MATHEMATICS HIGH SCHOOL

Penn stacks all of his snowballs in a square pyramid. The number of snowballs, P(n), in n layers of the square pyramid is given by P(n) = P(n-1) + n^2 Which could not be the number of snowballs Penn has? 5, 30, 25, 14

Answers

Answer 1

Answer:

Naturally, a pyramid of zero layers doesn't need any snowballs, so P(0) = 0. Then using the given recurrence, we find

P(1) = 1

P(2) = 1 + 4 = 5

P(3) = 1 + 4 + 9 = 14

P(4) = 1 + 4 + 9 + 16 = 30

and so on; luckily, three of these are listed among the answer choices, which leaves 25 as an insufficient number of snowballs to make such a pyramid.

More generally, we would end up with

$P(n) = 1^2 + 2^2 + 3^2 + \cdots + n^2 = \displaystyle \sum_(k=1)^n k^2 = \frac{n(n+1)(2n+1)}6$

Then given some number of snowballs S, you could try to solve for n such that

S = n (n + 1) (2n + 1)/6

and any S that makes n a non-integer would be the answer.

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what are the solutions of the equations x^2+14x=-130? (1point) a.2,-16 b.10,-13 c.-2,16 d.no solution

Answers

$x^2+14x=-130\nx^2+14x+49=-81\n(x+7)^2=-81$

no solutions in $\mathbb{R}$

in $\mathbb{C}$
$x+7=-√(-81) \vee x+7=√(-81)\nx=-7-√(-81) \vee x=-7+√(-81)\nx=-7-9i \vee x=-7+9i\n$

Kyla applied rm ◦ T0,3 to triangle ABC. What mistakes did she make? Check all that apply.She applied the rotation to the triangle first.
She applied the reflection to the triangle first.
She changed the size of the triangle instead of just applying a translation.
She translated the triangle down instead of just applying a reflection.
She applied a rotation instead of a reflection

Answers

Answer: she applied the reflection to the triangle first

she changed the size of the triangle instead of just applying a translation.

Step-by-step explanation:

Answer:

B & C

Step-by-step explanation:

Explain why the APR does not compare loans for different lengths of time.

Answers

I'm thinking because the woman/man taking out a loan would earn too much money for the loan

Deanna collected data on the favorite sports of the students of two grades. The table shows the relative frequencies of rows for the data collected: Favorite Sport Swimming Running Volleyball Row totals Grade 8 0. 14 0. 18 0. 22 0. 54 Grade 9 0. 17 0. 24 0. 05 0. 46 Column totals 0. 31 0. 42 0. 27 1 Based on the data, which statement is most likely correct? In Grade 8, 14 students liked swimming. In Grade 9, 31% of students liked swimming. In Grade 8, 22% of students liked volleyball. In Grade 9, 5 students liked volleyball.

Answers

Answer:

In Grade 8, 22% of students liked volleyball.

Step-by-step explanation:

Given:

The table representing the relative frequencies of different sports in different grades among the students.

Swimming Running Volleyball Row totals

Grade 8 0.14 0.18 0.22 0.54

Grade 9 0.17 0.24 0.05 0.46

Column totals 0.31 0.42 0.27 1

Relative frequency gives the ratio of the number of quantities of a particular kind and the total number of quantities.

From the above table, we can conclude the following points:

Grade 8:

14% liked swimming, 18% liked running and 22% liked volleyball. So, a total of 54% students liked playing sports.

Grade 9:

17% liked swimming, 24% liked running and 5% liked volleyball. So, a total of 46% students liked playing sports.

Combining students of grade 8 and 9:

31% liked swimming, 42% liked running and 27% liked volleyball.

From all the options available, we observe that, third option is only correct.

In Grade 8, 22% of students liked volleyball.

X + y = 155x - y = 9
Elimination method

(4, ? )

what number is the ?

Answers

The ? Is 11.

You add the equations to get rid of one variable, then you have 6x=24 then you divide both sides and you have x=4, then you substitute the given value of x and you are left with 5*4 - y = 9. And the solution or well possible solution is y = 11 which gives youuuuu. (x , y) = (4 , 11)

4 + y = 15....1
20 - y = 9.....2

....1*5
20 + 5y = 75....3

....3 - .....2
4y = 60
y = 15

the answer for (?) is 15
i’m not sure if this 100% correct but i’m trying my best to help you

If each number is rounded to the nearest hundred, which statement is true? A = 196.3 + 238.89 + 384.92 B = 329.11 + 288.06 + 106.4

Answers

A = 196.3 + 238.89 + 384.92 rounded to the nearest hundred
A = 200 + 200 + 400 = 800

B = 329.11 + 288.06 + 106.40 rounded to the nearest hundred
B = 300 + 300 + 100 = 700

800 is greater than 700. Thus, A > B.

Answer:

800 is greater than 700. Thus, A > B.

Step-by-step explanation:

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