Answer:
1a ) N_6 = 50 mg
1b) N_3 = 70.7 mg
1c) N_1 = 89.1 mg
2) f(t) = 100e^(-0.1155t)
Step-by-step explanation:
Formula to get amount remaining is;
N_t = N_o × ½^(t/t_½)
We are given;
N_o = 100 mg
t_½ = 6 years
We have; N_t = 100(½^(t/6))
Thus;
1a) amount left after 6 years is;
N_6 = 100 × ½^(6/6)
N_6 = 50 mg
1b) amount left after 3 years is;
N_3 = 100 × ½^(3/6)
N_3 = 70.7 mg
1c) amount left after 1 year is;
N_1 = 100 × ½^(1/6)
N_1 = 89.1 mg
2) to find the function to model the amount left after t years, let's use the formula;
f(t) = f_o × e^(-rt)
Where r is decay constant
Thus;
f(t) = 100e^(-rt)
We recall that N_t = 100(½^(t/6))
Thus;
100(½^(t/6)) = 100e^(-rt)
Divide both sides by 100 to get;
(½^(t/6)) = e^(-rt)
In (½^(t/6)) = In e^(-rt)
Using power rule, we have;
(t/6) In ½ = -rt In e
-0.6931t/6 = - rt (because In e = 1)
t will cancel out to give;
r = 0.6931/6
r = 0.1155
Thus;
f(t) = 100e^(-0.1155t)
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PLEASE SOLVE THIS FOR ME ITS MY MIDTERM
your class earned 90.00 saturday afternoon by washing cars to raise money for a class trip this is 1/6 of money needed for trip what is the total amount needed
Answer:
540
Step-by-step explanation:
We need 6 times 90 for the full amount.
Answer:
Total amount = 540
Step-by-step explanation:
let total amount = x
1/6 * x = 90
x = 540
The diagram below shows how you can find the volume of the prism on the left by multiplying the number of square units in the base by the number of layers.
Answer:
24
Step-by-step explanation:
Maryam has 12 cookies. She wants to give each of her 4 friends the same number of cookies. How many cookies will Maryam give each of her friends?
Answer: your answer is 3
Step-by-step explanation: 12/4=3
Hope I helped! :)
Can someone explain how to do this for me!
Answer:
x = 90 degrees
Step-by-step explanation:
the above figure is of a circle, so the sum of the measures of angles will be 360 degrees.
measure of arc = measure of the angle inscribed by the arc
therefore, the measure of arc JK will also be x...... ( vertically opposite angles)
therefore, x + x + 30 + (2x - 30) = 360 .....(1)
therefore, 2x + 30 + 2x - 30 = 360
therefore, 4x = 360.....( as -30 and +30 will be cancelled)
therefore, x = 90 degrees
Cross correction:-
by putting in x = 90 in (1)
90 + 90 + 30 + 2*90 - 30 = 360
180 + 30 + 180 - 30 = 360
180 + 180 = 360
so, x= 90 degrees is verified.
what is the probability of flipping a coin and it lands on heads
50/50 since there are 2 sides, and 1 is heads
---
hope it helps
if f(x)=x^2 domain=[-1,2], the range is ?
A veterinarian prescribed Christy, a 31-pound dog, an antibacterial medication in case an infection emerges after her teeth were cleaned. If the dosage is 8.75 mg for every pound, how much medicine was given?
Answer:
271.25 mg
Step-by-step explanation:
The amount of medicine will be equal to 271.25 mg.
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
It is given that a veterinarian prescribed Christy, a 31-pound dog, an antibacterial medication in case an infection emerges after her teeth were cleaned. The dosage is 8.75 mg for every pound.
The amount of medicine will be calculated as below:-
Amount = 31 x 8.75
Amount = 271.25 mg
Therefore, the amount of medicine will be equal to 271.25 mg.
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Samir just finished renovating a house during the renovation he added a steel beam as a support the steel beam was 15 feet long and cost $135 complete the statement by selecting the correct dollar amount from the provided list
the cost of the beam was _______per yard
Answer:
$27
Step-by-step explanation:
According to your question. The complete cost was $135 for a fifteen feet long beam. If you are looking for the price per yard, a yard has three feet, therefore in fifteen feet, there are five yards.
15 divided into 3 equals 5
$135 divided into five equals $27
I hope this helps.
What is the recursive formula for this arithmetic sequence?
-7, -1, 5, 11, ...
Answer:
The answer is A
Step-by-step explanation:
why it is a is...
the first like is the # your arithmetic sentence starts with which is -1
the second line is what you do to get to the next #
each time you are adding 6
An arithmetic sequence is a sequence of integers with its adjacent terms differing with one common difference. The correct option is A.
What is an arithmetic sequence?An arithmetic sequence is a sequence of integers with its adjacent terms differing with one common difference.
The explicit formula for any arithmetic series is given by the formula,
[tex]a_n = a_1 + (n-1)d[/tex]
Also, the recursive formula for any arithmetic series is given by the formula,
[tex]a_n = a_{(n-1)} + d\\\\[/tex]
Or, it can be also written as,
[tex]a_{(n+1)} = a_{n} + d[/tex]
where d is the difference and a₁ is the first term of the sequence.
For the given arithmetic sequence, the common difference can be written as,
Common difference = -1 - (-7)
= -1 + 7
= 6
Now, the recursive formula for this arithmetic sequence can be written as,
[tex]a_n = a_{(n-1)} + 6[/tex]
Also, the first term of the given arithmetic series is -7.
a₁ = -7
Hence, the correct option is A.
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Mrs. Evans opens a bank account and starts to gain money at a constant rate of $3 per day. What is the total amount of money that she will gain after a week?
Answer:
$21
Step-by-step explanation:
A recipe for potato casserole calls for 7/4 cups of cheese. Write the fractions as a mixed number.
[tex]4x - {x}^{3} [/tex]
An automobile engineer is redesigning a conical chamber that was originally specified to be 12 inches long with a circular base of diameter
5.7 inches. In the new design, the chamber is scaled by a factor of 1.5.
The volume of the original chamber is
V cubic inches. This i
v cubic inches less than the volume of the new
chamber.
Answer:
the original volume is lesser than the new volume by 242.47 in³
Step-by-step explanation:
Volume of a cone is;
V = ⅓πr²h
Where;
r is radius
h is height
For the original chamber;
r = 5.7/2 = 2.85 inches
h = 12 inches
Volume of this original chamber is;
V_orig = ⅓ × π × 2.85² × 12
V_orig = 102.02 in³
In the new design, the chamber is scaled by a factor of 1.5.
Thus;
r_new = 2.85 × 1.5 = 4.275 inches
h_new = 12 × 1.5 = 18 inches
V_new = ⅓ × π × 4.275² × 18
V_new = 344.49 inch³
V_new - V_orig = 344.49 - 102.02 =
Thus, the original volume is lesser than the new volume by 242.47 in³
point b is 8 units away for the origin
Answer:
ok
Step-by-step explanation:
Outside temperature over a day can be modeled as a sinusoidal function. Suppose you know the temperature is 45 degrees at midnight and the high and low temperature during the day are 54 and 36 degrees, respectively. Assuming t is the number of hours since midnight, find an equation for the temperature, D, in terms of t.
Answer:
D = 9sin(2π(t + a)/24) + 45
Step-by-step explanation:
Let's find the average temperature;
(54 + 36)/2 = 45°
Amplitude = 54 - 45 = 9
From the wave equation, we can write the temperature as;
D = 9sin(2π(t + a)/24) + 45
Where;
D is the temperature
t is the time in hours after midnight
a is a "phase" that is used to set the time at which temperature(D) occurs
A farmer is building a fence to enclose a rectangular area consisting of two separate regions. The four walls and one additional vertical segment (to separate the regions) are made up of fencing, as shown below.
If the farmer has 234 feet of fencing, what are the dimensions of the region which enclose the maximal area?
9514 1404 393
Answer:
58.5 ft by 39 ft
Step-by-step explanation:
Let x represent the length of the two horizontal segments. Then the three vertical segments will be ...
(234 -2x)/3
The total enclosed area is the product of these dimensions:
A = (x)(234 -2x)/3
A = (2/3)(x)(117 -x)
This is the equation of a downward-opening parabola with zeros at x=0 and x=117. The maximum of the parabola will be on the line of symmetry, halfway between these zeros. The value of x there is ...
x = (0 +117)/2 = 58.5
The lengths of the vertical segments are ...
(2/3)(117 -58.5) = 2/3(58.5) = 39
The dimensions of the region enclosing the maximum area are 58.5 ft by 39 ft. The additional vertical segment is 39 ft.
_____
Comment on maximum area problems
You may have noticed that the total length of the fence allocated to the long sides (2×58.5 = 117) is half the total length of fence and is equal to the total length of fence allocated to the short sides (3×39 = 117).
This relationship is true in all rectangular fencing problems where the area is being maximized for a given total fence length. It doesn't matter how many partitions there are in either direction: the total of horizontal lengths is equal to the total of vertical lengths.
The sixth grade class is going to the local art musem's dinoaurexhibit. There was 52 students in the class. The total cost of the tickets for all the students is $364. What is the cost of one student ticket?
Find the area of the shaded portion below.
Step-by-step explanation:
the area of the half-circle:
πr² /2= 3.14* 20² /2= 3.14 * 400 /2 =1256/2=628cm²
50*80/2=2000cm²
Shaded area:
2000-628=1372cm²
Answer:
Step-by-step explanation:
The shaded area is a trapezoid minus the area of half a circle.
T=h(b1+b2)/2
T=40(50+80)/2
T=2600cm^2
Now the area of the half circle
C=(pi r^2)/2
C=(400pi)/2
C=200pi
So the shaded area is
A=2600-200pi
A=1972 (rounded to nearest 1)
Use the values listed in the table to answer the question.
Which expression is equivalent to 0?
Answer:
B. (b x d) - c
Step-by-step explanation:
i. -(a x d) + b
= -(6 x [tex]\frac{1}{2}[/tex]) + 8
= -3 + 8
= 5
ii. (b x d) - c
(8 x [tex]\frac{1}{2}[/tex]) - 4
= 4 - 4
= 0
iii. 2(b x f) + a
= 2(8 x [tex]\frac{1}{4}[/tex]) + 6
= 4 + 6
= 10
iv. (a x e) - c
= (6 x [tex]\frac{1}{3}[/tex]) - 4
= 2 - 4
= -2
Thus, the expression which is equivalent to 0 is that of option B.
8. The dimensions of a lawn shaped like a trapezoid are given in meters.
18 m
4 m
5 m
12 m
The dimensions of a lawn shaped like a trapezoid are given in meters. What is the
area of the lawn?
108 m2
60 m2
72 m2
120 m2
Answer:
60m²
Step-by-step explanation:
Area of the trapezoid attached = 1/2(a+b)*h
a and b are the opposite sides
h is the height
Given
a = 18m
b = 12m
h = 4m
Substitute
Area of the trapezoid = 1/2(18+12)*4
Area of the trapezoid = 1/2 * 30 * 4
Area of the trapezoid = 120/2
Area of the trapezoid = 60m²
Hence the area of the lawn is 60m²
can someone help I need to fill in the blank
Answer:
240
Step-by-step explanation:
The directions says determine weather each rate of change is consistent. If it is, find the rate of change and explain what it represents.
I will give you tons of brainlist
Da.mn that sucks for you
— 5 3/4 - 3 1/2
I need help fast
Answer:
-9 1/4
Step-by-step explanation:
Answer:
i also need help
Step-by-step explanation:
do it yourself
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Jenny has some tiles in a bag. The tiles are of three different colors: purple, pink, and orange. Jenny randomly pulls a tile out of the bag, records the color, and replaces the tile in the bag. She does this 50 times. The results are recorded in the given table:
Color of Tile Purple Pink Orange
Number of times the tile is drawn 6 18 26
What is the experimental probability that Jenny will pull out an orange tile?
fraction 18 over 26
fraction 24 over 26
fraction 24 over 50
fraction 26 over 50
Answer:
26/50 bc she did it 26 out of 50 times ??
Write an equation in slope-intercept form for the line with slope -3/4 and y-intercept for 3
Answer:
y=-3/4x+3
Step-by-step explanation:
The formula is y=mx+b
m is the slope
b is the y-intercept
If you plug it in, you get y=-3/4x+3
Hope this helps!
is this a function ???????
what is the slope if it goes through (0, 2) and (-2, 3)
10 x 3 thousands how many thousands are in the answer
Answer:
30 thousands, or 30,000 units.
Step-by-step explanation:
Since the question refers to 10 x 3 thousands, to determine how many thousands are in the answer, the following calculation must be performed:
10 x 3 = 30
So there are 30 thousand in the answer, which is equal to 30,000.
In a filling line at A & C Foods, Ltd., the mean fill volume for rice bubbles is 475 grams and the standard deviation is 10 grams. The design specifications are [450, 495] grams. Any output outside of design specifications is treated as non-conforming. (1) Calculate the dpmo of the process (by calculating the area of non-conformance). Please type your answer in integers.
Answer:
The dpmo of the process is of 29000
Step-by-step explanation:
Dpmo of a process:
The dpmo of a process is the number of defects per million opportunities.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
In this question:
First, using the normal distribution, we calculate the proportion of defective bubbles. Then, using this proportion, we calculate the dpmo.
Mean fill volume for rice bubbles is 475 grams and the standard deviation is 10 grams.
This means that [tex]\mu = 475, \sigma = 10[/tex]
The design specifications are [450, 495] grams. Any output outside of design specifications is treated as non-conforming.
Below 450 and Above 495 are non-conforming.
Below 450:
The proportion is the pvalue of Z when X = 450. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{450 - 475}{10}[/tex]
[tex]Z = -2.5[/tex]
[tex]Z = -2.5[/tex] has a pvalue of 0.0062
Above 495:
The proportion is 1 subtracted by the pvalue of Z when X = 495. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{495 - 475}{10}[/tex]
[tex]Z = 2[/tex]
[tex]Z = 2[/tex] has a pvalue of 0.9772
1 - 0.9772 = 0.0228
The proportion of defectives is 0.0228 + 0.0062 = 0.0290
Dpmo:
Number of defects per million, that is, the proportion multiplied by 1000000.
1000000*0.0290 = 29000
The dpmo of the process is of 29000