The admission fee at an amusement park is $1.50 for children and $6.40 for adults. On a certain day, 286 people entered the park, and the admission fees collected totaled $1164. How many children and how many adults were admitted?

Answer:

yes ur on track

Step-by-step explanation:

Answer:

The terms are t, 8, and 3t

The like terms are t and 3t

Step-by-step explanation:

N/A

The correct answer is Using numerical integration techniques:Approximation using the Trapezoidal Rule (t10) is approximately [2.763211].Approximation using the Midpoint Rule (m10) is approximately [2.079728].Approximation using Simpson's Rule (s10) is approximately [2.094395].

To approximate the values of t10, m10, and s10 for the integral 0 to 8 sin(x) dx, we can use numerical integration techniques, such as the Trapezoidal Rule, Midpoint Rule, and Simpson's Rule.

Trapezoidal Rule (t10):

The Trapezoidal Rule estimates the integral by approximating the area under the curve using trapezoids. The formula for the Trapezoidal Rule is given by:

t10 = (b - a) * [(f(a) + f(b)) / 2 + ∑(f(xi))] / n

where a and b are the limits of integration (0 and 8 in this case), f(x) is the function (sin(x) in this case), xi are the equally spaced points between a and b, and n is the number of intervals.

Using n = 10, we can calculate t10:

t10 ≈ (8 - 0) * [(sin(0) + sin(8)) / 2 + ∑(sin(xi))] / 10

Midpoint Rule (m10):

The Midpoint Rule estimates the integral by approximating the area under the curve using rectangles. The formula for the Midpoint Rule is given by:

m10 = (b - a) * ∑(f(xi + h/2)) / n

where a, b, f(x), xi, and n have the same meanings as in the TrapezoidalRule, and h is the width of each interval (h = (b - a) / n).

Using n = 10, we can calculate m10:

m10 ≈ (8 - 0) * ∑(sin(xi + (8 - 0) / (2 * 10))) / 10

Simpson's Rule (s10):

Simpson's Rule estimates the integral by approximating the area using parabolic arcs. The formula for Simpson's Rule is given by:

s10 = (b - a) * [f(a) + 4 * ∑(f(xi)) + 2 * ∑(f(x2i)) + f(b)] / (3 * n)

where a, b, f(x), xi, and n have the same meanings as in the Trapezoidal Rule, and x2i represents the points with an even index.

Using n = 10, we can calculate s10:

s10 ≈ (8 - 0) * [sin(0) + 4 * ∑(sin(xi)) + 2 * ∑(sin(x2i)) + sin(8)] / (3 * 10)

By evaluating these formulas using numerical methods and rounding the results to six decimal places, you can find the approximations t10, m10, and s10 for the given integral 0 to 8 sin(x) dx.

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Answer:

Step-by-step explanation:

Let the number be x.

twice the square of the sum of a number and 3 is expressed as;

2(x+3)²

If the expression is equal to 98, then;

2(x+3)² = 98

divide both sides by 2;

2(x+3)²/2 = 98/2

(x+3)² = 49

square root both sides

√(x+3)² = √49

x+3 = ±7

x = ±7-3

x = 7-3 or -7-3

x = 4 or -10

Hence the number is 4 or -10

The number is -4 or 10

Let n represent the unknown number

The following equation can be used to summarise the information given in the question

2 × n² = 98

The first step to take in order to determine the value of n is to divide both sides of the equation by 2

n² = 98/2

n² = 49

The second step is to determine the square root of both sides of the equation

n =√49

n =-7 or +7

The number = - 7 + 3 = - 4 or 7 + 3 = 10

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The sequence for the cost of bracelet in dollars = $0, $3, $6, $9 and $12.

Also the sequence for the cost of necklace is = $0, $6, $12, $18, $24.

The column given concerning the products contains the following amounts of products such as 0, 1, 2, 3, and 4 pieces.

Therefore to calculate the amount to be used to buy each product of bracelet and necklace in each column multiplication is carried out.

That is, 0×3, 1 ×3, 2×3, 3×3, and 4×3

which is = $0, $3, $6, $9 and $12 respectively for the bracelet.

0×6, 1 ×6, 2×6, 3×6, and 4×6

Which is = $0, $6, $12, $18, $24. respectively for the necklace.

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Answer:

d

By the alternate interior angles theorem,

By the reflexive property, AB is congruent to itself.

Thus, the triangles will be congruent by ASA.

Answer:

d

Step-by-step explanation:

Answer:

hi its D

Step-by-step explanation:

you are seeing two similar things and each of them are showing 3 parts of 8 parts of the shape so

\(2 \times \frac{3}{8} \)

The vector equation for the line is:

r(t) = (1, 0, 6) + t(-4, 1, 4)

The parametric equations for the line.

x(t) = 1 - 4t

y(t) = t

z(t) = 6 + 4t

To find a vector equation and parametric equations for the line passing through the point (1, 0, 6) and perpendicular to the plane x + 4y + z = 7, we can first determine the direction vector of the line.

The normal vector of the plane x + 4y + z = 7 is (1, 4, 1) since the coefficients of x, y, and z represent the normal vector.

Any line perpendicular to this plane must have a direction vector orthogonal to the normal vector of the plane.

Let's call the direction vector of our line (a, b, c).

We know that the dot product of the direction vector and the normal vector of the plane is zero:

(a, b, c) ⋅ (1, 4, 1) = 0

This equation gives us a condition for the direction vector.

We can choose any values for a, b, and c as long as they satisfy this condition.

For simplicity, we can choose a = -4, b = 1, and c = 4, which gives us a direction vector (-4, 1, 4) orthogonal to the plane.

Now, let's denote the position vector of the given point (1, 0, 6) as (x₀, y₀, z₀) = (1, 0, 6).

The vector equation of the line can be written as:

r(t) = r₀ + t × v

where r₀ is the position vector of a point on the line (which is (1, 0, 6)), t is the parameter, and v is the direction vector of the line (-4, 1, 4).

Therefore, the vector equation for the line is:

r(t) = (1, 0, 6) + t × (-4, 1, 4)

Expanding this equation, we get:

x(t) = 1 - 4t

y(t) = t

z(t) = 6 + 4t

These are the parametric equations for the line passing through the point (1, 0, 6) and perpendicular to the plane x + 4y + z = 7.

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Based on the given conditions, formulate: 

34÷1 1/3

Find common denominator and write the numerators above common denominator:

34/3/3+1/3

Write the numerators over common denominator:

34/3+1/3

Calculate the sum or difference:

34/4/3

Divide a fraction by multiplying its reciprocal:34×3/4

Cross out the common factor:

17×3/2

Calculate the product or quotient:

51/2

get the result:

25.5 or 25 1/2

=25.5 or 25 1/2

The equation for traveling x miles in the cab can be written as:

Cost = $0.60 + $0.14 * x. The cab charges $0.88 for a ride of 2 miles. And the cab charges $1.72 for a trip of 8 miles.

a. The equation for traveling x miles in the cab can be written as:

Cost = $0.60 + $0.14 * x

b. To find the number of miles for a cab ride that costs $0.88, we can set up the equation:

$0.88 = $0.60 + $0.14 * x

Subtracting $0.60 from both sides, we get:

$0.88 - $0.60 = $0.14 * x

$0.28 = $0.14 * x

Dividing both sides by $0.14, we find:

x = $0.28 / $0.14

x = 2 miles

Therefore, the cab charges $0.88 for a ride of 2 miles.

c. To calculate the cost of a trip of 8 miles, we can substitute x = 8 into the equation:

Cost = $0.60 + $0.14 * 8

Cost = $0.60 + $1.12

Cost = $1.72

Therefore, the cab charges $1.72 for a trip of 8 miles.

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Answer: 19.6 feet

Step-by-step explanation:

Using the Pythagorean theorem,

\(x^2 +(x+6)^2 =48^2\\\\x^2 +x^2 +12x+36=2304\\\\2x^2 +12x-2268=0\\\\x^2 +6x-1134=0\\\\x=\frac{-6 \pm \sqrt{6^2 -4(1)(-1134)}}{2(1)}\\\\x \approx 30.8 \text{ } (x > 0)\\\\\implies x+(x+6) \approx 67.6\\\\\therefore (x+(x+6))-48 \approx 19.6\)

Answer:

-4y(3y + 1) (9y^2 - 3y + 1)

Step-by-step explanation:

-108y^4 - 4y

= -4y(27y^3 + 1)

= -4y(3y + 1) (3^2y^2 - 3y + 1)

= -4y(3y + 1) (9y^2 - 3y + 1)

Answer:

-4y(3y + 1) (9y^2 - 3y + 1)

Answer:

m = - 1

Step-by-step explanation:

Slope = rise/run or (y2 - y1) / (x2 - x1)

Pick 2 points (-2,0) (0, -2)

We see the y decrease by 2, and the x increase by 2, so the slope is

m = -2/2 = -1

So, the slope is -1

Answer:

m = - 1

Step-by-step explanation:

Step-by-step explanation:

the answer is how many times does 0.225 l fit wholly into 5 l :

5 / 0.225 = 22.22222222...

so, she can fill 22 glasses fully.

22 × 0.225 = 4.95 l

so, she has at the end (after filling the 22nd glass) 0.050 l (= 50 ml) left.

Answer:

the answer will be C

ik this bc I did the math

Answer:

A

Step-by-step explanation:

because I took the test

Answer: I think it's a. 84 cubic units

Hope it helped : D

a) X'Y' + X'Y + XY simplifies to X' + Y.

b) A'BC' + ABC' + BC'D simplifies to BC'.

Complement of the functions:

a) Complement is W' + X' + YZ.

b) Complement is (A' + B + C)(A'B' + C' + A'B).

a) To prove X'Y' + X'Y + XY = X' + Y, we can use Boolean algebra identities:

X'Y' + X'Y + XY

= Y'(X' + X) + XY(Distributive Law)

= Y' + XY(X + X' = 1)

= X' + Y(Commutative Law)

Therefore, X'Y' + X'Y + XY simplifies to X' + Y.

b) To prove A'BC' + ABC' + BC'D = BC', we can simplify the expression using Boolean algebra:

A'BC' + ABC' + BC'D

= BC'(A' + A) + BC'D   (Distributive Law)

= BC' + BC'D(A + A' = 1)

= BC'(BC' + BC'D = BC' + BC'(1) = BC')

Hence, A'BC' + ABC' + BC'D simplifies to BC'.

Complement of the given functions:

a) The complement of WX(Y'Z + YZ') + W'X'(Y' + Z)(Y + Z') is W' + X' + YZ.

b) The complement of (A + B' + C')(A'B' + C)(A + B'C') is (A' + B + C)(A'B' + C' + A'B).

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x + y = 100

x - y = 10

_____________ +

( x + y ) + ( x - y ) = 100 + 10

2x + y - y = 110

2x = 110

x = 110/2

x = 55

_________________________________

x - y = 10

55 - y = 10

- y = 10 - 55

- y = - 45

y = 45

♡♡♡♡♡♡♡♡♡♡♡♡♡♡♡♡

x = 55 ..**&**.. y = 45

The cost for 166.67 square feet is $80,000.

Let's call the cabin's square footage "x".

The first contractor quoted a price of $60,000 + $120 * x

The second contractor quoted a price of $80,000 + $100 * x

We can set their quotes equal to each other to find the square footage for which the two contractors will charge the same amount:

$60,000 + $120 * x = $80,000 + $100 * x

When we solve for x, we get:

$120 * x = $80,000 - $60,000

166.67 square feet / $120 * x = $20,000 x = $20,000

As a result, the two contractors will charge the same amount for 166.67 square feet. That sum is as follows:

$60,000 + $120 * 166.67 = $60,000 + $20,000 = $80,000.

So the cost for 166.67 square feet is $80,000.

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Since both conditions are satisfied, we can conclude that the series converges by the Alternating Series Test.

The given series is: `∑(n=1 to infinity) ((-1)^(n+1) / n^2(n^3 + 8))`.

To test for convergence or divergence, let us use the alternating series test.

The alternating series test states that if the alternating series `∑(-1)^(n-1) * b_n` satisfies the following conditions:the terms `b_n` are positive and decreasing as n increases,and `b_n` approaches zero as n approaches infinity,then the series converges.

It is to be noted that the series converges slowly if `b_n` approaches zero very slowly or if the terms are initially quite large.

To apply the alternating series test to the given series, we must first determine if `b_n` is positive, decreasing, and approaches zero as n approaches infinity.

In this case, `b_n = 1/(n^2(n^3 + 8))`.

Clearly, `b_n` is positive since the denominator is always positive.

Moreover, `b_n` is decreasing since increasing n will make both the numerator and denominator larger.

Finally, `b_n` approaches zero as n approaches infinity since the denominator grows much faster than the numerator. Therefore, the alternating series test applies to the given series.Hence, the given series is convergent.

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Answer:

In explanation below.

Step-by-step explanation:

Presumably, the proof you have in mind is to use a=b=2–√a=b=2 if 2–√2√22 is rational, and otherwise use a=2–√2√a=22 and b=2–√b=2. The non-constructivity here is that, unless you know some deeper number theory than just irrationality of 2–√2, you won't know which of the two cases in the proof actually occurs, so you won't be able to give aa explicitly, say by writing a decimal approximation.

Answer

100.57 square units

Explanation

The area of a circle is given as

Area = πr²

The area of a semi-circle is half of the area of a circle.

Area of a semi-circle = ½ (πr²)

r = radius = 8 units

Area of a semi-circle = ½ (πr²)

= ½ [π (8²)]

= ½ (64π)

= 32π

= 100.57 square units

Hope this Helps!!!

Answer:

Step-by-step explanation:

Choose your own x values and find the corresponding y values.

Here's a table of values

 x     y= 2x + 3    (x, y)

 0                  3    (0, 3)

 2    2(2) + 3 = 7  (2, 7)

and so on

Answer: 2/23

Step-by-step explanation: Absolute value is a term which is used to indicate the distance of a point or number from the origin of a number line or coordinate system.

Suppose x is a real number. Then the absolute value of x is defined as follows:

For x = 0 or x > 0, | x | = x

For x < 0, | x | = - x

Now, we have to find the absolute value of the given number  that means we have to find the distance of   from the origin of a number line.

Distance of  from the origin is  . As distance can never be negative.

Therefore, the absolute value of  is 2/23 .

Answer:

0.45

To find 0.45 you divide 45g by 100 to get 0.45!

Answer:12

Step-by-step explanation:

Your goal with variables should always be to isolate them.

so the first step is to subtract the 4

3x^2+4=436

       -4= -4

3x^2=432

The next step to isolate the variable x is to get rid of the 3. To get rid of the 3 you have to divide both sides by 3 since it is the opposite of multiplying.

3x^2=432

/3.    =/3

x^2=144

the last step to isolate the x is to do the opposite of what an exponent is, which is to find the square root. So when you square the x^2, the exponent cancels out.

square root of x^2=x

square root of 144=12

x=12

hope this helps!

Given

we have

Required

we need to write it in terms of linear factors.

Explanation

Here

the answer is (x+2)(x+i)(x-i)