The points are as selected on the graph.
How to select points on the graph?A function is an expression that shows the relationship between the independent variable and the dependent variable. A function is usually denoted by letters such as f, g, etc.
Since f(x) = -9. What this means is that the value of f(x) will always be -9 irrespective of the value of x. That is:
x f(x)
-2 -9
0 -9
2 -9
7 -9
9 -9
Check the attached image for the points on the graph
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Find the area of the irregular figure. Use 3.14 for π. Show your work. Round to the nearest tenth
The area of the irregular figure to the nearest tenth is 8.12 sq. ft.
What are irregular figures?Shapes classified as irregular lack both equal sides and equal angles. The entire area occupied by an irregular shape on a two-dimensional plane is referred to as the shape's area. An irregular form can be split into a number of regular shapes, such as triangles, squares, and rectangles, to determine its area. The area of those smaller shapes can then be added to determine the total area.
Given that, the diameter of the semicircle= 2.8 ft.
The radius of the semicircle = 1.4 ft.
The area of the semicircle is:
A = πr² / 2
A = (3.14)(1.4)²/2
A= 3.077 sq. ft
The area of the triangle is given as:
A = 1/2(b)(h)
A = 1/2(2.8)(3.6)
A = 5.04 sq. ft
The area of the irregular figure is:
A = Area of semicircle + area of triangle
A = 3.077 + 5.04
A = 8.117 sq. ft
Hence, the area of the irregular figure to the nearest tenth is 8.12 sq. ft.
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Looking for help with this one?
[tex] \frac{x + 2}{2x - 2} = \frac{1}{2} [/tex]
Answer:
No solution
Step-by-step explanation:
We are given the following equation and asked to solve for x
[tex]\dfrac{\left(x+2\right)}{2x-2}=\dfrac{1}{2}[/tex]
[tex]\mathrm{Apply\:fraction\:cross\:multiply:\:if\:}\dfrac{a}{b}=\dfrac{c}{d}\mathrm{\:then\:}a\cdot \:d=b\cdot[/tex]
[tex]\left(x+2\right)\cdot \:2=\left(2x-2\right)\cdot \:1[/tex]
[tex]\mathrm{Simplify}2x + 2 = 2x - 2\\\\\textrm{Subtract\;$2x$\;both\;sides}:\\-2 = 2[/tex]
Since the sides are not equal this indicates there is no solution to this system.
Krysta's Bakery recently spent a total of $264 on new equipment, and their average hourly
operating costs are $18. Their average hourly receipts are $26. The bakery will soon make
back the amount it invested in equipment. What would the total expenses and receipts both
equal? How many hours will that take?
Answer:
The net profit would be 26-18=6 dollars per hour.
we need hours such that 8h≥264 =>h≥33 hours
The function h(x) is a continuous quadratic function with a domain of all real numbers. The table lists some of the points on the function. x h(x) −6 12 −5 7 −4 4 −3 3 −2 4 −1 7 What are the vertex and range of h(x)?
The vertex of the parabola is at the point (-3/2, -21/4) and the range of the function would be (-21/4, infinity).
What is the quadratic function?
A quadratic function is a function of the form [tex]f(x) = ax^2 + bx + c,[/tex] where a, b, and c are constants, and a is not equal to 0. It is a type of polynomial function that can be graphed as a parabola, which is a symmetric curve that opens either upwards or downwards.
Given the table of points for the continuous quadratic function h(x), we can find the vertex and range of the function. Since the function is quadratic and continuous, it can be represented in the standard form [tex]f(x) = a(x - h)^2 + k[/tex], where (h, k) is the vertex of the parabola.
To find the vertex, we can use the fact that the x-coordinate of the vertex is given by -b/2a, where a and b are the coefficients of the quadratic term and the linear term, respectively. In this case, a = 1 (since the function is continuous and quadratic), and b can be found using any two points on the parabola:
[tex]b = (h(x2) - h(x1))/(x2 - x1) = (4 - 7)/(-2 + 1) = 3[/tex]
Therefore, the x-coordinate of the vertex is x = -b/2a = -3/2. To find the y-coordinate of the vertex, we can evaluate the function at this value of x:
[tex]h(-3/2) = (1)(-3/2 - h)^2 + k[/tex]
To solve for k, we can use one of the points on the parabola, say (-6, 12):
[tex]12 = (1)(-6 - h)^2 + k[/tex]
Expanding and simplifying, we get:
[tex]12 = (h - 6)^2 + k[/tex]
Substituting -3/2 for h, we get:
[tex]12 = (-(3/2) - 6)^2 + k\\\\12 = 81/4 + k\\\\k = -21/4[/tex]
Therefore, the vertex of the parabola is at the point (-3/2, -21/4).
To find the range of the function, we can look at the shape of the parabola. Since the coefficient of the quadratic term is positive, the parabola opens upwards, and the vertex is the lowest point on the graph. Therefore, the range of the function is all real numbers greater than or equal to the y-coordinate of the vertex, which is -21/4. In interval notation, we can write the range as (-21/4, infinity).
Hence, the vertex of the parabola is at the point (-3/2, -21/4) and the range of the function would be (-21/4, infinity).
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Please help me if you don’t mind
Answer:
C = .25m + 5.45
Step-by-step explanation:
c = (1..05 - .8)m + (16.40 - 10.95)
C = .25m + 5.45
The Luxury car cost 25 cents more per mile and an a higher initial cost of $5.45
An item is regularly priced at $15. John bought it at a discount of 35% off the regular price. How much did John pay
Answer:
Step-by-step explanation:
Item: $15
on sale:$15 -35% or 15*7/20=
$9.75~
Please help 13. Phil works at a department store and gets an employee discount. The price he pays can be modeled by the function d(c) = c - 0.08c , where is the original price of the item. Find d(25) and describe what this means in context.
With the original price at 25 units , he paid 23 units and d(25) means the price he paid when the original price is 25 units.
How to solve a function?Phil works at a department store and gets an employee discount. The price he pays can be modelled by the function d(c) = c - 0.08c , where c is the original price of the item.
Therefore, let's find d(25) and describes what it means.
Hence,
d(c) = c - 0.08c
where
c = original priceTherefore,
d(25) = 25 - 0.08(25)
d(25) = 25 - 2
d(25) = 23
Therefore, d(25) is the price he paid when the original price is 25 units. Therefore, he paid 23 units
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Consider a binary classification problem for which you know that the conditional class probabilities are given by: P2 (t) = Pr (Y; = 1|X, = x) = and po (I) = Pr (Y; = 0[Xi = 1) = 1 - P: (I). Find the optimal Bayesian classifier. (Hint: Your classifier should be of the form: if Xe [a, b] then yi = 1, where a and b are two scalars you need to find).
The optimal Bayesian classifier is the one that minimizes the probability of misclassification. This can be achieved by choosing the class that has the highest posterior probability given the observed data. In this case, we need to compare the conditional class probabilities P2(t) and P0(I) for each data point and choose the class with the higher probability.
To find the optimal Bayesian classifier, we need to find the values of a and b that define the decision boundary between the two classes. This can be done by setting P2(t) = P0(I) and solving for x:
P2(t) = P0(I)
Pr(Y; = 1|X, = x) = Pr(Y; = 0[Xi = 1)
1 - P2(I) = P2(I)
2P2(I) = 1
P2(I) = 0.5
Now we can solve for x to find the decision boundary:
0.5 = Pr(Y; = 1|X, = x)
0.5 = P2(I)
x = a + b
Therefore, the optimal Bayesian classifier is of the form:
if Xe [a, b] then yi = 1
if Xe [b, a] then yi = 0
where a and b are the values of x that satisfy P2(I) = 0.5.
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You may need to use the appropriate technology to answer this question.The Dow Jones Industrial Average (DJIA) and the Standard & Poor's 500 (S&P 500) indexes are used as measures of overall movement in the stock market. The DJIA is based on the price movements of 30 large companies; the S&P 500 is an index composed of 500 stocks. Some say the S&P 500 is a better measure of stock market performance because it is broader based. Suppose the closing price for the DJIA and the S&P 500 for 15 weeks of a certain year follow.Date DJIA S&P 500Week 1 12,350 1,279Week 2 12,412 1,290Week 3 12,730 1,314Week 4 12,670 1,315Week 5 12,852 1,346Week 6 12,811 1,344Week 7 12,960 1,363Week 8 12,993 1,367Week 9 12,988 1,371Week 10 12,932 1,370Week 11 13,223 1,403Week 12 13,091 1,398Week 13 13,202 1,409Week 14 13,050 1,399Week 15 12,840 1,369(a) Develop a scatter chart for these data with DJIA as the independent variable. What does the scatter chart indicate about the relationship between DJIA and S&P 500?The scatter chart indicates there may be no noticeable linear relationship between DJIA and S&P 500.The scatter chart indicates there may be a negative linear relationship between DJIA and S&P 500.The scatter chart indicates there may be a positive linear relationship between DJIA and S&P 500.(b)Develop an estimated regression equation showing how S&P 500 is related to DJIA. What is the estimated regression model? (Round your numerical values to four decimal places.)ŷ = ____________(c)What is the 95% confidence interval for the regression parameter ????1? (Round your answers to three decimal places.) _______ to ________Based on this interval, what conclusion can you make about the hypotheses that the regression parameter ????1 is equal to zero?Because this interval ---Select--- (does - does not) include zero, we ---Select--- (reject - fail to reject) the hypothesis that ????1 = 0.(d)What is the 95% confidence interval for the regression parameter ????0? (Round your answers to three decimal places.) ________ to ________Based on this interval, what conclusion can you make about the hypotheses that the regression parameter ????0 is equal to zero?Because this interval ---Select--- (does-does not) include zero, we ---Select--- (reject - fail to reject) the hypothesis that ????0 = 0.(e)How much of the variation in the sample values of S&P 500 (in %) does the model estimated in part (b) explain? (Round your answer to two decimal places.)__________ %(f)Suppose that the closing price for the DJIA is 13,600. Estimate the closing price for the S&P 500. (Round your answer to the nearest integer.)
Answer:
Step-by-step explanation:
(a) To develop a scatter chart, we plot the DJIA on the x-axis and the S&P 500 on the y-axis. The scatter chart indicates whether there is a linear relationship between the two variables.
(b) The estimated regression equation is ŷ = b0 + b1x, where x is the DJIA and ŷ is the predicted value of S&P 500. We can use a regression analysis to estimate the values of the regression coefficients b0 and b1. The estimated regression model is ŷ = 340.6548 - 0.0202x.
(c) The 95% confidence interval for the regression parameter b1 can be found using the t-distribution with n-2 degrees of freedom, where n is the sample size. The interval is ( -0.036, -0.004), which does not include zero. Therefore, we reject the null hypothesis that b1 = 0, and conclude that there is a significant linear relationship between DJIA and S&P 500.
(d) The 95% confidence interval for the regression parameter b0 can also be found using the t-distribution with n-2 degrees of freedom. The interval is ( 536.772, 144.537), which does not include zero. Therefore, we reject the null hypothesis that b0 = 0, and conclude that the intercept is significantly different from zero.
(e) The coefficient of determination R^2 measures the proportion of variation in the dependent variable (S&P 500) that is explained by the independent variable (DJIA). In this case, the model explains 73.23% of the variation in S&P 500.
(f) To estimate the closing price for the S&P 500 when the DJIA is 13,600, we substitute x = 13,600 into the regression equation:
ŷ = 340.6548 - 0.0202(13,600) = 88.572
Therefore, the estimated closing price for the S&P 500 is $88,572 (rounded to the nearest integer).
In AOPQ, p = 6.3 cm, m/O=149° and m/P=29°. Find the length of q, to the nearest
10th of a centimeter.
The length of q is approximately is 0.4 cm.
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
To solve for the length of q in triangle AOPQ, we can use the law of sines, which states:
a/sin A = b/sin B = c/sin C
where a, b, and c are the lengths of the sides opposite the angles A, B, and C, respectively.
In triangle AOPQ, we know that:
Side p = 6.3 cm (opposite angle P)
Angle O = 149° (opposite side q)
Angle P = 29° (opposite side p)
Let use angle sum property of triangles to find the measure of angle Q:
Angle Q = 180° - Angle O - Angle P
Angle Q = 180° - 149° - 29°
Angle Q = 2°
Now we can use the law of sines to solve for the length of q:
q/sin Q = p/sin P
q/sin(2°) = 6.3/sin(29°)
q = sin(2°) × (6.3/sin(29°))
q=0.034 × (6.3/0.484)
q = 0.442 cm
Therefore, the length of q is approximately is 0.4 cm.
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What is the value of x? (5 points) A right angle is shown divided into two parts. The measure of one part of the right angle is 10 degrees. The measure of the other part is 2x a 20 b 40 c 45 d 85
Based on the definition of a right angle, the value of x is: B. 40.
What is a Right Angle?A right angle is an angle that measures exactly 90 degrees, or one quarter of a full circle. The symbol used to represent a right angle is a small square placed in the corner where the two lines or rays meet
Therefore, if two parts of a right angle measures 10 degrees and 2x respectively, we would have:
2x + 10 = 90
Subtract 10 from both sides:
2x = 90 - 10
2x = 80
2x/2 = 80/2
x = 40
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What graph represents the function? G(x)={x if x < or equal to 2 -3 if x >2
The value of x for the function x > 2 is x ≤ -1. This is represented by the following graph.
What is a graph?A graph is a format similar to a set of elements in different mathematics, more categorically graph theory, in which some pairs of objects are conceptually "connected". Elements are represented by mathematical abstractions called vertices (sometimes called nodes or points), and each pair of allied vertices is called an edge (also called a link or line). A graph is usually characterized as a collection of points or circles defining vertices and lines or curves representing edges. One of the details studied in discrete mathematics is graphs.
The given function is:
G(x)={x if x < or equal to 2 -3 if x >2
Here, the value of x for x > 2 is x ≤ -1. This is represented by the following graph.
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Write a sequence of transformations that maps triangle ABC onto triangle A”B”C”.
The sequence of transformations that maps triangle ABC onto triangle A”B”C” is given as follows:
Reflection over the x-axis.Dilation centered around the origin by a scale factor of 4.How to obtain the transformations?First we must look at one vertex of the original triangle, and I am going to choose vertex A, which has the coordinates given as follows:
A(-1,1).
From the change in the orientation of the triangle, we can see that it was reflected over the x-axis, transformation for which the rule is (x,y) -> (x, -y), hence:
A'(-1,-1).
The coordinates of vertex A'' are given as follows:
A(-4,-4).
This means that each coordinate of vertex A' was multiplied by 4, thus the second transformation is a dilation with a scale factor of 4.
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A discount store buys a shipment of antique iron benches at a cost of $5,100 each. The antique iron benches will be sold for $8,715 apiece. What percentage is the mark-up?
Answer:
20000
Step-by-step explanation:
i think this is the right answer i could
Help me!!!!!!!!!!!!!!!!!!
Answer:
x = 10
Step-by-step explanation:
We know that it's a right triangle and it's two sides, which are 6 and 8
So we can find the third side, the Hypotenuse or x, using the Pythagoras Theorem
6² + 8² = Hypotenuse ²
36 + 64 = Hypotenuse²
100 = Hypotenuse²
Hypotenuse = root100
Hypotenuse = 10
Therefore x = 10
Graph y=3x−3/4
AND
Graph y=−x/3−3/2
Answer:
Photo below.
Step-by-step explanation:
Red Line = y=3x−3/4
Blue Line = y=−x/3−3/2
Hope it helped!
Consider this argument: Bob is 13 feet tall So, Bob is taller than most other people Suppose there are no implicit premises: this is the whole argument. Which of the following is true about this argument? A. The premise entails the conclusion because, if the premise is true, the conclusion has to be true B. The premise does not entail the conclusion because, if the premise is true, the conclusion could still be false (setting aside facts not supplied by the premise)
с. The premise entails the conclusion because, setting aside facts not supplied by the premise, there is no way the premise could be true and the conclusion false. D. The premise does not entail the conclusion because it has no suppositional strength.
The correct statement is Option - B →
The premise does not entail the conclusion because, if the premise is true, the conclusion could still be false.
What is argument in mathematics?A mathematical argument is a sequence of statements and reasons given with the aim of demonstrating that a claim is true or false.
Given is that Bob is 13 feet tall. So, Bob is taller than most other people.
The correct statement is -
The premise does not entail the conclusion because, if the premise is true, the conclusion could still be false.
Therefore, the correct statement is Option - B →
The premise does not entail the conclusion because, if the premise is true, the conclusion could still be false.
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based on the data in the graph, by approximately what percent did the sea ice decrease from 1980 to 2005 ?
Answer:
Step-by-step explanation:
find the measure of each marked angle
The sum of two opposite interior angles of a triangle is equal to the opposite exterior angle of a triangle
Therefore,
( 5x - 101 )° + ( x + 36 )° = ( 9x - 164 )°
5x + x - 106 + 36 = 9x - 164
6x - 65 = 9x - 164
6x - 9x = - 164 + 65
- 3x / - 3 = - 99 / - 3
x = 33
The first interior angle
= ( 5x - 101 )°
= ( 5 ( 33 ) - 101 ) °
= ( 165 - 101 )°
= 64°
The second interior angle
= ( x + 36 )°
= ( 33 + 36 )°
= 69°
The exterior angle
= ( 9x - 164 )°
= ( 9 ( 33 ) - 164 )°
= ( 297 - 164 )°
= 133°
Recall the Hotel Cardinality, described in Mindscapes 16, 17, and 18 of the previous section. Create a collection of people so that it would be impossible for the night manager to give each person a room. Thus, for a really big group of people, a No Vacancy sign (or actually a Not Enough Room sign) might actually be necessary. Explain why it is not possible to give each person from your group a room.
Giving each guest a room in a hotel is impossible if the group size exceeds the number of available rooms, resulting in some individuals having to share a room with someone else or not having a place to stay.
Describe Logical thinking.Logical thinking is a type of thinking that involves reasoning based on a set of premises or assumptions to arrive at a conclusion. It is a rational, systematic, and methodical way of thinking that involves analyzing information, identifying patterns, and drawing valid and sound conclusions.
Logical thinking involves using a combination of critical thinking skills, such as analysis, evaluation, and synthesis, to make reasoned judgments. It requires an ability to break down complex problems into smaller, more manageable parts, and to evaluate evidence in a clear and objective manner.
In logical thinking, conclusions are reached through a process of deduction or induction. Deduction involves starting with a general principle or premise and applying it to a specific situation to arrive at a conclusion. Induction, on the other hand, involves starting with specific observations or evidence and using them to make a general conclusion.
Logical thinking is essential in many fields, including science, mathematics, philosophy, and law, among others. It is also important in everyday life, such as when making decisions, solving problems, or evaluating arguments. By using logical thinking, individuals can make informed and reasoned judgments, and arrive at conclusions that are based on evidence and reason, rather than emotion or bias.
The Hotel Cardinality is a mathematical model that assumes that the hotel has an infinite number of rooms. However, in reality, hotels have a limited number of rooms. Therefore, if the group of people is larger than the number of available rooms, it would be impossible to give each person a room. For example, if the hotel has only 10 rooms and the group consists of 15 people, it is not possible to give each person a room. This is because there are more people than the number of available rooms, and some people will have to share a room or be left without a room. Hence, it is not always possible to accommodate all guests in a hotel, especially during peak seasons or when the hotel has limited capacity.
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Suppose that, in 2006, Germany produced 13.239 million bikes. The total world production that year totaled 84 million bikes. What percent of the world's total production of bikes is contributed by Germany? Round your answer to the nearest tenth of a percent.
Answer:
15.8%
Step-by-step explanation:
You want the percentage of world bike production represented by 13.239 million bikes out of a world production of 84 million bikes.
PercentageA fraction is converted to a percentage by multiplying it by 100%.
13.239/84 × 100% ≈ 15.8%
Germany contributed about 15.8% of the world's bike production in 2006.
The function that assigns every positive three-digit integer the sum of the largest and the smallest digits.
State the number of elements in the Domain and Range for this part only
Answer:
17 numbers in this range.
Step-by-step explanation:
For this function, the domain consists of all positive three-digit integers. There are 900 such integers, from 100 to 999.
The range consists of all numbers between 2 and 18, inclusive, since the smallest possible sum is 1+0+0 = 1 and the largest possible sum is 9+9+1 = 19, but the function only takes the sum of the largest and smallest digits. There are 17 numbers in this range.
Answer:
Step-by-step explanation:
The domain of this function consists of all positive three-digit integers. There are 900 three-digit integers in total, from 100 to 999 inclusive.
The range of this function consists of all integers between 2 and 18 inclusive, since the smallest and largest digits of a three-digit integer can range from 1 to 9, and their sum can range from 2 (1 + 1) to 18 (9 + 9). So the range has 17 elements in total: {2, 3, 4, ..., 18}.
help im gonna fail and my the teacher is scary saying shes gonna whoop me
Answer: greater than 6 cm. less than 20 cm
Step-by-step explanation:
What is the answer to this
Answer:
48
Step-by-step explanation:
2*4*6
Celine measured the high school and made a scale drawing. The scale she used was
1 millimeter: 10 meters. If the actual length of the parking lot is 120 meters, how long is the
parking lot in the drawing?
millimeters
Is ABES AGES? If so, identify the similarity postulate or theorem that
applies.
B
40 40
6
S
G
A. Similar - AA
B. Similar - SSS
C. Similar - SAS
D. Cannot be determined
Answer:
Step-by-step explanation:
similar - AA
The ΔBES is similar to ΔGES by AA similarity postulate.
What are Similar Triangles?Similar triangles are those triangles, where the angles of the triangles are equal and the sides are proportional.
Given a bigger triangle BEG.
There are two smaller right angled triangles BES and GES.
For ΔBES, ∠BES = 40° and ∠BSE = 90°
For ΔGES, ∠GES = 40° and ∠GSE = 90°
By AA similarity postulate, if two angles of one triangle is equal to two angles of another triangle, then the triangles are similar.
Here, two angles of ΔBES is equal to two angles of ΔGES.
So two triangles are similar.
Hence the two triangles are similar by AA similarity postulate.
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Your question is incomplete. The complete question with the image of the triangle is as given below.
X divided by 5 multiply by 12
Answer:
Step-by-step explanation:
The expression "X divided by 5 multiplied by 12" can be written as:
( X / 5 ) * 12
To simplify this expression, we can first multiply 12 by X/5, which gives:
( X / 5 ) * 12 = X * (12/5)
So the simplified expression is:
X * (12/5)
or
(12/5)X
which is equivalent to "12/5 times X".
**URGENT**
The monthly cost (in dollars) of a long-distance phone plan is a linear function of the total calling time (in minutes). The monthly cost for 34 minutes of calls is $14.69 and the monthly cost for 57 minutes is $17.68 . What is the monthly cost for 39 minutes of calls?
I will give brainliest. Just please help
The monthly cost for 39 minutes of calls is $14.30.
According to given information :Let's start by using the given information to find the slope and y-intercept of the linear function that gives the monthly cost in terms of the total calling time. We can use the point-slope form of a linear equation:
y - y1 = m(x - x1)
where (x1, y1) is a point on the line and m is the slope.
Using the points (34, 14.69) and (57, 17.68), we get:
m = (17.68 - 14.69) / (57 - 34) = 0.09
To find the y-intercept, we can use the point-slope form with either of the two points:
y - 14.69 = 0.09(x - 34)
y - 14.69 = 0.09x - 3.06
y = 0.09x + 11.63
So the monthly cost (y) is a linear function of the total calling time (x) with a slope of 0.09 and a y-intercept of 11.63.
To find the monthly cost for 39 minutes of calls, we simply substitute x = 39 into the equation:
y = 0.09(39) + 11.63 = 14.30
Hence, the monthly cost for 39 minutes of calls is $14.30.
What is cost price ?
Cost price refers to the amount of money that is paid to purchase an item or produce a good. It includes all the costs incurred in the production or acquisition of an item, such as the cost of raw materials, labor, and other expenses. Cost price is important for businesses because it helps determine the profit margin on a product, which is the difference between the selling price and the cost price. A business needs to set a selling price that covers the cost of producing or acquiring a product and leaves room for profit.
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Use the Commutative Property to complete the equation. 9 × 9 =
In the case of 9 x 9, using the Commutative Property, we can rewrite it as 9 x 9 = 9 x 9. The product of these two factors is 81, which is the same regardless of the order of the factors.
What is the Commutative property?The Commutative Property of Multiplication is one of the fundamental properties of arithmetic. It states that the order of the factors in a multiplication expression does not affect the product. In other words, you can multiply two numbers in any order and still get the same result.
For example, if you have the multiplication expression 2 x 5, you can switch the order of the factors and write it as 5 x 2, and the result is still the same:
2 x 5 = 5 x 2 = 10
Similarly, for the expression 3 x 4, you can switch the order of the factors and write it as 4 x 3, and the result is still the same:
3 x 4 = 4 x 3 = 12
The Commutative Property is a fundamental property of multiplication, and it is used in many mathematical operations, including simplifying expressions, solving equations, and more.
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Help! ASAP!! figure rst on the graph is reflected over the y axis creating figure r's't'. figure r's't' is translated down 2 units and left 1 unit creating r"s"t". tyler knows rst = r's't' because reflections produce congruent figures. he also knows that r's't' = r"s"t" because translations produce congruent figures. what can tyler determine based on these two statements? check all that apply. 1. RST = R’’S’’T’’
2. RS = ST = TR
3. R = S = T
4. R = R’ = R’’
5. TS = T’S’ = T’’S’’
Reflections and translations do not guarantee that all corresponding sides of the figures will be equal.
What is translation and reflection?
The translation is when we slide a figure in any direction. Reflection is when we flip a figure over a line.
Based on these two statements, Tyler can determine the following:
1. RST = R’’S’’T’’
4. R = R’ = R’’
5. TS = T’S’ = T’’S’’
Tyler cannot determine that RS = ST = TR, because reflections and translations do not necessarily produce congruent figures. Similarly, Tyler cannot determine that R = S = T, because reflections and translations do not guarantee that all corresponding sides of the figures will be equal.
Hence, Reflections and translations do not guarantee that all corresponding sides of the figures will be equal.
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