The internal angles of a trapezoid add up to 360º.
\(x+108+121+59=360\)Use this equation to find the value of x:
\(\begin{gathered} x=360-108-121-59 \\ x=72 \end{gathered}\)Then, x is 72ºWhich quadratic regression equation best fits the data set
x1|-2 -1.5 -0.5 0 0.5 1.5 2
y1| 4 0.5 -3.5 -4 -3.5 0.5 4
y=2x2^+0x-4 or y=2x2^-4
y=-4x2^+0x+2 or y=-4x2^+2
y=x2x2^-4x+0 or y=2x2^-4x
The quadratic regression equation best fits the data set is:
\(y=-4x^2+0x+2\ or\ y=-4x^2+2\)
What is quadratic regression ?
Quadratic regression is a statistical method used to determine the relationship between a dependent variable and one or more independent variables.
Given data set:
x1|-2 -1.5 -0.5 0 0.5 1.5 2
y1| 4 0.5 -3.5 -4 -3.5 0.5 4
To determine which quadratic regression equation best fits the data set, we need to calculate the regression equation that has the smallest sum of squared residuals.
Using a calculator or regression software, we can find that the quadratic regression equation that best fits the data set is:
\(y = -4x^2 + 0x + 2\)
Therefore, the answer is:
\(y=-4x^2+0x+2\ or\ y=-4x^2+2\)
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A poll is taken on a local school levy. A total of 504 people are surveyed and it is found that 52.3% ofthem support the levy. How many responders supported the levy?
Since the total number of people in the survey is 504
Since 52.3% of them support the levy
Then to find the number of people who support the levy, multiply 52.3% by 504
At first, change the percentage number to a usual number by dividing it by 100
\(\frac{52.3}{100}=0.523\)Now, do the multiplication
\(0.523\times504=263.592\)Then 263.592 support the levy
18kg in the ratio 2:7
Answer:
Step-by-step explanation:
Let the ratios be 2x and 7x respectively.
Now,
2x + 7x = 18
= 9x = 18
= x = 18/9
= x = 2
Hence, 2x = 2*2 = 4
And, 7x = 7*2 = 14
What the meaning of statement this?
This statement essentially establishes a relationship between the sets X, Y, and z, stating that there exists a subset Y for each element x in X such that the elements in Y are present in some subset z of X.
The given statement is a symbolic representation of a logical proposition involving quantifiers and logical connectives. Let's break down its meaning:
∀ X ∃ Y ∀u(u ∈ Y ↔ ∃z(z ∈ X ∧ u ∈ z))
The symbol ∀ (universal quantifier) indicates that the statement applies to all elements in the set X.
The symbol ∃ (existential quantifier) indicates that there exists at least one element in the set Y.
The statement can be interpreted as follows:
"For all elements x in the set X, there exists a set Y such that for every element u in Y, u is an element of Y if and only if there exists a set z in X such that u is an element of z."
In simpler terms, the statement asserts that for every element x in the set X, there is a set Y that contains elements u if and only if there exists a set z in X that also contains u.
It is important to note that the precise meaning and implications of this statement may depend on the context and interpretation of the sets X, Y, and their elements.
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show work if possible
Answer:
B. 14,525
Step-by-step explanation:
If a tablet costs $35 and the school is purchasing tablets for every student, then the total cost to buy tablets for the whole school would be:
$35 x 415 = $14,525
Therefore, the answer is B. $14,525.
Using only addition and multiplication, combine the single -digit numbers 1,2,3,4,5,6,7,8,9. So they total 100. the number must stay in the same order (Parentheses are not needed)
It is not possible to find a combination using addition and multiplication of the given single-digit numbers that totals exactly 100 while keeping the same order.
To combine the single-digit numbers 1, 2, 3, 4, 5, 6, 7, 8, and 9 using only addition and multiplication so that they total 100 while keeping the same order, we can form the following expression:
1 + 2 + 3 + 4 + 5 + 6 + 78 + 9
In this expression, we group the numbers 7 and 8 together to form 78. Then, we add all the other numbers from 1 to 6 and the number 9. Adding them up, we get:
1 + 2 + 3 + 4 + 5 + 6 + 78 + 9 = 108
Unfortunately, the sum obtained from this expression is 108, not 100 as required.
It is not possible to obtain a sum of exactly 100 by combining the single-digit numbers 1 to 9 in the given order using only addition and multiplication. This is because the largest single-digit number, 9, is relatively small compared to the desired total of 100.
Adding all the single-digit numbers in order without any multiplication would result in a sum of 45, which is significantly lower than 100. Multiplication can only further decrease the sum, making it even more difficult to reach 100.
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In Washington County,1/16 of the adults polled said they enjoyed gardening. In Webster County, 5 out of 76 adults polled said they liked to garden. Which county has a greater fraction of adults who enjoy gardening?
Step-by-step explanation:
1/16 for Washington County.
5/76 for Webster County.
so, let's bring both to the same denominator (bottom part of the fractions).
this is usual the LCM of both denominators.
since 16 = 2×2×2×2
76 = 2×2×19
the least common multiple (LCM) is the combination of the longest sequence per prime factor involved :
2×2×2×2×19 = 16×19 = 304
1/16 = 19/304
5/76 = 5× 1/76 = 5× 4/304 = 20/304
so, now we know, 20/304 > 19/304, and therefore Webster County has the greater fraction of adults, who enjoy gardening.
find the slope and y - intercept of x = 0
Answer:
When the equation is written in the slope-intercept form (y=mx+b) we can find the y-intercept by looking at the equation. The value of b is the y-intercept. This is because the y-intercept is when the x value equals 0. When x = 0, mx = 0, so when x = 0, y = b.
Step-by-step explanation:
trust the process
what is 6,383 in expended form?
Answer:
expanded notation form:
6,383 =
6,000
+ 300
+ 80
+ 3
expanded factors form:
6,383 =
6 × 1,000
+ 3 × 100
+ 8 × 10
+ 3 × 1
expanded exponential form:
6,383 =
6 × 103
+ 3 × 102
+ 8 × 101
+ 3 × 100
Step-by-step explanation:
i wasn't entirely sure what you needed but i hope this helps :) have a great day !!
9/4 as an improper fraction?
Answer:
9/4 is already an improper fraction but if u want a proper, it would b 2 1/4
Step-by-step explanation:
Points A, B, C, and D lie on circle M. Line segment BD is
a diameter. The measure of arc CD equals the measure
of arc DA.
M
D
B
A
D
What is the measure of angle ADM?
O22.5°
30.0⁰
45.0°
67.5°
The measure of angle ADM is 45.0°, as the intercepted arc AD is congruent to arc CD.
To find the measure of angle ADM, we need to consider that angle ADM is an inscribed angle and its measure is half the measure of the intercepted arc AD.
Given that the measure of arc CD equals the measure of arc DA, it means that these arcs are congruent.
Therefore, the intercepted arcs AD and CD have equal measures.
Since angle ADM is an inscribed angle intercepting arc AD, the measure of angle ADM is half the measure of arc AD.
Therefore, the measure of angle ADM is 45.0°, as the intercepted arc AD is congruent to arc CD.
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Find the area of the shape shown below.
Answer:
The answer is 32
Step-by-step explanation:
The formula for finding the area of a trapezoid is:
((base 1 + base 2)/ 2 )* h
Now all you have to do is substitute the numbers in.
Note: bases will always be the ones like 12 and 4 in this case. We have just named then 1 and 2.
Answer:
32 square units
Step-by-step explanation:
\(\displaystyle A=\frac{1}{2}(b_1+b_2)h=\frac{1}{2}(12+4)(4)=\frac{1}{2}(16)(4)=\frac{1}{2}(64)=32\)
Note that \(b_1\) and \(b_2\) are the lengths of each base of the trapezoid, so it doesn't matter which is which.
Select all statements below that are true about the binomial distribution shown on the right. The bar for any number k represents the probability of getting k successes in 5 flips. The number of successes, k, can range from 0 (no success) to 5 (all successes). Each coin flip is independent; it is not affected by any other coin flip. For 5 coin flips, P(2 heads) = P(3 heads). The sum of the probabilities shown in the binomial distribution is p.
Answer:
Step-by-step explanation:
Hello!
Distribution in attachment.
The variable of interest is:
X: Number of successes after flipping a coin 5 times.
If you check the binomial criteria:
The number of trials is fixed: n=5
There are only two possible outcomes "success" or "failure"
Each flip of the coin is independent of the others.
The probability of success in the same from one trial to another, in this case, if we consider the coin to be balanced, the probability of success is p=0.5
The histogram shows the probability of obtaining X number of success in 5ve flips of a coin (y-axis) vs the number of successes counted each (x-axis)
Statements:
1) The bar for any number k represents the probability of getting k successes in 5 flips. Correct. The histogram shows the probability of obtaining X number of success in 5ve flips of a coin (y-axis) vs the number of successes counted each (x-axis). Each bar represents the probability of success for each possible value.
2) The number of successes, k, can range from 0 (no success) to 5 (all successes). Correct. The variable count the number of successes after flipping a coin 5 times. It can happen that you flip it and all the flips turn to be failures (X=0), that you flip it 5 times and only one turns out to be a success and the other 4 are failures (X=1), and so on until you flip it 5 times and all flips are successes (X=5)
3) Each coin flip is independent; it is not affected by any other coin flip. Correct, if not, this variable wouldn't have a binomial distribution as specified in the text.
4) For 5 coin flips, P(2 heads) = P(3 heads). Correct
Looking at the histogram, the bars for "2 successes" and "3 successes" have the same height, a little above 0.3, this means that both values have the same probability of occurrence.
5) The sum of the probabilities shown in the binomial distribution is p.
Incorrect.
For the binomial distribution "p" represents the probability of success for each trial, in this case, flipping the coin once.
For this distribution, as well as for other probability distribution, the sum of all probabilities is always 1, if not, then it is not a probability distribution.
I hope this helps!
Answer:
Lets make this easier for you guys. The correct answers are 1 through 4.
The bar for any number k represents the probability of getting k successes in 5 flips.
The number of successes, k, can range from 0 (no success) to 5 (all successes).
Each coin flip is independent; it is not affected by any other coin flip.
For 5 coin flips, P(2 heads) = P(3 heads
Step-by-step explanation:
Correct on edge :))
When Mia volunteers to pick up trash onthe side of the highway, she can collect 5bags of trash in 2 hours. Mia works at aconstant rate. How many bags of trashcan Mia collect in 8 hours?
Solution:
Given that Mia volunteers to pick up trash on the side of the highway, she collects 5 bags of trash in 2 hours as shown in the table below:
According to the table, in 8 hours, she can collect 20 bags of trash.
The fourth option is the correct answer.
Mr. George has 5 bookcases in his classroom. Each bookcase has 3 shelves. Each
shelf has 20 books. How many total books are on Mr. George's 5 bookcases?
CLEAR
SUBMIT
300 books
160 books
100 books
60 books
Answer:
300
Step-by-step explanation:
i need help with the answer i also need to explain this question
Answer: B: 20
Step-by-step explanation: We can take 40% as a fraction to make it 4/10, simplifying gives 2/5. 2/5 of 50 is 20!
Hope this Helps!
A probability experiment is conducted in which the sample space of the experiment is S={ 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14}, event F={5, 6, 7, 8, 9}, and event G={9, 10, 11, 12}. Assume that each outcome is equally likely. List the outcomes in F or G. Find P(F or G) by counting the number of outcomes in F or G. Determine P(F or G) using the general addition rule.
List the outcomes in F or G. Select the correct choice belowand, if necessary, fill in the answer box to complete your choice.
A. F or G = { _____ }
(Use a comma to separate answers as needed.)
F or G = { 5,6,7,8,9,10,11,12 } is probability P(F or G) using the general addition rule.
What are examples and probability?
The likelihood that something will happen is called the probability. the total number of conceivable outcomes.
For instance, the chance of flipping a coin and obtaining heads is 1 in 2, as there is only one way to acquire a head and there are a total of 2 possible outcomes (a head or tail). P(heads) = 12 is what we write. the forerunners of the contemporary mathematical theory of probability (for example the "problem of points").
S={ 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14},
event F={5, 6, 7, 8, 9}, and
event G={9, 10, 11, 12}.
F or G = { 5,6,7,8,9,10,11,12 }
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Given that m2Q=63 and DQ-7, find z rounded to the nearest tenth.
Answer:
Ali is a boy
Step-by-step explanation:
Ali is a good boy
Is the point (-255,76) on the line shown below
Answer:
yes it's is shown in the diagram below and prosperity more than your expectation for me too anymore I just
in 2010 an earthquake below the ocean floor initiated a devastating tsunami in Samatra. scientists can approximate the velocity V in feet per second of a tsunami in water of depth d feet with the formula \(\sqrt{16} \\\) \(\sqrt{d}\). Determine the velocity of a tsunami in 300 feet of water. Write your answer in simplified radical form.
Its velocity is 69.28 feet/sec of a tsunami in 300 feet of water.
What is speed?Speed is measured as distance moved over time. The formula for speed is speed = distance ÷ time. To work out what the units are for speed, you need to know the units for distance and time. In this example, distance is in metres (m) and time is in seconds (s), so the units will be in metres per second (m/s).
here, we have,
Since the depth of the water 'd' (in feet) and the velocity of the wave 'v' (in feet per second) are related by the equation
v = √(16d)
a wave forms in water with a depth of 300 feet,
therefore d = 300 ft
so, we get,
velocity = √(16*300)
= 4√300
=4*17.32
=69.28
Hence, Its velocity is 69.28 feet/sec of a tsunami in 300 feet of water.
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suppose that grade point averages of undergraduate students at one university have a bell-shaped distribution with a mean of 2.56 and a standard deviation of 0.37 . using the empirical rule, what percentage of the students have grade point averages that are greater than 3.67 ? please do not round your answer.
93.7% of the students have a grade point average of 3.67
The Empirical Rule defines that for a normally distributed random variable:
1 standard deviation of the mean measures with 68%
2 standard deviations of the mean are measured at 95%.
3 standard deviations of the mean measures 99.7%.
The given information is:
Mean=2.56 and the standard deviation is 0.37.
By using the empirical rule, we can calculate the percentage of students who have a grade point of 3.67
3.67 = 2.56 + 3*0.37
So both the scores are within 3 standard deviations of the mean, which is 93.7% of the students have a grade point of 3.67.
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Which polynomial is prime?
O 3x³ + 3x² - 2x - 2
O 3x³ − 2x² + 3x − 4
-
O
4x³ + 2x² + 6x + 3
O
4x³+4x²-3x - 3
Answer:
B
Step-by-step explanation:
a prime polynomial is one which does not factor into 2 binomials.
its only factors are 1 and itself
attempt to factorise the given polynomials
3x³ + 3x² - 2x - 2 ( factor the first/second and third/fourth terms )
= 3x²(x + 1) - 2(x + 1) ← factor out common factor (x + 1) from each term
= (x + 1)(3x² - 2) ← in factored form
--------------------------------------------------
3x³ - 2x² + 3x - 4 ( factor the first/second terms
= x²(3x - 2) + 3x - 4 ← 3x - 4 cannot be factored
thus this polynomial is prime
----------------------------------------------------
4x³ + 2x² + 6x + 3 ( factor first/second and third/fourth terms )
= 2x²(2x + 1) + 3(2x + 1) ← factor out common factor (2x + 1) from each term
= (2x + 1)(2x² + 3) ← in factored form
-------------------------------------------------
4x³ + 4x² - 3x - 3 ( factor first/second and third/fourth terms )
= 4x²(x + 1) - 3(x + 1) ← factor out common factor (x + 1) from each term
= (x + 1)(4x² - 3) ← in factored form
--------------------------------------------------
the only polynomial which does not factorise is
3x³ - 2x² + 3x - 4
write each info entire radical √48
The value of the radical √48 is 4√3.
Radical is a symbol (√) that denotes square roots and nth roots. The number inside the symbol is called Radicand and the expression containing the radical or a square root is called a Radical expression.
Here, we are given the radical √48
To find the value of the radical, we will factorize 48
i.e., 48 = 2×2×2×2×3
= 16×3
Now, the square root of 48, that is, √48
= \(\sqrt{16\cdot3}\) =\(\sqrt{16} \cdot \sqrt{3}\)
We know 16 is a perfect square of 4, that is, the square root of 16= 4
⇒√16=4
Using this, we have √48= 4√3
The correct answer is 4√3.
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In a box there a total of four prizes: Two of them are worth $4, a single prize worth $26, and a single prize worth $241. A player will reach into the box and draw one of the prizes at random. What is the fair price for this game?
So,
First of all, the player has a 1/4 chance of drawing any of the 4 prizes.
This means that the probability of drawing a prize of $4 is 1/2 because there are 2 prizes worth of $4. The probability of drawing a prize of $26 is 1/4 and the probability of drawing a prize of $241 is also 1/4.
To find the fair price, we need to find the expected value of this problem:
This can be obtained by multiplying any possible value of a price for the probability of drawing a prize of that value and adding all these Hvalues together.
This is:
\(\begin{gathered} 4\cdot\frac{1}{2}+26\cdot\frac{1}{4}+241\cdot\frac{1}{4} \\ \\ =\frac{275}{4}=68.75 \end{gathered}\)Therefore, the fair price of this game is $68.75.
Which statements are correct? Select all that apply.
Expanding is the same as using the distributive property.
Factoring means going from ab + ac to a(b + c).
Factoring can only be done when an expression has two terms.
Factoring can only be done when an expression has plus signs.
Statement 1, 2 and 3 are correct about using the distributive property.
Expanding is the same as using the distributive property. Factoring means going from ab + ac to a(b + c).Factoring can only be done when an expression has two terms.
Statement 1: Expanding is the same as using the distributive property. The distributive property states that a(b + c) = ab + ac. When we expand an expression, we are multiplying everything out. So, expanding an expression is the same as using the distributive property. Therefore, this statement is correct.
Statement 2: Factoring means going from ab + ac to a(b + c).When we factor an expression, we are essentially undoing the distributive property. In other words, we are going from a common factor in the two terms to a product. This is exactly what happens when we factor ab + ac to a(b + c). Therefore, this statement is correct.
Statement 3: Factoring can only be done when an expression has two terms. Factoring is the process of breaking down an expression into simpler factors. However, in order to do that, the expression needs to have two or more terms. If the expression only has one term, then we cannot factor it. Therefore, this statement is correct.
Statement 4: Factoring can only be done when an expression has plus signs. This statement is incorrect. Factoring can be done when an expression has either plus signs or minus signs. For example, we can factor x² - 4 to (x + 2)(x - 2). Therefore, this statement is incorrect.
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14) Evaluate each indefinite integral. SHOW STEPS
As a result, -3/10 csc⁵-3x + C is the antiderivative of 9csc-3xcot-3x⋅ csc³-3x.
What is meant by an integral in math?In mathematics, an integral is either a number representing the region under a function's graph for a certain interval or an added to the initial, the derivative which is the previous function (indefinite integral).
9csc-3xcot-3x ⋅ csc³-3x = 9csc⁴-6x cot-3x
Then, we can use u-substitution, with u = csc-3x and du/dx = -3csc-3xcot-3x dx, as in the previous problem. We get:
∫9csc-3xcot-3x⋅ csc³-3x dx = -3/2 ∫u⁴ du
= -3/2 × u⁵ / 5 + C
= -3/10 csc⁵-3x + C
Therefore, the antiderivative of 9csc-3xcot-3x⋅ csc³-3x is -3/10 csc⁵-3x + C.
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Linear Functions
Quiz Active
1
2
3
-4
O-3
020
23
4
5
6
DI
What is the slope of the equation y-3 = -4(x - 5)?
By answering the presented question, we may conclude that As a result, the slope of \(y_3\) = -4(x - 5) is -4.
what is slope?The slope of a line indicates how steep it is. The term "gradient overflow" refers to a mathematical equation for the gradient (the change in y divided by the change in x).
The slope is defined as the ratio of the vertical change (rise) between two places to the horizontal change (run). The slope-intercept form of an equation is used to express a straight line's equation, which is written as y = mx + b.
The y-intercept is found where the slope of the line is m, b is b, and (0, b). For example, the slope and y-intercept of the equation y = 3x - 7 (0, 7). The slope of the line is m. b is b at the y-intercept, and (0, b).
The above equation is in point-slope form: y - \(y_1\)= m(x - \(x_1\)), where (\(x_1\), \(y_1\)) is a point on the line and m is the slope.
We can see by comparing the provided equation to the point-slope form that \(x_{1} ,y_1\)) = (5, 3) and m = -4.
As a result, the slope of \(y_3\) = -4(x - 5) is -4.
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A machine fills containers with 35 ounces of raisins
The correct graph will be the first one (A)
Given a number n, for each integer i in the range from 1 to n inclusive, print one value per line as follows: • If iis a multiple of both 3 and 5, print FizzBuzz. • If iis a multiple of 3 (but not 5), print Fizz. • If iis a multiple of 5(but not 3), print Buzz. • If i is not a multiple of 3 or 5, print the value ofi. Function Description Complete the function fizzBuzz in the editor below. fizzBuzz has the following parameter(s): int n: upper limit of values to test (inclusive) Returns: NONE Prints: The function must print the appropriate response for each value i in the set {1, 2, ... n}in ascending order, each on a separate line. Constraints • 0
The program is an illustration of loops and conditional statements and the part of the complete program is
n = int(input())
for i in range(1,n+1):
if not(i%3 == 0 or i%5==0):
How to determine the program using the conditions?The program written in Python where comments are used to explain each line is as follows:
#This gets input for n
n = int(input())
#This iterates through n
for i in range(1,n+1):
#If the current number is not a multiple of 3 and 5
if not(i%3 == 0 or i%5==0):
#This prints the number
print(i,end="")
else:
#This prints "Fizz", if the current number is a multiple of 3
if i%3 == 0:
print("Fizz",end="")
#This prints "Buzz", if the current number is a multiple of 5
if i%5==0:
print("Buzz",end="")
#This prints a new line
print()
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Mary has 6 blouses, 5 skirts and 4 belts. How many outfits can she make, consisting of a blouse, a skirt and a belt?
Answer:
120
Step-by-step explanation:
Use the counting principle.
6 × 5 × 4 = 120
Answer: 120