How do you write a recursive formula
The volume of a rectangular prism can be computed using the formula V = lwh. What is the height of a prism that has a volume of 2376 cubic centimeters, a length of 18 centimeters, and a width of 11 centimeters
Answer:
The height of the prism is approximately [tex]\(12\)[/tex] centimeters.
Explanation:
To find the height ([tex]\(h\)[/tex]) of the prism, we can rearrange the formula for volume to solve for [tex]\(h\):[/tex]
[tex]\[ V = lwh \][/tex]
We can rewrite this formula to solve for [tex]\(h\):[/tex]
[tex]\[ h = \frac{V}{lw} \][/tex]
Given:
- Volume ([tex]\(V\)[/tex]) = 2376 cubic centimeters
- Length ([tex]\(l\)[/tex]) = 18 centimeters
- Width ([tex]\(w\)[/tex]) = 11 centimeters
Substitute these values into the formula to find the height:
[tex]\[ h = \frac{2376}{18 \times 11} \][/tex]
[tex]\[ h = \frac{2376}{198} \][/tex]
[tex]\[ h \approx 12 \text{ centimeters} \][/tex]
So, the height of the prism is approximately [tex]\(12\)[/tex] centimeters.
Which pair of numbers is relatively prime? A. 102 and 321 B. 10 and 45 C. 3 and 51 D. 35 and 72
The pair of numbers 35 and 72 are relatively prime, which is the correct answer would be option (D).
What is the pair of relatively prime?If there is no integer greater than 1 that divides both integers, they are expressed to be relatively prime.
Consider the given pair of numbers to determine which pair is more prime.
A. Consider 102 and 321
3 is the number that divides by 102 and 321 both. Therefore, they are not relatively prime.
B. Consider 10 and 45
5 is the number that divides by 10 and 45 both. Therefore, they are not relatively prime.
C. Consider 3 and 51
3 is the number that divides by 3 and 51 both. Therefore, they are not relatively prime.
D. Consider 35 and 72
As there is no number greater than one, this divides both numbers. As a result, they are relatively prime numbers.
Therefore, the correct answer would be an option (D).
To learn more about the pair of relatively prime here :
https://brainly.com/question/11195956
#SPJ2
Please tell the answer
-8x+3>=27 and -13x+5>=57
Answer: The answer I got was x≤−4.Hopefully its right:)
A turtle fell to the bottom of a deep well. The turtle climbed up 2 meters on the first day, but slipped back 1 meter as he rested. The second day, the turtle climbed double the distance of the previous day, but slipped and lost ½ of the day’s climbed distance as he rested. This pattern continued until the end of the fourth day, when the turtle realized he was halfway to the top of the well. How deep was the well?
Analyzing the climbing pattern of the turtle for four days shows that it climbed 15 meters which is halfway to the top, thus the entire depth of the well is 30 meters.
The question asks for the determination of the depth of a well based on a pattern observed in a turtle's attempt to climb out of it. To do this, we need to analyze the climbing and slipping pattern for four days until the turtle is halfway out of the well.
On the first day, the turtle climbed up 2 meters and slipped back 1 meter, netting a 1 meter gain. On the second day, the distance climbed is double that of the previous day (2 meters x 2 = 4 meters), but the turtle loses half of it while resting, which means a gain of 2 meters for the second day (4 meters / 2 = 2 meters). Following the pattern:
Day 1: +2 - 1 = +1 meterDay 2: +(2 x 2) - (4 / 2) = +2 metersDay 3: +(4 x 2) - (8 / 2) = +4 metersDay 4: +(8 x 2) - (16 / 2) = +8 metersThe total distance climbed after four days is 1 + 2 + 4 + 8 = 15 meters. Since this is halfway to the top, the entire depth of the well would be 15 meters imes 2 = 30 meters.
a store has 7 red shirts 15 black shirts and 13 white sshirts
Which one of the following is an arithmetic sequence?
A. −2, 1, 4, 7, 10, . . .
B. 2, 3, 5, 7, 11, 13, 17, . . .
C. 5, 0, −1, −3, −7, . . .
D. .35, .5, .85, 1.1, 1.22, . . .
Final answer:
Option A (-2, 1, 4, 7, 10, ...) is an arithmetic sequence because there is a consistent common difference of +3 between each term. The other options do not show a constant difference between terms, so they are not arithmetic sequences.
Explanation:
To determine which of the sequences is an arithmetic sequence, we look for a constant difference between successive terms. An arithmetic sequence is a sequence of numbers in which each term after the first is found by adding a constant, known as the common difference, to the previous term.
A. −2, 1, 4, 7, 10, . . . - The difference between terms is consistently +3, so this is an arithmetic sequence.
B. 2, 3, 5, 7, 11, 13, 17, . . . - The sequence consists of prime numbers and does not have a consistent difference. Not an arithmetic sequence.
C. 5, 0, −1, −3, −7, . . . - The differences between terms here change; they are not constant. Not an arithmetic sequence.
D. .35, .5, .85, 1.1, 1.22, . . . - The differences between terms do not remain the same, so it's not an arithmetic sequence.
Our answer is A: −2, 1, 4, 7, 10, . . .. This is the only arithmetic sequence from the given options as it has a consistent common difference of +3 between each term.
What is a multiplication problem with a product that is greater than 0.1 but less than 0.2
What is the product in lowest terms?
1/6 x 5/7. ( / means fractions)
1. 6/13
2. 5/13
3. 1/7
4. 5/42
Thank you so much, if you could answer as fast and best as you can you really are very helpful!
Last year there were 52 Starbucks Coffee shops in Orlando. This year they are planning on increasing their numbers by 25%. How many Starbucks Coffee shops with there be now?
OR U COULD JUST MULTIPLY .25 BY 52 BC 25% IS 0.25. AND U GET 13. 52 PLUS 13 ISSSS
62
Miss Marcus Bulletin Board is 7 ft long and 4 feet High she has 26 ft of board to use Miss Marcus pool supplies 7 time 4 equals 28 to find the exact amount of the board she needs she concludes that she does not have enough border board for the bulletin board do you agree
Final answer:
Yes, I agree that Miss Marcus does have enough board for the bulletin board for the given information
Explanation:
The student is trying to determine if Miss Marcus has enough board to use for her bulletin board. The student calculates the area of the bulletin board as 7 ft x 4 ft = 28 ft². However, the student concludes that Miss Marcus does not have enough board because she only has 26 feet of board to use. This is incorrect, as 26 ft is greater than 28 ft². Therefore, Miss Marcus does have enough board for the bulletin board.
find A common denominator of 1/6 and 1/9. rewrite the pair of fractions using common denominator.
Answer:
the pair would be 3/18 and 2/18
The pair of fractions, 1/6 and 1/9, can be rewritten as 3/18 and 2/18, respectively, using the common denominator of 18.
We have,
The prime factorization of 6 is 2 * 3.
The prime factorization of 9 is 3 * 3.
To find the LCM, take the highest power of each prime factor:
LCM = 2 * 3 * 3 = 18
The common denominator for 1/6 and 1/9 is 18.
To rewrite the fractions using the common denominator of 18:
1/6 = (1/6) * (3/3) = 3/18
1/9 = (1/9) * (2/2) = 2/18
Thus,
The pair of fractions, 1/6 and 1/9, can be rewritten as 3/18 and 2/18, respectively, using the common denominator of 18.
Learn more about expressions here:
https://brainly.com/question/3118662
#SPJ4
Plzzzz Help meeeeee!!!!!!
Sara is selling cookies and brownies as a fundraiser for the school band. She charges $2.25 for two cookies and one brownie. She charges $5.75 for four cookies and three brownies. How much does Sara charge per cookie? How much per brownie?
A. $0.50 per cookie, $1.25 per brownie
B. $0.75 per cookie, $1.50 per brownie
C. $0.25 per cookie, $1.00 per brownie
D. $1.00 per cookie, $1.00 per brownie
Answer:
The cost of the $0.5 per cookies and $1.25 per brownie.
Option (A) is correct.
Step-by-step explanation:
Let us assume that the cost of the cookies =x
Let us assume that the cost of the brownie = y
As given
Sara is selling cookies and brownies as a fundraiser for the school band.
She charges $2.25 for two cookies and one brownie.
Than the equation becomes
2x + y = 2.25
She charges $5.75 for four cookies and three brownies.
4x + 3y = 5.75
Than two equation are
2x + y = 2.25 and 4x + 3y = 5.75
Multiply 2x + y = 2.25 by 3 and subtracted from 4x + 3y = 5.75
4x - 6x + 3y - 3y = 5.75 - 6.75
-2x = - 1
2x = 1
[tex]x = \frac{1}{2}[/tex]
x = $0.5
Put in the equation 2x + y = 2.25
2 × 0.5 + y = 2.25
1 + y = 2.25
y = 2.25 - 1
y = $1.25
Therefore the cost of the $0.5 per cookies and $1.25 per brownie.
Option (A) is correct.
Answer:
A is correct
Step-by-step explanation:
help i dont get this question!
Jenna says that no row or column contains products with only odd numbers do you agree explain.
Jenna's claim that no row or column contains products with only odd numbers is wrong. A counterexample can be found by examining a matrix.
Explanation:Jenna claims that no row or column contains products with only odd numbers. Let's examine whether this statement is true or not. Let's consider a matrix and see if we can find a row or column that contains products with only odd numbers.
For example, let's take the following matrix:
1 2
3 4
In this matrix, we can see that the 1st row contains the product 2 and the 2nd row contains the product 12 which are both even numbers.
So, Jenna's statement is not true as we have found a row that contains products with only even numbers.
Learn more about odd numbers in matrix here:https://brainly.com/question/32099210
#SPJ3
A ladder is leaning against the side of a building. The building and the ground form a right angle. How high on the building will the ladder touch if the ladder is 10 ft long and the base of the ladder is 6 ft from the base of the building?
The height of wall where the ladder touches it is 8 ft.
Given that, a ladder is leaned against a wall, the building and the ground form a right angle, we need to find that how high on the building will the ladder touch,
So, here using the Pythagoras theorem,
Formula =
a²+b² = c², a, b and c are the sides of a right triangle,
Here, c = 10 ft, b = 6 ft we need to find the a,
a²+6² = 10²
a² = 100-36
a² = 64
a = 8
Hence, the height of the wall where the ladder touches it is 8 ft.
Learn more about Pythagoras theorem, click;
https://brainly.com/question/343682
#SPJ2
how do i evaluate 256 1/4 .? this is algebra 2.
The value of the 256 1/4 is 384.25
What is a fraction?A fraction represents a part of a number or any number of equal parts.
A fraction consisting of a quotient and a remainder is a mixed fraction. we can convert the mixed fraction to an improper fraction by first dividing the numerator by denominator and then taking the quotient as whole number and the remainder as the numerator of the proper fraction keeping the denominator.
We have the fraction as 256 1/4
First, we will multiply 256 with 4.
256 x 4 = 1536
1536 + 1
= 1537
Then
1537 / 4 = 384.25
Learn more about fractions;
https://brainly.com/question/729654
#SPJ2
A theater sells adult tickets for $8.00 and children's tickets for $5.50. Sally bought some of each kind (not the same number) and paid a total of $78.50. Which equation represents this situation? A) x + y = 78.5 B) 13.5x = 78.5 C) 13.5xy = 78.5 D) 8x + 5.5y = 78.5
How do you solve -10=10(k-9)
A sneaker store salesman had $4125 in total monthly sales lath month. He made $165 in commission from those sales.
What is the saleman’s commission as a percent of his total monthly sales?
y and x have a proportional relationship, and y = 12 when x = 5. What is the value of y when x = 8?
I need help ..........
Answer:
The answer is B
Step-by-step explanation:
You need to graph the equation from the left of equality sign which is y=x*1/6 and the other is -2x+5
The first has a point (0,0) and other point could be (6,1) from there you can have your graph
The second has one point in (2.5, 0) and (0,5)
What is the equation of this line? y=12x−3 y=−12x−3 y=−2x−3 y=2x−3 Number graph ranging from negative 5 to 5 on both the x and y axis. A line passes through the point begin ordered pair 0 comma negative 3 end ordered pair and the point begin ordered pair 4 comma negative 1 end ordered pair
We are given that
A line passes through two points as
(0,-3) and (4,-1)
[tex](x_1,y_1)=(0,-3)[/tex]
[tex]x_1=0,y_1=-3[/tex]
[tex](x_2,y_2)=(4,-1)[/tex]
[tex]x_2=4,y_2=-1[/tex]
Firstly, we can find slope
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
now, we can plug values
[tex]m=\frac{-1+3}{4-0}[/tex]
[tex]m=\frac{2}{4}[/tex]
[tex]m=\frac{1}{2}[/tex]
now, we can use point slope form of line
[tex]y-y_1=m(x-x_1)[/tex]
we can plug values
[tex]y+3=\frac{1}{2} (x-0)[/tex]
[tex]y+3=\frac{1}{2}x[/tex]
[tex]y=\frac{1}{2}x-3[/tex]
so, the equation of line is
[tex]y=\frac{1}{2}x-3[/tex]...............Answer
i need to solve this equation: x= r-h/ y
for h and then for r
Answer:
[tex]h=r-xy[/tex]
[tex]r=xy+h[/tex]
Step-by-step explanation:
[tex]x=\frac{r-h}{y}[/tex]
Solve the equation for h
We need to get 'h' alone
[tex]x=\frac{r-h}{y}[/tex]
multiply y on both sides
[tex]xy=r-h[/tex]
Now add h on both sides
[tex]xy+h=r[/tex]
Subtract xy from both sides
[tex]h=r-xy[/tex]
Now solve the equation for 'r'
[tex]x=\frac{r-h}{y}[/tex]
multiply y on both sides
[tex]xy=r-h[/tex]
Now add h on both sides
[tex]xy+h=r[/tex]
[tex]r=xy+h[/tex]
What is the equation in point slope form of a line that passes through the points (-8,2) and had a slope of 1/2
Answer:
[tex]y-2=\dfrac{1}{2}(x+8)[/tex]
Step-by-step explanation:
It a line passes through the point [tex](x_1,y_1)[/tex] with slope m, then the point slope form of the line is
[tex](y-y_1)=m(x-x_1)[/tex] ....(i)
It is given that line passes through the point (-8,2) and had a slope of 1/2.
We neeed to find the equation in point slope form of the line.
Substitute [tex]x_1=-8,y_1=2\text{ and }m=\dfrac{1}{2}[/tex] in equation (i).
[tex](y-(2))=\dfrac{1}{2}(x-(-8))[/tex]
[tex]y-2=\dfrac{1}{2}(x+8)[/tex]
Therefore, the point slope form of the line is [tex]y-2=\dfrac{1}{2}(x+8)[/tex].
The O'Malley family is driving tlcross-country to see their cousins. So far, they have traveled 275 miles. This is 1/5 of the way to their cousins' house. How far do the O'Malleys live from their cousins?
In the talent show, 6 students plan to sing, 7 students plan to dance, and 2 students plan to tell jokes. Rick said that the ratio of singers to joke-tellers is 6 to 2. Leah said that the ratio of joke-tellers to singers is 1 to 3. Who is correct? Explain why.
Leah is correct because the ratio of 6 singers to 2 joke-tellers simplifies to 3 to 1. When we reverse this ratio to represent joke-tellers to singers, it becomes 1 to 3, which is what Leah stated
The question is asking us to compare two different ratios and decide which one is correct. Rick stated the ratio of singers to joke-tellers is 6 to 2. In its simplest form, this ratio can be reduced to 3 to 1 when we divide both numbers by 2. On the other hand, Leah stated the ratio of joke-tellers to singers is 1 to 3, which is the inverse of the first ratio.
Since the ratio of singers to joke-tellers is indeed 6 to 2, which simplifies to 3 to 1, that means for every 3 singers, there is 1 joke-teller. Therefore, Leah's statement of the ratio is correct, as it provides the simplified form while Rick gives the unsimplified form. The order of terms in a ratio is important, and Leah's presentation maintains the correct order while also presenting the simplest form of the ratio
1.56 x 10 to the 4th power in Standard notation
To write 1.56 × [tex]10^{4}[/tex] in standard notation, we will first begin with
1.56. Next, we look at the exponent. The exponent is 4 so this tells us we need to move the decimal point 4 places to the right.
1.56 → 15600.
Therefore, 1.56 × [tex]10^{4}[/tex] is written in standard notation as 15,600.
A Town's population went from 25800 to 42600 in 15 years. What was the percentage of change?