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The nth term of a sequence is 25 - 3n
a) Work out the first three terms of the sequence.
9
7
b) Work out the value of the first negative term of the sequence.
8

A camera store develops 2100 rolls of film in one month. Customize one that double prints from 1500 of these rolls, then the ratio of rolls with double prints to rolls develop would be 5:7.

What is the ratio in mathematics?

A ratio in mathematics shows how many times one number contains another. For example, if a bowl of fruit contains eight oranges and six lemons, the orange-to-lemon ratio is eight to six. Similarly, the lemon-to-orange ratio is 6:8, and the orange-to-total fruit ratio is 8:14.

A camera store develops 2100 rolls of film in one month. Customize one that double prints from 1500 of these rolls.

Then the ratio of rolls with double prints to develop = 1500/2100

Simplifying the above ratio we get

                                                                       = 5/7

Hence, the ratio of rolls with double prints to rolls develop would be 5:7.

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x=-20/13 and y=77/13 are solutions of 5x+4y=-16 and y= 2x+9

Two or more expressions with an Equal sign is called as Equation.

The two equations are

5x+4y=-16 ...(1)

Five x plus 4 y equal to minus sixteen.

y= 2x+9 ...(2)

y equal to two times of x plus nine.

Substitute 2 in 1.

5x+4y=-16

5x+4(2x+9)=-16

5x+8x+36=16

13x+36-16=0

13x+20=0

13x=-20

x=-20/13=-1.53

substitute the value of x in y.

y=2(-20/13)+9

y=(-40+117)/13

y=77/13

Hence the value of x is -20/13 and y value is 77/13.

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The solutions of the given equations are:

1. x = 5, -5

2. x = -6, 4

3. x = 3, -3

4. x = 1/2, -3

What is factorization?

Writing a number or other mathematical object as the result of numerous factors—typically smaller or simpler objects of the same kind—is known as factorization or factoring in mathematics.

Here, we have

1. x²-7= 18, by applying factorization

x² = 18 + 7

x² = 25

x = 5, -5

2. x² + 2x -24 = 0, by applying factorization

x² + 6x - 4x - 24 = 0

x(x+6)-4(x+6) = 0

(x-4)(x+6) = 0

x = 4,-6

3. 4x² + 2 = 38, by applying factorization

4x² = 36

x² = 9

x = 3, -3

4. 2x² + 5x -3 = 0, by applying factorization

2x² + 6x - x - 3 = 0

2x(x +3) -1(x+3) = 0

(2x-1)(x+3) = 0

x = 1/2, -3

Hence, The solutions of the given equations are:

1. x = 5, -5

2. x = -6, 4

3. x = 3, -3

4. x = 1/2, -3

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Applying the midpoint formula, the values of a and b are:

B. a = -8, b = -12

The midpoint formula is used to find the coordinates of the midpoint of a segment, which is given as:

M(x, y) = [tex](\frac{x_2 + x_1}{2}, \frac{y_2 + y_1}{2})[/tex].

Given the points below:

(10, a) = [tex](x_1, y_1)[/tex]

(b, 6) = [tex](x_2, y_2)[/tex]

M(-1, -1) = (x, y)

Plug in the values:

(-1, -1) = [(b + 10)/2, (6 + a)/2]

Solve the variables separately

-1 = (b + 10)/2

-2 = b + 10

-2 - 10 = b

b = -12

-1 = (6 + a)/2

-2 = 6 +a

-2 - 6 = a

a = -8

The answer is: B. a = -8, b = -12

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If Tina's score is in the 50th percentile and the grades were normally distributed, Tina's score on the exam is 78.

A percentile refers to the comparison score between a particular score and the scores of the rest of a group. It represents the percentage of scores that a specific score surpassed. For example, if the score of 75 points on a test is ranked in the 85th percentile, it implies that the score 75 is higher than 85% of the scores. The 50th percentile, which is also the median score implies that 50% of the score is below or above the average score in a normally distributed data. In the given situation, if the grades are normally distributed with a mean of 78, that implies that 50% of the scores are above 78 and 50% of the scores are below 78. The standard deviation in this case is irrelevant. As Tina’s score is at the 50th percentile, her score on the exam would be 78.

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Answer:

  162

Step-by-step explanation:

You want the sum of the first 9 terms described by ...

  a[n] = 7n -17

There are several ways the sum can be found. Most straightforward is simply adding up the terms:

  For n=1, 7n-17 = -10

  For n=2, 7n -17 = -3

The remaining 7 terms are 4, 11, 18, 25, 32, 39, 46.

The sum is ...

  -10 -3 +4 +11 +18 +25 +32 +39 +46 = 162

The terms form an arithmetic sequence with first term -10 and last term 46. The sum will be the average term multiplied by the number of terms:

  ((-10 +46)/2)(9) = 18(9) = 162

The sum can be decomposed into the sums whose formulas we know:

  [tex]\displaystyle \sum_{n=1}^9(7n-17)=7\sum_{n=1}^9{n}-17\sum_{n=1}^9{1} =7\cdot\left.\dfrac{n(n+1)}{2}-17n\right|_{n=9}\\\\= 7\cdot\dfrac{9\cdot10}{2}-17(9)=315-153=\boxed{162}[/tex]

Answer:

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

6[tex]x^{5}[/tex]

Step-by-step explanation:

For the first problem.  I am not sure what is going on with the -4.  Is it being added or multiplied by 2[tex]x^{2}[/tex]?  I left it out.

[tex](2x^{2}) ^{^{2} }[/tex] means 2[tex]x^{2}[/tex] (2[tex]x^{2}[/tex]) Which is 4[tex]x^{4}[/tex]

(2[tex]x^{2})\\[/tex]([tex]3x^{3)}[/tex]  multiple the 2 and the 3 and add the exonents

6[tex]x^{5}[/tex]

Answer:

Ummm I dont even kno but s1

Step-by-step explanation:

They take out one box from the warehouse because one box is sufficient for the requirement of 36 sweaters.

A number system is defined as a way to represent numbers on the number line using a set of symbols and approaches. These symbols, which are known as digits, are numbered 0 through 9. Based on the basic value of its digits, different types of number systems exist.

There are 7 boxes, which contain a total of 63 sweaters in a store's warehouse.

The store needs 36 sweaters.

Here one box is sufficient for the requirement of 36 sweaters because it contains 63 sweaters.

Therefore, they take out one box from the warehouse.

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The radius of the pool is 9.01 m.

Given,

In the question:

A circular pool is surrounded by a brick walkway 3 m wide.

The area of the walk- way is 198 m^2.

To find the Radius of the pool.

Now, According to the question:

"Area of the circle bounded by the outside edge of the walkway" minus "area of the pool" = "area of the walkway".

Let R = Radius of the pool

Area of the circle bounded by the outside edge of the walkway is:

[tex]\pi[/tex](R +3)^2

Area of the pool is:

[tex]\pi R^2[/tex]

Now, Our equation is:;

[tex]\pi[/tex](R +3)^2 - [tex]\pi R^2[/tex] = 198

[tex]\pi[/tex]((R+3)^2 - [tex]R^2[/tex]) = 198

Open the inner bracket :

[tex]\pi[/tex]([tex]R^2+6R+9-R^2[/tex]) = 198

[tex]\pi[/tex](6R +9) = 198

6R+9 = 198/[tex]\pi[/tex]

6R = 198/[tex]\pi[/tex] - 9

R = (198/[tex]\pi[/tex] - 9)/6

R = (198/(3.14) - 9)/6

R = (63.057 - 9)/6

R = 54.057/6

R = 9.01 meters

Hence, The radius of the pool is 9.01 m.

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A manufacturing machine has a 7% defect rate. If 4 items are chosen at random,

The probability of randomly choosing atleast one defective item would be 0.3043

Given the Parameters :

   Defect rate = P(defect) = 0.07

Probability = required outcome / Total possible outcomes

   P(atleast 1 is defective) = 1 - P(none is defective)

P(not defective) = 1 - P(defective) = 1 - 0.07 = 0.93

P(none is defective) = P(non defective)^4

P(none defective) = 0.93 × 0.93 × 0.93 × 0.93 = 0.7480

P(atleast one is defective) = 1 - 0.7480 = 0.252

Therefore, probability of atleast one defective item is 0.252.

Hence the answer is, the probability of randomly choosing atleast one defective item would be 0.3043

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Answer:

6

Step-by-step explanation:

24/6 = 4

36/6 = 6

6 bags, 4 lollipops and 6 pieces of gum in each bag.

Answer:

12 bags

Step-by-step explanation:

You would need to find the GCF of both numbers: 12

24*12 = 2

38*12 = 4

12 bags with 2 lollipops and 4 pieces of gum in each

Answer:

Step-by-step explanation:

1. Definition of Least common multiple: The least common multiple of two numbers is the smallest number that is a multiple of both of the numbers

2. Find the LCM 8 and 10=

Multiplies of 8= 8,16,24,32,40....

Multiplies of 10= 10,20, 30,40 ,50....

3. We found it!

40 is the least common multiple!

The amount invested in the account that yields a 5% interest is $18,000.

The amount invested in the account that yields a 5% interest is $12,000.

The system of equations that represent the question is:

a + b = 30,000 equation 1

0.05a + 0.13b = 2460 equation 2

Where:

The elimination method would be used to solve the system of equations.

Multiply equation 1 by 0.05

0.05a + 0.05b = 1500

Subtract equation 3 from equation 2:

0.08b = 960

Divide both sides of the equation by 0.08:

b = 960 / 0.08

b = $12,000

Substitute for b in equation 1:

a + 12,000 = 30,000

a = 30,000 - 12,000

a = 18,000

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Answer:

no because area is multiplication, but perimeter is adding.

Equation can be used to find  the number of candles (c) Katie ordered is 54 = 3c + 6. correct option is (C).

given that

3c+6=54                            --------------------------------- (1)

reduce the greatest common factor on both side of the equation, we get:

2+ c= 18                            ----------------------------------(2)

rearranging the equation (2), we get,

c + 2 = 18

⇒ c = 18 - 2

⇒ c= 16

∴ putting the value of c in option 3, we get,

    3 X 16 + 6 = 54

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The question was incomplete. Check below the complete question.

Katie ordered candle that cot $3 each from a webite. She wa charged a flat hipping fee of $6 and no ale tax. If he pent a total of $54, which equation can be ued to find c, the number of candle he ordered?

A. 3c = 54

B. 6c = 54

C. 3c + 6 = 54

D. 3c – 6 = 54

x = [tex]\sqrt[3]{40}[/tex]  = 3.42 ( approx.) is the value of x by given equation .

We often read numbers in words like hundred, thousand, hundred thousand, and ten million. Which number has more digits than we can read? For example, the mass of the Earth is 5972190000000000000000000 kg. This cannot be read in simple words. Therefore, exponents are used to pronounce these kinds of numbers.

Exponents can be observed in four different types: positive, negative, zero, and rational/fractional. Numerical values ​​can be interpreted  using exponents as the total number of times a base must be multiplied by the same base.

3x^3/5 = 24

3x^3 = 120

x^3 = 40

x = [tex]\sqrt[3]{40}[/tex]  = 3.42 ( approx.)

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A parabola has a vertex at (-3,2) and is opening left.

A symmetrical open plane curve formed by the intersection of a cone with a plane parallel to its side. The path of a projectile under the influence of gravity follows a curve of this shape.

So, a parabola has a vertex at (-3,2).

Now where is the axis of symmetry?

• Parabola opens downward or upward. The concept of the axis of symmetry is that, it is a line that when you fold the graph it will be one.

• in y=a(x-h)2+k where vertex is at (h,k), the axis of symmetry is x=h

Hence the answer is X=-3

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The exact value for the following expression {sec π/4 cos 2π/3}/{tan π/6 csc 3π/4} is - [tex]\sqrt{3} /2[/tex]

The expression is given that

{sec π/4 cos 2π/3}/{tan π/6 csc 3π/4}

Here we have to use the trigonometric functions

Find the each values of the term

sec π/4 = 1 / cos π/4

= 1 / (1 / [tex]\sqrt{2}[/tex] )

= [tex]\sqrt{2}[/tex]

Next term is cos 2π/3

cos 2π/3 = -1 / 2

Next term is tan π/6

tan π/6 = [tex]\sqrt{3}[/tex] / 3

Next term is csc 3π/4

csc 3π/4 =  [tex]\sqrt{2}[/tex]

Substitute the values in the expression

{sec π/4 cos 2π/3}/{tan π/6 csc 3π/4}

= (    [tex]\sqrt{2}[/tex] × (-1/2) ) / ( [tex]\sqrt{3}[/tex] / 3 ×  [tex]\sqrt{2}[/tex])

= - [tex]\sqrt{3} /2[/tex]

Hence, the exact value for the following expression {sec π/4 cos 2π/3}/{tan π/6 csc 3π/4} is - [tex]\sqrt{3} /2[/tex]

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The linear function that represents the cost of an adult ticket in dollars for a customer who contributes x cans of pet food is of:

y = 9.5 - 0.75x.

The graph is given by the image shown at the end of the answer.

The general format of a linear function is given by the rule shown as follows:

y = mx + b.

The terms of the linear function are listed and explained as follows;

The values of these terms in this function are given as follows:

The costs for the amounts of cans are given as follows:

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Answer:

largest angle is angle L

Step-by-step explanation:

the angle across the largest side of the triangle is the largest angle

Hence, there should be 5 pounds of apples and 7 pounds of grapes in 12 pounds.

acc to our question-

Hence, there should be 5 pounds of apples and 7 pounds of grapes in 12 pounds.

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The image of the point after the rotation is:

(-6, 7)

We have the point (-7, -6) and we want to apply a rotation of 270° counterclockwise.

This is equivalent to a rotation of 90° clockwise, so we will go from the third quadrant to the second quadrant, such that:

Then the image after the rotation is:

(-6, 7)

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Emmanuel paid $50 for each watch.

Profit describes the financial benefit realized when revenue generated from a business activity exceeds the expenses, costs, and taxes involved in sustaining the activity in question.

Given that, Emmanuel started a business selling watches. He sells each watch for 30% more than he pays for them. Last week, he sold 7 watches for a total of $455.

Let the original price of each watch be x

According to question,

x*130% = 455/7

x = 65*100/130

x = 50

Hence, Emmanuel paid $50 for each watch.

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Answer:

Step-by-step explanation:

the answer would be 73 since the angle is split in half which means that they are both equal to each other

Answer:

C. Both

Step-by-step explanation:

You would substitute the coordinates into the equation to find the answer.

(4,-1)

-1 + 1 = 3 (4-4)

0 = 0

(5,2)

2 + 1 = 3(5-4)

3 = 3

The angle in radians and the sector area are 2/9 π and 804.248 m² respectively

A sector of a circle is the part of a circle made of the arc along with its two radii

Given:  angle = 40° and distance(r) = 48m

To convert the angle to radians, multiply the angle by π/180:

Angle in radian(α) = 40 x π/180  = 2/9 π radian         (Note: π = 180°)

The formula for sector area = (α×r²)/2

Thus, sector area = (2/9π × 48²)/2 = 804.248 m²

Therefore, the angle in radians is 2/9 π and the sector area is 804.248 m²

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