Find HP
Round to the nearest whole meter

The boat's displacement is approximately 84,016.8 metric tons.

To convert the boat's top speed from knots to miles per hour, we can use the conversion factor of 1.15078 miles per hour per knot:

26 knots × 1.15078 miles per hour per knot = 29.86 miles per hour (rounded to two decimal places)

Therefore, the boat's top speed is approximately 29.86 miles per hour.

To convert the boat's displacement from tons to metric tons, we can use the conversion factor of 0.907185 metric tons per ton:

93,000 tons × 0.907185 metric tons per ton = 84,016.8 metric tons (rounded to one decimal place)

Therefore, the boat's displacement is approximately 84,016.8 metric tons.

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The complete factorization of the polynomial function f(x) = x³ - 4x² - 3x + 18 is (x + 2)(x - 22).

What is a polynomial ?

A polynomial is a mathematical expression involving a sum of powers in one or more variables (indeterminates) multiplied by coefficients.

where n is a non-negative integer (the degree of the polynomial), x is the variable, and (the coefficients of the polynomial). The highest power of x in the expression is n, and this term is called the leading term. The coefficient of the leading term, a_n, is called the leading coefficient.

To find the other linear factors of the polynomial function f(x) = x³ - 4x² - 3x + 18, we can use long division by dividing the polynomial function by (x + 2).

Here's how the long division would look like:

x³ - 4x² - 3x + 18

       ÷ x + 2

__________________________

x² - 6x - 20

             ÷ x + 2

__________________________

x - 22

       ÷ x + 2

__________________________

-20

here -20 is the remainder.

The complete factorization of the polynomial function f(x) = x³ - 4x² - 3x + 18 is (x + 2)(x - 22).

So, the other linear factors are x - 22.

Therefore, The complete factorization of the polynomial function f(x) = x³ - 4x² - 3x + 18 is (x + 2)(x - 22).

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Answer:

[tex]4x^{2} y^{3}[/tex]

Step-by-step explanation:

[tex]\frac{36x^{4}y^{5}}{(3xy)^{2}}[/tex]

In the denominator, all the terms in the brackets or parenthesis will be squared:

= [tex]\frac{36x^{4}y^{5}}{9x^{2} y^{2}}[/tex]

Law of indices is applied:

                                                    [tex]\frac{a^{n}}{a^{m}}[/tex]= [tex]a^{n - m}[/tex]

= [tex]4x^{4 - 2} y^{5 - 2}[/tex]

= [tex]4x^{2} y^{3}[/tex]

∴Option B

Answer:

  77.5°

Step-by-step explanation:

You want the measures of the angles formed when ray OX bisects the 155° angle AOB.

The angle bisector creates two equal angles, each of which is half the measure of the original angle. The measures of the angles formed are ...

  155°/2 = 77.5°

Answer: 266

Step-by-step explanation:

I = prt

p= 1900

r=.07

t=2

1900x.07x2=266

Answer:

To determine the balance in the Allowance for Doubtful Accounts on December 31, we first need to estimate the bad debts based on the credit sales.

Bad debts = 2% of credit sales = 2% * $400,000 = $8,000

The balance in the Allowance for Doubtful Accounts would then be equal to the estimated bad debts, which is $8,000.

Therefore, the Accounts Receivable and the Allowance for Doubtful Accounts would appear on the December 31 balance sheet as follows:

Current Assets:

Accounts receivable $120,000

Less: Allowance for doubtful accounts $8,000

Net accounts receivable $112,000

The number of widgets that Justin can make in 36 minutes is given as follows:

y = 36k.

In which the constant k is the number of widgets that can be made per minute, and is obtained dividing a value of y by it's respective value of x from the table.

A proportional relationship is defined as follows:

y = kx.

In which k is the constant of proportionality.

The variables for this problem are given as follows:

The constant is obtained as follows:

k = y/x.

For a time of 36 minutes, we have that x = 36, hence the number of widgets is given as follows:

y = 36k.

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Answer:

2

Step-by-step explanation:

1 plus 1 due to the characterisation of the number 1 increasing by 1 gives you 2

The number of bees that will equal the mass of a single moose is 5 × 10⁶.

Given the data in the question;

To determine the number of bees that will equal the mass of a single moose.

Let the number be represented by x.

Hence;

Number of bees × mass of bee = mass of moose

n × ( 2.5 × 10⁻⁴ ) = 1.25 × 10³

Divide both sides by ( 2.5 × 10⁻⁴ ).

n = ( 1.25 × 10³ ) / ( 2.5 × 10⁻⁴ )

n = 1250 / 0.00025

n = 5,000,000

Therefore, the number of bees is 5,000,000.

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1. The height of the cone is, 22.18 mm.

2. The slant height is, 28.14 mm.

3. The ant crawl to get from the base of the cone to the top of the hill is, 28.14 mm.

In mathematics, Space occupied by three dimensional objects is called Volume. Basically it is a space within a closed region of every three dimensional object.

The volume of cone V = (1/3)πr²h

Given that,

The volume  = 8792 mm³

1. by using the formula to solve for h,

we get h = (3V)/(πr²).

Plugging in the values given,

we have h = (3(8792 mm³))/(π(20 mm)²) ≈ 22.18 mm.

Therefore, the height of the cone is approximately 22.18 mm.

2. it is known that, from the Pythagoras theorem

s² = h² + r²,

where s is the slant height, h is the height, and r is the radius.

Plugging in the values we found in part 1,

we have s² = (22.18 mm)² + (20 mm)² ≈ 791.88 mm².

Taking the square root of both sides, we get s ≈ 28.14 mm.

Therefore, the slant height is approximately 28.14 mm.

3. To find the distance the ant crawls to get from the base of the cone to the top of the hill, we need to find the length of the slant height.

Using the value we found in part 2,

the length of the slant height is approximately 28.14 mm.

Therefore, that is the distance the ant would crawl to get from the base of the cone to the top of the hill.

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The volume of the cube  is 444.19 in³

The volume of the rectangular prism is 661.2 ft³

The volume of the triangular prism is 30.04 yd³

The volume of the cylinder is 380.57 km³

Volume of a cube is solved using the formula

= length³

= 7.63³

= 444.19 in³

Volume of a rectangular prism is solved using the formula

= Area of base * height

= 9.5 * 8.7 * 8

= 661.2 ft³

Volume of a triangular prism is solved using the formula

= 1/2 × base × height × length

= 1/2 * 5.84 * 3.08 * 3.34

= 30.04 yd³

Volume of a cylinder is solved using the formula

= π * radius² * height

= π * 3² * 13.46

= 380.57 km³

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Using a system of equations, the number of points given for an arrow in target B is 7.

A system of equations means two or more equations solved at the same time or concurrently.

A system of equations is also described as simultaneous equations since they are solved simultaneously.

                              Target A    Target B   Total Score

Rence shots                3                1                  19

Sunil shots                  2                2                22

Let the points for an arrow into target A = x

Let the points for an arrow into target B = y

3x + y = 19 ... Equation 1

2x + 2y = 22 ... Equation 2

Multiply Equation 1 by 2:

6x + 2y = 38 ... Equation 3

Subtract Equation 2 from Equation 3:

6x + 2y = 38

-

2x + 2y = 22

4x = 16

x = 4

From Equation 1, substitute x = 4:

3x + y = 19

3(4) + y = 19

12 + y = 19

y = 19 -12

y = 7

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Answer: D Im doing the quiz

Answer:D:the range is 5, and the IQR is 10.

Step-by-step explanation:

Answer:

Step-by-step explanation:

S+8=D

S+D equals 94.

94/2= 45+2=47

47-8=39

Sydney is 39

Answer:

43

Step-by-step explanation:

94-8= 86

86/2= 43

43+8= 51

a:43

prove it :

51+43= 94

Answer: Width = 73 m

Step-by-step explanation:

Perimeter = Length(2) + Width(2)

330 - (92 x 2)

330 - 184 = 146

146 = Width of 2 sides

146/2 = 73 m

Answer: A proper subset of a set A is a subset of A that is not equal to A

Step-by-step explanation:

A quadratic function could represent the data in the table, as the increase rate decreases as x increases, meaning that the function could be approaching it's vertex.

Traditionally, functions are classified as either linear or exponential, as follows:

As there is not a constant neither a multiplicative rate of change for the table, the function is neither linear nor exponential.

Considering that from x = 1 to x = 4 the rate of change is of 4/3, while from x = 16 to x = 25 the rate of change is of 4/9, that is, the increase rate decreases as x increases, the function is classified as a quadratic function.

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Answer:

Step-by-step explanation:

y = -3

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Answer:

x = -5

Step-by-step explanation:

15 - 2x = -4(x+1) + 9

-4(x+1) can be distributed and simplified to -4x - 4

15 - 2x = -4x - 4 + 9

15 - 2x = -4x +5

-2x + 4x = 5 - 15

2x = -10

x = -5

Answer:

[tex]x=-5[/tex]

Step-by-step explanation:

Given

[tex]15-2x=-4(x+1)+9[/tex]

Simplify the right side by applying the distributive property.

[tex]15-2x=(-4*x)+(-4*1)+9[/tex]

[tex]15-2x=-4x-4+9[/tex]

Add [tex]-4[/tex] and 9.

[tex]15-2x=-4x+5[/tex]

Add [tex]4x[/tex] to both sides of the equation.

[tex]15-2x+4x=5[/tex]

Add [tex]-2x[/tex] and [tex]4x[/tex].

[tex]15+2x=5[/tex]

Subtract [tex]15[/tex] from both sides of the equation.

[tex]2x=-10[/tex]

Divide both sides of the equation by [tex]2[/tex].

[tex]x=-5[/tex]

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Answer:

2 [tex]\frac{16}{17}[/tex] miles

Step-by-step explanation:

[tex]\frac{miles}{minutes}[/tex] = [tex]\frac{miles}{minutes}[/tex]

[tex]\frac{1 1/4}{8 1/2}[/tex] = [tex]\frac{x}{20}[/tex]

1 [tex]\frac{1}{4}[/tex] is the same as [tex]\frac{4}{4}[/tex] + [tex]\frac{1}{4}[/tex]   (1 = [tex]\frac{4}{4}[/tex] )

8 [tex]\frac{1}{2}[/tex] is the same as [tex]\frac{2}{2}[/tex] + [tex]\frac{2}{2}[/tex] + [tex]\frac{2}{2}[/tex] + [tex]\frac{2}{2}[/tex] + [tex]\frac{2}{2}[/tex] + [tex]\frac{2}{2}[/tex] + [tex]\frac{2}{2}[/tex] + [tex]\frac{2}{2}[/tex] + [tex]\frac{1}{2}[/tex] = [tex]\frac{17}{2}[/tex]   (1 = [tex]\frac{2}{2}[/tex])

[tex]\frac{\frac{5}{4} }{\frac{17}{2} }[/tex] = [tex]\frac{x}{20}[/tex]

[tex]\frac{17}{2}[/tex] x = 20  multiply both sides by [tex]\frac{2}{17}[/tex]

[tex]\frac{2}{17}[/tex] [tex](\frac{17}{2})[/tex]x = [tex]\frac{2}{17}[/tex][tex](\frac{20}{1})[/tex]

x = [tex]\frac{40}{17}[/tex]

[tex]\frac{5}{4}[/tex] [tex](\frac{40}{17})[/tex] = x

[tex]\frac{50}{17}[/tex] or 2 [tex]\frac{16}{17}[/tex]

The triangle's perimeter is roughly 25.29 cm.

The area around a form's edge is known as its perimeter. The perimeter of various forms can be calculated by summing the lengths of their sides.

Let's call the right triangle's shorter leg "x" for short.

The longer leg is then 5 cm longer than x, or x + 5, according to the situation.

The hypotenuse measures x + 10 cm longer than x.

By the Pythagorean theorem, we know that:

x² + (x+5)² = (x+10)²

Expanding and simplifying this equation gives:

2x² + 10x - 75 = 0

Dividing both sides by 2 gives:

x² + 5x - 37.5 = 0

We can find the value of x by using the quadratic formula:

x = (-5 ± sqrt(5² - 4(1)(-37.5))) / 2

x = (-5 ± sqrt(175)) / 2

x ≈ -8.68 or x ≈ 3.43

Since x represents a length, we must choose the positive solution x = 3.43 cm.

Therefore, the shorter leg of the triangle is 3.43 cm, the longer leg is 8.43 cm (3.43 + 5), and the hypotenuse is 13.43 cm (3.43 + 10). The perimeter of the triangle is the sum of the three sides, which is:

3.43 + 8.43 + 13.43 = 25.29 cm

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The volume of the cylinder will be 666 cubic centimeters. Then the correct option is D.

Volume is a measurement of three-dimensional space that is utilized. It is frequently mathematically quantified using SI-derived units or different imperial or US traditional units. The concept of length is linked to the notion of capacity.

The radius and height of the cone and the cylinder are the same. Then the ratio of the volume of the cylinder to the volume of the cone is 3. Then we have

(Volume of the cylinder) / (Volume of the Cone) = 3

Volume of the cylinder  / 222 = 3

Volume of the cylinder = 666 cubic cm

The volume of the cylinder will be 666 cubic centimeters. Then the correct option is D.

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The below area rate can also be further answered as 14, since the supplied border rate can be further answered as 12. Their areas are compared 4/16.

What's meant by rate?

Areas If the scale factor of the sides of two analogous polygons is m/ n

 also the rate of the areas is (m/n)^2.

Area of analogous Polygons Theorem). Because area is a two- dimensional volume, you square the rate.

It's given that, the rate of peripheries of two analogous quadrilateral is 2 4

 now,  

to find the rate of area, we can take two quadrilaterals, say square.

Square ABCD of side 2 units and Square PQRS of side 4 units.

now rate of areas,

[tex]=\frac{area \ of\ square\ ABCD }{area \ of\ square\ PQRS }[/tex]

[tex]=\frac{2 \times 2}{4 \times 4}[/tex]

= 4/16

= 1/4

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Answer:

B

Step-by-step explanation:

c=d*π

c=8*π

c=25.1 inches

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Answer:

the final answer is 7x + 5xy.

Step-by-step explanation:

3x + 4x = 7x

3xy + 2xy = 5xy

So, the final answer is 7x + 5xy.

Answer:

5xy+7x

Step-by-step explanation:

You see which ones have the same exact variables (x or xy)

Then you add the ones with the same variables together.

3x+4x=7x

3xy+2xy = 5xy

5xy+7x

(Depending on your teacher, they may not have to be in this order)

The sample distribution of (PM-PB) will not be normal, because w expect fewer than 10 electric cars in both samples.

There are two types of data sets are collected for the research. They are population and sample. Population includes all the elements from the data set. Sample is a part of population.

The company planned to take survey from the employees from both the main office and the branch office.

For this, the company took 100 employees from main office and 50 employees from a branch office.

We expect at least 10 successes and at least 10 failures in both samples, then the sampling distribution of [tex]p_{1 }and p_{2}[/tex] will be approximately normal.[tex]n_{1}p_{1}\ge 10 and n_1(1-p_1)\ge10[/tex]

[tex]n_{2}p_{2}\ge 10 and n_2(1-p_2)\ge10[/tex]

Let [tex]x_{1} and x_2[/tex] denotes the number of persons in the sample.

[tex]x_{1} =100\\n_{2} =50[/tex]

Also given 1.5% of employees at the main office have electric cars and 2% of employees at the branch office have electric cars.

so, [tex]p_{1}=0.015, p_{2}=0.02[/tex]

Combining this values we have,

[tex]n_1p_1=100(0.015)=1.5\le10[/tex] and

[tex]n_1(1-p_1)=100(1-0.015)=98.5 > 10[/tex]

Similarly, [tex]n_2p_2=50(0.02)=1\le10[/tex] and

[tex]n_2(1-p_1)=50(1-0.02)=49\ge10[/tex]

Hence, the sample distribution of PM-PB will not be normal, because w expect fewer than 10 electric cars in both samples.

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The inequality on the graph is written as:

-4 < x ≤ 5

Here we have an inequality graphed on a number line.

First, we can see that we have an open circle at x = -4 and then the line goes to the right.

That means that the value of x must be larger than -4, so we can start by writting:

-4 < x

Then we have a closed circle at x = 5.

That means that x can be smaller or equal to 5, then:

x ≤ 5

Then the inequality is:

-4 < x ≤ 5

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To convert inches to yards, we need to divide by 36, since 36 inches make 1 yard. Therefore, to convert the length of the shed and ramp from inches to yards, we can use the following expressions: (12 + 1) / 36 = 0.3611... yards, (12 / 36) + (1 / 36) = 0.3611... yards, 13 / 36 = 0.3611... yards

An expression in mathematics is a grouping of variables, numbers, and actions that can be evaluated to yield a value. A wide range of mathematical notions, from basic arithmetic computations to intricate algebraic formulas and beyond, are represented by expressions.

These components can be used to combine expressions in a wide range of different ways. For instance, we can construct straightforward arithmetic phrases such as "2 + 3" or "5 * 4" or more intricate algebraic expressions such as "3x2 + 2x + 1" or "sin(x) + cos(x)". In each instance, the expression denotes a mathematical idea that may be tested to provide a certain value.

Expressions play a significant role in mathematics and are utilized in a wide range of fields in science, engineering, and finance. By being aware of how expressions work, we can better understand and solve a wide variety of mathematical problems.

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