Solve the system. {4x^2+4y^2=36 {2x+3y=6

The central angle of the arc in degrees is 162 degrees.

The circumference of the circle is 10 units. The length of the arc is 9 / 2 units. The central angle can be calculated as follows;

We can find the central angle by comparing it to the length of the arc.

Therefore, we know the circle has a circumference of 10. We also know a circle is 360°.  The length of the arc is given as 9 / 2 units(4.5 units).

To determine the degrees of the central angle, we have to set up a ratio and set the unknown angle as x.

Hence,

length of the arc / circumference = angle of the arc / angle of the circle

4.5 / 10 = x / 360

cross multiply

360 × 4.5 = 10x

1620 = 10x

divide both sides by 10

x = 1620 / 10

x = 162 degrees

Hence,

central angle = 162 degrees.

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Answer:

To solve this problem, we need to use the formula for the volume of a cylinder: V = πr^2h, where V is the volume, r is the radius, and h is the height.

Step 1: We know that the radius of the tank is 2 feet and that it is being filled at a rate of 4 cubic feet per minute. We also know that the tank is half full, so we can assume that the height of the water in the tank is half the height of the tank itself.

Step 2: We can use the volume formula to find the volume of the tank when it is half full.

V = πr^2h

V = π(2^2)(h/2)

V = 4πh/2

Step 3: We can divide the rate of fill by the volume of the tank when it is half full to find the rate of change of the height of the water.

dh/dt = 4/(4π/2)

dh/dt = 2/π ft/min

Final Answer: The level of the water in the tank is rising at a rate of 2/π feet per minute when the tank is half full.

The area of the shaded portion of the figure is 272 units squared.

The figure above is a triangle inside a trapezium. The area of the shaded portion can be found when we subtract the area of the triangle from the area of the trapezium.

Therefore,

area of the shaded portion = area of the trapezium - area of the triangle

area of the triangle = 1 / 2 bh

where

Therefore,

area of the triangle = 1 / 2 × 18 × 16

area of the triangle = 288 / 2

area of the triangle = 144 units²

area of the trapezium = 1 / 2 (a + b)h

where

Therefore,

area of the trapezium = 1 / 2 (18 + 34)16

area of the trapezium = 1 / 2 (52)16

area of the trapezium =  832 / 2

area of the trapezium = 416 unit²

Therefore,

area of the shaded portion = 416 - 144

area of the shaded portion = 272 units²

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Listing of the angles and the sides in the order of smallest to largest is given by :

Side opposite to obtuse angle > Side opposite to acute angle and

side opposite to right angle > side opposite to acute angle.

As given in the question,

In the given triangle,

Ordering of the angles and sides from smallest to largest.

As per the property of the triangle:

Side opposite to the greatest angle is the largest side of the given triangle.

If the given triangle is obtuse angle triangle,

Then other two angles are acute.

Compare all the angles and sides arrange in ascending order.

Side opposite to obtuse angle  > Side opposite to acute angle

In the right angled triangle,

Other two angles are acute.

Same compare and write in ascending order.

side opposite to right angle > side opposite to acute angle

Therefore, the sides and angles can be written in smallest to largest order by comparison and is given by:

Side opposite to obtuse angle  > Side opposite to acute angle and

side opposite to right angle > side opposite to acute angle.

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Answer:

1. Write the number as the numerator of the fraction.

2. Write 1 as the denominator of the fraction.

Step-by-step explanation:

Example-

To turn the number 3 into a fraction, write 3 as the numerator and 1 as the denominator. The resulting fraction is 3/1.

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The number of non-empty subsets of the given set that consist entirely of prime numbers is [tex]$31-16=7$[/tex]

The total number of non-empty subsets of [tex]$\{1,2,3,4,5,6,7,8,9,10,11\}$[/tex] that consist entirely of prime numbers is 7. The prime numbers in the given set are {2,3,5,7,11}. The formula to calculate the number of non-empty subsets of a set with n elements is [tex]$2^n-1$[/tex]. Thus, the number of non-empty subsets of the given set is [tex]$2^{5}-1=31$[/tex]. To calculate the number of subsets that consist of prime numbers only, we need to subtract the number of subsets that contain at least one non-prime number from 31. There are 16 such subsets, as the non-prime numbers in the given set are[tex]$\{4,6,8,9,10\}$[/tex]. Thus, the number of non-empty subsets of the given set that consist entirely of prime numbers is[tex]$31-16=7$.[/tex]

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There is a statistically significant difference between the weights of the two cheeses at the 5% level of significance.

Standard deviation is a measure of how spread out a set of numbers is from the mean. It is calculated by taking the square root of the variance, which is the average of the squared differences from the mean. In other words, it is a measure of how much the values in a dataset differ from the mean, or average, value. Standard deviation is a useful tool for understanding the distribution of data and can be used to identify outliers and compare data sets.

To answer this question, we must use a two-tailed hypothesis test, where the null hypothesis is that there is no difference between the two cheeses. The alternative hypothesis is that there is a significant difference between the two cheeses.

Using the sample data provided, we are able to calculate the test statistic, which in this case is 2.02. This can be compared to the critical value from the t-distribution table, which is 1.711 for a 5% level of significance and 31 degrees of freedom.

Since the test statistic is larger than the critical value, we reject the null hypothesis and conclude that there is a statistically significant difference between the weights of the two cheeses at the 5% level of significance.

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On solving the provided question we can say that the linear regression results were: = 9.23 X [tex]10^{-3}[/tex]

When modeling the relationship between a scalar answer and one or more explanatory variables in statistics, linear regression is a linear method. Simple linear regression is used when there is only one explanatory variable. The procedure is known as multiple linear regression if there are numerous. A straight line is used to evaluate the relationship between the independent and dependent variables in a regression model known as simple linear regression. Both factors ought to be quantitative. The effect of the independent variable on the dependent variable is examined using simple linear regression. The second scenario, known as multiple linear regression, examines how various independent factors affect the dependent variable.

an education researcher gathers data about freshman students in an economics course.

he collects the number of hours that students study and the number of questions they missed (got wrong) on exams

the linear regression results were: = 9.23 X [tex]10^{-3}[/tex]

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Yes, Jackie is correct as the equation x = 0.25y could be written as x = ky which means x ∝ y. thus, 0.25 is a constant of proportionality.

The ratio between two proportional quantities has a constant value, which is known as the constant of proportionality. When either their ratio or their product produces a constant, two varying quantities are said to be in a proportional relationship. The Direct Variation and Inverse Variation types of proportion between the two given quantities determine the proportionality constant's value.

When two variables are directly or indirectly proportional to one another, their relationship can be expressed as y = kx or y = k/x, where k specifies how the two variables are related to one another. The proportionality constant, k, stands for this.

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Full question

Jackie was given a proportion x = 0.25y. Jackie says that the constant of proportionality in the equation is 0.25 is Jackie correct.

Yes, it makes sense that the number of cats falling from 5th floor would be greater since the terminal velocity of the cat would be greater at higher altitudes.

The pace at which an object's location changes in relation to a frame of reference and time is what is meant by velocity. Although it may appear sophisticated, velocity is just the act of moving quickly in one direction. Since it is a vector quantity, the definition of velocity requires both magnitude (speed) and direction.

A distance measurement between a reference datum and a point or object, typically in the vertical or "up" direction, is known as altitude, height, or depth.

The terminal velocity of the cat would be greater at higher altitudes; hence cats have higher risk of falling from heights.

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Answer:

  -4y²

Step-by-step explanation:

You want to simplify the expression -√(16y⁴), given that y < 0.

The square root can be simplified by removing squares from under the radical.

  [tex]-\sqrt{16y^4}=-\sqrt{(4y^2)^2}=\boxed{-4y^2}[/tex]

The sign of y is irrelevant.

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If the random variable X is distributed normally with a mean of 0 and a standard deviation of 1, the probability P(x = 0) =.50 is not correct.

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has included probability to forecast the likelihood of certain events. The degree to which something is likely to happen is basically what probability means.

The probability of all the events in a sample space adds up to 1.

Thus, If the random variable X is distributed normally with a mean of 0 and a standard deviation of 1, the probability P(x = 0) =.50 is not correct.

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The sequence of numbers for the expression -n² - 2n + 3 is

0, -5, -12, -21, and -32.

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,

-n² - 2n + 3

The sequence of numbers for n = 1, 2, 3, 4, 5 are:

n = 1,

-1 - 2 + 3

= -3 + 3

= 0

n = 2,

-4 - 4 + 3

= -8 + 3

= -5

n = 3,

-9 - 6 + 3

= -15 + 3

= -12

n = 4,

-4² - 2 x 4 + 3

= -16 - 8 + 3

= -21

n = 5,

-25 - 10 + 3

= -35 + 3

= -32

Thus,

The sequence of numbers is 0, -5, -12, -21, and -32.

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The number of pais of headphones that can be manufactured in a day = 576

Given that the time to manufacture a pair of headphones on each assembly line is 1/3 hour.

By unitary method the number of pairs of headphones can be manufactured in an hour :

1 ÷ (1/3)

= 1/ (1/3)

= 3

So, 3 pairs of headphones can be manufactured in an hour.

We need to determine the number of pairs of headphones that can be manufactured in a day.

Since we can operate assemply line 8 hours a day.

By unitary method the number of pairs of headphones can be manufactured in 8 hours:

3 × 8 = 24

And there are such 24 assembly lines.

So, the number of pais of headphones that can be manufactured in a day:

24 × 24 = 576

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Answer:

25,295.91

Step-by-step explanation:

304,770

1%=3047.7

0.1%=304.77

8%=24,381.6

0.3%=914.31

24,381.6+914.31=25,295.91

female viewers =25,295.91

Answer:

12 students earned B Honor Roll

Step-by-step explanation:

Let A be the number of students who earned A Honor Roll and B the number who earned B.

We are told that A = 24,

and that A = 3B-12  [ . . .were twelve less than three times the number of students who earned B Honor Roll]

Since we know the value of A (24) use the second equation to find B:

A = 3B-12

24 = 3B-12

3B = 36

B = 12

CHECK:

Is 24 12 less than three times B(12)?

 24 = 3*12 - 12?

 24 = 36 - 12?

  24 = 24

 YES

The expected value of the number of marbles Zuri removes from the bag is the sum of the number of red marbles plus the number of blue marbles.

The expected value of the number of marbles Zuri removes from the bag is the sum of the number of red and blue marbles. This is because the expected value of an event is the sum of the probability of each outcome multiplied by the associated outcome. Since Zuri is randomly removing marbles from the bag, one at a time and without replacement, the probability of each outcome (red or blue) is equal. Therefore, the expected value of the number of marbles Zuri removes from the bag is the sum of the number of red marbles plus the number of blue marbles. This is because each marble has an equal chance of being removed and, therefore, each marble has the same expected value.

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The range possible length of the third side of the triangle is greater than 11.

The lengths of two sides of a triangle are 7 cm and 17 cm.  The range of the possible length for the third side can be calculated as follows:

The triangle inequality theorem simply states that the sum of any two sides in a triangle must be greater than the length of the third side of the triangle.

Using triangle inequality theorem, if a, b and c are the sides of the triangle. Hence,

a + b > c

a + c > b

b + c > a

Hence,

7 + 17 > c

7 + c > 17

17 + c > 7

Therefore, using 7 + c > 17, c should be greater than 11.

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Answer:

The number that gives the same result if it is multiplied by 999/998 or if any number is added to it is zero (0).

The property of a number being unchanged after being multiplied by a fraction and a constant is called an "Identity element". The identity element for multiplication is 1 and for addition is 0.

When any number is multiplied by 1, it stays the same. So, if we multiply any number by 999/998, which is equivalent to multiplying by 1, it stays the same.

Similarly, when any number is added to zero, it stays the same. So, if we add any number to 0, it stays the same.

Therefore, the only number that gives the same result if it is multiplied by 999/998 or if any number is added to it is zero (0).

For Palanzios' Pizzeria and Guido’s Pizza to cost the same, the number of toppings needed is 2.

Let's begin by assigning a letter to represent our unknown:

   x = Number of toppings to be added to each pizza

Now,

Based on the Given information :

Expressions for the cost of each pizza with its toppings:

   Palanxio's Pizza:  6.80 + 0.90x

   Guido's Pizza:      7.30 + 0.65x

Now,

Equating the costs of both pizzas and solve for our unknown (x):

   ⇒ 6.80 + 0.90x = 7.30 + 0.65x

  ⇒ 0.90x - 0.65x = 7.30 - 6.80

   ⇒ 0.25x = 0.50

   ⇒ x = 0.50/0.25

   ⇒ x = 2

Therefore, There are 02 toppings to be added to each pizza.

Finally, we can verify our answer by putting the values back into our equation :

   6.80 + 0.90x = 7.30 + 0.65x    

   6.80 + 0.90(2) = 7.30 + 0.65(2)

   6.80 + 1.80 = 7.30 + 1.30

                       = $8.60        [both costs are the same]

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Answer:

Step-by-step explanation:

The power of 10 is the exponent of places we move the decimal point to get the first factor. For any number greater than 1, the power of 10 in scientific notation will be positive.

First Non-zero Power of 10

Example: Let’s look at the mass of Earth in kilograms.

What power? 9

Numbers can also be converted from scientific notation to standard notation.

Look at the number 6.51 × 108 . The power of 10 denotes the number of places the decimal point has to move. The power of 10 in this number is positive, so we move the decimal point to the right 8 places.

The number 6.51 × 108 written in standard notation is 651000000.

Step-by-step explanation:

we know

[tex]y = mx + c[/tex]

Answer:

y-intercept: -3

slope: 4

equation: y=4x-3

Step-by-step explanation:

To find the y-intercept, it shows in the table of value that when x is 0, y is -3 so y-intercept = -3. To find the slope, find the first differences which is 4.

For given function f(x) the y in the graph are f(2) = 4,f(0) = 3 ,f(-6) = -6 and f(4) = 5

A function is described as a relationship between a set of inputs, each of which has a single output. The simplest definition of a function is an association between inputs where each input is connected to a single, unique output. There is a codomain or range for each function. A function is frequently referred to as f(x), where x is the input.

Here,

In the given graph

when x = 2

y = 4

and x = 0

y = 3

Put it in slope formula

=> m =y2 - y1 / x2 -x1

=>  m =1/2

m = 1/2

Now we can just put them into slope formula

y - y₁ = m(x - x₁)

y - 4 = 1/2(x - 2)

y = 1/2(x) -1 + 4

y = 1/2(x) + 3

Now we can just put them into slope formula

y - y₁ = m(x - x₁)

y - 3 = 1/2(x - 0)

y = 1/2(x)  + 3

Thus, the function for given f(x) is solved

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Answer:

Step-by-step explanation:

true true false

Answer:

We can use the following steps to determine the different amounts of money that can be made from a collection of coins that consists of two pennies, one nickel, and one dime:

Step 1: List out all the different combinations of coins that can be used to make the different amounts of money.

Two pennies

One penny and one nickel

One penny and one dime

Two pennies and one nickel

Two pennies and one dime

One nickel and one dime

Two pennies, one nickel, and one dime

Step 2: Calculate the value of each combination of coins.

Two pennies = $0.02

One penny and one nickel = $0.06

One penny and one dime = $0.11

Two pennies and one nickel = $0.07

Two pennies and one dime = $0.12

One nickel and one dime = $0.15

Two pennies, one nickel, and one dime = $0.17

Step 3: Write down the total amount of money that can be made from each combination.

Final Answer: There are 7 different amounts of money that can be made from a collection of coins that consists of two pennies, one nickel, and one dime, they are $0.02, $0.06, $0.11, $0.07, $0.12, $0.15, and $0.17

Answer:

58.4%

Step-by-step explanation:

We can create a total number of 10 prime numbers from the set {1, 3, 6, 7}.

Given that,

The number is either 1-digit or 2-digit.

In the case of 1-digit, the only 1-digit primes are 3 and 7, for a total of 2 primes.

In the case of 2-digit, We have the following combinations of numbers: 13, 16, 17, 36, 37, 67, 76, 73, 63, 71, 61, 31. Out of these 12 numbers, it is easier to count the composites: 16, 36, 76, and 63 for a total of 4 composites, which we subtract from the original 12 numbers to yield 12-4=8 prime numbers.

Thus, We can create a total number of 10 prime numbers from the set {1, 3, 6, 7}.

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Answer: number 1: 0.1111 and number 2: 1.0909

Step-by-step explanation: I hope I did this right

  The ant's entire distance travelled along its semicircular journey is its total distance travelled overall. The ant is travelling around a circle with radius R, thus the distance it has travelled is equal to half of the circle's circumference, πR.

The change in the ant's position is represented by a vector quantity called the displacement of the ant. The ant in this scenario begins at one end of the semi-circular path and moves 2R away from the beginning point to reach the other end. The direction of the displacement vector is from the starting point to the ending point, and the displacement's magnitude is equal to the 2R distance between the two points.

    So, the option c is most suitable option.

Therefore, πR and 2R are the ant's displacement and the distance travelled, respectively.

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Answer:

y = -4x

Step-by-step explanation:

When equations are in the form

y = mx  the slope m (is y/x)