Answer:
The number by which the given number should be multiplied is 2.--------------------------
Find the prime factors of 1352:
1352 = 2*2*2*13*13 = 2³*13²We need another factor of 2 as a minimum added in order to have even number of same factors:
2⁴*13² = (2²*13)² = (4*13)² = 52²Hence we need to multiply the given number by 2.
Twelve of the workers received the following salaries: three of them earn P12,500 a month, four of them earn P11,000; twoearn P10,500 and the rest earn P9,000 a month. What is the median salary of the workers?
The median salary of the workers is P11,000.
What is median?In statistics, the median is a measure of central tendency that represents the middle value of a data set when the data set is ordered from least to greatest (or vice versa). If the data set has an odd number of values, the median is the middle value. If the data set has an even number of values, the median is the average of the two middle values. The median is used as a measure of central tendency when the data set has outliers or is not normally distributed.
How to calculate median?To calculate the median of a set of numbers:
Put the numbers in order from lowest to highest.If the number of items in the list is odd, the median is the middle number. For example, if the list is 3, 5, 7, 9, 11, the median is 7.If the number of items in the list is even, the median is the average of the two middle numbers. For example, if the list is 4, 6, 8, 10, the median is (6 + 8)/2 = 7.In the given question,
To find the median salary of the workers, we need to arrange the salaries in order from lowest to highest.
The salaries are:
P9,000, P9,000, P10,500, P10,500, P11,000, P11,000, P11,000, P11,000, P12,500, P12,500, P12,500, P12,500
There are 12 workers, so the median salary will be the average of the 6th and 7th salaries when arranged in order.
Median salary = (P11,000 + P11,000)/2
= P11,000
Therefore, the median salary of the workers is P11,000.
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The question is in the picture.
The composite function is obtained applying the inner function as the input to the outer function.
The functions for this problem are defined as follows:
Inner function: T(t) = 6t + 1.2.Outer function: N(T) = 20T² - 128t + 77.Hence the composite function is obtained replacing the two instances of T on the function N(t) by the definition of T(t), hence:
N(T(t)) = 20(6t + 1.2)² - 128(6t + 1.2) + 77
N(T(t)) = 720t² + 288t + 28.8 - 768t - 204.6.
N(T(t)) = 720t² - 480t - 175.8.
For a population of 18413 bacteria, we have that N(T(t)) = 18413, hence:
720t² - 480t - 175.8 = 18413
720t² - 480t - 18588.8 = 0.
The coefficients of the quadratic function are given as follows:
a = 720, b = 480, c = -18.588.8.
Using a quadratic function calculator, the positive solution is given as follows:
t = 4.76 hours.
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Andy has 4 red cards, 3 blue cards, and 2 green cards. He chooses a card and replaces it before choosing a card again. How many possible outcomes are in the sample space of Andy's experiment?
A) 18
B) 9
C)81
D)3
There are 81 potential outcomes in Andy's sample space.
What are the potential results?Potential Outcomes is a list of every scenario that could happen as a result of an occurrence. For instance, while rolling a dice, the possible results are 1, 2, 3, 4, 5, and 6. 6. Favorable Result - the intended outcome. For instance, if you roll a 4 on a dice, the only possible result is 4.
The total number of cards (i.e., 4 + 3 + 2 = 9) determines the number of outcomes that can occur in each draw.
We must multiply the total number of results for each draw in order to determine the total number of possible outcomes for the two draws.
For two draws with replacement, there are exactly as many outcomes available as the product of the amount of outcomes that could occur in each draw.
9 × 9 = 81.
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A TRIANGLE HAS TWO SIDES OF LENTHS 6 AND 9. WHAT VALUE COULD THE LENGTH OF THE THIRD SIDE BE
Answer:
The value could be any length between 3 and 15
Step-by-step explanation:
9 - 6 = 3
and
9 + 6 = 15
Census data for a certain county shows that 19% of the adult residents are Hispanic. Suppose 92 people are called to jury duty and only 11 of them are Hispanic. Does this apparent underrepresentation of Hispanics call into question the fairness of the jury selection process? Again run a test using the PHANTOMS method to complete all parts of your problem.
Yes, the apparent under representation of Hispanics on the jury duty calls into question the fairness of the jury selection system, as the results of the hypothesis test suggest that the system may be systematically excluding Hispanics.
To determine whether the apparent underrepresentation of Hispanics on the jury selection system is statistically significant and calls into question its fairness, we need to perform a hypothesis test.
First, we set up the null hypothesis, which is the assumption that there is no difference between the proportion of Hispanics in the county population and the proportion of Hispanics in the jury pool. That is, the proportion of Hispanics in the jury pool is expected to be equal to 19%.
The alternative hypothesis is that there is a difference between the proportion of Hispanics in the county population and the proportion of Hispanics in the jury pool.
We can use a one-tailed z-test to test the null hypothesis, where the test statistic is calculated as:
z = (p - P) / sqrt(P(1-P)/n)
where p is the proportion of Hispanics in the jury pool, P is the proportion of Hispanics in the county population (0.19), and n is the sample size (72).
Plugging in the values, we get
z = (9/72 - 0.19) / sqrt(0.19*(1-0.19)/72) = -2.39
Assuming a significance level of 0.05, we compare the calculated z-value with the critical z-value of -1.645 (obtained from a standard normal distribution table). Since the calculated z-value is less than the critical z-value, we reject the null hypothesis and conclude that the proportion of Hispanics in the jury pool is significantly different from the proportion of Hispanics in the county population.
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the formula for converting degrees fahrenheit (F) to degrees Kelvin is K= 5/9 (F = 459.67) Solve for F, terms of K
The formula for converting degrees Kelvin to degrees Fahrenheit is F = (9/5) K + 459.67.
What is degrees Fahrenheit and degrees Kelvin?Degrees Kelvin and Degrees Fahrenheit are two temperature measuring measures that are widely used across the globe. While Kelvin is an international standard unit of measurement, Fahrenheit is mostly used in the United States.
The fact that they measure temperature on distinct scales explains the difference between degrees Fahrenheit (F) and degrees Kelvin (K). Whereas Kelvin is based on a scale of 100 degrees between the freezing and boiling temperatures of water at normal atmospheric pressure, Fahrenheit is based on a scale of 180 degrees between these extremes.
Given that, K = 5/9 (F - 459.67).
To obtain F in term of K we isolate the value of F as follows:
K = 5/9 (F - 459.67)
Multiplying both sides by 9/5, we get:
(9/5) K = F - 459.67
Adding 459.67 to both sides, we get:
F = (9/5) K + 459.67
Hence, the formula for converting degrees Kelvin to degrees Fahrenheit is F = (9/5) K + 459.67.
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A dietician is planning a snack package of fruit and nuts. Each ounce of fruit will supply 1 unit of protein, 2 units of carbohydrates, and 1 unit of fat. Each ounce of nuts will supply 1 unit of protein, 1 unit of carbohydrates, and 1 unit of fat. Every package must provide at least 8 units of protein, at least 11 units of carbohydrates, and no more than 10 units of fat. Let x equal the ounces of fruit and y equal the ounces of nuts to be used in each package.
Let x be the number of ounces of fruit and y the number of ounces of nuts. Referring to the chart, give the three inequalities that x and y must satisfy because of the package's requirements for protein, fat, and carbohydrate.
__ _ 8
__ _ 11
__ _ 10
Give the inequalities that x and y must satisfy because they cannot be negative.
y ≥ __
x ≥ __
Answer:
Step-by-step explanation:
The three inequalities that x and y must satisfy because of the package's requirements for protein, fat, and carbohydrate are:
Protein: 1x + 1y ≥ 8 (at least 8 units of protein)
Carbohydrates: 2x + 1y ≥ 11 (at least 11 units of carbohydrates)
Fat: 1x + 1y ≤ 10 (no more than 10 units of fat)
The inequalities that x and y must satisfy because they cannot be negative are:
x ≥ 0
y ≥ 0
Step-by-step explanation:
To satisfy the requirements for protein, fat, and carbohydrates, the following three inequalities must be satisfied:
1. 1x + 1y ≥ 8 (At least 8 units of protein)
2. 2x + 1y ≥ 11 (At least 11 units of carbohydrates)
3. 1x + 1y ≤ 10 (No more than 10 units of fat)
To ensure that x and y are non-negative, the following inequalities must be satisfied:
x ≥ 0y ≥ 0
Therefore, the complete set of inequalities for x and y are:
x + y ≥ 82x + y ≥ 11x + y ≤ 10x ≥ 0y ≥ 0
can someone help me? please
evalute the following function h(x)=3x2+ax-1 for h(3) and find the value for a.
Answer:
Step-by-step explanation:
[tex]h(3)=3\times 3^2+3a-1 \rightarrow h(3)=26+3a[/tex]
But we cannot find [tex]a[/tex] unless we are told what [tex]h(3)[/tex] equals.
Which of the following is true regarding cross-sectional data sets? Check all that apply. The data consist of a sample of multiple individuals. It can be assumed that the data were obtained through a random sampling of the underlying population. These data require attention to the frequency at which they are collected (weekly, monthly, yearly, etc.). The data are collected at approximately the same point in time.
The correct options are:
The data contain a sample of multiple individuals.
The data are collected are approximately at the same point in time.
Cross-sectional data sets are a type of research design used in statistical analysis. They consist of a sample of multiple individuals or entities observed at a single point in time. One of the characteristics of cross-sectional data sets is that they do not involve any observation or measurement over time, making them different from longitudinal or time-series data sets.
One advantage of cross-sectional data sets is that they are relatively easy and inexpensive to collect. It can be assumed that the data were obtained through a random sampling of the underlying population, making them representative of the larger population. However, these data require attention to the frequency at which they are collected (weekly, monthly, yearly, etc.), as the timing of data collection can impact the results.
Overall, cross-sectional data sets can provide a snapshot of a population or phenomenon at a specific point in time, making them useful for a wide range of research questions in social, economic, and political sciences.
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Work out the size of angle x. 79°) 35
Answer: 66
Step-by-step explanation:
all 3 of them should equal to 180
so 79+35 is 114
180-114 will give us the answer which is 66
Please answer the attached question
The values of e and f in the given equation are: e = 2√3 ± √(4√3), e = 2√3 ± 2√2, and f = 4√3.
How are radicals solved?Equations containing radicals can be made simpler by solving the resultant equation after squaring both sides of the equation to remove the radical. Nonetheless, caution must be exercised to guarantee that any solutions found are reliable and adhere to any variables' limitations.
The given equation is [tex](e - 2\sqrt{3} )^2[/tex] = f - 20√3.
Expanding the left side of the equation we have:
[tex](e - 2\sqrt{3} )^2[/tex] = (e - 2√3)(e - 2√3)
= [tex]e^2[/tex] - 2e√3 - 2e√3 + 12
= [tex]e^2[/tex] - 4e√3 + 12
Substituting back in the function
[tex]e^2[/tex] - 4e√3 + 12 = f - 20√3
[tex]e^2[/tex] - 4e√3 - f + 20√3 - 12 = 0
Using the quadratic formula:
e = [4√3 ± √(16*3 + 4(f - 20√3 + 12))] / 2
e = [4√3 ± √(4f - 64√3)] / 2
e = 2√3 ± √(f - 16√3)
Now for,
(e - 2√3)² = f - 20√3
(2√3 + √(f - 16√3) - 2√3)² = f - 20√3
f - 20√3 = f - 16√3
f = 4√3
Hence, the values of e and f in the given equation are: e = 2√3 ± √(4√3), e = 2√3 ± 2√2, and f = 4√3.
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The odometer in Mr. Washington's car does not work correctly. The odometer recorded 14.3 miles for his last trip to the hardware store,but he knows the distant traveled is 17 miles.What is the percent error. Show steps
Find the percent errors, use the formula a-x/x ×100%
Answer:
15.8823% error
Step-by-step explanation:
Percent Error Formula
abs([tex]\frac{(a-x)}{x}[/tex]) * 100%
abs: absolute value
a: actual value
x: expected value
Percent Error = abs([tex]\frac{14.3 - 17}{17}[/tex]) * 100%
= abs(-0.158823) * 100%
15.8823% error
locate the absolute extrema of the function
on the closed interval
Answer:
To find the integral of f(x) = 2x + 5/3 over the interval [0, 5], we can use the definite integral formula:
∫[a,b] f(x) dx = F(b) - F(a)
where F(x) is the antiderivative of f(x).
First, we find the antiderivative of f(x):
F(x) = x^2 + (5/3)x + C
where C is the constant of integration.
Next, we evaluate F(5) and F(0):
F(5) = 5^2 + (5/3)(5) + C = 25 + (25/3) + C
F(0) = 0^2 + (5/3)(0) + C = 0 + 0 + C
Subtracting F(0) from F(5), we get:
∫[0,5] f(x) dx = F(5) - F(0)
= 25 + (25/3) + C - C
= 25 + (25/3)
= 100/3
Therefore, the definite integral of f(x) = 2x + 5/3 over the interval [0, 5] is 100/3.
$9,300 is invested in an account earning 8.9% interest (APR), compounded daily. Write a function showing the value of the account after � t years, where the annual growth rate can be found from a constant in the function. Round all coefficients in the function to four decimal places. Also, determine the percentage of growth per year (APY), to the nearest hundredth of a percent.
The function for the value of the account after t years can be written as:
V(t) = 93000(1.08900365)t
The coefficient of 1.08900365 is the annual growth rate (APR) compounded daily. After rounding to four decimal places, it becomes 1.0890.
The percentage of growth per year (APY) is 8.90%. This is the same as APR, but expressed as a percentage.
Below is the graph of a trigonometric function. It has a minimum point at
(1, 1.5) and an amplitude of 1.5. What is the midline equation of the function?
The midline equation of the function is y = 1.5.
What is amplitude of trigonometric functions?The gap between a trigonometric function's highest and least values is known as its amplitude. The difference between the greatest and minimum numbers is, in other words, divided by two. For instance, the amplitude is A in the equation y = A sin(Bx) + C. The amplitude, also known as the average value of the function across a period, denotes the "height" of the function above and below the midline. It gauges the magnitude or intensity of the oscillation of the function's representation of. The oscillation is more prominent and subtler depending on the amplitude, which ranges from higher to lower values.
Given that, the function has minimum point at (1, 1.5) and an amplitude of 1.5.
Using the definition of the amplitude the midline is the given amplitude.
Hence, the midline equation of the function is y = 1.5.
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Answer:
3
Step-by-step explanation:
Khan Academy
How do you write 0.38 as a percentage?
Write your answer using a percent sign (%).
Answer:
38%
Step-by-step explanation:
I learned in class on Friday.
Multiply both numerator and denominator by 100. We do this to find an equivalent fraction having 100 as the denominator.
[tex]0.38\times \dfrac{100}{100}[/tex]
[tex]= (0.38 \times 100) \times \dfrac{1}{100} =\dfrac{38}{100}[/tex]
Write in percentage notation: 38%
Question 20 (2 points)
Suppose a survey was given to students at WCC and it asked them if they voted for
the Democrat or Republican in the last election. Results of the survey are shown
below:
Democrat Republican
Male. 50. 75
Female. 125. 50
If a student from the survey is selected at random, what is the probability they voted
for the republican?
75/50
50/75
75/300
125/300
Answer:
The table given provides the number of male and female students who voted for each party, but it does not give the total number of students in the survey. To find the probability of selecting a student who voted for the Republican party, we need to know the total number of students who participated in the survey.
The total number of students in the survey is:
50 + 75 + 125 + 50 = 300
The number of students who voted for the Republican party is:
75 + 50 = 125
Therefore, the probability of selecting a student who voted for the Republican party is:
125/300 = 0.4167 (rounded to four decimal places)
So, the answer is option D: 125/300
(please mark my answer as brainliest)
f(x)
g(x)
=6x−4
=3x
2
−2x−10
Escribe (g∘f)(x) como una expresión en términos de x.
Answer:
g(x)
=6x−4
=3x
2
−2x−10
Escribe (g∘f)(x) como una expresión en términos de x.
Step-by-step explanation:
Primero necesitamos conocer la función f(x). Luego podemos sustituir f(x) en g(x) para obtener (g∘f)(x).
Como la función f(x) no se proporcionó en la pregunta, asumiré que f(x) es:
f(x) = x^2 - 2x + 1
Entonces, podemos sustituir f(x) en g(x) de la siguiente manera:
g(f(x)) = 6f(x) - 4
= 6(x^2 - 2x + 1) - 4 (sustituyendo f(x))
= 6x^2 - 12x + 2
Por lo tanto, (g∘f)(x) = 6x^2 - 12x + 2.
The table shows some points on the graph of exponential function g(x)
0 1 2 3 4 g(x) 1 3 9 27 81 What is the range of g?
the range of g is all positive numbers greater than or equal to 1. In set-builder notation, we can write the range of g as {g(x) | g(x) ≥ 1}.
How to solve and what is graph?
The range of a function refers to the set of all possible output values. Looking at the table, we can see that the output values of g(x) increase rapidly as x increases.
In fact, the output values of g(x) are the result of raising 3 to the power of x, which means that g(x) can never be negative. Therefore, the range of g is all positive numbers greater than or equal to 1. In set-builder notation, we can write the range of g as {g(x) | g(x) ≥ 1}.
A graph is a visual representation of data or mathematical functions. It is a diagram made up of points, lines, and curves that show the relationship between different variables or data points.
Graphs are used to display and analyze data, to illustrate trends and patterns, and to communicate complex information in an easily understandable way. There are many different types of graphs, including bar graphs, line graphs, pie charts, scatter plots, and more, each suited to different types of data and analysis.
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What gravitational force does the moon produce on the Earth if their centers are 3.88x108 m apart and the moon has a mass of 7.34x1022 kg?
The gravitational force that the moon produces on the Earth is approximately [tex]1.98 \times 10^{20}\ \mathrm{N}$.[/tex]
What is gravitational force?
Gravitational force is the force of attraction that exists between any two objects in the universe with mass. This force is directly proportional to the masses of the objects and inversely proportional to the square of the distance between their centers.
The gravitational force that the moon produces on the Earth can be calculated using the formula:
[tex]F = G \cdot \frac{m_1 \cdot m_2}{r^2}[/tex]
where:
[tex]G$ = gravitational constant = $6.67430 \times 10^{-11}\ \mathrm{N(m/kg)^2}$[/tex]
[tex]m_1$ = mass of the moon = $7.34 \times 10^{22}\ \mathrm{kg}$[/tex]
[tex]m_2$ = mass of the Earth = $5.97 \times 10^{24}\ \mathrm{kg}$ (approximate)[/tex]
[tex]r$ = distance between the centers of the Earth and the moon = $3.88 \times 10^8\ \mathrm{m}$[/tex]
Substituting these values into the formula, we get:
[tex]F &= 6.67430 \times 10^{-11} \cdot \frac{7.34 \times 10^{22} \cdot 5.97 \times 10^{24}}{(3.88 \times 10^8)^2} \&= 1.98 \times 10^{20}\ \mathrm{N}[/tex]
Therefore, the gravitational force that the moon produces on the Earth is approximately [tex]1.98 \times 10^{20}\ \mathrm{N}$.[/tex]
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How many proper subsets are in {2,4,6,8...100}
Answer:
159 proper subsets.
Step-by-step explanation:
Given a set {2, 4, 6, 8...100}, how many proper subsets are there?
First, find how many subsets there are in 2 - 10:
That's 16.
Then because there are 10 10s in 100, multiply by 10:
16 x 10 = 160
Finally, because it says proper subsets, subtract by 1:
160 - 1 = 159 proper subsets.
Therefore, there are 159 proper subsets in {2, 4, 6, 8...100}
What rotation centered about the origin maps (4, − 7) to (7,4) ? 90° counterclockwise 180° counterclockwise 270° counterclockwise I don't know. ←
Answer:
What rotation centered about the origin maps (4, − 7) to (7,4) ? 90° counterclockwise 180° counterclockwise 270° counterclockwise I don't know. ←
Step-by-step explanation:
To map the point (4, -7) to (7, 4) by a rotation centered about the origin, we need to find the angle of rotation and direction.
We can start by finding the vector from the origin to (4, -7), which is <4, -7>. We want to rotate this vector to the vector from the origin to (7, 4), which is <7, 4>.
To do this, we need to find the angle between these two vectors. Using the dot product, we have:
<4, -7> · <7, 4> = (4)(7) + (-7)(4) = 0
Since the dot product is zero, we know that the two vectors are orthogonal, and the angle between them is 90 degrees.
To map (4, -7) to (7, 4) with a 90-degree rotation counterclockwise, we can use the matrix:
[0 -1]
[1 0]
Multiplying this matrix by the vector <4, -7>, we get:
[0 -1] [4] = [-7]
[1 0] [-7] [ 4]
which corresponds to the point (-7, 4). This matches our desired endpoint, so the answer is 90° counterclockwise.
Answer:
90° counterclockwise
Step-by-step explanation:
I am not sure if the picture helps or not. I am trying to show that I traced the point (4,-7). Then I have a plus sign at (0,0). I start rotating the tracing paper counterclockwise until I get to the point (7,4). I needed to turn one turn of the plus sign. That would be 90°
Helping in the name of Jesus.
(a)A Chinese restaurant offers 10 different lunch specials. Each weekday for one week, Fiona goes to the restaurant and selects a lunch special. How many different ways are there for her to select her lunches for the week? Note that which lunch she orders on which day matters, so the following two selections are considered different.One possible selection:Mon: Kung pao chickenTues: Beef with broccoliWed: Kung pao chickenThurs: Moo shu porkFri: Beef with broccoliA different selection:Mon: Beef with broccoliTues: Kung pao chickenWed: Kung pao chickenThurs: Moo shu porkFri: Beef with broccoli(b)Now suppose that in addition to selecting her main course, she also selects between water or tea for her drink. How many ways are there for her to select her lunches?
(a) There are 100,000 different ways for Fiona to select her lunches for the week.
(b) There are 200,000 different ways for Fiona to select her lunches and drinks for the week.
(a) Since Fiona selects one lunch special each day, there are 10 options for Monday, 10 options for Tuesday, and so on, for a total of 10 options for each of the 5 weekdays. Therefore, the total number of ways for Fiona to select her lunches for the week is:
10 × 10 × 10 × 10 × 10 = 10^5 = 100,000
(b) In addition to the 10 lunch specials, Fiona now has 2 options for her drink, either water or tea. So for each of the 100,000 possible lunch selections from part (a), there are 2 possible drink options. Therefore, the total number of ways for Fiona to select her lunches and drinks for the week is:
100,000 × 2 = 200,000
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What does the point (5, 10) represent on the
graph?
Answer:
It means the point x = 5 and y = 10
Answer: The place 5 units right and 10 units up from the center of the graph (the origin).
Step-by-step explanation:
Starting at the origin, the 5 represents moving right 5, and the 10 represents going up 5.
The graph of y = 5x2 is
Answer:
................................
the circumference of a circle is 4.8m. Calculate the area of the circle
Answer:
A≈1.83m²
Step-by-step explanation:
Using the formulas
A=πr2C=2πr
Solving forAA=C24π=4.824·π≈1.83346m²
Answer:
1.83 (approximate)
Step-by-step explanation:
First, we need to find the radius of the circle.
Using the formula:
[tex]C=2 \pi r[/tex]
We have to reorganize terms:
[tex]r=\frac{C}{2\pi}[/tex]
[tex]\frac{4.8}{2 \times \pi}[/tex]
r ≈ 0.76
Now we have the radius and the circumference in order to find the area.
Use the formulas:
[tex]A= \pi r^2[/tex]
[tex]C=2 \pi r[/tex]
A = C^2/4[tex]\pi[/tex] = 4.8^2 / 4 * pi = 1.83
Question 13 (2 points)
Suppose you flip a coin and then roll a die. You record your result. What is the
probability you flip heads or roll a 3?
1/2
3/4
7/12
1
Step-by-step explanation:
a probability is always the ratio
desired cases / totally possible cases
we have 2 possible cases for the coin and 6 possible cases for the die.
so, we have 2×6 = 12 combined possible cases :
heads, 1
heads, 2
heads, 3
heads, 4
heads, 5
heads, 6
tails, 1
tails, 2
tails, 3
tails, 4
tails, 5
tails, 6
out of these 12 cases, which ones (how many) are desired ?
all first 6 plus (tails, 3) = 7 cases
so, the correct probability is
7/12
formally that is calculated :
1/2 × 6/6 + 1/2 × 1/6 = 6/12 + 1/12 = 7/12
the probability to get heads combined with the probability to roll anything on the die, plus the probability to get tails combined with the probability to roll 3.
Help pleaseeee!!
On January 1, 2014, the federal minimum wage was $7.25 per hour. Which graph has a slope that best represents this rate?
The horizontal line at $7.25 on the y-axis of the graph is the one with a slope that most accurately depicts the federal minimum wage of $7.25 per hour as of January 1, 2014.
Which federal minimum wage was the highest?Although it varies from state to state, the federally mandated minimum wage in the United States is $7.25 per hour. The District of Columbia had the highest minimum wage in the US as of January 1, 2023, at 16.50 dollars per hour.
How are minimum wages determined?The variable dearness allowance (VDA) component, which takes into account inflationary trends, such as an increase or fall in the Consumer Price Index (CPI), and, if applicable, the housing rent, are included in the computation of the monthly minimum salary.
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A simple random sample with n = 25 provided a sample mean of 30 and a sample standard deviation of 4. Assume the population is approximately normal. a. Develop a 90% confidence interval for the population mean. b. Develop a 95% confidence interval for the population mean. c. Develop a 99% confidence interval for the population mean. d. What happens to the margin of error and the confidence interval as the confidence level is increased?
Conversely, as the confidence level decreases, the margin of error becomes smaller, and the confidence interval becomes narrower.
What is confidence interval?In statistics, a confidence interval is a range of values that is likely to contain the true value of a population parameter (such as a mean or a proportion), based on a sample from that population. The confidence interval is typically expressed as an interval around a sample statistic, such as a mean or a proportion, and is calculated using a specified level of confidence, typically 90%, 95%, or 99%.
Here,
To develop a confidence interval, we need to use the following formula:
Confidence Interval = sample mean ± margin of error
where the margin of error is calculated as:
Margin of Error = z* (sample standard deviation/ √n)
where z* is the critical value from the standard normal distribution table based on the chosen confidence level.
a. For a 90% confidence interval, the critical value (z*) is 1.645. Thus, the margin of error is:
Margin of Error = 1.645 * (4 / √25) = 1.317
So, the 90% confidence interval for the population mean is:
30 ± 1.317, or (28.683, 31.317)
b. For a 95% confidence interval, the critical value (z*) is 1.96. Thus, the margin of error is:
Margin of Error = 1.96 * (4 / √25) = 1.568
So, the 95% confidence interval for the population mean is:
30 ± 1.568, or (28.432, 31.568)
c. For a 99% confidence interval, the critical value (z*) is 2.576. Thus, the margin of error is:
Margin of Error = 2.576 * (4 / √25) = 2.0656
So, the 99% confidence interval for the population mean is:
30 ± 2.0656, or (27.9344, 32.0656)
d. As the confidence level increases, the margin of error also increases, because we need to be more certain that our interval includes the true population mean. This means that the confidence interval becomes wider as the confidence level increases.
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what is the answer?
?
No, there is not enough information
Yes, because of the intermediate value theorem
Because g(x) is continuous on the interval, we can see that the correct option is the last one (counting from the top)
Does the value c exists in the given interval?Here we have the function g(x), and we know that it is continuous on the interval [1, 6], and that:
g(1) = 18
g(6) = 11
If it is continuous, then g(x) covers all the values between 18 and 11 in the given interval, this means that there must exist a value c in the given interval such that when we evaluat g(x) in that value c, we get the outcome 12, and we know this by the intermediate value theorem.
So the correct optionis the last one.
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