100 POINTS AND BRAINLST

Comparing the √17 and 29/7 using <, > or = , we have √17 < 29/7.

Mathematical number comparison is the process or method of comparing two numbers to determine whether one is less, bigger, or equal to the other. The comparison symbols for numbers are "=", which stands for "equal to," "=", which stands for "greater than," and " ", which stands for "less than." Comparing amounts is a technique for figuring out how much to compare units in relation to a different standard or reference unit. A common reference point is necessary for two comparing units to be compared; otherwise, they cannot be compared.

Given,

Comparing the following using <, > or = ,

Numbers:

√17 and 29/7

For √17

Simplifying,

√17 = 4.123

For 29/7

29/7 = 4.14

√17 < 29/7

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Using implicit differentiation dy/dx = -(2x + y)/(x + 2y) and d2y/dx² = -2(x² - 3xy - y²)/(x + 2y)³.

Implicit differentiation is the process of differentiating an equation in which it is not easy or possible to express y explicitly in terms of x.

Given the equation x² + xy + y² = 5,

we can differentiate both sides with respect to x using the chain rule as follows:

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

Simplifying this equation yields:

(x + 2y)dy/dx = -(2x + y)

Hence, dy/dx = -(2x + y)/(x + 2y)

Next, we need to find d^2y/dx^2 by differentiating the expression for dy/dx obtained above with respect to x, using the quotient rule.

That is:

d/dx(dy/dx) = d/dx[-(2x + y)/(x + 2y)](x + 2y)d^2y/dx² - (2x + y)(d/dx(x + 2y))

= -(2x + y)(d/dx(x + 2y)) + (x + 2y)(d/dx(2x + y))

Simplifying this equation yields:

d2y/dx² = -2(x² - 3xy - y²)/(x + 2y)³

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The equation that models the taxi fare F as a function of the number of miles driven is F = 2.40 + 0.40m

An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario.

In this case, the Topology Taxi Company charges 2.40 for the first fifth of a mile and 0.40 for each additional fifth of a mile.

The function will be:

F = 2.40 + (0.40 × m)

F = 2.40 + 0.40m

where m = number of miles

F = taxi fare.

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Answer:

18

Step-by-step explanation:

As an example, the 78-mph speed limit in the United States is equivalent to the 130 km/h restriction in Germany.

How quick is that speed?

A connection with a speed of 100 Mbps or higher is considered fast internet. Broadband internet speed is defined by the federal communications regulator (FCC) as 25 Mbps for downloading and 3 Mbps for upload.

We can increase each number by 0.6 to convert overall speed limitations from kilometers per hour into miles per hour. Here is the revised table:

Country Speed Limit (km/h)  Speed Limit (mph)

Germany         130                    78

France             110                     66

Italy                 150                     90

Japan              100                      60

Australia          110                       66

United Kingdom 113              67.8

Hence, Because one kilometer is equivalent to 0.6 miles, it is evident that speed limits in the form of miles per hour were lower than those in kilometers per hour.

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Answer and Step-by-step explanation:

To find out how many more yards of red fabric Reuben used, we need to subtract the amount of yellow fabric from the amount of red fabric. Since the two fractions have different denominators, we need to find a common denominator before subtracting them. The least common multiple of 8 and 4 is 8, so we can rewrite both fractions with a denominator of 8:

7/8 - 1/4 = 7/8 - (1/4) * (2/2) = 7/8 - 2/8 = (7 - 2)/8 = 5/8

So, Reuben used 5/8 yards more red fabric than yellow fabric.

Question 1:

(a) The equation representing Elaine's total parking cost is:

C = x * t

(b) So the cost of parking for a full 24 hours would be 24 times the cost per hour.

Question 2:

The given system of equations is inconsistent and has no solution.

(a) To represent Elaine's total parking cost, C, in dollars for t hours, we need to know the cost per hour. Let's assume the cost per hour is $x.

(b) If Elaine wants to park her car for a full 24 hours, we can substitute t = 24 into the equation from part (a):

C = x * 24

Question 2:

To solve the linear system:

-x - 6y = 5

x + y = 10

We can use the elimination method.

Multiply the second equation by -1 to create opposites of the x terms:

-x - 6y = 5

-x - y = -10

Add the two equations together to eliminate the x term:

(-x - 6y) + (-x - y) = 5 + (-10)

-2x - 7y = -5

Now we have a new equation:

-2x - 7y = -5

To check the answer, we can substitute the values of x and y back into the original equations:

From the second equation:

x + y = 10

Substituting y = 3 into the equation:

x + 3 = 10

x = 10 - 3

x = 7

Checking the first equation:

-x - 6y = 5

Substituting x = 7 and y = 3:

-(7) - 6(3) = 5

-7 - 18 = 5

-25 = 5

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Answer: B.792

Step-by-step explanation:

Answer:

32 bags

Step-by-step explanation:

0.5 × 16 = 32

hope it helps

To prove that (secx+tanx)² = (cscx+1)/(cscx-1), we will start with the left-hand side (LHS) of the equation and simplify it step by step until it matches the right-hand side (RHS) of the equation.

LHS: (secx+tanx)²

Using the trigonometric identities secx = 1/cosx and tanx = sinx/cosx, we can rewrite the LHS as:

LHS: (1/cosx + sinx/cosx)²

Now, let's find a common denominator and simplify:

LHS: [(1+sinx)/cosx]²

Expanding the squared term, we get:

LHS: (1+sinx)² / cos²x

Next, we will simplify the denominator:

LHS: (1+sinx)² / (1 - sin²x)

Using the Pythagorean identity sin²x + cos²x = 1, we can replace 1 - sin²x with cos²x:

LHS: (1+sinx)² / cos²x

Now, let's simplify the numerator by expanding it:

LHS: (1+2sinx+sin²x) / cos²x

Next, we will simplify the denominator by using the reciprocal identity cos²x = 1/sin²x:

LHS: (1+2sinx+sin²x) / (1/sin²x)

Now, let's simplify further by multiplying the numerator and denominator by sin²x:

LHS: sin²x(1+2sinx+sin²x) / 1

Expanding the numerator, we get:

LHS: (sin²x + 2sin³x + sin⁴x) / 1

Now, let's simplify the numerator by factoring out sin²x:

LHS: sin²x(1 + 2sinx + sin²x) / 1

Using the fact that sin²x = 1 - cos²x, we can rewrite the numerator:

LHS: sin²x(1 + 2sinx + (1-cos²x)) / 1

Simplifying further, we get:

LHS: sin²x(2sinx + 2 - cos²x) / 1

Using the fact that cos²x = 1 - sin²x, we can rewrite the numerator again:

LHS: sin²x(2sinx + 2 - (1-sin²x)) / 1

Simplifying the numerator, we have:

LHS: sin²x(2sinx + 1 + sin²x) / 1

Now, let's simplify the numerator by expanding it:

LHS: (2sin³x + sin²x + sin²x) / 1

LHS: 2sin³x + 2sin²x / 1

Finally, combining like terms, we get:

LHS: 2sin²x(sin x + 1) / 1

Now, let's simplify the RHS of the equation and see if it matches the LHS:

RHS: (cscx+1) / (cscx-1)

Using the reciprocal identity cscx = 1/sinx, we can rewrite the RHS:

RHS: (1/sinx + 1) / (1/sinx - 1)

Multiplying the numerator and denominator by sinx to simplify, we get:

RHS: (1 + sinx) / (1 - sinx)

Now, we can see that the LHS and RHS are equal:

LHS: 2sin²x(sin x + 1) / 1

RHS: (1 + sinx) / (1 - sinx)

Therefore, we have proven that (secx+tanx)² = (cscx+1)/(cscx-1).

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The amount of sinking fund payment is $2028.06.

So, the correct answer is option A.

The fee a customer pays to a lender for borrowing cash over time, expressed as a percentage of the loan amount. The interest rate is the amount charged by the lender to the borrower above and beyond the principal amount. In terms of the receiver, a person who deposits money in any bank or financial institution obtains additional income due to the time value of money, which is referred to as depositor interest.

The basic interest formula is as follows: P x R x T = Interest. P denotes the principal sum.

Given, Amount=35000

Time=4 years

Interest rate=4% compounded quarterly

i=4/4%

i=1%

35000=(1+(1/100))ⁿ

35000=(101/100)ⁿ

35000=x(1-(101/100)¹⁶)/((1-(1/100)))

x=2028.0609

Therefore, The amount is $2028.06

So, option A is correct

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To make lines u and v parallel, the indicated angle must be 108°.

So, if two parallel lines n and m intersect, then all the angles generated in line m must be exactly the same as the angles generated in line n.

According to the second (and previously used) criterion, we must have:

When we solve that, we get:

Therefore, to make lines u and v parallel, the indicated angle must be 108°.

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\(f(x)=2(3)^{x+1} \\\\[-0.35em] ~\dotfill\\\\ f(2)=2(3)^{(2)+1}\implies f(2)=2(3)^3\implies f(2)=2(3^3) \\\\\\ f(2)=2(27)\implies f(2)=54\)

Answer:

troop number and activity preference or b

Step-by-step explanation:

Answer:

y = 3x + 17

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

here m = 3 , then

y = 3x + c ← is the partial equation

to find c substitute (- 5, 2) , that is x = - 5, y = 2 into the partial equation

2 = - 15 + c ⇒ c = 2 + 15 = 17

y = 3x + 17 ← equation of line

Answer:

$31.94

Step-by-step explanation:

29.99 x 0.065 = 1.95

29.99 + 1.95= 31.94 :)

Answer:

$31.94

Step-by-step explanation:

Answer:

Step-by-step explanation:

To write y as a function of x using the given functions, we can substitute the value of "a" in the first equation with the expression "-5x + 1" from the second equation.

Given:

y = -3a + 3

a = -5x + 1

Substituting the value of "a" in the first equation:

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

Now, let's simplify this expression:

y = 15x - 3 + 3

y = 15x

Therefore, y can be expressed as a function of x as:

y = 15x

The answer is A

sin0 = p/h = 7/25

cos0 = b/h = -24/25

Therefore , p = 7 , b = -24

tan0 = p/b = 7 / -24 = -7/24

The function f(-9) is the -x value, find where the line is in the -y direction at -x = -9. The line crosses -y = -3 at -x = -9.

In mathematics, a graph is a visual representation or diagram that shows facts or values in an ordered way. The relationships between two or more items are frequently represented by the points on a graph.

In discrete mathematics, a graph is made up of vertices—a collection of points—and edges—the lines connecting those vertices. In addition to linked and disconnected graphs, weighted graphs, bipartite graphs, directed and undirected graphs, and simple graphs, there are many other forms of graphs. A graph is a diagram that depicts the connections between two or more objects.

The function f(-9) is the -x value, find where the line is in the -y direction at -x = -9. The line crosses -y = -3 at -x = -9.

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Answer:

The Question is not Correct but answer is f 3 and g 3

Answer:

The null and alternative hypothesis are:

\(H_0: \mu_1-\mu_2=0\\\\H_a:\mu_1-\mu_2> 0\)

where μ1 is the population mean sales with compensation plan, and μ2 is the populatiojn mean sales without compensation plan.

A Type I error is made when a true null hypothesis is rejected. In this case, it would be concluded that the compensation plan increases sales, when in fact it does not (at least, not significantly).

The consequences of this error would be that the compensation plan would have evidence to be implemented in the company when in fact it will not bring the results it is expected to have.

Step-by-step explanation:

This hypothesis test will test the claim that the compensation plan increases the average sales per salesperson. This claim will be stated in the alternative hypothesis, and will state that, with the compensation plan, the sales are significantly higher than without the compensation plan.

The null hypothesis, that Steve wants to falsify, will state that the sales will not differ with or withour compensation plan.

We can write this hypothesis as:

\(H_0: \mu_1-\mu_2=0\\\\H_a:\mu_1-\mu_2> 0\)

where μ1 is the population mean sales with compensation plan, and μ2 is the populatiojn mean sales without compensation plan.

A Type I error is made when a true null hypothesis is rejected. In this case, it would be concluded that the compensation plan increases sales, when in fact it does not (at least, not significantly).

The consequences of this error would be that the compensation plan would have evidence to be implemented in the company when in fact it will not bring the results it is expected to have. The sales would be expected to increase due to this implementation, and they will not increase, at least, not for the compensation plan.

Option 3 yielded the most money after 10 years is 171.7

Option 1 yielded the most total money by the time you were 60 years old is 8,771.56

A solution of an equation is a value or set of values that satisfy the equation, meaning that when the value(s) is substituted for the variable(s) in the equation, both sides of the equation are equal.

Based on the given equations, Option 1 yielded the most money after 10 years, and Option 3 yielded the most total money by the time you were 60 years old.

After 10 years:

Option 1: 50×(1.09)¹⁰ - 30 =  88.36

Option 2: 50×(1.08)¹⁰ - 20 =  87.94

Option 3: 100×(1.07)¹⁰ - 25 =  171.71

Therefore, Option 3 yielded the most money after 10 years is 171.7

By the time you were 60 years old:

Option 1: 50×(1.09)⁶⁰ - 30 =  8,771.56

Option 2: 50×(1.08)⁶⁰ - 20 =  5,042.85

Option 3: 100×(1.07)⁶⁰ - 25 =  5,769.64

Therefore, Option 1 yielded the most total money by the time you were 60 years old is 8,771.56

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Answer:

f(x) = x³ - 4x + 6

f'(x) = 3x² - 4

a) f'(2) = 3(2²) - 4 = 12 - 4 = 8

6 = 8(2) + b

6 = 16 + b

b = -10

y = 8x - 10

b) 3x² - 4 = 0

3x² = 4, so x = ±2/√3 = ±(2/3)√3

= ±1.1547

f(-(2/3)√3) = 9.0792

f((2/3)√3) = 2.9208

c) 3x² - 4 = 8

3x² = 12

x² = 4, so x = ±2

f(-2) = (-2)³ - 4(-2) + 6 = -8 + 8 + 6 = 6

6 = -2(8) + b

6 = -16 + b

b = 22

y = 8x + 22

f(2) = 6

y = 8x - 10

The equation perpendicular to the tangent is y = -1/8x + 25/4

-The smallest slope on the curve is 2.92

The curve has the smallest slope at the point (1.15, 2.92)

The equations at tangent points are y = 8x + 16 and  y = 8x - 16

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

y = x³ - 4x + 6

Differentiate

So, we have

f'(x) = 3x² - 4

The point is (2, 6)

So, we have

f'(2) = 3(2)² - 4

f'(2) = 8

The slope of the perpendicular line is

Slope = -1/8

So, we have

y = -1/8(x - 2) + 6

y = -1/8x + 25/4

We have

f'(x) = 3x² - 4

Set to 0

3x² - 4 = 0

Solve for x

x = √[4/3]

x = 1.15

So, we have

Smallest slope = (√[4/3])³ - 4(√[4/3]) + 6

Smallest slope = 2.92

So, the smallest slope is 2.92 at (1.15, 2.92)

Here, we set f'(x) to 8

3x² - 4 = 8

Solve for x

x = ±2

Calculate y at x = ±2

y = (-2)³ - 4(-2) + 6 = 6: (-2, 0)

y = (2)³ - 4(2) + 6 = 6: (2, 0)

The equations at these points are

y = 8x + 16

y = 8x - 16

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Answer:

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

Steps should be self-explanatory. Happy to explain if anything is not clear.

Answer:

Step-by-step explanation:

1) 4v + 7 = 7, for v?

→ 4v + 7 = 7

→ 4v = 7 - 7

→ v = 0/4

→ [ v = 0 ]

2) 3(u + 4) = 27, for u?

→ 3(u + 4) = 27

→ 3u + 12 = 27

→ 3u = 27 - 12

→ u = 15/3

→ [ u = 5 ]

3) -20 = 10(h + 5), for h?

→ -20 = 10(h + 5)

→ 10h + 50 = -20

→ 10h = -20 - 50

→ h = -70/10

→ [ h = -7 ]

4) -10 = (n - 52)/5, for n?

→ -10 = (n - 52)/5

→ n - 52 = -10 × 5

→ n = -50 + 52

→ [ n = 2 ]

5) (48/x) - 3 = 3, for x?

→ (48/x) - 3 = 3

→ 48/x = 3 + 3

→ 6x = 48

→ x = 48/6

→ [ x = 8 ]

6) 8r = 2r + 42, for r?

→ 8r = 2r + 42

→ 8r - 2r = 42

→ r = 42/6

→ [ r = 7 ]

These are required values.

When 30 statuses are uploaded, there are approximately 7939 visitors to the website.

What is the variation?
variation refers to how much a set of numbers or variables differ from each other. It is a measure of the spread or dispersion of a dataset. Variation can be measured in various ways, such as range, variance, and standard deviation.

Let's use the formula for direct variation: V = kS³, where k is the constant of variation.

To find k, we can use the data given when 8 statuses were uploaded:

1500 = k(8³) => k = 1500/512 = 2.93 (rounded to two decimal places)

Now we can find the number of visitors when 30 statuses are uploaded:

V = 2.93(30³) = 7938.9 (rounded to one decimal place)

Therefore, when 30 statuses are uploaded, there are approximately 7939 visitors to the website.

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Answer:

I got you

Step-by-step explanation:

c-11=25

c=25+11

c=36

Answer:

D.  18,535

Step-by-step explanation:

See attached picture

Answer:

The rocket's maximum height will be 1424 feet.

It will reach that height in 4 seconds.

It will reach the ground  in 8 seconds.

Step-by-step explanation:

One easy way to find the peak is to find the derivative and solve for zero:

h(t) = -16t² + 128t + 1680

To find the derivative of each term in that format, you simply multiply the coefficient by the exponent, and reduce the exponent by one.  In the case of terms with no variable, they disappear.  That gives us:

h'(t) = -32t + 128

This derivative describes the rate of change of h with respect to t, so to find the peak, we simply need to solve it for zero:

0 = -32t + 128

32t = 128

t = 4

So the maximum height occurs when t = 4.  Let's plug it in to the original equation:

h(t) = -16t² + 128t + 1680

h(4) = -256 + 512 + 1680

h(4) = 1424

So the rocket's maxiumum height is 1424 feet.

And we've already answered the second question, it happens at 4 seconds.

Also, the amount of time going up will be the same as the amount of time going down, which means that it will reach the ground in twice that time, or 8 seconds.