I got this from Khan academy.
Rewright the equation by completing the square. x^2 −14x+33=0
(x+_)^2
HELP!

D. No, because the probability of being left-handed is greater, x must count the number of left-handed adults.

The binomial probability formula can be used to calculate the probability of a certain number of successes (or left-handed individuals) in a given number of trials (100 adults). In order for the binomial probability formula to be used, the trials must be independent, meaning that the selection of one person does not affect the selection of the next one. Since the probability of being left-handed is greater, the binomial probability formula cannot be used in this case and x must count the number of left-handed adults.

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We have verified the identity [tex]csc^2(x)cos^2(x) = csc^2(x) - 1.[/tex]

What is trigonometry?

Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles, as well as the functions derived from these relationships. The most common trigonometric functions are sine, cosine, and tangent, which are abbreviated as sin, cos, and tan, respectively. These functions are used to model periodic phenomena such as sound waves, ocean tides, and the motion of planets.

To verify the identity [tex]csc^2(x)cos^2(x) = csc^2(x) - 1[/tex], we will start with the left-hand side and manipulate it until we get the right-hand side. Here's the full work:

[tex]csc^2(x)cos^2(x)[/tex] (given)

[tex]= (1/sin^2(x))(cos^2(x))[/tex] (definition of csc)

[tex]= (cos^2(x))/sin^2(x)[/tex] (multiply by reciprocal)

[tex]= (cos^2(x))/(1 - cos^2(x))[/tex](Pythagorean identity)

[tex]= (cos^2(x))/(1 - cos^2(x)) * [(1 + cos^2(x))/(1 + cos^2(x))][/tex] (multiply by conjugate)

[tex]= (cos^2(x)(1+cos^2(x)))/((1 - cos^2(x))(1 + cos^2(x)))[/tex](multiply and simplify)

[tex]= cos^2(x) * (1 + cos^2(x)) / (1 - cos^4(x))[/tex] (expand denominator)

[tex]= cos^2(x) / (1 - cos^2(x))[/tex] (cancel common factor of [tex]1 + cos^2(x))[/tex]

[tex]= csc^2(x) - 1[/tex](definition of csc and simplify)

Therefore, we have verified the identity [tex]csc^2(x)cos^2(x) = csc^2(x) - 1.[/tex]

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A critical t-value calculator is an online tool that helps you determine the critical value for the t-distribution for a given level of significance (alpha) and degrees of freedom (df). The critical t-value is the value that separates the area under the t-distribution curve into the rejection region and the non-rejection region for a two-tailed hypothesis test.

In statistical hypothesis testing, the t-distribution is used when the sample size is small, and the population standard deviation is unknown. The t-distribution is a family of distributions that depend on the degrees of freedom (df) and is bell-shaped, with a mean of 0 and a standard deviation of 1.

To use a critical t-value calculator, you need to input the significance level (alpha) and the degrees of freedom (df) and select whether the test is one-tailed or two-tailed. The calculator will then provide you with the critical t-value that separates the rejection and non-rejection regions for the given alpha and df.

It's important to note that the critical t-value depends on the level of significance (alpha) and the degrees of freedom (df). As the level of significant increases or the degrees of freedom decrease, the critical t-value also changes. Therefore, it's essential to use a critical t-value calculator to obtain the correct value for your hypothesis test.

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A critical t-value calculator is a tool used to calculate the critical value of t in a Student's t-test for a given significance level (alpha) and degrees of freedom (df).

When the sample size is small or the population standard deviation is unknown, the t-distribution is used to estimate the population mean.

The critical t-value in a Student's t-test is the value of t that separates the rejection region from the non-rejection region in a t-distribution. The null hypothesis is rejected if the calculated t-value is greater than the critical t-value, indicating that there is a significant difference between the sample mean and the population mean.

To use a critical t-value calculator, enter the t-significance test's level (alpha) and degrees of freedom (df). The degrees of freedom are defined as the number of observations minus one and are proportional to the sample size. The calculator will output the critical t-value for the given significance level and degrees of freedom once you enter these values.

For example, the degrees of freedom for a two-tailed t-test with a sample size of 20 and a significance level of 0.05 would be 20-1=19. The critical t-value at a significance level of 0.05 and 19 degrees of freedom is approximately 2.093, according to a critical t-value calculator.

Knowing the critical t-value is useful in hypothesis testing because it allows you to compare the calculated t-value from the sample data to the critical t-value to determine whether the null hypothesis should be rejected

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The amount of tip that Ethan receives on every order, we can use the formula Tip amount = (Tip percentage) x (Cost of order) and plug in the values accordingly.

To calculate the amount of tip that Ethan receives on every order, we can use the formula:

Tip amount = (Tip percentage) x (Cost of order)

In this case, the tip percentage is `15\%` and the cost of order is the variable we need to find.

Let's assume that the cost of an order is $100. Using the formula above, we can calculate the amount of tip that Ethan receives:

Tip amount = (`15\%`) x ($100)
Tip amount = $15

Therefore, Ethan receives a $15 tip on an order that costs $100.

If the cost of an order is different, we can simply plug in the new value into the formula and calculate the tip amount accordingly. For example, if the cost of an order is $50, the tip amount would be:

Tip amount = (`15\%`) x ($50)
Tip amount = $7.50

In conclusion, to calculate the amount of tip that Ethan receives on every order, we can use the formula Tip amount = (Tip percentage) x (Cost of order) and plug in the values accordingly.

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As a result, the rectangular pyramid has two conceivable dimensions: a base of 3 inches by 3 inches with a height of 3 inches, and a base of 1 inch by 9 inches with a height of 9 inches.

Volume is a fundamental physical quantity that measures the amount of three-dimensional space occupied by an object or a substance. In simpler terms, it refers to the amount of space that an object takes up or occupies. The standard unit of measurement for volume is the cubic meter (m3), which is defined as the amount of space occupied by a cube that has edges that measure one meter in length. However, in everyday life, other units of measurement are commonly used, such as liters, gallons, or cubic feet.

Here,

The volume of the rectangular prism is:

V = lwh = 6 * 1 * 1/2 = 3 cubic inches.

Let's call the base of the rectangular pyramid "b" and its height "h". The volume of a pyramid is given by:

V = (1/3)bh.

We want the volume of the pyramid to be the same as that of the rectangular prism, so we can set the two expressions for V equal to each other and solve for h:

3 = (1/3)bh

h = 9/b

Now we can choose any value for b and calculate the corresponding value for h that would result in the same volume as the original rectangular prism.

For example, we could choose b = 3, which would give us:

h = 9/b = 9/3 = 3

So one set of possible dimensions for the rectangular pyramid is a base of 3 inches by 3 inches, with a height of 3 inches.

Another set of possible dimensions could be b = 1, which would give us:

h = 9/b = 9/1 = 9

So another set of possible dimensions for the rectangular pyramid is a base of 1 inch by 9 inches, with a height of 9 inches.

Therefore, two sets of possible dimensions for the rectangular pyramid are: A base of 3 inches by 3 inches, with a height of 3 inches, A base of 1 inch by 9 inches, with a height of 9 inches.

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To simplify the expression, we can divide each term of the polynomial by the monomial:

30c^8d^3 / 12c^2d = 2.5c^6d^2

-3bc^6d^2 / 12c^2d = -0.25bc^4

6c^3d / 12c^2d = 0.5c

Therefore, the simplified expression is:

2.5c^6d^2 - 0.25bc^4 + 0.5c

One milliliter (mL) is equal to 0.033814 fluid ounces (fl oz). Therefore, to convert milliliters to fluid ounces, you need to divide the number of milliliters by 29.5735.

So, the value of 75 mL is equal to 2.53605 fluid ounces.

The metric system uses millilitres as the unit of volume, denoted by the letters ml or mL. One cubic centimetre, or one thousandth of a litre, is equivalent to one millilitre.

Fluid ounces is a measure of liquid; in Britain, 0.0284 of a litre.

Here, we want to convert the 75 mL into fluid ounces.

To convert milliliters (mL) to fluid ounces (oz), you can use the conversion factor of 0.033814.

So to convert 75 mL to ounces:

75 mL x 0.033814 oz/mL

= 2.53605 oz (rounded to five decimal places)

Therefore, 75 mL is approximately equal to 2.53605 fluid ounces.

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Using the probability formula the value for the largest piece is obtained as 3/4.

What is probability?

Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can range from 0 to 1, with 0 denoting an impossibility and 1 denoting a certainty.

Let X be the length of the largest piece when a unit stick is broken into three random pieces.

We want to find E(X), the expected value of X.

To solve for E(X), we can use the law of total probability and consider all possible lengths for the first cut.

Let Y be the length of the first piece, which can take any value between 0 and 1.

Then, we can write -

E(X) = ∫[0,1] E(X|Y=y) fY(y) dy,

where fY(y) is the probability density function of Y and E(X|Y=y) is the expected value of X given that the first piece has length y.

Now, let's consider the possible cases for the lengths of the other two pieces -

If the second cut is made in the interval [0,Y], then the largest piece has length Y.

If the second cut is made in the interval [Y,1-Y], then the largest piece has length 1-Y.

If the second cut is made in the interval [1-Y,1], then the largest piece has length Y.

Therefore, we can write -

E(X|Y = y)

= y × 1 + (1 - y) × 1/2 + (1 - y)×1  

= 1/2 + y/2.

Substituting this into the previous formula and using the fact that the density function for a uniform distribution on [0,1] is fY(y) = 1 for 0 ≤ y ≤ 1, we get -

E(X) = ∫[0,1] (1/2 + y/2) dy

= [y^2/4 + y/2] from 0 to 1

= 3/4.

Therefore, the expected length of the largest piece is 3/4.

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Answer: 43.2 minutes or 43 minutes and 12 seconds

Hi there, so first step I would do is to state the area of a cylinder which is 2πrh+2πr^2

Next step, I would place the value into the equation, so for the first pool, it is as follows: 2 x π x 20 x 5+2 x π x 20^2 which is = 1000π

which means 1000π = 50 minutes so each minutes must be equals to 20π

Then fit in the values for the second pool

2 x π x 18 x 6 + 2 x π x 18^2 = 864π

Then divide 864π by 20π to get how many minutes

The answer is equal to 43.2 minutes

Hope this helps

Answer:

Step-by-step explanation

To make the problem easier, we are gonna have to change the denominator into 16

8*2=16 after we times 8 with 2 we now have to do the same 7

So this would show 7*2=14

Now it would be 6 14/16 - 6 15/16

All we have to do now is minus 14 with 15 which equals -1.

Now for the whole numbers, you can just minus the 6’s with eachother 6-6=0. Taking the denominator, we now have -1/16.

Hope this is the answer you are looking for.

A) 500

B) 54 minutes

C) 68cents and 60 cents

D)

E) $40.95

A proportion is a statement that says that two ratios are equal. They can be used in many everyday situations like comparing sizes, cooking, calculating percentages, and more.

Proportions can be written as equivalent fractions or as equal ratios.

A) 42% = 210

100% = (210 x 100)/42

= 500 people

B) 135 berries = 15 minutes

    486 berries = ??minutes

= (486 x 15)/135

= 54 minutes

C) unit price = $6.75/10 = 0.675cents or 68cents

    ii) unit price = $7.25/12 = 0.604cents or 60cents

D) Inconclusive question.

E) 40% of 65 = $26

65 - 26 = $39

Tax = 5% = $1.95

Total = $39 + 1.95

Final Price of jacket = $40.95

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A pound is about equivalent to 0.453592 kilos. By multiplying the amount of pounds by 0.453592, you may convert pounds to kilogrammes.

So, the value of 77 kg is equal to 169.755 lbs.

The kilogramme is the primary mass unit in the metric system (kg). The masses of one kilogramme and one thousand cubic centimetres of water are comparable.

The weight of one pound is about equivalent to 454 grammes. A kilogramme is equivalent to 2.20462 pounds.

The value of One pound is 0.45359237 kilograms.

To convert kilograms to pounds,

We have to multiply given figure by 2.20462

To convert 77 kg to lbs, you can multiply 77 by 2.20462:

77 kg X 2.20462 lbs/kg

= 169.755 lbs

Therefore, 77 kg is nearly equal to 169.755 lbs.

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The following is a graph that illustrates the inequality system: (B) The graph displays a solid line with shading below it that goes through the points 0 commas 2, and 1 comma negative 3.

In mathematics, "inequality" refers to a relationship between two expressions or values that is not equal to each other.

Hence, inequality emerges from a lack of balance.

A mathematical statement that demonstrates the equality of two expressions is known as an equation, whereas a statement that demonstrates the greater or smaller value of one expression is known as an inequality.

For writing and comprehending an inequality plotted on a graph, there are two (2) main rules in mathematics, and these are as follows:

1. When the inequality symbol is (or), the line on a graph should be solid.

2. When the inequality symbol is (> or ), the line on a graph should be dashed (dotted).

The boundary line is dashed (dotted) and shaded above to indicate that the boundary is not part of the solution, and this must be indicated with the larger than (>) inequality sign.

Moreover, the y-value for this inequality graph meets the x-axis at -1.5.

Therefore, the following is a graph that illustrates the inequality system: (B) The graph displays a solid line with shading below it that goes through the points 0 commas 2, and 1 comma negative 3..

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Complete question:

The following inequalities represent a system.

y ≥ −5x + 2

y > 3x − 1.5

Which of the following graphs represents the system?

A. The graph shows a solid line that passes through 0 comma 2 and 1 comma negative 3, with shading above the line. There is also a dashed line that passes through 0 comma negative 1.5 and 1 comma 1.5, with shading above the line.

B. The graph shows a solid line that passes through 0 comma 2 and 1 comma negative 3, with shading below the line. There is also a dashed line that passes through 0 comma negative 1.5 and 1 comma 1.5, with shading above the line.

C. The graph shows a solid line that passes through 0 comma 2 and 1 comma negative 3, with shading above the line. There is also a dashed line that passes through 0 comma negative 1.5 and 1 comma 1.5, with shading below the line.

D> The graph shows a solid line that passes through 0 comma 2 and 1 comma negative 3, with shading below the line. There is also a dashed line that passes through 0 comma negative 1.5 and 1 comma 1.5, with shading below the line.

The conversion of 180 centimetres in feet is equals to the 5.90 feet. Thus, conversion factor for conversion of units, centimetres to feet is 5.90/180 = 0.032.

A conversion is defined as to convert one set of units into another set of units by multiplication or division. A number or value which used in conversion is called conversion factor. If conversion is necessary, a conversion factor suitable for equivalent value must be used. For example, to convert meters to centimetres, the appropriate conversion value is 100 centimetres equal 1 meter. It includes converting a value from inches to millimeters, for distance from miles to kilometers, feet or other units. How to convert centimeters to feet : One meter is a measure of length and equals approximately 3.28 feet. Thus conversion factor is 3.28 feet. So, 180 meters

= 180 × 3.28 feet

= 590.4 feet --(1)

But we need to convert 180 centimeters to feet. So, change meters to centimeters. As you know, 1 meter = 100 centimeters, so 180 meters = 18000 centimeters --(2). Now from equations (1) and (2),

18500 centimeters = 590.4 feet,

Divide both parts by 100,

=> 180 centimetres = (590.4/100 ) feet

= 5.90 feet

Hence required value is 5.90.

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The rank-nullity theorem states that the rank of a matrix plus the dimension of its null space equals the number of columns.

Thus, if the null space of a 4 x 5 matrix is three-dimensional, then the rank of the matrix is 5 - 3 = 2.

Answer to Question 2:

The dimension of the solution space of A x = 0 is 6 - 2 = 4, since the number of columns of A is 6 and its rank is 2. The solution space of A x = 0 is the null space of A, which has dimension 4 by the rank-nullity theorem.

Answer to Question 3:

No, the columns of A do not necessarily have to be linearly independent. The column space of A is the span of its columns, which has dimension p. However, the columns of A may be linearly dependent, which means that some columns can be expressed as linear combinations of the others.

Answer to Question 4:

To prove that H + K is a subspace of V, we need to show that it satisfies three conditions:

It contains the zero vector: 0 = 0 + 0 belongs to H + K, since it can be expressed as the sum of the zero vectors in H and K.

It is closed under vector addition: if w1 and w2 belong to H + K, then there exist h1 and k1 in H and K such that w1 = h1 + k1, and there exist h2 and k2 in H and K such that w2 = h2 + k2. Therefore, w1 + w2 = (h1 + h2) + (k1 + k2) belongs to H + K, since it can be expressed as the sum of vectors in H and K.

It is closed under scalar multiplication: if w belongs to H + K and c is a scalar, then there exist h and k in H and K such that w = h + k. Therefore, c w = c h + c k belongs to H + K, since it can be expressed as the sum of vectors in H and K.

Since H + K satisfies these three conditions, it is a subspace of V.

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Answer: A=77  B=103   C=90  D=90  E=103   F=77   G=77

Note: This may not be right.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

The answer is $11.60

Step-by-step explanation:

Recursive form of sequence is given by f(n)  = f(n-1) - 3

What is function?

Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable.

here, we have,

The explicit form of sequence is  given as

      f(n) = −3n + 2

So nth term is given by

           f(n) = −3n + 2

(n-1)th term is given by    

           f(n-1) = −3(n-1) + 2

We have

         f(n) -  f(n-1) = −3n + 2 - (−3(n-1) + 2)

          f(n) -  f(n-1) = −3n + 2 +3(n-1) - 2

          f(n) -  f(n-1) = −3n + 2 +3n -3 - 2

          f(n) -  f(n-1) = -3

          f(n)  = f(n-1) - 3

Recursive form of sequence is given by f(n)  = f(n-1) - 3

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Looking at z table you can find the probability = 0.8643.

Describe Probability?

The probability of an occurrence is a number used in science to describe how likely it is that the event will take place. In terms of percentage notation, it is expressed as a number between 0 and 1, or between 0% and 100%. The higher the likelihood, the more likely it is that the event will take place. A certain occurrence has a chance of 1, while an impossible event has a probability of 0. The odds of two complementing events A and B happening, either A happens or B happens, sum up to 1.

Probability that bulb will last at most 610 hours is same as bulb 1-probability that bulb will last more than 610 hours. Any way we can find the probability.

Pr <= 610 hours

Using Z statistic,

610-580/(900)^1/2 = 33/30 = 1.10

So we have z value = 1.10

Now looking at z table you can find the probability,

= 0.8643

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The value on conversion of 300 Fahrenheit to Celsius will be equal to 148.8 Celsius depending on the relation.

The temperature in degree celsius is calculated using the formula -

Celsius = 5/9 (F - 32)

Now we need to keep the value of fahrenheit in the formula where F represents Fahrenheit

Celsius = 5/9 (300 - 32)

Firstly solving the bracket where subtraction sign is present. So, performing the subtraction first.

Celsius = 5/9 × 268

Performing division and multiplication on Right Hand Side of the equation

Temperature in Celsius = 148.8

Therefore, the temperature in Celsius is 148.8.

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Based on the assertion and the reason regarding the weight of an object and upthrust experienced by the body in a fluid; Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A). The correct option is A.

The principle of floatation states that an object will float in a fluid if the upthrust that is experienced by the object is equal to or greater than the weight of the object.

The upthrust experienced by a body is the upward force that a liquid or gas exerts on a body floating in it.

Upthrust on a body depends on the acceleration due to gravity, the density of the liquid, and the volume of the body immersed in the liquid.

The weight of a body is the force of gravity acting on the body. The weight of a body acts downward.

Thus in a fluid, the weight of an object acts downward while the upthrust on the object acts in an upward direction.

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Answer: C. $725

Step-by-step explanation: To find the answer, let's first calculate the increase. A 16% increase causes the cost to go up by 16% of its own value, so let's calculate that by doing 0.16 x 12.5, giving us 2. Next, we add 2 to 12.50, giving us 14.5. Finally, we multiply 14.5 by 50 to find the cost for 50 students, giving us $725. So, $725 is our answer.

Hope this helped :D

The expression that can be used to determine if she has enough money to purchase the jeans would be discussed below.

The total amount of money given to Natalie by her mom= $40.

The original price of the jeans = $45

The discount percentage = 20% of 45

= 20/100 ×45/1

= 900/100 = $9

The price of the jeans after discount = $36

The percentage of tax deduction = 8% of 45

= 8/100 × 45

= 360/100

= $3.6

The price of the jeans after tax = 36+ 3.6 = $39.6

Therefore, the amount of money that the money gave to Natalie to purchase jeans will be enough.

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The required height of the triangle whose area and base are given is 9 yd.

The area of a triangle in a two-dimensional plane is the space that it completely encloses. A triangle is a closed shape with three sides and three vertices, as is pretty obvious.The area of a triangle is the total space occupied by its three sides. The general formula for determining the triangle's area is half of the product of its base and height.

In the given question, we have to find the height of the given triangle ,

we know that ,

Area of triangle = base x height x 1/2.

63.9 = 1/2 × 14.2 × height

Height = (63.9 × 2) ÷ 14.2

Height = 127.8 ÷ 14.2

Height = 9 yd

Therefore , the height of the triangle is 9 yd .

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Answer:  

Step-by-step explanation: To fidn the median I think you add all multiply by how many numbers you have and then divide I think PLS HELP MY QUESTION.

The figure W has one Rotational symmetries. This can be observed by rotating the figure by 0 or 180 degrees and noting that the shape remains unchanged. so the correct option is (b).

The letter W has one vertical line of symmetry that divides it into two identical halves. However, it does not have any rotational symmetry of order 2 or higher because there is no way to rotate the letter by a certain angle and have it look the same as before the rotation. Therefore, the answer is (b) 1, as W has only one line of symmetry and no rotational symmetry of order 2 or higher. In other words, if you rotate the letter by any angle other than 0 or 180 degrees, it will look different than before the rotation.

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______The given question is incomplete, the complete question is given below:

How many rotational symmetries does W alphabet have?

a. 0

b. 1

c. 2

d. 3

To convert 8 cups to quarts, you can divide the number of cups by 4 to get 2 quarts.

To convert cups to quarts, you can use the following conversion factor:

1 quart = 4 cups

Therefore, to convert 8 cups to quarts, you can divide the number of cups by 4:

8 cups ÷ 4 = 2 quarts

So, 8 cups is equal to 2 quarts.

It's important to keep in mind that cups and quarts are units of volume measurement commonly used in cooking and baking. Cups are often used to measure smaller amounts of liquid or dry ingredients, while quarts are used for larger amounts.

In many recipes, the measurements are given in cups, but in some cases, you may need to convert from cups to quarts or other units.

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As per the line segment, the location point of M is option (c) (16/5,19/5)

To answer the question, it is important to understand what a line segment is. A line segment is a part of a line that connects two points, usually denoted by X and Y.

Here we have consider that in this case, the line segment XY is divided by Point M such that XM/MY is equal to 2/3.

As we all know that this means that the ratio between the two parts of the line segment is 2:3. Therefore, the location point of M is (-16/5,19/5).

Therefore, the correct option is (c).

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Answer:

Below

Step-by-step explanation:

Similar triangles due to A - A - A

Set up ratios

QR is to RS   as  QP is to TS

(x+2) / (2x-5) = 3/5       Cross multiply to get

5x+10 = 6x-15               subtract 5x from both sides of the equation

10 = x - 15                     add 15 to both sides

25 = x