Write down in terms of n, an expression for the nth term
of the following sequences:
a) 4 1 -2 -5 -8
b) -7 -12 -17 -22 -27

Answer:

12:5

Step-by-step explanation:

To calculate the ratio, we must first find the values of the two expenditures. The amount spent on renting a hall was 60% of £1000. To represent percentages in decimals, we can simply divide the percentage by 100, resulting in 0.6 here. We can then multiply this value by 1000 to get the amount spent on renting a hall, which comes out to £600

The ratio is then 600 : 250,  60 : 25 (divide both sides by 10) , or 12:5 (divide both sides by another 5)

Answer:

Problem 1: 25

Problem 2: 693

Step-by-step explanation:

Problem 1:

f(x) = -5n + 1

g(x) = -6n + 2

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

f(-2) = -5(-2) + 1

f(-2) = 10 + 1

f(-2) = 11

g(-2) = -6(-2) + 2

g(-2) = 12 + 2

g(-2) = 14

(f + g)(-2) = 11 + 14

(f + g)(-2) = 25

Problem 2:

f(x) = 7 + 2x

g(x) = 5x - 2

fg(7) = f(7) × g(7)

f(7) = 7 + 2(7)

f(7) = 7 + 14

f(7) = 21

g(x) = 5(7) - 2

g(x) = 35 - 2

g(x) = 33

Therefore:

fg(7) = 21 × 33

fg(7) = 693

Answer:

B

Step-by-step explanation:

The line goes down 1 and right 4.  

Answer:

Option 2 represents a slope of 1/4.

Answer:

1/(5*12) = 1/60 = .016 = 1.6%

Step-by-step explanation:

Answer:

last one

Step-by-step explanation:

[tex]\frac{5}{7}[/tex] = [tex]\frac{10}{14}[/tex]

[tex]\frac{1}{2}[/tex] = [tex]\frac{7}{14}[/tex]

need common denominators to add fractions.

what ever is multiplied to the bottom needs to be multiplied to the top

for example : [tex]\frac{5}{7}[/tex] x [tex]\frac{2}{2}[/tex] = [tex]\frac{10}{14}[/tex]

Answer:

(10) Person B

(11) Person B

(12) [tex]P(5\ or\ 6) = 60\%[/tex]

(13) Person B

Step-by-step explanation:

Given

Person A [tex]\to[/tex] 5 coins (records the outcome of Heads)

Person [tex]\to[/tex] Rolls 2 dice (recorded the larger number)

Person A

First, we list out the sample space of roll of 5 coins (It is too long, so I added it as an attachment)

Next, we list out all number of heads in each roll (sorted)

[tex]Head = \{5,4,4,4,4,4,3,3,3,3,3,3,3,3,3,3,2,2,2,2,2,2,2,2,2,2,1,1,1,1,1,0\}[/tex]

[tex]n(Head) = 32[/tex]

Person B

First, we list out the sample space of toss of 2 coins (It is too long, so I added it as an attachment)

Next, we list out the highest in each toss (sorted)

[tex]Dice = \{2,2,3,3,3,3,4,4,4,4,4,4,5,5,5,5,5,5,5,5,6,6,6,6,6,6,6,6,6,6\}[/tex]

[tex]n(Dice) = 30[/tex]

Question 10: Who is likely to get number 5

From person A list of outcomes, the proportion of 5 is:

[tex]Pr(5) = \frac{n(5)}{n(Head)}[/tex]

[tex]Pr(5) = \frac{1}{32}[/tex]

[tex]Pr(5) = 0.03125[/tex]

From person B list of outcomes, the proportion of 5 is:

[tex]Pr(5) = \frac{n(5)}{n(Dice)}[/tex]

[tex]Pr(5) = \frac{8}{30}[/tex]

[tex]Pr(5) = 0.267[/tex]

From the above calculations: [tex]0.267 > 0.03125[/tex] Hence, person B is more likely to get 5

Question 11: Person with Higher median

For person A

[tex]Median = \frac{n(Head) + 1}{2}th[/tex]

[tex]Median = \frac{32 + 1}{2}th[/tex]

[tex]Median = \frac{33}{2}th[/tex]

[tex]Median = 16.5th[/tex]

This means that the median is the mean of the 16th and the 17th item

So,

[tex]Median = \frac{3+2}{2}[/tex]

[tex]Median = \frac{5}{2}[/tex]

[tex]Median = 2.5[/tex]

For person B

[tex]Median = \frac{n(Dice) + 1}{2}th[/tex]

[tex]Median = \frac{30 + 1}{2}th[/tex]

[tex]Median = \frac{31}{2}th[/tex]

[tex]Median = 15.5th[/tex]

This means that the median is the mean of the 15th and the 16th item. So,

[tex]Median = \frac{5+5}{2}[/tex]

[tex]Median = \frac{10}{2}[/tex]

[tex]Median = 5[/tex]

Person B has a greater median of 5

Question 12: Probability that B gets 5 or 6

This is calculated as:

[tex]P(5\ or\ 6) = \frac{n(5\ or\ 6)}{n(Dice)}[/tex]

From the sample space of person B, we have:

[tex]n(5\ or\ 6) =n(5) + n(6)[/tex]

[tex]n(5\ or\ 6) =8+10[/tex]

[tex]n(5\ or\ 6) = 18[/tex]

So, we have:

[tex]P(5\ or\ 6) = \frac{n(5\ or\ 6)}{n(Dice)}[/tex]

[tex]P(5\ or\ 6) = \frac{18}{30}[/tex]

[tex]P(5\ or\ 6) = 0.60[/tex]

[tex]P(5\ or\ 6) = 60\%[/tex]

Question 13: Person with higher probability of 3 or more

Person A

[tex]n(3\ or\ more) = 16[/tex]

So:

[tex]P(3\ or\ more) = \frac{n(3\ or\ more)}{n(Head)}[/tex]

[tex]P(3\ or\ more) = \frac{16}{32}[/tex]

[tex]P(3\ or\ more) = 0.50[/tex]

[tex]P(3\ or\ more) = 50\%[/tex]

Person B

[tex]n(3\ or\ more) = 28[/tex]

So:

[tex]P(3\ or\ more) = \frac{n(3\ or\ more)}{n(Dice)}[/tex]

[tex]P(3\ or\ more) = \frac{28}{30}[/tex]

[tex]P(3\ or\ more) = 0.933[/tex]

[tex]P(3\ or\ more) = 93.3\%[/tex]

By comparison:

[tex]93.3\% > 50\%[/tex]

Hence, person B has a higher probability of 3 or more

Answer:

no

Step-by-step explanation:

To determine if the point lies on the line, substitute x = - 3 into the equation and if the value obtained equals - 5 then it lies on the line.

y = 2(- 3) - 1 = - 6 - 1 = - 7 ≠ - 5

Then the point (- 3, - 5 ) is not on the line

Answer:

161 cm

Step-by-step explanation:

Since 115 cm is 5 boxes, we take 115 and divide it by 5. This will get us the cm of 1 box. 115/5=23

Now we take 23 and multiply it by 7 to get the final height. 23x7=161

Answer:

5 boxes have 115 cm height

Then 1 box height is 115 / 5 = 23 cm

7 boxes will have height of 23 * 7 = 161 cm

Give brianliest

Answer:

Logically that's not possible but if you want to prove it then, you have to use a trick.

Step-by-step explanation:

1 + 1 = 1 + [tex]\sqrt{1}[/tex]

        = 1 + [tex]\sqrt{(-1) * (-1)}[/tex]  

        = 1 + [tex]\sqrt{(-1)}[/tex] * [tex]\sqrt{(-1)}[/tex]

        = 1 + [tex]\sqrt{i^2}[/tex] * [tex]\sqrt{i^2}[/tex]

        = 1 + i * i  

        = 1 + i^2

        = 1 + (-1)

        = 1 - 1

        = 0

So, 1 + 1 = 0

Hope this will help. Please give me brainliest.

Step-by-step explanation:

the answer is in the above image

Answer:

15

Step-by-step explanation:

To find the mean you add all the numbers together then divide by how many numbers there are.

10+10+13+14+16+19+23=105

105÷7=15

So the student who found 15 as their mean is correct.

Answer:

1.false

2.true

3.true

4.true

5.120

6.105

7.85

8.100

9.115

10.40

11.13

12.30

13.36

14.65

15.35

16.75

Answer:

CA = 22.6 ft

Step-by-step explanation:

For the known angle A, leg CA is the adjacent leg.

Side AB is the hypotenuse.

The trigonometric ratio that relates the adjacent leg tot eh hypotenuse is the cosine.

cos A = adj/hyp

cos 41° = CA/(30 ft)

CA = 30 ft * cos 41°

CA = 22.6 ft

Answer:

Answer is 1st and Last

Step-by-step explanation:

Because if you use logic you should know why

Answer:

x = 21

Step-by-step explanation:

We can use ratios to solve

35            x

------  = ----------

25          15

Using cross products

35*15 = 25x

525 = 25x

Divide each side by 25

525/25 =25x/25

21 =x

Answer:

x=8

Step-by-step explanation:

assuming this is what you mean:

(5x+2)=42

try to

isolate the variable by subtracting 2 from both sides

5x=40

continue to isolate the variable

divide by 5 on both sides

5x/5=40/5

x=8

Answer:2 and 5

Step-by-step explanation:

The ratios that are equal to [tex]cos(B)[/tex] : [tex]\bold{\frac{BC}{AB}}[/tex] and [tex]\bold{\frac{EF}{DE}}[/tex]

"Two triangles are said to be similar

- if corresponding angles are equal and the sides

- if corresponding sides of the triangles are in proportion."

In a right triangle,

cos(Ф) = (adjacent side of angle Ф) ÷ hypotenuse

For given example,

Triangles ABC and DEF are similar triangles.

This means, ∠A = ∠D, ∠B = ∠E, ∠C = ∠F

And, [tex]\frac{AB}{DE} = \frac{BC}{EF} = \frac{AC}{DF}[/tex]               ..............(i)

For a right triangle ABC,

the cosine of angle B is,

[tex]cos(B)=\frac{BC}{AB}[/tex]

From (i),

[tex]\frac{BC}{AB}=\frac{EF}{DE}[/tex]

So, the cosine of angle B is,

[tex]cos(B)=\frac{EF}{DE}[/tex]

Therefore, the ratios that are equal to [tex]cos(B)[/tex] : [tex]\frac{BC}{AB}[/tex] and [tex]\frac{EF}{DE}[/tex]

Learn more about similar triangles here:

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Answer:

9

Step-by-step explanation:

Plug in 0 for y and solve for x.

0 = (-1/3)x + 3

(-1/3)x = -3

x = 9

Step-by-step explanation:

Zeros : -2

axis of symmetry : x = -2

Max or Min : min

Vertex : (-2, 0)

Answer:

i am a duck and i can confirm water is pretty poggers

Step-by-step explanation:

The Above triangles are similar, Therefore the corresponding sides would be proportional.

that is : -

[tex]\mathfrak{best \: \: of \: \: luck \: \: for \: \: your \: \: assignment}[/tex]

Answer:

[tex]-6 < k < 2[/tex]

Step-by-step explanation:

Given

[tex]y = x^2 - 2x[/tex]

[tex]y =kx -4[/tex]

Required

Possible values of k

The general quadratic equation is:

[tex]ax^2 + bx + c = 0[/tex]

Subtract [tex]y = x^2 - 2x[/tex] and [tex]y =kx -4[/tex]

[tex]y - y = x^2 - 2x - kx +4[/tex]

[tex]0 = x^2 - 2x - kx +4[/tex]

Factorize:

[tex]0 = x^2 +x(-2 - k) +4[/tex]

Rewrite as:

[tex]x^2 +x(-2 - k) +4=0[/tex]

Compare the above equation to: [tex]ax^2 + bx + c = 0[/tex]

[tex]a = 1[/tex]

[tex]b= -2-k[/tex]

[tex]c =4[/tex]

For the equation to have two distinct solution, the following must be true:

[tex]b^2 - 4ac > 0[/tex]

So, we have:

[tex](-2-k)^2 -4*1*4>0[/tex]

[tex](-2-k)^2 -16>0[/tex]

Expand

[tex]4 +4k+k^2-16>0[/tex]

Rewrite as:

[tex]k^2 + 4k - 16 + 4 >0[/tex]

[tex]k^2 + 4k - 12 >0[/tex]

Expand

[tex]k^2 + 6k-2k - 12 >0[/tex]

Factorize

[tex]k(k + 6)-2(k + 6) >0[/tex]

Factor out k + 6

[tex](k -2)(k + 6) >0[/tex]

Split:

[tex]k -2 > 0[/tex] or [tex]k + 6> 0[/tex]

So:

[tex]k > 2[/tex] or k [tex]> -6[/tex]

To make the above inequality true, we set:

[tex]k < 2[/tex] or [tex]k >-6[/tex]

So, the set of values of k is:

[tex]-6 < k < 2[/tex]

Answer:

1/20

Step-by-step explanation:

only a single number can be chosen out of 20. And 1/20 is the most simplified it can get.

Answer:

10 horas.

Step-by-step explanation:

Dado que una muestra de laboratorio contiene 32 bacterias inicialmente, y luego de aplicar una vacuna, se autodestruyen a la mitad cada una hora, para determinar al cabo de cuántas horas no quedará ninguna bacteria se debe realizar el siguiente cálculo:

32 / 2  = 16

16 / 2 = 8

8 / 2 = 4

4 / 2 = 2

2 / 2 = 1

1 / 2 = 0.5

0.5 / 2 = 0.25

0.25 / 2 = 0.125

0.125 / 2 = 0.0625

0.0625 / 2 = 0.03125

Por lo tanto, al cabo de 10 horas no quedará ninguna bacteria.

Answer:

Step-by-step explanation:

Area 32

rounded up 3/16

Noah needs 1063 square centimeters of clothes.

The area of the kite is 1063 square centimeters.

The correct option is B.

What is a kite's shape?

A kite is a quadrilateral with four sides that may be divided into two neighboring pairs of equal-length sides. A parallelogram, on the other hand, has two sets of equal-length sides, but they are opposed to one another as opposed to being adjacent.

To find the area of a kite, you need to use the formula:

Area = (diagonal 1 x diagonal 2) / 2

where "diagonal 1" and "diagonal 2" are the lengths of the two diagonals of the kite.

To use this formula, follow these steps:

Here, if "diagonal 1" measures (42.7 + 22.5) cm and "diagonal 2" measures (16.3 + 16.3) cm, the area of the kite would be:

Multiply the length of "diagonal 1" by the length of "diagonal 2".

That means the result is 2125.52

Divide the result by 2.

2125.52/2

= 1062.76

≈ 1063

Therefore, the area of the kite is 1063 square centimeters.

To learn more about the kite's shape;

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The complete question:

Noah wants to make the kite shown below out of cloth.

He wants to determine how much clothes he needs.

What is the area, rounded to the nearest square centimeter, of Noah's kite?

The image of the kite is given below.

Answer:

It is not a rectangle

Step-by-step explanation:

A rectangle is a shape with 4 sides, such that we have two pairs of parallel sides, where the length of the parallel sides is equal.

so we have two parallel sides with length L and two parallel sides with length L'.

In this figure ,we can see two sides with length 20 and other two with length 21, and this is a rectangle only if the sides meet at 90°degree angles (this would mean that the opposite sides are parallel)

To see this, we can think that the triangle formed by the diagonal and two sides is a triangle rectangle, then using the Pythagorean theorem we should have that:

20^2 + 21^2 = 28^2

841 = 784

So this is not a triangle rectangle, meaning that the angle between the side of 20 and the side of 21 is not a right triangle, then the figure is not a rectangle.

Therefore, it is not a rectangle

Hope u understand

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Thank You

The expression which represents the profit is 33x + 390, the correct option is D.

Expression in mathematics is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

We are given that;

The polynomial= 2x3 + 30x – 130

The cost, in dollars, of producing the skateboard= 2x3 – 3x – 520.

Now,

To find the expression that represents the profit, we need to subtract the cost from the revenue. So, we have:

profit = revenue - cost

profit = (2x^3 + 30x - 130) - (2x^3 - 3x - 520)

profit = 2x^3 + 30x - 130 - 2x^3 + 3x + 520

profit = 33x + 390

Therefore, the expression will be 33x + 390.

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Option C with h and k

see screenshot for an example

general formula is

r² = (x - x-center)² + (y - y-center)²