Mathematics Middle School

A plane traveled 972 miles to Berlin and back. The trip there was with the wind. It took 9 hours. The trip back was into the wind. The trip back took 18 hours. Find the speed of the plane in still air and the speed of the wind

Answers

Answer 1
With the wind, the plane's speed was (972 mi)/(9 h) = 108 mi/h.
Against the wind, the plane's speed was (972 mi)/(18 h) = 54 mi/h.

The speed of the plane in still air is the average of these speeds, 81 mi/h.
The speed of the wind is half the difference of the trip speeds, 27 mi/h.

Related Questions

How do you get the value of x

Answers

You add the angles, then set that total to 180°, the total of the angles in any triangle.
.. 5x = 180
.. x = 180/5 = 36

Web flixs charges $25 and $2 for each movie family video charges $10 plus $2.50 for each movie find the number of movie rental for both stores charge are the same

Answers

The number of movie rentals would be 30
To find the answer you have to do this
(M stands for movies)
$25 + 2m = $10 + 2.50m
-10     -2m   -10      -2
$15 = .50m
Divide .50/15
You get 30 
Check your answer $25 + 2(30) = $10 + 2.50(30)
$25 + $60 = $10 + $75
$85 = $85
Final answer:

The number of movie rentals for which Web Flixs and Family Video charge the same is 30.

Explanation:

To find the number of movie rentals for which Web Flixs and Family Video charge the same, we need to set up an equation and solve for the number of movies. Let's denote the number of movie rentals as 'x'.

For Web Flixs, the cost is $25 + $2 per movie, so the total cost can be expressed as 25 + 2x.

For Family Video, the cost is $10 + $2.50 per movie, so the total cost can be expressed as 10 + 2.50x.

To find the number of movie rentals for which the costs are the same, we set up the equation: 25 + 2x = 10 + 2.50x.

By rearranging the equation and solving for 'x', we can find the number of movie rentals:

25 - 10 = 2.50x - 2x

15 = 0.50x

x = 30

Therefore, when the number of movie rentals is 30, the charges at both Web Flixs and Family Video will be the same.

PLEASE HELP

If a student is chosen at random find the probability the student is male given that its a senior. Round to the nearest while percent.

Answers

Answer: 40%

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

Work Shown:

"given that it's a senior" is an important piece of info that tells us to only focus on the "seniors" column. The word "given" is an indication that we know this information 100%

There are 5 seniors (2+3 = 5) and 2 of them are male. So 2/5 = 0.40 = 40% of the seniors are male. The probability of selecting a male, if we know this person is a senior, is 40%

The probability that a randomly selected senior student is male is 40%.

Given Data:

We have a two-way table representing the number of students by gender and grade level.

The relevant information is that there are 2 male seniors.

Event Definitions:

Let’s define the following events:

A: Student is male.

B: Student is a senior.

Conditional Probability:

We want to find the probability that a student is male given that they are a senior: (P(\text{Male}|\text{Senior})).

We can use the formula for conditional probability: [tex][P(\text{Male}|\text{Senior}) = \frac{P(\text{Male and Senior})}[/tex][tex]{P(\text{Senior})}][/tex]

Calculations:

From the table, we know:

Number of male seniors (A and B): 2

Total number of seniors (B): 5

Therefore: [[tex]P(\text{Male}|\text{Senior}) = \frac{2}{5} = 0.4][/tex]

Rounded Answer:

Rounding to the nearest whole percent:

([tex]0.4 \times[/tex]100% = 40%)

Summary: The probability that a randomly selected senior student is male is 40%.

How do I solve 20% out of 75

Answers

20% -->decimal 0.2

75 x 0.2 = ?

? = 15
You take the decimal of 20 percent which is 0.2 and multiply it by 75. Then when you got your answer move the number of numbers after the decimal from the answer backwards. Now you got your answer . :)

The velocity of an airplane heading east is 400 knots with a wind velocity of 50 knots blowing toward the northeast. Calculate the resultant speed and direction of the plane. Round to the nearest tenth.

Answers

1. To Calculate the resultant speed of the plane, you need to find the speed of the air, add it to the plane speed, then find the resultant using trigonometry.

The velocity of the plane:
east=400 knots

The velocity of the air
50knots north east = 50/√2 north + 50/√2 east

The resultant speed would be:
total speed^2= east^2 + north^2
total speed= √(400+50/√2)^2 + (50/√2)^2
total speed= √(189534.254 + 1250)
total speed= 436.8 knots

2. To count the direction of the plane, you need to find the total speed of x(east/west) and y(north/south) axis separately then use tan formula.
east speed= 400knots + 50/√2 knots= 435.35 knots
north speed= 50/√2knots= 35.35 knots

tan a= opposite/adjacent
tan a = north speed/ east speed
tan a= 35.35/ 435.35 
tan a=0.0812
a= 4.6 degrees

what is the slope of the line (2,-2) and (9,3)

Answers

slope =  3-(-2) / 9-2
slope = 5/7
HI,
the slope of the line is 
m=5/7
i hope this helped you

if the temperature at 9:00 pm was 12 degrees farenheit,and after 6 hours the temperature dropped to 6 degrees Fahrenheit below 0,what was the rate of change in temperature per hour?

Answers

12-6 = 6
6-6=0
6 is the rate of change in temperature 6 hours
Then 1 is the rate of change in temperature is 1 hour

​ Quadrilateral ABCD ​ is inscribed in this circle.



What is the measure of angle B?

Enter your answer in the box.

m∠B=
°

Answers

Hello,

When you have an inscribed quadrilateral, the opposite sides are supplementary.

So you can write and solve the following equation.
x + 6x + 19 = 180
7x + 19 = 180
7x = 161
x = 23

Now, plug in 23 for X and we will find the measurement of B.
6(23) + 19
138 + 19
157

The measure of angle B is 157 degrees. (The picture is not drawn to scale)

Good luck,
MrEQ

Please help me, thanks.

Answers

1. Commutative Property of Addition.a + b = b + a 

Examples: 

1. real numbers 

2 + 3 = 3 + 2 

2. algebraic expressions 

x 2 + x = x + x 2

2. Commutative Property of Multiplication.a * b = b * a 

Examples: 

1. real numbers 

5 * 7 = 7 * 5 

2. algebraic expressions 

(x 3 - 2) * x = x * (x 3 - 2) 

3. Associative Property of Addition.(a + b) + c = a + (b + c) 

Examples: 

1. real numbers 

(2 + 3) + 6 = 2 + (3 + 6) 

2. algebraic expressions 

(x 3 + 2 x) + x = x 3 + (2 x + x) 

4. Associative Property of Multiplication.(a * b) * c = a * (b * c) 

Examples: 

1. real numbers 

(7 * 3) * 10 = 7 * (3 * 10) 

2. algebraic expressions 

(x 2 * 5 x) * x = x 2 * (5 x * x) 

5. Distributive Properties of Addition Over Multiplication.a * (b + c) = a * b + a * c 
and 
(a + b) * c = a * c + b * c 

Examples: 

1. real numbers 

2 * (2 + 8) = 2 * 2 + 2 * 8 

(2 + 8) * 10 = 2 * 10 + 8 * 10 

2. algebraic expressions 

x * (x 4 + x) = x * x 4 + x * x 

(x 4 + x) x 2 = x 4 * x 2 + x * x 2

6. The reciprocal of a non zero real number a is 1/a.and a*(1/a) = 1 

Examples: 

1. real numbers 

reciprocal of 5 is 1/5 and 5*(1/5) = 1 

7. The additive inverse of a is -a.a + (- a) = 0 

Examples: 

additive inverse of -6 is -(-6) = 6 and - 6 + (6) = 0 

8. The additive identity is 0. and a + 0 = 0 + a = a 

9. The multiplicative identity is 1.and a * 1 = 1 * a = a



find the slope of a line that is parallel to the line -0.75 x minus y equal 3 the slope of a parallel line is

Answers

In order for lines to be parallel, the slopes must be the same. Therefore, the slope of a parallel line would be -0.75. Unless you simplify the equation to y=0.75x+3 in which case the slope would be 0.75. 

is a simplified version of 5(x+8)-10x =60

Answers

5(x+8)-10x =60
5x + 40-10x = 60
5x-10x = -5x
40-5x = 60
Subtract 40 from both sides
-5x = 20
X= -4

Lavonne sold 4 times as many raffle tickets than Kenneth. Lavonne sold 56 raffle tickets. Write and solve an equation to find out how many tickets Kenneth sold.

PLEASE!!!!!! A+

Answers

14 tickets.

Hope this helped
take 56/4 and that equals 14.

56/4=14

then plug it in and you get 14 times 4 = 56

Please help

The profits for a large international bank were $2 934 569 000.

What is the scientific notation form of the profit figure? (Round the base/root to 1 decimal point.)

Answers

The scientific notations is 2.9x10^9
The scientific form is 2.9 * 10^9

Find an angle at home. Measure the angle. Record the measure. Classify the angle.

Answers

A table leg. It is 90 degrees from the floor. It is a right angle

351.68 rounded to the nearest hundredth?

Answers

351.60 would be the answer 
Hi there!

351.68 is already rounded to the nearest hundredth. The digit in the hundreds place is 8. 

Hope this helps! Tell me if you meant something else ;)

BRAINLIEST FOR THE FIRST RIGHT ANSWER

Instructions: Select the correct answer.

Audrey has a box that contains one caramel chocolate (C), one milk chocolate (M), one dark chocolate (D), and one white chocolate (W). She picks one chocolate and eats it. Then she picks another chocolate and eats it. What is the sample space of the event?

A. {M-D, M-W, M-C, D-W, D-C, W-C}

B. {M-D, M-W, M-C, D-M, D-C, D-W, W-M, W-C, W-D, C-M, C-D, C-W}

C. {M-D, M-W, M-M, D-M, D-C, D-D, W-M, W-W, W-D, C-M, C-D, C-C}

D. {M-D, M-W, M-C, M-M, D-M, D-C, D-W, D-D, W-M, W-C, W-D, W-W, C-M, C-D, C-W, C-C}

Answers

the answer would be B
 
 since there is only 1 flavor of each there would be 3 combinations containing each flavor
Hey there! :D

So, I know this can be confusing, but basically, it is just asking for all the possibilities of chocolates Audrey could've chosen. There are 4 choices. 

C, M, D, and W. 

You have 4 choices for the first pick. 

You have 4 choices for the second. 

4*4= 16

Which choice has 16 options? 

"D" has 16 options. It is the correct sample space.

I hope this helps!
~kaikers

A solid right pyramid has a square base. The base edge length is 2 cm longer than the height of the pyramid. If the height is 6 cm, the volume of the pyramid is cm3.

Answers

Base length = 2 + height
Height = 6
Base length = 8
Volume of pyramid = width x length x height /3 = 8 x 8 x 6/3 = 128 cm³

Answer:

128

Step-by-step explanation:

Just did the test ;)

The amount of money it takes to fill up your gas tank varies directly with the number of gallons you buy. You spent $16.56 to fill up your car with gasoline. If you bought 6 gallons of gasoline, what is the constant of variation

Answers

The constant of variation is 2.76 dollars per gallon

Let "m" represent the money required.

Let "n" represent the number of gallons filled.

Since it is given to us that the amount of money it takes to fill up your gas tank varies directly with the number of gallons you buy, therefore, this can be written mathematically as:

[tex] m\propto n [/tex]

We know that when we remove the "varies to" sign we have to replace it with the equal to sign and the constant of variation, which we will represent by the letter "k".

Therefore the above expression will become:

[tex] m=k\times n [/tex]

Now, it is given that m=$16.56 and n=6 gallons

Therefore, [tex] 16.56=k\times 6 [/tex]

Dividing both sides by 16.56 we get:

[tex] \therefore k=\frac{16.56}{6}=2.76 [/tex]

Thus, k=2.76 $/gallon is the value of the constant of variation.


A bakery supplier receives an order for 2 tons of flour from a bakery chain. The flour is shipped in crates. Each crate holds eight 10-pound bags of flour. How many crates does the supplier need to ship to fulfill the order?

Answers

2 tons = 4000 pounds
8 x 10 = 80
4000 \ 80 = 50
The supplier needs to ship 50 crates.
Hope this helps

triangle LMN is similar to triangle XYZ with altitudes KL and WX. Find KL

Answers

KL is 7.

Since LMN~XYZ, that means m∠N = m∠Z.

Since the angles are the same, we also know that 
sin N = sin Z

Sine is the ratio of the opposite side to the hypotenuse of a right triangle.  The sine of N would be the ratio of sides LK to LN, and the sine of Z would be the ratio of sides XW to XZ.  That gives us:

x/28 = 3/12

Cross multiply the proportion:

12*x = 28*3
12x = 84

Divide both sides by 12:
12x/12 = 84/12
x = 7

The side length (KL) of the triangle ΔLMN will be 7. Then the correct option is B.

What is the triangle?

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180 °.

The ratio of the matching sides will remain constant if two triangles are comparable to one another.

The triangle ΔLMN is similar to triangle ΔXYZ with altitudes KL and WX.

The ratio of the corresponding sides will remain constant. Then the equation is given as,

KL / XW = LN / XZ

KL / 3 = 28 / 12

KL = (28 x 3) / 12

KL = 84 / 12

KL = 7

The side length (KL) of the triangle ΔLMN will be 7. Then the correct option is B.

More about the triangle link is given below.

https://brainly.com/question/25813512

#SPJ5

Determine o X do triângulo na questão b

Answers

2x + 3x = 90

5x = 90

x = 18

Please could someone help with this one . Thanks I will brainlist

Answers

The answer to this is the third option choice: Reaches a maximum height of 549 after 5.75 seconds.
The answer is c I hope you get is right !

which one of the following tables is a relation that represents a function?

Answers

c is the correct answer homie
Answer:
Table 3

Explanation:
For a relation to be a function, each x value should have only one corresponding y value.

Now, let's check the givens: 
Table 1:
x = 1 has two corresponding y-values. Therefore, this is not a function

Table 2:
x = 10 has two corresponding y-values. Therefore, this is not a function.

Table 3:
each x value has only one corresponding y-value. Therefore, this one is a function

Table 4:
x = 7 has two corresponding y-values. Therefore, this is not a function.

Hope this helps :)

On Monday it snowed 9 inches. The next day it snowed 1/2 that amount. How much did it snow on the second day?

Answers

it probably snowed 4.5 inches

The original price of an item is $130. The item is on a discount of 1/5 off the original price. You then pay a sales tax of 10%. What is the amount you paid for the item?

Answers

Hello!

First, find 1/5 of $130, and then subtract that from the original price of the item, because it is a discount.

Divide the price of the item by 5.

130 ÷ 5 = 26

130 - 26 = 104

So, the price of the item (not including tax) is $104. Now, we must calculate the sales tax and then add that onto the price of the item, as tax is money collected by the government.

To calculate the tax, multiply the discounted price of the item by the percentage of tax, and then add it.

104 × 10% = 10.4

104 + 10.4 = 114.4

ANSWER:

The amount of money you paid fot the item is $114.4.

What is the volume of the composite figure ?

Answers

Do length x width x height for each of the shapes and add the products so )8 x 15 x 6) + (16 x 15 x 6) + (24 x 15 x 6) and the sum should be your answer. 4320 in[tex]^2[/tex]

What is the simplified version of (1/3) (9x - 9)

Answers

The answer is 3x-3 because of the distributive property. 1/3 times 9x is 3x and 1/3 of 9 is 3.

Can anyone solve this?

Answers

C because stating at 1 if you add 2 you get 3 for x
 then multiply 3 by 2 to get 6 so you would have (3,6)

Write 6 percent as a decimal

Answers

0.06 is 6% as a decimal
0.06 because Move the decimal point two places to the left, adding in zeros as needed and then thats it.

The area of a square garden is 50 m². How long is the diagonal? 100 m mc028-1.jpg m 25 m 10 m

Answers

a=s^2 50=S^2 s= sqrt50 s=7.071 ms  a^2+a^2=c^2 50+50=c^2 100=c^2 c= sqrt100 c=10ms  So the answer would be 10 hope this helped

Answer:

Option D, 10m

Step-by-step explanation:

The area of a square garden is 50 m²

We have to find the diagonal of the square garden  by Pythagoras theorem.

Since ( diagonal )² = 2(side)²

         ( diagonal )² = 2 × area

                              = 2 × 50 = 100 m²

      diagonal = √100

                     = 10 meter

Option D., 10m is the answer.

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