While waiting for his car to be repaired, a man rents a car for $17 per day and 33 cents per mile. His insurance
company will pay up to $200 of the rental fee. If he needs the car for four days, how many miles of driving will his
policy cover?

Answer:

11th term

Step-by-step explanation:

\(\\(1).\\\\(1.7898)^{2x} = (1.7898)^6\\\\\implies \ln(1.7898)^{2x} = \ln(1.7898)^6\\\\\implies 2x \ln(1.7898) = 6 \ln(1.7898)\\\\\implies 2x =6\\\\\implies x = \dfrac 62 =3\\\\(3).\\\\2^{5x -6} = 4^{x+9}\\\\\implies 2^{5x -6} = (2^2)^{x+9}\\\\\implies 2^{5x-6} = 2^{2x+18}\\\\\implies \ln(2^{5x-6}) = \ln(2^{2x+18})\\\\\implies (5x -6) \ln 2 = (2x +18) \ln 2\\\\\implies 5x -6 = 2x +18\\\\\implies 5x -2x = 18 +6\\\\\implies 3x = 24\\\\\implies x = \dfrac{24}3 =8\)

Answer:1.2

Step-by-step explanation:

then,

x-4=6x-10

-5x=-6

x=1.2

The results of the logical expressions are

Logical expressions are expressions that have a result of true or false.

These results are generally classified as boolean values

We start by solving the first expression

Logic expression (3)

¬ q v p

The above expression uses the or operator

The rule of the or operator is that:

This means that the expression ¬ q v p evaluates to false if q is true and p is false; otherwise, it evaluates to true

Logic expression (4)

¬ p ∧ ¬ q

The above expression uses the and operator

The rule of the and operator is that:

This means that the expression ¬ p ∧ ¬ q evaluates to true if q is false and p is false; otherwise, it evaluates to false

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Answer:The results of the logical expressions are¬ q v p: false if q is true and p is false¬ p ∧ ¬ q: true if q is false and p is falseWhat are logical expressions?Logical expressions are expressions that have a result of true or false.These results are generally classified as boolean valuesHow to solve the logical expressions?We start by solving the first expressionLogic expression (3)¬ q v pThe above expression uses the or operatorThe rule of the or operator is that:It evaluates to true, if at least one of the terms is trueOtherwise, it is falseThis means that the expression ¬ q v p evaluates to false if q is true and p is false; otherwise, it evaluates to trueLogic expression (4)¬ p ∧ ¬ qThe above expression uses the and operatorThe rule of the and operator is that:It evaluates to true, if both terms are trueOtherwise, it is falseThis means that the expression ¬ p ∧ ¬ q evaluates to true if q is false and p is false; otherwise, it evaluates to false

Step-by-step explanation:

A la sala de cine ingresaron 180 niños y 165 adultos.

De acuerdo con el enunciado, la sala de cine tiene capacidad para 345 espectadores y cobra 3 dólares por cada niño y 5 dólares por cada adulto. Asimismo, esta sala tiene un recaudo diario de 1365 dólares. La situación puede ser sintetizada en la siguiente ecuación algebraica:

3 · x + 5 · (345 - x) = 1365

Donde x es el número de niños que asistieron a la sala de cine.

Ahora despejamos la variable correspondiente mediante propiedades algebraicas:

3 · x + 1725 - 5 · x = 1365

1725 - 2 · x = 1365

2 · x = 1725 - 1365

2 · x = 360

x = 180

Ahora, el número de adultos es:

y = 345 - 180

y = 165

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The percentage of drivers who are at least 45 is 62%

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

The table of values

From the table, we have

Age 45 = 62 percentile

When represented properly

So, we have

Age 45 = 62%

This means that the percentage of drivers who are at least 45 is 62%

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Therefore, the rate of change, in cm per minute, of the height when the height is 6 cm is approximately -6 cm/min.

Given,The width of the box = 10 cm Length of the box = 17 cmThe volume of the box = 527 cubic cm/minWe need to find the rate of change, in cm per minute, of the height when the height is 6 cm.We know that the volume of the box is given as:V = l × w × h where, l, w and h are length, width, and height of the box respectively.It is given that the width and length are being held constant.

Therefore, we can write the volume of the box as

:V = constant × h Differentiating both sides with respect to time t, we get:dV/dt = constant × dh/dtNow, it is given that the volume of the box is decreasing at a rate of 527 cubic cm per minute.

Therefore, dV/dt = -527.Substituting the given values in the above equation, we get:

527 = constant × dh/dt

We need to find dh/dt when h = 6 cm.To find constant, we can use the given values of length, width and height.Substituting these values in the formula for the volume of the box, we get:

V = l × w × hV = 17 × 10 × hV = 170h

We know that the volume of the box is given as:V = constant × hSubstituting the value of V and h, we get:

527 = constant × 6 cm

constant = 87.83 cm/minSubstituting the values of constant and h in the equation, we get

-527 = 87.83 × dh/dtdh/dt = -6.0029 ≈ -6 cm/min

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The exponential model of the given data is f(t) = 30.18 × 1.06^t.

Some of the rules of exponents are as follows,

The product of two exponents having the same power is equal to the power of their base multiplied.

The product of two exponents having the same base is equal to the sum of the powers of different exponents to the same base.

Given that,

The average price for office space in 2004 is $30.18.

The average price for office space in 2015 is $66.85.

Suppose the average price in 2004 is taken as y₀.

The given situation can be represented in the form of exponential function f(t) = y₀b^t as,

Take t = 0 for 2004

Then,  f(0) = y₀b^0

⇒ f(0) = y₀ = $30.18.

Then, at 2015, t = 12. Substitute the respective values to get,

f(12) = 30.18 × b^12

⇒ 66.85 = 30.18 × b^12

⇒ b^12 = 66.85 / 30.18

⇒ b = 1.06

Thus in exponential form the given situation can be written as,

f(t) =30.18 × 1.06^t

Hence, the given data can be modeled in exponential function as  f(t) =30.18 × 1.06^t.

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Answer:

Step-by-step explanation:

your doing the calculation wrong

The two cars must be approximately 177.34 feet apart from each other for Spiderman to have different depression angles to each car.

To find the distance between the two cars, we can use trigonometry and the concept of similar triangles. Let's denote the distance between Spiderman and the nearest car as d1 and the distance between Spiderman and the farther car as d2.

In a right triangle formed by Spiderman, the height of the hotel, and the line of sight to the nearest car, the tangent of the depression angle (52 degrees) can be used:

tan(52) = 600 / d1

Rearranging the equation to solve for d1:

d1 = 600 / tan(52)

Similarly, in the right triangle formed by Spiderman, the height of the hotel, and the line of sight to the farther car, the tangent of the depression angle (46 degrees) can be used:

tan(46) = 600 / d2

Rearranging the equation to solve for d2:

d2 = 600 / tan(46)

Using a calculator, we can compute:

d1 ≈ 504.61 feet

d2 ≈ 681.95 feet

The distance between the two cars is the difference between d2 and d1:

Distance = d2 - d1

Plugging in the values, we have:

Distance ≈ 681.95 - 504.61

Distance ≈ 177.34 feet

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Reason:

We cannot divide by zero. This means the denominator cannot equal zero. If it was zero, then,

2x+10 = 0

2x = -10

x = -10/2

x = -5

Follow that chain in reverse to see that x = -5 causes the denominator 2x+10 to be zero. This is why we kick -5 out of the domain. Any other x value is valid.

Answer:

V= 17.64

Step-by-step explanation:

Answer:

The three numbers are 5,6&7

Answer:

225%

2*24=48, with 6 leftover. 6 is 25% of 24, so 200% (From when we multiplied 24 by 2) plus 25% (from the remainder) = 225%

\(x^2 -8x-2=0\\\\x^2 -8x=2\\\\x^2 -8x+16=18\\\\(x-4)^2 =18\\\\x-4=\pm \sqrt{18}\\\\\boxed{x=4 \pm \sqrt{18}}\)

The surface area of the solid formed is approximately, 598.3 in².

Surface area of the solid is the area covered by the solid all round.

The given parameters are:

Surface area of the solid formed = 5(10×10) + (0.5×10×8.67) + 3(10×1.83) = 598.3 in²

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The sum of the interior angle of a rhombus is 360° and each angle is 90°

The area of the circle is 81π. Option A.

The area of a given circle is the amount of space that the circle will cover when considered in a 2 dimensional plane. It can be determined by;

area of a circle = πr^2

where r is the radius.

The circumference of a circle is the curved boundary of a circle. It can be determined by;

circumference of a circle = 2πr

where r is its radius.

From the given information in the question, we have a circle's circumference to the circle's area;

circumference/ area = 2/ 9

But,

circumference/ area = 2πr/ πr^2

                                  = 2/ r

Then;

2/ r = 2/ 9

2r = 2*9

   = 19

r = 18/ 2

r = 9

Thus,

area of the circle = πr^2

                             = π(9)^2

                             = 81π

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Answer:

7. 28.8722

8. 21.7093

Step-by-step explanation:

458.29 x .063=28.8722

21.7093 x .0775= 21.7093

The equation to calculate the yearly interest earned on your investment of $750 at a 16% interest rate is: Interest = $750 * 0.16.

To write the equation for calculating the yearly interest earned on an investment, we can use the formula:

Interest = Principal * Rate

Where:

- Principal is the initial investment amount.

- Rate is the interest rate expressed as a decimal.

In this case, you invested $750, and the annual interest rate is 16%. To use the decimal form of the interest rate, we divide it by 100:

Rate = 16% = 16/100 = 0.16

Substituting the values into the equation:

Interest = $750 * 0.16

To calculate the interest, we multiply the principal by the interest rate:

Interest = $750 * 0.16 = $120

Therefore, the equation to calculate the yearly interest earned on your investment of $750 at a 16% interest rate is:

Interest = $750 * 0.16

Now, let's complete a table to show the growth of your investment over multiple years. We'll assume the interest is compounded annually.

Year | Initial Investment | Interest Earned | Total Value

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

 1        $750                 $120              $870

 2        $870                 $139.20          $1009.20

 3        $1009.20            $161.47          $1170.67

 4        $1170.67            $187.31          $1357.98

 5        $1357.98            $217.28          $1575.26

In each year, we calculate the interest earned by multiplying the initial investment by the interest rate (16% or 0.16). The total value is obtained by adding the initial investment and the interest earned. This process is repeated for each subsequent year.

The table shows the growth of your investment over five years, demonstrating how the interest compounds and increases the total value each year.

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Using the radius of the Ferris wheel and the angle between the two positions, the time spent on the ride when they're 28 meters above the ground is 12 minutes

The radius of the Ferris wheel is 30 / 2 = 15 meters.

The highest point on the Ferris wheel is 15 + 4 = 19 meters above the ground.

The time spent higher than 28 meters is the time spent between the 12 o'clock and 8 o'clock positions.

The angle between these two positions is 180 degrees.

The time spent at each position is 10 minutes / 360 degrees * 180 degrees = 6 minutes.

Therefore, the total time spent higher than 28 meters is 6 minutes * 2 = 12 minutes.

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Answer:

She made $105.75 working as a waitress

She made $367.50 working as a maths tutor

Step-by-step explanation:

Linda worked a total of 30 hours last week and she worked 9 of these hours as a waitress.

Hence, the number of hours worked as a maths tutor =

30 - 9

= 21 hours

When she works as a waitress she receives $11.75 per hour

Hence, $11.75 × 9 hours

= $105.75

Hence, she made $105.75 working as a waitress

When she works as a math tutor she received $ 17.50 per hour.

$17.50 × 21 hours

$367.50

Hence, she made $367.50 working as a waitress

Answer:

20/3

Step-by-step explanation:

Start with multiplying  the numerator by 5, keep the 6 then simply,

The statement is proved: PX = 12√6/5 and PY = 12√6/7.

To prove that PX = 12√6/5 and PY = 12√6/7, we will use the properties of similar triangles and the Pythagorean theorem.

First, let's denote the intersection point of the diagonals as O.  

We know that triangle ABP is similar to triangle CDP, as they share the same angles due to being vertical angles.

Therefore, we can write the following proportion:

AB/CD = BP/PD

Substituting the given values, we have:

6/12 = BP/PD

Simplifying, we find:

BP = PD/2

Since CP/PD = 1, we can conclude that CP = PD.

Now, let's consider triangle ABP and triangle CBO.

These triangles are similar because they share the same angles (due to being vertical angles) and have proportional sides.

We can write the following proportion:

AB/BC = BP/CO

Substituting the given values, we have:

6/7 = BP/CO

Rearranging the equation, we find:

CO = (7/6)BP

Now, let's focus on triangle ODP.

Using the Pythagorean theorem, we can write the following equation:

\(OD^2 = OP^2 + PD^2\)

Since we want to find PX and PY, which are the altitudes from P to AD and BC respectively, we need to express OP in terms of PX and PD, and OD in terms of PY and PD.

Looking at triangle ODP, we can see that OP = PX + OX and OD = PY + OY.

Substituting these expressions into the Pythagorean theorem equation, we have:

\((PX + OX)^2 = OP^2 = (PY + OY)^2 + PD^2\)

Expanding and simplifying the equation, we get:

\(PX^2 + 2PXOX + OX^2 = PY^2 + 2PYOY + OY^2 + PD^2\)

Since OX = OY = 0 (the altitudes are perpendicular to the bases), the equation simplifies to:

\(PX^2 = PY^2 + PD^2\)

Now, let's substitute the given values into this equation:

\((PX)^2 = (12\sqrt{6/7} )^2 + (PD)^2\)

Simplifying further, we get:

\((PX)^2 = 72/7 + (PD)^2\)

We know that PD = CP = CD - CP = 12 - PD, so we substitute this expression into the equation:

\((PX)^2 = 72/7 + (12 - PD)^2\)

Now, we can solve for \((PX)^2:\)

\((PX)^2 = 72/7 + 144 - 24PD + (PD)^2\)

Simplifying, we find:

\((PX)^2 = 216/7 - 24PD + (PD)^2\)

Since CP/PD = 1, we can write PD = 12 - PD, which gives us PD = 6.

Substituting this value into the equation, we have:

\((PX)^2 = 216/7 - 24(6) + (6)^2\)

Simplifying further, we get:

\((PX)^2 = 72/7\)

Taking the square root of both sides, we find:

PX = √(72/7) = 12√6/5

Similarly, we can prove that PY = 12√6/7.

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The probability of select 4 women from the group is, P = 35.

What is probability?

The area of mathematics known as probability deals with numerical descriptions of how likely it is for an event to happen or for a proposition to be true. A number between 0 and 1 is the probability of an event, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.

Given: You have a group of 20 people, 7 are women and the remaining people are men.

7 are women then 13 are men.

No. of ways in which 4 women can be chosen from 7 women are 7C4.

So, the probability of select 4 women from the group is,

\(P = {7_C_4} \\P = \frac{7!}{4!*(7-4)!} \\P=\frac{7!}{4!*3!} \\P = 35\)

Hence, the probability of select 4 women from the group is, P = 35.

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Answer:

y = 3x + 2

Step-by-step explanation:

Convert the equation to slope intercept form to get y = –1/3x + 2.  The old slope is –1/3 and the new slope is 3.  Perpendicular slopes must be opposite reciprocals of each other:  m1 * m2 = –1

With the new slope, use the slope intercept form and the point to calculate the intercept: y = mx + b or 5 = 3(1) + b, so b = 2

So y = 3x + 2

The area of the shaded region, with a frame of 3 units wide, is 264 square units. The inner rectangle is 6x4 units, and the outer rectangle is 18x16 units.

To solve the given problem, we have to find the area of the shaded region if the frame is 3 units wide. If the frame is 3 units wide, then the dimensions of the inner rectangle (the shaded region) will be (12 - 6) × (10 - 6) which simplifies to 6 × 4.

Therefore, we can say that the inner rectangle has a length of 6 units and a width of 4 units.The dimensions of the outer rectangle are (12 + 3 + 3) × (10 + 3 + 3) which simplifies to 18 × 16. Therefore, we can say that the outer rectangle has a length of 18 units and a width of 16 units.

The area of the shaded region can be obtained by subtracting the area of the inner rectangle from the area of the outer rectangle. Therefore, the Area of the outer rectangle = length × width= 18 × 16 = 288 square units

Area of the inner rectangle = length × width= 6 × 4 = 24 square units

Area of the shaded region = Area of the outer rectangle - Area of the inner rectangle = 288 - 24= 264 square units

Therefore, the area of the shaded region is 264 square units.

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Answer:

6

(If you like this answer i would appreciate if u give brainliest but otherwise, i hope this helped ^^)

Step-by-step explanation:

To find the missing number in the given sequence, let's analyze the pattern:

2, 4, 3, 6, 6, 3, 8, 9, 7, 9, 8, ???

Looking at the sequence, we can identify a few patterns:

The sequence alternates between increasing and decreasing numbers.

The first two numbers, 2 and 4, are increasing.

The next two numbers, 4 and 3, are decreasing.

The following two numbers, 3 and 6, are increasing.

The subsequent two numbers, 6 and 3, are decreasing.

The next two numbers, 3 and 8, are increasing.

The subsequent two numbers, 8 and 9, are increasing.

Based on these observations, it appears that the sequence is following a pattern where it alternates between increasing and decreasing numbers, but the specific values being added or subtracted are not consistent.

Now let's determine the missing number:

From the pattern, the next two numbers should be decreasing. Following the pattern of alternating between increasing and decreasing numbers, the missing number after the last given number (8) should be less than 9.

Let's assume the missing number is x:

8 - x

Since the previous decreasing sequence was 6 - 3, we can assume that x is 1 less than the previous number (3):

8 - (3 - 1) = 8 - 2 = 6

Therefore, the missing number in the sequence is 6.

The complete sequence is:

2, 4, 3, 6, 6, 3, 8, 9, 7, 9, 8, 6

The angle z is in the third quadrant, the value of cosz is negative. Hence, cosz = -3/5.So, the value of cosz is -3/5.

Given sinz = -4/5 for pi < z < (3pi)/2, we need to find the value of cosz. We can use the trigonometric identity of Pythagorean theorem to find the value of cosz.

According to Pythagorean theorem, sin2θ + cos2θ = 1, where θ is the angle in the right-angled triangle and sin, cos are the trigonometric ratios.

The negative sign for the given sinz indicates that the angle z is in the third quadrant. So, we can take the help of the unit circle to find the value of cosz as shown below:

Here, we have used the Pythagorean identity of sin2z + cos2z = 1 on the unit circle to find the value of cosz. Since the value of sinz is already given, we can find the value of sin2z as: sin2z = sinz x sinz = (-4/5) x (-4/5) = 16/25

Then, we can substitute the value of sin2z in the Pythagorean identity as: cos2z = 1 - sin2z = 1 - (16/25) = 9/25We need to find the value of cosz.

So, we can take the square root of cos2z as: cosz = ±(√(9/25)) = ±(3/5)The sign of cosz can be determined by considering the quadrant of the angle z.

Since the angle z is in the third quadrant, the value of cosz is negative. Hence, cosz = -3/5.So, the value of cosz is -3/5.

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