The same amount of principal is invested in different accounts earning the same interest rate. Which of the following accounts would have the greatest accumulated value at the end of one year?
a.
An account earning no interest
b.
An account earning simple interest
c.
An account earning interest compounded annually
d.
An account earning interest compounded daily
Answer:
D
Step-by-step explanation:
The height of a rocket a given number of seconds after it is released is modeled by h (t) = 6t2 + 32t + 10. What does t represent?
Answer: t represents the the number of seconds after rocket is released.
Step-by-step explanation:
Given: The height of a rocket a given number of seconds after it is released is modeled by [tex]h (t) = 6t^2 + 32t + 10[/tex].
Here h (height) is the dependent variable , which depends on the number of seconds after rocket is released (independent variable).
Since the independent variable in the function is t, then t must represents the the number of seconds after rocket is released.
The variable t represents the number of seconds that have passed since the rocket was released.
How to identify what a variable represents?Here we know that the height of a rocket a given number of seconds after it is released is modeled by:
h(t) = 6*t^2 + 32*t + 10
So this is a function that relates height with time in seconds, we know that the function models the height, so we must have that:
[h(t)] is equivalent to height.
This means that the other variable, t, must be related to time in seconds.
Then we can conclude that the variable t represents the number of seconds after the rocket has been released.
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A scuba diver descends at a rate of 40 feet per minute. How many feet will the scuba diver move in 2 minutes?
Write the equation in the slope-intercept form. 7x − 4y + 8 = 0
Final answer:
To convert the equation 7x - 4y + 8 = 0 to slope-intercept form, solve for y to get y = (7/4)x + 2, with a slope of 7/4 and a y-intercept of 2.
Explanation:
To write the equation 7x − 4y + 8 = 0 in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept, we want to solve for y. The steps are as follows:
Subtract 7x and 8 from both sides of the equation to isolate terms involving y: -4y = -7x - 8.Divide every term by -4 to solve for y: y = (7/4)x + 2.Thus, the equation of the line in slope-intercept form is y = (7/4)x + 2. Here, the slope is 7/4 and the y-intercept is 2.
On a particular road map 1/2 inch represents 18 miles about how many miles apart are 2 towns that are 21/2 inches apart on this map
Danielle can spend up to $600 buying small and large jackets for her employees. Small jackets cost $20 each and large jackets cost $25 each. To get a special discount, she needs the number of large jackets to be no more than twice the number of small jackets. Also, she needs to order at least 6 small jackets and 10 large jackets. The graph shows the feasible region, where x represents the number of small jackets and y represents the number of large jackets. Which ordered pairs meet all the constraints and make sense in context of the situation? Select each correct answer. (13, 11) (15, 11) (8, 9) (7, 15) (10,13)
Answer:
10,13 13, 15,11
Step-by-step explanation:
THANK YOU PREVIOUS PERSON YOU SAVED MY WHOLE MATH GRADE! I OWE YOU YOU MADE IT SO I CAN PASS 9TH GRADE.
Write what the expressions below best represent within the context of the word problem
How many quarts of water must be added to 4 quarts of an 80% mixture to obtain a 50% mixture?
x represents quarts of water to be added to the ____% mixture.
x + 4 represents the total quarts of the mixture at ____%.
first one is 80%
second one is 50%
1st. is 80%
2nd. is 50%
A line has a slope of 5 and a y-intercept of 4 what is the equation in slope intercept form
Write your answer using integers proper fraction and improper fractions in simplest form
Jacqui has grades of 79 and 76 on her first two algebra tests. if she wants an average of at least 71, what possible scores can she make on her third test?
Gary is looking over his receipts from his trip to Europe. When he was in Germany, he exchanged US dollars for euros at a rate of 1:0.7716, and when he was in Poland, he exchanged euros for Polish zloty at a rate of 1:4.0518. To four decimal places, what was the exchange rate of US dollars to Polish zloty?
For anyone who still needs it, the answer is 1:3.1264.
the total cost of a bus ride and a ferry ride is $8.00. in one month, bus fare will increase by 10% and ferry fare will increase by 25%. the total cost will then be 9.25. how much is the current bus fare?
Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. write the polynomial in standard form. (1 point) 4, -14, and 5 + 8i
The required polynomial function is x⁴ - 67x² + 1450x - 4984 = 0 with 4 degrees with real coefficients.
What is a polynomial?A polynomial is defined as a mathematical expression that has a minimum of two terms containing variables or numbers. A polynomial can have more than one term.
The zeros are given in the question as 4, -14, and 5 + 8i
The required polynomial function of minimum degree with real coefficients whose zeros include those listed above.
For the zero 4, you can write (x-4)
For the zero -14, you can write (x+14)
For the zero 5+8i since it is complex it will be accompanied by its conjugate 5-8i
So, you can write (x-(5+8i) and (x-(5-8i)) =(x²-10x+89)
(x - 4)(x + 14)(x² - 10x + 89)
Expanding the expression, we get
x⁴ - 67x² + 1450x - 4984 = 0
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What is h(10) equal to?
Triangle LMN is located at L(2,3), M(1,2), and N(4,4). The triangle is then transformed using the rule (x+5, y+2) to form the image L’M’N. What are the new coordinates of L’,M’, and N’?
Given:- L (2, 3), M (1, 2), and N make up the triangle known as LMN (4, 4). The image L'M'N' is created by first transforming the triangle according to the rule
To Locate:
What are L's, M's, and N's new coordinates?Solution:-
Rule for Points = (x + 2) on the x-axis.
Thus, the new x-points axis's are as follows:
L' = 2 + 5 = 7
M' = 1 + 5 = 6
N' = 4 + 5 = 9 .
and, Rule for y - axis Points = (y + 2) .
Therefore, New y - axis points of new ∆ are :-
L' = 3 + 2 = 5
M' = 2 + 2 = 4
N' = 4 + 2 = 6 .
Hence, New coordinates of L', M', and N' :-
L' = (7 , 5)
M' = (6, 4)
N' = (9, 6)
Find out more:
show that the point of trisection for the line connecting the points (-5,12) and (-1,12) is the midpoint of the line connecting the...
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Identify the range of the function shown in the graph
Answer:
Step-by-step explanation: the answer is b for apex
PLEASE HELP ASAP: A particle is moving with velocity v(t) = t2 – 9t + 18 with distance, s measured in meters, left or right of zero, and t measured in seconds, with t between 0 and 8 seconds inclusive. The position at time t = 0 sec is 1 meter right of zero, that is, s(0) = 1.
The average velocity over the interval 0 to 8 seconds
The instantaneous velocity and speed at time 5 secs
The time interval(s) when the particle is moving right
The time interval(s) when the particle is
going faster
slowing down
Find the total distance the particle has traveled between 0 and 8 seconds
Answer:
1) Average velocity = 10/3 m/s
2) Instantaneous velocity = -2 m/s
Speed = 2 m/s to the left
3) (0, 3) ∪ (6, 8]
4) Going faster: (3, 4.5) ∪ (6, 8]
Slowing down: (0, 3) ∪ (4.5, 6)
5) Total distance = 35.67 m (nearest hundredth)
Step-by-step explanation:
The relationships between position (displacement), velocity and acceleration are:
[tex]\boxed{\boxed{\begin{array}{c}\textbf{POSITION (s)}\\\\\text{Differentiate} \downarrow\qquad\uparrow\text{Integrate}\\\\\textbf{VELOCITY (v)}\\\\\text{Differentiate}\downarrow\qquad\uparrow \text{Integrate}\\\\\textbf{ACCELERATION (a)}\end{array}}}[/tex]
Given a particle is moving with velocity v(t) = t² - 9t + 18, to find its position s(t) we can integrate v(t):
[tex]\begin{aligned}\displaystyle s(t)=\int v(t)\;\text{d}t&=\int(t^2-9t+18)\;\text{d}t\\\\&=\dfrac{t^{2+1}}{2+1}-\dfrac{9t^{1+1}}{1+1}+18t+C\\\\&=\dfrac{t^{3}}{3}-\dfrac{9t^{2}}{2}+18t+C\end{aligned}[/tex]
As s(0) = 1, then:
[tex]\begin{aligned}s(0)=\dfrac{(0)^{3}}{3}-\dfrac{9(0)^{2}}{2}+18(0)+C&=1\\0-0+0+C&=1\\C&=1\end{aligned}[/tex]
Therefore, the position function s(t) is:
[tex]\large\boxed{s(t)=\dfrac{t^3}{3}-\dfrac{9t^2}{2}+18t+1}[/tex]
Given a particle is moving with velocity v(t) = t² - 9t + 18, to find its acceleration a(t) we can differentiate v(t):
[tex]\begin{aligned}a(t)=\dfrac{\text{d}}{\text{d}t}[v(t)]&=2\cdot t^{2-1}-1\cdot9t^{1-1}+0\\&=2t-9\end{aligned}[/tex]
Therefore, the acceleration function a(t) is:
[tex]\large\boxed{a(t)=2t-9}[/tex]
[tex]\hrulefill[/tex]
Question 1To find the average velocity over the interval [0, 8], use the formula:
[tex]\textsf{Average Velocity}=\dfrac{s(t_2)-s(t_1)}{t_2-t_1}[/tex]
In this case:
t₁ = 0t₂ = 8Calculate the position at t₁ and t₂ by substituting t = 0 and t = 8 into s(t):
[tex]s(0)=\dfrac{(0)^3}{3}-\dfrac{9(0)^2}{2}+18(0)+1}=1[/tex]
[tex]s(8)=\dfrac{(8)^3}{3}-\dfrac{9(8)^2}{2}+18(8)+1}=\dfrac{83}{3}[/tex]
Therefore:
[tex]\textsf{Average Velocity}=\dfrac{s(8)-s(0)}{8-0}=\dfrac{\frac{83}{3}-1}{8}=\dfrac{10}{3}\; \sf m/s[/tex]
Therefore, the average velocity is 10/3 m/s.
[tex]\hrulefill[/tex]
Question 2To find the instantaneous velocity at t = 5 seconds, substitute t = 5 into v(t):
[tex]\begin{aligned}v(5)&=(5)^2-9(5)+18\\&=25-45+18\\&=-2\end{aligned}[/tex]
So, the instantaneous velocity at t = 5 seconds is -2 m/s.
Speed is a scalar quantity that measures how fast an object is moving regardless of its direction. Therefore, speed is the magnitude of velocity:
[tex]\textsf{Speed}=|v(5)|=|-2|=2\;\sf m/s[/tex]
Therefore, the speed at t = 5 is 2 m/s to the left.
[tex]\hrulefill[/tex]
Question 2The particle changes direction when v(t) = 0.
[tex]\begin{aligned}v(t)&=0\\\implies t^2-9t+18&=0\\t^2-6t-3t+18&=0\\t(t-6)-3(t-6)&=0\\(t-3)(t-6)&=0\\\\t-3&=0\implies t=3\\t-6&=0\implies t=6\end{aligned}[/tex]
Therefore, the particle changes direction at t = 3 and t = 6.
We know that the position of the particle at t = 0 is 1 meter right of zero. Therefore:
It is moving to the right in the interval (0, 3).It is moving to the left in the interval (3, 6).It is moving to the right in the interval (6, 8].Therefore, the time intervals between 0 ≤ t ≤ 8 when the particle is moving right is:
(0, 3) ∪ (6, 8][tex]\hrulefill[/tex]
Question 4When a(t) > 0:
[tex]\begin{aligned}a(t)& > 0\\2t-9& > 0\\2t& > 9\\t& > \dfrac{9}{2}\\t& > 4.5\; \sf s\end{aligned}[/tex]
When a(t) < 0:
[tex]\begin{aligned}a(t)& < 0\\2t-9& < 0\\2t& < 9\\t& < \dfrac{9}{2}\\t& < 4.5\; \sf s\end{aligned}[/tex]
Therefore:
Velocity is positive in the interval (0, 3) and (6, 8].Velocity is negative in the interval (3, 6).Acceleration is positive in the interval (4.5, 8].Acceleration is negative in the interval (0, 4.5).(Refer to the attachment).
If velocity and acceleration have the same sign, it means the object is speeding up.
If velocity and acceleration have opposite signs, it means the object is slowing down.
Therefore, the time intervals when the particle is going faster and slowing down are:
Going faster: (3, 4.5) ∪ (6, 8]Slowing down: (0, 3) ∪ (4.5, 6)[tex]\hrulefill[/tex]
Question 5To find the total distance the particle has traveled between 0 and 8 seconds, we need to consider the distance traveled between the intervals when it changes direction.
To do this, find the position of the particle at t = 0, t = 3, t = 6 and t = 8.
[tex]s(0)=\dfrac{(0)^3}{3}-\dfrac{9(0)^2}{2}+18(0)+1=1[/tex]
[tex]s(3)=\dfrac{(3)^3}{3}-\dfrac{9(3)^2}{2}+18(3)+1=23.5[/tex]
[tex]s(6)=\dfrac{(6)^3}{3}-\dfrac{9(6)^2}{2}+18(6)+1=19[/tex]
[tex]s(8)=\dfrac{(8)^3}{3}-\dfrac{9(8)^2}{2}+18(8)+1=\dfrac{83}{3}\approx27.67[/tex]
Therefore, in the interval 0 ≤ t < 3, the particle travels:
[tex]|s(3)-s(0)|=|23.5-1|=22.5\; \sf meters\;(to\;the\;right)[/tex]
In the interval 3 < t < 6, it travels:
[tex]|s(6)-s(3)|=|19-23.5|=4.5\; \sf meters\;(to\;the\;left)[/tex]
In the interval 6 < t ≤ 8, it travels:
[tex]|s(8)-s(6)|=|27.67-19|=8.67\; \sf meters\;(to\;the\;right)[/tex]
So the total distance the particle has traveled between 0 and 8 seconds is:
[tex]\textsf{Total distance}=22.5+4.5+8.67=35.67\; \sf meters[/tex]
Parker bought a student discount card for the movies. The card cost $7 and and allows him to buy movie tickets for $5.50. After one month, Parker has spent $89.50 total. How many tickets has he bought since getting the discount card?
A) 12 tickets
B) 14 tickets
C) 15 tickets
D) 16 tickets
PLEASE HELP MATH!!!!!!
Sean used 3/4 cup of sugar to make a dozen brownies. How much sugar is in each brownie
Sean used 3/4 cups of sugar to make 12 brownies. By dividing 3/4 by 12, we find that there is 1/16 cup of sugar in each brownie.
Explanation:The subject of this problem is mathematics, specifically, it's about division in the context of fractions. In this scenario, Sean used 3/4 cups of sugar to make a dozen (12) brownies. To determine the amount of sugar in each brownie, we can divide the total amount of sugar by the total number of brownies.
So, 3/4 divided by 12 is 1/16. This means that there is 1/16 cup of sugar in each brownie.
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Choose the biconditional that is equivalent to the definition, "A skyscraper is a very tall building."
A skyscraper is a very tall building. The biconditional equivalent to this definition is 'A building is a skyscraper if and only if it is very tall.'
Explanation:The biconditional equivalent to the definition 'A skyscraper is a very tall building' is:
A building is a skyscraper if and only if it is very tall.
This biconditional statement means that for a building to be classified as a skyscraper, it must satisfy the condition of being very tall. Conversely, if a building is very tall, it can be classified as a skyscraper. This definition establishes a two-way relationship between being a skyscraper and being very tall.
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You have 6 pints of glaze. It takes 7/8 of a pint to glaze a bowl and 9/16 of a pint to glaze a plate. You want to glaze 5 bowls, and then use the rest for plates. How many plates can you glaze? How much glaze will be left over?
2 plates can be glazed and 0.50 glaze will be left over.
What is Unitary Method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.
for example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.
12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.
As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.
This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.
Given:
Total bowls= 5
fraction of pint to glaze bowl= 7/8
So, pint to glaze 5 bowls
= 5 bowls x 7/8 of a pint
= 4.375 pints
and, left over after glazing the bowls.
= 6 pints - 4.375pints
= 1.625
Now, we know to glaze plate pint used= 9/16
So, number of plates will be = 1.625 x 16/9
= 2.88 plates
Thus, we can only glaze 2 plates.
Also, glaze left over
= 1.625 - 1.125
= 0.50 glaze left over.
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Kyra is using rectangular tiles of two types for a floor design. A tile of each type is shown below: Two rectangular tiles, rectangle PQRS with vertices at P 1, 1. Q is at 8, 1. R is at 8, 5. S is at 1, 5. Rectangle JKLM with vertices J at 4, 1. K is at 8, 1. L is at 8, 4. M is at 4, 4. Which statement is correct? The two tiles are not similar because segment SP is to segment SR is 4:7 and segment MJ is to segment ML is 1:3. The two tiles are similar because segment PQ is to segment QR is 4:3 and segment JK is to segment KL is also 4:3. The two tiles are similar because segment SR is to segment ML is 7:4 and segment PQ is to segment JK is also 7:4. The two tiles are not similar because segment PQ is to segment QR is 7:4 and segment JK is to segment KL is 4:3.
The equation c = 6.5h represents the cost, c, of renting a bicycle for h hours. The table below can be used to show the same information.
If Francesca rents a bicycle for 2 hours and Phil rents a bicycle for 6 hours, how much more does Phil pay?
$13
$26
$39
$52
Answer:
26 (I got 100%)
Step-by-step explanation:
39 - 13
Phil payment - Francesca payment = 26
What is m∠JNM?
Enter your answer in the box.
°
we know that
Vertical angles are a pair of opposite and congruent angles formed by intersecting lines
In this problem
m∠JNM=m∠KNL -------> by vertical angles
so
[tex](4x+6)\°=(7x-21)\°[/tex]
Solve for x
[tex]7x-4x=6+21\\3x=27\\x=9\°[/tex]
Find the value of m∠JNM
m∠JNM=[tex](4x+6)\°[/tex]
substitute the value of x
m∠JNM=[tex](4*9+6)\°[/tex]
m∠JNM=[tex]42\°[/tex]
therefore
the answer is
m∠JNM=[tex]42\°[/tex]
In response to the increasing weight of airline passengers, the Federal Aviation Administration in 2003 told airlines to assume that passengers average 189.7 pounds in the summer, including clothing and carry-on baggage. But passengers vary, and the FAA did not specify a standard deviation. A reasonable standard deviation is 41.4 pounds. Weights are not Normally distributed, especially when the population includes both men and women, but they are not very non-Normal. A commuter plane carries 27 passengers.
What is the approximate probability (±0.0001) that the total weight of the passengers exceeds 5511 pounds?
The only way I can think of to solve this problem is to assume normal distribution.
Since the total weight excess 5511, hence the weight per passenger is at least:
x = 5511 / 27 = 204.1 pounds
Solve for the z score:
z = (x – u) / s
z = (204.1 – 189.7) / 41.4
z = 0.35
From the standard probability tables, the P value using right tailed test is:
P = 0.3632
Find the solution of the square root of the quantity of x plus 3 plus 4 equals 6, and determine if it is an extraneous solution
Answer:
[tex]x=1[/tex]
Step-by-step explanation:
We have been given an equation [tex]\sqrt{x+3}+4=6[/tex]. We are asked to find the solution of our given equation.
[tex]\sqrt{x+3}+4-4=6-4[/tex]
[tex]\sqrt{x+3}=2[/tex]
Now, we will square both sides of our given equation.
[tex]x+3=2^2[/tex]
[tex]x+3=4[/tex]
[tex]x+3-3=4-3[/tex]
[tex]x=1[/tex]
To see whether [tex]x=1[/tex] is an extraneous solution or not, we will substitute [tex]x=1[/tex] in our given equation as:
[tex]\sqrt{1+3}+4=6[/tex]
[tex]\sqrt{4}+4=6[/tex]
[tex]2+4=6[/tex]
[tex]6=6[/tex]
Since both sides of our given equation are equal, therefore, [tex]x=1[/tex] is a solution for our given equation.
A cab company charges an initial rate of $2.50 for a ride, plus $0.40 for each mile driven. What is the equation that models the total fee for using this cab company? Write into an equation and then graph it.
Answer:
The equation that models the total fee for using this cab company
[tex]y=\$2.50+\$0.40\times x[/tex]
Step-by-step explanation:
Initial rate charged by company = $2.50
Amount charged for an each mile = $0.40
Let the miles cover during a ride = x
Total cost of ride can given as = y
The equation that models the total fee for using this cab company
[tex]y=\$2.50+\$0.40\times x[/tex]
The graphical interpretation equation in an image.
A division of a company produces income tax apps for smartphones. each income tax app sells for $9. the monthly fixed costs incurred by the division are $25,000, and the variable cost of producing each income tax app is $4. (a) find the break-even point for the division.
The equation for profit is income – cost:
Profit = Income – Cost
Let us say that x is the number of sold amount
Profit = 9 x – (25,000 + 4 x)
Profit = 5 x – 25,000
Breakeven point occurs when Profit = 0, hence:
5 x = 25,000
x = 5,000
The breakeven is when 5,000 people uses the income tax app
What is the value of n in the numerical sentence below?
√16 ÷ 4³ = 4ⁿ
n = ?
Evaluate exactly the value of the integral from negative 1 to 0 of the product of the cube of the quantity 2 times x to the 4th power plus 8 times x and 4 times x to the 3rd power plus 4, dx. Your work must include the use of substitution and the antiderivative.
Answer:
-162
Step-by-step explanation:
Integration by substitution is a technique in calculus where a change of variables is made to simplify the integral by expressing it in terms of a new variable, making the integration easier to manage.
To evaluate the following integral, use the method of substitution:
[tex]\displaystyle \int_{-1}^0 (2x^4 + 8x)^3 (4x^3 + 4) \;\text{d}x[/tex]
Let u = 2x⁴ + 8x.
Differentiate u with respect to x using the power rule for differentiation by multiplying each term by its exponent and then subtracting 1 from the exponent:
[tex]\dfrac{\text{d}u}{\text{d}x}=4 \cdot 2x^{4-1}+1\cdot 8 x^{1-1}[/tex]
[tex]\dfrac{\text{d}u}{\text{d}x}=8x^{3}+8[/tex]
Rewrite it so that dx is on its own:
[tex]\text{d}u=8x^{3}+8\;\text{d}x[/tex]
[tex]\text{d}x=\dfrac{1}{8x^{3}+8}\;\text{d}u[/tex]
Change the limits of integration from x to u:
[tex]\begin{aligned}x=-1 \implies u&=2(-1)^4 + 8(-1)\\&=2(1)-8\\&=2-8\\&=-6\end{aligned}[/tex]
[tex]\begin{aligned}x=0 \implies u&=2(0)^4 + 8(0)\\&=2(0)-0\\&=0-0\\&=0\end{aligned}[/tex]
Rewrite the integral in terms of u:
[tex]\begin{aligned}\displaystyle \int_{-1}^0 (2x^4 + 8x)^3 (4x^3 + 4) \;\text{d}x&=\int_{-6}^0 u^3 (4x^3 + 4) \cdot \dfrac{1}{8x^{3}+8}\;\text{d}u\\\\&=\int_{-6}^0 u^3 (4x^3 + 4) \cdot \dfrac{1}{2(4x^{3}+4)}\;\text{d}u\\\\&=\int_{-6}^0\dfrac{u^3}{2} \;\text{d}u\end{aligned}[/tex]
Integrate with respect to u using the power rule for integration by adding 1 to the exponent of each term and then dividing by the new exponent:
[tex]\begin{aligned}\displaystyle \int_{-6}^0\dfrac{u^3}{2} &=\left[\dfrac{u^{3+1}}{2 \cdot (3+1)}\right]^0_{-6}\\\\&=\left[\dfrac{u^{4}}{8}\right]^0_{-6}\\\\&=\dfrac{(0)^4}{8}-\dfrac{(-6)^4}{8}\\\\&=0-\dfrac{1296}{8}\\\\&=-162\end{aligned}[/tex]
Therefore, the value of the given integral is -162.