As Venus revolves around the sun, it travels at a speed of approximately 22 miles per second. Convert this speed to miles per minute. At this speed, how many miles will Venus travel in 6 minutes?

The total number of non-fictional biography books in the library will be equal to 1/5.

The four basic operations of arithmetic can be used to add, subtract, multiply, or divide two or even more quantities.

They cover topics like the study of integers and the order of operations, which are relevant to all other areas of mathematics including algebra, data processing, and geometry.

As per the given information in the question,

Let the total number of books is x.

3/5 of total books are non-fiction, then,

3/5 × x = 3/5x

1/3x of them are biographies.

Then, the number of non-fictional biographies are,

3/5 × 1/3

=1/5

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The total number of ways there are for eight blue-shirt and five red-shirt to stand in a line so that no two red-shirts stand next to each other is 609638400.

A permutation of a set is, broadly speaking, a rearranging of its elements if the set is already ordered, or arranging its members into a sequence or linear order.

Given:

The eight blue-shirt and five red-shirt stands in a line,

Calculate the number of ways as shown below,

The total number of ways = Total no of permutations of blue ones × Total permutation of 9 positions, taken 5 at a time,

N = 8! × 9! / (9 - 5)!

N = 40320 × 362880 /24

N = 609638400

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The value of the composite function is 2x - 15

A function can be defined as a rule, law ore equation that explicitly shows the relationship between two variables.

These variables are called;

From the information given, we have the functions;

To determine the composite function (fog)(x), we have to substitute the value of g(x) as the variable 'x' in the function, f(x), we have;

(fog)(x) = 2 - (18 -2x) + 1

Now, expand the bracket

(fog)(x) = 2 - 18 + 2x + 1

collect like terms

(fog)(x) = 2x - 15

Hence, the function is 2x - 15

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If this answer helps you, brainliest is appreciated

The domain of a radical is the set of all values of the independent variable for which the radical is defined.

For example, consider the radical expression √x. This expression is defined for all nonnegative values of x, since the square root of a nonnegative number is always real. Therefore, the domain of the radical √x is the set of all nonnegative values of x:

{x | x ≥ 0}

This includes all real numbers that are greater than or equal to zero, such as 0, 1, 2, 3, and so on.

On the other hand, if we consider the radical expression √(x-2), this expression is defined for all values of x such that x-2 is nonnegative. This means that the domain of the radical √(x-2) is the set of all values of x such that x ≥ 2:

{x | x ≥ 2}

This includes all real numbers that are greater than or equal to 2, such as 2, 3, 4, 5, and so on.

In general, the domain of a radical is determined by the values of the independent variable that make the expression under the radical nonnegative. If the expression under the radical is always nonnegative, then the domain of the radical is the set of all real numbers. If the expression under the radical is not always nonnegative, then the domain of the radical is the set of all values of the independent variable that make the expression nonnegative.

Answer:

The domain of a radical is the set of all values that can be plugged into the radical without resulting in an undefined or imaginary value.For example, the domain of the square root function sqrt(x) is all non-negative real numbers, since the square root of a non-negative real number is always a real number. This means that the domain of sqrt(x) is the set of all real numbers x such that x >= 0.On the other hand, the domain of the square root function sqrt(x^2 - 4) is all real numbers except for the values x = 2 and x = -2, since the square root of a negative number is an imaginary number. This means that the domain of sqrt(x^2 - 4) is the set of all real numbers x such that x != 2 and x != -2.In general, the domain of a radical is the set of all values for which the expression inside the radical is greater than or equal to 0. This is because the radical of a negative number is an imaginary number, which is not included in the domain of the radical.

Step-by-step explanation:

Answer:

y = 2x - 3

Step-by-step explanation:

A (0,-3)

B (2,1)

slope = (-3-1)/(0-2)

-4/-2

2

y intercept = -3

By combination, Three men and three women must be chosen among the six men and seven women that are available. necessary number of methods =  [tex]^6C_3 * ^7C_3 = 20 * 35 = 700.[/tex]

The sequence of the selection is irrelevant since a combination in mathematics is a selection of items from a set having various members. Regardless of the sequence in which the items were chosen, a mathematical approach known as a combination may be used to calculate the number of alternative arrangements within a collection of objects. Any order can be chosen by a combination. Combinations and permutations are two alternative strategies to divide up a collection of items into subsets in mathematics. The subset's elements can be listed in any order in a combination. In a permutation, the components of a subset are listed in a certain order.

Three men and three women must be chosen among the six men and seven women that are available. necessary number of methods =  [tex]^6C_3 * ^7C_3 = 20 * 35 = 700.[/tex]

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The largest number of stones that could be in the box in the wagon will be 30.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

His wagon can carry 1.2 kg without falling apart.

And, The stones are in a wooden box that weighs 150 grams, and each stone weighs 35 grams.

Now,

Let the number of stones = x

So, We can formulate;

⇒ 150 + 35x = 1200

Solve for x as;

⇒ 35x = 1200 - 150

⇒ 35x = 1050

⇒ x = 1050/ 35

⇒ x = 30

Thus, There are 30 largest number of stones that could be in the box in the wagon.

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Answer:

x² - 3

Step-by-step explanation:

g(f(x))

=> g(x²)

=> x² - 3

The integer for vector 1 {2,6,-7}, integer for vector 2 is 10,8,-14}, integer for vector 3 is {4,12,-14}, integer for vector 4 is {14,-2,-7} and integer for vector 5 is {22,0,-14}. (all these vectors are in span {V1 and V2})

List five vectors in Span {v_1, v_2}?

1) V1+v2={8,2,-7 }+{-6,4,0 }

={2,6,-7}

2) 2v1+v2={16,4,-14}+{-6,4,0}

={10,8,-14}

3)2v1+2v2={16,4,-14}+{-12,8,0}

={4,12,-14}

4)V1-v2={8,2,-7}-{-6,4,0}

={14,-2,-7}

5)2v1-v2={16,4,-14}-{-6,4,0}

={22,0,-14}

All of these vectors are contained within the span.

{v1,v2}={av1+bv2:ab∈r}

A matrix is a rectangular variety of ordered numbers (real or complex) or functions .Assume we want to express the following information about   Ram and his two friends Rohan and Yash's possession of pens and pencils:
Ram       has      20     pens       and       7       pencils,

Rohan    has      15     pens       and       5       pencils,

Yash       has      12     pens       and       3       pencils

Now, this could be arranged in tabular form as follows,
⎢20  7⎢
⎢15   5⎢                            
⎢12   3⎢        

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The proof principle that you are describing is known as induction. Induction is a method of proof that is used to establish that a property holds for all natural numbers (or, more generally, for all elements of a well-ordered set).

The basic idea behind induction is as follows:

First, you start with a base case, which is a specific natural number (usually 0 or 1) for which you can directly prove that the property holds.

Next, you assume that the property holds for some natural number n. This is known as the induction hypothesis.

Using the induction hypothesis, you then prove that the property also holds for the natural number n+1. This is known as the induction step.

Since you have already established that the property holds for the base case, and you have shown that if it holds for one natural number, it must also hold for the next natural number, it follows that the property holds for all natural numbers.

Induction is a very powerful proof technique and is used extensively in mathematics to prove theorems about the properties of natural numbers and other well-ordered sets.

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Answer: Matthew’s milkshake

Step-by-step explanation: The ratio of ice cream to milk in Philips milkshake is 1:3/8. The ratio of ice cream to milk in Matthew’s milkshake is 1:1/3. 3/8>1/3. Since you want a thicker milkshake, you want less milk in the ratio, Matthew’s milkshake would be thicker.

The value of [tex]r^{\prime}(t)[/tex] is [tex]\left\langle 3,4 t, 12 t^2\right\rangle[/tex].

The value of unit tangent vector T(1) is [tex]\left\langle\frac{3}{13}, \frac{4}{13}, \frac{12}{13}\right\rangle \quad[/tex]

The value of r''(t) is [tex]\langle 0,4,24 t\rangle[/tex]

The value of r'(t) × r ''(t) is [tex]\left(48 t^2\right) \vec{i}-(68 t)\vec{j}+(12)\vec{k}[/tex]

As per the data given in the question r(t) = 3t, [tex]2t^{2}[/tex], [tex]4t^{3}[/tex]

From r(t) we can find the value of [tex]r^{\prime}(t)[/tex].

For that we have to differentiate each term of r(t).

[tex]r^{\prime}(t)=\left\langle 3,4 t, 12 t^2\right\rangle[/tex]

Tangent and Normal Vectors:

The tangent and unit normal vectors are calculated from the derivatives of the parameter settings of the curve.

In particular, to determine the unit tangent vector, we have:

[tex]& \vec{T}(t)=\frac{\partial^{\prime}(t)}{\left|r^{\prime}(t)\right|} \\[/tex]

Therefore [tex]\vec{T}(1)=\frac{\partial^{\prime}(1)}{\left|\partial^{\prime}(1)\right|}[/tex]

[tex]\partial^{\prime}(1)=\langle 3,4,12\rangle \\& \therefore\left|r^{\prime}(1)\right|=\sqrt{9+16+144}\\=\sqrt{169}\\=13[/tex]

[tex]\vec{T}(1)=\frac{\langle 3,4,12\rangle}{13}[/tex]

[tex]& =\left\langle\frac{3}{13}, \frac{4}{13}, \frac{12}{13}\right\rangle[/tex]

[tex]\vec{T}(1)=\left\langle\frac{3}{13},\frac{4}{13}, \frac{12}{13}\right\rangle[/tex]

[tex]\vec{T}(1)=\left\langle\frac{3}{13}, \frac{4}{13}, \frac{12}{13}\right\rangle \quad[/tex]

Now [tex]r^{\prime}(t)=\left\langle 3,4 t, 12 t^2\right\rangle \\[/tex]

From r'(t) we can find the value of r''(t).

For that we have to differentiate each term of r'(t)

[tex]r^{\prime \prime}(t)=\langle 0,4,24 t\rangle[/tex]

Now we have to find the value of r'(t) × r ''(t).

[tex]\partial^{\prime}(t) \times \partial^{\prime \prime}(t)=\left|\begin{array}{ccc}i & j & k \\3 & 4 t & 12 t^2 \\0 & 4 & 24 t\end{array}\right|[/tex]

[tex]&=i\left(96 t^2-48 t^2\right)-j(68 t)+k(12) \\&=\left(48 t^2\right) \vec{i}-\vec{j}(68 t)+\vec{k}(12) \\[/tex]

[tex]r^{\prime}(t) \times r^{\prime \prime}(t)=\left(48 t^2\right) \vec{i}-\vec{j}(68 t)+\vec{k}(12)[/tex]

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The total annual salary with a festive bonus is Rs (12r+2000)

In maths, multiply means the repeated addition of groups of equal sizes.

Given that, there is an annual salary at r rupees per month along with a Christmas bonus of, Rs 2000.

Here, a person is getting monthly salary  = Rs r

Therefore, his annual salary = Rs r × 12

= Rs 12r

He is also getting a bonus for Christmas = Rs 2000

So, in total, he will get =  Rs (12r+2000)

Hence, The total annual salary with a festive bonus is Rs (12r+2000)

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Answer:

1/11

Step-by-step explanation:

Add 1/5 + 2 then divide 1/5 by the result

Answer:

Step-by-step explanation:

so we start with Sara's

-3x+14=18-5x

for properties of equality, we need to isolate the x variable

-3x=4-5x

2x=4

x=2

that is correct

now we go to Ethan's

2x=5-1/2x

2 1/2x=5

x=2

now we have confirmed that x is equal to 2

hope this helped

Risk is the potential that a chosen action may lead to an undesirable outcome.

In simple terms, the definition of risk is a condition that is uncertain, but contains an element of danger as a consequence or result of something. Once again, this something is a business, business, activity, or decision that you make.

The risks themselves are divided into several types, complete with different characteristics.

1. Pure Risk 

This pure risk is certain, meaning that when the risk occurs, you will experience a loss. And vice versa, if pure risk does not occur, then you will make a profit.

2. Speculative Risk 

There are three possibilities that will happen, if you experience speculative risk, namely profits, losses, or maybe break even. What is meant by break even is the break even point.

Conditions where there are no profits or losses, so it's normal. The most obvious examples of speculative risk are the lottery, stock exchange, exchange risk, and others.

3. Particular Risk or Special Risk

Specific risks originate from individual activities, so the impact can still be estimated or anticipated at the outset because they are local in nature. For example, a turbine explosion, a shipwreck, or maybe a crash.

How to anticipate it (example for collision risk). You can take out insurance to provide guarantees or protection, both for the vehicle and for yourself.

4. Fundamental Risk 

Fundamental risks come from the surrounding environment or nature which can have quite a big impact, because humans are not able to control them.

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One solution for the equation [tex]\frac{1}{2} (6x - 2) = 2[/tex] is x = 1

A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions.

A mathematical statement known as an equation is made up of two expressions joined together by the equal sign.

According to the given information

The equation given to us is

[tex]\frac{1}{2} (6x - 2) = 2[/tex]

Solving the above equation

We get

3x - 1 = 2

3x = 2 + 1

3x = 3

x = 1

We have only

One solution for the equation [tex]\frac{1}{2} (6x - 2) = 2[/tex] is x = 1

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Answer:

To determine the missing coefficient "a" in the polynomial P(x) = x^4 - 3x^3 + ax^2 - 6x + 14, we can use the SOLVE process as follows:

S: Write down the given information and identify the problem.

We are given the polynomial P(x) = x^4 - 3x^3 + ax^2 - 6x + 14, and we need to find the value of the missing coefficient "a".

O: Organize the information and decide on a plan.

To find the value of "a", we can substitute specific values for x into the polynomial and solve for a.

L: Carry out the plan.

For example, let's say we substitute x = 2 into the polynomial. We get:

P(2) = 2^4 - 32^3 + a2^2 - 6*2 + 14

= 16 - 24 + 4a - 12 + 14

= -4 + 4a + 2

= 4a - 2

We are given that P(2) = 4a - 2 = 0, so 4a = 2.

Solving for a, we get:

a = 2 / 4

= 0.5

V: Check the solution.

We can check the solution by substituting 0.5 for a in the original polynomial and verifying that it gives us the correct result for P(x) when x = 2.

P(x) = x^4 - 3x^3 + 0.5x^2 - 6x + 14

Substituting x = 2 and a = 0.5, we get:

P(2) = 2^4 - 32^3 + 0.52^2 - 6*2 + 14

= 16 - 24 + 1 - 12 + 14

= 0

Since P(2) = 0, our solution appears to be correct.

Therefore, the missing coefficient "a" in the polynomial P(x) = x^4 - 3x^3 + ax^2 - 6x + 14 is 0.5.

Answer:

-3<c<11/2

Step-by-step explanation:

-7<2c-1

-7+1<2c

-6<2c

-3<c

and

2c-1<10

2c<10+1

2c<11

c<11/2

Final answer (combine both):

-3<c<11/2

The mean is $67,530 from the reported two average household incomes i.e, $49,445 and $67,530.

Averages can only be computed for numeric variables, regardless of whether the variables are discrete or continuous. This is obtained by simply dividing the sum of all values in the dataset by the number of values.

Mathematically, X-bar = Sum of x values/ number of values

We have, the current population survey is conducted by the US Census bureau,

Averages of household income are $49,445 and $67,530. Mean of average incomes is expected to be a right skewed distribution because some individuals belongs to exceptionally high income group which are outliers and which will cause the mean to inflate. Hence, value which is greater will be the mean i.e. $67,530

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The number of transgendered people would be expected to disagree with such a platform being allowed to exist in our society under the null hypothesis is 19.00

A statistical hypothesis known as a null hypothesis asserts that no statistical significance can be found in a collection of provided observations. Using sample data, hypothesis testing is performed to judge a theory' veracity. It is sometimes referred to as just "the null," and its symbol is H0.

To determine if a theory regarding markets, investing methods, or economies is correct or wrong, quantitative analysts employ the null hypothesis, often known as the conjecture.

The number of transgendered people would be expected to disagree with such a platform being allowed to exist in our society under the null hypothesis is 19.00

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The angles ∠ 5 and ∠ 7  are supplementary angles.

Supplementary angles are those angles that sum up to 180 degrees.

Given is a figure, with two parallel lines and a transversal

In the options,

(∠ 5 and ∠ 8) (∠ 2 and ∠ 3) are vertically opposite angles.

∠ 1 and ∠ 5 are corresponding angles

But ∠ 5 and ∠ 7 are forming linear pair, and we know that, two angles forming linear pairs are supplementary angles,

Hence, The angles ∠ 5 and ∠ 7  are supplementary angles.

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Answer:

D

Step-by-step explanation:

The last one- monetary support that is used to help pay educational costs

:)

Answer:

Unit price 12.16 for 4.07 pounds is $2.99 per pound

Unit price 14.99 for 5.11 pounds is $2.93 per pound

The best deal is the 14.99 per 4.11 pounds

Step-by-step explanation:

Unit price 12.16/4.07 = 2.99 rounded to the nearest cent

Unit price 14.99/5.11 = 2.93 rounded to the nearest cent.

Answer:

1) $2.99

2)$2.93

The better buy is the 4.07 pound bag

Step-by-step explanation:

To find the unit price you find the cost per pound

$12.16 : 4.07

? : 1

4.07x = 12.16

x = 2.98771499

$2.99

$14.99 : 5.11

? : 1

5.11x = 14.99

x= 2.9334638

43 is equivalent to 64(1/3)

Equivalent is different from equal. Equal means same in all aspects, whereas equivalent means similar but not identical.

For example, 2 is said to be equal to 2 but equivalent to 1 + 1.

Given that, if a=b(1/n) is equivalent to an=b then 43 is equivalent to

If we see the number 43, then converting it according to given pattern

4ⁿ(1/n)

Here, n = 3

So, 43 = 4³(1/3) = 64(1/3)

Hence, 43 is equivalent to 64(1/3)

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Answer:

A

Step-by-step explanation:

Sequence A works.

With sequence B, the triangles will be next to each other.

Answer: A

Answer:

-17

Step-by-step explanation:

p+5=-12

p=-12-5

p=-17

Answer:

p+5=-12

p=-12-5

p=-17

so the solution set is -17

Simple random sampling is a good way because he will have a more representative sample if he chooses randomly. which is the correct answer would be an option (B).

A sample is randomly chosen from the population in basic random sampling, guaranteeing that each person has an equal chance of being chosen.

Simple random sampling is a good way for a librarian to check a sample of books from the library to get an idea of how many need replacing because it will provide a more representative sample.

In simple random sampling, a sample is selected from the population at random, ensuring that each member of the population has an equal chance of being selected. This means that the sample will accurately represent the characteristics of the population as a whole.

Thus, He will have a more representative sample if he chooses randomly.

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The required Inequality is $12x + $150 ≥ $380 where x is the minimum number of lawns Jacob will need to mow in order to buy the ticket. The solution of inequation is x ≥ 19.2 ~ 19.

An inequality is a mathematical expression in which both sides are not equal. Unlike equations, inequalities compare two values. Equal signs between are replaced by less than (or less than and equal), greater than (or greater than and equal ) sign.

When solving an inequality:

We have, total cost of electronic ticket i.e with all taxes = $380

Saved cost = $150

Cost of one mowing lawn = $12

let "x" be the number of lawns mowed by Jacob for earning the rest of money .

Total cost of x mowed lawns by Jacob।

= $12x .

Now, $12x + $150 ≥ $380 --(*)

This is the required Inequality and x is minimum number of lawns which Jacob have to mowed .

The solution of above Inequality,

Substracts 150 from both sides in (*)

12 x + 150 - 150 ≥ 380 - 150

=> 12x ≥ 230

dividing by positive 12 both sides we get,

=> x/12 ≥ 230/12

=> x ≥ 19.16

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Complete question:

Jacob is saving to buy an electronic ticket that costs $380 including tax and has saved $150. Jared plans to earn the rest of the money by mowing lawns and will charge $12 for each lawn he mows. Write an inequality to find x, the minimum number of lawns Jacob will need to mow in order to buy the ticket. Show how to solve the inequality and what is solution.