74. REAL-WORLD APPLICATIONS
A car rental company offers two plans for renting a car. Plan A: $30 per day and $0.18 per mile Plan B: $50 per day with free unlimited mileage How many miles would you need to drive for plan B to save you money?

The angle for which the sine value is 0.6691 is found to be 42°.

What is the sine value?

A trigonometric function called sin x, where x is the angle under discussion stands for the sine of an angle. The sine function is the proportion between the perpendicular and hypotenuse of a right-angled triangle. In other words, the hypotenuse and its value change as the angle changes, and it is the ratio of the side opposite to the angle under discussion. In the study of physics, sound and light waves are represented by the sine function.

When the angle between a right-angled triangle's base and hypotenuse changes, the sine's value changes.

[tex]sin^{-1}(0.6691)[/tex]=41.99°≈42°

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Answer: a≈6,1.

Step-by-step explanation:

                                 The sine theorem states:

                                [tex]\boxed {\frac{a}{sinA^0} =\frac{b}{sinB^0}= \frac{c}{sinC^0} }[/tex],             ⇒

[tex]a=\frac{c*sinA^0}{sinC^0}[/tex]

m∡A=180°-(m∡B°+m∡C°)

=180°-(68°+76°)

=180°-144°

=36°.           ⇒

[tex]a=\frac{c*sin36^0}{sin76^0}\\ =\frac{10*sin36^0}{sin76^0} \\\approx6,1.[/tex]

Good luck an' have a nice day!

Probability is the ratio of the desired outcomes to all possible outcomes.

If there are no desired outcomes, the ratio is 0 over all possible outcomes, thus 0.

If the event is all possible outcomes, the ratio is all possible outcomes over all possible outcomes, thus 1.

Probability can never be below zero or negative because desired outcomes can never be negative. If an event is impossible that means there are no desired outcomes meaning that probability is zero, thus couldn't fall below

Probability can never exceed 1 as desired outcomes can never be greater than total outcomes.

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Answer:

A , B, D

Step-by-step explanation:

YX is the segment joining points Y and X and is defined (A)

∠ XYZ is the angle between XY and YZ and is defined (B)

∠ YXZ is the angle between YX and XZ

However there is no segment joining XZ ← not defined

YW is the segment joining points Y and W and is defined (D)

Answer:

288π

Step-by-step explanation:

The volume of a sphere can be evaluated by using the following formula:

[tex]A=\frac{4}{3}\pi r^{3}[/tex]

We are given that the radius is 6, so we can plug into the formula to solve:

[tex]A=\frac{4}{3}\pi*6^{3} =\frac{4}{3}*216*\pi =288\pi[/tex] (216/3 is 72, and 72*4 is 288)

Therefore, the volume is exactly 288π. The approximate answer, if you let π be 3.14 and evaluate it out, is around 904.78

It depends if you mean

[tex]f(x) = \sin(x^2+2x-1)^2 = \sin^2(x^2+2x-1)[/tex]

i.e. the sine part is getting squared, or

[tex]f(x) = \sin(x^2+2x-1)^2 = \sin\left((x^2+2x-1)^2\right)[/tex]

i.e. the argument to sine is getting squared. I'll assume the first case, since it's fairly common convention to write [tex]g(x)^2 = \bigg(g(x)\bigg)^2[/tex].

Now if

[tex]f(x) = \sin^2(x^2+2x-1)[/tex]

• by the power and chain rules we have

[tex]f'(x) = 2 \sin(x^2 + 2x - 1) \left(\sin(x^2+2x-1)\right)'[/tex]

• using the derivative of sine and the chain rule again we have

[tex]f'(x) = 2 \sin(x^2+2x-1) \cos(x^2+2x-1) \left(x^2+2x-1\right)'[/tex]

• with the power and chain rules we have

[tex]f'(x) = 2 \sin(x^2+2x-1) \cos(x^2+2x-1) (2x+2)[/tex]

Recalling the double angle identity for sine,

[tex]\sin(2x) = \sin(x) \cos(x)[/tex]

we can rewrite the derivative among several other ways as

[tex]\boxed{f'(x) = (2x+2) \sin(2x^2+4x-2)}[/tex]

Answer:

[tex]\textsf{Perimeter}=x^2+10x-1[/tex]

Step-by-step explanation:

The perimeter of a two-dimensional shape is the distance all the way around the outside.

Given sides of a triangle:

Therefore, to find the perimeter of the triangle, sum the given sides:

[tex]\begin{aligned}\sf Perimeter & = (2x+3)+(8x-4)+x^2\\& = 2x+3+8x-4+x^2\\& = x^2 + 2x+8x+3-4\\& = x^2+10x-1\end{aligned}[/tex]

Perimeter=

The functions that have complex roots are b and d.

Complex roots are the imaginary root of polynomial functions. The complex roots are represented as α = a + ib, and β = c + id.

When the quadratic equation has a discriminant value less than zero will have imaginary roots.

Out of the given functions, a ,b, c, and d, the function with complex roots are b and d.

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Answer:

b &d is correct. i just took the test. :)

Step-by-step explanation:

The required equation of the line is y = 5

The equation of a perpendicular line to a line in point-slope form is expressed as:

y-y1 = -1/m(x-x1)

m is the slope

(x1, y1) is any point on the line

Determine the slope

Slope = -3-3/2-2

y = ∞

Since there is no slope, hence the equation of the line will be in the form y = b

where b is the y-coordinate of the point. Hence the required equation of the line is y = 5

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Answer:

$6.40

Step-by-step explanation:

let d be the cost of 1 doughnut and b the cost of 1 burger.

set up 2 equations and solve for b

9b + d = 31.3 → (1)

6b + 3d = 26.7 → (2)

multiplying (1) by - 3 and adding to (2) will eliminate d

- 27b - 3d = - 93.9 → (3)

add (2) and (3) term by term to eliminate d

- 21b + 0 = - 67.2

- 21b = - 67.2 ( divide both sides by - 21 )

b = 3.2

then

cost of 2 burgers = 2 × $3.20 = $6.40

The population of squirrels in the Louisiana forest growing monthly at a rate of 5% currently from 100, will be 182 after a year.

The final value of any quantity growing constantly at a particular rate is given as [tex]V = V_{0}e^{rt}[/tex] ,

where V is the final value, V₀ is the initial value, r is the rate of growth per time period, and t is the number of time periods.

The current population of squirrels (V₀) = 100.

The growth rate (r) = 5% per month.

The time period (t) = 1 year = 12 months.

Hence, the final population of squirrels (V), is given as:

[tex]V = V_{0}e^{rt}[/tex] ,

or, [tex]V = 100e^{(0.05*12)}[/tex] ,

or, [tex]V = 100e^{0.60}[/tex] ,

or, V = 100*1.822119,

or, V = 182.2119 ≈ 182.

Therefore, the population of squirrels in the Louisiana forest growing monthly at a rate of 5% currently from 100, will be 182 after a year.

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Answer:

Step-by-step explanation:

Can 10 people be divided into two groups with a ratio of 1 : 2?

Explain.

10 : 3 = 3.33

or 10 : 3 = 9 remaining 1

since it is not possible to divide a person into three parts, your answer is no

Answer:

The slope of the line representing the linear function f(x) is determined as [tex]$-\frac{1}{2}$[/tex]. The function f(x) is decreasing because the slope is less than zero, i.e., m<0.

Step-by-step explanation:

A linear function f(x) is given with two points, (2,3) and (0,4) lying on the line representing f(x).

It is asked to determine the slope of the line and state if the function is increasing or decreasing. of the value of the slope obtained.

Step 1 of 1

Determine the slope of the line.

The points as given in the question are (2,3) and (0,4). Now, the formula for the slope is given as

[tex]$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$[/tex]

So, substitute [tex]$4 \& 3$[/tex] for [tex]$y_{2}$[/tex] and [tex]$y_{1}$[/tex] respectively, and [tex]$0 \& 2$[/tex] for [tex]$x_{2}$[/tex] and [tex]$x_{1}$[/tex] respectively in the above formula. Then simplify to get the slope as follows,[tex]$m=\frac{4-3}{0-2}$\\ $m=\frac{1}{-2}$\\ $m=-\frac{1}{2}$[/tex]

The slope of the line is obtained as [tex]$-\frac{1}{2}$[/tex]. Now, as [tex]$-\frac{1}{2} < 0$[/tex], so the function f(x) is decreasing.

Answer:

4x + 3y = 12

Step-by-step explanation:

Answer:

4x + 3y = 12

Step-by-step explanation:

At x-intercept, y = 0.

∴ When we substitute y = 0 into the equation, x should equal 3.

• 1st equation:     3x + 4(0) = 12  ⇒  x = 4       ❌

• 2nd equation:  4x + 3(0) = 7    ⇒  x = 7/4    ❌

• 3rd equation:   3x + 4(0) = 7    ⇒  x = 7/3    ❌    

• 4th equation:   4x + 3(0) = 12   ⇒  x = 3       ✅

This means the 4th option is the correct one.

To check, we can replace x = 0 into the 4th equation to see if the y-intercept value comes out to be 4:

4(0) + 3y = 12    ⇒    y = 4     ✅

Mean (m) = 498

Standard deviation (σ) = 12

Sample size (n) = 86

The probability that the sample mean would differ from Population mean by less than 494.7 watts

P(m - s < Z < m + s)

P(498-494.7 < Z < 498+ 494.7)

Using the Z formula :

Zscore = (x - m) / (σ/√n)

x = 498 - 494.7 = 3.3 , x = 498 + 494.7 = 992.7

Z = (3.3 - 498) / (12/√86) = -383.48

P(Z < -383.48)

Z = (992.7 - 498 ) / (12/√86) = 383.48

P(Z<383.48)

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Explanation:

Refer to the graph below. It should be similar to what your teacher gave you, based off the description.

Since we're approaching 3 from the right side, this means we'll be working with the horizontal line portion. We could start at something like x = 3.2 and move closer to 3 by getting to x = 3.1 then x = 3.01 then x = 3.001 and so on. We never actually get to 3 itself.

As x gets closer to 3 from this direction, the y values are approaching 3 since every point on this horizontal line has the same y coordinate. Technically the y value is already at 3, but it's the same idea.

In terms of notation, we can write [tex]\displaystyle \lim_{x\to3^{+}}f(x) = 3[/tex]

The portion [tex]x \to 3^{+}[/tex] means we're approaching 3 from the positive side, aka the right hand side on the number line.

Answer:

The third one of the first question.

Polynomials are mathematical expressions involving variables raised with non-negative integers and coefficients. The polynomial is x³- 7x² - 6x + 72.

Polynomials are mathematical expressions involving variables raised with non-negative integers and coefficients(constants who are in multiplication with those variables) and constants with only operations of addition, subtraction, multiplication and non-negative exponentiation of variables involved.

The polynomial using the given information can be made as shown below.

Given the zeros of the polynomial are -3, 4, and 6.

P(x) = (x+3)(x-4)(x-6) = x³- 7x² - 6x + 72

To check the end behaviour of the function, the graph of the function can be plotted as shown in the below image.

Hence, the polynomial is x³- 7x² - 6x + 72.

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The $378.49 was earned on the investment if the principal amount of $3000 is invested for 3 years at 4% compounded semi-annually.

It is defined as the interest on the principal value or deposit and the interest which is gained on the principal value in the previous year.

We can calculate the compound interest using the below formula:

[tex]\rm A = P(1+\dfrac{r}{n})^{nt}[/tex]

Where A = Final amount

          P = Principal amount

          r  = annual rate of interest

          n = how many times interest is compounded per year

          t = How long the money is deposited or borrowed (in years)

Here,

P = $3000

r = 4% = 0.04

n = 2

t = 3 years

After plugging all the values in the formula:

[tex]\rm A = 3000(1+\dfrac{0.04}{2})^{2\times 3}[/tex]

After solving:

A = $3,378.49

I = A - P = 3,378.49 - 3000 = $378.49

Thus, the $378.49 was earned on the investment if the principal amount of $3000 is invested for 3 years at 4% compounded semi-annually.

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Answer:

Hence, 0.00000103 can be expressed as [tex]$1.03 \times 10^{-6}$[/tex].

Step-by-step explanation:

- Given 0.00000103

- Move the decimal point so that the factor is greater than or equal to 1 but less than 10 .

- Then count n and write no. as a product with a power of 10 .

Step 1 of 1

Consider 0.00000103,

1.03

Decimal has moved 6 places to right.

The power will be negative as the original no. is less than 1 .

[tex]$$\begin{array}{r}1.03 \times 10^{-6} \\0.00000103=1.03 \times 10^{-6}\end{array}$$[/tex]

The student product is 81936 greater than the correct product

The student was suppose to multiply 4552 by 157 but instead he multiplied 4552 by 175.

Therefore, let's find how much his product is greater than the correct product.

incorrect product = 4552 × 175 = 796600

Correct product = 4552 × 157 = 714664

Therefore,

difference = 796600 - 714664 = 81936

Therefore, his product is 81936 greater than the correct product.

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Answer:

  x ≈ 0.499

Step-by-step explanation:

The value of x can be found by undoing the operations done to it.

The operations done to the variable are ...

We undo these operations in reverse order:

  7e^(2x) + 10 = 29 . . . . given

  7e^(2x) = 19 . . . . . . . . . subtract 10

  e^(2x) = 19/7 . . . . . . . . . divide by 7

  2x = ln(19/7) . . . . . . . . take the natural logarithm

  x = (ln(19/7))/2 . . . . . . divide by 2

The rounded result is ...

  x ≈ 0.499

Answer:

$11.62

Step-by-step explanation:

2.54×3=$7.62

0.76+7.62=8.38

20-8.38=$11.62

Answer:

Step-by-step explanation:

Discussion

3 cappuccinos at 2.54 each     2.54 * 3 = 7.62

1 bottle of water at 0.76              0.76*1  =   .76     Add

Total                                                             8.38

Change = 20 - 8.38 = 11.62

Answer

She should receive 11.62 in change.

Answer:

it is B

Step-by-step explanation:

that is because j3jejejdudduiwjsj

The requried pilot can make at least one round trip before having to refuel. Hence, the correct answer is: A) 1

To determine how many round trips the pilot can make before having to refuel, we need to consider both the fuel capacity and the flight time limit.

Given:

Maximum fuel capacity = 5,300 gallons

Flight time limit before refueling = 400 minutes

Fuel required for one-way flight = 2,000 gallons

Flight time for one-way flight = 190 minutes

First, let's calculate the maximum number of one-way trips the pilot can make based on the fuel capacity:

Max one-way trips based on fuel capacity = Maximum fuel capacity / Fuel required for one-way trip

Max one-way trips = 5,300 gallons / 2,000 gallons = 2.65 trips

Since we cannot have a fraction of a trip, we need to consider the flight time limit.

The total flight time for a round trip is twice the one-way flight time: 2 * 190 minutes = 380 minutes.

The pilot can fly a round trip as long as the flight time for the round trip is within the flight time limit. In this case, the round-trip flight time of 380 minutes is less than the flight time limit of 400 minutes.

Therefore, the pilot can make at least one round trip before having to refuel. Hence, the correct answer is: A) 1

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The possible values of x be  4.8, 5.6 and 6.4.

The statement of equality between two expressions consisting of variables and/or numbers.

Given:

5x -4y = 24

when y=0

5x = 24

x = 4.8

when y=1,

5x= 28

x= 5.6

when y=2,

5x= 32

x= 6.4

Hence, the possible values of x is 4.8, 5.6 and 6.4.

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The ship traveled 80 miles in 4 hours while the submarine traveled 75 miles in 5 hours.

Based on the information provided, we can logically deduce that the ship is initially 80 miles away from its destination. Thus, f(x) would be equal to 0, if it traveled 80 miles and 0 miles away from its destination:

f(x) = 80 - 20x

0 = 80 - 20x

20x = 80

x = 80/20

x = 4 hours.

By critically observing the graph (see attachment) for the submarine's voyage, we can logically deduce the following:

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Answer:

Ends with r and has five or fewer letters

Step-by-step explanation:

Answer:

The answer is : B

Step-by-step explanation:

trust me I did it on edge 2022