We need to find the resulting amount or future value of the presente value of $6000 with an interest rate of 0.03 after 5 years.
The compound interest formula is given by
[tex]A=P(1+\frac{r}{n})^{n\cdot t}[/tex]where A is the future value, P is the present value, r is the rate, n is the number of compounding periods per year and t is the time. In our case, we have
[tex]\begin{gathered} P=6000 \\ r=0.03 \\ n=1 \\ t=5 \end{gathered}[/tex]By substituting these values into the formula, we get
[tex]A=6000(1+\frac{0.03}{1})^{1\cdot5}[/tex]which gives
[tex]\begin{gathered} A=6000(1.03)^5 \\ A=6000(1.1592740743) \\ A=6955.6444 \end{gathered}[/tex]Therefore, in order to find the compound interest CI, we need to subtract the principal value P to the Future amount A
[tex]\begin{gathered} CI=A-P \\ CI=6955.6444-6000 \\ CI=955.6444 \end{gathered}[/tex]For which equation would x = 12 be a solution?12 - x = 448 ÷ x = 12x + 4 = 1212 x = 144
We need to determine which of the given equations has solution x = 12.
We can do so by replacing x with 12 on the left side of an equation and comparing the result to the right side. If they are equal, then x = 12 will be a solution to that equation.
We have:
[tex]12-12=0\ne4[/tex][tex]48\div12=4\ne12[/tex][tex]12+4=16\ne12[/tex][tex]12(12)=144[/tex]Therefore, x = 12 is a solution to the last equation.
Answer: 12 x = 144
The square canvas of a painting has an area of 64 ff?. How many feet of border should be ordered to make a frame for the painting? O 4 ft O 8 ft 0 32 ft O 128 ft
ANSWER
32 ft
EXPLANATION
The area of a square that has side length L is:
[tex]A=L^2[/tex]In this case, the area of the square is 64ft². The side length is:
[tex]L=\sqrt[]{A}=\sqrt[]{64}=8ft[/tex]Match the graph with the correct equation. A. Y-5=-(x+3)B. Y-3=(x+5)C. Y-3=-(x+5)D. Y+3=-(x+5)
step 1
Find the slope
we need two points
we take
(-4,2) and (-2,0)
m=(0-2)/(-2+4)
m=-2/2
m=-1
step 2
Find the equation in slope intercept form
y=mx+b
we have
m=-1
point (-2,0)
substitute
0=(-1)(-2)+b
0=2+b
b=-2
so
y=-x-2step 3
Verify option A, C and option D (because the slope is -1)
option A
y-5=-(x+3)
isolate the variable y
y-5=-x-3
y=-x+2 -------> is not the solution
option C
y-3=-(x+5)
y-3=-x-5
y=-x-2 ------> is the solution
therefore
answer is the option Cif b is between A and C and AB=3X, BC=6X+1, and AC=19. find x and BC
Let's draw the situation.
Based on the sum of segments property, we can define the following equation.
[tex]AC=AB+BC[/tex]Replacing the given expressions, we have
[tex]19=3x+6x+1[/tex]Let's solve for x
[tex]\begin{gathered} 19-1=9x \\ 9x=18 \\ x=\frac{18}{9} \\ x=2 \end{gathered}[/tex]We use this value to find BC.
[tex]BC=6x+1=6(2)+1=12+1=13[/tex]Therefore, segment BC is 13 units long.Recently, More Money 4U offered an annuity that pays 4.5% compounded monthly. If $1,643 is deposited into this annuity every month, how much is in the accountols after 11 years? How much of this is interest?
The rule of the FV (future value) is
[tex]FV=P\frac{(1+i)^n-1}{i}[/tex]P is the value each month
i is the rate divided by 12 month
n = number of years x 12 months
Since the deposit every month is $1643, then
[tex]P=1643[/tex]Since the annuity rate is 4.5%, then
[tex]\begin{gathered} i=\frac{4.5}{12}=0.375\text{ \%} \\ i=\frac{0.375}{100}=0.00375 \end{gathered}[/tex]Since the number of years is 11 years, then
[tex]\begin{gathered} n=11\times12 \\ n=132 \end{gathered}[/tex]Substitute them in the rule above
[tex]\begin{gathered} FV=1643\frac{(1+0.00375)^{132}-1}{0.00375} \\ FV=279958.5032 \end{gathered}[/tex]The account will have $279,959 after 11 years to the nearest dollar
To find the interest subtract $1643 x 132 months from the FV
[tex]\begin{gathered} I=FV-n\times P \\ I=279959-132\times1643 \\ I=63083 \end{gathered}[/tex]The amount of interest is $63,083 to the nearest dollar
Evaluate the following quotient. Leave your answer in scientific notation.(5.9 x 10°) = (4 x 104)AnswerKeyboХ
Statement Problem: Evaluate the following quotient. Leave your answer in scientific notation.
[tex](5.9\times10^9)\div(4\times10^4)[/tex]Solution:
[tex](5.9\times10^9)\div(4\times10^4)=\frac{5.9}{4}\times\frac{10^9}{10^4}[/tex]By law of indices;
[tex]\frac{a^b}{a^c}=a^{b-c}[/tex][tex]\begin{gathered} (5.9\times10^9)\div(4\times10^4)=\frac{5.9}{4}\times10^{9-4} \\ (5.9\times10^9)\div(4\times10^4)=1.475\times10^5 \end{gathered}[/tex]ANSWER:
[tex]1.475\times10^5[/tex]I need help on this logarithmic equation, If you can, please answer it step-by-step. Thank you!
Given a logarithmic equation as
[tex]\log _ba=x[/tex]It is expressed in an index form as
[tex]b^x=a[/tex]Thus, from the equation given as
[tex]\log _{32}q=3[/tex]We can express its index form as
[tex]\begin{gathered} 32^3=q \\ \text{Thus, } \\ q=32\times32\times32=32768 \end{gathered}[/tex]Hence, the value of q equals 32768
I need to know what to out in the missing boxes
1 A 9/ B 9 8 1
Then
981/109 = 9
So A = 0
and B = 9
41.How wide is the cabin? Round your measurement to the nearest 1/2 inch.A.5.3 ftB.8 ftC.10 ftD.12 ft
Height: 1in
Base/wide: 1.5 in
Square of the window: 0.25in
As 1in = 8ft, then
[tex]\text{wide}=1.5\times8=12[/tex]Answer: D. 12ft
drag each number to the best approximate location on the number line
Express all the numbers in decimal form:
3.42
2 4/5 = 2.8
π = 3.14
√5 = 2.24
Since each unit on the graph is divided by 4, each unit is 0.25
So:
8. Donny remodeled his home and rented some tools. He rented a tile sawfor 5 days. He rented a floor sander for 2 days. The total cost of therentals was $370. The floor sander cost $10 more per day to rent thanthe tile saw. How much did it cost to rent the floor sander for 2 days?C. $110A $60B. $100D. $120
Given -
He rented a tile saw for = 5 days.
He rented a floor sander for = 2 days
The total cost of the rentals was = $370
To Find -
How much did it cost to rent the floor sander for 2 days?
Step-by-Step Explanation -
Let the cost of renting a tile saw for one day = $x
So, the cost of renting a floor sander for one day = $x + $10
Now,
He rented a tile saw for 5 days.
So, cost of rent = 5($x) = $5x
He rented a floor sander for 2 days
So, the cost of rent = 2($x + $10) = $2x + $20
Now, according to the question:
Total Cost = $370
So,
$5x + $2x + $20 = $370
$7x = $350
$x = 350/7
$x = 50
So,
The cost of renting a floor sander for two day = $2x + $20
= $2(50) + $20
= $100 + $20
= $120
Final Answer -
The cost to rent the floor sander for 2 days =
Option (D). $120
Solve the equation for n 5n + 8=52 Show your work in the sketch feature. Input your solution below.
5n + 8 = 52
subtract 8 from both-side of the equation
5n + 8 - 8 = 52 - 8
5n =44
Divide both-side of the equation by 5
n = 8.8
helppppppppppppppppp
if the driver is driving at a constant speed, it should ook like this
then if stops at a red light, it should not increase on the y axis
after the red light changes he keeps on moving a constant speed meaning that it continuous on increasing
Nancy took a 3 hour drive. She went 65 miles before she got caught in a storm. Then she drove 92 miles at 12 mph less than she had driven when the weather was good. What was her speed, in miles per hour, driving in the storm
Explanation:
Let us start by listing out the given data:
To solve the question, we will make use of the basic formula:
[tex]\begin{gathered} Distance=time\times speed \\ time=\frac{distance}{speed} \end{gathered}[/tex]Let the initial speed before she got caught in the storm will be V
For the first part, before she got caught in a storm. The time it will take Nancy before she got caught in the storm will be
[tex]t_1=time=\frac{distance}{speed}=\frac{65}{V}[/tex]Then for the second part, because her speed has reduced by 12,
the time when she drives in the storm be t2 can be obtained as
[tex]t_2=\frac{92}{V-12}[/tex]Finally, we can sum the times t1 and t2 and equate them to 3
[tex]T=t_1+t_2=\frac{65}{v}+\frac{92}{v-12}=3[/tex]We can solve for v as follow: Multiplying by the lcm
[tex]65(v-12)+92(v)=3(v)(v-12)[/tex]Simplifying further
[tex]\begin{gathered} 65v-780+92v=3v^2-36v \\ 3v^2+101v+92v-780=0 \end{gathered}[/tex]Solving for v
[tex]\begin{gathered} v=60 \\ v=\frac{13}{3} \end{gathered}[/tex]But since she drove 12 mph less than the initial speed. so it is not logical to pick 13/3 mph
Thus, the value of V is v = 60 mph
So the speed, when she drives in the storm is
[tex]v-12=60-12\text{ =48mph}[/tex]Therefore, the answer is 48 mph
You are one of the 59 people whose names are put in a hat. A name will be drawn for a prize. What is your chance of winning the prize? Round your answer to the nearest 0.1%, if necessary.
Explanation
Total number of people =59
Desired number = 1
The chance of winning the prize is
[tex]pr(win)=\frac{1}{59}=1.7\text{\%}[/tex]Answer: 1.7%
2 What are the x- and y-intercepts of the linearfunction 2x - 3y = 12?F (-6, O) and (0, 4)G (-6, 0) and (0, -4)H (6, O) and (0,4)J (6,0) and (0, -4)
From the equation
2x - 3y = 12
To find x-intercept, make x the subject of the formula
2x = 3y + 12
divide through by 2
x = 3y/2 + 12/2
x = 3y/2 + 6
x intercept = 6
To find the y-intercept, make y the subject of the formula
2x - 3y = 12
2x - 12 = 3y
3y = 2x - 12
y = 2x/3 - 12/3
y = -2x/3 - 4
y-intercept = -4
(6,0) and (0,-4) J
the following triangles have the same angles and are similar. what is the ratio of hypotheses to base for triangles
In the first big triangle let take base as 8 and for the second triangle i.e. the smaller one take base as 4.
As given that the both triangles have same angle and both are similar so:
[tex]\begin{gathered} \frac{Base\text{ from 1 triangle}}{\text{Base from 2 triangle}}=\frac{8}{4} \\ \frac{Base\text{ from 1 triangle}}{\text{Base from 2 triangle}}=2 \end{gathered}[/tex]Given the function and the graph of the function below, which of the following best describes the continuity, interval of increase and interval of decrease?
The given function is
[tex]^3\sqrt[]{x-4}+2[/tex]The answer is,
the graph is continuouse for all the real numbers,
increasing
[tex]-\inftydecreasing -none.Find the value of a6PRх15I=
It is given that x is a variable that needs to be found.
By theorem of proportionality:
[tex]\begin{gathered} \frac{PS}{PQ}=\frac{RS}{RQ} \\ \frac{15}{9}=\frac{6}{x} \\ x=\frac{6\times9}{15} \\ x=3.6 \end{gathered}[/tex]Hence the value of x is 3.6
Simplify: 7x+6+5(4x+3)
This problem is about using the right order of operations. To do that we can recur to PEMDAS, which means Parenthesis, Exponents, Multiplication-Division, Addition-Subtraction, that's the order to solve this problem.
First, we solve parenthesis using the distributive property:
[tex]7x+6+5(4x+3)=7x+6+20x+15[/tex]Second, we solve like terms, that is, those terms which have variables, and those terms without variables.
[tex](20+7)x+15+6=27x+21[/tex]Therefore, the answer is 27x+21, that's the simplest form to the given expression.Christina is finding the values of x that make the following equation true.
Given
[tex]\tan^2(\frac{x}{2})+2\tan(\frac{x}{2})-5=3\tan(\frac{x}{2})[/tex]Find
Value of x that makes the equation true and what step will she take first
Explanation
to find the value of x , the first step we use
subtract
[tex]3\tan(\frac{x}{2})[/tex]from both sides
on subtraction , we obtain
[tex]\tan^2(\frac{x}{2})-\tan(\frac{x}{2})-5=0[/tex]now ,
[tex]\begin{gathered} \tan(\frac{x}{2})=\frac{-(-1)\pm\sqrt{(-1)^2-4\times1\times(-5)}}{2} \\ \\ \tan(\frac{x}{2})=\frac{1\pm\sqrt{21}}{2} \end{gathered}[/tex]Final Answer
The correct option is C.
How do I solve this? I know what domain is but how do I solve it like this
1) The first thing we need to do is to find the composite function. So, based on the ones we've got, we can do the following to get the f(g(x)) functions:
a)
[tex]\begin{gathered} f(x)=2^x,g(x)=\frac{2}{x} \\ f(g(x))=2^{\frac{2}{x}} \end{gathered}[/tex]Note that we have plugged into the x term of f(x) the whole function f(x). Now that we know the composite function, we can analyze it.
As the Domain is the set of entries for any function, we need to find the points of singularity, i.e. when the function is not defined.
[tex]\begin{gathered} f(g(x))=2^{\frac{2}{x}}\:\:\:Pick\:the\:denominator\:and\:equate\:it\:to\:zero \\ \\ x=0 \\ --- \\ Thus, \\ D=\:\left(-\infty\:,\:0\right)\cup\left(0,\:\infty\:\right) \end{gathered}[/tex]Note that when x=0, then there is an undefinition within the Real Set of Numbers. So, any point different than zero is an element of this Domain.
b)
In this case, we can find the composite function this way:
[tex]\begin{gathered} f(x)=\log(x),\:g(x)=x^3+1 \\ \\ f(g(x))=\log(x^3+1) \end{gathered}[/tex]Now, similarly to the previous one let's find the singularity points. We know that x has to be greater than -1 since the argument of a logarithm has to be greater than 0, according to the logarithm definition.
Thus the Domain is:
[tex]D=\:\left(-1,\:\infty\:\right)[/tex]In the diagram below, quadrilateral NOPQ is inscribed in circle R. Find themeasure of ZP.N70°o94RQ
Answer:
P = 110 degrees
Explanation:
We were given the following information:
A quadrilateral NOPQ is inscribed in a circle. This makes the quadrilateral a cyclic quadrilateral
[tex]\begin{gathered} \angle N=70^{\circ} \\ \angle O=94^{\circ} \end{gathered}[/tex]Angle P is supplementary to Angle N; both angles P & N sum up to 180 degrees:
[tex]\begin{gathered} \angle P+\angle N=180^{\circ} \\ \angle N=70^{\circ} \\ \angle P+70^{\circ}=180^{\circ} \\ \text{Subtract ''}70^{\circ}\text{'' from both sides, we have:} \\ \angle P=(180-70)^{\circ} \\ \angle P=110^{\circ} \\ \\ \therefore\angle P=110^{\circ} \end{gathered}[/tex]Therefore, the angle at P equals 110 degrees
For the function f(x) = (25 – 10), find f-'(x). of-1(x) = (V)+10 3 of-'(x) = V(x + 10) of-1(x) = x3 + 10 f-1(x) = x3 + 10
Answer::
[tex]f^{-1}(x)=\sqrt[5]{x^3+10}[/tex]Explanation:
Given f(x) defined below:
[tex]f(x)=(x^5-10)^{\frac{1}{3}}[/tex]To solve for the inverse, follow the steps below:
Step 1: Rewrite the equation using y.
[tex]y=(x^5-10)^{\frac{1}{3}}[/tex]Step 2: Next, swap x and y:
[tex]x=(y^5-10)^{\frac{1}{3}}[/tex]Step 3: Solve for y.
[tex]\begin{gathered} x^3=y^5-10 \\ y^5=x^3+10 \\ y=\sqrt[5]{x^3+10} \end{gathered}[/tex]Step 4: Replace y with the inverse function:
[tex]f^{-1}(x)=\sqrt[5]{x^3+10}[/tex]What is the surface area of a sphere with radius 3?O A. 36pi units²OB. 9pi units²O C. 3pi units²O D. 18pi units²
Given:
The radius of the sphere = 3
Find-:
The surface area of the sphere
Explanation-:
The surface area of spere is:
[tex]\text{ Area }=4\pi r^2[/tex]Where,
[tex]r\text{ = Radius}[/tex]Give radius is 3 then surface area is:
[tex]\begin{gathered} \text{ Area }=4\pi r^2 \\ \\ \text{ Area }=4\pi(3)^2 \\ \\ =4\pi\times9 \\ \\ =36\pi \end{gathered}[/tex]So the surface area is 36pi units²
Which confidence interval would have a larger width: A confidence interval using a large sample size or a confidence interval using a small sample size from a normal distribution?A) confidence interval with small sample size from normal distributionB) Confidence interval with large sample size
The following relation can be used to show the relationship between the confidence level and the sample size
[tex]\begin{gathered} \bar{\text{confidence interval(C.I)=}}\bar{x}\pm MOE \\ \text{where,} \\ \text{MOE}=\text{Margin of error} \end{gathered}[/tex]Also,
[tex]\text{MOE}=C.I\times S\tan dard\text{ error(S.E)}[/tex]And,
[tex]\begin{gathered} S\mathrm{}E=\frac{r}{\sqrt[]{n}} \\ \end{gathered}[/tex]There fore,
when the value of n is large, the standard error will be low
when the standard error is low margin of error(MOE) will also be low
Hence, if the Margin of error the confidence level will have a larger width
Therefore,
We can say that A confidence level would have a larger width with a small sample size from normal distribution
Final answer is OPTION A
What is the largest total area that can be enclosed
Let W = the three sides to make the width of the two corrals
Let L = the one side parallel to the river.
Area
A = L * W
Replace L with (300-3W)
A = (300-3W) * W
A = -3W^2 + 300W
A quadratic equation, the axis of symmetry will be the value for max area
Find that using x = -b/(2a)
In this equations: x = W; a = -3; b = 300
[tex]W=\frac{-300}{2\times-3}=\frac{-100}{2}=50[/tex]W = +50 yd is the width for max area.
Find the max area, substitute 50 for W in the area equation:
A = -3(50^2) + 300(50)
A = -3(2500) + 15000
A = -7500 + 15000
A = 7500 sq/yds is max area
Hence the largest total area that can be enclosed is 7500 sq. yd.
19) Geoff owns a computer store in 1990 he sold 2400 monitors and in 2000 he sold 4000. Let x represent the number of years since 1990. Write a linear equation in slope intercept form that represents this data. A) y = 160x + 4000 B) y=160x + 2400 C) y = 320x + 2400 D) y = 320x + 4000
We have the next informations
1990 ------ 2400
2000-------- 4000
the year 1990 represents x=0
for 2000 passed 10 years son x=10
we have then the next points
(0,2400) =(x1,y1)
(10,4000) =(x2,y2)
First we need to calculate the slope
[tex]m=\frac{y2-y1}{x2-x1}[/tex][tex]m=\frac{4000-2400}{10-0}=\frac{1600}{10}=160[/tex]then we can calculate the linear equation
[tex]y-y1=m(x-x1)[/tex][tex]y-2400=160(x-0)[/tex]the linear equation is
[tex]y=160x+2400[/tex]the correct answer is B
1 In an experiment, the probability that event B occurs is and the probability that event A occurs given 1 that event B occurs is - 3 What is the probability that events A and B both occur? Simplify any fractions.
The probability that event B occurs is 1/4
[tex]P(B)=\frac{1}{4}[/tex]The probability that event A occurs given that event B occurs is 1/3
[tex]P(A|B)=\frac{1}{3}[/tex]What is the probability that events A and B both occur?
[tex]P(A\: and\: B)=\text{?}[/tex]Recall that the conditional probability is given by
[tex]P(A|B)=\frac{P(A\: and\: B)}{P(B)}_{}[/tex]Re-writing the above formula for P(A and B)
[tex]P(A\: and\: B)=P(A|B)\cdot P(B)[/tex]So, the probability that events A and B both occur is
[tex]\begin{gathered} P(A\: and\: B)=P(A|B)\cdot P(B) \\ P(A\: and\: B)=\frac{1}{3}\cdot\frac{1}{4} \\ P(A\: and\: B)=\frac{1}{12} \end{gathered}[/tex]Therefore, the probability that events A and B both occur is 1/12
Solve the following system of linear equations using elimination. x+4y= -9 -2x + 3y= -4
(-1, -2)
1) Let's solve that system, by the Elimination Method.
Let's eliminate the x terms on both, to begin with. Multiply the first equation by 2
x+4y= -9 x2
-2x + 3y= -4
2x+8y= -18
-2x + 3y= -4
-------------------------
11y= -22 divide both sides by 11
y= -2
2) Let's plug into any of those two equations, usually the simplest one, y=-2
x +4y = -9
x +4(-2) = -9
x -8 = -9
x =-9+8
x= -1
3) Testing it:
-2x + 3y= -4
-2(-1) +3(-2) =-4
2 -6 = -4
-4 = -4 True!
Hence, the solution is (-1, -2)