X=20° is your answer
Step-by-step explanation:
X+3x+10°=90°
4x+10°=90°
4x=(90-10)°
X=80/4
X=20°
A radioactive substance decays to 30% of its original mass in 15 months. Determine the half-life of this radioactive substance to the nearest tenth. Show your work.
please help
Answer:
The half-life of this radioactive substance is of 8.6 months.
Step-by-step explanation:
Exponential decay of an amount:
The equation that models an amount after t units of time, subject to exponential decay, is given by:
[tex]A(t) = A(0)(1-r)^t[/tex]
In which A(0) is the initial amount and r is the decay rate, as a decimal.
A radioactive substance decays to 30% of its original mass in 15 months.
This means that [tex]A(15) = 0.3A(0)[/tex]. We use this to find 1 - r.
[tex]A(t) = A(0)(1-r)^t[/tex]
[tex]0.3A(0) = A(0)(1-r)^{15}[/tex]
[tex](1-r)^{15} = 0.3[/tex]
[tex]\sqrt[15]{(1-r)^{15}} = \sqrt[15]{0.3}[/tex]
[tex]1 - r = (0.3)^{\frac{1}{15}}[/tex]
[tex]1 - r = 0.9229[/tex]
So
[tex]A(t) = A(0)(0.9229)^t[/tex]
Determine the half-life of this radioactive substance to the nearest tenth.
This is t for which A(t) = 0.5A(0). So
[tex]A(t) = A(0)(0.9229)^t[/tex]
[tex]0.5A(0) = A(0)(0.9229)^t[/tex]
[tex](0.9229)^t = 0.5[/tex]
[tex]\log{(0.9229)^t} = \log{0.5}[/tex]
[tex]t\log{0.9229} = \log{0.5}[/tex]
[tex]t = \frac{\log{0.5}}{\log{0.9229}}[/tex]
[tex]t = 8.6[/tex]
The half-life of this radioactive substance is of 8.6 months.
GUYS PLEASE HELP ALMOST DUE
Answer:
1/5
Step-by-step explanation:
y = 12
12 = 1/5 x 60
12= 12
y = 9
9 = 1/5 x 45
9 = 9
and so on and it always results to one fifth
Pls help, answer within 5 minutes
Answer: I thin it’s Opposite of 2
Step-by-step explanation:
Answer:
The distance between A and D
Step-by-step explanation:
when it is |-2| (in the box) it changes to 2
The text book store sold a combined total of 326 history and chemistry textbooks in a week. The number of chemistry textbooks sold was 86 less than the number of history textbooks sold. How many textbooks of each type was sold?
Answer:
The sentence
"The Number of Chem textbooks sold is 86 less than the number of History textbooks"
This seems to be the confusing part.
Now look at it this way...
'If CHM text is 86 less than History text... It also means that History Text is 86 More than CHM'
This expression can be written as
Let History Text be "H"
Let CHM text be "C"
C - 86 = H
or
C=H + 86.......1
First line of this question is interpreted thus
H + C = 326.......2
From eqn 1... C=H+86
Substitute into Eqn 2
H + C=326
H + (H+86)=326
H+H=326-86
2H=240
H=240/2
H=120.
C=H+86
C=120+86
C=206.
This answer is correct... Why?
The key statement says .. The Number of CHM sold is 86 less than History...
Also interpreted as
The Number of CHM – 86 = History
206 - 86 =120.
Have a great day!!!
find the quotient of -75 divided (-15)
Answer:
5
Step-by-step explanation:
-75 divided (-15) = 5
pls help me with this, i’ll give brainly
Answer:
shirts = 15 when pants = 6
15
Step-by-step explanation:
Try two others that are given
shirts / pants = 10 / 4 = 2.5
shirts / pants = 30/12 = 2.5
So shirts/pants = 2.5 = x/6
2.5 = x / 6 Multiply by 6
2.5 * 6 = x
x = 15
Suppose we want to choose 5 letters without replacement from 16 distinct letters
Answer:
16P5
Step-by-step explanation:
16*15*14*13*12
A rectangle has a perimeter of 14 cm and length x cm. show that the width of the rectangle is (7-x)cm and hence that the area A of the rectangle is given by the formula A= x(7-x). Draw the graph, plotting x on the horizontal axis with a scale of 2cm to 1 unit, and A on the vertical axis with a scale of 1cm to 1 unit
take x from 0 to 7. From the graph find:
a) the area of the rectangle when x = 2.25cm
b) the dimensions of the rectangle when its area is 9cm^2
c) the maximum area of the rectangle
d) the length and width of the rectangle corresponding to the maximum area
e) what shape of the rectangle has the largest area
Answer:
B
Step-by-step explanation:
the dimensions of the rectangle when its area is 9cm^2
The odds of winning a contest are approximately 5:1476. How many winners are there likely to be if there are 50000 participants?
Answer:
Approximately 169
Step-by-step explanation:
Set up as fractions and use cross multiplilcation to solve for the unknown.
These are our fractions from the information we are given; the winners represent the numerators (and x is the unknown, becuase we don't yet know how many winners there will be with 50000 participants). Note that the denominator on the first fraction is (1476 + 5) because we want it to represent TOTAL amount of particpants in the ratio:
[tex]\frac{5}{1481} = \frac{x}{50000}[/tex]
Now cross multiply by multiplying numerators and denominators that are ACROSS from each other, so 5 * 50000 and 1481 * x; now we have:
250000 = 1481x
Now to isolate x (to know its value) we need to divide both sides by 1481, and we are left with:
168.8 = x
But I rounded up to 169.
Select the correct answer.
Which statement best defines the term principal?
OA.
It is an arrangement in which you buy now and pay later.
ов.
It is the annual rate of interest a bank charges for a loan.
OC.
It is the original amount of money the bank loans the borrower.
Help me plz
Answer:
C
Step-by-step explanation:
the bank loans the borrower
hope it help
A clothing vendor estimates that 78 out of every 100 of its online customers do not live within 50 miles of one of its physical stores. Using this estimate, what is the probability that a randomly selected online customer does not live within 50 miles of a physical store? .78 .50 .28 .22
Answer:
[tex]p' = 0.22[/tex]
Step-by-step explanation:
Given
[tex]p = \frac{78}{100}[/tex]
Required
Probability that a [tex]customer[/tex] does [tex]not[/tex] live [tex]within[/tex] [tex]50[/tex] miles
To do this, we make use of complement rule;
Which states that:
[tex]p + p' = 1[/tex]
Make p' the subject
[tex]p' = 1 - p[/tex]
So, we have:
[tex]p' = 1 - \frac{78}{100}[/tex]
Express fraction as decimal
[tex]p' = 1 - 0.78[/tex]
[tex]p' = 0.22[/tex]
medical research team is conducting a study to determine whether there is a relationships between aerobic walking and cholesterol levels. A random sample of 315 subjects is selected and represented in the table below. Test the claim that walking and cholesterol levels are related. Include appropriate statistical evidence to support your findings.
Answer:
Chi-Square and Linearization ... A random sample of 315 subjects is selected and represented in the table below. ... claim that aerobic walking and cholesterol levels are related.
the nearest 100 of 87682
What is the growth factor for 233% growth
Answer:
Here is what you do. Make it into vertex form and then whatever the x factor is is the growth factor
If f(x)
2x + 3, find f(-2)
Answer:
2x+3
f(-2)=:2x+3
2(-2)+3
-4+3
= -1
Please help me find x and y
Answer:
x = 33
y = 5
Step-by-step explanation:
Line BD splits AC in half so y is also 5Since the triangles are congruent (is known because of the congruence lines) and you know two angles you can find x57+90=147 and 180-147= 33 which is xWhat is 0.325 written as a percent?
Answer:
32.5%
Step-by-step explanation:
Answer:
32.5
Step-by-step explanation:
divided by 100 to get percentage
An artist buys a square canvas with a side length of 2.5 feet. What is the area of the canvas. Please help im on a test ;)
Answer:
The area of the canvas must be 30 feet.
Step-by-step explanation:
Find the first term and the common ratio of the following geometric
sequence: 8, 16, 32, ...
Answer:
The first term is 8
The common ratio is 2, because the ratio of 8:16 is 1:2 and the ratio of 16:32 is 1:2
Step-by-step explanation:
Answer:
The common ratio of the following geometric sequence is x2 everytime.
It’s simple math I’m just confused
Answer:
26 units
Step-by-step explanation:
make a proportion: so sides correspond alongside eachother.
so, 15/10 =24/Y, i know you need to solve for x, but you have to find the other blank length.
now cross multiply, 10*24=15*Y
240=15Y
240/15=
Y= 16
now add Y to the length 10 to get X. So you get 10+16=26
The radius of a circle is 18 millimeters. What is the circle's area?
Area = π × ( radius )^2
Area = π × ( 18 )^2
Area = π × 324
Area = 324 π mm^2
Find the first five terms that correspond with the following expression.
4n + 2
Answer:
6,10,14,18,22
Step-by-step explanation:
4n+2
Let n=1 4(1)+2 = 4+2 = 6
Let n=2 4(2)+2 = 8+2 = 10
Let n=3 4(3)+2 = 12+2 = 14
Let n=4 4(4)+2 = 16+2 = 18
Let n=5 4(5)+2 = 20+2 = 22
Fill in the missing values for this sequence of numbers.
Identify the start value and operation.
92, 110, ___, 146, ___, ___
92, 110, 128, 146, 164, 182. ✅
[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\orange{:}}}}}[/tex]
[tex]92,110,128,146,164,182 \\ ➵ \: 92 + 18 = 110 \\ ➵ \: 110 + 18 = 128 \\ ➵ \: 128 + 18 = 146 \\ ➵146 + 18 = 164 \\ ➵ \: 164 + 18 = 182[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\orange{Happy\:learning }}{\orange{.}}}}}[/tex]
Does y= x represent a function
for what value of x is the equation 2x-3 over -3+4 =3 true
Answer:5
Step-by-step explanation:
......
Can anyone help me find the function for this trig graph ? i need a specific answer for the function , 50 pts
Answer:
y = 5 sin (2x) + 4
Step-by-step explanation:
this is sines function,
the amplitude is [9 - (-1)]/2 = 10/2 = 5
the period is 2πx/π = 2x
the x-axis of actual function is at y = 4
so, the function is :
y = 5 sin (2x) + 4
-1/5 and +7 equals two
what is the question?? because this equation is false?
A landowner wants to find the distance d across a pond. The two overlapping right triangles are similar . Using the measurements shown , what is d?
Answer:
96 m
Step-by-step explanation:
It is given that the two overlapping triangles are similar in the figure.
The landowner wishes to find the distance across the pond. The distance is d.
From the figure, since the two triangles are similar, therefore we can write :
[tex]$\frac{d}{(24+40)}=\frac{60}{40}$[/tex]
[tex]$\frac{d}{64}=\frac{60}{40}$[/tex]
[tex]$d = \frac{60}{40} \times 64$[/tex]
[tex]$d = \frac{6}{4} \times 64$[/tex]
d = 6 x 16
= 96 m
Therefore, the distance across the pond is d = 96 m
What is the approximate volume of the cone
below?
Answer:
183 cm³
Step-by-step explanation:
V(cone) = 1/3πr²h
= (π5²·7) ÷ 3
= 175π ÷ 3
≈ 58π or 183 cm³
BONUS 1) You take the Math Time Machine into the past to save Julius Caesar and fix the calendar,
but you miss your timestamp and end up in Alexandria a few years early. You wander around before
ending up in front of the Great Library of Alexandria, which is guarded by a sphinx - known in
mythology for their tricky riddles. When you ask the sphinx what year it is, it refuses to answer
unless you solve a math problem. The sphinx shows you a right triangle with a base of 8 and a height
of 6, which you know has an area of 24. Then it tells you that if you that you can remove some
length x off of the 8 side, but if you do that you must add a rectangle under the 8 side with a height
equal to x, thus creating a trapezoid. How much length must you remove from the 8 side so the
trapezoid has the same area as the original triangle? X = 0 doesn't count.
a) X = 2
b) X = 3
c) X = 4
d) X = 5
Answer:
Gracias por los puntos :D