Raj takes a taxi to the airport. He expects the taxi to travel at an average speed of 50 mph.
The distance from Raj's house to the airport is 60 miles.
If Raj's taxi actually travels at an average speed of 40 mph, how many more minutes does the journey take than expected?

The solution to the inequality is all values of x less than 5. We can write the solution set using interval notation as (-∞, 5).

To solve the inequality -5x - 3 + 2x > -18, we need to isolate the variable x on one side of the inequality sign.

Starting with the given inequality:

-5x - 3 + 2x > -18

Simplifying the left-hand side by combining the like terms:

-3x - 3 > -18

Adding 3 to both sides:

-3x > -15

Dividing both sides by -3, and reversing the inequality sign since we are dividing by a negative number:

x < 5

Therefore, the solution to the inequality is all values of x less than 5. We can write the solution set using interval notation as (-∞, 5).

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Answer:

its 30 or 24

Step-by-step explanation:

but its most likely 30

Answer: y = 1x+4

the related between the x and y is x plus one and y plus 4

Step-by-step explanation:

Answer:

3.1 hrs  painting together

Step-by-step explanation:

Lucia rate = 1 room/ 5 hr

Marie rate = 1 room/8hr

now combine the rates

1 room / ( 1/5 + 1/8) = 3.077 hrs

Answer:

3 Feet

Step-by-step explanation:

The reason why it is 3 Feet is that 22 - 19 = 3. (Another anwser is 19 + 3 = 22)

To minimize the amount of tin used, the height of the can must be 4 inches (option D).

The volume of a cylindrical tin can is given by the formula V = πr²h, where V is the volume, r is the radius, and h is the height. To minimize the amount of tin used, we need to minimize the surface area, which is given by the formula A = 2πrh + 2πr².

Given the volume is 16π cubic inches, we have:

16π = πr²h

Now, we can find the relationship between r and h:

h = 16/r²

Now, substitute this into the surface area formula:

A = 2πr(16/r²) + 2πr²
A = 32π/r + 2πr²

To minimize the surface area, we can take the derivative with respect to r and set it to 0:

dA/dr = -32π/r² + 4πr

0 = -32π/r² + 4πr

Solving for r:

r³ = 8
r = 2 (since r > 0)

Now, substituting r back into the relationship between r and h:

h = 16/(2²)
h = 16/4
h = 4

Therefore, the height of the can must be 4 inches (option D) to minimize the amount of tin used.

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Given the following question:

Your exact solutions are...

In the given question function given is \(F(z)=1+3z^{-1} +4z^{-2}\) and by performing Z transform we get sampled time domain as f(n)=1 for all values of n          

                                                                                                                        In the given question function given is \(F(z)=1+3z^{-1} +4z^{-2}\) and by performing Z transform we get sampled time domain as f(n)=1 for all values of n            

In the given question function given is \(F(z)=1+3z^{-1} +4z^{-2}\) and by performing Z transform we get sampled time domain as f(n)=1 for all values of n                                                                                                                                                                        we need to perform the inverse Z-transform. The inverse Z-transform converts a function in the Z-domain back into the time domain.

The general form of the inverse Z-transform is given by:

f(n)= \(\frac{1}{2\pi j}\) ∮ \(_{C}\) \(F(z)z^{n-1} dz\)

​ where

F(z) is the function in the Z-domain, f(n) is the corresponding time-domain sequence, j is the imaginary unit, and ∮\(_{c}\)

​represents integration around a closed path in the Z-plane.

In this case, the function F(z) is a rational function, and we can find its inverse Z -transform using partial fraction decomposition. Let's find the inverse Z-transform step by step:

Step 1: Express F(z) in partial fraction form.

\(F(z)=\frac{1}{z^2} + \frac{3}{z} +4\)

Step 2: Find the roots of the denominator The roots of \(z^{2} =0\) and

z=0 (a double pole at the origin).

Step 3: Perform partial fraction decomposition.

We can write \(F(z)=\frac{A}{z} +\frac{B}{z^2} ​\)

​Multiplying through by \(z^{2}\) to clear the fractions we get,\(1+3z^{-1} +4z^{-2} = A+Bz^{-1}\)                                                                                                        Comparing coefficients, we get:

A=1

B=4

Step4: Apply the inverse Z transform for each term

Inverse Z transform for A/z is \(a^{n}\), where a is the root of corresponding term in the denominator. In this case a=0, so the inverse Z transform of A/z=1

The inverse Z transform of \(\frac{B}{z^2}\) is n.\(a^{n}\), where a is the root of the corresponding term in denominator. In this case a=0. So the inverse Z transform of \(\frac{B}{z^2}\) is n.\(a^{n}\)=0

therefore the time domain of function f(z) is

f(n)=1+0=1

So the sampled time domain representation of the function F(z)=\(1+3z^{-1} +4z^{-2}\) is f(n)=1 for all the values of n

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Answer:

Ex:

after 7 years you will have: $3074.68

Step-by-step explanation:

$2500 × 1.037 = $2500 × 1.2299 = $3074.68

Answer:

14.4

Step-by-step explanation:

Hope this helps you :)

Answer:

72/5 = 14.4

Step-by-step explanation:

In linear equation, 15.2% did the total number of students on the honor roll decrease.

What in mathematics is a linear equation?

50 × 24% = 12

50 × 14%= 7

12+ 7 = 19

50+75 = 125

19 ÷125= 15.2%

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a and g i think, hope this helps

Answer:

t = 0.06c

Step-by-step explanation:

Given the following :

Percentage sales tax on items = 6%

Cost of item = c

Amount of sales tax on item = t

Amount of sales tax is the product of the sales tax percentage and the cost of item purchased

Hence, Amount of sales tax;

t = 6% × cost of item (c)

t = 0.06 × c

t = 0.06c

Answer:

3cm

Step-by-step explanation:

those double hashes on those 5 sides mean they are equal. so essentially you have 5 sides that measure 3/10cm and one side that measures 1 1/2cm.

3/10 * 5 = 15/10 = 1 1/2cm

1 1/2cm + 1 1/2cm = 3cm

Answer:

d.

Step-by-step explanation:

Answer:

option c I guess - "It increases exponentially "

Answer:

30 is answer bro

Step-by-step explanation:

hope it wI'll help u

Sorry dude, diagram not visible, send a clear pic so I will help uh.

The  line with a slope of –5 that passes through the points (7,–2) and (8,q) has q as -7.

The equation of a line can be described as follows:

y = mx + b

where

Therefore, the line passes through  (7, –2) and (8, q) with a slope of - 5.

Hence, let's find q.

y = - 5x + b

Let's find y-intercept

-2 = -5(7) + b

b = -2  + 35

b = 33

Therefore,

y = -5x + 33

Hence, let's find q.

y = -5(8) + 33

q = -40 + 33

q = -7

Therefore, q = - 7

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Answer: C

Step-by-step explanation:

The triangle in the picture is an equilateral triangle. We know this is true because all sides are equal, as denoted by the tick marks. In equilateral triangles, each angle is 60° because when you add all the angles, you get 180°.

4x+8=60        [subtract both sides by 8]

4x=52            [divide both sides by 4]

x=13

Now, we know that C is the correct answer.

The next crow observed will be black is not supported by the premises in any meaningful way. The premises do not guarantee the outcome of the next observation.  Argument B is the stronger argument.

Argument A is an example of an inductive argument, as it generalizes from a limited sample to make a broader claim about the entire population. This argument form is called induction and can be evaluated on its strength.

Argument B is a deductive argument, as it uses a conditional premise to reach a definite conclusion. In this form of argument, the conclusion necessarily follows from the premises. The strength of a deductive argument depends on the logical structure of the premises and conclusion.

The better argument of the two is argument B. Because in deductive arguments, the conclusion necessarily follows from the premises if the premises are true.

And this argument, the premises state that if 90% of observed crows are black, then the next crow observed will be black.

Additionally, it is also claimed that 90% of observed crows are black. Therefore, it can be logically deduced that the next crow observed will be black

The argument in A, however, is an inductive argument, where the conclusion is not necessarily true even if the premises are true. Even if 90% of observed crows are black, it does not necessarily follow that 90% of all crows are black.

argument B is the stronger argument.

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Answer:

If r=0, there is absolutely no relationship between the two variables.

Step-by-step explanation:

Answer:

1. multiplication

2. division

3. bracket

4. division

5. bracket

6. division

The radius of the cone is 783.84/√h

A cone is the surface traced by a moving straight line (the generatrix) that always passes through a fixed point (the vertex).

Volume is defined as the space occupied within the boundaries of an object in three-dimensional space.

The volume of a cone is expressed as;

V = 1/3πr²h

643072 × 3 = 3.14 × r²h

r²h = 614400

r² = 614400/h

r = 783.84/√h

therefore the radius of the cone is 783.84/√h

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Answer:

24+56 is equivalent to 80.

The equation for BC is Y= -4/5(x + 1).

The equation for BC is Y= -4/5(x + 1), which is in slope-intercept form. This means that the slope of BC is -4/5, and the y-intercept is -4/5. The slope-intercept form of a linear equation is y=mx+b, where m is the slope and b is the y-intercept.

To find the equation for BC, we can use the point-slope form (y-y1=m(x-x1)) and plug in the coordinates of point B (-1,1) and the slope (-4/5). After simplifying, we get the equation Y= -4/5(x + 1). This equation represents the line that passes through point B with a slope of -4/5.

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Answer:

17.92

Step-by-step explanation:

The main answer is that the dimensions of the partner's scale drawing with a scale factor of 1:16 are approximately 1.125 inches long and 0.625 inches wide. Option A is the correct answer.

To find the dimensions of the partner's scale drawing with a scale factor of 1:16, we need to scale down the dimensions of the original drawing (1:8 scale).

If the original drawing is 9 inches long, dividing it by the scale factor of 8 gives us the length of the partner's drawing: 9 inches / 8 = 1.125 inches.

Similarly, if the original drawing is 5 inches wide, dividing it by the scale factor of 8 gives us the width of the partner's drawing: 5 inches / 8 = 0.625 inches.

Therefore, the dimensions of the partner's scale drawing are approximately 1.125 inches long and 0.625 inches wide, which corresponds to option A: The length is 4.5 inches and the width is 2.5 inches.

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The question is -

A gardener made a scale drawing of a lawn with a scale factor of 1:8. The dimensions of his drawing are 9 inches long by 5 inches wide. His partner plans to make another scale drawing of the lawn, but with a scale factor of 1:16. What are the dimensions of his scale drawing?

A. The length is 4.5 inches and the width is 2.5 inches.

B. The length is 10 inches and the width is 18 inches.

C. The length is 2.5 inches and the width is 4.5 inches.

D. The length is 18 inches and the width is 10 inches.

Given info:

Compound Interest = Rs.1290

Rate of Interest = 15% p.a

Time = 2 years

\( \dag{\underline{\boxed{\sf{C.I = P \bigg(1 + \dfrac{R}{100} \bigg)^{n} - 1}}}}\)

Where

C.I = Compound Interest

P = Principle

R = Rate of Interest

N = Time

\(\textsf{ \underline{Solution-}}\\\)

Here

C.I = Rs.1290

R = 15%

N = 2 years

Principle = ?

Now,Calculating the sum (Principle) borrowed by Rachna

\( \quad{: \implies{\sf{C.I = \Bigg[P \bigg(1 + \dfrac{R}{100} \bigg)^{n} - 1 \Bigg]}}}\)

Substituting the given values

\(\quad{: \implies{\sf{1290 = \Bigg[P \bigg(1 + \dfrac{15}{100} \bigg)^{2} - 1 \Bigg]}}}\)

\(\quad{: \implies{\sf{1290 = \Bigg[P \bigg(\dfrac{(1 \times 100) + 15}{100} \bigg)^{2} - 1 \Bigg]}}}\)

\(\quad{: \implies{\sf{1290 = \Bigg[P \bigg(\dfrac{115}{100} \bigg)^{2} - 1 \Bigg]}}}\)

\(\quad{: \implies{\sf{1290 = \Bigg[P \bigg(\dfrac{115}{100} \times \dfrac{115}{100} \bigg) - 1 \Bigg]}}}\)

\(\quad{: \implies{\sf{1290 = \Bigg[P \bigg(\dfrac{13225}{10000} \bigg) - 1 \Bigg]}}}\)

\(\quad{: \implies{\sf{1290 = \Bigg[P \bigg( \cancel{\dfrac{13225}{10000}} \bigg) - 1 \Bigg]}}}\)

\(\quad{: \implies{\sf{1290 = \Bigg[P \bigg({1.3225 - 1} \bigg) \Bigg]}}}\)

\(\quad{: \implies{\sf{1290 = P \times {0.3225}}}}\)

\(\quad{: \implies{\sf{\dfrac{1290}{0.3225} = P}}}\)

\(\quad{: \implies{\sf{\dfrac{1290 \times 1000}{0.3225 \times 1000} = P}}}\)

\(\quad{: \implies{\sf{\dfrac{12900000}{3225} = P}}}\)

\(\quad{: \implies{\sf{\cancel{\dfrac{12900000}{3225}} = P}}}\)

\(\quad{: \implies{\sf{Rs.4000 = P}}}\)

\(\quad{\dag{\underline{\boxed{\tt{\blue{Principle} = \purple{Rs.4000 }}}}}}\)

\(\begin{gathered}\end{gathered}\)

Hence,

The sum (Principle) is Rs.4000.