During a cake-eating contest, Dave ate three and a half pizza and Daisy
ate two-thirds of a pizza. How many pizzas did they eat altogether?

HELP EXPLAIN STEP BY STEP!

Answer:

b = 68°

Step-by-step explanation:

he's your solution

=> angle of a polygon is given by =

(2n -4)*90°

=>(2*8 - 4) *90°

=> 12*90°

=> sum of all angles = 1080°

=> now, 150°+144°+127°+2b+b+50°+2b+11°+2b-20°+2b+6° = 1080°

=> 9b + 468° = 1080°

=> 9b = 612°

=> b= 612°/9

=> 68°

hope it helps

The color that recorded the most is black.

The number of red cars is 150 cars.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

One circle = 40 cars

One circle can be divided into 4 parts.

Each part = 40 / 4 = 10.

Number of Red cars = 3 x 40 + 30 = 120 + 30 = 150

Number of Black cars = 5 x 40 = 200

Number of Silver cars = 2 x 40 + 20 = 80 + 20 = 100

Number of other cars = 3 x 40 + 10 = 120 + 10 = 130

Thus,

The color that recorded the most is black.

The number of red cars is 150 cars.

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So the equation of the parabola in standard form is y = (5/4)x^2 - (7/4)x + 2.

One way to approach this problem is to use the standard form of the equation for a parabola, which is y = ax^2 + bx + c. We can set up a system of three equations using the three points given and solve for the coefficients a, b, and c.

Starting with the point (-2, 18):

18 = a(-2)^2 + b(-2) + c

18 = 4a - 2b + c

Using the point (0, 2):

2 = a(0)^2 + b(0) + c

2 = c

Using the point (4, 42):

42 = a(4)^2 + b(4) + c

42 = 16a + 4b + c

Substituting c = 2 into the second equation, we get:

2 = 2

This is always true, so it doesn't provide any additional information.

Substituting c = 2 into the first and third equations, we get:

18 = 4a - 2b + 2

42 = 16a + 4b + 2

Simplifying each equation:

9 = 2a - b

20 = 4a + b

Solving this system of equations, we get:

a = 5/4

b = -7/4

Substituting these values for a and b, and c = 2, into the standard form equation for a parabola, we get:

y = (5/4)x^2 - (7/4)x + 2

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Answer: 2.9 in^3

Step-by-step explanation:

The formula for the volume of a right circular cone is: V = π*r^2*(h/3).

In order to find the radius, you must use the formula: Circumference = 2*π*r. Thus, divide 3.4 by 2 and pi in order to get .5411, the radius.

Plug the radius in and 9.5 in as the height in the formula in order to get the answer.

The sample that can best help the owner see the preferences of all the audience members is given as follows:

B) 5 people in VIP seats, 35 on the main floor, and 20 in the balcony.

The best sample is obtained considering the proportions in the sample, as follows:

Hence, considering 5 VIP seats, the amounts are given as follows:

Hence option B is the correct option for this problem.

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One statement that is necessarily true when a quadrilateral is inscribed in a circle is that the opposite angles of the quadrilateral are supplementary. In other words, the sum of the measures of two opposite angles is always 180 degrees.

To understand why this is true, let's consider a specific example. Imagine a quadrilateral PQRS inscribed in circle A. Let's say angle PQR measures 80 degrees. Since angle PQR is an inscribed angle that intercepts arc PS, it is equal in measure to half the measure of arc PS. Therefore, arc PS measures 160 degrees.

Now, let's focus on angle PSR. Angle PSR also intercepts arc PS, so it has the same measure as half the measure of arc PS, which is 160 degrees. Therefore, angle PSR measures 160 degrees as well.

If we add the measures of angles PQR and PSR, we get 80 + 160 = 240 degrees. This violates the fact that the sum of the measures of angles in a quadrilateral is always 360 degrees. Thus, it is clear that angles PQR and PSR cannot both measure 80 degrees.

Based on this example, we can conclude that the opposite angles of a quadrilateral inscribed in a circle are supplementary. This means that their sum is always 180 degrees.

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To find the values of x for which the series converges, we need to analyze the given series: Σ n = 0 to ∞ (x − 7)^n / 4^n.

This series is a geometric series with the general term (x - 7)^n / 4^n. A geometric series converges if the absolute value of its common ratio is less than 1: | (x - 7) / 4 | < 1, To find the interval for x, we solve the inequality: -1 < (x - 7) / 4 < 1
Multiplying by 4, we get: -4 < x - 7 < 4.

Adding 7 to all sides: 3 < x < 11, So, the series converges for x in the interval (3, 11). Now, to find the sum of the series for those values of x, we use the geometric series sum formula: S = a / (1 - r), Here, a is the first term, which is (x - 7)^0 / 4^0 = 1, and r is the common ratio, which is (x - 7) / 4. So, we have: S = 1 / (1 - (x - 7) / 4), Simplifying: S = 1 / (4 - x + 7) / 4, S = 4 / (11 - x). For x in the interval (3, 11), the sum of the series is S = 4 / (11 - x).

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Answer:

d=8√2 = 11.31

x=3√3 = 5.20

y=6√3 = 10.39

Step-by-step explanation:

d²=8²+8²

d²=64+64

d²=128

d=√128

d=√64*2

d=8√2 = 11.31

30-60-90 triangle

x-x√3-2x

x√3=9

x=9/√3

x=3√3

y=2x

y=2 * 3√3

y=6√3

Answer is

7 +g

Step-by-step explanation:

2+5+g

=7+g

Answer:

g+7

Step-by-step explanation:

Have an amazing day!

∫∫D x^2y dA = 128/15.

        x = r cos θ

        y = r sin θ

        dA = r dr dθ.

         x^2y = (r cos θ)^2 (r sin θ) = r^3 cos^2 θ sin θ.

         ∫∫D x^2y dA = ∫0^π ∫0^4 r^3 cos^2 θ sin θ r dr dθ

         ∫0^π ∫0^4 r^4 cos^2 θ sin θ dr dθ = (1/5) ∫0^π cos^2 θ sin θ dθ (∫0^4 r^5 dr)

        ∫0^4 r^5 dr

        (1/5) ∫0^π cos^2 θ sin θ dθ (4^6 / 6)

        ∫∫D x^2y dA = (2^7 / 15) ∫0^π cos^2 θ sin θ dθ

        ∫0^π cos^2 θ sin θ dθ = (1/2) ∫0^π sin θ dθ + (1/2) ∫0^π cos 2θ sin θ dθ

        ∫0^π cos^2 θ sin θ dθ = (1/2) (2) + (1/2) (0) = 1

        ∫∫D x^2y dA = (2^7 / 15) ∫0^π cos^2 θ sin θ dθ = (2^7 / 15) (1) = 128/15.

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Answer:.2 grams per year

Step-by-step explanation:you divide 6 by 30 and thats what you get:)

Answer:5

Step-by-step explanation:30/6=5

Answer:

The process capability index for this system is 0.9103

Step-by-step explanation:

Upper specification = 1.649 inches

Lowe Specification = 1.507 inches

Mean = 1.57 inches

Standard Deviation = 0.026 inches

Process Capability Index = PCI

PCI = (Upper specification - lower specification)/6(standard deviation)

So, we get,

PCI = (1.649 - 1.507)/((6)(0.026))

PCI = 0.142/0.156

PCI = 0.9102564

To four decimal places, we get,

PCI = 0.9103

Answer:

\(y-5=\frac{2}{3}(x-3)\)

Step-by-step explanation:

Hi there!

We are given the points (3,5) and (9,9) and we want to write the equation of the line that contains those two points in point-slope form

Point-slope form is written as \(y-y_1=m(x-x_1)\), where \((x_1, y_1)\) is a point and m is the slope

First, let's find the slope of the line

The formula for the slope calculated from two points is \(\frac{y_2-y_1}{x_2-x_1}\), where \((x_1, y_1)\) and \((x_2, y_2)\) are points

We are given two points, but let's label their values to avoid confusion and mistakes when calculating:
\(x_1=3\\y_1=5\\x_2=9\\y_2=9\)
Now substitute these points into the formula; remember that m is the value of the slope.
m=\(\frac{y_2-y_1}{x_2-x_1}\)
Substitute:

m=\(\frac{9-5}{9-3}\)
Subtract

m=\(\frac{4}{6}\)

Simplify the fraction

m=\(\frac{2}{3}\)

Now that we have the value of m (slope), and also the values of \(x_1\) and \(y_1\) (the points), let's substitute these values into the formula for point-slope form.

\(y-y_1=m(x-x_1)\)
\(m=\frac{2}{3}, x_1=3, y_1=5\)
Substitute these values into the formula

\(y-5=\frac{2}{3}(x-3)\)

Hope this helps!

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Answer:

30

Step-by-step explanation:

you have a 30-60-90 triangle so 15*2=30

man this concept of 30-60-90 triangles and 45-45-90 triangles is not hard. just read abt please its so ez

Answer:

10\(\sqrt{3}\), or 17.32050

Step-by-step explanation:

Answer:

JK = 72

Step-by-step explanation:

JL = JK + KL = (4x+8) + (6x-6) = 10x + 2 = 162

--> x = (162-2)/10 = 16

JK = 4x + 8 = 4 . 16 + 8 = 72

Answer:

0.05

Step-by-step explanation: if the total price in ounces is 1.30, you divide 1.30 by 26 ounces and you get 0.05 as the answer I also took a test with this question trust me it's right.

Answer:

i love uuuuuuuuuuuuuuuuuuuuuuuu

Step-by-step explanation:

Answer:

I believe the answer is triangle A.

Step-by-step explanation:

Since we know that sine is opposite over hypotenuse, and that the sine is being taken from angle A, triangle A is the correct answer.

Hope this helps!

The Fourier coefficient angle 02 of the combined trigonometric series for the periodic function r(t) = sin(4t) + cos(8t) + 7 + cos(16t) is zero.

To find the Fourier coefficient A₂ of the combined trigonometric series for the periodic function r(t) = sin(4t) + cos(8t) + 7 + cos(16t), we need to determine the coefficient of the term e^(j2ω₀t), where ω₀ is the fundamental frequency.

The combined trigonometric series for r(t) is given by:

r(t) = A₀/2 + ∑[n=1 to ∞] (Aₙcos(nω₀t) + Bₙsin(nω₀t))

where A₀/2 represents the DC component and Aₙ and Bₙ are the Fourier coefficients.

To determine A₂, we need to find the coefficient of the term cos(2ω₀t) in the series.

By comparing the original function r(t) and the trigonometric series, we can see that there is no term cos(2ω₀t) present in r(t). Therefore, the coefficient A₂ of the combined trigonometric series will be zero.

In summary, the Fourier coefficient angle 02 of the combined trigonometric series for the periodic function r(t) = sin(4t) + cos(8t) + 7 + cos(16t) is zero (A₂ = 0).

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Answer:

5x²-7x+2

step by step explanation:

(f•g)(x) = f(x)•g(x)

(x-1)•(5x-2)

x×5x-2x-5x-1×(-2)

5x²-2x-5x+2

=5x²-7x+2

Answer: 336

Step-by-step explanation:

8 * 3 * 14

The lexicographic preferences on apricots and bananas are transitive. They cannot be represented by a continuous utility function u(a, b).

1. To prove that the lexicographic preferences on apricots and bananas are transitive, let's assume the following:
(x1, y1)≻(x2, y2) (x2, y2)≻(x3, y3)

That implies the following:
1. x1 > x2 or (x1 = x2 and y1 > y2)
2. x2 > x3 or (x2 = x3 and y2 > y3)

Therefore, we have two cases:

Case 1: x1 > x2 > x3

If this is true, then we have

(x1, y1) > (x3, y3),

and the lexicographic preferences are transitive.

Case 2: x1 = x2 > x3

If this is true, then

y1 > y2, and x2 = x3,

which means

y2 > y3.

Therefore, (x1, y1) > (x3, y3), and the lexicographic preferences are transitive.

2. Now we need to prove that the lexicographic preferences on apricots and bananas cannot be represented by a continuous utility function u(a,b).

Suppose that there exists a continuous utility function u(a,b) that represents the lexicographic preferences on apricots and bananas.

Therefore, (a1, b1) ≻ (a2, b2) if and only if u(a1, b1) > u(a2, b2).

Let's consider two cases:

Case 1: a1 > a2.

Since

u(a1, b1) > u(a2, b2),

we have:

u(a1, b1) - u(a2, b2) > 0,

which means that

Δu = u(a1, b1) - u(a2, b2) > 0

Case 2: a1 = a2 and b1 > b2.

Since

u(a1, b1) > u(a2, b2),

we have:

u(a1, b1) - u(a2, b2) > 0,

which means that

Δu = u(a1, b1) - u(a2, b2) > 0

Therefore, we have Δu > 0 in both cases, which contradicts the fact that the lexicographic preferences on apricots and bananas are non-continuous.

Hence, they cannot be represented by a continuous utility function u(a,b).

In conclusion, the lexicographic preferences on apricots and bananas are transitive but cannot be represented by a continuous utility function.

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Answer:

13/18

Step-by-step explanation:

Therefore, 6.5 · 1/9 = 13/18.

Answer:

1479.2

Step-by-step explanation:

The code implementation of shell sort in C++ using the provided `city.h` header file and `cityArray[]`:

```cpp

#include "city.h"

City cityArray[] = {

   {"Tokyo", 38.98}, {"Delhi", 28.5}, {"Shanghai", 25.58}, {"São Paulo", 21.65},

   {"Mumbai", 21.04}, {"Mexico City", 20.99}, {"Beijing", 20.38}, {"Osaka", 19.28},

   {"Cairo", 18.77}, {"New York City", 18.6}, {"Dhaka", 18.24}, {"Karachi", 18},

   {"Buenos Aires", 15.59}, {"Istanbul", 15.29}, {"Kolkata", 14.85}, {"Manila", 14.7},

   {"Lagos", 14.37}, {"Rio de Janeiro", 14.31}, {"Tianjin", 13.4}, {"Kinshasa", 13.31},

   {"Guangzhou", 13.08}, {"Los Angeles", 12.82}, {"Moscow", 12.54}, {"Shenzhen", 12.44},

   {"Lahore", 11.13}

};

void shellSort(City arr[], int n) {

   for (int gap = n / 2; gap > 0; gap /= 2) {

       for (int i = gap; i < n; i += 1) {

           City temp = arr[i];

           int j;

           for (j = i; j >= gap && arr[j - gap].getPopulation() > temp.getPopulation(); j -= gap) {

               arr[j] = arr[j - gap];

           }

           arr[j] = temp;

       }

   }

}

int main() {

   int n = sizeof(cityArray) / sizeof(cityArray[0]);

   shellSort(cityArray, n);

   for (int i = 0; i < n; i++) {

       cityArray[i].print();

   }

   return 0;

}

```

Explanation:

The provided code demonstrates the implementation of the shell sort algorithm in C++. The `shellSort` function takes an array of `City` objects `arr[]` and its size `n` as parameters.

The outer `for` loop initializes the `gap` variable to `n/2`, representing the initial gap size for the first pass of shell sort. In each pass, the elements that are `gap` distance apart from each other are sorted. After each pass, the gap size is reduced by half until it reaches 0, indicating that the array is completely sorted.

The inner `for` loop iterates through the unsorted portion of the array, starting from the `gap` index and incrementing by 1. It performs an insertion sort on the sub-array by comparing and shifting elements that are greater than the key element (`temp`) to the right by `gap` distance. Finally, it inserts the key element into the correct position in the sub-array.

In the `main` function, the `shellSort` function is called to sort the `cityArray` based on the population of each city. After sorting, the sorted `cityArray` is printed using the `print` function defined in the `City` class.

This implementation demonstrates the shell sort algorithm's ability to sort the given array of `City` objects based on population in ascending order.

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Answer:

X = 12

Step-by-step explanation:

Since each angle is equivalent to each other, you can write the equation:

(9x-3) = (7x+21)

Then Simplify.

Subtract both sides by 7x

2x-3=21

Add 3 To Both Sides

2x=24

Divide by 2

X = 12

Answer:

9x-3=7x+21

9x=7x+24

2x=24

x=12

Step-by-step explanation:

(9x-3) and (7x+21) are corresponding angles that means that they are congruent. So they equal each other.

That day the number of adults was 95 and the number of children was 38

Let's define the variables:

x = number of adults.

y = number of children.

We know that 133 people used the public swimming pool. then we can write:

x + y = 133

We also know that the receipts for admission totaled 270.75, then we can write other equation as:

2.25x + 1.5y = 270.75

Then the system of equations is:

x + y = 133

2.25x + 1.5y = 270.75

In the first equation we can isolate x to get:

y = 133 - x

Now replace that in the other equation to get:

2.25x + 1.5*(133 - x) = 270.75

0.75x + 199.5 = 270.75

0.75x = 270.75 - 199.5

x = 71.25/0.75 = 95

Then the value of y is:

y = 133 - 95 = 38

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Answer:

20 is a tenth of 200

Step-by-step explanation:

Answer: 2

Step-by-step explanation:

x=10%(2)

20/x=10/100

200=100x

x=2

Answer:

x > 3

Step-by-step explanation:

Answer:

The value of the expression is 12 ⇒ B

Step-by-step explanation:

Let us solve the question

∵ The expression is 2n(n - 1)

→ Simplify it at first by multiply 2n by the bracket (n - 1)

∵ 2n(n - 1) = 2n(n) - 2n(1)

∴ 2n(n - 1) = 2n² - 2n

∵ n = 3

→ Substitute n by 3 in the expression to find its value

∴ 2n² - 2n = 2(3)² - 2(3)

∴ 2n² - 2n = 2(9) - 6

∴ 2n² - 2n = 18 - 6

∴ 2n² - 2n = 12 ⇒ at n = 3

∴ The value of the expression is 12