prove that: \((a+b)^-^1.(a^-^1 +b^-^1) = (ab)^-^1\)

Answer:

Since 26 out of a total of 520 batteries were defected and she wants to randomly select 20 batteries for it.

The formula she will be using will be randInt(1,520) to generate 20 random numbers.

A student's probability of having a sister are 1/2 or 0.5 if they do not have a brother.

Using the above data table, we must determine the likelihood that a student without a brother also has a sister. Analysing the table now

has a sibling: 5

possesses no sisters: 2

has an 18-year-old brother

possesses no brothers: 4

We are looking for the likelihood that a student has a sister and neither a brother (as indicated by the statement "Does not have a brother"). In this instance, there are two children who do not have a brother but do have a sister, making that number the number of positive outcomes.

No matter whether a student has a sister or not, the total number of outcomes is equal to the number of students who do not have a brother. According to the table, there are 4 students without brothers.

As a result, the likelihood that a student who doesn't have a brother will have a sister can be determined as follows:

Probability is calculated as the ratio of the number of favourable outcomes to all possible outcomes.

Probability equals 2/4

Probability equals 0.5 or half.

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Answer:

The answer to your question is 732 in³

Step-by-step explanation:

Data

Rectangular prism layers

Base layer = 12 in x 10 in x 4 in

Second layer = 3 in smaller x 4 in

Volume = ?

Formula

Total volume = Volume of the base layer + Volume of the second layer

Total volume = length 1 x width 1 x height +  length 2 x width 2 x height

Substitution

Total volume = 12 x 10 x 4 + (12 - 3)(10 - 3)(4)

Simplification

Total volume = 480 + (9)(7)(4)

Total volume = 480 + 252

Result

Total volume = 732 in³

A system of equations for this problem can be written as:

x + y = 10 (1) equation for the total number of herbs planted

0.50x + 0.25y = 3 (2) equation for the total cost of the herbs

Where x is the number of basil plants and y is the number of mint plants.

Using substitution, we can solve the system of equations.

Solving equation (1) for x, we get x = 10 - y

Substituting this into equation (2) we get:

0.50(10 - y) + 0.25y = 3

5 - 0.50y + 0.25y = 3

5 = 0.75y + 3

0.75y = -2

y = -2/0.75 = -8/3

So, Eden planted -8/3 mint plants, which doesn't make sense, as a fraction of plant are not possible. This implies that either the number of plants or the amount spent are incorrect or something is missing in the problem description.

The parent quadratic function is 2 unit right and 3 units up.

Given function is

f(x) = (x-2)² +3

= x² - 2² - 2×x×2 + 3

= x2 - 4 - 4X + 3

= X² - 4X -1

Parent function g(x) = x²

The parent function is shifted to 2 units in right and 3 units up.

Parent function transformations are shown in blue. This is a 1 unit shift down. Mirroring of the x-axis is done functionally by multiplying the superordinate function by the negative function.

A parent function is the simplest function that satisfies the definition of a particular function type. For example, consider linear functions that form a family of functions.

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Disclaimer:- your question is incomplete, Please see below for the complete question.

Which phrase best describes the transformation(s) of the following graph from the parent quadratic function? f(x)=(x-2)^2+3

a) U is subspace of R^3.

b) The set {(3, -2, 0), (0, 1/2, 1)} is a basis for U.

c) 2.

a) To show that U is a subspace of R^3, we need to verify the following three conditions:

i) The zero vector (0, 0, 0) is in U.

ii) U is closed under addition.

iii) U is closed under scalar multiplication.

i) The zero vector is in U since 0 + 2(0) - 3(0) = 0.

ii) Let (x1, y1, z1) and (x2, y2, z2) be two vectors in U. Then we have:

x1 + 2y1 - 3z1 = 0 (by definition of U)

x2 + 2y2 - 3z2 = 0 (by definition of U)

Adding these two equations, we get:

(x1 + x2) + 2(y1 + y2) - 3(z1 + z2) = 0

which shows that the sum (x1 + x2, y1 + y2, z1 + z2) is also in U. Therefore, U is closed under addition.

iii) Let (x, y, z) be a vector in U, and let c be a scalar. Then we have:

x + 2y - 3z = 0 (by definition of U)

Multiplying both sides of this equation by c, we get:

cx + 2cy - 3cz = 0

which shows that the vector (cx, cy, cz) is also in U. Therefore, U is closed under scalar multiplication.

Since U satisfies all three conditions, it is a subspace of R^3.

b) To find a basis for U, we can start by setting z = t (where t is an arbitrary parameter), and then solving for x and y in terms of t. From the equation x + 2y - 3z = 0, we have:

x = 3z - 2y

y = (x - 3z)/2

Substituting z = t into these equations, we get:

x = 3t - 2y

y = (x - 3t)/2

Now, we can express any vector in U as a linear combination of two vectors of the form (3, -2, 0) and (0, 1/2, 1), since:

(x, y, z) = x(3, -2, 0) + y(0, 1/2, 1) = (3x, -2x + (1/2)y, y + z)

Therefore, the set {(3, -2, 0), (0, 1/2, 1)} is a basis for U.

c) Since the basis for U has two elements, the dimension of U is 2.

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Answer:

z = 2

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Step-by-step explanation:

Step 1: Define

2z - 3 = 1

Step 2: Solve for z

Answer:

Amar will need 48 teaspoons of sugar to make lemonade

Step-by-step explanation:

If u need 4 teaspoons to make one tablespoon, then you just can do

4 x 1 = 4

so, having that now you can do

4 x 2 = 8

there you get 8 teaspoons

Now you do

4 X 12 = 48

Answer:

is there a picture

Step-by-step explanation:

Answer:b

Step-by-step explanation:did it

Answer: i believe its 15.12

Step-by-step explanation:

Answer:

b = 2a + c

Step-by-step explanation:

Given

a = \(\frac{1}{2}\) (b - c)

Multiply both sides by 2 to clear the fraction

2a = b - c ( add c to both sides )

2a + c = b

Answer:

c = 3/5 or 0.6

Step-by-step explanation:

5c + 16.5 = 13.5 + 10c

-5c                      - 5c

16.5 = 13.5 + 5c

-13.5  - 13.5

3 = 5c

3 ÷ 5 = c

c = 3/5

Answer:

D

Step-by-step explanation:

Opposite angles are always the same.

\(\sf \: D)∠ \: 2 \: and \: ∠ \: 4\)

\(\sf \: Vertically \: opposite \: angles \: are \: equal \: to \: each \: other. \\ \sf \: The \: other \: options \: are \: linear \: pairs \: and \: they \\ \sf \: may \: or \: may \: not \: be \: equal \: to \: each \: other.\)

Answer ⟶ \(\boxed{\bf{D)∠ \: 2 \: and \: ∠ \: 4}}\)

The solution to the given differential equation is y(t) = 2e^(-3t) - e^(-t) + e^(-3t).

To solve the given differential equation using Laplace transforms, we can follow these steps:

1. Take the Laplace transform of both sides of the equation.

  Apply the Laplace transform to each term in the equation and use the property of the Laplace transform that transforms derivatives as follows:

  Laplace {dy(t)/dt} = sY(s) - y(0)

  Applying the Laplace transform to the equation, we get:

  sY(s) - y(0) + 3Y(s) = e^(-s)

2. Solve for Y(s).

  Rearrange the equation to solve for Y(s):

  Y(s) = (1 + y(0))/(s + 3) + e^(-s)/[(s + 3)s]

3. Take the inverse Laplace transform to obtain the solution y(t).

  Apply the inverse Laplace transform to Y(s) using standard Laplace transform table or by using partial fraction decomposition. The inverse Laplace transform of e^(-s)/(s(s + 3)) can be obtained as:

  e^(-t) - e^(-3t)

  Therefore, the solution y(t) is:

  y(t) = (1 + y(0))e^(-3t) + (1 - y(0))(e^(-t) - e^(-3t))

Given that y(0) = 1, the solution becomes:

y(t) = 2e^(-3t) - e^(-t) + e^(-3t)

So, the solution to the given differential equation is y(t) = 2e^(-3t) - e^(-t) + e^(-3t).

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Answer:

Amaxesha amnandi ukuba unexesha elimnandi enkosi kuThixo ukuba unexesha elimnandi enkosi kuThixo ngokuba nexesha elimnandi enkosi kuThixo ngokuba nexesha elimnandi bulela uThixo ngokuba nexesha elimnandi

The surface area of the prism is 29 square units.

We have,

There are four triangles in the triangular prism.

So,

Area of a triangle.

= 1/2 x base x height

Now,

We find the area for each triangle.

Area = 1/2 x 4 x 2.2 = 4.4 square units

Area = 1/2 x 3 x 5 = 7.5 square units

Area = 1/2 x 3 x 5 = 7.5 square units

Area = 1/2 x 4 x 4.8 = 9.6 square units

Now,

The surface area of the prism.

= 4.4 + 7.5 + 7.5 + 9.6

= 29 square units

Thus,

The surface area of the prism is 29 square units.

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The graph which represents the function; y = 2 x - 2 is the second graph from the left.

By considering the slope-intercept form of the equation of a straight line;

By observation, the graph of the function has y-intercept, -2 and has slope, m = 2

The graph most comparable to the information above is the third graph and hence is the graph of the function.

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Answer:

3rd one or c

Step-by-step explanation:

There are 8 observations with x1 values greater than 30, when the data is sorted in ascending order the first observation has x1 value of 10, x2 value of 1 and x3 value of 1.

After sorting the data in ascending order,

Value of x1 - 10

Value of x2 - 1

Value of x3 - 1

c. Sort the data by xi and x2 both in descending order. What are the x1, x2, and x3 values of the first observation after the data are sorted? Value of X1 - 35

Value of x2 - 10

Value of x3 - 5

d. How many missing values are there in x1, x2, and x3?

The number of missing values in X1 - 0

The number of missing values in X2 - 0

The number of missing values in X3 - 0

a. How many observations have x1 values greater than 30? Number of observations - 8

b. Sort the data by x1, x2, and then x3 all in ascending order. What are the x1, x2, and x3 values of the first observation after the data are sorted? Value of x1 - 10

Value of x2 - 1

Value of X3 - 1

c. Sort the data by xi and x2 both in descending order. What are the x1, x2, and x3 values of the first observation after the data are sorted? Value of X1 - 35

Value of x2 - 10

Value of x3 - 5

d. How many missing values are there in x1, x2, and x3? The number of missing values in X1 - 0

The number of missing values in X2 - 0

The number of missing values in X3 - 0

There are 8 observations with x1 values greater than 30, when the data is sorted in ascending order the first observation has x1 value of 10, x2 value of 1 and x3 value of 1. When the data is sorted in descending order, the first observation has x1 value of 35, x2 value of 10 and x3 value of 5. There are no missing values in x1, x2, and x3.

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Equation is |x − 20| = 0.45

The min is x = 19.55

=====================================================

Explanation:

fl oz = fluid ounces

x = volume of the drink in fl oz

The expression |x-20| represents how far x is from the target of 20 fl oz. We use absolute value to ensure the result is never negative. It might help to draw out a number line.

Two examples:

We want this difference to be within 0.45 fl oz, i.e. we want |x-20| to either equal 0.45 or be smaller than it.

If we only cared about the min and max, then we set |x-20| equal to 0.45 to generate the equation |x − 20| = 0.45

----------------

Solve this equation to find the min and max.

|x - 20| = 0.45

x-20 = 0.45 or x-20 = -0.45

x = 0.45+20 or x = -0.45+20

x = 20.45 or x = 19.55

The min is 19.55 fl oz and the max is 20.45 fl oz.

Phrased another way: the x values span from 19.55 to 20.45, inclusive of both endpoints. We could write \(19.55 \le \text{x} \le 20.45\) as a compact way to describe what values x could be.

Answer:

C

Step-by-step explanation:

Step-by-step explanation:

Each square has a side length of 1/4 inch but you have said each square=1/4

Once you have found the amount of 1/4 inches you multiply the two numbers together, only then do you multiply it to $11 for the square area.

Area:-

Cost:-

The slope of the segment RT is equal to the slope of the segment TV.

A line's steepness and direction are measured by the line's slope. Without actually using a compass, determining the slope of lines in a coordinate plane can assist in forecasting whether the lines are parallel, perpendicular, or none at all.

Any two different points on a line can be used to calculate the slope of any line. The ratio of "vertical change" to "horizontal change" between two different locations on a line is calculated using the slope of a line formula.

The slope is given as rise / run thus,

The slope of the segment RT is:

RS / ST = 2/4 = 1/2

The slope of the segment TV is:

TU/UV = 1/2

Hence, the slope of the segment RT is equal to the slope of the segment TV.

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The correct question is:

Answer: He has 4 apples left.

Step-by-step explanation:

5-1=4

(hope this helps)

Answer:4

Step-by-step explanation: James had 5 apples which later he gave one to aliya so 5-1 is 4

The accident proportions differ between the two age groups is \(\frac{11}{100}\).

We have given that,

number of clients under age of 18 = 500

number of accident = 180

Proportion of client under age of 18 =  \(\frac{180}{500}\)  = \(\frac{18}{50}\)

number of clients over age of 18 = 600

number of accidents = 150

number of clients over age of 18 = \(\frac{150}{600}\) = \(\frac{15}{60}\) = \(\frac{1}{4}\)

Now we have to find proportion of difference between two age group,

\(\frac{18}{50}\)  -  \(\frac{1}{4}\) =  \(\frac{72 - 50}{200}\)

          = \(\frac{22}{200}\)

          =  \(\frac{11}{100}\)

Therefore the difference between two age groups is  \(\frac{11}{100}\) .

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Answer: v = 18

Step-by-step explanation:

26 = 8 + v

Now, subtract 8 from the right hand side and the left hand side, leave v alone: 18 = v

Answer:

it would be .1111111111

Hope this helps

Answer:

.1 repeating

Step-by-step explanation:

.1 repeating= .11111111111

Hope this helps.

Answer

before 'However'

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Answer:

Step-by-step explanation:

Write an equation of the line in slope intercept form that passes through (3, 1/2) and has a slope of 4.