The probability that the second crayon drawn is blue and the first crayon drawn is blue is 1/28.
To solve this problem, we can use the conditional probability formula:
P(A and B) = P(B|A) * P(A)
where:
P(A and B) is the probability that both events A and B occur
P(B|A) is the probability of event B given that event A has already occurred
P(A) is the probability of event A occurring
In this case, we want to find the probability of selecting a blue crayon on the second draw given that the first crayon selected was blue. So we have:
P(the second crayon is blue and the first crayon is blue) = P(blue on the second draw | blue on the first draw) * P(blue on the first draw)
To find each of these probabilities, we can start by calculating the total number of possible outcomes:
Total number of outcomes = 8 crayons in the box
Next, we need to find the probability of selecting a blue crayon on the first draw:
P(blue on the first draw) = 2/8 = 1/4
After the first blue crayon has been set aside, there are only 7 crayons left in the box, so the probability of selecting a blue crayon on the second draw given that the first crayon was blue is:
P(blue on the second draw | blue on the first draw) = 1/7
Putting it all together:
P(the second crayon is blue and the first crayon is blue) = P(blue on the second draw | blue on the first draw) * P(blue on the first draw)
= (1/7) * (1/4)
= 1/28
Therefore, the probability that the second crayon drawn is blue and the first crayon drawn is blue is 1/28.
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john is wallpapering a room and requires wallpaper. the wallpaper that he needs is charged at $12 per square meter, plus he must pay $20 for delivery. write down the cost function c(x), where x is the amount of wallpaper needed in square meters. if john has to pay a total cost of $500, how much wallpaper did he purchase?
The wallpaper cost $40 to John.
To find the amount of wallpaper John purchased, we have to solve for x in the cost function equation.
First, let's write down the cost function c(x) using the given information.Cost function equationc(x) = 12x + 20.
Here, x is the amount of wallpaper needed in square meters, and c(x) is the total cost John has to pay, including the cost of wallpaper and delivery.
Now, let's use the given total cost of $500 and solve for x.c(x) = 12x + 20Since the total cost John paid is $500, we can write the following equation:12x + 20 = 500
To solve for x, we can isolate x on one side by subtracting 20 from both sides.12x = 480x = 40Therefore, John purchased 40 square meters of wallpaper.
Answer: 40
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QUIZ:
Square Roots and Cube Roots to Solve Equations
Question
The volume of a cube can be found using the equation V = s³, where V is the volume and s is the measure of one side of the cube.
Match the equation for how to solve for the side length of a cube to its description.
Drag the equation to the box to match the description.
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
A cube has a volume of 2560 in³.
Answer:
Step-by-step explanation:
2560
Which of the filling best describes the expression 6(y+3)
Answer: 6y+18
Step-by-step explanation:
6 x y=6y
6 x 3= 18
Answer:
The product of a constant factor of six and a factor with the sum of two terms.
Step-by-step explanation:
Since we have given that
6(y+3)
It has sum of two terms i.e. y and 3.
Mathematically, it is expressed as
y+3
And the product of constant factor of six and a factor with the sum of two terms.
Mathematically, it is expressed as
6(y+3)
Hence, The product of a constant factor of six and a factor with the sum of two terms.
Determine which property(s) the following relation R on the set of all integers satisfy(s)?( a , b ) ∈ R iff a b ≥ 1 .
In conclusion, the relation R on the set of all integers satisfies reflexivity and symmetry but not transitivity.
To determine which properties the relation R on the set of all integers satisfy, we need to check for reflexivity, symmetry, and transitivity.
1. Reflexivity: A relation R is reflexive if for every element a in the set, (a, a) ∈ R.
In this case, we need to check if a * a ≥ 1 for all integers a.
Since any integer squared (a * a) is greater than or equal to 1, R is reflexive.
2. Symmetry: A relation R is symmetric if for every pair (a, b) ∈ R, (b, a) also ∈ R.
In this case, we need to check if a * b ≥ 1 implies b * a ≥ 1.
Since multiplication is commutative (a * b = b * a), the condition holds true, and R is symmetric.
3. Transitivity: A relation R is transitive if for every (a, b) ∈ R and (b, c) ∈ R, (a, c) also ∈ R.
In this case, we need to check if a * b ≥ 1 and b * c ≥ 1 imply a * c ≥ 1.
Let's take the counterexample: a = -1, b = 2, and c = -1. We have -1 * 2 ≥ 1 and 2 * -1 ≥ 1, but -1 * -1 ≥ 1 is false.
Therefore, R is not transitive.
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Costumers at Al's Toy Barn took a survey. The results showed that 90 customers rated the store's decorations as being "very festive." This number represented 45% of the total number of customer who took the survey. How many customers took the survey?
Answer: 200
Step-by-step explanation: x = 90 ÷ 0.45
x = 200
Hannah put 2,364 pieces of candy into a bags with 57 pieces of candy each. How many full bags did she make?
2,364 ÷ 57 ≈ 41. Therefore, Hannah made 41 full bags of candy.
To solve this problem, we use integer division to find the number of full bags Hannah made. We divide the total number of candy pieces by the number of pieces in each bag and take the integer part of the result. This is because we are only interested in the number of full bags, not partial bags. In this case, we have 2,364 pieces of candy and each bag holds 57 pieces, so 2,364 ÷ 57 ≈ 41. This means that Hannah made 41 full bags of candy.
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1)
The Polynomial Remainder Theorem states that if P(x) is divided by x-a, then the
remainder is equal to P(a). Given: 2x³ + 5x²-12x+9+x-3. Look at the divisor and
determine the value for "a". Evaluate P(a) and find the remainder.
The value for a is 1 and the remainder when P(x) is divided by x - 1 is 2.
What is polynomial remainder theorem?
It states that the remainder of the division of a polynomial f(x) by a linear polynomial x-r is equal to f(r).
The divisor in this case is x - a, where "a" is the value we need to determine.
We can see that the given polynomial 2x³ + 5x² - 12x + 9 + x - 3 has a term of x in addition to the other terms. This means that the divisor must also have a term of x in it.
So, we can write the divisor as x - a and set x - a = 0 to solve for "a":
x - a = 0
=> x = a
Therefore, "a" must be equal to 1 since there is a term of x in the polynomial.
To find the remainder, we need to evaluate P(a) where P(x) = 2x³ + 5x² - 12x + 9 + x - 3 and a = 1.
P(a) = 2(1)³ + 5(1)² - 12(1) + 9 + (1) - 3 = 2 + 5 - 12 + 9 + 1 - 3 = 2
So, the remainder when P(x) is divided by x - 1 is 2.
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|
Which expression is equivalent to √36x6 z2
x>0, and z> 0 ?
O 6x4
O 6x³ z
O 18x4
O 18x³ z
N
>
3
when
Finish
The expression √36x^6 z² can be simplified. The expression is equivalent to 6x³z.
What is simplified expression?A simplified expression is an algebraic expression that has been reduced or simplified as much as possible using various mathematical operations, such as combining like terms, factoring, or cancelling common factors.
According to question:The expression √36x^6 z² can be simplified using the properties of square roots as follows:
√36x^6 z² = √(36) √(x^6) √(z²)
Since 36 is a perfect square and x^6 and z² are perfect squares (since x and z are both greater than 0), we can simplify further as:
√36x^6 z² = 6x³ z
So the expression is equivalent to 6x³z.
Therefore, the correct answer is option B: 6x³z.
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the time to fly between new york city and chicago is uniformly distributed with a minimum of 50 minutes and a maximum of 100 minutes. what is the probability that a flight is less than 64 minutes
The probability that a flight between New York City and Chicago is less than 64 minutes is 0.28, or 28%.
Since the time to fly between New York City and Chicago is uniformly distributed between 50 and 100 minutes, we can use the formula for the uniform probability density function (PDF) to find the probability that a flight is less than 64 minutes:
f(x) = 1 / (b - a), for a ≤ x ≤ b
where a = 50 and b = 100 are the minimum and maximum times, respectively.
To find the probability that a flight is less than 64 minutes, we need to integrate the PDF from a to 64:
P(X < 64) = [tex]\int\limits^{64}_{50}[/tex] f(x) dx = [tex]\int\limits^{64}_{50}\\[/tex](1 / 50) dx = (1 / 50) * [x]|₅₀ ⁶⁴
= (1 / 50) * (64 - 50) = 0.28
This means that approximately 28% of flights will arrive in less than 64 minutes.
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Number of Years Since Last Census, X Estimated Population, f(x) 42,458 2 41,776 3 40,654 4 39,841 An exponential function would better model the data because as x increases, the y values change multiplicatively. The common ratio/multiplier/base of this function is approximately V
The common ratio/multiplier/base of the exponential function that better models the given data is approximately 1.123.
What is expression ?
In mathematics, an expression is a combination of numbers, variables, and mathematical operations (such as addition, subtraction, multiplication, division, exponents, and roots) that can be evaluated or simplified to obtain a numerical value or another expression.
To find the common ratio/multiplier/base of the exponential function that better models the given data, we need to use the formula for exponential functions:
[tex]f(x) = ab^x[/tex]
where a is the initial value and b is the common ratio/multiplier/base.
We can use the given data points to form a system of equations:
[tex]2 = ab^{(42,458)}\\ \\3 = ab^{(41,776)}\\ \\4 = ab^{(40,654)}\\ \\5 = ab^{(39,841)}\\ \\[/tex]
We can divide each equation by the previous equation to eliminate "a" and obtain a ratio of "b" values:
[tex]b^{(42,458-41,776)} = 3/2\\ \\ b^{(41,776-40,654)} = 4/3\\ \\ b^{(40,654-39,841)} = 5/4\\ \\[/tex]
Simplifying each exponent, we get:
[tex]b^{682} = 3/2\\ \\b^{1122} = 4/3\\ \\b^{813} = 5/4\\ \\[/tex]
Taking the cube root of the first equation, the fourth root of the second equation, and the fifth root of the third equation, we get:
[tex]b^{(682/3)} = (3/2)^{(1/3)} = 1.245\\ \\ b^{(1122/4)} = (4/3)^{(1/4)} = 1.090\\ \\ b^{(813/5)} = (5/4)^{(1/5)} = 1.035\\ \\[/tex]
Taking the average of these values, we get:
b ≈ (1.245 + 1.090 + 1.035) / 3 ≈ 1.123
Therefore, the common ratio/multiplier/base of the exponential function that better models the given data is approximately 1.123.
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Gary, Nancy, and Jamal are trying to write an inequality where all values in the set of numbers below make the inequality true. {0, 1, 3, 4, 6, 12} Consider their inequalities. Gary: 6>0.5t Nancy: 30−t≤18 Jamal: 12≤t+12 Which student(s) wrote an inequality that is true for all values in the set of numbers? Select your answer from the drop-down list.
Therefore , the solution of the given problem of inequality comes out to be Gary and Jamal are the students who created an inequality that holds true for all values in the collection "0, 1, 3, 4, 6, 12".
An inequality is what?Algebra does not have an equal symbol, but a partner or group of integers can be used to represent the difference. Equilibrium is typically followed by equity. Inequality comes from the continued divergence of ideals. Disparity and expression fairness are not identical. Despite the fact that the parts are typically not connected or close to one another, that was our most popular symbol. (). Any difference, no matter how small, can be used to determine worth.
Here,
We can test each inequality with each value in the set, 0 through 1, 3, 4, 6, and 12, to identify which inequality holds true for all values.
6 > 0.5t, where t is a member of the collection, is Gary's inequality. When we compare each value in the collection to this inequality, we discover:
When t = 6: 6 > 0.5(6) is true
When t = 12: 6 > 0.5(12) is true
Therefore, for each value in the collection, Gary's inequality holds true.
30 - t 18 is Nancy's inequality, where t is a number from the collection. When we compare each value in the collection to this inequality, we discover:
When t = 6: 30 - 6 ≤ 18 is true
When t = 12: 30 - 12 ≤ 18 is true
Therefore, not all values in the collection satisfy Nancy's inequality.
Gary and Jamal are the students who created an inequality that holds true for all values in the collection "0, 1, 3, 4, 6, 12".
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what is the volume of the large pyramid? (rounded to the nearest cubic meter) group of answer choices 20,833 41,666 10,417 16,817 375
The volume of the pyramid is 600 cubic centimeters (cm³).
The formula for the volume of a pyramid is given by
V = (1/3) × base area × height
Since the base of the pyramid is a square with sides of 10 cm, the base area can be calculated as
base area = side length × side length = 10 cm × 10 cm = 100 cm²
Substituting the given values into the formula for the volume of a pyramid, we get
V = (1/3) × base area × height
Substitute the values in the equation
= (1/3) × 100 cm² × 18 cm
Multiply the numbers
= 600 cm³
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I have solved the question in general as the given question is incomplete.
The complete question is:
What is the volume of a pyramid whose base is square? The sides of the base are 10 cm each and the height of the pyramid is 18 cm.
13. A group of students were asked if they play a sport or play an instrument. The results are shown
in the Venn diagram below. If one of these students is chosen at random, find each probability.
a) P(instrument)
b) P(does not play a sport)
(35)
(36)
d) P(sport but not an instrument)
(38)
Instrument
10
14
Sport
8 18
c) P(both instrument and a sport)
(37)
Answer:
a) 22/50
b) 24/50
c) 8/50
d) 18/50
Step-by-step explanation:
Total students= 18 + 8 + 14 + 10 = 50
students who play instruments = 14 + 8 = 22
--
students who play a sport = 18 + 8 = 26
students who dont play a sport = 50 - 26 = 24
--
c) students who play both instrument and sport = 8
--
d) students who play sports only = 18
Students who play instruments from Venn diagram is 22, students who play both instrument and sport is 8 and students who play sports only is 18.
What is Set?A set is a collection of well defined objects.
A group of students were asked if they play a sport or play an instrument
Total number of students= 18 + 8 + 14 + 10 = 50
students who play instruments from venn diagram
= 14 + 8
= 22
students who play a sport = 18 + 8
= 26
students who dont play a sport = 50 - 26 = 24
c) students who play both instrument and sport = 8
d) students who play sports only = 18
Hence, students who play instruments from venn diagram is 22, students who play both instrument and sport is 8 and students who play sports only is 18.
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Which situation can be represented by −10? A. a debt of $10 B. a temperature of 10°F C. a score of 10 in a soccer game D. an elevator that is on the 10th floor
Answer:
A debt of $10.
Step-by-step explanation:
A. If you have debt it means your supposed to give money back to someone. You could be low on money. THIS IS THE CORRECT ANSWER!
Here's why IT'S NOT the others.
B. Am pretty sure 10*F might seem cold. But isn't it equal to 50*F. Plus 10*F is above 0!
C. It's not -10 it's just 10. you can't score -10 in a game unless you broke a rule or smthing.
D. 10 floor in a building. It's not a underground building so it's not -10.
Have a nice day!
Your welcome!
Evaluate. 547+233×5−142 whats this anwser?
The answer is 1570. To evaluate the expression 547+233×5−142, we need to follow the order of operations, which is PEMDAS (parentheses, exponents, multiplication and division, and addition and subtraction).
There are no parentheses or exponents, so we start with multiplication and division from left to right.
233×5 = 1165
Then, we can simplify the expression to:
547 + 1165 - 142
Next, we add and subtract from left to right:
547 + 1165 = 1712
1712 - 142 = 1570
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If a tv is £800 plus 20% vat Whats the total cost of the telly
i need help with my home work
The expression or equation that correctly represents the situation given is y = 2x.
What is the relationship between the packages of cashews and the cans of peanuts?Based on the table, for each package of cashews 2 cans of peanuts are required. Here are some examples:
3 packages of cashews = 6 cans of peanuts = 6/3 = 24 packages of cashews = 8 cans of peanuts = 8/4 = 2Based on this relationship and assuming y represents the cans of peanuts and x represents the packages of cashews a possible equation to represent this situation would be y = 2x.
Note: This question is incomplete; below I attach the missing information:
Write an equation to represent this relationship:
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Nhan is getting dressed. He considers two different shirts, three pairs of pants, and three pairs of shoes. He chooses one of each of the articles at random. What is the probability that he will wear his jeans but not his sneakers?
Shirt
Pants
Shoes
collared
khakis
sneakers
T-shirt
jeans
flip-flops
shorts
sandals
Jacqui wants to prove that figures abc and def are similar. Which series of transformations would prove that these two figures are similar
One figure should be rotated to match the other's alignment. Expand one figure till it is the same size as another.
what is transformations ?A figure or object in a coordinate plane can be transformed to create a new figure or object that has been relocated, flipped, or altered in some other way. Translations, rotations, and reflections are the three primary forms of transformations. Moving a figure horizontally or vertically without altering its size or shape is known as translation. Rotation entails angling a figure around a fixed point, often known as the rotational center.
given
The subsequent transformations must be used in order to demonstrate similarity between two figures:
Translation (moving the figures to the same spot) (moving the figures to the same position)
Rotation (rotation one figure to fit the other) (rotating one figure to match the other)
Dilation (resizing the figures such that they have the same shape, but maybe different sizes) (resizing the figures so that they have the same shape, but possibly different sizes)
Consequently, the following set of transformations should be used to demonstrate that the figures abc and def are similar.
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Jen's total assets are $6,964. Her liabilities are $1,670 in credit card debt and $3,642 for a student loan. What is her net worth?
Responses
$1,652
$1,652
$6,964
$6,964
$5,312
$5,312
$12,276
$12,276
Answer: $1,652.
Step-by-step explanation:
To calculate Jen's net worth, we need to subtract her liabilities from her total assets:
Net worth = Total assets - Liabilities
In this case, Jen's total assets are $6,964, and her liabilities are $1,670 for credit card debt and $3,642 for a student loan. So:
Net worth = $6,964 - $1,670 - $3,642
Net worth = $1,652
Therefore, Jen's net worth is $1,652. Answer: $1,652.
a number is equal to . what is the smallest positive integer such that the product is a perfect cube?
The smallest positive integer y such that the product xy is a perfect cube is 3.
To find the value of y, we need to factorize x, which is 7 * 24 * 48.
We can then find the prime factorization of xy, which will help us determine the smallest integer y that will make the product a perfect cube.
Since 7, 24, and 48 are already factored, we can express x as:
x = 2⁴ * 3 * 7²
To make xy a perfect cube, we need to ensure that the exponents of all the prime factors are multiples of 3.
Therefore, we need to add a factor of 3 to the exponent of 2 in x to make it a multiple of 3. This gives us:
xy = 2⁷ * 3² * 7²
The smallest integer y that can make this product a perfect cube is 3, because we need to add a factor of 1 to the exponent of 2 in xy to make it a multiple of 3, and the smallest integer that can achieve this is 3.
Thus, the smallest positive integer y such that the product xy is a perfect cube is 3.
The question is: A number x is equal to [tex]$7\cdot24\cdot48$[/tex]. What is the smallest positive integer y such that the product xy is a perfect cube
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i need help pleaseeeeeee
By using the definition of inverse functions we can see that:
a) g(7) = -10
b)(-10,7) is a point on h(x).
c)(7, -10) is a point on j(x)
How to evaluate the functions?Remember that if two functions f(x) and g(x) are inverses, then:
f(y) = x
g(x) = y
And also g(f(x)) = x = g(f(x)).
Here we know that functions h(x) and j(x) are inverses, and we also know that:
h(-10) = 7
So for the input -10, we have the output 7.
Then, by using the relation written above, we know that for the inverse function we must have:
j(7) = -10
That is the answer for a.
And for b and c the notation is (input, output), then:
(-10, 7) is a point on h.(7, -10)is a point on jThese are the answers of points B and C of the question.
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John has a jar filled with juice. After he poured 350 ml of juice in each 8
glasses he was still left with 200 ml juice in the jar. What was the capacity
of jar in liters?
Answer:
Step-by-step explanation:
If there were 8 glasses of juice, and 350 ml was poured into each glass, then the total amount of juice poured into the glasses would be 8 x 350 = 2800 ml.
After pouring this much juice, John was still left with 200 ml juice in the jar.
Therefore, the capacity of the jar would be the total amount of juice poured into the glasses plus the amount remaining in the jar, which is 2800 ml + 200 ml = 3000 ml.
To convert this volume to liters, we can divide by 1000. Therefore, the capacity of the jar in liters would be 3000 ml / 1000 = 3 liters.
So, the capacity of the jar is 3 liters.
A castle has to be guarded 24 hours a day. Five knights are ordered to split each day's guard duty equally. how long will each knight spend on guard duty in one day???? Please help I am very stuck on this
Answer:
Step-by-step explanation:
If there are five knights and they need to divide the guard duty equally for the 24 hours in a day, each knight would spend 24/5 = 4.8 hours on guard duty in one day.
However, since it's not possible to guard for a fraction of an hour, they would need to round that number to the nearest whole number. In this case, each knight would spend 5 hours per day on guard duty.
a man standing 11 feet from the base of a lamppost casts a shadow 3 feet long. if the man is 6 feet tall and walks away from the lamppost at a speed of 200 feet per minute, at what rate, in feet per minute, will the length of his shadow be changing?
Step-by-step explanation:
Insects can show three types of development. One of them, holometaboly (complete development), consists of the stages of egg, larva, pupa and sexually mature adult, which occupy different habitats. Insects with holometaboly belong to the most numerous orders in terms of known species. This type of development is related to a greater number of species due to the a) protection in the pupa stage, favoring the survival of fertile adults. b) production of many eggs, larvae and pupae, increasing the number of adults. c) exploration of different niches, avoiding competition between life stages. d) food intake at all stages of life, ensuring the emergence of adults. e) use of the same food in all stages, optimizing the body's nutrition.
lucinda surveyed 50 students in her school to find out how many students enjoy playing sports. the resultsare shown in the table. do you think lucinda chose a random sample? why or why not?
If Lucinda used a random selection method, made an effort to ensure that the sample is representative, and the sample size is large enough, then it's possible that the sample is indeed random.
what are perpendicular lines?
Perpendicular lines are two lines that intersect at a 90-degree angle, forming four right angles at the point of intersection. In other words, if you were to draw a perpendicular line from one of the lines to the other at their point of intersection, it would form a right angle with each of the original lines.
Without having access to more information about how Lucinda selected the sample of students, it's difficult to determine whether or not the sample is truly random.
However, there are a few things that we can consider when trying to determine whether or not the sample is random. For example:
Did Lucinda use a random selection method to choose the students? If she simply surveyed her friends or classmates, for example, the sample would not be random.
Did Lucinda make any effort to ensure that the sample is representative of the larger population of students? For example, did she make sure to include students from a variety of grades, genders, and ethnic backgrounds.
Therefore, if Lucinda used a random selection method, and made an effort to ensure that the sample is representative, and the sample size is large enough, then it's possible that the sample is indeed random.
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Question
Find the surface area of the prism
HELP
Answer: 56 in
Step-by-step explanation:
4x7x2=56
Answer:
56 in
Step-by-step explanation:
4*7*2
Jared's average daily balance for the last month was $560. The finance charge was $8. 12. What was the monthly percentage rate? What was the APR?
The monthly percentage rate is 1.45%, and the APR is 17.4%.
To calculate the monthly percentage rate, we can divide the finance charge by the average daily balance, then multiply by 100 to convert to a percentage
Monthly percentage rate = (finance charge / average daily balance) x 100
Monthly percentage rate = ($8.12 / $560) x 100
Monthly percentage rate = 0.0145 x 100
Monthly percentage rate = 1.45%
To calculate the APR (annual percentage rate), we need to multiply the monthly percentage rate by the number of months in a year:
APR = Monthly percentage rate x 12
APR = 1.45% x 12
APR = 17.4%
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The function g(x) is shown on the graph.
The graph shows an upward opening parabola with a vertex at negative 3 comma negative 2, a point at negative 5 comma 2, and a point at negative 1 comma 2.
What is the equation of g(x) in vertex form?
g(x) = (x − 3)2 − 2
g(x) = (x − 3)2 + 2
g(x) = (x + 3)2 − 2
g(x) = (x + 3)2 + 2
Answer:
g(x) = (x + 3)2 - 2
Step-by-step explanation:
I think that's the one I just did this class so
Please help I’ll give brainliest
The standard form is 5x²-2x-4=0
A quadratic equation can be written in other forms.
Standard Form: ax²+bx+c=0
Vertex Form: a (x - h)2 + k = 0
Intercept Form: a (x - p)(x - q) = 0
This equation is called 'quadratic' as its degree is 2
The standard form of a quadratic equation is also known as its general form.
ax²+bx+c=0
with the conditions : a ≠ 0, and a, b, and c are real numbers
'a' is the coefficient of x²
'b' is the coefficient of x
'c' is the constant
here a= 5 b= -2 c= -4
Shift all the terms to one side and write in standard quadratic equations
=> 5x²-2x+1-5=0
=> 5x²-2x-4=0
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