A property tax rate of 16.3 mills is equal to

Most cars get their best gas mileage when traveling at a relatively slow speed. The gas mileage M for a certain new car is model

NeTakaya

In this item, it is assumed that we are to determine the speed at which the car will have the best gas mileage. This can be done by deriving the equation and equating it to zero.

M(s) = -1/28s² + 3s - 31

Deriving,
dM(s) = (-1/28)(2s) + 3 = 0

s = 42

Hence, the speed at which the best mileage is achieved is mi/h.

5 0

1 year ago

What's the hinge theorem and it's converse?

Elena L [17]

The converse of the hinge theorem is also true: If the two sides of one triangle are congruent<span> to two sides of another triangle, and the third side of the first triangle is greater than the third side of the second triangle, then the included angle of the first triangle is larger than the included angle of the second .</span>

7 0

2 years ago

A water tank leaks 5 gallons of water each day. What integer represents the change in the number of gallons of water in the tank

andrey2020 [161]

Answer:

35 is the integer that represents the change in number of gallons of water in the tank after 7 days

Step-by-step explanation:

The water tank leaks 5 gallons in one day.

So if there is leakage of 5 gallons a day, then after 7 days the total leakage will be:

Total Leakage = Leakage per day * Total number of days

= 5 Gal/day * 7 day

= 35 Gallons

So, 35 is the integer that represents the change in number of gallons of water in the tank after 7 days ..

5 0

2 years ago

Body armor provides critical protection for law enforcement personnel, but it does affect balance and mobility. The article "Imp

yKpoI14uk [10]

Answer:

No, there is not enough evidence to support the claim that true average task time with armor is less than 2 seconds.

Step-by-step explanation:

This is a hypothesis test for the population mean.

The claim is that true average task time with armor is less than 2 seconds.

Then, the null and alternative hypothesis are:

$H_0: \mu=2\\\\H_a:\mu< 2$

The significance level is 0.01.

The sample has a size n=52.

The sample mean is M=1.95.

As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=0.2.

The estimated standard error of the mean is computed using the formula:

$s_M=\dfrac{s}{\sqrt{n}}=\dfrac{0.2}{\sqrt{52}}=0.028$

Then, we can calculate the t-statistic as:

$t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{1.95-2}{0.028}=\dfrac{-0.05}{0.028}=-1.803$

The degrees of freedom for this sample size are:

$df=n-1=52-1=51$

This test is a left-tailed test, with 51 degrees of freedom and t=-1.803, so the P-value for this test is calculated as (using a t-table):

$P-value=P(t$

As the P-value (0.039) is bigger than the significance level (0.01), the effect is not significant.

The null hypothesis failed to be rejected.

There is not enough evidence to support the claim that true average task time with armor is less than 2 seconds.

3 0

1 year ago

Page:<br>If A+B+C=180 , then prove that:cosA+cosB+cosC= 1+4SINA/2SINB/2SINC/2

lakkis [162]

Answer:

A + B + C = π ...... (1)

...........................................................................................................

L.H.S.

= ( cos A + cos B ) + cos C

= { 2 · cos[ ( A+B) / 2 ] · cos [ ( A-B) / 2 ] } + cos C

= { 2 · cos [ (π/2) - (C/2) ] · cos [ (A-B) / 2 ] } + cos C

= { 2 · sin( C/2 ) · cos [ (A-B) / 2 ] } + { 1 - 2 · sin² ( C/2 ) }

= 1 + 2 sin ( C/2 )· { cos [ (A -B) / 2 ] - sin ( C/2 ) }

= 1 + 2 sin ( C/2 )· { cos [ (A-B) / 2 ] - sin [ (π/2) - ( (A+B)/2 ) ] }

= 1 + 2 sin ( C/2 )· { cos [ (A-B) / 2 ] - cos [ (A+B)/ 2 ] }

= 1 + 2 sin ( C/2 )· 2 sin ( A/2 )· sin( B/2 ) ... ... ... (2)

= 1 + 4 sin(A/2) sin(B/2) sin(C/2)

= R.H.S. ............................. Q.E.D.

...........................................................................................................

In step (2), we used the Factorization formula

cos x - cos y = 2 sin [ (x+y)/2 ] · sin [ (y-x)/2 ]

Step-by-step explanation:

6 0

1 year ago