To which graph does the point (2, 4) belong? (1 point) y ≥ x + 3 y ≥ −x + 8 y ≥ 4x − 5 y ≥ −2x + 9

Answer:

[tex] x_{1} = 3 + \sqrt {6} [/tex]

[tex] x_{2} = 3 - \sqrt {6} [/tex]

Step-by-step explanation:

Given the quadratic equation;

x² - 6x + 3 = 0

To find the roots of the quadratic equation, we would use the quadratic formula;

Note: the standard form of a quadratic equation is ax² + bx + c = 0

a = 1, b = -6 and c = 3

The quadratic equation formula is;

[tex] x = \frac {-b \; \pm \sqrt {b^{2} - 4ac}}{2a} [/tex]

Substituting into the formula, we have;

[tex] x = \frac {-(-6) \; \pm \sqrt {-6^{2} - 4*1*(3)}}{2*1} [/tex]

[tex] x = \frac {6 \pm \sqrt {36 - (12)}}{2} [/tex]

[tex] x = \frac {6 \pm \sqrt {36 - 12}}{2} [/tex]

[tex] x = \frac {6 \pm \sqrt {24}}{2} [/tex]

[tex] x = \frac {6 \pm 2 \sqrt {6}}{2} [/tex]

[tex] x_{1} = \frac {6 + 2 \sqrt {6}}{2} [/tex]

[tex] x_{1} = \frac {6}{2} + \frac {2 \sqrt {6}}{2} [/tex]

[tex] x_{1} = 3 + \sqrt {6} [/tex]

Or

[tex] x_{2} = \frac {6 - 2 \sqrt {6}}{2} [/tex]

[tex] x_{2} = \frac {6}{2} - \frac {2 \sqrt {6}}{2} [/tex]

[tex] x_{2} = 3 - \sqrt {6} [/tex]

Answer:

A = $29,201.97

A = P + I where

P (principal) = $20,000.00

I (interest) = $9,201.97

Step-by-step explanation:

First, convert R as a percent to r as a decimal

r = R/100

r = 9.5/100

r = 0.095 rate per year,

Then solve the equation for A

A = P(1 + r/n)nt

A = 20,000.00(1 + 0.095/12)(12)(4)

A = 20,000.00(1 + 0.007916667)(48)

A = $29,201.97

Summary:

The total amount accrued, principal plus interest, with compound interest on a principal of $20,000.00 at a rate of 9.5% per year compounded 12 times per year over 4 years is $29,201.97

Answer:

[tex]2*\pi *10=62.83185307[/tex]

[tex]20/2 = 10[/tex]

[tex](Radius)[/tex][tex]Or the C = \pi*d[/tex]

62.83185307 is the answer

Answer:

C≈60

Step-by-step explanation:

remember circumference formula

[tex] \displaystyle C = 2\pi r[/tex]

given that,d=20 therefore r would be 20/2=10 thus substitute:

[tex] \displaystyle C = 2\pi .10[/tex]

simplify mutilation:

[tex] \displaystyle C = 20\pi [/tex]

substitute the given value of π:

[tex] \displaystyle C = 20.3[/tex]

simplify multiplication:

[tex] \displaystyle C = 60[/tex]

and we are done!

Answer:

D

Step-by-step explanation:

shaped like a cone

Cone = 1/3

v = 1/3 x 3.14 x 2.5^2 x 4.2

v =27.475

The equation should the artist use to calculate the volume of the

cone is, 4. V=1/3π (2.5)²(4.2)

A cone is a three-dimensional geometric object with a smooth, curved top and a flat base. As a cone's height increases, its radius gradually decreases until it reaches a particular point.

The total surface area of a cone is πr(r + l).

The curved surface area is πrl.

Given, An artist is making a sculpture shaped like a cone having a radius of 2.5 inches and a height of 4.2 inches.

We know The volume of a cone is (1/3)πr²h.

Therefore, The volume of the cone would be,

= (1/3)π(2.5)²×4.2 cubic inches.

learn more about cones here :                                      

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Answer:

i got (-10/7, -44/7)

Answer:

B) 12

Step-by-step explanation:

2/7 is the original ratio

7 × 6 = 42

2 × 6 = 12

Answer:

All of the values that can go into a relation or function (input) are called the domain. ... The domain is the set of all first elements of ordered pairs (x-coordinates). The range is the set of all second elements of ordered pairs (y-coordinates). Only the elements "used" by the relation or function constitute the range.

Step-by-step explanation:

Math is a language

say you plant two posts that are 5ft apart and you want to get up to 60ft

right now you've covered 5ft and now have 60 - 5 = 55ft to go.

you plant the next one: 55 - 5 = 50ft to go

instead of subtracting many times and counting hiw many times we've subtracted, we can use division

60ft / 5ft = 12 posts

to verify, you can multiply 5 and 12 which is the same as adding 5 + 5 + 5 + 5 +... + 5 = 5ft x 12 Posts= 60ft in total length

There are 12 posts for 60 feet of straight line fence.

Here,

Given that,

Post are space 5 feet apart.

We have to find number of posts for 60 feet of straight line fence.

What is Division method?

This method of distributing a group of things into equal parts is termed as division.

Now,

We can division method to find number of posts for 60 feet of straight line fence.

Here, Post are space 5 feet apart.

Number of posts = [tex]\frac{60}{5} = 12[/tex]

Hence, There are 12 posts for 60 feet of straight line fence.

Learn more about the Division method visit:

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Answer:

Hello! answer: x = 16

Step-by-step explanation:

16 × 16 = 256

12 × 12 = 144

256 + 144 = 400

√400 = 20 therefore x = 16 hope that helps!

Answer:

23

Step-by-step explanation:

Answer:

snafnjnfnEWfnwenlfnwenflwenlfewfwefư

Answer:

200 boxes

Step-by-step explanation:

We can use ratios to solve

12 suits       2400 suits

------------ = ------------

1 box          x boxes

Using cross products

12x = 1*2400

12x = 2400

Divide by 12

12x/12 = 2400/12

x =200

We need 200 boxes

Answer:

200

Step-by-step explanation:

1 box = 12

Box? = 2400.

DIVIDE

Answer:

3rd option

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Here m = - [tex]\frac{5}{3}[/tex] and c = - 3 , then

y = - [tex]\frac{5}{3}[/tex] x - 3 ← equation of line

Answer:

62 square feet

Step-by-step explanation:

9 x 8 = 72

5 x 2 = 10

72 - 10 = 62

Answer:

option D

because every length is one fifth of the corresponding length of the bigger triangle

Answer:

As a statistical tool, a frequency distribution provides a visual representation for the distribution of observations within a particular test. Analysts often use frequency distribution to visualize or illustrate the data collected in a sample.

Answer:

a) cosA=5/13   b) sinA=12/13

Step-by-step explanation:

Look at the needed angle, then use SOHCAHTOA!

Answer:

cos A = 5/13,  sin A = 12/13

Step-by-step explanation:

Watch the picture for help.

sin A = a/c (According to the picture)

cos A = b/c (According to the picture)

Answer:

319,770 different task force groups might possibly be formed

Step-by-step explanation:

The order in which the members of the task force are chosen is not important, which means that the combinations formula is used to solve this question.

Combinations formula:

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

In this question:

Groups of 8 from a set of 22. So

[tex]C_{22,8} = \frac{22!}{8!(22-8)!} = 319770[/tex]

319,770 different task force groups might possibly be formed

Answer:                                                                                                                                                      

2                                                                                                                                                       Step-by-step explanation:

in the places there is X you put -3 , -3 squared minus 7 is equal to 9 , 9-7 is equal to 2

Answer:

[tex] \large{ \tt{❃ \: EXPLANATION}} : [/tex]

[tex] \large{ \tt{❁ \: LET'S \: START}} : [/tex]

[tex] \large{ \tt{⋆ \: f( - 3) = {( - 3)}^{2} - 7}}[/tex]

[tex] \large{ \tt{↦ \: f( - 3) = ( - 3) \times ( - 3) - 7}}[/tex]

[tex] \large{ \tt{↦f( - 3) = 9 - 7}}[/tex]

[tex]↦ \large{ \tt{f( - 3) = \boxed{ \tt{2}}}}[/tex]

[tex] \tt{✺ \: COMFORT \: IS \: THE \: ENEMY \: OF \: ACHIEVEMENT\: ♪}[/tex]

♡ Hope I helped! ♕

☃Have a wonderful day / evening ! ☼

# StayInAndExplore ! ☂

▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁

Answer:

B

Step-by-step explanation:

[tex]m = \frac{0 - ( - 2)}{ - 2 - 0} = - 1[/tex]

use the point (-5,3)

y-3=-(x-(-5)) = y-3= -(x+5)

Answer: B. y - 3 = -(x + 5)

Step-by-step explanation:

Find two easy points on the graph to calculate the slope:

The slope is calculated using [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1}}[/tex], so substitute in the values:

[tex](x_{1}, y_{1}) = (-2, 0)\\(x_{2}, y_{2}) = (0, -2)\\ \frac{y_{2}-y_{1} }{x_{2}-x_{1}} =\frac{(-2)-0}{0-(-2)} =\frac{-2}{0+2} =\frac{-2}{2} =-1[/tex]

The y-intercept is where it intersects the y-axis. It's -2.

Therefore, if you put it together, the function would be y = -x - 2                    

Solve each answer choices and find the one that matches the function:

B.[tex]y-3=-(x+5)\\y-3=-x-5\\y=-x-5+3\\y=-x-2[/tex]

Answer:

B = 31.6

Step-by-step explanation:

Since this is a right triangle, we can use trig functions

tan B = opp / adj

tan B = 28.2 / 45.8

taking the inverse tan of each side

tan ^ -1 ( tan B) = tan ^-1 (28.2/45.8)

B =31.62145

Rounding to the nearest tenth

B = 31.6

Answer:

we use side of triangle to find area and divide by 2 so first one is 15*15+ 8*15/2 225+60=285

Answer:

David had x amount of M&M's. He then ate 15 of them for snack. Now David only has 35 M&M's left. How many M&M's did David have in the beginning?

Step-by-step explanation:

Answer:

X= 20

Step-by-step explanation:

Hannah has 35 marbles. Hannah gives away 15 marbles. How many marbles does Hannah have left? Solve the equation X- 15=35.

Answer:

(a): The 95% confidence interval is (46.4, 53.6)

(b): The 95% confidence interval is (47.9, 52.1)

(c): Larger sample gives a smaller margin of error.

Step-by-step explanation:

Given

[tex]n = 30[/tex] -- sample size

[tex]\bar x = 50[/tex] -- sample mean

[tex]\sigma = 10[/tex] --- sample standard deviation

Solving (a): The confidence interval of the population mean

Calculate the standard error

[tex]\sigma_x = \frac{\sigma}{\sqrt n}[/tex]

[tex]\sigma_x = \frac{10}{\sqrt {30}}[/tex]

[tex]\sigma_x = \frac{10}{5.478}[/tex]

[tex]\sigma_x = 1.825[/tex]

The 95% confidence interval for the z value is:

[tex]z = 1.960[/tex]

Calculate margin of error (E)

[tex]E = z * \sigma_x[/tex]

[tex]E = 1.960 * 1.825[/tex]

[tex]E = 3.577[/tex]

The confidence bound is:

[tex]Lower = \bar x - E[/tex]

[tex]Lower = 50 - 3.577[/tex]

[tex]Lower = 46.423[/tex]

[tex]Lower = 46.4[/tex] --- approximated

[tex]Upper = \bar x + E[/tex]

[tex]Upper = 50 + 3.577[/tex]

[tex]Upper = 53.577[/tex]

[tex]Upper = 53.6[/tex] --- approximated

So, the 95% confidence interval is (46.4, 53.6)

Solving (b): The confidence interval of the population mean if mean = 90

First, calculate the standard error of the mean

[tex]\sigma_x = \frac{\sigma}{\sqrt n}[/tex]

[tex]\sigma_x = \frac{10}{\sqrt {90}}[/tex]

[tex]\sigma_x = \frac{10}{9.49}[/tex]

[tex]\sigma_x = 1.054[/tex]

The 95% confidence interval for the z value is:

[tex]z = 1.960[/tex]

Calculate margin of error (E)

[tex]E = z * \sigma_x[/tex]

[tex]E = 1.960 * 1.054[/tex]

[tex]E = 2.06584[/tex]

The confidence bound is:

[tex]Lower = \bar x - E[/tex]

[tex]Lower = 50 - 2.06584[/tex]

[tex]Lower = 47.93416[/tex]

[tex]Lower = 47.9[/tex] --- approximated

[tex]Upper = \bar x + E[/tex]

[tex]Upper = 50 + 2.06584[/tex]

[tex]Upper = 52.06584[/tex]

[tex]Upper = 52.1[/tex] --- approximated

So, the 95% confidence interval is (47.9, 52.1)

Solving (c): Effect of larger sample size on margin of error

In (a), we have:

[tex]n = 30[/tex]     [tex]E = 3.577[/tex]

In (b), we have:

[tex]n = 90[/tex]    [tex]E = 2.06584[/tex]

Notice that the margin of error decreases when the sample size increases.

Answer:

ANS.1

Freshmen F = 32

Sophomore S = 48

Total students = 80 students

P(F) = Favorables cases/Total cases

   = 32/80

Hope this helps!

Answer:

32/80 or 2/5 simplified

Step-by-step explanation:

P(Freshman) = 32/80 or 2/5 simplified

Answer:

The p-value of the test is 0.1314 > 0.05, which means that it cannot be concluded at the .05 level of significance that a lower proportion of men favor stricter gun control than women

Step-by-step explanation:

Before solving the question, we need to understand the central limit theorem, and subtraction of normal variables.

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.

Test if a lower proportion of men favor stricter gun control than women:

At the null hypothesis, we test if the proportion is the same, that is, the difference of the proportions if 0. So

[tex]H_0: p_M - p_W = 0[/tex]

At the alternative hypothesis, we test if it is less, that is, the subtraction of the proportions is negative. So

[tex]H_1: p_M - p_W < 0[/tex]

The test statistic is:

[tex]z = \frac{X - \mu}{s}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, and s is the standard error.

In a recent survey of gun control laws, a random sample of 564 women, 313 favored stricter gun control laws.

This means that:

[tex]p_W = \frac{313}{564} = 0.555[/tex]

[tex]s_W = \sqrt{\frac{0.555*0.445}{564}} = 0.0209[/tex]

In a random sample of 588 men, 307 favored stricter gun control laws.

This means that:

[tex]p_M = \frac{307}{588} = 0.522[/tex]

[tex]s_M = \sqrt{\frac{0.522*0.478}{588}} = 0.0206[/tex]

0 is tested at the null hypothesis:

This means that [tex]\mu = 0[/tex]

From the samples:

[tex]X = p_M - p_W = 0.522 - 0.555 = -0.033[/tex]

[tex]s = \sqrt{s_M^2+s_W^2} = \sqrt{0.0206^2+0.0209^2} = 0.029[/tex]

Value of the test statistic:

[tex]z = \frac{X - \mu}{s}[/tex]

[tex]z = \frac{-0.033 - 0}{0.029}[/tex]

[tex]z = -1.12[/tex]

P-value of the test and decision:

The p-value of the test is the probability of finding a sample proportion difference greater than 0.033, which is the p-value of z = -1.12.

Looking at the z-table, z = -1.12 has a p-value of 0.1314.

The p-value of the test is 0.1314 > 0.05, which means that it cannot be concluded at the .05 level of significance that a lower proportion of men favor stricter gun control than women

Answer:

No, it doesn't make sense, as we cannot have a negative population of owls.

Step-by-step explanation:

Obtaining a the quadratic model :

y = -1,34x2 - 10,75x - 11.3 ; by fitting the data above ;

To obtain the number of owls after 8 years, we have ;

y = -1,34x2 + 10,75x - 11.3

put x = 8 in the equation

y = -1,34(8)^2 + 10.75(8) - 11.3

y = - 85.76 + 86 - 11.3

y = - 11.06

y = - 11

This figure dies not make sense, as we cannot have a negative population of a certain specie such as owls at any given time.

Answer:

No, because you can't have a negative number of owls.

Step-by-step explanation:

Answer:

The rate of change of volume of the cone with respect to radius is [tex]\frac{2}{3}\pi\times rh\\[/tex].

Step-by-step explanation:

radius of come = r

height of cone = h

Volume of cone

[tex]V = \frac{1}{3}\pi\times r^2 h[/tex]

As the height is constant, the rate of change of volume with respect to radius is given by the derivative of volume with respect to radius.  

[tex]\frac{dV}{dr}=\frac{1}{3}\pi\times {2r}h\\\\\frac{dV}{dr}=\frac{2}{3}\pi\times rh\\\\[/tex]

Answer:

-5.5

Step-by-step explanation:

[tex]\frac{-7+-4}{2}\\\\\frac{-11}{2}\\\\-5.5[/tex]

Answer:

7 DAYS IN A WEEK

Step-by-step explanation:

MONDAY TUESDAY WEDNESDAY THURSDAY FRIDAY SATURDAY SUNDA

7 DAYS

Answer:

it depends... What is X in this situation?

Step-by-step explanation:

A week has seven days.

A day has one day..?

I dont know how to help you, Sorry

Answer:

[tex]y=-\frac{1}{4}x+2[/tex]

Step-by-step explanation:

Hi there!

What we need to know:

1) Determine the slope of line S using line R (m)

[tex]y=-\frac{1}{4} x+3[/tex]

We can identify clearly that the slope of the line is [tex]-\frac{1}{4}[/tex], as it is in the place of m. Because parallel lines always have the same slope, the slope of line S would also be [tex]-\frac{1}{4}[/tex]. Plug this into [tex]y=mx+b[/tex]:

[tex]y=-\frac{1}{4}x+b[/tex]

2) Determine the y-intercept of line S (b)

[tex]y=-\frac{1}{4}x+b[/tex]

Plug in the given point (-4,3) and solve for b

[tex]3=-\frac{1}{4}(-4)+b\\3=1+b[/tex]

Subtract 1 from both sides to isolate b

[tex]3-1=1+b-1\\2=b[/tex]

Therefore, the y-intercept is 2. Plug this back into [tex]y=-\frac{1}{4}x+b[/tex]:

[tex]y=-\frac{1}{4}x+2[/tex]

I hope this helps!