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.

The correct relation which shows the function is,

⇒ (-6, 2), (-2, 3), (2, 7), (6, 2)

Option B is true.

A relation between a set of inputs having one output each is called a function.

Now, We know that;

Function is a relation between a set of inputs having one output each.

So, By given options;

A. (-2, -2), (-6, -5), (2, 8), (2, 2)

Here, Two value of outputs 8, 2 have same input 2.

So, This is not a function.

B. (-6, 2), (-2, 3), (2, 7), (6, 2)

Here, A set of inputs having one output each.

So, This is function.

C. (6, -10), (-6, 7), (6, 6), (-6, 12)

Here, Two value of outputs - 10, 6 have same input 6.

So, This is not a function.

D. (-6, 0), (-2, 5), (-6, -3), (2, 9)

Here, Two value of outputs 0, -3 have same input -6.

So, This is not a function.

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The total number of servings of chicken the food bank can provide is 70 servings.

Per-unit is a technique of expressing a quantity's value in terms of a base or reference quantity. Each system variable or quantity in a per-unit system is normalized in relation to its own base value.

Two chickens make up the main course of a plate of food, according to the table's content. Each chicken served by the food bank weighs 12.6 ounces. 110.9 pounds of chicken are available at the food bank (1,774.4 ounces of chicken)

Thus,

The mass of chicken per serving = 2 × 12.6 = 25.2 oz/serving

The total number of servings of chicken the food bank can provide = (The quantity of chicken the food bank has)/(The mass of chicken per serving)

∴ The total number of servings of chicken the food bank can provide = (1,774.4 oz)/(25.2 oz/serving) ≈ 70.413

Given that the servings are in whole numbers, we have;

therefore, To the nearest whole number, the food bank can offer a maximum of 70 servings of chicken.

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On solving the provided question, we can say that Surface Area of central park = 2.5 × 0.5 = 1.25 square mile

An indication of the overall space occupied by an object's surface is its surface area. A three-dimensional shape's surface area is the total amount of space that surrounds it. A three-dimensional shape's entire surface area is known as its surface area. The surface area of a cuboid with six rectangular faces may be calculated by adding the areas of each face. As an alternative, you may use the formula below and name the box's dimensions as follows: Surface (SA) = 2lh + 2lw + 2hw. Surface area is a measurement of the entire amount of space filled by a three-dimensional shape's surface (a three-dimensional shape is a shape that has height, width, and depth).

Surface  Area of central park = 2.5 × 0.5 = 1.25 square mile

1 acre = 1/640 square mile

1.25 square mile = 1.25 ÷ 1/640 = 800 acre

Number of people in the park = 800 ÷ 15 = 53.3 ≈ 53 people

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The minimum number of entries needed in order to cover the total cost of the T-shirts is 94.

What is linear inequality?

A linear inequality is an inequality that can be written in the form of

ax + b > c or ax + b < c or ax + b = c

Where x and y are variables and a,b,c are constants.

The cost of the T-shirts plus VAT is £400 + (17.5/100) * £400 = £400 + £70 = £470

In order to cover the total cost of the T-shirts, you need to find out how much money you will make from the entry fees.

Let's call the number of entries N. The total revenue from the entry fees is N * £5 = £5N

So, in order to cover the cost of the T-shirts, the revenue from the entry fees must be greater than or equal to the cost of the T-shirts plus VAT:

£5N ≥ £470

To find the minimum number of entries needed, you can divide both sides of the inequality by 5:

N ≥ £470 / £5

N ≥ 94

Hence, the minimum number of entries needed in order to cover the total cost of the T-shirts is 94.

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The minimum number of entries needed in order to cover the total cost of the T-shirts is 94.

What is linear inequality?

A linear inequality is an inequality that can be written in the form of

ax + b > c or ax + b < c or ax + b = c

Where x and y are variables and a,b, and c are constants.

The cost of the T-shirts plus VAT is £400 + (17.5/100) * £400 = £400 + £70 = £470

In order to cover the total cost of the T-shirts, you need to find out how much money you will make from the entry fees.

Let's call the number of entries N. The total revenue from the entry fees is N * £5 = £5N

So, in order to cover the cost of the T-shirts, the revenue from the entry fees must be greater than or equal to the cost of the T-shirts plus VAT:

£5N ≥ £470

To find the minimum number of entries needed, you can divide both sides of the inequality by 5:

N ≥ £470 / £5

N ≥ 94

Hence, the minimum number of entries needed in order to cover the total cost of the T-shirts is 94.

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The population standard deviation of the data is 111.

1. Find the mean of the data:

Mean = (314 + 158 + 482 + 284 + 310 + 281) / 6 = 1029 / 6 = 171.5

2. Find the difference between each data point and the mean:

Feb: (314 - 171.5) = 142.5

Mar: (158 - 171.5) = -13.5

Apr: (482 - 171.5) = 310.5

May: (284 - 171.5) = 112.5

Jun: (310 - 171.5) = 138.5

Jul: (281 - 171.5) = 109.5

3. Square each of the differences:

Feb: (142.5)^2 = 20,312.5

Mar: (-13.5)^2 = 182.25

Apr: (310.5)^2 = 95,822.25

May: (112.5)^2 = 12,656.25

Jun: (138.5)^2 = 19,082.25

Jul: (109.5)^2 = 11,982.25

4. Sum all of the squared differences:

20,312.5 + 182.25 + 95,822.25 + 12,656.25 + 19,082.25 + 11,982.25 = 149,047.5

5. Divide the sum of the squared differences by the number of data points minus one:

149,047.5 / (6 - 1) = 149,047.5 / 5 = 29,809.5

Square root of 29,809.5 = 111 (rounded to the nearest integer)

Therefore, the population standard deviation of the data is 111.

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Answer:

y = 7/2x + 5

Step-by-step explanation:

The slope intercept form is: y = mx + b

Our equation is

7x -2y = -10

We subtract 7x both sides

-2y = -7x - 10

Divided by -2, both sides

y = 7/2x + 5

So, the answer is y = 7/2x + 5

One angle of a triangle measure 140°. The other two angles are in a ratio of 3:5.The smaller angle would measure 84°, and the larger angle would measure 56°. This can be found through the use of basic trigonometry.

A triangle is a three-sided polygon with three angles that add up to 180°. Since one of the angles is already known, the remaining two angles can be calculated by subtracting 140° from 180°, which equals 40°. This 40° can then be divided by the ratio 3:5, which is 8° and 32°.

If 8° is the smaller angle, then 32° must be the larger angle. To convert 8° and 32° to the final answer of 84° and 56°, 8° must be multiplied by 10 and 32° must be multiplied by 5. This gives a total of 84° and 56° for the other two angles.

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One angle of a triangle measures 140°. The other two angles are in a ratio of 3:5. What are the measures of that two angles?

Carlos needs a total of 400 Euros for buying 500 Euros.

The total amount available with Carlos for his holiday to Germany = 515 Euros

Amount spent to obtain these 515 Euros = £ 412

As it is clear that for buying 515 Euros he spent 412 Euros.

So, we will first find the Euros spent on buying 1 Euro.

For that, we will use Unitary Method:

So, the total Euros spent for buying 1 Euro will be = (412/515) = 0.8

So, for finding the total Euros spent for obtaining 500 Euros we will simply multiply the total Euros needed by the Euro spent for buying 1 Euro.

Thar will be equal to (0.8 * 500) = 400 Euros.

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The number 8 (eight) is represented by a number and numeral.

It is the natural number that follows seven and precedes nine. Given that it is an integer and a cardinal number, it can be counted. It is distinguished from imaginary numbers by being categorised as a real number.

Eight is a composite number, and its proper divisors are 1, 2, and 4. Eight can be written as 23, which when said aloud sounds like two cubed. It has a 7 aliquot total. All powers of two add up to an aliquot that is one less than their own.

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Therefore , the solution of the given problem of algorithm comes out to be halting problem is unsolvable.

An algorithm is a process for carrying out a computation or resolving a challenge. Algorithms work as a detailed set of guidelines that lead hardware- or software-based routines through a series of predetermined actions step by step. Algorithms are frequently used in all areas of IT.

Here,

The halting problem, which claims that no program can be created that can anticipate whether or not any other program will halt after a finite number of steps, is an intractable algorithmic challenge.

The inability to solve the stopping problem directly affects software development.

Therefore , the solution of the given problem of algorithm comes out to be halting problem is unsolvable.

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A guy wire is attached to an upright pole 6 meters above the ground. If the wire is anchored to the ground 5 meters from the base of the pole 7.81 m long is the wire. This can be solved by using the concept of Pythagoras theorem.

The widely accepted geometric principle known as the Pythagorean Theorem states that the square on the hypotenuse of a right triangle equals the sum of the squares on its legs (the side opposite the right angle).

The hypotenuse side of a right-angled triangle's square is equal to the sum of its other two sides, according to Pythagoras' Theorem. The perpendicular, base, and hypotenuse of this triangle are its three designated sides.

Let, assume ΔABC is a right-angled triangle

where, AC = 6m be the pole.

AB = 5m is the length of a guy wire and is attached to stake B

By Pythagoras theorem,

BC² = AB² + AC²

or, BC² = (5)² + (6)²

or, BC² = 36 + 25

or, BC =  √61 m

or, BC = 7.81 m

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The solution of equation is ∅.

According to the mathematical definition of inequality, neither side is equal. When a relationship leads to a non-equal comparison between two expressions or numbers, it is known as an inequality in mathematics. The equal sign "=" in this statement can be replaced with any of the inequality symbols.

Given equation |x| + 7 < 4

subtract 7 from both sides

|x| + 7 - 7 < 4 - 7

|x| < -3

but |x| ≥ 0, for all real values,

so solution is ∅.

Hence the solution of equation is ∅.

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Answer:

[tex]108\pi[/tex] or approx. [tex]339.3 m^{2}[/tex]

Step-by-step explanation:

The question asks us to find the total surface area of the given hemisphere. The question gave us the formula for total surface area of a sphere, [tex]SA_{tot} =4\pi r^2[/tex]. But we need it for a hemisphere, so multiply the equation by [tex]\frac{1}{2}[/tex].

[tex]SA} = (\frac{1}{2}) 4\pi r^2[/tex] => [tex]SA} =2\pi r^{2}[/tex]

We also need the area of the base, which is circle. [tex]A_{circle}=\pi r^{2}[/tex].

Now add these equations together to get our equation.

[tex]SA_{tot} =2\pi r^2 +\pi r^{2}[/tex] => [tex]SA_{tot} =3\pi r^2[/tex]

Now we have the proper equation for total surface area of a hemisphere, [tex]SA_{tot} =3\pi r^{2}[/tex]. Plug in the value of [tex]r[/tex] which is given in the problem, [tex]r=6m[/tex].

=> [tex]SA_{tot} =3\pi (6)^{2}[/tex] => [tex]SA_{tot} =3\pi (36)[/tex] => [tex]SA_{tot} =108\pi m^{2}[/tex] or approx. [tex]339.3 m^{2}[/tex]

The 9 inches side must be the hypotenuse, and the other two sides must be 3 inches and 5 inches.

n a triangle, the longest side (the hypotenuse) is opposite the largest angle, and the other two sides are opposite the smaller angles. According to the Triangle Inequality Theorem, the sum of any two sides of a triangle must be greater than the length of the third side. So, if the longest side of Karen's triangle measures 8 inches, it means that the sum of a and b (the two shorter sides) must be greater than 8 inches. Therefore [tex]a+b > 8 inches[/tex].

For the second part of your question, only one triangle can be drawn with side lengths 3, 5, and 9. The three numbers 3, 5, and 9 form a Pythagorean triple, meaning they can be used as the lengths of the sides of a right triangle. Since the longest side (the hypotenuse) must be greater than the other two sides, the 9 inches side must be the hypotenuse, and the other two sides must be 3 inches and 5 inches.

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Answer:

The answer is (4x² - 36x + 81)

Step-by-step explanation:

So,

(2x - 9)² = (2x)² - 2(2x)(9) + (9)²

(2x - 9)² = 4x² - 36x + 81

Thus, The product of (2x - 9)² is (4x² - 36x + 81)

The answers for Center of the circle is (-4,3) and radius is 2√10 units.

(x - h)2 + (y - k)2 = r2 is the equation of the center of the circle. The radius (r) is specified as 5 units, while the center's (h, k) coordinates are (0, 0). (x - 0)2 + (y - 0)2 = 52 is the result of substituting the values of h, k, and r in the equation.

Finding the simplified term of the given expression is the goal of simplifying the algebraic statement. We must first understand how to join like terms, factor a number, and the order of operations before we can factorize or simplify the statement. When like words are combined, the constant terms are divided for the purpose of simplicity and the variables with the same degree are grouped together.

Examples of  Algebraic Expressions

2x2+3xy+4x+7

Given,

[tex]x^2+y^2+8x-6y-15=0[/tex]

⇒ x².+8x+16–16+y²-6x+.9–9–15=.0

(x+4)²+(y-3)²-16–9–15=0

I.e. (x+4)²+(y-3)²=40

(x+4)²+(y-3)²={2√10}²

Hence center is (-4,3) and radius is 2√10 units.

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All values that are NOT in the domain of 9 are 5 /11 at x=9, where function  h=7.

All real numbers x, with the exception of those for which the denominator is 0, are included in the domain of a rational function. Equilibrate the denominator to zero and then solve for x to determine which x values are excluded from the scope of a rational function.

h(x)=x-2\sg(x)=(x-4)(x+2)

Suppose x = 9 and h(9) = 9-2 and g(9) = (9-4) (9+2) =5 /11

Because it is impossible to divide by zero while h is in the denominator, there will always be an issue anytime h = 7. After solving them, we discover that x cannot be either -2 or 5. So, the answer to part B would be x-5/11.or 5/11 are examples of x values that are beyond the domain.

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The number that belongs to both sequences is 26.

The formula known as the nth term allows us to locate any term in a series. The letter "n" stands for "number."

By changing the term number's value, we can create a series that uses the nth term (n).

To find the 10th term we would follow the formula for the sequence but substitute 10 instead of ‘n‘; to find the 50th term we would substitute 50 instead of n.

We have two sequences, let's call one as A and the other as B.

The n-th term of sequence A is written as:

aₙ = 3*n^2 - 1

the nth term of sequence B is written as:

bₙ = 30 - n^2

We want to find a term that belongs to both sequences, (it can be for different integers, we can use n for sequence A and x for sequence B)

Then we want to find:

aₙ = bₓ

where n and x are integer numbers.

Then we will heave:

3*n^2 - 1 = 30 - x^2

To find the pair, we could isolate one of the variables, then input different integers in the other variable and see if the outcome is also an integer.

Let's isolate n.

3*n^2 = 30 - x^2 + 1

3*n^2 = 31 - x^2

n^2 = (31 - x^2)/3

n = √(  (31 - x^2)/3)

Now let's input different values for x, and see if the outcome is also an integer, notice that x is in a negative term inside a square root, then we have only a few values of x such that the equation can be true.

Then let's start with x = 1.

n(1) = √(  (31 - 1^2)/3) = √(30/3) = √10

We know that √10 is not an integer.

now with x = 2,

n(2) = √(  (31 - 2^2)/3)  = √( (31 - 4)/3) = √(27/3) = √9 = 3

then if x = 2, we have n = 3.

Both of them are integers, then we get:

a₂ = 3*(3)^2 - 1 = 27 - 1 = 26

b₃ = 30 - 2^2 = 30 - 4 = 26

Therefore, The number that belongs to both sequences is 26.

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The amount of the proposed increase is, Rs 1071.4

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

Given that;

The annual gym subscription for a single member is Rs.1000,

And, An annual family membership is Rs.1500.

Here, A single membership increased cost 5/7 of a family membership.

Hence, The increased cost = 5/7 of 1500

                                          = 1071.4 Rupees

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Answer:

3/20

Step-by-step explanation:

To do this multiply the numerators (the top numbers) together first.

3 * 1 = 3

This is the numerator (the top number) of the answer fraction.

Next we take the bottom numbers:

5 * 4 = 20

We have 3/20 as our fraction. We know 3 is a prime number and can only be divided by 1 or 3. 20 cannot be divided by 1 or 3 so this fraction cannot be simplified any more.

Pick a random selection of students who attend the work lab.

Picking a random sample of students is the most effective strategy to ensure accurate results. The findings of a survey that the student conducts among those sat in the lab's front rows might be skewed.

The students seated in front of the lab could exhibit a certain trait (e.g., they might be particularly diligent students), which would undoubtedly yield a different outcome.  The survey is in good shape. No special equipment is required to evaluate our comprehension of statistical analysis.

Additionally, there won't be much of a difference if more students are included in the sample that are sat in front of the lab. Finally, it makes no sense to administer instruments to a group that does not visit the work laboratory. Effectiveness cannot be evaluated based on students who do not participate in class.

Therefore the correct option is B)  Select a random sample of students who go to the work laboratory

The complete question is:

A student researcher wishes to examine the effectiveness of a statistical work laboratory on graduate students' overall understanding of application of statistical analyses. The researcher administers a survey to 15 students who are seated at the front of the laboratory. How could this study be improved? Select all that apply.

A. Use an instrument to test statistical analysis understanding.

B. Select a random sample of students who go to the work laboratory

C. Use a larger sample size.

D. Administer instruments to a group who does not go to the work laboratory, as well.

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On solving the provided question, we can say that - so, percentage - 400/500 X 100 = 80%

A percentage in mathematics is a figure or ratio that is stated as a fraction of 100. The abbreviations "pct.," "pct," and "pc" are also occasionally used. It is frequently denoted using the percent symbol "%," though. The amount of percentages has no dimensions. With a denominator of 100, percentages are basically fractions. To show that a number is a percentage, place a percent symbol (%) next to it. For instance, if you correctly answer 75 out of 100 questions on a test (75/100), you receive a 75%. To compute percentages, divide the amount by the total and multiply the result by 100. The percentage is calculated using the formula (value/total) x 100%.

here,

total is 500

obtained is 400

so, percentage - 400/500 X 100 = 80%

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The exponential function showing the relationship between y and t is y = 4800e^(0.0625t).

An exponential function is a function of the form f(x) = bx, where b is a positive real number and x is a real number. This type of function is commonly used to model the rate of growth or decay of a quantity over time. Exponential functions have the property that their derivatives (slope) are proportional to the value of the function itself. This property makes them useful for modeling phenomena with compound growth or decay, such as populations, interest rates, and radioactive decay.

In this equation, 4800 is the original principal, 0.0625 is the interest rate (6.25%) and t is the number of years since the start of the investment. This equation can be used to calculate the value of the investment after any number of years. For example, if t = 5, then y would equal 6,842.50. This means that after 5 years, the value of the investment would be 6,842.50.

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The minimum value of the expression 3x² + 6x + 6 is 3.

Therefore the answer is 3.

A quadratic mathematical expression contains a variable of highest degree of 2 and it is of the general form ax² + bx + c, where a, b and c are constants.

Minimum value of a quadratic equation of form ax² + bx + c is when

x = -b/ 2a

Then minimum value is

a( -b/ 2a )² + b( -b/ 2a ) + c

= (b²a + -2ab² + 4a²c)/ 4a²

= ( - b² + 4ac)/ 4a

= c - b²/4a

In the expression 3x² + 6x + 6, a = 3, b =6 and c = 6. So minimum value is

= 6 - 6²/ (4×3)

= 3

--The question is incomplete, answering  to the question below--

"What will be the minimum value of the expression 3x² + 6x + 6?"

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The equation of the magnitude of the force applied at the back of otter is F is (P+P0)A F is ( P + P 0 ) A .

The amount that encapsulates the force's power is known as its magnitude. Consider the following scenario: the force is 10 N in the east. The direction is indicated by "towards east," while the force is indicated by "10." Magnitude may be thought of as simply the "value" or "amount" of any physical quantity.

The surface area of the otter's back is A = 0.55 m2.

The fluid pressure at the depth of the otter is P = 11500 Pa.

Thus, the equation of the magnitude of the force applied at the back of otter is F=(P+P0)A F = ( P + P 0 ) A .

The complete question is

An otter is swimming in the deep area of his tank at the zoo. The surface area of the otter's back is A = 0.55 m2. The fluid pressure at the depth of the otter is P = 11500 Pa.

Write an equation for the magnitude of the force F on the back of the otter in terms of the pressure P and the atmospheric pressure P0.

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Answer:

26$

Step-by-step explanation:

¼×48=12

so 12 was spent on calculator

12+14= 26

When you and your 3 friends decide to split the bill of $36 evenly and you leaving a 12% tip on your part, you pay a total of $13.32.

Therefore the answer is 13.32 dollars.

When you and your 3 friends decide to split the bill evenly, each person is responsible for paying 1/4 of the total bill. The total bill is $36, so each person is responsible for paying

$36 / 4 = $9

You also decided to leave a 12% tip on your part, so you need to calculate 12% of $36. To do this, you can multiply $9 by 0.12

$36 × 0.12 = $4.32  

So, you are responsible for paying $9 + $4.32 = $13.32

So you are responsible for paying $13.32 in total.

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Answer:

Step-by-step explanation:

c.120 i did the work and i came out with this answer. Hope it helps!

Reason: The degree is the largest exponent.

This rule only works when dealing with single variable polynomials.

The standard form is y = 3x^6+5x^2-10x-8; where the largest exponent term goes first, then the next largest, and so on.

Answer:

4 pounds of cheese

Step-by-step explanation:

4/5*5=4