simplify 4x to the power of 3 to power of 5

The distance covered on the triangular path to home along point A to B to C is 23.42 miles.

In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem. These triangle's three sides are known as the Perpendicular, Base, and Hypotenuse. Due to its position opposite the 90° angle, the hypotenuse in this case is the longest side. When the positive integer sides of a right triangle (let's say sides a, b, and c) are squared, the result is an equation known as a Pythagorean triple.

Given that the trip to home goes from point A to point B and then to point C.

The path traced thus, represents the hypotenuse of the two triangles. Triangle BHA and triangle BCH.

The Pythagorean theorem is given as follows:

a^2 + b^2 = c^2

For triangle BHA substitute the value of a = 4 and b =6.

4^2 + 6^2 = c^2

16 + 36 = c^2

c = 7.21

For triangle BHC, substitute the value of a = 7 and b =6.

7^2 + 6^2 = c^2

49 + 36 = c^2

c = 9.21

Now, from point B to point H the additional distance is 7 miles, hence the total distance traveled is:

D = 7.21 + 9.21 + 7

D = 23.42

Hence, the distance covered on the triangular path to home along point A to B to C is 23.42 miles.

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Line A is parallel to line B

We know, the slope of the line joining two points [tex](x_{1} ,y_{1} )[/tex] , [tex](x_{2} ,y_{2} )[/tex] is:

[tex]m = \frac{y_{2} - y_{1} }{x_{2}- x_{1}}[/tex]

Line A is passing through (2, 10) and (4,13).

The slope of line A

[tex]m_{1} = \frac{y_{2} - y_{1} }{x_{2}- x_{1}} = \frac{13 - 10}{4-2} =\frac{3}{2}[/tex]

Line B is passing through (4,9) and (6, 12)

The slope of line B

[tex]m_{2} = \frac{y_{2} - y_{1} }{x_{2}- x_{1}} = \frac{12 - 9}{6-4} =\frac{3}{2}[/tex]

Line C is passing through (2, 10), and (4,9).

The slope of line C

[tex]m_{3} = \frac{y_{2} - y_{1} }{x_{2}- x_{1}} = \frac{9- 10}{4-2} =\frac{-1}{2}[/tex]

We also know that if the slope of two lines is equal that is [tex]m_{1} = m_{2}[/tex] then the lines are parallel and

if the slope of the two lines has a relation [tex]m_{1} * m_{2} = -1[/tex] , the lines are perpendicular to each other.

Here, since the slope of lines A and lines B are equal.

Hence, line A is parallel to line B.

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To solve for x in this problem, we need to use the Law of Cosines.

We can set up the equation as follows:

a² = b² + c² - 2bc cos(x)

We can substitute the values for a, b, and c, which are 22, 10, and 10 respectively. This gives us the equation:

22² = 10² + 10² - 2(10)(10) cos(x)

Simplifying the equation gives us:

484 = 200 - 200cos(x)

Therefore,

200cos(x) = 284

We can divide both sides by 200 to get cos(x) = 1.42.

We can take the inverse cosine of both sides to get x = 54.15°.

Rounding to the nearest tenth, x = 54.

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The probability of exactly 4 of the 7 hens contracting the disease is ⁷C₄(0.15)⁴(0.85)³.. The ideal response is (A).

How can the binomial distribution be used to calculate probability?

The binomial theorem, which can be expressed as (a + b)n = nC0anb0 + nC1an1b1 + nC2an2b2 +....+ nCna0bn, is the foundation of the binomial distribution.Events must be independent of one another and have probabilities that add up to 1 in order for the probability to be used.

Due to that,There is a 15% chance that the chicken will be affected it is spelled as as,

15% P(infected)

= 15/100

= 0.15

Consequently, the likelihood of avoiding diseased chicken is,

P(not contaminated) = 1 - 0.15= 0.85

Seven chickens in all will be used for the test.

Now, the binomial distribution may be used to determine the likelihood of having exactly 4 sick chickens.

nCxpxqnx is a general expression for the binomial distribution.

n = 7 and x = 4 for the case where p = P(infected) and q = P(not infected) are given

Consequently, the likelihood is given as,

P = 7C4(0.15)4(0.85)3 (Exact 4 are infected).

Therefore, the likelihood that the virus infects precisely 4 out of the 7 chickens sampled is ⁷C₄(0.15)⁴(0.85)³.

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Answer:

3 times.

Step-by-step explanation:

30, 31, 32, 33, 34, 35, 36, 37, 38, 39,40,41,42,43,44,45,46,47,48,49,50,51,

52,53,54,55,56,57,58,59,60,61,62,63,64,65.

37,47,57.

3 times

Solid will this lesson focus on the regular square pyramid

Regular square pyramid.

The justification is stated below:

Four triangular faces, five vertices, and eight edges make up the typical square pyramid's square base. The main formulae for a square pyramid are volume and surface area.

By definition, a regular square pyramid is one that has a base that is square, meaning that each of its sides is the same length.

Because it has an apex, a height, lateral faces that are congruent isosceles triangles, and slant height, you can tell that it is a pyramid (the altitude of the lateral faces).

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The equation of the tangent line to the given curve at the point (1, 5) is y = 15x – 10.

The given function is f(x) = 6x2 - x3.

We need to find the equation of the tangent line to the given curve at the point (1, 5).

To find the equation of the tangent line, we need to find the slope of the tangent line. The slope of the tangent line is given by the derivative of the curve at the given point.

The derivative of the given curve is f' (x) = 3x2 + 12x.

Substituting the value of x as 1, we get the slope of the tangent line at (1, 5) as f' (1) = 3(1)2 + 12(1) = 15.

Therefore, the equation of the tangent line at (1, 5) is given by y – 5 = 15(x – 1).

This can be simplified to y = 15x – 10.

Hence, the equation of the tangent line to the given curve at the point (1, 5) is y = 15x – 10.

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The ratio for number of chairs with wheels and number of chairs without wheels is 7:2.

What is ratio?

Comparing two amounts of the same units and determining the ratio tells us how much of one quantity is in the other. Two categories can be used to categorise ratios. Part to whole ratio is one, and part to part ratio is the other. The part-to-part ratio shows the relationship between two separate entities or groupings.

The ratio value is given as 7/9.

There are 7/9 chairs that are with wheels.

This means that the total number of chairs is 9.

Out of the 9 chairs 7 chairs have wheels.

The number of chairs that have no wheels is -

Total number of chairs - Number of chairs with wheels

= 9 - 7

= 2

So, the number of chairs with no wheels is 2

The ratio for number of chairs with wheels to no wheels is -

7:2

Therefore, the ratio value is obtained as 7:2.

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The water volume in the kiddie pool is 6561π [tex]in^{3}[/tex], the correct answer is B. 6561π  [tex]in^{3}[/tex].

The volume can be found by using cylinder volume formula V = π[tex].r^{2}.h[/tex]

So, the kiddie pool has 6561π [tex]in^{3}[/tex] of water.

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The correct option is (A). The correct answer is Ursa Minor, the Little Bear, containing the bright star Polaris.

Whereas stars spin or revolve from the northern hemisphere is the center of the sky, also known as the North Celestial Pole. Additionally, it marks the precise location of the Polaris or Northern Star constellation in full view. In addition, this served as a point of reference for the construction of sundials in earlier times.

When people go outside, especially at night, and try to find the Polaris constellation, it is evident that the stars close to this star formation circle in an east-to-west direction, in contrast to the northern star, which makes no movement whatsoever as the evening wears on.

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Answer:

y=3/2x+86

Step-by-step explanation:

y=Mx+b

M is the slope and b is the y intercept. The slope of a line is rise/run, in this case 3/2 and the y intercept is where the line goes through the y axis which for this problem, is 86. So y=3/2x+86

ΔRED ≅ ΔBUL, by rule SSA criterion.

In geometry, two figures or objects are said to be congruent if their shapes and sizes match, or if one is the mirror image of the other.

We have the triangles,

ΔRED and ΔBUL.

And given:

RE ≅ BU

RD ≅ BL

And ∠RDE ≅ ∠BLU.

Hence,

ΔRED ≅ ΔBUL, by SSA criterion.

Therefore, ΔRED ≅ ΔBUL, by SSA criterion.

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Answer:

9 ft, 3 ft 7, ft  

Step-by-step explanation:

Perimeter = 19 ft

Let side 2 = x

Side 1 = 3x

Side 3 = x + 4

perimeter = 3x + x + x + 4 = 19

5x + 4 = 19

5x = 15

x = 3

Side 1: 3x = 3(9) = 9

Side 2: x = 3

Side 3: x + 4 = 3 + 4 = 7

Answer:

9 ft, 3 ft 7, ft  

The statement '9 less than 10 and 6 times the letter n' in the mathematical form will be 9 < 10 + 6n.

Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.

The act of converting a specified statement into an expression or equation is known as a sentence-to-equation transformation.

The statement is '9 less than 10 and 6 times the letter n'.

Convert the statement into a mathematical form. Then we have

9 < 10 + 6n

Simplify the inequality, then we have

9 < 10 + 6n

6n > - 1

n > - 1/6

The statement '9 less than 10 and 6 times the letter n' in the mathematical form will be 9 < 10 + 6n.

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There are a total of 720 possible gate codes for your apartment complex.

Gate codes are security codes used to control access to a restricted area. Gate codes are used in both residential and commercial settings to ensure the safety of the occupants and to protect the property. Gate codes can be used to unlock and lock a gate, door, or other access point, and typically consist of a combination of letters, numbers, and/or symbols.

This is because each code consists of three non-repeating digits (0-9).

For the first digit, there are 10 possible choices (0-9).

For the second digit, there are 9 possible choices (excluding the number chosen for the first digit).

For the third digit, there are 8 possible choices (excluding the numbers chosen for the first and second digits).

This means that the total number of possible gate codes is 10 x 9 x 8 = 720.

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The number of ways that the people can be arranged is given as follows:

120,960.

The number of possible permutations of x elements from a set of n elements is given by:

[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]

To choose four people from a set of 10, as the order matters, the permutation formula is used, hence:

10!/6! = 5040.

Then we have to consider the four strains, which can be arranged in 4! = 24 ways, hence the number of ways for which the statistics can be arranged is of:

24 x 5040 = 120,960.

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a. To determine if the sample differs from the claim, we can use a hypothesis test. The null hypothesis is that the mean life of the AA batteries in toys is 5 hours, and the alternative hypothesis is that the mean life is different from 5 hours.

What does a math equation mean?

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

Using a t-test with a significance level of 0.05, we can calculate the t-statistic and the p-value.

The t-statistic is calculated as (mean - hypothesized mean) / (standard deviation / sqrt(sample size))

t = (3.58 - 5) / (1.85 / sqrt(16)) = -2.06

The p-value is the probability of getting a t-statistic as extreme or more extreme than the one we calculated, assuming the null hypothesis is true.

p-value = P(t < -2.06) = 0.048

Since the p-value is less than 0.05, we can reject the null hypothesis and conclude that the sample mean of 3.58 hours differs significantly from the claim of 5 hours.

b. The p-value is the probability of getting a t-statistic as extreme or more extreme than the one we calculated, assuming the null hypothesis is true. If we change the significance level to 0.001, the p-value would be less than 0.001, which would still be less than the new significance level. Therefore the conclusion would still be the same, the sample mean of 3.58 hours differs significantly from the claim of 5 hours.

However, it's worth mentioning that a lower significance level (0.001) would require a stronger evidence against the null hypothesis, therefore it would be more stringent in accepting the alternative hypothesis.

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Answer:

f(g(8)) = 26

Step-by-step explanation:

to calculate f(g(8)) , evaluate g(8) , then substitute the value obtained into f(x)

g(8) = 8 - 6 = 2 , then

f(2) = 3(2)² + 2 + 12 = 3(4) + 14 = 12 + 14 = 26

The height rises by the drone each second is 6 meters.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that a drone rises 18 m every three seconds. After five seconds, the drone is at a height of 40 m.

The height will be calculated as:-

3 sec = 18 meters

1 sec = 18 / 3 meters

1 sec = 6 meters

Hence, the height in 1 second will be 3 meters.

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The capacity of the container is equal to 7.6 × 10⁻³ kiloliters.

This is a unit conversion question, in which we need to determine how many kiloliters are equivalent to the capacity of a container.

According to capacity tables, a cubic decimeter or 1000 cubic centimeters equals a liter. Then, we can determine the number of kiloliters by using the following cross multiplication:

x = 7.6 dm³ × (1 L / 1 dm³) × (1 kL / 1000 L)

x = 7.6 × 10⁻³ kL

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A general solution is one which involves the integer 'n' and gives all solutions of a trigonometric equation.

Given data :

dy / dx = 9 + [tex]\frac{9 + (5x)^{1/2} }{8 + (13y)^{1/2} }[/tex] ; x > 0

The general solution of a differential equation in implicit form is obtained as follows

dy / dx = h(x) / g(y)

g(y)dy = {8 + (13y)^{1/2}

h(x) dx = {9 + (5x)^{1/2}

F(x,y) = C

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Answer:

y²

Step-by-step explanation:

4y² - 3y² = (4 - 3) × y² = 1y² = y²

The average velocity of the top of the ladder on this time interval is 8.75.

What is an average velocity?

The directional speed of an item in motion, as measured by a specific unit of time and observed from a certain point of reference, is what is referred to as velocity.

Here, we have

Given: time interval [a,9] so that the average velocity of the top of the ladder on this time interval is -20 ft/sec.

v = Δy/Δt = 20 = (0 - √625 - (7+2a)²)/(9-a)

-20 = (-√4(144 - 7a - a²)/(9-a)

10 = √(16 + a)(9 - a)/(9-a)

10 = √(16 + a)/(9 - a)

a = √884/101 = 8.75

Hence, the average velocity of the top of the ladder on this time interval is 8.75.

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The smallest positive real number c that satisfies the above inequality is [tex]$c = \frac{2}{\sqrt{xy}}[/tex]

We can rewrite the inequality as [tex]$\sqrt{xy} c \ge \frac{2}{|x - y|}$[/tex]. To make the inequality hold for all nonnegative real numbers x and y, we need c to be minimized. We can do this by taking the reciprocal of the right side of the inequality, giving us [tex]$\sqrt{xy} c \ge \frac{2}{|x - y|}$[/tex]. The smallest positive value that c can take is[tex]$\frac{2}{\sqrt{xy}}$[/tex].

We can rewrite the inequality as [tex]$\sqrt{xy} c \ge \frac{2}{|x - y|}$[/tex]. To make the inequality hold for all nonnegative real numbers x and y, we need c to be minimized.

We can do this by taking the reciprocal of the right side of the inequality, giving us [tex]$c \ge \frac{2}{\sqrt{xy}|x - y|}$[/tex]. The smallest positive value that c can take is [tex]$\frac{2}{\sqrt{xy}}$[/tex].

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Iron, which is a magnetic substance, makes up most of the core of the Earth, where the magnetic field of the planet first appears. The fluid outer core's movement around the solid inner core causes electric currents, which in turn creates and maintains the Earth's magnetic field.

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The midpoint method is a numerical integration technique for solving ordinary differential equations. To use it to solve the given equation, we start by discretizing the interval [0, L] into smaller steps of size h = 2, and use the midpoint of each interval to estimate the deflection at that point. Here's the algorithm:

Initialize z = 0, y = 0, and dydz = 0

Repeat the following steps for z = z + h until z = 30:

a. Calculate f1 = dydz

b. Calculate ymid = y + h/2 * f1

c. Calculate f2 = d2y/dz2 = f/2EI * (L-z-h/2)^2

d. Update y = y + h * f2

e. Update dydz = dydz + h * f2

The final value of y is the estimated deflection at z = 30.

The midpoint method is a numerical integration technique for solving ordinary differential equations. To use it to solve the given equation, we start by discretizing the interval [0, L] into smaller steps of size h = 2, and use the midpoint of each interval to estimate the deflection at that point. Here's the algorithm:

Initialize z = 0, y = 0, and dydz = 0

Repeat the following steps for z = z + h until z = 30:

a. Calculate f1 = dydz

b. Calculate ymid = y + h/2 * f1

c. Calculate f2 = d2y/dz2 = f/2EI * (L-z-h/2)^2

d. Update y = y + h * f2

e. Update dydz = dydz + h * f2

The final value of y is the estimated deflection at z = 30.

Plugging in the given parameter values, we have:

f = 60, E = 1.25 * 10^8, I = 0.05, L = 30

h = 2

z = 0, y = 0, dydz = 0

while z < 30:

  f1 = dydz

  ymid = y + h/2 * f1

  f2 = f/2EI * (L-z-h/2)^2

  y = y + h * f2

  dydz = dydz + h * f2

  z = z + h

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For logx = 2, the value of x would be 100.

Option (C) is correct.

What is a logarithm?

A logarithm is a mathematical function that calculates the power to which a given number (called the base) must be raised to produce a given value. The most common base used in logarithms is base 10, but logarithms can be defined with any base. If the base of a logarithm is not specified, it is assumed to be base 10. The logarithm of a number is represented by the symbol log.

The value of x in the equation logx = 2 can be found by solving for x. The logarithm of a number is the exponent that the base must be raised to in order to produce that number. So, in the equation logx = 2, x is equal to the base raised to the power of 2.

So,

logx = 2

x = 10^2

x = 100

if the base of the logarithm is not specified it is assumed to be base 10.

So, logx = 2 means x = 10^2 = 100

Hence, for logx = 2, the value of x would be 100.

Option (C) is correct.

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A quadratic graph is a type of parabolic graph that can be represented by the equation y = ax^2 + bx + c, where a, b, and c are constants and x is the variable. The graph of this equation is a parabola that opens either up or down, depending on the value of a.

The equation y = x^2 + 2x - 3 is an example of a quadratic graph. It can be written in the standard form of a quadratic equation as y = x^2 + 2x - 3, where a = 1, b = 2 and c = -3.

The x^2 term in the equation is known as the quadratic term, and it is responsible for the parabolic shape of the graph. The x term and the constant term, 2x and -3, respectively, determine the location of the vertex and the direction of the parabola.

The vertex of the parabola is the point where the parabola changes direction. It can be found by using the formula x = -b/2a, which in this case is x = -2/2 = -1 and y = f(-1) = -1.

The graph of y = x^2 + 2x - 3 is a parabola that opens upwards and the vertex of the parabola is (-1,-1)

In summary, a quadratic graph is a parabolic graph represented by the equation y = ax^2 + bx + c, where a, b, and c are constants. The x^2 term gives the parabolic shape to the graph, the x term and the constant term determine the vertex and the direction of the parabola respectively.

Answer:

The difference in interest received from an investment of $750 from an account paying 4% simple interest per annum and an account paying 0.3% monthly compound interest, over a one-year period is $19.75. The account paying 0.3% monthly compound interest will pay the most interest, yielding $102.50 in total.

The amount of money that the worker will earn in a week if he works 4 hours overtime is; $3180

We are given;

Number of work hours per week = 40 hours

Regular rate of work = $15.90 per hour

Overtime rate of work = 1.5(15.90) per hour

Since the regular rate is $15.90 per hour, then for a week, the money earned is; (15.90 * 40)

Now, he also works 4 hours overtime in a week and as such amount earned for overtime in the week = 4 * 1.5(15.90)

Thus;

Total amount earned in the entire week = (15.90 * 40) + (4 * 1.5(15.90))

= $3180

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