Answer:
1/6
Step-by-step explanation:
Out of 30 tosses, 5 come up heads. So the estimated probability of heads is 5/30, or 1/6.
Answer: 0.17
Step-by-step explanation:
just got it right on quiz
PLEASE ANSWER THIS QUESTION! I BEG OF YOU
Two function are represent below.
FUNCTION A FUNCTION B
y=35x. (image below)
What is the difference in the rate of change between Function A and Function B? Be sure to include the rate of change of each function in your answer.
EXPLAIN THE ANSWER!j
Rate of change for Function A is: 35
Rate of change for Function B is: 50
Difference is: 15.
What is the Range of a Linear Function?
Rate of change = change in y / change in x.
The graph for function B is a proportional graph, therefore, rate of change = y/x.
Using a point on the line, (1, 50), rate of change for function B = 50/1 = 50.
Function A is given as y = 35x. Rate of change, is 35.
The difference = 50 - 35 = 15.
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Find the dimensions and volume of the right circular cylinder of maximum volume inscribed in a sphere with a radius of 25 cm.
The dimensions of the circular cylinder of maximum volume inscribed in sphere is r = 20.4 cm , h = 28.86 cm.
What is a sphere ?A sphere is a three dimensional round shaped figure , It has no vertices and the distance form the centre to any point on the sphere is same.
It is given that
A right circular cylinder is inscribed in a sphere
The circular cylinder has the maximum volume
Radius of the sphere is 25 cm.
Dimensions of the cylinder = ?
As it is a right cylinder.
The Pythagoras theorem can be applied
r² + (h/2)² = 25²
r² = 625 - h²/4
volume of the cylinder
= πh(625 - h²/4)
= π(625 h - h³/4)
As the volume is maximum ,
so the derivative of the expression = 0
π(625 - 3h²/4) = 0
so h = 50 /√ 3
so r² = 625 - 2500 / (3 *4 )
r = 20.4 cm
h = 28.86 cm
Therefore the dimensions of the circular cylinder of maximum volume inscribed in a sphere is r = 20.4 cm , h = 28.86 cm.
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the admission ticket to tyler amussement park is $1.25 per person. A total of 815 tickets were sold on saturday. the attendance decreased by 96 on sunday. how much money did the park receive from ticket sales in all?the admission ticket to tyler amussement park is $1.25 per person. A total of 815 tickets were sold on saturday. the attendance decreased by 96 on sunday. how much money did the park receive from ticket sales in all?the admission ticket to tyler amussement park is $1.25 per person. A total of 815 tickets were sold on saturday. the attendance decreased by 96 on sunday. how much money did the park receive from ticket sales in all?
The total revenue for Saturday and Sunday is $1917.50
How much money did the park receive from ticket sales in all?We know that 815 tickets were sold on Saturday, and on Sunday the number of tickets sold decreased by 96.
Then the total number of tickets sold in the two days is:
(815) + (815 - 96) = 1534
And we know that each ticket costs $1.25
Then the total revenue is:
R = $1.25*1534 = $1917.50
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The average waiting time to be seated for dinner at a popular restaurant is 23.8 minutes with a standard deviation of 6 minutes. What is the probability that 20 people will wait less than 21 minutes? Leave your answer exactly as it is taken from the table.
The probability that 20 customers will wait less than 21 minutes to be seated is
Using the normal distribution, it is found that there is a 0.3192 = 31.92% probability that 20 customers will wait an average of less than 21 minutes to be seated.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].The parameters for this problem are given as follows:
[tex]\mu = 23.8, \sigma = 6, n = 20, s = \frac{6}{\sqrt{20}} = 1.3416[/tex]
The probability that 20 customers will wait an average of less than 21 minutes to be seated is the p-value of Z when X = 21, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem:
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{21 - 23.8}{6}[/tex]
Z = -0.47
Z = -0.47 has a p-value of 0.3192.
0.3192 = 31.92% probability that 20 customers will wait an average of less than 21 minutes to be seated.
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Income Statements under Absorption Costing and Variable Costing
Gallatin County Motors Inc. assembles and sells snowmobile engines. The company began operations on July 1 and operated at 100% of capacity during the first month. The following data summarize the results for July:
Sales (19,500 units) $2,145,000
Production costs (25,000 units):
Direct materials $1,017,500
Direct labor 487,500
Variable factory overhead 245,000
Fixed factory overhead 162,500 1,912,500
Selling and administrative expenses:
Variable selling and administrative expenses $296,400
Fixed selling and administrative expenses 114,800 411,200
The Income Statements under Absorption Costing and Variable Costing are as follows:
Absorption Costing Variable Costing
Sales (19,500 units) $2,145,000 $2,145,000
Cost of goods sold $1,491,750 $1,365,000
Gross profit $653,250 $780,000
Selling and administrative expenses:
Fixed factory overhead $162,500
Variable selling and
administrative expenses $296,400 296,400
Fixed selling and
administrative expenses 114,800 411,200 114,800 573,700
Net Income $242,050 $206,300
What is the difference between Absorption Costing and Variable Costing?The difference between Absorption Costing and Variable Costing is that the Ending Inventory costs under Variable Costing include only direct materials, direct labor, and variable factory overhead. Absorption Costing includes all the variable factory costs plus fixed factory overhead (a period cost) in the Ending Inventory costs.
Data and Calculations under Absorption Costing:Sales (19,500 units) $2,145,000
Production costs (25,000 units):
Direct materials $1,017,500
Direct labor 487,500
Variable factory overhead 245,000
Fixed factory overhead 162,500
Total production costs 1,912,500
Cost per unit = $76.50 ($1,912,500/25,000)
Less Ending inventory 420,750 (5,500 x $76.50)
Cost of goods sold $1,491,750
Gross profit
Selling and administrative expenses:
Variable selling and administrative expenses $296,400
Fixed selling and administrative expenses 114,800 411,200
Data and Calculations under Variable Costing:Sales (19,500 units) $2,145,000
Production costs (25,000 units):
Direct materials $1,017,500
Direct labor 487,500
Variable factory overhead 245,000
Total variable production costs 1,750,000
Cost per unit = $70 ($1,750,000/25,000)
Less Ending inventory 385,000 (5,500 x $70)
Cost of goods sold $1,365,000
Gross profit
Selling and administrative expenses:
Variable selling and
administrative expenses $296,400
Fixed factory overhead 162,500
Fixed selling and administrative expenses 114,800 411,200
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The value of n from the set {6, 7, 8, 9} that holds true for 4n − 12 < 2n + 2 is
The value of n that satisfies the inequality is 6.
What is inequality?A statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.
Given:
4n − 12 < 2n + 2
For n= 6
4(6) - 12 = 12
2(6) + 2 = 14
Thus, n=6 satisfies
For n= 7
4(7) - 12 = 16
2(7) + 2 = 16
Thus, n=7 not satisfies
For n=8
4(8) - 12 = 20
2(8) + 2 = 18
Thus, n=8 not satisfies.
For n= 9
4(9) - 12 = 24
2(9) + 2 = 20
Thus, n=9 not satisfies.
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Identify all the inequalities that the graph represents.
X>10 10>x 8x>80 x+1>9 x+1>11
Identify all the inequalities that the graph represents.
How many turning points are in the graph of the polynomial function?
4 turning points
5 turning points
6 turning points
7 turning points
Answer:
There are 5 turning points
Step-by-step explanation:
In 1898, L. J. Bortkiewicz published a book called The Law of Small Numbers, where using data he collected for twenty years, he showed that the number of soldiers killed by horse kicks each year in the Prussian army followed a Poisson distribution with a mean of 0.61. What is the probability that there will be exactly three deaths in two years?
hurry please will pick brainly and step by step appreacite it
Answer:
given : 0.61 per year
formula poisson probability : p(x=k)=xke-x/k!
(a) The parameter λ is the product of the rate per year and the number of years. The number of years is 1 year in this case.
λ=0.61×1=0.61
Evaluate the formula of the Poisson probability at k=0,1:
P(X=0)= 0!
(0.61)
0
e
−0.61
≈0.5434
P(X=1)=
1!
(0.61)
1
e
−0.61
≈0.3314
Add the corresponding probabilities:
P(X≤1)=P(X=0)+P(X=1)=0.5434+0.3114=0.8748
Use the complement rule:
P(X>1)=1−P(X≤1)=1−0.8748=0.1252
Note: The solution in the back of the book is the probability of at least one death instead of more than 1 death, thus the solution in the back of the book is not correct.
Step-by-step explanation:
this is prob wrong so im sorry in advance!
In the card game Set, each card features a number of shapes, with four attributes:
Number: The number of shapes is 1, 2, or 3.
Color: Each shape is red, purple, or green.
Shape: Each shape is oval, diamond, or squiggle.
Shading: Each shape is hollow, shaded, or striped.
There is exactly one card for each possible combination of attributes.
In the game, several of the cards are dealt out, and the goal is to find a set. A set is formed by three cards, where for each attribute, either all three cards are the same, or all three cards are different. When three cards form a set, we can also count the number of attributes for which all three cards are the same.
(a) How many cards are in a complete deck of Set?
(b) How many unique sets are there?
(c) Find the number of sets where all three cards are the same for exactly 0 attributes.
(d) Find the number of sets where all three cards are the same for exactly 1 attribute.
(e) Find the number of sets where all three cards are the same for exactly 2 attributes.
(f) Find the number of sets where all three cards are the same for exactly 3 attributes.
A) The number of cards that are in a complete deck of Set is; 81
B) The number of unique sets are; 36
How to find the combination of a set of cards?a) We are given;
Number of shapes = 1, 2 or 3
Colour = Red, Purple or Green
Shape = Oval, Diamond or Squiggle
Shading = Hollow, Shaded or Striped
Now, since a set is formed by all 3 cards, then we can say that;
Number of cards in a complete deck of set = 3⁴ = 81 cards
(b) Let us first find all sets = 3² * 4 * 3 = 108.
Thus;
Unique sets = 108/3
= 36 unique sets.
(c) There are 3 ways to choose the number of the cards from the given order.
For the second one, there 2 choices, and then there is only 1 choice. Thus; Number of ways to choose the numbers = 3 * 2 * 1 = 6.
For the other attributes;
Number of ways = 6 * 6 * 24 *6 ways.
Now, since the order of cards doesn't matter in a set, then the number of sets where all three cards are the same for exactly 0 attributes is;
(6 * 6 * 24 *6)/3! = 864 sets
(d) If all the colors are the same, then;
Number of sets = 6 * 24 * 6/3! = 144 sets.
If all the numbers are the same, then there are 144 sets which is also same for shapes and shading. Thus;
The number of sets where all three cards are the same for exactly 1 attribute is; 4 * 144 = 576
(e) There are C(4, 2) = 6 ways of choosing two attributes.
For each of the two attributes, there are 3 options.
For the other two attributes, there are 3 ways of assigning the choices. Thus, number of sets = 6*3*3*3*3 = 486 sets.
(f) There are C(4,3) = 4 ways of choosing which attributes are the same. There are 3*3*4 = 36 ways to assign which is which for each of these three attributes, and there are 4 ways to assign the choices for the fourth attribute. Thus;
The number of sets where all three cards are the same for exactly 3 attributes = 4*36*4 = 576 sets.
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What are the vertices of A'B'C if ABC is dilated by a scale factor of 2?
The vertices of A'B'C' if A(0, 10), B(8, 6), C(4, 2) is dilated by a scale factor of 2 are;
C. A'(0, 20), B'(16, 12), C'(8, 4)Which method can be used to find the vertices of A'B'C'?Given that triangle ABC is dilated by a scale factor of 2, we have;
A'B' = 2 × AB
A'C' = 2 × AC
B'C' = 2 × BC
Length of AB = √((8-0)^2 + (6-10)^2) = 4•√5
Length of AC = √((4-0)^2 + (2-10)^2) = 4•√5
Length of BC = √((8-4)^2 + (6-2)^2) = 4•√2
By multiplying the given coordinates by the scale factor, we have;
A' = 2 × (0, 10) = (0, 20)
B' = 2 × (8, 6) = (16, 12)
C' = 2 × (4, 2) = (8, 4)
A'B' = √((16-0)^2 + (12-20)^2) = 8•√5
A'C' = √((8-0)^2 + (4-20)^2) = 8•√5
B'C' = √((16-8)^2 + (12-4)^2) = 8•√2
Therefore when we have;
A'(0, 20), B'(16, 12), C'(8, 4), we get;
A'B' = 2 × ABA'C' = 2 × ACB'C' = 2 × BCThe correct option is therefore;
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PLEASE HELP ME ASAP!!!!
Part A: Identify the diagonals in the parallelogram.
Part B: Determine the value for x and y. Show your work.
Part C: Identify the length of each diagonal. Show your work.
Part A
[tex]\overline{AC}[/tex] and [tex]\overline{BD}[/tex]
Part B
Diagonals of a parallelogram bisect each other, so
[tex]BE=ED \implies 2x+3=3y-4 \implies 3y=2x+7 \implies y=\frac{2}{3}x+\frac{7}{3}\\\\AE=EC \implies y+4=4x-6 \implies y=4x-10[/tex]
Solving by substitution,
[tex]\frac{2}{3}x+\frac{7}{3}=4x-10[/tex]
Multiplying both sides by 3,
[tex]2x+7=12x-30\\\\37=10x\\\\x=3.7[/tex]
So, [tex]y=\frac{2}{3}\left(\frac{37}{10} \right)+\frac{7}{3}=\frac{24}{5}[/tex]
Part C
[tex]BE=ED=2(3.7)+3=10.4\\\\AE=EC=4(3.7)-6=8.8[/tex]
[tex]\therefore BD=2(10.4)=20.8, AC=2(8.8)=17.6[/tex]
What is the least 6 digit multiple of 4 that has all different numbers?
Answer:
We can now take 2 as the third digit, 3 as the fourth digit, 4 as the fifth digit and finally 5 as the sixth digit. Therefore, the smallest 6-digit number having all different digits is 102345.
The smallest 6-digit multiple of 4 with all different numbers is 102,564. This number is obtained by incrementing from 100,000 until finding a divisible number with distinct digits.
A number that is the result of a given number plus another natural number is said to be a multiple of that number.
Since the smallest 6-digit number, is 100,000.
Check if this number is divisible by 4.
In this case, it is not.
Increment the number by 1 to get 100,001.
Repeat step 2. Not divisible by 4.
Increment the number by 1 to get 100,002.
Repeat step 2. Not divisible by 4.
Increment the number by 1 to get 100,003.
Repeat step 2. Not divisible by 4.
Continue this process until you find a number that is divisible by 4 and has all different digits.
After following these steps, we find that the smallest 6-digit multiple of 4 with all different numbers is 102,564.
Hence,
The required number is 102564.
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Find the sum of the first five terms of the geometric sequence: - 1, - 6, - 36
The sum of the first five terms of the geometric sequence is -1555
Sum of geometric sequenceThe formula for calculating the sum of geometric sequence is expressed as:
[tex]S_n=\frac{a(r^n-1)}{r-1}[/tex]
where
r is the common ratio = 6/1 = 6
a is the first term = -1
n = 5 (number of terms)
Substitute
[tex]S_5=\frac{-1(6^5-1)}{6-1}\\S_5=\frac{-7776+1}{5}\\S_5=-1555[/tex]
Hence the sum of the first five terms of the geometric sequence is -1555
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Find sin(c)
1.08
0.38
0.92
0.42
The measure of sin C from the figure is 0.92
Sine-tan-cos identityThese identity is used to determine the measure of sides and angles of a triangle.
From the triangle
Opposite side to m<C = 12
'Hypotenuse = 13
Using the expression
sinC = BC/ACC
sinC = 12/13
sinC = 0.92
Hence the measure of sin C from the figure is 0.92
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Question pictured below
Answer:
The third answer is correct.
Step-by-step explanation:
6 x 3-2x2+9x-8+4x3-2x+6
Combine like terms: [tex]6x^{3}[/tex] and [tex]4x^{3}[/tex] make [tex]10x^{3}[/tex]. At that point, disentangle constants: -8 + 6 rise to -2. Result:[tex]10x^{3} - 2x^{2} + 9x - 2[/tex].
How to simplify the expressionTo simplify the given expression, take after the arrangement of operations (PEMDAS/BODMAS):
Perform operations inside parentheses/brackets.Assess examples (powers).Perform increase and division from cleared out to right.Perform expansion and subtraction from cleared out to right.Given expression: [tex]6x^{3} - 2x^{2} + 9x - 8 + 4x^{3} - 2x + 6[/tex]
Step 1: Combine like terms (terms with the same variable and example):
[tex]6x^{3} + 4x^{3} = 10x^{3}[/tex]
Step 2: Combine the steady terms:
-8 + 6 = -2
The expression presently gets to be:
[tex]10x^{3} - 2x^{2} + 9x - 2[/tex]
So, the disentangled expression is [tex]10x^{3} - 2x^[2} + 9x - 2.[/tex]
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The complete question:
Simplify the expression:
6 x 3-2x2+9x-8+4x3-2x+6
Three randomly selected households are surveyed. the numbers of people in the households are 1,3,8 assume that samples of size n =2 are randomly selelcted with replacement from the population of 1,3,8. Listed below are the nine different sample 3,5 3,5 3,10,5,3 5,5 5,10 10,3 10,5 10,10 find the variance of each of the nine samples then summerize the sampling distribution of the variances in the format of a table representing the probability distribution of the distinct variance values
The estimator sample proportion is mathematically unbiased
What is the estimator sample proportion?Generally, the equation for is mathematically given as
Population sample \mu=1.3
The sample to sample proprotion table will have
first column= 3,5 3,5 3,10,5,3 5,5 5,10 10,3 10,5 10,10
Second coumn= 0,0,0.5,0,0,0.5,05,0.5, total 3
The probability distribution of the distinct variance values table will have
p row=0,0.5,1, Total
probability row= 4/9, 4/9, 1/9, 1
In conclusion, The mean sample
x=3/9
x=1.3
Where
population sample \mu=1.3
\mu= x
Therefore the estimator sample proportion is unbiased for population mean
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Graph the image using the given transformation
1) First find the coordinates of the shape:
G(-1, -2), F(-1, -1), E(2,2), D(2, -2)
2)It asked for dilation of 2 about the origin.
*What is dilation?
Dilation is the expanding/enlarging a transformation by a scale factor
Now we multiply all the coordinates with the factor of 2
G(-1*2, -2*2) = G'(-2, -4)
F(-1*2, -1*2) = F'(-2, -2)
E(2*2, 2*2) = E'(4, 4)
D(2*2, -2*2) = D'(4, -4)
3) Now plot these points and graph the transformation:
Assume a population of 40, 45, 47, and 53. Assume that samples of size n=2 are randomly selected with replacement from the population. Listed below are the sixteen different samples. Complete parts (a) through (c).
40,40 40,45 40,47 40,53 45,40 45,45 45,47 45,53
47,40 47,45 47,47 47,53 53,40 53,45 53,47 53,53
a. Find the median of each of the sixteen samples, then summarize the sampling distribution of the medians in the format of a table representing the probability distribution of the distinct median values. Use ascending order of the sample medians.
The median of each of the sixteen samples, the sampling distribution of the medians are shown in the table.
What is probability?It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.
We have data:
40,40 40,45 40,47 40,53 45,40 45,45 45,47 45,53
47,40 47,45 47,47 47,53 53,40 53,45 53,47 53,53
We can find the sample mean, median, and probability:
sample median probability sample median probability
40 1/16 46.5 2/16
42.5 2/16 47 1/16
43.5 2/16 49 2/16
45 1/16 50 2/16
46 2/16 53 1/16
Thus, the median of each of the sixteen samples, the sampling distribution of the medians are shown in the table.
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In the plane figure, only downward motion (movement leaving you relatively lower than where you were) is allowed. Find the total number of paths from A to B.
Plane figures are shapes with straight sides. Considering the movement to be lower than the initial path, there are eleven (11) paths from A to B.
A plane figure is given shape with straight sides. And these sides connect each edge of the figure one to another. Examples are triangles, quadrilaterals, polygons, etc.
A path is a connection or link between two reference points. This could be a footpath or a motorable path or other forms of the path.
Considering the given plane figure in the question, it can be observed that the total number of paths from A to B with respect to the given condition is eleven.
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Identify the area of the figure
Answer:
184cm²
Step-by-step explanation:
[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]
Area = 184 cm²[tex]\textsf{ \underline{\underline{Steps to solve the problem} }:}[/tex]
Divide the figure into two parts,
Part 1 : rectangle with, width = 7 cm and length = 20 cm
Area of part 1 :
[tex] \qquad❖ \: \sf \:20 \times 7[/tex]
[tex] \qquad❖ \: \sf \:140 \: \: {cm}^{2} [/tex]
Part 2 : Trapezoid with parallel sides - 7 cm and 4 cm,and height 8 cm
Area of part 2 :
[tex] \qquad❖ \: \sf \: \cfrac{1}{2} \cdot (7 + 4) \sdot(8)[/tex]
[tex] \qquad❖ \: \sf \:11 \times 4[/tex]
[tex] \qquad❖ \: \sf \:44 \: \: {cm}^{2} [/tex]
Area of whole figure =Area of part 1 + part 2
[tex] \qquad❖ \: \sf \:140 + 44 \: \: {cm}^{2} [/tex]
[tex] \qquad \large \sf {Conclusion} : [/tex]
[tex] \qquad❖ \: \sf \:area =184\: \: {cm}^{2} [/tex]
Write an equation of the line that passes through the point (5, 6) with slope 3.
Answer:
the answer to that would be y=3x-9
The city council of Pine Bluffs is considering increasing the number of police in an effort to reduce crime. Before making a final decision, the council asked the chief of police to survey other cities of similar size to determine the relationship between the number of police and the number of crimes reported. The chief gathered the following sample information.
City Police Number of Crimes City Police Number of Crimes
Oxford 12 17 Holgate 15 6
Starksville 15 13 Carey 8 18
Danville 20 6 Whistler 6 21
Athens 22 7 Woodville 17 7
Click here for the Excel Data File
a. Determine the regression equation. (Negative amounts should be indicated by a minus sign. Round your answers to 4 decimal places.)
The regression equation is calculated as: ŷ = -0.99299X + 26.39918
How to solve for the regression equationWe have these data for the x axis
12 15 20 22 15 8 6 17
These are the values for the y axis
17 15 6 7 6 18 21 7
Sum of X = 115
Sum of Y = 97
Mean X = 14.375
Mean Y = 12.125
Sum of squares (SSX) = 213.875
Sum of products (SP) = -212.375
Regression Equation = ŷ = bX + a
b = SP/SSX = -212.38/213.88 = -0.99299
a = MY - bMX = 12.13 - (-0.99*14.38) = 26.39918
ŷ = -0.99299X + 26.39918
These values where inputted into a regression analysis calculator and the output is ŷ = -0.99299X + 26.39918
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The Smiths have a pool that is 20 feet by 35 feet. A 5 foot wide deck completely surrounds the pool. The average depth of the pool is 6 feet. How much surface area is covered by the proposed pool deck?
Answer:
550 square feet
Step-by-step explanation:
There are 4 areas where the pool deck is situated on:
Top, Left, Right, and Bottom of the pool.
So if the deck is 5 feet wide:
Top = (35 feet * 5 feet) = 175
Bottom = (35 feet * 5 feet) = 175
Left = (20 feet * 5 feet) = 100
Right = (20 feet * 5 feet) = 100
175 + 175 + 100 + 100 = 550 square feet
a jar contains groundnuts and beans in a ratio of 1:1.There are 300 bean seeds in the jar.How many groundnuts seeds are in the jar?
Answer:
300
Step-by-step explanation:
if its 1:1 ratio, then its the same and so if there 300 bean seeds, there has to be 300 groundnut seeds
Write the domain and range of the function using interval notation.
A graph of an upward-facing parabola with endpoints (2,-2) and (6,-2). Both endpoints are solid circles. The vertex is (4,-6).
The domain is [2,6] and the range is [-2,0].
What is the Domain and Range of a Function?The Domain is all the possible input values to the function, while the range is all the possible values a function can have as an output.
The parabola has endpoints of (2,-2) and (6,-2).
The vertex is (4,-6)
The domain is [2,6]
The range is [-2,0]
Therefore, the domain is [2,6] and the range is [-2,0].
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The price of tickets for the dance was 1 ticket for $5 (for individuals) or 2 tickets for $8 (for couples). She looked inside the cash box and found $200 and ticket stubs for the 47 students in attendance. Does the dollar belong inside the cash box or not? Explain your reasoning.
The $1 belongs in the box.
What are the equations that represent the question assuming the $1 does not belong in the box?s + c = 47 equation 1
5s + 4c = 200 equation 2
How many singles and couples bought the ticket assuming that the $1 does not belong in the box?Multiply equation 1 by 5
5s + 5c = 235
Subtract equation 2 from equation 3
c = 35
Subtract 35 from 47
c = 47 - 35 = 12
35 couples tickets and 12 individual tickets were sold. This is not possible since the couples tickets were sold in 2.
What are the linear equations that represent the question if the 1 dollar belonged in the box?s + c = 47 equation 1
5s + 4c = 201 equation 2
How many couples tickets were sold?Multiply equation 1 by 5
5s + 5c = 235
Subtract equation 2 from equation 3
c = 34
34 is divisible by 2 so the $1 belongs in the box.
Here is the complete question:
Nola was selling tickets at the high school dance. At the end of the evening, she picked up the cash box and noticed a dollar lying on the floor next to it. She said,
I wonder whether the dollar belongs inside the cash box or not.
The price of tickets for the dance was 1 ticket for $5 (for individuals) or 2 tickets for $8 (for couples). She looked inside the cash box and found $200 and ticket stubs for the 47 students in attendance. Does the dollar belong inside the cash box or not?
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andrew has a cell phone plan that provides 300 free minutes each month fo a flat rate of $19 . for any minutes over 300, andrew is charged 0.39 per minute
The precise equation that represents the situation is as follows:
$19, x ≤ 300x > 300, f(x) = 19 + 0.39(x - 300)How to represent an equation?His cell phone plan provides 300 free minutes each month for a flat rate of $19.
let
x = number of minutes used
Therefore,
$19, x ≤ 300
For any minutes over 300, Andrew is charged 0.39 per minute.
Therefore,
if x > 300
f(x) = 19 + 0.39(x - 300)
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A carpenter purchased 60 ft of redwood and 80 ft of pine for a total cost of $308. A second purchase, at the same prices, included 90 ft of redwood and 70 ft of pine for a total cost of $397. Find the cost per foot of redwood and of pine?
Answer:
Price of redwood= $3.4
Pine =$1.3