The test static is 1.60 and the p-value is 0.1096, null hypothesis is not rejected and the population mean is not significantly different from $1000.
Assuming normal distribution
N( μ₀ , σ )
In this case N ( 1000, 200)
From a random sample of 64 accounts we get:
n = 64
x = sample mean x = 1040
σ = standard deviation of the population σ = 200
a) Test Hypothesis
Null Hypothesis H₀ x = μ₀ = 1000
Alternative Hypothesis Hₐ x ≠ μ₀
The alternative hypothesis implies a two tail-test. Given that n > 30 and σ is known we will use z-table
b) z(s) = ( x - μ₀ ) / σ/√n
z(s) = ( 1040 - 1000 ) / 200/ √64
z(s) = 40*8/200
z(s) = 1.60
c) P-value for z (score 1.6) p-value = 0.1096
d) If significance level is 0.05 then α = 0.05 and α/2 = 0.025
p-value > α/2
Then the z(s) < z(c) 1.6 < 1.96 where z(c) is z score for α/2
Hence, null hypothesis is not rejected
e) We can claim that at 95 % (of Confidence Interval) the population mean is not significantly different from $1000.
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Question is not complete. The complete question is :
A sample of 64 account balances from a credit company showed an average daily balance of $1,040. The standard deviation of the population is known to be $200. We are interested in determining if the mean of all account balances (i.e., population mean) is significantly different from $1,000. 1. State the null and alternative hypothesis. 2. Compute the test statistic. 3. Compute the p-value. 4. Based on the p-value and the significance level of 0.05% make a decision regarding the hypotheses. 5. Interpret your results in the context of the problem.
Volume of right circular cylinder if radius is 7 and hight is 1. 5
The volume of the right circular cylinder with a radius of 7 and a height of 1.5 is 110.25 cubic units.
The volume of a right circular cylinder can be calculated using the formula:
V = π * r² * h
Where r is the radius and h is the height of the cylinder.
Plugging in the values for r and h, we get:
V = π * 7² * 1.5
V = π * 49 * 1.5
V = 73.5 * 1.5
Therefore, V = 110.25
So the volume of the right circular cylinder with a radius of 7 and a height of 1.5 is 110.25 cubic units.
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Element X decays radioactively with a half life of 8 minutes. If there are 450 grams of Element X, how long, to the nearest tenth of a minute, would it take the element to decay to 37 grams?
If there are 450 grams of element and half life is 8 minutes, then it will take 28.83 minutes the element to decay to 37 grams
Half life of radio active element = 8 minutes
Initial quantity of radio active element = 450 gram
Final quantity of radio active element = 37 grams
y = a(0.5)^(t/h)
Substitute the values in the equation
37 = 450 (0.5)^(t/8)
Move 37 to left hand side of the equation
37 / 450 = 0.5^(t/8)
Convert the terms to logarithm
t/8 = [tex]log_{0.5}\frac{37}{450}[/tex]
t/8 = 3.60
t = 8 × 3.60
Multiply the numbers
t = 28.83 minutes
Therefore, the it will take 28.83 minutes to decay to 37 grams
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Why is it important to use the Order of Operations? (WHAT YOU THINK)
Answer:it guarantees that people can all read and solve a problem in the same way.
Step-by-step explanation:
HELP PLS! ITS DUE IN 30 MIN!!!!!!!
The altitude of an airplane coming in for a landing is represented by the equation shown below, where y represents the altitude, in feet, of the airplane and x represents the number of minutes the plane has been descending:
y = -10x + 300
Part A:
Create a table for the values when x = 0, 5, 8, 10, 30.
Include worked-out equations used to identify the values within the table.
Part B:
Identify the altitude after 5 minutes and after 30 minutes. Use 1-2 sentences to explain the altitude at these two times and describe what is happening to the airplane at these time intervals.
The altitude of an airplane coming in for a landing is represented by the equation shown below, where y represents the altitude, in feet, of the airplane and x represents the number of minutes the plane has been descending:
y = -10x + 300
Part A:
Create a table for the values when x = 0, 5, 8, 10, 30.
Include worked-out equations used to identify the values within the table.
Part B:
Identify the altitude after 5 minutes and after 30 minutes. Use 1-2 sentences to explain the altitude at these two times and describe what is happening to the airplane at these time intervals.
The table to explain the equation will be:
x (minutes) y (altitude, in feet) Worked-out equation
0 300 -10x + 300 = 300
5 250 -10x + 300 = 250
8 220 -10x + 300 = 220
10 200 -10x + 300 = 200
30 0 -10x + 300 = -0
What is an equation?An equation simply has to do with the statement that illustrates the variables given. In this case, it is vital to note that two or more components are considered in order to be able to describe the scenario
I used the equation y = -10x + 300 to find the altitude of the airplane for each x value.
The altitude after 5 minutes is 250 feet and 0 after 30 minutes.
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This season, the probability that the Yankees will win a game is 0. 61 and the probability that the Yankees will score 5 or more runs in a game is 0. 48. The probability that the Yankees lose and score fewer than 5 runs is 0. 32. What is the probability that the Yankees would score fewer than 5 runs when they lose the game? Round your answer to the nearest thousandth
Answer:
0.238
Step-by-step explanation:
Which measure of centre is meaningful when the data are qualitative?
A. The range
B. The mean
C. The mode
D. The median
The correct answer is C. The Mode.
What is data in math?Data is the collection of data term that is organized and formatted in a specific way it's typically contains fact observation or statistics that are collected through a process of measurement or research data set can be used to answer question and help make informed decision they can be used in a variety of ways such as to identify trends on cover patterns and make prediction.
This measure of centre is most meaningful when the data is qualitative because it shows the value that appears most frequently in the data set. The mode can be used to identify the most popular item or most commonly occurring outcome. It is the only measure of centre that can be used for qualitative data, as the other measures (mean, median, and range) require numerical data.
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Question 2 of 10
Frank is a champion fish charmer who can charm fish with .62 probability of
success. If he attempts to charm 100 fish, what's the probability he'll charm
between 60 and 80 inclusive? Solve using two methods: normal
approximation without the continuity correction, and normal approximation
with the continuity correction.
A. 332, 337
B. 323, .291
OC. 337,.332
OD. .660,.697
OE. 337,.323
The Solution using two methods are 323, .291, the correct option is B`.
How can we interpret probability?Probability of an event is a measurement of how likely an event can occur as an outcome of a random experiment.
Probability ranges from 0 to 1, both inclusive. Events whose probability is closer to 0 are rarer to occur than those whose probabilities are closer to 1 (relatively).
When converted to percentage, we just need to multiply its decimal representation by 100. In percentage form, the probability ranges from 0% to 100%.
Given;
Frank is a champion fish charmer who can charm fish with .62 probability of success
He attempts to charm 100 fish, what's the probability he'll charm
between 60 and 80 inclusive
Now, probability out of 100
=62
This is between 60 and 80
So, 323
Therefore, the probability will be 323 and .291
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true or false? a. a 95% confidence interval for the odds ratio between mi (yes, no) and treatment (placebo, aspirin) is (1.44, 2.33). if we form the table with aspirin in the first row (instead of placebo), the confidence interval is (1/2.33, 1/1.44)
The statement is true. A confidence interval is a range of values that is likely to contain the true value of the parameter with a certain degree of confidence.
In this case, we are interested in the odds ratio between MI (yes, no) and treatment (placebo, aspirin).
If the 95% confidence interval for the odds ratio between MI and placebo is (1.44, 2.33), this means that we can be 95% confident that the true odds ratio falls between these two values. This implies that the odds of having an MI are between 1.44 and 2.33 times greater for those taking the placebo compared to those taking aspirin.
When we switch the rows so that aspirin is in the first row, we need to take the reciprocal of the upper and lower bounds of the confidence interval to get the new interval. This is because the odds ratio is calculated as the odds of MI for one group divided by the odds of MI for the other group, and switching the groups changes the ratio.
So, if we take the reciprocal of the lower and upper bounds of the original interval, we get:
1/2.33 and 1/1.44
which is the new 95% confidence interval for the odds ratio when aspirin is in the first row. Therefore, the statement is true.
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A coffee shop recorded the drinks that were recently sold. There is 1 mocha, 3 macchiatos, 5 Americanos, 7 lattes, and 4 espressos! Considering this data, how many of the next 15 drinks sold would you expect to be espressos?
Answer:
one fifth would be espressos so 3
Step-by-step explanation:
a roller-coaster ride with 6 passengers takes 3 minutes. neglecting friction, a similar ride with 12 passengers aboard would take group of answer choices 1.5 minutes. 18 minutes. 3 minutes. 6 minutes.
Neglecting friction, a similar ride with 12 passengers aboard would take 6 minutes.
The time it takes for a roller coaster ride is directly proportional to the mass of the passengers. If we assume that each passenger has the same mass, then the time it takes for the ride is proportional to the number of passengers.
Let T1 be the time for the ride with 6 passengers, and T2 be the time for the ride with 12 passengers. Then, we have:
T2 = (12/6) * T1
Simplifying this expression, we get:
T2 = 2 * T1
We are given that T1 = 3 minutes, so we can substitute this value into the equation above to find T2:
T2 = 2 * 3 minutes = 6 minutes
Therefore, a similar roller coaster ride with 12 passengers aboard would take 6 minutes, as opposed to the 3 minutes it takes with 6 passengers aboard. The answer is 6 minutes.
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A student received a coupon for 43% off the total purchase price at a clothing store. Let b be the original price of the
purchase. Use the expression below for the new price of the purchase. Write an equivalent expression by combining like
terms.
b-0.43b
b-0.43b =
The equivalent expression by combining like terms is 0.57b
How to write an equivalent expression?
Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we substitute the same value(s) for the variable(s).
In order to write an equivalent expression by combining like terms, subtract 0.43b from b (Note: b = 1b). That is:
b-0.43b = 0.57b
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Pls help thank you will mark the Brainliest
the first choice is the right answer
please check my working for guidance
The distance a wheel can travel is proportional to its radius. What is a constant of proportionality for this relationship?
The constant of proportionality for this relationship is the circumference of the wheel.
What is the proportional relationship?A proportional relationship between two variables means that the ratio of the two variables is constant. In other words, if the independent variable (time in this case) increases, the dependent variable (the amount of money Steven charges) will increase proportionally.
The distance a wheel can travel is proportional to its radius.
wheel radius(in.) distance in 4 revolutions (in.)
4 32π
3.5 28π
0.25 2π
The distance a wheel can travel in one revolution is equal to the circumference of the wheel. So, if we know the radius of the wheel, we can calculate its circumference using the formula:
circumference = 2π × radius
Then, we can use the circumference to find the distance the wheel can travel in a given number of revolutions by multiplying the circumference by the number of revolutions. In the table provided, we can see that for each wheel radius, the distance traveled in 4 revolutions is a multiple of the circumference of the wheel, which confirms that the constant of proportionality is the circumference.
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In a simple linear regression model we use the normal quantile plot of the residuals to evaluate if it is reasonable to assume the _____ come from a normal distribution.
a. Response Variable
b. Explanatory Variable
c. Observations
d. Errors
To determine whether the errors from the linear regression model are from a normal distribution, examine the normal quantile plot of the residuals.
Calculating the regression equation is the first step in a straightforward linear regression model. The link between the explanatory variable (x) and the response variable is modelled using this equation (y). A linear function of the explanatory variable, an intercept term, and an error term make up the regression equation. The errors or residuals (e), which indicate the difference between the observed and expected values of the response variable, are calculated as the following step. To evaluate the regression model's accuracy, the residuals are crucial. The residuals are then plotted using a normal quantile to see whether it is acceptable to believe that the errors are derived from a normal distribution. Because linear regression models presume that the errors are regularly distributed, this is significant. The residuals' normal quantile plot shows the distribution of the mistakes graphically, making it simpler to determine whether the errors follow a normal distribution. The linear regression model might not be the optimal one to employ if the errors do not follow a normal distribution.
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The values of three consecutive even integers must be if their sum is 6000
If the sum of three successive integers even numbers is 6000, then their values must be 1998, 2000, and 2002.
In addition tangere is the root of the Latin word integer, which meaning "whole" and "untouched." The word "entire" is derived from the French word entier, which also means entire and integer. The expression was once used to describe a multiple of 1 or the whole part of a mixed number. The definition of the term was given as the collection of all positive integers, which is the same as the collection of all natural numbers. The concept of integer was expanded to include negative integers as the significance of those numbers came to be realized through time. For instance, in his 1765 book Elements of Algebra, Leonhard Euler stated that integers might contain both positive and negative values. Up until about the middle of the 20th century, most European mathematicians ignored negative numbers.
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17) On paper, graph the ordered pairs and label the points. Connect the points in order from A through D with
line segments. (a) What type of quadrilateral is formed? (b) What is the area of the quadrilateral?
A(-2,-1), B(7,-1), C(3,5), D(-2,5)
According to the information, the area of this quadrilateral, trapezoid is 42 cm.
How to calculate the area of this figure?To calculate the area of the figure we must first graph it. Once we have found its shape we must identify what type of quadrilateral it is, in this case we can affirm that it is a right trapezoid.
On the other hand, to calculate its area we must divide the figure in two, one part would be the quadrilateral and the other the triangle. So we need to find the area of both shapes and then add them.
6*5 = 306*4=2424 / 2 = 1212 + 30 = 42So the total area would be 42cm²
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please answer parts a and b correctly and let it make sense. if it's correct ill give it all stars and brainxvlest and also I will cavxsh app u
just put ur tag below. thank u
Answer:
11 inches
Step-by-step explanation:
If its cubic inches, we just need to cube root it
Plug it into the calculator and you get a number that rounds up to 11
Reasoning is because it is cubic, so to find the distance which is a normal number, you need to cube root it
What is the y-intercept of the line shown? (4 points)
A coordinate plane is shown. A line passes through the point -4 comma 1 and through the y-axis at 4.
3 over 4.
2
3
4
Answer:
y- intercept = 4
Step-by-step explanation:
the y- intercept is the value of y on the y- axis where the line crosses.
the line crosses the y- axis at 4
then y- intercept = 4
recent report suggests the proportion of general us population who believe in extraterrestrial life is 0.47. choose the appropriate null and alternative hypothesis that tests whether the proportion of college students who believe in extraterrestrial life in greater than the general population?
The null hypothesis assumes that the proportion of college students who believe in extraterrestrial life is the same or lower than the general population
The appropriate null and alternative hypothesis that tests whether the proportion of college students who believe in extraterrestrial life is greater than the general population can be expressed as follows:
Null hypothesis: The proportion of college students who believe in extraterrestrial life is equal to or less than the general population, or
H0: p <= 0.47
Alternative hypothesis: The proportion of college students who believe in extraterrestrial life is greater than the general population, or
Ha: p > 0.47
where p is the true proportion of college students who believe in extraterrestrial life.
In other words, the null hypothesis assumes that the proportion of college students who believe in extraterrestrial life is the same or lower than the general population (i.e., there is no difference between the two populations), while the alternative hypothesis assumes that the proportion of college students who believe in extraterrestrial life is higher than the general population.
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please help will give brainliest
Answer: D
Step-by-step explanation: I can't really see everything well but I think it is D
Calculate the area of a four-sided regular pyramid if its base edge is a=10cm, and its side edge is b=12cm.
The area of a four-sided regular pyramid, given the base edge and the side edge is 340 cm ² .
How to find the area ?The area of a four-sided regular pyramid can be found by the formula :
= Area of base + 1 / 2 x perimeter of base x side edge
Area of base :
= 10 x 10
= 100 cm ²
Perimeter of base ;
= 10 + 10 + 10 + 10
= 40 cm
The area of the four-sided regular pyramid is;
= 100 + ( 1 / 2 x 40 x 12 )
= 340 cm ²
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Put brackets into this calculation to make it correct.
6 x 1.5 + 4.9 x 4 = 55.6
Answer:
(6 x 1.5 + 4.9) x 4 = 55.6
Step-by-step explanation:
Use the picture
1. If the measure of the arc is 45 degrees, what is the length of the Arc and the area of the sector?
2. If the measure of the arc is 150 degrees, what is the length of the Arc and the area of the sector?
3. If the measure of the arc is what is the length of the Arc and the area of the sector?
4. If the measure of the arc is
3 I, what is the length of the Arc and the area of the sector?
The arc length and the sector area are l = 0.25πr and A = (πr²) / 8.
What is sector?The sector is essentially a section of a circle, and it may be described using the following three criteria:
The area of a disc that is surrounded by two radii and an arc is known as a circular sector.
The circle is divided into the Main Sector and the Minor Sector by a sector.
The region with a lesser extent is referred to as the Minor Sector, whereas the territory with a larger area is referred to as the Major Sector.
The arc length is given as:
l = α/360 (2πr)
The angle is 45 degrees thus,
l = (45/360)(2πr)
l = 0.25πr
The sector area is given as:
A = α/360 (πr²)
A = 45/360 (πr²)
A = (πr²) / 8
Hence, the arc length and the sector area are l = 0.25πr and A = (πr²) / 8.
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1. Dante mixes 30 milliliters of one liquid with 2 centiliters of a second
liquid. How many centiliters of liquid does he have altogether?
A. 5 cL
B. 32 cL
C. 50 CL
D. 302 CL
The total volume in centiliters is 5 cL, then the correct option is A.
How many centiliters of liquid does he have altogether?Here we know that Dante mixes 30 mililiters of one liquid with 2 centiliters of a second liquid, and we want to find the total volume in centiiters.
We know that:
1 milliliter = 0.1 centiliters.
Then:
30 mililiters = 30*( 0.1 centiliters) = 3 centilters.
Then the sum of the two volumes is:
3 centiliters + 2 centiliters = 5 centiliters.
Then the correct option is A.
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The answer is A. 5 cL.
What is liquid?Liquid is one of the three states of matter, alongside solid and gas. It is a form of matter that has a definite volume, but not a definite shape. Liquids take the shape of their container and are able to flow and be poured.
First, we need to convert 30 milliliters to centiliters, which is 3 centiliters (since 1 centiliter = 10 milliliters).
Then, we can add the 3 centiliters to the 2 centiliters of the second liquid to get a total of 5 centiliters.
Therefore, the answer is A. 5 cL.
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On a certain hot summer's day,482 people used the public swimming pool. The daily prices are $1. 50 for children and $2. 00 for adults. The receipts for admission totaled 815. 50 How many children and how many adults swam at the public pool that day?
There were 297 children and 185 adults who swam that day. Let x be the number of children and y be the number of adults who swam that day.
According to the problem, we know that:
x + y = 482 ---(1) (total number of people who swam)
1.5x + 2y = 815.5 ---(2) (total revenue generated)
To solve for x and y, we can use any method of solving a system of linear equations, such as substitution or elimination. Here's how to solve using the substitution method:
From equation (1), we can write:
x = 482 - y
Substituting this into equation (2), we get:
1.5(482 - y) + 2y = 815.5
Simplifying and solving for y, we find:
723 - 1.5y + 2y = 815.5
0.5y = 92.5
y = 185
Substituting this value of y back into equation (1), we find:
x + 185 = 482
x = 297
Therefore, there were 297 children and 185 adults who swam that day.
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Do the points in the following set lie on the same line? (1,3) (4,2) (-2,4) Explain. Does the point (2, 3) lie on the graph of y = 3x - 4? explain
The slope between the points is same, hence the points lie on the same line. The point (2, 3) does not lie on the graph of y = 3x - 4.
What is slope?A line's steepness and direction are measured by the line's slope. Without actually using a compass, determining the slope of lines in a coordinate plane can assist in forecasting whether the lines are parallel, perpendicular, or none at all.
Any two different points on a line can be used to calculate the slope of any line. The ratio of "vertical change" to "horizontal change" between two different locations on a line is calculated using the slope of a line formula.
The given points are, (1,3) (4,2) (-2,4):
Calculate the slope of the line formed by the points.
The slope of the line is given by:
m = (y2 - y1)/(x2 - x1)
For (1,3) (4,2):
m = (2 - 3) / (4 - 1) = -1/3
For (4,2) (-2,4):
m = (4 - 2) / (-2 - 4) = 2/ -6 = -1/3
The slope between the points is same, hence the points lie on the same line.
The equation of the graph is:
y = 3x - 4
The given point is (2, 3):
Substituting the point in the equation:
3 = 3(2) - 4
3 = 6 - 4
3 = 2
False.
Hence, the point (2, 3) does not lie on the graph of y = 3x - 4.
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Helppppppo meeeeeee plssssssssssssss
1)
it took
25 min : 35 mile
?? min : 70 mile
cross multiply we get 50 minutes
25 x 70 then divide by 35
2) we used:
4 cups : 90 batches
? cups. : 112.5 batches
cross multiply we get: 5 cups
112.5 x 4 then divide by 90
City officials conclude they should budget "s" million dollars for a new library
building if the population increases by "p" thousand people in a ten-year census. The formula:
s = 2 + 1/3(p + 1)^2/5
expresses the relationship between population and
library budget for the city. How much can the population increase without the city
going over budget if they have $5 million for a new library building?
In linear equation, 242 can the population increase without the city going over budget if they have $5 million for a new library building .
Which equation is linear equation?
An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.
The variables in the previous sentence, y and x, are referred to as a "linear equation with two variables" at times.
Substitute the value of s into formula for P -
P = ( 3(5-2)) 5/2 - 1
= (3(3))5/2 - 1
P = 95/2 - 1
P = 243 - 1
= 242
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A cookie company made 40 batches of
cookies in 8.25 hours. Assuming a constant
rate of production, at what rate, in hour(s) per
batch, was the cookies made?
The hourly rate that the batches of cookies were made is given as follows:
4.85 batches per hour.
How to obtain the hourly rate?The hourly rate is obtained applying the proportions in the context of the problem.
A proportion is applied as the rate is obtained dividing the total production by the time in hours.
The parameters for this problem are given as follows:
Production of 40 batches.Time of 8.25 hours.Hence the rate is given as follows:
40/8.25 = 4.85 batches per hour.
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Can somebody please look at the picture and help me
The relation does not relate y as a function of x because point (2,2) and (3,2) have the same y value. Hence, option 2 is the correct answer.
What is a function?A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain. The usual way to refer to a function is as f(x), where x is the input. A function is typically represented as y = f. (x).
We know that a function is a relationship between inputs where each input is related to exactly one output.
In the given graph (2,2) and (3,2) have the same y value that is two inputs have same output.
Hence, the relation does not relate y as a function of x because point (2,2) and (3,2) have the same y value and option 2 is the correct answer.
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