Answer:
311.36
Step-by-step explanation:
For a geometric series sum of first n terms is [tex]a(1-r^n)/(1-r)[/tex]
if r is less than 1.
where a is the first term and r is the common ratio.
____________________________\
given
a = 108
r = [tex]\frac{2}{3}.[/tex]
n = 8
thus , sum of n term is
[tex]a(1-r^n)/(1-r)\\=>108(1-(2/3)^8)/(1-2/3)\\=> 108 (1 - 256/6561)/1/3\\=> 108(6561-256)/ 6561/1/3\\=> 108(6305)/2187\\=>311.36[/tex]
Thus sum of first 8 terms is 311.36
Describe how the graph of y= x2 can be transformed to the graph of the given equation. y = x2 + 3 (5 points)
Answer:
x=-1 1/2,x=-1.5
Step-by-step explanation: x=-3/2
A student answered 12 out of 15 questions on an exam correctly.
a) What fraction of the 15 questions did the student answer correctly? Write your answer in
simplest terms.
b) What percent of the 15 questions did the student answer correctly?
Answer:
1. 4/5
2. 80%
Step-by-step explanation:
Pqrs is a rhombus. Find x, y and z. Justify your finding.
Answer:
x = 4, y = 2√21, z = 10
Step-by-step explanation:
Since all sides of a rhombus are congruent, z = SR = 10. Since the diagonals of a rhombus bisect each other, x = PO = 4. Using Pythagorean Theorem (look at ΔPSO, we know that PS = 10 and PO = 4), y = 2√21.
Need help again ?!???
Answer:
11.47
Step-by-step explanation:
Use SohCahToa. In this problem, you are given the hypotenuse and you are trying to solve for the adjacent side so it will be cosine. (cosine = [tex]\frac{adjacent}{hypotenuse}[/tex])
1. set up the equation
cos55 = [tex]\frac{x}{20}[/tex]
2. Multiply both sides by 20 to solve for x
20 · cos55 = 11.47
Answer:
11.47Solution,
From the figure,
[tex]cos \: 55 = \frac{PQ}{PR} [/tex]
[tex]cos \: 55 = \frac{PQ}{20} [/tex]
[tex]PQ = 20 \: cos \: 55[/tex]
[tex]PQ= 11.472[/tex]
[tex]PQ= 11 .47[/tex]
Hope this helps...
Good luck on your assignment...
Find the slope of the line
Answer:
3/2
Step-by-step explanation:
Using two points we can find the slope of a line
(0,1) and (2,4)
The slope is given by
m= (y2-y1)/( x2-x1)
= (4-1)/(2-0)
= 3/2
If 12^x = ^11√12, what value of x makes this equation true?
The root of a number is equivalent of being raised to its inverT
11 cubic root is = 1/11
X = 1/11
Again. I need help with this
Answer:
Option B.
Step-by-step explanation:
Scale factor of the image = [tex]\frac{\text{One side of the triangle FED}}{\text{Corresponding side of the triangleABC}}[/tex]
= [tex]\frac{\text{DF}}{\text{AC}}[/tex]
= [tex]\frac{3}{6}[/tex]
= [tex]\frac{1}{2}[/tex]
Coordinates of point C → (-2, 2)
Coordinates of the corresponding point C' after dilation with a scale factor [tex]\frac{1}{2}[/tex],
C(-2, 2) → C'(-1, 1)
Coordinates of point C' after reflection across y-axis,
C'(-1, 1) → C"(1, 1)
Followed by the translation of 2 units downwards,
C"(1, 1) → D[1, (1 - 2)]
→ D(1, -1)
From the graph we get the same coordinates of point D as (1, -1).
Therefore, ΔABC was dilated by a scale factor of [tex]\frac{1}{2}[/tex], reflected across the y-axis and moved through the translation of 2 units downwards.
exact value of :7 1/2 - 1 5/8 +(1 3/8 × 2 7/11 )
Answer:
261/44
Step-by-step explanation:
hope this helps. :)
Answer:
9 1/2
Step-by-step explanation:
7 1/2 - 1 5/8 + (1 3/8 × 2 7/11) =
= 7 4/8 - 1 5/8 + 11/8 * 29/11
= 6 12/8 - 1 5/8 + 29/8
= 5 7/8 + 3 5/8
= 8 12/8
= 8 + 8/8 + 4/8
= 9 1/2
Purple paint requires an exact mixture of blue and red. The ratio of blue paint to red paint is 2:5. Marissa needs 35 cups of purple paint to paint a wall. How much of each color would be needed to make a total of 35 cups of perfect purple paint?
Answer:
achievements
Step-by-step explanation:
Describe the effect of pollution on the environment
Answer:
Hello!
~~~~~~~~~~~~~~~~~
Pollution needs to be dramatically reduced because it is destroying the environment we live in, contaminating our food and water, causing diseases and cancers in humans and wildlife, and destroying the air we breathe and the atmosphere that protects us from harmful ultra-violet radiation.
Step-by-step explanation: This the wrong subject but here is the answer.
Hope this helped you! Brainliest would be nice!
Answer:
Answer:
Step-by-step explanation:
Due to pollution many diseases can occur to u...... So we should stop using fuel in vehicles and instead use compressed natural gas (CNG)..... And before sewage water is released into oceans hey should be treated with chemicals...... That's all...
Hope this answer helps.....
what is teh surface area of a rectangular prism, if its length is 17 meters, its width is 2 meters and its height is 3 meters
Answer:
102m^2
Step-by-step explanation:
2x3x17=102m^2
can u pls mark brainliest :)
Answer:
182 m²
Step-by-step explanation:
The formula for surface area of a rectangular prism is;
Surface Area = 2(wl) + 2(lh) + 2(hw) where w is the width, l is the length and h is the height.
SA = 2(2 * 17)m² + 2(17 * 3)m² + 2(3 * 2)m²
= 2(34)m² + 2(51)m² + 2(6)m²
= 68 m² + 102 m² + 12 m²
= 182 m²
g(x) = 4x + 1
What is g(3)?
————————————-
A. 13
B. 16
C. 12
D. 8
Answer:
A. 13.
Step-by-step explanation:
g(x) = 4x + 1
g(3) = 4 * 3 + 1 = 12 + 1 = 13
A. 13 is your answer.
Hope this helps!
Answer:
13
Step-by-step explanation:
g(x) = 4x + 1
Let x=3
g(3) = 4*3+1
= 12+1
= 13
En una casa de empanadas hornean 1.200 por día. Si las cocinan en fuentes de 75 unidades, colocando siempre la mayor cantidad posible, ¿Cuántas fuentes preparan?
Answer:
16 unidades preparan simultáneamente 1200 empanadas por día.
Step-by-step explanation:
Si cada fuente tiene una capacidad de 75 empanadas por horneada y que la mayor cantidad posible ocurre cuando el volumen de producción se cocina simultáneamente, entonces el total de fuentes es la cantidad total de producción dividida por la capacidad de empanadas por fuente. Es decir:
[tex]x = \frac{1200\,emp}{75\,\frac{emp}{und} }[/tex]
[tex]x = 16\,unidades[/tex]
16 unidades preparan simultáneamente 1200 empanadas por día.
14 + 18 divided by 2 * 18
Is the answer 86 or no?
Answer:
No.
Step-by-step explanation:
Order of Operations using BPEMDAS:
14 + 18/2(18)
14 + 9(18)
14 + 162
176
(2x + 3)(5x2 - 2x - 1) = Ax3 + Bx2 + Cx + D. What are the values of B and C?
Answer:
B = 11; C = -8
Step-by-step explanation:
When simplified I get 10x^3 + 11x^2 - 8x - 3
PLEASE HELP - Find the area of a regular octagon with a side length of 5 cm. Round to the nearest tenth. (Please explain in full detail the process, im trying to learn how to do these) thank you!!
Answer:
120.7
Step-by-step explanation:
The formula for finding the area of a regular octagon is: A = 2(1+[tex]\sqrt{2}[/tex])[tex]a^{2}[/tex].
Using the formula I got 120.7(rounded).
The area of the regular octagon with a side length of 5 cm is approximately 120.7cm².
We have,
To find the area of a regular octagon with a side length of 5 cm, you can use the following formula:
Area = 2 * (1 + √2) * (Side Length)²
Plugging in the values:
Area = 2 * (1 + √2) * (5 cm)² ≈ 120.7 cm²
Therefore,
The area of the regular octagon with a side length of 5 cm is approximately 120.7cm².
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The snail moved 6 inches in 120 minutes. What was the average speed of the snail in inches per minute?
Answer:
0.05 in per min.
Step-by-step explanation:
We simply divide 6 by 120 to find our unit rate:
6 in/120 min = 1/20 = 0.05 in/1 min
Answer:
1/20 Inch per. Minute
Step-by-step explanation:
6/120 -->
6/1 x 1/120 --> cancel out 6 and 120 for 1 and 20 respectively
1/1 x 1/20 --> 1 x 1/20 => 1/20
Hope this helps!
The figure is not drawn to scale. PQ and MN are straight lines. Find
Answer:
a = 138
Step-by-step explanation:
Notice that from the figure, we can see that ∠MOQ and ∠PON are vertical angles, which means that by definition, they're congruent in measure.
∠MOQ = ∠MOR + ∠ROQ = 90 + 48 = 138°
So, this means that ∠PON is also equal to 138, which means a = 138.
Thus, the answer is a = 138.
~ an aesthetics lover
Factor (x^2-1x)(-4x+4), with work shown
Answer:
4 ( -x^3 + 2x - x)
Step-by-step explanation:
refer the attachment
how to do this question plz
Answer:
adult = £7 and child = £2
Step-by-step explanation:
let a represent adult ticket and c child ticket, then
2a + 3c = 20 → (1)
a + 4c = 15 → (2)
Multiply (2) by - 2 and add to (1) to eliminate a
- 2a - 8c = - 30 → (3)
Add (1) and (3) term by term
- 5c = - 10 ( divide both sides by - 5 )
c = 2
Substitute c = 2 into either of the 2 equations and solve for a
Substituting into (1)
2a + 3(2) = 20
2a + 6 = 20 ( subtract 6 from both sides )
2a = 14 ( divide both sides by 2 )
a = 7
Cost of adult ticket is £7 and child ticket is £2
If (x+3) varies directly as y and x=3 when y=12, what is the value of x when y=8?
Answer:
x = 1.
Step-by-step explanation:
y = k(x + 3)
When x = 3 y = 12 so
12 = k(3 + 3)
6k = 12
k = 2.
So the relation is y = 2(x + 3)
When y is 8:
8 = 2(x + 3)
2x = 8 - 2*3 = 2
x = 1.
Natalie has 8 socks in a drawer.
5 of the socks are black.
3 of the socks are white.
Natalie takes out a sock at random, writes down its colour and puts it back into
the drawer.
Then Natalie takes out a second sock, at random, and writes down its colour.
Answer:
Probability that the two socks picked by Natalie are of the same colours = (17/32) = 0.53125
Step-by-step explanation:
Complete Question
Natalie has 8 socks in a drawer.
5 of the socks are black.
3 of the socks are white.
Natalie takes out a sock at random, writes down its colour and puts it back into
the drawer. Then Natalie takes out a second sock, at random, and writes down its colour.
Work out the probability that the two socks are of the same colour.
Solution
This is a probability that involves replacement.
Probability of an event is given as the number of elements in the event divided by the total number of elements in the sample space.
If the event that a black socks is picked = P(B)
Then, the event that a white socks is picked = P(W)
P(B) = n(B) ÷ n(S)
n(B) = 5
n(S) = 8
P(B) = (5/8)
P(W) = n(W) ÷ n(S) = (3/8)
Probability that the two socks picked by Natalie are of the same colours = (Probability that the two socks picked are black) + (Probability that the two socks picked by Natalie are white)
Probability that the two socks picked are black = (5/8) × (5/8) (since the socks are picked and replaced, the probability stays the same)
= (25/64)
Probability that the two socks picked by Natalie are white = (3/8) × (3/8) = (9/64)
Probability that the two socks picked by Natalie are of the same colours
= (25/64) + (9/64)
= (34/64)
= (17/32) = 0.53125
Hope this Helps!!!
need help asap!!! WILL GIVE THE MOST BRAINIEST TO WHOEVER ANSWERS IT RIGHT PUT THE ANSWER IN A BOX
Answer:
36PI
113.04
Step-by-step explanation:
4/3*PI*R^3=V
4/3*PI*27=V
36*PI=V
113.04
BRAINLIEST PLS
-ZYLYNN JADE
Answer:
113.10 (to the nearest hundredth)
Step-by-step explanation:
just google volume of a sphere
(06.01, 06.02 HC) I WILL MARK YOU BRAINIEST Part A: Create a fourth-degree polynomial in standard form. How do you know it is in standard form? (5 points) Part B: Explain the closure property as it relates to polynomials. Give an example. (5 points)
A fourth-degree polynomial in standard form is :
To write a polynomial in a standard form you have to set its terms according to the variable powers in a descending order.In this example it would give:
−6[tex]x^{4}[/tex]+3[tex]x^{2}[/tex]+4x +2
The degree of a polynomial is the maximum power of an unknown variable in the polynomial.Part B:
The closure property as it relates to polynomials are :
Polynomials are closed for addition and subtraction. This is because the power does not change. Only the coefficients are changed. This is illustrated by the examples below:(2x2 + 3x + 4) + (x2 - 5x - 3)
3x2 - 2x + 1.
The above operation does not change the degree. Only the number next to each variable changes.Therefore, the addition and subtraction of polynomials is closed.
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9.
((x - 2)2
The function f(x) = ax2 + bx
3x – 6
if x < -1
if - 1
if x 2
is continuous for all real values of x.
Find a and b.
Answer:
a = 0.3 and b = - 1.1
Step-by-step explanation:
(x - 2)² = x² -4x + 4
Hence, x² - 4x + 4 = 3x - 6
x² - 7x + 10 = 0
(x - 5)(x - 2) = 0
∴ x = 5 or 2
f(5) = 25a + 5b = 2 ----- (i)
f(2) = 4a + 2b = -1 ------ (ii)
(i) X 2: 50a + 10b = 4 ----- (iii)
(ii) X 5: 20a + 10a = -5 ---- (iv)
Subtract (iv) from (iii): 30a = 9
a = 0.3
Substitute a into (ii) to obtain b
4(0.3) + 2b = -1
2b = -1 - 1.2 = -2.2
∴ b = -1.1
Solve for x. Write both solution, separated by a comma. 4x^2-x-3=0.
Answer:
x = -3/4, 1
Step-by-step explanation:
Factor left side of the equation.
(4x + 3)(x - 1) = 0
Set factors equal to 0.
4x + 3 = 0
4x = -3
x = -3/4
x - 1 = 0
x = 1
Answer:
x₁ = -3/4
x₂ = 1
Step-by-step explanation:
4x² - x - 3 = 0
4x² + 3x - 4x - 3 = 0
xx(4x + 3) - 4x - 3 = 0
xx(4x + 3) - (4x + 3) = 0
(4x + 3) × (x - 1) = 0
4x + 3 = 0 → x = -3/4
x - 1 = 0 → x = 1
Hope this helps! :)
true or false rise is the horizontale change between any two points on a line
Answer:
False
Step-by-step explanation:
rise is the vertical change between any two points on a line.
Translate into an algebraic expressions: 120 is increased by d% and increased by 25% . What is the result ?
Answer:
The result is 150 + 1.5d
Step-by-step explanation:
We want to translate the wordings into algebraic expression.
Firstly, we increase 120 by d%
d% = d/100
So increasing 120 by d % means;
120 + (d/100 * 120)
= 120 + 1.2d
Then increase this by 25%
= (120 + 1.2d) + 25/100(120 + 1.2d)
= 120 + 1.2d + (120+1.2d)/4
= 120 + 1.2d + 30 + 0.3d
= 120 + 30 + 1.2d + 0.3d
= 150 + 1.5d
BRAINLIEST What is the volume of the right triangular prism, in cubic meters? Round to the nearest cubic meter.
1,771
2,071
3,542
4,143
Answer:
The answer to this would most likely be the first option: A. 1,771
Step-by-step explanation:
I've seen the question before.
The volume of the right triangular prism is 1771 cubic meters
What is the volume of a right triangular prism?The volume of a right triangular prism can be estimated by using the formula:
[tex]\mathbf{V = \dfrac{1}{2} \times b \times h \times l}[/tex]
where;
b = base length of the triangle = 14h = height of the triangle = 23l = length of the prism = 11[tex]\mathbf{V = \dfrac{1}{2} \times 14 \times 23 \times 11}[/tex]
V = 1771 m³
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At the beginning of year 1, Josie invests $400 at an annual compound interest rate of 5%. She makes no deposits to or withdrawals from the account. Which explicit formula can be used to find the account's balance at the beginning of year 3?
A. A(3) = 400 • (1 + 0.05)3 – 1
B. A(3) = 400 + (3 – 1)(0.05 • 400)
C. A(3) = 400 + (0.05 • 400)3 – 1
D. A(3) = 400 • (1 + 0.05)3
Answer: A
Step-by-step explanation:
Since she invested $400 in the beginning if the 1st year and we are asked to find the balance at the beginning of the third year, she earns interest only for the first two years. So, the formula will be
Amount = 400 (1 + 0.05) ^3-1
To find the balance in Josie's account at the beginning of the the third year we have to use A(3)=[tex]400*(1+0.05)^{3-1}[/tex]
What is Compound interest?It is the interest calculated on the initial principal amount and the accumulated interest. The formula to calculate the sum after compound interest is
Sum= [tex]P(1+r/m)^{tm}[/tex] where P=principal, r= rate of interest, m= number of times compounded in a year, t=time
How to calculate sum when interest is compounding?At the beginning of year 1, Josie invests $400 at an annual compound interest at the rate of 5%,then the amount at the beginning of year 3 is calculated as:
The amount in beginning of 1 year=$400
The amount at the end of the year 1=400+400*0.05=400(1+0.05)
The amount at the end of year 2=400(1+0.05)+400(1+0.05)*0.05
=[tex]400(1+0.05)^{2}[/tex]
=[tex]400(1+0.05)^{3-1}[/tex]
Hence the option A is correct which is to be used to calculate the amount in Josie's account at the beginning of year 3.
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