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kenny6666 [7]
3 years ago
6

Find the area of a square with a diagonal of 8 cm.

Mathematics
1 answer:
Fofino [41]3 years ago
3 0

Answer:

To find the area of a square with only the diagonal known,

Square the diagonal and divide by 2:

8^2 = 64

64/2 = 32

The area is 32 cm^2

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A rational number is such that when you multiply it by 5/2 and add 2/3 to the product, you get 7/12. What is the number?
Afina-wow [57]

Answer:A rational number is such that when you multiply it by 5/2 and add 2/3 to the product you get -7/12 . What is the number.

Step-by-step explanation:Let p/q (q ≠ 0) denote the rational number. Multiplying it by 5/2 gives (p/q)(5/2). Add 2/3 to the product and we get (p/q)(5/2) + 2/3 . The result is given to be -7/12.

∴ (p/q)(5/2) + 2/3 = -7/12 …………………………..……………………………………..(1)

Transposing 2/3 to right-hand-side and changing the sign to negative,

(p/q)(5/2) = -2/3 -7/12 = -(2/3 + 7/12) =- (2 x 4 + 7)/12 (Taking L.C.M.)

Or, (p/q)(5/2) = -(8+7)/12 = - 15/12

Multiplying both sides by 2/5,

(p/q)(5/2) x (2/5) = -15/12 . 2/5 = -(3x5)/(3x4) . 2/5 =- 5/4 .2/5

Since 2/5 is the multiplicative inverse of 5/2, 5/2 x 2/5 = 1 and we obtain

(p/q).1 = -1/4 . 2/1 = -1/2

⇒ p/q = -1/2 which is a negative rational number in which p = 1 and q = 2 ≠ 0 .

∴ the rational number = -1/2

3 0
3 years ago
Let Y be a random variable with a density function given by
Neporo4naja [7]

From the given density function we find the distribution function,

F_Y(y)=P(Y\le y)=\displaystyle\int_{-\infty}^y f_Y(t)\,\mathrm dt=\begin{cases}0&\text{for }y

(a)

F_{U_1}(u_1)=P(U_1\le u_1)=P(3Y\le u_1)=P\left(Y\le\dfrac{u_1}3\right)=F_Y\left(\dfrac{u_1}3\right)

\implies F_{U_1}(u_1)=\begin{cases}0&\text{for }u_1

\implies f_{U_1}(u_1)=\begin{cases}\frac{{u_1}^2}{18}&\text{for }-3\le u_1\le3\\0&\text{otherwise}\end{cases}

(b)

F_{U_2}(u_2)=P(3-Y\le u_2)=P(Y\ge3-u_2)=1-P(Y

\implies F_{U_2}(u_2)=\begin{cases}0&\text{for }u_2

\implies f_{U_2}(u_2)=\begin{cases}\frac32(u_2-3)^2&\text{for }2\le u_2\le4\\0&\text{otherwise}\end{cases}

(c)

F_{U_3}(u_3)=P(Y^2\le u_3)=P(-\sqrt{u_3}\le Y\le\sqrt{u_3})=F_Y(\sqrt{u_3})-F_y(\sqrt{u_3})

\implies F_{U_3}(u_3)=\begin{cases}0&\text{for }u_3

\implies f_{U_3}(u_3}=\begin{cases}\frac32\sqrt u&\text{for }0\le u\le1\\0&\text{otherwise}\end{cases}

5 0
3 years ago
What is the prduct of 33 and 6925?
liubo4ka [24]

Answer:

228525-Look below for steps:)

Step-by-step explanation:

Step 1:

6925

*   33

______

Step 2:

5*3=15

carry the one

3*2+1=7

9*3=27

carry the 2

6*3+2=20

SO your first number is 20775 but we are NOT done yet!

add a zero below 5

5*3=15

carry the one

3*2+1=7

9*3=27 carry the 2

then 6*3+2=20

then add 207750+20775

which equals....

228525

so 228525 is your answer!!!

<em>I really do hope this made sense!</em>

<em>Have a great day!</em>

<em>- Hailey: D</em>

<em>(NOTHING IS COPIED AND PASTED!!!!!)</em>

3 0
3 years ago
Plz help me answer these
givi [52]

Answer:

Lenne=10 Gilberto=10 Alana=7.50

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
Find the horizontal asymptote of of the graph of y=(-3x^6+5x+3)/9x^6+6x+4
NNADVOKAT [17]

Answer:

  y = -1/3

Step-by-step explanation:

As x gets large, the value of the expression approaches the ratio of the highest-degree terms in numerator and denominator:

  y = -3x^6/(9x^6) = -3/9

  y = -1/3

5 0
3 years ago
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