logx-log(x-l)^2=2log(x-1)​

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▹ Answer

D. 8x⁴ + x³ - 4x² + 1

▹ Step-by-Step Explanation

Remove the opposites:

x⁴ + 3x³ - 2x³ - 5x² + x² + 1 + 7x²

Collect like terms:

8x⁴ + 3x³ - 2x³ - 5x² + x² + 1

8x⁴ + x³ - 5x² + x² + 1

8x⁴ + x³ - 4x² + 1

Hope this helps!

CloutAnswers ❁

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Answer/Step-by-step explanation:

The idea to use in solving this problem using the model, is to express the number of shaded boxes in fraction form.

Thus, the blue red shaded boxes has 34 boxes shaded out of 100 boxes. This represents [tex] \frac{34}{100} [/tex]. This will give us 0.34.

The other shaded boxes represents [tex] \frac{49}{100} = 0.49 [/tex].

Using the model, we can solve 0.34 + 0.49.

Add both fractions together.

[tex] \frac{34}{100} + \frac{49}{100} = \frac{34+49}{100} [/tex]

[tex] \frac{83}{100} = 0.83 [/tex]

Answer:

102 cm

Step-by-step explanation:

Answer:

fraction bar. separates numerator and denominator in a fraction

Answer:

basically a dividing symbol, but specifically used for fractions

Step-by-step explanation:

Answer:

6 cm by 6 cm

Step-by-step explanation:

We know that the formula for area of a square is A = s² where A = area and s is the length of one side. We know that A = 36 so:

36 = s²

√36 = s

s = ±6

Note that s = -6 is an extraneous solution because you can't have a side length of -6, therefore the answer is s = 6 so the dimensions of the square are 6 cm by 6 cm.

The area of a square is found using the formula area = s^2, where s is the length of a side. ( a square has 4 equal sides).

Given the area you have:

36 = s^2

Find a by taking the square root of both sides:

S = sqrt(36)

S = 6

The square has a side length of 6 cm.

Answer:

[tex]Difference = 4.41[/tex]

Step-by-step explanation:

Given

Represent Christina's time with C and the other runner's time with R

C = 22.3

R = 4.41 + C

Required

Determine the difference using an equation

The difference between both runner's time is as follows;

[tex]Difference = R - C[/tex]

Substitute 4.41 + C for R

[tex]Difference = 4.41 + C - C[/tex]

[tex]Difference = 4.41[/tex]

Hence, the difference is 4.41 seconds

Answer:

(a) The probability that a study participant has a height that is less than 67 inches is 0.4013.

(b) The probability that a study participant has a height that is between 67 and 71 inches is 0.5586.

(c) The probability that a study participant has a height that is more than 71 inches is 0.0401.

(d) The event in part (c) is an unusual event.

Step-by-step explanation:

The complete question is: In a survey of a group of​ men, the heights in the​ 20-29 age group were normally​ distributed, with a mean of 67.5 inches and a standard deviation of 2.0 inches. A study participant is randomly selected. Complete parts​ (a) through​ (d) below. ​(a) Find the probability that a study participant has a height that is less than 67 inches. The probability that the study participant selected at random is less than inches tall is nothing. ​(Round to four decimal places as​ needed.) ​(b) Find the probability that a study participant has a height that is between 67 and 71 inches. The probability that the study participant selected at random is between and inches tall is nothing. ​(Round to four decimal places as​ needed.) ​(c) Find the probability that a study participant has a height that is more than 71 inches. The probability that the study participant selected at random is more than inches tall is nothing. ​(Round to four decimal places as​ needed.) ​(d) Identify any unusual events. Explain your reasoning. Choose the correct answer below.

We are given that the heights in the​ 20-29 age group were normally​ distributed, with a mean of 67.5 inches and a standard deviation of 2.0 inches.

Let X = the heights of men in the​ 20-29 age group

The z-score probability distribution for the normal distribution is given by;

                          Z  =  [tex]\frac{X-\mu}{\sigma}[/tex]  ~ N(0,1)

where, [tex]\mu[/tex] = population mean height = 67.5 inches

            [tex]\sigma[/tex] = standard deviation = 2 inches

So, X ~ Normal([tex]\mu=67.5, \sigma^{2}=2^{2}[/tex])

(a) The probability that a study participant has a height that is less than 67 inches is given by = P(X < 67 inches)

      P(X < 67 inches) = P( [tex]\frac{X-\mu}{\sigma}[/tex] < [tex]\frac{67-67.5}{2}[/tex] ) = P(Z < -0.25) = 1 - P(Z [tex]\leq[/tex] 0.25)

                                                                 = 1 - 0.5987 = 0.4013

The above probability is calculated by looking at the value of x = 0.25 in the z table which has an area of 0.5987.

(b) The probability that a study participant has a height that is between 67 and 71 inches is given by = P(67 inches < X < 71 inches)

    P(67 inches < X < 71 inches) = P(X < 71 inches) - P(X [tex]\leq[/tex] 67 inches)

    P(X < 71 inches) = P( [tex]\frac{X-\mu}{\sigma}[/tex] < [tex]\frac{71-67.5}{2}[/tex] ) = P(Z < 1.75) = 0.9599

    P(X [tex]\leq[/tex] 67 inches) = P( [tex]\frac{X-\mu}{\sigma}[/tex] [tex]\leq[/tex] [tex]\frac{67-67.5}{2}[/tex] ) = P(Z [tex]\leq[/tex] -0.25) = 1 - P(Z < 0.25)

                                                                = 1 - 0.5987 = 0.4013

The above probability is calculated by looking at the value of x = 1.75 and x = 0.25 in the z table which has an area of 0.9599 and 0.5987 respectively.

Therefore, P(67 inches < X < 71 inches) = 0.9599 - 0.4013 = 0.5586.

(c) The probability that a study participant has a height that is more than 71 inches is given by = P(X > 71 inches)

      P(X > 71 inches) = P( [tex]\frac{X-\mu}{\sigma}[/tex] > [tex]\frac{71-67.5}{2}[/tex] ) = P(Z > 1.75) = 1 - P(Z [tex]\leq[/tex] 1.75)

                                                                 = 1 - 0.9599 = 0.0401

The above probability is calculated by looking at the value of x = 1.75 in the z table which has an area of 0.9599.

(d) The event in part (c) is an unusual event because the probability that a study participant has a height that is more than 71 inches is less than 0.05.

Answer:

-All integers are whole numbers.

-All rational numbers are natural numbers.

Step-by-step explanation:

The statement which is correct about the sets of numbers is:

All integers are rational numbers.

Option D is the correct answer.

A rational number is a number that is expressed as the ratio of two integers, where the denominator should not be equal to zero.

We have,

Natural number:

Natural numbers are positive integers or non-negative integers which start from 1 and end at infinity.

Integer:

An integer is a number with no decimal or fractional part and it includes negative and positive numbers, including zero.

Whole number:

Whole numbers include all natural numbers and 0.

It does not include fractions, decimals, and negative integers.

Irrational numbers:

An irrational number is a type of real number which cannot be represented as a simple fraction.

It cannot be expressed in the form of a ratio.

Rational number:

A rational number is a number that is expressed as the ratio of two integers, where the denominator should not be equal to zero.

From the above definition, we can say that,

- Some integers are whole numbers but not all integers are whole numbers.

- No irrational numbers are integers.

-Some rational numbers are natural numbers but not all rational numbers are natural numbers.

- Yes, all integers are rational numbers.

Thus the statement which is correct about the sets of numbers is:

All integers are rational numbers.

Option D is the correct answer.

Learn more about rational numbers here:

https://brainly.com/question/24398433

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Answer:

The correct option is D

P(A or B) = 1.30

Step-by-step explanation:

Given two independent (or mutually exclusive) events with P(A) = 0.60, and P(B) = 0.70

P(A or B) = P(A) + P(B)

= 0.60 + 0.70

= 1.30

This is however absurd, as the probability of an event can only be less than or equal to 1, and not less than 0.

Based on the information given, the value of then P(A or B) will be D. 1.30.

From the information given, A and B are independent events with P( A) = 0.60 and P( B) = 0.70.

Then, the value of P(A or B) will be calculated thus:

= 0.60 + 0.70

= 1.30

In conclusion, the correct option is D.

Learn more about probability on:

https://brainly.com/question/24756209

Answer:

Renaissance Naturalism

Step-by-step explanation:

just took the quiz

Answer:

The diameter that will reward with the largest pizza is 14 in

Step-by-step explanation:

The perimeter of a sector of a circle is:

P = 2r + l

l = rθ

P = 2r + rθ

P=28 inches

28=2r + rθ

28-2r=rθ

θ=(28-2r/r)

=(2*14 - 2*r)/r

=2(14-r)/r

Area of the sector of the circle is:

A = r²/2 * θ

A = r²/2 * 2(14 - r)/r

A = r² * (14 - r)/r

A = r(14 - r)

A = 14r - r²

For the maximum area:

A = 14r - r²

A' = 14 - 2r

Set A' = 0

14 - 2r = 0

14= 2r

r = 7 in

The diameter (D) of the circle is twice of the radius:

D = 2r = 2 * 7= 14 in

The maximum area is:

A = 14r - r²

r = 7 in

A = 14 * 7 - 7²

A = 98 - 49

A = 49 in²

Answer:  [tex]\dfrac{(x+9)^2}{225}-\dfrac{(y+7)^2}{49}=1[/tex]

Step-by-step explanation:

The equation for a horizontal ellipse is: [tex]\dfrac{(x-h)^2}{a^2}-\dfrac{(y-k)^2}{b^2}=1[/tex]  where

Given: major axis (diameter on x) is 30 --> x-radius (a) = 15  -->  a² = 225

           minor axis (diameter on y) is 14 --> y-radius (b) = 7   --> b² = 49

           center (h, k) is (-9, -7)

Input those values into the equation for a horizontal ellipse and simplify:

  [tex]\dfrac{(x-(-9))^2}{15^2}-\dfrac{(y-(-7))^2}{7^2}=1\\\\\\\large\boxed{\dfrac{(x+9)^2}{225}-\dfrac{(y+7)^2}{49}=1}[/tex]  

Answer:

  -4

Step-by-step explanation:

(f+g)(1) = f(1) +g(1)

In each case, you need to locate the ordered pair with 1 as the first element.

  (1, f(1)) = (1, -2) . . . . f(1) = -2

  (1, g(1)) = (1, -2) . . . . g(1) = -2

  f(1) +g(1) = (-2) +(-2) = -4

(f+g)(1) = -4

Answer:

1978.2 or 630π feet

Step-by-step explanation:

The Ferris wheel will rotate 3 * 5 = 15 times during the 5 minute ride and the radius is 42 / 2 = 21 feet. Since C = 2πr, r = 21 and π ≈ 3.14, C = 2 * 3.14 * 21 = 131.88. However, this only accounts for one rotation so the answer is 131.88 * 15 = 1978.2 or 630π feet.

Answer:

300%

Step-by-step explanation:

1 year = 12 months

percent = part/whole * 100%

percent = 12/4 * 100% = 300%

Answer:

please can u follow me I've started following you

Answer:

The slope of Function 2 (m=1.1) is greater than the slope of Function 1 (m=1).  

Step-by-step explanation:

First, note that p is essentially the y and that r is the x. Thus, to make this easier to see, convert p to y and r to x. Thus:

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

From the above equation, we can determine that the slope is 1. Thus, the slope of Function 1 is 1.

To find the slope of the table, simply use the slope formula. Use any two points. I'm going to use the points (0,8) and (10,19). Let (0,8) be x₁ and y₁, and (10,19) be x₂ and y₂. Therefore:

[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{19-8}{10-0}=11/10=1.1[/tex]

Thus, the slope of Function 2 is 1.1.

1.1 is greater than 1.

Thus, the slope of Function 2 is greater than the slope of Function 1.

Answer:

Function 2 has the greater slope

Step-by-step explanation:

Answer: 1/24 of Ralph's land

Step-by-step explanation:

Ralph gave each of his children a 6th of his land.

= 1/6

Lynn being his daughter got 1/6 of his land. She then shared it to her 4 children.

Children got 1/4 of Lynn's land which is 1/6 of Ralph's land.

Lynn's children therefore got;

= 1/4 * 1/6

= 1/24 of the land

Answer:

32.5%

Step-by-step explanation:

Hey there!

To find the probability we first need to find the amount of prime numbers in the 1-40 set.

Prime - 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37

That’s 13 prime numbers.

Fraction - 13/40

Simplified is just 13/40.

13 / 40 = .325

Percent - 32.5%

Hope this helps :)

Answer:

As in explanation.

Step-by-step explanation:

A) SSE means "Error Sum of Squares". The source of it is the sum of squared deviations within groups.

B) SSTR means "Treatment Sum of Squares". It's source is the weighted sum of squared deviations of group means from grand mean. It's the sum of squares between groups.

C) SST means "Total Sum of Squares''. It's source is total sum of squared deviations from the grand mean. It is a sum of SSE and SSTR.

A) SSE means "Error Sum of Squares". The source of it is the sum of squared deviations that lies within groups.

B) SSTR means "Treatment Sum of Squares". It's source that represents the weighted sum of squared deviations of group means from the grand mean. It's the sum of squares between groups.

C) SST means "Total Sum of Squares''. It's source that represents total sum of squared deviations from the grand mean. It is a sum of SSE and SSTR.

learn more about sum here: https://brainly.com/question/6463206

Answer:

Geometric

Step-by-step explanation:

That is a geometric sequence, because the each number divided into 3. As we know if the pattern are multiply or divided it will be geometric, if it is sum or subtract will be arithmetic.

hope this helps

if u have question let me know in comments

The given sequence is geometric. The common ratio of the geometric sequence is 1/3.

A geometric progression (G.P.) is a sort of sequence in which each successive term is obtained by multiplying the prior term by a set number known as a common ratio.

This progression is also known as a pattern-following geometric sequence of integers.

The given sequence in the problem is;

81, 27, 9, 3, 1, …

Due to the fact that each number is split into three, that sequence is geometric. The pattern will be geometric if it is multiplied or divided, and arithmetic if it is the result of addition or subtraction.

The common ratio of the sequence is found as;

[tex]\rm r = \frac{27}{81} =\frac{9}{27} =\frac{3}{9} =\frac{1}{3} =\frac{1}{3}[/tex]

The common ratio of successive terms is equal.

Hence, the given sequence is geometric.

To learn more about the geometric progression, refer to https://brainly.com/question/14320920.

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Answer:

The equation is always false

Step-by-step explanation:

arctan1/4+arctan2/7=1/2arccos3/5

0.24497866+0.27829965=1/2(0.92729521)

0.52327832                 =0.46364760

not equivalent and will never be.

Answer:

(a) The 26th percentile for the number of chocolate chips in a bag is 1185

(b) The number of chocolate chips in a bag that makes up the middle 96% of the bags is between 1020 and 1504

Step-by-step explanation:

From the question, we have the following values:

μ =1262 and σ =118

(a) Let the value of x represents the 26th percentile. So the 26th percentile means 26% data is less than x. We can use the standard normal table to get the particular z-value that corresponds to this percentile.

P( Z<-0.65 )=0.2578 which is approximately 0.26

So for 26th percentile z-score will be -0.65.

Mathematically;

z-score = (x-mean)/SD

-0.65 = (x-1262)/118

-76.7 = x -1262

x = 1262-76.7 = 1185.3

This value is approximately 1,185

(b) Using a graph of standard normal distribution curve, if middle is 96% , then at both tails 2% each.

From z-table, we can find the closest probability;

P(-2.05<z<2.05) = 0.96

So we have two x values to get from the individual z-scores

-2.05 = (x-1262)/118

x = 1020(approximately)

For 2.05, we have

2.05 = (x-1262)/118

x = 1262 + 2.05(118) = 1504 (approximately)

Answer:

Slope of the tangent line (m) = 1 / 2

Step-by-step explanation:

Given:

Point A = (4,2)

Origin point = (0,0)

Find:

Slope of the tangent line (m)

Computation:

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

Slope of the tangent line (m) = (2-0) / (4-0)

Slope of the tangent line (m) = 2 / 4

Slope of the tangent line (m) = 1 / 2

Answer:

-6

Step-by-step explanation:

-18 + 2k    wherre k = 6

=> -18 + 2(6)

=> -18 + 12

=> -6

Answer:

A

Step-by-step explanation:

Let's find the ml per garlic for each sauce. Emily's has 1 clove of garlic for 62.5 ml. Raphael's has 1 clove of garlic for 7.438... ml. So, A, it will be too garlicky.

Answer:

Aiko should not have put both of the 'i' out of the brackets.

Step-by-step explanation:

As only one integer has i with it, it is not possible to take the i out of the bracket.

Answer:

n = 8

Step-by-step explanation:

Follow the question when turning the word equation into an equation

Because we know this is a quadratic equation, the product is a result of n multiplied by itself

[tex]n^{2} -4=60[/tex]

Solve for n

[tex]n^{2} =64[/tex]

[tex]\sqrt{n^{2} } =\sqrt{64}[/tex]

n = 8

Answer:

A

Step-by-step explanation:

r=10 and the angle bln 5√3 and -5 is 330 or 11π/6

Answer:

Take 5^x as y.  

Now the question becomes a simple equation.  

y + 20y - 125 = 0.

21y = 125.

Thus, y = 125/21.

Now resubstituting we get,

5^x = 125 /21.

Taking log on both sides,

xlog5 = log 125 - log 21

x = (log125/log5) - (log21/log 5)

x= 3- 1.89

Answer:

$5

Step-by-step explanation:

Using Promotion A, Jane would buy the first pair for $30 and the second for 1/2 * 30 = $15 for a total of 30 + 15 = $45. Using Promotion B, she would buy the first pair for $30 and the second for 30 - 10 = $20 for a total of 30 + 20 = $50. Since 45 < 50, Promotion A is the better deal, so Jane would save 50 - 45 = $5.