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F(x)= 3x^2 +12x+5

We have been given that a of sofa prices are normally distributed with a mean of 2500 dollars and a standard deviation of 200 dollars.  A leather sofa has a price of 2410 dollars. We are asked to find the proportion of sofa prices that are higher than the price of the leather sofa.

First of all, we will find the z-score corresponding to sample score 2410.

[tex]z=\frac{x-\mu}{\sigma}[/tex]

[tex]z=\frac{2410-2500}{200}[/tex]

[tex]z=\frac{-90}{200}[/tex]

[tex]z=-0.45[/tex]

Now we need to find area under normal curve that is greater than z-score of [tex]-0.45[/tex] that is [tex]P(z>-0.45)[/tex].

Using formula [tex]P(z>a)=1-P(z<a)[/tex], we will get:

[tex]P(z>-0.45)=1-P(z<-0.45)[/tex]

Now we will find area under curve using normal distribution table.

[tex]P(z>-0.45)=1-0.32636[/tex]

[tex]P(z>-0.45)=0.67364[/tex]

Upon rounding to 4 decimal places, we will get:

[tex]P(z>-0.45)\approx 0.6736[/tex]

Therefore, approximately 0.6736 of sofa prices are higher than the price of the leather sofa.

Answer:

0.6736

Step-by-step explanation:

khan academy

Answer:

cos Θ = [tex]\frac{4}{\sqrt{41} }[/tex]

Step-by-step explanation:

Given the angle passes through (4, 5 ) then the right triangle with sides 4 and 5 has hypotenuse h given by

h² = 4² + 5² = 16 + 25 = 41 ( take the square root of both sides )

h = [tex]\sqrt{41}[/tex]

In relation to Θ, 4 is adjacent and 5 is opposite, thus

cos Θ = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{4}{\sqrt{41} }[/tex]

Answer: 4√41/41

Step-by-step explanation:

Answer:

csc Θ = [tex]\frac{17}{15}[/tex]

Step-by-step explanation:

Given

tan Θ = - [tex]\frac{15}{8}[/tex] = [tex]\frac{opposite}{adjacent}[/tex] ← of a right triangle , then

hypotenuse h² = 15² + 8² = 225 + 64 = 289 ( square root both sides )

h = [tex]\sqrt{289}[/tex] = 17

Using the identity

csc x = [tex]\frac{1}{sinx}[/tex]

sin Θ = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{15}{17}[/tex]

Since Θ is in second quadrant then sinΘ and csc Θ > 0, thus

csc Θ = [tex]\frac{1}{\frac{15}{17} }[/tex] = [tex]\frac{17}{15}[/tex]

Answer:

You could have a square with side of 50 ft.

Step-by-step explanation:

Answer:

Step-by-step explanation:

If you think money, a question like this won't confuse you.

Which would you rather owe your parents

13 dollars or

10 dollars

The answer is obvious, isn't it? Most people would rather owe 10 dollars rather than 13.

The minus sign is the same as debt. - 13 is less than - 10. You are further and further in the hole when you owe 13 dollars than 10.

So the inequality is not correct. The answer is no.

So still with money

-13<- 11

13 > 11

you would rather have 13 dollars in your pocket than 10.

You would rather owe -10 dollars than - 13

Answer:

start at the origin (0,0) then move up 5 (Don't count the origin as the first move up). Now your point is (0,5)

Step-by-step explanation:

Look at the image below.

This is how you graph y=5

Answer:

55.4 m^3

Step-by-step explanation:

The volume of a pyramid of base area A and height h is V = (1/3)(A)(h).

Here, V = (1/3)(16.6 m)^2 * 10.1 m  = 55.4 m^3

Answer:

55.4 m^3

Step-by-step explanation:

Answer:

X = -12

Step-by-step explanation:

-10X + 1 +7X = 37

-10X + 7X + 1 = 37  {Add the like terms}

-3X + 1 = 37  {Subtract 1 form both sides}

-3X + 1 -1 = 37 -1

-3X = 36  {Divide both sides by (-3)}

[tex]\frac{-3x}{-3}=\frac{36}{-3}\\\\[/tex]

X = -12

Answer:

-12

Step-by-step explanation:

Answer:

113.04 meters

Step-by-step explanation:

pi*r^2

3.14*6*6= 113.04

Answer:

The Answer is 113.1m²

Step-by-step explanation:

Area is πr²

Sprinkler shoots 6m

a = π6²

a = 3.14 * 36

area is 113.1m²

Answer:

1km = 1000m

=> 60km = 60 x 1000 = 60000m

=> Option A is correct.

Hope this helps!

:)

Answer:

1/12piX^3

Step-by-step explanation:

Answer:

48

Step-by-step explanation:

64 times 0.75 is 48

Answer:

The volume of the cone is:

Step-by-step explanation:

The volume of a cone is:

Where:

r = radius.

h = height.

Since the exercise provides the diameter but not the radius, you simply have to divide the diameter in two:

Now we proceed to replace in the formula:

Answer:

$20

Step-by-step explanation:

Answer:

38

Step-by-step explanation:

j/-2=-19

j=38

Answer:

38

Step-by-step explanation:

J/-2+7=-12

     -7     -7

J/-2       -19

 x-2      x-2

J=          38

I was trying to edit but it kept saying "an error occured"

I'm sorry

Answer:

Angle pairs formed by parallel lines cut by a transversal When two parallel lines are given in a figure, there are two main areas: the interior and the exterior. When two parallel lines are cut by a third line, the third line is called the transversal.

Step-by-step explanation:

Answer:

Step-by-step explanation:

If a transversal intersects two parallel lines, then each pair of interior angles on the same side of the transversal is supplementary, i.e. they add up to 180°.

Answer:

a) A triangle which the angles ratio is 1 : 2 : 3 is a 30º - 60º - 90º right triangle.

b) The shortest side is opposite to the shortest angle. So, we can calculate it using sin 30º.

[tex]$\text{sin}(30\º)=\frac{\text{Opposite side to x}}{19} $[/tex]

[tex]$\frac{1}{2} =\frac{\text{Opposite side to x}}{19} $[/tex]

[tex]$\text{Opposite side to x}= 9.5$[/tex]

Answer:

see explanation

Step-by-step explanation:

(a)

Sum the parts of the ratio, 1 + 2 + 3 = 6 parts

Divide 180° ( sum of angles in a triangle ) by 6 to find the value of one part of the ratio.

180° ÷ 6 = 30° ← value of 1 part of the ratio, thus

2 parts = 2 × 30° = 60°

3 parts = 3 × 30° = 90°

Thus the triangle is right

-----------------------------------------

(b)

The sides of a 90°- 60°- 30° triangle are in the ratio

2 - [tex]\sqrt{3}[/tex] - 1 ( where 2 represents the hypotenuse )

Thus the other 2 sides of the triangle are

19 ÷ 2 = 9.5 , and

9.5 × [tex]\sqrt{3}[/tex] ≈ 16.45

The shortest side is 9.5

Answer:

Step-by-step explanation:

Answer:

try and put them do in order

Step-by-step explanation:

Thanks for coming to us with your question. I know this answer is quite late, but hopefully it'll be helpful to others.

Answer:

False --> 1011 > 1100

True --> 110 + 111 == 1101

50 --> 1010 x 101

13 --> 110 + 111

17 --> 1010101 / 101

Step-by-step explanation:

This solution is achieved by calculating the binary operations, then finding either their values or the validity of their statements.

1011 > 1100 is the same as 11 > 12, which is false.

110 + 111 == 1101 is the same as 6 + 7 = 13, which is true.

1010 x 101 is the same as 10 x 5, which is 50.

110 + 111 is the same as 6 + 7, which is 13.

1010101 / 101 is the same as 85 / 5, which is 17.

Answer:

Linear

Step-by-step explanation:

We see that in the left column, the integers increase by one at a time and that in the right column, the integers decrease by two at a time. Therefore, the rate of the increasing and decreasing of numbers is the same throughout the table so this line is linear.

Also, you could use desmos, a graphing calculator which is free on your computer to plot these points and to see that the line is linear.

Answer:

A

Step-by-step explanation:

Answer:

The answer is B.

Step-by-step explanation:

Because you have your slope (4.20) it doesn't matter what it is just as long as it is there.

THEORETICAL probability is the predicted ratio of favorable outcomes to the total number of outcomes.

Answer:

30%

Step-by-step explanation:

Answer:

x = 126/999

Step-by-step explanation:

Let x = .126126126 repeating

Multiply each side by 1000

1000x = 126.126126126 repeating

subtract the first equation from the second

1000x = 126.126126126 repeating

- x = .126126126 repeating

999x = 126

Divide each side by 999

999x/999 = 126/999

x = 126/999

Answer:

length of each side is 17cm

Answer: length of each side is 17cm

Step-by-step explanation:hoped this helped

Answer:

slope = 6

y-intercept = -5

Step-by-step explanation:

The equation is in slope-intercept form:

y = mx + b

where m is the slope and b is the y-intercept

Let's find the slope:

The slope is the number being multiplied by x.

y = mx + b

y = 6x - 5

Therefore, the slope is 6.

Let's find the y-intercept:

The y-intercept is the last number in the equation.

y = mx + b

y = 6x -5

Therefore, the y-intercept is -5.

Answer:

C

Step-by-step explanation:

Since the figures have equal perimeters we can equate them, thus

4(2p - 4) = 4p + 36 ← distribute left side

8p - 16 = 4p + 36 ( subtract 4p from both sides )

4p - 16 = 36 ( add 16 to both sides )

4p = 52 ( divide both sides by 4 )

p = 13

Substitute p = 13 into either of the 2 expressions, then

4p + 36 = 4(13) + 36 = 52 + 38 = 88 → C

The value of perimeter is found as 88 units. The correct option is (C).

A linear equation for the given case can be written by assuming any variable as the unknown quantity. Then, as per the given data the required operations are done and it is equated to some value.

As per the question the perimeters are equal.

The following equation can be written as,

4(2p - 4) = 4p + 36

⇒ 8p - 16 = 4p + 36

⇒ 4p = 52

⇒ p = 13

Thus, the perimeter value can be obtained by substituting p = 13 in 4p + 36 as below,

⇒ 4 × 13 + 36 = 88

Hence, the perimeter value is 88 units.

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Answer: True

Step-by-step explanation: the angle subtends, s, divided by the radius of the circle, r. One radian is the central angle that subtends an arc length of one radius (s = r). Since all circles are similar, one radian is the same value for all circles.

The given statement is correct. If an angle has a measure of one radian, the arc intercepted by that angle has an arc length equal to the radius of the circle.

Therefore,

Because the Latin word for length is spatium, arc lengths are denoted by s.

Length of an Arc = θ × r,

Where θ exists in radian.

Length of an Arc = θ × (π/180) × r,

Where θ exists in degree

To learn more about Arc length, refer to:

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