a child's weight at age 6 is 200% what it was at age 3. By what percent did the child's weight increase by

The $1314^\text{th}$ digit past the decimal point is 2.

To find the $1314^\text{th}$ digit past the decimal point in the decimal expansion of $\frac{5}{14}$, we can use long division to compute the decimal expansion of the fraction.

The long division of $\frac{5}{14}$ is as follows:

```

0.35    <-- Quotient

-----

14 | 5.00

   4.2    <-- Subtract: 5 - (14 * 0.3)

   -----

     80   <-- Bring down the 0

     70    <-- Subtract: 80 - (14 * 5)

     -----

     100   <-- Bring down the 0

      98    <-- Subtract: 100 - (14 * 7)

      -----

       20   <-- Bring down the 0

       14    <-- Subtract: 20 - (14 * 1)

       -----

        60   <-- Bring down the 0

        56    <-- Subtract: 60 - (14 * 4)

        -----

         40   <-- Bring down the 0

         28    <-- Subtract: 40 - (14 * 2)

         -----

         120   <-- Bring down the 0

         112    <-- Subtract: 120 - (14 * 8)

         -----

           80   <-- Bring down the 0

           70    <-- Subtract: 80 - (14 * 5)

           -----

           ...

```

We can see that the decimal expansion of $\frac{5}{14}$ is a repeating decimal pattern with a repeating block of digits 285714. Therefore, the $1314^\text{th}$ digit past the decimal point is the same as the $1314 \mod 6 = 0^\text{th}$ digit in the repeating block.

Since $1314 \mod 6 = 0$, the $1314^\text{th}$ digit past the decimal point in the decimal expansion of $\frac{5}{14}$ is the first digit of the repeating block, which is 2.

So, the $1314^\text{th}$ digit past the decimal point is 2.

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Answer:

y² +9y

Step-by-step explanation:

base = y +9

height = 2y

\(\sf \text{Area of triangle = $\dfrac{base *height}{2}$}\)

                         \(\sf =\dfrac{(y+9)*2y}{2}\\\\ = (y + 9) * y\)

                         \(\sf = y*y + 9*y\\\\ = y^2 + 9y\)

The Value is`9 + 9 tan^2(A) = 25`.

We know that:

`cos^2(A) + sin^2(A) = 1`

Squaring both sides of `cos(A) = 3/5`, we get:

`cos^2(A) = 9/25`

Substituting into the first equation, we get:

`9/25 + sin^2(A) = 1`

Solving for `sin^2(A)`, we get:

`sin^2(A) = 16/25`

Taking the square root of both sides, we get:

`sin(A) = ±4/5`

Since `cos(A) = 3/5` and `cos(A) > 0`, we have `sin(A) = 4/5`.

Therefore, `tan(A) = sin(A)/cos(A) = 4/3`.

Now, we can use the identity:

`tan^2(A) + 1 = sec^2(A)`

Substituting `tan(A) = 4/3`, we get:

`16/9 + 1 = sec^2(A)`

Simplifying, we get:

`25/9 = sec^2(A)`

Taking the square root of both sides, we get:

`5/3 = sec(A)`

Finally, we can use the identity:

`sec^2(A) - 1 = tan^2(A)`

Substituting `sec(A) = 5/3`, we get:

`(5/3)^2 - 1 = tan^2(A)`

Simplifying, we get:

`16/9 = tan^2(A)`

Multiplying both sides by 9, we get:

`16 = 9 tan^2(A)`

Adding 9 to both sides, we get:

`25 = 9 + 9 tan^2(A)`

Therefore, `9 + 9 tan^2(A) = 25`.

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The null hypothesis get rejected comparing the 95% confidence interval to the proportion of the given central valley residents and bay area residents .

As given in the question,

Total number of voters in California = 7525

x₁ = Number of voters of central valley residents approved California legislature

   = 68

n₁ = Total number of voters of central valley residents

   = 200

x₂ = Number of voters of bay area residents approved California legislature

   = 156

n₂= Total number of voters of bay area residents

   = 300

p₁ = proportion of voters of central valley

p₂= proportion of voters of bay area

p₁ = x₁/ n₁

   = 68/200

   = 0.34

p₂ = x₂/n₂

    = 156/300

    = 0.52

Standard error = √p₁(1 -p₁) / n₁ + p₂( 1- p₂)/n₂

                        = √0.34(1-0.34) / 200 + 0.52(1-0.52)/ 300

                        = √0.001122 + 0.000832

                        = 0.044

\(p_{w}\) = (68 + 156 )/ (200 + 300)

   = 0.448

\(q_{w} = 1- p_{w}\)

    = 1 - 0.448

    = 0.552

null hypothesis p₁ - p₂ = 0

z = ( 0.52 - 0.34 ) - 0/ √(0.448)(0.552)( 1/200 + 1/300)

  = 4

Tabular value for confidence interval 95% = 1.96

4 > 1.96

We reject the null hypothesis.

Therefore, the difference of proportion of central valley residents and the bay area residents rejection of null hypothesis as per given 95% confidence interval.

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Answer:

289m²

Step-by-step explanation:

Area of circle =πr²=π×17²=289m² when r=radius =17m

The equation of the degree 6 polynomial with a root at 3, a double root at 2, and a triple root at -1, and y-intercept at y = 5 is given as follows:

y = -5/12(x - 3)(x - 2)²(x + 1)³.

The equation of the function is obtained considering the Factor Theorem, as a product of the linear factors of the function.

The zeros of the function, along with their multiplicities, are given as follows:

Then the linear factors of the function are given as follows:

The function is then defined as:

y = a(x - 3)(x - 2)²(x + 1)³.

In which a is the leading coefficient.

When x = 0, y = 5, due to the y-intercept, hence the leading coefficient a is obtained as follows:

5 = -12a

a = -5/12

Hence the polynomial is:

y = -5/12(x - 3)(x - 2)²(x + 1)³.

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Answer:

y=13

Step-by-step explanation:

y=-x+6

x=-7

substitute

y=-(-7)+6

y=13

Answer:

y = 13

Step-by-step explanation:

y = -x + 6 if x = -7

since x = -7, -x = 7:

y = 7 + 6

7 + 6 = 13:

y = 13

hope dis helps ^-^

∠SQU ≅ ∠VQT by the Vertical angles theorem.

From the figure, lines UV and WZ are parallel.

We need to arrive at the conclusion that angle VQT is congruent to angle WRS. i.e., ∠WRS ≅ ∠VQT.

So first we have the angles ∠SQU and ∠VQT. Both are vertical angles or opposite angles at Q.

The Vertical Angles Theorem states that two vertical angles are congruent to each other.

Thus, ∠SQU ≅ ∠VQT by the Vertical angles theorem.

Then we have the angles ∠SQU and ∠WRS. They are corresponding angles from the figure.

The Corresponding Angles Theorem states that two corresponding angles are congruent to each other.

Thus, ∠SQU ≅ ∠WRS by The Corresponding Angles Theorem.

Finally, ∠VQT ≅ ∠WRS by the Transitive property of Equality .

The transitivity property can be defined as if a ≅ b and b ≅ c, then a ≅ c.

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Answer:

\(\frac{2}{6} =\frac{6}{18}\)

Step-by-step explanation:

Compare the denominators. Since  6 ⋅ 3 = 18 , multiply the numerator  2  by  3  to get  6

An isosceles right triangle has a perimeter of 16 square centimeters since the hypotenuse is 8 length.

A boundary is a closed path that surrounds, delimits, or includes a two-dimensional shape or a one-dimensional length. The outermost part of a circle or an ellipse is called the perimeter. The perimeter calculation has numerous real-world applications. A shape's perimeter is the measurement of its edge's radius. Discover how to calculate the perimeter by adding together the lengths of the sides of various forms. The perimeter of any shape can be calculated by multiplying its side lengths. An object's perimeter is the region that surrounds it. A good illustration of this at your house is a closed-off garden. Its perimeter is the space encircling something. For a 50 by 50 foot yard, a 200 foot fence will be required.

given

AC (hypotenuse) = 8 cm. ,

AB^2+BC^2 = AC^2

x^2+x^2 = 8^2

2x^2 = 64

x^2= 64/2=32

x = 4.2^1/2 cm.

Perimeter = {8 +4.(2)^1/2+4.(2)^1/2}

= {8+8.(2)^1/2}

=8(1+2^1/2) cm.

Area =( base×altitude)/2= (4.2^1/2×4.2^1/2)/2 = 16sq.cm.

An isosceles right triangle has a perimeter of 16 square centimeters since the hypotenuse is 8 length.

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32 bottles are needed to poured 4 gallons of chocolate milk.

The correct option is D.

A closed surface's volume, which is expressed as a scalar quantity, measures how much three-dimensional space is enclosed. The area that a material or 3D object takes up or contains, for instance. The SI-derived cubic metre is a common unit for quantifying volume quantitatively.

Pints to Gallons Ratio: 1:8

Permit x bottles to be present.

There are x bottles required for 4 gallons of chocolate milk.

Because of the direct proportion

4/x = 1/8

x = 4 x 8

x = 32

As a result, 32 bottles are required.

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If the area of a triangle is 96 sq. inches. its altitude is 2 inches greater than five times its base then the altitude is 32 inch

The area of a triangle is 96 sq. inches

Let base be b

Its altitude is 2 inches greater than five times its base.

a=5b+2

ab/2=A

(5b+2)b/2=96

(5b+2)b=192

5b²+2b=192

5b²2+2b-192=0

On solving the quadrartic equation,

we get

b=6

a=32

Therefore, if the area of a triangle is 96 sq. inches. its altitude is 2 inches greater than five times its base then the altitude is 32 inchs

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Answer:

The answer is D

Step-by-step explanation:

A 180 rotation on 1,1 which is the center will rotate it onto itself.

Answer:

V≥10

Step-by-step explanation:

V−6≥4

Add 6 to both sides.

V≥4+6

Add 4 and 6 to get 10.

V≥10

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~Hoped this helped :)

The critical path is the path with the longest duration, which in this case is A -> B -> D -> E with a duration of 11 days.

To determine the critical path of the project, we need to find the longest path of activities that must be completed in order to finish the project on time. This is done by calculating the earliest start time (ES) and earliest finish time (EF) for each activity.

Starting with activity A, ES = 0 and EF = 4. Activity B can start immediately after A is complete, so ES = 4 and EF = 7. Activity C can start after A is complete, so ES = 4 and EF = 6. Activity D can start after B is complete, so ES = 7 and EF = 9. Finally, activity E can start after C and D are complete, so ES = 9 and EF = 11.

The variance for each activity is also given, which allows us to calculate the standard deviation and determine the probability of completing the project on time. The critical path is the path with the longest duration, which in this case is A -> B -> D -> E with a duration of 11 days.

Using the expected durations and variances, we can calculate the standard deviation of the critical path. This information can be used to determine the probability of completing the project on time.

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Answer:

The price of the oven, including tax, before the discount is applied is $336.46. This is calculated by taking the sale price of $251.85 and multiplying that by 1.25 (which is 100% + 25% discount).

The angular coordinate, angular velocity, and angular acceleration of the flywheel are: (a) At t = 0, θ = θ0 = 0.5 rad, ω = 0, and α = 12π²θ0 = 23.55 rad/s².

(b) At t = 0.125 s, θ = 0.267 rad, ω = 4.116 rad/s, and α = -69.08 rad/s².

The given equation for the angular displacement of the flywheel is θ=θ0e(-3πcos(4πt)). Here, θ0 = 0.5 rad. To find the angular velocity and angular acceleration, we need to differentiate θ with respect to time.

θ = θ0e(-3πcos(4πt))

ω = dθ/dt = -12π²θ0e(-3πcos(4πt))sin(4πt)

α = d²θ/dt² = -48π³θ0e(-3πcos(4πt))(cos(4πt) - 2)sin(4πt)

Substituting t = 0, we get:

(a) At t = 0, θ = θ0 = 0.5 rad, ω = dθ/dt = 0, and α = d²θ/dt² = 12π²θ0 = 23.55 rad/s².

(b) At t = 0.125 s, θ = 0.267 rad, ω = dθ/dt = 4.116 rad/s, and α = d²θ/dt² = -69.08 rad/s².

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Answer:

87.92 m^3

Step-by-step explanation:

Volume = 3.14r^2*h

r = 1/2 of diameter

h = 7m

Diameter = 4m so r = 2m

Let’s solve

V = 3.14(2)^2*7

V = 87.92 meters cubed.

Answer: 20

Step-by-step explanation:

a^2=b^2 - c^2. i think i could be wrong

You can find this by using the pythagorean theorem.

The Pythagorean Theorem states that the squares of the legs add up to the square of the hypotenuse.

The hypotenuse is the longest side, which is opposite the right angle.

The other 2 sides are the legs.

Here, the hypotenuse is BC which is 17.

AC is one leg. We are trying to find the other leg.

So you set up the equation AB^2+ 15^2 = 17^2.

This simplifies to AB^2 + 225 = 289.

AB^2 = 64.

AB = 8.

Answer:

your answer is -4!

Step-by-step explanation:

plz mark me brainliest

Answer:

3!!

Step-by-step explanation:

trusttttt

The 95% confidence interval for the true proportion of families that own at least one television is (0.347, 0.542).,

The formula for the confidence interval of a proportion:

CI = p ± z* (√(p*(1-p)/n))

where:

p is the sample proportion (40/90 = 0.4444)

z* is the critical value of the standard normal distribution at the 95% confidence level (1.96)

n is the sample size (90)

Substituting the  values, we have

CI = 0.4444 ± 1.96 * (√(0.4444*(1-0.4444)/90))

CI = 0.4444 ± 1.96 * (√(0.00245))

CI = 0.4444 ± 1.96 * 0.0495

CI = 0.4444 ± 0.097

Hence, the 95% confidence interval for the true proportion of families that own at least one television is (0.347, 0.542) when rounded to three decimal places.

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The solution of the given recurrence relation `T(n) = 2T(n/2) + 23n` using all three methods are:`T(n) = Θ(nlog2n)`

Given recursive relation is `T(n) = 2T(n/2) + 23n`.

We have to solve the above recursion using all three methods in any order we choose and label each solution as recursion tree, substitution, or Master Theorem.

Now, let's solve the above recursion using all three methods one by one:

1. Recursion Tree method:

To solve the above relation using recursion tree method, we will create a tree and the value of each level will be the sum of the values of all nodes present in that level or the sum of all previous levels + current level.

The tree will look like:

Therefore, the answer of the given recurrence relation `T(n) = 2T(n/2) + 23n` using the recursion tree method is:

`T(n) = Θ(nlog2n)`

2. Substitution method:

To solve the above recurrence relation using the substitution method, we can assume a solution and prove it by the Mathematical induction method.

Let `T(n) = 2T(n/2) + 23n`

Then, `T(n/2) = 2T(n/4) + 23n/2`

Also, `T(n/4) = 2T(n/8) + 23n/4`

Therefore, `T(n) = 2(2T(n/4) + 23n/2) + 23n`Or, `T(n) = 2²T(n/2²) + 23n(1 + 2)`

In general, we have `T(n) = 2kT(n/2k) + 23n(1 + 2 + ... + 2k-1)`

When `n/2k = 1`Or, `k = log2n`

Therefore, `T(n) = 2log2nT(1) + 23n(1 + 2 + ... + 2log2n-1)`Or, `T(n) = 2log2nT(1) + 23n(2log2n - 1)`

As `T(1) = 1`

Therefore, `T(n) = Θ(nlog2n)`

Hence, the answer of the given recurrence relation `T(n) = 2T(n/2) + 23n` using the substitution method is:

`T(n) = Θ(nlog2n)`

3. Master Theorem method:

To solve the above recurrence relation using the Master theorem, we have to compare the function `nlogba` with the function `f(n)`.

Here, `a = 2`, `b = 2`, and `f(n) = 23n`.

As per the Master theorem:

`If f(n) = Θ(nlogba),

then T(n) = Θ(nlogba log2n)` `

               = Θ(nlog2n)` if

`f(n) = 23n

      = Θ(nlog2n)`

Therefore, the solution of the given recurrence relation `T(n) = 2T(n/2) + 23n` using the Master theorem is:

`T(n) = Θ(nlog2n)`

Hence, the solution of the given recurrence relation `T(n) = 2T(n/2) + 23n` using all three methods are:`T(n) = Θ(nlog2n)`

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The question is an illustration of scale drawing

The character have to travel 8.5 km in the game to visit all three destinations and return to their starting point

The distance on the map are given as:

A =2 cm

B = 8 cm

C = 7 cm

The total distance on the map would be:

\(Total =2cm + 8cm + 7cm\)

\(Total =17cm\)

The actual distance between the store and the dungeon is 4 kilometers.

This means that:

\(B' =4km\)

So, we have:

\(Scale = B : B'\)

\(Scale = 8cm : 4km'\)

Represent the required actual distance with x.

So, we have:

\(17cm : x = 8cm : 4km\)

Express as fraction

\(\frac{x}{17} = \frac 48\)

Multiply both sides by 17

\(x = \frac 48 * 17\)

\(x = 8.5\)

Hence, the actual distance travelled is 8.5 km

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Answer: 10x-6

Step-by-step explanation:

The probability of the sequence W, W, L, L, W is (0.4)³ + (0.6)².

Given data;

Five games are played. Each play has a probability of winning, P(W), of 0.4, and a probability of losing, P(L), of 0.6. The results of the plays are probabilistically independent.

To get the probability of the sequence W, W, L, L, W.

Now,

As the results are probabilistically independent,

The probability of the sequence is;

→ [(P(W)]³ + [(P(L)]²

→ (0.4)³ + (0.6)²

Hence, the probability of the sequence W, W, L, L, W is (0.4)³ + (0.6)².

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Answer:

60m/s is correct so I hope that helps

The derivative of the function y = x^2x using logarithmic differentiation is dy/dx = x^2x(2 + 2ln(x)).

To find the derivative of the function y = x^2x using logarithmic differentiation, we follow these steps:

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To find the derivative of the function y = x^(2x) using logarithmic differentiation, we take the natural logarithm of both sides, apply logarithmic properties, and then differentiate implicitly.

Start by taking the natural logarithm of both sides of the equation:

ln(y) = ln(x^(2x))

Apply the power rule of logarithms to simplify the expression:

ln(y) = 2x * ln(x)

Now, differentiate both sides of the equation implicitly with respect to x:

(1/y) * dy/dx = 2 * ln(x) + 2x * (1/x)

Simplify the expression:

(1/y) * dy/dx = 2 * ln(x) + 2

Multiply both sides by y to isolate dy/dx:

dy/dx = y * (2 * ln(x) + 2)

Substitute the original value of y = x^(2x) back into the equation:

dy/dx = x^(2x) * (2 * ln(x) + 2)

The derivative of the function y = x^(2x) using logarithmic differentiation is dy/dx = x^(2x) * (2 * ln(x) + 2). Logarithmic differentiation is a useful technique for differentiating functions that involve exponentials or complicated algebraic expressions, as it allows us to simplify the calculation by taking the logarithm of both sides and then differentiating implicitly.

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