good luck man i hate having to do this kind of thing in class
The formula [tex]\(A(t) = 2000(1.0075)^{4t}\)[/tex] represents the amount of money in a savings account with quarterly compounding interest over time.
The formula [tex]\(A(t) = 2000(1.0075)^{4t}\)[/tex] describes the amount of money, [tex]\(A(t)\),[/tex] in a savings account over time, where [tex]\(t\)[/tex] represents the number of years. The initial investment is $2000, and the account earns interest at a rate of 3%, compounded quarterly.
The term [tex]\((1.0075)^{4t}\)[/tex] represents the growth factor of the investment over time.
The base, [tex]\(1.0075\),[/tex] represents the factor by which the investment grows each quarter, considering the 3% annual interest rate.
Since the interest is compounded quarterly, it is raised to the power of [tex]\(4t\)[/tex] to account for the total number of quarters over [tex]\(t\)[/tex] years.
Multiplying the initial investment by this growth factor yields the total amount of money in the account after[tex]\(t\)[/tex]years.
As time increases, the exponential term increases, leading to exponential growth in the account balance.
This formula provides a mathematical model for calculating compound interest and understanding how investments grow over time.
What is the probability of rolling a 6-sided die and getting a 4 or a number
divisible by 3?
Event A = rolling a 4 on a single die
Event B = rolling a number divisible by 3 (3 or 6) on a single die
There are three outcomes possible in total if either event A happens or event B happens. This is out of six outcomes total.
Divide the values and reduce: 3/6 = 1/2
Final Answer: 1/2
assume that an avarage cell has a diameter of 7 micrometers (7x10^10 meter) which means it has a volume of 200 cubic micrometers. How many cells are ther in a cubic centimeter
Answer:
5x10⁸
Step-by-step explanation:
Cell = 200 cubic micrometers.
Te question is, how many 200 cubic micrometers are there in a cubic centimeter. 1st, we have to convert 200 cubic centimeter into cubic centimeter:
1cm = 1x10⁴micro, which is the same to:
1x10⁻⁴ cm = 1micro
Now, we have to cube both sides, to "equal the volumes"
(1x10⁻⁴cm)³ = (1micro)³
1x10⁻¹²cm = 1micro³
Multiple both sides by 200:
200 x 1x10⁻¹²cm = 1micro³ x 200
2x10⁻¹⁰cm³ = 200micro³
Finally, 1 cubic cm / 2x10⁻¹⁰cm³ = 5x10⁸
Final answer:
Explaining the number of cells in a cubic centimeter based on the volume of a 10 μm cell.
Explanation:
For a 10 μm cell:
Calculate the volume: V = (4/3)πr³
Convert diameter to radius: r = 5 μm
Substitute and calculate volume: V = (4/3)π(5)³ = 524 μm³
Convert to cubic centimeters: 1 μm³ = 10^-9 cm³, so 524 μm³ = 5.24 x 10^-7 cm³
Calculate the number of cells in 1 cm³: 1 cm³ / 5.24 x 10^-7 cm³ = 1.91 x 10^6 cells
3 thousand divided 10 in unit and standard form
Answer:
300
Step-by-step explanation:
Divide 3000 by 10 by striking out each zero one-by-one [300 ÷ 1] to get 300. This is one of the fastest ways to solve with zeros.
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The result would be 300 units and 320 units respectively.
3 thousand divided by 10 in unit and standard form:
To divide 3,000 by 10 in unit form: 3,000 ÷ 10 = 300 units.
To divide 3,000 by 10 in standard form: 3.2 × 10³ ÷ 10¹ = 3.2 × 10² = 320 units.
5. Write the phrase as an algebraic expression.
6 less than a number times 11
@ 6y - 11y © 11y - 6
6 11=Y
11+ y
Two coins are tossed simultaneously,Find the probability of getting.1.atleast one head.2.at most one tail
If two coins are tossed simultaneously, you will have one of the possible results
[tex]HH,\ HT,\ TH,\ TT[/tex]
with probability 1/4 each.
So, you'll have at least one head if you have HH, HT or TH, i.e. with probability 3/4.
Similarly, you have at most one tail if you get HH, HT or TH, so the probability will be the same.
In fact, both claims (at least one head and at most one tail) are verified by the same set of outputs HH, TH, HT, since they're not satisfied only by the output HH.
So, if those claims are not satisfied with probability 1/4, they're satisfied with probability 3/4.
Final answer:
The probability of getting at least one head when tossing two coins is 0.75.
When two coins are tossed simultaneously, the sample space consists of the following possible outcomes: {HH, HT, TH, TT}. To find the probability of getting at least one head, we can count the favorable outcomes which include at least one head: these are HH, HT, and TH. Thus, there are 3 favorable outcomes.
The total number of possible outcomes is 4. Therefore, the probability is 3 out of 4, or
0.75.
To find the probability of getting at most one tail, we consider the favorable outcomes: these are HH, HT, and TH. Again, we can see there are 3 favorable outcomes.
Since the total number of outcomes is the same, the probability remains
0.75.
I really don't know if I'm doing this right and I have a test coming up (I only need the answer for the odds)
Answer:
all work is shown and pictured
The book display has 8 histories, 12 biographies, and 24 novels. Write the ratio of biographies to histories.
Answer:
12:8
Step-by-step explanation:
The ratio of biographies to histories is 1.5, or more simply as a whole number ratio, 3:2. This means that for every 3 biographies, there are 2 history books.
Explanation:The question wants us to calculate the ratio of the number of biographies to the number of histories in the book display. To do this, simply divide the number of biographies by the number of histories. The problem provides the number of biographies as 12 and the number of histories as 8. Thus, the ratio is: 12 (biographies) / 8 (histories) = 1.5.
In other words, for every 1.5 biographies, there is 1 history book on the display. However, since ratios are commonly expressed as whole numbers, we can multiply both sides by 2 to get the ratio as 3:2, meaning for every 3 biographies, there are 2 history books. This provides a cleaner and more interpretable ratio.
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-50-2 - 8m) = 10 + 5m
Answer:
-4 10/13
Step-by-step explanation:
-52-8m = 10 + 5m
-8m = 62 +5m
-13m = 62
-m = 62/13
m = - 62/13
m = -4 10/13
HELP HELP HELP PLEASE ASAP
Answer:
Its Brand 2 :) also do you do connexus?
if so whats ur name :)
Step-by-step explanation:
Answer:
brand 4
Step-by-step explanation:
A taxi cab charges $1.75 for the flat fee and $0.25 for each mile. Write an in equality to determine how many miles Eddie can travel if he has $15 to spend.
Answer:
.25x+1.75=15 and x=53
Step-by-step explanation:
first subtract 1.75 from both sides
then divide by .25 on both sides
and you will get x=53
what is the substitution of 7+3x=1???
Answer:x= -2
Step-by-step explanation:
A circle passes through points A(7,4), B(10,6), C(12,3). Show that AC must be the diameter of the circle.
I've spent ages on this question and I still can't get it...
so we have three points, A, B and C, if indeed AC is the diameter of the circle, then half the distance of AC is its radius, and the midpoint of AC is the center of the circle, morever, since B is also on the circle, the distance from B to the center must be the same radius distance.
in short, half the distance of AC must be equals to the distance of B to the midpoint of AC, if indeed AC is the diameter.
[tex]\bf ~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ A(\stackrel{x_1}{7}~,~\stackrel{y_1}{4})\qquad C(\stackrel{x_2}{12}~,~\stackrel{y_2}{3}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left( \cfrac{12+7}{2}~~,~~\cfrac{3+4}{2} \right)\implies \left( \cfrac{19}{2}~~,~~\cfrac{7}{2} \right)=M\impliedby \textit{center of the circle}[/tex]
now, let's check the distance from say A to the center, and check the distance of B to the center, if it's indeed the center, they'll be the same and thus AC its diameter.
[tex]\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ A(\stackrel{x_1}{7}~,~\stackrel{y_1}{4})\qquad M(\stackrel{x_2}{\frac{19}{2}}~,~\stackrel{y_2}{\frac{7}{2}})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ AM=\sqrt{\left( \frac{19}{2}-7 \right)^2+\left( \frac{7}{2}-4 \right)^2} \\\\\\ AM=\sqrt{\left( \frac{5}{2}\right)^2+\left( -\frac{1}{2} \right)^2}\implies \boxed{AM\approx 2.549509756796392} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ B(\stackrel{x_1}{10}~,~\stackrel{y_1}{6})\qquad M(\stackrel{x_2}{\frac{19}{2}}~,~\stackrel{y_2}{\frac{7}{2}}) \\\\\\ BM=\sqrt{\left( \frac{19}{2}-10 \right)^2+\left( \frac{7}{2}-6 \right)^2} \\\\\\ BM=\sqrt{\left( -\frac{1}{2}\right)^2+\left( -\frac{5}{2} \right)^2}\implies \boxed{BM\approx 2.549509756796392}[/tex]
AC must be the diameter of the circle.
What is Circle?
A circle is a closed two dimensional figure in which the set of all the points in the plane is equidistance from a center.
Given that;
A circle passes through points A(7, 4), B(10, 6), C(12, 3).
Now,
If AC is diameter of the circle then half the distance of AC is its radius and midpoint of AC is the center of the circle.
Since, B is also on the circle , then distance from B to the center must be same radius distance.
Midpoint of AC is calculated as;
= (7 + 12 / 2 , 4 + 3/2)
= (19/2 , 7/2)
= (9.5 , 3.5)
Now, Distance from A to the center and check the distance of B to the center as;
AM = √(9.5 - 7)² + (3.5 - 4)²
AM = 2.5495
And,
BM = √(9.5 - 7)² + (3.5 - 6)²
BM = 2.5495
So, Distance from A to the center and the distance of B to the center is same.
Thus, AC must be the diameter of the circle.
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Henry can write 5 pages of his novel in 3 hours. At this rate, how many pages can Henry write in 8 hours?
Given that Henry can write 5 pages in 3 hours, his rate is 5/3 pages per hour. Multiplying this rate by 8 hours, we get approximately 13.33 pages. Therefore, Henry can write approximately 13 to 14 pages in 8 hours at the given rate.
Explanation:The subject of this question is mathematics, specifically, it is dealing with the concept of rates. Given that Henry can write 5 pages in 3 hours, we can set up a rate, which is simply a ratio that compares quantities in different units. So, Henry's rate of writing is 5/3 pages per hour.
To find out how many pages Henry can write in 8 hours at this rate, we multiply his rate (5/3) by the number of hours (8 hours). So, (5/3) x 8 = 40/3 = 13.33. However, since we cannot have a fraction of a page, we can round this to 13 pages for a conservative estimate or to 14 pages for a liberal estimate.
So, at the rate given, Henry can write approximately 13 to 14 pages in 8 hours.
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Henry can write approximately 13.33 pages in 8 hours.
Explanation:To find out how many pages Henry can write in 8 hours, we can set up a proportion using the given information.
Since Henry can write 5 pages in 3 hours, we can write the proportion as 5/3 = x/8.
To solve for x, we can cross multiply and then divide to find that x = 40/3.
So, Henry can write approximately 13.33 pages in 8 hours.
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Write 454.12kg with 3 significant
Answer: 454
Step-by-step explanation:
The first three digits will be the significant digits. Round the third digit.
454.12
the digit and the 4 is 1 so 454.12 is rounded to 454
this is really hard and I need help
Answer:
No solution
Step-by-step explanation:
Subtract 5k from both sides
Simplify
No solution
| n+2 | = 7 absolute value
Answer:
Step-by-step explanation:
| n+2 | = 7 : n+2 = 7 or n+2 = -7
n=5 or n = - 9
What is the domain of f(x)= x-4/square root x
Answer:
Step-by-step explanation:
f(x)= x-4/√x
f exist for : x > 0
so the domain is : D= ]0 ; + ∞[
A bakery sold 16 apple pie on Saturday they sold 4 more apple pies on Sunday than they did on Saturday how many apple pies did they sell on Sunday
Answer:
20 apple pies
Step-by-step explanation:
On Saturday they sold 16, while on Sunday they sold 4 more.
16+4 = 20.
20 apple pies.
Slope intercept form of y=3x+4 passing through (0,9)
Answer:
y = 3x + 9
Step-by-step explanation:
9 = 3[0] + b
0
9 = b
y = 3x + 9
This would be considered a parallel line, so 3 remains the way it is.
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A triangle has one side that is 5 inches long and the other two sides are both of length x. Write an expression for the perimeter of the triangle in terms of x and then use the expression to find the perimeter when x=10.
Let P = perimeter
P = 3x + 5
Let x = 10
P = 3(10) + 5
P = 30 + 5
P = 35
When members of the military are in a combat zone, they often eat meals-ready-to-eat (MREs). A typical MRE contains 1 comma 600 calories. If the average soldier eats 3 MREs per day and is deployed for 12 months, approximately how many calories will be consumed by a 37-member platoon of soldiers?
The number of calories by a 37-member platoon of soldiers will be 6,48,24000 calories.
What are calories?A calorie is a unit of energy. Energy is defined as the capacity to do work.
Now it is given that,
Calories contain in 1 MRE = 1,600
Number of MREs taken by a soldier per day = 3
Therefore, number of calories taken by soldier per day = 3*1600
= 4800 calories
Therefore, number of calories taken by 37 soldier per day = 37*4800
= 1,77,600 calories
Now since, 12 months = 365 days
⇒Number of calories taken by 37 soldier in 12 months = 365*1,77,600
⇒Number of calories taken by 37 soldier in 12 months =6,48,24000 calories.
Hence,The number of calories by a 37-member platoon of soldiers will be 6,48,24000 calories.
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Multiplier of 5/7=30/42
Answer:
6
Step-by-step explanation:
5*6=30
7*6=42
Hey!
---------------------
Solution:
30 / 5 = 6
42 / 7 = 6
5 x 6 = 30
7 x 6 = 42
---------------------
Answer:
Multiplier is 6!
---------------------
Hope This Helped! Good Luck!
The length of a rectangular frame is represented by the expression 2x+4 and the width of the rectangular frame is represented by the expression 2x+10. Write an equation to solve for the width of a rectangular frame that has a total area of 120 square inches
2x^2+20x-80=0
4x^2+28x+40=0
4x^2+28x-80=0
x^2+8x+20=0
Answer:
4x^2 + 28x - 80=0
Step-by-step explanation:
(2x+4)(2x+10) = 120
1. Use FOIL (Distribute):
4x^2 + 20x +8x + 40 = 120
2. Group like terms:
4x^2 + 28x+ 40 = 120
3. Subtract 120 from both sides:
4x^2 + 28x - 80 = 0
Answer:
Option 3 - [tex]4x^2+28x-80=0[/tex]
Step-by-step explanation:
We have given,
The length of a rectangular frame is represented by the expression L=2x+4.
The width of the rectangular frame is represented by the expression B=2x+10.
The total area of a rectangular frame is A=120 square inches.
To find : Write an equation to solve for the width of a rectangular frame ?
Solution :
The area of the rectangle is given by,
[tex]\text{Area}=\text{Length}\times \text{Breadth}[/tex]
Substitute the values,
[tex]120=(2x+4)\times(2x+10)[/tex]
[tex]120=4x^2+20x+8x+40[/tex]
[tex]4x^2+28x+40-120=0[/tex]
[tex]4x^2+28x-80=0[/tex]
The required equation is [tex]4x^2+28x-80=0[/tex]
Therefore, option 3 is correct.
For which of the following equations is (-4,-3) not a solution?
A.) 5x+2y=-26
B.) y=1+x
C.) 2y-3x=6
D.) -3x=4y
Answer:
D.) -3x = 4y
Step-by-step explanation:
[tex] -3(-4) ≠ 4(-3) \\ \\ 12 ≠ -12[/tex]
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The point (-4,-3) is not a solution to both Equation C: 2y-3x=6 and Equation D: -3x=4y. This is determined by substituting x with -4 and y with -3 in each equation and checking if the equation is balanced.
Explanation:To find which equation (-4,-3) is not a solution to, we substitute x with -4 and y with -3 into each equation, then see if both sides of the equation are equal.
For equation A: 5(-4) + 2(-3) equals -20 - 6, which is -26. So, (-4,-3) is a solution to this equation.For equation B: -3 equals 1 + (-4), which is -3. So, (-4,-3) is also a solution to this equation.For equation C: 2(-3) - 3(-4) equals -6 + 12, which equals 6. This equation does not equal 6. Therefore (-4,-3) is not a solution to this equation. For equation D: -3 equals 4*(-4), which is -16. This equation does not equal -16. So, (-4,-3) is also not a solution to this equation.So, (-4,-3) is not a solution to both Equation C: 2y-3x=6 and Equation D: -3x=4y.
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When is a linear model not a good fit for a set of data?
When there is not a constant rate of change.
When each input value has only one output value.
When the data set does not go through the origin.
When the data set does not increase.
ANSWER: when there is not a constant rate of change
Answer:
When there is not a constant rate of change
Step-by-step explanation:
A linear model shows a continuous response variable as a function of one or more predictor variables.
A linear model is a good fit for a set of data when the plotted points show a constant rate of change.
When a plot of values form a scatter plot, it is difficult to identify a linear model because the points will not appear to follow a trend.
To come up with a linear function in this case will require you to identify the line of best fit then extending the line to y-axis intercept so as to be able to find the slope.
there are 52 legs and they all belong to hamsters.how many hamsters are there
There are 52 legs and they all belong to hamsters. so 13 Hamsters are there.
Are hamsters a good pet?Hamsters are rodents from the subfamily Cricetinae, which includes 19 species divided into seven genera. They have established themselves as popular tiny pets. The golden or Syrian hamster is the most well-known species of hamster and is the variety most usually kept as a pet.Hamsters are terrific pets for many people. They don't take much attention, receive adequate exercise when running on their wheel, and are attractive, cuddly, and enjoyable to hold. Some children may find them to be a good first pet. Hamsters, however, do not come with care instructions.Total No. of legs = 52
Each hamsters have 4 legs.
No. of Hamster = 52/4 =13 Hamsters
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Given f(x) and g(x) = f(k⋅x), use the graph to determine the value of k.
A. 5
B. [tex]\frac{1}{5}[/tex]
C. -[tex]\frac{1}{5}[/tex]
D. -5
Answer:
Option A k=5
Step-by-step explanation:
step 1
Find the equation of f(x)
we have the points
(-10,-6) and (0,4)
Find the slope m
[tex]m=(4+6)/(0+10)=1[/tex]
The function in slope intercept form is equal to
[tex]f(x)=mx+b[/tex]
we have
[tex]m=1[/tex]
[tex]b=4[/tex] -----> the point (0,4) is the y-intercept
substitute
[tex]f(x)=x+4[/tex]
step 2
Find the equation of g(x)
we have the points
(-2,-6) and (0,4)
Find the slope m
[tex]m=(4+6)/(0+2)=5[/tex]
The function in slope intercept form is equal to
[tex]g(x)=mx+b[/tex]
we have
[tex]m=5[/tex]
[tex]b=4[/tex] -----> the point (0,4) is the y-intercept
substitute
[tex]g(x)=5x+4[/tex]
step 3
Find the value of k
we have
[tex]f(x)=x+4[/tex]
[tex]g(x)=5x+4[/tex] -----> equation A
[tex]g(x)=f(kx)[/tex] -----> equation B
[tex]f(kx)=kx+4[/tex] ----> equation C
substitute equation A and equation C in equation B and solve for k
[tex]kx+4=5x+4[/tex]
[tex]kx-5x=0\\kx=5x\\k=5[/tex]
The value of k in the equation g(x) = f(k*x), where g(x) and f(x) are graphs, signifies a horizontal compression, expansion, or reflection of the f(x) graph. It depends on the given graph to determine the exact value of k.
Explanation:Without the graphical representation, it's difficult to provide a definite value for k. However, understanding the relationship between f(x) and g(x) can help us make an educated guess. If g(x) is a horizontal compression of f(x) by a factor of k, then k is positive and larger than 1. If g(x) is a horizontal expansion of f(x), then k is positive and less than 1. If g(x) is a reflection of f(x) across the y-axis and has a horizontal compression or expansion, then k is negative. For example, if g(x) completes one cycle in a space where f(x) would complete 5 cycles, then k is 5. If g(x) completes 5 cycles in a space where f(x) would complete one cycle, then k equals 1/5.
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change 0.72 to a percent
Write 19h15min into a fraction
Answer:
19 1/4 hours
Step-by-step explanation:
19 h 15 min = 19 hours + 15 minutes
= 19 hours + (15/60) hours
= 19 + 1/4
= 19 1/4 hours
A train leaves the station at 6 pm traveling west at 80 mph. On a parallel track, a second train leaves the station 3 hours later traveling west at 100 mph. At what time will the second train catch up with the first?
Answer:
Step-by-step explanation:
Start train 1 at 6 pm an train 2 at 9pm