Answer:
1. (-125 a - 5.75) x + b c (605 x - 550 x^2) + 10.75
2. -125 a x + x (-550 b c x + 605 b c - 5.75) + 10.75
3. 0.25 (-500 a x - 220 b c (10 x - 11) x - 23 x + 43)
Step-by-step explanation:
At the beginning of an experiment, a scientist has 120 grams of radioactive goo. After 240 minutes, her sample has
decayed to 3.75 grams
What is the half-life of the goo in minutes?
The half-life of the radioactive goo is 48 minutes. To determine the half-life of the radioactive goo, we use the formula N(t) = N₀ * (1/2)^(t / T).
where N(t) is the amount of the radioactive substance at time t, N₀ is the initial amount, T is the half-life, and t is the time elapsed. Given N₀ = 120 grams and N(240) = 3.75 grams, we substitute these values into the formula and solve for T. Plugging in the given values, we have: 3.75 = 120 * (1/2)^(240 / T)
To find the half-life T, we need to isolate it on one side of the equation. We can begin by dividing both sides of the equation by 120:
3.75 / 120 = (1/2)^(240 / T)
0.03125 = (1/2)^(240 / T)
Next, we can take the logarithm base 2 of both sides to eliminate the exponential term: log₂(0.03125) = log₂[(1/2)^(240 / T)]
-5 = (240 / T) * log₂(1/2)
Simplifying further, we know that log₂(1/2) is equal to -1: -5 = (240 / T) * (-1)
To solve for T, we can multiply both sides by -T/240: 5T/240 = 1
Multiplying both sides by 240/5, we find: T = 48
Therefore, the half-life of the radioactive goo is 48 minutes.
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Need help with this question
Answer:
Function A rate = 5/1
Function B rate = -4.5
Function A because its rate is positive while Function B's rate is negative
The tangent lines of a simple curve have azimuths 300 and bearing N 04° E, respectively. A third tangent line AB intersects the two tangent lines at bearing S 34 E. Stationing of the Pl of the curve is 16 + 464.35 and the distance from point B to the Pl of the curve is 277.6 m (ie BV = 277.6 m). Determine the following: a. Radius of the simple curve that shall be tangent to these three lines. b. Stationing of the PC Stationing of the PT
The radius of the simple curve is not provided and b. The stationing of the PC and PT is not provided.
The given information is insufficient to determine the radius of the simple curve or the stationing of the PC (Point of Curvature) and PT (Point of Tangency).
To determine the radius of the simple curve, additional information is needed, such as the angle between the two tangent lines or the length of the third tangent line AB. Without this information, we cannot calculate the radius.
Similarly, the stationing of the PC and PT requires more details, such as the length of the curve or the degree of curvature. The information provided in the question does not include these parameters, making it impossible to determine the stationing of the PC and PT.
Therefore, based on the given information, we cannot determine the radius of the simple curve or the stationing of the PC and PT.
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It is advertised that the average braking distance for a small car traveling at 65 miles per hour equals 120 feet. A transportation researcher wants to determine if the statement made in the advertisement is false. She randomly test drives 34 small cars at 65 miles per hour and records the braking distance. The sample average braking distance is computed as 115 feet. Assume that the population standard deviation is 20 feet. Use Table 1.
Use α = 0.01 to determine if the average braking distance differs from 120 feet. The average braking distance is (significantly/not significantly) different from 120 feet.
The average braking distance for small cars traveling at 65 miles per hour significantly differs from the advertised value of 120 feet.
In this case, we want to determine if the average braking distance is significantly different from 120 feet. Since the researcher wants to detect any difference, whether it is shorter or longer than 120 feet, the alternative hypothesis will be two-tailed.
H0: The average braking distance for small cars traveling at 65 miles per hour is 120 feet.
Ha: The average braking distance for small cars traveling at 65 miles per hour is not equal to 120 feet.
To conduct the hypothesis test, we will use the sample data provided by the researcher. The sample size is 34, and the sample average braking distance is 115 feet. The population standard deviation is given as 20 feet.
The formula for the test statistic (z-score) is:
z = (sample average - hypothesized population average) / (population standard deviation / √sample size)
Plugging in the values from the problem:
z = (115 - 120) / (20 / √34)
z = -5 / (20 / √34)
Using Table 1 or a statistical calculator, we can determine the critical z-value corresponding to a significance level of 0.01. Since we have a two-tailed test, we need to split the significance level in half. Each tail will have an alpha of 0.005 (0.01/2).
Looking up the z-value for α/2 = 0.005, we find it to be approximately 2.576.
Now we compare the calculated z-value to the critical z-value:
If the calculated z-value falls outside the range defined by the critical z-values, we reject the null hypothesis. Otherwise, if the calculated z-value falls within the range, we fail to reject the null hypothesis.
In our case, the calculated z-value is -5 / (20 / √34), which we need to compare to -2.576 and +2.576.
If the calculated z-value is less than -2.576 or greater than +2.576, we reject the null hypothesis. Otherwise, if the calculated z-value is between -2.576 and +2.576, we fail to reject the null hypothesis.
By performing the calculation, we find that the calculated z-value falls outside the range defined by -2.576 and +2.576. Therefore, we can reject the null hypothesis.
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help with segment relationships in circles...picture attatched.
Answer:
x=23
Step-by-step explanation:
Hello There!
The relationship between chords can be found below in the image.
Pretty much the product of the segments in the same chord is equal to the product of the other segments in the other chord if that makes sense
So more specifically for this problem
10 * 18 = 9(x-3)
once we are able to create a formula/equation this problem is a lot easier to understand
Now we use basic algebra to solve for x
10 * 18 = 9(x-3)
step 1 combine like terms
10 * 18 = 180
now we have
180 = 9(x-3)
step 2 distribute the 9 to what's in the parenthesis (x and -3)
9*x=9x
9*-3=-27
now we have
180 = 9x - 27
step 3 add 27 to each side
-27 + 27 cancels out
180 + 27 = 207
now we have
207 = 9x
step 4 divide each side by 9
207/9 = 23
9x/9=x
we're left with x = 23
Now we want to check our answer
is 10 * 18 = 9*(23-3) then our answer is correct
10*18=180
23-3=20
20*9=180
180=180 is true hence the answer is 23
Given 15 patients 5 of them has a particular heath disease, what is the probability of taking 2 out of 4 selected patients has heart disease? 5. A certain clinic in the America is on average has a patient of 3 an hour. Find the probability that the clinic will have 4 patients in the next hour.
The probability of selecting 2 out of 4 patients with heart disease from a group of 15 patients, where 5 of them have the disease, can be calculated using the combination formula. The probability is approximately 0.595.
B. Explanation:
To calculate the probability, we need to use the concept of combinations. The formula for calculating combinations is given by:
C(n, k) = n! / (k!(n-k)!)
Where n is the total number of elements and k is the number of elements we want to choose.
In this case, we have a total of 15 patients, out of which 5 have the heart disease. We want to choose 2 patients with heart disease from a group of 4 patients.
The probability can be calculated as:
P(2 patients with heart disease) = C(5, 2) / C(15, 4)
C(5, 2) represents the number of ways to choose 2 patients with the heart disease from the group of 5 patients, and C(15, 4) represents the total number of ways to choose 4 patients from the group of 15 patients.
Using the combination formula, we can calculate C(5, 2) and C(15, 4) as follows:
C(5, 2) = 5! / (2!(5-2)!) = 10
C(15, 4) = 15! / (4!(15-4)!) = 1365
Substituting these values into the probability formula:
P(2 patients with heart disease) = 10 / 1365 ≈ 0.007
Therefore, the probability of selecting 2 out of 4 patients with the heart disease from the given group is approximately 0.595.
Moving on to the second part of the question, to find the probability that the clinic will have 4 patients in the next hour, we need to determine the average number of patients per hour and use the Poisson distribution.
The average number of patients per hour is given as 3. The Poisson distribution formula is:
P(x; λ) = (e^(-λ) * λ^x) / x!
Where P(x; λ) is the probability of x events occurring in a given interval, λ is the average rate of events, e is the base of the natural logarithm, and x! denotes the factorial of x.
In this case, we want to find P(4; 3), which represents the probability of having 4 patients when the average rate is 3.
Substituting the values into the formula:
P(4; 3) = (e^(-3) * 3^4) / 4!
Calculating the values:
P(4; 3) ≈ 0.168
Therefore, the probability that the clinic will have 4 patients in the next hour is approximately 0.168.
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The largest U.S flag in the world is 225 feet by 505 feet.
Is the ratio of the length to the width equivalent to 1:19,
the ratio for official government flags?
Answer:
Step-by-step explanation:
Remark
The ratio should be 10 : 19
Given
Flag Ratio: 225 : 505
Break the dimensions into prime factors.
225: 15 * 15 = 3*5 * 3*5
505: 5 * 101
Conclusion
101 is prime so this dimension cannot be broken down any further
The fives cancel out. The dimensions of this flag are in the ratio of 45/101 which is 0.4455
10/19 = 0.5263
I would say this is reasonably close.
Help me with this plsss
1.
a. 8 x 7 x 1/2 = 56 x 1/2 = 28
b. 24 x 14 x 1/2 = 336 x 1/2 = 168
c. 5 x 12 x 1/2 = 60 x 1/2 = 30
d. 4 x 4.8 x 1/2 = 19.2 x 1/2 = 9.6
2.
two triangles: 2(4 x 8 x 1/2) = 4 x 8 = 32
rectangle: 15 x 8 = 120
total area: 32 + 120 = 152
I need help Please i will give brainlist Please and thank you
Answer:
all I know is the answer for 5 so it is 2.0
Step-by-step explanation:
Answer:
4. 79.17%
5. 2.5
Step-by-step explanation:
4. Q3 - Q1 = 4.75 - 0 = 4.75
[tex]\frac{4.75}{6} *100[/tex] = 79.17
5. Q3 - Q1 = 4.75 - 2.25 = 2.5
please help!
PQRS is a kite. Enter coordinates
for point S.
P(0, b)
S
Q(a, 0)
R(0, -c)
S([ ? ] ,[ ? ])
Answer:
(-a, 0)
Step-by-step explanation:
By telling you that the quadrilaretal is a kite the problem is telling you that SQ is perpendicular to PR, and that PS=PQ (by simmetry, it follows that also RS=RQ). So S has to be the symmetric of Q to the center (intersection of the diagonals), which means that, since Py=0, its coordinates are (-a, 0)
Put the following numbers in order from least to greatest: √42, 7, 6, √38.
Answer:
6, √38, √42, 7
Step-by-step explanation:
The numbers in order from least to greatest is 6,√38,√42,7
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
Finding the least common multiples of the denominator expressions can help. Then using the similar method as we use in sum of fractions would give the sum of algebraic fractions.
Given;
√42, 7, 6, √38
√42=6.4
√38=6.1
Therefore, the order of algebra will be 6,√38,√42,7
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y = 100(1.25)^t
1. What is your initial value?
r17 is greater than or equal to 545.7
Answer:
r17 is that a mistake or actually the number?
Prince Ivan rides Grey Wolf at a constant speed from King's Castle to the Magic Apple Garden in 5 hours. On their return trip to King's Castle, Grey Wolf runs at that original constant speed for the first 36 km. Then he runs the rest of the way 3 km/h faster. What was Grey Wolf's original speed if the return trip took 15 minutes less than the trip from King's Castle to the Magic Apple Garden?
Answer:
48 and 9
Step-by-step explanation:
36/x + 5x-36/x+3 = 5-0.25
Answer:
9 and 48 km/hr
Step-by-step explanation:
The Formula [tex]S=\frac{D}{T}[/tex] along with its variations are used
Let's say for the initial ride, the speed was x. Because the time was 5 hours, the distance was 5x km. Now for the return. For the first part, the speed remains x but our distance is 36km. So, our time is 36/x hours. For the second part, the speed is x+3 but our distance is 5x-36 (The total minus the distance of the first part.) So, our time is [tex]\frac{5x-36}{x+3}[/tex]. Now we have the equation [tex]\frac{36}{x} + \frac{5x-36}{x+3}=5-\frac{1}{4}[/tex] as our times add up to 5 hours minus 1/4 of and hour. Solving, we get x=9, x=48.
here is a picture help me
Answer:
61
Step-by-step explanation:
add the numbers up and divide them by 7
Answer:
Step-by-step explanation:
added up the data = 427
divide by the number of days = 427/7 = 61
Please help me!!!!!!!!
Answer:
#6) A = 72 sq units
Step-by-step explanation:
area of ΔAOB = 6
area of ΔCOB = 6
area of ΔCOD = 30
area of ΔCOD = 30
A student-fare bus pass costs half as much as an adult-fare pass. Together, one student pass and one adult pass cost $129. How much does each pass cost?
Each pass costs $86 and $43 for an adult-fare and student-fare bus pass respectively.
Let the cost of an adult-fare bus pass be A student-fare bus pass costs half as much as an adult-fare pass, hence, the cost of a student pass will be $129 - A.
Mathematically, this is represented as:A = 2($129 - A) $A = $258 - 2A 3A = $258 A = $86Therefore, the cost of an adult-fare bus pass is $86.A student pass costs half as much as an adult-fare pass.
Since the cost of an adult-fare pass is $86, therefore the cost of a student pass will be half of $86. Mathematically, this can be represented as:Cost of student pass = 1/2 x $86 = $43
Therefore, each pass costs $86 and $43 for an adult-fare and student-fare bus pass respectively.
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If arc ED=(9x-3) , arc BF=(15x-39) and angle BCF=(11x-9) find arc ED
Answer:
ED = 105
Step-by-step explanation:
Answer:
ED=105 and x=12
Step-by-step explanation:
what is this answer?
A system of equations is created by using the line that is created by the equation 3x-2y=-4 and the line that is created
by the data in the table below.
Х
y
-9
-3
-1
-5
3
3
5
7
What is the y-value of the solution to the system?
Answer:
y=6x-8
Step-by-step explanation:
3x-2y=-4
3x^2-2y^2=-4^2
6x-y=8
y=6x-8
give the slope of the line with equation 17x = -34; then graph the line
yo someone help will give brainliest
Answer:
[tex]x=3[/tex]
Step-by-step explanation:
Equation - [tex]5=x+2[/tex]
Solve - subtract 2 from both sides - [tex]3 = x[/tex]
Answer:
X= 3 oz.
Step-by-step explanation:
Count left side. Minus the oz. on the right from that amount. You get 3. Chess piece weighs 3 oz.
Hope I helped.
The perimeter of a rectangle is 100 feet, and one side is 6 feet longer than the other side. An equation to find the length x of the shorter side is:
a. x + (x + 6) = 100
b. x + (x - 6) = 100
c. x + (x + 6) = 50
d. x + (x - 6) = 50
So the answer is not among the options provided. To find the equation that represents the relationship between the length of the shorter side (x) and the perimeter of the rectangle,
we can use the given information.
Let's denote the length of the shorter side as x. According to the problem, the other side is 6 feet longer, so the length of the longer side would be x + 6.
The perimeter of a rectangle is given by the sum of all its sides. In this case, the perimeter is 100 feet.
The equation to find the length x of the shorter side can be written as:
2x + 2(x + 6) = 100
Simplifying the equation, we have:
2x + 2x + 12 = 100
4x + 12 = 100
4x = 100 - 12
4x = 88
x = 88/4
x = 22
therefore, the correct equation to find the length x of the shorter side is:
2x + 2(x + 6) = 100
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The equation to find the length x of the shorter side is x + (x - 6) = 50.
Option (d) is the correct answer.
Given that the perimeter of a rectangle is 100 feet, and one side is 6 feet longer than the other side.
Let's suppose that x represents the length of the shorter side of the rectangle.
Therefore, the length of the longer side of the rectangle is (x + 6).
Using the formula of the perimeter of a rectangle, we get:
Perimeter = 2 × (Length + Width)
According to the problem,
Perimeter = 100
Length = (x + 6)
Width = x
Substituting the values,
Perimeter = 2 × (Length + Width)
100 = 2 × [(x + 6) + x]
50= 2x + 6
x = (50 - 6)/2
x = 22
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please help me out! I don’t understand
Answer:
10/26
Step-by-step explanation:
out of 26 student 10 have a brother 8 people have only a brother and 2 people have both a sister and a brother. so you have 10/26
0548 f(x) = 2100 The mean age of a woman in a certain country when her child is born can be approximated by the function where x = 10 corresponds to the year 2010. Estimate the mean age of the woman at the birth of her first child in the following years, The mean age of a woman at the birth of her first child in 2015 is
(a) Mean age in 2010 ≈ 23.9 years
(b) Mean age in 2013 ≈ 24.4 years
(c) Mean age in 2016 ≈ 24.9 years
To estimate the mean age of a woman at the birth of her first child in the given years, we can substitute the corresponding values of x into the function f(x) = 21 × [tex]x^{0.0521[/tex].
(a) For the year 2010 (x = 10):
f(10) = 21 × [tex](10)^{0.0521[/tex] ≈ 21 × 1.136 ≈ 23.856
The mean age of a woman at the birth of her first child in 2010 is approximately 23.9 years.
(b) For the year 2013 (x = 13):
f(13) = 21 × [tex](13)^{0.0521[/tex] ≈ 21 × 1.161 ≈ 24.381
The mean age of a woman at the birth of her first child in 2013 is approximately 24.4 years.
(c) For the year 2016 (x = 16):
f(16) = 21 × [tex](16)^{0.0521[/tex] ≈ 21 × 1.185 ≈ 24.885
The mean age of a woman at the birth of her first child in 2016 is approximately 24.9 years.
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The question is -
The mean age of a woman in a certain country when her child is born can be approximated by the function
f(x)=21x0.0521,
where
x=10
corresponds to the year 2010. Estimate the mean age of the woman at the birth of her first child in the following years.
(a) 2010
(b) 2013
(c) 2016
(a) The mean age of a woman at the birth of her first child in 2010 is?
(b) The mean age of a woman at the birth of her first child in 2013 is?
(c) The mean age of a woman at the birth of her first child in 2016 is?
(Type an integer or decimal rounded to one decimal place as needed.)
Does anyone know the answer to this and if you do pls give it to me I need it ASAP
Answer:
7,3 if rounded up...
not rounded up..... 7, 3.3????? I think???
Slope-intercept form: y = mx + b
First find the slope : [tex]\frac{rise}{run} = \frac{-1}{3}[/tex]
Slope = -1/3
Now we got y = -1/3x + b
Next find y-intercept. This is where your line crosses the y line (vertical)
Y-intercept = 3
b = 3
Answer: y = -1/3x + 3
An electrician deposits $6000 in a bank account with 7% simple interest. What is the total balance after 4 years?
Answer: $42,000
Step-by-step explanation:
Simple Interest: I=prt
I= (6,000)(7/4)(4)
I= 42,000
Expand 3(n + 7) show FULL work
Answer:
3n + 21
Step-by-step explanation:
3(n + 7)
3n + 21
Make a box and whicker plot of the following prices of some DVDs.
{10.99, 12.99, 15.99, 10.99, 26.99, 14.99, 19.99, 19.99, 9.99, 21.99, 20.99)
The box and whisker plot of the prices of some DVDs:
Minimum: 9.99
First Quartile: 12.99
Median: 15.99
Third Quartile: 19.99
Maximum: 26.99
The box and whisker plot shows that the median price of a DVD is $15.99. The prices range from $9.99 to $26.99. There are two outliers, one at $9.99 and one at $26.99.
The box and whisker plot can be used to identify the distribution of the data. In this case, the data is slightly skewed to the right, meaning that there are more DVDs priced at the lower end of the range than at the higher end.
The box and whisker plot can also be used to compare different sets of data. For example, we could compare the prices of DVDs from different stores or from different years.
Overall, the box and whisker plot is a useful tool for visualizing and summarizing data.
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Two positive numbers are in the ratio 2:3.
Find the numbers if (a) their sum is 75 and (b) their product is 150.
(a) If the sum of the numbers is 75, then the smaller number is 30 and the larger number is 45.
(b) If the product of the numbers is 150, then the smaller number is ____ and the larger number is ____
Answer:
60 and 90
Step-by-step explanation: