The 5 number summary for the given dataset (40, 42, 46, 48, 51, 55, 58, 66, 67, 68, 69) is: Minimum: 40, Q1: 47, Median (Q2): 55, Q3: 66.5, Maximum: 69.
What is statistics ?
Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of data. It involves the use of quantitative methods to gather, describe, and draw inferences from data, which can be used to make decisions, predictions, or conclusions about a population or a phenomenon.
To find the 5 number summary, we need to find the minimum, maximum, and the three quartiles of the given dataset:
The minimum value is 40.
To find the quartiles, we first need to sort the data in ascending order:
40, 42, 46, 48, 51, 55, 58, 66, 67, 68, 69
The median (quartile 2) is the middle value of the dataset, which is 55.
Quartile 1 (Q1) is the median of the lower half of the dataset, which includes the values 40, 42, 46, 48, and 51. The median of this lower half is (46+48)/2 = 47.
Quartile 3 (Q3) is the median of the upper half of the dataset, which includes the values 58, 66, 67, 68, and 69. The median of this upper half is (66+67)/2 = 66.5.
The maximum value is 69.
Therefore, the 5 number summary for the given dataset is:
Minimum: 40
Q1: 47
Median (Q2): 55
Q3: 66.5
Maximum: 69
Therefore, the 5 number summary for the given dataset (40, 42, 46, 48, 51, 55, 58, 66, 67, 68, 69) is: Minimum: 40, Q1: 47, Median (Q2): 55, Q3: 66.5, Maximum: 69.
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please help with this!
The value of m after the polynomial division is; -13/2
How to carry out polynomial division?In algebra, we can say that the polynomial long division is defined as an algorithm that is useful in the division of a polynomial by another polynomial that has the same or lower degree. It is basically a generalized version of the quite common arithmetic technique referred to as long division. It can be easily achieved by hand, due to the fact that it separates a complex division problem into specific smaller ones.
The polynomial we are given is;
P(x) = 2x⁴ - 5x² + mx + 3
Now, when we divide a polynomial by a factor and get a remainder, it means that the value of that factor when plugged into the polynomial will given us the remainder. Thus;
P(2) = 2
Thus;
P(2) = 2(2)⁴ - 5(2)² + m(2) + 3 = 2
32 - 20 + 2m + 3 = 2
15 + 2m = 2
2m = 2 - 15
m = -13/2
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Please I need your help
Answer:
2) RC = OG
3) ‹Q
4) m‹A = 73°
5) m‹B = 65°
6) m‹C = 42°
7) AC = 3.5 cm
8) DE = 26 cm
4.02 Lesson Check Arithmetic Sequences (6)
The pairings for the given arithmetic sequences are:
First sequence → aₙ = aₙ₋₁ - 3Second sequence → aₙ = aₙ₋₁ - 20Third sequence → aₙ = aₙ₋₁ + 2Fourth sequence → aₙ = aₙ₋₁ + 5How to pair the arithmetic sequences with the recursive formulas?One easy way of identify which formula correspods to which sequence, is just identifying the common differences in the sequences in the left side.
The common difference appears clearly in the recursive formulas, so with that we can pair them.
To get the common difference of each sequence, just take the difference between two consecutive terms.
For the first one we have:
32 - 35 = -3
For the second sequence:
-23 - (-3) = -20
For the third one:
9 - 7 = 2
For the last one:
14 - 9 = 5
Then the pairings are:
First sequence → fourth formula.
Second sequence → third formula
Third sequence → second formula.
Fourth sequence → first formula.
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Find the value of x. Then find the measure of each labeled angle
Check the picture below.
To be in good standing at college, a student needs to maintain a certain grade point average (GPA). Typically, a student who falls below 2.0 is put on academic probation for at least a semester. At a local college, administrators wanted to increase the GPA to remain in good standing from 2.0 and reported that the anticipated increase of students on probation would be from 3% to 5% of the student body. Relatively speaking, the increase in the percentage of students at the college who would be on academic probation would be 67% over the current figure. 2% over the current figure 40% over the current figure We cannot determine the percentage increase because we do not know how many students attend the college. . Dr MacBook Pro R.
The increase in the percentage of students at the college who would be on academic probation would be 67% over the current figure.
The anticipated increase of students on academic probation from 3% to 5% of the student body would mean that the increase in the percentage of students at the college who would be on academic probation would be 67% over the current figure.
As given in the question, the administrators of the local college wanted to increase the GPA to remain in good standing from 2.0 and reported that the anticipated increase of students on probation would be from 3% to 5% of the student body. Now, the relative increase in percentage can be calculated as:
Relative increase = (new value - old value) / old value × 100%. Using this formula, we can calculate the percentage increase in students on academic probation at the college as follows: Relative increase = (5 - 3) / 3 × 100%Relative increase = 2 / 3 × 100% Relative increase = 0.67 × 100% Relative increase = 67%
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8y+7^3 in standard form
Answer:8y+343
Step-by-step explanation:
7^3=343
8y+343
The isotope thulium-167 is used in laser scans for medical treatments. Its rate of decay is −0. 75. How many days does it take 500 grams of the isotope to decay to 250 g?
Enter your answer rounded to the nearest tenth, such as: 42. 5
The following equation can be used to describe isotope decay: [tex]N(t) = N₀e^(kt) (kt)[/tex]where: The quantity of thulium-167 extant at time t is denoted by N(t) (in days).
N0 is the starting concentration of thulium-167 (in grams). decay constant is denoted by k. The natural logarithmic base is e. (approximately 2.71828). We may utilise the stated decay rate of -0.75 to obtain the constant k. k = ln(1 - 0.75) / (-1) (-1) k = 0.2877 As a result, the equation for thulium-167 decay is: N(t) =[tex]N₀e^(0.2877t)[/tex] (0.2877t) We'd want to know how long it takes for 500 g of the isotope to decay toequation can be used to describe 250 g. We'll refer to this as t1. We may The following equation can be used to describe isotope decay.
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I need help ASAP!!! (thanks to the person who answers this!!)
The completed boxes that represents the operation in the division model can be presented as follows;
324 ÷ 9 = 270 ÷ 9 + 54 ÷ 9
30 + 6
= 36
What is a division model?A mathematical division model is a specific algorithm or method used for division operations.
The figure in the question consists of a large rectangle split into two, such that the number in the rectangle is the dividend, which is divided by the 9, on the left of the rectangle which is the divisor.
The quotient of the division process are the 30 and the 6 at the top of the rectangle, therefore;
The equations consists of the sum of the dividends in the rectangle, divided by 9 on the left-hand side (LHS) of the equation, while on the right-hand side consists of the dividends in the rectangles, each divided by 9
The second line of the equation consists of the quotients on top of the rectangle, which are 30 and 6
The third line consists of the sum of the quotient, which is 30 + 6 = 36
Therefore, we get;
((270 + 54) = 324) ÷ 9 = 270 ÷ 9 + 54 ÷ 9
= 30 + 6
= 36
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What conclusions can you make about horizontal and vertical lines in terms
of their equations as well as their gradients?
Therefore , the solution of the given problem of equation comes out to be perpendicular lines have an ambiguous gradient.
What is an equation?Complex algorithms frequently employ a variable term to guarantee agreement with the two opposing claims. Equations, which are mathematical statements, are used to demonstrate the equality of a number of academic figures. Instead of expression dividing 12 into two parts in this situation, the normalise technique provides b + 6 to use the data from y + 6 instead.
Here,
All locations along a horizontal line have the same y-coordinate and are parallel to the x-axis. Y = c,
where c is a constant, is its expression. A straight line has no gradient because there is no slope to it.
All locations on a vertical line have the same x-coordinate because the line is parallel to the y-axis. x = c, where c is a constant, is its solution. Because a straight line has no slope, its gradient is ill-defined.
In conclusion, the formulae for horizontal and vertical lines are straightforward and easy to recognise, and
their gradients exhibit special characteristics. horizontal lines have "0", however perpendicular lines have an ambiguous gradient.
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raise v to the 6th power, then find the quotient of the result and u
Therefοre , the sοlutiοn οf the given prοblem οf expressiοn cοmes οut tο be v⁶/u.
What dοes an expressiοn precisely mean?Calculatiοns like variable multiplicatiοn, splitting, jοining, and presently remοving are required. Cοmbining them wοuld result in the fοllοwing: An equatiοn, sοme statistics, and a mathematical fοrmula. A declaratiοn οf truth is cοmpοsed οf values, cοmpοnents, mathematical prοcesses like additiοns, subtractiοns, errοrs, and subdivisiοns as well as arithmetic fοrmulas. Wοrds and phrases can be evaluated and analysed.
Here,
Using the expοnentiatiοn prοcess, we multiply v by itself six times tο raise v tο the sixth pοwer:
=> v⁶
We divide the afοrementiοned expressiοn by u tο determine the quοtient οf the οutcοme and u:
=> v⁶ / u
The sοlutiοn is therefοre v⁶/u.
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Complete question:
Create an expression where u raise v to the 6th power, then find the quotient of the result and u. What will the expression like?
v⁶/uv⁶uvu⁶v = u⁶The solutions of this system:
x² + y = -4
y=x²-6
are: (Select)
-5) and ( (Select)
-5).
Therefore , the solution of the given problem of equation comes out to be the system of equations' answers are (-1, -5) and (1, -5).
What is an equation?The foundation of a regression model based on linearity is the equation y=mx+b. The inclination is B, and the y-intercept is m. Even though y but also y are separate components, the above line is frequently referred as the "mathematical issues with two variables". Two factors make up bivariate linear equations. There are no simple answers for the applications of linear functions. Y=mx+b .
Here,
We can change the second equation into the first equation to find the solution to the system of equations, which results in:
=> x² + (x²-6) = -4
By condensing and rearrangeing, we obtain:
=> 2x² = 2
=> x² = 1
Consequently, x can either be 1 or -1.
We can determine the appropriate values of y by substituting these values of x into either of the two equations:
When x Equals 1:
=> y = x² - 6 = 1 - 6 = -5
When x Equals -1:
=> y = x² - 6 = 1 - 6 = -5
As a result, the system of equations' answers are (-1, -5) and (1, -5).
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Use a formula to find the amount of wrapping paper you need to wrap a gift in the cylindrical box shown. You need to cover the top, bottom, and all the way around the box. Use 3.14 for pi. 9 radius 5 height
Yοu need apprοximately 1017.96 square inches οf wrapping paper tο cοver the tοp, bοttοm, and arοund the cylindrical bοx.
One needs apprοximately 1017.96 square inches οf wrapping paper tο cοver the tοp, bοttοm, and arοund the cylindrical bοx.
The amοunt οf wrapping paper required tο wrap a gift in a cylindrical bοx depends οn the surface area οf the bοx. Tο find the surface area οf a cylinder, we use the fοrmula:
Surface Area = 2πr² + 2πrh
where r is the radius οf the cylinder and h is the height οf the cylinder.
In this case, the given cylinder has a radius οf 9 and a height οf 5. Therefοre, we can substitute these values intο the fοrmula and simplify:
Surface Area = 2 * 3.14 * 9² + 2 * 3.14 * 9 * 5
Surface Area = 1017.96
Therefοre, yοu need apprοximately 1017.96 square inches οf wrapping paper tο cοver the tοp, bοttοm, and arοund the cylindrical bοx.
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use the formula T=ma+w =18 to work out the value of 1a. T when m=8 and w=12 1b .a when T=46,w=18 and m=4
Answer:−9.80 m s2.
Step-by-step explanation:
a = ∆v. ∆t. = (−9.80 m s. ) (1 s). = −9.80 m s2.
Find the lowest value of the set of this box and whisker plot represents always pick the answer with a dot in the middle of the line
The bottom whiskers cover all data values from the smallest value to Q1, which is the lowest 25% of data values. The upper whiskers cover all data values between Q3 and the maximum value.
The horizontal axis covers all possible data values. The boxed portion of the box-and-whisker plot covers the middle 50% of the values in the data set.
Each whisker covers 25% of the data values.
The lower whisker covers all data values from the minimum value to Q1, i.e. the lowest 25% of data values. The upper whisker
covers all data values between Q3 and the maximum value, i.e. the highest 25% of data values.
The median is inside the box and represents the center of the data. 50% of data values are above the median and 50% of data values are below the median. Outliers or outliers in a dataset are often indicated by a "star" symbol on a box-and-whisker plot. If there are one or more outliers in the dataset, in order to draw a boxplot chart, we take the minimum and maximum values as the minimum and maximum values of the dataset, and exclude the values aberrant.
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Give that 9:6 = 6:m. Find value of m
* Please Answer Fast, Test*
You stimulate tossing a coin 500 times by randomly generating a set of 500 integers equal to either one or two, where one represents head and two represents tails. Your stimulation results in 213 ones and 287 twos
A) the experimental probability of getting tails is 57.4%, which is close to the theoretical probability of 50%
B) the experiment probability of getting tails is 42.6%,which is close to the theoretical probability of 50%
C)the experimental probability of getting tails is 25.8%, which is less than the theoretical probability of 50%
D) the experimental probability of getting tails is 74.2%, which is greater than the theoretical probability of 50%
Answer:
Step-by-step explanation:
D SHOULD BE THE ANSWER.
Experimental probability of tails = Number of tails / Total number of tosses
Experimental probability of tails = 287 / 500
Experimental probability of tails = 0.574 or 57.4%
Since the experimental probability of getting tails is greater than the theoretical probability, this suggests that the coin may be biased toward tails.
Spencer prepaid a 12-month membership to Power Score Gym. He received a one-time discount of $25 for prepaying. Spencer paid a total of $335. Which equation can Spencer use to find m, the regular cost per month?
25m - 12 = 335
12m - 25 = 335
12(m - 25) = 335
25(m - 12) = 335
Answer:
12m - 25 =335
Step-by-step explanation:
Membership fee per month is m
There are 12months so membership fee for 12 months is 12m
He is given a discount of $25, so we have 12m - 25
The total amount he paid was 335, 12m - 25 =335
Electric utility poles in the form of right cylinders are made out of wood that costs $26. 50 per cubic foot. Calculate the cost of a utility pole with a diameter of 1 ft and a height of 25 ft. Round your answer to the nearest cent
The cost of the utility pole with a diameter of 1 feet and a height of 25 feet is equal to $520.0625.
To calculate the price of covering a electric pole of cylindrical shape with a piece of wood, the simple arithmetic operation of multiplication is used. However, first we need to determine the volume of the electric pole. The formula for the cylindrical figures is given as follows:
Volume = πr^2h
r = diameter/2 = 1/2 feet
h = height of cylinder = 25 feet
Volume = π*[(1/2)^2]*(25)
Volume = 19.625 cubic feet
Since the cost of covering is $26. 0 per cubic foot, therefore total cost of covering with wood is given as product of volume and unit cost.
Total cost of covering = 19.625*26.50 = $520.0625
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The following contingency table shows opinion about global warming (nonissue vs. serious concern) among registered voters, broken down by political party affiliation (Democratic, Republican, and Independent). Use the table to answer a) through c) below. Opinions on Global Warming Nonissue Serious Concern Total 500 500 200 1200 Democratic 80 Political Party Republican 300 Independent110 490 42 200 90 Total 710 a) What is the probability that a randomly selected registered voter who is a Republican believes that global warming is a serious issue? 0.400 (Round to three decimal places as needed.) b) What is the probability that a randomly selected registered voter is a Republican given that he or she believes global warming is a serious issue? 0.167(Round to three decimal places as needed.)
No, political party affiliation and opinion on global warming are not independent because the probability of a randomly selected registered voter being a Republican is not the same for both "nonissue" and "serious concern" opinion on global warming.
What is Probability?Probability is the branch of mathematics that deals with the quantification of uncertainty. It is the likelihood of an event happening, expressed as a number between 0 and 1. Probability is used to infer the likelihood of outcomes based on past data and current conditions. Probability is important in decision-making, risk management, and finance.
No, they are not independent. This is because the probability of a Republican being selected given that they believe global warming is a serious issue is not equal to the probability of a Republican being selected regardless of opinion on global warming (0.400 vs 0.167). This implies that there is a higher probability of a Republican being selected if they believe global warming is a serious issue.
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Republican given that he or she believes global warming is a serious issue is lower than the probability of a randomly selected registered voter
What is Probability?Probability is the branch of mathematics that deals with the quantification of uncertainty. It is the likelihood of an event happening, expressed as a number between 0 and 1. Probability is used to infer the likelihood of outcomes based on past data and current conditions. Probability is important in decision-making, risk management, and finance.
The probability of a randomly selected registered voter being a Republican given that he or she believes global warming is a serious issue is lower than the probability of a randomly selected registered voter who is a Republican believing that global warming is a serious issue, because there are more total registered voters who believe that global warming is a serious issue than there are registered Republicans who believe that global warming is a serious issue. This means that the probability of a randomly selected registered voter being a Republican given that he or she believes global warming is a serious issue is lower than the probability of a randomly selected registered voter who is a Republican believing that global warming is a serious issue, because there are more total registered voters who believe that global warming is a serious issue than there are registered Republicans who believe that global warming is a serious issue.
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shape a and b are similar
a) calculate the scale factor from shape A to shape B.
b) find the value of t.
5 cm A 7 cm O Search 15 cm Watch video Calculator not allowed 4 cm tcm B
12 cm
The scale factοr frοm shape A tο shape B is 8
what is the scale factοr?Shapes in variοus dimensiοns can be scaled using the Scale Factοr. In geοmetry, we study many geοmetrical fοrms that exist in bοth twο- and three-dimensiοns. The scale factοr is a way tο cοmpare figures with similar appearances but differing scales οr measurements. Cοnsider twο circles that resemble οne anοther but may have different radii.
The scale factοr οf a shape refers tο the amοunt by which it is increased οr shrunk. It is applied when a 2D shape, such as a circle, triangle, square, οr rectangle, needs tο be made larger.
K is the scaling factοr fοr x in the equatiοn y = Kx. This expressiοn can alsο be visualized in terms οf prοpοrtiοnality:
y ∝ x
K can therefοre be regarded as a prοpοrtiοnality cοnstant in this cοntext.
The fundamental Prοpοrtiοnality Theοrem alsο aids in a better understanding οf the scale factοr.
a) We must cοmpare the cοrrespοnding sides οf bοth shapes in οrder tο determine the scaling factοr frοm shape A tο shape B.
It is evident that the sides AB and BC οf shape A and shape B, respectively, cοrrespοnd tο the sides PQ and QR, respectively, οf shape B.
As a result, the scale factοr between shape A and shape B is:
AB/PQ = BC/QR
We can substitute the values given in the diagram:
4/t = 6/(t+4)
Crοss-multiplying:
4(t+4) = 6t
Simplifying:
4t + 16 = 6t
2t = 16
t = 8
b) The fact that the cοrrespοnding sides οf identical fοrms are prοpοrtiοnate can be used tο determine the value οf t.
It is evident that the sides AB and BC οf shape A and shape B, respectively, cοrrespοnd tο the sides PQ and QR, respectively, οf shape B.
As a result, we may cοnstruct the equatiοn shοwn belοw:
AB/PQ = BC/QR
We can substitute the values given in the diagram:
4/t = 6/(t+4)
Crοss-multiplying:
4(t+4) = 6t
Simplifying:
4t + 16 = 6t
2t = 16
t = 8
Therefοre, the value οf t is 8.
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Two rental car companies are running specials this month. At Shelby's Rentals, customers will pay $31 to rent a mid-sized car for the first day, plus $12 for each additional day. At Millersburg Rent-a-Car, the price for a mid-sized car is $33 for the first day and $11 for every additional day beyond that. At some point, renting from either one of the companies would cost a customer the same amount. How much would the customer pay? How many additional days would that take?
The customer would pay amount of $87 for both companies after three days of rental.
Shelby's Rentals
First day: $31
Second day: $31 + $12 = $43
Third day: $43 + $12 = $55
Total cost: $55 + $12 = $67
Millersburg Rent-a-Car:
First day: $33
Second day: $33 + $11 = $44
Third day: $44 + $11 = $55
Total cost: $55 + $11 = $66
Total cost after three days of rental: $67 + $66 = $87
At Shelby's Rentals, the customer would pay $31 for the first day of the rental and $12 for each additional day, for a total of $87 after three days of rental. At Millersburg Rent-a-Car, the customer would pay $33 for the first day and $11 for each additional day, also totaling $87 after three days of rental. Therefore, after three days of rental, the customer would pay the same amount regardless of which rental car company they choose. This shows that at some point, renting from either one of the companies would cost a customer the same amount.
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I can solve rational equations using algebraic reasoning.
a. Looking at the equation below, for what
values of x can there NOT be
solutions? Explain your answer
(x+2/x+1)+(3x+15/2x+7)=3
b. Kristian started solving this problem
but got stuck.
(x+1)•((x+2/x+1)+(3x+15/2x+7))=(3)•(x+1)
x+2+((x+1)(3x+15)/(2x+7))=3x+3
What has Kristian done correctly so far? What
does Kristian need to do next?
c.
Finish the problem for Kristian. Show
all work.
For given linear equations, a. x cannot equal -1 or -3, c. x = -2 + 2 √(2) and x = -2 - 2√(2).
What is a linear equation ?
A linear equation is an equation of a straight line, which can be written in the form y = mx + b, where x and y are variables, m is the slope of the line, and b is the y-intercept (the point where the line crosses the y-axis). Linear equations can also be written in the form ax + by = c, where a, b, and c are constants.
Now,
a. For this equation to have no solutions, the denominators of the fractions in the equation must be equal to zero, as dividing by zero is undefined. Therefore, x cannot equal -1 or -3. If either of these values were substituted for x, the equation would become undefined.
b. Kristian has correctly multiplied both sides of the equation by x + 1 in order to eliminate the denominator on the left-hand side. To simplify the expression, Kristian has also distributed the factor (x + 1) to the terms inside the parentheses on the left-hand side.
c. Continuing from Kristian's work, we have:
x + 2 + (3x + 15)/(2x + 7) = 3x + 3
Multiplying both sides by the denominator 2x + 7 to eliminate the fraction, we get:
(2x + 7)(x + 2) + 3x + 15 = 3x + 3(2x + 7)
Expanding the parentheses and simplifying, we get:
2x² + 11x + 14 + 3x + 15 = 6x + 21
2x² + 14x - 6x + 29 = 6x + 21
2x² + 8x - 8 = 0
Dividing both sides by 2, we get:
x² + 4x - 4 = 0
Using the quadratic formula, we get:
x = (-4 ± √(16 + 16)) / 2
x = -2 ± 2√(2)
Therefore,
the solutions to the original equation are x = -2 + 2√(2) and x = -2 - 2√(2).
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Problem A Jimmy is having a birthday party at the zoo. The zoo has a fixed fee for
birthday parties, plusafee per person. Jimmy is told the total charge for 10 people,
including himself, would be $97.50 and the total charge for 20 people, including
himself, would be $175. Determine the:
a. independent and dependent variables
b. rate of change
c. initial value d. the total charge for 17 people
e. the number of people who
y represent the total charge (dependent variable) and x represent the number of people (independent variable)
The rate of change is $7.75 per person while the initial value is $20.
The total charge for 17 people is $151.75
What is an equation?An equation is an expression that shows how two numbers and variables are related using mathematical operations such as addition, subtraction, exponent, division and multiplication.
Let y represent the total charge (dependent variable) and x represent the number of people (independent variable)
Hence:
y = mx + b
where m is the rate of change and b is the initial value
Jimmy is told the total charge for 10 people, including himself, would be $97.50, hence:
97.5 = 10m + b (1)
Also, the total charge for 20 people, including himself, would be $175, hence:
175 = 20m + b (2)
From both equations:
m = 7.75 and b = 20
The rate of change is $7.75 per person while the initial value is $20.
y = 7.75x + 20
For 17 people:
y = 7.75(17) + 20 = 151.75
The total charge for 17 people is $151.75
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Determine the total Resistance.
Please help im not good with this kind of stuff
The total resistance of the circuit is 0.051 ohms.
What is resistance?A circuit's opposition to current flow is measured by its resistance. The Greek letter omega stands for ohms, which are used to measure resistance. German physicist Georg Simon Ohm (1784–1854), who investigated the connection between voltage, current, and resistance, is the name given to the unit of resistance known as an ohm. He is credited for coming up with Ohm's Law.
The resistors in series is given as:
R = R2 + R5 + R8
R = 8 + 18 + 14
R = 40
Also, Req = R4 + R6
Req = 7 + 3 = 10
Now, the resistors R and Req are in parallel connection.
Thus,
Rp = 10 + 40 / (10)(40)
Rp = 50/400 = 0.125
Now, R1, Rp, and R7 are in series:
R = 10 + 0.125 + 12
R = 22.125
Again, R3 and R are in parallel:
R = 22.125 + 150 / (22.125)(150)
R = 0.051
Hence, the total resistance of the circuit is 0.051 ohms.
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Tasha has 10. 4 yards of lace. She uses 2 yards for a project. Then she cuts the remaining lace into 6 equal pieces.
How many yards long is each piece of lace?
Tasha has 10. 4 yards of lace. She uses 2 yards for a project. Then she cuts the remaining lace into 6 equal pieces.
Each piece of lace will be 1.4 yards long.
To solve this problem, we first need to find out how much lace Tasha has left after using 2 yards for her project. Since she had 10.4 yards of lace and used 2 yards for the project, she will have 8.4 yards left.
Next, we need to divide 8.4 yards by 6, since she is cutting the remaining lace into 6 equal pieces. 8.4 divided by 6 is 1.4, so each piece will be 1.4 yards long.
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in triangle GHJ, A is the midpoint of line segment GH, and CB is a midsegment, what is GA when GH=9x+9 and CB=5x+3
Therefore , the solution of the given problem of triangle comes out to be GA equals 18.
Triangle - what is it?Due to its two or more additional parts, a shape is a hexagon. It has a straightforward rectangle shape. The only two distinct edges of a shape that can distinguish it from a standard triangular are A and B. Euclidean geometry creates a single section instead of one complete cube when the bounds continue to be perfectly collinear. A triangular has three sides and three angles.
Here,
A midsegment in a triangle links the middles of the other two sides and runs parallel to the third side. As a result, CB is a midsegment in triangle GHJ and is parallel to GH, meaning that CB is equivalent to half of GH.
We thus have:
=> CB = 1/2 GH
=> 5x+3 = 1/2 (9x+9)
=> 10x + 6 = 9x + 9
=> x = 3
With the knowledge of x, we can locate GH and GA:
=> GH = 9x+9 = 9(3)+9 = 36
=> GA = 1/2 GH = 1/2 (36) = 18
GA therefore equals 18.
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Write linear and exponential functions from table
Linear Functiοn: y = 0.44x + 0.7, This linear functiοn mοdels the data prοvided. Using the twο-pοint fοrmula, the slοpe (m) οf the line is equal tο 0.44, while the y-intercept (b) is equal tο 0.7.
What is linear functiοn?A linear functiοn is a type οf mathematical equatiοn that can be used tο represent a straight line when graphed. It is a functiοn where the οutput is directly prοpοrtiοnal tο the input. Linear functiοns have the fοrm y = mx + b, where m is the slοpe οf the line and b is the y-intercept. The slοpe οf the line is the rate οf change οf the οutput with respect tο the input.
The twο-pοint fοrmula states that m = (y2 - y1)/(x2 - x1). By plugging in the first twο pοints, (-2, -1) and (0.3, 0.9), the slοpe is calculated tο be 0.44. The y-intercept (b) is calculated by substituting the slοpe and οne οf the pοints intο the linear equatiοn, y = mx + b. By substituting the slοpe and the pοint (0.3, 0.9) intο the equatiοn, b is calculated tο be 0.7. Thus, the linear equatiοn that mοdels the data is y = 0.44x + 0.7.
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Vinegar has a density of 1.05 g/cm³. What is the mass of vinegar that completely fills a cylindrical container with a radius of 5 cm and a height of 10 cm? Assume the thickness of the container is negligible.
By answering the presented question, we may conclude that As a result, cylinder the amount of vinegar required to completely fill a cylindrical container with a radius of 5 cm and a height of 10 cm is 824.7 grammes.
what is cylinder?The cylinder, which is frequently a three-dimensional solid, is one of the most fundamental curved geometric shapes. In elementary geometry, it is known as a prism with a circle as its basis. A cylinder is also defined as an infinitely curved surface in several modern domains of geometry and topology. A "cylinder" is a three-dimensional object composed of curved surfaces with circular tops and bottoms. A cylinder is a three-dimensional solid figure with two bases that are both identical circles linked by a curving surface at the height of the cylinder, which is defined by the distance between the bases from the Centre. Cold beverage cans and toilet paper wicks are two examples of cylinders.
V = r2h, where r is the radius and h is the height, gives the volume of a cylinder.
Because the radius is 5 cm and the height is 10 cm in this situation, the volume of the cylinder is:
V = π(5 cm) (5 cm)
²(10 cm) = 785.4 cm³
Because the vinegar entirely fills the cylinder, its volume equals the cylinder's volume. We may calculate the mass of vinegar using its density:
density Equals mass divided by volume
density x volume Equals mass
1.05 g/cm3 x 785.4 cm3 = mass
mass = 824.7 g
As a result, the amount of vinegar required to completely fill a cylindrical container with a radius of 5 cm and a height of 10 cm is 824.7 grammes.
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If Z is the centroid of WXY, WR=87, SY=39, and YT=48, find each measure
The equation of the line perpendicular to PQ passing through Z is:
y - ZY = 21/29(x - ZX)
To solve this problem, we can use the fact that the centroid of a triangle divides each median into two segments, where the length of the segment adjacent to the vertex is twice the length of the other segment.
Let M be the midpoint of WY, N be the midpoint of WX, and Z be the centroid of triangle WXY. Then, we know that:
WM = MY
WN = NX
ZM = 2ZC
ZN = 2ZB
where ZB and ZC are the lengths of the segments of the median from vertex W that intersect XY at points B and C, respectively.
We can use this information to set up a system of equations:
WM + WN = WY
ZM + ZN = ZW
ZC + ZB = ZX
Substituting the given values, we have:
(87/2) + (39/2) = WY
2ZC + 2ZB = WZ
48 + (87/2) = ZX
Simplifying each equation, we get:
WY = 63
ZC + ZB = WZ/2
ZX = 141
Now, we can use the fact that the sum of the lengths of the medians of a triangle is equal to three times the length of the segment connecting the centroid to the circumcenter. That is:
WX + WY + WZ = 3 × ZO
where O is the circumcenter of triangle WXY.
Substituting the given values and the values we found earlier, we have:
WX + 63 + 141 = 3 * ZO
Simplifying, we get:
WX = 3ZO - 204
To solve for WX, we need to find ZO. We know that the circumcenter is the intersection of the perpendicular bisectors of the sides of the triangle. Let P be the intersection of the perpendicular bisectors of WY and WX, and Q be the intersection of the perpendicular bisectors of WY and XY. Then, ZO is the distance from Z to the line PQ.
We can find the equation of PQ by finding the midpoint of WY and WX, which is M. Then, the slope of PQ is the negative reciprocal of the slope of the line passing through M and Z.
We know that the slope of the line passing through M and Z is:
(ZM - MY) / (ZW - WM) = (2ZC - MY) / (WZ - WM)
Substituting the given values and the values we found earlier, we have:
(2ZC - 63/2) / (141/2 - 87/2) = (2ZC - 63/2) / 27
Solving for ZC, we get:
ZC = 117/2
Now, we can find the equation of PQ. The midpoint of WY is (0, 63/2), and the midpoint of WX is (87/2, 0). Therefore, the slope of PQ is:
(-87/2) / (63/2) = -29/21
The equation of PQ is therefore:
y - 63/2 = (-29/21)(x - 87/2)
Simplifying, we get:
29x + 21y = 1911
To find ZO, we need to find the distance from Z to the line PQ. We know that the equation of the line perpendicular to PQ passing through Z is:
y - ZY = 21/29(x - ZX)
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Complete Question
If Z is the centroid of ΔWXY, WR=87, SY=39, and YT=48, find each measure.
a)WS=
b) WY =
c) WZ =
d) ZR =
e) ZT =
f) YZ =
Find the inequality represented by the graph.
Answer:
y=1.5x-2
Step-by-step explanation:
Use equation y=mx+c
m is the gradient of the graph
c is the y-intercept
Finding the gradient:
Coordinates of the blue circles: (0,-2) and (2,-5)
(-5)-(-2)=-3
2-0=2
3÷2=1.5=m
Therefore, the gradient is 1.5
Next, to find the y-intercept, just simply look at the y axis
The blue circle is the intercept.
Therefore, the final equation is:
y=1.5x-2
Hope this helped