Principal (P)= $1,450
Simple Interest rate (R) = 5%
time (T) = 3 years
n = 365
Future value = Amount. + Principal
[tex]FV=P(1+\frac{r}{n})^{nt}-P+P=P(1+\frac{r}{n})^{nt}[/tex][tex]\Rightarrow FV=1450(1+\frac{0.05}{365})^{365\times3}=1684.54[/tex]Therefore, the Future value = $1684.54
The rule general rule to add fractions
It is required to give a general rule for adding fractions.
The general rule is first to ensure the fractions' denominators are the same and then add the numerators.
Note that a common denominator must be found if the denominators are different.
Which of the following is the product of the rational expressions shown here?Х/x-2•3/x-2A. X+3/2x -4B. 3x/x^2- 4x + 4c. 3x/x^2-4
Step 1: Write out the expression
[tex]undefined[/tex]6x+8=28 find the value of X
Solve this system of equations. Fill in the blank with the correct point. a=-b + 5 2b+a=11
Answer:
The solution to the system of equations is:
a = -1
b = 6
Explanation:
Given the system of equations:
a = -b + 5 .............................................................(1)
2b + a = 11 ............................................................(2)
Substituting the expression for a in equation (1) into equation (2), we have:
2b + (-b + 5) = 11
2b - b = 11 - 5
b = 6
Using this value of b in equation (1), we have:
a = -6 + 5
= -1
Therefore,
a = -1
b = 6
In circle F, what is m EA if m ZDFE - 36°?АBFEDCa54°b104°C144°d324°
Note that the measurement of arc is equal to the central angle.
A central angle is an angle whose vertex is at the center of the circle.
Since DFA is a straight line, angle DFE and angle AFE will have a sum of 180 degrees
[tex]\angle\text{DFE}+\angle\text{AFE}=180[/tex]From the given, angle DFE = 36 degrees
[tex]\begin{gathered} 36+\angle\text{AFE}=180 \\ \angle\text{AFE}=180-36 \\ \angle\text{AFE}=144 \end{gathered}[/tex]From the notes above, arc EA = angle AFE
Therefore, arc EA = 144 degrees
The answer is Choice C. 144 degrees
One day, Jada takes home $90.45 after working h hours and after paying the bus fare. Write an equation to represent this situation.
The equation to represent this situation is t = b + h*p + 90.45.
It is given in the question that:-
Amount of money Jada takes home = $ 90.45
Number of hours Jada worked = h
We have to write an equation to represent the situation.
According to the data given in the question, we can write,
Total money with Jada = Bus fare + number of hours Jada worked*price per hour of working + amount of money Jada takes home
Let the bus fare be b.
The Total money with Jada be t.
Price per hour = p
Hence, we can write,
t = b + h*p + 90.45
To learn more about equation, here:-
https://brainly.com/question/10413253
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Alison Alix goes to the bank and borrows 150,000 pesos at 9.5% for 250 days. If the bank uses the ordinary interest method, how much interest will Alison have to pay?
In the ordinary interest method, interest (I) is computed as follows:
I = Prt
where P is the principal, r is the annual interest rate (as a decimal), and t is time in years. With this method, the year has 360 days instead of 365.
Substituting in the formula with P =150,000 pesos, r = 0.095 (= 9.5/100), and t = 250/360, we get:
[tex]\begin{gathered} I=150,000\cdot0.095\cdot\frac{250}{360} \\ I=9895.83\text{ pesos} \end{gathered}[/tex]
Alison will have to pay 9,895.83 pesos
Multiply: (5j + 3k) (5j - 3k)Multiply: (5j + 3k) (5j - 3k)
Answer:
25j^2 - 9k^2
Explanation:
A consumer research company wants to estimate the average cost of an airline ticket for a round trip within the continental United States. A random sample of 50 airfares was gathered and gave an average price of $438. Identify the variable
Answer
Option B is correct!
The variable here is the airfares that were gathered from the sample.
Explanation
In Statistics, variable is any number, quantity or characteristics that can be measured, counted or collected.
For this question, the data collected is the variable.
Hence, the variable here is the airfares that were gathered from the sample.
Hope this Helps!!!
I’m confused pls help
Answer:
there is not enough information
Step-by-step explanation:
in this image we can see 2 sides are congruent but we can’t see if an angle is congruent
Which number would go outside the circles?А. 0.3В. 0C. -7D. 2
First, what are whole numbers?
They are numbers of puppies you want
1,2,3,4,5........
That eliminates 2
Integers are positive and negative numbers of puppies including having no puppies
-5,-4,-3,-2,-1,0,1,2
That eliminates -7, 0 and 2
The decimal is neither a whole number or an integer so it would go outside the circle.
raph of y = f(x) is graphed below. What is the end behavior of f(2)?
By observing the graph we have got the following :
The graph is going down after the point (-7,0)
After the point (x,f(x)) =(-7,0) ,as x decreasing, the function f(x) is decreasing
[tex]as\text{ }x\rightarrow-\infty,\text{ f(x)}\rightarrow-\infty[/tex]The graph is going up after the point (4,0).
After the point (x,f(x)) =(4,0), as x increasing, the function f(x) is increasing
[tex]as\text{ }x\rightarrow\infty,\text{ f(x)}\rightarrow\infty[/tex]Hence we get
[tex]as\text{ }x\rightarrow\infty,\text{ f(x)}\rightarrow\infty\text{ and }as\text{ }x\rightarrow-\infty,\text{ f(x)}\rightarrow-\infty[/tex]
Hence the first option is correct.
A person is on the outer edge of a carousel that is rotating counterclockwise. Using the unit circle to model the carousel, what is the exact position of the riderafter the carousel rotates pi/12 radians
To determine the location of the rider, we need to convert the polar coordinate to rectangular form.
The given polar coordinate is (1, π/12).
To convert, here are the steps.
1. To get the x-coordinate, get r cos θ.
[tex]x=rcos\theta=1cos\frac{\pi}{12}=\frac{\sqrt{6}+\sqrt{2}}{4}[/tex]2. To get the y-coordinate, get r sin θ.
[tex]y=rsin\theta=1sin\frac{\pi}{12}=\frac{\sqrt{6}-\sqrt{2}}{4}[/tex]Hence, the exact location of the rider after the carousel rotates π/12 radians is given by the coordinates found in Option D.
) I want another BMW i-8 that costs $98,316.00 for 5 years at an APR of 1.02%. What is my monthly payment?
$1681.76
Explanation
Step 1
Let
M = the total monthly mortgage payment.
P = the principal loan amount=98316
Annual Percentage Rate=1.02%=0.0102
montly rate=0.0102/12=0.00085
n = number of payments over the loan’s lifetime=5*12=60 months
then
[tex]M=P(\frac{r(1+r)^n}{(1+r)^n-1})[/tex]then, replace
[tex]\begin{gathered} M=98310(\frac{0.0102(1+0.0102)^{60}}{(1+0.0102)^{60}-1}) \\ M=98310(\frac{0.018}{1.0102^{60}}) \\ MonthlyPayment=$1,681.76$ \end{gathered}[/tex]I hope this helps you
Ariana has created a paper airplane for her physics class, the physics teacher is requiring her paper airplane to swoop down at a single point to graze the ground before it rises back into the air. Her initial attempt is modeled by the function below where h is height in feet and X is time in seconds. In how many seconds will the paper airplane crash into the ground?
Given:
[tex]h(x)=x^2-12x+35[/tex]The given function h(x) represents the height in feet and (x) is time in seconds.
We will find the time the paper airplane will crash into the ground.
When the paper airplane crashes into the ground, h(x) = 0
So, substitute h = 0
[tex]x^2-12x+35=0[/tex]Solve the equation to find (x), we will factor the equation as follows:
[tex]\begin{gathered} (x-5)(x-7)=0 \\ x-5=0\rightarrow x=5 \\ x-7=0\rightarrow x=7 \end{gathered}[/tex]So, the answer will be the time = 5 seconds and 7 seconds
Which name would represent the angle shown in yellow? D A
We can name an angle with the 3 letters of the points that define it, being the vertex the point that is written in the middle of the 3 letters.
In this case, the yellow angle is defined by the points I, A and B, where A is the vertex of the angle.
Then, we can name the angle as It can also happens that more of 3 points can be use to define and angle, but it is not the case for the yellow angle in this example.
Answer:
0 Find the perimeter of the shaded region above, Question Heln
Define the perimeter of a shape
The perimeter of any shape is the distance around the edge of a shape. That is the total length of the outline of the shape
Draw the shape given with the appropriate dimension
The shape is shaded and the perimeter is the total length of the outline
Noted that line DE is equal to BC
[tex]DE=BC=8[/tex]Therefore, the perimeter is
[tex]AB+BC+CD+DE+EA[/tex][tex]P=6+8+7+8+6[/tex][tex]P=35\text{units}[/tex]find the distance of (-3, -5) and (4,4)
√130
1) To find the distance between two points. We can use a formula derived from the Pythagorean Theorem:
[tex]d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]In this case,
[tex]d=\sqrt[]{(4+3)^2+(4+5)^2}=\sqrt[]{130}[/tex]So the distance between those two points is √130
Write 25/9 as a decimal,if necessary use a bar to indicate which digit or group of digits repeats
As per given by the question,
There are given that the fraction
[tex]\frac{25}{9}[/tex]Now,
For decimal divide the numerator by the denominator.
So, the value is;
[tex]\frac{25}{9}=2.777777[/tex]Now,
According to the question, there are mention that use a bar to indicate which which digit repeats.
So,
[tex]\frac{25}{9}=2.\bar{7}[/tex]Hence, the decimal of given fraction is,
[tex]2.\bar{7}[/tex]The lines represented by the equations y + 3x = 9 and y 5x + 1 are O parallel Submit Answer O perpendicular O the same line O neither parallel nor perpendicular
To know the relation between the lines we have to calculate the slope with this expression:
[tex]y=mx+c[/tex]whre m is the slope and c the intersection with the y axis, so for the first line
[tex]\begin{gathered} y=-3x+9 \\ m=-3 \end{gathered}[/tex]and for the secon line:
[tex]\begin{gathered} y=-\frac{1}{3}x+1 \\ m=-\frac{1}{3} \end{gathered}[/tex]The slope is diferent, so they are not parallel, and they are not the same line. is they where perpendicular the slope of the second line should be the negative reciprocal of the first line. and in this case:
[tex]-3\to\frac{1}{3}[/tex]so they are not perpendicular. So the solution is numeral D) neither parallel nor perpendicular
questions A, B, C, D, E, F, G, H and I
A. The frequency is indicated in the vertical axis.
B. The horizontal axis indicates the classes, which in this case are the test scores intervals.
C. The horizontal axis has a class width of 10.
D. The frequency for the class 60-69 is 3.
E. The frequency for the class 70-79 is 9.
F. The frequency for the class 80-89 is 12.
G. The frequency for the class 90-99 is 7.
H. We can verify that 31 students took the test because we should have 31 data points (test scores) divided into the different classes.
We should obtain 31 when adding the frequency of all the classes:
[tex]3+9+12+7=31[/tex]I. The new scores are: 78, 81, 82, 85 and 88.
So the class 70-79 increases its frequency by one, while the class 80-89 increases its frequency by 4.
We can modify the histogram and obtain:
Learning Page? QUESTIONA certain brand of coffee comes in two sizes. An 11.5-ounce package costs $4.24. A 27.8-ounce package costs $9.98.Find the unit price for each size. Then state which size is the better buy based on the unit price.Round your answers to the nearest cent.74°FComputing unit prices to find the better buyStartUnit price for the 11.5-ounce package: $ per ounceUnit price for the 27.8-ounce package: $per ounceThe better buy:OO EXPLANATION0The 11.5-ounce packageThe 27.8-ounce packageNeither (They have the same unit price)I need help with this math problem
TEXPLANATION
For the 11.5-ounce package that costs $4.24. The unit price per pound is
[tex]unit\text{ price}=\frac{cost}{quantity}=\frac{4.24}{11.5}=0.37[/tex]For the 27.8-ounce package that costs $9.98.
[tex]unit\text{ price}=\frac{9.98}{27.8}=0.36[/tex]Answer: Box A = 0.37, Box B= 0.36. The better buy is the 27.8-ounce package
If you deposit $100 each month into an IRA earning 2.3% interest, how much will you have in the account after 17 years? Round your answer to the nearest cent.
Given:
The amount deposited each month, d=$100.
The rate of interest, R=2.3%.
The number of years after which the balance in the account is calculated, N=17.
The formula for the balance in the acoount after N years is,
[tex]P_N=\frac{d((1+\frac{r}{k})^{Nk}-1)}{(\frac{r}{k})}\text{ ---(1)}[/tex]Here, r is the interest rate in decimal form and k is the number of compounding periods in one year.
Since deposit is made every month, we use monthly compounding, k=12.
The rate of interest in decimal form is,
[tex]r=\frac{R}{100}=\frac{2.3}{100}=0.023[/tex]Now, substitute the known values in equation (1).
[tex]\begin{gathered} P_{17}=\frac{100((1+\frac{0.023}{12})^{17\times12}-1)}{(\frac{0.023}{12})}\text{ } \\ P_{17}=\frac{100((1+\frac{0.023}{12})^{204}-1)}{(\frac{0.023}{12})}\text{ } \\ P_{17}=24934.19 \end{gathered}[/tex]Therefore, after 17 years, the balance in the account will be $24934.19, to the nearest cent.
Mr. Gordon’s science class is studying blood types. The table below shows the probability that a person living in the US has a particular blood type. The probability of having a blood type: O= 9/20; A= 41/100; B= 1/10; and AB= 1/25What is the probability that three students selected randomly from the class will have A, B, and AB blood, respectively?A.) 41/25,000 or 0.16%B.) 41/2500 or 1.64%C.) 43/25,000 or 0.17%D.) 43/135 or 31.9%
Given the probability of having a blood type:
O = 9/20
A = 41/100
B = 1/10
AB = 1/25
Let's find the probability that three students selected at random from the class will have A, B, and AB blood respectively.
Let's first verify if the events are mutually dependent or independent:
[tex]\begin{gathered} \frac{9}{20}+\frac{41}{100}+\frac{1}{10}+\frac{1}{25} \\ \\ \frac{5(9)+1(41)+10(1)+4(1)}{100} \\ \\ \frac{45+41+10+4}{100} \\ \\ =\frac{100}{100} \\ \\ =1 \end{gathered}[/tex]Since the total probability is 1, the events are mutually independent.
Since the events are mutually independent, to find the probability a randomly selected student will have A, B, and AB blood respectivel, we have:
[tex]\begin{gathered} P(A)*P(B)*P(AB) \\ \\ =\frac{41}{100}*\frac{1}{10}*\frac{1}{25} \\ \\ =\frac{41*1*1}{100*10*25} \\ \\ =\frac{41}{25000} \\ \\ =0.00164\approx0.16\text{ \%} \end{gathered}[/tex]Therefore, the probability that three students selected randomly from the class will have A, B, and AB respectively is 41/25,000 or 0.16%
ANSWER:
A.) 41/25,000 or 0.16%
From the diagram below, if AC is a tangent line, and if PD = 3 and DC = 2, find the length of BC.
Explanation
From the diagram
[tex]\begin{gathered} radius\text{ of cicle =}PB=PD=3 \\ PC=PD+DC=3+2=5 \end{gathered}[/tex]Therefore;
[tex]\begin{gathered} PC^2=PB^2+BC^2 \\ 5^2=3^2+BC^2 \\ 25=9+BC^2 \\ BC^2=25-9 \\ BC^2=16 \\ BC=\sqrt{16} \\ BC=4 \end{gathered}[/tex]Answer: Option A
For each problem below, solve theequation for the missing variable.Then, use that equation to find themissing quantity in the situation. Showall steps.Question 3
Solution:
To find the area, A, of a triangle, the formula is
[tex]\begin{gathered} A=\frac{1}{2}bh \\ A\text{ is the area } \\ b\text{ is the base} \\ h\text{ is the height} \end{gathered}[/tex]Given that;
[tex]\begin{gathered} A=84\text{ m}^2 \\ h=12\text{ m} \end{gathered}[/tex]Substitute the values of the variables into the formula above
[tex]\begin{gathered} A=\frac{1}{2}bh \\ 84=\frac{1}{2}\times b\times12 \\ 84=6b \\ b=\frac{84}{6} \\ b=14\text{ m} \end{gathered}[/tex]Hence, the measure of the base, b is 14 m
For a moving object, the force acting on the object varies directly with the object's acceleration. When a force of 56 N acts on a certain object, the accelerationof the object is 8 m/s?. If the acceleration of the object becomes 3 m/s?, what is the force?
STEP 1
Establish relationship between force and acceleration.
From the 1st statement, there is a direct variation between the force and the acceleration. This is put mathematically as
[tex]F\text{ }\alpha\text{ a}[/tex]We introduce a constant, m
[tex]\begin{gathered} F\text{ = ma where} \\ m\text{ is the proportionality constant creating the relationship thus } \\ Nperm/s^2\text{ as its unit} \end{gathered}[/tex]STEP 2
Derive value for the constant, m
[tex]\begin{gathered} F\text{ = ma} \\ \text{Dividing both sides by a, we have} \\ \frac{F}{a}=m \\ where\text{ }f=56N,m=8m/s^2 \\ m=\frac{56}{8}=7Nperm/s^2=7Ns^2\text{ / m} \end{gathered}[/tex]STEP 3
Apply this value of m to solve related equations.
[tex]\begin{gathered} \text{where a = 3m/s}^2\text{ and m = }7Ns^2\text{ /m} \\ \text{and F = ma = 3 x 7 = 21}N \end{gathered}[/tex]Thus, the force when acceleration becomes 3 m/sq seconds is 21 N
Identify the quadratic equation with roots -2 and -1.
we know that
The roots -2 and -1.
so
The quadratic equation in factored form is equal to
[tex](x+1)(x+2)=0[/tex]Convert to standard form
[tex]\begin{gathered} x^2+2x+x+2=0 \\ x^2+3x+2=0 \end{gathered}[/tex]the answer is the third optiontable below shows the circumstances of a tree trunk as the tree ages. which statement describes the rate of change shown in the table?
Remember that
the arte of change is the the same that the slope
so
we take two points
(4,6) and (7,9)
m=(9-6)/(7-4)
m=3/3
m=1 in/year ------> rate of change
the equation is slope intercept form is
y=mx+b
we have
m=1 -
point (4,6)
substitute
6=1(4)+b
b=2
y=x+2
Verify the other ordered pairs with the equation
For x=11 ------> y=11+2=13 is ok
For x=16 -----> y=18 is ok
For x=22 -----> y=24 is ok
therefore
the answer is option AGive the equation for a circle with the given center and radius.Center at (-1, 3), radius = 4A. (x+3)2+(y−1)2=4B. (x−1)2+(y+3)2=16C. (x+1)2+(y−3)2=16D. (x−3)2+(y+1)2=4Don't need explanation just answer!
ANSWER:
C. (x + 1)² + (y − 3)² =16
STEP-BY-STEP EXPLANATION:
We have that the equation of the circle has the following structure:
[tex]\begin{gathered} \left(x−a\right)^2+\left(y−b\right)^2=r^2 \\ \\ \text{ Where \lparen a, b\rparen is the center and r is the radius.} \end{gathered}[/tex]We replace the center and the radius and we are left with the following:
[tex]\begin{gathered} \left(x-(-1)\right)^2+\left(y-3\right)^2=4^2 \\ \\ \left(x+1\right)^2+\left(y-3\right)^2=16 \end{gathered}[/tex]This means that the correct answer is C. (x + 1)² + (y − 3)² =16