find the slope-intercept equation of the line passing through the point (2,1) with the slope of m=3

Answer:

1. The 99% confidence interval is from 941.527 to 958.473

2. The 99% confidence interval is from 933.054 to 966.946

3. The 99% confidence interval is from 916.108 to 983.892

Step-by-step explanation:

The confidence interval is given by

[tex]\text {confidence interval} = \bar{x} \pm MoE\\\\[/tex]

Where [tex]\bar{x}[/tex] is the sample mean and Margin of error is given by

[tex]$ MoE = t_{\alpha/2}(\frac{s}{\sqrt{n} } ) $ \\\\[/tex]

Where n is the sample size,

s is the sample standard deviation,

[tex]t_{\alpha/2[/tex] is the t-score corresponding to some confidence level

The t-score corresponding to 99% confidence level is

Significance level = α = 1 - 0.99 = 0.01/2 = 0.005

Degree of freedom = n - 1 = 13 - 1 = 12

From the t-table at α = 0.005 and DoF = 12

t-score = 3.055

1. 99% Confidence Interval when s = 10

The margin of error is

[tex]MoE = t_{\alpha/2}(\frac{s}{\sqrt{n} } ) \\\\MoE = 3.055\cdot \frac{10}{\sqrt{13} } \\\\MoE = 3.055\cdot 2.7735\\\\MoE = 8.473\\\\[/tex]

So the required 99% confidence interval is

[tex]\text {confidence interval} = \bar{x} \pm MoE\\\\\text {confidence interval} = 950 \pm 8.473\\\\\text {confidence interval} = 950 - 8.473, \: 950 + 8.473\\\\\text {confidence interval} = (941.527, \: 958.473)\\\\[/tex]

The 99% confidence interval is from 941.527 to 958.473

2. 99% Confidence Interval when s = 20

The margin of error is

[tex]MoE = t_{\alpha/2}(\frac{s}{\sqrt{n} } ) \\\\MoE = 3.055\cdot \frac{20}{\sqrt{13} } \\\\MoE = 3.055\cdot 5.547\\\\MoE = 16.946\\\\[/tex]

So the required 99% confidence interval is

[tex]\text {confidence interval} = \bar{x} \pm MoE\\\\\text {confidence interval} = 950 \pm 16.946\\\\\text {confidence interval} = 950 - 16.946, \: 950 + 16.946\\\\\text {confidence interval} = (933.054, \: 966.946)\\\\[/tex]

The 99% confidence interval is from 933.054 to 966.946

3. 99% Confidence Interval when s = 40

The margin of error is

[tex]MoE = t_{\alpha/2}(\frac{s}{\sqrt{n} } ) \\\\MoE = 3.055\cdot \frac{40}{\sqrt{13} } \\\\MoE = 3.055\cdot 11.094\\\\MoE = 33.892\\\\[/tex]

So the required 99% confidence interval is

[tex]\text {confidence interval} = \bar{x} \pm MoE\\\\\text {confidence interval} = 950 \pm 33.892\\\\\text {confidence interval} = 950 - 33.892, \: 950 + 33.892\\\\\text {confidence interval} = (916.108, \: 983.892)\\\\[/tex]

The 99% confidence interval is from 916.108 to 983.892

As the sample standard deviation increases, the range of confidence interval also increases.

Answer: graphing calculator!

Step-by-step explanation: if you’re looking for the square root of a # that isn’t a perfect square (ie. sqrt4, sqrt 36) then you have to use a calculator for that. however the idea behind square roots is just a # multiplied by itself to give the original #. just ask yourself “what can i multiply by itself to get the original number”. hope that helped !

Answer:

By multiplying the number by its power 2.

E.g= 4^2

Answer:

Step-by-step explanation:

A trapezoid and two rectangulars are in the  opening form of the geometric shapes and you should calculate their surface areas seperately which is:

Answer:

Total surface area  = 3744 cm^2

Step-by-step explanation:

All linear measurements are in cm

Surface area of BOTH bases

Ab = 2*  (12+29)*24/2

= 984

Circumference of base

Cb = (25+12+26+29)

= 92

Height of prism

H = 30  (given)

Surface area of sides of prism

As= Cb*H

= 2760

Total Surface area of Prism

A = Ab + As

= 984 + 2760

= 3744 cm^2

Answer:

m∠s = 93°

Step-by-step explanation:

We know that any quadrilateral's sum of angles adds up to 360°. In that case,

360 - (56 + 132 + 79) = m∠s

m∠s = 93°

Answer:

S° = 93 °

Step-by-step explanation:

[tex]The- diagram- is- a- trapezoid (quadrilateral)\\Sum- of- angles-in a- quadrilateral = 360\\ 132\° + 56\° + 79\° + x\° = 360\° \\267\° + x\° = 360\° \\x = 360 \° - 267 \° \\x\° = 93\°[/tex]

Answer:

jc is 40 i think

Step-by-step explanation:

Answer:

40(Maybe)

Step-by-step explanation:

I'm not 100% sure that 40 is correct but I'm pretty sure it is.

Answer:

884,375

Step-by-step explanation:

The first digit can't be 0, so there are 9×10⁵ = 900,000 possible six-digit numbers.

Of those, the number of six-digit numbers that have only odd digits is 5⁶ = 15,625.

Numbers with at least one even digit are all numbers that don't have only odd digits.  So the number of six-digit numbers with at least one even digit is:

900,000 − 15,625 = 884,375

Answer:

here the order will be 104! =[tex]1.029e^{166}[/tex]

Step-by-step explanation:

since the cards are to arranged in  no particular order that is why we used combination to find the result.

Combination can simply be explained as the method of selecting items from a collection of items where the order of the selections does not matter.

Answer:

Step-by-step explanation:

Let's solve this by eliminating z, then we'll go from there.

Add 6 times the second equation to the first.

  (3x -3y +6z) +6(x +2y -z) = (3) +6(4)

  9x +9y = 27 . . . simplify

  x + y = 3 . . . . . . divide by 9 [eq4]

Add 13 times the second equation to the third.

  (5x -8y +13z) +13(x +2y -z) = (2) +13(4)

  18x +18y = 54

  x + y = 3 . . . . . . divide by 18 [eq5]

Equations [eq4] and [eq5] are identical. This tells us the system is dependent, and has an infinite number of solutions. We can find them in terms of z:

  y = 3 -x . . . . solve eq5 for y

  x +2(3 -x) -z = 4 . . . . substitute into the second equation

  -x +6 -z = 4

  x = 2 - z . . . . . . add x-4

  y = 3 -(2 -z)

  y = z +1

So far, we have written the solutions in terms of z. If we use the parameter "a", we can write the solutions as ...

  x = 2 -a

  y = 1 +a

  z = a

_____

Check

First equation:

  3(2-a) -3(a+1) +6a = 3

  6 -3a -3a -3 +6a = 3 . . . true

Second equation:

  (2-a) +2(a+1) -a = 4

  2 -a +2a +2 -a = 4 . . . true

Third equation:

  5(2-a) -8(a+1) +13a = 2

  10 -5a -8a -8 +13a = 2 . . . true

Our solution checks algebraically.

Answer:

3c - 7

Step-by-step explanation:

c - the number of miles Lawrence biked

Tammy biked seven less than three times the number of miles that Lawrence biked.

So, 3 x c (the # of miles Lawrence biked) - 7 (she biked seven less)

The answer is 3c - 7.

Answer:

The time period is 13 years.

Step-by-step explanation:

Interest rate (r )= 5% or 5%/12 = 0.42% per months

The investment amount (Present value) = $10500

Final expected amount (future value) = $20000

Since we have given the initial amount and final amount. Therefore we have to calculate the time period for which the initial amount is kept in the bank.

Use the below formula to find the time period.

Future value = present value (1 + r )^n

20000 = 10500(1+0.0042)^n

1.9047619 = (1+0.0042)^n

1.9047619 = 1.0042^n

n = 153.74 months.

Time in years = 153.74 / 12 = 12.8 years or 13 years (round off)

Answer:

v = Δs/Δt

Step-by-step explanation:

Velocity is equal to the displacement/distance (delta symbol s) over the change of time (delta symbol t).

Answer:

Step-by-step explanation:

For private Institutions,

n = 20

Mean, x1 = (43120 + 28190 + 34490 + 20893 + 42984 + 34750 + 44897 + 32198 + 18432 + 33981 + 29498 + 31980 + 22764 + 54190 + 37756 + 30129 + 33980 + 47909 + 32200 + 38120)/20 = 34623.05

Standard deviation = √(summation(x - mean)²/n

Summation(x - mean)² = (43120 - 34623.05)^2+ (28190 - 34623.05)^2 + (34490 - 34623.05)^2 + (20893 - 34623.05)^2 + (42984 - 34623.05)^2 + (34750 - 34623.05)^2 + (44897 - 34623.05)^2 + (32198 - 34623.05)^2 + (18432 - 34623.05)^2 + (33981 - 34623.05)^2 + (29498 - 34623.05)^2 + (31980 - 34623.05)^2 + (22764 - 34623.05)^2 + (54190 - 34623.05)^2 + (37756 - 34623.05)^2 + (30129 - 34623.05)^2 + (33980 - 34623.05)^2 + (47909 - 34623.05)^2 + (32200 - 34623.05)^2 + (38120 - 34623.05)^2 = 1527829234.95

Standard deviation = √(1527829234.95/20

s1 = 8740.22

For public Institutions,

n = 20

Mean, x2 = (25469 + 19450 + 18347 + 28560 + 32592 + 21871 + 24120 + 27450 + 29100 + 21870 + 22650 + 29143 + 25379 + 23450 + 23871 + 28745 + 30120 + 21190 + 21540 + 26346)/20 = 25063.15

Summation(x - mean)² = (25469 - 25063.15)^2+ (19450 - 25063.15)^2 + (18347 - 25063.15)^2 + (28560 - 25063.15)^2 + (32592 - 25063.15)^2 + (21871 - 25063.15)^2 + (24120 - 25063.15)^2 + (27450 - 25063.15)^2 + (29100 - 25063.15)^2 + (21870 - 25063.15)^2 + (22650 - 25063.15)^2 + (29143 - 25063.15)^2 + (25379 - 25063.15)^2 + (23450 - 25063.15)^2 + (23871 - 25063.15)^2 + (28745 - 25063.15)^2 + (30120 - 25063.15)^2 + (21190 - 25063.15)^2 + (21540 - 25063.15)^2 + (26346 - 25063.15)^2 = 1527829234.95

Standard deviation = √(283738188.55/20

s2 = 3766.55

This is a test of 2 independent groups. Let μ1 be the mean out-of-state tuition for private institutions and μ2 be the mean out-of-state tuition for public institutions.

The random variable is μ1 - μ2 = difference in the mean out-of-state tuition for private institutions and the mean out-of-state tuition for public institutions.

We would set up the hypothesis. The correct option is

-B. H0: μ1 = μ2 ; H1: μ1 > μ2

Since sample standard deviation is known, we would determine the test statistic by using the t test. The formula is

(x1 - x2)/√(s1²/n1 + s2²/n2)

t = (34623.05 - 25063.15)/√(8740.22²/20 + 3766.55²/20)

t = 9559.9/2128.12528473889

t = 4.49

The formula for determining the degree of freedom is

df = [s1²/n1 + s2²/n2]²/(1/n1 - 1)(s1²/n1)² + (1/n2 - 1)(s2²/n2)²

df = [8740.22²/20 + 3766.55²/20]²/[(1/20 - 1)(8740.22²/20)² + (1/20 - 1)(3766.55²/20)²] = 20511091253953.727/794331719568.7114

df = 26

We would determine the probability value from the t test calculator. It becomes

p value = 0.000065

Since alpha, 0.01 > than the p value, 0.000065, then we would reject the null hypothesis. Therefore, at 1% significance level, the mean out-of-state tuition for private institutions is statistically significantly higher than public institutions.

Answer:

a) 294

b) 180

c) 75

d) 174

e) 105

Step-by-step explanation:

I assume that for each problem, the first digit can't be 0.

a) There are 6 digits that can be first, 7 digits that can be second, and 7 digits that can be third.

6×7×7 = 294

b) This time, no digit can be used twice, so there are 6 digits that can be first, 6 digits that can be second, and 5 digits that can be third.

6×6×5 = 180

c) Again, each digit can only be used once, but this time, the last digit must be odd.

If only the last digit is odd, there are 3×3×3 = 27 possible numbers.

If the first and last digits are odd, there are 3×4×2 = 24 possible numbers.

If the second and last digits are odd, there are 3×3×2 = 18 possible numbers.

If all three digits are odd, there are 3×2×1 = 6 possible numbers.

The total is 27 + 24 + 18 + 6 = 75.

d) If the first digit is 3, and the second digit is 3, there are 1×1×6 = 6 possible numbers.

If the first digit is 3, and the second digit is greater than 3, there are 1×3×7 = 21 possible numbers.

If the first digit is greater than 3, there are 3×7×7 = 147 numbers.

The total is 6 + 21 + 147 = 174.

e) If the first digit is 3, and the second digit is greater than 3, then there are 1×3×5 = 15 possible numbers.

If the second digit is greater than 3, there are 3×6×5 = 90 possible numbers.

The total is 15 + 90 = 105.

Answer:Domain is x and range is y.For ex:-4 is domain and -7 is range.

Step-by-step explanatioFeel pleasure to help u:

Domain ( -4, 5) Range ( -7, 6)

The Domain includes the numbers between the least and the greatest x-values.

The range includes the numbers between the lowest and the highest y-values.

Answer:0.0081  or 0.81%

Step-by-step explanation:

The required probability is P(3,5,0.1)= C5 3 * p^3*q^2, where

C5 3=  5!/3/2=4*5/2=10

p is the probability that one randomly selected calculator is defective= 10%=0.1

q is the probability that one randomly selected calculator is non-defective.

q=1-p=1-0.1=0.9

So P(3,5,0.1)= 10*0.1^3*0.9^2=0.01*0.81=0.0081

Answer:

1 + 6v

Step-by-step explanation:

1+5v+v​

Combine like terms

1 + 6v

Answer:

6v + 1

Step-by-step explanation:

1 + 5v + v

Apply rule : a = 1a

1 + 5v + 1v

Combine like terms.

5v + 1v + 1

(5 + 1)v + 1

(6)v + 1

6v + 1

Answer:

5

Step-by-step explanation:

(14 × 5 × 4) ÷ (28 × 2)

Solve brackets.

280 ÷ 56

Divide.

= 5

Answer:

sum of the angles of the triangle are 180°

Step-by-step explanation:

To find the sum of the interior angles, we use the formula( s-2*180), where s is the number of sides of the shape. If it is a pentagon, 5-2*180= 3*180= 540,

which shows that the sum of the interior angles of a pentagon is 540.

since, it is a triangle in the figure with 3 sides, 3-2*180=1*180=180.

The interior angles are unknown= a, b and c. we know that a+b+c=180 degrees and the exterior angles are mentioned. And we know that, opposite angles are equal. So, a is 40 degrees considering that 40 degrees is the opposite angle of a, b is 95 degrees whereas c is 45 degrees.

now, lets check if the angles indeed have a sum of 180 degrees,

40+95+45= 135+45 which gives 180 degrees.

Answer:

180°

Step-by-step explanation:

→ Angles in a triangles always add up to 180, we can prove this by calculating a, b and c so,

a = 40° (vertical angles are equal)

b = 95° (vertical angles are equal)

c = 45° (vertical angles are equal)

40 + 45 + 95 = 85 + 95 = 180°

Answer:

1/9

Step-by-step explanation:

first, u need 9 ---> 1/3

then u need 8 ---> 1/3 also

Multiply them and get...1/9

Answer:

3: 2

Step-by-step explanation:

game Apps: education apps:

3: 2

Answer:

here,

a=b+12

b=a-12----> equation (i)

b= c+4

putting the value of b from the equation (I)

a-12=c+4

a=c+4+12

a=c+16

hope this helps...

Good luck on your assignment...

The value of a + c is 16.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

a=b+12

So, b=a-12 ---- equation (i)

and, b= c+4

Substitute the value of b from the equation (I)

a-12=c+4

a=c+4+12

a=c+16

Hence, the value of a+ c is 16.

Learn more about Algebra here:

https://brainly.com/question/24875240

#SPJ2

Answer:

Option B

Step-by-step explanation:

Again, another great question! Here we are given the following system of equations, bound by quadrant 1 -

[tex]\begin{bmatrix}2x+7y\le \:70\\ 8x+4y\le \:136\end{bmatrix}[/tex]

Convert this to slope - intercept form -

[tex]\begin{bmatrix}y\le \frac{70-2x}{7}\\ y\le \:2\left(-x+17\right)\end{bmatrix}[/tex]

Now the graphed solution of this intersects at a shaded region with which there are 3 important point that lie on the border. They are the following -

( 0, 10 ),

( 15, 9 ),

( 17, 0 )

When these point are plugged into the main function f ( x, y ) = 2x + 6y, the point ( 15, 9 ) results in the greatest solution of 84. Thus, it is our maximum point -

Option B

Answer:

1370754

Step-by-step explanation:

From what I can see, you are probably studying combinations and permutations at the moment. Since this is a question about how many groups of five can be produced from a sample size of 46, the groups are random and not in order, which may rule for us to use the combination formula.

Once you compute this, this answer is basically saying that 1370754 groups of 5 can be created from a sample size of 46

Answer:

Step-by-step explanation:

A) The constant of proportionality in terms of minutes per bracelet is

15/3 = 5 minutes per bracelet

B) The constant of proportionality represents man hour rate

C) let k = constant of proportionality, t = time in minutes and b = number of bracelets produced. Therefore,

t = kb

D) the constant of proportionality in terms of number of bracelets per minute is

3/15 = 1/5

E) The constant of proportionality represents production rate

F) let k = constant of proportionality, t = time in minutes and b = number of bracelets produced. Therefore,

b = kt

G) The constants of proportionality are reciprocals

H) Two equations are equivalent if they have the same solution. They are not equivalent. By inputting the different values of k, the solutions will always be the same. Therefore, they are equivalent.

Answer:the sample answers, change them up so you dont get in trouble

A To find the constant of proportionality in minutes per bracelet, divide the total time by the number of bracelets:

constant of proportionality=15 MINUTES/3 BRACELETS=5  minutes per bracelet.

B The proportionality constant of 5 minutes per bracelet means it takes Olivia 5 minutes to make 1 bracelet.

C Here’s one way to set up the equation:

time = constant of proportionality × number of bracelets

Let m be time in minutes and let b be the number of bracelets. Substitute the variables (m and b) and the value of the proportionality constant (5 minutes per bracelet) into the equation: m = 5b.

thats all ik srry

Step-by-step explanation:

Answer:

A)x=2pi/3 and x=-2pi/3

Step-by-step explanation:

The function [tex]y=\frac{5}{3}tan(\frac{3}{4}x)[/tex] has vertical asymptotes in the values where the tan(a) has vertical asymptotes.

we know that tan(a) has vertical asymptotes in [tex]a=\frac{\pi }{2}[/tex] and  [tex]a=\frac{-\pi }{2}[/tex], if we made [tex]a=\frac{3x}{4}[/tex] and solve for x, we get:

for [tex]a=\frac{\pi }{2}[/tex]

[tex]\frac{\pi }{2} =\frac{3x}{4}\\x = \frac{2\pi }{3}[/tex]

for [tex]a=\frac{-\pi }{2}[/tex]

[tex]\frac{-\pi }{2} =\frac{3x}{4}\\x = \frac{-2\pi }{3}[/tex]

Finally, the function [tex]y=\frac{5}{3}tan(\frac{3}{4}x)[/tex] has vertical asymptotes in the values x=2pi/3 and x=-2pi/3

Answer:

A

Step-by-step explanation:

Hey there! :)

Answer:

56 m².

Step-by-step explanation:

To find the area, simply split the figure into a triangle and rectangle. Solve for the areas separately:

Solve for the rectangle: (A = l × w)

A = 8 × 5

A = 40 m²

Solve for the triangle: (A = 1/2 (bh))

A = 1/2(4 · 8)

A = 1/2(32)

A = 16 m².

Add up the two areas:

40 + 16 = 56 m².

Answer:

Area of triangle+ the area of rectangle

Step-by-step explanation:

Since, area of triangle is 1/2×base×height in right angled triangle, 1/2×4×8: 1/2×32= 16m²

Area of rectangle is length × breadth= 5×8: 40 m²

Area of the shape is 40m²+16m²= 56m²

Answer:

[tex]r \approx 2.41\%[/tex]

Step-by-step explanation:

The computation of the approximate new interest rate is shown below:

As we know that there are four quarters in a year so

The new equation is

[tex]A = 250(1 + r)^{4t}[/tex]

Now to determine the value of interest rate,i.e r, so place this to the first equation.

So,

[tex]250(1.1)^{t} = 250(1 + r)^{4t}[/tex]

[tex]1.1^{t} = (1 + r)^{4t}[/tex]

1.1 = (1 + r)^4

[tex]\sqrt[4]{1.1} = 1 + r[/tex]

[tex]r = -1 + \sqrt[4]{1.1}[/tex]

[tex]r \approx 0.0241[/tex]

[tex]r \approx 2.41\%[/tex]

We simply applied the above formula so that the interest rate could come

Answer:

29.4

Step-by-step explanation:

Answer:

2.94

Step-by-step explanation:

4.2 × 0.7 = 2.94

Answer:

1140 ways.

Step-by-step explanation:

The applicable formula is: (n +r - 1)C(r-1), where n is the number of identical items (the candies), and r is the possible number of recipients (the kids).

The 17 identical candies, can be distributed among the 4 children in :  

=(17 + 4 - 1)C(4–1) = 20C3 ways.

= 20!/((20–3)!*3!) ways.

= 20*19*18*17!/(17!*(3*2*1)) = 20*19*18/6 ways

= 20*19*3 ways.  

=1140 ways.

Answer: 20 cm

If quadrilaterals WXYZ and BADC are congruent, then their corresponding sides are congruent.

Given that

WX≅DC,

XY≅BC,

you can state that

YZ≅AB,

WZ≅AD.

If AD = 4 cm and AB = 6 cm, then WZ = 4 cm and YZ = 6 cm. Opposite rectangle sides are congruent, then XY = 4 cm and WX = 6 cm.

The perimeter of WXYZ is

P = WX + XY + YZ + WZ = 6 + 4 + 6 + 4 = 20 cm.