Expand the logarithm as much as possible. Rewrite the expression as a sum, difference, or product of logs.



ln(1/49^k)

Answers

Answer 1

9514 1404 393

Answer:

  -2k·ln(7)

Step-by-step explanation:

49 is a perfect square, so the argument of the log function can be written as ...

  1/46^k = 1/(7^2)^k = 1/7^(2k) = 7^(-2k)

Then the log of it is ...

  ln(7^(-2k)) = -2k·ln(7)


Related Questions

solve the equation
r²-4s+s²=8r+2s=28​

Answers

Answer:

[tex] {r}^{2} - 4s + {s}^{2} = 8r + 2s = 28 \\ \\ r = \frac{24}{5 } - i \frac{ \sqrt[4]{129} }{5} \\ \: s = \frac{58}{5} + i \frac{ \sqrt[2]{129} }{5 } \\ \\ r = \frac{24}{5} + i \frac{ \sqrt[4]{129} }{5} \\ s = \frac{58}{5} - i \frac{ \sqrt[2]{129} }{5} [/tex]

A recipe calls for 2 1/2 tablespoons of oil and 3/4 tablespoons of vinegar. What is the ratio of oil to vinegar in this recipe?

Answers

Answer:

10:3

Step-by-step explanation:

Make 2 1/2 an improper fraction, you will get 5/2. You dont have to do anything to the 3/4.

For you to find the ratio of an fraction, you have to take the numerator but the denominator has to be the same.

So make 5/2 to a 10/4.

Take the numerator 10 & 3.

Your answer will be 10:3

No problem.

Find the midpoint of the line segment with end coordinates of: (-2,-2) and (2,8)​

Answers

Answer:

(0 ; 3)

Step-by-step explanation:

hello :

the midpoint of the line segment is : ((-2+2)/2 ;(-2+8)/2 )

(0 ; 3)

The correct answer is (0,3)

Angles are not necessarily drawn to scale.

X=?

Answers

Answer:

x = 76

Step-by-step explanation:

A line has an angle measurement of 180 degrees.

Knowing that, let's first find the angle measurement of DIJ:

180 - 107 = 73

Angle DIJ has an angle measurement of 73

To find the angle measurement of DJI, we have to apply knowledge of angles in a triangle. When you add all the angles in a triangle, they ALWAYS equal to 180 degrees.

Using that knowledge, we can add 73 and 31 and subtract that value from 180:

73 + 31 = 104

180 - 104 = 76

The angle measurement of Angle DJI is 76.

Because vertical angles are ALWAYS going to have the same angle measurement, Angle AJF is going to have an angle measurement of 76 as well.

So x = 76

Hope that helps (●'◡'●)

PLEASE HELP AND BE RIGHT BEFORE ANSWERING

Answers

9514 1404 393

Answer:

  see attached

Step-by-step explanation:

Since point P is the center of dilation, it doesn't move. (It is "invariant.") The other points on the figure move to 1/4 of their original distance from P. On this diagram, it is convenient that the distances are all multiples of 4 units, so dividing by 4 is made easy.

Simplificar expresiones algebraicas

Answers

Use Socratic it helps

Pleas help me in this question Find R

Answers

Answer:

R = 25.8

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

cos R = adj side / hyp

cos R = 9/10

Taking the inverse cos of each side

cos ^-1 ( cos R) = cos^ -1 ( 9/10)

R=25.84193

Rounding to the nearest tenth

R = 25.8

Answer:

[tex]\boxed {\boxed {\sf D. \ 25.8 \textdegree} }[/tex]

Step-by-step explanation:

We are asked to find the measure of an angle given the triangle with 2 sides. This is a right triangle because of the small square representing a right angle. Therefore, we can use trigonometric functions. The three major functions are:

sinθ= opposite/hypotenuse cosθ= adjacent/hypotenuse tanθ= opposite/adjacent

We are solving for angle R, and we have the sides TR (measures 9) and SR (measures 10).

The side TR (9) is adjacent or next to angle R. The side SR (10) is the hypotenuse because it is opposite the right angle.

We have the adjacent side and the hypotenuse, so we will use the cosine function.

[tex]cos \theta = \frac {adjacent}{hypotenuse}[/tex]

[tex]cos R = \frac {9}{10}[/tex]

Since we are solving for an angle, we must take the inverse cosine of both sides.

[tex]cos^{-1}(cos R) = cos ^{-1} ( \frac{9}{10})[/tex]

[tex]R = cos ^{-1} ( \frac{9}{10})[/tex]

[tex]R= 25.84193276[/tex]

If we round to the nearest tenth, the 4 in the hundredth place tells us to leave the 8 in the tenths place.

[tex]R \approx 25.8 \textdegree[/tex]

The measure of angle R is approximately 25.8 degrees and choice D is correct.

An inlet pipe can fill an empty swimming pool in 5hours, and another inlet pipe can fill the pool in 4hours. How long will it take both pipes to fill the pool?

Answers

Answer:

It will take 2 hours, 13 minutes and 20 seconds for both pipes to fill the pool.

Step-by-step explanation:

Given that an inlet pipe can fill an empty swimming pool in 5hours, and another inlet pipe can fill the pool in 4hours, to determine how long it will take both pipes to fill the pool, the following calculation must be performed:

1/5 + 1/4 = X

0.20 + 0.25 = X

0.45 = X

9/20 = X

9 = 60

2 = X

120/9 = X

13,333 = X

Therefore, it will take 2 hours, 13 minutes and 20 seconds for both pipes to fill the pool.

What is the chance of getting 3 of the same cards in a row in a 52 cards deck?

Answers

Answer:

1/425

Step-by-step explanation:

The first card can be any card, so we don’t have to evaluate the probability.

Now we can suppose that the exit card is a two

- For the second card we have 3/51 of possibilities that is a 2 = 1/17

- For the third card we have 2/50 of possibilities that is a 2 = 1/25

1/17 * 1/25 = 1/425

1+4=5
2+3=10
10+5=25
4+1?

Answers

the puzzle is
1+1(4)
2+2(3)
etc
so 4+1 = 8

Answer:

8

Step-by-step explanation:

To test the effectiveness of a business school preparation course, 8 students took a general business test before and after the course. The results are given below. Exam Score Exam Score Student Before Course (1) After Course (2) 1 530 670 2 690 770 3 910 1,000 4 700 710 5 450 550 6 820 870 7 820 770 8 630 610 If they hope that the prep course is effective in improving the exam scores, what is the alternative hypothesis?

Answers

Solution :

Group   Before     After

Mean    693.75    743.75

Sd         155.37     143.92

SEM        54.93     50.88

n              8            8

Null hypothesis : The preparation course not effective.

[tex]$H_0: \mu_d = 0$[/tex]

Alternative hypothesis : The preparation course is effective in improving the exam scores.

[tex]$H_a : \mu_d>0$[/tex]  (after -  before)

Bob's truck averages 23 miles per gallon. If Bob is driving to his mother's house, 72 miles away, how many gallons of gas are needed? Round to the nearest tenth.

Answers

Answer:

3.1 gallons

Step-by-step explanation:

To solve this, we need to figure out how many gallons of gas go into 72 miles. We know 23 miles is equal to one gallon of gas, and given that the ratio of miles to gas stays the same, we can say that

miles of gas / gallons = miles of gas / gallons

23 miles / 1 gallon = 72 miles / gallons needed to go to Bob's mother's house

If we write the gallons needed to go to Bob's mother's house as g, we can say

23 miles / 1 gallon = 72 miles/g

multiply both sides by 1 gallon to remove a denominator

23 miles = 72 miles * 1 gallon /g

multiply both sides by g to remove the other denominator

23 miles * g = 72 miles * 1 gallon

divide both sides by 23 miles to isolate the g

g = 72 miles * 1 gallon/23 miles

= 72 / 23 gallons

≈ 3.1 gallons

Which of the following exponential equations is equivalent to the logarithmic
equation below?
log 970 = x
A.x^10-970
B. 10^x- 970
C. 970^x- 10
D. 970^10- X

Answers

Given:

The logarithmic equation is:

[tex]\log 970=x[/tex]

To find:

The exponential equations that is equivalent to the given logarithmic equation.

Solution:

Property of logarithm:

If [tex]\log_b a=x[/tex], then [tex]a=b^x[/tex]

We know that the base log is always 10 if it is not mentioned.

If [tex]\log a=x[/tex], then [tex]a=10^x[/tex]

We have,

[tex]\log 970=x[/tex]

Here, base is 10 and the value of a is 970. By using the properties of exponents, we get

[tex]970=10^x[/tex]

Interchange the sides, we get

[tex]10^x=970[/tex]

Therefore, the correct option is B, i.e., [tex]10^x=970[/tex].

Note: It should be "=" instead of "-" in option B.

A group of rowdy teenagers near a wind turbine decide to place a pair of pink shorts on the tip of one blade, they notice the shorts are at its maximum height of 16 meters at a and it’s minimum height of 2 meters at s.

Determine the equation of the sinusoidal function that describes the height of the shorts in terms of time.

Determine the height of the shorts exactly t=10 minutes, to the nearest tenth of a meter

Answers

The equation of the sinusoidal function is 7 × sin((π/15)·(x - 2.5)) + 9

Question: The likely missing parameters in the question are;

The time at which the shorts are at the maximum height, t₁ = 10 seconds

The time at which the shorts are at the minimum height, t₂ = 25 seconds

The general form of a sinusoidal function is A·sin(B(x - h)) + k

Where;

A = The amplitude

The period, T = 2·π/B

The horizontal shift = h

The vertical shift = k

The parent equation of the sine function = sin(x)

We find the values of the variables, A, B, h, and k as follows;

The given parameters of the sinusoidal function are;

The maximum height = 16 meters at time t₁ = 10 seconds

The minimum height = 2 meters at time t₂ = 25 seconds

The time it takes the shorts to complete a cycle, (maximum height to maximum height), the period, T = 2 × (t₂ - t₁)

∴ T = 2 × (25 - 10) = 30

The amplitude, A = (Maximum height- Minimum height)/2

∴ A = (16 m - 2 m)/2 = 7 m

The amplitude of the motion, A = 7 meters

T = 2·π/B

∴ B = 2·π/T

T = 30 seconds

∴ B = 2·π/30 = π/15

B = π/15

At t = 10, y = Maximum

Therefore;

sin(B(x - h)) = Maximum, which gives; (B(x - h)) = π/2

Plugging in B = π/15, and t = 10, gives;

((π/15)·(10 - h)) = π/2

10 - h = (π/2) × (15/π) = 7.5

h = 10 - 7.5 = 2.5

h = 2.5

The minimum value of a sinusoidal function, having a centerline of which is on the x-axis, and which has an amplitude, A, is -A

Therefore, the minimum value of the motion of the turbine blades before, the vertical shift = -A = -7

The given minimum value = 2

The vertical shift, k = 2 - (-7) = 9

Therefore, k = 9

Therefore;

The equation of the sinusoidal function is 7 × sin((π/15)·(x - 2.5)) + 9

More can be learned about sinusoidal functions on Brainly here;

https://brainly.com/question/14850029

Consider A Triangle ABC. Suppose That A= 119 Degrees, B=53, And C=57. Solve The Traingle

Answers

9514 1404 393

Answer:

  a = 94.8, B = 29.3°, C = 31.7°

Step-by-step explanation:

Side 'a' can be found using the Law of Cosines:

  a² = b² +c² -2bc·cos(A)

  a = √(2809 +3249 -6042·cos(119°)) ≈ √8987.22 ≈ 94.8

Then one of the other angles can be found from the Law of Sines.

  sin(C)/c = sin(A)/a

  C = arcsin(c/a·sin(A)) ≈ arcsin(0.525874) ≈ 31.7°

Then the remaining angle can be found to be ...

  B = 180° -A -C = 180° -119° -31.7° = 29.3°

__

The solution is a ≈ 94.8, B ≈ 29.3°, C ≈ 31.7°.

PLEASE HELPPPPP ASAPPPPPPPPPPPPP PLEASEEEE

Answers

Answer:

0.5679

Step-by-step explanation:

From. The table Given above :

The probability of female Given an advanced degree ;

P(F|A) = p(FnA) / p(A)

From the table, p(FnA) = 322

P(Advanced degree), P(A) = (245 + 322) = 567

Hence,

P(F|A) = p(FnA) / p(A) = 322 / 567 = 0.5679

Consider the following results for two independent random samples taken from two populations.

Sample 1 Sample 2
n1=50 n2=35
x¯1=13.6 x¯2=11.6
σ1=2.2 σ2=3.0

Required:
a. What is the point estimate of the difference between the two population means?
b. Provide a 90% confidence interval for the difference between the two population means.
c. Provide a 95% confidence interval for the difference between the two population means.

Answers

Answer:

a. 2

b. The 90% confidence interval for the difference between the two population means is (1.02, 2.98).

c. The 95% confidence interval for the difference between the two population means is (0.83, 3.17).

Step-by-step explanation:

Before solving this question, we need to understand the central limit theorem and the subtraction of normal variables.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Subtraction between normal variables:

When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.

Sample 1:

[tex]\mu_1 = 13.6, s_1 = \frac{2.2}{\sqrt{50}} = 0.3111[/tex]

Sample 2:

[tex]\mu_2 = 11.6, s_2 = \frac{3}{\sqrt{35}} = 0.5071[/tex]

Distribution of the difference:

[tex]\mu = \mu_1 - \mu_2 = 13.6 - 11.6 = 2[/tex]

[tex]s = \sqrt{s_1^2+s_2^2} = \sqrt{0.3111^2+0.5071^2} = 0.595[/tex]

a. What is the point estimate of the difference between the two population means?

Sample difference, so [tex]\mu = 2[/tex]

b. Provide a 90% confidence interval for the difference between the two population means.

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1 - 0.9}{2} = 0.05[/tex]

Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].

That is z with a pvalue of [tex]1 - 0.05 = 0.95[/tex], so Z = 1.645.

The margin of error is:

[tex]M = zs = 1.645(0.595) = 0.98[/tex]

The lower end of the interval is the sample mean subtracted by M. So it is 2 - 0.98 = 1.02

The upper end of the interval is the sample mean added to M. So it is 2 + 0.98 = 2.98

The 90% confidence interval for the difference between the two population means is (1.02, 2.98).

c. Provide a 95% confidence interval for the difference between the two population means.

Following the same logic as b., we have that [tex]Z = 1.96[/tex]. So

[tex]M = zs = 1.96(0.595) = 1.17[/tex]

The lower end of the interval is the sample mean subtracted by M. So it is 2 - 1.17 = 0.83

The upper end of the interval is the sample mean added to M. So it is 2 + 1.17 = 3.17

The 95% confidence interval for the difference between the two population means is (0.83, 3.17).

1. Write a variable expression that matches the following situation: Marguerite wants to put a garland around her garden. If the length of the garden is 50 meters and the width of the garden is 2 more than the length, what is the perimeter of the garden?​

Answers

Answer:

3x2,−23y,√5m, 3 x 2 , − 2 3 y , 5 m

Step-by-step explanation:

that is the answer i think

Please help

4. The equation of a curve is y = (3 - 2x)^3 + 24x.
(a) Find an expression for dy/dx

5. The equation of a curve is y = 54x - (2x - 7)^3.
(a) Find dy/dx​

Answers

(4) y = (3 - 2x)³ + 24x

Use the power and chain rules:

dy/dx = 3 (3 - 2x)² d/dx [3 - 2x] + 24

dy/dx = 3 (3 - 2x)² (-2) + 24

dy/dx = -24x ² + 72x - 30

(5) y = 54x - (2x - 7)³

Same basic procedure:

dy/dx = 54 - 3 (2x - 7)² d/dx [2x - 7]

dy/dx = 54 - 3 (2x - 7)² (2)

dy/dx = -24x ² + 168x - 240

help please! i'm in class and i have 10 mins left. :)

Answers

Answer:

3:8

Step-by-step explanation:

i will gadit

that only

I really need help big time thank you

Answers

1) 2x² -5x+12
2) x² +7x+10
3) 3x² +5x-2

Factor the trinomial x^2-8x-65

Answers

Step-by-step explanation:

here's the answer to your question

Which function describes this graph? (CHECK PHOTO FOR GRAPH)

A. y = x^2 + 7x+10
B. y = (x-2)(x-5)
C. y = (x + 5)(x-3)
D.y = x^2+5x+12

Answers

Answer:

Option A. y = x² + 7x + 10

Step-by-step explanation:

We'll begin calculating the roots of the equation from the graph.

The roots of the equation on the graph is where the curve passes through the x-axis.

The curve passes through the x-axis at –5 and –2

Next, we shall determine the equation. This can be obtained as follow:

x = –5 or x = –2

x + 5 = 0 or x + 2 = 0

(x + 5)(x + 2) = 0

Expand

x(x + 2) + 5(x + 2) = 0

x² + 2x + 5x + 10 = 0

x² + 7x + 10 = 0

y = x² + 7x + 10

Thus, the function that describes the graph is y = x² + 7x + 10

I need help understanding how to get the answer.

Answers

Answer:

-157.87

Step-by-step explanation:

1) the rules are:

[tex]log_a(bc)=log_ab+log_ac;[/tex]

and

[tex]log_ab^c=c*log_ab.[/tex]

2) according to the rules above:

[tex]log_7(yz^8)=log_7y+8log_7z=-6.19-8*18.96=-157.87.[/tex]

A line passes through point (5, –3) and is perpendicular to the equation y = x. What's the equation of the line? Question 26 options: a) y = x b) y = –x – 7 c) y = x + 3 d)y = –x + 2

Answers

Answer:

sorry my bad bro I have no clue

Solve the following system of equations
x^2+2y^2=59
2x^2+y^2=43
(x ,y), (x, y) (x, y) (x, y)

Answers

Answer:

(-3,5),(-3,-5),(3,5),(3,-5)

Step-by-step explanation:

i changed my answer :)

A study conducted by the Center for Population Economics at the University of Chicago studied the birth weights of 614 babies born in New York. The mean weight was 3398 grams with a standard deviation of 892 grams. Assume that birth weight data are approximately bell-shaped. Estimate the number of newborns who weighed between 1614 grams and 5182 grams. Round to the nearest whole number.

Answers

Answer:

The number of newborns who weighed between 1614 grams and 5182 grams was of 586.

Step-by-step explanation:

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

The mean weight was 3398 grams with a standard deviation of 892 grams.

This means that [tex]\mu = 3398, \sigma = 892[/tex]

Proportion that weighed between 1614 and 5182 grams:

p-value of Z when X = 5182 subtracted by the p-value of Z when X = 1614.

X = 5182

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{5182 - 3398}{892}[/tex]

[tex]Z = 2[/tex]

[tex]Z = 2[/tex] has a p-value of 0.9772

X = 1614

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{1614 - 3398}{892}[/tex]

[tex]Z = -2[/tex]

[tex]Z = -2[/tex] has a p-value of 0.0228

0.9772 - 0.0228 = 0.9544.

Out of 614 babies:

0.9544*614 = 586

The number of newborns who weighed between 1614 grams and 5182 grams was of 586.

A strawberry and banana juice blend is made with a ratio of strawberry to banana of 2:3. Fill in the table to show different proportional amounts

Answers

Answer:

See Explanation

Step-by-step explanation:

Given

Let

[tex]s \to Strawberry[/tex]

[tex]b \to Banana[/tex]

So:

[tex]s:b = 2:3[/tex]

Required

Complete the table

The table, to be complete, is not given; so, I will generate one myself.

The table is generated as follows:

Multiply by 1.5

[tex]s : b = 3 : 4.5[/tex]

Multiply by 2

[tex]s : b = 2*2 : 2 * 3[/tex]

[tex]s : b = 4 : 6[/tex]

And so on....

In summary, whatever factor is multiplied to S must be multiplied to B

HELP!!!!!!!!!!! SOMEONE PLEASE HELP!!!

For the graph below, which of the following is a possible function for h?


A) h(x) = 4-x



B) h(x) = 2x



C) h(x) = 5x



D) h(x) = 3x

Answers

9514 1404 393

Answer:

  C)  h(x) = 5^x

Step-by-step explanation:

h(x) is shown on the graph as having the highest rate of growth. That means, relative to the other functions, the base of the exponential is larger. Of the choices offered, the one with the largest growth factor is ...

  h(x) = 5^x

_____

The general form of an exponential function is ...

  f(x) = (initial value) · (growth factor)^x

A cylindrical piece of iron pipe is shown below. The wall of the pipe is 1.25 inches thick: The figure shows a cylinder of height 14 inches and diameter 8 inches What is the approximate inside volume of the pipe?
332 cubic inches
69 cubic inches
703 cubic inches
99 cubic inches

Answers

Answer: 332 cubic inches

Step-by-step explanation:

You can eliminate 69 and 99 as those answers don't make any sense. This leaves you with 703 and 332.

It says the wall of the pipe is 1.25 inches thick so you multiply that by 2 and subtract it by the diameter to get the insider diameter of 5.5

Now you just use the equation V = (3.14)(r^2)(14) where the radius is half of 5.5.

So to finalize the equation you get V = (3.14)(5.5)^2(14) which comes out to 332 cubic inches

The best choice is 332 cubic inches.

69 cubic inches and 99 cubic inches are less and 703 cubic inches is a large approximation.

Diameter = d= 8 inches

Height= Length = l= 14 inches

Thickness= 1.25 inches

Outer Radius= R= diameter/2= 8/2=4 inches

Inner radius = r= Radius - thickness

                            = 4- 1.25= 2.75 inches

Volume of the cylinder = Area × length

                                      = π r²× l

                                       = 22/7 × (2.75)² × 14

                                          = 332. 616 inches cube

So the best answer is 332 cubic inches

https://brainly.com/question/21067083

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