Using an exponential function, it is found that the mass of the radioactive sample at the beginning of the 13th day of the experiment was of 169.1 mg.
What is an exponential function?A decaying exponential function is modeled by:
[tex]A(t) = A(0)(1 - r)^t[/tex]
In which:
A(0) is the initial value.r is the decay rate, as a decimal.At the beginning of the first day of the experiment the mass of the substance was 500 grams and mass was decreasing by 8% per day, hence A(0) = 500, r = 0.08, and the equation is given by:
[tex]A(t) = A(0)(1 - r)^t[/tex]
[tex]A(t) = 500(1 - 0.08)^t[/tex]
[tex]A(t) = 500(0.92)^t[/tex]
At the 13th day, the mass is given by:
[tex]A(13) = 500(0.92)^{13} = 169.1[/tex]
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A pillar is fixed in the centre of a circular meadow with diameter of 60 metres. The angle of elevation of its top was found to be 60%, when observed from a point of the circumference of circular meadow. Find the height of the pillar from the ground.
Answer:
17 meters
Step-by-step explanation:
|\ angle = 60 degrees here of triangle
| \ <-- digitaly drawn triangle
|___\
cirlcle diameter is 60 meters, since pillar is at the center then the distance of the pillar to the edge of the circlular meadow is (60/2) 30 meters.
30 meters is opposite of the angle.
The height of the pillar is adjacent to the angle so use tangent to solve
Tan(60) = 30/x
Tan(60) = 1.7; make sure that calculator is in degrees and not in radians to not get an incorrect value
1.7 = 30/x --> 1.7x = 30
x = 30/1.7
x = 17.3205 meters
using 2 significant figures gives us 17 meters
please help me solve this?
Answer:
there are none (sorry if I got it wrong)
Step-by-step explanation:
also, there is none because there other numbers are really close to the other number
outliers are a number that is really small in the pack of numbers and outliers can also be the number that is really big for example I have the numbers 3 24 28 32 43 and then 100. 3 and 100 are outliers because one number (3) is really small from the other numbers are bigger and one number (100) is really big from the other number but sometimes there are no outliers
Max was browsing Amazon on his phone and decided to purchase the newest Adidas shoes. He bought
them for $280. Unfortunately, a newer version was released a week later and his shoes began depreciating
in value rapidly. Every week the value of the shoes decreases by 8%. how much will the shoes be worth
in 2 months (8 weeks)?
Answer:
$143.70
Step-by-step explanation:
The multiplier of value each week is (1 -8%) = 0.92. After 8 weeks, the original value will have been multiplied by 0.92^8.
__
The value of the shoes after 8 weeks is ...
$280(0.92^8) ≈ $143.70
A figure was moved 5 units to the right, then a
mirror image was made. Which transformations were used? Rotation, dilation, reflection, translation
Answer:
Step-by-step explanation:
First a translation then a reflection.
Given A= (-3,6) and B=(10,-8) what is the length of AB
[tex]\text{Given that,}\\\\A(x_1,y_1) = (-3,6)~~ \text{and}~ B(x_2,y_2) =(10,-8)\\\\AB = \sqrt{(x_2-x_1)^2 + (y_2 -y_1)^2}\\\\~~~~~=\sqrt{(10+3)^2 + (-8-6)^2}\\\\~~~~~=\sqrt{13^2 + 14^2}\\\\~~~~~=\sqrt{365}\\\\~~~~~=19.105~ units[/tex]
please find the area
Answer:
254.34 m²
Step-by-step explanation:
The formula used to find the area of a circle is π · r².
The radius of a circle is half of it's diameter.
Using the given values, we can solve:
3.14 · 9²
3.14 · 81
= 254.34 m²
hope this helps!
Answer:
Area = 254.469004940773 m²
Step-by-step explanation:
formula : (area of a circle)
Area = π × r²
where r is the radius of the circle
[tex]\large \text r = \frac{\large \text Diameter \ of \ the \ circle }{2} = \frac{18}{2} =9\ m[/tex]
then
Area = π × 9²
= π × 81
= 254.469004940773 m²
write a word phrase that means the samme as x/4
Look At the picture I am not sure how to calculate the area
Answer:
height = 5.33 m (nearest hundredth)
area of wall = 41.66 m² (nearest hundredth)
Step-by-step explanation:
To find the height of A above the ground, find the height of the triangle and add it to the height of the rectangle.
The dashes on the sides of the triangle mean they are equal in length. Therefore, this triangle is an isosceles. If we draw a line down the center of the triangle to create 2 right triangles, their top angles will be 65° (half of 130°) and they will each have a base length of 5 m (see attached diagram).
To find the height, use the tan trig ratio:
[tex]\sf tan(\theta)=\dfrac{O}{A}[/tex]
where:
[tex]\theta[/tex] = angleO = side opposite the angleA = side adjacent to the angleGiven:
[tex]\theta[/tex] = 65°O = 5 mA = h[tex]\sf \implies tan(65)=\dfrac{5}{h}[/tex]
[tex]\sf \implies h=\dfrac{5}{tan(65)}[/tex]
[tex]\sf \implies h=2.331538291...[/tex]
Therefore, the height of A above the ground:
⇒ height = 3 + 2.331538191 = 5.33 m (nearest hundredth)
----------------------------------------------------------------------------------------
To find the area of the wall, sum the area of the rectangle and the area of the triangle.
Area of rectangle = width x height
= 3 x 10
= 30 m²
Area of triangle = 1/2 x base x height
= 1/2 x 10 x 2.331538191
= 11.65769145 m²
Total area of wall = 30 + 11.65769145 = 41.66 m² (nearest hundredth)
Use the Pythagorean Theorem to determine if a triangle with side lengths √2 ft., √3 ft., √5ft. is a right triangle.
A:) Yes it is a right triangle
B:) No it is not a right triangle
Answer:
A:) Yes it is a right triangle
Step-by-step explanation:
[tex]~~~~\left(\sqrt{5} \right)^2= \left(\sqrt{2} \right)^2+\left(\sqrt{3} \right)^2\\\\\implies 5=2+3\\\\\implies 5=5[/tex]
Answer:
A
Step-by-step explanation:
using the converse of Pythagoras' identity
If the square of the longest side is equal to the sum of the squares on the other 2 sides then the triangle is right.
longest side = [tex]\sqrt{5}[/tex] , and ([tex]\sqrt{5}[/tex] )² = 5
([tex]\sqrt{2}[/tex] )² + ([tex]\sqrt{3}[/tex] )² = 2 + 3 = 5
Thus the 3 sides form a triangle
Marco travels from his house to the beach. The total distance he travels
is 120 miles. In the first hour, Marco traveled 54 miles. What percent of
the distance did he travel the first hour?
Answer:
45%
Step-by-step explanation:
Since he drove 54 miles out of 120 in the first hour, the equation for this would be 54/120×100. This equals 45 and that is the percentage
What is the value of x if x * x + 2x - 35 = 0?
Answer:
x=5 or -7
step by step:
x2+2x−35=0
Step 1: Factor the left side of the equation.
(x−5)(x+7)=0
Step 2: Set factors equal to 0.
x−5=0 or x+7=0
x=5 or x=−7
Answer:
Your X value would equal to:
5 or -7
(images attached below show a step by step explanation)
Step-by-step explanation:
Have a great rest of your day
#TheWizzer
The sequence below is arithmetic:
{3, -6, -15,-24}
True
False
Answer:
True
Step-by-step explanation:
For the sequence to be arithmetic there must be a common difference d between consecutive terms.
a₂ - a₁ = - 6 - 3 = - 9
a₃ - a₂ = - 15 - (- 6) = - 15 + 6 = - 9
a₄ - a₃ = - 24 - (- 15) = - 24 + 15 = - 9
There is a common diffence between consecutive terms, thus the sequence is arithmetic.
find the area with 4cm, 8cm, 16cm
Answer:
u cant find the area if you dont add a picture or say if the cm is the width or the lenth.
L BOZO
Step-by-step explanation:
Answer:
PLEASE ADD PICTURE OR NOT ANSWER!
Step-by-step explanation:
We don’t know the problem. Pls apply it.
Choose the correct answer in each number.
1. It is the sum of all areas of lateral faces
and bases of solid figure.
A. Base area B. Lateral area C. Surface area D. None of the above
2. A flat pattern that you can fold to form a solid figure is called a/an _____.
A. Area B. Edge C. Face D. Net
3. The surface area of a cube is _____ times the area of its face.
A. Three B. Four C. Five D. Six
4. In a cylinder, the edge or length of the lateral surface is equal to _____ of its base.
A. Circumference B. Perimeter C. Radius D. All of the above
5. The lateral surface of a cylinder when it is unrolled will be _____
A. Rectangle B. Trapezoid C. Triangle D. All of the above
6. The solid figure that has surface area equivalent to for times the areas of circles of the same radii is _____.
A. Cube B. Cone C. Tetrahedron D. Sphere
7. To get the lateral area of a cone, we use the formula _____.
A. L.A.=πr2 B. L.A.=πrs C. L.A.=πrh D. L.A.=rh
8. The sum of the area of the square base and four triangular lateral faces is the surface area of _____.
A. Cube B. Rectangular prism C. Pyramid D. Cone
9. The unit for surface area is _____.
A. Cubic unit B. Linear unit C. Square unit D. Weight unit
10. A cone has a radius of 5 cm and slant height of 7.1 cm. What is the unit of measure appreciate for its surface area?
A. Square milimiter (mm2) B. Square centimeter (cm2) C. Square decimeter (dm2) D. Square meter (m2)
Answer:
A
B
A
C
D
C
A
B
B
D
Step-by-step explanation:
find the exact value of 2sin30 cos30
Answer:
[tex]\frac{\sqrt{3}}{2}[/tex]
Step-by-step explanation:
Let's take a look at the unit circle below.
Remmeber that cos represents the x-value and that sin represents the y-value.
We see that:
[tex]sin(30)= \frac{1}{2}\\\text{and}\\ cos(30) = \frac{\sqrt{3}}{2}[/tex]
Now we just multiply all the together and we get:
[tex]2*\frac{1}{2}*\frac{\sqrt{3}}{2} =\frac{\sqrt{3}}{2}[/tex]
Solve for x. Please help and please show work, thanks!
Answer: 5
Step-by-step explanation:
We can use ratios / proportions to solve for x. I am going to have the shorter segment on the top of our fractions (the numerator), and the longer segments on the bottom (the denominator).
[tex]\frac{10}{10+12} =\frac{4x-5}{33}[/tex]
[tex]\frac{10}{22} =\frac{4x-5}{33}[/tex]
Now I am going to cross multiply:
10 * 33 = 22(4x - 5)
330 = 88x - 110
440 = 88x
5 = x
x = 5
A regular octagon has an apothem of approximately 4.0 cm and a perimeter of approximately 26.4 cm. Find the area of the octagon.
Answer:
[tex]52.8cm^{2}[/tex]
Step-by-step explanation:
Perimeter = 26.4 cm
Apothem = 4.0 cm
The area of an regular octagon can be defined as the [tex]\frac{perimeter*apothem}{2}[/tex]
when we plug in our values we get the equation [tex]\frac{26.4cm*4.0cm}{2}=52.8cm^{2}[/tex]
In a survey, 125 people were asked to chose one card out of five cards labeled 1 to 5. The results are shown in the table. Compare the theoretical probability and experimental probability of choosing a card with the number 3
.
Answer:
There is no table, so I'll just calculate the theoretical.
125/5=25.
So, 20% to get a card with the number 3
PLEASE ANSWER! (4 - QUESTIONS) 50 POINTS + WILL RECEIVE BRAINLIEST!
1. The volume of a cylinder is 461.58 cubic inches. If the cylinder has a height of 3 units, what is the radius of the cylinder? Use 3.14 for pi.
2. Find the volume of the cone that has a height of 12 and diameter of 12. Use 3.14 for pi. Round your answer to the nearest tenths place.
3. Find the volume of the hemisphere that has a radius of 7 inches. Use 3.14 for pi. Round your answer to the nearest hundredth.
4. The volume of a sphere is 407.51 cubic units. What is the diameter of the sphere?
The radius of the cylinder is 7 in, the volume of the cone is 452.2 unit³, the volume of the hemisphere is 1436 in³ while the diameter of the sphere is 14.6 units
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
a) Volume of cylinder = π * radius² * height
461.58 = 3.14 * radius² * 3
radius = 7 in
b) Volume of cone = (1/3) * π * radius² * height
Volume = (1/3) * 3.14 * (12/2)² * 12
Volume = 452.2 unit³
c) Volume of sphere = (4/3) π * radius³
Volume of sphere = (4/3) * 3.14 * 7³
Volume = 1436 in³
d) Volume of sphere = (4/3) π * radius³
407.51 = (4/3) * 3.14 * radius³
Radius = 7.3
Diameter = 14.6 units
The radius of the cylinder is 7 in, the volume of the cone is 452.2 unit³, the volume of the hemisphere is 1436 in³ while the diameter of the sphere is 14.6 units
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angle properties pls help
Answer: Which question I’ll do a
Step-by-step explanation:
Since it is turned into an 100 degree angle you do length times width and you will get your answer 90 degrees
Was this helpful
how to solve (4s - 5t)²
Answer:
Step-by-step explanation:
What's the q1 and q2????
Answer:
Q1-298
Q2-422
Step-by-step explanation:
PLS HURRY AND TY!!!
Write eight and three hundred twenty-four thousandths in standard form.
Answer:
0.324 inch
Step-by-step explanation:
When asked to write two hundred thousandths as a decimal, three students gave three different answers as shown below. so you have to find by decimals..
Question below! :)
Brainliest!
The angle shown is less than 90 degrees so it is an acute angle.
answer: acute
9. The value of U.S. postage stamps increases ~5% per year. The current price is 55C. Estimate what the price will be in 20 years
Answer:
$1.46
Step-by-step explanation:
We can use the principal of compound interest to solve this with the formula:
[tex]A = P(1+\frac{r}{n})^{nt}[/tex]
where P = initial principal
r = interest rate
n = number of times applied per time period
t = time periods elapsed
In this specific case, P = 0.55, r = 0.05, n = 1, and t =20
[tex]0.55(1+\frac{0.05}{1})^{1*20} = 0.55(1.05)^{20} = 0.55(2.65) = 1.46[/tex]
5 7
What is the slope of the equation Y=74-7?
=
O -7
o -
O
O 5
Hey there!
y = 74 - 7
START at 74 and go back 7 spaces to your left and you should be left on your result of the y-value
y = 67
Therefore, your answer is: y = 67
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
before getting to school john has a few errands to run john has to walk 5 blocks to the galley and 9 blocks to the library before walking the final 7 blocks to arrive at school if john has already walked 12 blocks how many more blocks must he walked before arriving school
Answer:
9 blocks
Step-by-step explanation:
The total of what John has already walked and the number more he must walk will be equal to the number he has to walk to get to school.
12 + more = 5 + 9 + 7
more = 9 + 5 + 7 - 12 . . . . . subtract 12 from both sides
more = 9
John must walk 9 blocks more.
_____
We recognize that 5+7 = 12, so that last part of the sum totals zero.
Please help me ASAP.
The 3 inside angles of a triangle need to equal 180.
X = 180 - 70 - 20 = 90
x = 90 degrees
Find the length of the third side. If necessary, round to the nearest tenth
Pythagorean Theorem (Rounding)
Answer:
It's 3.5
(from the answer 3.464101615)
Hope this helps!
A hot-air balloon is released at ground level, and it rises into the air at a constant rate. After 5 seconds the height of the balloon is 20 feet. The balloon continues to rise at the same rate. Which table shows the relationship between the time in seconds, x, and the height of the balloon in feet, y?
The constant rate = 20 ft / 5 seconds = 4 feet per second
Find the chart that shows an increase of 4 feet for every second the balloon travels.
The height of the balloon over time is modeled by the linear equation y = 4x, so, the accurate choice is option D.
What are linear equations?A linear equation arises when multiple variables are connected, resulting in a linear model when graphed. This model is characterized by having a degree of one for each variable involved.
Imagine a hot air balloon taking off from the ground, ascending at a consistent speed. After 5 seconds, its altitude reaches 20 feet. The balloon maintains this rate of ascent.
The rate per second is calculated as follows:
m = 20/ 5
m = 4 ft/sec
Consequently, the equation is formulated as:
y = 4x
For x = 10 seconds, the corresponding y value will be:
y = 4 × 10
y = 40 ft
Similarly, for
x = 20 seconds:
y = 4 × 20
y = 80 ft
Hence, the linear equation representing the balloon's height over time is
y = 4x. The accurate option among the choices is D.
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