A scientist has a sample of the radioactive isotope bismuth-212. The isotope decays exponentially as shown in the table. Time (seconds) Mass (grams) 10 26.8 20 23.9 30 21.3 40 19.0 50 16.9 60 15.1 Which equation best represents the curve of best fit for this set of data? A. f(x) = 29 • 0.989x B. f(x) = 27 • 1.011x C. f(x) = 30 • 0.989x D. f(x) = 28 • 0.234x
Answer:
f(x) = 30 • 0.989x
Step-by-step explanation:
Given the data :
10 26.8
20 23.9
30 21.3
40 19
50 16.9
60 15.1
Using technology, the exponential model equation obtained by plotting the data is :
y = 30.068(0.989)^x
Based on the general exponential formula :
y = ab^x
y = predicted value
Initial value, a = 30.068
Rate = b = 0.989
The most appropriate model equation from the options given is :
f(x) = 30 • 0.989^x
Could someone please help me solve these?
what is the correct measure of m? 15, 5, n, m
Answer:
subtract 5 , m=(-15)
Step-by-step explanation:
15-5
=10
n:
5-10
=(-5)
m:
(-5)-10
=(-15)
hope it help
The question is in the image below
9514 1404 393
Answer:
B. y < -x +1
Step-by-step explanation:
The boundary line has a y-intercept of +1, eliminating choices A and C.
The boundary line has a negative slope, eliminating choices C and D.
The only viable choice is B: y < -x +1.
f(x) = 3x - 4
x is -2
Find the equation of the line that passes through points A and B.
Answer:
y = 2x + 5
Step-by-step explanation:
Step 1 : Find slope:
[tex]slope , m = \frac{y_B - y_A}{x_B - x_A}[/tex]
[tex]=\frac{-1 - 7}{-3-1} \\\\= \frac{-8}{-4}\\\\ = 2[/tex]
Step 2 : Find the equation of the line :
[tex](y - y_A) = m(x - x_A) \ or \ (y - y_B) = m(x - x_B)\\\\we \ will \ consider \ points \ of \ A :\\\\[/tex]
[tex](y - 7) = 2(x -1)\\\\y - 7 = 2x - 2\\\\y = 2x - 2 + 7\\\\y = 2x + 5[/tex]
Find x. Round to the nearest degree.
Answer: 56 degrees approximately
==========================================
Work Shown:
tan(angle) = opposite/adjacent
tan(x) = 15/10
tan(x) = 1.5
x = arctan(1.5)
x = 56.3099 approximately
x = 56 degrees
Note: arctan is the same as inverse tangent
SOMEONE PLEASE HELP ME! I NEED HELP BAD!
Answer:
gd
Step-by-step explanation:
line gd is congruent to kh
Solve each triangle. Round your answers to the nearest tenth.
Answer: The value of [tex]\angle B[/tex] is [tex]30^o[/tex], the length of BC and AC is 28 units and 25 units respectively.
Step-by-step explanation:
To calculate the value of each part of the triangle, we use:
1) Angle sum property
2) Law of sines
Starting with 1:
Calculating [tex]\angle B[/tex] by angle sum property:
[tex]\angle A+\angle B+\angle C=180^o\\\\34^o+\angle B+116^o=180^o\\\\\angle B=(180^o-116^o-34^o)=30^o[/tex]
Applying 2:
The Law of sines relates the length of the side with the sines of the angle opposite to it.
[tex]\frac{\sin 34^o}{BC}=\frac{\sin 116^o}{45}\\\\BC=\frac{\sin 34^o\times 45}{\sin 116^o}\\\\BC=28units[/tex]
Similarly,
[tex]\frac{\sin 30^o}{AC}=\frac{\sin 116^o}{45}\\\\AC=\frac{\sin 30^o\times 45}{\sin 116^o}\\\\AC=25units[/tex]
Hence, the value of [tex]\angle B[/tex] is [tex]30^o[/tex], the length of BC and AC is 28 units and 25 units respectively.
Is the spinner described below a fair spinner? If yes, explain why. If not describe a change that could make the spinner fair
There are 10 parts on the spinner 4 orange, 5 blue and 1 grey.
Answer:
no
Step-by-step explanation:
because it's unequal
can someone pls help for brainlest
Answer:
6 x 8 = 48 yd2 (square yards)
Step-by-step explanation:
Answer:
Area of triangle is 23 yd².
Step-by-step explanation:
Given :-
Base of triangle = 8 yd
Height of triangle = 6 yd
To find
Area of triangle
Solution :-
we know that,
Area of triangle = 1 / 2 × base × height
substitute the values
Area of triangle = 1/2 × 8 yd × 6 yd
multiplying the values
Area of triangle = 1/2 × 46 yd²
divide the values
Area of triangle = 46 yd ² /2 = 23 yd².
Therefore, Area of triangle is 23 yd ².
Find the median of the data. 43, 37, 49, 51, 56, 40, 44, 50, 36
Answer:
Median = 44
Step-by-step explanation:
Arrange the data in ascending order:
36, 37, 40, 43, 44, 49, 50 , 51, 56.
Choose the number in the middle.
Median = 44
At Safeway, a pound of apples cost $1.32. Mrs. Terry purchased 7.5 pounds of apples. How much money did
Mrs. Terry spend on apples?
Answer:
the answer is $1.32×7.5=$9.9
Answer:
£9.90
Step-by-step explanation:
There are 2 ways you can do this. Both are similar.
For the first method it's much quicker but you might need a calculator.
You would simply do 7.5 × 1.32 = £9.90 that should give you the answer.
If you were to do it with out a calculator then what you need to do is 7 × 1.32 = 9.24
Because there is still 0.5 (or 1/2) left from the 7 that you multiplied, you do 1.32 ÷ 2 = 0.66.
Add the 2 numbers together
0.66 + 9.24 = £9.90
What is the value of 4x + 9, when x = 4?
Answer:
The answer would be 25.
4x4=16
16+9=25
Step-by-step explanation:
I believe this is correct, if not feel free to let me know and I will fix it. I'm sorry in advance if it is incorrect.
Answer:
25
Step-by-step explanation:
rewrite the equation
(4x4)+9
do the equation
16+9=25
Select the correct answer from each drop-down menu.
The graph of the equation y = -x4 + x2 − 2
(A. Increases as x approaches negative infinity and decreases as x approaches positive infinity.)
(B. Decreases as x approaches negative infinity and increases as x approaches positive infinity)
(C. Increases as x approaches negative and positive infinity)
(D. Decreases as x approaches negative and positive infinity)
The graph of the equation y = x5 + x2 + 7
(A. Increases as x approaches negative infinity and decreases as x approaches positive infinity.)
(B. Decreases as x approaches negative infinity and increases as x approaches positive infinity)
(C. Increases as x approaches negative and positive infinity)
(D. Decreases as x approaches negative and positive infinity)
The graph of the equation y = x6 + 2x3 + 3
(A. Increases as x approaches negative infinity and decreases as x approaches positive infinity.)
(B. Decreases as x approaches negative infinity and increases as x approaches positive infinity)
(C. Increases as x approaches negative and positive infinity)
(D. Decreases as x approaches negative and positive infinity)
Answer:
y = -x⁴ + x² - 2 : D
y = x⁵ + x² + 7 : B
y = x⁶ + 2x³ + 3 : C
Step-by-step explanation:
anyways look at the part with the largest power of x. it will have the biggest impact on the overall value, when x approaches positive or negative infinity.
in the first one this is -x⁴
x⁴ is always positive (for positive and negative x). so, -x⁴ is always negative. therefore, it decreases in both cases when x approaches positive or negative infinity.
in the second one this is x⁵.
this goes with the sign of x. it is getting bigger (it increases), when x approaches positive infinity, and it is getting smaller (it decreases), when x approaches negative infinity.
in the third one this is x⁶.
this is always positive (for positive and negative x). therefore, it increases in both cases when x approaches positive or negative infinity.
One of the solutions to the equation 72 - 57– 24 – is 8. What is the other solution?
Answer:
72-57-24=-9
Step-by-step explanation:
simple subtraction
Need the question this is urgent!Please answer!
First, determine if the example is EXLUSIVE (M.E.) or
INCLUSIVE (Inc.) and circle the correct answer.
Then, find the probability of the example.
A die is rolled. What is the probability of rolling a 5 or a number greater than 3?
ME. Incl P (5 or >3) =
A die is rolled. What is the probability of rolling a 2 or a 6?
ME. Incl P (2 or 6) =
A card is drawn from a standard deck of cards. What is the probability of drawing a 6 or a king?
M. E. Incl P (6 or K) =
A card is drawn from a standard deck of cards. What is the probability of drawing a queen or a spade?
M. E. Incl P (Q or Spade) =
Answer:
Sorry I had to go to dinner here you go hope this helps! :D
Step-by-step explanation:
So, before we start, there are two things we have to go over.
First off, we have "or"
When using or between two probabilitess, you are basically adding them together.
For instance, you first question asks what the probability is of rolling a 5 or a number greater than 3(assuming this is a 6 sided dice).
So, rolling a 5 is a change of 1/6. Since 1 of the 6 dice iwll be 5. The other probability is a 1/2, since 3 of the 6 dice are over 3.
Now lets add these two together because of the "or":
1/2+1/6=3/6+1/6=4/6
So the probabily of rolling a 5 OR rolling a number greater than 3 is 4/6.
This is inclusive, since rolling a 5 is possible and greater than 3.
Now "and" is a bit different and more complex than or is.
Here is an example:
What is the change of rolling a even number or rolling a number above 4?
Well, rolling a even number has a probability of 1/2. Rolling a number above 4 is 1/3.
To find the "and", we multiply the two probabilities.
So 1/3*1/2=1/6
So the probability of rolling a even number and a number above 4 is 1/6.
Now, lets get back to the answers.
So what is the probability of rolling a 2 or a 6?
There is a 1/6 probability to get a 2, and a 1/6 probability to get a 6.
Add it together since they use or:
1/6+1/6=2/6
So the probability of rolling a 2 or a 6 is 2/6, or 1/3.
This is exlusive since you cant roll both a 6 and a 2 at the same time.
Next we have what the probability is of drawing a 6 or a king.
There are 13 different cards in a deck.
There is a 4/52 chance of drawing a 6(spade/heart/etc), and a 4/52 chance of drawing a king. This simplyfies to 1/13 for each.
This is:
1/13+1/13=2/13
So the probability of drawing a 6 or a king is 2/13
This is a exclusive event since a king and 6 cant be drawn at the same time.
Finally, we have:
What is the probability of drawing a queen or a spade?
Again, there is a 4/52 chance of drawing a queen. A spade, however, is different.
13 of the 52 cards can be spades, which simplies to 1/4.
So we have 1/13+1/4=4/52+13/52=17/52
So there is a 17/52 probability of drawing a queen or spade.
This is a inclusive event since it is possible to draw both a spade and queen at the same time.
Hope this answers all your questions and helps you understand what "and" "or" are in probability.
Question 8 of 1010 Points
Which of the following statements is false?
A. The diagonals of a rhombus are perpendicular and bisect each other.
B. A quadrilateral is a polygon with four angles.
C. In quadrilateral PQRS, ∠P and ∠S are opposite angles.
D. A rhombus is a quadrilateral.
Answer:
C
Step-by-step explanation:
In a quadrilatteral PQRS,angle P and angle S are not opposite anglesIn quadrilateral PQRS, ∠P and ∠S are opposite angles is false statement. Option c is correct.
False statement to be determine.
Quadrilateral is geometric shape encloses by 4 lines.
For A. The diagonals of a rhombus are perpendicular and bisect each other. This statement is true.
B. A quadrilateral is a polygon with four angles. Its also true.
C. In quadrilateral PQRS, ∠P and ∠S are opposite angles. Its false because ∠P is opposite to ∠R.
D. A rhombus is a quadrilateral. It is also true
Thus, In quadrilateral PQRS, ∠P and ∠S are opposite angles is false statement.
Learn more about quadrilateral here:
https://brainly.com/question/13805601
#SPJ5
Help ASAP. I will give branliest.
Answer:
( 1, 3)
Step-by-step explanation:
4x+y=7 * 2 = 8x + 2y = 14
8x + 2y = 14
- 3x + 2y = 9
--------------------
5x = 5
x = 1
Now substitute x into the equation for 1
8*(1) + 2y = 14
8 + 2y = 14
2y = 6
y = 3
The Art Club at Reynolds High School (ROCA) is selling paintings and clay coffee mugs to raise money for a trip to all the museums on the west coast. The cost for each painting is $20 and each mug is $15. The Art Club thinks they will sell at most 350 items. In order to meet their goal, they want to raise more than $4500. Write a system of linear inequalities to model the situation and then solve.
Answer:
See below and attached
Step-by-step explanation:
Let the number of paintings is x and the number of mugs is y.
We have following inequalities:
x + y ≤ 35020x + 15y > 4500The graphical solution is attached.
The solution is:
225 < x ≤ 350300 < y ≤ 3508 Luis put out 6 different pies at a picnic. At the end of the picnic, he noticed this about about the pies: 3 One whole apple pie was eaten, and of another apple pie was eaten 4 1 of the blackberry pie was eaten 2 NI 1 of the blueberry pie was eaten 5 of the cherry pie was eaten 8 3 of the peach pie was eaten 4 What is the total amount of Luis' pies that were left over? pies the scratchpad to show your work.
Answer:
2 1/4
Step-by-step explanation:
Here is the complete question used in answering this question :
Luis put out 6 different pies at a picnic at the end of the picnic, he noticed this about the pies: one whole apple pie was eaten, and 3/4 of another apple pie was eaten 1/2 of the blackberry pie was eaten 1/8 of the blueberry pie was eaten 5/8 of the cherry pie was eaten 3/4 of the peach pie was eaten. What is the total amount of pies that where left over
amount left of apple pie = 1 - 3/4 = 1/4
amount left of blackberry pie = 1 - 1/2 = 1/2
amount left of blueberry pie = 1 - 1/8 = 7/8
amount left of cherry pie = 1 - 5/8 = 3/8
amount left of peach pie = 1 - 3/4 = 1/4
add this figures together
[tex]\frac{2 + 4 + 7 + 3 + 2 }{8}[/tex] = [tex]\frac{18}{8}[/tex] = [tex]2\frac{2}{8}[/tex] = 2[tex]\frac{1}{4}[/tex]
What is 1 1/2 + 2 3/5
Answer:
i think its 5.7
Step-by-step explanation:
Answer:
4 1/10
Step-by-step explanation:
HELP WITH THIS SOMEONE!!!
Answer:
to blury
Step-by-step explanation:
What is the length of the side x?
Answer and Step-by-step explanation:
Solve for the middle side, then for x using Pythagorean Theorem.
[tex]A^2 + B^2 = C^2\\\\\\6^2 + 8^2 = C^2\\\\100 = C^2\\\\C = 10\\\\\\\\A^2 + 10^2 = 12^2\\\\A^2 + 100 = 144\\\\A^2 = 44\\\\A^2 = 2\sqrt{11} <-Answer[/tex]
#teamtrees #PAW (Plant And Water)
PLEASE HELP ME: Click on the graph to choose the correct answer to the equation.
x - 2y < 0
(Choose one of the graphs from the image as the answer)
It's the third one I believe. y>1/2x
570
1. Volume of a pyramid: 192 ftº: Volume of a rectangular prism:
2. Volume of a pyramid:
Volume of a rectangular prism: 729m
3. Volume of a cylinder: 285 cm: Volume of a cone:
4. Volume of a sphere:
Volume of a cylinder: 600cm
5. Volume of a cone: 50 m: Volume of a cylinder:
Answer:
576 FT^3
243 m^3
95 cm^3
400 cm^3
150 m^3
Step-by-step explanation:
Volume of a pyramid = 1/3 x ( length base x height)
Volume of a prism= ( length base x height)
1. prism = 192 x 3 = 576 FT^3
2. prism = 729 / 3 = 243 ft^3
volume of a cylinder = nr^2h
Volume of a cone = 1/3(nr^2h)
3. cone = 285/3 = 95
5. cylinder = 50 x 3 = 150
4. sphere = 600 / 1.5 = 400
No files just type it in please and thank you<3
Answer:
Option C is correct
Step-by-step explanation:
[tex]8 + 8 + 8 + 8 + 8 + 8 = 48[/tex]
[tex]6 \times 8 = 48[/tex]
Hope it is helpful...John got $30 for weeding the garden. He used money to buy a $15.25 video game and three snacks that cost $1.25 each. He bought his friend a snack too. If he went home with 1/6 of the money he started with, how much did his friends snack cost? A $5.00 B $6.00 C $8.50 D $11.00 E $13.50 F $14.75
Answer:
B
Step-by-step explanation:
His friends snack was 6 dollars.
15.25+1.25= 16
16+1.25= 17.25
17.25+1.25= 19
1/6 of 30 is 5 because 5x6=30.
30-19=11
He has to have 5 left over so the snack was 6 dollars.
The quantity five times a number y decreased by twelve. Group of answer choices 5y - 12 12 - 5y 12y - 5 12 + 5y
Answer:12 - 5y
Step-by-step explanation:
The quantity five times a number y decreased by twelve means that 5 multiplied by a number is subtracted from 12, it also means that 12 minus 5 times a number y and can be written mathematically as
12 - 5y
