1) Simplify and write your answer with one base and one exponent.
6^-5 x 6^2

Answer:

Concept :

✧Thorough solution is provided in the attachment.

Don't hesistate to reach out to me if you have further queries! Have fun studying! <3

The values of [tex]\( \sin \theta \)[/tex] are [tex]\( \frac{\sqrt{35}}{6} \)[/tex] and [tex]\( -\frac{\sqrt{35}}{6} \)[/tex],  and the value of [tex]\( \tan \theta \)[/tex] is [tex]\( \sqrt{35} \)[/tex].

Given that [tex]\( \cos \theta = \frac{1}{6} \)[/tex], we need to find [tex]\( \sin \theta \)[/tex] and [tex]\( \tan \theta \)[/tex].

First, we can find [tex]\( \sin \theta \)[/tex] using the Pythagorean identity:

[tex]\[\sin^2 \theta + \cos^2 \theta = 1\][/tex]

Substitute [tex]\( \cos \theta = \frac{1}{6} \)[/tex]:

[tex]\[\sin^2 \theta + \left(\frac{1}{6}\right)^2 = 1\][/tex]

[tex]\[\sin^2 \theta + \frac{1}{36} = 1\][/tex]

[tex]\[\sin^2 \theta = 1 - \frac{1}{36} = \frac{36}{36} - \frac{1}{36} = \frac{35}{36}\][/tex]

[tex]\[\sin \theta = \pm \sqrt{\frac{35}{36}} = \pm \frac{\sqrt{35}}{6}\][/tex]

So, [tex]\( \sin \theta \)[/tex] could be [tex]\( \frac{\sqrt{35}}{6} \)[/tex] or [tex]\( -\frac{\sqrt{35}}{6} \)[/tex].

Next, to find [tex]\( \tan \theta \)[/tex], we use the definition:

[tex]\[\tan \theta = \frac{\sin \theta}{\cos \theta}\][/tex]

Substitute [tex]\( \sin \theta = \pm \frac{\sqrt{35}}{6} \) and \( \cos \theta = \frac{1}{6} \)[/tex]:

[tex]\[\tan \theta = \frac{\frac{\sqrt{35}}{6}}{\frac{1}{6}} = \sqrt{35}\][/tex]

Answer:

38

Step-by-step explanation:

You need to add all of numbers together and then divide by the total number of numbers.

Answer:

REMA = 31

KEN = 19

Step-by-step explanation:

Let R be Rema

Let K be Ken

R+K = 50

R-K= 12

R-12= K

R+ R-12= 50

2R= 50+12

2R= 62

R= 31

R- 12= K

31-12= K

19= K

Upper Quartile: 38

Lower Quartile: 19

The lower quartile value is the median of the lower half of the data. The upper quartile value is the median of the upper half of the data.

Answer:

Step-by-step explanation:

The upper quartile is the median of the upper half of a data set.

The lower quartile value is the median of the lower half of the data.

Answer:

C

Step-by-step explanation:

Answer:

The answer is B

Step-by-step explanation:

2

Look at the attached picture ⤴

Hope it will help u ....

Answer:

11.31 ft

Step-by-step explanation:

Here in this problem ladder forms a right triangle with the wall of the house and it is acts as hypotenuse, length of one leg of right triangle given to be 4 feet.

Let the ladder reaches x ft height of the house.

Hence, by Pythagoras theorem:

[tex] {12}^{2} = {4}^{2} + {x}^{2} \\ 144 = 16 + {x}^{2} \\ {x}^{2} = 144 - 16 \\ {x}^{2} = 128 \\ x = \sqrt{128} \\ x = 11.3137085 \\ x = 11.31 \: ft[/tex]

Hence, the ladder reaches 11.31 ft height of the house.

Answer:

p^8 q^3

Step-by-step explanation:

When dividing exponents, you subtract the numerator by the denominator.

Example: Look at p. 5-(-3) will result with p^8. For q, find what subtracted from 6 will make 3.

Answer: [tex]q^3[/tex] and [tex]p^8[/tex]

When dividing exponents, if they have the same base, you subtract the exponents. For example, [tex]\frac{a^x}{a^y}[/tex] has the same base of [tex]a[/tex], so the answer would be [tex]a^{x-y}[/tex].

[tex]q^{6-3}[/tex] = [tex]q^3[/tex]

[tex]p^{5-(-3)}[/tex] = [tex]p^{5+3}[/tex] = [tex]p^8[/tex]

The solutions to the quadratic equation are x= 0.22 and x= -0.22.

The given quadratic formula is 2x²-5x+1=0.

The roots of a quadratic equation ax² + bx + c = 0 are given by x = [-b ± √(b² - 4ac)]/2a.

Here, x= [5± √(25 - 4×2×1)]/2×2

x= [5± √(25 - 8)]/4

x= (5± √17)/4

x= (5± 4.12)/4

x= 0.88/4 and x= -0.88/4

x= 0.22 and x= -0.22

Therefore, the solutions to the quadratic equation are x= 0.22 and x= -0.22.

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Answer: 168 because (9 × 6) + (9 × 5) + (9 × 5) + (6 × 4 × 0.5) + (6 × 4 × 0.5)  equals 168 :) good day humans

Answer:

24 books

steps:

If we take the amount 395 and subtract 35, we get a total that is unaffected by the video rack, and can be easily answered now

The total is 360, we are now able to divide 360 by 15, getting the total of 24 books

Answer:

3,500

Step-by-step explanation:

Answer:

-6 is the slope

Step-by-step explanation:

y = −6x + 5

This is of the form

y = mx+b where m is the slope and b is the y intercept

-6 is the slope and 5 is the y intercept

Answer:

D

Step-by-step explanation:

The slope is the change in y-coordinates divided by the change in x-coordinates.

Here, the y-coordinates are -4 and -1, and the x-coordinates are -3 and 0, so:

slope = m = (-4 - (-1)) / (-3 - 0) = -3 / -3 = 1

The slope is thus 1, so the answer is D.

We can use the points (-3, -4) and (0, -1) to solve.

Slope formula: y2-y1/x2-x1

= -1-(-4)/0-(-3)

= 3/3

= 1 (Option D)

Best of Luck!

Answer:

Step-by-step explanation:

The probability that a person chosen at random from a group of 30 people only visited one of the two landmarks, the Eiffel Tower or the Notre-Dame Cathedral in Paris, is 17/30.

To calculate the probability that a person in a group of 30 people who visited Paris only visited one of the two landmarks - the Eiffel Tower (ET) or the Notre-Dame Cathedral (NDC), we need to apply the principles of set theory and probability.

Firstly, we know that:

13 visited the ET

16 visited the NDC

7 did not visit either place

Adding the numbers of visitors to both places gives us a total of 29 (13 ET + 16 NDC). However, the total number of people is 30, and 7 did not visit either, which implies that 23 people (30 - 7) visited at least one site. Therefore, 29 - 23 gives us 6 people who have visited both places.

To find the number who visited only one place, we subtract those who visited both from the total who visited each:

For ET only: 13 (visited ET) - 6 (visited both) = 7

For NDC only: 16 (visited NDC) - 6 (visited both) = 10

Adding these gives us 17 (7 ET only + 10 NDC only) who visited just one site. Hence, the probability that a person chosen at random visited only one of the two places is:

P(visited only one site) = Number who visited only one site / Total number of people

P(visited only one site) = 17 / 30

Therefore, the probability is 17/30.

Answer:

5 units.

Step-by-step explanation:

For this problem, you will need to use the distance formula. The distance formula is as shown:

d= [tex]\sqrt{({x_{2}-x_{1})^{2}+({y_{2}-y_{1})^{2} }[/tex]

We can plug in the points which would result in:

d=  [tex]\sqrt{({-4-0)^{2}+(-3-0)^{2} }[/tex]

When solved:

d= [tex]\sqrt{25}[/tex]

d= 5 units

Answer:

A

Step-by-step explanation:

1/1-2/5

Answer:

78.5 cm^2

Step-by-step explanation:

The area of a circle can be found using:

[tex]a=\pi r^2[/tex]

We know that the radius is 5 cm. We also know that we are using 3.14 for pi. Therefore, we can substitute 5 in for r, and 3.14 in for pi.

a=3.14*5^2

Evaluate the exponent

a=3.14*(5*5)

a=3.14*25

Multiply

a=78.5

The area of the clock is 78.5 cm^2

Answer:

The correct answer would be 10 : 7

( OPINION ) I say this because we are comparing the apples in the fridge(10) to the apples on the table(7).

I hope this was helpful :3

STAY SAFE!! :)

The ratio of apples in the fridge to apples on the table is 10:7. This is calculated by dividing the number of apples in the fridge by the number on the table.

The question asks for the ratio of apples in the fridge to the apples on the table. In order to solve this, you need to understand what a ratio is. A ratio is a way of comparing quantities. Here, the quantity being compared is apples: those in the fridge versus those on the table.

To calculate the ratio, you simply divide the first quantity by the second quantity. So in this case, you have 10 apples in the fridge and 7 apples on the table.

The ratio is therefore 10/7. This can also be written as 10:7.

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Answer:

case 1 = 2592

case 2 =  729

case 1 + case 2 =  2916

(this is not a direct adition, because case 1 and case 2 have some shared elements)

Step-by-step explanation:

Case 1)

6 digits numbers that can be divided by 25.

For the first four positions, we can use any of the 6 given numbers.

For the last two positions, we have that the only numbers that can be divided by 25 are numbers that end in 25, 50, 75 or 100.

The only two that we can create with the numbers given are 25 and 75.

So for the fifth position we have 2 options, 2 or 7,

and for the last position we have only one option, 5.

Then the total number of combinations is:

C = 6*6*6*6*2*1 = 2592

case 2)

The even numbers are 2,4 and 6

the odd numbers are 3, 5 and 7.

For the even positions we can only use odd numbers, we have 3 even positions and 3 odd numbers, so the combinations are:

3*3*3

For the odd positions we can only use even numbers, we have 3 even numbers, so the number of combinations is:

3*3*3

we can put those two togheter and get that the total number of combinations is:

C = 3*3*3*3*3*3 = 3^6 = 729

If we want to calculate the combinations togheter, we need to discard the cases where we use 2 in the fourth position and 5 in the sixt position (because those numbers are already counted in case 1) so we have 2 numbers for the fifth position and 2 numbers for the sixt position

Then the number of combinations is

C = 3*3*3*3*2*2 = 324

Case 1 + case 2 = 324 + 2592 = 2916

Answer:

1. 2=1

2. No Solution

Step-by-step explanation:

edge 2022

The equation that shows the result as per the given scenario is 2=1. The correct option is A.

The way of representing huge numbers in terms of powers is known as an exponent. Exponent, then, is the number of times a number has been multiplied by itself.

In mathematics, a base number raised to an exponent is referred to as a power. The base number is the factor that is multiplied by itself, and the exponent indicates how many times the base number has been multiplied.

Given,

Equation = [tex](1/5000)^{2z}X5000^{2z+2}[/tex]

We have to rewrite the given equation so there is a single power of 5,000 on each side.

[tex]1/a^n=a^{-n}\\\\a^m/a^n=a^{a-n}\\\\a^mXa^n=a^{m+n[/tex]

So,

[tex](1/5000)^{2z}X5000^{2z+2}=5000[/tex]

[tex]5000^{-2z}X5000^{2z+2}=5000[/tex]

[tex]5000^{-2z+2z+2}=5000^1[/tex]

By this,

-2z+2z+2=1,

Thus, the value can be 2=1, so the correct option is A.

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Your question seems incomplete, the complete question is:

Rewrite the given equation so there is a single power of 5,000 on each side. then, set the exponents equal to each other.

(1/5000)^2z · 5000^2z+2 = 5000

which equation shows the result?

a) 2=1

b) z=1

c) -4z+2=1

d) -4z+1=1

Answer:

B) And D)

Step-by-step explanation:

8-2x1 = 6

Option B number line shows the solution set for |8 - 2p| = 6

A number line is a pictorial representation of numbers on a straight line. It can be used to represent any real number that includes every whole number and natural number. Arithmetic operations of numbers can be better explained on a number line.

According to the question the given expression is  |8 - 2p| = 6

Here the value of "p" is unknown. We have to assume a number and equate it to 6.

Let "p" be ±2, On applying ±2 in the set  |8 - 2(±2)| =0

so not ±2

Now assume ±1, On applying ±1 in the set  |8 - 2(±1)| =6

Value ±1 is shown in the 2nd number line.

Thus the correct option is B

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Answer:

47 inches.

I hope this helped!! :3

Edit- to find the height of a rectangular prism with a known volume, use the formula

V= AH.

3995= lwH

3995= 85h

If you don’t have the area, multiply the width and the length of one side to get that value.

Answer:

1

Step-by-step explanation:

Answer:

51.24 mg

Step-by-step explanation:

400 x (0.71^6) = 51.24

Final answer:

The distance between the points (-5,3) and (1,-1) is found using the distance formula and is approximately 7.2 units when rounded to the nearest tenth.

Explanation:

To find the distance between two points (-5,3) and (1,-1), we can use the distance formula: √((x2 - x1)² + (y2 - y1)²). Plugging in our values, we get the distance as √((1 - (-5))² + (-1 - 3)²) = √(6² + (-4)²) = √(36 + 16) = √52. To round to the nearest tenth, we calculate √52 and find it is approximately 7.2. Therefore, the distance between the points, rounded to the nearest tenth, is 7.2 units.

Answer:

quadratic

Step-by-step explanation:

i just took it on edge

Answer:

Step-by-step explanation:

Answer:

the absolute value of l9l is 9

Step-by-step explanation:

because if you look on a number line when you are calculating the absolute value it is how many numbers away from zero so it is always positive.

Answer: +9

Step-by-step explanation: When an integer is written with vertical bars on either side, it means that we take the absolute value of that integer.

The absolute value of an integer is its

distance from zero on a number line.

|9| is +9 because it's 9 units from zero on the number line.

Answer:

The most reasonable estimate for the number of Sunset Park Food  Festival attendees whose favorite type of burger is a sausage bacon  cheeseburger is 760.

Step-by-step explanation:

Assume that Bob's Burgers provides two types of burgers:

Of the random sample of N = 70 attendees, the number of people who said that bacon cheeseburgers were their favorite type of burgers is 32.

Then the number of people who said that sausage bacon cheeseburgers were their favorite type of burgers is, n (S) = 70 - 32 = 38.

Compute the probability that a randomly selected attendee like sausage bacon cheeseburger as follows:

[tex]P(S) = \frac{n(S)}{N}=\farc{38}{70}=0.543[/tex]

It is provided that there are 1400 Sunset Park Food Festival attendees.

Let the random variable X be defined as the number of attendee who likes sausage bacon cheeseburgers.

Then the random variable X will follows a Binomial distribution with parameter n = 1400 and p = 0.543.

This is because, there are a fixed number of trial in the experiment, each trial has the same number of outcomes, i.e. a person either likes bacon cheeseburgers or sausage bacon cheeseburgers and each trial has the same probability of success, i.e. P (S).

The expected value of a Binomial random variable is:

[tex]E(X)=n\times p[/tex]

Compute the expected number of attendees whose favorite type of burger is a sausage bacon  cheeseburger as follows:

[tex]E(X)=n\times p[/tex]

         [tex]=1400\times 0.543\\=760.2\\\approx 760[/tex]

Thus, the most reasonable estimate for the number of Sunset Park Food  Festival attendees whose favorite type of burger is a sausage bacon  cheeseburger is 760.

Answer:

A. 2x-13

Step-by-step explanation: