When finding the nth roots of a complex number, the exact values of these roots will be given in rectangular form, and the approximate values of these roots will be given in • form Find the cube roots of 117 441 Your answers should be in rectangular form, with all numbers rounded to the nearest hundredths. Select one or more! O a 3.00 +4.002 O b. –4.96 +0.604 OC -1.96 + 1.964 O d. - 124.10 + 11.95 e. 3.00 4.00 Of 4.68 - 1.764 Og 1.96 4.602 O h. 75.00+ 100.00 Di 49.10 - 114.951

The answer of the question based on expressing the side of the base of a rectangular prism in terms of V and b the answer is the side of the base a is equal to the square root of the volume V divided by the height b.

Volume is measure of  amount of space that  three-dimensional object takes up. It is typically expressed in units of cubic length, like cubic meters, cubic feet, or cubic centimeters.

The formula for volume of many common geometric shapes can be calculated using mathematical formulas, while volumes of irregular shapes can be determined by measuring  amount of water they displace or by using advanced imaging techniques like CT scans.

The formula for  volume of  rectangular prism are:

V = length×width×height

Since the base of the prism is a square, the length and width are both equal to a. Therefore:

V = a × a × b

Simplifying this expression:

V = a²b

Dividing both sides by b:

a² = V/b

Taking the square root of both sides:

a = √(V/b)

Therefore, the side of the base a is equal to the square root of the volume V divided by the height b.

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The probability that at least half of the 328 voters contacted in the telephone survey supported the current governor in the last election is 0.0532.

To calculate the probability that at least half of the 328 voters contacted in the telephone survey supported the current governor in the last election, we can use the binomial probability formula.

The formula is: P(x) = (ⁿCₓ) × pˣ × (1-p)⁽ⁿ⁻ˣ⁾

In this case, n = 328, p = 46.37%, and x = 164 (since half of 328 is 164).

Plugging in the numbers we get:

P(x) = ³²⁸C₁₆₄ × (0.4637)¹⁶⁴ × (0.5363)⁽³²⁸⁻¹⁶⁴⁾ = 0.0532

Therefore, the probability that at least half of the 328 voters contacted in the telephone survey supported the current governor in the last election is 0.0532.

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Answer:

[tex]\frac{-1}{3}[/tex]

Step-by-step explanation:

Look at the red slope triangle that is drawn. If you start at the point on the left, you go down 1 unit and then to the right 3 units.  This would be represented by -1/3.  Down would be negative and going right would be positive.  The slope is the rise over the run.

Helping in the name of Jesus.

Answer:

Step-by-step explanation:

Answer: D. Yes, the sum of the square of the legs is equal to the square of the hypotenuse.

Step-by-step explanation:

Pythagorean theorem is a^2 + b^2 = c^2

given side length of 6 and 8 and hypotenuse of 10

6^2 + 8^2 = 10^2

36 + 64 = 100

100 = 100

so yes, the sum of the square of the legs = the square of the hypotenuse.

Answer:

y = -2x + 12

Step-by-step explanation:

In order to put the equation in slope intercept form [tex]y=mx+b[/tex] we need to solve for y.

[tex]4x+2y=24[/tex]

Subtract 4x on both sides

[tex]2y=-4x+24[/tex]

Divide by 2

[tex]y=-2x+12[/tex]

Answer:

1

Step-by-step explanation:

Given values are:

x1 y1=(2,4)

x2 y2=( 4,6)

slop=(6-4)divide (4-2)=1

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The exponential function that models the quail population is:

P(t) = P0 * (1 + r)^t

where:

P0 is the initial population (385)

r is the annual growth rate (30% or 0.3)

t is the time in years

Substituting the values, we get:

P(t) = 385 * (1 + 0.3)^t

Simplifying:

P(t) = 385 * 1.3^t

To find the approximate population after 5 years, we substitute t = 5:

P(5) = 385 * 1.3^5

P(5) = 385 * 3.277

P(5) = 1262.45

Therefore, the approximate population after 5 years is 1262 quail

The products written in scientific notation are:

a) [tex]5.88*10^9[/tex]

b) [tex]15*10^{12}\\[/tex]

c) [tex]8.4*10^{-10}[/tex]

d) [tex]42*10^{-7}[/tex]

The first product we need to solve is:

[tex](4.2*10^6)*(1.4*10^3)[/tex]

We can reorder that product into the one below:

[tex](4.2*1.4)*(10^6*10^3)[/tex]

The exponents in the right side are added, so we get:

[tex](4.2*1.4)*(10^6*10^3) = 5.88*10^{3 + 6} = 5.88*10^9[/tex]

Now let's do the same in the others.

b)

[tex](5*10^5)*(3*10^7)\\= 5*3*10^{5 + 7}\\= 15*10^{12}\\[/tex]

Now we need to write the first number between 0 and 10, then we can rewrite this as:

[tex]1.5*10^{13}[/tex]

c) Again doing the same thing.

[tex](4*10^{-3})*(2.1*10^{-7}})\\= 4*2.1*10^{-3 - 7}\\= 8.4*10^{-10}[/tex]

d) Finally, this last product is:

[tex](6*10^{-2})*(7*10^{-5}})\\= 6*7*10^{-2 - 5}\\= 42*10^{-7}[/tex]

Again we need to have a number between 0 and 10, so we can rewrite this as:

[tex]4.2*10^{-8}[/tex]

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A system of linear inequalities that the graph represent include the following:

x ≥ 4.

y < -x - 2

y ≥ 3x + 3

y > x - 4

In Mathematics, the slope-intercept form of the equation of a straight line is given by this mathematical expression;

y = mx + c

Where:

At data points (-3, 0) and (0, 3), the slope of this line can be calculated as follows;

Slope = (3 - 0)/(0 + 3) = 3/3 = 1

y-intercept = 3.

Therefore, a linear inequality that models the line is given by:

y ≥ 3x + 3

At data points (-2, 0) and (0, -2), the slope of this line can be calculated as follows;

Slope = (-2 - 0)/(0 + 2) = -2/2 = -1

y-intercept = -2.

Therefore, a linear inequality that models the line is given by:

y < -x - 2

At data points (4, 0) and (0, -4), the slope of this line can be calculated as follows;

Slope = (-4 - 0)/(0 - 4) = -4/-4 = 1

y-intercept = -4.

Therefore, a linear inequality that models the line is given by:

y > x - 4

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Therefore , the solution of the given problem of unitary method comes out to be it weighs 0.01 times as much as the first nugget.

This common convenience, already-existing variables, or all important elements from the original Diocesan customizable survey that followed a particular event methodology can all be used to achieve the goal. If it does, there will be another chance to get in touch with the entity. If it doesn't, each of the crucial elements of a term proof outcome will surely be lost.

Here,

We can divide the weight of the second nugget by the weight of the first nugget to determine how many times as much the second nugget weights the first:

=> 0.8 oz / 0.008 oz = 100

The second piece is therefore 100 times heavier than the first.

We can divide the first nugget's weight by the second nugget's weight to determine how much the first nugget weights in relation to the second nugget:

=> 0.008 oz /0.8 oz = 0.01

In other terms, the second nugget weighs 100 times as much as the first nugget, or it weighs 0.01 times as much as the first nugget.

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Answer: 12.84

Step-by-step explanation:

if x = 3.2 and y = 6.1  and Z = 0.2

then plug in the numbers

(3.2)(0.2) + (6.1)(2)

0.64 + 12.2 = 12.84

Any variable next to a number means multiplication.

if I was wrong lmk

Answer:

If f(x)=x^3, evaluate f(x+h)-f(x)÷h, Where h* 0. Use your result to find the derivative of f(x) with respect to x. Differentiate with respect to x (x²-3x+5)(2x-7) .Find with respect to x the derivative of sinx ÷1– cosx​

Step-by-step explanation:

We are given f(x) = x^3. We need to find the value of (f(x+h) - f(x))/h.

f(x+h) = (x+h)^3 = x^3 + 3x^2h + 3xh^2 + h^3

Therefore, (f(x+h) - f(x))/h = [x^3 + 3x^2h + 3xh^2 + h^3 - x^3]/h

= 3x^2 + 3xh + h^2

Taking the limit of the above expression as h approaches 0, we get:

lim(h→0) [(f(x+h) - f(x))/h] = 3x^2

Therefore, the derivative of f(x) = x^3 with respect to x is 3x^2.

Next, we need to differentiate (x^2-3x+5)(2x-7) with respect to x.

Using the product rule, we get:

d/dx [(x^2-3x+5)(2x-7)] = (2x-7)(2x-3) + (x^2-3x+5)(2)

Simplifying, we get:

d/dx [(x^2-3x+5)(2x-7)] = 4x^2 - 20x + 11

Therefore, the derivative of (x^2-3x+5)(2x-7) with respect to x is 4x^2 - 20x + 11.

Finally, we need to find the derivative of sin(x)/(1-cos(x)) with respect to x.

Using the quotient rule, we get:

d/dx [sin(x)/(1-cos(x))] = [(1-cos(x))cos(x) - sin(x)(sin(x))]/(1-cos(x))^2

Simplifying, we get:

d/dx [sin(x)/(1-cos(x))] = cosec(x/2)^2

Therefore, the derivative of sin(x)/(1-cos(x)) with respect to x is cosec(x/2)^2.

Answer:

16x-20

Step-by-step explanation:

6(2x-3)-2(2x+1)

12x-18-4x+2

16x-20

You have given a relation R = {(x,y): y is the area of triangle x 3}. This means that for each value of x, which represents the base of a triangle, y is the area of that triangle with height 3.

To find out if this relation is a function, we need to check if there are any repeated x-values with different y-values. If there are none, then it is a function.

One way to do this is to use the formula for the area of a triangle: A = (1/2)bh, where b is the base and h is the height. Using this formula, we can find the y-values for some x-values:

[tex]x | y| - 0 | 0 1 | (1/2) * 1 * 3 = 3/2 2 | (1/2) * 2 * 3 = 3 3 | (1/2) * 3 * 3 = 9/2 4 | (1/2) * 4 * 3 = 6[/tex]

Therefore, As you can see, there are no repeated x-values with different y-values, this relation R is a function.

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Answer:

(2x - y)(3b + c + 2d)

Step-by-step explanation:

Factorize:

From the first two terms 6bx and (-3by) take out the common factor 3b.

From the third and fourth term 2cx and (-cy) take out the common factor c.

From the fifth and sixth term 4dx and (-2dy) take out the common factor 2d.

6bx - 3by  + 2cx - cy + 4dx - 2dy = 3b(2x - y) + c(2x - y) + 2d(2x - y)

                                                      = (2x - y)(3b + c + 2d)

Question: The heights of adult men can be approximated as normal, with a mean of 70 and a standard deviation of 3, the probability that a man is shorter than 65 inches is approximately 0.0475 or 4.75%.

Let X be the height of an adult man, which follows a normal distribution with mean μ = 70 and standard deviation σ = 3. Then, we need to find the probability that a man is shorter than some height, say x₀. We can write this probability as P(X < x₀).To find P(X < x₀), we need to standardize the random variable X by subtracting the mean and dividing by the standard deviation. This yields a new random variable Z with a standard normal distribution. Mathematically, we can write this transformation as:Z = (X - μ) / σwhere Z is the standard normal variable.

Now, we can find P(X < x₀) as:P(X < x₀) = P((X - μ) / σ < (x₀ - μ) / σ) = P(Z < (x₀ - μ) / σ)Here, we use the fact that the probability of a standard normal variable being less than some value z is denoted as P(Z < z), which is available in standard normal tables.

Therefore, to find the probability that a man is shorter than some height x₀, we need to standardize the height x₀ using the mean μ = 70 and the standard deviation σ = 3, and then look up the corresponding probability from the standard normal table.In other words, the probability that a man is shorter than x₀ can be expressed as:P(X < x₀) = P(Z < (x₀ - 70) / 3)We can now use standard normal tables or software to find the probability P(Z < z) for any value z.

For example, if x₀ = 65 (i.e., we want to find the probability that a man is shorter than 65 inches), then we have:z = (65 - 70) / 3 = -1.67Using a standard normal table, we can find that P(Z < -1.67) = 0.0475. Therefore, the probability that a man is shorter than 65 inches is approximately 0.0475 or 4.75%. Thus, P(X < 65) = 0.0475 or 4.75%. Therefore, the probability that a man is shorter than 65 inches is approximately 0.0475 or 4.75%.

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Answer:

169 - 144p²

Step-by-step explanation:

(13 - 12p) × (13 + 12p)

each term in the second factor is multiplied by each term in the first factor

13(13 + 12p) - 12p(13 + 12p) ← distribute parenthesis

= 169 + 156p - 156p - 144p² ← collect like terms

= 169 - 144p²

(a) The null hypothesis is that p = 0.5, and the alternative hypothesis is that p ≠ 0.5.

To conduct a hypothesis test, we need to define the null and alternative hypotheses. Let p be the proportion of US adults who believe raising the minimum wage will help the economy. The null hypothesis is that p = 0.5, and the alternative hypothesis is that p ≠ 0.5.

(b) The conditions for using a normal approximation to the binomial distribution are met since np = 1000(0.5) = 500 and n(1-p) = 1000(0.5) = 500 are both greater than 10.

(c) Using a significance level of α = 0.05, the test statistic is z = (0.42 - 0.5) / sqrt[(0.5)(0.5)/1000] = -2.38. The corresponding p-value is P(z < -2.38) = 0.017.

(d) Since the p-value is less than the significance level, we reject the null hypothesis. There is evidence to suggest that the proportion of US adults who believe raising the minimum wage will help the economy is not equal to 0.5. Therefore, we can conclude that a majority of US adults do not believe raising the minimum wage will help the economy.

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After solving the given equations we know that the value of x and y are -4 and -7 respectively.

A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions.

Ax+By=C is the usual form for two-variable linear equations.

A standard form linear equation is, for instance, 2x+3y=5. When an equation is given in this format, finding both intercepts is rather simple (x and y).

This form is also highly useful when solving systems involving two linear equations.

So, we have the equations:

y=2x+1 ...(1)

-4x+y=9 ...(2)

Now, substitute y=2x+1 in equation (2):

-4x+y=9

-4x+2x+1=9

-2x=8

x=-4

Now, insert x=-4 in equation (1):

y=2x+1

y=2(-4)+1

y=-8+1

y=-7

Therefore, after solving the given equations we know that the value of x and y are -4 and -7 respectively.

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The classmate's method is not correct because dividing the 1-week growth factor by 7 assumes that the growth rate is constant over each day of the week, which may not be the case so the correct 1-day correct growth factor is 1.036 and it is verified.

To calculate the correct 1-day growth factor, we can take the 7th root of the 1-week growth factor.

This is because if the height of the bamboo plant grows by a factor of x in one week, then the daily growth factor is the same as the weekly growth factor raised to the power of 1/7.

So the correct 1-day growth factor would be:

1-day growth factor = (1-week growth factor) raise to (1/7) = 1.27 raise to (1/7) ≈ 1.036

To verify that this is correct, we can raise the 1-day growth factor to the 7th power to obtain the 1-week growth factor:

1-week growth factor = (1-day growth factor)⁷ ≈ (1.036)⁷≈ 1.27

Therefore, the 1-day growth factor is approximately 1.036, and using this to find the 1-week growth factor yields approximately 1.27, which matches the given growth factor.

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Yes, the triangle is a right triangle, the correct option is A.

We can see that the vertices of the triangle are at:

A = (6, 4)

B = (-6, 9)

C = (0, 0)

Then the lenghts of each of the sides is:

AC = √( (6 - 0)² + (4 - 0)²) = √52

BC = √( (-6 - 0)² + (9 - 0)²) = √117

AB = √( (6 + 6)² + (4 - 9)²) = 13

If this is a right triangle, then the pythagorean theorem must be true, so:

AB² = AC² + BC²

13² =  √52²  + √117²

169 = 52 + 117

169 = 169

This means that BC is perpendicular to AC.

So yes, it is a right triangle. The correct option is A.

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We can see this by noticing that [tex]6^2 = 36 < 37 < 49 =[/tex] [tex]7^{2}[/tex]. Taking the square root of each expression, we get [tex]\sqrt36 < \sqrt37 < \sqrt49,[/tex] which simplifies to [tex]6 < \sqrt37 < 7[/tex].

The square root of a number is a value that, when multiplied by itself, gives the original number. In mathematical notation, the square root of a number "x" is represented by the symbol "√x". For example, the square root of 25 is 5, because 5 multiplied by 5 equals 25.

Given by the question.

[tex]\sqrt29[/tex] lies between 5 and 6.

We can estimate this by recognizing that. [tex]5^2 = 25 < 29 < 36 =[/tex] [tex]6^{2}[/tex]. Taking the square root of each expression, we get √25 < √29 < √36, which simplifies to [tex]5 < \sqrt29 < 6[/tex].

[tex]\sqrt37[/tex]lies between 6 and 7.

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RT arc length 3.31 units (rounded to two decimal places).

A circle is indeed a closed arc that extends outward from a set point known as the center, with each point on the curve being equally spaced from the center. [tex](x-h)2 + (y-k)2 = r2[/tex] is the equation for a circle having a (h, k) center and a r radius.

We may employ the following equation to determine that length of a circle's arc:

length of arc =[tex](central angle / 360 degrees) x 2πr[/tex]

Where the circle's radius, r, is.

According to the information provided in this problem, m/RST = 126, the arc RT's center angle is 126 degrees. We are also told that RS = 3 units, which indicates that the circle's radius is 3 units (since all radii of a circle have the same length).

Applying the formula with these values, we obtain:

length of arc [tex]RT = (126 / 360) x 2π(3) ≈ 3.31 units[/tex]

We obtain the final response by rounding to the closest hundredth:

RT arc length 3.31 units (rounded to two decimal places).

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This type of growth model is often used to model revenue or sales of a product, as these types of processes often grow in a linear fashion.

Growth models, like those used in ForecastX, are typically used to model situations where a process grows at an exponential rate. This is a type of growth where the rate of increase is proportional to the size of the process, meaning that the process increases quickly over time.

This type of growth model is often used to model population growth, technological growth, and financial growth. In these cases, the growth model is usually used to make predictions about future growth in the process.  

In some cases, a growth model can be used to model a process that grows in a more or less constant rate. In this situation, the rate of increase is not proportional to the size of the process, and the rate of increase remains relatively stable over time. This type of growth model is often used to model natural resources, as these resources typically increase or decrease at a steady rate.

Finally, growth models can also be used to model a process that grows in a linear fashion. In this case, the rate of increase is constant and increases in a straight line over time.

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Answer:

True

Step-by-step explanation:

To tell if you can make a triangle or not, it is necessary that the two shorter lengths added up must equal the longer length. In this case, the two shorter lengths are 5 and 5. 5 and 5 added up is 10 and 10>8 meaning that in this case, you can make a triangle

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The linear approximation of the given function f(x) is 40.5.

As f(X) = 4√(81+x) so by L(x) = f(a) + f'(a)(x-a) where a=0 and f(x)=4√(81+x) Then f'(x) = (1/2)(81+x)^(-1/2) So, f'(a) = (1/2)(81)^(-1/2) = 1/18.

Thus, L(x) = f(0) + f'(0)(x-0)

L(x) = 4√(81) + (1/18)x

L(x) = 36 + (1/18)x

Now we are asked to approximate the values 4√81.02 and 4√80.99 by using the linear approximation we found above. Let's solve the problems. Approximation of 4√81.02.L(x) = 36 + (1/18)x Now x=81.02. Thus, L(81.02) = 36 + (1/18)81.02L(81.02) = 36 + 4.5L(81.02) = 40.5.

Thus, the linear approximation of 4√81.02 is 40.5. Approximation of 4√80.99.L(x) = 36 + (1/18)x Now x=80.99. Thus, L(80.99) = 36 + (1/18)80.99L(80.99) = 36 + 4.49444...L(80.99) = 40.49444... ≈ 40.5. Thus, the linear approximation of 4√80.99 is approximately 40.5.

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The letters of the circled points based on their second coordinate values, from least to greatest R, A, T, I, and O.

A word that describes a way to compare quantities is RATIO.

In Mathematics, an ordered pair is sometimes referred to as a coordinate and it can be defined as a pair of two (2) elements that are commonly written in a fixed order within parentheses as (x, y), which represents the x-coordinate (abscissa) and the y-coordinate (ordinate) on the coordinate plane of any graph of a system of linear equations.

In this scenario, we can reasonably infer and logically deduce that the ordered pair representing the circled points are as follows:

Next, we would order the points by their second coordinate values, from least to greatest:

R = -4, A = 1, T = 2, I = 4, O = 5 ⇒ RATIO.

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The surface area of the object in the image is 80 cm². To find the surface area of the object in the image, we need to add up the areas of all the faces.

Most of the lateral faces are rectangular. Sometimes, it might even be a parallelogram. Here is the Prism Formula: A prism has a surface area of (2BaseArea) + Lateral Surface Area. Prism volume equals Base Area + Height.

The length of the rectangle is 4 cm and the width is 3 cm. Therefore, the area of the rectangular base is:

Area of rectangular base = length × width = 4 cm × 3 cm = 12 cm²

Area of each side = length × width = 5 cm × 3 cm = 15 cm²

Since there are four identical sides, the total area of all four sides is:

Total area of four sides = 4 × Area of each side = 4 × 15 cm² = 60 cm²

Area of each triangular face = 1/2 × base × height = 1/2 × 4 cm × 2 cm = 4 cm²

Since there are two triangular faces, the total area of both triangular faces is:

Total area of both triangular faces = 2 × Area of each triangular face = 2 × 4 cm² = 8 cm²

Now we can add up all the areas to get the total surface area:

Total surface area = Area of rectangular base + Total area of four sides + Total area of both triangular faces

= 12 cm² + 60 cm² + 8 cm²

= 80 cm²

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