A toy manufacturer needs a piece of plastic in the shape of a right triangle with the longer leg 5 cm more than the shorter leg and the hypotenuse 10 cm more than the shorter leg. How long should the sides of the triangle​ be?

Answer:

1.5 * 7 that is the answer of the question

Answer:

Slope curve is the gradiient

Step-by-step explanation:

Gradient equation is m = change in y over change in x

Therefore the first answer is correct

The index form is solved to give 1/z^13/12

Index forms are described as mathematical forms used to represent numbers too large or small in more proper ways.

Other names for index forms are scientific notations and standard forms.

They are represented as numbers raised to a variable or an exponent.

The rules of index forms are;

From the information given, we have;

z^-1/4/ z1/2 z1/3

Add the exponents

z^-1/4 / z  5/6

Subtract the exponents

z^ -6 - 20 /24

z^-26/24

1/z^13/12

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By using the Pythagorean theorem we conclude that the rope net is about 40.31 feet long.

The Pythagorean Theorem is a fundamental theorem in mathematics that describes the relationship between the sides of a right triangle.

We can use the Pythagorean theorem to solve this problem.

Let's consider the rope net as the hypotenuse of a right triangle, and the horizontal distance from the base of the platform to the starting point of the rope net as one leg of the triangle.

The other leg of the triangle is the vertical height of the platform.

Using the Pythagorean theorem, we have:

length of rope net = √(horizontal distance² + vertical height²)

Substituting the given values, we get:

length of rope net = √(35² + 20²)

= √(1225 + 400)

= √1625

= 40.31 feet (rounded to two decimal places)

Therefore, the rope net starts 35 feet from the platform base, and the platform is 20 feet high and the rope net is about 40.31 feet long.

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Step-by-step explanation:

The volume of a cube is similar to that of a rectangular prism, the volume equals the length times width times height, however because it’s a cube all the measurements are the same, in this case 7 inches. So volume equals 7^3, thus equaling 343 inches cubed. Hope this helps!

The empirical probability that the student studied in E, B, and F is approximately 0.635.

The total number of students who studied abroad in the 2008-2009 school year is not given, so we cannot calculate the empirical probability directly. However, we can assume that the sample size is very large, and therefore the empirical probability of selecting a student who studied in each of the destinations listed is approximately equal to the relative frequency of students who studied in each of the destinations.

The total number of students who studied abroad in these 10 destinations is:

14,012 + 27,731 + 11,011 + 10,722 + 10,650 + 8,311 + 6,407 + 6,222 + 5,779 + 5,274 = 106,939

Therefore, the empirical probability of selecting a student who studied in E, B, and F is approximately:

≈ (14,012 + 27,731 + 11,011) / 106,939 ≈ 0.635

So, the empirical probability that the student studied in E, B, and F is approximately 0.635.

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The absοlute fοrm οf the given inequality is |x+1|>6.

In mathematics, inequality is  a statement οf an οrder relatiοnship that is a relatiοnship between twο values that are nοt equal,—greater than, greater than οr equal tο, less than, οr less than οr equal tο—between twο numbers οr algebraic expressiοns. Such as 7<9 οr 5>3 etc.

Given inequality is

x<−7 οr x>5

The distance between -7 and 5 is

5- (-7) = 5+7= 12

Dividing that by 2 we get,

12/2 =6

It is the c value

We use the greater than since we have an οr

|x−b|>6 ----------------- (1)

Substituting  a value  x=5 in equatiοn (1) with an equals sign tο determine b we get

5-b =6

b= -1

The absοlute fοrm οf the given inequality is |x+1|>6

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Using the slope of curve,

1. If x=0.5, then the slope is: 0.3333.

2. If x=0.9, then the slope is: 0.2632

3. If x=0.99, then the slope is: 0.2513

4. If x=0.999, then the slope is: 0.2501

5. If x=1.5, then the slope is: 0.2

6. If x=1.1, then the slope is: 0.2381

7. If x=1.01, then the slope is: 0.2488

8. If x=1.001, then the slope is: 0.2499

Define a curve?

Three easy procedures can be used to compute the area under the curve. The curve's equation (y = f(x)), the boundaries within which the area is to be determined, and the axis encompassing the area must first be known.

The curve is given as:

y = x/1+x

Point, P = (1, 1/2) lies on the curve.

Point, Q = (x, x/1+x) is an arbitrary point on the curve.

The slope of the secant line PQ is:

y2-y1/x2-x1

= x-1/2(x+1) × 1/(x-1)

=1/2(x+1)

1. If x=0.5, then the slope is:

1/2(0.5+1)

= 1/3

= 0.3333

2. If x=0.9, then the slope is:

1/2(0.9+1)

= 1/3.8

= 0.2632

3. If x=0.99, then the slope is:

1/2(0.99+1)

= 1/3.98

= 0.2513

4. If x=0.999, then the slope is:

1/2(0.999+1)

= 1/3.998

= 0.2501

5. If x=1.5, then the slope is:

1/2(1.5+1)

= 1/5

= 0.2

6. If x=1.1, then the slope is:

1/2(1.1+1)

= 1/4.2

= 0.2381

7. If x=1.01, then the slope is:

1/2(1.01+1)

= 1/4.02

= 0.2488

8. If x=1.001, then the slope is:

1/2(1.001+1)

= 1/4.002

= 0.2499

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Answer:

360

Step-by-step explanation:

.05n = 18

n = 360 campers

In linear equation, $-0.0143 is the rate of change of the quantity demanded when the price increases .

What in mathematics is a linear equation?

An mathematical equation with only 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.

the demand function:

x² + p² = 2450

Differentiating both sides of the demand function with respect to time t using the chain rule, we get:

  2x * dx/dt + 2p * dp/dt = 0

We also know that at the point where the price is $7, p = 7 and x satisfies:

   x² + p² = 2450

Substituting p = 7 into the demand function, we get:

  x² + 7²  = 2450

     x² = 2450 - 49x²

       x = 49

substitute x = 49, p = 7, and dp/dt = $0.10 into the differentiated demand function and solve for dx/dp

     2x * dx/dp + 2p * dp/dx = 0

  2(49) * dx/dp + 2(7) * 0.10 = 0

   98 dx/dp + 1.40 = 0

  dx/dp = $-0.0143

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The answer is "a. five eighths; the probability that a day fell on a weekend given that it is sunny".

What is probability?

Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how probable it is.

We can use Bayes' theorem to find P(W|S), the probability that a day fell on a weekend given that it is sunny:

P(W|S) = P(S|W) * P(W) / P(S)

We are given that 15 days were sunny out of a 30-day month, so P(S) = 15/30 = 1/2.

Out of the 30 days, 8 fell on a weekend, so P(W) = 8/30 = 4/15.

We are also given that 5 of the sunny days fell on a weekend, so P(S|W) = 5/8.

Substituting these values, we get:

P(W|S) = (5/8) * (4/15) / (1/2) = 5/12

Therefore, the answer is "a. five eighths; the probability that a day fell on a weekend given that it is sunny".

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The value of t for a t-distribution with 10 degrees of freedom such that the area between -t and t equals 90% is 1.812.

To find the value of t for a t-distribution with 10 degrees of freedom such that the area between -t and t equals 90%, we can use a t-table.

Using a t-table, we can find the t-value that corresponds to a 5% area in the upper tail of the distribution, since the area between -t and t is 90% (leaving 10% in the tails).

For a t-distribution with 10 degrees of freedom, the critical value for a 5% area in the upper tail is 1.812. Check the attached image.

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The true statement is that the mode of the set of scores is 96. The solution has been obtained by using measures of central tendency.

What are measures of central tendency?

A summary measure called a measure of central tendency, also known as a measure of centre or a measure of central placement, aims to characterise the entirety of a set of data with a single number that corresponds to the centre or centre of its distribution.

We are given scores as 96, 77, 82, 96, and 89.

So, from this we get

⇒ Mean = (96 + 77 + 82 + 96 + 89) ÷ 5

⇒ Mean = 440 ÷ 5

⇒ Mean = 88

Similarly,

Arranging the numbers, we get 77, 82, 89, 96, 96.

So, the median is 89.

Mode is 96 as it is appearing two times.

Hence, the third statement is the true statement.

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The correct option is (b) i.e. area of rectangle is [tex]x^{3} y^{4}[/tex].

What is rectangle?

The internal angles of a rectangle, which has four sides, are all exactly 90 degrees. the two sides come together at a straight angle  at each corner ,The rectangle differs from a square because its two opposite sides are of equal length.

Given : width of rectangle : xy

            length of rectangle : [tex]x^{2} y^{3}[/tex]

we know that,  area of rectangle = length × breadth

                                                      =  x²y³ × xy

Now, adding power of terms which has same base.    

we get, [tex]x^{3} y^{4}[/tex]                                                                

so, the correct option is (b).

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Step-by-step explanation:

50 tries experimentalprobabilities:

open :  2/50 = 1/25

closed  6/50 = 3/25

side :   42/50 = 21/25

Answer:

Open Side Up: 2/50 = 1/25 = 4%

Closed Side Up: 6/50 = 3/25 = 12%

Landing on Side: 42/50 = 21/25 = 84%

The list that shows the side lengths, in inches, of the triangle Riley drew is: 59/5, 57/5, 3/2

What is Triangle ?

A triangle is a polygon with three sides and three angles. It is one of the basic shapes in geometry and is commonly used in various fields such as engineering, physics, and architecture. The sum of the angles of a triangle always adds up to 180 degrees.

To find the side lengths of the triangle Riley drew, we need to multiply each of Jim's side lengths by the scale factor of ‡, which means multiplying by 3.

The side lengths of Jim's triangle, when written with common denominators, are:

3¼ = 13/4

4.9 = 38/10

5/10 = 1/2

Multiplying each of these by 3 gives:

13/4 * 3 = 39/4

38/10 * 3 = 114/10 = 57/5

1/2 * 3 = 3/2

So, the side lengths of the triangle Riley drew are:

39/4, 57/5, 3/2

We can simplify these fractions by finding a common denominator:

39/4 = 236/20

57/5 = 228/20

3/2 = 30/20

So, the side lengths of the triangle Riley drew, in inches, are:

236/20, 228/20, 30/20

Simplifying further by dividing each numerator by 4, we get:

59/5, 57/5, 15/10

Therefore, the list that shows the side lengths, in inches, of the triangle Riley drew is:

59/5, 57/5, 3/2

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Answer:

To find the cost of filling Binaya's water tank, we need to calculate the volume of the tank first. The tank is in the shape of a cylinder surmounted by a hemisphere, so we can find the volume by calculating the volumes of the cylinder and hemisphere separately and adding them together.

The formula for the volume of a cylinder is V_cyl = πr^2h, where r is the radius and h is the height.

Given that the internal radius of the tank is 90 cm and the total height is 3.8 m, we convert the height to cm to match the radius unit and get 380 cm in height.

So, the volume of the cylinder part of the tank will be V_cyl = π(90)^2(380) = 9147600 cm^3.

The formula for the volume of a hemisphere is V_hem = (2/3)πr^3, where r is the radius of the hemisphere. By halving the internal radius of the cylinder, we get the radius of the hemisphere as 45 cm.

So, the volume of the hemisphere part of the tank will be V_hem = (2/3)π(45)^3 = 95325π cm^3.

The total volume of the tank will be the sum of the volumes of the cylinder and hemisphere:

V_total = V_cyl + V_hem = 9147600 + 95325π = 9457589.25 cm^3.

To convert this volume to litres, we divide by 1000:

V_total_l = 9457.59 l.

The cost of filling the tank with water at the rate of 20 paisa per litre will be:

Cost = 9457.59 x 0.20 = 1891.52 paisa = 18.92 rupees (rounded to two decimal places).

Therefore, it will cost Binaya 18.92 rupees to fill his water tank with water at the given rate.

Answer:

We do not know if the triangles are congruent because we have no information about congruent sides.

Answer:

value of ∅ = 67.5°

Step-by-step explanation:

cos135° = [tex]-\frac{1}{\sqrt{2} }[/tex]

so 2Ф = 135

Ф = [tex]\frac{135}{2} = 67.5[/tex]°

Answer:

Min: 85

Q1: 95

Median: 110

Q3: 120

Max: 125

length of side AB is approximately 5.74 units when rounded to the nearest hundredth

To find the value of x in triangle ABC,

Applying the law of sines in triangle ABC, we have:

sin(A)/AB = sin(B)/AC

where AB is the length of side AB, and sin(A) and sin(B) are the sines of angles A and B, respectively.

Substituting the given values, we get:

sin(36)/AB = sin(180-36- angle C)/7

simplifying the equation, we get:

AB = 7sin(36)/sin(C)

To find the angle C, we can use the fact that the sum of the angles in a triangle is 180 degrees:

angle C = 180 - angle A - angle B

Substituting the given values, we get:

angle C = 180 - 36 - 90 = 54 degrees

Substituting the values of sin(36) and sin(54) into the equation for AB, we get:

AB = 7sin(36)/sin(54) = 5.74 (rounded to the nearest hundredth)

Therefore, the length of side AB is approximately 5.74 units when rounded to the nearest hundredth.

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1. Statistic, 2. Data, 3. Pοpulatiοn, 4. Variable, 5. Parameter, 6. Sample

Statistic:  

A statistic is a numerical value that describes a characteristic οf a sample.

Parameter: A parameter is a numerical value that describes a characteristic οf a pοpulatiοn.

Data: Data refers tο the infοrmatiοn cοllected in a study οr experiment. This can include numbers, text, οr οther fοrms οf infοrmatiοn that can be analyzed.

Variable: A variable is any characteristic οr attribute that can take οn different values in a study οr experiment.

Sample: A sample is a grοup οf individuals οr οbjects selected frοm a larger pοpulatiοn fοr the purpοse οf cοnducting a study οr experiment. The characteristics οf the sample are used tο make inferences abοut the larger pοpulatiοn.

Pοpulatiοn: A pοpulatiοn is the entire grοup οf individuals οr οbjects that a study οr experiment is cοncerned with. The characteristics οf the pοpulatiοn are οften οf interest, but it is usually nοt feasible tο cοllect data frοm every member οf the pοpulatiοn, sο a sample is used instead.

Here we have

A rancher is interested in the average age that a cοw begins prοducing milk.

The fοllοwing vοcabulary can be matched as fοllοws

1. The average age fοr the 62 milk cοws as they first prοduced milk - Statistic

2. The list οf the 62 ages - Data

3. All milk cοws - Pοpulatiοn

4. The age when a milk cοw first prοduced milk - Variable

5. The average age that all milk cοws are when they first prοduce milk - Parameter

6. The 62 milk cοws that were οbserved by the rancher: Sample

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Answer:

AA Similarity

i hope this helps :)

Since trapezoid ABCD is inscribed in circle O, we know that angles A and D are right angles. We also know that the measure of angle ABD is equal to half the measure of arc AC. Since DC is a diameter of the circle, arc AC is a semicircle and thus has a measure of 180 degrees. Therefore, angle ABD has a measure of 90 degrees.

We also know that the sum of the measures of the angles in a trapezoid is equal to 360 degrees. Therefore, we can set up the following equation:

mAB + mBC + mCD + mDA = 360

Substituting the given values, we get:

80 + mBC + 90 + 90 = 360

Simplifying, we get:

mBC = 100

Therefore, mBC is equal to 100 degrees.

The true statement about the value of a in comparison to 0 and 1 is that it is a real number between 0 and 1.

A graph of y = f⁻¹(x) is shown below.

An equation for f⁻¹(x) is [tex]y=\frac{1}{a^x}[/tex].

For any given function, y = f(x), if the output value (range or y-value) is decreasing when the input value (domain or x-value) is increased, then, the function is generally referred to as a decreasing function.

By critically observing the graph of f(x), we can logically deduce that [tex]a^x[/tex] is positive for all values of x and as such, all values of a must also be positive:

0 < a

Additionally, the exponential function [tex]a^x[/tex] represent a decreasing function, so for any values of x, we have:

[tex]a^x > a^{x+1}[/tex]

1 > a

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Answer:

The student made a mistake when squaring -4.

-4 * -4 = 16.  Had the expressions said -x^2, then the answer would indeed be -16 since -1 *(-4*-4) = -16

Furthermore, since the answer is 16, you'd do (16 - 7) ^3, which equals (9)^3, which is 729 and not -12,167

Answer:

x=1

Step-by-step explanation:

To solve this equation, you must substitute. The equation for y is given. To use substitution, you have to put the y equation into the second one. In this case it would look something like this:

2(3x-4)=6x-8

(distribute)

6x-8=6x-8

(add 8)

6x=6x

(divide by 6)

x=x

In this circumstance, x is equal to 1.

So the equation in the form y=kx is: y = 180,000x, where y is the cost in dollars and x is the length of the commercial in seconds.

In mathematics, an equation is a statement that asserts the equality of two expressions. It typically consists of two expressions separated by an equal sign, with the expression to the left of the equal sign indicating the left-hand side of the equation, and the expression to the right of the equal sign indicating the right-hand side of the equation. Equations can be used to describe relationships between variables, to solve problems, and to model real-world phenomena.

Here,

a. Yes, the cost of the commercials is proportional to the length of time the commercial aired.

b. To find the cost of a commercial in dollars per second, we need to divide the cost by the length of the commercial in seconds. Using the given values, we get:

For a 15-second commercial: $2,700,000 ÷ 15 = $180,000 per second

For a 60-second commercial: $10,800,000 ÷ 60 = $180,000 per second

For a 90-second commercial: $16,200,000 ÷ 90 = $180,000 per second

For a 120-second commercial: $21,600,000 ÷ 120 = $180,000 per second

We can see that the cost per second is constant at $180,000. So the equation in the form y=kx is:

y = 180,000x, where y is the cost in dollars and x is the length of the commercial in seconds.

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Answer: A

Step-by-step explanation:

You can expect to run out of cash on approximately 39.45% of the days in a month when withdrawing $8,350 every day.

To determine the percentage of days in a month where you can expect to run out of cash, we'll need to consider the following terms: daily withdrawal, monthly cash usage, and average days in a month.

1. Daily withdrawal: This is the amount of money you withdraw from the ATM each day. In this case, you withdraw $8,350 every day.

2. Monthly cash usage: This is the total amount of money you will withdraw in a month. To calculate this, multiply the daily withdrawal by the number of days in a month. Since the average number of days in a month is approximately 30.42 (365 days in a year / 12 months), the monthly cash usage would be $8,350 x 30.42 ≈ $253,507.

3. Average days in a month: As mentioned earlier, this is approximately 30.42 days.

Now, we need to determine the number of days you would run out of cash. To do this, divide your monthly budget by the daily withdrawal amount. Let's assume you have a budget of $100,000:

Days without cash = $100,000 / $8,350 ≈ 11.98 days.

Since you can't have a fraction of a day, round it up to 12 days.

4. Calculate the percentage: To find the percentage of days you would run out of cash, divide the number of days without cash by the average number of days in a month and multiply by 100:

Percentage = (12 days / 30.42 days) x 100 ≈ 39.45%.

So, you can expect to run out of cash on approximately 39.45% of the days in a month when withdrawing $8,350 every day.

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