In a yacht race the second leg was half the length of the first leg, the third leg was two thirds of the length of the second leg, and the last leg was twice the length of the second leg. If the total distance was 153 km, find the length of each leg

Answer:

It is 8 children and 32 adults

Step-by-step explanation:

8+32=40

11*8=88

20*32=640

640+88=728

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Answer:

The answer is A

Step-by-step explanation:

In order for it to be a function every x value has to have a different y value or every input has to have a different output.

The given sequence is 64, 112, 196, 343. We will look for a pattern in the given sequence.

Step 1: The first term is 64.

Step 2: The second term is 112, which is the first term multiplied by 1.75 (112 = 64 x 1.75).

Step 3: The third term is 196, which is the second term multiplied by 1.75 (196 = 112 x 1.75).

Step 4: The fourth term is 343, which is the third term multiplied by 1.75 (343 = 196 x 1.75).

Step 5: Hence, we can see that each term in the sequence is the previous term multiplied by 1.75.So, the recursive formula that can be used to describe the given sequence is: a₁ = 64; aₙ = aₙ₋₁ x 1.75, n ≥ 2.

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The greatest possible number of intersection points for four circles of different sizes is 12.

The greatest possible number of intersection points of four circles of different sizes can be calculated by considering the maximum number of intersection points each pair of circles can have and then summing them up.

When two circles intersect, they can have a maximum of two intersection points. So, if we have four circles, we can find the maximum number of intersection points by considering each pair of circles separately.

For the first circle, it can intersect with the other three circles at most two times each, giving us a total of 2 * 3 = 6 intersection points.

For the second circle, it can intersect with the remaining two circles at most two times each, giving us a total of 2 * 2 = 4 intersection points.

The third circle can intersect with the last remaining circle at most two times, giving us a total of 2 * 1 = 2 intersection points.

Finally, the fourth circle doesn't have any other circle left to intersect with, so it doesn't contribute any additional intersection points.

Now, we can sum up the intersection points from each pair of circles: 6 + 4 + 2 + 0 = 12.

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Answer: 2289.06

Step-by-step explanation:

math expert

Answer:

r = 169.56 in. / 2π ≈ 27 in.

Now we can use the radius to find the area:

Area = πr^2 ≈ π(27 in.)^2 ≈ 2289.06 in^2

So the area of the circular table is approximately 2289.06 square inches, rounded to the nearest hundredth. The answer is option C.

a) This is a one-tailed test

b)  the decision rule is: Reject H0 when z > 1.645.

c) the value of the test statistic is approximately 2.21.

d) The test statistic is greater than the critical value, we reject the null hypothesis.

e) The p-value is approximately 0.0149.

a. This is a one-tailed test because the alternative hypothesis (H1) specifies a direction (µ > 23).

b. The decision rule depends on the chosen significance level (α) and the alternative hypothesis. Since the alternative hypothesis is µ > 23, we are interested in testing if the sample mean is significantly greater than 23. Therefore, we reject the null hypothesis (H0) when the test statistic (z) is greater than the critical value.

For a significance level of 0.05, the critical value can be obtained from the standard normal distribution table or calculator. In this case, since it is a one-tailed test with a significance level of 0.05, the critical value is 1.645.

So, the decision rule is: Reject H0 when z > 1.645.

c. The value of the test statistic (z) can be calculated using the formula:

z = (sample mean - population mean) / (population standard deviation / √sample size)

In this case:

sample mean = 24

population mean = 23

population standard deviation = 3

sample size = 44

z = (24 - 23) / (3 / √44) = 2.21

Therefore, the value of the test statistic is approximately 2.21.

d. To make a decision regarding H0, we compare the test statistic (2.21) with the critical value (1.645). Since the test statistic is greater than the critical value, we reject the null hypothesis.

e. The p-value is the probability of obtaining a test statistic as extreme as (or more extreme than) the observed value, assuming the null hypothesis is true. In this case, the p-value corresponds to the area under the standard normal distribution curve to the right of the test statistic (2.21).

Using a standard normal distribution table or calculator, we find that the area to the right of 2.21 is approximately 0.0149.

Therefore, the p-value is approximately 0.0149.

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Answer:

$10

Step-by-step explanation:

We Know

Terri pays a monthly cell phone fee of $10. She pays 5 cents for each minute that she talks.

Let C be the total cost, and x be the number of minutes she talks; we have the equation.

C = 0.05x + 10

If Terri does not make any calls, what would her bill be?

C = 0.05(0) + 10

C = $10

So, her bill will be $10

Either take the photo of that question or take screenshot and attach it. The question is not complete.

Answer:

-7/3

Step-by-step explanation:

the answer is the negative reciprocal.

Answer:

1?

Step-by-step explanation:

Diameter is the same

The difference between the polynomials 9x² + 8x and 2x² + 3x is 7x² + 5x.

A polynomial is formed mathematically by combining one or more algebraic terms (monomials). The roots of "polynomial" are poly- (many) and -nomial (terms). A polynomial can have exponents (powers), constants (numbers), and variables (letters), but not negative exponents or variable division.

Polynomials are typically expressed in standard form. Furthermore, because there are no similar terms among the exponents, they are arranged in descending order (largest to smallest).

To find the difference between

(9x² + 8x) - (2x² + 3x)

We do calculation

= 9x² + 8x - 2x² - 3x

= 9x² - 2x² + 8x - 3x

= 7x² + 5x

Thus, the difference between the polynomials is 7x² + 5x.

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1. The domain of the function in interval g(x) = 13x-15/x+4

Domain: (−∞,0)∪(0,∞),{x|x≠0

Range: (−∞,∞),{y|y∈R}

2. The domain of the function in interval y=x2-10x+2

Domain: (−∞,∞) {x|x∈R}

Range: (−23,∞),{y|y≥-23}

3. By rearranging the equation so that C is in terms of F, you may determine the inverse:

F= 5/9C+32

32 is deducted from both sides.

F−32= 5/9C

Add five to both sides:

5(F−32)=9C

multiply both sides by 9.

C= 5/9(F−32)

C=− 25​/9

−2.78C o 2.dp

The inverse is, in fact, a one-to-one function.

4. We are looking for the height at t=0 in order to determine the beginning height. To do this, replace t with 0 and find h.

h(t)= -16t2 + 32t + 24

h(0) = -16(0)2 + 32(0) + 24

h(0) = 24

24 feet is the initial height

The constant in the equation often represents height. 24 in this instance.

The coefficient of x, in this case 32, represents the beginning velocity.

32 feet per second is the beginning velocity.

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Answer:

$59.99 + 0.40(\(m\) - 900)

Step-by-step explanation:

Given that:

Per month charges for 900 minutes = $59.99

After 900 minutes, each minute is charged $0.40 per minute.

Also, there are \(m\) number of minutes used in February.

Plus, we know that:

\(m>900\)

To find:

Algebraic expression to represent the total bill in the month of February.

Solution:

Charges for the first 900 calls = $59.99

Total number of calls = \(m\)

Total number of calls above 900 = \(m\) - 900

Charges per call above 900 = $0.40

Charges for the calls above 900 = Number of calls above 900 \(\times\) Charges per call above 900 = 0.40(\(m\) - 900)

Therefore, total charges for \(m\) calls = $59.99 + 0.40(\(m\) - 900)

Answer:

Step-by-step explanation:

Wheelbarrows  is 30/3 = 10

Pair of shoes is (18 - 10) /2 = 4 so one shoe is 2

2 Seed bags is 4 - 2 = 2 so one bag is 1

Answer is 1(seed baf) + 10(wheelbarrows X 2(shoe) = 21

Answer:

A.

Step-by-step explanation:

Diameter = 4.4 cm

Radius = 2.2 cm

Now

Area of the circle = πr²

= (3.14)(2.2)²

= (3.14)(4.84)

= 15.1976 cm²

Answer:

A.

Step-by-step explanation:

D=4.4, therefore, the Radius is equal to 2.2, half of the diameter.

The formula for Area:

A=pir^2.

A=(3.14)(2.2)^2

A=(3.14)(4.84)

A=15.1976

A=15.1976, which is identical to option A.

As a result of answering the given question, we may state that When the cylinder radius is quadrupled, the volume increases by a factor of 9 (32).

A cylinder is a three-dimensional geometric object composed of two congruent parallel circular bases and a curving surface connecting the two bases. A cylinder's bases are always perpendicular to its axis, which is an imaginary straight line through the centre of both bases.  A cylinder's volume is equal to the product of its base area and height. The volume of a cylinder is calculated as V = r2h, where "V" represents the volume, "r" represents the radius of the base, and "h" represents the cylinder's height.

The volume of a cylinder is calculated as V = r2h, where r is the radius and h is the height.

Substituting the provided values yields:

(102 (8) V = 800 cubic metres

The new height is 3(8) = 24 metres if the height is tripled. When we enter this value into the formula, we get:

V = (102 + 24) = 2400 cubic metres

When the height is tripled, the volume is tripled.

If the radius is tripled, it becomes 3(10) = 30 metres. When we enter this value into the formula, we get:

(302)(8) V = 7200 cubic metres

When the radius is quadrupled, the volume increases by a factor of 9 (32).

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The student council sold $273$ t-shirts were sold at $\$10$ per shirt.

Let $x$ be the number of shirts sold at $\$10$

Let $y$ be the number of shirts sold at $\$12$

$x+y=661$

$10x+12y=3780$

$x=y+101$

$10y+12y=3780$

$22y=3780$

$y=172$

$x=172+101$

$x=273$

Hence $273$ t-shirts were sold at $\$10$ per shirt.

If they sold $661$ t-shirts in total, and they made a mistake when recording the amount of t-shirts sold at each price, then they actually sold more t-shirts at $\$10$ than they thought. This means that they thought they sold fewer t-shirts at $\$10$ than they actually did.

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The correct answer to this question is option D) number of populations minus 1.

The number of degrees of freedom (df) associated with the chi-square distribution in a test of independence is determined by the number of populations from which the samples are obtained minus one.

It is calculated by the formula: df = (r - 1) x (c - 1), where r is the number of rows and c is the number of columns in the contingency table used to perform the test. The chi-square distribution is used to analyze the difference between observed and expected values in a contingency table. It provides a measure of how closely the observed frequencies match the expected frequencies if there is no association between the variables being studied.

The degrees of freedom are important because they determine the critical values for the test statistic and help to determine the probability of obtaining the observed results if the null hypothesis is true.

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After one time constant has passed, 63.2% of the initial potential remains. After two time constants, 36.8% of the initial potential remains. After three time constants, 13.5% of the initial potential remains.


The time constant (τ) is a measure of how quickly a system reaches equilibrium or returns to its initial state after a disturbance. It is commonly used in electronics and other fields to describe the behavior of circuits, systems, and processes.

The equation for the percentage of initial potential remaining after a time constant is:

Percentage remaining = 100 * e^(-t/τ)

Where t is the time elapsed and τ is the time constant.

After one time constant (t = τ), the equation becomes:

Percentage remaining = 100 * e^(-1) = 63.2%

After two time constants (t = 2τ), the equation becomes:

Percentage remaining = 100 * e^(-2) = 36.8%

After three time constants (t = 3τ), the equation becomes:

Percentage remaining = 100 * e^(-3) = 13.5%

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CME 303 is a course offered at Stanford University that focuses on modeling, simulation, and optimization of complex systems.

It is an introduction to the fundamentals of mathematical optimization, which deals with the problem of finding the best solution to a given problem. The course covers basic optimization theory and algorithms, including linear programming, integer programming, nonlinear programming, dynamic programming, and stochastic programming. Furthermore, it introduces optimization software packages, such as MATLAB, GAMS, and CPLEX, and how to use them for solving real-world optimization problems. It also covers the application of optimization techniques to areas such as finance, engineering, economics, and computer science.CME 303 is a course offered at Stanford University that focuses on modeling, simulation, and optimization of complex systems.  The course is taught using lectures, tutorials, and computer lab assignments. In the final project, students apply the techniques learned in the course to solve a real-world problem.

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Answer:

50cm

200cm

50cm^2

Step-by-step explanation:

The big square is divided into 4 with a side length of 25cm. 2 small square side lengths make up the big squares.

25 * 2 =

50cm

50 + 50 + 50 +50 =

200

15 +2

17

8 + 2

10

17 * 10 = 170

15 * 8 = 120

170-120 = 50

50cm^2

Step-by-step explanation:

so, if car have 120km/hr it maximum speed will be 85-95km/hr so the car travel 300km in around 5 or 5 unhalf hour

Out of the 95 students surveyed, 7 students took none of the courses. To find the number of students who took none of the courses, we need to subtract the number of students who took at least one course from the total number of students surveyed.

First, let's find the number of students who took at least one course. We can do this by adding the number of students who took each course individually, and then subtracting the students who took two courses and the students who took all three courses.

The number of students who took math is 57, the number who took English is 57, and the number who took history is 62. To find the total number of students who took at least one course, we add these numbers: 57 + 57 + 62 = 176.

Now, we need to subtract the number of students who took two courses. We know that 32 students took math and English, 39 students took math and history, and 36 students took English and history. To find the total number of students who took two courses, we add these numbers: 32 + 39 + 36 = 107.

Next, we need to subtract the number of students who took all three courses. We know that 19 students took all three courses.

To find the number of students who took none of the courses, we subtract the students who took at least one course (176) from the students who took two courses (107) and the students who took all three courses (19):

95 - 176 + 107 - 19 = 7.

Therefore, the number of students who took none of the courses is 7.

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The image of the point (-2, 6) after a dilation by a scale factor of 1/2 centered at the origin is (-1, 3).

To find the image of the point (-2, 6) after a dilation by a scale factor of 1/2 centered at the origin, we need to multiply both the x-coordinate and y-coordinate by the scale factor.

The formula for dilation of a point (x,y) by a scale factor k centered at the origin is:

(x', y') = (kx, ky)

where (x', y') are the coordinates of the dilated point.

Using this formula with k = 1/2 and the point (-2, 6), we get:

(x', y') = (1/2 * (-2), 1/2 * 6)

= (-1, 3)

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The inference is that the variability in the results of the simulation is that when the outcomes of the Saint were independent, the simulated number of streaks varies from 1 to 12 games.

It should be noted that an inference simply means the conclusion that can be deduced based on the information given in the data.

Here, the inference is that the variability in the results of the simulation is that when the outcomes of the Saint were independent, the simulated number of streaks varies from 1 to 12 games.

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The first model of inequality satisfy the problem i.e 2w + 2* 4w ≤ 106

A rectangle is a four-sided, two-dimensional flat shape. The opposite sides of a rectangle's four sides are parallel and equal to one another. It belongs to a category of quadrilaterals where each of the four angles is a straight angle or measures 90 degrees. A particular kind of parallelogram that has all of its angles equal is the rectangle. A square is a rectangle with four equally sized sides. Let's now explore the characteristics of the rectangle in this essay.

Rectangles' essential characteristics are as follows:

A rectangle is a parallelogram.

The Perimeter of the rectangle is 2a + 2b where a and b are the two sides

Now , if w is the width of the rectangle then, the length is 4w given in problem.

Perimeter,

2w + 2* 4w

As it is given in the problem

2w + 2* 4w ≤ 106

The first model of inequality satisfy the problem.

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Answer: $3,250

Step-by-step explanation:

5% is the same as 0.05

$65,000 x 0.05 = $3,250

Answer:

x=10

Step-by-step explanation:

y=mx+b

y=9x+100

190=9x+100

x=10

Answer:

9x + 100 = 190

Step-by-step explanation:

Where x is hours.

The correct answer is option C: 30 pounds.

Based on the given information, the dog's weight increased by 50% over a period of 3 years, and at the end of the 3 years, the dog weighed 45 pounds. To determine how much the dog weighed 3 years ago, we can use a tape diagram to represent the weight changes.

Let's represent the initial weight of the dog as 100%. Since the dog's weight increased by 50%, we can represent the increased weight as 150%. According to the information, the dog's weight after 3 years is 45 pounds, which corresponds to 150% on the tape diagram.

To find the initial weight, we need to identify the value on the tape diagram that corresponds to 100%. From the diagram, it is evident that the initial weight, represented by 100%, is half of the distance between 0% and 150%. Therefore, the dog weighed 30 pounds 3 years ago.

In conclusion, the dog weighed 30 pounds 3 years ago, as indicated by the tape diagram and the given information. Therefore, the correct answer is option C: 30 pounds.

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If two lines have the same slope, then the lines are parallel. the lines do not intersect and do not share any common points, they are parallel to each other.

The statement "If two lines have the same slope, the lines are parallel" is a fundamental property of lines in Euclidean geometry.

In a Cartesian coordinate system, the slope of a line represents its steepness or inclination. It is defined as the ratio of the vertical change (change in y-coordinates) to the horizontal change (change in x-coordinates) between two points on the line.

If two lines have the same slope, it means that for any two corresponding points on the lines, the ratio of the vertical change to the horizontal change is equal.

Now, let's consider two lines with the same slope. If we take any point on the first line and draw a line with the same slope passing through that point, the two lines will never intersect.

This is because if the lines were to intersect, they would share a common point with the same x-coordinate but different y-coordinates. However, if the lines have the same slope, the ratio of the vertical change to the horizontal change will be the same for both lines, and therefore the y-coordinates at that common x-coordinate should also be the same.

Since the lines do not intersect and do not share any common points, they are parallel to each other.

Hence, if two lines have the same slope, the lines are parallel.

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