A boat is heading towards a lighthouse, whose beacon-light is 139 feet above the water. The boat’s crew measures the angle of elevation to the beacon, 5 degrees.
What is the ship’s horizontal distance from the lighthouse (and the shore)? Round your answer to the nearest hundredth of a foot if necessary.

Answer:

The original price of petrol is R12.58 per litre and the new price is R13.28 per litre. To find the percentage increase in the price, we can use the following formula:

Percentage increase = ((new price - old price) / old price) x 100%

Substituting the values, we get:

Percentage increase = ((13.28 - 12.58) / 12.58) x 100%

Percentage increase = (0.70 / 12.58) x 100%

Percentage increase = 0.0557 x 100%

Percentage increase = 5.57%

Therefore, the percentage increase in the price of petrol is 5.57%.

Step-by-step explanation:

Answer: 1979.2 meters

Step-by-step explanation:

Diameter of wheel is 63 cm. Circumference is 63π = 197.92 cm. 1000 revolutions of 197.92 = 197920 cm = 1979.2 meters.

let's reword it

what is the arc of a circle whose central angle is 100 revolutions and has a radius of 63÷2?

let's keep in mind that radius is half the diameter, and a revolution is 2π radians or 360°, so hmmm 100 revolutions will just be 360*100 = 36000°.

[tex]\textit{arc's length}\\\\ s = \cfrac{\theta \pi r}{180} ~~ \begin{cases} r=radius\\ \theta =\stackrel{degrees}{angle}\\[-0.5em] \hrulefill\\ \theta =36000\\ r=\frac{63}{2} \end{cases}\implies s=\cfrac{(36000)\pi (\frac{63}{2})}{180}\implies s=\cfrac{(36000)(\frac{22}{7}) (\frac{63}{2})}{180} \\\\\\ s=200(\frac{22}{7}) (\frac{63}{2})\implies s=(200)(99)\implies \boxed{s=19800}~metres[/tex]

Answer: June uses 192 jellybeans for every dozen (12) plastic eggs she fills, which means she uses 192/12 = <<192/12=16>>16 jellybeans per plastic egg.

To find how many plastic eggs can be filled with 1,152 jellybeans, we can divide 1,152 by the number of jellybeans per egg:

Number of eggs = 1,152 ÷ 16 = <<1152/16=72>>72

Therefore, June can fill 72 plastic eggs with 1,152 jellybeans.

Step-by-step explanation:

Mathematicians divide the world of numbers into seven subsets, namely natural numbers, whole numbers, integers, rational numbers, irrational numbers, real numbers, and complex numbers.

Natural numbers: These are the counting numbers, starting from 1 and continuing indefinitely. They can also be denoted as "N" or "ℕ".

Whole numbers: These are the natural numbers, as well as zero. They can also be denoted as "W" or "ℤ⁺⁰".

Integers: These are the whole numbers, as well as their negative counterparts. They can also be denoted as "Z" or "ℤ".

Rational numbers: These are numbers that can be expressed as a fraction, where the numerator and denominator are integers (and the denominator is not zero). They can also be denoted as "Q" or "ℚ".

Irrational numbers: These are numbers that cannot be expressed as a fraction of two integers. They are often represented by decimal expansions that neither terminate nor repeat. Examples include π and the square root of 2.

Real numbers: These are all the rational and irrational numbers, taken together. They can also be thought of as numbers that can be located on a number line. They are often denoted as "R" or "ℝ".

Complex numbers: These are numbers of the form a + bi, where a and b are real numbers and i is the imaginary unit (defined as the square root of -1). Complex numbers can be added, subtracted, multiplied, and divided, just like real numbers. They are often denoted as "C" or "ℂ".

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10.5% is better because 20 dollers is good but it not gonna increase like 10.5%

The transversal angle of 45 is angle6.

Two lines intersect at a location, creating an angle.

An "angle" is the term used to describe the width of the "opening" between these two rays. The character is used to represent it.

Angles are frequently expressed in degrees and radians, a unit of circularity or rotation.

In geometry, an angle is created by joining two rays at their ends. These rays are referred to as the angle's sides or arms.

An angle has two primary components: the arms and the vertex. T

he two rays' shared vertex serves as their common terminal.

Hence, The transversal angle of 45 is angle6.

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The required simplified forms are 3x - 1, 6x , 2x² - 10x , a + 2b , 15x - 8 , x² + 2x + 6 , x² - y² , 6x² - 22x.

the definition of an equation is a mathematical statement that demonstrates that two mathematical expressions are equal. For instance, the equation 3x + 5 = 14 consists of the two expressions 3x + 5 and 14, which are separated by the 'equal' symbol.

Simplified forms of the equation are

[tex]$c: 3(x-2)+5=3x-6+5=3x-1$[/tex]

[tex]$f: 2x(3-x)+x^2=6x-x^2+x^2=6x$[/tex]

[tex]$i: 7x^2-5x(x+2)=7x^2-5x^2-10x=2x^2-10x$[/tex]

[tex]$c: 2a-(a-2b)=2a-a+2b=a+2b$[/tex]

f: [tex]$3x-4(2-3x)=3x-8+12x=15x-8$[/tex]

[tex]$x(x+4)-2(x-3)=x^2+4x-2x+6=x^2+2x+6$[/tex]

[tex]$x(x+y)-y(x+y)=(x-y)(x+y)=x^2-y^2$[/tex]

[tex]$o: 4x(x-3)-2x(5-x)=4x^2-12x-10x+2x^2=6x^2-22x$[/tex]

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The graph of the system of equations is shown below:

The solution of the system is given by the point of intersection of the two lines which is (20/7, -7/2).

The minors and cofactors of the given matrix are:

|882 270 -72| |-490 194 198| |78 -44 -72|

To find the minors and cofactors of the given matrix, we first need to understand what a minor and a cofactor are.

The minor of an element a_ij is the determinant of the submatrix obtained by deleting the i-th row and j-th column of the original matrix.

The cofactor of an element a_ij is the minor of a_ij multiplied by (-1)^(i+j).

Using this definition, we can find the minors and cofactors of the given matrix as follows:

Minor of a_11:

|-7 9 5 -1|

|-5 -9 -7 9|

|-6 -3 -7 9|

Minor = (-7)(-9)(-7) + (9)(-7)(-6) + (5)(-5)(-3) + (-1)(-6)(9) = 882

Cofactor of a_11:

Cofactor = (-1)^(1+1) * 882 = 882

Minor of a_12:

|-6 -3 -7 9|

|-5 -9 -7 9|

|-5 -1 -9 5|

Minor = (-6)(-9)(-9) + (-3)(-7)(5) + (-7)(-5)(-1) + (9)(-5)(-5) = -270

Cofactor of a_12:

Cofactor = (-1)^(1+2) * (-270) = 270

Minor of a_13:

|-6 -6 -3|

|-5 -9 -7|

|-5 -1 -9|

Minor = (-6)(-9)(-9) + (-6)(-7)(-1) + (-3)(-5)(-1) + (-9)(-5)(-6) = -72

Cofactor of a_13:

Cofactor = (-1)^(1+3) * (-72) = 72

Minor of a_21:

|-5 -9 -7 9|

|-6 -3 -7 9|

|-5 -1 -9 5|

Minor = (-5)(-7)(-9) + (-9)(-5)(-5) + (-7)(-5)(-1) + (9)(-1)(-5) = 490

Cofactor of a_21:

Cofactor = (-1)^(2+1) * 490 = -490

Minor of a_22:

|-6 -6 -3|

|-5 -1 -9|

|-5 -1 -9|

Minor = (-6)(-9)(-1) + (-6)(-1)(-5) + (-3)(-5)(-1) + (-9)(-5)(-5) = 194

Cofactor of a_22

Cofactor = (-1)^(2+2) * 194 = 194

Minor of a_23:

|-6 -6 -3|

|-5 -9 -7|

|-5 -1 -9|

Minor = (-6)(-9)(-7) + (-6)(-7)(-1) + (-3)(-5)(-1) + (-7)(-5)(-6) = 198

Cofactor of a_23:

Cofactor = (-1)^(2+3) * (-198) = 198

Minor of a_31:

|-5 -9 -7|

|-6 -3 -7|

|-5 -1 -9|

Minor = (-5)(-3)(-9) + (-9)(-5)(-1) + (-7)(-6)(-1) + (-6)(-1)(-7) = -78

Cofactor of a_31:

Cofactor = (-1)^(3+1) * (-78) = 78

Minor of a_32:

|-6 -6 -3|

|-5 -1 -9|

|-5 -1 -9|

Minor = (-6)(-9)(-1) + (-6)(-1)(-5) + (-3)(-5)(-1) + (-1)(-5)(-5) = 44

Cofactor of a_32:

Cofactor = (-1)^(3+2) * 44 = -44

Minor of a_33:

|-6 -6 -3|

|-5 -9 -7|

|-6 -3 -7|

Minor = (-6)(-9)(-7) + (-6)(-7)(-3) + (-3)(-6)(-1) + (-7)(-5)(-6) = -72

Cofactor of a_33:

Cofactor = (-1)^(3+3) * (-72) = -72

Therefore, the minors and cofactors are:

|882 270 -72| |-490 194 198| |78 -44 -72|

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The probability of spinning a slice that is not yellow is equal to the total number of non-yellow slices divided by the total number of slices.

Total number of non-yellow slices = 9 (3 red + 5 blue)

Total number of slices = 12

Therefore, the probability of spinning a slice that is not yellow is 9/12 or 75%.

The number of words formed with letters of the word 'PROBLEM' which neither start with O nor end with E is 3600.

The word PROBLEM has 7 letters, which can be arranged in 7! (factorial) ways, i.e. [tex]7*6*5*4*3*2*1 = 5040.[/tex]

Now to calculate the number of words formed with letters of the word 'PROBLEM' which neither start with O nor end with E, we can first calculate the number of words which start with O or end with E.

For words starting with O, there are 6 letters left and these can be arranged in 6! ways, i.e.[tex]6*5*4*3*2*1 = 720.[/tex]

For words ending with E, there are again 6 letters left and these can be arranged in 6! ways, i.e. [tex]6*5*4*3*2*1 = 720[/tex].

Now the total number of words which start with O or end with E will be the sum of two, i.e. 720 + 720 = 1440.

Therefore, the number of words formed with letters of the word 'PROBLEM' which neither start with O nor end with E will be the total number of words minus the total number of words which start with O or end with E, i.e. 5040 - 1440 = 3600.

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The marginal probability function E(Y1) = 2/3, variance of a binomial distribution is V(Y1) = 4/9, and E(Y1-Y2) = 0, using the joint probability function for Y1 and Y2 and the fact that they have binomial distributions with n=2 and p=1/3.

The marginal probability function of Y1 is binomial with n=2 and p=1/3, as given in Exercise 5.19. Therefore, we have:

E(Y1) = np = 2(1/3) = 2/3.

The variance of a binomial distribution with parameters n and p is given by np(1-p), so we have:

V(Y1) = np(1-p) = 2(1/3)(2/3) = 4/9.

We can use the linearity of expectation to find E(Y1-Y2):

E(Y1 - Y2) = E(Y1) - E(Y2)

We know that E(Y1) = 2/3 from part (a), but we need to find E(Y2). Using the same reasoning as in part (a), we find that the marginal probability function of Y2 is also binomial with n=2 and p=1/3. Therefore, we have:

E(Y2) = np = 2(1/3) = 2/3.

Substituting these values into the expression for E(Y1-Y2), we get:

E(Y1 - Y2) = 2/3 - 2/3 = 0.

Therefore, E(Y1-Y2) is equal to 0.

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Answer:

680 ways

Step-by-step explanation:

C(17, 3) gives 17! / (14! 3!), or (17*16*15)/6 = 680 ways to select the 3 individuals.

Hope this helped!

Answer:

21 years old

Step-by-step explanation:

Set Alan's age as x, Bernice's age as y

2x=y

x-4+y-4=55

x+y=63

3y=63

x=21

y=42

To solve this equation, begin by expanding the parentheses.

y = 4x² + 40x + 100 + 16

Then, collect like terms on the left hand side.

y = 4x² + 40x + 116

Finally, rearrange the equation to get y on the left side.

4x² + 40x - (y - 116) = 0

The final answer will be a quadratic equation.

The negative of the gradient (-grad f(x)) points in the direction of the maximum decrease of f from x.

The gradient of a scalar-valued function is a vector that points in the direction of the maximum increase of the function.

In other words, if we consider a point in the domain of the function and take the gradient at that point, the direction of the gradient vector indicates the order in which the function increases the most from that point. Conversely, the negative gradient points in the direction of the maximum decrease of the function.

Specifically, let f be a scalar-valued function of n variables [tex](f: R^n - > R),[/tex]and let x be a point in the domain of f. The gradient of f at x is defined as the vector:

[tex]grad f(x) = (∂f/∂x1, ∂f/∂x2, ..., ∂f/∂xn)[/tex]

where ∂f/∂xi denotes the partial derivative of f with respect to xi evaluated at x, the direction of the gradient vector grad f(x) at x is the direction in which f increases the most from x, and the magnitude of the gradient vector is the rate of change of f at x in that direction.

The negative of the gradient (-grad f(x)) points in the direction of the maximum decrease of f from x.

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Answer: Consider the expression (2x − 3) − (-3x + 4).

First, distribute the negative sign and rewrite the expression:

2x − 3 + 3x – 4.

Then, model the polynomial.

There are no zero pairs, so the difference is 5x − 7.

Step-by-step explanation:

PLATO

Answer:157

Step-by-step explanation:

it just is =]

As a result, AB = 52 and AC = BC = 5 as AC and BC are both the circle's radii since A and B are points of tangency .

A circle is a closed object made up of all points in a plane that are separated from the center by a predetermined distance, known as the radius. The diameter is the distance across the circle that passes through its center, while the circumference is the distance around the circle. The ratio of a circle's circumference to its diameter is always pi (), or roughly 3.14. Pi is also known as the proportionality constant. Circles are significant geometric forms that are used frequently in mathematics, science, and daily life.

given

AC and BC are both the circle's radii since A and B are points of tangency. Hence, AC = BC = 5.

We can apply the Pythagorean theorem to segment AB as follows:

[tex]AB^2 = 52 + 52 \\AB^2 = AC^2 + BC^2[/tex]

AB² = 50

AB = √50 = 5√2

As a result, AB = 52 and AC = BC = 5 as AC and BC are both the circle's radii since A and B are points of tangency .

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The fixed price of the land is 296257.50.

What is discount?

Discount is the state of having a bond's price lower than its face value. The difference between the purchase price and the item's par value is the discount.

Discounts are different types of price reductions or deductions from a product's cost. It is frequently employed in consumer transactions when consumers receive discounts on a range of goods. The % discount rate is provided.

Here the discount on the fixed price = 10%

Commission for the broker = 5%

If total amount = 100%+10% = 110%

Then received amount = [tex]\frac{110}{100}\times256500[/tex]

=> Received amount =  282150

Now 5% commission then,

=> [tex]\frac{105}{100}\times 282150[/tex] = 296257.50.

Hence the fixed amount of the land before discount is 296257.50.

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it is false. 0 is not a natural number. it is a whole number

Answer: MN || VT

Step-by-step explanation:

We can see that MN is vertical, and the only angle that is vertical, is VT. And we can see that they don't obstruct their lines (meaning that they don't intersect), and keep going for infinity. So, VT would be the only parallel line to the one given.

Hope this helps

Answer:

x=12

Step-by-step explanation:

2x-y=15

y=9

2x-9=15

2x=24

x=12

Answer:

Step-by-step explanation:

Answer:

this is when you want to draw a sketch of a building

If there are 95 families to feed then each family will receive 11 cans of assorted tins.

Assorted tins typically refer to cans or containers of food items that come in different varieties or flavors.

To calculate the number of cans each family will receive, we need to first determine the total number of cans in the 19 boxes.

19 boxes × 55 cans per box = 1045 cans

Now we can divide the total number of cans by the number of families to determine the number of cans each family will receive:

1045 cans ÷ 95 families = 11 cans per family (rounded to the nearest whole number)

Therefore, each family will receive 11 cans of assorted tins.

For example, a box of assorted tins may contain cans of different types of vegetables, fruits, soups, or other food items. The specific assortment may vary depending on the context and the supplier. In the context of the given question, the 19 boxes of assorted tins likely contain cans of different types of food that will be packed into food parcels for the poor.

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