What is the approximate speed of sound in the experimental medium ( speed = frequency X wavelength )

The total money I have to pay will be 168.

What is the arithmetic operation?

The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or more quantities. Included in them is the study of numbers, especially the order of operations, which is important for all other areas of mathematics, including algebra, data management, and geometry. The rules of arithmetic operations are required in order to answer the problem.

If I and my brother pay for groceries and the total was 443.

If i pay 243 and get paid back 75

So the total I paid will be (243 - 75) = 168

Hence, the total money I have to pay will be 168.

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 The height of the top change when the lower end is feet from the wall by -4.5 ft/sec.

Given,

Assume that the horizontal floor is x and the vertical wall is y in distance (6 ft).

This creates a triangle, with the ladder serving as the 10 foot hypotenuse.

dy/dt = 6 feet per second.

Pythagoras' law states that there is a link between x and y.

(x²) + (y²) = (hypothenus²) = 10².

When both sides of the equation are distinct,

0 = 2x(dx/dt) + 2y(dy/dt)

(x/y) × (dx/dt) = dy/dt

y = √(10²) - (6²) = 8ft

Consequently, dy/dt = (6/8) × (6/1)= -4.5 ft/sec.

The rate is negative.

That is,

When the lower end is feet from the wall, the height of the top changes by -4.5 feet per second.

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The expression that represents the total cost on weekend job is 25x + 90y.

An algebraic expression can be obtained by doing mathematical operations on the variable and constant terms.

The variable part of an algebraic expression can never be added or subtracted from the constant part.

Given that,

The hourly charge of the electrician is $60.

And, the job fee is $25.

The additional percent charged on weekend is 50%.

Suppose the number of jobs on weekend is x and the total hour worked is y.

Then, as per the given case, the following expression can be written for the weekend cost as,

25x + 60y + (50% of 60y)

= 25x + 60y + 50/100 × 60y

= 25x + 90y

Hence, the expression for the total cost for a weekend job is given as 25x + 90y.

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well, we know that it was 195 in 1992, so "t" years later that'd be

[tex]\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &195\\ r=rate\to 1.2\%\to \frac{1.2}{100}\dotfill &0.012\\ t=years\dotfill &t\\ \end{cases} \\\\\\ A=195(1 + 0.012)^{t} \implies A =195(1.012)^t[/tex]

Answer:

Step-by-step explanation:

12.50

Answer:

B

Step-by-step explanation:

constant of proportionality = 10/20 = 1/2

y/x = 1/2

y = 1/2x

y = 1/2 * 25

y = 25/2

y = 12.5

Variable, x, represents the independent variable and the dependent variable is the distance, because the distance depends on the time. A function relating these variables is R(x) = 60x. So R(3) = 180 miles, meaning after 3, a distance of 180 miles was covered.

The dependent variable is the outcome or result that is being measured or observed, while the independent variable is the factor that is manipulated or changed to see its effect on the dependent variable.

Therefore, we can say that: the independent variable, x, represents the time and the dependent variable is the distance, because the distance depends on the time.

A function relating these variables is R(x) = 60x, representing the distance covered as a function of time at a constant speed of 60 miles per hour.

So, R(3) = 60 * 3 = 180 miles, meaning after 3 hours of driving, Hannah will have covered a distance of 180 miles.

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The independent variable x represents time in hours and the dependent variable R(x) represents distance in miles. The relationship between these variables is expressed by the function R(x) = 60x, signifying the distance (in miles) Hannah would have driven after x hours. For instance, R(3) equals 180, implying that after 3 hours, Hannah would have driven 180 miles.

In this context, the independent variable, x, represents the time in hours and the dependent variable, R(x), is the distance in miles, because the distance depends on the time. A function relating these variables is R(x) = 60x. This is because Hannah's speed is 60 miles per hour, so the formula for distance (Rate x Time) becomes 60 times the number of hours (x). So R(3) equals 180, meaning after 3 hours, Hannah would have driven 180 miles.

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Answer: 1x

Step-by-step explanation:-3+4=1 and then add a x

The probability that an endure all battery selected at random will last more than 610 hours is 0.3%

What is the Z score?

A Z-score is a metric that quantifies how closely a value relates to the mean of a set of values. Standard deviations from the mean are used to measure Z-score. If a Z-score is 0, it indicates that the data point's score is identical to the mean score.

Z score is used to determine by how many standard deviations the raw score is above or below the mean, The z score is given by:

[tex]z = \frac{x - \mu}{\sigma}[/tex]

where,

x = raw score

μ = mean

σ = standard deviation

Given that μ = 500, σ = 40, for x > 610:

z = (610 - 500) / 40

= 2.75

From the normal distribution table, P(z > 2.75) = 1 - P(z < 2.75) = 1 - 0.9970 = 0.0030 = 0.3%

Hence, the probability that an endure all battery selected at random will last more than 610 hours is 0.3%

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The joint distribution of X and Y probability is 1/6.

What is probability?

Probability is that the branch of arithmetic regarding numerical descriptions of however possible an occasion is to occur, or however possible it's that a proposition is true.

Main body:

Two dice are thrown  S = { (i,j) / i, j =1:6}

a) X : Number observed from the fair die.

   Y : Number observed from the unfair die.

   P(X=1, Y=1) = 1/6 * 1/9 =1/54  

Similarly we can obtained remaining probabilities.

P(X=2, Y=2 ) = 1/6 * 1/9 =1/54    

P(X=3, Y=3 ) = 1/6 * 1/9 =1/54

P(X=4, Y=4 ) = 1/6 * 1/9 =1/54

P(X=5, Y=5 ) = 1/6 * 3/9 =3/54 = 1/18

P(X=6, Y=6 ) = 1/6 * 2/9 =2/54 = 1/27

the joint distribution of X and Y is  =

⇒P(X=1, Y=1) = 1/6 * 1/9 =1/54  + P(X=2,  Y=2 )+ P(X=3, Y=3 ) +  P(X=4, Y=4)+

   P(X=5, Y=5 ) +P(X=6, Y=6 )

⇒1/54 +1/54+1/54+1/54 +3/54+2/54

⇒ 9/54

⇒1/6

Hence the joint distribution of X and Y probability is 1/6.

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The length of the 3rd side of the given triangle with 6 units and 9 units being the length of the 1st and 2nd side can be:

(B) 4 units

(C) 7 units

(F) 10 units

(E) 12 units

A triangle is a polygon with three vertices and three sides.

The angles of the triangle are formed by the connection of the three sides end to end at a point.

The triangle's three angles add up to 180 degrees in total.

So, knowing that the third side of a triangle must be longer than the sum of the first two sides and shorter than the difference between the first two sides allows us to obtain:

x > (9-6) so x > 3 and x < (9+6) so x < 15

Based on these findings, the third side length can be chosen from B. 4, C. 7, F. 10, and E. 12.

Therefore, the length of the 3rd side of the given triangle with 6 units and 9 units being the length of the 1st and 2nd side can be:

(B) 4 units

(C) 7 units

(F) 10 units

(E) 12 units

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Complete question:
A triangle has two sides of lengths 6 and 9. What value could the length of the third side be? Check all that apply

A.15

B.4

C.7

D.2

E.12

F.10

The largest number of bouquet are 9

What is Highest Common Factor?

The greatest common factor is the biggest whole number shared by the supplied numbers. For example, the common factors of 10 and 20 are 1, 2, 5, and 10, with 10 being the greatest; so, the highest common factor of 10 and 20 is 10.

Solution:

Total Red Roses = 18

Total Tulip = 27

Toal White Gardenia = 36

To find the largest number of bouquet we need to use Highest Common Factor

HCF of (18, 27, 36) = 9

The largest number of bouquet are 9

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The maximum height reached is 21.125ft

The squirrel was at its highest point when, v=0, which occurred 2.25 seconds after it jumped.

Squirrel reaches the ground in 5.5 seconds.

What is the relation between height and velocity?

We can find velocity if equation of height is given by differentiating the equation with respect to time.

According to the given question:

The squirrel can only have reached its maximum height when its velocity equals zero.

If h=-2t^2+9t-11

Then dh/dT=v=-4t+9

A) Therefore ,at the maximum height, the velocity ,v=0.

That is, 4t=9 , consequently, t=2.25s

Therefore, when t=2.25s

h=-2(2.25)^2 + 9(2.25)-11

The maximum height reached is then h=21.125ft

B) As explained above, the squirrel was at its highest point when, v=0, which occurred 2.25seconds after it jumped.

C) The squirrel reaches the ground when h=0...

0=-2t^2+9t+11

-2t^2-2t+11t+11=0

-2t(t+1)+11(t+1)=0

(-2t+11)(t+1)=0, since t>0 for this problem...

-2t+11=0

-2t=-11

t=5.5 seconds.

Therefore, squirrel reaches the ground in 5.5 seconds.

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here are some screen shots hope it helps

Answer: The at home printer prints faster, and you can print 6 more photos with it than the office printer.

Step-by-step explanation:

25 ÷ 12.5 = 2
15 ÷ 6 = 2.5

2 x 12 = 24
2.5 x 12 = 30

Twenty eight sixths is less than the square root of 26 which is  [tex]\sqrt[6]{28}[/tex] < [tex]\sqrt{26}[/tex]

Square root of a number is a value, which on multiplication by itself, gives the original number. The square root is an inverse method of squaring a number. Hence, squares and square roots are related concepts.

checking for square root of:

 [tex]\sqrt[6]{28}[/tex]    = 1.74

[tex]\sqrt{26}[/tex] = 5.09

which means 1.74 < 5.09

Therefore   [tex]\sqrt[6]{28}[/tex]  < [tex]\sqrt{26}[/tex]

In conclusion twenty eight sixths is less than the square root of 26 (   [tex]\sqrt[6]{28}[/tex]  < [tex]\sqrt{26}[/tex])

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Answer:

D (-3,4)

Step-by-step explanation:

This is the point that the two line intersect.  From (0.0) go three units left and 4 units up.  That is where the lines cross.

The width of the river is 1700m

What is the time, distance & speed relation?

Speed is calculated by dividing the distance traveled by the amount of time it took to get there. Divide the distance by the speed to find the passing time. To get the distance, multiply the speed by time.

Let 'x' be the distance from THE far bank where 700 is the distance to the NEAR bank

boat one has travelled 700 (rate = 700/unit time) boat two has travelled   x rate = x / unit time

boat one then travels   x  + 400  more      and boat two travels   700 + (700+x -400) more    when they meet

The time is the same:    

rate x time = distance  

distance/rate = time    

equate the distances divided by the respective rates

(700 + x + 400)/700     =    (  x  +  700     +  (700+x-400) )/x

1100x + x^2 = 1400x + 700000

x^2 - 300x - 700000 = 0                        

quadratic formula yields  x = 1000  

One boat travels 700 the other 1000 when they first meet.....width of the river =   700+ 1000 = 1700 m

Hence, the width of the river is 1700m

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The end behavior of the function is described by the following option:

f(x) -> 0 when x -> -∞ and f(x) -> -∞ when x -> ∞.

The end behavior of a function is given by the limits of the function as x goes to infinity.

On the graph, these limits are found looking at the behavior at the left end and at the right end of the graph, as follows:

From the graph, these limits are given as follows:

Hence the correct statement is given by the third option, as the other options give the wrong limits.

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The point on the line is (-4, 3) and the slope of the line is m=3

Divide the "vertical change" by the "horizontal change" between (any) two distinct points on the line to find the slope.

The slope's absolute value is used to calculate the steepness, incline, or grade of a line. A line's direction can be increasing, decreasing, horizontal, or vertical.

If a line runs up from left to right, it is growing. The slope is positive, implying that m>0.

If a line falls from left to right, it is diminishing. m<0 is the slope.

A horizontal line has a slope of zero. This is a function that never changes.

Given,

y=3+3(x+4)

y-3=3(x-(-4))

Here, the point on the line is (-4, 3)

And the slope of the line is m=3

Hence, the point on the line is (-4, 3) and the slope of the line is m=3

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At least 35% of all registered students, according to a university's academic planner, take summer courses. H0:p.35 Ha:p.35 is the appropriate set of hypotheses to test his theory with.

A hypothesis is a put-forth explanation for a phenomenon (plural: hypotheses).

A hypothesis must be testable according to the scientific method for it to be considered a scientific hypothesis.

Scientific hypotheses are typically based on prior observations that cannot be adequately explained by the current body of knowledge.

For example, a university's academic planner estimates that at least 35% of all enrolled students attend summer classes. The proper set of hypotheses to use in order to test his theory is H0:p.35 Ha:p.35.

Despite the frequent confusion between the terms "hypothesis" and "theory," a scientific hypothesis differs from a scientific theory.

A working hypothesis is an accepted theory that has been tentatively supported and is put up for further investigation.

Therefore, at least 35% of all registered students, according to a university's academic planner, take summer courses. H0:p.35 Ha:p.35 is the appropriate set of hypotheses to test his theory with.

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Answer:

[tex]\huge\boxed{\sf 60}[/tex]

Step-by-step explanation:

30 = a × 60

Divide both sides by 60

30/60 = a

0.5 = a

Now,

= 30/0.5

[tex]\rule[225]{225}{2}[/tex]

the limit of f (x) g(x) exists as x!0 is exist.

what is function existance ?

The EXISTS function returns a Boolean value to indicate whether a list contains at least one element.

let,

f(x)  =  1    at x=Q

also, f(x)  = -1  at x=Q'

now, g(x)  = -1  at x = Q

also, g(x) = 1 at x = Q'

Here,

[tex]\lim_{n \to \infty} f(x)[/tex]      and [tex]\lim_{n \to \infty} g(x)[/tex]   does not exist.

but,    f(x) + g(x)  =  (f+g)(x) = 0 at x = Q and also at x = Q'

⇒  (f+g)(x) = 0 ∀ x∈IR

⇒   [tex]\lim_{n \to \infty} (f+g)(x)[/tex]  = 0 exist.

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Answer:

Step-by-step explanation:

apples=$2 per pound

oranges=$3 per pound

If Ben bought x pounds of oranges and five pounds of fruit in total, then he bought 5-x pounds of apples.

oranges price: 3x

apples price: 2(5-x)

Final Equation: 3x+2(5-x)=12

3x+10-2x=12

x+10=12

x=2 -> amount of oranges

input in apples equation

apples= (5-x)->(5-2)=3

Final answer: 2 pounds of oranges, 3 pounds of apples

After Farmer Scott travelled for two weeks and left his acres of corn plants alone with no chemicals or other protection weeds began to grow and develop after farmer Scott returned to after the two weeks.

The farmer Scott will almost certainly come across the little weeds that had begun to sprout and flourish in his corn field while he was away this was as a result of not attending to the corn fields. The field was not safeguarded by pesticides or insecticides. The weeds would not have been eradicated for two weeks, resulting in greater growth. They will consume all of the nutrients, causing the corn plants to perish.

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Answer:

m = 3.99

Step-by-step explanation:

50.88 = 3 + 12 * m

50.88 - 3 = 12 * m

m = 47.88 / 12 = 3.99

Postoptimality analysis is another name for sensitivity analysis

What is sensitivity analysis?

According to a certain set of supposition, sensitivity analysis evaluates how various values of an independent variable affect a specific dependent variable. In other words, sensitivity studies look at how different types of uncertainty in a mathematical model affect the overall level of uncertainty in the model. This method is used within boundaries that are preset and depend on one or more input variables.

Both the corporate sector and the study of economics employ sensitivity analysis. It is often referred to as a what-if study and is frequently utilized by economists and financial experts.

Therefore, Postoptimality analysis is another name for sensitivity

analysis and thus option B is the correct answer

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The confidence interval of two populations means a) it must pool the sample variances

A confidence interval provides a range of possible values ​​for the difference between two population means. For example, a 95% confidence level indicates that given 100 random samples from the population, you can expect about 95 samples to yield intervals that include the population difference.

If the confidence interval for the between-groups difference contains zero, it means that if you run the experiment again, it is likely that you will not find a difference between the groups. Two populations from which two independent samples are selected are known to have the same variance.

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A quadratic function in standard form that represents each area as a function of the width is; A = -x² + 20

We are told that she is enclosing a new garden and has 40 ft of fencing.

Now, let the two sides be labelled x and y.

We know that area of a rectangle is;

A = length * width

Thus;

A = xy

Now, since she has 40 ft of fencing, then it means that;

y = 0.5(40) - x

y = 20 - x

Thus, the area expressed in quadratic function formula is;

A = x(20 - x)

A = 20x - x²

A = -x² + 20

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Complete question is;

Write a quadratic function in standard form that represents each area as a function of the width.

Remember to defi ne your variables

The  sketching of the vector field is attached herewith.

Since we know  the formula for the vector field is :

F(x, y, z) = -yi+ xj = xj -yi, where  x and y are the magnitude and i and j are the unit vectors for the x and y - axis .Since we the  points we are given with are:(-2, -2, -2) ,(-2, -2, 2) ,(-2, 2, -2),(-2, 2, 2),(2, -2, -2) ,(2, -2, 2),(2, 2, -2) , (2, 2, 2). So the  filed vectors  for individual points will be just substituting the magnitude of  the individual axis :

F(-2, -2, -2)   =  -2j +2i

F(-2, -2, 2)  =   -2j +2i

F(-2, 2, -2) =  -2j -2i

F(-2, 2, 2)  =   2j +2i

F(2, -2, -2)  =  -2j-2i

F(2, -2, 2)  =  -2j -2i

F(2, 2, -2)   =  2j -2i

F(2, 2, 2)    =  2j -2i

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If the partial derivative is equal to zero for all values of x then it indicates that the function is constant.

What is a partial derivative?

In differential calculus, partial derivative is defined as the rate of change of multivariable functions concerning change in just one of its variables.

Consider the restriction of f to a line y=c,

then

[tex] \frac{∂f}{∂x}(x \: c) = fx(f \: c) = 0[/tex]

Pick 2 points a and b, then by mean value theorem there is x0, such that

[tex]fx(x \: c) = \frac{f(b \: c) - f(a \: c)}{b - a} = 0[/tex]

[tex]⟹f(b \: c) - f( \: a \: c) = 0⟹f(b \: c) = f(a \: c)⟹f(x \: c) = const.[/tex]

We can show the same way that f(c,y)=const.

Combining f(x,c)=const and f(c,y)=const to get f(x, y)=const.

Hence, If the partial derivative is equal to zero for all values of x then it indicates that the function is constant.

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