NEED HELP WITH A MATH QUESTION

Answer:

Given:

POS system = 3,400

useful life = 10 years

salvage value = 400

double declining method means that the depreciation expense is higher in the early years than the later years of the asset.

Straight line depreciation = (3,400 - 400) / 10 yrs = 300 

300 / 3000 = 0.10 or 10%

10% x 2 = 20% double declining rate

Depreciation expense under the double declining method:

Year 1: 3,400 x 20% =  680 depreciation expense.

Year 1 book value = 3,400 - 680 = 2,720

Year 2 : 2,720 x 20% = 544 depreciation expense

Year 2 book value = 2,720 - 544 = 2,176

Answer:

8 units ^2

Step-by-step explanation:

The area of a triangle is given by

A = 1/2 bh  where b is the length of the base and h is the height

b = LK = 4 units

h = J to where LK would be extended to, which would be 4 units

A = 1/2 (4) * 4

A = 8 units ^2

Answer:

(25.732,30.868)

Step-by-step explanation:

Given that in a random sample of 42 ​people, the mean body mass index​ (BMI) was 28.3 and the standard deviation was 6.09.

Since only sample std deviation is known we can use only t distribution

Std error = [tex]\frac{s}{\sqrt{n} } =\frac{6.09}{\sqrt{42} } \\=0.9397[/tex]

[tex]df = 42-1 =41[/tex]

t critical for 99% two tailed [tex]= 2.733[/tex]

Margin of error[tex]= 2.733*0.9397=2.568[/tex]

Confidence interval lower bound = [tex]28.3-2.568=25.732[/tex]

Upper bound = [tex]28.3+2.568=30.868[/tex]

Answer:

i think its uh

Step-by-step explanation: carrot

[tex]\bf \boxed{A}\\\\ \stackrel{\textit{3 less than D}}{D-3}~\hspace{5em}A=(D-3)(D-3)\implies A=(D-3)^2 \\\\[-0.35em] ~\dotfill\\\\ \boxed{B}\\\\ \stackrel{\textit{area of rabbits' pen}}{25=(D-3)^2}\implies \stackrel{\stackrel{\textit{same exponents}}{\textit{same base}}}{5^2=(D-3)^2}\implies 5=D-3\implies 8=D \\\\\\ \boxed{C}\\\\ 5+5+5+5=20[/tex]

Final answer:

To find the expression that represents the area of the rabbit cage, use (D - 3)². The side of the rabbit cage, given the area, is 25 square feet, is 5 feet, so the dog pen's side length is 8 feet. The rabbit cage requires 20 feet of fencing to be enclosed.

Explanation:

To solve for the expression that represents the area of the rabbit cage, we'll start by defining the side of the square dog pen as D. Since each side of the rabbit cage is 3 feet less than the dog pen, the side of the rabbit cage would be D - 3. Therefore, the area of the rabbit cage, which is a square, is given by the expression (D - 3)². This tells us that the area is the side length squared. Now, we know that the area of the rabbit cage is 25 square feet.

To find the side length of the rabbit cage, we would take the square root of the area, which gives us 5 feet. Hence, to find the side length of the dog pen, we would add the 3 feet back to the side length of the rabbit cage. This gives us D - 3 = 5, which means D = 5 + 3, so D = 8 feet.

For part c, to find out how many feet of fencing is needed to enclose the rabbit cage, we take the side length of the rabbit cage, which is 5 feet, and multiply it by 4, since a square has four equal sides. This means we would need 5 feet x 4 sides = 20 feet of fencing to enclose the rabbit cage.

Answer:

15x12x10.

The roof is 12x15.

Two walls are each 12x10.

The other two walls are each 15x10.

12x15 + 12x10 + 15x10 = 180 + 120 + 150 = 450 ft^2

Step-by-step explanation:

Answer:

[tex]\frac{2x-20}{x^2+6x-40}[/tex]

Step-by-step explanation:

[tex]f(x)+g(x)[/tex]

[tex]\frac{x-16}{x^2+6x-40}+\frac{1}{x+10}[/tex]

I'm going to factor that quadratic in the first fraction's denominator to figure out what I need to multiply top and bottom of the other fraction or this fraction so that I have a common denominator.

I want a common denominator so I can write as a single fraction.

So since the leading coefficient is 1, all we have to do is find two numbers that multiply to be c and at the same thing add up to be b.

c=-40

b=6

We need to find two numbers that multiply to be -40 and add to be 6.

These numbers are 10 and -4 since (10)(-4)=-40 and 10+-4=6.

So the factored form of [tex]x^2+6x-40[/tex] is [tex](x+10)(x-4)[/tex].

So the way the bottoms will be the same is if I multiply top and bottom of my second fraction by (x-4).

This will give me the following sum so far:

[tex]\frac{x-16}{x^2+6x-40}+\frac{x-4}{x^2+6x-40}[/tex]

Now that the bottoms are the same we just need to add the tops and then we are truly done:

[tex]\frac{(x-16)+(x-4)}{x^2+6x-40}[/tex]

[tex]\frac{x+x-16-4}{x^2+6x-40}[/tex]

[tex]\frac{2x-20}{x^2+6x-40}[/tex]

Answer:

Step-by-step explanation:

The perimeter in each case is double the sum of the side dimensions. Since the perimeters are equal, the sum of side dimensions will be equal:

  2x +x = (x +12) +(x -3)

  3x = 2x +9 . . . . . . . . collect terms

  x = 9 . . . . . . . . . . . . . subtract 2x

Given this value of x, the dimensions of the first rectangle are ...

  {2x, x} = {2·9, 9} = {18, 9}

And the dimensions of the second rectangle are ...

  {x+12, x-3} = {9+12, 9-3} = {21, 6}

Answer:

[tex]4x^2-20x+25[/tex]

Step-by-step explanation:

[tex](2x-5)^{2} \\(2x)^2+2(2x)(-5)+(-5)^2\\4x^2-20x+25[/tex]

Answer:

[tex]4x^2-20x+25[/tex]

Step-by-step explanation:

You can use the formula:

[tex](u+v)^2=u^2+2uv+v^2[/tex].

[tex](2x-5)^2=(2x)^2+2(2x)(-5)+(-5)^2[/tex]

[tex](2x-5)^2=4x^2-20x+25[/tex].

You could also use foil:

[tex](2x-5)^2=(2x-5)(2x-5)[/tex]

First: 2x(2x)=4x^2

Outer: 2x(-5)=-10x

Inner: -5(2x)=-10x

Last: -5(-5)=25

--------------------------Add.

[tex]4x^2-20x+25[/tex]

Step-by-step explanation:

The coefficient of the x is 3, so it is horizontally shrunk by factor of 3.

The coefficient of the sine is 4, so it is vertically stretched by factor of 4.

The constant inside the sine is -pi, so it is horizontally shifted pi units to the right.

The constant outside the sine is 5, so it is vertically shifted 5 units up.

Answer:

The correct option is A. The graph will be continuous because the amount of gas that she added to the tank does not need to be an integer amount.

Step-by-step explanation:

Consider the given information.

If the value of a function is integer then the graph will be discrete, otherwise it will be a continuous graph.

The amount of gas that Jayne added does not need to be an integer. So, the graph will be continuous.

For example, 16.7 gallons of gas or 19.9 gallons of gas, etc. She can get amounts that are not integers.

This can be represent as:

y = x + 4

Where, y is total amount of gas in tank and x is number of gallons she added.

As it is a linear function which is continuous everywhere.

Thus, the correct option is A. The graph will be continuous because the amount of gas that she added to the tank does not need to be an integer amount.

Answer:

I want yo points

Step-by-step explanation:

Answer:

No, the triangle is not possible.

Step-by-step explanation:

Given,

A triangle ABC in which C = 38°, a = 19, c = 10,

Where, angles are A, B and C and the sides opposite to these angles are a, b and c respectively,

By the law Sines,

[tex]\frac{sin A}{a}=\frac{sin C}{c}[/tex]

[tex]\implies sin A = \frac{a sin C}{c}[/tex]

By substituting the values,

[tex]sin A = \frac{19\times sin 38^{\circ}}{10}[/tex]

[tex]=1.16975680312[/tex]

[tex]\implies A=sin^{-1}(1.16975680312)[/tex] = undefined

Hence, the triangle is not possible with the given measurement.

Step-by-step explanation:

Rate × time = distance

If x is the rate of the boat and y is the rate of the water:

(x − y) × 4 = 128

(x + y) × 2 = 128

Simplifying:

x − y = 32

x + y = 64

Solve with elimination (add the equations together):

2x = 96

x = 48

y = 16

The speed of the boat is 48 km/hr and the speed of the water is 16 km/hr.

bearing in mind that 4¾ is simply 4.75.

[tex]\bf ~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$600\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &3 \end{cases} \\\\\\ A=600\left(1+\frac{0.05}{1}\right)^{1\cdot 3}\implies A=600(1.05)^3\implies A=694.575 \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf ~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$750\\ r=rate\to 4.75\%\to \frac{4.75}{100}\dotfill &0.0475\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\dotfill &1\\ t=years\dotfill &3 \end{cases} \\\\\\ A=750\left(1+\frac{0.0475}{1}\right)^{1\cdot 3}\implies A=750(1.0475)^3\implies A\approx 862.032[/tex]

well, the interest for each is simply A - P

695.575 - 600 = 95.575.

862.032 - 750 = 112.032.

Answer:

(- 1, 4 )

Step-by-step explanation:

x = 1 is a vertical line passing through all points with an x- coordinate of 1

The point P(3, 4) is to units to the right of x = 1.

Hence the refection will be 2 units to the left of x = 1

P' = (1 - 2, 4 ) = (- 1, 4 )

Answer:

Part 1) For x=1 year, [tex]y=\$23,750[/tex]  

Part 2) For x=2 years, [tex]y=\$22,562.50[/tex]  

Part 3) For x=3 years, [tex]y=\$21,434.38[/tex]  

Step-by-step explanation:

we know that

The  formula to calculate the depreciated value  is equal to  

[tex]y=P(1-r)^{x}[/tex]  

where  

y is the depreciated value  

P is the original value  

r is the rate of depreciation  in decimal  

x  is the number of years  

in this problem we have  

[tex]P=\$25,000\\r=5\%=0.05[/tex]

substitute

[tex]y=25,000(1-0.05)^{x}[/tex]  

[tex]y=25,000(0.95)^{x}[/tex]  

Part 1) Find the value of the printer, to the nearest cent, in year 1

so

For x=1 year

substitute in the exponential equation

[tex]y=25,000(0.95)^{1}[/tex]  

[tex]y=\$23,750[/tex]  

Part 2) Find the value of the printer, to the nearest cent, in year 2

so

For x=2 years

substitute in the exponential equation

[tex]y=25,000(0.95)^{2}[/tex]  

[tex]y=\$22,562.50[/tex]  

Part 3) Find the value of the printer, to the nearest cent, in year 3

so

For x=3 years

substitute in the exponential equation

[tex]y=25,000(0.95)^{3}[/tex]  

[tex]y=\$21,434.38[/tex]  

Find the horizontal distance of 230 and find the Vertical distance , which is where the black dot is located.

The black dot is on 49 inches.

Now find the vertical distance f the black line at horizontal 230: This is on 47.5.

The difference between the two is : 49 - 47.5 = 1.5

The answer would be A. 1.5

Answer:

A) 1.5 inches

Step-by-step explanation:

If you draw a vertical line at 230", you will see that it will intersect the line of best fit at Vertical distance = 47.5"

However the actual vertical distance recorded was 49"

Hence the difference between the line of best fit and the actual distance,

= 49 - 47.5 = 1.5"

Answer:

  14a.  an = 149 -6(n -1)

  14b.  Evaluate the formula with n=8.

  15.  (no question content)

Step-by-step explanation:

14. Each week, sales decreases by 6, so the arithmetic sequence for sales has a first term of 149 and common difference of -6. The general formula for the n-th term is ...

  an = a1 + d·(n -1) . . . . . . where a1 is the first term, d is the common difference

Putting the numbers for this sequence into the general formula, we get ...

  an = 149 -6(n -1)

__

To predict the sales for the 8th week, put n=8 into the formula and do the arithmetic.

  a8 = 149 -6(8-1) = 107 . . . . predicted sales for week 8

_____

15. The graph is shown attached. There is no question content.

Answer:

3.6

Step-by-step explanation:

Divide 6 by 4

You get 1.5

Multiply 1.5 by 2.4

You get 3.6

Answer:

15 degrees

Step-by-step explanation:

The arc measure of BC is equal to angle created by B, C and the central angle.  The angle created by B,C, and the central angle is 15 degrees so the arc measure is 15 degrees.

Answer: 15°

Step-by-step explanation:

It is important to remember that, by definition:

[tex]Central\ angle = Intercepted\ arc[/tex]

Therefore, in this case, knowing that the angle BAC  (which is the central angle) in the circle provided measures 15 degrees, you can conclude that the measure of arc BC (which is the intercepted arc) is 15 degrees.

Then you get that the answer is:

[tex]BAC=BC[/tex]

[tex]BC=15\°[/tex]

Answer:

Step-by-step explanation:

6 types of lunch multiplied by 5 kinds of bread then multiplied by 4 types of sauces equals 120

Final answer:

The question involves the application of normal distribution and sample means in statistics to analyze per capita red meat consumption. The context provided includes dietary trend changes over time, reflecting shifts in consumer preferences and demand curves.

Explanation:

The student's question pertains to the normal distribution of red meat per capita consumption, a statistical concept used in mathematics to describe how values are spread around a mean. Based on a given mean of 107.107 pounds and a standard deviation of 39.339.3 pounds, we would analyze sample means for groups of 18 individuals. To do this, we use the Central Limit Theorem which states that the sampling distribution of the sample mean will be normally distributed if the sample size is large enough, typically n > 30, but even smaller samples from a normal population will be approximately normal.

As per the historical data from the USDA, we observe changes in per-capita consumption trends for chicken and beef, indicating shifts in consumer preferences affecting the demand curve over time. This information provides context to the type of data involved but does not directly affect the statistical analysis of sample means asked in the question.

Moreover, these statistical concepts could be used to estimate population parameters and analyze shifts in dietary patterns as suggested by the change in the consumption of chicken and beef over the years.

Answer:

Mean = 51.4.

Mode = 49.

Median = 52.

Range = 6.

Step-by-step explanation:

Mean = Sum of all observations / Number of observations.

Mean = (49+49+54+55+52+49+52)/7

Mean = 360/7

Mean = 51.4 (to the nearest tenth).

Mode = The most repeated values = 49 (repeated 3 times).

Range = Largest Value - Smallest Value = 55 - 49 = 6.

Median = The central value of the data.

First, arrange the data in the ascending order: 49, 49, 49, 52, 54, 55, 55.

It can be seen that the middle value is 52. Therefore, median = 52!!!

Answer:

D (assuming f(x)=-3x^2+4x+6)

Step-by-step explanation:

Let's find f(2) and f(3).

I'm going to make the assumption you meant f(x)=-3x^2+4x+6 (please correct if this is not the function you had).

f(2) means replace x with 2.

f(2)=-3(2)^2+4(2)+6

Use pemdas to simplify:  -3(4)+4(2)+6=-12+8+6=-4+6=2.

So f(2)=2

f(3) means replace x with 3.

f(3)=-3(3)^2+4(3)+6

Use pemdas to simplify:  -3(9)+4(3)+6=-27+12+6=-15+6=-9

So f(3)=-9

-9 is smaller than 2 is the same as saying f(3) is smaller than f(2) or that f(2) is bigger than f(3).

Answer:

The answer is statement D.

Step-by-step explanation:

In order to determine the true statement, we have to solve every statement.

In any function, we replace any allowed "x" value and the function gives us a value. This process is called "evaluating function". If we want to compare different values of the function for different "x" values, we just have to evaluate them first and then compare.

So, for x=2 and x=3

f(2)=-3*(2)^2+4*2+6=-12+8+6=2

f(3)=-3*(3)^2+4*3+6=-27+12+6=-9

f(2)>f(3)

According to the possible options, the true statement is D.

Answer:

The mid-point is:

[tex]=(\frac{-3}{2},\frac{-1}{2})[/tex]

Step-by-step explanation:

We are given:

[tex](x_1,x_2) = (3,5)\\(y_1,y_2) = (-6,-6)[/tex]

We have to find the midpoint of the segment formed by these points.

The formula for mid-point is:

[tex]Mid-point=(\frac{x_1+x_2}{2},\frac{y_1+y_1}{2})\\ Putting\ the\ values\\Mid-point=(\frac{3-6}{2},\frac{5-6}{2})\\=(\frac{-3}{2},\frac{-1}{2})[/tex] ..

Answer:

The answer above is correct, but in decimal form it's

(-1.5,-0.5)

Step-by-step explanation:

Answer:

0.688 or 68.8%

Step-by-step explanation:

Percentage of high school dropouts = P(D) = 9.3% = 0.093

Percentage of high school dropouts who are white = [tex]P(D \cap W)[/tex] = 6.4% = 0.064

We need to find the probability that a randomly selected dropout is​ white, given that he or she is 16 to 17 years​ old. This is conditional probability which can be expressed as: P(W | D)

Using the formula of conditional probability, we ca write:

[tex]P(W | D)=\frac{P(W \cap D)}{P(D)}[/tex]

Using the values, we get:

P( W | D) = [tex]\frac{0.064}{0.093} = 0.688[/tex]

Therefore, the probability that a randomly selected dropout is​ white, given that he or she is 16 to 17 years​ old is 0.688 or 68.8%

Answer: I believe it's 85° i have no explanation and am sorry if it's wrong x

Step-by-step explanation:

Answer:

Question 1.  Option (3) RT = 35°

Question 2. Option (3) y = 2

Step-by-step explanation:

By the definition of external angle, ∠PSY is the external angle formed by the secants PS and YS.

From the attached diagram.

Theorem says,

m(∠a) = [tex]\frac{1}{2}(\frac{y-x}{2})[/tex]°

Now we will apply this theorem in our question.

m(∠PSY) = 180° - [m(∠SMX) + m(∠MXS)]

               = 180° - (95° + 45°)

               = 180° - 140°

               = 40°

Since m(∠PSY) = [tex]\frac{1}{2}[m(arcPY)-m(arcRT)][/tex] [By the theorem]

m(arc PY) = m(arc PW) + m(arc WY)

               = (80 + 35)°

               = 115°

Now m(∠PSY) = [tex]\frac{1}{2}[115-RT][/tex]

40° = [tex]\frac{1}{2}(115-RT)[/tex]°

80 = 115 - RT

RT = 115 - 80

RT = 35°

Therefore, Option (3). RT = 35° is the answer.

Question 2.

By the theorem, every angle at the circumference of a semicircle, that is subtended by the diameter of the semicircle is a right angle.

Therefore, (53y - 16)° = 90°

53y = 90 + 16

53y = 106

y = 2

Therefore, Option (3). y = 2 is the answer.

so we know the angle is 180° < x < 270°, which is another way of saying that the angle is in III Quadrant, where cosine as well as sine are both negative, which as well means a positive tangent, recall tangent = sine/cosine.

the cos(x) = -(4/5), now, let's recall that the hypotenuse is never negative, since it's just a radius unit, thus

[tex]\bf cos(x)=\cfrac{\stackrel{adjacent}{-4}}{\stackrel{hypotenuse}{5}}\qquad \impliedby \textit{let's find the \underline{opposite side}} \\\\\\ \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \pm \sqrt{c^2-a^2}=b \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases} \\\\\\ \pm\sqrt{5^2-(-4)^2}=b\implies \pm\sqrt{9}=b\implies \pm 3 = b\implies \stackrel{III~Quadrant}{\boxed{-3=b}} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\bf tan(x)=\cfrac{\stackrel{opposite}{-3}}{\stackrel{adjacent}{-4}}\implies tan(x)=\cfrac{3}{4} \\\\\\ tan(2x)=\cfrac{2tan(x)}{1-tan^2(x)}\implies tan(2x)=\cfrac{2\left( \frac{3}{4} \right)}{1-\left( \frac{3}{4} \right)^2}\implies tan(2x)=\cfrac{~~\frac{3}{2}~~}{1-\frac{9}{16}}[/tex]

[tex]\bf tan(2x)=\cfrac{~~\frac{3}{2}~~}{\frac{16-9}{16}}\implies tan(2x)=\cfrac{~~\frac{3}{2}~~}{\frac{7}{16}}\implies tan(2x)=\cfrac{3}{~~\begin{matrix} 2 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}\cdot \cfrac{\stackrel{8}{~~\begin{matrix} 16 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}}{7} \\\\\\ tan(2x)=\cfrac{24}{7}\implies tan(2x)=3\frac{3}{7}[/tex]

Answer:

The value of given expression is [tex]-\frac{\sqrt{2}-\sqrt{6}}{4}[/tex].

Step-by-step explanation:

The given expression is

[tex]\cos\left(\dfrac{19\pi}{12}\right)[/tex]

The trigonometric ratios are not defined for [tex]\dfrac{19\pi}{12}[/tex].

[tex]\dfrac{19\pi}{12}[/tex] can be split into [tex]\frac{5\pi}{4}+\frac{\pi}{3}[/tex].

[tex]\cos\left(\dfrac{19\pi}{12}\right)=\cos (\frac{5\pi}{4}+\frac{\pi}{3})[/tex]

Using the addition formula

[tex]\cos (A+B)=\cos A\cos B-\sin A\sin B[/tex]

[tex]\cos (\frac{5\pi}{4}+\frac{\pi}{3})=\cos( \frac{\pi}{3})\cdot \cos (\frac{5\pi}{4})-\sin( \frac{\pi}{3})\cdot \sin (\frac{5\pi}{4})[/tex]

We know that, [tex]\cos(\frac{\pi}{3})=\frac{1}{2}[/tex] and [tex]\sin (\frac{\pi}{3})=\frac{\sqrt{3}}{2}[/tex]

[tex]\cos\left(\dfrac{19\pi}{12}\right)=\frac{1}{2}\cdot \cos (\frac{5\pi}{4})-\frac{\sqrt{3}}{2}\cdot \sin (\frac{5\pi}{4})[/tex]

[tex]\frac{5\pi}{4}[/tex] lies in third quadrant, by using reference angle properties,

[tex]\cos(\frac{5\pi}{4})=-\cos(\frac{\pi}{4})=-\frac{\sqrt{2}}{2}[/tex]

[tex]\sin(\frac{5\pi}{4})=-\sin(\frac{\pi}{4})=-\frac{\sqrt{2}}{2}[/tex]

[tex]\cos\left(\dfrac{19\pi}{12}\right)=\frac{1}{2}\cdot (-\frac{\sqrt{2}}{2})-\frac{\sqrt{3}}{2}\cdot (-\frac{\sqrt{2}}{2})[/tex]

[tex]\cos\left(\dfrac{19\pi}{12}\right)=-\frac{\sqrt{2}}{4}+\frac{\sqrt{6}}{4}[/tex]

[tex]\cos\left(\dfrac{19\pi}{12}\right)=-\frac{(\sqrt{2}-\sqrt{6})}{4}[/tex]

Therefore the value of given expression is [tex]-\frac{\sqrt{2}-\sqrt{6}}{4}[/tex].

Final answer:

To find [tex]\(\cos(\frac{19\pi}{12})\),[/tex] we express the angle as the sum of  [tex]\(\frac{4\pi}{3}\) and \(\frac{\pi}{4}\)[/tex] and then use the cosine addition formula. Calculating the values of cosine and sine for these angles gives us the exact value of [tex]\(\cos(\frac{19\pi}{12})\) as \(\frac{\sqrt{6} - \sqrt{2}}{4}\).[/tex]

Explanation:

To find [tex]\(\cos\left(\frac{19\pi}{12}\right)\)[/tex] using an angle addition or subtraction formula, let's break down the angle [tex]\(\frac{19\pi}{12}\)[/tex] into the sum or difference of angles whose cosine values we know. We can express[tex]\(\frac{19\pi}{12}\) as \(\frac{16\pi}{12} + \frac{3\pi}{12}\)[/tex] which simplifies to[tex]\(\frac{4\pi}{3} + \frac{\pi}{4}\).[/tex] Now we use the cosine addition formula [tex], \(\cos(a+b) = \cos a \cos b - \sin a \sin b\)[/tex], to find the answer:

[tex]\(\cos\left(\frac{19\pi}{12}\right) = \cos\left(\frac{4\pi}{3} + \frac{\pi}{4}\right) = \cos\left(\frac{4\pi}{3}\right)\cos\left(\frac{\pi}{4}\right) - \sin\left(\frac{4\pi}{3}\right)\sin\left(\frac{\pi}{4}\right)\)[/tex]

[tex]\(= (-\frac{1}{2})\cdot(\frac{\sqrt{2}}{2}) - (-\frac{\sqrt{3}}{2})\cdot(\frac{\sqrt{2}}{2})\)[/tex]

[tex]\(= -\frac{\sqrt{2}}{4} + \frac{\sqrt{6}}{4}\)[/tex]

Combining these, we get:

[tex]\(\cos\left(\frac{19\pi}{12}\right) = \frac{\sqrt{6} - \sqrt{2}}{4}\)[/tex]

Answer:  0.4013

Step-by-step explanation:

Given : The volumes of soda in quart soda bottles are normally distributed with : [tex]\mu=32.3\text{ oz}[/tex]

[tex]\sigma=1.2\text{ oz}[/tex]

Let x be the volume of randomly selected quart soda bottle.

z-score : [tex]z=\dfrac{x-\mu}{\sigma}[/tex]

[tex]z=\dfrac{32-32.3}{1.2}=-0.25[/tex]

The probability that the volume of soda in a randomly selected bottle will be less than 32​ oz = [tex]P(x<32)=P(z<-0.25)[/tex]

[tex]=0.4012937\approx0.4013[/tex]

Hence, the probability that the volume of soda in a randomly selected bottle will be less than 32​ oz is 0.4013

The probability that a randomly selected bottle of soda will be less than 32 oz is approximately 40.13%. This is calculated using the z-score and a standard normal distribution.

To find the probability that the volume of soda in a randomly selected bottle will be less than 32 oz, we can use the concept of z-score in statistics. The z-score is a measurement of how many standard deviations a data point is from the mean.

First, we need to calculate the z-score associated with 32 oz. The formula for the z-score is (X - μ) / σ, where X is the data point, μ is the mean, and σ is the standard deviation. Plugging our values in, we get (32 - 32.3) / 1.2 = -0.25.

Next, we consult a standard normal distribution table or use a calculator function to find the probability associated with this z-score. Using a TI-84 calculator, we perform the following steps: Go to the distribution menu ('2nd' then 'VARS'), choose '2: normalcdf(', input the following values: (-1E99, -0.25, 32.3, 1.2). Press 'ENTER' to get the result, which is approximately 0.4013. Thus, the probability that a randomly selected bottle of soda will be less than 32 oz is approximately 0.4013 or 40.13%.

https://brainly.com/question/14210034

#SPJ11

Answer:

-the elements in the domain of f(x) for which g(f(x)) is defined

Step-by-step explanation:

In order for g(f(x)) to exist we first must have that f(x) exist, then g(f(x)).

So the domain of g(f(x)) will be the elements in the domain of f(x) for which g(f(x)) is defined.

The description which best explains the domain of (gof)(x) is the elements in the domain of f(x) for which g(f(x)) is defined.

Composition of two functions f and g can be defined as the operation of composition such that we get a third function h where h(x) = (f o g) (x).

h(x) is called the composite function.

For two functions f(x) and g(x), the composite function (g o f)(x) is defined as,

(g o f)(x) = g (f(x))

So the domain of g(x) where x contains f(x).

Here when we defined g (f(x)), the domain of the composite function will be the elements in the domain of f(X).

Also these elements must be defined for g(x).

Hence the correct option is A.

Learn more about Domain of Functions here :

https://brainly.com/question/30194233

#SPJ7