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lora16 [44]
2 years ago
8

20 is what percent of 80? Choose the equation to solve the problem

Mathematics
1 answer:
Mila [183]2 years ago
5 0

Answer:

A

Step-by-step explanation:

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Prove the following limit. lim x → 5 3x − 8 = 7 SOLUTION 1. Preliminary analysis of the problem (guessing a value for δ). Let ε
Temka [501]

\displaystyle\lim_{x\to5}3x-8=7

means to say that for any given \varepsilon>0, we can find \delta such that anytime |x-5| (i.e. the whenever x is "close enough" to 5), we can guarantee that |(3x-8)-7| (i.e. the value of 3x-8 is "close enough" to the limit value).

What we want to end up with is

|(3x-8)-7|=|3x-15|=3|x-5|

Dividing both sides by 3 gives

|x-5|

which suggests \delta=\dfrac\varepsilon3 is a sufficient threshold.

The proof itself is essentially the reverse of this analysis: Let \varepsilon>0 be given. Then if

|x-5|

and so the limit is 7. QED

8 0
3 years ago
Find the length of the leg of a right triangle with leg length b= 21.5 inches and the hypotenuse c= 31.9 inches. Use a calculato
sweet [91]

Answer:

23.6 (approximate value)

Step-by-step explanation:

  • a*a+b*b=c*c Pythagorean thereom
  • (21.5)^2 + b*b = (31.9)^2
  • b*b= 1017.61 - 462.25
  • √b*b= √555.36
  • b=23.6(approximate value)
8 0
3 years ago
The table represents the temperature of a cup of coffee over time.
Harrizon [31]

Answer: first choice, exponential, because there is a relatively consistent multiplicative rate of change.

Explanation:

1) I have attached the figure with the data table that represents the temperature of a cup of coffee over time.

These are the data:

Time (min) ------ Temperature (°F)

0 ----------------------- 200

10 ---------------------- 180

20 --------------------- 163

30 --------------------- 146

40 ---------------------131

50 -------------------- 118

60 -------------------- 107

2) Since, the increase in time is constant, while the decrease in temperaute is not, you know that it is not linear.

3) The other two options involve exponential models.

The exponential models have a constant multiplicative rate of change, not additive. Therefore, the only feasible choice is the first one: temperature of a cup of coffee over time.

4) You can prove it:

i) Exponential models have the general form y = A [r]ˣ, where B is r is the multiplicative rate of change: any value is equal to the prior value multiplied by r:

y₁ = A [r]¹

y₂ = A[r]²

y₂ / y1 = r ← as you see this is the constant multiplicative rate of change.

ii) Test some data:

180 / 200 = 0.9

163 / 180 ≈ 0.906 ≈ 0.9

146 / 163 ≈ 0.896 ≈ 0.9

131 / 146 ≈ 0.897 ≈ 0.9

118 / 131 ≈ 0.901 ≈ 0.9

107 / 118 ≈ 0.907 ≈ 0.9

As you see all the data of the table have a relatively consistent multiplicative rate of change, which proves that the temperature follows an exponential decay; so the right choice is the first one.

6 0
3 years ago
Read 2 more answers
40 percent of students survey said that they are night owls . If 300 students said that they are night owls how many students we
sattari [20]

Based on the calculations that 300 is 40%, 375 is considered 50% or halfway.. in this case, we must multiply 375 by 2 and we will discover how many students were surveyed:

375 x 2 = 750

7 0
2 years ago
Can someone plzz help me with these 2 questions. thanks!
Deffense [45]

9514 1404 393

Answer:

  4. height: 5√3 cm; area: 25√3 cm²

  5. 30√2 ft ≈ 42.43 ft

Step-by-step explanation:

4. The height of an equilateral triangle is (√3)/2 times the side length, so is ...

  height = (√3)/2 × (10 cm) = 5√3 cm

The area is given by the formula ...

  A = 1/2bh

  A = 1/2(10 cm)(5√3 cm) = 25√3 cm²

__

5. The diagonal of a square is √2 times the side length, so the distance from 3rd to 1st base is ...

  (30 ft)√2 ≈ 42.43 ft

__

The length of the diagonal of a square is something you should be familiar with. If you're not, you can figure the distance using the Pythagorean theorem.

  d = √(30² +30²) = √1800 ≈ 42.43 . . . feet

6 0
2 years ago
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