Dipesh bought 3 notebooks and 2 pens for Rs. 80. His friend Ramesh said that price of each notebook could be
Rs. 25. Then three notebooks would cost Rs.75, the two pens would cost Rs. 5 and each pen could be for Rs. 2.50.
Another friend Amar felt that Rs. 2.50 for one pen was too little. It should be at least Rs. 16. Then the price of
each notebook would also be Rs.16.Dipesh bought 3 notebooks and 2 pens for Rs. 80. His friend Ramesh said that price of each notebook could be
Rs. 25. Then three notebooks would cost Rs.75, the two pens would cost Rs. 5 and each pen could be for Rs. 2.50.
Another friend Amar felt that Rs. 2.50 for one pen was too little. It should be at least Rs. 16. Then the price of
each notebook would also be Rs.16.

After answering the provided question, we can conclude that As a result, equation 315 kids did not select soda.

An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the phrase "2x + 3" equals the value "9". The purpose of equation solving is to determine the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complicated, regular or nonlinear, and include one or more elements. The variable x is raised to the second power in the equation "x2 + 2x - 3 = 0." Lines are utilised in many different areas of mathematics, such as algebra, calculus, and geometry.

According to the circle graph, 14% of pupils preferred soda. As a result, 100% - 14% = 86% of pupils did not select soda.

We know that 35% of students, or 110 kids, chose milk. Hence we may calculate the fraction of pupils that did not drink soda as follows:

35/100 = 110/x

When we solve for x, we get:

x = (110*100)/35 = 314.29

x = 315

As a result, 315 kids did not select soda.

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To vertically expand a function by a factor of 2, we multiply the function by 2. Thus, the transformed function becomes g(x) = 2f(x) = [tex]2(x^3)[/tex].

To translate a function down 2 units, we subtract 2 from the original function. Thus, the transformed function becomes h(x) = g(x) - 2 = 2[tex](x^3)[/tex] - 2.

So the equation of the transformed function is h(x) = 2[tex](x^3)[/tex] - 2.

Graphically, the transformation of the function f(x) = [tex]x^3[/tex] into h(x) = 2[tex](x^3)[/tex] - 2 means that the graph of h(x) is twice as tall as the graph of f(x) and shifted 2 units downwards. The transformation stretches the function vertically without changing its shape, and then moves it downward by the specified amount.

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Answer:

The formula is: x = -y + z

We are given that y = 3 and z = 1. Substituting these values in the formula, we get:

x = -y + z

x = -(3) + 1

x = -3 + 1

x = -2

Therefore, when y = 3 and z = 1, the value of x is -2.

Step-by-step explanation:

The given formula is: x = -y + z

We are given that y = 3 and z = 1.

Substitute the values of y and z into the formula.

x = -y + z

x = -(3) + 1

x = -3 + 1

Simplify the expression.

x = -2

Therefore, when y = 3 and z = 1, the value of x is -2.

Answer:

6.17 hours every week

Step-by-step explanation:

Answer:

Step-by-step explanation:

Depending on the correlations between the days, the answer can be anywhere from 25% (perfect correlation) to 100% (for example, first four days mutually exclusive).

If you assume the days are independent, which may be what you intended to ask but is not actually a good assumption when it comes to the weather, then the probability is 1 - (1-0.25)^5 = 76%

The issue pertains to probability theory, and specifically the calculation of the likelihood of precipitation on a particular day. We need to find the total probability that it rains at least three out of five days, and this would require enumerating and counting all possible outcomes.

This is a problem of probability related to weather forecasts, specifically concerned with the chance of rain. The first day has an independent probability of 1/2 (rain or no rain). Thereafter each day's weather depends on the previous day's. If it rained the day before, there's a 2/3 chance it will rain the next day, and 1/3 chance it won't. If it didn't rain, those chances are reversed.

To get the probability that it rains at least three out of five days, we will think about it in terms of the total possible outcomes and the desired outcomes. The problem can be solved by counting the number of ways that we can have 3, 4 or 5 rainy days out of 5 and then multiplying each by the probability of that particular event.

By following these steps, we will arrive at the total probability, which might require a sophisticated understanding of probability theory.

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A graph of the equation y = 2x - 3 is shown in the image attached below.

In order to to graph the solution to the given linear equation on a coordinate plane, we would use an online graphing calculator to plot the given linear equation and then take note of the point that lie on it;

y = 2x - 3

In this scenario and exercise, we would use an online graphing calculator to plot the given linear equation as shown in the graph attached below.

Based on the graph shown in the image attached below, we can reasonably infer and logically deduce that the domain for this linear equation is -2 < x < 4.

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Answer: Let's draw a diagram to visualize the situation:

                   C (water tower)

                  /|

                 / |  25°

         12000 /  |

               /   |

              /    |

             /     |

            /θ     | B (plane)

           A       |

In this diagram, the pilot of the airplane is located at point B and the water tower is located at point C. The angle of depression from the airplane to the base of the tower is 25°. We are asked to find the length of the line of sight from the airplane to the tower, which is the distance AC.

We can use trigonometry to solve for AC. In particular, we can use the tangent function, which relates the opposite side to the adjacent side of a right triangle:

tan(θ) = opposite / adjacent

In this case, the opposite side is BC (the height of the water tower) and the adjacent side is AB (the distance from the airplane to the base of the tower). We can rearrange the equation to solve for AB:

AB = BC / tan(θ)

We know that BC is the height of the water tower, but we don't have that information. However, we can use the fact that the angle of depression is 25° to find BC. The angle of depression is the angle between the horizontal line (which we can assume is the same as the ground level) and the line of sight from the airplane to the base of the tower. Therefore, the angle between the line of sight and the vertical line (which is perpendicular to the ground) is 90° - 25° = 65°. This means that the triangle ABC is a right triangle, with angle θ = 65°.

Now we can use trigonometry again to find BC, using the sine function:

sin(θ) = opposite / hypotenuse

In this case, the opposite side is BC (the height of the water tower) and the hypotenuse is AC (the line of sight from the airplane to the tower). We can rearrange the equation to solve for BC:

BC = sin(θ) x AC

We know that θ = 65° and sin(θ) ≈ 0.9063 (you can use a calculator to find this value). Substituting these values into the equation gives us:

BC = 0.9063 x AC

Now we can substitute this expression for BC into the equation we derived earlier:

AB = BC / tan(θ) = (0.9063 x AC) / tan(65°)

We can simplify this expression by noting that tan(65°) ≈ 2.1445 (you can use a calculator to find this value). Substituting this value gives us:

AB = (0.9063 x AC) / 2.1445

Multiplying both sides by 2.1445 gives us:

2.1445 x AB = 0.9063 x AC

Dividing both sides by 0.9063 gives us:

AC = (2.1445 x AB) / 0.9063

We know that AB is the altitude of the airplane, which is given as 12,000 feet. Substituting this value gives us:

AC = (2.1445 x 12,000) / 0.9063 ≈ 28,406 feet

Therefore, the length of the line of sight from the airplane to the water tower is approximately 28,406 feet.

Step-by-step explanation:

The frequency with largest amplitude  for the particular solution to the differential equation is w = 0.707 (approximately).

To find the frequency with the largest amplitude, we can assume that the particular solution to the given differential equation is of the form:

y(t) = Aeiwt

Taking the first and second derivatives of y(t), we get:

dy/dt = iwtAeiwt

d2y/dt2 = -w2Aeiwt

Substituting these into the differential equation, we get:

-w2Aeiwt + 2Aeiwt = eiwt

Simplifying, we get:

A = 1 / (1 - 2iw2)

The amplitude of y(t) is given by |A|, which is:

|A| = 1 / |1 - 2iw2|

To find the frequency w for which |A| is largest, we need to minimize the modulus of the denominator of A over all frequencies w. We can do this using numerical optimization methods. So, frequency is 0.707.

Therefore, the frequency with the largest amplitude is w = 0.707 (approximately).

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No, a binomial experiment cannot be used to determine the probability that the rods are the correct length or an incorrect length.

A binomial experiment has the following characteristics:

1. It consists of a fixed number of trials.

2. Each trial has only two possible outcomes: success or failure.

3. The trials are independent.

4. The probability of success is constant for each trial.

In the case of metal rods, the length can vary continuously, so it is not a binary outcome. Therefore, a binomial experiment cannot be used to determine the probability of the rods being the correct length or an incorrect length. Instead, a probability distribution such as a normal distribution could be used to model the distribution of rod lengths and calculate the probability of a rod being the correct length.

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The probability that the jury makes the correct decision is 0.9999

This is a binomial distribution problem where the event of interest is a juror making a correct decision (voting guilty) and the number of trials is 12 (the number of jurors).

The probability of a single juror making the correct decision is 0.80. Therefore, the probability of a single juror making the incorrect decision (voting not guilty) is 1 - 0.80 = 0.20.

To calculate the probability that at least 10 out of 12 jurors make the correct decision (voting guilty) if the defendant is guilty, we can use the binomial distribution formula:

P(X ≥ 10) = 1 - P(X < 10)

where X is the number of jurors who make the correct decision.

Since the probability of a single juror making the correct decision is 0.80, we can use the binomial probability formula to calculate the probability of X jurors making the correct decision

P(X = x) = (12 choose x) * 0.80^x * 0.20^(12-x)

where (12 choose x) is the number of ways to choose x jurors out of 12.

Using this formula, we can calculate the probability of fewer than 10 jurors making the correct decision:

P(X < 10) = P(X = 0) + P(X = 1) + ... + P(X = 9)

We can use a calculator or software to calculate this probability:

P(X < 10) = 0.00000436

Therefore, the probability of at least 10 out of 12 jurors making the correct decision if the defendant is guilty is:

P(X ≥ 10) = 1 - P(X < 10) = 1 - 0.00000436 = 0.99999564

Rounding to four decimal places, the probability is 0.9999.

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The length of the base of the given parallelogram is 2 feet.

The area of ​​a parallelogram is all the square units that fit inside, measured in square units (cm2, m2, in2, etc.). It is the area surrounded or enclosed by parallelograms in two places. The elements of a parallelogram. Since a rectangle and a parallelogram have the same properties, the area of ​​the rectangle is the same as that of the parallelogram.

Given us the area in sq. feet but height in yards, So let's convert the height in feet instead.

We know, 1 yard = 3 feet

∴ Height = 5 feet.

Now, We know

⇒ Area = Base × Height

⇒ 10 = Base × 5

⇒ Base = 2 feet

Hence, The length of the base of the given parallelogram is 2 feet.

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Answer:

slope= 1/4

Step-by-step explanation:

Answer:

- 1/2

Step-by-step explanation:

We can use the slope formula to find the slope.

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

    = ( -40 - -75)/(-15 - 55)

   = (-40+75)/( -15-55)

   =35/-70

  =- 1/2

Answer:

m = -0.5

Step-by-step explanation:

Given that, ( Coordinates of a line )

( 55, - 75 ) ⇒ ( x₁ , y₁ )

( - 15 , - 40 ) ⇒ ( x₂ , y₂ )

The formula to find the slope of a line is:

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

Let us find it now.

[tex]\sf m =\frac{y_1-y_2}{x_1-x_2} \\\\\sf m =\frac{-75-(-40)}{55-(-15)} \\\\\sf m =\frac{-75+40}{55+15} \\\\\sf m =\frac{-35}{70} \\\\m = -0.5[/tex]

In Linear equation, 121 the number of people per square mile.

What in mathematics is a linear equation?

An algebraic equation with simply a constant and a first-order (linear) component, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.

                                   Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables. Equations with variables of power 1 are known as linear equations. One example with only one variable is where ax+b = 0, where a and b are real values and x is the variable.

A = (12 + 21) * 14 * 1/2

    = 33 * 14 * 1/2

     = 231 mi²

 28000 ÷ 231  = 121 people

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The expressions are matched as;

5³· 5³    add the exponents

(4x³)⁵.  write as the product of the powers

6⁹ ÷ 6⁵.  subtract the exponents

(7²)³. multiply the exponents

Index forms are described as those mathematical models that are used to represent numbers too small or large in more convenient forms.

They are represented as variables or numbers that are being raised to an exponent.

Other names for index forms are;

The rules of the index forms are;

From the information given, we have that;

5³· 5³    multiply the exponents

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The scatter plot for the table shows the average cost of a gallon of gas each year for the past 8 years is attached.

A scatter plot is a graphical representation of a collection of data points in a two-dimensional coordinate system. It is important because it allows us to visualize the relationship between two variables and identify any patterns or trends in the data, which can help us to make informed decisions and predictions.

Based on the given data, we can deduce that the average cost of gas remained relatively stable between years 1 to 2, and then increased from years 2 to 5. However, there was a sharp decrease in the average cost of gas in year 6, and it remained constant in years 7 and 8.

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The exponential growth rate is approximately 3.1% per year, and the equation is C(t) = 0.22 * e^(0.031t). The cost of a bottle of ketchup in 2012 would be approximately $1.72.

To find the exponential growth rate, we use the formula:

r = (ln(P2/P1)) / (t2 - t1)

where P1 is the initial value, P2 is the final value, t1 is the initial time, t2 is the final time, and ln denotes the natural logarithm. Substituting the values we get:

r = (ln(1.39/0.22)) / (2007-1966) = 0.0271 or 2.7% (to the nearest tenth of a percent)

The equation for exponential growth is:

C(t) = C0 * e^(rt)

where C0 is the initial cost and C(t) is the cost at time t. Substituting the values we get:

C(t) = 0.22 * e^(0.0271t)

To find the cost of a bottle of ketchup in 2012, we substitute t = 2012 in the above equation:

C(2012) = 0.22 * e^(0.0271 * 2012) = $1.72 (rounded to the nearest cent)

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answer 5y - 12 = 8.

In order to use the subtraction property of equality to solve equations, the subtraction of the same quantity should be done on both sides of the equation.

Here are the equations in which you can use the subtraction property of equality to solve:7x + 2 = 25-2y = 10-4r = 28-1/3p = 15+9z = -27

The only equation from the options given in the question is 5y - 12 = 8. So, we can use the subtraction property of equality to solve this equation as follows:5y - 12 = 8Add 12 to both sides5y - 12 + 12 = 8 + 125y = 20Divide both sides by 55y/5 = 20/5y = 4 Therefore, the equation in which we can use the subtraction property of equality to solve is 5y - 12 = 8.

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Answer:

The function h(x) = -log(x + 5) has a vertical asymptote at x = -5, since the logarithm of a non-positive number is undefined. To find the intercepts of this function, we can set h(x) equal to zero and solve for x:

h(x) = 0

-log(x + 5) = 0

x + 5 = 1

x = -4

So the function has an x-intercept at (-4, 0). To find the y-intercept, we can set x equal to zero and evaluate h(x):

h(0) = -log(0 + 5) = -log(5)

So the function has a y-intercept at (0, -log(5)).

To verify these intercepts using the graph, we can look for the points where the graph intersects the x and y axes. The x intercept is where the graph crosses the x-axis, which in this case is at x = -4. The y-intercept is where the graph crosses the y-axis, which is at y = -log(5) or approximately -1.609. The vertical asymptote is the vertical line where the graph approaches but never touches. From the graph, we can see that this occurs at x = -5.

It is important to note that when graphing logarithmic functions, it is recommended to plot a few points, including the intercepts and vertical asymptote, to help visualize the graph accurately.

The answers of following questions are given as follows:- m∠R = 114°

m∠RSQ = 13°

TQ = SR = 3x

Quadrilateral which is made up of 2 pairs of parallel sides. The opposite sides are parallel and equal in length in a parallelogram.

Since QRST is a parallelogram, opposite angles are congruent. Therefore, we have:

m∠R = m∠T = 180° - m∠QTS = 180° - 66° = 114°

Also, since QRST is a parallelogram, opposite sides are congruent. Therefore, we have:

SR = TQ = 3x

Finally, we can use the fact that the sum of the angles in a triangle is 180° to find m∠RSQ:

m∠RSQ = 180° - m∠QST - m∠T = 180° - 53° - 114° = 13°

Note that we cannot solve for x since we have only one equation and two unknowns.

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Answer:

3cm or 1.5

Step-by-step explanation:

Long leg = radical of 3

Short leg = 1

Hypotenuse= 2

Increase in the level of confidence and increase in the population standard deviation will increase the width of a confidence interval and increasing the sample size will decrease the width of a confidence interval.

(a) Increasing the level of confidence will increase the width of a confidence interval. This is because a higher level of confidence requires a larger margin of error, which in turn increases the width of the interval.

(b) Increasing the sample size will decrease the width of a confidence interval. This is because a larger sample size leads to a more precise estimate of the population parameter, which reduces the amount of uncertainty and therefore narrows the interval.

(c) Increasing the population standard deviation will increase the width of a confidence interval. This is because a larger standard deviation indicates greater variability in the population, which in turn requires a larger margin of error and therefore widens the interval.

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The measure of m∠EFB is 68 degrees and the length of AC is 32 units

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

The triangle

The sum of angles in a triangle is 180

So, we have

∠EFB = 180 - 90 - 22

∠EFB = 68

By the congruent theorem, we have

AC = 2 *(6 + 10)

When evaluated, we have

AC = 32

Hence, the length of AC is 32 units

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Answer:

Step-by-step explanation:

The perimeter of a quarter circle can be calculated by adding the length of the arc and the two radii that make up the quarter circle.

The length of the arc of a quarter circle is given by (πr)/2, where r is the radius of the quarter circle and π is approximately 3.142 (as given in the question).

So, for a quarter circle with a radius of 7 cm, the length of the arc would be:

(πr)/2 = (3.142 x 7)/2 = 10.997 cm (rounded to 3 decimal places)

The two radii that make up the quarter circle are each equal to the radius of the quarter circle, so the total length of the two radii would be:

2r = 2 x 7 = 14 cm

Therefore, the perimeter of the quarter circle would be:

10.997 cm + 14 cm = 24.997 cm (rounded to 3 decimal places)

So the perimeter of the quarter circle is approximately 24.997 cm. The digits given by the calculator will depend on the specific calculator used.

The constant of proportionality for the work done when lifting an object is given as follows:

k = 14.78.

A proportional relationship is a type of relationship between two quantities in which they maintain a constant ratio to each other. This means that if one quantity is multiplied by a certain factor, the other quantity will also be multiplied by the same factor.

The equation that defines the proportional relationship is given as follows:

y = kx.

In which k is the constant of proportionality, representing the increase in the output variable y when the constant variable x is increased by one.

The work, W (in joules), done when lifting an object is jointly proportional to the product of the mass, m (in kilograms), of the object and the height, h (in meters), that the object is lifted, hence the equation is given as follows:

W = khm.

The work done when a 100-kilogram object is lifted 1.5 meters above the ground is 2116.8 joules, the the constant is given as follows:

150k = 2216.8

k = 2216.8/150

k = 14.78.

The problem asks for the constant of the proportional relationship.

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the equation to represent the number of hours, t, the bird will take to fly d kilometers at this rate is t = 2d / 71.2

We can use the formula for distance, rate, and time:

distance = rate x time

We can rearrange this formula to solve for time:

time = distance / rate

If we substitute the given distance of 71.2 km and rate of (71.2 km / 2 hours) into this formula, we can find the time it took the bird to fly 71.2 km:

time = 71.2 km / (71.2 km / 2 hours) = 2 hours

Now, we can use the same formula to find the time it will take the bird to fly d kilometers:

time = d km / (71.2 km / 2 hours) = 2d / 71.2 hours

Therefore, the equation to represent the number of hours, t, the bird will take to fly d kilometers at this rate is t = 2d / 71.2

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1)  The total number of computers they would buy if they get 10 notebooks and 19 desktop computers is: 54 computers

2) The total number of computers they would buy if they get n notebooks and d desktop computers is: (350/n) + (375/n)

The parameters given are:

Cost of notebook Computers = $350

Cost of Desktop desktop = $375

Thus, if they  get 10 notebooks and 19 desktop computers, then:

Total number of computers is:

(350/10) + (375/19) = 35 + 19

= 54 computers

(375/19) was approximated to 19 because we must use a whole number and not a decimal.

If they buy n notebooks and d desktop computers, then total computers will be:

(350/n) + (375/n)

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Answer: If it is pythagorean theorem than it is 10

Step-by-step explanation:

8^2+6^2=100

Squareroot of 100 is 10

An equation to find the fraction of punch that is either pineapple juice or orange juice is 1/6 + 1/9 = 5/8.

In Mathematics, a fraction simply refers to a numerical quantity (numeral) which is not expressed as a whole number. This ultimately implies that, a fraction is simply a part of a whole number.

Based on the information provided about the pineapple juice and orange juice, an equation that can be used for determining the fraction of punch that is either pineapple juice or orange juice is as follows;

Fraction = 1/6 + 1/9

Fraction = 3/18 + 2/18

Fraction = 5/18

In this context, we can reasonably infer and logically deduce that exactly 5/18 of the punch is either pineapple juice or orange juice.

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Complete Question:

About 1/6 of a fruit punch is pineapple juice. About 1/9 of the punch is orange juice. Write and solve an equation to find the fraction of the punch that is pineapple juice or orange juice.

The size of the angle PRQ is 300 degrees.

What is congruent?

The term “congruent” means exactly equal shape and size. This shape and size should remain equal, even when we flip, turn, or rotate the shapes.

In a regular 12-sided polygon, each interior angle has a measure of:

(12 - 2) × 180° / 12 = 150°

Since PR is diagonal, it divides the 12-sided polygon into two congruent triangles. Therefore, the angle PQR is half of the angle PRQ.

Let x be the measure of angle PRQ. Then we have:

x + 150° + 150° = 180° (sum of angles in triangle PQR)

Simplifying the equation, we get:

x = 180° - 150° - 150° = -120°

However, since x is an angle in a triangle, it must be positive. Therefore, we take the supplement of x, which is:

180° - x = 180° - (-120°) = 300°

Hence, the size of the angle PRQ is 300 degrees.

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