Answer:
13.5 years
Step-by-step explanation:
We are given the expression:
W(x)= 20 x (0.95)^x
Where W(x) = 20grams/2
= 10 grams
Hence:
10 = 20 x (0.95)^x
Divide both sides by 20
10/20 = 20 x (0.95)^x/20
0.5 = (0.95)^x
Take the log of both sides
log 0.5 = log (0.95)^x
log 0.5 = x log (0.95)
Divide both sides by log 0.95
x = log 0.5 / log 0.95
x = 13.513407334 years
Approximately to 1 decimal place =✓13.5 years
Therefore, it will take 13.5 years for the radioactive substance to be half of its original weight.
Find the the sum for the shown infinite geometric series?
2,2/3, 2/9, ...
Answer:
3
Step-by-step explanation:
The formula for the sum of an infinite geometric series is
[tex]\frac{a}{1-r}[/tex]
Where a is the first term and r is the common ratio. We can see that the first term is 2, and to find the common ratio, we can divide a term by the one before it. We can get:
[tex]\frac{\frac{2}{3}}{2} =\frac{2}{3} *\frac{1}{2}=\frac{1}{3}[/tex]
Now, we have all the values need to evaluate the formula. We can plug them in:
[tex]\frac{2}{1-\frac{1}{3} } \\\frac{2}{\frac{2}{3} } \\2*\frac{3}{2}\\3[/tex]
How many units is this value from zero on the number line?
-8
answers
A. 16
B. 8
C. 0
D. -8
pls help urgent
Answer:
answer is 8
Step-by-step explanation:
hope this helps
Factor the following, I will give 5 stars and thanks.
Answer:
5) [tex]x=3,-1[/tex]
6) [tex]r=-6,-4[/tex]
7) [tex]p=2,3[/tex]
8) [tex]n=-4,8[/tex]
Step-by-step explanation:
5) [tex](x-3)(x+1)=0[/tex]
[tex](3-3)(-1+1)=0[/tex] substitute x for a number that will make the statement true.
6) [tex](r+6)(r+4)=0[/tex]
[tex](-6+6)(-4+4)=0[/tex] substitute r for a number that will make the statement true.
7) [tex](p-2)(p-3)=0[/tex]
[tex](2-2)(3-3)=0[/tex] substitute p for a number that will make the statement true.
8) [tex](n+4)(n-8)=0[/tex]
[tex](-4+4)(8-8)=0[/tex] substitute n for a number that will make the statement true.
Find the measure of the angle indicated
=======================================================
Explanation:
The arc measures shown are 138 and 58. Subtract the arc measures and divide by 2 to get the answer
(138-58)/2 = 80/2 = 40 degrees
The general formula is
(A - B)/2
where A and B are the arc measures. The value of A is always the larger arc measure. This formula works for two secant lines as this diagram shows, and it also works for a secant line and tangent line, and lastly it works if both lines were tangent.
At the donut shop the cost for a dozen donut holes and a glass of milk is $3.50. The cost for three dozen donut holes and four glasses of milk is $11.80 which pair of equations can be used to determine D (the cost for donut holes) and M (the cost for the milk)
Answer:
Step-by-step explanation:
12 D + M = 3.50
3*12 D +4M = 11.80
the pair of equations are
12 D + M = 3.50
36 D +4M = 11.80
Answer:
I need points lol 2=yx thank you for letting me spam
A bank makes a profit of 20 million euro. The bank pays 500 thousand euro in tax. What percentage of the profit is paid in tax?
Answer:
2.5%
Step-by-step explanation:
Given data
Profit = Euro 20,000,000
Tax paid= Euro 500,000
The percentage tax paid is
% Tax= Tax paid/Profit*100
% Tax= 500,000/20,000,000*100
% Tax=0.025*100
% Tax=2.5
Hence the percentage tax paid is 2.5%
The hypotenuse of a right triangle is one inch longer than the longer leg. The shorter leg is seven inches shorter than the longer leg. Find the length of the hypotenuse.
Answer:
Length of hypotenuse is 13 unit or 5 unit
Step-by-step explanation:
Find;
Length of hypotenuse
Computation;
Assume;
Length of hypotenuse = h
Length of longer leg = h - 1
Length of shorter leg = h - 1 - 7
Using Pythagorean theorem
hypotenuse² = longer leg² + shorter leg²
h² = (h - 1)² + (h - 1 - 7)²
h² = (h - 1)² + (h - 8)²
h² = h² - 2h + 1 + h² - 16h + 64
h² = 2h² - 18h + 65
h² - 18h + 65 = 0
h² - 13h - 5h + 65 = 0
h(h - 13) -5(h - 13)
(h - 13)(h - 5)
So,
Length of hypotenuse is 13 unit or 5 unit
I really need some help please
Answer:
y - 1 = 3/2(x - 4)
Step-by-step explanation:
plug in the given(known) x and y coordinates into the point-slope form:
=> y - 1 = 3/2(x - 4)
Which of the following expressions is equal to squared +25? O A. (x+5012 O B. (x-50 O C. (x + 10 (x-151) O D. (X - 5)(x+51)
Answer:
(x-5i)(x+5i)
Step-by-step explanation:
Given the expression
(x-5i)²
Expand
(x-5i)(x+5i)
= x² - 5ix + 5ix - 25i²
= x² - 25i²
Since i² = -1, hence;
(x-5i)(x+5i) = x² - 25(-1)
(x-5i)(x+5i) = x² + 25
Hence the required expression is (x-5i)(x+5i)
can someone help me with these too please
Answer:
120 in³
Step-by-step explanation:
10 x 4 x 3 = 120
Please help. How do you find cosine, sine, cosecant and secant with this triangle?
Hi there! You have to remember these 6 basic Trigonometric Ratios which are:
sine (sin) = opposite/hypotenusecosine (cos) = adjacent/hypotenusetangent (tan) = opposite/adjacentcosecant (cosec/csc) = hypotenuse/oppositesecant (sec) = hypotenuse/adjacentcotangent (cot) = adjacent/oppositecosecant is the reciprocal of sinesecant is the reciprocal of cosinecotangent is the reciprocal of tangentBack to the question. Assuming that the question asks you to find the cosine, sine, cosecant and secant of angle theta.
What we have now are:
Trigonometric RatioAdjacent = 12Opposite = 10Looks like we are missing the hypotenuse. Do you remember the Pythagorean Theorem? Recall it!
a²+b² = c²Define that c-term is the hypotenuse. a-term and b-term can be defined as adjacent or opposite
Since we know the value of adjacent and opposite, we can use the formula to find the hypotenuse.
10²+12² = c²100+144 = c²244 = c²Thus, the hypotenuse is:
[tex] \large \boxed{c = 2 \sqrt{61} }[/tex]
Now that we know all lengths of the triangle, we can find the ratio. Recall Trigonometric Ratio above! Therefore, the answers are:
cosine (cosθ) = adjacent/hypotenuse = 12/(2√61) = 6/√61 = (6√61) / 61sine (sinθ) = opposite/hypotenuse = 10/(2√61) = 5/√61 = (5√61) / 61cosecant (cscθ) is reciprocal of sine (sinθ). Hence, cscθ = (2√61/10) = √61/5secant (secθ) is reciprocal of cosine (cosθ). Hence, secθ = (2√61)/12 = √61/6Questions can be asked through comment.
Furthermore, we can use Trigonometric Identity to find the hypotenuse instead of Pythagorean Theorem.
Hope this helps, and Happy Learning! :)
(I'm probably spammy lol)
More babes-
I just need help, like point me in the right direction, something.
I'm so tired-
Answer:
x= 9
Step-by-step explanation:
85 + 2x +2 + {180 -(11x + 6) }=180 (sum of angles in a triangle)
87 + 2x + 180 - 6 -11x = 180
87 -9x - 6 = 0
81 = 9x
x= 9
Ashley uses a mix of six base-ten blocks to model a 3 digit number. All 3 digits of the number are the same. What is the number?
Answer:
The number is 222
Step-by-step explanation:
The given parameters are;
The method Ashley models the 3 digit number = A mix of six base-ten blocks
The digits of the 3 digit number are equal
Therefore, given that in a 3 digit number, we have, hundreds, 100s, tens, 10s, and units, 1s, we can find the digits as follows;
Let 'x' represent the number of hundreds digits, let 'y' represent the number of tens digits and let 'z' represent the number of units digits, we have;
x = y = z...(1)
x + y + z = 6...(2)
Substituting the value of x = y, and x = z from equation (1), in equation (2), we get;
x + y + z = x + x + x = 6
∴ 3·x = 6
∴ x = 6/3 = 2
x = 2 = y = z
Therefore, the 3-digit numbers xyz = 222
What is the area of the figure composed of a parallelogram, a square, and a rectangle?
10 in.
3.5 in.
4 in.
6 in.
12,5 in.
A studio apartment has a floor that measures 120 feet by 60 feet. A scale drawing of the floor on grid paper uses a scale of 1 unit : 6 feet. What are the dimensions of the scale drawing?
Answer: [tex]20\ \text{unit}\times 10\ \text{unit}[/tex]
Step-by-step explanation:
Given
A studio apartment has a floor that measures [tex]120\ ft \times 60\ ft[/tex]
Scale used is 1 unit:6 feet i.e 6 feet of actual floor is considered 1 unit in drawing
The dimension of scale drawing is [tex]\frac{1}{6}[/tex] of actual
Dimensions are
[tex]\Rightarrow \dfrac{120}{6}\times \dfrac{60}{6}\\\\\Rightarrow 20\ \text{unit}\times 10\ \text{unit}[/tex]
[tex]3 + 9 - 2 12 \div 3[/tex]
what expression is equivalent to x^2-7x+12+(x-3)^2
Answer:
2x²−13x+21
Step-by-step explanation:
Hope this answer helps you :)
Have a great day
Mark brainliest
What is the radius of this circle?
Answer:
radius is 9
Step-by-step explanation:
radius is half the diameter which is 18 and half of 18 is 9
Kevin is 30 years old. He wants to take out a 15-year level term insurance policy with a face value of $500,000. The monthly premium is $56. What will be his total cost over the 15-year period?
Answer:
$10,080
Step-by-step explanation:
Monthly premium = $56
So, yearly premium = $56 × 12 = $672
Time period = 15 years
Now, we can calculate the total cost for 15 years period by using following formula,
Total cost = yearly premium × Time period
By putting the value, we get
Total cost = $672 × 15
= $10,080
Hence, total cost for 15 years period is $10,080.
Basit played and online Pin Ball game the first time we got our score of 25000 point then he is called 125000 point and third time he scored 30000 what was his Score per game ?
Answer:
Average score per game = 60,000 per game
Step-by-step explanation:
Given:
Points scored in first game = 25,000
Points scored in second game = 125,000
Points scored in third game = 30,000
Find:
Average score per game
Computation:
Average = Sum of observation / Number of observation
So,
Sum of all game = 25,000 + 125,000 + 30,000
Sum of all game = 180,000
Number of games = 3
Average score per game = 180,000 / 3
Average score per game = 60,000 per game
Stephen kicked a ball inside. The equation that represents the height h in feet of the ball after being kicked and elapsed amount of time t in seconds
Answer:
The maximum height of the ball is: 14.0625ft
Step-by-step explanation:
The missing information is:
[tex]h(t) = 30t - 16t^2[/tex]
Required
The maximum height the ball attained
First, we calculate the time to reach the maximum height.
For a function: [tex]h(t) = at^2 + bt + c[/tex]
The maximum is: [tex]t = \frac{-b}{2a}[/tex]
So, the maximum of [tex]h(t) = 30t - 16t^2[/tex] is:
[tex]t = \frac{-b}{2a}[/tex]
Where
[tex]a = -16; b = 30[/tex]
So:
[tex]t = -\frac{30}{2*-16}[/tex]
[tex]t = -\frac{30}{-32}[/tex]
[tex]t = \frac{30}{32}[/tex]
[tex]t = 0.9375[/tex]
The maximum height is then calculated as:
[tex]h(t) = 30t - 16t^2[/tex]
[tex]h(0.9375) = 30 * 0.9375- 16 * 0.9375^2[/tex]
[tex]h(0.9375) = 28.125- 14.0625[/tex]
[tex]h(0.9375) = 14.0625[/tex]
i need someone who could log into an acellus account and help solve 5 problems, they look something like this....( i will give 30 points)
Answer:
[tex]\huge\boxed{V=44cm^3}[/tex]
Step-by-step explanation:
(look at the picture)
The formula of a volume of a rectangular prism a × b × c:
[tex]V=abc[/tex]
We have two rectangular prisms.
[tex]1:\ 2cm\times2cm\times5cm\\2:\ 2cm\times2cm\times6cm[/tex]
Calculate the volume:
[tex]V_1=2\cdot2\cdot5=20(cm^3)\\\\V_2=2\cdot2\cdot6=24(cm^3)[/tex]
The volume of the irregular figure:
[tex]V_F=V_1+V_2\\\\V_F=20cm^3+24cm^3=44cm^3[/tex]
Find the area of the composite figure.
Answer:
Area of composite figure = 623.25 cm²
Step-by-step explanation:
Given:
Equal side of triangle = 39 cm
Diameter of semi-circle = 30 cm
Base of triangle = 30 cm
Find;
Area of composite figure
Computation:
Radius of triangle = 30 / 2
Radius of triangle = 15 cm
Height of triangle = √39² - 15²
Height of triangle = √1,521 - 225
Height of triangle = 36 cm
Area of composite figure = Area of semi-circle + Area of triangle
Area of composite figure = [πr² / 2] + [(1/2)(b)(h)]
Area of composite figure = [(3.14)(15)² / 2] + [(1/2)(15)(36)]
Area of composite figure = [(3.14)(225) / 2] + [(15)(18)]
Area of composite figure = [706.5 / 2] + [270]
Area of composite figure = 353.25 + 270
Area of composite figure = 623.25 cm²
A recipe for baba ghanoush cause for twice as much olive oil as lemon juice
Which expression represents the amount of olive oil needed for 4 tablespoons of lemon juice choose ALL that apply
A). 4•4
B). 4+2
C). 4•2
D). 4+4
Answer:
A. 4.4 I am doing good today
What is the midline equation of the function g(x) = 2 cos(7x + 5) + 1?
Answer:
y = 1
Step-by-step explanation:
The midline of h(x) = 2 cos(7x + 5) is y = 0.
The graph of g(x) = 2 cos(7x + 5) + 1 is the same, except that the entire graph of h(x) is translated up by 1 unit.
Thus, the midline of g(x) = 2 cos(7x + 5) is y = 1.
A DrillingRick was diggingA well in the valley it dug to a point of -50 Meters in one day After 18 hours at how many meters would the rig be if it moved at the same amount each hour? Show your work.Explain your answer
Answer:
37.5 meters
Step-by-step explanation:
depth of well : hours of digging
it dug to a point of -50 Meters in one day
= 50 meters : 24 hours
After 18 hours at how many meters would the rig
Let
x = depth that will be rigged
depth of well : hours of digging
= x meters : 18 hours
Equate the ratios
50 meters : 24 hours = x meters : 18 hours
50/24 = x/18
50 * 18 = 24 * x
900 = 24x
x = 900/24
x = 37.5
x = depth that will be rigged = 37.5 meters
hey! i’ll give brainliest please help
Answer:
D
hope this helps
have a good day :)
Step-by-step explanation:
Matthew worked a summer job and saved $900 each
summer for the last 4 years. He also has been awarded a
grant in the amount of $5,000 and he received $3,000 in
scholarships. He estimated the first year of college to cost
$13,000. If he uses his savings, the grant, and his
scholarship, how much more will he need to pay for the
first year of college?
Answer:
1400
Step-by-step explanation:
hope that helps <3
What is the product of V3 and 2V30 in simplest radical form?
Answer:
Step-by-step explanation:
[tex]\sqrt{3[/tex] *2[tex]\sqrt{30[/tex]
2[tex]\sqrt{30*3}[/tex]
2[tex]\sqrt{3*3*2*5}[/tex]
2*3[tex]\sqrt{2*5}[/tex]
6[tex]\sqrt{10}[/tex]
Someone please help me out!!!
Answer:
[tex] \sin(c) = \frac{ab}{ac} \\ \sin(c) = \frac{36}{45} \\ \sin(c) = \ \frac{4}{5} [/tex]