Answer:
$95
Step-by-step explanation:
Carmen invested $2,000 in a mutual fund with a loading rate of 4.75%. To calculate the loading charge, we can multiply the amount invested by the loading rate: $2,000 * 4.75% = $95. So, the loading charge for this mutual fund was $95.
Please help me l don’t understand new topic
Answer:
(x-3)(x+4)
Step-by-step explanation:
This way is how it s done in Greece. If u don't understand don't read the explanation Δ=β2-4αγ=81-32=49
χ1,2=-1+-7^2=3
=-4
Write the word form of the number in standard decimal form for: three and fifty-four thousandths
Answer: 350.214
Step-by-step explanation:
A clock pendulum swings back and forth once every two seconds. If its length is one meter and the greatest
angle that it makes with the vertical is 12 degrees, how many kilometers does the bottom end of the pendulum travel in
one day?
The bottom end of the pendulum travels 18,115.2 meters/day, which is approximately 18.12 kilometers/day (since 1 kilometer = 1000 meters).
The motion of the pendulum is a simple harmonic motion and the period of oscillation can be calculated as follows:
T = 2π√(l/g)
where l is the length of the pendulum and g is the acceleration due to gravity (approx. 9.81 m/s²).
Substituting l = 1 m, we get
T = 2π√(1/9.81)
T ≈ 2.006 s.
In one day, there are
24 hours x 60 minutes/hour x 60 seconds/minute
= 86,400 seconds.
The pendulum makes half a period (i.e., one back-and-forth swing) in 2/2 = 1 second. Therefore, it makes
86,400/2
= 43,200 back-and-forth swings in one day.
The distance traveled by the bottom end of the pendulum in one complete swing is equal to the length of the pendulum times twice the maximum angle it makes with the vertical, which is
2 x 12 degrees
= 24 degrees
= 0.419 radians.
Therefore, the distance traveled by the bottom end of the pendulum in one complete swing is
1 meter x 0.419
= 0.419 meters.
Multiplying by the number of swings in one day, we get:
0.419 meters/swing x 43,200 swings/day
= 18,115.2 meters/day.
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ERROR ANALYSIS Describe and correct the error in finding the area of sector XZY when the area of
OZ is 255 square feet.
X
W
Z
X
115°
Let n be the area
of sector XZY.
115
255
n≈ 162.35 ft²
n
360
=
The wrong formula was used. The correct method is: area of sector = 115/360 * 255 ≈ 81.46 square feet.
How to Find the Area of a Sector?The area of a sector is calculated by using the formula:
Area of sector = ∅/360 * πr², where:
r is the radius of the circle
∅ is the central angle measure.
The error made was that a wrong method/formula was used in finding the area of sector.
Given the following:
Area of circle = 255 square feet (πr²)
∅ = 115°
Note that πr² represents the area of a circle, therefore, substituting the values into the formula, we have:
Area of sector = 115/360 * 255
Area of sector ≈ 81.46 square feet
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please help with an explanation
It is financially beneficial for Harris Fishing Tours to replace the old boat with the new fuel-efficient model, as it has a net benefit of $12,000 compared to continuing to use the old boat.
To determine whether Harris Fishing Tours should replace the old boat with the new fuel-efficient model, we need to compare the costs and benefits of each option.
Option 1: Replace the old boat with the new fuel-efficient model
If Harris replaces the old boat with the new fuel-efficient model, they will have to pay $80,000 for the new boat. They can sell the old boat for $32,000, so the net cost of the new boat will be $48,000 ($80,000 - $32,000).
The new boat is expected to be extremely fuel efficient, which means that the fuel costs will be $15,000 per year lower than the old boat. Over the remaining four years of the old boat's useful life, this represents a total savings of $60,000 ($15,000 x 4).
Therefore, the total cost of replacing the old boat with the new fuel-efficient model is $48,000 - $60,000 = -$12,000, which means that this option has a net benefit of $12,000.
Option 2: Continue to use the old boat until it wears out
If Harris decides to continue using the old boat until it wears out, they will not incur the $80,000 cost of purchasing the new boat.
However, they will continue to pay $15,000 per year more in fuel costs than they would with the new boat. Over the remaining four years of the old boat's useful life, this represents a total cost of $60,000 ($15,000 x 4).
In addition, at the end of the four years, the old boat will have no salvage value since it will have reached the end of its useful life.
Therefore, the total cost of continuing to use the old boat until it wears out is $60,000, which means that this option has a net cost of $60,000.
Conclusion
Based on the analysis above, it is more financially beneficial for Harris Fishing Tours to replace the old boat with the new fuel-efficient model. This option has a net benefit of $12,000, while continuing to use the old boat until it wears out has a net cost of $60,000.
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Eve works out every 6 days and Jenna
works out every 4 days. If both Eve and
Jenna work out today, how many days will it
be until they work out on the same day
again?
In 12 days, both Eve and Jenna will work out on the same day again.
Calculating the number of days to work out againTo find the number of days until Eve and Jenna work out on the same day again, we need to find the least common multiple (LCM) of 6 and 4.
One way to find the LCM is to list the multiples of each number until we find a multiple that they have in common:
Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, ...
Multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, ...
From this list, we see that the least common multiple of 6 and 4 is 12.
This means that in 12 days, both Eve and Jenna will work out on the same day again.
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If there are 300 jellybeans in a container. You made a guess of 315 jellybeans. What is the percent error
Answer:
5%
Step-by-step explanation:
Percent error equation is:
(Absolute value of experimental value - actual value / actual value) * 100
Experimental Value: 315
Actual Value: 300
315 - 300 / 300 = 0.05
0.05*100 = 5
Percent error is 5%
Answer: the percent error is 5%
Step-by-step explanation:
A binomial experiment with probability of success p=0.45 and n=7 trials is conducted. What is the probability that the experiment results in exactly 1 success?
The calculated value of the probability that the experiment results in exactly 1 success is 0.08719
Calculating the probability that the experiment results in exactly 1 success?From the question, we have the following parameters that can be used in our computation:
n = 7
x = 1
p = 0.45
The probability is then calculated as
P(x = x) = nCr * p^x * (1 - p)^(n - x)
Substitute the known values in the above equation, so, we have the following representation
P(x = 1) = 7C1 * (0.45)^1 * (1 - 0.45)^(7-1)
Evaluate the expression
So, we have
P(x = 1) = 0.08719
Hence, the probability is 0.08719
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I need help pleaseeeeee
On performing the given row-operation on the given augmented-matrix:
(a) multiplying row1 by -2 and adding to row2, we have [tex]\left[\begin{array}{ccc}5&-2&6\\-10&10&-15\end{array}\right][/tex],
(b) interchanging row1 and row2, we have [tex]\left[\begin{array}{ccc}0&6&-3\\5&-2&6\end{array}\right][/tex],
(c) Multiplying row1 by 2, the matrix becomes [tex]\left[\begin{array}{ccc}10&-4&12\\0&6&-3\end{array}\right][/tex].
The augmented matrix on which we have to perform the row operation is
⇒ [tex]\left[\begin{array}{ccc}5&-2&6\\0&6&-3\end{array}\right][/tex],
Part(a) : We have to multiply row1 by -2 and and add to row2,
The row-operation is performed as : [tex]\left[\begin{array}{ccc}5&-2&6\\(5\times-2)+0&(-2\times-2)+6&(6\times-2)-3\end{array}\right][/tex];
Simplifying further ,
We get,
[tex]\left[\begin{array}{ccc}5&-2&6\\-10&10&-15\end{array}\right][/tex].
Part(b) : We have to interchange the "row1" and "row2",
On interchanging,
We get,
[tex]\left[\begin{array}{ccc}0&6&-3\\5&-2&6\end{array}\right][/tex].
Part(c) : We have to multiply the elements of "row1" by 2,
So, On multiplying the "row1" by 2,
We get,
⇒ [tex]\left[\begin{array}{ccc}5\times 2&-2\times 2&6\times 2\\0&6&-3\end{array}\right][/tex]
⇒ [tex]\left[\begin{array}{ccc}10&-4&12\\0&6&-3\end{array}\right][/tex].
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The rule to get from one term to the next in a
sequence is
Xn+1 = 2xn - 3
Calculate the value of x3 if
a) x₁ = 7
b) x₁ = 9
Answer:
Step-by-step explanation:
When x_1 =7 then you can figure out by given condition say X_n+1= 2X_n-3
then X_2= 11 by substituting the value of X_1 as 7 similarly you can find out the value of X_3 by substituting X_2 as 11 so X_3 =19.
Similarly you can find out b)
Match each drawing on the left with its word description on the right , some of the answer choices on the right may not be used. Line segment AB , Line AB , Point AB , Ray AB , Ray BA
1) Line AB
2) Ray AB
3) Line segment AB
4)Ray BA
The first drawing is a line AB because a line passing through two different points A and B
The second drawing is ray AB because it started at A
The third drawing is a line segment AB because it is part of a straight line that is bounded by two distinct end points, and contains every point on the line that is between its endpoints
The fourth drawing is ray BA
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Give the formulas for the following:
the partial sum of a geometric sequence where a₁ is the first term, n is the number of
the terms in the sum, and r is the common ratio.
the infinite sum of a geometric sequence where |r | < 1.
The formula for the partial sum of a geometric sequence with first term a₁, common ratio r, and n terms is given by:
Sₙ = a₁(1 - rⁿ)/(1 - r)
How to explain the formulaA geometric sequence is a non-zero numerical sequence in which each term after the first is found by multiplying the preceding one by a fixed, non-zero quantity known as the common ratio.
In the formula, Sₙ is the sum of the first n terms of the sequence.
Alternatively, the formula can be expressed as:
Sₙ = (a₁(rⁿ - 1))/(r - 1)
Both of these formulas give the same result and can be used to calculate the partial sum of a geometric sequence.
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Select the correct answer.
Simplify the expression so there is only one positive power for each base.
2.7^(-3) * 3.8^(2) * 2.7^(4) * 3.8^(3)
A. 2.7^(7) * 3.8^(5)
B. 2.7^(-7) * 3.8^(5)
C. 2.7 * 3.8^(5)
D. 2.7 * 3.8
E. 2.7^(7) * 3.8
The expression can be simplified to get:
2.7^(1)*3.8^(5)
The correct option is C.
How to simplify the expression?Remember that if we have the product of two powers with the same base, we only need to add the exponents.
Then we will get:
2.7^(-3) * 3.8^(2) * 2.7^(4) * 3.8^(3)
= (2.7^(-3)*2.7^(4)*3.8^(2)*3.8^(3))
= (2.7^(-3 + 4)*3.8^(2 + 3))
= 2.7^(1)*3.8^(5)
That is the expression simplified, we can see that the correct option is C.
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nueve números son escritos en orden ascendente, el número de en medio es el promedio de todos los números, el promedio de los cinco números más grande es 68 y el promedio de los cinco más pequeños es 44 ¿Cuál es la suma de todos los números?
a) 112
b) 504
c) 144
d) 560
e) 122
The sum of all the number is found to be 630 which is not given in the options.
Let the middle number be x. Then the five numbers smaller than x have an average of 44, so their sum is 544 = 220. Similarly, the five numbers larger than x have an average of 68, so their sum is 568 = 340.
The total of all the numbers is 9x since x is the median and average of all the numbers. The total of all the numbers equals 9x since we know that x is the average of all the numbers.
Therefore, we have,
9x = 220 + x + 340
Simplifying and solving for x, we get,
8x = 560
x = 70
Therefore, the sum of all the numbers is 9x = 970 = 630.
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Complete question - Nine numbers are written in ascending order, the middle number is the average of all the numbers, the average of the five largest numbers is 68, and the average of the five smallest is 44. What is the sum of all the numbers? ?
a) 112
b) 504
c) 144
d) 560
d) 122
Find tan A for the triangle below. A right triangle. The hypotenuse is 18.03, the side opposite to angle A is 10, and the side adjacent to angle A is 15. a. 1.5 b. 0.667 c. 0.832 d. 1.202
The value of tan A is 0. 667. Option B
How to determine the valueTo determine the value of the identity, we need to take note of the different trigonometric identities.
these identities are;
sinetangentcotangentcosinecosecantsecantWe also have that the ratio for the tangent identity is expressed as;
tan θ= opposite/adjacent
From the information given, we have that;
The hypotenuse is 18.03, the side opposite to angle A is 10, and the side adjacent to angle A is 15
Then, for the identity, we have;
tan A = 10/15
Divide the values
tan A = 0. 667
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In a class of 26 students, a teacher chooses a different student to each present five different homework problems. Which statement describes the number of ways the students can be chosen to present the problems? There are 26C5 = 65,780 ways the students can be chosen because the order they are chosen matters. There are 26P5 = 7,893,600 ways the students can be chosen because the order they are chosen matters. There are 26C5 = 65,780 ways the students can be chosen because the order they are chosen does not matter. There are 26P5 = 7,893,600 ways the students can be chosen because the order they are chosen does not matter.
"There are 26C₅ = 65,780 ways the students can be chosen because the order they are chosen does not matter." is correct statement. Therefore, the answer is option C.
The problem asks us to choose 5 students out of a class of 26 to present homework problems. Since the order in which the students present the problems does not matter, we need to use the combination formula. The combination formula is used to calculate the number of ways to choose a subset of k elements from a set of n elements without regard to order, and it is denoted by nCk.
Option A, "There are 26C₅ = 65,780 ways the students can be chosen because the order they are chosen matters," is incorrect because the order in which the students are chosen does not matter.
Option B, "There are 26P₅ = 7,893,600 ways the students can be chosen because the order they are chosen matters," is incorrect because we are choosing 5 students out of 26, and the order in which they are chosen does not matter.
Option D, "There are 26P₅ = 7,893,600 ways the students can be chosen because the order they are chosen does not matter," is also incorrect because the order in which the students are chosen does not matter.
Therefore, the answer is option C.
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Complete question is:
In a class of 26 students, a teacher chooses a different student to each present five different homework problems. Which statement describes the number of ways the students can be chosen to present the problems?
A) There are 26C₅ = 65,780 ways the students can be chosen because the order they are chosen matters.
B) There are 26P₅ = 7,893,600 ways the students can be chosen because the order they are chosen matters.
C) There are 26C₅ = 65,780 ways the students can be chosen because the order they are chosen does not matter.
D) There are 26P₅ = 7,893,600 ways the students can be chosen because the order they are chosen does not matter.
Students are making lemonade from a powdered lemon drink mix. Zachary mixes 11 cups of water and 5 cups of powdered lemon mix. Dianelys mixes 7 cups of water and 4 cups of powdered lemon mix. Use Zachary and Dianelys’s percent of powdered lemon mix to determine whose mix will be more lemony
The percentage of the powdered lemon mix in Dianelys's mix indicates that Dianelys's mix is more lemony.
What is a percentage?A percentage is an expression of a ratio of two quantities as a fraction of 100.
The number of cups of water Zachary mixes with 5 cups of powdered lemon mix = 11 cups of water
Number of cups of water Dianelys mixes with 4 cups of powdered lemon mix = 7 cups of water
Zachary's percentage of powdered lemon mix = (5/(11 + 5)) × 100 = 31.25%
Dianelys's percentage of powdered lemon mix = (4/(7 + 4)) × 100 = 36.[tex]\overline{36}[/tex]%
The percentage of powdered lemon mix for Dianelys which is more than the percentage in Zachary's powdered lemon mix indicates that Danialys mix is more lemony.
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A coach asked her athletes if they enjoy running. Fifty-five percent of the team do not like to run. Of those, 70% enjoy cycling, while 80% of those who enjoy running also enjoy cycling. The tree diagram shows how the athletes are divided into subgroups.
The tree diagram shows athletes branching off into two categories, enjoys running and does not enjoy running. Enjoys running branches off into two sub-categories, enjoys cycling and does not enjoy cycling. Does not enjoy running branches off into two subcategories, enjoys cycling and does not enjoy cycling.
What is the total percentage of the athletes who enjoy cycling?
9%
25.5%
55%
74.5%
Answer:
75%
Step-by-step explanation:
To determine the total percentage of athletes who enjoy cycling, we need to consider the percentages given in the problem.
According to the information provided:
55% of the team does not like to run.
Of those who do not like to run, 70% enjoy cycling.
Of those who enjoy running, 80% also enjoy cycling.
To calculate the total percentage of athletes who enjoy cycling, we need to consider the percentages from both branches of the tree diagram.
Percentage of athletes who do not like to run and enjoy cycling:
= (Percentage of athletes who do not like to run) * (Percentage of those who enjoy cycling within that group)
= 55% * 70% = 38.5%
Percentage of athletes who enjoy running and enjoy cycling:
= (Percentage of athletes who enjoy running) * (Percentage of those who enjoy cycling within that group)
= (100% - 55%) * 80% = 45% * 80% = 36%
Total percentage of athletes who enjoy cycling:
= Percentage of athletes who do not like to run and enjoy cycling + Percentage of athletes who enjoy running and enjoy cycling
= 38.5% + 36% = 74.5%
Therefore, the correct answer is:
74.5%
the visual fraction model shows the fractions of 1 cup of each kind of yogurt thats add to the blender
Therefore , the solution of the given problem of fraction comes out to be 3/4 cups of yoghurt to the blender.
What is a fraction?Any configuration of identically sized parts can be combined to represent the total. In Standard English, quantity is defined as "a portion" within a specific measurement. 8, 3/4. Wholes also include fractions. These serve as the divisor of the ratio, which in mathematical terms would be a pair of numbers. Here are a few illustrations of how to convert simple halves into whole numbers.
Here,
A visual fraction model can be used to illustrate the various fractions in a cup of yoghurt that you want to add in portions to a blender.
For instance, you may divide the cup into four equal parts and use one of those parts to represent 1/4 cup of yoghurt in the blender.
You can divide the cup into two equal parts and display two of those parts to symbolise the addition of 1/2 cup of yoghurt.
You would have added
=> 1/4 + 1/2 = 3/4 cups of yoghurt to the blender.
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A toy car travels 12 centimeters per second ehich graph best best represents why the number of centimeters the toy var travels in x seconds
Answer: The graph that best represents the number of centimeters the toy car travels in x seconds would be a linear graph with a slope of 12. The equation for this graph would be y = 12x, where y represents the distance traveled in centimeters and x represents the time in seconds.
Step-by-step explanation:
100 Points! Algebra question. Describe the scatter plot and an appropriate scale for the data set below. Photo attached. Thank you!
Note that the scatter plot (attached) for the given data is described below.
What is the description of the attached scatter plot?The scatter plot for the given data set shows a moderately strong negative linear relationship between x and y. The data points appear to form a somewhat linear pattern, indicating that there is a linear association between the variables.
The scatter plot suggests that as the x values increase, the corresponding y values decrease.
An appropriate sale for this data set would be a linear regression, which can provide a mathematical model for predicting y values based on x values.
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5 divided by -3 minus 3 times the square root of 3
The result of the operation that we have done here is -5√3.
How do you convert it to equation?We know that one of the most important things that we have to do in mathematics is that we have to convert word equations into mathematical equations and this is quite critical in how we can be able to work it so as to get the equation that we are looking for.
We now have that;
5/-3 * 3 * √3
5/-1 * √3
-5* √3
-5√3
We can see that after the computation of the word problem that we have here, the result is -5√3
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AP calc please help me
a) over the interval of 0 - 10 hours, the average rate of change of the temperature is 17,088°C/hr.
b) the average temperature of the water in the system is 1527.
c) over the interval of 10 - 20 hours, the total change in the temperature of the water in the solar steam power system is -14,351°C.
a) g'(x) = 2 + [tex]\int\limits^x_0[/tex] ƒ'(t) dt
g'(-3) = -2
b) The absolute maximum value of g on the closed interval [-5, 5]=
10 + 2√7.
c) The x-coordinates of the points of inflection of the graph of g are -1, 0 and 2.
What is right Riemann sum formula?
The right Riemann sum formula uses the right-most value of each interval as the value of the function over that interval.
a) g(5) = 2(5) + [tex]\int\limits^5_0[/tex] ƒ(t) dt
= 10 + 2√7
g'(x) = 2 + [tex]\int\limits^x_0[/tex] ƒ'(t) dt
g'(-3) = 2 + [tex]\int\limits^3_0[/tex]ƒ'(t) dt
= 2 - (4 + 0)
= -2
b) The absolute maximum value of g on the closed interval [-5, 5]=
10 + 2√7.
This is because the highest value of ƒ(t) dt on the interval= 4√7, which occurs at x = 2.
The highest value of g is thus given by 10 + 2√7.
c) The x-coordinates of the points of inflection of the graph of g are -1, 0 and 2.
This is because ƒ'(t) dt is undefined at these points, so the second derivative of g is also undefined.
a) To evaluate the S'(t) dt, we need to calculate the area under the curve of the temperature data given in the table. To do this, we use the trapezoidal rule. This gives us the following:
[tex]\int\limits^10_0[/tex] S'(t) dt = [(142 + 210 + 254 + 280 + 274 + 268)/2] × 8
= 17,088
This means that over the interval of 0 - 10 hours, the average rate of change of the temperature is 17,088°C/hr.
This can be interpreted in the context of the problem as the average rate at which the temperature of the water in the solar steam power system is changing over the given time interval.
b) To approximate the average temperature of the water in the system using a right Riemann approximation, we need to calculate the area under the curve of the temperature data given in the table. We can do this using the right Riemann sum formula, which gives us the following:
Right Riemann Approximation = [(210 + 254 + 280 + 274)/4] × 6 = 1527
In this case, the right-most value of each interval is lower than the true average over that interval, so the approximation will be lower than the true average.
c) To determine the total change in the temperature of the system for the interval 10≤t≤20, we need to calculate the area under the curve of the equation S'(t)=-√2xe (√x²-100)/x.
This can be done using the definite integral of the equation, which gives us the following:
Total Change = ∫1020-√2xe (√x²-100)/x dx
= -14,351
This means that over the interval of 10 - 20 hours, the total change in the temperature of the water in the solar steam power system is -14,351°C.
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Pls Help Parallelogram PQRS is shown in the coordinate plane below. What is the perimeter of parallelogram PQRS?
1) Find the missing side using the right triangle shown. 2) Then find the perimeter by adding all four sides of the parallelogram!
Note that the perimeter of the parallelogram is 42
How is this so?recall that opposite sides of a parallelogram are congruent always
We have to to find the distance between the points Q(6, 6 ) and R(1, -6) using the distance formula which is
d = √[(x2 - x1) ² + (y2 - y 1)²]
where d is the distance between two points with paris (x1 , y1)
and (x2, y2).
PS = QR = √(6-1)² + (6+6)²
= √5² + 12²
= √(25+144
= √(169)
= 13
PQ = SR = 8
Perimeter = 13 + 13 + 8 + 8
Perimeter = 42.
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Full Question:
Although part of your question is missing, you might be referring to this full question:
See attached image.
A researcher is interested in hamster wheel-running activity during the summer versus the winter. She suspects that either the hamsters will run less during the winter to conserve energy, or they will run more to keep warm. She records the activity of n = 30 hamsters during June, July, and August and compares their running-wheel revolutions per hour to the activity of the same hamsters during December, January, and February.
The data are collected, and the results show an average difference score of = 5. 7 and a sum of squares of SS = 2,851.44.
What is the value for degrees of freedom for this repeated-measures t test?
There are 29 degrees of freedom for this repeated-measures t-test.
Understanding the degree of freedomThe degrees of freedom (df) for a repeated-measures t-test is calculated as (n-1), where n is the number of paired observations.
In this case, each hamster's activity was measured during both summer and winter, resulting in a paired sample design. Therefore, the number of paired observations is equal to the number of hamsters, which is n = 30.
Hence, the degrees of freedom for this repeated-measures t-test is:
df = n - 1 = 30 - 1 = 29
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With workings, please help
Answer:
it's 4 cm
Step-by-step explanation:
A. Square = 50 cm²
A. Square = s × s
50 = s²
s = √50
SP = hypotenuse (c) = s
c = s = √50
b = √34
a = PT = ...?
use Pythagorean theorem to find PT
a² + b² = c²
a² + (√34)² = (√50)²
a² + 34 = 50
a² = 50 - 34
a² = 16
a = √16
a = 4 cm
#CMIIWACTIVITY 3: Given the following functions, find the following:
The values of the composite functions are (g o f)(x) = [tex]\frac{9x^2-18x+4}{4}-5[/tex], (j o g)(x) = 3x² - 15x + 1, (g o h)(x) = [tex]\frac{\left(2x-1\right)^2}{1089}-\frac{5\left(2x-1\right)}{33}[/tex] and (g o g)(-2) = 126
Calculating the composite functionsGiven that we have the function definitions
The composite functions are calculated below
(g o f)(x) = g(f(x))
(g o f)(x) = (f(x))² - 5f(x)
So, we have
(g o f)(x) = (3/2x + 1)² - 5(3/2x + 1)
Evaluate
(g o f)(x) = [tex]\frac{9x^2-18x+4}{4}-5[/tex]
Next, we have
(j o g)(x) = j(g(x))
(j o g)(x) = 3g(x) + 1
So, we have
(j o g)(x) = 3(x² - 5x) + 1
(j o g)(x) = 3x² - 15x + 1
Next, we have
(g o h)(x) = g(h(x))
(g o h)(x) = (h(x))² - 5h(x)
So, we have
(g o h)(x) = ((2x - 1)/33)² - 5((2x - 1)/33)
Evaluate
(g o h)(x) = [tex]\frac{\left(2x-1\right)^2}{1089}-\frac{5\left(2x-1\right)}{33}[/tex]
Lastly, we have
(g o g)(-2) = g(g(-2))
(g o g)(-2) = (g(-2))² - 5g(-2)
So, we have
(g o g)(-2) = ((-2)² - 5(-2))² - 5((-2)² - 5(-2))
(g o g)(-2) = 126
Hence, the values are (g o f)(x) = [tex]\frac{9x^2-18x+4}{4}-5[/tex], (j o g)(x) = 3x² - 15x + 1, (g o h)(x) = [tex]\frac{\left(2x-1\right)^2}{1089}-\frac{5\left(2x-1\right)}{33}[/tex] and (g o g)(-2) = 126
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Solve the following by completing the square or squaring both sides using steps illustrated in the lesson content.. Leave answers in radical (EXACT) form. Do not use decimals. -2x+6=-x^2
Answer:
Starting with the equation:
-2x + 6 = -x^2
First, we can rearrange it to put it in standard quadratic form:
x^2 - 2x - 6 = 0
To complete the square, we need to add and subtract a constant term that will make the left-hand side of the equation a perfect square. The constant we need to add is (b/2)^2, where b is the coefficient of x. In this case, b = -2, so:
x^2 - 2x + 1 - 1 - 6 = 0
The first three terms can be written as a perfect square:
(x - 1)^2 - 7 = 0
Add 7 to both sides:
(x - 1)^2 = 7
Now we can take the square root of both sides:
x - 1 = ±√7
Add 1 to both sides:
x = 1 ± √7
So the solutions to the equation are:
x = 1 + √7 or x = 1 - √7
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Cynthia is planning a trip to visit her friend who lives 460 miles away. Her car gets 32 miles per gallon of gas. How many gallons of gas will Cynthia use to get to her friend's house and then back home?
The length of the Green Route in miles is 64 miles.
What is miles?Miles is a unit of linear measurement. It is traditionally defined as 5,280 feet, or 1,760 yards, and is equivalent to 1.609 kilometers. Miles are commonly used to measure long distances, such as the distance between two cities. They are also used to measure the lengths of roads and other paths. Miles are one of the most commonly used units of measurement in the United States.
The length of the Green Route in miles can be calculated by subtracting the total mileage traveled on the Blue Route from the total mileage traveled on both routes.
Total miles traveled on Monday = 38 miles
Total miles traveled on Tuesday = 80 miles
Total miles traveled on the Blue Route = 5 + 11 = 16 miles
Therefore, the total miles traveled on the Green Route = 80 - 16 = 64 miles
Therefore, the length of the Green Route in miles is 64 miles.
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Jordan's monthly bank statement showed the following deposits and withdrawals:
$7.72,
−
−$84.26, $70.42,
−
−$50.15, $107.46
If Jordan's balance in the account was $92.66 at the beginning of the month, what was the account balance at the end of the month?
Jordan's account balance at the end of the month would be $143.85.
What is the basic arithmetic operations?
The four basic mathematical operations are Addition, subtraction, multiplication, and division.
To determine Jordan's account balance at the end of the month, we need to add up the deposits and withdrawals to the initial balance.
Initial balance: $92.66
Deposits: $7.72 + $70.42 + $107.46 = $185.60 (sum of positive amounts)
Withdrawals: -$84.26 + (-$50.15) = -$134.41 (sum of negative amounts)
To calculate the account balance at the end of the month, we can add the deposits and withdrawals to the initial balance:
Account balance at the end of the month = Initial balance + Deposits - Withdrawals
= $92.66 + $185.60 - $134.41
= $143.85
Hence, Jordan's account balance at the end of the month would be $143.85.
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