A ship's destination is 30 miles north and 12 miles east. At what angle should it head to go straight to its destination?
a) 22°east of north b) 24°east of north
c) 31°east of north d) 66°east of north

The weight of the contents in the container is 340 pounds

The space occupied within an object's borders in three dimensions is referred to as its volume. It is sometimes referred to as the object's capacity.

Volume is a measurement of three-dimensional space that is occupied. It is frequently expressed numerically in a variety of imperial or US-standard units as well as SI-derived units. Volume and the definition of length are related.

Given ,

volume of container = 20 x 8.5 x 8= 1360 cubic feet

weight = 0.25 pounds per cubic foot

0.25 x 1360 = 340 pounds

Therefore the weight of the contents in the container is 340 pounds

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Answer: A 3(5x-8)

Step-by-step explanation: 3 times 5x is 15x and 3 times -8 is -24

Answer:

p/gh=m

Step-by-step explanation:

divide both sides by gh to isolate m

Answer: 71

Step-by-step explanation:

Calculate c, ∠B, and ∠A based on given b, a, and ∠C.c = √b2 + a2 - 2ba·cos(C) = 13.67386∠B = arccos(c2 + a2 - b22ca)= 1.23918 rad = 71°∠A = arccos(c2 + b2 - a22cb)= 1.23918 rad = 71°

The smaller of the two number is 10.

What are Ratios?

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other. For example, if there is 1 boy and 3 girls you could write the ratio as: 1 : 3 (for every one boy there are 3 girls) 1 / 4 are boys and 3 / 4 are girls.

In simple words, the ratio is the number that can be used to express one quantity as a fraction of the other ones. The two numbers in a ratio can only be compared when they have the same unit. We make use of ratios to compare two things.

Given:

Ratio of two Positive number = 5:6

Let , the smaller number be 5x

then , the bigger number = 6x

According to the question,

product of these numbers = 120

Therefore,

[tex]5x * 6x = 120\\30x^{2} = 120\\x^{2} =4\\x = 2[/tex]

Smaller number = 5x = 5*2 = 10.

Hence, the smaller of the two number is 10.

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system of equations: n=2/3 ,a=14,x=−9
for each thing: x= −9  | a= 14  | n= 2/3

1. x = -9

2. a = 14

3. n = [tex]\frac{2}{3}[/tex]

1. Rearrange Terms

61 = 7 - 6x

61 = -6x + 7

2. Subtract 7 from both sides

61 = -6x + 7

61 - 7  = -6x + 7 - 7

3. Simplify

Subtract the numbers:

61 - 7 = -6x + 7 - 7

54 = -6x + 7 - 7

Subtract the numbers:

54 = -6x + 7 - 7

54 = -6x

4. Divide both sides by the same factor

54 = -6x

[tex]\frac{54}{6}[/tex] = [tex]\frac{-6x}{-6}[/tex]

5. Simplify

Divide the numbers:

[tex]\frac{54}{6}[/tex] = [tex]\frac{-6x}{-6}[/tex]

-9 = [tex]\frac{-6x}{-6}[/tex]

Cancel terms that are in both the numerator and denominator:

-9 = [tex]\frac{-6x}{-6}[/tex]

-9 = x

Move the variable to the left:

-9 = x

x = -9

x = -9

1. Combine multiplied terms into a single fraction

[tex]\frac{3}{2}[/tex]a - 26 = -5

[tex]\frac{3a}{2}[/tex] - 26 = -5

2. Find common denominator

[tex]\frac{3a}{2}[/tex] - 26 = -5

[tex]\frac{3a}{2}[/tex] + [tex]\frac{2(-26)}{2}[/tex] = -5

3. Combine fractions with common denominator

[tex]\frac{3a}{2}[/tex] + [tex]\frac{2(-26)}{2}[/tex] = -5

[tex]\frac{3a+2(-26)}{2}[/tex] = -5

4. Multiply the numbers

[tex]\frac{3a+2(-26)}{2}[/tex] = -5

[tex]\frac{3a - 52}{2}[/tex] = -5

5. Multiply all terms by the same value to eliminate fraction denominators

[tex]\frac{3a - 52}{2}[/tex] = -5

2 · [tex]\frac{3a - 52}{2}[/tex] = 2(-5)

6. Cancel multiplied terms that are in the denominator

2 · [tex]\frac{3a - 52}{2}[/tex] = 2(-5)

3a - 52  = 2(-5)

7. Multiply the numbers

3a - 52 = 2(-5)

3a - 52 = -10

8. Add 52 to both sides

3a - 52 = -10

3a - 52 + 52 = -10 + 52

9. Simplify

Add the numbers:

3a - 52 + 52 = -10 + 52

3a = -10 + 52

Add the numbers:

3a = -10 + 52

3a = 42

10. Divide both sides by the same factor

3a = 42

[tex]\frac{3a}{3}[/tex] = [tex]\frac{42}{3}[/tex]

11. Simplify

Cancel terms that are in both the numerator and denominator:

[tex]\frac{3a}{3}[/tex] = [tex]\frac{42}{3}[/tex]

a = [tex]\frac{42}{3}[/tex]

Divide the numbers:

a = [tex]\frac{42}{3}[/tex]

a = 14

a = 14

1. Divide the numbers

4 = n  + [tex]\frac{-10}{-3}[/tex]

4 = n + [tex]\frac{10}{3}[/tex]

2. Subtract [tex]\frac{10}{3}[/tex] from both sides

4 = n + [tex]\frac{10}{3}[/tex]

4 - [tex]\frac{10}{3}[/tex] = n + [tex]\frac{10}{3}[/tex] - [tex]\frac{10}{3}[/tex]

3. Simplify

Subtract the numbers:

4 - [tex]\frac{10}{3}[/tex] = n + [tex]\frac{10}{3}[/tex] - [tex]\frac{10}{3}[/tex]

[tex]\frac{2}{3}[/tex] = n + [tex]\frac{10}{3}[/tex] - [tex]\frac{10}{3}[/tex]

Subtract the numbers:

[tex]\frac{2}{3}[/tex] = n

Move the variable to the left:

[tex]\frac{2}{3}[/tex] = n

n = [tex]\frac{2}{3}[/tex]

n = [tex]\frac{2}{3}[/tex]

I hope my answer helped you! If you need more information or help, comment down below and I will be sure to respond if I am online. Have a wonderful rest of your day!

The image for quadrilateral PQRS is attached below

The image for  Triangle QRM  is attached below

Generally, To construct a quadrilateral PQRS with the given dimensions, you can use a straightedge and a compass. Here is a step-by-step guide:

To construct a triangle QRM with an area equal to quadrilateral PQRS, you can use the same method as above. Here is a step-by-step guide:

To verify that the area of triangle QRM is equal to the area of quadrilateral PQRS, you can use the formula for the area of a triangle:

Area of triangle QRM = (1/2) * QM * QR * sin(angle QRM)

And the formula for the area of a quadrilateral:

Area of quadrilateral PQRS = (PQ * QR * sin(angle PQR))/2

Substituting the given values and solving for sin(angle QRM), we find that:

sin(angle QRM) = (2 * area of quadrilateral PQRS)/(QM * QR)

= (2 * (5 * 5.5 * sin(75)))/(5 * 5.5)

= sin(75)

Thus, the area of triangle QRM is equal to the area of quadrilateral PQRS, as desired.

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The equation of the line that passes through (7, 10) and its perpendicular to the line y = (1/2)x - 9 is y = -2x + 24

The coordinates of the line passing through the point = (7, 10)

The equation of the perpendicular line

y = (1/2)x - 9

The slope of the line = 1/2

The slope of the original line = - 1 / (1/2)

= -1 × 2

= -2

The slope intercept form is

y = mx + b

Substitute the values in the equation and find the value of b

10 = -2(7) + b

10 = -14 + b

b = 10 + 14

b = 24

Substitute the value of b and m is the equation

y = -2x + 24

Therefore, the slope of the line is y = -2x + 24

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The Type of taxation system in this table represent is Option C Regressive Tax.

Taxation System is an obligatory fee or financial charge is referred to as a tax when it is imposed by a government on a person or an organisation in order to raise money for public projects that fund the greatest services and infrastructure. Various public spending programmes are then funded with the money that was gathered.

Type of Taxation

There are mainly four types of Taxes, these are Regressive, progressive, Indirect, and Proportional. In the given question the Regressive Taxation system is represented.

A Regressive Taxation system is one where Companies which have lower income have higher tax rate in comparison to big companies. In the given question the company which have lowest income is giving 15% of total income, while the largest company is giving 10% of their income.

Therefore, taxation system in this table represent is Option C Regressive Tax.

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The given statement " chi-square tests are used for testing hypotheses of the association between two categorical values. " is true

The term chi square test defines if there is a significant relationship between two nominal variables.  

Here we have given the statement, chi-square tests are used for testing hypotheses of the association between two categorical values.

And we need to find whether the statement is true or not.

As per the definition of chi square test, we know that the frequency of each category for one nominal variable is compared across the categories of the second nominal variable.  

Here we also know that the data can be displayed in a contingency table where each row represents a category for one variable and each column represents a category for the other variable.  

Therefore, based on these facts the given statement is true.

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Answer:

Step-by-step explanation:135 degrees

An expression which shows the correct substitution of the values a, b, and c from the equation 0 = – 3x2 – 2x + 6 into the quadratic formula is: expression A. Therefore, the correct answer option is A.

A quadratic equation can be defined as a mathematical expression (equation) that can be used to define and represent the relationship that exists between two or more variable on a graph. In Mathematics, the standard form of a quadratic equation is given by;

ax² + bx + c = 0

Mathematically, the quadratic formula is modeled or represented by this mathematical expression:

[tex]x = \frac{-b\; \pm \;\sqrt{b^2 - 4ac}}{2a}[/tex]

From the information provided, we have the following values;

0 = -3x² - 2x + 6

Where:

a = -3

b = -2

c = 6

Substituting the values into the quadratic formula, we have;

[tex]x = \frac{-(-2)\; \pm \;\sqrt{(-2)^2 - 4(-3)(6)}}{2(-3)}\\\\x = \frac{2\; \pm \;\sqrt{4^2 - 4(-3)(6)}}{2(-3)}[/tex]

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Answer:

1/9

Step-by-step explanation:

The y intercept of a line is when x = 0

y = 1/9

Answer:

y = 1/9

Step-by-step explanation:

y = -10x + 1/9

Substitute 0 for x

y = -10 x 0 +1/9

-10 x 0 = 0

y = 1/9

If i clap my hands 20 times in 12 seconds. 200 times will i do it in 2 minutes.

The friend can clap his hands 28 times in 12 seconds, according to our knowledge. The first thing we need to know is how many times he can clap in a second:

What is clap ?

Gonorrhea is known by the slang term "the clap." Gonorrhea is also referred to as "the drip." Someone who has an may feel stigmatized and shamed by these words.

To do it, we must divide the number of seconds by the number of times he can clap his hands:

20/12 =1.6667

He can clap his hands 1.6667 times in 1 second:

Now we want to know how many times will he clap his hands in 2 minutes

We have to change 2 minutes into seconds:

1 (minute) = 60 (seconds in 1 minute)

2 (minutes) * 60 (seconds in 1 minute) = 120seconds

After we get the seconds he is going to clap his hands, we have to multiply the times he claps times the seconds:

1.6667 times * 120 seconds = 200

200 times in 2.25 minutes

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Answer: 52.5°

Step-by-step explanation:

sin59 = 45/x

sin59(x) = 45

x = 45/sin59 = 52.5°

The expression 5t + (-9) + (-8t) + (-5) in the simplified form will be negative (3t + 14).

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

The expression is given below.

⇒ 5t + (-9) + (-8t) + (-5)

Simplify the expression, then the value of the expression is given as,

⇒ 5t + (-9) + (-8t) + (-5)

⇒ 5t - 9 - 8t - 5

⇒ – 3t – 14

⇒ – (3t + 14)

The expression 5t + (-9) + (-8t) + (-5) in the simplified form will be negative (3t + 14).

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The computer will cost £ 33512.32

Given,

the cost of the computer = 2500

Depreciation = 12%

Cost after 3 years =?

compound interest is calculated as,

A = P(1 + r/n)nt

r = 12/100 = 0.12

So, A= P(1 + r/n)nt

A = 2500 (1+.12/1)1*3

A= 2500 (1.12)³

A= 2500 * 1.404928

A = 3512.32

So, The computer will cost £ 33512.32

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By using the concept of arrangement, it can be concluded that-

The correct order is Beto, Alex, Valentin

The act of arranging people and things towards a certain goal is referred to as arrangement. the arrangement or arrangement of details in a written work. Readers to whom a piece of writing is addressed; those who read or hear what you have written.

Your reader could feel disoriented and lose interest if there is no obvious organizational structure. Your essay's organization will aid readers in making connections between the essay's body and thesis, as well as help you stay on task as you plan and compose the essay.

It is known that:

• Alex sits next to Beto and Valentin.

• Valentin sits to the right of Beto.

So the correct order is Beto, Alex, Valentin

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Persons cannot be in decimals we can expect about 9 passengers will not keep their reservation.

Given,

In the question:

An airline finds that about 8 percent of the time, a person who makes an advance reservation does not keep the reservation.

Therefore, for each of their 105105105-passenger planes, the company schedules 113113113 people with advance reservations.

Now, According to the question:

Capacity of the airline per trip = 105 only

But company schedules = 113 people with advance reservations

Since 8% do not turn up

Out of 113 passengers who reserved in advance we can say

that 8% of 113 passengers will not keep their reservation

Based on this information, number  of the scheduled people will not keep their reservation

= 8% x 113

= 0.08*113

=9.04

Hence, Persons cannot be in decimals we can expect about 9 passengers will not keep their reservation.

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The equation is 55 = 5t and the graph is attached with the answer.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that a painting crew bought 55 gallons of paint for a job, The crew members used 5 gallons of paint per hour until they used all the paint.

The equation can be written as,

55 = 5t

Here, t is the number of hours.

The graph is attached with the answer below.

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Answer:

Step-by-step explanation:

The slope of a linear function is a measure of the rate at which the value of the function changes as the input (x) changes. A slope of -5/3 means that for every 3 units of change in the input, the output (y) changes by -5 units.

In general, a negative slope indicates that the graph of the function is decreasing. As the input increases, the output decreases. A slope of -5/3 is a relatively steep negative slope, which means that the graph of the function will have a steep downward slope.

A slope of -5/3 also tells us that the function is not a horizontal line. A horizontal line has a slope of 0, which means that the output does not change as the input changes. A slope of -5/3 is not equal to 0, which means that the function is not a horizontal line.

Overall, the slope of a linear function tells us about the direction and steepness of the graph of the function. A slope of -5/3 indicates that the graph of the function is decreasing and relatively steep.

Answer:

$54,742.76

Step-by-step explanation:

The equation for an exponential function is  [tex]f(x)=ab^x\\[/tex], where [tex]a[/tex] is the starting value, which is 40,000. This value increases by 4%, so [tex]b[/tex] is 1.04. Finally, [tex]x[/tex] is the term that the value is increasing for, which in this case is 8.

So, the equation is [tex]f(x)=40000*1.04^8[/tex]

** [tex]f(x)[/tex] can be replaced with [tex]y[/tex]

The expense type which is true is , indebtedness expense as because they are the  minimum monthly payments you make on your loans and credit card.

Being in debt to someone else or owing them money is the state of being indebted. A person who owes money has either borrowed money or obtained goods or services in exchange for a promise to repay the money.

Someone can owe money for both present-day obligations and obligations that they anticipate having in the future. For instance, the term "indebtedness" can relate to a person's mortgage or a car loan.

The majority of people cannot afford to buy a home or a car outright, thus they owe the bank the amount of the loan that was granted to them. When you use a credit card to make purchases like apparel or travel expenses, you become indebted. Being in debt is not the same as not making payments.

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The equation of line in slope intercept form is y = -1/3 x + 1.

What is equation of a line?

The set of points that make up a line in a coordinate system are represented algebraically by a line's equation. An equation of a line is an algebraic expression that represents the many points that together make up a line in the coordinate axis as a set of variables, x, and y. The slope of the line and a point on the line can be used to create the equation of a line.

The points on the line are (3,0) and (0,1).

The slope of a line that passes through the points (x₁, y₁) and (x₂, y₂) is (y₂ - y₁)/(x₂ - x₁).

The slope of line is (1 - 0)/(0 - 3) = -1/3.

The line cuts y-axis at (0,1). Thus y-intercept of the line is 1.

The slope-intercept form of the line is

y =  -1/3 x + 1

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The p-value associated with the null hypothesis = 0.05

Fail to reject the null hypothesis. The​ P-value is greater than the level of significance.

Candice should reject the null hypothesis as the 50% confidence interval does not contain 10 hours

Small p-values offer proof that the null hypothesis is false. The stronger the evidence is against the null hypothesis, the smaller (closer to 0) the p-value. The null hypothesis is rejected if the p-value is less than or equal to the chosen significance level; otherwise, it is not.

You have the Hypothesis that "students study less than 10 hours, on average, per week"

Symbolically:

H₀:μ≥10hours

H₁:μ<10hours

The significant level for this case study is 50% - 0.05. If the results gotten is less than the significance level, we reject the null hypothesis, but if greater, we fail to reject the null hypothesis.

The p-value of 0.05 is one of the most often used numbers. When the calculated p-values are less than 0.05, the faulty hypothesis is considered to be fraudulent or invalid (subsequently the name invalid theory). Additionally, the faulty theory is taken into consideration to be clear if the value is greater than 0.05.

The edge for that likelihood in our model is 0.05, and it represents the probability that our results will be similar to the invalid speculation. Therefore, if the calculated p-value is less than 0.05, it actually means that there is a very little likelihood that we would have the same results as the flawed hypothesis. Additionally, if the p-value is greater than 0.05, there is a very strong probability that the results will be similar to the flawed speculation, leading us to conclude that it is legitimate.

Therefore,

Fail to reject the null hypothesis. The​ P-value is greater than the level of significance.

The p-value associated with the null hypothesis = 0.05

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The minimum sample size needed to guarantee a given margin of error increases , the correct option is (b) .

What is Margin Of Error ?

The term margin of error is defined as an estimate of a small sample that is drawn from a relatively large population data.

the margin of error is usually governed by the parameters such as the standard deviation , sample size and desired confidence level.

to find missing term in the given statement , let us consider the values ,

where σ ⇒ Standard deviation for population

and m as "Margin of error"  and Z as "Empirical value of Z-score" at a given confidence level .

So , minimum sample size for given confidence level is given by

⇒ (Z×σ)²/m²

from above formula we can conclude that minimum sample size is directly related to population's standard deviation.

Therefore, the minimum sample size required would "increase" with the increase in population "standard deviation" .

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The equation of the line will be y = 6x - 25

Given, the point is (4, -1)

The slope is m = 6.

We have to write an equation of the line in slope-intercept form.

The standard form of equation of the line in slope-intercept form is given by

y = mx + c

Where, m is the slope.

Now, substituting the values of x, y and m in the equation,

-1 = 6(4) + c

-1 = 24 + c

c = -1 - 24

c = -25

Put the value of c in the standard equation,

y = 6x - 25

Therefore, the equation of the line is y = 6x - 25

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The length of segment AB is 13 units.

The distance between the two points (a,b) and (c,d) is given by:
[tex]d=\sqrt{(c-a)^2+(d-b)^2}[/tex].

The given coordinates of A  and B are A(0,12) and B(5,0).

The length of segment AB is given by:

[tex]AB = \sqrt{(5-0)^2 + (0 - 12)^2}\\\\AB=\sqrt{25 + 144}\\\\AB = \sqrt{169}\\\\AB = 13[/tex]

Hence, the length of segment AB is 13 units.

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The slope of NO is 2/3 and the slope of LO is -3/2 after using the slope formula.

The ratio that y increase as x increases is the slope of a line. The slope of a line reflects how steep it is, but how much y increases as x increases. Anywhere on the line, the slope stays unchanged (the same).

[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]

The parallel lines have same slope

The slope of LM = the slope of NO

The slope of LM = (-1-(-5))/(4-(-2))

The slope of LM = 4/6 = 2/3

Slope of NO = 2/3

If LMNO is rectangle:

The slope of LO = -1/(slope of LM)

The slope of LO = -1(2/3)

The slope of LO = -3/2

Thus, the slope of NO is 2/3 and the slope of LO is -3/2 after using the slope formula.

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