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The largest prime number that divides the given expression is 229.

We can factorize the given expression as follows:

[tex]$0! \times 1 \times 1! \times 2 \times 2! \times 3 \times 3! \times \cdots \times 50! \times 50$[/tex]

Now, we can cancel out all the factorials from both sides, leaving us with:

[tex]$1 \times 1 \times 2 \times 2 \times 3 \times 3 \times \cdots \times 50 \times 50$.[/tex]

The largest prime factor of any composite number is the largest prime factor of its prime factorization. By the fundamental theorem of arithmetic, we know that the prime factorization of any composite number is unique.

The prime factorization of a number can be found by dividing the number by prime numbers and keeping dividing the quotient by prime numbers until the quotient is prime.

Now, we can start dividing the given number (the product of all numbers from 1 to 50) by the smallest prime number, 2, and keep dividing the quotient by the next prime number until the quotient is prime.

The largest prime factor of the given expression is the largest prime factor of the final quotient.

The final quotient is

[tex]2^{24} \times 3^{12} \times 5^9 \times 7^7 \times 11^5 \times 13^4 \times 17^3 \times 19^3 \times 23^2 \times 29^2 \times 31^2 \times 37^2 \times 41^2 \times 43^2 \times 47^2 \times 53^2 \times 59^2 \times 61^2 \times 67^2 \times 71^2 \times 73^2 \times 79^2 \times 83^2 \times 89^2 \times 97^2 \times 101^2 \times 103^2 \times 107^2 \times 109^2 \times 113^2 \times 127^2 \times 131^2 \times 137^2 \times 139^2 \times 149^2 \times 151^2 \times 157^2[/tex]

[tex]\times 163^2 \times 167^2 \times 173^2 \times 179^2 \times 181^2 \times 191^2 \times 193^2 \times 197^2 \times 199^2 \times 211^2 \times 223^2 \times 227^2 \times 229^2$[/tex]

The largest prime factor of the final quotient is the largest prime factor of the prime factorization, which is 229.

So the largest prime number that divides the given expression is 229.

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The volume of solid generated when region s is revolved about the horizontal line y is 93.04919.

We have to find the volume of the solid generated when region s is revolved about the horizontal line y.

As shaded region is revolved around y = -3.

Outer radius = f(x) + 3

Inner radius = g(x) + 3

Width = dx

Thus small volume "dv" formed when shaded region in above diagram is revolved around y = -3.

dv = π[tex](f(x) + 3)^3[/tex]dx - π[tex](g(x) + 3)^2[/tex]dx

dv = π([tex]f^2[/tex](x) + 6f(x) + 9)dx - π([tex]g^2[/tex](x) + 6g(x) + 9)dx

dv = π([tex]f^2[/tex](x) + 6f(x))dx - π([tex]g^2[/tex](x) + 6g(x))dx

Now integrating on both side:

[tex]\int dv=\pi\int^{3}_{0}9(1+x)\cos(\pi x/6) + 6\int^{3}_{0}f(x)dx-\pi\times 5.32021-6\times3.24125[/tex]

Using the provided result or a scientific calculator, the entire definite integral was discovered.

v = π × 25.54298 + 6 × 8.16083 - π × 5.32021 - 6 × 3.24125

v = 93.04919

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The complete question is given below:

The total distance of the trip Ella's family took is 700 miles.

A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.

Given, Ella slept through the last 14% of the trip.

So, Before Ella fell to asleep they covered (100 - 14)% = 86% of the trip.

Let The total distance be 'x'.

Therefore, 602 miles is 86% of 'x' which can be numerically expressed as,

(86/100)×x = 602.

0.86x = 602.

x = 602/0.86.

x = 700 miles.

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The mean for the low income group is the average of all the values in the group.

It is calculated by adding up all the values and then dividing by the total number of values. In the low income group, the mean is calculated by adding up all the incomes, and then dividing by the total number of people.

The median for the low income group is the middle value when all the values are arranged in order. To calculate the median, first arrange the incomes in order from lowest to highest, and then find the middle value.

The standard deviation for the low income group is a measure of how spread out the values are. It is calculated by taking the square root of the variance, which is calculated by taking the average of the squared difference between each value and the mean, and then dividing by the number of values.

The mean for the high income group is the average of all the values in the group. It is calculated by adding up all the values and then dividing by the total number of values. In the high income group, the mean is calculated by adding up all the incomes, and then dividing by the total number of people.

The median for the high income group is the middle value when all the values are arranged in order. To calculate the median, first arrange the incomes in order from lowest to highest, and then find the middle value.

The standard deviation for the high income group is a measure of how spread out the values are. It is calculated by taking the square root of the variance, which is calculated by taking the average of the squared difference between each value and the mean, and then dividing by the number of values.

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Answer:

¿Qué quieres comer?

Step-by-step explanation:

The slope is -Ea/R and the intercept is equal to ln(A)

The Arrhenius equation is a mathematical equation that describes the relationship between the rate constant of a chemical reaction and temperature:

k = Ae^(-Ea/RT)

where k is the rate constant, A is the pre-exponential factor, Ea is the activation energy, R is the gas constant, and T is the temperature in Kelvin.

The slope and intercept of the linear plot of the Arrhenius equation using a semilogarithmic (semilog) plot can be determined by transforming the equation into a linear form. The semilog plot is created by taking the logarithm of the rate constant (k) on the y-axis and the reciprocal of the temperature (1/T) on the x-axis:

ln(k) = ln(A) - Ea / RT

The slope of the plot is equal to -Ea/R and the intercept is equal to ln(A). By fitting a straight line to the semilog plot, the values of Ea and A can be determined.

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Answer:

x = 6

Step-by-step explanation:

[tex]\frac{8}{12}[/tex] = [tex]\frac{x}{9}[/tex] ( cross- multiply )

12x = 72 ( divide both sides by 12 )

x = 6

Applying proportion, 2520 ounces of solution Z will contain 44040 ounces of ingredient a.

To determine the number of ounces of ingredient a in 2520 ounces of solution Z, we need to first calculate the proportion of ingredient a in solutions X and Y, and then use that information to determine the proportion of ingredient a in solution Z.

Solution X contains 2 ounces of ingredient a and 3 ounces of ingredient b in one ounce of solution, so the proportion of ingredient a is 2/(2+3) = 2/5.

Solution Y contains 1 ounce of ingredient a and 2 ounces of ingredient b in one ounce of solution, so the proportion of ingredient a is 1/(1+2) = 1/3.

Solution Z is created by mixing solutions X and Y in a ratio of 3:11, so 3 ounces of solution X are mixed with 11 ounces of solution Y.

Thus, the proportion of ingredient a in solution Z = (32/5) + (111/3) = 6/5 + 11/3.

To find out the number of ounces of ingredient a in 2520 ounces of solution Z, we need to multiply the proportion of ingredient a with the number of ounces of solution Z

2520 * (6/5 + 11/3) = 2520 * (6/5 + 11/3) = 2520 * (252/15 + 11/3) = 2520 * (16+11/3) = 2520 * (16+11/3) = 2520 * (16+11/3) = 2520 * (16+37/3) = 2520 * (16+37/3) = 2520 * (53/3) = 252053/3 = 252017.66666 = 44040 ounces of ingredient a.

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The information shows that Larry is incorrect as a composite number is a positive integer that has at least one positive divisor.

It should be noted that composite numbers are those numbers that have more than two factors. Composite numbers have factors other than 1 and itself

Larry is incorrect. A composite number is a positive integer that has at least one positive divisor other than one and itself. For example, 4 is composite because it can be divided by 2 (and 1). However, a number's ones place simply refers to the digit in the units place and has no bearing on whether a number is prime or composite.

For example, the number 22 is composite because it is divisible by 2 and 11, but the number 12 is composite because it is divisible by 2,3,4 and 6.

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Answer:

A ≈ 34.91 m²

Step-by-step explanation:

the area (A) of the sector is calculated as

A = area of circle × fraction of circle

  = πr² × [tex]\frac{40}{360}[/tex] ( r is the radius )

  = π × 10² × [tex]\frac{1}{9}[/tex]

  = [tex]\frac{100\pi }{9}[/tex]

  ≈ 34.91 m² ( to 2 decimal places )

Answer:

(round 35m²)

Step-by-step explanation:

360° : 40° = 9  

Area of Circle Formulas · Area = π × r2, where 'r' is the radius

Area = π × r2

Area = π × 10²

Area = π × 100

Area = 3.14 × 100

Area = 314 m²

314 : 9 = 34.88m² (round 35m²)

Answer: 16

Step-by-step explanation:

You need to divide 12 by 3/4

To do this you turn 12 into a fraction by making it 12/1

Then you do Keep Change Flip

Keep 12/1

Change the division into multiplication

Flip 3/4 into 4/3

Then you do 12/1 × 4/3 which is 48/3

Finally you simplify 48/3 into 16

Check the picture below.

Due to the lack of a common ratio, the above sequence is not geometric.

A series of integers with a common ratio is referred to as a geometric sequence. A geometric sequence has a next number that is a multiple of the one before it.

if the sequence is geometric.the common ratio of the number's

-1, 1, 4, 8, are

-1/1 = -1 ratios of the numbers in the sequence

4/1 = 4

8/4 = 2

There isn't a ratio that unites the numbers.

The lack of a common ratio leads us to the conclusion that the presented sequence is not geometric.

Due to the lack of a common ratio, the above sequence is not geometric.

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The measure of the angle m∠GEH  = 33° for the given Quadrilateral EFGH which is a rectangle.

Examples:

For this stated question:

In the rectangle EFGH.

m∠FEG=57°

Then,

m∠FEG + m∠GEH  = 90 (complimentary angles)

57° + m∠GEH  = 90

m∠GEH  = 90 - 57

m∠GEH  = 33°

Thus, the measure of the angle m∠GEH  = 33° for the given Quadrilateral EFGH which is a rectangle.

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According to exponent rules, when we multiply terms with the same base add the exponents. Hence, the correct answer is option D.

Exponent rules are a set of rules that dictate how exponents (numbers written as a superscript) can be manipulated in mathematical operations. Some of the most commonly used exponent rules include:

        For example, [tex]x^4 * x^5 = x^{4+5} = x^9[/tex]

       For example, [tex]x^7 / x^3 = x^{7-3} = x^4[/tex]

        For example,[tex](x^3)^5 = x^{3*5} = x^{15}[/tex]

        For example,[tex](xy)^3 = x^3 * y^3[/tex]

       For example,[tex](x/y)^3 = x^3 / y^3[/tex]

According to the product of the power rule, we get that we add the exponents when we multiply terms with the same base.

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Answer:

Yes, the friend is correct in finding the sum of -3.7 + (-0.25) = 3.95.

To find the sum, the friend first takes the absolute value of each number (ignoring the negative sign) to find that the absolute value of -3.7 is 3.7 and the absolute value of -0.25 is 0.25.

Then, the friend adds the absolute values of the numbers (3.7 + 0.25) to get 3.95 which is the final answer.

The order of operation is correct and the arithmetic is also correct, so the final result is the correct sum of the two given numbers.

Answer:

Step-by-step explanation:

The equation of a line in slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept (the point where the line crosses the y-axis).

Given that the slope of the line is m = 4/6, we can substitute it into the equation.

We know that the line passes through the point (1, -1), so we can use that point to find the value of b.

Plugging in the point (1, -1) into the equation, we get:

-1 = (4/6)(1) + b

Solving for b, we get:

b = -1 - (4/6) = -1 - 2/3 = -5/3

So the equation of the line is:

y = (4/6)x - (5/3)

which can be rewritten as

y = (2/3)x - (5/3)

this line is the equation of the line you are looking for.

Answer:

Y--1=m(x-1) this is the rule of the equation of straight line

a. The angular velocity of the ball is 1.57rad/sec

b. The angular acceleration of the bicycle is 0.23 rad/sec²

angular is the rate of change of angular distance . it is measured in rad/sec. it is represented by w. Angular acceleration is the rate of change in angular velocity with time.

angular velocity = change in angle/ time

w = 2π/t

w = 2× 3.14/4

w = 6.28/4

w = 1.57 rad/sec

angular acceleration =( final angular velocity - initial angular velocity )/time

= (4.2 - 3.5)/3

= 0.7/3

= 0.23 rad/s²

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Yes, each of the four sections for books is a rectangle because all four sides of the section are straight lines and the opposite sides are the same length.

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The length of the segment PS is 100 units.

In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem. These triangle's three sides are known as the Perpendicular, Base, and Hypotenuse.

From the given image we can see that the segments PT, PQ, and TQ form a right- angled triangle PQT.

Applying Pythagorean theorem to this triangle we have:

PQ^2 + TQ^2 = PT^2

(45)^2 + (TQ)^2 = (53)^2

2025 +  (TQ)^2 = 2809

(TQ)^2 = 2809 - 2025

(TQ)^2 = 784

TQ = 28

Similarly, segments PR, PS, and SR form a right-angled triangle PRS, where TQ = SR = 28 and PR = 96.

Applying Pythagorean theorem to this triangle we have:

PR^2 + SR^2 = PS^2

(96)^2 + (28)^2 = (PS)^2

(PS)^2 = 9216 + 784

(PS)^2 = 10000

PS = 100

Hence, the length of the segment PS is 100 units.

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Answer:

.................................................................................

Step-by-step explanation:

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ok

Answer:

opposite angles are equal and parallel

If the  height of the football could be described by the model: f(x) = -16x² + 64x , then the time at which the ball at its highest point after being kicked is t = 2 seconds .

In order to find time at which ball is at its highest point,

we have to find the time at which the derivative of height function is = 0.

the height function is ⇒ f(x) = -16x² + 64x ;

So , the derivative of the height function will be :

⇒  f'(x) = -32x + 64 ;

equating the derivative of height function to 0 , and solving for x ,

we get ;

⇒ -32x + 64 = 0

⇒ -32x = -64

⇒ x = 2

Therefore , the time at which the ball is at its highest point is 2 seconds .

The given question is incomplete , the complete question is

Justin punts a football. The height of the football could be described by the model: f(x) = -16x² + 64x. h describes the height of the ball in feet and the time in seconds after the ball was kicked.

At what time in seconds is the ball at its highest point after being kicked ?

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Answer:

1: 0.15x = 0.15x * x = discount (percentage) * original price = discount

2: x - 0.15x = x (1 - 0.15) = original price - discount

3: 0.15 x 15.99 = 2.39

15.99 - 2.39= 13.59

x= $13.59

Tubby is not correct. 1.15x is not an expression that represents the new price for the ornament. It represents the original price plus a 15% increase, not a discount. To find the new price after a discount, you need to multiply the original price by (1- the percentage discount) or subtract the percentage discount from the original price.

Step-by-step explanation:

Using the triangle inequality theorem, the length of the third side is: D. 4 < c < 42.

The triangle inequality theorem states that for any triangle, the sum of the lengths of any two sides must be greater than the length of the third side.

In this case, we know that side A measures 23 inches and side B measures 19 inches. To find possible values for side C, we can use the triangle inequality theorem by adding the lengths of sides A and B and comparing the sum to all possible values of side C.

A + B > C

23 + 19 > C

42 > C

So, the length of side C must be less than 42 inches.

Also

C > A - B

C > 23 - 19

C > 4

So, the length of side C must be greater than 4 inches.

Therefore, the possible side lengths of the third side, C, must be between 4 inches and 42 inches (not including 4 inches and 42 inches).

The answer is: D. 4 < c < 42

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Plan 2 can be used to save $500 in less than 16 weeks and have $20 extra.

The number of weeks and y, which is the equation we wish to utilise, stand in for the total amount saved. Our equation will then be 15 x. Instead of the other way around, he will save 330.

Plan  Amount saved per week Total amount saved in 16 weeks

1      $31.25                                         $500

2      $35                                             $560 (with $60 extra)

3      $40                                              $640 (with $140 extra)

Plan 2 can be used to save $500 in less than 16 weeks and have $20 extra.

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The verification of the given trig identity is shown in below.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

⇒ (1 - sin x) / (1 + sin x) = (sec x - tan x)²

Now, We can simplify as;

⇒ (1 - sin x) / (1 + sin x) = (sec x - tan x)²

LHS;

⇒ (1 - sin x) / (1 + sin x)

⇒ (1 - sin x) (1 - sin x) / (1 + sin x) (1 - sin x)

⇒ (1 - sin x)² / (1 - sin²x)

⇒ (1 - sin x)² / cos²x

⇒ ( (1 - sin x )/ cos x )²

RHS;

⇒ (sec x - tan x)²

⇒ ( 1/cos x - sin x / cos x)²

⇒ ( (1 - sin x) / cos x )²

Hence, We get;

⇒ (1 - sin x) / (1 + sin x) = (sec x - tan x)²

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Answer:

14 dollars

Step-by-step explanation:

They vary in direct proportion

Thus; If 15 copies = 6dollars

35 copies = (35 × 6) ÷ 15

= 210 ÷ 15

= 14

It would cost 18$

Every fifteen copies you have to pay 6$, and since 35 is 3 times 15, it would also be 3 times the price, or 6 * 3$ which equals 18$

7.21

The Pythagoras theorem allows us to solve for unknown sides of right triangles.

Right Triangles

Right triangles are triangles that have one 90-degree angle (aka a right angle). The side directly across from the right angle is called the hypotenuse. The hypotenuse is always the longest side of a triangle. The other 2 sides of a right triangle are called the legs of the triangle.

Pythagorean Theorem

The Pythagorean theorem states that a² + b² = c², where a and b are the legs of the triangle and c is the hypotenuse. To find the missing side we can plug in the values we know and solve for b.

Then, subtract 12² from both sides.

Finally, take the square root of both sides. When you square root a number, the resulting value is plus or minus, but since we are finding a distance, we will only take the positive answer.

Answer:   255

Step-by-step explanation:

Try thinking backwards first; 51*(0.20)=10.2, or 10.2 is 20% of 52

To find 20% of the unknown number, just divide 51 by 0.20

51/0.20=255

Whatever the answer is, you know it has to be larger than the original number.