14/15 divided by 7/5

The probability that the slope of the line determined by p and the point (5/8, 3/8) is greater than or equal to 1/2 is 5/8.

Let the coordinates of point p be (x,y). Then, the slope of the line determined by p and the point (5/8, 3/8) is:

For the slope to be greater than or equal to 1/2, we must have:

Solving for y, we get:

Graphing this inequality on the unit square, we see that the region satisfying this inequality is a trapezoid with vertices (5/8,3/8), (1,1/2), (1,1), and (3/4,1).

The area of this trapezoid is (1/2)*((5/8 - 3/4) + (1 - 5/8) + (1 - 1/2) + (3/8 - 3/16)) = 5/16.

The area of the unit square is 1, so the probability we seek is 5/16.

Hence, the answer is 5/16 written as a fraction in its simplest form, which is 5/16.

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Answer:

-486

Step-by-step explanation:

-9 × 6 × 9 ×6=

-9 × 6 × 9 = -486

First let's calculate the radius of the cost

Step-by-step explanation:

y = ax + b => ax +b = y

-5= a.1+ b => a + b = -5

-9= a.2+b => 2a+b = -9

________-

-a = 4

=> a = -4

a+b=-5 => b = -5 -a

b = -5+4 = -1

so, the Equation : y = -4x -1

Given

(x + 2 < 5) (x - 7 > -6).

Answer

x + 2 < 5

x < 3 (1)

x - 7 > - 6

x > - 6 + 7

x > 1 (2)

From 1 and 2

1 < x < 3

When 'a' is 10, 'c' is approximately 142.97. You can repeat this process for different values of 'a' to find corresponding values of 'c'. Keep in mind that there are infinitely many solutions to this equation

To use the elimination method to solve the equation 2a + c = 162.97, we need another equation with the same variables. However, as there is only one equation given, we cannot apply the elimination method directly.

The elimination method typically involves adding or subtracting equations to eliminate one of the variables, resulting in a new equation with only one variable. Since we have only one equation, we don't have the opportunity to eliminate variables using another equation.

In this case, we can solve the given equation directly by isolating one variable in terms of the other. Let's solve for 'c':

2a + c = 162.97

Rearrange the equation to isolate 'c':

c = 162.97 - 2a

Now, we have an expression for 'c' in terms of 'a'. This equation represents a line in the 'a-c' coordinate plane. We can choose any value for 'a', substitute it into the equation, and calculate the corresponding 'c' value.

For example, let's say we choose 'a' = 10:

c = 162.97 - 2(10)

c = 162.97 - 20

c = 142.97

So, when 'a' is 10, 'c' is approximately 142.97.

You can repeat this process for different values of 'a' to find corresponding values of 'c'. Keep in mind that there are infinitely many solutions to this equation since we have one equation and two variables.

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Answer: The answer would be 30.

Step-by-step explanation:

Answer:

  x = 36

Step-by-step explanation:

Given a tangent segment of length 24, and a secant segment from the same point with an external length of 12 and a total length of (12+x), you want to find the value of x.

The product of lengths from the common point to the two intersections with the circle are the same for both segments. In the case of the tangent, the two intersections with the circle are the same point, so the square of the length is used.

  24² = 12(12 +x)

  2·24 = 12 +x . . . . . . . divide by 12

  36 = x . . . . . . . . . subtract 12

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The experimental probability of the rolling a 6 is 13%.

Probability is the likelihood of a desired event happening. Experimental probability is a probability that relies mainly on a series of experiments.

From the table:

The total number of times all the numbers appear is:

total number of times = 7 + 4 + 4 +  5 + 6 + 4 = 30

The number six (6) occurred 4 times.

Experimental probability = (occurrence of 6 / total number of times)

Experimental probability = 4/30 * 100

Experimental probability = 13%

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The probability that four batteries connected in series will have a combined voltage of 60.8 or more volts is approximately 0.0228 or 2.28%.

To find the probability that four batteries connected in series will have a combined voltage of 60.8 or more volts, we need to use the concept of the Central Limit Theorem.

In this case, we know that the mean voltage of a single battery is 15 volts and the standard deviation is 0.2 volts. When batteries are connected in series, their voltages add up.

The combined voltage of four batteries connected in series is the sum of their individual voltages. The mean of the combined voltage will be 4 times the mean of a single battery, which is 4 * 15 = 60 volts.

The standard deviation of the combined voltage will be the square root of the sum of the variances of the individual batteries. Since the batteries are connected in series, the variance of the combined voltage will be 4 times the variance of a single battery, which is 4 * (0.2)^2 = 0.16.

Now, we need to calculate the probability that the combined voltage of four batteries is 60.8 or more volts. We can use a standard normal distribution to calculate this probability.

First, we need to standardize the value of 60.8 using the formula:

Z = (X - μ) / σ

Where X is the value we want to standardize, μ is the mean, and σ is the standard deviation.

In this case, the standardized value is:

Z = (60.8 - 60) / sqrt(0.16)

Z = 0.8 / 0.4

Z = 2

Next, we can use a standard normal distribution table or calculator to find the probability associated with a Z-score of 2. The probability of obtaining a Z-score of 2 or more is approximately 0.0228.

Therefore, the probability that four batteries connected in series will have a combined voltage of 60.8 or more volts is approximately 0.0228 or 2.28%.

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The area of the triangle with the given vertices is 11.5 square units.

The area of a triangle can be calculated using the coordinates of its vertices using the following formula.

To find the area of a triangle with vertices (x₁, y₁), (x₂, y₂), and (x₃, y₃), we can use the following formula:

A = (x₁(y₂ − y₃) + x₂(y₃ − y₁) + x₃(y₁ − y₂))/2

Using this formula with the given vertices (0, 6), (2, −3), and (3, 4), we get:

A = (0(-3 − 4) + 2(4 − 6) + 3(6 − (-3)))/2

A = (0 - 4 + 27)/2

A = 23/2

A = 11.5

Therefore, the area of the triangle with the given vertices is 11.5 square units.

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The requried ball reached a maximum height of approximately 62 feet

Let the ball is thrown vertically upward, we can use the following formula to find the maximum height it reaches:

\(h(t) = -16t^2 + vt + h_0\)

here, h(t) is the height of the ball at time t, v is the initial velocity of the ball (in feet per second), and h0 is the initial height of the ball (in feet). We can also use the fact that the ball remains in the air for 3.8 seconds, which means that the time it takes to reach the maximum height is half of that or 1.9 seconds.

At the highest point, the ball's velocity is zero, so we can find the initial velocity by setting v = 0 in the above formula and solving for h₀:

h₀ = h(t) + 16t²

   = 4 + 16(1.9)²

   ≈ 4 + 57.76

   ≈ 61.76

Therefore, the ball reached a maximum height of approximately 62 feet

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Answer:

0.95 = 95% probability that a randomly selected student at this university recycles at least some of the time

Step-by-step explanation:

For a randomly selected student, we have these following probabilities:

0.55 probability that they always recicle.

0.25 probability that they usually recicle.

0.15 probability that they recicle only when it's convenient.

0.05 probability that they never recicle.

What is the probability that a randomly selected student at this university recycles at least some of the time?

Always, usually or only when it's convenient.

0.55 + 0.25 + 0.15 = 0.95

0.95 = 95% probability that a randomly selected student at this university recycles at least some of the time

The amount of work done is Option A) 12 N/m

Work done is simply defined as the product of the magnitude of displacement, (d) and the component of the force that in the direction of displacement.

It measures energy transfer that occurs when an object is moved to a distance by an external force which is applied in the direction of the displacement.

Work done on a body is equivalent  to the increase in the energy of the body, because it transfers energy to the body.

The formula for work done is;

W = fd

Where, 'f' is the applied force and d is the distance

Substitute the values

Work done = 6(2)

Work done = 12 N/m

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Given

To find

Let the purchase value be P,

ATQ,

P -3 x 0.1P = Rs 43,740

P-0.3P = Rs 43,740

0.7P = Rs 43,740

P = Rs 43,740/0.7

P = Rs 62,486 (approx)

Hence, the purchase value of the machine would be Rs 62,486

Answer:

The smaller number in 0.01

Step-by-step explanation:

To find this answer, just take the fraction and find the quotient of both numbers.

1.789/178 = 0.01005056179

Now take the quotient and compare it to 0.05.

Is 0.01 larger or 0.05 - the answer is 0.01.

The range of the exponential function is B. y > 0.

The range of the exponential function f(x) = 11 × (1/3)ˣ can be determined by analyzing the behavior of the function as x approaches positive and negative infinity.

As x approaches positive infinity, (1/3) becomes smaller and smaller, tending towards zero.

f(x) approaches 11 × 0, which is equal to 0.

As a result, the function approaches 0 as x goes to infinity.

On the other hand, as x approaches negative infinity, (1/3)ˣ becomes larger and larger.

Since 1/3 is between 0 and 1, raising it to a negative power causes it to grow exponentially.

f(x) approaches infinity as x goes to negative infinity.

Combining these two behaviors, we can conclude that the range of the function f(x) = 11 × (1/3)ˣ is all positive real numbers, excluding zero.

In other words, the range is y > 0.

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Answer:

2.371

Step-by-step explanation:

subtract 8.63 to 11.001

B

Step-by-step explanation:

because the figure is based on the graphic law

Answer:

X=32, Y=148

Step-by-step explanation:

X is 32 degrees because it is parallel to that 32 between f and b.

Y is 148 degrees because x and y together make a straight line and a straight line is 180 degrees therefore, 180-32 = 148.

Angle EFG is an angle with a measure of 42 degrees is drawn below.

Given that, angle EFG= 42 degrees.

Angle EFG is an angle with a measure of 42 degrees. To draw angle EFG, first draw a line segment and mark two points on the line segment. Label the two points E and F. Then, using a protractor, measure out an angle with a measure of 42 degrees from the line segment EF, starting from point E. Finally, mark the end of the angle as point G.

Therefore, angle EFG is an angle with a measure of 42 degrees is drawn below.

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Sara need 9/4 ounces of chopped nuts

Sara wants to make dinner for herself
The recipe she will use calls for 13 1/2 ounces

The recipe feeds 6 people

The number of ounces of chopped nuts that Sara needs can be calculated as follows

13 1/2

= 27/2 ÷ 6

= 27/2 × 1/6

= 27/12

= 9/4

Hence Sara needs 9/4 ounces of chopped nuts for one serving

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==================================================

Explanation:

When we reflect any point (x,y) over the line y = x, the x and y coordinates swap. So for instance, we have K = (5, -9) turn into K ' = (-9, 5).

Consider a point like (1,2). We can move it down 1 unit to have it land on the line y = x, then we can move it one unit to the right to move it to (2,1). These two translations effectively move the original point to its reflected location. The distance from (1,2) to y = x, is the same as the distance from (2,1) to y = x. Furthermore, the line connecting (1,2) to (2,1) is perpendicular to y = x.

Answer:

5.75

Step-by-step explanation:

1.25 +4.5 =5.75(the time =the addition of the both times)

Answer:

x = 54, so the vertical angles are 110°.

Step-by-step explanation:

\(2x + 2 = 3x - 52\)

\(2 = x - 52\)

\(x = 54\)

\(2(54) + 2 = 108 + 2 = 110\)

\(3(54) - 52 = 162 - 52 = 110\)

Answer:

130 degrees

Step-by-step explanation:

DE+DA=130

Answer:

Step-by-step explanation:

The Order of Operations is very important when simplifying expressions and equations. The Order of Operations is a standard that defines the order in which you should simplify different operations such as addition, subtraction, multiplication and division.

This standard is critical to simplifying and solving different algebra problems. Without it, two different people may interpret an equation or expression in different ways and come up with different answers. The Order of Operations is shown below.

Parentheses and Brackets -- Simplify the inside of parentheses and brackets before you deal with the exponent (if any) of the set of parentheses or remove the parentheses.

Exponents -- Simplify the exponent of a number or of a set of parentheses before you multiply, divide, add, or subtract it.

Multiplication and Division -- Simplify multiplication and division in the order that they appear from left to right.

Addition and Subtraction -- Simplify addition and subtraction in the order that they appear from left to right.

Before we begin simplifying problems using the Order of Operations, let's examine how failure to use the Order of Operations can result in a wrong answer to a problem.

Without the Order of Operations one might decide to simplify the problem working left to right. He or she would add two and five to get seven, then multiply seven by x to get a final answer of 7x. Another person might decide to make the problem a little easier by multiplying first. He or she would have first multiplied 5 by x to get 5x and then found that you can't add 2 and 5x so his or her final answer would be 2 + 5x. Without a standard like the Order of Operations, a problem can be interpreted many different ways

We cannot combine the variable terms before using the distributive property when solving the equation as it will results in wrong answer.

What is distributive property of multiplication over addition ?

If we multiply a number by the sum of more than two, we use the distributive property of multiplication over addition.

Here the expression given is :

7(x+5)-x=42

The Order of Operations is very important when simplifying expressions and equations. The Order of Operations is a standard that defines the order in which you should simplify different operations such as addition, subtraction, multiplication and division.

Parentheses and Brackets -- Simplify the inside of parentheses and brackets before you deal with the exponent (if any) of the set of parentheses or remove the parentheses.

Exponents -- Simplify the exponent of a number or of a set of parentheses before you multiply, divide, add, or subtract it.

Multiplication and Division -- Simplify multiplication and division in the order that they appear from left to right.

Addition and Subtraction -- Simplify addition and subtraction in the order that they appear from left to right.

Without the Order of Operations one might decide to simplify the problem working left to right. He or she would add two and five to get seven, then multiply seven by x to get a final answer of 7x. Another person might decide to make the problem a little easier by multiplying first. He or she would have first multiplied 5 by x to get 5x and then found that you can't add 2 and 5x so his or her final answer would be 2 + 5x. Without a standard like the Order of Operations, a problem can be interpreted many different ways.

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