Answer:
Series A has an r value of 2/5 and series A has an r value of 3. The sum of the series A is 50/3
Step-by-step explanation:
A geometric sequence is in the form a, ar, ar², ar³, . . .
Where a is the first term and r is the common ratio = [tex]\frac{a_{n+1}}{a_n}[/tex]
For series A: 10+4+8/5+16/25+32/125+⋯ The common ratio r is given as:
[tex]r=\frac{a_{n+1}}{a_n}=\frac{4}{10} =\frac{2}{5}[/tex]
For series B: 1/5+3/5+9/5+27/5+81/5+⋯ The common ratio r is given as:
[tex]r=\frac{a_{n+1}}{a_n}=\frac{3/5}{1/5} =3[/tex]
For series A a = 10, r = 2/5, which mean 0 < r < 1, the sum of the series is given as:
[tex]S_{\infty}=\frac{a}{1-r}=\frac{10}{1-\frac{2}{5} } =\frac{50}{3}[/tex]
the equation y=2(3^t) shows the number of infected people from an outbreak of the norovirus. the variable y represents the number of infected people and t represents time in weeks.
in how many weeks will the number if infected people reach 1458?
Answer:
Step-by-step explanation:
We have the equation
[tex] 2(3^t) = 1458[/tex]
Dividing by 2 on both sides we get
[tex] 3^t = 729[/tex]
Taking the natural logarithm on both sides we get
[tex] t \ln(3) = \ln(729)[/tex]
So t = \frac{\ln(729)}{\ln(3)} = 6.
So at 6 weeks we get 1458 infected people.
Determine the inequality represented by the following diagram
How many three-digit numbers can you make if you are not allowed to use any other digits except 1 and 2? (You may use 1 and 2 in a number more than once or not at all!)
The first digit can be 1 or 2.
For each one ...
The second digit can be 1 or 2.
For each one ...
The third digit can be 1 or 2.
That's (2•2•2)= 8 different possibilities.
The athletic club at school sold raffle tickets to raise money for equipment. The club sold a total of 1050 tickets,515 to teachers and 235 tickets to staff. If the winning ticket was picked at random what is the probability of the teacher or other staff member?
Answer:
Probability of the teacher or other staff is 0.7143
Step-by-step explanation:
pr(teacher or other staff) = pr(teacher) + pr(other staff) - pr(teacher and other staff)
Total number of tickets = 1050
Number of tickets sold to teachers = 515
Number of tickets sold to other staff = 235
pr(teacher) = [tex]\frac{515}{1050}[/tex]
= 103 [tex]\frac{2}{10}[/tex]
= 0.4905
pr(other staff) = [tex]\frac{235}{1050}[/tex]
= 47 [tex]\frac{2}{10}[/tex]
= 0.2238
Since the picking of the wining ticket is mutually exclusive, then;
pr(teacher and other staff) = 0
Thus,
pr(teacher or other staff) = 0.4905 + 0.2238 - 0
= 0.7143
8³=512 indique o expoente
1. Following is the Receipt and Payment A/c. of a club for the year ended 31-03-2014.
Receipt ₹ Payment ₹
To Balance b/d 75,000 By Salaries 22,000
To Subscription By office expenses 8,000
2012-13 35,000 By Sports equipment
2013-14 9,50,000 (Purchased on 1-10-2013) 6,00,000
2014-15 55,000 10,40,000 By Telephone charges 12,000
To Donation 90,000 By Electricity charges 18,000
To Entrance Fees 60,000 By Travelling Expenses 6,000
To Locker rent 20,000 By 10% Fixed Deposit
To Donation for Building 1,50,000 (made on 1-07-2013) 7,00,000
By balance c/d. 69,000
14,35,000 14,35,000
Additional information:
a) Outstanding subscription for 2013-14 ₹80,000. Outstanding salaries as on 1-04-2013 were ₹2,000 and as on 31-03-2014 were ₹4,000.
b) One third of Entrance fee to be treated as General income.
c) Locker rent rate is ₹2,000 per month.
d) Depreciation on sports equipment 10% p.a.
Prepare Income and Expenditure A/c. for the year ending 31-03-2014.
Answer:
Excess of income over expenditure is ₹1,185,500.
Step-by-step explanation:
Note: The data in this question are merged together. They are therefore sorted before answering this question. See the attached pdf file for the sorted question.
The question is now answered as follows:
Question: Prepare Income and Expenditure A/c. for the year ending 31-03-2014.
Answer and explanation:
Note: See the attached excel file for the Income and Expenditure A/c. for the year ending 31-03-2014.
Both receipts and payments account and income and expenditure account are prepared by not-for-profit organizations such as charity organizations, human right campaign, clubs, etc.
Receipts and payments account is an account gives a summary of all the cash transitions, cash received and paid, that the organization engaged in during a particular period. It is similar to the cash book prepared by profit making organizations. The receipts and payments account is prepared in or to determine the balance of cash in hand or at bank or bank overdraft at the end of the period.
Income and expenditure account is an account gives a summary of all incomes and expenses of an organization during a particular period. It is similar to the trading and profit and loss account prepared by profit making organizations. The income and expenditure account is prepared in order to determine whether there is a surplus or a deficit balance during the period.
On a trip mrs. ahmed drove 188 miles in 4 hours. On the return trip, she took a different route and traveled 197 miles in 4.5 hours. What was the average rate of speed for the trip?
Answer:
45.29 miles per hour
Step-by-step explanation:
Speed is the distance over time. To find the average rate of speed for a trip, we simply need to take the total distance divided by the total time.
Avg. Speed = (188 miles + 197 miles) / (4 hours + 4.5 hours)
Avg. Speed = 45.29 miles per hour
Hence the average rate of speed for the trip was 45.29 miles per hour.
Cheers.
--------------------------------------------------------
Edit: Thanks to Chegsnut36 for calculation correction
Answer:
≅45.29
Step-by-step explanation:
Hey there!
To find the average rate speed we need to add all the same number.
188 + 197 = 385
4 + 4.5 = 8.5
Now to find the average rate we do,
385 ÷ 8.5 ≅ 45.29
Hope this helps :)
Given: EG - diameter m arc FG =41°, m arc EH =53° Find: m∠E, m∠GPF
Answer: m∠E = 20.5°
m∠GPF = 47°
Step-by-step explanation: An inscribed angle is an alge formed with its vertex on the circle. Its relation with arc is that the measure of an inscribed angle is half the measure of the intersected arc. For that reason:
m∠E = [tex]\frac{arcFG}{2}[/tex]
m∠E = [tex]\frac{41}{2}[/tex]
m∠E = 20.5°
Angle in F is:
m∠F = [tex]\frac{arcEH}{2}[/tex]
m∠F = [tex]\frac{53}{2}[/tex]
m∠F = 26.5°
The angle GPF is external to the triangle EPF, so the angle can be found by the following definition: The measure of an external angle of a triangle equals the sum of the non-adjacent angles, i.e.:
m∠GPF = m∠E + m∠F
m∠GPF = 20.5 + 26.5
m∠GPF = 47°
Answer:
b
Step-by-step explanation:
A climbing structure needs to be built in the shape of a square-based pyramid. Look at the diagram below. What is the perimeter of the flat, orange shape? PLEASE HELP A GIRL OUT
Answer:
40 m
Step-by-step explanation:
The perimeter of the flat, orange shape is the sum of all the sides that forms a boundary around the shape.
The shape is made up of 4 triangles having 2 equal side lengths each, which surrounds the center square.
Each side length of the triangle, that forms a boundary round the shape = 5 m.
There are 8 of this equal side length.
Perimeter = 8(5m) = 40 m
How much material would you need to fill the following cylinder? Radius 13 in. and Height 9 in.
39π in3
117π in3
1053π in3
1521π in3
Answer:
1521 pi in^3
radius x radius x height x pi = volume
13 x 13 x 9 = 1521
We do not multiply by pi because it is already included
Hope this helps
Step-by-step explanation:
Solve for x. 60 10 20 120
Answer:
Hey there!
We have the angle is equal to half the measure of the arc of 120 degrees. (Just another rule for circles)
7x-10=0.5(120)
7x-10=60
7x=70
x=10
Hope this helps :)
Answer:
x = 10
Step-by-step explanation:
Tangent Chord Angle = 1/2 Intercepted Arc
7x-10 = 1/2 ( 120)
7x -10 = 60
Add 10 to each side
7x -10+10 = 60+10
7x = 70
Divide by 7
7x/7 = 70/7
x = 10
Let f(x) = 3x + 5 and g(x) = x2. Find g(x) − f(x).
Answer:
2x-(3x+5) = -x-5
Step-by-step explanation:
2x + 0
-
3x + 5
-———————-
-x - 5
...............................
Answer:
[tex]2 \sqrt{10} [/tex]Option C is the correct option.
Step-by-step explanation:
√ 8 • √ 5
Calculate the product
[tex] = \sqrt{40} [/tex]
Simplify the radical expression
[tex] = \sqrt{2 \times 2 \times 10} [/tex]
[tex] = 2 \sqrt{10} [/tex]
Hope this helps...
Best regards!!
which graph represents exponential decay
Answer:
1
Step-by-step explanation:
BEGINNING COORDINATES:
A- 2,2
B- 0,2
C- 4,4
Triangle ABC is dilated by a factor of 2 with the center of dilation at the origin to form triangle A′B′C′. What are the coordinates of triangle A′B′C′?
Question 1 options:
A)
A′ (0, 4), B′ (4, 0), C′ (16, 16)
B)
A′ (0, –4), B′ (–4, 0), C′ (–8, –8)
C)
A′ (0, 4), B′ (4, 0), C′ (8, 8)
D)
A′ (4, 0), B′ (0, 4), C′ (8, 8)
Answer:
The correct option is;
A'(4, 4), B'(0, 4), C'(8, 8).
Step-by-step explanation:
The beginning coordinates are;
A -2, 2
B - 0, 2
C - 4, 4
Given that triangle ABC is dilated by 2, the center of dilation being the origin, (0, 0), we have;
Given that the center of dilation is the origin, we multiply the x, and y values by the scale factor as follows;
(x, y) → (2·x, 2·y)
Which gives;
A - (2, 2) → A'(2×2, 2×2) = A'(4, 4)
B - (0, 2) → B'(2×0, 2×2) = B'(0, 4)
C - (4, 4) → C'(2×4, 2×4) = C'(8, 8)
The correct option is A'(4, 4), B'(0, 4), C'(8, 8).
Gemma wants to draw a triangle with side lengths of 4 inches, 12 inches, and 17 inches. Which statement is true? This triangle exists because the sum of any two side lengths is greater than the length of the third side. This triangle exists because the sum of 4 and 12 is less than 17. This triangle does not exist because the sum of any two side lengths is greater than the length of the third side. This triangle does not exist because the sum of 4 and 12 is less than 17.
Answer:
The triangle inequality states that the sum of the lengths of the two shortest sides of a triangle must be greater than the length of the largest side. Because 4 + 12 > 17 is not a true statement, the answer is "This triangle does not exist because the sum of 4 and 12 is less than 17."
Answer:
This triangle does not exist due to the fact that the sum of 4 and 12 is less than 17
Step-by-step explanation:
The triangle formaction rule states that the 2 smaller sides must be able to combine and be greater than the greatest side.
Triangle
Sides - 3, 4, 5
3+4=7
Meaning the two smaller sides add up to because greater than 5.
Non-Triangle
Sides - 5, 6, 13
5+6=11
This means that this is not a triangle because the smaller sides ‘5 and 6’ do not add up to become greater than 13.
Gemma’s Triangle
Sides - 4, 12, 17
4+12=16
Hence, Gemma‘s figure is not a triangle because the 2 smaller sides ‘4 and 12’ don‘t add up to be greater than 17.
Which of these workers is paid less than the minimum hourly wage? Bartender Electrician Hotel Manager Plumber
Answer:
It's A, the bartender
Step-by-step explanation:
What the answer question now
Answer:
UW=41
Step-by-step explanation:
the tangent line and the radius always meet at a right angle(90 degrees)
UWV is a right angle triangle, apply the Pythagorean theorem:
a²+b²=c² (a=40, b=9, c=UW)
40²+9²=c²
c=√40²+9²=√1600+81=√1681
c= 41
can someone explain how to use sin cos and tan on right angled triangles
Round this however you need to
=================================================
Explanation:
The reference angle is 56 degrees. The side 26.5 is adjacent to this angle as it is the leg closest to the angle (in contrast to the opposite leg or opposite side that is furthest from the reference angle)
The hypotenuse is d. The hypotenuse is always the longest side. The longest side is always opposite the largest angle of a triangle.
We will use the cosine ratio as it is the ratio of adjacent over hypotenuse
cos(angle) = adjacent/hypotenuse
cos(56) = 26.5/d
d*cos(56) = 26.5
d = 26.5/cos(56)
d = 47.3897287242421
You use your calculator for the last step shown above. Make sure your calculator is in degree mode. Round that value however you need to.
Here is the formula of sin cos tan :
sin x = opposite/hypotenuse
cos x = adjacent / hypotenuse
tan x = opposite / adjacent
d = hypotenuse
x = the angle known in your pic
like example if in your picture:
adjacent = 26.5
if want to find the d
cos x = adjacent / hypotenuse
cos 56 = 26.5 / d
d = 26.5 : cos(56)
d = 47.390 (3 significant figures)
and if want to find the opposite
tan x = opposite/adjacent
tan 56 = opposite/ 26.5
opposite = 26.5 × tan(56)
opposite = 39.288
-> Sorry if im wrong
g(x)=sqrt8x what is domain of g
Answer:
x > or equal to 0
Step-by-step explanation:
you're welcome
Answer:
x > or equal to 0
Which graph shows the solution to the system of linear inequalities? 2x -3y ≤ 12 y < -3
First solve for y in [tex]2x - 3y \le 12[/tex] to get [tex]y \ge \frac{2}{3}x-4[/tex]. The inequality sign flips because we divided both sides by a negative value.
To graph [tex]y \ge \frac{2}{3}x-4[/tex] we need to graph the boundary line y = (2/3)x - 4. This line has a y intercept of (0,-4) and another point on the line is (6,0).
Draw a solid line through (0,-4) and (6,0). The boundary line is solid because of the "or equal to" part of the inequality sign. The last part is to shade above the boundary line because of the "greater than" sign in [tex]y \ge \frac{2}{3}x-4[/tex].
---------------
As for graphing y < -3, we draw a horizontal dashed line through -3 on the y axis. The line is dashed because there is no "or equal to" here. We do not include boundary points as part of the solution set. Shade below this dashed line due to the "less than" sign.
---------------
After doing both of these things on the same xy grid, you'll get something that looks like choice C. I'm assuming choice C has a dashed line for the red region.
Answer: Choice CThe graph is image 2. (last option)
We first draw the lines 2x - 3y = 12 and y=-3. Image 1.
For 2x - 3y ≤ 12
or, 2x - 12 ≤ 3y
or, 3y ≥ 2x - 12
or, y ≥ (2x - 12)/3
we shade upwards.
For y < - 3 we shade below.
So the graph is image 2.
Learn more: https://brainly.com/question/8806877
Write each of the following expressions without using absolute value.
|a−7|−|a−9|, if a<7
PLEASE HELP!!!! D:
=======================================================
If a < 7, then |a-7| = -(a-7) = -a+7 based on how absolute value functions are constructed. We're using the idea that
[tex]|x-k| = \begin{cases}x-k \ \text{ if } \ x \ge k\\ -(x-k) \ \text{ if } \ x < k\end{cases}[/tex]
Also, if a < 7, then |a-9| = -(a-9) = -a+9. This is true whenever 'a' is less than 9 for similar reasoning as above.
---------
So we have,
|a-7| - |a-9| = -a+7 - (-a+9) = -a+7+a-9 = -2
As long as a < 7, the result of |a-7| - |a-9| will always be -2.
---------
As an example, let's say a = 0
|a-7| - |a-9| = |0-7| - |0-9|
|a-7| - |a-9| = |-7| - |-9|
|a-7| - |a-9| = 7 - 9
|a-7| - |a-9| = -2
I recommend you try out other values of 'a' to see if you get -2 or not. Of course only pick values that are smaller than 7.
PLEASE I NEED HELP ASAP! The function below represents the interest Jessi earns on an investment. Identify the term that represents the amount of money originally invested. f(x) = 1,000(1 + 0.05)x 1,000 1 0.05 1.05
Answer:
1000
Step-by-step explanation!
The formula for the amount accrued [ƒ(x)] on an investment earning compound interest is f(t) = P(1 + r)^t where:
P = the amount of money invested (the principal)
r = the interest rate per payment period expressed as a decimal fraction
t = the number of periods
Your formula is
f(x) = 1000(1 + 0.05)^x
In comparison, we can see that the term that represents the amount of money originally invested is 1000.
Answer:
(A) 1,000
Step-by-step explanation:
i just took the test
Daniel had 80 more stickers than Elle. He gave 1/4 of his stickers to Elle. She then gave 3/5 of her stickers to Daniel. In the end, Daniel had 92 more stickers than Elle. How many stickers did Daniel have at first? (please refrain from using algebra to solve this question as this is a primary 6 question thanks.)
Answer:
Daniel had 108 stickers at first
Step-by-step explanation:
Number of Daniel's stickers = d
Number of Elle's stickers = e
Since Daniel had 80 more stickers than Elle, d = 80 + e
e = d - 80
Daniel gave 1/4 of his stickers to Elle, Daniel is left with (d - d/4) = 3d/4
Elle now has e + d/4 = d - 80 + d/4 = (5d/4) - 80 = (5d - 320)/4
Elle now gave 3/5 of her remaining stickers to Daniel:
Elle now has:
[tex]e_{new} = \frac{5d -320}{4} - \frac{3}{5} * \frac{5d -320}{4}\\\\e_{new} = \frac{5d -320}{4} - \frac{15d -960}{20}\\\\e_{new} = \frac{25d - 1600 - 15d + 960}{20} \\\\ e_{new} = \frac{10d-640}{20}[/tex]
Daniel now has:
[tex]d_{new} = \frac{3d}{4} + \frac{3}{5} (\frac{5d - 320}{4} )\\d_{new} = \frac{3d}{4} + \frac{15d - 960}{20} \\d_{new} = \frac{30d - 960}{20}[/tex]
Daniel now had 92 more stickers than Elle
[tex]d_{new} = E_{new} + 92[/tex]
[tex]\frac{30d - 960}{20} = \frac{10d - 640}{20} + 92[/tex]
Multiply through by 20
30d - 960 = 10d - 640 + 1840
20d = -640 + 1840 + 960
20 d = 2160
d = 2160/20
d = 108
Five years ago, Alan was thrice as old as Aron. After ten years, Alan will be twice as old as Aron. How old are Alan and Aron?
Alan will be 50 yrs old and Aron will be 20 yrs old
Juanita is cutting a piece of construction paper in the shape of a parallelogram. Two opposite sides of the parallelogram have lengths (5n − 6) cm and (3n − 2) cm. A third side measures (2n + 3) cm. What are the lengths of two adjacent sides of the parallelogram? 2 cm and 2 cm 4 cm and 7 cm 7 cm and 9 cm 13 cm and 19 cm
=======================================================
Explanation:
For any parallelogram, the opposite sides are the same length. Think of a rectangle, though we could have angles that aren't 90 degrees.
(5n-6) and (3n-2) are the lengths of the opposite sides. Set them equal to one another and solve for n.
5n-6 = 3n-2
5n-3n = -2+6
2n = 4
n = 4/2
n = 2
We can use this to find the length of the opposite sides
5n-6 = 5*2-6 = 10-6 = 4
3n-2 = 3*2-2 = 6-2 = 4
We get 4 each time which helps confirm we have the correct value for n.
The opposite sides are 4 cm each. The other side is
2n+3 = 2*2+3 = 4+3 = 7
Looking at adjacent sides (sides that are next door neighbors), we see 4 cm and 7 cm.
We could easily say "7 cm and 4 cm" as order doesn't matter. Though this isn't listed so we'll go with "4 cm and 7 cm" instead.
HELP ME PLEASE THE DIAGRAM SHOWS A CIRCLE INSIDE A CIRCLE WORK OUT THE AREA OF THE CIRCLE
Answer:
64π
Step-by-step explanation:
Since the diameter of the circle is 16, the radius is half of that which is 8.
Area = πr² = 64π
Answer:
200.96 units[tex] {}^{2} [/tex]Step-by-step explanation:
Radius = 8 cm
Now, finding the area of circle:
[tex]\pi \: {r}^{2} [/tex]
Plug the values
[tex] = 3.14 \times {8}^{2} [/tex]
Evaluate the power
[tex] = 3.14 \times 64[/tex]
Calculate the product
[tex] = 200.96 \: {cm}^{2} [/tex]
Hope this helps..
Best regards!!
Multiply: (6x - 1)(6x +1)
Answer:
36x^2 -1
Step-by-step explanation:
6x times 6x= 36x^2
6x times 1= 6x
-1 times 6x= -6x
-1 times 1= -1
so, ...
36x^2+6x+(-6x)+(-1) = 36x^2 -1
A driver decends 20 feet in the water from the boat at the surface of the lake. He then rose 12 feet and decends another 18 feet. At this point what is his depth in the water
Answer:
-26 ft or 26 ft below the surface
Step-by-step explanation:
Starting at the surface
0
Descending 20 ft
0 -20 = -20
Rose 12 ft
-20 +12 = -8
Descends 18 ft
-8 -18= -26 ft
Please help I’m being timed!!! System shows there is no profit made until the price reaches $95 per unit, a maximum profit at a price of $140 per unit, and no profit at a price over $185 per unit. Which graph models the function?
Answer:
4th one
Step-by-step explanation: