How to Calculate Z Scores?

Answer:

it just dots that all

Step-by-step explanation:

no step need

To solve for theta in the equation 3sin(theta) = sin(theta) + 1:

First, we can simplify the equation by subtracting sin(theta) from both sides:

2sin(theta) = 1

Then, we can isolate sin(theta) by dividing both sides by 2:

sin(theta) = 1/2

Using the unit circle or a calculator, we can find the two possible solutions for theta:

theta = pi/6 + 2npi or theta = 5pi/6 + 2npi, where n is an integer.

"Karen wants to buy a new smartphone that costs $46. She currently has some money saved up, represented by the expression 6x - 4, where x is the number of weeks she has been saving. Can Karen buy the smartphone now, or does she need to save for more weeks? Use the inequality 6x - 4 < 46 to help you answer the question."

In mathematics, an algebraic expression is a combination of variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. Algebraic expressions are used to represent and solve problems in various areas, including science, engineering, economics, and mathematics.

An algebraic expression can contain one or more variables, which represent unknown or changing quantities, and one or more constants, which represent fixed values. The variables are usually represented by letters, such as x, y, or z. The operations of addition, subtraction, multiplication, and division are represented by the symbols +, -, ×, and ÷, respectively. Parentheses are also used to group terms and indicate the order of operations.

For example, the algebraic expression 3x + 2y - 5 represents a combination of two variables, x and y, and three constants, 3, 2, and 5. The terms 3x and 2y are the variables multiplied by their coefficients, while -5 is a constant term.

Algebraic expressions can be simplified by combining like terms, which are terms that have the same variable raised to the same power. For example, in the expression 3x + 2y - 5 + 4x - 3y, the like terms are 3x and 4x, and 2y and -3y. Combining these terms yields the simplified expression 7x - y - 5.

Algebraic expressions are used in various mathematical operations, such as solving equations, graphing functions, and evaluating formulas. They are also used in real-world applications, such as calculating interest rates, solving optimization problems, and modeling physical phenomena.

Sure, here's a word problem that fits the inequality 6x - 4 < 46:

"Karen wants to buy a new smartphone that costs $46. She currently has some money saved up, represented by the expression 6x - 4, where x is the number of weeks she has been saving. Can Karen buy the smartphone now, or does she need to save for more weeks? Use the inequality 6x - 4 < 46 to help you answer the question."

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The probability that a continuous random variable equals any of its values is called Continuous probability distribution.

Continuous probability distribution:

A probability distribution in which the random variable X can take on any value (which is continuous). Since there are infinitely many possible values ​​for X, the probability that X takes on any particular value is zero. So we often talk about a range of values ​​[p(X >0] = 0.50).

An absolutely continuous probability distribution is a probability distribution of real numbers with an uncountable set of possible values, such as the full interval of a solid line, where the probability of any event can be expressed as an integral. More precisely, there exists a function f: R − [0, so that for each interval[ 0,∞] ⊂ R, the probability that X belongs to [a, b] is given by the integral of f over I.

[tex]P(a\leq X\leq b) = \int\limits^a_b {f(x)} \, dx[/tex]

Since this is the definition of a probability density function, an absolutely continuous probability distribution is exactly equivalent to a probability density function. In particular, the probability that X takes any single value a (i.e. a≤X≤b) is zero because integrals with the same upper and lower bounds are always zero. If the interval [a, b] is replaced by the measurable set A, then the equivalence remains valid.

P(X ∈ A) = [tex]\int\limits^a_b {f(x)} \, dx[/tex]

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Based on angle relationship, the missing angles are:

1. Angle a = 108°; reason: alternate interior angles

2. Angle b = 43°; reason: corresponding angles

3. Angle c = 114°, reason: corresponding angles are congruent.

4. Angle d = 101°; reason: same-side interior angles .

5. Angle e = 82°, reason: alternate interior angles

angle f = 82°, reason: vertical angles

6.  Angle g = 67°, reason: corresponding angles

Angle h = 113°, reason: same-side interior angles

7. Angle i = 127°, reason: corresponding angles

Angle j = 53° [reason: linear pair angles]

8. k = = 156° [reason: supplementary angles]

l = 24° [reason: alternate exterior angles]

9. m = 72° [reason: alternate exterior angles]

10. n = 86° [reason: supplementary angles]

11. p = 25° [reason: supplementary angles]

12. q = r = 61° [reason: supplementary angles]

To calculate a missing angle in a figure using angle relationships, follow these steps:

Therefore:

1. Angle a = 108°, the reason is: alternate interior angles are congruent.

2. Angle b = 43°, the reason is: corresponding angles are congruent.

3. Angle c = 114°, the reason is: corresponding angles are congruent.

4. Based on the same-side interior angles theorem (angle relationship), we have:

d = 180 - 79

d = 101°

5. Angle e = 82°, the reason is: alternate interior angles are congruent.

angle f = 82°, because, vertical angles are congruent.

6.  Angle g = 67°, the reason is: corresponding angles are congruent.

Angle h = 180 - 67 = 113°, the reason is: same-side interior angles are supplementary.

7. Angle i = 127°, the reason is: corresponding angles are congruent.

Angle j = 180 - 127 = 53° [reason: linear pair angles]

8. k = 180 - 24 = 156° [reason: supplementary angles]

l = 24° [reason: alternate exterior angles are congruent]

9. m = 72° [reason: alternate exterior angles are congruent]

10. n = 180 - 94 = 86° [reason: supplementary angles]

11. p = 180 - 155 = 25° [reason: supplementary angles]

12. q = r = 180 - 119 = 61° [reason: supplementary angles]

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The value of temperature 75degrees Fahrenheit converted to Celsius is 23.89 degrees Celsius.

To convert 75 degrees Fahrenheit to Celsius, you can use the formula

(F - 32) x 5/9.

Here's how to use this formula:

Subtract 32 from 75: 75 - 32 = 43

Multiply 43 by 5/9: 43 x 5/9 = 23.89

So 75 degrees Fahrenheit is equivalent to 23.89 degrees Celsius. To remember this formula easily, you can use the mnemonic "Fahrenheit to Celsius, subtract 32, then divide by 1.8".

This is a useful formula to know if you're traveling internationally or working with scientific data that uses Celsius instead of Fahrenheit.

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Note that the angle indicated by the question mark is 75°. See the explanation below.

Given that the angle at the vertex that they (the equilateral triangle and the square share) is a right angle or 90 degrees.

This means that the middle angle of the equilateral triangle is 60° this is because an "equilateral" triangle has 3 equivalent sides and, therefore, 3 equivalent angles.

Since the sum of the 3 angles of ANY triangle is 180°, then 180/3 = 60° for each angle.

Because the angle at the vertex is "splitting" a right angle, or 90 degrees which belongs to the square, then that leaves 2 smaller angles on each side of the 60° angle,

or 90 - 60

=30/2

=15° each.

That is the top angle of the triangle you are trying to solve.

Therefore, since that small triangle is a right triangle, then: 180 - 90 - 15 =75°, which is the angle with a question mark (?)

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Full Question:

An equilateral triangle and a square are inscribed in a circle as shown.  ABCis isosceles. The triangle and square share a common vertex. What is the number of degrees in the measure of the angle indicated by the question mark? (See attached)

The linear inequality 32,500<x<36,000 best represents age of the tusk, where x is the age of ivory tusk.

What exactly are linear inequalities?

Inequality is a mathematical statement in which neither side is equal. In Math, an inequality occurs when a connection produces a non-equal comparison between two expressions or two integers. The equal sign "=" in the phrase is substituted by any of the inequality symbols, such as greater than symbol (>), less than symbol (<), greater than or equal to symbol (≥), less than or equal to symbol (≤), or not equal to symbol (≠). In mathematics, there are three types of inequalities: polynomial inequalities, rational inequalities, and absolute value inequalities.

The symbols '<' and '>' represent severe inequalities, whereas " and " represent slack inequalities.

Now,

Given that

An archaeologist estimated the age of an ivory tusk to be at least 32,500 years old and less than 36,000 years old.

Let x be the age of ivory tusk

then x>32,500 years

and x<36,000 years

hence,

          The linear inequality 32,500<x<36,000 best represents age of the tusk.

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All the angle measures are;

m∠A = 160°

m∠B  = 142°

m∠C = 120°

m∠D  = 156°

m∠E = 31°

m∠F = 111°

Angles inside a polygon are referred to as interior angles. A triangle, for instance, has three internal angles. Interior angles are sometimes defined as "angles confined in the interior area of two parallel lines when they are crossed by a transversal."

Given:

Mr. Smith is putting a brick border around his irregularly shaped yard.

Before installing the border,

he must cut the bricks to fit the angles of the garden.

There are 6 sides to the polygon.

The total sum of the irregular angle = (4 - 2) x 180° = 720°.

So,

7x - 8 + 4x + 46 + 5x + 6x + 12 + x + 7 + 5x - 9 = 720°.

28x = 720 - 48

x = 24

Now, all the measures are:

m∠A = 7x - 8 = 160°

m∠B = 4x + 46 = 142°

m∠C = 5x = 120°

m∠D = 6x + 12 = 156°

m∠E = x + 7 = 31°

m∠F = 5x - 9 = 111°

Therefore, all the measures are given above.

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Answer: A random variable.

Step-by-step explanation:

a numerical description of the outcome of an experiment is called a random variable.

Burt saves $1,500 from each pay check.

What is the percentage?

A percentage is a way of expressing a number or quantity as a fraction of 100. It is commonly used to express the proportion of one quantity relative to another or the amount of change between two quantities.

For example, if you received a score of 80 out of 100 on a test, you can express that score as a percentage by dividing 80 by 100 and multiplying by 100. The result is 80%, which means you scored 80% of the total possible points.

Percentages are often used in finance, such as when calculating interest rates, taxes, and discounts. They are also used in statistics to express the probability or likelihood of an event occurring.

Understanding percentages are important in everyday life, as they are commonly used to compare and evaluate different quantities and values.

Burt earns a semi-monthly income of $3,250, which means he earns $6,500 per month.

He spends 24% of his income on his mortgage, which is:

0.24 x $6,500 = $1,560

He spends 6.5% of his income on utilities, which is:

0.065 x $6,500 = $422.50

He spends 15% of his income on food, which is:

0.15 x $6,500 = $975

He spends 8% of his income on miscellaneous items, which is:

0.08 x $6,500 = $520

Therefore, his total expenses are:

$1,560 + $422.50 + $975 + $520 = $3,477.50

To find out how much he saves from each paycheck, we need to subtract his total expenses from his monthly income:

$6,500 - $3,477.50 = $3,022.50

Since he gets paid semi-monthly, he saves half of this amount from each paycheck:

$3,022.50 / 2 = $1,511.25

Rounding this amount to the nearest $100, we get:

$1,500

Therefore, Burt saves $1,500 from each paycheck.

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The chain rule is a formula used in calculus to find the derivative of a composition of functions. It is an important tool for solving problems in many areas of mathematics and science.

The chain rule formula can be stated as follows:

If y = f(g(x)), then the derivative of y with respect to x is given by:

dy/dx = (df/dg) * (dg/dx)

In other words, the derivative of y with respect to x is equal to the derivative of f with respect to g, multiplied by the derivative of g with respect to x.

Here, f and g are functions of x, and y is a function of g. The chain rule formula tells us how to find the derivative of y with respect to x, by taking into account the effect of both f and g on the function y.

The chain rule can be extended to more complex compositions of functions, by applying the formula repeatedly. For example, if y = f(g(h(x))), then the chain rule can be applied twice, as follows:

dy/dx = (df/dg) * (dg/dh) * (dh/dx)

This formula tells us how to find the derivative of y with respect to x, by taking into account the effects of all three functions f, g, and h on the function y.

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A 6 pack of bouncy ball costs 2.76$ and the unit price of a bouncy ball is $0.46

To find the unit price of the bouncy balls, we need to divide the total cost by the number of bouncy balls in the pack. Since there are 6 bouncy balls in the pack and the cost is $2.76, we can calculate the unit price as follows: Unit price = total cost ÷ number of units

Unit price = $2.76 ÷ 6

Unit price = $0.46

Therefore, the unit price of a bouncy ball is $0.46.

Unit price is a measure of the cost of a single unit of a product. It is calculated by dividing the total cost of a product by the number of units in the package. The unit price is helpful when comparing the costs of different package sizes or brands of the same product. It allows consumers to make informed decisions about their purchases based on the value they receive for their money. Unit pricing is required by law in some countries, including the United States, to ensure transparency in pricing and to protect consumers from deceptive marketing practices. Overall, knowing the unit price of a product can help consumers save money and make more informed purchasing decisions.

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LCM is the smallest number that is completely by the given numbers. It can be calculated using different techniques. LCM of 6 and 8 is found to be 24.

LCM of 6 and 8 means the smallest number that can be divisible by both 6 an 8. LCM can be calculated by three methods.

        Multiples of 6  are 6, 12, 18, 24, 30, 36.....

         Multiples of 8  are 8, 16, 24, 32.....

      The smallest common multiple or LCM is 24

        6 - 2×3

        8 - 2×2×2

LCM = 2×3×2×2 = 24

           2    |  6, 8                                                                                                                      

          2     |  3, 4

                    3, 2

LCM = 2×2×3×2 = 24

So the LCM of 6 and 8 is found to be 24 by all methods.

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To find the minimum score needed to be in the top 7%, we need to find the score that corresponds to the 93rd percentile, since the top 7% is the complement of the bottom 93%.

Using a standard normal distribution table or a calculator, we can find the z-score that corresponds to the 93rd percentile, which is approximately 1.44. This means that a score of 1.44 standard deviations above the mean corresponds to the 93rd percentile.

To find the actual score, we can use the formula:

z = (x - μ) / σ

where z is the z-score, x is the actual score, μ is the mean, and σ is the standard deviation. Solving for x, we get:

x = z * σ + μ

= 1.44 * 6.1 + 76.4

= 85.084

So, the minimum score needed to be in the top 7% is approximately 85.084 points.

The solution is (1, -1), which is the point where the two lines intersect.

What is linear equation ?

Linear equation can be defined as equation in which highest degree is one.

To graph the system of equations, we can first write them in slope-intercept form:

y = -2x + 1 (equation 1)

y = 3x - 4 (equation 2)

From equation 1, we can see that the y-intercept is 1 and the slope is -2. This means that if we go down 2 units and to the right 1 unit, we will find another point on the line. From equation 2, we can see that the y-intercept is -4 and the slope is 3. This means that if we go up 3 units and to the right 1 unit, we will find another point on the line.

To graph the system, we can plot these two points and draw a line through them:

(0, 1) and (1, -1)

Now, to find the solution, we need to find the point where these two lines intersect. One way to do this is to set the equations equal to each other:

-2x + 1 = 3x - 4

Adding 2x to both sides gives:

1 = 5x - 4

Adding 4 to both sides gives:

5 = 5x

Dividing both sides by 5 gives:

x = 1

Substituting this value of x into either equation gives:

y = -2(1) + 1 = -1

Therefore, the solution is (1, -1), which is the point where the two lines intersect.

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The conversion of 5kg in pounds is 11.0231 pounds (rounded to four decimal places).

A kilogram is greater than a pound. I know that a kg is greater than a lb because of something called conversion factors.

Put very simply, a conversion factor is a number that can be used to change one set of units to another, by multiplying or dividing it. So when we need to convert 5 kilograms into pounds, we use a conversion factor to get the answer.

The conversion factor for kg to lb is:

1 kg = 2.2046244201838 lb

Now that we know what the conversion factor is, we can easily calculate the conversion of 5 kg to lb by multiplying 2.2046244201838 by the number of kilograms we have, which is 5.

5 x 2.2046244201838 = 11.023122100919 lb

To convert 5kg to pounds, you can use the conversion factor of 2.20462 pounds per kilogram. Multiplying 5kg by this conversion factor gives:5 kg * 2.20462 pounds/kg = 11.0231 pounds.

Therefore, 5kg is equivalent to 11.0231 pounds (rounded to four decimal places).

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Answer:

Step-by-step explanation:

180-55-85=180-140=40

The volume of the solid generated when r is revolved about the​ y-axis is 3.2π.

Volume of Solid:

The volume of a solid is a measure of the space occupied by an object. This article explains how to calculate the volume of solids and the volume of regular and irregular solids.

According to the Question:

We know that:

A ( y ) = π × (f₁ (y)² - f₂ (y)²)

where,

f₁ (y) is the function further away from y axis

f₂ (y) is the function closer to y axis

f₁ (y) = 2

f₂ (y) = 2y²

A ( y ) = π × [2² - (2y)²]

A (y) = π × (4 - 4y²)

A (y) = 4π (1 - y²)

Now,

Computing V (y)

[tex]V =\int\limits^1_0 {A(y)} \, dy[/tex]

[tex]V = 4\pi \int\limits^1_0 {(1-y^2)} \, dx[/tex]

V = 4π (1 - 0.2)

V = 3.2π

Therefore, The volume of the solid generated when r is revolved about the​ y-axis is 3.2π.

Complete Question:

Let R be the region bounded by the following curves. Use the disk or washer method to find the volume of the solid generated when R is revolved about the​ y-axis. y= square root of (x/2) , y=0 , x=2

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Answer:

Step-by-step explanation:

b

Answer:

Step-by-step explanation:

Answer:

The integral of the constant function f(x) = k is: kx + C. This is because when you integrate a constant function, you are essentially finding the area under the graph. In this case, the area of the graph is equal to the value of k multiplied by the width of the graph (x) plus a constant.

The value x = 3 will result in the greatest relative frequency given discrete random variable X.

What is relative frequency?

A frequency is the number of times an event takes place. It's experimental, not theoretical, to study relative frequency. As it is an experimental one, it is likely that when we repeat the trials, we will get different relative frequencies.

The relative frequency of a discrete random variable increases with decreasing variable value.

This implies that,

A variable with x = 0 would occur more frequently than one with x = n, where n > 0.

So, the greatest relative frequency given discrete random variable X, when X ∼ B (4, 1/10) is  x = 3.

Hence, the value x = 3 will result in the greatest relative frequency given discrete random variable X.

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SKLearn or Scikit-learn's linear regression is a machine learning algorithm that models the relationship between a dependent variable and one or more independent variables by fitting a linear equation to the observed data.

In simpler terms, linear regression is a statistical method used to predict a numerical outcome based on one or more input variables. Scikit-learn's implementation of linear regression is widely used in the field of machine learning for tasks such as predicting house prices, stock prices, and other numeric outcomes.

The linear regression model assumes a linear relationship between the input and output variables and seeks to minimize the sum of the squared differences between the predicted and actual values. Scikit-learn's implementation provides a powerful and flexible interface for fitting, evaluating, and using linear regression models for a wide range of predictive tasks.

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The results of the first three trials are:

Trial 1: 8 girls, 12 boys

Trial 2: 13 girls, 7 boys

Trial 3: 11 girls, 9 boys

What is permutation and combination ?

Permutation and combination are two related concepts in mathematics that deal with counting and arranging objects.

Permutation refers to the number of ways in which a set of objects can be arranged or ordered. In other words, it involves selecting objects from a set and arranging them in a specific order. The formula for finding the number of permutations of n objects taken r at a time is given by:

nPr = n! / (n-r)!

According to given condition:

To simulate the number of male and female births using a random digit table, the nurse has assigned the digits 0-4 to represent girls and 5-9 to represent boys. She selects samples of 20 and records the digits in order.

For the first trial, the digits are:

1 7 9 3 9 6 7 7 6 4 0 7 1 3 4 9 9 0 4 7

Interpreting these digits using the nurse's coding scheme, we see that there are:

8 girls (represented by the digits 0-4)

12 boys (represented by the digits 5-9)

For the second trial, the digits are:

6 2 4 5 4 8 1 0 6 9 0 7 8 7 9 8 5 4 2 8

Interpreting these digits using the nurse's coding scheme, we see that there are:

13 girls

7 boys

For the third trial, the digits are:

5 9 3 9 8 4 1 8 2 2 4 6 4 8 0 3 3

Interpreting these digits using the nurse's coding scheme, we see that there are:

11 girls

9 boys

Therefore, the results of the first three trials are:

Trial 1: 8 girls, 12 boys

Trial 2: 13 girls, 7 boys

Trial 3: 11 girls, 9 boys

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With regards to the probabilities of getting each color in the game played by Larry and Jessica, the correct answer is B. No, the probabilities are NOT equally likely.

In the game being played by Larry and Jessica, the colors that can be picked by either person include:

The probability of picking blue is:

= Number of blue sections / Total sections

= 3 / 8

The probability of picking red is :

= 3 / 8

The probability of picking green is:

= 2 / 8

= 1 / 4

The probabilities are therefore not equally likely.

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The solution of the quadratic equation using quadratic formula are x = (√181 - 19)/2 or x = (-√181 - 19)/2.

Quadratic equations are defined as the polynomial equations with the highest degree of the variable being 2.

The standard form of a quadratic equation is ax² + b x + c = 0.

Given quadratic equation is,

-x² - 19 = 45

Subtracting both sides by 45,

-x² - 19 - 45 = 0

Multiplying throughout by -1,

x² + 19 + 45 = 0

Quadratic formula for the general quadratic equation is,

x = [-b ± [tex]\sqrt{b^2-4ac}[/tex]] / 2a

Here, [tex]\sqrt{b^2-4ac}[/tex] is called discriminant.

Discriminant of given equation = [tex]\sqrt{19^2-(4*1*45)}[/tex] = √181

x = (-19 ± √181) / 2

x = (√181 - 19)/2 or x = (-√181 - 19)/2

Hence the solutions are x = (√181 - 19)/2 or x = (-√181 - 19)/2.

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Answer:

x = 5, y = 2

Step-by-step explanation:

    x - 5.2y = -5.4

+ (-x + 4.3y = 3.6)

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

         -0.9y = -1.8

                   y = 2

x - 5.2(2) = -5.4

x - 10.4 = -5.4

x = 5

The addition (elimination) method is a good choice for solving this system  because the x's are already opposites, and will cancel out when the two equations are added together. If one was to solve for x first, this method wouldn't be as good of a choice since it involves extra steps to eliminate the y's from the equation.