add the following - 4/9,7/12and - 3/8​

Answer:

events at A and B are independent because P(A)(B)≠P(A)

Answer:

The range is 5.

Step-by-step explanation:

You can deduce this by concluding all other statements are true, or by calculating the range. 10 - 1 = 9

Answer:  infinitely many solutions

Step-by-step explanation: A system of two equations can be classified as follows:

If the slopes are the same but the y-intercepts are different, the system has no solution.

If the slopes are different, the system has one solution.

If the slopes are the same and the y-intercepts are the same, the system has infinitely many solutions.

The equation of the transformed function is y = 5f(x)

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

y = f(x)

If we want to stretch the graph of y = f(x) vertically by a factor of 5, we can use the following equation:

y = 5f(x)

This equation multiplies the y-values of the function f(x) by 5, which will result in a vertical stretching of the graph.

Note that the shape of the graph will remain the same

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After answering the presented question, we can conclude that As a result, the expression for the rectangle's perimeter in terms of w is: 6w + 5 is the perimeter.

A boundary is a closed path that encompasses, surrounds, or delimits a length or shape in two dimensions in one direction. A circle's or an ellipse's outermost portion is known as its perimeter. Numerous circumstances in everyday life call for the application of the perimeter calculation. The radius of an edge determines a form's perimeter. Learn how to add the side lengths of various forms to determine the perimeter.

The length of the rectangle is 2w + 5/2 units, and its width is w units.

The formula for calculating the perimeter of a rectangle is:

2(length + width) = perimeter

Substituting the length and width expressions yields:

2(2w + 5/2 + w) perimeter

When we simplify, we get:

circumference = 2(3w + 5/2)

circumference = 6w + 5

As a result, the expression for the rectangle's perimeter in terms of w is:

6w + 5 is the perimeter.

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The lengths of the right-angled triangle are 6 and 8.

A right-angled triangled is a triangle that has one of its angles equal to 90°. The sum of the other two interior angles is also equal to 90°.

The Pythagoras theorem relates the three sides of a right-angled triangle through a simple equation. According to the Pythagoras theorem,

hypotenuse^2 = base^2 + opposite^2

Let base = b, so opposite = b + 2

So,

10^2 = b^2 + (b+2)^2

100 = b^2 + b^2 + 4b + 4

100 = 2b^2 + 4b + 4

50 = b^2 + 2b + 2

b^2 + 2b - 48 = 0

solving this quadratic equation gives, b = 6 and b = -8. Since length cannot be negative, the base is 6 feet and the opposite is 8 feet.

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Answer:

The base is: \(3 \sqrt[3]{4}\)

Step-by-step explanation:

Given

\(f(x) = \frac{1}{4}(\sqrt[3]{108})^x\)

Required

The base

Expand 108

\(f(x) = \frac{1}{4}(\sqrt[3]{3^3 * 4})^x\)

Rewrite the exponent as:

\(f(x) = \frac{1}{4}(3^3 * 4)^\frac{1}{3}^x\)

Expand

\(f(x) = \frac{1}{4}(3^3^\frac{1}{3} * 4^\frac{1}{3})^x\)

\(f(x) = \frac{1}{4}(3 * 4^\frac{1}{3})^x\)

Rewrite as:

\(f(x) = \frac{1}{4}(3 \sqrt[3]{4})^x\)

An exponential function has the following form:

\(y=ab^x\)

Where

\(b \to base\)

By comparison:

\(b =3 \sqrt[3]{4}\)

So, the base is: \(3 \sqrt[3]{4}\)

Answer:

B

Step-by-step explanation:

good luck

The probability of selecting 50 jars is 0%

The z score determines by how many standard deviations the raw score is above or below the mean. It is given by:

\(z=\frac{x-\mu}{\sigma/\sqrt{n} } \\\\where \mu=mean,\sigma=standard\ deviation, x=raw\ score,n=sample\ size\\\\Given\ that\ \mu=17,\sigma=0.68,n=50,x=16.8\\\\z=\frac{16.8-17}{0.65/\sqrt{50} } =-5\)

The P(z < -5) = 0%

Therefore the probability of selecting 50 jars is 0%

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Answer:

Trapezoid

Step-by-step explanation:

One pair of parallel sides.

Answer:

Step-by-step explanation:

.................8908989

Answer:

$250

Step-by-step explanation:

Reverse division is multiplication. So one fifth of 50 is ?/5=50. Now reverse this to 50*5=?. This should come out to 250, because you can leave off the zero, and do 5*5, which equals 25, and add the zero back in you get 250. So your answer is $250.

The area between -

C{x} = 0.01x² - 3x + 229, R{x} = 429 - 2x and {x} = 0 is 492097.4 square

units.

A function is a relation between a dependent and a independent variable. Mathematically we can write the function as -

y = f(x)

Given is that a factory selling cell phones has a marginal cost function C(x) = 0.01x² - 3x + 229, where {x} represents the number of cellphones, and a marginal revenue function given by R(x) = 429 - 2x.

We can write the area between -

C{x} = 0.01x² - 3x + 229, R{x} = 429 - 2x and {x} = 0 as -

Area = ∫C(x) dx  +  ∫{C(x) - R(x)} dx

We can write the area with limits as -

Area =

∫(0.01x² - 3x + 229) dx             {limits from 229 to 429}

+

∫(0.01x² - 3x + 229 - 429 + 2x) dx       {limits from 429 to 629}

Area = 71548.7 + 420548.7

Area = 492097.4 square units

Therefore, the area between -

C{x} = 0.01x² - 3x + 229, R{x} = 429 - 2x and {x} = 0 is 492097.4 square

units.

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Answer:20 m/s

Step-by-step explanation:

Answer:

20 m/s

Step-by-step explanation:

700 ÷ 35 = 20 m/s

The quadratic function graphed is defined as follows:

y = x² - 10x + 9.

We are given the roots for each function, hence the factor theorem is used to define the functions.

The function is defined as a product of it's linear factors, if x = a is a root, then x - a is a linear factor of the function.

From the graph, the roots are given as follows:

x = 1 and x = 9.

Hence the function as a product of it's linear factors is defined as follows:

y = a(x - 1)(x - 9)

y = a(x² - 10x + 9).

When x = 5, y = -16, hence the leading coefficient a is obtained as follows:

-16 = a(5² - 10(5) + 9)

-16a = -16

a = 1.

Thus the function is:

y = x² - 10x + 9.

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Onto but not one-to-one. is f(x)  which is obtained by removing the second bit from x and placing the bit at the end of the string.

The function f is said to be "onto" because it maps every element in its codomain (the set of possible output values) to at least one element in its domain (the set of possible input values). In this case, the codomain is the set of all binary strings of length 3, and the domain is the set of all binary strings of length 2. However, the function is not one-to-one, because there are multiple elements in the domain that are mapped to the same element in the codomain. For example, both "10" and "01" are mapped to "100". This means that the function f is not one-to-one, meaning that it doesn't map every element in its domain to a unique element in its codomain. A function is said to be one-to-one if every element in its domain (the set of possible input values) is mapped to a unique element in its codomain (the set of possible output values). In other words, no two elements in the domain have the same image (output) under the function. A function is said to be onto if every element in the codomain is mapped to by at least one element in the domain. In other words, every element in the codomain has at least one pre-image (input) under the function. In the case of the function f described in the previous question, it is onto because every binary string of length 3 can be obtained as the output of the function for some binary string of length 2. However, it is not one-to-one because there are multiple binary strings of length 2 that are mapped to the same binary string of length 3. For example, both "10" and "01" are mapped to "100".

So, the function f is described as "onto but not one-to-one".

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The equation given in slope-intercept form does not represent the graph because the y-intercept of the graph is equal to 4 while the y-intercept of the equation is equal to 5.

In Mathematics, the slope-intercept form of a line can be calculated by using this linear equation:

y = mx + c

Where:

In Mathematics, the y-intercept of any graph such as a linear function, generally occur at the point where the value of "x" is equal to zero (x = 0).

Based on the information provided regarding the equations and graphs, the y-intercept are as follows:

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Answer:

First Option = No

\( \sf \frac{1}{ {x}^{ - 3} } = \frac{1}{ \frac{1}{ {x}^{3} } } = {x}^{3} \: ( \red{wrong})\)

Second Option = No

\( \sf - \sqrt[3]{x} = - {x}^{ \frac{1}{3} } \: ( \red{wrong})\)

Third Option = Yes

\( \sf {x}^{ - \frac{1}{3} } = \frac{1}{ {x}^{ \frac{1}{3} } } ( \green{true})\)

Fourth Option = Yes

\( \sf {x}^{ - \frac{1}{3} } =( \sqrt[3]{x} {)}^{ - 1} = \frac{1}{ \sqrt[3]{x} } ( \green{true})\)

Hope it helps!

Answer:

No, No, Yes, Yes

Step-by-step explanation:

I just took it EDGE2022

The three consecutive numbers that have a sum of 12 is 3, 4 and 5. The formula for calculation is x + x + 1 + x + 2 = 12.

Let the first number in three consecutive numbers be x. So, the next two numbers will be (x+1) and (x+2). Now, their sum wil be represented as mathematical equation -

x + x + 1 + x + 2 = 12

Performing addition on Left Hand Side of the equation

3x + 3 = 12

Rewriting the equation

3x = 12 - 3

Performing subtraction on Right Hand Side of the equation

3x = 9

x = 9/3

Performing division on Right Hand Side of the equation

x = 3

So, next number = x+1

Second number = 3+1

Second number = 4

Third number = x+2

Third number = 3+2

Third number = 5

Hence, the three consecutive numbers are 3, 4 and 5.

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Answer:  first choice is correct

Step-by-step explanation:

\(\sqrt{10} = 3.16\\\\ \sqrt{13} = 3.6\)

22/9 = 2.44

Therefore Point A is 22/9, Point B is \(\sqrt{10}\),  Point C is \(\sqrt{13}\)

Answer:

x < 3

Step-by-step explanation:

5(3 - x) < -2x + 6

Distribute;

15 - 5x < -2x + 6

Add 2x to both sides;

15 - 3x < 6

Subtract 15 from both sides;

-3x < -9

Divide both sides by -3

x < 3

To solve the savings plan balance, we have to calculate the interest for 19 months. The formula for calculating interest for compound interest is given below:$$A = P \left(1 + \frac{r}{n} \right)^{nt}$$where A is the amount, P is the principal, r is the rate of interest, t is the time period and n is the number of times interest compounded in a year.

The given interest rate is 11% per annum, which will be converted into monthly rate and then used in the above formula. Therefore, the monthly rate is $r = \frac{11\%}{12} = 0.0091667$.

The monthly payment is $PMT = $250. We need to find out the amount after 19 months. Therefore, we will use the formula of annuity.

$$A = PMT \frac{(1+r)^t - 1}{r}$$where t is the number of months of the plan and PMT is the monthly payment. Putting all the values in the above equation, we get:

$$A = 250 \times \frac{(1 + 0.0091667)^{19} - 1}{0.0091667}$$$$\Rightarrow

A = 250 \times \frac{1.0091667^{19} - 1}{0.0091667}$$$$\Rightarrow

A =250 \times 14.398$$$$\Rightarrow A = 3599.99$$

Therefore, the savings plan balance after 19 months with an APR of 11% and monthly payments of $250 is $3599.99 (approx).

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Answer: There is no solution.

Answer:

There is no solution

Step-by-step explanation:

The statement that describes inverse function best is the amount of time she has walked (in hours) when she is kilometers from tomsville i.e. option A

According to the question,

The given function denotes the distance travelled by Kira in kilometers from tomsville after hours of walking

D(t) =  10.4 - 4t

The inverse of the function is D⁻¹(x)

=> D(t) =  10.4 - 4t

Converting equation in terms of t,

=>  D(t) + 4t = 10.4

=> 4t = 10.4 - D(t)

=> t = 10.4 - D(t) /4

Inverse function =  D⁻¹(x) = 10.4 - D(x) /4

It denotes the amount of time she has walked (in hours) when she is kilometers from tomsville.

From the following statements in the question

Option (a) is correct about inverse function

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Answer:

0.5,4,3/2,15,V16

Step-by-step explanation:

Be cause if you want ur estimate u have to but the numbers in order so thst how u get ur anwser got to put the numbers small to large.

HOPE IT HELPS GIVE BRAINLEAST :)

The missing term in the geometric sequence, 12, ?, 27/4, is +9 or -9

From the question, we are to find the missing term in the given geometric sequence.

The given geometric sequence is

12, ?, 27/4

To find the missing term in the geometric sequence 12, ?, 27/4, we need to find the common ratio, r, first.

Let the missing term be x

r = 2nd term / 1st term

r = x / 12

Also

r = 3rd term / 2nd term

r = 27/4 / x

Thus,

x/12 = (27/4) / x

x² = 12 × 27/4

x² = 3 × 27

x² = 81

x = ±√81

x = ±9

Hence, the missing term is +9 or -9

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Answer:

9

Step-by-step explanation:

Acellus

Answer:

f(x)=(x-22)^2

Step-by-step explanation:

Subtract 22 from x and then square.

Answer:

Step-by-step explanation:

For step explanation:

1. write the problem

2. distinguishing the neg sign

3. distributing 3

4. moving like terms next to each other through commutative property

5.  Combining like terms

6. getting rid of parentheses

Therefore, the solutions to the equation 0 = |3x + 3| + 3 are x = -2 and x = 0.

To solve the equation 0 = |3x + 3| + 3, we need to eliminate the absolute value. Remember that the absolute value of a number is always non-negative.

First, let's isolate the absolute value term on one side of the equation:

|3x + 3| = -3

Since the absolute value cannot be negative, there are no solutions to the equation as it stands. However, if we modify the equation to make the right side positive, we can find a solution.

To eliminate the absolute value, we can rewrite the equation as two separate equations, considering both the positive and negative cases:

   3x + 3 = -3

   -(3x + 3) = -3

Solving equation 1:

3x + 3 = -3

3x = -6

x = -2

Solving equation 2:

-(3x + 3) = -3

-3x - 3 = -3

-3x = 0

x = 0

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Humanity would achieve a life expectancy of 110 years in approximately 60 years.

To calculate the number of years it would take for humanity to achieve a life expectancy of 110 years, we need to determine the number of decades required to reach this goal based on the given rate of increase.

In 2009, the life expectancy was about 80 years. From that point, we need to calculate the difference between the current life expectancy and the target life expectancy of 110 years.

110 years - 80 years = 30 years

Since the rate of increase is 5.3 years every decade, we can divide the difference by the rate to determine the number of decades required:

30 years / 5.3 years per decade ≈ 5.66 decades

Since we can't have a fraction of a decade, we need to round up to the nearest whole number. Therefore, it would take approximately 6 decades for humanity to achieve a life expectancy of 110 years.

To calculate the number of years, we multiply the number of decades by 10:

6 decades * 10 years per decade = 60 years

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