Answer:
The correct answer is:
Between 600 and 700 years (B)
Step-by-step explanation:
At a constant decay rate, the half-life of a radioactive substance is the time taken for the substance to decay to half of its original mass. The formula for radioactive exponential decay is given by:
[tex]A(t) = A_0 e^{(kt)}\\where:\\A(t) = Amount\ left\ at\ time\ (t) = 75\ grams\\A_0 = initial\ amount = 1000\ grams\\k = decay\ constant\\t = time\ of\ decay = 2500\ years[/tex]
First, let us calculate the decay constant (k)
[tex]75 = 1000 e^{(k2500)}\\dividing\ both\ sides\ by\ 1000\\0.075 = e^{(2500k)}\\taking\ natural\ logarithm\ of\ both\ sides\\In 0.075 = In (e^{2500k})\\In 0.075 = 2500k\\k = \frac{In0.075}{2500}\\ k = \frac{-2.5903}{2500} \\k = - 0.001036[/tex]
Next, let us calculate the half-life as follows:
[tex]\frac{1}{2} A_0 = A_0 e^{(-0.001036t)}\\Dividing\ both\ sides\ by\ A_0\\ \frac{1}{2} = e^{-0.001036t}\\taking\ natural\ logarithm\ of\ both\ sides\\In(0.5) = In (e^{-0.001036t})\\-0.6931 = -0.001036t\\t = \frac{-0.6931}{-0.001036} \\t = 669.02 years\\\therefore t\frac{1}{2} \approx 669\ years[/tex]
Therefore the half-life is between 600 and 700 years
5 2/3 divided by 2 1/8
Answer:
[tex]2 \frac{2}{3} [/tex]
M/x =n-p, x for p ??
Answer:
the answer is A) X=m/n-p
Step-by-step explanation:
m/x=n-p
n-p=m/X
(n-p)×x=m
X=m/n-p
Double line graphs are used to compare two sets of data over the same period of time.
-True
-False
Answer:
the answer is true! :)
Step-by-step explanation:
What are the solutions of this quadratic equation?
x + 10 = 0
Let V be the volume of the pyramid of height 11 whose base is a square of side length 6. Find a formula for the area A of the horizontal cross section at a height y.
Answer:
Base area = 36
Volume of the pyramid = 132
Step-by-step explanation:
Volume of a pyramid = Base Area × Height/3
Base area = Length × Length (since base of the pyramid is a square)
Given the side length of the square = 6
Base area = 6×6
Base area = 36
Given height of pyramid =11
Volume of the pyramid = 36×11/3
Volume of the pyramid = 12×11
Volume of the pyramid = 132
miguel writes the expression 2n^4. He say that when you double the value of n, you double the value of the expression. Do you agree or disagree? Explain
Answer:
No, I disagree
Step-by-step explanation:
2n^4
let's put n to a real number. How about 2.
(2*2)^4=256
(2*4)^4=4096
No, I disagree, it doesn't double the expression.
Disagree. When you double the value of n, you quadruple the value of the expression.
What is proportionality?In mathematics, proportionality indicates that two quantities or variables are related in a linear manner. If one quantity doubles in size, so does the other.
Now the given expression is,
2n^4
Let y = 2n^4
Since 2 is the constant and y and n are variables.
Thus we can write,
y ∝ n^4
This means when value of y increases one time, the value of n increases 4 times.
Thus,you Disagree. When you double the value of n, you quadruple the value of the expression.
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Jayden's family watched 8 hours of TV last week. This week, they watchec
25% more than that. How many hours of TV did they watch this week? *
Answer:
I THINK that it is 10 hours
Step-by-step explanation:
(Sorry if I am wrong)
25% = 1/4 SO 8 divided by 4 = 2
Since they watched 25% MORE you add 2 to 8 and get 10
A 6000-seat theater has tickets for sale at $25 and $40. How many tickets should be sold at each price for a sellout performance to generate a total revenue of $174,000?
Step-by-step explanation:
Let x be the amount of tickets sold for $25 and y be the amount of tickets sold for $40, since there are 6000 seats theatre then;
x+y = 6000 .............. 1
If x tickets cost $25 and y tickets are sold for $40 with total revenue of $174,000, then;
25x + 40y = 174,000................ 2
From 1, x = 6000-y ............ 3
Substitute equation 3 into 2:
25x + 40y = 174,000.
25(6000-y) + 40y = 174,000
150,000-25y + 40y = 174,000
150,000+15y = 174,000
15y = 174,000-150,000
15y = 24,000
y = 24,000/15
y = 1600
Substitute y = 1600 into equation 3:
x = 6000-y
x = 6000-1600
x = 4400
Hence 4400 $25 tickets and 1600 $40 tickets must be sold to generate a revenue of $174,000
The table below shows the weekly change in the price of one gram of gold for four weeks.
ONE GRAM OF GOLD
Week
Weekly Change in the Price (dollars)
1
+ 1.
2
-3.
3
+ 2.
4
+3.
By how much did the price of one gram of gold change from the beginning of week 1 to the end of week 4? Did the price increase or decrease? explain
At the end of week 4, the price per gram of gold was $39. What was the price per gram of gold at the beginning of week 1?
Show your work in the box below.
Answer _____________ price per gram of gold
Answer:
THEY DIDN'T IT WAS BECAUSE THEY MADE UP A FAKE RUMER AND HAD TO MAKE IT LOOK REAL
Step-by-step explanation:
M/2+ m evaluate if m =-6
A model of the American flag was made out of 1,776 colored tiles. The star field took 444 blue tiles. The rest of the tiles were split evenly to form the red and white stripes. Choose the correct answer that represents the number of red or white tiles.
A. 540
B. 444
C. 1,332
D. 666
Answer:
D
Step-by-step explanation:
The number of red and white stripes = 666
Given, A model of the American flag was made out of 1,776 colored tiles.
The star field took 444 blue tiles.
The rest of the tiles were split evenly to form the red and white stripes.
Number of red or white stripes = (Total number of colored tiles - number of blue tiles)/2
= (1776 - 444)/2
= (1332)/2
= 666
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A cube has edges of 8 inches, what is the volume of the cube? Use the formula V = S3
24 cubic inches
64 cubic inches
512 cubic inches
4,096 cubic inches
resta y suma de valor absoluto
Answer: Éstos son los pasos para usar la estrategia del valor absoluto. Para sumar dos enteros con el mismo signo, suma sus valores absolutos. Luego, coloca el mismo signo de los dos enteros originales a la respuesta. Para sumar dos enteros con signos diferentes, resta el valor absoluto menor al valor absoluto mayor.
Step-by-step explanation: Ojalá esto ayude !
Answer:
El valor absoluto de un número consiste en su valor, sin importar su signo. Cuando tomamos el valor absoluto de un número, éste es siempre positivo o cero. ... Por ejemplo, el valor absoluto de 5 es 5. El valor absoluto de -5 es también 5.
Step-by-step explanation:
ANSWER PLEASE NEED HELP ASAP
Answer: 43 should be divided into 0.37 to find “x”.
Step-by-step explanation:
What is the equation of the line that passes through the point (4,0) and has a slope of 5/4
Answer:
The answer is y=5/4x-5
Step-by-step explanation:
The required equation of the line that goes through the point (4, 0) and has a slope of 5/4 is y = 5/4x - 5.
What is the intercept in the equation?In the equation intercept is the value of the linear function where either of the variables is zero.
The equation of a line with slope m and passing through the point (x₁, y₁) can be found using the point-slope formula:
y - y₁ = m (x - x₁)
Plugging in m = 5/4, x₁ = 4, and y₁ = 0, we get:
y - (0) = 5/4 (x - (4))
Simplifying, we get:
y = 5/4x - 5
Thus, the equation of the line is y = 5/4x - 5
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24. Critical Thinking Anika wants to determine the maximum
number of tulip bulbs (t) she can purchase if each bulb costs $1.50.
She will also need to purchase separate pots for each bulb at $1.25
each and a bag of potting soil for $10.00. Set up an inequality to
determine how many tulip bulbs Anika can purchase without
spending more than $20.00, and solve it. Can Anika buy exactly
enough bulbs and pots to spend the full $20.00? Explain. Can you
think of a better inequality to describe the answer?
Answer:
t ≤ 3 ; kindly check explanation for more explanation
Step-by-step explanation:
Given that :
Number of tulip (t) =?
Cost of bulb = $1.50
Pot for each bulb purchased at =$1.25
Bag of potting soil = $10.00
Number of tulip bulb that can be purchased without spending more than $20
Cost of tulip bulb = [(cost per bulb + cost per pot) * number purchased (t) + cost of bag of potting soil]
Cost = [(1.50 + 1.25)t + 10]
If spending should not exceed $20
2.75t + 10 ≤ 20
2.75t ≤ 20 - 10
2.75t ≤ 10
t ≤ 10/2.75
t ≤ 3.64
He cannot purchase more than 3 tulip bulbs
Anika cannot buy exactly enough tulip bulbs an pot to spend the full $20 because the number obtained is a fraction and not a whole number.
The Area of a rectangle is 46sq in, length is 4 times width find dimensions
Answer:
I guess you need all your numbers to be multiblyed to get 46
Step-by-step explanation:
what is basikly the question
Write 8x10 3 in standard notation
PLEASE HELP
(10 3 = ten to the third power)
Answer:
8,000
Step-by-step explanation:
you have to move the decimal to the right 3 times. so you take 8 and move the decimal 3 times. which gives you 8000.
or 8,000
The solution is: 8x10^3 in standard notation is 8,000.
Here, we have,
given that,
the expression is: 8 x 10^3
now, we have to write 8 x 10^3 in standard notation.
we know that,
A standard notation is a form of writing a given number, an equation, or an expression in a form that follows certain rules.
For example, 4.5 billion years is written as 4,500,000,000 years.
we know,
To change a number from scientific to standard notation, move the decimal point the number of places shown in the exponent of 10.
here, we have,
8 x 10^3
= 8 x 1000
so, we have to move the decimal to the right 3 times. so we take 8 and move the decimal 3 times. which gives 8000.
we get,
8 x 10^3 = 8000
Hence, The solution is: 8 x 10^3 in standard notation is 8000.
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Simplify the polynomial, then evaluate for x=-3
-x^2+2x-2x^2-3x+4+x^2
Step-by-step explanation:
Let's simplify step-by-step.
−x2+2x−2x2−3x+4+x2
=−x2+2x+−2x2+−3x+4+x2
Combine Like Terms:
=−x2+2x+−2x2+−3x+4+x2
=(−x2+−2x2+x2)+(2x+−3x)+(4)
=−2x2+−x+4
Answer:
=−2x2−x+4
Solve for x: 4x +
(2x + 4) > 12
Quick help me pls
Answer:
x > 2
Step-by-step explanation:
Original Equation:
4x + 0.5(2x + 4) > 12
0.5 multiplied by 2x = 1x
0.5 multiplied by 4 = 2
4x + 1x + 2 > 12
4x + 1x = 5x
5x + 2 > 12
Subtract 2 from both sides.
5x > 10
Divide both sides by 5
x > 2
Hope I helped :)
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Lucy is making the same bracelet for 8 of her friends. She has 32 beads. How many beads can she put on each bracelet?
Answer:
4 beads in each bracelet
Step-by-step explanation:
You divide 32 by 8 which gives you 4 because 8 multiplied by 4 equals 32
write the expression useing exponents 4×4×4×4
Please answer if you can! Really important worksheet due and I can’t figure this one out
Answer:
Step-by-step explanation:
Find the solution for the equation. 3 (n - 4) = -12
Answer:
0
Step-by-step explanation:
3n-12=-12
-3n=-0
n=0
Answer:
n=0.0
Step-by-step explanation:
3(n-4) = -12
3n-12 = -12
3n = 0
n = 0
solve each system by substitution
x – y = -4
2x + y = 4
Answer:
Step-by-step explanation:
x -y = -4
2x + y = 4
3x = 0
x = 0
0 + y = 4
y = 4
(0,4)
Solve for k for the equation h+p=3(k-8)
Answer:
h/3 + p/3 + 8 = k
Step-by-step explanation:
h+p=3(k-8)
h+p=3k-24
h+p+24=3k
h/3 + p/3 + 8 = k
Answer
k=(h+p+24)/3
Step-by-step explanation:
h+p=3(k-8)
h+p=3k-24
h+p+24=3k
k=(h+p+24)/3
If the points P(5,2),Q(0,7) and R(-5,2) are drawn on coordinate plane,where must point S be located so that figure PQRS is square.
Answer:
(0, -7) i think
hope this helps :3
sorry if im wrong
ABX Clothing manufactures expensive jackets for sale to college stores in runs of up to
150. Its cost (in dollars) for a run of jackets is
() = + + .
, ( ≤ ≤ )
(a)ABX Clothing sells the jackets at $90 each. Find the revenue function.
(b) Find the profit function.
(c) How many should ABX Clothing manufacture to make a profit? (Round your answer up to
the nearest whole number.)
Answer:
a. R(x) = 90x b. -1500 -10x - 0.2x c. 148
Step-by-step explanation:
a. Since we have x jackets produced at a rate of $90 per jacket, the revenue function, R(x) = rate × number of jackets = 90 × x = 90x
R(x) = 90x
b. Since the cost function is C(x) = 1500 + 100x + 0.2x, the profit function P(x) = Revenue function - cost function = R(x) - C(x) = 90x - (1500 + 100x + 0.2x)
P(x) = -1500 + 90x - 100x - 0.2x
P(x) = -1500 - 10x - 0.2x
c. For a profit, P(x) > 0
-1500 - 10x - 0.2x > 0
0.2x + 10x + 1500 < 0
10.2x + 1500 < 0
10.2x < -1500
x < -1500/10.2
x < -147.05
x < -147
So, ABX Clothing needs to produce greater than 147 jackets to make a profit. So, they need to make 148 jackets to make a profit.
Solve for x . − 9 x + 2 > 18 AND 13 x + 15 ≤ − 4
Answer:
x<−
9
--
16
and x≤−
13
--
19
Step-by-step explanation:
please help me........
Answer:
Step-by-step explanation:
so the y axes is up and down and the x axes is left to right so point d and point e have the same y axes but they have opposite x axes so instead of negative four to the left its positive 4 to the right
