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3 years ago

Simify

Mathematics

1 answer:

Harlamova29_29 [7]3 years ago

4 0

Step-by-step explanation:

1. -9x - 3 - 3 + 2x

-7x - 6

3. 3 - 4x - 7x - 2

-11x - 1

4. 5x - 1 + 3 + 2x

7x + 2

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The waiting times at a certain bank are normally distributed with a mean waiting time of 3.7 minutes and a standard deviation of

muminat

Answer:

From the given options we can say the correct answer is d.) 6.3

Step-by-step explanation:

The waiting times at the bank are given to be normally distributed.

The mean of the waiting time is given as = 3.7 minutes

The given standard deviation is = 1.4 minutes

It is required to find the waiting time at the 97th percentile.

So we are required to find the time which can be said to be the waiting time which occurs with 97 % probability.

Let the time required be designated as y.

Therefore we can write p(X < y) = 0.97 (where 0.97 means the 97th percentile)

This is a left tailed test.

Using the formula from MSEXCEL to find y we get

y = NORMINV(0.97, 3.7, 1.4) = 6.333.

The other approach would to find the Z value corresponding to the probability value from the Z Table

The Z value for a probability of 0.97 gives us Z = 1.881 .

Therefore $\frac{y - 3.7}{1.4} = 1.881$ . Therefore y = (1.881 × 1.4) + 3.7 = 6.33

Therefore from the given options we can say the correct answer is d.) 6.3

7 0

3 years ago

Does anyone know what the measure of angle 1 would be?

svlad2 [7]

Answer:

Angle 1 = 119 degrees.

Step-by-step explanation:

3x + 31 = 6x + 1 (exterior alternate angles)

30 = 3x

x = 10

So the angle marked 6x + 1 = 6(10)+1

= 61

Angle 1 is adjacent to this so it is 180-61 = 119 degrees.

3 0

4 years ago

A water tank has a diameter of 15 ft and is 22 ft high. a. What is the volume of the tank in ft?? b. In m?? c. In cm?

rodikova [14]

Answer:

a) $V = 3887.72 ft^{3}$

b) $V = 104.97 m^{3}$

c) $V = 104,968,468.538 cm^{3}$

Step-by-step explanation:

A tank has the format of a cylinder.

The volume of the cylinder is given by:

$V = \pi r^{2}h$

In which r is the radius and h is the heigth.

The problem states that the diameter is measured to be 15.00 ft. The radius is half the diameter. So, for this tank

$r = \frac{15}{2} = 7.50$ ft

The height of the tank is 22 ft, so $h = 22$ .

a) Volume of the tank in $ft^{3}$ :

$V = \pi r^{2}h$

$V = pi*(7.5)^2*22$

$V = 3887.72 ft^{3}$

b) Volume of the tank in $m^{3}$ :

We must convert both the radius and the height to m.

Each feet has 0.30 m, so:

Radius:

1 feet - 0.30m

7.5 feet - r m

$r = 7.5*0.30$

$r = 2.25m$

Height

1 feet - 0.30m

22f - h m

$h = 22*0.30$

$r = 6.60m$

The volume is:

$V = \pi r^{2}h$

$V = pi*(2.25)^2*6.60$

$V = 104.97 m^{3}$

c) Volume of the tank in $cm^{3}$ :

Each m has 100 cm.

So $r = 2.25m = 225cm$

$h = 6.60m = 660cm$

The volume is:

$V = \pi r^{2}h$

$V = pi*(225)^2*660$

$V = 104,968,468.538 cm^{3}$

7 0

4 years ago

The slope of the graph of the equation y=2x-2 is 2 what is the y intercept

Natali5045456 [20]

Answer:

-2

Step-by-step explanation:

the equation is y=2x-2 and the constant is the y-intercept

8 0

3 years ago

7-18 use part 1 of the fundamental theorem of calculus to find the derivative of the function.

blondinia [14]

$\displaystyle h(x)=\int\limits_{1}^{\sqrt{x}}~\cfrac{z^2}{z^4+1}dz~\hspace{10em}\cfrac{dh}{du}\cdot \stackrel{chain~rule}{\cfrac{du}{dx}\implies \cfrac{dh}{dx}} \\\\[-0.35em] ~\dotfill\\\\ u=\sqrt{x}\implies \cfrac{du}{dx}=\cfrac{1}{2\sqrt{x}} \\\\[-0.35em] ~\dotfill$

$\cfrac{dh}{dx}\implies \displaystyle \cfrac{d}{du}\left[ \int\limits_{1}^{u}~\cfrac{z^2}{z^4+1}dz \right]\cdot \cfrac{1}{2\sqrt{x}}\implies \left[ \cfrac{u^2}{u^4+1} \right]\cdot \cfrac{1}{2\sqrt{x}} \\\\\\ \stackrel{substituting~back}{\left[ \cfrac{(\sqrt{x})^2}{(\sqrt{x})^4+1} \right]\cdot \cfrac{1}{2\sqrt{x}}}\implies \cfrac{x}{x^2+1}\cdot \cfrac{1}{2\sqrt{x}}\implies \cfrac{\sqrt{x}}{2x^2+2}$

7 0

2 years ago