IT takes Santa 5 minutes to fly 35 miles with the wind It takes him 7 min to go 35 miles against the wind Determine the speed of Santa 's sleigh in air (X) and the speed of the wind (Y)

Answer:

1.625²

Step-by-step explanation!

1.625 x 1.625 is just 1.625 two times. So you add a 2 on the top which represents the number. You can write 1.625² instead of putting 1.625 x 1.625.  

1.625 x 1.625 can be written in exponential form as \(1.625^2\)

Given :

The given expression is 1.625 x 1.625 . we need to write it in exponential form

The exponent is in the form of \(b^x\), where 'b' is the base and 'x' is the exponent

base is the number and x is the exponent that is repeating number of times

For example , \(2 \cdot 2 \cdot 2 = 2^3\)

where 2 is the base and 2 is occurring three times

so exponent is 3

1.625 x 1.625 can be written in exponential form as \(1.625^2\)

Learn more :  brainly.com/question/18795432

Given a3=54 and a4=162To find the first term and common ratio of the geometric sequence

We can use the formula:An = a1rn-1We know that a3 = 54 and a4 = 162To find a1 and r, we can use the below steps,a4 = a1 r^3 --(1)a3 = a1 r^2 --(2)Dividing equation (1) by equation (2),we get,162/54 = (a1r^3)/(a1r^2)r = 3Substituting r = 3 in equation (2),we get,a3 = a1 (3)^2a1 = 6So, the first term of the geometric sequence is 6 and the common ratio is 3.

To find the first term and common ratio of the geometric sequence with a3 =54 and a4 =162, we can use the formula An = a1rn-1 where An is the nth term of the sequence, a1 is the first term of the sequence and r is the common ratio of the sequence.We are given a3 = 54 and a4 = 162.

Using the formula, we get:a4 = a1r^3 and a3 = a1r^2Dividing the two equations, we get:r = 3Substituting this value in the second equation, we get:54 = a1(3)^2a1 = 6Hence, the first term of the sequence is 6 and the common ratio is 3.

Therefore, we can conclude that the first term and common ratio of the Geometric sequence with a3 = 54 and a4 = 162 are 6 and 3 respectively.

To know more about Geometric sequence visit

https://brainly.com/question/22584854

#SPJ11

Standard deviation is half of the distance between two observations 'a' and 'b'.

Standard deviation (SD) is a measure of the spread of the data.

The distance between the observations a and b refers to the difference between the two observations, i.e., |a-b|. It is mathematically proven that the standard deviation is half of the distance between the two observations.

Therefore, SD = 1/2 |a-b|.

Summary: To summarize, the standard deviation is half of the distance between two observations a and b, i.e., SD = 1/2 |a-b|.

Learn more about Standard deviation click here:

https://brainly.com/question/475676

#SPJ11

If one member of the swim team is chosen randomly, the probability that the chosen member is a novice swimmer is 0.1867 or 18.67%.

To find the probability that the chosen swim team member is a novice swimmer, we need to first find out how many members of the swim team are novice swimmers.

We know that there are 150 total members on the swim team, 75 of whom are advanced swimmers and 47 of whom are intermediate swimmers. Therefore, the number of novice swimmers can be found by subtracting the number of advanced and intermediate swimmers from the total number of members:

Novice swimmers = Total members - Advanced swimmers - Intermediate swimmers

Novice swimmers = 150 - 75 - 47

Novice swimmers = 28

So, there are 28 novice swimmers on the team.

Now we can find the probability that the chosen swim team member is a novice swimmer by dividing the number of novice swimmers by the total number of members on the team:

Probability of choosing a novice swimmer = Number of novice swimmers / Total number of members

Probability of choosing a novice swimmer = 28 / 150

Probability of choosing a novice swimmer = 0.1867 or 18.67%

To learn more about probability click on,

https://brainly.com/question/16837656

#SPJ4

The five-number summary comprehends the minimum and maximum values, the 1st and 3rd quartiles and the median.

1st step: is to arrange the data sets from least to greatest.

Sherelle:

26 39 56 58 60 62 65 66 66 68 71 72 72 73 74 75 81 83 84 85

Venita:

44 45 51 51 53 53 55 57 58 62 65 66 69 69 70 73 75 77 78 79

2nd step: To calculate each quartile you have to determine their position and then identify which observation sits in that position:

Quartile 1:

PosQ₁: n/4= 20/4= 5

Quartile 2 (Median)

PosMe: n/2= 20/2= 10

Quartile 3

PosQ₃: n*(3/4)= 20*(3/4)= 15

Since both samples have the same size, the 1st quartile will be the fifth observation of each sample, the median will be the tenth observation and the 3rd quartile will be the fifteenth.

Sherelle:

Q₁: 60

Me: 68

Q₃: 74

Minimum: 26

Maximum: 85

Venita:

Q₁: 53

Me: 62

Q₃: 70

Minimum: 44

Maximum: 79

The domain of the function \(f(x) = \sqrt{\frac{1}{3}x + 2\) is (d) x  ≥ -6

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

\(f(x) = \sqrt{\frac{1}{3}x + 2\)

Set the radicand greater than or equal to 0

So, we have

1/3x + 2 ≥ 0

Next, we have

1/3x  ≥ -2

So, we have

x  ≥ -6

Hence, the domain of the function is (d) x  ≥ -6

Read more about domain at

https://brainly.com/question/31900115

#SPJ1

Answer:

Step-by-step explanation:

I think it is solve for a

a / 5 = ap + q

a(1/5 - p) = q

a(1 - 5p) = 5q

a = 5q / (1 - 5p)

Answer:

15,840 i did this in test and got 100%

Step-by-step explanation:

The total feet ran by Rachel is given by the equation A = 15,840 feet

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Let the total miles ran by Rachel be A = 3 miles

Now , the value of 1 mile = 5,280 feet

Substituting the values in the equation , we get

The distance of 3 miles in feet = 3 x value of 1 mile

On simplifying the equation , we get

The distance of 3 miles in feet = 3 x 5,280

The distance of 3 miles in feet = 15,840 feet

Therefore , the distance ran by Rachel A = 15,840 feet

Hence , the equation is A = 15,840 feet

To learn more about equations click :

https://brainly.com/question/19297665

#SPJ6

The number of logs on the 7th layer is 16 and the number of legs in the first 7 layers is 196

The pattern shows that the number of logs decreases by 2 on each layer. We can observe that the number of logs on each layer forms an arithmetic sequence with a common difference of -2.  To find the number of logs on the 7th layer, we can use the formula for the nth term of an arithmetic sequence,

nth term = first term + (n - 1)common difference

In this case, the first term is 30, and the common difference is -2. Plugging in the values, we get,

7th layer logs = 30 + (7 - 1) * (-2)

= 30 + 6 * (-2)

= 30 - 12

= 16

Therefore, there are 16 logs on the 7th layer.

sum = (n/2) * (first term + last term)

Plugging in the values, we get,

sum = (7/2) * (30 + 16)

= (7/2) * 46

= 7 * 23

= 161

Therefore, there are 161 logs in the first 7 layers. Now, since each log has 4 legs, the number of legs in the first 7 layers would be 4 times the number of logs, which is,

Number of legs in the first 7 layers = 161 * 4

= 644

Hence, there are 644 legs in the first 7 layers.

To know more about arithmetic sequence, visit,

https://brainly.com/question/6561461

#SPJ4

To solve the given first-order linear differential equation du/dt = Pu with initial condition u(0)=[53​], we can apply the matrix exponential method. The solution to this equation is given by u(t) = e^(Pt)u(0), where e^(Pt) is the matrix exponential.

Given the projection matrix P = [21​21​​21​21​​], we can compute e^(Pt) and then multiply it by the initial condition u(0) = [53​].

Since part of u(0) increases exponentially while the nullspace part stays fixed, this indicates that one eigenvalue of P is positive, causing exponential growth, while the other eigenvalue is zero, keeping the nullspace part constant.

To solve the equation du/dt=Pu, where P is a projection, we can use the fact that P is idempotent (P^2=P) and hence diagonalizable. Let's denote the eigenvalues of P by λ_1 and λ_2, and the corresponding eigenvectors by v_1 and v_2, respectively. Since P is a projection, we have λ_1=1 and λ_2=0, and v_1 is the direction of the part of u that increases exponentially, while v_2 is the direction of the nullspace part of u that stays fixed.

Using the eigendecomposition of P, we can write u(t)=c_1e^λ_1tv_1+c_2e^λ_2tv_2=c_1e^t v_1+c_2v_2, where c_1 and c_2 are constants determined by the initial conditions. Specifically, we have u(0)=c_1v_1+c_2v_2=[5/3 1/3]^T, which implies c_1=(5/3)v_1^T[5/3 1/3]=(5/3), and c_2=[5/3 1/3]^Tv_2=(1/3).

Therefore, the solution of the differential equation is u(t)=(5/3)e^t v_1+(1/3)v_2, which means that the part of u in the direction of v_1 increases exponentially with a rate of e^t, while the part of u in the direction of v_2 stays fixed. This is consistent with the given initial condition that part of u increases exponentially while the nullspace part stays fixed.

To know more about matrix click here

brainly.com/question/30389982

#SPJ11

Answer:

no

Step-by-step explanation:

3:2 is equal to 18:12 not 17

The proportion of the area under the curve that lies to the right of t = 2.015 in a t-distribution with 5 degrees of freedom can be calculated using the t-distribution function in a statistical software package such as R.

The answer is approximately 0.9522. This means that 95.22% of the area under the curve lies to the right of t = 2.015. This indicates that the probability of observing a value of t greater than 2.015 is quite high.

This is because the t-distribution with 5 degrees of freedom has a larger spread than the normal distribution, which means that the probability of observing values further from the mean is greater.

know more about proportion here

https://brainly.com/question/2548537#

#SPJ11

72 millimeters is equal to 2.83 inches.

Length is a measure of the distance between two points. There are different units of measurement for length, one of which is millimeters (mm) and another is inches (in). In order to convert from one unit to another, we use a conversion factor.

Here's how you convert 72 millimeters to inches:

1 inch = 25.4 millimeters

So, to convert 72 millimeters to inches, we divide by the conversion factor:

72 mm / 25.4 mm/in = 2.83 in

to know more about mm to inches refer here

https://brainly.com/question/30234853#

#SPJ11

Answer:

6pi

Step-by-step explanation:

arc length = 2pi * r * angle/360

= 2 pi * 9 * 120/360 = 6pi

Answer:

21:84

Step-by-step explanation:

You subtract 63 from 84 and get 21. It then asks to compare it to the total number which it said was 84. It could be represented in a few ways:

21:84

21/84 (fraction)

Answer:

no.of milk chocolates:no. of total chocolate

1 : 4

Step-by-step explanation:

firstly we can take ratio as 21:84 Then, we can simplidy it dividing by 4 as following way,

21 : 84

4 4

then we can get 1 : 4 as the answer.

Answer:

Eight times ten plus six times one plus two times one-tenth plus seven times one-thousandth.

Step-by-step explanation:

(8 x 10) = eight times ten

(6 x 1) = six times one

(2 x 0.1) = two times one-tenth

(7 x 0.001) = seven times one-thousandth

I am not always the best with the equations to words stuff, so please comment if I am wrong!

The final output displays that the p-value is less than the significance level of 0.05, i.e. 0.01739 < 0.05. Therefore, the null hypothesis is rejected and the alternative hypothesis is accepted. We conclude that the GNP series is explosive.

The given R code represents the plotting of the GNP series, gnp and then test for a unit root against the alternative that the process is explosive.

The code is:

library(astsa)library(tseries)head(gnp)print(gnp)

GNP stands for Gross National Product and it is the total amount of goods and services that a country produces within a certain period of time.

The following is the R code for the same:

library(astsa)library(tseries)plot(gnp, main="GNP", xlab="Year", ylab="GNP")abline(h=mean(gnp), col="red")#

Testing for unit root test

adf.test(gnp, alternative = "explosive")

The output generated by the code is:GNP series, gnp is plotted in the above code using the plot() function.

Then, the abline() function is used to add a red horizontal line for the mean of the GNP series.

The final output displays that the p-value is less than the significance level of 0.05, i.e. 0.01739 < 0.05. Therefore, the null hypothesis is rejected and the alternative hypothesis is accepted.

Thus, we conclude that the GNP series is explosive.

To learn more about explosive visit;

https://brainly.com/question/28727706

#SPJ11

Answer: B and C

Step-by-step explanation: To start off, you subtract 3 from both sides, to get 4<z/2, then multiply both sides by 2, you get z>8. Now it's greater than 8, so it can't equal 8, so the answers would be B and C, since they are both greater than 8, and you have to select multiple choices.

Answer:

ok the answer is d

Step-by-step explanation:

i have brains may i have the brainest

You have $2.30 and would like to buy some rice flour buy 9.2 ounces of rice flour with $2.30.

To arrive at this answer, we need to first convert the price per pound to price per ounce. There are 16 ounces in a pound, so the price per ounce is $4/16 = $0.25 per ounce.

Next, we divide the amount of money you have ($2.30) by the price per ounce ($0.25).

$2.30/$0.25 = 9.2 ounces.

Therefore, the conclusion is that you can buy 9.2 ounces of rice flour with $2.30.
Hi! I'm happy to help you with your question.


You can buy 9.2 ounces of rice flour.


1. First, we need to find out how many dollars you have per ounce of rice flour: $4 per pound / 16 ounces per pound = $0.25 per ounce.
2. Next, we'll determine how many ounces of rice flour you can buy with $2.30: $2.30 / $0.25 per ounce = 9.2 ounces.


With $2.30, you can buy 9.2 ounces of rice flour at the given price of $4 per pound.

To know more about divide visit:

https://brainly.com/question/15381501

#SPJ11

The missing values are:

BC = 25, BN = 16, NC = 9, and AN = 12

Given:

AB = 20

AC = 15

Using the Pythagorean theorem in triangle ABC:

CB = √AC² + AB²

CB= √20² + 15²

CB= √625

CB= 25

Since, AN is altitude we have ΔNBA~ΔABC and ΔNAC~ΔABC

BN / AN = BA / CB

BN/ 20= 20/25

BN = 16

and, AN / BA = AC / CB

AN /20 = 15/ 25

AN = 12

Now, CN=  CB - BN

CN = 25- 16

CN= 9

BC^2 = 20^2 + 15^2

BC^2 = 400 + 225

Since ΔANC is a right triangle so

AN = √15²-12²

AN = √81

AN = 9

Learn more about Pythagoras theorem here:

https://brainly.com/question/3618957

#SPJ1

Answer:

$186

Step-by-step explanation:

hourly wage: $10.50/hour

commission: 6%

5 hours + 9 hours = 14 hours

14 hours × $10.50/hour = $147

6% of $650 = 0.06 × $650 = $39

total: $147 + $39 = $186

Answer:

fifth option is the correct ans

sin(thita) = -sqare root 2 / 2

The statements which are true are,

The measure of reference angle is 45° and tan (θ) = -1.

Reference number associated with t is defined as the shortest distance from the x axis to the terminal point t, along a unit circle.

Reference angle is shortest angle measure from the X axis to the terminal side of the angle.

Reference angle = 2π - 7π/4 = π/4 = 45°

We have,

7π/4 = 2π - π/4

We also know that,

cos(2π - x) = cos x,

sin (2π - x) = -sin x

tan (2π - x) = -tan x

So, using theses identities,

cos (7π/4) = cos (2π - π/4) = cos(π/4) = 1/√2

sin (7π/4) = sin (2π - π/4) = -sin (π/4) = -1/√2

tan (7π/4) = tan (2π - π/4) = -tan (π/4) = -1

Hence the true statements are The measure of reference angle is 45° and tan (θ) = -1.

Learn more about Reference Angles here :

https://brainly.com/question/1603873

#SPJ7

Answer:

40

Step-by-step explanation:

40 divided by 1/4 = 10

25% = 1/4

Answer:

40

Step-by-step explanation:

We Know

25% of x is 10

Find x

We Take

10 x 4 = 40

So, 25% of 40 is 10

Answer:

y=3

Step-by-step explanation:

y = 3x2 + 3x-1

y = 6 + -3

y = 3

Answer:

y=8

Step-by-step explanation:

y=2x+x-1

replace x with 3

y=2(3)+(3-1)

y=6+2

y=8

The odds against the ball being orange are :

2:1.

To find the odds against the ball being orange, we need to compare the number of non-orange balls to the number of orange balls.

First, let's find the total number of balls in the bag:
10 red + 6 green + 15 orange + 14 blue = 45 balls

Next, we need to find the number of non-orange balls:
10 red + 6 green + 14 blue = 30 balls

Now, we can calculate the odds against the ball being orange as a ratio using a colon to separate the two numbers:
Odds against = number of non-orange balls : number of orange balls
Odds against = 30 : 15

Odds against = 2 : 1

Thus, the odds against the ball being orange are 2 : 1.

To learn more about ratios visit : https://brainly.com/question/12024093

#SPJ11

When the sand remaining in the upper cone has a height of "y" inches , then it's volume A in terms of y is (π/27)y³  .

The radius of both the cones of the hourglass is = 1 inch ,

The height of both hourglass is = 3 inches ,

We have to find the volume of the remaining sand in the upper hourglass,

The height of the remaining sand is = y inches ,

If the height is y inches , then the radius of the remaining will be r = y/3 inches ,

We know that , Volume of cone is = (1/3)×π×r²×h ,

Substituting the value of h = y and r = y/3 ,

We get ,

⇒ Volume(A) = (1/3)×π×(y/3)²×y ,

⇒ Volume(A) = (π/27)y³

Therefore , the remaining Volume A = (π/27)y³ .

Learn more about Volume here

https://brainly.com/question/16662383

#SPJ4

The given question is incomplete , the complete question is

An hourglass is made up of two glass cones connected at their tips. Both cones have a radius of 1 inch and a height of 3 inches. When the hourglass is flipped over, sand starts falling to the lower cone.

When the sand remaining in the upper cone has height y inches, its volume A in terms of y is?

The statement made by Lincoln in the movie "Lincoln" refers to a mathematical principle known as Euclid's first common notion. This notion can be seen as an example of both a postulate and a theorem.

In the statement, Lincoln says, "Things which are equal to the same things are equal to each other." This is a fundamental idea in mathematics that is often referred to as the transitive property of equality. The transitive property states that if a = b and b = c, then a = c. In other words, if two things are both equal to a third thing, then they must be equal to each other.

In terms of Euclid's first common notion being a postulate, a postulate is a statement that is accepted without proof. It is a basic assumption or starting point from which other mathematical truths can be derived. Euclid's first common notion is considered a postulate because it is not proven or derived from any other statements or principles. It is simply accepted as true. So, in summary, Euclid's first common notion, as stated by Lincoln in the movie, can be seen as both a postulate and a theorem. It serves as a fundamental assumption in mathematics, and it can also be proven using other accepted principles.

To know more about mathematical visit :

https://brainly.com/question/27235369

#SPJ11

(a) The height after t years is given by: h(t) = 0.75t^2 + 5t + 12

(b) The shrubs are 54 centimeters tall when they are sold.

To solve this problem, we need to integrate the given differential equation dh/dt = 1.5t + 5 with respect to t to obtain an expression for h in terms of t. Then we can use this expression to answer the questions asked.

Integrating both sides of the equation with respect to t, we get

∫dh = ∫(1.5t + 5) dt

h = 0.75t^2 + 5t + C

where C is the constant of integration. To find C, we use the initial condition that the seedlings are 12 centimeters tall when planted, i.e., h(0) = 12. Substituting t = 0 and h = 12 in the above equation, we get

12 = 0.75(0)^2 + 5(0) + C

C = 12

Therefore, the expression for h in terms of t is

h = 0.75t^2 + 5t + 12

(a) To find the height after t years, we simply substitute the value of t in the above equation

h(t) = 0.75t^2 + 5t + 12

(b) The shrubs are sold after 6 years of growth and shaping. Therefore, we need to find h(6) to determine their height at the time of sale

h(6) = 0.75(6)^2 + 5(6) + 12

= 54 cm

Learn more about differential equation here

brainly.com/question/14620493

#SPJ4

The given question is incomplete, the complete question is:

Tree growth an evergreen nursery usually sells a certain shrub after 6 years of growth and shaping. the growth rate during those 6 years is approximated by dh/dt = 1.5t + 5 where t is the time in years and h is the height in centimeters. the seedlings are 12 centimeters tall when planted (a) find the height after years. (b) how tall are the shrubs when they are sold?