A truck driver is driving from Nome, Alaska to Death Valley, California. Because he is traveling between locations with extreme temperatures, he needs to check the weather continuously to make sure the gas in his truck remains in liquid form. The gas he uses freezes at −40° F and evaporates at 140° F.

Part A: Write an inequality to represent the temperatures at which the gas in the truck will remain in liquid form. (2 points)

Part B:Describe the graph of the inequality completely from Part A. Use terms such as open/closed circles and shading directions. Explain what the solutions to the inequality represent. (4 points)

Part C: In January 1989, the temperature in Nome, Alaska dropped to −49° F. Would the gas in the driver's truck have remained in liquid form so he could have driven on this day? Why or why not?

Answer:

No, Yes, No, No.

Step-by-step explanation:

"It is not the case that x is equal to 100." This means that x ≠ 100.

"x is not equal to 300." The problem has nothing to do with 300. We know that x ≠ 100, but the fact that x ≠ 300 doesn't prove or deny anything about the statement x ≠ 100.

"x is equal to 100." This is the complete opposite of the original statement! If x = 100, then this completely denies or negates the fact that x ≠ 100.

"It is not the case that x is equal to 400." Again, 400 has nothing to do with the statement x ≠ 100, so the statement neither proves nor denies the statement x ≠ 100.

"x is equal to 300." Same story: 300 has nothing to do with x ≠ 100, so it doesn't change anything about x ≠ 100.

Answer:

EVALUATE THE FUCTION WHEN: f (1/2 % 32)////////21+×_37- 4 = 37.2

EVALUATE THE FUNCTION WHEN f(3+38 x + formula of angle are = _1/2 decimals point 78.32)*/% =3( 92.03

Step-by-step explanation:

HOPE IT HELPS A LOT!!

Answer:

The answer will be, 105.26

Answer:

Step-by-step explanation:

Find the exact frequency table in the diagram attached. x is the midpoint of the interval f is the frequency. Using the formula below to find the mean;

\(\overline x = \frac{\sum fx}{\sum f} \\\)

\(\sum fx = (42*2)+(47*7)+(52*9)+(57*5)+(62*1)\\\sum fx = 84+329+468+285+62\\\sum fx = 1,228\\\sum f = 24\\\\\overline x = \frac{1,228}{24} \\\overline x = 51.17^{0} F\)

The mean of the frequency distribution compare to the actual mean of 50.7°F is 51.2°F(to nearest tenth)

Randy's error is in the first step of the division, where he subtracts 4x² instead of adding it. The correct subtraction should be: x³ + 2x² + 5x - 3

Randy made an error in the step where he subtracted (2x² - 2x + 1) from (2x² - 3x³ - 3x² + 7x - 3).

Instead of getting -x³ + 4x² + 6x - 4 as the result, he got 2x⁴ - 4x³ + 2x². This error occurred because he forgot to change the sign of all the terms in (x² - 2x + 1) when subtracting it from the polynomial.

It should be (3x³ - 2x² + 7x - 3) divided by (x² - 2x + 1).

Let me proceed with this corrected version of the question.

Randy divides (3x³ - 2x² + 7x - 3) by (x² - 2x + 1) as,
2x² + x + 3
____________
x² - 2x + 1) 3x³ - 2x² + 7x - 3
2x³ - 4x² + 2x
_____________
x³ - 2x² + 5x
x³ - 2x² + x
____________
-3x² + 4x - 3
-3x² + 6x - 3
___________
\(-2x^2\) + x - 3

3x³ - 2x² + 7x - 3
-(2x³ - 4x² + 2x)
______________
x³ + 2x² + 5x - 3

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Randy made an error while dividing (2x⁴ - 3x³ - 3x² + 7x - 3) by (x² - 2x + 1). He mistakenly subtracted intermediate results from zero instead of the original polynomial, leading to an incorrect division.

Randy made an error in his division of the polynomial (2x⁴ - 3x³ - 3x² + 7x - 3) by (x² - 2x + 1). Let's go through the division process step by step to identify the mistake:

Randy correctly started by dividing 2x⁴ by x², which gives him 2x² as the first term of the quotient.

He then multiplied (x² - 2x + 1) by 2x², which resulted in 2x⁴ - 4x³ + 2x². So far, so good.

Randy should have subtracted this result from the original polynomial (2x⁴ - 3x³ - 3x² + 7x - 3), but he mistakenly subtracted it from 0. The correct step should have been to subtract 2x⁴ - 4x³ + 2x² from (2x⁴ - 3x³ - 3x² + 7x - 3).

Here's the corrected division:

(2x⁴ - 3x³ - 3x² + 7x - 3) - (2x⁴ - 4x³ + 2x²) = -3x³ - 5x² + 7x - 3

Now, Randy should have continued the division by bringing down the next term, which is -3x², and repeated the process. However, he incorrectly moved to the next step without subtracting -3x³ - 5x² + 7x - 3 from (x² - 2x + 1).

So, Randy's error is that he failed to properly subtract the intermediate result from the original polynomial, causing the division process to go awry.

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rational + irrational = irrational

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

Proof:

The claim is that A+B = C where,

Because A is rational, we can write it like A = p/q for some integers p,q. The value of q cannot be zero.

Let's for a moment consider the opposite scenario and let's assume that A+B was rational. We'll prove that a contradiction arises from this (hence this is a proof by contradiction).

If A+B = C was rational, then C = r/s for some integers r,s. The s cannot be zero.

From there we can have these steps to isolate B

A+B = C

B = C - A

B = (r/s) - (p/q)

B = (rq - ps)/(qs)

B = (some integer)/(some other nonzero integer)

B = some rational number

But this directly contradicts B set up as an irrational number.

So if A is rational and B is irrational, then A+B cannot possibly be rational due to the proof by contradiction above. The only other possibility is that A+B must be irrational.

Answer:

Step-by-step explanation:

Use the order of operations to solve this problem.

\(\Longrightarrow: \sf{\sqrt{28-3(4)} }\)

Remove parentheses.

→ (4)=4

Rewrite the problem down.

\(\Longrightarrow:\sf{\sqrt{28-3*4} }\)

PEMDAS stands for:

→ 28-3*4

Multiply.

→ 3*4=12

→ 28-12

Subtract.

→ 28-12=16

\(\Longrightarrow:\sf{\sqrt{16} }\)

\(\Longrightarrow\sf{\sqrt{16}=4^2 }\)

Use the radical rule.

\(\Longrightarrow: \sf{4^2=\boxed{\sf{4}}\)

I hope this helps you! Let me know if my answer is wrong or not.

Answer:

\(\±4\)

Step-by-step explanation:

Given expression: \(\sqrt{28 - 3(4)}\)

Here, we can see that the terms, 28 and 3(4) are inside the root. Since the two terms are inside the root, we can subtract them. Therefore:

Usually, \(\sqrt{16}\) can also be written as \(\sqrt[2]{16}\). Therefore:

Therefore, the simplified expression is ±4.

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Answer:

see below

Step-by-step explanation:

every stage is 60m

stage one = -340+60 = -280

stage 2: -280 +60 = -220

stage 3: -220 +60 = -160

stage 4: -160+60 = -100

stage 5: -100+60= -40

stage 6: -40+60 =20

it'll take it 6 stages to fully surface

Answer:

Step-by-step explanation:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89,144,233,377,610,987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368, 75025, 121393, 196418, 317811, 514229, ... Can you figure out the next few numbers?

for (-3)^4, if there were more numbers in the parentheses, the exponent would apply to all numbers in the parentheses

for -3^4, the exponent would only apply the -3.

hope this helps!

Answer:

-3^4=-81 and (-3)^4=81

Step-by-step explanation:

Following the rules of PEMDAS you will do exponents before multiplcation.

A negative sign means that you are multiplying by -1.

-3^4 means you will raise 3 to the 4th power and then multiply by -1. So you will do 3^4 first which is 81 and then multiply by -1. Making the answer -81.

When you put parentheses around the -3 it means you are raising the entire -3 to the power of 4 instead of only the 3. So it will be -3*-3*-3*-3 which is 81.

The component form of the following vectors is Option A. V = (38.3, 32.1).

To find the component form of a vector given its magnitude and direction angle, we can use trigonometry.

The component form of a vector in two dimensions is represented as (x, y), where x is the horizontal component and y is the vertical component.

In this case, the magnitude of the vector is given as 50, and the direction angle θ is 50°. We can use this information to calculate the horizontal and vertical components.

The horizontal component (x) can be found using the formula x = magnitude * cos(θ), and the vertical component (y) can be found using y = magnitude * sin(θ).

Let's calculate the components:

x = 50 * cos(50°) ≈ 38.3

y = 50 * sin(50°) ≈ 32.1

Rounding the answers to the nearest tenth, we get the component form of the vector V as (38.3, 32.1).

Therefore, the correct answer is A. V = (38.3, 32.1).

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The question is incomplete. Find the full content below:

Find the component form of the following vectors. Round your answers to the tenth.

Magnitude of v = 50, direction angle θ = 50°

A. V = (38.3, 32.1)

B. V = (33.8, 31.2)

C. V = (32.1, 38.3)

D. V = (31.2, 33.8)

Answer:

0.6, 1.2, 1.8, _, _, _

1. 2.4

2. 3.0

3. 3.6

Step-by-step explanation:

You increase the number by .6 each time.

Answer:

X=6

Step-by-step explanation:

To find the answer you could do 21 - 15 and that gets you an answer of 6 and thats how to get your answer.

Answer:

centre = (5, - 6 ) , radius = 7

Step-by-step explanation:

the equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k ) are the coordinates of the centre and r is the radius

given

x² + y² - 10x + 12y + 12 = 0 ( subtract 12 from both sides )

x² + y² - 10x + 12y = - 12 ( collect terms in x/ y )

x² - 10x + y² + 12y = - 12

using the method of completing the square

add ( half the coefficient of the x/ y terms )² to both sides

x² + 2(- 5)x + 25 + y² + 2(6)y + 36 = - 12 + 25 + 36

(x - 5)² + (y + 6)² = 49 = 7² ← in standard form

with centre (5, - 6 ) and radius = 7

Answer:

Center = (5, -6)

Radius = 7

Step-by-step explanation:

To find the center and the radius of the circle represented by the given equation, rewrite the equation in standard form by completing the square.

To complete the square, begin by moving the constant to the right side of the equation and collecting like terms on the left side of the equation:

\(x^2-10x+y^2+12y=-12\)

Add the square of half the coefficient of the term in x and the term in y to both sides of the equation:

\(x^2-10x+\left(\dfrac{-10}{2}\right)^2+y^2+12y+\left(\dfrac{12}{2}\right)^2=-12+\left(\dfrac{-10}{2}\right)^2+\left(\dfrac{12}{2}\right)^2\)

Simplify:

\(x^2-10x+(-5)^2+y^2+12y+(6)^2=-12+(-5)^2+(6)^2\)

       \(x^2-10x+25+y^2+12y+36=-12+25+36\)

       \(x^2-10x+25+y^2+12y+36=49\)

Factor the perfect square trinomials on the left side:

\((x-5)^2+(y+6)^2=49\)

The standard equation of a circle is:

\(\boxed{(x-h)^2+(y-k)^2=r^2}\)

where:

Comparing this with the rewritten given equation, we get

Therefore, the center of the circle is (5, -6) and its radius is r = 7.

The approximate number of guests that were children are 172 and adults are 278

From the complete question, we have the following system of equations

25x + 12y = 9014

x + y = 450

Make y the subject in x + y = 450

y = 450 -x

Substitute y = 450 - x in 25x + 12y = 9014

25x + 12(450 - x) = 9014

Expand the expression

25x + 5400 - 12x = 9014

Evaluate the like terms

13x = 3614

Divide both sides by 12

x = 278

Substitute x = 278 in y = 450 -x

y = 450 - 278

Evaluate

y = 172

Hence, the approximate number of guests that were children are 172 and adults are 278

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Answer:

a). slope = 0 so it is zero slope

b). slope = -3/2 , it is negative

c). slope is undefined

d). slope = 1/3 , it is positive

Step-by-step explanation:

The slope formula is slope = (y2-y1)/(x2-x1) keeping this in mind we will begin with a):

a): (-3,2) and (4,2)

2-2/4-(-3) = 0/7 = 0 -> this is your slope for a) and it is simply zero slope

b): (-1,3) and (1,0)

0-3/1-(-1) = -3/2 -> this is your slope for b) and it is negative

c): (1,2) and (1,4)

4-2/1-1 = 2/0 = undefined. this simply can not happen. if it was flipped it would be 0. (for example. 0/2 = 0 but 2/0 = undefined.) so your slope for c) -> undefined

d): (4,4) and (1,3)

3-4/1-4 = -1/-3 = 1/3 -> this is your slope for d) and it is positive because the negatives " - " cancels out.

Answer:

y = 60*

x = 30*

Step-by-step explanation:

the bottom angle is the same angle as y and it says 2x meaning that x is 1/2 of y. the full angle across the line is 180* so divide that by 3.

180 / 3 = 60

Answer:

75%

Step-by-step explanation:

Answer: 75

Step-by-step explanation: there ya go M8

Answer:its 15.7

Step-by-step explanation:

Answer:

15.7

Step-by-step explanation:

Answer:

The original price of the shirt was Ksh 500 and it was sold for Ksh 550.

The discount is the difference between the original price and the selling price, which is Ksh 500 - Ksh 550 = Ksh -50.

To find the percentage discount, we can use the formula:

percentage discount = (discount ÷ original price) × 100%

percentage discount = (-50 ÷ 500) × 100%

percentage discount = -10%

Therefore, the percentage discount is 10%.

About 92.7% of shirt prices would be between $37 and $59.35, assuming a normal distribution with a mean of $45 and a standard deviation of $5.

To solve this problem, we can first standardize the values using the z-score formula: z = (x - μ) / σ, where x is the observed value, μ is the mean, and σ is the standard deviation.

For the lower limit of $37, the z-score would be (37 - 45) / 5 = -1.6.

For the upper limit of $59.35, the z-score would be (59.35 - 45) / 5 = 2.87.

Next, we can use a standard normal distribution table or calculator to find the proportion of values between these z-scores. For example, using a calculator, we can find that the area between -1.6 and 2.87 under a standard normal curve is approximately 0.927.

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Complete question is:

A set of shirt prices are normally distributed with a mean of 45 dollars and a standard deviation of 5 dollars. What proportion of shirt prices are between 37 dollars and 59.35 dollars?

Answer:

42,5000

Step-by-step explanation:

The slope of the tangent line is:

a = (df(x1)/dx)

The slope of the normal one is:

a' = -1/(df(x1)/dx)

For any function y = f(x), we define the slope of the tangent line at the point x as the derivative evaluated in x.

So if we want to find the slope of the tangent line at the point (x1, y1), we just need to differentiate and evaluate in x1, then the slope will be given by:

df(x1)/dx

And the normal slope is the slope of the perpendicular line, two slopes are perpendicular if the product is -1, then:

a*(df(x1)/dx) = -1

a = -1/(df(x1)/dx)

Where df/dx reffers to the derivative of f(x).

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Answer:

The equation of the tangent line to the curve at the given point is \(y = \frac{1}{14}(x - 49) + 7\)

Step-by-step explanation:

Equation of the tangent line:

The equation of the tangent line to a function f(x) at a point \((x_0,y_0)\) is given by:

\(y - y_0 = m(x - x_0)\)

In which m is the slope, which is given by the derivative of f(x) at \(x_{0}\)

y=√x, (49,7)

This means that \(x_0 = 49, y_0 = 7\)

The derivative is:

\(y^{\prime} = \frac{1}{2\sqrt{x}}\)

At \(x = 49\)

\(m = y^{\prime} = \frac{1}{2\sqrt{49}} = \frac{1}{14}\)

So

\(y - y_0 = m(x - x_0)\)

\(y - 7 = \frac{1}{14}(x - 49)\)

\(y = \frac{1}{14}(x - 49) + 7\)

The equation of the tangent line to the curve at the given point is \(y = \frac{1}{14}(x - 49) + 7\)

Answer:

589

Step-by-step explanation:

l x w

19x11

5x31

5x45

589

Answer:

589 is the answer

Step-by-step explanation:

A=2(wl+hl+hw)=2x(14x7+7x7+7x14)=490

Option B is the correct answer

The equation of the line perpendicular to the line y = 3x+7 is 3y = -x-17

The slope or gradient of a line is a number that describes both the direction and the steepness of the line.

Given that, a line is perpendicular to line y = 3x+7 and passing through points (-2,-5)

The slope of perpendicular lines is negative reciprocal of each other.

Therefore, the slope of the asked line is -1/3

Finding c,

-5 = -1/3x(-2)+c

c = -17/3

Therefore, the equation of the line is y = -1/3x-17/3 or 3y = -x-17

Hence, The equation of the line perpendicular to the line y = 3x+7 is

3y = -x-17

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Answer:

Three inches

Step-by-step explanation:

If 1 inch is = to 2 ft, and Andy has a length of 6ft for his tree house:

6/2 = 3

Answer: We can solve this problem by counting the total number of ways to select three members and then subtracting the number of ways to select three members without any officers.

The total number of ways to select three members from a group of 13 is given by the combination formula:

C(13,3) = 286

To count the number of ways to select three members without any officers, we need to choose three members from the 8 non-officers. This can be done in C(8,3) = 56 ways.

Therefore, the number of ways to select three members with at least one officer is:

C(13,3) - C(8,3) = 286 - 56 = 230

There are 230 ways to select three members for the search and rescue mission such that at least one officer is included.

Step-by-step explanation:

Answer:

25 a    18p

Step-by-step explanation:

4x5  5+5+4+4