Part A: Cassie hiked 4 tenths of a 4.7-mile trail. How many miles did Cassle have left to hike?
Part B: Dana was 1.6 miles ahead of Cassie. How many miles did Dana hike already?

Answer:

18 + 30 + 57 + 30 + 15 = 150

P(1) = 18/150 = 3/25 = .12 = 12%

The probability that a teenager has exactly 1 pair of shoes in their closet is [tex]\( \dfrac{3}{25} \)[/tex].

Given the distribution:

Pairs of Shoes | Frequency

--------------------------

1             | 18

2             | 30

3             | 57

4             | 30

5             | 15

The frequency of teenagers with exactly 1 pair of shoes is 18.

The total number of teenagers is the sum of all the frequencies:

Total number of teenagers = 18 + 30 + 57 + 30 + 15

                                             = 150

Now, the probability:

[tex]\[ P(1) = \frac{\text{Number of teenagers with exactly 1 pair of shoes}}{\text{Total number of teenagers}} = \frac{18}{150} \][/tex]

[tex]\[ P(1) = \frac{3}{25} \][/tex]

So, the probability is [tex]\( \dfrac{3}{25} \)[/tex].

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The highlighted part of the circle is an inscribed angle.

Given that a circle is centered at O.

From the provided diagram,

A circle is centered at O.

YH is the diameter of the circle.

BK is the tangent of the provided circle at K.

And a secant of the circle BR.

As per the given choices,

Tangent: the line BK is tangent to a given circle.

center: the center of the circle is at O.

Central angle: ∠ROH.

Inscribed angle: ∠OYR.

An inscribed angle is the angle that an arc at any point on the circle subtends.

Therefore, an inscribed angle is ∠OYR.

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Answer: 50°

Step-by-step explanation:

7 and 6 are vertical angles, which means they are equal. m<7 and m<6 are 130 degrees. Then. m<4 and m<6 are supplementary angles, and if m<6 is 130°, then you subtract that from 180 to get 50 = m<4. m<4 and m<1 are vertical angles, so that means m<1 is 50°.

Therefore, the control represented by the decimal value 15 is the one with all four bits set to 1.

In digital electronics, binary digits (bits) are used to represent numbers and control various devices. Each bit can have a value of either 0 or 1, and by combining multiple bits, we can represent larger numbers or control signals. The decimal system, which we are most familiar with, uses 10 digits (0-9) to represent numbers. In contrast, the binary system uses only 2 digits (0 and 1) to represent numbers or controls. To convert a decimal number to binary, we repeatedly divide the number by 2 and keep track of the remainders. The binary representation of a number is the sequence of remainders read in reverse order.

The decimal value 15 can be represented as a control with four binary digits (bits), as follows:

1 1 1 1

Each bit represents a power of 2, from right to left: 2^0, 2^1, 2^2, 2^3. Adding up the powers of 2 where there is a 1 in the binary representation gives us the decimal value.

So, in this case, we have:

1x2^0 + 1x2^1 + 1x2^2 + 1x2^3 = 1 + 2 + 4 + 8 = 15

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The sum of the lengths of the two parallel sides, a + b, is equal to 30 centimeters.

Let's denote the lengths of the two parallel sides of the trapezoid as a and b. The formula for the area of a trapezoid is given by:

Area = (1/2) * (a + b) * h

where h represents the height of the trapezoid.

We are given that the area is 120 square centimeters and the height is 8 centimeters. Substituting these values into the formula, we have:

120= 1/2*(a+b)*8  

Multiplying both sides of the equation by 2 and dividing by 8, we get:

240 = a + b

a+b = 120*2/8

= 30 cm

Therefore, the sum of the lengths of the two parallel sides, a + b, is equal to 30 centimeters.

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To prove the identity sinh(2x) = 2 sinh(x) cosh(x), we can use the definitions of sinh(x) and cosh(x) and apply trigonometric identities for exponential functions.

We start with the left-hand side of the identity, sinh(2x). Using the definition of the hyperbolic sine function, sinh(x) = (e^x - e^(-x))/2, we can substitute 2x for x in this expression, giving us sinh(2x) = (e^(2x) - e^(-2x))/2.

Next, we focus on the right-hand side of the identity, 2 sinh(x) cosh(x). Again using the definitions of sinh(x) and cosh(x), we have 2 sinh(x) cosh(x) = 2((e^x - e^(-x))/2)((e^x + e^(-x))/2).

Expanding this expression, we get 2 sinh(x) cosh(x) = (e^x - e^(-x))(e^x + e^(-x))/2.

By simplifying the right-hand side, we have (e^x * e^x - e^x * e^(-x) - e^(-x) * e^x + e^(-x) * e^(-x))/2.

This simplifies further to (e^(2x) - 1 + e^(-2x))/2, which is equal to the expression we derived for the left-hand side.

Hence, we have proved the identity sinh(2x) = 2 sinh(x) cosh(x) by showing that the left-hand side is equal to the right-hand side through the manipulation of the exponential functions.

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The solution is: the approximate surface area of the cone is 103.6 in², which is closest to option (B).

To find the exact surface area of the cone, we need to know the slant height of the cone. Since we are not given the slant height, we can use the Pythagorean theorem to find it:

Slant height² = h² + r²

Slant height² = 4² + 3²

Slant height² = 16 + 9

Slant height² = 25

Slant height = 5

Now that we know the slant height, we can use the formula for the surface area of a cone:

Surface area = πr² + πr×s

where s is the slant height

Surface area = π(3²) + π(3)(5)

Surface area = 9π + 15π

Surface area = 24π

Therefore, the exact surface area of the cone is 24π square units.

The surface area of a cone is given by:

Surface area = πr² + πr×s

where r is the radius of the circular base and s is the slant height.

We are given that the diameter of the circular base is 6 inches, so the radius is 3 inches. We are also given that the slant height is 8 inches. Using these values, we can calculate the surface area of the cone:

Surface area = π(3²) + π(3)(8)

Surface area = 9π + 24π

Surface area = 33π

We can approximate π as 3.14, so:

Surface area ≈ 33(3.14)

Surface area ≈ 103.62

Therefore, the approximate surface area of the cone is 103.6 in², which is closest to option (B).

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complete question:

PLEASE ANSWER THESE QUESTIONS THROUGHLY FOR BRAINLIEST!!

1.)

In this figure, h = 4, and r = 3.

What is the exact surface area of the cone?

(picture inserted below!!!!)

2.)

The diameter of a cone's circular base measures 6 inches, and the slant height of the cone is 8 inches.

What is the approximate surface area of the cone?

94.2 in²

103.6 in²

131.9 in²

257.5 in²

3.)

The slant height of a cone measures 15 centimeters. The height of the cone measures 12 centimeters.

What is the exact surface area of the cone?

4.)

The radius of the circular base of a cone measures 1.6 inches, and its slant height measures 2.5 inches.

What is the approximate lateral area of the cone?

Use π≈3.14.

round to the nearest tenth.

5.) The area of the circular base of a cone is 9π cm², and the slant height of the cone is four times the radius of the cone.

What is the approximate lateral area of the cone?

Use π≈3.14.

round to the nearest whole number.

Step-by-step explanation:

SA = 2 ( 3x6 + 6x3 + 3x3) = 90   ft^2     now double everything

SA = 2 ( 6x12 + 12 x6 + 6x 6 ) = 360   ft^2     FOUR times larger SA

When the depth reaches 8 inches, the rate at which the grain level is rising is approximately (15 / (2 * sqrt(3))) ft/min.

To find the rate at which the grain level is rising when the depth reaches 8 inches, we can consider the volume of the grain in the trough and its rate of change with respect to time.

The trough is in the shape of an equilateral triangle, so the cross-sectional area of the trough at any depth can be calculated using the formula: A = (sqrt(3)/4) * s^2, where s is the length of the side of the equilateral triangle.

In this case, the length of the side of the equilateral triangle is 2 feet, so the cross-sectional area of the trough is A = (sqrt(3)/4) * 2^2 = sqrt(3) square feet.

Given that the trough is 8 feet long, the volume V of the grain in the trough at any depth h can be calculated as V = A * h.

Now, let's differentiate both sides of the equation with respect to time t to find the rate at which the volume is changing: dV/dt = d(Ah)/dt.

Since the length of the trough remains constant, dh/dt represents the rate at which the depth is changing.

Therefore, dV/dt = A * (dh/dt).

We are given that the grain is poured into the trough at a rate of 5 cubic feet per minute, so dV/dt = 5 ft^3/min.

At the depth of 8 inches (or 8/12 = 2/3 feet), we want to find the rate at which the grain level is rising, which is dh/dt.

Plugging in the known values, we have: 5 = (sqrt(3) * h) * (dh/dt).

Simplifying the equation, we find: dh/dt = 5 / (sqrt(3) * h).

Substituting h = 2/3 (depth in feet), we can calculate the rate at which the grain level is rising.

dh/dt = 5 / (sqrt(3) * (2/3)) = 5 / (sqrt(3) * 2/3) = 5 / (2 * sqrt(3) / 3) = 5 * 3 / (2 * sqrt(3)) = (15 / (2 * sqrt(3))) ft/min.

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Answer:

4(x+1)+5(5x-4)

=4x+4+25x-20

=29x-16

The dimensions of the largest rectangle that can be formed if all the sides (including the partition) sum to 600 units are 150 units x 150 units. This solution yields an area of 22,500 square units.

To find the dimensions of the largest rectangle that can be formed if all the sides (including the partition) sum to 600 units, we can use the concept of optimization. Let's assume that the rectangle has a length of L and a width of W, with a partition dividing it into two smaller rectangles.
Since all the sides (including the partition) sum to 600 units, we can express this mathematically as:
L + W + 2x = 600
where x represents the length of the partition. Rearranging the equation, we get:
L + W = 600 - 2x
The area of a rectangle is given by the formula A = L x W. To find the largest possible area of the rectangle, we need to maximize this function.
Substituting the above equation into the area formula, we get:
A = (600 - 2x - W) x W
Expanding and simplifying, we get:
A = 600W - 2W^2 - Wx
To find the maximum value of A, we can differentiate it with respect to W and set it equal to zero:
dA/dW = 600 - 4W - x = 0
Solving for W, we get:
W = (600 - x)/4
Substituting this value of W back into the equation for A, we get:
A = (600 - x)^2/16
To maximize A, we need to minimize x. Since x represents the length of the partition, this means that the partition should be as small as possible. Therefore, the largest rectangle that can be formed will be a square with sides of 150 units, and the partition will have a length of zero.
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The product of 8759 x 2391 x 2391 x 7759 is 388,895,526,171,961.

To find the product of 8759 x 2391 x 2391 x 7759, we can use the associative property of multiplication. This property states that the way in which we group the factors does not affect the result of the multiplication.

So, we can group the factors in pairs and multiply each pair together before multiplying the products. Let's start with 8759 x 7759 and then multiply the products of 2391 x 2391.

8759 x 7759 = 67,907,881
2391 x 2391 = 5,716,881

Now, we can multiply these two products together to get the final result.

67,907,881 x 5,716,881 = 388,895,526,171,961

Therefore, the product of 8759 x 2391 x 2391 x 7759 is 388,895,526,171,961.

Using the associative property of multiplication can make it easier to find the product of a large number of factors. By grouping the factors in pairs and multiplying each pair together, we can simplify the problem and make it more manageable.

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Answer:

y = 0.833x + 2.67

Step-by-step explanation:

Important Info:

Slope intercept form:

y = mx + b

where;

m = slope

b = y - intercept

x,y = distance of the line from x-axis/y-axis

Slope formula:

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Solve:

Find two point on the graph:

(-2,1) (4,6)

Using slope formula to find slope:

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]m=\frac{6-1}{4-(-2)}[/tex]

[tex]m=\frac{6-1}{4+2}[/tex]

[tex]m=\frac{5}{6}[/tex]

[tex]m=0.833[/tex]

Now, put it in slope intercept form:

y = 0.833x + b

To find "b" we have to chose one order pair. Let's use (-2,1) and use it to substitute x and y.

y = mx + b

1 = 0.833x(-2) + b

1 = -1.67 + b

b = 2.67

Now, put it in slope intercept form:

y = 0.833x + 2.67

Hence, the equation for that graph is; y = 0.833x + 2.67

RevyBreeze

Bar graph best displays the data. Therefore, the correct option is option C among all the given options.

In mathematics, a graph is a visual representation or diagram that shows facts or values in an ordered way.  The relationships between two or more items are frequently represented by the points on a graph. Bar graph best displays the data.

Therefore, the correct option is option C.

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To calculate Mrs Jendor's profit, we first need to determine the cost price of the radio set.

Let's assume that the cost price of the radio set is "x".

We know that Mrs Jendor made a profit of 10% on the cost price. This means that the selling price is 110% of the cost price.

We can write this as:

Selling price = Cost price + Profit

29,700 = x + 0.1x

Simplifying this equation, we get:

1.1x = 29,700

x = 27,000

So, the cost price of the radio set is 27,000.

Now, we can calculate the profit made by Mrs Jendor:

Profit = Selling price - Cost price

Profit = 29,700 - 27,000

Profit = 2,700

Therefore, Mrs Jendor made a profit of 2,700 on the sale of the radio set.

a is correct

Step-by-step explanation:

The equation in point-slope form that represents this relationship is y - 1 = 3(x - 7). So, the correct option is OA.

To write an equation in point-slope form, we need to use the formula: y - y1 = m(x - x1), where (x1, y1) is a point on the line, and m is the slope.
In this case, we are given that Hani sells postcards for $3 each (slope = 3), and he sold 7 postcards for a net profit of $1. So, we have a point (7, 1) on the line, where 7 represents the number of postcards sold (x1) and 1 represents the net profit (y1).
Using this information, we can plug the values into the point-slope form equation:
y - 1 = 3(x - 7)
Thus, the correct answer is OA: y - 1 = 3(x - 7).

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The approximate probability the 11 players on a team will have a mean height of less than 72 inches is 0.047.

probability was calculated, we need to use the central limit theorem. This theorem states that the sample mean of a large enough sample (in this case, n=11 is considered large enough) taken from a population with any distribution will follow a normal distribution with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size.

Using this theorem and the given information, we can calculate the standard error of the sample mean as follows:

Standard error = standard deviation / square root of sample size
= 3.75 / sqrt(11)
= 1.13

Next, we need to standardize the sample mean using the z-score formula:

z = (sample mean - population mean) / standard error
= (72 - 73) / 1.13
= -0.88

Finally, we can use a standard normal distribution table or calculator to find the probability that a z-score is less than -0.88, which is approximately 0.047.

the approximate probability the 11 players on a team will have a mean height of less than 72 inches is 0.047, calculated using the central limit theorem and the z-score formula.

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The input - output pairs of the linear function are given as follows:

The slope-intercept representation of a linear function is given by the equation shown as follows:

y = mx + b

The coefficients m and b have the meaning presented as follows:

From the table, when x increases by 8, y increases by 16, hence the slope m is given as follows:

m = 16/8

m = 2.

Hence:

y = 2x + b.

When x = 7, y = 16, hence the intercept b is given as follows:

16 = 14 + b

b = 2.

Hence the function is:

y = 2x + 2.

The output for an input of 25 is given as follows:

y = 2 x 25 + 2

y = 52.

The input for an output of 22 is given as follows:

22 = 2x + 2

2x = 20

x = 10.

The output for an input of 2x is given as follows:

y = 2(2x) + 2

y = 4x + 2.

The output for an input of x + 3 is given as follows:

y = 2(x + 3) + 2

y = 2x + 8.

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Volume of cylinder is, V = 99π km³

And, Volume of sphere is, V = 457.3π meter³

Given that;

8) In cylinder;

Diameter = 18 km

Height = 11 km

9) In sphere,

Diameter = 14 m

Since, We know that;

Volume of cylinder is,

V = πr²h

V = π × 18/2 × 11

V = π × 9 × 11

V = 99π km³

And, We know that;

Volume of sphere is,

V = 4/3πr³

Hence, WE get;

V = 4/3 × π × (14/2)³

V = 4/3 × π × 7³

V = 457.3π meter³

Thus, We get;

Volume of cylinder is, V = 99π km³

And, Volume of sphere is, V = 457.3π meter³

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Disjoint events are events that cannot happen at the same time. Two events A and B are independent if the occurrence of A does not affect the probability of B happening, and vice versa. Mathematically, this can be written as P(A and B) = P(A)P(B).

In the case of disjoint events, P(A and B) = 0 because they cannot occur at the same time. Therefore, the condition for A and B to be independent is that either P(A) = 0 or P(B) = 0, since any non-zero probability for either event would make the product P(A)P(B) also non-zero.

Two disjoint events are independent if and only if at least one of them has zero probability.

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The general solution of the given system of differential equations is:

y = -37 × (1/2)x² + 5x + C, where C is the constant of integration.

The general solution of a system of derivative equations refers to a set of equations or formulas that represent all possible solutions of the given system. It includes an arbitrary constant or constants, which can take different values to yield different specific solutions.

The form of the general solution depends on the nature of the equations and the techniques used to solve them.

Here we have

dx/dt = 7x + y and dy/dt = -2x + 5y

To find the general solution of the given system of differential equations:

=> dx/dt = 7x + y  __ (1)

=> dy/dt = -2x + 5y  __(2)

Solve it using the method of simultaneous equations.

Solve Equation (1) for y:

y = dx/dt - 7x

Substitute the value of y in Equation (2):

dy/dt = -2x + 5(dx/dt - 7x)

Simplify the equation:

dy/dt = 5dx/dt - 2x - 35x

dy/dt = 5dx/dt - 37x

Rearrange the equation:

dy/dt - 5dx/dt = -37x

Multiply through by dt:

dy - 5dx = -37x dt

Integrate both sides of the equation:

∫(dy - 5dx) = ∫(-37x) dt

Integrate each term:

y - 5x = -37 * (1/2)x² + C

Simplify the equation:

y = -37 × (1/2)x² + 5x + C

Therefore,

The general solution of the given system of differential equations is:

y = -37 × (1/2)x² + 5x + C, where C is the constant of integration.

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A linear programming problem with two decision variables can be solved by a graphical solution method. In this method, the constraints and the objective function of the linear programming problem are graphed on a two-dimensional coordinate plane, and the optimal solution is found at the intersection of the feasible region (the area defined by the constraints) and the level curve of the objective function.

The graphical solution method is a simple and intuitive way to solve linear programming problems with few decision variables, but it becomes impractical as the number of decision variables and constraints increase. In such cases, more complex algorithms, such as the simplex method or interior point methods, are used to find the optimal solution.

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The factored expression of the expression 4x³ - 6x² + 8x is 2x(2x² - 3x + 2)

From the question, we have the following parameters that can be used in our computation:

4x³ - 6x² + 8x

The above expression is a polynomial expression

So, we have the following

4x³ - 6x² + 8x

Factor out x in 4x³ - 6x² + 8x

This gives

4x³ - 6x² + 8x = x(4x² - 6x + 8)

Factor out 2 in 4x² - 6x + 8

This gives

4x³ - 6x² + 8x = 2x(2x² - 3x + 2)

Hence, the factored expression is 2x(2x² - 3x + 2)

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Answer:

f

Step-by-step explanation:

Statement B may or may not be true, depending on whether AM = MT, and statement D may or may not be true, depending on the Orientation of LA.

In triangle MAH with MT as the perpendicular bisector of AH, let's consider the given statements.

A. AMAH is isosceles.

If MT is the perpendicular bisector of AH, then AM = MH. Therefore, triangle AMAH is isosceles, and statement A is always true.

B. AMAT is isosceles.

Since MT is the perpendicular bisector of AH, then AT = TH. However, there is not enough information to determine whether AM = MT. Therefore, statement B may or may not be true, depending on whether AM = MT.

C. MT bisects ZAMH.

Since MT is the perpendicular bisector of AH, then MT also bisects the base of triangle MAH, which is ZAMH. Therefore, statement C is always true.

D. LA and ZTMH are complementary.

Since MT is the perpendicular bisector of AH, then ZTMH is a right angle. However, there is not enough information to determine whether LA is perpendicular to MT. Therefore, statement D may or may not be true, depending on the orientation of LA.

statement B may or may not be true, depending on whether AM = MT, and statement D may or may not be true, depending on the orientation of LA. Therefore, the statement that is not always true is:

B. AMAT is isosceles.

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[tex]\stackrel{ \textit{\LARGE sum of all exterior angles} }{(6x+24)+(6x+26)+(4x+10)+(3x-22)+(5x-14)~~ = ~~360} \\\\\\ 24x+24=360\implies 24x=336\implies x=\cfrac{336}{24}\implies x=14[/tex]