Given
The functions,
[tex]\begin{gathered} f(x)=x^2 \\ g(x)=x^2-3 \end{gathered}[/tex]To complete the ordered pairs for f(x)=x².
Explanation:
It is given that,
[tex]\begin{gathered} f(x)=x^2 \\ g(x)=x^2-3 \end{gathered}[/tex]That implies, for x=-2,
[tex]\begin{gathered} f(-2)=(-2)^2 \\ =4 \end{gathered}[/tex]Also, for x=-1.
[tex]\begin{gathered} f(-1)=(-1)^2 \\ =1 \end{gathered}[/tex]For x=0,
[tex]\begin{gathered} f(0)=0^2 \\ =0 \end{gathered}[/tex]For x=1,
[tex]\begin{gathered} f(1)=1^2 \\ =1 \end{gathered}[/tex]For x=2,
[tex]\begin{gathered} f(2)=2^2 \\ =4 \end{gathered}[/tex]Hence, the ordered pairs are,
[tex]\left(-2,4\right),(-1,1),(0,0),(1,1),(1,4).[/tex]Consider the system of linear equalities:2+>26+3<12This is the graph of the solution.
Given inequality is 2x+y>2 and 6x+3y<12.
Solve 2x+y>2 for y:
[tex]undefined[/tex]What is 1584 in terms of pi?
TED BORROWED $1,200 FOR TWO YEARS AND HE MADE MONTHLY PAYMENTS. IF THE TOTAL FINANCE CHARGE IS $175.92 WHAT IS THE APR?
Given: Ted Borrowed $1200 for two years and made monthly payments. The total finance charge is $175.92
Required: To determine the Annual Percentage Rate.
Explanation: The formula for APR is as follows-
[tex]APR=\lbrace\frac{(Fees+Interest)}{\frac{Principal}{n}}\frac{}{}\times365\rbrace\times100[/tex]where n is the total number of days in the loan term.
Here, the total finance charge is $175.92, and the Principal amount is $1200.
Also, n=2 years or 730 days. Substituting these values into the formula as-
[tex]APR=(\frac{175.92}{\frac{1200}{730}}\times365)\times100[/tex]Further solving as-
[tex]APR=7.29\%[/tex]Final Answer: The Annual Percentage Rate is 7.29%
Food Express is running a special promotion in which customers can win a free gallon of milk with their food purchase if there is a star on their receipt. So far, 219 of the first 264 customers have not received a star on their receipt. What is the experimental probability of winning a free gallon of milk?options: 3/11....15/88....73/88.....1/78
Solution:
Experimental probability is a probability that is determined on the basis of a series of experiments. A random experiment is done and is repeated many times to determine their likelihood, and each repetition is known as a trial.
[tex]\begin{gathered} P(E)=\frac{n(E)}{n(T)} \\ \\ Where; \\ n(E)=\text{ number of event} \\ \\ n(T)=\text{ total outcome} \end{gathered}[/tex]If 219 of the first 264 customers have not received a star on the receipt, then a customer that would win a free gallon of milk would be among (264 - 219) customers. Thus;
The experimental probability of winning a free gallon of milk is;
[tex]\begin{gathered} =\frac{264-219}{264} \\ \\ =\frac{45}{264} \\ \\ =\frac{15}{88} \end{gathered}[/tex]CORRECT OPTION:
[tex]\frac{15}{88}[/tex]
Find both the x-intercept and the y-intercept of the line given by this equation 7.2x-9.6y-5.7=0
To find the x intercept of the line we have to replace y for 0 and solve for x:
[tex]\begin{gathered} 7.2x-9.6y-5.7=0 \\ 7.2x-9.6(0)-5.7=0 \\ 7.2x-5.7=0 \\ 7.2x=5.7 \\ x=\frac{5.7}{7.2} \\ x=0.79 \end{gathered}[/tex]To find the y intercept of the line we have to replace x for o and solve for y:
[tex]\begin{gathered} 7.2x-9.6y-5.7=0 \\ 7.2(0)-9.6y-5.7=0 \\ -9.6y-5.7=0 \\ -9.6y=5.7 \\ y=\frac{5.7}{-9.6} \\ y=-0.59 \end{gathered}[/tex]It means that the x intercept is 0.79 and the y intercept is -0.59.
Write the point-slope form of the equation of the line that passes through the point (-1, 5) and has a slope of -1.
a. Using variables, write out the formula for the point-slope form of the equation.
b. Identify the values for m, x1, and y1.
c. Fill these values into the point-slope form of the equation from part (a), and simplify as needed.
Use the box provided to submit all of your calculations and final answers. Simplify the answer as needed.
[tex](\stackrel{x_1}{-1}~,~\stackrel{y_1}{5})\hspace{10em} \stackrel{slope}{m} ~=~ - 1 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{5}=\stackrel{m}{- 1}(x-\stackrel{x_1}{(-1)}) \implies {\large \begin{array}{llll} y -5= -(x +1) \end{array}}[/tex]
Using the table, what is the average daily balance of the credit card for the December 1 - December 31 billing period? Round your answer to the nearest cent. Do not include a dollar sign or comma in your answer. For example, $5,678.00 should be entered as 5678.00.
Answer
ADB= 8145.16
Problem Statement
The question tells us to calculate the Average Daily Balance (ADB) for a period of December 1 - December 31 using the balances given in the table.
Method
To find the Average Daily Balance (ADB), we apply the formula given below:
[tex]\text{ADB}=\sum ^n_{i=1}\frac{(\text{Balance after Day}_i)}{Total\text{ number of days in Billing cycle}}[/tex]The question has given us the Balance after Day 1 - Day 10 (10 days) to be 11,000. We are also given that the Balance from Day 11 to Day 20 (10 days) is 8000, from Day 21 to 30 (10 days), the Balance is 5500 while Day 31 (1 day) with a balance of 7500.
The total number of days in the billing cycle is from Day 1 to Day 31, which is 31 days altogether.
Thus we can use the above formula to find the Average Daily Balance (ADB).
Implementation
[tex]\begin{gathered} \text{ADB}=\frac{(10\times11,000)+(10\times8,000)+(10\times5,500)+(1\times7,500)}{31} \\ \\ \text{ADB}=\frac{252,500}{31} \\ \\ \therefore ADB=8,145.16 \end{gathered}[/tex]
Final Answer
The Answer is:
ADB= 8145.16
This table shows how many sophomores and juniors attended two school events.What is the probability that a randomly chosen person from this group is a sophomore and attended the jazz band concert?Round your answer to two decimal places.
Given:
Number of sophomores attended jazz band concert = 35
Total number of students = 137
Required: Probability that a randomly chosen person from this group is a sophomore and attended the jazz band concert.
Explanation:
The formula to find probability is
[tex]p=\frac{\text{Number of favorable outcomes}}{\text{ Total number of outcomes}}[/tex]Probability that a randomly chosen person from this group is a sophomore and attended the jazz band concert
[tex]\begin{gathered} =\frac{\text{Number of sophomores attended jazz band concert}}{\text{ Total number of students in this group}} \\ =\frac{35}{137} \\ =0.26 \end{gathered}[/tex]Option D is correct.
Final Answer: Probability that a randomly chosen person from this group is a sophomore and attended the jazz band concert is 0.26.
Analyze the diagram below and complete the instructions that follow.F45E28DSolve AEFD. Round the answers to the nearest hundredth.
Since this is a right triangle we can use trig functions
First we can find the length of the hypotenuse using the Pythagorean theorem
a^2 + b^2 = c^2 where a and b are the legs and c is the hypotenuse
28^2 + 45^2 = c^2
784+2025 = c^2
2809 = c^2
Taking the square root of each side
sqrt(2809) = sqrt(c^2)
53 = c
The hypotenuse, DR = 53
Then we can find the measurements of the angles
sin F = opp/ hyp
sin F = 28/53
Taking the inverse sin of each side
sin D = opp/ hyp
sin D = 45/53
Taking the inverse sin of each side
Six times the sum of a number and 7 is 3.
and solve x
[tex]\begin{gathered} x+7=\frac{3}{6} \\ \\ x=\frac{1}{2}-7 \\ \\ x=-\frac{13}{2}=-6.5 \end{gathered}[/tex]the number is -6.5
Write a simplified expression for the model below. 1 1 -1 -1 х X X х х -X -X 1 1 ו-ווו-| 1 1 1 -1 ||-1
we have the following:
[tex]\begin{gathered} 4\cdot(x)+2\cdot(-x)+6\cdot(1)+6\cdot(-1) \\ 4x-2x+6-6 \\ 2x \end{gathered}[/tex]therefore, the answer is 2x
Please help me to classify each of the numbers below as an integer or not
The integers are the number that are written without a factional component.
The fraction -6/19 can be expressed with fraction. So it is not a integer.
The fraction -10/5 can be expressed as -2, so this is a integer.
The number -40 is expressed wth fraction component. So it is a integer.
The number -33 is expressed with fraction component. So it is a integer.
The decimal number 8.98 can be expressed as fraction and not expressed without fraction. So it is not a interger.
Answer:
-6/19 No
-10/5 Yes
-40 Yes
The radius of a quarter circle is 3 millimeters. What is the quarter circle's perimete r=3 mm ude 3.14 for .. millimeters Submit can you explain
Given:
The radius of the quarter circle is given 3 mm.
To find:
The perimeter of the quarter circle.
Solution:
It is known that the perimeter of the quarter circle is given by:
[tex]2r+\frac{\pi r}{2}[/tex]So, the perimeter of the quarter circle:
[tex]\begin{gathered} P=2r+\frac{\pi r}{2} \\ =2(3)+\frac{3.14\times3}{2} \\ =6+4.71 \\ =10.71 \end{gathered}[/tex]Thus, the perimeter of the quarter circle is 10.71 mm.
Find the volume of a cylinder with a height of 3 m and a diameter of 3 . Round to the nearest tenth
EXPLANATION
The volume of a cylinder will be:
Volume= π*(d/2)^2*h
Substituting:
Volume= π*(3/2)^2*3 = 21.2 m^2
The answer is 21.2 m^2
3.If F, G, and H are the midpoints of the sidesof AJKL, FG = 37, KL = 48, and GH = 30,find each measure.Ka) FH=Gb) JL =F>Lc) KJ =H||Jd) FJ =
3.If F, G, and H are the midpoints of the sides of AJKL, FG = 37, KL = 48, and GH = 30,
Find each measure.
a) FH = 1/2 KL; FH= 24
b) JL = 2* FG = 2* 37
c) KJ = 2* GH = 2*30 =
d) FJ = 1/2 KJ = GH = 30
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I'm working on your image, please give me a few minutes
Ed spends 21 hours practicing drums over a fortnight. At that rate, how much time will he spend on practicing drums over a 7 week period?
This problem can be solve with the simple rule of three:
[tex]\begin{gathered} 1\text{ fortnight}\to21\text{hours of practice} \\ 7\text{ weeks}\to x \\ x=\frac{7weeks\cdot21\text{ hours of practice}}{1fortnight} \\ 7\text{ we}eks=7\cdot7days=49days \\ 1\text{ fortnight=15days} \\ x=\frac{49days\cdot21\text{ hours of practice}}{15\text{ days}}=68.6\text{ hours of practice} \end{gathered}[/tex]In 7 weeks Ed practice 68.6 hours.
Note we convert week and fortnight to days.
use the circle unit to evaluate csc(-/2)
The definition of the cosecant function is
[tex]\csc \theta=\frac{1}{\sin \theta}[/tex]Therefore,
[tex]\Rightarrow\csc (-\frac{\pi}{2})=\frac{1}{\sin (-\frac{\pi}{2})}[/tex]To find sin(-pi/2), use the diagram below.
Consider that the circumference has a radius equal to 1. Then, the coordinates of the orange point are (0,-1). Furthermore, the points on the circumference are given as (cos(theta), sin(theta)); therefore,
[tex]\begin{gathered} \Rightarrow(0,-1)=(\cos (-\frac{\pi}{2}),\sin (-\frac{\pi}{2})) \\ \Rightarrow\sin (-\frac{\pi}{2})=-1 \\ \Rightarrow\csc (-\frac{\pi}{2})=\frac{1}{-1}=-1 \\ \Rightarrow\csc (-\frac{\pi}{2})=-1 \end{gathered}[/tex]Thus, the answer is csc(-pi/2)=-1
is this left continuous at x=2?from those intervals pleases answer the part of the question asking if left or right continuous and where
Not, the left graph is discontinuous in x=2, the kind of discontinuity is removable discontinuity. It is not continuous because in x=2 there us a abrupt change in the function value.
To determine if the function is left or right continuous you identify if the function in a jump discontionuity has the defined point on the left or on the right.
The function given in number 11 has a jump discontinuity at x=3, as the defined point is on the part of the graph on the left, you say the function is left continuous at x=3.
Answer: left continuous at endpoint x=3What did I do wrong? Need help with this equation
Recall that :
1) A function
[tex]f\mleft(x\mright)[/tex]translated n-units to the left is
[tex]f\mleft(x-n\mright).[/tex]2) A function
[tex]h\mleft(x\mright)[/tex]translated m-units up is:
[tex]h\mleft(x\mright)+m.[/tex]3) A function g(x) reflected over the x-axis is:
[tex]-g(x)\text{.}[/tex]The parent function is:
[tex]y=\sqrt[]{x}\text{.}[/tex]The function of the graph of the above function translated horizontally 3 units to the left is:
[tex]y=\sqrt[]{x+3}.[/tex]The function of the graph of the above function translated vertically 4 units up is:
[tex]y=\sqrt[]{x+3}+4.[/tex]The function of the graph of the above function reflected over the x-axis is:
[tex]y=-(\sqrt[]{x+3}+4)=-\sqrt[]{x+3}-4.[/tex]Finally, the function of the graph of the above function stretched vertically by a scale factor of 2 is:
[tex]y=-2\sqrt[]{x+3}-4.[/tex]Answer:
The graph of the function has a horizontal translation Left 3 and vertical translation Up 4. The graph has been reflected over the x-axis and has been Vertically stretched.
Bob had three 10' lengths of conduit. If he used a total of 13.75' of conduit to install a motor, how much total conduit does he have left?
Given that Bob had three 10' lengths of conduit and he used a total of 13.75' of conduit to install a motor.
To find how much total conduit he has left we would subtract the initial from what was used.
The initial length = three 10' lengths = 30'
Length used = 13.75'
[tex]\begin{gathered} \text{Conduit left = Initial length - length used} \\ \text{Conduit left }=\text{ 30 - 13.75} \\ =16.25 \\ \end{gathered}[/tex]
The total conduit he has left is
Answer: 16.25 feet
The perimeter of a geometric figure is the sum of the lengthsof its sides. If the perimeter of the pentagon (five-sided figure)to the right is 140 meters, find the length of each side.
Given figure is a regular pentagon, it means it will have 5 sides of equal length.
Let the length of each side of the polygon be 'x' meters.
The perimeter of the pentagon will be the sum of all its 5 sides,
[tex]\begin{gathered} P=x+x+x+x+x \\ P=5x \end{gathered}[/tex]Given that the perimeter of the pentagon is 140 meters,
[tex]P=140[/tex]Substitute the value in the equation,
[tex]\begin{gathered} 140=5x \\ x=\frac{140}{5} \\ x=28 \end{gathered}[/tex]Thus, the length of each side of the regular pentagon is 28 meters.
If you can help me with this I would be thankful
When a function is compose by its inverse, the result is its original input. Therefore,
[tex]f(f^{-1}(x))=x[/tex]The figure below is a right rectangular pyramid. Which of the following is not a cross-section from a right rectangular pyramid?
Answer:
(B)
Explanation:
The base of a right rectangular pyramid is a rectangle, so if we cut the pyramid with a plane that is parallel to the base, we will get a cross-section with a rectangular form or (A)
We can also cut the pyramid with a plane that is perpendicular to the base, In this case, we will get a cross-section with a triangular form (C)
Finally, we can cut the pyramid with a transversal plane and get a cross-section with the form of a trapezoid (D)
Therefore, the answer is (B) because a square is not a cross-section for the right rectangular pyramid.
Which equation is represented by the table of values below
Choosing two points: A(0, 3) and B(3, -9)
• Sope (m):
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1}=\frac{-9-3}{3-0}=\frac{-12}{3}=-4 \\ m=-4 \end{gathered}[/tex]• Find b: choosing point A
y = mx + b
[tex]\begin{gathered} y=mx+b \\ 3=-4\cdot(0)+b \\ b=3 \end{gathered}[/tex]• Education:
[tex]\begin{gathered} y=m\cdot x+b \\ y=-4x+3 \end{gathered}[/tex]
Answer: A. y= -4x + 3
a bank account principal is $1,000 and accumulate yearly interest at 6%. assuming that no withdrawals are made, use the compound interest formula to compute the amount in the account after 10 yearsIf interest is compounded yearly, what is the amount of money after t = 10 years?
The rule of the compounded interest is
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]A is the new amount
P is the initial amount
r is the rate in decimal
n is the number of periods per year
t is the time in years
Since the principal is $1000, then
P = 1000
Since the yearly interest rate is 6%, then change it to decimal by dividing it by 100
r = 6/100 = 0.06
Since the interest is compounded yearly, then
n = 1
Since the time is 10 years, then
t = 10
Substitute them in the rule above
[tex]\begin{gathered} A=1000(1+\frac{0.06}{1})^{(1)(10)} \\ A=1000(1.06)^{10} \\ A=1790.847697 \end{gathered}[/tex]The amount of money in the account after 10 years is $1790.847697
PLS HELP ME I BEG OF YPU PLS PLS
Answer: Y= 2x + 4
Step-by-step explanation:
The line is going up which means it is positive, giving it a positive slope of 2x. It intersects with the Y-axis at (0, 4), giving it a positive Y-int of 4. You can use rise over run to find the slope; pick two easy points and count how many units up and over it is to the next point!
Raina got a prepaid debit card with $30 on it .For her first purchase with the card ,she bought some bulk ribbon at a craft store. The price of the ribbon was 6 cents per yard.If after that purchase there was $27.90 left on the card ,how many yards of ribbon did Raina buy?
Data:
• Total: $30
,• Price of ribbon: 6 cents per yard
,• Left after purchase: $27.90
Procedure:
[tex]30-27.90=2.1[/tex]Raina spent a total of $2.1 on ribbons.
To know how many yards she bought, we have to homogenize the units. For that, a conversion to dollars must be made.
[tex]6\frac{cents}{\text{yard}}\cdot\frac{0.01dollar}{1cent}=0.06\frac{\text{dollars}}{\text{yard}}[/tex]The yard is $0.06 per yard.
Finally, we can get the yards bought:
[tex]2.1dollars\cdot\frac{1\text{yard}}{0.06\text{dollars}}=35[/tex]Answer: 35 yards
Explain why we need math? (Need three sentences)
1. Mathematics is necessary for engineering. Without them we could not have the technological advances that make our lives easy.
2. Mathematics is necessary just as art is necessary. For its beauty. They have a spiritual and aesthetic value.
3. Mathematics is necessary for our daily life. From calculating the cost of things or calculating how we can carry out our dreams.
4. Mathematics is fundamental for the intellectual development of human beings: that is, because it helps them to be logical, to reason in an orderly manner and to have a mind prepared for thought, criticism and abstraction
Find f(5) for f(x)= 2(2)*O A. 32B. 2O C. 4D. 8
Given function is
[tex]2^x[/tex]Fo
Use the graph to find the appropriate solutions to the equation
The first thing that you should notice is that you have two functions:
[tex]f(x)=\text{ -}2|x\text{ -}3|+1;\text{ and }g(x)=\text{ -}2\sqrt{x\text{ -}1}[/tex]Then their respective graphs are given by the blue and the red functions in your picture. Now, the main idea, is to know the points where they are equal and in that way, you will have the initial equation as follows:
[tex]f(x)=\text{ -}2|x\text{ - }3|+1=\text{ -}2\sqrt{x\text{ - }1}\text{ }=g(x)[/tex]The equation will be satisfied in terms of their graphs at the points where they intersect themselves, at the x-coordinate.
The intersection points A and B at the x-coordinate are the answer for the equation. Then
[tex]x\approx1.7\text{ or }x\approx5.7[/tex]