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Complete Question
Determine the common difference, the fifth term, the nth term, and the 100th term of the arithmetic sequence.
7/6, 5/3, 13/6, 8/3
Answer:
a) Common difference = 1/2
b) Fifth term = 19/6
c) nth term = 7/6 + (n - 1)1/2
= 7/6 + n/2 - 1/2
d) 100th term = 152/3
Step-by-step explanation:
We solve using the formula for arithmetic sequence
an = a1 + (n - 1)d
a1 = First term
n= nth term
d = common difference
a) Common difference = Second term - first term or Third term - second term
= d = 5/3 - 7/6
d = LCD (Lowest Common Denominator = 15
d = 5 × 6 - 3 × 7/18
d = 30 - 21/15
d = 9/18
d = 1/2
b) Fifth term =
an = a1 + (n - 1)d
a1 = First term = 7/6
n= nth term = 5
d = 1/2
a5 = 7/6 + (5 - 1)1/2
a5 = 7/6 + (4)1/2
a5 = 7/6 + 4/2
a5 = 7/6 + 2
a5 = LCD = 6
= 7× 1 + 2 × 6/6
= 7 + 12/6
= 19/6
c) nth term
an = a1 + (n - 1)d
a1 = First term = 7/6
n= nth term = n
d = 1/2
= 7/6 + (n - 1)1/2
= 7/6 + n/2 - 1/2
d) 100th term
an = a1 + (n - 1)d
a1 = First term = 7/6
n= nth term = 100
d = 1/2
a5 = 7/6 + (100- 1)1/2
a5 = 7/6 + (99)1/2
a5 = 7/6 + 99/2
a5 = 7/6 + 99/2
a5 = LCD = 6
= 7× 1 + 3 × 99/6
= 7 + 297/6
= 304/6
= 152/3
Lisa has collected data to find that the number of pages per book on a book shelf has a normal distribution. What is the probability that a randomly selected book has less than 168 pages if the mean is 192 pages and the standard deviation is 24 pages? Use the empirical rule. Enter your answer as a percent rounded to two decimal places if necessary.
Answer:
The answer is "Thus a chosen random book has a 15.87% chance of fewer than 170 pages".
Step-by-step explanation:
[tex]Mean = 190\\\\\text{Standard devaition} \ \sigma= 20\\\\\to P(\bar{x}<70)\\\\Z = \frac{(170-190)}{20}[/tex]
[tex]= \frac{-20}{20} \\\\=-1[/tex]
It found a p-value from its empirical rule:
[tex]\to P(\bar{x}<170) = 0.1587[/tex]
Q14.
Solve the simultaneous equations
2x - 3y = 24
6x + 2y = -5
landimorament
4x + 16y = -19
-2x - 8y = 10
Answer:
No solution.
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDASEquality PropertiesAlgebra I
Solving systems of equations using substitution/eliminationSolving systems of equations by graphingStep-by-step explanation:
Step 1: Define systems
4x + 16y = -19
-2x - 8y = 10
Step 2: Rewrite systems
-2x - 8y = 10
Add 8y to both sides: -2x = 8y + 10Divide -2 on both sides: x = -4y - 5Step 3: Redefine systems
4x + 16y = -19
x = -4y - 5
Step 4: Solve for y
Substitution
Substitute in x: 4(-4y - 5) + 16y = -19Distribute 4: -16y - 20 + 16y = -19Combine like terms: -20 ≠ -19Here we see that -20 does not equal -19.
∴ This systems of equations has no solution
Step 5: Graph
Check the systems.
Hard to see, but they are parallel lines.
Petra jogs 3 miles in 30 minutes at this rate how long would it take a jog 10 miles
Answer:
100 minutes or 1 hour and 40 minutes
Step-by-step explanation:
3 miles in 30 minutes means 1 mile in 10 minutes
10 miles takes 100 minutes or 1 hour and 40 minutes.
1 hour and 40 minutes
What is the value of x?
Enter your answer in the box.
Answer:
35
Step-by-step explanation:
Since all the angles are the same in this triangle, all the sides should be the same too.
Hence, 3x - 5 = 4x - 30
5 + -1x = -30
-1x = -35
x = 35
Hope this helped!
Answer:
Considering the fact that this is an equilateral triangle, x would equal 25
Step-by-step explanation:
since in an equilateral triangle all sides are equal, just pick 2 and solve for x
3x-5=2x+20
3x-2x=20+5
x=25
to check work,
4(25)-30=70
3(25)-5=70
2(25)+20=70
Martina ordered a set of blue and orange pins. She received 96 pins in all. 24 of the pins were
blue. What percentage of the pins were blue?
Write your answer using a percent sign (%).
Answer:
25%
Step-by-step explanation:
This is like a part over whole problem, where 24 blue pens is the part and 96 pens total is the whole.
24/96 = 0.25 * 100 = 25%
Answer:
Of the 96 pins, 25% of the pins were blue.
Step-by-step explanation:
We are given that Martina ordered 96 pins in total. We are also given that she ordered 24 blue pins.
With this, we can determine how many of the pins were not blue pins by subtracting the amount of blue pins from the number of total pins.
[tex]96 \ \text{total pins} - 24 \ \text{blue pins} = 72 \ \text{orange pins}[/tex]
Now, we can divide the number of blue pins by the number of total pins to determine the fraction of blue pins to total pins.
[tex]\displaystyle \frac{24}{96} = \frac{12}{48} = \frac{6}{24} = \frac{3}{12} = \frac{1}{4}[/tex]
Then, we can convert our fraction to a decimal.
[tex]\displaystyle \frac{1}{4} = 0.25[/tex]
And finally, we can convert our decimal to a percentage by multiplying the determined decimal by 100.
[tex]0.25\times100 = 25\%[/tex]
Therefore, of the 96 pins that Martina ordered, 25% of them were blue.
PLZ Help Urgent. 15 POINTS, BRAINLY Guaranteed.
Plz Answer honestly or you will be reported.
Evaluate.
(2/7)^3
A: 8/343
B: 8/7
C: 3/343
D: 6/7
Answer:
8/343
so A
Step-by-step explanation:
2+4 i need help right now
Answer:
6?
Step-by-step explanation:
Answer:
6
Step-by-step explanation:
2 + 4 =6
just add 2 by 4 than ans 6
13. The population of a city is currently 45,000 and is declining at a rate of 2% each year. Estimate the population after a period of 5 years. Use the formula ƒ(t) = aert.
Given:
Initial population = 45,000
Decreasing rate = 2%
Time = 5 year
To find:
The population after a period of 5 years.
Solution:
Formula used:
[tex]f(t)=ae^{rt}[/tex]
where, a is initial population, r is rate and t is time.
[tex]r=\dfrac{2}{100}=0.02[/tex]
Decreasing rate represented by -0.02.
Substitute a=45000, r=-0.02 and t=5 in the above formula.
[tex]f(5)=45000e^{-0.02(5)}[/tex]
[tex]f(5)=45000e^{-0.1}[/tex]
[tex]f(5)=45000(0.904837418)[/tex]
[tex]f(5)=40717.68381 [/tex]
Approximate the value to the previous integer.
[tex]f(5)\approx 40717 [/tex]
Therefore, the population after 5 years is 40717.
Answer:
40,718
Step-by-step ex
The population of a city is currently 45,000 and is declining at a rate of 2% each year. Estimate the population after a period of 5 years. Use the formula ƒ(t) = aert. planation:
Express rational numbers in reduced form for 27/36
Answer:
3\4
Step-by-step explanation:
hihihihihihihihihihi
Harry wants a fence around his garden.
Height: 16.7m
Length: 16.3m
What is the perimeter of the whole garden?
Answer:
66m
Step-by-step explanation:
perimeter is the distance all round a figure
perimeter(p)= 2( length(l) + width(w)) or perimeter= 2 length + 2 width
p= 2(l + w) or p = 2l + 2w
p= 2(16.3 +16.7) or p= 2(16.3) + 2(16.7)
p=2(33) or p= 32.6 + 33.4
p=66m or p= 66m
A bicycle is traveling at 21 miles per hour. How many feet will it cover in 35 second?
find area of triangle formed by (1,1) (2,3) (4 ,5) using heron's formula
Answer:
The area of a triangle is:
A = 1 unit²Step-by-step explanation:
Given the points of a triangle
A(1, 1)
B(2, 3)
C(4, 5)
[tex]\mathrm{Compute\:the\:distance\:between\:}\left(x_1,\:y_1\right),\:\left(x_2,\:y_2\right):\quad \sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}[/tex]
Distance between AB:
[tex]AB=\sqrt{\left(2-1\right)^2+\left(3-1\right)^2}[/tex]
[tex]=\sqrt{1+4}[/tex]
[tex]=\sqrt{5}[/tex]
so
[tex]a=\sqrt{5}[/tex]Distance between BC:
[tex]BC=\sqrt{\left(4-2\right)^2+\left(5-3\right)^2}[/tex]
[tex]=\sqrt{2^2+2^2}[/tex]
[tex]=\sqrt{2^3}[/tex]
[tex]=2\sqrt{2}[/tex]
so
[tex]b=2\sqrt{2}[/tex]Distance between AC:
[tex]AC=\sqrt{\left(4-1\right)^2+\left(5-1\right)^2}[/tex]
[tex]=\sqrt{3^2+4^2}[/tex]
[tex]=\sqrt{5^2}[/tex]
[tex]=5[/tex]
so
[tex]c=5[/tex]Semiperimeter = sum of sides ÷ 2
[tex]s=\frac{\sqrt{5}+2\sqrt{2}+5}{2}=5.03224[/tex]
Area of the triangle:
[tex]A=\sqrt{s\left(s-a\right)\left(s-b\right)\left(s-c\right)}[/tex]
[tex]a=\sqrt{5}[/tex][tex]b=2\sqrt{2}[/tex][tex]c=5[/tex][tex]A=\sqrt{s\left(s-\sqrt{5}\right)\left(s-2\sqrt{2}\right)\left(s-5\right)}[/tex]
[tex]A=\sqrt{5.03224\dots \left(5.03224\dots -\sqrt{5}\right)\left(5.03224\dots -2\sqrt{2}\right)\left(5.03224\dots -5\right)}[/tex]
[tex]A=1[/tex]
Therefore, the area of a triangle is:
A = 1 unit²6. Evaluate f(-1).
7. What value of a will make the equation f(a) = 6 true?
someone please help lol I have a test <3
Answer:
6. -f 7. f= 6/8
Step-by-step explanation:
Hope dis helps!!
1/6 * 3/4
could be answers
3/10
1/6
1/8
4/10
Answer:
it's a sooooooo it's the first one
Answer:
1/8
Step-by-step explanation:
i used the calculator.
A taxi cab charges a flat fee of $1.75 plus $0.30 for each half-mile or fraction of a half-mile.
a) Fill in the chart.
b)write and equation for the function.
Answer:
a) there is no chart but we can elaborate one:
taxi fee half-miles driven
$1.75 0
$2.05 1
$2.35 2
$2.65 3
$2.95 4
$3.25 5
$3.55 6
b) y = 0.3x + 1.75
where:
y = taxi fee
x = half miles driven
the point that doesn't lie to a straight line y=-4x+12 is
Answer:
12?
Step-by-step explanation:
1+1+2+2+8+19+1234385993 hehe i will brainlest
Answer: 1234386026
Step-by-step explanation:
Answer:
1,234,386,030
Step-by-step explanation:
A sequence of steps for solving the equation 3(x - 2) = 4 is shown. Match a property to each blank box to show the reason for each step. Question 6 options: 3(x - 2) = 4 3x - 6 = 4 3x = 10 x = 103 1. Given 2. Distributive Property 3. Addition property of equality 4. Division property of equality
Step-by-step explanation:
Given the equation;
3(x-2) = 4
A sequence of steps for solving the equation is as shown;
Step 1: Open the parenthesis by applying distributive law to distribute 3 over x and 2 as shown;
3(x-2) = 4
3(x)- 3(2) = 4
3x - 6 = 4
Step 2: Add 6 to both sides of the equation (Addition property)
3x-6+6 = 4+6
3x = 10
Step 3: Division property of equality. Divide both sides by 3;
3x = 10
3x/3 = 10/3
x = 10/3
guys help plz What is the coefficient of y^2 in the expression 2x^2y – 10xy^2 + 5y^2?
Can someone please help, ty!!
(Will mark brainliest)
Answer:
Yellow is correct.
You can add the valued and divide by how many values there are to find the mean
The score of 20 is an outlier and brings the mean score down by almost 10%
Step-by-step explanation:
Answer:
3: The low score causes the mean to decrease.
Step-by-step explanation:
If you add a significantly lower number, it will bring down the overall average.
Hope this helps!
can somone help me pls ?
[tex]\huge\mathtt{Hello!}[/tex]
[tex](6x - 23) = (4x + 9)[/tex]
[tex]6x -4x = 9 + 23[/tex]
[tex]2x = 32[/tex]
[tex]x = 16[/tex]
It is because the sides are equal, so the angles opposite to them also are equal.
Have a nice day!
A person on a moving sidewalk travels 56 feet in 8 seconds. The moving sidewalk has a length of 210 feet. How long will it take to move from one end to the other?
PLEASE HELP ME WILL REPORT IF TROLL
Answer:
The answer is 1470 seconds.
Step-by-step explanation:
yler's brother earns $12 per hour. The store offers him a raise— a 5% increase per hour. after the raise,how much will tyler make per hour
Answer:
$12.60
Step-by-step explanation:
12/100 × 12 = 0.60
12 + 0.60 = 12.60
Last year, the cost of a family-sized dinner at a picnic was $8.50. This year, the cost is $11.56. What is the percent of increase of the price? ( I need a step-by-step explanation not just the answer) ill give brainliest
help me please somone
Answer:
Iscoccecles
Sorry if i spelled it wrong.
Step-by-step explanation:
giving brainliest it’s due asap pls help
Answer:
AB is parallel to CD - the reasoning looks right aswell although I don't know exactly what I'm answering here.. are you asking to check it?
Plzzz answer thank you :))
Answer:
booger
Step-by-step explanation:
bc
indicate in standard form the equation of the line passing through the given points, in the equation box below. X(0, 6), Y(5, 6)
Answer:
0x + y = 6
Step-by-step explanation:
Equation of the Line
The equation of a line passing through points (x1,y1) and (x2,y2) can be written as follows:
[tex]\displaystyle y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
It can be later converted to any other form of the line. For example, the standard form is:
[tex]Ax + By = C[/tex]
Let's find the equation by using the given points (0,6) (5,6):
[tex]\displaystyle y-6=\frac{6-6}{5-0}(x-0)[/tex]
Operating:
[tex]\displaystyle y-6=\frac{0}{5-0}(x-0)[/tex]
y - 6 = 0
Or, equivalently:
0x + y = 6
This corresponds to a horizontal line
Joy is going to a sub shop for a sandwich. At the restaurant, she can choose either a roll (R), bread (B), or a wrap
(W). There are two meat choices, ham (H) and turkey (T), and 2 kinds of cheese, Swiss (S) and American (A)
Before she goes, Joy wants to make a list of her choices. If she chooses one item from each selection, which will be
part of her list?
O RBW, RBH RBT, RBS, RBA
ORSA, BSA, RHT, BHT, HSA
RH, RT, BH, BT, WH
O RHS, RHA, RTS, RTA, BHS
Answer:
The answer is D
Step-by-step explanation:
Answer:
RHS, RHA, RTS, RTA, BHS
Step-by-step explanation: