It will take approximately 12.85 hours until only 1 gram of the element remains.
If after 2 hours, 36% of the initial amount remains, then the remaining amount is 0.36 times 100 grams, which is 36 grams. Let's define the amount of the element remaining after time t in hours as R(t). Since the element is decaying exponentially, we can model it with the equation R(t) = 100[tex](0.36)^t[/tex].
We want to find how many hours it will take until only 1 gram remains. We can set R(t) equal to 1 gram and solve for t:
1 = 100[tex](0.36)^t[/tex]
Taking the logarithm of both sides, we get:
ln(1) = ln(100[tex](0.36)^t[/tex])
0 = ln(100) + t*ln(0.36)
t = -ln(100)/ln(0.36)
Using a calculator, we find that t ≈ 12.85 hours.
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What is the relation between the variables in the equation
The equation x⁴/y = 7 represents a relationship of direct proportionality between x and y, where x⁴ and y are inversely proportional to each other.
The equation x⁴/y = 7 represents a relationship between the variables x and y. Specifically, it shows that the fourth power of x divided by y is equal to 7.
This equation can be rewritten as x⁴ = 7y, which means that if we know the value of y, we can determine the corresponding value of x that satisfies the equation. For example, if y = 1, then x⁴ = 7, and taking the fourth root of both sides of the equation gives us x = ± √7.
Conversely, if we know the value of x, we can solve for y by rearranging the equation as y = x⁴/7. This shows that y is directly proportional to x raised to the fourth power, meaning that as x increases, y will also increase, but at a faster rate due to the exponent of 4.
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Draw a line representing the "rise" and a line representing the "run" of the line. State
the slope of the line in simplest form.
-409-8
Click twice to plot each segment.
Click a segment to delete it.
Slope of the Line:
-3 -2 7
10
9
Submit Answer
5
4
7
9
10
The rise and run of the line is shown in the image below, where: slope of the line (m) = -3/4.
What is the Slope of a Line?The slope refers to how steep a line is. To find the slope of a line on coordinate plane, find the rise and the run of the line, then find their ratio.
Slope of a line (m) = change in y / change in x = rise / run
The red line in the image below represents the rise of the line while the blue line represents the run of the line.
The rise = 3 units
The run = 4 units
Therefore, we have:
Slope (m) = rise/run = -3 units / 4 units
Slope (m) = -3/4.
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Please help will mark Brainly
Emma brought $23.75 to the art supply store. She bought a brush, a sketchbook, and a paint set. The brush was 1 /4 as much as the sketchbook, and the sketchbook cost 2/ 3 the cost of the paint set. Emma had $4.50 left over after buying these items.
Emma bought a brush for $1.75, a sketchbook for $7, and a paint set for $10.5.
How to solve for the costB = 1/4 * S
S = 2/3 * P
B + S + P = 23.75 - 4.50
Emma spent 23.75 - 4.50 = $19.25 on the brush, sketchbook, and paint set.
Now we have the equation:
B + S + P = 19.25
Substitute the expressions from relationships 1 and 2 into the equation:
(1/4 * S) + S + (3/2 * S) = 19.25
Now combine the terms:
(1/4 * S) + (4/4 * S) + (6/4 * S) = 19.25
(11/4 * S) = 19.25
Now, to solve for S, multiply both sides of the equation by the reciprocal of the fraction (4/11):
S = (4/11) * 19.25
S = 7
The sketchbook cost $7. Now we can find the costs of the brush and the paint set using relationships 1 and 2:
B = 1/4 * S = 1/4 * 7 = 1.75
P = 3/2 * S = 3/2 * 7 = 10.5
Emma bought a brush for $1.75, a sketchbook for $7, and a paint set for $10.5.
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Complete question
Emma brought $23.75 to the art supply store. She bought a brush, a sketchbook, and a paint set. The brush was 1 /4 as much as the sketchbook, and the sketchbook cost 2/ 3 the cost of the paint set. Emma had $4.50 left over after buying these items. What is the total cost for each item
There are 6 bottles of water.
Each bottle is 1/2 full. If you
were to combine all the
water, how many full bottles
of water would there be?
Answer:3
Step-by-step explanation: 1/2 X 6 = 3
Answer:
6 x 1/2 = 3 full bottles
Step-by-step explanation:
7
35cm
42cm
X =
6cm
cm
N
HELP ME FAST GUYS!! Asap
The value of x in the polygon is 5 centimetres.
How to find the side of similar polygon?A polygon is a two-dimensional geometric figure that has a particular number of sides.
Two polygons are similar if their corresponding angles are congruent and the corresponding sides have a constant ratio .
Therefore, using the ratio of the similar polygon, let's find the value of x as follows:
35 / x = 42 / 6
cross multiply
35 × 6 = 42x
210 = 42x
divide both sides of the equation by 42
x = 210 / 42
x = 5 cm
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I know is blurry just pls help
12 - 2^2 x 2
---Remember: PEMDAS
---In this case exponents are first, then multiplication, then subtraction
12 - 4 x 2
12 - 8
4
Answer: 4
Hope this helps!
5.
Andre is playing a new card game. This game uses 4 sets of cards:
green, blue, yellow, and red. Each set has 15 cards numbered from
1 to 15. Select all of the actions that have more than 4 possible
outcomes. 7.SP.8, 7.SP.8b
0
selecting a blue card less than 5
selecting a red card greater than 13
selecting a yellow 12 card
selecting an 8 or 9 card of any color
selecting an even-numbered green card greater than 4
selecting a yellow card greater than 4²
selecting a blue card that is a multiple of 3
The actions that have more than 4 possible outcomes are:
- Selecting an 8 or 9 card of any color (each set has 2 cards for a total of 8 possible outcomes)
- Selecting a yellow card greater than 4² (there are 7 yellow cards that meet this criteria)
- Selecting a blue card that is a multiple of 3 (there are 5 blue cards that meet this criteria)
Therefore, only three of the given actions have more than 4 possible outcomes.
Ocarolyn and Abby
went camping and
caught a total of a fish.
How many fish
weighed 8 1/4 pounds
or less?
XX
XX
X X
x+
XX-
X
8 8
8
8 9
Weight of Fish in Pounds
1
Write the equation of a line perpendicular to y = −5/9x + 4 and that passes through point (-5,-4) in slope intercept form.
Answer: y = (9/5)x + 5.
Step-by-step explanation:
The slope of the given line is -5/9. The slope of a line perpendicular to it would be the negative reciprocal of -5/9, which is 9/5. Using the point-slope form of a line, we can write the equation of the line as y - (-4) = (9/5)(x - (-5)). Simplifying this equation gives y + 4 = (9/5)x + 9. Solving for y, we get y = (9/5)x + 5. This is the equation of the line in slope-intercept form.
In summary, the equation of a line perpendicular to y = −5/9x + 4 and that passes through point (-5,-4) is y = (9/5)x + 5.
Can anybody help me quick 21 points
According to a recent poll, 22% of US adults get an average of 7 or more hours of sleep per night. Assume this is the parameter value for the population. Suppose you select a simple random sample of 50 US adults and find that 10 of them get an average of 7 or more hours of sleep per night. Let p(hat) = the proportion in the sample who get an average of 7 or more hours of sleep per night.
Assuming the polling information is true, the probability that 20% or less of US adults get an average of 7 or more hours of sleep per night is ?
answer is .3664
If needed, use the z-table to answer the question.
assuming the polling information is true, is 0.4019 or approximately 0.3664 when rounded to four decimal places.
What is probability?
By simply dividing the favorable number of possibilities by the entire number of possible outcomes, the probability of an occurrence can be determined using the probability formula. Because the favorable number of outcomes can never exceed the entire number of outcomes, the chance of an event occurring might range from 0 to 1.
The mean of the sample proportion distribution is given by:
μp(hat) = p = 0.22
The standard deviation of the sample proportion distribution is given by:
σp(hat) = sqrt((p*(1-p))/n) = sqrt((0.22*0.78)/50) = 0.0802
To find the probability that 20% or less of US adults get an average of 7 or more hours of sleep per night, we need to find the z-score corresponding to this value:
z = (0.20 - 0.22) / 0.0802 = -0.2494
Using a standard normal table or calculator, we find that the probability of obtaining a z-score of -0.2494 or less is 0.4019. Therefore, the probability that 20% or less of US adults get an average of 7 or more hours of sleep per night,
Hence assuming the polling information is true, is 0.4019 or approximately 0.3664 when rounded to four decimal places.
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Solve the equation without using a calculator
[tex](x^2-9x-1)^{10}+99x^{10}=10x^9(x^2-1)[/tex]
Answer:
x = 5 ± √26-------------------------
Convert the given equation as below:
[tex](x^2-9x-1)^{10}+99x^{10}=10x^9(x^2-1)[/tex][tex](x^2-9x-1)^{10}+99x^{10}=10x^9(x^2-9x-1)+10x^9(9x)[/tex][tex](x^2-9x-1)^{10}+99x^{10}=10x^9(x^2-9x-1)+90x^{10}[/tex][tex](x^2-9x-1)^{10}+9x^{10}=10x^9(x^2-9x-1)[/tex][tex](x^2-9x-1)^{10}-9x^9(x^2-9x-1)=x^9(x^2-9x-1)-9x^9x[/tex]Let's substitute x² - 9x - 1 = t, then the equation is:
[tex]t^9t-9x^9t=x^9t-9x^9x[/tex]Comparing both sides, we see that x = t, so:
x² - 9x - 1 = xx² - 10x - 1 = 0Solving this quadratic equation we get:
x = 5 ± √26A swimming pool holds 450, 000 L
of water and has two drainage
pipes.
Pipe A, by itself, can drain the pool
in 150 minutes. Pipe B, by itself, can
drain the pool in 225 minutes.
If you turned on both pipes at the
same time, how many minutes
would it take to drain the pool?
Using a linear equation, the minutes it would take both pipes to drain the swimming pool that holds 450,000 liters is 90 minutes.
What is a linear equation?A linear equation is an equation of a straight line written in the form of y = mx +b, where m is the slope.
The quantity of water the swimming pool holds = 450,000 liters
The drainage time of Pipe A working alone = 150 minutes
Drainage rate of Pipe A = 3,000 liters per minute (450,000 ÷ 150)
The drainage time of Pipe B working alone = 225 minutes
Drainage rate of Pipe B = 2,000 liters per minute (450,000 ÷ 225)
The drainage rate of the combined pipes = 5,000 liters per minute (3,000 + 2,000)
Let the number of minutes for both pipes to drain the pool = x
Therefore, the linear equation is 5,000x = 450,000
x = 90 minutes (450,000 ÷ 5,000)
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Given (x – 7)2 = 36, select the values of x. x = 13 x = 1 x = –29 x = 42
The solution for x in the equation (x – 7)^2 = 36 are x = 13 and x = 1
Solving for x in the equationWe can solve for x by taking the square root of both sides of the equation:
(x – 7)^2 = 36
Taking the square root of both sides:
x - 7 = ±6
Adding 7 to both sides:
x = 7 ± 6
Therefore, the values of x are:
x = 7 + 6 = 13
x = 7 - 6 = 1
So the correct answers are x = 13 and x = 1. The values x = -29 and x = 42 are not solutions to the equation.
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what is the sum of 14, 12, 8, and 6
Answer:
Step-by-step explanation:
14+12 = 26+8 = 34 + 6 is 40
the answer is 40.
Answer:
[tex]2\sqrt{10[/tex]
Step-by-step explanation:
Add all the numbers together on your calculator
A local maximum of the function f(x) occurs for which x-value? A 2-column table with 6 rows. The first column is labeled x with entries negative 4, negative 3, negative 2, negative 1, 0, 1. The second column is labeled f of x with entries 16, negative 2, 0, 6, 0, negative 2. Group of answer choices –4 –3 –2 –1
There is a local maximum at the point (-1,6), therefore, for x = -1
option D is correct
What do we mean by local maximum point?A local maximum point on a function is described as a point (x,y) on the graph of the function whose y coordinate is larger than all other y coordinates on the graph at points "close to'' (x,y).
We see that the function adopts values smaller than 6 to the left of x = -1, and to the right of it:
(-3, -2), (-2, 0) to the left of x = -1 where the function's value is 6
and (0, 0), and (1, -2) to the right of x = -1
Therefore, we can say that the pints (-1, 6) is a maximum, that is for x = -1, where the function renders a value of 6.
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Factor the polynomial, if possible. Check your answer using foil.
y² + 49
Answer:
its prime
Step-by-step explanation:
it can not be factored using foil
find the probability that a randomly selected point within the large square falls in the red shaded square 6 6 15 15 p= enter as a decimal rounded to the nearest hundredth
The probability that a randomly selected point within the red-shaded square is 0.16
Finding the probability of a pointFrom the question, we have the following parameters that can be used in our computation:
Red square of 6 by 6White square of length 15The areas of the above shapes are
Red square = 6 * 6 = 36
White square = 15^2 = 225
The probability is then calculated as
P = Red square /White square
So, we have
P = 36/225
Evaluate
P = 0.16
Hence, the calculated value of the probability that the point falls in the red square is 0.16
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i need an answer for this with explanation
Answer: 76
Step-by-step explanation:
The surface area is all of the area faces added together
The blue is 5*4 but I have 2 of those faces so I multiply by 2
(5*4*2)=40
The red is 4*2 but I have 2 of those faces so I multiply by 2
(4*2*2)=16
The green is 5*2 but I have 2 of those faces so I multiply by 2
(5*2*2)=20
Add those together
A=40+16+20=76
I need help i don't know how to do this please
The size of matrix cM is given as follows:
9 x 10.
What happens when a matrix is multiplied by a constant?When a matrix is multiplied by a constant, we have that every element in the matrix is multiplied by the constant. Hence, the dimension of the matrix remains constant.
The parameters for this problem are given as follows:
Constant c.Matrix M of dimensions 9 x 10.Hence the size of matrix cM is given as follows:
9 x 10.
(same size as the original matrix, as we simplify multiply each element in the matrix by the constant, hence the dimensions remain the same).
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Elin chose C as the correct answer. Explain how she got her answer.
Answer:
Elin concluded that car B travels a distance of 265.8 km during the same time based on her interpretation of the given information.
Step-by-step explanation:
My apologies for the confusion. Let's analyze how Elin arrived at her answer.
According to the given information, car A travels 221.5 km at a given time. Elin interpreted the statement "car B travels 1.2 times the distance car A travels at the same time" to mean that the distance traveled by car B is 1.2 times the distance traveled by car A.
To calculate the distance traveled by car B, Elin multiplied the distance of car A (221.5 km) by 1.2:
Distance of Car B = 1.2 * Distance of Car A
Distance of Car B = 1.2 * 221.5 km
Distance of Car B = 265.8 km
Therefore, Elin concluded that car B travels a distance of 265.8 km during the same time based on her interpretation of the given information.
7. The towns of Washington, Franklin, and Springfield are
connected by straight roads. The towns wish to build an
airport to be shared by all of them.
a. Where should they build the airport if they want it to be the same distance from
each town's center? Describe how to find the precise location.
b. Where should they build the airport if they want it to be the same distance from
each of the roads connecting the towns? Describe how to find the precise
location.
They should build the airport at the
They should build the airport at the
n be found by locating the intersection of at least
which can be found by locating the intersection of a
a circumcenter
medians
A research institute poll asked respondents if they felt vulnerable to identity theft. In the poll, n=918 and x=592 who said "yes." Use a 90% confidence level.
The values received after utilizing confidence interval are (0.614, 0.674)
Poll = n = 918
X = 592
Calculating the value of p -
p = x/n
= 592/918
= 0.644
The mean of an estimate plus and minus the range of that estimate constitutes a confidence interval. inside a specific degree of confidence, this is the range of values that anticipates the estimate to fall inside if the test is repeated.
Using the formula of confidence interval -
[tex]CI = p + z\sqrt{} p ( 1-p/n)[/tex]
Substituting the values -
[tex]CI = 0.644 + 1.645 \sqrt{} ( 0.644 ( 1 - 0.644) / 918)[/tex]
= 0.644 ± 0.030
Thus, the interval values are -
= 0.644 + 0.030 = 0.674
= 0.644 - 0.030 = 0.614
With 90% certainty that this range represents the true percentage of the population who feel vulnerable to identity theft.
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The National Academy of Science reported in a 1997 study that 40% of research in mathematics is published by U.S. authors. The mathematics chairperson of a prestigious university wishes to test the claim that this percentage is no longer 40%. He has no indication of whether the percentage has increased or decreased since that time. He surveys a simple random sample of 130 recent articles published by reputable mathematics research journals and finds that 62 of these articles have U.S. authors. Does this evidence support the mathematics chairperson's claim that the percentage is no longer 40%? Use a 0.05 level of significance.
There is evidence to suggest that the percentage of mathematics research published by U.S. authors is no longer 40%.
How to test for the evidenceTo test the claim that the percentage of research in mathematics published by U.S. authors is no longer 40%, we can use a hypothesis test with a 0.05 level of significance.
Let p be the true proportion of mathematics research published by U.S. authors.
The null hypothesis is that p = 0.4, and the alternative hypothesis is that p ≠ 0.4 (two-tailed test).
sample proportion, x/n = 62/130 = 0.477
The test statistic for a two-tailed test is given by:
z = (0.477 - 0.4) / √(0.4 * 0.6 / 130)
= 2.41
Using a z-table, we find that the p-value for a two-tailed test with z = 2.41 is approximately 0.016.
Since 0.016 < 0.05
, we reject the null hypothesis and conclude that there is evidence to suggest that the percentage of mathematics research published by U.S. authors is no longer 40%.
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For any positive values x and y, f(xy) = f(x) + f(y). f(1/2021) = 1.
Find f(2021).
I will give BRAINLIEST to correct answer.
OAB is a minor sector of the circle below.
Calculate the length of the minor arc AB in terms of pi
Not drawn accurately
AWARDING BRAINLIEST TO FIRST ANSWER
The Length of the arc in the circle shown is calculated to one decimal place, in terms of pi, as approximately 3.6π cm.
How to Calculate the Length of an Arc?The length of an arc in a given circle can be calculated by applying the formula as expressed below:
Length of arc (s) = ∅/360 * 2πr, where:
Reference angle = ∅
Radius of the circle = r.
Given the parameters:
Radius (r) = 16 cm
Reference angle (∅) = 40 degrees.
Plug in the values:
Length of the arc (s) = 40/360 * 2 * π * 16
Length of the arc (s) = 3.6π cm
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Answer:
To calculate the length of the minor arc AB in terms of pi, you need to know the measure of the central angle that intercepts the arc and the radius of the circle. Do you have that information?
Step-by-step explanation:
3. Point F(21, -14) is rotated-90° clockwise about the origin. What are the coordinates of F’
Answer: The coordinates of F' are (14, 21).
Step-by-step explanation:
Since we are rotating -90° clockwise about the origin (or 90° counterclockwise), we will apply (x, y) becoming (-y,x). I have also graphed this, see attached.
(21, -14) ➜ (14, 21)
The coordinates of F' are (14, 21).
Suppose that the function g is defined, for all real numbers, as follows.
The graph of the piecewise function is given by the image presented at the end of the answer.
What is a piece-wise function?A piece-wise function is a function that has different definitions, depending on the input of the function.
All the three definitions of the function in this problem are constant, hence the graph will be composed by horizontal lines.
The definitions are given as follows:
y = 2 to the left of x = 0.y = -1 at x = 0.y = -3 to the right of x = 0.More can be learned about piece-wise functions at brainly.com/question/19358926
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Piston movement compresses air in this type of air compressor. Medium size compressors Industrial compressors Small compressors Horizontal compressors
Piston movement compresses air in Small compressors type of air compressor
Piston movement compresses air in small compressors. Small compressors, also known as portable compressors, are commonly used for home improvement projects, powering tools, and inflating tires or other objects. The piston moves back and forth inside a cylinder, compressing air and increasing its pressure. The compressed air is then stored in a tank until it is needed to power a tool or inflate an object.
Small compressors are generally less powerful than medium or industrial compressors, but they are more affordable, portable, and easier to use for smaller tasks. They can be powered by electricity or gasoline, and they come in a range of sizes and capacities to meet different needs. Overall, piston-driven small compressors are an efficient and cost-effective way to compress air for various applications.
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