if i break a stick of unit length into three random pieces, what is the expected length of the largest piece?

We can convert 162 cm to feet by multiplying by the conversion factor to get , 162 cm equivalent to 5.32 feet .

The length or the distance between two points is measured with the help of units such as : meter , centimeter , inches , feet .

We have to convert the length of 162 centimeter to feet ;

We know that , 1 centimeter is approximately equal to 0.0328 feet ;

So , the conversion factor is 0.0328 ;

So , for the conversion  we multiply the given length by 0.0328 ;

On multiplication we get ;

⇒ 162 centimeter = 162 × 0.0328 ;

⇒ 162 centimeter = 5.3136 feet .

Therefore , 162 cm is approximately equal to 5.32 feet .

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The highest 5% of all IQs in the N(100, 15) Normal model are bounded by a value of 124.68, while the lowest 30% are bounded by a value of 92.64. The middle 80% of IQs are bounded by values between 80.77 and 119.23.

In the Normal model N(100, 15):

The highest 5% of all IQs are bounded by a z-score of 1.645, which corresponds to a value of 100 + (1.645 * 15) = 124.68. This means that an IQ of 124.68 or higher is in the top 5% of all IQs in this model.

The lowest 30% of the IQs are bounded by a z-score of -0.524, which corresponds to a value of 100 + (-0.524 * 15) = 92.64. This means that an IQ of 92.64 or lower is in the lowest 30% of all IQs in this model.

The middle 80% of the IQs are bounded by z-scores of -1.282 and 1.282, which correspond to values of 100 + (-1.282 * 15) = 80.77 and 100 + (1.282 * 15) = 119.23, respectively. This means that IQs falling between 80.77 and 119.23 are in the middle 80% of all IQs in this model.

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Answer:

15.585 is the radius of the cone

The 1 1/2 cups divided by 2 is 0.75  cups

Division is the opposite of multiplication. If 3 groups of 4 are multiplied by 12, then dividing 12 into 3 equal groups yields 4 in each group when divided.

Dividend: The dividend is the number that is being divided in the division process.

Divisor: The number by which the dividend is being divided by is called the divisor.

Quotient: The quotient is a result obtained in the division process.

Remainder: Sometimes, we cannot divide things exactly. There may be a leftover number. That leftover number is called the remainder.

The relationship between these four parts can be expressed as follows:

Dividend = Divisor x Quotient + Remainder

The main purpose of sharing is to see how many equal groups form, or how many people belong to each group, when sharing equitably.

In the above example, to divide the 12 donuts into 3 similar groups, we need to place 4 donuts in each group. So dividing 12 by 3 gives 4.

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Suav deposits $450 every quarter into an account earning a quarterly interest rate of 2.225%. After 10 years, he would have $7,395 in the account to the nearest dollar.

The formula for calculating the future value (FV) of an investment is: FV = PV(1 + r/n)nt, where PV is the present value, r is the interest rate per period, n is the number of compounding periods per year, and t is the number of years.

In this problem, PV is $450, r is 2.225%, n is 4 (quarters in a year), and t is 10 years. Plugging these values into the formula gives us:

FV = 450(1 + 0.02225/4)4*10 = 450(1.0055625)40 = 450(2.7326) = $7,395

Therefore, after 10 years, Suav would have $7,395 in the account to the nearest dollar.

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The ratio of the time Thabo spent doing homework to the time he spent at school is 2:7.

Ratio refers to the relative size of a quantity compared to another.

Ratios are expressed as percentages, from 0% to 100%, as fractions, as proportions or decimals, from zero to one, and in ratio forms (:).

To compute the ratio as a decimal, it is the quotient of one quantity and another comparative quantity.

Activity                      Time

Sleeping                   8 hours

At school                  7 hours

Doing homework    2 hours

Playing sport            4 hours

Watching TV            2 hours

Eating                       1 hour

Total hours =        24 hours

Ratio of time doing homework to the time spent at school = 2:7

The sum of ratios = 9 (2 + 7)

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The shape of the cross section is circle from the following option given.

A cylinder has traditionally been a three-dimensional solid, one of the most basic of curvilinear geometric shapes.

When a cylinder is sliced parallel to its bases, the shape of the cross section will be a circle. This is because the bases of a cylinder are circular, and any plane that is parallel to the bases will intersect the cylinder in a circle of the same radius as the bases. Therefore, regardless of the position of the slice, the shape of the cross section will always be a circle.

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Explanation:

1 balloon needs 12 ft of string.

48 balloons need 48*12 = 576 ft of string.

Divide by 3 to convert from feet to yards. This is because 1 yard = 3 ft.

576 ft = 576/3 = 192 yards

Answer:

Step-by-step explanation:

of is *

20% is 1/5

1/5 *2000= 2000/5= 400

The shoreline is reduced by 0.5 feet every 10 years. Then the correct option is A.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

A group of scientists studied the amount of erosion at a beach. The scientist determined that the equation is given below.

y = -0.5 x + 26

Hence, The shoreline is reduced by 0.5 feet every 10 years. Then the correct option is A.

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scientists determined that the equation y=0.5x+26 models the amount of shoreline at the beach, y, in feet, x decades after 1950. Which statement is true based on the model

The shoreline is reduced by 0.5 feet   every 10 years.

The shoreline is increased by 0.5 feet  every 10 years.

The shoreline is reduced by 26 feet  every 10 years.

The shoreline is increased by 26 feet  every 10 years.

The conversied value of 152 centimetres in feet is equals to the 4.98 feet.

Unit conversion, by definition, is the conversion between different units and measurements of the same quantity done in the process of multiplication or division. In mathematics, conversion is the process of changing a value from one form to another, such as converting a value from inches to millimeters, for time minutes to hours, or other units.

How to convert centimeters to feet : 1 meter is a measure of length and equals approximately 3.28 feet.

152 meters = 152×3.28 feet = 498.56 feet --(1)

But we need to convert 152 centimeters to feet. So change meters to centimeters. As you know, 1 meter is 100 centimeters, so 152 meters = 15200 centimeters --(2). Now from equations (1) and (2),

15200 centimeters = 498.56 feet,

Divide both parts by 100,

=> 152 centimetres = 498.56/100 feet

= 4.98 feet

Hence required value is 4.98 feet.

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The initial position is the starting point, and the final position is the endpoint.

We proceed to explain the initial and final position:

For example, if an object starts at the 2 meter mark (initial position) and moves 3 meters to the right, its final position would be at the 5 meter mark.

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Answer:

42 meters

Step-by-step explanation:

The length of the factory floor will be 42 meters. This is found by multiplying the length of 0.3 meters by the scale factor of 140, which yields 42 meters.

Answer:

42 meters

Step-by-step explanation:

its correct :)

slides off the 0.86 m high counter and lands 1 m from the base. what was its initial speed ⇒ Ø = 56.87˚ beneath the horizontal

A. Suppose the horizontal component of the velocity is vx and the vertical is vy.

At first at t=0 (as the mug leaves the counter) the components are v0x and v0y.

v0y = 0 since the customer slides it horizontally so applied force is in the x component as it were.

The equations for horizontal and vertical shot movement are:

x = x0 + v0x t

y = y0 + v0y t - 1/2 g t^2 = y0 - 1/2 g t^2

Setting the beginning to be the end corner of the counter so that x0=0 and y0=0, thus:

x = v0x t

y = - 1/2 g t^2

Given esteem are: x=1.50m and y=-1.15m (y is negative since mug is going down)

1.50m = v0x t - - - - > v0x= 1.50/t

-1.15m = - (1/2) (9.81) t^2 - - - - - > t =0.4842 s

Working out for v0x:

v0x = 3.10 m/s

B. v0x is constant since there could be no other horizontal forces so, v0x=vx=3.10m/s

vy can be calculated from the recipe:

vy = v0y + at where a=-g (negative since going down)

vy = - gt = - 9.81 (0.4842)

vy = - 4.75 m/s

Presently to get the point beneath the horizontal, tan(90-Ø) = - vx/vy

tan(90-Ø )= 3.1/4.75

Ø = 56.87˚ beneath the horizontal

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The answer to the question is 17/140 fraction.

A fraction is a numerical expression that represents a part of a whole or a ratio of two numbers. It consists of two parts: a numerator (the number on top) and a denominator (the number on the bottom). For example, 3/4 is a fraction that represents 3 parts out of 4. It can also represent the ratio of 3 to 4.

To move the fraction to each box, you would need to multiply the denominator of the first fraction (10) by the numerator of the second fraction (14). The result is 140. Then, you would add the numerator of the first fraction (3) to the numerator of the second fraction (14), giving you 17. The answer to the question is 17/140.

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The number outcomes in the sample space is option (3) 64

In mathematics, combination is a way of selecting a group of objects from a larger set, where the order in which the objects are selected does not matter.

The number of outcomes in the sample space can be calculated by finding the total number of possible combinations of genders for the six children.

For each child, there are two possible genders: male or female. Therefore, the number of possible outcomes for one child is 2.

To find the total number of outcomes for six children, we need to multiply the number of possible outcomes for each child together:

2 × 2 × 2 × 2 × 2 × 2 = 64

Therefore, the correct option is (3) 64

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The TI-84 calculator can be used to find the p-value associated with a hypothesis test, given the test statistic and the degrees of freedom (df).

Here are the steps to find the p-value on a TI-84 calculator:

Press the "2nd" button and then the "VARS" button (which is above the "STAT" button). This will open the DISTR menu.

Select "3: tcdf" from the menu by scrolling down with the arrow keys and pressing "ENTER".

Enter the test statistic and degrees of freedom. For a two-tailed test, enter the test statistic with the appropriate sign (positive or negative) and enter a very large number (such as 100 or 999) for the second argument.

For a one-tailed test, enter the test statistic and select "1" or "2" for the third argument, depending on the direction of the test.

Press "ENTER" to calculate the p-value.

The result displayed on the calculator screen will be the p-value associated with the hypothesis test, based on the test statistic and degrees of freedom entered.

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The question is -

How to find the p-value from the TI-84 calculator?

This is a word problem and the value of the unknown number is equal to 5.5.

We can write algebraically the second question as 3(x - 1).

Simplifying fully 15xy ÷ 15xy = 1/y

Word problems are mathematical problems which involves the use of ordinary words, instead of mathematical symbols.

Let us represent the unknown number with the letter x so that we derive the equation;

2x - 2 = 9

we add 2 from both sides of the equation

2x - 2 + 2 = 9 + 2

2x = 11

divide through by the coefficient of x which is 2

2x/2 = 11/2

x = 5.5.

Using x as the unknown, we can write the statement in the second question as 3(x - 1).

15xy ÷ 15xy = 1/y

Therefore, the value of the unknown number for the word problem is equal to 5.5

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Answer:

in order from last to first

3y

(x-1)3

x2-2=9

Step-by-step explanation:

(I also included the image for your previous question))

Answer: 5, 6, 7, 8, 9, or the numbers 5-9 inclusive.

Step-by-step explanation: The Triangle Inequality Conjecture states that any two sides of a triangle added up will be larger than the third. To easily prove this, you can add the two smaller sides to see if it is bigger than the larger side. Using this conjecture, we can calculate that 5 works, 6 works, 7 works, 8 works (8 is larger than 7 so now we do 3+7), and 9 works.

The required reflection of the given figure across the line y = x is shown.

Transform the shapes on a coordinate plane by rotating, reflecting, or translating them. Felix Klein introduced transformational geometry, a fresh viewpoint on geometry, in the 19th century.

Here,
A figure on a coordinate plane is shown, and we have to determine the reflection of that figure across the line y = x,

In order to determine the reflection across the line y = x,
The Abscissa inside the line gets interchanged by the ordinate of the corresponding Absciss as.
(x, y) ⇒ (y, x)

Thus, the required reflection of the given figure across the line y = x is shown.

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Using the ratios we know that out of 102 cans, 34 cans will be of green beans that John will use.

In mathematics, a ratio shows how frequently one number appears in another.

For instance, the ratio of oranges to lemons in a fruit plate would be eight to six if there were eight oranges and six lemons.

Oranges make up 8:14 of the total fruit, whereas lemons make up 6:8 of the total fruit.

If you enter this into a calculator, the result will come out as 0.6 decimal.

In other words, 3/5 is equal to any two numbers that divide to provide the same result.

So, the total cans that John wants to use:
102

Then, the ratio of pumpkin to green beans:
4:2

Sum: 4+2 = 6

Then, out of 102 cans, the cans of green beans would be:

= 102 * 2/6

= 102 * 1/3

= 34

Therefore, using the ratios we know that out of 102 cans, 34 cans will be of green beans that John will use.

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An algebra over a field F is a vector space over F equipped with a bilinear operation called multiplication.

Let F be a field and let A be a vector space over F. An algebra over F is a triple (A, ×, 1) where × is a bilinear operation A x A -> A, and 1 is an element of A such that:

a × (b × c) = (a × b) × c for all a,b,c in A (associativity)

There exists an element 1 in A such that a × 1 = a = 1 × a for all a in A (existence of identity)

a × (b + c) = (a × b) + (a × c) and (a + b) × c = (a × c) + (b × c) for all a,b,c in A (distributivity)

a × b = b × a for all a,b in A if and only if A is commutative

The operation × is usually referred to as multiplication and the element 1 as the unit or identity element.

Examples of algebras over a field F include the set of n x n matrices over F, the polynomial ring F[x], and the complex numbers C, which can be viewed as an algebra over the field of real numbers R.

Therefore, the algebra over a field F has been explained

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The required value table is  

x    -1     0     1      2    3

y    -3    1      5     9    13

To find the value table of a linear function take, any values for 'x' and from that find the 'y' values for each corresponding value of 'x'.

Here in this problem, we are taking x values as 0, 1, 2, and 3. Now substitute each of the 'x' values and find the 'y' values and make the table of values.

Here we have  

The linear function given is y = 4x + 1

To find the value table we are taking x values as - 1, 0, 1, 2, 3  

At x = - 1 => y = 4(-1)  + 1

=> y = - 4 + 1

=> y = - 3

At x = 0 => y = 4(0) + 1

=> y = 0 + 1

=> y = 1

At x = 1 => y = 4(1) + 1

=> y = 4 + 1

=> y = 5

At x = 2 => y = 4(2) + 1

=> y = 8 + 1

=> y = 9

At x = 3 => y = 4(3) + 1

=> y = 12 + 1

=> y = 13

Therefore,

The required value table is  

x    -1     0     1      2    3

y    -3    1      5     9    13

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Answer:

true

Step-by-step explanation:

log2(5x+3)=log2(4x-3)

log2(5x+3)/log2(4x-3)

division turns to minus

log2(5x+3-4x-3)

log2(x)

A balanced chemical equation calculator is an online tool that assists in the balancing of chemical equations by automatically computing the coefficients for each reactant and product to verify that the equation obeys the rule of mass conservation.

According to the law of conservation of mass, matter cannot be generated or destroyed in a chemical process, just rearranged.

A balanced chemical equation includes the chemical formulae for the reactants and products of a chemical reaction, as well as the factors that balance the amount of atoms of each element on both sides of the equation. Balancing a chemical equation is a necessary step in addressing many sorts of chemistry issues, such as forecasting the quantity of product generated or reactant required in a reaction.

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The surface area of the cylinder is approximately 951.44 square inches, rounded to the nearest hundredth.

What is the surface area of the cylinder?

To find the surface area of a cylinder, we need to find the sum of the areas of its curved surface (lateral area) and its two circular bases.

The formula for the lateral area of a cylinder is L = 2πrh, where r is the radius and h is the height. The formula for the area of each circular base is B = πr^2.

We are given that the height of the cylinder is 11 inches and the radius is 8 inches. Therefore, we can calculate:

L = 2πrh = 2 × 3.14 × 8 × 11 = 549.52 in²

B = πr^2 = 3.14 × 8^2 = 200.96 in²

The total surface area is the sum of the lateral area and the two base areas:

Surface area = L + 2B = 549.52 + 2(200.96) = 951.44 in²

Hence, the surface area of the cylinder is approximately 951.44 square inches, rounded to the nearest hundredth.

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The length of the side AC of the right-angled triangle is equal to 24cm by comparison using the trigonometric ratio of sine of angle B.

The trigonometric ratios is concerned with the relationship of an angle of a right-angled triangle to ratios of two side lengths.

The basic trigonometric ratios includes;

sine, cosine and tangent.

Considering the right-angled triangles ABC and DBC, we shall evaluate for the length AC using the trigonometric ratio of sine for the angle B° to derive an equation as follows:

For ∆ABC;

sin B = AC/BC {opposite/hypotenuse}

For ∆DBC;

sin B = 24cm/BC {opposite/hypotenuse}

thus;

AC/BC = 24cm/BC

Therefore, by comparison using the trigonometric ratio of sine for the angle B, we have the length of AC equal to 24cm.

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Answer:

Let's define the variables:

h: the number of hours the driver worked.

d: the number of miles the truck drove.

We know that the driver is paid $16 per hour, so the cost of the driver's labor is:

16h

We also know that the truck incurs an expense of $1.25 per mile driven, so the cost of gas and maintenance is:

1.25d

The total expenses for the driver, gas, and maintenance were $205, so we can set up the following equation:

16h + 1.25d = 205

We also know that the average speed of the truck was 20 miles per hour, so we can set up the following equation:

d = 20h

So the system of equations that could be used to determine the number of hours the driver worked and the number of miles the truck drove is:

16h + 1.25d = 205

d = 20h

These two equations can be solved simultaneously to find the values of h and d that satisfy both equations.

The dimensions of the park on the scale drawing are 2 inches by 0.5 inches

The dimensions of the park on the scale drawing can be determined by using the scale factor between the actual dimensions and the scale drawing dimensions. The scale factor can be found by dividing the actual dimensions by the scale drawing dimensions.

Scale factor for length = Actual length / Scale drawing length = 1000 feet / 2 inches = 500 feet per inch
Scale factor for width = Actual width / Scale drawing width = 600 feet / 0.5 inches = 1200 feet per inch

Now, we can use the scale factor to determine the dimensions of the park on the scale drawing.

Length of park on scale drawing = Actual length / Scale factor for length = 1000 feet / 500 feet per inch = 2 inches
Width of park on scale drawing = Actual width / Scale factor for width = 600 feet / 1200 feet per inch = 0.5 inches

Therefore, on the scale drawing, the park measures 2 inches by 0.5 inches.

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Answer:

92%

Step-by-step explanation: