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3 years ago

How does h

Mathematics

1 answer:

Agata [3.3K]3 years ago

4 0

Answer:

h(t) = 16t changes 16 units every t. in the interval t=7 to t=2,

if its asking for:

$\int\limits^2_7 {16t} \, dt$

then it's

16(2) - 16(7) = 32 - 112 = -80

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lianna [129]

Answer:

1) The slope of the line is $m=\frac{5}{2}$ or $m=2.5$

2) The equation of the line is $y=2.5x-4$

Step-by-step explanation:

step 1

Find the slope

we know that

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

take any two points from the values in the table

(2,1) and (4,6)

substitute the values in the formula

$m=\frac{6-1}{4-2}$

$m=\frac{5}{2}$

$m=2.5$

step 2

Find the equation of the line in point slope form

$y-y1=m(x-x1)$

we have

$m=2.5$

$point\ (2,1)$

substitute

$y-1=2.5(x-2)$

Convert to slope intercept form

isolate the variable y

$y-1=2.5x-5$

$y=2.5x-5+1$

$y=2.5x-4$

7 0

2 years ago

We have two coins, A and B. For each toss of coin A, we obtain Heads with probability 1/2 ; for each toss of coin B, we obtain H

ycow [4]

Answer:

The expected value is 5.

Step-by-step explanation:

Let X represent the number of tosses until the event described in the question happens.
Let Y represent the number of tosses with coin A until Heads is obtained.

Let Z represent the number of tosses with coin B until Heads is obtained.

As we can see, X=Y+Z. Then, by the linearity of the expected value operator, we have that

$E(X)=E(Y)+E(Z).$

We will compute E(Y) and E(Z).

Observe that Y and Z have countable sets of outcomes (1,2,3,....) then,

$E(X)=\sum^\infty_{n=1}nP(Y=n)$ ,

$E(Z)=\sum^\infty_{n=1}nP(Z=n)$ ,

Then:

for each $n\in \mathbb{N}$ , the probability of Y=n is given by $(0.5)^{n-1}(0.5)=(0.5)^{n}$ (because the first n-1 tosses must be Tails and the n-th must be Heads). Therefore

$E(Y)=\sum^\infty_{n=1}nP(Y=n)=\sum^\infty_{n=1}n(\frac{1}{2} )^n=\\\\\sum^\infty_{m=1}\sum^\infty_{n=m}(\frac{1}{2} )^n=\sum^\infty_{m=1}(\frac{1}{2} )^{m-1}=\sum^\infty_{m=0}(\frac{1}{2} )^{m}=2.$

For each $n\in \mathbb{N}$ , the probability of Z=n is given by $(\frac {2}{3})^{n-1}(\frac {1}{3})$ (because the first n-1 tosses must be Tails and the n-th must be Heads). Therefore

$E(Z)=\sum^\infty_{n=1}nP(Z=n)=\frac{1}{3}\sum^\infty_{n=1}n(\frac{2}{3} )^{n-1}=\frac{1}{3}\sum^\infty_{m=1}\sum^\infty_{n=m}(\frac{2}{3} )^{n-1}$

Observe that, by the <u>geometric series formula</u>:

$\sum^\infty_{n=m}(\frac{2}{3} )^{n-1}=\sum^\infty_{n=1}(\frac{2}{3} )^{n-1}-\sum^{m-1}_{n=1}(\frac{2}{3} )^{n-1}=3-\sum^{m-1}_{n=1}(\frac{2}{3} )^{n-1}=\\\\3-\sum^{m-2}_{n=0}(\frac{2}{3} )^{n}=3-\frac{1-(\frac{2}{3})^{m-1} }{1-\frac{2}{3}}=3(\frac{2}{3})^{m-1}$

Therefore

$E(Z)=\frac{1}{3}\sum^\infty_{m=1}\sum^\infty_{n=m}(\frac{2}{3} )^{n-1}=\frac{1}{3}\sum^\infty_{m=1}3(\frac{2}{3})^{m-1} =\\\\ \sum^\infty_{m=1}(\frac{2}{3})^{m-1} = \sum^\infty_{m=0}(\frac{2}{3})^{m} =3.$

Finally, E(X)=E(Y)+E(Z)=2+3=5.

4 0

2 years ago

Given the following rectangle and circle, what appropriate value of x are the two areas equal? A: x= 3.4 B: x=5.8 C: x= 10.2 D:

Yuki888 [10]

The correct option is D:

the curves do not intersect, so there is no solution

<h3>For what values of x are the two areas equal?</h3>

The area of the rectangle is given by:

f(x) = (x + 7)*(5x - 3)

f(x) = 5x² -3x + 35x - 21

f(x) = 5x² + 32x - 21

For the circle, the area is:

g(x) = 2*pi*(x + 6)^2

g(x) = 2pi*x^2 + 12pi*x + 72pi

The solution is given g(x) = f(x).

By graphing both functions (the green curve is the area of the rectangle, the orange one is the area of the circle). The two curves never do intercept, so the correct option is D.

If you want to learn more about areas:

brainly.com/question/24487155

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5 0

2 years ago

The circle graph below shows the colors of flowers in a garden

Kruka [31]

Purple and white make up less than 30 %

5 0

2 years ago

Read 2 more answers

The Two sets A and B are said to be disjoint sets if A n B=_____

asambeis [7]

The Two sets, A and B, are said to be disjoint sets if A n B=ϕ

<h3>What does it mean for two sets to be disjoint?</h3>

Disjoint sets are a pair of sets that do not share any elements. For instance, sets A=2,3 and B=4,5 are not connected sets.
When two sets don't share elements, they are considered disjoint sets. In other words, the null set will result if we find the intersection of two sets. The process is straightforward; two sets are given in this procedure.
When using a disjoint set union, it is possible to add new sets, combine existing sets, and check whether two sets of elements are the same in almost real-time.

The Two sets, A and B, are said to be disjoint sets if A n B=ϕ

To learn more about two sets to be disjoint, refer to:

brainly.com/question/13100777

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4 0

1 year ago