Given:-
[tex]7,14,21,28,\ldots[/tex]To find the sequence inside the pattern.
Since the number are the numbers in 7th table the function can be,
[tex]f(n)=7n[/tex]So the required function is f(n)=7n
consider the function f(x) whose second derivative is f''(x)=4x+4sin(x). if f(0)=4 and f'(0)=2, what is f(3)?
what is the area of a sector bounded by a 114 arc
Step1: Write out the given parameter
Θ=114°,r= 6ft
Step2; Write out the formula
The area of a sector is given as
[tex]\frac{\theta}{360}\times\pi r^2[/tex]Step3: substitute the parameters into the formula
[tex]\frac{114}{360}\times\pi\times6^2[/tex][tex]\begin{gathered} \frac{114}{10}\pi \\ \frac{57}{5}\pi \end{gathered}[/tex]Hence the area of the sector is (57/5)π interms o
function c is defined by the equation c(n)=50+4n. it gives the monthly cost in dollars of visitiing a gym as a function of the number of visits v. find the value of c (7). show your reasoning and explain what the value means in this situation
The cost function is defined as
[tex]c(n)=50+4n[/tex]The value of c(7) can be determined by substituting 7 for n into the function.
Therefore, c(7) becomes;
[tex]\begin{gathered} c(7)=50+4(7) \\ c(7)=50+28 \\ c(7)=78 \end{gathered}[/tex]This means the cost of 7 visits to the gym is $78.
The cost function shows that there is an amount that doesnt change and that is 50. Then there is one that varies or changes with every visit, or n. That means as the value of n increases or decreases, the total amount also increases or decreases. When n equals zero, then the total cost becomes 50. This means when there is no visit to the gym, the cost still remains $50.
Therefore, n is a variable that can determine changes in the total cost.
Answer: c(7)=78
Step-by-step explanation:
C(n)=50+4n
c(7)=50+4(7)
=50+28
=78
C(7)=78
The following data are the distances from the workplace (in miles) for the 5 employees of a small business.
1. Given that the population data is : 15,5,8,2,5
• number of sample in data , ,n = 5
,• Mean = sum of sample in the data / number of sample
= (15+5+8+2+5)/5
= 35/5
Therefore mean = 7
2. Calculate varience as in the box below:
[tex]\begin{gathered} _{}\text{Varience = }\frac{1}{n}\mleft\lbrace(x_i-\vec{x}\mright)^2 \\ \text{ = }\frac{1}{5}\mleft\lbrace(7-15)^2+(7-5)^2+(7-8)^2+(7-2)^2+(7-5)^2\mright\rbrace \\ \text{ = }\frac{1}{5}\mleft\lbrace(-8^2\mright)+(-2)^2+(-1^2)+(5^2)+(2^2)\} \\ \text{ =}\frac{1}{5}\mleft\lbrace64\text{ + 4+ 1 +25+4}\mright\rbrace \\ \text{ = }\frac{1}{5}(98) \\ \text{ = }\frac{98}{5} \\ \therefore S\tan dard\text{ deviation = }\sqrt[]{varience\text{ }} \\ \text{ = }\sqrt[]{\frac{98}{5}}\text{ } \\ \text{ =4.427} \end{gathered}[/tex]• This means that Standard deviation = 4.43
Round the value 23.731 g to three significant figures.Express your answer numerically using three significant figures.
23.731 g rounded to three significant figures is 23.7 g.
Rule for significant figures:
All non-zero numbers are significant.
In 23.731, there are 5 non-zero numbers. So, there are 5 significant figures. To get number in 3 significant figures round the number at the first decimal place.
Now, the 23.731 g can be expressed in 3 significant figures as 23.7 g.
Which of the equations below could be the equation of this parabola?5Vertex(0,0)10A. x = 2y2B. y= 2x2C. y = -2x2O D. x = -2y2
Given:
Vertex = (0,0)
General vertex from of equation is:
[tex]y=a(x-h)^2+k[/tex][tex]\text{vertex = (h,k)}[/tex]So:
h = 0
k = 0
then equation is:
[tex]\begin{gathered} y=a(x-h)^2+k \\ h=0;k=0 \\ y=a(x-0)^2+0 \\ y=ax^2 \end{gathered}[/tex]Here value of "a" is negative because the graph is move downward . and all option give mode value is 2 then the equation of functuion:
[tex]y=-2x^2[/tex]solve the following: a. 1/14 - 3 1/8 b. -7/2x^2y^2. + 5/2xy^2 + 3/x^2yc. -2 1/3 + 1 1/9
First we analyze the denominators
2x^2y^2 is the greatest common factor for all three fractions, now we just divide each denominator with that factor and then multiply the answer by numerators
Then, the new fraction will be:
e)
A line is drawn over this rectangle . Is the line a line of symmetry?
Answer:
The line is not a line of symmetry because the two parts are not an exact match when you fold the rectangle over the line.
Explanation:
A line of symmetry is a line that divides the figure into two equal parts, so when you fold the figure over the line, the two parts will match exactly. So, taking into account the figure, the line drawn is not a line of symmetry.
The answer is
The line is not a line of symmetry because the two parts are not an exact match when you fold the rectangle over the line.
6. Sheila simplified an expression using the following steps. Which property justifies Step 3?
The distributive property of multiplication is represented by the following expression:
[tex]a\cdot(b+c)=a\cdot b+a\cdot c[/tex]Notice that Sheila uses distributive property to simplify the expression:
[tex]\begin{gathered} 5x+4(3+2x) \\ =5x+4\cdot3+4\cdot2x \\ =5x+12+8x \\ =13x+12 \end{gathered}[/tex]I want to know the answer and steps please I would appreciate it.
ANSWER
[tex]578.05yd^2[/tex]EXPLANATION
Given;
[tex]\begin{gathered} diameter(d)=8yd \\ radius(r)=\frac{d}{2}=\frac{8}{2}=4 \\ height(h)=19yd \end{gathered}[/tex]Recall, the formula for finding the surface area of a cylinder is;
[tex]A=2\pi rh+2\pi r^2[/tex]Substituting the values;
[tex]\begin{gathered} A=2\pi rh+2\pi r^2 \\ =2\times3.14\times4\times19+2\times3.14\times4^2 \\ =477.28+100.48 \\ =578.05 \end{gathered}[/tex]Convert: 3 days = minutes
ANSWER
4320 minutes
EXPLANATION
To convert from days to minutes, first, we have to convert from days to hours. It is known that 1 day has 24 hours, so 3 days have,
[tex]3\text{ }days\cdot\frac{24\text{ }hours}{1\text{ }day}=72\text{ }hours[/tex]Then, we convert from hours to minutes. If 1 hour has 60 minutes,
[tex]72\text{ }hours\cdot\frac{60\text{ }minutes}{1\text{ }hour}=4320\text{ }minutes[/tex]Hence, there are 4320 minutes in 3 days.
Cameron is playing 9 holes of golf. He needs to score a total of at most 14 over par on the last four holes tobeat his best golf score. On the last four holes, he scores 7 over par, 1 under par, 4 over par, and 1 underpar.Part 1 out of 3Enter and find the value of an expression that gives Cameron's score for 4 holes of golf.The expression isCameron's score is✓ CheckNext
In golf:
[tex]\begin{gathered} \text{ par corresponds to 0 on the number line} \\ \text{ under par corresponds to negative numbers on the number line} \\ \text{over par corresponds to positive numbers on the number line} \end{gathered}[/tex]Hence, in this case,
[tex]\begin{gathered} 7\text{ over par corresponds to +7 on the number line} \\ 1\text{ under par corresponds to -1 on the number line} \\ 4\text{ over par corresponds to +4 on the number line} \end{gathered}[/tex]Hence, the value of an expression that gives Cameron's score for 4 holes of golf is given by
[tex]7-1+4-1=6+4-1=10-1=9[/tex]The expression is : 7 - 1 + 4 - 1
Camerons's score is: 9
If f(x) = 2x2 + x - 3, which equation can be used to determine the zeros of the function?
Given the function:
[tex]f(x)=2x^2+x-3[/tex]to find the zeros of the function, we have to solve the equation f(x) = 0, this means the following:
[tex]\begin{gathered} f(x)=0 \\ \Rightarrow2x^2+x-3=0 \end{gathered}[/tex]solving for 'x', we get the zeros of the function, if there are any.
Example(-9, -2) (1,3)Find the slopeWrite in point slopeWrite in slope intercept formComplete the same three steps for 50extra points using the points(-6,7)(-3,6)
The slope, m, of a line passing therough the points (x₁, y₁ ) and (x₂, y₂) can be calculated using the formula
[tex]m\text{ = }\frac{y_2-y_1}{x_2-x_1}[/tex]For the points (-9, -2) and (1, 3):
x₁ = -9, y₁ = -2, x₂ = 1, y₂ = 3
Substituting these points into the slope formula given above
[tex]\begin{gathered} m\text{ = }\frac{3-(-2)}{1-(-9)} \\ m\text{ = }\frac{5}{10} \\ m\text{ = }\frac{1}{2} \end{gathered}[/tex]The slope, m = 1/2
The point-slope form of the equation of a line passing through the points (x₁, y₁ ) and (x₂, y₂) can be calculated using the formula
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y\text{ - (-2) = }\frac{1}{2}(x\text{ - (-9))} \\ y\text{ + 2 = }\frac{1}{2}(x\text{ + 9)} \end{gathered}[/tex]The slope-intercept form of the equation will be of the form y = mx + c
Reduce the point-slope form written above to the intercept-slope form
[tex]\begin{gathered} y\text{ + 2 = }\frac{1}{2}(x\text{ + 9)} \\ y\text{ + 2 = }\frac{x}{2}+\text{ }\frac{9}{2} \\ y\text{ = }\frac{x}{2}+\frac{9}{2}-2 \\ y\text{ = }\frac{1}{2}x\text{ +}\frac{5}{2} \end{gathered}[/tex][tex] {x}^{2} - [/tex]which could be the missing term in the expression if a factor of the expression is x-2ya) 2xyb) -2yc) [tex] {4y}^{2} [/tex]d)4y
This is a difference of two squares.
If one factor is
[tex]x+2y[/tex]An the other is
[tex]x-2y[/tex]We have that the expression is:
[tex](x+2y)\cdot(x-2y)=x^2-4y^2[/tex]So the missing term is 4y², option c
I have no idea how to do this please help
Answer:
Initial Value: 19,900
Value after 11 years: 7953
Explanation:
The initial value of the car is its value at t =0. Therefore, to find this initial value, we put in t = 0 to get
[tex]v(0)=19,900(0.92)^0[/tex][tex]\boxed{v\mleft(0\mright)=19,900}[/tex]Hence, the initial value is $19,900.
Now, to find the value after 11 years, we put t = 11 into the equation and get
[tex]v(11)=19,900(0.92)^{11}[/tex]which gives (rounded to the nearest dollar)
[tex]\boxed{v\mleft(11\mright)=7953}[/tex]which is our answer!
Hence, the value after 11 years is $7953.
The amount of money Jeremy makes varies directly with the number of hours he works. Ifhe earns $195 for 3 days of work, how much will he earn if he works 12 days?
Given:
a.) Jeremy earns $195 for 3 days of work.
To be able to determine how much will he earn if he works 12 days, we will be using ratios and proportions.
Let,
x = his earnings if he works for 12 days.
[tex]\text{ 195 : 3 = x : 12}[/tex][tex]\text{ 195 : 3 = x : 12 }\rightarrow\text{ }\frac{\text{ 195}}{3}\text{ = }\frac{\text{ x}}{12}[/tex][tex]\frac{\text{ 195}}{3}\text{ = }\frac{\text{ x}}{12}[/tex][tex]\text{ (195)(12) = (x)(3)}[/tex][tex]\text{ 2,340 = 3x}[/tex][tex]\text{ }\frac{\text{2,340}}{3}\text{ = }\frac{\text{3x }}{3}[/tex][tex]\text{ 780 = x}[/tex]Therefore, he'll earn $780 for working 12 days.
X 0 1 | 2 3 4 y 7 15 23 31 39
step 1
Find the slope
we take the points
(0,7) and (1,15)
m=(15-7)/(1-0)
m=8/1
m=8
step 2
Find the equation in slope intercept form
y=mx+b
we have
m=8
b=7 -------> (0,7) is the y-intercept
substitute
y=8x+7Find the real part and the imaginary part of the following complex number. - 14 - 14/13
Please help. I’m not sure how to do this. the options are a)1.3b)0.3c) 2.2d)0.4
Step 1
Given;
Step 2
[tex]\begin{gathered} constant=\text{ height}\times width \\ let\text{ us use height=0.2} \\ width=2 \end{gathered}[/tex][tex]constant=0.2\times2=0.4[/tex]Answer;
[tex]0.4[/tex]how to compare fractions 15/8 and 12/7
Answer:
To compare fractions 15/8 and 12/7
In order to comapare any two fractions, the denomiator of the two fractions must be same.
For the given fractions denominators are different.
To make the denomiator of the given fractions same, find the LCM of the denominators.
LCM of 8,7: 56
The fractions become,
[tex]\frac{15}{8}=\frac{15\times7}{8\times7}=\frac{105}{56}[/tex][tex]\frac{12}{7}=\frac{12\times8}{7\times8}=\frac{96}{56}[/tex]we get that,
[tex]\frac{105}{56}>\frac{96}{56}[/tex]we get,
[tex]\frac{15}{8}>\frac{12}{7}[/tex]15/8 is greater than 12/7.
Answer is: 15/8 is greater than 12/7
2. There were 132 students on the field trip. The students were divided into as many groups of 8 as possible. One group was smaller. How many students were in the smaller group? A 17 students B. 16 students C. 8 students D. 4 students
So, there were 132 students divided in groups of 8.
If we divide:
So, there will be 8 groups of 16 and 1 group of 4 students. (The smaller group).
Fill in the blank. The set {x|XS - 4.3) written in interval notation is
The given expression is :
[tex]\mleft\lbrace x\mright|x\leq-4.3\}[/tex]In the given expression x is less than equal to - 4.3
so, it's domain will lie from - infinity to - 4.3
Thus :
[tex]\text{ Interval Notation: (-}\infty,-4.2\rbrack[/tex]Answer :
[tex]\text{ Interval Notation: (-}\infty,-4.2\rbrack[/tex]What is the intersection of the sets C = {5, 7, 10, 13, 19) and D = {3, 9, 14, 15}?O null setO (5, 7, 9, 10, 13, 14, 15, 19}O {5, 9, 14)O {3, 19)
We are given the following two sets C and D
C = {5, 7, 10, 13, 19}
What is the solution to the following equation?
3(x-4)-5 = x - 3A. x = 12B. x=3C. x=8D. x = 7
Given:
3(x-4)-5 = x - 3
Required:
To calculate which option is correct
Explanation:
[tex]\begin{gathered} 3(x-4)-5=x-3 \\ \\ 3x-12-5=x-3 \\ \\ 3x-17=x-3 \\ \\ 3x-x=-3+17 \\ \\ 2x=14 \\ \\ x=\frac{14}{2} \\ \\ x=7 \end{gathered}[/tex]Required answer:
Option D (x=7)
To find the measure of
You have the following expression:
(2z - 3) + (5z - 6) = 180
in order to solvet the previous expression for z, proceed as follow:
(2z - 3) + (5z - 6) = 180 cancel out parenthesis
2z - 3 + 5z - 6 = 180 simplify like terms left side
7z - 9 = 180 add 9 both sides
7z = 180 + 9
7z = 189 divide by 7 both sides
z = 189/7
z = 27
Hence, the value of z is 27
Next, replace the values of z into the expression for the measureof angle M:
Hence, the measure of angle M is 129°
Hello, I need help with this precalculus homework question, please? I just need help with section D for the graph. HW Q3
The answer would be option B
An easy way to see this is to look for the Y-intercept (when X=0)
So:
(13x + 13) / (8x +16) = 13/16 = 0.81
So, which graph has a Y intercept of approximately 0.81? The B
find the slope (1, 2), (-3, 3)
Given:
The points are (1, 2), (-3, 3).
The slope is calculated as,
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ (x_1,y_1)=\mleft(1,2\mright) \\ (x_2,y_2)=(-3,3) \\ m=\frac{3-2}{-3-1} \\ m=\frac{1}{-4} \\ m=-\frac{1}{4} \end{gathered}[/tex]Answer: slope = -1/4
Lynn lines the bottom of her first pan with aluminum foil. The area of the rectangular piece of foil is 11 1/4 square inches. It's length is 4 and 1/2 inches. what is the width of the foil
The area of the rectangular foil is
[tex]\begin{gathered} \text{area}=11\frac{1}{4}inches^2=\frac{45}{4}inches^2 \\ \text{length}=4\frac{1}{2}inches=\frac{9}{2}inches^2 \\ \text{width =?} \\ \text{area}=\text{length}\times width \\ \frac{45}{4}=\frac{9}{2}w \\ \text{cross multiply} \\ 90=36w \\ w=\frac{90}{36}=\frac{30}{12}=\frac{10}{4}=\frac{5}{2}\text{ inches} \\ \end{gathered}[/tex]A group of friends wants to go to the amusement park. They have no more than $225to spend on parking and admission. Parking is $5, and tickets cost $20 per person,including tax. Write and solve an inequality which can be used to determine p, thenumber of people who can go to the amusement park.3Inequality:рSubmit AnswerPrivacy Policy Terms of Service
Answer:
Inequality: 5 + 20p ≤ 225
p ≤ 11
Explanation:
The total cost can be calculated as the sum of the parking and ticket costs. So, we can calculate the total cost as:
5 + 20p
Because 20p represents the total ticket cost for p people.
Then, this total cost should be less than or equal to 225. It means that the inequality that represents the situation is:
5 + 20p ≤ 225
Finally, we can solve the inequality by subtracting 5 from both sides as:
5 + 20p - 5 ≤ 225 - 5
20p ≤ 220
Then, divide both sides by 20, to get:
20p/20 ≤ 220/20
p ≤ 11
So, the number of people who can go to the amusement park is less than or equal to 11.
Therefore, the answers are:
Inequality: 5 + 20p ≤ 225
p ≤ 11