1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
solong [7]
3 years ago
9

Chnstopher earned $142.20. He saved $24.50. He spent the rest on 2 new pairs

Mathematics
2 answers:
pogonyaev3 years ago
6 0

Answer:

$58.25

Step-by-step explanation:

142.20 - 24.50 = 117.50

117.50 / 2 = 58.25

Jobisdone [24]3 years ago
6 0

Answer:

$118.00

Step-by-step explanation:

$142.50- $24.50= $118.00

You might be interested in
PLEASE HELP
Lunna [17]
Well what’s the base and what’s the height and then times then
8 0
3 years ago
How many modes does the data set shown below contain?<br><br><br> 1, 3, 3, 4, 6, 6, 7, 7, 7, 10, 12
kipiarov [429]

Answer:

There are 3 modes

Step-by-step explanation:

There are two 3s, two 6s, and three 7s

4 0
3 years ago
Prove or disprove (from i=0 to n) sum([2i]^4) &lt;= (4n)^4. If true use induction, else give the smallest value of n that it doe
ddd [48]

Answer:

The statement is true for every n between 0 and 77 and it is false for n\geq 78

Step-by-step explanation:

First, observe that, for n=0 and n=1 the statement is true:

For n=0: \sum^{n}_{i=0} (2i)^4=0 \leq 0=(4n)^4

For n=1: \sum^{n}_{i=0} (2i)^4=16 \leq 256=(4n)^4

From this point we will assume that n\geq 2

As we can see, \sum^{n}_{i=0} (2i)^4=\sum^{n}_{i=0} 16i^4=16\sum^{n}_{i=0} i^4 and (4n)^4=256n^4. Then,

\sum^{n}_{i=0} (2i)^4 \leq(4n)^4 \iff \sum^{n}_{i=0} i^4 \leq 16n^4

Now, we will use the formula for the sum of the first 4th powers:

\sum^{n}_{i=0} i^4=\frac{n^5}{5} +\frac{n^4}{2} +\frac{n^3}{3}-\frac{n}{30}=\frac{6n^5+15n^4+10n^3-n}{30}

Therefore:

\sum^{n}_{i=0} i^4 \leq 16n^4 \iff \frac{6n^5+15n^4+10n^3-n}{30} \leq 16n^4 \\\\ \iff 6n^5+10n^3-n \leq 465n^4 \iff 465n^4-6n^5-10n^3+n\geq 0

and, because n \geq 0,

465n^4-6n^5-10n^3+n\geq 0 \iff n(465n^3-6n^4-10n^2+1)\geq 0 \\\iff 465n^3-6n^4-10n^2+1\geq 0 \iff 465n^3-6n^4-10n^2\geq -1\\\iff n^2(465n-6n^2-10)\geq -1

Observe that, because n \geq 2 and is an integer,

n^2(465n-6n^2-10)\geq -1 \iff 465n-6n^2-10 \geq 0 \iff n(465-6n) \geq 10\\\iff 465-6n \geq 0 \iff n \leq \frac{465}{6}=\frac{155}{2}=77.5

In concusion, the statement is true if and only if n is a non negative integer such that n\leq 77

So, 78 is the smallest value of n that does not satisfy the inequality.

Note: If you compute  (4n)^4- \sum^{n}_{i=0} (2i)^4 for 77 and 78 you will obtain:

(4n)^4- \sum^{n}_{i=0} (2i)^4=53810064

(4n)^4- \sum^{n}_{i=0} (2i)^4=-61754992

7 0
3 years ago
Find the unit rate of 8 teaspoon for 4 cups.
Igoryamba

Answer:

2 teaspoons for 1 cup

Step-by-step explanation:

8 divided by 4 is 2

4 divided by 4 is 1

3 0
3 years ago
Read 2 more answers
Please answer this question, will give brainliest!
Alika [10]

There are 360° in a circle and this circle is divided into 8 equal parts. 360/8 = 45 which means that each angle is 45°. The central angle subtended by minor arc BC is 2 portions of the circle, or 45 * 2 which is 90°. The answer is B.

7 0
3 years ago
Read 2 more answers
Other questions:
  • I am thinking of a number. It is increased by 7. The sun is 21. What is my number?
    11·2 answers
  • On the blueprint of a house, 39 millimeters represents 6 meters. The length of the living room is 52 millimeters on the blueprin
    10·1 answer
  • Three consecutive integers whose sums is 66
    10·1 answer
  • Can you please help me with this question?​
    6·1 answer
  • 123333333333333333333
    12·1 answer
  • In 1846 the depth of the river was 2.5 feet deep. In 1847 it rose 9%. This year, 1848, it dropped 6%. How deep is the river now?
    14·1 answer
  • Can someone help me in these questions please
    6·1 answer
  • Solve variable 3/4x-5=7
    8·1 answer
  • Which polynomial identity will prove that 49<br> = (2 + 5)2?
    15·1 answer
  • The polynomial x^3-kx^2+kx+2 has a factor of (x-2). What is the value of k?
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!