Ms.Liu has $60 to buy candy and soda at the movies theater for her family. Candy cost $6 per box and soda cost $4 per cup .Write an algebraic expression that can be used to find the amount of money mr.Liu will have left if she buys a number of boxes of candy (c)and cups of soda (s).

Given equation is 2x² - y² = t²Also, x = t cos θDifferentiating x w.r.t t using the product rule, we get\(dx/dt = (d/dt)(t cos θ) + (d/dθ)(t cos θ)(dθ/dt)dx/dt = cos θ + (-tsinθ)(dθ/dt).\)

We are required to find (dx/dt)θ which means the differentiation of x with respect to t keeping θ as constant. Therefore, we can say that (dθ/dt) is 0 anddx/dt = cos θDifferentiating the given equation w.r.t t, we get:4x (dx/dt) - 2y (dy/dt) = 2t (dt/dt)2x (dx/dt) - y (dy/dt) = tHere, we need to find (dt/dy)x which means the differentiation of t with respect to y keeping x as constant.

Hence, we can say that (dx/dt) is 0.Thus,\(2x(0) - y (dy/dt) = t(dy/dt) = -t/y Therefore, (dx/dt)θ = cos θ and (dt/dy)x = -t/y.\)

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As a claims handler, Maria is responsible for managing and processing claims submitted by customers or clients. This role involves handling various types of claims, such as insurance claims, warranty claims, or product return claims, depending on the nature of the business.

In this capacity, Maria's ongoing work as a claims handler involves receiving and reviewing claim submissions, verifying the validity of the claims, gathering necessary documentation or evidence to support the claims, and assessing the coverage or liability.

She acts as a liaison between the customers and the organization, ensuring that the claims process is smooth and efficient. Maria may also need to investigate the circumstances surrounding the claims and make decisions on the appropriate course of action, such as approving or denying claims or negotiating settlements.

Additionally, she may be responsible for documenting and maintaining records of claims, communicating with customers to provide updates or resolve any issues, and ensuring compliance with applicable regulations and policies.

Overall, as a claims handler, Maria plays a crucial role in providing timely and fair resolutions to customer claims, maintaining customer satisfaction, and protecting the interests of the organization.

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Answer:So to get a 6 when rolling a six-sided die, probability = 1 ÷ 6 = 0.167, or 16.7 percent chance. So to get two 6s when rolling two dice, probability = 1/6 × 1/6 = 1/36 = 1 ÷ 36 = 0.0278, or 2.78 percent.

Step-by-step explanation:

Answer:

C.72

Step-by-step explanation:

rolling a six-sided number cube(6) x flipping a coin(2) x  rolling a six-sided number cube again(6)= 72

6x6= 36

         36 x 2 = 72

6x2=12

12 x 6 = 72

By using factoring by grouping or synthetic division, we find that \(x = -2\) is a real solution.

Checking for Rational Roots

Using the rational root theorem, the possible rational roots of the polynomial are given by the factors of the constant term (24) divided by the factors of the leading coefficient (-4).

The possible rational roots are ±1, ±2, ±3, ±4, ±6, ±8, ±12, ±24.

By substituting these values into \(f(x)\), we find that \(f(-2) = 0\). Hence, \(x + 2\) is a factor of \(f(x)\).

Dividing \(f(x)\) by \(x + 2\) using long division or synthetic division, we get:

Now, we have reduced the problem to factoring \(-4x³ + 18x² - 16x + 12\).

Attempt 2: Factoring by Grouping

Rearranging the terms, we have:

Factoring out common factors, we obtain:

Now, we have \(2x^2(-2x + 9) + 4(4x - 3)\). We can further factor this as:

Therefore, the fully factored form of \(f(x) = -4x⁴  + 26x³  - 50x² + 16x + 24\) is \(f(x) = (x + 2)(2x² + 4)(-2x + 9)\).

Solutions to the polynomial equations:

Using polynomial division or synthetic division, we can find the quadratic equation \((x + 2)(x² + 2x - 3)\). Factoring the quadratic equation, we get \(x² + 2x - 3 = (x +

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Answer:

x is 11

Step-by-step explanation:

\({ \sf{ \sqrt{x + 5} - 3 = 1}} \\ { \sf{ \sqrt{x + 5} = 4 }} \\ { \sf{x + 5 = 16}} \\ { \sf{x = 11}}\)

Answer:

\(x = 11\)

Step-by-step explanation:

\( \sqrt{x + 5} −3=1\)

\( \sqrt{x + 5} = 1 + 3\)

\( \sqrt{ {x} + 5 } = 4\)

\( \sqrt{x + {5}^{2} } = {4}^{2} \)

\(x + 5 = 16\)

\(x = 16 - 5\)

\(x = 11\)

The price of the two pencils is Rs.100 (expensive) and Rs.60 (cheaper).

Let the price of the expensive pencil be = x

And the price of the cheaper one be = y.

According to the question:

The difference between the price of 2 = 40

Therefore,

x- y =40

Total amount = 1800.

The number of Expensive pencils that can be bought = 1800/x.

The number of Expensive pencils that can be bought = 1800/y.

According to the question,

1800/y -1800/x = 15 (the number of extra pencils)

= (1800x -1800y)/xy = 15

= 1800x -1800y =15xy

= 1800 (x-y) =15xy

Substituting x-y as 40

1800 x 40 =15xy

xy = 4800.

We know that x-y =40

Therefore, x = y+ 40

xy = 4800

(y+40) y = 4800

\(y^{2}\) + 40 y = 4800

Using the quadratic equation formula,

y = 52.111 or y = -92.111

Thus, the cost of the cheaper pencil (y)= Rs. 52.111

The cost of the expensive pencil (x) = 52.111 + 40 = Rs 92.111

Therefore the cost of two pencils is =   Rs. 52.111 and Rs 92.111.

Since each coupon decreases the price by 0.75, we can represent its value as (-0.75).

Then, the customer used 3 coupons, so the total discount is 3 times (-0.75), therefore the expression that represents this scenario is:

Correct option: B.

Answer: The scale factor from the first map to the second map is 4:3 (four to three) The side lengths of the landmark on the second map is 9/4 mm, 3 mm, 15/4mm.

Step-by-step explanation:

The scale factor is 8:6 which can be simplified to 4:3.

The side lengths of the landmark on the second map follows the same scale 4:3, so going in order:

4:3 = 3:x

4x = 9

x = 9/4

4:3 = 4:y

y = 3

4:3 = 5: z

4z = 15

z = 15/4

Answer:

there are 10 girls in the club

Step-by-step explanation:

25*40% is equal to 10

Answer:

white sold = 16

yellow sold = 12

Step-by-step explanation:

w = # of white sold

y = # of yellow sold

w + y = 28   solve this for w

w = 28 - y

9.95w + 13.5y = 321.20     substitute w = 28-y into this expression and solve for y

9.95(28-y) + 13.5y = 321.20

278.60 - 9.95y + 13.50y = 321.20

278.60 + 3.55y = 321.20

3.55y = 321.20 - 278.60 = 42.60

y = 42.60/3.55 = 12   substitute this into w = 28 - y and solve for w

w = 28 - 12 = 16

The area of the shaded region is  4 cm².

The area of the shaded region is calculated by applying Cavalieri's principle.

Cavalieri's principle states that if two three-dimensional objects have the same cross-sectional area along a height and the same height, then the figures have the same volume.

The area of the shaded figure is calculate as follows;

from the diagram the width of the shaded region = 2 cm

The height of the shaded region = 2 cm

Area = 2 cm x 2 cm = 4 cm²

Thus, the area of the shaded region is determined by considering Cavalieri's principle.

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Answer:

R 270

Step-by-step explanation:

Amount paid for one hour =  \(\frac{360}{12}\)

Amount paid for one hour = Rs 30

Amount paid for 9 hours = 9 × 30

Amount paid for 9 hours = Rs 270

The painter will be paid Rs 270 for 9 hours of work.

Answer:

  y(x) = -(2/e)x +3

Step-by-step explanation:

You want the equation of the line tangent to the parametric curve at t=1.

  (x, y) = (e^(√t), t -2·ln(t))

At t=1, the point of tangency is ...

  (x, y) = (e^(√1), 1 -2·ln(1)) = (e, 1)

The derivatives with respect to t are found using the chain rule:

  dx = d(e^u)du = d(e^√t)(1/(2√t))dt

  dx = (e^√t)/(2√t))·dt

  dy = (1 -2/t)·dt

Then the slope of the tangent line is ...

  m = dy/dx = (1 -2/t)(2√t)/e^√t

For t=1, this is ...

  m = (1 -2/1)(2√1)/(e^1) = -2/e

The equation for a line with slope m through point (h, k) is ...

  y = m(x -h) +k

The equation for a line with slope -2/e through point (e, 1) is ...

  y = (-2/e)(x -e) +1

  y = (-2/e)x +3

Answer:

  y(x) = -(2/e)x +3

Step-by-step explanation:

You want the equation of the line tangent to the parametric curve at t=1.

  (x, y) = (e^(√t), t -2·ln(t))

At t=1, the point of tangency is ...

  (x, y) = (e^(√1), 1 -2·ln(1)) = (e, 1)

The derivatives with respect to t are found using the chain rule:

  dx = d(e^u)du = d(e^√t)(1/(2√t))dt

  dx = (e^√t)/(2√t))·dt

  dy = (1 -2/t)·dt

Then the slope of the tangent line is ...

  m = dy/dx = (1 -2/t)(2√t)/e^√t

For t=1, this is ...

  m = (1 -2/1)(2√1)/(e^1) = -2/e

The equation for a line with slope m through point (h, k) is ...

  y = m(x -h) +k

The equation for a line with slope -2/e through point (e, 1) is ...

  y = (-2/e)(x -e) +1

  y = (-2/e)x +3

The equation representing the relationship between dy/dt and dx/dt that is rate at which the length of the woman's shadow is changing is equal to option C. dy/dt =4× (dx/dt).

Woman is walking towards the street lamp.

Rate at which the length of her shadow is changing as she walks.

Let us consider the height of the street lamp as h = 20 feet.

Height of the woman be w = 5 feet.

And the distance between the woman and the street lamp be x.

Length of the woman's shadow be y.

Triangles formed by the woman, the street lamp, and their shadows are similar.

Sides of similar triangles are in proportion,

This implies,

h / y = (h + w) / (x + y)

Solving for y we get,

⇒h(x + y) = y(h + w)

⇒hx + hy = hy + wy

⇒y = hx / w

Rate at which the length of the woman's shadow is changing by differentiating both sides of this equation with respect to time,

⇒ dy/dt = h(dx/dt) / w

Substitute in the values for dx/dt = 3 ft/s, h and w we get,

⇒dy/dt = (20)(3) / 5

⇒dy/dt = 60 /5

⇒dy/dt =12

⇒dy/dt = 4(3)

⇒dy/dt =4× (dx/dt)

Therefore, the rate at which the length of the woman's shadow is changing is given by option C. dy/dt =4× (dx/dt) .

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The probability distribution's mean and standard deviation, Y, will be 0.4899 and 0.699, respectively, based on the information provided.

By dividing the sum of the supplied numbers by the entire number of numbers, the mean—the average of the given numbers—is determined.

The middle value in a sorted, ascending or descending list of numbers is known as the median, and it has the potential to describe a data collection more accurately than the average does. It reflects the midway of the data since it is the point above and below which half (50%) of the observed data falls.

Mean= (Sum of All Observations/Total number of Observations).

How is a probability distribution made?

It should be noted that the probability distribution for y will be as follows given the probability distribution:

Y                         0           1         . 2

Probabilities      0.63     0.25,  0.12

The median value of Y is:

Mean = (0 × 0.63) + (1 × 0.25) + (2 × 0.12)

Mean = 0 + 0.25 + 0.25

Mean = 0.49

The variance will be 0.4899. Therefore, the standard deviation will be:

standard deviation = ✓0.4899

=> Standard Deviation = 0.699

So, The probability distribution's mean and standard deviation, Y, will be 0.4899 and 0.699, respectively

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If Hilda has $210 worth of $10 and $12 stock shares and the number of $10 shares is 5 more than twice the number of $12 shares, then the number of $10 shares and $12 shares she has is equal to 15 and 5 respectively.

The number of $10 shares and $12 shares can be calculated by forming linear equations.

Consider the number of $10 shares to be x and the number of $12 shares to be y.

x = 2y + 5

10x + 12y = 210

Putting the value x = 2y + 5 in the second equation,

10x + 12y = 210

10 (2y + 5) + 12y = 210

20y + 50 + 12y = 210

32y + 50 = 210

32y = 210 - 50

32y = 160

y = 160 ÷ 32

y = 5

Putting y = 5 in the first equation,

x = 2y + 5

x = 2(5) + 5

x = 10 + 5

x = 15

Hence the number of $10 and $12 shares she has is calculated to be 15 and 5 respectively.

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The dimensions of the rectangle are:

To find the dimensions of the rectangle:

Let,

Extend the area equation as follows:

Rearrange:

Substitute known information for A:

To solve quickly, factor the left side (or use the quadratic formula):

The factorial solutions for w are -2 and 7/2.

Assuming this is a genuine rectangle, the width must be positive.

As a result, the length is:

That is,

Therefore, the dimensions of the rectangle are:

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The complete question is given below:
The area of a rectangle is 14 yd², and the length of the rectangle is 3 yd less than double the width. find the dimensions of the rectangle.

Answer:

0.565 m^3 to the nearest thousandth.

Step-by-step explanation:

The volume of the cylinder = π r^2 h

Here the radius r = 1/2 diameter

= 1/2 * 3 = 1.5 m

8 cm = 0.08 m.

So the volume = π (1.5)^2 * 0.08

= 0.565 m^3 to the nearest thousandth.

Answer: 32 miles

Step-by-step explanation:

48-16

48

-16

__

32

The standard form of the given numbers is 207360 × 10¹⁷.

The number system is a way to represent or express numbers.

A decimal number is a very common number that we use frequently.

Since the decimal number system employs ten digits from 0 to 9, it has a base of 10.

Any of the multiple sets of symbols and the guidelines for utilizing them to represent numbers are included in the Number System.

Given the numbers is  (5 x 1,000,000) (6 x 100,000) (4 x 10,000) (8 x 1,000) (3 x 100) (2 x 10) (4 x 0.1) (9 x 0.001)

Now standard form means we need to write the exponents form.

So,

5 x 6 x 4 x 8 x 3 x 2 x 4 x 9 = 207360

And

1,000,000 x  100000 x 10000 x 1000 x 100 x 10 x 0.1 x 0.001 = 10¹⁷

So, combine 207360 x  10¹⁷

Hence "The standard form of the given numbers is 207360 × 10¹⁷".

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3  is the answer

you're welcome

Step-by-step explanation:

4 is the answer since the question asks if the student would prefer so to get a better opinion you'd have to ask ever student in all grade

Answer: 45ft

Step-by-step explanation:

You do 8 x 5 first which you get 40 then you do 10 x 5 which you get 50 you add 40 and 50 you get 90 and since it’s made out of triangles you do bh1/2 so you do 90 x 1/2 or 90 / 2 and you get 45ft

Answer:

(m,n) is (-2,2)

Step-by-step explanation:

Elimination means that we should rewrite one of the two equations as an expression of one of the variables isolated, and then use that definition isn the other equation.  It is also called "substitution."

Lets use the first equation and rewrite it so that the variable m is isolated:

3m-4n=-14

-4n = -3m-14

n = (3/4)m +(7/2)

Now use this definition of n in the second equation:

3m+2n=-2

3m+2((3/4)m +(7/2)) = -2

3m + (3/2)m + 7 = -2

4.5m = -9

m = -2

Now use m= -2 in either equation to find n.

3m-4n=-14

3(-2)-4n=-14

-6 -4n = -14

-4n = -8

n = 2

The solution of this system of equations is (-2,2).

See the attached graph, with x and y used in place of m and n.

Answer:

Step-by-step explanation:

The first step is to find the slope of the tangent line. To do that, we need to find the derivative of f(x):

f(x) = sin(x) + 2cos(x)

f'(x) = cos(x) - 2sin(x)

Now we can find the slope of the tangent line at x=0 by plugging in x=0 into f'(x):

f'(0) = cos(0) - 2sin(0) = 1

Therefore, the slope of the tangent line at x=0 is 1.

Next, we need to find the y-coordinate of the point on the graph where x=0. To do that, we simply plug in x=0 into f(x):

f(0) = sin(0) + 2cos(0) = 2

Therefore, the point on the graph where x=0 is (0, 2).

Now we can use the point-slope form of the equation of a line to find the equation of the tangent line:

y - y1 = m(x - x1)

where m is the slope and (x1, y1) is the point on the line. Plugging in m=1 and (x1, y1) = (0, 2), we get:

y - 2 = 1(x - 0)

Simplifying, we get:

y = x + 2

Therefore, the equation of the tangent line is y = x + 2.

Answer:

The equation of the tangent line at x = 0 can be found by differentiating the function f(x) and using the point-slope form of a line.

The derivative of f(x) is f'(x) = cos(x) - 2sin(x). Substituting x = 0 into f'(x) gives f'(0) = cos(0) - 2sin(0) = 1 - 0 = 1.

Therefore, the equation of the tangent line is y = 1x + b, or y = x + b.

To find the value of b, we can plug in x = 0 and y = f(0) = sin(0) + 2cos(0) = 2 into the equation. Solving for b, we get 2 = 0 + b, so b = 2.

Therefore, the slope-intercept equation of the line tangent to the graph of y = f(x) at the point (0,2) is y = x + 2.

Answer: x ≥ 17

Step-by-step explanation:

We know that she worked 7 hours at a dinner, for $10 per hour last week.

Then in the last week, she did make:

7*$10 = $70

Now she babysits, she wins $8 per hour, then if she works x hours, she will win:

w(x) = $8*x

if we add the $70 that she already had, we have:

$70 + $8*x

And we know that she wants to have, at least, $206, then we can write the inequality.

$70 + $8*x ≥ $206.

Now let's solve this for x.

first, we can subtract $70 in both sides:

($70 + $8*x) - $70 ≥ $206 - $70

$8*x ≥ $136

now we can divide by $8 in both sides:

($8*x)/$8 ≥ $136/$8

x ≥ 17

This means that she must babysit for at least 17 hours if she wants to buy the dress.

Answer:

The number is → 56

Step-by-step explanation:

tens digit \(\Rightarrow x\)

unit digit \(\Rightarrow y\)

"The difference between the digits of a two-digit number is 1...", " ...the unit digit is greater than the tens digit..."

\(y-x=1 \qquad \textbf{ec.1}\)

"The number itself is one more (unit) than five times the sum of its digits..."

\(10x+y=5(x+y)+1\\ 10x+y= 5x + 5y+1\\5x= 4y+1 \qquad \textbf{ec.2}\)

we clear "y" in equation 1:

\(y=1+x \qquad \textbf{ec.3}\)

then we substitute in equation 2:

\(5x=4(1+x)+1\\5x=5+4x\\\boxed{x=5}\)

Finally, we substitute in equation 3:

\(y=1+5\\\boxed{y=6}\)

With this we have solved the exercise.

\(\text{-B$\mathfrak{randon}$VN}\)

Carolyn made an error in her work because she did not correctly distribute the negative in Step 3.

A system of equations is the given term math for two or more equations with the same variables. The solution of these equations represents the point of the intersection.

You can solve a system of equations by the adding or substitution methods. In the addition method, you eliminate a variable, on the other hand, in the substitution method you replace a variable for the other.

The question gives:3x-2y=7 (1)y=x+2The question shows that Carolyn applies the substitution method because she replaces the variable y (equation 2) in equation 1. See the given step 2.

3x – 2y = 7

3x – 2(x + 2) = 7

3x – 2x - 4 = 7 - here it is the mistake. (Carolyn did not correctly distribute the negative).

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Answer:

Undefined or Infinity

Step-by-step explanation:

(x1,y1)=(-11,8)

(x2,y2)=(-11,-17)

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

= (-17-8)/(-11-(-11))

= -25/0

= Undefined