Estimate sixty-two percent of one hundred twenty-four.
Find the sum of the first 8 terms of the following series, to the nearest integer.
36, 30, 25, ...
Answer:
The sum of the first 8 terms will be:
[tex]\frac{1288991}{7776}[/tex]Step-by-step explanation:
Given the sequence
[tex]36, 30, 25, ...[/tex]
A geometric sequence has a constant ratio and is defined by
[tex]a_n=a_0\cdot r^{n-1}[/tex]
computing the common ratio
[tex]\frac{30}{36}=\frac{5}{6},\:\quad \frac{25}{30}=\frac{5}{6}[/tex]
[tex]r=\frac{5}{6}[/tex]
As the first element is
[tex]a_1=36[/tex]
so the nth term will be:
[tex]a_n=a_0\cdot r^{n-1}[/tex]
[tex]a_n=36\left(\frac{5}{6}\right)^{n-1}[/tex]
Geometric sequence sum formula
[tex]a_1\frac{1-r^n}{1-r}[/tex]
Plugin the values to determine the sum of the first 8 terms
[tex]n=8,\:\spacea_1=36,\:\spacer=\frac{5}{6}[/tex]
[tex]=36\cdot \frac{1-\left(\frac{5}{6}\right)^8}{1-\frac{5}{6}}[/tex]
[tex]=\frac{\left(1-\left(\frac{5}{6}\right)^8\right)\cdot \:36}{1-\frac{5}{6}}[/tex]
[tex]=\frac{36\left(-\left(\frac{5}{6}\right)^8+1\right)}{\frac{1}{6}}[/tex]
[tex]=\frac{36\left(-\frac{390625}{1679616}+1\right)}{\frac{1}{6}}[/tex]
[tex]=\frac{\left(1-\frac{390625}{1679616}\right)\cdot \:36\cdot \:6}{1}[/tex]
[tex]=\frac{216\left(-\frac{390625}{1679616}+1\right)}{1}[/tex]
[tex]=\frac{216\cdot \frac{1288991}{1679616}}{1}[/tex]
[tex]=216\cdot \frac{1288991}{1679616}[/tex]
[tex]=\frac{1288991\cdot \:216}{1679616}[/tex]
[tex]=\frac{278422056}{1679616}[/tex]
[tex]=\frac{1288991}{7776}[/tex]
Therefore, the sum of the first 8 terms will be:
[tex]\frac{1288991}{7776}[/tex]Expression A: X+3 Expression B: 1 + x + 2 Which statement can be used to show that these expressions are equivalent?
OA. Each expression includes the term x.
OB. The expressions name the same number regardless of the value of x.
OC. X+3 can be rewritten as 1 + x + 2 using distributive property.
O D. Both expressions involve addition,
Please help! May give brainlists. (Idk how to spell it-)
Answer:
The expressions name the same number regardless of the value of x
Step-by-step explanation:
Answer: C
Step-by-step explanation:
Because 3 can become 1 and 2
Solve the right triangle. Round decimal answers to the nearest tenth
Answer:
AB = 15
m∠A = 53.1°
m∠B = 36.9°
Step-by-step explanation:
From the picture attached,
By Applying Pythagoras theorem,
AB² = AC² + BC²
AB² = 9² + (12)²
AB² = 81 + 144
AB = √225
AB = 15
tan(B) = [tex]\frac{\text{Opposite side}}{\text{Adjacent side}}[/tex]
= [tex]\frac{12}{9}[/tex]
= 1.3333
B = [tex]\text{tan}^{-1}(1.3333)[/tex]
= 53.13
≈ 53.1°
Since, m∠A + m∠B + m∠C = 180°
m∠A + 53.1° + 90° = 180°
m∠A = 180°- 143.1°
= 36.9°
Answer:
AB = 15
m∠A = 53.1°
m∠B = 36.9°
A.) how much does it cost to buy 5 tickets?
B.) How many tickets can buy with $130?
Answer:
A) $77.50
B) 8 tickets
Step-by-step explanation:
A) c(x) = 17.5x - 10
Substitute 5 for x
c(x) = 17.5(5) - 10
Multiply
c(x) = 87.5 - 10
Subtract
c(x) = 77.5
B) 130 is the cost, so substitute 130 for c(x)
130 = 17.5x - 10
Add 10 to each side to move the constants to one side
140 = 17.5x
Divide each side by 17.5 to isolate the variable
8 = x
Pls give me the answer to this geometry problem smart people
Answer:
25
Step-by-step explanation:
Since it is a rhombus all the parallel lines are always divided by half at the intersection. Basically divide 50 by 2 because QN=50 and QS is half of that
find the slope of the line
Answer:
[tex]\frac{2}{3}[/tex]
Step-by-step explanation:
The line goes up 2 units and right 3 units.
Answer:
the slope is 6/7
Step-by-step explanation:
Are there any five-digit numbers which are reversed when multiplied by 8?
At a department store, the price of a freezer is marked up 15% to $450.50.
What was the price of the freezer BEFORE the mark up?
Answer:
The price was $391.30.
Step-by-step explanation:
We can answer this using algebra:-
Let the original price be $x, then:
x + 15% of x = 450
x + 0.15x = 450
1.15x = 450
x = 450/1.15
x = 391.304
An advertisement reads “All Books 28 Percent Off.” A best-selling novel is originally priced at $18.99. About how much money will Gio save if he buys the novel on sale?
Answer:
6dollars
Step-by-step explanation:
Answer:
the answer is B 6 dollars
Step-by-step explanation:
Point (x, y) lies on the perpendicular bisector of . What is the value of x?
Record your answer and fill in the bubbles on your answer document.
Answer:5
Step-by-step explanation:
You play a game that involves spinning the money wheel shown. You spin the wheel twice. Find the probability that you get more than $500 on your first spin and then go bankrupt on your second spin. Round your answer to the nearest tenth.
Answer:
about 2.8%
Step-by-step explanation:
Convert the following:
(a) 300 cm into metre
Answer:
3m
Step-by-step explanation:
1 meter equals 100 cmWe know that [tex]1meter=100centimeters[/tex] Now how many (100 cm)'s are in (300 cm)'s? There are 3 right?So if every 100 cm is also a meter and there are 3 of these (100cm)s then they are just the same as 3 meters[tex]100cm=1m\\300cm=(x)m[/tex] cross multiply[tex]100cm(x)m=300cm1m[/tex] divide both sides by 100cm[tex](x)m=3m[/tex]Answer:
Convert the following:
(a) 300 cm into metre
3 metres
that is the question
How do you write 462 in scientific notation?
x 10
Answer:
could you explain more?
Step-by-step explanation:
There is a snowstorm in a certain town. In 1/2 hour, there was 7/8 inches of snow. It continues at the same rate for a total of 2 hours. Which statement is true about the amount of snow in the 2-hour period
Answer:
Since I don't know the statements, I'm gonna guess that if there is 7/8 snow in 1/2 hour then in 2 hours there is 3.5 inches of snow or 28/8 inches of snow in 2 hours.
Step-by-step explanation:
Use the distributive property to remove the
6(v+4)
A rectangular park is 135 yards long and 90 yards wide.
Give the length and width of another rectangular park that has the same perimeter but a smaller area.
Answer:
l = 140 yards , w = 85 yards
Step-by-step explanation:
1). l = 135 yards , w = 90 yards
P = 2 × 135 + 2 × 90 = 450 yards
A = 135 × 90 = 12,150 yards²
2). l = 140 yards , w = 85 yards
P = 2(140 + 85) = 450 yards
A = 140 × 85 = 11,900 yards²
Answer:
width= 100 yards
length= 125 yards
Step-by-step explanation:
I think.
In △ACD, if AC ≅ AD, m∠A = (3x – 4)°, m∠C = (5x + 1)°, and m∠D = (7x – 27)°, find x and the measure of each angle. *
Answer:
x = 14
A = 38
B = 71
C = 71
Step-by-step explanation:
Since we have a triangle, the addition of the measure of all the measure of the angles give 180
Thus;
3x-4 + 5x + 1 + 7x-27 = 180
15x-30 = 180
15x = 180 + 30
15x = 210
x = 210/15
x = 14
To get the measure of each of the angles, we substitute for x
A = 3x-4 = 3(14) - 4 = 38
B = 5x + 1 = 5(14) + 1 = 70 + 1 = 71
C = 7x - 27 = 7(14) - 27 = 98-27 = 71
estimate each quotient by rounding the dividend and the divisor to the largest place value
1. 2,756 divided by 532.
2. 22,528 divided by 98
3. 7,790 divided by 210
4. 17,658 divided by 360
5. 916 divided by 320
Answer:
5
230
3
0
3
Step-by-step explanation:
1)5.2 estimated is 5
2)229.9 estimated is 230
3)37.1 estimated is 3
4)0.0 estimated is 0
5)2.9 estimated is 3
Audrina goes to the mall with $50. She buys 3 shirts for $8.50 each, and 2 pairs of pants for $11 each. How much money does Audrina have left?
Answer:
2.5
Step-by-step explanation:
she has buys 3 shirts for 8.50 which = 25.5
then she buys 2 pair of pants for $22 because 2 x 11=22
so then 22 + 25.5 = 47.50
50.00- 47.50= 2.50
Classify the polynomial as a monomial, binomial, trinomial, or none of these. x2 - 10x + 25
It is a trinomial because it follows the pattern of x^2 + bx + c. In this case, x^2 - 10x + 25. Also, it only has three numbers and two operation symbols, signifying a trinomial (three = tri).
On a certain hot summer's day, 151 people used the public swimming pool. The daily prices are $1.50 for children and $2.00 for adults. The receipts for admission totaled $270.50 How many children and how many adults swam at the public pool that day?
Answer: 63 children and 88 adults swam at the public pool that day.
Step-by-step explanation:
Let x = Number of children
y= Number of adults
As per given , we have
x+y=151 (i)
1.50x+2y=270.50 (ii)
Multiply 2 on both sides of (i)
2x+2y = 302 (iii)
Eliminate (ii) from (iii)
0.5x=31.5
⇒ x = 63 [Divide both sides by 0.5]
Put value of x in (i) , we get
63+y= 151
⇒ y= 151-63 =88
Hence, 63 children and 88 adults swam at the public pool that day.
what is significant figures
Answer:
Significant figures are the number of digits in a value, often a measurement, that contribute to the degree of accuracy of the value. We start counting significant figures at the first non-zero digit.
Step-by-step explanation:
i have multiple question but for that i will give u lots of points and who ever gets it first ALL OF THEM will also get brainlest :)
1:
2:
3:
4:
5:
Answer:
1. slope is 1/2
2. slope is 1/3
3. slope is 2/3
4. slope is 3
5. y=3x-2
Step-by-step explanation:
marcys breakfast table has a square table top with an area of 36 square feet. what is the diagonal length of the table top
Answer:
√36 = 6
a^2 + b^2 = c^2
6^2 + 6^2 = c^2
36 + 36 = c^2
72 = c^2
√72 = c
2 36
2 18
2 9
3 3
6√2 = c
6√2 = (estimate rounded up, 8.49)
Please help will mark brainliest if correct
Answer:
Step-by-step explanation:
ASA
Help plz:))) I’ll mark u brainliest
ASAP!!!
Answer:
46
x=46 degrees
please help I'm actually crying! Find A and B if the graph of Ax + By = 7 passes through (2,1) and is parallel to the graph of 2x - 7y = 3.
i have less sympathy for ur crying when you copy and paste this question and ask it again three times. why dont you just ask it once? everyone answers anyway
Lionheart Ranch has bought a new herd of race horses. If there is one stable for every four horses, which equation shows the correct relationship between the number of stables (S) and the number of horses (H)?
Answer:
1S=4H
Step-by-step explanation