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2 years ago

How do I rename the number 5 hundreds 8 tens

Mathematics

2 answers:

Phantasy [73]2 years ago

7 0

5 hundred is 500

8 tens is 80

So 5 hundred 8 tens is 580

scZoUnD [109]2 years ago

6 0

So 5 hundred 8 tens is 580

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Please help me with the below question.

Snezhnost [94]

6a. By the convolution theorem,

$L\{t^3\star e^{5t}\} = L\{t^3\} \times L\{e^{5t}\} = \dfrac6{s^4} \times \dfrac1{s-5} = \boxed{\dfrac5{s^4(s-5)}}$

6b. Similarly,

$L\{e^{3t}\star \cos(t)\} = L\{e^{3t}\} \times L\{\cos(t)\} = \dfrac1{s-3} \times \dfrac s{1+s^2} = \boxed{\dfrac s{(s-3)(s^2+1)}}$

7. Take the Laplace transform of both sides, noting that the integral is the convolution of $e^t$ and $f(t)$ .

$\displaystyle f(t) = 3 - 4 \int_0^t e^\tau f(t - \tau) \, d\tau$

$\implies \displaystyle F(s) = \dfrac3s - 4 F(s) G(s)$

where $g(t) = e^t$ . Then $G(s) = \frac1{s-1}$ , and

$F(s) = \dfrac3s - \dfrac4{s-1} F(s) \implies F(s) = \dfrac{\frac3s}{\frac{s+3}{s-1}} = 3\dfrac{s-1}{s(s+3)}$

We have the partial fraction decomposition,

$\dfrac{s-1}{s(s+3)} = \dfrac13 \left(-\dfrac1s + \dfrac4{s+3}\right)$

Then we can easily compute the inverse transform to solve for f(t) :

$F(s) = -\dfrac1s + \dfrac4{s+3}$

$\implies \boxed{f(t) = -1 + 4e^{-3t}}$

6 0

1 year ago

The equation for the circle below is x^2+y^2=4. what is the length of the circle’s radius

Inessa05 [86]

2 because in the equation of a circle it is x^2 + y^2 = r^2, r=radius so you would take the square root of 4, leaving the radius of the circle to be 2.

6 0

3 years ago

Which expression has a value greater than 43 ? PLEASEEE HELP!

lozanna [386]

Answer:

7^2

Step-by-step explanation:

7*7=49

4^3=43

49>43

8 0

2 years ago

HELP!!! URGENT!!! I WILL GIVE BRAINLEIST THING

lisov135 [29]

Answer:

Horizontal distance = 0 m and 6 m

Step-by-step explanation:

Height of a rider in a roller coaster has been defined by the equation,

y = $\frac{1}{3}x^{2}-2x+8$

Here x = rider's horizontal distance from the start of the ride

i). $y=\frac{1}{3}x^{2}-2x+8$

$=\frac{1}{3}(x^{2}-6x+24)$

$=\frac{1}{3}[x^{2}-2(3x)+9-9+24]$

$=\frac{1}{3}[(x^{2}-2(3x)+9)+15]$

$=\frac{1}{3}[(x-3)^2+15]$

$=\frac{1}{3}(x-3)^2+5$

ii). Since, the parabolic graph for the given equation opens upwards,

Vertex of the parabola will be the lowest point of the rider on the roller coaster.

From the equation,

Vertex → (3, 5)

Therefore, minimum height of the rider will be the y-coordinate of the vertex.

Minimum height of the rider = 5 m

iii). If h = 8 m,

$8=\frac{1}{3}(x-3)^2+5$

$3=\frac{1}{3}(x-3)^2$

(x - 3)² = 9

x = 3 ± 3

x = 0, 6 m

Therefore, at 8 m height of the roller coaster, horizontal distance of the rider will be x = 0 and 6 m

6 0

2 years ago

A professor thinks that the students in her statistics class this term are less creative than most students at this university.

choli [55]

Answer:

It is not enough evidence to reject null hypothesis. It is not enough evidence to say that mean score is not equal to 35.

Step-by-step explanation:

$\mu=35\\n=23\\\=x=33\\s=5\\\alpha=0.1$

1. Null and alternative hypothesis

$H_{0}:\mu=35\\H_{1}:\mu$

2. Significance level

$\alpha=0.1\\1-\alpha=0.99$

Freedom degrees is given by:

$v=n-1\\v=23-1=22$

For a sgnificance level of 0,01 and 22 freedom degrees, t-student distribution value is:

$t_{0.01;23}=-2. 5083$

3. Test statistic

$t=\frac{\=x-\mu}{\frac{s}{\sqrt{n} } }$

$t=\frac{33-35}{\frac{5}{\sqrt{23} } }$

$t=-1,918$

In this case, we have an one left tailed analysis, it means that null hypothesis is rejected if $t$

$-1.918>-2.5083$

Conclusion:

It is not enough evidence to reject null hypothesis. It is not enough evidence to say that mean score is not equal to 35.

3 0

3 years ago