Mathematics College

(Write your answers on the space provided) The World Health Organization (WHO) reported that about 16 million adolescent girls between 15 and 19 years of age give birth each year. Knowing the adverse effects of adolescent childbearing on the health of the mothers as well as their infants, a group of students from Magiting High School volunteered to help the government in its campaign for the prevention of early pregnancy by giving lectures to 7 Barangays about the WHO guidelines on teenage pregnancy. The group started in Barangay 1 and 4 girls attended the lecture. Girls from other barangays heard about it, so 8 girls attended from Barangay 2, 16 from Barangay 3, and so on. a. Make a table representing the number of adolescent girls who attended the lecture from Barangay 1 to Barangay 7 assuming that the number of attendees doubles each Barangay 4 3 5 6 2 7 1 Barangay Number of Attendees b. Form a sequence representing the number of adolescent girls who attended the lecture from Barangay 1 to Barangay 7. C. Because people who heard about the lecture given by the group thought that it would be beneficial to them, five more different barangays requested the group to do the lectures for them. If the number of young girls who will listen to the lecture from these five Barangays will increase in the same manner as that of the first 7 Barangays, determine the total number of girls who will benefit from the lecture.​

(Write Your Answers On The Space Provided) The World Health Organization (WHO) Reported That About 16

Answers

Answer 1

The sequence of the number of girl attendees at each Barangay is nonzero, given by multiplying the number of attendees in the previous Barangay by 2

The required values are;

a. The completed table is presented as follows;

[tex]\underline{\begin{array}{|l|c|c|c|c|c|c|c|}\mathbf{Barangay}&1&2&3&4&5&6&7\\\mathbf{Number \ of \ attandees}&4&8&16&32&64&128&256\end{array}}[/tex]

b. The sequence of the number of girls attendees aₙ = 4×2⁽ⁿ⁻¹⁾

c. The sum of beneficiaries of the lecture from the twelve Barangay is 16,384 girls

Reason:

Known parameters are;

Number of girls that attended the lecture at Barangay 1 = 4 girls

Number of girls that attended from Barangay 2 = 8 girls

Number that attended from Barangay 3 = 16 girls

a. The required table with the assumption that the number of girls that attended at each Barangay from Barangay 1 to Barangay 7 doubles, is presented as follows;

[tex]\begin{array}{|l|c|c|c|c|c|c|c|}Barangay&1&2&3&4&5&6&7\\Number \ of \ attandees&4&8&16&32&64&128&256\end{array}[/tex]

b. The sequence of the number of girls who attended the lecture from Barangay 1 to Barangay 7 is presented as follows;

The sequence is a geometric progression having the form, aₙ = a·r⁽ⁿ⁻¹⁾

The first term of the sequence, a = 4

The common ratio, r = 2 (each term is twice the previous term)

n = The number of terms

The sequence is therefore;

aₙ = 4·2⁽ⁿ ⁻ ¹⁾

c. The total number of girls in the geometric progression, (G. P.) is given by the sum of a G. P. as follows

[tex]S_n = \dfrac{a \cdot (r^n - 1 )}{r - 1}[/tex]

Where;

n = The number of terms = 7 + 5 = 12

Which gives;

[tex]S_{12} = \dfrac{4 \times (2^{12} - 1 )}{2 - 1} = \dfrac{4 \times 4,096 }{1} = 16,384[/tex]

The total number of girls who will benefit from the lectures, S₁₂ = 16,384 girls

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Related Questions

what is 5.6 less than 25.3

Answers

Answer:

19.7

Step-by-step explanation:

HELP!! ASAP
A graphic designer makes a sketch for an image that will appear on a poster. The width of the sketch is 14 in. She figures that it should be enlarged to 220% to make the final image. How wide will the final image be?

Answers

Answer:

220

Step-by-step explanation:

The final image will be 30.8 inches!

17 - (-25) =
I need help

Answers

17 - (-25)
Negatives cancel each other
=17+25
Answer is 42

Answer:

42

Step-by-step explanation:

rewrite by changing subtraction sign to addition and the following number to opposite

- always involves two sign changes

have a good day

can someone plz help me with this

Answers

Answer:

option D .....11

Option c 36

If f(1) = 160 and

f(n)=1/2f(n-1) what is f(5)?

Answers

Answer:

10

Step-by-step explanation:

[tex]f(n) = \frac{160}{ {2}^{(n - 1)} } [/tex]

Answer:

This is 10

f(5) = 5f

Martha Stewart has developed a new perfume. She decides to test its side effects by spraying the perfume in 31 randomly chosen houses. She records the level of antigens that create an allergic response. If the antigen level is high enough, the person will go into anaphylactic shock. The mean of her sample is a lot bigger than the median, but Martha hopes that a 90% confidence interval will contain zero. Her confidence interval is (0.116, 1.884). Disappointed, she offers you $144 to find an acceptable, realistic way to change the confidence interval to contain zero. What could you say to earn the money

Answers

The acceptable and realistic ways to to change the confidence interval to contain zero are;

Martha should decrease x-bar by providing medicine to treat shock to the perfume users.Decrease sample size than 30Increase the confidence level, till the interval contains zero

Reasons:

The confidence interval is given by the following formula;

[tex]CI=\bar{x}\pm t_{\alpha/2} \cdot \dfrac{s}{\sqrt{n}}[/tex]

When the mean, [tex]\overline x[/tex], is positive and large, both values, [tex]\bar{x}+ t_{\alpha/2} \cdot \dfrac{s}{\sqrt{n}}[/tex], and [tex]\bar{x} -t_{\alpha/2} \cdot \dfrac{s}{\sqrt{n}}[/tex], will be positive.

Therefore, Martha has to either intervene to reduce the mean also known as x-bar

Increasing the confidence level will increase the allowable error such that [tex]\bar{x} < t_{\alpha/2} \cdot \dfrac{s}{\sqrt{n}}[/tex], and the interval will contain zero

Therefore;

Martha should decrease x-bar, [tex]\overline x[/tex], by providing medicine to treat shock to the perfume usersUse a much smaller sample size, n, such that [tex]t_{\alpha/2} \cdot \dfrac{s}{\sqrt{n}} > \bar{x}[/tex]

Increase the confidence level to 95% or 99%, thereby increasing the error bound

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What is the fourth term of an arithmetic sequence whose first term is 23 and whose seventh term is 5?

A) 78
B) 32
C) 14
(Explain your work)

Answers

We have that  the fourth term of an arithmetic sequence is

a_4=14

Option C

From the question we are told

What is the fourth term of an arithmetic sequence whose first term is 23 and whose seventh term is 5?

A) 78

B) 32

C) 14

(Explain your work)

Generally the equation for the  arithmetic sequence  is mathematically given as

[tex]a_4=a_1+(n-1)d[/tex]

Therefore

For seventh term

[tex]5=23+(6)d\\\\d=5-23/(6)\\\\d=-3[/tex]

Therefore

For Fourth term

[tex]a_4=23+(3*(-3))[/tex]

a_4=14

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A phone company offers two monthly plans. Plan A costs $10 plus an additional $0.12 for each minute of calls. Plan B costs $15 plus an additional $0.10 for
each minute of calls.
For what amount of calling do the two plans cost the
Same?

Answers

Answer:

250 minutes

Step-by-step explanation:

10 + 0.12x = 15 + 0.10x

0.02x + 10 = 15

0.02x = 5

x = 250

Your welcome!

Kayden Kohl

8th Grade Student

AAA help I need to do this for schoosleldkdk

Answers

Answer:

[tex] \frac{1}{8} [/tex]

Step-by-step explanation:

The total amount of cards is 8, and the stack have 4 even numbers, so the probability is

4/8 Simplify it and

1/2

Now, there are just 6 cars bigger than 6, so:

2/8. Simplify it

1/4

Now you have to multiply the two values:

1/2×1/4 = 1/8

look at the pictuse below i would copy and paste but I can't copy a picture

Answers

Answer:

I can't really see it so i don't know I'm sorry

Answer:

15

Step-by-step explanation:

how do i write the word form and the expanded form for 3.4 and 2.51

Answers

Answer:

(3×1)+(4/10) & two and fifty-one hundredths

Step-by-step explanation:

In order to write a decimal in expanded form you need to create a equation that equals the decimal you are trying to expand, and for writing decimal in word form you need to remember the names of place values.

1. 3.4

[tex]3.4=(3\times`1)+(\frac{4}{10} )[/tex]

2.2.51

two and fifty-one hundredths

Hope this helps.

NEED HELP FOR REAL 69 points!!!!!!!!!!!!!! ASAP
The physicist from the last problem lets the particle fall another 100 times, and finds that the average travel time is now 16 sec. Remember that when running the simulation many times it took 15 seconds, on average, for the particle to fall to the bottom, with a standard deviation of 1.5 seconds. What does she conclude and why?

Answers

It concludes that newtons laws of motion are at work

what does n equal in 4n − 2n = 4

Answers

Answer:

Step-by-step explanation:

4 = 2

find the value of a square + b square when a+b = 6 a_b = 4

Answers

Answer:

a+b=6

a-b =4

______subtract

(a-a)+(b-(-b))=6-4

0+2b = 2

b= 1

put the value of b at any equation

a+1 =6

then a=6-1=5

a square+b square= 25+1= 26

Use polar coordinates to find the volume of the given solid.
Below the plane
2x + y + z = 4
and above the disk
x2 + y2 ≤ 1

Answers

Using polar/cylindrical coordinates, we take

x = r cos(t )

y = r sin(t )

z = z

so that

dV = dx dy dz = r dr dt dz

The solid is given by the set

D = {(x, y, z) : x ² + y ² ≤ 1 and 0 ≤ z ≤ 4 - 2x - y}

or in cylindrical coordinates,

D = {(r, t, z) : 0 ≤ r ≤ 1, 0 ≤ t ≤ 2π, and 0 ≤ z ≤ 4 - 2r cos(t ) - r sin(t )}

Then the volume of the solid is

[tex]\displaystyle \iiint_D \mathrm dV = \iiint_Dr\,\mathrm dr\,\mathrm dt\,\mathrm dz \\\\ = \int_0^{2\pi} \int_0^1 \int_0^{4-2r\cos(t)-r\sin(t)} r\,\mathrm dz\,\mathrm dr\,\mathrm d t \\\\ = \int_0^{2\pi}\int_0^1 (4r-2r^2\cos(t)-r^2\sin(t))\,\mathrm dr\,\mathrm dt \\\\ = \int_0^{2\pi} \left(2 - \frac23 \cos(t) - \frac13 \sin(t)\right) \,\mathrm dt \\\\ = \boxed{4\pi}[/tex]

The volume of the given solid below the plane 2x + y + z = 4 and above the disk x2 + y2 ≤ 1 is 4π.

What is the volume of the solid in polar coordinates?

The volume of the solid in polar coordinates can be calculated by the double integral in polar coordinates.

[tex]V = \iint_R f(x,y) \,dA.\\[/tex]

Similarly, by polar coordinates,

x = r cost

y = r sint

z = z

we get, dV = dx dy dz = r dr dt dz

The solid is given

D = {(x, y, z) : x ² + y ² ≤ 1 and 0 ≤ z ≤ 4 - 2x - y}

or in polar coordinates,

D = {(r, t, z) : 0 ≤ r ≤ 1, 0 ≤ t ≤ 2π, and 0 ≤ z ≤ 4 - 2r cos(t ) - r sin(t )}

The volume of the solid is

[tex]\rm \int \int\int\ dV = \int \int\int\ rdr dt dz\\ \rm = \int\limits^{2\pi}_0\int\limits^1_0 \int\limits^{4-2rcost-rsint}_0 rdr dt dz\\\rm =\int\limits^{2\pi}_0\int\limits^1_0 {4r-2r^{2} cost-r^{2} sint} dr dt\\\rm =\int\limits^{2\pi}_0( 2-2/3cost-1/3sint) dt\\\rm =4\pi[/tex]

Hence, The volume of the given solid below the plane 2x + y + z = 4 and above the disk x2 + y2 ≤ 1 is 4π.

Learn more about the volume of the solid;

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No links just answer
Simplify

Answers

Answer:

first option _32\21 is the answer

Step-by-step explanation:

the answer will

-32/21

I'm indian just came in Canada

indians are very intelligent in maths

Which of the following expressions is equivalent to 24/8 ·6/3 · 3?

-7 · 6/3 · 3

-28/4 · 3

-28/24/9

-7 ·6/9

Answers

Answer:

I think second one is the ans

Click this if you are a savage

Answers

Answer:

i  am

Step-by-step explanation:

pro!

uhfy1gujhqfvwtfu

6. a + 6 < -2; a = -8
I
0. yes
P. no

Answers

Answer:

yes

Step-by-step explanation:

A 4-quart jug of juice costs $4.48. What is the price per cup?

Answers

Answer:

28 cents.

Step-by-step explanation:

There are 4 cups in 1 quart. So, 4 quarts is 16 cups.

If 4 quarts costs $4.48, to find the price per cup, you need to divide $4.48 by 16.

4.48 ÷ 16 = 0.28

This means each cup is 28 cents.

I hope this helps! :)

Step-by-step explanation:

you devide 4.48by 16 and your answer is 0.28

Alyssa purchased 3 pounds of peanuts for $8.25. Write an equation that shows the relationship between the cost and the number of pounds purchased

Answers

Answer:$8.25 ÷ 3= x or 3·x =8.25

Step-by-step explanation:

3*x=8.25

Mr. Cruz bought 9 3/5 kg of meat. He used 2 3/5 kg for adobo, 4 3/5 kg for menudo and the rest for afritada. How many kilograms of meat did he use for afritada?​​

Answers

Answer:

Loading,please wait...

Step-by-step explanation:

Write a three digit number that gives same answer when rounded to the nearest ten and to the nearest hundred .explain

Answers

Answer:

Numbers can be rounded to the nearest ten, the nearest hundred, the nearest thousand, the nearest million, and so on. All the numbers to the right of the place you are rounding to become zeros. Rounded numbers are easier to remember and easier to use.

If 5 pieces of steel bar each 6 1/2" long are welded together, how long will the new
bar be?

Answers

The new car will be 32.5” long.
6.5 x 5= 32.5

Person 2 worked for 200 minutes and checked 1,325 comments every 5 minutes

Answers

Answer: 33.125

Step-by-step explanation:

So you would do 200 divdied by 5 which is 40 then you would do 1,325 divided by 40 which is the anwser 33.125. If you did it another way let me know.

9% out of 432 kids want to be lawyers. How many kids did not want to be lawyers?

Answers

Answer:

393.12 kids. This is technically impossible, as you can't have 0.12 of a kid, so I will round down to 393 kids.

Step-by-step explanation:

9% = 0.09

x = amount of kids who want to be lawyers

y = amount of kids who do not want to be lawyers

x = 0.09(432)

x = 38.88

y = 432 - 38.88

y =  393.12

2x - 7= -11
What’s the answer?!?!?

Answers

Answer:

×=9

Step-by-step explanation:

2× - 7=11

2× - 7+7=11+7

How does the test variable of an object affect the amount of mechanical energy it contains?

Answers

Answer:

rg53º

Step-by-step explanation:

grnrgnrn

3 Select the correct answer from each drop-down menu. The boundary of a park is shaped like a circle. The park has a rectangular playground in the center and 2 square flower beds, one on each side of the playground. The length of the playground island its width is w. The length of each side of the flower beds is a Which two equivalent expressions represent the total fencing material required to surround the playground and flower beds. Assume that the playground and beds do not overlap The total fending material required to fence the playground and both flower beds is​

Answers

Answer:

Get the perimeter of the each shape and add it all up to get the total fencing material required. 2 square flower beds = 2 x 4a = 8a 1 rectangular play ground = 2l + 2w  total fencing material = 8a + 2l + 2w  

Answer:

2l + 2w + 8a

Step-by-step explanation:

PLEASEEE!! HEPPPP!!

It takes Shonda of an hour to dry one load of laundry in her dryer. How many hours will it take her to dry 4 loads of laundry?

A. 1/5
B. 1 3/5
C. 3 1/5
D. 4/5​

Answers

Shonda takes an hour to dry one load of laundry.No of loads =4

No of hours

[tex]\\ \sf\longmapsto 4(1)[/tex]

[tex]\\ \sf\longmapsto 4 hours[/tex]

None of the above

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