Answer:
The domain is {-1, 3, 5}, so D is correct.
Which of the following functions is graphed below?
Note that the function that is graphed below is y = x + 7.
What is the explanation for the above response?The equation y = x + 7 represents a linear function, where x is the independent variable and y is the dependent variable.
It has a slope of 1, which means that for every unit increase in x, y increases by 1. The y-intercept is 7, which is the value of y when x is zero. This equation can be graphed as a straight line on a coordinate plane, with a positive slope and y-intercept of (0, 7).
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geometry-
A vendor is using an 8-ft by 8-ft tent for a craft fair. The legs of the tent are 9ft tall and the tent top forms a square pyramid with a height of 3 ft. What is the volume, in cubic feet, of space the tent occupies?
The tent occupies 640 cubic feet of space.
What is volume of a space?Volume is a measurement of the amount of three-dimensional space occupied by an object or substance. It is the measure of the amount of space that an object or substance occupies in three dimensions, typically expressed in cubic units such as cubic meters, cubic centimeters, or cubic feet.
For example, the volume of a cube can be calculated by multiplying its length by its width by its height (or side cubed):
V = l x w x h = [tex]s^3[/tex],
where V is the volume, l is the length, w is the width, h is the height, and s is the length of a side.
Volume is an important measurement in fields such as physics, engineering, architecture, and chemistry, where it is used to calculate quantities such as the amount of fluid that can be held by a container, the amount of material needed to construct a building, or the amount of a substance that can react with another substance in a chemical reaction.
The volume of the tent can be found by calculating the volume of the square pyramid and then adding the volume of the rectangular box formed by the tent's base.
The base of the tent is an 8-ft by 8-ft square, so its area is 8 x 8 = 64 square feet. The height of the pyramid is 3 ft, so its volume is:
V(pyramid) = (1/3) x base area x height
V(pyramid) = (1/3) x 64 x 3
V(pyramid) = 64 cubic feet
The rectangular box formed by the tent's base has dimensions of 8 ft by 8 ft by 9 ft, so its volume is:
V(box) = length x width x height
V(box) = 8 x 8 x 9
V(box) = 576 cubic feet
Therefore, the total volume of space the tent occupies is:
V(total) = V(pyramid) + V(box)
V(total) = 64 + 576
V(total) = 640 cubic feet
So the tent occupies 640 cubic feet of space.
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12' of framing materical can be used to make a rectangular window with a semicircle top. what are the dimensions for the largest area
The dimension for the largest area is 181 sq ft.
The rectangle has width. [tex]$w$[/tex] and height [tex]$h$[/tex],and let the radius of the semicircle be [tex]$r$[/tex]. We want to maximize the area [tex]$A$[/tex] of the window, which is given by:
[tex]A= 21 \pi r 2 +wh[/tex]
We also have the constraint that the total length of framing material is 12 feet:
[tex]2r+2w+h=12[/tex]
Solving this equation for [tex]$h$[/tex] we get:
[tex]h=12-2r-2w[/tex]
Substituting this expression for [tex]$h$[/tex] into the equation for [tex]$A$[/tex], we get:
[tex]A= 21 \pi r ^2+w(12-2r-2w)[/tex]
Expanding this expression, we get:
[tex]A= 21\pi r^2 +12w-2rw-2w^2[/tex]
To find the values of [tex]$r$[/tex], [tex]$w$[/tex], and [tex]$h$[/tex] that maximize[tex]$A$[/tex], we take the partial derivatives of [tex]$A$[/tex] with respect to each variable, set them equal to zero, and solve for the variables.
We get:
[tex]\partial r/\partial A=\pi r-2w=0 \Rightarrow r= 2w/\pi[/tex]
[tex]\partial w/\partial A=12-2r-4w=0 \Rightarroww= (6-r)/2= (6-2w/\pi)/2=3- w/\pi[/tex]
Substituting the expression for [tex]$w$[/tex] into the equation for [tex]$r$[/tex], we get:
[tex]r= 2/\pi (3-w/\pi )= 6/\pi - 2/\pi^2w[/tex]
Substituting these expressions for [tex]$r$[/tex] and [tex]$w$[/tex] into the equation for [tex]$h$[/tex], we get:
[tex]h=12-2r-2w=12- (4/\pi)w[/tex]
So the dimensions that maximize the area are:
[tex]w= \pi/2,r= 3\pi /4 ,h= (48-8\pi) / \pi[/tex]
The area of the window is:
[tex]A= (1/2)\pir^2 +wh= (1/2)\pi ( 3\pi/4)^2 + (\pi/2)\cdot (48-8\pi)/\pi = 9\pi/8+24-4\pi\approx 18.1 sq ft[/tex]
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Therefore, the dimensions of the largest area rectangular window with a semicircle top that can be made with 12' of framing material are approximately 1.55' * 3.38'. The maximum area is: Area = 4.82 square feet.
To find the dimensions for the largest area of a rectangular window with a semicircle top using 12' of framing material, we need to use optimization techniques.
Let's denote the width of the rectangular window as "w" and the height of the rectangular portion as "h". We also know that the semicircle top will have a radius equal to the width of the rectangular portion, so its diameter will be 2w.
The perimeter of the window is given by:
Perimeter = 2w + h +[tex]\pi w[/tex]
Since we have 12' of framing material available, we can write:
2w + h + [tex]\pi w[/tex] = 12
We can rearrange this equation to solve for h:
h = 12 - 2w - [tex]\pi w[/tex]
The area of the window is given by:
Area = w * h + 1/2 * [tex]\pi w^2[/tex]
Substituting the expression for h from the perimeter equation, we get:
Area = w(12 - 2w - [tex]\pi w[/tex]) + 1/2 * [tex]\pi w^2[/tex]
Expanding and simplifying, we get:
Area = 12w - [tex]2\pi w^2[/tex] - [tex]w^2[/tex]
To find the dimensions that maximize the area, we need to take the derivative of the area equation with respect to w and set it equal to zero:
d(Area)/dw = 12 - [tex]4\pi w[/tex] - 2w = 0
Solving for w, we get:
w = 12/(4\pi+2) ≈ 1.55'
Substituting this value back into the perimeter equation, we can find the height:
h = 12 - 2w - \piw ≈ 3.38'
Therefore, the dimensions of the largest area rectangular window with a semicircle top that can be made with 12' of framing material are approximately 1.55' * 3.38'. The maximum area is:
Area ≈ 4.82 square feet.
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A rectangular mural measures 890 centimeters by 2891
centimeters. Hailey creates a new mural that is 66 centimeters
longer
The perimeter of the rectangular mural after increasing the dimensions by Hailey is equal to 7826 centimeters.
Measures of rectangular mural are,
length = 890 centimeters
Width = 2891 centimeters
New mural is 66 centimeters longer.
The new dimensions of the rectangular mural will be,
New length = 890 cm + 66 cm
= 956 cm
New width = 2891 cm + 66 cm
= 2957 cm
The perimeter of the new mural can be calculated by adding up the lengths of all four sides,
Perimeter = 2(length + width)
⇒Perimeter = 2(956 cm + 2957 cm)
⇒Perimeter = 2(3913 cm)
⇒ Perimeter = 7826 cm
Therefore, the perimeter of Hailey's new mural will be 7826 centimeters.
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The above question is incomplete , the complete question is:
A rectangular mural measures 890 centimeters by 2891centimeters. Hailey creates a new mural that is 66 centimeters longer. What's is the perimeter of Hailey new mural?
Starting at noon the temperature changed steadily at a rate of -0. 8°C every hour how many hours does it take for the temperature to change by -4. 4°C
Number of hours does it take for the temperature to change by -4. 4°C is 5.5 hours
To solve this problem, we can use the formula for finding the change in temperature
Change in temperature = rate of change × time
where the rate of change is -0.8°C per hour and the change in temperature we want to find is -4.4°C. So, we can plug in these values and solve for time
-4.4°C = (-0.8°C / hour) × time
Dividing both sides by -0.8°C / hour, we get
time = 5.5 hours
Therefore, it will take 5.5 hours for the temperature to change by -4.4°C.
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g a generic drug is being tested to test its efficacy (effectiveness) at reducing blood pressure in patients with hypertension (a.k.a. high blood pressure). in a randomized, double-blind experiment with 200 patients, 100 are given the name-brand drug (control group) and 100 are given a generic version of the drug (treatment group). in the control group, the average reduction in blood pressure is 15.2 mmhg with a standard deviation of 11.5 mmhg. in the treatment group, there is an average reduction of 14.6 mmhg and a standard deviation of 12.5 mmhg. neither group has any outliers. a researcher claims that this study shows the generic drug is not as effective as the name-brand drug. what would be the reply of a statistician? you have two attempts for this problem so choose wisely. if you do not receive 5 points in the gradebook after submitting this assignment then you have answered incorrectly. make sure to try it again before the deadline.
A statistician would reply that in order to determine if the generic drug is less effective than the name-brand drug, a hypothesis test needs to be conducted.
The null hypothesis (H0) would be that there is no difference in the average blood pressure reduction between the two drugs, while the alternative hypothesis (H1) would be that the name-brand drug has a higher average reduction in blood pressure than the generic drug.
To test these hypotheses, a t-test would be appropriate since we have two independent samples (control and treatment groups) with known means, standard deviations, and sample sizes. The t-test will provide a p-value, which can be compared to a chosen significance level (e.g., α = 0.05).
If the p-value is less than the significance level, we reject the null hypothesis and conclude that there is a significant difference in the average blood pressure reduction between the two drugs. If the p-value is greater than the significance level, we fail to reject the null hypothesis, meaning we do not have enough evidence to claim that the name-brand drug is more effective than the generic drug.
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a number g multiplied by 67
Answer:
67g
Step-by-step explanation:
the correct form of g multiplied by 67 is 67g
fractions to decimals
Answer: 1 is .4
2. is .6
3 is .5
4 is .375
5 is .18
6 is .71
7 is .16
8 is .66 repeating
9 is .91
and 10 is .25
Step-by-step explanation:
to get all these and fractions to decimals in the future just divide the numerator by the denominator in other words the top number by the bottom number
1): 0.4
2): 0.67 or 0.7
3): 0.5
4): 0.37 or 0.4
5): 0.18
6): 0.42 or 0.5
7): 0.17
8): 0.7
9): 0.97 or 1
10): 0.25
a machine that is programmed to package 1.30 pounds of cereal is being tested for its accuracy in a sample of 43 cereal boxes, the sample mean filling weight is calculated as 1.32 pounds. the population standard deviation is known to be 0.06 pounds. find the 95% confidence interval for the mean.
The 95% confidence interval for the mean filling weight of the cereal boxes is (1.300, 1.340) pounds.
To find the 95% confidence interval for the mean filling weight of the cereal boxes, we can use the formula
CI = x ± z × (σ/√n)
where:
x = sample mean filling weight = 1.32 pounds
σ = population standard deviation = 0.06 pounds
n = sample size = 43
z = z-score corresponding to the desired level of confidence (95% in this case)
To find the z-score, we can use a standard normal distribution table or calculator. For a 95% confidence level, the z-score is 1.96.
Plugging in the values, we get
CI = 1.32 ± 1.96×(0.06/√43)
CI = 1.32 ± 0.020
Therefore, the 95% confidence interval for the mean filling weight of the cereal boxes is (1.300, 1.340) pounds. This means that we can be 95% confident that the true population mean filling weight falls within this range.
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The line graph below charts the time spent playing video games during a one week period.
*LOOK AT THE PICTURE*
The line graph contains an error. Study the graph carefully and use complete sentences to describe the error.
A piecewise function is a function that is defined by different equations or formulas on different intervals or pieces of its domain. In other words, a piecewise function is a function that consists of multiple functions "stitched" together.
When looking at the line graph, it is clear that there is a error because the scales don't begin at 0.
What is a line graph?An example of a chart that shows data trends over time or other continuous periods is a line graph. The x-axis represents time or another continuous variable, while the y-axis represents the value of the data. It consists of a sequence of data points connected by a line.
The visualisation of trends and patterns in data, such as variations in temperature, stock prices, or sales numbers over time, is frequently done using line graphs. Due to the ability to draw many lines in a variety of colors and patterns, they are particularly helpful for comparing different data series on the same graph.
When looking at the line graph, it is clear that there is a flaw because the scales don't begin at 0.
It presents information that is incongruous, as if it were saying that the highest hour on Friday is 7, but that it is precisely 1 to 7, making it equivalent to 6.
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10. Sarah has a new job of slicing and
stocking the lunchmeat in a deli case.
She keeps track of how many pounds
she puts in the case, while her manager
keeps track of the number of pounds
they sell from the case.
Sarah's List
6
10.60
Day
143.46 1
2
3
bropez
10
bro
Day
Number of Pounds
Added to Case
0.5
10
0.5
10de
2
erit
aby
List ole qu zmlwz
Manager's List
Number of Pounds Soldot
exom S
from Case
wan 11 svib ed EdW
24/4
3
If there were 12 pounds in the case
when Sarah started on Day 1, how
many pounds will be in the case at the
start of Day 4?
The total number of pounds in the case at the start of Day 4 would be 12.50 pounds found by using an arithmetic operation.
What is the arithmetic operation?Arithmetic operations refer to the basic mathematical operations used to perform calculations involving numbers. These operations include Addition, Subtraction, Multiplication, Division, Exponential, Modulo.
According to the given information:
Based on the information provided, Sarah's list shows the number of pounds she added to the deli case each day. According to her list:
Day 1: 6 pounds
Day 2: 10.60 pounds
Day 3: 0.5 pounds
So the total number of pounds Sarah added to the case from Day 1 to Day 3 is 6 + 10.60 + 0.5 = 17.10 pounds.
Since Sarah's manager's list shows the number of pounds sold from the case each day, and no information about the pounds sold on Day 4 is given, we can assume that no pounds were sold on Day 4.
Therefore, at the start of Day 4, the total number of pounds in the case would be the initial 12 pounds plus the pounds added by Sarah on Day 3, which is 0.5 pounds. So the total number of pounds in the case at the start of Day 4 would be 12 + 0.5 = 12.50 pounds.
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this table lists the lengths, to the nearest inch, of a random sample of 21 2121 brown bullhead fish. the outlier measurement of 24 2424 inches is an error. of the mean, median, and range of the values listed, which will change the most if the 24 2424-inch measurement is removed from the data?
The range will change the most, if the 24-inch measurement is removed from the data.
The correct answer is an option (c)
Consider the table with outlier 24.
The mean of this sample of 21 brown bullhead fish would be,
x₁ = (8 + (3 × 9) + (2 × 10) + (2 × 11) + (4 × 12) + (3 × 13) + (2 × 14) + (2 × 15) + 16 + 24) / 21
x₁ = 262/21
x₁ = 12.476
And the median would be,
m₁ = 12
And the range would be,
R₁ = 24 - 8
R₁ = 16
If we remove outlier 24 then,
mean x₂ = 11.9
median m₂ = 12
range R₂ = 16 - 8
= 8
Therefore, the range will change the most.
The correct answer is an option (c)
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The complete question is:
The table lists the lengths, to the nearest inch, of a random sample of 21 brown bullhead fish. The outlier measurement of 24 inches is an error. Of the mean, median, and range of the values listed, which will change the most if the 24-inch measurement is removed from the data?
a) mean
b) median
c) range
d) They will all change by the same amount.
A chef used some bouillon cubes when making chicken noodle soup. The volume of each of the bouillon cubes was 1/27
cubic inch. How long was an edge of one of the bouillon cubes that the chef used?
Answer: 1/3
Step-by-step explanation:
1/3x1/3x1/3=1/27
Kira will run less than 29 miles this week. So far, she has run 12 miles. What are the possible numbers of additional miles she will run? Use t the number of additional miles she will run. Write your answer as an inequality solved for .
Answer:
t < 17
Step-by-step explanation:
If Kira has already run 12 miles and she will run less than 29 miles this week, then the total number of additional miles she will run is less than 29 - 12 = 17 miles. So, the inequality that represents the possible number of additional miles Kira will run is t < 17.
HELP!! VIEW PHOTO THANKS!!
Step-by-step explanation:
Total people surveyed = 246
total female = 122
divorced = 15 + 13 BUT the 13 was already counted in 'female'
soooo
female OR divorced = 122 + 15 out of 246 = 137/246 = .5569
which of the following null hypothesis statistical tests require calculating degrees of freedom? group of answer choices all of the above two-sample t-test chi-squared one-sample t-test
The two null hypothesis that are correct answer are two-sample t-test and one-sample t-test.
Among the group of answer choices provided, the tests that require calculating degrees of freedom are the two-sample t-test and the one-sample t-test. Both of these tests belong to the t-test family and involve using degrees of freedom to determine the critical t-value.
In summary:
- Null hypothesis: The assumption that there is no significant difference between the sample and population or between two samples.
- T-test: A statistical test used to determine if there is a significant difference between the means of two groups or between a sample and population mean.
- Degrees of freedom: A value used in statistical tests that represents the number of independent values in a data set, which can affect the outcome of the test.
So answer is: two-sample t-test and one-sample t-test.
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The null hypothesis statistical tests that require calculating degrees of freedom are the two-sample t-test and the one-
sample t-test. The degrees of freedom are necessary to calculate the t-value for these tests. The chi-squared test also
requires degrees of freedom, but it is not a test for a null hypothesis.
The correct answer is: all of the above.
All these tests require calculating degrees of freedom:
1. Two-sample t-test:
Degrees of freedom are calculated using the formula (n1 + n2) - 2, where n1 and n2 are the sample sizes of the two
groups being compared.
2. Chi-squared test:
Degrees of freedom are calculated using the formula (rows - 1) * (columns - 1), where rows and columns represent the
number of categories in the data.
3. One-sample t-test:
Degrees of freedom are calculated using the formula n - 1, where n is the sample size.
The null hypothesis statistical tests that require calculating degrees of freedom are the two-sample t-test and the one-
sample t-test. The degrees of freedom are necessary to calculate the t-value for these tests. The chi-squared test also
requires degrees of freedom, but it is not a test for a null hypothesis.
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Calculate the slope of the line between pairs of points in each of the tables to determine which table represents a linear function? A. B. C. D.
Answer:
Table D represents the linear function
y = x + 1.
Complete the inequality.
1/4 ___ 3/16
>
=
Answer:
1/4 > 3/16
Step-by-step explanation:
1/4 = 4/16
4/16 > 3/16
1/4 > 3/16
hope this helps:)
~~~Wdfads~~~
Please help me with this homework
Answer: Area = 144 π cm²
Step-by-step explanation:
We can use this formula to find the area of a circle:
➜ r is equal to the radius, also known as half the width of a circle.
A = πr²
We will substitute our known values and solve for C by multiplying. Since the answer option includes π in our units, we do not multiply this into the 144.
A = πr²
A = π(12)²
A = 144 π cm²
What is the answer and how do I get there?
The value of the missing side length is 2√6. Option C
How to determine the value
We have that the six trigonometric identities are;
sinecosinetangentcotangentsecantcosecantFrom the information given, we have that;
Using the tangent identity,
tan 60 = 6√6/y
find the value
y = 6√6 /√3
Using the sine identity
sin 45 = 6√6 /√3/x
sin45 =6√18/3 × 1/x
√2/2x = 6√18/3
x = 2√18/√2
x = 2√36
x = 2√6
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Martin has read 10 percent of a book he has 54 more page to finish how many pages are in the book
Step-by-step explanation:
If he read 10 % , then he has 90 % to go...and this 90% is 54 pages
x = number of pages in book
90% * x = 54
.90x = 54
x = 54/.90 = 60 pages in book
the iq scores and english test scores of fifth grade students is given by the line of best fit y=-26.7+0.9346s, whereby is the predicted english score and s is the iq score. an actual english test score for a student is 65.7 with an iq of 96 find and interpret the residual
The residual for the given student is approximately 2.77.
This indicates that the student performed better on the English test than what would have been expected based on their IQ score according to the line of best fit.
What is Linear regression?
Linear regression is a statistical technique used to model the relationship between two variables by fitting a linear equation to observed data points.
To find the residual for the given student, we can substitute the student's IQ score (s = 96) into the equation for the best-fit line, y = -26.7 + 0.9346s.
Plugging in s = 96 into the equation, we get:
y = -26.7 + 0.9346(96)
y = -26.7 + 89.6304
y ≈ 62.93 (rounded to two decimal places)
So, the predicted English test score for a student with an IQ score of 96 is approximately 62.93.
To calculate the residual, we subtract the actual English test score (65.7) from the predicted English test score (62.93):
Residual = Actual English test score - Predicted English test score
Residual = 65.7 - 62.93
Residual ≈ 2.77 (rounded to two decimal places)
The residual for the given student is approximately 2.77.
Interpretation:
The positive residual of 2.77 suggests that the actual English test score for the student (65.7) is higher than the predicted English test score based on their IQ score (62.93).
Hence, This indicates that the student performed better on the English test than what would have been expected based on their IQ score according to the line of best fit.
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Write the nth term rule for the arithmetic sequence with the given term and common difference. Fill in the formula: a = a₁ + d(n-1) below.
a1=-10 and d=0.5
Answer:
The nth term rule for an arithmetic sequence with a first term of -10 and a common difference of 0.5 is given by:
an = a₁ + (n-1)d
where a₁ = -10 and d = 0.5.
Substituting these values into the formula gives:
an = -10 + (n-1)0.5
Simplifying this expression gives:
an = -10 + 0.5n - 0.5
an = -10 + 0.5n - 0.5
an = -10 + 0.5n - 0.5
an = -10 + 0.5n - 0.5
an = -10 + 0.5n - 0.5
an = -10 + 0.5n - 0.5
an = -0.5n - 9.5
I hope that helps! Let me know if I'm wrong!
Step-by-step explanation:
Distance between (7,-2) and (-1,-1)
Answer: The distance formula between two points (x1, y1) and (x2, y2) is:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Using this formula, we can find the distance between (7, -2) and (-1, -1):
d = sqrt((-1 - 7)^2 + (-1 - (-2))^2)
= sqrt((-8)^2 + (1)^2)
= sqrt(64 + 1)
= sqrt(65)
Therefore, the distance between (7, -2) and (-1, -1) is sqrt(65), or approximately 8.06 units.
Step-by-step explanation:
a plane cuts through a sphere with diameter 20 cm, but the closest it gets to the center is 3 cm. what is the area of the intersection of the sphere and the plane in sq cm?
The area of the intersection of the sphere and the plane in sq cm is 286.46 square centimeters.
The sphere is divided into two equal halves by the plane. The closest point on the plane is 3 cm away from the sphere's center. As a result, a right triangle is formed, with one leg equal to the sphere's radius and the other to the sphere's radius from the plane.
We may calculate the radius of the sphere using the Pythagorean theorem:
r^2 = (20/2)^2 - 3^2
r = sqrt(91) 9.54 cm and r2 = 91
A circle with a radius of 9.54 cm forms the point where the sphere and the plane cross. Its area is therefore: A = r2 A = (9.54)2 A 286.46 sq cm.
The sphere and plane's intersection therefore has a surface area of about 286.46 square centimeters.
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Establishing causality is often a main focus of statistical studies. What is the best type of study to conduct to establish causality? Use the situation in this task to support your answer.
The best type of study to establish causality is a randomized controlled experiment.
What is the best type of study to conduct to establish causality?In this type of study, participants are randomly assigned to different groups, and at least one group is given a specific treatment or intervention, while the other group(s) serve as a control group. By randomly assigning participants to groups, researchers can control for potential confounding variables that could impact the results.
For example, let's say we want to determine if a new medication reduces blood pressure. In a randomized controlled experiment, we could randomly assign some participants to receive the medication and others to receive a placebo. This would allow us to compare the effects of the medication on blood pressure to the effects of the placebo, while controlling for other variables that could impact blood pressure.
In contrast, observational studies, such as cohort studies or case-control studies, can only establish correlations between variables, not causation. This is because researchers do not have control over the variables being studied, and there may be other factors that are influencing the relationship between the variables.
Therefore, to establish causality, a randomized controlled experiment is the best type of study to conduct.
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Determine the type of variable for:The number of counties in California.
Qualitative nominal
Quantitative Continuous
Qualitative ordinal
Quantitative discrete
Determine the type of variable for: The stages of childhood: Infant, Toddler, Preschooler, School age, Preteen, Teen
Qualitative nominal
Quantitative Continuous
Qualitative ordinal
Quantitative discrete
Suppose the average time for a class of 28 students (taken from a campus of 1200 students) to drive to campus was 23 minutes.
Select the choice
In the scenario above, 23 minutes is a parameter/ statistic , because 28 students is a sample/ population.
At a Track field, a coach keeps track of an athletes mile time. The coach reported that the mean mile time of a particular athlete was 7 minutes and the standard deviation of the mile time was 1 minute. Assume that the coach also gave us the information that the distribution of the mile time was bell shaped. Use the empirical rule to find:
What percent of the athlete's mile times are expected to be between 6 minutes and 8 minutes?
What percent of the athlete's mile times are expected to be between 4 minutes and 7 minutes?
What percent of the athlete's mile times are expected to be less than 9 minutes?
The type of variable for,
a. The number of counties in California: Quantitative discrete.
b. The stages of childhood: Qualitative ordinal.
c. In the scenario above, 23 minutes is a statistic, because 28 students is a sample.
d. Between 6 minutes and 8 minutes: Approximately 68% of the athlete's mile times are expected to be between 6 and 8 minutes, according to the empirical rule.
e. Between 4 minutes and 7 minutes: Approximately 68% of the athlete's mile times are expected to be between 4 and 10 minutes, according to the empirical rule.
f. Less than 9 minutes: Approximately 84% of the athlete's mile times are expected to be less than 9 minutes, according to the empirical rule.
In statistics, variables can be categorized into two types: qualitative and quantitative.
Qualitative variables describe characteristics or qualities that cannot be measured numerically, such as gender or hair color.
Quantitative variables, on the other hand, represent numerical values that can be measured or counted.
There are two types of quantitative variables: continuous and discrete. Continuous variables can take any numerical value within a range, such as age or weight.
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Joe solved the equation 3+x/2=10 and justified each step as shown.
Explain in words Joe’s error and fix his mistake.
Step Justification
3+x/2=10 Given equation
x/2=7 Multiplication Property of Equality
x = 14 Subtraction Property of Equality
The correct solution for the given equation is x = 17.
What is distributive property?The distributive property is a mathematical property that relates multiplication and addition or subtraction. It states that multiplying a number by a sum (or difference) is equivalent to multiplying the number by each term of the sum (or difference) and then adding (or subtracting) the results.
According to question:Joe's error is due to not using the order of operations correctly. In step 2, he did not use parentheses to isolate the x term before dividing by 2. Instead, he divided both 3 and x by 2, resulting in x/2 = 7.
To fix Joe's mistake, we need to apply the distributive property by adding parentheses around the numerator of the left-hand side of the equation, like this:
(3 + x)/2 = 10
Then we can multiply both sides by 2 to eliminate the fraction:
3 + x = 20
Finally, we can solve for x by subtracting 3 from both sides:
x = 17
Therefore, the correct solution is x = 17.
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How will the mean be affected if 68 is added to the data set below?
58,60,62,64,66
A.
The mean will increase by 5.
B.
The mean will increase by 1.
C.
The mean will not change.
D.
The mean will decrease by 1.
Answer:
b
Step-by-step explanation:
in order to find the mean you have find the sum of the numbers and divide them by the amount of numbers.without 68 the sum is 310 divide it by 5 and tge answer is 62.however if you add 68 the sum is 378 divide it by 6 and the answer is 63.
therefore the answer increased by 1.
hope this helps :)
Using the graph, determine the coordinates of the vertex of the parabola.
Based on the information given, the vertex of the parabola can be found using the coordinates of the turning point (also known as the vertex).
What is the explanation for the above response?The vertex is located at (4,-4), which means that the value of x is 4 and the value of y is -4. Therefore, the coordinates of the vertex are (4,-4).
The fact that the curve is on the upper and lower quadrants of the right side of the cartesian coordinate system suggests that the parabola opens upwards.
Also, since the curve meets the x-axis at two points, this indicates that the parabola intersects the x-axis at those two points, which are (2,0) and (6,0).
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