What’s 523.15 in word from?

Answer:

  20 mi/h

Step-by-step explanation:

You want the speed of separation after 3 hours between two cars that started from the same point. One is moving at 16 mi/h south, the other is moving at 12 mi/h west.

Since both cars started from the same point, the speed of separation is the magnitude of the difference between the respective velocity vectors. A graphical representation of the velocity vectors shows them to be the legs of a right triangle. Their difference is the length of the hypotenuse, which can be found using the Pythagorean theorem.

  s = √(16² +12²) = √(256 +144) = √400

  s = 20

The speed of separation is a constant 20 mi/h.

__

Additional comment

If the cars did not start at the same point, then the speed of separation would be changing with time. It could be found using the derivative of the distance between the cars, or by considering the car speeds in the direction each car is from the other at the time of interest.

We note that the problem here makes use of a 3-4-5 right triangle, with a multiplier of 4 mph.

(a) A quadratic equation is in the form: y = -12.87x² + 42.22x + 1.18

(b) The height of the rocket after 3 seconds would be 12.01 feet.

A quadratic equation is a polynomial equation with a maximum degree of two. Any equation that can be written in the standard form where x is an unknown value, a, b, and c are known quantities, and a 0 is a quadratic equation.

Here, we have

Given: A rocket is launched upwards from the ground.

(a) A quadratic equation is in the form:

y = -12.87x² + 42.22x + 1.18

(b) When x = 3 seconds

y = -12.87(3)² + 42.22(3) + 1.18

y = 12.01 feet

Hence, the height of the rocket after 3 seconds is 12.01 feet.

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Answer:

31.01

Step-by-step explanation:

A= πr^2= π · 3.142 ≈31.01432

Suppose a trapezoid is defined as a quadrilateral with at least 1 pair of parallel sides. Thus, trapezoids will change the venn Diagram by being classified as under 1 pair of parallel sides.

In geometry, a quadrilateral with at least one set of parallel sides is referred to as a trapezium in American or Canadian English, or a trapezium in British as well as other forms of English. In Euclidean geometry, a trapezium is a convex quadrilateral by definition. The bases of a trapezium are the parallel sides. Thus, trapezoids will change the venn Diagram by being classified as under 1 pair of parallel sides.

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The total area from the graph is 2.737.

Area is the amount of space occupied by a two-dimensional figure. In other words, it is the quantity that measures the number of unit squares that cover the surface of a closed figure. The standard unit of area is square units which is generally represented as square inches, square feet, etc.

First of all, lets calculate the points of intersection (P, Q, R)

x²+3=(x+2) +5

x²-2=√(x+2)

x⁴+4-4x²=x+2

x⁴-4x²-x+2=0

(x-2)(x³+2x²-1)=0

(x-2)(x+1)(x²+x-1)=0

x=2, -1, -1±√(1+4)/2

Clearly, the x-coordinate of Q is -1, P is -1-√5/2, R is -1+√5/2, S is 2

So the limit of integration will be

P( (-1-√5)/2, (-1-√5/2)² +3)=P((-1-√5)/2, (3+√5/2))

Q(-1, (-1)²+3)=Q(-1, 4)

Area A:

\(\int\limits^\frac{3+\sqrt{5} }{2} _4 {-\sqrt{-y-3}-((y-5)^2 -2)} \, dx\)

= \([\frac{-(y-3)^\frac{3}{2} }{\frac{3}{2} }-\frac{(y-5)^3}{3}+3y]^{\frac{3+\sqrt{5} }{2} }_4\)

= 2.07

Area B:

\(\int\limits^\frac{-1+\sqrt{5} }{2} _4 {-\sqrt{x+2}+5-(x^2+3)} \, dx\)

= \([\frac{-(x+2)^\frac{3}{2} }{\frac{3}{2} }+5x-\frac{x^3}{3}-3x]^{\frac{-1+\sqrt{5} }{2} }_{-1}\)

= 0.667

Total area = 2.07+0.667

= 2.737

Therefore, the total area from the graph is 2.737.

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The two equations of a system that can be used to find the ages of both girls are y - x = 6 and 3x - y = 0.

A group of two or more equations that must be solved all at once is known as a system of equations. The objective is to determine the values of the variables that make both equations true in a system of two equations with two variables. These numbers represent the system of equations' answer. There are several ways to solve a system of equations, including substitution, elimination, and graphing. They are used to simulate and resolve issues in many branches of mathematics, science, engineering, and other disciplines.

Let us suppose the age of Celine = x.

Let us suppose the age of Cindy = y.

Given that, Celine is 6 years younger than her sister Cindy.

x = y - 6

She is also one third as old as Cindy.

x = 1/3y or y = 3x.

Substitute the value of y in equation 1:

x = 3x - 6

6 = 2x

x = 3

Substitute the value of x:

y = 3(3) = 9

Hence, the two equations that can be used to find the ages of  both girls are y - x = 6 and 3x - y = 0.

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Answer:

9. x = 2

Step-by-step explanation:

9. The corresponding side lengths of two similar polygons are proportional to each other. This means the ratio of their corresponding side lengths are equal.

Thus:

8/x = 12/3

8/x = 4

Cross multiply

4x = 8

4x/4 = 8/4

x = 2

The required distance c between the point of marching formation is given as C = √61.

Distance is defined as the object traveling at a particular speed in time from one point to another.

Here,

The distance formula is given as,

C = √[[x₂ - x₁]² + [y₂+ - y₁]²]

Put the given point in the above equation,
C = √[[3 + 2₁]² + [4 + 2]²]
C = √25+36
C = √61

Thus, the required distance c between the point of marching formation is given as C = √61.

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The surface area of the \(132cm^2.\)

The surface area of a triangular prism is also referred to as its total surface area. The total surface area of a triangular prism is the sum of the areas of all the faces of the prism. A triangular prism has three rectangular faces and two triangular faces. The rectangular faces are said to be the lateral faces, while the triangular faces are called bases. If the bases of a triangular prism are placed horizontally, they are referred to as the top and the bottom (faces) of the prism, respectively.

Surface area of given triangular shaped prism

= 2 ×area of right angle triangle + area of3 rectangles

= 2(1/2 ab)+(ah+bh+ch)

=(3 cmx4 cm) +(3cm×10 cm +4cm×10cm+5cm×10cm)

=\(12 cm^2 +30cm^2+40cm^2+50cm^2=132cm^2\)

Volume of prism = Area of base × height

=> V=( 1/2 ab) × height= 1/2 × 3 cm×4cm× 10 cm =\(60 cm^3\)

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Answer:

D

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

Use of formula:

According to above and based on given:

(a) | BD | bisects | AC | (reason : Given)

(b) |AD| ≅ |CD| (reason: |BD| is the perpendicular bisector of segment AC).

(c) ∠ABD ≅ ∠CBD (reason: | BD |  bisects angle ABC)

(d) ∠A ≅ ∠ C (reason: complementary angles of a right triangle)

Congruent angles are the angles that have equal measure. So all the angles that have equal measure will be called congruent angles.

From the first statement, we will complete the flow chart as follows;

line BD bisects line AC (reason : Given)

line AD is congruent to line CD (reason: line BD is the perpendicular bisector of segment AC)

Angle ABD is congruent to angle CBD (reason: line BD bisects angle ABC)

Angle A is congruent to angle C (reason: angle ABD = angle CBD, and both triangles ABD and CBD are right triangles).

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Answer:

Step-by-step explanation:

Total amount of money = cost of 13 manicures + tips for 13 manicures

        = 13x ( ∵ Given cost of 1 manicure = x) + 52 ( given she get 52 in tips)

= 13x + 52

Answer:

y = ±√100-x

Step-by-step explanation:

To work out the inverse of this function :

We solve for x then swap x and y :

Solving for x :

y = 100 - x²

Add x² to both sides :

x² + y = 100

Subtract y from both sides :

x² = 100-y

Square root both sides :

x = ±√100-y

Now we have solved for x. Now swap x and y :

y = ±√100-x

This is our final answer and is the first option.

Hope this helped and have a good day

Answer:

\( \sqrt{ {13.5}^{2} - {8.6}^{2} } = \sqrt{108.29} = 7 \sqrt{2.21} = \frac{7}{10} \sqrt{221} \)

V = (1/2)(8.6)(.7√221)(22.4) = 1,002.33 square meters

The closest answer is 1,001.73 square meters.

Answer:

1

Step-by-step explanation:

The maximum of f(x) = sin(x) is 1. The sine function has a range of -1 ≤ sin(x) ≤ 1. The sine function oscillates between -1 and 1, reaching a maximum of 1 when x = π/2 and a minimum of -1 when x = -π/2.  If you look at a graph of

y = sin(x) you can see this.  

Answer: The Maximum Value of f(x)=sin(x) is 1 , when x=90°.

Step-by-step explanation:

Property of Sine function:

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Answer:

26 and 27

Step-by-step explanation:

Let the numbers be x and y

x + y = 53

xy = 702

x = 702/y

702/y + y = 53

Multiply through by y

702 + y^2 = 53y

y^2 - 53y + 702 = 0

y^2 - 27y - 26y + 702 = 0

y(y - 27) - 26(y - 27) = 0

(y - 27) (y - 26) = 0

y = 26 or 27

Solve for x in x + y = 53

if y = 26,

x = 53 - 26 = 27

if y = 27,

x = 53 - 27 = 26

The numbers are 26 and 27

The formula for the centripetal force, as a function of the radius, is given as follows:

F = 896/r.

The equation that defines a direct proportional relationship is given as follows:

y = kx.

In which k is the constant of proportionality.

For an inverse proportional relationship, the equation is given as follows:

y = k/x.

The centripetal force varies inversely with the radius, hence the equation is given as follows:

F = k/r.

When F = 56, r = 16, hence the constant k is obtained as follows:

56 = k/16

k = 56 x 16

k = 896.

Hence the equation is given as follows:

F = 896/r.

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The equation for the total cost of all adult tickets (a) and student tickets (s).

4a + 2.5s = 2,820  

a + s = 900

The number of adults ticket and student tickets is 380 and 520.

We have,

Adults ticket cost = $4

Student ticket cost = $2.5

Now,

Total amount earned = $2,820

The equation for the total cost of all adult tickets (a) and student tickets (s).

4a + 2.5s = 2,820   ______(1)

And,

The number of tickets sold = 900.

We can write as equation as:

a + s = 900 ______(2)

Now,

We have two equations.

4a + 2.5s = 2820

a + s = 900

Solving for s.

s = 900 - a

Substituting in (1)

4a + 2.5(900 - a) = 2820

Simplifying and solving for a.

4a + 2250 - 2.5a = 2820

1.5a = 570

a = 380

Now,

a + s = 900

380 + s = 900

s = 520

Therefore,

The number of adults ticket and student tickets is 380 and 520.

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Answer:

\(P(z<\frac{a-\mu}{\sigma})=0.10\)

and we can set up the following equation

tex]z=-1.282<\frac{a-104.5}{23.62}\)

And if we solve for a we got

\(a=104.5 -1.282*23.62=74.22\)

And the best answer for this case would be:

b) $74.23

Step-by-step explanation:

Let X the random variable that represent the stocks price of a population, and for this case we know the distribution for X is given by:

\(X \sim N(104.5,23.62)\)  

Where \(\mu=104.5\) and \(\sigma=23.62\)

For this part we want to find a value a, such that we satisfy this condition:

\(P(X>a)=0.90\)   (a)

\(P(X<a)=0.10\)   (b)

As we can see on the figure attached the z value that satisfy the condition with 0.10 of the area on the left and 0.90 of the area on the right it's z=-1.282. On this case P(Z<-1.282)=0.10 and P(z>-1.282)=0.90

If we use condition (b) from previous we have this:

\(P(X<a)=P(\frac{X-\mu}{\sigma}<\frac{a-\mu}{\sigma})=0.10\)  

\(P(z<\frac{a-\mu}{\sigma})=0.10\)

and we can set up the following equation

tex]z=-1.282<\frac{a-104.5}{23.62}\)

And if we solve for a we got

\(a=104.5 -1.282*23.62=74.22\)

And the best answer for this case would be:

b) $74.23

Answer:

x = 1 (?)

i dont rlly know

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Answer:

count the number of places it is. The 5 in 458,039 is in the 10,000 place and the 5 in 271,145 is in the ones place so the 5 in 458,039 is 10,000 times greater

Complete Question

Suppose that the random variable X represents the length of a punched part in

centimeters. Let Y be the length of the part in millimeters. If E(X) = 5 and V(X) = 0.25,

what are the mean and variance of Y?

Answer:

The mean

\(E(Y) =50 mm\)

The variance

\(V(Y) = 25 mm\)

Step-by-step explanation:

From the question we are told that  

   Length in cm is  X

   Length in mm is Y

  Generally  10 mm  =  1 cm

So

    \(Y = 10 X\)

Hence the expected mean of Y is  

  \(E(Y) = E (10 X)\)

=>    \(E(Y) = 10 E(X)\)

From the question \(E(X) = 5\)

So

      \(E(Y) = 10 * 5\)

=> \(E(Y) =50 mm\)

Gnerally the variance of  X is  

      \(V(X) = E [X^2] -E[X]^2\)

From the question we are told that \(V(X) = 0.25\)

=> \(0.25 = E [X^2] -E[X]^2\)

Gnerally the variance of Y

    \(V(Y) = E [Y^2] -E[Y]^2\)

=> \(V(Y) = E [10X^2] -E[X]^2\)

=> \(V(Y) = 10^2[ E [X^2] -E[X]^2]\)

=> \(V(Y) = 10^2* V(X)\)

=> \(V(Y) = 10^2* 0.25\)

=> \(V(Y) = 25 mm\)

The given polynomial 81a² − 25z⁶ is not a difference of two squares because −25z⁶ is not a perfect square.

We can see that 81a² is a perfect square because it is equal to (9a)². However, 25z⁶ is not a perfect square because it can't be written as the square of a single term.

Therefore, we cannot factor 81a² − 25z⁶ into the difference of two squares.

\( \: \: \: \)

Answer:

7 + 6z

Step-by-step explanation:

3z + 3z = 6z, and that isolates the variable (z).