The
/_ M =55 the measure of arc LN=37 what is the measure of arc KT

When the volume of this sphere is [tex]$\frac{K \sqrt{6}}{\sqrt{\pi}}$[/tex], then the value of K is 8

As per the data given:

The length of the cube is 2 units.

First, we have to determine the surface area of the cube.

The formula for the surface area of the cube:

A = 6 (side × side)

A = 6 (2 × 2)

A = 6 (4)

A = 24 square units

The surface area of a cube is 24 square units.

Also given that the surface area of a cube and the surface area of a sphere is equal.

The formula for the surface area of the sphere.

A = 4π [tex]r^{2}[/tex]

Where r is the radius of the sphere.

4π [tex]r^{2}[/tex] = 24

π [tex]r^{2}[/tex] = 6

[tex]r^{2}[/tex] = [tex]\frac{6}{\pi }[/tex]

r = [tex]\sqrt{\frac{6}{\pi } }[/tex]

The radius of the sphere is [tex]\sqrt{\frac{6}{\pi } }[/tex]

Also given the volume of the sphere as [tex]$\frac{K \sqrt{6}}{\sqrt{\pi}}$[/tex]

Here we have to determine the value of K.

The volume of sphere = [tex]\frac{4}{3} \pi r^{3}[/tex]

Where r is the radius of the sphere.

[tex]\frac{4}{3} \pi r^{3}[/tex] =    [tex]$\frac{K \sqrt{6}}{\sqrt{\pi}}$[/tex]

[tex]\frac{4}{3} \pi (\sqrt{\frac{6}{\pi } }) ^{3} = \frac{K \sqrt{6} }{\sqrt{\pi } }[/tex]

[tex]\frac{4}{3} \pi {\frac{6}{\pi } }= K[/tex]

K = 4 × 2

K = 8.

Therefore the value of K = 8.

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Assuming that each site is equally likely to be chosen, there are 1820 ways the sites for the new stores can be selected.

The department store chain is planning to expand into a new market and is considering 16 different sites on which to locate 4 stores. In order to determine the number of ways to select the sites for the new stores, we need to calculate the number of ways to select 4 sites from the 16 available sites. This can be done by using the binomial coefficient "16 choose 4" which is also written as,

16C4 = 16!/(4! * 12!)

Using this formula, we can calculate the number of ways to select 4 sites out of 16 as 1820 ways.

This means that the store chain has 4845 different ways to select the 4 sites from the 16 available sites assuming each site is equally likely to be chosen.

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Angle C is 70°

Angle A is 30°

Side AC is 12 cm.

Is associated with motor impairment but does not cause it

Autism is defined as the development of disability caused by differences in the brain.

People with autism often have problems with social communication and interaction, restricted or repetitive behaviors or interests, and also have different ways of learning, moving, or paying attention.

The study didn't explain the timeline of their findings, so we can conclude this research takes data at one time.

Research that doesn't take before and after exposure data cannot be used to derive causation since we can't prove that the condition happens after exposure.

But this study still can predict association by risk ratio or odds ratio depending on the study design.

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The volume of the three dimensional figure is 102π m³

An equation is an expression composed of variables and numbers linked together by mathematical operations.

Diameter = 6 m, radius = 6/2 = 3 m

Volume of hemisphere = (2/3) * π * radius³ = (2/3) * π * 3³ = 18π m³

Volume of cylinder = π * radius² * height = π * 3² * 8 = 72π m³

Volume of cone = (1/3) * π * radius² * height = (1/3) * π * 3² * 4 = 12π m³

Volume of solid = sum of all volumes = 18π m³ + 72π m³ + 12π m³ = 102π m³

The volume of the solid is 102π m³

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The volume of the figure is the sum volume of the cone, hemisphere and cylinder which is 320.4m²

To determine the volume of the figure, we have to find the volume of the hemisphere, the volume of the cylinder and the volume of the cone.

The formula of volume of a hemisphere is given as;

V = 2/3πr³

Substituting the values into the formula above;

v = 2/3(π) × 3³

v = 56.5m³

The formula of volume of a cylinder is given as

V = πr²h

Substituting the values into the formula

v = π * 3² * 8

v = 226.2m³

The formula of volume of a cone is given as;

v = 1/3πr²h

Substituting the values into the formula

v = 1/3 × π × 3² * 4

v = 37.7m³

The volume of the figure = volume of cone + volume of cylinder + volume of hemisphere

volume of figure = 56.5 + 226.2 + 37.7

volume of figure = 320.4m³

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Answer:

Step-by-step explanation:

1

At a constant speed of 45 miles per hour it will take 0.71 hours for Darla to run her errands and get back home.

What is constant speed?

An object is considered to be moving at a constant speed when it covers the same distance in the same amount of time. When moving at a constant pace, an object covers a certain distance in a fixed amount of time.

Darla drives at a constant speed of 45 miles per hour.

She drives for y miles and it takes her x hours.

The number of miles Darla can drive in x hours is y = 45x.

Darla drives to the market, 14 miles from her house.

Then she drives to the post office, 3 miles from the market.

Then she drives back to her house, 15 miles from the post office.

Calculate Darla's total distance travelled -

14 + 3 + 15 = 32 miles

Now, substituting the value of y with 32 -

32 = 45x

x = 32/45

x = 0.71

Therefore, the time taken by Darla is 0.71 hours.

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The probability of drawing exactly three face cards is given as follows:

0.0660 = 6.60%.

The mass probability formula is presented as follows:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

Considering that a standard deck is composed of 52 cards, of which 12 are face cards, and 5 cards are taken, the values of the parameters are given as follows:

N = 52, k = 12, n = 5.

The probability of drawing exactly three face cards is P(X = 3), obtained as follows:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]P(X = 3) = h(3,52,5,12) = \frac{C_{12,3}C_{40,2}}{C_{52,5}} = 0.0660[/tex]

The problem asks for the probability of drawing exactly three face cards.

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From the given information, the value of x in the given table is 42.5.

To find the value of x, we can use the formula for the arithmetic mean (average) of a set of numbers:

Arithmetic mean = (sum of all numbers) / (number of numbers)

Given that the average score on the test is 62, we can use this information to find the sum of all the scores.

Given that number of students is 1,2,3 and 4 with scores of 40,55,70 respectively, we can use this information to find the sum of all the scores.

Sum of all scores = (1 * 40) + (2 * 55) + (3 * 70) + (4 * x)

Now we can substitute the given average score and the number of students into the equation and solve for x.

62 = (1 * 40) + (2 * 55) + (3 * 70) + (4 * x) / 10

620 = 40 + 110 + 210 + 4x

4x = 170

x = 42.5

So, the value of x is 42.5

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The complete question is -

ten students wrote a test, and the distribution of scores is shown in the frequency table. if the average (arithmetic mean) score is 62, what is the value of x?

Score - 40, 55, 70, x

Number of students - 1, 2, 3, 4

Answer:

Step-by-step explanation:

a) To find u1, we can use the term-to-term rule given in the problem:

Un+1 = U²₁ + 5

We know that u1 = 1, so we can substitute that into the equation:

u2 = 1² + 5 = 1 + 5 = 6

b) To find u2, we can use the same term-to-term rule and substitute the value of u1 (which is 6) into the equation:

u3 = 6² + 5 = 36 + 5 = 41

c) To find un, we can use the term-to-term rule and substitute the value of un-1 into the equation.

un = un-1² + 5

It's important to note that the value of n is not given so we can't calculate the value of un.

Therefore, u1 = 6, u2 = 41, and we can't calculate un without knowing the value of n.

The equation that shows the power of a power property by obtaining the product of the exponents is given as follows:

(y^a)^b = y^(a x b).

Meaning that the lower right option is the correct option.

The power of a power rule is used when a single base is elevated to multiple exponents.

Then the simplified expression is obtained keeping the base, while the exponents are multiplied.

A simple example is given as follows:

(2²)³ = 2^(2 x 3) = 2^6.

Hence the general format of the expression is presented as follows:

(y^a)^b = y^(a x b).

Which gives the correct option in the context of this problem, and the correct option is the bottom right option.

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Answer:

The length of the third side (Hypotenuse) is 7.1556411313

Step-by-step explanation:

In order to find the third side(Hypotenuse) we use a formula called the phytogorean theorem which was invented by a philosopher named Pythagoras.

[tex]a^{2} +b^{2} =c^{2}[/tex]

We now apply the given values to the equation

[tex]5.96^{2} + 3.96^{2} = c^{2}[/tex]

Squaring the numbers we get,

[tex]35.5216+15.6816 = c^{2}[/tex]

[tex]51.2032[/tex] [tex]= c^{2}[/tex]

We now find the root of the number to find the hypotenuse which is,

[tex]\sqrt{51.2032} = c[/tex]

[tex]7.1556411313 = c[/tex]

Hence ,  the length of the third side (Hypotenuse) is 7.1556411313

An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles.

Given data :

1 ) 6x - 4y = 2

- 2x + 4y = 18

( 5. 7 )

=

=         6x-4y=2

    {-2x+4y=18(5.7)}

= [ -2{1+2y}{3}+4y=18. 5.7 ]

= [tex]\frac{-2+8y}{3}[/tex] = 102.6

= y = 38.725

= x = [tex]\frac{1+2\cdot \:38.725}{3}[/tex]

x = 26.15

2)  -4x - 12y=-24

    -2x - 4y =-10

         (3,1)

Solve the equation for x

x = 12 − 4y

− 24 − 2x−4y = −31

Solve using substitution

−24 −2 (12−4y) − 4y = −31

Simplify

− 48 + 4y = −31

Move the constant to the right side

4y= −3 1− (−48)

Subtract the terms

4y = 17

​Multiply both sides

4y × [tex]\frac{1}{4}[/tex]  = 17 x [tex]\frac{1}{4}[/tex]

Simplify

4y × [tex]\frac{1}{4}[/tex]  = [tex]\frac{17}{4}[/tex]

Substitute the given value of y into the equation x = 12 − 4y

x = 12 − 4 ×  [tex]\frac{17}{4}[/tex]

Simplify the expression

x=−5

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​

According to the concept of differentiation the length of his shadow changing when he is 10 feet from the base of the light is 10 feet.

Here we have given that the height of man = 6 feet

And the Height of light is 15 feet

Then the Rate of walk by man is written as

=>dx/dt = 5 feet per second.

Here we have to find the rate at which the tip of his shadow is moving when he is 10 feet from the base of the light.

Here by using ratio of similar triangles we have write it as,

=> 15/y = 6/(y - x)

When we do the cross multiplication on it, then we get

=> 15(y - x) = 6y

=> 15y - 6y = 15x

=> 9y = 15x

When we dividing by 3 on both sides then we get

=> 3y = 5x

While we differentiating both sides with respect to t then we get

=> 3(dy/dt) = 5(dx/dt)

=> dy/dt = (5/3)(6)

When we simplify this one, then we get

=> dy/dt =  10 ft/s

Hence the rate at which the tip of his shadow is changing is 10 ft/s.

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The 1 1/4 cups of sugar and 1 1/2 cups of flour used in making one batch, indicates that the number of cups of flour Lesley should use in the new batch of cookies, expressed as a mixed fractions is 1 1/5 cups

A mixed fraction consists of the sum of the quotient and the fraction of the remainder divided by the divisor, of a fraction which has a larger numerator than the denominator.

The amount of sugar and flour required to make one batch of cookies specified in mixed fractions are;

Amount of sugar = 1 1/4 cups

Amount of flour = 1 1/2 cups

The amount of sugar in the additional batch = 1 cup of sugar

The ratio of the quantities of the sugar and flour between original batch and the new batch is therefore;

Sugar in original batch/(Sugar in new batch) = (Flour in original batch)/(Flour in the new batch)

[tex]\frac{1\frac{1}{4} }{1} =\frac{1\frac{1}{2} }{y}[/tex]

Where;

y = The number of cups of flour required in the new batch

Cross multiplying, we get;

[tex]y \times 1\frac{1}{4} = 1\frac{1}{2}[/tex]

[tex]y = \frac{1\frac{1}{2} }{1\frac{1}{4} } = \frac{6}{5} =1\frac{1}{5}[/tex]

The number of cups of flour needed in the new batch is, y = 1 1/5 cups

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The total area of the two non-shaded crescent-shaped regions =25π ^2

The length of hypotenuse = 10

(6^2 + 8^2 = 10^2 )

Therefore, the radius of the large semicircle equals 5.            
area of large semi-circle = 25π

As a result, the total area of the two non-shaded regions is 25π^ 2

A semicircle is formed when a circle is divided in half along its diameter

The circumference of a semicircle is curved, and the diameter is straight.
A semicircle has a right angle of 90.


For example PR is a diameter and (angle PRQ=25.  The size of (angle QPR) is  (angle PQR=90circ) because it is the angle in a semicircle. The sum of  triangle's three angles is 180.    
   
     
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All the Individuals solutions are solved below:

a) To verify that y = e^m_1x - e^m_2 x/m_1 - m_2 is a solution of the differential equation y" - (m_1 + m_2)y' + m_1 m_2y = 0, we can substitute y into the equation and simplify:

y" = m_1^2e^m_1x - m_2^2e^m_2x

y' = m_1e^m_1x - m_2e^m_2x

so:

y" - (m_1 + m_2)y' + m_1 m_2y = m_1^2e^m_1x - m_2^2e^m_2x - (m_1 + m_2)(m_1e^m_1x - m_2e^m_2x) + m_1 m_2(e^m_1x - e^m_2x/m_1 - m_2) = 0

b) To find the limit of the solution in part (a) as m_1 right arrow m_2, we can use I'Hospital's rule. The limit is:

lim (m_1 -> m_2) e^m_1x - e^m_2 x/m_1 - m_2 = e^m_2x - e^m_2 x/m_2 - m_2 = e^m_2x - e^m_2x - m_2 = -m_2

c) To verify that the limit in part (b) satisfies the differential equation obtained from the equation in part (a) by replacing mi by m_2, we can substitute -m_2 into the equation:

y" - (m_2 + m_2)y' + m_2 m_2y = 0

y" - 2m_2y' + m_2^2y = 0

which is the differential equation of a constant function, and -m_2 is a constant function. Therefore, the limit in part (b) satisfies the differential equation.

It should be noted that the solution y = e^m_1x - e^m_2 x/m_1 - m_2 is a linearly independent solution of the differential equation y" - (m_1 + m_2)y' + m_1 m_2y = 0, and it can be used in combination with the general solution y = c_1e^m_1x + c_2e^m_2x to find the general solution of the differential equation.

Therefore, All the Individuals' solutions are solved.

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Shaded picture where tree can be planted is attached below as per the scaling given.

The ratio between a distance on a map and its actual distance on the ground is known as the map's scale. Since scale must vary throughout a map due to the curvature of the Earth's surface, this straightforward idea is made more difficult. This change makes the idea of size significant in two different ways.

Given, Here is a scale drawing of a garden. The scale is 1 cm to 2m

A tree is going to be planted. The tree must be more than 4 m from the patio. The tree must be more than 6m from the pond.

Since Scale is 1: 200

Planted tree distance from Patio = 4 m = 400 cm

in picture = 400 *  1: 200

in picture, Planted tree distance from Patio= 2 cm

Planted tree distance from Ppnd = 6 m = 600 cm

in picture = 600 *  1: 200

in picture, Planted tree distance from Patio= 3 cm

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Answer:

(5n + 2.29n) + (5.82 + 7.67)

Step-by-step explanation:

The percentage of oil that has leaked​ from the tank is 14.29%.

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100.

Given that,

The capacity of the tank = 49 litres.

Total litres of oil leaked = 7 litres.

Mathematically, the percentage for the amount of oil leakage in this tank is given by this formula:

Percentage = oil leakage/tank capacity *100

Substituting the given parameters into the formula, we have:

Percentage = 7/49 *100 =  14.29%

Thus, The percentage of oil that has leaked​ from the tank is 14.29%.

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The difference would be $61.60 in favor of the daily compounded scenario.

Compound interest is the interest on a loan or deposit calculated based on both the initial principal and the accumulated interest from previous periods.

To calculate the difference between the two scenarios you have provided:

$1,000 compounded daily at 5% for 8 years would earn $1,472.11

$1,000 compounded semiannually at 5% for 8 years would earn $1,410.51

Hence, the difference would be $61.60 in favor of the daily compounded scenario.

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1 is a universal factor. It is a factor of all numbers. The number itself is a factor of the number as it divides itself entirely.

A factor is a number that divides another number and leaves no remainder. In other words, if multiplying two whole numbers gives us a product, the numbers we are multiplying are factors of the product because they are divisible by the product. There are two processes for finding factors: multiplication and division.

For example, 3 and 6 are factors of 12 because 12 ÷ 3 = 4 absolutely and 12 ÷ 6 = 2 absolutely. The other factors of 12 are - 1, 2, 4, and 12.

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They tend to satisfice, meaning they settle on a satisfactory solution rather than searching for the optimal solution.

This type of decision making is known as bounded rationality. Bounded rationality acknowledges that people often make decisions based on incomplete and imperfect information but seek the best possible outcome. People use heuristics and mental shortcuts to make decisions and tend to satisfice, which means they settle on a satisfactory solution rather than searching for the optimal solution. This type of decision making is often used when the complexity of a problem is too great to be solved analytically.

Bounded rationality is a type of decision making which acknowledges that people often make decisions based on incomplete and imperfect information, and seek the best possible outcome using heuristics and mental shortcuts. They tend to satisfice, meaning they settle on a satisfactory solution rather than searching for the optimal solution.

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The amount paid for the dress to the nearest dollar is $109

From the question, we are to calculate the amount paid for the dress

From the given information,

Atiku is allowed a discount of 12.5% on a dress that cost $125

First, we will calculate the discount

Discount = 12.5% of $125

Discount = 0.125 × $125

Discount = $15.625

Amount paid = Cost - Discount

Thus,

Amount paid = $125 - $15.625

Amount paid = $109.375

Amount paid ≈ $109

Hence, the amount paid is $109

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Answer:

Step-by-step explanation:

21

Answer:

Sam bikes at a faster rate.  He can go 42.6 km in one hour while Alex is only able to go 39.6 km in the same amount of time.

Step-by-step explanation:

Alex's unit rate:

198/5 = 39.6 km per hour

Sam's unit rate:

298/7 = 42.6 km per hour rounded to the nearest tenths'

The given expression 1 2/3+(-8 1/2) is equivalent to -41/6.

what are expressions?

Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between. The mathematical operators can be of addition, subtraction, multiplication, or division. For example, x + y is an expression, where x and y are terms having an addition operator in between. In math, there are two types of expressions, numerical expressions - that contain only numbers; and algebraic expressions- that contain both numbers and variables.

e.g. A number is 6 more than half the other number, and the other number is x. This statement is written as x/2 + 6 in a mathematical expression. Mathematical expressions are used to solve complicated puzzles.

Now,

Given expression is 1 2/3+(-8 1/2)

=5/3+(-17/2)

=5/3-17/2

Taking LCM 6

=(10-51)/6

=-41/6

Hence,

        The given expression 1 2/3+(-8 1/2) is equivalent to -41/6.

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No, it is not the same as receiving a 35% discount of all the $100 items.

A discount can be defined as the amount of money a seller deducts for their customers from the normal price of the products they are selling.

The percentage discount that is generally on products that are sold for the price of $100 = 35%

The additional discount Josh received were 25% and 10% which is a total of 35% which is different from the general discount.

Therefore, it is not the same as receiving a 35% discount of all the $100 items.

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Complete question:

Josh went into a store to buy a $100 item. There was a sale of 35% off all. The sales person gave Josh a 25% discount and then an additional merchandise.

10% discount. Is that the same as receiving a 35% discount? Prove your answer.

Answer:

Step-by-step explanation:

Let x be the number of tickets sold before the tournament.

The number of tickets sold on the day of the tournament is x - 150 (since 150 fewer tickets were purchased on the day of the tournament than before the tournament)

The total number of tickets sold is the sum of the number sold before the tournament and on the day of the tournament.

x + (x - 150) = 898

Combining like terms:

2x = 1048

To find the number of tickets sold on the day of the tournament, we need to divide by 2:

x = 1048/2

x = 524

Therefore, 524 tickets were sold before the tournament and x - 150 = 524 - 150 = 374 tickets were sold on the day of the tournament.

Answer:

c its the answer jus did it on edge 2022

Step-by-step explanation: