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3 years ago

Simplify and solve for the unknown. Use order of operations as needed. Check your work.

Mathematics

1 answer:

antiseptic1488 [7]3 years ago

3 0

Answer:

Step-by-step explanation:

Given: 5^3– 10^2 = X(8 – 2) + 2X – 3X

Solving the equation to find the value of x.

⇒ $5^{3} -10^{2} = x(8-2)+2x-3x$

Using the distributive property of multiplication, multiplying x with 8 and -2

⇒ $125-100= 8x-2x+2x-3x$

cancelling out -2x and 2x

⇒ $25= 8x-3x$

⇒ $25= 5x$

Multiplying both side by 5

⇒ x= $\frac{25}{5}$

∴ x= 5

Hence, the value of unknown is 5.

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A city hosted a music festival that included three concerts. According to the sales database, 28% of the audience attended the f

Vitek1552 [10]

Answer:

$P(X\cap Y\cap Z)=0.05$

Step-by-step explanation:

From the question we are told that:

Percentage of audience in first concert $P(X)=0.28$

Percentage of audience in second concert $P(Y)=0.42$

Percentage of audience in third concert $P(Z)=0.30$

Audience Percentage at at-least one concert $P(X \cup Y \cup Z)=0.80$

Percentage of audience at first & second concert $P(X \cap Y)=0.10$

Percentage of audience in first & third concert $P(X \cap Z)=0.08$

Percentage of audience in second & third concert $P(Y\cap Z)=0.07$

Generally the equation for probability of attending all concerts $P(X\cap Y\cap Z)$ is mathematically given by

$P(X \cup Y \cup Z)=P(X)+P(Y)+P(Z)-P(X \cap Y)-P(X \cap Z)-P(Y\cap Z)+P(X\cap Y\cap Z)$

$P(X\cap Y\cap Z)=P(X \cup Y \cup Z)-P(X)-P(Y)-P(Z)+P(X \cap Y)+P(X \cap Z)+P(Y\cap Z)$

$P(X\cap Y\cap Z)=0.80-0.28-0.42-0.30+0.10+0.80+0.70$

$P(X\cap Y\cap Z)=0.05$

Therefore the probability that a randomly selected audient attended all the concerts

$P(X\cap Y\cap Z)=0.05$

8 0

3 years ago

Consider a tree T storing 100,000 entries. What is the worst-case height of T in the following cases?

Darina [25.2K]

Answer:

Step-by-step explanation:

a.) The worst-case height of an AVL tree or red-black tree with 100,000 entries is 2 log 100, 000.

b.) A (2, 4) tree storing these same number of entries would have a worst-case height of log 100, 000.

c.) A red-black tree with 100,000 entries is 2 log 100, 000

d.) The worst-case height of T is 100,000.

e.) A binary search tree storing such a set would have a worst-case height of 100,000.

6 0

3 years ago

Find one positive angle and one negative angle that are coterminal with the given angle. Explain.

Setler [38]

Answer: 10) 615° & -105°

12) -440° & 280°

Step-by-step explanation:

Coterminal means it is in the exact same spot on the Unit Circle but one or more rotations clockwise or counterclockwise.

Since one rotation = 360°, add or subtract that from the given angle until you get a positive or negative number.

10) 255° + 360° = 615° (this is a POSITIVE coterminal angle to 255°)

255° - 360° = -105° (this is a Negative coterminal angle to 255°)

12) -800° + 360° = -440° (this is a Negative coterminal angle to -800°)

-440° + 360° = -80° (this is a Negative coterminal angle to -800°)

-80° + 360° = 280° (this is a POSITIVE coterminal angle to -800°)

3 0

3 years ago

What is the length of a car if the length on the scale model car is 17 cm and the scale is 2 cm : 50 cm?

LenaWriter [7]

The length of the car is equal to 425cm! You can convert the scale to 1 cm : 25cm. Multiply 25 by 17 (the scale model car length) to get 425 cm

5 0

3 years ago

HELP PLEASE GAHAHAHAHAHAHAHAHA

kenny6666 [7]

Answer:

Angle QPS= 42

Angle ONP= 180-42 = 138

Hence Angle RSU= 138

Corresponding angles have same angles.

4 0

3 years ago