Out of 138 seventh graders, 86 voted math was their favorite subject. What percent is this?

A new gas- and electric-powered hybrid car has recently hit the market. The distance traveled on 1 gallon of fuel is normally di

Doss [256]

Answer:

a) P [ Z > 70 ] = 0.1075 or 10.75 %

b) P [ Z < 60 ] = 0.1038 or 10.38 %

c) P [ 55 ≤ Z ≤ 70 ] = 0.8882 or 88.82 %

Step-by-step explanation:

Normal Distribution μ = 65 and σ = 4

a) The probability of the car travels more than 70 miles per gallon is:

P [ Z > 70 ] = (Z-μ) ÷ σ ⇒ P [ Z > 70 ] = (70-65) ÷4 P [ Z > 70 ] = 1.25

the point 1.25 corresponds at values, from left tail up to 70 so we must go and look for the area for the point 1.24 which is 0.8925. Then we have the area or probability of all cars traveling up to 70 miles therefore we have to subtract 1 -0,8925

P [ Z > 70 ] = 0.1075 or 10.75 %

b)The probability of the car travels less than 60 miles per gallon is:

P [ Z < 60 ] = ( 60 - μ ) ÷ σ ⇒ P [ Z < 60 ] = (60-65)÷ 4 P [ Z < 60 ] = -1.25

Again -1.25 corresponds to 60 miles per gallon threfore we move to the left and find for point -1.26 which area is 0.1038 so

P [ Z < 60 ] = 0.1038 10.38 %

c) P [ 55 ≤ Z ≤ 70]

For point Z = 70 or 1.25 (case a above) P [ Z ≤ 70] = (70-65)÷4

P [ Z ≤ 70] = 1.25

In this case we got the whole area from the left tail up to 1.25

P [ Z ≤ 70] = 0.8944 (includes the area of the point from the left tail up to the point assocciated to 55 miles and for that reason we have to subtract that area)

P [ Z ≥ 55 ] = (55-65) ÷ 4 P [ Z ≥ 55 ] = -2.5 and the area is 0.0062

So P [ 55 ≤ Z ≤ 70 ] = 0.8944 - 0.0062 = 0.8882

8 0

3 years ago

Please help!!!!!!!!!!! ASAPPPPPPPPP

Zanzabum

When you match the pattern of (x+y)⁴ to (a+b)ⁿ, you see that a=x, n=4. Then the first term aⁿ can be found by substituting these values for "a" and "n":

... x⁴

7 0

3 years ago

The position of an object moving horizontally after t seconds is given by the function s equals 3 t minus t cubed, for t greate

Anton [14]

Answer:

Step-by-step explanation:

The position of an object moving horizontally after t seconds is given by the function

s = 3t - t³

a) The object is stationary when there is no external force acting on the body. When the body is at rest, the body remains in a position and here is no distance covered by the object i.e s = 0

b) velocity is the change in displacement of a body with respect to time.

v = ds/dt

S = 3t - t³

V = ds/dt = 3-3t²

at t = 2

Velocity = 3-3(2)²

Velocity = 3-12

Velocity = -9m/s

c) acceleration is the change in velocity of a body with respect to time.

acceleration = dv/dt

If v = 3-3t²

a = dv/dt = -6t

When v = 0

0 = 3-3t²

-3 = -3t²

t² = 1

t = ±√1

t = 1sec

The acceleration of the object at v = 0 occurs at t = 1sec and -1sec

a = -6(1)

a = -6m/s²

d) Given the speed of the body v modelled by the function

v = 3-3t²

The speed is decreasing when it is less than zero as shown:

3-3t²< 0

3<3t²

1<t²

±1<t

1<t and -1<t

t>±1

t >1 and t>-1

The speed is decreasing when

3-3t²<0 and t>1 or t>-1

6 0

3 years ago

Is the equation x9 - 5x3 + 6 = 0 quadratic in form? explain why or why not.

Varvara68 [4.7K]

Answer:

Yes.

Step-by-step explanation:

Yes, because we can replace x^3 by another variable, say y:

x^9 - 5x^3 + 6 = 0

Let x^3 = y, then we have x^9 = (x^3)^2 = y^2:

y^2 - 5y + 6 = 0 which is quadratic from.

6 0

3 years ago

Read 2 more answers

You are considering buying a 30-year U.S. Treasury bond but are nervous about the effect on bond price if the yield to maturity

Savatey [412]

Answer:

The corresponding change in bond price = 17.1%

Step-by-step explanation:

In this question, we are interested in calculating the percentage change in the bond price using the approximation method based on bond duration;

Mathematically;

% change in bond price = Duration * Change in yield

From the question;

Duration = 19 years

Change in yield = 0.9%

Thus;

% change in bond price = 19 * 0.9% = 17.1%

7 0

2 years ago