The constant p is determined by the half-life of 1600 years, and since after one half-life, the amount of the element is half of its initial value, we find that x=1/2 and y=1/1600, as e^p can be expressed as (1/2)^(1/1600). Therefore, option (a) is the correct answer.
The equation Q(t) = Q(0)e^pt describes an exponential decay process, such as the decay of a chemical element over time. Given that the half-life of the chemical element is 1600 years, after this period the quantity of the element will be half of its original amount. According to the properties of exponential decay, we know that after one half-life, Q(t) = Q(0)/2.
Substituting t = 1600 into the equation and knowing that Q(1600) = Q(0)/2, we get Q(0)/2 = Q(0)e^(1600p). Simplify by dividing both sides by Q(0), resulting in 1/2 = e^(1600p). To find p, take the natural logarithm of both sides, yielding ln(1/2) = 1600p ln(e), and since ln(e) = 1, we have p = ln(1/2)/1600.
Now, to express e^p as x^y, with both x and y being rational numbers, we look for a rational base x that can represent e^ln(1/2), which simplifies to (1/2). So, x would be 1/2, and because the half-life is 1600 years, y will be proportional to the fraction of that time. Hence, y = t/1600, where t is time in years. From this, you can infer that the base x equals 1/2 and y is 1/1600 for each year surpassing the half-life. Therefore, the correct answer is (a) x = sqrt(1/2), y = 1/1600.
Which of the following numbers can be expressed as repeating decimals? 3/7, 2/5, 3/4, and 2/9.
Answer:
Step-by-step explanation:
2/9 when you divide it is 0.22222222222222
Answer:
First option: [tex]\frac{3}{7}[/tex]
Fourth option: [tex]\frac{2}{9}[/tex]
Step-by-step explanation:
Repeating decimals are also known as "Recurring decimals", are those decimal numbers whose digit or group of digits repeats indefinitely.
To know which of the given fractions can be expressed as Repeating decimals, you need to divide the numerator by the denominator in each option. Then:
First option: [tex]\frac{3}{7}=0.428571428571[/tex] (It can be expressed as repeating decimal)
Second option: [tex]\frac{2}{5}=0.4[/tex]
Third option: [tex]\frac{3}{4}=0.75[/tex]
Fourth option: [tex]\frac{2}{9}=0.2222222222[/tex] (It can be expressed as repeating decimal)
How will you write 7^5 as a multiplication expression?
A.
7 * 5
B.
7*7*777
C.
5 x 5 x 5 x 5 x 5 x 5 x 5
Answer:
The answer is 7*7*7*7*7
Step-by-step explanation:
The correct way to write 7^5 as a multiplication expression is by writing it as 7 multiplied by itself 5 times, which is 7 x 7 x 7 x 7 x 7.
The question asks how to write 7^5 as a multiplication expression. To correctly express 7^5, we represent it as 7 being multiplied by itself 5 times. So, the correct way to write 7^5 as a multiplication expression is 7 \u00d7 7 \u00d7 7 \u00d7 7 \u00d7 7. This clearly demonstrates the concept of an exponent, where the base (7) is multiplied by itself a certain number of times (5 times in this case), which is fundamentally different from just multiplying 7 by 5.
Help fast please!!! Find the value of each variable.
Answer: third answer
Step-by-step explanation:
Answer:
a = 10√3, b = 5√3, c = 15; d = 5
Step-by-step explanation:
d = 10/2 = 5
b = 5√3
a = 2 * 5√3 = 10√3
c = 5√3 * √3 = 15
Answer is the second option
a = 10√3, b = 5√3, c = 15; d = 5
Susan plans on visiting her friend in the next state over the distance to her friend is 1497 miles . If she leaves on Friday and drives 8 hours at a time 60 mph when will she get there
A. The next day
B. In 3 days
C. In 5 days
D. In 2 days
The Answer Is B
Explanation : If you divide 1497 by 60 you get 24.95 24 divide by 8 is 3
The number of days, she will be there are 3 days. Then the correct option is B.
What is speed?The distance covered by the particle or the body in an hour is called speed. It is a scalar quantity. It is the ratio of distance to time.
We know that the speed formula
[tex]\rm Speed = \dfrac{Distance}{Time}[/tex]
Susan plans on visiting her friend in the next state the distance to her friend is 1497 miles.
If she leaves on Friday and drives 8 hours at a time at 60 mph. Then the number of days, she will be there.
The distance she covers in a day will be
D = 60 × 8
D = 480 miles
Then the number of the days will be
→ 1497 / 480
→ 3.11875
→ 3 days and 1 hour.
More about the speed link is given below.
https://brainly.com/question/7359669
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The table below represents the height of a bird above the ground during flight, with p(t) representing height in feet and t representing time in seconds
calculate the average rate of change from 3 to 9 seconds
Answer:
calculate the difference height (P) is -6 and (t) is 2.85
Δy divided by Δx = rate of change
3-9 = -6
6.23-3.41 = 2.85
then divide
2.85 / -6 = .475
Your answer will be - .475
Step-by-step explanation:
Using the table, the average rate of change from 3 to 9 seconds is of -0.475 feet per second.
The average rate of change of a function P(x) over an interval [a,b] is given by:
[tex]A = \frac{P(b) - P(a)}{b - a}[/tex]
In this problem, we want the rate from 3 to 9 seconds, hence [tex]a = 3, b = 9[/tex].
From the table, [tex]P(3) = 6.26, P(9) = 3.41[/tex], hence:[tex]A = \frac{3.41 - 6.26}{9 - 3} = -0.475[/tex]
Considering the units, the average rate of change from 3 to 9 seconds is of -0.475 feet per second.
You can learn more about the average rate of change at https://brainly.com/question/24313700
If 0° ≤ θ ≤ 90° and cosθ =
11
15
, what is the value of sin (90° - θ)?
Answer:
11/15.
Step-by-step explanation:
If we consider a right angled triangle we see that
in this case cos θ = sin (90 - θ) so the answer is 11/15.
My dog died but answer is 0
If 90 students were surveyed and 50 said they would buy a wristband, how many wristbands should Monty order for the school of 1800 students?
He should buy 1000 wristbands.
Since 50/90 students said they would buy a wristband, we can set up this proportion.
[tex]\frac{50}{90}[/tex] [tex]\frac{x}{1800}[/tex]
multiply 50 * 1800 divided by 90 = 1000
Why did most Americans reject Marxism in the early 1900s? They believed that a government-run economy was best for all. They believed in a system owned and run by the individual. They believed that factory workers should make more than factory owners. They believed that the proletariat should control the means of pr
Answer:
They believed in a system owned and run by the individual
Step-by-step explanation:
In the early 1900's the majority of the Americans rejected the Marxist ideology, and they saw it as usurpation of their country and its foundations. The majority of the Americans favored the capitalism, and they saw their country as the country of opportunities where everyone can achieve everything if the person is smart enough and works hard enough. The Marxism suggested the total opposite of it, that everyone should be equal, have the same earnings, there's no prosper on a career level, so for the Americans was not attractive, and we can comfortably say that they made the right choice considering what happened in the countries that adopted this ideology.
Answer:
B They believed in a system owned and run by the individual
Step-by-step explanation: B
Explain how you drew and used a tape diagram to model and solve problem 1.
Answer:
800
Step-by-step explanation:
you follow the draeing above so you know that 4+5= 9 so u do 1800÷9 which equals 200 so u do 200×4=800
Answer:
Step-by-step explanation:
you follow the draeing above so you know that 4+5= 9 so u do 1800÷9 which equals 200 so u do 200×4=800
Select all the correct answers.
Look at the graphs of y = 4x2 + 7x - 11 and y = 3x + 4. At which points are the two equations equal?
410
-
8
7
6
5
4
3
27-1
y = 3x + 4
Answer:
Second point (-5/2, -7/2)
First point (3/2, 17/2)
Step-by-step explanation:
We have two equations, and we want to know at wich poin are equal. Hence, we have a system of equations and the solution is nothing more that the point (x,y) where those functions intercepts.
4x2+ 7x -11=y
3x+4=y
Lets use substitute method
4x2+7x-11=3x+4
This can be re arrange as the following eq:
4x2+4x-15=0
A quadratic equation, its solution can be obtained using the below eq.
[tex]x=\frac{-b+/- \sqrt{x^{2}-4ac } }{2a}[/tex]
where a=4, b=4, c=-15.
Remember, the quadratic equation as a +/- sign, meaning that you will obtain one answer using the + operator and other using the - operator.
By doing the above, we have x=-5/2 and x=3/2
By using x=3/2 in equation of line (3x+4=y) we have y=17/2
First point (3/2, 17/2)
By using x=-5/2 in equation of line (3x+4=y) we have y= -7/2
Second point (-5/2, -7/2)
Those points are the ones where the line and the parabola intercept.
Solve the inequality:
3x-3<9
5x+2<32
Answer:
x < 4x < 6Step-by-step explanation:
[tex]3x-3<9\qquad\text{add 3 to both sides}\\3x-3+3<9+3\\3x<12\qquad\text{divide both sides by 3}\\\dfrac{3x}{3}<\dfrac{12}{3}\\\boxed{x<4}\\\\============================\\\\5x+2<32\qquad\text{subtract 2 from both sides}\\5x+2-2<32-2\\5x<30\qquad\text{divide both sides by 5}\\\dfrac{5x}{5}<\dfrac{30}{5}\\\boxed{x<6}[/tex]
What is the reciprocal of 3 ?
What is the reciprocal of 11/8
Answer:
1 / 3 and 8 / 11
Step-by-step explanation:
When you find the reciprocal of something you flip the number over e.g
Find the reciprocal of 1 /2,
You ' flip it ' and it becomes 2 / 1 or 2
Answer: 1/3 and 8/11
Step-by-step explanation:
2x+y=4
Y=3x-1
Is (1,2) a solution to both equations
Answer:
yes they are
Step-by-step explanation:
Just test it
2x+y=4
(1,2)
1 is x
2 is y
2+2=4
y=3x-1
3-1=2
X=1 y=2................
Find the surface area of a right prism whose bases are equilateral triangles with side lengths of 6 in. The height of the prism is 10in
Answer:
The surface area of the prism is [tex](18\sqrt{3}+180)\ in^{2}[/tex]
Step-by-step explanation:
we know that
The surface area of the triangular prism is equal to
[tex]SA=2B+PH[/tex]
where
B is the area of the triangular base
P is the perimeter of the triangular base
H is the height of the prism
Find the area of the base B
Applying the law of sines to find the area of a equilateral triangle
[tex]B=\frac{1}{2}b^{2} sin(60\°)[/tex]
we have
[tex]b=6\ in[/tex]
[tex]sin(60\°)=\sqrt{3}/2[/tex]
substitute
[tex]B=\frac{1}{2}6^{2}(\sqrt{3}/2)[/tex]
[tex]B=9\sqrt{3}\ in^{2}[/tex]
Find the perimeter P
[tex]P=3*6=18\ in[/tex]
we have
[tex]H=10\ in[/tex]
substitute the values
[tex]SA=2(9\sqrt{3})+(18)(10)=(18\sqrt{3}+180)\ in^{2}[/tex]
What is the point slope form of a line with slope 3/2 that contains the point (-1,2) ?
The options are in the picture ... please help !
y-2=3/2 (x+1) must be first
Solve 2p = 18
Help!!!!!!
Answer:
9
Step-by-step explanation:
2p= 18
p = 18 ÷ 2
p = 9 hope it helps u
Answer:
p=9
Step-by-step explanation:
mary's job pays her $8.75 per hour which of the following expressions best represents her total earnings if she works two hours or monday three hours on tuesday for hours on wednesday 5 hours on thursday and 6 hours on friday
Around 175 dollars with that because that’s 20 hours
Answer:
$170
Step-by-step explanation:
add the hours first
2+3+4+5+6= 20 hours
multiply that by how much she makes per hour
20*8.75= 175
If f(x) = 4x + 12 is graphed on a coordinate plane, what is the y-intercept of the graph? 4 8 12 16
Answer:
The y-intercept would be 12.
Step-by-step explanation:
In the problem:
4x=slope
12=y-intercept
AnswBetty correctly determined that the ordered pair (–3, 5) is a solution to the system of linear equations 6 x + 5 y = 7 and x + 4y = 17. Based on this information, which statement is correct?
(–3, 5) satisfies neither the equation 6x + 5y = 7 nor the equation x + 4y = 17.
(–3, 5) satisfies the equation 6x + 5y = 7 but not the equation x + 4y = 17.
(–3, 5) satisfies the equation x + 4y = 17 but not the equation 6x + 5y = 7.
(–3, 5) satisfies both the equation 6x + 5y = 7 and the equation x + 4y = 17.
Ms Sharp baked 21 trays of cookies with 35 cookies on each trays if she needs to bake 840 cookies how many more trays will she need to make
Answer:
3 more trays
Step-by-step explanation:
At 35 cookies per tray, x trays is sufficient for an output of 840 cookies. Dividing 840 cookies by 35 cookies/tray, we get 24 trays.
But Ms. Sharp already has 21 trays.
Thus, she needs 3 more to be able to bake 840 cookies.
Ms Sharp will need to bake 3 more trays of cookies to meet the requirement of 840 cookies.
To determine how many more trays of cookies Ms. Sharp needs to bake, we first calculate the total number of cookies she has already baked. She baked 21 trays with 35 cookies on each tray:
[tex]\[21 \text{ trays} \times 35 \text{ cookies per tray} = 735 \text{ cookies}\][/tex]
Ms. Sharp needs a total of 840 cookies. Therefore, we need to find out how many more cookies are required:
[tex]\[840 \text{ cookies} - 735 \text{ cookies} = 105 \text{ cookies}\][/tex]
Each tray contains 35 cookies, so we need to determine how many more trays are required to bake 105 cookies:
[tex]\[\frac{105 \text{ cookies}}{35 \text{ cookies per tray}} = 3 \text{ trays}\][/tex]
Therefore, Ms. Sharp will need to bake an additional:
[tex]\[\boxed{3}\][/tex] trays of cookies.
what are expressions are equivalent to 6x-18y
Answer:
Step-by-step explanation:
6 is common to both terms, so 6x - 18y is equivalent to 6(x - 3y).
What is the factored form of x2 − 4x − 5?
Answer:
[tex]\large\boxed{x^2-4x-5=(x+1)(x-5)}[/tex]
Step-by-step explanation:
[tex]\text{The factored form:}\\\\ax^2+bx+c=a(x-x_1)(x-x_2)\\\\x_1,\ x_2-the\ zeros\\==============================\\\\\text{We have}\ x^2-4x-5:\\\\x^2-4x-5=x^2+x-5x-5=x(x+1)-5(x+1)\\\\x^2-4x-5=(x+1)(x-5)[/tex]
4708.06 rounded to nearest thousand
Answer
5,000
Explanation
1. Examine the number next to the thousands value (hundreds place)
2. Should that number be greater than 5, round the thousands value up one.
To round 4708.06 to the nearest thousand, we look at the hundreds place value which is '7'. Since it's higher than 5, we round up the thousands of places and the number becomes 5000.
Explanation:The process of rounding involves deciding which multiple of a certain number is closest to the number you're trying to round. If to round the number 4708.06 to the nearest thousand, we look at the hundreds place. In our case, it's '7', a digit that is 5 or higher.
Thus, we increase the digit at the thousands place by '1' and change all the subsequent digits to '0'. Therefore, 4708.06 rounds to 5000 when rounded to the nearest thousand.
Learn more about Rounding Numbers here:https://brainly.com/question/19166897
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The width of a rectangle is y feet long. The rectangle is 4 feet longer than it is wide. What is the area of the rectangle? Which expression represents the area?
Answer:
y²+4y
Step-by-step explanation:
y multiplies with (y+4)
y times y is y²
y times 4 is 4y
That leaves you with y²+4y
Answer: [tex]y^2+4y[/tex] expresses the area.
Step-by-step explanation:
Let the width of a rectangle be 'y' feet.
Let the length of a rectangle be 'y+4' feet.
As we know the area of rectangle :
Area of rectangle is given by
[tex]Length\times breadth\\\\=y\times (y+4)\\\\=y^2+4y[/tex]
Hence, [tex]y^2+4y[/tex] expresses the area.
A cup of cereal can contain 480
480
milligrams of salt, which is 20%
20
%
of the recommended daily amount.
What is the recommended daily amount of salt?
480 x 5 = 2400. 2400 milligrams of salt is the recommended daily amount.
Answer:
2400 milligrams because 480 is 20% of the recommended amount
Step-by-step explanation:
20*5 = 100% so 480* 5 = 100% or recommended amount
Hope this helps!
URGENT: Can someone help me solve these problems?
Answer:
12
Step-by-step explanation:
21=31
31=7+2-3+0=12
This is correct because linear equations mean add subtract divide and multiply instead of finding roots and squares
It is asking for the standard form for the quadratic function.
well factored would be f(x)= (x+4)(x+2) and standard for would be
f(x)= x^2+6x+8
Liz earns a salary of $2,500 per month, plus a commission of 6% of her sales. She wants to earn at least $2,700 this month. Enter an inequality to find amounts of sales that will meet her goal. Identify what your variable represents. Enter the commission rate as a decimal.
Final answer:
To find the amounts of sales that will meet Liz's goal, we can set up an inequality using her salary and commission. Liz needs to earn at least $2,700 this month, and with her salary and commission, we can create the inequality $2,500 + 0.06x ≥ $2,700. Solving this inequality gives us x ≥ $3,333.33. Therefore, the amounts of sales that will meet Liz's goal are any values of x that are greater than or equal to $3,333.33.
Explanation:
To find the amounts of sales that will meet Liz's goal of earning at least $2,700 this month, we can set up an inequality. Let's represent the amount of sales as 'x'.
Liz's salary is $2,500 per month, and her commission is 6% of her sales. So her total earnings for the month can be calculated as:
Total Earnings = Salary + Commission
Total Earnings = $2,500 + 0.06x (since the commission is 6% of sales)
We want Liz to earn at least $2,700, so we can set up the following inequality:
$2,500 + 0.06x ≥ $2,700
To solve this inequality, we can subtract $2,500 from both sides:
0.06x ≥ $2,700 - $2,500
0.06x ≥ $200
Finally, we divide both sides by 0.06 to isolate 'x', the amount of sales:
x ≥ $200 ÷ 0.06
x ≥ $3,333.33
Therefore, the amounts of sales that will meet Liz's goal are any values of 'x' that are greater than or equal to $3,333.33.
Need help please someone
The answer to 9 would be (-3,-4) and (2,6) because if you plug in -3 for x in either of the equations and plug in 4 for y in the equations, both sides of the equation are the same number. also, if you plug in 2 for x and 6 for y both sides of the equation equal each other. The answer to 10 is (-1,1) and (7,33). if you plug them in they are equal:)
pls help me i really need it
Look at the prism and its net.
What is the surface area of this rectangular prism?
a. 112 m²
b. 140 m²
c. 280 m²
d. 292 m²
Answer:
The answer would be C
Step-by-step explanation:
have a wonderful day, please mark brainlest and thank me.... I do flvs as well
Answer:
Step-by-step explanation: SA= Arec1*2+Arec2*2+Arec3*2
SA=l*w*2+l*w*2+l*w*2
SA=4*14*2+4*5*2+5*14*2
and you do the math
NEED HELP ASAP
if f(x)=sqrt x-3 and g(x)=1-x^2 then what did you notice about the domain of (f o g)(x)?
ANSWER
The domain is an empty set
EXPLANATION
The given functions are:
[tex]f(x) = \sqrt{x - 3} [/tex]
and
[tex]g(x) =1 - {x}^{2}[/tex]
[tex](f \circ \: g)(x) = f(g(x))[/tex]
[tex](f \circ \: g)(x) = f(1 - {x}^{2} )[/tex]
[tex](f \circ \: g)(x) = \sqrt{(1 - {x}^{2} ) - 3} [/tex]
[tex](f \circ \: g)(x) = \sqrt{ - {x}^{2} - 2} [/tex]
This function is defined if and only if
[tex] - {x}^{2} - 2 \geqslant 0[/tex]
[tex] {x}^{2} + 2 \leqslant 0[/tex]
There is no real values that satisfies this inequality, because
[tex] {x}^{2} + 2[/tex]
is always positive.
The domain of this composite function is a null set.
Answer:
The domain of f, and thus the range of g, is restricted to values greater than or equal to 3.
If 1 minus x squared is greater than or equal to 3, then x squared must be less than –2.
Since x squared cannot be less than a negative number, the function is undefined for all values of x.
Step-by-step explanation: