equal, we can determine them by using the equation n/k, where n is the total number of observations and k is the number of categories. This equation helps us distribute the total number of observations equally among the categories when the expected frequencies are equal.

Expected frequencies do not necessarily have to be whole numbers. They can be decimals or fractions depending on the context and calculations involved.

Goodness-of-fit hypothesis tests can be left-tailed, right-tailed, or two-tailed. These different types of tests allow us to assess whether the observed data significantly deviates from the expected frequencies. The choice of the tail depends on the specific research question and the alternative hypothesis being tested.

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Answer:

9 of 32 invitations were mailed

fraction = 9/32

Decimal = this can be derived by dividing 9 by 32 = 0.28

Percentage = this can be derived by multiplying the decimal by 100 = 28%

Step-by-step explanation:

Number of invitations mailed = 1/3 x (total invitation - invitation mom delivered)

1/3 x (32 - 5)

1/3 x (27)

= 9

This figure can be expressed as a fraction

A fraction is a quantity that is not a whole number. In maths, a fraction usually has a numerator and a denominator.

The numerator is the number above. While the denominator is the number below

an example of a fraction =  \(\frac{1}{2}\)

1 is the numerator while 2 is the denominator

fraction = 9/32

Decimal = this can be derived by dividing 9 by 32 = 0.28

Percentage = this can be derived by multiplying the decimal by 100 = 28%

The Law of Detachment states:

If a ⇒ b is true and a is true, then b is true

if two figures are congruent, their areas are equal.

a = two figures are congruent

b = their areas are equal

We are given b

The area of ABCD equals the area of PQRS.

We cannot use the law of detachment in this case because we need to be given a for the law of detachment to apply.

ABCD could be a rectangle with area 10

PQRS could be a rhombus with area 10

They are not congruent

Answer:

x = 4

Step-by-step explanation:

−6x + 8x − 5 = 3

Step 1: Simplify both sides of the equation.

−6x + 8x −5 = 3

−6x + 8x + −5 = 3

(−6x + 8x) + (−5) =3 (Combine Like Terms)

2x + −5 = 3

2x −5 = 3

Step 2: Add 5 to both sides.

2x−5+5=3+5

2x=8

Step 3: Divide both sides by 2.

2x/2 = 8/2

x = 4

Answer: The index of refraction for the unknown wavelength is approximately 1.355.

Step-by-step explanation:

We can use Snell's law to relate the incident angle and refracted angle to the indices of refraction:

n1 sinθ1 = n2 sinθ2

where n1 and θ1 are the index of refraction and incident angle of the light in air, and n2 and θ2 are the index of refraction and refracted angle of the light in glass. Since the incident angle is 45.00 degrees, we have:

sinθ1 = sin(45.00) = √2/2

Since we know the index of refraction for the 450.0 nm light is 1.482, we can solve for the refracted angle θ2:

1.000 * √2/2 = 1.482 * sinθ2

sinθ2 = 1.000 * √2/2 / 1.482 = 0.4951

θ2 = sin^(-1)(0.4951) = 29.07 degrees

Now, we can use Snell's law again to relate the index of refraction to the refracted angle for the unknown wavelength:

n1 sinθ1 = n3 sinθ3

where n3 is the index of refraction for the unknown wavelength, and θ3 is the refracted angle for the unknown wavelength. We know that θ3 is 0.8000 degrees greater than θ2:

θ3 = θ2 + 0.8000 = 29.87 degrees

Substituting all the known values into Snell's law, we get:

1.000 * √2/2 = n3 * sin(29.87)

n3 = 1.000 * √2/2 / sin(29.87) = 1.355

Therefore, the index of refraction for the unknown wavelength is approximately 1.355.

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The probability of getting one defective component per customer is very low, less than 1/14,254. The probability of getting five defective components to a single customer is also low, 1/14,254. And the probability of getting two defective components to two different customers and the rest of the customers getting none is 10/14,254.

(a) The probability that each customer will receive one defective component is the probability that the five defective components will be drawn in a specific order, divided by the total number of ways the 50 components can be drawn. There are 5049484746 ways that the 50 components can be drawn, and 5! (5 factorial) ways that the defective components can be drawn in a specific order. So the probability is (5!)/(5049484746) = 1/14,254.

(b) The probability that one customer will have drawn five defective components is the probability that all five defective components will be drawn in a row, divided by the total number of ways the 50 components can be drawn. There are 5049484746 ways that the 50 components can be drawn, and 5! (5 factorial) ways that the defective components can be drawn in a row. So the probability is (1!)/(5049484746) = 1/14,254,

(c) The probability that two customers will receive two defective components each, two none, and the other one, is the probability that the five defective components will be drawn in a specific order and then divided among the five customers in a specific way, divided by the total number of ways the 50 components can be drawn. The number of ways to divide the defective components among the customers is 5!/(2!2!1!) = 10. There are 5049484746 ways that the 50 components can be drawn, and 5! (5 factorial) ways that the defective components can be drawn in a specific order, so the probability is (105!)/(50494847*46) = 10/14,254.

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The weight of a kilogram is 2.20462262185 pounds.

14 kilos equals 30.86446653 pounds (14 x 2.20462262185).

14 kilos are therefore equivalent to 30.86 pounds.

Thirty-one and 0/7 pounds are equal to fourteen kilos. Understanding the conversion factor—1 kilogramme is equal to 2.20462262185 pounds—will help you figure out the solution. The formula is 14 x 2.20462262185 = 30.86446653 pounds to convert 14 kilogrammes to pounds. The answer, when rounded to the nearest hundredth, is 30.86 pounds. 14 kilos are therefore equivalent to 30.86 pounds.

It's crucial to remember that pounds are a unit of force and kilogrammes are a unit of mass. Thus, it is crucial to guarantee that the conversion is made between the appropriate units. The International System of Units provides a conversion of 1 kilogramme to 2.20462262185 pounds (SI). As a result, it is the most trustworthy method for converting between the two units .In conclusion, 14 kilogrammes, rounded to the closest hundredth, is equivalent to 31.07 pounds, or 30.86 pounds. This can be found by multiplying 14 by the conversion factor of 2.20462262185 pounds per kilogramme.

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To sketch the region in the plane consisting of points whose polar coordinates satisfy the conditions \(1 < r \leq 2\) and \(\frac{3}{4} \leq \theta \leq \frac{5}{4}\), we can visualize the region as follows:

1. Start by drawing a circle with radius 1. This represents the condition \(r > 1\).

2. Inside the circle, draw another circle with radius 2. This represents the condition \(r \leq 2\).

3. Now, mark the angle \(\theta = \frac{3}{4}\) on the circle with radius 1, and mark the angle \(\theta = \frac{5}{4}\) on the circle with radius 2.

4. Shade the region between the two angles \(\frac{3}{4}\) and \(\frac{5}{4}\) on both circles.

The resulting sketch should show a shaded annular region between the two circles, with angles \(\frac{3}{4}\) and \(\frac{5}{4}\) marked on the respective circles. This annular region represents the set of points whose polar coordinates satisfy the given conditions.

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Answer:

no, because for each input, there is not exactly one output.

Step-by-step explanation:

the relation is not a function because the input 0 has multiple outputs (1-to-many means that the relation is not a function).

Answer:

-6x²+11x-4

Step-by-step explanation:

Apply the distributive property by multiplying each term of -3x+4 by each term of 2x-1

-6x²+3x+8x-4

Answer:

Part A: 4           Part B: every day the amount of people that know are multiplied by 4.

Step-by-step explanation:

Answer:

5<8

Step-by-step explanation:

A) ) To compute f '(a) algebraically, we need to find the derivative of f(x) and then evaluate it at x = a.

f '(-5) = -6
b) \(f '(x) = 8x^3 + 6x^2 - 0\\So, f '(x) = 8x^3 + 6x^2\)
c) the derivative of y with respect to x is 0.
dy/dx = 0
d) To find the derivative of f(x), we apply the power rule and chain rule.  \(f '(x) = 3/x^{0.5} + 3/x^{1.5}\)

A) To compute f '(a) algebraically, we need to find the derivative of f(x) and then evaluate it at x = a.
f(x) = −6x + 7
f '(x) = -6 (by power rule for derivatives)
f '(-5) = -6

B) To use the shortcut rules to mentally calculate the derivative of f(x), we apply the power rule and constant multiple rule.
\(f(x) = 2x^4 + 2x^3 - 2\\f '(x) = 8x^3 + 6x^2\)
(Note that the derivative of a constant is 0.)
\(f '(x) = 8x^3 + 6x^2 - 0\\So, f '(x) = 8x^3 + 6x^2\)

C) To obtain the derivative dy/dx, we need to recognize that y is a constant function (always equal to 13). Therefore, the derivative of y with respect to x is 0.
dy/dx = 0

D) To find the derivative of f(x), we apply the power rule and chain rule.
\(f(x) = 6x^{0.5} + 3x^{-0.5}\\f '(x) = 3x^{-0.5} + (6)(0.5)x^{(-0.5-1)}\\f '(x) = 3x^{-0.5} + 3x^{(-1.5)}\)
(Note that we simplified the second term using negative exponent rules.)
So, \(f '(x) = 3/x^{0.5} + 3/x^{1.5}\)

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19.8% of the molecules are in the upper energy level and 80.2% are in the lower energy level. Therefore, the upper energy level is less populated than the lower energy level.

The population of molecules in each energy level depends on the temperature, the energy difference between the levels, and the number of molecules in the system. The Boltzmann distribution gives us the relative populations of the molecules in each energy level as:

n1/n2 = e^(-ΔE/kT)

where n1 and n2 are the populations of the upper and lower energy levels, respectively, ΔE is the energy difference between the two levels, k is the Boltzmann constant, and T is the temperature in Kelvin.

Substituting the given values, we get:

n1/n2 = e^(-2.0x10^-22/(1.38x10^-23 x 298))

n1/n2 = 0.198 = 19.8%

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Total stockholders’ equity 7,800,000

Statement of stockholders’ equity for CC for the year ended December 31, 2012:Particulars Amount ($)
Common Stock 100,000

Additional Paid-in Capital 4,100,000
Retained Earnings (Opening Balance) 3,000,000
Add: Net Income for the year ended December 31, 2012 800,000
Total retained earnings 3,800,000

Less: Cash Dividend Declared on July 1 and paid on July 31 (200,000)
Retained earnings (Closing balance) 3,600,000
Total stockholders’ equity 7,800,000

Explanation:The given information is as follows:Common Stock on January 1, 2012 = $100,000Additional Paid-in Capital on January 1, 2012 = $4,100,000

Retained Earnings on January 1, 2012 = $3,000,000Net Income for the year ended December 31, 2012 = $800,000Cash Dividend Declared on July 1 and paid on July 31 = $200,000

To prepare the statement of stockholders’ equity for the year ended December 31, 2012, we will begin by preparing the opening balances of each of the equity accounts. We will then add the net income to the retained earnings account.

The closing balance for retained earnings is then computed by subtracting the cash dividend declared and paid from the total retained earnings. Finally, the total stockholders' equity is calculated by adding the balances of all the equity accounts.

Calculations:Opening balance of common stock = $100,000

Opening balance of additional paid-in capital = $4,100,000

Opening balance of retained earnings = $3,000,000

Net Income for the year ended December 31, 2012 = $800,000

Retained earnings (Opening Balance) = $3,000,000

Add: Net Income for the year ended December 31, 2012 = $800,000

Total retained earnings = $3,800,000Less: Cash Dividend Declared on July 1 and paid on July 31 = $200,000Retained earnings (Closing balance) = $3,600,000

Total stockholders’ equity = Common Stock + Additional Paid-in Capital + Retained Earnings (Closing balance) = $100,000 + $4,100,000 + $3,600,000 = $7,800,000

Therefore, the statement of stockholders’ equity for CC for the year ended December 31, 2012, is as follows:Particulars Amount ($)
Common Stock 100,000
Additional Paid-in Capital 4,100,000

Retained Earnings (Opening Balance) 3,000,000
Add: Net Income for the year ended December 31, 2012 800,000
Total retained earnings 3,800,000

Less: Cash Dividend Declared on July 1 and paid on July 31 (200,000)
Retained earnings (Closing balance) 3,600,000
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Answer:

Step-by-step explanation:

56