Analyze and Persevere
Javi is building
a birdhouse. Each of the four walls of the
birdhouse needs to be 5.5 inches long.
Javi has a piece of board that is 24.5 inches
long. Is the board long enough to be
cut into the four walls of the birdhouse?
Estimate using compatible numbers.

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

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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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:

33

Step-by-step explanation:

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

= 3(6 + 5)

= 3(11)

= 3 × 11

= 33

On solving the provided question, we can say that by equation

30 tons of veggies were sold on the first day, 33 tons on the second day, and 35 tons on the third day.

An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.

x = amount (ton) of vegetables sold on day one; y = amount (ton) of vegetables sold on day two. Z = the amount of vegetables sold on the third day (in tons).

[tex]x=y-3\\z=(5/9)*(x+y)\\x+y+z=98\\x+y+[(5/9)*(x+y)]=98\\ 9x+9y+5x+5y=882\\14x+14y=882\\x=y-3\\14x+14y=882[/tex]

solution

[tex]x=30\\y=33\\x+y+z=98---- > z=98-(x+y)---- > z=98-63--- > 35[/tex]

30 tons of veggies were sold on the first day, 33 tons on the second day, and 35 tons on the third day.

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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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If the total charge for yogurt is dependent on the base price of the bowl of yogurt plus the number of toppings added, the value of y at the y-intercept of the line representing this situation is  C $4.00

The y-intercept of a line is the point where the line crosses the y-axis. In this case, the y-intercept is the cost of the bowl of yogurt without any toppings. The base price of the bowl of yogurt is $4.00, so the y-intercept of the line representing this situation would have a value of $4.00.

This means that the cost of a bowl of yogurt without any toppings is $4.00. The cost of the bowl of yogurt with toppings is determined by adding the cost of the bowl of yogurt plus the cost of the toppings. Therefore, the y-intercept of the line representing this situation would have a value of $4.00.

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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 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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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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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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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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Answer:

Step-by-step explanation:

x=11

y=14

Recursive formula for a(n) , the nth term of the sequence is

⇒ a(n) = 125 × (5)ⁿ⁻¹

An sequence has the ratio of every two successive terms is a constant, is called a Geometric sequence.

We have to given that;

The sequence is,

⇒ 125, - 25, 5 , ....

Clearly, The sequence is a geometry sequence with common ratio - 5 and first term 125.

We know that;

The nth term of geometry sequence is,

⇒ a(n) = a rⁿ⁻¹

Where, 'r' is common ratio and 'a' is first term of the sequence.

Substitute all the values, we get;

The nth term of the given sequence is,

⇒ a(n) = a rⁿ⁻¹

⇒ a(n) = 125 × (5)ⁿ⁻¹

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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)

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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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

0.71 percentage points greater is wyatt’s effective interest rate than his nominal interest rate.

Interest is a fee paid by a borrower to a lender for the use of borrowed money. It is calculated as a percentage of the amount borrowed, and is usually paid periodically at intervals. Interest is generally considered to be a form of compensation for the time and risk taken by the lender in providing a loan or other form of credit.

The effective interest rate is calculated by taking the (1 + nominal interest rate/number of compounding periods per year) to the number of compounding periods per year power minus 1. In this case, the effective interest rate would be 0.1362 x (1 + 0.1362/4)^4 - 1, which is 0.1439 or 14.39%. The difference between the nominal interest rate of 13.62% and the effective interest rate of 14.39% is 0.71 percentage points.

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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.

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 median of the data is 1

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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When a building is 40 meters long in shadow cast by another building of the same height, there are 10 levels there.

equation that can be used to explain the mathematical relationship between two variables, where one variable is equal to a constant multiplied by the other. A direct variation's (proportional relationship's) graph is a straight line that pierces the origin. On a graph of direct variation, the graph will always pass through (1, k), where k is the proportionality constant. Direct variation refers to a change in one quantity that directly affects the other. The complete opposite of this is inverse variation.

The equation that describes this variation is:

h =kx

1st Data                                                            2nd Data

s=22 m                                                                    s  = 40 m

h=6 stories                                                               h = find 2nd

k=find 1st                                                                  k = 0.27 story/m

Find k:                                                                       Find h :

h=kx                                                                           h = kx

6 stories=k(22 m)                                                 h = ( 0.27 story/m ) ( 40 m)                                                                                                                                                                                                

k=6 stories/22 m                                                           h = 10    stories

k=0.27 story/m

so its direct variation .

When a building is 40 meters long in shadow cast by another building of the same height, there are 10 levels there.

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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? ​

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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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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On solving the provided question, we can say that - the area of the provided circle is A = [tex]113.04 cm^2[/tex]

Every point in the plane that is a certain distance away from a certain point forms a circle (center). It is, thus, a curve formed by points moving in the plane at a fixed distance from a point. At every angle, it is also rotationally symmetric about the center. A circle is a closed two-dimensional object where every pair of points in the plane are equally spaced out from the "center." A line that goes through the circle creates a specular symmetry line. At every angle, it is also rotationally symmetric about the center.

here,

radius, r = 6 cm

Area of circle = [tex]\pi X r^2 = 3.14 X 6 X 6 \\[/tex]

A = [tex]113.04 cm^2[/tex]

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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