The optimal height h of the letters of a message printed on pavement is given by the formula [tex]h = \frac{0.00252 d^{2.27}}{e}[/tex]. Here d is the distance of the driver from the letters and e is the height of the​ driver's eye above the pavement. All of the distances are in meters. Find h for the given values of d and e.
d = 92.4 m, e = 1.7 m.

Step-by-step explanation:

[tex] \because \: a_n = - 1 + 3(n - 1) \\ \\ \therefore \: a_{55} = - 1 + 3(55 - 1) \\ \\ \therefore \: a_{55} = - 1 + 3 \times 54 \\ \\ \therefore \: a_{55} = - 1 + 162\\ \\ \huge \blue { \boxed{\therefore \: a_{55} = 161}}\\ \\ [/tex]

Hence, the 55th term of the sequence is 161.

Answer with Step-by-step explanation:

We are given that

DE

[tex]x''+x=2e^t[/tex]

Function:[tex]x=C_1sint+C_2cost+e^t[/tex]

We have to show that given function is  a solution of the equation for all values of the constants.

If given function is  solution of DE then it satisfied the given DE.

Differentiate  function w.r.t.t

[tex]x'=C_1cost-C_2sint+e^t[/tex]

Again differentiate w.r.t. t

[tex]x''=-C_1sint-C_2cost+e^t[/tex]

Substitute the values in the given DE

[tex]-C_1sint-C_2cost+e^t+C_1sint+C_2cost+e^t=2e^t[/tex]

LHS=RHS

Given function satisfied the given DE.Therefore, it is solution of given DE for all values of the constants.

Answer:

i think it' =-8abc(a+b-c)

Step-by-step explanation:

answer is C: [tex]\frac{EF}{DF}[/tex]

Answer:option C is the correct answer

Step-by-step explanation:

Triangle DEF is a right angle triangle.

From the given right angle triangle,

DF represents the hypotenuse of the right angle triangle.

With m∠θ as the reference angle,

EF represents the adjacent side of the right angle triangle.

DE represents the opposite side of the right angle triangle.

To determine Cos ∠θ, we would apply

the cosine trigonometric ratio.

Cos θ = adjacent side/hypotenuse. Therefore,

Cos θ = EF/DF

Answer:

a. Form B would be better because statistical methods can be applied to the ordinal data.

Step-by-step explanation:

Ordinal data can be ranked. This teacher evaluation can be ranked on a scale of 1-10 for example. Ordinal data can  provide good information about the choice of the person who is responding. And these informations are quantitative in nature.

Tens is the correct answer

Answer:

Correct answer is (a). Simple random sampling

Step-by-step explanation:

Simple random sampling (SRS) is a statistical techniques used in choosing subset of members of the population randomly without given special priority to anyone to be chosen. It gives every members of the population equal chance.

By randomly selecting 6060 customers from the customer's database, Maytag has employed Simple Random Sampling method of survey.

Answer:

Step-by-step explanation:

Simplify.

4n + 12 + 7n  

16n + 7

23n

11n + 12

4n + 19

Answer:

Step-by-step explanation:

An arc is a portion of the circle's circumference bounded by 2 radii

The formula for determining the length of an arc is expressed as

Length of arc = θ/360 × 2πr

Where

θ represents the central angle or angle which the 2 radii subtends at the center of the circle.

r represents the radius of the circle.

π is a constant whose value is 3.14

From the information given,

Radius, r = 5 inches

θ = 170 degrees

Therefore,

Length of arc = 170/360 × 2 × π × 5

Length of arc = 4.7222π feet

rounding up to 2 decimal places, it becomes

4.72π feet

Bob can buy 15 cupcakes for the price of 18 cookies.

Step-by-step explanation:

Answer:

For the sequence is [tex]-\frac{2}{3}[/tex] ,-4 ,-24 ,-144 ,...

Hence the formula [tex]f(x)=-\frac{2}{3}(6)^{x-1}[/tex] for x=1,2,3,... represents the given geometric sequence

Step-by-step explanation:

Given sequence is [tex]-\frac{2}{3}[/tex] ,-4 ,-24 ,-144 ,...

To find the formula to describe the given sequence :

Let [tex]a_1=\frac{-2}{3}[/tex] ,[tex]a_2=-4[/tex] ,[tex]a_3=-24[/tex],...

First find the common ratio

[tex]r=\frac{a_2}{a_1}[/tex] here  [tex]a_1=\frac{-2}{3}[/tex] and,[tex]a_2=-4[/tex]

[tex]=\frac{-4}{\frac{-2}{3}}[/tex]

[tex]=\frac{4\times 3}{2}[/tex]

[tex]=\frac{12}{2}[/tex]

[tex]r=6[/tex]

[tex]r=\frac{a_3}{a_2}[/tex] here  [tex]a_2=-4[/tex] and [tex]a_3=-24[/tex]

[tex]=\frac{-24}{-4}[/tex]

[tex]=6[/tex]

[tex]r=6[/tex]

Therefore the common ratio is 6

Therefore the given sequence is geometric sequence

The nth term of the geometric sequence is

[tex]a_n=a_1r^{n-1}[/tex]

The formula which describes the given geometric sequence is

[tex]f(x)=a_1r^{x-1}[/tex] for x=1,2,3,...

[tex]=\frac{-2}{3}6^{x-1}[/tex] for x=1,2,3,...

Now verify that [tex]f(x)=a_1r^{x-1}[/tex] for x=1,2,3,... represents the given geometric sequence or not

put x=1 and the value of [tex]a_1[/tex] in [tex]f(x)=a_1r^{x-1}[/tex] for x=1,2,3,...

we get [tex]f(1)=-\frac{2}{3}(6)^{1-1}[/tex]

[tex]=-\frac{2}{3}(6)^0[/tex]

[tex]=-\frac{2}{3}[/tex]

Therefore [tex]f(1)=-\frac{2}{3}[/tex]

put x=2 we get [tex]f(2)=-\frac{2}{3}(6)^{2-1}[/tex]

[tex]=-\frac{2}{3}(6)^1[/tex]

[tex]=-\frac{12}{3}[/tex]

Therefore [tex]f(2)=-4[/tex]

put x=3 we get [tex]f(3)=-\frac{2}{3}(6)^{3-1}[/tex]

[tex]=-\frac{2}{3}(6)^2[/tex]

[tex]=-\frac{2(36)}{3}[/tex]

Therefore [tex]f(3)=-24[/tex]

Therefore the sequence is f(1),f(2),f(3),...

Therefore  the sequence is [tex]-\frac{2}{3}[/tex] ,-4 ,-24 ,-144 ,...

Hence the formula [tex]f(x)=a_1r^{x-1}[/tex] for x=1,2,3,... represents the given geometric sequence is verified

Therefore the formula [tex]f(x)=-\frac{2}{3}(6)^{x-1}[/tex] for x=1,2,3,... represents the given geometric sequence

Answer:

a

Step-by-step explanation:

Answer:

x = 9

Step-by-step explanation:

if the perimeter os square JKLM is 48  

each side has 48/4

so each side has 12

now if JK is x + 3 = 12

we only need to solve that

x + 3 = 12

x = 12 -3

x = 9

Answer:

B. 9

Step-by-step explanation:

Answer:

(x⁻¹)(x⁻⁵) = x⁻⁶

Step-by-step explanation:

When multiplying number with the same base, you add up their exponent.

(x⁻¹)(x⁻⁵) =

= x⁽⁻¹⁾ ⁺ ⁽⁻⁵⁾

= x⁻⁶

you can also write x⁻⁶ as 1/x⁶. The negative sign in the exponent just flip the numerator and denominator with each others.

Answer:

The answer to your question is   x⁻⁶ or 1/x⁶

Step-by-step explanation:

Multiplying exponents

-To multiply exponents they must have the same base and the result will be the base and the exponents will add.

Ex

              (a³)(a²)

base = a

exponents = 3 and 2

result     a³ ⁺ ²  = a⁵

In your question

             (x⁻¹)(x⁻⁵) = x⁻¹⁻⁵ = x⁻⁶ = 1/x⁻⁶

Answer:

Wm = 43.2 pounds

Step-by-step explanation:

If the ratio of the weight of an object on Mars to its weight on Earth is 9 to 25, this means that what on Mars weighs 9 units on earth weighs 25 units, therefore:

Data

ratio = 9/25

Weight on Mars (Wm) = ?

Weight on Earth (We) = 120 pound

Wm = (9/25)*120 pound = 43.2 pounds

Answer :

The required number is 2.

Step-by-step explanation:

Given : The sum of six fifths and six times a number is equal to four fifths subtracted from seven times the number.

To find : The number ?

Solution :

Let the number be 'x'.

The sum of six fifths and six times a number i.e.  [tex]\frac{6}{5}+6x[/tex]

Four fifths subtracted from seven times the number i.e. [tex]7x-\frac{4}{5}[/tex]

According to question,

[tex]\frac{6}{5}+6x=7x-\frac{4}{5}[/tex]

[tex]7x-6x=\frac{6}{5}+\frac{4}{5}[/tex]

[tex]x=\frac{10}{5}[/tex]

[tex]x=2[/tex]

The required number is 2.

Answer:

Step-by-step explanation:

total height, H = 113 inches

height of each stair case, h = 7.25 inches

Number of stair case, n = total height / height of each stair case

n = 113 / 7.25 = 15.6

Answer:

[tex]sec\ E = \frac{4\sqrt{7} }{7}[/tex]

[tex]Cos\ F = \frac{3}{4}[/tex]

[tex]Tan\ F =\frac{\sqrt{7}}{3}[/tex]

Step-by-step explanation:

Given

EF = 8

FG = 6

We need to find the trigonometric ratios.

Solution:

First we will find the length of the third side.

Now we know that;

△EFG is a right angled triangle with right angle at G.

Now applying Pythagoras theorem which states.

"The sum of square of the two legs of the triangle is equal to square of the hypotenuse."

so we can say that;

[tex]FG^2=EF^2+EG^2\\\\EG^2=FG^2-EF^2[/tex]

Substituting the given values we get;

[tex]EG^2=8^2-6^2=64-36=28[/tex]

Taking square roots on both side we get;

[tex]\sqrt{EG^2} =\sqrt{28}=\sqrt{4\times7}\\ \\EG = 2\sqrt{7}[/tex]

Now we will find the trigonometric values.

[tex]secE=\frac{Hypotenuse}{Adjacent\ side}[/tex]

Here Hypotenuse = EF = 8

Adjacent side of E = EG = [tex]2\sqrt{7}[/tex]

[tex]secE=\frac{8}{2\sqrt{7}} =\frac{4}{\sqrt{7}}[/tex]

Now rationalizing the denominator by multiplying numerator and denominator by [tex]\sqrt{7}[/tex] we get;

[tex]secE=\frac{4\times \sqrt{7} }{\sqrt{7}\times \sqrt{7} }\\\\secE = \frac{4\sqrt{7} }{7}[/tex]

Now,

[tex]Cos F = \frac{Adjacent \ side}{Hypotenuse}[/tex]

Adjacent side to F =GF = 6

Hypotenuse = EF = 8

[tex]Cos\ F = \frac{6}{8}\\\\Cos\ F = \frac{3}{4}[/tex]

Now,

[tex]Tan F = \frac{opposite \ side}{adjacent\ side}[/tex]

Here Opposite side of F = EG = [tex]2\sqrt{7}[/tex]

Adjacent side of F = GF = 6

[tex]Tan\ F= \frac{2\sqrt{7}}{6}\\\\Tan\ F =\frac{\sqrt{7}}{3}[/tex]

Hence Below are required details.

[tex]sec\ E = \frac{4\sqrt{7} }{7}[/tex]

[tex]Cos\ F = \frac{3}{4}[/tex]

[tex]Tan\ F =\frac{\sqrt{7}}{3}[/tex]

The value of the trigonometric ratio of an angle of the triangle is;

[tex]\rm SecE=\dfrac{8}{2\sqrt{7}}=\dfrac{4}{\sqrt{7} }\\\\CosF = \dfrac{6}{8}=\dfrac{3}{4}\\\\Tan F =\dfrac{2\sqrt{7}}{3}=\dfrac{\sqrt{7} }{3}\\[/tex]

Given

Right △EFG has its right angle at G, EF=8, and FG=6.

The Pythagoras theorem states that the square of the length of the hypotenuse is equal to the sum of squares of the lengths of the other two sides of the right-angled triangle.

In right-angle △EFG, in which E is a right angle.

[tex]\rm EF^2=FG^2-EG^2\\\\8^2=6^2-EG^2\\\\EG^2=8^2-6^2\\ \\EG^2=64-36\\\\EG^2=28\\\\EG = 2\sqrt{7}[/tex]

The value of the trigonometric ratio of an angle of the triangle is;

[tex]\rm SecE=\dfrac{8}{2\sqrt{7}}=\dfrac{4}{\sqrt{7} }\\\\CosF = \dfrac{6}{8}=\dfrac{3}{4}\\\\Tan F =\dfrac{2\sqrt{7}}{3}=\dfrac{\sqrt{7} }{3}\\[/tex]

To know more about the Pythagoras theorem click the link given below.

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Answer:

The length of the room in the drawing is 5 inches.

Step-by-step explanation:

Given:

Kenneth measured a hotel and made a scale drawing the scale he used was 1 inch= 4 feet.

The actual length of a room in the hotel is 20 feet.

Now, to find the length of the room in the drawing.

Let the length of the room in the drawing be [tex]x.[/tex]

The actual length of the room = 20 feet.

The scale used in drawing is 1 inch = 4 feet.

As, 1 inch is equivalent to 4 feet.

Thus, [tex]x[/tex] is equivalent to 20 feet.

Now, to get the length of the room in the drawing we use cross multiplication method:

[tex]\frac{1}{4} =\frac{x}{20}[/tex]

By cross multiplying we get:

[tex]20=4x[/tex]

Dividing both sides by 4 we get:

[tex]5=x[/tex]

[tex]x=5\ inches.[/tex]

Therefore, the length of the room in the drawing is 5 inches.

Answer:

B

Step-by-step explanation:

360/6

6 is number of sides

You get 60

Rotate twice to reach 120

Moving F Counter clockwise twice is where B was

The image of point F after the rotation of 120°, r(120°), will be point B.

So, we need to rotate point F a total angle of 120°.

As you can see, in the image we have 6 sections, and equally distributed in these 6 sections we will have an angle of 360° (a complete rotation). So each section has an angle of:

360°/6 = 60°.

Then a rotation of 120°  (two times 60°) will rotate the point F two sections counterclockwise. Then the image of the point after the rotation will be point B.

If you want to learn more about rotations, you can read:

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Answer:

3/2

Step-by-step explanation:

Answer:

3/2

Step-by-step explanation:

9 to 6 means  

                                                          [tex]\dfrac{9}{6}[/tex]

Now we will cancel that fraction - we will divide numerator and denominator both by 3:

9 divided by 3 equals 3

6 divided by 3 equals 2

Hence,

                                        [tex]\dfrac{9}{6} = \dfrac{3\cdot 3}{2\cdot 3} = \dfrac{3}{2}[/tex]

Answer:

Constant of proportionality = 24

Equation: [tex]y=24x[/tex]

Step-by-step explanation:

Given:

'x' and 'y' are proportional to each other.

At [tex]x=3,y=72[/tex]

Now, for a proportional relationship, the constant of proportionality is given as the ratio of the two values of the two variables that are in proportion.

Here, 'x' and 'y' are in proportion. So, the constant of proportionality is given as:

[tex]k=\frac{y}{x}\\\\k=\frac{72}{3}=24[/tex]

Therefore, the constant of proportionality is 24.

Now, a proportional relationship in 'x' and 'y' is given as:

[tex]y=kx[/tex]

Now, plug in the given value of 'k' and complete the equation. This gives,

[tex]y=24x[/tex]

Therefore, the equation that relates 'x' and 'y' is [tex]y=24x[/tex]

Answer:

a) 43 m b) 55 m

Step-by-step explanation:

a) From question at t = 0, initial velocity [tex]V_{o}[/tex] = 15 m/s

   Using equation of motion, [tex]S = V_{o}t + \frac{1}{2} at^{2}[/tex] ; at t = 2 secs , a = 4 m/[tex]s^{2}[/tex]

    S = (15 x 2) + (0.5 X 4 x [tex]2^{2}[/tex])

    S = 30 + 8 = 38 m , Therefroe;

  car is (38 + 5)m from the sign post

  car is 43 m from the sign post at t = 2 secs

b) Also from equation of motion, [tex]V^{2} = V_{o} ^{2} + 2aS[/tex]

    [tex]25^{2} = 15^{2}[/tex] + (2 x 4 x S)

     625 - 225 = 8S

S = 50 m

 Car is (50 + 5) m from the sign post

Car is 55 m from the sign post at V = 25 m/s

At t=2s, the motorcyclist is at position 29m east of the signpost with a velocity of 23m/s. When his velocity is 25m/s, he is at a position 38.75m east of the signpost.

Given that the motorcyclist starts 5 m east of the signpost with an initial velocity of 15 m/s and a constant acceleration of 4.0 m/s2, we can use the equation of motion to find his position and velocity at any given time.

(a) At t=2s, the motorcyclist's position (x) and velocity (v) can be determined using the following two equations respectively:

(b) When the velocity is 25 m/s, the time can be calculated using the equation v = v0 + a*t. By setting v=25m/s, v0=15m/s, and a=4.0m/s2, we get t = (25m/s-15m/s) / 4.0m/s2 = 2.5s. Substituting this time into the position equation gives x = 5m + 15m/s*2.5s + 0.5*4.0m/s2*(2.5s)2, which results in the motorcyclist being at position 38.75 m.

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Answer:

300 programs

Step-by-step explanation:

Let’s work with cents to make this easier. We convert the $12 to cents, making 1200 cents

Let the number of copies Alden printed be x. His total printing cost would be x * 54 = 54x cents.

He sold at 75 cents each and still had left 100 copies. This means his total sale would be (x - 100)75

He lost $12 on the venture. This means his cost price minus his selling price is $12 since it’s a loss.

Computing this:

54x - 75(x - 100) = 1200

54x - 75x + 7500 = 1200

-21x = 1200 - 7500

-21x = -6,300

x = 6300/21 = 300 programs

Answer:1)2804m^2=4s.f

2)84Km^3=2s.f

3)5.029m=4s.f

4)0.00003068m=4s.f

5)4.6×10^5m=2s.f

6)4.06×10^-5m=3s.f

7)750m=3s.f

8)75m=2s.f

9)75,000.0m=5s.f

10)75.00m=2s.f

11)75,000.00m=5s.f

12)10cm=2s.t

B) to four significant figures

1)3.682

2)860100

3)375.7

4)51150

5)4673

C to 1 decimal places

1)1.4

2)4735.0

3)687524.0

4)7.6

5)235.0

Dto 2d.p

1)22.49

2)25880.00

3)30623.00

4)412541.00

5)866323.00

E)

1)6.201cm+7.4cm+0.68cm+12.0cm=26.281cm

2)1.6km+1.62km+1200km=1203.22km

3)8.264g-7.8g=0.464g

4)10.4168m-6m=4.4168m

5)12.00m+15.001kg=12.00m+15.001kg

6)1.31cm×2.3cm=3.013cm^2

7)5.7621m×6.201m=35.7308m^2

8)20.2cm/7.41s=2.726cm/s

Step-by-step explanation:

S.f means significant figures or Digits.

2)cm +kg is impossible because they are unlike termsi.e they do not have any thing in common, hence 12.00m+15.001kg cannot be added up.

This detailed answer involves the concept of significant figures, rounding off significant figures, and performing calculations while maintaining the appropriateness of significant figures in measurement.

Number of significant digits

Significance figures involve the digits in a number that carry meaningful information about its precision.

Rounding off to Significant Figures

To round to a certain number of significant figures, start from the first non-zero number and count the number of digits required, rounding the last one if necessary. Here are your rounded numbers:

Performing Calculations

In adding or subtracting numbers, the result should retain the smallest number of decimal places in the input values. In multiplication or division, the result should retain the smallest number of significant figures in the input values. Here are your answers:

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Answer:

11/92

Step-by-step explanation:

G = 11

R = 7

B = 6

P(b) = 6/24 = 1/4

P(g) = 11/23

P(blue first and then green(without replacement)) = 1/4 * 11/23

= 11/92

The probability of randomly selecting a blue marble followed by a green marble from a jar of 24 marbles (6 blue, 7 red, 11 green) is 11/92.

The number of outcomes considered favorable or desired is compared to the total number of outcomes possible. In this situation, we're interested in choosing a blue marble first, then a green marble. The total number of marbles is 11 green + 7 red + 6 blue = 24 marbles.

Initially, the probability of selecting a blue marble is 6/24 = 1/4

because there are 6 blue marbles out of a total of 24.

After taking one marble out (assuming it's blue), you have 23 marbles left, with 11 of them being green. So, the probability of selecting a green marble next is 11/23.

Therefore, the probability of both of these events happening (selecting a blue marble followed by a green marble) is found by multiplying these two probabilities together, which gives (1/4) * (11/23) = 11/92.

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Answer:

The Final answer will be [tex]2x^2+5x+2[/tex] with remainder 0.

Step-by-step explanation:

We have attached the division for your reference.

Given:

Dividend = [tex]6x^3 + 11x^2 - 4x -4[/tex]

Divisor= [tex]3x - 2[/tex]

Explaining the division we get;

Step 1: First when we divide the Dividend [tex]6x^3 + 11x^2 - 4x -4[/tex] with divisor [tex]3x - 2[/tex] we will first multiply [tex]2x^2[/tex] with the divisor then we get the Quotient as [tex]2x^2[/tex] and Remainder as [tex]15x^2-4x-4[/tex]

Step 2: Now the Dividend is [tex]15x^2-4x-4[/tex] and Divisor is [tex]3x - 2[/tex] we will now multiply [tex]5x[/tex] with the divisor then we get the Quotient as [tex]2x^2+5x[/tex] and Remainder as [tex]6x-4[/tex]

Step 3: Now the Dividend is [tex]6x-4[/tex] and Divisor is [tex]3x - 2[/tex] we will now multiply 2 with the divisor then we get the Quotient as [tex]2x^2+5x+2[/tex] and Remainder as 0.

Hence The Final answer will be [tex]2x^2+5x+2[/tex] with remainder 0.

Answer:

Fractional form = [tex]\frac{95}{100}=\frac{19}{20}[/tex]

Percent form = 95%

Trisha got 95% of her problems correct.

Step-by-step explanation:

Given:

Total number of questions (N) = 100

Number of correct questions (C) = 95

Therefore, the ratio of the correct answers to the total number of problems is given by dividing the the number of correct questions by the total number of questions. This is given as:

Ratio expressed as a fraction = [tex]\frac{C}{N}=\frac{95}{100}=\frac{95\div 5}{100\div 5}=\frac{19}{20}(Simplest\ form)[/tex]

Now in order to express this ratio in percentage form, we need to multiply the given ratio by 100. This gives,

Ratio expressed as a percent = [tex]\frac{C}{N}\times 100=\frac{95}{100}\times 100=95\%[/tex]

Therefore, Trisha got 95% of her problems correct.

Answer:

1: the first one

2:the third one

3:the third one

Step-by-step explanation:

Answer:

The winner completed the race in 96 hours and 52 minutes.

Step-by-step explanation:

Given:

Distance of the cycling race = 2292 miles

Average speed of the winner = [tex]23.66\ mph[/tex]

We need to find time required by winner to complete the race.

Solution:

Now we know that;

Time required can be calculated by dividing Total Distance from the Average speed.

framing in equation form we get;

time required by winner to complete the race = [tex]\frac{2292}{23.66} = 96.87\ hrs[/tex]

Now converting [tex]0.87\ hrs[/tex] into minutes we get;

[tex]0.87\times 60= 52.2\approx 52\ mins[/tex]

Hence the winner completed the race in 96 hours and 52 minutes.

Answer:

Additive inverses for complex numbers are just like they are for real numbers: they mean the number you'd add to get back to 0. Just like real numbers, this means that you change the signs. Thus, the additive inverse of -4+7i is 4-7i

hope it helps

Step-by-step explanation: