The exponential decay function for 24 mg sample is given as
[tex]F(t) = 24 (0.5)^{\frac{t}{5730} }[/tex]) and 0.64mg carbon - 14 will remain after 30 millennia.
Exponential function that represent the decay is given as :
[tex]F(t) = a (0.5)^{\frac{t}{h} }[/tex] (1)
where, F(t) = amount remaining after time t
a = amount of sample is decayed
t = time in years
h = half life years
The values that we have been given are :
a = 24 mg sample
h = 5730 years
Putting the required values in equation (1) we get
[tex]F(t) = 24 (0.5)^{\frac{t}{5730} }[/tex] (2)
Now we need to find how much carbon-14 remains after 30 millennia.
That is we have to find F(t) for t = 30 millennia = 30000 years
[As 1 millennium = 1000 years]
Putting the required values in equation (2) we get
[tex]F(t) = 24 (0.5)^{\frac{30000}{5730} }[/tex]
[tex]F(t) = 24 (0.5)^{5.236}[/tex]
F(t) = 24*0.027
F(t) = 0.64 mg
Thus 0.64mg carbon - 14 will remain after 30 millennia.
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Solve. Check for extraneous solutions. √x+7 +5=x
x = 3 and x = 6 is extraneous solution.
√(x+7) +5=x
Subtracting 5 on both sides of the equation
√(x+7) + 5 - 5 = x - 5
√(x+7) = x - 5
Squaring both sides of the equation
(√(x+7))² = (x - 5)²
x + 7 = x² + 25 - 10x
x² - 9x + 18 = 0 ...(1)
By middle term splitting equation (1) can be written as
x² - 6x - 3x + 18 = 0
x(x - 6) -3(x - 6) = 0
(x - 3)(x - 6) = 0
x - 3 = 0 and x - 6 = 0
x = 3, 6
Check extraneous solution by putting the value of x in the original equation, we get
Let x = 3
√(3+7) +5 = 3
✓10 + 5 = 3
which is a contradiction, so, x = 3 is an extraneous solution.
Let x = 6
√(6+7) +5 = 3
✓13 + 5 = 3
which is a contradiction, so, x = 6 is an extraneous solution.
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Which expression is equal to √49/100
A. 7√10/10
B. √7/10
C. 7/10
D. 7/50
Answer:
A
Step-by-step explanation:
70-271=20
Answer: it's 7/10
Step-by-step explanation:
the 49 simplifies to 7, and the 100 simplifies to 10
Find the value of x.
-2x = 3x + 6
Answer:
x= -6/5
Step-by-step explanation:
-2x=3x +6
collect like terms
-6=3x+2x
-6=5x
x= -6/5
Answer: x= -6/5 make that a fraction
decimal form: x= -1.2
mixed number form: x= - 1 1/5, 1 is the whole number
Step-by-step explanation: Isolate the variable by dividing each side by factors that don't contain the variable.
How do I set up the equations for these two problems so I can find X?
The values of x and measures of angles are:
1. x = 12; m<PQS = 71°; m<PQT = 142°; m<TQR = 41°
2. x = 8; m<GDH = 126°; m<FDH = 200°; m<FDE = 137°
How to Find the Measures of Angles?1. Since QS bisects angle PQT, therefore:
measure of angle PQS = measure of angle SQT
Given:
m<SQT = 8x - 25
m<PQT = 9x + 34
m<SQR = 112°
Thus:
m<PQT = 2(m<SQT)
Substitute
9x + 34 = 2(8x - 25)
9x + 34 = 16x - 50
9x - 16x = -34 - 50
-7x = -84
x = 12
m<PQS = m<SQT = 8x - 25
Plug in the value of x
m<PQS = 8x - 25 = 8(12) - 25
m<PQS = 71°
m<PQT = 9x + 34 = 9(12) + 34
m<PQT = 142°
m<TQR = m<SQR - m<SQT [angle addition theorem]
m<TQR = 112 - 71
m<TQR = 41°
2. Given:
m<GDE = 8x - 1
m<EDH = 6x + 15
m<CDF = 43
m<GDE = m<EDH [reason: DE bisects GDH]
Substitute
8x - 1 = 6x + 15
8x - 6x = 1 + 15
2x = 16
2x/2 = 16/2
x = 8
m<GDH = 2(m<GDE)
m<GDH = 2(8x - 1)
m<GDH = 16x - 2 = 16(8) - 2
m<GDH = 126°
m<FDG = 180 - m<CDF - m<GDE
m<FDG = 180 - 43 - (8x - 1)
m<FDG = 180 - 43 - (8(8) - 1)
m<FDG = 180 - 43 - 63
m<FDG = 74°
m<FDH = m<FDG + m<GDH
m<FDH = 74 + 126
m<FDH = 200°
m<FDE = m<FDG + m<GDE
m<FDE = 74 + 63
m<FDE = 137°
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Given that 2x+7=27 and 3x+1=28 does 2x+7=3x+1 explain
It is false that 2x + 7 = 3x + 1
How to determine the true statement?The equations are given as
2x + 7 = 27
3x + 1 = 28
The above equations have different values
This means that
It is false that 2x + 7 = 3x + 1
The above statement is true because 27 does not equal 28
Hence, it is false that 2x + 7 = 3x + 1
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The scale on a map is 1 : 200,000.
The length of a road on the map is 4 cm.
What is the length of the road in real life?
Give your answer in kilometres.
According to the solving the length of the road in real life will be = 8 km.
What is a map scale?The relationship (or ratio) between the distance on a map and the comparable distance on the ground is referred to as map scale. For example, on a 1:100000 scale map, 1cm on the map represents 1km on the ground.
Why is a scale used on maps?You've probably seen maps with just a scale bar representing equal sections, each marked with kilometres or miles. These divisions have been used to calculate ground distance on a map. In other words, a map scale specifies the relationship between the map and indeed the entire or a portion of the earth's surface depicted on it.
According to the given data:scale on a map is 1 : 200,000.
= 1 : (200,000/(100*1000))
= 1:2
= 2km
So,
length of a road on the map is 4 cm.
= 4*2
= 8km
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Kate and Ismaila were trying to describe parts of the expression 20xy.
• Ismaila said, "20 is a factor in the product 20xy."
. Kate said, "20 is the coefficient."
Who is correct?
Both Katie and Ismailia are both correct because 20 is a coefficient and factor of the expression 20xy.
How to find factor and coefficient of an expression?A coefficient is a number multiplied by a variable.
In other word, a coefficient is a number or any symbol representing a constant value that is multiplied by the variable of a single term or the terms of a polynomial.
A factor is a number that divides another number, leaving no remainder.
Therefore, the coefficient of the expression 20xy is 20.
The factor of the expression 20xy is also 20.
Therefore, Both Katie and Ismailia are both correct.
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Answer:
there both right
Step-by-step explanation:
✔✔✔♂️♂️♀️
Pencils are sold in boxes of 10
Erasers are sold in boxes of 14
A teacher wants to buy the same number of pencils and erasers.
Work out the smallest number of boxes of each item she should buy.
Answer:a
Step-by-step explanation:a cult
what is the slope of the line that passes through the points (6,-8) and (6,-3)
We have a vertical line, so we have an undefined slope.
How to get the slope of the line?The general linear equation in the slope-intercept form is given by:
y = m*x + k
Where we define k as the y-intercept and m as the slope.
If we know that the line passes through two points (a, b) and (c, d), then the slope is given by the formula:
m = (d - b)/(c - a)
In this case we have the points (6,-8) and (6,-3), then the slope will give:
m = (-3 + 8)/(6 - 6)
Notice that the denominator becomes zero, so we have a "slope of infinity", thing that happens for vertical lines
Basically, these lines have undefined slopes, so that is the correct answer.
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PLSS HELP :((
will mark brianlist if its the correct answer ty
Answer is B
because i did it out i dont feel like explaning lol
The ratio of impressions to fans is a measure of:_____.
a. fan acquisition
b. community
c. engagement
d. amplification
The ratio of impressions to fans is a measure of fan acquisition.
What is social media marketing?Social media marketing is the use of social media platforms and websites to promote a product or service. Although the terms e-marketing and digital marketing are still dominant in academia, social media marketing is becoming more popular for both practitioners and researchersGiven is to find the ratio of impressions to fans.
The ratio of impressions to fans is a measure of fan acquisition. Social marketing campaigns begin with fan acquisition, which involves using any of a variety of means, from display ads to News Feed and page pop-ups, to attract people to your Web page.
Therefore, the ratio of impressions to fans is a measure of fan acquisition.
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5. (01.06 MC)
Solve the following equation for x: 5x + 3y = 15.
Answer:
x = [tex]\frac{15-3y}{5}[/tex]
Step-by-step explanation:
5x + 3y = 15 ( isolate the term in x by subtracting 3y from both sides )
5x = 15 - 3y ( isolate x by dividing both sides by 5 )
x = [tex]\frac{15-3y}{5}[/tex]
We know 5×8=56
Which of the following statements are also true?
Choose 2 answers:
A. 8 is a factor of 56.
B. 7 is a multiple of 56.
C. 7 is a factor of 56.
Answer:
A and C
Step-by-step explanation:
Factors are numbers that can multiplied with another number to create a product. The factors of 56 are 1, 2, 4, 7, 8, 14, 28, and 56.
Use the Change of Base Formula to evaluate each expression.
log₃54
The value of the expression log₃54 is 3.6.
Given that the expression is log₃54.
We are required to find the value of the expression by using the change of base formula.
The change of base formula is the formula that will give us the answer of a log with a different base by using only log calculations with a base of 10.
The expression is log₃54.
log₃54= log (54)/log (3)
(We know that [tex]log_{a}b[/tex]=log b/ log a)
Now we have to use the values of logarithms in the above expression to find its value.
=1.73/0.48
=3.6
Hence the value of the expression log₃54 is 3.6.
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2x + kx = m solve for x
Answer:
x=m/2+k , k≠-2
Step-by-step explanation:
2x+kx=m
Factor out x from the expression:
(2+k)x=m
Assume 2+k≠0 and divide both sides of the equation by 2+k:
x=m/2k , 2+k≠0
Rewrite the restriction:
x=m/2+k≠-2
Solution:
x=m/2+k , k≠-2
The value of x in the given expression is x = m / (k+2)
What is an expression?An expression is a mathematical statement containing variables, numerical, and they are related by at least one mathematical operation.
Given an expression, 2x + kx = m
We are asked to rearrange the values and find the value of x.
Therefore,
2x + kx = m
Since, two terms have same variable, therefore, taking x common from both,
x(2+k) = m
x(k+2) = m
Now, transpose (k+2) to right side, we get,
x = m / (k+2)
Hence, we get the value of x as, x = m / (k+2)
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Micah sketches the graph below to represent a scenario his teacher gave him
Which scenario could Micah's graph represent?
1.Micah's plant is 1 inch and then grows at a rate of 2 inches per week (where x is the number of weeks), for a total of
y inches.
2.Micah's plant is 2 inches tall and grows at a rate of 1 inch per week (where x is the number of weeks), for a total of y
inches.
3.Micah's plant grows 2 inches per week (where x is the number of weeks) and has a starting height of 1 inch, for a
total of y inches.
4.Micah's plant grows 1 inch per week (where x is the number of weeks) and has a starting height of 1 inch, for a total
of y inches.
A scenario which Micah's graph could represent is: 2. Micah's plant is 2 inches tall and grows at a rate of 1 inch per week (where x is the number of weeks), for a total of y inches.
What is a graph?A graph can be defined as a type of chart that's commonly used to graphically represent data on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis and y-axis.
How to calculate the average rate of change?Mathematically, the average rate of change (slope) of any straight line can be calculated by using this formula;
[tex]Slope = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}[/tex]
Substituting the given points into the formula, we have;
Average rate of change = (6 - 2)/4 - 0)
Average rate of change = 4/4
Average rate of change = 1.
Therefore, Micah's plant is 2 inches tall and grows at a rate of 1 inch per week (where x is the number of weeks), for a total of y inches.
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Answer: b or Micah’s plant is 2 inches tall and grows at a rate of 1 inch per week (where x is the number of weeks), for a total of y inches.
Step-by-step explanation:
Solve each equation. Check your answers.
ln 4 r²=3
After solving the equation the value of r in 4 r²=3 is [tex]\sqrt{3/4}[/tex].
We have to find r in 4 r²=3
⇒ 4 r² = 3
⇒ r² = 3/4
⇒ r = [tex]\sqrt{3/4}[/tex]
So, r is equal to [tex]\sqrt{3/4}[/tex]
How to solve an equation?To solve linear equations, utilize the steps that are provided below.
Remove parentheses from each side of the equation and combine similar terms to make it simpler.To separate the variable term on one side of the equation, use addition or subtraction.To find the variable, use division or multiplication.The common denominator can be multiplied by each side of the equation to eliminate fractions.Lets take an example of solve z for 7z – (3z – 4) = 12
Here is no multiplication or division, so this will be easy to solve
⇒ 7z – (3z – 4) = 12
⇒ 7z – 3z + 4 = 12
⇒ 4z = 12 – 4
⇒ 4z = 8
⇒ z = 8/4
⇒ z = 2
See, that was so simple, using the mentioned methods, every linear equation can be solved easily.
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What is the slope of a line perpendicular to the line whose equation is 6x+y=8
The slope intercept form of a line is y=mx+c, where m is slope.slope of a line perpendicular to 6x+y=8 is 1/6
What is slope intercept form?The slope intercept form of a line is y=mx+c, where m is slope.
The equation of a line is 6x+y=8.
We need to convert to slope intercept form
y=8-6x
y=-6x+8
where m=-6 is slope of a line.
Two lines are said to be perpendicular when m1m2=-1
m1 is slope of given line and m2 is slope of other line which we have to find.
-6.m2=-1
m2=1/6.
Therefore slope of a line perpendicular to 6x+y=8 is 1/6.
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Maria wants to write a linear function to describe the cost of a cab ride. The cab costs $3 per ride plus an additional $0.20 per mile. a. What is the function that describes the cost of the cab ride for any number of miles? b. how much is the fare for a 15-mile trip? c. How far can she afford to travel if she only has 10$
Answer:
add then simplify
Step-by-step explanation:
Pleaseeeee helpppppp
Answer:
56°
Step-by-step explanation:
The angles are supplementary. They add up to 180°
So ∠AYZ + ∠AYX = 180
6x+4 + 3x - 4 = 180
9x = 180
x = 20
Measure of ∠AYX = 3x - 4 = 3 x 20 - 4 = 60 -4 = 56°
Solve for x and write your answer in simplest form.
-1/2 -1/2(4/5x+1) = -2 -3x
The solution of the equation which is as described in the task content when expressed in its simplest form is; -5/13.
What is the solution of the equation as described in the task content?It follows from the task content that the solution to the equation is to be determined and expressed in its simplest form.
Given;
-1/2 -1/2(4/5x+1) = -2 -3x
By distributing the coefficients: we have;
-1/2 - 2/5x - 1/2 = -2 -3x
Hence, by collecting like terms; we have;
-1/2 - 1/2 + 2 = -3x + (2/5)x
1 = -13x/5
Therefore; by cross-multiplication; we have;
5 = -13x
Divide both sides by; -13.
x = -5/13.
Ultimately, the solution of the equation which is as described in the task content when expressed in its simplest form is; -5/13.
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25 students submitted the HW this week, which was 77% of the class. How many students are in the class?
Answer:
Step-by-step explanation:
25 divide 77 = 0.32467532 x 100 = 32 (Leave off the rest, there is no such thing as a fraction of a person in this)
Simplified: (25/77)*100 = 32
To check our answer we would do 32 x 77%(.77) = 24.64 round-up and you get 25!
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Let f(x)=4 x, g(x)=1/2 x+7 , and h(x)=-2 x+4 . Perform each function operation. (g⁰ f)(x)
The answer to this question is (gof)(x)=2x+7
According to question:
Given: f(x)=4 x, g(x)=1/2 x+7,h(x)=-2 x+4
(gof)(x)=g(f(x))=g(4x)=1/2×4x+7=2x+7(fog)(x)=f(g(x))=f(x/2+7)=4×(x/2+7)=2x+28We always simplify everything in brackets first using BODMAS. Therefore, in order to compute f(g(x)), g(x) must first be calculated and then substituted within f(x). Similar to this, in order to determine g(f(x)), f(x) must first be computed and then substituted in g(x). In other words, the sequence is important when locating the composite functions. It implies that g(f(x)) and f(g(x)) may not be equal. The following procedures are used to obtain the composite function f(g(a)) for any two functions f(x) and g(x).
By changing x = a in g, find g(a) (x).
Put x = g(a) into f to find f(g(a)) (x)
∴(gof)(x)=2x+7
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Simplify.
√81x6y2
Assume all variables are nonnegative.
Answer:
9x³y²
Step-by-step explanation:
To simplify, factorize 81 in powers of 2 ; x⁶ in powers of 2 and y² in powers of 2.
[tex]\sf \sqrt{81x^6y^2}=\sqrt{9^2 * x^{3*2}*y^2}[/tex]
[tex]\sf = \sqrt{9^2* (x^3)^2)* y^2}\\\\ = 9 * x^3*y^2\\\\=9x^3y^2[/tex]
A cube had dimensions of 2cm, 4cm, and 6cm. It also has a density of 24g/cm3. Will it Sink or Float in water?
Answer:
Step-by-step explanation:
Volume of the cube = 2*4*6 = 48 cm^3.
Its density is 24 g / cm^3
The density of water is 1g /cm^3 so it will sink in water.
legend has it that the great mathematician carl friedrich gauss (1777–1855) at a very young age was told by his teacher to find the sum of the first 100 counting numbers. while his classmates toiled at the problem, carl simply wrote down a single number and handed the correct answer in to his teacher. the young carl explained that he observed that there were 50 pairs of numbers that each added up to 101. so the sum of all the numbers must be 50•101
The sum of numbers from 1 to 100 is 50 × 101.
Carl Friedrich Gauss is a renowned mathematician. He has contributed many theories to the fields of mathematics and physics.
The sum of the first hundred numbers is calculated by making pairs of two numbers. The sum of these pairs is 101.
And there is a total of 50 pairs.
So, the sum of all these numbers is,
101 ×50
= 5050
Therefore, the sum of numbers from 1 to 100 is 5050.
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NEED ANSWER ASAP WILL GIVE 40 POINTS
-6≥ 10-8x
Answer:
x≥2
Step-by-step explanation:
-16≥ -8x
x≥2
Courtney, the buyer for a small produce store and she sells 25 bags of oranges at $12 per bag. Her cost of goods sold per bag is $7. What is Courtney’s gross profit?
a. $293
b. $300
c. $175
d. $125
Solve. Check for extraneous solutions. (x+3)¹/₂-1=x
-2 is the extraneous solution of the equation.
The equation is:
[tex](x + 3)^{1/2}[/tex] - 1 = x
To find the extraneous solution of the expression first we need to find the value of x.
[tex](x + 3)^{1/2}[/tex] = x + 1
Squaring both sides we have,
[tex](x+ 3)^{}[/tex] = [tex](x + 1)^{2}[/tex]
x + 3 = [tex]x^{2}[/tex] + 2x + 1
[tex]x^{2}[/tex] + x - 2 = 0
[tex]x^{2}[/tex] + 2x - x - 2 = 0
x ( x + 2 ) - 1 (x + 2) = 0
(x+2) (x-1)=0
x = -2, 1
Now we have to put the value of x in the equation:
x = -2
[tex](-2 +3)^{1/2}[/tex] - 1 = -2
1-1 =-2
0≠ -2
x = 1
[tex](1 + 3)^{1/2}[/tex] - 1= 1
2 - 1 = 1
1= 1
Therefore we get x = -2 is as extraneous solution of the equation and x= 1 is the solution of the equation.
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Pedro went to the store and spent $36.85. He paid with a $50 bill. How much money will he get back as
change? Show All Your Work for full credit
Answer: 13.15
Step-by-step explanation:
50
-
36.85
Answer:
Step-by-step explanation:
13.50