Answer: To produce treatment groups with similar characteristics
Step-by-step explanation:
The purpose of this experiment is to determine that the treatments groups with similar characteristics are produced. Every groups is taking different amount of the supplement so this study ensures that by randomly assigning the supplements, we can check the cholesterol level in the blood. In this way, similar characteristics in groups are imparted so we can then make treatment groups of same characteristics.
The purpose of random assignment in experiments is to avoid bias, increase the research results' accuracy, help in producing treatment groups with similar characteristics, and control confounding variables. In this case, it ensures that all participants have an equal chance of receiving any level of omega-3 fatty acid or placebo.
Explanation:The purpose of random assignment in this experiment is multifold. Firstly, it ensures all participants, regardless of their cholesterol levels, have an equal chance of being selected. This prevents bias in the sample selection. Secondly, it increases the accuracy of the research results by preventing skewness in the data. The random assignment ensures that every participant has an equal chance of receiving any level of the omega-3 fatty acid supplement or the placebo. This helps produce treatment groups with similar characteristics, which in turn allows for fair comparisons to be made. Finally, it aids in controlling confounding variables. These are factors other than the independent variable (in this case, omega-3 fatty acid supplements) that may affect the dependent variable (cholesterol level), and random assignment helps to equalize these among the groups.
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What is the sum of the linear expression 3x + 9 and 2x + 4
Answer:
5x + 13
Step-by-step explanation:
(3x + 9 ) + (2x + 4)
It's quite simple, we just have to add the parts that have x to each other and those that don't have x to each other
3x + 2x + 9 +4 =
then the result is
5x + 13
Looking into the sky one night, Tori wondered how far into outer space she would get if she drove a car for 3.21 × 103 hours at a rate of 70mph. She calculated and determined that a car travelling at 70 mph covers approximately 1.13 × 105 meters per hour. Tori wrote this expression to determine the distance she would travel into outer space. (3.21 × 103)(1.13 × 105) Estimate the distance travelled
Answer:
[tex]\large\boxed{\large\boxed{3\times 10^8meters}}[/tex]
Explanation:
One of the applications of scientific notation is to make estimations rounding the whole part of the numbers, i.e. the digits before the decimal point, to the nearest integer, and adding the exponents of the powers of base 10.
Here, you must estimate this product of two numbers written is scientific notation:
[tex](3.21\times 10^3)(1.13\times 10^5)[/tex]
Then, for an estimation you round 3.21 to 3 and 1.13 to 1, then multiply 3 × 1 = 3. That will be the coefficient of your new power of 10.
The power or exponent will be the sum of the powers of the numbers that are being multiplied, i.e. 3 + 5 = 8.
And the result is [tex]3\times 10^8[/tex]
The unit is meters, so you write your answer as: [tex]3\times 10^8meters[/tex]
Answer:
b. 3*10^8
Step-by-step explanation:
PLEASE HELP ASAP!!! I NEED CORRECT ANSWERS ONLY PLEASE!!!
Find m∠R.
Write your answer as an integer or as a decimal rounded to the nearest tenth.
m∠R = °
Answer:
Therefore,
[tex]m\angle R = 69.4\°[/tex]
Step-by-step explanation:
Given:
In Right Angle Triangle PQR at ∠Q = 90° such that
RQ = 3 ....Adjacent side of angle R
PQ = 8 ....Opposite side of angle R
To Find:
m∠R = ?
Solution:
In Right Angle Triangle PQR, Tan Identity,
[tex]\tan R= \dfrac{\textrm{side opposite to angle R}}{\textrm{side adjacent to angle R}}[/tex]
Substituting the values we get
[tex]\tan R= \dfrac{PQ}{QR}=\dfrac{8}{3}=2.6666\\\\\angle R=\tan^{-1}(2.666)=69.439=69.4\°[/tex]
Therefore,
[tex]m\angle R = 69.4\°[/tex]
Tim drove 4 hours at an average speed of 60 miles per hour. How many hours would it take Tim to drive the same distance at an average speed of 50 miles per hour?
Answer:
4.8 hours
Step-by-step explanation:
Distance = speed × time
If Tim drove 4 hours at 60 miles per hour
Than he drove a total of 4×60 miles
He drove 240 miles
Time = distance ÷ speed
If he drove 240 miles at 50 miles per hour
Than he took 240÷50 hours
He took 4.8 hours (4 hours and 48 minutes)
The length of the sandbox will be 6 less than 3 times the width. The perimeter of the sandbox must be less than or equal to 116 feet. What would be the maximum length and width of the sandbox.
Answer: the maximum length of the sandbox is 42 feet.
the maximum width of the sandbox is 16 feet.
Step-by-step explanation:
Let L represent the length of the sandbox.
Let W represent the width of the sandbox.
The formula for determining the perimeter of a rectangle is expressed as
Perimeter = 2(L + W)
The perimeter of the sandbox must be less than or equal to 116 feet. This means that
2(L + W) ≤ 116
Dividing through by 2, it becomes
L + W ≤ 116/2
L + W ≤ 58 - - - - - - - - -1
The length of the sandbox will be 6 less than 3 times the width. This means that
L = 3W - 6
Substituting L = 3W - 6 into equation 1, it becomes
3W - 6 + W ≤ 58
4W ≤ 58 + 6
4W ≤ 64
W ≤ 64/4
W ≤ 16
L = 3W - 6 = 3 × 16 - 6
L ≤ 42
Scott purchased a $146,000 home with a 7/23 balloon mortgage. His initial rate was 3.5%. At the end of the initial rate he decided to refinance a balloon payment with a 30 year mortgage fixed at 5%. What is his new mortgage payment
A:$654.87
B:$707.63
C:$655.61
D:$666.55
Answer:D
Step-by-step explanation:
The solution is: : $117,783.05 will be her balloon payment at the end of 7 years if she chooses this mortgage.
What is interest?Interest is the price you pay to borrow money or the cost you charge to lend money. Interest is most often reflected as an annual percentage of the amount of a loan. This percentage is known as the interest rate on the loan.
here, we have,
Step 1
Calculate the number of monthly payments for 7 years.
The formula we would be using is given as:
Monthly payment = [Loan amount × (rate/number of year)] ÷ [1 - (1 +r/n)^nt)]
Loan amount =$146,000
Rate = 4.75% = 0.0475
n = number of payments = 12
t= number of years = 23
Monthly payment = [ 146,000× (0.0475/12)] ÷ [1 - (1 +0.0475/12)^-276)]
Monthly payment = $870.49
Step 2
Calculate the amount left after 7 years using the formula
Ballon payment after 7 years = Loan amount ( 1 + r)ⁿ - P[(1 +r)ⁿ - 1 /r]
r = 4.75% for 12 years
= 146,000( 1 + 0.0475/12)^84 - 870.49[((1 + 0.0475/12)^84 - 1)/0.0475/12]
= $117,783.05
Hence, The solution is: : $117,783.05 will be her balloon payment at the end of 7 years if she chooses this mortgage.
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complete question:
Yvette is considering a 7/23 balloon mortgage with an interest rate of 4.75%
to purchase a house for $146,000. What will be her balloon payment at the end of
7 years if she chooses this mortgage?
Two particles travel along the space curves r1(t) = t, t2, t3 r2(t) = 1 + 4t, 1 + 16t, 1 + 52t . Find the points at which their paths intersect. (If an answer does not exist, enter DNE.) (x, y, z) = (smaller x-value) (x, y, z) = (larger x-value) Find the time(s) when the particles collide. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) t =
Final answer:
To find the intersection points of the paths of two particles, one needs to set their position functions equal and solve for the variable t. If no solution exists, then the intersection points do not exist, and the answer is DNE.
Explanation:
To find the points where the paths of two particles intersect, we set their respective position functions r1(t) and r2(t) equal to each other and solve for t. The position functions given are:
r1(t) = (t, t^2, t^3)
r2(t) = (1 + 4t, 1 + 16t, 1 + 52t).
Their paths intersect when:
x1 = x2
y1 = y2
z1 = z2.
By solving these equations, we find the common t values that make both position vectors equal. If there is no common t that satisfies all three conditions, then the particles never collide, and the answer is DNE (Does Not Exist).
Which of the following has a finite solution for a three-variable system of equations?
A. three planes intersecting at a point
B. three planes intersecting at a line
C. three parallel planes
D. two parallel planes
Answer:
A. three planes intersecting at a point
Step-by-step explanation:
Whenever three planes intersect at a point, then we have an ordered triplet (x,y,z) that is a solution to the associated system of equation.
This is a unique solution and it is finite.
However three planes intersecting at a line gives infinitely many solutions.
Three or two parallel planes may have no solution or or infinitely many solutions when they coincide.
A player of a video game is confronted with a series of four opponents and an 80% probability of defeating each opponent. Assume that the results from opponents are independent (and that when the player is defeated by an opponent the game ends).
A. What is the probability that a player defeats all four opponents in a game?
B. What is the probability that a player defeats at least two opponents in a game?
C. If the game is played three times, what is the probability that the player defeats all four opponents at least once?
Answer:
(a) 0.4096
(b) 0.64
(c) 0.7942
Step-by-step explanation:
The probability that the player wins is,
[tex]P(W)=0.80[/tex]
Then the probability that the player losses is,
[tex]P(L)=1-P(W)=1-0.80=0.20[/tex]
The player is playing the video game with 4 different opponents.
It is provided that when the player is defeated by an opponent the game ends.
All the possible ways the player can win is: {L, WL, WWL, WWWL and WWWW)
(a)
The results from all the 4 opponents are independent, i.e. the result of a game played with one opponent is unaffected by the result of the game played with another opponent.
The probability that the player defeats all four opponents in a game is,
P (Player defeats all 4 opponents) = [tex]P(W)\times P(W)\times P(W)\times P(W)=[P(W)]^{4} =(0.80)^{4}=0.4096[/tex]
Thus, the probability that the player defeats all four opponents in a game is 0.4096.
(b)
The probability that the player defeats at least two opponents in a game is,
P (Player defeats at least 2) = 1 - P (Player losses the 1st game) - P (Player losses the 2nd game) = [tex]1-P(L)-P(WL)[/tex]
[tex]=1-(0.20)-(0.80\times0.20)\\=1-0.20-0.16\\=0.64[/tex]
Thus, the probability that the player defeats at least two opponents in a game is 0.64.
(c)
Let X = number of times the player defeats all 4 opponents.
The probability that the player defeats all four opponents in a game is,
P(WWWW) = 0.4096.
Then the random variable [tex]X\sim Bin(n=3, p=0.4096)[/tex]
The probability distribution of binomial is:
[tex]P(X=x)={n\choose x}p^{x} (1-p)^{n-x}[/tex]
The probability that the player defeats all the 4 opponents at least once is,
P (X ≥ 1) = 1 - P (X < 1)
= 1 - P (X = 0)
[tex]=1-[{3\choose 0}(0.4096)^{0} (1-0.4096)^{3-0}]\\=1-[1\times1\times (0.5904)^{3}\\=1-0.2058\\=0.7942[/tex]
Thus, the probability that the player defeats all the 4 opponents at least once is 0.7942.
Final answer:
The probability of defeating all four opponents in one game is 40.96%. The probability of defeating at least two opponents is 87.04%. Playing the game three times, the probability of defeating all four opponents at least once is 88.47%.
Explanation:
To calculate the probability of different outcomes when playing a video game against four opponents, we'll use basic probability rules and assumptions given in the question.
A. Probability of Defeating All Four Opponents
The probability of defeating each opponent is 80% or 0.8. Since the fights are independent, to find the probability of defeating all four, we multiply the probabilities together:
0.8 × 0.8 × 0.8 × 0.8 = 0.4096 or 40.96% chance of defeating all four opponents.
B. Probability of Defeating At Least Two Opponents
To find the probability of defeating at least two opponents, we must consider all possible combinations of winning 2, 3, or 4 opponents' fights, and add those probabilities together. Let W represent a win and L represent a loss:
P(WWLL) + P(WLWL) + P(WLLW) + P(LWWL) + P(LWLW) + P(LLWW)We already calculated P(WWWW) as 0.4096. The other probabilities can be calculated using similar multiplication of respective individual probabilities (0.8 for W, 0.2 for L). After calculation, we sum these to find the cumulative probability, which is 0.8704 or 87.04%.
C. Probability of Defeating All Four Opponents At Least Once Over Three Games:
The probability of not defeating all four opponents in one game is 1 - P(WWWW) = 0.5904. The events in each game are independent, so the probability of not defeating all four opponents in all three games is (0.5904)^3. Therefore, by subtracting this result from 1, we get the probability of defeating all opponents at least once: 1 - (0.5904 × 0.5904 × 0.5904) = 0.8847 or 88.47%.
Which of the following is a consequence of increasing variability? Group of answer choices A.The distance from one score to another tends to increase, and a single score tends to provide a more accurate representation of the entire distribution. B.The distance from one score to another tends to increase, and a single score tends to provide a less accurate representation of the entire distribution. C.The distance from one score to another tends to decrease, and a single score tends to provide a more accurate representation of the entire distribution. D. The distance from one score to another tends to decrease, and a single score tends to provide a less accurate representation of the entire distribution.
Answer:
Step-by-step explanation:
Variability refers to the degree in which a set of data set spreads out or dispersed or clustered together. There are four measure of variability namely: range, interquartile range (IQR) variance and standard deviation. The consequence of increasing variability is that the distance from one score to another tends to increase, and a single score tends to provide a less accurate representation of the entire distribution.
In the context of a data set, increasing variability implies that scores in the dataset are dispersing more, increasing the distance from one score to another. Therefore, a single score provides a less accurate reflection of the entire distribution. The correct answer to the question is B.
Explanation:The subject of the question relates to the concept of variability in a data set, which is a measure of how much scores differ from each other in a distribution. The question asks about the consequences of increasing variability.
If variability increases, it means that the scores in the dataset are spreading out more. In other words, the distance from one score to another tends to increase. Consequently, a single score tends to provide a less accurate representation of the entire distribution because the scores are more spread out and there is a higher level of diversity in the scores. So, the correct answer is B.
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The Quick Change Oil Company has a number of outlets in the metropolitan Seattle area. The numbers of oil changes at the Oak Street outlet in the past 20 days are:
65 98 55 62 79 59 51 90 72 56
70 62 66 80 94 79 63 73 71 85
The data are to be organized into a frequency distribution.
How many classes would you recommend?
What class interval would you suggest?
What lower limit would you recommend for the first class?
Organize the number of oil changes into a frequency distribution.
Comment on the shape of the frequency distribution. Also determine the relative frequency distribution.
The recommended number of classes is 5, and the class interval is 10. The first class's lower limit would be 50. To create a relative frequency distribution, divide each class frequency by the total
Explanation:First, we have to calculate the range of the data by subtracting the smallest number from the highest number (98-51 = 47). A typical choice for the number of classes might be between five and 20. The
square root rule
suggests a round number near the square root of the number of observations, which is approx 4.47 in this case; you can round to 5. Now we divide the range by the number of classes (47/5 approximately 9). So, the class interval would be 10 (we round up as it does not make sense to have a fraction of an oil change). If the smallest number is 51, the lower limit for the first class would be 50. Hence, the
frequency distribution
would break down like this: 50-59, 60-69, 70-79, 80-89, 90-99. To create a relative frequency distribution, divide each class frequency by the total number of observations and multiply by 100 to convert to percentages. As for the shape, you would need to plot the data to see, but it may have a normal distribution as service levels often do.
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Compare the ratios of sauce to dough. Which of the
following are true? Check all that apply.
Adrian's recipe has a greater ratio of sauce to
dough.
Juliet's recipe has a greater ratio of sauce to dough.
Adrian's and Juliet's recipes have equal ratios of
sauce to dough.
The ratios can be compared by comparing 15 to 18
because 30 is in both dough columns.
Answer:b also d
Step-by-step explanation:
Adrian's recipe has a greater ratio of sauce to dough, and the ratios can be compared by comparing 15 to 18 because 30 is in both dough columns.
In Adrian's recipe, the ratio of sauce to dough is 15:30, which simplifies to 1:2.
In Juliet's recipe, the ratio of sauce to dough is 18:30, which also simplifies to 1:2.
Since both ratios simplify to the same value of 1:2, it means that Adrian's and Juliet's recipes have equal ratios of sauce to dough.
Therefore, the statement "Adrian's and Juliet's recipes have equal ratios of sauce to dough" is true.
The reason we can compare the ratios by looking at 15 and 18 is because both of these values represent the amount of sauce, and 30 represents the amount of dough in both recipes.
By comparing the sauce portions directly, we can determine that the ratios are indeed equal.
It's important to note that the absolute values of the sauce and dough quantities are less relevant in this context than their proportions, which are expressed in the ratios.
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Katy earns $10 per hour. She worked 4 hours on Friday, 9 hours on Saturday, and 6 hours on Sunday. How much money did Katy earn in all on Friday, Saturday, and Sunday? Answer: $
Answer: In total Katy earned $190
Katy earn $190 in all on Friday, Saturday, and Sunday.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS is; Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
Given that Katy earns $10 per hour. She worked 4 hours on Friday, 9 hours on Saturday, and 6 hours on Sunday.
Therefore, total time = 4+9+6=19
Then 19 x 10 = 190
so, she made $190
Hence, Katy earn $190 in all on Friday, Saturday, and Sunday.
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A company wants to determine the amount of a vitamin mix that can be enclosed in a capsule like the one shown. The capsule has a radius of 3millimeters (mm) and a length of 10 mm. How much vitamin mix is needed?
Answer:
226.08 mm³
Step-by-step explanation:
The figure below shows a capsule mad of;
Two hemisphere and an open cylinderTo determine the amount of vitamin that can be enclosed in the capsule, we determine the volume of the capsule;
First we determine the volume of the two hemisphere;Volume of a hemisphere = 2/3 πr³
Therefore; Taking π to be 3.14
Then;
Volume of the hemisphere = 2/3 × 3.14 × 3³
= 56.52 mm³
But, since there are two equal hemispheres;
Then;
Volume of hemispheres = 56.52 mm³ × 2
= 113.04 mm³
Second we determine the volume of the cylinderVolume of the cylinder is given by;
Volume = πr²h
Height = (10 mm - (2× 3mm)
= 4 mm
Thus, taking π to be 3.14
Then;
Volume of the cylinder = 3.14 × 3² × 4
= 113.04 mm³
Thus, Volume of the capsule = 113.04 mm³ + 113.04 mm³
= 226.08 mm³
Derek wants to determine the height of the top of the backboard on the basketball goal at the playground. He places a standard 12-inch ruler next to the goal post and measures the shadow of the ruler and the backboard. If the ruler has a shadow of 10 inches and the backboard has a shadow of 8.5 feet, then how high is the top of the backboard?
Answer:
10.2 feet.
Step-by-step explanation:
We have been given that Derek places a standard 12-inch ruler next to the goal post and measures the shadow of the ruler and the backboard. If the ruler has a shadow of 10 inches. We are asked t find the height of the backboard, if the backboard has a shadow of 8.5 feet.
We will use proportions to solve our given problem as ratio between sides ruler will be equal to ratio of sides of background.
[tex]\frac{\text{Actual height of ruler}}{\text{Shadow of ruler}}=\frac{\text{Actual height of backboard}}{\text{Shadow of backboard}}[/tex]
[tex]\frac{12}{10}=\frac{\text{Actual height of backboard}}{8.5}[/tex]
[tex]\frac{12}{10}*8.5=\frac{\text{Actual height of backboard}}{8.5}*8.5[/tex]
[tex]1.2*8.5=\text{Actual height of backboard}[/tex]
[tex]10.2=\text{Actual height of backboard}[/tex]
Therefore, the actual height of the back-board is 10.2 feet.
Answer:
Step-by-step explanation:
Since the backboard and the ruler are both vertical and the sun is at the same position in the sky, the triangle made by the backboard and its shadow is similar to the triangle made by the ruler and its shadow.
The ratio of the corresponding sides of the triangles are equal and the height of the backboard can be determined by solving the following proportion.
Therefore, the top of the backboard is 7.64 feet high.
Triangle FGH is translated using the rule (x,y) > (x+3,y-1). What are the coordinates of H ?
Answer: [tex]H'(4,-3)[/tex]
Step-by-step explanation:
For this exercise you must remember that the original figure (before a transformation) is called "Pre-Image" and the one obtained after the transformation is called "Image".
A Translation is defined as a transformation in which the figure is moved a fixed distance in a fixed direction. In this kind of transformatiosn the size and shape do not change and the figure is not flipped.
In this case you know that the Pre-Image is the Triangle FGH.
You can identify in the picture that its vertex H has these coordinates:
[tex]H(1,-2)[/tex]
Where:
[tex]x=1\\y=-2[/tex]
Since the rule is:
[tex](x,y)[/tex] → [tex](x+3,y-1)[/tex]
You can substitute the coordinates of H into the given rule in order to find the coordinates of H'. This is:
[tex]H'=(1+3,-2-1)=(4,-3)[/tex]
The coordinates of H after translation using the rule (x,y) > (x+3,y-1) are obtained by adding 3 to the x-coordinate and subtracting 1 from the y-coordinate of H's original position.
Explanation:To determine the coordinates of H after applying the translation rule (x,y) > (x+3,y-1), you have to add 3 to the x-coordinate and subtract 1 from the y-coordinate of point H's original position.
For example, if H originally has coordinates (a,b), then after the translation, the new coordinates of H will be (a+3, b-1).
The given translation rule does not change regardless of the element being translated, be it point or vector, as the rule is applied to each coordinate independently.
Therefore, if you know the original coordinates of point H, you just apply the rule directly to find the translated coordinates.
A baby otter was born 3/4 of a month early at first it's weight was 7/8 kg which is 9/10 kg less than the average weight of newborn otter in the aquarium what is the average weight of a newborn otter
Answer:
The average weight of the newborn otter is [tex]\frac{71}{40}\ kg.[/tex]
Step-by-step explanation:
Given:
A baby otter was born 3/4 of a month early at first it's weight was 7/8 kg which is 9/10 kg less than the average weight of newborn otter in the aquarium.
Now, to find the average weight of the newborn otter.
Let the average weight of the newborn otter be [tex]x.[/tex]
It's weight was = [tex]\frac{7}{8} \ kg.[/tex]
It's weight is less than the average weight of newborn by = [tex]\frac{9}{10} \ kg.[/tex]
According to question:
[tex]x-\frac{9}{10}=\frac{7}{8}[/tex]
Adding both sides by [tex]\frac{9}{10}[/tex] we get:
[tex]x=\frac{9}{10} +\frac{7}{8}[/tex]
[tex]x=\frac{36+35}{40}[/tex]
[tex]x=\frac{71}{40} \ kg.[/tex]
Therefore, the average weight of the newborn otter is [tex]\frac{71}{40}\ kg.[/tex]
Help pls!! I need answer asap
Answer:
m<7=65
m<4 = 115
m<6 = 115
m<1=65
m<16 = 60
m<18 = 60
m<21 = 120
m<10 = 55
m<11 = 125
m<12 = 55
Step-by-step explanation:
(1) m<7 = 65° (corresponding angles are equal)
(2) m<4 = 180 - 65 = 115 (angles on a straight line)
(3) m<6 = 115 (angles on a straight line)
(4) m<1 = 180-115 = 65
(5) m<16 = 180 - 120 = 60°
(6) m<18 = m<14 = 60°(corresponding angles are equal)
(7) m<21 = 180 - 60 = 120
(8) m<10 = m<12 = 180-(65+60)=55(sum of angles in a triangle)
m<10 = 55°
(9) m<11 = 180 - 55 = 125°
(10)m<12 = 55°(sum of angles in a triangle)
Answer:
Step-by-step explanation:
Combine like terms in the expression. 3r + r *
Answer:
4r
Step-by-step explanation:
If you take away the variable, add the 3 and metaphorical 1
3 + 1 = 4
Adding like terms (3+1) and then putting the variable back in makes 4r
Hope this helps, mark brainliest
Answer:
4r
Step-by-step explanation:
3r + r = 4rI hope this helps!
Write the sum using summation notation, assuming the suggested pattern continues. 5 - 15 + 45 - 135 + ...
summation of five times three to the power of the quantity n plus one from n equals zero to infinity
summation of five times negative three to the power of n from n equals zero to infinity
summation of five times three to the power of n from n equals zero to infinity
summation of five times negative three to the power of the quantity n plus one from n equals zero to infinity
Answer:
summation of five times negative three to the power of n from n equals zero to infinity
Step-by-step explanation:
Summation Notation
It represents the sum of a finite or infinite number of terms. Let's analyze the terms of the given succession:
5-15+45-135+...
If we take 5 as a common factor, we have
5(1-3+9-27+...)
The parentheses contain the alternate sum/subtraction of powers of 3. The odd terms are positive, the even terms are negative, thus the exponent must be n starting from 0 or n-1 starting from 1
The summation is then represented by
[tex]\sum_{n=0}^{\infty}5(-3)^n[/tex]
This corresponds with the option:
summation of five times negative three to the power of n from n equals zero to infinity
Final answer:
The correct summation notation for the series 5 - 15 + 45 - 135 + ... is the summation of five times negative three to the power of n from n equals zero to infinity.
Explanation:
The given sequence is 5 - 15 + 45 - 135 + ... which can be seen as a geometric series with a pattern of alternating signs and a common ratio of -3. The first term of the sequence is 5 (when n=0), and each subsequent term is multiplied by -3. Therefore, to write this pattern using summation notation, the nth term can be represented as 5 × (-3)^n. So, the summation notation for the entirety of the series from n equals 0 to infinity is:
Σ [5 × (-3)^n], from n = 0 to infinity
This matches the option: summation of five times negative three to the power of n from n equals zero to infinity.
Do these basic math problems please
Answer:
.
Step-by-step explanation:
a.) 72 ÷ 8 × 9 = 81 (we divide 72 by 8 first then multiply the result with 9)
b.) -72 ÷ 8 × 9 = -81 (it's same with a only differ by negative sign)
c.) 72 ÷ (-8) × 9 = -81 (dividing 72 by -8 will give us -9 and multiplying -9 by -9 will give the result of -81)
d.) 72 ÷ 8 × (-9) = -81 (divide 72 by 8 and it will be 9, mutliply it by -9 and again it will give -81)
e.) -72 ÷ 8 × (-9) = 81 (divide -72 by 8 and it will be -9 multiplying it by -9 will give a positive 81 since two negative signed numbers multiplied or divided gives positive result)
Answer:
A)81
B)-81
C)-81
D)-81
E)81
Step-by-step explanation:
A tower 125 feet high stands on the of a hill. At a point 240 feet from the foot of the tower, measured straight down the hill, the tower subtends an angle of 25 degrees. What angle does the side of the hill make with the horizontal?
11°
The solution is in the attachment
The angle of subtends the hill will make with horizontal is 17.04 degrees.
What is a trigonometric function?The trigonometric functions found in the four quadrants, as well as their graphs, domains, and differentiation and integration, will all be understood.
The trigonometric function is very good and useful in real-life problems.
Given below is the image of the situation,
In triangle ABC →
Tan25° = (125+240)/x
x = 782.745 feet
Now in triangle ADC →
Tan(y) = 240/x
Tan y = 240/782.745
y = 17.04°
Hence "The angle of subtends the hill will make with horizontal is 17.04 degrees".
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If 2/3 of the distance from the y-axis to point A (−30, −45) is equal to 1/4 of the distance from the x-axis to point B(a, a), where a > 0, what is the value of a?
The value of a is 80
Step-by-step explanation:
The distance of a point [tex](x_0,y_0)[/tex] from the y-axis can be written as
[tex]d_y = |x_0|[/tex]
because the x-coordinate of the y-axis is zero.
Similarly, the distance of a point [tex](x_0,y_0)[/tex] from the x-axis can be written as
[tex]d_x=|y_0|[/tex]
Since the y-coordinate of the x-axis is zero.
In this problem:
- The distance of the point A (−30, −45) from the y-axis can be written as
[tex]d_A = |-30|=30[/tex]
- The distance of point B (a,a) from the x-axis can be written as
[tex]d_B = |a| = a[/tex]
Since [tex]a>0[/tex].
We are told that 2/3 of the distance from the y-axis to point A (−30, −45) is equal to 1/4 of the distance from the x-axis to point B(a, a), which means
[tex]\frac{2}{3}d_A = \frac{1}{4}d_B[/tex]
Therefore,
[tex]\frac{2}{3}(30)=\frac{1}{4}a[/tex]
And solving for a,
[tex]20=\frac{1}{4}a\\a=80[/tex]
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Answer:
40
Step-by-step explanation:
Resorts-R-Us charges $ 125 a night to rent a suite. If you purchase their oneyear membership fee for $350, you only pay $75 a night. Which is a better deal?
Answer:
Step-by-step explanation:
Let x represent the number of nights for which you rent a suite.
Resorts-R-Us charges $ 125 a night to rent a suite. If you choose this plan, the total cost of renting the suite for x nights would be
125 × x = 125x
If you purchase their one year membership fee for $350, you only pay $75 a night. This means that the total cost of renting a suite for x nights would be
75x + 350
For the plan involving membership to be a better deal,
75x + 350 < 125x
350 < 125x - 75x
350 < 50x
50x > 350
x > 350/50
x > 7
After 7 nights, the membership option would be a better deal. If you intend to rent the suite for lesser than 7 nights in a year, then the first option is a better deal.
A 13 foot ladder is leaning against a wall. The distance from the top of the ladder to the bottom of wall is 7 ft more than the distance from the bottom of the ladder to the wall. Find the distance from the bottom of the ladder to the wall.
Using the Pythagorean theorem, the distance from the bottom of the ladder to the wall is found to be 5 ft, after solving the quadratic equation that arises from the conditions given.
Explanation:The question asks for the distance from the bottom of the ladder to the wall when a ladder is leaning against it. We can use the Pythagorean theorem to solve this problem as it forms a right-angled triangle. Let's denote the distance from the bottom of the ladder to the wall as x, then the distance from the top of the ladder to the bottom of the wall would be x + 7 ft. Since the ladder's length, which represents the hypotenuse, is 13 ft, we can set up the equation:
x2 + (x + 7)2 = 132
Expanding this, we get:
x2 + x2 + 14x + 49 = 169
Combining like terms:
2x2 + 14x - 120 = 0
Dividing everything by 2 to simplify:
x2 + 7x - 60 = 0
Factoring the quadratic equation:
(x + 12)(x - 5) = 0
The possible values for x are -12 and 5. Since distance cannot be negative, the distance from the bottom of the ladder to the wall is 5 ft.
There are 5 ships in a port.
1. The Greek ship leaves at six and carries coffee.
2. The ship in the middle has a black chimney.
3. The English ship leaves at nine.
4. The French ship with a blue chimney is to the left of a ship that carries coffee.
5. To the right of the ship carrying cocoa is a ship going to Marseille.
6. The Brazilian ship is heading for Manila.Next to the ship carrying rice is a ship with a green chimney.
7. A ship going to Genoa leaves at five.
8. The Spanish ship leaves at seven and is to the right of the ship going to Marseille.
9. The ship with a red chimney goes to Hamburg.Next to the ship leaving at seven is a ship with a white chimney.
10. The ship on the border carries corn.
11. The ship with a black chimney leaves at eight.
12. The ship carrying corn is anchored next to the ship carrying rice.
13. The ship to Hamburg leaves at six.
Which ship goes to Port Said? Which ship carries tea?
Answer:
The Spanish ship goes to Port Said and the French ship carries tea. However, tea can be carried by the Brazilian ship, too.
Step-by-step explanation:
French 5:00 tea blue Genoa
Greek 6:00 coffee red Hamburg
Brazilian 8:00 cocoa black Manila
English 9:00 rice white Marseille
Spanish 7:00 corn green Port Said
Pratap puri Row 22 miles down a river in two hours but the return trip took him 5 1/2 hours find the rate pratap Control in Stillwater and find the rate of the current X equal rate pratap can row in still water and y equals rate of the current
Answer:
x= 7.5 mile/h
y= 3.5 miles / h
Step-by-step explanation:
Given x and y
so, x+y = speed down river
and x-y= speed up river
using
travel time = distance / speed for each case;
we get;
22/x+y=2 ---(1)
and
22/x-y=5.5 -----(2)
Solving equations simultaneously
eq 1 gives
2x+2y=22 ---(3)
eq 2 gives
5.5x-5.5y=22 ----(4)
Multiply eq 3 by 2.75
==> 5.5x+5.5y=60.5 --- (5)
adding eq 4 with eq 5
==> 11x =82.5
==> x= 7.5 miles/h
put this value in eq 3
==> 2(7.5)+2y=22
==> 2y=22-19.8
==> 2y=7
==> y = 3.5
Once setting up two equations based on downstream and upstream velocities, using variables x for Pratap's rowing speed and y for the current's speed, you can solve for these variables. The results show Pratap can row at a speed of 7.5 mph in still water, while the rate of the current is 3.5 mph.
Explanation:Firstly, we have to understand that Pratap's speed with the current and against the current will be affected. Let's say x is the speed of Pratap rowing in still water, and y is the speed of the current. When going downstream (in the direction of the current), Pratap's speed is (x + y) since the current helps him. He covered a distance of 22 miles in 2 hours, so the rate (velocity) can be found by dividing distance by time. Hence, x + y = 22/2 = 11 miles per hour.
On the other hand, when rowing upstream (against the current), Pratap's speed is (x - y), because now the current hinders his rate. He covered the same distance in 5 1/2 hours, so x - y = 22/(5.5) = 4 miles per hour.
Now, we have two equations: x + y = 11 and x - y = 4. Solving these equations (by adding them), we find that 2x = 15 hence x = 7.5. Pratap can row in still water at a speed of 7.5 miles per hour. Substituting x=7.5 into either of the original equations we get y = 3.5. Hence, the rate of the current is 3.5 miles per hour.
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Connor went to New York for vacation. He spent 3 nights at a hotel and rented a car for 4 days. Jillian stayed at the same hotel, but spent 4 nights and rented a car for 5 days from the same company. If Connor paid $675 and Jillian paid $875, how much did one night at the hotel cost?
A) $75
B) $100
C) $125
D) $150
Answer: option C is the correct answer
Step-by-step explanation:
Let x represent the cost of one night at the hotel.
Let y represent the cost of renting the car for one day.
Connor went to New York for vacation. He spent 3 nights at a hotel and rented a car for 4 days. If Connor paid $675, it means that
3x + 4y = 675 - - - - - - - - - - - 1
Jillian stayed at the same hotel, but spent 4 nights and rented a car for 5 days from the same company. If Jillian paid $875, It means that
4x + 5y = 875 - - - - - - - - - - - -2
Multiplying equation 1 by 4 and equation 2 by 3, it becomes
12x + 16y = 2700
12x + 15y = 2625
Subtracting, it becomes
y = 75
Substituting y = 75 into equation 1, it becomes
3x + 4 × 75 = 675
3x + 300 = 675
3x = 675 - 300 = 375
x = 375/3 = $125
Can plurality violate the majority fairness criteria? (Fairness Investigation)
Answer:
No
Step-by-step explanation:
The majority fairness criteria states that a person with majority of votes should be the winner and it is not violated by the plurarity method. Rather pluarity is always satisfied with majority fairness criterion.
A town’s January high temperatures average 36 degrees (F) with a standard deviation of 10 degrees while in July the mean high temperature is 74 degrees and the standard deviation is 8. In which month is it more unusual to have a day with a high temperature of 55? explain
Final answer:
After calculating the z-scores for a high temperature of 55 degrees in both January and July, it was found that a temperature of 55 degrees is more unusual in July than in January due to the higher absolute value of its z-score.
Explanation:
To determine in which month it is more unusual to have a day with a high temperature of 55 degrees, we compare the standardized scores (z-scores) of 55 degrees for January and July. The z-score is calculated by subtracting the mean from the observation and then dividing the result by the standard deviation. For January, with a mean of 36 and standard deviation of 10, the z-score is (55 - 36) / 10 = 1.9. For July, with a mean of 74 and standard deviation of 8, the z-score is (55 - 74) / 8 = -2.375.
Comparing the absolute values of the z-scores, the z-score for July is higher in absolute value, indicating that a temperature of 55 degrees is more unusual in July than it is in January.