1. Drag the cards so that each number sentence is true. (You will have one card left over.)
2. Describe your thinking.
Answers
The figures paired are given as follows:
| -3| = 3
|-2| > 1
0 < |-1|
The left over is 2. This is based on the principle of absolute values.
What is absolute values?The absolute value (or modulus) of a real number x is its non-negative value regardless of its sign. For example, 5 has an absolute value of 5, and 5 has an absolute value of 5.
A number's absolute value can be conceived of as its distance from zero along the real number line.
As a result, the absolute value of -3 is 3, which suggests that |-3| = 3.
-2 in absolute terms equals 2. That is |-2| greater than 1.
the inverse value of -1 equals 1. This equals 0 |-1|.
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Related Questions
NO LINKS!!! URGENT HELP PLEASE!!!
3. A virus has infected 400 people in the town and is spreading to 25% more people each day. Write an exponential function to model this situation, then find the number of 3000 people are infected.
4. The population of a small town was 10,800 in 2002. Since then, the population has decreased at a rate of 2.5% each year. Write an exponential function to model the situation, then find when the popuation reaches half the 2002 value?
Answers
Step-by-step explanation:
3. Let P(t) be the number of people infected by the virus at time t (in days). We can model the situation with the following exponential function:
P(t) = 400 * 1.25^t
Here, 400 represents the initial number of infected people, and 1.25 represents the growth factor, since the virus is spreading to 25% more people each day.
To find the number of people infected after t days, we can substitute t = (log(3000) - log(400)) / log(1.25) into the equation:
P(t) = 400 * 1.25^t
P(t) = 400 * 1.25^((log(3000) - log(400)) / log(1.25))
P(t) ≈ 2,343
Therefore, approximately 2,343 people are infected when the total number of infections reaches 3000.
4. Let P(t) be the population of the town at time t (in years). We can model the situation with the following exponential function:
P(t) = 10,800 * 0.975^t
Here, 10,800 represents the initial population in 2002, and 0.975 represents the decay factor, since the population is decreasing at a rate of 2.5% each year.
To find when the population reaches half the 2002 value, we can set P(t) = 5,400 and solve for t:
5,400 = 10,800 * 0.975^t
0.5 = 0.975^t
log(0.5) = t * log(0.975)
t ≈ 28.2
Therefore, the population will reach half the 2002 value in approximately 28.2 years, which corresponds to the year 2030.
Answer:
3) 9.03 days
4) 27.38 years
Step-by-step explanation:
Question 3To model the spread of the virus over time, we can use an exponential function in the form:
[tex]\large\boxed{P(t) = P_0(1 + r)^t}[/tex]
where:
P(t) is the number of infected people after t days.P₀ is the initial number of infected people.r is the daily growth rate (as a decimal).t is the time elapsed (in days).Given the virus has infected 400 people in the town and is spreading to 25% more people each day:
P₀ = 400r = 25% = 0.25Substitute these values into the formula to create a function for P in terms of t:
[tex]P(t) = 400(1 + 0.25)^t[/tex]
[tex]P(t) = 400(1.25)^t[/tex]
To find how many days it will take for 3000 people to be infected, set P(t) equal to 3000 and solve for t:
[tex]\begin{aligned}P(t)&=3000\\\implies 400(1.25)^t&=3000\\(1.25)^t&=7.5 \\\ln (1.25)^t&=\ln(7.5)\\t \ln (1.25)&=\ln(7.5)\\t &=\dfrac{\ln(7.5)}{\ln (1.25)}\\t&=9.02962693...\end{aligned}[/tex]
Therefore, it will take approximately 9.03 days for the virus to infect 3000 people, assuming the daily growth rate remains constant at 25%.
Note: After 9 days, 2980 people would be infected. After 10 days, 3725 people would be infected.
[tex]\hrulefill[/tex]
Question 4To model the population of the town over time, we can use an exponential function in the form:
[tex]\large\boxed{P(t) = P_0(1 - r)^t}[/tex]
where:
P(t) is population after t days.P₀ is the initial population.r is the annual decay rate (as a decimal).t is the time elapsed (in days).Given the initial population was 10,800 and the population has decreased at a rate of 2.5% each year:
P₀ = 10,800r = 2.5% = 0.025Substitute these values into the formula to create a function for P in terms of t:
[tex]P(t) = 10800(1 -0.025)^t[/tex]
[tex]P(t) = 10800(0.975)^t[/tex]
To find how many days it will take for the population to halve, set P(t) equal to 5400 and solve for t:
[tex]\begin{aligned}P(t)&=5400\\\implies 10800(0.975)^t&=5400\\(0.975)^t&=0.5 \\\ln (0.975)^t&=\ln(0.5)\\t \ln (0.975)&=\ln(0.5)\\t &=\dfrac{\ln(0.5)}{\ln (0.975)}\\t&=27.3778512...\end{aligned}[/tex]
Therefore, it will take approximately 27.38 years for the population to reach half the 2002 value, assuming the annual decay rate remains constant at 2.5%.
PLS HELP ME OUT MARKING AS BRAINlist
Answers
Answer:
The answer is 176
Step-by-step explanation:
First lets find the area of rectangle by multiplying 16 by 8 to get 128.
Now lets find the area of each triangle. We know that one side is 6 cm and the base of both is 16.
So to find the base of one triangle we divide 16 by 2 to get 8.
Now we know that the base of one triangle is 8, so lets sub. that into the equation for a triangle. 1/2(b)(h) to get
1/2(6)(8)=24
Since there are two triangle 24+24=48 for area of both triangles
Now lets add that to the answer for the rectangle to get area for whole structure
128+48 = 176
So the answer is 176
HOPE THAT HELPS :)
Pretest: Unit 5
Question 6 of 25
If a sample proportion is 0.65, which range of possible values best describes
an estimate for the population parameter?
OA. (0.6, 0.69)
B. (0.65, 0.7)
O C. (0.5, 0.89)
OD. (0.5, 0.8)
SUBMIT
Answers
The range of possible values for the population parameter can be estimated using the margin of error, which is calculated as the critical value times the standard error.
Assuming a 95% confidence level, the critical value is approximately 1.96. The standard error for a sample proportion can be calculated as:
SE = sqrt[(p * (1 - p)) / n]
Where p is the sample proportion and n is the sample size. Substituting the values given in the question, we get:
SE = sqrt[(0.65 * 0.35) / n]
We do not know the sample size, so we cannot calculate the standard error exactly. However, we can use a rule of thumb that states that if the sample size is at least 30, we can use the normal distribution to estimate the margin of error.
With a sample proportion of 0.65, the margin of error can be estimated as:
ME = 1.96 * sqrt[(0.65 * 0.35) / n]
We do not know the sample size, so we cannot calculate the margin of error exactly. However, we can use the rule of thumb that a margin of error of about ±5% is typical for a 95% confidence level.
Using this margin of error, we can construct the following range of possible values for the population parameter:
0.65 ± 0.05
This range can be expressed as (0.6, 0.7), which corresponds to option A.
Therefore, the correct answer is option A) (0.6, 0.69).
Please help I’ll mark you as brainliest if correct!
Answers
Using similar side theorem, the side with equivalent proportion to the given side is RQ/SQ
What is similar side theorem?Similar triangles are triangles that have the same shape, but their sizes may vary. All equilateral triangles, squares of any side lengths are examples of similar objects. In other words, if two triangles are similar, then their corresponding angles are congruent and corresponding sides are in equal proportion.
In this problem, we can use this same theory to find the equivalent side of the given proportion.
OQ / PQ = RQ / SQ
The equivalent side is RQ/SQ
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Explain why you cannot use the product of powers property to simplify (3z + y)^3. Be specific.
Any badd answer will be reported
Answers
The product of powers of exponents cannot be used to simplify the binomial expansion
Given data ,
Let the binomial expansion be represented as A
A = ( 3z + y )³
According to the property of products of powers, exponents can be multiplied when a power is increased to a higher power.
The product of powers characteristic cannot be applied to the equation (3z + y)³. This is due to the fact that (3z + y)³ is a binomial raised to the power of 3, not just a power of a single word.
These terms cannot be simplified further using the product of powers property because they involve different variables or variable combinations.
In this case, it is more appropriate to expand the expression using the binomial expansion
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What is the end behavior of this radical function? f(x) = -2½ + 7
Answers
Answer:
Step-by-step explanation:
The function you provided, f(x) = -2.5 + 7, represents a linear function rather than a radical function. A linear function has a constant slope and a constant y-intercept.
The end behavior of a linear function is determined by its slope. In this case, the slope of the function is 0 since there is no term involving x. When the slope is 0, it means the function is a horizontal line.
The function f(x) = -2.5 + 7 represents a horizontal line at y = 4.5. As x approaches positive infinity (∞) or negative infinity (-∞), the value of y remains constant at 4.5. Therefore, the end behavior of this linear function is that y approaches 4.5 as x approaches both positive and negative infinity.
In conclusion, the end behavior of the function f(x) = -2.5 + 7 is that y approaches 4.5 as x approaches positive and negative infinity.
jasmine bikes the same distance every day. in 8 days, she biked a total of 32 miles. How far will she bike in 5 days?
Answers
Answer:
20
Step-by-step explanation:
She biked an equal amount each day for 8 days to a total of 32 miles. We can write that as 8x = 32. 32/8 = 4 so x = 4. To find how much shell bike in 5 days, we multiply it by x(4). 5*4 = 20.
Which model represents the expression 87 - 42?
Answers
The model that represents the expression 87 - 42 is (d)
Identifying the model that represents the expression 87 - 42?From the question, we have the following parameters that can be used in our computation:
87 - 42
Using their place values, we have
87 = 8 tens 7 units
42 = 4 tens 2 units
This means that
87 - 42 = 8 tens 7 units - 4 tens 2 units
Subtract the tens
87 - 42 = 4 tens 7 units - 2 units
Subtract the units
87 - 42 = 4 tens 5 units
The model that represents the expression 87 - 42 is 4 tens 5 units
This is represented by model (d) bottom right
Hence, the model that represents the expression 87 - 42 is (d)
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(10)
In 2008, the average new car price was approximately $27,700. In 2010,
the average new car price had increased to $29,200. Assuming a linear
relationship, what will be the approximate new car price in 2014?
A $33,700
B. $32,200
C. $30,700
D. $29,950
Answers
The approximate price of the new car in 2014 is:
B. $32,200
How to find the approximate new car price in 2014?The general form of a linear equation is given by:
y = mx + c
where y is the future price of the car, x is the number of years, m is the rate of change of price and c is the initial price of the car
c = $27,700
m = ($29,200 - $27,700)/(2010 - 2008)
m = 1500/2
m = $750 per year
In 2014, x = 2014 - 2008 = 6 years
Substituting into y = mx + c:
y = 750(6) + 27,700
y = 4500 + 27700
y = $32,200
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How is the graph of y(x-1)²-3 transformed to produce the graph of y(x+4)²
O The graph is translated left 5 units, compressed vertically by a factor of 2, and translated up 3 units.
O The graph is stretched vertically by a factor of 2, translated left 5 units, and translated up 3 units.
The graph is translated left 5 units, compressed horizontally by a factor of 2, and translated down 3 units.
O The graph is stretched horizontally by a factor of 2, translated left 5 units, and translated down 3 units.
Mark this and return
Save and Exit
Next
Submit
Answers
The transformations are:
Shift up 3 units.
Shift left 5 units.
Vertical compression of scale factor 2.
The correct option is the first one.
Here, we have,
Here we start with the original function:
y = (x - 1)^2 - 3
And it will be transformed into the new function:
y = (1/2)*(x + 4)^2
So let's start with the first function, and apply transformations until we reach the new one.
y = (x - 1)^2 - 3
If we shift it up by 3 units, then we get:
y = [ (x - 1)^2 - 3 ] + 3 = (x - 1)^2
If now we shift it to the left 5 units, then we get:
y = ( (x + 5) - 1)^2 = (x + 4)^2
finally, we compress the graph by a factor of 2, so we get:
y = (1/2)*(x + 4)^2
The order may be different, but from that we conclude that the correct option is the first option.
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complete question:
graph of y = (x- 1)2 -3 transformed to produce the graph of y = - 1/2(X+-4)2?
O The graph is translated left 5 units, compressed vertically by a factor a of 2, and translated up 3 units.
The graph is stretched vertically by a factor of 2, translated left 5 units, and translated up 3 units.
• The graph is translated left 5 units, compressed horizontally by a factor of 2, and translated down 3 units.
• The graph is stretched horizontally by a factor of 7, translated left 5 units, and translated down 3 units:
WHAT IS THE FIRST STEP TO SOLVE 3(4x + 5) = 12
Answers
Multiplying 3 by each term inside the parentheses, we get:
12x + 15 = 12
Me mason likes to work around the yard during the weekends
Answers
A) One way to write mixed fractions [tex]6\frac{2}{4} \\[/tex] is 3 + 3 + [tex]\frac{1}{4}[/tex] +[tex]\frac{1}{4}\\[/tex]
B) Saturday: 3 to 4 hours work = trim bushes and weed garden
Sunday: 4 to 5 hour work = paint sheet and mow lawn
A) [tex]6\frac{2}{4} \\[/tex] can be written as a simple fraction 6 + [tex]\frac{2}{4}[/tex]
This can be further broken into and written as
3 + 3 + [tex]\frac{1}{4}[/tex] +[tex]\frac{1}{4}\\[/tex]
B) Saturday : 3 to 4 hours of work
Trim bushes + Weed garden
[tex]1\frac{1}{6} +2\frac{2}{6}[/tex]
1 + [tex]\frac{1}{6}[/tex] + 2+ [tex]\frac{2}{6}\\[/tex]
3 + [tex]\frac{3}{6}[/tex]
3 + [tex]\frac{1}{2}[/tex]
[tex]3\frac{1}{2}[/tex]
Sunday: 4 to 5 hours of work
Paint sheet + mow lawn
[tex]1\frac{3}{6} +3 \frac{4}{6}[/tex]
1 + 3 + [tex]\frac{3}{6} +\frac{4}{6}[/tex]
4 + [tex]\frac{8}{6}[/tex]
[tex]4\frac{8}{6}[/tex]
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The Given question is incomplete the complete question is :
Mr. mason likes to work around the yard during the weekends
Which of the following can be used to evaluate the series 8∑k=1 5(2/3)^k-1?
Answers
The evaluation of the geometric series is found as:
[tex]5(1- \frac{2}{3}^{8} / 1- \frac{2}{3} )[/tex]
How do we evaluate any given series?The given series is
[tex]8∑k=1 5(2/3)^k-1[/tex]
A geometric series is described as the sum of an infinite number of terms that have a constant ratio between successive terms.
Since this is a geometric series, we apply formula for the sum of the first k terms.
[tex]S= a( 1- r^{k} / 1-r )[/tex]
From the series, first term a = 5, common ratio r = 2/3 , k = 8
We substitute the values to obtain:
he evaluation of the series is found as:
[tex]5(1- \frac{2}{3}^{8} / 1- \frac{2}{3} )[/tex]
Geometric series finds its applications in Physics, engineering, biology, economics, computer science, queueing theory, and finance.
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complete question is attached in image
Ivy Corporation gave 74 people a bonus. If Ivy had given 3 more people bonuses, Ivy would have rewarded 13
of the workforce. How large is Ivy’s workforce?
Answers
If Ivy had given 3 more people bonuses, Ivy would have rewarded 13 of the workforce, Ivy Corporation's workforce has 592 employees.
Let's assume that the total workforce at Ivy Corporation is represented by "x".
According to the problem statement, Ivy Corporation gave a bonus to 74 people. Therefore, the remaining non-bonus-receiving employees would be (x-74).
If Ivy had given 3 more people bonuses, then the number of employees that would receive the bonus would be (74+3)=77.
According to the problem, 77 is equal to 13% of the total workforce (x):
77 = 0.13x
We can solve for x by dividing both sides by 0.13:
x = 592
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Solve.
10 - 9x^2 + 4x = -6x^210−9x
2
+4x=−6x
2
Answers
Answer: the solutions to the equation are x = √(10/3) and x = -√(10/3).
Step-by-step explanation:
To solve the equation 10 - 9x^2 + 4x = -6x^2 + 4x, we can simplify it and then solve for x.
Rearranging the equation, we have:
10 - 9x^2 + 4x = -6x^2 + 4x
Combining like terms, we get:
10 - 9x^2 = -6x^2
Subtracting -6x^2 from both sides, we have:
10 - 9x^2 + 6x^2 = 0
Simplifying further, we get:
10 - 3x^2 = 0
To solve for x, we can isolate the term with x^2:
-3x^2 = -10
Dividing both sides by -3, we have:
x^2 = 10/3
Taking the square root of both sides, we get:
x = ±√(10/3)
Therefore, the solutions to the equation are x = √(10/3) and x = -√(10/3).
The population of bees worldwide has been in decline. There are estimated to be 2,000,000,000 bees worldwide and each year there is estimated to be 10% less. How many bees worldwide will there be in 10 years?
Answers
ANSWER: 100% of 2000000000 is 2000000000
What is 100 Percent of 2000000000?
100 percent *2000000000
= (100/100)*2000000000
= (100*2000000000)/100
= 200000000000/100 = 2000000000
Now we have: 100 percent of 2000000000 = 2000000000
Question: What is 100 percent of 2000000000?
We need to determine 100% of 2000000000 now and the procedure explaining it as such
Step 1: In the given case Output Value is 2000000000.
Step 2: Let us consider the unknown value as x.
Step 3: Consider the output value of 2000000000 = 100%.
Step 4: In the Same way, x = 100%.
Step 5: On dividing the pair of simple equations we got the equation as under
2000000000 = 100% (1).
x = 100% (2).
(2000000000%)/(x%) = 100/100
Step 6: Reciprocal of both the sides results in the following equation
x%/2000000000% = 100/100
Step 7: Simplifying the above obtained equation further will tell what is 100% of 2000000000
x = 2000000000%
Therefore, 100% of 2000000000 is 2000000000
Write the equation of the circle for which ý(22, 21) and p(6, 23) are the endpoints of
a diameter of the circle.
Answers
Answer:
[tex](x-14)^2 +(y-22)^2 = (\sqrt{65})^2[/tex]
Step-by-step explanation:
If the two given points are the extremes of the diameter, the center of the circle has to be its middle point - that we can find by taking the average of the coordinates. The center thus sits in
[tex](\frac{22+6}2; \frac{21+23}2)[/tex] or [tex](14; 22)[/tex]. At this point we either find the length of the diameter and halve it, or the distance between the center and either point. Let's go for the diameter.
[tex]r=\sqrt{(22-6)^2+(21-23)^2}=\sqrt{16^2+2^2} = \sqrt {260}=2\sqrt{65}[/tex]. That makes our radius half of that. We can easily write the equation of the circle now:
[tex](x-14)^2 +(y-22)^2 = (\sqrt{65})^2[/tex]
Now, in theory you can improve it by multiplying it out and taking every term to the LHS, but I think it's good enough like that.
Can someone help me find the surface area of these cylinders??
Answers
The surface area for each of the cylinders is given as follows:
13. 126 yd².
14. 490 m².
15. 283 mm².
16. 297 cm².
How to obtain the surface area of a cylinder?The surface area of a cylinder of radius r and height h is given by the equation presented as follows, which combines the base area with the lateral area:
S = 2πrh + 2πr²
S = 2πr(h + r)
Item 13:
r = 2 yd and h = 8 yd, hence the surface area is given as follows:
S = 2π x 2(2 + 8)
S = 126 yd².
Item 14:
r = 6 m and h = 7 m, hence the surface area is given as follows:
S = 2π x 6(6 + 7)
S = 490 m².
Item 15:
r = 3 mm and h = 12 mm, hence the surface area is given as follows:
S = 2π x 3(3 + 12)
S = 283 mm².
Item 16:
r = 3.5 mm and h = 10 mm, hence the surface area is given as follows:
S = 2π x 3.5(3.5 + 10)
S = 297 cm².
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Sophia says that you can solve the problem in the example by multiplying both quantities and the ratio is 60 to 36 by 1/6 is Sofia correct explain
Answers
This is a ratio problem and Sophia is expected to simplify the ratio by finding the smallest possible values and not compounding them by multiplying them by some values.
We can represent the given ratio as 60:36,
60/36
We proceed to reduce the fraction by dividing both the numerator and the denominator by a common factor say 6,
10/6
We can further reduce this with a common factor of 2
5/2
Thus, the ratio we have 5:2
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Do it please i will reward brainlest
Answers
Answer:
Step-by-step explanation:
A softball player hits a pitched ball when it is 4 feet above the ground. The initial velocity is 75 feet per second. Use the formula h=-16t^2+vt+s. How long will it take for the ball to hit the ground?
Answers
If the initial velocity is 75 feet per second, it will take approximately 5.125 seconds for the ball to hit the ground.
The given formula h= -16t²+vt+s represents the height (h) of an object thrown vertically in the air at time (t), with initial velocity (v) and initial height (s). In this case, we are given that the initial height of the softball is 4 feet and the initial velocity is 75 feet per second.
We want to find out how long it will take for the ball to hit the ground, which means we want to find the time (t) when the height (h) is 0.
Substituting the given values into the formula, we get:
0 = -16t² + 75t + 4
This is a quadratic equation in standard form, which we can solve using the quadratic formula:
t = (-b ± √(b² - 4ac)) / 2a
Where a=-16, b=75, and c=4. Substituting these values into the formula, we get:
t = (-75 ± √(75² - 4(-16)(4))) / 2(-16)
t = (-75 ± √(5625 + 256)) / (-32)
t = (-75 ± √(5881)) / (-32)
We can simplify the expression under the square root as follows:
√(5881) = √(49121) = 711 = 77
So we have:
t = (-75 ± 77) / (-32)
Simplifying further, we get two possible solutions:
t = 0.5 seconds or t = 5.125 seconds
Since the softball player hits the ball when it is 4 feet above the ground, we can disregard the solution t=0.5 seconds (which corresponds to when the ball is at its maximum height) and conclude that it will take approximately 5.125 seconds for the ball to hit the ground.
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A cone has a volume of 2560 Pi cm cubed and a height of 30cm. Find the radius
Answers
•A volume of 2560 pi cm cube
•A height of 30 centimeters
The the required one
•The radius of the cone
Then find the solution
Using the formula
V=πr squared * h/3
Solving for
r=3V 3·2560
π·30≈9.02703
πh=
A plane takes off from an airport andtravels 13 miles on its path.
if the plane is 12 milesfrom its takeoff poin horizontally, what is its height?
Answers
The height of the plane is 5 miles.
To solve this problem, we can visualize it as a right triangle. The horizontal distance traveled by the plane forms the base of the triangle, which is 12 miles. The total distance traveled by the plane forms the hypotenuse of the triangle, which is 13 miles. We need to find the height, which corresponds to the vertical side of the triangle.
Using the Pythagorean theorem, we can calculate the height as follows:
height^2 + 12^2 = 13^2
height^2 + 144 = 169
height^2 = 169 - 144
height^2 = 25
Taking the square root of both sides, we get:
height = √25
height = 5
Therefore, the height of the plane is 5 miles.
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a certain radioactive isotope has leaked into a small stream. one hundred days after the leak 8% of the original amount of substance remained. Determine the half life of this radioactive isotope
Answers
Answer:
The half-life of a radioactive substance is the time it takes for half of the initial amount of the substance to decay. We can use the fact that 8% of the original amount remains after 100 days to determine the half-life of the isotope.
Let's assume that the initial amount of the substance is 1 unit (it could be any amount, but we're assuming 1 unit for simplicity). After one half-life, half of the original amount remains, or 0.5 units. After two half-lives, half of the remaining amount remains, or 0.25 units. After three half-lives, half of the remaining amount remains, or 0.125 units. We can see that the amount of substance remaining after each half-life is half of the previous amount.
We can use this information to set up the following equation:
0.08 = (1/2)^n
where n is the number of half-lives that have elapsed. We want to solve for n.
Taking the logarithm of both sides, we get:
log(0.08) = n*log(1/2)
Solving for n, we get:
n = log(0.08) / log(1/2) = 3.42
So the number of half-lives that have elapsed is approximately 3.42. Since we know that 100 days is the time for three half-lives (from the previous calculation), we can find the half-life by dividing 100 days by 3.42:
Half-life = 100 days / 3.42 = 29.2 days (rounded to one decimal place)
Therefore, the half-life of the radioactive isotope that leaked into the stream is approximately 29.2 days.
100 tickets are sold for $1 each there is $25 prizes and a $10 prize what is the expected value for a person that buys a ticket round to the nearest cent
Answers
The expected value for a person buying a ticket is $0.35 rounded to the nearest cent.
What is the expected value for the person who buys the ticket?The expected value is calculated considering the probabilities of winning each prize and the corresponding values of each prize.
Assuming:
P($25) as the probability of winning the $25 prize
P($10) as the probability of winning the $10 prize
There are 100 tickets sold, therefore, the probabilities can be found as follows:
P($25) = 1/100 (since there is only 1 $25 prize)
P($10) = 1/100 (since there is only 1 $10 prize)
The expected value (E), will then be:
E = P($25) * $25 + P($10) * $10
E = (1/100) * $25 + (1/100) * $10
E = $0.25 + $0.10
E = $0.35
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A volunteer walks 1 mile to a dog
shelter. She walks 4 dogs for 1/2mile
each. Then she walks 1 mile
home. She does this each day for
3 days, How many miles does she
walk in all?
Answers
She walks 4 dogs for 1/2 mile each, so she walks 4 x 1/2 = 2 miles with the dogs each day.
Therefore, she walks a total of 2 + 2 = 4 miles each day.
Over the course of 3 days, she walks a total of 4 x 3 = 12 miles.
So, the volunteer walks 12 miles in all.
Using the present value approach, solve the following:
Tom has $100 in a bank account that pays a guaranteed 5% interest rate each year. How much would Tom have at the end of Year 3?
Answers
Answer:
Step-by-step explanation:
$100x0.5x1=$5
6x^2=-3x+1 to the nearest hundredth
Answers
The solutions to the quadratic equation 6x² = -3x + 1 to the nearest hundredth are -0.73 and 0.23.
What are the solutions to the quadratic equation?Given the quadratic equation in the question:
6x² = -3x + 1
To solve the quadratic equation 6x² = -3x + 1, we can rearrange it into standard form, where one side is set to zero:
6x² + 3x - 1 = 0
Now we can solve the equation using the quadratic formula, which states that for an equation in the form ax² + bx + c = 0, the solutions for x are given by:
[tex]x = \frac{-b \±\sqrt{b^2-4ac} }{2a}[/tex]
Here; a = 6, b = 3, and c = -1.
Let's substitute these values into the quadratic formula:
[tex]x = \frac{-b \±\sqrt{b^2-4ac} }{2a}\\\\ x= \frac{-3 \±\sqrt{3^2-4\ *\ 6\ *\ -1} }{2*6}\\\\x = \frac{-3 \±\sqrt{9+24} }{12}\\\\x = \frac{-3 \±\sqrt{33} }{12}\\\\x = -0.73, \ x=0.23[/tex]
Therefore, the values of x are -0.73 and 0.23.
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-8.915444681 round to nearest hundred miles
Answers
On rounding the given number to nearest hundred miles will give the result -8.92.
Rounding to nearest hundred miles refers to changing the number present on hundreds place. We see that the number 8 is at unit's place, 9 is at tenth's place and 2 is at hundred's place.
Based on the rules of rounding, we will check the number to the right of number on hundred's place. Since the next number is 5, the number we will round the number 1 present at hundred's place. Hence, the final number will be -8.92.
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A rectangle has an area of 114cm squared and a perimeter of 50cm. What are the dimensions
Answers
If rectangle has an area of 114cm squared and a perimeter of 50 cm, the dimensions of the rectangle are approximately 5 cm by 22.8 cm.
Let's assume the length of the rectangle is "l" and the width is "w". We can start by using the formula for the area of a rectangle, which is A = lw. From the given information, we know that the area is 114cm².
So, we have:
lw = 114
Next, we can use the formula for the perimeter of a rectangle, which is P = 2l + 2w. From the given information, we know that the perimeter is 50cm.
So, we have:
2l + 2w = 50
We now have two equations with two variables, which we can solve using substitution or elimination. Let's use substitution by solving the first equation for l:
l = 114/w
We can then substitute this expression for l in the second equation:
2(114/w) + 2w = 50
Multiplying both sides by w to eliminate the fraction, we get:
228 + 2w² = 50w
Rearranging and simplifying, we get a quadratic equation:
2w² - 50w + 228 = 0
We can solve for w using the quadratic formula:
w = [50 ± √(50² - 4(2)(228))]/(2(2)) ≈ 11.4 or 5
Since the length and width must be positive, we can discard the solution w = 11.4. Therefore, the width of the rectangle is approximately 5 cm. We can then use the equation lw = 114 to solve for the length:
l(5) = 114
l ≈ 22.8
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