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KATRIN_1 [288]
3 years ago
9

Heather drew the scaled drawing of a train car shown below. She used the scale of 2 cm = 5 ft to complete the

Mathematics
1 answer:
lora16 [44]3 years ago
3 0

Answer: c

Step-by-step explanation:

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Pleasee help ASAP!! No links pleaseee!!!
Ilya [14]

Given:

The vertices of the rectangle ABCD are A(0,1), B(2,4), C(6,0), D(4,-3).

To find:

The area of the rectangle.

Solution:

Distance formula:

D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

Using the distance formula, we get

AB=\sqrt{(2-0)^2+(4-1)^2}

AB=\sqrt{(2)^2+(3)^2}

AB=\sqrt{4+9}

AB=\sqrt{13}

Similarly,

BC=\sqrt{(6-2)^2+(0-4)^2}

BC=\sqrt{(4)^2+(-4)^2}

BC=\sqrt{16+16}

BC=\sqrt{32}

BC=4\sqrt{2}

Now, the length of the rectangle is AB=\sqrt{13} and the width of the rectangle is BC=4\sqrt{2}. So, the area of the rectangle is:

A=length \times width

A=\sqrt{13}\times 4\sqrt{2}

A=4\sqrt{26}

A\approx 20

Therefore, the area of the rectangle is 20 square units.

3 0
3 years ago
There are 96 female staff in an office. If the ratio of male staff to female staff is 3:4, find the number of male staff​.
Alex

Answer:60 male staff

Step-by-step explanation:

Ok, there are 96 female staff. The ratio of male to female is 3:4. We’re going to use a proportion which looks like this. 3/4 = x/96. X is a variable that takes the place of the male staff since we don’t know what it is. Now, the question is what do we do to get from 4 to 96. So 96/4 = 24, so 4 x 20 = 96. To keep this ratio equivalent whatever you do to the top you have to do to the bottom so 4 x 20 = 96 and 3 x 20 = 60. So there are 60 male staff.

4 0
3 years ago
Find an equation equivalent to r = 10sin ø in rectangular coordinates.
kherson [118]

Answer: x^2 + y^2 -10y = 0

Step-by-step explanation:

Cartesian coordinates, also called the Rectangular coordinates, isdefined in terms of x and y. So, for the problem θ has to be eliminated or converted using basic foundations that are described by the unit circle and the right triangle trigonometry.

r= 10sin(θ)

Remember that:

x= r × cos(θ)

y= r × sin(θ)

r^2= x^2 + y^2

Multiply both sides of the equation by r. This will give:

r × r = 10r × sin(θ)

r^2 = 10r × sin(θ)

x^2 + y^2= 10r × sin(θ)

Because y= r × sin(θ), we can make a substitution. This will be:

x^2 + y^2= 10y

x^2 + y^2 -10y = 0

The above equation is the Rectangular coordinate equivalent to the given equation.

4 0
3 years ago
The scores on an achievement test are normaly distributed with mean µ = 100 and standard deviation σ = 100. What should the scor
ser-zykov [4K]

Answer:

the student should score atleast 229 to be among the top 10%.

Step-by-step explanation:

in terms of the normal distribution, and if the table that you're using calculates the area of the normal distribution from the mean to a point x, only then what we are actually finding the value 'x' at which the z-score is at 40% (the rest 50% is already skipped by the table)

P(0.4) = \dfrac{x - \mu}{\sigma}

after finding the the value at this z-score, we can find the value of x at which the score is in the top 10% range.

we can find the z-score either using a normal distribution table or calculator. (but be sure what area is it calculating)

looking at the table the closest value we can find is, 0.4015 at z = 1.29 ((it is above 40% because we want to be in the top 10% range)

P(0.4015) = \dfrac{x - 100}{100}

1.29 = \dfrac{x - 100}{100}

x = 1.29(100) + 100

x = 229

the student should score atleast 229 to be among the top 10%.

7 0
3 years ago
Solve the given initial-value problem. x^2y'' + xy' + y = 0, y(1) = 1, y'(1) = 8
Kitty [74]
Substitute z=\ln x, so that

\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{\mathrm dy}{\mathrm dz}\cdot\dfrac{\mathrm dz}{\mathrm dx}=\dfrac1x\dfrac{\mathrm dy}{\mathrm dz}

\dfrac{\mathrm d^2y}{\mathrm dx^2}=\dfrac{\mathrm d}{\mathrm dx}\left[\dfrac1x\dfrac{\mathrm dy}{\mathrm dz}\right]=-\dfrac1{x^2}\dfrac{\mathrm dy}{\mathrm dz}+\dfrac1x\left(\dfrac1x\dfrac{\mathrm d^2y}{\mathrm dz^2}\right)=\dfrac1{x^2}\left(\dfrac{\mathrm d^2y}{\mathrm dz^2}-\dfrac{\mathrm dy}{\mathrm dz}\right)

Then the ODE becomes


x^2\dfrac{\mathrm d^2y}{\mathrm dx^2}+x\dfrac{\mathrm dy}{\mathrm dx}+y=0\implies\left(\dfrac{\mathrm d^2y}{\mathrm dz^2}-\dfrac{\mathrm dy}{\mathrm dz}\right)+\dfrac{\mathrm dy}{\mathrm dz}+y=0
\implies\dfrac{\mathrm d^2y}{\mathrm dz^2}+y=0

which has the characteristic equation r^2+1=0 with roots at r=\pm i. This means the characteristic solution for y(z) is

y_C(z)=C_1\cos z+C_2\sin z

and in terms of y(x), this is

y_C(x)=C_1\cos(\ln x)+C_2\sin(\ln x)

From the given initial conditions, we find

y(1)=1\implies 1=C_1\cos0+C_2\sin0\implies C_1=1
y'(1)=8\implies 8=-C_1\dfrac{\sin0}1+C_2\dfrac{\cos0}1\implies C_2=8

so the particular solution to the IVP is

y(x)=\cos(\ln x)+8\sin(\ln x)
4 0
3 years ago
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