Which logarithmic equation is equivalent to the exponential equation below?
67.21 = ea
A. In a = 67.21
B. loga 67.21 = 2.43
C. lo967.21 2.43 = e
O D. In 67.21 = a

Answers

Answer 1

Answer:

[tex]log_e^{67.21}= a[/tex]

Step-by-step explanation:

The equation is ,

[tex]\implies 67.21 = e^a [/tex]

Here e is the Euler's Number . The log which are defined on the base e are called Natural logarithms.

Say if we have a expoteintial equation ,

[tex]\implies a^m = n [/tex]

In logarithmic form it is ,

[tex]\implies log_a^n = m [/tex]

Similarly our required answer will be ,

[tex]\implies\boxed{ log_e^{67.21}= a }[/tex]


Related Questions

What is the slope of the line on the graph

Answers

the answer to this question is 3,3

Answer:

slope of the line(m) =(y2-y1)/(x2-x1)

or, m=(16-10)/(6-3)

or, m=6/3

So, m=2

Christopher needs to buy wooden boardes to build a box that is 12 inches long, 6 inches wide, and 8 inches high. How many square inches of wooden boards is needed to build the box

Answers

Answer:

432 in²

Step-by-step explanation:

To Obtian the square inches of wooden boards required :

Area of box = 2(l * w) + 2(l * h) + 2(h * w)

Length = 12 ; width = 6 ; height = 8

Hence,

Area of box = 2(12 * 6) + 2(12 * 8) + 2(8 * 6)

Area of box = 2(72) + 2(96) + 2(48)

Area of box = 432 in²

can someone help me with this ?

Answers

Answer:

de goes with bc ab goes with fd and angle f is angle A and angle d is angle B

Step-by-step explanation:

Answer:

Step-by-step explanation:

Which value below shows the strongest correlation?
A. 0.72
B. 0.35
C. 0.91
D. 0.99
E. 0.88
F. 0.29
G. 0.06
H. -0.55

Answers

Answer:

The answer is D. = 0.99

What was Dimitri's mistake? He mixed up the coordinates of the ordered pair when Substituting it into the equations 7x+9y=-4 and 5x-2y=6

Answers

Answer:

He made a mistake in his calculations when simplifying 5x - 2y

Step-by-step explanation:

Given

The coordinate pair

[tex](x,y) = (2,-2)[/tex]

The equations

[tex]7x + 9y = ?[/tex]

[tex]5x - 2y = ?[/tex]

Dimitri's Solution

[tex]Equation\ 1: 7x + 9y = -4.[/tex]

[tex]7(2) + 9 (-2) = -4.[/tex]

[tex]14 + (-18) = -4.[/tex]

[tex]-4 = -4.[/tex]

[tex]Equation\ 2: 5x -2y = 6.[/tex]

[tex]5(2) - 2 (-2) = 6.[/tex]

[tex]10 - 4 = 6.[/tex]

[tex]6 = 6.[/tex]

Required

Identify Dimitri’s mistake

In the first equation, Dimitri made no mistake.

However, he made a mistake when simplifying the second equation.

We have:

[tex]5x - 2y[/tex]

and

[tex](x,y) = (2,-2)[/tex]

Substitute [tex]x = 2[/tex] and [tex]y = -2[/tex]

So, we have:

[tex]5(2) -2(-2)[/tex]

Open bracket

[tex]10 +4[/tex]

Finally, we have:

[tex]14[/tex]

Identify each pair of angles in the diagram below as adjacent, vertical,
corresponding, alternate interior, or none of these.

Answers

Answer:

1) corresponding

2) alternate interior

3) corresponding

4) alternate exterior

5) vertical

6) supplementary

Write the equation of the line that passes through the points (4,1) and (-6,9). Put your answer in fully reduced point-slope form, unless it is a vertical or horizontal line.​

Answers

Answer:

Find the slope:

[tex]m = \frac{y2-y1}{x2-x1} = \frac{9 - 1}{-6 - 4} = -\frac{8}{10} = -\frac{4}{5}[/tex]

Use point-slope form and one of the points:

y - y₁ = m(x - x₁)[tex]y - 1 = -\frac{4}{5}(x - 4)[/tex]

PLZ HELP

How many solutions does the equation 3s + 7 = 3 + 4 + 3s have? (5 points)

a
Two

b
None

c
One

d
Infinitely many

Answers

Answer:

(d) infinitely many solutions

Step-by-step explanation:

Subtract 3s from both sides of 3s + 7 = 3 + 4 + 3s.  We get

7 = 3 + 4, or 7 = 7.  This is always true.  There are (d) infinitely many solutions.

Answer:

(d) infinitely many solutions.

How many​ flowers, spaced every 6 ​in., are needed to surround a circular garden with a ​100-ft ​radius?

Answers

Answer:

Number of flowers required = 1256

Step-by-step explanation:

Circumference of a circle is given by the formula,

Circumference = 2πr

Here, r = radius of the circle

For a circle with radius = 100 in.

Therefore, circumference = 2π(100)

                                           = 200π

                                           = 628.32 ft

Distance between each flower = 6 in

                                                   ≈ [tex]\frac{6}{12}[/tex]

                                                   = 0.5 ft

Number of flowers = [tex]\frac{\text{Circumference}}{\text{Space between each flower}}[/tex]

                               = [tex]\frac{628.32}{0.5}[/tex]

                               = 1256.63

                               ≈ 1256

Therefore, number of flowers required = 1256

Use this data to answer the questions below:
2, 4, 7, 8, 9, 12, 13
What is the range of the data?

What is the second quartile Q2 (or what is the median)?

What is the interquartile range? (Q1-Q3)

Answers

Answer: The Range is 11

The Q2 is 8

The Interquartile range is 8

x-y=3 what is this in slope intercept form

Answers

Answer:

y=x-3

Step-by-step explanation:

Can I get help with this please?

Answers

First equation:
5(x+1)=20 —— distribute the 5 to the x and 1
5x+5=20 ——- subtract 5 from 20
5x=15 ———— divide by 5 from both sides
X=3 ————— answer

Second equation:
5x+1=20——— subtract 1 from 20
5x=19 ———— divide by 5 from both sides
X=19/5———— answer in fraction form
X=3.8————- answer in decimal form

Suppose IQ scores were obtained for 20 randomly selected sets of siblings. The 20 pairs of measurements yield x overbarequals103.29​, y overbarequals103.75​, requals0.899​, ​P-valueequals​0.000, and ModifyingAbove y with caret equals negative 9.5 plus 1.1 x​, where x represents the IQ score of the younger child. Find the best predicted value of ModifyingAbove y with caret given that the younger child has an IQ of 105​? Use a significance level of 0.05.

Answers

Answer:

106

Step-by-step explanation:

Given :

Number of the set of siblings = 20

This 20 pair yields [tex]$\overline x$[/tex] = 103.29, [tex]$\overline y$[/tex] = 103.75, requals = 0.899, P-value = 0.000

Let x represents the IQ score of the younger child.

And y is the predicted value of Y(^).

So according to the question,

x = 105

and y = -9.5 + 1.1 x

Then,

y = -9.5 + 1.1 (105)

y = -9.5 + 115.5

y = 106

So the best predicted value of Y(^) is 106

Need some help on this question. Will award brainliest to a correct answer.

A car is moving at a fixed speed. The distance D that the car covers is then directly proportional to the time T it moves. Find the speed of the car. Write a formula that connects D and T. What is the coefficient of variation k equal to?

Answers

The formula is D=kT where k is the constant

tasha purchased an ipad for $625. a year later, it was selling for $500. what was the percent of change?

a. 20% increase
b. 25% increase
c. 20% decrease
d. 25% decrease

Answers

I believe this answer is (C) 20% decrease

A jar contains 4 green marbles 2 pink marbles 3 striped marbles. One marble is picked at random and then replaced. Then another marble is drawn at random again. What is the probability that both marbles are striped?

Answers

Answer:

25%

Step-by-step explanation:

Answer: It’s 1/9 I got the same question on my test.

The radius of a cylindrical cup is 6 ft and its volume is 420 cubic ft. Find the
height of the cup.
A.5 ft
B.3.71 ft
C.2.98 ft
D.6 ft

Answers

Answer:

Step-by-step explanation:

Volume of cylinder=pir^h

420={22/7×6×6]h=792/7h=113.14h

h=420/113.14

h=3.712

The answer is B. 3.71

Claire had 4 1/6 feet of string. She used some string to hang out decorations. Now she has 1 5/6 feet of string left. How much string did claire use? Draw a model and solve.

Answers

Answer:

Length of string used by Claire = 7 / 3 feet

Step-by-step explanation:

Given:

Length of string Claire in starts = [tex]4\frac{1}{6}[/tex] feet

Length of string Claire in end = [tex]1\frac{5}{6}[/tex] feet

Find:

Length of string used by Claire

Computation:

Length of string Claire in starts = [tex]4\frac{1}{6}[/tex] feet = 25 / 6 feet

Length of string Claire in end = [tex]1\frac{5}{6}[/tex] feet = 11 / 6 feet

Length of string used by Claire = Length of string Claire in starts - Length of string Claire in end

Length of string used by Claire = [25 / 6] - [11 / 6]

BY taking LCM

Length of string used by Claire = [25 - 11] / 6

Length of string used by Claire = 14 / 6

Length of string used by Claire = 7 / 3 feet

hii please help i’ll give brainliest

Answers

Answer:

18

Step-by-step explanation:

Multiples of 6: 6, 12, 18, etc.

Multiples of 9: 9, 18, etc.

the least common multiple here is 18

Answer:

Example: 9 and 12

Step-by-step explanation:

9: 9, 18, 27, 36, 48, 54, 63, 72..

12: 12, 24, 36, 48, 60, 72

36 is the first number that occurred in both list, so 36 is the least common multiple of 9 and 12

A quality control manager samples 700 LED bulbs and finds defects in 8 of them. What is the probability that a bulb selected at random will have a defect?

Answers

Answer: 0.0114

Step-by-step explanation:

Since we are given the information that the quality control manager samples 700 LED bulbs and finds out that 8 bulbs have defects in them.

The probability that a bulb selected at random will have a defect will be calculated as follows:

= Number of defected bulbs / Total number of bulbs sampled

= 8/700

= 0.0114

Therefore, the probability is 0.0114.

OKAY, guys give me a really brilliant explanation on how 2+2=4. It should be 22. It doesn't make sense.

Answers

It 22 what are you talking about

Answer:

It does make perfect sense... Count with ya fingers and see 4 yourself.

Step-by-step explanation: Go back to kindergarten buddy...

~ thx 4 the points my dude!~

Assume that 80 yen = $1.
What is the yen price of $1?
What is ths dollar price of 1 yen?
How many dollars would you need to buy a 20,000 yen iphone?​

Answers

Answer:

250$

Step-by-step explanation:

[tex]80/1 = 20000/x\\20000/80=250\\1 * 250=250\\\\80/1 = 20000/250\\[/tex]

Given the diagram shown below, find the value of 3x

Answers

Answer:

x= 6

Step-by-step explanation:

by using Pythagoras theorem

(30)={(9x^2+ 16x^2)}1/2

30= 5x

x= 30/5

x= 6

Answer:

18

Step-by-step explanation:

The triangle is a right triangle with sides 3x, 4x, 5x.

5x = 30

x = 6

3x = 3(6) = 18

Answer: 18

What is the center of the data?




Number of Green Candies in a Bag


A dot plot going from 10 to 15. 10 has 1 dot, 11 has 3 dots, 12 has 1 dot, 13 has 2 dots, 14 has 3 dots, and 15 has 3 dots.



The center is

.

Answers

Answer:

[tex]Median = 13[/tex]

Step-by-step explanation:

Given

See attachment for dot plot

Required

The center of data

This implies that, we calculate the median

From the attached plot,

[tex]n = 13[/tex] --- number of observation

So, the median is:

[tex]Median = \frac{n + 1}{2}[/tex]

[tex]Median = \frac{13 + 1}{2}[/tex]

[tex]Median = \frac{14}{2}[/tex]

[tex]Median = 7th[/tex]

The median is at the 7th position

At the  7th position, is 13

Hence:

[tex]Median = 13[/tex]

Answer:

i think it would be 13?

Step-by-step explanation:

just guessing but im pretty sure its 13

how to solve for x? i need help please help fast

Answers

Hi!

x² = 11,2² - 8,5²

x² = 125,44 - 72,25

x² = 53,19 |√

x ≈ 7,3

Point R′ (−2, 8) is the image of point R (−2, 2). Which of the following algebraic representations could be used for that transformation?
Select one:

(x,y)→(−x,y)

(x,y)→(4x,4y)

(x,y)→(x,y+6)

(x,y)→(x+6,y)

Answers

Answer:

C) (x,y) → (x,y+6)

Step-by-step explanation:

As the x value stays the same after the transformation, we know that there can be no changes to the value x, automatically limiting the options to answer C.

The mathematical way to find the value y is changed by would be by setting up a small equation as follows:

[tex]8 = 2 + n[/tex], where n is some number that the y value is altered by.

Solving for n gives the value 6, proving that the translation must add 6 to the y value.

Find the volume of the cylinder. Use 3.14 for u. Round to the nearest whole number.
Radius-34 m
Height-45 m

Answers

Answer:

1530 cubic centimeters

9
?
Find the arc length of the semicircle,
Either enter an exact answer in terms of ar or use 3.14 for 7 and enter your answer as a decimal.
units

Answers

Answer:

28.26 units

Step-by-step explanation:

Given:

Radius (r) = 9

π = 3.14

Required:

Arc length

Solution:

Arc length = θ/360 × 2πr

θ = 180° (half of a circle = 180°)

Plug in the values into the formula

Arc length = 180/360 × 2 × 3.14 × 9

Arc length = ½ × 56.52

Arc length = 28.26 units

please help
2y+x=-15
y=2x

Answers

Answer: x = -3

Step-by-step explanation:

2y + x = -15

y = 2x

2y = 2(2x) = 4x

4x + x = -15

5x = -15

x = -3

In a popular online role playing game, players can create detailed designs for their character's "costumes," or appearance. Boubacar sets up a website where players can buy and sell these costumes online. Information about the number of people who visited the website and the number of costumes purchased in a single day is listed below.
120 visitors purchased no costume.
235 visitors purchased exactly one costume.
3 visitors purchased more than one costume.

Based on these results, express the probability that the next person will purchase no costume as a percent to the nearest whole number.

Answers

Answer:

Step-by-step explanation:

p[p

Answer: 34%

Step-by-step explanation:

(Trust me)

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