Answer:There will be 10 grams left because you subtract half of the current amount from it every 9 years.
Step-by-step explanation:
Starting with 40 grams of europium which has a half-life of 9 years, after the first half-life, there would be 20 grams left, and after the second half-life (a total of 18 years), there would be 10 grams remaining.
The question is about calculating the amount of a radioactive substance that remains after a certain period of time has passed, which is based on the substance's half-life. Given that the half-life of europium is 9 years, after one half-life (9 years) 50% of the substance would remain, and after two half-lives (18 years) only 25% would remain. Since we started with 40 grams of europium, we apply this decay process step by step:
After the first half-life (9 years), 40 grams become 20 grams.After the second half-life (another 9 years, total of 18 years), the remaining 20 grams become 10 grams.Therefore, after 18 years, there will be 10 grams of the radioactive europium left.
Write a fraction that is equivalent to 8
8/1 or 16/2 or 24/3 or 32/4 or 40/5
SOMEONE PLEASE HELP ME!!!
if f(x)=x^2+2x-3 and g(x)=x^2-9, find (f/g)(4) and (f+g)(4)
Replace x in each equation with 4:
f(x) = x^2 +2x-3 = 4^2 + 2(4) -3 = 16 + 8 -3 = 21
g(x) = x^2-9 = 4^2 -9 = 16-9 =7
Now you have values for f(x) and g(x) now you can solve for f/g and f+g:
f/g = 21 / 7 = 3
f+g = 21 + 7 = 28
For this case, we have that by definition:
[tex](f + g) (x) = f (x) + g (x)\\(\frac {f} {g})(x) = \frac {f (x)} {g (x)}[/tex]
We have the following functions:
[tex]f (x) = x ^ 2 + 2x-3\\g (x) = x ^ 2-9[/tex]
So:
[tex](f + g) (x) = x ^ 2 + 2x-3 (x ^ 2-9)\\(f + g) (x) = x ^ 2 + 2x-3 x ^ 2-9\\(f + g) (x) = 2x ^ 2 + 2x-12\\(f + g) (4) = 2 (4) ^ 2 + 2 (4) -12\\(f + g) (4) = 2 * 16 + 8-12\\(f + g) = 32 + 8-12\\(f + g) (4) = 28[/tex]
On the other hand:
[tex](\frac {f (x)} {g (x)}) = \frac {x ^ 2 + 2x-3} {x ^ 2-9}\\Evaluated\ at\ x = 4[/tex]
[tex](\frac {f (x)} {g (x)}) = \frac {4 ^ 2 + 2 (4) -3} {4 ^ 2-9} = \frac {16 + 8-3} {16 -9} = \frac {21} {7} = 3[/tex]
Answer:
[tex](f + g) (4) = 28\\(\frac {f} {g}(4)) = 3[/tex]
I need help with this anybody know it?
3(2n-7)=9
Answer:
5
Step-by-step explanation:
3(2n-7)=9
^ ^
6n-21=9
+21 +21
6n=30
6 6
n=5 :)
A rectangular field is enclosed by 360 feet of fencing. What is the length, in feet, of the field if it’s length is 6 feet more than it’s width?
Answer:
The Field's length is 93ft
Step-by-step explanation:
P=2L+2w
360=2(w+6)+2w
360=2w+12+2w
360=4w+12
348=4w
348/4=w
87=w
L=w+6
L=87+6
L=93
The width of a rectangular field surrounded by 360 feet of fencing is 87 feet. The length of the field, which is 6 feet more than the width, is 93 feet.
Explanation:We are dealing with a rectangular field here, and we know that the length of a rectangle is equal to the total fencing (perimeter), divided by two, minus the width. Now, the problem states that the length is 6 feet more than the width. Therefore, we can create the following equation: 2x + 2(x + 6) = 360, where x is the width.
After simplifying this equation, we find that 4x + 12 = 360. Subtract 12 from both sides to get 4x = 348, and then divide by 4 to find that x = 87 feet. Thus, the width of the field is 87 feet. Since the length is 6 feet more than the width, we add 6 to 87 to get a length of 93 feet.
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help on 8, 9, and 12?
Answer:
8.) x = 15
Step-by-step explanation:
8.) divide 40 by 2 = 20 to only find half the triangle..
20^2 + b^2 = 25^2
400 + b^2 = 625
-400 -400
√b^2 = √225
b = 15
Asa owed $25 to his friend. He then borrowed another $14 after paying back $12 to his sister. Which expression could be used to find how much money Asa owes or has?
Answer:
Asa has $13 and owes $39
Step-by-step explanation:
25 + 14 = 39$ (amount of money he owes)
25 - 12 = 13$ (amount of money he has)
Simplify.
38√
3√4
6√8
24√8
6√4
Answer:
the first one i believe
Step-by-step explanation:
hope this helps
Answer:
3√4
Step-by-step explanation:
The button on Monica's shirt has a radius of 1 centimeter. What is the button's diameter?
Final answer:
To find the diameter of Monica's shirt button with a radius of 1 centimeter, we multiply the radius by 2, resulting in a diameter of 2 centimeters.
Explanation:
The question asks to determine the diameter of a button given its radius. The radius of Monica's shirt button is 1 centimeter. In geometry, the diameter of a circle is defined as twice the radius. Therefore, to find the button's diameter, you simply multiply the radius by 2.
Formula: Diameter = 2 × Radius
Calculation: Diameter = 2 × 1 cm = 2 cm.
Thus, the diameter of Monica's shirt button is 2 centimeters
A map of a highway has a scale of 2 inchesequals39 miles. The length of the highway on the map is 9 inches. There are 7 rest stops equally spaced on the highway, including one at each end. You are making a new map with a scale of 1 inch equals 30 miles. How far apart are the rest stops on the new map?
The distance between rest stops on the new map is approximately 4.262 miles.
Explanation:To find the distance between the rest stops on the new map, we need to determine the distance between each rest stop on the original map and then convert it to the new scale. The original map has a scale of 2 inches = 39 miles, so the distance between each rest stop on the original map is (9 inches / 7 rest stops) * 39 miles. Simplifying this gives us 5.571 miles. To convert this distance to the new scale, we use the scale of 1 inch = 30 miles. So, the distance between each rest stop on the new map is (5.571 miles / 39 miles) * 30 miles, which equals approximately 4.262 miles.
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The rest stops on the new map are approximately 19.2857 miles apart.
Explanation:To find the distance between the rest stops on the new map, we need to determine the distance between the rest stops on the original map and then convert it to the new scale.
In the original map, the length of the highway is 9 inches and there are 7 rest stops.
Therefore, the distance between each rest stop on the original map is 9 inches / 7 rest stops = 1.2857 inches.
To convert this distance to the new scale, we multiply it by the ratio of the scales: 1.2857 inches * (1 inch / 2 inches) * (30 miles / 1 inch) = 19.2857 miles.
So, the rest stops on the new map are approximately 19.2857 miles apart.
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a rectangle has a perimeter of 72 ft the side lengths are whole numbers what is the area
Answer:
Minimum area is : 1 * 35 = 35
Maximum area is : 19 * 17 = 323
Step-by-step explanation:
The parameter (P) of rectangle is calculated using:
P = 2(a+b)
We are given that,
P = 72
=> 2(a+b) = 72
=> a+b = 36
In rectangle, the lengths of both sides are different and a whole number (as mentioned in question), Therefore, the length of smaller side a can be varied from 1 to 17. Similarly, the length of larger side varies from 19 to 35.
The area can be easily calculated using a*b.
Minimum area is : 1 * 35 = 35
Maximum area is : 19 * 17 = 323
Select the numbers which should be hyphenated when written in words. 17 20 23 46 99 1/3 1/2 7/8
Answer:
23
46
99
1/3
1/2
7/8
Step-by-step explanation:
Let's find out by writing out each of the numbers.
17 = Seventeen (Seventeen stands alone)
20 = Twenty (Twenty stands alone)
23 = Twenty-three will be hyphenated
46 = Forty-six will be hyphenated
99 = Ninety-nine will be hyphenated
1/3 = one-third will be hyphenated
1/2 = one-half will be hyphenated
7/8 = seven-eights will be hyphenated
Now we ask ourselves why are they hyphenated?
We hyphenate because we need the two words to be glued together to show readers that the two or more elements of a sentence are link to each other.
Answer:
23
46
99
1/3
1/2
7/8
If sheena buys 5 bags of apples that cost for $12.25, what is the unit price for the apples
Answer:
It should be $2.45.
Step-by-step explanation:
12.25 divided by 5 equals 2.45.
The names Jessica,Joshua,Jill,and Jimmy are written on slips of paper. The slips of paper are placed in a bag. One name is picked. Name an event that is impossible. Name an event that is certain. Name an event that is as likely as not. Name an event that is more likely than not.
Answer:
Name an event that is impossible: Drawing the name "John" out of the bag
Name and event that is certain: Drawing a name that starts with the letter "J"
Name an event that is as likely as not: Drawing a girl's name or a boy's name
Name an event that is more likely than not: Drawing a name that is longer than 4 letters.
Step-by-step explanation:
The price of a plane ticket has increased from $150 to $200. By what percent has the price increased? A) 15% Eliminate B) 25% C) 33% D) 50%
Answer:
c
Step-by-step explanation:
The price of a plane ticket has increased by 33% from $150 to $200, determined by computing the difference between the new and old prices, dividing by the original price, and converting to a percentage.
Explanation:The question is asking by what percent the price of a plane ticket has increased from $150 to $200. To calculate the percentage increase, you subtract the original price from the new price and divide by the original price. Then multiply by 100 to convert it to a percentage. Using this method:
Price Increase = New Price - Original Price = $200 - $150 = $50Percentage Increase = (Price Increase ÷ Original Price) × 100 = ($50 ÷ $150) × 100 = 33.33%So, the price of the plane ticket has increased by 33%, which means the correct answer is C) 33%.
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Solve for the roots in the following equation. Hint: Factor both quadratic expressions. (x 4 + 5x 2 - 36)(2x 2 + 9x - 5) = 0 x = a0 a1, ± a2, - a3, ± a4 i
Answer:
The final solution is all the values that make
( x 4 + 5 x 2 − 36 ) ( 2 x 2 + 9 x − 5 ) = 0 true. x = − 2 , 2 , 3 i , − 3 i , 1 2 , − 5
Step-by-step explanation:
x 4 + 5 x 2 − 36 = 0 2 x 2 + 9 x − 5 = 0
Answer:
1,2,2,5,3
Step-by-step explanation:
it's right you idiots
what is the nth term in the sequence -4/3,-1,-4/5,-2/3,-4/7 with work please
-4/3 is the nth term
What is the sum of the geometric sequence 1,3,9.. if there are 12 terms?
Answer:
The sum of terms 12 the geometric sequence 1,3,9... = 265720
Step-by-step explanation:
Formula:-
Sₙ = a₁(1 - rⁿ)/(1 - r)
Where Sₙ - sum of n terms in the GP
a - First term of GP
r - Common ratio
n - Number
It is given the geometric sequence 1,3,9....
To find the sum of 12 terms
Here a = 1, r = 3 and n = 12
Sₙ = a₁(1 - rⁿ)/(1 - r) = 1(1 - 3¹²)/(1- 3) = 265720
Answer:
The sum of the 12 terms = 265720
Step-by-step explanation:
* Lets study the geometric sequence rule
- If a1 = a , a2 = ar , a3 = ar² , a4 = ar³ , .........................
∴ an = a[(r)^(n-1)]
- Where a is the first term and r is the common ratio and
n is the position of the term in the sequence
- The rule of the sum of some terms is Sn = [a(1 - r^n)]/(1 - r)
- Where n is the number of terms we want to add
* Lets check our terms in the sequence
- The terms are 1 , 3 , 9 , ..........
- To find the common ratio divide the 2nd term by 1st term
∵ the second term is 3 and the first term is 1
∴ 3/1 = 3
∴ The common ratio is 3
∵ n = 12 and a = 1
* Lets substitute the values of a , r , n in the rule of the sum to
find the sum of the 12 terms
∴ S12 = [1(1 - 3^12)]/(1 - 3) = (1 - 3^12)/-2 = 265720
* The sum of the 12 terms = 265720
How Find the solution set of the inequality
−4x+35>2
Answer:
[tex]x<8\frac{1}{4}[/tex]
Step-by-step explanation:
[tex]-4x+35>2\\-4x>-33\\x<\frac{33}{4} \\x<8\frac{1}{4}[/tex]
Remember to flip the sign when you divide or multiply both sides by a negative number! You don't need to flip the sign with adding or subtracting as in the case of step one subtracting 35 from both sides.
The solution of the inequality −4x+35>2 will be x < (33 / 4).
What is inequality?The relationship between two phrases using a symbol like "not equal to," "greater than," or "less than" indicates that they are not equal.
The given inequality will be solved as below:-
−4x+35>2
−4x>- 35 + 2
−4x > - 33
−4x > - 33
x < ( 33 / 4 )
Therefore, the solution of the inequality −4x+35>2 will be x < (33 / 4).
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If A=3x^2+5x−6 and B=−2x−6x+7, then what is A-B
Answer:
A=3x^2+5x-6
B=-2x^2-6x+7
A-B=(3x^2+5x-6)-(-2x^2-6x+7)
remove parentheses
A-B=3x^2+5x-6+2x^2+6x-7
combine like terms
A-B=5x^2+11x-13
The length a rectangle is 2 cm grater than its width .the area is the rectangle is 80 cm square what is the width of the rectangle
Answer:
Step-by-step explanation:
If breadth =x
length =x+2
Area =length *breadth
Area =x(x+2)=80
X^2+2x-80=0
X^2 +10x - 8x - 80=0
X(x+10)- 8(x+10)=0
(X-8)(x+10)=0
X=8 or x=-10
X=8(since breadth cannot be a negative value x cannot be negative)
Help me accidentally checked it in !!!!!!!!!
Answer: 16
Step-by-step explanation:
[tex]64^{\frac{2}{3}}=(2^6)^{\frac{2}{3}}=2^{\frac{12}{3}}=2^4=\boxed{16}[/tex]
Suppose you buy an appliance costing $2450 at a store charging 9% add-on interest, you make a down payment of $ 600, and you agree to monthly payments over 4 years.
Find the total cost for the appliance plus interest.
Answer:
$3116
Step-by-step explanation:
First off, we need to find the value of the appliance after the down payment.
$2450 - $600 = $1850
This then makes our principal $1850.
P = $1850
r = 9% or 0.09
t = 4 years
To find the total cost of the appliance plus interest, we need to look for our accrued amount first.
A = P + Prt
A = $1850 + $1850(0.09)(4)
A = $1850 + $666
A = $2516
Now that we know our accrued amount, we then add our down payment to find the total cost.
Total cost = $2516 + $600
Total cost = $3116
To calculate the cost of an appliance with added interest, subtract the down payment from the purchase price to determine the amount of the loan. This is followed by the calculation of the total interest over the length of the loan. Adding these two amounts provides the total cost of the appliance plus interest, which in this case is $2516.
Explanation:The total cost of the appliance plus interest can be calculated by first determining the amount of the loan made, which is the cost of the appliance minus the down payment. This comes out to $2450 - $600 = $1850.
Then, the add-on interest over 4 years is calculated by multiplying the amount of the loan by the annual interest rate and by the number of years. For this question, that is $1850 * 0.09 * 4 = $666.
So, the total cost of the appliance with interest added is the sum of the amount of the loan and the amount of the interest. Therefore, $1850 + $666 = $2516 is the total cost for the appliance plus interest.
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A right triangle has coordinates A(6, 0), B(0, 0), and C(0, 8). What is the perimeter of the triangle?
A. 18 units
B. 20 units
C. 24 units
D. 28 units
Answer:
C
Step-by-step explanation:
From the given coordinates
A(6, 0), B(0, 0) then AB = 6 - 0 = 6
B(0, 0), C(0, 8) then BC = 8 - 0 = 8
To calculate AC use Pythagoras' theorem on the right triangle formed
AC² = AB² + BC² = 6² + 8² = 36 + 64 = 100
Take the square root of both sides, hence
AC = [tex]\sqrt{100}[/tex] = 10
Perimeter = AB + BC + AC = 6 + 8 + 10 = 24 → C
Use the net to find the approximate surface area of the cylinder to the nearest square meter.
Radius=5
Height=9
Answer:
S.A. = 440 m²Step-by-step explanation:
Look at the picture.
We have the rectangle 2πr × h and two circles.
Therefore the formula of a Surface Area is:
[tex]S.A.=2\pi rh+2\pi r^2[/tex]
We have r = 5m and h = 9m. Substitute:
[tex]S.A.=2\pi(5)(9)+2\pi(5^2)=90\pi+50\pi=140\pi\ m^2[/tex]
[tex]\pi\approx3.14\to S.A.\approx(140)(3.14)\approx440\ m^2[/tex]
Final answer:
To calculate the surface area of the cylinder, use the formula 2π(radius)(height) + 2π(radius)², with radius = 5m and height = 9m. The answer is approximately 440 square meters when rounded to the nearest square meter.
Explanation:
To find the approximate surface area of the cylinder, we can use the formula: Surface area = 2π(radius)(height) + 2π(radius)². Given a radius of 5 meters and a height of 9 meters, we can plug these values into our formula.
The area of the two circular bases is 2π(radius)² = 2π(5)² = 2π(25) = 50π square meters.
The area of the side (the rectangular part when the cylinder is unrolled) is 2π(radius)(height) = 2π(5)(9) = 90π square meters.
Adding both of these areas together gives us the total surface area:
50π + 90π = 140π square meters.
Using 3.14159 as an approximation for π, we get 140π = 140(3.14159) ≈ 439.8226 square meters, which can be rounded to the nearest square meter as 440 square meters.
2pt 4 fl oz, 5 cups 39fl oz. What is the greatest amount of paint?
Answer:
5 cups 39 fl oz
Step-by-step explanation:
There are 2 cups to a pint, so 2pt 4 fl oz becomes 4 cups 4 fl oz, which is less than 5 cups 39 fl oz
Jason and Shawn both begin riding their bikes from different points away from the ranger station. They both ride their bikes in the direction away from the station along the same trail.
Jason starts biking 1 mile away from the station. Jason rides at a constant speed of 20 miles per hour.
Shawn starts biking 2 miles away from the station. Shawn rides at the same constant speed as Jason.
Let y represent the total miles away from the station.
At how many hours, x, will it take Shawn to catch up with Jason?
Based on the information provided, complete each expression below and determine the number of solutions.
The answer is: There is no solution, it's not possible for Shawn to catch up with Jason since both are riding at the same constant speed, there is always be a distance of 1 mile between.
Why?If it's possible to Shawn to catch up with Jason, the following equation will be true:
Let be the station our origin, so:
[tex]ShawnPosition=JasonPosition\\20mph.x-2miles=20mph.x-1mile\\-2=-1[/tex]
So, since the equation is not fulfilled, there is not solution, meaning that it's not possible to Shawn to catch up with Jason since both started riding from different points keeping the same constant speed, there will always be a distance of 1 mile between them if they keep the speed constant.
Also, Shawn could have caught up with Jason if he were started with a speed of 21mph instead the Jason speeds (20mph), let's prove that:
[tex]ShawnPosition=JasonPosition\\21mph.x-2miles=20mph.x-1mile\\\\21mph.x-20mph.x=2miles-1mile\\\\mph.x=1mile\\x=1h[/tex]
So, by substituting "x" into the equations, we have:
[tex]ShawnPosition=JasonPosition\\21mph.1h-2mile=20mph.1h-1mile\\21miles-2miles=20miles-1mile\\19miles=19miles[/tex]
So, Shawn could have caught up with Jason if he were started with a 21 mph speed instead starting with the Jason speed (20 mph).
Have a nice day!
The dance committee of Pine Bluff Middle School earns $72 from a bake sale and will earn $4 for each ticket they sell to the Spring Fling dance. The dance will cost $400
Write an inequality to determine the number, ttt, of tickets the committee could sell to have money left over after they pay for this year's dance.
AND
What is the solution set of the inequality?
Choose 1 answer:
A) t<82
B) t≤82
C) t>82
D) t≥82
Answer:
c
Step-by-step explanation:
The coordinates of 3 of the vertices of a parallelogram are (–7, 3), (–6, 1), and (–4, 5). What is the equation for the line containing the side opposite the side containing the first two vertices? (Remember, opposite sides of a parallelogram are parallel.)
Answer: [tex]y=-2x-3[/tex]
Step-by-step explanation:
The equation of the line in slope-intercept form, is:
[tex]y=mx+b[/tex]
Where m is the slope and b is the y-intercept.
By definition, parallel lines have the same slope.
Then:
- Find the slope of the the line that connects the points (-7,3) and (-6,1), as following:
[tex]m=\frac{y_2-y_1}{x_2-x_1}\\\\m=\frac{1-3}{-6-(-7)}=-2[/tex]
- We know that the other line is connected with the point (-4,5), therefore, you can substitute values and solve for b:
[tex]5=-2(-4)+b\\5=8+b\\5-8=b\\b=-3[/tex]
Then, the equation for the line containing the side opposite the side containing the first two vertices is:
[tex]y=-2x-3[/tex]
Which number line shows the solution set for |m| = 4
Answer:
Last choice that shows points on +4 and -4 is the correct graph.
Step-by-step explanation:
We have been given equation [tex]|m|=4[/tex]. Now we need to find out which of the given number lines shows the corret solution set for [tex]|m|=4[/tex].
We know that [tex]|x|=a[/tex] can be broken into two parts as:
[tex]x=+a[/tex] and [tex]x=-a[/tex]
Same way we can break [tex]|m|=4[/tex] into two parts as:
[tex]m=+4[/tex] and [tex]m=-4[/tex]
Hence last choice that shows points on +4 and -4 is the correct graph.
Answer:
D is correct
Step-by-step explanation:
Find a linear equation in your life?
My life is not linear. Time is not constant. My life (and time included) is just a series of times that do not run parallel to each other. Instead, they drift further or closer as a function of velocity and curvature of space time.
Answer: If you are looking for a linear equation in your life, an example could be the rate of the grass growing in your lawn. The y axis could be the height and the x axis could be the time. As it grows, the line representing the grass could go up gradually; when you cut it, the line can stop. Keep doing that for however long you'd like to represent the grass growing/getting cut.