Answer:
It would take 74.5 minutes for the element to decay 17 grams.
Step-by-step explanation:
The amount of element X after t minutes is given by the follwoing equation:
[tex]X(t) = X(0)e^{rt}[/tex]
In which X(0) is the initial amount of the substance and r is the decay rate.
Half life of 14 minutes.
This means that [tex]X(14) = 0.5X(0)[/tex]
So
[tex]X(t) = X(0)e^{rt}[/tex]
[tex]0.5X(0) = X(0)e^{14r}[/tex]
[tex]e^{14r} = 0.5[/tex]
[tex]\ln{e^{14r}} = \ln{0.5}[/tex]
[tex]14r = \ln{0.5}[/tex]
[tex]r = \frac{\ln{0.5}}{14}[/tex]
[tex]r = -0.0495[/tex]
So
[tex]X(t) = X(0)e^{-0.0495t}[/tex]
There are 680 grams of element X
This means that [tex]X(0) = 680[/tex]
[tex]X(t) = X(0)e^{-0.0495t}[/tex]
[tex]X(t) = 680e^{-0.0495t}[/tex]
How long would it take the element to decay 17 grams
This is t for which X(t) = 17. So
[tex]X(t) = 680e^{-0.0495t}[/tex]
[tex]17 = 680e^{-0.0495t}[/tex]
[tex]e^{-0.0495t} = \frac{17}{680}[/tex]
[tex]e^{-0.0495t} = 0.025[/tex]
[tex]\ln{e^{-0.0495t}} = \ln{0.025}[/tex]
[tex]-0.0495t = \ln{0.025}[/tex]
[tex]0.0495t = -\ln{0.025}[/tex]
[tex]t = -\frac{\ln{0.025}}{0.0495}[/tex]
[tex]t = 74.5[/tex]
It would take 74.5 minutes for the element to decay 17 grams.
Which expression is equivalent to 2(3x − 1.75) − 3(1.5x − 2.5)?
Answer:
1.5x+4
Step-by-step explanation:
Step-by-step explanation:
Step 1: Distribute
[tex]2(3x - 1.75) - 3(1.5x - 2.5)[/tex]
[tex](2 * 3x) + (2 * -1.75) + (-3 * 1.5x) + (-3 * -2.5)[/tex]
[tex](6x) + (-3.5) + (-4.5x) + (7.5)[/tex]
Step 2: Combine like terms
[tex](6x - 4.5x) + (7.5 - 3.5)[/tex]
[tex]1.5x + 4[/tex]
Answer: [tex]1.5x + 4[/tex]
2x + 3y = 12
Complete the missing value in the solution to the equation.
,8)
i need help with this problem x/56=7/8 Thank you
[tex] \dfrac{x}{56} = \dfrac{7}{8} \\ x = \dfrac{56 \times 7}{8} \\ x = 49[/tex]
You roll a six-sided number cube (die). What is the BEST answer for the probability that the number rolled is between 1 and 6, inclusive?
A) certain
B) unlikely
C) impossible
D) very likely
Answer: It is A certain.
Step-by-step explanation:
Because all the numbers on a six-sided cube is between 1 and 6 so it is certain or 100/100 that the number will land on a number between 1 and 6.
Suppose the round-trip airfare between Philadelphia and Los Angeles a month before the departure date follows the normal probability distribution with a mean of $387.20 and a standard deviation of $68.50. What is the probability that a randomly selected airfare between these two cities will be between $325 and $425?
Answer:
52.74% probability that a randomly selected airfare between these two cities will be between $325 and $425
Step-by-step explanation:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.
In this question, we have that:
[tex]\mu = 387.20, \sigma = 68.50[/tex]
What is the probability that a randomly selected airfare between these two cities will be between $325 and $425?
This is the pvalue of Z when X = 425 subtracted by the pvalue of Z when X = 325. So
X = 425
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{425 - 387.20}{68.50}[/tex]
[tex]Z = 0.55[/tex]
[tex]Z = 0.55[/tex] has a pvalue of 0.7088
X = 325
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{325 - 387.20}{68.50}[/tex]
[tex]Z = -0.91[/tex]
[tex]Z = -0.91[/tex] has a pvalue of 0.1814
0.7088 - 0.1814 = 0.5274
52.74% probability that a randomly selected airfare between these two cities will be between $325 and $425
The owner of a bicycle store had a sale on bicycles (two-wheelers) and tricycles (three-wheelers). Each cycle had two pedals. When he counted the total number of pedals of the cycles, he got 50. When he counted the total number of wheels of the cycles, he got 64. Explain how you figured out how many tricycles were offered in the sale.
Let x represent number of bicycles and y represent number of tricycles.
We know that a bicycle has 2 pedals and a tricycle has 32 pedals as well.
We have been given that when the owner counted the total number of pedals of the cycles, he got 50. We can represent this information in an equation as:
[tex]2x+2y=50...(1)[/tex]
[tex]2x=50-2y...(1)[/tex]
We know that a bicycle has 2 wheels and a tricycle has 3 wheels.
We have been given that when the owner counted the total number of wheels of the cycles, he got 64. We can represent this information in an equation as:
[tex]2x+3y=64...(2)[/tex]
Upon substituting equation (1) in equation (2), we will get:
[tex]50-2y+3y=64[/tex]
[tex]50+y=64[/tex]
[tex]50-50+y=64-50[/tex]
[tex]y=14[/tex]
Therefore, 14 tricycles were offered in the sale.
Figure A is translated 3 units right and 2 units up. The translated figure is labeled figure B. Figure B is reflected over the x-axis. The reflected figure is labeled figure C. Which best explains why figure A is congruent to figure C? On a coordinate plane, triangle A has points (1, negative 2), (3, negative 2), (3, negative 5). Triangle B has points (4, 0), (6, 0), (6, negative 3). Triangle C has points (4, 0), (6, 0), (6, 3). A Is congruent to B and B Is congruent to C A Is congruent to A, B Is congruent to B, C Is congruent to C Each triangle is a right triangle. Each triangle is an isosceles triangle.
Answer:
A Is congruent to B and B Is congruent to C
Step-by-step explanation:
Let's look at the answer choices:
A: "A Is congruent to B and B Is congruent to C"
Well, clearly, if A ≅ B and B ≅ C, then by the transitive property, we can say that A ≅ C. So, A is very likely correct.
B: "A Is congruent to A, B Is congruent to B, C Is congruent to C"
Just because A is congruent to itself (and same with B and C) doesn't necessarily mean that they're congruent to each other. So, B is wrong.
C: "Each triangle is a right triangle."
Again, there are so many right triangles out there with different dimensions. For example, there are some with sides 3, 4, and 5, and others with sides 5, 12, and 13. They are not congruent, however. So, rule out C.
D: "Each triangle is an isosceles triangle."
This is just like choice C since there are so many variations of isosceles triangles. So D is wrong.
The answer is thus A.
Answer:
First one:
A Is congruent to B and B Is congruent to C
Step-by-step explanation:
Since B is obtained by translating A, it has the same measure angles and sides as A, hence B is congruent to A
C is obtained by reflecting B, which doesn't alter the measure of sides and angles, so C is congruent to B
Therefore by transition, C is congruent to A
What is the vertex of the graph of the function f(x) = x2 + 8x - 2 ?
(-4, 18)
(0, -2)
(-8, -2)
(-4, -18)
Answer: (-4,-18)
Step-by-step explanation: If you use desmos you can graph the equation to find the vertex.
The vertex of the graph of function f(x) = x² + 8x - 2 is (-4, -18)
What is the vertex of the graph of a quadratic function?In a quadratic function, the vertex of the graph refers to the highest or lowest possible outcome of the function. In a graph, the vertex is the highest or lowest point on the parabola,
Given that:
f(x) = x² + 8x - 2
where;
a = 1b = 8c = - 2By using the vertex formula to find the x-value;
[tex]\mathbf{x = \dfrac{-b}{2a}}[/tex]
[tex]\mathbf{x = \dfrac{-8}{2(1)}}[/tex]
x = -4
So,
y = (-4)² + 8(-4) - 2
y = 16 -32 -2
y = -18
Therefore, the vertex of the graph of function f(x) = x² + 8x - 2 is (-4, -18)
Learn more about the vertex of the graph function here:
https://brainly.com/question/1305555
#SPJ2
Which is a solution of the system of equations shown?
A. (−4, 0)
B. (2, −4)
C. (0, −2)
D. (2, 0)
Answer:
D. (2, 0)
Step-by-step explanation:
The solutions are the two points of intersection of the graphs:
(-2, -4) and (2, 0)
The latter of these corresponds to choice D, the one you have marked.
PLEASE HELP ME:)
(50points)
WILL MARK THE BRAINLIEST !!
Answer:
3. L(15055) is the number of pages ...
4. true
Step-by-step explanation:
3. The problem tells you that L( ) is a function of the number of words. (That means the number in parentheses in L( ) is a word count.) The first two answer choices describe the function as being of a number of pages, so are incorrect. The last answer choice matches the description of the function.
__
4. Compound interest represents a growth function. Account values in later years will be more than values in earlier years. So ...
D(2) < D(7) is TRUE
Can someone help me please
To the nearest tenth of a cubic centimeter, what is the volume of
the sphere if r = 17 cm?
Answer:
V≈20579.53
Step-by-step explanation:
[tex]V=\frac{4}{3} \pi r^3[/tex]
David is preparing a report to show
Answer:
cool?
who's david den
Step-by-step explanation:
Answer:
He shoud use a table or chart.
Step-by-step explanation:
I answered this question before
During Ashland High School basketball games, the snack bar sells both cheese and pepperoni pizza slices. Last night, the snack bar sold 143 slices of pizza. They sold 10 times as many pepperoni slices as cheese slices.
How many slices of cheese pizza did the snack bar sell last night?
slices of cheese pizza
Answer:
13 slices of cheese pizza
Step-by-step explanation:
Consider grouping the slices so there are 10 pepperoni and 1 cheese in each group of 11. Then 143 slices represents 143/11 = 13 groups. Since there is 1 cheese slice in each group, ...
13 slices of cheese pizza were sold
There are 12 inches in 1 foot. Write 75 inches in feet and inches
Answer:6.25
Step-by-step explanation:
Plz help ..............!!!!!
Answer:
1.8
is the median
Answer: 1.8
Step-by-step explanation: 1.8 is the median
Which expression is equivalent to m n + z?
n m + n
z + m z
m z + n
z + n m
Answer:
z + n m
Step-by-step explanation:
These expressions are equivalent because the commutative property of addition, which states that when adding two terms, the order doesn't matter.
If this answer is correct, please make me Brainliest!
Answer:
It's "c"
Step-by-step explanation:
i just did this on edge
A celebrity called Wayne East has been having some money problems recently. He is thinking of investing in the greatest record in the world, and wants to know how the value will change over time. He has an exponential regression model where his predictor is time in months, and response variable is money, measured in thousands of dollars. The alpha value is 4.2, and beta is 1.03. Based on this model, how much money (in thousands) will he have after six months
Answer:
Wayne west would have $5,015 in six months
Step-by-step explanation:
The formula for exponential regression model is y = αβˣ
Where y is amount of money in 1000 dollars
x is time in months
We are given that α = 4.2 and β = 1.03 and x = 6 months
Therefore, based on this model, y = αβˣ, the amount he would have in 6 months, y = [tex]4.2*(1.03) ^{6}[/tex]
y = 5.015 × 1000 = $ 5,015
9. The circumference of a circle is 601 cm. What is the diameter of the circle?
O 120 cm
90 cm
30 cm
60 cm
Answer:191.4 cm
Step-by-step explanation:
Circumference=601 cm
π=3.14
Diameter=circumference ➗ π
Diameter=601 ➗ 3.14
Diameter=191.4 cm
Solve.
A European swallow flies about 12 meters in 1 second.
How many kilometers could it fly in 15 minutes?
It could fly |
Answer:
It could fly 10,8 kilometers.
Step-by-step explanation:
The European swallow fly speed is 12 meters per second.
We have to calculate how many kilometers it could fly in 15 minutes.
This can be calculated using the equivalent factors for each of the units:
- 1 km is equivalent to 1,000 meters.
- 1 minute is equivalent to 60 seconds.
We know that the distance travelled by the fly is the product of the speed and the time, so we have:
[tex]D=v\cdot t\\\\\\D=12\,\dfrac{m}{s}\cdot15\, min\\\\\\D=12\,\dfrac{m}{s}\cdot(\dfrac{1\,km}{1,000\,m})\cdot15\, min\cdot (\dfrac{60\,s}{1\,min})\\\\\\D=\dfrac{12\cdot 15\cdot 60}{1,000}\,km=\dfrac{10,800}{1,000}\,km\\\\\\D=10,8 \,km[/tex]
lan ran 24 laps in a charity run and then walked 0.2 kilometer to the presentation table the total; distance lan traveled was 29.6 kilometer what was the distance of each lap explain how you solve the problem
Answer:
Step-by-step explanation:
1.225km is equal to each laps
Step-by-step explanation:
Since Kristy total distance traveled = 29.6km
And Kristy ran 24 laps and later walk 0.2km. it simply implies that
Total distance traveled = distance covered running + distance covered walking
Since we know that
Total distance traveled = 29.6km
distance covered running = 24 laps
distance covered walking = 0.2km
Distance covered running in km = total distance traveled - distance covered walking
Distance covered running in km = 29.6km - 0.2km = 29.4km.
To now find the distance for each lap.
Since we have:
Distance covered running in km = 29.4km.
Distance covered running in lap = 24 laps
i.e
24 laps = 29.4km
1 lap = x
Use cross-multiple
24 laps * x = 29.4km × 1 lap
x = 29.4km / 24
x = 1.225km
Therefore
1.225km is equal to each laps.
Answer:1.225km is equal to each laps
Step-by-step explanation:
The length of a rectangle is seven less than twice the length of its width. If the area of the rectangle is 15 square meters, find the value of x.
Answer:
Length is 3 meters and the Width is 5 meters
Step-by-step explanation:
L*W=15
L=2W-7
(2W-7)W=15
[tex]2W^{2} -7W=15\\2W^{2} -7W-15=0[/tex]
(2W+3)(W-5)=0, don't use (2W+3)=0, because it gives you a negative dimension.
W=5, L=3
What’s the correct answer for this?
Answer:
A.
Step-by-step explanation:
tan x= 6/8
usually tan θ = perpendicular / base
So,
we get perpendicular = 6, base = 8
Now using Pythagorean Theorem to find hypotenuse
hyp² = base² + Perp²
hyp² = 8² + 6²
hyp²= 64 + 36
hyp²=100
Taking sq root on both sides
hypotenuse = 10
Now
sin θ = Perpendicular / Hyp
sin x = 6 / 10
Now
cos θ = base / Hyp
cos x = 8 / 10
4 ÷ 1/5 = 20 because
Step-by-step explanation:
BECAUUUUSE ;
[tex]4 \div \frac{1}{5} = 20 \\ \frac{4}{1} \div \frac{1}{5} = 20 \\ \frac{4}{1} \times \frac{5}{1} = 20 \\ \frac{20}{1} = 20[/tex]
Answer:Because the divide sign change to multiplication sign, and when this happens denominator in the right hand side will become numerator,while the formal numerator will become denominator.
Step-by-step explanation:
4 ➗ 1/5
4 x 5/1=20
If a zero is
then the graph of its function only touches the x-axis at that zero.
Ifa zero is
then the graph of its function crosses the x-axis at that zero.
Answer: The first one is of even multiplicity and the second one is of odd multiplicity.
Answer:
even
odd
Step-by-step explanation:
Is z = 5 in the solution set of the inequality 6z > 15
YES
OR
NAA
Answer:
Yes
Step-by-step explanation:
6z > 15
z > 15/6
z > 2.5
So all numbers greater than 2.5 is in the solution set of the inequality 6z > 15.
For the past 50 days, daily sales of laundry detergent in a large grocery store have been recorded (to the nearest 10). Units sold Number of Times. 30 8 40 12 50 15 60 10 70 5 a). Determine the relative frequency for each number of units sold. Please show your work on EXCEL. b). Suppose that the following random numbers were obtained using Excel .12 .96 .54 .55 .66 .77 .88 .99 .33. 304894 Use these random numbers to simulate 10days of sales. Please show your work on EXCEL.
Answer:
The answer to this question can be described as follows:
Step-by-step explanation:
Please find the attachment
Find the area of a semi-circle with radius, r = 83cm.
Give your answer rounded to 1 DP.
how many square feet of of outdoor carpet will we need for this hole?
Answer:
To convert the feet to square feet we have to multiply the length by the width. In which, we should get the answer as well.
Our length is 2ft, since it's a rectangle the other side is 2ft as well.
The width is 3ft, and the other half is 3ft.
So, basically to get the area of the hole, it'd be 3*2=
Which, it's 6sq ft.
Step-by-step explanation:The actual answer is 36. If I am wrong i am sorry ;3
HELP ME ASAP! Will give BRAINLIEST! Please read the question THEN answer correctly! No guessing.
Answer:
C. x=2 ± √13
Explanation:
