The eighth term of the geometric sequence 4, -20, 100,... is 9600, calculated using the formula aₙ = arⁿ⁻¹ with a = 4, r = -5, and n = 8.
The eighth term of the geometric sequence 4, -20, 100,... is 9600.
To find the eighth term of a geometric sequence, you can use the formula: aₙ = arⁿ⁻¹, where a is the first term, r is the common ratio, and n is the term number. In this case, a = 4, r = -5, and n = 8.
Plug the values into the formula: 4 x (-5)⁸⁻¹ = 9600.
"what is the binary equivalent of the decimal value 97?"
Final answer:
To find the binary equivalent of the decimal number 97, one divides it by 2 repeatedly and records the remainders in reverse order, resulting in the binary number 1100001.
Explanation:
The binary equivalent of the decimal value 97 can be found using a process of dividing by 2 and keeping track of the remainders. Firstly, divide 97 by 2, which gives a quotient of 48 and a remainder of 1. We write down the remainder. Continuing this process:
48 divided by 2 equals 24 with 0 remainder.24 divided by 2 equals 12 with 0 remainder.12 divided by 2 equals 6 with 0 remainder.6 divided by 2 equals 3 with 0 remainder.3 divided by 2 equals 1 with 1 remainder.1 divided by 2 equals 0 with 1 remainder (as we have now reached a value less than 2).After collecting all the remainders in reverse order, the binary equivalent of decimal 97 is 1100001.
Jack and Andrea want to create a right triangle together using values of x and y and the polynomial identity to generate Pythagorean triples. If Andrea picks a value of x = 2, and the hypotenuse of the resulting right triangle is 5, what natural number value of y did Jack pick? y = 1 y = 2 y = 3 y = 4
A right triangle can be considered as a special type because the relationship of its sides can be described using the hypotenuse formula:
c^2 = a^2 + b^2
or
c^2 = x^2 + y^2
where,
c is the hypotenuse of the triangle and is the side opposite to the 90° angle
while a and b are the sides adjacent to the 90° angle
In the problem statement, we are given that one of the side has a measure of 2 = x, while the hypotenuse is 5 = c, therefore calculating for y:
y^2 = c^2 – x^2
y^2 = 5^2 – 2^2
y^2 = 21
y = 4.58
The natural number is the number before the decimal. Therefore the answer is:
y = 4
Answer:
it is now y=4, i swear!! I put this, and it was wrong!!!
Step-by-step explanation:
what is the unit rate
The front of an a frame cabin in a national park is the shape of a triangle, with an area of 189 ft.². If the height is 1 foot less than twice the base, find the base and the height of the front of the cabin.
Final answer:
The student needs to solve a quadratic equation to find the base and height of a triangle using the area formula and the given relationship between height and base. The solution involves substitution, expansion, and application of the quadratic formula or factoring.
Explanation:
The problem involves finding the base and height of a triangular front of an A-frame cabin based on its given area and a relationship between the height and base. It's a typical quadratic equation problem found in the high school mathematics curriculum when dealing with geometry and algebra.
To find the base (b) and height (h) of the triangle, we first use the area formula of a triangle A = 1/2 × base × height. We know that the area (A) is 189 ft² and that the height (h) is 1 foot less than twice the base, so h = 2b - 1. Substituting h into the area formula, we get 189 = 1/2 × b × (2b - 1). Solving this quadratic equation, we find the values for the base (b) and substitute back to find the height (h).
The process entails expanding the equation, moving all terms to one side to set the equation to zero, and then using the quadratic formula or factoring to find the value of b. Once the base is found, we use the relationship h = 2b - 1 to determine the height.
Jeremiah is asked to write the equation of an ellipse. He is given one vertex along the major axis and the location of the center. He realizes he does not have enough information to write the equation. He asks his teacher for one additional piece of information. What information could Jeremiah ask for to help him write the equation? Check all that apply.
-the location of the focus nearest the given vertex
-the location of the focus nearest the other vertex
-the location of the other vertex along the major axis
-the location of one covertex along the minor axis
-the location of the directrix nearest the given vertex
-the location of the directrix nearest the other vertex
-the length of the minor axis
Jeremiah needs additional information such as the location of the foci, the other vertex on the major axis, a covertex along the minor axis, or the length of the minor axis to write the equation of the ellipse that is options A, B, C, D and G are correct.
Jeremiah is asked to write the equation of an ellipse given one vertex along the major axis and the location of the center.
He realizes he does not have enough information. He could ask for the following additional pieces of information to help him write the equation:
The location of the focus nearest the given vertexThe location of the focus nearest the other vertexThe location of the other vertex along the major axisThe location of one covertex along the minor axisThe length of the minor axisWith any of these pieces of information, he could determine the necessary parameters to complete the equation of the ellipse.
Jeremiah could ask for the other information that is the location of the other vertex along the major axis, the location of one covertex along the minor axis, the length of the minor axis and the location of the focus nearest the given vertex.
To write the equation of an ellipse, Jeremiah needs more information. Given the center and one vertex along the major axis, he can ask for:
The location of the other vertex along the major axis: This will help determine the length of the major axis.The location of one covertex along the minor axis: This will help find the length of the minor axis.The length of the minor axis: Directly needed to formulate the equation.The location of the focus nearest the given vertex: This helps identify the distance from the center to the foci, which is necessary for finding the equation.With any of this additional information, Jeremiah can confidently determine the parameters required to write the equation of the ellipse.
Can the sum of two irrational numbers ever be a rational number?
110 students are surveyed about their pets. The results are shown in the table. Which statement is true?
The only true statement is b. 40% of the boys surveyed have at least one pet.
To determine which statement is true, let's analyze the data provided in the table:
- Total number of boys surveyed: 45
- Total number of girls surveyed: 65
Now, let's break down the information based on the provided table:
1. **At least one pet:**
- Boys: 18
- Girls: 39
- Total: 57
2. **No pets:**
- Boys: 27
- Girls: 26
- Total: 53
Now, let's check each statement:
a. 27% of the boys surveyed have no pets.
- Percentage of boys with no pets = (Number of boys with no pets / Total number of boys surveyed) * 100%
- = (27 / 45) * 100% ≈ 60%
- This statement is false.
b. 40% of the boys surveyed have at least one pet.
- Percentage of boys with at least one pet = (Number of boys with at least one pet / Total number of boys surveyed) * 100%
- = (18 / 45) * 100% = 40%
- This statement is true.
c. 49% of the girls surveyed have no pets.
- Percentage of girls with no pets = (Number of girls with no pets / Total number of girls surveyed) * 100%
- = (26 / 65) * 100% ≈ 40%
- This statement is false.
d. 57% of the students surveyed have at least one pet.
- Percentage of students with at least one pet = (Total number of students with at least one pet / Total number of students surveyed) * 100%
- = (57 / 110) * 100% ≈ 52%
- This statement is false.
So, the only true statement is b. 40% of the boys surveyed have at least one pet.
The probable question may be:
110 students are surveyed about their pets. The results are shown in the table. Which statement is true?
Boys | Girls | Total
At least one pet | 18 | 39 | 57
No pets | 27 | 26 | 53
Total | 45 | 65 | 110
a. 27% of the boys surveyed have no pets.
b. 40% of the boys surveyed have at least one pet.
c. 49% of the girls surveyed have no pets.
d. 57% of the students surveyed have at least one pet.
Which of the following are solutions to the equation below? (4x - 1)2 = 11
Answer:
X = - sqrt 12 / 4
X = sqrt 11 + 1 / 4
Explain how the phrase "oh heck another hour of algebra" can help a student recall the trigonometric ratios
The phrase "oh heck another hour of algebra" can help a student recall the trigonometric ratios by associating key words in the phrase with math concepts. The phrase contains words related to math, such as "algebra" and "hour," as well as a word similar to "angle." By linking these words to the trigonometric ratios, a student can better remember and understand them.
Explanation:The phrase "oh heck another hour of algebra" can help a student recall the trigonometric ratios by focusing on the key words within the phrase. The phrase contains the words "algebra" and "hour," which are related to math, and the word "heck," which is similar to the word "angle." By associating these words with the phrase, a student can remember the trigonometric ratios, which involve angles and algebraic calculations. For example, the phrase can remind a student that the sine ratio involves the ratio of opposite and hypotenuse sides, similar to finding lengths in algebraic equations.
Learn more about Recalling trigonometric ratios here:https://brainly.com/question/25122832
#SPJ3
What is 16.35 written as a fraction
Which of the following are true statements about any regular polygon? Check all that apply.
A. All of its angles measure 90.
B. It is a quadrilateral.
C. It is a closed figure.
D. It is a hexagon.
E. All of its angles have equal measures.
F. Its sides are congruent line segments.
Answer:
Statement C, E and F are true.
Step-by-step explanation:
We have to find the true statements about a regular polygon.
Regular Polygon
A regular polygon is a polygon that is equiangular that is all angles are equal in measure and equilateral that is all sides have the same length.A) False
This is not a necessity that all angles measure 90 degrees.
B) False
It may or may not be a a quadrilateral.
C) True
All regular polygons are closed figure.
D) False
All regular polygons are not hexagon but hexagon is a polynomial.
E) True
All the angles of a regular polygon are equal.
F) True
Since all the sides of a regular polygon are equal, thus, its sides are congruent line segments.
Given p(a)=0.40, p(b)=0.50. if a and b are independent, what is the value of p(a intersection b)?
Final answer:
The value of P(A intersection B) is 0.20.
Explanation:
Given that events A and B are independent, the probability of their intersection can be found by multiplying their individual probabilities. So, P(A ∩ B) = P(A) * P(B). From the given information, P(A) = 0.40 and P(B) = 0.50. Therefore, P(A ∩ B) = 0.40 * 0.50 = 0.20.
IHELP ME OUT WITH THIS MATH QUESTION
f DE is a mid segment of the triangle, then the measure of AC:
7.5
15.
30.
None of the choices are correct.
Let r(t)=⟨t2,1−t,4t⟩. calculate the derivative of r(t)⋅a(t) at t=5, assuming that a(5)=⟨−4,4,−5⟩ and a′(5)=⟨−5,9,3⟩
3. A carpenter is framing a window with wood trim where the length of the window is 6 and 2\3 feet. If the width of the window is 7 and3\4 feet, how many feet of the wood is needed to frame the window?
57% of men consider themselves professional baseball fans. you randomly select 10 men and ask each if he considers himself a professional baseball fan. find the probability that the number who consider themselves baseball fans is (a) exactly five, (b) at least six, and (c) less than four.
(a) [tex]\( P(X = 5) \approx 0.234 \)[/tex]
(b) [tex]\[ P(X \geq 6) \approx 0.892 \][/tex]
(c) [tex]\[ P(X < 4) \approx 0.020 \][/tex]
To solve this problem, we can use the binomial probability formula since each man's response (considering themselves a baseball fan or not) is independent and there are only two possible outcomes (success or failure).
Given:
- Probability of success (considering themselves a baseball fan) [tex]\( p = 0.57 \)[/tex]
- Probability of failure (not considering themselves a baseball fan) [tex]\( q = 1 - p = 1 - 0.57 = 0.43 \)[/tex]
- Number of trials [tex]\( n = 10 \)[/tex]
We'll calculate the probabilities for each case:
(a) To find the probability that exactly five men consider themselves baseball fans:
[tex]\[ P(X = 5) = \binom{10}{5} \times (0.57)^5 \times (0.43)^{10 - 5} \][/tex]
(b) To find the probability that at least six men consider themselves baseball fans, we can find the probability of six, seven, eight, nine, and ten men being baseball fans, and then sum them up.
(c) To find the probability that less than four men consider themselves baseball fans, we need to find the probabilities of zero, one, two, and three men being baseball fans, and then sum them up.
Let's calculate each probability:
(a) [tex]\[ P(X = 5) = \binom{10}{5} \times (0.57)^5 \times (0.43)^{5} \][/tex]
(b) To find the probability of at least six men being baseball fans:
[tex]\[ P(X \geq 6) = P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10) \][/tex]
(c) To find the probability of less than four men being baseball fans:
[tex]\[ P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) \][/tex]
We'll use these formulas to find the probabilities for each case. Let me do the calculations.
(a) To find the probability that exactly five men consider themselves baseball fans:
[tex]\[ P(X = 5) = \binom{10}{5} \times (0.57)^5 \times (0.43)^{5} \][/tex]
Using the binomial coefficient formula [tex]\(\binom{n}{k} = \frac{n!}{k!(n - k)!}\)[/tex], where [tex]\(n = 10\)[/tex] and [tex]\(k = 5\)[/tex]:
[tex]\[ \binom{10}{5} = \frac{10!}{5!(10 - 5)!} = \frac{10 \times 9 \times 8 \times 7 \times 6}{5 \times 4 \times 3 \times 2 \times 1} = 252 \][/tex]
Now, we plug in the values:
[tex]\[ P(X = 5) = 252 \times (0.57)^5 \times (0.43)^{5} \][/tex]
[tex]\[ P(X = 5) \approx 0.234 \][/tex]
(b) To find the probability of at least six men being baseball fans:
[tex]\[ P(X \geq 6) = P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10) \][/tex]
For each [tex]\(k = 6, 7, 8, 9, 10\)[/tex], we calculate [tex]\(P(X = k)\)[/tex] using the binomial formula and sum them up.
(c) To find the probability of less than four men being baseball fans:
[tex]\[ P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) \][/tex]
Similarly, for each [tex]\(k = 0, 1, 2, 3\)[/tex], we calculate [tex]\(P(X = k)\)[/tex] using the binomial formula and sum them up. Let me do the calculations.
(a) [tex]\( P(X = 5) \approx 0.234 \)[/tex]
(b) To find the probability of at least six men being baseball fans:
[tex]\[ P(X \geq 6) = P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10) \][/tex]
Using the binomial formula for each [tex]\( k = 6, 7, 8, 9, 10 \)[/tex] and summing the probabilities:
[tex]\[ P(X \geq 6) \approx 0.892 \][/tex]
(c) To find the probability of less than four men being baseball fans:
[tex]\[ P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) \][/tex]
Using the binomial formula for each [tex]\( k = 0, 1, 2, 3 \)[/tex] and summing the probabilities:
[tex]\[ P(X < 4) \approx 0.020 \][/tex]
In how many ways can 5 starting positions on a basketball team be filled with 8 men who can play any of the positions?
8 men, 5 positions
so multiply 8*7*6 =336
divide by 3*2 =6
336/6 =56
56 different ways
which of the following is irrational? 7.51•(-4)
The irrational number among the options is root 3 + 8.486. option C.
An irrational number is a number that cannot be expressed as a fraction of two integers and has a non-repeating, non-terminating decimal expansion.
Let's examine each option:
A. [tex]\(7.51\ldots \times -4\)[/tex]
This is a rational number because it's the product of a rational number [tex](\(7.51\ldots\)) and \(-4\),[/tex] which is also rational. So, option A is not irrational.
B. [tex]\(\sqrt{16} + \frac{3}{4}\)[/tex]
[tex]\(\sqrt{16} = 4\)[/tex], so this expression simplifies to [tex]\(4 + \frac{3}{4}\)[/tex], which is a rational number. So, option B is not irrational.
C. [tex]\(\sqrt{3} + 8.486\)[/tex]
If [tex]\(\sqrt{3}\)[/tex] is not exactly equal to 8.486 , then this expression is irrational because it's the sum of an irrational number and a rational number. However, if [tex]\(\sqrt{3}\)[/tex] does happen to be exactly 8.486, then this expression would be rational. To determine if [tex]\(\sqrt{3}\)[/tex] is exactly 8.486, we need to compute [tex]\(\sqrt{3}\).[/tex] Since [tex]\(\sqrt{3}\)[/tex] is irrational (it's not a perfect square), 8.486 is not [tex]\(\sqrt{3}\)[/tex], so this expression is irrational. Therefore, option C is the correct answer.
D.[tex]\(8 \frac{2}{3} \times 17.75\)[/tex]
This is a rational number because it's the product of a rational number [tex](\(8 \frac{2}{3}\)) and \(17.75\),[/tex] which is also rational. So, option D is not irrational.
Complete question: Which of the following is irrational?
A. 7.51... x -4
B. root 16 + 3/4
C. root 3 + 8.486
D. 8 2/3 x 17.75
Kim uses decals to decorate 5 cars and 2 motorbikes. She uses 2/3 of the decals on the cars and 2/5 of the remaining on the motorbikes. She has 6 decals left. How many decals does Kim use on each car?
What is 2/15 in simplest form
What is the value of s in the equation 3r=10+5s when r=10
Answer:
[tex]s=4[/tex].
Step-by-step explanation:
We have been given an equation [tex]3r=10+5s[/tex]. We are asked to find the value of 's', when [tex]r=10[/tex].
To find value of 's', we will substitute [tex]r=10[/tex] in our given equation as shown below:
[tex]3(10)=10+5s[/tex]
[tex]30=10+5s[/tex]
Upon subtracting 10 from both sides of our given equation, we will get:
[tex]30-10=10-10+5s[/tex]
[tex]20=5s[/tex]
Now, we will divide both sides of our equation by 5.
[tex]\frac{20}{5}=\frac{5s}{5}[/tex]
[tex]4=s[/tex]
Therefore, the value of 's' is 4, when [tex]r=10[/tex].
Tatiana wants to give friendship bracelets to her 32 classmates. She has 5 bracelets now. She can buy more bracelets in packages of 4. If p is the number of packages Tatiana needs to buy to have at least 32 bracelets, the inequality representing the problem is: 4p+5≥32 What is the minimum number of packages Tatiana needs to buy?
Let
p--------> the number of packages Tatiana needs to buy
we know that
[tex] 4p+5 \geq 32\\ 4p \geq (32-5)\\ 4p \geq 27\\\\ p \geq \frac{27}{4} \\ \\ p \geq 6.75 [/tex]
therefore
the minimum number of packages does Tatiana needs to buy is [tex] 7 [/tex]
let's check
[tex] 7*4+5=33 [/tex] bracelets
[tex] 33 \geq 32 [/tex] ------> is ok
the answer is
the minimum number of packages is [tex] 7 [/tex]
The sum of the roots of 8x² - 2x = 1 is:
-1/4
1/4
-1/8
In a literal question what does f and c represent
Write an appropriate inverse variation equation if y = 9 when x = 3.
Of 13 possible books, you plan to take 6 with you on vacation. How many different collections of 6 books can you take?
Taking into account the definition of combination, you can take 1716 different collections of 6 books.
CombinationCombinations of m elements taken from n to n (m≥n) are called all the possible groupings that can be made with the m elements in which the order in which the elements are chosen is not taken into account and repetition is not possible.
The combination is calculated by:
[tex]C=\frac{m!}{n!(m-n)!}[/tex]
The term "n!" is called the "factorial of n" and is the multiplication of all numbers from "n" to 1.
Collections of 6 books that you can takeIn this case it is possible to apply a combination, not all the elements enter, the order in which the books are chosen does not matter, and they are not repeated.
Being m= 13 and n=6, the combination is calculated by:
[tex]C=\frac{13!}{6!(13-6)!}[/tex]
Solving:
[tex]C=\frac{13!}{6!7!}[/tex]
C= 1716
Finally, you can take 1716 different collections of 6 books.
Learn more about combination:
https://brainly.com/question/25821700
A box contains 5 plain pencils and 7 pens. A second box contains 3 color pencils and 3 crayons. One item from each box is chosen at random. What is the probability that a plain pencil from the first box and a color pencil from the second box are selected?
,,,Help Please.. Question in the file.
The population of a town is modeled by the equation P = 16,581e0.02t where P represents the population t years after 2000. According to the model, what will the population of the town be in 2020?
2020 is 20 years after 2000, so put 20 where t is in the equation and evaluate.
P = 16,581e^(0.02·20) = 16,581e^0.4
P ≈ 24,736
The model predicts the population in 2020 will be about 24,736.
What is the value 6,035