Answers
Answer:
The horizontal translation of the function is 3 units to the right (from the parent function). Therefore, we subtract 3 from the x-value of the function.
The equation of the graphed function in vertex form is:
[tex]\boxed{y = (x - 3)^2- 2}[/tex]
Step-by-step explanation:
The given graph shows a parabola that opens upwards.
Therefore, the equation for this function is a quadratic equation with a positive leading coefficient.
The vertex of a parabola is the minimum point of a parabola that opens upwards, or the maximum point of a parabola that opens downwards.
From inspection of the given graph, the vertex of the function is (3, -2).
The parent function of a parabola that opens upwards is y = x². This has a vertex at (0, 0).
Therefore, given the vertex of the given function is (3, -2), the parent function has been translated 3 units right and 2 units down.
For a horizontal translation to the right, we subtract the number of units from the x-value of the function.
For a vertical translation down, we subtract the number of units from the function.
Therefore, a translation of 3 units right and 2 units down from the parent function y = x² is:
[tex]\boxed{y = (x - 3)^2- 2}[/tex]
This function is written in vertex form.
To write the equation in standard form, expand the brackets and simplify:
[tex]\implies y=(x-3)(x-3)-2[/tex]
[tex]\implies y=x^2-3x-3x+9-2[/tex]
[tex]\implies y=x^2-6x+7[/tex]
[tex]\hrulefill[/tex]
Additional comments
The vertex form of a quadratic equation is y = a(x - h)² + k, where (h, k) is the vertex. Therefore, the "k" value refers to the y-value, which is the vertical translation from the parent function.
As your question refers to the "k" value for the horizontal translation, we assume that it is not referring to the k-value of the vertex form.
Related Questions
how many different samples of size 4 (without replacement) can be taken from a finite population of size 10? a. 10,000 b. 210 c. 40 d. 5,040
Answers
Answer:
Step-by-step explanation:(10,4)=10.9.8.7/4.3.2.1=210
The number of different samples of size 4 that can be taken from a finite population of size 10, without replacement, is 210.
The formula for calculating the number of different samples of size r that can be taken from a finite population of size n without replacement is given by the combination formula: nCr = n! / (r! * (n-r)!), where n! denotes n factorial (n × (n-1) × (n-2) × … × 1).
In this case, we want to find the number of different samples of size 4 that can be taken from a population of size 10, so we use the combination formula with n=10 and r=4:
10C4 = 10! / (4! × (10-4)!) = (10987) / (4321) = 210
Therefore, there are 210 different samples of size 4 that can be taken from a population of size 10 without replacement.
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the name of a function identifies it and must be used when the function is called. group of answer choices true false
Answers
The name of a function identifies it and must be used when the function is called - True
A function serves as its unique identifier and must be used when calling the function. A function in a computer language is given a name when it is created so that the user can invoke it later on in their particular code. The function is identified by its name which also serves to set it apart from similar functions with potentially different titles.
Depending on its definition, the parentheses that come after the function name may or may not contain arguments or parameters when calling a function. A function is called, executed, and its outcomes are returned to the caller code. Due to the reason that it is a crucial part of the function's definition, its name must always be employed when a function is called.
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Find the value of x
3 : 25 = x : 75
Answers
Answer:
Step-by-step explanation:
x = 9
how many ways are there to write a 3 digit positive number integer using the digits 1,3,5,7, and 9 if no digit is used more than once
Answers
Answer: 60
Step-by-step explanation:
To form a 3-digit positive integer using the digits 1, 3, 5, 7, and 9 without repeating any digit, we can use the counting principle.
There are 5 choices for the first digit (hundreds place) since any of the 5 digits (1, 3, 5, 7, or 9) can be placed there.
5 (choices for the first digit) × 4 (choices for the second digit) × 3 (choices for the third digit) = 60
There are 60 ways to write a 3-digit positive integer using the digits 1, 3, 5, 7, and 9 without using any digit more than once.
A 12 ft ladder is leaning against a building. The top of the ladder is 7 ft above the ground.
How far from the building is the ladder?
Answers
Answer:
The ladder is approximately 9.75ft from the building
Step-by-step explanation:
We can use Pythagoras theorem:
[tex]c^2=a^2+b^2[/tex]
where:
[tex]c =[/tex] it's the size of the ladder, 12ft
[tex]b=[/tex] it's the top of the ladder above the ground, 7ft
so:
[tex]c^2-b^2=a^2\\\implies a=\sqrt{c^2-b^2}\\ a=\sqrt{(12)^2-(7)^2}\\a=\sqrt{95}\\ a\approx 9.75ft[/tex]
[tex]\text{-B$\mathfrak{randon}$VN}[/tex]
The
dimensions
(in inches)
of a rectangular
tile can be
modeled by A(x)=x² + 5
and B(x) = 2x - 1.
a. Find (A + B)(x) and
(AB)(x).
Answers
The composite functions are (A + B)(x) = x² + 2x + 4. and (AB)(x) = 2x³ - x² + 10x - 5.
Evaluating the composite functionsTo find (A + B)(x), we add the two functions A(x) and B(x):
(A + B)(x) = A(x) + B(x)
So, we have
= x² + 5 + 2x - 1 (substituting the given expressions for A(x) and B(x))
= x² + 2x + 4
Therefore, (A + B)(x) = x² + 2x + 4.
To find (AB)(x), we multiply the two functions A(x) and B(x):
(AB)(x) = A(x)B(x)
= (x² + 5)(2x - 1) (substituting the given expressions for A(x) and B(x))
= 2x³ - x² + 10x - 5
Therefore, (AB)(x) = 2x³ - x² + 10x - 5.
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Determine the equation of the circle with radius 8 and center (-2,9).
Answers
According to the solution we have come to find that, The equation of the circle with radius 8 and center (-2,9) is [tex](x + 2)^2 + (y - 9)^2 = 64.[/tex]
What is radius?
Radius is a straight line segment that joins the center of a circle to any point on its circumference. It is half of the diameter of the circle. The length of the radius is denoted by the letter "r".
The equation of a circle with center (a,b) and radius r is given by:
[tex](x - a)^2 + (y - b)^2 = r^2[/tex]
Substituting the given values, we have:
[tex](x - (-2))^2 + (y - 9)^2 = 8^2[/tex]
Simplifying, we get:
[tex](x + 2)^2 + (y - 9)^2 = 64[/tex]
Therefore, the equation of the circle with radius 8 and center (-2,9) is [tex](x + 2)^2 + (y - 9)^2 = 64.[/tex]
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A quadratic function has the equation y=a (x +6)(x -2)
(3,36), and passes through the point
. What is the value of
?
Answers
We are given that the quadratic function has the equation:
y = a(x + 6)(x - 2)
To find the value of a, we can use the fact that the function passes through the point (3, 36). This means that when x = 3, y = 36. Substituting these values into the equation, we get:
36 = a(3 + 6)(3 - 2)
36 = 9a
a = 4
Therefore, the value of a is 4.
kevin is building a dog house. for the trim around the roof, he bought 4 pieces of wood for a total of $6.52 how much was each piece of trim
Answers
The cost of each piece of trim is $1.63
To find the cost of one piece of trim, we can use the unitary method, which involves dividing the total cost by the number of pieces. In this case, we can use the following formula
Cost of one piece of trim = Total cost / Number of pieces
We know that Kevin bought 4 pieces of trim for a total of $6.52, so we can substitute these values into the formula
Cost of one piece of trim = $6.52 / 4
Simplifying this expression, we get
Cost of one piece of trim = $ 1.63
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in a hypothesis test, what does it mean to say that the null hypothesis was rejected? rejecting the null hypothesis means that the sample data provide convincing evidence against the ---select--- hypothesis and in favor of the ---select--- hypothesis.
Answers
When it is said that the null hypothesis was rejected in a hypothesis test, it means that the sample data has given strong evidence against the null hypothesis and in favor of the alternative hypothesis.
What is a hypothesis?
A hypothesis is a statement that proposes a potential relationship between two variables. It's a conjecture about the nature of the relationship between the two variables that a researcher might test.In hypothesis testing, the null hypothesis is always the hypothesis being tested. A null hypothesis is a statement that assumes there is no relationship between the variables being studied. It is denoted by H0.The alternative hypothesis is a statement that negates the null hypothesis. It suggests that there is a relationship between the variables being studied. It is denoted by Ha.When it is said that the null hypothesis was rejected in a hypothesis test, it means that the sample data has given strong evidence against the null hypothesis and in favor of the alternative hypothesis. As a result, the researcher may conclude that the alternative hypothesis is true with a certain level of confidence.If the null hypothesis is not rejected in a hypothesis test, it means that there is insufficient evidence to support the alternative hypothesis. As a result, the researcher cannot conclude that the alternative hypothesis is true with a certain level of confidence.
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graph f(x) = x^2 and g(x) = 2^x for x
Answers
Answer:
Step-by-step explanation:
if club members charge $3 admission to a classic car show, 1000 people will attend, and for each $1 increase in price, 100 fewer people will attend. what price will give the maximum revenue for the show? $ per ticket find the maximum revenue. $
Answers
the price per ticket that will give maximum revenue is $6.5, and the maximum revenue in dollars per ticket is $2.925.
As given,If club members charge $3 admission to a classic car show, 1000 people will attend, and for each $1 increase in price, 100 fewer people will attend.
We need to determine the price that will give the maximum revenue for the show and the maximum revenue in dollars per ticket.
Let the number of $1 increases in price be x. Then the number of people attending will be (1000 - 100x), and the price per ticket will be $(3 + x).The total revenue will be:
Revenue = Price × Quantity= $(3 + x) × (1000 - 100x)= $3000 - $100(x^2 + 7x)
The revenue function is quadratic, with the coefficient of the x^2 term being negative. Hence the graph of the function is a parabola which opens downwards, with a maximum at the vertex of the parabola.To find the value of x that will give maximum revenue, we first find the x-coordinate of the vertex.
For a quadratic function of the form f(x) = ax^2 + bx + c, the x-coordinate of the vertex is given by x = -b / (2a).In this case, a = -100, and b = -100(7) = -700. Therefore, the x-coordinate of the vertex is:x = -b / (2a)= 7/2= 3.5
Therefore, the value of x that will give maximum revenue is 3.5. Substituting this value of x in the revenue function, we get:Revenue = $3000 - $100(x^2 + 7x)= $3000 - $100(3.5^2 + 7(3.5))= $2925
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Can someone please help thank you, I will give brainliest to the first person that answers
Answers
The following are answers to the probability questions;
1. 2/3 or 0.67 or 0.7 chances
2. 2/3 or 0.67 or 0.7 chances
3. No probability is greater than the other. They are both 2/3.
4. There are 36 possible outcomes
5. 3/36 or 1/12
What is probability?
Probability is a measure of the likelihood of an event occurring. It is expressed as a number between 0 and 1, with 0 indicating that the event is impossible and 1 indicating that the event is certain.
To calculate the probability of choosing a password with no Y's and With no O's we need to consider all the combinations that do not have Y and O. There are 20 combinations with no Y's and 20 combinations with no O.
Therefore, the probability of choosing a password with no Y's or O's are 20 each. When then calculate by sating
20/30, which simplifies to 2/3 or 0.67.
The number of possible outcomes for a single number cube is as follows;
1 2 3 4 5 6
1 1,1 1,2 1,3 1,4 1,5 1,6
2 2,1 2,2 2,3 2,4 2,5 2,6
3 3,1 3,2 3,3 3,4 3,5 3,6
4 4,1 4,2 4,3 4,4 4,5 4,6
5 5,1 5,2 5,3 5,4 5,5 5,6
6 6,1 6,2 6,3 6,4 6,5 6,6
In total, there are 36 combinations.
! There are three ways to obtain a sum of 10: rolling a 4 and a 6, rolling a 6 and a 4, or rolling two 5's. Since there are 36 possible outcomes in total (as we determined earlier), the probability of rolling two numbers that have a sum equal to 10 is:
P(sum of 10) = number of outcomes that add up to 10 / total number of possible outcomes
P(sum of 10) = 3 / 36
P(sum of 10) = 1/12
So the probability of rolling two numbers that add up to 10 is 1/12.
The answers provided is based on the full questions below as seen in the picture;
12. Higher Order Thinking The table shows the sample space of picking a 2-character password using the letters Y, B, R, O, G, and P. If double letters are not allowed, what is the probability of choosing a password with no Y's? With no O's? Is one probability greater than the other? Explain.
Possible Combinations
Y, B B, R R, O O, G G, P P. Y
Y, R B, O R, G O, P G, Y P, B
Y, O B, G R, P O, Y G, B P, R
Y, G B, P R, Y O, B G, R P, O
Y, P B, Y R, B O, R G, O P,G
13. A single number cube is rolled twice.
PART A
Determine the number of possible outcomes. Explain how you know you have found all the possible outcomes.
PART B
Find the probability of rolling two numbers that have a sum equal to 10.
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Find the area and perimeter
Answers
Answer:
A=240 P=64
Step-by-step explanation:
A=240 because you take lxw and that gives you the answer
P=64 because you just add 12+12+10+10
Answer: The area is 240 and the perimeter is 64
Step-by-step explanation:
To get the area you need to do 20 x 12 = 240
And to get the perimeter you need to add up all the sides;
20 + 20 + 12 + 12 = 64
All of the quadrilaterals in the shape below are squares. Find the area of the shaded
region.
Answers
To find the area of the shaded region subtract the unshaded region from the total area, so we got 87.
What are the square area formulae?Square Area equals Side x Side. The square's size is therefore equal to side square units. and a square's circumference equals four side units.
To find the area of the shaded region first we need to find the sum of the area of all quadrilaterals and then subtract the area of the unshaded region.
Area of first quadrilateral A1 = [tex]16^{2}[/tex] = 256
Area of first quadrilateral A2 = [tex]3^{2}[/tex] = 9
Area of first quadrilateral A3 = [tex]3^{2}[/tex] = 9
Area of first quadrilateral A4 = [tex]19^{2}[/tex] = 361
To find the area of the shaded region subtract the unshaded region from the total area = Area of first quadrilateral A4 - (Area of first quadrilateral A1 + Area of first quadrilateral A2 + Area of first quadrilateral A3)
= 361 - (9 + 9 + 256)
=87
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hey!!!!! i need help asap! assignment due in 30 minutes
Answers
Answer:
x ≈ 19,47°
Step-by-step explanation:
Use trigonometry:
[tex] \sin(∠cab) = \frac{cb}{ab} [/tex]
[tex] \sin(x°) = \frac{2}{6} [/tex]
[tex]x ≈19.47°[/tex]
the earths diameter is approzimentley 13000km find the distance around the equator
Answers
The distance around the equator is 40,820 km, when the Earth's diameter is approximately 13000km. The distance around the Earth is the circumference.
Why are Earth's distances significant to astronomers?The Earth is nearly a perfect sphere, but not quite. Astronomers utilized the diameter of the Earth as their primary measuring tool to gauge the extent of the solar system during the 18th and 19th centuries. Today's astronomers typically don't need to be aware of the Earth's size for their regular research tasks.
Nonetheless, the Earth's diameter continues to be the starting point for us, the inhabitants of this planet, in our quest to comprehend the cosmic distance scale. Eratosthenes measured the polar radius, and the number he obtained using the conversion of 0.15 km/stadium sits halfway between the polar and equatorial values.
Given:
Diameter = 13,000 km
Circumference = pi x diameter
Circumference = 3.14 x 13,000 = 40,820 km
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Rua and Liz have a bag of 24 cherries. Liz keeps most for herself, but gives some to Rua. He complained, so she gave him five more. She then had one Cherry fewer than 1.5 times the number of cherries that Rua had. Write an equation and solve it to find how many cherries she gave to Rua at the start.
Answers
Answer:
8 cherries
Step-by-step explanation:
Let r represent the number of cherries Rua was given
24 - r - 5 = 1.5r - 1
Simplify and solve for r.
19 - r = 1.5r - 1
-2.5r = -20
r = 8
So Liz gave Rua 8 cherries at the start.
guy makes a drink by mixing apple juice and water in the ratio 1:4 kim makes a drink by mixing apple juice and water in the ratio 2:7 who has the drink with the higher proportion of apple juice?
Answers
The second guy‘s drink has a ratio of 2:7
1:4 2:7 = 1/4, 2/7
LCM of 4 and 7 = 28
1/4 -> 7/28
2/7 = 8/28
Answer : The second guy’s drink has the higher proportion of apple juice (8/28)
solve the inequality 4x - 9 > 23
Answers
Add 9 to both sides:
\left(4~x-9\right)+9=23+9
Simplify the arithmetic:
4x=23+9
Simplify the arithmetic:
4x=32
Answer :8
an urn contains 1 green ball, 1 red ball, 1 yellow ball and 1 white ball. i draw 3 balls with replacement. what is the probability that exactly two balls are of the same color?
Answers
The probability that exactly two balls are of the same color when drawing 3 balls with replacement from an urn containing 1 green ball, 1 red ball, 1 yellow ball and 1 white ball is 4/16 or 1/4.
There are three ways to draw two balls of the same color: two green balls and one of any other color, two red balls and one of any other color, or two yellow balls and one of any other color. Each of these ways can occur in 4 different orders (e.g. GGR, GRG, RGG, etc.) for a total of 12 possible outcomes. The probability of each of these outcomes is (1/4)^3 = 1/64. Therefore, the probability of exactly two balls being of the same color is 12/64 or simplified to 3/16, which is equivalent to 1/4.
Therefore, the probability of exactly two balls being of the same color when drawing 3 balls with replacement from an urn containing 1 green ball, 1 red ball, 1 yellow ball and 1 white ball is 1/4.
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A pizzeria charges $3.50 for a slice of pizza and $1.75 for a bottle of soda. Write an equation that models the number of slices of pizza(p) and bottles that can be purchased for $35.00.
WILL GIVE BRAINLIEST
Answers
Answer:
A
Step-by-step explanation:
If bottles of soda are marked S, and one bottle costs $1,75
And slices of pizza - P, and one slice costs $3,5
Then the equation would be:
3,50p + 1,75s = 35,00
The points N
(
6
,
−
3
)
(6,−3), O
(
0
,
−
1
)
(0,−1), and P
(
2
,
5
)
(2,5) form a triangle. Plot the points then click the "Graph Triangle" button.
Answers
Answer:
Step-by-step explanation:
The first number within the the x axis.
The second number is the y axis.
the point you're looking is where they both intersect,
Do that for the 3 points, and you get 3 dots.
Make a line connecting each other in order.
And you made a shape.
Happy Solving
suppose that, of women who undergo routine screening, 1/101 have breast cancer. of the women who undergo screening and do have breast cancer, 80% will have a positive test. of the women who undergo screening but don't have breast cancer, only 5% have a positive test. a woman of this age undergoes routine screening and has a positive test. what is the probability that she has breast cancer? give your answer as a numerical value between 0 and 1, to three decimal places. (do not give it as odds, a fraction, or a percentage!)
Answers
Answer:
The probability that she has breast cancer if she gives a positive test result is P=0.16
Step-by-step explanation:
And according to the Bayes theorem I got 0.16
The probability that the woman who underwent routine screening and has a positive test has breast cancer is 0.017.
Let A denote the event that the woman has breast cancer, and let B denote the event that she has a positive test result. Then we need to find P(A|B), the probability that A occurs given that B has occurred. By Bayes' theorem, we have:
P(A|B) = P(B|A)P(A) / [P(B|A)P(A) + P(B|not A)P(not A)]
where P(not A) = 1 - P(A) is the probability that the woman does not have breast cancer.
From the problem statement, we have:
P(A) = 1/101, P(B|A) = 0.8, and P(B|not A) = 0.05.
Therefore,
P(not A) = 100/101,
and
P(A|B) = (0.8 x 1/101) / [(0.8 x 1/101) + (0.05 x 100/101)] = 0.017 (to three decimal places).
Therefore, the probability that the woman who underwent routine screening and has a positive test has breast cancer is 0.017.
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The equation for the line of fit shown is y = 8.2x + 25, where x
represents the number of minutes the water has been heated and y represents the temperature of the water.
Based on the equation for the line of fit, what will be the estimated temperature of the water, to the tenth of a degree, when it has been heated for 8 min?
Answers
Answer:
90.6°
Step-by-step explanation:
It is given that x represents the number of minutes. You are solving for 8 minutes. Therefore, plug in 8 for x in the given equation, and simplify:
[tex]y = 8.2x + 25\\y = 8.2(8) + 25[/tex]
Simplify. Remember to follow PEMDAS. PEMDAS is the order of operations and stands for:
Parenthesis
Exponent (& Root)
Multiplication
Division
Addition
Subtraction
~
First, multiply 8.2 with 8:
[tex]y = (8.2 * 8) + 25\\y = (65.6) + 25\\[/tex]
Next, add:
[tex]y = 65.6 + 25\\y = 90.6[/tex]
90.6 is your answer.
~
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Can someone please help
Answers
The total possible outcomes are 36 and the probability of rolling a 5 and a 6 is 2.78 approximately.
What is dice?
Dice are small objects with different numbers of dots or pips on each side used in games of chance or strategy. Most commonly, dice are cubes with each of the six faces marked with a different number of pips from one to six. When rolled, the number that appears on the top face of the die is used to determine the outcome of the game or the action of the player.
Dice are used in a wide variety of games, including board games, tabletop games, role-playing games, and gambling games. They can also be used for randomization in decision-making or statistical analysis. Some games use dice with more or less than six sides, with various shapes and markings, or even electronic versions that simulate rolling.
When rolling two six-sided dice, the total number of possible outcomes is 6 x 6 = 36, as there are 6 possible outcomes for each die.
To determine the probability of rolling a 5 and a 6, we first need to determine the number of ways this outcome can occur. There is only one way to roll a 5 and a 6, which is to have one die show a 5 and the other die show a 6.
So, the probability of rolling a 5 and a 6 is
P(rolling a 5 and a 6) = number of ways to roll a 5 and a 6 / total number of possible outcomes
= 1 / 36
Therefore, the probability of rolling a 5 and a 6 is 1/36, or approximately 0.0278, or about 2.78%.
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Identify the combination of angle measures that could form a triangle. (1 point)
O 40,55", and 95°
O 25°, 65°, and 90°
O 30,75°, and 85°
O 45,65", and 75"
Please help I am so confused
Answers
Answer:
25°, 65°, and 90°
Step-by-step explanation:
To form a triangle the 3 angles must sum to 180 degrees.
at a price of $7.75 per ticket, a musical theater group can fill every seat in their 1200 seat performance hall. for every additional dollar charged for admission, the number of tickets sold drops by 50. a) what ticket price maximizes revenue? round your answer to the nearest cent.
Answers
The musical theater group should charge $14.25 per ticket to maximize revenue. To find the ticket price that maximizes revenue, we need to determine the revenue function and then differentiate it with respect to the ticket price to find the critical points.
We can then evaluate the revenue at these points to determine the maximum. Let x be the number of dollars charged for admission above the base price of $7.75, and let y be the number of tickets sold at that price. Then, the revenue function is given by:
R(x) = (1200 - 50x)(7.75 + x)
Expanding this expression, we get:
R(x) = 9300 + 650x - 50x^2
To find the ticket price that maximizes revenue, we need to find the critical points of the revenue function. We can do this by differentiating the revenue function with respect to x and setting the derivative equal to zero:
R'(x) = 650 - 100x = 0
Solving for x, we get:
x = 6.5
This means that the additional charge above the base price that maximizes revenue is $6.50. Therefore, the ticket price that maximizes revenue is:
7.75 + 6.50 = $14.25
So, the musical theater group should charge $14.25 per ticket to maximize revenue.
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Two observers are 500 ft apart on opposite sides of a
flagpole. The angles of elevation from the observers to
the top of the pole are 16° and 19° Find the height of the
flagpole.
Answers
Nikki used the calculations shown to determine whether a carton of 12 eggs or a carton of 18 eggs was the better buy.
A carton of 12 eggs cost $2.39 , and a carton of 18 eggs cost $3.39 .
Unit price of the 12 -egg carton = ($2.39)(12 eggs) = $28.68 per egg
Unit price of the 18 -egg carton = ($3.39)(18 eggs) = $61.02 per egg
The 12 -egg carton has the lower unit cost, so it is the better buy.
What was her first error?
Answers
Answer:
She was supposed to DIVIDE the amount of money by the amount of eggs in the carton.
Step-by-step explanation:
12 egg carton = $2.40, 1 egg = $2.40 ÷ 12 = 0.2c
18 egg carton = $3.40, 1 egg = $3.40 ÷ 18 = 0.188 (1.9)
The 18 egg carton was more affordable by about 1.22 cents. Nikki was supposed to divide the amount of money it was worth by the quantity in it.