Answer:
Yes all of the logs can be used in such a grouping.
We'll have 19 logs in the bottom row (and have 19 rows)
========================================================
Explanation:
Let n be the number of layers. Let T(n) represent how many logs there are total.
If you have 1 layer, then you have 1 log. So we can say that T(1) = 1.If there are n = 2 layers, then we have 1 log on top of two other logs, which leads to 1+2 = 3 logs total. This shows that T(2) = 3.If there are n = 3 layers, then we have 1 log on top of 2 which are on top of 3 at the very bottom. We have 1+2+3 = 6 logs total. So T(3) = 6.Having n = 4 layers gives 1+2+3+4 = 10 logs. So T(4) = 10Having n = 5 layers gives 1+2+3+4+5 = 15 logs. So T(5) = 15This process continues for however long you like. The sequence 1,3,6,10,15 is the set of triangular numbers, since the logs form a triangular or pyramid shape when stacked this way. To get the nth value in the triangular number sequence, use this formula
T(n) = 0.5*n*(n+1)
---------------
For example, let's say we wanted to find how many logs there were in the fifth layer
T(n) = 0.5*n*(n+1)
T(5) = 0.5*5*(5+1)
T(5) = 15
This matches from earlier.
The purpose of bringing in a formula is to see if we can get T(n) = 190 for some integer n.
-------------------
T(n) = 0.5*n*(n+1)
190 = 0.5*n*(n+1)
190*2 = n(n+1)
380 = n^2+n
0 = n^2+n-380
n^2+n-180 = 0
Applying the quadratic formula will lead to the two solutions: n = -20 and n = 19. We ignore the negative value of n as we can't have a negative number of rows. Therefore, n = 19 is the only valid solution here.
If we wanted to stack 190 logs in this triangular pyramid fashion, then we'll need to have 19 rows. The bottom row will have 19 logs.
----------
Check:
1+2+3+4+5+6+7+8+9+10 = 55
11+12+13+14+15+16+17+18+19 = 135
55+135 = 190
Or you could say,
T(n) = 0.5*n*(n+1)
T(19) = 0.5*19*(19+1)
T(19) = 190
Either way, the answer is confirmed.
Consider points a, b, and c in the graph below. Determine which of these points are relative maxima on the interval x = 1 to x = 3
Answer:
c
Step-by-step explanation:
Relative Maxima means "a point that is higher than the points directly beside it on both sides", or when looking at derivatives, when the derivative of a function changes from above zero to below zero. If you're looking at a graph, all you have to do is find those points that seem to be poking out of the graph, aka c, when x=2.
Also look at the interval - (1,3), so... really, just by that, c would be your answer
Air is being pumped into a spherical balloon at the rate of 7 cm3/sec. What
is the rate of change of the radius at the in stant the volume equals 36π cm3
? The volume of
the sphere of radius r is (4 over PI )r power of 3
Answer:
Step-by-step explanation:
[tex]V=\frac{4}{3} \pi r^3\\\frac{dV}{dt} =\frac{4}{3} ~\pi \times ~3r^2\frac{dr}{dt} \\\frac{dV}{dt} =4\pi r^2\frac{dr}{dt} \\7=4\pi r^2\frac{dr}{dt} \\\frac{dr}{dt} =\frac{7}{4\pi r^2} \\when~V=36 \pi cm^3\\36\pi =\frac{4}{3} \pi r^3\\r^3=\frac{36\pi \times 3}{4\pi } =27=3^3\\r=3~cm\\\frac{dr}{dt} =\frac{7}{4\pi \tmes 3^2} \\\frac{dr}{dt} =\frac{7}{36 \pi } cm/sec[/tex]
Can someone please help me
Answer: B
Step-by-step explanation: I beilieve it's B but, don't take my word.
What is the area of a triangle with the Base of √10 and a height of √13
Answer:
5.70
Step-by-step explanation:
[tex] a = \frac{1}{2} bh \\ \frac{ \sqrt{10} \sqrt{13} }{2} \\ \frac{ \sqrt{130} }{2} [/tex]
[tex]a = \frac{11.401}{2} \\ = 5.70[/tex]
Answer:
5.70
Step-by-step explanation:
mark me as brainliest
evaluate the following expression . 2*[4+(12+16)/7
Answer:
16
Step-by-step explanation:
[tex]2 \times (4 + (12 + 16) \div 7 \\ (12 + 16) = 28 \div 7 = 4 + 4 = 8 \\ 2 \times 8 = 16[/tex]
HURRY HELP PLEASE! SERIOUS ANSWERS ONLY!
Living Space?
You have the opportunity to live in a 3 bedroom 3.5 bath on Miami Beach in a Luxury Condo or in Laurel Mississippi in a 5-bedroom 7 bath home. Money for either is not an issue. The only stipulation is that you and your present family situation will remain intact. Given your present situation, which would you choose and why? (Students will receive full credit for their completion of the project; steps 2 and 3)
1. Look up property and amenities
a. Condo on: unaresidencemiami.com/price-list
b. Home on: 2230 Ridgewood Dr, Laurel, MS 39440 (type in address)
2. Look up the community in which EACH is located
3. Solve for the intersection of the two properties (two variable systems of equations using the
cost and the Square Footage as the variables)
a. Condo: $2.2 million / 1946 sq feet
b. House : $.3 million / 4681 sq feet
4. Which would you choose and why?
Answer:
The Mississippi home
Step-by-step explanation:
I would get the Mississippi home because it has 5 bedrooms with 7 bathrooms, it would be a great home for a family and guest to go to. and it also depends on the condition of the home and the amount of people in you family.
The question is in the picture
Answer:
8
Step-by-step explanation:
f (x) = x5 − 8x4 + 21x3 − 12x2 − 22x + 20
Three roots of this polynomial function are −1, 1, and 3 + i.
Which of the following describes the number and nature of all the roots of this function?
f (x) has two real roots and one imaginary root.
f (x) has three real roots.
f (x) has five real roots.
f (x) has three real roots and two imaginary roots.
Answer:
f(x) has three real roots and two imaginary roots.
Step-by-step explanation:
The function is degree 5, so will have 5 roots in total. 2 real roots and one complex root are shown. Complex roots come in pairs, so there will be one more, but cannot be two more.
f(x) has three real roots and two imaginary roots.
__
All five roots must be accounted for. This leaves out the first two choices. The given complex root eliminates the third choice.
Answer:
D
Step-by-step explanation:
did the test
Today is my birthday. My age today, in months, is 72 times my age 5 years ago,
in years. My age today, in years, is
Answer:
Happy Birthday!
Step-by-step explanation:
after a party 3/4 cake is leftover. Dennis eats 1/2 of the leftover cake. Which fraction model represents the amount of cake Dennis eats?
Help I’m so confused
Answer:
5x: linear; monomial
-7: constant; monomial
x^2 + 4: quadratic, binomial
x^2 - 3x + 11: quadratic, trinomial
2x - 9: linear, binomial
Step-by-step explanation:
Name using degree: just count the highest number of variables in a single term. if it's 0, its a constant polynomial, if it's 1 it's linear, 2 quadratic, 3 cubic
Name using number of terms: just count the number of "things" added or subtracted. If there's one, it's a monomial, two: binomial, three: trinomial.
Question : Explore criteria of congruency of triangles using a set of triangle cut outs
Answer:
Explore Various Criteria for Congruence TrianglesSASASAAASSSSRHS23+4⋅2−7
the 23 is 2 to the third power.
Answer:
12618
Step-by-step explanation:
23x23x23=12617
4•2=8
12617+8=12625
12625-7=12618
Answer: 9
Step-by-step explanation:
The correct answer to [tex]2^{3} + 4[/tex] ⋅ [tex]2 - 7 = 9[/tex]
I hope that helps :)
Please help, I will give good rating and brainliest of possible!!
Thank you!!!!!!!!
Answer:
[tex]g(x)=x+8[/tex]
Step-by-step explanation:
Translating a function up is very simple, all you need to do here is add 8.
If you want to think of it logically,
[tex]f(x)=x[/tex]
the whole right side of the function here can be our output. If x is 8, then the output, or height, is also 8. if you wanted to translate that up to 10, you'd simply need to add 2 to it, meaning [tex]x+2[/tex]. Then, at any given point on the function, it'd be 2 higher than it would be otherwise.
Simplify the following expression.
Answer:
-1
Step-by-step explanation:
[tex]3 + \sqrt{10 - {3}^{2} } + - 5 \\ = 3 + \sqrt{10 - 9} - 5 \\ = 3 + \sqrt{1} - 5 \\ = 3 + 1 - 5 \\ = 4 - 5 \\ = - 1[/tex]
Answer:
-1
Hope you could get an idea from here.
Doubt clarification - use comment section.
12+13×4 what is the answer best explanation will get brainliest
Hello there, this is just a basic PEMDAS problem
[tex]{\huge{\boxed{\mathbb{QUESTION}}}[/tex]
12+13×4 what is the answer
[tex]{\huge{\boxed{\mathbb{EQUATION}}}[/tex]
[tex]12+13\cdot4[/tex]
_______________
[tex]{\huge{\boxed{\mathbb{PEMDAS\:RULE}}[/tex]
Follow PEMDAS rule
Parenthesis Exponents Multiplication or Division Addition or Subtraction_______________
So first we will multiply [tex]13[/tex] by [tex]4[/tex] giving us [tex]52[/tex]. Now just add [tex]12+52=64[/tex]
_______________
[tex]{\huge{\boxed{\mathbb{ANSWER}}[/tex]
64
Consider the following data for 120 mathematics students at a college concerning the languages French, German, and Russian:
65 study French, 45 study German,
42 study Russian , 20 study French and German,
25 study French and Russian,
15 study German and Russian.
8 study all three languages.
Determine how many students study exactly 1 subject and fill the correct numbers of students in each eight region of Venn diagram shown in figure.
Answer:
check online for more information
The Venn diagram for given situation is as shown below.
The number of students who study exactly one subject = 56
What is set?"It is a collection of well-defined elements"
What is Venn diagram?"It is a pictorial representation that uses circles to show the relationships among sets."
For given example,
We have been given the data for 120 mathematics students at a college concerning the languages French, German, and Russian
Let set A, B and C represents the number of students who study French, German and Russian respectively.
⇒ n(A) = 65
⇒ n(B) = 45
⇒ n(C) = 42
20 study French and German
⇒ n(A ∩ B) = 20
25 study French and Russian,
⇒ n (A ∩ C) = 25
15 study German and Russian.
⇒ n(B ∩ C) = 15
8 study all three languages.
⇒ n(A ∩ B ∩ C) = 8
So, the Venn diagram for given situation is shown below.
Now, we find the number of students who study exactly one subject.
28 students study French only, 18 students study German only and 10 students study Russian only.
So, the total number of students who study exactly one subject is,
28 + 18 + 10 = 56
Therefore, 56 students study exactly one subject
Learn more about Venn diagram here:
https://brainly.com/question/1605100
#SPJ2
Can anyone please help me answer this Math question ? As soon as possible !
The We-Make-It factory in the United States pays its 250 workers an average of $21 per hour, including benefits. The average number of work hours per employee in a year is 1,924. The owners of the factory are considering relocating overseas to a country where they can pay workers an average of $6 per hour, including benefits, to achieve the same production levels. Assuming that the company would hire the same number of workers for the same number of hours in a new location, how much could We-Make-It save in wages alone in the first year by moving to the proposed overseas location?
Assuming that this would not be destroying the lives of many in a community by locating overseas. The factory would save $2,886,000 in payroll wages during the first year of relocation.
Step-by-step explanation:
$15 saved in wages/working hour × 250 workers × 1924 hours per year/worker = $2,886,000
PLEASE HELP ME PLEASE
Answer:
5
Step-by-step explanation:
Determine the area of the yellow sector
Answer:
146 is the answer im positive
3. Tom's entered a snowman building contest in which the person who builds the tallest
snowman wins. Currently, the record is 13.4 feet high. If Tom's snowman is currently 9 feet
high, how many more feet does he need to build on, in order to win the competition
tom's snowman has to increase by anything greater than 4.4 ft
Answer:
4.5 feet
Step-by-step explanation:
9+4.5=13.5
13.5>13.4
If the ratio y/x is the same for all related pairs of x and y, what does that mean about the relationship between x and y?
Answer:
The the relationship is linear
Step-by-step explanation:
If y/x is same for all pairs of x and y, slope is a constant value that is not changed by value of x or y. Hence, it is linear function.
A jar contains 28 marbles. Half of the marbles are red. Half of the non-red marbles are white and the rest are blue. Todd chose a white marble at random and kept it. What is the probability that when Hosea now draws a marble it will also be white
Answer:
2/9
Step-by-step explanation:
28 marbles in all
"Half of the marbles are red."
28/2 = 14 red
"Half of the non-red marbles are white..."
14/2 = 7 white
"...and the rest are blue."
25 -14 -7 = 7 blue
"Todd chose a white marble at random... " -from the bag that has...
14 red 7 white 7 blue
"... and kept it."- so now the marbles left in the jar are...
14 red 6 white 7 blue
P (white) = Number of white marbles/ Total number of marbles = 6/27 = 2/9
PLEASE HELP IMMEDIATELY
THANN YOU!
(Image attached above)
Answer: x = 2, explanation below
area of rectangles and squares is l * h or h * l (h is height and l is length)
length of left rectangle/square is
4*(6x+6) and for the right quadrilateral, it is 4x*9
4x*9 is 36x
and we use the distributive property for 4*(6x+6)
4*6x+4*6
4*6x = 24x
4*6 = 24
24x+24
They have equal areas, so we can make an equation making their areas equal.
36x = 24x+24
Subtract 24x from both sides
12x=24
divide 12 by both sides
x = 2
Step-by-step explanation:
(X+2b)(x-4b) simplified
Answer:
I will ASSUME X = x
x² + 2bx - 4bx - 8b²
x² - 2bx - 8b²
Answer:
[tex]\\\\\\-8b^2-2bx+x^2[/tex]
Step-by-step explanation:
[tex](x+2b)(x-4b)\\=(x+2b)(x+(-4b)\\=(x)(x)+(x)(-4b)+(2b)(x)+(2b)(-4b)\\\\x^2-4bx+2bx-8b^2\\\\-8b^2-2bx+x^2[/tex]
Francine recorded today's high
temperature as 78.6°F. Today's low
temperature was 4.7°F less than
that. How much cooler was today's
low temperature than yesterdays low
temperature, which was 77.4°F?
Answer:
3.5
Step-by-step explanation:
the problem says 4.7 less than which refers to subtraction so we can plug our numbers into a subtraction problem like so
78.6-4.7 which equals 73.9
the second part of the problem asks the difference between yesterday's low and today's.
we can take the two lows and subtraction them to find this answer.
77.4-73.9 which equals 3.5
so today's low was 3.5 degrees cooler than yesturdays
Determine whether each graph shows a positive correlation, a negative
correlation, or no correlation. If there is a positive or negative correlation,
describe its meaning in the situation.
Answer:
Positive correlation.Step-by-step explanation:
From the graph we can see overall increasing trend.
It means there is a positive correlation.
The meaning of this is the more time you spend on study the better test score you get.
Answer:
Negative correlation
Step-by-step explanation:
As TV hours increase, exercise
hours decrease.
50 POINTS!!!
Which is the graph of linear inequality x - 2y = -12?
Find the future value of $124,357 deposited at 8% compounded quarterly for 4 years
Answer:
Future value, $63,398.79; Interest, $16,798.79
Step-by-step explanation:
A bus traveling at a constant rate of 50 miles per hour. At this rate, how far will the bus travel 3 1/4 hours?
First, let's do the easy part! Multiplying 50 by 3 will give us how far the bus would travel in 3 hours. 50 x 3 = 150.
Now let's do the quarter. 50 / 4 = 12.5. Simply add these two together now!
The bus will travel 162.5 miles!
Hope this helps :)
