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
Alenkinab [10]
3 years ago
5

You have a mixture of dimes and

Mathematics
1 answer:
Stels [109]3 years ago
6 0

0.06 I hope that helped

You might be interested in
Prove or disprove (from i=0 to n) sum([2i]^4) <= (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
Consider the following figure.
Karolina [17]

Answer:

BD = 16

Step-by-step explanation:

By applying mean proportional theorem in the given right triangles,

\frac{AD}{BD}=\frac{BD}{CD}

AD × CD = BD²

8 × 32 = BD²

BD = √256

BD = 16

Therefore, measure of side BD = 16 units.

4 0
2 years ago
What is the next term of the geometric sequence?<br>375,75,15​
Damm [24]

Answer:

Step-by-step explanation:

ΔΔπФ⇵β³Δ⊄⊇≡⊕⊕π⇆ω∩∨

3 0
3 years ago
Read 2 more answers
Triangle A is reflected in the x-axis to give B.
nikitadnepr [17]

Answer:

The answer is below

Step-by-step explanation:

Transformation is the movement of a point from its initial location to a new location. Types of transformation is rotation, reflection, translation and dilation.

If a point A(x, y) is reflected over the x axis, the new point is at A'(x, -y). If a point B(x, y) is reflected over the y axis, the new point is at A'(-x, y).

Triangle A has vertex at (-4, -2), (-4, -5) and (-2, -5). If triangle A is reflected in the x axis to give triangle B, the vertex of triangle B is (-4, 2), (-4, 5) and (-2, 5).

If triangle B is reflected in the y axis to give triangle C, the vertex of triangle C is at (4, 2), (4, 5) and (2, 5). Hence the transformation is:

(x, y) ⇒ (-x, -y)

8 0
3 years ago
Which inequality is true? Use the number line to help
Nuetrik [128]

There is no image posted

6 0
3 years ago
Read 2 more answers
Other questions:
  • Solution for 8.5+4(1-2.5k)= -25.5
    12·1 answer
  • ILL CHOOSE BRAINLIEST!!!Which region represents the solution to the given system of inequalities?
    15·2 answers
  • Can someone please help me
    9·1 answer
  • The points A(0, 0), B(0, 4a - 5) and C(2a + 1, 2a + 6) form a triangle. If angle ABC = 90, what is the area of triangle ABC?(A)
    15·1 answer
  • A city's population is currently 150,500. If the population doubles every 62 years, what will
    11·1 answer
  • Tallulah biked 84 miles at a rate of 10.5 miles per hour. Determine how many hours she biked. Use d=rt​
    6·1 answer
  • Select the two answer choices that apply.
    7·1 answer
  • help me no link dummys jk A venue is preparing for a concert on the floor shown.The width of the red carpet is 1/6 of the width
    8·1 answer
  • I dont get it so can someone explain
    13·1 answer
  • if an object is dropped from a height of 144 ft the function h t equals negative 16 t squared + 144 gives the height of the obje
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!