Answer:
3.25 years (nearest hundredth)
Step-by-step explanation:
Compound Interest Formula
[tex]\large \text{$ \sf A=P\left(1+\frac{r}{n}\right)^{nt} $}[/tex]
where:
A = final amountP = principal amountr = interest rate (in decimal form)n = number of times interest applied per time periodt = number of time periods elapsedGiven:
A = $4916P = $4000r = 6.4% = 0.064n = 4 (quarterly)Substitute the given values into the formula and solve for t:
[tex]\implies \sf 4916=4000\left(1+\frac{0.064}{4}\right)^{4t}[/tex]
[tex]\implies \sf 4916=4000\left(1.016\right)^{4t}[/tex]
[tex]\implies \sf \dfrac{4916}{4000}=\left(1.016\right)^{4t}[/tex]
[tex]\implies \sf \dfrac{1229}{1000}=\left(1.016\right)^{4t}[/tex]
[tex]\implies \sf \ln \left(\dfrac{1229}{1000}\right)=\ln \left(1.016\right)^{4t}[/tex]
[tex]\implies \sf \ln \left(\dfrac{1229}{1000}\right)=4t \ln \left(1.016\right)[/tex]
[tex]\implies \sf t=\dfrac{\ln \left(\frac{1229}{1000}\right)}{4\ln \left(1.016\right)}[/tex]
[tex]\implies \sf t=3.247594892...[/tex]
Therefore, it will take 3.25 years (nearest hundredth) for the account to grow to $4916.
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If m < ACD = 100 , then m < ACE = ?
If m ∠ACD = 100°, then m ∠ACE = 80°, as ∠ACD and ∠ACE are supplementary angles.
Supplementary angles are the angles whose sum is equal to 180°. The angles formed when one straight line intersects the other, on the point of intersection on the same side of any line are always supplementary.
In the given question, AB and DE are two straight lines intersecting at point C. ∠ACD and ∠ACE lie on the same side of the line DE, thus they are supplementary angles.
Therefore, m ∠ACD + m ∠ACE = 180°.
But we know that m ∠ACD = 100°. So,
m ∠ACD + m ∠ACE = 180°,
or, 100° + m ∠ACE = 180°,
or, m ∠ACE = 180° - 100° = 80°.
Therefore, if m ∠ACD = 100°, then m ∠ACE = 80°, as ∠ACD and ∠ACE are supplementary angles.
For the complete question, check attachment 1.
For reference to the solution, check attachment 2.
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What’s the correct answer answer asap
Answer:
I think A
Step-by-step explanation:
f(x)=5x-25 What is the domain of the function?
Answer:
Domain: All Real Numbers
Step-by-step explanation:
Since this function is a linear function, it will use any x-value in order to continue with being a linear function. Therefore, if the line goes on for infinity, every x-value will be used for infinity. Therefore, the domain will be All Real Numbers since every number on the x-axis has a possibility of being used.
Which of these is an exponential parent function? OA. f(x)=2x-2 OB. f(x) = 2x C. f(x) = 2x + 3 OD. f(x) = 24x
The answer to this question is choice B
The table shows three values of x and their corresponding values of f (x) for a linear function f, such that f (r) = 0 and f (0) = s, where r and s are constants. What is the value of rs?
Using a linear function, it is found that the product rs is rs = 81.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.In this problem, when x changes by 68(from -64 to 68), y changes by -16(from 12 to -4), hence the slope is given by:
m = -16/64 = -0.25.
Hence:
y = -0.25x + b.
When x = 34, y = -4, hence this is used to find b.
-4 = -0.25(34) + b
b = 4.5.
Hence the function is:
y = -0.25x + 4.5.
f(r) = 0, hence:
-0.25x + 4.5 = 0
x = 4.5/0.25
x = 18
r = 18.
f (0) = s, hence s = 4.5.
Then the value of the product is:
rs = 18 x 4.5 = 81.
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During a radio contest, $50 is added to the prize money each time a caller answers the contest question incorrectly. the first caller has a chance to win $100. which equation represents the amount the 10th caller receives if this caller is the first to answer the question correctly?
Answer:
50x+100=y
y=550
Step-by-step explanation:
Since the first caller can win $100, you add 100 onto the end. After you add 50 for every person who answered incorrectly. X being amount tried/answered incorrectly, and Y being the amount you can win at that given time
Answer:
A. a10=100+(10-1)50
Step-by-step explanation:
Can someone explain step by step how to get this please?
3) Alternate interior angles theorem
4) Definition of congruent angles
help me help me please guys send me in 5 minutes I really need it
Answer:
a) If the question is 18 and 13, then 1. If 18 and 3, then 3.
b) 10
c) 5
d) 15
e) 11
f) 20
Have a nice day :)
What is the length of focal chord of the equation y^2 + 6y - 2x + 13 = 0?
Answer:
2 units
Step-by-step explanation:
The given equation graphs as a parabola that opens to the right. It can be written in the form ...
(4p)x = ay² +by +c
Interpreting the equationWhen the equation is written in the form ...
(4p)x = ay² +by +c
The value of p is the focus-to-vertex distance. The length of the latus rectum (focal chord) is 4 times the value of p, so is the coefficient of x in the equation.
ApplicationRewriting the given equation to the form shown above, we have ...
2x = y² +6y +13
That is, the value of 4p, the coefficient of x, is 2. The length of the focal chord is 2 units.
evaluate this piecewise function at x= -6 and x=2
The values of the piecewise function are f(-6) = 6 and f(2) = 1
How to evaluate the function?The complete question is in the attached image.
The value x = -6 is in the domain: -8 <= x < 1
The function at this domain is:
f(x) = |x|
So, we have:
f(-6) = |-6|
Evaluate
f(-6) = 6
Also, we have:
The value x = 2 is in the domain: x >= 1
The function at this domain is:
f(x) = 3
So, we have:
f(2) = 1
Hence, the values of the piecewise function are f(-6) = 6 and f(2) = 1
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What are the x-intercepts and the y-intercepts of the graph of 12x−3y=36
Answer:
Step-by-step explanation:
12x −3y=36 ⇔ 3y = 12x - 36
y = 4x - 12
y = 0 ⇔ 4x - 12 = 0 ⇔ 4x = 12 ⇔ x = 12/4 = 3
So (0 ; - 12) and (3 ; 0)
Answer:
x-intercept=3, y-intercept=-12
Step-by-step explanation:
at x-intercept y=0 such that:
12x-3(0)=36
12x=36
[tex]x=\frac{36}{12} =3[/tex]
additionally, at y-intercept x=0 such that
12(0)-3y=36
-3y=36
[tex]y= \frac{36}{-3}=-12[/tex]
A group of friends was working on a student film that had a budget of $700. They used $658 of their budget on costumes. What percentage of their total budget did they spend on costumes?
[tex]\huge\boxed{94\%}[/tex]
Simply use division to solve this problem.
[tex]\dfrac{\$658}{\$700}=0.94[/tex]
Now, multiply this by 100 to get a percentage.
[tex]0.94=\large\boxed{94\%}[/tex]
Direction: Given the following scatter plot, determine if there is a relationship occurred. HANDWRITTEN.
COPY AND ANSWER WITH COMPLETE SOLUTION. AVOID COPYING OR CHEATING IN ANY FORM.
1.
A = points in upper left + points in lower right = ______
B = points in upper right + points in lower left = ______
Q = the smaller of A and B = ______
N = A + B = ______
Is there a relationship? ____ Yes ____ N
there's relationship between the points upper left and points in d lower left
Step-by-step explanation:
points in upper right nd points in lower left
the smaller of A+B=a+b
yes
How many hectometers are in 16 decimeters
Answer:
0.016 decimeters
Step-by-step explanation:
16 x 10^-3 = 0.016dm
Answer:
0.016 hm
Step-by-step explanation:
i dont cap
Shania owns a gym for women clients. She advertises that women can lose 1/2 pound per week by visiting her gym 3 times a week. If this is the case, how many pounds can women lose in a month?
(4 wks/mo)(1/2 lb/wk) = 2 lb/mo
(4_1/3 wks/mo)(1/2 lb/wk) = 2.17 lb/mo
Women who visit Shania's gym three times per week have the ability to drop two pounds in a month.
If women visit Shania's gym three times a week and can lose 1/2 pound per week, we can calculate how many pounds they can lose in a month (assuming a month has four weeks on average).
The rate of weight loss is 1/2 pound per week. So in one month, which is four weeks, the weight loss would be:
Weight loss per week × Number of weeks in a month = (1/2) × 4 = 2 pounds
Therefore, women visiting Shania's gym three times a week can potentially lose 2 pounds in a month.
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Calculus help please 10 points for 18&19
thanks!
First function - The function is not continous on [0, 5] because h(5) is not defined.
Second function - There are no discontinuities.
How to determine the continuity of a function
In this problem we have two functions, whose continuity has to be checked. The first equation is a rational function and the second one is a polynomic function. There is a discontinuity in a function f at a given point if and only if the function evaluated at such point does not exist.
The discontinuities of rational functions are those x-values such that the denominator equals zero. The first function is defined for the interval [0, 5] and it is continuous if the function exists for all value of the interval. Thus:
5 - x = 0
x = 5
The rational function has a discontinuity at x = 5. The function is not continous on [0, 5] because h(5) is not defined. (Correct choice: C)
In accordance to algebra, polynomic functions are continuous as there exist a result for all value of x. There are no discontinuities.
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3) A diameter divides a circle into two congruent arcs. What is the measure in degrees for each arc?
A. 60°
B. 45°
C. 180°
D. 90°
Answer:
C. 180°
Step-by-step explanation:
The degree measure of the arc of a full circle is 360°
A diameter divides a circle into two parts of equal size, so the degree measure of each part is half of the degree measure of a full circle.
360°/2 = 180°
what is the reminder when X³ +4X² - 2X + I is divided by X + 1 what is the reminder when X³ + 4X² - 2X + I is divided by X + 1
Answer:
6
Step-by-step explanation:
do synethtic wig curls only come out if you put heat on it Answer Asap for brainlist
Answer:
. It will curl without heat. You Never attempt to use hot tools, like a curling iron, on a synthetic wig – unless the label specifically says that the wig can tolerate heat. If not, you can use foam rollers to curl the wig using the method below.
Step-by-step explanation:
Answer:
Yes, it is possible to curl a synthetic wig. But you should never attempt to use hot tools, like a curling iron, on a synthetic wig, unless the label specifically says that the wig can tolerate heat. If not, you can use foam rollers to curl the wig.
What is the slope and the y-intercept of the line on the graph below? On a coordinate plane, a line goes through points (0, 1) and (4, 0). a slope = –4, y-intercept = 1 b slope = –4, y-intercept = 4 c slope = Negative one-fourth, y-intercept = 1 d slope = Negative one-fourth, y-intercept = 4
Answer:
the slope of the coordinates will be 0-0/4-1 then you will get the coordinates of the graph
2.1. The following is a recipe for making 18 scones: 1 cup white sugar, cup butter, 2
teaspoons vanilla essence, 1 cups flour, 2 eggs, 12 teaspoons baking powder, cup of milk
On your birthday you decide to use this recipe to make scones for the staff at your school. How
would you adjust the recipe so that you can make 60 scones?
(10)
man
The adjusted recipe for 6scones is shown as;
4.2 cup white sugar, cup butter,
7.2 teaspoons vanilla essence,
4.2 cups flour,
7.2 eggs,
37.2 teaspoons baking powder, cup of milk
Ratio and proportionsFractions are written as a ratio of two integers. Given the recipe for 18scones as
1 cup white sugar, cup butter,
2 teaspoons vanilla essence,
1 cups flour,
2 eggs,
12 teaspoons baking powder, cup of milk
For the given 60 scone;
4.2 cup white sugar, cup butter,
7.2 teaspoons vanilla essence,
4.2 cups flour,
7.2 eggs,
37.2 teaspoons baking powder, cup of milk
This given the adjusted recipe for 60 scones
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(y + 4)^2 – 2(y + 4) + 1
Answer:
y = -3 and y = -3
or y = -3 with a multiplicity of 2
Step-by-step explanation:
[tex](y+4)^2-2(y+4)+1[/tex]
If you want to factor this, heres what you do:
[tex](y+4)(y+4)-2(y+4)+1[/tex]
[tex]y^2+8y+16-2y-8+1[/tex]
[tex]y^2+6y+9[/tex]
Then factor:
[tex](y+3)(y+3)[/tex]
[tex](y+3)^2[/tex]
The value of y:
y + 3 = 0 and y + 3 = 0
y = -3 and y = -3
or y = -3 with a multiplicity of 2
The solution of the given function are; y = -3 and y = -3 or y = -3 with a multiplicity of 2.
What is a quadratic equation?A quadratic equation is the second-order degree algebraic expression in a variable. the standard form of this expression is ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.
The given function is;
[tex](y + 4)^2 -2(y + 4) + 1[/tex]
To solve;
[tex](y + 4)(y + 4) -2(y + 4) + 1\\\\y^{2} + 8y + 16 - 2y -8 + 1\\\\y^{2} + 6y + 9 \\[/tex]
Then the factor are;
(y + 3)(y + 3)
The value of y:
y + 3 = 0 and y + 3 = 0
y = -3 and y = -3
or y = -3 with a multiplicity of 2
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What is the value of this expression when x=2 and y=-4? -3(x-y)2
Answer:
-108
Step-by-step explanation:
[tex] - 3 \times { (2 - ( - 4)) }^{2} = \\ - 3 \times ( {2 + 4})^{2} = \\ - 3 \times 36 = - 108[/tex]
Answer:
108 is correct hjgbjbvmbhbjnnn
L.C.Mof 16, 28, 42,60
Answer:
1680
Step-by-step explanation:
First do the prime factorization:
16=2x2x2x2
28=2x2x7
42=2x3x7
60=2x2x3x5
To find least common multiple (LCM), write down all prime factors of one of the number and multiply by factors from other numbers that was not in that number:
LCM=2x2x3x5x7x2x2=1680
Select the correct answer from each drop-down menu.
A researcher is examining the claims made by a water softener salt manufacturer. He performs an experiment using water from a variety of sources. For each water source, he has a sample with no treatment and a sample treated with the recommended amount of the water softener salt.
He then tests each sample to measure the softness and compares the results, determining that the claims made by the manufacturer are true.
The conclusion drawn from the study is _____ because the sample is _____. In this instance, an ______study was performed.
The conclusion is valid in this experiment because the sample is homogenous and an experimental study was performed.
What is an experimental study?It should be noted that an experimental study is one in which there is a dependent variable and there is a dependent variable. Also a control is used to establish the validity of the results.
In this case, the dependent variable is the level of softness after treatment while the independent variable is the type of water softener used.
The conclusion is valid in this instance because the sample is homogenous and an experimental study was performed.
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Hi, need help please to get my HS diploma...did not graduate :(
Let V(x)=−x2+2x−4 and W(x)=−x3+2x2+x+5. Find V(x)⋅W(x)
Answer:
B
Step-by-step explanation:
I assume this should look like
V(x) = -x² + 2x - 4
W(x) = -x³ + 2x² + x + 5
when doing arithmetic operations with whole functions, we simply do these operations with the whole expressions :
V(x) × W(x) =
(-x² + 2x - 4) × (-x³ + 2x² + x + 5) =
= x⁵ - 2x⁴ - x³ - 5x² - 2x⁴ + 4x³ + 2x² + 10x + 4x³ - 8x² - 4x - 20 =
= x⁵ - 4x⁴ + 7x³ - 11x² + 6x - 20
In a country 55% of the male population has houses in cities while 30% have houses both in cities and in villages . Find the percentage of the population that has houses only in villages.
15%
{100-(55+30)}%
={100-(85)}%
=15%
Choose the definition for the function.
-2x + 1
a.y = {=
a.y=-x+ 2
(-2x + 1
b.y = -x + 2
{
x ≤ 1
x>1
x < 1
x ≥ 1
-2x + 1 x > 1
x ≤ 1
c. y = -x + 2
{-2x+2
(-2x + 1
d. y = -x + 2
{
x ≥ 1
x < 1
Answer: its d
Step-by-step explanation:
above answer is wrong and D is right.
PLEASE ANSWER PROBLEM IN THE IMAGE PLEASE GIVE EXPLANATION IF YOU DON’T WANT TO GIVE A EXPLANATION DON’T ANSWER WILL GIVE BRAINLEST THANK YOU
image below
Answer:
30
Step-by-step explanation:
We can determine the number of different sets of reports by determining how many possible options are available per subject and then multiplying them.
There are 5 total options for geography, 3 for English, 1 for sciences, and 2 for maths. Multiplying these gets us 30.
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Calculate total choices for individual then multiply
Geography=5English=3Science=1Math=2Total choices
5(3)(2)(1)30Option C
1.25 +1.25+1.25+1.25
Answer:
5
Step-by-step explanation:
1.25+1.25+1.25+1.25=5