Suppose log5=b , then what is the exact value of log5^4?

Answer:

(a) B ∩ D' = {k}

(b)  (B ∪ D)' = {s}

Step-by-step explanation:

Set Notation

[tex]\begin{array}{|c|c|l|} \cline{1-3} \sf Symbol & \sf N\:\!ame & \sf Meaning \\\cline{1-3} \{ \: \} & \sf Set & \sf A\:collection\:of\:elements\\\cline{1-3} \cup & \sf Union & \sf A \cup B=elements\:in\:A\:or\:B\:(or\:both)}\\\cline{1-3} \cap & \sf Intersection & \sf A \cap B=elements\: in \:both\: A \:and \:B} \\\cline{1-3} \sf ' \:or\: ^c & \sf Complement & \sf A'=elements\: not\: in\: A \\\cline{1-3} \sf - & \sf Difference & \sf A-B=elements \:in \:A \:but\: not\: in \:B}\\\cline{1-3} \end{array}[/tex]

Given sets:

Part (a)

[tex]\begin{aligned}\sf B \cap D' & = \sf B \cap \left( \text{U}-D\right)\\ &= \sf \{k, q, x, y \} \cap \left(\{f, k, q, s, x, y, z \} - \{f, q, x, y, z \}\right)\\& = \sf \{k, q, x, y \} \cap \{ k, s \}\\ & = \sf \{k \}\end{aligned}[/tex]

Part (b)

[tex]\begin{aligned}\sf \left(B \cup D\right)' & = \sf \text{U}-\left(B \cup D\right)\\& = \sf \{f, k, q, s, x, y, z \}-\left(\{k, q, x, y\} \cup \{f, q, x, y, z\}\right)\\& = \sf \{f, k, q, s, x, y, z \}-\{ f, k, q, x, y, z\}\\& = \sf \{s\}\\\end{aligned}[/tex]

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Now we have to find,

→ B ∩ D'

→ (B ∪ D)'

Let's solve for the following sets,

a) B ∩ D' = ?

→ B ∩ D'

→ {k, q, x, y} ∩ ({f, k, q, s, x, y, z} - {f, q, x,y,z})

→ {k, q, x, y} ∩ {k, s} = {k}

Hence, the required set is {k}.

b) (B ∪ D)' = ?

→ B' ∩ D'

→ ({f, k, q, s, x, y, z} - {k, q, x, y}) ∩ ({f, k, q, s, x, y, z} - {f, q, x, y, z})

→ {f, s, z} ∩ {k, s} = {s}

Hence, the required set is {s}.

Answer:

0.125 liters per day

Step-by-step explanation:

0.5/4=.125

The actual dimensions of Sarah's classroom are 20 feet by 30 feet, based on a scale of 1 inch representing 10 feet on the floor plan.

If 1 inch on the floor plan represents 10 feet in reality, we can determine the actual dimensions of Sarah's classroom by multiplying the dimensions on the floor plan by 10.

The width of Sarah's classroom on the floor plan is 2 inches, so the actual width would be 2 inches * 10 feet/inch = 20 feet. Similarly, the length of Sarah's classroom on the floor plan is 3 inches, so the actual length would be 3 inches * 10 feet/inch = 30 feet.

Therefore, the actual dimensions of Sarah's classroom are 20 feet by 30 feet. This means that the classroom occupies a rectangular space with a width of 20 feet and a length of 30 feet. It is important to note that these measurements are scaled up from the floor plan according to the given ratio of 1 inch to 10 feet.

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Answer:

B

Step-by-step explanation:

Given a quadratic equation in standard form

ax² + bx + c = 0 ( a ≠ 0 )

Then the discriminant is

Δ = b² - 4ac

• If b² - 4ac > 0 then 2 real irrational roots

• If b² - 4ac > 0 and a perfect square then 2 real rational roots

• If b² - 4ac = 0 then 1 real double root

• If b² - 4ac < 0 then 2 complex roots

Given

x² + 3x - 7 = 0 ← in standard form

with a = 1, b = 3, c = - 7 , then

b² - 4ac

= 3² - (4 × 1 × - 7) = 9 + 28 = 37

Since b² - 4ac > 0 then 2 real irrational roots

right now I know you have to go out for the first half of the most people who have been in touch and time to the right now I know you have to go out for the first half of the most people who have been in touch and time to the right now I know you have to go out for the first half of the most people who have been in touch and time to the right now I know you have to go out for the first half of the most people who have been in touch and time to the right now I know you have to go out for the first half of the most people who have been in touch and time to the right now I know you have to go out for the first half of the most people who have been in touch and time to the right now I know you have to go out for the first half of the most people who have been in touch and time to the right now I know you have to go out for the first half of the most people who have been in touch and time to the right now I know you have to go out for the first half of the most people who have been in touch and time to the right now I know you have to go out for the first half of the most people who have been in touch and time to the right now I know you have to go out for the first half of the most people who have been in touch and time to the right now I know you have to go out for the first half of the most people who have been in touch and time to the right now I know you have to go out for the first half of the most people who have been in touch and time to the right now I know you have to go out for the first half of the most people who have been in touch and time to the right now I know you have to go out for the first half of the most people who have been in touch and time to the right now I know you 2have to go out for the first half of the most people who have been in touch and time to the right now I know you have to go out for the first half of the most people who have been in touch and time to the right now I know you have to go out for the first half of the most people who have been in touch and time to the right now I know you have to go out for the first half of the most people who have been in touch and time to the right now I know you have to go out for the first half of the most people who have been in touch and time to the right now I know you have to go out for the first half of the most people who have been in touch and time to the right now I know you have to go out for the first half of the most people who have been in touch and time to the right now I know you have to go out for the first half of the most people who have been in touch and time to the

The value of the probability is P(Large or Blue) = 7/10

The given parameters are represented on the table

Using the table parameters, we have

P(Large or Blue) = [(Large) + (Blue) - (Large and Blue)]/Total

This gives

P(Large or Blue) = ((17 + 8) + (17 +3) - 17)/(17 + 3 + 8 + 12)

This gives

P(Large or Blue) = 28/40

Simplify

P(Large or Blue) = 7/10

Hence, the value of the probability is P(Large or Blue) = 7/10

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Answer:

h = 15.8

Step-by-step explanation:

200 = 42 + 10h

10h = 200 - 42

10h = 158

h = 15.8

Answer:

15.8 hours

Step-by-step explanation:

Answer: 10 1/3 or 31/3

Step-by-step explanation:

Following bedmas first we do division then addition ( this case you would also switch your fraction into mixed fractions)

(55/6 / 5/1) + 3 1/3

(55/6 x 1/5) + 10/3

11/6 + 10/3

To add fraction you have to have the same denominator, so you multiply it till it has the same denominator

11/6 + 20/3

31/3 = 10 1/3 is your final answer

The required nonreal solution of the given equation 4x⁴ – 8x³ + 4x² – 128x – 960 = 0 is –4i, 4i.

The equation is the relationship between variables and is represented as y =ax +b is an example of a polynomial equation.

Here,
The given expression,
4x⁴ – 8x³ + 4x² – 128x – 960 = 0.
Factorization
4.(x + 3).( x - 5).(x² + 16) = 0
Now,
x + 3 = 0    ; x - 5 = 0      ; x² + 16 = 0
x = -3         ; x = 5           ; x = ± 4i

Thus, the required nonreal solution of the given equation is –4i, 4i.

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Answer:

B

Step-by-step explanation:

Answer:

1,080

Step-by-step explanation:

QUICK MATH

The length of the ladder is 58.31 inches and the angle made by the ladder with the ground is θ = 59.04°.

The distance between the ladder and the wall is 30 inches.

The height at which the ladder touches the wall is 50 inches from the ground.

Let x be the slant height when the ladder touches the wall.

Then, by using a Pythagorean theorem:

(Base)² + (Altitude)² = (Hypotenuse)²

(30)² + (50)² = x²

x² = 900 + 2500

x² = 3400 inches²

x = √[ 3400 inches²]

x = 10√34 inches

x = 58.31 inches

Then the angle made by the ladder with gound is :

tan (θ) = opposite / adjacent

tan (θ) = 50/30

tan (θ) = 5/3

θ = tan⁻¹ ( 5/3 )

θ = 59.04°

Therefore, the ladder is 58.31 inches long and the angle between the ground and the ladder is 59.04°.

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Answer:

A-B=C

A= a house

B=destruction

C= aftermath

158.93 yd³ water it would take to completely fill the swimming pool.

Given that, a swimming pool has a volume of 32,100 gal and we have to find out that how many cubic yards of water it would take to completely fill the swimming pool.

1 cubic yard (yd³) ≈ 201.97 gallon (gal)

So, by using the conversion given above we can simply find the water in cubic yards that it would take to completely fill the swimming pool.

Volume of the swimming pool = 32,100 gal

and we know that, 1 cubic yard (yd³) ≈ 201.97 gallon (gal)

Now, we get

water needed in cubic yards to completely fill the swimming pool

= 32,100/201.97

= 158.93 yd³

Hence, 158.93 yd³ water it would take to completely fill the swimming pool.

Therefore, 158.93 yd³ is the required answer.

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Answer:

50= 2x2x5 is the prime factorization of 50.

Answer:

27.893m in 27m 8dm 9cm 3mm​

Step-by-step explanation:

Just put in the digits from left to right since:

10dm = 1m

10cm = 1 dm

10mm = 1cm

Answer:

the probability to flip a head is 50%

Step-by-step explanation:

I think.

Answer:

C

Step-by-step explanation:

9y-1=180-127

9y-1=53

9y=54

y=6

Answer: B

Step-by-step explanation:

Answer:

3/2

Step-by-step explanation:

K = Y/X

why the grade tent truck fico duck session duck duck drink dunno rbi Thu to ft ft ft ft tho

Answer:

The distance between w=1+2i and z=3-i is 3.61

Step-by-step explanation:

We need to find the distance between w=1+2i and z=3-i

The formula used is: [tex]Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

We have [tex]x_1=1, y_1=2, x_2=3, y_2=1[/tex]

We will use only real numbers and not i for calculating distance.

Putting values and finding distance

[tex]Distance=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}\\Distance=\sqrt{(1-3)^2+(-1-2)^2} \\Distance=\sqrt{(-2)^2+(-3)^2} \\Distance=\sqrt{4+9} \\Distance=\sqrt{13}\\Distance=3.61[/tex]

So, The distance between w=1+2i and z=3-i is 3.61

Answer:

2t^2−7t−4 (b)

Step-by-step explanation:

=(2t+1)(t+−4)

=(2t)(t)+(2t)(−4)+(1)(t)+(1)(−4)

=2t^2−8t+t−4

=2t^2−7t−4

Answer:

Gymnastics

Step-by-step explanation:

Answer:

Step-by-step explanation:

Since lines 1 and 2 are parallel, <2=<6 because corresponding angles of parallel lines are congruent. <8 is the vertical angle of <6 meaning it's equal to <6. <8=115 degrees. <7 is the supplement of <6 and therefore 180-<6=<7. 180-115=65.

The total account balance after forty-five years will be $68.15

As per the known facts, the simple interest is calculated using the formula -

S. I. = (P × R × T) ÷ 100, where S.I. is simple interest, P is principal, R is rate of interest and T is time. Keep the values in formula to find the value of interest.

S.I. = (29 × 3 × 45) ÷ 100

S.I. = 3915 ÷ 100

S.I. = 39.15

To calculate the amount, we will simply add the principal and simple interest.

Amount = 29 + 39.15

Amount = $68.15

Therefore, the total account balance after forty-five years will be $68.15.

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Given:

The table of score and frequency.

To find:

The probability that on the next roll the score will be 4.

Solution:

From the given table it is clear that the score 4 occurs 10 times.

Number of times the dice was rolled = 17 + 24 + 23 + 10 + 16 + 30

                                                             = 120

The probability that on the next roll the score will be 4 is

[tex]\text{Required probability}=\dfrac{\text{Number of times 4 occurs}}{\text{Number of times the dice was rolled}}[/tex]

[tex]\text{Required probability}=\dfrac{10}{120}[/tex]

[tex]\text{Required probability}=\dfrac{1}{12}[/tex]

Therefore, the required probability is [tex]\dfrac{1}{12}[/tex].