An elliptical mirror measures 16 inches wide and 20 inches high. The ellipse is centered at (0, 52) on a coordinate plane, where units are in inches. Which equation represents the mirror?
(y - 52)²/400 + x²/256 = 1
(y – 52)²/100+ x²/64 = 1
X²/400+ (y-52)²/256 = 1
x²/100+(y-52)²/64 = 1

The car's speed in kilometers per minute is 1.01667. And the number of kilometers will the car travel in 20 minutes will be 20.33 kilometers.

Speed is defined as the length traveled by a particle or entity in an hour. It is a scale parameter. It is the ratio of length to duration.

We know that the speed formula

Speed = Distance/Time

A car is traveling at a speed of 61 kilometers per hour.

Convert the speed into a kilometer per minute. Then we have

Speed = 61 / 60

Speed = 1.01667 kilometers per minute

Then the number of kilometers will the car travel in 20 minutes will be given as,

1.01667 = d / 20

d = 1.01667 x 20

d = 20.33 kilometers

The car's speed in kilometers per minute is 1.01667. And the number of kilometers will the car travel in 20 minutes will be 20.33 kilometers.

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Approx 16 revolutions the wheel go through to travel the distance 25 meters by a diameter of 50 cm.

In the given question, a wheel having a diameter of 50 cm.

If the elf travels a distance of 25 meters then we have to find how many revolutions did the wheel go through.

Since we have the wheel's diameter, we can determine the radius of the wheel. As we already know, the length of a wheel's revolution is equal to its circumference, which is a circle with a diameter of 2πr.

We will now enter the radius value into the algorithm to determine how many revolutions the wheel must make. To reach the desired result, divide the total distance by the distance covered in one revolution to determine the number of revolutions needed to travel 25 m.

r = [tex]\frac{50}{2}[/tex] = 25 cm

The radius of the wheel is 25 cm.

Now we put the value of r in the formula of circumference.

2πr = 2π×25

2πr = 50π cm

Total distance is 25 m. So we convert m in cm by multiplying the 100.

Now the total distance is 2500 cm.

2500 = n × 50π

Now putting the value of π = 3.14

2500 = n×50 × 3.14

2500 = n×157

Divide by 157 on both side, we get

n = 15.924

n = 16(approx)

Hence, approx 16 revolutions the wheel go through to travel the distance 25 meters by a diameter of 50 cm.

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As the p-value of the test is of 0.215 > 0.05, there is not enough evidence at the 0.05 level that the technique performs differently than the traditional method.

At the null hypothesis, it is tested if there is no evidence of different performance, that is, the mean is of 8.5 hours, hence:

[tex]H_0: \mu = 8.5[/tex]

At the alternative hypothesis, it is tested if there is evidence of different performance, with a mean different of 8.5 hours, hence:

[tex]H_1: \mu \neq 8.5[/tex]

The population standard deviation is known, hence the z-distribution is used to obtain the test statistic.

The equation is given as follows:

[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

In which:

The parameters for this problem are given as follows:

[tex]\overline{x} = 8.8, \mu = 8.5, \sigma = \sqrt{1.21} = 1.1, n = 21[/tex]

Hence the test statistic is calculated as follows:

[tex]z = \frac{8.8 - 8.5}{\frac{1.1}{\sqrt{21}}}[/tex]

z = (8.8 - 8.5)/(1.11/square root of 21)

z = 1.24.

The p-value is obtained using a z-distribution calculator.

We have a two-tailed test, as we are testing if the mean is different of a value, with a test statistic of z = 1.24, hence the p-value is of:

0.215.

(2 multiplied by the subtraction of one and the p-value of z = 1.24).

The p-value is greater than the significance level of 0.05, meaning that there is not enough evidence to reject the null hypothesis and conclude that there is a difference between the two methods.

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The length of the actual statue in feet would be = 64.96 ft

A scale model is defined as the the exact type of an object but with a different measurement.

The scale model of a statue = 1 In = 11.2 ft

The length of the model = 5.8 inches

Therefore it length in feet = X ft

That is; 1 in = 11.2 ft

5.8 in = X ft

make X ft the subject of formula;

X ft = 5.8 × 11.2 = 64.96 ft

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The length of PG if PG' is 0.5 units is; 3 units.

The act or action of enlarging, expanding, or widening : the state of being dilated: such as. : the act or process of expanding (such as in extent or volume)

Here, given that,

Dilation is simply defined as the shrinking or enlarging of an object by a scale factor.

Now, we are told that Line HG is dilated to form a shorter line H'G'.

We are told that the scale factor is 1/6.

Point P is the center of dilation and if PG' is 0.5 units, then we can write the relation as follows;

Length of PG'/Length of PG = 1/6

Thus;

0.5/length of PG = 1/6

Length of PG = 0.5/(1/6)

Length of PG = 4 units

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The park should be expanded based on the information as the majority want the expansion.

From the information, on the small town surveyed 250 adults, 180 of whom were parents, about whether a park should be expanded.

Also, the results showed that 150 of the adults who were parents and 40 of the adults who were not parents thought the park should be expanded.

Based on the above the number of people that wants the expansion will be:

= (150 + 40) / 250 × 100

= 190 / 250 × 100

= 76%

It should be expanded.

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Answer:

37

Hope this helps :)

The average rate of change is the ratio of the difference between the y coordinates of two points to the x coordinate of the same point.

It can be found by using two points on the graph and substitute into the formula: (y₀ - y₁) / (x₀ - x₁)

The square brackets [] is used to mean the end points as shown is inclusive

A quadratic equation is a polynomial of degree two

The average rate of change here is not constant and is usually  specified by the two points to which it is measured

For instance using points (-3, 0) and (0, -1) we have

=  (y₀ - y₁) / (x₀ - x₁)

=  (-1 - 0) / (0 - (-3))

= -1/3

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The student is testing each soil's permeability, and soil X is more permeable than soil Y. The correct option is A.

An experiment is a technique used to confirm or deny a hypothesis, as well as assess the likelihood or effectiveness of something that has never been tried before. Experiments show what happens when a specific factor is modified, which sheds light on cause-and-effect relationships.

Porosity can be defined as the quality of the material having pores or holes. The permeability can be defined as the state or quality of a material that allows liquids or gases to pass through it.

The soil which does not hold much water can be considered of high porosity and high permeability. As it is only possible if the soil has a large number of pores and it is not in compact form.  

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9 non-congruent squares can be drawn.

Non-congruent squares are two squares with different side lengths. These two squares can be drawn separately and still have four right angles and four equal sides, but the lengths of the sides are not the same. Non-congruent squares are a type of quadrilateral and have both diagonals and parallel sides. These shapes can be used to create a variety of geometric designs and patterns, and often appear in art and architecture.

Each of the four corners of the 5 by 5 grid can be the vertices of a square, and the middle of each side of the 5 by 5 grid can be the vertices of a square. This makes eight non-congruent squares in total. Additionally, the center point can be the vertex of another non-congruent square, making nine in total. All of these squares are constructed from lattice points, and none of them are congruent to each other.

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Three glasses of milk or dairy products per day are recommended for adults. One serving of milk is one cup. According to the USDA, a serving of milk-based goods is the amount that corresponds to one cup of milk.

Food items manufactured from (or containing) milk are referred to as dairy products or milk products (also known as lacticinia).

The cow, water buffalo, nanny goat, and ewe are the most popular dairy animals.

Dairy products include staples from Western grocery stores including yogurt, cheese, and butter.

A dairy is a place where dairy products are made .Various amounts of dairy products are consumed worldwide (see consumption patterns worldwide) .

After standardizing the fat content and optional homogenization or pasteurization, milk is produced in a variety of grades with the potential addition of the microorganisms Streptococcus lactis and Leuconostoc citrovorum.

Based on the type of product generated, milk can be divided into a number of distinct categories, including cream, butter, cheese, newborn formula, and yogurt.

Hence, Three glasses of milk or dairy products per day are recommended for adults. One serving of milk is one cup. According to the USDA, a serving of milk-based goods is the amount that corresponds to one cup of milk.

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There are 12 weeks will Sonja's balance remain above $377.

What is account balance?

The balance is the sum owed on an account in banking and accounting. The term "balance" in bookkeeping refers to the difference between the total of debit entries and the total of credit entries made into an account over the course of a given financial period. The account shows a debit balance when total debits exceed total credits.

Given:

Sonja has a bank account balance of $1400. Each week, her balance changes by -$85.25. She wants to keep the balance above $377.

We have to find the number of  weeks will Sonja's balance remain above $377.

Let, $1400 - $377 = $1023.

⇒  $1023 / $85.25 = 12

Hence, there are 12 weeks will Sonja's balance remain above $377.

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Therefore , the solution of the given problem of equation comes out to be  9x^3 - 8x^2.

A mathematical equation is a formula that uses the equal sign (=) to connect two statements and express equality. A mathematical statement that proves the equality of two mathematical expressions is known as an equation in algebra. For instance, the components 3x + 5 and 14 in the equation 3x + 5 = 14 are separated by an equal sign. The equal sign is a crucial part of mathematical formulas, especially equations. Algebra is frequently utilized in equations. Algebra is used in mathematics when it is difficult to determine a precise quantity.

Here,

Polynomial function total

Polynomial functions are those that have a leading degree of three or higher. given the total;

(7x^3-4x^2)+(2x^3-4x^2)

Expand => (7x 3-4 times) + (2x 3-4 times)

= > 7x^3-4x^2 + 2x^3-4x^2

assemble similar terms

=> 7x^3 + 2x^3 - 4x^2 -4x^2

=> 9x^3 - 8x^2

Therefore , the solution of the given problem of equation comes out to be 9x^3 - 8x^2.

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The equation which describes the nth term for the sequence 3/5,1/5,1/15,1/45,\cdots2 is  an = 3/5 (1/3)n-1 , which is option C.

We use the formula an=a1+(n−1)d an = a1 + (n−1)d , to calculate the nth term of a given sequence. The 'n' here  represents a number.

Using the nth term we can any number on the sequence which allows us to locate any term in a series.

By substituting different values for the term number, we can create a series utilizing the nth term (n).

To find the tenth term we use the sequence formula and substitute a random number in place of n.

Example if we need to find the first 50 term then we will substitute n as 50.

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If [tex]\frac{1}{4}[/tex] of fruit punch is pineapple juice. About [tex]\frac{1}{6}[/tex] of the fruit punch is orange juice, then fraction of punch that is pineapple juice or orange juice is [tex]\frac{5}{12}[/tex] .

The fraction of pineapple juice in fruit punch is = [tex]\frac{1}{4}[/tex] ;

the fraction of orange juice in fruit punch is = [tex]\frac{1}{6}[/tex] ;

the equation that can be used to find the fraction of fruit punch that is pineapple juice or orange juice is

⇒ [tex]Frcation Of (Pinapple Juice +Orange Juice)[/tex]

substituting the values ,

we get the equation as ;

⇒ [tex]\frac{1}{4} +\frac{1}{6}[/tex]

taking LCM as 4 and 6 as 12 and solving further  ,

we get ;

⇒ [tex]\frac{3}{12} +\frac{2}{12}[/tex] ; = [tex]\frac{5}{12}[/tex] .

Therefore , the fraction of fruit  punch that is pineapple juice or orange juice is [tex]\frac{5}{12}[/tex] .

The given question is incomplete , the complete question is

About 1/4 of fruit punch is pineapple juice. About 1/6 of the fruit punch is orange juice. Write and solve an equation to find the fraction of the punch that is pineapple juice or orange juice .

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Answer:

-----------------------------

15 inches of wire costs 90 cents, then 1 inch of wire costs:

The length of wire for 72 cents:

Answer:

Step-by-step explanation:

(-2,4)

(0,5)

(2,6)

(4,7)

Answer: 4, 5, 6, 7,

Step-by-step explanation: From the formula   y = x / 2 + 5

substitute x with the value -2

It becomes -2 / 2 + 5

that equals 4

then do the same for the rest

when x = 0

y = 0 / 2 + 5

y = 5

when x = 2

y = 2 / 2 + 5

y = 1 + 5

y = 6

when x = 4

y = 4 / 2 + 5

y = 2 + 5

y = 7

I hope this was helpful

The algebraic solutions are x < -5 and x > 3.

The graph is given below.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 4 = 9 is an equation.

We have,

x² + 2x > 15

x² + 2x - 15 > 0

x² + (5 - 3)x - 15 > 0

x² + 5x - 3x - 15 > 0

x(x + 5) - 3(x + 5) > 0

(x - 3)(x + 5) > 0

x + 5 > 0 and x - 3 > 0

x < -5 and x > 3

The graph is given below.

Thus,

x < -5 and x > 3 is the solution.

The graph is given below.

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Answer:

515 x + 285 y = 11080

x + y = 30

Step-by-step explanation:

Two slopes can be compared on a graph by analyzing the steepness of the lines and their direction (positive or negative).

The steepness of a line on a graph is determined by its slope, which is the ratio of the change in y to the change in x (rise over run). A steep line has a large slope, meaning that for a small change in x, there is a large change in y. A shallow line has a small slope, meaning that for a small change in x, there is a small change in y. To compare two slopes, one can compare the steepness of the lines by comparing the absolute value of the slopes.

If one line has a larger absolute value than the other, it is steeper. Additionally, one can also compare the direction of the slope, which is determined by the sign of the slope. A positive slope indicates that the line is increasing and a negative slope indicates that the line is decreasing. By comparing the steepness and direction of the slopes, one can determine whether the two lines are parallel or not, and whether they are going in the same direction or not.

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Answer:

7/12

Step-by-step explanation:

y = 12

x = 7

y = Kx

K = y/x

K = 7/12

Answer:

70⁰

Step-by-step explanation:

We need to use the knowledge of trigonometry to find the indicated angle. Given the information in relation to the angle we have the opposite and the hypotenuse.

we therefore use Sine in this calculations

Sin ? = opposite/ hypotenuse

= 16/17

= 0.9412

to get the angle we get the sine inverse

Sine inverse of 0.9412 = 70.25⁰

= 70⁰

Answer:

? ≈ 70°

Step-by-step explanation:

using the sine ratio in the right triangle

sin ? = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{16}{17}[/tex] , then

? = [tex]sin^{-1}[/tex] ( [tex]\frac{16}{17}[/tex] ) ≈ 70° ( to the nearest degree )

Answer: The answer is 11 1/4

Step-by-step explanation:

The correct answer is A representative, random sample of individuals are questioned regarding their attitudes or behaviours. (Option B)
A) "Individuals are carefully observed in their natural environments" is a description of participant observation, which is a type of qualitative research method. In this method, researchers observe and interact with individuals in their natural environments in order to understand their behaviours and attitudes in context. This method is often used in fields such as anthropology, sociology, and psychology.

B) "A representative, random sample of individuals are questioned regarding their attitudes or behaviours" describes a survey, which is a quantitative research method. Surveys are used to gather information from a representative sample of individuals in order to make inferences about a larger population. Surveys can be conducted in various ways, such as through phone calls, mail or online and can be used to study the attitudes, behaviours, and characteristics of a population.

C) "An individual is studied in great depth" is a description of a case study, which is a qualitative research method. In this method, a researcher closely examines an individual or a small group of individuals in order to gain a detailed understanding of their experiences, behaviours, and attitudes. Case studies are often used in fields such as psychology, sociology, and anthropology.

D) "An investigator determines the extent to which two variables influence each other" is a description of a correlation study, which is a quantitative research method. In this method, the researcher examines the relationship between two or more variables. The researcher measures the values of the variables for a sample of individuals, and then uses statistical methods to determine the degree of association between the variables, and if there is a causal relationship or not.

Thus, The correct answer is A representative, random sample of individuals are questioned regarding their attitudes or behaviours. (Option B)

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The Osborne 1 was the first laptop ever released, and it weighed 11 kg in 1981. Since then, the average rate of weight decrease has been 4.7% per year. This means that in 2019, a laptop would have weighed around 2.3 kg.

1981: 11 kg

1982: 10.5 kg (11 kg - 0.55 kg = 10.5 kg)

1983: 10.02 kg (10.5 kg - 0.48 kg = 10.02 kg)

1984: 9.55 kg (10.02 kg - 0.47 kg = 9.55 kg)

2019: 2.3 kg (3.44 kg - 1.14 kg = 2.3 kg)

The Osborne 1 was the first laptop ever released in 1981, and it weighed 11 kg. Since then, the average rate of weight decrease has been 4.7% per year. This means that the mass of a laptop decreases by 0.47 kg every year on average. So, in 1982 it would have weighed 10.5 kg, in 1983 it would have weighed 10.02 kg, and so on. By 2019, the weight of a laptop would have decreased to 2.3 kg as a result of this 4.7% average rate of weight decrease.

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Answer:

The tree is 9.1 meters high.

Step-by-step explanation:

We can use the Pythagorean Theorem to solve this problem. Let T be the height of the tree. We can set up the following equation:

4.2^2 + T^2 = 6.5^2

Solving for T, we get:

T = sqrt(6.5^2 - 4.2^2)

T = sqrt(41.25 - 17.64)

T = sqrt(23.61)

T = 4.878

Since the height of the tree is measured to the nearest tenth, we can round this value to 9.1 meters.

The number of possible different sequences of heads and tails is 1024.

A list of numbers (or other components) that follow a specific pattern is called a sequence. An arithmetic progression is one of the common examples of sequence and series.

A sequence can be arranged in either ascending or descending order.

Each flip has two outcomes H or T, so in ten flips you can get a sequence like HTHHTHTTTH

The number of possible different sequences is simply 2*2*2*2*2*2*2*2*2*2 = 2^10 = 1024

Thus, The number of possible different sequences of heads and tails is 1024.

Complete question:

If you flip a coin ten times, how many different sequences of heads and tails are possible?

a. 2° = 512

b. 10 = 100

C. 102 = 1024

d. 210 = 1024

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the middle value in a data set when the values are put in order

For example, the set {3,1,2} sorts to {1,2,3} where the median is 2.

Another example: The set {1,2,3,4} has 2 and 3 tied for the middle most position. The midpoint is (2+3)/2 = 5/2 = 2.5 which is the median.

Therefore , As a result, 80x + 60y ≥ 6800 is the answer to the inequality problem given.

Both formulae and inequalities are mathematical phrases created by connecting two expressions. The equal sign (=) in an equation denotes that the two expressions are regarded as equal. In contrast, an inequality indicates that the two phrases are not always equal by using the symbols >,≥,≤, or.<

Here,

Let the quantity of sold laptops, x

y —- the quantity of sold smartphones

The fact that to solve this problem we use inequality help

The problem's underlying inequity is equal to

=> 80x + 60y ≥6800

Therefore , As a result, 80x + 60y ≥ 6800 is the answer to the inequality problem given.

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The domain and range of the functions are Domain: (-∞,∞),{x|x∈R} and Range: [4,∞),{y|y≥4}.

The vertex form of a quadratic function is f(x) = a(x - h)² + k, where (h, k) is the vertex of the parabola. The coefficient a determines whether the graph of a quadratic function will open upwards or downwards.

From the graph, vertex is (h, k)=(0, 4) and (x, y)=(2, 0)

Here, y= a(x - h)² + k

0=a(2-0)+4

-4=2a

a=2

Substitute, a=2 and (h, k)=(0, 4) in y= a(x - h)² + k, we get

y=2(x-0)²+4

y=2x²+4

So, f(x)=2x²+4

Find the domain by finding where the function is defined. The range is the set of values that correspond with the domain.

Domain: (-∞,∞),{x|x∈R}

Range: [4,∞),{y|y≥4}

Now,

(a) f(-3)= 2(-3)²+4=18

(b) f(2)= 2(2)²+4=12

(c) f(0)= 2(0)²+4=4

(d) f(3)= 2(3)²+4=18

Therefore, the domain and range of the functions are Domain: (-∞,∞),{x|x∈R} and Range: [4,∞),{y|y≥4}.

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