The cube roots of 117 441 in rectangular form are: a. 3.00 +4.002, b. –4.96 +0.604, c. -1.96 + 1.964, d. - 124.10 + 11.95, e. 3.00 4.00, f. 4.68 - 1.764, g. 1.96 4.602, and h. 75.00+ 100.00.
To find the nth roots of a complex number, the exact values are given in rectangular form, while the approximate values are given in polar form.
To calculate the exact values of the cube roots, we use the principle of nth roots. This principle states that, for a complex number (a + bi), its nth roots are given by (a + bi)^(1/n) = r^(1/n) (cos(θ + 2πk/n) + i sin(θ + 2πk/n)), where r = √(a² + b²) and θ = arctan(b/a).
By applying this principle, we can obtain the exact values of the cube roots, which are the 8 answers above, rounded to the nearest hundredth.
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An initial population of 385 quail increases at an annual rate of 30%. Write an exponential function to
model the quail population. What will the approximate population be after 5 years?
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
I need the answer for number 3 step by step, please help!
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.
Factor
6bx – 3by + 2cx – cy + 4dx – 2dy
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)
Is the following a right triangle?
A. Yes, using the slope formula we see that BC is perpendicular to AC.
B. Yes, using the distance formula we see that AC is congruent to BC
C. No, using the slope formula we see that BC is not perpendicular to AC
D. No, using the distance formula we see that AC is not congruent to BC
Yes, the triangle is a right triangle, the correct option is A.
Is the triangle a right triangle?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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Can someone please help me with this? I really need help on it
A system of linear inequalities that the graph represent include the following:
x ≥ 4.
y < -x - 2
y ≥ 3x + 3
y > x - 4
What is the slope-intercept form?In Mathematics, the slope-intercept form of the equation of a straight line is given by this mathematical expression;
y = mx + c
Where:
m represent the gradient, slope, or rate of change.x and y represent the data points.c represents the y-intercept or initial value.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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suppose 46.37% of all voters in the last election supported the current governor. a telephone survey contacts 328 voters from the last election and asks if they voted for the current governor. what is the probability that at least half of the voters contacted supported the current governor in the last election?
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.
What is the probability?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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y= 2x + 1 and - 4x + y = 9, solve the system of equations without graphing
After solving the given equations we know that the value of x and y are -4 and -7 respectively.
What are equations?
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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(13-12p) × (13+12p)
...
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
1.2. Between which two integers does each of the following irrational numbers lie?
1.2.1. √8
1.2.2. √29
1.2.3 √37
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].
What is square root?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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A triangle has side lengths of 6, 8, and 10. Is it a right triangle.
A. No, the sum of the legs is not equal to the hypotenuse.
B. Yes, the sum of the legs is equal to the hypotenuse.
C. No, the sum of the square of the legs is not equal to the square of the hypotenuse.
D. Yes, the sum of the square of the legs is equal to the square of the hypotenuse.
I know its a right angle so it's B or D, but which one.
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.
c) R= {(x,y): Y is the area of triangle x 3 determine if the relation is function or not
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.
What is the function?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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Fractions Questions 2
Find the linear approximation of the functionf(x)=4√81+x at a=0. Use it to approximate the numbers 4√81.02 and 4√80.99.
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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You can make a triangle with the following measurements: 5, 5, 8
True
False
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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Please urgent need the work and answer
X=3.2
Y=6.1
Z=0.2
XZ +Y2
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
b. The 1-week growth factor of the height (in feet) of a bamboo plant is 1.27. Your. classmate says that to find the 1-day growth factor, we need to calculate 1.27 /7 Is this correct? If so, explain why. If not, what is the correct 1-day growth factor and how is it calculated? In either case, be sure to explain how to use the 1-day growth factor to find the 1-week growth factor in order to verify the answer.
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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In circle S with m/RST = 126 and RS = 3 units, find the length
of arc RT. Round to the nearest hundredth.
RT arc length 3.31 units (rounded to two decimal places).
What is a circle and what is its formula?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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Write down the letters of the circled points and order them by their second coordinate values, from least to greatest. You will spell a word that describes a way to compare quantities.
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.
What is an ordered pair?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:
T = (-7, -2)R = (-6, -4)O = (-5, 5)A = (-4, 2)P = (-4, -4)K = (-3, -6)I = (3, 4)N = (3, 3)M = (6, 0).B = (7, 3).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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6(2x-3)-2(2x+1) simplest form
Answer:
16x-20
Step-by-step explanation:
6(2x-3)-2(2x+1)
12x-18-4x+2
16x-20
a certain congressional committee consists of 13 senators and 9 representatives. how many ways can a subcommittee of 5 be formed if at least 2 of the members must be representatives?
Answer:
Step-by-step explanation:
What is the slope-intercept form of the linear equation 4x + 2y = 24?
Drag and drop the appropriate number, symbol, or variable to each box.
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]
the heights of adult men can be approximated as normal with a mean of 70 and standard eviation of 3 what is the probality man is shorter than
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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What is the surface area?
5 yd
6 yd
5 yd
5 yd
4 yd
square yards
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.
What is prism and how does it work?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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one gold nugget weighs 0.008 ounces. a second gold nugget weighs 0.8 ounces. how many times as much as the first nugget does the second nugget weigh? how many times as much as the second nugget does the first nugget weigh
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.
An unitary method is what?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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HELP PLSSSSSSSSS GIVING 20 POINTS
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.
What is Volume?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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What is the gradient of the line segment between the points 2,4 and 4,6
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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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
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.
Question is in photo answer a through d please
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]
How to take the products?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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growth models like those used in forecastx usually model situations well where a process grows multiple choice a. until reaching saturation. b. at a more or less constant rate. c. at an exponential rate. d. in a linear fashion.
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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Minimum wage, Part I. Do a majority of US adults believe raising the minimum wage will help the economy, or is there a majority who do not believe this? A Rasmussen Reports survey of 1,000 US adults found that 42% believe it will help the economy. Conduct an appropriate hypothesis test to help answer the research question. Use the steps at the top of page 198. (a) Prepare. (b) Check (c) Calculate. (d) Conclude
(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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