the confidence intervals for the two groups overlap, and one cannot conclude that one group clearly has a higher proportion in the population than the other.
One cannot say with certainty that in the population more people clearly like buying food at the movies based solely on the given poll results. While 49% of individuals in the poll indicated that they liked buying food at movies, the margin of error is +/- 2%, which means that the true proportion of individuals who like buying food at movies could be as low as 47% or as high as 51%. Similarly, the true proportion of individuals who do not like buying food at movies could be as low as 40% or as high as 44%.
what is proportion?
proportion refers to a measure that expresses the size of one subset (e.g., the number of individuals with a certain characteristic) relative to the size of the entire group or population being considered.
To learn more about proportion visit:
brainly.com/question/30657439
#SPJ11
two students proposed two different designs for their system in their course project. the first student performed 5 experiments to determine the number of customers served within 5 minutes and the second student performed 7 experiments for the same measure. student number of customers served within 5 minutes 1 102 86 98 109 92 2 81 165 97 134 92 87 114 what would each student obtain as their 90% confidence interval for the mean number of customers served within 5 minutes using their respective designs.
Therefore, the 90% confidence interval for Student 1 is (89.61, 105.19). Therefore, the 90% confidence interval for Student 2 is (84.96, 131.24).
To calculate the 90% confidence interval for the mean number of customers served within 5 minutes for each student, we need to use the formula:
CI = X ± (tα/2 * s/√n)
where X is the sample mean, s is the sample standard deviation, n is the sample size, and tα/2 is the critical value from the t-distribution with (n-1) degrees of freedom at the desired confidence level (in this case, 90%).
For Student 1:
X = (102 + 86 + 98 + 109 + 92)/5
= 97.4
s = √([(102-97.4)² + (86-97.4)² + (98-97.4)² + (109-97.4)² + (92-97.4)²]/(5-1))
= 7.94
n = 5
tα/2 = 1.895 (from t-distribution table with 4 degrees of freedom at 90% confidence level)
CI = 97.4 ± (1.895 * 7.94/√5)
= 97.4 ± 7.79
= (89.61, 105.19)
For Student 2:
X = (81 + 165 + 97 + 134 + 92 + 87 + 114)/7
= 108.1
s = √([(81-108.1)² + (165-108.1)² + (97-108.1)² + (134-108.1)² + (92-108.1)² + (87-108.1)² + (114-108.1)²]/(7-1))
= 30.18
n = 7
tα/2 = 1.895 (from t-distribution table with 6 degrees of freedom at 90% confidence level)
CI = 108.1 ± (1.895 * 30.18/√7)
= 108.1 ± 23.14
= (84.96, 131.24)
To know more about confidence interval,
https://brainly.com/question/24131141
#SPJ11
Your fishing bobber oscillates in simple harmonic motion from waves in the lake where you fish. Your bobber moves a total of 1.5 inches from its high point to its low point and returns to its high point every 3 seconds. After how many seconds is the bobber at the midpoint between its highpoint and its low point for the first time?
Using the amplitude of the motion, After approximately 0.89 seconds, the bobber will be at the midpoint between its high point and low point for the first time.
The bobber will be at the midpoint between its high point and low point for the first time after 1.5/4 seconds.
To find the answer, we need to first find the amplitude of the motion, which is half of the total distance the bobber travels, so amplitude = 1.5/2 = 0.75 inches.
Next, we can use the formula for the period of a simple harmonic motion: T = 2π√(m/k), where T is the period, m is the mass, and k is the spring constant. In this case, we can use the formula T = 3 seconds.
Solving for k, we get k = (4π²)m/T². Since we don't know the mass of the bobber, we can assume it's negligible and use k = 4π²/T². Plugging in T = 3 seconds, we get k = 4π ²/⁹.
Now we can use the formula for the displacement of a simple harmonic motion at time t: x = Acos(ωt), where A is the amplitude and ω is the angular frequency (ω = 2π/T). We want to find when the displacement x = 0.5A (i.e. the midpoint between the high and low points), so we can solve for t:
0.5A = Acos(ωt)
0.5 = cos(2πt/3)
2πt/3 = arccos(0.5)
t = 3arccos(0.5)/2π
t ≈ 0.89 seconds
So after approximately 0.89 seconds, the bobber will be at the midpoint between its high point and low point for the first time.
Learn more about the amplitude:
https://brainly.com/question/30696138
#SPJ4
Kylie explained that (-4x+9)2 will result in a difference of squares because (-4x+9)²-(-4x)²+(9)²-16x²+81. Which statement best describes Kylie's explanation?
The correct expansion of (-4x + 9)² is 16x² - 72x + 81.
We have,
Step 1: Start with the expression (-4x + 9)².
Step 2: To expand this expression, we use the formula for the square of a binomial: (a - b)² = a² - 2ab + b².
Step 3: In this case, a is -4x and b is 9.
Applying the formula, we have:
(-4x + 9)² = (-4x)² - 2(-4x)(9) + (9)².
Step 4: Simplify each term in the expansion:
(-4x)² = 16x² (square the first term).
-2(-4x)(9) = 72x (multiply -2, -4x, and 9 together).
(9)² = 81 (square the second term).
Step 5: Combine the simplified terms:
(-4x + 9)² = 16x² - 72x + 81.
Thus,
The correct expansion of (-4x + 9)² is 16x² - 72x + 81.
Learn more about expressions here:
https://brainly.com/question/3118662
#SPJ12
john runs a computer software store. he counted 120 people who walked by his store in a day, 53 of whom came into the store. of the 53, only 26 bought something in the store. estimate the probability that a person who walks into the store will buy something. round your answer to the nearest hundredth. group of answer choices 0.66 0.49 0.22 0.44 none of these choices
For a computer software store, the estimate the probability that a person who walks into the store will buy something is equals to the 0.22. So, option(c) is right one.
Probability is the chances of occurrence of an event. It is calculated by dividing the favourable outcomes to the total possible outcomes.
We have, John runs a computer software store. Number of people walked by his store = 120/ day
Number of people came in his store = 53
Number of people who buy something from the store = 26
We have to determine the estimate the probability that a person who walks into the store will buy something. Let E be an event such that a person walk and buying something from store. Here, total possible outcomes for occurrence an event = 120
Favourable outcomes for event E = 26
So, probability that a person who walks into the store will buy something, P(E) =
[tex] \frac{ 26}{120}[/tex] = 0.21666 ~ 0.22
Hence, required value is 0.22.
For more information about probability, refer:
https://brainly.com/question/25870256
#SPJ4
Complete question:
john runs a computer software store. he counted 120 people who walked by his store in a day, 53 of whom came into the store. of the 53, only 26 bought something in the store. estimate the probability that a person who walks into the store will buy something. round your answer to the nearest hundredth. group of answer choices
a) 0.66
b) 0.49
c) 0.22
d) 0.44
e) none of these choices
As x approaches infinity, the limit [(2x-1)(3-x)]/[(x-1)(x+3)] is
As x approaches infinity, the limit of function [(2x-1)(3-x)]/[(x-1)(x+3)] is equal to -2.
What is function?
In mathematics, a function is a relation between a set of inputs (called the domain) and a set of possible outputs (called the codomain) with the property that each input is related to exactly one output.
To find the limit of [(2x-1)(3-x)]/[(x-1)(x+3)] as x approaches infinity, we need to consider the highest power of x in the numerator and the denominator.
In the numerator, the highest power of x is [tex]x^2[/tex], which comes from the product of (2x)(3). In the denominator, the highest power of x is also [tex]x^2[/tex], which comes from the product of (x)(x).
Thus, we can use the rule that when the highest powers of x in the numerator and denominator are equal, the limit is the ratio of the coefficients of these highest powers. Therefore:
lim [(2x-1)(3-x)]/[(x-1)(x+3)]
= lim [([tex]-2x^2[/tex] + 7x - 3)/([tex]x^2[/tex] + 2x - 3)]
= lim [-2 + (7/x) - (3/[tex]x^2[/tex])] / [1 + (2/x) - (3/[tex]x^2[/tex])]
= -2/1
= -2
Therefore, as x approaches infinity, the limit of [(2x-1)(3-x)]/[(x-1)(x+3)] is equal to -2.
To learn more about function visit:
https://brainly.com/question/11624077
#SPJ4
Rearrange your equation from part A by setting it equal to 0 and substituting y for 0. Then write the equation in the form y=(x-h)^2-c
Rearrange the equation from part A, we get y = (x - 1)^2 - 8
Rearrange the equation from part AFrom the comlete question, the equation from part A
y = x^2 - 2x - 7
To rearrange the equation, we have the following
y = x^2 - 2x - 7
Set to 0
So, we have
x^2 - 2x - 7 = 0
This gives
x^2 - 2x = 7
Take the coefficient of x; divide it by 2 and then add the squared quotient to both sides
So, we have
x^2 - 2x + 1 = 7 + 1
Factorize
(x - 1)^2 = 8
So, we have
(x - 1)^2 - 8 = 0
Replace 0 with y
y = (x - 1)^2 - 8
Hence, the equation is y = (x - 1)^2 - 8
Read complete the square at
https://brainly.com/question/13981588
#SPJ1
There were 70 enrolled students in STAT 3355 during the year 2020 . The population of adults, 18 years or older, in the United States was 258.3 million in 2020 . A student surveyed 30 of her classmates in 2020 and found that 22 students liked to play video games. If this student computed a 95% confidence interval, would it have contained the value of 65%, which was known to be the proportion of adults that liked to play video games in the United States in 2020. (Hint: Calculate the confidence interval by hand at first, and then try to use R ).
The confidence interval for proportion of adults who liked video game is (0.575091,0.8915756 ) from sample. It has a parameter 65%.
Number of enrolled students in STAT during year 2020 = 70
The population of adults that is 18 or above in 2020 = 258.3 million
Number of students are classmates= 30
Out of 30, number of students who like video game = 22
level of significance = 0.95
Let p denote the proportion of students in sample who liked video games. it is p = 22/30 = 0.733.
Using the distribution table, value of z for 95% is equals to the 1.96. From the formula of confidence interval, [tex]CI = p ± z\sqrt{ \frac{ p( 1 - p)}{n}}[/tex]
[tex]= 0.733 ± \sqrt{ \frac{0.733( 1 - 0.733)}{30}}[/tex]
= (0.575091, 0.8915756), the lower limit and upper limit of interval. This interval contains 65% which is population parameter. Hence, required value is (0.575091, 0.8915756).
For more information about confidence interval, visit:
https://brainly.com/question/15712887
#SPJ4
a classroom of children has 10 boys and 12 girls in which five students are chosen at random to do presentations. what is the probability that more boys than girls are chosen?
The probability that more boys than girls are chosen is approximately 39.67%.
To determine the probability that more boys than girls are chosen from a classroom with 10 boys and 12 girls, we need to consider the possible ways this can happen. There are two scenarios:
1. 3 boys and 2 girls are chosen.
2. 4 boys and 1 girl are chosen.
First, calculate the total number of ways to choose 5 students from 22 (10 boys + 12 girls) using the combination formula: C(n, k) = n! / (k! * (n-k)!)
C(22, 5) = 22! / (5! * 17!) = 26,334
Now, calculate the probabilities for the two scenarios:
1. 3 boys and 2 girls are chosen:
C(10, 3) = 10! / (3! * 7!) = 120
C(12, 2) = 12! / (2! * 10!) = 66
Total combinations: 120 * 66 = 7,920
2. 4 boys and 1 girl are chosen:
C(10, 4) = 10! / (4! * 6!) = 210
C(12, 1) = 12! / (1! * 11!) = 12
Total combinations: 210 * 12 = 2,520
Add the combinations for both scenarios: 7,920 + 2,520 = 10,440
Now, calculate the probability:
P(more boys than girls) = Number of favorable outcomes / Total possible outcomes = 10,440 / 26,334 ≈ 0.3967 or 39.67%
So, the probability that more boys than girls are chosen is approximately 39.67%.
To know more probability, visit:
https://brainly.com/question/28207189
#SPJ11
Consider again the question of comparing arm strength regimens. This time we assign regimen type by first splitting the males and females, then randomly assigning treatments within each group. What kind of experimental design is this?
The experimental design in this scenario is a randomized block design. The blocks are the male and female groups, and the treatments (different arm strength regimens) are randomly assigned within each block.
This design allows for better control of potential confounding variables, such as gender, and helps to increase the precision of the results.
This experimental design is called a Stratified Randomized Controlled Trial (RCT). In this design, participants are first divided into separate groups based on a specific characteristic, such as gender (males and females in this case). Then, within each group, treatments are randomly assigned to compare arm strength regimens.
This approach helps ensure that each treatment group has a similar proportion of males and females, reducing potential confounding factors and increasing the of the study's results.
Visit here to learn more about potential confounding : https://brainly.com/question/28450965
#SPJ11
For each one-year period after a car was purchased, its value at the end of the year was 15% less than its value at the beginning of the year
State whether the value of the car as a function of time after it was purchased is best modeled with a linear function, a quadratic function, or an exponential function, and explain why.
Enter your answer and your work or explanation in the space provided.
PART B
If the value of the car 2 years after it was purchased is $17,918, what was the value of the car when it was purchased? Show your work or explain your answer.
Part A) The value of the car as a function of time after it was purchased is best modeled with an exponential decay function.
Part B) The value of If the value of the car 2 years after it was purchased is $17,918, its value when it was purchased was $24,800.
What is an exponential decay function?Exponential functions are classified into two: exponential growth and exponential decay functions.
Exponential decay functions are modeled as y = a(1 - r)ˣ, where y is the decreased or decay value, a is the initial value, r is the decay rate, while x is the exponent, representing the number of periods.
Annual decreasing rate in value = 15% = 0.15
Decay factor = 0.85 (1 - 0.15)
f(x) = a(1 - 0.15)^t
Where x = the value of the car after t years
a = the initial or purchase value of the car
t = the years expired after the purchase date
B) If t = 2 years
x = $17,918
f(x) = a(1 - 0.15)^t
17,918 = a(0.85)^2
a = $24,800
Learn more about exponential functions at https://brainly.com/question/2456547.
#SPJ1
Weights of females have approximately a normal distribution with mean 135 lbs. and standard deviation 20 lbs. Allison weighs 145 lbs. What is the z-score for her weight?
After using the formula: z = (x - μ) / σ , the z-score for Allison's weight is 0.5.So, the z-score for Allison's weight is 0.5.
To find the z-score for Allison's weight, we use the formula:
z = (x - μ) / σ
where x is Allison's weight (145 lbs), μ is the mean weight of females (135 lbs), and σ is the standard deviation (20 lbs).
Substituting the values, we get:
z = (145 - 135) / 20
z = 0.5
Therefore, the z-score for Allison's weight is 0.5.
To calculate the z-score for Allison's weight, we can use the following formula:
z-score = (Allison's weight - mean weight) / standard deviation
Plugging in the given values:
z-score = (145 lbs - 135 lbs) / 20 lbs = 10 lbs / 20 lbs = 0.5
So, the z-score for Allison's weight is 0.5.
Visit here to learn more about standard deviation : https://brainly.com/question/23907081
#SPJ11
What is the median of this data set?
Rainfall (in inches)
Answer:
2, 3, 1, 3, 5, 4---->1, 2, 3, 3, 4, 5
The median is 3.
what is the equation of the major axis of y=1/x
The equation of the major axis of y = 1 / x would be y = x and y = -x.
How to find the equation ?The equation y = 1/x constitutes a rectangular hyperbola. Not like ellipses possessing broadly characterized principal axes, no finite line exists representing the major axis of the given hyperbola.
This is due to the symmetrical relationship around both x- and y-axes where its core remains positioned at (0, 0). In place of a definite line, the asymptotes operate in replaceable fashion, defined as the lines y = x and y = -x, which are values approached at near limit by this specific hyperbola yet never collided with.
Find out more on major axis at https://brainly.com/question/30950392
#SPJ1
What is the slope of the line with an equation of y = 4x + 8?
Answer: 4
Step-by-step explanation:
Answer:
Step-by-step explanation:
there u go
Can somebody help me please I'm in a bit of a rush.
Answer:
a) multiply
b) 16
Step-by-step explanation:
a) To convert a smaller unit of measurement into a larger unit, multiply because more of a smaller unit is required to cover up a larger measurement.
b) We know that there are 16 ounces in a pound, which is the unit rate.
Kiran is thinking about building a structure like this for his younger cousins to play on.
The entire structure is made out of soft foam so the children don't hurt themselves.
How much foam-would-Kiran need to build this play structure?
Kiran would need?
cubic inches of foam to build this play structure.
The entire structure is covered with vinyl so it is easy to wipe clean.
How much vinyl would Kiran need to cover this play structure?
Kiran would need?
square inches of vinyl to cover this play structure.
The foam costs 0.008¢ per in³.
The vinyl costs 0.006€ per in².
What is the total cost for all the foam and vinyl needed to build this play structure?
The cost for the foam needed is $
The cost for the vinyl needed is $
The total cost for all the foam and vinyl needed to build this play structure is $
The total cost for all the foam and vinyl needed to build the play structure would be $419.91
How to calculate the costLet's say the play structure is a cube with each side measuring 36 inches. The total volume of the foam needed to build this cube would be:
V = (36 in)³ = 46,656 in³
Since the structure is a cube, the surface area would be:
A = 6 × (36 in)² = 7,776 in²
The cost for the foam would be:
46,656 in³ × $0.008/in³ = $373.25
The cost for the vinyl would be:
7,776 in² × $0.006/in² = $46.66
Total cost will be:
$373.25 + $46.66 = $419.91
Learn more about cost on
https://brainly.com/question/25109150
#SPJ1
Select the TRUE statements: a A sufficiently large sample size for the central limit theorem is greater than 30 b The variability of sampling distribution of the mean (X-bar) is less than the variability of the individual observations (X) c A sufficiently large sample size for the central limit theorem is greater than 50 d The variability of sampling distribution of the mean (X-bar) is more than the variability of the individual observations (X)
The true statements are:
b. The variability of the sampling distribution of the mean ([tex]\overline x[/tex]) is less than the variability of the individual observations (x)
a. A sufficiently large sample size for the central limit theorem is greater than 30.
The central limit theorem:The CLT states that if a sample is drawn randomly from any population, the distribution of sample means will approach a normal distribution, regardless of the shape of the population distribution, as the sample size increases.
This means that for large enough sample sizes, the mean and standard deviation of the sample mean can be estimated using a normal distribution.
Let's check each option as follows
Statement c is false because a sample size of 30 or greater is often considered sufficiently large for the central limit theorem.
Statement d is false because the variability of the sampling distribution of the mean decreases as the sample size increases, which is why the central limit theorem is useful.
Therefore,
The true statements are:
b. The variability of the sampling distribution of the mean (X-bar) is less than the variability of the individual observations (X)
a. A sufficiently large sample size for the central limit theorem is greater than 30.
Learn more about Central limit theorem at
https://brainly.com/question/18403552
#SPJ4
Consider the function f(x)=9x+4x^â1. For this function there are four important intervals: (â[infinity],A], [A,B) (B,C], and [C,[infinity]) where A, and C are the critical numbers and the function is not defined at B.
Find A
and B
and C
For this function, A is -2/3, B is 0 and C is 2/3.
To find the critical numbers of the function f(x) = 9x + 4[tex]x^{-1}[/tex] , we need to find the values of x where the derivative of the function is equal to zero or undefined.
The derivative of f(x) is:
f'(x) = 9 - 4[tex]x^{-2}[/tex] = 9 - 4/[tex]x^{2}[/tex]
To find where the derivative is equal to zero, we set f'(x) = 0 and solve for x:
9 - 4/[tex]x^{2}[/tex] = 0
4/[tex]x^{2}[/tex] = 9
[tex]x^{2}[/tex] = 4/9
x = ±2/3
Therefore, the critical numbers of f(x) are x = 2/3 and x = -2/3.
To find the intervals where the function is not defined, we need to look for values of x that make the denominator of the expression 4[tex]x^{-1}[/tex] equal to zero. In this case, the function is not defined at x = 0.
Now we need to determine the sign of the derivative in each of the intervals (−∞,A], [A,B), (B,C], and [C,∞).
For x < -2/3, f'(x) is negative because 4/[tex]x^{2}[/tex] is positive and 9 is greater than 4/[tex]x^{2}[/tex] . Therefore, the function is decreasing on the interval (−∞,−2/3).
For −2/3 < x < 0, f'(x) is still negative because 4/[tex]x^{2}[/tex] is positive and 9 is still greater than 4/[tex]x^{2}[/tex] . Therefore, the function is decreasing on the interval (−2/3,0).
For 0 < x < 2/3, f'(x) is positive because 4/[tex]x^{2}[/tex] is positive and 9 is less than 4/[tex]x^{2}[/tex] . Therefore, the function is increasing on the interval (0,2/3).
For x > 2/3, f'(x) is still positive because 4/[tex]x^{2}[/tex] is positive and 9 is still less than 4/[tex]x^{2}[/tex] . Therefore, the function is increasing on the interval (2/3,∞).
Finally, the function is not defined at x = 0, so the interval [A,B) is (−∞,0) and the interval (B,C] is (0,∞).
Therefore, we have:
A = -2/3
B = 0
C = 2/3
To learn more about function here:
https://brainly.com/question/12431044
#SPJ4
8. You and your family are preparing to go on a ski trip tomorrow to Lake Tahoe, and you
decide to watch the weather forecast. In the forecast, you can read the probability of
it snowing tomorrow. Match each term to the corresponding probability of it snowing
yaba
there tomorrow.
Likely Impossible Certain
Probability
P(snow)
P(snow) > 1/
P(snow) = 1
P(snow) = 0
Unlikely
OTALugz al sonnige s
wwportileil erh zidW
Suid
sidizzogmi
Answer:
Step-by-step explanation:
To match each term to the corresponding probability of it snowing tomorrow, we can use the following definitions:
Likely means that the event has a high chance of happening, so the probability is close to 1. For example, P(snow) = 0.9 means that it is very likely to snow tomorrow.
Unlikely means that the event has a low chance of happening, so the probability is close to 0. For example, P(snow) = 0.1 means that it is very unlikely to snow tomorrow.
Certain means that the event will definitely happen, so the probability is exactly 1. For example, P(snow) = 1 means that it will surely snow tomorrow.
Impossible means that the event will never happen, so the probability is exactly 0. For example, P(snow) = 0 means that it will not snow tomorrow at all.
Using these definitions, we can match each term to the corresponding probability as follows:
Likely: P(snow) > 0.5
Unlikely: P(snow) < 0.5
Certain: P(snow) = 1
Impossible: P(snow) = 0
Sketch a curve y = f(x) that satisfies: f(0) = 3, and dy/dx =-2. What is f(x)?
The curve f(x) is f(x) = -2x + 3.
Given that dy/dx = -2, we can integrate both sides with respect to x to obtain:
dy/dx = -2
dy = -2 dx
Integrating both sides, we get:
y = -2x + C
where C is the constant of integration. To find the value of C, we use the initial condition f(0) = 3:
y = -2x + C
f(0) = 3
-2(0) + C = 3
C = 3
Thus, the equation of the curve is:
y = -2x + 3
Therefore f(x) is -2x + 3
We can sketch the curve by plotting a few points. For example, when x = 0, y = 3 (as required by the initial condition). When x = 1, y = 1. When x = -1, y = 5. We can also note that the slope of the curve is always -2, meaning that the curve is a straight line with a negative slope.
Learn more about differentiation here
https://brainly.com/question/31404817
#SPJ4
The 5 owners of Mei's Restaurant remodeled their business. They bought 6 tables, 48 chairs, and 4 crystal light fixtures. The cost of these purchases was divided equally among the owners. Excluding tax, how much did each owner pay?
Answer:
$391.2 per owner
Step-by-step explanation:
find the total price of the items and divide it by five
which of the following run-time complexity orders ranks between the other two? group of answer choices o(2^n) exponential none of these o(n^2) quadratic (or polynomial) o(log n) logarithmic time
As per the question, the complexity that ranks between the other two is O(n^2) - Quadratic (or Polynomial).
How to solveAs we compare the run-time complexities, it's crucial to examine the function’s growth with an increase in input size (n).
Let us analyze the growth rates:
Exponential (O(2^n)): The function doubles for each increment in n. This is very fast growth.
Quadratic (O(n^2)): The function grows proportional to the square of n. This is slower growth compared to exponential but faster than logarithmic.
Logarithmic (O(log n)): The function grows very slowly as n increases. The growth rate is less than linear (O(n)).
So the ranking, from slowest to fastest growth, is:
O(log n) - Logarithmic
O(n^2) - Quadratic (or Polynomial)
O(2^n) - Exponential
As per the question, the complexity that ranks between the other two is O(n^2) - Quadratic (or Polynomial).
Read more about quadratic run-time complexity here:
https://brainly.com/question/24488401
#SPJ1
k = -1
1) If there are parentheses, use the distributive property to dissolve them
−18 − 6k = 6(1 + 3k)
−18 − 6k = 6 + 18k
2) Combine like terms and solve
−18 − 6k + 6k = 6 + 18k + 6k
-18 - 6 = 6 - 6 + 24k
-24 ÷ 24 = 24k ÷ 24
-1 = k
The solution to the equation −18 − 6k = 6(1 + 3k) in terms of k is k = -3/4.
What is equation?A statement that affirms the equivalence of two expressions joined by the equals symbol "=" is known as an equation.
Your steps are correct, and here's the solution to the equation:
−18 − 6k = 6(1 + 3k)
To solve for k, we first use the distributive property to remove the parentheses:
−18 − 6k = 6 + 18k
Then, we simplify the equation by combining like terms:
−18 − 6k + 6k = 6 + 18k + 6k
-18 = 24k
Finally, we isolate k by dividing both sides by 24:
-18/24 = 24k/24
-3/4 = k
Therefore, the solution to the equation −18 − 6k = 6(1 + 3k) in terms of k is k = -3/4.
Learn more about equation on:
https://brainly.com/question/27893282
#SPJ4
The complete question is:
Solve for the value of k in the equation:
-18 - 6k = 6(1 + 3k)
where k is an unknown constant.
a sample of a material has 2000 radioactive particles in it today. your grandmother measured 4000 radioactive particles in it 80 years ago. how many radioactive particles will the sample have 80 years from today?
Radioactive particles 2000 the sample have 80 years from today.
We have the information:
There is 2000 radioactive particles in a sample.
and, your grandmother measured 4000 radioactive particles in it 80 years ago.
We have to find the samples of radioactive particles present it in 80 years from today.
By the definition of Half line, The half line of the item is 80 years.
=> 80 years from now, means that another half life is achieved means, 2000 will reduced to half on decay.
Learn more about Exponential growth and decay at:
https://brainly.com/question/12490064
#SPJ4
Approximately 72% of the U.S. population recycles. According to a green survey of a random sample of 250 college students, 182 said that they recycled. Akz - 0.10, Is there sufficient evidence to conclude that the proportion of college students who recycle is greater than 72%? Use a graphing calculator. Part 1 out of 4 State the hypotheses and identify the claim with the correct hypothesis. (select) H,:P (select) H:p (select) (select) The hypothesis test is a (select) test.
The hypothesis test is a one-tailed test, since we are testing for a specific direction (greater than 72%).
What is hypothesis?An assumption is said to as a hypothesis when it is supported by evidence. Any investigation that turns the research questions into predictions must start here. Variables, the population, and the relationships between the variables are among its constituent parts.
The hypotheses for the test are:
H0: p = 0.72 (null hypothesis)
Ha: p > 0.72 (alternative hypothesis)
The claim is that the proportion of college students who recycle is greater than 72%, which corresponds to the alternative hypothesis.
The hypothesis test is a one-tailed test, since we are testing for a specific direction (greater than 72%).
Learn more about hypothesis on:
https://brainly.com/question/14587073
#SPJ4
find the average rate of change of over the interval . for how many values of in the interval does the instantaneous rate of change of equal the average rate of change of over that interval?
there are two values of x in the interval where the instantaneous rate of change of is equal to the average rate of change of over the interval.
To find the average rate of change of over the interval , we need to calculate the slope of the line passing through the two endpoints of the interval.
The slope of the line passing through the points and is given by:
( - )/( - ) = ( -3 - 3)/(1 - (-1)) = -6/2 = -3
Therefore, the average rate of change of over the interval is -3.
To find how many values of in the interval have instantaneous rate of change equal to the average rate of change, we need to find the derivative of :
f'(x) = 3x^2 - 3x - 3
Setting f'(x) equal to the average rate of change, we get:
3x^2 - 3x - 3 = -3
Simplifying the equation, we get:
3x^2 - 3x = 0
Factoring out 3x, we get:
3x(x - 1) = 0
Therefore, the solutions are x = 0 and x = 1.
To learn more about solutions visit:
brainly.com/question/30665317
#SPJ11
find y using Pythagoras theory
8.2 cm
20.2 cm
The value of y in the right triangle is 27.3 cm.
How to find the side of a right angle triangle?A right angle triangle is a triangle that has one of its angle as 90 degrees.
The sum of angles in a triangle is 180 degrees.
Therefore, let's apply Pythagoras's theorem to find the sides of the right triangle as follows:
c² = a² + b²
where
c = hypotenuse sidea and b are other legsTherefore,
20.2² - 16.4² = h²
408.04 - 268.96 = h²
h = √677
h = 26.0192236625
h = 26.0 cm
Let's find y as follows:
y² = 26² + 8.2²
y = √676 + 67.24
y = √743.24
y = 27.2624283585
y = 27.3 cm
learn more on right triangle here: https://brainly.com/question/29169306
#SPJ1
a pharmaceutical lab states that a drug causes negative side effects in 3 of every 100 patients. to confirm this affirmation, another laboratory chooses 10 people at random who have consumed the drug. assume that these 10 patients are not related to each other. find the expected number of people who experienced negative side effects
In this scenario, we are dealing with a probability problem that involves pharmaceutical and people. The pharmaceutical lab claims that 3% of patients experience negative side effects when taking a particular drug.
However, to confirm this, another lab randomly selects 10 PEOPLE who have taken the drug and wants to determine the expected number of people who experienced negative side effects.
To solve this problem, we can use the binomial distribution formula, which states that the probability of x successes in n trials is given by:
P(x) = (nCx) * p^x * q^(n-x)
Where nCx is the binomial coefficient, p is the probability of success, q is the probability of failure (1-p), and x is the number of successes.
In this case, n = 10, p = 0.03, and q = 0.97 (since the drug causes negative side effects in 3 out of 100 patients, or 0.03). To find the expected number of people who experienced negative side effects, we can simply multiply the number of trials (n) by the probability of success (p):
Expected number of people = n * p
Expected number of people = 10 * 0.03
Expected number of people = 0.3
Therefore, we can expect that 0.3 (or 3 out of 10) of the randomly selected patients experienced negative side effects from the drug. It's important to note that this is only an expected value and does not guarantee that exactly 3 patients will experience negative side effects. The actual number may vary.
learn more about drug here: brainly.com/question/13294633
#SPJ11
ratio problems pls sssss
Answer:
see explanation
Step-by-step explanation:
ratio of sides = 8 : 5 : 7 = 8x : 5x : 7x ( x is a multiplier )
given the perimeter = 480 , then
8x + 5x + 7x = 480
20x = 480 ( divide both sides by 20 )
x = 24
then
8x = 8 × 24 = 192
5x = 5 × 24 = 120
7x = 7 × 24 = 168
the sides of the triangle are 192 inches, 120 inches, 168 inches
-------------------------------------------------------------------------------------------
ratio of angles = 8 : 15 : 17 = 8x : 15x : 17x ( x is a multiplier )
the sum of the angles in a triangle = 180° , then
8x + 15x + 17x = 180
40x = 180 ( divide both sides by 40 )
x = 4.5
Then
8x = 8 × 4.5 = 36
15x = 15 × 4.5 = 67.5
17x = 17 × 4.5 = 76.5
the angles in the triangle are 36°, 67.5°, 76.5°
Is it true that Every square matrix is a product of elementary matrices.
It is true that every invertible square matrix can be written as a product of elementary matrices. because, it depends on whether you are talking about invertible square matrices or all square matrices.
An elementary matrix is a matrix that can be obtained from the identity matrix by performing a single elementary row operation (such as swapping two rows, multiplying a row by a scalar, or adding a multiple of one row to another).
Moreover, any matrix that can be expressed as a product of elementary matrices is invertible.
However, not every square matrix is invertible, and so not every square matrix can be written as a product of elementary matrices. For example, the zero matrix cannot be written as a product of elementary matrices since it is not invertible.
So, it depends on whether you are talking about invertible square matrices or all square matrices.
for such more question on square matrix
https://brainly.com/question/3617398
#SPJ11
