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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3.4 The rectangular box has the length of 8x² and the breadth of 6x² - 4x 3.4.1 What is the area of the box? 3.4.2 Factorise the area of the box? 3.4.3 If x = 2 what will be the value of the length and the breadth?
Answer:
3.4.1) (8x^2)(6x^2 - 4x) = 48x^4 - 32x^2
3.4.2) 48x^4 - 32x^2 = (16x^2)(3x^2 - 2)
3.4.3) Length = 16(2^2) = 16(4) = 64
Width = 3(2^2) - 2 = 3(4) - 2
= 12 - 2 = 10
Area = 64(10) = 640
please help for this question
The single transformation that maps shape A to shape B is: Reflection about the line x = -2
What is the transformation rule?There are different ways of carrying out transformation of objects and they are:
Reflection whereby all the points of an object are reflected or flipped on a line called the axis of reflection or line of reflection
Rotation whereby all points are rotated about a point.
Dilation where the object is reduced or increased by a scale factor.
Translation where the object is moved from one point to another.
Looking at the given image, we can tell that this denotes a reflection because it is the exact same shape and looks like a mirror image which was reflected over the line x = -2
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If GI and JL are parellel lines and m
The measure of angle IHE is 23°.
Since DF and GI are parallel, we know that angle HJF is congruent to angle GHJ. Therefore, we have:
mHJF = mGHJ = 134°
We can now use this information to find the measure of angle IHE. To do this, we need to use the fact that the sum of the angles in a straight line is 180°. Since H, J, F, and I lie on a straight line, we have:
mHJF + mFJI + mIHE = 180°
Substituting the values we know, we get:
134° + mFJI + mIHE = 180°
Simplifying the equation, we get:
mFJI + mIHE = 46°
We still need to find the measure of angle FJI. To do this, we can use the fact that the angles in a triangle add up to 180°. Triangle GHJ is a straight line, so its angles add up to 180°. Therefore, we have:
mGHJ + mHJF + mFJI = 180°
Substituting the values we know, we get:
134° + mFJI + mFJI = 180°
Simplifying the equation, we get:
2mFJI = 46°
Dividing both sides by 2, we get:
mFJI = 23°
Finally, we can substitute this value back into our earlier equation to find the measure of angle IHE:
mFJI + mIHE = 46°
23° + mIHE = 46°
Subtracting 23° from both sides, we get:
mIHE = 23°
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Complete Question:
If DF and GI are parallel lines and mGHJ = 134°, what is mIHE?
Johnny's cafe serves desserts. One serving of ice cream and two servings of blueberry pie provides 790 calories. Three servings of ice cream and two serving of blueberry pie provides 1290 calories
The caloric content for ice cream C is 250 calories while the caloric content for ice cream B is 270 calories.
How to determine the caloric contentTo determine the caloric content, we will assign algebraic notations to each of the dessert types.
1 Icecream + 2 Blueberry pie = 790 calories
3 icecream + 2 Blueberry pie = 1290 calories
Now the first equation will be subtracted from the second equation as follows:
2 icecream = 500 calories
So, 1 ice cream is 250 calories.
Also, since, 1 icecream serving equals 250 calories, 2 Blueberry pies = 790 - 250 = 540 calories, and 1 Blueberry pie equals 270 calories.
Complete question:
Johnny's cafe serves desserts. One serving of ice cream and two servings of blueberry pie provides 790 calories. Three servings of ice cream and two servings of blueberry pie provides 1290 calories. Find the caloric content of each item.
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Trundle wheels are used to measure distances along the ground.
The radius of the trundle wheel is 30 cm.
Jim wants to work out the distance between two junctions on a road.
He rolls the trundle wheel between the two junctions.
The trundle wheel rotates exactly 48 times.
Work out the distance between the two junctions.
Give your answer in metres correct to the nearest metre.
The distance between the two junctions is, 90 meters, when rounded off to the nearest meter.
:: Radius of trundle wheel = 30 cm = 0.3 meter (as 100 cm = 1 m)
:: No. of rotations = 48
:: Circumference of a circle = ( 2 x π x r )
where, r is radius of the circle
So, as,
Distance between junctions = [ (circumference of trundle wheel) x (no. of rotations) ]
Therefore,
Distance = (2 x π x 0.3) x (48)
Distance = 2 x (3.14) x 0.3 x 48
Distance = 90.432 meters
When rounded off to the nearest meter,
Distance = 90 meters.
So, The distance between the two junctions is, 90 meters, when rounded off to the nearest meter.
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I understand the lower and upper class limits but there are only one number but I don't know what to do
The class mark of the modal class is: 25
How to solveFrom the given histogram, the following Frequency Distribution is obtained:
Class Interval Mid point Frequency
625-675 650 3
676-726 701 5
727 - 777 752 7
778 - 828 803 8
829 - 879 854 6
880 - 930 905 2
931 - 981 956 0
982 - 1032 1007 1
b. To find the lower class limit of the first class:
First class: 625
c. The upper limit of the first class is:
First class: 676
The class mark of the modal class is:
The modal class is: 803
The class mark is upper limit + lower limit/2
Thus, 828-778/2
=> 50/2
The class mark of the modal class is: 25
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if my circular garden requires 2 cups of water per 10 square feet, how many cups of water do i need when the radius is 3 feet
The mean monthly salary of female employees of a company is 3750 Birr, while the mean monthly salary of male employees is 4500 Birr. It is known that the mean monthly salary of male and female employees combined is 4000 Birr. a) What is the ratio of the number of female employees to male employees? b) What percentage of employees are females?
A map shows the vertices of a campsite are (25,10), (25,-5), (-5,-5), and (-5,10). The vertices of your tent are (0,-3), (0,6), (10,6), and (10,-3). The coordinates are measured in feet. What percent of the campsite is not covered by your tent?
The percent of the area that is not covered is 80 percent
How to calculate the area that is not coveredIn mathematics area is defined as the absolute or total space that an object or shape occupies. It is usually measured using centimeters, cm ² square or the use of meter square m ².
area of tent
= (10 - 0) * (6 - (-3))
= 90
The area of the campsite would be:
(25 - (-5) x (10 - (-5))
= 450
Then the area would be 450 - 90
= 360
the percentage that is not covered by tent = 360 / 450 x 100
= 80 percent
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Find the consumers' surplus at a price level of $1 for the price-demand equation
p= D(x) = 20-0.1x
where p is the price and x is the demand. Do not include a dollar sign or any commas in your answer.
The consumers' surplus at a price level of $1 for the price-demand equation is -1072.5.
Given that price-demand equation p= D(x) = 20-0.1x, we need to find the consumers' surplus at a price level of $1.
So,
From the equation we have,
20-0.1x = 1
0.1x = 19
x = 190
Therefore, the equilibrium point = (190, 1) = (xe, Pe)
Now,
Cs = [tex]\int\limits^{x_e}_0 {D(x)} \ dx\, -Pexe[/tex]
[tex]\int\limits^{190}_0 {20-0.1x} \ dx\, -(190)[/tex]
= 20-0.1{9025}-190
= -1072.5
Hence the consumers' surplus at a price level of $1 for the price-demand equation is -1072.5
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‼️HELP CUZ IM SO LOST PLEASE‼️
Using two column proof we have been able to show that AB ║ EC
by definition of alternate interior angles
How to use two column proof?A two-column proof is defined as a two-column table labeled with statements on the left-hand side and reasons on the right-hand side.
The two column proof of the given diagram is as follows:
Statement 1: ΔADE is an Isosceles Triangle
Reason 1: Given
Statement 2: ∠DEA ≅ ∠DAE
Reason 2: Properties of Isosceles Triangles
Statement 3: ∠ADE = 20°
Reason 3: Sum of angles in a triangle
Statement 4: ∠BAD ≅ ∠EDA
Reason 4: Congruent Angles
Statement 5: ∠BAD and ∠EDA are alternate angles
Reason 5: Alternate angles are congruent
Statement 6: AB ║ EC
Reason 6: Definition of alternate interior angles
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A company produces two products, A and B. At
least 30 units of product A and at least 10 units of
product B must be produced. The maximum
number of units that can be produced per day is
80. Product A yields a profit of $15 and product B
yields a profit of $8. Let a = the number of units of
product A and b = the number of units of product
B.
What objective function can be used to maximize
the profit?
P=
DONE✔
a+
b
The objective function that can be used to maximize the profit is Profit = 15a + 8b
Let a is the number of units of product A and b is the number of units of product B.
Profit = 15a + 8b
This function represents the total profit earned by producing a units of product A and b units of product B
Given that the profit per unit of product A is $15 and the profit per unit of product B is $8.
To maximize the profit, we would need to find the values of a and b that satisfy the constraints given in the problem and maximize the value of the objective function
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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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The cost of a pen is $15. Find the cost of 162 pens
Answer: 15 x 162 = 2430$
Find the degree of the monomial. 3a^8b^7
6 yards 2 feet 5 inches equals
Answer:
245 inches
Step-by-step explanation:
Yards->Inches
1 yard = 36 inches
Therefore, 6 yards = 36 x 6 = 216 inches
Feet->Inches
1 feet = 12 inches
Therefore, 2 feet = 2 x 12 = 24 inches
Adding all inches,
=> 216 + 24 + 5
=> 245 inches
Find the volume of the cone shown. Use 3.14 for pi. Round your answer to the nearest hundredth.
Answer: 100.48 cubic feet
Step-by-step explanation:
Lines and Angles
10) In the figure below BD is the perpendicular bisector of AC. Find the value of x.
3(2x-8)
4425
Enter your answer in the box.
x=
Since BD is the perpendicular bisector of AC, then AB = BC, which implies 2x - 8 = 5x - 17.
Solving for x, we have:
3(2x - 8) = 4425
6x - 24 = 4425
6x = 4451
x = 741.83
Rounding to the nearest whole number, we have x = 742.
Therefore, x = 742.
.If $10,000 is deposited in an account earning 5 ¾ % interest compounded monthly. How much money will be in the account in 5 years.
The total amount in the acount in 5 years is approximately $13,321.76.
What is the accrued amount in the account in 5 years?The formula accrued amount in a compounded interest is expressed as;
[tex]A = P( 1 + \frac{r}{n} )^{n*t}[/tex]
Where A is accrued amount, P is principal, r is interest rate and t is time.
Given that:
Principal P = $10,000Compounded monthly n = 12Time t = 5 yearsInterest rate r = 5 3/4% = 5.75%Accrued amount A = ?First, convert R as a percent to r as a decimal
r = R/100
r = 5.75/100
r = 0.0575
Plug the given values into the above formula and solve for A.
[tex]A = P( 1 + \frac{r}{n} )^{n*t}\\\\A = 10000( 1 + \frac{0.0575}{12} )^{(12*5)}\\[/tex]
A = $13,321.76
Therefore, the accrued amount is $13,321.76.
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Models that represent z+9=14 ASAP
To represent z+9=14, we can start by subtracting 9 from both sides of the equation:
z + 9 - 9 = 14 - 9
Simplifying the left side of the equation gives:
z = 5
Therefore, the solution to the equation z+9=14 is z=5.
Rosie earns $25 for travel time plus $18 an hour working at her uncle’s shop. Write an expression that can be used to find the amount Rosie will earn for working, 7, hours.
Answer:
Earned = 25 + 18h
Earned = 151
Step-by-step explanation:
The amount earned is the travel time plus the amount per hour times the hours
Earned = 25 + 18h
She works 7 hours
Earned = 25 + 18*7
Earned = 25 + 126
Earned = 151
A 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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A local radio station is running a contest were 35 people have qualified. From these qualifiers, 3 will be randomly selected to win a trip to the Bahamas. How many different possibilities are there for the outcome of this contest?
Answer:
39270
Step-by-step explanation:
When the first person is picked, there is a 1 in 35 chance that it will be Person 1. If they are selected, that leaves 34 people left in the pool. After Person 2 is selected, there are 33 people left in the pool for Person 3.
35*34*33=39270
A spinner divided into three equal sections marked A A and Z is spun 570 times approximately how many times will it be expected to land on an A
If a spinner divided into three equal sections marked A A and Z is spun 570 times . The number of times it will be expected to land on an A is 380 times.
How to find the Expected number of time ?Since the spinner has three equal sections in which two of them are marked A. The probability of landing on an A in a single spin will be 2/3 while the probability of landing on Z will be 1/3.
So,
Expected number of time E(A) =Number of spins x Probability of landing on A
Expected number of time E(A) = 570 x (2/3)
Expected number of time E(A) = 380
Therefore the Expected number of time E(A) is 380 times.
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Find the probability that
event A or B takes place.
The probability that event A or B takes place is P ( A ∪ B ) = 6/17
Given data ,
Let the probability that event A or B takes place is P ( A ∪ B )
Now , the probability of A is P ( A ) = 2/17
And , the probability of B is P ( B ) = 4/17
where P ( A ∩ B ) = 0
On simplifying the equation , we get
P ( A ∪ B ) = P ( A ) + P ( B ) - P ( A ∩ B )
So , P ( A ∪ B ) = 2/17 + 4/17
P ( A ∪ B ) = 6/17
Hence , the probability is 6/17
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Consider the line y = -8x + 7.
Find the equation of the line that is perpendicular to this line and passes through the point (-5, 3).
Find the equation of the line that is parallel to this line and passes through the point (-5, 3).
The equation of the line that is parallel to the line that passes through the point (7, 6) is y = 8x - 50.
What is a line?A line is an object in geometry that is indefinitely long and has neither breadth nor depth nor curvature.
Since lines can exist embedded in two, three, or higher dimensions environments, they are one-dimensional objects.
The term "line" can also be used to describe a line segment in daily life that contains two locations that serve as its ends.
So, the lines with the same slope but a different y-intercept are said to be parallel.
Therefore, we must use the same slope to plug in the point (7, 6) and solve for the y-intercept.
We thus have:
y = 8x + b
6 = 8(7) + b
6 = 56 + b
b + 56 = 6
b + 56 - 56 = 6 - 56
b = -50
The equation is: y = 8x - 50
Therefore, the equation of the line that is parallel to the line that passes through the point (7, 6) is y = 8x - 50.
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Correct question:
Consider the line y = 8x - 4. Find the equation of the line that is parallel to this line and passes through the point (7, 6).
Plsss help meeee quick
Answer:
B
Step-by-step explanation:
Lateral surface contains B,C and D (because A and E are bases)
A (lateral surface area) = 70 + 70 + 56 = 196 cm^2
A population of rabbits is increasing at a rate of 1.5% per month. If there are 60 rabbits today, how many will there be after 10 months? Round to the nearest whole.
If population of rabbits is increasing at a rate of 1.5% per month, after 10 months, there will be approximately 71 rabbits in the population.
To solve this problem, we need to use the formula for exponential growth:
A = P(1 + r)ᵗ
where A is the final amount, P is the initial amount, r is the growth rate as a decimal, and t is the time period. In this case, we have P = 60, r = 0.015 (1.5% expressed as a decimal), and t = 10.
Plugging these values into the formula, we get:
A = 60(1 + 0.015)¹⁰
A ≈ 71
t's important to round to the nearest whole, so we can't be exact, but we know the answer will be somewhere between 70 and 72 rabbits.
Exponential growth is a model that assumes continuous growth over time, which may not be entirely accurate in real-world scenarios.
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PLEASE HELP ME QUICK!!!
Answer:
Option D. [tex]g(x)=5(0.8)^{x}+2[/tex]
Step-by-step explanation:
Main concepts
Concept 1: identifying horizontal asymptote
Concept 2: assuring decreasing exponential function
Concept 1. identifying horizontal asymptote
Any exponential function of the form [tex]y=a*b^x[/tex] has a horizontal asymptote on the x-axis. A constant (positive or negative) added to the end of the exponential expression will shift the graph of the exponential function up (if positive) or down (if negative) the number of units equal to the magnitude of the number. Since the original function f(x) has a "+2" at the end, it has been shifted up 2 units. Thus, we can eliminate answers A and C from feasible answers since they each shift the exponential function up 3 units, not 2.
Concept 2. assuring decreasing exponential function
Exponential functions of the form [tex]y=a*b^x[/tex] increase or decrease based on the value of "b".
If "b" is between 0 and 1 (a "small" number), the function will decrease.If "b" is larger than 1 (a "big" number), the function will increase.Observe that the graph of the function f(x) is decreasing, and the value of b=0.5.
To ensure that g(x) also decreases, the b-value must be between 0 and 1, which eliminates option B.
Option D is the correct answer because the value of "b" is between 0 and 1 (making the graph of the function a decreasing exponential), and the number added at the end is "+2", causing the horizontal asymptote to be at a height of positive 2.
Find the exact value of each of the remaining trigonometric functions of θ.
tan θ= -3/5, sec θ>0.
If given trigonometric functions of θ are tan θ= -3/5, sec θ>0, the exact value of sin θ is 3/√(34).
To find the value of sin θ, we can use the Pythagorean identity: sin²θ + cos²θ = 1.
First, we need to find the value of cos θ. We know that sec θ = 1/cos θ and sec θ > 0, which means that cos θ > 0. Therefore, we can use the identity: tan²θ + 1 = sec²θ to find the value of cos θ.
tan θ = -3/5
tan²θ = 9/25
sec²θ = tan²θ + 1 = 34/25
cos²θ = 1/sec²θ = 25/34
cos θ = √(25/34) = 5/√(34)
Now, we can use the Pythagorean identity to find sin θ:
sin²θ + cos²θ = 1
sin²θ = 1 - cos²θ
sin²θ = 1 - 25/34
sin²θ = 9/34
sin θ = √(9/34) = 3/√(34)
In trigonometry, the six trigonometric functions (sine, cosine, tangent, cosecant, secant, and cotangent) are used to relate the angles of a triangle to its sides. The sine function is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse. In other words, sin θ = opposite/hypotenuse.
Knowing the value of sin θ is important because it allows us to calculate the values of the other trigonometric functions. For example, cosine is defined as the ratio of the length of the adjacent side to the length of the hypotenuse, so we needed to find the value of cos θ to calculate sin θ.
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