Yes, the truck fit in the parking space for the given rectangle dimensions through which 13.5ft<19ft or 11ft>8.5ft
What about rectangle dimensions?
The dimensions of a rectangle refer to its length and width, which are the two perpendicular sides of the rectangle. The length is the longer side of the rectangle, while the width is the shorter side. The dimensions are usually denoted by the letters "l" and "w", with the length written first.
For example, if a rectangle has a length of 6 units and a width of 4 units, its dimensions would be written as "6 x 4", or "l = 6, w = 4". The area of a rectangle can be calculated by multiplying its length by its width, while its perimeter is given by the sum of twice its length and twice its width.
According to the given information:
We know the are of parking space = [tex]209ft^{2}[/tex]
So, 19 x b = 209
b = 11
13.5 ft < 19 ft and 11 ft > 8.5 ft
So, the truck fit in the parking space (parallelogram area formula)
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What is the value of the y-coordinate of the ordered pair that reflects (2-12) over the x-axis?
Solve for y in the two equations below using substitution.
3x - 9y =8
-2x + 2y= 8
Using the substitution method we know that the value of y in the given situation is 2 respectively.
What is the substitution method?The substitution method is typically used in mathematics to solve an equation system.
In this approach, you solve the equation for one variable first, then you enter its value into the other equation.
A false statement is produced if the variables x = 3 and y = 2 are substituted into the first equation: 2(2) = 3 + 9.
Try changing the first equation as x = 2y 8 to solve this system.
Next, change x in the second equation to 2y 8, and then solve for y.
The right response is x = 2, y = 3.
So, get the value of y as follows:
3x - 9y =8 ...(1)
-2x + 2y= 8 ...(2)
Now, take equation (1):
3x - 9y =8
3x = 8 + 9y
x = (8 + 9y)/3
Now, substitute x = (8 + 9y)/3 in equation (2):
-2x + 2y= 8
-2[(8 + 9y)/3] + 2y= 8
-2[(8 + 9y)] + 2y= 8*3
-16 + 18y + 2y = 24
20y = 24 + 16
20y = 40
y = 40/20
y = 2
Therefore, using the substitution method we know that the value of y in the given situation is 2 respectively.
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Chad drinks 64. 88 fluid ounces of water per day. How much water does he drink in 6 days
Chad drinks 389.28 fluid ounces of water in 6 days.
What is ounces?A unit of weight equal to ¹/₁₂ troy pound see Weights and Measures Table. : a unit of weight equal to ¹/₁₆ avoirdupois pound. : a small amount. an ounce of sense.
An ounce (oz) is a unit of weight that is equal to one-sixteenth of a pound. Items that weigh approximately one ounce include a slice of bread and a pencil. A fluid ounce is a unit of liquid volume that is equal to one-eighth of a cup. A medicine cup has a volume of approximately one fluid ounce.
given that,
chad drinks 64.88 fluid ounces of water per day,
so in 6 days
he will drink = 6 x water drink per day
= 6 x 64.88
= 389.28
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I NEED HELP ON THIS ASAP!
The exponential function for the new participants is f(x) = 3 * 4^x
Writing the exponential function for the new participantsLet's start with the initial number of participants who sent selfies on Day 0.
We know that Aliyah, Kim, and Reese each sent selfies to 4 friends, so there are 3 x 4 = 12 participants on Day 1.
On Day 2, each of these 12 participants will send selfies to 4 friends, so we will have 12 x 4 = 48 new participants.
We can see that the number of new participants each day is increasing exponentially. In fact, the number of new participants each day is multiplied by 4, since each participant sends selfies to 4 friends.
Therefore, we can write an exponential function of the form:
f(x)=a * 4^x
Where x is the number of days since the challenge started, and $a$ is the initial number of participants who sent selfies on Day 0.
We know that a = 12 from our earlier calculations.
So, we have
f(x) = 3 * 4^x
Hence, the function is f(x) = 3 * 4^x
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math please. its for a quiz
The quotient function of f(x) and g(x) is given as follows:
(f/g)(x) = 3x^(3/4).
How to obtain the quotient function?The functions in the context of this problem are defined as follows:
f(x) = 3x.g(x) = x^(1/4).When we want to divide two functions, we just divide each other, hence:
(f/g)(x) = f(x)/g(x) = 3x/x^(1/4).
When we divide two terms with the same base and different exponents, we keep the base and subtract the exponents, hence:
x/x^(1/4) = x^(1 - 1/4) = x^(3/4).
Hence the function is:
(f/g)(x) = 3x^(3/4).
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Construct a two-way frequency table for the data. Include row and column totals. Hint: Let column categories be labeled by after school activity.
Every student at Georgia Southern Middle School participates in exactly one after school activity. The school activities coordinator recorded data on after extracurricular activity
and grade for all 254 students in 7th grade and 8th grade.
The counselor's findings for the 254 students are the following:
• Of the 80 students enrolled in music, 42 are in 7th grade.
.
. Of the 21 students enrolled in student government, 9 are in 8th grade.
.
Of the 65 students enrolled in theatre, 20 are in 7th grade.
. Of the 88 students enrolled in sports, 30 are in 8th grade.
Answer:
[tex]\begin{array}{|c|c|c|c|c|c|} \cline{1-6} & \text{Music} & \text{Gov} & \text{Theater} & \text{Sports} & \text{Total}\\\cline{1-6}\text{7th grade} & 42 & 12 & 20 & 58 & 132\\\cline{1-6}\text{8th grade} & 38 & 9 & 45 & 30 & 122\\\cline{1-6}\text{Total} & 80 & 21 & 65 & 88 & 254\\\cline{1-6}\end{array}[/tex]
"Gov" refers to "Student Government".
==================================================
Explanation:
The rows are labeled "7th grade", "8th grade" and "Total".
The columns are labeled "Music", "Student Government", "Theater", "Sports", and "Total".
I'll abbreviate "Student Government" to "Gov" so that the table doesn't get too wide.
There are 254 students total. This value goes in the bottom right corner of the table. This is the grand total.
----------
We have 80 students in music. This value goes at the bottom of the "music" column since we're in a "total" row. Basically it's the total of all the music students regardless of grade.
Of those 80 students in music, 42 are in seventh grade. Write 42 in the first row of this column and 38 just underneath it (because 80-42 = 38). The two values 42 and 38 should add to the 80 mentioned.
----------
There are 21 students in student government. This value goes at the bottom of the "student government" column.
9 of these students are in eighth grade, so the remaining 21-9 = 12 must be in seventh grade.
----------
There are 65 students in theater. This value goes at the bottom of the "theater" column.
There are 20 such students in 7th grade and 45 in 8th grade (because 65-20 = 45).
----------
There are 88 students in sports.
30 are in 8th grade, so 88-30 = 58 must be in 7th.
----------
At this point, you should have these values along the bottom row:
80, 21, 65, 88, 254
The first four values (80, 21, 65, 88) should add to the grand total 254.
Along each row, add up the values to get the row total.
7th grade: 42 + 12 + 20 + 58 = 132
8th grade: 38 + 9 + 45 + 30 = 122
There are 132 seventh graders and 122 eighth graders.
Those subtotals add to 132+122 = 254 total students, which helps confirm we did things correctly.
Choose the algebraic description that maps abc onto abc in the given figure.
So the transformation is: (x, y) → (x + -8, y - 4) which is equivalent to option B.
What is transformation?In mathematics, a transformation is a process that manipulates the position, size, or shape of a geometric object. Transformations can include translations, rotations, reflections, and dilations. They are used to study geometric properties and relationships and are often used in fields such as geometry, algebra, and computer graphics. Transformations are important in understanding symmetry and congruence, as well as in solving problems involving geometric figures.
Here,
We can see that the transformation takes each point of the form (x, y) in ABC to a corresponding point of the form (x', y') in A'B'C'. To find the correct transformation, we need to determine how the coordinates of the points in ABC are related to the coordinates of the corresponding points in A'B'C'. One way to do this is to use the fact that the transformation should preserve the relative distances and angles between the points. Another way is to use the known coordinates of three corresponding points to determine the transformation directly.
In this case, we can see that the transformation maps (-3,-2) to (5,2), (-1,-4) to (7,0), and (-6,-5) to (2,-1). We can use these points to find the transformation:
(x, y) → (x', y')
To map (-3,-2) to (5,2), we need to add 8 to the x-coordinate and add 4 to the y-coordinate:
x' = x + 8
y' = y + 4
To map (-1,-4) to (7,0), we again add 8 to the x-coordinate, but this time we only add 4 to the y-coordinate:
x' = x + 8
y' = y + 4
To map (-6,-5) to (2,-1), we subtract 4 from the x-coordinate and subtract 4 from the y-coordinate:
x' = x - 4
y' = y - 4
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Look across each row of the table what pattern do you see
When we look across each row of the table the pattern we observe is that the multiplication of the table leads to 12.
What is volume?The quantity of space a three-dimensional item occupies is measured by its volume. Usually, it is expressed in cubic units like cubic metres or cubic feet. If an object has irregular or curved shapes, the volume can be determined by using its measurements, such as length, breadth, and height, or by employing more difficult mathematical calculations. In several disciplines, such as physics, engineering, and architecture, volume is a crucial notion.
From the table we see that the arrangement of the 12 cubes is made in different length and width, such that the multiplication of the three is 12.
Here we have,
Long wide tall
2 3 2
2 6 1
3 1 4
3 2 2
3 4 1
4 1 3
6 2 1
Hence, when we look across each row of the table the pattern we observe is that the multiplication of the table leads to 12.
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The complete question is:
I need help ASAP mean absolute deviation (mad)
The absolute deviation for the observation of 16 in the data-set is given as follows:
5.
How to calculate the mean of a data-set?The mean of a data-set is given by the sum of all observations in the data-set divided by the number of observations, which is also called the cardinality of the data-set.
Hence the mean of the data-set in this problem is given as follows:
(19 + 16 + 4 + 9 + 7)/5 = 11.
The absolute deviation of 16 is given by the difference between 16 and the mean of 11, hence:
16 - 11 = 5.
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Learning Task 4. Multiply each of the following. Use cancellation method
if possible. Write your answer in your notebook.
1. 5/7•14/35
2. [4/5][10/11]
3. 8 3/4 multiplied by 2/9
4. [4/5]10/11][7/8]
please answer this
Answer:1
1. is 2/7
2. is .5
3 is 1.94 repeating and
4 is 7/11
Step-by-step explanation:
what time does a 12-hour clock read a) 80 hours after it reads 11:00? b) 40 hours before it reads 12:00? c) 100 hours after it reads 6:00?
a) 80 hours after 11:00 on a 12-hour clock would be 7:00.
b) 40 hours before 12:00 on a 12-hour clock would be 4:00.
c) 100 hours after 6:00 on a 12-hour clock would be 10:00.
a, To find this, we need to divide 80 by 12 (the number of hours on the clock), which gives us a quotient of 6 and a remainder of 8. We then add the remainder to the starting time of 11:00, giving us 7:00.
b, To find this, we need to subtract 40 from 12 (the number of hours on the clock), which gives us 8. We then subtract 8 from the starting time of 12:00, giving us 4:00.
c, To find this, we need to divide 100 by 12 (the number of hours on the clock), which gives us a quotient of 8 and a remainder of 4. We then add the quotient (which represents a full cycle of 12 hours) to the starting time of 6:00, giving us 6+8=14:00, which is equivalent to 2:00 on a 12-hour clock. Finally, we add the remainder of 4 to 2:00, giving us 10:00.
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a production process produces 2.5% defective parts. a sample of five parts from the production process is selected. what is the probability that the sample contains exactly two defective parts? group of answer choices 0.2637 0.0058 0.0000 0.0250
The probability that the sample contains exactly two defective parts is 0.0058.
We may utilize the binomial probability formula to resolve this issue:
P(X = k) is equal to (n pick k) * p * k * (1-p) (n-k)
where n is the sample size, k denotes the number of successes, p denotes the likelihood that a success will occur, and (n pick k) denotes the binomial coefficient, which indicates the number of possible ways to select item k from n.
Here, n = 5, k = 2, and p = 0.025 (due to the fact that 2.5% of the pieces are flawed).
P(X = 2) therefore equals (5 pick 2)*0.025*2*(1 - 0.025)*3
We calculate P(X = 2) = 0.0058 using a calculator.
As a result, there is a 0.0058 percent chance that the sample has exactly two defective components.
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5x(x - 4) = 3x + 4 someone help me pls
Answer: x=23±√609/10
Step-by-step explanation:
PLS HELP ME ON THIS
WHAT COULD BE THE LARGEST WHOLE NUMBER?
Step-by-step explanation:
7 + x = 2x, so x = 7
In an all boys school, the heights of the student body are normally distributed with a mean of 69 inches and a standard deviation of 3.5 inches. What is the probability that a randomly selected student will be taller than 63 inches tall, to the nearest thousandth?
The probability that a randomly selected student will be taller than 63 inches tall is 0.9332, to the nearest thousandth.
the number of square feet per house are normally distributed with a population standard deviation of 154 square feet and an unknown population mean. a random sample of 16 houses is taken and results in a sample mean of 1550 square feet. what is the correct interpretation of the 80% confidence interval? select the correct answer below: we estimate that 80% of the number of square feet per house are between 1501 and 1599 square feet. we estimate with 80% confidence that the sample mean is between 1501 and 1599 square feet. we estimate with 80% confidence that the true population mean is between 1501 and 1599 square feet.
The 80% confidence interval is 1501 to 1599 square feet, indicating with 80% confidence that the true population mean of square feet per house falls within this range based on the sample data.
How to find correct interpretation of the 80% confidence interval?Based on the given information, we can calculate the 80% confidence interval for the true population mean of the number of square feet per house using the sample mean of 1550 square feet and the population standard deviation of 154 square feet. The interval is 1501 to 1599 square feet. This means that if we were to repeat the sampling process and construct confidence intervals in the same way for an infinite number of times, approximately 80% of these intervals would contain the true population mean. Therefore, we can estimate with 80% confidence that the true population mean falls within the range of 1501 to 1599 square feet.
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Ages of 12 players on a basketball team: {11,10,11,11,8,11,12,11,9,10,11,12}
Best Center:
Why?:
The best center is the mean because there are no outliers
To determine the best center, we need to examing the ages of the player withing the range of age.
The ages of the players are: 11, 10, 11, 11, 8, 11, 12, 11, 9, 10, 11, 12
In the above list of age, we can seee that there are no outliers are
When there are no outliers in a dataset, the best center to use is the mean
Hence, the best center is the mean
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20 POINTS!!!!!!
4. Find the value of x and y.
3y - 5
x =
y =
y+1
2x+6
II
work:
Answer:
x = 8, y = 3
Step-by-step explanation:
Assuming the figure is a parallelogram, opposite sides on a parallelogram are equal.
This means that 3x-2 = 2x+6 and 3y-5 = y+1.
To solve these equations:
3x-2 = 2x+6 (collect like terms)
3x-2x = 6+2
x = 8
3y-5 = y+1 (collect like terms)
3y-y = 1+5
2y = 6 (divide both sides by 2)
y = 3
∴ x = 8, y = 3
Madison is reading a book that is 860 pages long. She reads 25 pages in 0.5 hours. At that rate, how long will it take for her to read the entire book
Answer:
17.2 hours, or 17 hours and 12 minutes
Step-by-step explanation:
If she reads 50 pages per hour, then 860/50 = 17.2
If 2 inches represents 75 miles on a map, then how many inches will represent 11 miles?
We can use proportions to solve this problem. If 2 inches represent 75 miles, then we can set up a proportion:
2 inches / 75 miles = x inches / 11 miles
To solve for x, we can cross-multiply:
2 inches * 11 miles = 75 miles * x inches
22 inches = 75 miles * x inches
Divide both sides by 75 miles:
22 inches / 75 miles = x inches
Simplify:
0.2933 inches = x inches
Therefore, 11 miles on the map would be represented by approximately 0.2933 inches.
true or false? use cases can help with developing quantitative and measurable usability tests. group of answer choices
The given statement about developing quantitative and measurable usability tests is true.
Explain about how this given statement is true?Use cases can help with developing quantitative and measurable usability tests. Use cases are scenarios that describe how a user might interact with a system or product in a specific situation.
By developing use cases, researchers can identify specific tasks that users may need to perform and design usability tests to measure how well users can perform those tasks.
This can help make the usability tests more objective and measurable, as researchers can use metrics such as completion rates, task time, and errors to assess the usability of the system or product.
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what is the probability that a five-card poker hand contains a straight, that is, five cards that have consecutive kinds? (note that an ace can be considered either the lowest card of an a-2-3-4-5 straight or the highest card of a 10-j-q-k-a straight.)
The probability of getting a straight in a five-card poker hand is 0.0019, which is calculated by dividing the total number of possible straights by the total number of possible five-card hands.
How to find probability that a five-card poker hand contains a straight?To calculate the probability of getting a straight in a five-card poker hand, we need to first understand the concept of a straight. A straight is a combination of five cards that are in consecutive ranks, such as 6-7-8-9-10 or 10-J-Q-K-A.
The total number of possible five-card hands is given by the mathematical formula 52 choose 5, which is equal to 2,598,960. To calculate the number of possible straights, we need to consider the number of ways that we can choose five consecutive ranks out of the thirteen ranks available in a standard deck of cards. There are 10 ways to do this, since we can start with each of the 10 possible ranks (A, 2, 3, 4, 5, 6, 7, 8, 9, 10) and have one unique straight for each.
However, there are different ways to arrange the cards in a straight. For example, the straight 10-J-Q-K-A can be arranged in five different ways (10-J-Q-K-A, A-10-J-Q-K, K-A-10-J-Q, Q-K-A-10-J, J-Q-K-A-10). Therefore, the total number of possible straights is 10 * 5 = 50.
To calculate the probability of getting a straight, we divide the number of possible straights by the total number of possible five-card hands. Thus, the probability of getting a straight in a five-card poker hand is 50/2,598,960, or approximately 0.0019. Therefore, the chances of getting a straight are relatively low, but not impossible.
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hel me please please
The incorrect expressions are given as follows:
h^9/h³ = h^6 -> keep the base and subtract the exponents.9b^7/3b² = 3b^5 -> we have to divide the bases.d^5 x d²/d³ = d^4 -> add the exponents in the numerator, then subtract the exponent with the denominator.How to simplify the exponential expressions?When two terms with the same base and different exponents are multiplied, we keep the base and add the exponents.
When two terms with the same base and different exponents are divided, we keep the base and subtract the exponents.
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Questions seven and eight please
The results are:
7a) Explicit = h(n) = [tex]0.87^{n-1}[/tex] * 200.
Recursive = h(0) = 200 and h(n) = 0.87 * h(n-1)
7b) Rebound height = 99.76 cm (rounded to the nearest hundredth).
8a) Explicit formula: A(n) = 575 + 47.50n
Recursive formula: A(0) = 575, A(n) = A(n-1) + 47.50
8b) 30 weeks to save $2000'
Step by step explanation:7a) Explicit: h(n) = [tex]0.87^{n-1}[/tex] * 200 (
where h(n) = height of the golf ball after n bounces,
0.87 is the rebound factor,
200 is the initial height)
h(n) = [tex]0.87^{n-1}[/tex] * 200
Recursive: h(0) = 200
h(n) = 0.87 * h(n-1)
where h(n) = the height after n bounces,
h(n-1) = height after (n-1) bounces,
0.87 = rebound factor.
Apply given values:
h(0) = 200
h(n) = 0.87 * h(n-1)
7b) Rebound height, using recursive formula:
h(0) = 200
h(1) = 0.87 * 200 = 174
h(2) = 0.87 * 174 = 151.38
h(3) = 0.87 * 151.38 = 131.70
h(4) = 0.87 * 131.70 = 114.71
h(5) = 0.87 * 114.71 = 99.76 (rounded to the nearest hundredth)
8a)Explicit: A(n) = 575 + 47.50n,
where A(n) = amount of money Jessica has after n weeks,
575 = initial amount given by grandfather,
47.50 = amount Jessica adds each week.
Recursive: A(0) = 575, A(n) = A(n-1) + 47.50,
where A(n) = the amount of money Jessica has after n weeks,
A(n-1) = amount Jessica has after (n-1) weeks
47.50 = amount Jessica adds each week.
8b) Weeks to save $2000:
A(n) = 575 + 47.50n = 2000
Solving for n:
575 + 47.50n = 2000
47.50n = 2000 - 575
47.50n = 1425
n = 1425 / 47.50
= 30 weeks.
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ladder 13 feet long is leaning against a wall. if the foot of the ladder is pulled away from the wall at the rate of 0.5 feet per second, how fast will the top of the ladder be dropping when the base is 5 feet from the wall?
The top of the ladder is dropping at a rate of -5/24 ft/s (approximately -0.208 ft/s) when the base is 5 feet from the wall.To answer your question, we'll use the Pythagorean theorem for the right triangle formed by the ladder, wall, and ground.
Let x be the distance from the base of the ladder to the wall, and y be the distance from the top of the ladder to the ground. The ladder's length (13 ft) is the hypotenuse of the triangle.
According to the Pythagorean theorem:
x² + y² = 13²
When the base is 5 feet from the wall:
5² + y² = 13²
y² = 144
y = 12 ft
Now, we'll differentiate the equation with respect to time (t):
2x(dx/dt) + 2y(dy/dt) = 0
Given that the base is being pulled away at 0.5 ft/s (dx/dt = 0.5 ft/s), we can find the rate at which the top of the ladder is dropping (dy/dt) when x = 5 ft and y = 12 ft:
2(5)(0.5) + 2(12)(dy/dt) = 0
5 + 24(dy/dt) = 0
dy/dt = -5/24
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The top of the ladder is dropping at a rate of [tex]5/\sqrt(119)[/tex]feet per second.
Let's begin by drawing a diagram of the situation:
|\
| \
| \ <-- ladder
| \
| \
| \
| \
|______\
wall
A right triangle formed by the ladder, the wall, and the ground.
Let's call the distance from the foot of the ladder to the wall "x" and the height of the ladder "y".
The ladder is 13 feet long and that the foot of the ladder is being pulled away from the wall at a rate of 0.5 feet per second.
The height of the ladder is changing when the foot of the ladder is 5 feet from the wall.
Using the Pythagorean theorem,
the Pythagorean theorem or Pythagoras' theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle.
It states that the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares on the other two sides.
This theorem can be written as an equation relating the lengths of the sides a, b and the hypotenuse c, often called the Pythagorean equation
[tex]{\displaystyle a^{2}+b^{2}=c^{2}.}[/tex]
The theorem is named for the Greek philosopher Pythagoras, born around 570 BC.
The theorem has been proven numerous times by many different methods – possibly the most for any mathematical theorem.
The proofs are diverse, including both geometric proofs and algebraic proofs, with some dating back thousands of years.
[tex]x^2 + y^2 = 13^2[/tex]
Differentiating both sides with respect to time t, we get:
[tex]2x dx/dt + 2y dy/dt = 0[/tex]
We want to find. [tex]dy/dt[/tex] when [tex]x = 5[/tex], so, we need to substitute. [tex]x = 5[/tex] and [tex]dx/dt = 0.5[/tex] into the equation above:
[tex]2(5)(0.5) + 2y dy/dt = 0[/tex]
[tex]y dy/dt = -5[/tex]
[tex]dy/dt = -5/y[/tex]
Pythagorean theorem to solve for y when. [tex]x = 5[/tex]:
[tex]5^2 + y^2 = 13^2[/tex]
[tex]y^2 = 144 - 25[/tex]
[tex]y^2 = 119[/tex]
[tex]y = \sqrt(119)[/tex]
The foot of the ladder is 5 feet from the wall, the height of the ladder is:
[tex]y = \sqrt(119) feet[/tex]
And the rate of change of the height of the ladder is:
[tex]dy/dt = -5/y = -5/\sqrt(119) feet per second[/tex]
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please help !!!!!!
MULTIPLY (3x + 4)(4x + 5)
Answer:
B. 12x^2 + 31x + 20
Step-by-step explanation:
Use FOIL (First, Outer, Inner, Last)
(3x + 4)(4x + 5)
12x^2 + 15x +16x + 20
12x^2 + 31x + 20
Answer:
B
Step-by-step explanation:
You are going to want to use the FOIL method. First outer inner last. Multiply 3x*4x to get 12x^2 then multiply 3x*5 to get 15x then multiply 4*4x to get 16x and last multiply 4*5 to get 20. Since 15x and 16x are like terms we add them together to get 31x
what is the proportional relationship between x 2 6 8 10 and y 6 18 24 30
The proportional relationship is y = 3x.
What is the proportional relationship?
If the corresponding elements of two sequences of numbers, frequently experimental data, have a constant ratio, known as the coefficient of proportionality or proportionality constant, then the two sequences of numbers are proportional or directly proportional.
Here, we have
Given:
x: 2, 6, 8, 10
y: 6, 18, 24, 30
We have to find the proportional relationship between x and y.
So, we can see from inspection and visual observation that there is a proportional relationship between x and y.
6 = 3 2, 18 = 3 6, 24 = 3 8, 30 = 3 10.
Hence, The proportional relationship is y = 3x.
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In the figure, what is the value of z?
Answer:
The answer for z=137°
Step-by-step explanation:
y=43°
x=z
x+z+y+43=360(angles at a point)
Note:x=z
x+x+43+43=360
2x=86=360
2x=360-86
2x=274
divide both sides by 2
x=137°
Remember x=z
therefore
z=137°
you wish to buy 10 pieces of fruit. there are (indistinguishable) bananas, apples, pears, and strawberries. how many ways are there to buy 10 pieces of fruit so that you buy at most 2 pieces with inedible cores (i.e., apples and pears).
The total number of ways to buy 10 pieces of fruit so that you buy at most 2 pieces with inedible cores is 137.
To determine the number of ways to buy 10 pieces of fruit so that you buy at most 2 pieces with inedible cores, we can use a combination of counting techniques.
First, we can consider the total number of ways to buy 10 pieces of fruit without any restrictions. This can be represented by the number of solutions to the equation:
x1 + x2 + x3 + x4 = 10
where x1 represents the number of bananas, x2 represents the number of apples, x3 represents the number of pears, and x4 represents the number of strawberries. Using the stars and bars method, we can find that there are C(13,3) = 286 ways to do this.
Next, we need to subtract the number of ways to buy 10 pieces of fruit where we buy 3 or more pieces with inedible cores.
We can do this by considering the number of ways to buy 3, 4, or 5 apples and pears, and then finding the number of ways to distribute the remaining pieces of fruit. Using the same method as before, we can find that there are C(12,2) + C(11,2) + C(10,2) = 221 ways to do this.
Finally, we can subtract the number of ways to buy 10 pieces of fruit where we buy 3 or more pieces with inedible cores twice, since we double-counted these cases in the previous step. Using the inclusion-exclusion principle, we can find that there are 2 * C(9,2) = 72 ways to do this.
Therefore, the total number of ways to buy 10 pieces of fruit so that you buy at most 2 pieces with inedible cores is 286 - 221 + 72 = 137.
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Steven has a bag of 20 pieces of candy. Five are bubble gum, 8 are chocolates, 5 are fruit chews, and the rest are peppermints. If he randomly draws one piece of candy what is the probability that it will be chocolate?
A. 0. 4
B. 0. 45
C. 0. 2
D. 0. 8
The opportunity of drawing a chocolate from the bag is 0.4, therefore, the answer is A. 0.4.
Steven has a bag of 20 pieces of candy, out of which 8 are chocolates. If he draws one piece of sweet at random, the opportunity of it being a chocolate may be calculated through dividing the wide variety of chocolates in the bag with the aid of the full quantity of chocolates inside the bag. In this situation, there are 8 chocolates out of 20 total candies.
The formulation to calculate the opportunity is:
P(chocolate) = number of candies / total range of candies
Substituting the given values, we get:
P(chocolate) = 8 / 20
Simplifying this fraction, we get:
P(chocolate) = 0.4
Consequently, the opportunity of drawing a chocolate from the bag is 0.4
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