Which calculation should be used to calculate s9 for the arithmetic sequence an=3n-1

The perimeter (P∆AKL) of triangle AKL is 21.294 m, and the area is 20.25 m². Triangle AKL is a 30-60-90 triangle, with sides in the ratio 1:√3:2, allowing for straightforward calculations of the perimeter and area using the given side lengths and right triangle properties.

To find the perimeter (P∆AKL) and the area of triangle AKL (∆AKL), we can use the properties of a right triangle. Since we have one angle of 60°, and the right angle 90°, the remaining angle must be 30°. With this information, we recognize that triangle AKL is a 30-60-90 special right triangle.

For a 30-60-90 triangle, the lengths of the sides are in the ratio 1:√3:2. Knowing one side, AK (the side opposite the 60° angle), is 9 m, we determine the side opposite the 30° angle (AL) is half that length, so AL = 9m / 2 = 4.5 m. The side opposite the 90° angle (KL) is √3 times the side opposite the 30° angle, so KL = 4.5m * √3 = 7.794 m.

Now we can find the perimeter (P) by adding all the sides:

The area (A) of a right triangle is (½)*base*height.

Answer: the base is: 3 units

The height is: 5 units

The area is: 7.5 units

Step-by-step explanation: I just answered this question ❤️

The base of triangle is, 3 units

The height of triangle is, 5 units

And, The area of triangle is, 7.5 units²

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

The triangle is shown in image.

Now, We get by graph of triangle;

The base of triangle is, 3 units

The height of triangle is, 5 units

We know that;

⇒ Area of triangle = 1/2 × base × height

⇒ Area of triangle = 1/2 × 3 × 5

⇒ Area of triangle = 7.5 units²

Thus, The base of triangle is, 3 units

The height of triangle is, 5 units

And, The area of triangle is, 7.5 units²

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Answer :

(a) The number of rows need will be, 57 rows.

(b) The amount in pounds of food a circus horse eat each day is, 35.71 pounds.

Step-by-step explanation :

Part A:

As we are given that the there are 9 seats in each row that means 9 people can sit in each row.

Now we have to determine the number of rows will need to be set up if 513 people are expected to attend the show.

As, 9 people can sit in 1 row

So, 513 people can sit in [tex]\frac{513}{9}=57[/tex] row

Thus, the number of rows need will be, 57 rows.

Yes, the rows be divided into a number of equal sections as, 3 rows would be 19 sections or, 19 rows would be 3 sections.

Part B:

As we  are given that circus horses eat about 250 pounds of horse food per week. Now we have to determine the amount in pounds of food does a circus horse eat each day.

Given : 1 week = 7 days

As, in 1 week the circus horses eat about 250 pounds of horse food

or, in 7 days the circus horses eat about 250 pounds of horse food

So, in 1 day the circus horses eat about [tex]\frac{1day}{7day}{\times 250=35.71[/tex] pounds of horse food

Thus, the amount in pounds of food a circus horse eat each day is, 35.71 pounds.

Answer:

5575

Step-by-step explanation:

its just subtraction you take the 6000 and subtract 425 and thats how you get whats left they try to trick you using the time im guessing correct me if im wrong

Answer:

S22 for the arithmetic sequence is:

First option: 15.4

Step-by-step explanation:

a12=2.4

d=3.4

S22=?

Sn=(a1+an)n/2

n=22

S22=(a1+a22)22/2

S22=(a1+a22)11

ak=aj+(k-j)d

a12=a1+(12-1)d

2.4=a1+11(3.4)

2.4=a1+37.4

Solving for a1: Subtracting 37.4 both sides of the equation:

2.4-37.4=a1+37.4-37.4

Subtracting:

-35=a1

a1=-35

a22=a12+(22-12)d

a22=2.4+10(3.4)

a22=2.4+34

a22=36.4

S22=(a1+a22)11

S22=(-35+36.4)11

S22=(1.4)11

S22=15.4

Answer: A

Step-by-step explanation:

[tex]\stackrel\frown{XY}[/tex] ≅ [tex]\stackrel\frown{YZ}[/tex]

⇒ ∠XOY ≅ ∠ZOY

[tex]\overline{XO}[/tex] ≅ [tex]\overline{ZO}[/tex] since they are both a radius

[tex]\overline{OY}[/tex] ≅ [tex]\overline{OY}[/tex] based on reflexive property

∴ ΔXOY ≅ ΔZOY by SAS

So, [tex]\overline{XY}[/tex] ≅ [tex]\overline{ZY}[/tex] by CPCTC

ZY = 10.2 is given

so, XY = 10.2 by substitution property

Final answer:

A total of 4 more students need to sign up for all 56 students to be placed on teams of 10 in the flag football league.

Explanation:

The question is asking how many additional students will need to sign up to ensure that all students can participate in a flag football league, with the stipulation that each team is made up of 10 students. With 56 students currently signed up, we can divide this number by the team size to see how many complete teams can be formed:

56 students ÷ 10 students per team = 5 teams with 6 students left over.

To have a complete additional team, 10 students are needed. Since there are already 6 students without a team, the number of additional students required is:

10 students needed for a complete team - 6 students already signed up but not placed on a team = 4 additional students needed.

Answer:

t=4 seconds

Step-by-step explanation:

The equation given to us is

d=30 + vt + 4t²

d=126 feet

v= 8 ft per second

to find t =?

Now putting the values in the above equation gives

126 = 30 + 8t + 4t²

126 - 30 = 8t + 4t²

96 = 8t + 4t²

Dividing the whole equation by 4

[tex]\frac{96}{4}=\frac{8t}{4}+\frac{4t^{2} }{4}[/tex]

it will become

24 = 2t + t²

taking 24 to other sides of equality

0 = 2t + t² -24

t²+2t-24=0

Now we will do mid term breaking of the eqaution

t²+6t-4t-24=0

taking common from the equation

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

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

so it becomes

t+6 = 0                  or   t-4 =0

t =-6                       or   t = 4 seconds

as time can not be negative

so t=4 seconds

Answer:

Johnny had 5 items and Bobby had 13 items.

Step-by-step explanation:

Let us assume that Johnny has x items and Bobby has y items in their list.

Bobby had 3 more than twice as many items on it than Johnny. So,

[tex]\Rightarrow y=3+2x[/tex]  ----------1

Johnny asked for 8 fewer items than bobby. So,

[tex]\Rightarrow y-8=x[/tex]  -----------2

Putting the value of x from equation 2 in equation 1, we get

[tex]\Rightarrow y=3+2(y-8)[/tex]

[tex]\Rightarrow y=3+2y-16[/tex]

[tex]\Rightarrow 2y-y=16-3[/tex]

[tex]\Rightarrow y=13[/tex]

Putting the value of y in equation 2,

[tex]\Rightarrow 13-8=x[/tex]

[tex]\Rightarrow x=5[/tex]

So, Johnny had 5 items and Bobby had 13 items.

Answer:

The correct answer option is: [tex]a_n=\frac{5}{2} n-\frac{11}{2}, 37[/tex].

Step-by-step explanation:

We are given the following arithmetic sequence and we are to write an explicit formula for it and the find the 17th term of the sequence:

{[tex]a_n[/tex]}={[tex]-3, -\frac{1}{2} ,2,\frac{9}{2} ,7[/tex]}

From the given options, we can put in the values of n and check if it proves to be true.

For  [tex]a_n=\frac{5}{2} n-\frac{11}{2}[/tex], put values of [tex]n[/tex] from 1 to 5 which the number of the term.

[tex]a_1=\frac{5}{2} (1)-\frac{11}{2}\\\\a_1=-3[/tex]

[tex]a_2=\frac{5}{2} (2)-\frac{11}{2}\\\\a_2=-\frac{1}{2}[/tex]

[tex]a_3=\frac{5}{2} (3)-\frac{11}{2}\\\\a_3=2[/tex]

[tex]a_4=\frac{5}{2} (4)-\frac{11}{2}\\\\a_4=\frac{9}{2}[/tex]

[tex]a_5=\frac{5}{2} (5)-\frac{11}{2}\\\\a_5=7[/tex]

Therefore, the formula for the given sequence is  [tex]a_n=\frac{5}{2} n-\frac{11}{2}[/tex].

Also, [tex]a_{17}=\frac{5}{2} (17)-\frac{11}{2}=37[/tex]

Answer: The correct one is an=5/2n-11/2,37 so A :)

The correct hypotheses are:

b. [tex]\(H_0: \mu_1 = \mu_2 = \mu_3\) and \(H_a: \mu_1, \mu_2, \mu_3\) are not all equal.[/tex]

To determine the appropriate hypotheses for testing the relationship between the type of school attended and verbal reasoning scores for Irish students, we first need to understand the nature of the comparison being made.

We have three groups of students: those who attended secondary school, vocational school, and primary school only. We want to investigate if there is a difference in the mean verbal reasoning scores among these groups.

The null hypothesis  [tex](\(H_0\)) states that there is no difference in the mean verbal reasoning scores among the three types of schools, expressed as \( \mu_1 = \mu_2 = \mu_3 \), where \( \mu_1 \), \( \mu_2 \), and \( \mu_3 \)[/tex] are the population means for students attending secondary school, vocational school, and primary school only, respectively.

The alternative hypothesis  [tex](\(H_a\)) suggests that at least one of the population means is different from the others, expressed as \( \mu_1, \mu_2, \mu_3 \)[/tex] are not all equal.

Option b correctly represents these hypotheses:

[tex]\(H_0: \mu_1 = \mu_2 = \mu_3\) \(H_a: \mu_1, \mu_2, \mu_3\) are not all equal.[/tex]

This formulation allows for the testing of differences in mean verbal reasoning scores across the three types of schools. The null hypothesis assumes equality among the means, while the alternative hypothesis considers the possibility of inequality.

Answer:

Step-by-step explanation:

they are opposite angles, same value of 45°

Answer:

[tex]\frac{40}{3}[/tex]

Step-by-step explanation:

Here a= 20, r = -1/2

Here, the absolute value of r is 1/2 which is less than 1. So, the series converges.

The sum of an infinite geometric series is given by

S = [tex]\frac{a}{1-r}[/tex]

Substituting the values in the above equation, we have

[tex]S = \frac{20}{1-(-1/2)} =\frac{20}{3/2} =\frac{40}{3}[/tex]

∴ The sum of the given infinite series is 40/3

Answer:

A. 40/3 hope thats helpful

When the function f(x) is replaced with -1/2f(x), it results in vertical reflection over x-axis and vertical compression of the graph.

When the function f(x) is replaced with -1/2f(x), it means that the values of the original function are multiplied by -1/2. This has two effects on the graph of the function:

Therefore, the correct answer is B) vertical reflection over x-axis and vertical compression.

Answer:

5 single rolls  or 3 double rolls.

Step-by-step explanation:

Ignoring doors and windows, we need to find the lateral surface ares.  We are not papering the ceiling or floor.

The lateral surface areas = P*h

                                            = 2(l+w) * h

                                             = 2(10+12) * 8  

                                             = 2(22)*8

                                              =352  ft^2

A single roll covers 72 ft^2 so we divide the number of ft^2 that we need (352^2) by the amount of a single roll

352/72 =4.88888(repeating)

Rounding up since we need to buy in full rolls.

We will need 5 rolls

Assuming a double roll will cover  twice that of a single roll

2*72 = 144 ft^2

Take 572/144 =2.4444444

Rounding up since we need to buy in full rolls.

We will need to buy 3 double rolls

Adia will need 5 single rolls or 3 double rolls of wallpaper to cover her 10' by 12' bedroom with 8' ceilings.

Adia needs to calculate the amount of wallpaper needed to cover the walls of her bedroom. To find the total wall area, we calculate the perimeter of the room and multiply it by the ceiling height. The perimeter is two times the length (12 feet) plus two times the width (10 feet), giving us 44 feet. Multiplying the perimeter by the ceiling height (8 feet) gives us the total wall area: 44 feet × 8 feet = 352 square feet.

Since each single roll covers 72 square feet, dividing the total wall area by the coverage of one roll gives us the number of rolls needed: 352 square feet / 72 square feet/roll = 4.89, which means Adia will need 5 single rolls of wallpaper.

For double rolls, we need to consider that each double roll is equivalent to two single rolls.

Therefore, we divide the number of single rolls needed by 2 to get the number of double rolls: 5 single rolls / 2 = 2.5, which means Adia will need 3 double rolls (since she can't purchase half a roll, she'll have to round up).

Answer:

(-4,-2) U (-2,4]

Step-by-step explanation:

Domain is the set of x values for which the function is defined.

We look at the x  values on the graph

the graph starts at -4 and we have a hole at x=-4

For a hole we use parenthesis

Graph starts at -4  and ends at -2. Both -4  and -2  have hole, so we use parenthesis.

So interval is (-4,-2)

From -2  to  4 , there is no hole or break in between. the graph is continuous from -2  to 4

so interval is (-2, 4]

combine both intervals

(-4,-2) U (-2,4]

Answer:

B. (-4,-2) (-2,4)

Answer:

25

Step-by-step explanation:

let x questions on the text, so we get:

56/100=14/x,   4/100=1/x,

x=25

Answer:

[tex]\frac{1}{3}[/tex]

Step-by-step explanation:

On a standard cube there are the numbers 1, 2, 3, 4, 5, 6

Only 2 are divisible by 3, that is 3 and 6, hence

P(divisible by 3 ) = [tex]\frac{2}{6}[/tex] = [tex]\frac{1}{3}[/tex]

Answer:

150

Step-by-step explanation:

We can write a proportion to find the total amount in the choir using the information given. A proportion is two equivalent ratios set equal to each other.

[tex]\frac{24}{100}=\frac{36}{y}[/tex]

We will cross multiply the numerator of one ratio with denominator of the other. And then solve for y.

24y=100(36)

24y=3600

y=150.

There are 150 students in the choir.

Answer:

The Correct Answer Is A.) 25 Square Units

Step-by-step explanation:

The area of the corkboard that is not covered by the target is 25 sq. units.

(Option A).

The area of the corkboard that is not covered by the target is calculated from the difference between the area of the square and area of the target.

Area of the square is calculated as;

A = L²

A = ( 5 + 5)²

A = 100 sq units

The area of the target is 75 sq. units, so we wil use this value

The area of the corkboard that is not covered by the target is calculated as;

A = 100 - 75

A = 25 sq. units.

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See the attached explanation and diagram.

Answer:

1/48

Step-by-step explanation:

To find the probability of 2 independent events, we multiply their probabilities together.

Probability of getting a 2 on the spinner, 1 of 8 spots

1/8  =

Probability of getting a 3 on the die, 1 of 6

1/6 =

Multiply these probabilities together

1/8 * 1/6 = 1/48

Answer: [tex]\bold{y=\dfrac{24}{x}}[/tex] ; indirect variation ; x = 2.4

Step-by-step explanation:

direct variation is when: [tex]\dfrac{y}{x}=k[/tex]   ; where k is the constant rate

indirect variation is when: xy = k  ; where k is the constant rate

In the table provide: x * y = 24 for each coordinate provided, so this is indirect variation, with equation: [tex]y = \dfrac{24}{x}[/tex]

since k = 24, then input y = 10 and k = 24 into the equation above:

[tex]10 = \dfrac{24}{x}[/tex]

[tex]10x = 24[/tex]

[tex]x = \dfrac{24}{10}[/tex]

x = 2.4

Answer:

Step-by-step explanation:

100% = $15

20% = 1.2*15 = $18

Quick check

Answer:

i think Banu is 40 and Binu is 20

Step-by-step explanation:

if Banu was 35 and Binu was 15, 5 years go by Banu is 40 so still 20 years older and Binu is 20, Binu is half the age of Banu.

Answer:

Decimal represents the number of people who earned a perfect score is 0.009 .

Step-by-step explanation:

As given

At a county fair, 9 people out of 1,000 earned a perfect score in a carnival game.

[tex]Number\ of\ people\ who\ earned\ a\ perfect\ score = \frac{People\ who\ earned\ perfect\ score}{Total\ number\ people}[/tex]

people who earned a perfect score = 9

Total number of people = 1000

Put in the above

[tex]Number\ of\ people\ who\ earned\ a\ perfect\ score = \frac{9}{1000}[/tex]

Number of people who earned a perfect score = 0.009

Therefore  decimal represents the number of people who earned a perfect score is 0.009 .

Answer: 8 hours

Step-by-step explanation:

Company 1: 3.25x + 26

Company 2: 3.50x + 24

3.50x + 24 = 3.25x + 26

0.25x  +24 = 26        subtracted 3.25x from both sides

0.25x = 2            subtracted 24 from both sides

x = 8               divided both sides by 0.25

Check:

Company 1: 3.25x + 26  =  3.25(8) + 26  = $52

Company 2: 3.50x + 24  = 3.50(8) + 24  = $52