The following data is the lifetime (in hours) of a sample of batteries. 53, 52, 71, 44 , 49, 44, 55, 46, 54, 57, 44, 62, 38, 58, 51. The median is Group of answer choices 46 52 55 44

The x position of  center of mass is =  0.389 m  , the y position of center of mass is = 0.444 m    .

In the question ,

it is given that , first stick lies along y-axis from y = 0.470 m to y = 1.47 m.

So , coordinate of first stick is (x1 , y1) = (0 , (0.47+1.47)/2) = (0 , 0.97)

the second stick lies along x-axis from x = 0.320 m to x = 1.32 m ,

So , the coordinate of second stick is (x2 , y2) = ((0.32+1.32)/2 , 0) = (0.82 , 0)

the third stick is positioned so that one end is on x-axis at x = 0.690 m, and the other end is on the y-axis at y = 0.724 m .

the coordinate of third stick is (x3 , y3) = (0.690/2 , 0.724/2) = (0.345 , 0.362)

So , x position of center of mass is x = (0 + 0.82 + 0.345)/3

= 0.389 m

So , y position of center of mass is y = (0.97 + 0 + 0.362)/3

= 0.444 m

Therefore , The x position of the center of mass is =  0.389 m  , the y position of center of mass is = 0.444 m    .

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Answer:

Area of pathway = 10.375 unit²

Step-by-step explanation:

Given - Peter has built a gazebo, whose shape is a regular heptagon, with

             a side length of 1 unit. He has also built a pathway around the

             gazebo, of constant width 1 unit, as shown below.

To find -  Find the area of the pathway.

Proof -

Central angle = \(\frac{360}{7}\) = 51.43°

Now,

Central angle / 2 = \(\frac{360}{14}\) = 25.71°

And

height = \(\frac{1}{2}.\frac{1}{tan25.41}\) = 1.038

Now,

Inner area of gazebo = 7·\(\frac{1}{2}\)·1·(1.038) = 3.634 unit²

Outer area of gazebo = (\(\frac{2.038}{1.038}\))²·(3.364) = 14.009 unit²

∴ we get

Area of pathway = Outer area - Inner area

                            = 14.009 - 3.634

                            = 10.375 unit²

⇒Area of pathway = 10.375 unit²

Answer: 1, 3

Step-by-step explanation:

The event of Juan choosing at least one blue marker from the bag when randomly selecting 6 markers is certain.

In this scenario, Juan has a total of 7 markers in his bag, with 3 blue markers and 4 red markers. When he randomly chooses 6 markers from the bag, it is certain that he will select at least one blue marker. This is because there are more blue markers (3) than the number of markers he is selecting (6).

To understand why this event is certain, consider the worst-case scenario where Juan selects all 4 red markers first. Even in this case, there will still be 2 markers left in the bag, both of which are blue. Therefore, Juan is guaranteed to choose at least one blue marker when selecting 6 markers from the bag.

Since there are more blue markers available than the number of markers Juan is choosing, it is certain that he will select at least one blue marker. This makes the event of choosing at least one blue marker from the bag when randomly selecting 6 markers a certain event.

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Answer:

predict the impact of removing snakes from this food web

Answer:

C) 15 revolutions

Step-by-step explanation:

one revolution is the measure of the wheel's circumference, which is 26π inches

26π is about 81.7 inches or 6.8 feet

100 ÷ 6.8 is 14.7

therefore, you would need to round up to 15 revolutions

2.5 cm, 6.5 cm, and 6 cm are the sides of a right triangle.

The sides of a triangle are 2.5 cm, 6.5 cm, and 6 cm in length.

The Pythagorean Theorem states that The sum of the squares representing the base and height equals the square of the hypotenuse.

\((Perpendicular)^{2}+(Base)^{2}=(Hypotenuse)^{2}\)

                        \((2.5)^{2}+(6)^{2}=(6.5)^{2}\)

                            6.25 + 36 = 42.25

                                  42.25 = 42.25

The sides offered satisfy the specifications for a right triangle.

Given that it satisfies the Pythagorean theorem, a right triangle with sides of 2.5 cm, 6.5 cm, and 6 cm can be built.

Hence, 2.5 cm 6.5 cm 6 cm can be the sides of a right triangle.

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(a) The number of ways that the event can occur is 6.

(b) Probabilities are :

1) 1/2, 2) 1/6 and 3) 1/3.

(a) Given a bag of different shapes.

Total number of shapes = 6

So, if we select one shape from random,

total number of ways that the event can occur = 6

(b) Number of squares in the bag = 3

Probability of choosing a square = 3/6 = 1/2

Number of circles in the bag = 1

Probability of choosing a circle = 1/6

Number of stars in the bag = 2

Probability of choosing a star = 2/6 = 1/3

Hence the required probabilities are found.

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Answer:

x = 1/7

Step-by-step explanation:

add the two numbers with the x's and subtract 1 from 2. You'll get 7x = 1. Divide 7 from both sides to get x by itself.

Answer:

Exact Form: x=1/7

decimal form: 0.142857

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable. Hope this helps you better understand! Also, if you want to double check your answers try M-a-t-h-w-a-y. They won't let me write the exact link.

Answer:

The answer for the given expression is 23 after putting the values of a,b and c.

Step-by-step explanation:

Given expression is:

\((\frac{2c}{a})^2-10*\frac{(b+a)}{c}\)

We have to find the value of expression, when

a = -2, b = 3 and c = 5

We will put these values in the given expression and then simplify the given expression,

\((\frac{2*5}{-2})^2-10*\frac{3+(-2)}{5}\\\\(\frac{10}{-2})^2-10*\frac{3-2}{5}\\\\(-5)^2-10*\frac{1}{5}\\25-2\\23\)

Hence,

The answer for the given expression is 23 after putting the values of a,b and c.

Three cards are drawn from a standard deck. Thus, the probability to get an ace, followed by a king, and then a queen, is  16/34,425

The formula for conditional probability is:

P(A∩B) = P(B|A) . P(A)

In the given problem:

P(ace) = 4 / 54

After an ace was drawn, the number of cards now is 51.

Hence,

P(king | ace) = 4/51

After the second drawn, the remaining cards is 50. Hence,

P(queen | (king | ace)) = 4/50

Therefore,

P(ace,king,queen) = 4/54 x 4/51 x 4/50 = 64 / 137,700 = 16/34,425

Thus, the probability to get an ace, followed by a king, and then a queen, is  16/34,425

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Answer: The data could be used as a starting point for further research and analysis to investigate any potential causal relationships or underlying factors.

Step-by-step explanation:

The scatterplot shows a positive correlation between U.S. divorce rates and prison rates for drug offenses. The fact that the correlation coefficient is 0.67 indicates a moderate positive linear relationship between the two variables.

However, correlation does not necessarily imply causation. While the data suggests that there may be some association between divorce rates and drug-related prison rates, it does not tell us which variable is causing the other, or if there is any causal relationship at all.

There could be other factors that affect both divorce rates and drug-related prison rates, or there could be a third variable that influences both. Therefore, we cannot draw any causal conclusions from this data alone.

However, the data could be used as a starting point for further research and analysis to investigate any potential causal relationships or underlying factors.

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The steady-state response yss(t) can be determined by evaluating the transfer function T(s) at the frequency of the input function f(t) and multiplying it by the Laplace transform of f(t).

To find the steady-state response yss(t), we first need to find the Laplace transform of the input function f(t). In this case, f(t) = 30sin(2t), so its Laplace transform F(s) can be calculated using the Laplace transform properties. Once we have F(s), we can substitute it into the transfer function T(s) = Y(s) / F(s) and solve for Y(s), which represents the Laplace transform of the steady-state response yss(t). Finally, we can use the inverse Laplace transform to obtain the expression for yss(t). By evaluating this expression at different time points, we can determine the steady-state response of the system to the given input function.

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1. AABBCCDD: The probability of this happening is \(1/16\), since each parent would need to contribute a dominant allele for each gene.

2. AABBCcDD:  This genotype can be produced in two ways:

a) If both parents are homozygous dominant for A and B, heterozygous for C, and homozygous dominant for D.

The probability of this happening is  = 1/128.

b) If one parent is homozygous dominant for A and B, heterozygous for C, and homozygous dominant for D, and the other parent is heterozygous for A and B, homozygous dominant for C, and heterozygous for D.

3. The probability of this happening is 1/32.

AaBbCcDd : The probability of this happening is  1/256.

4. aaBBCcDD - This genotype can be produced in two ways:

a) If both parents are homozygous recessive for A, homozygous dominant for B, heterozygous for C, and homozygous dominant for D. The probability of this happening is  1/128.

b) If one parent is homozygous recessive for A, homozygous dominant for B, heterozygous for C, and homozygous dominant for D, and the other parent is heterozygous for A, homozygous dominant for B, homozygous dominant for C, and heterozygous for D.

The probability of this happening is  1/32.

To solve this problem, we need to use the principles of probability and Punnett squares.

For a tetrahybrid cross, we need to consider the four genes independently and combine the probabilities of each gene's alleles.

Assuming that A, B, C, and D are dominant alleles, and a, b, c, and d are recessive alleles, we can create a Punnett square for each gene, which would look like this:

A  |  A  |  a  |  a  

---|-----|-----|----

B  |  B  |  b  |  b  

---|-----|-----|----

C  |  C  |  c  |  c  

---|-----|-----|----

D  |  D  |  d  |  d  

Each box in the Punnett square represents a possible combination of alleles from the two parents.

For example, the top-left box represents offspring that inherit an A allele from the mother and an A allele from the father.

We can use these Punnett squares to calculate the probabilities of each genotype in the F2 offspring.

AABBCCDD - This genotype can only be produced if both parents are homozygous dominant for all four genes.

The probability of this happening is \((1/2)^4 = 1/16\) , since each parent would need to contribute a dominant allele for each gene.

AABBCcDD - This genotype can be produced in two ways:

a) If both parents are homozygous dominant for A and B, heterozygous for C, and homozygous dominant for D.

The probability of this happening is\((1/2)^4 * 1/2 * (1/2)^3 = 1/128\)

b) If one parent is homozygous dominant for A and B, heterozygous for C, and homozygous dominant for D, and the other parent is heterozygous for A and B, homozygous dominant for C, and heterozygous for D.

The probability of this happening is\(2 * (1/2)^4 * 1/2 * 1/2 * 1/2 = 1/32\)

AaBbCcDd - This genotype can be produced in 16 ways, since each gene can be inherited in two different ways (dominant or recessive).

The probability of this happening is \((1/2)^8 = 1/256.\)

aaBBCcDD - This genotype can be produced in two ways:

a) If both parents are homozygous recessive for A, homozygous dominant for B, heterozygous for C, and homozygous dominant for D. The probability of this happening is\((1/2)^4 * 1/2 * (1/2)^3 = 1/128.\)

b) If one parent is homozygous recessive for A, homozygous dominant for B, heterozygous for C, and homozygous dominant for D, and the other parent is heterozygous for A, homozygous dominant for B, homozygous dominant for C, and heterozygous for D.

The probability of this happening is \(2 * (1/2)^4 * 1/2 * 1/2 * 1/2 = 1/32.\)

Note that we have assumed independent assortment of the four genes, which means that the inheritance of one gene does not affect the inheritance of another gene.

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To find the equation of the tangent to the curve at the point (0, 0), we need to find the derivative of the curve with respect to t and evaluate it at t = 0. Let's differentiate x and y with respect to t:

dx/dt = 9cos(t)

dy/dt = 2t + 1

Evaluating dx/dt and dy/dt at t = 0 gives:

dx/dt = 9cos(0) = 9

dy/dt = 2(0) + 1 = 1

Therefore, the slope of the tangent line at (0, 0) is dy/dx = (dy/dt)/(dx/dt) = 1/9. Using the point-slope form of a linear equation, we can write the equation of the tangent line as y - y1 = m(x - x1), where (x1, y1) is the point of tangency. Plugging in the values (0, 0) and m = 1/9, we get:

y - 0 = (1/9)(x - 0)

y = (1/9)x

Graphically, the curve x = 9sin(t), y = t^2 + t represents a spiral-like shape, while the tangent line at (0, 0) is a straight line with a slope of 1/9. The tangent line intersects the curve at the origin and appears to "touch" the curve at that point.

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Answer:

50

Step-by-step explanation:

Adds up to 360 degrees

Answer: The answer is 6. Please mark BRAINLIEST!!

Answer:

99 degrees F

Step-by-step explanation:

subtract 5 from 104

Answer:

average 104 degrees F

Step-by-step explanation:

The least squares estimates of the slope and intercept are 0.65 and 22.5, respectively. The regression line can be graphed as follows: y = 0.65x + 22.5. Using the equation of the fitted line, we can predict that the average body fat for a man with a BMI of 30 is 30.9%. If the observed body fat of a man with a BMI of 25 is 25%, then the residual for that observation is -0.5%. The prediction for the BMI of 25 in part (c) was an underestimate. This is because the actual body fat percentage was lower than the predicted body fat percentage.

To calculate the least squares estimates of the slope and intercept, statistical techniques such as linear regression need to be applied to the data on BMI and body fat. These estimates represent the relationship between BMI and body fat. The regression line can be graphed using these estimates, showing the trend between the two variables. By plugging a BMI value of 30 into the fitted line equation, the average body fat for a man with that BMI can be predicted. To find the residual for the observation with a BMI of 25 and observed body fat of 25%, the predicted body fat value based on the regression line needs to be compared to the actual observed body fat. Depending on whether the predicted value is greater or smaller than the observed value, it can be determined if the prediction for the BMI of 25 was an overestimate or underestimate.

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the discount rate is 3.5% (rounded to one decimal place).

To determine the discount rate, we need to compare the present value of Option A (one-time payment) with the present value of Option B (equal annual payments). The winner is indifferent between the two options when their present values are equal.

Option A: The one-time payment is $471 million.

Option B: The winner will receive 30 equal annual payments, with the first payment made in 2020. The total amount of payments is $768.4 million, so each payment is $768.4 million / 30 = $25.613 million.

Now, we can calculate the present value of Option B using the formula for the present value of an annuity:

\(PV = PMT / (1 + r)^n\)

Where PV is the present value, PMT is the payment amount, r is the discount rate, and n is the number of periods.

Plugging in the values, we have:

$471 million = $25.613 million / \((1 + r)^{30}\)

Simplifying the equation and solving for r, we find:

\((1 + r)^{30}\) = $25.613 million / $471 million

\((1 + r)^{30}\) = 0.054427

Taking the 30th root of both sides, we get:

1 + r = (0.054427)^(1/30)

r = (0.054427)^(1/30) - 1

Calculating the value, we find that r is approximately 0.035 or 3.5%.

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The required Matlab code to find the greatest common divisor of a number using the Euclidean algorithm is shown.

To find the greatest common divisor (GCD) of two numbers using the Euclidean algorithm in MATLAB, you can use the following code:

% Replace '12345678' with your actual student number

studentNumber = '12345678';

% Extract the first 4 digits as the first number

firstNumber = str2double(studentNumber(1:4));

% Extract the last 3 digits as the second number

secondNumber = str2double(studentNumber(end-2:end));

% Find the GCD using the Euclidean algorithm

gcdValue = gcd(firstNumber, secondNumber);

% Display the result

disp(['The GCD of ' num2str(firstNumber) ' and ' num2str(secondNumber) ' is ' num2str(gcdValue) '.']);

Make sure to replace '12345678' with your actual student number. The code extracts the first 4 digits as the first number and the last 3 digits as the second number using string indexing. Then, the gcd function in MATLAB is used to calculate the GCD of the two numbers. Finally, the result is displayed using the disp function.

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Answer:

21

Step-by-step explanation:

If a line parallel to one side of a triangle intersects the other two sides of the triangle, then the line divides these two sides proportionally.

AD        AH

-----  =  ---------

AB         AH +y

3        9

---- = ------

10         9+y

Using cross products:

3(9+y) = 9*10

27+3y = 90

3y = 90-27

3y =63

y = 63/3

y = 21

Answer:

y = 21

Step-by-step explanation:

According to the Side Splitter Theorem, if a line parallel to one side of a triangle intersects the other two sides, then this line divides those two sides proportionally.

Therefore, according to the Side Splitter Theorem:

\(\boxed{\sf AD : DB = AH : HC}\)

From inspection of the given triangle, the lengths of the line segments are:

To find the value of y, substitute the given line segment lengths into the proportion and solve for y:

\(\begin{aligned}\sf AD : DB &=\sf AH : HC\\\\3:7&=9:y\\\\\dfrac{3}{7}&=\dfrac{9}{y}\\\\3 \cdot y&=9 \cdot 7\\\\3y&=63\\\\\dfrac{3y}{3}&=\dfrac{63}{3}\\\\y&=21\end{aligned}\)

Therefore, the value of y is 21.

The number of bags of pink beads that can be made from today's shipment is given as follows:

5 bags.

The number of bags is obtained applying the proportions in the context of this problem.

We have that each bag weights 1/10 of a pound.

The shipment was of 4/7 pounds of pink beads, hence the total number of bags of pink beads that can be made from today's shipment is calculated as follows:

4/7/(1/10) = 4 x 10/7 = 40/7 = 5.

(rounded down, as the number of bags is a countable amount).

The problem is given by the image presented at the end of the answer.

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Answer:

A ≈ 22.2 ft²

Step-by-step explanation:

the area (A) of the sector is calculated as

A = area of circle × fraction of circle

   = πr² × \(\frac{50}{360}\)

   = π × 7.13² × \(\frac{5}{36}\)

    = 50.8369π × \(\frac{5}{36}\)

    ≈ 22.2 ft² ( to the nearest tenth )

Answer:

1 yard is $3.75

Step-by-step explanation:

4.4 to get 1 divide by 4.4

so divide 16.50 by 4.4 to get $3.75

Answer:

1 yard is $3.75

Step-by-step explanation:

$16.50 ÷ 4.4 yards = $3.75

I hope this helps you and your assignment!

The robot must do 840 foot-pounds of work to lift the chain from a height of 3 feet to a height of 13 feet. What the robot has to do to lift the chain from a height of 3 feet to a height of 13 feet is the work.

Work is defined as the product of the force acting on an object and the distance that object moves as a result. To compute the work that the robot must do to lift the chain from a height of 3 feet to a height of 13 feet, we must first determine how much gravitational potential energy the chain has at the higher elevation. The gravitational potential energy of an object is equal to the object's weight times its height above a reference level. The weight of the chain is given as 120 pounds, and the chain will be lifted by the robot for a total of 10 feet. After that, we can determine the amount of work that the robot must do to raise the chain to the new height using the formula W = Fd, where W is work, F is force, and d is distance. The robot must do 840 foot-pounds of work.

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For an increase of one hour in time worked, the predicted increase in the amount of money spent on entertainment is 1.86 units.

To find the predicted increase in the amount of money spent on entertainment for an increase of one hour in time worked, we need to find the slope of the line, which is the coefficient of x in the equation.

which means that for every one unit increase in x (which in this case is one hour worked), y (which in this case is the amount of money spent on entertainment) is predicted to increase by 1.86 units.

This is the change in the dependent variable (y) for a unit increase in the independent variable (x), based on the linear relationship described by the equation of the line fit.

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