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Zepler [3.9K]
2 years ago
5

Solve the equation for x: 2.5x = 50

Mathematics
2 answers:
oksano4ka [1.4K]2 years ago
6 0

Answer:

x = 20

Step-by-step explanation:

2.5x= 50

x= 50/2.5

x = 20

maria [59]2 years ago
4 0

Answer:

x = 20

Step-by-step explanation:

x = 50/2.5 = 2.5x = 50

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Suppose I have an urn with 9 balls: 4 green, 3 yellow and 2 white ones. I draw a ball from the urn repeatedly with replacement.
Mrrafil [7]

Answer:

E(X_n)=\frac{2(n-1)}{27}

E(y)=\frac{14}{9}

Step-by-step explanation:

From the question we are told that:

Sample size n=9

Number of Green g=4

Number of yellow y=4

Number of white w=4

Probability of Green Followed by yellow P(GY) ball

 P(GY)=\frac{4}{9}*\frac{3}{9}

 P(GY)=\frac{4}{27}

Generally the equations for when n is even is mathematically given by

 Probability of success P(S)=\frac{4}{27}

 Probability of Failure P(F)=\frac{27-4}{27}

 Probability of Failure P(F)=\frac{23}{27}

Therefore

 E(X_n)=\frac{n}{2}*P

 E(X_n)=\frac{n}{2}*\frac{4}{27}

 E(X_n)=\frac{2n}{27}

Generally the equations for when n is odd is mathematically given by

 \frac{n-1}{2}

 E(X_n)=\frac{n-1}{2}*\frac{4}{27}

 E(X_n)=\frac{2(n-1)}{27}

b)

Probability of drawing white ball

 P(w)=\frac{2}{9}

Therefore

 E(w)=\frac{1}{p}

 E(w)=\frac{1}{\frac{2}{9}}

 E(w)=\frac{9}{2}

Therefore

 E(y)=[E(w)-1]\frac{4}{9}

 E(y)=[\frac{9}{2}-1]\frac{4}{9}

 E(y)=\frac{14}{9}

5 0
3 years ago
You go to the mall to make some purchases. You buy 3 dresses which cost $59.99 each and a pair of shoes that cost $75. What is t
mina [271]
Combine costs
59.99(3) + 75 = 179.97 + 75
179.97 + 75 = $254.99 (total cost)
Now add tax: 8% = 0.08
254.99 * 0.08 = 20.3992
254.99 + 20.3992 = 275.3892

Solution: bill would be around $275
6 0
2 years ago
An open box is to be made out of a 6-inch by 14-inch piece of cardboard by cutting out squares of equal size from the four corne
lawyer [7]

Answer:

The dimensions of the resulting box that has the largest volume is 1.3 inches x 1.3 inches

Step-by-step explanation:

Card board size is L= 14 inches and

W = 6 inches

Let x be the size of equal squares cut from 4 corners and bent into a box whose size is now;

L = 14 − 2x , W = 6 −2x and h = x inches.

Volume of the box is given as;

V = (14 −2x)(6−2x)x

V =(4x² − 40x + 84)x

= 4x³ − 40x² + 84x.

Now, for the maximum value,

dV/dx =0

Thus,

dv/dx = 12x² - 80x + 84 = 0

Using quadratic formula

x = [-(-80) ± √(-80²) - 4(12 x 84)]/(2 x 12)

x = [80 ± √(6400 - 4032)]/24

x = (80 + 48.66)/24 or (80-48.66)/24

x = 5.36 or 1.31

Looking at the two values, 1.31 would be more appropriate because if we use 5.36,we will get a negative value of the width (W).

Thus, x = 1.31 inches

Let us use the Second Derivative Test to verify that V has a local maximum at x = 1.31.

Thus;

d²v/dx² = 24x - 80 = 24(1.31) - 80 = -48.56

This is less than 0 and therefore, the volume of the box is maximized when a 1.31 inch by 1.3 inch square is cut from the corners of the cardboard sheet.

3 0
3 years ago
Lawrence's parents pay him a base allowance of $20 per week and $3.55 per hour for extra chores he completes. Mrs. Johnson pays
sergey [27]

Answer:

7.15x + 3.55y + 20 = weekly income

Step-by-step explanation:

7.15x + 3.55y + 20 = weekly income


6 0
3 years ago
-0.4a + 3 = 7 <br> a = <br> plz help
Papessa [141]

Answer:

a = -10

Step-by-step explanation:

-0.4a + 3 = 7

subtract 3 from each side

-0.4a + 3-3 = 7-3

-.4a = 4

Divide each side by -.4

-.4a/ -.4 = 4/-.4

a = - 10

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3 years ago
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