Which table best represents the relationship between n, the position of the term in a sequence, and the value of the term defined by the rule 5n-3 ?

Answer:

0.89

Step-by-step explanation:

Nunber of samples = 100

City mpg :

Mean = 28

Standard deviation =9.2

Highway mpg:

Mean = 35

Standard deviation = 8.6

correlation Coefficient (r) between city mpg and highway mpg = 0.95.

The value of the slope of the regression line that predicts highway mpg based on city mpg can be obtained by:

(Standard deviation of highway mgp / standard deviation of city mpg) × correlation Coefficient

Slope = (8.6 / 9.2) × 0.95

Slope = (0.934782 × 0.95) = 0.8880

Slope = 0.89 ( two decimal place)

Answer:

a+9 = b

Step-by-step explanation:

a=b-9

Add 9 to each side

a+9=b-9+9

a+9 = b

25.5 is the runners' median age.

What in maths is median?

When a data set's median value is used, 50% of the data points in the collection have values that are lower or equal to the median and 50% of them have values that are higher or equal to the median.

                           When working with a tiny data collection, you must first count the number of data points (n) and organise them in ascending order.

22, 31, 16, 19, 15, 24, 27, 27, 14, 31, 32, 30

We must first arrange the ages from youngest to oldest in order to determine the median

 14,15,16,19,22,24,27,27, 30 , 31, 31, 32,

The median will be the average of the sixth and seventh values in this sorted list because there are 12 runners

               24 +27/2 =  25.5  is the median.

Hence, 25.5 is the runners' median age.

Learn more about median

brainly.com/question/28060453

#SPJ1

Answer:

Step-by-step explanation:

\(\mathrm{6n - 9 \; when\;n = 4}\)

Let's substitute n with 4 :-

Multiply 6*4 = 24:-

Subtract:-

____________________

Hope this helps!

1. Mean = 33.61

2. Standard Deviation = 11.3284

3. Variance = 128.33

The given data are: \(22.8, 49.8, 17.5, 44.1, 33.2, 20.6, 43.2, 37.7\)

To get mean, we will sum up all the numbers and divide by the total count. The mean is:

= (22.8 + 49.8 + 17.5 + 44.1 + 33.2 + 20.6 + 43.2 + 37.7) / 8

= 268.9 / 8

= 33.62

Standard Deviation: \(\sqrt((22.8 - 33.61)^2 + (49.8 - 33.61)^2 + (17.5 - 33.61)^2 + (44.1 - 33.61)^2 + (33.2 - 33.61)^2 + (20.6 - 33.61)^2 + (43.2 - 33.61)^2 + (37.7 - 33.61)^2) / 8\)

= \(\sqrt{128.3336}\)

= 11.3284420818

= 11.3284

Variance = (Standard Deviation)^2

Variance = \(11.3284 ^2\)

Variance = 128.33264656

Variance = 128.33.

Read more about measure of centres

brainly.com/question/15214370

#SPJ1

(11/44)^ 3 = 11^3/14^3 = 1331/2744 = 0.48505

Round the answer as needed.

The random variable is the number of cars held up at the intersection.

A random variable is one whose value is aleatory, then you can not know anticipatedly the outcome for sure. In this case, the number of cars held up at the intersection may be different at any time inside the range given and you cannot know the number of cars that there will be in a future moment.

Let's assume that the corresponding side of the second triangle is \(\displaystyle\sf x\).

The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides. Therefore, we can set up the following proportion:

\(\displaystyle\sf \left( \dfrac{x}{6.3} \right)^{2} =\dfrac{49}{81}\)

To find \(\displaystyle\sf x\), we can solve the proportion above:

\(\displaystyle\sf \left( \dfrac{x}{6.3} \right)^{2} =\dfrac{49}{81}\)

Taking the square root of both sides:

\(\displaystyle\sf \dfrac{x}{6.3} =\sqrt{\dfrac{49}{81}}\)

Simplifying the square root:

\(\displaystyle\sf \dfrac{x}{6.3} =\dfrac{7}{9}\)

Cross-multiplying:

\(\displaystyle\sf 9x = 6.3 \times 7\)

Dividing both sides by 9:

\(\displaystyle\sf x = \dfrac{6.3 \times 7}{9}\)

Calculating the value:

\(\displaystyle\sf x = 4.9\)

Therefore, the corresponding side of the second triangle is \(\displaystyle\sf 4.9 \, cm\).

\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)

♥️ \(\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

Answer:

Step-by-step explanation:

let's assume that the corresponding side of the second triangle is .

The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides. Therefore, we can set up the following proportion:

To find , we can solve the proportion above:

Taking the square root of both sides:

Simplifying the square root:

Cross-multiplying:

Dividing both sides by 9:

Calculating the value:

Therefore, the corresponding side of the second triangle is 4.9cm


hope it helped u dear...........

Answer:

3/4= .75 3/16= .0625 .

Step-by-step explanation:

3/4 =.75 3/16 = .1875

.75/.1875 = 4

Answer:

6.5 yards of cord were bought

Step-by-step explanation:

234/36=6.5

Answer:

\(\huge\boxed{f(x)=-5(x-4)^2-1=-5x^2+40x-81}\)

Step-by-step explanation:

The vertex form of an equation of a parabola:

\(f(x)=a(x-h)^2+k\)

\((h;\ k)\) - vertex

We have

vertex \((4;\ -1)\to h=4;\ k=-1\)

\(f(3)=-6\)

Therefore we have:

\(f(x)=a(x-4)^2+(-1)=a(x-4)^2-1\)

Substitute \(x=3\) and \(f(3)=-6\)

\(a(3-4)^2-1=-6\qquad|\text{add 1 to both sides}\\\\a(-1)^2=-6+1\\\\a(1)=-5\\\\a=-5\)

Finally:

\(f(x)=-5(x-4)^2-1=-5(x^2-2(x)(4)+4^2)-1\\\\=-5(x^2-8x+16)-1=-5x^2+(-5)(-8x)+(-5)(16)-1\\\\=-5x^2+40x-80-1=-5x^2+40x-81\)

Answer:

AC = 12

Step-by-step explanation:

If BC is parallel to DE then ∠D ≅ ∠B and ∠E ≅ ∠C. Therefore

ΔABC is similar to ΔADE.

The sides of smaller triangle are in proportion with sides of bigger triangle.

Therefore we have the equation:

AC/AE = AB/AD

Substitute the given numbers:

x/x+15 =8/18

18x= 8(x+15)

18x = 8x+120

10x = 120

x = 12

AC=12

A. The total value of the loan with quarterly compounded interest is $52,400.

B. The total value of the loan with monthly compounded interest is $52,010.04

Part A: Total value of the loan with the quarterly compounded interest

To find the total value of the loan, we'll use the formula for compound interest:

A = P * (1 + r/n)^(nt)

Where:

A = final amount (loan + interest)

P = principal amount (initial loan) = $20,000

r = interest rate = 7% = 0.07

n = number of times compounded per year = 4 (quarterly)

t = number of years = 10

Plugging in the values, we get:

A = $20,000 * (1 + 0.07/4)^(4 * 10)

A = $20,000 * (1.0175)^40

A = $20,000 * 2.620075

A = $52,401.51

Rounding to the nearest hundred, the total value of the loan with quarterly compounded interest is $52,400.

Part B: Total value of the loan with the monthly compounded interest

To find the total value of the loan with monthly compounded interest, we'll use the same formula with a different value of n:

A = P * (1 + r/n)^(nt)

Where:

n = number of times compounded per year = 12 (monthly)

Plugging in the values, we get:

A = $20,000 * (1 + 0.07/12)^(12 * 10)

A = $20,000 * (1.005833)^120

A = $20,000 * 2.600502

A = $52,010.04

Rounding to the nearest hundredth, the total value of the loan with monthly compounded interest is $52,010.04

The difference between the two loans is $52,401.51 - $52,010.04 = $391.47

The difference between the two loans is due to the higher frequency of compounding in the monthly compounded interest loan. The interest is compounded more times per year, so the interest is accumulating on the interest more quickly, leading to a higher overall interest charge.

learn more about compound interest: https://brainly.com/question/24274034

#SPJ1

Answer:

D the amount of money he pays for each lunch

Step-by-step explanation:

In each lunch Devante has, he pays 2,50 $ according to:

Money in t = t₀     he has  35,50 $      paid 3 lunches and spent

35,50 - 28  =  7,5

Then the cost of each lunch is    7,5 / 3   =  2,5 $

After that

bought    5 lunches and spent   28  - 15,5  = 12,50

Again    12,5 / 5   =  2,5 $

Now the model for the situation is a straight line with a slope 2,5

In an  x , y cartesian system in which  y is money in the account  and x is the number of lunches, such a straight line will be

y  =  b  -  m*x      ( b the intercept on y  and  m the negative slope)

y  =  35,50 - 2,5*x

So  answering the question is lyrics  D  the amount of money he pays for each lunch

Answer:

5 feet

Step-by-step explanation:

\(f(t) = 3 cos \bigg( \frac{\pi}{6} t\bigg) + 5 \\ \\ plug \: t = 9 \\ \\ \implies \: f(9) = 3 cos \bigg( \frac{\pi}{6} \times 9 \bigg) + 5 \\ \\\implies \: f(9) = 3 cos \bigg( \frac{3\pi}{2}\bigg) + 5 \\ \\\implies \: f(9) = 3 cos \bigg( \pi + \frac{\pi}{2}\bigg) + 5 \\ \\\implies \: f(9) = - 3 cos \bigg( \frac{\pi}{2}\bigg) + 5 \\ [ \because \: cos ({\pi}+\theta) = -\cos \theta]\\\\\implies \: f(9) = - 3 (0) + 5 \\ ( \because \: cos \frac{\pi}{2} = 0) \\ \\ \implies \: f(9) = 0 + 5 \\ \\ \implies \: \huge{ \orange{f(9) = 5 }}\)

Using L'hopital we can see that the limit is equal to 1/22

Here we want to take the limit of x tending to zero for x/sin(22x)

Notice that when x = 0, both numerator and denominator are zero, so we need to take the limit of the first derivatives, for:

y = x

y' = 1

And for:

y = sin(22x)

y' = 22*cos(22x)

Now taking the limit we will get:

\(\lim_{x \to 0} \frac{1}{22cos(22x)} = \frac{1}{22cos(0)} = 1/22\)

That is the value of the limit.

Learn more about limits at.

https://brainly.com/question/5313449

#SPJ1

Answer:

Jade Howey

Step-by-step explanation:

Answer:

Maria

Step-by-step explanation:

yodjdjdjdkdkdjekrnrjr

Lucio is 64 meters from the starting point.

The square has four sides of equal length, so Lucio has walked half the length of one side.

To return to the starting point, he needs to walk the other half of the side, which is 64 meters.

The angle Lucio turns is irrelevant, as long as he turns 180 degrees in total.

With this in mind, it can be seen that based on the parameters and the conditions, Lucio is 64 meters from the starting point because the angle to which he turns is irrelevant.

Read more about angles here:

https://brainly.com/question/25716982

#SPJ1

The question in English:

In a square Lucio walks in straight sections, starting from the flagpole, at one point he changes direction turning 150º to his left, advances 64 meters and stops. To return to the pole you have to turn 75º to the left. How far are you from the starting point?

Answer:

730.236

the answer

a) The dot product of v and -v is -1.

b) The dot product of v + w and v – w is 2v.w

c) The dot product of v – 2w and v + 2w is 4||w||^2 - 4v.w

(a) For any unit vector v, the dot product of v and -v can be found as follows:

v · -v = ||v||||-v||cos(θ) = ||v||||v||cos(180°) = -||v||^2 = -1, where ||v|| represents the magnitude of the vector v and θ is the angle between the vectors.

Since v and -v are unit vectors, their magnitudes are equal to 1, so ||v||^2 = 1. Thus, the dot product of v and -v is -1.

(b) For any unit vectors v and w, the dot product of v + w and v – w can be found as follows:

(v + w) · (v – w) = ||v + w||||v – w||cos(θ) = (||v||||v|| + 2v · w + ||w||||w||)cos(θ) = 2v · w

where θ is the angle between the vectors v + w and v – w, and v · w is the dot product of v and w.

(c) For any unit vectors v and w, the dot product of v – 2w and v + 2w can be found as follows:

(v – 2w) · (v + 2w) = ||v – 2w||||v + 2w||cos(θ) = (||v||||v|| + 4||w||||w|| - 4v · w)cos(θ) = 4||w||^2 - 4v · w

where θ is the angle between the vectors v – 2w and v + 2w, and v · w is the dot product of v and w.

To learn more about vectors click on,

https://brainly.com/question/14376687

#SPJ4

Answer:

= a^2 + 2.a.b + b^2

The expression "F = {(x, y) : φ(x, y, p)}" represents a set of ordered pairs (x, y) that satisfy a condition defined by the function φ. The interpretation and nature of the set F depend on the specific function φ and the parameter p, which determine the relationship between the variables x, y, and p.

The expression "F = {(x, y) :  φ(x, y, p)}" represents a set F consisting of ordered pairs (x, y) that satisfy a particular condition defined by the function  φ, which takes the variables x, y, and p as inputs.

To fully understand the meaning of F, we need to delve into the function  φ and its relationship with the variables x, y, and p. The function φ could represent a wide range of mathematical relationships or conditions that determine the inclusion of certain pairs (x, y) in the set F.

For instance, let's consider a specific example where vraphi(x, y, p) is defined  φ(x, y, p) = \(x^2 + y^2 - p^2.\)In this case, F = {(x, y) : \(x^2 + y^2 - p^2\)= 0} represents a set of ordered pairs (x, y) that satisfy the equation \(x^2 + y^2 - p^2 = 0.\) This equation represents a circle with radius p centered at the origin (0, 0). Consequently, F corresponds to all the points lying on the circumference of this circle.

It is important to note that the specific meaning and implications of F heavily rely on the nature of the function  φ and the parameter p. Different functions and parameters will yield distinct sets F with their own unique characteristics and interpretations.

For more such information on: expression

https://brainly.com/question/28602085

#SPJ8

Answer:

x = 27692903

Step-by-step explanation:

x - 2 + 3 = 27692904

x + 1 = 27692904         Combine like terms

x = 27692903        Subtract 1 from both sides

Hey there!

x - 2 + 3 = 27,692,904

COMBINE the LIKE TERMS

x + 1 = 27,692,904

SUBTRACT 1 to BOTH SIDES

x + 1 - 1 = 27,692,904 - 1

CANCEL out: 1 - 1 because it give you 1

KEEP: 27,692,904 - 1 because it gives you the x-value

NEW EQUATION: x = 27,692,904 - 1

SIMPLIFY IT!

x = 27,692,903

Therefore, your answer is:

x = 27,692,903

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

The coordinates of the vertices of trapezoid J'K'L'M' with its graph include the following:

J' (-3, 0).

K' (-3, -3).

L' (-8, 6).

M' (-8, 1).

In Mathematics and Geometry, the rotation of a point 90° about the center (origin) in a clockwise direction would produce a point that has these coordinates (y, -x).

By applying a rotation of 90° clockwise to the vertices of trapezoid JKLM, the coordinates of the vertices of the image are as follows:

(x, y)               →                ((y - b) + a, -(x - a) + b)

J (2, 1)           →     ((1 - 3) - 1, -(2 + 1) + 3) = (-2 - 1, -3 + 3) = J' (-3, 0).

K (5, 1)           →     ((1 - 3) - 1, -(5 + 1) + 3) = (-2 - 1, -6 + 3) = K' (-3, -3).

L (8, -4)           →     ((-4 - 3) - 1, -(8 + 1) + 3) = (-7 - 1, -9 + 3) = L' (-8, 6).

M (1, -4)           →     ((-4 - 3) - 1, -(1 + 1) + 3) = (-7 - 1, -2 + 3) = M' (-8, 1).

Read more on rotation here: brainly.com/question/28854313

#SPJ1

Answer:

Step-by-step explanation:

Given the expression in rectangular coordinate as x²+y²−4x=0, in order to write the given expression in polar coordinates, we need to write the value of x and y as a function of (r, θ).

x = rcosθ and y = rsinθ.

Substituting the value of x and y in their polar form into the given expression we have;

x²+y²−4x=0

( rcosθ)²+( rsinθ)²-4( rcosθ) = 0

Expand the expressions in parenthesis

r²cos²θ+r²sin²θ-4rcosθ = 0

r²(cos²θ+sin²θ)-4rcosθ = 0

From trigonometry identity, cos²θ+sin²θ =1

The resulting equation becomes;

r²(1)-4rcosθ = 0

r²-4rcosθ = 0

Add 4rcosθ to both sides of the equation

r²-4rcosθ+4rcosθ = 0+4rcosθ

r² = 4rcosθ

Dividing both sides by r

r²/r = 4rcosθ/r

r = 4cosθ

Hence the correct equation in polar coordinates is r = 4cosθ

Answer: I hope this helps.

Step-by-step explanation:

Answer:

The triangles are similar.

Explanation:

Similar triangles have 3 pairs of congruent angles. In this diagram, we can see that the triangles WXP and WYZ share angle W, which is congruent to itself; therefore, they have at least 1 pair of congruent angles. We are given that angle X is congruent to angle Y, so that is a second pair of congruent angles. Finally, we know that angle P is congruent to angle Z because if two pairs of corresponding angles are congruent, then the third pair must also be congruent because the measures of the interior angles of both triangles have to add to 180°.

For the fractions, the calculation of 3/5 of 2/3 of 3/4 of 560 is equal to 168.

To calculate 3/5 of 2/3 of 3/4 of 560, break it down step by step:

Step 1: Calculate 3/4 of 560:

3/4 × 560 = (3 × 560) / 4 = 1680 / 4 = 420

Step 2: Calculate 2/3 of the result from Step 1:

2/3 × 420 = (2 × 420) / 3 = 840 / 3 = 280

Step 3: Calculate 3/5 of the result from Step 2:

3/5 × 280 = (3 × 280) / 5 = 840 / 5 = 168

Therefore, 3/5 of 2/3 of 3/4 of 560 is equal to 168.

Find out more on fractions here: https://brainly.com/question/78672

#SPJ1