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A 10 1/2-inch candle burns down in 7 hours. If b represents how much of the candle, in inches, has burned away at any time given in hours, t, write a proportional equation for b in terms of t that matches the context.

Using function concepts, it is found that:

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

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

Thus means that:

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The price of a pack of balloons is 4. 39

The price of a pack of party favors is 0. 36

We have that;

Let the cost of balloons be x

Let the cost of party favors by y

From the information given, we have that;

3x + 4y = 14. 63   (1)

2x + 4y = 16. 03  (2)

Now, let's make 'x' the subject from equation (1)

x = 14. 63 - 4y/ 3  (3)

Substitute in equation (2)

3( 14. 63 - 4y/ 3) = 16. 03

expand the bracket

43. 69 - 12y /3 = 16. 03

cross multiply

43. 69 - 12y = 48. 09

collect like terms

- 12y =  - 4. 4

make 'y' the subject

y = 0. 36

substitute in equation (3)

x = 14. 63 - 4(0. 36)/ 3

x = 13. 1/ 3

x = 4. 39

Hence, the prices are 4. 39 and 0. 36 respectively.

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Answer:

You will end up at (-5, -4)

Step-by-step explanation:

you find where (1, -4) is on the graph than from that point move left 6 units.

Answer:

$7 total

Step-by-step explanation:

$5 + $2 = $7

The solution to the quadratic equation is x = negative two-thirds, negative four-fifths. Option C

From the information given, we have that;

15 x squared + 22 x = negative 8

This is represented mathematically as;

15x² + 22x = -8

Equate the quadratic expression to zero, we get;

15x² + 22x + 8 = 0

Find the pair factors of the product of 15 and 8 that sum up to 22. The value is 120

Now, substitute the value into the formula

15x² + 12x + 10x + 8 = 0

Evaluate the equation in pairs, we have;

(15x² + 12x) + (10x + 8) = 0

Factor the common terms

3x(5x + 4) + 2( 5x + 4)= 0

Then, we have;

(3x + 2) (5x + 4) = 0

If 3x + 2 = 0

x = -2/3

If 5x + 4 = 0

x = -4/5

Hence, the values are -2/3 and -4/5

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Answer:

9.8

Step-by-step explanation:

In the first question, the statement "Using logarithmic differentiation we obtain that the derivative of the function y = x² satisfies the equation y = 4x log x + 2x" is true.

In the first question, using logarithmic differentiation on the function y = x², we differentiate both sides, apply the product rule and logarithmic differentiation, and simplify to obtain the equation y = 4x log x + 2x, which is correct.

In the second question, the statement is false. When using logarithmic differentiation on the function y = (1+x²)²(1 + sin x)²/(1-x²), the derivative is calculated correctly, but the equation given is incorrect. The correct equation after logarithmic differentiation should be y' = (4x/(1 + x²)(1 + sin x))(1-x²) - (2x(1+x²)²(1 + sin x)²)/(1-x²)².

In the third question, the product z²w is calculated correctly as 30-10%.

It is important to accurately apply logarithmic differentiation and perform the necessary calculations to determine the derivatives and products correctly.

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According to the given graph, the diameter is 16 feet long, which means the radius is 8 feet.

Let's find the volume of the sphere using the proper formula

Answer:

5.1416

Step-by-step explanation:

L = πr + d = 1 * π + 2 [meter] ≈ 5.1416 [meter]

Answer:

D. y = -4/5x + 10

Step-by-step explanation:

If you graph it, whether that be on paper or typing the equation out on a website so it can do the graphing for you, it's a straight line with a negative slope unlike the other choices. Therefore, it's a linear function. A quick tip is that, usually, a linear function can be easily shown in the form of y = mx + b (slope-intercept form), and that's the exact form y = -4/5x + 10 is in. y being y (dependent variable, or result/output), -4.5 being m which represents the slope, x being x (independent variable, or input), and +10 being b which represents the y-intercept. If the x is in the denominator like in y = 5/x - 3, it's very likely that it's not a linear function.

Answer:

5/11

Step-by-step explanation:

there are 72 boys and 60 girls. that means there are 132 students on total.

60/132 = 5/11

Answer:

5/11

Step-by-step explanation:

Black= 22 b + 17 g

Brown= 4 b + 18 g

Blonde= 25 b + 10 g

Red= 21 b + 15 g

Answer:

2

Step-by-step explanation:

Since rounding to the one place relies on the decimal part, the part to focus on is the .5

becuase anything greater or equal to 5 is rounded up, the answer is 2

1.5 rounded to one decimal place will be 2.

Place value can be defined as the value represented by a digit in a number on the basis of its position in the number.

Given a fraction number 1.5 that needed to be rounded to one decimal place. Since it's at the equidistance from the nearest whole number then we will follow the even number rule.

Rounds towards the nearest neighbor, but if equidistant, it rounds towards the even number. Both 1.5 and 2.5 are rounded to 2

therefore, 1.5 will be 2, when rounded to the nearest tenth.

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The calculated expectation of X is 0.1

From the question, we have the following parameters that can be used in our computation:

P{X = -1}=0.2, P{X = 0} = 0.5, P{X = 1}=0.3

The expectation of X is calculated as

E(x) = ∑xp(x)

So, we have

E(x) = -1 * 0.2 + 0 * 0.5 + 1 * 0.3

Evaluate

E(x) = 0.1

Hence, the expectation of X is 0.1

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In order to determine the sensitivity, if the optimal value of x2  is positive, we know that increasing c2 will increase the optimal solution, while if the optimal value of x2 is negative, we know that decreasing c2 will increase the optimal solution.

To determine the sensitivity of the optimal solution to a change in c2 using the objective function 25x1 c c2x2, we need to perform a sensitivity analysis. This involves finding the range of values for c2 that will not change the optimal solution, as well as the range of values that will change the optimal solution.

Assuming we have a linear programming problem with the objective function 25x1 c c2x2 and constraints, we can use the simplex method to solve the problem and find the optimal solution. Once we have the optimal solution, we can then perform the sensitivity analysis by calculating the shadow price for the constraint involving c2.

The shadow price for a constraint is the amount by which the objective function would increase or decrease with a one-unit increase in the right-hand side of the constraint, while all other variables are held constant at their optimal values. In this case, the constraint involving c2 is the coefficient of x2 in the objective function, so the shadow price for c2 is simply the optimal value of x2.

If the optimal value of x2 is positive, this means that the objective function is sensitive to changes in c2, and that increasing c2 will increase the optimal solution. Conversely, if the optimal value of x2 is negative, this means that the objective function is also sensitive to changes in c2, but that decreasing c2 will increase the optimal solution.

Therefore, to determine the sensitivity of the optimal solution to a change in c2, we need to calculate the optimal value of x2 and determine whether it is positive or negative. If it is positive, we know that increasing c2 will increase the optimal solution, while if it is negative, we know that decreasing c2 will increase the optimal solution.

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Answer:

\( \sqrt {196}\)

Step-by-step explanation:

\(\bigg \{ - 12.6, \: \frac{11}{15}, \: \red{ \boxed{\sqrt{196} }}, \: \: 0 \bigg\}\)

The missing value in the set will be √196.

What is Rational number ?

In mathematics, a rational number is any number that can be written as a fraction, in which the numerator (the top number) and the denominator (the bottom number) are both integers, and in which the numerator is not equal to zero. In other words which can be written in p/q form.

Here, the number given are 8π, √196, 14.32641..., √105

if we consider one by one the above numbers except √196 all are irrational numbers that is cannot be written in p/q form.

Therefore, the missing value in the set will be √196.

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Answer:

Step-by-step explanation:

-9

As k(-x) = -k(x), the function k is indeed an odd function. By switching the words in f, we can observe that f(-x) Equals f(x) (x). Hence, f is an even function.

A collection of inputs or one output for each input are referred to as a "function" in this sentence. Simply described, a function is a connection between inputs where each input is connected to exactly one output. Each function has a domain, codomain, or range.

1.The function k is an odd function.

A function is odd if f(-x) = -f(x) for all x. In the case of function k, we have:

k(-x) = 2 - 1(-x) = 1 + 2x

k(x) = 2 - 1(x) = 1 + 2x

Therefore, k(-x) = -k(x), and the function is odd.

2.The function f is an even function.

A function is even if f(-x) = f(x) for all x. In the case of function f, we have:

f(-x) = 3^(-x) + 3^x

f(x) = 3^x + 3^(-x)

We can see that f(-x) = f(x) by swapping the terms in f(x). Therefore, f is an even function.

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The calculation for correctly rounded 20.0030 - 0.491 g is as follows:

20.0030
- 0.491
= 19.5120

To correctly round this answer, we need to consider the significant figures of the original values. The value 20.0030 has five significant figures, while 0.491 has only three. Therefore, the answer should be rounded to three significant figures, which gives us:

19.5 g

When subtracting values with different significant figures, the answer should be rounded to the least number of significant figures in either value. In this case, the value 0.491 has only three significant figures, so the answer should be rounded to three significant figures.

The correctly rounded answer for 20.0030 - 0.491 g is 19.5 g. It is important to consider the significant figures when rounding the answer, as this ensures that the result is accurate and precise.

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Answer:

6.00 %

Step-by-step explanation:

205.00 × 0.060= 12.3

205.00 + 12.3= $217.30

Answer:

15*10^15

Step-by-step explanation:

5*10^6= 5*1,000,000

5*1,000,000=5,000,000

3*10^9=3*1,000,000,000=3,000,000,000

5,000,000*3,000,000,000=15,000,000,000,000,000

15*10^15=15,000,000,000,000,000

Hope this helps

Answer:

0

Step-by-step explanation:

its a negative rational number

The solution involves calculating the likelihood function, maximizing it, and using the estimated value to find the probability of no dropped connections in the next two calls.

(a) To find the maximum likelihood estimate of λ, the mean number of dropped connections per call, we need to use the Poisson distribution to calculate the likelihood function L(λ) for the given data. The Poisson distribution is given by:

P(X = x | λ) = (λ^x * e^(-λ)) / x!

where X is the random variable representing the number of dropped connections per call, λ is the parameter representing the mean number of dropped connections per call, and x is the observed number of dropped connections in a call.

The likelihood function for four calls with observed numbers of dropped connections 2, 0, 3, and 1 can be expressed as:

L(λ) = P(X = 2 | λ) * P(X = 0 | λ) * P(X = 3 | λ) * P(X = 1 | λ)

= (λ^2 * e^(-λ)) / 2! * (e^(-λ)) / 0! * (λ^3 * e^(-λ)) / 3! * (λ^1 * e^(-λ)) / 1!

= (λ^6 * e^(-4λ)) / 6

Taking the derivative of L(λ) with respect to λ, setting it equal to zero, and solving for λ.

d/dλ [L(λ)] = d/dλ [(λ^6 * e^(-4λ)) / 6]

= [(6λ^5 * e^(-4λ) - 4λ^6 * e^(-4λ)) / 6]

Setting this derivative equal to zero, we get:

2λ - 3λ^2 = 0

λ = 0 or λ = 2/3

Since λ = 0 is not a valid solution for a Poisson distribution, the maximum likelihood estimate of λ is λ = 2/3.

Therefore, the maximum likelihood estimate of the mean number of dropped connections per call is 2/3.

(b) To obtain the maximum likelihood estimate that the next two calls will be completed without any accidental drops, we can use the estimated value of λ = 2/3 to calculate the probability of no dropped connections in each of the next two calls, using the Poisson distribution:

P(X = 0 | λ = 2/3) = (2/3)^0 * e^(-2/3) / 0! = e^(-2/3) ≈ 0.5134

P(both calls have no drops | λ = 2/3) = P(X = 0 | λ = 2/3)^2 ≈ 0.2637

Therefore, the maximum likelihood estimate that the next two calls will be completed without any accidental drops is approximately 0.2637.

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Answer:

Step-by-step explanation:

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

The factors of 96 are 1,2,3,4,6,8,12,16,24,32,48,96

The Greatest Common Factor (GCF) for 42 and 96

(Notation Form) (42,96): is 6

6

the factors of 42 and 96 are 1,2,3,6,7, 14,21,42

1,2,3,4,6,8,12,16,24,32,48,96

Answer:

\( 4,220.16 \: {units}^{3} \)

Step-by-step explanation:

Diameter of cone = 24 units

Radius of cone (r) = 24/2 = 12 units

Height of cone (h) = 28 units

\(V_{cone} = \frac{1}{3} \pi {r}^{2}h \\ \\ = \frac{1}{ 3} \times 3.14 \times {(12)}^{2} \times 28 \\ \\ = \frac{1}{3} \times 3.14 \times 144 \times 28 \\ \\ = 3.14 \times 1,344 \\ \\ = 4,220.16\: {units}^{3} \)

To determine the probability of choosing a fruit snack and then choosing a granola bar, assuming each snack is chosen independently and with replacement, we multiply the probabilities of each event.

Let's assume the probability of choosing a fruit snack is 0.6 (or 60%) and the probability of choosing a granola bar is 0.4 (or 40%).

The probability of choosing a fruit snack and then choosing a granola bar is:

P(Fruit snack and Granola bar) = P(Fruit snack) * P(Granola bar)

                              = 0.6 * 0.4

                              = 0.24

Therefore, the best probability that she chooses a fruit snack, puts it back, and then chooses a granola bar is 0.24, or 24%.

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Answer:

46

Step-by-step explanation:

length x width x height

7 x 5 x 3

Answer: surface area = 142

Volume = 105

* make sure to add labels (units^2, etc.)

Step-by-step explanation:

Area = length x height

Volume = length x width x height

Answer:

THERE IS NO SIMPLEST FORM OMG THIS IS SO HARD. I'M EINSTEINS GREAT NEICE AND THIS IS STILL HARD

Step-by-step explanation:

Answer:

The big container holds 60 gallons

The small container holds 40 gallons

Step-by-step explanation:

If the small container held 40 gallons of gasoline then double that would be 80 gallons and 20 gallons less than that would be 60 gallons.