A rectangular pool has a length of 15 meters and a width of 10 meters.
How many 25 cm x 25 cm tiles will you need to cover the entire surface of the pool?

Answer:

197

Step-by-step explanation:

To show that dy/dx = 1 - x·ln(x)/x·e^x, we shall first find the derivative of y with respect to x using the chain rule and the quotient rule.

According to the Quotient Rule, the derivative of a quotient is the denominator times the derivative of the numerator minus the numerator times the derivative of the denominator, all divided by the square of the denominator.

Given the equation: y = ln(x)/e^x

First, apply the quotient rule to differentiate y = ln(x)/e^x

dy/dx = [(e^x)(d/dx)(ln(x)) - (ln(x))(d/dx)(e^x)] / (e^x)^2

Next, differentiate ln(x) using the chain rule

(d/dx)(ln(x)) = 1/x

Next, differentiate e^x using the chain rule

(d/dx)(e^x) = e^x

Then, substitute the derivatives of ln(x) and e^x back into the quotient rule expression

dy/dx = [(e^x)(1/x) - (ln(x))(e^x)] / (e^x)^2

Simplify the expression:

dy/dx = (e^x/x - ln(x)e^x) / e^(2x)

Next, multiply the numerator and denominator by x

dy/dx = (xe^x/x^2 - ln(x)e^x/x) / (xe^(2x)/x^2)

Then, simplify the expression

dy/dx = (e^x/x - ln(x)e^x/x) / (xe^(2x)/x^2)

And multiply the numerator and denominator by x^2

dy/dx = (xe^x - xln(x)e^x) / (xe^(2x))

Next, factor out e^x from the numerator

dy/dx = e^x (x - xln(x)) / (xe^(2x))

And simplify the numerator

dy/dx = e^x (x(1 - ln(x))) / (xe^(2x))

Next, simplify further

dy/dx = (x - xln(x)) / (xe^(x))

Finally, rearrange the terms

dy/dx = 1 - xln(x) / xe^(x)

Therefore, the derivative of y with respect to x is given by dy/dx = 1 - xln(x)/xe^(x).

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Answer:

[tex]v(t) = 10500( {.86}^{t} )[/tex]

The original recipe requires 6 cups of flour and 4 cups of water. If the water is reduced to 2 cups, then 3 cups of flour should be used, found by setting up a proportion.

The recipe calls for 6 cups of flour and 4 cups of water.

To decrease the amount of water used to 2 cups, we can set up a proportion

(flour)/(water) = (6)/(4) = (x)/(2)

where x is the amount of flour needed when 2 cups of water are used.

Simplifying this proportion, we get

4x = 12

Dividing both sides by 4, we get

x = 3

Therefore, when the recipe uses 2 cups of water, 3 cups of flour should be used.

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Answer:133.4

Step-by-step explanation:

The calculated value of the car 5 years after its purchase is 7250

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

Equation of line of fit is y = -750x + 11000

The value of a car 5 years after its purchase means that the value of x is 5

i.e. x = 5

Substitute the known values in the above equation, so, we have the following representation

y = -750 * 5 + 11000

Evaluate

y = 7250

Hence, the value of a car 5 years after its purchase is 7250

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The distance between the given points in the coordinate plane is equal to 15 units.

In the coordinate plane ,

Let us consider the points in the coordinate plane is represented by

( x₁ , y₁ ) = ( 8 , 35 )

( x₂ , y₂ ) = ( 8 ,20 )

Using the distance formula between two points ( x₁ , y₁) and ( x₂ , y₂ ) we have,

Distance =  √( y₂ - y₁)² + ( x₂ - x₁ )²

Substitute the values we have in the formula,

⇒ Distance = √( 20 - 35)² + ( 8 - 8 )²

⇒ Distance = √ (-15)² + ( 0)²

⇒ Distance = √225

⇒ Distance = 15

Because distance cannot be negative.

Therefore, the distance between the two points (8 , 35) and (8 , 20) is equal to 15 units.

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Miss Anna needs ⅔ cup of sugar, and one tablespoon is equivalent to ⅓ of a cup.

What might an equivalent look like?

The entire amount of water distributed is roughly comparable to 35 inches of rainfall. Being a noble meant you were barred from holding public office, which effectively disfranchised the whole noble order.

What in academics is equivalent?

The terms "or equivalent" may occasionally be used in conjunction with educational requirements. This means that you may be able to fulfil some or all of the educational prerequisites using your work experience or other experiences in the same or a closely related field.

Therefore, we can find out how many tablespoons of sugar she needs by dividing ⅔ by ⅓.

⅔ ÷ ⅓ = 2

So Miss Anna needs 2 tablespoons of sugar to make peanut biscuits.

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The p-value for this test is 0.012, which is the probability of observing a sample mean as extreme as 380 (or more extreme) if the null hypothesis were true.

If the significance level of the test was α = 0.05, for example, we would reject the null hypothesis since the p-value (0.012) is less than the significance level.

To find the p-value for this test, we first need to determine the appropriate test statistic. Since we do not know the population standard deviation, we will use a t-test. The test statistic is calculated as:

t = (X - μ) / (s / √n)

Where X is the sample mean, μ is the null hypothesis population mean, s is the sample standard deviation, and n is the sample size.

In this case, the null hypothesis might be that μ = 400 (for example, if we were testing whether the mean weight of a certain type of fruit was 400 grams). Using the given sample information, we can calculate the t statistic as:

t = (380 - 400) / (39 / √18) = -2.82

Next, we need to find the corresponding p-value from the t-distribution table. Looking at the table with 17 degrees of freedom (since n - 1 = 18 - 1 = 17), we find that the p-value for a two-tailed test with a t-value of -2.82 is approximately 0.012.

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The scale factor used. in the dilation is 1/3

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

The scale factor is calculated as

Scale factor  = A'/A

substitute the known values in the above equation, so, we have the following representation

Scale factor  = (-1, -1)'/(-3, -3)

Evaluate

Scale factor  = 1/3

Hence, the scale factor  = 1/3

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Answer:

$66.24

Step-by-step explanation:

The area of Vince's porch is:

8 feet x 12 feet = 96 square feet

To find the cost of the stain, we need to multiply the area of the porch by the cost per square foot:

96 square feet x $0.69 per square foot = $66.24

So it will cost $66.24 to buy enough stain for the whole porch.

Answer:

The slope of the line is -1/4. To find the slope of the line, we can use the formula m = (y2 - y1)/(x2 - x1). In this case, y2 = 2, y1 = 3, x2 = 4, and x1 = 0. Plugging these values into the formula gives us m = (2 - 3)/(4 - 0) = -1/4.

The number of middle school students prefer the Documentaries television genre is108.

To get that, we need to multiply the total number of students by the correspondent percentage (in decimal form).

We know that there are 450 students, and 24%  (just add the other percentages, and 24% is the amount missing to reach 100%) like the documentaries.

That percentage in decimal form is 24%/100% = 0.24

Then the estimation will be:

450*0.24 = 108

So that is the correct answer.

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Brian deposited $9,808 into a savings account that compounds interest on a daily basis, at a rate of 3.78%. If we want to find out how much interest he will earn after 12 years, we can use the formula:

A = P(1 + r/n)^(nt)

where A is the amount of money after t years, P is the principal amount (which is $9,808 in this case), r is the annual interest rate (3.78% in this case), n is the number of times the interest is compounded per year (which is 365 since it compounds daily), and t is the number of years (which is 12).

So, plugging in the values we get:

A = $9,808(1 + 0.0378/365)^(365*12)

A = $9,808(1.000103972)^4380

A = $9,808(1.496812899)

A = $14,682.54

Therefore, the interest Brian will earn after 12 years is $14,682.54 - $9,808 = $4,874.54. When we round this answer to the hundredths place, we get $4,874.54.

To get a result of 4 on the numerical expression, Barry added 4 to the expression on the number line. So, the correct answer is C).

The expression involves adding up the values at different points on the number line. We can see that the value at the point labeled "x" is the missing value that needs to be found.

By adding up the values at each point, we get the following equation

-5 + (-3) + x - (-7) = 1

Simplifying this equation gives

-5 - 3 + x + 7 = 1

Simplifying further

-x = -4

Solving for x, we get

x = 4

Therefore, the value of x that Barry added to the expression on the number line to get a result of 4 is 4. So, the correct option is C).

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--The given question is incomplete, the complete question is given

" Barry used a number line to simplify a numerical expression on a math test. Which number did Barry add to get a result of 4 on the numerical expression he simplified? A –14, B −6, C 4, D 14 "--

The 95% confidence interval estimate for the population proportion of car deals that used 0% financing is (0.1612, 0.2308). So, the correct option is (b).

To construct a confidence interval estimate for the population proportion of car deals that used 0% financing, we can use the formula

CI = p ± z√((p(1-p))/n)

where

p = sample proportion = 98/500 = 0.196

n = sample size = 500

z = z-score for the desired level of confidence, which is 95% in this case. From a standard normal distribution table, the z-score corresponding to 95% confidence level is approximately 1.96.

Substituting the values, we get

CI = 0.196 ± 1.96√((0.196(1-0.196))/500)

= (0.1612, 0.2308)

Therefore, the 95% confidence interval estimate is (0.1612, 0.2308).

The correct answer is (b).

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The height of the cone is 4cm

The parameters given in the question are

volume= 36

radius= 3

The formula for calculating the height of a cone is

height= 3(v/πr²)

= 3(36/3.14×3²)

= 3(36/28.26)

= 3(1.273)

= 3.8

⇒4

Hence the height of the cone is 4 cm

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Answer: Euclid

Step-by-step explanation:

Answer:  4

Which geometer developed the deductive reasoning method for geometric proofs that is used today?

1.  Rene Descartes

2. Pythagoras

3. Girard Desargues

4. Euclid

Deductive reasoning, unlike inductive reasoning, is a valid form of proof.  Euclid using his definitions, common notions and postulates as an axiomatic system, was able to produce deductive proofs of a number of important geometric propositions.

Step-by-step explanation:

Answer:

Step-by-step explanation:

I haven't answered because I'm thrown off by (x-1) in exponent but typically the ratio is the base.

The exponent is base with exponent (here  not sure if it's from parent or with(x-1 ) depends on professor.

and y int comes from plugging in x=0

       Exponential Function            Ratio          y-int

A          [tex]3^{x-1}[/tex]                                         3             -2/3

B           [tex]2^{x-1}[/tex]                                        2            45/2

C        [tex].1^{x-1}[/tex]                                        .1 or 1/10       12340

D      [tex](1/2)^{x-1}[/tex]                                  1/2                     -10

I'm positive about y-int and pretty sure about ratio and iffy about ex. function.  

Hope this helps.

Answer: $1.74 worth of coins

Step-by-step explanation:

Let's say Tom throws x amount of money in coins on the table. Then Joe throws twice as much, which is 2x.

The total value of coins on the table is $5.22, so we can write an equation:

x + 2x = 5.22

Simplifying the equation, we get:

3x = 5.22

Dividing both sides by 3, we get:

x = 1.74

Therefore, Tom threw $1.74 worth of coins on the table.

Keisha sold 48 gallons of basic paint and 92 gallons of premium paint last weekend.

Let's denote the number of premium paint gallons sold by "x" and the number of standard paint gallons sold by "y".

According to the problem statement, we have:

[tex]x = 2y - 4[/tex] (the number of standard paint gallons sold was four less than twice as many premium gallons sold)

The total sales revenue from paint sales can be expressed as:

[tex]40.5x + 24.5y = 4914[/tex]

We can substitute x in the second equation with 2y - 4:

40.5(2y - 4) + 24.5y = 4914

Simplifying and solving for y, we get:

[tex]81y - 162 + 24.5y = 4914\\105.5y = 5076\\y = 48[/tex]

Substituting y in the equation [tex]x = 2y - 4[/tex], we get:

[tex]x = 2(48) - 4\\x = 92[/tex]

Therefore, last weekend, Keisha sold 48 gallons of normal paint and 92 gallons of premium paint.

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g(x) is a translation of f(x), and it can be written as:

g(x) = f(x + 2)

So f(x) is the graphed function and g(x) is the one in the table. We can see that the slopes of both functions are 2, so there is no change in the slope nor any type of reflection.

This means that we have a translation.

Now, comparing values:

f(0) = 1   and g(0) =5

f(1) = 3   and g(1) = 7

and so on.

in any of the values we can see that g(x) is 4 units above f(x), then there are two possible transformations:

g(x) = f(x) + 4

g(x) = f(x + 2)

(The +2 in the argument is equivalent because of the slope of 2, when we take that product we will get a 4)

Thus the correct option is the second one.

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The transformations are matched as follows

f(x) = eˣ to the graph of g (x) = [tex]e^{x + 5} + 1[/tex]

f(x) = eˣ to the graph of g(x ) = -eˣ - 4

f(x) = eˣ to the graph of g (x) = [tex]e^{x + 5} + 1[/tex]

f(x) = eˣ to the graph of g(x ) = -eˣ - 4

Translation transformation refers to the movement of an object or figure in a straight line without rotation or distortion in this transformation all points of an object or shape move parallel and in the same direction

The negative sign in g(x) = -eˣ - 4 lead to reflection while the -4 is a translation 4 units downwards.

For the graph of g (x) = [tex]e^{x + 5} + 1[/tex]

The +1 represents a vertical shift up by 1 unit and Horizontal shift left is represented by +5

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Putting it all together, we get:

A:

[-3 0 0]

[ 0 1 0]

[ 0 0 -1]

which is an orthogonal matrix with the first row being a multiple of (3, 3, 0).

An orthogonal matrix is a square matrix whose columns and rows are orthonormal vectors, i.e., each column and row has unit length and is orthogonal to the other columns and rows.

Let's start by finding a vector that is orthogonal to (3, 3, 0). We can take the cross product of (3, 3, 0) and (0, 0, 1) to get such a vector:

(3, 3, 0) x (0, 0, 1) = (3*(-1), 3*(0), 3*(0)) = (-3, 0, 0)

Note that this vector has length 3, so we can divide it by 3 to get a unit vector:

(-3/3, 0/3, 0/3) = (-1, 0, 0)

So, the first row of the orthogonal matrix A can be (-3, 0, 0) or a multiple of it. For simplicity, we'll take it to be (-3, 0, 0).

To find the remaining two rows, we need to find two more orthonormal vectors that are orthogonal to each other and to (-3, 0, 0). One way to do this is to use the Gram-Schmidt process.

Let's start with the vector (0, 1, 0). We subtract its projection onto (-3, 0, 0) to get a vector that is orthogonal to (-3, 0, 0):

v1 = (0, 1, 0) - ((0, 1, 0) dot (-3, 0, 0)) / ||(-3, 0, 0)||^2 * (-3, 0, 0)

= (0, 1, 0) - 0 / 9 * (-3, 0, 0)

= (0, 1, 0)

We can then normalize this vector to get a unit vector:

v1' = (0, 1, 0) / ||(0, 1, 0)|| = (0, 1, 0)

So, the second row of the orthogonal matrix A is (0, 1, 0).

To find the third row, we take the cross product of (-3, 0, 0) and (0, 1, 0) to get a vector that is orthogonal to both:

(-3, 0, 0) x (0, 1, 0) = (0, 0, -3)

We normalize this vector to get a unit vector:

v2' = (0, 0, -3) / ||(0, 0, -3)|| = (0, 0, -1)

So, the third row of the orthogonal matrix A is (0, 0, -1).

Putting it all together, we get:

A:

[-3 0 0]

[ 0 1 0]

[ 0 0 -1]

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The proof of trigonometric identity (sin(x) + tan(x))/sin(x) = 1 +secx is given below.

The given trigonometric identity is,

(sin(x) + tan(x))/sin(x).

We know that tan(x) = sin(x)/cos(x), so we can substitute that in:

sin(x)/ sin(x) + sin(x)/cos(x) / sin(x)

We can simplify the fraction in the numerator:

sin(x)/ sin(x) + sin(x)/sin(x)cos(x)

We know that sin(x)/sin(x) = 1, so we can simplify further:

1+ 1/cos(x)

We know that 1/cos(x) = sec(x), so we can substitute that in:

1 + sec(x).

Now we have the same expression as the right-hand side of the identity, so we have proven that:

sin(x) + tan(x)/sin(x) = 1 + sec(x)

Therefore, (sin(x) + tan(x))/sin(x) = 1 +secx.

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Answer:

Step-by-step explanation:

The correct answer is:

The theoretical probability of pulling a brown marble from the bag is 10/40 or 1/4, which is equivalent to 25%. This is because there are 10 brown marbles out of 40 total marbles in the bag.

The experimental probability of pulling a brown marble is 13/40 or 0.325, which is equivalent to 32.5%. This is because the student pulled a brown marble 13 times out of 40 total trials.

Therefore, the correct answer is: The theoretical probability, P(brown), is 25%, and the experimental probability is 32.5%.

Answer:

720.33 square inches.

Step-by-step explanation:

To find the amount of leather needed to create the travel case, you need to find the surface area of the cylinder. The surface area of a cylinder is given by the formula:

SA=2πr2+2πrh

where r is the radius of the base and h is the height of the cylinder. In this case, the radius is half of the diameter, so r = 17/2 = 8.5 inches. The height is given as 5 inches. Using π = 3.14, we can plug in these values and get:

SA=2×3.14×8.52+2×3.14×8.5×5

SA=452.38+267.95

SA=720.33

Therefore, the amount of leather needed is approximately 720.33 square inches. The closest answer is C. 720.63 square inches.

Answer:

720.63 square inches

To find the surface area of the cylindrical travel case, we need to add the areas of the two circular bases and the lateral surface area.

The diameter of the circular bases is given as 17 inches, so the radius is 17/2 = 8.5 inches. Using the formula for the area of a circle, we can find the area of one base:

Area of one base = πr^2 = 3.14 x 8.5^2 = 226.96 square inches

Since there are two circular bases, the total area of both bases is:

Total area of both bases = 2 x 226.96 = 453.92 square inches

The lateral surface area is a rectangle with height 5 inches and length equal to the circumference of the circular base. We can find the circumference using the formula:

Circumference = 2πr = 2 x 3.14 x 8.5 = 53.38 inches

So, the lateral surface area is:

Lateral surface area = height x circumference = 5 x 53.38 = 266.9 square inches

Therefore, the total surface area of the cylindrical travel case is:

Total surface area = 453.92 + 266.9 = 720.82 square inches (rounded to two decimal places)

So, the answer is approximately 720.63 square inches (rounded to two decimal places).

Step-by-step explanation:

we know the area A = B

10(6 + x) = A

5(15.5 + x) = B

A = B

10(6 + x) = 5(15.5 + x)

solve for x to get

x = 3.5

Add up to get the perimeter is 80

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Step-by-step explanation:

3^x eventually gets larger......it has exponential growth....the other is only linear growth

If the area code must have a 0 or1 for the second digit, and neither the area code nor the seven-digit number can start with 0 or 1, 1 280 000 000 different ways are possible.

Therefore option B is correct.

In this scenario we apply our  knowledge of probability to find the phone number, so:

We can establish the following facts:

Therefore, if we calculate the possibilities of occurrence, we have:

8 times 2 times 10 times 8 times 10 times 10 times 10 times 10 times 10 times 10 = 1,280,000,000

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