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The number of adults in the museum, using the fractional value of girls and boys, is 75.

A fractional value refers to a portion of the total value.

A fractional value can be depicted in fractions, decimals, or percentages.

A fractional value can also be represented as a ratio or proportion.

In this situation, the fractional number of adults is determined using subtraction.

The total number of people in a museum = 250

The fraction of girls in the museum = 2/5

2/5 of 250 = 100 girls

The fraction of boys in the museum = 3/10

3/10 of 250 = 75

Alternatively:

2/5 + 3/10 = 7/10

7/10 of 250 = 175

Therefore, the number of adults = 75 [250 - (100 + 75)]

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There are 250 people in the museum.

2/5 of the 250 people are girls.

3/10 out of the 250 people are boys.

The rest of the 250 people are adults.

Work out the number of adults in the museum.

Answer:

3x(2x - 3)

Step-by-step explanation:

Given

y = 6x² - 9x ← factor out 3x from each term

  = 3x(2x - 3)

Answer:

Step-by-step explanation:

answer:X=k/n-3

explain:move all terms to the left side and set equal to zero. then set each factor equ to zero!

I hope this helps

Answer:

3.29%

Step-by-step explanation:

Answer:

3.2925. Divide 0.15 from 21.95

Hoped this helped.

Answer:

For the first one: they increase in  by 14, so the three could be 73,87,101

Second: Sequential, increasing by 20, next could be 110, 130, 150

Third: Increase by 27, next three could be 122,149,176

The area under the curve over [2,5] is 24.

Given function is f(x) = 2xIntervals [2, 5] is given and it is to be divided into subintervals.

Let us consider n subintervals. Therefore, width of each subinterval would be:

$$
\Delta x=\frac{b-a}{n}=\frac{5-2}{n}=\frac{3}{n}
$$Here, we are using right-hand end point. Therefore, the right-hand end points would be:$${ c }_{ k }=a+k\Delta x=2+k\cdot\frac{3}{n}=2+\frac{3k}{n}$$$$
\begin{aligned}
\therefore R &= \sum _{ k=1 }^{ n }{ f\left( { c }_{ k } \right) \Delta x } \\&=\sum _{ k=1 }^{ n }{ f\left( 2+\frac{3k}{n} \right) \cdot \frac{3}{n} }\\&=\sum _{ k=1 }^{ n }{ 2\cdot\left( 2+\frac{3k}{n} \right) \cdot \frac{3}{n} }\\&=\sum _{ k=1 }^{ n }{ \frac{12}{n}\cdot\left( 2+\frac{3k}{n} \right) }\\&=\sum _{ k=1 }^{ n }{ \frac{24}{n}+\frac{36k}{n^{ 2 }} }\\&=\frac{24}{n}\sum _{ k=1 }^{ n }{ 1 } +\frac{36}{n^{ 2 }}\sum _{ k=1 }^{ n }{ k } \\&= \frac{24n}{n}+\frac{36}{n^{ 2 }}\cdot\frac{n\left( n+1 \right)}{2}\\&= 24 + \frac{18\left( n+1 \right)}{n}
\end{aligned}
$$Take limit as n → ∞, so that $$
\begin{aligned}
A&=\lim _{ n\rightarrow \infty  }{ R } \\&= \lim _{ n\rightarrow \infty  }{ 24 + \frac{18\left( n+1 \right)}{n} } \\&= \boxed{24}
\end{aligned}
$$

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Given function f(x) = 2x. The interval is [2,5]. The number of subintervals, n is 3.

Therefore, the area under the curve over [2,5] is 21.

From the given data, we can see that the width of the interval is:

Δx = (5 - 2) / n

= 3/n

The endpoints of the subintervals are:

[2, 2 + Δx], [2 + Δx, 2 + 2Δx], [2 + 2Δx, 5]

Thus, the right endpoints of the subintervals are: 2 + Δx, 2 + 2Δx, 5

The formula for the Riemann sum is:

S = f(c1)Δx + f(c2)Δx + ... + f(cn)Δx

Here, we have to find a formula for the Riemann sum obtained by dividing the interval [2.5] subintervals and using the right hand endpoint for each ck. The width of each subinterval is:

Δx = (5 - 2) / n

= 3/n

Therefore,

Δx = 3/3

= 1

So, the subintervals are: [2, 3], [3, 4], [4, 5]

The right endpoints are:3, 4, 5. The formula for the Riemann sum is:

S = f(c1)Δx + f(c2)Δx + ... + f(cn)Δx

Here, Δx is 1, f(x) is 2x

∴ f(c1) = 2(3)

= 6,

f(c2) = 2(4)

= 8, and

f(c3) = 2(5)

= 10

∴ S = f(c1)Δx + f(c2)Δx + f(c3)Δx

= 6(1) + 8(1) + 10(1)

= 6 + 8 + 10

= 24

Therefore, the Riemann sum is 24.

To calculate the area under the curve over [2, 5], we take the limit of the Riemann sum as n → ∞.

∴ Area = ∫2^5f(x)dx

= ∫2^52xdx

= [x^2]2^5

= 25 - 4

= 21

Therefore, the area under the curve over [2,5] is 21.

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In triangle ABC, side AC and the perpendicular bisector of BC meet in point D, and BD bisects ∠ABC。 If AD = 9 and DC = 7, 145–√5  is the area of a triangle.

I supposed here that [ABD] is the perimeter of ▲ ABD.

As  BD  is a bisector of  ∠ABC ,

ABBC=ADDC=97

Let  ∠B=2α

Then in isosceles  △DBC

∠C=α

BC=2∗DC∗cosα=14cosα

Thus  AB=18cosα

The Sum of angles in  △ABC  is  π  so

∠A=π−3α

Let's look at  AC=AD+DC=16 :

AC=BCcosC+ABcosA

16=14cos2α+18cosαcos(π−3α)

[1]8=7cos2α−9cosαcos(3α)

cos(3α)=cos(α+2α)=cosαcos(2α)−sinαsin(2α)=cosα(2cos2α−1)−2cosαsin2α=cosα(4cos2α−3)

With  [1]

8=cos2α(7−9(4cos2α−3))

18cos4−17cos2α+4=0

cos2α={12,49}

First root lead to  α=π4  and  ∠BDC=π−∠DBC−∠C=π−2α=π2 . In such case  ∠A=π−∠ABD−∠ADB=π4, and  △ABD  is isosceles with  AD=BD. As  △DBC  is also isosceles with  BD=DC=7,  AD=7≠9.

Thus first root  cos2α=12  cannot be chosen and we have to stick with the second root  cos2α=49. This gives  cosα=23  and  sinα=5√3.

The area of a triangle ABD=12h∗AD  where h  is the distance from  B  to  AC.

h=BCsinC=14cosαsinα

Area of  triangle ABD=145–√5

= 145–√5.

Incomplete question please read below for the proper question.

In triangle ABC, side AC and the perpendicular bisector of BC meet in point D, and BD bisects ∠ABC。 If AD = 9 and DC = 7, what is the area of triangle ABD?

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Answer:

Your answer should be x = 2

Step-by-step explanation:

149 + 13(2) + 5 = 180.

Hope this helps.

Answer:

x=2

Step-by-step explanation:

You add 149 and 5, which is 154. Then you take the total which is 180, and subtract it by 154. So 180-154=26 Then you take and do 26/13 which is 2.

149+13(2)+5=180

149+26+5=180

Definitely 2.

Hope this helps!!!

Answer:

1.1

Step-by-step explanation:

As we move left, we multiply by 10 to obtain the new place value.

The scientist descends from 83 feet below sea level to 151 feet below sea level, a change in depth of 151 - 83 = 68 feet. This change occurs over a time of 5 seconds.

The rate of change in depth, or the speed at which the submarine is descending, is given by the ratio of the change in depth to the time taken:

Rate of change in depth = (final depth - initial depth) / time taken

Rate of change in depth = (151 ft - 83 ft) / 5 s

Rate of change in depth = 13.6 ft/s (rounded to one decimal place)

Therefore, the rate of change in the submarine's elevation is 13.6 feet per second.

To prove that the intersection H ∩ K of subgroups H and K is Abelian, we need to show that for any two elements a and b in H ∩ K, their product ab is equal to their product ba.

In other words, we want to show that the order in which we multiply elements in H ∩ K does not matter.

Since H and K are subgroups, they must both contain the identity element e of the group. Therefore, e ∈ H ∩ K. Now, consider an arbitrary element a ∈ H ∩ K.

Since a ∈ H, we know that the order of a divides the order of H, which is 24. Similarly, since a ∈ K, the order of a divides the order of K, which is 20. Therefore, the order of a must divide both 24 and 20, so it must be a divisor of their greatest common divisor (GCD).

By observing the possible divisors of 24 and 20, we find that the only possible orders for elements in H ∩ K are 1, 2, 4, and 8. This is because the GCD of 24 and 20 is 4. Therefore, all elements in H ∩ K have an order that is a divisor of 4.

Now, let's take two arbitrary elements a and b in H ∩ K. We want to show that ab = ba. Since the order of a and b must divide 4, we have four cases to consider:

Case 1: The order of a is 1 or the order of b is 1.

In this case, both a and b are the identity element e, so ab = ba = e.

Case 2: The order of a is 2 and the order of b is 2.

In this case, we have \(a^2 = e\) and \(b^2 = e\).

Thus, \((ab)^2 = a^2b^2 = e\), which implies that ab has order 1 or 2.

Similarly, \((ba)^2 = b^2a^2 = e\), so ba also has order 1 or 2.

Since the only elements in H ∩ K with order 1 or 2 are the identity element e, we have ab = ba = e.

Case 3: The order of a is 4 and the order of b is 2.

In this case, \(a^4 = e\) and \(b^2 = e.\)

Multiplying both sides of \(a^4 = e\) by b, we get \(ab^2 = eb = e\).

Since \(b^2 = e\), we can multiply both sides by b^{-1} to obtain ab = e. Similarly, multiplying both sides of \(a^4 = e\) by \(b^{-1\),

we get \(a^4b^{-1} = eb^{-1} = e.\)

Since \(a^4 = e\), we can multiply both sides by \(a^{-4\) to obtain \(b^{-1} = e.\)

Thus, multiplying both sides of ab = e by \(b^{-1\), we have \(ab = e = b^{-1}\). Therefore, ab = ba.

Case 4: The order of a is 4 and the order of b is 4.

In this case, \(a^4 = e\) and \(b^4 = e.\)

Since the order of a is 4, the powers \(a, a^2, a^3,a^4\) are all distinct.

Similarly, the powers \(b, b^2, b^3, b^4\) are all distinct.

Therefore, we have eight distinct elements in the set

{\(a, a^2, a^3, a^4, b, b^2, b^3, b^4\)}.

However, the group H ∩ K has at most four elements (since the order of each element in H ∩ K divides 4), so there must be an element in the set {\(a, a^2, a^3, a^4, b, b^2, b^3, b^4\)} that is not in H ∩ K.

This contradicts the assumption that a and b are both in H ∩ K. Therefore, this case cannot occur.

In each of the cases, we have shown that ab = ba. Since these cases cover all possibilities, we can conclude that H ∩ K is Abelian.

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The total cost  of he meat with tax and tip is $ 22.42

To calculate the total cost with tax and tip, we need to follow these steps:

multiply the meal cost by the tip rate. when  the tip rate is 18%, we have:

Tip amount = $19.00 * 0.18 = $3.42

Add the meal cost, sales tax, and tip amount to get the total cost:

Total cost = Meal cost + Sales tax + Tip amount

= $19.00 + $3.42

= $ 22.42

Therefore, the total cost with tax and tip is $22.42

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Answer:

i dont know because u didnt give me how many numbers

Step-by-step explanation:

Answer:

4/9 16/36 12\27 are all equivalent fraction

Answer:

16/36, 12/27 are equivalent to 4/9.

Step-by-step explanation:

Hope this helps!

Step-by-step explanation:

To dilate the figure by a factor of 2, I will multiply the x and y-value of each point by 2. I plotted all the new points to find the new triangle. To dilate the figure by a factor of 2, I will multiply the x-value of each point by 2.

The line integral ∫[C] (Pdx + Qdy) over the given curve C consisting of the arc of the parabola y = x² from (0,0) to (1, 1), and the line segment from (1,1) to (0,1) is equal to 2/5.

What is integral?

The value obtained after integrating or adding the terms of a function that is divided into an infinite number of terms is generally referred to as an integral value.

To evaluate the line integral using Green's theorem, we need to find a vector field F = (P, Q) such that ∇ × F = Qₓ - Pᵧ, where Qₓ represents the partial derivative of Q with respect to x, and Pᵧ represents the partial derivative of P with respect to y.

Let's consider F = (P, Q) = (x²y², xy).

Now, let's calculate the partial derivatives:

Qₓ = ∂Q/∂x = ∂(xy)/∂x = y

Pᵧ = ∂P/∂y = ∂(x²y²)/∂y = 2x²y

The curl of F is given by ∇ × F = Qₓ - Pᵧ = y - 2x²y = (1 - 2x²)y.

Now, let's find the line integral using Green's theorem:

∫[C] (Pdx + Qdy) = ∫∫[R] (1 - 2x²)y dA,

where [R] represents the region enclosed by the curve C.

To evaluate the line integral, we need to parameterize the curve C.

The arc of the parabola y = x² from (0, 0) to (1, 1) can be parameterized as r(t) = (t, t²) for t ∈ [0, 1].

The line segment from (1, 1) to (0, 1) can be parameterized as r(t) = (1 - t, 1) for t ∈ [0, 1].

Using these parameterizations, the region R is bounded by the curves r(t) = (t, t²) and r(t) = (1 - t, 1).

Now, let's calculate the line integral:

∫∫[R] (1 - 2x²)y dA = ∫[0,1] ∫[t²,1] (1 - 2t²)y dy dx + ∫[0,1] ∫[0,t²] (1 - 2t²)y dy dx.

Integrating with respect to y first:

∫[0,1] [(1 - 2t²)(1 - t²) - (1 - 2t²)t²] dt.

Simplifying:

∫[0,1] [1 - 3t² + 2t⁴] dt.

Integrating with respect to t:

[t - t³ + (2/5)t⁵]_[0,1] = 1 - 1 + (2/5) = 2/5.

Therefore, the line integral ∫[C] (Pdx + Qdy) over the given curve C consisting of the arc of the parabola y = x² from (0,0) to (1,1), and the line segment from (1,1) to (0,1) is equal to 2/5.

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a) The set {1, 2, 3} does not represent vectors, but rather a collection of scalars. Therefore, there are no vectors in {1, 2, 3}.

b) The number of vectors in "col a" cannot be determined without additional context or information. "Col a" could refer to a column vector or a collection of vectors associated with a variable "a," but without further details, the exact number of vectors in "col a" cannot be determined.

c) Without knowing the specific context of "p" and "col a," it is impossible to determine if "p" is in "col a." The inclusion of "p" in "col a" would depend on the definition and properties of "col a" and the specific value of "p."

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The equation of the hyperbola for the cross section of the cooling tower is x²/8100 - y²/9506.25 = 1.

We must take into account its characteristics in order to formulate the hyperbola's equation for the cooling tower's cross section.

Since the origin serves as the hyperbola's centre, its coordinates are (0, 0).

The left/right opening of the hyperbola indicates that the primary axis is horizontal.

The cooling tower's smallest diameter is 180 metres, which is the same length as the minor axis.

The primary axis' 195 m length and the diameter at its highest point are matched.

The hyperbola's highest point is 80 metres above the centre.

These characteristics allow us to write the hyperbola's equation in standard form:

(x - h)²/a² - (y - k)²/b² = 1

Where (h, k) represents the center of the hyperbola.

Substituting the given values:

Center: (h, k) = (0, 0)

Minor axis: 2a = 180 m, so a = 90 m

Major axis: 2b = 195 m, so b = 97.5 m

Vertical shift: c = 80 m

Now we can write the equation of the hyperbola:

x²/90² - y²/97.5² = 1

Simplifying, we have:

x²/8100 - y²/9506.25 = 1

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Answer:

$9257.5

Step-by-step explanation:

plug into the equation  known variables

Answer:

2257.50

Step-by-step explanation:

B=p(1+r)^t

p= principal amount= $7000 in the saving account

r= interest rate= 15%= .15

t- number of years = 2

B= 7000(1+.15)^2

B= 7000(1.15)^2

B= 7000(1.15)(1.15)

B= 9257.50

She has a total of 927.50 dollars in the account after two years. To find out how much of that is interest we take the Balance and subtract what she invested.

B-p= 9257.50-7000= 2257.50 earned in interest.

The equation of the plane that passes through the point (3, 4, 5) and contains the given line is 5x + y - z - 14 = 0.

To find an equation of the plane that passes through the point (3, 4, 5) and contains the given line, we can use the fact that a plane is determined by a point on the plane and a vector that is parallel to the plane.

First, let's find a vector that is parallel to the given line. We can do this by taking the direction vector of the line, which is the coefficients of t in the parametric equations of x, y, and z. In this case, the direction vector is <5, 1, -1>.

Next, we use the point-normal form of the equation of a plane. The equation of a plane passing through a point (a, b, c) with a normal vector <d, e, f> is given by:

d(x - a) + e(y - b) + f(z - c) = 0

Substituting the values from the given point (3, 4, 5) and the direction vector <5, 1, -1>, we have:

5(x - 3) + 1(y - 4) - 1(z - 5) = 0

Simplifying the equation, we get:

5x - 15 + y - 4 - z + 5 = 0

5x + y - z - 14 = 0

Therefore, the equation of the plane that passes through the point (3, 4, 5) and contains the given line is 5x + y - z - 14 = 0.

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Answer:

$3360

Step-by-step explanation:

7% of $6000=$420

$420 time 8= $3360

Hope this helped! :)

Answer:

$3,360

Step-by-step explanation:

So first of all you want to start by finding what P, r and t would be.

P = Principal amount ($$)

r = interest rate (%)

t = time (years)

Once I found all of those I put them into the equation (l = Prt) and solved (by putting it into a calculator obviously). That is how I came up with my answer. Check the screenshot provided to see what P, r and t would be and to see all my work! :)

Hope this helps! :)

Have a great day!

Answer:

It is true

Step-by-step explanation:

20/-7 is ~2.56

-2.8 (8 repeating) is -2.8......

So it is true

Hope this helps!

Answer:

True

Step-by-step explanation:

Answer:

Step-by-step explanation:

2 numbers that differ by 3 and have a product of 88 are 11 and 8.

Let's say that the very first figure is x and the next is y.

x - y = 3 -----> y=x-3 .........(i)

xy=88 .......(ii)

Substitute (i) to (ii)

xy=88

x(x-3)=88

x\(x^{2} - 3x = 88\\x^{2} - 3x - 88 = 0\)

(x+8)(x-11)=0

x+8=0 or x-11=0

x=-8 or x=11

Substitute x=-8 to (i)

y=x-3

y=-8-3=-11

Substitute x=11 to (i)

y=x-3

y=11-3=8

Thus, x = -8 and y =- 11 or x = 11 and y = 8

2 numbers that differ by 3 and have a product of 88 are 11 and 8.

A 2nd equation with the form ax2 + bx + c = 0 denotes a quadratic equation, where a, b, and c are real-number coefficients and a 0.  For instance, if school administration decides to build a chapel with a floor size of 400 sq metres and a length that is two meters longer than its width, we will need the aid of a quadratic equation to determine the length and breadth. 

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Answer:

Step-by-step explanation:

y = -½(x-3)²-1

This is the equation of a vertical parabola with vertex at (3,-1). The leading coefficient is negative, so the parabola opens downwards.

The variance of the random variable X, denoted as Var[X], can be calculated as σ^2 / (1 - ρ^2), where σ^2 is the variance of X₁ and ρ is the constant linking consecutive variables.

1. We start with the given information that Xᵢ₊₁ = ρXᵢ, where i = 1, 2, ..., n-1. This implies that X₂ = ρX₁, X₃ = ρ²X₁, X₄ = ρ³X₁, and so on.

2. To find the variance of X, denoted as Var[X], we need to find the variance of X₁, which is given as σ².

3. Since X₂ = ρX₁, we can calculate the variance of X₂ as Var[X₂] = ρ²Var[X₁]. Similarly, Var[X₃] = ρ⁴Var[X₁], Var[X₄] = ρ⁶Var[X₁], and so on.

4. Notice that the power of ρ in the variance expression increases by 2 for each subsequent variable.

5. The total variance of X can be expressed as the sum of the variances of all the variables: Var[X] = Var[X₁] + Var[X₂] + Var[X₃] + ... + Var[Xₙ].

6. Using the information from step 3, we can rewrite Var[X] as Var[X₁] + ρ²Var[X₁] + ρ⁴Var[X₁] + ... + ρ²ⁿ⁻²Var[X₁].

7. Factoring out Var[X₁], we get Var[X] = Var[X₁] * (1 + ρ² + ρ⁴ + ... + ρ²ⁿ⁻²).

8. The sum of the terms inside the parentheses is a geometric series with a common ratio of ρ² and n-1 terms. Using the formula for the sum of a geometric series, we have Var[X] = Var[X₁] * [(1 - ρ²ⁿ⁻²) / (1 - ρ²)].

9. Finally, substituting Var[X₁] with σ² (given in the question), we obtain Var[X] = σ² / (1 - ρ²).

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