The product of two consecutive natural numbers, with the first being [tex]\( N \),[/tex]is [tex]\( N \times (N + 1) \).[/tex]
The product [tex]\( P \)[/tex] of two consecutive natural numbers can be expressed as the product of a number and its consecutive number. So, if the first number is [tex]\( N \),[/tex] then the second number would be [tex]\( N + 1 \).[/tex] Therefore, the product [tex]\( P \)[/tex] can be written as:
[tex]\[ P = N \times (N + 1) \][/tex]
Expanding this, we get:
[tex]\[ P = N^2 + N \][/tex]
This represents the product of two consecutive natural numbers where [tex]\( N \)[/tex] is the first number.
Answers matching "The combined average weight of an okapi and a llama is 450 kilograms. The average weight of 3 llamas is 190 kilograms more than the average weight of one okapi. On average, how much does an okapi weigh, and how much does a llama weigh?"
Let us say that:
x = weight of llamas
y = weight of okapi
From the problem, we can create the equations:
x + y = 450 --> 1
3 x = y + 190 --> 2
Rewriting equation 1:
x = 450 – y
From equation 2:
3 (450 – y) = y + 190
1350 – 3 y = y + 190
4 y = 1160
y = 290
From equation 1:
x = 450 – 290
x = 160
Therefore a llama weighs 160 kilograms while okapi weigh 290 kilograms on average.
at 1:00 pm you have 24 megabytes of a movie. at 1:15 pm you have 96 megabytes what is the download rate in megabytes per minute
Monique Fournier deposited $12,500 into a savings account paying 6.5% annual interest compounded monthly. What amount will she have in her account after 3 years? How much compound interest will she have earned?
Explaining the calculation of the amount in the account after 3 years and the compound interest earned.
Amount in the account after 3 years:
Calculate the monthly interest rate: 6.5% annual interest divided by 12 (months) = 0.0054167
Calculate the total amount using the compound interest formula: $12,500 * (1 + 0.0054167)^36 = $15,183.41
Compound interest earned:
Subtract the initial deposit from the total amount: $15,183.41 - $12,500 = $2,683.41
What is 32,020.20 rounded to the nearest square mile
Given the function f(x) = −2x2 + 4x − 7, find f(−4). −55 −7 9 25
Answer:
Option (a) is correct.
The value of function [tex]f(x) = -2x^2 + 4x- 7[/tex] at x = -4 is -55
Step-by-step explanation:
Given : [tex]f(x) = -2x^2 + 4x- 7[/tex]
We have to find the value at f(-4) and choose the correct option from the given options.
Consider the given function [tex]f(x) = -2x^2 + 4x- 7[/tex]
Since, we have to find the value of f(-4) that is value of f(x) at x = -4
Substitute, value of x = -4 in given function, we have,
[tex]f(-4) = -2(-4)^2 + 4(-4)- 7[/tex]
Simplify, we have,
[tex]f(-4) = -55[/tex]
Thus, the value of function [tex]f(x) = -2x^2 + 4x- 7[/tex] at x = -4 is -55
Option (a) is correct.
How many boxes of carrots are left? 75 boxes − 68 boxes = 7 boxes
The question pertains to a basic subtraction operation where the student is left with 7 boxes of carrots after subtracting 68 boxes from an initial count of 75 boxes.
The subject of the question is mathematics, specifically involving subtraction and the concept of determining the number of items remaining after a reduction. The mathematical operation presented in the question is 75 boxes - 68 boxes = 7 boxes, which indicates that when you start with 75 boxes of carrots and remove 68 boxes, you are left with 7 boxes of carrots.
This type of problem is common in elementary mathematics and does not involve complex concepts such as permutations, probability, or statistical distributions.
At the frozen yogurt shop, a machine fills cups with 4 ounces of frozen yogurt before adding the toppings. After the cups are filled, customers add as many toppings as they want without exceeding a total weight of 6 ounces. Which of the following represent the acceptable weights for the frozen yogurt options? Select all that apply.
For the number 4768.325, what is the sum of the tens digit and the tenths digit
A line has a slope of -1/2 and a y-intercept of –2.
what is the x-intercept of the line?
y = (slope)x + (y-intercept)
y = -1/2x - 2
x-intercepts occur when y = 0
0 = -1/2x - 2
2 = -1/2x
x = -4
Thus, the x-intercept is at (-4,0)
Find the point p where the line x = 1 + t, y = 2t, z = -3t intersects the plane x + y - z = 3.
I need help someone explain?????
Henry is making a corn grits recipe that calls for 14 cup of corn grits for every 12 cup of water. How much water will he need if he uses 112 cups of corn grits? Enter the number in the box
Trygg has 3/4 package of marigold seeds. He plants 1/6 of those seeds in his garden and divides the rest equally into 10 flower pots. What fraction of a packege of seeds is planted in each flower pot? Show your work.
Answer:
[tex]\frac{1}{16}[/tex]
Step-by-step explanation:
We are given that
Trygg has package of marigold seeds=[tex]\frac{3}{4}[/tex]
He plants seeds in garden=[tex]\frac{1}{6}\times \frac{3}{4}=\frac{1}{8}[/tex]
Remaining seeds=[tex]\frac{3}{4}-\frac{1}{8}=\frac{5}{8}[/tex]
He divide remaining seeds equally into 10 flower pots.
We have to determine the fraction of a package of seeds is planted in each flower pot.
Seeds in each pot=[tex]\frac{\frac{5}{8}}{10}=\frac{1}{16}[/tex]
Hence, seeds planted in each pot=[tex]\frac{1}{16}[/tex]
It takes 40 min for a bus to travel the 36 miles from Framingham to Worcester. A car traveling from Worcester to Framingham moves 1.5 times as fast as the bus. If the car and the bus start moving towards each other simultaneously, after how many minutes will they meet?
The velocity of the bus is:
velocity (bus) = 36 miles / 40 min
velocity (bus) = 0.9 miles / min
Since the car is 1.5 times faster, so the velocity of the car is:
velocity (car) = 1.5 * 0.9 miles / min
velocity (car) = 1.35 miles / min
At the meeting point, the sum of the distance is equal to 36 miles. Therefore:
1.35 t + 0.9 t = 36
2.25 t = 36
t = 16 min
So they will meet after 16 minutes.
Write a user-defined function that determines the polar y coordinates of a point from the cartesian coordinates in a two-dimensional plane.
Daniel ate 1/3 of the left over pizza. If there were 2 1/2 pizzas left, how much did Daniel eat?
WILL GIVE BRAINEST
Identify one characteristic of exponential decay.
Answer: A
Step-by-step explanation:
Find the measures of two angles, one positive and one negative, that are coterminal with pi divided by five.
Find the area of one segment formed by a square with sides of 6" inscribed in a circle.
(Hint: use the ratio of 1:1: to find the radius of the circle.)
Which of the following is a measurement of the space between two objects? A. Area B. Pounds C. Circumference D. Miles
Final answer:
The space between two objects is measured as distance or length, with miles being the correct unit of measurement among the given options.
Explanation:
The measurement of the space between two objects is referred to as length or distance. If we look at the options provided: A. Area, B. Pounds, C. Circumference, D. Miles, it is clear that miles is a unit of measurement that describes distance. Area measures the size of a surface, pounds measure weight or mass, and circumference measures the distance around a circle. When considering distances, especially those that are long such as between two cities, miles is an appropriate unit to use. For example, the distance between your house and school would best be measured in kilometers or miles, rather than in smaller units like inches or centimeters, or in unrelated units like pounds or areas.
Help!
Math Torture!
Adam is constructing an equilateral triangle. He has already constructed the line segment and arcs shown.
What should Adam do for his next step?
A. Place the point of the compass on point X and draw an arc, using a width for the opening of the compass that is greater than 12XR.
B. Place the point of the compass on point X and draw an arc, using XR as the width for the opening of the compass.
C. Use the straightedge to draw XR←→ and XS←→.
D. Use the straightedge to extend RS¯¯¯¯¯ in both directions.
Answer:
C. Use the straightedge to draw XR←→ and XS←→.
Step-by-step explanation:
Adam has drawn the arcs by using RS distance as the radius of the circle and mid points as R and S.
So the point X is the same distance from R and S.
So now Adam has to use the straightedge to draw XR←→ and XS←→.
Then, XR = XS = RS
So it is an equilateral triangle.
Therefore, the correct answer is C.
Adam should do for his next step to use the straightedge to draw [tex]\( XR \)[/tex] and [tex]\( XS \).[/tex] The option (C) is correct.
The construction process for the equilateral triangle:
To construct an equilateral triangle using a straightedge and compass:
Construct [tex]\( XR \)[/tex]: Adam has already constructed segment [tex]\( XR \).[/tex]
Draw [tex]\( XS \)[/tex]: Using the straightedge, Adam should draw a line segment [tex]\( XS \)[/tex] from point [tex]\( X \)[/tex] to another point [tex]\( S \)[/tex] such that [tex]\( XS = XR \)[/tex]. This ensures that two sides of the equilateral triangle are equal in length.
Draw [tex]\( RS \)[/tex]: After drawing [tex]\( XS \)[/tex], Adam should use the straightedge to draw segment [tex]\( RS \)[/tex], completing the equilateral triangle [tex]\( \triangle XRS \).[/tex]
This method aligns with the steps typically used in geometric constructions to form an equilateral triangle: ensuring that all three sides are equal in length by first establishing two sides of equal length and then completing the triangle.
Therefore, upon reconsideration, option (C) is indeed the correct next step for Adam to construct his equilateral triangle.
Carmen is making 5 parts strawberry juice to 3 parts water. Carmen would like to make 64 fluid ounces of the strawberry drink. How many fluid ounces of strawberry juice and water does Carmen need?
Ok so if she needs 64 floz, If u add 5+3 you get 8. 64/8 = 8
Now You multiply your parts of water and juice by 8.
5*8= 40 <---- Answer
3*8 =24 <----Answer
To check your answer you would add up the parts of each. 40+24= 64
A dealer dealt the following cards from a shuffled deck: 3 , 2 , 2 , A , K , Q , K , 5 , 2 , 6 4 , 5 , K , 2 , 7 , 6 , A , J , J , A What was the experimental probability of dealing a black card?
Answer:
Total number of cards in shuffled deck=3 , 2 , 2 , A , K , Q , K , 5 , 2 , 6, 4 , 5 , K , 2 , 7 , 6 , A , J , J , A .
Total number of cards in a deck of card = 52 cards, out of which 26 are black cards and 26 are red card.
As, it is not given that out of the 20 cards dealt by dealer is either red card or black card.
A=3=2B +1 R or 1 B + 2 R
2=4=2 R +2 B
3=1=1 R or 1 B
4=1=1R or 1 B
5=2=2 R or 2 B
6=2=2 R or 2 B
7=1=1 R or 1 B
8=0
9=0
10=0
J=2= 2 R or 2 B
K=3= 2 R + 1 B or 1 R +2 B
Q=1=1 R or 1 B
If you count total number of black cards among the number of cards dealt by dealer, the possibilities of black card drawn is either 15 or 16 from 20 cards drawn.
As, Experimental probability is the probability obtained through experiment which is different from theoretical Probability.
Total number of cards =52
So, Probability of dealing with black cards by dealer which is either 15 or 16 in number is given by
[tex]=\frac{\text{total favorable outcome}}{\text{total possible outcome}}\\\\\frac{15}{52} {\text{or}} \frac{16}{52}=\frac{4}{13}.[/tex]
40%
Step-by-step explanation:There are 20 cards in total.
8 are black: 3,2,K,5,6,4,A,J
12 are red: 2,A,K,Q,2,5,K,2,7,6,J,A
so that means 8 of the 20 are black or 8/20
and 8/20 is 40% which is your answer.
There are about 4200 college presidents in the United States, and they have annual incomes with a distribution that is skewed instead of being normal. Many different samples of 40 college presidents are randomly selected, and the mean annual income is computed for each sample. What is the approximate shape of the sample means?
Final answer:
The distribution of sample means for college presidents' incomes, based on many different samples of size 40, will approximate a normal distribution due to the Central Limit Theorem.
Explanation:
The question regarding the distribution of sample means for college presidents' incomes pertains to a concept in statistics known as the Central Limit Theorem. When dealing with a population whose distribution is skewed, the distribution of sample means tends to become approximately normal if the sample size is large enough, which is usually considered to be over 30. As multiple samples of size 40 are taken in this case, the distribution of the sample means for the college presidents' annual incomes should approximate a normal distribution.
Which of the following numbers is the smallest?
4/9
0.44
3/7
400%
Harvey invested $6000 for 2 years in a savings account paying simple interest with a yearly interest rate of 5.5%. How much simple interest did he earn.
Harvey earned a simple interest of $660 over 2 years on his $6000 investment.
What is Multiplication?To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
Since, We know that;
Simple interest is calculated using the formula:
I = P r t
Where: I = Interest earned P = Principal amount (amount invested) r = Annual interest rate t = Time period (in years)
Now, In this case,
Harvey invested $6000 for 2 years at an annual interest rate of 5.5%.
So, using the formula:
I = 6000 x 0.055 x 2
I = $660
Therefore, Harvey earned a simple interest of $660 over 2 years on his $6000 investment.
Learn more about the multiplication visit:
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What is the rate of change of y with respect to x for this function?
HELP FOR BRAINLYEST
hannah and anthony are siblings who have ages that are consecutive odd integers. the sum of their ages is 92 . which equations could be used to find hannah's age,h, if she is the older sibling?
I would like to create a rectangular orchid garden that abuts my house so that the house itself forms the northern boundary. The fencing for the southern boundary costs $30 per foot, and the fencing for the east and west sides costs $15 per foot. If I have a budget of $120 for the project, what are the dimensions of the garden with the largest area I can enclose?
The largest rectangular orchid garden that can be enclosed within a $120 budget, considering the given costs of fencing, has dimensions of 2 feet by 2 feet, resulting in an area of 4 square feet.
You wish to create a rectangular orchid garden with the house forming the northern boundary, and you're working with a budget of $120 for fencing. The cost per foot for the southern boundary is $30, and for the east and west sides, it's $15 each. We need to determine the dimensions that maximize the area.
Let's denote the width of the garden (east and west sides) as w feet, and the length (only the southern side, as the northern side is the house) as l feet. The total cost of fencing is therefore the sum of the costs for all three sides: Cost = $30l + 2($15w), which simplifies to Cost = $30l + $30w. Since your budget is $120, we can write the equation $30l + $30w = $120, which simplifies further to l + w = 4.
To find the dimensions that give you the largest area, we need to maximize the area A of the rectangle, which is A = l imes w. Substituting w with 4 - l (from our previous equation), we get A = l imes (4 - l). To find the maximum area, take the derivative of A with respect to l and set it to zero, solving for l. This gives us l = 2 feet. Substituting back, we find w = 2 feet as well.
The dimensions for the garden that will give you the largest enclosed area within a $120 budget are 2 feet in width by 2 feet in length, resulting in an area of 4 square feet.
Which function has an inverse that is also a function? a {(–1, 3), (0, 4), (1, 14), (5, 6), (7, 2)} b {(–1, 2), (0, 4), (1, 5), (5, 4), (7, 2)} c {(–1, –2), (0, 4), (1, 3), (5, 14), (7, 4)} d {(–1, 4), (0, 4), (1, 2), (5, 3), (7, 1)}
Answer:
Which function has an inverse that is also a function? a {(–1, 3), (0, 4), (1, 14), (5, 6), (7, 2)} b {(–1, 2), (0, 4), (1, 5), (5, 4), (7, 2)} c {(–1, –2), (0, 4), (1, 3), (5, 14), (7, 4)} d {(–1, 4), (0, 4), (1, 2), (5, 3), (7, 1)}
Step-by-step explanation:
It is called the inverse or reciprocal function of f to another function f − 1 that fulfills that:
If f (a) = b, then f − 1 (b) = a.
The inverse of a function when it exists is unique, so that neither "X" nor "Y" can be repeated.
If we analyze the possibilities, in the case of b, c, and d, the value 4 of the "Y" is repeated twice; in the case of a, that does not happen, therefore the answer is: a {(–1, 3), (0, 4), (1, 14), (5, 6), (7, 2) }