Set up the ratio for cos(A)

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

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).

Answer:

Step-by-step explanation:

The most obvious answer is the line y = 1.

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

Answer:

?

Step-by-step explanation:

Brainly challenge.

Answer:

Step-by-step explanation:

no body is answering

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.

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

Answer:

Step-by-step explanation:

find the value of a and b if 5+√3/7+2√3=a-b√3

The required inequality that expresses the given condition is 36 + 29x ≤ 210.

Given that,
A rental car company charges $29 per day to rent a car and $0.09 for every mile driven. Claire wants to rent a car, knowing that she plans to drive 400 miles. she has at most $210 to spend.

Inequality can be defined as the relation of the equation containing the symbol of ( ≤, ≥, <, >) instead of the equal sign in an equation.

Here,
Let the number of days be x,
Total cost to drive 400 miles = 400(0.09) = $36.
According to the question,
36 + 29x ≤ 210

Thus, the required inequality that expresses the given condition is 36 + 29x ≤ 210.

Learn more about inequality here:

brainly.com/question/14098842

#SPJ5

Answer:

p(a) =|2a+2|

p(–9) = | 2 (–9) +2 | = | –18 +2 | = | – 16 | = + 16

I hope I helped you^_^

The simplification of the expression [tex]xy-5x+y^2xy-5x+y ^2[/tex]  gives - 335.

Usually, simplification involves proceeding with the pending operations in the expression.

Simplification usually involves making the expression simple and easy to use later.

Given;

[tex]xy-5x+y^2xy-5x+y ^2[/tex]

Substitute x = -3 and y = 5.

[tex]-3\times 5-5\times -3+5^2\times -3\times 5-5\times -3+5 ^2[/tex]

= -15 + 15 - 375 + 15 + 25

= -335

Learn more about simplification;

https://brainly.com/question/17579585

#SPJ1

Answer:

The answer is "(27.030,29.770)"

Step-by-step explanation:

[tex](\bar{x}) = 28.4[/tex]

[tex](n)= 49[/tex]

[tex](\sigma) = 6[/tex]

[tex](CI) = \bar{x}\pm z^*_{\frac{\alpha}{2}} \frac{\sigma}{\sqrt{n}}[/tex]

[tex]z^*_{\frac{\alpha}{2}}\ for \ 89\%\ confidence = 1.598 \\\\\text{Using z table }\\\\ NORM.S.INV(1-\frac{(1-0.89)}{2})[/tex]

[tex]CI = 28.4 \pm 1.598 \times \frac{6}{\sqrt{49}}=(27.030,29.770)[/tex]

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

Answer:

y = 11/5x - 32/5

Step-by-step explanation:

y2 - y1 / x2 - x1

-2 - 9 / 2 - 7

-11 / -5

= 11/5

y = 11/5x + b

-2 = 11/5(2) + b

-2 = 22/5 + b

-32/5 = b

Answer:

cos a = 12/13

tan a = 5/12

You use these properties to solve the question,

sin²a+cos²a=1

tana=sina/cosa

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

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.

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

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.

Answer:

Domain is all real numbers, and range is all numbers greater than or equal to -2.  If thee was anything you didn't understand let me know.  

Step-by-step explanation:

The domain is what x values work, or it may be better to say the horizontal axis.  is there any number you cannot use?  if you cannot tell, this is a parabola, like x^2.  Is there any number you cannot plug into x^2.  The answer is no, the domain for all parabolic functions is all real numbers.

The range you really want to look at visually here.  Range is y values you can get, or values on the vertical axis.  I would also compare it to x^2 again.  You should know you can make it as high as you want, here is the same.  but at -2, there is no point below that.  so the range is -2 and up

The other options are just specific numbers.  you can disprove those by choosing a number not on their lists.  For the domain literally any other number.  For range any number not on the list greater than -2

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

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, 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.

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

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

Answer:

i think iys 6 lol

Step-by-step explanation:

its wright

=============================================================

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