[tex]\qquad \textit{Amount for Exponential Decay} \\\\ A=P(1 - r)^t\qquad \begin{cases} A=\textit{current amount}\dotfill & \$ 500\\ P=\textit{initial amount}\dotfill &3300\\ r=rate\to 75\%\to \frac{75}{100}\dotfill &0.75\\ t=years \end{cases}[/tex]
[tex]500 = 3300(1 - 0.75)^{t} \implies \cfrac{500}{3300}=0.25^t\implies \cfrac{5}{33}=0.25^t \\\\\\ \log\left( \cfrac{5}{33} \right)=\log(0.25^t)\implies \log\left( \cfrac{5}{33} \right)=t\log(0.25) \\\\\\ \cfrac{\log\left( \frac{5}{33} \right)}{\log(0.25)}=t\implies 2\approx t\qquad \qquad \textit{to be exact, about 1 year and 131 days}[/tex]
Could you please help me with 13, 14, and 15 please
Answer:
your mom a cow your dad left for milk
A bone fragment has 10% of the parent Pb-210 remaining. The half-life of Pb-210 is 22 years.
How old is the bone fragment?
A bone fragment that has 10% of the parent Pb-210 remaining with half-life of Pb-210 is 22 years, the bone fragment is approximately 51 years old.
To determine the age of the bone fragment, you need to calculate the number of half-lives that have elapsed since the bone was formed. The age of the bone can be calculated using the formula:
age = number of half-lives * half-life
To calculate the number of half-lives, you need to determine how much of the original Pb-210 has decayed. If a bone fragment has 10% of the parent Pb-210 remaining, then 90% has decayed.
You can calculate the number of half-lives by taking the natural logarithm of the ratio of the remaining amount of Pb-210 to the original amount:
number of half-lives = ln(0.10) / ln(0.5)
Using the half-life of Pb-210, which is 22 years, you can now calculate the age of the bone fragment:
age = number of half-lives * 22 years
Substituting the values and calculating the number of half-lives and the age of the bone fragment, you get:
number of half-lives = ln(0.10) / ln(0.5) = 2.302
age = number of half-lives * 22 years = 51.064 years
So, the bone fragment is approximately 51 years old.
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Select the false statement involving p, and the arbitrary events A and B. a) P( A^c n B^c)=P(A^c) P(B^c) b). P( A n B)=P( A) + P( B) -P( A U B). c). P(A^) + P(A)=1. d). P(A n B^c)= P(A)-P(A n B).e). P(A^c n B)=P(B)-P(A n B). f). None of the above.
The deceptive amount claim is b). P (A n B) = P (A) + P (B) -P ( A U B). This assertion is false since it omits the point where A and B intersect, which is P. (A n B).
The deceptive claim is b). P (A n B) = P (A) + P (B) -P ( A U B). This claim is false because it disregards the fact that P is where A and B overlap (A n B). The stated statement does not take into consideration the intersection of two events, which is the likelihood that both occurrences will occur.
One must factor in the likelihood that the two occurrences will intersect when calculating the likelihood that two events will occur simultaneously. The given statement deducts the probability of the union of two occurrences from the sum of the probabilities of the two separate events because the probability of the union of two events is the chance that at least one of the events occurs. As it ignores the intersection, this method is inaccurate for estimating the likelihood of both occurrences occurring simultaneously. The probability of the intersection must be considered in order to calculate the likelihood of two occurrences occurring simultaneously.
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a high school has 40 players on the football team. the summary of the players' weights is given in the box plot. what is the median weight of the players?
The median weight of the players on the football team is approximately 160 lbs.
The box plot provides a visual summary of the data which shows the distribution of the weights of the players on the football team. The box plot consists of a box and two "whiskers" which represent the upper and lower quartiles of the data. The box is bounded by the upper quartile and lower quartile and the two whiskers represent the highest and lowest values in the data set, excluding any outliers. The median weight of the players is represented by the line in the middle of the box, which is approximately 160 lbs. The box plot is a useful tool for summarizing the data and provides a quick and easy way to visualize the distribution of the players' weights. The median weight of 160 lbs gives us an idea of the average weight of the players, which can be used to determine the overall strength of the team.
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The complete question is
a high school has 40 players on the football team. the summary of the players' weights is given in the box plot. what is the median weight of the players and find lbs.
The function f(x) = 500(1 − 0.19 )x2
models the price of a share of stock over time.
Part A
The price of the stock models exponential
Choose...
.
What is the rate of exponential growth or exponential decay?
%
Part B
Which expression is equivalent to the function f(x) = 500(1 − 0.19 )x2
?
A. f(x) = 202.5x
B. f(x) = 20.1246x
C. f(x) = 500(0.9)x
D. f(x) = 500(1.0909)x
The rate of exponential decay is 0.19.
f(x) = 202.5x is the equivalent function.
The correct option is A.
What is exponential decay?An exponential function's curve is created by a pattern of data called exponential decay, which exhibits higher decreases over time.
The exponential decay function:
Aₙ = A₀(1-r)ˣ, where y = Final amount, A₀ = Initial amount, r = Rate of decay in decimal form, x = Time.
Given:
The function f(x) = 500(1 − 0.19 )ˣ/2,
models the price of a share of stock over time.
Compared to the definition,
we get,
The rate of exponential decay is 0.19.
When x = 0,
Then f(x) = 202.5x
Therefore, f(x) = 202.5x is the equivalent function.
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Manny took home a couple of his friends after soccer practice. He originally had 6 gallons of gas in his car. He used 1.04 gallons of gas to take one friend home and two fifths gallons to take the other friend home. How much gas did he have left in his car after taking both friends home?
The quantity of has he had left in his car after taking both friends home would be = 4.76gallons
How to calculate the quantity of gallons?The total amount of gas in gallons in his car = 6 gallons
The amount of gas he used to take one of his friends home = 1.04 gallons.
The second friend he used a total of = 1/5 = 0.2 gallons.
The total amount of gas he uses = 1.04+0.2 = 1.24 gallons.
Then the amount of gas remaining = 6 - 1.24 = 4.76gallons.
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Answer: For every one who is annoyed with the dude aboves answer the correct answer is: D 4.56
Step-by-step explanation:
36 divided s =4; 9,10,11,
Answer:
Step-by-step explanation:
The expression 36 divided by s = 4 can be solved for s by dividing both sides of the equation by 36:
36/s = 4
Dividing both sides of the equation by 4:
s = 36/4 = 9
So, the value of s that makes the equation true is 9. This means that if you divide 36 by 9, the result will be 4.
A local bike race is broken into 12 parts. Each stage is 14 1/2 miles. What is the total distance of the bike race?
Answer: 174 miles
Step-by-step explanation: 14.5 (14 1/2) times 12 is 174
i forgot what this is even though i learned it someone please help me or at least explain to me what I'm looking at and how to solve it
Answer: C, I hope this helps
8t+1+(−4t)+(−6) ?????????????
What is the circumference, in centimeters, of the circle? Use 3. 14 for π. Enter your answer in the box. Cm
the circumference of the circle is 19.4568 cm or, rounded to two decimal places, 94.68 cm.
94.68 cm
The formula for circumference of a circle is C = 2πr, where r is the radius of the circle. Therefore, to find the circumference of the circle, we need to first calculate the radius.
The area of the circle is given as A = πr2.
Therefore, we can rearrange this equation to solve for the radius, which is
r = √(A/π)
Plugging in the given area, A = 3.14, we get
r = √(3.14/π) = √(3.14/3.14) = 1
Now, we can use the circumference formula to calculate the circumference, which is
C = 2πr = 2π(1) = 2π × 3.14 = 6.28 × 3.14 = 19.4568
Therefore, the circumference of the circle is 19.4568 cm or, rounded to two decimal places, 94.68 cm.
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5-8(3+x) simplified expression
Answer: -8x - 19
Step-by-step explanation:
Distribute: 5-8(x+3) = 5-8x-24
5-8x-24= -19 - 8x
= -8x - 19
Answer:
-8x - 19
Step-by-step explanation:
1. Rearrange terms: 5 - 8 (3 + x)
2. Distribute terms: 5 - 8 ( x + 3) = 5 - 8x - 24
3. Subtract the numbers: 5 - 8x - 24 = -19 - 8x
4. Rearrange terms again: -19 - 8x to -8x - 19
5. Here's your answer! Hope this helped :)
Which property is demonstrated below?
A. associative property
B. distributive property
C. commutative property
D. identity property
The property which is demonstrated by this expression 6 + 7 = 7 + 6 include the following: C. commutative property.
What is the Commutative Property of Addition?In Mathematics, the Commutative Property of Addition states that when two (2) or three (3) numerical values (numbers) are added together, the output (end result) would always remain the same, irrespective of the way in which the numerical values are arranged.
Generally speaking, the Commutative Property of Addition allows the addends to be re-ordered without causing a change in the result, output, or outcome.
By applying the Commutative Property of Addition, we have the following;
6 + 7 = 7 + 6
13 = 13
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Complete Question:
Which property is demonstrated below?
6 + 7 = 7 + 6.
A. associative property
B. distributive property
C. commutative property
D. identity property
Enter the interval equivalent to
2
<
x
≤
5
or
x
>
7
2,5
this is how I got the answer
help meeeeee please lol
Answer:A
Step-by-step explanation:
every matrix transformation is a linear transformation . t/f
"Every linear transformation is a matrix transformation." This is false. Not all linear transformations are matrix transformations, even if all matrix transformations are linear transformations.
A point, line, or geometric object can be changed in four different ways that are all referred to as transformations. The Pre-Image refers to the object's initial shape, and the Image, after transformation, refers to the object's ultimate shape and location.
Bring out the pattern blocks, tangrams, and geoboards for another low-prep, high-engagement method of teaching geometric transformations. Students can produce an original design and then hand it off to a partner so that they can add a reflection, rotation, or translation to it.
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Using the given diagram,
The length of the side x is 60.
What is the value of x?Pythagorean Theorem is a mathematical statement that states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. It can be written as c^2 = a^2 + b^2
Let the unknown side in the first triangle be a
We know that;
a^2 = 55^2 - 25^2
a= 49
Then again;
x^2 = 35^2 + 49^2
x = 60
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A group of researchers is studying the relationship between cortisol (stress hormone) levels and memory, and they want to see if a sample of 25 adults that has been recruited is a good representation of the population it came from, before they conduct additional research. The population has been found to have an average cortisol level of 12 mcg/dL, with a standard deviation of 2 mcg/dL. The sample was found to have an average cortisol level of 15 mcg/DL, with a standard deviation of 3 mcg/dL. For this assignment, construct a confidence interval to determine if this sample mean is significantly different from the population mean. Explain how you know, based on the confidence interval, and specific the confidence level you used. Be sure to show your work and calculations. This can be tricky with Word, so if necessary you may take a photo of your hand calculations and add it to the Word document
The sample mean is significantly different from the population mean. The confidence level used was 95%.
To build a confidence interval to decide whether this example mean is fundamentally not the same as the populace mean, there are a few stages that should be taken.
To begin with, work out the standard error of the mean (SEM) for the example, which is the standard deviation separated by the square base of the example size (SEM = σ/√n). For this situation, the SEM is 3/5 = 0.6 mcg/dL.
Then, compute the critical value for the confidence interval picked by increasing the SEM by the t-esteem from the t-dissemination for the given confidence interval. For instance, in the event that a 95% confidence interval is picked, the t-esteem is 1.96. This provides us with a basic worth of 0.6 x 1.96 = 1.176 mcg/dL.
At last, build the certainty span utilizing the example mean and the basic worth. The certainty span is (15 - 1.176, 15 + 1.176), or (13.824, 16.176). This implies that we are 95% sure that the genuine populace mean exists in this reach.
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Please help!! Urgent!
Answer:
-1, 7
Step-by-step explanation:
Based on the graph (it's a little blurry!) it looks like f(x) = 0 when x = -1 and x = 7. The question is asking, for what values of x is y=0? Answer is x = -1, 7
if the work required to stretch a spring 3 ft beyond its natural length is 6 ft-lb, how much work (in ft-lb) is needed to stretch it 18 in. beyond its natural length?
A total of 2.25 ft-lb work is needed to stretch it 18 in. beyond its natural length.
One foot is equal to 12 inches, so 3 ft is equal to 36 inches. To stretch the spring 18 inches beyond its natural length, we need to perform work on it to stretch it an additional 18/36 = 1/2 of the 3 ft distance. If the work required to stretch it 3 ft is 6 ft-lb, then to stretch it 1/2 of that distance, we would need 1/2 of the work, or 6/2 = 3 ft-lb. The work needed to stretch the spring 18 inches beyond its natural length is 3 ft-lb * 18 inches/12 inches/ft = 2.25 ft-lb.
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Triangle JKL is similar to triangle MNO. Find MN. Round your answer to the
nearest tenth if necessary. Figures are not drawn to scale.
N
L
19
J
26
K
58
X
M
The length of MN is roughly 13.89 units.
Describe a triangleThe polygonal shape of a triangle has three sides and three corners. It is one of the fundamental geometric shapes. Triangle ABC is a symbol for a triangle with vertices A, B, and C. When three points are not collinear, unique triangles and planes are found using Euclidean geometry.
Triangle JKL and triangle MNO are comparable, thus we can use the aspect ratio to determine the appropriate side lengths.
MN is 'x' in length. Then, it appears as follows:
JK/MN = 26/x, and KL/NO = 19/x
We can use their ratio to get x because we are aware of the lengths of JK and KL. We obtain: using the first ratio.
26/x = 58/26
x=26*26/58
x = 26^2/58
x = 13.89 (rounded to nearest integer)
Therefore, MN is approximately 13.89 units long.
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Mr. Gonzales has only $42.50 to spend at a clothing store. He wants to buy a shirt that costs $29, including tax, and some bracelets that cost $4.50 each, including tax.
Choose an equation to determine x, the maximum number of bracelets Mr. Gonzales could buy.
The equation to determine the maximum number of bracelets Mr. Gonzales could buy is 29 + 4.50x = 42.50 and the maximum number of bracelets is 3.
According to the question Gonzales has $42.50.
Cost of shirt = $29
Cost of bracelets = $4.50 each.
so, the equation becomes
Total cost = money that Gonzales has.
The cost is $29 + 4.50x, where x is the number of bracelets he can buy.
29 + 4.50x = 42.50
4.50x = 42.50 - 29
x = 13.50/4.50
x = 3
So we have that Mr. Gonzales can buy a total of 3 bracelets.
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Answer: The equation is $29 + x$4.50 = $42.50, and the solution is x = 3
Step-by-step explanation:
The data we have is: Gonzales has $42.50. He wants to buy a shirt that costs $29. SOME bracelets that cost $4.50 each.
The equation that we need to solve is: Total cost = money that Gonzales has. The expression to find the cost is $29 + $4.50x
X represents the number of bracelets he can buy. The equation that we need to solve is: $29 + $4.50x = $42.50
To solve it we must isolate the x
$4.50x = $42.50 - $29 = $13.50x = 13.50/4.50 = 3
So we have that Mr. Gonzales can buy a total of 3 bracelets.
Find an equation of the line L.
L is perpendicular to y = - 2x.
4
On solving the provided question, we can say that the new equation of the line is = (y +6) = 1/2(x-3) => x - 2y = 9
What is equation?A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences on either side of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 2x – 4 = 2.
coordinates are (3, -6)
the perpendicular equation is y = -2x
so, m. the slope = 1/2
the new equation of the line is = (y +6) = 1/2(x-3)
2y + 12 = x = 3
x - 2y = 9
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The ratio of boys to girls Ms. Garcia’s class is 4:5.
b. If she randomly selects a student from the class to present their solution to a math problem, what is the probability the student will be a girl?
The probability of randomly selecting a girl from Ms. Garcia's class is 5/9.
The ratio of boys to girls in Ms. Garcia's class is 4:5Which means that for every 5 students in the class, 4 of them are boys and 5 of them are girls.
To calculate the probability of selecting a girl from the class, we need to divide the number of girls by the total number of students:
Number of girls: 5 students
Total number of students: 4 students + 5 students = 9 students
Probability of selecting a girl: 5 students / 9 students = 5/9
So the probability of randomly selecting a girl from Ms. Garcia's class is 5/9.
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An equestrian club orders magazine subscriptions for new members. Last year, it had 32 new members and spent $576 on subscriptions. Solve the equation 32m = 576 to find the cost of each subscription, in dollars.
Answer:
$ 18
Step-by-step explanation:
To find the cost of each subscriptions, divide the cost of total subscriptions by 32.
32m = 576
m = 576 ÷ 32
m = $ 18
The ratio of the measures of the sides of a
triangle is 4:7:5. If the perimeter of the
triangle is 128 yards, find the length of the
longest side.
Answer: 56 yards
Step-by-step explanation:
4 + 7 + 5 = 16
128 / 16 = 8 yards
7 is the highest ratio in the set so
7 x 8 yards = 56 yards
What is 2 1/5 + 1 5/6??
A baker uses 2/3 cup of rye flour in each loaf of bread. How many cups of rye flour will the baker use in 3 loaves? in 7 loaves? in 10 loaves?
Answer:
3 loaves? 2 rye flour
7 loaves? 4⅔ rye flour
10 loaves? 6⅔ rye flour
Step-by-step explanation:
To get how many cups of rye flour the baker will use, for example: to get how many cups of rye flour the baker will use in 3 loaves? we multiply the number of cups the baker uses to make one loaf of bread
[tex]3 \: loaves \: = \frac{2}{3} \times 3[/tex]
[tex] \frac{2}{3} \times 3 = 2[/tex]
Now let's work out the others using the same method shown above
[tex] \frac{2}{3} \times 7 = 4 \frac{2}{3} [/tex]
[tex] \frac{2}{3} \times 10 = 6 \frac{2}{3} [/tex]
Hope that helpsAnswer:
2 cups = 3 loaves, 4 2/3 (4.66666667 in decimal form) cups of rye in 7 loaves, and 6 2/3 (6.66666666667 in decimal form) cups of rye in 10 loaves.
Step-by-step explanation:
What do we know? We know that 2/3 cups of rye is equal to one loaf of bread. We need to figure out how many cups of rye are in three loaves, seven loaves, and ten loaves. To do this, we will first figure out how many cups of rye are in three loaves. Since we know that 2/3 cups of rye is in 1 loaf, we take 2/3 cups and multiply it by three over one, or, three, for the three loaves. That comes out to 6/3. Now, we simplify. Three goes into six, evenly, twice with no remainder. So, 2 cups of rye goes into 3 loaves. The decimal for this would be 2.0.
Applying the same method, 2/3 cups times 7. We get 14/3. Three goes into fourteen 4 times with a remainder of 2. So, the answer would be 4 2/3 cups of rye in 7 loaves. To get the decimal version, divide 14 into 3.
2/3 times 10 equals 20/3. 3 goes into twenty six times with a remainder of two. So, 6 2/3 cups of rye in 10 loaves. To get the decimal version, simply divide 20 into 3.
simplify 2m exponent of 0 n exponent of 6 over 3n exponent of 5
The simplified expression is equal to 2/3.
Simplifying Math ExpressionThe expression can be simplified as follows:2m⁰ * n⁶ / (3n⁵)
Since m⁰ is equal to 1, the expression becomes:2 * n⁶ / (3n⁵)
Dividing both numerator and denominator by n⁵ gives:2 * n / (3n) = 2/3
So the simplified expression is equal to 2/3.
The rules of arithmetic and exponentiation that I used to simplify the expression are general mathematical principles that are applicable to many mathematical problems. However, the specific techniques for simplifying an expression will depend on the particular expression and the context in which it is being used.
For example, there might be additional rules or simplification techniques that are specific to a particular field of mathematics, such as algebra, calculus, or geometry. In these cases, it's important to understand the specific rules and techniques that apply to the problem at hand in order to simplify an expression effectively.
In general, the goal of simplifying an expression is to make it easier to understand and manipulate mathematically, either for further calculations or for understanding the relationships between the variables involved.
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t-9.25=5.45 what is the answer pls it due tomorrow and my mom has no clue how to do sixth grade math.....???
Answer:
[tex]t=14.7[/tex]
Step-by-step explanation:
In the equation: [tex]t-9.25=5.45[/tex] we need to get [tex]t[/tex] by itself. To do that, we need to add [tex]9.25[/tex] from one side to the other. We do this because on the side where [tex]t[/tex] is, [tex]9.25[/tex] is being subtracted and we have to do the opposite of that. So:
[tex]t-9.25=5.45[/tex]
[tex]+9.25[/tex] [tex]+9.25[/tex]
In this case, we got [tex]t[/tex] by itself. The new equation is:
[tex]t=14.7[/tex]