Step-by-step explanation:
58 g = 660 g * ( 1/2)^n
58 / 660 = (1/2) ^n LOG both sides
-1.056 = n log 1/2
n = 3.508 half lives
3. 508 x 10 min = ~ 35.1 min
[tex]\textit{Amount for Exponential Decay using Half-Life} \\\\ A=P\left( \frac{1}{2} \right)^{\frac{t}{h}}\qquad \begin{cases} A=\textit{current amount}\dotfill & 58\\ P=\textit{initial amount}\dotfill &660\\ t=minutes\dotfill &t\\ h=\textit{half-life}\dotfill &10 \end{cases} \\\\\\ 58 = 660\left( \cfrac{1}{2} \right)^{\frac{t}{10}} \implies \cfrac{58}{660}=\left( \cfrac{1}{2} \right)^{\frac{t}{10}}\implies \cfrac{29}{330}=\left( \cfrac{1}{2} \right)^{\frac{1}{10}\cdot t}[/tex]
[tex]\log\left( \cfrac{29}{330} \right)=\log\left[ \left( \cfrac{1}{2} \right)^{\frac{1}{10}\cdot t} \right]\implies \log\left( \cfrac{29}{330} \right)=t\log\left[ \left( \cfrac{1}{2} \right)^{\frac{1}{10}} \right] \\\\\\ \cfrac{ ~~ \log\left( \frac{29}{330} \right) ~~ }{\log\left[ \left( \frac{1}{2} \right)^{\frac{1}{10}} \right]}=t\implies 35.1\approx t[/tex]
Please see the attached
0.6/(-0.9- -0.5 x -0.3)
The value of the expression is -0.8
What is PEDMAS?PEDMAS can be described as a mathematical acronym that is used for the representation of arithmetic operations on the basis of how they are to be carried out sequentially in an equation.
The alphabet represents different operations. They are;
P represents parenthesesE represents exponentsD represents divisionM represents multiplicationA represents additionS represents subtractionFrom the information given, we have that;
0.6/(-0.9- -0.5 x -0.3)
Multiply the values
0.6/(-0.9 +0. 15)
add the values
0.6/0. 75
Now, divide the values
-0.8
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36 is 15% of what number
In a coordinate plane, what is the distance between the points (6,−10)
and (6,−7)
?
The distance between the points (6,−10) and (6,−7) is 3 units
What is the distance between the points (6,−10) and (6,−7)?From the question, we have the following parameters that can be used in our computation:
Points (6,−10) and (6,−7)
Because the points have the same x coordinate, the distance between the points (6,−10) and (6,−7) is the difference between the y coordinates
Using the above as a guide, we have the following:
Distance = -7 - -10
Evaluate
Distance = 3
Hence, the distance between the points (6,−10) and (6,−7) is 3 units
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which fraction is greater than the fraction by the model if the fraction is 3/8
The calculated value of the fraction that is greater than the fraction by the model is 1/2
Which fraction is greater than the fraction by the modelFrom the question, we have the following parameters that can be used in our computation:
Model fraction = 3/8
A fraction that is greater than the fraction by the model is represented as
Fraction > Model fraction
Substitute the known values in the above equation, so, we have the following representation
Fraction > 3/8
Add 1 to the numerator
So, we have
Fraction = 4/8
Simplify
Fraction = 1/2
Hence, the fraction that is greater than the fraction by the model is 1/2
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Write the equation of a line parallel to 2y = x – 3 and that passes through point (-4,3) in slope intercept form.
Answer:
The equation of the line parallel to 2y = x – 3 and passing through point (-4,3) in slope-intercept form is y = (1/2)x + 5.
Step-by-step explanation:
To find the equation of a line that is parallel to 2y = x – 3, we need to determine the slope of the given line.
2y = x - 3 can be written in slope-intercept form y = (1/2)x - 3/2.
The slope of this line is 1/2.
Since we want a line parallel to this line, the slope of the new line will also be 1/2.
Next, we can use the point-slope form of a line to write the equation of the new line.
Point-slope form: y - y1 = m(x - x1)
where (x1, y1) is the given point and m is the slope of the line.
Substituting the values, we get:
y - 3 = (1/2)(x - (-4))
Simplifying, we get:
y - 3 = (1/2)x + 2
Adding 3 to both sides, we get the final equation in slope-intercept form:
y = (1/2)x + 5
Therefore, the equation of the line parallel to 2y = x – 3 and passing through point (-4,3) in slope-intercept form is y = (1/2)x + 5.
HELP ASAP!!!
(Appropriate Measures MC)
A charity needs to report its typical donations received. The following is a list of the donations from one week. A histogram is provided to display the data.
10, 10, 10, 10, 15,15,15,19, 20, 20, 20, 25, 25, 25, 30, 30, 55, 55
A graph titled Donations to Charity in Dollars. The x-axis is labeled 10 to 19, 20 to 29, 30 to 39, 40 to 49, and 50 to 59. The y-axis is labeled Frequency. There is a shaded bar up to 8 above 10 to 19, up to 6 above 20 to 29, up to 2 above 30 to 39, and up to 2 above 50 to 59. There is no shaded bar above 40 to 49.
Which measure of variability should the charity use to accurately represent the data? Explain your answer.
The IQR of 10 is the most accurate to use, since the data is skewed.
The range of 10 is the most accurate to use, since the data is skewed.
The IQR of 45 is the most accurate to use to show that they need more money.
The range of 45 is the most accurate to use to show that they have plenty of money.
A measure of variability which the charity should use to accurately represent the data include the following: D. The range of 45 is the most accurate to use to show that they have plenty of money.
What is a box-and-whisker plot?In Mathematics and Statistics, a box plot is a type of chart that can be used to graphically or visually represent the five-number summary of a data set with respect to locality, skewness, and spread.
Based on the information provided about the data set, the five-number summary for the given data set include the following:
Minimum (Min) = 10.
First quartile (Q₁) = 13.75.
Median (Med) = 20.
Third quartile (Q₃) = 26.25.
Maximum (Max) = 55.
For the IQR, we have:
IQR = Third quartile (Q₃) - First quartile (Q₁)
IQR = 26.25 - 13.75
IQR = 12.50
For the range, we have;
Range = maximum - minimum
Range = 55 - 10
Range = 45.
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The height y(in feet) of a ball thrown by a child isy=−114x2+2x+3
where x is the horizontal distance in feet from the point at which the ball is thrown.
(a) How high is the ball when it leaves the child's hand? (Hint: Find y
when x=0)
Your answer is y=____
(b) What is the maximum height of the ball? _____
(c) How far from the child does the ball strike the ground?_____
Solve for x. Round to the nearest tenth, if necessary.
Using the sine ratio, the value of x in the right triangle shown is calculated to the nearest tenth as: 2.6 units.
How to Find the Value of x Using the Sine Ratio?The sine ratio is part of the trigonometry ratios that can be applied to solve a right triangle, and it is written as:
sin ∅ = length of the opposite side / length of the hypotenuse of the right triangle
We are given the following information from the image above:
Reference angle (∅) = 75 degrees
length of the opposite side = x
length of the hypotenuse = 9
Plug in the values:
sin 75 = x/9
9 * sin 75 = x
x = 8.7 [to the nearest tenth]
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One respondent said they watched 10 movies. This seems to be an
symmetrical
This graph is
skewed
to the
left
because the data is stacked on the left with a "tail" going to the right.
Most people watched
[ Select ]
movies
The graph seems to be a left symmetrical distribution and most people watched action movies
Calculating the skewness of the graphFrom the question, we have the following parameters that can be used in our computation:
The graph (see attachment)
From the graph, we have the following readings and observations
The movie with the highest frequency is Action moviesThe data is stacked on the right with a "tail" going to the left.Using the above as a guide, we have the following conclusions
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Find m/_U. Write your answer as an integer or as a decimal rounded to the nearest tenth.
The measure of angle U = 41.83 degree.
In the given right angle triangle
VW = 6
UV = 9
Since sinΘ = (opposite side)/(hypotenuse)
Therefore,
sin U = VW/UV
= 6/9
= 0.667
Take inverse of sin both sides
∠U = arcsin(0.667)
= 41.83
Hence ∠U = 41.83 degree
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the cost of a luna bar is 2 dollars at harmons. what is the cost of 30 luna bars
Answer:
60
Step-by-step explanation:
2$ times 30 luna bars at harmons is $60
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
HELP ME PLEASEEEE The matrix below represents a system of equations.
Which matrix represents the solution to this system of equations?
The matrix that represents the solution to this system of equations is
1 0 0 2
0 1 0 -4
0 0 1 3
Therefore option B is correct.
What is a matrix in mathematics?A matrix is described as a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns, which is used to represent a mathematical object or a property of such an object.
We solve a matrix by Arranging the elements of equations in matrices and find the coefficient matrix, variable matrix, and constant matrix.
We then go ahead to write the equations in AX = B form.
we then take the inverse of A by finding the adjoint and determinant of A. Multiply the inverse of A to matrix B, thereby finding the value of variable matrix X.
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100 Points! Algebra question. Please show as much work as possible. Photo attached. Thank you!
The value of the constant term k in the exponential model of the bacteria population is k ≈ 0.0972
What is an exponential function?An exponential function is one in which the input variable is part of the exponent of the expression for the function.
The function for the population of the bacteria indicates;
[tex]P(t) = \frac{22,000 }{1 + 1.2\cdot e^{(-k\cdot t)}}[/tex]
The population of the bacteria after t = 1 hour is P(1) = 10,532
Therefore;
[tex]P(1) = \frac{22,000 }{1 + 1.2\cdot e^{(-k\times 1)}} = 10,532[/tex]
[tex]1 + 1.2\cdot e^{(-k\times 1)} = \frac{22,000}{10,532}[/tex]
[tex]1.2\cdot e^{(-k\times 1)} = \frac{22,000}{10,532} - 1[/tex]
[tex]e^{(-k\times 1)} = \frac{\frac{22,000}{10,532} - 1}{1.2}[/tex]
Taking the natural logarithm of both sides, we get;
[tex]\ln (e^{(-k\times 1)}) = \ln (\frac{\frac{22,000}{10,532} - 1}{1.2})[/tex]
[tex]\ln (e^{(-k)}) = \ln (\frac{\frac{22,000}{10,532} - 1}{1.2})[/tex]
[tex]\ln (e^{(-k)}) = -k = \ln (\frac{\frac{22,000}{10,532} - 1}{1.2})[/tex] ≈ -0.0972 (rounded to 4 decimal places)
-k ≈ -0.0972
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john want to buy a new bike that costs 337and he already has save 103 estimates to find about how much more john needs to save to buy the bike
To find the estimated amount John needs to save to buy the bike, we can subtract the amount he already has saved from the cost of the bike:
Estimated amount = Cost of bike - Amount already saved
Estimated amount = $337 - $103
Estimated amount = $234
Therefore, John needs to save an estimated $234 more to buy the bike.
Answer:
John needs to save about $234 more to buy the bike. Note that this is an estimate, as we do not know if John will need to pay any taxes or additional fees when purchasing the bike.
Step-by-step explanation:
To find out how much more John needs to save to buy the bike, we can subtract the amount he has already saved from the cost of the bike:
337 - 103 = 234
Therefore, John needs to save about $234 more to buy the bike. Note that this is an estimate, as we do not know if John will need to pay any taxes or additional fees when purchasing the bike.
use synthetic division
PLEASE HELP!!
The quotient using a synthetic method of division is 8x² + 15x + 7/8 and the remainder is 71/64
How to evaluate the quotient using a synthetic methodThe quotient expression is given as
(8x³ + 14x² - 2x + 1) divided by x - 1/8
Using a synthetic method of quotient, we have the following set up
1/8 | 8 14 -2 1
|__________
Bring down the first coefficient, which is 8:
1/8 | 8 14 -2 1
|__________
8
Multiply 8 by 1/8 to get 1, and write it below the next coefficient and repeat the process
1/8 | 8 14 -2 1
|_____1_15/8__7/64_
8 15 7/8 71/64
So, the quotient is 8x² + 15x + 7/8 and the remainder is 71/64
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a) Close the following accounts. 9
K. Emmanuel
$
2020
$
640
360
2020
800
Feb. 10 Bank Cash
25
200
Feb. 1 15
Sales Sales
J. Amaze
$
$
2020
2020
260 1090
1350
Mar. 12
Returns inwards
Mar4
Sales
18
Bank
Z. Ventour
2020
$
2020
$
May 13
Cash
518
May 10
Purchases
518
FSampath
2020
$
2020
July 14 22
Returns outwards
Bank
$
220
July 3
Purchases Purchases
8
25
Bank
800
1500
830
350
Answer:
I dont know the answer I dont know what it is I just needed points bye
Step-by-step explanation:
An ant crawled 2/8 yard from an ant mount. On which number line does point A represent the ants position after crawling 2/8 yard?
The number line on which point A represents the ant's position after crawling 2/8 yard would be a number line labeled in units of yards, with O representing 0 and A representing 1/4 yard to the right of O.
To decide the place of the insect subsequent to creeping 2/8 yard from the insect mount, we really want to address this distance on a number line.
Since 2/8 can be rearranged to 1/4, we can address the distance crept by the subterranean insect as 1/4 of a yard.
To develop a number line to address this distance, we can begin with the point addressing the subterranean insect mount (we should call it point O) and separate a distance of 1/4 of a yard to one side of O. This point, which we can name as point A, addresses the place of the insect subsequent to creeping 2/8 yard (or 1/4 yard) from the insect mount.
The number line would have units of yards, with the distance between every unit separated similarly. The point O would address 0 on the number line, and the point A would address 1/4 yard on the number line.
Thus, the number line on which point An addresses the insect's situation in the wake of creeping 2/8 yard would be a number line named in units of yards, with O addressing 0 and An addressing 1/4 yard to one side of O.
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The complete question is:
An ant crawled 2/8 yard from an ant mount. On which number line does point A represent the ants position after crawling 2/8 yard?
It’s due tomorrow I really need help
Answer:
B.
Step-by-step explanation:
As the steps imply,
Step 1 is to first convert the 3.5% (0.035) and then multiply it by 16 to find out by how many grams the amount should decrease (0.035 * 16 = 0.56). Step 2 is to subtract this amount from 16 to find the amount remaining after one hour (16 - 0.56 = 15.44). Step 3 is to convert 4.25% to a decimal (0.0425) and multiply it by the amount remaining at the end of one hour to find out by how many grams this amount should decrease after two hours (0.0425 * 15.44 = 0.6562)Step 4 finally is to subtract this amount from 15.44 to find the amount remaining after two hours (15.44 - 0.6562 = 14.7838)20x^2-7x-6=0 by factoring
Answer:
x = -2/5
x = 3/4
Step-by-step explanation:
Factoring:
20x²-7x-6=0
20x²+8x - 15x - 6 = 0
4x * (5x + 2) - 3 * (5x + 2) = 0
(5x + 2) * (4x - 3) = 0
Cases:
5x + 2 = 0
4x - 3 = 0
x = -2/5
x = 3/4
Answer:
20x^2 -x(15-8)-6=0 here 6×20=120an by subtracting 15-8 we got seven where the 15×8 is also 120
Step-by-step explanation:
now,
20x^2 -15x+8x -6 =0 (here -×-is equal to +thus we write +8)
5x(4x-3) +2(4x-3)=0
(5x+2) (4x-3)=0
Either 5x=-2
X=-2/5
Or
4x=3
X=3/4
Question is done below. Just multiple sqrts inside of each other.
The solution to the prompt of multiple square roots is 5.
How to solve for the sum of the multiple square rootsTo obtain the sum of the multiple square roots, we need to first find the square of 30, sum it up in four places and find the square root of the last figure we obtained.
So this gives
√30 =5.47
5.47 + 5.47 + 5.47 + 5.47
= 21.88
=4.67 approximately 5
So. option 5 is the solution.
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A solution has a total mass of 400 g. If the solvent has a mass of 236 g of the total mass, what is the strength of the drug?
In a case whereby A solution has a total mass of 400 g. If the solvent has a mass of 236 g of the total mass, the strength of the drug can be expressed as 41%.
How can the strength of the drug be calculated?From the question, the total mass =400 g
The solvent mass = 236 g
Then the mass of the drug = 400-236
= 164
Then the mass percentage of the drug can be calculated as 164/400 * 100
= 41%
Therefore, the strenght of the drug can be expressed as 41%
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Jim bought a pair of shoes for $50 and laces for $1. If the sales tax is 7%, how much tax must he pay?
(a) $3.57
(c) $0.36
(b) $350
(d) $35.70
Jim must pay tax $3.57.
The correct answer is (a) $3.57.
To calculate the sales tax that Jim must pay, we need to find 7% of the total cost of the shoes and laces.
The total cost of the shoes and laces is $50 (shoes) + $1 (laces) = $51.
To calculate the sales tax, we multiply the total cost by the tax rate:
Sales tax = 7% of $51
[tex]= 0.07 \times $51[/tex]
= $3.57.
Therefore, Jim must pay $3.57 in sales tax.
The correct answer is (a) $3.57.
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Can someone help me please
The resulting matrix will be in the form :
5 9 -4
0 -14 15
What is a matrix in mathematics ?A matrix is described as a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns, which is used to represent a mathematical object or a property of such an object.
To get a 1 in row 1, column 1, we perform the following elementary row operation:
R2 - 2R1 -> R2
This will subtract 2 times the first row from the second row and give us the result:
5 9 -4
0 -14 15
Matrices are useful for describing systems of linear or differential equations, as well as representing a linear application.
In conclusion, in a matrix function, the input and the output values are matrices.
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Please help !!!!!!!!!
Find the value of x.
The value of x in the circle is 4.2
Calculating the value of x in the circleFrom the question, we have the following parameters that can be used in our computation:
The circle
Using the intersecting chords equation, we have
(5x - 8) * 4 = (x + 1) * 10
When solved for x, we have
x = 4.2
Hence. the value of x is 4.2
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Which equations represent circles that have a diameter of 12 units and a center that lies on the y-axis? Select two options. x2 + (y – 3)2 = 36 x2 + (y – 5)2 = 6 (x – 4)² + y² = 36 (x + 6)² + y² = 144 x2 + (y + 8)2 = 36
The equations that represent circles that have a diameter of 12 units and a center that lies on the y-axis are:
A. x² + (y - 3)² = 36.
D. x² + (y + 8)² = 36.
What is the equation of a circle?In Mathematics and Geometry, the standard form of the equation of a circle is represented by the following mathematical equation;
(x - h)² + (y - k)² = r²
Where:
h and k represents the coordinates at the center of a circle.r represents the radius of a circle.Note: A center that lies on the y-axis simply means the value of h on the x-axis is equal to 0.
Based on the information provided above, we have the following parameters:
Radius, r = diameter/2 = 12/2 = 6 units.
Center, (h, k) = (0, 3).
By substituting the given parameters into the equation of a circle formula, we have the following;
(x - h)² + (y - k)² = r²
(x - 0)² + (y - 3)² = 6²
x² + (y - 3)² = 36.
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Which statement concerning the equation x² - 1 = x is true?
1. Its discriminant is 0, so it has no solution.
2. Its discriminant is 5, so it has two real solutions.
3. Its discriminant is 0, so it has one real solution.
4. Its discriminant is -3, so it has two complex solutions.
Answer:
The equation x² - 1 = x can be rewritten as x² - x - 1 = 0. We can use the quadratic formula to find the solutions:
x = (-b ± sqrt(b² - 4ac)) / 2a
In this case, a = 1, b = -1, and c = -1. So:
x = (1 ± sqrt(1 - 4(1)(-1))) / 2(1)
x = (1 ± sqrt(5)) / 2
Therefore, the equation has two real solutions, and the discriminant is positive. The answer is 2. Its discriminant is 5, so it has two real solutions.
18. The volumes of two similar solids are 857.5 mm^3 and 540 mm^3. The surface area of the smaller solid is 108 mm^2. What is the surface area of the larger solid?
Answer:
64.14
Step-by-step explanation:
Reading the passage I see that you have to multiply then divide
The surface area of the larger solid is, 171.7 mm²
What is Proportional?Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.
Given that;
The volumes of two similar solids are 857.5 mm³ and 540 mm³.
And, The surface area of the smaller solid is 108 mm².l
Now, Let us assume that;
The surface area of the larger solid is, x
Hence, We get;
857.5 / x = 540 / 108
Solve for x as;
857.5 x 108 = 540 x
92,718 = 540x
x = 171.7 mm²
Thus, The surface area of the larger solid is, 171.7 mm²
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