Answer:
40 + 20 + 10 + 5 is a geometric series
Step-by-step explanation:
* Lets revise the geometric series
- There is a constant ratio between each two consecutive numbers
- Ex:
# 5 , 10 , 20 , 40 , 80 , ………………………. (×2)
# 5000 , 1000 , 200 , 40 , …………………………(÷5)
* General term (nth term) of a Geometric Series:
∵ U1 = a , U2 = ar , U3 = ar2 , U4 = ar3 , U5 = ar4
∴ Un = ar^n-1, where a is the first term , r is the constant ratio
between each two consecutive terms , and n is the position of
the term in the series
* Now lets check the answers to find the correct one
# 40 + 50 + 60 + 70
∵ 50/40 = 5/4
∵ 60/50 = 6/5
∵ 5/4 ≠ 6/5
- No common ratio between each two consecutive terms
∴ Not geometric series
# 40 + 42 + 44 + 46
∵ 42/40 = 21/20
∵ 44/42 = 22/21
∵ 21/20 ≠ 22/21
- No common ratio between each two consecutive terms
∴ Not geometric series
# 40 + 80 + 40 + 120
∵ 80/40 = 2
∵ 40/80 = 1/2
∵ 2 ≠ 1/2
- No common ratio between each two consecutive terms
∴ Not geometric series
# 40 + 20 + 10 + 5
∵ 20/40 = 1/2
∵ 10/20 = 1/2
∵ 5/10 = 1/2
- There is a common ratio between each two consecutive terms
∴ 40 + 20 + 10 + 5 is a geometric series
Answer:
D 40 + 20 + 10 + 5
The first day of Sam's vacation was a Monday. What day of the week was the Day 36 of Sam's vacation?
A. Monday
B. Tuesday
C. Wednesday
D. Thursday
Answer:
A. Monday
Step-by-step explanation:
The solution to this problem can be found by creating a table
If Day 1 was Monday, then
Mon Tues Wed Thur Fri Sat Sun
1 2 3 4 5 6 7
8 9 10 11 12 13 14
...............
We can see that the multiples of 7 are falling on Sundays so we will divide 36 by 7 to get the closest multiple of 7 to 36.
The closest multiple of 7 near 36 is 35 so Day 35th will fall on Sunday and Day 36 will be on Monday
Hence, Option A is the correct answer..
Answer:
A. Monday
Step-by-step explanation:
The solution to this problem can be found by creating a table
If Day 1 was Monday, then
Mon Tues Wed Thur Fri Sat Sun
1 2 3 4 5 6 7
8 9 10 11 12 13 14
...............
We can see that the multiples of 7 are falling on Sundays so we will divide 36 by 7 to get the closest multiple of 7 to 36.
The closest multiple of 7 near 36 is 35 so Day 35th will fall on Sunday and Day 36 will be on Monday
Hence, Option A is the correct answer..
Which of the following are identities? Check all that apply.
Answer:
Options A and D.
Step-by-step explanation:
To check the identities we have to check each option given.
A. tan(x - π) = tanx
We take left hand side (L.H.S.) of the equation.
tan(π - x) = tanx [ since we know tan(π ± x) = tanx ]
So L.H.S. = R.H.S.
It's an identity.
B. sin(x + y) + sin(x - y) = 2cosx siny
We take L.H.S. first
sin(x + y) + sin(x - y)
= sinx coxy + siny cosx + sinx cosy - cosx siny
= 2sinx cosy ≠ R.H.S.
Option B is not an identity.
C. cos(x + y) - cos(x - y) = 2cosx cosy
We take L.H.S. of the equation.
cos(x + y) - cos(x - y) = cosx cosy - sinx siny - (cosx cosy + sinx siny)
= -2sinx siny ≠ R.H.S.
Therefore, option C is not an identity.
D. cos(x + y) + cos(x - y) = 2cosx cosy
We take L.H.S. of the equation.
cos(x + y) + cos(x - y) = cosx cosy - sinx siny + cosx cosy + sinx siny
= 2cosx cosy = R.H.S.
Therefore, option D is an identity.
Options A and D are the identities.
What is the reverse of “multiply by 6”
Answer:
Divide by 6
Step-by-step explanation:
The reverse or inverse of multiply by 6 is divide by 6.
Jeff has a cube train that is 22 inches long. he removes 8 inches of cubes from the train. How long is Jeff's cube train now?
Answer:
14 inches long
Step-by-step explanation:
Answer:
14 inches long
Step-by-step explanation:
I need help please??!!
Answer:
Step-by-step explanation: (5,-2)
Answer:
(5,-2)
Step-by-step explanation:
Original price: $32
Discount: ?
Sale price: $8
Answer: 75%
Step-by-step explanation:
32 dollars times 75% = 24
32 - 24 = $8
The Discount is of amount $32.
What is Discount?The discount is equivalent to the difference between the purchase price and the par value. A discount is a decrease or deduction in a product's cost price.
Discount = Original price – Sale price.
We have,
Original price: $32
Sale price: $8
So, Discount Price = Original price - Sale price
= 32 - 8
= $24
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The table below shows two equations:
Equation 1 |4x − 3|− 5 = 4
Equation 2 |2x + 3| + 8 = 3
Which statement is true about the solution to the two equations?
* Equation 1 and equation 2 have no solutions.
* Equation 1 has no solution, and equation 2 has solutions x = −4, 1.
* The solutions to equation 1 are x = 3, −1.5, and equation 2 has no solution. *
* The solutions to equation 1 are x = 3, −1.5, and equation 2 has solutions x = −4, 1.
Answer:
Option C is correct.
Step-by-step explanation:
Equation 1 |4x − 3|− 5 = 4
Adding +5 on both sides
|4x − 3|− 5 +5 = 4 +5
|4x − 3| = 9
Apply absolute rule:
IuI = a and a>0 then u = a and u = -a
so, 4x-3 = 9 and 4x-3 = -9
Solving
4x = 9+3 and 4x = -9+3
4x = 12 and 4x = -6
x = 12/4 and x = -6/4
x = 3 and x = -3/2 or -1.5
Equation 2 |2x + 3| + 8 = 3
Adding -8 on both sides
|2x + 3| + 8 -8 = 3 -8
|2x + 3| = -5
Apply absolute rule:
IuI = a and a>0 then u = a and u = -a
But we cannot apply absolute rule because in our case a < 0 i.e -5
So, Equation 2 has no solutions.
Hence Option C The solutions to equation 1 are x = 3, −1.5, and equation 2 has no solution is correct.
Please help will give brainliest
Answer:
[tex]b = 17[/tex]
Step-by-step explanation:
For this triangle we have to
[tex]a=18.2\\B=62\°\\C=48\°[/tex]
We want to find the length of b
We know that the sum of the internal angles of a triangle is 180 °
So
[tex]A + 62 +48=180\\\\A=180-62-48\\\\A=70\°[/tex]
Now we use the sine theorem to find the length of b:
[tex]\frac{sin(A)}{a}=\frac{sin(B)}{b}=\frac{sin(C)}{c}[/tex]
Then:
[tex]\frac{sin(A)}{a}=\frac{sin(B)}{b}\\\\b=\frac{sin(B)}{\frac{sin(A)}{a}}\\\\b=a*\frac{sin(B)}{sin(A)}\\\\b=(18.2)\frac{sin(62)}{sin(70)}\\\\b=17[/tex]
Owen uses colored pencils on his homework assignment. His red pencil is 12.195 centimeters long. His blue pencil is 9.13 centimeters long.
What is the total length of these two pencils if he lines them up end to end
Enter your answer, as a decimal
Answer:
21.325 is the correct answer
please gimme brainliest :))!!Answer: 21.325
Explanation: 12.195+9.13
Match each cross section with its perimeter
64 inches
26 inches
48 inches
34 inches
Answer:
64 inches : cross-section, cube, 16 inches
26 inches : right rectangular prism, 10x 3 x 14 inches
48 inches : cube with 12-inches edges
34 inches : rectangular prism, 5x12x4 diagonal of 13 inches
Step-by-step explanation:
right rectangular prism, 10x 3 x 14 inches
The cross-section is parallel to the base, so it cuts the height, maintaining the length and width. So, we have:
P = 10 + 3 + 10 + 3 = 26 inches
cube with 12-inches edges
This time, the cross-section is done perpendicular to the base, but in this case it doesn't matter since it's a cube... so it could be done in any direction and it wouldn't change the result.
P = 12 + 12+ 12 + 12 = 48 inches
rectangular prism, 5x12x4 diagonal of 13 inches
The cut is done perpendicular to the base, but along a diagonal of 13 inches, so the height is preserved, and the diagonal length becomes the new side other than height.
P = 13 + 4 + 13 + 4 = 34 inches
cross-section, cube, 16 inches
Again, the cross-section is done parallel to the base, but in this case it doesn't matter since it's a cube... so it could be done in any direction and it wouldn't change the result.
P = 16 + 16 + 16 + 16 = 64 inches.
Answer:
points
Step-by-step explanation:
Triangle ABC was rotated 90° clockwise. Then it underwent a dilation centered at the origin with a scale factor of 4. Triangle A'B'C' is the resulting image. Compare the perimeters of ΔABC and ΔA'B'C'. Explain your reasoning.
Answer:
it is 170 degrees
Step-by-step explanation:
Answer: The image will be the same shape by all the sides will be 4 times larger than the original triangle but all 3 angles will be the same as the original.
Step-by-step explanation:
a photograph of a full moon is enlarged so that the diameter is 8 times larger. how much larger is the circumfrence?
Answer:
25.13
Step-by-step explanation:
Since the Diameter is 8 the equation to find the Circumference is pi time D
3.14 x 8 equals 25.13274...
let's recall that the radius of a circle is half of the diameter, now, if the diameter say "d" got enlarged 8 times, to it became 8d, then the radius "r" got enlarged 8 times as well, namely 8r.
[tex]\bf \textit{circumference of a circle}\\\\ C=2\pi r~~ \begin{cases} r=radius\\ \cline{1-1} r=8r \end{cases}\implies \stackrel{\textit{is 8 times larger than that of the original}}{C=2\pi (8r)\implies C=\stackrel{\downarrow }{8}[2\pi r]}[/tex]
What is the midpoint of AC
ANSWER
B) (m+p,n+r)
The coordinates are :
A(2m,2n)
B(2p,2r)
To find the x-coordinate of the midpoint of AB, we add the x-coordinates of the two points and divide by 2.
[tex]x = \frac{2m + 2p}{2} [/tex]
Factor
[tex]x = \frac{2(m + p)}{2} [/tex]
Simplify:
[tex]x = m + p[/tex]
Similarly, the y-coordinate is
[tex]y = \frac{2n + 2r}{2} [/tex]
[tex]y = \frac{2(n + r)}{2} [/tex]
[tex]y = (n + r)[/tex]
Hence the midpoint is
(m+p,n+r)
Please answer quickly!!!
Answer:
1. 64cm² , 2. 240yd² , 3.≈220.5cm² , 4.≈193.4m² , 5. 38.6ft² , 6. ≈78.1yd² , 7. ≈120.7
Step-by-step explanation:
1. A=12x4.5+2x5 , 2. A=24x8+0.5x12x8 3. A=0.5x16x15+0.5x8²π ,4. A=7x15+0.5(15/2)² 12 ,5. A=3.6(16/2)+0.5x7x2.8 ,6. A=8(16/2)+0.5x9π ,7. A=(8/4)x5²xcot(180/8)
Which of the following shapes is convex?
D. Is a convex shape.
A convex shape will have no angles less than 180 degrees pointing inward. A, B, and C all have at least one of these angles. Whereas D, only has outward angles.
Only the shape D is convex structure.
What is convex?A form that curves outward is convex.
We know that the convex structure has no inward shape.
In the shape A,B and C;
all of the shape have inward structure.
Whereas shape D has only outward structure.
Therefore, Only shape D is convex.
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Which is larger 0.08 or 0.028
Answer:
0.028
Step-by-step explanation:
0.08 Is Bigger Than 0.028
The probability of a given event is . If the experiment is repeated n times, what is the probability that the event does not occur in any of the trials?
ILL GIVE U BRAINLIEST AND 30 POINTS
HELP
Final answer:
The probability that a given event does not occur in any of the trials when an experiment is repeated n times is calculated using the formula (1 - P(A))^n, where P(A) is the probability of the event occurring in a single trial.
Explanation:
The question is about finding the probability that a given event does not occur in any of the trials when an experiment is repeated n times. Let's denote the probability of the event occurring as P(A) and the probability of the event not occurring as P(~A). The probability that an event does not occur in a single trial is 1 - P(A). Therefore, if the experiment is repeated n times independently, the probability that the event does not occur in any of these trials is given by (1 - P(A))^n. This formula arises from the principle that for independent events, the probability of both events A and B occurring is the product of their individual probabilities, P(A) and P(B). Since each trial is independent, and we are looking for the event not happening across all n trials, we multiply the probability of it not happening in one trial by itself n times.
Which ratio is not equivalent to 5/3
4/3 I hope this helps
today Kylee put a kitchen table on layaway by making a down payment of 120 and agreeing to pay $48 a month starting next month for 24 months when will I receive the kitchen table
Answer:
2 1/2 months by the 3rd month
Step-by-step explanation:
Answer:
Kylee will receive the table in 24 months.
Step-by-step explanation:
Layaway is a type of purchasing method where the buyer places a deposit on an item to secure it or lay it aside. The buyer will pick up the item later when he pays the full balance.
This system allows the buyer to make smaller payments on the item until the full amount has been paid off.
So, if Kylee put the kitchen table on layaway, and agrees to pay $48 a month starting next month for 24 months. She will get the table in 24 months after completing her payment.
Find the median of the following data:
8, 17, 12, 14, 8, 21, 10, 11, 19, 20, 10, 5, 17, 12, 10, 20
O A. 10
O B. 16
O c. 12
O D. 14
The correct answer is C. 12
If you were to line up all the numbers in chronological order, the order would be: 5, 8, 8, 10, 10, 10, 11, 12, 12, 14, 17, 17, 19, 20, 20, 21. Twelve is the center of all the numbers. There's eight numbers on each side of 12. Hope this helps! Please mark brainliest! Thank you v much! :)
Answer:
C) 12
Step-by-step explanation:
Step 1: List the numbers in order from least to greatest. Take a look at the data and cross out numbers as you place them. There are 16 numbers. The order of these numbers are:
5, 8, 8, 10, 10, 10, 11, 12, 12, 14, 17, 17, 19, 20, 20, 21
Step 2: Cross out numbers from each side to the furthest left and right. By the time you do this, the remaining numbers should be 12 and 12.
Step 3: Find the median. Because there are two numbers left, you do this by adding the two remaining numbers and divinding them by 2. However, because they are the same number, you can safely say that the median is 12.
PLEASE BRANLIESTTT
A pop star is coming for a live concert in your area. The ticket proceeds will benefit a nonprofit organization helping underprivileged children interested in music education. They would like to raise $1,500.
Stage-level seats are on sale for \$10 each and balcony-level seats are on sale for \$5 each. How many of each seat type would need to be sold to reach the goal of \$1,500?
You can set up an equation to help solve this problem. Translate the situation above by letting x represent the number of stage-level seats and by letting y represent the number of balcony-level seats.
Answer:
You would need to sell 100 of each
Step-by-step explanation:
$5 times 100 people equals $500.
$10 times 100 people equals $1,000.
$1,000+$500=1,500
I hope this helped!
Answer:
100 each
Step-by-step explanation:
The distance around a circular park is 88 yards. What is the area of the park?
Answer:
A = 617 yd², to the nearest yard
That distance is called the "circumference," and its formula is C = 2πr.
We need r to find the area of the park. So we solve C = 2πr for r:
C
r = -------
2π
Substituting 88 yd for C, we get r = (88 yd) / (6.28) = 14.01 yd
The formula for the area of this circular park is A = πr².
Here, r = 14.01 yd, so the area of this park is:
A = π(14.01 yd)² = 3.14(196.36 yd²) = 617 yd², to the nearest yard.
The area of the park is [tex]A = 617 yd^2[/tex], to the nearest yard.
That distance is called the circumference and
We have to determine the area of the park
What is the formula for the circumference of the circle?The circumference of the circle is C = 2πr.
We need r to find the area of the park.
So we solve C = 2πr for r:
[tex]r=\frac{C}{2\pi}[/tex]
Substituting 88 yd for C,
We get r = (88 yd) / (6.28)
r= 14.01 yd
The formula for the area of this circular park is
A = πr².
Here, r = 14.01 yd, so the area of this park is,
[tex]A = \pi (14.01 yd)^2[/tex]
[tex]A = 3.14(196.36 yd^2)[/tex]
[tex]A = 617 yd^2[/tex], to the nearest yard.
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What is 15/7 as a mixed number
Answer:
Fraction can't be reduced (simplified). /7 = - 15/7 = - 2 1/7 = - 2.142857142857; Result written as a negative improper fraction, a mixed number (also called a mixed fraction) and a decimal number. Ordinary (simple, common) math fraction reducing to lowest terms (simplifying), answer with explanations below.
Step-by-step explanation:
2 1/7 Is Your Answer.
First, divide the numerator (the 15) by the denominator (the 7). This will give
you 2, with a remainder of 1.
The mixed number can be created by using the 2 as the whole number, the 1 as the numerator
and the 7 as the denominator.
When a warehouse opened, it had an inventory of 6,000 items. Every month, the inventory increases by 3,000 items.
Which graph has the most appropriate scales and units for this situation?
Answer:
The graph in the attached figure
Step-by-step explanation:
Let
x----> the time in months
y ----> the total inventory of the warehouse
we know that
The linear equation that represent this situation is equal to
[tex]y=3,000x+6,000[/tex]
using a graphing tool
see the attached figure
Answer: Guessing this is off the test.
The graph with
6
12
18
21
30 should be correct.
Step-by-step explanation:
Let me know the answer plz
Answer:
The correct answer option is H. 4374.
Step-by-step explanation:
We are given the following geometric sequence and we are to find its 8th term:
[tex]\frac{2}{9}, \frac{2}{3}, 2,...[/tex]
Here [tex]a_1=\frac{2}{9}[/tex] and common ratio [tex](r) = \frac{\frac{2}{3} }{\frac{2}{9} } =3[/tex].
The formula we will use to find the 10th term is:
nth term = [tex]a_1 \times r^{(n-1)}[/tex]
Substituting the values in the formula to get:
10th term = [tex]\frac{2}{9} \times 3^{(10-1)}[/tex]
10th term = 4374
The equation of a circle is given below.
(x-20)^{2}+(y-0.05)^{2} = 81(x−20)
2
+(y−0.05)
2
=81left parenthesis, x, minus, 20, right parenthesis, start superscript, 2, end superscript, plus, left parenthesis, y, minus, 0, point, 05, right parenthesis, start superscript, 2, end superscript, equals, 81
What is its center?
((left parenthesis
,,comma
))right parenthesis
What is its radius?
If necessary, round your answer to two decimal places.
Answer:
Part 1) The center is the point [tex](20,0.05)[/tex]
Part 2) The radius is equal to [tex]r=9\ units[/tex]
Step-by-step explanation:
we know that
The equation of the circle in standard form is equal to
[tex](x-h)^{2}+(y-k)^{2}=r^{2}[/tex]
where
(h,k) is the center of the circle
r is the radius of the circle
In this problem we have
[tex](x-20)^{2}+(y-0.05)^{2}=81[/tex]
[tex](x-20)^{2}+(y-0.05)^{2}=9^{2}[/tex]
so
[tex](h,k)=(20,0.05)[/tex]
[tex]r=9\ units[/tex]
What is the vertex of the quadratic function f(x) = (x – 8)(x – 2)?
Answer:
(5, - 9)
Step-by-step explanation:
Given
f(x) = (x - 8)(x - 2) ← in factored form
Find the zeros by equating f(x) to zero, that is
(x - 8)(x - 2) = 0
Equate each factor to zero and solve for x
x - 8 = 0 ⇒ x = 8
x - 2 = 0 ⇒ x = 2
The vertex lies on the axis of symmetry which is located at the midpoint of the zeros, hence
[tex]x_{vertex}[/tex] = [tex]\frac{8+2}{2}[/tex] = 5
Substitute x = 5 into f(x) for corresponding y- coordinate
f(5) = (5 - 8)(5 - 2) = (- 3)(3) = - 9
vertex = (5, - 9)
Answer: (5,-9)
Step-by-step explanation:
Make the multiplication indicated:
[tex]f(x) = x^2-2x-8x+16[/tex]
Add the like terms:
[tex]f(x) = x^2-10x+16[/tex]
Now find the x-coordinate of the vertex with this formula:
[tex]x=\frac{-b}{2a}[/tex]
In this case:
[tex]b=-10\\a=1[/tex]
Then:
[tex]x=\frac{-(-10)}{2(1)}=5[/tex]
Rewrite the expression with [tex]f(x)=y[/tex]
[tex]y = x^2-10x+16[/tex]
Now substitute [tex]x=5[/tex] into the function to find the y-coordinate of the vertex:
[tex]y = (5)^2-10(5)+16[/tex]
[tex]y =-9[/tex]
Therefore, the vertex is:
(5,-9)
Find the interest earned and the future value of an annuity with semiannual payments of $1,500 for 16 years into an account that pays 9% interest per year compounded semiannually.
Answer:
interest earned= 1853.98
the future value of an annuity= 2453.98
Step-by-step explanation:
Given Data:
Interest rate= 9%
time,t = 16 years
Semi-Annual payment, P= 600
n= 2 as Semi-Annual
At the end of 16 years, final investment A= ?
As per the interest formula for compounded interest
A= P(1+r/n)^nt
Putting the values in above equation
= 600(1+0.09/2)^32
= 2453.98
Interest earned = A-P
= 2453.98-600
= 1853.98 !
Some doctors recommend that men drink 3 liters of water every day . There are approximately 29.6 milliliters in 1 fluid ounce. Which measurement is closest to the number of fluid ounces in 3 liters ?
Answer:
[tex]\boxed{\text{101 fl oz}}[/tex]
Step-by-step explanation:
Step 1. Convert litres to millilitres
[tex]\text{V} = \text{3 L} \times \dfrac{\text{1000 mL}}{\text{1 L}} = \text{3000 mL}[/tex]
Step 2.Convert millilitres to fluid ounces
[tex]\text{v} = \text{3000 mL} \times \dfrac{\text{1 fl oz}}{\text{29.6 mL}} = \boxed{\textbf{101 fl oz}}[/tex]
Clara's class is going on a trip to the local science museum. Twenty-five students, one teacher, and three parents are going on the trip. The museum charges $3.50 admission for each student and $5.00 for each adult. How much will it cost for all the students and the adults to enter the museum?
Question 2 options:
a $87.50
b $101.50
c $102.50
d $107.50
Answer:
$107.50
Step-by-step explanation:
$3.50 = 1 STUDENT
$5.00 = 1 ADULT
TWENTY FIVE STUDENTS = $3.50 × 25 = $87.50
FOUR ADULTS (ONE TEACHER AND THREE PARENTS) = $5.00 × 4 = $20.00
TOTAL COST = $87.50 + $20.00 = $107.50