Answer: 3 11/12
Step-by-step explanation:
1 1/3 * 2 = 2 2/3
5/8 * 2 = 1 1/4
2 2/3 + 1 1/4 = 3 11/12
Find a function whose graph is a parabola with vertex (4,-5) and that passes through the point (2, 3).
Answer:
4 ,-5
Step-by-step explanation:
I hope it's helpful for youThe value of x is 6. What is the value of y ?
Answer: y = 4.5
scale factor = 4/3
[tex]\large \rm \sum \limits_{n = 0}^ \infty \frac{( { - 1)}^{1 + 2 + 3 + \dots + n} }{(2n + 1 {)}^{2} }[/tex]
The sum we want is
[tex]\displaystyle \sum_{n=0}^\infty \frac{(-1)^{T_n}}{(2n+1)^2} = 1 - \frac1{3^2} - \frac1{5^2} + \frac1{7^2} + \cdots[/tex]
where [tex]T_n=\frac{n(n+1)}2[/tex] is the n-th triangular number, with a repeating sign pattern (+, -, -, +). We can rewrite this sum as
[tex]\displaystyle \sum_{k=0}^\infty \left(\frac1{(8k+1)^2} - \frac1{(8k+3)^2} - \frac1{(8k+7)^2} + \frac1{(8k+7)^2}\right)[/tex]
For convenience, I'll use the abbreviations
[tex]S_m = \displaystyle \sum_{k=0}^\infty \frac1{(8k+m)^2}[/tex]
[tex]{S_m}' = \displaystyle \sum_{k=0}^\infty \frac{(-1)^k}{(8k+m)^2}[/tex]
for m ∈ {1, 2, 3, …, 7}, as well as the well-known series
[tex]\displaystyle \sum_{k=1}^\infty \frac{(-1)^k}{k^2} = -\frac{\pi^2}{12}[/tex]
We want to find [tex]S_1-S_3-S_5+S_7[/tex].
Consider the periodic function [tex]f(x) = \left(x-\frac12\right)^2[/tex] on the interval [0, 1], which has the Fourier expansion
[tex]f(x) = \frac1{12} + \frac1{\pi^2} \sum_{n=1}^\infty \frac{\cos(2\pi nx)}{n^2}[/tex]
That is, since f(x) is even,
[tex]f(x) = a_0 + \displaystyle \sum_{n=1}^\infty a_n \cos(2\pi nx)[/tex]
where
[tex]a_0 = \displaystyle \int_0^1 f(x) \, dx = \frac1{12}[/tex]
[tex]a_n = \displaystyle 2 \int_0^1 f(x) \cos(2\pi nx) \, dx = \frac1{n^2\pi^2}[/tex]
(See attached for a plot of f(x) along with its Fourier expansion up to order n = 10.)
Expand the Fourier series to get sums resembling the [tex]S'[/tex]-s :
[tex]\displaystyle f(x) = \frac1{12} + \frac1{\pi^2} \left(\sum_{k=0}^\infty \frac{\cos(2\pi(8k+1) x)}{(8k+1)^2} + \sum_{k=0}^\infty \frac{\cos(2\pi(8k+2) x)}{(8k+2)^2} + \cdots \right. \\ \,\,\,\, \left. + \sum_{k=0}^\infty \frac{\cos(2\pi(8k+7) x)}{(8k+7)^2} + \sum_{k=1}^\infty \frac{\cos(2\pi(8k) x)}{(8k)^2}\right)[/tex]
which reduces to the identity
[tex]\pi^2\left(\left(x-\dfrac12\right)^2-\dfrac{21}{256}\right) = \\\\ \cos(2\pi x) {S_1}' + \cos(4\pi x) {S_2}' + \cos(6\pi x) {S_3}' + \cos(8\pi x) {S_4}' \\\\ \,\,\,\, + \cos(10\pi x) {S_5}' + \cos(12\pi x) {S_6}' + \cos(14\pi x) {S_7}'[/tex]
Evaluating both sides at x for x ∈ {1/8, 3/8, 5/8, 7/8} and solving the system of equations yields the dependent solution
[tex]\begin{cases}{S_4}' = \dfrac{\pi^2}{256} \\\\ {S_1}' - {S_3}' - {S_5}' + {S_7}' = \dfrac{\pi^2}{8\sqrt 2}\end{cases}[/tex]
It turns out that
[tex]{S_1}' - {S_3}' - {S_5}' + {S_7}' = S_1 - S_3 - S_5 + S_7[/tex]
so we're done, and the sum's value is [tex]\boxed{\dfrac{\pi^2}{8\sqrt2}}[/tex].
write and solve an equation twice a number is 26
Answer:
2x = 26, x = 13
Step-by-step explanation:
Write and solve an equation twice a number is 26
x = unknown number
Equation: 2x = 26
Solve:
2x = 26
/2 /2 <== divide both sides by 2
x = 13
Check your answer:
2x = 26
2(13) = 26
26 = 26
This stament is correct
Hope this helps!
Quadrilateral A B C D is shown. Sides A D and B C are parallel. Sides A B and C D are congruent. Angle A is 115 degrees.
What is the measure of ADC in quadrilateral ABCD?
45°
65°
115°
135°
Since no diagram attached there are two possible options.
Option 1
The quadrilateral is parallelogram.
In this case ∠A and ∠D sum up to 180°, therefore:
∠ADC = 180° - 115° = 65°Option 2
The quadrilateral is isosceles trapezoid.
In this case ∠A is congruent with ∠D, therefore:
∠ADC = ∠A = 115°Answer:
115
Step-by-step explanation:
How large a sample must a pollster take in order to estimate with 95% confidence and to within 3 percentage points, the proportion of voters who are in favor of a certain measure
========================================================
Work Shown:
[tex]n = \hat{p}*(1-\hat{p})\left(\frac{z}{E}\right)^2\\\\n \approx 0.5*(1-0.5)\left(\frac{1.96}{0.03}\right)^2\\\\n \approx 1067.111\\\\n \approx \boldsymbol{1068}\\\\[/tex]
Notes:
At 95% confidence, the z critical value is roughly z = 1.96 which is determined using a Z table.E = 0.03 to represent the 3% error. We're not told the value of [tex]\hat{p}[/tex], so we assume the most conservative estimate of 0.5Always round up to the nearest integer. The value 1067.111 is closer to 1067, but we round up to 1068 to clear the hurdle needed. A chemist has one solution that is 20% alcohol and another that is 60% alcohol.
How much of each solution must the chemist use to get 200 mL of a solution that is 52%
alcohol?
Answer:
solution 1= 40ml
solution 2= 160ml
Step-by-step explanation:
%alcohol= amount of alcohol/total solutionx100
0.52x200=104ml of alcohol present
0.2x L=0.2Lml of alcohol in solution one
0.6 x M=0.6Mml of alcohol in solution two
1st equation
0.2L+0.6M=104ml alcohol
times 10 to get whole
2L+6M=1040ml
2nd
same for this equation
10L+10M=2000ml
10L+10M=2000
2L+6M=1040
elimination method
=20L+20M=4000
-
=20L+60M=10400
-40M=-6400
M=160ml
2L+6 (160)=1040
2L=1040-960
2L=80
L=40ml
solve the equation
answer: x=
Answer:
Hope the picture will help you
Which is the graph of x2 − y2 = 16?
Answer:
see attached
Step-by-step explanation:
When the signs of the x^2 and y^2 terms of a relation quadratic in both x and y are different, the relation represents a hyperbola. The graph of the hyperbola is shown in the attachment.
__
If the signs are the same, the relation represents an ellipse. If the coefficients of the squared terms are also the same, then that ellipse is a circle.
Help me please with math for points
Answer:
The answer is 72
Step-by-step explanation:
because you take the 8 times it by the 9
9×8=72 square³
9
These lists show the ages of attendees in a yoga class and a dance dass
Yoga: 18, 31, 17, 14, 20, 33, 36
Dance: 20, 47, 23, 38, 26, 42, 30
Select from the drop-down menus to correctly complete each statement about the attendees in the two cases
The median age of the attendees in the yoga class is
the median age of the attendees in the dance
The range of ages of the attendees in the yoga class is
the range of ages of the attendees in the conce
Answer:
median is 20
Step-by-step explanation:
due to both of them having it in there 1 time
Answer:
The Median Age: Yoga Class (31) Dance Class (30)
The Range: Yoga Class (17-44) Dance Class (20-47)
Step-by-step explanation:
Judi Salem opened a law office on July 1, 2022. On July 31, the balances in the accounts were as follows: Cash $5,000, Accounts Receivable $1,500, Supplies $500, Equipment $6,000, Accounts Payable $4,200, and Owner’s Capital $8,800. During August, the following transactions occurred.
1. Collected $1,200 of accounts receivable.
2. Paid $2,800 cash on accounts payable.
3. Recognized revenues of $7,500 of which $3,000 is collected in cash and the balance is due in September.
4. Purchased additional equipment for $2,000, paying $400 in cash and the balance on account.
5. Paid salaries $2,500, rent for August $900, and advertising expenses $400.
6. Withdrew $700 in cash for personal use.
7. Received $2,000 from Standard Federal Bank—money borrowed on a note payable.
8. Incurred utility expenses for month on account $270.
Step-by-step explanation:
what is that called into the comet or ok
Is (8, 7) a solution of y > 4x − 6?
No, (8, 7) is not a solution of y > 4x − 6.
Yes, (8, 7) is a solution of y > 4x − 6.
Answer:
no
Step-by-step
Use the slope-intercept form to find the slope and y-intercept.
Tap for fewer steps...
The slope-intercept form is
y
=
m
x
+
b
, where
m
is the slope and
b
is the y-intercept.
y
=
m
x
+
b
Find the values of
m
and
b
using the form
y
=
m
x
+
b
.
m
=
4
b
=
−
6
The slope of the line is the value of
m
, and the y-intercept is the value of
b
.
Slope:
4
y-intercept:
(
0
,
−
6
)
Any line can be graphed using two points. Select two
x
values, and plug them into the equation to find the corresponding
y
values.
Tap for fewer steps...
Find the x-intercept.
Tap for fewer steps...
To find the x-intercept(s), substitute in
0
for
y
and solve for
x
.
0
=
4
x
−
6
Solve the equation.
Tap for fewer steps...
Rewrite the equation as
4
x
−
6
=
0
.
4
x
−
6
=
0
Add
6
to both sides of the equation.
4
x
=
6
Divide each term by
4
and simplify.
Tap for fewer steps...
Divide each term in
4
x
=
6
by
4
.
4
x
4
=
6
4
Cancel the common factor of
4
.
Tap for fewer steps...
Cancel the common factor.
4
x
4
=
6
4
Divide
x
by
1
.
x
=
6
4
Cancel the common factor of
6
and
4
.
Tap for fewer steps...
Factor
2
out of
6
.
x
=
2
(
3
)
4
Cancel the common factors.
Tap for fewer steps...
Factor
2
out of
4
.
x
=
2
⋅
3
2
⋅
2
Cancel the common factor.
x
=
2
⋅
3
2
⋅
2
Rewrite the expression.
x
=
3
2
x-intercept(s) in point form.
x-intercept(s):
(
3
2
,
0
)
Find the y-intercept.
Tap for fewer steps...
To find the y-intercept(s), substitute in
0
for
x
and solve for
y
.
y
=
4
(
0
)
−
6
Solve the equation.
Tap for fewer steps...
Remove parentheses.
y
=
4
(
0
)
−
6
Simplify
4
(
0
)
−
6
.
Tap for fewer steps...
Multiply
4
by
0
.
y
=
0
−
6
Subtract
6
from
0
.
y
=
−
6
y-intercept(s) in point form.
y-intercept(s):
(
0
,
−
6
)
Create a table of the
x
and
y
values.
x
y
0
−
6
3
2
0
Graph the line using the slope and the y-intercept, or the points.
Slope:
4
y-intercept:
(
0
,
−
6
)
x
y
0
−
6
3
2
0
Q. 1. Solve for x using determinants, x + y = 9, x - y + 3z = 2 and 4y - 32 - 5 = 0.
Hello!
x + y = 9,
x= 9-y
x - y + 3z = 2
x= 2+y -3z
4y - 32 - 5 = 0.
4y = 32+5
4y = 37
y = 37/4
What is M G to the nearest tenth
Answer:
tan m‹G = 28.2/45.8
m‹G= 31.62°
what is the measure of the space occupied by a solid. (Measured in cubic units)
You spin the spinner, flip a coin, then spin the spinner again. Find the probability of the compound event. Write your answer as a fraction or percent rounded to the nearest hundredth. (the spinner is 1-9)
The probability of spinning a 4, flipping heads, then spinning a 7 is
Answer:
1/162
Step-by-step explanation:
first spin 1/9
land heads 50/50
second spin 1/9
so (9 x 2) x 9
= 162
1
Answer:
1/162 or 0.62 % to the nearest hundredth.
Step-by-step explanation:
Prob(spinning a 4) = 1/9
Prob(spinning a 7) = 1/9
Prob(flipping a head) = 1/2
Required Probability = 1/9 * 1/2 * 1/9
1/162.
a newspaper editor hired a writer for jokes cartoons. the cost for 8 jokes and 6 cartoons is 610usd. the cost of 6 jokes and 8 cartoons is 510usd how much do a joke and a cartoon together cost
Answer:
a joke and a cartoon together cost $80
c=$15 j=$65
Step-by-step explanation:
j=joke
c=cartoon
8j +6c = 610
6j+8c = 510
Multiply the first by 8
Multiply the second by -6
64j +48c = 4880
-36j -48c = -3060
ADD both (c will cancel)
28j = 1820
j= 65
PLUG j
8(65) + 6c = 610
520+6c = 610
6c= 90
c = 15
j + c = 65+15 = 80
Peter is buying a circular rug for his bedroom. The rug has an area of 40 square feet. What is the approximate diameter of the rug? Show your work or explain your answer.
The approximate diameter of the rug with an area of 40 ft² is 7.14 feet.
What is area?Area is the amount of space occupied by a two dimensional shape or object.
The area of a circle is given by:
Area = π * diameter²/4
The rug has an area of 40 square feet. Hence:
40 = π * diameter²/4
Diameter = 7.14 feet
The approximate diameter of the rug with an area of 40 ft² is 7.14 feet.
Find out more on area at: https://brainly.com/question/25292087
∠45° is complementary to which of the following angles?
∠45°
∠135°
∠315°
∠55°
The answers people keep on giving is 90 but it doesnt say it here. Can someone help me?
Answer:
45°
Step-by-step explanation:
complementary angles add up to 90° so it's 90-45
April is 19, Bryan is 20, Carla is 20, and Dave is 21, how old is Erica is the average of their given ages is 23?
Answer: 35
Step-by-step explanation:
The average can be found by adding their ages together and dividing by the number of ages.
Given:
[tex]\frac{19+20+20+21+x}{5}[/tex] = 23
Multiply both sides of the equation by 5:
19 + 20 + 20 + 21 + x = 115
Combine like terms:
80 + x = 115
Subtract 80 from both sides of the equation:
x = 35
Erica is 35.
The dimensions of triangle A are three times the dimensions of triangle B. The area of triangle B is 28 cm What is the area of triangle A?
Answer:
Below in bold.
Step-by-step explanation:
The ratio of theire areas is 1^2 : 3^2
= 1:9.
So the area of triangle A = 28 * 9
= 252 cm^2.
Answer:
[tex]252cm {}^{2} [/tex]
step by step explanation:
[tex]since \: \: dimension \: of \: traiangle \: a \: = 3 times \: dimension \: of \: triangle \: b \\ note \: that \: area \: is \: square \: of \: dimension \: \\ therefore \: area \: of \: triangle \: a \: = 3 {}^{2} \: area \: of \: triale \: \: b \\ area \: of \: trianle \: a = 9 \times 28 = 252cm {}^{2} [/tex]
please help
me answer this question
Answer:
x ≥ 4
Step-by-step explanation:
Given:
[tex]\displaystyle \large{3x-1\geq 11}[/tex]
Add both sides by 1:
[tex]\displaystyle \large{3x-1+1\geq 11+1}\\\displaystyle \large{3x\geq 12}[/tex]
Divide both sides by 3:
[tex]\displaystyle \large{\dfrac{3x}{3} \geq \dfrac{12}{3}}\\\displaystyle \large{x\geq 4}[/tex]
Hence, the solution is x ≥ 4
How to solve 4 divided by 5
Answer: HELLO THERE! Here's what I found from study dot com "4 divided by 5 is equal to 0.8. This decimal can also be written as a fraction. 0.8 = eight tenths or 8/10 (4/5 in its reduced form)."
Step-by-step explanation:
Hope this helps, have a good day!
what is the difference of 21 1/4 - 18 2/4
Answer: Difference between 21 1/4 - 18 2/4 =2 3/4
Step-by-step explanation:
If line segment AB is 400%, what is the length of a line segment that is 100%?
the length of the line would be 1 inch
Question 7 (3 points)
A right rectangular prism is shown. Find the surface area of this prism. Refer to your
STAAR 8th Grade Math Reference Sheet for the appropriate formula.
Answer:
196 square feet
Step-by-step explanation:
(learn it before u submit. im here to help not cheat;w;
-ur fellow classmate)
S=ph+2b
s=(p=l+l+w+w) (h)+ (2) (b=lxw)
s=(8+8+10+10) (1) + (2) (8x10)
s=( 36x1 )+ (2x80)
s= 36+160
s=196
God bless ya:)
The area of this prism is 196 square feet.
What is the area of the prism?The prism's area can be calculated by adding its lateral area to the base areas. The process of calculating these areas ends up being facilitated because the two bases of a prism are the same, therefore, it is enough to calculate the area of a base and multiply the result by 2
The formula for the area of the prism is given by:
[tex]S=ph+2b[/tex]
Where:
p=l+l+w+wb=lxwSo we have that:
[tex]s=(p=l+l+w+w) (h)+ (2) (b=lxw)\\s=(8+8+10+10) (1) + (2) (8*10)\\s=( 36*1 )+ (2*80)\\s= 36+160\\s=196[/tex]
See more about area at brainly.com/question/11952845
Which of the following are not polynomials?
A. x^2+2sqrtx+1 B. 2/x^2+x+1 C. 2/3x^2+x+1 D. x^2+ sqrt2x + 1 E. x^-2+x+1
Answer:
A
Step-by-step explanation:
(3√7 +5)^2
simplify the problem to its simplest form.
Answer:
88 + 30[tex]\sqrt{7} \\[/tex]
Step-by-step explanation:
Expand to make easier:
(3[tex]\sqrt{7} \\[/tex] + 5) x (3[tex]\sqrt{7} \\[/tex] + 5)
FOIL:
9(7) + 15 [tex]\sqrt{7}[/tex] + 15[tex]\sqrt{7}[/tex] + 25
Simplify:
63 + 30[tex]\sqrt{7}[/tex] + 25
88 + 30[tex]\sqrt{7}[/tex]
can some one help i need to pass