Answer:
D. A discrete data set because there are a finite number of possible values.
Step-by-step explanation:
Assuming in a test of a method of gender selection, 725 couples used the XSORT method and 368 of them had baby girls. The value given is from a discrete data set because there are a finite number of possible values.
In Mathematics, a discrete data is a data set in which the number of possible values are either finite or countable.
On the other hand, a continuous data is a data set having infinitely many possible values and those values cannot be counted, meaning they are uncountable.
Hence, if 725 couples used the XSORT method and 368 of them had baby girls; this is a discrete data because the values (725 and 368) are finite and can be counted.
Eight less than four times a number is less than 56. What are the possible values of that number?
Answer:
The numbers should be less than 16 . The numbers can be 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 ............15
Step-by-step explanation:
Eight less than four times a number is less than 56 . The expression can be written below
let
the number = a
4a - 8 < 56
add 8 to both sides
4a - 8 + 8 < 56 + 8
4a < 64
divide both sides by 4
a < 64/4
a < 16
The numbers should be less than 16 . The numbers can be 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 ............15
HELP! EASY! WILL GIVE BRAINLIEST!
Answer:
c
Step-by-step explanation:
Jackson's robot moved 5 meters in 2 seconds How far did he move in 30 sec? (please explain and use fractions)
75 meters
Step-by-step explanation:
5 x 30/2
= 5 x 15
= 75 meters
The graph of a polynomial is shown below. At which value of x does this polynomial have an extreme?
Answer:
A. x = 4.
Step-by-step explanation:
An extreme is the highest or lowest value of the function. In this case, the extreme of the parabola is the lowest point, or the vertex.
We can see that point is at about A. x = 4.
Hope this helps!
Volume of cylinder height=20 and B= 32????
Answer:
16076.8
Step-by-step explanation:
Volume of Cylinder=πr²h
h= 20 m
r = 32/2 = 16
=πr²h
= (3.14)(16^2)(20)
=16076.8 m^2
HOPE IT HELPS :)
PLEASE MARK IT THE BRAINLIEST!
Rotate the figure 90 counterclockwise about the origin. Determine the orientation of the rotated figure and place it in the correct position (PLS HELP)
Answer:
see below
Step-by-step explanation:
The rotated location of D' is (-2, 1). The "arrow" points to the left. The attached figure is the best I could do with your distorted image.
You have to rotate the figure 90 counterclockwise about the origin.
In a study of the progeny of rabbits, Fibonacci (ca. 1170-ca. 1240) encountered the sequence now bearing his name. The sequence is defined recursively as follows.
an + 2 = an + an + 1, where a1 = 1 and a2 = 1.
(a) Write the first 12 terms of the sequence.
(b) Write the first 10 terms of the sequence defined below. (Round your answers to four decimal places.)
bn =
an + 1/
an, n ? 1.
(c) The golden ratio ? can be defined by
limn ? In a study of the progeny of rabbits, Fibonacci (cbn = ?
, where
? = 1 + 1/?. Solve this equation for ?. (Round your answer to four decimal places.)
The question in part c is not clear, nevertheless, part a and part b would be solved.
Answer:
a. The first twelve terms are:
1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144.
b. The first ten terms are:
1.000, 1.000, 1.500, 1.667, 1.600, 1.625, 1.615, 1.619, 1.618, 1.618.
Step-by-step explanation:
a. Given
an + 2 = an + an + 1
where a1 = 1 and a2 = 1.
a3 = a1 + a2
= 2
a4 = a2 + a3
= 3
a5 = a3 + a4
= 5
a6 = a5 + a4
= 8
a7 = a6 + a5
= 13
a8 = a7 + a6
= 21
a9 = a8 + a7
= 34
a10 = a9 + a8
= 55
a11 = a10 + a9
= 89
a12 = a11 + a10
= 144
The first twelve terms are:
1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144.
(b)
Given
bn = an+1/an
b1 = a2/a1
= 1/1 = 1.000
b2 = a3/a2
= 2/1 = 1.000
b3 = a4/a3
= 3/2 = 1.500
b4 = a5/a4
= 5/3 = 1.667
b5 = a6/a5
= 8/5 = 1.600
b6 = a7/a6
= 13/8 = 1.625
b7 = a8/a7
= 21/13 = 1.615
b8 = a9/a8
= 34/21 = 1.619
b9 = a10/a9
= 55/34 = 1.618
b10 = a11/a10
= 89/55 = 1.618
The first ten terms are:
1.000, 1.000, 1.500, 1.667, 1.600, 1.625, 1.615, 1.619, 1.618, 1.618.
The gas mileage for a certain vehicle can be approximated by m=−0.05x2+3.5x−49, where x is the speed of the vehicle in mph. Determine the speed(s) at which the car gets 9 mpg. Round to the nearest mph.
Answer:
14mphStep-by-step explanation:
Given the gas mileage for a certain vehicle modeled by the equation m=−0.05x²+3.5x−49 where x is the speed of the vehicle in mph. In order to determine the speed(s) at which the car gets 9 mpg, we will substitute the value of m = 9 into the modeled equation and calculate x as shown;
m = −0.05x²+3.5x−49
when m= 9
9 = −0.05x²+3.5x−49
−0.05x²+3.5x−49 = 9
0.05x²-3.5x+49 = -9
Multiplying through by 100
5x²+350x−4900 = 900
Dividing through by 5;
x²+70x−980 = 180
x²+70x−980 - 180 = 0
x²+70x−1160 = 0
Using the general formula to get x;
a = 1, b = 70, c = -1160
x = -70±√70²-4(1)(-1160)/2
x = -70±√4900+4640)/2
x = -70±(√4900+4640)/2
x = -70±√9540/2
x = -70±97.7/2
x = -70+97.7/2
x = 27.7/2
x = 13.85mph
x ≈ 14 mph
Hence, the speed(s) at which the car gets 9 mpg to the nearest mph is 14mph
Write these as normal numbers
Hi there!! (✿◕‿◕)
⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐⭐
A.) 7.2 x 10^-5 = 0.000000072
B.) 6.3 x 10^-9 = 0.0000000063
C.) 4.54 x 10^-5 = 0.0000454
D.) 7.041 x 10^-10 = 0.0000000007041
Hope this helped!! ٩(◕‿◕｡)۶
The numbers can be written as;
A.) 7.2 x 10^{-5} = 0.000000072
B.) 6.3 x 10^{-9} = 0.0000000063
C.) 4.54 x 10^{-5} = 0.0000454
D.) 7.041 x 10^{-10} = 0.0000000007041
What is the fundamental principle of multiplication?Multiplication is the mathematical operation that is used to determine the product of two or more numbers. If an event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.
We are given the parameters
We need to Write these as normal numbers
A.) 7.2 x 10^{-5} = 0.000000072
B.) 6.3 x 10^{-9} = 0.0000000063
C.) 4.54 x 10^{-5} = 0.0000454
D.) 7.041 x 10^{-10} = 0.0000000007041
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Copy the problem, mark the givens in the diagram, and write a Statement/Reason proof. Given: CS ≅ HR ∠CHS ≅ ∠HCR ∠CSH ≅ ∠HRC Prove: CR ≅ HS
Answer:
Step-by-step explanation:
Given: CS ≅ HR
∠CHS ≅ ∠HCR
∠CSH ≅ ∠HRC
Prove: CR ≅ HS
ΔCHS ≅ ΔHCR (Angle-Angle-Side, AAS, congruence property)
ΔICR ≅ ΔIHS (congruence property)
IS ≅ IR (similarity property)
CS ≅ HR (given)
Thus,
IC = IS + SC (addition property)
IH = IR + RH (addition property)
IC ≅ IH
Then,
CR ≅ HS (similarity property of triangles SCH and RHC)
Harry is trying to complete his hill walking scouts badge. He is using a map with a scale of 1 cm : 2 km. To earn the badge he needs to walk 14 km. What is the distance he needs to walk on the map?
Answer:
7 cm
Step-by-step explanation:
14 / 2 = 7 cm
7cm is the distance Harry needs to walk on the map?
What is Distance?Distance is a numerical or occasionally qualitative measurement of how far apart objects or points are.
Given that,
Harry is trying to complete his hill walking scouts badge.
He is using a map with a scale of 1 cm : 2 km.
To earn the badge he needs to walk 14 km.
Let the distance he needs to walk on the map is x.
By given data we write an equation
1/2=x/14
Apply Cross Multiplication
14/2=x
7=x
Hence, 7cm is the distance he needs to walk on the map.
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NEED HELP LIKE NOW PLSSS HELP 50 POINTS Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar and ^ to indicate an exponent. Find the missing term.
Answer:
The expression that fits into the box is x¹⁵⁸
Step-by-step explanation:
Let the empty box be y
(x¹²)⁵ × (x⁻²)⁹ × y = (x⁴⁰)⁵
Here, we will apply the laws of indices.
The laws of indices gives the answer for the expressions
1) xᵏ × xˢ = xᵏ⁺ˢ
2) xᵏ ÷ xˢ = xᵏ⁻ˢ
3) (xᵏ)ˢ = xᵏ•ˢ
So,
(x¹²)⁵ = x⁶⁰
(x⁻²)⁹ = x⁻¹⁸
(x⁴⁰)⁵ = x²⁰⁰
(x¹²)⁵ × (x⁻²)⁹ × y = (x⁴⁰)⁵
Becomes
x⁶⁰ × x⁻¹⁸ × y = x²⁰⁰
x⁶⁰⁻¹⁸ × y = x²⁰⁰
x⁴² × y = x²⁰⁰
y = x²⁰⁰ ÷ x⁴²
y = x²⁰⁰⁻⁴² = x¹⁵⁸
Hope this Helps!!!
Given the function below, find value (s) of x if f(x)=7
Explanation:
f(x) and y are often used interchangeably. We are asked to find the x value(s) when y = 7.
Circle the rows where 7 shows up in the y column. You should find that x = -1 and x = 1 are circled as well.
So f(x) = 7 leads to x = -1 or x = 1. In other words, f(-1) = 7 and f(1) = 7 also.
For the function given the value of x can be two, one is 1 and the other one is -1 if the f(x)=7
What is a Function?
A function relates an input to an output means it is a kind of relationship between the variable y and x. It is denoted through f(x).
What is a Variable?A variable is defined as a quantity that may assume any one of a set of values.
How to find the value of x in a function?
In the question the function is given as:
Function is denoted through f(x) and f(x) shows the value of x. We know that the value of f(x)=7 which is given in the question. So we will take the value of x in the front of 7 which is written in the y column. We have got two values in this which are 1 and -1. So they both will be the values of x.
Hence the value of x for the function given in the question are -1 and 1
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50 POINTS!!!! I ALSO GIVE BRAINLIEST, BUT YOU HAVE TO ANSWER QUICK Choose the correct graph of the given system of equations. A pair of linear equations is shown: y = −x + 1 y = 2x + 4 Which of the following statements best explains the steps to solve the pair of equations graphically? On a graph, plot the line y = −x + 1, which has y-intercept = −1 and slope = 1, and y = 2x + 4, which has y-intercept = 2 and slope = 4, and write the coordinates of the point of intersection of the two lines as the solution. On a graph, plot the line y = −x + 1, which has y-intercept = 1 and slope = 1, and y = 2x + 4, which has y-intercept = 1 and slope = 4, and write the coordinates of the point of intersection of the two lines as the solution. On a graph, plot the line y = −x + 1, which has y-intercept = 1 and slope = −1, and y = 2x + 4, which has y-intercept = −2 and slope = 2, and write the coordinates of the point of intersection of the two lines as the solution. On a graph, plot the line y = −x + 1, which has y-intercept = 1 and slope = −1, and y = 2x + 4, which has y-intercept = 4 and slope = 2, and write the coordinates of the point of intersection of the two lines as the solution.
Answer:
D. On a graph, plot the line y = −x + 1, which has y-intercept = 1 and slope = −1, and y = 2x + 4, which has y-intercept = 4 and slope = 2, and write the coordinates of the point of intersection of the two lines as the solution.
Step-by-step explanation:
Correct answer is in bold. Incorrect answer have the mistakes put between stars *** ***.
50 POINTS!!!! I ALSO GIVE BRAINLIEST, BUT YOU HAVE TO ANSWER QUICK Choose the correct graph of the given system of equations. A pair of linear equations is shown: y = −x + 1 y = 2x + 4 Which of the following statements best explains the steps to solve the pair of equations graphically?
A. On a graph, plot the line y = −x + 1, which has y-intercept = ***−1*** and slope = 1, and y = 2x + 4, which has y-intercept = 2 and slope = 4, and write the coordinates of the point of intersection of the two lines as the solution.
B. On a graph, plot the line y = −x + 1, which has y-intercept = 1 and slope = ***1***, and y = 2x + 4, which has y-intercept = 1 and slope = 4, and write the coordinates of the point of intersection of the two lines as the solution.
C. On a graph, plot the line y = −x + 1, which has y-intercept = 1 and slope = −1, and y = 2x + 4, which has y-intercept = ***−2*** and slope = 2, and write the coordinates of the point of intersection of the two lines as the solution.
D. On a graph, plot the line y = −x + 1, which has y-intercept = 1 and slope = −1, and y = 2x + 4, which has y-intercept = 4 and slope = 2, and write the coordinates of the point of intersection of the two lines as the solution.
PLEASE ANSWER FAST I WILL MARK BRAINLEIST AMD 20 POINTSBased on the figure below what is the value of X
Answer:
[tex]\boxed{9}[/tex]
Step-by-step explanation:
The two angles are complementary to each other.
That means they add up to 90 degrees.
[tex]5x+15+30=90[/tex]
[tex]5x+45=90[/tex]
[tex]5x=45[/tex]
[tex]x=9[/tex]
Answer:
x = 9
Step-by-step explanation:
So you know that the total is 90 degrees.
What you need to do is create an equation.
5x + 15 + 30 = 90
Then, solve the equation like this.
5x + 15 + 30 = 90
5x + 45 = 90
5x = 90 - 45
5x = 45
x = 45 ÷ 5
x = 9
Hope this helps! :)
helpppppppppppppppppppppppppppppppppppppppppppppppppppppp
Answer:
4
Step-by-step explanation:
Answer:
1/8 < 1/6
Step-by-step explanation:
The top is divided into 8 and 1 part is shaded so 1/8
The bottom is divided into 6 and 1 part is shaded so 1/6
Comparing
1/8 < 1/6
The total cost of a sweater and a jacket was $71.55 If the price of the sweater was $3.19 less than the jacket, what was the price of the sweater? Express your answer as a simplified fraction or a decimal rounded to two places.
Answer: $34.18
Step-by-step explanation:
Let the cost of the Jacket = $x and
The cost of the sweater. = $y
Now total price. = $71.55.
So, $x + $y. = $71.55 -- 1
From the second statements, the price of the sweater was $3.19 less than the price of the jacket. Transforming that into equation
y = ( x - $3.19 )
Now substitute for y in the equation (1) above.
x + ( x - 3.19 ) = 71.55
Now solve the equation
x + x - 3.19 = 71.55
2x - 3.19. = 71.55
2x = 71.55 + 3.19
2x. = 74.74
x = 74.74/2
= $37.37. cost of the jacket
Now to determine the cost of the sweater,
$71.55 - $37.37 = $34.18
The cost of the sweater = $34.18.
Identify the type of hypothesis test below. H0:X=10.2, Ha:X>10.2 Select the correct answer below: The hypothesis test is two-tailed. The hypothesis test is left-tailed. The hypothesis test is right-tailed.
Answer:
The hypothesis test is right-tailed
Step-by-step explanation:
To identify a one tailed test, the claim in the case study tests for the either of the two options of greater or less than the mean value in the null hypothesis.
While for a two tailed test, the claim always test for both options: greater and less than the mean value.
Thus given this: H0:X=10.2, Ha:X>10.2, there is only the option of > in the alternative claim thus it is a one tailed hypothesis test and right tailed.
A test with the greater than option is right tailed while that with the less than option is left tailed.
Answer:
Please help with questions on my profile somebody
Step-by-step explanation:
What is the answer? I'm stuck
Answer:
[tex]g(2)=1[/tex]
Step-by-step explanation:
So first, we know that:
[tex]f(1)=g(1)+1[/tex]
And:
[tex]f(2)=2[/tex]
This means that instead of 1, if we put two in like so:
[tex]f(2)=g(2)+1[/tex]
Then we can substitute the f(2):
[tex]2=g(2)+1\\g(2)=1[/tex]
Therefore, g(2)=1.
Write 3 expressions containing exponents so that each expression equals 81
Answer:
9x9= 81
3x3x3x3=81
81 to the first power.
Step-by-step explanation:
I hope this helps in any way:)
Listed below are the top 10 annual salaries (in millions of dollars) of TV personalities. Find the range, variance, and standard deviation for the sample data. Given that these are the top 10 salaries, do we know anything about the variation of salaries of TV personalities in general?
42 40 39 31 22 18 15 12 11.7 10.5
____________________________________________________________________________
The Range of the sample data is $[ ] million. (Type an integer or a decimal)
The variance of the sample data is [ ]. (Round to three decimal places as needed.)
The standard deviation of the sample data is $[ ] million. (Round to three decimal places as needed)
Is the the standard deviation of the sample a good estimate of the variation of the salaries of the TV personalities in general ?
A. yes, because the standard deviation is an unbiased estimator
B. no, because the sample is not representative of the whole population.
C. no, because there is an outlier in the sample data.
D. yes, because the sample is random.
Answer:
If you do not need that actual numbers, the answer is B.
Step-by-step explanation:
In order to find a fully comprehensive study, you would need many more people than just 10, not to mention these are the top 10 people in the world.
(Brainliest would be much appreciated!)
Of the cartons produced by a company, % have a puncture, % have a smashed corner, and % have both a puncture and a smashed corner. Find the probability that a randomly selected carton has a puncture or a smashed corner. The probability that a randomly selected carton has a puncture or a smashed corner nothing%. (Type an integer or a decimal. Do not round.)
Full Question
Of the cartons produced by a company, 10% have a puncture, 6% have a smashed corner, and 0.4% have both a puncture and a smashed corner. Find the probability that a randomly selected carton has a puncture or a smashed corner. The probability that a randomly selected carton has a puncture or a smashed corner nothing ____%. (Type an integer or a decimal. Do not round.)
Answer:
[tex]P(Punctured\ or\ Smashed\ Corner) = 0.156[/tex]
Step-by-step explanation:
Given
[tex]Puncture\ Corner = 10\%[/tex]
[tex]Smashed\ Corner = 6\%[/tex]
[tex]Punctured\ and\ Smashed\ Corner = 0.4\%[/tex]
Required
[tex]P(Punctured\ or\ Smashed\ Corner)[/tex]
For non-mutually exclusive event described above, P(Punctured or Smashed Corner) can be calculated as thus;
[tex]P(Punctured\ or\ Smashed\ Corner) = P(Punctured\ Corner) + P(Smashed\ Corner) - P(Punctured\ and\ Smashed\ Corner)[/tex]
Substitute:
10% for P(Puncture Corner),
6% for P(Smashed Corner) and
0.4% for P(Punctured and Smashed Corner)
[tex]P(Punctured\ or\ Smashed\ Corner) = 10\% + 6\% - 0.4\%[/tex]
[tex]P(Punctured\ or\ Smashed\ Corner) = 15.6\%[/tex]
Convert % to fraction
[tex]P(Punctured\ or\ Smashed\ Corner) = \frac{15.6}{100}[/tex]
Convert to decimal
[tex]P(Punctured\ or\ Smashed\ Corner) = 0.156[/tex]
Using Venn probabilities, it is found that:
The probability that a randomly selected carton has a puncture or a smashed corner is 15.6%.In this problem, the events are:
Event A: Puncture.Event B: Smashed corner.The "or" probability is given by:
[tex]P(A \cup B) = P(A) + P(B) - P(A \cap B)[/tex]
10% have a puncture, hence [tex]P(A) = 0.1[/tex]6% have a smashed corner, hence [tex]P(B) = 0.06[/tex].0.4% have both a puncture and a smashed corner, hence [tex]P(A \cup B) = 0.004[/tex].Then:
[tex]P(A \cup B) = 0.1 + 0.06 - 0.004 = 0.156[/tex]
The probability that a randomly selected carton has a puncture or a smashed corner is 15.6%.
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It takes four painters working at the same rate 1.25 work-days to finish a job. If only three painters are available, how many work-days will it take them to finish the job, working at the same rate? Express your answer as a mixed number.
Answer:
.9375 days
Step-by-step explanation:
1.25 / 4 = 0.3125
0.3125 x 3 - 0.9375
Home health aide trades in old car a gas mileage of 18 1/4 miles per gallon.starting with a full tank of gas in her new car she travels 390 7/8 miles it takes 14 3/4 gallons to fuel the tank. How many miles further can she travel on a full tank of gas with the new car if the gas tank hold 30 gallons of gas
Answer:
The new car travels 247.5 miles more than the old one on 30 gallons of gas.
Step-by-step explanation:
The fuel consumption of the old car was:
[tex]car_{old} = 18 + \frac{1}{4} = \frac{73}{4} \text{ miles per gallon}[/tex]
The new one can travel a distance of 390 7/8 miles by using 14 3/4 gallons of fuel, therefore the consumption is:
[tex]car_{new} = \frac{390.875}{14.75} = 26.5 \text{ miles per gallon}[/tex]
If the tank holds 30 gallons, on the old car the distance would be:
[tex]distance_{old} = 18.25*30 = 547.5 \text{ miles}[/tex]
On the new one it will be:
[tex]distance_{new} = 26.5*30 = 795 \text{ miles}[/tex]
So the new car is able to travel 247.5 miles more than the old one on 30 gallons of gas.
Please help. I’ll mark you as brainliest if correct!
Answer:
Quantity (lbs) of type 1 candy x = 8
Quantity (lbs) of type 2 candy y = 17,5
Step-by-step explanation:
Let´s call "x" quantity (in pounds) of candy type 1 in the mixture, and "y" quantity (in pounds ) of candy type 2, then according to the problem statement.
x + y = 25,5
2,20*x + 7,30*y = 5,70 * 25,5 ⇒ 2,20*x + 7,30*y = 145,35
Then we have a two equation system
x + y = 25,5 ⇒ y = 25,5 - x
2,20*x + 7,30*y = 145,35 ⇒ 2,20*x + 7,30* (25,5 - x ) = 145,35
2,20*x + 186,15 - 7,30*x = 145,35
5,1*x = 40,8
x = 40,8/5,1
x = 8 lbs
And y = 25,5 - 8
y = 17,5 lbs
Find the value of x.
A. 6
B. 7
C. 4
D. 5
Answer:
A. 6
Step-by-step explanation:
We see that 20 is a diameter that goes through the center of the point. This means that the top half of the black line is 10 and the top half of the blue line is 8. Use the Pythagorean Theorem to find out the length of the shortest side by doing 10^2 - 8^2 = x^2. x^2 = 36; x = 6.
1
?
x + 5and
Which line is parallel to the line y =
passes through the point (-2, 1)?
x+
O y=x+3
1
y =
+2
1
y =
4
*-
oy-
1
-X
y=-2
Answer:
second option
Step-by-step explanation:
Parallel lines have the same slope, and since the slope of the given line is 1/2, we know the slope of the answer will be 1/2, which eliminates the first and last options. We know the slope and a point that belongs to the line, (-2, 1), so we can use point-slope formula to derive the equation of the line.
y - 1 = 1/2(x + 2)
y - 1 = 1/2x + 1
y = 1/2x + 2
Find the values of x,y,and z. The diagram is not to scale.
*check attachment for the correct figure given in this question with the right labelled angles
Answer:
[tex] x = 86, y = 67, z = 94 [/tex]
Step-by-step explanation:
From the given figure attached below, values of x, y, and z can be found as follow:
Value of x:
[tex] x = 180 - (38 + 56) [/tex] => sum of angles in a triangle
[tex] x = 180 - 94 [/tex]
[tex]x = 86[/tex]
Value of z:
[tex] z = 180 - 86 [/tex] => angles on a straight line
[tex]z = 94[/tex]
Value of y:
[tex] y = 180 - (19 + 94) [/tex] => sum of angles in a triangle.
[tex] y = 180 - 113 [/tex]
[tex]y = 67[/tex]
[tex] x = 86, y = 67, z = 94 [/tex]
The half-life of iron-52 is approximately 8.3 hours. Step 1 of 3: Determine a so that A(t)=A0at describes the amount of iron-52 left after t hours, where A0 is the amount at time t=0. Round to six decimal places.
Answer:
Step-by-step explanation:
Given the half like of a material to be 8.3 hours and the amount of iron-52 left after t hours is modeled by the equation [tex]A(t) = A_0 a^{t}[/tex], we can get A(t) as shown;
At t = 8.3 hours, A(8.3) = 1/2
Initially at t = 0; A(0) = 1
Substituting this values into the function we will have;
[tex]\frac{1}{2} = 1 * a^{8.3}\\\\Taking \ the \ log \ of\ both \ sides;\\\\log(\frac{1}{2} ) = log(a^{8.3} )\\\\log(\frac{1}{2} ) = 8.3 log(a)\\\\\fr-0.30103 = 8.3 log(a)\\\Dividing\ both\ sides\ by \ 8.3\\\\\frac{-0.30103}{8.3} = log(a)\\\\log(a) = - 0.03627\\\\a =10^{-0.03627} \\\\a = 0.919878 (to\ 6dp)[/tex]
Assume that females have pulse rates that are normally distributed with a mean of mu equals 75.0 beats per minute and a standard deviation of sigma equals 12.5 beats per minute. Complete parts (a) through (c) below. a. If 1 adult female is randomly selected, find the probability that her pulse rate is less than 78 beats per minute.
Answer:
0.40517 is the probability
Step-by-step explanation:
The first thing to do here is to calculate the corresponding z-score
Mathematically;
z-score = x-mean/SD
from the question,
x = 78, mean = 75 and SD = 12.5
Plugging these values in the z-score equation, we have;
z-score = (78-75)/12.5 = 3/12.5 = 0.24
So the probability we want to calculate is that;
P(z < 0.24)
we can get this by using the standard normal distribution table,
The value according to the table is;
0.40517