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3 years ago

The perimter of a rectangle is 90 centimeters.the length is 27 centimeters what is the width of the rectangle

Mathematics

1 answer:

Sati [7]3 years ago

3 0

Answer:

18 cm

Step-by-step explanation:

The perimeter of a rectangle is given by the formula ...

P = 2(L +W)

Fill in the given information and solve for the width.

90 = 2(27 +W)

45 = 27 +W . . . . . divide by 2

18 = W . . . . . . . . . subtract 27

The width of the rectangle is 18 cm.

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You tell your 3 friends that you are going to a magic show. It turns out, in an amazing coincidence, they each

Inga [223]

Answer:

$\frac{1}{4845}$ probability that you and your 3 friends will be selected.

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

In this question, the order in which the volunteers are chosen is not important, which means that the combinations formula is used to solve this question.

Combinations formula:

$C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

Desired outcomes:

You and the 3 friends(4 people), from a set of 4. So

$D = C_{4,4} = \frac{4!}{4!0!} = 1$

Total outcomes:

20 people from a set of 20. So

$T = C_{20,4} = \frac{20!}{4!16!} = 4845$

Probability:

$p = \frac{D}{T} = \frac{1}{4845}$

$\frac{1}{4845}$ probability that you and your 3 friends will be selected.

8 0

3 years ago

The game commission observes the fish population in a stream and notices that the number of trout increases by a factor of 1.5 e

just olya [345]

Answer:

A - $f(t)=80(1.5)^t$

B - Graph given below

C - Number of trouts in 5th week are 607.2

D - Population of trouts will exceed 500 on the 5th week.

Step-by-step explanation:

We are given that,

The number of trout increases by a factor of 1.5 each week and the initial population of the trout is observed to be 80.

Part A: So, the explicit formula representing the situation is,

$f(t)=80(1.5)^t$ , where f(t) represents the population of trouts after 't' weeks.

Part B: The graph of the function can be seen below.

It can be seen that the function is an exponential function.

Part C: It is required to find the number of trouts in the 5th week.

So, we have,

$f(5)=80(1.5)^5$

i.e. $f(5)=80\times 7.59$

i.e. f(5) = 607.2

Thus, the number of trouts in 5th week are 607.2

Part D: We are given that the trout population exceeds 500.

It is required to find the week in which this happens.

So, we have,

$50$

i.e. $(1.5)^t>\frac{500}{80}$

i.e. $(1.5)^t>6.25$

i.e. $t\log 1.5>\log 6.25$

i.e. $t\times 0.1761>0.7959$

i.e. $t>\frac{0.7959}{0.1761}$

i.e. t > 4.5

As, t represents the number of weeks. So, to nearest whole, t = 5.

Thus, the population of trouts will exceed 500 on the 5th week.

7 0

3 years ago

The Colvilles are buying a new car. The cash price is $35,000.00. They will make a down payment of 20% or $5,000. The balance wi

Varvara68 [4.7K]

9514 1404 393

Answer:

2.01% for a down payment of $5000

5.49% for a down payment of 20%

Step-by-step explanation:

There is no formula for the APR of a loan, given its other parameters. The value must be found using iterative or graphical means. The attached shows a graphical solution for each of the two cases for a 4-year loan.

For 20% down payment, APR ≈ 5.49%

For $5,000 down payment, APR ≈ 2.01%

4 0

3 years ago

Read 2 more answers

The average weight of a package of rolled oats is supposed to be at least 18 ounces. A sample of 18 packages shows a mean of 17.

Rom4ik [11]

Answer:

Step-by-step explanation:

The average weight of a package of rolled oats is supposed to be at least 18 ounces

Null hypothesis: u >= 18

Alternative: u < 18

Using the t-test formula, we have

t = x-u/ (sd/√n)

Where x is 17.78, u = 18, sd = 0.41 and n = 18

t = 17.78-18 / (0.41/√18)

t = -0.22 / (0.41/4.2426)

t = -0.22/ 0.0966

t = -2.277

Since, this is a left tailed test, at a significance level of 0.05, the p value is 0.01139. Since the p value is less than 0.05, we will reject the null hypothesis and conclusion that the true mean smaller than the actual specification.

6 0

3 years ago

Find the vertex of the parabola whose equation is y = -2x2 + 8x - 5.

VladimirAG [237]

The vertex is the point where the graph is horizontal, which you can find by setting the first derivative to zero.

derivative: -4x + 8 = 0 => x=2
fill it in in the equation:

y=-2*2² + 8*2 - 5 = 3

So the answer is the point (2,3)

8 0

4 years ago

Read 2 more answers