It is the same distance from second base to first base, and from second base to third base. The angle formed by first base, second base, and home plate has the same measure as the angle
formed by third base, second base, and home plate. What can you conclude about the distance from first base to home plate, and from home plate to third base? Explain using your knowledge of congruent triangles.

The derivative of the function y = [tex]tan^{-1}[/tex] √[(1 - x)/(1 + x)] is given by

y' = -1/[(1 + x)²× √[(1 - x)/(1 + x)]].

To find the derivative, we use the chain rule. The derivative of the outermost function, arctan, is

1/[1 + (√[(1 - x)/(1 + x)])²], and the derivative of the innermost function, the square root, is

-1/2×(1 - x)/[[tex](1+x)^{3/2}[/tex])]. Multiplying these two derivatives together gives us the final result.

1/[1 + (√[(1 - x)/(1 + x)])²]×-1/2×(1 - x)/[[tex](1+x)^{3/2}[/tex])]

=-1/[(1 + x)²× √[(1 - x)/(1 + x)]].

When we take the derivative of a function, we are essentially finding the slope of the tangent line of a function at a given point. This derivative will tell us the rate at which y changes with respect to x. The derivative of the function y = [tex]tan^{-1}[/tex] √[(1 - x)/(1 + x)] is a negative value, which means that as x increases, y decreases. Therefore, this function has a negative slope.

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According to the table the wavelength that has the least amount of electromagnetic energy is B having a wavelength of 4.0 x 10⁻⁶ m

Radiant energy that moves in waves at the speed of light is called electromagnetic energy. It can also be referred to as radiant energy, electromagnetic radiation, electromagnetic waves, light, or the movement of radiation.

Wavelength is the separation between identical points (adjacent crests) in successive cycles of a waveform signal traveling through space or over a wire.

This length is often stated in meters when using wireless technology (m),

The relationship between a electromagnetic energy and wavelength is in inverse relation. This means that the least wavelength will result to greatest electromagnetic energy

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complete question

(03.05 MC) The table below shows the wavelength of four electromagnetic waves in meters (m).

Electromagnetic Wave      Wavelength

A                                         3.0 x 10² m

B                                         4.0 x 10^-6 m

C                                         1.2 x 10-¹2 m

D                                         2.0 x 10 m

According to the table, which electromagnetic wave has the least amount of energy? ​

Answer:

Step-by-step explanation:

Derivation of composite functions concept.

h'(x)=g'(f(x))·f'(x)=(sin(5x))'×(5x)'=cos(5x)×5=5cos(5x)

It takes 560 of 1/3 inch cubes to fill a box with width 2 2/3 inches, length 3 1/3 inches, and height 2 1/3 inches.

In Math's or in Geometry, a Cube is a solid three-dimensional figure, which has 6 square faces, 8 vertices and 12 edges.

It is also said to be a regular hexahedron.

We will convert the dimensions of the given box into simple fractions for easy calculations.

The dimensions of the given box:

Length = 3 + 1/3 inches = 10/3 inches

Breadth = 2 + 2/3 inches = 8/3 inches

Height = 2 + 1/3 inches = 7/3 inches

The side of each cube = 1/3 inches

Therefore,

The no. of cubes required to fill the box is,

= (volume of the box) / (volume of each 1/3 inch cube)

= ( 10/3 * 8/3 * 7/3 ) / (1/3)^2

= 10 * 8 * 7

= 560

Thus, it takes 560 of 1/3 inch cubes to fill a box with width 2 2/3 inches, length 3 1/3 inches, and height 2 1/3 inches.

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Answer: 29 ft

Step-by-step explanation:

Based on the description we are given. we know that we can form a right triangle, where 20 and 21 are the legs. The length from the girl to the bike would be the hypotenuse. To do this, we need to use the Pythagorean Theorem, which is [tex]a^2+b^2=c^2[/tex], where a and b are legs, and c is hypotenuse. We can go ahead and plug them in.

[tex]20^2+21^2=c^2[/tex]            [exponent]

[tex]400+441=c^2[/tex]            [add]

[tex]841=c^2[/tex]                      [square root both sides]

[tex]c=29[/tex]

Therefore, the distance from the girl to the bike is 29 ft.

Answer:

Step-by-step explanation:

x=11

y=14

He must purchase 3 packages of hot dogs and 2 packages of hot dog buns for a total of 24 hot dogs with buns if he doesn't want to have any leftover hot dogs or buns. You should be aware that students might respond with 24, which is the least common multiple of 8 and 12.

The hot dog buns most frequently used in the American region of New England and its cuisine are New England-style hot dog buns, also referred to as New England hot dog buns or top-loading hot dog buns.

As you can see, "hot dog" is a versatile word that can be used as a noun, verb, adjective, or even as an exclamation.

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If Shapera mowed 7 lawns and worked for 36 hours at pet store and delivered newspapers 7 days , then she earned $497 which is not enough to buy the computer .

the amount that she earns in mowing each lawn is = $15 ;

So , the amount earned for mowing 7 lawns is = [tex]15\times 7[/tex] = $105 ;

the amount that she earns per hour working at pet store is = $7 ;

So , amount earned for working 36  hours is = [tex]36\times 7[/tex] = $252 ;

the amount that she earns by delivering newspapers per day is = $20 ;

So , amount earned by delivering newspapers for 7 days =[tex]20\times7[/tex] = $140 ;

The total amount earned by Shapera is = [tex]\$ 105 + \$252+\$140[/tex]

On adding all the amount earned ,

we get ;

= $497 ;

The amount earned by Shapera is $497 .

Therefore , Shapera will not be able to buy the $499 computer as she is $2 less than the price .

The given question is incomplete , the complete question is

Shapera has three sources of income. She earns $15 for each lawn she mows. She earns $7 per hour working part-time at a pet store She earns $20 each day she delivers newspapers.

In the six weeks, Shapera mowed 7 lawns, worked 36 hours at the pet store, and delivered newspapers 7 days. Did she make enough to buy the $499 computer ?

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Step-by-step explanation:

there are a few things from school everybody has to burn into their brains for life. one of them : Pythagoras for right-angled triangles :

c² = a² + b²

c is the Hypotenuse (the triangle side opposite of the 90° angle), a and b are the triangle legs.

now, it depends on what you teacher agreed with you regarding naming the sides of such a triangle.

sometimes "base" is the Hypotenuse (baseline), sometimes it is one of the legs, and then the height is the second leg (as the legs are standing at a 90° or right angle at each other).

we have to assume the second one, as for the first one we have not enough information to solve the question (because with just a given Hypotenuse and the height to the Hypotenuse we can draw infinitely many different triangles with different perimeters).

so, we have

Hypotenuse² = 24² + 7² = 576 + 49 = 625

Hypotenuse = sqrt(625) = 25 m

the perimeter of the triangle is then

25 + 24 + 7 = 56 m

Using percentages we know that the value of a car decreases by 34% on average.

A % is a quantity or ratio that, in mathematics, represents a portion of one hundred.

A dimensionless relationship between two numbers can be represented in a variety of ways, such as through ratios, fractions, and decimals.

The symbol "%" is frequently written after the number to indicate percentages.

So, we know that:
Annie brought a car at: $32000

Current price of the car: $21000

The decline in car percentage:

21000/32000 * 100

65.625%

⇒ 100 - 65.625 = 34.375%

Rounding off: 34%

Therefore, using percentages we know that the value of a car decreases by 34% on average.

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Complete question:
Annie bought a brand-new car for $32,000. The car is now worth $21,000.

By what percentage does the car's worth decrease?

Answer:

33

Step-by-step explanation:

18 + 15 ← factor out 3 ( the GCF ) from each term

= 3(6 + 5)

= 3(11)

= 3 × 11

= 33

The required scale factor that Amir will use to go from Polygon F to G is 1/9.

The scale factor is defined as the ratio of the modified change in length to the original length.

here,
Area of polygon F = 36 square units
Area of polygon G = 4 square units

Now,
The scale factor to go from polygon F to polygon G is given as,
SF = Area of polygon G / Area of polygon F
SF= 4/36
SF = 1/9

Thus, the required scale factor that Amir will use to go from F to G is 1/9.

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Answer: 4/5 minus 5/10 can be simplified as:

(4/5) - (5/10)

It can also be re-written as

(4/5) - (1/2)

To subtract these fractions, we need a common denominator, which is 10 in this case.

So it becomes

(4/5)(2/2) - (1/2)(5/5) = 8/10 - 5/10 = 3/10

So the result of 4/5 minus 5/10 is 3/10 on a number line.

Step-by-step explanation:

Answer:

9, after being converted to a mixed number

Step-by-step explanation:

Just divide 27 by 3, it’ll equal 9

yw :)

hope i helped, reach out if it’s wrong (it’s not lol)

Have a great day :3

Answer: 9

Step-by-step explanation:

since fraction means we divide the numerator by denominator, we divide 27 by 3

⇒27/3

⇒27 ÷ 3

⇒9 answer

hope that helps ...

The Least Common Multiple (LCM) of 2, 6, and 11 is 66.

We shall divide the numbers (6, 11) by their prime factors in order to determine the LCM of 6 and 11 using the division method (preferably common). The LCM of 6 and 11 is determined by the product of these divisors.

Step 1:Find the smallest prime number that at least one of the numbers, 6, or 11, can be factored into. As indicated by the ladder arrangement, place this prime number (2) to the left of the supplied numbers (6 and 11).

Step 2: Divide any of the supplied integers (6, 11) by 2 and write the quotient below it if it is a multiple of 2. Any number that is not divisible by the prime number should be brought down.

Step 3: Continue the procedure until there are only 1s left in the

The LCM of 6 and 11 is the product of all prime numbers on the left, i.e. LCM(6, 11) by division method = 2 × 3 × 11 = 66

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The pair of linear equations 3x + 2y = 5 and 2x + 3y = 7 has no solution.

To solve these equations, we will use the method of elimination.

We start by multiplying the first equation by 2:

6x + 4y = 10

Now we add both equations together:

6x + 4y + 2x + 3y = 10 + 7

Combining like terms, we have:

8x + 7y = 17

We can now solve for x by dividing both sides by 8:

x = 17/8

Now we can substitute this value of x into either of the original equations to solve for y:

3(17/8) + 2y = 5

51/8 + 2y = 5

2y = 5 - 51/8

2y = -41/8

y = -41/16

However, this value for y is not a real number, so there is no solution for the pair of linear equations.

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The lower bound for the number of minutes that it takes for all people to leave is of:

70 minutes.

At a football match, there are 29 800 people, correct to the nearest 100. The fewest number of people that can be there, hence, is of:

29,750.

(as 29749 would be rounded to 29,700).

At the end of the football match, the people leave at a rate of 400 people per minute, correct to the nearest 50 people, hence the fastest rate is given as follows:

424 people per minute.

(as 425 people would be rounded to 450).

Hence the time it would take is obtained applying the proportion as follows:

29750/424 = 70 minutes.

(lower bound is fewest time, hence lowest number of people leaving at the fastest rate).

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The builder should buy x meters of $20/m fence for the front side and 3x + 2y meters of $10/m fence for the other three sides.

To minimize the cost of the fence, the builder needs to use the least expensive type of fence for the three sides of the land that are not the front. Since the fence along the front of the land costs $20 per meter and the fence for the other three sides costs $10 per meter, the builder should use the $10 per meter fence for the other three sides.

To find out how much of each type of fence the builder needs to buy, we need to determine the total length of the three sides that are not the front. Since the land is a rectangular shape, we can use the formula for the perimeter of a rectangle:

Perimeter = 2(length) + 2(width)

Let's assume the length of the front side is x and the width of the land is y, the perimeter of the land is:

2x + 2y = 60,000

To find out the total length of the three sides that are not the front, we need to subtract the length of the front side from the perimeter of the land:

60,000 - x = 3x + 2y

The total length of the three sides that are not the front is 3x + 2y.

Now we can calculate how much the builder will pay for each type of fence:

Total cost of the fence = $20x + $30x + $20y = $50x + $20y

To minimize the cost, the builder should choose the values of x and y that minimize the total cost of the fence. To do this, the builder should set the derivative of the total cost function with respect to x and y and then set them equal to zero and solve for x and y.

However, in this case, we can simply see that the total cost is minimized by using the $10/m fence for the other three sides and using the $20/m fence only for the front side. Therefore, the builder should buy:

This way, the builder minimizes the cost of the fence and ensures that the security of the land is maintained.

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After solving, the possible domain in interval notation is (0, 7).

In the given question, a researcher is following the growth of a particular type of flower.

The equation to show the height of the plant f(n), in cm, after days (n) = 8(1.05)^n

According to the given information,

The height of the plant is modeled by the function= f(n)

The height of the plant is approximately 11.04cm when the number of days = 7

The days are started from n > 0 and n<=7

Hence the possible domain in interval notation = (0, 7)

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The complete question is:

A scientist is studying the growth of a particular species of plant. He writes the following equation to show the height of the plant f(n), in cm, after days (n) = 8(1.05)^n

Part A: When the scientist concluded his study, the height of the plant was approximately 11.26 cm What is a reasonable domain toplot the growth function?

Part B: What does the y-intercept of the graph of the function () represent?

Part C: What is the average rate of change of the function f(n) from n = 2 ton, and what does it represent?

Answer: The Seed Calculator app is used to calculate the amount of seed required in order to produce a desired crop yield.

Step-by-step explanation:

Answer:

Step-by-step explanation:

it B.

just put in the calculator and it gives  you the reduced fraction

Answer:

B. 3/4

Step-by-step explanation:

Find the GCD (or HCF) of the numerator and denominator

GCD of 15 and 20 is 5

Next, divide both the numerator and denominator by the GCD

15 ÷ 5 = 3

20 ÷ 5 = 4

Finally, put them back into a fraction

[tex]\frac{3}{4}[/tex]

Therefore, 15/20 simplified to the lowest terms is 3/4.

The values of x , y and z are 80,2,110 respectively from the given figure where JKLM ~ EFGH

What is Quadrilateral ?

Quadrilateral can be defined as the type of the polygon in which it contains four sides.

Given ,

JKLM ~ EFGH

Since , JKLM ~ EFGH

3/30 = 11/z

 z = 30*11/3

z =110

3 / 30 = 8/ x

3 * x = 8 * 30

x = 80

3 / 30 = y/ 20

y = 20 * 3 / 30

y = 2

Hence the values of x , y and z are 80,2,110 respectively.

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Answer:  [tex]3x^4 / 2y^4[/tex]

Step-by-step explanation: [tex](3x7x^6y^5)divide(2x7x^2y^9)[/tex]    then [tex]x^6 divided by x^2 = x(^6 ^- ^2) = x^4[/tex]   then

[tex]y^5 divided by y^9 = y(^5 ^- ^9) = y(^-^4) = 1/y^4[/tex]  then

Canceling out  7  as it appears on both sides of the fraction line.

Hope this is clear and is helpful

X²-3There are a number of ways to factor equations like x2 -3x+2=3x+2=0. If all the terms are positive: (x + ) (x + )=0,  If the center term is negative: ( (-)( x -)=0 • If the last or if both terms are negative: ( x +)(x-)=0

The following are the rulesIf, ll trinomial terms are positive, then all binomial terms will be positive.If the trinomial’s last term is negative but the middle and first terms are positive, one term of the binomial will be negative and the other will be positive.

If we can find two numbers whose product is A * C and whose sum is B, we may factor a trinomial of the type Ax2 + Bx + C. Exemplification 1. Determine if 4x2 + 8x + 3 can be factored. Solution. We want for two numbers whose product is (4)(3) = 12 and whose total is 8. (the coefficient of x).

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The expectation of X, when X is log-normal and log(X) follows a normal distribution with mean m and standard deviation k, is exp(m + k²/2).

Therefore the answer is exp(m + k²/2).

The log-normal distribution is a probability distribution of a random variable whose logarithm is normally distributed. In other words, if X is log-normal, then log(X) follows a normal distribution with mean m and standard deviation k.

The expectation of a random variable is the expected value of the variable, which is a measure of the central tendency of the distribution. For a continuous probability distribution, the expectation is also known as the population mean. The expected value of X can be calculated using the probability density function (PDF) of X.

The expectation of X is calculated as the integral of X × f(X) over the range of X. Where f(X) is the probability density function of X and X is the random variable.

For log-normal distribution, the expectation of X is calculated as follows:

E(X) = exp(m + k²/2)

where m is the mean of log(X) and k is the standard deviation of log(X).

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Total profit earned = 25000000 dollars

Profit is a financial achievement which is the difference between the amount of money or resources people earned and the amount is spent in various purpose. In case of a business organization, the difference between production and cost is termed as profit. Let, someone invested money for operating business, he needs to spend money for workers, for the welfare of business and after all these he has amount that comes from business that is called profit.

Given, profit earned = $ 2.5 × 10⁴ in the 1×10³ days in a row

total profit earned during this time = $(2.5 × 10⁴ × 10³)

                                                         $2.5 × 10⁷

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Answer:

a) 48 portions
b) $157.25

Step-by-step explanation:

1) 15.36/.32 to get 48 portions

2) Since it's asking for 6.25 0.32kg portions, multiply 6.25 by $25.16 to get $157.25

The number of 1/3 inch cubes that will fill the box is 26.

The volume of an object is the amount or quantity of substance that it would conveniently contain. Different objects has their method of determining their volume depending on their shapes.

Given a cube of length 1/3 inch. The volume of the cube can be determined as;

volume of a cube = length x width x height

The volume of the cube = 1/3 * 1/4 * 1/3

                            = 1/9 cube inches

The volume of the box can be determined as;

Volume of the box = length x width x height

                       = 1 1/3 * 1 1/3 * 1 2/3

                       = 2.963 cubic inches

Volume of the box = 2.963 cubic inches

The number of 1/3 inch cubes that will fill the box = 2.963/ (1/9)

                                                        = 26.667

The number of 1/3 inch cubes that will fill the box is 26.

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