Expand the log completely

The point of intersection between the function f(x) and g(x) is x = 4 then, g(x)=18 where option E (4,18) is correct answer.

What is a function?

A function is defined as a relation between a set of inputs having one output each.

We have,

f(x) = ( x + 5 ) ( x - 2 )

g(x) = ( 2x + 1 ) ( x - 2 )

To find the points of intersection between the two functions we must equal the function.

f(x) = g(x)

( x + 5 ) ( x - 2 ) = ( 2x + 1 ) ( x - 2 )

( x - 2 ) gets canceled

x + 5 = 2x + 1

5 - 1 = 2x - x

4 = x

x = 4

This means that at x =4 the function f(x) and g(x) intersect.

we can see that at x = 4 both the functions have the same value.

f(x) = ( x + 5 ) ( x - 2 ) = ( 4 + 5 ) ( 4 - 2 ) = 9 x 2

f(x) = 18

g(x) = ( 2x + 1 ) ( x - 2 ) = ( 2 x 4 + 1 ) ( 4 - 2 ) = ( 8 + 1 ) ( 4 - 2 )

     = 9 x 2

g(x) = 18

Thus the point of intersection between the function f(x) and g(x) is x = 4 then, g(x) =18 where option E (4,18) is correct answer.

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If 25% of Tolla's salary is Birr 135.75, then the full amount of his salary is 4 times this amount, since 25% is one quarter of the total amount.

Therefore, the full amount of Tolla's salary is 4 * Birr 135.75 = Birr 543.

This is the amount of Tolla's full salary.


LOL

A series that is neither mathematical nor geometric is described by the provided sequence. Which is the proper response would be a choice (B).

A grouping of numbers in a specific order is known as an arithmetic sequence.

The following question gives the sequence as follows: 1, 6, 7, 13,...

We must determine the kind of the current sequence.

According to the question, we have 1, 6, 7, 13,...

For verification as an arithmetic series:

The usual deviation between 1 and 6 is given by d = 6 - 1 = 5.

Commonly, 6 and 7 differ by 1 when d = 7 - 6

It is not an arithmetic sequence since the common difference between subsequent terms is not the same.

In order to verify it as a geometric sequence:

r = 6/1 = 6 is a common ratio between 1 and 6.

r = 7/6 is a common ratio between 6 and 7.

It is not a geometric sequence since the common ratio between subsequent terms is not the same.

A series that is neither mathematical nor geometric is described by the provided sequence.

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The probability of selecting chocolate such that:

(a) both have cherry centers: 0.1630

(b) one has a cherry center and one does not: 0.507

In this question, we have been given a box of chocolates contains 24 chocolates.

n(S) = 24

Ten of the chocolates with cherry centers.

n(A) = 10

So, the number of chocolates with no cherry centers are:

n(B) = 14

We need to find the probability of selecting chocolate such that

(a) both have cherry centers

P = (10/24)(9/23)

P = 90/552

P = 15/92

P = 0.1630

(b) one has a cherry center and one does not

P = 2*(10/24)(14/23)

P = 0.507

Therefore, the probability of selecting chocolate:

(a) both have cherry centers

P = 0.1630

(b) one has a cherry center and one does not

P = 0.507

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The interval of true average price of a regular room with a king size bed in the resort community with 99% confidence is ( 14.74, 48.89 ).

One method of determining the actual population mean is by using a confidence interval for the mean. A confidence interval provides a lower estimate and an upper estimate rather than just the mean.

A confidence interval expresses the degree of uncertainty surrounding a given statistic. A margin of error is frequently used with confidence intervals. It reveals the degree to which you may be certain that the findings of a poll or survey correspond to what you would anticipate discovering if it were possible to poll the complete population. Levels of confidence are inextricably linked to confidence intervals.

x = mean;

99% confidence interval for μ is

(x - t * S) /√n  <  μ <( x + t * S) /√n;

(135 - 2.898 * 25 )/√18 < μ < (135 + 2.898 * 25)/√18;

14.74<  μ< 48.89;

99% CI is ( 14.74, 48.89 ) ;

critical value at 0.01 significance level with 17 df = 2.898

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By using the distance formula, the length of the interval AC 10.8, After rounding it will be 11 units.

The distance formula is given as:

Distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Give the example of two decimal rounding off.

Here are two examples of rounding off to two decimal places:

12.3456 rounded to two decimal places is 12.35

0.678 rounded to two decimal places is 0.68

Plugging in the coordinates of the two points, we get:

Distance = sqrt((5 - (-1))^2 + (4 - 13)^2)

= sqrt(6^2 + (-9)^2)

= sqrt(36 + 81)

= sqrt(117)

= approximately 10.8

Therefore, the distance between the points (-1,13) and (5,4) is approximately 10.8.

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The minimum sample size is needed to be 90% confident that the sample mean is within 5 minutes of the true population mean is 40.

In frequentist statistics, a confidence interval is a range of estimates for an unknown parameter.

We have that to find our α level, that is the subtraction of 1 by the confidence interval divided by 2.

α = (1 - 0.90)/2 = 0.05.

Now, we have to find z in the Ztable as such z has a p-value of 1 - α.

So it is z with a pvalue of  1 - 0.05 = 0.95 = 1.96.

Now, find the margin of error M as such,

M = z×(sigma/√n).

5 = 1.96×(16/√n).

5√n = 31.36.

n = 39.9.

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Answer: 4x^2(7x+1)

Step-by-step explanation: Divide by the common divisible of 4x^2 and you will get your answer/.

Answer:4x^2(1+7x)

Step-by-step explanation:

4x^2(1+7x)

The solution is

a) The amount Connor has to pay for parking if he left his car for y hours is given by the equation A = 8 + 2y where y is the number of hours

b) The amount Connor has to pay for parking if he left his car for t hours is given by the equation B = 8 + 2t where t is the number of hours

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the first equation be represented as A

Let the second equation be represented as B

Now , the value of A is

The automatic fee for parking = $ 8

The additional fee for parking every hour = $ 2

So , for x number of hour , the additional parking fee = 2x

And , the total parking fee including x hours = automatic fee for parking + additional parking fee

Substituting the values in the equation , we get

The total parking fee including x hours = 8 + 2x

Now , when x = y hours

The total parking fee including y hours A = 8 + 2y

And , when x = t hours

The total parking fee including t hours B = 8 + 2t

Hence , the equations are A = 8 + 2y and B = 8 + 2t where y and t are number of hours

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The value of r(x) approaches as x approaches Infinity is; 0

Limit is defined as the value that a function approaches for the given input value.

We have been given a function;

r (x) = Start Fraction a x Superscript b Baseline + 8 Over c x Superscript d Baseline End Fraction

We can rewrite this function as;

r(x) = (axᵇ + 8)/(cx^d)

where a, b, c, and d are positive integers and b < d.

We need to find the value of r(x) approach as x approaches Infinity.

This means, we need to find the value of the limit [tex]\lim_{x \to \infty} r(x)[/tex]

Now, we find the value of limit for given function;

[tex]\lim_{x \to \infty} \frac{ax^b + 8 }{cx^d}[/tex]

This simplifies to;

[tex]\lim_{x \to \infty} \frac{8 }{cx^d}[/tex] (since d > b)

Thus;

[tex]\lim_{x \to \infty} r(x) = 0[/tex]

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Answer:

13

Step-by-step explanation:

The box plot ends at 13.

Box plots show the average score of the data. It shows the minimum, median and maximum. The line inside the box is the median. The minimum, in this case is 0 and the max is 13.

Answer:

10/7 or 1 3/7

Step-by-step explanation:

1. change from mixed fraction to improper fraction, 5/2 and 7/4

2. instead of the dividing the fractions as is, multiply the reciprocal which would be 5/2 multiplied by 4/7. Then you cross multiply. 2 into 2, 1 and 2 into 4, 2. So now you're left with 5 and 2/7 since 5/1 is basically 1.

3. simplify to just 10/7

Answer:

10/7 or 1 3/7

I took a test with that question.

The maximum area is 12.25 square feet

From the question, we have the following parameters that can be used in our computation:

Perimeter = 14 feet

This means that

P = 2(l + w)

So, we have

2(l + w) = 14

Divide by 2

l + w = 7

Make l the subject

l = 7 - w

The area is calculated as

A = lw

So, we have

A = (7 - w)w

Expand

A = 7w - w²

Differentiate and set to 0

7 - 2w = 0

So, we have

w = 3.5

Substitute w = 3.5 in A = (7 - w)w

A = (7 - 3.5) * 3.5

Evaluate

A = 12.25

Hence, the area is 12.25 square feet

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Complete question

There is 14 feet of fencing available to enclose a rectangular region. For what value of area is the area maximum

Answer:

150 in^2

Step-by-step explanation:

It is a cube...it has six equal sides

  the surface area of one side is 5 x 5 = 25 in^2

       there are six   ....    so   6 x 25 = 15o in^2

Edited:  should be in^2    not cm^2 as originally posted...wrong units

Answer:

150

Step-by-step explanation:

To find the surface area of a cube, you do 6a^2. That would mean it is 150.

Answer:

answer for no.10 is {11,12,13,14}

Step-by-step explanation:

According to question domain and equation is given. At first we have to write equation as f(y)=5x+1 and at the place of y we have to write the given domain respectively then we can get the answers

Answer:

Step-by-step explanation:

P = 4 a

a = √p^2 + q^2 / 2

P = 2√p^2 + q^2 = 2 x √42^2 + 40^2 = 116cm

∴ the perimeter of a rhombus when the diagonals are 42cm and 40cm is 116cm

Answer:

the range of the graph would move down by 4 units.

Step-by-step explanation:

f(x) is the original/basis equation

g(x) is the translation equation

-4 does not have any x's attached to it, so it would affect the range, or the y of the equation

for example:

f(x) = 2x + 8

if you subtracted 4 from that it would be:

f(x) = 2x - 4, so the range would be affected

Answer:

880 is the answer

Step-by-step explanation:

hope this helps

Answer:

To solve this problem, we can set up the following system of equations:

Let x be the rate at which Joe flew in still air and y be the rate of the wind.

1000 km / 4 hours = x + y

700 km / 7 hours = x - y

Solving this system of equations using the elimination method, we get:

x + y = 250

x - y = 100

Adding these two equations together, we get 2x = 350, so x = 175 km/hour.

Subtracting the second equation from the first equation, we get 2y = 150, so y = 75 km/hour.

Therefore, the rate at which Joe flew in still air is 175 km/hour and the rate of the wind is 75 km/hour.

Step-by-step explanation:

The  level of confidence as a would accompany each of the given intervals are a. 95%, b. 90%, c. 99%

Instead of being expressed as a percentage, the confidence level is expressed as a proportion using the confidence coefficient. For instance, the confidence coefficient would be. 99 if you had a confidence level of 99%. In general, the greater the coefficient, the more confident you can be in the accuracy of your findings.

The most typical levels of confidence are 90%, 95%, and 99%. A summary of the values corresponding to these typical confidence levels can be seen in the following table. The "confidence coefficient" is simply the confidence level presented as a proportion .

for a:

Z1=a/2=1.96

1-a/2=0.975

a=0.05

so,

(1-a)x100

=95%

Hence, the level of confidence is 95%

for b:

Z1=a/2=1.645

1-a/2=0.95

a=10

so,

(1-a)x100

=90%

Hence, the level of confidence is 90%

for c:

Z1=a/2=2.576

1-a/2=0.995

a=0.01

so,

(1-a)x100

=99%

Hence, the level of confidence is 99%

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The measure of AB in the figure is C. 100 degree

The measure of AB in the figure is the length of arc, this is given by the formula

given angle / 360 * 2πr

However, the measure in degree is equal to the angle given which is 100 degree.

The size or the measure of the angle is same at any point within same lines that formed the angel AB.

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The probability that the average score of golfers exceeded = 0.0228

A measurement of a data set's deviation from the mean is referred to as "standard deviation.". A low standard deviation means that the data are grouped around the mean, whereas a large standard deviation says that the data are more spread out.

According to the given information

We are given that,

[tex]& \mu=80 \\[/tex]

[tex]& \sigma=3.5 \\[/tex]

[tex]& n=49 \\& \mu \bar{x}=\mu=80 \\[/tex]

[tex]& \sigma \bar{x}=\sigma / \sqrt{n}=3.5 / \sqrt{ } 49=0.5 \\& P(\bar{x} > 81)=1-P(\bar{x} < 81) \\& =1-P[(\bar{x}-\mu \bar{x}) / \sigma \bar{x} < (81-80) / 0.5] \[/tex]

[tex]& =1-P(z < 2) \\&[/tex]

Using standard normal table

[tex]& =1-0.9772 \\& =0.0228[/tex]

Probability [tex]$=0.0228$[/tex]

The probability that the average score of golfers exceeded = 0.0228

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The correlation of two pairs of data values tells about the degree of movement that can occur. The correct option is A, C, and D.

The degree of movement that can occur in one of the data values when another data value is increased or decreased is indicated by the correlation of two pairs of data values.

A.) There is a positive relationship between depth under water and pressure.

Because water pressure increases with depth, this is a casual relationship that can be observed while swimming in a deep swimming pool.

C.) A positive relationship between the age and weight of a puppy.

This is a casual relationship because the puppy's weight and size both increase as it grows.

D.) A negative relationship between temperature and the number of snowboards sold

This is a casual relationship because as the weather warms up, fewer people prefer to go snowboarding.

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a) The values are given as follows:

b) The solution of the equation is of: -0.25410169644.

The equation in this problem is given as follows:

y = (x³ - 1)/4.

The solution is obtained using a iterative solution method, until the difference between previous iterations is less than 10^-6, as the solution is exact to 6 decimal places.

Then the values are given as follows:

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Answer:

44.8

Step-by-step explanation:

Volume = Length * Height * Width

Volume = 10 * 1.5 * 3.2

Volume = 44.8cm

Option 1: An initial investment of $5 that increases by 50% every year

as after 20 years, it amounts to a greater value.

An arithmetic sequence is a set of numbers in which every no. next to the previous number has the same common difference

d = aₙ - aₙ₋₁ = aₙ₋₁ - aₙ ₋₂.

In a geometric sequence numbers are written in the same constant ratio(r).

It means every next number is a multiple of a common constant and the previous number.

r = aₙ/aₙ₋₁ = aₙ-₁/aₙ₋₂.

The given situations can be modeled as a geometric sequence.

Option A :

a₁ = 5, r = 1.5.

We know Sₙ = a₁(rⁿ - 1)/(r -1).

Sₙ = 5(1.5ⁿ - 1)/(1.5 - 1).

Sₙ = 5(1.5ⁿ - 1)/(0.5).

Let us see for n = 20, 20th year.

S₂₀ = 5(1.5²⁰ - 1)/(0.5).

S₂₀ = 5(3324.25)/(0.5).

S₂₀ = 33242.5.

Option B :

a₁ = 0.01 and r = 2.

Sₙ = 0.01(2ⁿ - 1)/(1).

S₂₀ = 0.01(2²⁰ - 1)/(1).

S₂₀ = 10,485.75

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Solution

Given series is [tex]$5+11+17+\ldots .+95$.[/tex]

Thus,

[tex]$\mathrm{a}=5, \mathrm{~d}=11-5=6,1=95$$$\begin{aligned}& \mathrm{n}=\frac{1-a}{d}+1 \\& =\frac{95-5}{6}+1 \\& =\frac{90}{6}+1=15+1=16\end{aligned}[/tex]

Therefore, [tex]$\mathrm{S}_{\mathrm{n}}=\frac{\mathrm{n}}{2}(\mathrm{a}+1)$$$\begin{aligned}& =\frac{16}{2}(5+95) \\& =8(100) \\& =800\end{aligned}$$[/tex]

What is arithmetic series?

The total of the terms in an arithmetic sequence with a predetermined number of terms is known as an arithmetic series. Here is a straightforward formula for calculating the sum: Formula 1: If the sum of an arithmetic series of terms is represented by S n, then The first and last terms' values, as well as the total number of terms, are needed for this formula.

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Answer:

Step-by-step explanation:

A

The number of movies rented when the cost for Movies Plus and Movies-To-Go is the same is 10.

An equation is written in the form of variables and constants separated by the operation of multiplication and division,

An equation states that terms in different forms on both sides of the equality sign are equal.

Multiplication and division do not separate the terms of an equation.

Let the no. of movies be 'm' and the total cost is 'C'

Movies Plus charges a one-time fee of $20 plus $5 per movie

which is, C = 5m + 20.

Movies-To-Go charges $7 per movie

which is, C = 7m.

Now,  the number of movies rented when the cost for Movies Plus and Movies-To-Go is the same will be when we equate both equations.

∴ 7m = 5m + 20.

2m = 20.

m = 10.

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