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Let's use the following formula:
[tex]A=A_0(0.5)^{\frac{t}{h}}[/tex]where:
Ao= Initial amount
t = time
h = half-life
[tex]\begin{gathered} A=0.2A_0 \\ so\colon \\ 0.2A_0=A_0(0.5)^{\frac{t}{5730}} \end{gathered}[/tex]solve for t:
[tex]\begin{gathered} 0.2=0.5^{\frac{t}{5730}} \\ \ln (0.2)=\frac{t}{5730}\ln (0.5) \\ t=5730\cdot\frac{\ln (0.2)}{\ln (0.5)} \\ t\approx13305 \end{gathered}[/tex]Related Questions
please look at screenshots
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Answer:
c
Step-by-step explanation:
it not linear relationship
i know the answer i just don’t know the steps.
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Answer:
x = 4Step-by-step explanation:
1/2x - 2 = 0
1/2x = 2
x = 2 * 2/1
x = 4
----------------------------
check1/2(4) - 2 = 0
2 - 2 = 0
0 = 0
the answer is good
Percents are the result of expressing numbers as a part of
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Answer:
percentage of fractions
Write a quadratic function in standard form whose graph has the given characteristics.
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The quadratic function in standard form that passes through (-2, 0), (4, 18), and (10, 0) is y = (- 1/2) x² + 4x + 10.
Given that, (-2, 0), (4, 18) and (10, 0).
What is a quadratic function in standard form?The standard form of a quadratic equation is given as:
ax² + bx + c = 0 where a, b, c are real numbers and a ≠ 0.
Now, the equation passes through (- 2, 0)
y = ax² + bx + c
0 = 4a - 2b + c ----------------(1)
The equation passes through (4, 18)
y = ax² + bx + c
18 = 16a + 4b + c ----------------(2)
The equation passes through (10, 0)
y = ax² + bx + c
0 = 100a + 10b + c ----------------(3)
Using the Gauss elimination method to solve the system of equations we get,
a = -1/2, b = 4, and c = 10
The quadratic equation will be:
y = ax² + bx + c
y = (- 1/2) x² + 4x + 10
Therefore, a quadratic function in standard form with the given characteristics is y = (- 1/2) x² + 4x + 10.
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Determine if triangle EFG and triangle HIJ are or are not similar, and, if they are, state how you know. (Note that figures are NOT necessarily drawn to scale.)
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Given the triangles EFG and HIJ, you can identify that:
[tex]EG=19\text{ }[/tex][tex]EF=18[/tex][tex]\begin{gathered} FG=16\text{ } \\ \\ \text{ }HI=90 \\ \\ IJ=80 \end{gathered}[/tex][tex]\begin{gathered} m\angle F=67\text{ \degree} \\ \\ m\angle I=67\text{ \degree} \end{gathered}[/tex]By definition, two triangles are similar if the lengths of the corresponding sides are in proportion and their corresponding angles are congruent.
In this case, you can identify that you know two pairs of corresponding sides. Then, you can find in they are in proportion. Set up that:
[tex]\frac{EF}{HI}=\frac{FG}{IJ}[/tex]Substituting values and simplifying, you get:
[tex]\begin{gathered} \frac{18}{90}=\frac{16}{80} \\ \\ \frac{1}{5}=\frac{1}{5} \end{gathered}[/tex]Notice that they are in proportion.
You can also identify that the corresponding angles F and I are congruent because they have equal measure.
Therefore, since you know that two sides are proportionate and the included angles are congruent, you can conclude that the triangles are similar, based on the Side-Angel-Side Theorem (SAS).
Hence, the answer is: Third option.
Use synthetic division to determine whether the first expression is a factor of the second. If it is, indicate the factorization. (If the first expression is not a factor of the second, enter DNE.)x − 2, 9x^4 − 35x^2 − 4(x − 2)
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[tex]9x^4-35x^2-4[/tex]
Lets divide this polynomial by x - 2
9x^4 0x³ -35x² 0x -4 | x - 2
-9x^4 +18x³ | 9x³
18x³ -35x² 0x -4 | x - 2
-18x³ 36x² | 9x³ + 18x²
x² 0x -4 | x - 2
-x² +2x |9x³ + 18x² + x
2x -4 |x - 2
-2x + 4 |9x³ + 18x² + x +2
0
Since there is no rest for the division, x - 2 is a factor of the given polynomial:
[tex]9x^4-35x^2-4=(x-2)\cdot(9x^3+18x^2+x+2)[/tex]f(x)=x^2-8, g(x)=17-x
(f/g)(-4)=?
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The quotient between the two functions evaluated in -4 is equal to 8/21.
How to find the quotient?
Here we have the two functions:
f(x) = x^2 - 8
g(x) = 17 - x
And we want to find:
(f/g)(-4)
That can be rewritten as:
f(-4)/g(-4)
By evaluating the two functions we get:
f(-4) = (-4)^2 - 8 = 16- 8 = 8
g(-4) = 17 - (-4) = 17 + 4 = 21
replacing that in the quotient we get
f(-4)/g(-4) = 8/21
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Write a quadratic function in standard form, with a leading coefficient of 1, given x-intercepts 7 and 10. Use "y" as the dependent variable
and "x" as the independent variable.
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Standard form of quadratic function with leading coefficient 1,
x-intercept 7 and 10 and y as dependent variable and x as independent variable is equal to y = x² -17x +70.
As given in the question,
Given :
y is the dependent variable of the required quadratic function.
x is the independent variable of the required quadratic function.
Leading coefficient of quadratic function is 1
X-intercept of the required function is 7 and 10
Standard form of required quadratic function is equal to
y = k (x-a)(x -b)
Here k=1 , a=7 , b=10
y = 1 (x -7)(x - 10)
⇒ y = x² -7x -10x +70
⇒ y= x² -17x +70
Therefore, standard form of quadratic function with leading coefficient 1, x-intercept 7 and 10 and y as dependent variable and x as independent variable is equal to y = x² -17x +70.
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Rewrite y = a (2)¹/3 in the form y = a(1+r) or y = a(1-r)'. Round each value to the nearest hundredth, if necessary. Then state the growth or decay rate.yoThe rate is about %.This is a rate.
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we have the equation
[tex]y=a(2)^{\frac{t}{3}}[/tex]Rewrite the given equation
[tex]\begin{gathered} y=a(2^{\frac{1}{3}})^t \\ y=a(1.26)^t \\ y=a(1+0.26)^t \end{gathered}[/tex]the base of the exponential function is b=1.26
1.26 > 1
that means
is an exponential growth function
1+r=1.26
r=1.26-1
r=0.26
therefore
The rate is about 26%This is a growth rateI only need help with the gauss elimination and back substitution, and cramers rule. I know hwo to do everything else.
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To solve the equation by Gauss elimination method first convert the equation in matrix form.
The cramers rule is as follows;
A college student realized that he was spending too much money on music. For the remaining 5 months of the year his goal is to spend a mean of $50 a month towardsmusic. How much can he spend in December, taking into consideration that in the other 4 months he spent $20, $70, S30, and $85, respectively? Round your answerto two decimal places. If necessary
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The mean is given by the sum of all the months divided by the number of months.
Then:
Let's set x for the spending money for December.
There are 5 months.
Hence:
[tex]\operatorname{mean}=\frac{20+70+30+85+x}{5}[/tex]We need to have a mean equal to $50. Set mean = 50.
[tex]50=\frac{20+70+30+85+x}{5}[/tex]Solve for x:
[tex]\begin{gathered} 50=\frac{20+70+30+85+x}{5} \\ 50=\frac{205+x}{5} \\ 5\cdot50=205+x \\ 250=205+x \\ \text{Therefore:} \\ x=250-205 \\ x=45 \end{gathered}[/tex]Hence, If the student wants to complete his goal, he will need to spend $45 in December.
Need to study for finals need help on this problem on my study guide find the measure of each angle calculate the length of each side
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Answer:
[tex]\begin{gathered} m\angle B\text{ = 28}\degree \\ AB\text{ = 9.75} \\ BC\text{ = 7.7} \end{gathered}[/tex]Explanation:
Here, we want to calculate the measure of each of the missing angles and sides
We have one missing angle and 2 missing sides
a) Let us get the angle at B
Mathematically, the sum of angles in a triangle is 180 degrees
Thus:
[tex]\begin{gathered} 90\text{ + 62 + B = 180} \\ B\text{ = 180-90-62} \\ B\text{ = 28}\degree \end{gathered}[/tex]b) Let us get the measure of AB
We can use the appropriate trigonometric ratio here
The side that measures 6 is an opposite to the angle B
Since AB is the hypotenuse (the side facing the right angle and the longest side of in the triangle), we use sine
Sine is the ratio of the opposite and the hypotenuse
Mathematically:
[tex]\begin{gathered} sin\text{ 38 = }\frac{6}{AB} \\ \\ AB\text{ =}\frac{6}{sin\text{ 38}} \\ \\ AB\text{ = 9.75} \end{gathered}[/tex]c) side BC
We can use tan to get this
Tan is the ratio of the opposite to the adjacent side
The opposite side here is the side AC, while the adjacent is BC
Thus, we have it that:
[tex]\begin{gathered} Tan\text{ 38 = }\frac{6}{BC} \\ \\ BC\text{ = }\frac{6}{Tan\text{ 38}} \\ \\ BC\text{ = 7.7} \end{gathered}[/tex]What is the value of 7 + z ÷ 2, when z = 10?
Answers
Answer:
12
Step-by-step explanation:
7 + z ÷ 2 ,z=10(bodmas , division is the first)
7 + 10 ÷2
7 + 5
12
Answer:
12
Step-by-step explanation:
Substitute 10 for z
7+10 ÷ 2
divide first
7+5=
12
What is the reflection image of p (0,0) after two reflections,first across x=4 and Than across y= -3
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After two reflections, P(0, 0)'s reflection image is P (8,-6).
What do we mean by reflection of image?A reflection is the shape's mirror image. A line, called the line of reflection, will allow an image to reflect through it. Every point in a figure is said to reflect the other figure when it is equidistant from every corresponding point in the other figure.The given point is(0,0)
A point will reflect across x = 4 ,then(x,y) → (-x+8,Y)(0,0)→(-0+8,0)(0,0)→(8,0)A point will reflect across x = -3 ,then(X,Y)→(X,-Y-6)(8,0)→(8,-0-6)(8,0)→(8,-6)Therefore, P' is the reflection image of P(0, 0) following two reflections (8,-6).
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What was done to the linear parent function, f(x) = x, to get the functiong(x) = ?A. Horizontally compressed by a factor of 6B. Vertically stretched by a factor of 6C. Vertically compressed by a factor of 6D. Shifted unit up
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Given
Two functions
[tex]\begin{gathered} f(x)=x \\ g(x)=\frac{1}{6}x \end{gathered}[/tex]Procedure
When we multiply a function by a positive constant, we get a function whose graph is stretched or compressed vertically in relation to the graph of the original function.
10s = 12 help!!!! pls
Answers
Answer:
12-10=2 which means an extra 2seconds was added therefore it's impossible for 10seconds to be equal to 12
What type of transformation is illustrated in the picture below? A. rotationB. translation
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Rotation simply means turning around a centre . From the diagram above the vehicle rotated in a clockwise fashion.
Philip purchased s pairs of shoes for the school year. He also purchased jeans and T-shirts.
The number of pairs of jeans is 3 more than the number of pairs of shoes and the number of
T-shirts is twice as many as the number of pairs of jeans. How many shoes did he purchase if he purchased a total of 17 items?
Answers
Answer:
3 pairs of shoes
Step-by-step explanation:
You can represent the amount of each item with these:
2(jeans) = t-shirts
shoes + 3 = jeans
shoes + t-shirts + jeans = 17
By plugging in 3 for s, you get:
(3) + 3 = 6
(6) × 2 = 6
3 + 6 + 6 = 17
operations of rational algebraic expression 1/4+2/4
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Answer:
3/4
Step-by-step explanation:
Washing his dad's car alone, Matt takes 6 hours. If his dad helps him, then it takes 2 hours. How long does it take Matt's dad to wash the car by himself?
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If it takes 6 hours for Matt to wash the car, then he washes at a rate of 1/6 cars per hour:
[tex]\begin{gathered} \frac{1}{x}=6 \\ x=\frac{1}{6} \end{gathered}[/tex]Let y be the time in which Matt's dad washes the car and state an equation that describes the situation in which Matt and his dad wash the car together:
[tex]\begin{gathered} \frac{1}{6}+\frac{1}{y}=2 \\ \frac{1}{y}=2-\frac{1}{6} \\ \frac{1}{y}=\frac{11}{6} \\ y=\frac{6}{11} \end{gathered}[/tex]It means that he washes the car in 6/11 hours (approximately 0.54hours).
Can anyone answer this question fast?
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Sauce = 15
15/3 = 5
Cheese = 12
12/3 = 4
To make 1 pizza you need 5 sauce and 4 cheese.
Multiply these ingredients by 7 to make 7 pizzas:
5*7 = 35
4*7 = 28
You need 35 sauce and 28 cheese
which expression is equivalent to (4^2)^-2?
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Answer:
[tex](4^2)^{-2}=\frac{1}{x^4}[/tex]Explanation: We need to simplify the given expression to get an equvilant expression: The given is as follows.
[tex](4^2)^{-2}[/tex]Simplification:
Using the following exponent property:
[tex](x^a)^{-b}=x^{a\times(-b)}^{}=x^{-ab}^{}=\frac{1}{x^{ab}}[/tex]The equvilant expression we get is:
[tex](4^2)^{-2}=x^{2\times-2}=x^{-4}=\frac{1}{x^4}[/tex]Consider the following equation. State any restrictions on the variable, if they exist.
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In equation like this one, the restriction happens when there are variables in the denominator. Since the denominator can't be equal to zero, when we have a variable in the denominator, we have to find the restrictions to the variable.
However, in this case, no denominator have variables in it.
So, in this case, there is no restriction for the values of x.
10 Caleb divides powers of 10 using exponents . He says that 0.6 divided by increases the value of the 6. Do you agree with Caleb ? 10 ^ 2 Explain your thinking
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I disagree with Caleb because the value decreased after the quotients are carried out
How to determine the true statement?From the question, the statement is given as
He says that 0.6 divided by 10² increases the value of the 6.
The mathematical expression of the above statement is represented as
0.6 divided by 10²
So, we have
0.6/10²
When the above quotient is evaluated, we have
0.6/10² = 0.006
The above result is different from Caleb's reasoning
This is so because 0.6 divided by 10² decreases the value of the 0.006, instead of increasing the value to 6, as stated by Caleb
Hence, Caleb's reasoning is incorrect
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Complete question
Caleb divides powers of 10 using exponents. He says that 0.6 divided by 10² increases the value of the 6.
Do you agree with Caleb? Explain your thinking
What is the magnitude of -5 + 121?
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Question:
Solution:
For a complex number z = x + yi, we define the magnitude, |z|, as follows:
[tex]|\text{ z |=}\sqrt[]{x^2+y^2}[/tex]thus, according to this, we can conclude that the magnitude of the given complex number is:
[tex]|\text{ z |=}\sqrt[]{(-5)^2+(12)^2}\text{ = 13}[/tex]so that, the correct answer is:
[tex]13[/tex]
HELPP ASPP PLS HELP Combine "like terms" in this expression:
6x - 8x - 4y - x + 5y - 2y
A. -6x - y
B. -3x + y
C. -3x -2y
D. -3x - y
Answers
Answer:-3x-y
Step-by-step explanation:
6-8-1=-3
-4+5-2=-1
-3x-y
A gift wrapping store has 8shapes of boxes, 14types of wrapping paper, and 12 different bows. How many different gift-wrapping options are available at this store?
Answers
14*12*8=1344
1344 options
I believe the answer to be 0.15 but I just want to make sureSuppose that grade point averages of undergraduate students at one university have a bell-shaped distribution with a mean of 2.57 and a standard deviation of 0.44. Using the empirical rule, what percentage of the students have grade point averages that are greater than 3.89? Please do not round your answer
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First, we need to find the z-score for the measure x=3.89. This is given by
[tex]z=\frac{x-\mu}{\sigma}=\frac{3.89-2.57}{0.44}[/tex]which gives
[tex]z=3[/tex]Now, from the empirical rule :
we can see that
[tex]P(x>3.89)=P(z>3)\approx0.15\text{ \%}[/tex]Then, the answer is 0.15%
HELP! How do I solve this!!?
Answers
x ki power 3 is the answer
Step-by-step explanation:
use x is equal to root over x
Write the correct expression for the following statement:
A difference of x and six