3. consider all triangles formed by lines passing through the point ( 8 9 , 3) and both the x- and y-axes. find the dimensions of the triangle with the shortest hypotenuse.

It is not possible to determine the area of square 3 based on the information given. The area of a square is determined by its side length, which is not mentioned in the problem. In order to find the area of a square, you need to know the length of at least one side. The perimeter of a square, which is the total length of all its sides, is not sufficient to determine the area of the square. You would need to know the side length of square 1 in order to calculate its area.

Answer:400

Step-by-step explanation:

Answer:

So, it will take between 4 and 5 bags of quickrete to fill the tube.

Step-by-step explanation:

To find the volume of the sonotube, you can use the formula for the volume of a cylinder: V = πr^2h, where r is the radius of the tube and h is the height.

First, you need to find the radius of the tube. The diameter of the tube is 10 inches, so you can divide that by 2 to get the radius: r = 10 inches / 2 = 5 inches.

Then, you can plug the radius and height into the formula to find the volume of the tube: V = πr^2h = π(5 inches)^2(48 inches) = about 235.61 inches^3.

To find the number of bags of quickrete you will need to fill the tube, you need to convert the volume of the tube to cubic feet and then divide by the number of cubic feet in a bag of quickrete.

First, you can convert the volume of the tube to cubic feet by dividing by 1728 (the number of cubic inches in a cubic foot): V = 235.61 inches^3 / 1728 inches^3/ft = about 0.14 cubic feet.

Then, you can divide this volume by the number of cubic feet in a bag of quickrete to find the number of bags you need: 0.14 cubic feet / (1 cubic foot / 30-40 bags) = about 4-5 bags.

So, it will take between 4 and 5 bags of quickrete to fill the tube.

Answer:

Step-by-step explanation:

The rate of hiking is 4 miles per hour.  The rate of driving is 40 miles per hour.

What is the mile?

Mile, any of various units of distance, such as the statute mile of 5,280 feet (1.609 km). It originated from the Roman mile passus, or “thousand paces,” which measured 5,000 Roman feet.

We have given,

A camper traveled 80 miles to a destination for recreation before doing a 4-mile stroll through the woods. The camper's speed while driving was ten times that of the hiker. Three hours were spent driving and hiking together.

We have to determine the camper's hiking speed.

We know that,

Let x represent the increasing rate and 10x represent the driving rate

Time equation is

80/10x + 4/x = 3

Simplify

8/x + 4/x = 3

12/x = 3

x = 12/3

x = 4

Therefore, Driving is done at a 40 mph speed when a camper traveled 80 miles to a destination for recreation before doing a 4-mile stroll through the woods.

Hence, the rate of hiking is 4 miles per hour.  The rate of driving is 40 miles per hour.

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If you made a pie and then ate two slices of it, the first pie would be missing two slices of pie. If you then made two more slices of pie for another pie, the first pie would be missing a total of four slices of pie. This is because you took two slices of pie from the first pie and added them to the second pie, leaving the first pie with two fewer slices than it originally had.

Answer:

The first pie would be missing four slices in total

Step-by-step explanation:

If you make a pie and then eat two slices of it, there would be two missing slices from the first pie. If you then make two more slices of pie for another pie, the first pie would be missing a total of four slices. The first pie would be missing four slices in total.

The values of the expression (1)  (r*s)(x) is 4x²+22x+10 (2) (r-s)(x) is -3x +3 (3) (r+s)(1) is 5x +7

The given parameters that will help us to calculate the values are

r(x) = x+5

s(x) = 4x +2

(1)  r*s(x) will be

(x+5)(4x+2)

Opening the brackets we have

4x²+2x+20x+10

= 4x²+22x+10

(2) (r-5)(x)

Putting the values of r and s

(x+5)- (4x+2)

Open the brackets to have

x+5-4x-2

Collecting like terms to get

-3x+3

(3) (r+s)(x)

By substitution we have

x+5+4x+2

⇒5x +7

In conclusion the values of the expressions are (1)  (r*s)(x) is 4x²+22x+10 (2) (r-s)(x) is -3x +3 (3) (r+s)(1) is 5x +7

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The solutions to the system of equations 2x + y = 3 and y - 3 = 2x - 2 are (1,5) and (-2,-1).

A mathematical statement that has two expressions with equal values separated by the symbol "equal to" is called an equation. Consider the formula 3x + 5 = 15. Different types of equations exist, including linear, quadratic, cubic, and others. Let's read this article to learn more about math equations.

The definition of an equation in algebra is a mathematical statement proving the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 has the two expressions 3x + 5 and 14 that are separated by the 'equal' sign.

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If the mean is 8.5 minutes and the variance is 9 minutes then the upper confidence limit is 9.3765  .

In the question ,

it is given that ,

the number of sales person in the random sample (n) = 45 ,

the mean = 8.5 minutes

the variance is = 9 minutes .

So , the standard deviation is = 3.

For the 95% confidence interval the level of significance (α) is 0.05 .

So , α/2 = 0.05/2 = 0.025 .

So , from Z table ;

the value of [tex]Z_{\frac{\alpha }{2} }[/tex] is = 1.96 .

The formula for the confidence interval is

= [ mean ±  [tex]Z_{\frac{\alpha }{2} }[/tex](SD/√n)]

Substituting the values from above ,

we get ,

= [8.5 - 1.96*0.4472 , 8.5 + 1.96*0.4472]

Simplifying further ,

we get ,

= [ 7.6235 , 9.3765 ]

Therefore , the upper limit of the 95% confidence interval is 9.3765  .

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The value of the function at -4 is f(-4) = -14.

What is the value of a function?

When the variables and constants in a mathematical expression are given values, the outcome of the computation it describes is the expression's value. The quantity that the function assumes for these argument values is the value of a function, given the value(s) assigned to its argument(s).

Given:

f(x) = 2x - 6

We have to find the value of f(-4).

So, plug x = -4 in the above equation.

Above equation becomes,

f(-4) = 2(-4) - 6

f(-4) = -8 - 6

f(-4) = -14

Hence, the value of the function at -4 is f(-4) = -14.

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The features of the linear function in this problem are given as follows:

The slope of a linear function represents the rate of change of the output variable y relative to the input variable x.

Hence, if we are given two points in a linear function, the slope is calculated as the division of the change in y by the change in x.

The two points for the function in this problem are given as follows:

(0, -4) and (2,5).

Hence the slope of the function is calculated as follows:

m = (5 - (-4))/(2 - 0) = 9/2 = 4.5.

The intercept of a linear function is given by the value of y when the graph of the function crosses or touches the y-axis, that is, the value of y when x = 0. One point for this problem is (0,-4), hence the intercept is given by y = -4.

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If figure A is a scale image of figure B. The value of x will be 72.

The ratio among comparable dimensions of an object and a model with that object is known as an exponent in algebra. The replica will be larger if the scale factor is a whole number. The duplicate will be lowered if the step size is a fraction.

It is given that, Figure A is a scale image of Figure B.

We have to find the value of x, which is obtained by taking the ratio of the sides.

Since figure A is a scale image of figure B, there is a proper scale factor for the given data which is obtained by the ratio.

24/20=x/60

x=(60×24) / 20

x=72

Thus, if figure A is a scale image of figure B. The value of x will be 72.

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The standard deviation of X is $2.00.

Probability is the likelihood that a specific occurrence will occur. Probabilities can be written as proportions with a 0 to 1 or 0% to 100% range.

Let X be the amount one wins. If the die is 4 or 5, the amount one wins is $1. If the die is 6, the amount one wins is $4. If the die is 1, 2, or 3, the amount is $0. Then, the probability of winning from 1 to 6 is 1/6.

The value of the expected mean (μ) is,

[tex]\begin{aligned}\mu&=\sum X P(X)\\&=1\times \frac{1}{6}+1\times \frac{1}{6}+4\times \frac{1}{6}+0\times\frac{1}{6}+0\times\frac{1}{6}+0\times\frac{1}{6}\\&=\frac{6}{6}\\&=1\end{aligned}[/tex]

Therefore, the standard deviation (σ)is [tex]\begin{aligned}\sigma&=\frac{\sum(X-\mu^2)}{n}\\&=\frac{(1-1)^2+(1-1)^2+(4-1)^2+(0-1)^2+(0-1)^2+(0-1)^2}{6}\\&=\frac{12}{6}\\&=2\end{aligned}[/tex]

The answer is $2. The correct option is option E.

The complete question is -

In a particular game, a fair die is tossed. If the number of spots showing is either 4 or 5 you win $1, if the number of spots showing is 6 you win $4, and if the number of spots showing is 1, 2, or 3 you win nothing. Let X be the amount that you win. Use Scenario 6-2. Which of the following is the standard deviation of X? A. $1.00 B. $1.35 C. $1.41 D. $1.78 E. $2.00

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Answer:

Below

Step-by-step explanation:

To find the area, you need to multiply L x W....so find those first

2 ( L + W) = 36 m

2 * ( W+2    +  W ) = 36 m

4W + 4 = 36  m

W = 8 m     then  L = 10  m

8 m  x 10 m  = 80 m^2

Answer:27,299

Step-by-step explanation:

45 people used credit card on that particular day , this could be found out using simplified multiplication.

What is proportion?

A quantitative relation is an ordered try of numbers a and b, written a / b wherever b doesn't equal zero.

A proportion is an equation within which 2 ratios ar set up to one another.

Main body:

We have been given that during one particular sales day, 75% of the store's customers paid with credit cards. There were 60 customers that day.

To find the number of people, who used credit card, we will find 75% of 60.

The number of people who used credit card = (75 / 100 )* 60

The number of people who used credit card = 0.75 *60

The number of people who used credit card = 45

Therefore, 45 people used credit card on that particular day.

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The required age of Liza's sister is given as 6 years.

Given that,
Liza is one year older than her sister. In four years she will be 3 times as old as she is now. How old is her sister now is to be determined.

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,

Here,
Let the age of Liza be x and of her sister be y,
According to the question,
x = y + 1
After 4 years,
4 + (y + 1) = 3(y + 1)
5 + y = 3y + 1
y = 2
The age of her sister now,
y = 2 + 4 = 6 years.

Thus, the required age of her sister is given as 6 years.

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To Bisect the line segment CD, the next step is option B. Swing an arc on both sides of line segment CD.

Bisection is a process of dividing a given line, or angle into two equal parts or measures respectively. This could either be a line bisector or an angle bisector as the case may be.

Thus to bisect the line CD, the following steps are required:

The next step for Ian is to swing an arc on both sides of line segment CD i.e option B.

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Answer:

b

Step-by-step explanation:

took test

95% confidence interval for the true mean breaking strength of the white wood is (71.66 MPA, 78.74 MPA)

The result above means that the lower limit of the true mean breaking strength of the white wood is 69.89 MPA and the upper limit is 81.51 MPA.

The definition says, "A confidence interval is a range of values ​​derived from a sample statistic that likely includes the value of an unknown population parameter."

To calculate the confidence interval, we need to know three parameters of the sample: the mean (average value) μ, the standard deviation σ, and the sample size n (number of measurements). Then you can calculate standard error and tolerance using the following formulas:

                      standard error = σ/√n

Given in the question:

Confidence interval = mean + or - Error margin (E)

Mean = 75.2 MPA

Standard deviation = 8.6 MPA

Sample size, n = 25

Now,

Degree of freedom = n - 1 = 25 - 1 = 24

Confidence level (C) = 95% = 0.95

Significance level = 1 - C

                              = 1 - 0.95

                              = 0.05 = 5%

Therefore, t-value corresponding to 24 degrees of freedom and 5% significance level is 2.06

Again,

E = t × sd/√n

  = 2.06 × 8.6/√25

  = 2.06 × 1.72

  = 3.54 MPA

Lower limit = Mean - E

                  = 75.7 - 5.81

                  = 69.89 MPA

Upper limit = Mean + E

                   = 75.7 + 5.8

                   = 81.51 MPA

95% confidence interval is (69.89 MPA, 81.51 MPA)

The result means that the true mean breaking strength of the white wood is between 69.89 and 81.51 MPA.

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The sum of the series is 25/3

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

5, 2, 4/5, ....

The sum of the series to infinity is

Sum = First term/1 - common ratio

In this, we have

First term = 5

common ratio = 2/5

So, we have

Sum = 5/(1 - 2/5)

Evaluate

Sum = 25/3

Here, we have

Initial population, a = 79000

Rate = 5%

An exponential function is represented as

P(x) = a *(1 + r)^x

So, we have

P(x) = 79000 *(1 + 5%)^x

In 2003. we have

x = 2003 - 1990 = 13

So, we have

P(13) = 79000 *(1 + 5%)^13

Evaluate

P(13) =148966

This means that

P(x) = 3a

So, we have

3a = a *(1 + 5%)^x

This gives

3 = (1 + 5%)^x

Take the logarithm of both sides

x = log(3)/log(1 + 5%)

Evaluate

x = 23

So, the year is

Year = 1990 + 23 = 2013

Hence, the year is 2013

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Answer:

it is using the Pythagorean theorem its basically a^2 + b^2 = c^2 watch videos on it, it will explain better

Hence, the current yield is [tex]1212.897[/tex]

What is the calculation?

A calculation is a deliberate mathematical process that transforms one or more inputs into one or more outputs or results.

Here given that,

Leah Long bought one bond of Vick Company for [tex]147[/tex]. The original bond was [tex]8.25 10[/tex].

So,

[tex]8.2510(147)=1212.897[/tex]

Hence, the current yield is [tex]1212.897[/tex]

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A rhombus is a quadrilateral with 4 equal sides. A shape with four sides of equal length. The shape has two sets of parallel sides and does not have right angles.

A rhombus is a closed two-dimensional plane figure. It is considered a special parallelogram, and because of its unique properties, it gets an individual identity as a quadrilateral. A rhombus is also called an equilateral quadrilateral since all of its sides are equal in length. The term ‘rhombus’ has been derived from the ancient Greek word ‘rhombos', which actually means something that spins

given that

a parallelogram with all sides of equal length without any right angles

A rhombus is a quadrilateral with 4 equal sides. A shape with four sides of equal length. The shape has two sets of parallel sides and does not have right angles.

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Answer: 84 feet and 10 ¼ inches

Step-by-step explanation:

An angle is formed when two lines or rays meet at a common point. The common point is known as the vertex.

An angle measurement can be defined as the measure of the angle formed by the two rays or arms at a common vertex. Angles are measures in degrees. There are many kinds of angles in geometry such as acute, obtuse, reflex, straight and right angle. Each angle has a different measure.

Angle relationship between the angles made when a line intersects a pair of parallel lines.

In geometry, there are five fundamental angle pair relationships such as complementary angles, supplementary angles, adjacent angles, linear pair, vertical angles.

The more familier unit of measurement is that of degrees. A circle is divided into 360 equal degrees, so that a right angle is 90°. Two angles are complementary if the sum of their measures is 90°.

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A Coordinate Plane is a two-dimensional plane formed by the intersection of two number lines. One of these number lines is a horizontal number line called the x-axis and the other number line is a vertical number line called the y-axis.

What is a Coordinate Plane?

A Coordinate Plane is a two-dimensional plane formed by the intersection of two number lines. One of these number lines is a horizontal number line called the x-axis and the other number line is a vertical number line called the y-axis.

Elements of the Coordinate Plane

Quadrants: The two number lines divide the coordinate plane into 4 regions. These regions are called Quadrants. The quadrants are denoted by roman numerals and each of these quadrants have their own properties.

Quadrant I: The upper right Quadrant is the first Quadrant denoted as Quadrant I. In this quadrant, the x-axis and the y-axis both have positive numbers.

Quadrant II: The upper left Quadrant is the second Quadrant denoted as Quadrant II. In this quadrant, the x-axis has its negative numbers and the y-axis has positive numbers.

Quadrant III: The bottom left Quadrant is the third Quadrant denoted as Quadrant III. In this quadrant, both the x-axis and the y-axis have negative numbers.

Quadrant IV: The bottom right Quadrant is the fourth Quadrant denoted as Quadrant IV. In this quadrant, the x-axis has positive numbers and the y-axis has negative numbers.

1.The coordinate plane was created hundreds of years ago. The system is commonly referred to as the Cartesian coordinate system because French mathematician René Descartes invented it.

2.The points on the x-axis have their y-coordinate 0 so the points on x-axis are represented as (x,0) and similarly the points on y-axis have their x-coordinate 0, so they are represented as (0,y).

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Answer:

Definition - The plane containing the "x" axis and "y" axis.

Examples - (4,9), (24,90), etc

Facts - The coordinate plane is a two-dimension surface formed by two number lines. One number line is horizontal and is called the x-axis. The other number line is vertical number line and is called the y-axis. The two axes meet at a point called the origin.

Step-by-step explanation:

Area: [tex]3.14*3^2=28.26 cm^2\\[/tex]

Circumference: [tex]2*3.14*3=18.84cm[/tex]

The worth of the CD at the end of the 5-year term would be = $3605.25

Annual interest is the amount of money that is being added to an primary capital of an investment or a property which increases with time.

The rate of annual interest = 5.3%

The time for the term = 5 years

The principal amount invested in the CD = $2,850

The simple interest = P×T×R/100

=2850×5×5.3/100

= 75525/100

= $755.25

Therefore, the worth of the CD at the end of the 5-year term would be =$2,850 + $755.25

= $3605.25

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Answer:

14/2

Step-by-step explanation:

We can write 7 as 7/1

Multiply the top and bottom by 2/2

7/1 * 2/2 = 14/2

We could multiply by any number over itself

7/1 * 3/3 = 21/3

This is an equivalent fraction

Answer:

See below

Step-by-step explanation:

Examples ( choose one)

14/2

7/1

21/3

98/14