What bearing and airspeed are required for a plane to fly 500 miles due north in 2. 5 hours if the wind is blowing from a direction of 344° at 10 mph?

The amount of water for washing x cars is y = 12x, and 72 gallons would be needed to wash 6 cars.

An equation is an expression that shows the relationship between two or more numbers and variables.

The standard form of a linear equation is given as:

y = mx + b

Where m is the rate of change and b is the y intercept (initial value of y)

Let y represent the amount of water Jaquan uses to wash x cars, Using the point (2, 24) and (5, 60):

y - 24 = [(60 - 24)/(5- 2)](x - 2)

y = 12x

For 6 cars:

y = 12(6) = 72

The amount of water for washing x cars is y = 12x, and 72 gallons would be needed to wash 6 cars.

Find out more on equation at: https://brainly.com/question/2972832

#SPJ1

Answer: Jaquan uses 72 L to wash 6 cars

Step-by-step explanation:

Answer:

the triangle is a right angle triangle. I can't see the correct explanation here so I will explain

Step-by-step explanation:

to work out whether triangles are right angle you do :

square root of (5² + 12²) so it would be 25 + 144 =169 and the square root of 169 is 13 . we do this because the square root of both of the side lengths squares should make ths longer side in this case it makes 13 so it is a right angled triangled

i hope this helps . if you need any more help pls ask :)

The amount in the ira's account s = $187,159.62.

How do you interest rate?

Future Value of an Ordinary Annuity

[tex]s = R(( 1 + i)^{n} - 1 ) / i[/tex]

where

S = the future value;

R = the periodic payment;

i = the interest rate per period;

n = the number of periods.

[tex]s = 5000 ( 1 + 0.032)^{25} - 1)/ 0.032[/tex]

[tex]s = 5000((1.032)^{25} - 1 )/0.032[/tex]

[tex]s = 5000( 2.19782157471 - 1)/0.032[/tex]

[tex]s = 5000(1.19782157471)/0.032[/tex]

[tex]s = 5000 * 37.4319242096[/tex]

s = $187,159.62

Learn more about interest rate

brainly.com/question/8755688

#SPJ4

Based on the given table which shows the number of years with a company in relation to the employee salary, the conclusion that can be drawn is There is a weak positive correlation between the variables.

When two variables are said to be positively correlated, then it means that when one variable increases, the other variable would increase as well.

If the correlation between them is strong, then the increase between the variables would be more uniform i.e. we can tell with higher accuracy, how the increase in one variable would affect the other.

In the table, we see that with every increase in the number of years with the company, there is an increase in the salary. This means that there is a positive correlation.

The increase is not uniform however. Sometimes it increases by $1,000, and other times by $7,000. As the increase is not uniform, it means that the correlation is weak.

In conclusion, there is a weak positive correlation between number of years and salary.

Find out more on positive correlation at https://brainly.com/question/17104826

#SPJ1

The volume of the cone is  84.9 km³

Volume of a cone = 1 / 3 πr²h

where

Therefore,

radius = 3 km

height = √9.5² - 3²

height = √81.25

height = 9.01387818866

height = 9.014 km

Volume of a cone = 1 / 3 × 3.14 × 3² × 9.014

volume of the cone = 254.732197612 / 3

volume of the cone = 84.9107325372

volume of the cone = 84.9 km³

learn more on volume here: https://brainly.com/question/17075150

#SPJ1

Using the normal distribution, we have that the desired information is given as follows:

a) X ~ N(3,1.8).

b) 3 days.

c) Z = 0.5556.

d) 0.33 = 33%.

e) 0.2048 = 20.48%.

f) 5.3 days.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The mean and the standard deviation are given, respectively, by:

[tex]\mu = 3, \sigma = 1.8[/tex]

Hence the distribution is X ~ N(3,1.8), and, as is standard in the normal distribution, the median is the same as the mean, which is of 3 days.

The Z-score for a patient that took 4 days to recover is Z when X = 4, hence:

Z = (4 - 3)/1.8 = 0.5556.

The probability of spending more than 3.8 days in recovery is one subtracted by the p-value of Z when X = 3.8, hence:

Z = (3.8 - 3)/1.8 = 0.44.

Z = 0.44 has a p-value of 0.67.

1 - 0.67 = 0.33.

The probability is of 0.33 = 33%.

The probability of spending between 3.2 and 4.2 days in recovery is the p-value of Z when X = 4.2 subtracted by the p-value of Z when X = 3.2, hence:

X = 4.2:

Z = (4.2 - 3)/1.8

Z = 0.67.

Z = 0.67 has a p-value of 0.7486.

X = 3.2:

Z = (3.2 - 3)/1.8

Z = 0.11.

Z = 0.11 has a p-value of 0.5438.

0.7486 - 0.5438 = 0.2048 = 20.48%.

The 90th percentile is X when Z = 1.28, hence:

1.28 = (X - 3)/1.8

X - 3 = 1.8 x 1.28

X = 5.3 days.

More can be learned about the normal distribution at https://brainly.com/question/15181104

#SPJ1

The perimeter of the triangle can be express as follows:

12b + 11d + 2c

The perimeter of a figure is the sum of the whole sides of the figure.

A triangle has three sides. Therefore, the perimeter of a triangle is the sum of the three sides.

Therefore, the sides of the triangle are of lengths (2b + 5c) centimetres, (10b + 7d) centimetres, and (4d-3c) centimetres.

Hence, the perimeter of the triangle can be represented as follows:

Perimeter of the triangle = 2b + 5c + 10b + 7d + 4d - 3c

Perimeter of the triangle = 2b + 10b + 7d + 4d + 5c - 3c

Perimeter of the triangle = 12b + 11d + 2c

Therefore, the perimeter of the triangle can be express as follows:

12b + 11d + 2c

learn more on triangle here: https://brainly.com/question/20725699

#SPJ1

Using the arrangements formula, it is found that:

a) There are 1365 possible outcomes that contain exactly four tails.

b) There are 1,307,674,399,889 possible outcomes that contain at least three heads.

The number of possible arrangements of n elements is given by the factorial of n, that is:

[tex]A_n = n![/tex]

When there are repetitions, the number of ways is given as follows:

[tex]A_{n}^{n_1, n_2, \cdots, n_n} = \frac{n!}{n_1!n_2! \cdots n_n!}[/tex]

In which [tex]n_1, n_2, \cdots, n_n[/tex] are the numbers of repetitions.

Item a:

11 heads and 4 tails, hence:

[tex]A_{15}^{11,4} = \frac{15!}{11!4!} = 1365[/tex]

There are 1365 possible outcomes that contain exactly four tails.

Item b:

The total number is:

[tex]A_{15} = 15! = 1,307,674,400,000[/tex]

With no heads:

[tex]A_{15}^{15,0} = \frac{15!}{15!0!} = 1[/tex]

With one head:

[tex]A_{15}^{14,1} = \frac{15!}{14!1!} = 15[/tex]

With two heads:

[tex]A_{15}^{13,2} = \frac{15!}{13!2!} = 95[/tex]

Hence the number of outcomes with less than three heads is:

1 + 15 + 95 = 111

With at least three heads, the number of outcomes is:

[tex]1,307,674,400,000 - 111 = 1,307,674,399,889[/tex]

There are 1,307,674,399,889 possible outcomes that contain at least three heads.

More can be learned about the arrangements formula at https://brainly.com/question/24648661

#SPJ1

Answer: 10

Step-by-step explanation: 5 less than 15 is 10 because 15 - 5 is 10. If it was 15 less from 5, only then it would be -10.

Answer:

5 less than 15 is Option D, 10. This is because using mathematical symbols, it says 15-5 which equals to 10.

For Ann and Tom to have ​$20,000 at the end of 10 ​years, they must deposit a sum of $6,131.14.

To calculate the sum of money they must deposit, use the compound interest formula.

From the compound interest formula;

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

Given that;

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

P = 20,000 / ( 1 + 0.12/4 )^(4×10)

P = 20,000 / ( 1.03)^40

P = 20,000 / 3.26203779

P = $6,131.14

Therefore, for Ann and Tom to have ​$20,000 at the end of 10 ​years, they must deposit a sum of $6,131.14.

Learn more about compound interest here: brainly.com/question/27128740

#SPJ1

The solution to the following mathematical problems are;

Solve using

BODMAS

5² -3⁴ / (2³-5)(6² ÷ 9)

= 25-81 / (8-5)(36÷9)

= -56 / (3)(4)

= -56/12

= - 14/3

20² ÷ {3(5-9)² + 2}

= 400 ÷ {3(-4)² + 2}

= 400 ÷ {3(16) + 2}

= 400 ÷ (48+3)

= 400 ÷ 50

= 8

84/12 + (5-7)² -72 ÷ 6×2

= 7 + (-2)² - 12 × 2

= 7 + (4) - 24

= 11 - 24

= -13

Learn more about evaluation:

https://brainly.com/question/17884446

#SPJ1

The minimum value of f(4) - f(1) is 6.

The maximum value of f(4) - f(1) is 12.

In the question, we are given that, 2 ≤ f'(x) ≤ 4 for all values of x.

Taking the given inequality as (i).

We are asked to find the minimum and maximum possible values of f(4) - f(1).

We multiply (i) by dx throughout, to get:

4dx ≤ f'(x)dx ≤ 5dx.

To find this, we integrate (i) in the definite interval [4, 1] with respect to dx, to get:

[tex]\int_{1}^{4}2dx \leq \int_{1}^{4}f'(x)dx \leq \int_{1}^{4}4dx\\\Rightarrow [2x]_{1}^{4} \leq [f(x)]_{1}^{4} \leq [4x]_{1}^{4}\\\Rightarrow 2*4 - 2*1 \leq f(4)-f(1) \leq 4*4 - 4*1\\\Rightarrow 6 \leq f(4) -f(1) \leq 12[/tex]

Thus, the minimum value of f(4) - f(1) is 6.

The maximum value of f(4) - f(1) is 12.

Learn more about definite integrals at

https://brainly.com/question/17074932

#SPJ4

Answer:

(a) k = 4
(b) y = - 2x + 9

Step-by-step explanation:

x2-x1, y2-y1  
= 3-2, 3-5

= 1,-2
3,3 + 1,-2 = (4,1)

x=4

480 Ways can the letters be arranged.

What is the meaning of probability ?

First letter can't be n or l

=   4! × [tex]5P_{3}[/tex]

=    24 × 5! /3!

=     24 × 5 × 4

=         480

Therefore, 480 ways can the letters be arranged.

Learn more about Probability

brainly.com/question/3087951

#SPJ4

Answer: 480 ways

Step-by-step explanation:

Answer:

See below

Step-by-step explanation:

x = largest

x-1   previous

x -2  smallest

sum =   x   +    x-1      +   x-2

sum = 3x -3    

Answer:

The answer is B, 2.78 hours

Step-by-step explanation:

Answer:

  6 hours 15 minutes, or 6.25 hours

Step-by-step explanation:

We assume Hank reads at a constant rate. His reading time will be proportional to the number of pages.

We know that 15 minutes is 1/4 hour, so the proportion can be written ...

  hours/pages = (book hours)/(250 pages) = (1/4 hour)/(10 pages)

Multiplying by 250 pages gives ...

  book hours = 250(1/4 hour)/10 = 25/4 hour = 6 1/4 hour

It will take Hank 6 1/4 hours to read the book.

Answer:Maria

Step-by-step explanation: Maria uses a cup per 2 gallons while Franco uses a cup for 5 gallons. Maria has a 1:16 ratio while Franco has a ratio of 1: 80 because a gallon is 16 cups. It is clear now that Franco has a smaller ratio so, Maria's sports drink is stronger.

Answer: 26.39

Step-by-step explanation:

2xπxr

The expression 40 + 30m = c represents the cost of the gym membership for m months option (A) 40 + 30m = c is correct.

It is defined as the combination of constants and variables with mathematical operators.

It is given that:

The local gym is offering this new promotion:

An enrollment fee of $40 and a monthly fee of $30.

Let m be the total number of months

Total monthly fee = 30m

Total cost(including the enrollment fee of $40) = 40 + 30m

Let the total cost is c:

c = 40 + 30m

If in the linear expression, one variable is present, then the bis known as the linear expression in one variable.

Thus, the expression 40 + 30m = c represents the cost of the gym membership for m months option (A) 40 + 30m = c is correct.

Learn more about the expression here:

brainly.com/question/14083225

#SPJ2

The probability of not choosing red when choosing one marble from the bag is 90%.

S = {1, 2, 3, 4, 5, 7}

Flipping a fair, two-sided coin.

probability that a student studied for exactly 1 hour is 0.23.

The probability of landing on yellow is less than the probability of landing on blue.

Sandy's experimental probability was exactly the same as the theoretical probability for all three experiments.

The theoretical probability, P(brown), is 25%, and the experimental probability is 32.5%.

The experimental probability of drawing a spade is 0.15.

The probability of not choosing red when choosing one marble from the bag will be:

= (3 + 15 + 9)/30

= 27/30

= 90%

The sample space for rolling a fair seven-sided die will be S = {1, 2, 3, 4, 5, 7}.

The event that will have a sample space of S = {h, t} will be flipping a fair, two-sided coin.

The probability that a student studied for exactly 1 hour will be:

= 8/(1+8+2+5+9+7+3)

= 8/35

= 0.23

The true statement is that the probability of landing on yellow is less than the probability of landing on blue.

Sandy's experimental probability was exactly the same as the theoretical probability for all three experiments.

The theoretical probability, P(brown), is 25%, and the experimental probability is 32.5%. This was 13/40 = 32.5%.

The experimental probability of drawing a spade will be:

= 3/(7+3+6+4)

= 3/20

= 0.15.

Learn more about probability on:

brainly.com/question/24756209

#SPJ1

Answer: the sample space of the experiment from simultaneously flipping a coin and rolling a die consisted of: 2 × 6 = 12 possible outcomes.

Step-by-step explanation:

The sample space of 52 cards is all 52 possible outcomes, which is {Ace of Hearts, two of hearts, three of hearts...etc}.

Step-by-step explanation:

g(f(a))=4(a²+2a) + 5

= 4a²+8a+5

Based on the given function, the equivalent function that best shows the x-intercepts on the graph is f(x) = (6x - 1)(6x + 1)

Equivalent functions are different functions that have equal values when evaluated and compared

The function is given as:

f(x) = 36x^2 - 1

Express 1 as 1^2

f(x) = 36x^2 - 1^2

Express 36x^2 as (6x)^2

f(x) = (6x)^2 - 1^2

Apply the difference of two squares.

This is represented as:

(a + b)(a - b) = a^2 - b^2

So, we have the following equation

f(x) = (6x - 1)(6x + 1)

Based on the given function, the equivalent function that best shows the x-intercepts on the graph is f(x) = (6x - 1)(6x + 1)

Read more about equivalent function at:

https://brainly.com/question/2972832

#SPJ1

The option A is correct. A circle is the shape of the cross section taken parallel to the base of a cylinder.

According to the statement

We have given that the cylinder and we have to tell that the which shape required for the cross section taken parallel to the base of a cylinder.

So, For this purpose,

We know that the

A cylinder is a three-dimensional solid, one of the most basic geometric shapes.

In this shape the surface formed by the points at a fixed distance from a  line segment, which is  known as the axis of the cylinder.

As the bases of cylinder are two identical circles which are parallel to the curved surface.

The curved surface when we open will be circle rather than the circle.

So, Due to this reason the answer is a circle.

Therefore, a circle is the shape of the cross section taken parallel to the base of a cylinder.

Learn more about base of cylinder here

https://brainly.com/question/76387

#SPJ1

Assuming that the variable h is the same for each figure, the figures from the least to the greatest is:

The value of h is the same for all the shape so assume the value of h is 2 units.

The volume of a cylinder is:

= πr²h

First cylinder area:

= 22/7 x 3 x 2

= 56.54867 units

The second cylinder area:

= 22/7 x 6 x 2

= 226.19467 units

The volume of a cone is:

= πr²h/3

First cone volume:

= 22/7 x 3 x 2/3

= 18.84956 units

Second cone volume:

= 22/7 x 6 x 2/3

= 75.39822 units

The order is therefore:

Cone with radius of 3 units < Cylinder with radius of 3 units < Cone with radius of 6 units < Cylinder with radius of 6 units

In conclusion, the shapes with the larger radius of 6 units will have more volume.

Find out more on the volume of a cone at https://brainly.com/question/1082469

#SPJ1

Your net worth change by zero dollars.

Net worth is the difference between asset and liability.  

In other words net worth is the sum of all assets owned by a person or a company, minus any obligations or liabilities.

Therefore, since he took $5,000 out of the bank to purchase a car worth $5,000 his net worth will change by zero dollars.

learn more on net worth here: https://brainly.com/question/20511222

#SPJ1

Answer:

You did not list any choices but if you simplify that the answer is 6√2x-3√2

Step-by-step explanation:

If they want you to factor it instead of simplifying the answer is 3√2(2x-1)

Answer:

[tex]6x\sqrt{2} - 3\sqrt{2}[/tex]

Step-by-step explanation:

So you haven't provided any options, but I'm assuming they want it in most simplified form.

To do this, we simply combine like terms, and in this case you can see the [tex]\sqrt{2}[/tex] as a variable, if it makes it easier to think about why we can combine terms. So just like how we can do: [tex]2y + y = 3y[/tex] we can do the same thing here, since sqrt(2) constant and it's in each expression.

So if it makes a bit easier to represent, I'll rewrite the equation such that sqrt(2) = y

[tex]5xy-3y+xy[/tex]

So in here, think of y as the variable and the 5x, -3, and x as the coefficients.

In doing this we can combine the terms by adding them, since they all have the same "variable" (sqrt(2))

[tex](5x-3+x)y[/tex]

Simplify this expression to get

[tex](6x-3)y[/tex]

Now just plug the sqrt(2) back in as y and you get the expression

[tex](6x-3)\sqrt{2}[/tex]

Since we can't combine the 6x and -3 in any way, we we can just distribute this back into the sqrt(2)

[tex]6x\sqrt{2} - 3\sqrt{2}[/tex]

Answer:

Step-by-step explanation:

12

Answer:296 m

I’m assuming “breadth” is width and garderean is just the park.

(25+25+12+12) times 4.

A is never defined