[tex]\textit{Amount for Exponential Decay using Half-Life} \\\\ A=P\left( \frac{1}{2} \right)^{\frac{t}{h}}\qquad \begin{cases} A=\textit{current amount}\dotfill &75\\ P=\textit{initial amount}\dotfill &2400\\ t=seconds\\ h=\textit{half-life}\dotfill &13.8 \end{cases} \\\\\\ 75=2400\left( \frac{1}{2} \right)^{\frac{t}{13.8}}\implies \cfrac{75}{2400}=\left( \frac{1}{2} \right)^{\frac{t}{13.8}}\implies \cfrac{1}{32}=\left( \frac{1}{2} \right)^{\frac{1}{13.8} t}[/tex]
[tex]\log\left( \cfrac{1}{32} \right)=\log\left[ \left( \frac{1}{2} \right)^{\frac{1}{13.8} t} \right]\implies \log\left( \cfrac{1}{32} \right)=t\log\left[ \left( \frac{1}{2} \right)^{\frac{1}{13.8}} \right] \\\\\\ \cfrac{\log\left( \frac{1}{32} \right)}{\log\left[ \left( \frac{1}{2} \right)^{\frac{1}{13.8}} \right]}=t\implies \cfrac{\log\left( \frac{1}{32} \right)}{\log\left[ \sqrt[13.8]{\frac{1}{2}} \ \right]}=t\implies 69\approx t[/tex]
The area of a circle is 9π m². What is the circumference, in meters? Express answer in terms of π
Answer:
20.25 pi
Step-by-step explanation:
The circumference of a circle is given by
C = 2 * pi *r
9 pi = 2 * pi *r
Divide each side by 2pi
9pi / 2 pi = 2 pi r / 2 pi
4.5 = r
Now we can find area
A = pi r^2
= pi ( 4.5)^2
20.25 pi
An architech was designing a rectangular room with a length of 16 feet, a width of 14 feet, and a height of 10 feet. what is the volume, in cubic feet , or the room?
Write the number in scientific notation. 0.0805
a)8.05 × 10
b)0.805 × 10–1
c)80.5 × 100–3
d)8.05 × 10–2
A fruit company guarantees that 94% of the pineapples it ships will ripen within four days of delivery. Find the probability that at least 10 pineapples in a case of 12 are ripe within four days.
The probability that at least 10 pineapples in a case of 12 are ripe within four days as described in the task content is; 0.783
Probability of PercentageFrom the task content;
It follows that 94% of the pineapples shipped will ripen within four days of delivery.On this note, the probability for ripening of each apple is; 0.94.
Ultimately, the probability that at least 10 pineapples in a case of 12 are ripe within four days is therefore; 0.94 × 10/12 = 0.783.
Read more on probability;
https://brainly.com/question/18916756
At the frozen yogurt shop, a machine fills cups with 4 ounces of frozen yogurt before adding the toppings. After the cups are filled, customers add as many toppings as they want without exceeding a total weight of 6 ounces. Which of the following represent the acceptable weights for the frozen yogurt options? Select all that apply:
A.) 0 < x ≤ 6
B.) 0 < x ≤ 3
C.) 4 ≤ x ≤ 6
D.) x ≤ 6
E.) |x - 5| ≤ 1
F.) |x - 2| ≤ 6
Answer
4 ≤ x ≤ 6 and |x - 5| ≤ 1
Step-by-step explanation:
I answered the question...i got it right...
Solve the problem.
Two cylindrical cans of beef stew sell for the same price. One can has a diameter of 6 inches and a
height of 4 inches. The other has a diameter of 4 inches and a height of 6 inches. Which can contains
more stew and is therefore, a better buy?
Answer:
The first can.
Step-by-step explanation:
formula: Pi x diameter x height
1st can has a volume of 113.10
2nd can has a volume of 75.40
A car rental agency rent compact, midsize, and luxury cars. Its goal is to purchase 48 cars for a total of $932,000 and to earn a daily rental of $ 1,265 from all the cars. The compact cars cost $13,000 each earn $ 20 per day in rental, the midsize cars cost $ 25,000 each earn $ 27 per day, and the luxury cars cost $ 29,000 each and earn $ 45 per day. Your task will be to find the number of each type of car the agency should purchase to meet its goal.
Answer:
25 compact15 midsize8 luxuryStep-by-step explanation:
The set of relationships can be formulated as three equations in three unknowns. These can be written as an augmented matrix and solved using a calculator.
Let x, y, z represent the numbers of compact, midsize, and luxury cars, respectively. Then the relations are ...
x + y + z = 48 . . . . . . total number of cars purchased
13x +25y +39z = 932 . . . . . total cost in thousands
20x +27y +45z = 1265 . . . . daily rental revenue
The augmented matrix of coefficients looks like ...
[tex]\left[\begin{array}{ccc|c}1&1&1&48\\13&25&39&932\\20&27&45&1265\end{array}\right][/tex]
And its solution is ...
(x, y, z) = (25, 15, 8)
The agency should purchase 25 compacts, 15 midsize, and 8 luxury cars.
Graph the parabola. Plot five points on the parabola. button.
Step-by-step explanation:
The graph looks like the above picture
Answer:
Image Attached
Step-by-step explanation:
Hello!
To have points with whole numbers, multiples of 3 need to be used for x.
x = 3
y = (1/3)(3)²y = (1/3)(9)y = 3
x = 6
y = (1/3)(6)²y = (1/3)(36)y = 12
x = 9
y = (1/3)(9)²y = (1/3)(81)y = 27
x = 12
y = (1/3)(12)²y = (1/3)(144)y = 48
x = 15
y = (1/3)(15)²y = (1/3)(225)y = 75
Two images are attached, one in correlation to y = x^2, and the original graph with the given points (3,3), (6,12), (9,27), (12,48), (15, 75).
MATH. Someone please answer this for me :) 50 points
Image attached
Answer:
A=0.51
B=0.73
C=0.41
D=A student taking algebra II is dependent on whether they prefer it and a student being in 10th grade is dependent on their age
Step-by-step explanation:
These answers are all in fractions btw
A)5/255+20/245+65/225+90/725=0.514267 which rounds to 0.51
B)100+65=165
165/225=0.73
C)100/245=0.41
Hope it helps !
Well has -55.00 in his account if he saves $2.50 his mom gives him lunch every day, how many days will it be until he has a balance of at least $0
Answer:
22 days
Step-by-step explanation:
55 divided by 2.5=22 days
Answer: 22 Days
Step-by-step explanation:
-55.00/2.50= -22
But since you can’t have a negative answer then you have to make it positive for your amount of days! So it would take that person 22 days to have 0 in his account!
- I hope this helped! I tried my best but definitely double check with your teacher for this answer!
X - 8 = 1 what does X equal to?
Answer:
9
Step-by-step explanation:
To answer this we add 8 to both sides:
x-8+8 = 1+8
x = 9
This is our answer
Given:-
X - 8 = 1To find :-
The value of xSolution :-
X - 8 = 1
Transferring 8 to Right sideX = 1 + 8 ( signs change when transferred to opposite side )
X = 9
Can you help me solve this
Answer:
27 miles
Step-by-step explanation:
27 miles is your answer
this is k 12 help,
please!!! for (100 points)
Answer:
14 m²
area of sqaure pyramid: a² + 2(a)(l)
a = side of the base l = slant heightarea:
(2)² + 2(2)(2.5)14 m²Data from a sample of 576 people in a city was used to estimate the mean monthly bill
paid by city residents for internet service to be $45 with a standard deviation of $0.48.
Enter a number in the box to complete the sentence below.
S
Use the formula M=1.96 x to calculate the margin of error for a 95% confidence
VN
interval, to the nearest hundredth, $
dollars.
Using the z-distribution, it is found that the margin of error for a 95% confidence interval is of $0.04.
What is a z-distribution confidence interval?The confidence interval is:
[tex]\overline{x} \pm z\frac{\sigma}{\sqrt{n}}[/tex]
In which:
[tex]\overline{x}[/tex] is the sample mean.z is the critical value.n is the sample size.[tex]\sigma[/tex] is the standard deviation for the sample.The margin of error is given by:
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In this problem, the values of the parameters are:
[tex]z = 1.96, \sigma = 0.48, n = 576[/tex].
Hence, the margin of error, in dollars, is given by:
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]M = 1.96\frac{0.48}{\sqrt{576}}[/tex]
M = 0.04.
More can be learned about the z-distribution at https://brainly.com/question/25890103
i need an answer in 5 minutes please!
Find a unit vector in the direction of the given vector, w = 6i - 3j
Step-by-step explanation:
hope this helps, you can ask any questions for clarification
Each interior angle of a regular polygon has a measure of 40.how many sides does the polygon have?
Given Information :-
⠀
Each exterior angle of a regular polygon has a measure of 40°⠀
To Find :-
⠀
The number of sides of the polygon⠀
Formula Used :-
⠀
[tex] \qquad \star \: \underline{ \boxed{ \green{ \sf No.~of~sides = \dfrac{360^ \circ}{exterior ~angle}}}} \: \star[/tex]
⠀
Solution :-
⠀
Using the formula,
⠀
[tex] \sf \dashrightarrow No. ~of~sides= \dfrac{360}{40} \\ \\ \\ \sf \dashrightarrow No. ~of~sides= \frac{ \cancel{360}}{ \cancel{40} } \\ \\ \\ \sf \dashrightarrow No. ~of~sides= \underline{ \boxed{ \blue { \frak{9}}}} \: \star[/tex]
⠀
Thus, the polygon is a nonagon, and hence has 9 sides.
⠀
[tex] \underline{\rule{227pt}{2pt}} \\ \\ [/tex]
I WILL GIVE 20 POINTS TO THOSE WHO ANSWER THIS RIGHT NOOOO SCAMS AND EXPLAIN WHY THAT IS THE ANSWER
Simplify (x-2 divided by 2x+6) - (x-3 divided by 5x+15)
Answer:
3x - 4
---------
10(x + 3)
Step-by-step explanation:
x -2 x - 3
----------- ( - ) ----------
2x + 6 5x + 15
Multiply both sides by the denominator
5(x - 2) 2( x - 3)
----------- ( - ) ----------
5(2)(x + 3) 2(5)(x + 3)
multiply the numbers together
5x - 10 2x - 6
----------- ( - ) ---------
10(x + 3) 10(x + 3)
Subtract the numberator
5x - 10 - (2x - 6)
5x - 10 - 2x + 6
5x - 2x = 3x
-10 + 6 = -4
3x - 4
3x - 4
----------
10(x + 3)
I hope this helps!
What is the LCD of -1 2/8 and 2 3/4?
Answer:
The least common denominator of [tex]-1\frac{2}{8}[/tex] and [tex]2\frac{3}{4}[/tex] is 8
Question
A pole that is 3 m tall casts a shadow that is 1 m long. At the same time, a nearby tower casts a shadow that is 44.5 m long. How tall is the tower?
Answer: 1,33.5 m
Step-by-step explanation:
We can set up a proportion to solve. I will have the length of the pole / tower on the top (numerator), and the length of the shadow on the bottom (denominator). All units will be in m.
[tex]\frac{3}{1} =\frac{x}{44.5}[/tex]
Now, I will cross multiply and solve for x. This will give us the height of the tower.
x * 1 = 3 * 44.5
x = 133.5 m
A locker combination has three nonzero digits, and digits cannot be repeated. If the first digit is 3, what is the probability that the next digit is odd?
A. 4/9
B. 1/5
C. 1/2
D. 5/9
Answer:
1/5 is the answer in my calculations
Find the solutions to the equation below.
Check all the apply.
16x^2 - 64 = 0
A. x = 4
B. x = 2
C. x = -64
D. x = -2
E. x = -4
F. x = -8
Answer:
x = 2
x = - 2
Step-by-step explanation:
⇒ 1: Common Factor
16x² - 64 = 016(x² - 4) = 0⇒ 2: Use the sum-product pattern
16 (x² - 4) = 016 (x² + 2x - 2x - 4) = 0⇒ 3: Common factor from the two pairs
16((x² + 2x) + (-2x - 4) = 016(x(x+2)-2(x+2))=0I dont feel like adding more details.
- rewrite in factored form
16(x(x+2)-2(x+2))=0
16(x-2)(x+2)=0
- create seperate equations
16(x-2)(x+2)=0
x-2=0
x+2=0
- solve
*rearrange and isolate the variable to find each solution
x = -2
x = 2
Answer:
B.x=2
Step-by-step explanation:
[tex]16x ^{2} - 64 = 0[/tex]
[tex]16x ^{2} = 64[/tex]
[tex]4 ^{2} {x}^{2} = {4}^{3} [/tex]
[tex] {x}^{2} = \frac{4 ^{3} }{4 ^{2} } [/tex]
[tex]x^{2} = 4[/tex]
[tex] \sqrt{x ^{2} } = \sqrt{4} [/tex]
[tex]x = 2[/tex]
7. Given: AD || BC and AD=BC.
B
Prove: AB || DC
시
Answer:
Step-by-step explanation:
PLEASE HELP PLEASE PLEASE HELP
Answer:
5x10x9 Is the correct answer meaning that the answer is 450
Brainliest would be very appriciated
Step-by-step explanation:
EDIT: my bad i read the question wrong, the answer is D:450
sorry for any confusion ;^;
6) The frequency table represents lunch choices for 22 middle school students. Each student may only make one choice. What frequency count should be recorded for the soup category?
-------
A) 2
B) 4
C) 6
D) 8
The frequency count that should be recorded for the soup category is 6.
What does subraction mean?
Subtraction is the process of taking one number away from another number. The sign used to represent subtraction is -.
What is the frequency count for the soup category?The frequency count on the table should be equal to the number of students. Thus, in order to determine the frequency count for the soup category, subtract 22 from the total frequency count.
The frequency count for the soup category = 22 - (5 + 8 + 2 + 1 ) = 6
To learn more about subtraction, please check: https://brainly.com/question/915789
18.) A cylinder and a cone have the same radius and
the same volume. How do the heights compare?
Answer:
If a cone and a cylinder have the same base and the same height, then the volume of the cone is of the volume of the cylinder. For example, the cylinder and cone shown here both have a base with radius 3 feet and a height of 7 feet. The cylinder has a volume of cubic feet since .
Step-by-step explanation:
PLEASE HELP ASAP!! 30 POINTSSSS!!!!! EXPLANATION PLEASEEEEE, IM BEGGING PLEASE DONT JUST PUT AN ANSWER
Solve for 'x' in both of the following problems.
Answer:
x = 73° , x = 7
Step-by-step explanation:
(1)
the measure of an inscribed angle is half the measure of its intercepted arc.
∠ B = [tex]\frac{1}{2}[/tex] AC = [tex]\frac{1}{2}[/tex] × 128° = 64°
the sum of the 3 angles in Δ ABC = 180°
then
x = 180° - (64 + 43)° = 180° - 107° = 73°
(2)
2 chords iintersecting in a circle, then
the products of the parts of one chord is equal to the product of the parts of the other chord, that is
KH × HI = JH × HG ( substitute values )
10x = 14 × 5 = 70 ( divide both sides by 10 )
x = 7
I’ve been stuck on this question can someone help?
practice harder and harder you will get what you want
please help! math
(3/7) (-2/5 x 9/11)
Answer:
-54/385
Step-by-step explanation:
A can of juice is 5cm in diameter and 8cm high. How much juice is in a pack of 6cans
Answer:
942.84 cm³
Step-by-step explanation:
volume of 1 can = πr²h = 22/7 × 5/2 × 5/2 × 8
= 157.14 cm³
volume of juice in 6 cans = 6 × 157.14 = 942.84cm³
