Simplify the expression (7^6) ^5

The side length of a cube with a volume of 64 mm^3 is found by taking the cube root of the volume, which is 4 mm.

To find the side length of a cube with a given volume, you apply the formula for the volume of a cube, which is V = s3, where V is the volume and s is the side length of the cube. Since the volume of the cube is given as 64 mm3, you need to take the cube root of 64 to find the side length.

The steps are as follows:

Substitute the value into the formula: V = s^3, so 64 mm3 = s3.

Undo the cube by applying the cube root: s = ∛64 mm3, which simplifies to s = 4 mm.

Therefore, the side length of the cube is 4 mm.

Answer:

c. Place the point of the compass on point G and draw an arc, using the same width for the opening of the compass as the first arc.

Step-by-step explanation:

I took the k12 test and it was correct.

To construct the perpendicular bisector of GH, Louis should place the point of the compass on point G and draw an arc using the same opening as the first arc. The intersecting point of these arcs is the midpoint of GH, which separates GH into two equal halves.

Louis should place the point of the compass on point G and draw an arc, using the same width for the opening of the compass as the first arc. This is a required step in constructing a perpendicular bisector. After Louis has created this arc, the intersection of the two arcs is the midpoint of GH. If a line is drawn from this point to GH, it will create two equal halves, creating the perpendicular bisector.

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The equation of the circle is x² + y²=20

Step-by-step explanation:

The equation of circle is written as

(x-h)² +( y-k)²=r²

x² + y²=r²

The circle passes through (0,0) and (4, -2)

The equation of the circle is x² + y²=20

I have attached the document for the explanation part

Answer:

B = 612.2 ft

Step-by-step explanation:

Solution:-

- The elevation of person, H = 235 ft

- The angle of depression, θ = 21°

- We will sketch a right angle triangle with Height (H), and Base (B) : the boat's distance to the edge of the cliff and the angle (θ) between B and the direct line of sight distance.

- We will use trigonometric ratios to determine the distance between boat and the edge of the cliff, using tangent function.

                             tan ( θ ) = H / B

                             B = H / tan ( θ )

                             B = 235 / tan ( 21 )

                             B = 612.2 ft    

Answer:

The distance of the boat from the edge of the cliff is 655.75 ft

Distance of the boat from the base of the cliff is 251.72 ft

Step-by-step explanation:

Height of person above sea level = 235 ft

Angle of depression of sight to the boat from the person = 21°

Therefore, based on similar angle between person and angle of depression and the boat with angle of elevation we have,

Angle of elevation of the location of the person as sighted from the boat θ = 21°

Distance from the edge of the cliff of the boat is then given by;

[tex]Sin\theta = \frac{Opposite \, side \, to\, angle}{Hypothenus\, side \, of\, triangle} = \frac{Height\, of\, person\, above \, ses \, level}{Distance\, of\, boat\, from \, edge\, of \, cliff}[/tex]

[tex]Sin21 =\frac{235}{Distance\, of\, boat\, from \, edge\, of \, cliff}[/tex]

[tex]Distance\, of\, boat\, from \, edge\, of \, cliff=\frac{235}{Sin21 } = \frac{235}{0.358} = 655.75 \, ft[/tex]

Distance of the boat from the base of the cliff is given by

[tex]Distance\, of\, boat\, from \, base\, of \, cliff=\frac{235}{cos21 } = \frac{235}{0.934} = 251.72 \, ft[/tex].

Answer:

Step-by-step explangghdhc6vyation:

Hhyvvh

Answer:

The answer to your question is Kevin is 6 years old.

Step-by-step explanation:

Process

1.- Assign a letter to Daniel and another letter to Kevin

Daniel = d

Kevin = k

2.- Write equation that help to solve this problem

      k = d + 3         equation l

       k = 4d             equation ll          four years ago

3.- Solve the system by substitution. Substitute equation ll in equation l

       4d = d + 3

-Solve for d

       4d - d = 3

       3d = 3

         d = 1

-Find k

       k = 1 + 3

       k = 4

4.- Calculate the age Kevin has now

Kevin's age = 4 + 2

                   = 6  

Answer:

where are your answers?

I need all the question to answer becbecause it seems it is incomplète.

Step-by-step explanation:

however, Reflection in algèbre is something that changes place or position but it never changes its size. for example you can flippe a triangle's position and it will remind the same but it just changes place or position .

I hope this helps .

Answer:

A B E

Step-by-step explanation:

Answer:

∠ ABC ≈ 137.9°

Step-by-step explanation:

Using the Cosine rule in Δ ABC

cos B = [tex]\frac{a^2+c^2-b^2}{2ac}[/tex]

with a = 89, b = 144, c = 65

cos B = [tex]\frac{89^2+65^2-144^2}{2(89)(65)}[/tex] = [tex]\frac{7921+4225-20736}{11570}[/tex] = [tex]\frac{-8590}{11570}[/tex] , thus

B = [tex]cos^{-1}[/tex] ( - [tex]\frac{8590}{11570}[/tex] ) ≈ 137.9° ( to the nearest tenth )

Answer:

50.27

Step-by-step explanation:

Answer:

50.27

Step-by-step explanation:

A=1 /4 πd squared

A≈50.27

Hope this helps

The circumference of Cole's bass drum is 25.12 inches.

The formula to find the circumference (C) of a circle is C = 2πr, where r is the radius and π is approximately 3.14.

Since Cole's bass drum has a radius of 4 inches, we substitute the values into the formula to get

C = 2 × 3.14 × 4 inches.

So, the circumference of Cole's drum is C = 2×3.14 × 4 = 25.12 inches.

Answer:

0.1835

Step-by-step explanation:

This question can be solved by way of binomial distribution.

Let’s have the probability of success as p which is the probability that they stay with the company for more than five years;

p = 8/100 = 0.08

probability of failure, meaning not staying is q = 1-p = 1-0.08 = 0.92

Now let’s write the expression for the binomial distribution. That would be;

probability = 12C2 * 0.08^2 * 0.92^10

= 0.1835

Probabilities are used to determine the chances of an event.

The probability that exactly two stays more than 5 years is 0.1835

The given parameters are:

[tex]\mathbf{n = 12}[/tex] ---- sample

[tex]\mathbf{x = 2}[/tex] --- selected

[tex]\mathbf{p = 80\%}[/tex] --- sample proportion

So, the probability that exactly two stays more than 5 years is calculated using the following binomial probability:

[tex]\mathbf{P(x) = ^nC_x p^x (1 - p)^{n -x}}[/tex]

So, we have:

[tex]\mathbf{P(x) = ^{12}C_2 (8\%)^2 (1 - 8\%)^{12 -2}}[/tex]

[tex]\mathbf{P(x) = ^{12}C_2 (8\%)^2 (92\%)^{10}}[/tex]

Solve 12C2 using a calculator

[tex]\mathbf{P(x = 2) = 66 \times (8\%)^2 \times (92\%)^{10}}[/tex]

[tex]\mathbf{P(x = 2) = 0.1835}[/tex]

Hence, the probability that exactly two stays more than 5 years is 0.1835

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Answer:

j=70

im sure of it

Answer:

j = 70

Step-by-step explanation:

j + j - 60 = 80

=> 2j - 60 = 80

=> 2j = 80 + 60

=> 2j = 140

=> j = 140/2

=> j = 70

Answer:

15(2a - 2)= 5(a2 - 1)

The simplified form of the given equation is 5a²-30a-31=0.

The given equation is 15/(a²-1)=5/(2a-2).

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

By cross-multiplying we get,

15/(a²-1)=5/(2a-2)

⇒ 15(2a-2)=5(a²-1)

⇒ 30a-30=5a²-1

⇒ 5a²-30a-31=0

Therefore, the simplified form of the given equation is 5a²-30a-31=0.

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Answer:

Niles and Bob were traveling for 6 hours.

Step-by-step explanation:

The speed or rate at which an object is moving can be computed using the formula:

[tex]s=\frac{d}{t}[/tex]

Here:

s = speed

d = distance traveled

t = time taken

It is provided that Niles and Bob sailed at the same time for the same length of time.

Speed of Niles sailboat is, s₁ = 6 mph.

Distance traveled by Niles' sailboat is, d₁ = 36 miles.

Speed of Bob's sailboat is, s₂ = 16 mph.

Distance traveled by Bob's sailboat is, d₂ = 96 miles.

It took both Niles and Bob the same time to travel the respective distance.

Compute the time it took Niles to travel 36 miles at 6 mph speed as follows:

[tex]t_{1}=\frac{d_{1}}{s_{1}}[/tex]

   [tex]=\frac{36}{6}\\=6[/tex]

It took Niles 6 hours to travel 36 miles at 6 mph speed.

Compute the time it took Bob to travel 96 miles at 16 mph speed as follows:

[tex]t_{2}=\frac{d_{2}}{s_{2}}[/tex]

   [tex]=\frac{96}{16}\\=6[/tex]

It took Bob 6 hours to travel 96 miles at 16 mph speed.

Thus, Niles and Bob were traveling for 6 hours.

Answer:

Brad picked 130 apples. Andy picked 45 apples. Krystal picked 115 apples.

Step-by-step explanation:

B = 2Y                A = Y - 20            K = Y + 50        B + A + K + Y = 355

130 = 2(65)        45 = 65 - 20        115 = 65 + 50     130 + 45 = 115 + 65 = 355

130 = 130           45 = 45                115 = 115      

If this answer is correct, please make me Brainliest!

Answer:

36 km

Step-by-step explanation:

Let time taken by upstream=x hours

Upstream speed=12 km/h

Time spend  for sightseeing=2 hours

Total time=7 hours

Traveling time=7-2=5 hours

Time taken by downstream=5-x

Downstream speed=18km/h

Distance=[tex]speed\times time[/tex]

Using the formula

Distance traveled when Delta Duchess paddled upstream=12 x

Distance traveled when  Delta Duchess paddled back=18(5-x)

According to question

[tex]12x=18(5-x)[/tex]

[tex]12x=90-18x[/tex]

[tex]12x+18x=90[/tex]

[tex]30x=90[/tex]

[tex]x=\frac{90}{30}=3 hours[/tex]

Substitute the values

Distance traveled when Delta Duchess paddled upstream=[tex]12\times 3=36 km[/tex]

Answer:

Total amount paid for the Car=$24,832

Finance Charge=$2,382

Step-by-step explanation:

Down payment on the Car=$2800

Number of Monthly Installments=36

Amount Paid Per Installment=$612

Total Monthly Installment Paid=36*$612=$22032

Therefore, the Total Amount Paid for the Car=Down Payment+Total Installmental Payment=2800+22032=$24,832

Next, we determine the finance charge.

Finance Charge=Total Amount Paid for the Car - Delivered Price of the Car

=24832-22450

=$2,382

Therefore:

Total amount paid for the Car=$24,832

Finance Charge=$2,382

Answer:

316

Step-by-step explanation:

The question has a little problem:

"the probability that they chose the same book is m n for relatively prime positive integers m and n. Compute 100m + n."

The correct sentence:

the probability that they chose the same book is "m/n" for relatively prime positive integers m and n.

Total number of books = 4

We have:

Number of 200page book = 1

Number of 400page book = 1

Number of 600page book = 1

Number of 800page book = 1

Probability of picking same book:

Velma read page 122 of her book Daphne read page 304 of her book

If it is same book, it must contain atleast 400page.

Therefore, 400page, 600page and 800 page would be considered in the probability.

Pr(one 400page) = 1/4

Pr(picking two 400page) = 1/4 * 1/4 = 1/16

Pr(one 600page) = 1/4

Pr(picking two 600page) = 1/4 * 1/4 = 1/16

Pr(one 800page) = 1/4

Pr(picking two 800page) = 1/4 * 1/4 = 1/16

Pr(picking same book page)=

Pr(picking two 400page) or Pr(picking two 600page) or Pr(picking two 800page)

= Pr(picking two 400page) + Pr(picking two 600page) + Pr(picking two 800page) = 1/16+ 1/16+ 1/16

Pr(picking same book page)= 3/16

This answer satisfies the probability as m/n for relatively prime positive integers m and n.

Two numbers are said to be relatively prime integers if the only positive integer that divides both of them is 1. It means the numerator and denominator of the fraction have been reduced to the lowest form.

m/n = 3/16

m = 3, n= 16

100m + n = 100(3) + 16

= 316

Answer:

100m+n = 6425

Step-by-step explanation:

Let X be the book Velma picks and Y the book that Daphne picks. Note that X and Y are independent and identically distributed, so for computations, i will just focus on X for now.

Lets denote with A, B, C and D the books with 200, 400, 600 and 800 pages respectively.

Note that, without any restriction P(X=A) = P(X=B) = P(X=C) = P(X=D) = 1/4. However, if we also add the condition that R = 122, where R is the page picked, we will need to apply the Bayes formula. For example,[tex]P(X=A|R=122) = \frac{P(R = 122|X=A)*P(X=A)}{P(R=122)}[/tex]

P(X=A) is 1/4 as we know, and the probability P(R=122|X=A) is basically the probability of pick a specific page from the book of 200 pages long, which is 1/200 (Note however, that if he had that R were greater than 200, then the result would be 0).

We still need to compute P(R=122), which will be needed in every conditional probability we will calcultate. In order to compute P(R=122) we will use the Theorem of Total Probability, in other words, we will divide the event R=122 in disjoint conditions cover all possible putcomes. In this case, we will divide on wheather X=A,  X=B, X=C or X=D.

[tex]P(R=122) = P(R=122 | X=A)*P(X=A) + P(R=122|X=B)*P(X=B)+P(R=122|X=C)*P(X=C)+P(R=122|X=D)*P(X=D) = 1/200 * 1/4 + 1/400*1/4 + 1/600*1/4+1/800*1/4 = 1/4*(12/2400 + 6/2400 + 4/2400 + 3/2400) = 1/384[/tex]

Thus, P(R=122) = 1/396

With this in mind, we obtain that

[tex]P(X=A|R=122) = \frac{\frac{1}{200}*\frac{1}{4}}{\frac{1}{396}} = \frac{384}{800} = \frac{12}{25}[/tex]

In a similar way, we can calculate the different values that X can take given that R = 122. The computation is exactly the same except that for example P(R=122|X=B), is 1/400 and not 1/200 because B has 400 pages.

[tex]P(X=B|R=122) = \frac{\frac{1}{400}*\frac{1}{4}}{\frac{1}{384}} = \frac{384}{1600} = \frac{6}{25}[/tex]

[tex]P(X=C|R=122) = \frac{\frac{1}{600}*\frac{1}{4}}{\frac{1}{384}} = \frac{384}{2400} = \frac{4}{25}[/tex]

[tex]P(X=D|R=122) = \frac{\frac{1}{800}*\frac{1}{4}}{\frac{1}{384}} = \frac{384}{3200} = \frac{3}{25}[/tex]

We can make the same computations to calculate the probability of Y = A,B,C or D, given that R=304. However, P(Y=A|R=304) will be 0 because A only has 200 pages (similarly, P(R=304|Y=A) = 0, R=304 and Y=A are not compatible events). First, lets compute the probability that R is 304.

[tex]P(R=304) = P(R=304|Y=A)*P(Y=A)+P(R=304|Y=B)*P(Y=B)+P(R=304|Y=C)*P(Y=C)+P(R=304|Y=D)*P(Y=D) = 0+1/400*1/4+1/600*1/4+1/800*1/4 = 13/9600[/tex]

Thus, P(R=304) = 13/9600. Now, lets compute each of the conditional probabilities

[tex] P(Y=A|R=304) = 0[/tex] (as we stated before)

[tex]P(Y=B|R=304) = \frac{\frac{1}{400}*\frac{1}{4}}{\frac{13}{9600}} = \frac{9600}{1600*13} = \frac{6}{13}[/tex]

[tex]P(Y=C|R=304) = \frac{\frac{1}{600}*\frac{1}{4}}{\frac{13}{9600}} = \frac{9600}{2400*13} = \frac{4}{13}[/tex]

[tex]P(Y=D|R=304) = \frac{\frac{1}{800}*\frac{1}{4}}{\frac{13}{9600}} = \frac{9600}{3200*13} = \frac{3}{13}[/tex]

We want P(X=Y) given that [tex] R_x = 122 [/tex] and [tex] R_y = 304 [/tex] (we put a subindex to specify which R goes to each variable). We will remove the conditionals to ease computations, but keep in mind that we are using them. For X to be equal to Y there are 3 possibilities: X=Y=B, X=Y=C and X=Y=D (remember that Y cant be A given that [tex] R_y = 304). Using independence, we can split the probability into a multiplication.

[tex] P(X=Y=B) = P(X=B|R=122)*P(Y=B|R=304) = \frac{6}{25} * \frac{6}{13} = \frac{36}{325} [/tex]

[tex] P(X=Y=C) = P(X=C|R=122)*P(Y=C|R=304) = \frac{4}{25}*\frac{4}{13} = \frac{16}{325} [/tex]

[tex] P(X=Y=D) = P(X=D|R=122)*P(Y=D|R=304) = \frac{3}{25}*\frac{3}{13} = \frac{9}{325} [/tex]

Therefore

[tex] P(X=Y) = \frac{36}{325} + \frac{16}{325} + \frac{9}{325} = \frac{61}{325} [/tex]

61 is prime and 325 = 25*13, thus, they are coprime. Therefore, we conclude that m = 61, n = 325, and thus, 100m+n = 6425.

Answer:

Price decrease = 24 %

Step-by-step explanation:

Given:

Initial price of the 60 inch television = $ 1050

Final price of the same television = $ 798

We have to find by what percent did the price of the television decrease.

Let the percent decrease be "x".

Formula to be used:

⇒ [tex]Percent\ decrease =\frac{(Initial\ price) - (Final\ price)}{Initial\ price}\times 100[/tex]

Using the above formula:

And plugging the values.

⇒ [tex]\%\ decrease =\frac{(Initial\ price) - (Final\ price)}{Initial\ price}\times 100[/tex]

⇒ [tex]\%\ decrease =\frac{(1050) - (798)}{1050}\times 100[/tex]

⇒ [tex]\%\ decrease =\frac{252}{1050}\times 100[/tex]

⇒ [tex]\%\ decrease =0.24\times 100[/tex]

⇒ [tex]\%\ decrease =24[/tex]

By 24 percent did the price of the television decreases.

Answer:

D

Step-by-step explanation:

The range of the data is 10.

Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.

The range of the data can be determined by finding the difference between the maximum and minimum values.

The maximum value is given by the upper whisker, which is 15, and

the minimum value is given by the lower whisker, which is 5.

Therefore, the range of the data is:

Maximum value - Minimum value = 15 - 5 = 10

So, the range of the data is 10.

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Answer:

a= 11rad6/2

Step-by-step explanation:

sin45=a/11rad3

Answer:

1) first two (A & B)

2. -1,533

Step-by-step explanation:

Sum to infinity is finite when

-1 < r < 1

Option 1: r = -¼

Option 2: r = 27/81 = ⅓

Option 3: r = 3/2

Option 4: r = 17.75/7.1 = 2.5

a = -3

r = -6/-3 = 2

S9 = -3 × (2⁹ - 1)/(2 - 1)

= -1533

Answer:

-7/3 pi radians

Step-by-step explanation:

To convert from degrees to radians, multiply by pi/180

-420 * pi/180

-42/18 *pi

Divide by 6 on the top and bottom

-7/3 pi

Answer:

The area of the larger circle is 9 times greater than that of the smaller circle.

Step-by-step explanation:

Let d be the diameter of the smaller circle and d be the diameter of the larger circle. If d₁ = 3d

Since Area of a circle A = πd²/4 ⇒ A ∝ d²

Let A be the area of the smaller circle and A₁ be the area of the larger circle.

So, A₁/A = d₁²/d² = (3d)²/d² = 9

A₁/A = 9

A₁ = 9A

So the area of the larger circle is 9 times greater than that of the smaller circle.

Answer:

9 times greater

Step-by-step explanation:

Let radius of small circle b r

radius of big circle = 3×(r) = 3r

Area of small circle  = πr²

Area of big circle = π(3r)² = 9πr²

How many times area of big circle is larger = 9πr²/ πr² = 9

The set 2 contains an outlier.

The range measure of spread was most impacted by the outlier.

A box and whisker plot displays a "box" with its left edge at Q₁, right edge at Q₃, "center" at Q₂ (the median), and "whiskers" at the maximum and minimum.

Given:

Set 1: 8, 15, 13, 7, 11, 17, 13

Median = 13

Lower quartile = 8

Upper quartile = 15

Range = 10

Interquartile range = 7

And Set 2: 8, 15, 13, 7, 11, 17, 13, 100

Median = 13

Lower quartile = 9.5

Upper quartile = 16

Range = 93

Interquartile range = 6.5

Set two contains the value 100 as an outlier.

The range is the component of spread that was most adversely affected by the outlier.

This is due to the fact that set two's median, quartiles, and interquartile range are all closely clustered together, but the range is 93, which is extremely disproportional high compared to any of those other numbers.

Therefore, set 2 contains an outlier.

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You can construct a pie chart by calculating the percentage each item contributes to the total in your table. Each percentage point represents a slice of the pie, with the size of the slice proportional to the percentage of the total.

In a pie graph, each slice of the pie represents a share of the total, or a percentage. For example, 50% would be half of the pie and 20% would be one-fifth of the pie. The pie graphs allow you to get a feel for the relative size of the different historical data sets.

To create your pie chart based on your table, you will want to find the percentage of the total that each holiday destination in your table represents. Once you've calculated these percentages, you can begin creating your pie chart. Each slice of your pie will correlate to a holiday destination, with the size of the slice representative of the percentage of people that chose that destination.

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Step-by-step explanation:

Given

it is a right angled triangle so

with reference angle x

hypotenuse (h) = 12

base (b) = 5

Now

cos x = b / h

cos x = 5 / 12

x = cos ^-1 ( 5/12)

Therefore x = 65.4°

Hope it will help :)

Answer:

Step-by-step explanation:

Answer:

cant

Step-by-step explanation:

Answer:

Correct answer:  x = 217

Step-by-step explanation:

Given:

N = 350 customers

62%  made additional purchases

x = ?  the number of customers that is made additional purchases

Solution is:

x = (62 / 100) · 350 = 217

x = 217

God is with you!!!

Answer:

R(t)=401−10t

Step-by-step explanation:

Given the data, there appears to be a negative linear relationship between time and radius as the balloon deflates. This suggests a model of the form R(t) = a - bt best fits the data.

The subject matter here is a Mathematical topic related to model fitting - a statistical method that estimates the relationship between variables. In this case, the variables are Time (t) and radius (R). From the given data, it seems that the radius is reducing as the time increases, which likely indicates a negative linear relationship.

We can also observe that the data points reduce at a constant rate (e.g., it goes down by 50 cm every 5 seconds initially), which further supports the idea of a linear model.

Therefore, considering this rate of change and the mathematical relationship between the variables, a linear model of the form R(t) = a - bt (where a is the initial radius and b is the rate of decrease) would likely be the best option.

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Answer: 34.25

Step-by-step explanation:

Answer:

34.3 the real answer is 34.25 but rounded it is 34.3