I have 14 tens, 6 hundred, 7 tens /thousands, and 15 ones

How much is 20 times 96

Iteru [2.4K]

Answer:

1920

Step-by-step explanation:

Hope this helps :)

4 0

3 years ago

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Write a polynomial of least degree with rational coefficients and with the root -19-5 square root 2.

iogann1982 [59]

Answer:

y = x² + 38x + 311

Step-by-step explanation:

If a polynomial has rational coefficients and irrational roots, then the roots must be conjugate pairs.

y = (x − (-19-5√2)) (x − (-19+5√2))

y = (x + 19+5√2) (x + 19−5√2)

Use FOIL to distribute:

y = x² + x (19−5√2) + x (19+5√2) + (19+5√2)(19−5√2)

y = x² + 19x − 5√2 x + 19x + 5√2 x + (19+5√2)(19−5√2)

y = x² + 38x + (19+5√2)(19−5√2)

Use FOIL to distribute the last term:

y = x² + 38x + 19² − 95√2 + 95√2 − 50

y = x² + 38x + 361 − 50

y = x² + 38x + 311

5 0

3 years ago

Find the volume of a cone with base area 16pi ft squared and height 9 ft.

yulyashka [42]

Answer:

$volume = \frac{1}{3} \pi {r}^{2} h \\ = \frac{1}{3} \times16\pi \times 9 \\ =48\pi \: cubic \: ft$

6 0

3 years ago

(a) A parachutist lands at a point on the line between the points A and B, and the target is an operation at A. The operation fa

mr Goodwill [35]

Answer:

a) $\frac{B-\frac{A+5B}{6}}{B-A}= \frac{6B -A-5B}{6(B-A)}=\frac{B-A}{6(B-A)}=\frac{1}{6}$

b) $P(X>1) = 1-P(X\leq 1)=1-\int_{0}^1 \frac{1^{2} x^{2-1} e^{- x}}{\gamma(2)}=0.736$

Step-by-step explanation:

Part a

We assume that the parachutist lands at random point in the interval (x=A,y=B) we have a continuous random variable X. And the distribution of X would be uniform $Y\sim Unif(A,B)$ . And the density function would be given by:

$f(x) =\frac{1}{B-A} , A$

And 0 for other case.

The operation fails, if parachutist's distance to A is more than five times as much as her distance to B.

So the point P in the interval (A,B) at which the distance to A is exactly 5 times the distance to B is given by:

$P= A + \frac{5}{6} (B-A)= \frac{6A +5B -5A}{6}=\frac{A+5B}{6}$

And we can find the probability desired like this:

$P(d(P,A) \geq 5 d(P,B))= P(\frac{A+5B}{6} < X< B)$

And from the cumulative distribution function of X ficen by $F(X)\frac{X-A}{B-A}$ we got:

$\frac{B-\frac{A+5B}{6}}{B-A}= \frac{6B -A-5B}{6(B-A)}=\frac{B-A}{6(B-A)}=\frac{1}{6}$

Part b

For this case we assume that $X\sim Gamma (2,1)$

On this case we assume that $\alpha=2, \beta= 1$

The density function for the Gamma distribution is given by:

$P(X)= \frac{\beta^{\alpha} x^{\alpha-1} e^{-\beta x}}{\gamma(\alpha)}$

And on this case we can find the probability using the complement rule like this:

$P(X>1) = 1-P(X\leq 1)=0.736$

We can solve this problem with the following excel code:

"=1-GAMMA.DIST(1;2;1;TRUE)"

And if we do it by hand we need to do this:

$P(X>1) = 1-P(X\leq 1)=1-\int_{0}^1 \frac{1^{2} x^{2-1} e^{- x}}{\gamma(2)}=0.736$

6 0

3 years ago

A speed walker covered 4 1/2 mi in 3/4 hour. How far will he walk with the same pace in 3.5 hours?

alisha [4.7K]

Distance = Speed × Time

Distance = (4.5 mi)/(0.75 h) × (3.5 h) = 21 mi

The walker will cover 21 miles in 3.5 hours at that pace.

6 0

3 years ago

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