Bakery rolls are being prepared to go to grocery stores. Divide 72 rolls into 2 groups so the ratio is 3 to 5.

The equation h = -16t 2+ 53x + 8 gives the height h, in feet, of a football as a function of time t, in seconds, after it is kic

Elanso [62]

Answer: The maximum height the football reaches = 51.89 feet.

Step-by-step explanation:

Given: The equation $h = -16t^2+ 53t + 8$ gives the height h, in feet, of a football as a function of time t, in seconds, after it is kicked.

Differentiate the given equation, we get

$h'=-(2)16t+53=-32t+53$ (i)

Put $h'=0$

$\Rightarrow\ -32t+53=0\\\\\Rightarrow\ t=\dfrac{53}{32}\approx1.65625$

Differentiate (i) w.r.t. t, we get

$h''=-32$ < 0 i.e. h is maximum at t= 1.65625

The value of h at t= 1.65625 will be $-16(1.65625)^2+53(1.65625)+8=51.890625\approx51.89\text{ feet}$

Hence, the maximum height the football reaches = 51.89 feet.

8 0

3 years ago

On average, Nancy has noticed that 20 trucks pass by her apartment daily (24 hours). In order to find the probability that more

sukhopar [10]

Answer: Our required probability is 0.384.

Step-by-step explanation:

Since we have given that

In 24 hours,

λ = 20

In 6 hours,

$\lambda=\dfrac{20}{24}\times 6=\dfrac{20}{4}=5$

As we know that it is a Poisson distribution.

E[X] = λ = 5

Probability that more than 6 trucks will pass her apartment is given by

$P(X>6)=\sum_{x=6}^{20}\dfrac{e^{-5}\times 5^x}{x!}=0.384$

Hence, our required probability is 0.384.

4 0

3 years ago

Karen notices that segment BC and segment EF are congruent in the image below:

LenaWriter [7]

Answer:

Givens:

$A(-2;2) \ B(-2;4) \ C(0;3) \ D(2;1) \ E(2;3) \ F(0;2)$
$BC \cong EF$
$\angle C \cong \angle F$

Using this information we could recur to SAS postulate to demonstrate the congruence of this pair of triangles. We already have one side and one angle congruent, we just need to demonstrate that $AC \cong DF$ , that will prove the complete congruence.

So, based on the given coordinates, we're able to calculate the length of each side and find if they are the same. We use this formula:

$d=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}\\d_{AC} =\sqrt{(0-(-2))^{2}+(3-2)^{2}}=\sqrt{4+1}=\sqrt{5}\\\\\d_{DF} =\sqrt{(0-2)^{2}+(2-1)^{2}}=\sqrt{4+1}=\sqrt{5}$

Therefore, $AC \cong DF$ , because they have the same length.

Now, based on these congruences:

$BC \cong EF$
$\angle C \cong \angle F$
$AC \cong DF$

We demonstrate by the Side-Angle-Side (SAS) postulate that ΔABC ≅ ΔDEF.

6 0

3 years ago

Let f(x) = x² + 3x<br> What is f(-1) ?<br><br> Need help ASAP !!!!

Karo-lina-s [1.5K]

Answer:

-2

Step-by-step explanation:

f(x) = x² +3x

so f(-1) means f(x= -1) so wherever you see a "x" in your equation you put a "-1"

f(-1) = (-1)² +3*(-1) = 1 -3 = -2

8 0

2 years ago

An animal is randomly selected from a group consisting of 5 cats, 11 dogs, and 14 rabbits. Find the probability of the outcome.

ohaa [14]

1. There are 30 animals, so the probability of picking a cat is 5/30, or 1/6. (o.16)
The probability of picking a dog is 11/30 or (0.36)
The probability of picking a rabbit is 14/30 or 7/15 (0.46)

2. The probability of picking a number less than 12 is 11/44, or 1/4 (0.25)

5 0

3 years ago