Two lines defined by the equations $y = mx + 4$ and $y = 3x + b$, where $m$ and $b$ are constants, intersect at the point $(6, 10)$. What is the value of $b + m$?

Answer:

80% confidence interval for the proportion of homes that are "eclectic" is [0.59 , 0.78].

Step-by-step explanation:

We are given that James takes a random sample of 42 homes form the Austin MLS (that's where Realtors go for information) and finds that 29 of them are listed as "eclectic" style.

Firstly, the pivotal quantity for 80% confidence interval for the population proportion is given by;

                              P.Q. =  [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex]  ~ N(0,1)

where, [tex]\hat p[/tex] = sample proportion of homes that are "eclectic" = [tex]\frac{29}{42}[/tex] = 0.69

            n = sample of homes = 42

            [tex]\mu[/tex] = population proportion of homes that are "eclectic"

Here for constructing 80% confidence interval we have used One-sample z proportion statistics.

So, 80% confidence interval for the population proportion, p is ;

P(-1.282 < N(0,1) < 1.282) = 0.80  {As the critical value of z at 10% level

                                                     of significance are -1.282 & 1.282}  

P(-1.282 < [tex]\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] < 1.282) = 0.80

P( [tex]-1.282 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] < [tex]{\hat p-p}[/tex] < [tex]1.282 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ) = 0.80

P( [tex]\hat p-1.282 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] < p < [tex]\hat p+1.282 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex] ) = 0.80

80% confidence interval for p = [ [tex]\hat p-1.282 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex],[tex]\hat p+1.282 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }[/tex]]

= [ [tex]0.69-1.282 \times {\sqrt{\frac{0.69(1-0.69)}{42} } }[/tex] , [tex]0.69+1.282 \times {\sqrt{\frac{0.69(1-0.69)}{42} } }[/tex] ]

= [0.59 , 0.78]

Therefore, 80% confidence interval for the proportion of homes that are "eclectic" is [0.59 , 0.78].

Answer:

y = 4x-7

Step-by-step explanation:

We have a slope and a point

m = 4    (2,1)

Using the slope intercept form of the equation

y = mx+b

y = 4x+b

From the point x=2 and y =1

1 = 4(2)+b

1 = 8+b

Subtract 8 from each side

1-8 =8-8+b

-7 = b

We can write the equation by using m=4 and b = -7

y = 4x-7

Answer:

y = 4x - 7

Step-by-step explanation:

y = mx + b

y = 4x + b

1 = 4(2) + b

b = 1 - 8

b = -7

y = 4x - 7

Find the difference:

$127 - $85 = $42

Divide the difference by the original price:

42 / 127 = 0.3307

Rounded to 2 decimal places = 0.33

Multiply by 100:

0.33 * 100 = 33% decrease

Answer: it was reduced by 33%

Step-by-step explanation:

127x0.67 is 85.09 which is about 33%

Answer:

1/10

Step-by-step explanation:

So first we need to find the probability of the cards, there is 5 cards and one card needs to be chosen, so the probability is 1/5

Then we need to find the probability of the dice, there is 3 even numbers in 1,2,3,4,5,and 6, so the probablity is 3/6 which is also equal to 1/2

Finaly we need to multiply 1/5 with 1/2, which is 1/10

Answer:

infinitely many solutions

Step-by-step explanation:

x + 6y = -5

3x + 18y = -15

Multiply the first equation by 3

3(x + 6y) = -5*3

3x + 18y = -15

The two equations are identical.  This means they have infinite solutions along the line x+6y = -5

Answer:

5,5

Step-by-step explanation:

(5, 5)

This is very correctamundo

Answer:

4.5

Step-by-step explanation:

It's the right answer 2 is wrong.

The value of the third-term arithmetic sequence will be 4.5. Then the correct option is A.

A series of integers called an arithmetic succession or arithmetic chain of events has a fixed difference between the terms.

Let a₁ be the first term and d be a common difference.

Then the nth term of the arithmetic sequence is given as,

aₙ = a₁ + (n - 1)d

From the graph, the first term is 1.5 and the common difference is given as,

d = 3 - 1.5

d = 1.5

Then the arithmetic equation is given as,

aₙ = 1.5 + (n - 1)(1.5)

The value of the third term will be given as,

a₃ = 1.5 + (3 - 1)(1.5)

a₃ = 1.5 + 3

a₃ = 4.5

The value of the third-term arithmetic sequence will be 4.5. Then the correct option is A.

More about the arithmetic sequence link is given below.

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A "triangle" with the angles 0, 90, and 90 degrees cannot be considered a triangle since the two 90 degree angles make a right angle, and 0 degrees would mean a flat line. Rather it would resemble something like a straight U that is stretched sideways.

Final answer:

A figure with angles of 0, 90, and 90 degrees cannot be considered a triangle because the angles must sum to 180 degrees and each angle must be greater than 0 degrees and less than 180 degrees to form a three-sided figure.

Explanation:

A triangle is defined as a three sided figure lying on a plane, with three angles that add up to 180 degrees. In the case of the angles provided (0, 90, and 90), they do not add up to 180 degrees; instead, they sum up to 180 degrees if you exclude the 0-degree angle, which cannot be a valid angle for a triangle since every angle in a triangle must be greater than 0 degrees and less than 180 degrees. Therefore, a figure with angles of 0, 90, and 90 degrees cannot be considered a triangle.

In addition, the shape with two 90-degree angles would be a straight line, which does not meet the criteria of a triangle having three sides. An example of a valid right-angled triangle is one having angles of 90, 45, and 45 degrees, which correctly sum up to 180 degrees and form a closed three-sided figure.

Answer:

x = 8 inches length

Step-by-step explanation:

Dimension of box:

12 inches  by 2 inches by length x

with total surface area = 272 square inches,

There are 6 faces.

Area =  2 *(12 * 2) + 2 *(2*x) + 2 *(12*x)

Area = 272 sq. in.  = 48 + 4x + 24x

272 = 48 + 28x

272 - 48 = 28x

224 = 28x

x = 8 inches

To find the length of the box, use the surface area formula of a rectangular prism and solve for the length. The length of the box is 59 inches.

To find the length of the box, we need to calculate the dimensions of the cereal box. The surface area of a rectangular prism is given by the formula: Surface Area = 2lw + 2lh + 2wh, where l is the length, w is the width, and h is the height of the box. From the given information, we have:

12(2) + 12(1) + 2(2)x = 272

Simplifying the equation gives us: 24 + 12 + 4x = 272

Combining like terms, we have 4x + 36 = 272. Subtracting 36 from both sides gives us 4x = 236. Finally, dividing by 4 gives us x = 59.

Therefore, the length of the box is 59 inches.

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Answer: there is no picture so can you eidt it and show it please

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

i did it on egunity i know u hate it as much as i do....

Answer:

B

Step-by-step explanation:

Answer:

True

Step-by-step explanation:

Answer: no, it does not mean the same thing

Answer:  No, a millimeter is much smaller than a meter.

Step-by-step explanation:

Answer:

answers are highlighted below!   I hope this helps! please do not copy my work!   ^-^     :)

Step-by-step explanation:

okay, on the first one we are told we have 15% off of $729.99

which then takes off about $109.50

after we subtract the $109.50 from the $729.99 we are left with $620.49, that's not including tax

sales ax is 8.25% or $51.19      that comes out to equal $671.69

so we can conclude that the big tv sale at the big box store is equal to the amount of $671.69

on the second one, its normally $699.99

we have the coupon  for $100 off of that price so that leaves us with $599.99

but we have the $50 charge for delivery. so now its at $649.99

now we need to determine the price after tax. the price of tax is $53.62

add the tax amount to $649.99 to get $703.61

$703.61

the initial price of the tv is $734.95

$150 in rebate (refund)

$734.95 - $150 = $584.95

now we need to find the price including the delivery cost

$584.95 + $35 = $619.95

now lets find the tax price

$51.15

After Tax Price: $671.10

The TV from the Electronic Warehouse is the best option. You pay only $671.10!  The prices from the two other stores are $703.61 and $671.69.

We are paying .59 cents less than one of the TV's, and we are also paying $32.51 less than the other TV! So the best option would be the TV from the Big Box store!

Answer:

can u take another picture

Step-by-step explanation:

Answer:

Area = 2375.83

Step-by-step explanation:

[tex]Area=\pi r^{2} \\Radius = Diameter/2\\r=55/2\\r=27.5\\Area=\pi(27.5)^{2} \\Area=2375.83[/tex]

Answer:

-8

Step-by-step explanation:

x less than or equals to -8

Answer:

If you are moving up the line toward the 0, the answer would be more than

If you are moving down the line, -72 would be more than -64.

Step-by-step explanation:

8 times negative 8 is -64     --- I think

Answer:

18/m - 3

Step-by-step explanation:

Answer:

The result for the volume of the cylinder:

[tex]V \approx452.389[/tex]

Step-by-step explanation:

-To find the volume of a cylinder, you need the formula:

[tex]V = \pi r^2 h[/tex]

-Use the radius and the height for the formula:

[tex]V = \pi 4^2 9[/tex]

-Then, you solve:

[tex]V = \pi 4^2 9[/tex]

[tex]V = \pi[/tex] × [tex]4^2[/tex] × [tex]9[/tex]

[tex]V = \pi[/tex] × [tex]16[/tex] × [tex]9[/tex]

[tex]V = \pi[/tex] × [tex]V = 144\pi \approx 452.389[/tex]

So, therefore, the volume is [tex]452.389[/tex] .

Answer: 37.5% of 24 = (9)

The number of students is an illustration of proportions

9 students that got a ride

From the question, we have:

Total = 24

37.5% of the 24 students walk to school.

So, the number of students that walk to school is:

Students = 37.5% * 24

Students = 9

One third of the walkers got a ride to school today from their parents.

So, the number of students that got a ride is:

Ride =1/3 * 9

Ride = 3

Hence, the number of students that got a ride 3

Read more about proportions at:

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Answer:

The vertex of the function is at (1,-25)

Step-by-step explanation:

I think your question missed key information, allow me to add in and hope it will fit the orginal one.

Part of the graph of the function f(x) = (x + 4)(x-6) is shown  below.

Which statements about the function are true? Select two

options.

The vertex of the function is at (1,-25).

The vertex of the function is at (1,-24).

The graph is increasing only on the interval -4< x < 6.

The graph is positive only on one interval, where x <-4.

The graph is negative on the entire interval  

My answer:

Given the factored form of the function:

f(x) = (x + 4)(x-6)

<=> f(x) = [tex]x^{2} - 2x -24[/tex]

We will convert to vertex form

<=> f(x) = ([tex]x^{2} - 2x +1[/tex]) - 25

<=> f(x) = [tex](x-1)^{2} -25[/tex]

=> the vertex of the function is: (1,-25)

We choose: a. The vertex of the function is at (1,-25)

Let analyse other possible answers:

c. The graph is increasing only on the interval -4< x < 6.

Because the parameter a =1 so the graph open up all over its domain and the vertex is the lowest point.

So the graph is increasing in the domain (1, +∞)

=> C is wrong

d. The graph is positive only on one interval, where x <-4

Wrong, The graph is positive only on one interval, where x > 6

e. The graph is negative on the entire interval

Wrong, The graph is negative only on one interval, where -4< x < 6.

Answer:

$19.60

Step-by-step explanation:

Take the amount and multiply by the tax rate to determine the sales tax

tax = 245 * 8%

Change to decimal form

tax =245*.08

     = 19.60

Answer:

$19.6

Step-by-step explanation:

8% of 245

8/100 × 245

19.6

Answer:

Faith means to believe in something you cannot see.

Step-by-step explanation:

An example can be oxygen. To a naked eye, you cannot see oxygen, yet you "believe" that it is there, or you have faith that there is oxygen around you to sustain you.

This is what faith is, the belief of something that you cannot see with the naked eye.

~

Answer:

Faith is a trust or confidence in a person, object, or concept.

Example:

"The dog remained faithful to his owner."

"They lost faith when he lied to them."

Answer:

They spent 9 weeks in Australia, 11 weeks in Japan and 7 weeks in Sweden.

Step-by-step explanation:

A rock group plans to travel for a total of 27 weeks, making three concert stops in Japan, Australia and Sweden.

Let the number of weeks spent in Sweden be s.

Let the number of weeks spent in Japan be j.

Let the number of weeks spent in Australia be a.

This means that:

s + j + a = 27___________(1)

They will be in Japan for 2 more weeks than they will be in Australia. This means that:

j = a + 2 ______________(2)

Their stay in Sweden will be 2 weeks shorter than that in Australia. This means that:

s = a - 2 ______________(3)

We can replace s and j in (1) with (2) and (3):

=> a - 2 + a + 2 + a = 27

Collecting like terms:

a + a + a - 2 + 2 = 27

3a = 27

a = 27 / 3 = 9

The number of weeks they will spend in Australia is 9 weeks.

Putting this value of a in (2) and (3):

j = 9 + 2 = 11

and

s = 9 - 2 = 7

Therefore, they will spend 11 weeks in Japan and 7 weeks in Sweden.

Answer:

-5a(2a^3+a-1)

Step-by-step explanation:

I factored -5a out of 5a -5a^2-10a^4

hope this helped you

Final answer:

The given expression 5a−5a²−10a⁴ is factored as a product by factoring out the common factors, resulting in 5a(1 - a - 2a³).

Explanation:

To write the expression 5a−5a²−10a⁴ as a product, we need to factor out the common factors in each term. The term with the lowest exponent in 'a' is '5a', which indicates we can factor out 'a' from the entire expression. However, we can also factor out a '5' since it is common to all terms. Here are the steps:

Doing this, we get: 5a(1 - a - 2a³)

The expression can now be expressed as the product of '5a' and '(1 - a - 2a³)'.

Answer:

A

Step-by-step explanation:

option A is correct,  2a³/b⁴ is expanded to log2+3loga-4logb

An expression is combination of variables, numbers and operators.

The given expression is 2a³/b⁴

We have to expand this by using logarithms.

logab=loga +log b

log(a/b)=loga-logb

log(2a³)/log(b⁴)

log2+loga³ - log(b⁴)

Another property of logarithm

logaˣ=xloga

log2+3loga-4logb

Hence, option A is correct,  2a³/b⁴ is log2+3loga-4logb

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Answer:

First one:

Subtract 3 and one-fifth from both sides of the equation

Step-by-step explanation:

3 and one-fifth + n = 9

3⅕ + n = 9

3⅕ + n - 3⅕ = 9 - 3⅕

n = 5⅘

Answer:

first choice

Step-by-step explanation:

give brainileast to the other guy plas