Answer:
common difference is 0.5
first term is 5
Step-by-step explanation:
use the formula for the nth term of an ap Tn=a+(n-1)d
T12=10.5
T18=13.5
therefore come up with two equations
T12=a+(12-1)d
10.5=a+11d(1st equation)
T18=a+(18-1)d
13.5=a+17d(2nd equation)
then solve both as a simultaneous equation
a+11d=10.5
a+17d=13.5
-6d/-6=-3/-6
d=0.5
use one of the equations to find the first term
a+11(0.5)=10.5
a+5.5=10.5
a=10.5-5.5
a=5
I hope this helps
please mark as brainliest
A candidate for one of Ohio's two U.S. Senate seats wishes to compare her support among registered voters in the northern half of the state with her support among registered voters in the southern half of the state. A random sample of 2000 registered voters in the northern half of the state is selected, of which 1062 support the candidate. Additionally, a random sample of 2000 registered voters in the southern half of the state is selected, of which 900 support the candidate. A 95% confidence interval for the difference in proportion of registered voters that support this candidate between the northern and southern halves of the state is:
Answer:
The 95% confidence interval for the difference in proportion of registered voters that support this candidate between the northern and southern halves of the state is (0.05, 0.112).
Step-by-step explanation:
Before building the confidence interval, the central limit theorem and subtraction of normal variables is explained.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
Subtraction between normal variables:
When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.
Northern half:
1062 out of 2000, so:
[tex]p_N = \frac{1062}{2000} = 0.531[/tex]
[tex]s_N = \sqrt{\frac{0.531*0.469}{2000}} = 0.0112[/tex]
Southern half:
900 out of 2000, so:
[tex]p_S = \frac{900}{2000} = 0.45[/tex]
[tex]s_S = \sqrt{\frac{0.45*0.55}{2000}} = 0.0111[/tex]
Distribution of the difference:
[tex]p = p_N - p_S = 0.531 - 0.45 = 0.081[/tex]
[tex]s = \sqrt{s_N^2 + s_S^2} = \sqrt{0.0112^2 + 0.0111^2} = 0.0158[/tex]
Confidence interval:
The confidence interval is:
[tex]p \pm zs[/tex]
In which
z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].
95% confidence level
So [tex]\alpha = 0.05[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].
The lower bound of the interval is:
[tex]p - zs = 0.081 - 1.96*0.0158 = 0.05[/tex]
The upper bound of the interval is:
[tex]p + zs = 0.081 + 1.96*0.0158 = 0.112[/tex]
The 95% confidence interval for the difference in proportion of registered voters that support this candidate between the northern and southern halves of the state is (0.05, 0.112).
A student said that since -9 is less than 4, then |-9| is less than |4|. Is the student correct? Explain why or why not.
Answer:
No.
Step-by-step explanation:
They are not correct because the "| |" signs mean absolute value. What ever is inside the signs must be positive. So -9 becomes 9 and 9 is greater than 4. So, the student is not correct.
Can anyone help me with this question?
x^{2} + 7x -144
quadratic equations
Answer:
?
Step-by-step explanation:
Brainly challenge.
worth 10pts can someone help?
Answer:
y = -x+2
Step-by-step explanation:
The y intercept is 2
The slope is found by using 2 point
I picked (0,2) and (2,0)
m = ( y2-y1)/(x2-x1)
= ( 0-2)/(2-0)
= -2/2 = -1
Slope intercept form is
y = mx+b where m is the slope and b is the y intercept
y = -1x+2
y = -x+2
13. A pair of shoes sell for $27 per pair. There is a sale tomorrow on shoes offering two pairs for $45.
How much will 3 pairs of shoes cost today?
Answer:
$72
Step-by-step explanation:
The sale offers 2 pair of shoes for $45, but the price is same for 1 pair of shoes.
The cost of 3 pair of shoes
= The sale price of 2 pair of shoes + Regular price of 1 pair of shoes
= $45 + $27
= $72
So, 3 pairs of shoes will cost $72 today.
Taehyung was sitting on the ground flying a kite. He had 22 feet of line let out to fly his kite, and the kite was 14 feet in front of him. How high was the kite?
30^∘ Another boy is standing on the roof of a 10 second string be x mIn Δ ABC sin 30^∘ = AC/AB 1/2 = AC/100 AC =
Answer: hope this helps ♡
The kite was 16.9 feet high.
Step-by-step explanation:
Pythagorean theorem
b = [tex]\sqrt{c^{2} - a^{2} }[/tex]
b = [tex]\sqrt{22^{2} - 14^{2} }[/tex]
b = [tex]\sqrt{484 - 196}[/tex]
b = [tex]\sqrt{288}[/tex]
b = 16.9
Find the exact value of the indicated trigonometric function for the acute angle a:
Given: sin a=5/13, Find: cos a and tan a
Answer:
cos a = 12/13
tan a = 5/12
You use these properties to solve the question,
sin²a+cos²a=1
tana=sina/cosa
Given two consecutive even integers whose sum is 186, find the smaller of the two integers.
Answer:
92 is the smaller even integer
Step-by-step explanation:
x = first even integer
x+2 = second even integer
(x) + (x+2) = 186
Combine like terms
2x+2 = 186
Subtract 2 from each side
2x+2-2 =186-2
2x = 184
Divide by 2
2x/2 = 184/2
x = 92
x+2 = 94
Step-by-step explanation:
let,two even consecutive number be x and x+2
now,according to the question
x+x+2=186
or, 2x=186-2
or, 2x= 184
or, x= 184/2
:- x= 92
Hence,
x=92 and x+2= 94
two even consecutive numbers are 92 and 94
a person has 2 balls, a second one had (2)^2 = 4 balls, a third had (4)^2 = 16, how many balls will the tenth person have?
Answer:
256
Step-by-step explanation:
because all of them are squared so
2^2= 4 balls
2 x 2
4^2 = 16 balls
4 x 4
16^2 = 256 balls
16 x 16
Plzzzz someone help. Will mark brainiest is correct!!!!
Photo attached
Answer:
Your last step ( step 5 ) :
[tex] {x}^{2} + \frac{b}{a} x + \frac{ {b}^{2} }{4 {a}^{2} } = - \frac{c}{a} + \frac{ {b}^{2} }{4 {a}^{2} } [/tex]
Step 6:
[tex]{ \boxed{x + ( \frac{b}{2a}) = ± \frac{ \sqrt{ {b}^{2} - 4ac } }{ \sqrt{4a^2} } }}[/tex]
Step-by-step explanation:
[tex] {x}^{2} + \frac{b}{a} x + \frac{ {b}^{2} }{4 {a}^{2} } = - \frac{4ac}{4 {a}^{2} } + \frac{ {b}^{2} }{4 {a}^{2} } \\ \\ {x}^{2} + \frac{b}{a} x = \frac{4ac}{4a {}^{2} } \\ \\ {x} = \sqrt{ \frac{ - 4ac + b {}^{2} }{4a {}^{2} } } [/tex]
.,............. ..... ..nnkkjk
Geometry, please answer question ASAP
Answer:
D. 101
Step-by-step explanation:
(25x+1)+(25x-2)+(20x-1)+82=360
70x=360-1+2+1-82
70x=280
x=4
A=25x+1=101
Find the value of a. Round
the nearest tenth.
Answer:
a = 24.0
Step-by-step explanation:
We can use the law of sines to solve
sin 150 sin 12
---------- = ----------
a 10
Using cross products
10 sin 150 = a sin 12
10 sin 150 / sin 12 = a
a=24.04867
To the nearest tenth
a = 24.0
find the value of a and b if 5+√3/7+2√3=a-b√3
Answer:
Step-by-step explanation:
find the value of a and b if 5+√3/7+2√3=a-b√3
Một ôtô đi từ A đến B với vận tốc 60km/h và đi từ B về A với vận tốc 45km/h. Thời gian cả đi và về hết 7giờ. Tính quãng đường AB
Please explain in english
Answer:
Đáp án: 180km
Step-by-step explanation:
Giải thích các bước giải:
Gọi quãng đường AB là x (km)
(x > 0)
Thời gian ô tô đi từ A -> B là x/60 (h)
Thời gian ô tô đi từ B -> A là x/45 (h)
Vì thời gian cả đi và về hết 7h
=> x/60 + x/45 = 7
=> x = 180 (TM)
Vậy quãng đường AB là 180 km
Write the ratio as a fraction in simplest form with whole numbers in the numerator and denominator
Answer:
3:8
Step-by-step explanation:
1.2 to 3.2 is 12:32 or 3:8
Answer:
3/8
Step-by-step explanation:
1.20/3.20
= 12/32
= 3/8 (divide top and bottom by 4)
I hope this helped! :D
A bag contains 42 red, 45 green, 20
yellow, and 32 purple candies. You
pick one candy at random. Find the
probability that it is green or yellow.
Answer:
=65/139
Step-by-step explanation:
42 red, 45 green, 20yellow, and 32 purple candies = 139 candies
P( green or yellow) = green or yellow / total
=(45+20) / 139
=65/139
You are driving 2760 miles across the country. During the first 3 days of your trip, you drive 1380 miles. If you continue to drive at the same rate each day, how many days will the entire trip take? Show your work and circle your answer.
The entire trip will take 6 days.
(Encircle this answer, as said on the directions)
Step-by-step explanation:
We know that the first three days of the trip, we traveled 1380 miles.
Find the UNIT RATE of MILES PER day:
1380/3 = 460
Unit rate = 460 miles per day
If we were to drive at this (460 mi per day) rate EACH day and the whole journey takes 2760 miles across the country.
FInd the NUMBER of DAYS of the ENTIRE TRIP:
2760/460 = 6
It will take us 6 days to drive to the destination.
Can someone help me please?
Answer:
p(a) =|2a+2|
p(–9) = | 2 (–9) +2 | = | –18 +2 | = | – 16 | = + 16
I hope I helped you^_^
Write a slope-intercept equation for a line passing through the point (5,-5) that is parallel to the line x = -2. Then write a second equation for a line passing through the point (5,-5) that is perpendicular to the line x=-2.
Answer:
1. y=-2x+5
2. y=1/2x-7.5
Step-by-step explanation:
you plug in the cordinates for the y intercept and you already have the slope.
y=mx+b
m= slope which is -2
2. Mr. McGrath is ordering pizza for the girls soccer team. A large cheese pizza costs $10, plus 80¢ for each
additional topping (including extra cheese!).
Complete the table below.
Answer:
i think iys 6 lol
Step-by-step explanation:
its wright
A room is twice as long as it is broad and its height is 8 m. if the cost of painting its walls at Rs. 20 per m² is Rs 9600 , find the cost of carpeting its floor at Rs. 400 per m²
Answer:
Step-by-step explanation:
no body is answering
125 Children get one pen, there are 8
pens in a pack. How many pens are
needed?
Answer:
16 packs
Step-by-step explanation:
Take the number of children and divide by the number of pens in a pack
125/8
15.625
We need to round up to get the number of packs
16 packs
Answer:
125 pens and 16 packs.
Step-by-step explanation:
Given:
Each child gets 1 pen.There are 125 children.Each pack has 8 pens.Each child gets 1 pen, so there needs to be 125 pens.
Since there are 8 pens in a pack, there will need to be:
125 / 8 = 15.62
Estimate:
16 packs
There needs to be 16 packs for the 125 children.
Please help me solve this fast!
Answer:
base = 18.89
legs = 16.89
Step-by-step explanation:
x + x + 68 = 180
2x + 68 = 180
2x = 112
x = 56
The altitude = 14
Tan(56) = opposite / adjacent
adjacent = base
opposite = altitude
Tan(56) = opposite / base Multiply both sides by the base
base * Tan(56) = opposite Divide by Tan(56)
base = opposite / Tan(56)
base = 14/tan(56)
base = 9.443
The base is actually twice this length because the altitude lands on the midpoint of the opposite side and is perpendicular to the third side (base).
base = 18.886
Legs are the hypotenuse formed by 1/2 the base and the attitude.
Sin(56) = opposite / hypotenuse
Sin(56) = altitude / hypotenuse
hypotenuse = altitude / Sin(56)
hypotenuse = 14 / sin(56)
hypotenuse = 16.887
Rounded
base = 18.89
legs = 16.89
pls helppppppp it’s due in 20 minutes
Answer:
hope this helps you
havea great dayy
Answer:
39
Step-by-step explanation:
3(6m-17)
3(30-17)
3(13)
39
What is the value of x in the equation 4(2x + 14) = 0?
A. 9
B. 7
C. -7
D. -9
Answer:
-7
Step-by-step explanation:
2(2x+14)=0
2x+14=0
2x=-14
x=-14/2
x=-7
Answered by GAUTHMATH
Please help me i need this
fast
Answer:
just restart your device
Since opening night, attendance at Play A has increased steadily, while attendance at Play B first rose and then fell. Equations modeling the daily attendance y at each play are shown below, where x is the number of days since opening night. On what day(s) was the attendance the same at both plays? What was the attendance?
Play A: y=25x+136
Play B: y=-x^2+44x+76
Answer: Day 4 and 15
Step-by-step explanation:
Set up system of equations:
[tex]25x+136=-x^2+44x+76[/tex]
Simplify:
[tex]x^2-19x+60=0[/tex]
Factor: Both factors must be positive as the days can only be natural numbers.
[tex](x-15)(x-4)=0[/tex]
x=4,15
please help me solve this exercise.!!
find the value of tanx if sinx+cosx=1/5 and 0<x<π.
=============================================================
Explanation:
Let's square both sides and do a bit of algebra to get the following.
[tex]\sin(x) + \cos(x) = 1/5\\\\\left(\sin(x) + \cos(x)\right)^2 = \left(1/5\right)^2\\\\\sin^2(x) + 2\sin(x)\cos(x) + \cos^2(x) = 1/25\\\\\sin^2(x) + \cos^2(x) + 2\sin(x)\cos(x) = 1/25\\\\1 + 2\sin(x)\cos(x) = 1/25\\\\\sin(2x) = 1/25 - 1\\\\\sin(2x) = 1/25 - 25/25\\\\\sin(2x) = -24/25\\\\[/tex]
Now apply the pythagorean trig identity to determine cos(2x) based on this. You should find that cos(2x) = -7/25
This then means tan(2x) = sin(2x)/cos(2x) = 24/7.
From here, you'll use this trig identity
[tex]\tan(2x) = \frac{2\tan(x)}{1-\tan^2(x)}\\\\[/tex]
which is the same as solving
[tex]\tan(2x) = \frac{2w}{1-w^2}\\\\[/tex]
where w = tan(x)
Plug in tan(2x) = 24/7 and solve for w to get w = -4/3 or w = 3/4
So either tan(x) = -4/3 or tan(x) = 3/4.
If we were to numerically solve the original equation for x, then we'd get roughly x = 2.21; then notice how tan(2.21) = -1.345 approximately when your calculator is in radian mode.
Since tan(x) < 0 in this case, we go for tan(x) = -4/3
a 4 pint carton of frozen yogurt costs 6.08 what is the price per cup
Answer:
?
Step-by-step explanation:
My last person to ask a question
Answer:
$0.76 per cup or 76 cents per cup
Step-by-step explanation:
1 pint is 2 cups
4 pints is 8 cups
We can use ratios to solve
8 cups 1 cup
------------------ = -----------------
6.08 dollars x dollars
Using cross products
8x = 6.08
Divide each side by 8
x =6.08/8
x=.76
PLEASE ANSWER ASAP THANK YOU!!!
How much money will be in a bank account after 3 years if $9 is deposited at an interest rate of 5% compounded annually? Round to the nearest dollar.
Answer:
$10.42
Step-by-step explanation:
Compound interest formula: A=p(1+r/n)^nt
9=p, r=0.05, n=1, and t=3
A=9(1+0.05)^3
A=9(1.05)^3
Plug this into calculator and you get $10.42
Answer:
A = $10.42
Step-by-step explanation:
The appropriate formula is the "compound amount" formula given by
A = P(1 + r)^t,
where P is the initial amount, r is the annual interest rate as a decimal fraction, and t is the number of years elapsed.
Here:
A = $9(1 + 0.05)^3, or
A = $9(1.05)^3, or
A = $10.42
