Answers
Answer:
a. 31/6; 33/6; 35/6
b. + 2/6
c. 37/6; 39/6; 41/6
d. 49/6
Step-by-step explanation:
First we need to find the first three terms.
To do so solve the equations in the boxes.
When dividing by a fraction you multiply by the reciprocal so the equations are now as follows:
2 * 31/12
3 * 11/6
5 * 7/6
Solve these to get
62/12 = 31/6
33/6
35/6
The term to term rule as shown above is adding 2/6 or 1/3.
To find the next three terms in the sequence add 2/6 to the term.
35/6 + 2/6 = 37/6
37/6 + 2/6 = 39/6
39/6 + 2/6 = 41/6.
To find the 10th term you need to write out the arithmetic sequence equation.
an = a1 + (n-1)d
an is the term you want to find and n is the term number in this case that is 10. D is the common difference which in this case is 2/6. Plug these into the equation. A1 is the first term in the equation which in this case is 31/6.
31/6 + (10-1) 2/6
31/6 + (9)2/6
31/6 + 18/6 = 49/6
Related Questions
A survey was given to a random sample of 80 residents of a town to determine whether they support a new plan to raise taxes in order to increase education spending. Of those surveyed, 52 respondents said they were in favor of the plan. Determine a 95% confidence interval for the proportion of people who favor the tax plan, rounding values to the nearest thousandth.
Answers
With a 95 percent confidence interval, the proportion of people who favor the tax plan is 0.546 ,0.755
How to solve for the intervalThe value of n is the random sample n = 80
we have x as the number of people surveyed, = 52 respondents
Then p = x / n
p = 52 / 80
p = 0.65
From the z critical table, 95% confidence level = 1.96
we would have to use the confidence interval formula. This is given as:
[tex]p +- Z * \sqrt{\frac{p*(1-p)}{n} }[/tex]
we have to put in the values
[tex]0.65 +- 1.96 * \sqrt{\frac{0.65*(1-0.65)}{80} }[/tex]
0.65 ± 1.96 * 0.053326822
0.65 - 0.10452 , 0.65 + 0.10452
0.546 ,0.755
Therefore the proportion of persons that are in favor of this tax has been calculated as 0.546 ,0.755
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Ashley's company makes solid spherical balls out of scrap metal for various industrial uses. A large order just came in to make aluminum balls with a radius of 4.5 in. If Ashley uses 74,325in^3 on average, of aluminum each day making these balls, how many balls does she make, on average, each day?
Answers
Using the formula of volume of a sphere, Ashely's company made 195 balls
Volume of SphereThe volume of sphere is the measure of space that can be occupied by a sphere. If we draw a circle on a sheet of paper, take a circular disc, paste a string along its diameter and rotate it along the string. This gives us the shape of a sphere.
The formula of volume of a sphere is given as
v = 4/3πr³
r = radius = 4.5in
volume of each spherical ball = 4/3π(4.5)³
volume of sphere = 381.7in³
The number of balls she made from 74325 in³ can be found by dividing it by 381.7in³
Number of balls = 194.7≅195 balls
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Find a polynomial f(x) of degree 5 that has the following zeros.
-2, 3, 7, 0, 4
Leave answer in factored form
Answers
The polynomial f(x) of degree 5 that has the following zeros is
f(x) = (x+2) (x-3) (x-7)(x-0) (x-4).
What is meant by polynomial?Using mathematical operations like addition, subtraction, multiplication, and division, a polynomial is an expression made up of variables, constants, and exponents. In many branches of mathematics and science, polynomials are used. For instance, they are used to define polynomial functions, which show up in settings ranging from basic chemistry and physics to economics and social science. They are also used in calculus and numerical analysis to approximate other functions. Polynomial equations are used to form these functions.
The function's zeros are expressed as follows:
f(x) = (x-a)(x-b)..... where the a, b are the zeros
f(x) = (x-(-2)) (x-3) (x -7)(x-0) ( x-4)
f(x) = (x+2) (x-3) (x-7)(x-0) (x-4)
Therefore, the polynomial f(x) of degree 5 that has the following zeros is
f(x) = (x+2) (x-3) (x-7)(x-0) (x-4)
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What is 4 1/4 x (-12.2)?
Answers
A population of lizards in a large region doubles every year. The number of lizards can be
modeled by the equation y = 500 * 2 ^ x where
× is the number of vears after a researcher
measures the population size . When x = - 3
-3what does the value of y represent ?
Answers
The value of y when the value of x is -3 for the equation,y = 500×2ˣ will be y=62.5.
What is the equation?An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.
It is given that, the given equation of is, y = 500×2ˣ
We have to find the value of y when x = - 3.
y = 500×2ˣ
y=500×2⁻³
y=62.5
Thus, the value of y when the value of x is -3 for the equation,y = 500×2ˣ will be y=62.5.
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The cleaning service charges $15 per hour. Mr. Henrickson is hiring the cleaning service but does not want to spend more that $75. What is the maximum number of hours that he can hire the cleaning service? Write an inequality and solve.
Answers
The maximum number of hours that he can hire the cleaning service would be 5.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Consider that the number of hours for which the total cost would be the same be x
The first inequality is;
$15x > $75
Now equate equations
$15x - $75 = 0
15x = 75
x = 5
Hence, the maximum number of hours that he can hire the cleaning service would be 5.
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(01.06 MC)
Solomon invested money in his bank account. He had a principal, P,
of $100 in his account at the beginning of the period, which
increased at a rate, r, of 0.15 per year. At the end of the period, he
had interest, I, of $135 in his account. Use the simple interest
formula 1 = Prt, to solve for the time, t, in months that it took to
earn this amount. (1 point)
Answers
Answer:
700 months
Step-by-step explanation:
Which equation is perpendicular to y = 2/3 x - 4?
a. y = -3/2 x + 4
b. y= 2/3 x - 4
c. y = -2/3 x + 4
d. y = 3/2 x - 4
Answers
Answer:
Your answer is A) [tex]y=-\frac{3}{2}x-4[/tex]
Step-by-step explanation:
This is because the slope of a perpendicular line is a negative reciprocal in relation to the original line. In this example, [tex]\frac{2}{3}[/tex] is flipped to [tex]-\frac{3}{2}[/tex]
If the simple interest on $2000 for 4 years is $480, then what is the interest rate?
Answers
Answer: 6%
Step-by-step explanation:
R=100×480/2000×4
R=6%
Answer:
R
=
6
%
Step-by-step explanation:
The formula for Simple Interest is
S
I
=
P
R
T
100
Change the subject to be R.
R
=
100
×
S
I
P
T
Once that is done, we just need to substitute the values.
R
=
100
×
480
2000
×
4
R
=
6
%
À class counted how many banks were in all the nearby cities.
Richmond has________more banks than Dollarville
Answers
Answer:
4
Step-by-step explanation:
Richmond has 7 and Dollarville has 3. 7 - 3 = 4
Montraie has 1 1/2 cups of yogurt to make smoothies. Each smoothie uses cup of 3/4 yogurt. How many smoothies can Montraie make with the yogurt?
Answers
Montraie can make 2 cups of smoothies with the yogurt
How to determine the number of smoothies in the yogurtFrom the question, we have the following parameters that can be used in our computation:
Cups of yogurt = 1 1/2
Each smoothie = 3/4 yogurt
Assume there exist a proportional relationship between the cups and the yogurt
The number of smoothies in the yogurt can be calculated using the following equation
Smoothies = (1 1/2)/(3/4)
Evaluate the quotient
Smoothies = 2
Hence, the cups is 2 yogurt
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kay walks upstairs yo make her legs stronger . Every day at work, she walks up 9 flights of stairs . If there are 13 steps in 1 flight of stairs in 1 flight of stairs , how many steps does kay climb in 5 days at work
Answers
In 5 days at work, kay climbs 585 steps
How to find how many steps kay climbsIf there are 13 steps in 1 flight of stairs then 9 flights of stairs will be
= 13 * 9
= 117 steps
Every day Kay climbs 117 steps in 9 flights in 5 days kay will climb
= 117 * 5
= 585 steps
Kay climbs 585 steps in a 5 days at work
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Please help I was sick and missed out on class.Thank you
Answers
Answer:
Step-by-step explanation:
Start with y intercept (Where the line crosses the y-axis)
You place the first dot on (0,2)
Negative slope goes down
For the second dot, you go down one and move two to the right
A car travels 120 miles and one and a half hours what is the average speed for miles per hour
Answers
Answer:
80
Step-by-step explanation:
120 divided by 3 (for per half hr) is 40 and if you add 2 of the half hrs together (40+40) its 80
4) The trapezoid I'J'K'L' is a dilation of the trapezoid IJKL. What is the scale factor of the
dilation?
I
-10 -8 -6 -4
I'
~
104
8
6
4
2
2
-4
-6
-8
L'
L
J'
K'
4
6
J
K
10
10
4) Simplify your answer and write it as a proper fraction, an improper fraction, or a whole
number.
Answers
Answer:4
Step-by-step explanation:
16/4=4
The scale factor of the dilation is, 1/4.
What is Division method?Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.
We have to given that;
The trapezoid I'J'K'L' is a dilation of the trapezoid IJKL.
Here, The length of IJ = 16
And, The length of I'J' = 4
Hence, The scale factor of the dilation is,
⇒ I'J' / IJ = 4 / 16
= 1/4
Thus, The scale factor of the dilation is, 1/4.
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Is the system of equations consistent and independent, consistent and dependent, or inconsistent?
y=−3x+12y=−6x+2
Select the correct answer from the drop-down menu.
consistent and independent
Answers
The system of equation is consistent and independent because it has one unique solution.
How to solve system of equation?If a system has at least one solution, it is said to be consistent . If a consistent system has exactly one solution, it is independent.
Therefore, let's solve the equation,
y = -3x + 12
y = -6x + 2
Using substitution,
-6x + 2 = -3x + 12
-6x + 3x = 12 - 2
-3x = 10
x = - 10 / 3
y = -6(-10 / 3) + 2
y = 60 / 3 + 2
y = 20 + 2
y = 2
Therefore, the system of equation is consistent and independent.
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In order to accumulate enough money for a down payment on a house, a couple deposits $406 per month into an account paying 3% compounded monthly. If payments are made at the end of each period, how much money will be in the account in 6 years?
Answers
In 6 years, the couple will have $32,916.38 in the account.
Solve using order of operations
16÷2×6-3
Answers
48 - 3
=46
The Order of Operations, also referred to as PEMDAS, is the rule that defines the sequence in which an expression with multiply operations can be solved.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
In this scenario, we are dividing, multiplying, adding, and subtracting numbers. This being laid out, lets begin.
1. Multiply and divide (left to right).
[tex]16[/tex] ÷ [tex]2 * 6 = 48[/tex]
[tex]=48-3[/tex]
2. Add and subtract (left to right).
[tex]48-3=45[/tex]
Hence, our final solution after using the order of operations would be [tex]45[/tex].
Hope this helps!
Can anyone help me? Thank you
Answers
Answer:162
Step-by-step explanation:
1.5 ft = 18 inches
so
9 * 18 = 162
Express cos L as a fraction in simplest terms.
15
39
K
36
Answers
The representation of cos L in simplest term is 5/13. It can be obatined by trigonometric ratios.
What are trigonometric ratio?
The ratio of sides of a right angled triangle is known ars trigonometric ratios. There are six trigonometric ratios. Which are as follows:
sin = P/H, cos = B/H, tan = P/B
cosec = H/P, sec = H/B, cot = B/P
Here, P is perpendicular, H is hypotaneous, and B is base. These ratios simplify the calculation.
SInce the angle is not specified hence, consider the given angle is L. Now, L is given angle hence, the base will be 15 and hypotenous will be 39.
Now, consider the trigonometric ratio of cos.
[tex]cosL=\frac{Base}{Hypotenuse}\\[/tex]
Subsitute 15 for base and 39 for hypotenuse in the above expression.
[tex]cosL=\frac{15}{39}\\=\frac{5}{13}[/tex]
Hence, the representation of cos L in simplest term is 5/13. It can be obatined by trigonometric ratios.
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Given L(-6, -7) and M(3, 6), what is the length of LM to the nearest tenth?
LM
Answers
Answer:
LM ≈ 15.8
Step-by-step explanation:
calculate the length d using the distance formula
d = [tex]}\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]
with (x₁, y₁ ) = L (- 6, - 7 ) and (x₂, y₂ ) = M (3, 6 )
LM = [tex]\sqrt{(3-(-6))^2+(6-(-7))^2}[/tex]
= [tex]\sqrt{(3+6)^2+(6+7)^2}[/tex]
= [tex]\sqrt{9^2+13^2}[/tex]
= [tex]\sqrt{81+169}[/tex]
= [tex]\sqrt{250}[/tex]
≈ 15.8 ( to the nearest tenth )
marking brainiest
:)
Answers
Answer:
Step-by-step explanation:
4x^2 + 4x =3
help pls
Answers
Answer:
x = .5, - 1.5
Step-by-step explanation:
4x^2 + 4x =3
To solve for x, we can complete the square.
4 ( x^2 + x) = 3
x^2 + x = 3/4
Take the coefficient of x, divide by 2, and square.
(1/2)^2
Then add to each side.
x^2 + x + 1/4= 3/4 +1/4
(x+1/2) ^2 = 1
Take the square root of each side.
x+1/2 = ±1
x = ±1 -1/2
x = 1-1/2 or -1-1/2
x = 1/2, -3/2
x = .5, - 1.5
Answer:
x = 1/2 or -3/2
Step-by-step explanation:
Rewrite in Standard Form:
4x²+4x=3 ==> 4x²+4x-3=0
Identify: a=4 b=4 c= -3
Quadratic Formula:
[tex]x=\frac{-b+\sqrt{b^2-4ac}}{2a} or \frac{-b-\sqrt{b^2-4ac}}{2a}\\ \\=\frac{-4+\sqrt{4^2-4(4)(-3)}}{2(4)} or \frac{-4-\sqrt{4^2-4(4)(-3)}}{2(4)}\\\\=\frac{-4+\sqrt{16+48}}{8} or \frac{-4-\sqrt{16+48}}{8}\\\\=\frac{-4+\sqrt{64}}{8} or \frac{-4-\sqrt{64}}{8}\\\\=\frac{-4+8}{8} or \frac{-4-8}{8}\\\\=\frac{4}{8} or \frac{-12}{8}\\\\=\frac{1}{2} or -\frac{3}{2}[/tex]
Kyla finished a 100 meter race in one and three-eighths minutes. The winner of the raced finished in one-third of Kyla's time.
How many minutes did it take for the winner of the race to finish?
eight thirty-thirds
eleven twenty-fourths
one and three twenty-fourths
one and four-elevenths
Answers
11/24 many minutes did it take for the winner of the race to finish.
What is Fraction?A fraction represents a part of a whole.
Given,
Kyla finished a 100 meter race in one and three-eighths minutes.
Kylas time is [tex]1\frac{3}{8}[/tex] minutes.
Convert mixed fraction to improper fraction.
11/8 minutes.
The winner of the raced finished in one-third of Kyla's time.
Which means 1/3 of 11/8
1/3×11/8
11/24
Hence, 11/24 many minutes did it take for the winner of the race to finish.
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Hello can someone please help me out? Thank you so much I’ll give brainly :)
Answers
Answer:
Step-by-step explanation:
the answer is a 28.27
Answer:
a) 28.27
Step-by-step explanation:
Formula we use,
→ πr²
Now the required area will be,
→ 3.14 × 3²
→ 3.14 × 9
→ 28.27 in²
Hence, the area is 28.27 in².
what is the value of the expression 0.307+13.16+0.8
Answers
Answer:
The Answer of the 0.307+13.16+0.8 is 14.267
HELP THANKS SO MUCH!!!!!!
Answers
Answer:
.62 each
Step-by-step explanation:
Evaluate each expression if w = 2, x = 3, y = 5, and z = 6.
1. 2w
2. y + 5
4. x+ w
7. y²
5. 3+ 4z
8. y - x
Fvaluate each evnreccion if m
n
3.9-2
6. 6y-5
Nov 30
Answers
2. 10
4. 5
7. 25
5. 27
8. 2
3. 7
6. 25
Hope this helped:))
need help pelase i need it
Answers
Door:80( actual height) 44( height on set)
Table 28( actual height) 15.4 ( height on set)
Stool 18 ( actual height) 9.9 ( height on set)
Step-by-step explanation:
Times the actual height inches by 0.55 and you get your height on set.
(x+1)+(x+4)+(x+7)+...+(x+40)=442
Answers
The value of the unknown variable x in the given sequence is; 14
What is the sum of the Arithmetic Sequence?
The formula for sum of an arithmetic sequence is;
Sₙ =ⁿ/₂(2a + (n − 1)d)
where;
a is first term
d is common difference
n is position of term
We are given the sequence as;
(x + 1) + (x + 4) + (x + 7) +...+ (x + 40) = 442
The common difference is;
x + 4 - (x + 1)
= 3
Now, to get the number of terms, we will say that the function follows the pattern;
aₙ = (x + 1) + 3n
Thus;
(x + 1) + 3n = x + 40
3n = 39
n = 13
Thus, there are n = 13 terms
Sₙ = ¹³/₂(2(x + 1) + (14 − 1)3) = 442
6.5(2x + 40) = 442
2x + 40 = 442/6.5
2x = 68 - 40
x = 28/2
x = 14
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