Answer:
a = -3, b = 2.5, c = - 1/2Step-by-step explanation:
1)
\(3^a=1/27\)\(3^a=1/3^3\)\(3^a=3^{-3}\)\(a=-3\)2)
\(3^b=9\sqrt{3}\)\(3^b=3^2*3^{1/2}\)\(3^b=3^{2+1/2}\)\(3^b=3^{2.5}\)\(b=2.5\)3)
\(3^c=1/\sqrt{3}\)\(3^c=1/3^{1/2}\)\(3^c=3^{-1/2}\)\(c = - 1/2\)A train travels a total of 67 km at a constant speed of 110 km/h.
How long is its journey? Give your answer in minutes and seconds, to the nearest second.
Answer:
36 m 32 s
Step-by-step explanation:
67 /110 = 0.609 hour
0.609 × 60 minutes = 36.54 minutes
36 minutes + 0.54×60 second
= 36 minutes 32 seconds
Answer:
36 mins 32 secs
Step-by-step explanation:
4. Car dealer Lisa Kovach paid 82% of a car's options totaling $3,098. She paid 85% on a base price of $15,480.
The destination charge was $890. What is the dealer's cost?
a. $13,158.00
b. $16,588.36
c. $18,020.36
d. $19.001.20
Part (c) is the correct option i.e. The total dealer's cost is $16588.36.
What is Percentage ?
Percentage, which is a relative figure used to denote hundredths of any quantity. Since one percent (symbolised as 1%) is equal to one hundredth of something, 100 percent stands for everything, and 200 percent refers to twice the amount specified.
Given, Cost paid for car's options = 82 % $3,098 = $2540.36
Cost paid for base price = 85 % $15,480 = $13158.
Destination charge = $890
∴ The total dealer's cost will be :
= Cost paid for car's options + Cost paid for base price + Destination charge
= $2540.36 + $13158 + $890
= $16588.36.
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A random number generator is used to select a number from 1 to 50 (inclusively). What is the probability of selecting the number 28?
(Type an integer or a decimal. Do not round.)
Answer:
the answer is 1/50
Step-by-step explanation:
A random number generator is used to select an integer from 1 to 50. Since random number generator generates any number randomly, all the numbers from 1 to 50
5) Explain in your own words what is meant by the son of a mention Include a practical example of a differential equation used to model wito your specific engineering course நmata) b) Solve the following first order differential equation using the integrating factor method. dy cos(t) + sin(t) y = 3cos (t) sin(t) - 2 dx [10 marks) c) Explain the following MATLAB code shown and sketch the output plot from program 19 marks) 01 t=0 02 while t<10 03 if (t<5) 04 y=3*(1-exp(-)): 05 else if (t>=5) 06 y=3*exp(-t+5); 07 end 08 end 09 t = t + 0.05 10 pause (0.002) + Figure Q4 Q4 Total
The output of this code will be a signal that starts at zero and gradually increases to three. After five seconds, the signal starts decreasing to zero, with an exponential decay rate. The output plot will look like a ramp that rises linearly and falls exponentially after five seconds.
The term "son of a mention" is not familiar in mathematics. The correct term might be "son of a gun" or "son of a function."A differential equation used to model your specific engineering course is called an engineering differential equation. Such equations are used to predict, control, and monitor various physical processes, ranging from the dynamics of mechanical systems to the motion of fluids and gases, and electrical and electronic circuits. It's essential to know the form of the differential equations, the initial and boundary conditions, and the physical meaning of the parameters to use them effectively in modeling physical systems.
The following MATLAB code represents a simple for loop with a nested if-else statement and a plotting command. The code generates a signal with two segments: a rising ramp from zero to three and a falling ramp from three to zero. The signal has a total duration of 10 seconds, a sampling interval of 0.05 seconds, and a plotting delay of 0.002 seconds.
01 t=0 02 while t<10 03
if
(t<5) 04 y=3*(1-exp(-t)); 05 else if
(t>=5) 06 y=3*exp(-t+5); 07 ends 08 end 09
t = t + 0.05 10 pauses (0.002)
The output of this code will be a signal that starts at zero and gradually increases to three. After five seconds, the signal starts decreasing to zero, with an exponential decay rate. The output plot will look like a ramp that rises linearly and falls exponentially after five seconds.
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Math school please need help
Answer:
r² = (9 - 4)² + (6 - 4)² = 5² + 2² = 25 + 4 = 29
So the equation of this circle is
(x - 4)² + (y - 4)² = 29
Help (the answer isn't the 3rd one my friend did this test and chose that and got it wrong please )
Answer:
3 and 1/3
Step-by-step explanation:
It is 3 and 1/3 because there are 3 fully shaded circles (3) then one of the three parts for one circle (1/3)
If it was wrong there is something wrong with the test lol.
students in a large statistics class were randomly divided into two groups. the first group took the midterm exam with dave matthews band playing in the background while the second group took the exam with death cab for cutie playing in the background. the scores of the two groups on the exam were compared. what is the explanatory variable in this experiment?
The response variable in this experiment is the scores on the midterm exam. The response variable is the one that is measured or observed to determine whether it has been affected by the explanatory variable.
What is variable?The alphabetic character that expresses a numerical value or a number is known as a variable in mathematics. A variable is used to represent an unknown quantity in algebraic equations.
The explanatory variable in this experiment is the type of music played in the background during the exam. The explanatory variable is the one that is deliberately manipulated or changed by the researcher in order to observe its effect on the response variable. In this case, the researcher wanted to investigate whether the type of music played during the exam would have an effect on the students' performance, so they manipulated the type of music and observed its effect on the exam scores.
The response variable in this experiment is the scores on the midterm exam. The response variable is the one that is measured or observed to determine whether it has been affected by the explanatory variable. In this case, the researcher measured the exam scores of the two groups to see if there was a difference between the group that listened to Dave Matthews Band and the group that listened to Death Cab for Cutie.
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Which equation could represent a linear combination of the system?
The equation that could represent a linear combination of the system 2/3x + 5/2y = 15 and 4x + 15y = 12 is 0 = 26
What are linear equations?Linear equations are equations that have constant average rates of change, slope or gradient
How to determine the linear combination to the system?A system of linear equations is a collection of at least two linear equations.
In this case, the system of equations is given as
2/3x + 5/2y = 15
4x + 15y = 12
Multiply the first equation by 6, to eliminate the fractions.
6 * (2/3x + 5/2y = 15)
This gives
4x + 15y = 90
Subtract the equation 4x + 15y = 90 from 4x + 15y = 12
4x - 4x + 15y - 15y = 12 - 90
Evaluate the difference
0 + 0 = -78
Evaluate the sum
0 = -78
The above equation is the same equation as option (b) 0 = 26
This is so because they both represent that the system of equations have no solution
Hence, the equation that could represent a linear combination of the system is 0 = 26
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Complete question
The system of equations below has no solution.
2/3x + 5/2y = 15
4x + 15y = 12
Which equation could represent a linear combination of the system?
consider the system of equations 2x −5y =1 4x −10y =3 how many solutions does this system have? explain.
Solutions for the system of equations 2x −5y =1 , 4x −10y =3 has no solution as ( 2 /4 ) = (-5/-10) ≠ (1/3) .
Simplify the system of equations to get the solution of the system :
2x - 5y = 1
⇒ 2x = 1 + 5y
⇒ x = ( 1+ 5y ) / 2 __(1)
4x -10y = 3
⇒ 2 ( 2x - 5y ) = 3
⇒2x - 5y = 3/2 ___(2)
Standard form of the system of equations are :
a₁x + b₁y + c₁ = 0
a₂x + b₂y + c₂ = 0
Substitute the value of x from (1) into (2) we get,
2 ( 1 + 5y )/2 - 5y = 3/2
⇒1 + 5y -5y = 3/2
⇒1 = 3/2
⇒2 = 3 which is not true.
System of the equation has no solution.
Here, ( a₁ /a₂ ) = (b₁ /b₂) ≠ (c₁ /c₂ ) that is ( 2 /4 ) = (-5/-10) ≠ (1/3) .
Therefore, the system of equations has no solution.
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A special deck of cards has 6 red cards, and 5 black cards. The red cards are numbered 1, 2, 3, 4, 5, and 6. The black cards are numbered 1, 2, 3, 4 and 5. The cards are well shuffled and you randomly draw one card.
a) Number of elements in sample size is 11.
b) Probability P(E) is 0.45.
a) The sample space is the set of all possible outcomes when drawing a single card from the deck. Since there are 11 cards in total, the sample space has 11 elements.
b) We want to find the probability of drawing an even-numbered card, which includes the red cards numbered 2, 4, and 6, and the black cards numbered 2 and 4. There are five such cards in total, so the probability of drawing an even-numbered card is:
P(E) = number of even-numbered cards / total number of cards
P(E) = 5 / 11
P(E) = 0.4545 or approximately 0.45
Therefore, the probability of drawing an even-numbered card from the deck is about 0.45.
Correct Question:
A special deck of cards has 6 red cards, and 5 black cards. The red cards are numbered 1, 2, 3, 4, 5, and 6. The black cards are numbered 1, 2, 3, 4 and 5. The cards are well shuffled and you randomly draw one card.
R = card drawn is Red
E = card drawn is even-numbered
a) How many elements are there in the sample space.
b) What is the probability P(E).
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A new drug is being tested to see whether it can increase the chance of a quick recovery in people who have come down with the flu in the past week. The rate of quick recovery in the population of concern is 0.87. The null hypothesis is that p​ (the population proportion using the new drug that have a quick recovery​) is 0.87. What is the correct alternative​ hypothesis?
This alternative hypothesis is either greater than or less than 0.87, but not exactly equal to it.
The alternative hypothesis (H1) is the hypothesis that is tested when the null hypothesis (H0) is rejected.
The null hypothesis is that the population proportion using the new drug that have a quick recovery is 0.87.
The alternative hypothesis would be that the population proportion using the new drug that have a quick recovery is different from 0.87.
This can be expressed as:
H1: p ≠ 0.87
The alternative hypothesis in this scenario would be that the new drug being tested is effective in increasing the chance of a quick recovery in people who have come down with the flu in the past week.
The alternative hypothesis would state that the population proportion of those who use the new drug and experience a quick recovery is greater than 0.87.
The alternative hypothesis is necessary because it allows us to determine whether the results of the study are statistically significant.
If the null hypothesis is accepted, it means that there is no significant difference between the rate of quick recovery with or without the new drug.
The alternative hypothesis is accepted, it means that the new drug has a significant effect on increasing the rate of quick recovery.
To test this hypothesis, a statistical analysis will need to be performed using the data collected from the study.
This analysis will allow us to determine whether the results are statistically significant and whether we can reject the null hypothesis in favor of the alternative hypothesis.
Ultimately, this will provide valuable information on the effectiveness of the new drug and whether it should be recommended for use in treating the flu.
The "≠" symbol means "not equal to".
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factoring trinomials 4x^2-15x-25
Answer:
For a polynomial of the form ax2+bx+c a x 2 + b x + c , rewrite the middle term as a sum of two terms whose product is a⋅c=4⋅−25=−100 a ⋅ c = 4 ⋅ - 25 ...
Step-by-step explanation:
Una catedral esta situada en la cima de una colina. Cuando la punta de su torre se observa desde el ple de la loma, el angulo de elevacion es de 48°. Cuando se ve desde un punto a una distancia de 6096 m del pie del promontorio, el angulo de elevacion es de 41° la cuesta de la colina forma un angulo de 32° Aproxima la altura de la catedral
Answer:
La altura de la catedral es de 15119,97 m.
Step-by-step explanation:
Para una respuesta única, la pregunta se formula de la siguiente manera:
Una catedral se encuentra en la cima de una colina. Cuando se ve la parte superior de su torre desde la parte inferior de la colina, el ángulo de elevación es de 48 °. Cuando se ve desde un punto a 6096 m del pie del promontorio, el ángulo de elevación es de 41 °, la pendiente de la colina forma un ángulo de 32 ° Se aproxima a la altura de la catedral
Deje que la base de la colina = C
El punto 6096 m de la base = A
La cima de la catedral = B
∴ ∠A = 41 °
∠C = 180-48 = 132 °
∠B = 180 - (41 + 132) = 7 °
\(\dfrac{6096}{sin7} = \dfrac{CB}{sin41}\)
∴ CB = 32816.59 m.
Punto E = Base de la catedral.
Punto D = Punto debajo de la base de la catedral al nivel del pie de la colina
Por lo tanto, la altura de la catedral = BE
∡ABE = 90-41 = 49 °
∡CED = 90-32 = 58 °
∴ ∡CEB = 180 - 58 ° = 122 °
De la regla seno tenemos;
\(\dfrac{CB}{sin(\angle CEB)} = \dfrac{BE}{sin(\angle ECB)}\)
∠EBA = 90 - 48 = 42°
∠EBC = 42 - 7 = 35°
∠ECB = 180 - 35 - 122 = 23°
\(\therefore \dfrac{32816.59 }{sin(122)} = \dfrac{BE}{sin(23)}\)
\(BE = \dfrac{32816.59 }{sin(122)} \times sin(23) = 15119.97 \ m\)
La altura de la catedral = 15119,97 m.
Translate the sentence into an inequality.
The sum of 2 and b is less than 18.
Answer:
2+b<18
Step-by-step explanation:
a gym knows that each member, on average, spends 70 minutes at the gym per week, with a standard deviation of 20 minutes. assume the amount of time each customer spends at the gym is normally distributed. a. what is the probability that a randomly selected customer spends less than 65 minutes at the gym? b. suppose the gym surveys a random sample of 49 members about the amount of time they spend at the gym each week. what are the expected value and standard deviation (standard error) of the sample mean of the time spent at the gym?
(a) The probability that a randomly selected customer spends less than 65 minutes at the gym is 0.4013. (b) The expected value and standard deviation (standard error) of the sample mean of the time spent at the gym is 2.857 minutes
a) The probability that a randomly selected customer spends less than 65 minutes at the gym is calculated using the standard normal distribution formula.
z = (x - μ) / σ
where,μ = 70 minutes, σ = 20 minutes, x = 65 minutes
Substituting the given values, we get
z = (65 - 70) / 20
z = -0.25
Using a standard normal table or calculator, the probability that a randomly selected customer spends less than 65 minutes at the gym is 0.4013.
b) The standard deviation (standard error) of the sample mean can be calculated using the formula:
SE = σ/√n
where,σ = 20 minutes, n = 49
Substituting the given values, we get
SE = 20/√49
SE = 2.857 minutes
Therefore, the expected value and standard deviation (standard error) of the sample mean of the time spent at the gym is 2.857 minutes, respectively.
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Write an equation that can be solved using multiplication and has a solution of x=12
Answer:3x4=x
Step-by-step explanation:
some alkenes have geometric cis trans isomers because
Some alkenes have geometric cis-trans isomers because of the presence of a double bond between two carbon atoms. In a carbon-carbon double bond, the carbon atoms are connected to two different groups of atoms, which can be oriented differently in space. In the cis configuration, the two substituent groups on each carbon atom are on the same side of the double bond, while in the trans configuration, the two substituent groups on each carbon atom are on opposite sides of the double bond.
The cis-trans isomerism arises due to the restricted rotation around the carbon-carbon double bond. In the case of cis isomers, the substituent groups are too bulky to rotate around the double bond, and they remain on the same side of the double bond. In contrast, in the trans isomers, the substituent groups are oriented on opposite sides of the double bond, which allows them to rotate freely around the bond.
The presence of cis-trans isomers has important consequences for the physical and chemical properties of alkenes, including their reactivity, solubility, and melting points. The two isomers can have different properties and can exhibit different biological activities, making them important targets for drug design and synthesis.
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karen wants to advertise how many chocolate chips are in each big chip cookie at her bakery. she randomly selects a sample of 43 cookies and finds that the number of chocolate chips per cookie in the sample has a mean of 13.9 and a standard deviation of 2.9. what is the 80% confidence interval for the number of chocolate chips per cookie for big chip cookies? enter your answers accurate to one decimal place (because the sample statistics are reported accurate to one decimal place).
There were 13.9 chocolate chips on average in each cookie, with a standard deviation of 2.9. Based on this sample, it is estimated that there are between 13.3 and 14.5 chocolate chips per cookie within the 80% confidence interval.
To calculate the 80% confidence interval for the number of chocolate chips per cookie, we can use the formula:
Confidence Interval = Mean ± (Z * (Standard Deviation / √( SampleSize))) First, we need to find the critical value (Z) for an 80% confidence level.
The Z-value corresponds to the desired confidence level and can be obtained from a standard normal distribution table or calculated using a statistical software. For an 80% confidence level, the Z-value is approximately 1.282.
Confidence Interval = 13.9 ± (1.282 * (2.9 / √43))
Calculating the expression inside the parentheses:
Confidence Interval = 13.9 ± (1.282 * 0.442)
Calculating the final confidence interval:
Confidence Interval ≈ 13.9 ± 0.567
Therefore, the 80% confidence interval for the number of chocolate chips per cookie for big chip cookies is approximately (13.3, 14.5).
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Write an
equation in slope-intercept form for the line that passes
through the points (6, –3) and (0,2).
The populations of two towns, town A and town B, are being compared. The population of town A is 4×104 and the population of B is 2×105. How many times greater is the population of town B than town A?
Answer:
The population of town A is greater than B. Town A is 206 times greater than town B.
Step-by-step explanation:
Population of town B is 0.505 times greater than the population of town B.
The population of Town A is:
= 4 x 104
= 416 people
The population of Town B is:
= 2 x 105
= 210 people
In relation to town A, the population of town B is:
= Town B population / Town A population
= 210 / 416
= 0.505 times greater
In conclusion, the population of town A is more than that of town B so town B is only 0.505 times greater than town A to show that it is smaller than town A.
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Show that the equation of the lime in R^2 through distinct points (x1,x2) and (x2,y2) can be written as det =[\begin{array}{ccc}1&x&y\\1&x1&y1\1&x2&y2\end{array}\right]=0
The equation of the lime in R^2 through distinct points (x1,x2) and (x2,y2) can be written as det as 0
Let (x1,y1) and (x2,y2) be two distinct points in R^2.
The equation of a line passing through two points in the plane can be written in the form y = mx + b, where m is the slope of the line and b is the y-intercept.
We can find the slope of the line by:
m = (y2 - y1)/(x2 - x1)
We can rewrite this equation in the form:
y - y1 = m(x - x1)
Expanding this equation, we get:
y - y1 = (y2 - y1)/(x2 - x1) (x - x1)
Multiplying both sides by (x2 - x1), we get:
(x2 - x1)(y - y1) = (y2 - y1)(x - x1)
Simplifying, we get:
x(y2 - y1) - y(x2 - x1) + x2y1 - x1y2 = 0
This equation can be written as:
\begin{vmatrix}
1 & x & y\
1 & x1 & y1\
1 & x2 & y2
\end{vmatrix} = 0
which is the same as the determinant expression given in the problem statement.
Therefore, we have shown that the equation of the line passing through two distinct points (x1,y1) and (x2,y2) can be written as det = 0.
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Sofia earns $9 per hour mowing lawns. The total amount earned (t) equals the amouont earned per hour times the number of hours (h) . Which equation gives the total amount earned t if Lina works (h) hours ?
Answer:
9h
Step-by-step explanation:
Given data
Sofia earns $9 per hour mowing lawns
Let the total amount earned be t
and let the time worked be h
Hence
t= 9*h
t= 9h
The expression is 9h
Find the slope of the line in the graph.
SAVE ME!! THIS IS DUE IN LIKE 2 MINUTES
Answer: m = -1
Step-by-step explanation:
m = slope
The slope is 1/-1 which is just -1.
Hope this helps!
Triangle F E D is cut by line segment H G. Line segment H G goes from side F D to side E D. The length of E G is 6 and the length of F H is 8. Lines E F and G H are parallel.
What is the length of Line segment G D?
Answer:
10.5
Step-by-step explanation:
The length of the segment HD will be 5.5.
What is geometry?One of the first areas of mathematics is geometry, along with arithmetic. It is concerned with spatial characteristics like the separation, shape, size, and relative placement of objects.
Given that triangle, F E D is cut by line segment H G. Line segment H G goes from side F D to side E D. The length of E G is 6 and the length of F H is 8.
The length of the segment HD will be calculated as,
EG / GD = FH / HD
4 / 11 = 2 / HD
HD = 22 / 4
HD = 5.5
The missing image is attached with the answer below.
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Find the sum of the first 7 terms of the following series, to the nearest integer. 125,50,20,...
Answer:208
Step-by-step explanation:
i really need help with pls help
Answer:
1. A
2. B
3. D
The square root of 28 is equivalent to 2 x the square root of 7
the square root of 252 is equivalent to 6 x the square root of 7
the square root of 36 is 6
show that (x-1) is a factor of x¹⁰-1
Answer:
The answer is 0 X=1
1. x10-1
(1)10-1
1-1
=0
2. x11-1
(1)11-1
1-1
=0
Step-by-step explanation:
Which pair of undefined terms is used to define the term parallel lines?
point and line
plane and line
point and ray
ray and line
Answer-
B) Plane and line
The pair which is undefined terms are used to define the term parallel lines is B. plane and line
What is meant by parallel line?Parallel lines are lines in a plane that are always the same distance apart. Parallel lines never intersect.
What are the properties of parallel lines?Properties of Parallel Lines
Corresponding angles are equal. Vertical angles/ Vertically opposite angles are equal. Alternate interior angles are equal. Alternate exterior angles are equal.
What is an example of a parallel?My dog not only likes to play fetch but also chase cars. Parallel: My dog not only likes to play fetch, but he also likes to chase cars. My dog likes not only to play fetch but also to chase cars. When you connect two clauses or phrases with a word of comparison, such as than or as, use parallel structure.
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3.2.2 Determine how many boxes of tiles Tshego will need if an extra 10% of the number of tiles must be added for cutting and breakages. (9)
The number of required tiles including the breakage and cut-offs are 37.
Firstly we will calculate the number of required tiles based on below mentioned formula-
Number of tiles required to cover the floor = Area covered by one tile × Total area to be tiled
Number of required tiles = 33.984
Rounding off the number
Number of required tiles = 34
Number of extra tiles required for breakage and cut-offs = 34 + 10% × 34
Number of extra tiles = 34 + 10/100×34
Performing multiplication, division, addition along with cancelling common zeroes of the number
Number of extra tiles = 34 + 3.4
Adding the values
Number of extra tiles = 37.4
Again rounding off the number
Number of extra tiles = 37
Hence, the total required number of tiles are 37 according to stated percentage of waste.
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A sample of n=8 scores has a mean of M=14. One person with a score of 0 is removed from the sample. What is the new value of the sample mean? 28. A researcher collects two samples. The first sample has n 1
=4 scores has a mean of M 1
=7. The second sample has n 2
=4 scores has a mean of M 2
=9. What is the mean of the combined samples?
The new value of the sample mean is approximately 16. The mean of the combined samples is 8.
To find the new value of the sample mean after removing a score, we need to calculate the mean of the remaining scores.
Given that the original sample had n = 8 scores with a mean of M = 14, we can calculate the sum of the scores (ΣX) using the formula ΣX = M * n.
ΣX = 14 * 8 = 112
Since one person with a score of 0 is removed, we subtract this score from the sum of the scores:
New ΣX = ΣX - 0 = 112 - 0 = 112
Now, we need to calculate the new sample mean by dividing the new sum of the scores by the new sample size (n - 1).
New Mean = New ΣX / (n - 1) = 112 / (8 - 1) = 112 / 7 ≈ 16
Therefore, the new value of the sample mean is approximately 16.
For the second question regarding the mean of the combined samples, we can find the overall mean by calculating the weighted average of the individual means, weighted by their respective sample sizes.
Given that the first sample has n1 = 4 scores with a mean of M1 = 7, and the second sample has n2 = 4 scores with a mean of M2 = 9, the overall mean (M_combined) can be calculated as:
M_combined = (n1 * M1 + n2 * M2) / (n1 + n2)
= (4 * 7 + 4 * 9) / (4 + 4)
= (28 + 36) / 8
= 64 / 8
= 8
Therefore, the mean of the combined samples is 8.
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