Answer:
Time 2 540 years
Step-by-step explanation:
T = 5 600 yares - Half-life
73% - Carbon content
N = 0.73·N₀
Decay constant:
λ = ln 2 / T = 0.693 / 5600 ≈ 0.000124 (years)⁻¹
Law of radioactive decay:
N = N₀·e^(-λ·t)
0.73·N₀ = N₀·e^(-λ·t)
0.73 = e^(-λ·t)
ln (0.73) = -λ·t
t = ln (0.73) / (-λ) = ln (0.73) / (- 0.000124) ≈ 2 540 years
Determine an nth degree polynomial that satisfies the aforementioned conditions.
The polynomial of p(x) is 20/13(x³+4x²-9x-36) with the satisfying's conditions degree 3.
Given that,
An nth degree polynomial p meets the requirements listed below:
p is of degree 3.
-3 is a multiplicity 1 zero of p.
-4 is a zero, with multiplicity 1, of p.
3 is a root, with multiplicity 1, of p.
p(-2)=-40
We have to determine an nth degree polynomial that satisfier the conditions.
Let the polynomial be p(x) whose zero are -3,-4 and 3.
a be the coefficient.
p(x)=a(x+3)(x+4)(x-3)
p(x)=a(x²-3²)(x+4)
p(x)=a(x²-9)(x+4)
p(x)=a(x³+4x²-9x-36)
Now, take x=-2
p(-2)=a((-2)³+4(-2)²-(-2)-36)
-40=a(-8+16+2-36)
-40=a(-26)
a=-40/-26
a=40/26
a=20/13
We get,
p(x)=20/13((x+3)(x+4)(x-3))
p(x)=20/13(x³+4x²-9x-36)
Therefore, the polynomial of p(x) is 20/13(x³+4x²-9x-36) with the satisfying's conditions degree 3.
To learn more about degree visit: https://brainly.com/question/364572
#SPJ1
You have four sweaters, five pairs of pants, and three pairs of shoes. How many different combinations can you make, wearing one of each? Explain your answer. a. 4 times 5 + 3 = 23 b. 4 times 5 = 20 c. 4 times 5 times 3 = 60 d. 4 + 5 + 3 = 12 Please select the best answer from the choices provided A B C D
There are total 4*5*3 = 60 ways of wearing one each.
What is Fundamental Counting Principle?
A rule used to count the entire number of alternative outcomes in a circumstance is known as the fundamental counting principle.
Solution:
Let,
for three events A, B, and C, number of outcomes be a,b, and c respectively.
So, the total number of outcomes is given by the product of outcomes of all the events i.e. by using Fundamental Counting Principle.
In the question mentioned,
a = 4
b = 5
c = 3
So, total outcomes = 4*5*3 = 60 ways
To learn more about Fundamental Counting Principle from the given link
https://brainly.com/question/10275154
#SPJ9
A doctor prescribes 100 milligrams of a therapeutic drug that decays by about 15% each hour. To the nearest hour, what is the half-life of the drug?
The drug administered to the patient by the doctor has a half-life of 5 hours
Half-LifeHalf-life is the time required for a quantity to reduce to half of its initial value. The term is commonly used in nuclear physics to describe how quickly unstable atoms undergo radioactive decay or how long stable atoms survive. The term is also used more generally to characterize any type of exponential decay.
The formula is given as;
T1/2 = ln2 / λ
Where;
λ = disintegration constant.But λ = 15% = 0.15/hr
t1/2 = ln2 / 0.15
T1/2 = 0.693/0.15
T1/2 = 4.62 = 5 hours.
The drug has an half-life of approximately 5 hours
Learn more on half-life here;
https://brainly.com/question/10525285
#SPJ1
Solve for x. Round to the nearest tenth, if necessary.
Value of x rounded to nearest tenth is 25.5 units.
Given in question,
Right angled triangle CDE
θ = 20°
CD = perpendicular = 24 units
CE = Hypotenuse = x
Therefore,
cosθ = Perpendicular/Hypotenuse
cos 20 = 24/x
0.9397 = 24/x
x = 24/0.9397
= 25.54
Hence, value of x rounded to nearest tenth is 25.5 units.
To learn more about rounded to nearest here:
https://brainly.com/question/1285194
#SPJ1
The cellular phone service for a business executive is $35 per month plus $0.40 per minute of phone use over 900 min. For a month in which the executive's cellular phone bill was $87.80, how many minutes did the executive use the phone?
The number of minutes that the executive use the phone is 131 minutes.
How to calculate the number of minutes?From the information, the cellular phone service for a business executive is $35 per month plus $0.40 per minute of phone use.
Let the number of minutes be m.
This will be illustrated as:
35 + 0.40m = 87.80
Collect like terms
0.40m = 87.80 - 35
0.40m = 52.80
Divide
m = 52.40 / 0.40
m = 131
The number of minute is 131 minutes.
Learn more about expressions on:
brainly.com/question/723406
#SPJ1
the line segment from (0,0) to (6,18) is revolved about the x-axis to form a cone. what is the volume of this cone?
Answer:
Step-by-step explanation:
do you happen to know the formula for finding the area of a cone?
V=π*[tex]r^{2}[/tex]*h/3
does that formula look familiar?
we know the radius , r, is 18 and the height, h is 6 :) can you figure this out now? just plug those into the formula above :)
You move left 1 unit and right 8 units. You end at (5, 5). Where did you start?
The coordinates of the starting point is (12, 5)
What are ordered pairs?Ordered pairs refers to the arrangement of 2 numbers in the form (a, b)
The rule to move ordered pair one unit left 1 will be subtracted in the x coordinates
(5, 5) → one unit left → ( 5 - 1, 5 ) = (4, 5)
The rule to move ordered pair 8 units left, 8 will be added in the x coordinates
(4, 5) → one unit left → ( 4 + 8, 5 ) = (12, 5)
Learn more about ordered pairs here:
https://brainly.com/question/29232584
#SPJ1
An ostrich farmer wants to enclose a rectangular area and then divide it into three pens with fencing parallel to one side of the
rectangle (see the figure below). There are 700 feet of fencing available to complete the job. What is the largest possible total
area of the three pens?
The largest possible total area of the three pens is 15312.5sq.units.
What is a rectangular area?
The quantity of space occupied by a flat surface with a specific shape is referred to as the area.
Area of a Rectangle = (Length × Breadth) square units.
Here,
We let x be the length and y be the breadth of a rectangle area.
Given equation : 2y + 4x = 700
y + 2x = 350
y = 350 - 2x .......(1)
Area of rectangular field (A)= xy
A = x(350 - 2x)
A = 350x - 2x²
Differentiating w.r.t x we get,
A' = 350 - 4x
Again, differentiating w.r.t x we get,
A" = -4
Let A' = 0
350 - 4x = 0
4x = 350
x = 87.5
A is maximum at 87.5feets.
Hence, the largest possible total area of the three pens = XY = 87.5×175 = 15312.5 sq. units.
To learn more about the rectangular area from the given link
https://brainly.com/question/25292087
#SPJ4
Evaluate the expression 23.5 − 6.8x when x = 3.
Answer:
3.1
Step-by-step explanation:
23.5-6.8x
x=3
first put 3 in for x
23.5-6.8(3)
now solve the expression
23.5-20.4
3.1
A solve the first question
Answer:
A or C
Step-by-step explanation:
it takes matilda twice as long to complete a research project
Jaclyn bought new shoes priced at $98 and sales tax is 8%. What is the total cost of the shoes after-tax?
The total cost of the shoes after tax is 105.84 dollars.
How to solve sales tax?Sales tax is a tax on goods and services purchased and is normally a percentage added to the buyer's cost.
Jaclyn bought new shoes priced at $98 and sales tax is 8%. The total cost of the shoes after tax can be calculated as follows;
Therefore, the cost after tax is the sum of the cost and the sales tax.
Hence,
sales tax = 8% of 98
sale tax = 8 / 100 × 98
sales tax = 784 / 100
sales tax = $7.84
Hence,
total cost after tax = 7.84 + 98 = 105.84 dollars
learn more on sales tax here: https://brainly.com/question/8648684
#SPJ1
write the number 4 as a fraction with a denominator of 15
Answer:
60/15
Step-by-step explanation:
A fraction is simply a portion of a whole number, so 1/15 is the number 1 split into fifteen equal parts, therefore 15/15 = 1.
So 4 as a fraction with fifteen as the denominator would be 15/15 x 4, which equals 60/15.
Determine whether the series converges or diverges...
The series as represented in the task content is divergent and hence; diverges.
What convergence and divergence in series?It follows from the task content that the series defined by the summation expression as represented above is to be identified as divergent or convergent.
It is noteworthy to know that;
If a sequence converges, it means that the limit of the sequence exists as n → ∞. Also, if the limit of the sequence as n → ∞ does not exist, Then, such series is said to diverges.
Therefore, by evaluation as the limit of the expression k sin²k / 1 + k³ as k → ∞ is; Undefined and hence does not exist.
Read more on convergence and divergence of series;
https://brainly.com/question/28169281
#SPJ1
in a major need of help
Answer:
B and D are the correct answers.
we want to factor the following expression: (x - 3)^2 - 64y^4 which pattern can we use to factor the expression? u and v are either constant integers or single variable expression.
The factored expression of (x - 3)^2 - 64y^4 is given as follows:
(x - 3)^2 - 64y^4 = (x - 3 + 8y²)(x - 3 - 8y²).
What is the subtraction of perfect squares?The subtraction of perfect squares is a notable product that gives the simplification of an expression containing the subtraction of perfect squares as follows:
a² - b² = (a - b)(a + b).
In this problem, the expression is presented as follows:
(x - 3)^2 - 64y^4
This expression is a subtraction of perfect squares, as the terms are given as follows:
Term a: square root of (x - 3)² = x - 3.Term b: square root of 64y^4 = 8y².Then the expressions are given as follows:
a - b = x - 3 - 8y².a + b = x - 3 + 8y².Then the factored expression is presented as follows:
a² - b² = (a - b)(a + b).
(x - 3)² - 64y^4 = (x - 3 + 8y²)(x - 3 - 8y²).
More can be learned about the subtraction of perfect squares at https://brainly.com/question/28792378
#SPJ1
Find the equation of a parabola with a focus at (–2,–3) and a directrix at y = –5.
A)
y = 1∕4(x + 2)2 – 4
B)
y = –1∕16(x + 2)2 – 4
C)
y = 1∕4(x – 2)2 – 4
D)
y = 1∕4(x + 2)2 – 8
The vertex form of Parabola is y= 1/4(x + 2)² -4 .
What is Vertex form of Equation?The general equation of a parabola is given by y = a(x – h)² + k or
x = a(y – k)² +h. Here (h, k) is vertex.
Given:
focus at (–2,–3) and a directrix at y = –5.
We know, the standard form is (x - h)² = 4p (y - k),
where the focus is (h, k + p) and the directrix is y = k - p
So, (h, k + p) = (-2, -3)
h = -2, k + p = -3
Directrix is y = k - p:
k - p = -5
k + p = -3
so, 2k = -8
k = -4
and, p = -3+ 4 = 1
Thus, the vertex is at (-2, -4) and p = 1, the equation is:
(x + 2)² = 4(y+ 4)
1/4(x + 2)² = y+4
y= 1/4(x + 2)² -4
Learn more about Vertex form of Parabola here:
https://brainly.com/question/1504592
#SPJ1
what is y times equals negative 42
Answer:
I am thinking the answere is -6 x 7 but I'm not completely
50 POINTS!!
One Thursday night, Joel the delivery boy earned $43 in tips plus his usual $12/hr. He made $85. Write an equation for this situation.
Answer:
Step-by-step explanation:
This is a simple linear equation.
Y=12x + 43
The 12x represents the money he makes hourly, as x represents each hour he works
+43 represents the amount of money in tips he made since this was added on top of the hourly pay he was making.
Answer:
your welcome
Step-by-step explanation:
42+43=85$
to get the 42 you have to do 83-43 and that leaves you with 42
If you are god in math the I have a question do it
Answer:
I am definitely not one...Lol
Step-by-step explanation:
The graph represents the function f(x) = x2 + 3x + 2. If g(x) is the reflection of f(x) across the x-axis, g(x) = . (Write the function in standard form. Use ^ to indicate an exponent.)
The reflection of the graph in the x-axis gives the function
g(x) = -x² - 3x - 2
The given function is of the form f(x) = x² + 3x + 2 which represents a parabola.
The vertex of the function is at (-3/2 , -1/4)
The focus is at ( 3/2 , 0 )
The axis of symmetry is 2x+3 = 0 and the directrix is at 2x + 1 = 0
Now when the parabola is reflected along the x-axis we get
the focus at ( -3/2 , 0 )
the vertex is at (-3/2 , 1/4)
Axis of symmetry remains the same
The directrix becomes 2y-1 =0
The red graph denotes the function f(x) while the blue graph denotes the function g(x) reflected on the x-axis.
Hence the reflection on the x-axis gives the function g(x) = -x² - 3x - 2
To learn more about reflection visit:
https://brainly.com/question/13206012
#SPJ1
HURRY PLS!! TEST!!!!
consider the line y=5x-5
find the equation of the line that is parallel to this line and passes through the point (3,4)
find the equation of the line that is perpendicular to this line and passes through the point (3,4)
Answer:
y=-5x+19
Step-by-step explanation:
yeah -ya...... right?
can anyone help? thanks!
Answer: 175
Step-by-step explanation:
7 x 1 x 5^2
7 x 1 x 25
7 x 25
175
Answer:
175
Step-by-step explanation:
Since we have 7ca^2 and since we know a = 5 and c = 1, we can just plug in these values for a and c and follow the order of operations:
[tex]7ca^2\\7(1)(5)^2\\7(1)(25)\\7*25=175[/tex]
Try It
Solving Equations with Rational Numbers
Solve this equation: -7x+12 - 2x = 23 + 13x
Step 1: Simplify by combining like terms that are on the
same side of the equation. Which terms can be
combined?
Check
-7x+12-2x = 23+13x
Answer:
-6/11
Step-by-step explanation:
please follow me to mark me on brainliest
What can be concluded about line that passes through the points (1,-2) and (4,-2)? Check all that apply.
The slope is 0.
The y-intercept is -2.
The line is vertical.
O The line is horizontal.
The line has no y-intercept.
The equation of the line is Y--2
All that apply are:
The slope is 0.
The y-intercept is -2
The line is horizontal.
The equation of the line is Y = -2.
Given points:
(1,-2) and (4,-2)
slope m = -2-(-2) / 4 - 1
= -2+2/3
= 0
so slope is 0
y = mx + c
(1,-2) passes
-2 = 0*1 + c
c = -2
y = 0*x + -2
y = -2
so the line is horizontal and equation of the line is y = -2.
The y-intercept is -2.
Learn more about the equation here:
https://brainly.com/question/10413253
#SPJ1
Which expression is equivalent to 1/3(x+6)−4
The expression that must be equivalent to the one give must be 1/3x - 2
Equivalent ExpressionEquivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value for the variable. Two expressions are said to be equivalent if they have the same value irrespective of the value of the variable(s) in them.
In this problem, we just need to simply the expression to get the answer to this.
1/3(x + 6) - 4
Step 1 : Expand or open the bracket
1/3x + 2 - 4
Step 2: Simplify the expression.
1/3x + 2 - 4 = 1/3x - 2
The equivalent expression must be 1/3x - 2
Learn more on equivalent expression here;
https://brainly.com/question/15775046
#SPJ1
[tex]\frac{5x^{6}5x^{-2}125x2x^{4}2x^{-5} }{2x^{5}5x^{-3}2x^{6\\} }[/tex]
[tex]\cfrac{5x^6 5x^{-2}125x 2x^4 2x^{-5}}{2x^5 5x^{-3} 2x^6}\implies \cfrac{5\cdot 5\cdot 125\cdot 2\cdot 2}{2\cdot 5\cdot 2}\cdot \cfrac{x^6 x^{-2}x x^4 x^{-5}}{x^5 x^{-3} x^6} \\\\\\ \cfrac{ 5\cdot 125}{1}\cdot \cfrac{x^{6-2+1+4-5}}{x^{5-3+6}}\implies 125\cdot \cfrac{x^4}{x^8}\implies 125\cdot \cfrac{1}{x^8 x^{-4}}\implies \cfrac{125}{x^{8-4}}\implies {\Large \begin{array}{llll} \cfrac{125}{x^4} \end{array}}[/tex]
Write the equation of a line in
y = mx + b form that passes
through (5,-5) and (-5, -3)
The equation of a line in y = mx + b form that passes through (5,-5) and (-5, -3) is y = (-1/5)x - 4.
The formula to calculate the slope between two points is equal to
[tex]m = y2-y1/(x2-x1)[/tex]
Find the slope of Line a
We have the points
(5,-5) and (-5, -3)
Substituting the value in the formula
[tex]m = -3 - (-5)/(-5-5)\\m = (-3 + 5)/(-10)\\m = 2/-10\\m = -1/5[/tex]
The slope is -1/5.
Finding the y-intercept from the below-given equation:
y = mx + b ...... (1)
Putting value of y = - 5, x = 5, m = -1/5
-5 = (-1/5) x (5) + b
-5 = - 1 + b
=> b = - 4
Putting the value of b = - 4 and m = -1/5 in equation (1). We get,
y = (-1/5)x - 4
Hence, the equation of the line is y = (-1/5)x - 4.
To learn more about the line visit: https://brainly.com/question/19448440
#SPJ1
25% of 0÷4 = 0÷1 True or False?
Answer:
false
Step-by-step explanation:
25% is equivalent to 0.25
You have to make a balloon payment on your house five years from now of $15,000. If money can earn an average of 6 percent a year for the five-year period, how much will you have to place in the account today to have the $15,000 in five years?
The future value of an investment with such details must have a present value of $11120.58
Present ValuePresent value (PV) formula finds application in finance to calculate the present day value of an amount that is received at a future date. The present value formula (PV formula) is derived from the compound interest formula. The compound interest formula is,
FV = PV(1 + r/n)^nt
We can substitute the values into the formula
15000 = PV(1 + 0.06/12)^12*5
15000 = PV(1.005)^60
PV = 11120.58
The present value of an investment to give a future value of $15000 at 6% rate in 5 years is $11120.58
Learn more on present value here;
https://brainly.com/question/24703884
#spj1