Answer: 4 years
Step-by-step explanation:
A(0) has to be amount at start. Assume that's 5mg
Then A(t) = 5×(0.5)^(0.25t) = 5×2^(-t/4),
(also known as 5 exp(-λ t) with λ = ln(2)/4, incidentally).
We need to such that A(t) = 2.5mg, or 2^(-t/4) is 1/2, which happens when -t/4 is -1, or t is 4.
The exponential function given can be used to model how radioactivity decays. Solving this function for when half the material remains, we find it takes approximately 2.8 years for half of the radioactive material to decay.
Explanation:The amount of radioactive material remaining in a container over time can be modelled by the exponential decay function given in the question: A(t) = 5(0.5)0.25t. Here, A(t) stands for the amount left after time t, and the function gives a general rule for how radioactivity decays over time. Specifically, this rule tells us that after 1 year (t=1), approximately 74% of the radioactive material remains.
However, you're asking for the time it takes for half of the original material to remain. To solve this, we need to set A(t) to half its initial value, which is 2.5 milligrams: 2.5 = 5(0.5)0.25t. This translates to a simple equation 0.5 = (0.5)0.25t. Solving for t, we find that approximately 2.8 years are needed for half of the material to remain. Please note, this relies on the assumptions and limitations of the exponential decay model.
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Wyatt is training for a race. He will run 3/4 of a mile a day for 8 days. How far will Wyatt run altogether?
Answer:
6 miles all together in them 8 days
Step-by-step explanation:
3/4 times 8
Answer:
6 miles in all
Step-by-step explanation:
3/4 *8 duh
Which shape best describes the object generated when the rectangle is rotated about the axis?
hollow rectangular prism
hollow cylinder
solid cylinder
solid rectangular prism
If the shape shown is rotated about the axis, a solid cylinder would be formed.
What is a cylinder?A cylinder is a three dimensional shape (has length, width and height) which has two parallel bases joined by a curved surface, at a fixed distance.
If the shape shown is rotated about the axis, a solid cylinder would be formed.
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When a rectangle is rotated about an axis, it forms a solid cylinder.
Explanation:The shape that best describes the object generated when a rectangle is rotated about an axis is a solid cylinder. When a rectangle is rotated around an axis, it forms a three-dimensional shape that is similar to a cylinder. The base of the shape is a rectangle, and the height is equal to the length of the original rectangle. The shape has a curved surface and two circular faces at the top and bottom, just like a cylinder.
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A basketball hoop is 10 feet high. Army is 5 feet tall. How many times is the basketball hoop than army
Answer:2 times
Step-by-step explanation:
i did the assinment
Martha can paint a room in 2 hours. Jamie can paint the same room in 6 hours. How long, to the nearest tenth of an hour, will it take them to paint the room together?
Tim is measuring the weight (in ounces) of a substance for a science experiment. Tim added a mystery substance (m) to his experiment. Tim used the equation 12.93 + m = 17.0 to find out how much he added. How much of the mystery substance (m) did Tim add to his experiment?
A)4.07 ounces B)4.97 ounces C)5.03 ounces D)5.17 ounces
Answer:
A: 4.07 ounces
Step-by-step explanation:
17.0 - 12.93 = 4.07
Answer:
The weight of the mystery substance added by Tim is 4.07 ounces. Hence option A is correct.
Solution:
Given, Tim is measuring the weight (in ounces) of a substance for a science experiment.
Tim added a mystery substance (m) to his experiment.
Tim used the equation 12.93 + m = 17.0 to find out how much he added.
We have to find how much of the mystery substance (m) did Tim add to his experiment?
Now, from the given equation, 12.93 + m = 17.0 → m = 17.0 – 12.93 → m = 4.07
Hence, the weight of the mystery substance is 4.07 ounces, i.e. option A is correct.
Joe ate 7 pies on wednesday. If that is only 1/4 of the world record for pie eating what is the pie record
Answer:
The answer would be 24
Step-by-step explanation:
7 pies= 1/4 so 7 times four (to equal whole) = 24
the sum of 7 2/9 and 2 7/9 in simpliest form
Answer:
10
Step-by-step explanation:
7 2/9 + 2 7/9 common denominators already the same so add
7+2=9 first start with the whole number
2/9 + 7/9= 9/9 = 1 then add the fractions
9+1=10 then add the whole number and fraction
Answer:
10
Step-by-step explanation:
The formula for the lateral surface area of a cylinder is S=2πrh , where r is the radius of the bases and h is the height. Solve for r. r=2hπ/S r=S/2πh r=2Sπh r=h/2πS
Answer:
Option B is correct.
[tex]r = \frac{S}{2\pi h}[/tex]
Step-by-step explanation:
It is given that :
The formula for the lateral surface area of a cylinder is [tex]S = 2\pi rh[/tex]
where
S represents the lateral surface area of cylinder,
r represents the radius of the bases and
h represents the height of the cylinder.
Solve for r;
Given: [tex]S = 2\pi rh[/tex]
Divide both sides by [tex]2 \pi h[/tex],
[tex]\frac{S}{2\pi h} =\frac{2\pi rh}{2\pi h}[/tex]
Simplify:
[tex]r = \frac{S}{2\pi h}[/tex]
Therefore, the radius of the bases of the cylinder is, [tex]r = \frac{S}{2\pi h}[/tex]
Final answer:
The radius of the base of a cylinder, denoted as 'r', can be solved from the lateral surface area formula 'S=2πrh' by rearranging the formula to 'r = S / (2πh)'.
Explanation:
The question requires solving for r (the radius of the bases) from the formula for the lateral surface area of a cylinder, which is S=2πrh. To solve for r, we start by isolating r on one side of the equation. Here's how we can do it step by step:
Start with the formula for lateral surface area: S=2πrh.Divide both sides of the equation by 2πh to isolate r: S / (2πh) = r.Thus, the formula for r is r = S / (2πh).This equation shows that the radius can be found by dividing the lateral surface area by twice the product of π and the height of the cylinder.
If f(x)=2x+7 and g(x)=11x-4, find (f+g)x.
Answer:
(f+g)(x) = 13x + 3
Step-by-step explanation:
Rewrite f(x)=2x+7 and g(x)=11x-4 in columns, as follows:
f(x)=2x+7
+g(x)=11x-4
----------------
Now add each column separately.
f(x)+g(x) = (f+g)(x) ("the sum of functions f and g")
2x + 11x = 13x, and, finally, 7-4 = 3.
Therefore,
f(x)=2x+7
+g(x)=11x-4
----------------
(f+g)(x) = 13x + 3
What is your real rate of return is your savings account pays 2.5% interest and inflation is at 1%
Answer:
1.5
Step-by-step explanation:
The real rate of return is calculated as the difference between rate of interest and the inflation.
so,Interest=2.5%
Inflation=1%
=2.5-1
=1.5%
Answer:
1.485 % ( approx )
Step-by-step explanation:
We know that,
[tex]\text{Real rate of return}=\frac{1+\text{Nominal rate}}{1+\text{Inflation rate}}-1[/tex]
Given,
Nominal rate = 2.5 % = 0.025
Inflation rate = 1 % = 0.01,
[tex]\implies \text{Real rate of return}=\frac{1+0.025}{1+0.01}-1[/tex]
[tex]=\frac{1.025}{1.01}-1[/tex]
[tex]=1.01485149-1=0.01485149\approx 0.01485[/tex]
Thus, the real rate of return is 0.01485 or 1.485 %.
Three of the angles of quadrilateral are 100 degrees, 104 degrees and 44 degrees. What is the size of the 4th angle
Mrs.Padre drives 2 hours at a n average speed of 35 miles per hour then she drives 3 hours at a speed of 48 miles per hour what is her average speed for the whole trip
She drove 2 hours at 35 miles per hour for a total of 35 * 2 = 70 miles.
She drove 3 hours at 48 miles per hour for a total of 48 * 3 = 144 miles.
Her total miles were: 70 + 144 = 214.
Her total driving time was 3 + 2 = 5 hours.
Divide her total miles by total time for her average speed:
214 / 5 = 42.8 miles per hour average speed.
Not sure if you need to round the answer or not.
Mrs. Padre's average speed for the entire trip is 42.8 miles per hour, which is calculated by dividing the total distance (214 miles) by the total time (5 hours).
To determine Mrs. Padre's average speed for the whole trip, we need to use the formula for average speed:
Average speed = Total distance / Total time
First, we calculate the distance traveled during each part of the trip:
For the first part: 2 hours * 35 miles/hour = 70 milesFor the second part: 3 hours * 48 miles/hour = 144 milesNext, we sum up the total distance and total time:
Total distance = 70 miles + 144 miles = 214 milesTotal time = 2 hours + 3 hours = 5 hoursNow we can calculate the average speed:
Average speed = 214 miles / 5 hours = 42.8 miles per hour
The cost of a car rental is thirty dollars a day plus fifteen cents a mile. If the total cost to rent the car was one hundred and eighty dollars, how many miles was the car driven if it was rented for four days?
Answer:
Step-by-step explanation:
Alright, lets get started.
Suppose car was driven x miles in its 4 days trip.
Cost of a car rental is thirty dollar per day.
So, for 4 days, the car rental will be = [tex]30*4=120[/tex] $
For 1 mile, it adds fifteen cents,
So, for x miles, the cost will be = [tex]0.15 x[/tex] $
As per question, total rent is 180 $
Total rent will be = [tex]120 + 0.15 x = 180[/tex]
Subtracting 120 in both sides
[tex]0.15 x = 180-120=60[/tex]
[tex]x=\frac{60}{0.15}[/tex]
[tex]x=400[/tex]
It means car was driven 400 miles. : Answer
Hope it will help :)
the price of a pair of shoes increases from $52 10 $64. What i the percent increase?
Answer:
Step-by-step explanation:
Step 1: Calculate the change by subtracting old cost ($52) from the new cost ($64)
Step 2: Divide that change by the old cost ($52). You will get a decimal number
Step 3: Convert the decimal number to a percentage by multiplying by 100%
A rectangular garden has a total area of 48 square yards.Draw and label2 possiblerectangular garden with different side lengths that have the same area.
Two possible rectangular gardens with different side lengths and an area of 48 square yards are:
Square garden: 6 yards by 6 yards
Long and narrow garden: 8 yards by 6 yards
Explanation:Given:
Total area of the garden = 48 square yards
Objective:
Find possible combinations of side lengths for rectangular gardens with the same area.
Step 1: Square Garden
Let the side length of the square garden be x.
Area of the square garden = x^2
Set the area equation: x^2 = 48
Solve for x:
Take the square root of both sides: x = √48
Approximate the value: x ≈ 6.928 yards
Therefore, a square garden with sides of approximately 6.93 yards will have an area of 48 square yards.
Step 2: Long and Narrow Garden
We know the total area is 48 square yards.
Try different values for the width (w) and calculate the corresponding length (l) using the area formula: l * w = 48
For example, if w = 6 yards:
Calculate the length: l = 48 / w = 48 / 6 = 8 yards
Verify that the area matches: l * w = 8 * 6 = 48 square yards
Therefore, a long and narrow garden with a length of 8 yards and a width of 6 yards will also have an area of 48 square yards.
45 trucks, each with 3.5-ton payload, are needed to unload a freight train. How many trucks with a 2.5-ton payload would be needed to do the same job?
Answer:
The answer is 63 trucks.
Step-by-step explanation:
If we need 45 trucks with 3.5 ton each to do the job; then we have a 157.5 ton payload. So if we divide the 157.5 ton into 2.5 ton trucks we get a total of 63 trucks.
3.5 x 45 = 157.5
2.5 x 63 = 157.5
The number of trucks required with 2.5 payloads will be 32.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that 45 trucks, each with a 3.5-ton payload, are needed to unload a freight train.
The number of trucks for 2.5 tons of payloads will be calculated as,
3.5 Tons of payload = 45 Trucks
2.5 Ton = ( 45 x 2.5 ) / 3.5
2.5 Ton = 32 Trucks
Therefore, the number of trucks required with 2.5 payloads will be 32.
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Find the inverse.
f(x)= 2x-5/3x+4
Answer:
F.MBFFBLKFDKGBKK FGLK doingTDKDT
Step-by-step explanation:
Help me with these math questions......
Answer: y = 0
Step-by-step explanation:
[tex]\frac{x^{0}}{x^{2}}[/tex]
exponent of denominator > exponent of numerator so, y = 0
*****************************************************************************
Answer: [tex]y=\frac{x^{2}+8}{3}[/tex]
Step-by-step explanation:
y = [tex]\sqrt{3x-8}[/tex]
To find the inverse, swap the x's and y's and solve for "y":
x = [tex]\sqrt{3y-8}[/tex]
x² = 3y - 8
x² + 8 = 3y
[tex]\frac{x^{2}+8}{3}=y[/tex]
*****************************************************************************
Answer: -6x - 3h
Step-by-step explanation:
f(x + h) = 7 - 3(x + h)²
= 7 - 3(x² + 2xh + h²)
= 7 - 3x² - 6xh - 3h²
-f(x) = -(7 - 3x²)
= -7 + 3x²
f(x + h) - f(x) = 7 - 3x² - 6xh - 3h² -7 + 3x²
= -6xh - 3h²
= h(-6x - 3h)
[tex]\frac{f(x+h)-f(x)}{h}=\frac{h(-6x-3h)}{h}[/tex]
= -6x - 3h
ABCD is a parallelogram. if side AB=6x-10, side BC=4x-5, and side CD =3x+5, find the value of x
x=
Answer:
x=5
Step-by-step explanation:
If ABCD is a parallelogram, then AB = CD
AB=CD
6x-10 = 3x+5
Subtract 3x from each side
6x-3x -10 = 3x-3x+5
3x-10 = 5
Add 10 to each side
3x-10+10 = 5+10
3x = 15
Divide by 3 on each side
3x/3 =15/3
x=5
Answer:
6
i just did the test rn
Step-by-step explanation:
___ can be found by making x=0
Answer:
y intercept
Step-by-step explanation:
At first I didn't think there was enough information, but there is. In general terms, for any polynomial which is also a function, making x = 0 gives the point where (0,b) = the y intercept.
For example
using f(x) = x^2 + 4x + 6 when x = 0 the result left is f(0) = 6 so the y intercept is (0,6)
If you have x^2 + 6x the y intercept is (0,0)
At the city museum, child admission is $6.10 and adult admission is $9.30 . On Sunday, four times as many adult tickets as child tickets were sold, for a total sales of $909.30 . How many child tickets were sold that day?
Answer:
21 child tickets
Step-by-step explanation:
For this problem, you'd use a system of equations.
First, define your variables.
x = # of child tickets sold
y = # of adult tickets sold
There were 4 times as many adult tickets (y) as child tickets (x) sold, so:
4 x = y
4 x - y = 0
93 (4 x - y = 0)
372 x - 93 y = 0
The total revenue was $909.30, adult tickets were $9.30 each, child tickets were $6.10 each, so:
6.10 x + 9.30 y = 909.30
10 (6.10 x + 9.30 y = 909.30)
61 x + 93 y = 9093
372 x - 93 y = 0
433 x = 9093
433 x / 433 = 9093 / 433
x = 21
For vectors t, u, v, and w defined as shown, select the TRUE equation.
i dont really unserstand what this is?
Answer:
t= u+v+w
Step-by-step explanation:
i did the test and got it right
A store Is having a 20% off sale on all merchandise if my buyers one item and save $13 what was the original price of their of her precio is having a 20% off sale on all merchandise if my buyers one item and save $13 what was the original price of her purchase
The following ordered pairs are solutions to a linear equation: (-20, 11.5), (-21, 12), and (-22, 12.5).
Which of the following graphs shows all of the ordered pairs in the solution set of this linear equation?
Answer:
option A
Step-by-step explanation:
The following ordered pairs are solutions to a linear equation: (-20, 11.5), (-21, 12), and (-22, 12.5).
Frame the equation of line y=mx+b using ordered pairs
(-20, 11.5), (-21, 12)
[tex]slope m = \frac{y_2-y_1}{x_2-x_1} =\frac{12-11.5}{-21+20}=-0.5[/tex]
m= -0.5
Now plug in (-21,12) and find out b
y=mx+b
12= -0.5(-21) + b
12= 10.5 +b
Subtract 10.5 on both sides
So b= 1.5
Equation of line is y=-0.5x + 1.5
Slope is negative so graph will be decreasing
Option A and option C graphs are decreasing
y intercept is the b values = 1.5
y intercept is (0,1.5)
Lets find x intercept
Plug in 0 for y in the equation y=-0.5x+1.5
0 = -0.5x+1.5
subtract 1.5 on both sides
1.5 = -0.5x
Divide by -0.5
so x= 3
So x intercept is (3,0)
Option A graph has x intercept (3,0) and y intercept (0,1.5)
A line that intersects a circle at exactly one point is called a ______
Chord
Tangent
Secant
A line that intersects a circle at exactly one point is called a tangent.
What is a tangent to a circle?A line segment that touches a circle specified to only one point is called a tangent to that circle.
The point where it touches the circle is called the point of tangency.
We can see that point line segment PT is the tangent of our circle and point P is the point of tangency.
Therefore, A line that intersects a circle at exactly one point is called a tangent.
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Someone please help!!!
A company is selling two types of treadmills. Treadmill x sells for $750 and treadmill y sells for $900. Three times the number of treadmill y sold must be less than or equal to twice the number of treadmill x sold. The company has at most 100 treadmills to sell. What is the maximum revenue that the company can make from the treadmill sales?
$75,000
$81,000
$84,000
$90,000
Answer:
Option B is correct
The maximum revenue that the company can make from the treadmill sales is, $81,000
Step-by-step explanation:
Let x represent the number of treadmill x sold and y represents the number of treadmill y sold
As per the statement: Three times the number of treadmill y sold must be less than or equal to twice the number of treadmill x sold.
⇒[tex]3y\leq 2x[/tex] ......[1]
Also, it is given that the company has at most 100 treadmills to sell.
⇒[tex]x+y\leq 100[/tex]
using a graph tool for equation [1] and [2] as shown in figure given below;
⇒ the solution is the shaded area
The maximum revenue that the company can make is for the point, (60, 40)
⇒ x = 60 treadmills
and y = 40 treadmills
Maximum Revenue = [tex]60 \times 750 + 40 \times 900 = 45000+36000 = \$81,000[/tex]
Therefore, the maximum revenue that the company can make from the treadmill sales is, $81,000
Henry is saving money for college. He earns $210 each week working part time after school and the weekends. Henry currently has $2,240 in savings. His parents put $100 in his savings account each week and he saves one-third of his paycheck each week. Which expression represents the situation? (n represents the number of weeks) A) 2,240 + 170n B) 2,240 + 310n C) 2,240 + 210n + 100n 3 D) 2,240 + 210n + 100n 3 Eliminate
The answer is 2,240 + 170n
2,240 in savings
210n
3
Henry saves each week
100n parents put in savings each week
thus,
2,240 + 210n
3
+ 100n
2,240 + 70n + 100n
2,240 + 170n
Order the numbers from least to greatest: –13, 16, 3, –20, 15, –10.
Answer:
-20,-15,-13,-10,3,15,16
Step-by-step explanation:
negative to positive
Use the Polygon tool to draw the image of the given quadrilateral under a dilation with a scale factor of 34 and center of dilation (0, 0) .
Answer:
See attached diagram
Step-by-step explanation:
Given quadrilateral has vertices at points A(-8,4), B(4,-4), C(0,-8) and D(-4,-4).
A dilation with a scale factor of [tex]\dfrac{3}{4}[/tex] and a center of dilation (0,0) has a rule
[tex](x,y)\mapsto \left(\dfrac{3}{4}x,\dfrac{3}{4}y\right).[/tex]
Then
A(-8,4)→E(-6,3);B(4,-4)→F(3,-3);C(0,-8)→G(0,-6);D(-4,-4)→H(-3,-3).See attached diagram for details.
Remark: If a scale factor is 34, then the rule is (x,y)→(34x,34y) and image vertices have coordinates (-272,136), (136,-136), (0,-272), (-136,-136).
In the formula for the volume of a cylinder, how is the area of the base determined?
Answer:
area of base = [tex]\pi r^2[/tex]
where 'r' is the radius
Step-by-step explanation:
Volume of the cylinder formula = [tex]\pi r^2h[/tex]
volume of cylinder = area of base * height
The base of a cylinder is a circle. so we use the area of circle for the base of cylinder while finding volume
We know area of the circle is [tex]\pi r^2[/tex]
So area of the base of cylinder is [tex]\pi r^2[/tex]
To find volume of the cylinder , we multiply the base of the cylinder with height
To determine the base of the cylinder we need radius of the cylinder
area of base = [tex]\pi r^2[/tex]
where 'r' is the radius
Answer: c
Step-by-step explanation: teehee