Answer:
The slopes are equal. You should calculate the point's slopes by using rise-run:\(\frac{(y_2-y_1)}{(x_2-x_1)}\) for \((x_1,y_1),(x_2,y_2)\).
(b) Given the matrix D = k 0 0 3 k² k³ 0 kª k³ kº k k k 0 0 0 k¹⁰ Find all possible value(s) of k if det(D) = 1024."
To find the possible values of k, we need to calculate the determinant of matrix D and set it equal to 1024.
Given matrix D:
D = | k 0 0 |
| 3 k² k³ |
| 0 kª k³ kº |
| k k k |
| 0 0 0 |
| k¹⁰ |
The determinant of D can be calculated by expanding along the first row or the first column. Let's expand along the first row:
det(D) = k(det | k³ k k |
| 0 k³ kº |
| 0 0 k¹⁰ |)
- 0(det | 3 k² k³ |
| 0 kª k³ |
| k k k |)
+ 0(det | 3 k² k³ |
| k k k |
| k k k |)
Simplifying further, we have:
det(D) = k(det | k³ k k |
| 0 k³ kº |
| 0 0 k¹⁰ |)
Now, we can calculate the determinant of the 3x3 submatrix:
det | k³ k k |
| 0 k³ kº |
| 0 0 k¹⁰ |
This determinant can be found by expanding along the first row or the first column. Expanding along the first row gives us:
det = k(k³(kº) - 0(k)) - 0(0(k¹⁰)) = k⁴kº = k⁴+kº
Now, we can set det(D) equal to 1024 and solve for k:
k⁴+kº = 1024
Since we are looking for all possible values of k, we need to solve this equation for k. However, solving this equation may require numerical methods or approximations, as it is a quartic equation.
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A 4.00-kg particle moves along the x axis. Its position varies with time according to x= t +2.0
, where x is in meters and t is in seconds. Find (and remember to state the units in each case):
(a) the kinetic energy of the particle at any time t
(b) the acceleration of the particle
(c) the force acting on it at time t
(d) the power being delivered to the particle at time t.
(e) the work done on the particle in the interval t = 0 to t =2.00s.
The kinetic energy of the particle at any time t is 2 J. The acceleration of the particle is zero. The force acting on it at any time t is zero. The power being delivered to the particle at any time t is zero. The work done on the particle in the interval t = 0 to t = 2.00s is zero.
The given function is: x= t + 2 ...(1)
Differentiating with respect to time gives: dx/dt = v ...(2)
d²x/dt² = a ...(3)
We know that v = dx/dt
From equation (1), we have;
dx/dt = d/dt(t + 2)
dx/dt = 1
From equation (2), we have;
v = dx/dtv
= 1 m/s
(a) The kinetic energy of the particle at any time t. We know that the kinetic energy of an object of mass m moving with a velocity v is given by:
K.E = 1/2 mv²
From the above, we can see that the kinetic energy of the particle is dependent on its velocity. From equation (1), we have;
x = t + 2 ...(1)
Differentiating with respect to time gives: dx/dt = v ...(2)
Now, substituting v = 1 into equation (2), we have;
v = 1 m/s
Therefore, the kinetic energy of the particle at any time t is:
K.E = 1/2 mv²
K.E = 1/2(4)(1)²
K.E = 2 J
Therefore, the kinetic energy of the particle is 2 J.
(b) The acceleration of the particle. From equation (3), we have;
d²x/dt² = ad²x/dt²
= 0 m/s²
Therefore, the acceleration of the particle is zero.
(c) The force acting on it at time t. We know that: F = ma
From part (b), we know that the acceleration is zero, therefore, the force acting on the particle at any time t is zero.(d) The power being delivered to the particle at time t. We know that power is the rate at which work is done. Therefore, we need to find the work done on the particle in the interval t = 0 to t = 2.00s. The work done on the particle is given by:
W = FΔx
Where F is the force acting on the particle and Δx is the distance covered by the particle. From equation (1), we have;
x = t + 2
Δx = x2 - x1
Δx = (2+2) - (0+2)
Δx = 2 m
Now, F = 0.
Therefore, the work done on the particle is zero, hence the power being delivered to the particle at any time t is zero.
(e) The work done on the particle in the interval t = 0 to 2.00s. We know that the work done on the particle is given by:
W = FΔx
From part (c), we know that the force acting on the particle is zero. Therefore, the work done on the particle is zero.
Conclusion: (a) The kinetic energy of the particle at any time t is 2 J.(b) The acceleration of the particle is zero.(c) The force acting on it at any time t is zero.(d) The power being delivered to the particle at any time t is zero.(e) The work done on the particle in the interval t = 0 to 2.00s is zero.
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given a set of data and a corresponding regression line, describe all values of x that provide meaningful predictions for y. a. prediction value are meaningful for all x-values that are realistic in the context of the original data setb. prediction value are meaningful only for x-values that are not included in the original data setc. prediction value are meaningful only for x-values in (or close to) the range of the original data
4. because we are using a coin flip app, this experiment really tests only that app inventor's random integer block generates 1 around half the time. is this a sufficient test for app inventor's prng? what other experiments might you do to increase your confidence in app inventor's prng?
App inventor's random integer block test is sufficient for app inventor's prng . but to increase our confidence in app inventor's prng we can do other tests like random fraction test and random set speed test.
The Coin Flip Experiment app allows you to run experiments aimed at determining how "good" the App Inventor PRNGs are. The app allows the user to "flip a coin" her N times and the results are displayed. They should record and count the results and calculate the average head percentage. The expectation of should reach 50% on average as N increases.
To properly test an App Inventor PRNG, you must test both the Random Integer and Random Fraction blocks along with the Random Fraction and Random set speed to blocks. Create dice simulations to get better than 50/50 predictions and reuse dice simulators for all combinations of different App Inventor random blocks. If such a combination yields the same results, then you can be confident that her PRNG in App Inventor provides a good model of randomness from all angles.
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Aaliyah and Phildres are joining a gym that offers two different payment plans. Aaliyah
chooses Plan A, and Phildres chooses Plan B.
Plan A
No yearty fee
Plan B
$200 yearly fee
$50 for each class
$10 for each class
Which equation can be used to solve for the number of classes, c, for which the cost
of Plan A equals Plan B?
Based on the two different payment plans, the equation which can solve for the number of classes that equates both plans is 50x = 200 + 10x.
What equation can lead to both plans being equal?Plan A has no yearly fee but charges $50 per class.
Plan B has a $200 yearly fee and charges $10 per class.
Assuming the number of classes was x, the equation of Plan As total cost is:
= 50x
The equation of Plan B is:
= 200 + 10x
The equation to find the number of classes where the plans are equal is:
50x = 200 + 10x
Solving gives 5 classes.
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Answer:
Step-by-step explanation:
Using 6 bits in your answer, convert the base-10 value -21 to 2's complement binary.
2.Express the integer -4 in excess-16. Use 5 bits in your representation.
3.Using 6 bits in your answer, write the integer -26 using sign-magnitude binary representation.
4.The binary number shown here is a 6-bit excess-26 representation. What is its equivalent decimal (base 10) value?
101101
5.
A modified IEEE-754 floating-point representation uses 7 bits for the exponent and 10 bits for the fractional mantissa. The exponent is expressed in binary, excess-k. What is an appropriate value for k?
6. An IEEE-754 floating-point representation uses 3 bits for the fractional mantissa and 4 bits for the exponent (represented in excess-k). What is the largest positive value that can be represented? Express your answer in decimal (base 10).
1. To convert -21 to 2's complement binary using 6 bits:
- First, convert the absolute value of the number (21) to binary: 10101.
- Then, invert all the bits: 01010.
- Finally, add 1 to the inverted value: 01011.
So, the 6-bit 2's complement binary representation of -21 is 01011.
2. To represent -4 in excess-16 using 5 bits:
- Add the excess value (16) to the absolute value of the number (4): 20.
- Convert 20 to binary: 10100.
So, the 5-bit excess-16 representation of -4 is 10100.
3. To represent -26 in sign-magnitude using 6 bits:
- Convert the absolute value of the number (26) to binary: 11010.
- Set the leftmost bit as the sign bit (1 for negative).
- So, the 6-bit sign-magnitude representation of -26 is 111010.
4. To convert the 6-bit excess-26 binary number (101101) to decimal:
- Subtract the excess value (26) from the binary value: 101101 - 26 = 101075.
- The resulting decimal value is 75.
So, the decimal equivalent of the 6-bit excess-26 binary number 101101 is 75.
5. In IEEE-754 floating-point representation, the exponent is expressed in binary, excess-k. The value of k is determined by the number of bits used for the exponent. Since 7 bits are used for the exponent in this case, the value of k would be 2^(7-1) - 1 = 63. So, an appropriate value for k is 63.
6. In IEEE-754 floating-point representation, the largest positive value that can be represented depends on the number of bits used for the exponent and the fractional mantissa.
Since 3 bits are used for the fractional mantissa and 4 bits are used for the exponent in this case, the largest positive value that can be represented is determined by the maximum exponent value of 2^(4-1) - 1 = 7. Therefore, the largest positive value that can be represented is 2^7 = 128 in decimal (base 10).
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Help me please please
Answer:
4. c = 10
5. True
6. t = 3
Answer:
#4. 10
#5. true
#6. 3
Select the correct answer. You’re laying a new kitchen floor with square tiles that are one yard by one yard. Your rectangular kitchen is 24 feet by 33 feet, and each tile costs $54. You determine that the tiles will cost you $3,960. If you made a mistake in your pricing estimate, what most likely occurred?
A. You determined the number of tiles was 19 instead of 88.
B. You multiplied the number of tiles by $45 instead of $54.
C. You calculated the dimensions of your kitchen to be 3 yards by 4 yards instead of 8 yards by 11 yards.
D. No mistake was made.
Answer: Your estimate is wrong, and it should be $4,752
Step-by-step explanation:
We are given that:
Size of tile = 1yard by 1yard
Let convert yard to feet, so as to find the covered by the tile in feet.
Since 1yard = 3feet
Size of tile = 3feet by 3feet
Area cover by tile = 3x3 = 9ft²
Size of kitchen floor = 24ft by 33ft
Area covered by floor = 24 x 33 = 792ft²
Total number of tile needed for the kitchen floor = Area of kitchen/Area of tiles
= 792/9
= 88 tiles
Given that each tile cost $54
Total cost of 88 tiles = 54 x 88 = $4752
Therefore the answer is
B. Your estimate is wrong, and it should be $4,752
which one ? please help! I’ll mark brainliest!
Answer:
w ≥ 66
Step-by-step explanation:
You know that anything less than 66 would not cause any effect, so you need something that is exactly 66 or more than 66 for the airbag to deploy.
Thus, w ≥ 66
≥ means that w is more than or equal to 66. (66 and above)
< means that w is less than 66. (65 and below)
> means that w is more than 66. (67 and above)
≤ means that w is less than or equal to 66. (66 and below)
Answer:
w<66 is the answer i believe
What is the Answer to this
========================================================
Explanation:
For now, let's focus on triangle AFG.
This is a right triangle with the following sides:
FA = unknown horizontal leg = xFG = vertical leg = 6.1AG = hypotenuse = 11.2We'll use the pythagorean theorem to solve for x.
a^2 + b^2 = c^2
(FA)^2 + (FG)^2 = (AG)^2
x^2 + (6.1)^2 = (11.2)^2
x^2 + 37.21 = 125.44
x^2 = 125.44 - 37.21
x^2 = 88.23
x = sqrt(88.23)
x = 9.39308 approximately
Side FA is roughly 9.39308 units long.
-----------
Let's say for a moment we don't know where point G is located, but we do know where points A, C, and E are located. We can determine G's location by determining the perpendicular bisectors for segments AE and EC, and then intersecting said perpendicular bisectors.
Put another way:
FG is a perpendicular bisector for AEDG is a perpendicular bisector for ECBecause of the first bullet point, we know that AE is split into two equal pieces FA and FE, ie FA = FE.
We just found that FA = 9.39308 back in the last section, which means this is the length of FE as well.
Therefore,
AE = FA + FE
AE = 9.39308 + 9.39308
AE = 18.78616
AE = 18.8 when rounding to the nearest tenth, aka one decimal place.
Answer:
18.79
Step-by-step explanation:
→ Use Pythagoras theorem
√11.2² - 6.1²
→ Simplify
9.39
→ Now double the answer
18.79
Can someone tell me why is nobody helping me with my question I be POSTING 4 TIMES PLEASE YALL Help me please
Answer:
x = 4
y = 5
Step-by-step explanation:
4x = x + 12
^(subtract x from both sides)^
3x = 12
^(divide both sides by 3)^
x = 4
3y = 15
(divide both sides by 3)
y = 5
cmon guys, just tell me if i’m right! no guesses.
how to know the correct number of significant figures when doing a calculation?
This applies for division, multiplication, addition & subtraction
Answer:
When doing addition or subtraction with measured values, the answer should have the same precision as the least precise measurement (value) used in the calculation.The following rule applies for multiplication and division: The LEAST number of significant figures in any number of the problem determines the number of significant figures in the answer.
Step-by-step explanation:
Expand abs simplify root 5 ( root 10 + root 2)
Answer:
5\sqrt{2} + \sqrt{10}
Step-by-step explanation:
I assume the exp as \(\sqrt{5} (\sqrt{10} + \sqrt{2} )\)
\(\sqrt{50 } + \sqrt{10}\)
\(\sqrt{25*2} +\sqrt{10}\)
\(5\sqrt{2} + \sqrt{10}\)
The simplified form of the given expression \(\sqrt{5} (\sqrt{10} +\sqrt{2} )\) will be \(5\sqrt{2} + \sqrt{10}\).
What is a perfect square?A perfect square is a number system that can be expressed as the
square of a given number from the same system.
The given expression is as follows;
\(\sqrt{5} (\sqrt{10} +\sqrt{2} )\\\\\sqrt{5} \times \sqrt{10} +\sqrt{5} \times\sqrt{2} \\\\\sqrt{25 \times 2} +\sqrt{10}\\\\5\sqrt{2} +\sqrt{10}\)
Hence, the simplified form of the given expression is \(5\sqrt{2} + \sqrt{10}\).
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A local restaurant advertises that the mode cost of their most popular meals is $8. If the costs of their most popular meals are $7, $8, $8, $12, $13, $15, $17, $18, and $20, which word or phrase best describes this kind of advertising?
accurate
inaccurate
accurate, but misleading
inaccurate and misleading
Judging the humorousness of "lawyer" jokes. Stillman, Baumeister, and DeWall (2007) conducted a study where participants listened to a variety of jokes. To determine how funny the jokes were, the researchers asked a group of 86 undergraduates to rate the jokes on a scale from 1 (very unfunny) to 21 (very funny). Participants rated a "lawyer joke" as one of the funniest jokes, with a rating of 14.48 ± 4.38 (M ± SD). Assuming that these data are normally distributed:
What was the rating that marks the cutoff for the top 10% of participant ratings for this joke? ___________________________
How many of the 86 undergraduates gave the joke a rating of at least 10?
To find the rating that marks the cutoff for the top 10% of participant ratings for this joke, we need to determine the z-score corresponding to the 90th percentile of the normal distribution.
The z-score indicates the number of standard deviations from the mean. To calculate the z-score, we use the formula:
z = (x - M) / SD
where x represents the rating, M represents the mean, and SD represents the standard deviation. Given that the mean (M) is 14.48 and the standard deviation (SD) is 4.38, we can calculate the z-score for the 90th percentile.
Using a standard normal distribution table or a statistical calculator, we find that the z-score corresponding to the 90th percentile is approximately 1.28.
To find the rating, we rearrange the formula and solve for x:
x = z * SD + M
x = 1.28 * 4.38 + 14.48
x ≈ 20.52
Therefore, the rating that marks the cutoff for the top 10% of participant ratings for this joke is approximately 20.52.
To determine how many of the 86 undergraduates gave the joke a rating of at least 10, we need to compare the rating of 10 with the mean rating. Since the mean rating is 14.48, any rating of 10 or higher would meet the criteria.
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robin is twice as old as earl and adam is 8 years younger than earl. in 6 years robin will be three times as old as adam. find their present ages
The present age of Earl is 12 years, Robin is 24 years and Adam is 4 years old.
Let us consider the present age of Earl to be x years.
According to the given question, the present age of Robin is twice that of Earl = 2x
And since it is given that Adam is 8 years younger than Earl, then his age
= x - 8
After 6 years, the age of Earl will be x + 6
Robin's age will be = 2x + 6
Adam's age will be = x - 8 + 6 = x - 2
According to the given question, Robin's age will be thrice the age of Adam.
Hence, 2x + 6 = 3 (x - 2)
⇒ 2x + 6 = 3x - 6 ⇒ 6 + 6 = 3x - 2x ⇒ 12 = x
Thus, the present age of Earl is 12 years,
Robin's age = 2x = 2 x 12 = 24 years
Adam's age = x - 8 = 12 - 8 = 4 years
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Giving right ANSWER branleist
Answer:
the answer to this question is 58
Martin is interested in the effects of different kinds of instruction on videogame performance. Martin asks 30 college freshmen to each play 1 hour of Ratchet and Klank. Participants are randomly assigned to one of three instruction groups: (1) complete the tasks as quickly as possible, (2) conserve as much health as possible (i.e., play more carefully), or (3) find gold bolts (worth lots of money in equipment and ammunition). Obviously, even in a single instruction group, not all players will obtain the same final score. These differences in an instruction group reflect:
Answer:
Between - groups variance
Step-by-step explanation:
From the question we see that the college freshmen are assigned to one of the three given groups. This means that they are exposed to different experimental conditions and thus it means that the variation differs as a result of different experimental conditions between the groups.
Thus, these differences reflect between - group variance.
|-6+8| = simplify the expression
Answer:
2
Step-by-step explanation:
|-6+8|
Add/subtract the numbers: -6 + 8 = 2
= |2|
Apply the absolute value rule: |a| = a, a ≥ 0
= 2
A student has the following test scores in English class. 98 87 86 100 79 92 88 95 89 86 96 What is the IQR (interquartile range) of the student's scores? Enter your answer in the box. IQR =
We have the set of values: 98 87 86 100 79 92 88 95 89 86 96.
We have to calculate the IQR:
\(\text{IQR}=Q_3-Q_1\)where Q3 is the third quartile and Q1 is the first quartile.
The first step is to sort the values in ascendent order:
Which of these numbers is prime? Choose 1 answer: 3 30 63 77 E 91
Answer:
3
Step-by-step explanation:
3 is the only number here with factors of itself (3) and 1
Answer:
3
Step-by-step explanation:
What is the vertex angle of an isosceles triangle?.
The vertex angle is defined as the angle opposite the base. It can be calculated by formula, 180° - 2B = A where, B=base angle and A=vertex angle.
The two sides of an isosceles triangle are congruent, which means they are the same length. The third side of an isosceles triangle is larger than the other two and is known as the base.
Every triangle has three angles that add up to a total of 180°. The base angles are the two angles located along the base of isosceles triangles. In isosceles triangles, the base angles are always congruent, or equal.
The vertex angle is defined as the angle opposite the base. The vertex angle is always greater than the sum of the two base angles. The vertex angle is always calculated by subtracting the base angles from 180°, using the general formula: 180° - 2B = A, where B represents the base angle and A represents the vertex angle.
Thus, vertex angle is defined as the angle opposite the base.
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Please help asap. I give brainliest and points plz no links i grinded for these points
LOOK AT THE PIC
Represent the following expressions as a power of the number a where a not = 0
((a^-2)^-1)^-1 divided by ( a divided by a ^-1)^2
Step-by-step explanation:
\(((a^{-2})^{-1})^{-1}:(a:a^{-1})^2 =\)\(a^{(-2)*(-1)*(-1)}:(a^{1-(-1)})^2 =\)\(a^{-2}:(a^2)^2 =\)\(a^{-2}:a^4=\)\(a^{-2-4}=\)\(a^{-6}\\ or\\ 1/a^6\)\(\\ \rm\leadsto ((a^{-2})^{-1})^{-1}/(a\div a^{-1})^2\)
\(\\ \rm\leadsto (a^2)^{-1}/(a^2)^2\)
\(\\ \rm\leadsto (a^2)^{-1-2}\)
\(\\ \rm\leadsto (a^2)^{-3}\)
\(\\ \rm\leadsto a^{-6}\)
how do you solve for x.
Answer:
X=10
Step-by-step explanation:
71+50=121
180-121=59
So (6x-1)=59
(6x-1)=59
+1 +1
6x=60
6x/6=60/6
x=10
X is a normally distributed random variable with mean 61 and standard deviation 8.
What is the probability that X is greater than 53?
The probability that X is greater than 53
What is probability ?
The area of mathematics known as probability deals with numerical descriptions of how likely it is for an event to happen or for a claim to be true. A number between 0 and 1 is the probability of an event, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.
A probability is a number that expresses the possibility or likelihood that a specific event will take place. Probabilities can be stated as proportions with a range of 0 to 1, or as percentages with a range of 0% to 100%.
Formula for calculating the standard score or z score:
z = x-μ/σ, where:
z is the standard score
x is the raw score
μ is the population mean
σ is the population standard deviation
In this question: μ = 61 and σ = 8
The score is greater than 53
Let’s calculate the z score, for x = 53 and then find the probability for x greater than 53
z = (53 - 61)/8
= -8 / 8
= -1
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find the rate of change of the area of a square when the side of the square is 2 meters and the side is growing at a rate of 3 meters per second.
The rate of change of the area of a square is 12m^2/sec.
What do you mean by rate of change?
The term "rate of change" refers to the rate at which one quantity changes in respect to another. Consequently, if y value is the dependent variable and x value is the independent variable.
Rate of Change is equal to \(\frac{Change in y}{Change in x}\).
Change rates may be positive or negative. This reflects a change in the y-value between the two data points, either up or down. Zero rate of change is the state where a quantity does not change over time.
Solution Explained:
Given,
S = 2m and ds/dt = 3m/s
So, we use
Area = s^2
dA/dt = 2s ds/dt
= 2 X 2 X 3
Therefore, the rate of change of the area is 12m^2/s.
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Write the equation of the line that passes througlī the points (-2, 6)
and (4,6). Put your answer in fully reduced point-slope form, unless it
is a vertical or horizontal line.
Answer:
Horizontal line (0 slope)
Step-by-step explanation:
The equation is \(\frac{y2-y1}{x2-x1}\), so you'd just insert what you know.
It would look like this: \(\frac{6-6}{4-(-2)}\).
We would solve. 6-6=0, while 4-(-2)=6.
So, we have 0/6, which gives you 0, and it would be a horizontal line, since a horizontal line is portrayed by 0 slope.
we want to determine if there a significant difference in the average amount of saturated fat in solid and liquid fats. what is the test statistic? (assume the population data is normally distributed
The test statistic is t = 24.135. (option d)
To perform the hypothesis test, we need to calculate a test statistic. In this case, we can use a two-sample t-test since we are comparing the means of two independent samples. The formula for the t-test is:
t = (x₁ - x₂) / (s_p * √(1/n₁ + 1/n₂))
where x₁ and x₂ are the sample means, s_p is the pooled standard deviation, n₁ and n₂ are the sample sizes.
Using the data provided, we can calculate the sample means and standard deviations for the two samples:
x₁ = 26.3%, s₁ = 0.37%, n₁ = 6
x₂ = 16.9%, s₂ = 0.57%, n₂ = 6
As per the percentage, we can then calculate the pooled standard deviation:
s_p = √(((n₁-1)*s₁² + (n₂-1)*s₂²) / (n₁+n₂-2))
s_p = √(((6-1)*0.37² + (6-1)*0.57²) / (6+6-2)) = 0.471%
Finally, we can calculate the t-statistic:
t = (26.3 - 16.9) / (0.471 * √(1/6 + 1/6)) = 24.135
Therefore, the test statistic is d) t = 24.135.
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Complete Question:
Solid fats are more likely to raise blood cholesterol levels than liquid fats. Suppose a nutritionist analyzed the percentage of saturated fat for a sample of 6 brands of stick margarine (solid fat) and for a sample of 6 brands of liquid margarine and obtained the following results:
Stick = [26.1, 26.5, 26.5, 25.8, 26.7, 26.2]
Liquid = [16.6, 16.5, 17.1, 17.5, 17.7, 16.3]
We want to determine if there a significant difference in the average amount of saturated fat in solid and liquid fats. What is the test statistic? (assume the population data is normally distributed)
a) t = 34.225
b) z = 34.225
c) z = 34.725
d) t = 24.135
e) t = 34.725
ill give brainliest please help :(
Answer:
okay so god,dog,now,won,noon,doom,mood,not,ton,pool
Step-by-step explanation: