What are the first five terms of the arithmetic sequence defined explicitly by the formula an=14 - 3n

Answer:

23

Step-by-step explanation:

The corresponding speed of pulleys B, C and D are 300rpm, 1200rpm and 240 rpm

The speed of the pulleys can be determined by using the formula that relates the speed and diameters of the pulleys

N1/N2 = D2/D1

Where: D1 is the diameter of the driven pulley, D2 is the diameter of the drive pulley, N1 is the speed of the driven pulley and N2 is the speed of the drive pulley

Given: Da = 2'', Db =4''  Dc = 1'', Dd =5'' and Na = 600rpm

Na/Nb = Db/Da

600/Nb = 4/2

2Nb = 600

Nb = 600/2 = 300 rpm

Nb/Nc = Dc/Db

300/Nc = 1/4

Nc = 300 x 4 = 1200rpm

Nc/Nd = Dd/Dc

1200/Nd = 5/1

5Nd = 1200

Nd = 1200/5 = 240 rpm

Therefore, the speed of pulleys B, C and D are 300rpm, 1200rpm and 240 rpm respectively

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George made 75 percent of the shots.

First, let us understand the percentage:

A percentage is a fraction of a whole expressed as a number between 0 and 100. Nothing is zero percent, everything is 100 percent, half of everything is fifty percent, and nothing is zero percent.

To determine a percentage, we need to divide the portion of the whole by the whole itself and multiply by 100.

We are given the following:

George shot the basketball 20 times in his game on Saturday.

Of those 20 shots, he made 15.

We need to find the percentage of the shots George made.

The percentage of shots George made is given by:

Percentage = 15 / 20 * 100 = 15 * 5 = 75 %

So, 75 % of the shots did George make.

Thus, George made 75 percent of the shots.

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Answer 3rd one

Step-by-step explanation:

The cost of a jar of peanut butter is $2.36.

Let cost of one jar of jelly be x and the cost of jar of peanut butter be y.

According to question, total cost of 4 jars of jelly and 6 jars of peanut butter is $19.32.

So, 4x+6y = 19.32 ..............(i)

According to question again, the cost of 3 jars of jelly and 5 jars of peanut butter is $15.67.

So, 3x+5y = 15.67 ...........(ii)

4*(ii) - 3*(i) we get,

12x+20y - (12x+18y) = 62.68 - 57.96

2y = 4.72

y = 4.72/2 = 2.36

Substituting the value of y in (i) we get,

4x+6*2.36 = 19.32

4x+14.16 = 19.32

4x = 19.32-14.16

4x = 5.16

x = 5.16/4

x = 1.29

Hence the cost of jar of peanut butter is $2.36.

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The right answer to your question is b: 10-2=8 which is a counting number

the given expression is,

put x = -1 in the above expression

so the answer is 2

(7, -3) are the coordinates of R' after dilation with center (0, 0) and with the scale factor of 2.

A graph's basic relationship is represented by a point.

A pair of numbers containing two coordinates define each point.

A coordinate is one of a set of numbers used to locate a point on a graph.

Each point is assigned an x and a y coordinate.

Each point is identified by an ordered pair of numbers: an x-coordinate on the x-axis and a y-coordinate on the y-axis.

Parentheses indicate ordered pairs (x-coordinate, y-coordinate).

The starting point is at (0,0).

The horizontal and vertical distances from the two reference axes are used to describe the position of a point on a coordinate plane.

So, after dilation with center (0, 0) and with the scale factor of 2, the coordinates will be:
R' are (7, -3)

P' are (4,-3)

Q' is (4,4)

Hence,  the coordinates of R are (7, -3).

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ABC's vertices are points A, B, and C. ABC's sides are made up of the AB, BC, and CA segments.

Determine the length of the median across vertex A of triangle ABC, which has vertices A (7,3), B (5,3), and C.

Assume M(x,y) represents the ABC median from A to BC.

M will be the point at which BC splits in half.

x 1​ =5, y1 =3

x 2 =3,y2 =−1

Using the midpoint formula, x=(x 1 + x 2)/2

∴x=(5+3)/2=8/2=4

Using the midpoint formula, y=(y 1 + y 2 )/2

∴y=(3+(−2))/2=2/2=1

Consequently, M's coordinates are (4,1).

The distance formula reads d(AM)=

By distance formula, d(AM)=  √[(x2 - x1)² + (y2 -y1)²]

x1 = 7,y1 = -3

x2 = 4,y2 = 1

∴d(AM) = √[(4- 7)² + (1 - (-3)²]

∴d(AM) = √(-3)² + (4)² = √9 + 16

∴d(AM) = √25 = 5

As a result, the median AM is 5 units long.

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The m∠2 is m∠2 = 14°.

What is degree measure?

Since an angle is measured in degrees, the term "degree measure" is used. Since 360 degrees make up one full revolution, it is divided into 360 equal sections. A degree is what the revolution is at each stage.

As given in the figure,

m ∠WHI = 160°,

m ∠EHI = 104°

m ∠THE = 42°

We have to find the m ∠2

From figure,

m ∠WHI = m ∠WHT + m ∠THE + m ∠EHI

m ∠WHT = m ∠WHI - m ∠THE - m ∠EHI

m ∠WHT = 160° - 42° - 104°

m ∠WHT = 14°

Hence the measure of angle 2 is, m ∠2 = 14°.

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Ecuaciones

Llamemos x al primer número del camión y y al segundo número.

Tenemos que su suma es 11, así que:

x+y=11

También sabemos que su producto es 24:

xy=24

De esta forma, tenemos un sistema de ecuaciones. Vamos a despejar la x de la primera ecuación:

x=11-y

Y la reemplazamos en la segunda:

(11-y)y=24

Operamos y ordenamos el poninomio para formar la ecuación cuadrática:

Para hallar las soluciones de esta ecuación, tomemos los coeficientes de la ecuación de segundo grado:

a=1, b=-11, c=24

Y aplicamos la fórmula resolvente

Tenemos dos posibles respuetas:

y=16/2=8

y=6/2=3

Sustituimos ambas respuestas para hallar x:

x=11-y

x=11-8=3

x=11-3=8

En cualquier orden que los tomemos, los números del camón eran 3 y 8

The theoretical probability is given by 1 over the number of hobbies.

If there is a total of 8 hobbies, the probability of a student having a specific hobby is:

The experimental probability is given by the number of students with that hobby over the total number of students. If 3 students have the hobby roller skating among the 24 students surveyed, the probability is:

To find out the rate of change, divided 110,400 miles by 24 hours

so

110,400/24=4,600 miles per hour

To obtain the surface area of a triangular prism, the formula to employ is:

From the image, a=18in, b=21in, c =15in and h=12in

We have to obtain the value of 's' first, from the equation:

The final step is to obtain the area of the triangular, having gotten the values needed to be inputted in the formula;

Hence, the surface area of the triangular prism is 912.54 square inches

Using <, >, or = to compare each pair of expressions, we get:

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement.

It's possible to multiply, divide, add, or subtract with this mathematical operation.

So, using <, >, or = to compare each pair of expression:

Given expressions: (-5)², -5² (-5)³, -53

Then,

(A) (-5)²__-5² (-5)³

(B) -5² (-5)³ __ -53

(C) (-5)² __ -53

Now calculate as follows:

(A) (-5)²__-5² (-5)³

25 __ 25(-125)

25 > -3,125

(B) -5² (-5)³ __ -53

-3,125 < -53

(C) (-5)² __ -53

25 > -53

Therefore, using <, >, or = to compare each pair of expressions, we get:

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Explanation:

The y-intercept is the point where the line crosses the y-axis. This always happens when x = 0.

In this case x = 0 represents 0 days. The y-intercept is 400 pages remaining

Answer:

The answer is option a. At 0 days there are 400 pages remaining

Answer: she has been in book club for 3 months

Step-by-step explanation:

The reason is that she can read 10 books in one months than you would multiply it by three.

Answer:

3 months

Step-by-step explanation:

20:2/2=

10:1

10:1 x 3 = 30:3

30 books= 3 months.

The number obtained 9/4 is the reciprocal of the number 4/9.

For the given number.

Divide 1 by 4/9

This can be written as;

= 1/(4/9)

= 9/4

Then, the number obtained 9/4 is the reciprocal of the number 4/9.

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Factorization  of 49n^3 -- 25m^3 is (5m + 7n) × (5m - 7n)

A difference of two perfect squares,  A2 - B2  can be factored into  (A+B×(A-B)

(A+B) • (A-B)

=   A2 - AB + BA - B2

= A2 - AB + AB - B2

= A2 - B2

AB = BA is the commutative property of multiplication.

- AB + AB equals zero and is therefore eliminated from the expression.

⇒ 25  is the square of  5

⇒ 49 is the square of 7

⇒ m2  is the square of  m1

⇒ n2  is the square of  n1

Hence, The Factorization is (5m + 7n) × (5m - 7n)

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1) Gathering the data

555 gallons ----- $ 1.74

2) If 8000 gallons could be spent

If a Family conserves 8000 gallons this family would not have an expense of?

Let's set a proportion for that:

555 g-----$1.74

8000g ---x

555x =13920 Dividing both sides by 555

x=25.08

If a family conserves 8000 gallons of water. They save $25.08 per month assuming that $1.74 is equal to 555 gallons of water.

Answer:

The missing number: 6

The property used: Distributive Property of Multiplication

Explanation:

Given the below;

The below shows an example of the distributive property of multiplication;

Applying the distributive property in the given equation, we can see that;

So the missing number is 6 and the equation can be written as;

The two endpoints we have are (-1,7) and (3,-3).

And we need to find the midpoint.

Step 1. Label the given coorfinates as (x1,y1) and (x2,y2):

Step 2. Use the midpoint formula:

Substituting the values for x1, x2, y1, and y2 that we found in step 1:

Step 3. Solve the resulting operations to find the coordinates of the midpoint:

Solving the divisions:

The midpoint is (1,2).

Answer: (1,2)

We were told that Mr. Newman packed 16 large - size ornaments and 29 medium - size ornaments into a box. This means that the number of large and medium ornaments in each box is 16 + 29. Given that there were 13 boxes and x represents the total number of ornaments, the equation would be

x = (16 + 29)13

x = 45 * 13

x = 585

Option F is correct

B. 3y = 2x – 9

is not perpendicular to the given line.

The slopes of perpendicular lines are negative reciprocals

Given the line

y = -1.5x + 11

The slope is -1.5 or -3/2

Any line perpendicular to the one above must have its slope as 2/3

A. The slope is 2/3 . CORRECT

B. The slope is 2/3. CORRECT

C. The slope is 3/2. WRONG

D. The slope is 2/3. CORRECT

7m-m is equal to 6m.

Answer: Intenisy = 83.2 milliroentgens per hour

Let the intensity from the radiation = I

Let the distance = d

The intensity is inversely proportional to the square of its distance

The solution to the expression (12-√-8)/2 as a complex number is 6 - i√2.

What is expression?

In mathematics, an expression is a combination of numbers, variables, and mathematical operations, such as addition, subtraction, multiplication, division, exponents, and roots.

The expression (12-√-8)/2 involves a square root of a negative number, which cannot be represented by a real number. Therefore, we need to extend the real numbers to the complex numbers to solve this expression.

To evaluate the square root of a negative number, we can use the imaginary unit, denoted by i, which is defined as the square root of -1. Then, we have:

√-8 = √(8) √(-1) = 2i√2

Substituting this value back into the original expression, we get:

(12-√-8)/2 = (12 - 2i√2)/2

Simplifying the expression by dividing both the numerator and denominator by 2, we get:

(12 - 2i√2)/2 = 6 - i√2

Therefore, the solution to the expression (12-√-8)/2 as a complex number is 6 - i√2.

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1750 megabytes has been downloaded.

What do you mean by percentage?

In mathematics, a percentage is a number or ratio that can be expressed as a fraction of 100. If you need to calculate the percentage of a number, divide the number by the whole number and multiply by 100. Percentages therefore mean 1 in 100. The word percent means around 100. Represented by the symbol '%'.Percentages have no dimension. Hence it is called a dimensionless number.

It is given that 273 megabytes has been downloaded and it is 15.6% of complete.

Let x be the complete storage

15.6% of x = (15.6/100) × x

(15.6/100) × x  = 273

x = (273/15.6) × 100 = 2730/15.6 =  1750

Therefore, 1750 megabytes has been downloaded.

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The total amount of water Nicholas drank is 47/ 30 liters of water.

Given : Amount of water Nicholas drinks in the morning = 2/3 liters

Amount of water he drinks at lunch = 1/2 liters

Amount of water he drinks during his basketball practice = 2/5 liters

Thus to calculate the total amount of water he drank in the whole we would you the operation of addition in which we will add all the above mentioned value.

The value which comes after adding all of the above mentioned numbers is called sum .

Thus the total amount of water Nicholas drank = 2/3 + 1/2 + 2/5

On taking the LCM we will get

= [tex]\frac{20 + 15 + 12}{30}[/tex]

= 47 / 30

Thus the total amount of water Nicholas drank is 47/ 30 liters of water.

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Although both fluid ounces and quarts are measurements for volume, the mug would be a very small fraction of a quart.

Thereby, the most likely unit of measurement used for the capacity of a mug would be fluid ounces.