g(x) = 2 log(x - 1)
what is the inverse

Answer:

0.625

Step-by-step explanation:

I just entered this in a calculator what are you learning in math?

Answer:

y = 40 / x^1/3

Step-by-step explanation:

Given that :

y α x^1/3

y = k * 1 / x^1/3

y = k / x^1/3

When x = 125 ; y = 8

8 = k / 125^1/3

Cube root of 125 = 5

8 = k / 5

8 * 5 = k ; k = 40

Hence, expression becomes :

y = 40 / x^1/3

y α k/∛x is the relationship of the variables x and y whose values are 125 and 8.

Two or more expressions connected with an equal sign is called Equation.

The relationship of the given variables. y varies inversely as the cube root of x.

By given data we can write as

y α k/∛x

The cube root of 125 is 5.

y α k/∛125

y α k/5

8=k/5

k=40

Hence y α 40/∛x is the relationship of the variables x and y whose values are 125 and 8.

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Answer:

x= -3

Step-by-step explanation:

3x-1= -10

   +1   +1

 3x=-9  =  -3

The volume of the funnel to the nearest cubic centimeter is 38.

The given funnel is in the shape of cone, so volume of cone gives the volume of funnel. The formula of volume of the cone is as follows:

\(V=\frac{1}{3} \pi r^{2} h\)

Where r is the radius and h is the height of the cone and π=3.14.

The funnel is in the shape of cone with height 9 centimeter and diameter 4 centimeter.

Radius of cone  \(=\frac{4}{2} =2 c m\)

Now, putting the value of h, r and π in the formula of volume of cone,

\(V=\frac{1}{3} \pi r^{2} h\\\\V=\frac{1}{3} \times 3.14\times 2^{2}\times 9\\\\V=37.68\)

Approximating to nearest cubic centimeter, we get

\(V\approx38cm^3\)

Hence, the volume of the funnel with diameter 4 centimeter and height 9 centimeter is 38 cubic centimeter.

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Answer:

The experimental probability of the coin landing heads up is 110/200 = 11/20.

The probability is 1/2.

The correct statement in Mai's experiment is, The experimental probability of the coin landing heads up is (11/20) and the theoretical probability of the coin landing heads up is (1/2)

Probability is the chance of occurrence of a certain event out of the total no. of events that can occur in a given context.

Experimental probability is repeating an experiment and observing the outcomes and theoretical probability is the expected value.

In the given context the expected value is 200×(1/2) = 100, As P(H) = 1/2 and P(T) = 1/2.

Upon experiment, the coin landed 110 times heads up.

Therefore, The theoretical likelihood of the coin landing heads up is (1/2), while the experimental probability is (11/20).

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When the null hypothesis is rejected in ANOVA analysis, we can test for differences between treatment means by doing a t-test.

It is statistically possible to compare the means of two or more groups of data using the ANOVA approach. It includes comparing the null hypothesis, which states that the means of the groups are equal, to the alternative hypothesis, which states that at least one of the means is different. If the null hypothesis is disproved, it signifies that the group means deviate significantly from one another.To test for these differences, we may use a t-test, which is a statistical test used to evaluate if the means of two groups are significantly different from one another. With the use of a t-test, we may assess if there are any statistically variations in terms of the 2 groups.

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Answer:

(405x ^ 7)²

405²x^14

164025x^14 is a square of 405x ^ 7

Step-by-step explanation:

Answer:ab power of 5 c

Step-by-step explanation: bc it stayed

The scale factor of the dilation that maps triangle ABC onto triangle DBE is approximately 0.75. Option B.

To find the scale factor of the dilation that maps triangle ABC onto triangle DBE, we need to compare the corresponding side lengths of the two triangles.

Let's consider the length of side AC in triangle ABC, which is given as 16.12. Correspondingly, the length of side DE in triangle DBE is given as 12.09.

To find the scale factor, we divide the length of side DE by the length of side AC:

Scale factor = Length of DE / Length of AC

= 12.09 / 16.12

≈ 0.75 Option B is correct.

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Answer:

\(-\frac{8}{45}\)

Step-by-step explanation:

So when multiplying fractions, you would multiply the numerator of the first fraction by the numerator of the second fraction and make that product the numerator of the resulting fraction and multiply the denominator of the first fraction by the denominator of the second fraction and make that product the denominator of the resulting fraction. In other words:

\(\frac{a}{b}*\frac{c}{d}=\frac{a*c}{b*d}\)

So lets multiply the two fraction together:

\(\frac{4}{5}*(-\frac{2}{9})==-(\frac{4*2}{5*9})=-\frac{8}{45}\)

So now we found the product. Now we have to try to try to simplify the fraction. To do this, we must find the GCF of the numerator, 8, and the denominator, 45.

Factors of 8: 1, 2, 4, 8

Factors of 45, 1, 3, 5, 9, 15, 45

As we can see, the GCF of 8 and 45 are 1. The fraction is simplified as much as possible.

I hope you find my answer and explanation to be helpful. Happy studying. :)

Answer:

\(3 \times \frac{1}{3 } + \frac{1}{2} \times - 12( \frac{1}{3} ) = \frac{1}{3} \)

It will take Vincent 24 number of days to build the cubby house by himself.

Let's assume that Vincent can build the cubby house alone in h days.

From the given information, we know that Nadia takes 12 days to build the cubby house, and when Nadia and Vincent work together, they can finish it in 8 days.

We can use the concept of "work done" to solve this problem. The amount of work done is inversely proportional to the number of days taken.

Nadia's work rate is 1/12 of the cubby house per day, while the combined work rate of Nadia and Vincent is 1/8 of the cubby house per day.

When Nadia and Vincent work together, their combined work rate is the sum of their individual work rates:

1/8 = 1/12 + 1/h

To solve for h, we can rearrange the equation:

1/h = 1/8 - 1/12

1/h = (3 - 2) / 24

1/h = 1/24

Taking the reciprocal of both sides, we find:

h = 24

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Answer:

19

Step-by-step explanation:

Substitute the value of x for 5 in the function.

f(x) = 3x + 4

f(5) = 3(5) + 4

f(5) = 19.

Answer:

Answer is 19

Step-by-step explanation:

\(f |x| = 3x + 4 \: \: \: \: \: f |5| = \\ f |5 | = 3 \times 5 + 4 \\ f |5| = 19\)

I hope this helps you

The conditional probability that the size of the family is less than 6 given that it is at least 3 is 1.

To find the conditional probability that the size of the family is less than 6 given that it is at least 3, we need to use the formula for conditional probability.

Let's denote A as the event that the size of the family is less than 6, and B as the event that the size of the family is at least 3.

The conditional probability of A given B, denoted as P(A|B), is calculated as follows:

P(A|B) = P(A and B) / P(B)

First, we need to find P(B), the probability that the size of the family is at least 3. Since the family is selected at random, we can assume that all possible family sizes have an equal chance of being selected.

Let's assume the total number of possible family sizes is n. The probability of selecting a family with at least 3 members is the sum of the probabilities of selecting a family with exactly 3 members, exactly 4 members, and exactly 5 members.

P(B) = P(3) + P(4) + P(5)

Next, we need to find P(A and B), the probability that the size of the family is both less than 6 and at least 3. Since any family size less than 6 is also at least 3, P(A and B) will be the same as P(B).

Finally, we can substitute the values into the formula for conditional probability:

P(A|B) = P(A and B) / P(B) = P(B) / P(B) = 1

Therefore, the conditional probability that the size of the family is less than 6 given that it is at least 3 is 1.

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Answer:

B:6

Step-by-step explanation:

Which is 6 different 3- digit numbers.

I hope this helped you!

Please put brainliest :)

If lidocaine is injected intra-arterially, it can quickly lead to systemic toxicity. The first signs of toxicity may include circumoral numbness and tongue paresthesia, but these symptoms may be followed by more severe manifestations such as dizziness, seizures, and cardiac arrest.

The systemic effects of lidocaine are dose-dependent, meaning that the higher the dose, the more severe the symptoms.

Lidocaine is a local anesthetic that is commonly used for minor surgical procedures or dental work. It works by blocking the nerve signals that transmit pain to the brain. However, if it is injected into an artery, it can rapidly spread throughout the body and affect other organs, leading to potentially life-threatening complications.

If you suspect that a patient has been injected with lidocaine intra-arterially, it is important to act quickly. The first step is to stop the injection and monitor the patient closely for signs of toxicity. If the patient is experiencing severe symptoms, such as seizures or cardiac arrest, emergency treatment should be initiated immediately. Treatment may include administering medications to counteract the effects of the lidocaine or performing cardio-pulmonary resuscitation (CPR) if necessary.

In conclusion, the first signs of lidocaine toxicity may include circumoral numbness and tongue paresthesia, but more severe symptoms may follow, such as dizziness, seizures, and cardiac arrest. If you suspect that a patient has been injected with lidocaine intra-arterially, it is important to act quickly to prevent potentially life-threatening complications.

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Answer:

A. & B. are the corect answers

Step-by-step explanation:

Answer:

A and B

x is \(\frac{1}{3}\) of y

AND

y is \(\frac{3}{4}\) of (x+y)

Step-by-step explanation:

x:y is 1:3

=>  y is bigger than x

=>  y is 3x bigger than x

=>  y = 3 lots of x

=>  \(y =\) \(3x\)

=>  \(\frac{y}{3}\) \(= x\)

=>  \(\frac{1}{3} y\) \(= x\)

So x is \(\frac{1}{3}\) of y

y is \(\frac{3}{4}\) of (x+y)

If x = 1 and y = 3 (substitute in values)

=>  3 is \(\frac{3}{4}\) of (4)

=>  3 is \(\frac{3}{4}\)(4)

=>  3 is (\(\frac{3}{4}\)x4)

=>  3 = 3

Therefore, y is \(\frac{3}{4}\) of (x+y) is true

So the answers are:

x is \(\frac{1}{3}\) of y

AND

y is \(\frac{3}{4}\) of (x+y)

The simplified and rationalized equivalent of the fraction (sqrt(8) / sqrt(2)) - sqrt(2) is 2 - (sqrt(2) / 2).

To rationalize the denominator and simplify the fraction (sqrt(8) / sqrt(2)) - sqrt(2), we can follow these steps:

1. Rationalize the denominator:

  Multiply both the numerator and denominator by sqrt(2) to eliminate the square root from the denominator:

  [(sqrt(8) / sqrt(2)) - sqrt(2)] * (sqrt(2) / sqrt(2))

  This simplifies to (sqrt(16) - sqrt(2)) / 2.

2. Simplify the numerator:

  sqrt(16) is equal to 4, so we have (4 - sqrt(2)) / 2.

3. Simplify the fraction:

  Divide both the numerator and denominator by 2 to simplify the fraction:

  (4 - sqrt(2)) / 2 = 4/2 - sqrt(2)/2 = 2 - (sqrt(2) / 2).

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Answer:

hope your get it but it's hard because I did that I didn't pass it

The value of x must be between -18 and -6. The solution has been obtained using Triangle inequality theorem.

What is Triangle inequality theorem?

The triangle inequality theorem explains how a triangle's three sides interact with one another. This theorem states that the sum of the lengths of any triangle's two sides is always greater than the length of the triangle's third side. In other words, the shortest distance between any two different points is always a straight line, according to this theorem.

We are given three sides of a triangle as 8, 6 and x+20

Using Triangle inequality theorem,

⇒8+6 > x+20

⇒14 > x+20

⇒-6 > x

Also,

⇒x+20+6 > 8

⇒x+26 > 8

⇒x > -18

Also,

⇒x+20+8 > 6

⇒x+28 > 6

⇒x > -22

From the above explanation it can be concluded that x is less than -6 but greater than -22 and -18.

This means that x must lie between -18 and -6.

Hence, the value of x must be between -18 and -6.

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The number of marbles that represent each vegetable option are: carrots - 3 marbles, green beans - 7 marbles, asparagus - 2 marbles, and vegetable medley - 8 marbles.

To model the situation of the catering company, we need to use percentages to represent the number of customers who choose each vegetable option. We are given that 15% of customers choose carrots, 35% choose green beans, and 10% choose asparagus. The remaining customers, who choose vegetable medley, can be represented by subtracting the sum of the other three percentages from 100%.

To represent this situation using marbles, we can assign a certain number of marbles to each vegetable option based on the percentage of customers who choose it. For example, if we use 20 marbles in total, 15% of 20 is 3, so we can assign 3 marbles to carrots. Similarly, 35% of 20 is 7, so we can assign 7 marbles to green beans. 10% of 20 is 2, so we can assign 2 marbles to asparagus. Finally, the remaining 8 marbles would represent the customers who choose vegetable medley.

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Answer:

Perimeter of the hexagon = 90 Unit

Step-by-step explanation:

Given:

A(-12, -8). B(-12, 7), C(0, 16), D(12,7), E(12, -8), F(0, -17)

Find:

Perimeter of the hexagon

Computation:

Length = √(x1 - x2)² + (y1 - y2)²

AB = √(-12 + 12)² + (-8 - 7)²

AB = 15

BC = √(-12 + 0)² + (7 - 16)²

BC = 15

CD = √(0 - 12)² + (16 - 7)²

CD = 15

DE = √(12 - 12)² + (-7 - 8)²

DE = 15

EF = √(12 - 0)² + (-8 + 17)²

EF = 15

FA = √(0 + 12)² + (-17 + 8)²

FA = 15

Perimeter of the hexagon = AB + BC + CD  + DE + EF + FA

Perimeter of the hexagon = 15 + 15 + 15 + 15 + 15 + 15

Perimeter of the hexagon = 90 Unit

Answer:

4 step by step explanation

The at {x} = 10, the value of the function remains +8.

A function is a relation between a dependent and independent variable. We can write the examples of functions as -

y = f(x) = ax + b

y = f(x, y, z) = ax + by + cz

Given is that the function f(x) is defined as -

f(x) = + 8

The given function is a constant function. This means that the value of the function remains the same irrespective of the value of {x} or the value in the function domain. So, at {x} = 10, the value of the function remains +8 only. This is true for all the values of {x}.

Therefore, the at {x} = 10, the value of the function remains +8.

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Answer:

1/4

Step-by-step explanation:

i hope this helps :)

The total amount of money that Mike made during summer by solving the equation formed is $3360. And the time that Mike worked whole summer at Six flags was 360 hours.

An equation, like 6 x 4 = 12 x 2, is used to demonstrate that two amounts or values are equal. Numerical noun An equation is a circumstance in which two or more components must be taken into account in order to perceive or comprehend the circumstance as a whole.

a) Let's denote the number of hours that Milk worked at Six Flags as x. Then, the amount of money he earned from Six Flags is given by:

9x

The amount of money he earned from babysitting his sister is given by:

120

Therefore, the total amount of money he made over the summer is:

9x + 120= $3360

b) We are given that the total amount of money Milk earned over the summer is $3,360. Setting this equal to the equation for the total amount of money he made above, we get:

9x + 120 = 3360

Subtracting 120 from both sides:

9x = 3240

Dividing both sides by 9:

x = 360

Therefore, Mike worked 360 hours at Six Flags over the summer.

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The percentage of the total expenses spent on food is 50%.

Expense Distribution:

Food: GH₵ 450.00

Housing: GH₵ 120.00

Clothing: GH₵ 120.00

Tobacco and Drink: GH₵ 170.00

Entertainment: GH₵ 40.00

B) Percentage of Total Expenses on Food:

To find the percentage of the total expenses spent on food, we need to divide the expense on food by the total expenses and then multiply by 100.

Total expenses = Food + Housing + Clothing + Tobacco and Drink + Entertainment

Total expenses = GH₵ 450.00 + GH₵ 120.00 + GH₵ 120.00 + GH₵ 170.00 + GH₵ 40.00

Total expenses = GH₵ 900.00

Percentage of total expenses on food = (Expense on food / Total expenses) x 100

Percentage of total expenses on food = (GH₵ 450.00 / GH₵ 900.00) x 100

Percentage of total expenses on food = 50%

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Spherical harmonics are an integral part of quantum mechanics. They describe the shape of the orbitals, which electrons occupy in atoms. Moreover, the spherical harmonics provide the angular distribution of a wave in spherical coordinates. In 3D, the spherical harmonics can be written as:

Ylm(θ, φ) = √(2l + 1)/(4π) * √[(l - m)!/(l + m)!] * Plm(cosθ) * e^(imφ)

Here, l and m are known as the angular quantum numbers. They define the shape and orientation of the orbital. Plm(cosθ) represents the associated Legendre polynomial, and e^(imφ) is the exponential function. The spherical harmonics have various forms, including:

Y1,1 = -Y1,-1 = 1/2 √(3/2π) sinθe^(iφ)

Y1,0 = 1/2 √(3/π)cosθ

Y2,2 = 1/4 √(15/2π)sin²θe^(2iφ)

Y2,1 = -Y2,-1 = 1/2 √(15/2π)sinθcosφ

Y2,0 = 1/4 √(5/π)(3cos²θ-1)

Y0,0 = 1/√(4π)

The spherical harmonics have various applications in physics, including quantum mechanics, electrodynamics, and acoustics. They play a crucial role in understanding the symmetry of various systems. Hence, the spherical harmonics are an essential mathematical tool in modern physics. Thus, this is how one can show another form for spherical harmonics.

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Answer:

f(3)=7

Step-by-step explanation:

just plug in the number

f(3)=2×3+1

=7