A professor is looking at how many calories is in a Big Mac so he looks at how much
water the big mac can boil. The 240 g big mac boiled in hot water at 130 °C. If the Big
Mac has a specific heat of 4.18 J/g°C what is the amount of heat added to the water?

Step-by-step explanation:

ABCD is a quadrilateral triangle,where AD=BC and <DAB =<CBA.

In ∆ABD and ∆BAC

•AD=BC. (given)

•<DAB=<CBA (given)

•AB=BA. (common side)

Therefore, ∆ABD ≌ ΔBAC. {SAS congruence rule}

The equation that represents a hyperbola with a center at (0, 0), a vertex at (−48, 0), and a focus at (50, 0) is (x^2 / 48^2) - (y^2 / b^2) = 1.

A hyperbola is a type of conic section with two branches that are symmetric to the x-axis and y-axis. The center of the hyperbola is given as (0, 0), which means the x-axis and y-axis intersect at the center. The vertex is given as (-48, 0), which is on the x-axis. This means that the hyperbola opens horizontally.

The standard form equation for a hyperbola with a horizontal transverse axis is (x^2 / a^2) - (y^2 / b^2) = 1, where a represents the distance from the center to the vertex, and b represents the distance from the center to the foci.

In this case, since the vertex is at (-48, 0), a = 48. The focus is given as (50, 0), which is 2 units to the right of the center. Therefore, c = 2. The relationship between a, b, and c for a hyperbola is given by the equation c^2 = a^2 + b^2.

Substituting the values into the equation, we have:
(2^2) = (48^2) + (b^2)
4 = 2304 + b^2
b^2 = -2300

Since b^2 is negative, this hyperbola does not exist. There is no equation that represents a hyperbola with the given conditions.

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Answer:

P=22.6, T=67.4

Step-by-step explanation:

\(sin(P)=\frac{5}{13}\\ P= 22.6\\\\tan(T)=\frac{12}{5}\\ T=67.4\\\\cos(T)=\frac{5}{13} \\T=67.4\)

We cannot conclude that the earth science book has more words per page than the math book based on the mean alone.

Based on the data provided, it is not a valid inference to conclude that the earth science book has more words per page than the math book just because the mean number of words on each page in the earth science book is greater than the mean number of words on each page in the math book.

Firstly, the median number of words on each page in the math book is actually higher than the median for the earth science book (44 vs 41), which suggests that there may be some outliers or extreme values in the earth science book that are pulling the mean up.

Secondly, there is a much larger mean absolute deviation (MAD) for the earth science book (9.2) compared to the MAD for the math book (1.9). This indicates that the data points in the earth science book are much more spread out and variable than in the math book, further suggesting that the mean may not be a reliable measure of central tendency for this dataset.

Therefore, we cannot conclude that the earth science book has more words per page than the math book based on the mean alone.

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Answer:

mean   (1/6){92 + 97 + 53 + 90 + 95 + 98}

= 87.5

variance (1/6){(92-87.5)^2 + (97-87.5)^2 + (53-87.5)^2 + (90-87.5)^2 + (95-87.5)^2 + (98-87.5)^2}

= 245.6

standard deviation   √{1/6*[(92-87.5)^2 + (97-87.5)^2 + (53-87.5)^2 + (90-87.5)^2 + (95-87.5)^2 + (98-87.5)^2]}

= 15.7

To find the probability that exactly 15 defective components are produced, with exactly 10 of them being repairable, we can use the concept of the Poisson distribution and the probability of repairability.

Step 1: Calculate the probability of producing exactly 15 defective components.
Using the Poisson distribution formula, we can plug in the mean (19) and the desired value (15) to calculate this probability:
\(P(X = 15) = (e^(-19) * 19^15) / 15!\)

Step 2: Calculate the probability of 10 out of the 15 defective components being repairable.
Given that each defective component has a probability of 0.62 of being repairable, we can calculate the probability of 10 being repairable out of the 15 defective components using the binomial distribution formula:
\(P(X = 10) = (15 choose 10) * (0.62^10) * (0.38^5)\)

Step 3: Multiply the probabilities from Step 1 and Step 2 to get the desired probability:
\(P(X = 15 and X = 10) = P(X = 15) * P(X = 10)\)

Alternatively, we can directly calculate the probability that 15 defective components are produced and 10 out of the 15 are repairable:
\(P(X = 15 and X = 10) = (e^(-19) * 19^15) / 15! * (15 choose 10) * (0.62^10) * (0.38^5)\)

Note: To obtain the actual numerical value of the probability, you will need to substitute the values into the formulas and perform the calculations.

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a- The probability that exactly 15 defective components are produced is approximately 0.0310.
b- The probability that exactly 10 of the 15 defective components are repairable is approximately 0.1064.
c- The probability that exactly 15 defective components are produced and 10 of them are repairable is approximately 0.0033.

The probability that exactly 15 defective components are produced, with exactly 10 of them being repairable, can be calculated using the Poisson distribution and the given information.

The Poisson distribution is used to model the number of events occurring in a fixed interval of time or space, given the average rate of occurrence. In this case, the average rate of defective components produced by the process is 19.

To calculate the probability, we need to use the formula for the Poisson distribution:

\(\[ P(X = k) = \frac{e^{-\lambda} \lambda^k}{k!} \]\)

where P(X = k) is the probability of exactly k events occurring, λ is the average rate of occurrence, e is the base of the natural logarithm (approximately 2.71828), and k! represents the factorial of k.

First, let's calculate the probability that exactly 15 defective components are produced:

\(\[ P(X = 15) = \frac{e^{-19} \cdot 19^{15}}{15!} \]\)

To simplify the calculation, we can use a calculator or software that can evaluate exponentials and factorials. The result is approximately 0.0310.

Next, let's calculate the probability that exactly 10 of the 15 defective components are repairable. We can use the binomial distribution, since each defective component has a probability of 0.62 of being repairable.

The formula for the binomial distribution is:

\(\[ P(X = k) = \binom{n}{k} \cdot p^k \cdot (1-p)^{n-k} \]\)

where P(X = k) is the probability of exactly k successes, n is the number of trials, p is the probability of success, and (nCk) represents the number of ways to choose k successes from n trials.

In this case, we have n = 15 (the number of defective components) and p = 0.62 (the probability of a defective component being repairable).

\(\[ P(X = 10) = \binom{15}{10} \cdot 0.62^{10} \cdot (1-0.62)^{15-10} \]\)

Again, using a calculator or software to evaluate combinations, exponents, and subtraction, the result is approximately 0.1064.

Finally, to calculate the probability that exactly 15 defective components are produced and 10 of them are repairable, we can multiply the two probabilities together:

P(15 defective components and 10 repairable) = P(X = 15) * P(X = 10)

Multiplying the two probabilities, we get approximately 0.0033.

So, the probability that exactly 15 defective components are produced, with exactly 10 of them being repairable, is approximately 0.0033.

Please note that the calculations and results provided are based on the information given in the question.

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Answer:

d= 8 t

Step-by-step explanation:

In 1 hour 30 minutes it ran for 12 miles.

So, time t =1.5 hours(Because 1 hour 30 minutes)

distance d =12

We know distance d= rate 'r' * time 't'.

So, using given information , find the rate

12= r *1.5

Divide both sides by 1.5

8=r

So,  equation would be d =8 t.

Where 't' is in hours.

To write the equation that represents the situatio, as y is in function of x, you multiply the rate by the number of minutes (x):

In 7.5 minutes he can type:

 answer

steb by step explanation:

the inflation rate (π) is found to be 3%, the nominal interest rate (i) is calculated as 7%, and if the money growth rate is increased by 2% per year, the new nominal interest rate (i') would be 9%. These calculations provide insights into the relationships between inflation, real interest rates, and monetary policy decisions.

a. To solve for the inflation rate (π), we subtract the real interest rate (r) from the sum of the growth rates of M and Y. In this case, π = (M + Y) - r. Substituting the given values, π = 5% + 2% - 4% = 3%.

b. To solve for the nominal interest rate (i), we add the real interest rate (r) to the inflation rate (π). In this case, i = r + π. Substituting the given values, i = 4% + 3% = 7%.

c. If the Fed increases the money growth rate by 2% per year, it will affect the nominal interest rate. The new nominal interest rate (i') can be calculated using the same formula as in part b: i' = r + π'. However, since the money growth rate (M) increases by 2%, the new inflation rate (π') will be (M + Y) - r = (5% + 2% + 2%) - 4% = 5%. Therefore, the new nominal interest rate (i') would be 4% + 5% = 9%.

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The cost is directly proportional to the lateral area, the silo with the smallest lateral area, which is Silo D, will also have the lowest cost to paint.

To determine which silo will cost the least to paint, we need to calculate the lateral area for each silo using the formula for the lateral area of a cylinder, which is LA = 2πrh.

Silo A:

Radius (r) = 6 feet

Height (h) = 60 feet

Lateral Area (LA) = 2π(6)(60) = 720π square feet

Silo B:

Radius (r) = 8 feet

Height (h) = 50 feet

Lateral Area (LA) = 2π(8)(50) = 800π square feet

Silo C:

Radius (r) = 10 feet

Height (h) = 34 feet

Lateral Area (LA) = 2π(10)(34) = 680π square feet

Silo D:

Radius (r) = 12 feet

Height (h) = 20 feet

Lateral Area (LA) = 2π(12)(20) = 480π square feet

To compare the costs, we multiply the lateral area of each silo by the cost per square foot, which is $1.20:

Cost of Silo A = 720π * $1.20 = 864π dollars

Cost of Silo B = 800π * $1.20 = 960π dollars

Cost of Silo C = 680π * $1.20 = 816π dollars

Cost of Silo D = 480π * $1.20 = 576π dollars

Since the cost is directly proportional to the lateral area, the silo with the smallest lateral area, which is Silo D, will also have the lowest cost to paint.

Therefore, Silo D will cost the least to paint.

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Answer:

10, 8

Step-by-step explanation:

l + w = 18

l*w = 80

8 and 10 works

Answer:

Step-by-step explanation:

To solve this problem, we need to find the Least Common Factor between 15 and 9.

15    9   | 3

5      3  |  3

5      1   |  5

1

So, the Least Common Factor would be 3x3x5 = 45. But, we need a multiple of this number which must be between 150 and 200. So,

45 x 4 = 180.

Therefore, the cable measures 180 meters.

Answer:

the correct option is (B) (x-3)(x+10).

Step-by-step explanation:

To factorize the trinomial x²+7x-30, we need to find two binomials whose product is equal to this trinomial. These binomials will have the form (x+a) and (x+b), where a and b are constants.

To find a and b, we need to look for two numbers whose product is -30 and whose sum is 7. One pair of such numbers is 10 and -3.

Therefore, we can factorize the trinomial as follows:

x²+7x-30 = (x+10)(x-3)

Answer:

a) R(randy)

expression: Randy's brother= 2R

b) 16 years old

c) Randy's sister=R+3

Step-by-step explanation:

because maths

A) R2 = 16

B) Randy's brother is 16 years old.

C) R - 3 = 5

Randy is 8 years old, his brother is 16 years old, and his little sister is 5 years old.

Answer:

  XED is 2

  demand will likely be based on price

Step-by-step explanation:

You want the XED for Coke and Pepsi, given that a decrease in price of Pepsi from $2 to $1.75 per liter causes demand for Coke to fall from 6,000 to 4500 liters.

XED is the abbreviation for "cross-elasticity of demand." It is the ratio of the percentage change in the demand for one good to the percentage change in price for another.

  XED = (∆Q/Q)/(∆P/P)

  XED = ((4500 -6000)/(6000))/((1.75 -2.00)/(2.00)) = (2/6000)(-1500/-0.25)

  XED = 2

The XED is positive for substitute goods, and negative for complementary goods (bought together).

The relatively large positive XED for Coke and Pepsi indicates these brands are nearly interchangeable. Consumers will tend to choose one over the other based on price. Apparently, the price of $1.75 per liter of Pepsi is sufficiently low to cause a switch from Coke.

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Answer:

y(y+27)

Step-by-step explanation:

as per it is y2 it is two times counted so

y(y+27)

True mean of the numbers is 3.5 .

True standard deviation is 1.8708

Given,

The population : 1, 2, 3, 4, 5, 6

The table shows the calculations for population mean and SD. (Image attached below) .

Mean = ΣX/n

ΣX = 21

n = 6

Substitute the values,

Mean = 21/6

Mean = 3.5

Now,

Standard deviation:

σ = √Σ(X - X(mean))²/n

Substituting the values from the table,

= √(17.5) /5

= 1.8708

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Answer: 12

Step-by-step explanation:

x/6 = 2

you have to divide x equally into 6 two times to find x you have to

Times the Denominator and the answer (6·2)

which results in being 12

and to check you plug 12 into x and get this 12/6 = 2

6*2 = 12

so 12 was divided 2 times into 6 and you get 2 = 2  

I know the way I summed it up was lengthy sorry about that.

To find the Taylor series at \(x=0\) for the function \(ln(1+7x^4)\), we can use the formula for the Taylor series expansion of \(ln(1+x)\):

\(\ln(1+x) = x - \frac{{x^2}}{2} + \frac{{x^3}}{3} - \frac{{x^4}}{4} + \ldots\)

Now we substitute \(7x^4\) in place of x in the above formula:

\(\ln(1+7x^4) = 7x^4 - \frac{{(7x^4)^2}}{2} + \frac{{(7x^4)^3}}{3} - \frac{{(7x^4)^4}}{4} + \ldots\)

Simplifying each term, we have:

\(7x^4 - \frac{{49x^8}}{2} + \frac{{343x^{12}}}{3} - \frac{{2401x^{16}}}{4} + \ldots\)

The general expression for the nth term in the Taylor series at \(x=0\) for \(ln(1+7x^4)\) is:

\((-1)^{n+1} \cdot 7^n \cdot x^{4n} / n\)

Therefore, the Taylor series at \(x=0\) for ln\((1+7x^4)\) is:

\(\sum_{n=1}^\infty \left((-1)^{n+1} \cdot \frac{{7^n \cdot x^{4n}}}{n}\right)\)

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Statistical hypothesis testing employs the null and alternate hypotheses.

The alternative hypothesis of a test expresses the prediction of an effect or relationship based on your study, while the null hypothesis of the test does not yet predict an effect or an association between the variables.

A statement that there is no relationship between two variables is called a null hypothesis. Another hypothesis is that the two variables are statistically correlated.

Alternative unilateral (directional) or the bilateral (non-directional) hypotheses are also possible. Simple, complex, true, and false are the four main categories of null hypotheses. If the p-value is greater than the statistical significance level, null hypothesis is preferred.

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Since c must be between 1 and 3, we can eliminate the negative solution and calculate that c = 2.089. Therefore, the answer is 0. The correct option is (A).The Mean Value Theorem states that if a function is continuous on a closed interval and differentiable on the open interval, then there exists at least one point in the open interval where the slope of the tangent line.

Applying this theorem to the function f(x) = 2x³ - 4x² + 1 on the interval [1,3], we know that there exists a value c in (1,3) such that the slope of the tangent line at c is equal to the slope of the secant line between f(1) and f(3).
To find the value of c, we can start by calculating the slope of the secant line:
slope = (f(3) - f(1)) / (3 - 1)
= (2(3)³ - 4(3)² + 1 - 2(1)³ + 4(1)²⁻¹) / 2
= 26
Next, we need to find the derivative of f(x):

f'(x) = 6x² - 8x
Now we can set the slope of the tangent line equal to the slope of the secant line and solve for c:
6c² - 8c = 26
3c² - 4c - 13 = 0
Using the quadratic formula, we get:
c = (4 ± sqrt(4² - 4(3)(-13))) / (2(3))
c = (4 ± sqrt(160)) / 6
c = 2.089 or c = -1.422
Therefore, the answer is 0.

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Answer:

The determined equation for number 321411 factorisation is 3 * 107137.

There is only 1 power of 7 contained in 10.

Students use powers of numbers to solve this problem and learn what is occurring to the numbers as a result.

Students also learn how to divide a seemingly vast and challenging equation into smaller, more accessible components. The pupils should understand that raising 7 to a power only produces a finite number of unit digits. Furthermore, as the power of 7 rises, these particular numbers "circle round." 7, 9, 3, and 1 make up this cycle.

The digit in the tens place is the same.

The total number of times we multiply a number is known as its exponent or power. For instance, 2 to the power 3 denotes a 3x3 multiplication of 2.

The largest power of 7 that is less than 10 is 7^1 = 7, therefore there is only 1 power of 7 contained in 10.

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There is only 1 power of 7 contained in 10.

Students use powers of numbers to solve this problem and learn what is occurring to the numbers as a result.

Students also learn how to divide a seemingly vast and challenging equation into smaller, more accessible components. The pupils should understand that raising 7 to a power only produces a finite number of unit digits. Furthermore, as the power of 7 rises, these particular numbers "circle round." 7, 9, 3, and 1 make up this cycle.

The digit in the tens place is the same.

The total number of times we multiply a number is known as its exponent or power. For instance, 2 to the power 3 denotes a 3x3 multiplication of 2.

The largest power of 7 that is less than 10 is 7^1 = 7, therefore there is only 1 power of 7 contained in 10.

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Answer:24.5

Step-by-step explanation:

a^2+ (25)^2 =35^2

a^2 +625=1225

a^2=600

a=24.494897

a=24.5

The population of birds to increase by 50% in 31.25 years.

The differential equation for the population of birds is:

dp/dt = 0.016P

where P is the population of birds and t is time in years.

To obtain the time it takes for the population to increase by 50%, we need to solve for t when P increases by 50%.

Let P0 be the initial population of birds, and P1 be the population after the increase of 50%.

Then we have:

P1 = 1.5P0 (since P increases by 50%)

We can solve for t by integrating the differential equation:

dp/P = 0.016 dt

Integrating both sides, we get:

ln(P) = 0.016t + C

where C is the constant of integration.

To obtain the value of C, we can use the initial condition that the population at t=0 is P0:

ln(P0) = C

Substituting this into the previous equation, we get:

ln(P) = 0.016t + ln(P0)

Taking the exponential of both sides, we get

:P = P0 * e^(0.016t)

Now we can substitute P1 = 1.5P0 and solve for t:

1.5P0 = P0 * e^(0.016t

Dividing both sides by P0, we get:

1.5 = e^(0.016t)

Taking the natural logarithm of both sides, we get:

ln(1.5) = 0.016t

Solving for t, we get:

t = ln(1.5)/0.016

Using a calculator, we get:

t ≈ 31.25 years

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Answer:

The square root of 33 is 5.74456264654

Answer:

5.74456264654

Step-by-step explanation:

Hope its help u

The time that the ball is lower than the building in interval notation is 3 seconds.

It should be noted that from the information, the ball is thrown straight up from the top of a tower that is 280 ft high with an initial velocity of 48 ft/s and the height of the object can be modeled by the equation s(t) = -16t² + 48t + 280.

It should be noted that the height is illustrated as 280 ft.

Therefore, the time that the ball is lower than the building will be:

-16t² + 48t + 280 - 280 = 0

-16t² + 48t = 0

-16t² = -48t

t = -48t / -16t

t = 3 seconds

Therefore, the time that the ball is lower than the building in interval notation is 3 seconds.

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Answer:

d 150 +50x = y

Step-by-step explanation:

Answer:

$51.20

Step-by-step explanation:

36% of 80 is 28.8

80 - 28.8 = 51.2

Formatted properly, the answer is $51.20

Answer:

Step-by-step explanation:

The answer is $51.20!

Hope this helps!