(4i+1)² can be simplified to 8i-15
What is Complex number?A complex number is a number of the form a + bi, where a and b are real numbers
Given expression is (4i+1)²
four times of i plus one whole square.
(4i+1)² can be expanded by using algebraic identity
(a+b)²=a²+b²+2ab
(4i+1)²
Now put a as 4i and b as 1
(4i+1)²=16i²+1+2(4i)(1)
Where i²=-1
=-16+1+8i
=8i-15
Hence (4i+1)² can be simplified to 8i-15
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Describe the sampling distribution of p. Assume the size of the population is 30,000. n 700, p 0.388 Describe the shape of the sampling distribution of p. Choose the correct answer below. O A. The shape of the sampling distribution of p is not normal because n s0.05N and np(1-p)210. O B. The shape of the sampling distribution of p is approximately normal because ns0.05N and np(1-p) <10. C. The shape of the sampling distribution of pis not normal because n s05N and np(1-p)<10 O D. The shape of the samplingdistrbution of p is approximately normal because n s0.05N and np(1 -p)210 Determine the mean of the sampling distribution of p. Round to three decimal places as needed.) Determine the standard deviation of the sampling distribution of p. Round to three decimal places as needed.)
The correct option regarding the sampling distribution of p, considering the Central Limit Theorem, is given as follows:
D. The shape of the sampling distrbution of p is approximately normal because n <= 0.05N and np(1 -p) > 10.
The mean of the sampling distribution of p is of:
0.388.
The standard deviation of the sampling distribution of p is of:
0.0184.
What is defined by the Central Limit Theorem?The Central Limit Theorem defines the distribution of the sampling distribution of sample proportions of a proportion p in a sample of size n, in which:
The mean is [tex]\mu = p[/tex].The standard deviation is [tex]s = \sqrt{\frac{p(1 - p)}{n}}[/tex]The shape is approximately normal.As long as these two conditions are respected:
[tex]n \leq 0.05N[/tex][tex]np(1 - p) > 10[/tex]The values of the parameters in this context are given as follows:
N = 30000, n = 700, p = 0.388.
Hence the conditions are:
n/N = 700/30000 = 0.0233 < 0.05.np(1 - p) = 700 x 0.388 x 0.612 = 166 > 10.Then the shape is approximately normal and option D is correct.
The mean of the distribution is of:
[tex]\mu = p = 0.388[/tex]
The standard error of the distribution is of:
[tex]s = \sqrt{\frac{p(1 - p)}{n}} = \sqrt{\frac{0.388(0.612)}{700}} = 0.0184[/tex]
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81% of the tickets sold at an amusement park were discount tickets. If the park sold 800 tickets in all, how many discount tickets did it sell?
Answer:
40% = 0.40800 / 0.40 = 2000 total tickets were sold
Step-by-step explanation:
Answer:
648
Step-by-step explanation:
ans: 81/100 x800
=648
SOMEONE HELP PLEASE
⇒The volume is given and the height is give. In the equation [tex]V=\pi r^{2} h[/tex]plug in the known value V which is equal to [tex](160\pi )m^{3}[/tex] and h which is equal to 8m and solve for r which is the radius
⇒[tex]160\pi =\pi r^{2} *(8)\\\frac{160\pi}{\pi } =\frac{\pi r^{2} *(8)}{\pi } \\160=8r^{2} \\8r^{2} -160=0\\8(r^{2} -20)=0\\\frac{8(r^{2} -20)}{8} =\frac{0}{8} \\r^{2} -20=0\\(r+\sqrt{20} )(r-\sqrt{20} )=0\\r+\sqrt{20} =0\\or\\r-\sqrt{20} =0\\\\r=2\sqrt{5} \\or\\r= -2\sqrt{5}[/tex]
⇒Note radius is a distance therefore it cannot be negative meaning radius r is equal to [tex]\sqrt{20} =2\sqrt{5}[/tex]m
expressed in decimal is 4.5m
The graph below illustrates the decay of a radioactive substance over t days.
Use the graph to estimate the average decay rate from t = 5 to t = 15 Note: Your answer will be negative.
The estimate of the average decay rate of change is -0.6
How to estimate the average decay rate of the function?From the question, we have the graph and the interval is given as
t = 5 to 15
This can also be represented and expressed as
(a, b) = [5, 15]
From the attached graph, we have
f(5) = 12
f(15) = 6
The estimate of the average decay rate of change is calculated as
Rate = [f(b) - f(a)]/[b - a]
This gives
Rate = [f(15) - f(5)]/[15 - 5]
So, we have
Rate = [6 - 12]/[15 - 5]
Evaluate
Rate = -0.6
Hence, the average decay rate of change is -0.6
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You use a line of best fit for a set of data to make a prediction about an unknown value. The correlation coefficient for your data set is 0. How confident can you be that your predicted value will be reasonably close to the actual value?
Responses
I can’t be confident at all; this is about as close to a random guess as you can get.
I can be a little confident; it might be close, or it might be way off.
I can be very confident; it will be close, but it probably won’t be exact.
The correct option regarding the correlation coefficient is that A. I can’t be confident at all; this is about as close to a random guess as you can get.
What is a correlation coefficient?The correlation coefficient is a statistical measure of the strength of a two-variable linear relationship. Its values can range between -1 and 1. A correlation coefficient of -1 denotes a perfect negative, or inverse, correlation, in which values in one series rise while those in the other fall, and vice versa.
A coefficient of one indicates that there is a perfect positive correlation, or a direct relationship. A correlation coefficient of 0 indicates that no linear relationship exists. In science and finance, correlation coefficients are used to assess the degree of association between two variables, factors, or data sets.
In this case, the fat that the person gets 0 implies that it's probably a random guess. In conclusion, the correct option is A.
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A theatre contains 439 seats and the ticket prices for a recent play were $48 for adults and $28 for children. if the total proceeds we $15,852 for a sold-out matinee, how many of each type of ticket were sold?
The theatre sold 178 adult tickets and 261 children tickets for the play.
It is given that the total number of seats is 439 seats.
There are two types of tickets available- children and adults.
The price for adult tickets is $48 and that for children is $28.
Let the number of adult tickets sold be x
Let the number of children's tickets sold be y.
The show was a sold-out
Hence,
x + y = 439 [1]
48x + 28y = 15852 [2]
From equation [1] we get
x = 439 - y
putting this result in equation [2] gives us
48(439 - y) + 28y = 15852
or, 21072 - 48y + 28y = 15852
or, -20y = - 5220
or, y = -5220/ -20
or, y = 261
Therefore,
x + 261 = 439
or, x = 439 - 261
or, x = 178
Hence, 178 adult tickets were sold and 261 children's tickets were sold.
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Simplify.
ab2−−−√+39ab2−−−−√−34ab2−−−−√
Assume all variables are nonnegative.
Answer:In this item, I take it that we are to get the cube root of the given expression, -64x6y9. First, we look into the numerical coefficient, this is the product when -4 is multiplied to itself three times as shown below.
-64 = (-4)(-4)(-4)
Then,
x6 = x2 (x2) (x2)
and,
y9 = (y3)(y3)(y3)
If we take the cube root, we consider only one item per product. Thus, the answer is,
-4x²y³
Step-by-step explanation:
A cockroach can travel at a speed of 80 centimeters per second. A centipede can travel at 30 meters per
minute. Which can travel faster?
Answer:
The cockroach is faster
Step-by-step explanation:
a grocery store has an average sales of $7,100 per day. the store introduced several advertising campaigns in order to increase sales. to determine whether or not the advertising campaigns have been effective in increasing sales, a sample of 100 days of sales was selected. it was found that the average was $7,275 per day. from past information, it is known that the standard deviation of the population is $1,500. we know that the test statistic is 1.1667. find the p-value.
The P value of the question in the given condition is less than 0.05 hence it reject the null hypothesis.
What is null hypothesis?According to the null hypothesis, an independent variable and a dependent variable have no association with one another. The results might be the result of an experimental or sampling error if the hypothesis indicates a link between the two factors. There is a relationship in the measured phenomena, but, if the null hypothesis is incorrect.
First we find the value of small z
z = (x - μ) / (α / [tex]\sqrt{100}[/tex])
z = (7275 - 7100) / (1500/[tex]\sqrt{100}[/tex])
z = (175) / 150
z = 1.1667
As we have verified the test statistic value and it matched.
Then,
P value approach
Hence P value must be equal to 0.0013
As p value is less than 0.05 , Reject the null hypothesis.
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help meeeeeeeeeeeeeee pleaseee
The vertex of the curve is at (-2, -4) and the axis of symmetry is at -2
The curve opens downward.
from, the graph, the roots of the equation are -4 and 0
so if -4 is a root, (x + 4) is a factor and if 0 is a root, then x is a factor.
The equation of the curve is the product of the factors of the curve which is y = x(x + 4)
y = [tex]x^{2}[/tex] + 4x
the x coordinate of the vertex = -b/2a = axis of symmetry
where a is the coefficient of [tex]x^{2}[/tex] and b is the coefficient of x
so a = 1, b = 4
x coordinate of vertex = -4/2 = -2
substitute x = -2 into y = [tex]x^{2}[/tex] + 4x to find the y-coordinate of the vertex
y = [tex](-2)^{2}[/tex] + 4(-2)
y = 4 -8
y = -4
vertex = (-2, -4)
The axis of symmetry is -b/2a which is -2
The curve opens downward as the vertex is at -4
In conclusion, the vertex of the parabola is (-2, -4) and the axis of symmetry is -2 and the parabola opens downward
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X=3/5
Y=1/3
z=2 4/5
work out Z + X x Y
The value of the summation will be equal to 3.
What is an expression?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 X=3/5, Y=1/3, and z=2⁴/₅.
The value of the Z+ ( X x Y ) will be calculated as,
E = Z + ( X x Y )
E = 2⁴/₅ + ( 3 / 5 ) x ( 1 / 3 )
E = 14 / 5 + 1 / 5
E = 15 / 5
E = 3
Therefore, the value of the summation will be equal to 3.
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An object attached to a coiled spring is pulled down a distance of 10 centimeters from its rest position and then released.
Assuming that the motion is simple harmonic
with a period of 2 seconds, write an equation that relates the displacement d of the object from its rest position after t seconds.
Also assume that the positive direction of
the motion is up. At time t=0 the object is at its resting position and moving down.
Answer: The general form for an equation that models a wave is this: (+/-) a (sin/cos) (2π(x-p)/T), where a is your amplitude, p is your phase shift, and T is your period. The (+/-) becomes + if the graph is to start in the positive direction, and - if it is to start in the negative direction. The (sin/cos) becomes sine if the graph is to start at 0 before being shifted, while it becomes cosine if the graph is to start at the amplitude.
In this case, our graph starts out negative, and at the amplitude with no phase shift, so the (+/-) becomes -, (sin/cos) becomes cos, and p is zero. Substituting in the values given in the problem, a = 9 and T = 7, we find this equation: d = -9cos(2πt/7).
Step-by-step explanation:
Write an equation of the line, in point-slope form, that passes through the two given points.
points: (-2,10), (10 -14)
The required equation of the line will be y = 2x + 6 which passes through the points (-2,10), (10 -14).
What is the slope of the line?The slope of a line is defined as the gradient of the line.
Given that line passes through the points (-2,10), (10 -14)
Let the required line would be y - y₁ = (y₂ - y₁)/(x₂ -x₁ )[x -x₁]
x₁ = -2, y₁ = 10
x₂ = 10, y₂ = -14
⇒ y - y₁ = (y₂ - y₁)/(x₂ -x₁ )[x -x₁]
Substitute values in the equation, we get
⇒ y - 10 = (-14 - 10)/(10-(-2))[x -(-2)]
⇒ y - 10 = (-24)/(12 )[x +2]
⇒ y - 10 = -2(x +2)
⇒ y = -2x - 4 + 10
⇒ y = -2x + 6
Therefore, the equation of the line would be y = 2x + 6 which passes through the points (-2,10), (10 -14).
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hello please help
I WILL GIVE BRAINLIEST!
describe the nature of the roots of this equaition. 2x^2 - x+1=0
According to the discriminant, the quadratic equation y = 2 · x² - x + 1 has two roots that are complex and conjugate.
How to determine the nature of the roots in a quadratic equation
Quadratic equations are algebraic expressions of the form a · x² + b · x + c, where a, b, c are real coefficients. In this case, we can infer the nature of its roots by means of a discriminant:
D = b² - 4 · a · c
Whose possible results are listed below:
D > 0, two distinct real roots.D = 0, two equal real roots. D < 0, two conjugate complex roots.If we know that a = 2, b = - 1 and c = 1, then the nature of the roots of the polynomial:
D = (- 1)² - 4 · 2 · 1
D = 1 - 8
D = - 7
Then, the quadratic equation has two conjugate complex roots.
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Segment RS is reflected over the line y = and then translated by (x +3, y + 4). The resulting segment
R" S" has coordinates R" (-1,4) and S" (-3,-2). What are the coordinates of the segment RS?
R=
S =
Answer:
-1,-2
Step-by-step explanation:
get the x and y value and combine the coordinates using the slope formula
Write a polynomial f (x) that satisfies the given conditions.
Degree 3 polynomial with integer coefficients with zeros 7i and 9/5
If the degree of the polynomial is 3 with zeros 7i and 9/5, then the polynomial f(x) = [tex]5x^3-9x^2+245x-441[/tex]
The zeros of the polynomial = 7i and 9/5
Here the degree of polynomial is 3, therefore there will be three zeros in polynomial, here only 2 zeros are given. We have to find the third zero of the polynomial.
Here one of the polynomial is complex number, therefore another zero will be the conjugate of the complex zero
Therefore the equation will be
(x+7i)(x-7i)(5x-9) = 0
We have to solve the equation
([tex]x^2[/tex] -7ix+7ix+49)(5x-9) = 0
([tex]x^2[/tex] + 49)(5x - 9) = 0
[tex]5x^3-9x^2+245x-441 =0[/tex]
Therefore
f(x) = [tex]5x^3-9x^2+245x-441[/tex]
Hence, if the degree of the polynomial is 3 with zeros 7i and 9/5, then the polynomial f(x) = [tex]5x^3-9x^2+245x-441[/tex]
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Mrs. Robinson made the table below showing the number of cells in a biology experiment after a number of days. Which type of function best models Mrs. Robinson’s data?
Days / Number of Cells
2 / 4
3 / 8
4 / 16
5 / 32
6 / 64
7 / 128
a) an exponential function
b) a quadratic function
c) an absolute value function
d) a linear function
The type of function best models Mrs. Robinson’s data is A. exponential function.
What is an exponential function?The formula f(x) = a^x defines an exponential function, where x is the input variable as an exponent. The exponential curve is determined by the exponential function and the value of x. Where an is greater than zero and less than one. x can be any actual number.
Mrs. Robinson created the table, which shows the number of cells in a biology experiment after a certain number of days. The independent variable, or x-value, in an exponential function is the exponent, while the base is a constant.
In this case, we can see that:
2 days = 2² = 4
3 days = 2³ = 8
4 days = 2⁴ = 16
This is an exponential function.
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What is the solution set for 5 - 5 = 15, given the replacement set {0, 1, 2, 3, 4}? O x = 4 O x = 3 O x = 2 O x = 1 x = 0
The solution set for the given equations is x = 4.
What is a set?
A set contains elements or members that can be mathematical objects of any kind, including numbers, symbols, points in space, lines, other geometric shapes, variables, or even other sets. A set is a mathematical model for a collection of various things.
Here,
we put the value of x in the given equation and justify our answer
when we x=4, we get
5x−5=15
5(4) - 5 = 15
20 - 5 = 15
15 = 15
Hence, the solution set for the given equations is x = 4.
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Write the equation of the line in slope - intercept form
The equation of line in slope-intercept form is y = 2x + 1
Q. What is Equation of line ?
A straight line's general equation is y = mx + b, where m denotes the gradient or slope and y = b denotes the point at which the line crosses the y-axis. On the y-axis, this value b is referred to as the intercept.
We know the equation of line is
y = mx + b
where,
m = slope
b = y - intercept
To form an equation we need to find 'b' and 'm'.
so, first find 'b' i.e, y - intercept
For that, you just need to see the red line cuts the y-axis at its sharp grid means not in middle of the grid.
So, by observing the graph we see y = 1 where the red line cuts the y-axis
so we get, b = 1 means y-intercept
Now, we need to find slope (m).
For that, we know slope = rise / run
So take any point on graph which is easily to recognize the (x,y) points on graph.
Here I take the point (2, 5).
Now mark that point and find rise and run values.
rise = 4 (count from y = 1 to y = 5 )
run = 2 (count from x = 0 to x = 2)
Now, put the values and get the slope.
slope (m) = 4 / 2
= 2
Now, put the y-intercept and slope values in equation of line .
y = mx + b
y = 2x + 1
Hence, the equation of line in slope-intercept form is y = 2x + 1
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Complete the statement.
48 cm = mm
The value of the 48 cm will be equal to 480 mm.
What is a unit conversion?Multiplication or division by a numerical factor, selection of the correct number of significant figures, and unit conversion are all steps in a multi-step procedure.
Given that the number is 48 cm. Here 48 cm is the length of any object the value of 48 cm in the unit mm will be calculated as below,
1 cm = 10 mn
48 cm = 48 x 10 mm
48 cm = 480 mm
Therefore, the value of the 48 cm will be equal to 480 mm.
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Naomi is cutting patches in the shape of right triangles to make a quilt. Each triangle has a diagonal side of 14.5 inches and a short side of 5.5 inches. What is the length of the third side of each triangular patch?
Help? Fractions/visual
3/3 * 3/4 is fraction of green color .
What is fraction in math?
Part of a whole is a fraction. In mathematics, the number is represented as a quotient, where the numerator and denominator are divided. Both are integers in a simple fraction. Whether it is in the numerator or denominator, a complex fraction contains a fraction. The numerator and denominator of a correct fraction are opposite each other.green colored boxes = 3
blue colored boxes = 3
fraction of green = 3/3 * 3/4
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Above are two different models of the same triangle. If the area of the model on the left is 24 sq cm, what is the area of the model on the right?
A.
120 sq cm
B.
26.5 sq cm
C.
48 sq cm
D.
96 sq cm
The area of the model on the right is given by 96 sq cm
The correct answer option is option D.
What is a Model?A model represents a real object on a drawing paper.
Given that the model is triangular in shape, the model on the right is 2 times the model on the left.
Area of model on the left = 24 square cmTherefore, area of model on the left = area of model on the left × 2².
Area of model on the left = 24 × 4
Area of model on the left = 96 square cm.
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Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two
different proportional relationships represented in different ways.
Will give points to first correct answer that follows all the steps right.
Answer:
I Need Help On That Too
Step-by-step explanation:
What are the two square roots of 1/121
Answer:
-1/11, +1/11
Step-by-step explanation:
You want the two square roots of 1/121.
Square rootA square root can be either positive or negative.
[tex]\pm\sqrt{\dfrac{1}{121}}=\pm\dfrac{1}{\sqrt{121}}=\boxed{\pm\dfrac{1}{11}}[/tex]
__
Additional comment
The √ symbol generally means the principal square root, the positive root. To get the negative root, we precede the symbol with a minus sign. So, both square roots are identified as ±√( ).
please help will mark u brainliest
The expressions that are not polynomials are the second and third ones:
3 + 1/nq^(1/2) + 5Which expressions are polynomials?A polynomial is a lineal combination of terms of powers of variables, such that the exponents must be positive integers or zero.
So, for example, a polynomial of degree n is:
p(x) = aₙ*xⁿ + ... + a₂*x² + a₁*x + a₀
Where we also can have more than one variable.
Then, for example the first one:
-4p + 7
Is a polynomial of degree 1.
The options that are not polynomials are:
p(n) = 3 + 1/n
p(q) = q^(1/2) + 5
Which are the second and third options.
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Answer:
Those are the answers
Step-by-step explanation:
3 + 1/n
q^(1/2) + 5
please help with this im strugglingggggggg
The dimensions of the kennel and the size of the cylinder indicates;
4.1.1. The two 3D objects which the figure consists of are a triangular prism that lays on top of a rectangular prism at the bottom.
4.1.2. The area of the wood needed to build the dog kennel is approximately 2.85 m²
4.1.3. The number of containers of sealant needed to paint one coat on the dog kennel is approximately 2 containers
4.2. The new height of the water in the container will be approximately 18 cm.
What is the surface area of a solid?The surface area of a solid is found by adding together the area of the surfaces that enclose the solid.
4.1.1. The two 3D objects in the figure are;
A triangular prismA rectangular prism4.1.2. The amount of wood needed is found by finding the surface area, A, of the dog kennel as follows;
A = 2×80×60+2×50×60+50×80+2×0.5×80×40+2×√(40²+40²)×50
A = 22800 + 80·√2×50 = 22800 + 4000·√2
The amount of wood needed = (22800 + 4000·√2) cm²
1 m² = 10,000 cm²
(22800 + 4000·√2) cm² = ((22800 + 4000·√2))/10,000 m²
((22800 + 4000·√2)) cm² = (2.28 + 0.4·√2) m² ≈ 2.85 m²
The amount of wood needed is approximately 2.85 m²4.1.3. 500 milliliters of paint is enough to for 1.5 m² area
The number of containers of paint containers required, n, is therefore;
[tex]n = \dfrac{(2.28 + 0.4\cdot \sqrt{2}) \, m^2 }{1.5 \, m^2/container} = (1.52+0.\overline 6\cdot\sqrt{2} ) \, containers \approx 2 \, containers[/tex]
The number of containers of sealant needed to paint one coat on the dog kennel is approximately 2 containers4.2 Diameter of the base of the water container = 20 cm
Radius of the base = (20 ÷ 2) cm = 10 cm
Height of water in the container = 15 cm
Volume of water added = 1,000 cm³
The new height will be 15 + (1,000/(π×10²)) = (15 + 10/π) cm ≈ 18 cm
The height of the water in the container will rise to approximately 18 centimeters
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Sheri has $15,200 to invest in mutual funds and in bonds. sheri has selected a mutual fund that earns 1% a year and a bond that earns 4% a year. if she wants to earn $548 at the end of the first year, how much does she need to invest into each type of account?
Sheri should invest $2000 in mutual fund and $13,200 in bond.
Let the amount to be invested in mutual fund be x. So, the amount to be invested in bond will be (15,200 - x). Forming the equation now -
1%×x + 4%×(15,200 - x) = 548
x/100 + 60,800/100 - 4x/100 = 548
60,800 - 3x = 54800
3x = 60800 - 54800
3x = 6000
x = 6000 ÷ 3
x = 2000
Amount to be invested in mutual fund = $2000
Amount to be invested in bond = 15,200 - 2000
Amount to be invested in bond = $13,200
Sheri should invest $2000 and $13,200 in mutual fund and bond respectively.
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The hypotenuse of a right triangle measures 8 cm and one of its legs measures 4 cm.
Find the measure of the other leg. If necessary, round to the nearest tenth.
Answer:
4√3 (about 6.9) cm.
Step-by-step explanation:
In a 30°-60°-90° triangle, the length of the hypotenuse is twice the length of the shorter leg, and the length of the longer leg is √3 times the length of the shorter leg.
Here, the length of the longer leg is 4√3, or about 6.9, cm.
