The function g is defined by g(x)=2x^2-3.
Find g(2y)

To calculate the work done to lift the leaking water, consider the average weight of the water over each part of the journey and calculate force x distance. After doing this, it is found that the total work done is 160 ft-lb.

This problem is a example of work done against gravity. Gravity pulls the water downward, whereas the rope lifts it upward. Remember the formula for work is Work = force x distance. In this case, the force is the weight of the water being lifted (decreasing as the water leaks out) and the distance is the height the bucket is raised.

Let's start by assuming that the rate of the water leaking out is linear. This means that if the bucket is lifted halfway up the rope when it's half empty, then its average weight over the first 10 feet is 0.75 * 16 lb (12 lb), and its average weight over the next 10 feet is 0.25 * 16 lb (4 lb).

So the work done is calculated as follows:

Therefore, the total work done in lifting the water alone is Work1 + Work2 = 160 ft-lb.

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To solve this problem, you can use calculus to determine the work done lifting the water as it leaks out of the bucket. To find the amount of work done to lift the water to the top, you'll need to integrate the varying weight of the water over the distance it's lifted. Since the water leaks out at a constant rate, it will linearly decrease in weight from 16 pounds to 0 pounds over the course of the 20-foot ascent.
You're given that the bucket starts with 16 pounds of water, which is equal to 2 gallons. That's because 1 gallon of water weighs approximately 8 pounds. The water weight decreases to 0 pounds as the height reaches 20 feet.
The weight of the water as a function of height, \( w(x) \), can be modeled as a linear function that starts from 16 lb at the ground (when \( x = 0 \)) and goes to 0 lb at 20 ft (when \( x = 20 \)). Thus, the weight function is:
\[ w(x) = 16 - \frac{16}{20}x \]
This simplifies to:
\[ w(x) = 16 - 0.8x \]
The work done lifting the water from height \( x \) to \( x + dx \) is \( w(x) \cdot dx \).
Work, \( W \), is the integral of this force over the distance it's applied:
\[ W = \int_{0}^{20} w(x) \, dx \]
Substitute \( w(x) \) into the equation:
\[ W = \int_{0}^{20} (16 - 0.8x) \, dx \]
Evaluating this integral involves finding the antiderivative:
\[ W = \left[ 16x - 0.4x^2 \right]_{0}^{20} \]
Apply the bounds of the integration (from 0 to 20):
\[ W = \left( 16(20) - 0.4(20)^2 \right) - \left( 16(0) - 0.4(0)^2 \right) \]
\[ W = (320 - 0.4(400)) - (0 - 0) \]
\[ W = 320 - 160 \]
Therefore, the total work done lifting the water alone is:
\[ W = 160 \text{ foot-pounds} \]

Answer:

Area of the rectangle is increasing with the rate of 84 cm/s.

Step-by-step explanation:

Let l represents the length, w represents width, t represents time ( in seconds ) and A represents the area of the triangle,

Given,

[tex]\frac{dl}{dt}=6\text{ cm per second}[/tex]

[tex]\frac{dw}{dt}=5\text{ cm per second}[/tex]

Also, l = 12 cm and w = 4 cm,

We know that,

A = l × w,

Differentiating with respect to t,

[tex]\frac{dA}{dt}=\frac{d}{dt}(l\times w)[/tex]

[tex]=l\times \frac{dw}{dt}+w\times \frac{dl}{dt}[/tex]

By substituting the values,

[tex]\frac{dA}{dt}=12\times 5+4\times 6[/tex]

[tex]=60+24[/tex]

[tex]=84[/tex]

Hence, the area of the rectangle is increasing with the rate of 84 cm/s.

Answer:

2.5 ml for a dosage of 20 mg.

Step-by-step explanation:

Hello, great question. These types are questions are the beginning steps for learning more advanced Ratio problems.

Since this is basically a ratio problem we can use the simple Rule of Three property to solve this problem. The Rule of Three property can be seen in the photo below. Now we just plug in the values and solve for x.

 8 mg.   ⇒   1 ml.

20 mg.   ⇒   x

[tex]\frac{20mg*1ml}{8mg} = 2.5ml[/tex]

Now we can see that we should administer a 2.5 ml for a dosage of 20 mg.

I hope this answered your question. If you have any more questions feel free to ask away at Brainly.

Answer:

$15400

Step-by-step explanation:

Principle amount, P = $14000

Time, T = 1 year

Rate of interest, R = 10%

We know that maturity amount,

[tex]A = P\left (1+\frac{R}{100} \right )^{n}[/tex]

where n is number of years

[tex]A = P\left (1+\frac{R}{100} \right )^{n}[/tex]

[tex]A = 14000\left (1+\frac{10}{100}\right )^{1}[/tex]

[tex]A = 14000\left (1+\frac{1}{10}\right )[/tex]

[tex]A = 14000\left (\frac{11}{10}\right )[/tex]

[tex]A = 15400[/tex]

The maturity amount is $15400

Kayla should take out a loan of $12,727.27 to have $14,000 after accounting for a 10% discount rate over one year.

Kayla needs to determine the amount she must borrow so that after accounting for the interest rate of 10%, she will have proceeds of $14,000 to invest in new equipment for her shop. The equation to calculate this is the present value (amount borrowed) equals the future value (amount after interest) divided by one plus the interest rate to the power of the period, which in this case is one year.

Using this formula:

Amount Borrowed = $14,000 / (1 + 0.10)1

Amount Borrowed = $14,000 / 1.10

Amount Borrowed = $12,727.27

Therefore, Kayla should ask for a loan of $12,727.27 to receive $14,000 after one year.

Answer:

-1

Step-by-step explanation:

Move all terms containing  x

to the left side of the equation.

Tap for fewer steps...

Subtract  4x from both sides of the equation.

2 x−10−4x= −8 y=4x−8

Subtract  4 x  from  2 x − 2 x− 10= − 8 y = 4 x − 8

Move all terms not containing  x  to the right side of the equation.

Tap for more steps...

− 2 x = 2 y = 4 x − 8

Divide each term by  − 2  and simplify.

Tap for fewer steps...

Divide each term in  − 2 x= 2  by  − 2 .

− 2 x − 2 = 2 − 2 y = 4 x − 8

Simplify the left side of the equation by cancelling the common factors.

Tap for fewer steps...

Reduce the expression by cancelling the common factors.

Tap for more steps...

− ( − 1 ⋅ x ) = 2 2 y = 4 x − 8

Rewrite  

− 1 ⋅ x  as  - x . x = 2 − 2 y = 4 x − 8

Divide  2  by  − 2 .

x = − 1 y = 4 x − 8

Replace all occurrences of  x  with the solution found by solving the last equation for  x . In this case, the value substituted is  − 1 . x= − 1 y = 4 ( − 1 ) − 8

Simplify  4 ( − 1 ) − 8 .

Tap for fewer steps...

Multiply  4 by  − 1 .

x = − 1 y = − 4 − 8

Subtract  8  from  - 4 .

x = − 1 y = − 12

The solution to the system of equations can be represented as a point.

( − 1 , − 12 )

The result can be shown in multiple forms.

Point Form:  ( − 1 , − 12 )

Equation Form:  x  =− 1  ,y = − 12

By the chain rule,

[tex]\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{\mathrm dy}{\mathrm dt}\dfrac{\mathrm dt}{\mathrm dx}[/tex]

Then for all [tex]t[/tex] the first derivative has a value of 7.

By the product rule,

[tex]\dfrac{\mathrm d^2y}{\mathrm dx^2}=\dfrac{\mathrm d}{\mathrm dx}\left[\dfrac{\mathrm dy}{\mathrm dt}\dfrac{\mathrm dt}{\mathrm dx}\right]=\dfrac{\mathrm d\left(\frac{\mathrm dy}{\mathrm dt}\right)}{\mathrm dx}\dfrac{\mathrm dt}{\mathrm dx}+\dfrac{\mathrm dy}{\mathrm dt}\dfrac{\mathrm d^2t}{\mathrm dx^2}[/tex]

but [tex]t=x\implies\dfrac{\mathrm dt}{\mathrm dx}=1\implies\dfrac{\mathrm d^2t}{\mathrm dx^2}=0[/tex], so we're left with

[tex]\dfrac{\mathrm d^2y}{\mathrm dx^2}=\dfrac{\mathrm d\left(\frac{\mathrm dy}{\mathrm dt}\right)}{\mathrm dx}[/tex]

By the chain rule,

[tex]\dfrac{\mathrm d^2y}{\mathrm dx^2}=\dfrac{\mathrm d\left(\frac{\mathrm dy}{\mathrm dt}\right)}{\mathrm dx}=\dfrac{\mathrm d\left(\frac{\mathrm dy}{\mathrm dt}\right)}{\mathrm dt}\dfrac{\mathrm dt}{\mathrm dx}=\dfrac{\mathrm d^2y}{\mathrm dt^2}[/tex]

but [tex]y=7t-2\implies\dfrac{\mathrm dy}{\mathrm dt}=7\implies\dfrac{\mathrm d^2y}{\mathrm dt^2}=0[/tex] so the second derivative is 0 for all [tex]t[/tex].

The derivative dy/dx for the given parametric equations is 7, and the second derivative d2y/dx2 is zero. The slope at t = 9 is 7, and the curve does not exhibit concavity since it is linear.

To find dy/dx for the parametric equations x = t and y = 7t - 2, we need to compute the derivatives of both x and y with respect to t and then use the chain rule to find dy/dx as dy/dt divided by dx/dt. Since the derivative of x with respect to t is 1, and the derivative of y with respect to t is 7 (as the derivatives of the constants -2 and 1 are zero), dy/dx equals 7/1, which is 7. To find the second derivative d2y/dx2, we note that since dx/dt is constant (equals 1), the second derivative is zero. Therefore, the concavity of the curve does not change and is neither concave up nor down.

At the given value of the parameter t = 9, the slope of the tangent line is 7, as it is for all values of t. Since the second derivative is zero, the curve is linear and does not exhibit concavity at any point, including t = 9.

Check the picture below.

so the hyperbola looks more or less like so, with a = 6, and its center at the origin.

[tex]\bf \textit{hyperbolas, vertical traverse axis } \\\\ \cfrac{(y- k)^2}{ a^2}-\cfrac{(x- h)^2}{ b^2}=1 \qquad \begin{cases} center\ ( h, k)\\ vertices\ ( h, k\pm a)\\ c=\textit{distance from}\\ \qquad \textit{center to foci}\\ \qquad \sqrt{ a ^2 + b ^2}\\ asymptotes\quad y= k\pm \cfrac{a}{b}(x- h) \end{cases} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]

[tex]\bf \begin{cases} a=6\\ h=0\\ k=0\\ \stackrel{asymptotes}{y=\pm\frac{3}{4}x} \end{cases}\implies \stackrel{\textit{using the positive asymptote}}{0+\cfrac{6}{b}(x-0)=\cfrac{3}{4}x}\implies \cfrac{6x}{b}=\cfrac{3x}{4}\implies 24x=3xb \\\\\\ \cfrac{24x}{3x}=b\implies 8=b \\\\[-0.35em] ~\dotfill\\\\ \cfrac{(y- 0)^2}{ 6^2}-\cfrac{(x- 0)^2}{ 8^2}=1\implies \cfrac{y^2}{36}-\cfrac{x^2}{64}=1[/tex]

Answer: 50% is the probability

Step-by-step explanation:

There are to people showing up at to different times now the probability is out of a 100%.

So 100 divided by 2 will equal to a 50

Answer: Dividend paid = $750,000

Explanation:

In order to compute the dividends paid by the firm in 2014 , we'll use the following formula :

Retained earning at end = Retained earning at beginning +Net income -Dividend paid

$5,200,000 = $4,900,000 +  $1,050,000 - Dividend paid

Dividend paid = $4,900,000 +  $1,050,000 - $5,200,000

Dividend paid = $750,000

Answer:

  (a) increasing: (-ln(2)/3, ∞); decreasing: (-∞, -ln(2)/3)

  (b) minimum: (-ln(2)/3, (9/8)∛2) ≈ (-0.21305, 1.41741); maximum: DNE

  (c) inflection point: DNE; concave up: (-∞, ∞); concave down: DNE

Step-by-step explanation:

The first derivative of f(x) = e^(8x) +e^(-x) is ...

  f'(x) = 8e^(8x) -e^(-x)

This is zero at the function minimum, where ...

  8e^(8x) -e^(-x) = 0

  8e^(9x) -1 = 0 . . . . . . multiply by e^x

  e^(9x) = 1/8 . . . . . . .  add 1, divide by 8

  9x = ln(2^-3) . . . . . . take the natural log

  x.min = (-3/9)ln(2) = -ln(2)/3 . . . divide by the coefficient of x, simplify

This value of x is the location of the minimum.

__

The function value there is ...

  f(-ln(2)/3) = e^(8(-ln(2)/3)) + e^(-(-ln(2)/3))

  = 2^(-8/3) +2^(1/3) = 2^(1/3)(2^-3 +1)

  f(x.min) = (9/8)2^(1/3) . . . . . minimum value of the function

__

A graph shows the first derivative to have positive slope everywhere, so the curve is always concave upward. There is no point of inflection. The minimum point found above is the place where the function transitions from decreasing to increasing.

To find the intervals on which f(x) = [tex]e^8^x + e^(^-^x^)[/tex] is increasing and decreasing, analyze the first derivative. The function is increasing on (-1/8, ∞) and decreasing on (-∞, -1/8). The local minimum is at x = -1/8, and the function is concave up on (-∞, -1/8) and concave up on (-1/8, ∞).

To find the intervals on which the function f(x) = [tex]e^8^x + e^(^-^x^)[/tex] is increasing and decreasing, we need to analyze the first derivative of the function. The first derivative is f'(x) = [tex]8e^8^x - e^(^-^x^)[/tex]. We set this derivative equal to zero and solve for x to find the critical points. There is one critical point at x = -1/8. We can test intervals to the left and right of this critical point to determine the behavior of the function. The function is decreasing on (-∞, -1/8) and increasing on (-1/8, ∞). Therefore, the function is increasing on the interval (-1/8, ∞) and decreasing on the interval (-∞, -1/8).

To find the local minimum and maximum values of f, we analyze the second derivative of the function. The second derivative is f''(x) =[tex]64e^8^x + e^(^-^x^)[/tex]. We evaluate this second derivative at the critical point x = -1/8. The second derivative at x = -1/8 is positive, so the function has a local minimum at x = -1/8.

The inflection point of the function can be found by analyzing the points where the concavity changes. The second derivative changes sign at x = -1/8. Therefore, the inflection point of the function is (-1/8, f(-1/8)). To find the intervals on which the function is concave up and concave down, we analyze the sign of the second derivative. The second derivative is positive on (-∞, -1/8) and positive on (-1/8, ∞), meaning the function is concave up on (-∞, -1/8) and concave up on (-1/8, ∞).

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Answer:Given below

Step-by-step explanation:

Using mathematical induction

For n=1

[tex]2!=2^1[/tex]

True for n=1

Assume it is true for n=k

[tex]2!\cdot 4!\cdot 6!\cdot 8!.......2k!\geq \left ( k+1\right )^{k}[/tex]

For n=k+1

[tex]2!\cdot 4!\cdot 6!\cdot 8!.......2k!2\left ( k+1\right )!\geq \left ( k+1\right )^{k}\dot \left ( 2k+2\right )![/tex]

because value of [tex]2!\cdot 4!\cdot 6!\cdot 8!.......2k!=\left ( k+1\right )^{k}[/tex]

[tex]\geq \left ( k+1\right )^{k}\dot \left ( 2k+2\right )![/tex]

[tex]\geq \left ( k+1\right )^{k}\left [ 2\left ( k+1\right )\right ]![/tex]

[tex]\geq \left ( k+1\right )^{k}\left ( 2k+\right )!\left ( 2k+2\right )[/tex]

[tex]\geq \left ( k+1\right )^{k+1}\left ( 2k+\right )![/tex]

Therefore [tex]2!\cdot 4!\cdot 6!\cdot 8!.......2k!2\left ( k+1\right )! must be greater than \left ( k+1\right )^{k+1}[/tex]

Hence it is true for n=k+1

[tex]2!\cdot 4!\cdot 6!\cdot 8!.......2k!2\left ( k+1\right )!\geq \left ( k+1\right )^{k+1}[/tex]

Hence it is true for n=k

a. This recurrence is of order 2.

b. We're looking for a function [tex]A(x)[/tex] such that

[tex]A(x)=\displaystyle\sum_{n=0}^\infty a_nx^n[/tex]

Take the recurrence,

[tex]\begin{cases}a_0=a_0\\a_1=a_1\\a_n-5a_{n-1}+6a_{n-2}=0&\text{for }n\ge2\end{cases}[/tex]

Multiply both sides by [tex]x^{n-2}[/tex] and sum over all integers [tex]n\ge2[/tex]:

[tex]\displaystyle\sum_{n=2}^\infty a_nx^{n-2}-5\sum_{n=2}^\infty a_{n-1}x^{n-2}+6\sum_{n=2}^\infty a_{n-2}x^{n-2}=0[/tex]

Pull out powers of [tex]x[/tex] so that each summand takes the form [tex]a_kx^k[/tex]:

[tex]\displaystyle\frac1{x^2}\sum_{n=2}^\infty a_nx^n-\frac5x\sum_{n=2}^\infty a_{n-1}x^{n-1}+6\sum_{n=2}^\infty a_{n-2}x^{n-2}=0[/tex]

Now shift the indices and add/subtract terms as needed to get everything in terms of [tex]A(x)[/tex]:

[tex]\displaystyle\frac1{x^2}\left(\sum_{n=0}^\infty a_nx^n-a_0-a_1x\right)-\frac5x\left(\sum_{n=0}^\infty a_nx^n-a_0\right)+6\sum_{n=0}^\infty a_nx^n=0[/tex]

[tex]\displaystyle\frac{A(x)-a_0-a_1x}{x^2}-\frac{5(A(x)-a_0)}x+6A(x)=0[/tex]

Solve for [tex]A(x)[/tex]:

[tex]A(x)=\dfrac{a_0+(a_1-5a_0)x}{1-5x+6x^2}\implies\boxed{A(x)=\dfrac{a_0+(a_1-5a_0)x}{(1-3x)(1-2x)}}[/tex]

c. Splitting [tex]A(x)[/tex] into partial fractions gives

[tex]A(x)=\dfrac{2a_0-a_1}{1-3x}+\dfrac{3a_0-a_1}{1-2x}[/tex]

Recall that for [tex]|x|<1[/tex], we have

[tex]\displaystyle\frac1{1-x}=\sum_{n=0}^\infty x^n[/tex]

so that for [tex]|3x|<1[/tex] and [tex]|2x|<1[/tex], or simply [tex]|x|<\dfrac13[/tex], we have

[tex]A(x)=\displaystyle\sum_{n=0}^\infty\bigg((2a_0-a_1)3^n+(3a_0-a_1)2^n\bigg)x^n[/tex]

which means the solution to the recurrence is

[tex]\boxed{a_n=(2a_0-a_1)3^n+(3a_0-a_1)2^n}[/tex]

d. I guess you mean [tex]a_0=2[/tex] and [tex]a_1=5[/tex], in which case

[tex]\boxed{\begin{cases}a_0=2\\a_1=5\\a_2=13\\a_3=35\\a_4=97\\a_5=275\end{cases}}[/tex]

e. We already know the general solution in terms of [tex]a_0[/tex] and [tex]a_1[/tex], so just plug them in:

[tex]\boxed{a_n=2^n+3^n}[/tex]

Answer:

y=2/5x+3/5

Step-by-step explanation:

Use the slope formula to get the slope:

m=4/10

m=2/5

The y intercept is 3/5

The equation is y=2/5x+3/5

Answer:

y = (2/5)x + 3/5

Step-by-step explanation:

Points to remember

Equation of the line passing through the poits (x1, y1) and (x2, y2)  and slope m is given by

(y - y1)/(x - x1) = m    where slope m = (y2 - y1)/(x2 - x1)

To find the slope of line

Here (x1, y1) =  (-4, -1) and  (x2, y2) = (6, 3)

Slope = (y2 - y1)/(x2 - x1)

 = (3 - -1)/(6 - -4)

 = 4/10 = 2/5

To find the equation

(y - y1)/(x - x1) = m  

(y - -1)/(x - -4) = 2/5

(y + 1)/(x + 4) = 2/5

5(y + 1) = 2(x + 4)

5y + 5 = 2x + 8

5y = 2x + 3

y = (2/5)x + 3/5

The numbers on a six sided die are: 1, 2, 3, 4 ,5 ,6

There are 4 numbers that are either equal to 3 or greater than 3: 3, 4, 5 ,6

The probability of getting one is 4 chances out of 6 numbers, which is written as 4/6.

4/6 can be reduced to 2/3 ( simplified fraction)

Final answer:

The probability of rolling a number greater than or equal to 3 on a six-sided die is 2/3 or 0.6667 when rounded to four decimal places.

Explanation:

To find the probability of rolling a number greater than or equal to 3 on a standard six-sided die, we count the favorable outcomes and then divide this number by the total number of possible outcomes. The sample space, S, of a six-sided die is {1, 2, 3, 4, 5, 6}.

Numbers greater than or equal to 3 are 3, 4, 5, and 6. So, there are 4 favorable outcomes. The total number of possible outcomes is 6 (since there are 6 sides on the die).

The probability is thus the number of favorable outcomes (4) divided by the total number of possible outcomes (6), which simplifies to 2/3 or approximately 0.6667 when rounded to four decimal places.

Answer:

Step-by-step explanation:

Given that [tex]r = 0.952[/tex]

We have coefficient of determination

[tex]r^2 =0.952^2\\=0.906304[/tex]

=90.63%

This implies that nearly 91% of variation in change in dependent variable is due to the change in x.

The coefficient of determination is the square of the correlation (r) between predicted y scores and actual y scores; thus, it ranges from 0 to 1.

An R2 of 0 means that the dependent variable cannot be predicted from the independent variable.

An R2 of 1 means the dependent variable can be predicted without error from the independent variable.

Answer: [tex]R^{2}[/tex] = 0.89

Step-by-step explanation:

Coefficient of determination is represented by [tex]R^{2}[/tex]. This tells us that how much of the variation in the dependent variable is explained by the independent variable.

It is the ratio of explained variation by the independent variables to the total variation in the dependent variable.

Hence,

Coefficient of determination = [tex]\frac{Explained\ Variation}{Total\ Variation}[/tex]

= [tex]\frac{18.592}{20.711}[/tex]

[tex]R^{2}[/tex]= 0.89

∴ 89% of the variation in the dependent variable is explained by the independent variables.

The coefficient of determination is calculated by dividing the explained variation by the total variation. For the student's data, the coefficient of determination is approximately 0.8978, which translates to about 89.78% of the variation in the dependent variable being explained by the regression line.

The student is asking about the coefficient of determination, which is a statistical measure in a regression analysis. To find the coefficient of determination, we use the explained variation and the total variation from the regression equation. It is calculated by dividing the explained variation by the total variation and then squaring the result if needed to find r squared.

In this case, the explained variation is 18.592 and the total variation is 20.711. The formula to find the coefficient of determination (r²) is:

r² = Explained Variation / Total Variation

Plugging in the values we have:

r² = 18.592 / 20.711

r² ≈ 0.8978

Expressed as a percentage, the coefficient of determination is approximately 89.78%, which means that about 89.78% of the variation in the dependent variable can be explained by the independent variable using the regression line.

Answer:

The slope is -6 and the y intercept is -1

Step-by-step explanation:

Lets put the  equation in slope intercept form (y=mx+b) where m is the slope and b is the y intercept

-6x-y =1

Add y to each side

-6x-y+y = 1+y

-6x = 1+y

Subtract 1 from each side

-6x-1 = y+1-1

-6x-1 =y

y = -6x-1

The slope is -6 and the y intercept is -1

Answer:

A∩(A∪B)=A

Step-by-step explanation:

Let's find the answer as follows:

Let's consider that 'A' includes all numbers between X1 and X2 (X1≤A≥X2), and let's consider that 'B' includes all numbers between Y1 and Y2 (Y1≤B≥Y2). Now:

A∪B includes all numbers between X1 and X2, as well as the numbers between Y1 and Y2, so:

A∪B= (X1≤A≥X2)∪(Y1≤B≥Y2)

Now, A∩C involves only the numbers that are included in both, A and C. This means that 'x' belongs to A∩C only if 'x' is included in 'A' and also in 'C'.

With this in mind, A∩(A∪B) includes all numbers that belong to 'A' and 'A∪B', which in other words means, all numbers that belong to (X1≤A≥X2) and also (X1≤A≥X2)∪(Y1≤B≥Y2), which are:

A∩(A∪B)=(X1≤A≥X2) which gives:

A∩(A∪B)=A

Answer:

Step-by-step explanation:

Sugar and Salt even thought they both dissolve in water they both dissolve in different ways. When salt dissolves in water, its individual types of ions are torn apart from each other, while Sugar molecules stay together when dissolved in water, and therefore the molecules remain the same when dissolved in water.

This being said in science using your senses can be just as valuable as using calculations. In this case both Sugar and Salt taste differently. Sugar is sweet while Salt is salty. Therefore tasting the substance can be the easiest and most accurate way of determining the substance.

I hope this answered your question. If you have any more questions feel free to ask away at Brainly.

Final answer:

To determine if an unknown sample contains sugar, salt, or both, examine their solubility properties and chemical reactivity. Comparing the density of the sample against reference values of pure substances can provide preliminary identification, while testing for chloride ions with silver nitrate confirms the presence of salt.

Explanation:

Identifying Sugar and Salt in an Unknown Sample

To determine whether an unknown sample contains sugar, salt, or both, we must identify the physical and chemical properties that distinguish these substances. Salt (sodium chloride) and sugar (sucrose) have distinct solubility properties and chemical reactivity, which we can use to identify them when dissolved in water.

Solubility and Density Test

Both sugar and salt are highly soluble in water, but we can compare their densities to make a preliminary identification. A known volume of each substance is weighed and their densities calculated. Salt generally has a greater density than sugar. If the unknown sample has a certain mass, comparing it with the reference densities may provide an initial indication.

Chemical Reactivity Test

To confirm the identity of the substances, a chemical reactant such as silver nitrate can be introduced to the water solution of the unknown sample. If a white precipitate forms, it indicates the presence of chloride ions, which suggests the presence of salt. Since sugar does not produce a precipitate with silver nitrate, its absence would indirectly indicate the presence of sugar.

Performing these tests will allow us to determine if the unknown sample is sugar, salt, or a mixture of both. The greater the discrepancy between the calculated density and the known densities of pure sugar or pure salt, the more likely it is that the sample is a mixture.

Answer: 0.0192

Step-by-step explanation:

Given : The mean per capita consumption of milk per year : [tex]\mu=140\text{ liters}[/tex]

Standard deviation : [tex]\sigma=22\text{ liters}[/tex]

Sample size : [tex]n=233[/tex]

Let [tex]\overline{x}[/tex] be the sample mean.

The formula for z-score in a normal distribution :

[tex]z=\dfrac{\overline{x}-\mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]

For  [tex]\overline{x}=137.01[/tex]

[tex]z=\dfrac{137.01-140}{\dfrac{22}{\sqrt{233}}}\approx-2.07[/tex]

The P-value = [tex]P(\overline{x}<137.01)=P(z<-2.07)= 0.0192262\approx 0.0192[/tex]

Hence, the probability that the sample mean would be less than 137.01 liters is 0.0192 .

The probability that Little Joe, who has no brothers, is an only child is calculated using conditional probability and results in a 1/4 chance.

The question asks us to find the probability that Little Joe, who has no brothers, is an only child. The sample space for the number of children in a family can be defined as {1, 2, 3, 4}, since each of these outcomes has an equal probability of 1/4. We will define event A as Little Joe being an only child, and event B as the family having no additional male children. Since Little Joe is a boy and has no brothers, cases with more than one male child should not be a part of our conditional sample space.

To solve this, we are looking at the conditional probability P(A|B). The probability that Little Joe is an only child given he has no brothers is P(A|B) = P(A and B) / P(B). We can determine that P(A and B) is simply the probability that there is one child and that child is a boy (Little Joe), which is 1/4. Event B can happen in three scenarios: Little Joe is an only child, Little Joe has one sister, or Little Joe has two or three sisters, and each scenario has an equal probability. Therefore, P(B) = 1/4 (only child) + 1/4 (one sister) + 1/4 (two sisters) + 1/4 (three sisters), which adds to 1/4 * 4 = 1.

The answer therefore is P(A|B) = (1/4) / 1 = 1/4. There is a 1/4 chance that Little Joe, who has no brothers, is an only child.

Answer:  The lines L1 and L2 are parallel.

Step-by-step explanation:  We are given to determine whether the following lines L1 and L2 passing through the pair of points are parallel, perpendicular or neither :

L1 : (–5, –5), (4, 6),

L2 : (–9, 8), (–18, –3).

We know that a pair of lines are

(i) PARALLEL if the slopes of both the lines are equal.

(II) PERPENDICULAR if the product of the slopes of the lines is -1.

The SLOPE of a straight line passing through the points (a, b) and (c, d) is given by

[tex]m=\dfrac{d-b}{c-a}.[/tex]

So, the slope of line L1 is

[tex]m_1=\dfrac{6-(-5)}{4-(-5)}=\dfrac{6+5}{4+5}=\dfrac{11}{9}[/tex]

and

the slope of line L2 is

[tex]m_2=\dfrac{-3-8}{-18-(-9)}=\dfrac{-11}{-9}=\dfrac{11}{9}.[/tex]

Therefore, we get

[tex]m_1=m_2\\\\\Rightarrow \textup{Slope of line L1}=\textup{Slope of line L2}.[/tex]

Hence, the lines L1 and L2 are parallel.

Answer:

Parallel

Step-by-step explanation:

Answer:

[tex]H_0:\mu =873\\\\H_a: \mu<873[/tex]

Step-by-step explanation:

Given : In a study investigating a link between walking and improved​ health, researchers reported that adults walked an average of 873 minutes in the past month for the purpose of health or recreation.

Claim : The true average number of minutes in the past month that adults walked for the purpose of health or recreation is lower than 873 minutes.

i.e. [tex]\mu<873[/tex]

We know that the null hypothesis contains equal sign , then the set of hypothesis for the given situation will be :-

[tex]H_0:\mu =873\\\\H_a: \mu<873[/tex]

The null hypothesis assumes no difference, so it reflects an average walking time of 873 minutes (H0: μ = 873). The alternative hypothesis reflects the research query, suggesting the true average is less than 873 minutes (Ha: μ < 873).

In statistics, the null hypothesis and the alternative hypothesis are often used to test claims or assumptions about a population. In this case, the research is about whether the true average number of minutes in the past month that adults walked for the purpose of health or recreation is lower than 873 minutes.

The null hypothesis (H0) is often a statement of 'no effect' or 'no difference'. Here, it would be: H0: μ = 873. This means that the population mean (μ) of walking time is equal to 873 minutes.

The alternative hypothesis (Ha) is what you might believe to be true or hope to prove true. In this study, it would be: Ha: μ < 873. This means that the population mean of walking time is less than 873 minutes.

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Answer:

2/7

Step-by-step explanation:

For the president position, there are 4 females from a total of 7 people.

For the vice president position, there are 3 males from 6 people left over.

So the probability is 4/7 × 3/6 = 2/7.

Answer: [tex]\dfrac{2}{7}[/tex]

Step-by-step explanation:

Given : Number of males = 3

Number of females = 4

The number of ways to select a female is elected president and a male is elected vice president :-

[tex]^3P_1\times ^4C_1=\dfrac{3!}{(3-1)!}\times\dfrac{4!}{(4-1)!}=3\times4=12[/tex]

The total number of ways to select 2 people from 7 :_

[tex]^7P_2=\dfrac{7!}{(7-2)!}=42[/tex]

Now, the probability that a female is elected president and a male is elected vice president will be :-

[tex]\dfrac{12}{42}=\dfrac{2}{7}[/tex]

Answer: Option (4) is correct.

Step-by-step explanation:

Given that,

B = {John, Paul, George, Ringo, Pete, Stuart}

Now, we have select the Set that is equal to the Set B.

From all the options given in the question, option (4) is correct.

It contains all the elements of Set B but only the arrangement or sequence of the Set is different.

Correct Set 4 = {Paul, Ringo, Pete, John, George, Stuart} = Set B

The set matching B = {John, Paul, George, Ringo, Pete, Stuart} from the options provided is {Paul, Ringo, Pete, John, George, Stuart}, as it contains all the same members regardless of order and no other elements.

The question asks to select all answers that are equal to the set B = {John, Paul, George, Ringo, Pete, Stuart}. A set, in this context, is defined as a collection of distinct objects, considered as an object in its own right. In a set, the order of elements does not matter, but duplication of elements is not allowed. From the provided options, the only answer that matches set B exactly is {Paul, Ringo, Pete, John, George, Stuart}, since it contains all the same elements as set B, regardless of order, and does not include any additional elements.

Answer:

The correct answer is last option

Step-by-step explanation:

From the figure we can see two right angled triangle.

Points to remember

If two right angled triangles are congruent then their hypotenuse and one leg are congruent

To find the correct options

From the figure we get all the angles of 2 triangles are congruent.

one angle is right angle. But there is no information about the hypotenuse and legs.

So the correct answer is last option

There is not enough information to determine congruency.

Answer:

Accumulated amount will be $2504.90.

Step-by-step explanation:

Formula that represents the accumulated amount after t years is

A = [tex]A_{0}(1+\frac{r}{n})^{nt}[/tex]

Where A = Accumulated amount

[tex]A_{0}[/tex] = Initial amount

r = rate of interest

n = number of times initial amount compounded in a year

t = duration of investment in years

Now the values given in this question are

[tex]A_{0}[/tex] = $1000

n = 12

r = 4.6% = 0.046

t = 20 years

By putting values in the formula

A = [tex]1000(1+\frac{0.046}{12})^{240}[/tex]

  = [tex]1000(1+0.003833)^{240}[/tex]

  = [tex]1000(1.003833)^{240}[/tex]

  = 1000×2.50488

  = 2504.88 ≈ $2504.90

Therefore, accumulated amount will be $2504.90.

Answer:

  a) 297°

  b) 4.52 minutes

Step-by-step explanation:

a) Consider the attached figure. The boat's actual path will be the sum of its heading vector BA and that of the current, vector AC. The angle of BA north of west has a sine equal to 5/11. That is, the heading direction measured clockwise from north is ...

  270° + arcsin(5/11) = 297°

__

b) The "speed made good" is the boat's speed multiplied by the cosine of the angle between the boat's heading and the boat's actual path. That same value can be computed as the remaining leg of the right triangle with hypotenuse 11 and leg 5.

  boat speed = √(11² -5²) = √96 ≈ 9.7980 . . . . miles per hour

Then the travel time will be ...

  time = distance/speed

  (3900 ft)×(1 mi)/(5280 ft)×(60 min)/(1 h)/(9.7980 mi/h) ≈ 4.523 min

Answer:

0.0726mL

Step-by-step explanation:

Let's find the answer by using the following formula:

(subcutaneous dose)=(milliliters of the injection)*(drug concentration)/(child weight)

Using the given data we have:

(0.01mg/kg)=(milliliters of the injection)*(1mg/mL)/(16lbs)

milliliters of the injection=(0.01mg/kg)*(16lbs)/(1mg/mL)

Notice that the data has different units so:

1kg=2.20462lbs then:

16lbs*(1kg/2.20462lbs)=7.25748kg

Using the above relation we have:

milliliters of the injection=(0.01mg/kg)*(7.25748kg)/(1mg/mL)

milliliters of the injection=0.0726mL