What is the interquartile range of the set of data this box-and-whisker plot represents?

The (f + g)(x) = 15x - 2 is represent the total round trip time.

According to the statement

we have given that the f(x) represents the time it takes a boat to travel upstream and g(x) represents the time it takes a boat to travel downstream.

And we have to find the total round trip time.

So, For this purpose, the given information is:

f(x) = 3x − 10 and g(x) = 12x + 8

And

The total round trip time is represented by the term (f + g)(x)

We know that the

(f + g)(x) = f(x) + g(x)

Substitute the given values in it

So, (f + g)(x) = f(x) + g(x)

(f + g)(x) = (3x - 10) + (12x + 8)

(f + g)(x) = 15x - 2

Hence, The (f + g)(x) = 15x - 2 is represent the total round trip time.

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Answer:

[tex] {x}^{4} [/tex]

Step-by-step explanation:

[tex] { {( - x}^{2} )}^{2} = ( - {x}^{2} )( - {x}^{2} ) = {x}^{4} [/tex]

An expression is defined as a set of numbers, variables, and mathematical operations. The value of the given expression when simplified is equal to x⁴.

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

The given expression can be simplified as shown below,

(-x²)²

= (-x × -x)²

Since the product of two negatives is always positive, therefore, we can write,

= -x² × -x²

As per the rule of exponents, the expression can be written as,

= x⁴

Hence, the value of the given expression when simplified is equal to x⁴.

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The number is 841

So we can see that the number is odd.

Here we have a 3-digit number that can be written as:

a*100 + b*10 + c

Here we know that:

"the tens digit of a number is 4 times the units digit"

b = 4*c

"the hundreds digit is twice the tens digit"

a = 2*b

Now, remember that a, b, and c, are numbers on the set {0, 1, ..., 8, 9}

And if we replace the first equation into the second, we get:

a = 2*(4*c) = 8*c

Now, the only value of c that we can use such that a is a single digit whole number is c = 1

(if c = 0, then our number is zero)

a = 8*1 = 8

b = 4*1 = 4

c = 1

The number is 841

So we can see that the number is odd.

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Answer:

31. (98,765 x 9) + 3 = 888,888

32. (12,345 x 9) + 6 + 111,111

33. 3367 x 15 + 50,505

34. 15,873 x 28 = 555,555

35. 33,334 x 33,334 = 1,111,155,556

36. 11,111 x 11,111 = 123,454,321

41. 3 + 9 + 27 + 81 + 243 = 3(243 -1) / 2

42.  1/1x2 + 1/2x3 + 1/3x4 + 1/4x5 + 1/5x6 = 5/6

hope this helps

Answer:

see the step-by-step explanation

Step-by-step explanation:

31. (98,765 x 9) + 3 = = 888,888

32. (12,345 x 9) + 6 + 111,111

33. 3367 x 15 + 50,505

34. 15,873 x 28 = 555,555

35. 33,334 x 33,334 = 1,111,155,556

36. 11,111 x 11,111 = 123,454,321

41.3+9+27+81 +243 = 3(243-1)/2

42. 1/1x2 + 1/2x3 + 1/3x4 + 1/4x5 + 1/5x6 = 5/6

The area of the parallelogram is 55 square feet

From the figure, we have the following dimensions:

Height = 5 ft

Base = 11 ft

The area of the parallelogram is calculated as:

Area = Base * Height

This gives

Area = 5ft * 11ft

Evaluate the product

Area = 55 square feet

Hence, the area of the parallelogram is 55 square feet

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The intermediate value theorem applies to the indicated interval and the importance of c guaranteed by the theorem is c=2,3.

Especially, he has been credited with proving the following five theorems:  a circle is bisected via any diameter; the bottom angles of an isosceles triangle are the same;  the other (“vertical”) angles are shaped by means of the intersection of two traces are same; two triangles are congruent (of identical form and size.

In mathematics, a theorem is an announcement that has been proved or may be proved. The evidence of a theorem is a logical argument that makes use of the inference guidelines of a deductive system to set up that the concept is a logical result of the axioms and formerly proved theorems.

In line with the Oxford dictionary, the definition of the concept is ''a rule or principle, especially in arithmetic, that may be proved to be true''. For example, in arithmetic, the Pythagorean theorem is a  theorem and is maximum extensively used in the domain of science.

2-1and interval = [4]

since function text is continuous in a given interval. And also

+(4) = 42+4 = 4-1

20 = 6667

$(5/4) = ($145/2

stone-1

= 5.833

simple, f(4) > $(5/2), hence Intermediate

Theorem & applies to the indicated proved.

Now,

= 6 C-1

C-5c +6 = 0

C=2 or c=3

1=3 or

C= 2, 3

<= 2

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The values of [tex]x[/tex] are [tex]1+\sqrt{89}[/tex] and [tex]1-\sqrt{89}[/tex].

To find the values of x:

Given equation: [tex](x+7)(x-9)=25[/tex]

Then: [tex]x(x-9)+7(x-9)=25[/tex]

Using the distributive property: [tex]a.(b+c)=a.b+a.c[/tex]

[tex]x^{2} -9x+7x-63=25[/tex]

Combine like terms:

[tex]x^{2} -2x-63=25[/tex]

Subtract 25 from both sides and obtain:

[tex]x^{2} -2x-88=0[/tex]

Using completing square form:

Add and subtract [tex](\frac{2}{2} )^{2} =1[/tex] we have:

[tex]x^{2} -2x-88+1-1=0\\(x-1)^{2} -89=0[/tex]

Add 89 to both sides we have:

[tex](x-1)^{2} =89[/tex]

Taking square roots on both sides, obtain:

[tex]x-1=[/tex] ± [tex]\sqrt{89}[/tex]

Add 1 to both sides we have:

[tex]x=1[/tex]±[tex]\sqrt{89}[/tex]

Therefore, the values of [tex]x[/tex] are [tex]1+\sqrt{89}[/tex] and [tex]1-\sqrt{89}[/tex].

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The complete question is given below:

Use completing the square to solve (x + 7)(x – 9) = 25 for x.

With respect to the parent function y = cos x, the interval closest to the range of the transformed function is ( 0,50). the correct option is D.

Mathematically speaking, cosines are periodic functions, and period (T) is the distance in the horizontal axis such that f(t + T) = f(t). The period of the parent cosine function is 2π. The period in daughter functions may vary by means of the following form:

y = cos Ax     (1)

Where:

x - Independent variable

y - Dependent variable

A - Period width

From the graph, it is observed that with respect to the parent function y = cos x, the interval closest to the range of the transformed function is ( 0,50). the correct option is D.

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Answer: The answer is [0,65]

Step-by-step explanation:

The value of angle ABT is 40 degrees if PTR is the tangent of a circle option (a) 40° is correct.

It is described as a set of points, where each point is at the same distance from a fixed point (called the center of a circle)

It is given that:

A circle is shown in the picture.

PTR is the tangent of a circle.

AT=PT

Angle APT=20°

Let O is the center of the circle:

Angle BOT = 2 Angle PAT = 40 degrees

BO = TO = r

Angle BOT = Angle TBO = (1/2)(180 - 40) = 70 degrees

RTP is the tangent

OT ⊥ PTR

Angle OTA = 90 - Angle ATR = 50 degrees

Angle ABT = 180 - Angle PAT - Angle BTA

= 180 - 20 -  (170 + 50)

= 40 degrees

Thus, the value of angle ABT is 40 degrees if PTR is the tangent of a circle option (a) 40° is correct.

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x > 1 is the required solution of the given inequality - 3x + 7 < 4. This can be obtained by solving the inequality the same way as we solve an algebraic equation.

The inequality can be solved as the same way as we solve an algebraic equation.

Here in the question the inequality to be solved is given:

- 3x + 7 < 4

By subtracting 7 from both sides of the inequality we get,

⇒ - 3x + 7 - 7 < 4 - 7

⇒ - 3x < - 3

To make the side of the inequality with variable x positive we multiply the whole equation with - 1, then we have to reverse the sign of inequality since we have to multiply the whole inequality with a negative term,

we get,

⇒ 3 x > 3

Now finally by dividing the whole inequality by 3 we get,

⇒ x > 1

The number line representation can be done by marking values from 1 to numbers greater than 1.

Hence x > 1 is the required solution of the given inequality - 3x + 7 < 4.

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Answer:

9.72 lb

Step-by-step explanation:

Yield = the amount or quantity produced or returned.

Given:

To determine how many pounds of eggplant you will be able to use, calculate 81% of the amount of eggplant purchased.

[tex]\begin{aligned}\sf 81\% \: of \: 12 \: lb & = \sf \dfrac{81}{100} \cdot 12\\\\& = \sf \dfrac{81 \cdot 12}{100}\\\\& = \sf \dfrac{972}{100}\\\\& = \sf 9.72\:lb\end{aligned}[/tex]

Therefore, you will be able to use 9.72 lb (nearest hundredth).

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Purchase=12lb

Amount to be used

You will be able to use 9.72pounds

Answer:

Step-by-step explanation:

The rational root theorem tells you any rational roots of the expression will be found from the constant and the leading coefficient:

  rational roots = ±{divisor of 25} / {divisor of 3}

The list of divisors in each case is pretty short, so this is ...

  rational roots = ±{1, 5, 25) / {1, 3} = ±{1/3, 1, 5/3, 5, 25/3, 25}

We find the only actual rational root is x = 5/3 when we graph the function.

(Factoring out that root, we find the remaining roots are ±i√5, irrational imaginary values.)

Answer:  [tex]h(\text{x}) = -4\text{x}^2 - 6\text{x} + 6[/tex]

Work Shown:

[tex]h(\text{x}) = f(\text{x}) - g(\text{x})\\\\h(\text{x}) = ( 8\text{x}^2 - 2\text{x} + 3) - ( 12\text{x}^2 + 4\text{x} - 3 )\\\\h(\text{x}) = 8\text{x}^2 - 2\text{x} + 3 - 12\text{x}^2 - 4\text{x} + 3 \\\\h(\text{x}) = (8\text{x}^2-12\text{x}^2) + (- 2\text{x} - 4\text{x}) + (3 + 3) \\\\h(\text{x}) = -4\text{x}^2 - 6\text{x} + 6 \\\\[/tex]

Answer:

81

Step-by-step explanation:

If a number is divisible by 11, then you can make those numbers by multiplying 11 by any number. Like 33 is divisible by 11 because 3×11 is 33.

Of course, 33 is too small, we are looking for 3-digit numbers...

see image.

330 ways can the instructor choose the first group of four education students.

What is probability in math?

Given:

12 students

3 groups consisting of 4 students.

Mark can't be in the first group.

The combination formula that I used is =  n! / r!(n-r)!

where: n = number of choices ; r = number of people to be chosen.

This is the formula I used because the order is not important and repetition is not allowed.

Since Mark can't be considered in the first group, the value of n would be 11 instead of 12. value of r is 4.

numerator: n! = 11! = 39,916,800

denominator: r!(n-r)! = 4!(11-4)! = 4!*7! = 120,960

Combination = 39,916,800 / 120,960 = 330

Therefore, There are 330 ways that the instructor can choose 4 students for the first group.

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Answer:  [tex]35 cm^2[/tex]

Step-by-step explanation:

Area of trapezium =

2X = 2 + 2 = 4 cm

2Z = 5 + 5 = 10 cm

Y = 5 cm

[tex]\dfrac{ \left( 4+10 \right) }{ 2 } \times 5[/tex]

                 |

                 |--------> 35 [tex]cm^2[/tex]

We can infer and logically deduce that airplane’s ground speed is equal to 658.94 kph.

Given the following data:

Speed can be defined as the distance covered by an object per unit of time. Thus, speed can be measured in kilometer per hour (kph).

Mathematically, speed can be calculated by using this formula;

Speed = distance/time

In order to calculate the airplane’s ground speed, we would apply the law of cosine:

C² = A² + D² - 2(A)(D)cosθ

Substituting the given parameters into the formula, we have;

C² = 700² + 60² - 2(700)(60)cos45

C² = 434,203.03

C = √434,203.03

C = 658.94 kph.

In conclusion, we can infer and logically deduce that airplane’s ground speed is equal to 658.94 kph.

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The regression equation that represents the relationship between velocity and time is:

To find the equation, we need to insert the points (x,y) in the calculator.

For this problem, the points (t,v), that is, time and velocity, are given as follows:

(0, 6.1), (2.1, 12.2), (5.3, 17.4), (8.2, 26.4), (10, 28.1), (12.1, 32.8).

Hence, inserting these points into a calculator, the equation is given by:

v = 2.19t + 6.7.

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Considering the definition of an inequality, the number of people who can go to the amusement park is 3.

An inequality is the existing inequality between two algebraic expressions, connected through the signs:

An inequality contains one or more unknown values ​​called unknowns, in addition to certain known data.

Solving an inequality consists of finding all the values ​​of the unknown for which the inequality relation holds.

In this case, you know that:

Being "p" the number of people who can go to the amusement park, the inequality that expresses the previous relationship is

$9.75 + $16.25×p ≤$65

Solving:

$16.25×p ≤$65 - $9.75

$16.25×p ≤$55.25

p ≤$55.25÷ $16.25

p≤ 3.4

Finally, the number of people who can go to the amusement park is 3.

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Answer:

7/6π, 1/6π

Step-by-step explanation:

We know that tan is sine/cosine, so cot is cosine/sine.

In this case, we know cotθ = √3

As the number is positive, using the unit circle, we now can say that the two solutions are in quadrants I and III.

Taking a look at the unit circle, we can finalize our answer.

Step-by-step explanation:

180(n-2)/n=90 ( this is the solution for the 90)

cross multiplying

180n-360=90n

180n-90n=360

90n=360

90n/90=360/90

n=4, the number of sides for the polygon with 90° is 4 sides

Solution for 100°

180(n-2)/n=100

180n-360=100n

180n-100n=360

80n=360

80n/80=360/80

n=4.5

Same applies to the rest 110°,125° ,150°,175°

Step-by-step explanation:

3. B

because the figure to the left of the y-axis yields the one to the right when you reflect it across y = x.

4. C

Flip either of the figures vertically across x = -1 which is their intersection point and you'll get the other.

5. D

it can't be clockwise because the x value of the vertices would have been negative. so it is 270° counterclockwise resulting in ( -y , x )

6. A

Similar to #4 which except this time, you flip it horizontally like how you lay a book or pick it up.

The answer is A. Winter.

As the pattern is : F, W, Sp, Su, F... (letters used for convenience), then the next word in the pattern will be Winter, because that was shown in the previous sequence.

Answer:

(4x - 1)^2.

Step-by-step explanation:

16x^2 - 8x + 1

Multiplying the first and last coefficients:

16 * 1 = 16

We need 2 numbers whose product is 16 and whose sum is -8.

These are - 4 and -4.

So we now write:

16x^2 - 4x - 4x + 1

Now factor by grouping :

= 4x(4x - 1) - 1(4x - 1)

= (4x - 1)(4x - 1)

= (4x - 1)^2

This method of factoring quadratics is called the 'ac' method - you split the middle term ( in this case the -8x) into 2 parts.

Answer:

[tex](4x-1)^2[/tex]

Step-by-step explanation:

Given quadratic expression:

[tex]16x^2-8x+1[/tex]

To factor a quadratic in the form [tex]ax^2+bx+c[/tex], find two numbers that multiply to ac and sum to b:

Therefore, two numbers are: -4 and -4

Rewrite the middle term as the sum of these two numbers:

[tex]\implies 16x^2-4x-4x+1[/tex]

Factorize the first two terms and the last two terms separately:

[tex]\implies 4x(4x-1)-1(4x-1)[/tex]

Factor out the common term (4x - 1):

[tex]\implies (4x-1)(4x-1)[/tex]

Apply the exponent rule:  aa = a²

[tex]\implies (4x-1)^2[/tex]

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Taking into account the definition of proportion, 12 students said their favorite color was blue.

The ratio is the comparison of two quantities and is measured from the division of two values. In other words, the ratio between two magnitudes is defined as their ratio or division; that is, given the quantities a and b, the ratio between them is a÷b.

The result of this division can be understood as how many times one quantity is in another.

The relationship of equality that exists between two ratios, that is, between two comparisons between two determined quantities, is known as a proportion. So if a/b corresponds to the ratio, then a/b = c/d equals a proportion.

At school, the teacher surveyed the color preferences of 21 students. Out of every 7 students surveyed, 4 said they liked blue the best. This can be expressed as a proportion as follow:

4÷7= x÷ 21

where x is the number of students of the 21 students surveyed who like blue.

Solving:

(4÷7)×21= x

12= x

Finally, 12 students said their favorite color was blue.

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Answer:

20 pounds

Step-by-step explanation:

i took the test trust me i got 2 points

Answer:cost(weight)

Step-by-step explanation:

The options A, C, E are correct. On the basis of the theory of the rotation and transformation on the parallelogram.

According to the statement

we have given that the

Parallelogram 1 is in quadrant 1 and sits on the x-axis with a point at (0, 0). Parallelogram 2 is in quadrant 4 and sits on the y-axis with a point at (0, 0)

And we have to find that the which terms are corrected from the given options when Parallelogram 1 is rotated 270 degrees counter-clockwise to form parallelogram 2.

So, For this purpose we know that the

A rotation is a type of transformation that takes each point in a figure and rotates it a certain number of degrees around a given point.

And According to the given statement

when parallelogram 1 is rotated 270 degrees counter-clockwise to form parallelogram 2.

Then the conditions A, C, E are applicable because on rotation these things are applicable.

So, The options A, C, E are correct. On the basis of the theory of the rotation and transformation on the parallelogram.

Disclaimer: This question was incomplete. Please find the full content below.

Question:

Figure 2 was constructed using figure 1.

On a coordinate plane, 2 parallelograms are shown.

Parallelogram 1 is in quadrant 1 and sits on the x-axis with a point at (0, 0). Parallelogram 2 is in quadrant 4 and sits on the y-axis with a point at (0, 0).

Parallelogram 1 is rotated 270 degrees counter-clockwise to form parallelogram 2.

For the transformation to be defined as a rotation, which statements must be true? Select three options.

A. The segment connecting the center of rotation, C, to a point on the pre-image (figure 1) is equal in length to the segment that connects the center of rotation to its corresponding point on the image (figure 2).

B. The transformation is rigid.

C. Every point on figure 1 moves through the same angle of rotation about the center of rotation, C, to create figure 2.

D.Segment CP is parallel to segment CP'.

E. If figure 1 is rotated 180° about point C, it will be mapped onto itself.

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Matt's BAC the equation for is  mathematically given as

X= 4 standard drinks

This is further explained below.

Blood Alcohol Content, sometimes known as BAC, is a measurement that expresses the amount of alcohol present in the blood as a percentage. Because it is measured in grams per 100 milliliters of blood, a blood alcohol concentration (BAC) of 0.08 indicates that your blood contains 0.08 percent alcohol by volume.

Generally, One standard drink is equal to twelve ounces of beer.

He drank a total of 48 ounces of beer since he had three cups of beer that were each 16 ounces.

In conclusion, the number of standard drinks that Matt consumed

X= 48/12

X= 4 standard drinks

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