Given the expression:
[tex]-k+10m^2-6-n^{2^{}}[/tex]The second term in the expression means the 2nd term from left to right of an expression.
Here, the second term is 10m².
A coefficient is a number that is being multiplied by the variable.
Therefore, the coefficient of the term 10m² is 10.
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
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.
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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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
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]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
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]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
Compute P(7,4)
From probability and statistics
The resultant answer from computing P(7,4) from probability and statistics is 840.
What is probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.The probability is computed by dividing the total number of possible outcomes by the number of possible ways the event could occur.So, P(7,4):
This is a permutation and can be calculated as:
ₙPₓ= n! / (n - x)!Here, n = 7 and x = 4Put the values in the given formula:
P(7, 4) = 7! / (7 - 4)!P(7, 4) = 7! / 3!P(7, 4) = 840Therefore, the resultant answer from computing P(7,4) from probability and statistics is 840.
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The initial directions are in the pic below. I’m sending 2 pics now. And the other 2 soon. For a total of 4.
Recall that the rule of transformation of a point reflected over the y-axis is as follows:
[tex](x,y)\rightarrow(-x,y).[/tex]Therefore, the transformed coordinates of the vertices of the triangle are:
[tex]\begin{gathered} N(4,6)\rightarrow N^{\prime}(-4,6), \\ P(1,6)\rightarrow P^{\prime}(-1,6), \\ Q(3,4)\rightarrow Q^{\prime}(-3,4)\text{.} \end{gathered}[/tex]Therefore, the image of the triangle is the triangle with the above vertices.
Answer:
х3,2y=x?(x, y)00(0,0)2.4(2, 4)For which value of x is the row in the table of values incorrect?3The function is the quadratic function y = -x?4366를18(3,6)(5,18 )5
Since the given equation is
[tex]y=\frac{3}{4}x^2[/tex]If x = 0, then
[tex]y=\frac{3}{4}(0)^2=0[/tex]Then x = 0 is correct because it gives the same value of y in the table
If x = 2
[tex]\begin{gathered} y=\frac{3}{4}(2)^2 \\ y=\frac{3}{4}(4) \\ y=3 \end{gathered}[/tex]Since the value of y in the table is 4
Then x = 2 is incorrect
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]
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]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]Rewrite 25% as a fraction in simplest form.
Answer:
1/4
Step-by-step explanation:
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
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]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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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
An online bookstore is having a sale. All paperback books are $6.00 with a flat shipping fee of $1.25. you purchase "b" booms and your total is "c". What is the independent variable?$6.00"c" cost"b" books$1.25
Let:
c = total
a = cost of each book
w = flat shipping fee
Therefore, the total is given by:
[tex]c=ab+w[/tex]where:
b = number of books
[tex]c=6x+1.25[/tex]The independent variable is:
"b" books
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]Michael earned some Money doing odd jobs last summer and put it in a savings account that earns 13% interest compounded quarterly after 2 years there is 100.00 in the account how much did Michael earn doing odd jobs
Michael earned some Money doing odd jobs last summer and put it in a savings account that earns 13% interest compounded quarterly after 2 years there is 100.00 in the account How much did Michael earn doing odd jobs?
____________________________________
13% interest compounded quarterly
after 2 years there is 100.00
_________________________________-
interest compounded
A = P(1 + r/n)^nt
A= Final amount
P= Principal Amount
r= interest
n= number of compounding periods (year)
t= time (year)
_____________________
Data
A= 100.00
P= Principal Amount (The question)
r= interest (0.13)
n= number of compounding periods (4)
t= time (2)
_________________
Replacing
A = P(1 + r/n)nt
P = A / ((1 + r/n)^nt)
P = 100.00/ ((1 + 0.13/4)^4*5)
P= 100.00/ (1.0325^20)
P= 52
________________
Michael earns doing odd jobs 52 dollars.
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,
3x - 7 = 3(x - 3) + 2
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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given the parent function f (x) identify whether g (x) is a reflection about a horizontal line of reflection or vertical line of reflectionf (x) = 6^x and g (x) = - (6^x)
The relation between this two functions is g(x) = -f(x)
This means that g(x) is a reflection of f(x) about the x-axis, that is, a reflection about a horizontal line
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]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
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)