The equation is [tex]f(t)=50(0.5)^{\frac {10}{5.3}}[/tex] and approximately 13.52 milligram remains
How to determine the equation?The missing information in the question is:
[tex]f(t)=m(0.5)^{\frac th}[/tex]
When the mass is 50 mg, it means that:
m = 50
So, we have:
[tex]f(t)=50(0.5)^{\frac th}[/tex]
When 10 years remain in the life of the substance, it means that:
t = 10
So, we have:
[tex]f(t)=50(0.5)^{\frac {10}h}[/tex]
The half life is 5.3. So, we have
[tex]f(t)=50(0.5)^{\frac {10}{5.3}}[/tex]
Evaluate the equation
f(t) = 13.52
Hence, the required equation is [tex]f(t)=50(0.5)^{\frac {10}{5.3}}[/tex] and approximately 13.52 milligram remains
Read more about half life at:
https://brainly.com/question/15575933
#SPJ1
Answer:c
Step-by-step explanation:
Based on an architectural drawing, a roof slopes to a drain along the function represented in the table that defines the edge of slope, where x is the horizontal distance in feet and f(x) is the vertical distance in feet.
If the drain is at the minimum point, how far is it from the wall defined by the y-axis?
0 feet
8 feet
80 feet
160 feet
The distance from the wall defined by the y-axis will be 8 feet. Then the correct option is B.
What is the equation of line?The equation of line is given as
y = mx + c
Where m is the slope and c is the y-intercept.
The table is given below.
Then the equation of the line will be
(y – 8) = [(8 – 6) / (0 – 20)](x – 0)
y = -0.1x + 8
If the drain is at the minimum point.
Then the distance from the wall defined by the y-axis will be 8 feet.
Then the correct option is B.
The complete question is given below.
More about the equation of line link is given below.
https://brainly.com/question/21511618
#SPJ1
If g(x) is the inverse of f(x), what is the value of f(g(2))?
0-6
O-3
02
O 5
Answer:
2
Step-by-step explanation:
When a function and its inverse are composed, the output is equal the input.
Larry likes skeet shooting. a clay disc is shot into the air and the participant tries to shoot it. he rarely misses, because he knows that the flight of the disc can be modeled by a quadratic function. the discs are released from a firing mechanism that sits at ground level and shoots the disc on average a horizontal distance of 120m. the average maximum vertical height that the disc reaches is 40 m.
a)The functions that represent the flight of the clay disc in Factored Form will be,[tex]\rm y = - \frac{1}{90} (x-60)^2+40[/tex]
b)The function in its standard form is,[tex]\rm y =- \frac{1}{90} x^3 + \frac{4}{3} x[/tex].
c) The domain and range of the quadratic function with the context provided will be [0,120] and [0,40] respectively.
What exactly is a function?A function is a statement, rule, or law that specifies the connection between two variables. Functions are common in mathematics and are required for the formulation of physical connections.
The given points represent on the graph is;
x = 0 , y = 0
x = 120 , y = 0
x = 60 , y = 40
The standard equation is;
[tex]\rm y = a(x-h)^2 +k \\\\ y = a(x-60)^2 +40 \\\\ 0 = sA(120-60) +40\\\\ 0= a \times 3600 + 40 \\\\ 3600 a = -40 \\\\ a = - \farc{1}{90}[/tex]
Substitute the value as;
[tex]\rm y = - \frac{1}{90} (x-60)^2+40[/tex]
b)
The above equation in the standard form is found as;
[tex]\rm y = \frac{-1}{90}(x^2 +3600 -120 x )+40 \\\\ y =- \frac{1}{90}(x^2 -40 + \frac{4}{3}x +40 \\\\ y = \frac{-1}{90} x^2 + \frac{4}{3}x[/tex]
c)The domain and range of the quadratic function with the context provided will be [0,120] and [0,40] respectively.
Hence, the functions that represent the flight of the clay disc in the factored form will be,[tex]\rm y = - \frac{1}{90} (x-60)^2+40[/tex]
To learn more about the function, refer to:
https://brainly.com/question/5245372
#SPJ1
Trout Street and Salmon Street are the same distance from the boardwalk to the intersection of 1st Street, Trout Street, and Salmon Street as shown in the diagram. Abby walks down 1st Street and stops when she reaches the boardwalk.
How far of a walk does she have to get to Trout Street?
Abby's walk to Trout Street is _______ yards.
Answer:
800
Step-by-step explanation:
I did it on the test
Answer:
800
Step-by-step explanation:
I just fifnished test
Damek has five number cards lying on the table. There are two number cards with digit 1, two number cards with digit 2 and one number card with 0. How many different three-digit numbers can Damek form? (Number cannot being with 0).
(P.S. Is there a way to find the answer without listing all the possibilities?)
Damek can form 14 three-digit numbers from the given situation. Hence, only 14 possibilities.
There are five number cards on the table.
2- digit 1 card
1- digit 0 card
2- digit 2 card
There is a possibility of putting 1 or 2 in the hundredth place.
If 1 is put in the hundredth place then there are 3 possibilities for tenth place 1,0,2
If 1 is put there then there is a possibility of 2 numbers 0,2 in ones place
If 2 is put then there is a possibility of 3 numbers 0,1,2 in ones place
If 0 is put then there is a possibility of 2 numbers 1,2 in ones place.
So, there are 7=(2+3+2) possibilities that the hundredth place is filled by 1.
Similarly, there will be 7 possibilities that the hundredth place is filled by 2.
Hence, there are 14 possibilities as required by the problem.
So, the possibilities of 3-digit numbers are (given the number cannot start with 0) 14.
Learn more about permutation here-
brainly.com/question/1216161
#SPJ10
find area of shape below to 1 dp
The shape will have a surface area of 189.25 cm². There are two distinct pieces to the figure: a rectangle and a semicircle.
What is the area?The space filled by a flat form or the surface of an item is known as the area.
The number of unit squares that cover the surface of a closed-form is the figure's area. Square centimeters and other similar units are used to measure area.
The figure is divided into two parts one is a rectangle and the second is a semicircle.
Area of figure = Area of rectangle + Area of a semicircle
Area of figure = L × B + (πr²/2)
A = 10 cm × 15 cm + (3.14 ×(5)^2/2)
A= 189.25 cm²
Hence the area of the shape will be 189.25 cm²
To learn more about the area, refer to the link;
https://brainly.com/question/11952845
#SPJ1
A car manufacturer has parked some new cars in 2 car parks.In the first car park there are 60 cars in the ratio 1 red car for every 2 blue cars and 3 silver cars.In the second car park there are 80 cars in the ratio 2 blue cars for every 3 red cars and 5 silver cars.
11. How many red cars are there altogether?
12.How many blue cars are there altogether?
13.How many silver cars are there together?
(PLS BE FAST!!)
The number of red car altogether is 34
The number of blue cars altogether is 36
The number of silver car altogether 70
How to use the ratio to find the number of cars?The car manufacturer has parked some cars in 2 car parks .
The first car park has 60 cars.
In the ratio 1 :2:3
Therefore,
red car = 1 / 6 × 60 = 10 cars
blue car = 2 / 6 × 60 = 20 cars
Silver car = 60 - 30 = 30 cars
The second car park has 80 cars.
The ratio are
In the ratio 3:2 5
Therefore,
red cars = 3 / 10 ×80 = 24
blue cars = 2 / 10 × 80 = 16
silver cars = 5 / 10 × 80 = 40
Therefore,
The number of red car altogether is 24 + 10 = 34 red car
The number of blue cars altogether is 20 + 16 = 36 blue cars
The number of silver car altogether is 30 + 40 = 70 silver cars
learn more on ratio here: https://brainly.com/question/12754973
#SPJ1
which graph correctly represents 3x+y > 7
Answer:
What graph? add a photo?
Each car on the lot at a car dealership has 4 tires and 2 headlights. Which pair correctly describes tires and headlights?
Answer: 4 : 2
Step-by-step explanation:
I am going to assume you want a ratio between number of tires to headlights which is
4 : 2
Please help!
Find m<1
1
60°
63°
Answer:
i think 150 degrees
Step-by-step explanation:
the 30° angle and ∠1 are a linear pair, and are supplementary. therefore they add up to 180°
∠1 + 30° = 180°
The presence of a midpoint will result in what type of segments?
Answer: two congruent segments.
Step-by-step explanation:
idlk im not smart
I need help explanation if possible
Step-by-step explanation:
tan x = sin x / cos x
[tex]tan \: x \: = \frac{ \frac{7}{15} }{ \frac{4 \sqrt{11} }{15} } = \frac{7}{4 \sqrt{11} } [/tex]
Someone please help with this !!!!!
Answer:
[tex]5^{\circ}[/tex]
Step-by-step explanation:
[tex]~~~~~~~\tan \theta = \cot 85^{\circ}\\\\\implies \tan \theta = \tan\left(90^{\circ} - 85^{\circ} \right)\\\\\implies \tan \theta = \tan 5^{\circ}\\\\\implies \theta = 5^{\circ}[/tex]
This is from the last question
Answer:
huh
Step-by-step explanation:
what are you trying to figure out-
Write an equation of the line that passes through the point P (2,-2) and is parallel to the line
-2x+y=-3
Step-by-step explanation:
Solution:
The slope of the line -2x+y = -3 is m1 =
- coefficient of x ÷ coefficient of y
= -(-2) ÷1
=2
Then, according to the question ;
It is stated that the lines are parallel
i.e.
m1=m2
or, 2 = m2
Hence, m2 =2
Again,
The required equation of the line passing through the point P(2,-2) = (x1,y1) is
y-y1 = m2(x- x1)
or, y-(-2) = 2(x-2)
or, y+2 = 2x-4
or, 2+4 = 2x-y
or, 2x-y = 6
Therefore; 2x-y = 6.
Which of the following does the function [tex]y=-4cos(3x)-9[/tex] not have?
a) horizontal translation
b)vertical translation
c)horizontal compression
d)reflection
Answer:
horizontal translation ( this would require an x - k or x+k type of a factor)
Step-by-step explanation:
It DOES have :
vertical due to the -9
horizontal compression due to the 3x
reflection due to the -4
Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options.
x < 5
–6x – 5 < 10 – x
–6x + 15 < 10 – 5x
A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right.
A number line from negative 3 to 3 in increments of 1. An open circle is at negative 5 and a bold line starts at negative 5 and is pointing to the left.
The correct simplified inequality is - 6x + 15 < 10 - 5x and the number line representation is "an open circle is at 5 and a bold line starts at 5 and is pointing to the right".
The given inequality is -3(2x - 5) < 5(2 - x)
We need to simplify the inequality.
What is inequality?In mathematics, inequality is a statement of an order relationship greater than, greater than or equal to, less than, or less than or equal to between two numbers or algebraic expressions.
Consider LHS and simplify -3(2x - 5) = -3(2x)-5(-3)
⇒ -3(2x - 5) = - 6x + 15 [∵(-)(-) = (+)]
Consider RHS and simplify 5(2 - x) = 5(2) + 5(-x)
⇒5(2 - x) = 10 - 5x [∵(+)(-) = (-)]
Now, - 6x + 15 < 10 - 5x
By subtracting 15 from both sides, we get
- 6x < -5 - 5x
By adding 5x to both sides, we get - x < - 5
The coefficient of x is -1. So, divide both sides by -1
Then we get x > 5
Hence, the correct simplified inequality is - 6x + 15 < 10 - 5x and the number line representation is "an open circle is at 5 and a bold line starts at 5 and is pointing to the right".
To learn more about inequalities visit:
https://brainly.com/question/20383699.
#SPJ1
What is the probability that a random chosen male voter is a registered Democrat? Round your answer to the nearest tenth of a percent.
what is the slimpelst form for ratio 21:28
Answer:
3:4
Step-by-step explanation:
We know this because the GCD of 21 and 28 is 7
so we divide both numbers by 7 and get 3 and 4
so the answer is 3:4
pls tell the answer with explanation, i have finish this hw
Answer:
7 and 8
Step-by-step explanation:
49 - 1 = 48. (1)
48 - 3 = 45. (2)
45 - 5 = 40. (3)
40 - 7 = 33. (4)
33 - 9 = 24. (5)
24 - 11 = 13. (6)
13 - 13 = 0. (7) The answer is 7
64 - 1 = 63. (1)
63 - 3 = 60. (2)
60 - 5 = 55. (3)
55 - 7 = 48. (4)
48 - 9 = 39. (5)
39 - 11 = 28. (6)
28 - 13 = 15. (7)
15 - 15 = 0. (8) the answer is 8
Answer:
Step-by-step explanation:
Finding square root by repeated subtraction method:In this, the given number is subtracted by consecutive odd numbers (1,3,5,7,9.....) till we fer zero at the end. Count the number of steps performed and this number will be square root of the given number.
a) 49
49 -1 = 48 48 - 3 = 4545 - 5 = 4040 - 7 = 3333 - 9 = 2424 - 11 = 1313 - 13 = 0√49 = 7
b) 64
64 - 1 = 6363 - 3 = 6060 - 5 = 5555 - 7 = 4848 -9 = 3939 -11 = 2828 - 13 = 1515 - 15 = 0√64 = 8
p varies jointly as q and the square of r, and p = 200 when q = 2 and r = 3. Find p when q = 5 and r= 2.
Step-by-step explanation:
If a variables varies jointly, we can just divide it by the other variables in relation to it.
For example, since p variables jointly as q and square of r, then
[tex] \frac{p}{q {r}^{2} } = k[/tex]
where k is a constant
First, let find k. Substitute p= 200
q= 2, and r=3.
[tex] \frac{200}{2(3) {}^{2} } = k[/tex]
[tex] \frac{200}{18} = k[/tex]
[tex] \frac{100}{9} = k[/tex]
Now, since we know our constant, let find p.
[tex] \frac{p}{q {r}^{2} } = \frac{100}{9} [/tex]
Q is 5, and r is 2.
[tex] \frac{p}{5( {2}^{2}) } = \frac{100}{9} [/tex]
[tex] \frac{p}{20} = \frac{100}{9} [/tex]
[tex]p = \frac{2000}{9} [/tex]
The two-way table below shows the number of students in a school who like mathematics and/or physics: Like Mathematics Do Not Like Mathematics Total Like Physics 15 20 35 Do Not Like Physics 5 25 30 Total 20 45 65 How many more students like physics than mathematics? 10 15 20 25
The number of students like physics more than mathematics is 15 , Option B is the correct answer.
What is a Number ?A mathematical way of expressing quantity of a substance is called a Number.
Number of students in a school who like mathematics = 20
Number of students in a school who like physics = 35
number of students in a school who like only physics is 20
number of students who like only Mathematics is 5
the number of students like physics more than mathematics is 20-5 = 15
Therefore Option B is the correct answer.
To know more about Number
https://brainly.com/question/17429689
#SPJ1
PLEASE ANSWER ASAP!!!!!!!!
A Ferris wheel completes 7 revolutions in 14 minutes. The radius of the Ferris wheel is 30 feet.
What is the linear velocity of the Ferris wheel in inches per second?
Enter your answer, rounded to the nearest tenth, in the box.
The linear velocity of the Ferris wheel in inches per second is 18.9 inches/second.
What is the speed of an object?The speed of an object is the ratio of the total distance covered by the object and the total time taken by the object to complete that distance.
Here, the radius of the Ferris wheel is (r) = 30 feet.
The circumference of the wheel is
C= 2πr
C= 2 × π × 30 feet
C= 60π feet
Here, the Ferris wheel completes 7 revolutions.
Therefore, it covers the linear distance of
D= 7 × circumference of the wheel
D= 7 × 60π feet
D= 420π feet
Now, the Ferris wheel took 14 minutes to complete 420π feet.
Therefore, the speed of the wheel is
S= (420π/14) feet/minute
S= 30π feet/minute
S= (30π × 12)/60 inches/second
S= 6π inches/second
S= 18.9 inches/second
Therefore the linear velocity of the object will be 18.9 inches/second
Learn more about the speed of an object here: brainly.com/question/16123156
#SPJ1
Two-thirds of the tokens in the box are red and 2/5 of the remaining tokens are blue.
If the remaining 24 tokens are green, how many tokens are there in the box?
Answer:
After solving this question I got and 120 tokens
The slope of the line below is -2. Write the equation of the line in point-slope
form, using the coordinates of the labeled point. Do not use parenthesis on
the y side.
(-2,1)
Answer:
y - 1 = -2(x + 2)
Step-by-step explanation:
The general structure of an equation in point-slope form is:
y - y₁ = m(x - x₁)
In this form, "x" and "y" stand for the values of one point and "x₁" and "y₁" stand for the values of another point. The variable "m" represents the value of the slope. You have been given the values of one point and the slope. When you plug them into the general form, you get this answer:
Point: (-2, 1)
m = -2
y - y₁ = m(x - x₁) <----- Point-slope form
y - y₁ = -2(x - x₁) <----- Plug -2 in "m"
y - 1 = -2(x - (-2)) <----- Plug in values from point
y - 1 = -2(x + 2) <----- Simplify
what is the explict formula for this sequence 5, 10, 20, 40, 80, 160, ...
Step-by-step explanation:
as we see in the sequence, each term is twice of the previous term.
we mark the Nth as a(N), then:
a(N)=2a(N-1)
Answer:
[tex]a_{n}[/tex] = 5[tex](2)^{n-1}[/tex]
Step-by-step explanation:
there is a common ratio between consecutive terms , that is
10 ÷ 5 = 20 ÷ 10 = 40 ÷ 20 = 80 ÷ 40 = 2
this indicates the sequence is geometric with explicit formula
[tex]a_{n}[/tex] = a₁[tex](r)^{n-1}[/tex]
where a₁ is the first term and r the common ratio
here a₁ = 5 and r = 2 , then
[tex]a_{n}[/tex] = 5 [tex](2)^{n-1}[/tex]
I need help with this please
2534+? but its not that clear cant understand it
Please help very urgent I’m on a time limit and I need the answer this is a test
An isosceles triangle is one with two equal-length sides. The value of l is 8 ft.
What is an isosceles triangle?An isosceles triangle is one with two equal-length sides. It is sometimes stated as having exactly two equal-length sides, and sometimes as having at least two equal-length sides, with the latter form containing the equilateral triangle as a particular case.
In the given image it can be observed except 140° angle, the other two angles are congruent to each other which means the triangle is an isosceles triangle.
As per the base angle theorem in an isosceles triangle the sides opposite to the congruent triangle are equal therefore, the length of side l will be 8 ft as well.
Hence, the value of l is 8 ft.
Learn more about Isosceles Triangle:
https://brainly.com/question/2456591
#SPJ1
Marcy and her sister watched a cartoon movie that was 2 hours and 18 minutes long. after the movie, they played a card game for 34 minutes and then played soccer for 1 hour and 12 minutes. when they came in from playing soccer, it was 5:28 p.m. what time did marcy and her sister start watching the movie?
Answer:
1:24pm
Step-by-step explanation:
Couple of ways to solve this. Here is one method
Convert all times to minutes and find the total number of minutes they spent on all 3 activities. Then convert to hours and minutes and subtract from the end time of 5;28 to get the start time of all activities which is also the start time of watching the movie (first activity)
So time spent:
Movie: 2 hours 18 minutes = 2 * 60 + 18 = 120 + 18 = 138 minutes
Card game: 34 minutes
Soccer: 1 hour 12 minutes = 1 * 60 + 12 = 72 minutes
Total time spent = 138 + 34 + 72 = 244 minutes = 4 hours and 04 minutes
Subtract 4:04 from 5:28 to get 1:24pm
Check
Movie watch starts at 4:04, ends at 1:24 + 2:18 or 3:42pm
Card game starts at 3:42pm ends at 3:42+0:34 ==> 4:16pm
Soccer starts at 4:16pm ends at 4:16pm + 1:12 ==> 5;28pm
Martin uses of a gallon of paint to cover of a wall. What is the unit rate at which Martin paints in walls per gallon?
The unit rate at which Martin paints in walls per gallon is 1 7/25 walls per gallon
Unit rateUnit rate of paint per gallon = Quantity of wall / gallon of paint
= 4/5 ÷ 5/8
= 4/5 × 8/5
= (4 × 8) / (5 × 5)
= 32/25
= 1 7/25 walls per gallon
Complete question:
Martin uses 5/8 of a gallon of paint to cover4/5 of a wall. What is the unit rate at which Martin paints in walls per gallon
Learn more about unit rate:
https://brainly.com/question/620388
#SPJ1
