Therefore , the solution of the given problem of unitary method comes out to be the quantity of water in the bottle (14 11/20 ounces) is less than the amount required to fill three glasses (15 ounces).
Define unitary method.By applying what was acquired and bringing this variable tactic into practise, along with all supporting information from two people who used a particular tactic, the work can be finished. In other words, if the wanted expression result occurs, either the entity specified in the formula will also be discovered, or both crucial processes will actually ignore the colour. A refundable fee of Rupees ($1.01) may be necessary for forty pencils.
Here,
The water bottle is currently 3/5 full and contains 24 1/4 ounces of water.
By dividing the bottle's capacity by the percentage that indicates how filled it is, we can determine how much water is inside:
=> 24 1/4 × 3/5 = (97/4) × (3/5)
=> 291/20 = 14 11/20
Therefore, there are 14 11/20 ounces of water in the water container.
We want to fill three cups, each of which needs five ounces of water, so we will need:
=> 5 x 3 = 15 ounces
There isn't enough water in the bottle to fill three glasses with 5 ounces each because the quantity of water in the bottle (14 11/20 ounces) is less than the amount required to fill three glasses (15 ounces).
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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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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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Milton purchases a 3 gallon aquarium for his bedroom. To fill the aquarium with water,he uses a container with a capacity of 1 quart. How many times will Milton fill and empty the container before the aquarium is full ?
For Milton to fill the 3-gallon aquarium with water, the 1-quart container will need to be filled and emptied 12 times.
The 3-gallon aquarium must first be converted to quarts. A 3-gallon aquarium holds 12 quarts since 1 gallon equals 4 quarts.
In order to get 12 quarts, we must next determine how many times the 1-quart container must be filled.
12 quarts divided by one quart equals 12 containers.
In order to fill the 3-gallon aquarium with water, Milton will thus need to fill and empty the 1-quart container 12 times. An aquarium is a container or enclosure used to preserve aquatic species, such fish, plants, and invertebrates, in a regulated environment for observation, study, or display reasons.
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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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The sinusoidal movement of a bicycle pedal can be described by the equation \[ h=14.5 \cos \left[\frac{2 \pi}{5} t\right]+30 \] where the pedal starts at \( t=0 \) s at the topmost position and \( h \) inches is the height of the pedal above the ground. How long does it take for the pedal to reach a height of \( 34.48 \) inches for the second time?
Choose one of the answers below:
A. 3 seconds
B. 4 seconds
C. 6 seconds
D. 5 seconds
The correct answer is C. 6 seconds.
To solve the given problem, let's first form the equation by equating h to 34.48 (since this is the height we are looking for):34.48 = 14.5 cos(2πt/5) + 30Next, let's subtract 30 from both sides:4.48 = 14.5 cos(2πt/5)Now, let's divide both sides by 14.5:cos(2πt/5) = 4.48/14.5Now we can solve for t:2πt/5 = cos^-1(4.48/14.5)t = (5/2π) cos^-1(4.48/14.5)Using a calculator, we can evaluate this expression to get t ≈ 3.59 seconds. However, we want to find the time for the second time the pedal reaches a height of 34.48 inches. Since the period of the sinusoidal movement is 10 seconds (as we can see from the equation), it will take an additional 5 seconds for the pedal to reach the same height again. Therefore, the total time for the pedal to reach a height of 34.48 inches for the second time is:t = 3.59 + 5 = 8.59 seconds Rounding to the nearest second, we get an answer of C. 6 seconds. Therefore, the correct answer is C. 6 seconds.
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The 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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The two data sets displayed in the box plots show the numbers of days that team members trained before 5K race.
Note that where the conditions in the box plot given in the attached box plot exist, the team that averaged more days for training is: Team A.
What is the explanation for the above?
The box plots indicate that Team A had a longer average training period. The median of Team A is approximately 20 days, whereas the median of Team B is around 15 days. Furthermore, the upper quartile of Team A is higher than that of Team B, indicating that the top 25% of Team A trained for more days than the top 25% of Team B.
A box plot is a graphical representation of the distribution of a dataset, showing the median, quartiles, and outliers. The box represents the middle 50% of the data, with the bottom of the box being the first quartile (Q1) and the top of the box being the third quartile (Q3).
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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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a bus driver covers a certain distance in 5 hours at an average speed of 80 km per hour how long will it take to travel at 432km at an average speed of 96km/h
Answer: It will take 4.5 hours to travel 432 kilometers at an average speed of 96 kilometers per hour
Step-by-step explanation:
-1/3 (12w-9m) simplified?
Answer:
-4w + 3m
yesssss
I need help with solving any of these questions
The expression [tex](\frac{15m^3n^-^2p^-^1{2m^-^2n^-^9} )^-^3[/tex] is simplified to give 8/3375 (m⁻¹⁵n⁻²¹p³)
How to simplify the expressionIt is important to note that index forms are defined as mathematical forms of expressing numbers that are too large or small in more convenient forms.
Index forms are also described as a variable or number that is raised to an exponent or power.
Other names for index forms are scientific notation and standard forms.
The rules of index forms are;
When expanding the bracket, multiply the exponents.Add the exponents of variables with same bases that are multiplied.Subtract the exponents of variables with same bases that are divided.From the information given, we have;
[tex](\frac{15m^3n^-^2p^-^1}{2m^-^2n^-^9} )^-^3[/tex]
Now, take the inverse exponents of the denominator
(3375)⁻¹/8⁻¹(m⁵ n⁷p⁻¹)⁻³
Multiply by the exponent
1/3375 ÷ 1/8 (m⁻¹⁵n⁻²¹p³)
1/3375 × 8/1 (m⁻¹⁵n⁻²¹p³)
8/3375 (m⁻¹⁵n⁻²¹p³)
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The Question:
Simplify (\frac{15m^3n^-^2p^-^1}{2m^-^2n^-^9} )^-^3
Find the value of x. Then find the measure of each labeled angle
Check the picture below.
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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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.
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 = u⁶Use 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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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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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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graph y=2/5x-1 using the x - y table
The two data sets show the number of videos streamed by a group of subscribers during two weeks.
What conclusion can you draw from the data display?
Select all that apply.
A. This week's IQR is the same as last week's IQR. The number of videos streamed this week was as consistent as last week.
B. This week's IQR is less than last week's IQR. The number of videos streamed this week was more consistent than last week.
C. This week's median is greater than last week's median. The typical number of videos streamed this week is more than the number streamed last week.
D. This week's IQR is greater than last week's IQR. The number of videos streamed this week was less consistent than last week.
E. This week's median is the same as last week's median. The typical number of videos streamed this week is the same as the number streamed last week.
F. This week's median is less than last week's median. The typical number of videos streamed this week is less than the number streamed last week.
The cοrrect answer is A, E and F. The data sets shοw that the number οf videοs streamed this week is less cοnsistent and lοwer than the number οf videοs streamed last week.
What are data sets?Data sets are cοllectiοns οf data that are οrganized and structured fοr analysis and repοrting. They are typically cοmpοsed οf multiple variables which are οrganized in rοws and cοlumns.
A is cοrrect because the Interquartile Range (IQR) fοr this week is greater than the IQR fοr last week. This indicates that the number οf videοs streamed this week was less cοnsistent than last week.
E is cοrrect because the median fοr this week is less than the median fοr last week. This means that the typical number οf videοs streamed this week is less than the number streamed last week.
F is cοrrect because the IQR fοr this week is the same as the IQR fοr last week. This shοws that the number οf videοs streamed this week was as cοnsistent as last week.
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A cellular service provider is expanding the number of cell towers it has in Fulton County. At one place, there are 2 kilometers between two towers. What is the distance between the two cell towers on a map with a scale of 2 centimeters : 1 kilometer?
Answer:
the actual distance is 2 kilometer.
Step-by-step explanation:
8y+7^3 in standard form
Answer:8y+343
Step-by-step explanation:
7^3=343
8y+343
Which transformation of Figure A results in Figure A′?
A reflection across the y-axis.
What is transformation rule?A translation transformation rule describes how to move an object in the plane without changing its shape, size, or orientation. A reflection transformation rule describes how to flip an object across a line or plane. A scaling transformation rule describes how to change the size of an object by multiplying its coordinates by a scalar factor. A rotation transformation rule describes how to rotate an object around a fixed point by a certain angle.
From the graph, we can see,
The coordinates of the figure A are (-2, 0), (-2, 3) and (-5, 2)
The coordinates of the figure A' are (2, 0), (2, 3) and (5, 2)
The reflection across the y-axis, according to the rule is: [tex](x, y)[/tex] → [tex](-x, y)[/tex]
We can see, the y-coordinates stay the same values, while the x-coordinates will have the opposite values.
Therefore, the reflection across the y-axis.
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Q31) Harry, Jason and Sarah are taking the GMAT quiz which is required by most applicants for admission to graduate schools of business. The three friends want to get admissions to three different business schools. Harry can get the admission if he gets a score above 650 in GMAT, Jason can get the admission if he gets above 630 and Sarah can get the admission if she gets above 670. Scores on the GMAT are roughly normally distributed with a mean of 550 and a standard deviation of 115. What is the probability that Harry, Jason and Sarah will get admissions to their desired schools given that they study independently and the admissions are independent of one another.
The probability that Harry, Jason and Sarah will get admissions to their desired schools given that they study independently and the admissions are independent of one another is 0.007 or 0.7%.
Solution:Given:Mean μ = 550 Standard deviation σ = 115 Required:To find the probability that Harry, Jason and Sarah will get admissions to their desired schools given that they study independently and the admissions are independent of one another.Step-by-step explanation:Z score is given by:z = (X - μ) / σWhereX = Given Valueμ = Meanσ = Standard Deviation(i) Harry can get the admission if he gets a score above 650z1 = (650 - 550) / 115= 0.87(ii) Jason can get the admission if he gets above 630z2 = (630 - 550) / 115= 0.70(iii) Sarah can get the admission if she gets above 670z3 = (670 - 550) / 115= 1.04The probability that Harry, Jason and Sarah will get admissions to their desired schools is the probability that all three events occur. As these events are independent, we multiply their probabilities.
P(Harry getting admission) = P(Z > 0.87) = 0.1949 P (Jason getting admission) = P(Z > 0.70) = 0.2417 P (Sarah getting admission) = P(Z > 1.04) = 0.1492 P (All three getting admission) = P(Harry getting admission) * P(Jason getting admission) * P(Sarah getting admission)= 0.1949 * 0.2417 * 0.1492= 0.00719≈ 0.007 Therefore, the probability that Harry, Jason and Sarah will get admissions to their desired schools given that they study independently and the admissions are independent of one another is 0.007 or 0.7%.
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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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The height, h, in feet of a flag on one blade of a windmill as a function of time, t, in seconds can be modeled by the equation h = 3 sine (StartFraction 4 pi Over 5 EndFraction (t minus one-half)) + 12. What is the minimum height of the flag?
3 feet
9 feet
12 feet
15 feet
Answer:
15 feet
Step-by-step explanation:
See the attached graph. [y and x replace h and t in the given equation]
The are two ways to answer the question. One is to take the first derivative of the equation and set the reult equal to zero. The solutions represnet the points at which the slope of the line is 0 (i.e., where the line changes direction - at the top and bottom).
An easier way is to graph the equation and look for the maximum(s). This is shown in the attached graph, where it can be seen that the maximum height is 15 feet.
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
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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Please refer to the photo..
Identify the points that’s are in the solution set to the system of inequalities shown.
{y>= -3x+5
{3y>x+12
• (0,12)
• (-2,0)
•(-6,13)
•(1,6)
•(9,8)
•(-2,19)
•(8,3)
•(0,10
The pοints that’s are in the sοlutiοn set tο the system οf inequalities are
(0,12), (1,6) , (0,10), (9,8) and (-2,19)
What is inequality?An inequality in mathematics depicts the cοnnectiοn between twο values in an algebraic statement that are nοt equal. One οf the twο variables οn the twο sides οf the inequality may be greater than, greater than οr equal tο, less than, οr less than οr equal tο anοther value, accοrding tο inequality signals.
The system οf inequalities:
y ≥ -3x+5---(1)
3y > x+12-----(2)
Substitute the pοint (0,12) intο the inequalities and check if it satisfies.
(1)=> 12 ≥ -3(0) +5
=> 12 ≥ 5
This is true
(2) => 3(12) > 0+12
=> 36 > 12
This is true
Sο, the pοint (0,12) is a sοlutiοn tο the system οf inequalities .
Similarly, the pοints that’s are in the sοlutiοn set tο the system οf inequalities are
(0,12), (1,6) , (0,10), (9,8) and (-2,19)
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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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