a train is 2500m long crosses a platform whose length is 1900 meters in 40 seconds . if a dog is running at the speed of 6 m\s in the direction of the train and the train is 936 meters away from the dog , then how much time will the train catch up with the dog

Answer:

16.53

Step-by-step explanation:

Start by finding the length of the line in the center. I will call this line a. Using the Pythagorean Theorem with 12.3 as the hypotenuse:

[tex]c^2=a^2+b^2\\a=\sqrt{c^2-b^2} \\a=\sqrt{12.3^2-5.4^2} \\a=\sqrt{122.13} \\a=11.05[/tex]

Now that this line is known, x can be found. Once again using the Pythagorean Theorem:

[tex]x^2=a^2+b^2\\x=\sqrt{a^2+b^2} \\x=\sqrt{12.3^2+11.05^2} \\x=\sqrt{273.39} \\x=16.53[/tex]

The indoor temperature ranges between 68.5 and 76.5 degrees Fahrenheit.

Given data;

According to the equation |x - 72. 5| = 4, the home's heating system is configured to maintain the minimum and maximum temperatures (in degrees Fahrenheit).

To find the minimum and maximum temperatures in the house,

We know that modulus is used to make a negative value into a positive;

|x - 72. 5| = 4

|A| = -A < x < A

|x - 72. 5| = 4

⇒ x - 72.5 = -4  x - 72.5 = +4

   x = 72.5 - 4    x = 4 + 72.5

   x = 68.5         x = 76.5

Hence, the minimum and maximum temperatures in the house are 68.5 and 76.5 Fahrenheit.

To learn more about Fahrenheit click here:

brainly.com/question/516840

#SPJ4

The measure of the angle SQR is 68 degrees if m/PSR = 134 and Angle QPS = Angle PSQ  = Angle SQP = 60 degrees.

When two lines or rays converge at the same point, the measurement between them is called a "Angle."

It is given that:

m/PSR = 134,

PQ = QS = PS

Angle QPS = Angle PSQ  = Angle SQP = 60 degrees

Angle QSR = QRS

Angle SQR = 180 - (180 - 134)x2

= 180 - 112

= 68 degrees

Thus, the measure of the angle SQR is 68 degrees if m/PSR = 134 and Angle QPS = Angle PSQ  = Angle SQP = 60 degrees.

Learn more about the angle here:

brainly.com/question/7116550

#SPJ1

The polynomial representing length, breadth and height of th e container is

Volume is measure in liters, cubic meters and so on

The formula for volume calculation is given by

volume = length * width * height

from the question

height is 0.15 m more than their width

width = w

height = 0.15 + w

length = L

volume = 652 m³

652 = L * w * (w + 0.15)

652 = (w^2 + 0.15w)L

652 = Lw^2 + 0.15Lw

Lw^2 + 0.15Lw - 652

Learn more about volume calculation here:

https://brainly.com/question/29400663
#SPJ1

Answer:

Step-by-step explanation:

First calculate 55% of 150:

= 150 x 55/100

= 82.5 ans

Now decrease it from 150:

= 150-82.5

= 67.5 ans Hope it helps!!

The first four terms of the sequence defined by the rule f(n) = n³-1 are -1, 0, 7 and 26.

According to the question,

We have the following expression:

f(n) = n³-1

Now, in order to find the first four values of the given expression, we will change the values of n from 0 to 3.

So, putting the value of n as 0, we have:

f(0) = 0³-1

0-1 = -1

Now, putting the value of n as 1, we have:

1³-1

1-1

0

Now, putting the value of n as 2, we have:

2³-1

8-1

7

Now, putting the value of n as 3, we have:

3³-1

27-1

26

Hence, the first four terms of the sequence defined by the rule f(n) = n³-1 are -1, 0, 7 and 26.

To know more about terms of the sequence here

https://brainly.com/question/28615767

#SPJ1

Answers:

V = 30 cubic cm

D = 4 grams per cubic cm

=========================================================

Explanation:

The volume of a rectangular solid (aka block or brick) is equal to its length times width times height

V = length*width*height

V = 5*2*3

V = 10*3

V = 30 cubic cm

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

You haven't mentioned it, but the "D" probably refers to the density. This is a measure how much stuff occupies a certain volume of space. The higher the density, the more stuff in that space. Think of it like cramming more packing peanuts in a box.

To find the density, we divide the mass over the volume

density = mass/volume

density = (120 grams)/(30 cubic cm)

density = 4 grams per cubic cm

In each cubic centimeter of space, there are 4 grams of mass.

The needed sample size Smaller if the margin of error .

Given,

In the question:

This question in the form of: Fill in the blanks.

So, You want to estimate the proportion of students at your university in favor of a longer spring break. changing the confidence level from 95% to 90% will decrease the needed sample size_____ if the margin of error.

Hence, The answer is smaller the margin of error.

Let's Know:

What is Confidence level?

The confidence level is the percentage of times you expect to get close to the same estimate if you run your experiment again or resample the population in the same way. The confidence interval consists of the upper and lower bounds of the estimate you expect to find at a given level of confidence.

Learn more about Confidence Level at:

https://brainly.com/question/9386257

#SPJ4

Answer:

$2300

Step-by-step explanation:

1. Her yearly allowable debt

36% × 85000 = 30600

2. Her monthly allowable debt

30600/12 = 2550

3. Her monthly existing debt

car payment = 200

car insurance = 300/6 =50

monthly utility bill = na this is an estimation

4. allowable debt - existing debt

2550 -200-50= 2300

ps: i may be wrong

The expression can be written without negative exponents as 1/(bm)³

Exponent is defined as the method of expressing large numbers in terms of powers. That means, exponent refers to how many times a number multiplied by itself. For example, 6 is multiplied by itself 4 times, i.e. 6 × 6 × 6 × 6. This can be written as 6⁴. Here, 4 is the exponent and 6 is the base.

Simplifying exponents is a method of simplifying the algebraic expressions involving exponents into a simpler form such that they cannot further be simplified. There are rules in algebra for simplifying exponents with different and same bases that we can use.

Steps to removing exponents are;

Step 1

remove parentheses by multiplying factors.

Step 2

use exponent rules to remove parentheses in terms with exponents.

Step 3

combine like terms by adding coefficients.

Step 4

combine the constants.

In this case, we have an expression;

(bm)⁻³ which can be rewritten using cube.

(bm)⁻³ = 1/ (bm)³

Learn more on exponents here;

https://brainly.com/question/847241

#SPJ1

The given exponential function will grow at rate of 4%

Given, the following exponential function,

y = 530(1.04)ˣ

we are asked to  identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease.

we have:

y = 530(1.04)ˣ

The equation represents exponential growth because the growth factor is greater than 1.

The general form equation is:

y(x) = a(1-r)ˣ

⇒ 1+r = 1.04

⇒ r = 0.04

⇒ r = 4%

Hence the given exponential function will grow at 4%.

Learn more about Exponential functions here:

brainly.com/question/2456547

#SPJ9

Answer:

No

Step-by-step explanation:

parallel is when 2 lines never touch and move in the same direction and these touch and move in different directions

Hopes this helps please mark brainliest

Answer:

90 m

Step-by-step explanation:

because the helicopter is 60 m up and the submarine is 30 m under so combining the two helps us identify the difference between the two objects

Answer:

I'll try my best B r u h ....

Step-by-step explanation:

Bowling:

15+5x  where x is the number of people

Skating:

20+3x

We have 50 dollars so the amount must be less than or equal to 50

Bowling

15+5x≤50

Subtract 15 from each side

15-15+5x≤50-15

5x ≤35

Divide each side by 5

5x/5 ≤35/5

x ≤7

She can have 7 or less people

Skating

We have 50 dollars so the amount must be less than or equal to 50

20+3x  ≤50

Subtract 20 from each side

20-20+3x  ≤50-20

3x  ≤30

Divide each side by 3

3x/3 ≤30/3

x ≤10

She can have up to 10 people

She can invite more people skating

Hope this helped.

Answer:

3√13

Step-by-step explanation:

4 : y = y = 9

y^2 = 36

y = 6

z = [tex]\sqrt{9^2 + 6^2} = \sqrt{81 + 36} = \sqrt{117}[/tex]

117 = 3^2 * 13

[tex]\sqrt{117} = \sqrt{3^2 * 13} = 3\sqrt{13[/tex]

Answer:

9. train a = 8.33 hours

train b = 5 hours

time of coincidence = 3.33 hours

Step-by-step explanation:

I'm not sure about this but I think it's correct.

Answer:

B

Step-by-step explanation:

[tex]x-y=-4 \\ \\ x-f(x)=-4 \\ \\ f(x)-x=4 \\ \\ f(x)=x+4[/tex]

Answer:

Yolanda bought 48 yards of ribbon, and spent 7.68 cents on it.

Step-by-step explanation:

First Step: Find out how much Yolanda spent

20.00 -12.32 = 7.68

Second Step: Divide Total Cost by Price of one Yard

7.68/0.16 = 48

Third Step: Double Check

48 x 0.16 = 7.68

I hope my answer helped you, good luck on your homework!

It is true that the eigenvectors of the covariance matrix are equal to the principal components. Concretely, the first principal component (i.e. the largest eigenvector and associated largest eigenvalue) gives you the direction of the maximum variability in your data

The covariance matrix's eigenvectors are identical to its major components, which is a well-known fact. In more concrete terms, the direction of the most variability in your data is provided by the first principal component, which is represented by the largest eigenvector and related largest eigenvalue. After that, each primary component provides you decreasingly variable output. The fact that each primary component is orthogonal to the others is also important to note.

The above picture was taken from the Principal Component Analysis article on Wikipedia, which I previously referred to. This is a scatter plot of samples having a bivariate Gaussian distribution with a center at (1,3), a standard deviation of 3 roughly in the (0.878, 0.478) direction, and a standard deviation of 1 roughly in the orthogonal direction. The first principal component is the one with a standard deviation of 3, and the second is the orthogonal component. The shown vectors are the eigenvectors of the covariance matrix scaled by the relevant eigenvalue's square root and moved to place their tails at the mean.

Learn more about eigenvectors here:

brainly.com/question/14415835

#SPJ4

If the equation is 4y - 6x = 12, then (-4, -3) and (0, 3) are the solutions of the equation

The equation is given that

4y - 6x = 12

The first solution =(-4, -3)

The value of x = -4

The value of y = -3

Substitute the values in the equation

4(-3) - 6(-4) = 12

-12 - (-24) = 12

-12 + 24 = 12

12 = 12

Therefore (-4, -3) is the solution of the equation

Next solution is (0, 3)

The value of x = 0

The value of y = 3

Substitute the values in the equation

4(3) - 6(0) = 12

12 - 0 = 12

12 = 12

Therefore (0, 3) is the solution of the equation

Hence, if the equation is 4y - 6x = 12, then (-4, -3) and (0, 3) are the solutions of the equation

Learn more about equation here

brainly.com/question/14603452

#SPJ1

Answer: ?

Step-by-step explanation:

that's how you do it.

Answer:

x has no real solution/roots

Step-by-step explanation:

please see the attached image:

Answer:

10

Step-by-step explanation:

tbh i am confused

please if you see this, i am really trying my best and you guys gave me the hardest question i ever had. sincerely apologize

A Paired t-test evaluates data from dependent samples in which the two

treatments are applied to the same individual.

T-test is a statistical statistics mainly use when population variance is

unknown and sample size is small.

In Paired t-test , we compare means of two dependent samples. It gives

hypothesis examination on difference between of mean.

It uses same items or people in both sample that's why they are also known as dependent t-test or Paired t-test also increases the statistical power of our analysis.

Formula of paired t-test :

t = m / S / n

with (n-1) degree

where , m --> mean difference

S ---> standard deviation difference

n --> sample size

To know more about Paired t-test, refer:

brainly.com/question/28020847

#SPJ4

The number of nickels is 25

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

We have,

The total number of nickels and quarters = 63

Total value = $10.75

20 nickels = 1 dollar

4 quarters = 1 dollar

Now,

1 nickel = $0.05

1 quarter = $0.25

Let the number of nickels = x

Let the number of quarters = y

We can make equations as,

0.05x + 0.25y = 10.75 _____(1)

x + y = 63 ______(2)

From (2) we get,

x = 63 - y

Putting in (1) we get,

0.05 (63 - y) + 0.25y = 10.75

3.15 - 0.05y + 0.25y = 10.75

3.15 + 0.20y = 10.75

0.20y = 10.75 - 3.15

0.20y = 7.6

y = 7.6/0.20

y = 38

Now,

x = 63 - y = 63 - 38 = 25

Thus,

The number of nickels is 25

Learn more about equations here:

https://brainly.com/question/17194269

#SPJ1

Answer:

[tex]u=-25.6[/tex]

Step-by-step explanation:

Take a look at the attachment...

Hope this helps! :)