−4 3/3 − 5/3 subtract then simplify

The sample standard deviation is approximately 0.83.

Sample size \(($n$)\) = 36

Population mean \(($\mu$)\) = 50

Population standard deviation \(($\sigma$)\) = 5

The sample standard deviation, denoted as \($s$\) can be estimated using the formula:

\(\[ s = \sqrt{\frac{\sum_{i=1}^{n}(x_i - \bar{x})^2}{n-1}} \]\)

where:

\($x_i$\) represents the individual data points in the sample

\($\bar{x}$\) is the sample mean

In this case, since we don't have individual data points, we can use the population standard deviation as an estimate for the sample standard deviation when the sample size is relatively large (as in this case \($n = 36$\)). This approximation is known as the standard error of the mean.

Therefore, the sample standard deviation can be approximated as:

\(\[ s \approx \frac{\sigma}{\sqrt{n}} \]\)

Substituting the given values:

\(\[ s \approx \frac{5}{\sqrt{36}} = \frac{5}{6} \] = 0.83\)

Hence, the sample standard deviation is approximately 0.83.

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The correct answers are: The test is statistically significant. We have observed something unusual if the null hypothesis is true. The other statements are not necessarily true on the given p-value of 1.5%.

Based on the information provided, we can determine the following:

The test is statistically significant: A p-value of 1.5% indicates that the observed result is unlikely to have occurred by chance, given the null hypothesis.

We have observed something unusual if the null hypothesis is true: A small p-value suggests that the observed data is unlikely to be a result of random chance, which implies that the data is unusual if the null hypothesis is true.

The null hypothesis is not necessarily false: The p-value alone does not provide direct information about the truth or falsehood of the null hypothesis. It only indicates the level of evidence against the null hypothesis.

The alternative hypothesis is not necessarily true: Similarly, the p-value does not provide evidence for the alternative hypothesis being true. It only indicates the strength of evidence against the null hypothesis.

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Han's retirement account earns $247,163.25 in simple interest.

To find the simplest interest, we need to use the formula:

Simple Interest = Principal × Rate × Time

In this case, the Principal is $410,000 and the Rate is $15,785 per year. We don't know the time period, but we can solve for it using the formula:

Time = Simple Interest ÷ (Principal × Rate)

Plugging in the values, we get:

Time = $15,785 ÷ ($410,000 × 1) = 0.0385 years

Therefore, the simplest interest is:

Simple Interest = $410,000 × $15,785 × 0.0385 = $247,163.25

So Han's retirement account earns $247,163.25 in simple interest.

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Answer:

Option B) \(y - 1= -4 [x-(-3)]\)

Step-by-step explanation:

Slope = m = -4

Point = (x1,y1) = (-3,1)

So, x1 = -3, y1 = 1

Putting it in the point slope equation:

=> \(y-y1 = m(x-x1)\)

=> \(y - 1= -4 [x-(-3)]\)

1. Probability of exactly 7 students majoring in STEM: is 0.1312

2. Probability of exactly 2 students needing another math class: is 0.3186

3. Probability of at most 2 students needing another math class: 0.0997

4. Probability of at least 2 students needing another math class: 0.9537

5. Probability of between 2 and 3 students needing another math class: 0.9829

6. Mean for the number of people with the genetic mutation: 24

7. Standard deviation for the number of people with the genetic mutation: 4.49

1. Probability of exactly 7 students majoring in STEM:

The probability of exactly 7 students majoring in STEM can be calculated using the binomial probability formula:

P(X = k) = (nCk) × (\(p^k\)) × (\((1-p)^{(n-k)\))

Where:

n = Total number of trials (34)

k = Number of successful trials (7)

p = Probability of success (25% or 0.25)

Plugging in the values:

P(X = 7) = (34C7) × (\(0.25^7\)) × (\((1-0.25)^{(34-7)\))

Using a calculator or statistical software, calculate P(X = 7) = 0.1312 (rounded to 4 decimal places).

2. Probability of exactly 2 students needing another math class:

The probability of exactly 2 students needing another math class can be calculated using the binomial probability formula:

P(X = k) = (nCk) × (\(p^k\)) × (\((1-p)^{(n-k)\))

Where:

n = Total number of trials (4)

k = Number of successful trials (2)

p = Probability of success (64% or 0.64)

Plugging in the values:

P(X = 2) = (4C2) × (0.64²) × (\((1-0.64)^{(4-2)\))

Using a calculator or statistical software, calculate P(X = 2) = 0.3186 (rounded to 4 decimal places).

3. Probability of at most 2 students needing another math class:

To calculate the probability of at most 2 students needing another math class, we sum up the probabilities of exactly 0, 1, and 2 students needing another math class:

P(X ≤ 2) = P(X = 0) + P(X = 1) + P(X = 2)

Using the binomial probability formula as in the previous steps, calculate P(X ≤ 2) = 0.0997 (rounded to 4 decimal places).

4. Probability of at least 2 students needing another math class:

To calculate the probability of at least 2 students needing another math class, we subtract the probability of 0 students needing another math class from 1:

P(X ≥ 2) = 1 - P(X = 0)

Using the binomial probability formula, calculate P(X ≥ 2) = 0.9537 (rounded to 4 decimal places).

5. Probability of between 2 and 3 students needing another math class:

To calculate the probability of between 2 and 3 students needing another math class (inclusive), we sum up the probabilities of exactly 2 and exactly 3 students needing another math class:

P(2 ≤ X ≤ 3) = P(X = 2) + P(X = 3)

Using the binomial probability formula, calculate P(2 ≤ X ≤ 3) = 0.9829 (rounded to 4 decimal places).

6. Mean for the number of people with the genetic mutation:

The mean for the number of people with the genetic mutation can be calculated using the formula:

Mean = n × p

Where:

n = Total number of trials (600)

p = Probability of success (4% or 0.04)

Plugging in the values, calculate the mean = 600 × 0.04 = 24 (rounded to 2 decimal places).

7. Standard deviation for the number of people with the genetic mutation:

The standard deviation for the number of people with the genetic mutation can be calculated using the formula:

Standard deviation = √(n × p × (1 - p))

Where:

n = Total number of trials (200)

p = Probability of success (8% or 0.08)

Plugging in the values, calculate the standard deviation = √(200 × 0.08 × (1 - 0.08)) = 4.49 (rounded to 1 decimal place).

So, the mean for the number of people with the genetic mutation in groups of 600 is 24, and the standard deviation for the number of people with the genetic mutation in groups of 200 is 4.49.

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Answer:

Growth

Step-by-step explanation:

When x value increase, y value also increase, So growth.

When x = 1   ;f(1) = 2

When x = 2  ; f(2) = 2² = 4

When x = 3  ; f(3) = 2³ = 8

Answer:

Exponential Growth

Step-by-step explanation:

I found this photo that helps differentiate both growth and decay :)

I hope this helps! :)

Answer:

The cost in 2007 - 2008  =  $15,795.5

The linear model for the data is y = $650.5·x + $9290.5

Step-by-step explanation:

The given data can be presented as follows;

College year,                         x,                 Estimated tuition, y

1997-1998,                             0,                 $9412

1998-1999,                             1,                  $9941

1999-2000,                            2,                 $10561

2000-2001,                            3,                 $11242

2001-2002,                            4,                  $11965

2002-2003,                            5,                  

2003-2004,                            6,                  

2004-2005,                            7,                

2005-2006,                            8,                

2006-2007,                            9,                  

2007-2008,                            10,                  

With points (1, 9941) and (3, 11242), we have the slope given by the equation;

\(m = \dfrac{y_2 - y_1}{x_2 - x_1}\)

Which gives;

\(m = \dfrac{11242 - 9941}{3 - 1}= 650.5\)

Therefore;

y - 11242 = 650.5 × (x - 3)

y= 650.5·x - 650.5 ×3 + 11242

y = 650.5·x + 9290.5

Therefore from the above table at 2007 - 2008, the value of x should be 10, we therefore have;

y = 650.5×10 + 9290.5 = $15,795.5

The cost (estimated tuition) in 2007 - 2008  =  $15,795.5

The linear model for the data is y = 650.5·x + 9290.5.

The linear model for the data is y = 650.5x + 9290.5 and The cost of college tuition in 2007-2008 is $15795.5

A linear equation is in the form:

y = mx + b

where y, x are variables, m is the rate of change and b is the initial value of y.

Let y represent the cost of tuition of battery after x years.

From the table using the points (1, 9941) and (3, 11242):

\(y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\ \\ y-9941=\frac{11242-9941}{3-1}(x-1)\\ \\ y=650.5x+9290.5\)

The linear model for the data is y = 650.5x + 9290.5

At 2007-2008 (x = 10:

y = 650.5(10) + 9290.5 = 15795.5

The cost of college tuition in 2007-2008 is $15795.5

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The solution of the system of equations is; (7, 45).

The solution in this situation means that after 7 days, Adela and Isaiah would each have 45 bracelets.

It follows from the task content that the solution to the system of equations is to be determined and interpreted accordingly.

Since the given equations are;

By elimination, we must subtract Isaiah's equation from Adela's so that we have;

(y - y) = (3x - 5x) + (24 - 10)

0 = -2x + 14

2x = 14; x = 7.

Consequently, y = 3 (7) + 24

y = 21 + 24; y = 45.

Consequently, the solution to the system of equations as given in the task content is; (7, 45).

This means that after 7 days, Adela and Isaiah would both have; 45 bracelets.

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Answer:

1, 2 and 3  (I, II and III)

Step-by-step explanation:

Since the slope is positive (3) in the equation y = 3x + 1, it means that the graph has a positive slope, meaning the line slopes up from left to right.

The y intercept is 1

the x intercept is:  

0 = 3x + 1

x = 1/3

Therefore, the graph of y = 3x + 1 lies in quadrants I, II and III.  Graph the equation to prove this.  

Answer

There are 3 pairs of rectangular faces on this figure.

Total surface area = 276 cm²

Explanation

A cuboid or a rectangular prism has 3 pairs of rectangular faces.

Hence, the surface area is given as

Total surface area = 2 (LB + LH + BH)

where

L = Length of the cuboid = 7 cm

B = Breadth of the cuboid = 4cm

H = Height of the cuboid = 10 cm

Total surface area = 2 (LB + LH + BH)

Total surface area = 2 [(7×4) + (7×10) + (4×10)]

Total surface area = 2 [28 + 70 + 40]

Total surface area = 2 (138) = 276 cm²

Hope this Helps!!!

The probability density function of Z = X + Y can be determined by finding the CDF and then differentiating it to obtain the PDF.

To find the probability density function (PDF) of the random variable Z = X + Y, we need to determine the cumulative distribution function (CDF) of Z and then differentiate it to obtain the PDF.

First, let's find the cumulative distribution function (CDF) of Z:

FZ(z) = P(Z ≤ z) = P(X + Y ≤ z)

To find this probability, we can integrate the joint probability density function over the region where X + Y is less than or equal to z:

FZ(z) = ∫∫R fX,Y(x, y) dx dy

Where R is the region defined by 0 ≤ x ≤ y ≤ 1.

Integrating the joint PDF over this region, we get:

FZ(z) = ∫∫R 2(x + y) dx dy

To evaluate this integral, we split it into two parts:

FZ(z) = ∫[0, z] ∫[x, 1] 2(x + y) dy dx + ∫[z, 1] ∫[0, 1] 2(x + y) dy dx

After evaluating these integrals, we obtain the expression for the CDF of Z.

Finally, to find the PDF of Z, we differentiate the CDF with respect to z:

fZ(z) = d/dz FZ(z)

By differentiating the obtained CDF expression, we can find the PDF of Z.

Therefore, the probability density function of Z = X + Y can be determined by finding the CDF and then differentiating it to obtain the PDF.

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The president's choices for the three dimensional containers packaging, indicates;

A. The shape of the figure in the question is a prism

A three dimensional figure is a  figure that has dimensions of length, breadth, and width.

The possible question, obtained from a similar question on the internet includes to identify the figure as either a prism, pyramid, cylinder or cone

The figure in the question has a shape that differs from a cylinder or cone

A pyramid is a three dimensional figure consisting of triangular faces and a polygonal base that meet at a point

A prism consists of two polygonal bases that are are parallel and congruent and lateral rectangular or parallelogram faces. The name of a prism is based on the name of the polygonal base.

The shape of the polygonal base in the figure is an isosceles trapezium, therefore, the name of the solid is a trapezoidal prism

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The exact answer on Edge is

"Use the product of powers property to simplify the numerator by removing the parentheses.  Follow the order of operations by removing the innermost parentheses first.  Cube the quantity to get the product of 2 to the third power, r to the 6th power, and t to the third power, or 2^3r^6t^3 in the numerator. "

a) The rate at which shoppers are entering the store 3 hours after the start of the sale is 432.5 shoppers per hour.

b) The integral ∫₀¹₂ S'(t) dt represents the net change in the number of shoppers in the store over the entire 12-hour sale and its value is 4400.

c) According to the model, approximately 6708 shoppers are in the store at the end of the sale (time = 12).

d) The time at which the number of shoppers in the store is the greatest is approximately 4.32 hours.

a) To find the rate at which shoppers are entering the store 3 hours after the start of the sale, we need to find the derivative of the function S(t) with respect to t and evaluate it at t = 3.

S'(t) = d/dt (0.5t* - 16t³ + 144t²)

= 0.5 - 48t^2 + 288t

Plugging in t = 3:

S'(3) = 0.5 - 48(3)² + 288(3)

= 0.5 - 432 + 864

= 432.5 shoppers per hour

Therefore, the rate at which shoppers are entering the store 3 hours after the start of the sale is 432.5 shoppers per hour.

b) To find the value of ∫S'(t)dt, we integrate the derivative S'(t) with respect to t from 0 to 12, which represents the total change in the number of shoppers over the entire sale period.

∫S'(t)dt = ∫(0.5 - 48t² + 288t)dt

= 0.5t - (16/3)t³ + 144t² + C

The meaning of ∫S'(t)dt in this context is the net change in the number of shoppers during the sale, considering both shoppers entering and leaving the store.

c) To find the number of shoppers in the store at the end of the sale (t = 12), we need to evaluate the function S(t) at t = 12.

S(12) = 0.5(12)³ - 16(12)³ + 144(12)²

= 216 - 27648 + 20736

= -6708

Rounding to the nearest whole number, there are approximately 6708 shoppers in the store at the end of the sale.

d) To find the time at which the number of shoppers in the store is greatest, we can find the critical points of the function S(t). This can be done by finding the values of t where the derivative S'(t) is equal to zero or undefined. We can then evaluate S(t) at these critical points to determine the maximum number of shoppers.

However, since the derivative S'(t) in part a) was positive for all values of t, we can conclude that the number of shoppers is continuously increasing throughout the sale period. Therefore, the maximum number of shoppers in the store occurs at the end of the sale, t = 12.

So, at t = 12, the number of shoppers in the store is the greatest.

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The ratio of corresponding sides for the given similar triangles is 2/5.

In the given options, the ratio of corresponding sides is provided for each set of similar triangles. Let's analyze each option to determine the correct ratio:

a. 10

This option only provides a single number and does not specify the ratio of corresponding sides. Therefore, it is not the correct answer.

b. 4/5

This option provides the ratio 4/5 for the corresponding sides of the similar triangles. However, the ratio can be simplified further.

To simplify the ratio, we divide both the numerator and denominator by their greatest common divisor (GCD). In this case, the GCD of 4 and 5 is 1.

Dividing 4 and 5 by 1, we get:

4 ÷ 1 = 4

5 ÷ 1 = 5

Therefore, the simplified ratio is 4/5.

c. 10/85

This option provides the ratio 10/85 for the corresponding sides of the similar triangles. However, this ratio cannot be simplified further, as 10 and 85 do not have a common factor other than 1.

Therefore, the correct ratio of corresponding sides for the given similar triangles is 2/5, as determined in option b.

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Answer:

4/5

Step-by-step explanation:

Square of 1: 1*1=1

Square of 2: 2*2=4

Square of 3: 3*3=9

Square of 4: 4*4=16

Square of 5: 5*5=25

Square of 6: 6*6=36

Square of 7: 7*7=49

Square of 8: 8*8=64

Square of 9: 9*9=81

Square of 10: 10*10=100

Those are the basics.

I hope this helps!

pls ❤ and give brainliest pls

Answer:

\( \large{ \tt{❊ \: S \: O \: L \: U \: T \: I \: O \: N \:❊ }}\)

\( \underline{\large{ \tt{۵ \: S \: T \: E \: P \: S} }} : \)

\( \large{ \tt{❁ \: \sqrt{ \frac{16}{25} }→\sqrt{ \frac{ {4}^{2} }{ {5}^{2} } }→ \sqrt{ (\frac{4}{5} ) ^{2} } → (\frac{4}{5} )}^{ \frac{2}{2} } → \boxed{ \tt{ \frac{4}{5} }}} \)

\( \boxed{ \boxed{ \tt{⤳ \: OUR \: FINAL \: ANSWER : \boxed{ \frac{4}{5} }}}}\)

Answer:

78.3% which would be a C+

Step-by-step explanation:

If the project was worth 20% of your grade and you got 50% on that project, we can multiply the decimal values of these percentages together to know exactly by how much your grade will drop.

0.2 * 0.5 = 0.1 or 10%

Now, we see that your grade will drop 10%. Meaning, that from your 87% you will actually have only 90% of that which is...

87 * 0.90 = 78.3

Therefore, your grade will go down to a 78.3% which would be a C+

The value of the function if the independent variable is equal to -1 is -2

Given the function p(x) = x^3 - 1

The input variable "x" is the independent variable. If the independent variable is equal to -1, the value of the function will be expressed as:

P(-1) = (-1)^3 - 1

P(-2) = -1 -1

P(-2) = -2

Hence the value of the function if the independent variable is equal to -1 is -2

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The percentage of the flock that has spots is 35%.

To find the percentage of the flock that has spots, we need to divide the number of sheep with spots by the total number of sheep and then multiply by 100 to get the percentage.

In this case, we have 182 white sheep and 98 spotted sheep, so the total number of sheep in the flock is 182 + 98 = 280.

To find the percentage of sheep with spots, we divide the number of spotted sheep (98) by the total number of sheep (280) and then multiply by 100:

(98/280) x 100 = 35%

This means that 65% of the flock is white.

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Answer:

C: peasants were dependent on the lord and his land.

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

i did it already.

To find the value of x, we can use the fact that the sum of the angles in a triangle is 180 degrees. By subtracting the given angles a and b from 180 degrees, we can find the measure of angle x.

In a triangle, the sum of all three angles is always 180 degrees. Therefore, we can set up the equation:

a + b + x = 180

Substituting the given values for a and b:

78° + 47° + x = 180°

To solve for x, we can subtract 78° and 47° from both sides of the equation:

x = 180° - 78° - 47°

x = 55°

Hence, the value of angle x is 55 degrees.

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The answer is ,the statement  that are true are: A. The small popcorn has  volume of about 25.13 cubic inches , C. The volume of two small popcorn is less than  volume of one large popcorn , E. The volume of  large popcorn is about 34.68 cubic inches greater than  volume of small popcorn (135.09 - 25.13 = 109.96).

A cone is  three-dimensional geometric shape that tapers smoothly from  flat, usually circular base to  point called the apex or vertex. The base of  cone can be any closed shape, but is usually a circle. A cone can be right or oblique, depending on whether or not the axis passing through the apex and the center of the base is perpendicular to the base.

The formula for volume of  cone are V = (1/3)πr^2h, where r is radius and h is height.

For the small popcorn cone:

radius =diameter/2 =4/2=2 inches

V = (1/3)π(2²)(6) ≈ 25.13 cubic inches

For the large popcorn cone:

radius = diameter/2 = 5/2 = 2.5 inches

V = (1/3)π(2.5²)(9) ≈ 59.81 cubic inches

Therefore, the statements that are true are:

A. The small popcorn has  volume of about 25.13 cubic inches

C. The volume of two small popcorn is less than volume of one large popcorn

E. The volume of  large popcorn is about 34.68 cubic inches greater than  volume of small popcorn (135.09 - 25.13 = 109.96)

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We are going to apply the Triangle Inequality Theorem in this problem.

Given sides a, b, and c, a triangle exists if:

If each of these inequalities hold, we can say that the triangle does, in fact, exist.

The quickest way to test any triangle is to add the shortest side and the medium side to determine if their sum is greater than the longest side.

Option 1: 15, 17, 25

15, 17, 25 is a triangle.

Option 2: 8, 15, 6

This is false.

Option 3: 19, 9, 13

19, 9, 13 is a triangle.

Option 4: 24, 15, 33

24, 15, 33 is a triangle.

Option 5: 9, 21, 29

9, 21, 29 is a triangle.

Option 6: 3, 7, 10

This is false.

The following groups of sides form triangles: 15, 17, 25; 19, 9, 13; 24, 15, 33; 9, 21, 29.

Answer: 35.90

Step-by-step explanation:

Answer:

Step-by-step explanation:

do I

Answer:

(x-1)(x-2)

x=1, x=2

Step-by-step explanation:

Step-by-step explanation:

the FH seems to be option b.6.0

........

Answer:

yes they will be equal in 1.3 years

Step-by-step explanation:

A Z-score is a metric that quantifies the connection between a value and the mean of a set of values.

z-scores are calculated by (observed value - mean)/standard deviation

Mean = 40

Standard Deviation = 8

Observed Value = 52

z-score = (52 - 40)/8 = 2

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Answer: y = 3.75x + 2.50

Step-by-step explanation:

The equation that can be used to find y, the total cost of renting a bike, if x represents the number of hours Violet rents the bike is:

y = 3.75x + 2.50

Explanation:

Violet pays an initial fee of $2.50, which is a fixed cost that does not depend on the number of hours she rents the bike. Additionally, she pays $3.75 per hour she rents the bike, which is a variable cost that depends on the number of hours. Therefore, the total cost of renting a bike (y) can be expressed as the sum of the fixed cost ($2.50) and the variable cost ($3.75x), which gives the equation: