In order to factor your quadratic polynomials, the box method, as its name suggests, uses a box. You can divide your quadratic into its factors by using the box, which is essentially a square divided into four equal parts.
What is box method ?Be aware that not all quadratics can be factored. Some just lack relevant components. But if a quadratic polynomial does have components, you can utilize the box approach to simplify the operation.Drawing a square divided into four equal sections or a two-by-two grid is the first step. You then enter your first squared term into the upper left box and your final term into the lower right box. the product of your final term and first term.These new term's contributing components are found. You're seeking for a specific combination of elements that, when added together, give you your middle word. Write these elements in the two remaining empty boxes once you've identified this group of components. Your answer will remain the same no matter which empty box each term is entered into. Find the largest common factor for each row and column to determine the quadratic factors. The factors of your polynomial will then be determined by finding the biggest common factors from your columns and rows, respectively.Employing the Box Method
For our first quadratic, 6x2 - x - 12, let's utilize the box approach to solve it.
The first step is to create a two by two grid, as shown here:
using a box
Following that, we place the first term in the upper left box and the last term in the lower right box.
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The figure below is a cone with the vertex at A and diameter BC. The cone is cut off along 15 cm B =B 6 cm 49 cm-a)find the base radius of the smaller cone.
b) find the volume of the frustum.
divide the lateral height in half, Height squared lateral height squared is subtracted from height squared, the answer from step three, and find its square root. The radius of the cone is the outcome.
What is the volume formula of frustum?The following are the conical Frustum formulas in terms of r and h: V = (1/3) * * h * (r12 + r22 + (r1 + r2)) is the formula for a conical frustum's volume.The base's radius is the same as the cylinder's radius. The cylinder's height is equal to the length of the altitude, which is a segment running perpendicular to the planes of each of its bases.Radius = Diameter/ 2 applies when the diameter is known. Radius = Circumference/2 can be calculated after the circumference is known. The radius is calculated using the formula Radius = ((Area of the circle/π).To learn more about radius refer to:
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Therefore , the solution of the given problem of volume comes out to be 9,003.75π cubic cm.
What is the volume formula of frustum?The following are the conical Frustum formulas in terms of r and h: V = (1/3) * * h * (r12 + r22 + (r1 + r2)) is the formula for a conical frustum's volume. The base's radius is the same as the cylinder's radius. The cylinder's height is equal to the length of the altitude, which is a segment running perpendicular to the planes of each of its bases.
Here,
Given :
=> 15 cm is the AB
=> radius = 49/2 = 24.5 cm
The radius of base is 24.5 cm
and
the volume of frustrum:
=> π(24.5)(24.5)(15)
=> 9,003.75π cubic cm
Therefore , the solution of the given problem of volume comes out to be
9,003.75π cubic cm.
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Question 1:
The average cost of a scientific calculator was $96.50 in 1970. The same type of calculator cost $22 in 2016. Assuming the exponential decay model applies, what will a similar calculator cost in the year 2023? Round your answer to the nearest cent.
Question 2:
Part A:
Reshanda was invited for coffee at 2:00 pm, but she normally goes to sleep at 10:00 pm. If a 16-oz coffee has 122 mg of caffiene, and the half-life of caffiene is 5.5 hours, how much caffiene would still be in her system at bedtime? (Round your answer to the nearest tenth of a milligram)
Part B:
Suppose Reshanda cannot sleep if she has 15 or more mg of caffeine in her system. How many hours before she goes to sleep could she drink a 16-oz coffee? (Round your answer to the nearest tenth of an hour)
Assuming the exponential decay model applies, a similar calculator will cost $10.19 in the year 2023.
Question 2:
Part A:
The amount of caffiene that would still be in her system at bedtime is 28.36 mg
Part B:
The hours before she goes to sleep which she could drink a 16-oz coffee is 6.51 hours.
How do we determine the values?The average cost of a scientific calculator was $96.50 in 1970 and $22 in 2016. Using the exponential decay model, the cost of a similar calculator in 2023 would be $10.19.
Question 2:
Part A:
Reshanda was invited for coffee at 2:00 pm, and she normally goes to sleep at 10:00 pm. The half-life of caffeine is 5.5 hours. To determine how much caffeine would still be in her system at bedtime, we can use the formula:
C(t) = C0(1/2)^(t/T),
where C(t) is the amount of caffeine in her system at time t, C0 is the initial amount of caffeine (122 mg), t is the time in hours since she consumed the coffee, and T is the half-life of caffeine (5.5 hours).
At 10:00 pm, 8 hours after drinking the coffee, t = 8 hours. Plugging these values into the formula and solving for C(t), we get: C(8) = 122(1/2)^(8/5.5) = 28.36 mg
Part B:
Reshanda cannot sleep if she has 15 or more mg of caffeine in her system. We can use the formula from part A to solve for the time t when the caffeine level drops below 15 mg.
C(t) = 15, C0 = 122, T = 5.5
15 = 122(1/2)^(t/5.5)
then we can isolate t:
t = 5.5 * ln(122/15) = 6.51 hours
So, Reshanda could drink the coffee 6.51 hours before she goes to sleep.
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Meredith plays softball, she gets a hit about 35% of the time. Write this as a fraction.
A 1/4
B 2/5
C 1/35
D 7/20
The depiction of 35% as a fraction is 7/ 20, and option D is the correct answer.
What are percentages?A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the term percent signifies. The letter "%" stands for it.
Given that the chance of getting hit by the ball is 35%.
35 % = 35/100
Simplifying the fraction:
35/100 = 7/ 20
Hence, depiction of 35% as a fraction is 7/ 20, and option D is the correct answer.
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Kathy and Mark Smith believe investing in their retirement is critical. Kathy began investing 20% of each paycheck in a retirement account when she was 20 years old. She has saved four times more than Mark who began saving when he was 35. If their total retirement savings equals $1,560,000, how much are Kathy’s and Mark's investments worth?
Kathy’s and Mark's investments worth will be $1248000 and $312000.
How to calculate the worth of each individual?From the information, Kathy and Mark Smith believe investing in their retirement is critical. Kathy began investing 20% of each paycheck in a retirement account when she was 20 years old. She has saved four times more than Mark who began saving when he was 35.
Let Mark = x
Kathy = 4 × x = 4x
The equation to represent this will be:
4x + x = 1560000
5x = 1560000
Divide
x = 1560000 / 5
x = 312000
Mark contributed $312000
Kathy contributed
= 312000 × 4
= 1248000
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please help! giving 20 points for this answer please!
Answer:
6 divided by 2/3 = 9
Step-by-step explanation:
Steven cuts the 6 ft long rope by 2/3 to make 9 pieces and the answer is mathematically correct, via calulcator
IS 1.5 MORE OR LESS THAN -1.5
Answer:
1.5 is more than -1.5
Step-by-step explanation:
Positive numbers, like 1.5, are always greater than negative numbers, like -1.5
An instructor asked her students how much time to the nearest hour) they spent studying for the midterm. The data are displayed in the following histogram: What percentage of students study to or more hours for the midterm? 3 % Round your answer to the nearest whole number
Based on the data displayed in the histogram, the percentage of students who study 2 or more hours for the midterm is 88%.
A histogram is a graphical representation of data that shows the distribution of a dataset. It is used to show the frequency or the relative frequency of different values within a set of data. It is a bar chart that displays the data in a continuous format, with the bars touching each other.
Based on the histogram, the number of students studying 2 or more hours for the exam are:
= 9 + 6 + 3 + 2 + 1 + 1
= 22 students
While the total number of students studying is :
= 3 + 9 + 6 + 3 + 2 + 1 + 1
= 25 students
The percentage of students study to or more hours can be determined by dividing the number of students studying 2 or more hours with the total number of students studying multiply by 100.
percentage = 22/25 x 100
percentage = 0.88 x 100
percentage = 88%
Therefore, 88% of students study to or more hours for the midterm.
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2. You are single and your gross pay for this week is $710. Using the
percentage method of withholding, what amount will you pay in federal
income tax if you claim 3 allowances. Each weekly allowance is $80.80.
(Use percentage method table.)
The amount that you would have to pay in federal income tax if you claim 3 allowances would be: $65.46
How to solve for the claimable amount?To calculate the amount you will pay in federal income tax using the percentage method of withholding, you will need to know the withholding percentage for your gross pay and the number of allowances you are claiming.
If you claim 3 allowances, each allowance is $80.80, and you gross pay for the week is $710, your taxable income is:
$710 - 3*$80.8 = $710 - $242.4 = $467.6
To find the amount of federal income tax you will pay, you will need to use the withholding percentage for your taxable income. You can find this information by consulting the IRS Circular E (Employer's Tax Guide) or by using an online withholding calculator.
If we use the IRS Circular E, we can find that if you are single and claim 3 allowances, the withholding percentage for a taxable income of $467.6 is 14%.
So the amount you will pay in federal income tax is:
$467.6 * 14% = $65.46
Therefore, you will pay $65.46 in federal income tax if you claim 3 allowances, and your gross pay for the week is $710.
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Please help its due today also please show me how you solve it
Answer:
y < x + 6
Step-by-step explanation:
The line is broken so that mean that points on the line are not a solution. The shaded part is below the line so that means that we would use the less than sign.
The slope is 1. Rise over Run. We go up 1 and right 1. 1/1 = 1. The graph crossed the y axis at 6
To find the slope of the line given the points (-6,0) and (0,6), we can use the formula: m = (y2 - y1) / (x2 - x1).
m = (6 - 0) / (0 - (-6)) = 6/6 = 1
Using point-slope form, we can write the equation of the line as:
y - 0 = 1(x + 6)
y = x + 6
To get the inequality we just need to change the equation to the inequality by replacing the equal sign with the inequality sign.
So the linear inequality for the points (-6,0) and (0,6) is:
y > x + 6
There are 100 teachers in a school. 60 teach science, 25 teach humanities, 15 teach both science and humanities. 6Find the number of teachers who teach: (a) science but not humanities. (b) Humanities but not science. (c) Humanities or science.
Answer:
(a) 45
(b) 10
(c) 70
Step-by-step explanation:
(a) The number of teachers who teach science but not humanities is:
Number who teach science - Number who teach both subjects
==> 60 - 15 = 45
(b) The number of teachers who teach humanities but not science is:
Number who teach humanities - Number who teach both subjects
==> 25 - 15 = 10
(c) The number who teach humanities or science is Number who teach humanities + number who teach science - number who teach both
60 + 25 - 15 = 70
There are 30 teachers who teach neither humanities nor science = 100 - 70
A small town surveyed 250 adults one Haiti of whom were parents about whether a Park should be expanded the results showed that 150 of adults who were parents and 40 of the adult who were not parents thought the park should be expanded useless information to complete the two way table
Based on the information, we can infer that of the 250 adults surveyed, 190 wanted the park to be expanded and 60 did not want the park to be expanded.
How to complete the table?To complete the table we must take into account the available information. In this case, they are only referring to the adults who wanted the park to be expanded:
40 non-parent adults wanted it expanded.150 adult parents wanted it expanded.40 + 150 = 190According to the above, if we add these two values we would have a group of 190 adults who want the park to be expanded. So the number of adults who do not want the park to be expanded would be 60.
250 - 190 = 60Finally, if there are 60 people who do not want the park to be expanded, we can infer that there may be 30 who are parents and 30 who are not parents.
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standard form y-100=-50x-3
Answer:
Answer in attached photo.
Step-by-step explanation:
SolutionSolution in attached photo, do take note the standard form of an equation is:
y = mx + c,
where m is the gradient and c is the y-intercept.
Answer: (x– 8)2= 4(1)(y+ 3); vertex: (8, –3); opens upward
Which of the following is (are) true concerning the confusion matrix? [select all that apply]
a. It is so named because it is traditionally confusing to read
b. It is a matrix that tabulates correct and incorrect predictions of the choice categories
c. It is useful to determine the predictive accuracy of a choice model
d. None of the above
It is useful to determine the predictive accuracy of a choice model and hence option c is correct for confusion matrix
the misclassification error rate for the following xlminer confusion matrix and the accuracy value of the confusion matrix is 10.82% .
In the field of machine learning, specifically the problem of statistical classification (in unsupervised learning, it is typically referred to as a matching matrix), a confusion matrix, also known as an error matrix, is a specific table structure that enables visualizing the performance of an algorithm.
The literature describes both iterations of the matrix, where each row represents instances in an actual class and each column represents instances in a predicted class. Since it is straightforward to tell whether the system is combining two classes, the name was chosen (i.e. commonly mislabeling one as another).
accuracy is given by the formula :
Accuracy(%) = (true positive + true negative)/(positive + negative)
Here TP true positive =10
and TN true negative is 8.2
hence accuracy = (10+8.2) / (1+0) %
Accuracy = 10.82%
Therefore the accuracy value of the confusion matrix is 10.82% .
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A child is sitting at the edge of a merry-go-round that has a 3m radius. If the merry-go-
round rotates through 120 degrees, how far does the child end up from his starting
point. Note that you are trying to find the straight line distance from the starting point to
the ending point, not the distance around the circle that the child traveled.
Answer: To find the distance the child travels, we can use the arc length formula: s = r * θ, where s is the arc length, r is the radius of the circle, and θ is the angle of rotation in radians. Since the merry-go-round has a radius of 3m and rotates through 120 degrees, we can convert the angle to radians by multiplying by pi/180.
120 degrees * pi/180 = 2pi/3 radians
Now we can plug in the values into the arc length formula:
s = r * θ
s = 3 * (2pi/3)
s = 2pi
The distance the child travels is 2pi meters, which is the circumference of the circle.
Step-by-step explanation:
Sarina shares a phone plan with her brother, Quentin. Each month, they are allowed to send a limit of 1000 text messages. Last month, they did not go over their 1000 text message limit. Sarina knows she sent 400 text messages.
How many text messages, on average, could Quentin have sent per day in the month? Last month, there were 30 days.
Graph the number of text messages as an inequality on the number line.
The average number of text messages that Quentin could have sent is given as follows:
At most 20.
How to obtain the average number?The maximum number of text messages that can be sent on the entire plan is given as follows:
1000.
The amount sent by Sarina is given as follows:
400.
Hence the maximum amount of text messages that Quentin can send is given as follows:
1000 - 400 = 600.
Hence the maximum average over 30 days is given as follows:
600/30 = 20.
Hence the inequality is:
0 ≤ x ≤ 20.
(as the average number of messages cannot be negative).
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segment ac is called a diagonal. on your paper, put a mark on it to indicate that it is congruent to itself. now, look at all of the markings on your paper. you should see that triangle abc is congruent to triangle cda. based on your markings, why are these triangles congruent?
The triangles abc and cda are congruent by sss congruence criteria.
The full form of CPCT is Corresponding parts of Congruent triangles. After proving triangles congruent, the remaining dimension can be predicted without actually measuring the sides and angles of a triangle. Different rules of congruency are as follows. SSS (Side-Side-Side)
SAS (Side-Angle-Side)ASA (Angle-Side-Angle)AAS (Angle-Angle-Side)RHS (Right angle-Hypotenuse-Side)SSS (Side-Side-Side)SSS (Side-Side-Side) :-If all the three sides of one triangle are equivalent to the corresponding three sides of the second triangle, then the two triangles are said to be congruent by SSS rule.
so, sides
AB=CD
BC=DA
AC=CA
Hence by SSS (Side-Side-Side) the triangles are congruent.
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AC=A, C, equals Round your answer to the nearest hundredth. A right triangle A B C. Angle A C B is a right angle. Angle A B C is twenty-five degrees. Side A C is unknown. Side B C is five units.
The unknown side AC will be equal to 2.33.
What is trigonometry?The branch of mathematics that sets up a relationship between the sides and the angles of the right-angle triangle is termed trigonometry.
The trigonometric functions, also known as a circular, angle, or goniometric functions in mathematics, are real functions that link the angle of a right-angled triangle to the ratios of its two side lengths.
Given that a right triangle ABC. Angle ACB is a right angle. Angle ABC is twenty-five degrees. The side AC is unknown. Side BC is five units.
The unknown side will be calculated as:-
tan(25) = P / B
tan(25) = AC / BC
AC = BC x tan(25)
AC = 5 x tan(25)
AC = 2.33
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Give f(x) = 3x^3+kx-13, and x-1 is a factor of f(x), then what is the value of k?
Answer: If x-1 is a factor of f(x) = 3x^3+kx-13, then f(x) can be written as (x-1)g(x) for some polynomial g(x). This means that f(1) = 0.
We can substitute x = 1 into f(x) to get f(1) = 3(1)^3 + k(1) - 13 = 3 + k - 13 = 0.
Therefore k - 10 = 0, so k = 10
So the value of k is 10.
Step-by-step explanation:
PLEASE HELP DONT IGNORE!!
Answer:
[tex]m=-\frac{1}{2}[/tex]
Step-by-step explanation:
[tex]\Delta y=-1,\,\Delta x=2\\\rightarrow \frac{\Delta y}{\Delta x}=\frac{-1}{2}=-\frac{1}{2}[/tex]
[tex]\Delta[/tex] represents change in both variables, so we calculate the slope this way.
Answer:
m=-1/2
Step-by-step explanation:
Use slope formula: [tex]m=\frac{y_{2} -y_{1}}{x_{2}-x_{1}}[/tex]
Which of the following is false regarding the use of simulation?one answer
A. we might choose to conduct a simulation because gathering the desired data by means of an experiment may be considered unethical.
B. We might choose to conduct a simulation because we want to gain insight into real world probabilities or expected values.
C. Conducting a well designed simulation can mimic real world outcomes.
D.Conducting a simulation can help to establish a cause and effect relationship between two variables.
E.A simulation must be repeated many times in order to provide reliable information about probabilities
Conducting a simulation can help to establish a cause and effect relationship between two variables is false regarding the use of simulation.
How would you define simulation?By enabling the testing of various scenarios or process improvements, a simulation is a modeling that replicates the operation of a current or proposed system. It provides evidence for decision-making. This can be integrated with virtual reality technologies for a more engaging experience.
The purpose of simulation in daily lifeUsing simulation modeling, real-world issues can be safely and effectively solved. It provides a crucial analytical method that is easy to verify, interpret, and explain. Through providing precise insights into complex systems, simulation modeling offers beneficial solutions across sectors and disciplines.
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For which of the following sets of data should a stacked bar chart be used?
The total number of planes landing at O’Hare Airport categorized by type
The number of white cars vs, the number of white trucks
The average age of male high school grads vs. the age of female graduates
The average golfers vs the average age of tennis players
Answer:
The total number of planes landing at O’Hare Airport categorized by type.
Calcula la raíz de √144
Answer:
12
Step-by-step explanation:
√144 =12 answer
12 is right answer
Two airplanes leave Philadelphia for Rochester. The first airplane to leave travels at an average speed of 590 kilometers per hour. The second airplane, which leaves 3 hours later, travels at an average speed of 650 kilometers per hour. How long does it take the second airplane to overtake the first?
it would take 29.5 hours the second airplane to overtake the first.
What is Speed?speed is described as. the pace at which an object's location changes in any direction. Speed is defined as the distance traveled divided by the travel time. Speed is a scalar quantity because it just has a direction and no magnitude.
Given, Two airplanes leave Philadelphia for Rochester. The first airplane to leave travels at an average speed of 590 kilometers per hour. The second airplane, which leaves 3 hours later, travels at an average speed of 650 kilometers per hour.
So, in 3 hours first airplane will reach at;
Distance = speed *time
Distance = 590 * 3
Distance travels by first airplane in 3 hours will be = 1770 km
Since, Relative speed of given two planes = 650 - 590
Relative speed of given two planes = 60 km/hour
To reach 1770 km it would take = 1770/60 hours
Thus,
To reach 1770 km it would take = 29.5 hours
therefore, it would take 29.5 hours the second airplane to overtake the first.
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f it is, state the domain and range of the function. (enter your answers using interval notation. if it is not a function, enter naf in all blanks.) domain correct: your answer is correct. range incorrect: your answer is incorrect. your answer cannot be understood or graded. more information
The domain and range of the function is input value and output values respectively.
In math function is defined as a correspondence from one value x of the first set A to another value y of the second set B.
Here we have to state the domain and range of the function.
AS per the definition of the function, we have identified that the domain of a function is the set of values that we are allowed to plug into our function. Which refers that this set is the x values in a function such as f(x).
And the term range of a function is defined as the set of values that the function assumes and which includes the set is the values that the function shoots out after we plug an x value in.
Complete Question:
State the domain and range of the function for the function f. And enter your answers using interval notation. if it is not a function, enter it in all blanks.
Domain: ____
Range: _____
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find the solution of the system of equations -7 -7y =-41 x-6y = -37
Answer:
x = -55/7, y = 34/7
Step-by-step explanation:
Solve the following system:
{-7 y - 7 = -41 | (equation 1)
-6 y + x = -37 | (equation 2)
Express the system in standard form:
{0 x - 7 y = -34 | (equation 1)
x - 6 y = -37 | (equation 2)
Swap equation 1 with equation 2:
{x - 6 y = -37 | (equation 1)
0 x - 7 y = -34 | (equation 2)
Multiply equation 2 by -1:
{x - 6 y = -37 | (equation 1)
0 x + 7 y = 34 | (equation 2)
Divide equation 2 by 7:
{x - 6 y = -37 | (equation 1)
0 x + y = 34/7 | (equation 2)
Add 6 × (equation 2) to equation 1:
{x + 0 y = -55/7 | (equation 1)
0 x + y = 34/7 | (equation 2)
Collect results:
Answer: {x = -55/7, y = 34/7
The following data show the miles per gallon of small SUVs. Sketch a box plot. Calculate the smallest, Q1, median, Q3, largest value, range, and the interquartile range for a box plot. 19 22 22 26 23 24 21 16 16
Smallest = 16, median=22, largest value of data=26 , interquartile range=Q3-Q1=23-19=4.
In statistics and probability theory, the median is the value separating the higher half from the lower half of a data sample, a population, or a probability distribution. For a data set, it may be thought of as "the middle" value.
We have the data 19 22 22 26 23 24 21 16 16, and we have to calculate smallest, Q1, median ...
First rearrange the data 16,16,19,21,22,22,23,24,26
So, Smallest = 16
Median of the data = middle number of data=22
Q1=middle of smallest and median=19
Q3=23
largest value of data=26
range= 19-26
interquartile range=Q3-Q1=23-19=4
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six friends met for a book club at a local coffee shop. Each person ordered a small cup of coffee and a muffin. The total for the order, including taxes, was $38.10, if the cost of a small coffee is $3.79 after taxes find the cost of one muffin after taxes
Please help me
The cost of one muffin after taxes is $2.56. The solution has been obtained by using the arithmetic operations.
What are arithmetic operations?
For all the real numbers, there are four basic mathematical operations which are:
1. Addition(‘+’) wherein the sum of the numbers is obtained.
2. Subtraction(‘-’) wherein the difference of the numbers is obtained.
3. Multiplication(‘×’) wherein the product of the numbers is obtained.
4. Division(‘÷’) wherein the quotient of the numbers is obtained.
Let cost of one muffin after taxes be 'x'
We are given that there were six friends and each person ordered a small cup of coffee and a muffin.
The total for the order, including taxes, was $38.10
Also, the cost of a small coffee is $3.79 after taxes.
So, we get
⇒ 6(3.79 + x) = 38.10
⇒ 22.74 + 6x = 38.10
⇒ 6x = 15.36
⇒ x = $2.56
Hence, the cost of one muffin after taxes is $2.56.
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5. To predict the performance of her first
period class on their next quiz, a teacher
randomly selects eight students from the
class and takes the mean of their scores on
the last quiz. Is this sample representative
of the class's performance on the quiz?
Explain your reasoning.
Yes this sample(straightforward random sample)representative of the class's performance on the quiz
What is average?In mathematics, the middle value—which is determined by dividing the sum of all the values by the total number of values—is the average value in a set of numbers. To calculate the average of a set of data, add up all the values and divide the result by the total number of values.
According to data:A teacher randomly selects eight students from the class and averages their test scores to forecast how well her first period class will fare on their upcoming quiz. Is this sample indicative of how the class performed on the test?
Yes, since it is a straightforward random sample.
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John is creating a Thanksgiving display at the store where he works, using only canned pumpkin and canned green beans. He
needs to maintain a ratio of pumpkin to green beans of 4 to 2. If he wants to use a total of 114 cans, how many cans of green beans
should he use?
A. 36 cans
B. 38 cans
C.6 cans
D. 21 cans
Answer: B
Step-by-step explanation:
The pumpkin to green bean ratio is 2:1
That means x, the amount of green beans, has to be 1/2 the amount of pumpkin. Therefore the amount of pumkin is 2x.
The total amount of cans would be 3x, which is 114
3x = 114
114/3 = x
x = 38 cans of green beans
Three vertices of a parallelogram are shown in the figure below.
Give the coordinates of the fourth vertex.
(-4,9)
(-6,-5)
(1.-7)
Answer:
(3, 7)
Step-by-step explanation:
Given that points (-4,9), (-6,-5), and (1.-7) are three vertices of a parallelogram with segments connecting them in order, you want the point that is the fourth vertex.
ParallelogramThe diagonals of a parallelogram bisect each other, which means they have the same midpoint:
((-4, 9) +(1, -7))/2 = ((-6, -5) +(x, y))/2
Multiplying by 2 and subtracting the point on the right side, we have ...
(-4, 9) +(1, -7) -(-6, -5) = (x, y)
(-4 +1 +6, 9 -7 +5) = (x, y) = (3, 7)
The fourth vertex is (3, 7).
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Additional comment
In general three points can define three possible parallelograms. Here, the segments connecting the points are presumed to be the sides of the parallelogram, so reducing the number of possibilities to just one.
The fact that the diagonal midpoints are the same is useful for solving a variety of problems involving parallelograms.