The confidence interval for the population mean at significance level is
2.724<μ<30.76 .
A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".
The margin of error is the range of values below and above the sample statistic in a confidence interval.
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
Population standard deviation: σ = 0.45
Sample size: n = 25
Sample Mean: x= 2.90
Х=2.90 represent the sample mean for the sample
μ population mean (variable of interest)
σ = 0.45 represent the population standard deviation
n=25 represent the sample size
We have the following distribution for the random variable:
X≈N(μ,σ =0.45)
And by the central theorem we know that the distribution for the sample mean is given by:
X≈N( μ, [tex]\frac{σ}{\sqrt{n} }[/tex])
Since the Confidence is 0.95 or 95%, the value of [tex]\alpha =0.05[/tex] and[tex]\frac{\alpha }{2} =0.025[/tex], and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.025,0,1)" and we see that
Z₁ =±1.96
Now we have everything in order to replace into formula:
[tex]2.90-1.96\frac{0.45}{\sqrt{25} }=2.724[/tex]
[tex]2.90+1.96\frac{0.45}{\sqrt{25} }=3.076[/tex]
So on this case the 95% confidence interval would be given by (2.724:3.076) .
At a significance level, the population mean's confidence interval is 2.724–30.76.
To learn more about confidence interval visit:
brainly.com/question/24131141
#SPJ4
Hi i need help with this question.
The perimeter of the state of Wyoming, given the rectangle ABCD and the vertices, is 1, 282 miles
How to find the perimeter?The perimeter is the distance around the shape so to find the perimeter of the shape, you need to find the distance between the sides of the rectangle and then add them up.
The distance between vertices can be found by the formula :
= ((x2 – x1)² + (y2 – y1)²)
The distance between AB is therefore 3.65 miles.
The distance between BC is 2.76 miles
The distance between CD is 3.65 miles.
The distance between AD is 2.76 miles
The perimeter of Wyoming is therefore :
= ( 3.65 x 2) + ( 2.76 x 2 )
= 12.82 miles x 100
= 1, 282 miles
Find out more on perimeter at https://brainly.com/question/21249260
#SPJ1
Find the inverse of y = 5x² - 6.
Answer:
The correct answer is the 3rd option
EXAMPLE 6 The Heaviside function H is defined by
H(t) = {(0 text( if ) t < 0,1 text( if ) t >= 0)
[This function is named after the electrical engineer Oliver Heaviside (1850-1925) and can be used to describe an electric current that is switched on at time t = 0.] Its graph is shown in the figure.
As t approaches 0 from the left, H(t) approaches
. As t approaches 0 from the right, H(t) approaches . Therefore the limit as t approaches 0 of H(t) does not exist.
H(t) = [tex]\left \{ {{0 if t < 0} \atop {1 if t \geq 0}} \right.[/tex]
As t→0 from the left, H(t) approaches 0, as t→0 from right H(t) approaches 1.
From Laplace transformation definition:
L{f(t)} = [tex]\int\limits^\alpha _0 {e^{-st} f(t)} \, dt[/tex]
Given, H(t) = [tex]\left \{ {{0 if t < 0} \atop {1 if t \geq 0}} \right.[/tex]
Then
L{H(t)} = [tex]\int\limits^1_0 {e^{-st} H(t) } \, dt+\int\limits^\alpha _1 {e^{-st} H(t) } \, dt[/tex]
[tex]=\int\limits^1_0 {e^{-st} (0) } \, dt+\int\limits^\alpha _1 {e^{-st} (1) } \, dt[/tex]
[tex]=[\frac{e^{-st} }{-s} ]^{\alpha }_{1}[/tex]
[tex]=\frac{e^{-st} }{s}[/tex]
L{H(t)} =[tex]\frac{e^{-st} }{s}[/tex]
As t→0 from the left, H(t) approaches 0, as t→0 from right H(t) approaches 1.
For such more questions about Heaviside function
https://brainly.com/question/13189084
#SPJ4
PLEASE HELP WILL MARK BARINLIEST
Answer:
Your answer is A.
Step-by-step explanation:
I tried but i doubt that's the answer (NO USELESS ANSWERS I WILL REPORT YOU )
Answer:
Step-by-step explanation:
So, they want the equation of the 4 colored lines, not a coordinate.
a --> x=-4
b --> x=4
c --> y=4
d --> y=-2
bc they are horizontal and vertical lines so only one value is staying the same, depending on whether it's vertical or horizontal.
The functions f and g are defined by the following tables:
Function
Find the following composition of two functions: (f o g)(0) and (g o f)(1).
Write the appropriate formula(s). What is the domain of the function g(x) ? What is the range of the function f(x) ?
The following composition of two functions ( f o g ) ( 0 ) = 1 and ( g o f ) ( 1 ) = 1 .
Given :
The functions f and g are defined by the following tables:
Tables :
x -2 -1 0 1
f ( x ) 1 2 1 0
x 1 -3 0 -4
g ( x ) -2 0 1 5
( f o g ) ( 0 ) = ( f ( g ( 0 ) )
from the table g ( 0 ) = 1
= ( f ( 0 ) )
= 1
( g o f ) ( 1 ) = ( g ( f ( 1 ) )
= ( g ( 0 ) )
= 1
Learn more about the function here:
https://brainly.com/question/9046022
#SPJ4
Nellie is shopping for a new bicycle. She is most interested in color and type of tires.
What is the probability that a randomly selected bike is green given that the bike has bike tires?
Simplify any fractions.
The probability that a randomly selected bike is green given that the bike has road bike tires is 0.66
Given :
Nellie is shopping for a new bicycle. She is most interested in color and type of tires.
Probability :
Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event .
From the table given :
Total number of 6 road bikes = 4
Total road bikes = 2 + 4 = 6
Probability = 4 / 6
= 2 / 3
= 0.66
Hence the probability that a randomly selected bike is green given that the bike has road bike tires is 0.66 .
Learn more about the probability here:
https://brainly.com/question/14210034
#SPJ4
Find a parametric representation for the part of the sphere (a surface, not a solid) of radius 4 centered at the origin that lies (a) inside the cone z= 3(x2 +y 2) (b) inside the cone x= 31(y 2 +z 2 )
c) inside the cone y= x +z 2
Hint: you may want to use spherical-like coordinates, where the roles of x,y and z are permuted.
Answer:
Read carefully below
Step-by-step explanation:
We can use spherical coordinates to represent the points on the sphere. These coordinates are typically denoted as (r, θ, φ), where r is the radius of the sphere, θ is the polar angle, and φ is the azimuthal angle.
In order to find a parametric representation of the part of the sphere that lies inside the given cones, we can use the following approach:
First, we need to find the intersection of the sphere and the cone. This is the set of points that satisfy the equations of both the sphere and the cone.
Then, we can use spherical coordinates to represent these points on the sphere.
Finally, we can use these spherical coordinates as parameters in a parametric equation of the form x = x(r, θ, φ), y = y(r, θ, φ), z = z(r, θ, φ) to represent the points on the part of the sphere that lies inside the cone.
Let's use this approach to find a parametric representation of the part of the sphere that lies inside the cone z = 3(x^2 + y^2) in the first case.
To find the intersection of the sphere and the cone, we need to solve the following system of equations:
x^2 + y^2 + z^2 = 16 (equation of the sphere)
z = 3(x^2 + y^2) (equation of the cone)
Substituting the second equation into the first equation, we get:
x^2 + y^2 + 9(x^4 + y^4) = 16
This equation represents an ellipse in the xy-plane. We can use the parametric equations of an ellipse to represent the points on this ellipse:
x = a * cos(t)
y = b * sin(t)
where a and b are the semi-major and semi-minor axes of the ellipse, respectively, and t is a parameter that varies from 0 to 2π.
We can now use spherical coordinates to represent the points on the part of the sphere that lies inside the cone. We can let r be the radius of the sphere (r = 4), θ be the polar angle (0 ≤ θ ≤ π), and φ be the azimuthal angle (0 ≤ φ ≤ 2π).
The parametric equations of the sphere in spherical coordinates are:
x = r * sin(θ) * cos(φ)
y = r * sin(θ) * sin(φ)
z = r * cos(θ)
Substituting the equations for x and y from the ellipse into the equations for x and y from the sphere, we get:
x = 4 * sin(θ) * cos(φ) = a * cos(t)
y = 4 * sin(θ) * sin(φ) = b * sin(t)
z = 4 * cos(θ) = 3(x^2 + y^2) = 3(a^2 * cos^2(t) + b^2 * sin^2(t))
We can solve for a and b in terms of r and θ:
a = 4 * sin(θ)
b = 4 * sin(θ)
Therefore, the parametric equations for the part of the sphere that lies inside the cone z
Solve the problem by finding x. I don’t know how to? Do you.
The solution of the logarithmic equation:
ln(x - 7) = 3
Is x = 27.09
How to solve the logarithmic function?Here we have the following logarithmic function:
ln(x - 7) = 3
And we want to solve this for x.
Remember that the logarithmic function is the inverse of the exponential function, so now we can use the exponential function in both sides so we get:
exp( ln(x - 7) ) = exp(3)
x - 7 = exp(3)
Now we can add 7 in both sides so we isolate x, we will get:
x = exp(3) + 7
x = 27.09
That is the solution of the logarithmic equation.
Learn more about logarithmic equations by reading:
https://brainly.com/question/28041634
#SPJ1
Question 12
The plans for a zipline are shown. Use two points to determine the slope of the zipline. Then verify that the slope is the same by choosing a
different set of points.
y
B
A
C
The slope of the zipline is Enter your answer as a fraction or decimal.
The slope of the zipline in the given diagram is; -1/3
How to find the slope of the line?The slope of a line is defined as the change in y values divided by change in corresponding x-values.
The formula to find slope here will be;
Slope = (y₂ - y₁)/(x₂ - x₁)
Let us pick two points along line BD namely points C and D.
Coordinate of point C is (7, 2)
Coordinate of point D is; (10, 1)
Thus;
Slope = (1 - 2)/(10 - 7)
slope = -1/3
Let us pick point B and point D now.
Coordinate of point B is; (1, 4)
Thus slope of BD = (4 - 1)/(1 - 10)
= -3/9 = -1/3
The slopes are equal and as such that is the slope of the zip line
Read more about slope of line at; https://brainly.com/question/16949303
#SPJ1
Company A has three times as many customers as company B while company C has 10 customers more than company B. Let x represent the number of customers held by company B, what is the expression so that it represents the total number of customers held by all three companies?
The expression that represents the total number of customers held by all three companies is 5x + 10.
What is a mathematical expression?A mathematical expression is a combination of numbers, variables, and mathematical operands (multiplication, division, subtraction, and addition).
What differentiates a mathematical expression from an equation is the equal symbol because a mathematical expression does not have it.
In simple terms, a mathematical expression is like a phrase in the English language without the complete form of a sentence.
The number of customers held by Company B = x
The number of customers held by Company A = 3x
The number of customers held by Company C = x + 10
The total number of customer for all three companies = x + 3x + x + 10
= 5x + 10
Thus, mathematically, we can conclude that the three companies have 5x + 10 customers.
Learn more about mathematical expressions at https://brainly.com/question/1859113
#SPJ1
The expression that represents the total number of customers held by all three companies is; 5X + 10
What is an Expression?An expression consists of one or more numbers or variables along with one more operation.
X + 1 is an example of an expression.
"X" is the variable, "+" is the operation and 1 is a number. Think of "X" as any number that is unknown.
Representing the variables;
X, Y and Z represents number of customers
Let Company A = Y
Let Company B = X
Let Company C = Z
But,
Company A = 3X
Company C = 10 + X
Therefore;
Total number of customers = Y + X +Z
Substituting;
Total number of customers = 3X + X + 10 + X
Total number of customers = 5X + 10
Learn more about expressions here:https://brainly.com/question/1859113
#SPJ1
what is the answer. a b c or d
all can be the answer I guess
Customers depart from a bookstore according to a Poisson process with rate A per hour Each customer buys a book with probability p, independent of everything else. Find the distribution of the time until the first sale of a book. Find the probability that no books are sold during a particular hour. Find the expected number of customers who buy a book during a particular hour.
The distribution of the time until the first sale of a book [tex]f(x)=\lambda p e^{\wedge_{-}} \lambda p x[/tex]
The probability that no books are sold during a particular hour [tex]\mathrm{P}(\mathrm{y}=0)=\mathrm{e}^{\wedge}-\lambda \mathrm{p}[/tex].
The expected number of customers who buy a book during a particular hour [tex]\mathrm{E}(\mathrm{y})=\lambda \mathrm{p}[/tex]
As per the details share in the above question are as follow,
Poisson process with a rate λ per hour
While customer buys a book with probability p
First we have to find the distribution of the time until the first sale of a book.
Second to find the probability that no books are sold during a particular hour.
Third to find the expected number of customers who buy a book during a particular hour.
Giving the duration till a book sells its first copy
Consider,
Following are some instances of waiting times,
[tex]f(x)=\lambda p e^{\wedge_{-}} \lambda p x[/tex]
The distribution of the time until the first sale of a book [tex]f(x)=\lambda p e^{\wedge_{-}} \lambda p x[/tex]
Now, to calculate the likelihood that no books will be sold at a specific time.
[tex]\mathrm{P}(\mathrm{y}=0)=\mathrm{e}^{\wedge}-\lambda \mathrm{p}[/tex]
The probability that no books are sold during a particular hour [tex]\mathrm{P}(\mathrm{y}=0)=\mathrm{e}^{\wedge}-\lambda \mathrm{p}[/tex].
Consider the Poisson distribution to determine the anticipated number of book purchases during a specific hour.
[tex]\mathrm{E}(\mathrm{y})=\lambda \mathrm{p}[/tex]
The expected number of customers who buy a book during a particular hour [tex]\mathrm{E}(\mathrm{y})=\lambda \mathrm{p}[/tex].
For more such question on Poisson process.
https://brainly.com/question/9123296
#SPJ4
One man can paint a garage in 28 hours. After working for 12 hours, he was given a new job, and a second man finished the painting in 18 hours. How long would it take the second man to paint the whole garage alone? Show the setup/equation used to solve.
The number of hours taken by man to paint the whole garage alone is 31.5 hours.
Given that, one man can paint a garage in 28 hours.
What is time and work?The basic concept of Time and Work is similar to that across all Arithmetic topics, i.e. the concept of Proportionality. Efficiency is inversely proportional to the Time taken when the amount of work done is constant.
Let x be number of hours taken by second man paint the whole garage.
Work done by first man be 1/28
So, work completed by first man =1/28 ×12
= 12/28
= 3/7
Remaining work is 1-3/7 =4/7
1/x ×18 =4/7
⇒ 18/x=4/7
⇒ 4x=126
⇒ x=126/4
⇒ x=31.5 hours
Therefore, the number of hours taken by man to paint the whole garage alone is 31.5 hours.
To learn more about the time and work visit:
https://brainly.com/question/3854047.
#SPJ1
use the given information to complete the proof of the following theorem. the angles opposite the two congruent sides of an isosceles triangle are congruent.
The angle opposite to the two congruent sides of an isosceles triangle are congruent.
To prove that the angles opposite the two congruent sides of an isosceles triangle are congruent, we can use the following steps:
Draw a diagram of an isosceles triangle with two congruent sides and two corresponding angles opposite these sides. Label the vertices A, B, and C, with B being the vertex opposite the base of the triangle.Since the triangle is isosceles, AB = AC.Since the sides AB and AC are congruent, we can apply the SAS Congruence Theorem to triangles ABC and ACB. This states that if two sides of a triangle are congruent and the included angle is congruent, then the triangles are congruent.Therefore, triangles ABC and ACB are congruent.Since triangles ABC and ACB are congruent, the corresponding angles are congruent. In particular, ∠BAC is congruent to ∠CAB.Therefore, the angles opposite the two congruent sides of an isosceles triangle are congruent.This completes the proof of the theorem
Learn more about Isosceles triangle at:
brainly.com/question/1475130
#SPJ4
ratio is the quantitative relation between two amounts showing the number of times one value contains or is contained within the other
Ratio is the relation between two amounts that shows the number of times one value contains within the other.
What is Ratio?
A ratio in mathematics illustrates how many times one number contains another. For example, if a dish of vegetables contains eight tomato and six carrots, the tomato-to-carrot ratio is eight to six (that is, 8:6, which is equivalent to the ratio 4:3). Similarly, the proportion of carrots to tomato is 6:8 (or 3:4), while the proportion of tomato to overall fruit is 8:14. (or 4:7). A ratio's numbers can be any quantity, such as a count of persons or things, or measures of lengths, weights, time, and so forth. In most situations, both numbers must be positive.
Ratio is the relation between two amounts that shows the number of times one value contains within the other.
To learn more about Ratio from the given link
brainly.com/question/2328454
#SPJ4
PLEASE HURRY PLEASE I WILL GIVE BRAINLYIST Your friend just returned to the United States from their trip to Nepal and wants to exchange their 9,576 Nepalese rupees for U.S. dollars.
How many dollars will they receive if the current exchange rate is 1 U.S. dollar to 112 Nepalese rupees?
$11.69
$85.50
$95.76
$107.25
There are $85.50 will they receive if the current exchange rate is 1 U.S. dollar to 112 Nepalese rupees.
What is convertibility of rupee?
Convertibility is the simplicity with which a national currency can be changed into gold or another asset through international exchanges. The rupee is a partially convertible currency in India; while smaller amounts can be exchanged at market rates, larger ones require permission.
Given:
Your friend just returned to the United States from their trip to Nepal and wants to exchange their 9,576 Nepalese rupees for U.S. dollars.
Since,
1 U.S dollar = 112 Nepalese rupees
Suppose x be the U.S dollars for 9576 Nepalese rupees.
So,
x = 9576/112 = 85.5
Hence, there are $85.50 will they receive if the current exchange rate is 1 U.S. dollar to 112 Nepalese rupees.
To know more about convertibility of rupees, click on the link
https://brainly.com/question/16627643
#SPJ1
Considered the father of sociology, a French philosopher who in 1822 used the term sociology or social physics, highlighting its scientific nature by comparing it to the queen of natural sciences.
The French character who is considered the father of sociology has been Auguste Comte.
¿Who was Auguste Comte?This character was a Frenchman, he himself was a philosopher and is recognized mainly by:
Start what is positivism and its associated elements.Start scientific sociology, that is, sociology with scientific elements and components.Due to the above, Auguste Comte is considered the initiator of the social sciences, which are currently very important sciences for the study of various events.
¡Hope this helped!
Sarah budgeted $100 for new art supplies. When Sarah purchased the supplies, she
spend $75. What type of variance does this represent?
(XA) 26. In a certain community, 65% people speak Newar language and 45% people speak Gurung language. Find percentage of people who can speak (i) both the languages. (ii) Newari only (iii) Gurung language only.
Answer: (i) 10% (ii) 60% (iii) 40%
Step-by-step explanation:
(i) Newar language = 65%
Gurung language = 45%
Total covers = 110 but to sum it up to base that is 100% then 110-100 is 10.
so, 10% of people speak both the language.
(ii) people who speak only Newari only would be 60% as 5% among them speak Gurung language.
(iii) people who speak only Gurung only would be 40% as 5% among them speak Newari language.
Find all the roots for this polynomial using the steps below.
P(X)=x^3+3x^2+3x+2
List the 4 possible rational roots.
Plug each possible rational root into P(x) to determine which is a root of the polynomial.
Divide P(x) by the root you found in part 2 using synthetic division.
Write the fully factored form of P(x).
Use the quadratic formula to find the solutions of the quadratic factor.
List the 3 solutions of the P(x).
Answer:
[tex]p(x)=(x+2)(x^2+x+1)[/tex]
[tex]x=-2[/tex]
[tex]x=\dfrac{-1 + \sqrt{3}\:i}{2}[/tex]
[tex]x=\dfrac{-1- \sqrt{3}\:i}{2}[/tex]
Step-by-step explanation:
Given polynomial:
[tex]p(x)=x^3+3x^2+3x+2[/tex]
Rational Root Theorem
If P(x) is a polynomial with integer coefficients and if p/q is a root of P(x), then p is a factor of the constant term of P(x) and q is a factor of the leading coefficient of P(x).
Possible p-values
Factors of the constant term: ±1, ±2
Possible q-values
Factors of the leading coefficient: ±1
Therefore, all the possible values of p/q:
[tex]\sf \dfrac{p}{q}=\dfrac{\pm 1}{\pm 1}, \dfrac{\pm 2}{\pm 1}=\pm1,\pm2[/tex]
Substitute each possible rational root into the function:
[tex]x=-1 \implies p(-1) =(-1)^3+3(-1)^2+3(-1)+2=1[/tex]
[tex]x=1 \implies p(1) =(1)^3+3(1)^2+3(1)+2=9[/tex]
[tex]x=-2 \implies p(-2) =(-2)^3+3(-2)^2+3(-2)+2=0[/tex]
[tex]x=2 \implies p(2) =(2)^3+3(2)^2+3(2)+2=28[/tex]
Therefore, x = -2 is a root of the polynomial since f(-2) = 0.
Divide the polynomial by the root using synthetic division:
[tex]\begin{array}{c|crrr}-2 & 1 & 3 & 3 & 2\\\cline{1-1} & \downarrow &-2&-2&-2\\ \cline{2-5} & 1&1&1&0\end{array}[/tex]
The bottom row (except the last number) gives the coefficients of the quotient. Therefore, the quotient is:
[tex]x^2+x+1[/tex]
So the fully factored form of p(x) is:
[tex]p(x)= (x+2)(x^2+x+1)[/tex]
[tex]\boxed{\begin{minipage}{3.6 cm}\underline{Quadratic Formula}\\\\$x=\dfrac{-b \pm \sqrt{b^2-4ac}}{2a}$\\\\when $ax^2+bx+c=0$ \\\end{minipage}}[/tex]
Therefore, the solutions to the quadratic factor are:
[tex]\implies x=\dfrac{-1 \pm \sqrt{1^2-4(1)(1)}}{2(1)}[/tex]
[tex]\implies x=\dfrac{-1 \pm \sqrt{-3}}{2}[/tex]
[tex]\implies x=\dfrac{-1 \pm \sqrt{3\cdot -1}}{2}[/tex]
[tex]\implies x=\dfrac{-1 \pm \sqrt{3} \sqrt{-1}}{2}[/tex]
[tex]\implies x=\dfrac{-1 \pm \sqrt{3}\:i}{2}[/tex]
The 3 solutions of p(x) are:
[tex]x=-2[/tex][tex]x=\dfrac{-1 + \sqrt{3}\:i}{2}[/tex][tex]x=\dfrac{-1- \sqrt{3}\:i}{2}[/tex]To show 4 dimensional matching is NP complete, we want to reducte from 3 dimensional matching. The trick is to just pad each triple with an extra coordinate. We need to do this in a way that we don't really change the problem. One way to do this is to just repeat the last coordinate - so that the triple [a, b, c] is mapped to the quadruple [a, b, c, c].
NP finished. Only two jobs share resources with the reduction provided in section A.
what is coordinate?to put in the same order or rank. : to bring into a common action, movement, or condition : harmonize. coordinate schedules. She'll be coordinating the relief effort.
The overall issue is NP-complete. From Independent Set, this is a decrease. We substitute jobs for the graph's vertex points. If there is an edge connecting vertices v and w, we establish a resource called r v,w that v and w can share.
If k = 2, we are simply checking to see if there are any jobs that are resource-exclusive. By checking every pair of jobs, we can accomplish this using sheer force.
NP finished. Only two jobs share resources with the reduction provided in section A.
To know more about coordinate visit:-
https://brainly.com/question/27749090
#SPJ4
Which of the following designs involves repeated measurement of a variable before and after some event?
Group of answer choices
nonequivalent control group design
interrupted time-series design
matched group factorial design
multiple regression design
The design that involves repeated measurement of a variable before and after some event will be matched group factorial design. Hence, option C is correct.
What is Matched group factorial design?In this kind of experimental design, the research's participants are divided into groups, and key factors are matched to each group. The variables that are used to match the respondents must have an impact on the original study conclusion (the dependent variable).
The benefit of using matched group factorial design is,
Fewer people are needed for this kind of investigation, which could also produce more accurate results and results that are based on more information.
To know more about Factorial design:
https://brainly.com/question/29668399
#SPJ1
kari is thinking about buying a laptop that cost $750 on sale if the sales tax is 7.5% how much money will she need in total to buy the computer
Answer: 806.25
Step-by-step explanation: First, we need to find how much the sales tax is worth in dollars. Recall the formula:
Worth = Wole number x part percent / 100
Now, plug in the numbers:
Worth = 750 x 7.5 / 100
So, 750 x 7.5 = 5625
So, 5625 / 10 = 56.25
But remember, $56.25 is the amount of the SALES TAX. To find the total, we need to add 56.25 to 750. So,
750 + 56.25 = 806.25
Therefore, $806.25 is the TOTAL AMOUNT she needs to pay.
ANSWER PLEASE! DEADLINE 11:00 45+ POINTS
1.
The list represents the number of students who left school early in a 12-day period.
48, 62, 75, 43, 32, 52, 70, 63, 81, 40, 38, 67
Find the mean and interpret its meaning as it relates to the number of students who left school early.
2. The ages of a group of teachers are listed.
25, 32, 33, 35, 41, 43, 45, 48, 52, 55, 60, 62
If another teacher with an age of 45 is added to the data, how would the mean be impacted?
THANKS! ANSWER FAST!
Answer: To find the mean of the number of students who left school early, we must add all of the numbers together and then divide the sum by the number of days.
48 + 62 + 75 + 43 + 32 + 52 + 70 + 63 + 81 + 40 + 38 + 67 = 671
The mean of the number of students who left school early is 56.75 (671 / 12).
This mean represents the average number of students who left school early each day over the 12-day period. It tells us that on average, about 56.75 students left school early each day.
Step-by-step explanation: 2. The mean of the group of teachers' ages is currently (25+32+33+35+41+43+45+48+52+55+60+62)/12=45.5. If another teacher with an age of 45 is added to the data, the mean will be (25+32+33+35+41+43+45+45+48+52+55+60+62)/13=44.5. The mean will be slightly lower, as the additional value of 45 is being added to the sum, but the number of values being averaged is also increasing by 1.
3x-12=2x+7 subtract 7 from both sides and subtract 3x from both sides
x=19
According to question,
3x-12=2x+7
Subtracting 7 from both sides
3x-12-7=2x+7-7
⇒3x-19=2x
Subtracting 3x from both sides
3x-19-3x=2x-3x
⇒-19=-x
⇒x=19
∴The value of x is 19.
For further information regarding linear equation in one variable
https://brainly.in/question/39414007
The complete question is Find the value of x in the equation 3x-12=2x+7 when 7 and 3x is subtracted from both sides.
How do you find the general solutions for tanx−3cotx=0?
The general solutions for tanx−3cotx=0 is [tex]\frac{\pi}{3} \text { and } \frac{2 \pi}{3}[/tex]
[tex]\begin{aligned}& \tan x-\frac{3}{\tan x}=0 \\& \tan ^2 x-3=0 \text { (condition } \tan \times \text { not zero) } \\& \tan ^2 x=3 \rightarrow \tan x=\pm \sqrt{3}\end{aligned}[/tex][tex]a. $\tan x=\sqrt{3} \rightarrow x=\frac{\pi}{3}$b. $\tan x=-\sqrt{3} \rightarrow x=\frac{2 \pi}{3}$Extended answers:$$\begin{aligned}& x=\frac{\pi}{3}+k \pi \\& x=\left(2 \frac{\pi}{3}\right)+k \pi\end{aligned}[/tex]
What is the general equation for tan's solution?
Tan + Tan Equals Tan
n Z (i.e., n = 0, 1, 2, 3, etc.), so n = n + n. Therefore, n Z (i.e., n = 0, 1, 2, 3, etc.) is the value for which the general solution of tan = tan is given as = n +. Because cot = 1/tan and cot = 1/tan, the expression cot = cot is identical to tan = tant
To learn more about tan's solution visit:
https://brainly.com/question/24268805?
#SPJ4
If the distance between points P(3.a) and Q(3, 1) is 4 units then find the value of a.)
Answer:
a = -3
Step-by-step explanation:
The explanation is in the image
Under an anticockwise rotation about the point O, AOAB is mapped onto AOA'B'. Determine the angle of rotation.
Check the picture below.
let's notice that the triangle is an equilateral triangle, meaning all its sides are congruent and likewise, all its angles are also congruent.
hw11.3. projection onto a subspace consider the subspace of spanned by the orthogonal vectors let . compute the orthogonal projecti
The Projectile Motion of vectors will be [tex]Proj_{v}(w)[/tex] = [tex]\left[\begin{array}{c}-1.5 \\0 \\-1.5\end{array}\right][/tex]
What is Projectile Motion ?An item or particle that is projected in a gravitational field, such as from the surface of the Earth, and moves along a curved route while solely being affected by gravity is said to be in projectile motion.
According to the given information
Given, [tex]$\quad b_1=\left[\begin{array}{c}2 \\ 2 \\ -2\end{array}\right], \quad b_2=\left[\begin{array}{l}2 \\ 0 \\ 2\end{array}\right], \quad w=\left[\begin{array}{c}-2 \\ 1 \\ -1\end{array}\right]$[/tex]
We know,
[tex]Proj_{v}(w)[/tex] = [tex]Proj_{b1}(w) + Proj_{b2}[/tex]
[tex]& =\left(\frac{w \cdot b_1}{b_1 \cdot b_1}\right) b_1+\left(\frac{w \cdot b_2}{b_2 \cdot b_2}\right) b_2[/tex]
[tex]w \cdot b_1 &[/tex] =[tex]\left[\begin{array}{c}-2 \\1 \\-1\end{array}\right] \cdot\left[\begin{array}{c}2 \\2 \\-2\end{array}\right][/tex][tex]=-4+2+2=0 \\[/tex]
[tex]w \cdot b_2 &[/tex] =[tex]\left[\begin{array}{c}-2 \\1 \\-1\end{array}\right] \cdot\left[\begin{array}{l}2 \\0 \\2\end{array}\right][/tex] =[tex]-4+0-2=-6 \\[/tex]
[tex]b_2 \cdot b_2 &[/tex] =[tex]\left[\begin{array}{c}2 \\0 \\2\end{array}\right] \cdot\left[\begin{array}{l}2 \\0 \\2\end{array}\right][/tex] =[tex]4+0+4=8[/tex]
Therefore
[tex]Proj_{v}(w)[/tex] = [tex]\left(\frac{0}{b_1 \cdot b_1}\right) b_1+\left(\frac{-6}{8}\right)\left[\begin{array}{l}2 \\0 \\2\end{array}\right] \\[/tex]
[tex]& =0+\frac{-3}{4}\left[\begin{array}{l}2 \\0 \\2\end{array}\right] \\[/tex]
[tex]& =\left[\begin{array}{c}\frac{-3}{2} \\0 \\-3 \\2\end{array}\right] \\[/tex]
[tex]Proj_{v}(w)[/tex] = [tex]\left[\begin{array}{c}-1.5 \\0 \\-1.5\end{array}\right][/tex]
The Projectile Motion of vectors will be [tex]Proj_{v}(w)[/tex] = [tex]\left[\begin{array}{c}-1.5 \\0 \\-1.5\end{array}\right][/tex]
To know more about Projectile Motion
https://brainly.com/question/11049671
#SPJ4