Evaluate the expression: (16 ÷ 4)3 – 6 The solution is _____.

Answer:

- \(\frac{27}{25\\}\)

Step-by-step explanation:

4x−5y=39

for x=3

12 - 5y = 39

-5y = 39 -12

-5y = \(\frac{27}{5\\}\)

-y = \(\frac{27}{25\\}\)

y = - \(\frac{27}{25\\}\) = -1 \(\frac{2}{25\\}\\\)

-27/5 or -5 2/5

Step-by-step explanation:

4x-5y=39 while x=3

4(3)-5y=39 add x into bracket

12-5y=39 result of 4*3

12-5y-12=12-39 substrate non variable number to each side

5y = -27 the result from upper substraction

y= -27/5 the result mixed fraction form -5 2/5

SOLUTION:

Step 1:

In this question, we are given the following:

Step 2:

The details of the solution are as follows:

The sum of interior angles of a polygon is:

CONCLUSION:

The final answer is:

Answer:

2

Step-by-step explanation:

Scale factor tells how much the size of the figure increases or decreases. Part A shows that the larger figure is twice the size of the smaller figure. So, the scale factor of this dilation is 2.

Answer:

The cost of the dryer is $375.

Step-by-step explanation:

We can call the washer "w", and the dryer "d".

w+d=815

w=d+65

Now we solve. We can substitute d+65 in for w.

(d+65)+d=815

2d+65=815

2d=750

d=375

w=d+65

Substitute 375 in for d.

w=375+65

w=440

We can check our work. 375+440=815.

Therefore, the dryer cost $375 (and the washer cost $440, but you don't need to know that for this question.)

Hope this helps! If you have any questions, I'll be happy to answer them :)

The probability that exactly two of the three people selected also travel by train is 4/9

The probability of an event occurring is specified by the ratio of the number of  required outcomes to the number of possible outcomes.

The number of people that travelled from London to Manchester for the conference = 30

Number of people that traveled by train = 15

Number of people that travelled by plane = 9

Number of people that did not travel by travel by either train or plane = 12

Number of people chosen from those that traveled by plane = 3

The probability that two of those selected also traveled by train can be found as follows;

The number of people that traveled by either train of plane = 30 - 12 = 18

The number of people that traveled by plane and train = 15 + 9 - 18 = 6

The binomial probability distribution formula that can be used to find the probability of an event, p, occurring exactly r times is as follows;

P(p) = \(_nC_r\cdot p^r\cdot q^{n-r}\)

Where;

n = Number of people chosen = 3

r = Number of people chosen that also traveled by train = 2

p = Probability that a person chosen also traveled by train = 6/9 = 2/3

q = Probability that a person chosen did not travel by train = 3/9 = 1/3

Therefore;

\(P = _3C_2\times \left(\dfrac{2}{3}\right) ^2\times \left(\dfrac{1}{3} \right)^{3-2} = \dfrac{4}{9}\)

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Answer:

b

Step-by-step explanation:

If increasing the sides of a square field by five feet will increase the area by 245 ft², then the area of the original square is 484 ft².

To find the area of the original square, we can use the following formula:

Area of the original square = x²

where x is the original length of the square field.

Given that the increase in the length and width of the square field is 5 ft, the side length of the new square is (x + 5) ft. Therefore, the area of the new square is (x + 5)² ft².

Given that the area of the new square is 245 ft² more than the area of the smaller square, we can write:

(x + 5)² = 245 + x²

Expanding the left-hand side of the equation and simplifying, we get:

x² + 10x + 25 = 245 + x²

Solving for x, we get:

10x + 25 = 245

x = 22

Plugging x = 22 into the formula, we can find the area of the original square:

Area of the original square = x² = 22² = 484 ft²

Therefore, the area of the original square is 484 ft².

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The probability that the obstetrician has delivered no child with polydactyly is 0.8187.

To find the probability that the obstetrician has delivered no child with polydactyly, we can use the formula:

P(no polydactyly) = \((1 - P(polydactyly))^{number of births}\)

First, we need to find the probability of a child having polydactyly. This is given as 1 in every 500, which can be expressed as a decimal: 1/500 = 0.002.

Next, we find the probability of a child not having polydactyly: 1 - 0.002 = 0.998.

Now, we can find the probability of the obstetrician delivering no child with polydactyly in 100 unrelated and independent births by raising the probability of no polydactyly to the power of the number of births (100):

P(no polydactyly in 100 births) = (0.998)¹⁰⁰ ≈ 0.8187

So, the probability that the obstetrician has delivered no child with polydactyly is approximately 0.8187.

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Here to solve the probability of this sum, it is difficult to say that the probability without no information.

(a)The probability that the team wins the debate with a junior giving the closing argument is 0.083.

(b) To design a simulation to estimate the probability that a sophomore is never selected to give the closing argument in the next 3 debates, one could randomly assign a closing argument speaker for each debate using a table of random digits. The table would have two columns: one for sophomores and one for juniors and seniors. The probability of a sophomore being selected would be 20%, and the probability of a junior or senior being selected would be 80%. The simulation would be run for 3 debates and the number of times a sophomore is never selected would be recorded. This process would be repeated a number of times to estimate the probability of a sophomore never being selected. (e) Based on the dot plot, it appears that there is some evidence that the sophomores were purposely ignored, as there are several simulated sets of 5 debates where a sophomore was not selected to give the closing argument. However, without more information, it is difficult to say for certain if this is enough evidence to support the claim that the sophomores were purposely ignored.

A larger sample size or a more detailed analysis of the simulation results may be needed to make a more convincing determination.

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Answer:

The missing fraction is 6/12

(you can further simplify this but the question requires that you don't do that)

Step-by-step explanation:

To add fractions easily, their denominators should have the same value, so the denominator should be 12,

Then, to get 16 in the numerator, we need to find a number that on adding to 10, gives 16, or,

10 + x = 16

x = 16 - 10

x = 6

So, the numerator should be 6

so we get the fraction, 6/12

We can also solve it in an alternate way,

\(10/12 + x = 16/12\\x = 16/12 - 10/12\\x = (16-10)/12\\x = 6/12\)

Using the distance between two points to find the side lengths, the perimeter of the triangle is of 25.66 units.

The perimeter of a polygon is given by the sum of all the lengths of the outer edges of the figure.

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

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

This formula is derived from the Pythagorean Theorem, as the points form a right triangle in the xy-plane, with the hypotenuse being the distance between them.

Hence the side lengths are given as follows:

Hence the perimeter is given by:

P = 9 + 8.6 + 8.06 = 25.66 units.

The triangle is graphed at the end of the answer.

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Responder:

2,40

Explicación paso a paso:

Dado que:

Dejar :

Tomate = t

Cebolla = n

(2 kilo de t) + (1 kilo de n) = 8.40

(1 kilo de t) + (2 kilo de n) = 7.80

2t + n = 8,40 - - (1)

t + 2n = 7,80 - - (2)

De (2);

t = 7,80 - 2n

Ponga t = 7.80 - 2n en (1)

2 (7,80 - 2n) + n = 8,40

15,6 - 4n + n = 8,40

15,6 - 3n = 8,40

-3n = 8,40 - 15,6

-3n = - 7,2

n = 2,4

t = 7,80 - 2 (2,40)

t = 7,80 - 4,80

t = 3

Por lo tanto, el costo de 1 kilo de cebolla es 2,40

The correct symbol to fill in the blank is " = " so Fraction of equation is 23/5 = 4(3/5).

What is fraction ?

A fraction is a numerical representation of a part of a whole or a ratio between two quantities. It is written as a pair of numbers, one above the other, separated by a horizontal line called a fraction bar.

The number above the fraction bar is called the numerator, which represents the number of parts being considered. The number below the fraction bar is called the denominator, which represents the total number of equal parts that make up the whole.

According to the question:
The expression we're given is:
23/5 ? 4(3/5)

We need to fill in the blank with one of the symbols <, >, or = to make the expression true.

To compare fractions, we can cross-multiply and compare the resulting numerators.

Let's start by simplifying 4(3/5) to an improper fraction:
4(3/5) = (4*5 + 3)/5 = 23/5

So, our expression becomes:

23/5 ? 23/5

To make this expression true, we need to fill in the blank with the symbol =, since 23/5 is equal to 23/5:
23/5 = 4(3/5)

Therefore, the correct symbol to fill in the blank is =.

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Answer:

\(b = 3\)

The value of y triples

Step-by-step explanation:

Given:

\(\begin{array}{cccccc}x & {-2} & {-1} & {0} & {1} & {2} \ \\ y & {\frac{2}{9}} & {\frac{2}{3}} & {2} & {6} & {18} \ \end{array}\)

Required

Determine b value

An exponential equation is:

\(y = ab^x\)

When \(x = 0; y =2\)

So:

\(y = ab^x\)

\(2 = a * b^0\)

\(2 = a\)

\(a = 2\)

When \(x = 2; y = 18\)

So:

\(18 = a * b^2\)

Substitute 2 for a

\(18 = 2 * b^2\)

Divide by 2

\(9 = b^2\)

Take positive square roots of both sides

\(3 = b\)

\(b = 3\)

The derivatives of the given functions with respect to x are as follows:

i) For y = \(ln(x^4 + 3x^2 + 6)\), the derivative is dy/dx = \((4x^3 + 6x)/(x^4 + 3x^2 + 6)\).

This is obtained using the chain rule and the derivative of ln(u) = (1/u)(du/dx).

ii) For y =\(2x - 12x^2 - x +\)4, the derivative is dy/dx = 2 - 24x - 1. This is obtained by taking the derivative of each term separately, as the derivative of a constant is zero and the derivative of \(x^n is nx^(n-1)\).

iii) For y = \(4(x^2 - 4x + 6)^3\), the derivative is dy/dx = 1\(2(x^2 - 4x + 6)^2(2x - 4)\). This is obtained using the chain rule and the power rule, where the derivative of \((u^n) = n(u^{n-1})(du/dx)\).

In summary, the derivative of \(ln(x^4 + 3x^2 + 6)\) with respect to x is \((4x^3 + 6x)/(x^4 + 3x^2 + 6)\). The derivative of \(2x - 12x^2 - x + 4\) with respect to x is 2 - 24x - 1. The derivative of\(4(x^2 - 4x + 6)^3\) with respect to x is \(12(x^2 - 4x + 6)^2(2x - 4)\).

i) The derivative of \(ln(x^4 + 3x^2 + 6\)) is obtained by applying the chain rule. The derivative of ln(u) is (1/u)(du/dx), where \(u = x^4 + 3x^2 + 6\). By finding the derivative of u with respect to x and substituting it into the chain rule formula, we get\((4x^3 + 6x)/(x^4 + 3x^2 + 6)\).

ii) The derivative of \(2x - 12x^2 - x + 4\) is obtained by taking the derivative of each term separately. The derivative of 2x is 2, the derivative of \(-12x^2 is -24x\) (using the power rule), and the derivative of -x is -1. The derivative of a constant term is zero. Combining these derivatives, we get dy/dx = 2 - 24x - 1.

iii) The derivative of \(4(x^2 - 4x + 6)^3\) is obtained using the chain rule and the power rule. We first apply the power rule by multiplying the exponent (3) by the expression inside the parentheses, resulting in \((x^2 - 4x + 6)^2\). Then, using the chain rule, we multiply by the derivative of the expression inside the parentheses, which is 2x - 4. Combining these results, we get dy/dx = \(12(x^2 - 4x + 6)^2(2x - 4).\)

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Answer:

Given that a circle of radius 5 miles has an arc of length 3 miles.

The central angle of the arc can be found using the formula:\(\[\text{Central angle} = \frac{\text{Arc length}}{\text{Radius}}\]\)

Substitute the given values into the formula to get:\(\[\text{Central angle} = \frac{3}{5}\]\)

To get the answer in degrees, multiply by 180/π:\(\[\text{Central angle} = \frac{3}{5} \cdot \frac{180}{\pi}\]\)

Simplify the expression:\(\[\text{Central angle} \approx 34.38^{\circ}\]\)

Therefore, the measure of the central angle that subtends the arc of length 3 miles in a circle of radius 5 miles is approximately 34.38 degrees.

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30-degree is the smallest value of the \(\theta\\\).

If sin(θ) = 1/2 and 0° < θ < 180°, then we know that θ is an acute angle in the first or second quadrant of the unit circle, since sine is positive in those quadrants.

To find the value of θ, we can use the inverse sine function (sin^-1) on both sides of the equation:

\(sin^{-1}(sin(\theta)) = sin{^-1}(1/2)\)

θ = 30° or 150°

Since 0° < θ < 180°, the smaller value of θ is 30°.

Therefore, the smaller value of θ is 30°.

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The horizontal distance along the grid line from the highest grid elevation point to the 97 contour is 52.38 feet.

To solve this problem, we first need to determine the location of the highest grid elevation point on the grid line labeled 96.33 and 97.48.

Let's assume that the highest grid elevation point is located at a distance of x feet from the grid line labeled 96.33. Therefore, the distance from the same point to the grid line labeled 97.48 would be 50 - x feet (as the total length of the grid line is 50 feet).

Now, we need to determine the location of the 97 contour on the same grid line. Let's assume that the 97 contour intersects the grid line at a distance of y feet from the grid line labeled 96.33.

Since the highest grid elevation point is on the same grid line, it must also be on the 97 contour. Therefore, we can set the elevation at the highest point equal to 97 and use this information to solve for x and y.

We can set up two equations based on the information we have:

x² + y² = d² (Equation 1)

x + (50 - x) = y (Equation 2)

where d is the horizontal distance we are trying to find.

We can simplify Equation 2 to:

50 = y

Substituting this into Equation 1, we get:

x² + 50² = d²

Rearranging this equation, we get:

d² = x² + 2500

Now we can substitute 97 for the elevation at the highest point, and solve for x:

(97 - 96.33)/0.01 = x/50

x = 33.5 feet

Substituting this value of x into the equation for d², we get:

d² = (33.5)² + 2500 = 2742.25

Taking the square root of both sides, we get:

d = 52.38 feet (approx.)

Therefore, the horizontal distance along the grid line from the highest grid elevation point to the 97 contour is approximately 52.38 feet.

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Answer:

the first one

Step-by-step explanation:

to know weather the graph is function or not we use vertical line test meaning we draw vertical line and if this line intersects once we say the graph is a function, unless it's not function.

Answer:at his party's national convention

Step-by-step explanation:

Answer:

35 liters of Jam.

Step-by-step explanation:

20/4 = 5.

5 liters of jam would be jarred per d

ay.

7 (days) x 5 (únit rate) = 35

Answer:

inferno

Step-by-step explanation:

bb u the reason why hells so hot hell so not ohhhhhhh lallalalala

Answer:

For both sets of data, the median is equal to the mean.

The interquartile range (IQR) is greater for M's classes than J's classes.

Step-by-step explanation:

J's Classes:

23, 25, 27, 28, 32

Median: 27

Mean: 27

Mean Absolute Deviation: 2.4

Interquartile Range: 3

M's Classes:

20, 24, 26, 29, 31

Median: 26

Mean: 26

Mean Absolute Deviation: 3.2

Interquartile Range: 5

The value of the patent is

$50,000 ($500,000 - $450,000)

due to the increased value at fair value and the remaining life of the patent is 10 years.Thus, the excess of amortization for 2019 would be

$5,000 {($50,000 / 10)}.

Therefore, the correct option is a.

$5,000.

On January 1, 2019, X Corporation acquired

100% of Y

Company's stock for

$150,000.

On the acquisition date, y company net assets of

$450,000

valued at book value and

$500,000

stated at fair value. The difference ($50,000) was due to the increased value of patent with a remaining life of 10 years. What amount of amortization excess for 2019?The excess amortization in 2019 is ($5,000).Explanation:Excess of amortization

= (fair value of asset - book value of asset)/remaining life of asset. The value of the patent is

$50,000 ($500,000 - $450,000)

due to the increased value at fair value and the remaining life of the patent is 10 years.Thus, the excess of amortization for 2019 would be

$5,000 {($50,000 / 10)}.

Therefore, the correct option is a.

$5,000.

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The corresponding intervals for diameters of the washers as given in the task content is; 3.44 ≤ d ≤ 3.76.

It follows from the task content that the corresponding interval for ths diameter of the washers is to be determined given the circumference interval.

On this note, since the formula given is;

C = 3.14d.

By making d the subject of the formula;

d = C / 3.14.

Therefore, since the lower limit of the circumference is; 10.8 and the upper limit is; 11.1

The lower and upper limit of the diameter, d can be evaluated as follows;

lower limit of d is; d = 10.8 / 3.14 = 3.44

Upper limit of d is; d = 11.1 / 3.14 = 3.76

Therefore, the required interval for diameters of the washers is; 3.44 ≤ d ≤ 3.76.

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In Chapter 6, Problem 10P, the constraints are derived based on the given problem scenario and the objective of the optimization problem. Without specific details about Problem 10P in Chapter 6, it is challenging to provide a precise explanation.

However, I can provide a general understanding of how constraints are typically formulated in optimization problems. In optimization problems, constraints are used to represent the limitations or restrictions on the decision variables. These constraints can arise from various sources, such as physical constraints, resource constraints, budget constraints, or technical constraints. To derive the constraints, you need to carefully analyze the problem statement and identify the conditions or limitations that must be satisfied. These conditions are then translated into mathematical inequalities or equations that relate the decision variables. For example, if the problem involves allocating limited resources among different activities, the constraints would represent the availability of those resources and ensure that the total allocation does not exceed the available amount. Similarly, if the problem involves production planning, constraints might include demand requirements, capacity limitations, or inventory constraints. In general, the process of formulating constraints requires careful consideration of the problem's requirements, objectives, and limitations. It often involves translating real-world constraints into mathematical expressions to create a well-defined optimization problem that can be solved using appropriate techniques.

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