(b) The perimeter of a rectangular painting is 250 cm.

1. Last year a fishing license cost $52.00. This year the license will cost $46.80.

Talja [164]

Answer:

10%

Step-by-step explanation:

First, get the drop in value by deducting the price this year from last year's price.

Value decrease=$52.00-$46.80=$5.20

To express it as a percentage, we divide it by the original price which was $52.00 then multiply by 100 hence the percentage decrease will be

$\frac {5.20}{52.00}\times 100=10\ %$

Therefore, the price decreases by 10%

6 0

3 years ago

5x - 4y = 19 <br> x + 2y = 8

klemol [59]

Answer:

(5x-4y)=19

5×19-4×19

95-76

19

Step-by-step explanation:

x+2y=8

x=8-2

x=6

7 0

3 years ago

Each year, all final year students take a mathematics exam. It is hypothesised that the population mean score for this test is 1

Yuri [45]

Answer:

90% confidence interval for the population mean test score is [95.40 , 106.59]

Step-by-step explanation:

We are given that the population mean score for mathematics test is 115. It is known that the population standard deviation of test scores is 17.

Also, a random sample of 25 students take the exam. The mean score for this group is 101.

The, pivotal quantity for 90% confidence interval for the population mean test score is given by;

P.Q. = $\frac{Xbar-\mu}{\frac{\sigma}{\sqrt{n} } }$ ~ N(0,1)

where, X bar = sample mean = 101

$\sigma$ = population standard deviation

n = sample size = 25

So, 90% confidence interval for the population mean test score, $\mu$ is ;

P(-1.6449 < N(0,1) < 1.6449) = 0.90

P(-1.6449 < $\frac{Xbar-\mu}{\frac{\sigma}{\sqrt{n} } }$ < 1.6449) = 0.90

P(-1.6449 * $\frac{\sigma}{\sqrt{n} }$ < ${Xbar-\mu}$ < 1.6449 * $\frac{\sigma}{\sqrt{n} }$ ) = 0.90

P(X bar - 1.6449 * $\frac{\sigma}{\sqrt{n} }$ < $\mu$ < X bar + 1.6449 * $\frac{\sigma}{\sqrt{n} }$ ) = 0.90

90% confidence interval for $\mu$ = [ X bar - 1.6449 * $\frac{\sigma}{\sqrt{n} }$ , X bar + 1.6449 * $\frac{\sigma}{\sqrt{n} }$ ]

= [ 101 - 1.6449 * $\frac{17}{\sqrt{25} }$ , 10 + 1.6449 * $\frac{17}{\sqrt{25} }$ ]

= [95.40 , 106.59]

Therefore, 90% confidence interval for the population mean test score is [95.40 , 106.59] .

7 0

3 years ago

Fill in the blanks to complete the equation that describes the diagram.

Nimfa-mama [501]

Based on the picture I would say:
-4 + -2 = -6

8 0

3 years ago

Find constants a and b such that the function y = a sin(x) + b cos(x) satisfies the differential equation y'' + y' − 5y = sin(x)

vichka [17]

Answers:

a = -6/37

b = -1/37

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Explanation:

Let's start things off by computing the derivatives we'll need

$y = a\sin(x) + b\cos(x)\\\\y' = a\cos(x) - b\sin(x)\\\\y'' = -a\sin(x) - b\cos(x)\\\\$

Apply substitution to get

$y'' + y' - 5y = \sin(x)\\\\\left(-a\sin(x) - b\cos(x)\right) + \left(a\cos(x) - b\sin(x)\right) - 5\left(a\sin(x) + b\cos(x)\right) = \sin(x)\\\\-a\sin(x) - b\cos(x) + a\cos(x) - b\sin(x) - 5a\sin(x) - 5b\cos(x) = \sin(x)\\\\\left(-a\sin(x) - b\sin(x) - 5a\sin(x)\right) + \left(- b\cos(x) + a\cos(x) - 5b\cos(x)\right) = \sin(x)\\\\\left(-a - b - 5a\right)\sin(x) + \left(- b + a - 5b\right)\cos(x) = \sin(x)\\\\\left(-6a - b\right)\sin(x) + \left(a - 6b\right)\cos(x) = \sin(x)\\\\$

I've factored things in such a way that we have something in the form Msin(x) + Ncos(x), where M and N are coefficients based on the constants a,b.

The right hand side is simply sin(x). So we want that cos(x) term to go away. To do so, we need the coefficient (a-6b) in front of that cosine to be zero

a-6b = 0

a = 6b

At the same time, we want the (-6a-b)sin(x) term to have its coefficient be 1. That way we simplify the left hand side to sin(x)

-6a -b = 1

-6(6b) - b = 1 .... plug in a = 6b

-36b - b = 1

-37b = 1

b = -1/37

Use this to find 'a'

a = 6b

a = 6(-1/37)

a = -6/37

8 0

2 years ago