Answers
Solving the exponential function, it is found that the times that will take to have the desired measures are given by:
a) 3.6 hours.
b) 38.51 hours.
c) 56.98 hours.
What is the exponential function for the amount of Carbon-10 after t hours?The function is given by:
[tex]A(t) = 140(0.5)^{\frac{t}{19.255}}[/tex]
Solving for t, we have that:
[tex](0.5)^{\frac{t}{19.255}} = \frac{A(t)}{140}[/tex]
[tex]\log{(0.5)^{\frac{t}{19.255}}} = \log{\frac{A(t)}{140}}[/tex]
[tex]\frac{t}{19.255} = \frac{\log{\frac{A(t)}{140}}}{\log{0.5}}[/tex]
[tex]t = 19.255\frac{\log{\frac{A(t)}{140}}}{\log{0.5}}[/tex]
In item A, we have that A(t) = 123, hence:
[tex]t = 19.255\frac{\log{\frac{123}{140}}}{\log{0.5}}[/tex]
t = 3.6 hours.
In item B, we have that A(t) = 35, hence:
[tex]t = 19.255\frac{\log{\frac{35}{140}}}{\log{0.5}}[/tex]
t = 38.51 hours.
In item C, we have that A(t) = 18, hence:
[tex]t = 19.255\frac{\log{\frac{18}{140}}}{\log{0.5}}[/tex]
t = 56.98 hours.
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Related Questions
Find the value of x.
Answers
So we can assume that side b is also equivalent to side a. Here we use the pythagorean theorem to find x
a^2 + b^2 = c^2
5^2 + 5^2 = c^2
25+25=50
The square root of 50 is 7.1
x= 7.1
For ten school days, the numbers of bikes parked at a school bike rack are 10, 12, 8, 11, 13, 9, 2, 1, 9, and 12.
a. What is the mean number of bikes per day? [already answered]
b. Identify two outliers for the data. Describe how the outliers affect the mean.
"the numbers, Mason, what do they mean??"
Answers
The mean number is 8.7 and the outliers 1 and 2 reduce the mean value
How to determine the mean number?The dataset is given as:
10, 12, 8, 11, 13, 9, 2, 1, 9, and 12.
The mean number is calculated using:
Mean = Sum/Count
So, we have:
Mean = (10+ 12+ 8+ 11+ 13+ 9+ 2+ 1+ 9+12)/10
Evaluate
Mean = 8.7
Hence, the mean number is 8.7
The outlier and how it affects the meanOutliers are relatively far from other data elements of the dataset
In the given dataset, 1 and 2 are far from other data element.
So, the outliers are 1 and 2
Because 1 and 2 smaller than other data elements, they affect the mean by reducing the mean value
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Answer:87/10 is the answer because there are no tens
Step-by-step explanation:
f(x) = 3 and g(x) = x – 2
3 = x – 2
5 = x
Answers
Answer:
3=1×5-2
Step-by-step explanation:
you minus 5-2 is 3 and one threes three
erved.
6
What is the reason for step 3 of this proof?
OA
Alternate Interior Angles Theorem
OB.
Corresponding angles in congruent triangles are congruent.
OC. For parallel lines cut by a transversal, corresponding angles are congruent.
OD.
Vertical Angles Theorem
OE.
SAS criterion for congruence
Answers
Vertical Angles Theorem is the reason for step 3 of this proof. Hence, option D is correct.
What is Vertical Angles Theorem?Theorem of vertical angles or angles that are vertically opposing According to the theorem, two opposing vertical angles that are created when two lines cross one other are always equal to one another.
As AE = EC and BE = ED (by the definition of bisection) suggest that triangles AEB and CED are congruent (by the SAS criterion for congruence),
It is claimed in step 3 of the provided proof that mAEB = mCED. The corresponding angles of two triangles are equal when they are congruent. Since mAEB = mCED, it follows that the measure of angle AEB must be equal to the measure of angle CED.
This step is crucial because it proves the equality of the respective angles in the congruent triangles AEB and CED. This equality is then utilized in step 4 to prove that the two triangles satisfy the SAS criterion, which is a congruence criterion.
Steps 5 through 11 then employ the congruence of triangles AEB and CED to demonstrate that the quadrilateral ABCD is a parallelogram.
Thus, option D is correct.
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The complete question is given below-
What is the reason for step 3 of this proof?Given: and bisect each other.
Prove: Quadrilateral ABCD is a parallelogram.
Proof:
Statement Reason
1. and bisect each other. given
2. AE = EC
BE = ED definition of bisection
3. mAEB = mCED
4. ABE CDE SAS criterion
5. ACD CAB Corresponding angles of congruent triangles are congruent.
6. converse of Alternate Interior Angles Theorem
7. mBEC = mAED Vertical Angles Theorem
8. BEC DEA SAS criterion for congruence
9. DBC BDA Corresponding angles of congruent triangles are congruent.
10. converse of Alternate Interior Angles Theorem
11. Quadrilateral ABCD is a parallelogram. definition of a parallelogram
a Alternate Interior Angles Theorem
B. Corresponding angles in congruent triangles are congruent.
C. For parallel lines cut by a transversal, corresponding angles are congruent.
D. Vertical Angles Theorem
E. SAS criterion for congruence
NEED HELP ASAP!!!!
A flavored drink is made using a mixture of a powder drink mix and water, with ratio of powder to water that is 3:2 based on weight. If 20 g of the powdered mix is needed for a certain amount of the flavored drink, how much water will be needed?
Answers
Answer:
[tex]13.\overline 3[/tex]
Step-by-step explanation:
We can use proportions to find the amount of water needed
Let [tex]x[/tex] be the amount of water needed
[tex]\frac{3}{2} = \frac{20}{x}[/tex] (with the ratio being 3 powder to 2 water)
Now we can cross multiply and solve for [tex]x[/tex]
[tex]3(x) = 20(2)\\3x = 40\\x = \frac{40}{3}\\ x = \boxed{13.\overline3}[/tex]
You will need [tex]13.\overline3[/tex] grams of water to make the flavored drink.
Type the correct answer in each box. Round the vector's magnitude to the nearest tenth.
Vector u has its initial point at (14,-6) and its terminal point at (-4, 7). Write the component form of u and find its magnitude.
Answers
Component form of u is (-18,13) and The magnitude of u is 22.2
What is a vector?A vector is a two-dimensional entity with both magnitude and direction. A vector can be visualized geometrically as a directed line segment.
The component form of a vector is an ordered pair that describes the change in x and y values
This is mathematically expressed as (Δx, Δy) where Δx=x₂-x₁ and Δy=y₂-y₁
Given ;
Initial points of the vector as (14,-6)
The terminal point of the vector is (-4,7)
Here x₁=14,x₂=-4, y₁=-6,y₂=7
The component form of the vector u is (-4-14,7--6) =(-18,13)
Finding the Magnitude of the vector
u=√(x₂-x₁)²+(y₂-y₁)²
u=√-18²+13²
u=√324+169
u=√493
u=22.2
Therefore the Component form of u is (-18,13) and The magnitude of u is 22.2
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Solve for x. Round to the nearest tenth of a degree, if necessary.
Answers
[tex]~~~~~\sin \theta = \dfrac{\text{Perpendicular}}{\text{Hypotenuse}}\\\\\\ \implies \sin x = \dfrac{HI}{GI}\\\\\\\implies \sin x = \dfrac{39}{62}\\\\\\\implies x= \sin^{-1} \left( \dfrac{39}{62} \right)\\\\\\\implies x =38.9^{\circ}[/tex]
Which statements are true for the functions g(x) = x2 and h(x) = –x2 ? Check all that apply.
For any value of x, g(x) will always be greater than h(x).
For any value of x, h(x) will always be greater than g(x).
g(x) > h(x) for x = -1.
g(x) < h(x) for x = 3.
For positive values of x, g(x) > h(x).
For negative values of x, g(x) > h(x).
Answers
Using translation concepts, it is found that the correct statements are given as follows:
g(x) > h(x) for x = -1.For positive values of x, g(x) > h(x).For negative values of x, g(x) > h(x).What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
In this problem, the functions are:
g(x) = x².h(x) = -x².h(x) = -x² = -g(x), which means that h(x) is a reflection of g(x) over the x-axis. Since [tex]g(x) \geq 0[/tex] for all values of x, [tex]h(x) \leq 0[/tex] for all values of x, which means that they are equal at the origin and g is greater for other values of x, hence the correct statements are:
g(x) > h(x) for x = -1.For positive values of x, g(x) > h(x).For negative values of x, g(x) > h(x).More can be learned about translation concepts at https://brainly.com/question/4521517
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A restaurant's seating is completely full. There
are some four-person tables and 8 tables withcouples. If there are 56 people here, how many
four-person tables are there?
Answers
Final answer: 10 four-person tables.
tìm số hữu tỉ
(x-5/6)^2=1/36
Answers
Answer:
x = [tex]\frac{2}{3}[/tex] , x = 1
Step-by-step explanation:
(x - [tex]\frac{5}{6}[/tex] )² = [tex]\frac{1}{36}[/tex] ( take square root of both sides )
x - [tex]\frac{5}{6}[/tex] = ± [tex]\sqrt{\frac{1}{36} }[/tex] = ± [tex]\frac{1}{6}[/tex] ( add [tex]\frac{5}{6}[/tex] to both sides )
x = [tex]\frac{5}{6}[/tex] ± [tex]\frac{1}{6}[/tex] , then
x = [tex]\frac{5}{6}[/tex] - [tex]\frac{1}{6}[/tex] = [tex]\frac{4}{6}[/tex] = [tex]\frac{2}{3}[/tex]
x = [tex]\frac{5}{6}[/tex] + [tex]\frac{1}{6}[/tex] = [tex]\frac{6}{6}[/tex] = 1
Find the median and mean of the data set below:
11,48,6,25,31
Answers
Answer:
mean 24.2
median 25
Step-by-step explanation:
6 11 25 31 48
Bella can rake the leaves in 3 hours and Jordan can complete the same task in 4 hours. If they work together, how long will it take Bella and Jordan to rake the leaves? Round your answer to the nearest hundredth of an hour.
Answers
Using the together rate, it is found that it will take 1.71 hours for Bella and Jordan to rake the leaves.
What is the together rate?It is the sum of each separate rate.
In this problem, the rates are given as follows:
Together: 1/x.Bella's: 1/3.Jordan's: 1/4.Hence:
[tex]\frac{1}{x} = \frac{1}{3} + \frac{1}{4}[/tex]
[tex]\frac{1}{x} = \frac{4 + 3}{12}[/tex]
[tex]x = \frac{12}{7}[/tex]
x = 1.71.
It will take 1.71 hours for Bella and Jordan to rake the leaves.
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Geometry: Solve for x
Answers
Answer:
[tex]4\sqrt{3}[/tex]
Step-by-step explanation:
Since <PDA is right, the vertical angle, <BDC is right as well. Using sum of angles in a triangle, the angles in triangle BDC sum to 180, and for solving for <DCB, you get 30 degrees.
The line connecting the intersection of the tangents to the radius bisects the angle formed by the tangents; therefore, m<PCA is also 30 degrees.
A radius drawn to the point of tangency is perpendicular to the tangent, so <PAC is a right triangle. We can use sum of angles in a triangle for triangle PAC. Since <PCA is 30 and <PAC is right, <DPA is 60 degrees.
Now, we can look at triangle DPA, using sum of angles in a triangle, we can conclude triangle DPA is a 30-60-90 special right triangle. The leg opposite the 60 degree angle is √3 times the leg opposite the thirty degree angle. Since <DPA is 60 degrees and <PAD is 30:
[tex]DP\sqrt{3} = 6\\DP = \frac{6}{\sqrt{3} } \\DP = \frac{6}{\sqrt{3} } \times \frac{\sqrt{3} }{\sqrt{3} } \\DP = \frac{6\sqrt{3} }{3} \\DP = 2\sqrt{3}[/tex]
Also, in a 30-60-90, the hypotenuse is twice the leg opposite the 30 degree angle, so x is 2 * 2√3. or [tex]4\sqrt{3}[/tex].
Drag each tile to the correct box.
Match each equation with its solution.
Equation
Solution
arrowRight
arrowRight
arrowRight
arrowRight
Answers
The correct match of each tile of the equation with its solution is:
n - 13 = - 12 →→→ 1n/5 = -1/5 →→→ -1n + 15 = - 10 →→→ -25How do we match each tile to the correct box?To match each tile to the correct box, we have to solve the arithmetic operations in the box, then drag the correct tile that matches our answer into the box.
From the image attached below;
1.
n - 13 = - 12
Let us add (+13) to both sides to eliminate (-13), i.e.
n - 13 + 13 = - 12 + 13
n = 1
2.
n/5 = -1/5
multiply both side by 5
n/5 × (5) = -1/5 × (5)
n = -1
3.
n + 15 = - 10
n +15 - 15 = - 10 - 15
n = -25
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The chart below shows conversion between yards and inches.
Conversion Chart
Yards
Inches
3
108
6
?
8
288
11
396
What is the missing value in the table?
144
180
198
216
Answers
step by step explanation :
to converting yard to inches you have to multiply whatever number u are given in yard by 36 to get your figure in inches
o multiply whatever number u are given in yard by 36 to get your figure in inches so we multiply 6 *36 to give us 216
o multiply whatever number u are given in yard by 36 to get your figure in inches so we multiply 6 *36 to give us 216answer:
216
Find the area of the polygon.
2 cm
3 cm
1 cm
3 cm
4 cm
Answers
Answer:
the area of the problem is 20
lolllll helppppp it’s probably simple buttttt
Answers
4951 to the nearest 1000
Answers
Answer:
5000
makes the best sense
The ratio of legs to dogs in the cat shelter was 4 to 1. If there were 8 cats , then how many cats were there?
Answers
Answer:
if there were 8 cats then theres 8 cats, or 32 dogs
Step-by-step explanation:
Which function is positive for the entire interval [–3, –2]? On a coordinate plane, a curved line with a minimum value of (0, negative 3) crosses the x-axis at (negative 3, 0) and (3, 0), and crosses the y-axis at (0, negative 3). On a coordinate plane, a curved line with a minimum value of (2, negative 3) crosses the x-axis at (negative 1, 0) and (5, 0), and crosses the y-axis at (0, negative 1.5). On a coordinate plane, a curved line with a minimum value of (2, 4) and a maximum value of (0.5, 6), crosses the x-axis at (negative 1.5, 0) and crosses the y-axis at (0, 5). On a coordinate plane, a curved line with a minimum value of (negative 1.75, negative 3.9) and a maximum value of (0, 2), crosses the x-axis at (negative 2.2, 0), (negative 0.75, 0), and (0.75, 0), and crosses the y-axis at (0, 2).
Answers
The function that is positive for the entire interval [–3, –2] is the graph of the function (b)
How to determine the function?See attachment for the proper representation of the available options
For a function to be positive on the interval [-3,-2];
It means that the y values must be in the positive quadrant from x = -3 to x =-2
From the list of options, we have:
The y values from x = -3 to x =-2 is at the positive quadrant for the second graph i.e. option B
Hence, the function that is positive for the entire interval [–3, –2] is the graph of the function (b)
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Find the missing base of the triangle when the area is 94.5cm2
Answers
Answer:
this is your answer
hope it will help you
help pls i need it really fast
Answers
Answer:19 for first answer. Second answer is subtract 16 from both sides
Step-by-step explanation:76/4 first answer
Abc car share inc. offers car sharing for a $199 yearly fee plus $14/hr for the
use of its car share. what is the total cost for a person who purchases a car
share and uses it for 72 hours total time?
Answers
The total cost for a person who purchases a car share and uses it for 72 hours is $1207.
What is the total cost?The total cost is a function of the yearly fee and the cost per hour.
Total cost = yearly fee + (total hours the car was used for x cost per hour)
$199 + (72 x $14)
$199 + $1008 = $1207
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i need help. due today
Answers
Explanation:
This expression is vertical from the angle 135, meaning it is congruent. With that being said, we would need to find what 7 multiplies by to give us 2 less than 135, which would be 133. Because 133 divided by 7 equals 19, x = 19. If we plug this in, we get the following equation: 7(19) + 2 = 135.
Answer:
19
Step-by-step explanation:
7x +2 = 135. Vertically opposite angles
7x=133
x=19
How many combinations exist of the letters W, X, Y, Z, taking two at a time?
04
06
012
Answers
Step-by-step explanation:
C(4,2)
Use combinations formula,
c(n,r)=n!/r!(n-r)!
c(n,r)=4!/2!(2!)
[tex]c = \frac{4 \times 3 \times 2 \times 1 }{2 \times 1 \times 2 \times 1} [/tex]
[tex]c = 3 \times 2 \times 1[/tex]
[tex]c = 6[/tex]
please help me with this if you can? thanks alot :)))
Answers
The probabilities are:
P(red) = 5/24P(orange) = 0 P(blue) = 1/3P(not green)= 17/24P(green or black) = 11/24P(not yellow) = 1.How to find the probabilities?
The probability of getting a particular color of marble, is given by the quotient between the number of marbles of that color and the total number of marbles.
Here we have:
5 red marbles.7 green marbles.4 black marbles.8 blue marbles.So the total number is 5 + 7 + 4 + 8 = 24.
Then:
P(red) = 5/24P(orange) = 0/24 = 0 (because there are 0 orange marbles).P(blue) = 8/24 = 1/3P(not green) = (24 - 7)/24 = 17/24P(green or black) = (4 + 7)/24 = 11/24P(not yellow) = 24/24 = 1 (because there aren't yellow marbles).If you want to learn more about probability, you can read:
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Work out the area of a circle with diameter 1.8cm.
Take pi to be 3.142 and give your answer to 1 decimal place
Answers
Step-by-step Explaination:
Diameter = 1.8 cm
Radius (r) = 1.8/2 = 0.9
According to formula...
Area of circle = π(r)^2
= 3.142 * 0.9 * 0.9
= 2.54502 cm
Answer to 1 decimal place :-2.5 cm...ans Hope it helps you!!Select the correct answer from each drop-down menu.
This graph shows the relationship between demand and price for goods sold at a shop. Anna plots the data on a scatter plot and draws a line of best fit to represent the relationship as shown.
This is not the line of best fit because the line . Anna could get a better fit by the y-intercept and the slope.
Answers
This is not the line of best fit because the line is not through the middle of the data points.
What is line of best fit?
The line of best fit is a line through a scatter plot of data points that best expresses the relationship between those points.
In this case, this is not the line of best fit because the line is not through the middle of the data points.
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grades are do today please help
Answers
Answer:
length of PR is [tex]4\sqrt{5}[/tex]
Is an isosceles triangle
because PQ is congruent to QR
Step-by-step explanation:
Calculate length of P(-6,0) R(2,4)
=> apply distance formula
[tex]\left(x_1,\:y_1\right),\:\left(x_2,\:y_2\right):\quad \sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}[/tex]
[tex]\sqrt{\left(2-\left(-6\right)\right)^2+\left(4-0\right)^2}[/tex]
[tex]4\sqrt{5}[/tex]
Calculate length of P(-6,0) Q(-3,4)
[tex]\sqrt{\left(-3-\left(-6\right)\right)^2+\left(4-0\right)^2}[/tex]
= 5
5(PQ) = 5(QR)
What is the solution to the system of equations graphed below?
(0, 4)
(3, 1)
(1, 3)
(4, 0)
Answers
Answer:
(c) (1, 3)
Step-by-step explanation:
The solution to the system of equations shown on the graph is the point where the lines intersect.
__
The coordinates of the point of where the lines cross are (1, 3).
The solution to the system of equations is (x, y) = (1, 3).