Each piece is 24 inches long. One yard is equal to 36 inches, so two yards are equal to 72 inches.
To solve this problem, we need to convert the length of the board from yards to inches and then divide it into 3 equal parts.
First, we convert 2 yards to inches by multiplying by 36 (since there are 36 inches in a yard):
2 yards × 36 inches/yard = 72 inches
So, the board is 72 inches long.
Next, we divide 72 inches by 3 to find the length of each piece:
72 inches / 3 = 24 inches
Therefore, each piece is 24 inches long. In summary, to find the length of each piece of a board that is 2 yards long and cut into 3 equal pieces, we convert 2 yards to inches by multiplying by 36 and then divide by 3 to get each piece's length, which is 24 inches.
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a company conducted a marketing survey for families with young children and found that 113 113 families own a nintendo ds and 192 192 families own a nintendo wii. if 22 22 own a wii and a ds, how many own either a wii or ds, but not both?
out of the families that have DS, 20 have both, so subtract them from the absolute to get 124 - 20 = 104.
out of the families that have WII, 20 have both, so subtract them from the all-out to get 186 - 20 = 166.
you presently have 3 classifications that are unadulterated.
104 own DS in particular.
266 own WII in particular.
20 own both.
the complete that possesses either a DS or a WII however not both is equivalent to 104 + 266 = 370.
you need to subtract 20 from every classification since it is remembered for both.
it is remembered for DS and it is remembered for WII.
Market surveys are apparatuses to straightforwardly gather criticism from the interest group to grasp their qualities, assumptions, and prerequisites. Marketers foster previously unheard-of techniques for impending items/benefits however there can be no affirmation about the outcome of these methodologies.
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the complete question is:
A company conducted a marketing survey for families with young children and found that 124 families own a Nintendo DS and 186 families own a Nintendo Wii. If 20 own a Wii and a DS, how many own either a Wii or DS, but not both?
Sara cut a 2 1/2 meter rope to hang a swing for her sister. How many centimeters is the rope
Length of the Sara's rope of 2 1/2 meter in centimeter is 25 centimeters.
To convert 2 1/2 meters to centimeters, we can use the conversion factor 1 meter = 100 centimeters. This means that:
2.5 meters = 2.5 x 100 centimeters
= 250 centimeters
Therefore, the length of the rope is 250 centimeters. It's important to understand and be able to convert between different units of measurement, as this is a common task in many fields such as science, engineering, and finance. For example, in science, it's important to be able to convert between different units of length, mass, and volume when making measurements or analyzing data. Similarly, in finance, it's common to convert between different currencies or units of time when dealing with investments or loans. Being able to make these conversions accurately is essential to avoid errors or misunderstandings. In this case, converting the length of the rope from meters to centimeters allows us to work with a more convenient unit for the task at hand, which is hanging a swing for Sara's sister.
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a random sample of 120 college seniors found that 30% of them had been offered jobs. what is the standard error of the sample proportion?
A random sample of 120 college seniors found that 30% of them had been offered jobs. the standard error of the sample proportion is 0.045.
When dealing with random samples and proportions, the standard error can be calculated using this formula:
SE_p =[tex]sqrt [ p × ( 1 - p ) / n ][/tex]
Where,
SE_p is the standard error of the sample proportion,
p is the sample proportion,n is the sample size.
Using the given information, a random sample of 120 college seniors found that 30% of them had been offered jobs. Hence, p=0.30 and n=120.
Substituting p=0.30 and n=120 in the above formula, we get:
SE_p = [tex]sqrt [0.30 × (1 - 0.30) / 120][/tex]
Simplifying,
SE_p = [tex]sqrt [0.21 / 120]SEp = 0.045[/tex]
Hence, the standard error of the sample proportion is 0.045.
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solve ABC subject to the given conditions if possible. Round the lengths of the sides and measures of the angles (in degrees) to one decimal place it necessary.
B=64 degrees, a=25, b=41
To solve triangle ABC, we can use the Law of Cosines, which states that for any triangle with sides a, b, and c and opposite angles A, B, and C, respectively:
c^2 = a^2 + b^2 - 2ab*cos(C)
We are given B, a, and b, so we can solve for c as follows:
c^2 = 25^2 + 41^2 - 2(25)(41)cos(64)
c^2 = 625 + 1681 - 2135cos(64)
c^2 = 1829 - 2135*cos(64)
c^2 = 311.90
Taking the square root of both sides, we get:
c ≈ 17.7
So the length of side c is approximately 17.7 units.
To find the measures of angles A and C, we can use the Law of Sines, which states that for any triangle with sides a, b, and c and opposite angles A, B, and C, respectively:
a/sin(A) = b/sin(B) = c/sin(C)
We know a, b, and c, and we just solved for c, so we can use the Law of Sines to solve for angles A and C:
a/sin(A) = c/sin(C)
sin(A) = asin(C)/c
A = sin^{-1}(asin(C)/c)
A = sin^{-1}(25*sin(C)/17.7)
Similarly,
b/sin(B) = c/sin(C)
sin(B) = bsin(C)/c
B = sin^{-1}(bsin(C)/c)
B = sin^{-1}(41*sin(C)/17.7)
To find angle C, we can use the fact that the sum of the angles in a triangle is 180 degrees:
C = 180 - A - B
Using a calculator, we get:
A ≈ 41.6 degrees
B ≈ 74.1 degrees
C ≈ 64.3 degrees
Therefore, the measures of the angles in triangle ABC are approximately:
A ≈ 41.6 degrees
B = 64 degrees
C ≈ 64.3 degrees
And the lengths of the sides are approximately:
a = 25
b = 41
c ≈ 17.7
in 2011, the average home in the region of the country studied in exercise 13 lost $9010. was the community studied in exercise 13 unusual? use a t-test to decide if the average loss observed was significantly different from the regional average.
To find out whether the community studied in Exercise 13 was unusual or not, a t-test should be utilized to determine whether the average loss observed was significantly different from the regional average.
T-test is a statistical test that assesses whether two population means are statistically different from one another. It is often used in hypothesis testing to determine whether there is a significant difference between two means.
A t-test is utilized when the mean of one variable for two groups is compared to the mean of another variable for those same two groups.
The steps to perform a t-test are given below:
Determine the level of significance (alpha).
Determine the degrees of freedom (DF) for the sample.
Determine the critical value of t.
Calculate the t-value.
Compare the calculated t-value with the critical value of t.
Draw a conclusion as to whether there is a significant difference between the two means or not.
A t-test can be performed using the following formula:
t = (X1 - X2) / [s (1 / n1 + 1 / n2)]
Where:
X1 and X2 are the means of the two samples.
s is the pooled standard deviation of the two samples.
n1 and n2 are the sample sizes for the two groups.
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Angela is using a game piece with faces labeled A, B, C, and D. What is the sample space for rolling the game piece?
The sample space for rolling the game piece is S = {A, B, C, D}
Describe Sets?In mathematics, a set is a well-defined collection of distinct objects, which can be anything like numbers, letters, people, or even other sets. A set is usually denoted by curly braces {} enclosing its elements separated by commas. For example, the set of natural numbers less than or equal to 5 can be denoted as {1, 2, 3, 4, 5}.
Sets can also be described by various methods such as by listing its elements, by set-builder notation, or by using a Venn diagram to visualize relationships between sets. A set can have any number of elements, including none (empty set), and can also have infinite number of elements.
Sets can be combined through set operations such as union, intersection, and complement. The union of two sets A and B is a set that contains all the elements that belong to either A or B (or both). The intersection of two sets A and B is a set that contains all the elements that belong to both A and B. The complement of a set A is the set of all elements that are not in A.
The sample space for rolling the game piece can be represented by the set of possible outcomes, which are the labels on the faces of the game piece. Therefore, the sample space is:
S = {A, B, C, D}
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I need help finding the subsets and proper subsets. Please help it’s due tonight!!
Answer:
Step-by-step explanation:
# elements = 292 - 268 - 1 = 23 elements
G has 2^23 subsets = 8388608
G has 2^23 - 1 proper subsets = 8388607
the atmospheric carbon dioxide levels in parts per million (ppm) in a town can be modeled using the function defined by where is in years and corresponds to 1950. find and interpret the result. round to 2 decimal places as needed. answer: with unit
The atmospheric carbon dioxide levels in parts per million (ppm) in a town can be modeled using the function defined by , where is in years and corresponds to 1950.
Substituting in gives , which means that the atmospheric carbon dioxide levels in parts per million (ppm) in the town is 386.50 in 2019.
This means that since 1950, the atmospheric carbon dioxide levels in parts per million (ppm) in the town have increased by 386.50.
This is a significant increase and reflects the growing levels of atmospheric carbon dioxide emissions globally due to human activity, leading to climate change.
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most people in the united states with a mental disorder in any given 12-month period receive treatment during the same time frame.
Explanation:
Most people with a mental illness in the United States receive care at some point in their lives, but most receive insufficient or inappropriate care. In any given year, fewer than one-third of people with a diagnosable mental illness obtain treatment.
However, according to a study, most people in the United States with a mental disorder in any given 12-month period receive treatment during the same time frame.
According to the National Survey on Drug Use and Health (NSDUH), about one in five adults (18.5%) had a mental illness in 2019. It is said that roughly 22.3 million people aged 18 and above received care for a mental health condition in the preceding year.
Treatment may involve medication, therapy, support groups, or a combination of these methods. The majority of people with mental illness may significantly benefit from these treatments.
As per a study, most people in the United States with a mental disorder in any given 12-month period receive treatment during the same time frame. This statement is true.
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the number of hours needed to complete a trip, h, varies inversely with the driving speed, s. a trip can be completed in 5 hours at a speed of 60 miles per hour. find the equation that represents this relationship.
The equation that represents the relationship between the number of hours needed to complete a trip, h, and the driving speed, s, is h = 5/s. This means that the number of hours needed to complete the trip is inversely proportional to the driving speed.
When the driving speed is 60 miles per hour, the number of hours needed to complete the trip is 5 (h = 5/60). If the driving speed is increased to 90 miles per hour, the number of hours needed to complete the trip is 5/90 (h = 5/90).
In general, as the driving speed increases, the number of hours needed to complete the trip decreases.
To summarize, the equation that represents the inverse relationship between the number of hours needed to complete a trip and the driving speed is h = 5/s. This equation can be used to determine the number of hours needed to complete a trip at any given speed.
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A line passes through the point (-8, 7) and has a slope of -5/4
Write an equation in slope-intercept form for this line.
The slope-intercept form of the equation of a line is y = mx + b, where m is the slope and b is the y-intercept.
We are given that the line passes through the point (-8, 7) and has a slope of -5/4. So we can substitute these values into the slope-intercept form and solve for b:
y = mx + b
7 = (-5/4)(-8) + b
7 = 10 + b
b = -3
Therefore, the equation of the line in slope-intercept form is:
y = (-5/4)x - 3
Help me with the even numbers. 2,4,6,and8
2= 2
4=10
i cant see 6 or 8
a 4 card hand is dealt from a deck of 52 playing cards. assuming that each hand is equally likely, what is the probability that the hand contains cards from exactly one suit
Answer:The given problem can be solved with the help of the following steps:Step 1: Finding the total number of ways to form a hand of four cards from 52 cards can be calculated by using the formula,Number of ways = (52 C 4) = (52! / 4! (52-4)!) = 270725Step 2: Finding the total number of ways to form a hand of four cards containing cards from exactly one suit. For this, we can use the following approach:a) Select one of the four suits available in the deckb) Choose four cards from the selected suitThe total number of ways to form a hand of four cards containing cards from exactly one suit can be calculated by using the following formula,Number of ways = (4 C 1) × (13 C 4) = 4 × (13! / 4! (13-4)!) = 5148Step 3: Finding the probability that the hand contains cards from exactly one suit can be calculated by using the following formula,Probability = (Number of ways to form a hand of four cards containing cards from exactly one suit) / (Total number of ways to form a hand of four cards from 52 cards) = 5148 / 270725 = 0.019Summary:Therefore, the probability that the hand contains cards from exactly one suit is 0.019.
stephen weighs 185 pounds and is at 17% body fat. he wants to drop down to 10% body fat. how many pounds does he need to lose?
Stephen needs to lose approximately 13 pounds to reach his desired body fat percentage of 10%.
To calculate how many pounds Stephen needs to lose to reach his desired body fat percentage, we first need to determine his current fat mass and lean mass. We can use the following formula:
Fat mass = body weight x body fat percentage
Lean mass = body weight - fat mass
Using Stephen's current weight of 185 pounds and body fat percentage of 17%, we can calculate his fat mass and lean mass as follows:
Fat mass = 185 x 0.17 = 31.45 pounds
Lean mass = 185 - 31.45 = 153.55 pounds
Next, we can calculate Stephen's desired fat mass using his desired body fat percentage of 10%:
Desired fat mass = 185 x 0.10 = 18.5 pounds
To reach his desired body fat percentage of 10%, Stephen needs to lose the difference between his current fat mass and his desired fat mass:
Pounds to lose = current fat mass - desired fat mass
= 31.45 - 18.5
= 12.95 pounds
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^-AB IS THE MID SEGMENT of triangle CDE what is the value of x? Show all work please
In response to the stated question, we may state that As a result, the trigonometry value of x is 11/4.
what is trigonometry?The study of the connection between triangle side lengths and angles is known as trigonometry. The concept first originated in the Hellenistic era, during the third century BC, due to the application of geometry in astronomical investigations. The subject of mathematics known as exact techniques deals with certain trigonometric functions and their possible applications in calculations. There are six commonly used trigonometric functions in trigonometry. Sine, cosine, tangent, cotangent, secant, and cosecant are their separate names and acronyms (csc). The study of triangle characteristics, particularly those of right triangles, is known as trigonometry. As a result, geometry is the study of the properties of all geometric forms.
Because AB is the midpoint of triangle CDE, it is parallel to CD and equal to half of CD.
As a result, we have:
AB = 1/2 CD
We also know that AD has a length of 3x - 1 and DB has a length of x + 4.
Given that AB is the mid-segment, we may write:
1/2 (AD + DB) = AB
In place of the values we have:
3x - 1 + x + 4 = 2AB
4x + 3 = 2AB
We also know that AB = 7, therefore we may use this number instead:
4x + 3 = 2(7) (7)
4x + 3 = 14
4x = 11
x = 11/4
As a result, the value of x is 11/4.
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How do I work this out ?
Answer:
Step-by-step explanation:
First, I believe you would go in and mulitiply that 3 and the 1/6 and from there we will get 0.5. Next you are going to add the 2/5 to that 0.5 and you will get 0.9.
Answer: 0.9
Which of the following best describes the expression 7(x + 9)? (1 point)
a
The product of a constant factor 7 and a 2-term factor x + 9
b
The sum of a constant factor 7 and a 2-term factor x + 9
c
The sum of constant factors 7 and x + 9
d
The product of constant factors 7 and x + 9
d. The expression 7(x + 9) is the product of the constant factor 7 and the 2-term factor x + 9.
Write an equation of the line that has a slope of 6 and passes through the point (1,-2) in slope-intercept form
Answer:
y=6x-8
Step-by-step explanation:
The slope-intercept form of a line is y = mx + b, where m is the slope and b is the y-intercept. We are given the slope m = 6 and a point on the line (1,-2). We can use point-slope form to find the equation and then simplify it to slope-intercept form.
Point-slope form: y - y1 = m(x - x1)
Substitute the values of m, x1, and y1:
y - (-2) = 6(x - 1)
Simplify the right side:
y + 2 = 6x - 6
Subtract 2 from both sides:
y = 6x - 8
This is the equation of the line in slope-intercept form.
Solve the system of equations.
–6x + y = –21
2x − 1
3
y = 7
What is the solution to the system of equations?
(3, 3)
(2, –9)
infinitely many solutions
no solutions
The closest option is (A) (3,3), which is the correct solution to the system of equations.
EquationsTo find the solution to the system of equations, we need to substitute the value of y in the first equation with the value given in the second equation:
-6x + y = -21 ...(1)
2x - 1/3 y = 7 ...(2)
Substituting y=7 in the first equation, we get:
-6x + 7 = -21
Simplifying the above equation:
-6x = -28
Dividing both sides by -6, we get:
x = 28/6 = 14/3
Substituting x=14/3 and y=7 in the second equation, we get:
2(14/3) - 1/3(7) = 7
Simplifying the above equation, we get:
28/3 - 7/3 = 7
21/3 = 7
Therefore, the solution to the system of equations is (14/3, 7).
Hence, the answer is not in the given options, but the closest option is (A) (3,3), which is not the correct solution to the system of equations.
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Angie made a scale drawing of the town library. The parking lot is 348 centimeters long in the drawing. The actual parking lot is 120 meters long. What scale did Angie use for the drawing?
29 centimeters :
meters
The scale ratio that Angie used for the drawing is 25 centimeters : 862 meters.
What is scale ratio?Scale ratio is a mathematical expression of the relationship between the measurements of an object or space in a drawing or model compared to the measurements of the actual object or space.
What is fraction?A fraction is a mathematical expression that represents a part of a whole. It is written as one number (the numerator) over another number (the denominator), separated by a horizontal or diagonal line.
According to given information:We can use the scale ratio formula to find the scale that Angie used for the drawing:
Scale ratio = length in drawing / actual length
In this case, the length of the parking lot in the drawing is 348 centimeters, and the actual length of the parking lot is 120 meters. We can convert the units so that they are consistent, for example, by converting the length in the drawing to meters:
Scale ratio = 348 cm / 120 m
Simplifying this ratio, we can convert the length in centimeters to meters by dividing by 100:
Scale ratio = 3.48 m / 120 m
Simplifying further, we can divide both terms by 3.48 to get:
Scale ratio = 1 / 34.48
To express this ratio in the form of a fraction of centimeters to meters, we can multiply the numerator and denominator by 100 to get:
Scale ratio = 100 cm / 3448 cm = 25 / 862
So the scale that Angie used for the drawing is 25 centimeters : 862 meters.
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The variables x and y vary inversely, and y=10 when x=5. Write an equation that relates x and y
[tex]\qquad \qquad \textit{inverse proportional variation} \\\\ \textit{\underline{y} varies inversely with \underline{x}} ~\hspace{6em} \stackrel{\textit{constant of variation}}{y=\cfrac{\stackrel{\downarrow }{k}}{x}~\hfill } \\\\ \textit{\underline{x} varies inversely with }\underline{z^5} ~\hspace{5.5em} \stackrel{\textit{constant of variation}}{x=\cfrac{\stackrel{\downarrow }{k}}{z^5}~\hfill } \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{\textit{"y" varies inversely with "x"}}{y = \cfrac{k}{x}}\hspace{5em}\textit{we also know that} \begin{cases} x=5\\ y=10 \end{cases} \\\\\\ 10=\cfrac{k}{5}\implies 50=k\hspace{12em}\boxed{y=\cfrac{50}{x}}[/tex]
if the five teachers have an average salary of $49,000, should we be concerned that the sample does not accurately reflect the population?
As a result, we should not be concerned that the sample does not accurately reflect the population.
We can learn more about average, population, and sample.
What is the population?
The entire group of people, items, or objects that we want to draw a conclusion about is known as the population. For example, if we want to learn about the average age of people in the United States, then the entire population is every individual in the United States.
What is a sample?
A smaller group of individuals, objects, or items that are selected from the population is known as a sample. A random sample is a sample in which every individual in the population has an equal chance of being selected for the sample.
What is an average?
A statistic that summarizes the central tendency of a group of numbers is known as an average.
The mean is the most commonly used average in statistics. The mean is calculated by adding up all the numbers in a group and then dividing by the number of numbers in the group. If we want to learn about the average salary of all teachers in the United States, we'd have to sample every teacher. That's not a feasible option. Instead, we take a smaller sample, which should be representative of the population, and then use the information gathered from that sample to make predictions about the population as a whole.
If we assume that the five teachers in the example are a random sample of all teachers in the United States, then we can conclude that the average salary of all teachers in the United States is around $49,000. As a result, we should not be concerned that the sample does not accurately reflect the population.
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I need a bit of help
Substitute r = 2 and s = 3 into the expression:
5r + 7s - 3(r + s) + 4 = 5(2) + 7(3) - 3(2 + 3) + 4
= 10 + 21 - 15 + 4
= 20
Therefore, the value of the expression when r = 2 and s = 3 is 20.
Given:-
[tex] \texttt{r = 2}[/tex][tex] \: [/tex]
[tex] \texttt{s = 3}[/tex][tex] \: [/tex]
Solution:-
[tex] \texttt{5r+ 7s - 3( 2 + 3 ) + 4}[/tex][tex] \: [/tex]
put the given values in the equation
[tex] \texttt{5( 2 ) + 7 ( 3 ) - 3( 2 + 3 ) + 4.}[/tex][tex] \: [/tex]
[tex] \texttt{10 + 21 - 6 - 9 + 4}[/tex][tex] \: [/tex]
[tex] \texttt{31 - 15 + 4}[/tex][tex] \: [/tex]
[tex] \texttt{16 + 4}[/tex][tex] \: [/tex]
[tex] \texttt{ \red{20}} \: [/tex][tex] \: [/tex]
━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━
hope it helps ⸙
this answer to the problem. Kind of tricky.
suppose we should solve the following equation:
[tex]s = \frac{13}{2} (12 + 75)[/tex]
which equals 565.5
in a mid-size company, the distribution of the number of phone calls answered each day by each of the 12 receptionists is bell-shaped and has a mean of 47 and a standard deviation of 5. using the empirical rule, what is the approximate percentage of daily phone calls numbering between 42 and 52?
Using empirical rule, the approximate percentage of daily phone calls numbering between 42 and 52 is 68%.
A statistical principle known as the empirical rule, also known as the three-sigma rule or 68-95-99.7 rule, holds that with a normal distribution, virtually all observed data will lie within three standard deviations (denoted by ) of the mean or average (denoted by ).
The empirical rule specifically states that 68% of observations will fall inside the first standard deviation, 95% will fall within the first two standard deviations, and 99.7% will fall within the first three standard deviations.
Mean = 47
SD = 5
Using Empirical Formula ,approximate percentage of daily phone calls numbering between 42 and 52
Normal Distribution has bell shape curve
The Empirical Rule states that in a normal distribution
68% of the data falls with in one standard deviation ( -1 to 1)
95% of data falls with in two standard deviations, and (-2 to 2)
99.7% of data falls with in three standard deviations from the mean. (-3 to 3)
z score = ( Value - mean)/SD
Calculate z score for 60
Z = (42 - 47)/5
Z = -1
Calculate z score for 66
Z = (52 - 47)/5
Z = 1
As data lies between -1 and 1 hence with in one standard deviation from the mean Hence using Empirical data approximate percentage of daily phone calls numbering between 42 and 52 is 68%.
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a street light is at the top of a pole that has a height of 15 ft . a woman 5 ft tall walks away from the pole with a speed of 4 ft/s along a straight path. how fast is the tip of her shadow moving away from the pole when she is 36 ft from the base of the pole? (leave your answer as an exact number.)
The tip of the woman's shadow is moving away from the pole at a rate of 16/3 ft/s when she is 36 ft from the base of the pole.
Let x be the distance of the woman from the pole, and let y be the length of her shadow on the ground. Since the sun's rays are parallel, the triangles formed by the woman, her shadow, and the pole are similar triangles. Therefore, we can use the following proportion:
(woman's height) / (length of woman's shadow) = (height of pole) / (total length of pole's shadow)
Substituting the given values, we get:
5 / y = 15 / (x + y)
Cross-multiplying and simplifying, we get:
3y = 5(x + y)
3y = 5x + 5y
2y = 5x
y = (5/2)x
We can now differentiate both sides of this equation with respect to time t:
dy/dt = (5/2)dx/dt
We want to find dx/dt when x = 36 ft. To do this, we need to find y when x = 36 ft:
y = (5/2)x = (5/2)(36) = 90 ft
Now we can substitute x = 36 ft and y = 90 ft into the differentiated equation:
dy/dt = (5/2)dx/dt
Solving for dx/dt, we get:
dx/dt = (2/5)dy/dt
We know that dy/dt is the rate at which the woman's shadow is changing, which is given by her walking speed of 4 ft/s. Therefore, dy/dt = 4 ft/s. Substituting this value, we get:
dx/dt = (2/5)(4) = 8/5 ft/s
Therefore, the tip of the woman's shadow is moving away from the pole at a rate of 8/5 ft/s, which is equivalent to 1.6 ft/s or 16/3 ft/s.
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An arithmetic series of A has first term a and common difference d.
The sum of Sn of the first n termof A is given by Sn=(15+2n)
(a) Find the value of a and d
(b) Find the 20th term of A
Given that S2p - 2Sp = 1 + S(p-1)
(c) find the value of p
PLS HELP ME THIS IS REALLY ESSENTIAL FOR MY SCORE.
Answer:
(a) To find the value of a and d, we use the formula for the sum of first n terms of the arithmetic series A which is given by:Sn = n/2[2a + (n-1)d]We are also given that Sn = 15 + 2n. So we can equate these two expressions to get:15 + 2n = n/2[2a + (n-1)d]Multiplying both sides by 2 and simplifying, we get:30 + 4n = n[2a + (n-1)d]Expanding the brackets and simplifying, we get:2an + nd - d + 30 = 2n^2Rearranging terms, we get:2a = 2n^2 - nd + d - 30Now we also know that the first term of the series A is a. So we can substitute this value of a in the formula above to get:a = (2n^2 - nd + d - 30)/2Simplifying, we get:a = n^2 - (n-1)d - 15Therefore, we have found the values of a and d in terms of n. (b) To find the 20th term of A, we use the formula for the nth term of an arithmetic series which is given by:an = a + (n-1)dSubstituting the value of a and d that we found in part (a) we get:a20 = (20^2 - 19d - 15) + 19dSimplifying, we get:a20 = 391 - dTherefore, the 20th term of A is given by a20 = 391 - d.(c) Given that S2p - 2Sp = 1 + S(p-1), we can use the formula for the sum of first n terms of an arithmetic series which we used in part (a) to get:2p/2[2a + (2p-1)d] - 2p/2[2a + (p-1)d] = 1 + p/2[2a + (p-2)d]Simplifying, we get:2apd = d(p^2 - 3p + 2)Dividing both sides by d and simplifying, we get:2ap = p^2 - 3p + 2Rearranging terms, we get:p^2 - 3p + (2-2ap) = 0This is a quadratic equation with coefficients a=1, b=-3, and c=2-2ap. We can use the quadratic formula to solve for p:p = [3 ± sqrt(9 - 4(1)(2-2ap))]/2Simplifying, we get:p = [3 ± sqrt(4ap + 1)]/2Therefore, we have found the value of p in terms of a.
In a certain chemical, the ratio of zinc to copper is 3 to 13. A jar of the chemical contains 429 grams of copper. How many grams of zinc does it contain?
Answer: 93 grams Zinc
Step-by-step explanation:
cross multiply, and solve for the variable:3(403) = 13(x)3(31) = x93 = x .
hector has 24 oranges. he puts 4 oranges in each basket. how many baskets does hector need for all the orangers
Answer: He needs 6 baskets
Step-by-step explanation: Its division 24 divided by 4 equals 6
Terrance and his three friends earned $359 in August, $522 in July, and $420 in September selling lemonade. How much would they each earn if they divided their earnings equally?
In Linear equation, 260.2 would they each earn if they divided their earnings equally.
What in mathematics is a linear equation?
A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept. Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.
Equations with variables of power 1 are referred to be linear equations. One example with only one variable is where ax+b = 0, where a and b are real values and x is the variable.
three friends earned $359 in August, $522 in July, and $420 in September
= $359 + $522 $ 420
= 1301/5 = 260.2
Learn more about Linear equation
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