What is the y-value of the vertex of the function f(x)=â’(xâ’3)(x 11)?.

At the lowest temperature he could get a water and salt solution to attain, Fahrenheit set zero.

Fahrenheit is named for German scientist Daniel Gabriel Fahrenheit, who was born there in 1686 as part of the Polish-Lithuanian Commonwealth. He was the first to develop a constant, accurate method of measuring temperature. At the lowest temperature he could get a water and salt solution to attain, Fahrenheit set zero.

To assist us remember that we go from colder to hotter as we walk up the scale on our thermometer, let's label it. In other terms, a higher number of degrees Fahrenheit is hotter than a lower number.

\($$\begin{aligned}& \text { Given:- } \mathrm{C}=\frac{5}{9}(\mathrm{~F}-32) \\& \Rightarrow \mathrm{F}=\frac{9}{5} \mathrm{C}+32\end{aligned}$$\)

(I) If \($F^{\prime}=F+1$\)

\($$\begin{aligned}\mathrm{C}^{\prime} & =\frac{5}{9}\left(\mathrm{~F}^{\prime}-32\right) \\\mathrm{C}^{\prime} & =\frac{5}{9}(\mathrm{~F}+1-32) \\\mathrm{C}^{\prime} & =\frac{5}{9}(\mathrm{~F}-32)+\frac{5}{9} \times 1 \\\mathrm{C}^{\prime} & =\mathrm{C}+\frac{5}{9}\end{aligned}$$\)

Hence, a temperature increase of 1 degree Fahrenheit is equivalent to a temperature increase of \($\frac{5}{9}$\) degree Celsius.

Therefore, statement I exists true.

(II) If \($\mathrm{C}^{\prime}=\mathrm{C}+1$\)

\($$\begin{aligned}& \mathrm{F}^{\prime}=\frac{9}{5} \mathrm{C}^{\prime}+32 \\& \mathrm{~F}^{\prime}=\frac{9}{5}(\mathrm{C}+1)+32 \\& \mathrm{~F}^{\prime}=\left(\frac{9}{5} \mathrm{C}+32\right)+\frac{9}{5} \\& \mathrm{~F}^{\prime}=\mathrm{F}+\frac{9}{5} \\& \mathrm{~F}^{\prime}=\mathrm{F}+1.8\end{aligned}$$\)

Therefore, a temperature increase of 1 degree Celsius exists equivalent to a temperature increase of 1.8 degrees Fahrenheit.

Therefore, statement II exists true.

\($$\begin{aligned}& \text { (III) If } F^{\prime}=F+\frac{5}{9} \\& C^{\prime}=\frac{5}{9}\left(F^{\prime}-32\right) \\& C^{\prime}=\frac{5}{9}\left(F+\frac{5}{9}-32\right) \\& C^{\prime}=\frac{5}{9}(F-32)+\frac{5}{9} \times \frac{5}{9} \\& C^{\prime}=C+\frac{25}{81}\end{aligned}$$\)

Therefore, a temperature increase of \($\frac{5}{9}$\) degree Fahrenheit exists equivalent to a temperature increase of \($\frac{25}{81}$\) degree Celsius.

Therefore, statement III exists false.

To learn more about Fahrenheit refer to:

https://brainly.com/question/30403835

#SPJ4

Answer:

9.6

Step-by-step explanation:

20%of 8=8*20/100 =1.6 and the new price of the cashews is1. 6+8=9.6

The length of side DE is 3cm

Since the line AC is equivalent to DE, hence AC = DE

To get the length of DE, we will need to get the length oF AC using the Pythagoras theorem:

Given the following parameters

Hypotenuse = 5

Opposite = 4

Required

Adjacent side

Substitute the given parameters into the formula of Pythagoras theorem.

AC² = 5² - 4²

AC² = 25 - 16

AC² = 9

AC = 3

Hence the length of side DE is 3cm

Learn more on Pythagoras theorem here: https://brainly.com/question/12306722

Answer: 1. 9:342 Rate: 38 cans per bag

2. 38:152 Rate: 4 tickets per person

3. 2:40 Rate: 20 commercials per hour

1. Divide 4 both sides

2. Graph the inequality

The amount of bacteria that will be there in 100 milliliters of water will be: 1.5 × 10⁸.

A standard notation is a method of writing a given number, equation, or expression in a specific format that adheres to certain rules. 4.5 billion years, for example, is written as 4,500,000,000 years.

The main reason for converting numbers to scientific notation is to make calculations involving unusually large or small numbers easier.

Even though zeros are no longer always seemed to set the decimal point, all digits in a scientific notation number are significant.

Here, it is given that,

The number of bacteria found in  1 milliliter of water = 1,500,000.

So,

The number of bacteria in 100 milliliters of water = 1,500,000 x 100

The number of bacteria in 100 milliliters of water = 15,00,00,000

The number of bacteria in 100 milliliters of water = 1.5 × 10⁸.

Correct option: e

To know more about standard notation refer to:

brainly.com/question/10253124

#SPJ4

Answer:

f ≤ 1

Step-by-step explanation:

1) Subtract 2 from both sides.

1 - 2 ≤ - f

2) Simplify 1 - 2 to - 1.

- 1 ≤ - f

3) Multiply both sides by - 1.

1 ≥ f

4) Switch Sides.

f ≤ 1

\(\\ \sf\longmapsto 1\leqslant 2-f\)

\(\\ \sf\longmapsto 1-2\leqslant -f\)

\(\\ \sf\longmapsto -1\leqslant -f\)

Multiply -1 on both sides

\(\\ \sf\longmapsto f\leqslant 1\)

So look at the first one like this: AB=BC which means its an isosceles triangle(search that for more details) and automatically has the 2 angles of equal measures.

The second one the same thing but reversed.(angles first)Sides opposite to the equal angles of a triangle are equal. Proof: In a triangle ABC, base angles are equal and we need to prove that AC = BC or ∆ABC is an isosceles triangle.

My advice search the web for a more mathematical explanation of the isosceles triangle

Answer:

4,999

Step-by-step explanation:

4,999 is the number in standard form, hope this helps!!

Your answer is 4,999

I hope this helps!

Answer:

40 is

But it is not an

Answer:

what do you need help with?

Step-by-step explanation:

Answer:

28,568 feet

Step-by-step explanation:

Mt. Rainer is 14,410 feet in elevation

Point success is 14,158 feet in elevation

Therefore if both mountains were climbed then the total distance can be calculated as follows

= 14,410 feets + 14,158 feets

= 28,568 feet

Hence the total distance is 28,568 feet

Answer: 28,568

Step-by-step explanation:

Mt. Rainier in washington is 14,410.

Point success is 14,158.

Therefore 14,410 feet + 14,158 = 28,568 feet.

Answer:

18,0

Step-by-step explanation:

By useing desmos, the line has an x intercept of 18 making that the answer.

PLZ MARK AS BRAINLIEST

Answer:

D = 18

Step-by-step explanation:

\(6 = \frac{1}{3}d\)

\(3*(\frac{1}{3} d) = (3)*(6)\)

\(d=18\)

Answer:

  32 square units

Step-by-step explanation:

You want the area of a polygon with the vertices (1,2) (1,6) (7,6) (7,2) (5,0) (3,0).

The graphed figure can be decomposed into a rectangle 4 units high and 6 units wide, together with a trapezoid with bases 6 and 2, and height 2.

The area formulas for these parts are ...

  A = HW . . . . area of a rectangle of height H and width W

  A = 1/2(b1 +b2)h . . . . area of a trapezoid with bases b1, b2, and height h

The rectangle area is ...

  A = (4)(6) = 24

The trapezoid area is ...

  A = 1/2(6+2)(2) = 8

So, the total area of the polygon is ...

  A = 24 +8 = 32 . . . . square units.

The area of the polygon is 32 square units.

Answer:

More than 8 seconds

Step-by-step explanation:

Xandler

Leon

Time  = x

Inequality for the required condition is:

Answer:

Step-by-step explanation:

A series Σ(-1)"an converges if (an) is a positive, decreasing sequence with limit an = 0. A series converges absolutely if Σan converges, and it converges conditionally if it converges but an diverges.

For a series Σan to converge absolutely, it means that the series Σan converges. In other words, the sum of the terms an in the series converges to a finite value. This can happen regardless of the signs of the terms an.

On the other hand, a series Σan converges conditionally if it converges but the terms an themselves diverge. In this case, the sum of the terms in the series converges, but only because the positive and negative terms cancel each other out.

An example of a series that converges conditionally is the alternating harmonic series Σ((-1)^n)/n. This series satisfies the conditions for the Alternating Series Test, which states that if a series has alternating positive and negative terms that decrease in magnitude and approach zero, then the series converges. However, when considering the absolute values of the terms, Σ|((-1)^n)/n| becomes the harmonic series Σ(1/n), which is a well-known divergent p-series. Therefore, the alternating harmonic series converges conditionally.

To learn more about converges - brainly.com/question/29258536

#SPJ11

Answer:

-2

Step-by-step explanation:

Step-by-step explanation: -40/20=-2, 20x-2=-40.

Answer:

x=18

M=18

L= 63

K= 99

Step-by-step explanation:

Answer: P=7+3√5+2√13 units      S=21 quadratic units

Step-by-step explanation:

\(A(1,-2)\ \ \ \ B(1.5)\ \ \ \ C(7,2)\\\)

                  The perimeter of a triangle

\(|AB|=\sqrt{(x_B-x_A)^2+(y_B-y_A)^2} \\|AB|=\sqrt{(1-1)^2+(5-(-2))^2} \\|AB|=\sqrt{0^2+(5+2)^2}\\|AB|=\sqrt{0+7^2}\\ |AB|= \sqrt{7^2} \\|AB|=7\)

\(|BC|=\sqrt{(x_C-x_B)^2+(y_C-y_B)^2} \\|BC|=\sqrt{(7-1)^2+(2-5)^2}\\ |BC|=\sqrt{6^2+(-3)^2}\\ |BC|=\sqrt{36+9}\\ |BC|= \sqrt{45} \\|BC|=\sqrt{9*5}\\ |BC|=3\sqrt{5}\)

\(|AC|=\sqrt{(x_C-x_A)^2+(y_C-x_A)^2}\\ |AC|=\sqrt{(7-1)^2+(2-(-2)^2} \\|AC|=\sqrt{6^2+(2+2)^2}\\ |AC|=\sqrt{36+4^2}\\ |AC|=\sqrt{36+16} \\|AC|=\sqrt{52}\\ |AC|=\sqrt{4*13} \\|AC|=2\sqrt{13} \\\)

\(Thus,\\\\P_{ABC}=|AB|+|BC|+|AC|\\\\P_{ABC}=7+3\sqrt{5}+2\sqrt{13}\ units\)

                        The area of a triangle

Taking A as the first vertex, we find:

\(\displaystyle\\Find\ |\overline{AB}*\overline{AC}|\\\left|\begin{array}{cc}x_A-x_C&y_A-y_C\\x_B-x_C&y_B-y_C\\\end{array}\right|=\\\\\left|\begin{array}{ccc}1-7&-2-2\\1-7&5-2\\\end{array}\right| =\\\\\left|\begin{array}{ccc}-6&-4\\-6&3\\\end{array}\right| =\\\\|(-6)*3-(-6)*(-4)|=\\\\|-18-24|=\\\\|-42|=\\\\42\\\\S_{ABC}=\frac{1}{2} |\overline{AB}*\overline{AC}|\\\\S_{ABC}=\frac{1}{2}(42)\\\\S_{ABC}=21 \ quadratic\ units\)

Answer:

3.5 m

Step-by-step explanation:

PQ = 5/(5+5) × 7

= 5/10 × 7

= 3.5 m

Answer:

12 inches

Step-by-step explanation:

The storage bin is in the shape of a rectangular prism.

Its volume is 5400 cubic inches and its base area is 450 square inches.

The volume of a rectangular prism is given as:

V = L * W * H

where L = length

W = width

H = height

The product of the length and width gives the base area of the rectangular prism:

A = L * W

This implies that:

V = A  * H

=> 5400 = 450 * H

H = 5400 / 450

H = 12 inches

The height of the bin is 12 inches.

The approximate probability that at most 30 of the 200 circuit boards are defective is 0.5295.

To find the probability that at most 30 of the 200 randomly selected circuit boards are defective, we can use the normal approximation.

Given that the probability of a circuit board being defective is 15% (or 0.15), we can define the random variable X as the number of defective boards out of the 200 selected.

The mean (μ) of the binomial distribution is given by μ = n * p, where n is the sample size and p is the probability of success (defective board). In this case, μ = 200 * 0.15 = 30.

The standard deviation (σ) of the binomial distribution is given by σ = sqrt(n * p * (1 - p)). Therefore, σ = sqrt(200 * 0.15 * 0.85) ≈ 6.32.

To apply the normal approximation, we need to use the continuity correction. We consider the probability that at most 30 boards are defective, which is equivalent to the probability that X is less than or equal to 30.

We standardize the distribution using the z-score formula:

z = (x - μ) / σ,

where x is the number of defective boards we are interested in.

In this case, we need to calculate P(X ≤ 30), which is equivalent to finding P(X < 30 + 0.5) using the continuity correction. Therefore, we calculate P(X < 30.5).

Converting to z-scores:

z = (30.5 - 30) / 6.32 ≈ 0.079

Now, we can find the probability using the standard normal distribution table or a calculator. The probability that X < 30.5 is approximately 0.5295.

Therefore, the approximate probability that at most 30 of the 200 circuit boards are defective is 0.5295. The answer obtained using the normal approximation is an approximation, as we are assuming the binomial distribution can be approximated by the normal distribution due to a large sample size. If a more exact answer is desired, the binomial distribution itself can be used with the appropriate calculations.

Learn more about probability here

https://brainly.com/question/25839839

#SPJ11

Answer:

b=98 and a=82

Step-by-step explanation:

b and 98 are corrisponding angles which means that they are both 98

a+b=180 because it is a straight line

a+98=180 subtract 98 from both sides a d you get a=82

Answer:

2.4

Step-by-step explanation:

tan(theta) is defined as: \(tan(\theta)=\frac{\text{opposite}}{\text{adjacent}}\)

in the given diagram we only have the opposite and hypotenuse, but we can use the Pythagorean Theorem to solve for the other two missing sides.

Pythagorean Theorem: \(a^2+b^2=c^2\), where c is the hypotenuse.

Plugging in known values we get the following:

\(a^2+12^2=13^2\)

in this case the missing side, or the adjacent side is simply "a"

from here we simplify the bases with exponents

\(a^2+144=169\)

now subtract 144 from both sides

\(a^2=25\)

take the square root of both sides

\(a=5\)

So now we know the adjacent side so we can plug it into the tan equation

\(tan(z)=\frac{12}{5}\\\\tan(z)=2.4\)

The approximate average rate at which the area decreases as the rectangle's length goes from 13 cm to 16 cm is equal to the width (w) of the rectangle.

To determine the approximate average rate at which the area decreases as the rectangle's length goes from 13 cm to 16 cm, we need to calculate the change in area and divide it by the change in length.

Let's denote the length of the rectangle as L (in cm) and the corresponding area as A (in square cm).

Given that the initial length is 13 cm and the final length is 16 cm, we can calculate the change in length as follows:

Change in length = Final length - Initial length

= 16 cm - 13 cm

= 3 cm

Now, let's consider the formula for the area of a rectangle:

A = Length × Width

Since we are interested in the rate at which the area decreases, we can consider the width as a constant. Let's assume the width is w cm.

The initial area (A1) when the length is 13 cm is:

A1 = 13 cm × w

Similarly, the final area (A2) when the length is 16 cm is:

A2 = 16 cm × w

The change in area can be calculated as:

Change in area = A2 - A1

= (16 cm × w) - (13 cm × w)

= 3 cm × w

Finally, to find the approximate average rate at which the area decreases, we divide the change in area by the change in length:

Average rate of area decrease = Change in area / Change in length

= (3 cm × w) / 3 cm

= w

Therefore, the approximate average rate at which the area decreases as the rectangle's length goes from 13 cm to 16 cm is equal to the width (w) of the rectangle.

learn more about rectangle here

https://brainly.com/question/15019502

#SPJ11

Answer:

NO=OP

Step-by-step explanation:

To identify the false statement in the diagram, analyze the given options and compare with the information presented. In this case, the false statement is that the figure has four sides. It actually has three sides, making it a triangle.

In order to identify the false statement based on the diagram, you need to analyze the given options and compare them with the information presented in the diagram.

Let's assume the options are:

The figure is not a triangle.

There are three blue items in the diagram.

The figure has four sides.

The figure is a square.

After examining the diagram, you can determine that option 3, 'The figure has four sides,' is false. The diagram clearly shows a figure with three sides, making it a triangle. The false statement contradicts the information depicted in the diagram.

Learn more about the topic of False statement in a diagram here:

https://brainly.com/question/18746205

#SPJ3