How many modes are in the data set?


2. 20, 2. 30, 2. 30, 1. 70, 2. 00, 1. 50, 2. 40, 2. 40, 2. 00, 2. 00, 2. 00


A. 0

B. 1

C. 2

D. 3

The magnitude of the vector is approximately 7.3 and the direction of the vector is approximately 74 degrees which is option B.

We have,

To find the magnitude and direction of the vector <2, 7>, we can use trigonometric concepts. Let's break down the steps:

Magnitude (Length) of the Vector:

The magnitude of a vector <x, y> is given by the formula:

Magnitude = √(x² + y²)

For the given vector <2, 7>:

Magnitude = √(2² + 7²) = √(4 + 49) = √53 ≈ 7.3 (rounded to the nearest tenth)

Direction (Angle) of the Vector:

The angle θ that the vector makes with the positive x-axis can be found using trigonometric functions:

θ = arctan(y / x)

For the given vector <2, 7>:

θ = arctan(7 / 2) ≈ 74° (rounded to the nearest degree)

Thus,

The magnitude of the vector is approximately 7.3 and the direction of the vector is approximately 74 degrees which is option B.

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Answer:

Were sorry! Answer is not available right now check in later.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Let's use "n" to represent the number of slices in each pizza. Then the equation to describe the situation is:

999n = 727272

To solve for "n", we divide both sides by 999:

n = 727272/999

Using a calculator or long division, we get:

n ≈ 728.56

Therefore, each pizza has approximately 728 slices.

Answer:

proofs attached to answer

Step-by-step explanation:

proofs attached to answer

In conclusion  the values of p that satisfy this inequality are p = 11, p = 12, p = 13, etc.  The equation showing that Elena saves exactly $20 is:

5 + (1.5)p = 20

Why it is?

The expression for how much money Elena saves after selling p pens is:

Total money saved = 5 + (1.5)p

The equation showing that Elena saves exactly $20 is:

5 + (1.5)p = 20

Solving the equation:

5 + (1.5)p = 20

(1.5)p = 15

p = 10

We notice that the value of p is a whole number, which makes sense since Elena cannot sell a fractional number of pens.

If Elena wants to have some money left over, we can write the inequality:

5 + (1.5)p > 20

Some values for p where Elena would have money left over are p = 11, p = 12, p = 13, etc.

To describe the values of p where Elena would be able to buy the t-shirt and still have money left over, we can write the inequality:

5 + (1.5)p > 20

(1.5)p > 15

p > 10

Therefore, the values of p that satisfy this inequality are p = 11, p = 12, p = 13, etc.

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$17.5 price should she charge in order to make the highest possible gross income.

Given two points are (400, 10) and  (392, 10.5)

slope = (10.5-10)/(392 -400) = 0.5/ - 8 = -0.0625

Equation is

p -10 = -0.0625(x-400)

p-10 = -0.0625x + 25

p = -0.0625x + 35

find revenue as

R=x*p

-0.0625x² + 35x

To maximize,

R'(x) =0

-0.125x + 35 = 0

35/0.125  = x

280 = x

when x is equal to 280, find

p= -0.0625(280) + 35

p= -17.5 +35

p= 17.5

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The value of the standard error of the mean in each of the following cases:

a. The population size is infinite = 1.4142

b. The population size is N = 50,000 = 1.4135

c. The population size is N = 5000 = 1.4073

d. The population size is N = 500 = 1.343

The standard error is a statistical technique used to measure variability. SE is the abbreviation. A statistic's or parameter estimate's standard error is the standard deviation of its sample distribution. It can be defined as an approximation of that standard deviation.

Standard error calculation:

σ = 10

n = 50

A) when size is infinite, the standard deviation of the sample mean is given by the formula;

σ_x' = σ/√n

Thus,

σ_x' = 10/√50

σ_x' = 1.4142

B) size is given, thus, the standard deviation of the sample mean is given by the formula;

σ_x' = (σ/√n)√((N - n)/(N - 1))

Thus, with size of N = 50,000, we have;

σ_x' = 1.4142 x √((50000 - 50)/(50000 - 1))

σ_x' = 1.4142 x 0.9995

σ_x' = 1.4135

C) at N = 5000;

σ_x' = 1.4142 x √((5000 - 50)/(5000 - 1))

σ_x' = 1.4073

D) at N = 500;

σ_x' = 1.4142 x √((500 - 50)/(500 - 1))

σ_x' = 1.343

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Answer:x=33/4096=0.008

Step-by-step explanation: 1.1     16 = 24

(16)3 = (24)3 = 212

Equation at the end of step

1

:

 ((212 • x) -  1) -  32  = 0

STEP

2

:

Equation at the end of step 2

 4096x - 33  = 0

STEP

3

:

Solving a Single Variable Equation:

3.1      Solve  :    4096x-33 = 0

Add  33  to both sides of the equation :

                     4096x = 33

Divide both sides of the equation by 4096:

                    x = 33/4096 = 0.008

Answer:2.4 inches

Step-by-step explanation:

if 6 is for 30 feet, we can use a proportional statement to find what the length of the line will be for a room that is 12 feet.

We will consider two cases: n is even and n is odd. In this step, you will complete the proof of the first case. Proof. Case 1: n is even Let n be an even integer. By the definition of even, for some integer k. This follows that `nº + 17n - 1 = 2:( 2k )+1`

Since is an integer, `n^3+17n + 1` must be an integer. Since `na +17n – 1` equals times an integer plus `n+ 17n – 1` is 2The solution explains the concept of even integer. Let n be an even integer, and by the definition of even, for some integer k. This follows that `nº + 17n - 1 = 2:( 2k )+1`.Since 2k is an integer, n^3 + 17n + 1 must also be an integer. This is because even times even is even and even times odd is even, which means that (2k + 1) is always odd. The integer n^3 can be written as (n*n*n). Given that n is an even integer, it follows that n*n is even. And since an even number times an even number is always even, it follows that (n*n*n) is even. Since the sum of an even number and an odd number is always odd, adding 1 to n^3 + 17n gives an odd number, and thus an integer, as desired. The equality `na +17n – 1 = 2` is not needed in this proof.

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Yes, the data give convincing evidence to support Phoebe's hunch. As the result of the test is a p-value that is 0.1 of less than 0.05.

The p-value is the probability of obtaining a result as extreme or more extreme given that the null hypothesis is true. The p-value is calculated by comparing the test statistic to the probability distribution under the null hypothesis.

The ratio of seniors bringing a bag lunch= 78/104 or 0.75,

while the ratio of sophomores bringing a bag lunch= 52/80 or 0.65.

This indicates that the proportion of seniors bringing a bag lunch is higher than the proportion of sophomores bringing a bag lunch.

Further, the difference between the proportions is

0.75-0.65 = 0.1,

which is a large enough difference to be considered significant.

The result of the test is a p-value of less than 0.05, which is statistically significant and indicates that the difference in the proportions is due to the different ages, and not due to chance.

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Answer:

Area: 391.92 ft²

Perimeter: 84.4 ft

Step-by-step explanation:

Area of rectangle = L × W

We Take

13.8 × 28.4 = 391.92 ft²

Find the Perimeter of the Rectangle

We Take

28.4 + 13.8 + 28.4 + 13.8 = 84.4 ft

So, Area: 391.92 ft²

     Perimeter: 84.4 ft

Answer:

Area = 391.92 square feet

Perimeter = 84.4 feet

Step-by-step explanation:

The area of a rectangle is the product of its width and length.

The perimeter of a rectangle is twice the sum of its width and length.

Given the width of the rectangle is 28.4 feet and its length is 13.8 feet:

[tex]\begin{aligned}\textsf{Area of the rectangle}&=\sf width \times length\\&=28.4 \times 13.8\\&=391.92 \sf \;\;square\;feet\end{aligned}[/tex]

[tex]\begin{aligned}\textsf{Perimeter of the rectangle}&=\sf 2(width +length)\\&=2(28.4 +13.8)\\&=2(42.2)\\&=84.4 \sf \;\;feet\end{aligned}[/tex]

The final value in cell D2 using the following formula:

price - price× discount = $ 101.19

Take the original price. Multiply that by the discount percentage and divide the result by 100. Subtract the result from the original price. this is your final price

According to the Question:

The final value in cell D2 using the following formula:

(price - price) × discount.

Given that:

Price = $114.99

Discount = 12%

By the above formula:

(price - price) × discount.

= ($114.99 - $114.99) × 12%

= $101.19

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the given side that measures 2 1/4 inches with the corresponding length measurement. Label the angle between these sides as 60°.

A triangle is a polygon with three sides, three vertices, and three angles. The sum of the interior angles of a triangle is always 180 degrees, and the longest side of a triangle is opposite to the largest angle, and the shortest side is opposite to the smallest angle. Triangles can be classified according to their side lengths and angles. For example, an equilateral triangle has three equal sides and three equal angles of 60 degrees each, while an isosceles triangle has two equal sides and two equal angles. A scalene triangle has no equal sides or angles. Triangles are important in geometry and have many applications in mathematics and other fields, such as architecture, engineering, physics, and computer graphics.

by the question.

Draw a straight-line segment and label it as the given side that measures 1 1/2 inches.

From one endpoint of the first line segment, draw another line segment that forms a 60° angle with the first line segment. Label this second line segment as the given side that measures 2 1/4 inches.

Draw a third line segment that connects the endpoints of the first two-line segments. This will complete the triangle.

To label the triangle, label the given side that measures 1 1/2 inches with the corresponding length measurement, and label the given side that measures 2 1/4 inches with the corresponding length measurement. Label the angle between these sides as 60°.

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Answer: 100:3

Step-by-step explanation:

Answer:

the ratio of first-year college basketball players to high school seniors playing basketball is 3:100.

Step-by-step explanation:

The problem states that for every 75,000 high school seniors playing basketball, about 2,250 play college basketball as first-year students. To write the ratio of first-year college basketball players to high school seniors playing basketball, we need to compare the two quantities.

The ratio is a way of expressing the relationship between two numbers as a fraction or a pair of numbers separated by a colon (:). In this case, we want to express the ratio of the number of first-year college basketball players to the number of high school seniors playing basketball.

To write the ratio, we start by putting the number of first-year college basketball players (2,250) in the numerator of a fraction. We put the number of high school seniors playing basketball (75,000) in the denominator of the same fraction.

So the ratio can be expressed as:

2,250/75,000

To simplify this fraction, we can divide both the numerator and denominator by a common factor. In this case, both 2,250 and 75,000 are divisible by 750. Dividing both numbers by 750 gives:

2,250/75,000 = 3/100

The volume is 63.717 cubic units

The limits of integration for rho are 0 and 4 cos phi, since the sphere has radius 4 cos phi. The limits for phi are π/4 and π/2, since we want to consider the region outside the cone but inside the sphere, and phi is the angle between the positive z-axis and the position vector of a point. Finally, the limits for theta are 0 and 2π, since theta is the azimuthal angle and we want to integrate over the entire azimuthal angle.

Thus, the volume of the region is given by:

V = 8 x ∫(0 to 2π) ∫(π/4 to π/2) ∫(0 to 4 cos phi) ρ² sin phi dρ dphi dtheta

Simplifying the integral using basic calculus, we get:

V = 8 x (64/3 - 16/3√2π) = 63.717

Therefore, the volume of the region outside the cone phi = π/4 and inside the sphere rho = 4 cos phi is 8(64/3 - 16/3√2π), which is an exact answer using π as needed.

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The strike price of the option is $101.5, rounded to the nearest integer, whicch is given as the APE(s,t)= -0.5.

The asset price elasticity (APE) of a European Put Option at time 't' is the ratio of the change in the option price to the change in the stock price, given that all other factors remain constant.

The APE(s,t) of a European put option is calculated using the formula APE(s,t) = -S+Ke-rτ.

In this case, the current stock price is $100 and the time until expiration is 4 years.

We can solve for K, the strike price of the option, given the APE(s,t) is -0.5.

K = S + APE(s,t) + reτ

K = 100 - 0.5 + (0.5 x 4)

K = 101.5

The strike price of the option is $101.5, rounded to the nearest integer.

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Answer:

Para calcular el precio original de los auriculares antes del descuento, podemos usar la fórmula:

Precio original = Precio después del descuento / (1 - Porcentaje de descuento)

Donde "Precio después del descuento" es el costo de los auriculares después del descuento, y "Porcentaje de descuento" es el porcentaje aplicado como descuento. En este caso, el porcentaje de descuento es del 20%, es decir, 0.2 en términos decimales.

Sustituyendo los valores conocidos, obtenemos:

Precio original = 260 / (1 - 0.2)

Precio original = 260 / 0.8

Precio original = 325

Por lo tanto, el costo original de los auriculares antes del descuento era de $325.:

Answer:

The answer is D. (1-0.2)h=260

Step-by-step explanation:

Based on the picture, we can use the Pythagorean theorem to find MBC. Therefore, MBC is equal to  [tex]7[/tex]√2.

Theorem of Linear Pairs Two angles are supplementary if they create a linear pair. Additional theorem, Two angles are congruent if they are supplements of the same angle.

Theorem of congruent complements an of thes., but it will be the first of a series of events that will result in a new set of rules and the.

First, we can find AB:

AB = √(AD² + BD²)

= √ [tex](3^2 + 4^2)[/tex]

= √[tex](9 + 16)[/tex]

= √ [tex]25[/tex]

[tex]= 5[/tex]

Next, we can find AC:

AC = √(AD² + CD²)

= √[tex](3^2 + 8^2)[/tex]

= √ [tex](9 + 64)[/tex]

= √[tex]73[/tex]

Finally, we can find BC:

[tex]BC = √(AB^2 + AC^2)[/tex]

= √(5² + (√73)²)

= √(25 + 73)

= √98

= 7√2

Therefore, m Bc is = 7√2

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Stefanie bought a package of pencils for 1. 75$ and some erasers that cost 0. 25 each. She paid a total of 4. 25 for these items, before tax. Stefanie bought total 10 erasers.

Equation:

In mathematics, an equation is a formula that connects two expressions with the equal sign = to indicate that they are equal.

According to the Question:

The number of erasers bought by Stefanie:

Let we denote the number of erasers bought by her by x (an unknown variable)

Then we will have:

Total amount before tax = cost of one package of pencil + cost of  erasers

   $4.25 = $1.75 + X × $0.25

⇒ 4.25 = 1.75 + 0.25x

Now,

we will perform subtraction by 1.75 and division by 0.25 on both sides.

4.25 = 1.75 + 0.25x

Subtracting 1.75 both side:

   4.25 -1.75 = 0.25x

⇒ 2.5 = 0.25x

Dividing by 0.25 on both sides:

   2.5/0.25 = 0.25x/0.25

⇒ x = 10

Thus, Stefanie bought total 10 erasers.

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To solve the question asked, you can say:  So the dolphin's new location expressions is 3 feet above sea level. Option OD explains this process correctly and gives the correct answer. 

In mathematics, an expression is a set of numbers, variables, and mathematical operations such as addition, subtraction, multiplication, division, and exponentiation that represent quantities or values. Expressions can be as simple as "3 + 4" or as complex as they can contain functions like "sin(x)" or "log(y)" . Expressions can be evaluated by substituting values ​​for variables and performing mathematical operations in the order specified. For example, if x = 2, the expression "3x + 5" is 3(2) + 5 = 11. In mathematics, formulas are often used to describe real-world situations, create equations, and simplify complex math problems. 

Move 3 units to the right on the outer diameter number line. Exit with -3. The dolphin was 3 feet below sea level.

To find the dolphin's new location, we need to determine the dolphin's direction of movement and distance traveled. In this case the dolphin swam to the bottom. This means it has moved in the negative direction on the number line. Then she swam three feet. This means she has moved 3 units to the right (or positive side) on the number line.

So we need to start at the dolphin's original position of -6 and move it 3 units to the right to -3. So the dolphin's new location is 3 feet above sea level. Option OD explains this process correctly and gives the correct answer. 

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To see if there is a significant difference in the costs of airline flights between the west and east coasts to Lincoln, Nebraska, one can use a two-sample t-test. It is okay to perform the inference procedure, but the following assumptions and conditions must be checked.

Assumptions: Independence: The airfares for each coast should be independent of each other. Normality: The populations of airfares for both coasts should be approximately normally distributed .Equal variances: The population variances for both coasts should be equal.

Conditions: Sample sizes: Both samples should be large enough so that the Central Limit Theorem applies. Rule of thumb for t-tests is that the sample size should be at least 30.Random sampling: Both samples should be random .To test if the conditions are met, one can create a boxplot for each coast, check the normal probability plots, perform the F-test to check for equal variances, and check the sample sizes. If the assumptions and conditions are met, a two-sample t-test can be used to determine if there is a significant difference in the costs of airline flights between the west and east coasts to Lincoln, Nebraska.

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If an access code for a car's security system consist of six digits and the  first digit cannot be zero and the last digit must be even, then the number of different codes available are 4,500,000

Since the first digit cannot be zero, we have 9 choices for the first digit. For each of these 9 choices, there are 10 possibilities for the second digit (0-9).

Similarly, there are 10 possibilities for the third digit, 10 for the fourth digit, 10 for the fifth digit, and 5 (0, 2, 4, 6, 8) for the last digit.

Therefore, the total number of possible access codes is:

9 x 10 x 10 x 10 x 10 x 5 = 4,500,000

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Random sampling 50 batteries throughout the day and testing to see if they would provide most valid results.

A sample is described as a smaller, more manageable representation of a larger group. A smaller population with characteristics of a larger one. A sample is used in statistical analysis when the population size is too large to include all participants or observations in the test.

The sample may be biased if it is taken from the first 25 batteries made each day or the last 25 batteries made each day.

The first and last battery made each day could not be an accurate representation of the total quality of the batteries produced that day if the battery manufacturing process is not consistent thought the day.

Although the battery quality can change during the day, sampling the first 50 batteries produced each day may also add bias into the sample.

The ideal course of action is to randomly select 50 batteries throughout the day, since this helps to ensure that the sample is reflective of the general calibre of batteries manufactured that day.

A more accurate image of the quality of the batteries manufactured can be obtained using this method, which is also more likely to capture any variations in battery quality over the day.

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Answer:

  y = -1/3x +6

Step-by-step explanation:

You want the equation of the line through the point (3, 5) and perpendicular to y = 3x +2.

The slope-intercept form of the equation of a line is ...

  y = mx +b

where m is the slope, and b is the y-intercept.

Comparing this to the given equation, we see that m=3 for the given line.

The slopes of perpendicular lines are opposite reciprocals of one another. This means the slope of the line we want is ...

  desired slope = -1/m = -1/3

The slope-intercept equation above can be solved for b to give ...

  b = y -mx

Then the y-intercept for the line we want is ...

  b = 5 -(-1/3)(3) = 5 +1 = 6

The equation of the desired line is y = -1/3x +6.

__

Additional comment

Once you understand how to find the slope of the given line and of the desired line, you can write down the desired equation in point-slope form.

Given slope = 3; perpendicular slope = -1/3

Point-slope equation: y -k = m(x -h) . . . . line through (h, k) with slope m

  y -5 = -1/3(x -3) . . . . . line through (3, 5) with slope -1/3

The only "work" required is to rearrange this equation to whatever form you may want. In standard form it is x +3y = 18.

Answer:

34

Step-by-step explanation:

1/2 multiplied by 68=34

34 is 1 half of 68 .

Here, we have,

given that,

what is 1 half of 68

we know that,

Half of a number can be found by dividing the number by 2.

i.e. we have to find half of 68,

for that, we need to divide 68 by 2

so, we get,

To find half of 68:

68 / 2 = 34

Therefore, half of 68 is 34.

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The answer of the given factor and multiplication term for the positive integers are 3.

Positive, negative, and zero digit whole numbers are all included in the category of integers. They can be stated without any fractional or decimal components and are a subset of the real numbers. On a number line, integers can be visualized as positive numbers to the right of zero and negative numbers to the left.

In mathematics, a multiplication term is a mathematical expression that involves the multiplication of two or more factors. The factors can be numbers, variables, or a combination of both. Multiplication terms are commonly represented using the multiplication symbol "×" or the dot "." symbol.

For example, in the expression 2x × 3y, the multiplication term is 2x × 3y, which involves the multiplication of the factors 2x and 3y.

If you want to find the smallest possible value of the given term we have that,The smallest factor of 15 is 1.

The smallest multiple of 3 is 3so, the smallest answer is 1x3 = 3.

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The correct option is C, A 95% confidence interval for the average starting salary of all attorneys in the city is (91331.94, 113352.06)

We have that to find our level, that is the subtraction of 1 by the confidence interval divided by 2. So:

∝= [tex]\frac{1-0.95}{2} = 0.025[/tex]

Now, we have to find z in the Ztable as such z has a p-value of 1-∝.

So it is z with a value of, so [tex]1-0.025=0.975,Soz= 1.96[/tex]

Now, find M as such

[tex]M= z*\frac{1}{\sqrt{n} } *[/tex]σ

In which is the standard deviation of the population and n is the size of the sample.

[tex]M= 1.96* \frac{21756}{\sqrt{15}} =11010.06[/tex]

The lower end of the interval is the sample mean subtracted by M. So it is 102342 - 11010.06 = 91331.94.

The upper end of the interval is the sample mean added to M. So it is 102342 + 11010.06 = 113.352.06.

So the correct answer is:

(91331.94, 113352.06)

Standard deviation is a measure of how much the values in a data set vary from the average or mean value. It is a statistical measure that indicates the extent to which the values are spread out from the mean. A low standard deviation indicates that the values are clustered around the mean, while a high standard deviation indicates that the values are more widely spread out.

Standard deviation is commonly used in statistics and probability theory to measure the uncertainty or risk associated with a particular event or outcome. It is also used in fields such as finance, economics, and engineering to analyze data and make predictions. Standard deviation can provide valuable insights into the distribution of data and help identify trends and patterns in the data set.

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Complete Question:

A random sample of 15 recent college graduates found that starting salaries for attorneys in New York City had a mean of $102,342 and a standard deviation of $21,756. There are no outliers in the sample data set. Construct a 95% confidence interval for the average starting salary of all attorneys in the city. Group of answer choices

A). (89869.82, 114814.18)

B). (90292.73, 114391.27)

C). (91331.94, 113352.06)

D). (90371.37, 114312.63)

Answer:28/445 or 6.2921 %

Step-by-step explanation:

There are 90 nuts all together. There are 14 pecans so it would be a 14/90 chance. Then since you are not replacing the nut there are 89 nuts. There are 36 cashews which would be a 36/89 chance. Because in the problem it says to find the probability of the selecting a pecan and then a cashew we know it is an and situation. Since it is an and situation you would multiply. You would do 14/90 times 36/89. This gives you 504/8010 which reduced is 28/445 or 6.2921%. Do you have and questions?