Find the nth term of this quadratic sequence
4, 9, 16, 25, 36, ..
The nth term of this quadratic sequence 4,9,16,25,36 is [tex]n^{2} + 2n + 1[/tex]
Given that:
the given sequence is 4,9,16,25,36
nth term of quadratic sequence is [tex]an^{2}+bn+c[/tex]
Now lets find out the value of each variable a,b,c
a = second difference divide by 2
lets find out second difference
4,9,16,25,36
the first difference between the terms are
5,7,9,11
The second difference between the terms
2,2,2
the value of a = second difference / 2
[tex]a = \frac{2}{2} = 1\\[/tex]
a = 1
Now we find the value of b
3a + b = first term of first difference
3a + b = 5
3(1) + b = 5
3 + b = 5
b = 5 - 3
b = 2
Now find the value of c
a + b + c = first term
a + b + c = 4
1 + 2 + c = 4
3 + c = 4
c = 1
Now we replace all the values to find the nth term
[tex]an^{2}+bn+c\\ \\n^{2}+2n+1[/tex]
Hence the answer is the nth term of this quadratic sequence 4,9,16,25,36 is [tex]n^{2} + 2n + 1[/tex].
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which of the following is an example of a paired design? question 7 options: a teacher compares the scores of students in her class on a standardized test with the national average score. a teacher compares the pre-test and post-test scores of students. a teacher calculates the average score of students on a pair of tests and wishes to see if this average is larger than 80%. a teacher compares the scores of students using a computer-based method of instruction, with the scores of other students using a traditional method of instruction. question 8 (1 point)
The statement “A teacher compares the pretests and posttest scores of students” is an example of matched pairs design.
Given data;
A teacher contrasts the results of her class's standardized test with the entire country's results. An instructor contrasts the results of the students' pre-and post-tests. A teacher computes the average grade received by students on two tests and checks to see if it is greater than 80%. An instructor contrasts the results of students who were taught using a computer-based method with those of post-students whose students ought to use a more conventional approach.
⇒
The statement “A teacher compares the pretests and posttest scores of student” using here would be approach-test because the sample “the students’ scores” are being compared with the two different treatments” and pretest and posttest scores.
A matched pairs design is demonstrated with the sentence "A teacher compares the pretests and posttest scores of students."
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HELP MEEEEE PLEASEE TYYY
Answer:
4 metters por el significado
28/63 en la forma más simple
plss ayuda para que suba al 70% en el khann
The value of the fraction 28/63 in the simplest form is 4/9.
What is a fraction?A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.
In this case, we want to reduce 28/63 yo the simplest term. This will be illustrated thus:
= 28/63
= (7 × 4) / (9 × 7)
= 4 / 9
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Given (x – 7)^2 = 36, select the values of x.
x = 13, x = 1, x = –29, x = 42
Answer:
x = 13 x = 1
Step-by-step explanation:
(13-7) = 6
6^2 = 36
1-7 = -6
(-6)^2 = 36
In a class of 25 students, 14 are boys and 11 are girls. On a unit test, 6 boys and 6 girls made an A grade. If a student is chosen at random from the class, what is the probability of choosing a boy or an A student?
If in a class of 25 students, 14 are boys and 11 are girls. On a unit test, 6 boys and 6 girls made an A grade. If a student is chosen at random from the class, The probability of choosing a boy or an A student 4 / 5
How to solve for the probabilityFrom the question, we have the following data
Total number of students = 25
The total number of boys = 14
The students that are A male students = 6
Then we would have probability of having an A male student to be:
Total boys + A male students / total
= 14 + 6 / 25
= 4 / 5
Hence the probability is 4 / 5
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the food and drug administration (fda) is a u.s. government agency that regulates (you guessed it) food and drugs for consumer safety. one thing the fda regulates is the allowable insect parts in various foods. you may be surprised to know that much of the processed food we eat contains insect parts. an example is flour. when wheat is ground into flour, insects that were in the wheat are ground up as well. the mean number of insect parts allowed in 100 grams (about 3 ounces) of wheat flour is 75. if the fda finds more than this number, they conduct further tests to determine if the flour is too contaminated by insect parts to be fit for human consumption. the null hypothesis is that the mean number of insect parts per 100 grams is 75. the alternative hypothesis is that the mean number of insect parts per 100 grams is greater than 75. is the following a type i error or a type ii error or neither?
Since in the question we reject the alternative hypothesis hence type II error occurs.
What is Type I error?
When the null hypothesis is true but rejected in hypothesis testing, type 1 errors often confused with false positives occur. A general assertion or default attitude that there is no connection between two measurable phenomena is known as the null hypothesis.
What is Type II error?
Type II errors take place when you fail to reject the null hypothesis even though it is untrue.
The average number of insect parts per 100 gm in this problem is 75. This number cannot be demonstrated by the test to be larger than 75. This indicates that the test is producing a "false negative" since it is not detecting these insect parts.
Hence, this is a Type II error.
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I need help please!!
Answer:
1/2
Step-by-step explanation:
(-6-(-4)/(3-7)
(-6+4)/-4
-2/-4
1/2
I need help please!!!
the slope of the given point is m=−3/4
Whenever you are asked to construct and interpret a confidence interval, what are the steps to the process you must complete?
A. plan, state, do, conclude
B. state, plan, do, conclude
C. plan, do, state, conclude
D. state, do, conclude, plan
ANSWER IS B
A tudy invetigated the tatitical quetion: ""How many hour per week do teenager pend playing a port or outdoor game?"" Here are the data that wa collected from a ample of 10 teenager howing the number of hour per week pent playing a port or a game outdoor: 3; 2; 0; 6; 3; 3; 3; 1; 1; 2
The numbers of hours per week teenagers spend playing a sport or outdoor game is 2.4 or 2[tex]\frac{1}{15}[/tex] hours.
What is Averaging?
This refers to the mean value, which is equal to the ratio of all the numbers added and divided by the number of a given set of values present in the set of values.
Average= x₁+x₂+x₃+x₄..........xn
n
Where,
x₁+x₂+x₃+x₄..........xn = Given set of values
n= Number of a given set of values
From the question:
The number of hour per week spent playing a port or a game outdoors:
3; 2; 0; 6; 3; 3; 3; 1; 1; 2
number of teenagers,n =10
Average= 3+ 2+ 0+ 6+3+3+3+ 1+ 1+2
10
=2.4 or 2[tex]\frac{1}{15}[/tex] hours.
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Identify the slope and y-intercept for the following equation.
-2y-10+2x=0
Slope:
Y-intercept:
Giving 50 points :)))
Pls need help on #7!!!
Answer:
6
Step-by-step explanation:
Each coordinate is six times the corresponding coordinate in the preimage.
How do you approximate on a calculator?
Answer:
enter a function and from there you approximate hope it helps
Suppose that F(x) = x² and G(x) = -1/4 (x+7)². Which statement best compares
the graph of G(x) with the graph of F(x)?
A. The graph of G(x) is the graph of F(x) stretched vertically, flipped
over the x-axis, and shifted 7 units to the right.
B. The graph of G(x) is the graph of F(x) stretched vertically, flipped
over the x-axis, and shifted 7 units to the left.
C. The graph of G(x) is the graph of F(x) compressed vertically,
flipped over the x-axis, and shifted 7 units to the right.
OD. The graph of G(x) is the graph of F(x) compressed vertically,
flipped over the x-axis, and shifted 7 units to the left.
The statement that best compares the graph of G(x) with the graph of F(x) is the graph of G(x) is the graph of F(x) compressed vertically, flipped over the x-axis, and shifted 7 units to the left.
According to the question,
We have the following information:
F(x) = x² and G(x) = -1/4 (x+7)²
Now, the graph of G(x) will be the graph of F(x) but there will be certain changes in the graph according to its function.
Now, in this function, 7 is added to x then it means that it will shift 7 units to left.
There is a negative sign before the function which says that is flipped over the x-axis.
Now, the factor 1/4 in the multiplication says that it has been compressed.
Hence, the correct option is D.
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Pls answe only 9 and 10 and this is due tomorrow
The value is 5/2 and 35/2 pounds.
What is meant by ratio?Comparing two amounts of the same units and determining the ratio tells us how much of one quantity is in the other. Two categories can be used to categorize ratios.
Part to whole ratio is one, and part to part ratio is the other. The part-to-part ratio shows the relationship between two separate entities or groupings.
For instance, a class has a 12:15 boy-to-girl ratio, whereas the part-to-whole ratio refers to the relationship between a particular group and the entire.
The ratios of the given table
Table 10,
[tex]\begin{aligned}&\Rightarrow \frac{5}{3}=\frac{1}{x} \\&\Rightarrow x=\frac{3}{5} \\&\Rightarrow \frac{5}{3}=\frac{12}{x}=\frac{12+3}{15} \\&\Rightarrow x=\frac{12}{5}\end{aligned}[/tex]
Table 9,
[tex]\begin{aligned}&\frac{10}{4}=\frac{5}{2} \\&\frac{5}{2}=\frac{x}{1} \\&x=\frac{5}{2} \\&\frac{5}{2}=\frac{x}{7} \\&x=\frac{35}{2}\end{aligned}[/tex]
[tex]\begin{array}{rccc}\text { 9) pounds } & 10 & \frac{5}{2} & \frac{35}{2} \\\text { Weeks } & 4 & 1 & 7 \\\text { 10) tons } & 5 & 1 & 12 \\\text { days } & 3 & \frac{3}{5} & \frac{12}{5}\end{array}[/tex]
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the diameter of a circle is 24 feet. what is the approximate circumference of the circle? use 3.14 for pie
Circumference = pi x d
Circumference = 3.14 x 24 = 75.36
I hope this helps!
For his phone service, Chang pays a monthly fee of $27, and he pays an additional $0.07 per minute of use. The least he has been charged in a month is
$121.71.
What are the possible numbers of minutes he has used his phone in a month?
Use m for the number of minutes, and solve your inequality for m.
1353 numbers of minutes he has used his phone in a month.
What do you mean by algebraic expression?
In mathematics, an algebraic expression is an expression composed of integer constants, variables, and algebraic operations (addition, subtraction, multiplication, division, and exponentiation by exponents that are rational numbers).
Algebraic equations are equations that contain only algebraic expressions.
Algebraic expression is the idea of using letters or alphabets to represent numbers without specifying the actual value. Algebra Basics taught us how to use letters like x, y, and z to represent unknown values. These characters are called variables here.
It is given that Chang pays a monthly fee of $27, and he pays an additional $0.07 per minute of use.
Let m be the additional minutes
Then charge for additional minutes is $0.07m
Now , it is also given that least he has been charged in a month is
$121.71.
⇒ 0.07m + 27 = 121.71
⇒ 0.07m = 121.71 - 27
⇒ 0.07m = 94.71
⇒ m = 94.71/0.07 = 1353
Therefore, 1353 numbers of minutes he has used his phone in a month.
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how many numbers must be randomly selected from the set \{1,3,5,7,9,11,13,15\}{1,3,5,7,9,11,13,15} to guarantee that at least one pair of these numbers add up to 1616?
The number of pairs that must be randomly selected from the set {1,3,5,7,9,11,13,15} to guarantee that at least one pair of these numbers add up to 16 is 5.
In the given set {1,3,5,7,9,11,13,15}, there are four pairs that sum up to 16, which are (1,15), (3,13), (5,11), and (7,9). Let k numbers be picked from the set. Consider k = 5, then using the pigeonhole principle, for one of the pairs described above, both of the endpoints must have been picked. Hence, if 5 numbers are picked from the set, then there exists a pair with a sum of 16.
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the sides of a square are dilated by a scale factor of 1/2. the perimeter of the bigger square is 24 ft. what is the perimeter of the smaller square? A. 48 feet B. 12 feet C. 8 feet D. 4 feet
The perimeter of the smaller square would be = 12feet. That is option B.
What is perimeter?Perimeter can be defined as the summation of all the sides and edges of an object.
Scale factor is also defined as the ratio of difference between an original object and a newly formed object.
A square has four sides and it's perimeter = 24 ft
This means that the sides of the square= 24/4 = 6ft.
If the original (smaller square) dialted by a factor of 1/2 to have 6 ft as its sides, it means that it's original side of the small square is 3ft.
This is because to form the bigger square, 1/2 × 6 = 3ft.
Therefore, the perimeter of small square = 3+3+3+3 = 12ft.
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11 Find the value of x.
(x+8)
fo
-(6x-58)
12 FT
Determine the size of all missing angles:
angle a =
angle b =
angle c =
angle d =
angle e =
Answer:
angle a = 74 degrees
angle b = 106 degrees
angle c = 106 degrees
angle d = 65 degrees
angle e = 65 degrees
Step-by-step explanation:
Angle a:
the Alternate Interior Angles Theorem makes angle a equal to 74 degrees
Angle b:
First find angle c, and angle b is equal to angle c because angle b and c are Corresponding angles
Angle c:
angle c = 180 degrees - 74 degrees
angle c = 106 degrees
Angle d:
angle d corresponds with 65 degrees, therefore the are the same.
Angle e:
angle d and e are opposite angles, therefore they are the same.
The residents of a city voted on whether to raise property taxes. The ratio of yes votes to no votes was 2 to 3. If there were 4335 total votes, how many yes
votes were there?
Answer: The number of no votes is 1876 votes.
What is the ratio?
"The ratio is a term that is used to compare two or more numbers. It is used to indicate how big or small a quantity is when compared to another".
For the given situation,
Let x be the number of votes.
The ratio of yes votes : no votes = 3x:2x
Total = 5x
Total votes = 4690 votes
⇒
Divide by 5 on both sides,
⇒
Thus the number of no votes =
⇒
⇒
Hence we can conclude that the number of no votes is 1876 votes.
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Step-by-step explanation:
-18t=-3(t+5) distributive property and using division first HELP PLEASE
Answer: T= 1
Step-by-step explanation:
Which of the following is true of prime numbers?
A.
A prime number may be an even number or an odd number.
B.
A prime number is always an even number.
C.
A prime number is always an odd number.
D.
A composite number may be an even number or an odd number.
Answer:
a is right (prime number is always a even number)
Answer:
A.
a prime number may be an even or an odd number
PLEASE ANSWER I WILL MARK BRAINLIEST!!!!!!
Deon throws a ball into the air. The height h of the ball in meters at time T seconds is modeled by the function h(t) =-5t^2+9t+2. will the ball reach a height of 5 m??
(Also what is the discriminant)
It is possible that the ball may reach a height of 5 meters in accordance with the quadratic formula.
May the ball reach a height of 5 meters?
The height of the ball as a function of time is represented by a quadratic equation, in which we must determine if the ball may reach a height of 5 meters. First, substitute the height in the quadratic equation:
- 5 · t² + 9 · t + 2 = 5
5 · t² - 9 · t + 3 = 0
Second, use the quadratic formula to determine the roots of the resulting quadratic equation:
t = - (- 9) / (2 · 5) ± [1 / (2 · 5)] · √[(- 9)² - 4 · 5 · 3]
t = 9 / 10 ± (1 / 10) · √(81 - 60)
t = 9 / 10 ± √21 / 10
t = (9 ± √21) / 10
Since all roots of the quadratic equations are real, then the ball can reach a height of 5 meters above the ground.
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An element with a mass of 200 grams decays by 15.7% per minute. To the nearest minute, how long will it be until there are 60 grams of the element remaining?
Answer:
3.82%
Step-by-step explanation:
Please help
What is the area, in square feet, of the shape below? Express your answer as a fraction in simplest form.
2/3 ft
4/3 ft
Answer:
4/9
Step-by-step explanation:
Area of a triangle is 1/2*base*height
1/2*2/3*4/3 = 8/18 = 4/9
Tyrone can type 87 words in three minutes at this rate how long will it take him to type 1624 words
Find the length of x
The length of x is 4.1.
Given:
Base = 9 + 4.5 = 13.5
From figure:
= [tex]\sqrt{9^{2}+5^{2} }[/tex]
= [tex]\sqrt{81+25}[/tex]
= [tex]\sqrt{96}[/tex]
= 9.797
4.5 opposite is equal to 4.5.
5 opposite equal to 5 and remaining to x - 5.
According to pythagorean theorem:
= [tex]\sqrt{4.5^{2}+(x-5)^{2} }[/tex]
[tex]13.5^{2} +x^{2} =(\sqrt{96}+\sqrt{4.5^{2} +(x-5)^{2} })^{2}[/tex]
[tex]\sqrt{13.5^{2} +x^{2} }[/tex] - [tex]\sqrt{96} = \sqrt{20.25+x^{2} +25 -10x}[/tex]
squaring on both sides
182.25 + [tex]x^{2}[/tex] - 96 = [tex]x^{2}[/tex] - 10x + 45.25
10x = 45.25 + 96 - 182.25
10x = 41
x = 4.1.
Therefore the value of x is 4.1.
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