On solving the provided question we cans ay that the half life of the given exponential growth radioactive isotope will be 3.2894067399 years.
What is exponential growth?The process of quantity growth over time is called exponential growth. occurs when the rate at which a quantity changes instantaneously with time is proportionate to the quantity itself. A data pattern that shows bigger increases with time is known as exponential growth. Compound interest yields exponential rewards in the world of finance. Savings accounts with compound interest sometimes see exponential growth. characterized by an extremely fast exponential growth rate rise (in size or extent). exponentially. The exponential function has the formula f(x)=abx where a and b are positive real values. Sketch exponential functions using the app below for different values of a and b. Describe verbally how modifying a and b changes the graph's form.
Here, Element X starts with 490 grams
After 1 year we have (490 X 0.81 grams) or 396.9 grams
Now, We can solve for half-life by this equation:
Half life = (time X log 2) / log (beginning amount / ending amount)
Half-life = (1 year X 0.30102999566) / log (490 / 396.9)
Half life = (1 year X 0.30102999566) / log (1.2345679012 )
Half life = (0.30102999566) / 0.091514981109
Half-Life = 3.2894067399 years
Thus, the half life of the given exponential growth radioactive isotope will be 3.2894067399 years.
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Manjit bought a house. The value of her house went up by 5% in the first year. In the second year, the value went up by 2%. At the end of the two years her house was worth £171360.
What was the total percentage increase?
Work out the amount Manjit paid for her house
Answer:
The percentage increase is 7%.
She paid £160150 for her house.
Step-by-step explanation:
first year : increase 5%
second year : increase 2%
after 2 years : £171360
100%+5%+2%= 107%
107%= £171360
1%= £171360÷107
= £1601.5 (to 5 s.f.)
100%= £1601.5×100
= £160150
Lucy made 247 for 13 hours of work. At the same rate, how much would she make for 9 hours of work?
Answer: $171
Step-by-step explanation:
$247 divided by 13 hrs = $19/hr
$19/hr times 9 hrs = $171
The speed of sound is 3.43 x 10² meters per second. How far does sound travel in 3.3 x 10-5 second? Write your answer in
scientific notation. Round to the nearest hundredth, if necessary.
Distance: meters
The distance will be 1.1319 × 10⁻¹ meters .
Speed of the sound = 3.43 x 10² meters per second
Time to calculate the distance traveled = 3.3 x 10-5 seconds
Since,
Distance = Speed x Time
Using the values we get:
Distance = 3.43 x 10² * 3.3 x 10-5
Distance = 11.319 × 10⁻³ meters
Since the calculators show the final answer is scientific notation, the above answer in scientific notation would be:
Distance = 1.1319 × 10⁻¹ meters
Hence , the distance will be 1.1319 × 10⁻¹ meters .
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Mr. Winston was selling toilet paper at Ikea. He sold 281 toilet papers in one hour. How much toilet papers did Mr.Winston sell in 5 hours?
Answer:
і мой тоєе если что какти зн
Answer:
In 5 hours he sold around 1405 toilet papers at ikea
a quiz consists of 10 multiple-choice questions, each with 6 possible answers. for someone who makes random guesses for all of the answers, find the probability of passing if the minimum passing grade is 50 %.
The probability of passing a 10-question multiple-choice quiz by random guessing is about 2.4%.
How to find the probabilityA quiz consists of 10 multiple-choice questions, each with 6 possible answers. for someone who makes random guesses for all of the answers, find the probability of passing if the minimum passing grade is 50 %.
The probability of a random guess being correct for a single multiple-choice question with 6 options is 1/6, or approximately 0.17.
To find the probability of passing the quiz with a minimum passing grade of 50%, we need to calculate the probability of getting 5 or more correct answers out of 10.
This can be calculated as the sum of the probabilities of getting exactly 5, 6, 7, 8, 9, or 10 correct answers:
P(pass) = P(5) + P(6) + P(7) + P(8) + P(9) + P(10)
where P(x) is the probability of getting exactly x correct answers.
This can be calculated using the binomial distribution and its cumulative distribution function (CDF). The result is approximately 0.024, or 2.4%.
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A passenger train and a freight train leave cities 260 mi apart and travel toward each other. The passenger train is traveling
15 mph faster than the freight train. Find the speed of each train if they pass each other after 4 hr.
Step-by-step explanation:
x = speed of the passenger train
x - 15 = speed of the freight train
remember, the passenger train is traveling 15 mph faster than the freight train. that also means the freight train travels 15 mph slower than the passenger train.
we could define the variable also the other way around (x = freight train, x + 15 = passenger train).
speed = distance/time period
distance = speed × time period
so,
x×4 + (x - 15)×4 = 260
because when both trains meet somewhere in the middle, it means that the sum of both of their ways traveled is the whole distance between both cities : 260 miles.
4x + 4x - 60 = 260
8x = 320
x = 320/8 = 40 mph
so, the passenger train traveled at 40 mph.
the freight train traveled at 40-15 = 25 mph.
A. Neither
B. SSS
C. SAS
Choose SSS,
SAS, or neither
to compare these
two triangles.
No Criteria used to compare the Triangles.
What is Congruence?Two figures are said to be "congruent" if they can be positioned perfectly over one another. Both of the bread slices are the same size and shape when stacked one on top of the other. Congruent refers to things that are exactly the same size and shape.
Given:
As from the Figure in two Triangles ACB and ECD.
<ACB = <ECD (Vertically Opposite Angle)
AC= CE (Given)
But we do not have any third pair for make it Congruent.
Thus, None of the Rule is used to prove Congruency in Triangles.
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Answer:
Its Neither
Step-by-step explanation:
A savings account gathers compound interest at a rate of 7% per annum. The amount of money in the account over the first two years is shown below. Copy and complete the expression below for the amount of money in the account after n years
The equation that gives the balance of the account after n years is given as follows:
[tex]A(t) = P(1.07)^t[/tex]
In which P is the initial amount in the account.
What is compound interest?The amount of money earned, in compound interest, after t years, is given by:
[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]
In which:
P is the principal, which is the value of deposit/loan/....r is the interest rate, as a decimal value.n is the number of times that interest is compounded per year, annually n = 1, semi-annually n = 2, quarterly n = 4, monthly n = 12.The parameters for the function in thisp roblem are given as follows:
r = 0.07, n = 1.
Hence the function is given as follows:
[tex]A(t) = P(1.07)^t[/tex]
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identify the circumstances in which the median rather than the mean is the preferred measure of central tendency. check all that apply.
The circumstances in which the median rather than the mean is the preferred measure of central tendency is when there is a skewed distribution (a few extreme scores), an open-ended distribution or undetermined scores.
What is central tendency?Central tendency is defined as the summative measure that tries to describe the entire set of data with a single value representing the mean or center of the distribution.
A skewed distribution occurs when one tail is longer than the other.
Therefore, in this type of distribution, the median should be chosen as the preferred measure of central tendency.
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find the number of ways the digits 0,1,2 and 3 can be permuted to give rise to a number greater than 2000
The number of ways the digits 0,1,2 and 3 can be permuted to give rise to a number greater than 2000 is 9.
What is permutation?A permutation is a word that describes the number of ways things can be ordered or arranged.
Given are numbers, 0,1, 2, 3
We asked for numbers greater than 2000, so those numbers will start either from 2 or 3.
2 _ _ _ = 3! = 6
3 _ _ _ = 3!/2! = 3
Hence, total possible ways are 6+3 = 9
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Given sin O
= -√35/6 and angle is in Quadrant IV, what is the exact value of
cos O in simplest form? Simplify all radicals if needed.
The value of trigonometric function be [tex]$\cos (\theta)=-\frac{\sqrt{35}}{6}$[/tex].
What is meant by trigonometric function?A subfield of mathematics called trigonometry is concerned with the study of triangles. It is sometimes known by the colloquial term "trig." In trigonometry, mathematicians look at how triangles' sides and angles relate to one another.
The sine, cosine, and tangent are the trigonometric functions that are employed in modern mathematics the most frequently.
There are many applications for trigonometry and its functions in daily life. For instance, it is employed in astronomy to gauge the distances between nearby stars, in geography to gauge the separations between landmarks, and in the satellite navigation system.
Let the value of sin [tex]\theta[/tex] be -√35/6.
The value of trigonometric function: [tex]$\cos (\theta)$[/tex]
[tex]$=-\frac{\sqrt{35}}{6}$$[/tex]
[tex]$\cos (\theta)=-\frac{\sqrt{35}}{6}$[/tex]
Therefore, the value of trigonometric function be [tex]$\cos (\theta)=-\frac{\sqrt{35}}{6}$[/tex].
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santa clara county, ca, has approximately 27,873 japanese-americans. what percentage of the community is under age 35?
The percentage of Japanese-Americans under 35 in Santa Clara County, CA is approximately 11.3%.
Santa Clara County, CA is home to approximately 27,873 Japanese-Americans. To determine what percentage of this population is under age 35, it is necessary to first calculate the total number of Japanese-Americans under 35. To do this, we can subtract the estimated number of Japanese-Americans over age 35 from the total population of Japanese-Americans. We can then divide this number by the total population of Japanese-Americans to find the percentage of Japanese-Americans under age 35. In Santa Clara County, CA, the estimated number of Japanese-Americans over age 35 is 24,672, and the total population of Japanese-Americans is 27,873. Subtracting 24,672 from 27,873 yields 3,201 Japanese-Americans under age 35. We can then divide 3,201 by 27,873 to get a percentage of 11.3%. Therefore, approximately 11.3% of the Japanese-American population in Santa Clara County, CA is under age 35.
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Helen and Reid are walking to their classes at Cedarburg College. Helen comes from her dorm room, walking at a speed of 4 miles per hour down a straight path. Reid comes from the gymnasium on the other end of campus, moving up the same path at 3 miles per hour. If they start out 3 miles apart, how long will it be before they meet?
The time it will take for Helen and Reid to meet is given as follows:
3/7 of an hour = 26 minutes.
What is the relation between velocity, distance and time?Velocity is distance divided by time, hence the following equation is built to model the relationship between these variables:
v = d/t.
The parameters for this problem are given as follows:
Distance of 3 miles.Relative velocity of 7 miles, as they are moving in opposite directions, and 4 + 3 = 7.Hence the time is obtained as follows:
7 = 3/t
7t = 3
t = 3/7 of an hour = 26 minutes.
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Triangle ABC with points A (9,1) B (2,7) C(-2,-5) was translated 3 units left, 2 units down and then was reflected across the line y = x. What is the image point of C?
The point of C is, (- 7, - 5).
What is mean by Triangle?A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
Given that;
Triangle ABC with points A (9,1) B (2,7) C(-2,-5) was translated 3 units left, 2 units down and then was reflected across the line y = x.
Now, Triangle ABC with points A (9,1) B (2,7) C(-2,-5) was translated 3 units left, 2 units down.
Hence, The point of C is,
⇒ C = (- 2, -5) + (- 3, - 2)
⇒ C = (- 5, - 7)
Since, It was reflected across the line y = x.
Hence, The point of C is,
⇒ C = (- 7, - 5)
Thus, The point of C is, (- 7, - 5).
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if a state wants each of its license plates to contain any 7 digits, how many different license plates are possible?
There are 10 million possible 7-digit license plates that a state can issue.
This is because each digit position can be filled with any of the 10 digits (0-9), giving us 10 options for each digit position.
By multiplying these 10 options for each of the 7-digit positions,
we get 10 * 10 * 10 * 10 * 10 * 10 * 10 = 10^7.
This amount is sufficient to guarantee that every citizen can have a distinctive license plate number.
It is significant to note that some restrictions, such as those that constitute a profane word or imply an official status, may prevent the issuance of particular license plate numbers.
So there are 10 million possible 7-digit license plates that a state can issue.
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hank owns a fruit stall he sells 11 apple and 5 oranges for 2.71. one apple costs 16p how much does one orange cost?
Answer:
11*0.16=1.76
2.71-1.76=0.95
0.95/5=0.19
One orange costs 0.19
Step-by-step explanation:
2. A worker is tiling the floor of a rectangular room that is 12 feet by 15 feet. The tiles
are square with side lengths 11
3 feet. How many tiles are needed to cover the entire
floor? Show your reasoning.
165 tiles are needed to cover the entire floor of the room.
First, we need to find out the area of the room in square feet. We do this by multiplying the length and width of the room:
12 feet x 15 feet = 180 square feet
Next, we need to find out the area of one tile in square feet. We do this by squaring the length of one side of the tile:
11 3/11 feet x 11 3/11 feet = 128/121 square feet
Now, we can divide the total area of the room by the area of one tile to find out how many tiles are needed:
180 square feet / (128/121 square feet) = 180 x 121/128 = 165 tiles
So, 165 tiles are needed to cover the entire floor of the room.
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Find the missing dimension. Use the scale 2: 5.
2:5
L
Model
Actual
2. Depth: 10 km
3. Length: 5 in.
Depth: _5 km
Length: in.
4. Length:
ft
Length: 24 ft
5. Diameter:
m
Diameter: 32. 5 m
The model on the fifth row has a diameter of 32.5 meters, hence the actual diameter is 32.55 = <<32.55=162.5>>162.5 meters.
What are dimensions?The minimal number of coordinates required to specify each point within a mathematical space (or object) is known as the dimension in physics and mathematics.
Because only one coordinate is required to identify a point on a line, such as a point at 5 on a number line, a line is said to have one dimension (1D).
Because two coordinates are necessary to identify a point on a surface, such as the perimeter of a sphere or cylinder, it is referred to as having a dimension of two (2D).
For instance, a point on the surface of a sphere requires both a latitude and a longitude to be located.
So, we can use a scale of 2:5 as a conversion factor to identify the table's missing dimensions.
For instance, the model's length in the second row is 2 inches, but the real length is 5 inches.
This implies that the model's 1 inch corresponds to the actual object's 5 inches.
The actual depth is 10 5 = 50 km because the model's depth is 10 km.
Since the model's length is not specified in the fourth row, we are unable to determine its true length.
Therefore, the model on the fifth row has a diameter of 32.5 meters, hence the actual diameter is 32.55 = <<32.55=162.5>>162.5 meters.
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Correct question:
Find the missing dimension. use the scale 2: 5.
2:5
l
model
actual
2. depth: 10 km
3. length: 5 in.
depth: _5 km
length: in.
4. length:
ft
length: 24 ft
5. diameter:
m
diameter: 32.5 m
an arithmetic sequence with first term 1 and common difference not equal to 0 has second, tenth, and thirty-fourth terms that form a geometric sequence. what is the thirty-fourth term of the arithmetic sequence?
The thirty-fourth term of the arithmetic sequence is the thirty-second term plus the common difference, which is not equal to 0.
The thirty-fourth term of the arithmetic sequence is calculated by adding the common difference to the thirty-second term. The common difference is the amount by which each successive term increases or decreases. As the common difference is not equal to 0, the thirty-fourth term is not the same as the tenth or second terms. The second, tenth, and thirty-fourth terms form a geometric sequence, which means that the ratio between any two successive terms is always the same. This ratio is determined by the common difference of the arithmetic sequence, and the thirty-fourth term can be calculated by adding the common difference to the thirty-second term.
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mr . france wants to have a party they want to celebrate . out of all the students in the class , 5 wants a ice cream part , 7 want a movie party , 10 want a costume party , and the rest are undecided , if 20% want a ice cream party , how many students are in the class
Answer:
there is 27 percent In the class
Step-by-step explanation:
you need black bla bla times bla = ur racist
A ball is dropped from 2 meters and rises up by 75%
When a ball is droped from 2m heights and rises by 75%, then the height of ball after forth bounce is equals to 0.632 meters.
If an object is thrown from high and has a bouncing feature, each bouncing is less than the initial height until it stops. Each bounce reduces the growth rate until it reaches zero. In order to calculate the height of each bounce, so we can estimate what percentage the object will reach after each bounce. If we get the percentage of each bounce, we can easily determine the height of each bounce. We have, a ball is droped from 2 meters and bounce up to 75%. That is height of first bounce is determined by using percentage, height is 2 m × 75% = 2 m×0.75 = 1.5 m
In second bounce, height is 1.5 m × 75%
= 1.5 m×0.75 = 1.12 m
In third bounce, 1.12 m× 75%
= 1.12 m×0.75 = 0.843 m
In forth bounce, height is 0.843× 75%
= 0.843× 0.75 = 0.632 m
The height the ball reaches on its forth bounce is 0.632 m.
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Complete question :
A ball is dropped from a height of 2 meters and rises up by 75% of its height on each bounce. How high would the forth bounce be?
Solve for x. Enter the solutions from least to greatest.
3x²+36x + 81 = 0
lesser x =
greater x =
Answer:
Step-by-step explanation:
Simplify.
x^2 + 12x + 27
Factor.
(x + 9)(x + 3)
Solutions.
x = -9
x=-3
Answer:
x=-3 or x=-9
Step-by-step explanation:
No need to explain
What’s the math discount for $249.99 20% off now 199.99
Small work…
Answer:
The discount amount is $50.00. To calculate the discount, you can multiply the original price by the discount rate (expressed as a decimal), $249.99 * 0.20 = $49.998. Then, subtract the discount amount from the original price: $249.99 - $49.998 = $199.992.
Step-by-step explanation:
Prove angle ABC is a right angle
Pleasee help I need ASAP
Answer: A + B = C + D
Step-by-step explanation:
A company’s stock opened at 68 3/8 dollars per share. The stock dropped 1 7/8 dollars on Monday. The stock dropped another 2 1/2 dollars on Tuesday. On Wednesday, the stock gained back 4 1/4 dollars. brainly
Answer:
273/4
Step-by-step explanation:
We know
A company’s stock opened at 68 3/8 dollars per share
68 3/8 = 547/8
The stock dropped 1 7/8 dollars on Monday
1 7/8 = 15/8
547/8 - 15/8 = 532/8
The stock dropped another 2 1/2 dollars on Tuesday.
2 1/2 = 5/2
532/8 - 5/2 = 532/8 - 20/8 = 512/8
On Wednesday, the stock gained back 4 1/4 dollars.
4 1/4 = 17/4
512/8 + 17/4 = 512/8 + 34/8 = 546/8
546/8 = 273/4
So, the answer is 273/4
Your family drives 126 miles from Key West to the Florida mainland about 15% of this distance is spent on bridges how many miles of the bridges do you come travel over
Answer:
Step-by-step explanation:
The 15% of 126 is 18.96 thus, my family travels 18.96 miles over the bridge.
What is the percentage?
The percentage is defined as a given amount in every hundred. It is a fraction with 100 as the denominator percentage is represented by the one symbol %.
The percentage is also called the indicating hundredths. Thus, 2% is two-hundredth, which means 2%=2/100=0.02.
As per the given,
Total travel = 126
Percentage travel over the bridges = 15% of 126
15% of 126 = (15/100)126 = 18.96 miles
Hence "The 15% of 126 is 18.96 thus, my family travels 18.96 miles over the bridge".
a survey of 25 grocery stores revealed that the average price of a gallon of milk was $2.98, with a standard error of $0.10. what is the 98% confidence interval to estimate the true cost of a gallon of milk? $2.85 to $3.11 $2.73 to $3.23 $2.95 to $3.01 $2.94 to $3.02
The 98% confidence interval to estimate the true cost of a gallon of milk is $2.73 to $3.23.
What do you mean by standard error?The standard error is a measure of the variability or spread of a set of sample values. In statistics, the standard error is used to quantify the precision of an estimate of a population parameter, such as the mean or standard deviation. It is calculated as the standard deviation of the sampling distribution of a statistic, usually the mean. The standard error is a useful measure because it provides a way to compare different estimates of a population parameter, and it can be used to construct confidence intervals, which provide a range of values within which the true population parameter is likely to lie with a specified degree of confidence.
The 98% confidence interval to estimate the true cost of a gallon of milk can be calculated using the following formula:
CI = (sample mean) ± (critical value) * (standard error)
Where critical value can be obtained from a standard normal distribution table, corresponding to a given level of confidence.
For 98% confidence, the critical value is 2.33.
CI = $2.98 ± 2.33 * $0.10 = $2.98 ± $0.23 = $2.73 to $3.23
Therefore, the 98% confidence interval to estimate the true cost of a gallon of milk is $2.73 to $3.23
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) let x be an exponential random variable. then, its mean and its standard deviation are equal. true or false?
False. The mean and the standard deviation of an exponential random variable are not equal.
An exponential random variable has a probability density function given by:
[tex]$f(x) = \lambda e^{-\lambda x}$ for $x > 0$[/tex]
where[tex]$\lambda > 0$ i[/tex]s the rate parameter.
Mean for exponential random variable:
[tex]$\frac{1}{\lambda}$[/tex]
Standard deviation for exponential random variable:
[tex]$\frac{1}{\lambda}$[/tex]
Thus, the mean and the standard deviation of an exponential random variable are not equal, and they have different values depending on the value of [tex]$\lambda$[/tex]
It is important to note that exponential random variables have a memoryless property, which means that the future behavior of an exponential random variable is independent of its past values. This property makes exponential random variables useful for modeling various real-world phenomena such as the time between failures in reliability engineering or the time between events in a Poisson process.
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Solve. Write both set-builder notation and interval notation for the answer.
X/5+4≤3
The solution set is {x|_}
(Type an inequality. Use integers or fractions for any numbers in the inequality.)
The solution set is
(Type your answer in interval notation. Use integers or fractions for any numbers in the expression
Answer: We can solve for x by subtracting 4 from both sides of the inequality:
X/5 + 4 <= 3
X/5 <= -1
Multiplying both sides of the inequality by 5:
X <= -5
The solution set for x can be expressed in set-builder notation as:
{x | x <= -5}
And in interval notation as:
(-∞, -5]
Step-by-step explanation:
The value of x is x≤ -5
What is inequality?inequality, In mathematics is a statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.
greater than is >
less than is <
greater then or equal to is ≥
less than or equal to is ≤
x/5 +4 ≤ 3
collect like terms
x/5 ≤3-4
x/5 ≤ -1
multiply both sides by 5
x ≤ -5
therefore the value of x≤ -5
in interval notation
= infinity < x ≤ -5
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I need help with this problem
Answer: 33
Step-by-step explanation:
There are lots of things you have to remember in parallel lines with transversal lines (the lines that cut through the parallel lines). In this picture, the angles shown are co-interior angles. Co-interior angles add up to 180°.
Given this, we can make and solve the following equation:
[tex](x + 20) + (4x-5) = 180\\x + 20 + 4x - 5 = 180\\5x + 15 = 180\\5x = 165\\x = 33[/tex]
If there are any steps you don't understand, I can go through it again, so please tell me :)