a ship leaves a harbor. it travels 35 miles due east and then adjusts its course 40 degrees northward. after traveling 45 miles in that direction, how far is the ship from its point of departure?

we need 31/2 pounds mirepoix to make 31/2 gallons of soup.

let we need x% (percent) of mirepoix to make 1 gallon of soup

given we have 1 pound of mirpoix which yeilds 1 gallon soup of soup

so total amount of mirepoix that required in the solution is = [tex]\frac{x}{100} *1 pound[/tex]

so x/100 = 1 gallon / pound

we will use this equation for further calculation

let we need y pounds of mirepoix to make 31/2 gallon of soup  ans we know that x% of mirepoix is required for this solution.

so [tex]\frac{x}{100} * y = 31/2[/tex]

ans in the above equation x/100 =1 gallon / pound

so  1 * y= 31 /2

and hence y = 31/2 pounds

so we need 31/2 pounds of mirepoix to form requied amount of soup.

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Answer:

The perimeter of Elie's vegetable garden is 34 meters.

Step-by-step explanation:

The formula for area is: a=w*l.

A = area

W = width

L = length

If the length is 9 meters, then we know two of the values, the area, and the length. Substitute.

72=w*9

You can divide both sides by 9 to get the width, which is 8 meters.

To find perimeter, we add l+w+l+w, or 2l+2w. Substitute for our values:

2(9)+2(8)=34

The perimeter of Elie's vegetable garden is 34 meters.

The graphs in this problem that show continuous data are given as follows:

Continuous and discrete graphs have different formats to show the data, which are presented as follows:

For a continuous data, the data shown is all the real numbers in an interval, hence a continuous graph is represented by solid lines. This means that the second and third graphs in this problem, that is, the top right and the bottom left graphs represent continuous data.

For discrete data, only certain values are represented in an interval, hence the graph of discrete data is composed only by dots, which is the case for the first and last graphs in this problem, that is, the top left graph and the bottom right graph.

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Answer:

a

Step-by-step explanation:

Answer:

2184

Step-by-step explanation:

This question involves permutations. We can solve it using the formula

[tex]\frac{n!}{(n-r)!}[/tex]

where n=14 (because we are choosing from 14 people)

and r=3 (because we are choosing 3 people)

and we are using the permutation formula because the order or placement in which these 3 people are choosing matters (having a person 1 being a director is different from having person 1 being a chief executive officer)

14!/(14-3)!

= 14!/11!

= 14 x 13 x 12

= 2184

Answer:

1. ΔCDE≅ΔJEH

2. ΔIHG≅ΔIHD

3. ΔIHJ≅ΔIXT

4. ΔIJT≅ΔJIH

5. ΔEFD≅ΔDKJ

6.ΔGWY≅ΔGHI

Answer:

y – 5 = m(x – 6)

Step-by-step explanation:

using y =mx +c as our guide line

Step 1 : identification of coordinates

(6,5) ;x1= 6,y1 = 5

step 2 : applying the formula

y – y1 = m(x – x1)

y – 5 = m(x – 6)

The value of first quartile of the given data set is 2.5

The lower quartile, or first quartile (Q1), is the value under which 25% of data points are found when they are arranged in increasing order.

Given is a data set,

According to the data,

The lower quartile is between 0 and 2.5, which under 25% of the data.

Hence, The value of first quartile of the given data set is 2.5

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The solution to the expression is (b) -3.07n - 8.2

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

(7.43n − 2.2) − (6 + 10.5n)

Remove the brackets

So, we have

(7.43n − 2.2) − (6 + 10.5n) = 7.43n − 2.2 − 6 - 10.5n

Evaluate the like terms

(7.43n − 2.2) − (6 + 10.5n) = -3.07n - 8.2

Hence, the solution is (b) -3.07n - 8.2

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Answer:

There is one unique solution, (−6, 5).

Step-by-step explanation:

2x + 4y = 8

2x + 6y = 18

2x + 4y = 8  ==> solve for 2x

2x + 4y - 4y = 8 - 4y

2x = 8 - 4y

2x + 6y = 18  ==> solve for 2x

2x + 6y - 6y = 18 - 6y

2x = 18 - 6y

8 - 4y = 18 - 6y  ==> 2x = 8 - 4y   and   2x = 18 - 6y

8 - 4y + 6y = 18 - 6y + 6y  ==> solve for y by first adding 6y on both sides to

                                                remove negative y

8 + 2y = 18  ==> simplify

8 - 8 + 2y = 18 - 8  ==> isolate y

2y = 10

y = 5

2x + 4(5) = 8  ==> substitute 5 for y in 2x + 4y = 8

2x + 20 = 8

2x - 20 + 20 = 8 - 20  ==> subtract 20 on both sides to isolate 2x

2x = -12

x = -6

x = -6, y = 5  ==> (6, 5)

Answer: There is one unique solution, (−6, 5).

Answer:

Use this site, it will help you in the long run.

Answer:

d = 0

Step-by-step explanation:

We have the equation

7.5d = 2.5d

We divided both sides by factors and get

d = 0

Value of d is 0.

According to question

7.5d=2.5d

Lin divides each side by 2.5d

∴7.5d÷2.5d=2.5d÷2.5d

⇒3=1

which is not possible and Lin is doing wrong

Elena subtract 2.5d from each side

∴7.5d-2.5d=2.5d-2.5d

⇒5d=0

⇒d=0

So Elena is right and the value of d is 0.

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Answer:

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

Complete the square as follows:

Answer:_18

replace _4 instead of x

-5*-4=_20

_20+2=_18

Step-by-step explanation:

Answer:

here is the answer with proper steps.

Answer:

<E=180-60=120

t=60 degrees

u=8

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To find the decimal number that corresponds to the message "10101111", you can convert the binary number to decimal.

By using the following formula:

decimal = [tex]sum(binary[i] X 2^{(n-i-1)})[/tex]

binary = converting binary number

i = index of the current digit in the binary number

n = total number of digits in the binary number

[tex]2^{(n-i-1)}[/tex] is the corresponding power of 2

use the following steps to convert the binary number "10101111"

Calculate the decimal value for each digit in the binary number:

binary[0] = 1, [tex]2^{(8-0-1)}[/tex]  = [tex]2^7[/tex] = 128

binary[1] = 0, [tex]2^{(8-1-1)}[/tex] = [tex]2^6[/tex] = 64

binary[2] = 1, [tex]2^{(8-2-1)}[/tex] = [tex]2^5[/tex] = 32

binary[3] = 0, [tex]2^{(8-3-1)}[/tex] = [tex]2^4[/tex] = 16

binary[4] = 1, [tex]2^{(8-4-1)}[/tex] = [tex]2^3[/tex] = 8

binary[5] = 1, [tex]2^{(8-5-1)}[/tex] = [tex]2^2[/tex] = 4

binary[6] = 1, [tex]2^{(8-6-1)}[/tex] = [tex]2^1[/tex] = 2

binary[7] = 1, [tex]2^{(8-7-1)}[/tex] = [tex]2^0[/tex] = 1

Adding decimal values for each digit

Total decimal value = 1128 + 064 + 132 + 016 + 18 + 14 + 12 + 11

= 128 + 0 + 32 + 0 + 8 + 4 + 2 + 1

= 175

Hence, the decimal number that corresponds to the binary number "10101111" is 175.

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Answer:

a is 30 degrees.

Step-by-step explanation:

The degree of a triangle is 180, which means that all the degrees in any triangle will always add up to 180. Since CB and DB are congruent, the angles C and D will be the same. This means that to get the answer, just subtract the value we already have from 180 and divide the sum by 2.

[tex]\frac{180-120}{2} = \frac{60}{2} = 30[/tex]

The probability that at least one person receives his/her own hat is 1 - (1/n)^n, using the inclusion-exclusion principle.

The inclusion-exclusion principle states that the probability of event A or B occurring is equal to the probability of event A plus the probability of event B minus the probability of event A and B occurring. In this case, the probability of at least one person receiving his/her own hat is the probability of one person receiving his/her own hat plus the probability of two people receiving their own hats minus the probability of three people receiving their own hats, and so on. This can be expressed mathematically as 1 - (1/n)^n, where n is the number of guests. This formula can be applied to any situation where a random event is being repeated multiple times with the same set of outcomes.1 - (1/10)^10 = 0.99.

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Answer:

(x + 2)(x + 4)

Step-by-step explanation:

for the denominator we have (x + 2)(x + 4)(x + 4).

divide the denominator by (x + 4), you would be left with (x + 2)(x + 4).

The statue is 4. 6 meter high. The angle of elevation from the opposite corner of the courtyard to the top of the statue is 8,Tan 8 = 4.6/opposite and opposite = 4.6/tan 8 = 5.8 meters

First, we calculate the opposite side of the triangle using the tangent function. To do this, we need to use the angle of elevation (8 degrees) and the height of the statue (4.6 meters). We use the tangent function to calculate this, which is written as:

tan 8 = 4.6/opposite

Solving for the opposite, we get:

opposite = 4.6/tan 8 = 5.8 meters

This means that the opposite corner of the courtyard to the top of the statue is 5.8 meters away.

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Answer:

Alternative Hypothesis

Answer:

[tex]y=-\frac{2}{3}x+1[/tex]

Step-by-step explanation:

Parallel means same slope.

[tex]y=-\frac{2}{3}x+b[/tex]

[tex]5=-\frac{2}{3} (-6)+b[/tex]

5 = 4 + b

b = 1

[tex]y=-\frac{2}{3}x+1[/tex]

Answer:

B. Alternate exterior angles

Step-by-step explanation:

Alternate exterior angles are angles that are outside two lines intersected by the transversal and are located on opposite sides of the transversal. Also, they have the same degree! So, the answer is B.

Different x values must be taken into account in order to graph h (x). So the graph of the h(x) is given below.

In the given question, we use the graphs of f and g to graph h(x) = (f + g)(x).

A diagram that compares the fluctuation of one variable to that of one or more other variables, such as a collection of points, lines, line segments, curves, or regions.

The graph is given below:

h (x) = (f + g) (x)

The function h(x) can be written as

h (x) = f (x) + g (x)

Different x values must be taken into account in order to graph h (x).

h (0) = f (0) + g (0) = 2 - 1 = 1

h (1) = f (1) + g (1) = 3 + 0 = 3

h (2) = f (2) + g (2) = 1 + 0.5 = 1.5

h (3) = f (3) + g (3) = 2 + 0 = 2

So the graph of the h(x) is given below:

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Moussa's age if the product of their ages is 24 is 4 years.

An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario.

Moussa is younger than Sophia. Their ages are consecutive even integers.

Let the ages be x and x + 2.

This will be illustrated as:

x(x + 2) = 24

x² + 2x = 24

x² + 2x - 24 = 0

x² + 6x - 4x - 24 = 0

x(x + 6) -4(x + 6) = 0

x - 4 = 0

x = 4

x + 2 = 4 + 2 = 6

The ages are 4 and 6 years.

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If the product of Sophia age and Moussa age is 24, the age of Moussa is 4 years.

Moussa is younger than Sophia.  Their ages are consecutive even integers.

The product of there ages is 24. Moussa's age can be found as follows:

Even numbers are those numbers that can be divided into two equal groups or pairs and are exactly divisible by 2.

Hence,

Let

x = age of Moussa

x + 2 = age of Sophia

Hence, the product of their age will be as follows:

x(x + 2) = 24

x² + 2x = 24

x² + 2x - 24 = 0

lets factorise the quadratic equation. The numbers one can multiply to get -24 and add to get 2 are -4 and 6. Therefore,

x² - 4x + 6x - 24 = 0

x(x - 4) + 6(x - 4) = 0

(x + 6)(x - 4) = 0

Therefore,

x = - 6 and x = 4

We can only use positive numbers.

Therefore, the age of Moussa is 4 years

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Answer:

40mins

Step-by-step explanation:

4hrsx60

=240mins

240mins/6 lessons

=40mins per lesson

Answer:

The value of the car at the end of 3 years will be $13707.

Step-by-step explanation:

If the original value of the car is $20000, then after the first year, the value of the car will be $20000 - (12/100)*$20000 = $17600.

After the second year, the value of the car will be $17600 - (12/100)*$17600 = $15552.

After the third year, the value of the car will be $15552 - (12/100)*$15552 = $13707.

Therefore, the value of the car at the end of 3 years will be $13707.

After the end of the lease period the pay, the rent would increase to $3030.83 approx.

A lease is a legal agreement by which the owner of a building, a piece of land, or something such as a car allows someone else to use it for a period of time in return for money.

Given here,  a 2-year lease is - $2,657 per month plus a $200 security deposit. Now, the average increase in the rate in the U.S is 14.07%

thus, at the end of the two-year lease period, the new rent would be

= (1+14.07/100) × $2,657

= $3030.83

Hence, the new rent with a security deposit is $3030.83 + security deposit.

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