In a survey, the ratio of students who prefer popcorn to potato chips is 3 to 4. If the number of the students surveyed who prefer popcorn is 360, how many preferred potato chips?

Answer:

N/A  (if on delta math leave blank)

Step-by-step explanation:

(3.4905745)=ERROR

Sine cannot be greater than 1.

The given conditions cannot form a triangle, there is no possible value of K.

In trigonometry, the law of sines, sine law, sine formula, or sine rule is an equation relating the lengths of the sides of any triangle to the sines of its angles.

Given that, in a triangle Δ IJK, k = 64 inches, j = 17 inches and ∠J = 68°.

We need to find value of ∠K,

So, using the sine law,

Sin K / k = Sin J / j = Sin I /i

So,

Sin K / k = Sin J / j

Sin K / 64 = Sin 68° / 17

Sin K = 3.5

K = Sin⁻¹(3.5)

K = ERROR

Hence, the given conditions cannot form a triangle, there is no possible value of K.

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A stochastic process X(t) is called a martingale if the expected value of X(t) given all information available up to and including time s is equal to the value of X(s).

Thus, to show that the process X(t):=e^(t/2)cos(W(t)), 0 ≤ t ≤ T is a martingale w.r.t. any filtration for Brownian motion, we need to prove that E(X(t)|F_s) = X(s), where F_s is the sigma-algebra of all events up to time s.

As X(t) is of the form e^(t/2)cos(W(t)), we can use Itô's lemma to obtain the differential form:dX = e^(t/2)cos(W(t))dW - 1/2 e^(t/2)sin(W(t))dt

Taking the expectation on both sides of this equation gives:E(dX) = E(e^(t/2)cos(W(t))dW) - 1/2 E(e^(t/2)sin(W(t))dt)Now, as E(dW) = 0 and E(dW^2) = dt, the first term of the right-hand side vanishes.

For the second term, we can use the fact that sin(W(t)) is independent of F_s and therefore can be taken outside the conditional expectation:

E(dX) = - 1/2 E(e^(t/2)sin(W(t)))dt = 0Since dX is zero-mean, it follows that X(t) is a martingale w.r.t. any filtration for Brownian motion.

Now, let's represent X(t) as an Itô process on the interval [0,T]. Applying Itô's lemma to X(t) gives:

dX = e^(t/2)cos(W(t))dW - 1/2 e^(t/2)sin(W(t))dt= dM + 1/2 e^(t/2)sin(W(t))dt

where M is a martingale with M(0) = 0.

Thus, X(t) can be represented as an Itô process on [0,T] of the form:

X(t) = M(t) + ∫₀ᵗ 1/2 e^(s/2)sin(W(s))ds

Hence, we have shown that X(t) is a martingale w.r.t. any filtration for Brownian motion and represented it as an Itô process on any time interval [0,T], T > 0.

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Answer:

the daylilies cost: $5

The roses cost:$3

The tulips cost:$1

Step-by-step explanation:

Answer:

In math, a unit fraction can be defined as a fraction whose numerator is 1. It represents 1 shaded part of all the equal parts of the whole.

Step-by-step explanation:

Answer:

Is it .04

Step-by-step explanation:

Answer:

Step-by-step explanation:

The strength of a linear relationship between two variables is typically measured by the correlation coefficient (r) or the coefficient of determination (r^2). A value of r or r^2 closer to 1 indicates a stronger positive linear relationship, whereas a value closer to -1 indicates a stronger negative linear relationship. A value of r or r^2 closer to 0 indicates a weaker or no linear relationship.

Looking at the given regression equations and their correlation coefficients, the regression with the weakest linear relationship between x and y is Regression 3:

Regression 1: y = -5.8x - 6.5, r = -0.7621

Regression 2: y = 2.4x - 14.7, r = 0.809

Regression 3: y = -7.4x - 17.4, r = -0.233

Regression 4: y = -3.4x - 8.5, r = -0.6121

Regression 3 has the lowest absolute value of r (0.233), indicating the weakest or no linear relationship between x and y. Therefore, Regression 3 represents the weakest linear relationship between x and y among the given options.

Net present value is a measure of profitability. The NPV of an investment is the net cash inflow received over the project's life, less the initial cash outflow, adjusted for the time value of money.

A higher NPV means the project is more lucrative. The profitability index measures the benefit-cost ratio of a project and is calculated by dividing the present value of future cash flows by the initial cash outflow. A profitability index greater than one indicates that the project will be profitable, whereas a profitability index less than one indicates that the project will not be profitable.

Calculation of Net Present Value (NPV) of Project AInitial Outlay = $454,000Net annual cash flows = $68,000Discount Rate = 9%Use the PV of an annuity of $1 table to determine the PV of net cash flows.Using the formula for NPV,NPV of Project A = PV of net cash flows – Initial OutlayNPV of Project A = 68,000 × 7.63930 – 454,000NPV of Project A = $56,201.85Calculation of Profitability Index of Project AProfitability Index of Project A = Present value of future cash flows / Initial OutlayProfitability Index of Project A = 68,000 × 7.63930 / 454,000Profitability Index of Project A = 1.14

Calculation of Net Present Value (NPV) of Project BInitial Outlay = $300,000Net annual cash flows = $47,000Discount Rate = 9%Use the PV of an annuity of $1 table to determine the PV of net cash flows.Using the formula for NPV,NPV of Project B = PV of net cash flows – Initial OutlayNPV of Project B = 47,000 × 6.10338 – 300,000NPV of Project B = $37,100.86Calculation of Profitability Index of Project BProfitability Index of Project B = Present value of future cash flows / Initial OutlayProfitability Index of Project B = 47,000 × 6.10338 / 300,000Profitability Index of Project B = 0.96

The NPV and profitability index calculations show that project A is the better investment since it has a higher NPV and profitability index than project B.

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The expressions that represent the number of hats Tracy has now will be 5j + 10x. Then the correct option is A.

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

Tracy had 5j hats.

Barbara and Claudia each give Tracy an additional 5x hats each.

The number of hats given by Barbara will be 5x.

And the number of hats given by Claudia will be 5x.

Then the expressions that represent the number of hats Tracy has now will be

⇒ 5j + 5x + 5x

⇒ 5j + 10x

Thus, the expressions that represent the number of hats Tracy has now will be 5j + 10x.

Then the correct option is A.

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Answer:

32.7 degrees

Step-by-step explanation:

The total exterior angle of any polygon is 360 degrees

Each exterior angle can be calculated by dividing this total by the number of sides

So we have each measure as 360/n

where n is the number of sides

here, we have n = 11

So we have each exterior angle as:

360/11 = 32.7 degrees

Answer:

40

Step-by-step explanation:

Answer: \(Heyaa!\)

Your Answer Is... 2

Step-by-step explanation:

Simplify the radical by breaking the radicand up into a product of known factors, assuming positive real numbers.

Hopefully this helps you!

- Matthew ~

Answer:

Step-by-step explanation:

Adding the same number to both sides of equation doesn't change the equality.

¹/₉ + t    =   7

+(-¹/₉)        +(-¹/₉)

   t = 7 + (-¹/₉) = 7 - ¹/₉ = 6⁸/₉

addition property of equality

Answer:

Step-by-step explanation:

The circumference equation:

Given:

The circumference is:

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

Circumference of the circle is :

now, here radius (r) = 6 mm, let's find the circumference :

The theorem (A) CPCTC represents the given condition of the triangle.

According to the formula CPCTC, which stands for "corresponding portions of congruent triangles are congruent," if two or more triangles are congruent, their corresponding angles and sides must also be congruent.

When demonstrating the congruence of triangles or other shapes, the term CPCT is employed.

When a student is asked to demonstrate that two angles or two sides are congruent, CPCTC is frequently employed at the end of the proof or close to it.

So, in the given triangle:

The angles are bold and the lines are not bold.

This represents that it is proved first that the angles are congruent.

And through CPCTC, we are concluding that the sides of the triangles are also congruent.

Therefore, the theorem (A) CPCTC represents the given condition of the triangle.

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Multiplicative inverse of 4 doesn't exist in modulo 30, 32, 33, and 34. It exists in modulo 31 and 35.

For a number to have a multiplicative inverse in modulo n, it must be relatively prime to n. Now let's find the multiplicative inverse of 4 modulo 30, 31, 32, 33, 34, and 35. In modulo 30, GCD(4, 30) = 2. Hence, 4 does not have a multiplicative inverse in modulo 30. In modulo 31, 4 and 31 are relatively prime. Therefore, the multiplicative inverse of 4 in modulo 31 is 8. Hence, 4 * 8 = 1 (mod 31). In modulo 32, GCD(4, 32) = 4. Therefore, 4 does not have a multiplicative inverse in modulo 32.

In modulo 33, GCD(4, 33) = 1. However, 33 is not a prime number. Therefore, it is not relatively prime to 4, and 4 does not have a multiplicative inverse in modulo 33.In modulo 34, GCD(4, 34) = 2. Hence, 4 does not have a multiplicative inverse in modulo 34.

In modulo 35, 4 and 35 are relatively prime. Therefore, the multiplicative inverse of 4 in modulo 35 is 9. Hence, 4 * 9 = 1 (mod 35). Therefore, we can conclude that the multiplicative inverse of 4 exists in modulo 31 and 35, and does not exist in modulo 30, 32, 33, and 34.

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Answer:

See below

Step-by-step explanation:

To find the mean, you take each data point, add them together, and divide it by the number of data points.

Problem 1

Mean of High Temperatures = (65+67+54+52+63+69+75)/7 = 445/7 = between 63 and 64

Problem 2

Mean of Low Temperatures = (61+55+37+29+34+42+54)/7 = 312/7 = between 44 and 45

Using percentages we know that Terrel has the best free throw statistics which is 70.83%.

In mathematics, a quantity or ratio known as A% stands for a percentage of 100.

There are several different ways to depict a dimensionless connection between two numbers, including ratios, fractions, and decimals.

To represent percentages, the symbol "%" is typically written after the number.

In mathematics, a percentage is a number or ratio that is expressed as a fraction of 100.

So, in the given situation where we need to get whose statistics are the best.

We need to calculate the percentages in all cases as follows:

Jack: 18/39*100 = 46.15%

Henry: 54%

Terrel: 17/24*100 = 70.83%

Riley: 9/23*100 = 39.13%

Since Terrel has the highest %, so he has the best free throw statistics.

Therefore, using percentages we know that Terrel has the best free throw statistics which is 70.83%.

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Using it's formula, the distance between the points A(13,2) and B(7,10) is of 10 units.

Suppose that we have two points, \((x_1,y_1)\) and \((x_2,y_2)\). The distance between them is given by:

\(D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

In this problem, the points are A(13,2) and B(7,10), hence the distance is given by:

\(D = \sqrt{(13 - 7)^2+(2 - 10)^2}\)

D = sqrt(100)

D = 10 units.

The distance between the points A(13,2) and B(7,10) is of 10 units.

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Answer:

The price per serving is $0.315, therefore, it's less than $0.5

Step-by-step explanation:

In order to calculate the price per serving, we can first calculate the price per cup, this is done by dividing the total value of the box by the number of cups it can serve:

\(price_{cup} = \frac{3.8}{9} = 0.42\)

Since each serving is \(\frac{3}{4}\) of a cup, then it's price has the same proportion and is given by:

\(price_{serving} = \frac{3}{4}*0.42 = 0.315\)

The price per serving is $0.315, therefore, it's less than $0.5

Answer:

2/12

Step-by-step explanation:

a red and blue is two

a die is six

two dice is twelve

2/12=1/6

The range at which Dan's car can go is 3.33 miles

A car's range is the distance it can travel with the current amount of fuel in the tank.

The vehicle calculates the range based on the amount of fuel, how the accelerator and brakes are used, and how quickly the car is travelling.

The range of a car can be measured in the unit of distance.

Therefore the range of a car can be calculated as;

R = distance per gallon/ number of gallon.

Dan's car is 40mpg and has 12 gallons in it's tank.

Therefore it's range = 40/12

= 3.33miles.

therefore the range of Dan's car is 3.33miles

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The altitude of the airplane after 4 minutes of descent, descending at a rate of 172 feet every 30 seconds is 11,109 feet.

The descent rate of the airplane is given as 172 feet every 30 seconds. To calculate the altitude after 4 minutes (240 seconds) of descent, we need to determine the number of descent intervals and subtract the cumulative descent from the initial altitude.

The number of descent intervals in 4 minutes can be calculated as follows:

4 minutes * (60 seconds/1 minute) / (30 seconds/interval) = 8 intervals

Next, we calculate the cumulative descent:

8 intervals * 172 feet/interval = 1,376 feet

Finally, we subtract the cumulative descent from the initial altitude:

12,645 feet - 1,376 feet = 11,109 feet

Therefore, the altitude of the plane after 4 minutes of descent is 11,109 feet.

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The airplane, initially at an altitude of 12,645 feet, descends at a rate of 172 feet every 30 seconds for a total of 4 minutes. This totals a descent of 1376 feet, leaving the airplane at an altitude of 11,269 feet after the 4 minute descent.

The subject of this problem is Mathematics and it involves calculating the new altitude of a descending airplane. The scenario involved is that an airplane, flying at an altitude of 12,645 feet, starts to descend at a rate of 172 feet every 30 seconds. The pilot continues this descent for 4 minutes.

The first step in solving this is to know how many 30-second intervals are in 4 minutes. Since there are 2 intervals per minute, this means there are 8 intervals in 4 minutes. If the plane descends 172 feet per interval, over 8 intervals, it descends a total of 172 feet x 8 = 1376 feet.

The final altitude of the plane would be the original altitude minus the total decline. In this case, it would be 12,645 feet - 1376 feet, which equals 11,269 feet. Therefore, the airplane will be at an altitude of 11,269 feet after 4 minutes of descent.

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Answer: False

Step-by-step explanation:

If t<-3, and t>2, that means that all values less than 3, and all values greater than 2 are true.

In the inequality -3<t<2, only values between -3 and 2 are true, so this means they are not equivalent.

Step-by-step explanation:

t>-3 or t<2

THE STATEMENT ABOVE CONTRADICTS THE GIVEN STATEMENT THEREFORE IT IS FALSE

Answer:

a)  0.356

b)  1.1397

Step-by-step explanation:

a) log₇2

b) log₇ (¹⁴⁷/₁₆)

          log (7)

Answer:

heart

Step-by-step explanation:

Answer:

It would be the heart <3

Step-by-step explanation:

Answer:

4th one

Step-by-step explanation:

18/6=3      3 units on the y-axis / vertical

That's the only one with (-4,-2)

The maximum number of phases that can be in mutual equilibrium in two-component system is 3.

The maximum number of phases that can be in mutual equilibrium in two-component system will be 3. This is known as the Gibbs phase rule, which states that the number of phases that can coexist in equilibrium is given by: F = C - P + 2

where F is the number of degrees of freedom (the maximum number of intensive variables that can be varied independently without changing the number of phases in the system), C is the number of components in the system (in this case, 2), and P is the number of phases.

Substituting C = 2 and F = 0 (since we are considering mutual equilibrium) into the Gibbs phase rule gives:

0 = 2 - P + 2

Simplifying gives:

P = 3

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Using the Bisection method, we need to find solutions accurate to within \(10^{-5}\) for the equations \(x^{2}\)+ 2x - 3 = 0 in the range -2 < x < 2 and x - \(2^{-4}\) = 0 in the range 0 < x < 1.

For the equation \(x^{2}\) + 2x - 3 = 0:

We start with an initial interval [-2, 2] and evaluate the function at the midpoint of the interval. If the function value is close to 0, we consider it as the solution. Otherwise, we narrow down the interval by dividing it in half and selecting the subinterval where the function changes sign. This process is repeated until the desired accuracy is achieved (within \(10^{-5}\)). The number of iterations required will be recorded.

For the equation x - \(2^{-4}\)= 0:

We follow the same steps as above but with the initial interval [0, 1]. Again, we iterate until the desired accuracy is reached and keep track of the number of iterations.

By applying the Bisection method and counting the number of iterations for each equation, we can find solutions accurate to within 10^-5 for both equations and determine the required number of iterations for each case.

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Answer:

See below

Step-by-step explanation:

20 minutes = 1/3 hr

distance / rate = time

x = rate1      x+6 = rate2

39 mi / (  x +     x+6    m/hr ) = 1/3 hr

39/(1/3) = 2 x + 6

x = 55.5 mi/hr       x+6 = 61.5 mi/hr

1000 cubic centimeters would need to be placed in a tub of water to displace 1 Lter of water

Conversion of units simply refers to the method used in determining the equivalent of one unit in relation to another.

From the information given, we have that;

Number of cubic centimeters that would be placed in a tub of water to displace 1 L of water

So, we have that there is 1 liter of water in the tub

In order to displace, you need to put something in that is the same amount

Now, let's convert the units

1 liter = 1000 cubic cm

Hence, you need 1000 cubic cm to displace 1 liter

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