Frahan travels from Town A to Town B at an average speed of 4 Km/h and from Town B to Town A at an average
speed of 3 Km/h. He takes 25 minutes to complete the entire journey.
(a) Convert 25 minutes into hours.
(b) Find his total distance travelled.

According to the above, we have to add the surface area of each face. So, the surface area of this solid would be 127.

To calculate the surface area of the composite solid we have to perform the following procedure:

Sides (a) area

Sides (b) area

Face (c) area

Base area

4 * 7 = 28

Total surface area

To calculate the total surface area we have to add the value of each face as shown below:

According to the above, the surface area of this solid would be 127.

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Answer:

The unit rate is 35 pages per minute.

Step-by-step explanation:

Divide 175 by 5, or 175/5  to get the unit rate, which is 35.

A population has a mean μ=135 and a standard deviation Ï=28.

The mean of the sampling distribution of sample means is equal to the population mean, that is 135.

The standard deviation of the sampling distribution of sample means can be calculated by using the formula

SE = Ï /[tex]\sqrt{n}[/tex]

Where Ï is the population standard deviation and n is the sample size.

By putting the given values we get

SE = 28 / [tex]\sqrt{57}[/tex] = 3.7

Hence, the mean of the sampling distribution of sample means is 135, and the standard deviation is 3.7.

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The density of the given metal is 19.3g/cm³ . Then, the correct answer to this given question is Option E.

The given mass of  the metal is 611 g  and it is kept in a elevated cylinder that contains 25.1 mL of water,
Now, let us increase the water level to 56.7 mL. The metal  volume can be evaluated by subtracting the initial volume  from the final volume of water released by the metal.

Hence,
Metal volume = final volume - initial volume
= 56.7 mL - 25.1 mL
= 31.6 mL

Therefore,
Density = Mass / Volume
= 611 g/31.6 mL
= 19.3 g/cm³

The density of the given metal is 19.3g/cm³ . Then, the correct answer to this given question is Option E.


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the average rate of change over the interval (-1, 2] in the given function is 1.17.all three functions have the same average rate of change over the interval [1, 2], which is 2

A function is a mathematical rule that takes an input and produces an output. The average rate of change of a function over an interval is the average amount the output changes per unit change in the input over that interval.

For the function f(x) = 2x + 3:

Let x1 = -1 and x2 = 2

f(x1) = 2(-1) + 3 = 1

f(x2) = 2(2) + 3 = 7

The average rate of change is:

[f(x2) - f(x1)] / [x2 - x1] = [7 - 1] / [2 - (-1)] = 6 / 3 = 2

Therefore, the average rate of change of f(x) over the interval (-1, 2] is 2.

For the function g(x) = x^2 - 1:

Let x1 = -1 and x2 = 2

g(x1) = (-1)^2 - 1 = 0

g(x2) = 2^2 - 1 = 3

The average rate of change is:

[g(x2) - g(x1)] / [x2 - x1] = [3 - 0] / [2 - (-1)] = 3 / 3 = 1

Therefore, the average rate of change of g(x) over the interval (-1, 2] is 1.

For the function h(x) = 2^x + 1:

Let x1 = -1 and x2 = 2

h(x1) = 2^(-1) + 1 = 1.5

h(x2) = 2^2 + 1 = 5

The average rate of change is:

[h(x2) - h(x1)] / [x2 - x1] = [5 - 1.5] / [2 - (-1)] = 3.5 / 3 = 1.17 (rounded to 2 decimal places)

Therefore, the average rate of change of h(x) over the interval (-1, 2] is approximately 1.17.

b)To determine which function has the greatest average rate of change over the interval [1, 2], we need to calculate the average rate of change for each function over that interval and compare the results.

Let's assume the functions are f(x), g(x), and h(x).

The average rate of change for f(x) over the interval [1, 2] is:

[f(2) - f(1)] / [2 - 1] = (2(2) + 3 - 2(1) - 3) / 1 = 2

The average rate of change for g(x) over the interval [1, 2] is:

[g(2) - g(1)] / [2 - 1] = (2^2 - 1 - 1^2 + 1) / 1 = 2

The average rate of change for h(x) over the interval [1, 2] is:

[h(2) - h(1)] / [2 - 1] = (2^2 + 1 - 2^1 - 1) / 1 = 2

Therefore, all three functions have the same average rate of change over the interval [1, 2], which is 2.

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The rate of change for the function f(x) is 9.5 over the interval.

How I calculated the rate of change for f(x):

f(2) = 12, f(6) = 50

slope = (50 - 12) / (6 - 2) = 9.5

The rate of change for the function g(x) is -2 over the interval.

How I calculated the rate of change for g(x):

g(2) = -10, g(6) = -18

slope = (-18 - (-10)) / (6 - 2) = -2

To find the rate of change for a function over an interval, we need to calculate the slope of the secant line that connects the two endpoints of the interval.

The slope of a line can be found using the formula:

slope = (y2 - y1) / (x2 - x1)

For the quadratic function f(x) = (x + 1)² + 8, we can find the values of f(2) and f(6) by substituting x = 2 and x = 6 into the function:

f(2) = (2 + 1)² + 8 = 12

f(6) = (6 + 1)² + 8 = 50

Therefore, the rate of change for f(x) over the interval 2 ≤ x ≤ 6 is:

slope = (f(6) - f(2)) / (6 - 2) = (50 - 12) / 4 = 9.5

So the answer is: The rate of change for f(x) is 9.5 over the interval.

To find the rate of change for the linear function g(x) = -2x - 6, we can use the same formula:

g(2) = -2(2) - 6 = -10

g(6) = -2(6) - 6 = -18

Therefore, the rate of change for g(x) over the interval 2 ≤ x ≤ 6 is:

slope = (g(6) - g(2)) / (6 - 2) = (-18 - (-10)) / 4

slope = -2

So the answer is: The rate of change for g(x) is -2 over the interval.

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The LCM of 63 and 42 is 126 where 63 is the required number lying in between 60 and 70.

Let the missing number be x.

The number x lies in between 60 and 70.

The LCM ( Least Common Multiple) refers to the least value that is divisible by any two (or more) numbers.

Here LCM of x and 42 is 126.

Simplifying 126 we can write it as,

126 = 2*3*21

Thus, one of the number having 126 is as multiple is 42  (as already given).

The other number, that is x, having 126 as multiple lying between 60 and 70 is,

x = 3*21 = 63

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LaTisha's calculation of the distance for the brake anchor placement is incorrect because she didn't take into account the height at which the cable is attached to the starting tree.

The bungee cord is attached 16 feet above the ground, which will also contribute to the length of the cable needed to reach the ending tree.

To correctly calculate the distance, we can use the Pythagorean theorem, considering the height (16 feet) and the length of the stretched bungee cord (24 feet + 18 feet = 42 feet). Let's denote the horizontal distance from the base of the ending tree to the brake anchor as 'd'. We have:

d² + 16² = 42²

Now, we can solve for d:

d² + 256 = 1764

d² = 1508

d = √1508 = 38.8 feet (rounded to one decimal place)

The brake anchor should be placed approximately 38.8 feet from the base of the ending tree.

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Answer:

$10,244.14 after 12 years

Step-by-step explanation:

To solve this problem, we can use the formula for compound interest:

A = P(1 + r/n)^(n*t)

A = the final amount of the investment

P = the principal amount ($4200 in this case)

r = the annual interest rate (8% or 0.08 as a decimal)

n = the number of times the interest is compounded per year (once annually in this case)

t = the number of years the money is invested (12 years in this case)

Substituting the given values into the formula, we get:

A = 4200(1 + 0.08/1)^(1*12)

A = 4200(1.08)^12

A = 4200(2.44140625)

A = $10,244.14 (rounded to the nearest cent)

(a) The simplified and correct expression is (6×7)-(5 +4) = 16

(b) The simplified and correct expression is (-2x²) + (24÷12)-4 = 2

a. 6×7-5 +4= 16

In this calculation, we need to use brackets to ensure the correct order of operations, which is typically remembered using the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division [from left to right], Addition and Subtraction [from left to right]).

Without brackets, the calculation would be evaluated as follows:

6×7-5 +4 = 42-5 +4 (applying multiplication first)

= 37 +4 (applying subtraction)

= 41 (applying addition)

However, the desired result is 16. To achieve this, we can use brackets to group the addition and subtraction operations together, like this:

(6×7)-(5 +4) = 42 - 9 (applying addition within the brackets first)

= 33 (applying subtraction)

b. -2x²+24÷12-4=2

Similarly, in this calculation, we need to use brackets to ensure the correct order of operations.

Without brackets, the calculation would be evaluated as follows:

-2x²+24÷12-4 = -2x²+2-4 (applying division first)

= -2x²-2 (applying addition and subtraction)

However, the desired result is 2. To achieve this, we can use brackets to group the division and subtraction operations together, like this:

-2x²+(24÷12)-4 = -2x²+2-4 (applying division within the brackets first)

= -2x²-2 (applying addition and subtraction)

By adding brackets to each calculation to ensure the desired order of operations, we arrive at the correct results of 16 and 2, respectively.

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The average score of 100 students taking a statistics final was 70, with a standard deviation of 7. The test score esteem that isolates the beat 2.5% of normal distribution from the rest of the understudies is roughly 83.72.

To discover the test score esteem that isolates the best 2.5% of the understudies, we got to discover the z-score comparing to that rate utilizing the standard ordinary conveyance table.

z = (x - μ) / σ

To discover the z-score compared to the best 2.5%, we see up the region of the right-hand tail of the standard normal distribution table, which is 0.025. This compares to a z-score of roughly 1.96.

Presently ready to utilize the z-score equation to unravel for x:

1.96 = (x - 70) / 7 Increasing both sides by 7, we get:

x - 70 = 13.72

Including 70 to both sides, we get:

x = 83.72

Hence, the test score esteem that isolates the beat 2.5% of the understudies from the rest of the understudies is roughly 83.72.

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The percentage of pens that are blue =18%

Let's assume that r represents the red pens, b represents the blue pens and g represents the green pens.

From the statements we can observe that the blue appears in both ratio.

The ratios are,

r:b=5:9 and b:g=1:4

Consider ratio b:g,

b:g

= 1:4

= (1×9) : (4×9)

=9:36

i.e., b:g = 9:36 and r:b = 5:9

So, we can conclude that, b=9, g=36, r=5

so, the total number of pens would be,

n = b + g + r

n = 9 + 36 + 5

n = 50

Now we need to find the percentage of pens that are blue.

Using percentage formula,

p = (b/n) × 100

p = (9/50) × 100

p = 18%

Hence, the percentage of blue pens are 18%.

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Answer:

a=60 (12*5=60)

b=7 (45/9=5 5+2=7)

c=62

d=25 (11*5=55 55-30=25)

The equation is linear and can be written in the slope intercept form as: y = -3x/5 + 6.

A linear equation is an algebraic equation that represents a straight line on a graph. It can be written in the form y = mx + b, where x and y are variables, m is the slope of the line, and b is the y-intercept, which is the point where the line crosses the y-axis.

given the slope m = -3/5 and y intercept b = 6, we can write the equation as;

y = (-3/5)x + 6

y = -3x/5 + 6.

Therefore, the equation is linear and can be written in the slope intercept form as: y = -3x/5 + 6.

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The a is rational , b is irrational and product of a and b is rational.

The number a=0.444444444444 is rational

Because it can be expressed as the ratio of two integers.

a = 4/9

The number b=0.354355435554 is irrational

Because it cannot be expressed as the ratio of two integers.

It has an infinite non-repeating decimal expansion.

To determine whether the product of a and b is rational or irrational, we can simply multiply them together:

a × b = (4/9) × 0.354355435554

= 0.158919191574

This product is a rational number, because it can be expressed as the ratio of two integers.

Hence, a is rational , b is irrational and product of a and b is rational.

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The circle with equilateral triangle is constructed.

What is triangle?

A triangle is a form of polygon with three sides; the intersection of the two longest sides is known as the triangle's vertex. There is an angle created between two sides. One of the crucial elements of geometry is this.

Here we need to construct the circle  with center D.

Now we know that in equilateral triangle , side length of the all sides are equal.

Then, AB=BC=CA.

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Step-by-step explanation:

Perimeter =  2 m + 2 * 7m

Perimeter = 2 ( m + 7m)

Perimeter = 2m + 14m

Perimeter = 16 m                          Pick any of them

The acceptable conclusions to a hypothesis test are option a, c, d, f.

What is hypothesis test?

Hypothesis Testing is a way of statistical analysis in which a person can  put his assumptions about a population parameter to the test. It usually  used to estimate the relationship between two statistical variables.

By the property of hypothesis test the following can be stated.

⇒The value of the test statistic lies in the non rejection region. Therefore, there is no evidence to suggest that the alternative hypothesis is true.

⇒ The value of the test statistic lies in the rejection region. Therefore, there is evidence to suggest that the null hypothesis is not true.

⇒The value of the test statistic does not lie in the rejection region. Therefore, there is no evidence to suggest that the alternative hypothesis is true.

⇒ The value of the test statistic lies in the rejection region. Therefore, there is evidence to suggest that the alternative hypothesis is true.

Hence the correct options are a, c, d, f.

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Answer: The amount of planes of symmetry a right pyramid with an isosceles triangle base has four.

Hope this helps!

The calculated value of each boy's share is shown below

Let's call the amount of oranges the third boy gets "x".

According to the problem, the second boy gets twice the amount of oranges as the third boy, so he gets 2x oranges.

And the first boy gets twice more oranges than the second boy, so he gets 2(2x) = 4x oranges.

So the total number of oranges is x + 2x + 4x = 7x, and we need to divide this equally among the three boys.

Therefore, the first boy gets 4/7 of the total oranges, which is 4x/3, the second boy gets 2/7 of the total oranges, which is 2x/3 and the third boy gets 1/7 of the total oranges, which is x/3.

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Step-by-step explanation:

Radius simply means half of the diameter. In other words radius is the distance between the center of the circle to the outside of the circle

The acceleration of this classroom table is equal to 1.5 meter per seconds square.

From Newton's Second Law of Motion, the force exerted on the classroom table is modeled or represented by this mathematical equation (formula):

F = ma

Where:

By making "acceleration" the subject of formula, we have the following:

Acceleration, a = force/mass

Acceleration, a = 36/24

Acceleration, a = 1.5 meter per seconds square.

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Answer:

the y is always gonna be a difrent like a negative and a postive

Step-by-step explanation:

the y on the left if it's a positive the y on the right Is nightie ect

The system of equations that models this scenario is:

Let p be the number of bags of popcorn.

Let s be the number of sodas Dave buys.

Since Dave needs to buy at least one of each item for all six kids, we have:

p + s = 6 -----(1)

Given:

The cost of a bag of popcorn is $2.50.

The cost of a soda is $4.00.

The total cost of Dave's purchase can be expressed as:

2.50p + 4.00s = C -----(2) where the C is the total cost of Dave's purchase.

Since Dave can spend at most $40, we have:

2.50p + 4.00s ≤ 40 -----(3).

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The given piecewise function has a range of:

Range = {46, 48, 50, 52, 54, 56}.

The range of a function is the set of all possible output values, or the set of all y-coordinates that correspond to the x-coordinates in the domain of the function.

It is, in other words, the entire set of values that the function is capable of returning as its result.

From the given piecewise function, we can see that the y-coordinates of the function are limited to the values 46, 48, 50, 52, 54, and 56.

These values correspond to the y-intercepts of each of the line segments in the graph.

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Therefore, the temperature at the summit of the 3,000-foot mountain on a sunny day is estimated to be 10.8 F°.

In mathematics, an equation is a statement that indicates the equality of two expressions. An equation typically contains one or more variables, which are placeholders for unknown values or quantities. The variables can take on different values, and the goal is often to find the values that satisfy the equation.

Here,

Let's start by calculating the rate of change of temperature with respect to elevation:

=-5.4 F° / 1,000 ft

This means that for every 1,000-foot increase in elevation, the temperature will decrease by 5.4 F°.

Next, we can calculate how much the temperature will decrease from the base of the mountain to the summit:

3,000 ft / 1,000 ft = 3

This means that the elevation difference between the base of the mountain and the summit is 3,000 - 0 = 3,000 ft.

So, the temperature decrease from the base to the summit is:

-5.4 F° / 1,000 ft * 3,000 ft = -16.2 F°

This means that the temperature at the summit will be:

27 F° - 16.2 F° = 10.8 F°

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Answer:

Step-by-step explanation:

angle L is 106 degrees

x= 2

angle LMK is 37 degrees

its equal, you can check by adding up all the angles to 360 degrees

Here he formula for v is:

v = √(2gh)

What is meant by the term formula?

A formula is a mathematical relationship or rule that is expressed using symbols and mathematical operations. It is used to represent a relationship between quantities or to calculate a value based on given variables or inputs. Formulas are often used in various branches of mathematics, science, and engineering.

According to the given information

To change the subject of the formula mgh = (1/2)mv² to v, we need to isolate v on one side of the equation.

First, we can multiply both sides of the equation by 2 to eliminate the fraction:

2mgh = mv²

Next, we can divide both sides of the equation by m:

(2mgh) / m = v²

Simplifying the left side, we get:

2gh = v²

Finally, we can take the square root of both sides of the equation to solve for v:

v = √(2gh)

Therefore, the formula for v is:

v = √(2gh)

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Answer:

409 > 1.008

Step-by-step explanation:

409 is greater than 1.008