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.
True or False (See Image)
The remainder theorem can be used to check if a binomial is a factor of a larger polynomial.
Answer: true
Step-by-step explanation:
8) A school community had planned to reduce the number of grade 9 students per class room by constructing additional class rooms. However, they constructed 4 less rooms than they planned. As the result, the number of students per class 10 more than they planned. If there are 1200 grade nine students in the school, determine the current number of class rooms and the number of students per class.
Step-by-step explanation:
Let "c" be the original number of classrooms.
The 1200/c was the original number of students per classroom.
----
Equation:
1200/(c-4) = (1200/c)+10
Multiply thru by c(c-4)
---
1200c = 1200(c-4)+10c(c-4)
---
1200c = 1200c-4800 + 10c^2-40c
----
10c^2-40c-4800 = 0
c^2-4c-480 = 0
Factor:
(c-24)(c+20) = 0
---
Positive solution:
c = 24 (# of classrooms originaly planned)
Solve. x 2 = 7
pls help!!
Answer:
x = 14
Step-by-step explanation:
1) Multiply both sides by 2.
x = 7 * 2
2) Simplify 7 * 2 to 14.
x = 14
Answer:
D.
Step-by-step explanation:
when using diversions in fractions to whole numbers you will always multiply the denominator by the whole number. So 2 x 7 equals 14. :))
A rock is launched from a cannon. Its height, h(x), can be represented by a
quadratic function in terms of time, x, in
seconds.
After 1 second, the rock is 94 feet in the
air; after 2 seconds, it is 176 feet in the
air.
Complete the height function, h(x), for this situation
h(x) =
Answer:
The height, in feet, of the rock after 5 seconds = 875 feet
Step-by-step explanation:
The mass of a an atom of helium is 6.65 x 10−24. Use scientific notation to express the mass of 250 helium atoms. A) 1.6625 x 10−21 B) 1.6625 x 10−22 C) 1.6625 x 10−24 D) 1.6625 x 10−26
Answer: its A
Step-by-step explanation:
i know this is it
subtract 8 and 1/5 - 4 2/5
Answer: = -3
Step-by-step explanation:
138.4divided by16 show works it possible to show your work
B = {x|x ∈ N and 1 ≤ x < 9}
Answer:
Set membership x ∈ X means x is an element of the set X. (Non-membership is written x ∈ X.) Set inclusion X ⊆ Y means every element of X is an element of Y ; X is a subset of Y .
Step-by-step explanation:
Carry on learning
Given f(x) = 21 - 1, complete the missing values in the table
Answer:
first one is f(x)=-5
second one is f(x)=7
third one is x=-3
4th one is x=0
5th one is f(x)=1
6th one is x=-4
Step-by-step explanation:
first one. plug in x as -2:
f(x)=2*-2-1=-4-1=-5
second one is the same way:
f(x)=4*2-1=8-1=7
third one is a different one:
2x-1=-7
2x=-6
x=-3
4th one is the same way:
2x-1=-1
2x=0
x=0
5th way is the same thing as previous:
f(x)=2*1-1=2-1=1
Finally, the 6th one is the same thing as the 4th one:
2x-1=-9
2x=-8
x=-4
Done!
he Nassau Bahamas Community College (NBC) claims that students who take statistics spend on average 19 hours a week working. The population standard deviation is not known. Statistics students in MAT 102 believe students work more than 19 hours because they want to make more money.
Using the t-distribution, it is found that since the test statistic is greater than the critical value for the right-tailed test, it is found that there is enough evidence to conclude that the students' claim that they work more than 19 hours is correct.
At the null hypothesis, it is tested if they spend on average 19 hours a week working, that is:
[tex]H_0: \mu = 19[/tex]
At the alternative hypothesis, it is tested if they spend more than 19 hours a week working, that is:
[tex]H_1: \mu > 19[/tex]
We have the standard deviation for the sample, hence, the t-distribution is used.
The test statistic is given by:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
The parameters are:
[tex]\overline{x}[/tex] is the sample mean. [tex]\mu[/tex] is the value tested at the null hypothesis. s is the standard deviation of the sample. n is the sample size.Searching the problem on the internet, it is found that the values of the parameters are:
[tex]\overline{x} = 24.2, \mu = 19, s = 12.59, n = 25[/tex]
Hence, the value of the test statistic is:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
[tex]t = \frac{24.2 - 19}{\frac{12.59}{\sqrt{25}}}[/tex]
[tex]t = 2.07[/tex]
The critical value for a right-tailed test, as we are testing if the mean is greater than a value, with a significance level of 0.05 and 25 - 1 = 24 df is of [tex]t^{\ast} = 1.71[/tex]
Since the test statistic is greater than the critical value for the right-tailed test, it is found that there is enough evidence to conclude that the students' claim that they work more than 19 hours is correct.
To learn more about the t-distribution, you can take a look at https://brainly.com/question/13873630
Simplify Exponents and Roots
Solve -2/3x > 8 or -2/3x < 4.
{x | x > -12 or x < -6}
{x | -12 < x < -6}
{x | x < -12 or x > -6}
{x | x < -12 or x > -6}
=========================================================
Explanation:
Let's solve the first inequality for x.
(-2/3)x > 8
-2x > 8*3
-2x > 24
x < 24/(-2)
x < -12
The inequality sign flips when we divide both sides by a negative value.
Let's do the same for the second inequality.
(-2/3)x < 4
-2x < 4*3
-2x < 12
x > 12/(-2)
x > -6
The conclusion of each section is that x < -12 or x > -6 which points us to choice C as the final answer.
Side note: The intervals x < -12 and x > -6 do not overlap in any way. There's a gap between the two pieces. We consider these intervals to be disjoint. The number line graph is below.
Solve for x + (1/x):
3x + (2/x) - 4 = 2(x+9) - (7 - (1/x))
Answer:
Step-by-step explanation:
The radius of a circle wheel is 35 cm. How many revolutions does it make to cover a distance of 81.40
Answer:
.37 resolutions
Step-by-step explanation:
2×22/7×35
44.5×=220
0.37 revolutions
The dot product of u ∙ u = 45 what is the length of u?
Answer:
67 hah why you solve this
[tex]\textbf{u} \cdot \textbf{u} = 45\\\\\implies |\textbf{u}|^2 =45\\\\\implies |\textbf{u}| = 3\sqrt{5}[/tex]
A 2ft-by-2ft square is divided into smaller squares and portions are shaded. What is the area of the shaded portion?
Answer:
1.5 ft^2
Step-by-step explanation:
Since the length is divided into 4 parts,
Length of a small square = 2/4
= 0.5 ft
Hence,
Area of 1 small square = (0.5)(0.5)
= 0.25 ft^2
Area of shaded portion = Area of 6 small squares
= 6(0.25)
= 1.5 ft^2
Step-by-step explanation:
The area of the shaded cubes is 3 square feet.
What is a square?A square is a two-dimensional figure that has four sides and all four sides are equal.
The area of a square is given side²
We have,
Since the 2 ft-by-2 ft square is divided into 16 smaller squares, each smaller square has an area of:
(2/4)ft = 0.5ft.
Now,
Out of the 16 smaller squares, 6 smaller cubes are shaded.
Since each smaller cube occupies the space of one of the smaller squares, the total area of the shaded cubes is 6 times the area of one of the smaller squares.
The area of the shaded cubes is:
6 x 0.5ft² = 3ft²
Thus,
The area of the shaded cubes is 3 square feet.
Learn more about squares here:
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Find
∂f
∂x
,
∂f
∂y
, and
∂f
∂z
.
f(x, y, z) = 32xyz
Answer:
what are the measurements for 1 and 2?
Step-by-step explanation:
George Washington
please get this done asap
Answer:
1)2 2)2y=4 y=2 x=1
Step-by-step explanation:
Plot 1[tex]\frac{2}{5}[/tex] −12, and −2[tex]\frac{1}{10}[/tex] on the number line.
Answer:
1st= 2.4 on the line
2nd= -0.5 on the line
3rd=2.1 on the line
Step-by-step explanation:
1st=because each line represents 1 part so if it is split into 5 you have to treat 2 lines as one
2nd 1/2=0.5 so -1/2= -0.5
3rd if one line is one part then it is 2.1
Write an expression that is the product of two factors and is equivalent to -2x - 10
PLEASE HELP
Answer:
-2(x + 5)
Step-by-step explanation:
For what values of k
If y = cos(kt), then its first two derivatives are
y' = -k sin(kt)
y'' = -k² cos(kt)
Substituting y and y'' into 49y'' = -16y gives
-49k² cos(kt) = -15 cos(kt)
⇒ 49k² = 15
⇒ k² = 15/49
⇒ k = ±√15/7
Note that both values of k give the same solution y = cos(√15/7 t) since cosine is even.
Bill wanted to know how many times students at his middle school go to the beach each week during the summer. He surveyed every other middle school student at the mall last Saturday. After analyzing the data collected, Bill determined that the average student from his middle school goes to the beach about 2.4 times a week during the summer. What error did he make in the survey?
The survey was intended for Bill's middle school during the summer. The
survey was administered to students of other schools on a Saturday.
The type of error is the selection bias error.Reasons:
The type of error made is a non sampling error, given that the target of the
study is the number of times in a week students at his middle school
attend the beach during the summer.
The errors are; Selection bias error.
The given that the students survey are not from his middle school.The survey was carried out once on a Saturday, where the target was during the summer.The selection bias error is a type error that is due to the researcher
chooses what to study, such that the participant have common
characteristics rather than being random.
Learn more about selection bias error here:
https://brainly.com/question/13727092
Would you use SSS or SAS to prove the triangles congruent? If there is not enough information to prove the triangles by SSS or SAS, write "not enough information". Explain your answer.
Write a congruence statement and give a reason why the triangles are congruent. Select the correct choice below and, if necessary, write the vertices of the second triangle in the correct order.
Answer:
option B is correct answer. ∆SVZ~=∆YVX, SSS
Step-by-step explanation:
reasons,
VY=VS, S
YX=SZ, S
VX=VZ, S
therefore, ∆SVZ~=∆YVX.
hope this helps you.
The two triangles are congruent by side angle side property. The correct option is A.
What is congruency?In geometry, two figures or objects are said to be congruent if their shapes and sizes match, or if one is the mirror image of the other. The meaning of congruency is that the two shapes are similar as well as equal in size.
Given that there are three triangles and these three triangles are connected to each other at the centres' A, B, and C.
The diameter of the three circles is HF, DF, and DH. The three diameters are similar in shape and are also equal to each other.
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When a retired police officer passes away, he leaves $325,000 to be divided among his five children and three grandchildren. The will specifies that each child is to get twice as much as each grandchild. How much does each get?
How can one determine the number of x-intercepts of the graph of a quadratic function without graphing the function?
Answer:
The easiest method is to find the x-intercepts of the quadratic function by substituting y=0 in the function and solving it to find the possible values of x. The number of all possible values of x is the number of x-intercepts of the graph.
Which represents the RANGE of the following relation? {(-6, 5), (-4, 3), (-1, 0), (4, 3)}
Answer:
5, 3, 0, 3 are all the ranges! Hope this helps
Step-by-step explanation:
Ranges are on the right, domains are on the left
HELP! Due in 5 minutes
ANSWER:
the first one: 30x+48
The second one: x y^2(10 y + 15)
The third one: 30 x y - 5 x^2
Hope this helped!
sorry if im wrong. :)
GOOD LUCK!! <3
For what value of x does 32X – 9^3x-4?
Answer: X = 4/61
Step-by-step explanation
Evaluate ( f/g)(x) if f(x) = 2x and g(x) = 3x – 2 when x = 2.
Answer:
1
Step-by-step explanation:
(f/g)(x)
= [tex]\frac{f(x)}{g(x)}[/tex]
= [tex]\frac{2x}{3x-2}[/tex] ← substitute x = 2 into the expression
= [tex]\frac{2(2)}{3(2)-2}[/tex]
= [tex]\frac{4}{6-2}[/tex]
= [tex]\frac{4}{4}[/tex]
= 1
HELP ME PLEASEEEEEE I WILL GIVE BRAINLIEST
Answer:
DE, EW, WD
Step-by-step explanation:
From shortest line to longest line this would be the correct order.