When a car travels 100 km at a speed of 60km/h and returns back with a speed of 40km/h What will be average speed for whole journey?

The value of the variable 'x' in the first case and the second case will be 9° and 1.

It is a polygon with four sides. The total interior angle is 360 degrees. A parallelogram's opposite sides are parallel and equal. And the sum of the adjacent angles is 180°.

In part 61, the equation is given as,

100° + 9x - 1° = 180°

Simplify the equation, then we have

9x + 99° = 180°

9x = 81°

x = 9°

In part 62, the equation is given as,

22x - 1 = 21

Simplify the equation, then we have

22x - 1 = 21

22x = 22

x = 1

The value of the variable 'x' in the first case and the second case will be 9° and 1.

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The balloon will be collapsed due to the excess pressure.

if we press on a balloon that is already filled by air stretched over the jar, the air of the jar will enter the balloon and create excess pressure beyond its tolerance and finally the balloon will be collapsed.

as the air-filled balloon is pressed directly over a jar, there is no way to leakage of air, besides the air of jar enter the balloon causes high pressure on the wall of balloon and finally it is destroyed. The result represents the presence of gases inside any empty bottle as well as any jar.

hence, we understand that every empty jar or bottle has gaseous substances with them.

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Using the percentage increase formula, we know that the rate of increase in the advertising cost of the company is 93.5%.

In mathematics, a percentage is a number or ratio that is expressed as a fraction of 100.

The percent symbol, "%," is widely used to denote it even if the abbreviations "pct," "pct," and rarely "pc" are also employed.

A% is a number that has neither dimensions nor a defined unit of measurement.

For instance, if you properly answered 75 out of 100 questions on a test, you would have received a 75% grade (75/100).

So, the percentage increase formula:

% increase: original - increase/original * 100

Increase: 76680-72000 - 4680

Now, substitute values as follows:

% increase: original - increase/original * 100

% increase: 72000 - 4680/ 72000* 100

% increase:93.5

Therefore, using the percentage increase formula, we know that the rate of increase in the advertising cost of the company is 93.5%.

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The appropriate null and alternative hypothesis for calculating number of gogles is H0 : No linear relation H1 : there is a relation

Correlation is a statistical measure that expresses the extent to which two variables are linearly related (meaning they change together at a constant rate).

It's a common tool for describing simple relationships without making a statement about cause and effect.

According to the question,

A group of scientist randomly selected 20 piknits from the sea-floor and measured their respective weights in grams.

Also, They wanted to know if the weight of the piknits can be used to predict the number of gogles.

From the given information,

Null hypothesis : H0 : There is no linear relationship between the weight of piknits and the number of gogles

Alternative hypothesis : Ha: There is a linear relationship between the weight of piknits and the number of gogles

Option 4 is correct about null and alternative hypothesis

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The product to the nearest whole number is equivalent to zero.

Given is to write the product (0.7 x 0.85) to the nearest whole number.

We have the product as -

0.7 x 0.85

(7/10) x (85/100)

(7/10) x (17/100)

119/1000

0.119

0.12

0.1

0

Therefore, the product to the nearest whole number is equivalent to zero.

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The equation to represent the total amount of money Richard make in an hour is  y = 9 + 2x    .

In the question ,

it is given that ,

Richard is working at a retail shop ,

let the number of membership sold in an hour be = "x" ,

let the total amount of money earned be = "y" .

amount of money earned in hour = $9 ,

amount that he gets for each membership sold = $2 .

So , According to the question ,

the equation that represent the given situation is given as

y = 9 + 2x

Therefore , the equation for the situation is y = 9 + 2x .

The given question is incomplete the complete question is

Richard works at a retail shop. he makes $9 an hour, plus $2 for each membership he sells. let x represent the number of memberships sold and y represent the total amount of money he will make in an hour. write an  equation represents this situation ?

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The percent decrease of water in the tank is 50%.

What is the percent decrease?

The difference between starting and final numbers is the percentage drop. It displays a percentage loss of value compared to the original regardless of the units. The difference between the initial and final amounts is the amount of decline.

We have,

a tank contained 6 in. of water.

After several​ hours, it contained 3 in. of water.

percent decrease of water in the​ tank?

A tank contained 6 in of water.

After several hours, it contained 3 in of water

So, decrease in water =  6 in - 3 in = 3 cm

The percent decrease of water in the tank = (change in amount of water/initial amount) * 100

The percent decrease of water in the tank = (3/6) * 100

= 50

Hence, the percent decrease of water in the tank is 50%.

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The percentage comparing the size of the large milkshake to the size of the small milkshake is 140%.

Let the size of small milkshake he x. So, the size of large milkshake will be 1.4x. Now, for percentage calculation the formula will be -

Percentage = size of large milkshake/size of small milkshake × 100

As we need to find the percentage of ratio, we need to simply take large and small size of milkshake.

Keep the values in formula -

Percentage = 1.4x/x ×100

Cancelling x from numerator and denominator

Percentage = 1.4 ×100

Performing multiplication

Percentage = 140%

Hence, the percentage is 140%.

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Answer:

I believe it is C.

Step-by-step explanation:

Answer:

To write a system of inequalities that has the point (6, 6) as a solution but not (6, -6), we can use the fact that the point (6, 6) is above the graph of the quadratic function, but the point (6, -6) is below the graph. Therefore, we can write a system of inequalities that includes the condition that the y-value must be greater than the value of the quadratic function at a given x-value.

For example, we could use the quadratic function y = x^2 and write the following system of inequalities:

y > x^2

y > 6

The first inequality states that the y-value must be greater than the value of the quadratic function at a given x-value. The second inequality is added to ensure that the y-value is greater than 6, which is necessary for the point (6, 6) to be a solution.

Since the point (6, 6) satisfies both of these inequalities, it is a solution to the system. However, the point (6, -6) does not satisfy the first inequality, since the y-value is less than the value of the quadratic function at x = 6. Therefore, it is not a solution to the system.

Overall, the system of inequalities would be as follows:

y > x^2

y > 6

The selected statement that are true about the equilateral triangle ABC are

An equilateral triangle is a triangle in which all sides are equal and angles are also equal.

The value of each angle of an equilateral triangle is 60 degrees therefore, it is also known as an equiangular triangle. Equiangular triangle because the angles are congruent.

Therefore, the true statement about the equilateral triangle ABC are as follows:

Recall AD is a perpendicular bisector of BC. Therefore, it divides BC into two equal halves.

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Answer:

gradient = -2

Step-by-step explanation:

gradient = difference of y-coordinates / difference of x-coordinates

gradient = (y2-y1) / (x2-x1)

gradient = (-14)-0 / 1-(-6)

gradient = (-14)/7

gradient = -2

Answer:using gas

Step-by-step explanation:

The number of sides an interior angle of polygon 3240 degree have is 20 sides.

Divide the number of triangles in the polygon by 180 degrees to determine the sum to its inner angles.

(n-2) *180, where n= the number of sides. since we have 5 sides. therefore, the sum is 360 degrees.

formula for finding sum of interior angles of polygon is (n-2)180

3240=(n-2)180

expand, we have;

3240=180n-360

collect like terms

3240+360=180n

3600=180n

divide both side by 180

therefore

n= 20

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Answer: 100 pi, or 314.15926...

Step-by-step explanation:

The circumference is 2r pi. r is 10. The area is r squared pi. 10 squared in 100, so 100 pi.

The solution range of the inequality {5x+7<3  and  3x-4>11} to is in range : x < -4/5 or x > 5.

Given are the following inequalities -

5x+7<3  and  3x-4>11

We have -

5x + 7 < 3

5x < - 4

x < -4/5

and

3x - 4 > 11

3x > 15

x > 5

So, we can write the solution of the inequality as -

x < -4/5 or x > 5

Therefore, the solution to the inequality is in range : x < -4/5 or x > 5.

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Answer:

1 1/5

Step-by-step explanation:

So first we need to realize that 4/5 can be turned into 8/10. Plus since they need 3 cups, not 2 (which we have been provided with the cups for) then we have to split it in half. So it would be 8/10 + 4/10. Which is 12/10 or 1 2/10 or 1 1/5

Hope this makes sense!!!

The function f(x) = -7x + 22 and g(x) is f(x) translated up 5 thus option (D) is correct.

Transformation is rearranging a graph by a given rule it could be either increment of coordinate or decrement or reflection.

Reflection is a mirror image of a graph about any axis.

If we reflect any graph about y = x then the coordinate will interchange it that (x,y) → (y,x).

As per the given table,

The function f(x) = -7x + 22 is satisfying the table.

For example at x = 2

f(2) = -7 x 2 + 22 = 8

Now, since, g(x) = f(x) + 5 thus g(x) is translated up to 5 units.

Hence "The formula f(x) = -7x + 22 and the translation of f(x) up 5 is g(x).".

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After the discount and the tax, the total cost will be $24.19

So, suppose we have a known price P.

If we apply a discount of X (in percentage) then the new price will be:

P' = P*(1 - X/100%)

If instead, we apply an increase of X, the new price willbe:

P' = P*(1 + X/100%).

In this case the original price is $30, then we apply a discount of 25% and then an increases of 7.5%, then the total cost will be:

C = $30*(1 + 7.5%/100%)*(1 - 25%/100%)

C = $30*(1 + 0.075)*(1 - 0.25) = $24.19

That is the final cost of the jeans.

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the eigenvalues of the matrix a^ta t is λ(Ax).

What is matrix?

The plural version of the word matrix is a matrix, which refers to the arrangements of numbers, variables, symbols, or phrases in a rectangular table with varying numbers of rows and columns. These arrays have a rectangular shape, and several operations like addition, multiplication, and transposition are specified for them. The components of the matrix are referred to as its entries or numbers. Vertical and horizontal entries in matrices are referred to as columns and rows, respectively. A matrix with m rows and n columns will contain m n entries. The uppercase letter 'A', which here stands for "matrix," Aij.

Let λ be an eigenvalue of ATA, i.e.

ATAx=λx

for some x≠0. We can multiply A from the left and get AAT(Ax)=λ(Ax).

Hence the eigenvalues of the matrix a^ta t is λ(Ax).

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By using function, it can be concluded that

The domain of the function is all real numbers greater than zero.

What is a function

A function from A to B is a rule that assigns to each element of A a unique element of B. A is called the domain of the function and B is called the codomain of the function.

There are different operations on functions like addition, subtraction, multiplication, division and composition of functions.

Here the values on the horizontal axis is the domain and the values on the vertical axis is the range.

From the graph, it can be seen that the function is defined for all real numbers greater than or equal to zero.

So the domain of the function is all real numbers greater than zero.

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The value of 'x' is 60.

We are given with [tex]\frac{-5}{6}x-\frac{-7}{30}x+\frac{1}{5}x=-52[/tex]

⇒ [tex]\frac{-25x-7x+6x}{30}=-52[/tex]

⇒ [tex]\frac{-26x}{30}=-52[/tex]

⇒ [tex]x = 2 \times 30[/tex]

[tex]\therefore x=60[/tex]

So the value of 'x' is 60.

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Answer:

1

Step-by-step explanation:

41 is prime, so its only factors are 1 and 41.

Since 1 is a factor of 78 but 41 isn't a factor of 78, the greatest common factor is 1.

The linear equation 8(u + 6) = 24 has a solution of u = -3

A linear equation is an algebraic equation where each term has an exponent of 1 and when this equation is graphed, it always results in a straight line.

In the given question, we are required to solve the linear equation following some steps.

Step one

8(u + 6) = 24

This is the given equation

Step two

8u + 48 = 24

This done using distributive property

Step Three

8u + 48 - 48 = 24  - 48

This is done using subtraction property

Step four

8u = -24

This done using collection of like terms

Step five

8u / 8 = -24 / 8

This is done using division property

u = -3

This is the answer to the question

The solution of the linear equation is - 3

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Line passing through AB is perpendicular. A pair of angles that are linear have an angle sum of 180 degrees. The lines are therefore shown to be perpendicular to one another because the angles are 90 degrees in size.

Two lines intersect to generate perpendicular lines, and the angle formed between the two lines must be 90 degrees (right angle).

Given,

Create another line perpendicular to AB passing through C on AB..

Line passing through AB is perpendicular.

Two lines are perpendicular if they cross at a point where a pair of linear congruent angles results. In a plane, a transversal is perpendicular to the other line if it is parallel to one of the two parallel lines.

A pair of angles that are linear have an angle sum of 180 degrees. The lines are therefore shown to be perpendicular to one another because the angles are 90 degrees in size. The linear pair perpendicular theorem is demonstrated by this.

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By using the concept of probability, it can be calculated that-

P(F|E) = [tex]\frac{P(F \ and \ E)}{P(E)} = \frac{6}{17}[/tex]

What is probability?

Probability gives us the information about how likely an event is going to occur

Probability is calculated by Number of favourable outcomes divided by the total number of outcomes.

Probability of any event is greater than or equal to zero and less than or equal to 1.

Probability of sure event is 1 and probability of unsure event is 0.

Here P(F|E) means probability of happening of event F knowing event E will happen

P(E) = 0.85, P(F) = 0.40, and P(E and F) = 0.30.

P(F|E) = [tex]\frac{P(F \ and \ E)}{P(E)} = \frac{0.30}{0.85} = \frac{6}{17}[/tex]

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The probability that the first failed inspection occurs on Fatima's 5th inspection i.e P(c = 5) is 0.05..

In probability and statistics,the geometric distribution defines the probability of the first success occurring after k trials. The probability of success is p

P r ( X = k ) = ( 1 − p )⁽ᵏ⁻¹⁾ p.

We have given that,

An emissions inspections on cars is conducted by Fatima.

Probability that car fail the inspection, p = 6% = 0.06

let c denoted the number of cars that are inspected until one car fail to inspection.

The random variable c here. Here c follow geometric probability distribution with probability of success (0.06).

Plugging all known values in above formula we get, p(c= 5) = (1-0.06)⁴ × 0.06

= (0.94)⁴ (0.06)

=0.0468449376~ 0.05

so, the answer is 0.05

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Complete question:

Fatima conducts emissions inspections on cars. She finds that 6%, percent of the cars fail the inspection. Let C be the number of cars Fatima inspects until a car fails an inspection. Assume that the results of each inspection are independent.

Required:

Find the probability that the first failed inspection occurs on Fatima's 5th inspection

The term "standard error of the mean" refers to the sample mean's standard deviation. And the formula for the standard deviation is σ/√n.

The square root of a random variable's variance is the standard deviation of a sample, statistical population, data collection, or probability distribution. Compared to the average absolute deviation, it is algebraically easier but less reliable in practice. The standard deviation has the advantage of being represented in the same unit as the data, unlike the variance, which is a desirable characteristic.

The standard error of a statistic (such the sample mean) is related to the standard deviation of a population or sample, however they are very different. Standard deviation of the population divided by the square root of sample size yields the standard deviation of the sampling distribution of means. "Standard error of the mean" is the term for the sampling distribution's standard deviation.

The term "standard error of the mean" refers to the sample mean's standard deviation.

And the formula for the standard deviation is given by σ/√n.

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Using the provided conditions and rule of inequality, The required expression is 11.25x + 14.75 <=80.

Both mathematical phrases, equations and inequalities, are created by connecting two expressions.

The Different Types of Equations are:

x= number of friends

Total parking cost = 14.75

Total ticket cost =11.25x

Total money = 80

Since, The total money to be spend can't cross $80, The inequality is given by 11.25x + 14.75 <= 80

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