data
Area = 126pi m^2
diameter = 22
TA = pi r h + pir^2
126pi = LA + pi(11)^2
LA = 126pi - 121pi
LA = 5pi
Letter B.
Rewrite 25% as a fraction in simplest form.
Answer:
1/4
Step-by-step explanation:
Sketch the graph of the polynomial function. Use synthetic division and the remainder theorem to find the zeros.
GIVEN:
We are given the following polynomial;
[tex]f(x)=x^4-2x^3-25x^2+2x+24[/tex]Required;
We are required to sketch the graph of the function. Also, to use the synthetic division and the remainder theorem to find the zeros.
Step-by-step solution;
We shall begin by sketching a graph of the polynomial function.
From the graph of this polynomial, we can see that there are four points where the graph crosses the x-axis. These are the zeros of the function. One of the zeros is at the point;
[tex](-1,0)[/tex]That is, where x = -1, and y = 0.
We shall take this factor and divide the polynomial by this factor.
The step by step procedure is shown below;
Now we have the coefficients of the quotient as follows;
[tex]1,-3,-22,24[/tex]That means the quotient is;
[tex]x^3-3x^2-22x+24[/tex]We can also divide this by (x - 1) and we'll have;
We now have the coefficients of the quotient after dividing a second time and these are;
[tex]x^2-2x-24[/tex]The remaining two factors are the factors of the quadratic expression we just arrived at.
We can factorize this and we'll have;
[tex]\begin{gathered} x^2-2x-24 \\ \\ x^2+4x-6x-24 \\ \\ (x^2+4x)-(6x+24) \\ \\ x(x+4)-6(x+4) \\ \\ (x-6)(x+4) \end{gathered}[/tex]The zeros of this polynomial therefore are;
[tex]\begin{gathered} f(x)=x^4-2x^3-25x^2+2x+24 \\ \\ f(x)=(x+1)(x-1)(x-6)(x+4) \\ \\ Where\text{ }f(x)=0: \\ \\ (x+1)(x-1)(x-6)(x+4)=0 \end{gathered}[/tex]Therefore;
ANSWER:
[tex]\begin{gathered} x+1=0,\text{ }x=-1 \\ \\ x-1=0,\text{ }x=1 \\ \\ x-6=0,\text{ }x=6 \\ \\ x+4=0,\text{ }x=-4 \end{gathered}[/tex]Assume the random variable X has a binomial distribution with the given probability of obtaining a success. Find the following probability, given the number of trials andthe probability of obtaining a success. Round your answer to four decimal places.P(X= 15), n = 18, p = 0.8TablesKeynad
Recall that the probability of a binomial distribution is given by
[tex]P(X=x)=^^nC_r\cdot p^x\cdot(1-p)^{n-x}[/tex]Where n is the number of trials, p is the probability of success, and x is the variable of interest.
nCr is the number of combinations.
For the given case, we have
n = 18
p = 0.8
x = 15
Let us find the probability P(X=15)
[tex]\begin{gathered} P(X=15)=^{18}C_{15}\cdot0.8^{15}\cdot(1-0.8)^{18-15} \\ P(X=15)=816\cdot0.8^{15}\cdot0.2^3 \\ P(X=15)=0.2297 \end{gathered}[/tex]Therefore, the probability P(X=15) is 0.2297
Segment AB and segment CD intersect at point E. Segment AC and segment DB are parallel.
To begin we shall sketch a diagram of the line segments as given in the question
As depicted in the diagram, line segment AC is parallel to line segment DB.
This means angle A and angle B are alternate angles. Hence, angle B equals 41 degrees. Similarly, angle C and angle D are alternate angles, which means angle C equals 56.
Therefore, in triangle EAC,
[tex]\begin{gathered} \angle A+\angle C+\angle AEC=180\text{ (angles in a triangle sum up to 180)} \\ 41+56+\angle AEC=180 \\ \angle AEC=180-41-56 \\ \angle AEC=83 \end{gathered}[/tex]The measure of angle AEC is 83 degrees
a certain number was multiplied by 3. then, this product was divided by 10.2. finally, 12.4 was subtracted from this quotient, resulting in a difference of -8.4. what was this number
Answer:
13.6
Step-by-step explanation:
[tex] \frac{3x}{10.2} - 12.4 = - 8.4[/tex]
[tex] \frac{3x}{10.2} = 4[/tex]
[tex]3x = 40.8[/tex]
[tex]x = 13.6[/tex]
For how many integers n is 28÷n an interger
An integer, pronounced "IN-tuh-jer," is a whole number that can be positive, negative, or zero and is not a fraction. Integer examples include: -5, 1, 5, 8, 97, and 3,043. The following numbers are examples of non-integers: -1.43, 1 3/4, 3.14,.09, and 5,643. 1.
How do you determine an integer's number from a number?
Basic Interest Calculator
Simple interest is calculated by multiplying the principal by the time, interest rate, and time period. "Simple Interest = Principal x Interest Rate x Time" is the written formula. The simplest method for computing interest is using this equation.
The answer to the question "How many integers are there in n?" is n-1.
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Explain the behavior of f(x)= ln (x-a) when x=a. Give values to x and a such that x-a=0
SOLUTION:
Step 1:
In this question, we are given the following:
Explain the behavior of :
[tex]f(x)\text{ = ln\lparen x-a\rparen}[/tex]when x=a.
Give values to x and a such that:
[tex](x-a)\text{ = 0}[/tex]Step 2:
The graph of the function:
[tex]f(x)\text{ = In \lparen x- a \rparen}[/tex]are as follows:
Explanation:
From the graph, we can see that the function:
[tex]f(x)\text{ = ln\lparen x-a\rparen}[/tex]is a horizontal translation, shift to the right of its parent function,
[tex]f(x)\text{ = In x}[/tex]Missed this day of class and have no idea how to solve this last problem on my homework
From the given expression
a) The linear system of a matrix form is
[tex](AX=B)[/tex]The linear system of the given matrix will be
[tex]\begin{gathered} 2x+y+z-4w=3 \\ x+2y+0z-7w=-7 \\ -x+0y+oz+w=10 \\ 0x+0y-z+3w=-9 \end{gathered}[/tex]b) The entries in A of the matrix is
[tex]\begin{gathered} \text{For }a_{22}=2 \\ a_{32}=0 \\ a_{43}=-1 \\ a_{55}\text{ is undefined} \end{gathered}[/tex]c) The dimensions of A, X and B are
[tex]\begin{gathered} A\mathrm{}X=B \\ \begin{bmatrix}{2} & 1 & {1} & -4 \\ {1} & {2} & {0} & {-7} \\ {-1} & {0} & {0} & {1} \\ {0} & {0} & {-1} & {3}\end{bmatrix}\begin{bmatrix}x{} & {} & {} & {} \\ {}y & {} & {} & {} \\ {}z & {} & {} & {} \\ {}w & {} & {} & {}\end{bmatrix}=\begin{bmatrix}3{} & {} & {} & {} \\ {}-7 & {} & {} & {} \\ {}10 & {} & {} & {} \\ {}-9 & {} & {} & {}\end{bmatrix} \end{gathered}[/tex]Given the points (3, -2) and (4, -1) find the slope
Slope is
[tex]\text{slope}=\frac{y2-y1}{x2-x1}[/tex]Then:
[tex]\text{slope}=\frac{-1-(-2)}{4-3}=\frac{-1+2}{1}=\frac{1}{1}=1[/tex]Answer: slope = 1
A rectangular athletic field is twice as long as it is wide. If the perimeter of the athletic field is 360 yards, what are its dimensions?
Answer:
The width is 60 and the length is 120
Step-by-step explanation:
Let l = length
Let w = width
l = 2w
Perimeter
l + l + w + w = 360 Substitute 2w for l
2w + 2w + w + w =360 Combine line terms
6w = 360 Divide both sides by 6
w = 60
If w = 60 then l = 120
What are examples of vertical stretch and compression and horizontal stretch and compression?
Examples of vertical stretch and compression and also horizontal stretch/vertical compression are explained below considering x² and
sin(x) function.
What is vertical stretch/vertical compression ?
A vertical stretch is derived if the constant is greater than one while the vertical compression is derived if the constant is between 0 and 1.Vertical stretch means that the function is taller as a result of it being stretched while vertical compress is shorter due to it being compressed and is therefore the most appropriate answer.example : If the graph of x² is is transformed to 2x² Then the function is compressed Vertically.
If the graph of x² is is transformed to x²/2 Then the function is stretch Vertically.
What is horizontal stretch/vertical compression ?
We know that if f(x) is transformed by the rule f(x+a) then the transformation is either a shift ''a'' units to the left or to the right depending on a is positive or negative respectively this phenomenon is horizontal stretch and compression.example : If the function y = sin(x) is transformed to y = sin(2x) Then the function is compressed horizontally.
example : If the function y = sin(x) is transformed to y = sin(x/2) Then the function is stretch horizontally.
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Simplify the square root of 25x^4
In this case, we'll have to carry out several steps to find the solution.
Step 01:
data:
[tex]\sqrt{25x^4}[/tex]Step 02:
simplify (radical):
[tex]\sqrt{25x^4}=\sqrt{5^2x^4}=5x^2[/tex]The answer is:
5x²
Answer ASAP please and thank you :)
We can see the pairs (-1, 4) and (1, 4), so the function is not invertible.
Is the function g(x) invertible?
Remember that a function is only invertible if it is one-to-one.
This means that each output can be only mapped from a single input (the outputs are the values of g(x) and the inputs the values of x).
In the table, we can see the pairs (-1, 4) and (1, 4).
So both inputs x = -1 and x = 1 have the same output, this means that the function is not one-to-one, so it is not invertible.
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11. Let the supply and demand functions for sugar is given by the following equations. Supply: p = 0.4x Demand: p = 100 - 0.4x (a) Find the equilibrium demand.
SOLUTION:
Step 1:
In this question, we are given the following:
Let the supply and demand functions for sugar be given by the following equations. Bye
Supply: p = 0.4x
Demand: p = 100 - 0.4x
a) Find the equilibrium demand.
Step 2:
At Equilibrium,
[tex]\begin{gathered} \text{Supply}=\text{ Demand} \\ 0.\text{ 4 x = 100 - 0. 4 x} \end{gathered}[/tex]collecting like terms, we have that:
[tex]\begin{gathered} 0.4\text{ x + 0. 4 x = 100} \\ 0.8\text{ x = 100} \end{gathered}[/tex]Divide both sides by 0.8, we have that:
[tex]\begin{gathered} x\text{ = }\frac{100}{0.\text{ 8}} \\ x\text{ = 125} \end{gathered}[/tex]
Step 3:
Recall that:
[tex]\begin{gathered} \text{Equilibrium Demand : p = 100 - 0. 4 x } \\ we\text{ put x = 125, we have that:} \\ p\text{ = 100 - 0. 4 (125)} \\ p\text{ =100 -50} \\ p\text{ = 50} \end{gathered}[/tex]CONCLUSION:
Equilibrium Demand:
[tex]p\text{ = 50 units}[/tex]I need help on my practice sheet. needs to be simplified
then
[tex]\begin{gathered} \frac{x+6}{3x}\times\frac{3(x-6)}{(x+6)(x-6)} \\ \frac{x+6}{3x}\times\frac{3}{x+6} \\ \frac{(x+6)\times3}{3x\times(x+6)} \\ \frac{3}{3x} \\ \frac{1}{x} \end{gathered}[/tex]answer: 1/x
I need help graphing 3x+y=-1I already found the x intercept= -1/3
Here, we want to graph the line
To do this, we need to get the y-intercept and the x-intercept
The general equation form is;
[tex]y\text{ = mx + b}[/tex]M is the slope while b is the y-intercept
Let us write the equation in the standard from;
[tex]y\text{ = -3x-1}[/tex]The y-intercept is -1
So we have the point (0,-1)
To get the x-intercept, set y = 0
[tex]\begin{gathered} 0\text{ = -3x-1} \\ -3x\text{ = 1} \\ x\text{ = -}\frac{1}{3} \end{gathered}[/tex]So, we have the x-intercept as (-1/3,0)
Now, if we join the two points, we have successfully graphed the line
TRIGONOMETRY Given a unite circle what is the value for y?
Let's put more details in the given figure:
To find y, we will be using the Pythagorean Theorem.
[tex]\begin{gathered} c^2=a^2+b^2 \\ \text{r}^2=x^2+y^2 \\ \end{gathered}[/tex]Where,
r = radius
x = 1/3
y = uknown
We get,
[tex]\text{r}^2=x^2+y^2[/tex][tex]\begin{gathered} y^2\text{ = r}^2\text{ - }x^2 \\ y^{}\text{ = }\sqrt{\text{r}^2\text{ - }x^2} \end{gathered}[/tex][tex]\text{ y = }\sqrt[]{1^2-(\frac{1}{2})^2}\text{ = }\sqrt[]{1\text{ - }\frac{1}{4}}[/tex][tex]\text{ y = }\sqrt[]{\frac{3}{4}}\text{ = }\frac{\sqrt[]{3}}{\sqrt[]{4}}[/tex][tex]\text{ y = }\frac{\sqrt[]{3}}{2}[/tex]Therefore, the answer is:
[tex]\text{ y = }\frac{\sqrt[]{3}}{2}[/tex]Use the sample data and confidence level given below to complete parts (a) through (d). A drug is used to help prevent blood clots in certain patients. In clinical trials, among 4519 patients treated with the drug. 133 developed the adverse reaction of nausea Construct a 90% confidence interval for the proportion of adverse reactions. a) Find the best point estimate of the population proportion p.
We will have the following:
*First: We determine the standard deviation of the statistic, this is:
[tex]\sigma=\sqrt[]{\frac{\sum ^{133}_1(x_i-\mu)^2}{N}}[/tex]So, we will have:
[tex]\mu=\frac{\sum^{133}_1x_i}{N}\Rightarrow\mu=\frac{8911}{133}\Rightarrow\mu=67[/tex]Then:
[tex]\sigma=\sqrt[]{\frac{\sum^{133}_1(x_i-67)^2}{133}}\Rightarrow\sigma=\sqrt[]{\frac{196042}{133}}\Rightarrow\sigma=\sqrt[]{1474}\Rightarrow\sigma=38.39270764\ldots[/tex]And so, we obtain the standar deviation.
*Second: We determine the margin of error:
[tex]me=cv\cdot\sigma[/tex]Here me represents the margin of error, cv represents the critical value and this is multiplied by the standard deviation. We know that the critica value for a 90% confidence interval is of 1.645, so:
[tex]me=1.645\cdot38.39270764\ldots\Rightarrow me=63.15600407\ldots\Rightarrow me\approx63.156[/tex]*Third: We determine the confidence interval as follows:
[tex]ci=ss\pm me[/tex]Here ci is the confidence interval, ss is the saple statistic and me is the margin of error:
[tex]ci\approx133\pm63.156\Rightarrow ci\approx(69.844,196.256)[/tex]And that is the confidence interval,
A ball bounces to a height of 6.1 feet on the first bounce. Each subsequent bounce reaches a height that is 82% of the previous bounce. What is the height, in feet, of the fifth bounce? Round your answer to the thousandths place.
In the first bounce, the height is
[tex]6.1\times(0.82)^0=6.1[/tex]In the second bounce, the height is
[tex]6.1\times(0.82)^2=5.002[/tex]Then, we can note that the pattern is
[tex]6.1\times(0.82)^{n-1}[/tex]where n represents the number of bounces of the ball. Then, for n=5 (fifth bounce), we get
[tex]\begin{gathered} 6.1\times(0.82)^{5-1} \\ 6.1\times(0.82)^4 \end{gathered}[/tex]which gives
[tex]6.1\times(0.82)^4=2.7579[/tex]Therefore, by rounding to the nearest thousandths, the answer is 2.758 feet
3x - 7 = 3(x - 3) + 2
hi can you see if I did this estimate right?
Mr Manet need 5 guitars for his 4 grandsons and 1 granddaughter.
Each guitar costs $88,
So the total cost of guitars is $88 x 5 = $440
The best estimate among the choices is Choice B. $450
The estimate should always be higher than the actual cost.
152. ) Find all real x such that square root x + 1 = x - Square root x - 1.
Given the equation:
[tex]\sqrt[]{x}+1=x-\sqrt[]{x}-1[/tex]Solving for x:
[tex]\begin{gathered} \sqrt[]{x}+\sqrt[]{x}=x-1-1 \\ 2\sqrt[]{x}=x-2 \end{gathered}[/tex]Now, we take the square on both sides of the equation:
[tex]\begin{gathered} 4x=x^2-4x+4 \\ 0=x^2-8x+4 \end{gathered}[/tex]Now, using the general solution of quadratic equations:
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]From the problem, we identify:
[tex]\begin{gathered} a=1 \\ b=-8 \\ c=4 \end{gathered}[/tex]Then, the solutions are:
[tex]\begin{gathered} x=\frac{-(-8)\pm\sqrt[]{(-8)^2-4\cdot1\cdot4}}{2\cdot1}=\frac{8\pm\sqrt[]{64-16}}{2} \\ x=\frac{8\pm4\sqrt[]{3}}{2}=4\pm2\sqrt[]{3} \end{gathered}[/tex]But the original equation √(x), so x can not be negative if we want a real equation. Then, the only real solution of the equation is:
[tex]x=4+2\sqrt[]{3}[/tex]Identify the graph that has a vertex of (-1,1) and a leading coefficient of a=2.
To determine the vertex form of a parabola has equation:
[tex]f(x)=a(x-h)^2+k[/tex]where V(h,k) is the vertex of the parabola and 'a' is the leading coefficient.
From the question, we have that, the vertex is (-1, 1)
and the leading coefficient is a = 2
We substitute the vertex and the leading coefficient into the vertex form to
get:
[tex]\begin{gathered} f(x)=2(x+1)^2\text{+}1 \\ f(x)=2(x+1)^2+1 \end{gathered}[/tex]The graph of this function is shown in the attachment.
Hence the equation of parabola is
[tex]f(x)=2(x+1)^2+1[/tex]Find 5 number summary for data given
The 5 number summary of the data given is:
Minimum = 59
Q1 = 66.50
Median = 78
Q3 = 90
Maximum = 99
What is the 5 number summary?A stem and leaf plot is a table that is used to display a dataset. A stem and leaf plot divides a number into a stem and a leaf. The stem is the first digit in a number while the leaf is the second digit in the number.
The minimum is the smallest number in the stem and leaf plot. This is 59. Q1 is the first quartile.
Q1 = 1/4 x (n + 1)
Where n is the total number in the dataset
1/4 x 19 = 4.75 term
(64 + 69) / 2 = 66.50
Q3 is the third quartile.
Q1 = 3/4 x (n + 1)
Where n is the total number in the dataset
3/4 x 19 = 14.25 term = 90
The median is the number that is at the center of the dataset.
Median = 1/2(n + 1)
1/2 x 19 = 8.5 term
(76 + 80) / 2 = 78
The maximum is the largest number in the dataset. This number is 99.
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Write a rule for the given translation.P(-3,6) to P^1(-4,8)
To turn P(-3,6) to P'(-4,8), we have to
•Move 1 unit to the left (from -3 to -4)
•Move 2 units up (from 6, to 8)
1. Ms. Oates is going to plant grass in her backyard. It is 14feet wide and 20.5 feet long. What is the area of thebackyard that will need to be covered with grass?
Area of a rectangle is given by the expression:
[tex]A=\text{base}\times height[/tex]Then:
[tex]\begin{gathered} A=20.5\times14 \\ A=287\text{ square f}eet \end{gathered}[/tex]The area that will need to be covered is 287 square feet.
Lesson 12.03: Plot Twists Printable Assessment: Plot Twists Plot Twists Show your work. 1. Use the data set provided to create a line plot. Distance of Ski Trails (miles) 1 2 3 2 7 8 4 м 3 - - - - 2 8 1 8 8 -|+ 100 - mlo 2 2 7 8 -100 100-00 글 1 2 2 1 3 8 3 HH 士。 8 2. What is the total number of ski trails? 3. What is the difference in length between the longest ski trail and the shortest ski trail? 7 4. What is the total length of all the ski trails that are 2 miles long? 8 25 5. What is the sum of the lengths of the shortest and longest ski trails? 6. Sam says the longest ski trail is more than three times the length of the shortest ski trail. Eli says it is less than three times the length. Who is correct? Explain.
The length of a rectangle is 6 more than three times the width. If the perimeter of the rectangle is equal to 274 feet then what are the length and width equal to ?(Both of your answers are decimals)The width =The length =
Given data:
The gieven length of the rectangle in erms of width is L=3w.
The perimeter of rectangel is P=274 feet.
The expressio for the perimeter of the rectangle is,
P=2(L+w)
Substitute the given values in the above expression.
274 feet=2(3w+w)
274 feet=8w
w=34.25 feet.
The length of the rectangle is,
L=3(34.25 feet)
=102.75 feet.
Thus, the width is 34.25 feet and lenth of rectangle is 102.75 feet.
In the accompanying diagram of circle O, COA is adiameter, O is the origin, OA = 1, and mLBOA = 30. Whatare the coordinates of B?
Given:
COA is a diameter
O is the origin
OA = 1
m< BOA = 30
Re-drawing the diagram to show the coordinates of the B:
Let the coordinates of B be (x,y)
Using trigonometric ratio, we can find the length of side AB
From trigonometric ratio, we have:
[tex]tan\text{ }\theta\text{ = }\frac{opposite}{adjacent}[/tex]Substituting we have:
[tex]\begin{gathered} tan\text{ 30 = }\frac{y}{1} \\ Cross-Multiply \\ y\text{ = tan30 }\times\text{ 1} \\ y\text{ = 0.577} \\ y\text{ }\approx\text{ 0.58} \end{gathered}[/tex]Hence, the coordinates of B is (1, 0.58)
Determine the transformations that produce the graph of the functions g (T) = 0.2 log(x+14) +10 and h (2) = 5 log(x + 14) – 10 from the parent function f () = log 1. Then compare the similarities and differences between the two functions, including the domain and range. (4 points)
The transformation to get g(x) from f(x) are:
translate 14 units to the left and 10 unit upwards
[tex]h(x)=5\log (x+14)-10[/tex]the transformatio to get h(x) from f(x) are:
translate 14 units to the left and 10 units downwards