The time since the rock reached its closure temperature is approximately 579.8 years. When the rock was discovered, it had 4.375 grams of europium-151.
To find the time since the rock reached its closure temperature, we can use the following formula
t = t(1/2) * log(N0/Nt)
where t is the time elapsed, t(1/2) is the half-life, N0 is the initial amount of the isotope, and Nt is the amount of the isotope at the time it was discovered.
Substituting the given values, we get
t = 96.6 * log(5/0.625) ≈ 579.8 years
Therefore, the time since the rock reached its closure temperature is approximately 579.8 years.
To find the amount of europium-151 in the rock when it was discovered, we can use the fact that the total amount of samarium-151 and europium-151 in the rock is constant.
Since the rock originally contained 5 grams of samarium-151, it must have contained 5 - 0.625 = 4.375 grams of europium-151 when it was discovered.
Therefore, the rock had 4.375 grams of europium-151 when it was discovered.
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Determina la altura del papalote con respecto al piso considerando los datos presentados.
The length of the string required to fly the kite at a height of 75 meters from the ground is 86.6 meters.
The sine of an angle is defined as the ratio of the length of the opposite side to the length of the hypotenuse. In this case, the opposite side is the height of the kite (75 m), and the hypotenuse is the length of the string that we need to find. We can set up an equation using the sine function:
sin(60 degrees) = opposite/hypotenuse
sin(60 degrees) = 75/hypotenuse
We can simplify the equation using the value of the sine of 60 degrees, which is √3/2.
√3/2 = 75/hypotenuse
To solve for the length of the string, we can cross-multiply and simplify:
hypotenuse = 75/(√3/2)
hypotenuse = (75*2)/√3
hypotenuse = 150/√3
hypotenuse = (150/√3) * (√3/√3) (to rationalize the denominator)
hypotenuse = (150√3)/3
hypotenuse = 50√3 meters = 86.6 meters.
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Complete Question:
A kite is flying at a height of 75 m from the level ground, attached to a string inclined at 60 ∘ to the horizontal. Find the length of the string, assuming that there is no slack in it. [Take √ 3 =1.732].
If a square has an area of 94 square units. How big is its side length?
The requried side length of the square is approximately 9.695 units.
To find the side length of a square with an area of 94 square units, we need to take the square root of the area.
a² = 94
a = √94
a ≈ 9.695
Therefore, the side length of the square is approximately 9.695 units.
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Express as a trinomial.
(
2
�
−
3
)
(
3
�
−
4
)
(2x−3)(3x−4)
Answer: 6x^2 - 17x + 12.
Step-by-step explanation:
To multiply these two binomials, we can use the FOIL method, which stands for First, Outer, Inner, Last. This gives us:
(2x - 3)(3x - 4) = (2x)(3x) + (2x)(-4) + (-3)(3x) + (-3)(-4)
Simplifying each term, we get:
(6x^2) + (-8x) + (-9x) + 12
Combining like terms, we can simplify this to:
6x^2 - 17x + 12
Therefore, (2x-3)(3x-4) can be expressed as the trinomial 6x^2 - 17x + 12.
a food shop offers 5 different sandwiches and 8 different drink choices. how many choices are possible for a single sandwich and a drink?
Answer:
Step-by-step explanation:
5
UO
Graph each figure and classify it. Then find the area.
6. R(3,-2), S(7, -2), T(8, -6), V(1, -6)
22 unit² is the area of trapezoid .
In arithmetic, what is a polygon?
A polygon is a closed, one-dimensional, flat or planar structure that is circumscribed by straight sides. There are no curves on its sides. Polygonal edges are another name for the sides of a polygon. A polygon's vertices (or corners) are the places where two sides converge.
this is trapezoid .
area of trapezoid = 1/2 * sum of parallel side * height
= 1/2 * (3 + 8 ) * 4
= 22 unit²
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Find the line parallel to y=5x+3 that includes the point (-1,6)
Write in y-y1=m(x-x1)
Answer:
y=5x-6
Step-by-step explanation:
PLEASE HELP PLEASE HELP FAST PLEASEEEE
The number of outcomes that are in the sample space = 20
The number of outcomes that are in the event = 5
How to calculate the probability of the selected events?To calculate the probability of an event, the formula that should be used is given as follows;
Probability = possible event/sample space.
possible outcome = 5
sample space = 20
Probability = 5/20 = 1/4
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(-4,-6) and (8,9). Slope
slope= y2 - y1/ x2 - x1 ( take (-4, -6) as 1 and (8,9) as 2 where 9 and -6 are y2 and y1 respectively and 8 and -4 as x2 and x1 respectively)
- slope = 9 - (-6) / 8 - (-4)= 9 + 6/ 8 + 4
- slope = 15 / 12 (simplify)
- slope = 5/ 4
financial planner puts $3,500 into a college savings plan that pays 7.5% simple interest annually. If no additional deposits are made into the savings plan, how much interest is accumulated at the end of 5 years? A. $262.50 |B. $1,312.50* C. $ 2,625.00 D. $4,812.50
Thus, the amount of simple interest accumulated on the given principal of $3500 after 5 years is $1312.50.
Define about the term simple interest:Simple interest (SI) is calculated as a percentage added to the principle amount deposited or borrowed for a given period of time. SI is typically expressed as years.
As a result, it represents the real expense incurred on the main sum. The accrued interest is not included in this. SI and CI are very dissimilar to one another. CI is the interest rate applied to both the principal amount and the total amount of unpaid interest.Given data:
Principal P = $3,500Simple Interest rate R = 7.5%Time T = 5 yearsSimple interest formula:
SI = PRT / 100
SI = 3500*7.5*5 / 100
SI = 1312.5
Now,
Amount = principal + simple interest
Amount = 3500 + 1312.5
Amount = $4812.50
Thus, the amount of simple interest accumulated on the given principal of $3500 after 5 years is $1312.50.
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hello! i need help thru out 10-12!!!
what u need to do : decide if each figure is symmetric. then, tell how much lines each figure has
THANKS!!
How can 25% of one item be different from 25% of another? Explain
The difference between the two items are depends on sample size, the method of counting, or the criteria for classification can all impact the percentage calculation.
Percentage is a measure of the proportion of one value to another expressed as a fraction of 100. For example, if there are 100 apples, and 25 of them are red, then the percentage of red apples is 25%. Similarly, if there are 200 bananas, and 50 of them are ripe, then the percentage of ripe bananas is also 25%.
However, the context in which these percentages are calculated can be different. For instance, the way in which the 25% of red apples was calculated could be different from how the 25% of ripe bananas was calculated.
To illustrate this, let's consider an example. Suppose there are two cities, A and B, with populations of 10,000 and 5,000, respectively. In city A, 2,500 people have blue eyes, while in city B, 1,250 people have blue eyes. At first glance, it may seem that the percentage of people with blue eyes is the same in both cities, at 25%.
However, if we look closer, we can see that the actual number of people with blue eyes is different between the two cities. City A has twice as many people with blue eyes as city B, even though the percentage is the same.
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Bret bought his family lunch. Before tax, the bill came to $42. The sales tax was 6% and Bret tipped the waitress 20% before tax was added. How much money did Bret spend?
Answer: Bret spent $52.92 on the lunch, including tax and tip.
Step-by-step explanation:
Given:
The bill before tax = $42
Sales tax = 6%
Tip = 20% before tax
To find:The total amount of money Bret spent
Solution: Calculate the sales tax:
Sales tax = 0.06 * $42 = $2.52
Calculate the total bill, including tax:
Total bill = $42 + $2.52 = $44.52
Calculate the bill before tax, based on which the tip is calculated:
Bill before tax = $44.52 - $2.52 = $42
Calculate the tip amount:
Tip = 0.2 * $42 = $8.40
Calculate the total amount spent by Bret:
Total spent = $44.52 + $8.40 = $52.92
Therefore, Bret spent $52.92 on the lunch, including tax and tip.
A circle has a center of (1, -1). The circumference passes through (1, 2). Find the length of the circumference of the circle. Use 3.14 for pi. Then, Find the area of the circle.
Answer:
The radius of the circle is 3, so
Circumference = 2(3)π = 6π = 18.84
Area = π(3^2) = 9π = 28.26
3 Marcus has 500 g of flour. He uses 200g to bake
bread and 120g to make biscuits.
Work out the percentage of the flour:
A he uses for bread
B he uses for biscuits
C he does not use
Answer:
40% , 24% , 36%
Step-by-step explanation:
first express each as a fraction then multiply the fraction by 100%
A
[tex]\frac{200}{500}[/tex] × 100% = 0.4 × 100% = 40% used for bread
B
[tex]\frac{120}{500}[/tex] × 100% = 0.24 × 100% = 24% used for biscuits
C
percentage not used = 100% - (40 + 24)% = 100% - 64% = 36%
the scatter graph shows the maximum temperature and the number of hours of sunshine in 13
The coordinates of the point which is an outlier would be ( 14, 13).
The correlation between the 13 British towns is Linear.
The number of hours of sunshine for the British town with the maximum of 17.4 degrees Celsius is 13 hours of sunshine.
How to find the hours of sunshine ?The coordinates of the outlier would be ( 14, 13). This is because, that point on the graph is far from the other points and does not follow their correlation.
The rest of the towns seem to be increasing in the same direction so they are linear.
The number of hours of sunshine in the British town with the maximum temperature of 17.4 degrees Celsius, based on the line of best fit drawn, would be 13 hours of sunshine.
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Full question is:
The scatter graph shows the maximum temperature and the numbers of hours of sunshine in 13 British towns in one day.
A line of best fit has also been drawn.
One of the points in an outliner.
a) Write down the coordinates of this point. (1)
b) For all the other points write down the type of correlation in just one word. (1)
On the same day, in another British town, the maximum temperature was 17.4C.
c) Estimate the number of hours of sunshine in this town on this day. (2)
Find the vectors that join the center of a clock to the hours 1:00, 2:00, and 3:00. Assume the clock is circular with a radius of 1 unit.
at
1:00
2:00
3:00
The vectors that join the center of a clock to the hours :
At 1:00: (cos(π/6), sin(π/6)) = (√3/2, 1/2)
At 2:00: (cos(π/3), sin(π/3)) = (1/2, √3/2)
At 3:00: (cos(π/2), sin(π/2)) = (0, 1)
What is Vector?
A vector is a object that has both magnitude (size) and direction. In other words, a vector is a quantity that can be represented by an arrow or line segment, where the length of the arrow corresponds to the magnitude of the vector.
To find the vectors that join the center of a clock with radius 1 unit to the hours 1:00, 2:00, and 3:00, we can use basic trigonometry.
First, we can find the angle (in radians) between the 12:00 position and each of the desired hour positions. Since there are 12 hours on a clock and the circle has a circumference of 2πr = 2π(1) = 2π, the angle between each hour mark is:
2π/12 = π/6 radians
Therefore, the angles between the center of the clock and the hour marks are:
At 1:00, the angle is π/6 radians clockwise from the 12:00 position.
At 2:00, the angle is 2π/6 = π/3 radians clockwise from the 12:00 position.
At 3:00, the angle is 3π/6 = π/2 radians clockwise from the 12:00 position.
Next, we can use the cosine and sine functions to find the x and y components of each vector. The x-component of each vector is given by the radius times the cosine of the angle, and the y-component is given by the radius times the sine of the angle.
Therefore, the vectors that join the center of the clock to the hours 1:00, 2:00, and 3:00 are:
At 1:00: (cos(π/6), sin(π/6)) = (√3/2, 1/2)
At 2:00: (cos(π/3), sin(π/3)) = (1/2, √3/2)
At 3:00: (cos(π/2), sin(π/2)) = (0, 1)
Note that these vectors are unit vectors, meaning that they have a length of 1 unit.
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A random sample of 100 middle schoolers were asked about their favorite sport. The following data was collected from the students.
Sport Basketball Baseball Soccer Tennis
Number of Students 17 12 27 44
Which of the following graphs correctly displays the data?
histogram with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled basketball going to a value of 17, the second bar labeled baseball going to a value of 12, the third bar labeled soccer going to a value of 27, and the fourth bar labeled tennis going to a value of 44
histogram with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled baseball going to a value of 17, the second bar labeled basketball going to a value of 12, the third bar labeled tennis going to a value of 27, and the fourth bar labeled soccer going to a value of 44
bar graph with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled basketball going to a value of 17, the second bar labeled baseball going to a value of 12, the third bar labeled soccer going to a value of 27, and the fourth bar labeled tennis going to a value of 44
bar graph with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled baseball going to a value of 17, the second bar labeled basketball going to a value of 12, the third bar labeled tennis going to a value of 27, and the fourth bar labeled soccer going to a value of 44
The graph that correctly displays the data is this: C. bar graph with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled basketball going to a value of 17, the second bar labeled baseball going to a value of 12, the third bar labeled soccer going to a value of 27, and the fourth bar labeled tennis going to a value of 44.
How to obtain the correct graphA graph plots values to show the relationship between two variables often depicted by the x and y axes. The correct graph to display this data is a bar graph with the title "Favorite Sport" and the x-axis labeled "Sport" and the y-axis labeled "Number of Students."
The first bar should be labeled "Basketball" and go to a value of 17, the second bar should be labeled "Baseball" and go to a value of 12, the third bar should be labeled "Soccer" and go to a value of 27, and the fourth bar should be labeled "Tennis" and go to a value of 44.
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jim tosses a fair coin to decide whether his next vacation will be in hawaii or alaska. if it is a head, jim visits hawaii, or else he decides to visit alaska. if in hawaii, jim surfs during the vacation with a probability of 0.9. if in alaska, jim is going to surf in the ocean with probability 0.1 only. given that we know that jim went on surf- ing during the vacation, what is the conditional probability that his vacation was in alaska?
the conditional probability that Jim's vacation was in Alaska given that we know he went surfing during the vacation is 0.1, or 10%.
Let A be the event that Jim's vacation was in Alaska, and let S be the event that Jim went surfing during the vacation. We want to find P(A|S), the conditional probability that Jim's vacation was in Alaska given that we know he went surfing during the vacation.
By Bayes' theorem, we have:
P(A|S) = P(S|A) * P(A) / P(S)
We can calculate each term as follows:
P(S|A) = 0.1: the probability that Jim went surfing during the vacation given that he was in Alaska.
P(A) = 0.5: the probability that Jim's vacation was in Alaska, since he tosses a fair coin to decide between Hawaii and Alaska.
P(S) = P(S|A) * P(A) + P(S|H) * P(H) = 0.1 * 0.5 + 0.9 * 0.5 = 0.5: the total probability of Jim going surfing during the vacation, since he either went surfing in Alaska with probability 0.1 or went surfing in Hawaii with probability 0.9.
Therefore, we have:
P(A|S) = P(S|A) * P(A) / P(S) = 0.1 * 0.5 / 0.5 = 0.1
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1870003# gave an answer about Sean and his aquarium in ratios. He had 7 guppies to 12 cichlids which came out to be 7:12 and 4 tetras to 11 catfishes in ratios it is 4:11 and lastly he had a ratio of corydoras catfishes 9 to the total number of fishes is how many ratio to the total number of fish? I had 11:34 is that right?
The simplified ratio of corydoras catfishes to the total number of fish is 9:34, which is equivalent to 0.26:1 or approximately 1:3.88.
How to find the the ratioTo find the ratio of corydoras catfishes to the total number of fish, we need to add up the number of corydoras catfishes to the total number of fish, and express the ratio as a simplified fraction.
The total number of fish is 7 + 12 + 4 + 11 = 34.
The ratio of corydoras catfishes to the total number of fish is 9:34.
To simplify this ratio, we can divide both sides by the greatest common factor, which is 1 in this case.
So the simplified ratio of corydoras catfishes to the total number of fish is 9:34, which is equivalent to 0.26:1 or approximately 1:3.88.
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Question 2
Mike deposited $3,000 in the first year of a retirement account, and then increased the deposits by $300 each year. The account earned 8.35%. What was the account value after forty years?
The account value after forty years is approximately $489,074,140.57.
What is formula for the future value of an annuity?To calculate the account value after forty years, we need to use the formula for the future value of an annuity:
[tex]FV = P * [(1 + r)^n - 1] / r[/tex]
where FV is the future value, P is the annual payment, r is the interest rate, and n is the number of periods.
In this case, we have:
P = $3,000 in year 1, and then $3,300 in year 2, $3,600 in year 3, and so on
r = 8.35% = 0.0835 (assuming the interest rate is compounded annually)
n = 40 years
To compute the future worth of the annuity, we really want to ascertain the aggregate sum of installments over the 40 years. This should be possible involving the equation for the amount of a number-crunching series:
S = n/2 * [2a + (n-1)d]
where S is the sum, a is the first term, d is the common difference, and n is the number of terms.
In this case, we have:
a = $3,000
d = $300
n = 40
Plugging these values into the formula, we get:
S = 40/2 * [2($3,000) + (40-1)($300)] = $2,340,000
Thus, the aggregate sum of installments more than 40 years is $2,340,000.
We can now enter these figures into the formula for annuity future value:
[tex]FV = P * [(1 + r)^n - 1] / r[/tex]
[tex]FV = $2,340,000 * [(1 + 0.0835)^{40} - 1] / 0.0835[/tex]
FV = $2,340,000 * 209.251
FV = $489,074,140.57
Consequently, after forty years, the account's value is approximately $489,074,140.57.
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A recipe calls for 23\frac{2}{3}
3
2
cup of brown sugar. Marilyn is making 5 batches. How many cups of brown sugar should Marilyn use?
Marilyn needs 3 and 1/3 cups of brown sugar to make 5 batches of the recipe.
To find the total amount of brown sugar Marilyn needs, we need to multiply the amount required for one batch by the number of batches.
One batch requires 2/3 cup of brown sugar. To find the amount required for five batches, we can multiply 2/3 by 5.
2/3 * 5 = 10/3
So Marilyn needs 10/3 cups of brown sugar to make 5 batches of the recipe. However, it's usually easier to work with mixed numbers or whole numbers.
To convert the fraction 10/3 to a mixed number, we divide the numerator (10) by the denominator (3) and get a quotient of 3 with a remainder of 1. So:
10/3 = 3 1/3
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PLEASE HELP MY MOMS GONNA KICK MT BUTT AND I JUST DONT GET THIS!!!Add.
(2h + 8) + (9h² + 2h)
find x. provide an explanation
Applying the inscribed angle theorem, the value of x is calculated as: 47 degrees.
How to Apply the Inscribed Angle Theorem?If an inscribed angle intercepts an arc in a circle, according to the inscribed angle theorem, we have:
measure of inscribed angle = 1/2(measure of intercepted arc) or 1/2(measure of central angle)
x is an inscribed angle, while 94 degrees is a central angle. Therefore, we have:
x = 1/2(94)
x = 47 degrees.
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If the dimensions of the following cylinder are tripled, what will be the volume of the new cylinder?
15,260.4 cm 3
61,041.6 cm 3
183,124.8 cm 3
45,781.2 cm 3
Radius 12cm Height 15cm
Answer:
C) 183,124.8 cm^3.Step-by-step explanation:
The volume of a cylinder can be calculated using the formula V = πr^2h, where V is the volume, r is the radius, and h is the height.
The current volume of the cylinder is:
V = π(12cm)^2(15cm)
V = π(144cm^2)(15cm)
V = 2160π cm^3
If the dimensions of the cylinder are tripled, then the new cylinder will have a radius of 3(12cm) = 36cm and a height of 3(15cm) = 45cm.
The new volume of the cylinder is:
V = π(36cm)^2(45cm)
V = π(1296cm^2)(45cm)
V = 58320π cm^3
Simplifying the expression, we get:
V ≈ 183,124.8 cm^3
Therefore, the volume of the new cylinder, when the dimensions are tripled, is approximately 183,124.8 cm^3.
The answer is C) 183,124.8 cm^3.
Hi,
-The correct answer should be "option 4," 45,781.2 cm ^3.
Let me know if my answer is wrong or not what you were looking for because I would like to help all I can.
If you have any questions let me know and I may be able to help.
I hope that my answer helped you out. :)
Here is the correct figure if anybody needs it. ⇅
water leaks from a tank at a rate of 2 5t liters/hour, where t is the number of hours after 7 am. how much water is lost between 9 and 11 am?
the total amount of water lost between 9 and 11 am is 5 liters.
To find out how much water is lost between 9 and 11 am, we need to calculate the total amount of water that leaks out during that time period.
First, we need to find the number of hours between 7 am and 9 am, which is 2 hours. Similarly, the number of hours between 7 am and 11 am is 4 hours.
Next, we can use the given rate of water leakage to calculate the amount of water lost during each of these time periods:
Amount of water lost between 7 am and 9 am:
2.5 liters/hour × 2 hours = 5 liters
Amount of water lost between 7 am and 11 am:
2.5 liters/hour × 4 hours = 10 liters
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2. Given: MNOP is a rectangle.
Show: The diagonals bisect each other, and the diagonals are congruent.
M
a
AC and BD are the diagonals of the MNOP, the diagonals of the rectangle MNOP bisect each other and are congruent.
What is a rectangle and its properties?
A rectangle and a rectangle are quadrilaterals that share the following properties: Opposite sides are equal. Two diagonals are the same length. It has two class 2 reflection symmetries and a rotational symmetry (through 180°). To show that the diagonals of a rectangle bisect each other and are congruent, we can use the following proof:
Proof:
Let MNOP be a rectangle whose diagonal MO and diagonal NP intersect at Q.
First we show that the diagonals bisect each other. Since MNOP is a rectangle, we know that opposite sides are parallel and congruent. Therefore, we can draw segment MP and segment NO which are both parallel and congruent to each other.
Now consider the triangle MON. Since segment MP is parallel to segment NO, we know that angles MNO and MON are alternate interior angles and are congruent. Similarly, the angles NMO and ONM are also congruent. Therefore, triangle MON is an isosceles triangle with legs MO and NO. This means that the height drawn from Q to the side MN (which is the perpendicular bisector of MO and NO) bisects MO and NO. Similarly, the height drawn from Q to the side OP bisects OP. Therefore we have shown that the diagonals of a rectangle bisect each other.
Next, we show that the diagonals are congruent. Since MNOP is a rectangle, we know that opposite sides are parallel and congruent. Therefore, MP is compatible with NO and MO is compatible with NP. Using the fact that the diagonals bisect each other, we can write:
MQ = QO (because the height drawn by Q to the side MN divides MO and NO)
and
NQ = QP (because the height drawn from Q to the side OP divides NP and MO)
Combining these two equations, we get:
MQ + NQ = QO + QP
But we also know that MO is NP-consistent, so we can substitute:
MQ+ NQ = MO + MO
Simplification:
MQ + NQ = 2MO
Therefore, we have shown that the diagonals of a rectangle are congruent. Therefore, we have shown that the diagonals of a rectangle bisect each other and are congruent as necessary.
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what is 55/63 in simplest form
55/63 is already in its simplified form.
To simplify 55/63, we can divide both the numerator and denominator by their greatest common factor (GCF). To find the GCF of 55 and 63, we can use prime factorization:
55 = 5 × 11
63 = 3 × 3 × 7
The common factors of 55 and 63 are 1, so the GCF is 1. We can divide both the numerator and denominator by 1:
55/1/63/1
Therefore, 55/63 in simplest form is 55/63.
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I need some help please
Step-by-step explanation:
'3' is greater than 0 so we use the second portion of f(x)
f(3) = x+1
= 3 + 1 = 4
Your friend in college decides to purchase textbooks using his credit card, which has an APR
(Annual Percentage Rate) of 12.5% compounded continuously. He charges $500 for the
textbooks. Without making any payments, after how many years will his credit card balance be
$1360? Round your answer to the nearest year.
The time that it will take for the balance to be of $1360 is given as follows:
8 years.
How to model continuous compounding?The balance of an account after t years, using continuous compounding, is modeled by the equation presented as follows:
A(t) = A(0)e^(kt).
In which:
A(0) is the initial amount.k is the continuous compounding rates.The parameters for this problem are given as follows:
A(t) = 1360, A(0) = 500, k = 0.125.
Hence the time is obtained as follows:
500e^(0.125t) = 1360
e^(0.125t) = 1360/500
0.125t = ln(1360/500)
t = ln(1360/500)/0.125
t = 8 years.
More can be learned about continuous compounding at brainly.com/question/7513822
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GIVING 50 POINTS, BRAINLYEST, 5 STARS, AND THANKS IF YOU ANSWER CORRECTLY!!!
A coin is flipped at the start of every game to determine if Team A (heads) or Team B (tails) will get the ball first.
Part A: Find the theoretical probability of a fair coin landing on heads. (2 points)
Part B: Flip a coin 15 times and record the frequency of each outcome. (4 points)
Part C: Determine the experimental probability of landing on heads. (4 points)
Part D: Compare the theoretical and experimental probabilities. Explain your answer. (2 points)
Answer:
Part A: 1/2 or 0.5
Part B: heads is 8, tails is 7.
Part C: 8/15 or 0.533.
Part D: The theoretical and experimental probabilities are close but not exactly the same. This is because the theoretical probability is based on an ideal situation where the coin is fair, and the outcomes are equally likely. The experimental probability is based on actual data that may vary due to chance or other factors. The more trials we perform, the closer the experimental probability will get to the theoretical probability. It's like when you practice a skill and get better at it over time, but you still make mistakes sometimes.
Step-by-step explanation:
Part A: The theoretical probability of a fair coin landing on heads is 1/2 or 0.5. This is because there are two possible outcomes (heads or tails) and only one favorable outcome (heads). This is also the same probability of me winning the lottery, finding a unicorn, or getting a date.
\(∘-∘)/ <-------- single pringle
Part B: I flipped a coin 15 times and got the following results:
H T H H T T H H T H T H T T H
or (in a more orderly fashion)
HHHHHHHH
TTTTTTT
The frequency of heads is 8 and the frequency of tails is 7. This means that I was slightly luckier than average, but not enough to make a difference. Maybe I should have used a different coin, or a different hand, or a different day.
Part C: The experimental probability of landing on heads is the ratio of the frequency of heads to the total number of trials. In this case, it is 8/15 or 0.533. This is slightly higher than the theoretical probability, but still within the margin of error. It's like when you order a pizza and get one extra slice, but it's the one with pineapple.
Part D: The theoretical and experimental probabilities are close but not exactly the same. This is because the theoretical probability is based on an ideal situation where the coin is fair, and the outcomes are equally likely. The experimental probability is based on actual data that may vary due to chance or other factors. The more trials we perform, the closer the experimental probability will get to the theoretical probability. It's like when you practice a skill and get better at it over time, but you still make mistakes sometimes.
✧☆*: .｡. That's all folks, have fun with math! (✧ω✧) .｡.:*☆✧