I need a clear explanation please bc i don't get how I'm supposed to do this. :,)
Answers
The half-life [tex]t_{1/2}[/tex] is the amount of time it takes for some quantity [tex]N_0[/tex] of carbon-14 to decay to half the original amount, or [tex]N=\frac{N_0}2[/tex].
In terms of the formula, it's the time such that
[tex]\dfrac{N_0}2=N_0e^{-kt_{1/2}}[/tex]
and we can divide both sides by the original amount to get
[tex]\dfrac12=e^{-kt_{1/2}}[/tex]
We want to find the time [tex]t[/tex] it takes for 57%, or 0.57, of the original amount to remain. This means we solve for [tex]t[/tex] in
[tex]0.57N_0=N_0e^{-kt}[/tex]
or
[tex]0.57=e^{-kt}[/tex]
We're given [tex]k=0.0001[/tex]; plug this in and solve for [tex]t[/tex]:
[tex]0.57=e^{-kt}\implies\ln0.57=-kt\implies t=-\dfrac{\ln0.57}k\approx\boxed{5621\,\mathrm{years}}[/tex]
Related Questions
ASAP!! Please help me. I will not accept nonsense answers, but will mark as BRAINLIEST if you answer is correctly with solutions.
Answers
Answer:
The function has two real roots and crosses the x-axis in two places.
The solutions of the given function are
x = (-0.4495, 4.4495)
Step-by-step explanation:
The given quadratic equation is
[tex]G(x) = -x^2 + 4x + 2[/tex]
A quadratic equation has always 2 solutions (roots) but the nature of solutions might be different depending upon the equation.
Recall that the general form of a quadratic equation is given by
[tex]a^2 + bx + c[/tex]
Comparing the general form with the given quadratic equation, we get
[tex]a = -1 \\\\b = 4\\\\c = 2[/tex]
The nature of the solutions can be found using
If [tex]b^2- 4ac = 0[/tex] then we get two real and equal solutions
If [tex]b^2- 4ac > 0[/tex] then we get two real and different solutions
If [tex]b^2- 4ac < 0[/tex] then we get two imaginary solutions
For the given case,
[tex]b^2- 4ac \\\\(4)^2- 4(-1)(2) \\\\16 - (-8) \\\\16 + 8 \\\\24 \\\\[/tex]
Since 24 > 0
we got two real and different solutions which means that the function crosses the x-axis at two different places.
Therefore, the correct option is the last one.
The function has two real roots and crosses the x-axis in two places.
The solutions (roots) of the equation may be found by using the quadratic formula
[tex]$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$[/tex]
[tex]x=\frac{-(4)\pm\sqrt{(4)^2-4(-1)(2)}}{2(-1)} \\\\x=\frac{-4\pm\sqrt{(16 - (-8)}}{-2} \\\\x=\frac{-4\pm\sqrt{(24}}{-2} \\\\x=\frac{-4\pm 4.899}{-2} \\\\x=\frac{-4 + 4.899}{-2} \: and \: x=\frac{-4 - 4.899}{-2}\\\\x= -0.4495 \: and \: x = 4.4495 \\\\[/tex]
Therefore, the solutions of the given function are
x = (-0.4495, 4.4495)
A graph of the given function is also attached where you can see that the function crosses the x-axis at these two points.
Katya has $20.00 to spend at her college bookstore, where all students receive a 20% discount . katya wants to purchase a copy of a book that normally sells for $22.50 plus 10% sales tax. how much dose the book sell for dose katya have enough money bc bc?
Answers
Answer:
here you go :)
Step-by-step explanation:
You would take 20% of $22.50 (22.5 multiplied by .2). You would get $4.50 off of the book with the discount. So you would subtract 4.5 from 22.5 and get $18. Then you would take 10% of $18 for the sales tax. (18 multiplied by .1). You would get $1.80 towards sales tax. you would then add $1.80 to $18 and get $19.80.
The graph of g(x) resembles the graph of f(x)=x^2, but it has been changed. Which of these is the equation of g(x)?
Answers
Answer:
A.
Step-by-step explanation:
Anwer A has the following equation:
[tex]g(x)=\frac{3}{5}x^2-3[/tex]
In this equation, we can calculated the intercept replacing x by 0, as:
[tex]g(x)=\frac{3}{5}0^2-3=-3[/tex]
if this is the answer, the graph of g(x) should be through the point (0,-3) and that happens.
Additionally, the roots of the equations are calculated replacing g(x) by 0 and solving for x, so:
[tex]0=\frac{3}{5}x^2-3\\x_1=\sqrt{5}=2.236\\x_2=-\sqrt{5}=-2.236[/tex]
It means that the graph of g(x) should be through the points (2.236,0) and (-2.236,0) and that happens too.
So, the answer is A, [tex]g(x)=\frac{3}{5}x^2-3[/tex]
PLEASE ANSWER FAST.What is the probability that only girls bought lunches? 25% 41.6% 75% 50%
Answers
Answer:
The correct answer is 50.6195
Step-by-step explanation:
The probability that only girls bought lunches is given as D. 50%
How to solve
To find the probability that only girls bought lunches, we solve:
We can see that the total number of girls is 30 and the total number of both boys and girls is 60
So, to solve, it becomes:
30/60= 50%
Probability is a mathematical concept used to measure the likelihood of an event occurring, ranging from 0 (impossible) to 1 (certain), and is calculated using ratios, frequencies, or subjective judgments.
Read more about probability here:
https://brainly.com/question/23417919
#SPJ2
A cube has a side length of 5 cm. Determine the surface area of the largest pyramid that will fit inside the cube. Round if necessary.
Answers
Answer:
The surface area of the pyramid is 80.9 cm²
Step-by-step explanation:
The side length, s of the cube is given as 5 cm
Therefore, the largest pyramid that can fit into the cube will have a base side length, s = The side length of the cube = 5 cm
The height, h of the largest pyramid = The height of the cube = 5 cm.
The surface area of a pyramid = Area of base, A + 1/2 × Perimeter of base, P × Slant height, S
The slant height of the pyramid = √(h² + (s/2)²) = √(5² + (5/2)²) = (5/2)×√5
The perimeter of the base = 4×5 = 20 cm
The area of the base = 5×5 = 25 cm²
The surface area of a pyramid = 25 + 1/2×20×(5/2)×√5 = 80.9 cm².
The surface area of a pyramid = 80.9 cm².
Find the measure of d.
Answers
Answer:
[tex] d = 123 [/tex]
Step-by-step explanation:
The given figure above is an inscribed quadrilateral with all four vertices lying on the given circle, thereby forming chords each.
Therefore, the opposite angles of the above quadrilateral are supplementary.
This means:
[tex] c + 31 = 180 [/tex] , and
[tex] d + 57 = 180 [/tex]
Find the measure of d:
[tex] d + 57 = 180 [/tex]
Subtract 57 from both sides.
[tex] d + 57 - 57 = 180 - 57 [/tex]
[tex] d = 123 [/tex]
Please help me to solve this . Thank you so much .
And if possible , could you explain the answer too ?
Base on the diagram , state
a) The point which is 2 cm from R and 4 cm from P
b) The point which is more than 2 cm from R and 4 cm from T
c) The location of a moving point X in the diagram such that it is less than 4 cm from P and more than 2cm from R
d) The location of a moving point Y in the diagram such that YR < 2 cm and YP < 4 cm
e)The location of a moving point Z in the diagram such that ZT > 4 cm , ZP > 4 cm and ZR > 2 cm
Answers
Answer:
a) N
b) L
c) area I
d) area II
e) area VI
Step-by-step explanation:
a) the points that are 2cm from R are Q, N, M, S. Then, points that are 4cm from P are K, N, R. So, the only one point that works for both is N.
b) the points that are >2cm from R are P, K, L, T. We do not count those are exactly 2cm from R. Then, points that are 4cm from T are R, M, L. Ans is L.
c) <4cm from P, are area I and II. Then area that are >2cm from R are I, VI, and V. So, the only area that works for both is I.
d) <2cm from R, are areas II, III, and IV. Then, <4cm from P, are areas I and II. So, the only one works for both is area II.
e) >4cm from T, are areas I, II, III, VI. Then, >4cm from P, are III, IV, V, VI. Finally, >2cm from R, are areas I, VI, V. The only one that works for all three conditions is area VI.
20 POINTS!!!
The functions f(x) and g(x) are shown on the graph.
f(x)=|x|
What is g(x)
Answers
Answer:
Option B
Step-by-step explanation:
As shown in the picture, g(x) is the red one which can be obtained by translating f(x) - the blue one toward +x-axis direction 4 units.
=> g(x) = f(x) + 4 = |x| + 4
Answer: Choice D
g(x) = |x-4|
=================================================
Explanation:
Replacing x with x-4 shifts the xy axis four units to the left. If we fix the blue V shape to not move while the xy axis does move, then it gives the illusion of the V shape moving 4 units to the right to end up producing the red curve.
You can use a table of values to compare the two functions or you could use a graphing tool to confirm the answer.
--------
Extra info:
Choice A will move the blue graph 4 units down
Choice B will move the blue graph 4 units up
Choice C will move the blue graph 4 units to the left
Rationalise the denominator and simplify
A) 2sqrt3/sqrt12
B) 5sqrt7/sqrt35
Answers
Answer: A) 1 B) [tex]\sqrt5[/tex]
Step-by-step explanation:
[tex]A)\quad \dfrac{2\sqrt3}{\sqrt{12}}=\dfrac{2\sqrt3}{2\sqrt3}=1\\\\\\\\B)\quad \dfrac{5\sqrt7}{\sqrt{35}}=\dfrac{5\sqrt7}{\sqrt5\cdot \sqrt7}=\dfrac{5}{\sqrt5}\bigg(\dfrac{\sqrt5}{\sqrt5}\bigg)=\dfrac{5\sqrt5}{5}=\sqrt5[/tex]
A sector with an area of 30 pi cm^2 has a radius of 10cm. What is the central angle measure of the sector of the degree?
Answers
Answer:
108
Step-by-step explanation:
help me Please!!!!!!!
Answers
Answer:
[tex]2\sqrt{14\\}[/tex] = q
Step-by-step explanation:
use geometric mean method
4/s = s/10
s^2 = 40
s = 2[tex]\sqrt{10}[/tex]
consider the triangle STR and using the Pythagorean theorem
[tex]s^{2} +16 = q^{2} \\[/tex]
[tex](2\sqrt{10})^{2} +16 = q^{2}[/tex]
40 + 16 = q^2
56 = q^2
[tex]2\sqrt{14\\}[/tex] = q
How many x-intercepts does the graph of y=2x^2-8x+15 have?
Answers
The graph of y=2x^2-8x+15 has no x-intercepts.
Using the two-way table, what percentage of the students that do not like camping like traveling out of state? Round to the
nearest whole percent.
Likes Traveling Out of State Does Not Like Traveling Out of State Row totals
Likes Camping
52
38
90
Does Not Like Camping 36
74
110
Column totals
88
112
200
30%
33%
36%
41%
Answers
Answer:
In Grade 8, 17% of students like running.
Step-by-step explanation:
Let's do process of elimination.
For the first choice, we have that In Grade 8, 14 students liked swimming. This is wrong because based on the two-way frequency table, we are dealing with decimals, which can written as percentages. Also, you can't have 0.14 of a person.
Therefore, the first choice is incorrect.
Now for the third choice. The statement is that in Grade 9, 31 percent of students liked volleyball. Okay, so we have a percentage this time. That is a good thing, but we have to know what this percentage means. This answer is incorrect because 31 percent goes with the column of running, not volleyball. It would also be a marginal frequency as well. The 31 percent actually means that 31 percent of all students in both grades liked running. In other words, a total of 31 percent of students in both 8th and 9th grade liked running.
Therefore, the third choice is incorrect.
For the last choice. The statement is 22 students like volleyball. Just like the first choice, we are dealing with percentages, not people.
Therefore, the last choice is incorrect.
Now for the second choice. We are given that in Grade 8, 17 percent of students liked running. We have a percentage, so that is good. This choice is correct because if you were to go to Grade 8 and running. Draw some lines down. You do get to 17 percent. This 17 percent means that 17 percent of students did actually like running. It also means that out of all 8th graders, 17 percent enjoyed running.
Therefore, the second choice is correct.
Hope this helps! I hope you enjoy the rest of your day.
Fill in the blank with a constant, so that the resulting expression can be factored as the product of two linear expressions: 2ab-6a+5b+___ Please include an explanation too!
Answers
Answer:
[tex]2ab - 6a + 5b - 15[/tex]
Step-by-step explanation:
Given
[tex]2ab - 6a + 5b + \_[/tex]
Required
Fill in the gap to produce the product of linear expressions
[tex]2ab - 6a + 5b + \_[/tex]
Split to 2
[tex](2ab - 6a) + (5b + \_)[/tex]
Factorize the first bracket
[tex]2a(b - 3) + (5b + \_)[/tex]
Represent the _ with X
[tex]2a(b - 3) + (5b + X)[/tex]
Factorize the second bracket
[tex]2a(b - 3) + 5(b + \frac{X}{5})[/tex]
To result in a linear expression, then the following condition must be satisfied;
[tex]b - 3 = b + \frac{X}{5}[/tex]
Subtract b from both sides
[tex]b - b- 3 = b - b+ \frac{X}{5}[/tex]
[tex]- 3 = \frac{X}{5}[/tex]
Multiply both sides by 5
[tex]- 3 * 5 = \frac{X}{5} * 5[/tex]
[tex]X = -15[/tex]
Substitute -15 for X in [tex]2a(b - 3) + 5(b + \frac{X}{5})[/tex]
[tex]2a(b - 3) + 5(b + \frac{-15}{5})[/tex]
[tex]2a(b - 3) + 5(b - \frac{15}{5})[/tex]
[tex]2a(b - 3) + 5(b - 3)[/tex]
[tex](2a + 5)(b - 3)[/tex]
The two linear expressions are [tex](2a+ 5)[/tex] and [tex](b - 3)[/tex]
Their product will result in [tex]2ab - 6a + 5b - 15[/tex]
Hence, the constant is -15
Help me to solve this problem ASAP please, also {} is incorrect.
Answers
Answer:
8/9
Step-by-step explanation:
2/3 + 1 / ( 2 2/5) - 1/x = 1/3 - 1 / ( 2 2/3)
Changing to improper fractions
2 2/5 = ((5*2+2) / 5 = 12/5
2 2/3 = ( 3*2+2) /3 = 8/3
2/3 + 1 / ( 12/5) - 1/x = 1/3 - 1 / ( 8/3)
1 over and improper fraction flips the improper fraction 1 / ( a/b) = b/a
2/3 + 5/12 - 1/x = 1/3 -3/8
Subtract 2/3 from each side
5/12 -1/x = 1/3 -2/3 -3/8
5/12 -1/x = -1/3 -3/8
Subtract 5/12 from each side
-1/x = -1/3 -3/8-5/12
Multiply each side by 24 to get rid of the fractions
-24/x = -24/3 -3*24/8 -5*24/12
-24/x = -8 -9 -10
-24/x = -27
Multiply each side by x
-24 = -27x
Divide by -27
-24/-27 =x
8/9 =x
Pls help I need help with 12
Answers
Answer:
B. 14
Step-by-step explanation:
22/x = 11/(21-x)
462 - 22x = 11x
462 = 33x
x = 14
Answer: The value of x is 14, answer choice B
Let y be the other line segment connected to x
Using proportions:
[tex]\dfrac{11}{22}=\dfrac{y}{x}[/tex]
Cross multiply and simplify
[tex]22y=11x[/tex]
[tex]y=\dfrac{1}{2}x[/tex]
We know that x and y add to 21, so we can create the following equation:
[tex]x+y=21[/tex]
Substitute y=(1/2)x
[tex]x+\dfrac{1}{2}x=21[/tex]
Simplify by adding like terms
[tex]\dfrac{3}{2}x=21[/tex]
Divide both sides by 3/2
[tex]x=14[/tex]
Let me know if you need any clarifications, thanks!
PLEASE HELP ME WITH THIS PROBLEM ASAP!!!
Answers
Answer:
220 units
Step-by-step explanation:
ER = ET = 33 tangents from same poiint
DE = 59 => DS = DR = 59-33 = 26
DC = 77 => CR =CT = 77-26 = 51
Perimeter
= 2 *( ES + DR + CT )
= 2* (33 + 26 + 51)
= 220
Credit and thanks to ValerieUlbrich. :)
To mix mortar to lay bricks,you need 2.5Kg of cement,4kg of sand and 3 liters of water.Sand is sold in 10kg bags.How much cement and water will I need to add to make mortar?
Answers
Answer:
6.25 kg cement, 7.5 L water
Step-by-step explanation:
2.5 kg cement / 4 kg sand = x kg cement / 10 kg sand
x = 6.25
3 L water / 4 kg sand = y L water / 10 kg sand
y = 7.5
What is (5+5×5÷5-5)⁵/5
Answers
Answer:
625.
Step-by-step explanation:
(5+5×5÷5-5)⁵/5
=[ ( 5 + 25 / 5 - 5)^5] / 5
= [(5 + 5 - 5)^5] / 5
= [ (10 - 5)^5] / 5
= 5^5 / 5
= 5^4
= 625.
Answer:
625
Step-by-step explanation:
The rule is to do Parentheses/Brackets, then Exponents/Orders, followed by doing Multiplication and Division from left to right, and finally Addition and Subtraction from left to right. The answer is 625
When deriving the quadratic formula by completing the square, what expression can be added to both sides of the equation to create a perfect square trinomial?
Answers
Answer:
According to steps 2 and 4. The second-order polynomial must be added by [tex]-c[/tex] and [tex]b^{2}[/tex] to create a perfect square trinomial.
Step-by-step explanation:
Let consider a second-order polynomial of the form [tex]a\cdot x^{2} + b\cdot x + c = 0[/tex], [tex]\forall \,x \in\mathbb{R}[/tex]. The procedure is presented below:
1) [tex]a\cdot x^{2} + b\cdot x + c = 0[/tex] (Given)
2) [tex]a\cdot x^{2} + b \cdot x = -c[/tex] (Compatibility with addition/Existence of additive inverse/Modulative property)
3) [tex]4\cdot a^{2}\cdot x^{2} + 4\cdot a \cdot b \cdot x = -4\cdot a \cdot c[/tex] (Compatibility with multiplication)
4) [tex]4\cdot a^{2}\cdot x^{2} + 4\cdot a \cdot b \cdot x + b^{2} = b^{2}-4\cdot a \cdot c[/tex] (Compatibility with addition/Existence of additive inverse/Modulative property)
5) [tex](2\cdot a \cdot x + b)^{2} = b^{2}-4\cdot a \cdot c[/tex] (Perfect square trinomial)
According to steps 2 and 4. The second-order polynomial must be added by [tex]-c[/tex] and [tex]b^{2}[/tex] to create a perfect square trinomial.
Answer: D
Step-by-step explanation:
EDGE 2023
Bao can eat 12 chicken wings in 3 minutes.She eats the chicken wings at a constant rate how many chicken wings can bao eat in 12 minutes
Answers
Answer:
48 wings
Step-by-step explanation:
12:3 is the ratio. So multiply both of it by 4. Then it would be 48:12
Answer:
48 chicken wings
Step-by-step explanation:
If Bao can eat 12 chicken wings in 3 minutes and 12 minutes is 3 minutes times 4, then the answer would be 12 chicken wings times 4, so 12 times 4, which is 48, so the answer would be 48 chicken wings.
PLZ HELP ASAP!!! I WILL NAME BRAINLIEST!! 65 POINTS!! (:
Answers
Answer:
1. 44 + 3x
2. 2y - 8
3. x - 6
15. [tex]5\frac{7}{8}[/tex]
16. [tex]6\frac{1}{3}[/tex]
17. [tex]3\frac{7}{9}[/tex]
Step-by-step explanation:
1. 7² + 2² - 5 - 4 + 3x
49 + 4 - 5 - 4 + 3x
53 - 5 - 4 + 3x
48 - 4 + 3x
44 + 3x
2. - y - 5 + y + 2(2y-y) - 3
-y - 5 + y + 4y - 2y -3
-y - 5 + 5y - 2y - 3
4y - 2y - 5 - 3
2y - 8
3. 5x -3 - x - 3(x + 1²)
5x - 3 - x - 3x - 3
4x - 3x - 3 -3
x - 3 -3
x - 6
15. [tex]7\frac{1}{4} - 1\frac{3}{8}[/tex]
= [tex]7 \frac{2}{8} - 1\frac{3}{8}[/tex]
= [tex]\frac{58}{8} - \frac{11}{8}[/tex]
= [tex]\frac{47}{8}[/tex] → [tex]5\frac{7}{8}[/tex]
16. [tex]9 - 2\frac{2}{3}[/tex]
= [tex]\frac{54}{6} - 2\frac{4}{6}[/tex]
= [tex]\frac{54}{6} - \frac{16}{6}[/tex]
= [tex]\frac{38}{6}[/tex] → [tex]6\frac{2}{6}[/tex] → [tex]6\frac{1}{3}[/tex]
17. [tex]10\frac{1}{3} - 6\frac{5}{9}[/tex]
= [tex]10 \frac{3}{9} - 6\frac{5}{9}[/tex]
= [tex]\frac{93}{9} - \frac{59}{9}[/tex]
= [tex]\frac{34}{9}[/tex] → [tex]3\frac{7}{9}[/tex]
Hope this helps.
asap help !!
How much additional interest is earned if $8000 is invested for 7 years at 6.5% when
interest is compounded annually, as compared with simple interest paid at the same
rate?
Answers
Answer:
put it in a calculator, 8,000 times whatever number u need
How many of the terms in the simplified expression are negative? -3x2 + 2y2 + 5xy - 2y + 5x2 - 3y2
Answers
Step-by-step explanation:
-3x² + 2y² + 5xy -2y + 5x² - 3y²
= -3x² + 5x² +2y² -3y² + 5xy -2y
= 2x² - y² +5xy -2y
2 terms
HELPPPPPPPPPPPPPPPpppp
Answers
Answer:
Option (A)
Step-by-step explanation:
Two bases of the the given cylinder are circular in shape in the given picture.
When we take a cross-section of the cylinder parallel to the bases or perpendicular to the height, we get a circle exactly same as the bases (As shown on the rectangular slide).
Cross-section will have the same radius as the bases of the cylinder.
Therefore, Option (A) will be the answer.
The total value of a collection of nickels and dimes is $3.05. If the number of nickels is 19 greater than the number of dimes, how many nickels are in the collection?
Answers
Answer:
N = 33
Step-by-step explanation:
N = D + 19
.05N + .10 D = 3.05
N = 33
D = 14
Determine if the question is statistic or not, college in Jacksonville do tennis coaches get paid more than football coaches
Answers
Answer:
Yes, because to get the answer for this question one of the things you would do is most likely look at a group of statistics average them, and see who gets paid more.
what are the like terms??? 5x2+3x-10+7x2-8x+11 PLEASE HELP!!!! ASAP!!!!
Answers
Answer:
5x² and 7x² are like terms because they contain x².
3x and 8x are like terms because they contain x.
10 and 11 are like terms because they are constants.
Step-by-step explanation:
Let's recall that the definition of like terms is that they are terms that contain the same variables raised to the same power and only like terms can be combined.
Upon saying that, we have:
5x² and 7x² are like terms because they contain x²
3x and 8x are like terms because they contain x
10 and 11 are like terms because they are constants.
a cord of a circle is a line segment connecting any point on the circle to the center of a circle. true or false?
Answers
Answer:
true if I'm wrong I'm so sorry:/
15. To save for retirement, Karla Harby put $625 each month into an ordinary annuity for 14 years. Interest was compounded monthly. At the end of the 14 years, the annuity was worth $156 comma 700. What annual interest rate did she receive? The interest rate she received was approximately _______%. (Round to two decimal places as needed.)
Answers
Answer:
40.08%
Step-by-step explanation:
From the given information;
the annual interest rate can be determined using the formula:
[tex]A =P \times( 1+ \dfrac{r}{n})^{nt}[/tex]
where;
A = amount
P is the installment per period = $625
r = interest rate
nt = number of installments= 14×(12) =168
i = rate of interest per year
[tex]156700 = 625 \times( 1+ \dfrac{r}{12})^{168}[/tex]
[tex]\dfrac{156700}{625} = {(1+ \dfrac{r}{12})^{168}[/tex]
[tex]250.72 = {(1+ \dfrac{r}{12})^{168}[/tex]
[tex]\sqrt[168]{250.72} = {(1+ \dfrac{r}{12})[/tex]
1.0334 = [tex]{(1+ \dfrac{r}{12})[/tex]
1.0334 -1 = r/12
0.0334 = r/12
r = 0.0334 × 12
r = 0.4008
r = 40.08%
Thus; Karla Harby received an interest rate of 40.08%