brenna goes on a cave tour with her family.she spots a mysterious crystal that is shaped like a cube the crystal has edge lengths of 5 centimeters what is the volume of the crystal

The width of the river using the similar triangle is 43.3 metres.

The surveyor wants to determine the width of the river . Let's use the pair of similar triangle to find the width of the river.

Therefore, two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion.

Hence, let's find the width of the river.

Therefore,

18.6 / 34.2 = AB / 79.6

cross multiply

18.6 × 79.6 = 34.2 AB

34.2 AB = 1480.56

divide both sides of the equation by 34.2

AB = 1480.56 / 34.2

AB = 43.2912280702

AB = 43.3 metres

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Answer:

x=2, x=-3

Step-by-step explanation:

The rate at which the volume of the cylinder is changing at that moment is 1200π mm³/min.

The rate at which the surface area of the cylinder is changing at that moment is 240π mm²/min.

The rate at which the volume and surface area of a cylinder are changing, we can use the given information and the formulas for volume and surface area.

Given:

Rate of change of the radius, dr/dt = 3 mm/min

Height, h = 20 mm

Radius at the moment of interest, r = 10 mm

Rate of change of volume (dV/dt):

The formula for the volume of a cylinder is V = πr²h.

Differentiating both sides with respect to time (t), we get:

dV/dt = 2πrh(dr/dt) + πr²(dh/dt)

Since the height (h) is constant, dh/dt = 0.

Substituting the given values:

dV/dt = 2π(10)(20)(3) + π(10)²(0)

dV/dt = 1200π + 0

dV/dt = 1200π mm³/min

Rate of change of surface area (dA/dt):

The formula for the surface area of a cylinder is A = 2πrh + 2πr².

Differentiating both sides with respect to time (t), we get:

dA/dt = 2πr(dh/dt) + 2πh(dr/dt) + 4πr(dr/dt)

Again, since the height (h) is constant, dh/dt = 0.

Substituting the given values:

dA/dt = 2π(10)(0) + 2π(20)(3) + 4π(10)(3)

dA/dt = 0 + 120π + 120π

dA/dt = 240π mm²/min

Your calculations were correct.

The rate of change of volume is 1200π mm³/min, and the rate of change of surface area is 240π mm²/min.

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a. The rate at which the volume of the cylinder is changing when the radius is 10 mm is 1200π mm³/min.

b. The rate at which the surface area of the cylinder is changing when the radius is 10 mm is 120π mm²/min.

To find the rate at which the volume and surface area of the cylinder are changing, we can use the formulas for volume and surface area of a cylinder and apply the chain rule of differentiation.

Given:

Rate of change of radius (dr/dt) = 3 mm/min

Height (h) = 20 mm

Radius (r) = 10 mm

1. Rate of change of volume (dV/dt):

Volume (V) = πr²h

Differentiating both sides with respect to time (t):

dV/dt = d/dt (πr²h)

Using the chain rule:

dV/dt = 2πrh(dr/dt) + πr²(dh/dt)

Substituting the given values:

dV/dt = 2π(10)(20)(3) + π(10²)(0)

dV/dt = 1200π + 0

dV/dt = 1200π mm³/min

Therefore, the rate at which the volume of the cylinder is changing when the radius is 10 mm is 1200π mm³/min.

2. Rate of change of surface area (dSA/dt):

Surface Area (SA) = 2πrh + 2πr²

Differentiating both sides with respect to time (t):

dSA/dt = d/dt (2πrh + 2πr²)

Using the chain rule:

dSA/dt = 2πh(dr/dt) + 2πr(dh/dt)

Substituting the given values:

dSA/dt = 2π(20)(3) + 2π(10)(0)

dSA/dt = 120π + 0

dSA/dt = 120π mm²/min

Therefore, the rate at which the surface area of the cylinder is changing when the radius is 10 mm is 120π mm²/min.

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The closest projection will have a value of -29/360.

we will follow these steps to use the Gram-Schmidt orthonormalization procedure for producing an orthonormal basis for the subspace spanned by 1, x, and x²,

Set u₁ = 1, a unit vector.

Set v₂ = x and u₂ = v₂ / ||v₂||.

Set v₃ = x² - (x², u₁)u₁ - (x², u₂)u₂, and u₃ = v₃ / ||v₃||.

Thus we get the orthonormal basis for the subspace spanned by 1, x, and x² to be {u₁, u₂, u₃}.

Now we will use the formula for the projection of a vector onto a subspace to find the closest-point projection of x³ into this subspace,

proj_subspace(x³) = (x³, u₁)u₁ + (x³, u₂)u₂ + (x³, u₃)u₃

The inner products will be calculated as follows:

(x³, u₁) = ∫x³ X 1 dx = 1/4

(x³, u₂) = ∫ x³ X x dx = 1/5

(x³, u₃) = ∫ x³ * (x² - (x², u₁)u₁ - (x², u₂)u₂) dx

Here all the integrals will have limits of 0 and 1.

Hence we get

= 1/9 - 1/4 X 1/2 - 1/5 X 1/3

= 1/9 - 1/8 - 1/15

= (40 - 45 - 24)/360

= -29/360

Thus, the projection of x³ onto the subspace spanned by 1, x, and x² is:

proj_subspace(x³) = 1/4 X u₁ + 1/5 X u₂ + (1/9 - 1/4 X 1/2 - 1/5 X 1/3) X u₃

This projection is the closest point in the subspace to x³, in the sense that the distance between x³ and proj_subspace(x³) is minimized.

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The coordinates of the resulting point, E' are (-3, -5)

The point is given as:

E = (3, -5)

The reflection is given as:

Reflection across the y-axis

The rule of reflection across the y-axis is

(x, y) = (-x, y)

So, we have:

E' = (-3, -5)

Hence, the coordinates of the resulting point, E' are (-3, -5)

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Answer:

Substitute the value of the variable into the expression and simplify.

121

Step-by-step explanation:

Step-by-step explanation:

(y + z)^2

substitute in the given

y = -8, z = 19

(-8 + 19)^2

(11)^2

121

Hope this helps :)

Answer:

x=3y

y=x

3

Step-by-step explanation:

x-3y=2 equation 1

-2x+6y=2 equation 2

x-3y= -2x+6y

x+2x=6y+3y

3x=9y

x=3y

x-3y= 2

3y-3y=2

0≠2

-2x+6y=2

-2(3y)+6y=2

-6y+6y=2

0≠2

The solutions to the equation 1x² - 16x = 20 are x = 8 + 2√21 and x = 8 - 2√21.

To solve the quadratic equation 1x² - 16x = 20, we need to rearrange it into the standard form ax² + bx + c = 0. Let's simplify the equation step by step:

1x² - 16x = 20

First, move all terms to one side of the equation:

1x² - 16x - 20 = 0

Now we have a quadratic equation in the standard form. To solve it, we can use factoring, completing the square, or the quadratic formula. In this case, factoring may not be straightforward, so let's use the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a)

For our equation, a = 1, b = -16, and c = -20. Substituting these values into the quadratic formula:

x = (-(-16) ± √((-16)² - 4(1)(-20))) / (2(1))

Simplifying further:

x = (16 ± √(256 + 80)) / 2

x = (16 ± √336) / 2

x = (16 ± √(16 * 21)) / 2

x = (16 ± 4√21) / 2

Simplifying:

x = 8 ± 2√21

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The value of y in simplest form for the point P = (1/2, y) lying on the unit circle is y = ± √(3)/2.

To find the value of y in simplest form for the point P = (1/2, y) lying on the unit circle, we can use the equation of the unit circle, which states that for any point (x, y) on the unit circle, the following equation holds: x^2 + y^2 = 1.

Plugging in the coordinates of the point P = (1/2, y), we get:

(1/2)^2 + y^2 = 1

1/4 + y^2 = 1

y^2 = 1 - 1/4

y^2 = 3/4.

To simplify y^2 = 3/4, we take the square root of both sides:y = ± √(3/4).

Now, we need to simplify √(3/4). Since 3 and 4 share a common factor of 1, we can simplify further: y = ± √(3/4) = ± √(3)/√(4) = ± √(3)/2.

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Answer:

\(\boxed{\sf \ \ 25 \ \ }\)

Step-by-step explanation:

Hello,

we can see that

\(x^2-10x = x^2-2*5x\)

is the beginning of

\(x^2-2*5x+5^2=(x-5)^2\)

so we must add 5*5=25 to both sides of the equation to make the left side a perfect square trinomial

hope this helps

Answer:

25.

Step-by-step explanation:

To find the value that will make the left side a perfect-square trinomial, you need to find (b/2)^2. In this case, b = -10.

(-10 / 2)^2

= (-5)^2

= (-5) * (-5)

= 25

Once you add 25 to both sides, the left side becomes x^2 - 10x + 25, which is equal to (x - 5)^2.

Hope this helps!

Answer:

we have

y=16-4x²

4x²=16

x²=\(\frac{16}{4}\)

x=\(\sqrt{4}\)

x=±2

Let's do

Let y be 0

Answer:

All real numbers

Step-by-step explanation:

The domain of the function is the set of real values that can be substituted into a function to produce a valid output. Any real number can be substituted into the function (y = x), and produce a valid output. Thus, the domain is all real numbers.

Answer:

number is 5

Step-by-step explanation:

let the number be n, then

30 subtracted from 14 times the number is

14n - 30

the result is 20 more than 4 times the number, that is

4n + 20

the equation is then

14n - 30 = 4n + 20 ( subtract 4n from both sides )

10n - 30 = 20 ( add 30 to both sides )

10n = 50 ( divide both sides by 10 )

n = 5

the number is then 5

Answer:

9/10 bc it would be .90 in decimals

Step-by-step explanation:

Answer:

9/10 is

Step-by-step explanation:

9/10 as a decimal is 0.9 and if you line them up, 0.9 is greater than 0.45

Answer:

They paid her $23 at most

Step-by-step explanation: 4+12+7=23

Answer:

Ken;

Step-by-step explanation:

Ken grew 4/5 of an inch. 4/5=0.8

Sang grew 3/8 of an inch. 3/8= 0.375

0.8 > 0.375 so Ken grew more.

0.8 - 0.375 = 0.425

So, Ken grew 0.425 more inches than Sang grew. 0.425 is also the same thing as 17/40.

To find the distance above the ground at which the tack is, we need to calculate the vertical displacement of the front wheel when the tack was picked up.

First, let's determine the circumference of the front wheel. The circumference of a circle is given by the formula C = πd, where C is the circumference and d is the diameter. Given that the diameter is 26 inches, we can calculate the circumference:

C = π × 26

C ≈ 81.64 inches

This means that for every complete revolution of the wheel, Devon travels a distance of approximately 81.64 inches.

Next, we need to determine how many complete revolutions the front wheel made as Devon rolled another 100 feet (1200 inches). Since the circumference of the wheel is 81.64 inches, we can divide 1200 inches by 81.64 inches to find the number of revolutions:

1200 / 81.64 ≈ 14.68 revolutions

Now, we know that the tack was picked up after one full revolution. Therefore, out of the 14.68 revolutions, 13 complete revolutions have occurred. The tack is located at the point where the 14th revolution starts.

Since each revolution covers a distance equal to the circumference of the wheel, the vertical displacement of the tack is the height of the wheel, which is the radius of the wheel. The radius is half the diameter, so in this case, it is 26 / 2 = 13 inches.

Therefore, the tack is located 13 inches above the ground.

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Answer:

3

Step-by-step explanation:

Usually, when there is contamination the smallest amount can have huge ramifications in the data collected. In this scenario, if in a "clean" environment the trait is found in 2/10 frogs then anything above this number should be considered contaminated. This is because data above this ratio would be considered uncommon or rare and this unique occurrence can be most likely tied to the only new factor which would be the contamination. Therefore the minimum number of frogs with this trait in the sample would be 3.

The solution is,  2.5 miles per hour was her walking rate in miles per hour.

We know that,

Speed is measured as distance moved over time.

The formula for speed is speed = distance ÷ time.

To work out what the units are for speed, you need to know the units for distance and time.

In this example, distance is in metres (m) and time is in seconds (s), so the units will be in metres per second (m/s).

Speed = Distance/ Time.

Here, given that,

Bao walked 15 miles in 6 hours.

so, we get,

in 6 hours = 15 miles

so, in 1 hour = 15 / 6 miles

                    =2.5 miles

Hence, The solution is,  2.5 miles per hour was her walking rate in miles per hour.

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Answer:

Four hundred thirdy seven and six hundred and eight thousandths.

437.068

Step-by-step explanation:

Hope it helps! =D

The number formed by these terms is 437.068.

To solve this problem, we first need to understand the place value system and what each term represents.

As per the place value system used in decimals:

- Hundreds: It is the third digit to the left of the decimal point and each unit represents 100.
- Tens: It is the second digit to the left of the decimal point and each unit represents 10.
- Ones: It is right next to the decimal point, all the digits to the left of it are the ones. Each unit represents 1.
- Hundredths: It is the second digit to the right of the decimal point and each unit represents 0.01.
- Thousandths: It is the third digit to the right of the decimal point and each unit represents 0.001.

In the given context, we know that there are 4 hundreds, 3 tens, 7 ones, 6 hundredths, and 8 thousandths.

To start, we calculate each term separately:

- 4 hundreds = 4 x 100 = 400
- 3 tens = 3 x 10 = 30
- 7 ones = 7 x 1 = 7
- 6 hundredths = 6 x 0.01 = 0.06
- 8 thousandths = 8 x 0.001 = 0.008

After evaluating each term separately, we sum them up together for the final answer:

- Sum = 400 + 30 + 7 + 0.06 + 0.008 = 437.068

Hence, the number formed by these terms is 437.068.

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Your question is not complete, however, I have provided answers to it by suggesting that the question goes like this;

Twelve different video games showing drug use were observed. The duration times of drug use​ (in seconds) were recorded. When using this sample for a t test of the claim that the population mean is greater than 85​sec, what does df​ denote, and what is its​ value

Answer:

df denote degree of freedom.

degree of freedom df is 11.

Step-by-step explanation:

what does df​ denote?

df denote degree of freedom

To find it value,

we have twelve different video games showing drug use, then, it means that the sample size "n" is 12

the degree of freedom is 1 < n ( i.e, one less than sample size)

df = n -1 = 12 -1 = 11

So, degree of freedom df is 11.

Note; use your sample size to solve the question as I don't know the exact value you were given. Thanks.

As per the given data, the number of integers in R ∩ S is 2, and the correct answer is (B) Two.

In mathematics, the intersection of two sets is a set containing all elements that are members of both sets.

In symbols, the intersection of two sets A and B is denoted by A ∩ B, and it contains all elements that belong to both A and B.

The intersection of two sets contains only the elements that are present in both sets. In this case,

R ∩ S = {x | x > 0 and x < 3}

The integers that are present in this set are 1 and 2.

Therefore, the number of integers in R ∩ S is 2, and the correct answer is (B) Two.

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Answer:

\( \pink{ \rm{SOLUTION:-}}\)

\( \pink{ \rm{Here,}}\)

\(\boxed{162}\) can be a perfect square if the factor \(\boxed{2}\) is a paired.

Hence,\(\boxed{162×2}\),will be a perfect square.

\(: \implies{324 = {3}^{2} \times {3}^{2} \times {2}^{2} }\)

Hence,the square root is \(3×3×2,i.e. 18\)

\({\rm{162 \: must \: be \: multiplied \: by \: 2 \: to \: make \: it \: a \: perfect \: square.}}\)

Answer:

2

Step-by-step explanation:

\(\\ \rm\Rrightarrow \sqrt{162}\)

\(\\ \rm\Rrightarrow \sqrt{2\times 3\times 3\times 3\times 3}\)

Now there is one 2 left .

We need another 2

So we get

\(\\ \rm\Rrightarrow 2(3)(3)\)

Answer:

A

Step-by-step explanation:

DE is the shortest side because it's is opposite to the smallest angle (<F)

180 - 60 = 3X +2X + 5,

X = 23

<F = 2*(23) +5 = 51

The mean could be used to describe a data set by itself, while interquartile range would almost never be used to describe a data set by itself.

These are operations which are used to summarize certain characteristics a set of data has.

Mean and range deals with the full set of data while interquartile range measures just the middle half of the data and is denoted as option A.

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Answer:

(2) 6x^2+40x +50

Step-by-step explanation:

(4x+10)*(2x+5) = 8x^2 +40+50

minus 2x^2

=6x^2 +40 +50

Answer:

1 - Paco

2 - Tim

3 - Jenny

4 - Maria

Step-by-step explanation:

Tim will not be in positions 1 or 4, as 1 and 4 represent the ends of the line.  Jenny cannot be in positions 1 or 4, as she is between two people.  Paco will not be in positions 2 or 4, as he is only in an odd numbered position. Maria will be in position 4, as none of the other three can be at position 4.  Paco will be in position 1, as Tim and Jenny cannot be at position 1.  The two positions left are 2 and 3. We'll assume that 1 represents the front of the line. Since Tim has to be in front of Jenny, he will take the position with the lower number, which is 2. This leaves Jenny with 3.