In the figure, ABCD is a square, E is the midpoint of side AD, and F is the midpoint of side BC. The area of the shaded region is
what fraction of the area of square region ABCD?

Answer:

6 and 4

Step-by-step explanation:

the first number is x and the second is y , then triple x is 3x , so

3x + y = 22 → (1)

the second number y is equal to twice x , less 8 , that is 2x - 8 , so

y = 2x - 8 → (2)

solving the 2 equations simultaneously.

substitute y = 2x - 8 into (1)

3x + 2x - 8 = 22

5x - 8 = 22 ( add 8 to both sides )

5x = 30 ( divide both sides by 5 )

x = 6

substitute x = 6 into (2) for y

y = 2(6) - 8 = 12 - 8 = 4

first number is 6 and second number is 4

Therefore, the given statement that the t-distribution has more area in the tails than the standard normal distribution

SO ITS TRUE

Answer: true

Step-by-step explanation:

A fraction in simplest form M = 3/4

Part A is 1/4 of the whole

Part B is 3/4 of the whole

Assuming there are no other parts,

the Whole = A + B is the denominator:

Whole = 3 + 9 = 12

Part A = 3 and Part B = 9 are numerators for each fraction.

The fractions are then:

3/12 and 9/12

Meaning:

Part A is 3/12 of the whole

Part B is 9/12 of the whole

Reducing the fractions, it is also true that:

Part A = 1/4 of the whole

Part B = 3/4 of the whole

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Answer:

See below

Step-by-step explanation:

Your question lacks context, but zero would be in the quotient if the dividend is 0 and the divisor is some natural number (all integers but 0).

Answer:

I believe the answer is C... I might be wrong but I hope it helps you!!

Step-by-step explanation:

Answer:

I think the answer is b

-1,2

The length of side x is √2 units. The solution has been obtained by using the trigonometry formulas.

What is trigonometry?

The study of the sides, angles, and connections of the right-angle triangle is the main goal of the field of mathematics known as "trigonometry." In order to find the unknown or missing angles or sides of a right triangle, one can apply the trigonometric formulas, functions, or identities. Angles can be expressed in radians or degrees in trigonometry. The most frequent trigonometric angles used in calculations are 0, 30, 45, 60, and 90 degrees.

We are given a right-angled triangle with hypotenuse 2units.

We know that sin theta = opposite side/hypotenuse

Also, sin 45° = 1/√2

So,

⇒sin 45° = x/2

⇒1/√2 = x/2

⇒2/√2 = x

⇒√2 = x

Hence, the length of side x is √2 units.

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Me. I definitely want to take a break

The proportion of the individuals that spend more than $400 is 0.35 and  the percent of calls answered in less than 5 minutes is 5.3%

Probability 1

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

Mean = 384

Standard deviation = 48

x = 400

The z-score is calculated as

z = (x - Mean)/Standard deviation

So, we have

z = (400 - 384)/40

z = 0.4

The required probability is

P = P(z > 0.4)

So, we have

P = 0.345

Probability 2

Here, we have

Mean = 12.4

Standard deviation = 4.3

x = 5

The z-score is calculated as

z = (x - Mean)/Standard deviation

So, we have

z = (12.4 - 4.3)/5

z = 1.62

The required probability is

P = P(z > 1.62)

So, we have

P = 5.3%

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Answer: Multiplying both sides of the original equation by 100 gives the same

the solution as follows;

100 × (2.3·p - 10.1) = 100 × (6.5·p - 4 - 0.01·p)

230·p - 1010 = 650·p - 400 - p

Step-by-step explanation:

The equation of the exponential function in the table is

Exponential function is a type of function of the form: f(x) = a(b)^x. It is made up of  3 main parts

a = the starting or initial value

b = the base function

x = the exponents

Considering the given problem, as in the table

the starting = is f(0) = 0.2

Solving for the base

f(x) = a(b)^x at x = 1

0.6 = 0.2(b)^1

0.6 = 0.2b

b = 0.6 / 0.2

b = 3

hence the equation is f(x) = 0.2(3)ˣ

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Answer:

Step-by-step explanation:

The value of the improper fraction will be:

1. 2 2/3 = 8/3

2. 4 1/2 = 9/2

3. 1 7/10 = 17/10

4. 2 3/8 = 19 / 8

5. 5 5/9 = 50/9

6. 1 7/12 = 19/12

A fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split. In this situation, in a simple fraction, the numerator as well as the denominator are both integers.

The improper fraction will be:

1. 2 2/3 = (2 × 3 + 2) / 3 = 8/3

2. 4 1/2 = (4 × 2 + 1) / 2 = 9/2

3. 1 7/10 = (1 × 10 + 7) / 10 = 17/10

4. 2 3/8 = (2 × 8 + 3) / 8 = 19 / 8

5. 5 5/9 = (5 × 9 + 5) / 9 = 50/9

6. 1 7/12 = (1 × 12 + 7) / 12 = 19/12

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The complete statement would be, confounding  in a study occurs when the effects of two or more explanatory variables are not separated. Therefore, any relation that may exist between an explanatory variable and the response variable may be due to some other variable or variables not accounted for in the study.

We know that an  extraneous variable is a variable that has the potential to affect the results and it is not a independent variable.

A confounding variable is nothing but a type of extraneous variable which is related to a study’s independent and dependent variables.

These variables (confounding variables) are also known as confounders or confounding factors.

Any variable must follow following conditions to be a confounding variable:

1) A variable must be correlated with the independent variable.

2) It must be related to the dependent variable.

Thus, confounding occurs when the effects of two or more explanatory variables are not separated. therefore, any relation that may exist between an explanatory variable and the response variable may be due to some other variable not accounted for in the study.

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The complete question is:

__________ in a study occurs when the effects of two or more explanatory variables are not separated. Therefore, any relation that may exist between an explanatory variable and the response variable may be due to some other variable or variables not accounted for in the study.

The number of seconds in a year in scientific notation is 31,536,000 seconds or [tex]3.154 * 10 ^{7}[/tex]

In one hour [tex]60 \ sec * 60\ min = 3600 \ sec[/tex]

For one day we have to multiply [tex]3600 * 24 = 86400\ sec[/tex]

For one calendar year (365 days) = [tex]86400 * 365 = 31536000 \ sec[/tex]

It Can be written as : [tex]3.154 * 10 ^{7}[/tex]

∴ In a year, there are 31,536,000 seconds.

Numbers that are either too large or too little to be conveniently stated in decimal form can be expressed using scientific notation.

We must adhere to the following rule in order to calculate the power or exponent of 10:

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The following question may be like this:

Express the number of seconds in a year in scientific notation (1year= 365days)​

The number of seconds in a year is 31,536,000 seconds. Rounded to three significant figures, the number of seconds in a year can be written as 3.15 x 10^7 seconds in scientific notation.

Scientific notation is a way to represent numbers as a decimal multiplied by a power of 10. The decimal part is always between 1 and 10, and the power of 10 gives the number of zeros or decimal places in the original number. For example, the number of seconds in a year can be written as 31,536,000 seconds in scientific notation as 3.1536 x 10^7.

The number of seconds in a year is 31,536,000 (60 seconds x 60 minutes x 24 hours x 365 days).

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Answer:

The first option (angle 2 and 5)

Step-by-step explanation:

Vertical angles are angles that are opposite of each other when two lines cross. Vertical angles are congruent, meaning that they have the same angle measure.

In this case, angle 2 and angle 5 are vertical angles. So, the measure of angle 2 is equal to the measure of angle 5. Angle 6 and angle 3 are also vertical angles. So, the measure of angle 6 is equal to the measure of angle 3.

The table of values is not a function

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

The table of values

The general rule of functions is that

Each y value must have different x values

In the table of values, the y values 2 and 5 all have the same x value

Hence, it is not a function

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The solution is Option B.

The rotation of the line JK around the point P by 180° will be J'K'

The measure of the amount a figure is rotated about the center of rotation is called the angle of rotation. The angle of rotation is usually measured in degrees. We specify the degree measure and direction of a rotation.

90° clockwise rotation: (x,y) becomes (y,-x)

90° counterclockwise rotation: (x,y) becomes (-y,x)

180° clockwise and counterclockwise rotation: (x, y) becomes (-x,-y)

270° clockwise rotation: (x,y) becomes (-y,x)

270° counterclockwise rotation: (x,y) becomes (y,-x)

Given data ,

Let the rotation angle be represented as A

Now , the value of A is 180°

Let the points be represented as J and K

Let the rotated point be represented as J'K'

And , when a point is rotated by and angle 180° , the x and y coordinates of the point will become their additive inverse

For a 180° clockwise and counterclockwise rotation: (x, y) becomes (-x,-y)

And , the figure which represents the coordinates of the point J' and K' is when K' is below and J' is above

Hence , the solution is Option B.

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1) Note that the dark triangles are outliers.

2) Omitting the outlines changed the correlation between the variables because outliers can skew the data and make the relationship between the variables appear stronger or weaker than it actually is.

3) Outliers can greatly affect the data by distorting the overall relationship pattern between the variables.

An outlier in statistics is a data point that deviates considerably from other observations.

It is correct to state that an outlier can be caused by measurement variability, a hint of new data, or an experimental mistake; the latter is sometimes eliminated from the data set.

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Answer:Answer: $532.50

Step-by-step explanation:

564.45 = 1.06x

564.45/1.06 = x

532.50=x

Check: 532.50 × .06 = 31.95

532.50+31.95 = 564.45 True!

The range of the function will exist on all real numbers. Option D is correct.

what is the Range?

The range gives an idea of how spread out the values in a dataset are and it's a simple measure of dispersion.

The formula for range is:

Range = Maximum value - Minimum value

Given the function  f (x) = x^2 + 2x – 6,

The function of the table will also give a quadratic function of degree two.

The sum of the functions will also lead to a quadratic function and since for all input values of the function, there will be a corresponding output, hence the range of the function will exist on all real numbers.

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The ratio of AB to BC is 4.3 : 5 and the ratio of AD to DC is 2 : 2.3

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

A = (0, 4)

B = (-5, -3)

C = (5, -3)

D = (2.4, 0.8)

Next, we calculate the distance between the points using

Distance = √[(x2 - x1)² + (y2 - y1)²]

So, we have

AB = √[(0 + 5)² + (4 + 3)²] = 8.6

BC = √[(5 + 5)² + (-3 + 3)²] = 10

AD = √[(0 - 2.4)² + (4 - 0.8)²] = 4

DC = √[(2.4 - 5)² + (0.8 + 3)²] = 4.6

The ratios are then represented as

AB : BC = 8.6 : 10

AD : DC = 4 : 4.6

Simplify the ratios

AB : BC = 4.3 : 5

AD : DC = 2 : 2.3

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The function's description is accurate if (b) The graph of g(x) will ultimately surpass the graph of f. (x).

A relationship between a group of inputs and one output is referred to as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output. A domain, codomain, or range exists for every function. Typically, f(x), where x is the input, is used to represent a function.

Graphs can be used to represent functions.

The correct statement that describes the function is: (b) The graph of g(x) will eventually exceed the graph of f(x).

From the graphs, we have the following highlights

The graph of g(x) is constantly increasing as the value of x increases

The graph of f(x) is on decreasing (not constantly) as the value of x increases

The above highlights mean that: the value of g(x) would exceed g(x), at some point.

Hence, the correct statement that describes the function is: (b) The graph of g(x) will eventually exceed the graph of f(x).

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To compare the two different numbers 12 and 23 using different sentences are :

a. Twelve is less than twenty three or twenty three is greater than twelve.

b. 12 < 23 or 23 > 12.

Choose two numbers:

Let the numbers be 12 and 23.

Two different sentence to compare the considered numbers we have,

First method is using words.

a. twelve is less than twenty three.

Twenty three is greater than twelve.

Second method is symbolic method :

b. 12 < 23

'<' symbol represents less than.

23 > 12

'>' symbol represents the greater than.

Therefore, using two different method to compare two numbers are :

a. Word method : Twelve is less than twenty three or twenty three is greater than twelve .

b. Symbolic method : 12 < 23 or 23 > 12.

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No, 35/24 will never be on the board because the arithmetic and harmonic means can only generate positive integers.

No, 35/24 will never be on the board because the arithmetic and harmonic means can only generate positive integers. To calculate the arithmetic mean of two numbers, one adds the two numbers and divides the sum by two. The harmonic mean of two numbers is calculated by taking the reciprocals of the two numbers and dividing their sum by two. In the case of 1 and 2, the arithmetic mean is 1.5 and the harmonic mean is 2/3. So, the numbers on the board will be changed to 1.5 and 2/3 every day. 35/24 is a fraction and cannot be generated from the arithmetic and harmonic means of 1 and 2. Therefore, it will never be on the board.

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Answer:

the slope of the line is -11/7 and the y-intercept is 8.

Step-by-step explanation:

First, we'll add 11x + 7y to both sides:

-11x - 7y + 11x + 7y = -56 + 11x + 7y

0 = -56 + 11x + 7y

Then, we'll add 56 to both sides:

0 + 56 = -56 + 11x + 7y + 56

56 = 11x + 7y

Finally, we'll divide both sides by 7:

56/7 = (11x + 7y)/7

8 = (11x + 7y)/7

Now we have the equation in slope-intercept form:

y = -(11/7)x + 8

So in this case, the slope of the line is -11/7 and the y-intercept is 8.

Answer: There are a few different ways to approach this problem, but one common method is to use the complement rule, which states that the probability of an event happening is equal to 1 minus the probability of the event not happening. In this case, we want to find the probability of at least one psychologist being chosen, which is the same as 1 minus the probability of no psychologists being chosen.

To find the probability of no psychologists being chosen, we first need to calculate the total number of ways to choose 3 people from a group of 54, which is:

54 choose 3 = 54! / (3! * 51!) = 19,958

Then we need to find the number of ways to choose 3 psychiatrists from a group of 24, which is:

24 choose 3 = 24! / (3! * 21!) = 1,344

Now, we can use these values to calculate the probability of no psychologists being chosen:

P(no psychologists) = (24 choose 3) / (54 choose 3) = 1,344 / 19,958 = 0.067 or 6.7%

Finally, we can use the complement rule to find the probability of at least one psychologist being chosen:

P(at least one psychologist) = 1 - P(no psychologists) = 1 - 0.067 = 0.93 or 93%

So the probability that at least one psychologist is chosen from the conference is 93%

Step-by-step explanation:

The total number of drinks Roxanne buy is 124

Roxanne bought 7 packs of bottled water and 9 boxes of soda. There were 10 bottles of water in each pack and 6 cans of soda in each box.

Roxanne bought 7 pack of bottled water.

1 pack of water bottle contains 10 bottles of water,

Hence 7 pack of water bottle contains. [tex]$7 \times 10=70$[/tex] water bottles

Roxanne bought 9 boxes of soda, 1 box of soda contain 6 cans of soda, then 9 boxes of soda contains. [tex]$x=$[/tex] cans of soda,

Then the total number of drinks Roxanne buy[tex]$=70=1$[/tex]

The total number of bottles calculate by the Multiplication of number of packet of bottles and per packet bottles.

Therefore, the total number of drinks Roxanne buy = 124

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The theoretical yield of Fe₂(SO₄)³ if 20.00 g of FePO₄ reacts with an excess of Na₂SO₄ is 26.52g.

The amount of a product produced by a reaction is expressed in terms of the reaction's yield.

Given the chemical equation:

2FePO₄ + 3Na₂SO₄ → Fe₂(SO₄)₃ + 2Na₃PO₄

Theoretical molar ratios:

2 mol FePO₄  : 3 mol Na₂SO₄ : 1 mol Fe₂(SO₄)₃ : 2 mol Na₃PO₄

Convert 20.00 g of FePO₄  into a number of moles

number of moles = mass in grams / molar mass

molar mass of FePO₄  = 150.82 g/mol

Number of moles = 20.00 g / 150.82 g/mol = 0.1326 mol FePO₄

Proportionality

1 mol Fe₂(SO₄)₃                x

----------------------- =  ------------------------

2 mol FePO₄            0.1326 mol FePO₄

Solve for x:

x = (0.1326 / 2) x 1 mol Fe₂(SO₄)₃ = 0.0663 mol Fe₂(SO₄)₃

Convert 0.0663 mol Fe₂(SO₄)₃ into grams

mass in grams = number of moles x molar mass

molar mass Fe₂(SO₄)₃ = 399.88 g/mol

mass = 0.0663 mol x 399.88 g/mol = 26.51 g

Depending on the number of decimal digits used by one or other you might obtain 26.52 instead 26.51, that difference does not count.

Therefore, the theoretical yield of Fe₂(SO₄)³ is 26.52g.

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Answer: 3.5

Step-by-step explanation:

70/20=3.5

2 apples is equivalent to 6 bananas.

Linear equations help in representing the relationship between variables such as x, y, and z, and are expressed in exponents of one degree. In these linear equations, we use algebra, starting from the basics such as the addition and subtraction of algebraic expressions.

Given here; Scale1 as 20 bananas equal to 4 pineapples

Scale 2 as 2 pineapple equals 4 bananas and 2 apple

Let the weights of pineapple, bananas , apple as x,y,z respectively

Thus 20y=4x

      or x=5y

Again 2x=4y+2z

or      10y=4y+2z

          6y=2z

           z=3y

Thus 2 apples or 2z=6y that is 6 bananas

Hence, 2 apples is equivalent to 6 bananas.

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Answer:

Area of a trapezoid=1/2(a+b)h where a and b are the bases and h is the height.

Step-by-step explanation: