Answer:
[tex]15\text{ grams}[/tex]
Step-by-step explanation:
Since the mass of the radioactive isotope is halved every 69 years, we want to multiply its initial mass by [tex]1/2[/tex] every 69 years.
We can model this using the following equation:
The remaining mass, [tex]f(x)[/tex], is equal to the initial mass multiplied by [tex]\frac{1}{2}^{(\frac{t}{69})}[/tex], where [tex]t[/tex] is the number of years that have passed from the initial mass. The reason why the exponent is [tex]\frac{t}{69}[/tex] is because we only want to half the mass every 69 years, so [tex]\frac{69}{69}=1[/tex] and [tex]\frac{1}{2}^1=\frac{1}{2}[/tex].
Thus, we have:
[tex]f(x)=20\cdot \frac{1}{2}^{(t/69)}[/tex]
Substituting [tex]t=30[/tex], we get:
[tex]f(x)=20\cdot \frac{1}{2}^{(30/69)}=20\cdot 0.73980522316=14.7961044632\approx \boxed{15\text{ grams}}[/tex]
On a coordinate plane, parallelogram H I J K is shown. Point H is at (negative 2, 2), point I is at (4, 3), point J is at (4, negative 2), and point K is at (negative 2, negative 3).
HIJK is a parallelogram because the midpoint of both diagonals is __________, which means the diagonals bisect each other.
(1,−1)
(1,1)
(1,0)
(0,1)
============================================================
Explanation:
Point H is at (-2,2) and J is at (4,-2)
Focusing on the x coordinates, the midpoint is (x1+x2)/2 = (-2+4)/2 = 1.
The y coordinates have a midpoint of (y1+y2)/2 = (2+(-2))/2 = 0.
The midpoint is at (1,0). That's why the answer is choice C.
--------------------------
This next section is optional.
Points I and K are located at (4,3) and (-2,-3) respectively
Averaging the x coordinates gets us (x1+x2)/2 = (4+(-2))/2 = 1
Doing the same for the y coordinates gets us (y1+y2)/2 = (3+(-3))/2 = 0
We end up with the same midpoint (1,0)
The midpoint being the same for both diagonals proves that each diagonal is bisected, ie cut in half.
Answer:
C is the correct answer
Step-by-step explanation:
Please help. It’s a multiple choice question. I’ve my answer, but I’m not sure.
Answer:
66 degree
Step-by-step explanation:
given:
angle FAB = 48 degree
angle ECB = 18 degree
in triangle HBC , angle H is also 48 degree degree since the line is parallel the connection between angle H and angle A is alternate interior angle and alternate interior angle are always equal.
so angle H = 48 degree
in triangle HBC
angle H + angle C = angle ABC (sum of two interior opposite angles are equal to the exterior angle formed)
48 + 18 = angle ABC
66 = angle ABC
how many joules of work are done against a cart when a force of 50N pushes it 1000m anway
Math help due soon thanks
Answer: The figures appear to be similar
============================================================
Explanation:
You'd need to use a protractor, or perhaps some trig tricks that I can't think of right now, to determine that the angles are the same. They appear to be the same so, let's assume that the angles are the same.
That means we just need to focus on the sides being proportional or not. We simply divide the corresponding sides in the correct order. If we get the same result each time, then we have similar figures.
I've marked your drawing adding color coded circles to show which sides are corresponding. We'll divide the red values together, the green values together, etc like so
2.5/2 = 1.253.75/3 = 1.255/4 = 1.256.25/5 = 1.252.5/2 = 1.255/4 = 1.25I started with the stuff in red, moved to stuff in green, working clockwise around each figure. We get the same result each time, so it seems to suggest we have similar figures. Again, we have to assume the angle measures are the same for the two figures to officially be considered similar.
Put these numbers in order from greatest to least.
0.32,1/2,0.66, and 0.45
The moon Phobos orbits Mars
(mass = 6.42 x 1023 kg) at a distance
of 9.38 x 106 m. What is its period of
orbit?
Answer:
27583.78 s
Step-by-step explanation:
Use the orbit equation to get v, then v=distance/time to get time.
Correct on Acellus
Evaluate
tan 332°30'
Cos 229°47'
and sec(-38°22')
HELPPP
A gallon of paint covers 400 square feet. How many square feet will 2 __ 3 8 gallons of paint cover?
Answer:
2 gallons of paint
Step-by-step explanation:
If 3/4 of a gallon covers 2/5 of a wall, this means that a half of 3/4 gallons can cover 1/5 of a wall.
By knowing this, you can just make up your own expression
(the trick is to find a way to break it down to one, so you can multiply and manipulate it to save yourself some brain cells)
Hoped this helped you :3
Answer:
30,400 sq ft
Step-by-step explanation:
1 gallon = 400 sq ft
2×38=76 gallons
76×400=
30,400sq ft
URGENT!!!!! I really suck at these help please I beg of you
Answer:
Step-by-step explanation:
1) ∠WVZ and ∠VWX are right angles & VX = = WZ Given
2) WV = VW Reflexive property
3) ΔWVZ ≅ ΔVWX HL
4) ∠Z = ∠X CPCT
CPCT --> Corresponding parts of congruent triangle.
through:(-1, -2), slope = 5
Answer:
y=5x+3
Step-by-step explanation:
Hi there!
We're given the point (-1, -2) and a slope of 5. We need to find the equation of the line in slope intercept form.
Slope-intercept form is given as y=mx+b, where m is the slope and b is the y intercept
Since we're already given the slope, we can substitute that immediately into the equation
here it is so far:
y=5x+b
now we need to solve for b
Since the line will pass through the point (-1,-2), we can use it to solve for b
substitute -1 as x and -2 as y into the equation
-2=5(-1)+b
multiply
-2=-5+b
add 5 to both sides
3=b
substitute that into the equation
therefore, the equation of the line is y=5x+3
Hope this helps! :)
which function has a domain of all real numbers
please answer accurately I need this to pass my class. thank you.
Answer:
a.y=-x½+5
Step-by-step explanation:
from the above functions ,the highest degree or power is ½ on a.⅓,¼,⅙ are smaller than ½
PLZZZZZZ HELPPPPP!!!!!!
Answer:
1
Step-by-step explanation:
1/2×2 = 2/2 = 1
_____________________
What is the product on this Brainly test
Answer:
I have no clue to be honest
pls explaing by tep by step
Answer:
a = 3
Step-by-step explanation:
If (x+3) is a factor of f(x) = x³+ax²+x+3,
From remainder theorem,
When we substitute -3 into the expression, we equate to zero
That is,
F(-3) = 0
(-3)³+a(-3)²+(-3)+3 = 0
-27+9a-3+3 = 0
9a = 27
divide both sides by the coefficient of a
a = 27/9
a = 3
Hence the value of a = 3
Find the volume of this sphere.
Use 3 for TT.
Using the formula shown replace r with 11 and pi with 3:
Volume = 4/3 x 3 x 11^3
Volume = 5,324 in^3
what is x when tan24 = 5/x
Answer:
x ≈ 11.23
Step-by-step explanation:
Given
tan24° = [tex]\frac{5}{x}[/tex] ( multiply both sides by x )
x × tan24° = 5 ( divide both sides by tan24° )
x = [tex]\frac{5}{tan24}[/tex] ≈ 11.23 ( to 2 dec. places )
For EASY BRAINLIEST!!!
Answer that question
Step-by-step explanation:
my answer is in the image above
Assignment
1
Which is rational?
a. 64
b. 17
C. 67.714819...
22. Which is irrational?
a. 75.106
c. 101
Identify each of the following as Rational or Irrational.
3 -42
4 65.4279
5
98
16
6
25
7 57.013013..
8
18.44333777...
9
-139.04
24
10
What are the domain and range of f(x) = 2|x -4|?
plz i'm in need
Answer:
Domain: (-∞, ∞)
Range: [0, ∞)
Step-by-step explanation:
The domain represents what x can be. In this scenario, we do not have x as a denominator, and there is nothing limiting x, so its domain is (-∞, ∞)
The range represents what f(x) can be, Because |x-4| is in absolute value, the lowest |x-4| can be is 0, and as a result, the lowest value of 2|x-4| is 2*0=0. The maximum value of f(x) is ∞ as an absolute value does not limit the maximum, making the range [0, ∞)
You will take a test with multiple choice questions and short answer questions. The multiple choice questions are worth 1 point and the short answer questions are worth 3 points. There is a total of 100 points on the test and 70 total questions. How many questions of each type? Set up a system and solve. Let x = number of multiple choice questions and y = number of short answer questions.
9514 1404 393
Answer:
15 short answer (3 points)55 multiple choice (1 point)Step-by-step explanation:
Your system of equations will be ...
x + y = 70 . . . . . . . there are 70 total questions
x + 3y = 100 . . . . . there are 100 total points
__
We can use the first equation to write an expression for x that can be substituted into the second.
x = 70 -y
(70 -y) +3y = 100
70 +2y = 100 . . . . . . collect terms
2y = 30 . . . . . . . . . . subtract 70
y = 15 . . . . . . . . . . . divide by 2
x = 70 -15 = 55
The test has 15 short answer questions and 55 multiple-choice.
HELLPPP DUE IN 10 MINUTES
Answer:
Step-by-step explanation:
The Letter B
PLEASE HELP ME THANK YOU
Answer:
Step-by-step explanation:
That exterior angle of 111 is equal to the sum of the triangle's remote interior angles. We add the 37 + 35 to get a total angle measure of 72. That means that the base angle on the right is 111 - 72 = 39. That 39 degree angle is vertical to x; that means that x = 39 as well.
Answer:
39deg
Step-by-step explanation:
HELP HELP HELP HELP HELP HELP
Answer:
148 Degrees
Step-by-step explanation:
32-180=148
148+32=180
For which equation would x = 0 be a solution?
6x = 1/6
4x = -4
(7)x = 0
1,000x = 0.001
QUESTIONS:- For which equation would x = 0 be a solution?
ANSWER:- (7)x = 0
as 7x= 0
x=0 ANSWER
Please help!!
The slope of a line that passes through the points (-6, w) and (-10, 4) ls 1/8. What is the
value of w?
Answer:
[tex]\displaystyle w=\frac{9}{2}=4.5[/tex]
Step-by-step explanation:
We can use slope formula:
[tex]\displaystyle m=\frac{y_2-y_1}{x_2-x_1}[/tex]
So:
[tex]\displaystyle m=\frac{4-w}{-10-(-6)}=\frac{4-w}{-10+6}=\frac{4-w}{-4}[/tex]
We are given that this equals 1/8. Therefore:
[tex]\displaystyle \frac{4-w}{-4}=\frac{1}{8}[/tex]
Solve for w. Cross-multiply:
[tex]-4(1)=8(4-w)[/tex]
Distribute:
[tex]-4=32-8w[/tex]
Isolate:
[tex]-8w=-36[/tex]
So:
[tex]\displaystyle w=\frac{-36}{-8}=\frac{9}{2}=4.5[/tex]
Yuron is sketching a scale drawing of a famous painting. The painting is 54 inches wide and 72 inches long. He used a scale factor of Two-thirds to make his sketch. How many inches wide is Yuron's sketch? 36 48 81 84
Answer: 36 inches
Step-by-step explanation:
From the information given in the question, we are informed that Yuron is sketching a scale drawing of a famous painting and that the painting is 54 inches wide and 72 inches long.
We are further informed that he used a scale factor of ⅔ to make his sketch, then the measure of the width of the sketch will be ⅔ of the original width and this will be:
= ⅔ × 54 inches
= 36 inches
The width of Yuron's sketch is 36 inches.
How many inches wide is Yuron's sketch?
We know that the original painting is 54 inches wide and 72 inches long, and Yuron makes a sketch that uses a scale of 2/3 of the original dimensions.
Then the width of Yuron's sketch will be 2/3 times the original width:
W = (2/3)*54 inches = 36 inches.
The width of Yuron's sketch is 36 inches.
If you want to learn more about scales, you can read:
https://brainly.com/question/15891755
please help me guys I am in trouble
2. What is the mode for the data set 13, 11, 10, 12, 14, 9,
11, 8, 11?
A.10
B. 11
C. 12
D. none of the above
Answer:
11
Step-by-step explanation:
mode is the number that is most frequent
11
Answer:
11
Step-by-step explanation:
Mode means the highest repeated observation in the data set,
Therefore Mode = 11, as 11 has repeated 3 times, the most in the data set
The sum of two numbers is 10. The larger number is 4 times the smaller number. What are the two numbers?
Let x = the smaller number.
Let y = the larger number.
Which two equations represent the system for this word problem?
Equation 1:
Equation 2:
Step-by-step explanation:
everything can be found in the picture
Answer:
Step-by-step explanation:
Which two equations represent the system for this word problem?
Equation 1:
✔ x + y = 10
Equation 2:
✔ y = 4x
Ayúdenme con esto
Por favor
Answer:
sir, this is a english app, search a spanish app
señor, esta es una aplicacion en ingles, busque una en español
Step-by-step explanation:
Brainly.lat