The amount of money that he should have at the closing of December should be $227.69.
The correct answer choice is option C
How to find total savings?Given that,
Starting amount = $24And, it plans to save 10% more as compared to the last month.
The amount of money that he should have at the closing of December can be solved using the concept of geometric sequence.
First term, a = $24
Common ratio, r = 1.10
Number of terms, n = 7
So,
Sn = a1×(r^n -1)/(r -1)
S7 = 24×(1.10^7 -1)/(1.10 -1)
= (24×0.948717) / 0.10
= $227.69
The total amount Cory will have saved by the end of December is approximately $227.69
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Answer:
(c) $227.69
Step-by-step explanation:
The amounts Cory will be adding to his account comprise a geometric series with first term $24 and each successive term 10% more, or 1.10 times the previous term. The total amount Cory will have saved by the end of December is the sum of 7 terms of the series.
__
sum of geometric seriesThe sum of ...
24 +1.10×24 +1.10²×24 +... +1.10⁶×24
is given by the formula ...
Sn = a1×(r^n -1)/(r -1)
where a1 is the first term (24), and r is the common ratio (1.10).
formula applicationFor the series representing Cory's deposits, we have ...
S7 = 24×(1.10^7 -1)/(1.10 -1) = 24×0.948717/0.10 ≈ 227.69
At the end of December, Cory will have about $227.69.
_____
Additional comment
A financial calculator or app can also tell you the value of an annuity with a 10% increase per period.
Michael Jordan scores the following points over 8 games: 24, 17, 28, 19, 23, 20, 13, 19. What is the mean (average) number of points she scored over those 8 games
Answer:
19
Step-by-step explanation:
Answer:
20.375
Step-by-step explanation:
To calculate the mean, in this situation, you first add up the game scores and divide it by the amount of games.
So, first we add 24+17+28+19+23+20+13+19 = 163
Because there are 8 games, we do 163 / 8 = 20.375
or 20.4 to 1dp
Hope this helped! If anything requires clarification, don't hesitate to ask me. I can assure you this is the right answer.
- profparis
Which of the following is equidistant from a given directrix and focus?
The term used to describe the equidistance from a given directrix and focus is: C. a locus of points called a parabola.
What is a Parabola?A parabola can be defined as a curve on a plane where any given point is at equal distance from the focus (fixed point), and from a directrix (fixed straight line).
Thus, we can conclude that what is a locus of points called a parabola is equidistant from a given directrix and focus.
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Maurisa gets $8 per week for an allowance. She saves 25% of her allowance each week.How long will it take maurisa to save $16?
Answer:
8weeks
Step-by-step explanation:
$16÷(25/100×$8)=8
On Monday Marcos droves 20 miles and on Thursday he drove 40 miles. How much further did Marcos drive on Thursday than on Monday?
Answer:
20 miles
Step-by-step explanation:
We are finding the difference. Take the larger number and subtract the smaller number
40-20 = 20
The difference is 20 miles
_multiply(-26) = -468
please help who will give me full solution I will mark him/her brainlist please help please please
Answer:
Step-by-step explanation:
Note
I think the question means "What do you multiply -26 by to get - 468
call the number that you need x
x * -26 = - 468 Divide both sides by - 26
-26x/-26 = - 468/ - 26 There are 2 minus signs on the right. They cancel.
x = 18
Conclusion
When you multiply 18 * -26 the answer is --468
Answer: 18
What are the vertical and horizontal asymptotes for the function f(x)=3^2/x^-4
O horizontal asymptote: y = -2, y = 2
vertical asymptote: x = 3
O horizontal asymptote: y = -4, y = 1
vertical asymptote: x = 3
O horizontal asymptote: y = 3
vertical asymptote: x=-4, x=1
O horizontal asymptote: y = 3
vertical asymptote: x= -2, x=2
3x²242
?
-4
The vertical asymptotes x = - 2, 2 and Horizontal asymptotes y = 3
Option A is the correct answer.
What are Function?Function are mathematical statement which links an independent variable to dependent variable.
It always comes with a defined domain and range.
The equation mentioned is incorrect in the question w.r.t. to the solutions mentioned, The right equation is
[tex]\rm f(x) = \dfrac{3 x^2}{x^{2}-4}[/tex]
This function can also be written as
[tex]\rm f(x) = \dfrac{3 x^2}{x^{2}-2^2}\\\\\rm f(x) = \dfrac{3 x^2}{(x+2)(x-2)}[/tex]
Vertical asymptotes are defined when the denominator of a rational function tends to zero.
To find the equation/s let the denominator equal zero.
Denominator tends to zero for x = -2 and x = +2
Horizontal Asymptote is when the function f(x) is tending to zero.
for x = +∞ and x = - ∞
Let the rational function [tex]f(x)= \dfrac{mx^a}{nx^b}[/tex] where and a and b are degree of numerator and denominator.
If a < b , then the y axis y = 0 is a horizontal asymptote.
If b = a then horizontal asymptote is the line y = p/q
Here the value is b = 2 and a = 2
Since b = a the horizontal asymptote is the line
y = m/n where m = 3 and n = 1
Therefore y = 3
So , vertical asymptotes x = - 2, 2
Horizontal asymptotes y = 3
Option A is the correct answer.
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Answer:
A
Step-by-step explanation:
just took the test
The graph of a logarithmic function is shown below.
On a coordinate plane, a curve starts at y = negative 2 in quadrant 4 and curves up into quadrant 1 and approaches y = 2.
What is the domain of the function?
x < 0
x > 0
x < 1
all real numbers
The domain of the function is x > 0.
The correct option is (B)
What is domain of function?Domain of a function is defined by the set of x-values of the graph of a function.
as, domain of a function is defined by the set of x-values of the graph of a function.
From the graph we can see that,
x-values are starts from x > 0 [Since x ≠ 0]
Also, moves towards infinity,
Hence, domain of the function be, (0, ∞) or x > 0
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Answer:
B
Step-by-step explanation:
x² + 10x + 3 = -21?!?!!?!?!!!?
Answer:
-6,-4
Step-by-step explanation:
if you have to evaluate its 4
and there is 2 solutions
50 POINTS!! What is (-4, 3) (-3, -1) in point slope form?
Y=4x+16
Y-3=-4(x+4)
Explanation:
[tex]\bf point \ slope \ form: y-y_{1}=m\left(x-x_{1}\right)[/tex]
Find the slope: given points: (-4, 3), (-3, -1)
[tex]\sf slope: \dfrac{y_2 - y_1}{x_2- x_1} \ \ where \ (x_1 , \ y_1), ( x_2 , \ y_2) \ are \ points[/tex]
Insert values
[tex]\rightarrow \sf slope: \ \dfrac{-1-3}{-3-(-4)} =-4[/tex]
Equation in point slope form:
[tex]\sf\rightarrow y - 3 = -4(x - (-4))[/tex]
[tex]\sf\rightarrow y - 3 =-4(x + 4)[/tex]
Additional, in slope intercept form:
[tex]\sf\rightarrow y = mx + b \quad where \ 'm \ is \ slope' \ and \ 'b \ is \ y-intercept'[/tex]
[tex]\sf\rightarrow y = -4 x - 16 +3[/tex]
[tex]\sf\rightarrow y = -4x -13[/tex]
Find x. Give your answer in the simplest form.
45
Y
x = [?]
45
X
Enter the number that belongs in the green box.
Answer:
see the attachment photo!
Use the drawing tools to form the correct answer on the graph. Draw a point that belongs to the solution region of this system of inequalities.
#1
y>1.5^x+4Find y intercept
y>1+4y>5#2
y<2/3x+6Y intercept
y<6Both graphs attached
An point should be (1,6)
Answer:
< or > = dashed line
≤ or ≥ = solid line
< or ≤ = shade below the line
> or ≥ = shade above the line
To draw:
[tex]y < \dfrac{2}{3}x+6[/tex]
Treat as a linear equation.
Find 2 points:
[tex]x=0 \implies y=\dfrac{2}{3}(0)+6=6 \implies (0,6)[/tex]
[tex]x=3 \implies y=\dfrac{2}{3}(3)+6=8 \implies (3,8)[/tex]
Plot the 2 points and draw a dashed straight line through them.
To draw:
[tex]y > 1.5^x+4[/tex]
Treat as an exponential equation.
Find y-intercept:
[tex]x=0\implies y=1.5^0+4=5\implies (0,5)[/tex]
End behaviors:
[tex]\textsf{As } x \rightarrow \infty, f(x) \rightarrow \infty[/tex]
[tex]\textsf{As } x \rightarrow - \infty, f(x) \rightarrow 4[/tex]
Draw the curve as a dashed line.
Once both lines are drawn, shade the overlapping region below the linear inequality and above the exponential inequality.
A point that belongs to the solution is any point in the shaded area,
e.g. (1, 6)
How many years will Samsung galaxy 2 in 1 laptop last
Answer:
i think 6 years because i always used it
Step-by-step explanation:
make me my brainliest answer
Charles would like to buy a new car that costs $32 000. The dealership offers to finance the car at 2.4%/a compounded monthly for five years with monthly payments. The dealer will reduce the selling price by$3000 if Charles pays cash. Charles can get a loan from his bank at 5.4%/a compounded monthly. Which is the best way to buy the car? Justify your answer with calculations.
Charles would like to buy a new car that costs $32 000. The dealership offers to finance the car at 2.4%/a, it's best for Charles loans from the bank to buy car.
Which is the best way to buy a car?Generally, the equation for the monthly loan payment is mathematically given as
[tex]R=\frac{\frac{iP}{N}}{1-(\frac{1}{N})^{NY}}[/tex]
Therefore
[tex]R=\frac{\frac{0.024*32000}{12}}{1-(\frac{0.024}{12}+1)^{-12*5}}[/tex]
R=566.51
Hence the total payment is
T=R*N*Y
T=33990.34
By taking a loan of 29000, and applying the equation
T'=33155.77
In conclusion, it is best for Charles loans from the bank to buy a car.
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I need help please asap?!!!
Answer:
3660
Explain
3660ml×1L/100ml
= 3.66L
93/100
Natalie needs 3 1/2 cups of flour to make 4 dozen cookies. How many.cups will she
need to make 2 dozen cookies?
7 cups
1 cup
13/4 cups
11/2 cups
Answer:
3/4 cups
Step-by-step explanation:
3 1/2 divided by 2
A centroid is the intersection of three
altitudes in a triangle.
perpendicular bisectors in a
triangle.
angle bisectors in a triangle.
medians in a triangle.
Answer: medians in a triangle.
The intersection of the three altitudes is the orthocenter.The intersection of the three perpendicular bisectors is the circumcenter.The intersection of the three angle bisectors is the incenter.The intersection of the three medians is the centroid.Under what condition is √x > √25?
[tex]\sqrt x > \sqrt{25} \qquad( x\geq 0)\\\sqrt x > 5\\x > 25[/tex]
When [tex]x > 25[/tex].
Please help you can see how stressed I am
answer send in this photo there is answer any doubt you can ask again
Translate the following expression to an equation in terms of p: "151.8 is what percent of 69?"
The statement "151.8 is what percent of 69 is expressed as 0.69p = 151.8
Equations and expressionsEquations are expressions separated by an equal sign. Words can be translated to equations.
Let the unknown variable be "p". If p percent of 69is 151.8, this is expressed as;
p% of 69 = 151.8
Convert to decimals
p/100 * 69 = 151.8
0.01p * 69 = 151.8
0.69p = 151.8
Hence the statement "151.8 is what percent of 69 is expressed as 0.69p = 151.8
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A pulley is used to pull a boat to the dock. The rope is attached to the boat 7 feet below the level of the pulley. What is the distance from the boat to the dock when the rope is 25 feet long?
Answer: 24 ft
Step-by-step explanation:
By the Pythagorean theorem,
[tex]7^{2}+x^{2}=25^{2} \\ \\ 49+x^{2}=625 \\ \\ x^{2}=576 \\ \\ x=\boxed{24 \text{ ft}}[/tex]
You play a game that requires rolling a six-sided die and then randomly choosing a colored card from a deck containing 3 red cards, 6 blue cards, and 8 yellow cards. Find the probability that you will roll a 5 on the die and then choose a red card.
The probability of getting a red card and rolling a 5 is = 3/85
How to find the probability?First, we want to find the probability of rolling a 5.
There are 6 outcomes on the six-sided die, so the probability of getting a particular value is:
P = 1/5.
Then, the probability of randomly drawing a red card is given by the quotient between the number of red cards and the total number of cards:
P' = 3/(3 + 6 + 8) = 3/17
The joint probability is given by the product between the individual probabilities:
prob = P*P' = (1/5)*(3/17) = 3/85
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A patient has been prescribed 1 gram (g) of Drug A. The stock dose is available in 250 milligram (mg) tablets. How many tablets would you administer per dose?
Answer:
4
Step-by-step explanation:
1 g = 1,000 mg
1,000/250 = 4
your recipe calls for 2 over 3 cups of sugar. you are only making 2 over 4 of the recipe. how much sugar do you need? not simplified
The quantity of sugar required for 2/4 of the recipe is 1/3 cups
How to solve fraction?let
x = quantity of sugar neededRatio of sugar to recipe
2/3 : 1 = x : 2/4
2/3 ÷ 1 = x ÷ 2/4
2/3 × 1/1 = x × 4/2
2/3 = x × 2
2/3 = 2x
x = 2/3 ÷ 2
x = 2/3 × 1/2
= 2/6
x = 1/3 cups
Therefore, the quantity of sugar required for 2/4 of the recipe is 1/3 cups
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The graph represents the height of a ball after being thrown versus time. Which statement is true? A. The ball attains a maximum height of 70 meters at 4 seconds. B. The ball attains a maximum height of 4 meters at 70 seconds. C. The ball attains a maximum height of 70 meters at 2 seconds. D. The ball attains a maximum height of 2 meters at 4 seconds.
The statement which is true about the thrown ball is that A. The ball attains a maximum height of 70 meters at 4 seconds
What is a Maximum Height?
This refers to the highest vertical projectile that an object can attain when acted upon by an external force.
Given the attached diagram that shows the graph of the projectile of the ball, we can observe that its maximum height before it began to fall is 70 meters at 4 seconds based on the values on the x and y-axis.
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#SPJ1If one factor of x² + 2x - 24 is (x+6), what is the other factor?
O (x+8)
O (x-8)
O (x+4)
O(x-4)
The other factor for the given equation will be ( x - 4 ). The correct option is D.
What is a quadratic equation?The polynomial having a degree of two or the maximum power of the variable in a polynomial will be 2 is defined as the quadratic equation and it will cut two intercepts on the graph at the x-axis.
The solution of the given quadratic equation will be:-
x² + 2x - 24 = ( x² + 6x -4x -24 )
= [ x( x + 6) - 4 ( x + 6 ) ]
= ( x + 6 ) ( x - 4 )
Therefore another factor for the given equation will be ( x - 4 ). The correct option is D.
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Which property was used to simplify the expression?
O distributive property
O commutative property
O associative property
O inverse property
4(b+2)=4b+8
The expression is
4(b+2)=4b+8See
4(b)+4(2)4b+8Its distributive property which states that
a(b+c)=ab+acOption A
Which of the following best describes the graph below?
54 -3 -2 -1
PINT
123 to
3
A. It is not a function.
B. It is a many-to-one function.
C. It is a function, but it is not one-to-one.
D. It is a one-to-one function.
I need help with this question please
The changes in Z would be = 6.1× 10^-4.
Calculation of the unknown valueZ = Sin (x³ +y³)
Where X = 0.3
y = 0.2
Z= Sin ( 0.3³ + 0.2³)
Z= Sin ( 0.027 + 0.008)
Z= Sin ( 0.035)
Z= 6.1× 10^-4
Therefore, the changes in Z would be = 6.1× 10^-4.
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Expand and simplify: (-7y - 8) (y - 4)
To expand an expression, use FOIL method.
F - FirstMultiply the first term in each expression inside the parentheses.-7y and y are the first terms in each expression.
(-7y)(y) = -7y²
O - Outside Next is to multiply the terms outside. (The first term in the first expression and the last term in the second expression)-7y is the first term in the first expression
-4 is the last term of the second expression
(-7y)(-4) = 28y
I - InsideThe next step is to multiply the terms inside. (The last term in the first expression and the first term in the last expression)-8 is the last term in the first expression
y is the first term in the second expression
(-8)(y) = -8y
L - LastLast step is to multiply the last term in each expression.-8 is the last term of the first expression
-4 is the last term of the second expression
(-8)(-4) = 32
Combine all simplified terms.
-7y² + 28y - 8y + 32-7y + 20y + 32Answer:
-7y + 20y + 32Wxndy~~
I want to learn more about mean.
What is the mean?
Numbers:
4.5, 1, 9.25, 2, 6, 9.