Which expression is equivalent to 3(–2x – 1)?
*

The slope of the line that passes through given points is -0.87. Option B is the correct answer.

In mathematics, slope is usually defined by the letter "m" and includes the change in y coordinate (vertical change) divided by the change in x coordinate (horizontal shift) between two points on a line.

We know that slope of a line that passes through two points is :

slope,   [tex]m = \frac{y_{2} - y_{1} }{x_{2}-x_{1} }[/tex]

The given points are (-3.9,4.1) and (5.5,-4.1).

y2 = -4.1

y1 = 4.1

x2 = 5.5

x1 = -3.9

Substituting all these values  in the above equation  we get,

slope,  [tex]m = \frac{-4.1 - (4.1)}{5.5 - (-3.9)}[/tex]

m = -8.2 / 9.4

m = -0.87

So, the slope of the line formed by given points is -0.87. Therefore , option B is correct answer.

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(f x g)(x) = √(1/x + 2)

(g x f)(x) = 1/(√(x + 2))

To find (f x g)(x), we need to evaluate the composition of functions f and g, which is denoted as f(g(x)).

Similarly, to find (g x f)(x), we need to evaluate the composition of functions g and f, which is denoted as g(f(x)).

Let's calculate (f x g)(x) and (g x f)(x) for the given pair of functions f(x) = √(x + 2) and g(x) = 1/x:

1. (f x g)(x):

We start by substituting g(x) into f(x) wherever we see an x in f(x):

(f x g)(x) = f(g(x)) = f(1/x)

Substitute 1/x into f(x):

(f x g)(x) = f(g(x)) = f(1/x) = √(1/x + 2)

2. (g x f)(x):

We start by substituting f(x) into g(x) wherever we see an x in g(x):

(g x f)(x) = g(f(x)) = g(√(x + 2))

Substitute √(x + 2) into g(x):

(g x f)(x) = g(f(x)) = g(√(x + 2)) = 1/(√(x + 2))

Therefore, we have:

(f x g)(x) = √(1/x + 2)

(g x f)(x) = 1/(√(x + 2))

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There must exist a vertex u in T such that the distance between u and v is at most (n-1)/2.

To prove the existence of a vertex u in tree T such that the distance between u and v is at most (n-1)/2, we can employ a contradiction argument. Assume that such a vertex u does not exist.

Since the number of vertices in T is odd, there must be at least one path from v to another vertex w such that the distance between v and w is greater than (n-1)/2.

Denote this path as P. Let x be the vertex on path P that is closest to v.

By assumption, the distance from x to v is greater than (n-1)/2. However, the remaining vertices on path P, excluding x, must have distances at least (n+1)/2 from v.

Therefore, the total number of vertices in T would be at least n + (n+1)/2 > n, which is a contradiction.

Hence, there must exist a vertex u in T such that the distance between u and v is at most (n-1)/2.

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The angle formed is 91.84° which can be obtained using Cosine Rule since all the three sides are given.

CosC = (a²+b²-c²) /2(ab)

a = 31

b = 42

c = 53

Substituting the values into the relation

CosC = (31² + 42² - 53²) / 2(31×42)

CosC = - 84 / 2604

CosC = −0.032258

C =

[tex]C = {cos}^{ - 1} (- 0.03225)[/tex]

C = 91.84°

Hence, the angle formed is 91.84°

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The GDP at FC from the following data: GDP at MP = Rs. 2,000 billion Indirect taxes = Rs. 300 billion Subsidies = Rs. 100 billion​ is: Rs. 1,800 billion.

Using this formula to determine the GDP at FC

GDP at FC = GDP at MP - Indirect taxes + Subsidies

Where:

GDP at MP (Market Price) = Rs. 2,000 billion

Indirect taxes = Rs. 300 billion

Subsidies = Rs. 100 billion

Let plug in the formula

GDP at FC = 2,000 billion - 300 billion + 100 billion

GDP at FC = 1,800 billion

Therefore the GDP at factor cost (FC) is Rs. 1,800 billion.

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KM, JK, PK, and MJ are shown on the diagram.

Then the correct options are B, C, D, and F.

Since, Coordinate geometry is the study of geometry using the points in space. Using this, it is possible to find the distance between the points, the dividing line is m:n ratio, finding the mid-point of the line, etc.

A line segment in mathematics has two different points on it that define its boundaries.

All the line segments will be

JK, JM, KM, MP, PK, and KL

The triangle KPM.

And the angle will be ∠LKJ, ∠PKM. ∠KMP. and ∠MPK.

Then the correct options are B, C, D, and F.

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Answer:

False

Step-by-step explanation:

1. The inverse function should have c(n) isolated
2. When finding the inverse of a function, the variables c(n) and n are interchanged (and then c(n) is isolated).
It would look like this --->c(n)=50+4n--->n=50+4(c(n)) ---> c(n)=(n-50)/4

Based on the LCM, Jaziel, Elisa, and Sofía will coincide again after 60 days.

From the information, in the family business, the siblings Jaziel Elisa and Sofía must help take care of it, so he comes every four days, Elisa every five days and Sofía that at six o'clock.

In order to determine when Jaziel, Elisa, and Sofía will coincide again, we need to find the least common multiple (LCM) of their visit intervals.

The intervals for Jaziel, Elisa, and Sofía are 4 days, 5 days, and 6 days, respectively. We need to find the smallest number that is divisible by all three of these intervals.

The LCM of 4, 5, and 6 is 60. Therefore, Jaziel, Elisa, and Sofía will coincide again after 60 days.

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In the family business, the siblings Jaziel Elisa and Sofía must help take care of it, so he comes every four days, Elisa every five days and Sofía that at six o'clock if the three have coincided on March 4 after how many days will they coincide again

Answer: $4,998

Step-by-step explanation:

34000*1.147

38998-34000=4998

Answer:

608 in²

Step-by-step explanation:

To figure out how much wrapping paper we need to cover the box, we can find its surface area.

The surface area of a rectangular prism (a box) is defined as:

[tex]SA = 2A + (P \cdot d)[/tex]

where [tex]A[/tex] is the area of the base, [tex]P[/tex] is the perimeter of the base, and [tex]d[/tex] is the prism's depth.

From the diagram, we can identify the following values for these variables:

[tex]A=16\cdot 12 = 192 \text{ in}^2[/tex]

[tex]P = 16 + 12 + 16 + 12 = 56 \text{ in}[/tex]

[tex]d = 4\text{ in}[/tex]

Now, we can plug these values in for the variables in the above formula and solve for the prism's surface area.

[tex]SA = 2A + (P \cdot d)[/tex]

[tex]SA = 2(192) + (56 \cdot 4)[/tex]

[tex]SA = 384 + 224[/tex]

[tex]SA = 608 \text{ in}^2[/tex]

So, we need 608 in² of paper to cover the box.

The horizontal distance from the base of the skyscraper out to the ship is 1140 m

Under the horizontal line, the angle of depression is measured, typically in degrees. It aids in figuring out how steep or incline the line of sight is in relation to the horizontal plane. The line of sight is steeply directed downward and increases with the angle of depression.

In many different disciplines, such as surveying, navigation, engineering, and physics, the angle of depression is frequently utilized.

We know that;

Tan 45 = x/1140

x = 1140 Tan 45

= 1140 m

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The marginal frequency of students who chose dancing is 37.

The correct answer to the given question is option 3.

The marginal frequency of students who chose dancing can be calculated by adding up the number of students who chose dancing in each row or column. In this case, we need to add up the number of art students who chose dancing (22) and the number of music students who chose dancing (15), which gives us a total of 37. This is the marginal frequency of students who chose dancing.

Based on the survey results, it appears that a slightly higher percentage of art students prefer dancing (41.5%) compared to music students (31.9%). However, both groups of students seem to be fairly evenly split between dancing and playing sports, with a slight preference for playing sports overall.

It's worth noting that cardiovascular activity is important for overall health and well-being, and both dancing and playing sports can provide great opportunities for exercise and physical activity. Additionally, both activities can also be enjoyable and provide a sense of community and social connection, which is important for middle school students who are still developing their social skills and relationships. Ultimately, the choice between dancing and playing sports will depend on individual interests, preferences, and abilities.

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The class has collected a total of 74 pounds of food so far.

The class collected 33 pounds on the first day and 41 pounds on the second day.

To find the total pounds of food collected, we add these two amounts together:

33 pounds + 41 pounds = 74 pounds

On the first day, the students gathered 33 pounds, and on the second day, they collected 41 pounds.

We combine these two figures together to get the total number of pounds of food collected:

33 lbs. plus 41 lbs. equals 74 lbs.

On the first day, the class brought in 33 pounds, and on the second, 41 pounds.

We combine these two figures to get the total weight in pounds of food collected:

44 pounds plus 33 pounds equals 74 pounds.

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Answer:

Entrance fee for children: $1.92

Entrance fee for adults: $3.92

Step-by-step explanation:

Total expenses for this year: $214.00

The child fee will be: $x

and the adult fee will be $(x+2)

Last year the number of children was 44

and the number of adults was 33

this year also has the same number of children and adults.

which means the entrance fee total for children will be $44x and for adults will be $33(x+2).

44x + 33(x+2) = 214

--> 44x + 33x + 66 = 214

--> 77x = 214 - 66 = 148

--> x = 148/77 = 1.92

So children's price is $1.92 and adults price is $1.92 + 2

hence:

Entrance fee for children: $1.92

Entrance fee for adults: $3.92

Which is the standard equation for a circle centered at the origin with radius r be,

⇒   x² + y²  = r²

Hence option D is correct.

We have to find the standard equation of circle,

Given that,

Center of circle is at (0, 0)

And radius is r

Let a point (x, y) on the circle.

We know that,

The distance between the point (x, y) and origin is also known as radius of the circle,

Since we know that,

The distance between two points (x₁ , y₁) and (x₂, y₂) is,

⇒ d = √ (x₂ - x₁)² + (y₂ - y₁)²

Therefore distance between (0, 0) and (x, y),

⇒   √[ (x - 0)² + (y - 0)²] = r

Squaring both sides we get,

⇒   (x - 0)² + (y - 0)²  = r²

⇒   x² + y²  = r²

This  is the standard equation of circle.

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The volume of the solid generated by rotating the figure is 62.8 cubic units

From the question, we have the following parameters that can be used in our computation:

The figure

The figure is a rectangle with the following dimensions

Length = 5

Width = 2

When rotated around the given axis, we have a cylinder with the following dimensions

Height = 5

Radius = 2

So, we have

Volume = πr²h

This gives

Volume = 3.14 * 2² * 5

Evaluate

Volume = 62.8

Hence, the volume of the solid generated by rotating the figure is 62.8 cubic units

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Answer:

----------------------

Let d be the number of dimes and q be the number of quarters.

We can set up two equations based on the information given:

Use substitution here:

So he has 5 quarters.

We can plug that back into either equation to find the number of dimes:

So he has 9 dimes and 5 quarters.

The two mathematical symbols that William Oughtred introduced are "×" for multiplication and "::" for proportion.

Given is a statement about William Oughtred.

William Oughtred is most famous not for his mathematical discoveries, but rather for introducing two mathematical symbols.

We have to find those symbols.

William Oughtred is actually an English priest who basically teaches the students in mathematics subject.

He did invent other famous things like slide rule.

But the most famous invention of him is two mathematical symbols which are "×" for multiplication and "::" for proportion which are still widely used symbols.

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Answer:

c=19

Step-by-step explanation:

11=c-8

+8  +8

19=c

11=c-8

move the variable to the left - hand side and change it sign: 11-c= -8

move the constant to the right-hand side and change its sign: -c= -8-11

calculate the difference: -c = -19

change the signs on each side c=19

Brynen will use 7.71 gallons of gas driving to and from work this week.

To calculate the gallons of gas Brynen will use driving to and from work this week, we need to consider the round trip distance and the car's fuel efficiency.

Given:

Brynen drives 27 miles each way to work.

His car gets 35 miles per gallon of gas.

To find the total distance Brynen will travel in a week, we need to calculate the round trip distance for each workday and multiply it by the number of workdays (five days).

Round trip distance = 27 miles (one-way distance) * 2 = 54 miles (round trip distance)

Total distance traveled in a week = 54 miles (round trip distance) * 5 days = 270 miles

Next, we can determine the total gallons of gas Brynen will use using his car's fuel efficiency.

Gallons of gas used = Total distance / Fuel efficiency

Gallons of gas used = 270 miles / 35 miles per gallon

Gallons of gas used ≈ 7.71 gallons (rounded to the nearest tenth)

Therefore, Brynen will use approximately 7.71 gallons of gas driving to and from work this week.

It's important to note that this calculation assumes that Brynen's car maintains a consistent fuel efficiency of 35 miles per gallon throughout the entire week and that no additional driving outside of the work commute is considered. Factors such as traffic, variations in fuel efficiency, or additional trips would affect the actual gas consumption.

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Answer:

6

Step-by-step explanation:

(3√3)^2/3 = (∛3)²  X ∛(√3)²  

= 3

27^2/3 = (∛27)²

= 3² = 9

9^-1/2 = 1/√9

= 1/3

so the answer is  3 + (9 X 1/3)

= 3 + 3

= 6

[tex]2\cdot20\text{ m}\cdot n+2\cdot20\text{ m}\cdot 5\text{ m}+2\cdot 5\text{ m}\cdot n=1100\text{ m}^2\\40n\text{ m}+200\text{ m}^2+10n\text{ m}=1100\text{ m}^2\\50n\text{ m}=900\text{ m}^2\\n=18\text{ m}[/tex]

Answer:

The answer is 16pi or 50.3cm² to 1 d.p

Step-by-step explanation:

The non shaded=area of shaded

d=8

r=d/2=4

A=pir³

A=p1×4²

A=pi×16

A=16picm² or 50.3cm² to 1d.p

Answer:

3.45 cm (3 s.f.)

Step-by-step explanation:

We have been given a 5-sided regular polygon inside a circumcircle. A circumcircle is a circle that passes through all the vertices of a given polygon. Therefore, the radius of the circumcircle is also the radius of the polygon.

To find the radius of a regular polygon given its side length, we can use this formula:

[tex]\boxed{\begin{minipage}{6 cm}\underline{Radius of a regular polygon}\\\\$r=\dfrac{s}{2\sin\left(\dfrac{180^{\circ}}{n}\right)}$\\\\\\where:\\\phantom{ww}$\bullet$ $r$ is the radius.\\ \phantom{ww}$\bullet$ $s$ is the side length.\\\phantom{ww}$\bullet$ $n$ is the number of sides.\\\end{minipage}}[/tex]

Substitute the given side length, s = 8 cm, and the number of sides of the polygon, n = 5, into the radius formula to find an expression for the radius of the polygon (and circumcircle):

[tex]\begin{aligned}\implies r&=\dfrac{8}{2\sin\left(\dfrac{180^{\circ}}{5}\right)}\\\\ &=\dfrac{4}{\sin\left(36^{\circ}\right)}\\\\ \end{aligned}[/tex]

The formulas for the area of a regular polygon and the area of a circle given their radii are:

[tex]\boxed{\begin{minipage}{6 cm}\underline{Area of a regular polygon}\\\\$A=\dfrac{nr^2\sin\left(\dfrac{360^{\circ}}{n}\right)}{2}$\\\\\\where:\\\phantom{ww}$\bullet$ $A$ is the area.\\\phantom{ww}$\bullet$ $r$ is the radius.\\ \phantom{ww}$\bullet$ $n$ is the number of sides.\\\end{minipage}}[/tex]

[tex]\boxed{\begin{minipage}{6 cm}\underline{Area of a circle}\\\\$A=\pi r^2$\\\\where:\\\phantom{ww}$\bullet$ $A$ is the area.\\\phantom{ww}$\bullet$ $r$ is the radius.\\\end{minipage}}[/tex]

Therefore, the area of the regular pentagon is:

[tex]\begin{aligned}\textsf{Area of polygon}&=\dfrac{5 \cdot \left(\dfrac{4}{\sin\left(36^{\circ}\right)}\right)^2\sin\left(\dfrac{360^{\circ}}{5}\right)}{2}\\\\&=\dfrac{5 \cdot \left(\dfrac{4}{\sin\left(36^{\circ}\right)}\right)^2\sin\left(72^{\circ}\right)}{2}\\\\&=\dfrac{\dfrac{80\sin\left(72^{\circ}\right)}{\sin^2\left(36^{\circ}\right)}}{2}\\\\&=\dfrac{40\sin\left(72^{\circ}\right)}{\sin^2\left(36^{\circ}\right)}\\\\&=110.110553...\; \sf cm^2\end{aligned}[/tex]

The area of the circumcircle is:

[tex]\begin{aligned}\textsf{Area of circumcircle}&=\pi \left(\dfrac{4}{\sin\left(36^{\circ}\right)}\right)^2\\\\&=\dfrac{16\pi}{\sin^2\left(36^{\circ}\right)}\\\\&=145.489779...\; \sf cm^2\end{aligned}[/tex]

The area of the shaded area is the area of the circumcircle less the area of the regular pentagon plus the area of the small central circle.

The area of the unshaded area is the area of the regular pentagon less the area of the small central circle.

Given the shaded area is equal to the unshaded area:

[tex]\begin{aligned}\textsf{Shaded area}&=\textsf{Unshaded area}\\\\\sf Area_{circumcircle}-Area_{polygon}+Area_{circle}&=\sf Area_{polygon}-Area_{circle}\\\\\sf 2\cdot Area_{circle}&=\sf 2\cdot Area_{polygon}-Area_{circumcircle}\\\\2\pi r^2&=2 \cdot \dfrac{40\sin\left(72^{\circ}\right)}{\sin^2\left(36^{\circ}\right)}-\dfrac{16\pi}{\sin^2\left(36^{\circ}\right)}\\\\2\pi r^2&=\dfrac{80\sin\left(72^{\circ}\right)}{\sin^2\left(36^{\circ}\right)}-\dfrac{16\pi}{\sin^2\left(36^{\circ}\right)}\\\\\end{aligned}[/tex]

                                                 [tex]\begin{aligned}2\pi r^2&=\dfrac{80\sin\left(72^{\circ}\right)-16\pi}{\sin^2\left(36^{\circ}\right)}\\\\r^2&=\dfrac{40\sin\left(72^{\circ}\right)-8\pi}{\pi \sin^2\left(36^{\circ}\right)}\\\\r&=\sqrt{\dfrac{40\sin\left(72^{\circ}\right)-8\pi}{\pi \sin^2\left(36^{\circ}\right)}}\\\\r&=3.44874763...\sf cm\end{aligned}[/tex]

Therefore, the radius of the small circle is 3.45 cm (3 s.f.).

A construction of the box-and-whisker plot representing the data set is shown below.

In Mathematics and Statistics, a box-and-whisker plot and it can be defined as a type of chart that can be used to graphically or visually represent the five-number summary of a data set with respect to locality, skewness, and spread.

Based on the data (information) provided above, the five-number summary for the given data set include the following:

In conclusion, we can logically deduce that the maximum number is 100 while the minimum number is 35, and the median is equal to 88.

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Answer:

0.5ml/hr

Step-by-step explanation:

Given:

Infusion rate: 0.002 units/min

To convert the infusion rate from units/min to ml/hr, we need to know the flow rate conversion factor specific to the medication and solution being administered.

In this case, we have the information that the patient is receiving 10 units of oxytocin (Pictocin) in 250 ml of D5W solution.

To calculate the ml/hr rate, we can use the following formula:

ml/hr = (Infusion rate in units/min * Volume in ml) / Time in min

ml/hr = (0.002 units/min * 250 ml) / 1 min

ml/hr = 0.5 ml/min

Therefore, the infusion rate of 0.002 units/min is equivalent to 0.5 ml/hr.

Answer:

5541.77 cm^2

Step-by-step explanation:

The mean number of text messages that Julianna sent per day is 7.

To calculate the mean number of text messages that Julianna sent per day, we need to sum up the number of text messages she sent each day and divide it by the total number of days.

Total number of text messages sent:

13 + 0 + 4 + 4 + 5 + 6 + 17 = 49

Total number of days: 7

Mean = Sum of all observations/number of observations

Mean =Total number of text messages sent/Total number of days

Mean number of text messages per day: 49 / 7

= 7

Therefore, 7 is the  mean number of text messages that Julianna sent per day.

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Use julianna’s text message data to answer the questions.

Text messages sent:

Sun: 13 Mon: 0 tues: 4 wed: 4 thurs: 5 fri: 6 sat: 17

1. What was the mean number of text messages that julianna sent per day ?

A. 4

B.6

C.8

D.7

Answer:

  B.  2

Step-by-step explanation:

You want the predicted number of missed shots after 8 weeks if the trend line equation is ...

  y = -1/2x +6

Using x=8 in the given equation, we find the prediction to be ...

  y = -1/2(8) +6 = -4 +6 = 2

The number of missed shots is predicted to be 2.

__

Additional comment

We can see that the trend line (red) goes through the point (8, 2). That tells you the prediction is 2 missed shots at 8 weeks of practice.

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Answer:

The answer is 69.63cm²

Step-by-step explanation:

d=18

r=d/2=18/2=9cm

Area of shaded portion =Area of square -Area of circle

A=18²-pi×9²

A=69.53cm²

Answer:

69.53 centimeters squared.

Step-by-step explanation:

The area is the total space taken up by a flat (2-D) surface or shape. The area is always measured in square units.

To solve for the area of the shaded region, we must figure out what the length and width is. Assuming this is a square, the length and width of the shape are 18cm. To solve for the area of a square, we can use the formula:

Inserting 18 as our side length:

Therefore, the area of the square without the circular gap is 324 [tex]cm^{2}[/tex].

To solve for the area of a circle, we can use the formula:

But wait, we are given the diameter, not the radius!

No worries, the radius is simply half the size of the diameter, so we can just divide 18 by 2.

Inserting 9 into the formula for the radius:

Now we can subtract this from the squares area.

The closest to match this approximation is [tex]69.53cm^{2}[/tex].