Solve for x
5x-1= 2x+5

The value of the integral \(\int\limits^{pi/2}_0\) cos⁷(x) dx is 4/35 π.

The alternative method using Wallis' formula can simplify the process. Wallis' formula states that:

∫[0, π/2] cosⁿ(x) dx = (n-1)(n-3)(n-5)...(3)(1) / (n)(n-2)(n-4)...(4)(2) π/2

In this case, we have n = 7. Let's apply Wallis' formula:

∫[0, π/2] cos⁷(x) dx = (7-1)(7-3)(7-5)(7-7)(7-9)(7-11)(7-13) / (7)(7-2)(7-4)(7-6)(7-8)(7-10)(7-12)  π/2

Simplifying the expression:

\(\int\limits^{pi/2}_0\)cos⁷(x) dx = 6 x 4 x 2 / 7 x  5 x 3  π/2

\(\int\limits^{pi/2}_0\)cos⁷(x) dx = 48 / 210 * π/2

\(\int\limits^{pi/2}_0\)cos⁷(x) dx = 8/35 x π/2

Finally, we can simplify the expression:

∫[0, π/2] cos⁷(x) dx = 4/35 π

Therefore, the value of the integral \(\int\limits^{pi/2}_0\) cos⁷(x) dx is 4/35 π.

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The integer that represents this change is -5.

We have,

The change in temperature is represented by the difference between the temperature before and after the storm.

In this case,

The temperature dropped, which means it decreased.

The integer that represents the change in temperature is negative because it indicates a decrease or a loss.

In particular,

The integer that represents a decrease of 5 degrees is -5.

Therefore, if the temperature before the storm was, for example, 20 degrees, the temperature after the storm would be 20 - 5 = 15 degrees, which is 5 degrees lower.

Thus,

The integer that represents this change is -5.

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Answer:

This equation shows that the pet groomer uses 3.75 ounces of shampoo per dog.

The relationship between the amount of shampoo used and the number of dogs groomed is proportional. We can represent this relationship with an equation using the form y = kx, where y is the amount of shampoo used, x is the number of dogs groomed, and k is the constant of proportionality.

Given that the pet groomer uses 26.25 ounces of shampoo per day when 7 dogs need to be groomed, we can use this information to find the value of k.

26.25 = k * 7

Solving for k, we get:

k = 26.25/7

k = 3.75

So the equation representing the relationship between the amount of shampoo used and the number of dogs groomed is y = 3.75x

This equation shows that the pet groomer uses 3.75 ounces of shampoo per dog.

\(\qquad \qquad \textit{direct proportional variation} \\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad \stackrel{\textit{constant of variation}}{y=\stackrel{\downarrow }{k}x~\hfill } \\\\ \textit{\underline{x} varies directly with }\underline{z^5}\qquad \qquad \stackrel{\textit{constant of variation}}{x=\stackrel{\downarrow }{k}z^5~\hfill } \\\\[-0.35em] ~\dotfill\)

\(\stackrel{\textit{"s"ampoo varies directly with "d"ogs}}{s = k(d)}\hspace{5em}\textit{we also know that} \begin{cases} d=7\\ s=26.25 \end{cases} \\\\\\ 26.25=k(7)\implies \cfrac{26.25}{7}=k\implies 3.75=k~\hfill \boxed{s=3.75d}\)

Answer:

76.

Step-by-step explanation:

It is given that N is a 2-digit number.

Last two digits of N^2 is the same as N.

We know that, a number is even if it ends with 0,2,4,6,8.

\(2^2=4,4^2=16,6^2=36,8^2=64\)

If 0 is in end then we get two zeros in the square of that number.

It is clear that, number should ends with 6 to get the same number at the end.

\(16^2=256\)

\(26^2=676\)

\(36^2=1296\)

\(46^2=2116\)

\(56^2=3136\)

\(66^2=4356\)

\(76^2=5776\)

\(86^2=7396\)

\(96^2=9216\)

It is clear that last two digits of (76)^2 is the same as 76.

Therefore, the required number is 76.

Each individual result of a probability experiment is called an "outcome" (d).

An outcome refers to a specific result or occurrence that can happen when conducting a probability experiment. It represents the different possibilities or potential results of an experiment.

For example, when flipping a fair coin, the possible outcomes are "heads" or "tails." In this case, "heads" and "tails" are the two distinct outcomes of the experiment.

Similarly, when rolling a fair six-sided die, the possible outcomes are the numbers 1, 2, 3, 4, 5, or 6. Each number represents a different outcome that can occur when rolling the die.

In summary, an outcome is a specific result or occurrence that can happen during a probability experiment. It is essential to understand outcomes as they form the basis for calculating probabilities and analyzing the likelihood of different events occurring.

Thus, each individual result of a probability experiment is called an "outcome" (d).

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Yes, the walls form a right angle.

To determine if the walls form a right angle, we can use the Pythagorean theorem. The question states that a wall 12 feet long makes a corner with a wall that is 14 feet long, and the other ends of the walls are about 18.44 feet apart.

The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. In this case, let's consider the 12-foot and 14-foot walls as the two shorter sides, and the 18.44-foot distance as the potential hypotenuse.

Step 1: Calculate the square of the lengths of the 12-foot and 14-foot walls.

12² = 144

14² = 196

Step 2: Calculate the sum of the squares of these two sides.

144 + 196 = 340

Step 3: Calculate the square of the length of the 18.44-foot distance.

18.44² ≈ 339.95

Since 339.95 is very close to 340, we can conclude that the walls form a right angle.

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Answer:

20

Step-by-step explanation:

\(x + 60 + 2x + 100 + 3x + 80 = 360\)

\(x = 20\)

The value of the standard deviation of the variance S is equivalent to 250 and the value of the variance (S) is equivalent to 62500.

Given that:

2Ax = 0.08

Ax = 0.2

A fully discrete whole life insurance issued to (x) is 1000.

Firstly we have to find out the value of variance S.

Variance S = (insurance issued)^2 * [2Ax - Ax^2]/(1- Ax)^2

Variance S = (1000)^2 * [0.08 -  0.2^2]/(1- 0.2)^2

Variance S = (1000)^2 * [0.04]/.64

Variance S = (1000)^2 * .0625

Variance S = 62500

Standard deviation of S = (insurance issued) * [\(\sqrt{2Ax - Ax^2}\)]/(1- Ax)

Standard deviation = 1000 * [\(\sqrt{0.08 - 0.2^2}\)]/(1- 0.2)

Standard deviation = 1000 * 0.2/0.8

Standard deviation = 1000 * 1/4 = 250

The value of the standard deviation of the variance S is equivalent to 250 and the value of the variance (S) is equivalent to 62500.

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(a) No, a triangle cannot have two obtuse angles. (b) No, a triangle cannot have two right angles.
(c) If no angle of a triangle measures more than 60°, then the triangle is an acute triangle.


(a) In a triangle, the sum of all three angles must be 180°. Since two obtuse angles would sum to more than 180°, it is not possible for a triangle to have two obtuse angles.
(b) In a triangle, the sum of all three angles must be 180°. Since two right angles would sum to 180°, it is not possible for a triangle to have two right angles.
(c) In an acute triangle, all three angles are less than 90°. If no angle of a triangle measures more than 60°, then all three angles are less than 90°, making it an acute triangle.

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Answer:

X= 15

Step-by-step explanation:

3x - 15 + 150 = 180

X = 15

Answer: Step 1

Find the scale factor

we know that

If the two cylinders are similar

then

The ratio between the circumference of the larger cylinder to the circumference of the smaller cylinder is equal to the scale factor

Step 2

Find the lateral area of the smaller cylinder

we know that

If the two cylinders are similar

then

The ratio between the lateral area of the larger cylinder to the lateral area of the smaller cylinder is equal to the scale factor squared

Let

x--------> the lateral area of the larger cylinder

y-------> the lateral area of the smaller cylinder

z--------> the scale factor

In this problem we have

substitute in the formula and solve for y

therefore

the answer is

33.6π mm2

The correct option is Option D: the lateral area of the smaller cylinder is 84π mm².

The lateral area of the cylinder is the area of the curved surface which can be calculated by the formula given below

lateral area of the cylinder= 2πrl

where r is the radius of the cylinder and l is the length of the cylinder.

Here given that the two cylinders are similar.

The larger cylinder has base of circumference = 60π mm

As we know the circumference of base of cylinder= 2πR

⇒60π= 2πr

⇒2πR= 60π

Given the lateral area of the larger cylinder is 210π mm²

From above formula, it is clear that the lateral area of the cylinder= 2πrl

⇒ 210π = 2πrl

⇒2πRl= 210π

⇒60πl= 210π (as from above it is derived that 2πr= 60π)

⇒l= 210π/ 60π= 7/2

⇒l= 3.5 mm

the smaller cylinder has base of circumference = 24π mm

⇒ 2πr= 24π mm

then the lateral area of the smaller cylinder is= 2πrl= 24π*3.5= 84π mm²

Therefore the correct option is Option D: the lateral area of the smaller cylinder is 84π mm².

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Answer:

the answer would be:

3 (t+2)

Step-by-step explanation:

Answer:

3 (t+2)

Step-by-step explanation:

Answer:

42 cubic units

Step-by-step explanation:

7 x 3 x 2 = 21 x 2 = 42

The specific gravity of the combined product is 1.22

Specific gravity is the ratio of the density of a substance to the density of some substance (such as pure water) taken as a standard when both densities are obtained by weighing in air.

Given,

The total quantity of portion= 50 ml

Specific gravities of the three syrups = 1.10,1.25 and 1.32

Then,

The specific gravity of the combined product= \(\frac{1.10+1.25+1.32}{3}\)

= 1.22

Hence, the specific gravity of the combined product is 1.22.

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Answer:

Step-by-step explanation:

\(\frac{146}{\pi}\\ \\ \text{Pi is irrational and cannot be expressed as a ratio of two integers.}\\ \\ \frac{146}{\pi}\approx 46.47\)

Answer:

\(x \4 = 5 \\ x = 5 \times 4 = 20 \\ x = 20.\)

Answer:

yes. ........ .........

Recall that the domain of a function is the set of numbers to which the function is defined. That is, if you replace the value of the independant variable (normally represented as x), then the function will give another number as a result.

In this case, we are given the function 400+13x. Since x is the independant variable, to determine the domain we must think on what possible values the variable x can take. Since in this case x represents the number of products made, it is impossible that it takes negative values, since in real life you can't produce negative amounts of products.

So far, we know that x should be greater or equal to zero. Once again, in this context, it doesn't make sense that, for example, x=7.8, since this would mean that 7.8 number of products were made. Since x represents the number of products made, it can only take values as x=0,x=1, x=2, x=3 and so on.

This set receives the name of whole numbers.

40 m³ is the volume of pyramid .

What is a pyramid defined as?

A three-dimensional shape is a pyramid. A pyramid's flat triangular faces and polygonal base all come together in a summit known as the apex. By fusing the bases together at the peak, a pyramid is created. The lateral face, a triangular feature formed by the connection of each base edge to the apex, is present.

  L= 5

h = 4

s = 6

V = 6 * 4 * 5/3

   = 120/3

   = 40 m³

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The direction of the difference between the 2 measurements.

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The value of X = 25.

Solution:

The two equations are

(i) the first condition is difference of x and y is 14

x - y = 14 ---------equation 1

(ii) the second condition of the given data is value of x is 3 times more than two times of y value.

x - 2y = 3 --------equation 2

From equation 2, we have to separate two variables x and y,

x = 3 + 2y  --------equation 3

We have to Substitute equation 3 in equation 1

3 + 2y - y = 14

3 + y = 14

y = 14 - 3

y = 11

Substitute y = 11 in equation 1........

x - 11 = 14

x = 14 + 11

x = 25

So, the value of x is 25 and y is 11.

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Answer:

Step-by-step explanation:

Given the difference of x and y is 14, and the difference of x and 2y is 3, you want two equations, their graph, and the value of x.

The difference of 'a' and 'b' is (a -b). Here, the two differences are expressed as the equations ...

The attachment shows a graph of these equations. Their point of intersection is (25, 11), meaning the value of x is 25.

The graph of the first equation is easily drawn by recognizing the x- and y-intercepts are 14 and -14, respectively.

The graph of the second equation will go through the x-intercept point of (3, 0) and the y-intercept point of (0, -3/2). It is probably easier to graph this by hand by considering the x-intercept point and the slope of 1/2.

Since we're only interested in the value of x, it is convenient to eliminate the variable y. We can to that by subtracting the second equation from twice the first:

  2(x -y) -(x -2y) = 2(14) -(3)

  x = 25 . . . . . . . . . simplify

Answer:

A). Scale factor = \(\frac{1}{4}\)

B). Length of the unknown side = 2.75 feet

Step-by-step explanation:

Part A

Since, the large rectangle was scaled by a scale factor 'k' to form the smaller rectangle,

Scale factor = \(\frac{\text{Side length of the image}}{\text{Side length of the preimage}}\)

                    = \(\frac{\text{Side length of the smaller rectangle}}{\text{Side length of the larger rectangle}}\)

                    = \(\frac{4}{16}\)

                    = \(\frac{1}{4}\)

Part B

Scale factor = \(\frac{\text{Side length of the smaller rectangle}}{\text{Side length of the larger rectangle}}\)

\(\frac{1}{4}=\frac{\text{Side length of the smaller rectangle}}{11}\)

Therefore, side length of the unknown side = \(\frac{11}{4}\) = 2.75 feet

The system of equations that matches the given graph is:

A. 3x - 6y = 12

9x - 18y = 36

To determine which system of equations matches a given graph, we need to analyze the slope and intercepts of the lines in the graph.

Looking at the options provided:

A. 3x - 6y = 12

9x - 18y = 36

B. 3x + 6y = 12

9x + 18y = 36

Let's analyze the equations in each option:

For option A:

The first equation, 3x - 6y = 12, can be rearranged to slope-intercept form: y = (1/2)x - 2.

The second equation, 9x - 18y = 36, can be simplified to 3x - 6y = 12, which is the same as the first equation.

In option A, both equations represent the same line, as they are equivalent. Therefore, option A does not match the given graph.

For option B:

The first equation, 3x + 6y = 12, can be rearranged to slope-intercept form: y = (-1/2)x + 2.

The second equation, 9x + 18y = 36, can be simplified to 3x + 6y = 12, which is the same as the first equation.

In option B, both equations also represent the same line, as they are equivalent. Therefore, option B does not match the given graph.

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The period of the Markov chain is 2.

The period of this Markov chain is determined by the number of times you have to go through the probability transition matrix before you return to the same state. The period for this Markov chain is 2, as you can see from the probability transition matrix below:

 P(i,j)   State 0   State 1    State 0   0.5   0.5    State 1   0.3   0.7  


Starting from State 0, the probability of transitioning to State 0 is 0.5, and the probability of transitioning to State 1 is 0.5. If we start from State 1, the probability of transitioning back to State 0 is 0.3, and the probability of transitioning back to State 1 is 0.7.

Therefore, it takes two steps for the chain to return to its original state and the period of this Markov chain is 2.

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Answer:

n = -1.25

Step-by-step explanation:

S(ABCD) = AB × AD

S(ABCD) = 2n × (4n + 5)

S(ABCD) = CD × AD

2n × (4n + 5) = CD × (4n + 5)

n = -1.25

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The number of yards, as a mixed number, will you drive until you reach this exit is 333 1/3 yards

The complete question is added as an attachment

From the attached figure, we have:

Exit = 1000 feet

From the question, we have

3 feet = 1 yard

So, the number of yards is

Number of yard =Exit/3 yards

This gives

Number of yard = 1000/3 yards

Evaluate the quotient

Number of yard = 333 1/3 yards

Hence, the number of yards, as a mixed number, will you drive until you reach this exit is 333 1/3 yards

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The numerator of the z-score test statistic measures the difference between the sample mean and the population mean (or the hypothesized population mean, depending on the context) in terms of the standard error of the mean.

It can use z- test only if the population standard deviation is known (or given) and the sample is large (more than 30 units)

If the mean and standard deviation is known, then the z-score is calculated using the formula.

z = (x - μ) / σ

where x is data;

μ is the mean and σ is the standard deviation.

Thus, the actual distance between a sample mean x and a population mean µ is measured by the numerator of z- score test statistic.

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Answer:

\(f(x) = {x}^{4} - 16\)

Step-by-step explanation:

\(f(x) = (x + 2i)(x - 2i)(x - 2)(x + 2)\)

\(f(x) = ( {x}^{2} + 4)( {x}^{2} - 4) \)

\(f(x) = {x}^{4} - 16\)

The weekly rate of change in the mass of the sample can be determined by examining the function provided:\(M(t) = (0.97)^(7t + 5)\).  

To find the factor by which the mass is multiplied every week, we can compare the mass at two different times, such as t = 0

and t = 1.

When t = 0,

the function becomes \(M(0) = (0.97)^(7(0) + 5)\)

= (0.97)⁵.

When t = 1,

the function becomes \(M(1) = (0.97)^(7(1) + 5)\)

= (0.97)¹².

To find the factor by which the mass is multiplied every week, we can divide M(1) by M(0):
Factor = M(1) / M(0)

= (0.97)¹²/ (0.97)⁵

= (0.97)⁷

= (0.97)⁷.

Rounding this value to two decimal places, we find that every week, the mass of the sample is multiplied by a factor of approximately 0.73.

The weekly rate of change in the mass of the sample is approximately 0.73, which means the mass decreases by about 27% each week.

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