Olivia is an athlete. During training this morning, she ran three laps. It took her 5 6minute to finish the first lap. The second lap took her 1 12more minutes than the first lap. The third lap took her 1 10less minutes than the second lap. How much time did it take her to finish the third lap?

We will write greater than 20 using Inequality sign as ( > 20).

The first number in every inequality sign tells us how the first and second numbers relate to one another, so  > 20 means "A number is greater than 20."

In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to one another.

Greater than and less than symbols are used to indicate whether one number is greater than or less than another. The greater than symbol (>) is used when the first number exceeds the second number. The less than symbol (<) is used when the first number is less than the second number.

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Omar would most likely use a line graph to show changes in water depth. A line graph would allow him to plot the water depth readings against a timeline and visualize how the depth changes over the duration of the drought.

A line graph is the most appropriate method of displaying data to show changes in water depth over the duration of the drought. A line graph is a type of chart that plots data points on a two-dimensional coordinate system. It is used to show how one set of data changes over a period of time. Omar would plot the water depth readings along the vertical y-axis and the days of the drought along the horizontal x-axis. A line would then be drawn to connect the data points, depicting the changes in water depth over the period of the drought. Additionally, the data points can also be labeled to provide more detailed information about the water depth readings at each point. This would allow Omar to compare the readings over time and monitor the effects of the drought on the water depth.

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The probability that exactly two of the students are juniors is given as follows:

0.270 = 27%.

The mass probability formula is presented as follows:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

The values of these parameters for this problem are given as follows:

[tex]N = 60, n = 4, k = 18[/tex]

Hence the probability that exactly two of the students are juniors is calculated as follows:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]P(X = 2) = h(2,60,4,18) = \frac{C_{18,2}C_{42,2}}{C_{60,4}} = 0.270[/tex]

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From the concept of algebra of venn diagram we obtain that
P(A or B) = 0.75.

A set is a collection of well-defined objects.

A subset contains all the elements or few elements of the given set.

The improper subset is when it contains all the elements of the given set and the proper subset is when it doesn't contain all the elements of the given set.

From set theory, we know that N(A∪B) = N(A) + N(B) - N(A∩B).

It states that N(A) or N(B) is the sum of N(A) and N(B) minus the common intersecting region N(A∩B) as we have already considered the region in the sum of N(A) and N(B) twice.

Similarly, P(A or B) = P(A) + P(B) - P(A∩B)>

Therefore, P(A or B) = 0.50 + 0.40 - 0.15.

P(A or B) = 0.90 - 0.15.

P(A or B) = 0.75.

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The multiplicity of a number is the number of times a number is a factor of another number.

In general, the multiplicity of a number can be determined by dividing the number by the factor. If the result is a whole number, then the multiplicity of the factor is equal to the result of the division. If the result is a decimal or fraction, then the multiplicity of the factor is 0.

For example, if we wanted to find the multiplicity of 5 in 25, we would divide 25 by 5: 25/5 = 5. This means that the multiplicity of 5 in 25 is 5.

The multiplicity of 5 can also be determined by finding the prime factorization of the number. For example, if we wanted to find the multiplicity of 5 in 30, we would factorize 30: 30 = 2 x 3 x 5. This means that the multiplicity of 5 in 30 is 1, because there is only one 5 in the prime factorization of 30.

In summary, the multiplicity of a number is the number of times a number is a factor of another number. The multiplicity of a number can be found by dividing the number by the factor, or by finding the prime factorization of the number.

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By using the concept of conjugate, it can be calculated that

Conjugate of [tex]x + \sqrt{y}[/tex] is [tex]x - \sqrt{y}[/tex]

What is conjugate?

Conjugating is the process of changing a verb in a sentence to match the person, number, gender, tense, mood, and voice of the subject. For example, the verb "to walk" changes to "walked" when conjugated in the past tense. Conjugation is important in many languages, including English, as it helps to make communication more precise. Conjugation involves making changes to the base form of the verb, such as adding suffixes or prefixes, or changing the spelling of the word. Different languages have different rules for conjugating verbs, so it is important to understand the language’s system of conjugation before attempting to use it.

Here the expression is [tex]x + \sqrt{y}[/tex]

Conjugate of [tex]x + \sqrt{y}[/tex] is [tex]x - \sqrt{y}[/tex]

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The factors of  2x² - 7x - 15 are (2x + 3) and (x - 5).

By splitting the middle term and factoring the polynomial,

2x² - 7x - 15

= 2x² - 10x + 3x - 15

= 2x(x - 5) + 3(x - 5)

= (2x + 3)(x - 5)

The factors of  2x² - 7x - 15 are (2x + 3) and (x - 5).

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When the mean is 6, the mean deviation of a given collection of data is 2.4.

The deviation is a metric used in statistics and mathematics to discover the difference between the actual and predicted values of a variable. The deviation is just the distance from the central point. The mean deviation is a statistical metric that computes the average departure from the mean value of a given data collection. Using the following approach, you can simply determine the mean deviation of the data values. We categorize the data and describe the frequency distribution of each group to provide it in a more concise way. These are referred to as class intervals.

Here,

To find out the mean deviation, just follow the steps given below.

Step 1: Find the mean for the given set of values

Step 2: Find the distance. (i.e) Subtract the mean value from each given values, and ignore minus symbol if any

Step 3: Finally, find the mean of the obtained distance, which is called the mean deviation.

=(2+4+6+8+10)/5

=6

mean deviation,

=(4+2+0+2+4)/5

=2.4

The mean deviation of given set of values is 2.4 when mean is 6.

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The lines p and q are perpendicular in the coordinate plane.

The name of the other number line, which is a vertical one, is called the y-axis. To graph points, lines, and other objects, one can utilize the coordinate plane. A pair of numerical coordinates that uniquely identify each point in a Cartesian coordinate system in a plane are called the coordinates. These numerical coordinates are signed length measurements that represent the separations between two fixed perpendicular oriented lines and the point.

Let the equation of the line is:

y-y'=m₁(x-x')

m₁=2/6

m₁=1/3

Therefore, the equation of a line with the point (3, 4) and slope m₁=1/3

y-4=(1/3)(x-3)

y=(1/3)x-1+4

y=(1/3)x+3

And m₂= -3

The line equation that is passing through (2,7) and m₂= -3

y-7=(-3)(x-2)

y-7= -3x+6

y= -3x+13

m₁×m₂= -1

(1/3)(-3)= -1

So, the lines that are given in the coordinate plane p and q are perpendicular.

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Using the roots of the quadratic equation the equation is solved to be

Information from the problem include

The quadratic function f(x) has roots of −2 and 3 and point (2, −4) lies on f(x)

from the roots

x = -2 and x = 3

x + 2 = 0 and x - 3 = 0

(x + 2)(x - 3)

passing through points (2 , -4)

y = a(x + 2)(x - 3)

-4 = a(2 + 2)(2 - 3)

-4 = a * 4 * -1

-4 = -4a

a = 1

the quadratic  equation is f(x) = (x + 2)(x − 3)

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Answer: X=20 Y=70

Step-by-step explanation:

There’s no labels so it might be hard to explain this one otherwise

-We’ll call the point at the top left with y°: A

-the bottom right point with x°: C

-the point in between them with 40°: B

-the bottom left point with the right angle: D

angle DBC = 140° because angles on a straight line sum to 180°

so x must equal 20 because the other angles in an isosceles triangle are equal and 180-140=40 and 40/2=20

90-20=70 so angle ADB=70

meaning that y must equal 70 because 70+40=110 and 180-110=70

Counting to 100 frequently and accurately can be mastered between the ages of three and a half and five and a half, but no later than the age of six.

The series of physical, language, mental, and emotional changes that occur in a kid from birth to the beginning of maturity is referred to as child development. During this phase, a kid moves from being dependent on their parents/guardians to be more self-sufficient.

Most parents will notice their children can count to 100 without any assistance around this age.

So it was apparent that they had a lot of practice time and focused specifically on counting to 100. The average age of parents in the discussion cable ranged from tardily 5 to early 6 years old.

Some parents expressed concern about their children not being able to count to 100 by the age of six, but they were apathetic because it was apparent their child was capable of other developmental goals.

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Answer:

(D) 1/9

Step-by-step explanation:

9x-2=-3

9x=1

x=1/9

(i) Large Table Required are 3 and Small Table required are 8

(ii) Price of Student Ticket is $5.5 and Adult Ticket is $7.5

What is Linear Equation in Two Variable?

A linear equation in two variables is one that is stated in the form ax + by + c = 0, where a, b, and c are real integers and the coefficients of x and y, i.e. a and b, are not equal to zero.

Solution:

(i)

Seats in Large Table = 12

Cost of Large Table = $50

Seats in Small Table = 8

Cost of Small Table = $25

Let, Number of Large Tables = x

Number of Small Tables = y

According to the Question:

12x + 8y = 100

50x + 25y = 350

x = 3, y = 8 (refer graph 1)

(ii)

Cost of Student Ticket = x

Cost of Adult Ticket  = y

According to the Question:

16x + 3y = 110.5

12x + 4y = 96

x = $5.5, y = $7.5 (refer graph 2)

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Answer:

Greg is correct

Step-by-step explanation:

To determine which of them is experiencing warmer weather, you need to compare the temperatures in the same unit of measurement. 77°F is equivalent to 25°C, while 30°C is equivalent to 86°F. Therefore, Greg is experiencing warmer weather than Josh.

The difference in the temperatures they reported is due to the fact that they are using different temperature scales. The Fahrenheit scale is used in the United States, while the Celsius scale is used in most other countries. The two scales are related by the equation:

C = (F - 32) / 1.8

To convert from Fahrenheit to Celsius, you can use this equation to determine the temperature in Celsius. To convert from Celsius to Fahrenheit, you can use the equation:

F = C * 1.8 + 32

Using these equations, you can compare temperatures in different scales to determine which is warmer.

Answer:

1/ simplify polynomial is x^3 y^2 - x^2 y^3 + xy

2/ Answer is -86

Step-by-step explanation:

x²yxy-xy²xy +xy

Simplify each term, and I get

x^3 y^2 - x^2 y^3 + xy

I may be wrong!

Now let's put -3 in for x and 2 in y and evaluate

(-3)^3  (2)^2 -  (-3)^2  (2)^3  +  (-3 times 2)

(27) (4) - (9) (8) - 6

-86

I may be wrong, but I tried my best to help you since this question has been on for a long time, but no one answered. If I am wrong, I am sorry!

Answer:

Step-by-step explanation:

You want the measures of the numbered angles in the figure comprised of overlapping right triangles.

The acute angles in a right triangle are complementary, as are the two angles into which a right angle is divided.

  ∠1 +35° = 90°   ⇒   ∠1 = 55°

  ∠3 +35° = 90°   ⇒   ∠3 = 55°

The angle marked 70° is exterior to the bottom right triangle, so is equal to the sum of angles 3 and 4.

  ∠3 +∠4 = 70°

  55° +∠4 = 70°   ⇒   ∠4 = 15°

Angle 2 is the other acute angle in the bottom right triangle, so ...

  ∠2 = 90° -∠4 = 90° -15°

  ∠2 = 75°

Therefore, we can construct the only one quadrilateral can I construct with the following data quadrilateral  PQ 4.5 cm angle P 70 ∘ angle Q 100 ∘ angle r 80 ∘ and angle S 110  with the above diagram.

An example of a closed quadrilateral is a polygon, which has four sides, four vertices, and four angles. It has four non-collinear points that are joined together. The interior angles of quadrilaterals are all sums of 360 degrees.

Here,

the following construction steps:

I Build a line segment with a QR of 4.5 cm.

(ii) Create a ray QX with an angle of 80 degrees and cut off QP = 4 cm at the point Q.

(iii) Create a ray at the point R that forms an angle of 110 degrees, and then cut it off at RS = 4.5 cm.

Now join PS. (iv)

PQRS is hence the necessary quadrilateral.

Therefore, we can construct the quadrilateral can I construct with the following data quadrilateral  PQ 4.5 cm angle P 70 ∘ angle Q 100 ∘ angle r 80 ∘ and angle S 110  with the above diagram.

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Answer: The answer is B

Step-by-step explanation:

Answer:

Step-by-step explanation:

The symbol that represents an expression in statistics are That is option A , B and C.

Statistics is defined as the area of study that is concerned with the collection, organization, analysis, interpretation, and presentation of data.

The importance of statistics is that it helps in conducting research, evaluating results, developing critical thinking and making informed decisions.

The various symbols use in statistics include the following:

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The parallel marks the northern limit of the Southern Ocean (though some organisations and countries, notably Australia, have other definitions) and of the Antarctic Treaty System.

Parallel lines are straight lines that never meet each other no matter how long we extend them

Parallel lines are any two or more lines that all lie in the same plane and never cross one another. They are equally spaced apart and have the same incline.

Numerous pairs of angles are created when a transversal line intersects any two parallel lines. While some angles are additional, others are congruent (equal).

The fundamental characteristics listed below make it simple to recognise parallel lines.

Parallel lines are defined as straight lines that are always the same distance apart.

No matter how far apart they are from one another, parallel lines can never intersect.

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Answer and Step-by-step explanation:

Lydia must sell at least $680 worth of tacos and burritos each day, and she only has enough supplies to make 115 tacos or burritos. If she sells each taco for $4, then she can make a maximum of 115 tacos * $4/taco = $<<115*4=460>>460 by selling tacos.

Therefore, in order to make at least $680, Lydia must sell burritos in addition to the tacos. The minimum number of burritos she must sell in order to make at least $680 is $680 - $460 = $<<680-460=220>>220.

Since Lydia sells each burrito for $6.75, she must sell at least $220 / $6.75/burrito = <<220/6.75=32.5>>32.5 burritos to make at least $680. Since she only has enough supplies to make 115 tacos or burritos, and she has already accounted for 115 tacos, she must sell a minimum of 32.5 burritos to meet the requirements.

56.6 years  is the mean of the modes of the given set of numbers.

What are the mean, median, and example?

The most frequent number, or the one that happens the most frequently, is known as the mode.

                     Example: Since the number 2 appears three times, more than any other number, it is the mode of the numbers 4, 2, 4, 3, and 2.

The mean is calculated by adding together all the values

                 =  (54+54+54+55+56+57+57+58+58+60+60

                  = 623

                  =  56.6 years.

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If the value x =12 then 2x - 5 = 19 the statement is true if 2x -5 = 19 then x = 12. The correct options are A and D.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the statements are:-

x = 12, then 2x - 5 = 19.

2x - 5 = 19

(2 x 12 ) - 5 = 19

24 - 5 = 19

19 = 19

If 2x - 5 = 19, then x = 12. The value of x will be calculated as,

2x - 5 = 19

2x = 19 + 5

2x = 24

x = 24 / 2

x = 12

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Hannah's thought that the original photo is congruent and similar to the final image is false

From the question, we have the following parameters that can be used in our computation:

Translation creates congruent and similar shapes

However, dilation only create similar shapes,  but not congruent shapes

This means that the shapes are similar, but not congruent

Hence. Hannah is incorrect

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The mean squared error is 4.67. So the option a is correct.

In the given question, demand for a product and the forecasting department's forecast for a product are given.

We have to compute the mean squared error.

Period          Actual        Forecasted      Error       Absolute      Squared

                 Demand(E)    Demand (F)     (E-F)        Error |E-F|    Error |(E-F)|^2

1                12    

2                15                12              3               3             9

3                14                15              -1                1              1

4                18                16              2                2              4

                                                                Total=6        Total=14

Now we finding the mean squared error (MAE)

Mean squared error = ∑|(E−F)|^2/n

Mean squared error = 14/3

Mean squared error = 4.67

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The second tile represents the missing alternatives.

In mathematics, a sequence is an enumerated collection of objects in which repetitions are allowed and order matters

Given is a square array of tiles as shown in the image attached.

The tile given at the second number is the missing tile of the given alternatives.

Therefore, the second tile represents the missing alternatives.

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