If x= 45, then √x is between
4 and 5
44 and 46
22 and 23
6 and 7

Answer:

Answer is in attached photo.

Step-by-step explanation:

The solution is in the attached photo, do take note to solve this question, we can assign 2 variables to the 2 conditions stated in the question, and solve them simultaenously.

Using combinatorial reasoning, the expression of[tex](x y)5 is x^5y^5 + 5x^4y^6 + 10x^3y^7 + 10x^2y^8 + 5xy^9 + y^10[/tex]. Using the binomial theorem, it is[tex]1x^5 + 5x^4y + 10x^3y^2 + 10x^2y^3 + 5xy^4 + y^5[/tex].

a) Combinatorial reasoning involves breaking the expression down into different combinations of x and y, and then multiplying each combination. In this case, (x y)5 can be broken down into

[tex]x^5y^0 + x^4y^1 + x^3y^2 + x^2y^3 + x^1y^4 + x^0y^5[/tex],

and the coefficient of each term is the number of ways that combination can be derived from the expression. For example, there are 5 ways to arrange the combination [tex]x^4y^1[/tex], so its coefficient is 5. When the coefficients are multiplied with the combinations, they become

[tex]5x^4y^1 + 10x^3y^2 + 10x^2y^3 + 5xy^4 + y^5[/tex],

which is the expansion of (x y)5.

b) The binomial theorem states that for any expression of the form [tex](x + y)^n[/tex], the expansion can be found by multiplying the term[tex]x^n[/tex]with the coefficient of each term in Pascal’s triangle. For example, for[tex](x + y)^5[/tex], the coefficient of[tex]x^5[/tex] is 1, the coefficient of[tex]x^4y[/tex]is 5, the coefficient of[tex]x^3y^2[/tex]is 10, the coefficient of [tex]x^2y^3[/tex]is 10, the coefficient of[tex]x^1y^4 is 5[/tex], and the coefficient of[tex]y^5[/tex]is 1. Thus, the expansion of [tex](x + y)^5 is 1x^5 + 5x^4y + 10x^3y^2 + 10x^2y^3 + 5xy^4 + y^5.[/tex]

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Answer: The equation represents the value (in dollars) of a car t years after its purchase, so the purchase price of the car would have been the value of the car when t = 0. Plugging in t = 0 into the equation, we get:

V = 23900 * (0.91)^0

V = 23900

So the purchase price of the car was $23,900.

Regarding the rate of decrease in the value of the car, we can observe that the value decreases at a rate proportional to (0.91)^t, so the rate of decrease is proportional to 0.91.

Step-by-step explanation:

The graph of the y+2x=6 is given in the attachment.

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

The standard equation of a line is expressed as y = mx + b, m is the slope

and b is the y-intercept.

Given the equation y = 2x - 2

If x = -2

y = 2(-2) - 2

y = -4-2

y = -6

If x  = 4

y = 2(4) - 2

y = 8-2

y = 6

The point (-2, -6) and (4, 6 )must be on the line graph.

Hence, the graph of the y+2x=6 is given in the attachment.

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There are 4 zeros in the graph and the multiplicity is 5.

The zeros of a function are defined as the values of the variable of the function such that the function equals 0. Graphically, the zeros of a function are the points on the x-axis where the graph cuts the x-axis. In other words, we can say that the zeros of a function are the x-intercepts of its graph. The number of zeros of a polynomial function is equal to the degree of the polynomial.

In the given graph,

There are 4 turning points in the graph.

The 4 zeros from the graph are

(-3, 0), (-2, 0), (1, 0) and (1.5, 0)

The graph touches the x-axis and bounces off of the axis, it is a zero with  multiplicity is 5.

Therefore, there are 4 zeros in the graph and the multiplicity is 5.

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Answer:

Improper, proper, proper, improper

Step-by-step explanation:

Step-by-step explanation:

To be a proper fraction the numerator (top number) must be less the the denominator (bottom number). Let’s start at the top.

27/27

This would be an improper fraction because the numerator is equal to the denominator, not less.

6/17

Because 6 is less then 17 this would make it a proper fraction

8/9

Same case as the last one, this is a proper fraction because the numerator is less then the denominator

21/5

21 is definitely more the 5 making this a improper fraction.

Hope this helped :)

The average T2, T7, T6, T4, and T10 in Processor 1

T8, T9, T3, T1, and T5 on Processor 2.

Work on tasks t2, t7, t6, t4, and t10 will be done by processor 1. The first task to be finished is task t2, followed by tasks t7, t6, t4, and lastly t10. Work on tasks t8, t9, t3, t1, and t5 will be done by processor 2. The first work to be finished is task t8, followed by t9, t3, t1, and ultimately t5. In order to finish the job quickly, both processors will cooperate, with Processor 1 concentrating on the early tasks and Processor 2 concentrating on the later duties. This guarantees that the project is finished on schedule and that all the tasks are carried out in the proper order.

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He should expected tomorrows's score to be about 75 points greater than today's score.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

The input and output variables for this problem are given as follows:

The slope is given as follows:

m = 5.

Meaning that when the input increases by one, the output increases by 5, hence the expected score's increase with an increase in the input of 15 is given as follows:

15 x 5 = 75.

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The publisher nedds to produce 2414 books and sell so that production cost will equal the money from sales.

Equations whose variables have a power of one are called linear equations. One example with one variable is where ax+b = 0, where a and b are real values and x is the variable.

Given:

A small publishing company is planning to publish a new book.

The production costs will include one-time fixed costs (such as editing) and variable costs (such as printing).

The one-time fixed costs will amount to $27,160.

The variable costs will be $8.75 per book.

The publisher will sell the finished product to bookstores at a price of $20.00 per book.

Let x be the number of books.

Cost = 8.75x + 27160

Revenue = 20x

Revenue = cost

20x = 8.75x + 27160

11.25x = 27160

x = 2414.2

x ≈ 2414 books.

Therefore, the required number of books are 2414 books.

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Answer: 13

Step-by-step explanation: The two numbers are 967 and 445 making a=4 and b=9. We know a+b= 9+4 which is 13. For starters, you add the last digits of b67 and aa5 so 7+5=12 which is why the four digit number ends in two. When adding, the one from 12 would carry so the second to last digit on the four digit number would have to be 11. To get eleven you would add 7 and 4. The seven comes from the second digit in the b67 number including the one that came from 7+5=12. Now we know a=4. Knowing this now aa5= 445 and 1a12= 1412. We can now substract 445 from 1412 to get 967. b67= 967. To check 967+445=1412.  

Answer:4/3

Step-by-step explanation: rise over run when finding slope, and the first point i can find (-3,-5) is 4 up and 3 right away from (0,-1)

A. The thickness of the rectangular sheet of sugar paste is 1/5 cm.

B. The volume of the remaining pastry can be expressed as approximately 45.84 cm³.

The volume of a cuboid is equal to the product of the length, width, and height of a cuboid.

The volume of a cuboid is length × breadth× height

A) The volume of the cuboid pack of sugar paste is 5 cm x 8 cm x 9 cm = 360 cm³.

To find the thickness of the rolled-out rectangular sheet, we need to divide the volume of the pack by the area of the rectangular sheet:

thickness = volume/area

thickness = 360 cm³ / (30 cm x 60 cm)

thickness = 360 cm³ / 1800 cm²

thickness = 1/5 cm

So the thickness of the rectangular sheet of sugar paste is 1/5 cm.

B) The two circular pieces of pastry each have a diameter of 25 cm and thus a radius of 25/2 = 12.5 cm.

The volume of each circular piece of pastry can be calculated as:

V = π × (radius)² × thickness

V = π × (12.5 cm)² × 1/5 cm

V = π × 156.25 × 1/5 cm³

V = 50 × π cm³

Since Mary cuts out two circular pieces, the total volume of pastry that she removes is 2 x 50 x π cm³. The remaining volume of pastry is the original volume of the pack minus the volume of the two circular pieces:

Volume remaining = 360 cm³ - 2 × 50 × π cm³ = 45.84 cm³

The volume of the remaining pastry can be expressed as approximately 45.84 cm³.

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The monomial is 6² completes it and makes it (6p - 7q)².

A polynomial is an algebraic expression.

A polynomial of degree n in variable x can be written as,

a₀xⁿ + a₁xⁿ⁻¹ + a₂xⁿ⁻² +...+ aₙ.

We know a monomial is a polynomial that consists of a single term.

Given, __ - 42pq + 49q².

= ___ - 42pq + 7²q².

Now, 6×7 = 42,

Therefore,  ___ - 42pq + 7²q²,

= 6²p² - 42pq + 7²q².

= (6p)² - 42pq + (7q)².

= (6p - 7q)².

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Answer:

150 in cubed

Step-by-step explanation:

You spend 480 minutes per day at school. We will assume that you go to school for 5 days per week.

480 minutes × 5 days = 2,400 minutes per week

There are 4 weeks in a month, so we will multiply the minutes per week by 4 weeks to get the monthly time spent in school.

2,400 minutes per week × 4 weeks = 9,600 minutes per month

You are in school for 10 months, so we will multiply the minutes per month by 10.

9,600 minutes per month × 10 months = 96,000 minutes in school

Now, we will divide the time in school by the number of minutes in school per day.

96,000 minutes in school ÷ 480 minutes per day = 200 days in school

Answer: 96,000 hours or 200 days

The fraction of the entire space jenny use for pink roses is 1/8 of the whole garden

A word problem in math is a math question written as one sentence or more that requires children to apply their math knowledge to a 'real-life' scenario.

These word problem are translated into mathematical equations.

Represent the total garden by x

Jenny uses 1/2 of the garden to plant roses

= 1/2×x = x/2

She uses 1/4 of the space to plant pink roses

= 1/4 × ×/2

= x/8

Therefore she uses 1/8 of the whole garden to plant pink roses.

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Answer:

-4

4

14

Step-by-step explanation:

A:

5 + (-3)(3) = 5 -9 = -4

B:

5+ (-3)(1/3) = 5 - 1 - 4

C:

5 + (-3)(-3) = 5 + 9 = 14

Answer: maybe look up the answer and ask ur teacher what to do

Step-by-step explanation:

Answer: 12 feet

Step-by-step explanation: If the length of the garden is 20 feet then that means 40 feet of fence was used to make both lengths of the garden. So we subtract 40 from 64 which leaves us with 24 feet and then we divide 24 by 2 to get 12 because there are 2 widths.

Hope this helps!

The linear equation on the graph is:

y = x + 3

Here we have a linear equation.

Remember that the general one is y = a*x + b where b is the y-intercept, here we can see that the line intercepts the y-axis at y = 3

y = a*x + 3

And it passes through the point (-3, 0), replacing these values we get:

0 = a*-3 + 3

3a =  3

a = 3/3 = 1

The linear equation is:

y = x + 3

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The equation for the given scenario is y=50/57x-3.16.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The formula to find the slope of a line is slope = (y₂-y₁)/(x₂-x₁).

From the given figure, the coordinate points are (129, 110) and (300, 260).

Substitute (x₁, y₁)=(129, 110) and (x₂, y₂=(300, 260) is slope formula, we get

Slope (m) =(260-110)/(300-129)

= 150/171

= 50/57

Substitute, m=50/57 and (x, y)=(129, 110) in y=mx+c, we get

110=50/57 (129)+c

110=113.16+c

c= -3.16

Substitute, m=50/57 and c= -3.16 in y=mx+c, we get

y=50/57x-3.16

Therefore, the equation for the given scenario is y=50/57x-3.16.

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As a result, the coordinate of the picture of point B (4, 9) under dilation with the origin as the center and a scale factor of 2 is (8, 18).

Coordinates are a pair of integers that are used to locate a point or object in a two-dimensional plane. A point's location on a 2D plane is defined by two integers called the x-coordinate and the y-coordinate. The distance between two points is known as the x-coordinate, or abscissa, while the distance between two points is known as the y-coordinate, or ordinate. Point (3, 2), for example, is three units distant from the positive y-axis and two units away from the positive x-axis.

Here,

A dilation with center at the origin and scale factor of 2 will stretch or shrink the distances from the origin by a factor of 2. If the given point B is (4,9), its image under the dilation will be:

(2 * 4, 2 * 9) = (8, 18)

So the coordinate of the image of point B (4, 9) under the dilation with center at the origin and scale factor of 2 is (8, 18).

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Step-by-step explanation:

Median IJK = IM = PN + 2

Median PQR = PN

Therefore, IM = PN + 2

IM = PN + 2

PN = IM - 2

IM = (15 + 9 + PN)/2

PN = (15 + 9 + IM - 2)/2

15 + 9 + PN = 2IM

15 + 9 + IM - 2 = 2PN

25 + PN = 2IM

25 + IM - 2 = 2PN

PN = 2IM - 25

PN = 2PN - 25

3PN = 25

PN = 25/3

IM = PN + 2

IM = 25/3 + 2

IM = 29/3

Therefore, IM = 29/3 and PN = 25/3.

(a). There is a 57.16 Mbps difference. (b). There is a 2.74 standard deviation difference. (c). 2.74 is the z-score (d). The maximum data rate offered by the carrier is more than 2.

When something is careful and purposeful, you use the word measured to describe it. The men's voices were measured and quiet. Voters will be attracted to her more considered reaction. These are a couple of those illustrations. using a thermometer to measure body temperature using a measuring cylinder to determine the weight of produce in a store. Measuring the stature of an infant to retain his/her growth record.

(a). (74.5 - 17.34) = 57.16

(b). 57.16/20.79

= 2.74

(c). z = (X - μ)/sd

= (74.5 - 17.34)/20.79

= 2.74

(d). Because it is higher than 2, the carrier's greatest data speed is noteworthy.

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The solution is Option C.

The value of the quadratic equation is A = 3a² + 4a - 4 , where the factor of a is given by a = 2/3

A quadratic equation is a second-order polynomial equation in a single variable x , ax² + bx + c=0. with a ≠ 0. Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.

The roots of the quadratic equations are

x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )

where ( b² - 4ac ) is the discriminant

when ( b² - 4ac ) is positive, we get two real solutions

when discriminant is zero we get just one real solution (both answers are the same)

when discriminant is negative we get a pair of complex solutions

Given data ,

Let the quadratic equation be represented as A

Now , the value of A is

A = 3a² + 6a - 2a - 4   be equation (1)

On simplifying the equation , we get

A = 3a² + 4a - 4

Now , when the factor of the equation is ( 3a - 2 ) = 0

Adding 2 on both sides of the equation , we get

3a = 2

Divide by 3 on both sides , we get

a = 2/3

Substitute the value of a in the equation , we get

A = 3 ( 2/3 )² + 4 ( 2/3 ) - 4

On simplifying the equation , we get

A = 3 ( 4/9 ) + 8/3 - 4

A = ( 4/3 + 8/3 ) - 4

A = ( 12/3 ) - 4

A = 4 - 4

A = 0

Hence , the binomial ( 3a - 2 ) is a factor of the equation

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Using the Chinese Remainder Theorem, the smallest positive integer solution is x1 = 62.

We can use the Chinese Remainder Theorem to find the smallest positive integer solution for this problem.

The Chinese Remainder Theorem states that if x ≡ a (mod m) and x ≡ b (mod n), then x is congruent to a unique value modulo mn. That is, there exists a unique solution x such that x is congruent to a modulo m and congruent to b modulo n, and the solution x is between 0 and mn - 1.

So, we want to find the smallest x such that:

x ≡ 6 (mod 8) and x ≡ 7 (mod 9)

We can start by finding a solution x1 such that x1 ≡ 6 (mod 8) and x1 ≡ 7 (mod 9). One such solution is:

x1 = 6 + 8k for some integer k

We can use the formula x1 = 6 + 8k to find a solution x1 that is also congruent to 7 (mod 9):

x1 = 6 + 8k = 7 + 9l (mod 9)

Expanding the right side of this equation, we get:

6 + 8k = 7 + 9l (mod 9)

6 - 7 = 9l - 8k (mod 9)

-1 = 9l - 8k (mod 9)

Since 9 and 8 are relatively prime, we can use the Extended Euclidean Algorithm to find integers r and s such that:

8r + 9s = gcd(8, 9) = 1

Using the Euclidean Algorithm, we can find r = -1 and s = 1. So,

-8 = 9(l - rk) (mod 9)

Since 9 is relatively prime to 8, l - rk is a multiple of 9. We can then rewrite the equation as:

-8 = 9j (mod 9)

Adding 9 to both sides of the equation, we get:

1 = 9j (mod 9)

So, j = 1.

Now, we have:

k = (1 - l) / r

Since r = -1, we can replace k with -l:

k = -l

So, we have:

x1 = 6 - 8l

And,

x1 = 7 + 9l (mod 9)

Combining these two equations, we get:

6 - 8l = 7 + 9l (mod 9)

Subtracting 9l from both sides, we get:

-2l = 13 (mod 9)

Dividing both sides by -2, we get:

l = -13 / -2 = 7 (mod 9)

So,

k = -l = -7 (mod 9)

And,

x1 = 6 - 8(-7) = 6 + 56 = 62 (mod 8)

So,

x1 = 62 (mod 8) and x1 = 7 (mod 9)

The smallest positive integer solution is x1 = 62

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The solution of the inequality are shown in figure.

A relation by which we can compare two or more mathematical expression is called an inequality.

Given that;

The inequalities are,

⇒ x + 1 < 9

⇒ 4x ≤ 8

Now, We can simplify as;

⇒ x + 1 < 9

Subtract 1 both side;

⇒ x < 9 - 1

⇒ x < 8

⇒ 4x ≤ 8

Divide by 4;

⇒ x ≤ 4

Thus, The solution of the inequality are shown in figure.

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To find the derivative of a piecewise function, you need to take the derivative of each individual piece and then combine them into one piecewise function.

The derivative of each piece can be found using the usual rules of differentiation (such as the power rule, sum rule, product rule, etc.).

Once you have the derivatives of each piece, you can write the overall derivative as a piecewise function, where the expression for each piece is limited to a specific range of x-values. The limits of each piece are defined by the breakpoints in the original function.

For example, if the original function is given as:

f(x) = {x^2 for x < 0,

x for 0 <= x < 1,

2x for x >= 1}

Then the derivative of f(x) can be found as:

f'(x) = {2x for x < 0,

1 for 0 <= x < 1,

2 for x >= 1}

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Correct Answer is c. Phyllis has a comparative advantage in producing cakes.

What is comparative advantage?

Comparative advantage is an economic concept that refers to the ability of an individual, firm, or country to produce a particular good or service more efficiently compared to others.

The opportunity cost of producing one cake for John is (20 loaves of bread) / (18 cakes) = 1.11 loaves of bread per cake.

The opportunity cost of producing one cake for Phyllis is (30 loaves of bread) / (15 cakes) = 2 loaves of bread per cake.

Since Phyllis has a lower opportunity cost of producing cakes (2 loaves of bread per cake) compared to John (1.11 loaves of bread per cake), Hence, Phyllis has a comparative advantage in producing cakes.

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