The formula we need to use is as follows:
[tex]A=P\mleft(1+\frac{r}{n}\mright)^{nt}[/tex]Where:
A - Ajusted amount
P - Starting amount
r - Annual interest rate
n - How many times it is compounded per year
t - Time of the period in years
Since we want to find the compounded amount, that is, the adjusted A, the value given below, $20,000, is the starting amount, P.
Assuming the 5% is the annual interest, this is r.
Since the interest is compounded quarterly, it is compounded 4 times per year, so n is 4.
And the period is given to be 3/4 of an year.
So:
[tex]\begin{gathered} A=? \\ P=20000 \\ r=5\%=0.05 \\ n=4 \\ t=\frac{4}{3} \end{gathered}[/tex]So, substituting the values into the formula, we can evaluate A:
[tex]\begin{gathered} A=P\mleft(1+\frac{r}{n}\mright)^{nt} \\ A=20000\mleft(1+\frac{0.05}{4}\mright)^{4\cdot\frac{3}{4}} \\ A=20000\mleft(1+0.0125\mright)^3 \\ A=20000(1.0125)^3 \\ A=20000\cdot1.03797\ldots \\ A=20759.4140\ldots\approx20759.41 \end{gathered}[/tex]So, the compounded amount is approximately $20,759.41.
Evaluate each expression using the graph of y=f(x) & y=g(x) shown in the figure.1.f(2)+g(-1)
f(2) + g(-1) = ??
Using the graph of y = f(x) to find the value of f(2)
the coordinates of each point is ( x , f(x) )
Looking for the point at which x = 2
so, the answer is the point (2 , -2)
so, f(2) = -2
By the same way, we will find the value of g(-1)
looking for the point at which ( x = -1 ) and lie on the graph y = g(x)
so, the point will be (-1 , 3)
so, g(-1) = 3
So, f(2) + g(-1) = -2 + 3 = 1
I need to find the rate and unit rate of 480 hours of work in 12 weeks
Explanation
To help understand the question we need an example.
A unit rate means a rate for one of something. We write this as a ratio with a denominator of one. For example, if you ran 70 yards in 10 seconds, you ran on average 7 yards in 1 second. Both of the ratios, 70 yards in 10 seconds and 7 yards in 1 second, are rates, but the 7 yards in 1 second is a unit rate.
Using the above idea we case say that;
The rate is
Answer
[tex]\frac{480}{12}=40\text{hours i}n\text{ 1 w}eek[/tex]Similarly, the unit rate will be
[tex]40\text{ hours in 1 w}eek[/tex]Brian needs to buy plastic forks. Brand A has a box of 12 forks for $1.12. Brand B has a box of 25 forks for $2.69.Find the unit price for each brand. Then state which brand is the better buy based on the unit price.Round your answers to the nearest cent.Unit price for the Brand A forks:Unit price for the Brand B forks:s] for each fork$for each forkThe better buy:Brand ABrand BNeither (They have the same unit price)
Given
Brand A
12 forks for $ 1.12
Then, the unit price is:
[tex]\frac{1.12}{12}=0.0933[/tex]Unit price for the Brand A forks: $0.093
Brand B
25 forks for $2.69
So, the unit price is:
[tex]\frac{2.69}{25}=0.1076[/tex]Unit price for the Brand B forks: $0.11
Finally, the better buy based on the unit price is: Brand A
A car travels 10 km southeast andthen 15 km in a direction 60° north ofeast. Find the direction of the car'sresultant vector.
We need to find the angle x, so let's find the angle of the first two vectors:
[tex]\theta_1=\frac{270+360}{2}=315[/tex][tex]\theta_2=60[/tex]so:
[tex]v_x=10cos(315)+15cos(60)=14.57[/tex][tex]v_y=10sin(315)+15sin(60)=5.91[/tex]Therefore, the angle is:
[tex]\begin{gathered} \theta_r=tan^{-1}(\frac{v_y}{v_x})=tan^{-1}(\frac{5.91}{14.57}) \\ \theta_r=22.11^{\circ} \end{gathered}[/tex]Answer:
The direction of the car's resultant vector is 22.11⁰
What else isneeded to provethese trianglescongruent usingthe ASA postulate?A. The angles at point A need to be congruent, and AD=AB.B. Nothing else is needed to use the ASA postulate.C. The two angles at point A need to be congruent.
The angles at point A need to be congruent, and AD ≅ AB. In this way, the angle-side-angle (ASA) postulate is satisfied with the two angles at point A, angles B and D, and the side between them, which are AD and AB, respectively.
How do I find the zeros of the function and write as an ordered pair? f(x) = 3x^2 - 11x -20
f(x) = 3x^2 - 11x -20
To find the zeros of the function, first we factor the expression as follows:
f(x) = (3x + 4)(x - 5)
Now we equal the expression to zero:
(3x + 4)(x - 5) = 0
If the expression is equal to zero, that means at least one of the factors is equal to zero, so:
3x + 4 = 0, then x = - 4/3
or
x - 5 = 0, then x = 5
The zeros of the function are:
(-4/3, 0) and (5, 0)
Which fraction is equivalent to 4/10? a.4/10 b.10/4 c.1/4 d.1/10
ANSWER:
a. 4/10
STEP-BY-STEP EXPLANATION:
We have the following fraction:
[tex]\frac{4}{10}[/tex]The fraction equivalent to 4/10, is the same fraction 4/10, since the other fractions give a different numerical value
A runner ran for 3.5 hours and traveled 14 miles. What is the rate of the runner in miles/hour?
From the question we can derive the following?
Time = 3.5 hours
Distance traveled = 14 miles
We are asked to find the runners rate in miles/hour.
recall:
Distance = Rate x Time
Rate = Distance
Time
Rate = 14/3.5
Rate = 4 miles/hour.
Therefore, the rate of the runner is 4 mile/hour.
8+4^2 times 2 I’m not sure how to answer this
We need to evaluate the expression:
[tex]8+4^2\cdot2[/tex]We start by evaluating the power 4²:
[tex]4^2=4\cdot4=16[/tex]And multiplication has priority over addition. Thus, we evaluate the product:
[tex]4^2\cdot2=16\cdot2=32[/tex]Then, the addition:
[tex]8+4^2\cdot2=8+32=40[/tex]Answer: 40
Seventeen hundred tickets costing $5 each were sold for a scholarship fund-raiser. One prize of $2,000, 3 prizes of $1,000, and 5 prizes of $250 were given away. How much money did the scholarship fund-raiser make?
An object is thrown into the air going 9 m/s. How fast is it going 2 seconds later?-10.6 m/sO 10.6 m/s0 m/sO 0.8 m/s
To answer this question we have to remember that
[tex]a=\frac{v_f-v_0}{t}[/tex]In this case a=-9.81, t=2 and v0=9. Then
[tex]\begin{gathered} -9.81=\frac{v_f-9}{2} \\ 2(-9.81)=v_f-9 \\ v_f=2(-9.81)+9 \\ v_f=-10.62 \end{gathered}[/tex]Therefore the speed after two seconds is -10.62 m/s.
bus2.NextPiecewise and Absolute Value Functions: Mastery Test2.Use the drawing tool(s) to form the correct answer on the provided graph,Graph the function.f(t) = |x + 2 - 1Drawing ToolsClick on a tool to begin drawing,8 DeleteSelectRay10Line8
The function
[tex]f(x)=|x+2|-1[/tex]Step 1: Get the x-intercept by substituting f(x) =0
0=|x+2| -1
=> |x+2|=1
Square both sides
x+2= 1
Mke x the subject of the formula
x=1-2
x= -1
Hence, we will have (-1,0) as one of the coordinates
Step 2: Get the y-intercept by putting x=0 into the equation
f(x) => |0+2| -1
f(x)=> 2-1
f(x)=>1
Hence the coordinate will be (0,1)
Therefore, to plot the graph, we will use the two coordinates (-1,0) and (0,1)
The graph is shown below.
which coordinate K on the line segment with endpoints J (4, 2) and L (4, 6) divide JL such that the ratio of JK : KL is 3:1 ?
From the question;
we are given the line with endpoints J(4,2) and L(4,6)
We are to divide the line in ratio 3:1
we will use the formular
[tex]undefined[/tex]The sugar sweet company is going to transport its sugar to market. It will cost 5500 to rent trucks plus $175 for each ton of sugar transported. The total cost C (in dollars) for transporting n tons is given by the following functionC(n)=5500+175nWhat is the total cost of transporting 12 tons?If the cost is $9525, how many tons is the company transporting?
The cost function is given as:
[tex]C(n)=5500+175n[/tex]a)
[tex]\begin{gathered} The\text{ cost of transporting 12 tons:} \\ C(12)=5500+175(12) \\ C(12)=\text{ \$7600} \end{gathered}[/tex]b)
[tex]\begin{gathered} C(n)=5500+175n \\ \Rightarrow9525=5500+175n \\ \Rightarrow9525-5500=175n \\ \Rightarrow4025=175n \\ \Rightarrow n=\frac{4025}{175} \\ n=23\text{ tons} \end{gathered}[/tex]use the graph to answer the question is the function even odd neither or both
Remember that
The odd functions are functions that return their negative inverse when x is replaced with –x. This means that f(x) is an odd function when f(-x) = -f(x)
and
A function is an even function if f of x is equal to f of −x for all the values of x
In this problem
the function is neitherEvaluate the expression when y= 7 and : =1.3(v+-)2- 5ySimplify your answer as much as possible.
Evaluate the expression when m=-5.7 and n=7.8.5m-7n
Evaluating Algebraic Expressions
We are given the expression
Q = 5m - 7n
And we're required to evaluate it for m=-5.7 and n=7.8.
Substituting:
Q = 5(-5.7) - 7(7.8)
Operating the products separately:
Q = -28.5 - 54.6
Operating:
Q = -83.1
The expression results -83.1
Find the circumcenter of the triangle ABC.A(-8,-5), B(7,6), C(-8,6).
The circumcenter of a triangle is the intersection point of the perpendicular bisector from the sides of the triangle.
4. Identify the domain and range, draw a mapping, then state if the relation is a function.a) (4, 6) (6,-5) (4, 2) (6, 6)
We can start by looking at the points.
We can see that the relation is defined for x=4 and x=6.
[tex]\begin{gathered} \text{Dom}\colon x\in\left\lbrace 4,6\right\rbrace \\ \end{gathered}[/tex]The image, that is the values that the dependant variable takes, are y=6, -5 and 2
[tex]\operatorname{Im}\colon y\in\left\lbrace -5,2,6\right\rbrace [/tex]For this relation to be a function, we have to have one and only one value for "y" for each value of "x" in the domain.
We can already see that for x=4, we have two values for y (y=6 and y=2), so we can conclude that this relation is not a function.
We can draw the points in an xy-plane and get:
how would you factor the polynomial expression x4+x2-20
We have the following:
[tex]x^4+x^2-20[/tex]factoring:
[tex]\begin{gathered} x^4+x^2-20 \\ u=x^2 \\ u^2+u-20=(u+5)(u-4) \\ (x^2+5)(x^2-4)=(x^2+5)(x+2)(x-2) \end{gathered}[/tex]The anwer is:
[tex](x^2+5)(x+2)(x-2)[/tex]Based on the table, what is the y-value of the vertex of the parabola that models the data?
We have a table that represents a parabola.
The vertex will represent the extreme point of the parabola where the minimum or maximum value happens.
In this case, we can see that for x = 5, we have an extreme value of y = 1125.
We can also check that for x = 3 and x =7, 2 units from x = 5, we have the same value (y = 1105).
Then, we have to have the vertex at point (5, 1125), as we have an axis of symmetry in the line x = 5.
The value for y for the vertex is then y = 1125.
Answer: 1125
A box contains 77 red marbles, 6 white marbles, and 94 blue marbles. If a marble is randomly selected from the box, what is the probability that it is red or white? Express your answer as a simplified fraction or a decimal rounded four decimal places.
Given:
A box contains 77 red marbles, 6 white marbles, and 94 blue marbles.
Required:
We need to find the probability to select a marble that is red or white.
Explanation:
Let A be the event that selects a red or white marble.
The total number of marbles in the box = 77+6+94 =177 marbles.
The possible outcomes = the total number of marbles = 177 marbles.
[tex]n(S)=177[/tex]The favorable outcomes = The number of red marbles + the number of white marbles =77 + 6 = 83marbles.
[tex]n(A)=83[/tex]The probability of selecting a red or white marble.
[tex]P(A)=\frac{n(A)}{n(S)}=\frac{83}{177}[/tex]Final answer:
The probability of selecting a red or white marble is 83/177.
graph the following equationy=3x-4
Since a single line passes through two points, then you can take two values of x and replace them in the given equation to obtain their corresponding values in y. Then you graph the points found and join them.
So for example, if you take the values of x, x = 2, and x = -3, you have
[tex]\begin{gathered} x=2 \\ y=3x-4 \\ y=3(2)-4 \\ y=6-2 \\ y=-2 \\ \text{ Then you have the point} \\ (2,-2) \end{gathered}[/tex][tex]\begin{gathered} x=-3 \\ y=3x-4 \\ y=3(-3)-4 \\ y=-9-4 \\ y=-13 \\ \text{ Then you have the point} \\ (-3,-13) \end{gathered}[/tex]is prediction for the mone, in dollars from selling cranberis hsserside can seseorang where thegs) = -4502 +503 +2,700
SOLUTION AND EXPLANATION
The giving function are
[tex]f(x)=-750x^2+1500x+2250[/tex][tex]g(x)=-450x^2+450x+2700[/tex]The function h(x) which represent the total monthly revenue is the sum of F(x) and g(x)
[tex]\begin{gathered} h(x)=f(x)+\text{g(x)} \\ h(x)=-750x^2+1500x+2250-450x^2+450x+2700 \end{gathered}[/tex]Then we rearrange the terms according to their degrees and simplify them
[tex]\begin{gathered} h(x)=-750x^2-450x^2+1500x+450x+2700+2250 \\ h(x)=(-1200)x^2+(1950)x+4950 \end{gathered}[/tex]4. Lilly's old car seat hada maximum weight of 40 pounds. Her now car seat has a max weight of 70 pounds. find the percent increase or decrease
Lilly's old car seat hada maximum weight of 40 pounds.
Her now car seat has a max weight of 70 pounds.
Find the percent increase or decrease?
SOLUTION:
New increase in weight = 70 pounds - 40 pounds = 30 pounds
Percentage increase = 30 / 40 x 100 / 1 = 75 % increase
Graph the parabola.y=x2-4Plot five points on the parabola: the vertex, two points to the left of the vertex, and two points to the right of the vertex. Then click on the graph-a-functionbuttonХ5?
Given the Quadratic Function:
[tex]y=x^2-4[/tex]You need to remember that the Quadratic Parent Function (the simplest form of a Quadratic Functions) is:
[tex]y=x^2[/tex]And its vertex is at the Origin:
[tex](0,0)[/tex]The function given in the exercise was obtained by shifting the parent function 4 units down. That means that the y-coordinate of the vertex changes, but the x-coordinate is the same. Therefore, the vertex of this parabola is:
[tex](0,-4)[/tex]To find two points to the left of the vertex, you can choose this value for "x":
[tex]x=-1[/tex]Substituting this value into the function and evaluating, you can find the corresponding value of "y":
[tex]y=(-1)^2-4=1-4=-3[/tex]Now you have this point:
[tex](-1,-3)[/tex]You can choose this value of "x":
[tex]x=-4[/tex]And apply the same procedure:
[tex]y=(-4)^2-4=16-4=12[/tex]Then, the other point is:
[tex](-4,12)[/tex]To find the first point to the right of the vertex, you can substitute this value of "x" into the function and evaluate:
[tex]x=1[/tex]Then, you get:
[tex]y=(1)^2-4=-3[/tex]The point is:
[tex](1,-3)[/tex]To find the second point, substitute this value into the equation and evaluate:
[tex]x=4[/tex]Then:
[tex]y=(4)^2-4=16-4=12[/tex]So the other point is:
[tex](4,12)[/tex]Now you can plot the points and graph the function.
Therefore, the answer is:
1. P(non fiction)2. P(teen or adult books)3. P(fiction or kids book)4. P(teen books and non fiction)5. P(adult books/fiction book)6. P(non fiction book/teen book)Fill in the missing cells of the table and answer the following questions base off of the completed table make sure your answer is a reduced fraction.
Using the given data on the table, we must fill the missing cells with the correct answer.
First, let's try to solve for the FICTION Books for ADULTS.
Since we are given the total number of Fiction books, as well as the number of Kids and Teens Fiction books, we can add up the number of Kids and Teens Fiction book to the Total number of fictions book in order to get how many Adult Fiction books there are.
ADULT FICTION = TOTAL FICTION - (KIDS FICTION + TEENS FICTION)
ADULT FICTION = 105 - (75 + 20)
ADULT FICTION = 105 - 95
ADULT FICTION = 10
Therefore, there are 10 Adult Fiction Books.
Next, we will find the number of KIDS NON FICTION books.
Just like what we did on the first one, we are given the total, and the number of KIDS FICTION book. Therefore, we just need to substract the number of KIDS FICTION to the TOTAL amount of kids book.
KIDS NON FICTION = TOTAL KIDS BOOK - KIDS FICTION
KIDS NON FICTION = 80 - 75
KIDS NON FICTION = 5
Therefore, we have 5 Non Fiction Books for Kids.
We will use the same process for finding how many TEEN NON FICTION books are there.
TEENS NON FICTION = TOTAL TEENS BOOK - TEENS FICTION BOOK
TEENS NON FICTION = 50 - 20
TEENS NON FICTION = 30
Therefore, we have 30 Non Fiction Books for Teens.
Next, to find the total number of NON FICTION Books, we just need to add up the number of KIDS NON FICTION books, TEENS NON FICTION books, and ADULT FICTION books.
TOTAL N-FICTION=KIDS N-FICTION+TEENS N-FICTION + ADULT N-FICTION
TOTAL NON FICTION BOOKS = 5 + 30 + 15
TOTAL NON FICTION BOOKS = 50
Therefore, the total number of Non Fiction books are 50.
Next, we will do the same to find the total number of ADULT BOOKS.
TOTAL ADULT BOOKS = ADULT FICTION + ADULT NON FICTION
TOTAL ADULT BOOKS = 10 + 15
TOTAL ADULT BOOKS = 25
Therefore, we have a total of 25 Adult Books.
Finally, we will just add up the number of TOTAL NON FICTION books and TOTAL NON FICTION books to get the TOTAL NUMBERS OF BOOKS.
TOTAL NUMBER OF BOOKS = TOTAL FICTION + TOTAL NON FICTION
TOTAL NUMBER OF BOOKS = 105 + 50
TOTAL NUMBER OF BOOKS = 155
Therefore, we have a total of 155 books altogether.
I also need help with these 2 questions.
The value of the variable w associated to the two line segments is equal to 3.5.
How to determine the value of a variable behind two line segments of equal length
In this question we find two line segments that are supposed to be of equal length. We need to determine the value of a variable w both by definitions and theorems from Euclidean geometry and algebra properties. The complete procedure is now shown:
Step 1 - Given:
JK = LM, JK = 4 · w + 1,
Step 2 - Given:
LM = 6 · w - 6
Step 3 - Steps 1 & 2 / Algebra properties:
4 · w + 1 = 6 · w - 6
Step 4 - Algebra properties:
2 · w = 7
Step 5 - Algebra properties / Result
w = 3.5
The value of the variable w is equal to 3.5.
To learn more on congruent line segments: https://brainly.com/question/15730595
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I having trouble understanding these questions over pythagorean theorem. I can send photos so it's understandable.
We will be creating two triangles: Triangle ABC and Triangle CDE
From the two figures drawn above, Triangle ABC is similar to Triangle CDE
Line AB = Line DE
Line BC = Line DC
Line AC = Line CE
< D is equal to 90 degrees and this is similar to angle B
Hence, < D = < B
Also, triangle similarity proportion can be establish
[tex]\frac{AB}{DE}\text{ = }\frac{BC}{DC}\text{ = }\frac{AC}{CE}[/tex]Use a scientific calculator to find the values of the following.
For the given triangle, we have that the trigonometric functions are defined as follows:
[tex]\begin{gathered} sinA=\frac{opposite\text{ side}}{hypotenuse}=\frac{1}{2}=0.5 \\ cosA=\frac{adjacent\text{ side}}{hypotenuse}=\frac{\sqrt{3}}{2}=0.86 \\ tanA=\frac{opposite\text{ side}}{adjacent\text{ side}}=\frac{1}{\sqrt{3}}=0.58 \end{gathered}[/tex]