3. Point A(–31, 72) is 407 to the right, 209 down from the point
C, what is the coordinate of C?

Answer:

17.5 kg of water.

Step-by-step explanation:

The amount of alcohol in the 15% solution = 20*0.15 =  3kg.

If 3 kg is equivalent to 8% solution

then 100%  is  3*100 / 8 = 37.5 kg.

So the amount of water to be added to make 8% solution = 37.5 - 20

= 17.5 kg.

Answer:

\( F = mt +b\)

From the info given we know that m =-11 and we have a condition given:

\( F =90 , t =4\)

Using this condition we have:

\( 90 = -11*4 +b\)

And solving for b we got:

\( 90 +4*11 = 90 +44= 134\)

So then the original temperatue for this case is 134 F

Step-by-step explanation:

For this case we know that after four hours the temperature was 90 f and the temperature dropped 11 f per hour.

We can use a linear model to solve the problem given by:

\( F = mt +b\)

Where F represent the temperature, t the time in hours and m the slope and b the intercept.

From the info given we know that m =-11 and we have a condition given:

\( F =90 , t =4\)

Using this condition we have:

\( 90 = -11*4 +b\)

And solving for b we got:

\( 90 +4*11 = 90 +44= 134\)

So then the original temperatue for this case is 134 F

Answer:

I honestly don't know what to say other than.....I'm sorry to hear that. I really am

Step-by-step explanation:

Answer:

1/3

Step-by-step explanation:

Answer:

18 cm^2

Step-by-step explanation:

The legs of a right triangle are the base and height of the triangle.

Since C is a right angle, AB is the hypotenuse.

AC and BC are the legs and the base and height.

sin 75 = BC/12

BC = 12 sin 75

cos 75 = AC/12

AC = 12 cos 75

area = bh/2 = (12 sin 75)(12 cos 75)/2

area = 18 cm^2

Answer:

Conclusion:

Step-by-step explanation:

Given

We know that the diagonals of a parallelogram bisect each other.

Therefore,

Given RT = x and TP = 5x-28, so

x = 5x-28

5x = x+28

5x-x = 28

4x = 28

divide boh sides by 4

4x/4 = 28/4

x = 7

Thus, the value of x = 7

Similarly,

QT = TS

Given QT = 5y and TS = 2y+12, so

5y = 2y+12

5y-2y = 12

3y = 12

divide both sides by 3

3y/3 = 12/3

y = 4

Thus, the value of y = 4

Conclusion:

Answer:

w = -10.5

Step-by-step explanation:

p = 21 +2w

get 2w by its self

p= 21 + 2x

-21  -21

p - 21 = 2w

cancel out p

p(0) - 21 = 2w

-21 = 2w

divide both sides by 2

w= -10.5

Hope this helps!!!

Answer: x = 18.9 to 1dp

Step-by-step explanation: Using SOH CAH TOA,

Sin 25 = 8/x

Making x subject of the formula:

x = 8/Sin 25

x = 18.92961267

x = 18.9 to 1dp

Explanation:

The reciprocal function of y = f(x) is the function y = 1/f(x)

So, to graph the reciprocal function, we need to identify the values of y for some points in the graph.

For example, y is equal to 0 at x = 0, x = 2π, and x = -2π.

It means that at x = 0, x = 2π, and x = -2π, the reciprocal function will be

1/f(x) = 1/0

Since the division by 0 is not defined, there will be vertical asymtotes at x = 0, x = 2π, and x = -2π.

On the other hand, we can see that at x = π and x = -3π, y is equal to 0.5, so the reciprocal function will be equal to:

1/f(x) = 1/0.5 = 2

And at x = -π and x = 3π, y is equal to -0.5, so the reciprocal function will be equal to:

1/f(x) = 1/(-0.5) = - 2

Therefore, we have the following for the reciprocal function:

It passes through the points (π, 2), (-3π, 2), (-π, -2), and (3π, -2)

It has vertical asymptotes in x = 0, x = 2π and x = -2π

So, the graph is:

y=-x-4 (a)

y=3x (b)

Put (b) into (a) and solve for x:

3x=-x-4

3x+x = -4

4x= -4

Divide both sides by 4

4x/4 = -4/4

x= -1

Replace the value of x on any equation:

y=3x = 3(-1) = -3

Solution : (-1,-3)

Graph:

The number of different paintings possible for the given figure is (3^66 + 3) / 6. after rotation.

To determine the number of different paintings possible, we need to consider the symmetries of the figure and apply the concept of Burnside's Lemma.

In this case, we have a figure with 66 disks that are to be painted in three different colors: blue, red, and green. We want to count the number of different paintings that can be obtained by rotating or reflecting the entire figure.

Let's analyze the symmetries of the figure:

1. Identity (no rotation or reflection): This symmetry leaves all the disks in their original positions. There is only one way to paint the figure in this case.

2. Rotation by 120 degrees clockwise: This symmetry can be achieved by rotating the figure one-third of a full rotation. Since we have three colors, each disk can be painted in any of the three colors independently. Therefore, there are 3^66 possible paintings that remain the same under this rotation.

3. Rotation by 240 degrees clockwise: This symmetry can be achieved by rotating the figure two-thirds of a full rotation. Similar to the previous case, there are 3^66 possible paintings that remain the same under this rotation.

4. Reflection along a vertical axis: This symmetry can be achieved by flipping the figure horizontally. Since the figure has an even number of disks, the reflection will result in the same pattern. Therefore, there is only one way to paint the figure that remains the same under this reflection.

5. Reflection along a horizontal axis: This symmetry can be achieved by flipping the figure vertically. Similar to the previous case, there is only one way to paint the figure that remains the same under this reflection.

6. Reflection along the main diagonal: This symmetry can be achieved by reflecting the figure along the main diagonal (from the top left to the bottom right). Again, since the figure has an even number of disks, the reflection will result in the same pattern. Therefore, there is only one way to paint the figure that remains the same under this reflection.

7. Reflection along the secondary diagonal: This symmetry can be achieved by reflecting the figure along the secondary diagonal (from the top right to the bottom left). Similar to the previous case, there is only one way to paint the figure that remains the same under this reflection.

Applying Burnside's Lemma, the number of distinct paintings is given by the average number of fixed points (paintings that remain the same) under each symmetry. Therefore, the total number of distinct paintings is:

(1 + 3^66 + 3^66 + 1 + 1 + 1) / 6 = (3^66 + 3) / 6

Calculating this expression may not be feasible due to the large exponent. Therefore, it is recommended to use a calculator or computer program to obtain the numerical value.

In conclusion, the number of different paintings possible for the given figure is (3^66 + 3) / 6.

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The decrease in diameter of the bar due to the applied load is -0.005434905d and the final diameter of the bar is 1.005434905d.

A compressive load of 80,000 lb is applied to a bar with a circular section of 0.75 in diameter and a length of 10 in.

if the modulus of elasticity of the bar material is 10,000 ksi and the Poisson's ratio is 0.3.

We have to determine the decrease in diameter of the bar due to the applied load.

Let d be the initial diameter of the bar and ∆d be the decrease in diameter of the bar due to the applied load, then the final diameter of the bar is d - ∆d.

Length of the bar, L = 10 in

Cross-sectional area of the bar, A = πd²/4 = π(0.75)²/4 = 0.4418 in²

Stress produced by the applied load,σ = P/A

= 80,000/0.4418

= 181163.5 psi

Young's modulus of elasticity, E = 10,000 ksi

Poisson's ratio, ν = 0.3

The longitudinal strain produced in the bar, ɛ = σ/E

= 181163.5/10,000,000

= 0.01811635

The lateral strain produced in the bar, υ = νɛ

= 0.3 × 0.01811635

= 0.005434905'

The decrease in diameter of the bar due to the applied load, ∆d/d = -υ

= -0.005434905∆d

= -0.005434905d

The final diameter of the bar,

d - ∆d = d + 0.005434905d

= 1.005434905d

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(a)The two descriptive statistics that can be cited are as follows: A. Of those investment managers surveyed, 44% were bullish or very bullish on the stock market.

B. Of those investment managers surveyed, 23% selected health care as the sector most likely to lead the market in the next 12 months.

(b)Inference about the population of all investment managers concerning the average return expected on equities over the next 12 months:By looking at the descriptive statistic given, we can say that the average expected return over the next 12 months for equities was 11.3%. Therefore, the inference about the population of all investment managers concerning the average return expected on equities over the next 12 months would be that most investment managers expect a return of about 11.3% on equities over the next 12 months.

(c)Inference about the length of time it will take for technology and telecom stocks to resume sustainable growth:By looking at the descriptive statistic given, we can say that the managers' average response when asked to estimate how long it would take for technology and telecom stocks to resume sustainable growth was 2.3 years. Therefore, the inference about the length of time it will take for technology and telecom stocks to resume sustainable growth would be that investment managers believe it will take about 2.3 years for technology and telecom stocks to resume sustainable growth.

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Options A and D are both correct. UV = 14 feet and mTUV = 45 degrees D. ST = 20 feet, UV = 14 feet, and mUST = 98 degrees by using congruence of triangles.

Two triangles are congruent if their corresponding sides are the same length and their corresponding angles are the same size.

According to the SAS criterion for triangle congruence, two triangles are congruent if they have two pairs of congruent sides and the included angle (the one between the congruent sides) in one triangle is congruent to the included angle in the other triangle.

Given

See the attachment for the triangle.

What evidence do you have?

SAS is used by STU and VTU.

To demonstrate their resemblance, we must examine the corresponding sides and angles of both triangles.

To begin, UST must equal UVT.

As a result, UST=UVT=98⁰.

Then, UV must equal US.

So:

UV = US = 14⁰

Furthermore, ST must equal VT.

So:

Furthermore, ST must equal VT.

As a result, ST = VT = 200.

Finally, TUV must be equal to TUS.

So: TUV = TUS = 450

Options A and D are both correct. UV = 14 feet and mTUV = 45 degrees D. ST = 20 feet, UV = 14 feet, and mUST = 98 degrees.

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Answer:

(i) This equation is not true, which means that the three squares cannot exactly surround a right-angled triangle.

(ii) It is not always possible for three squares to surround a right-angled triangle. One way to see this is to note that the side lengths of a right-angled triangle satisfy the Pythagorean theorem, which means that they must be in a certain relationship to each other. On the other hand, the areas of three squares can take any values, so it is not always possible to find three squares whose side lengths satisfy the Pythagorean theorem.

Step-by-step explanation:

To determine whether the three squares can exactly surround a right-angled triangle, we need to use the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.

Let's assume that the three squares have side lengths a, b, and c, with areas of 7 cm², 17 cm², and 10 cm², respectively. Then, we have:

a² = 7 cm²

b² = 17 cm²

c² = 10 cm²

We need to find out whether there exist values of a, b, and c that satisfy the Pythagorean theorem. If such values exist, then the three squares can surround a right-angled triangle.

We can rearrange the equations above to solve for a, b, and c:

a = √7 cm ≈ 2.65 cm

b = √17 cm ≈ 4.12 cm

c = √10 cm ≈ 3.16 cm

Now, we can check whether the Pythagorean theorem holds:

c² = a² + b²

(√10 cm)² = (√7 cm)² + (√17 cm)²

10 cm = 7 cm + 17 cm

This equation is not true, which means that the three squares cannot exactly surround a right-angled triangle.

In general, it is not always possible for three squares to surround a right-angled triangle. One way to see this is to note that the side lengths of a right-angled triangle satisfy the Pythagorean theorem, which means that they must be in a certain relationship to each other. On the other hand, the areas of three squares can take any values, so it is not always possible to find three squares whose side lengths satisfy the Pythagorean theorem.

Answer:

c

Step-by-step explanation:

0.0125

so it is 1.25 because the thousand place onward, it is in the decimal place of the percent

If P(B)=0.3, P(A|B)=0.5, P(B')=0.7and P(A|B')=0.8, then the value of the probability P(B|A)= 0.2113

To find the value of P(B|A), follow these steps:

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Answer:

40

Step-by-step explanation:

x is being multiplied by 8 to get y

so 5 x 8 = 40

Answer:

9x² + 42x + 49

Step-by-step explanation:

Identity

In this case, x = 3x and a = 7, so substitute the values.

Answer:

\(9x^2 + 42x + 49\)

Step-by-step explanation:

Step 1:  Factor out the expression

\((3x + 7)^2\)

\((3x + 7)(3x + 7)\)

\((3x * 3x) + (3x * 7) + (7 * 3x) + (7 * 7)\)

\(9x^2 + 21x + 21x + 49\)

\(9x^2 + 42x + 49\)

Answer: \(9x^2 + 42x + 49\)

Answer:

804

Step-by-step explanation:

1240- 436= 804

Answer:

12^5

Step-by-step explanation:

36^5=3^5×x^5

36÷3=12

Answer:

B and C are correct

Answer:

1.043kg

Step-by-step explanation:

2.3lb = 1.043 kg

a) Probability that all four are the same suit = 0.0106 b) Probability that all four are red =0.055 c) Probability each has a different suit = 0.105

Total number of cards =52

No. of cards for each suit =13

Total types of four suit =4 (heart, spades, diamonds, clubs)

Total numbers of ways = \(^{52}C_4\) =270,725 ways

a) number of ways choosing four cards of the same suit

= \(^{13}C_4+^{13}C_4+^{13}C_4+^{13}C_4\)

= \(4 \times ^{13}C_4\\\)

= \(4 \times \frac{13!}{4!(13-4)!}\)

=2860 ways

Probability that all four are the same suit is 2860/270,725 = 0.0106

b) Number of ways all four cards are red

=\(^{26}C_4\)

= 4,950 ways

Probability that all four are red = 4950/270,725 =0.055

c)  Number of ways each card has a different suit

=\(^{13}C_1\times^{13}C_1\times^{13}C_1\times^{13}C_1\)

= 28,561 ways

Probability each has a different suit is 28561/270725 = 0.105

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Answer:

$26.75 per scarf

Step-by-step explanation:

3 scarves = $80.25 (quite expensive)

1 scarf = $80.25/3

1 scarf = $26.75

Answer:

$8.75 because 26.25 divided by 3 equals 8.75.

Step-by-step explanation:

The number of oranges that are expected to weigh more than 4 oz is:

1400 - (1400 × 0.0228)≈ 1368.

The mean weight of the oranges growing in an orchard is 8 oz and standard deviation is 2 oz, the distribution of the weight of oranges can be represented as normal distribution.

From the batch of 1400 oranges, the number of oranges is expected to weigh more than 4 oz can be found using the formula for the Z-score of a given data point.

\(z = (x - μ) / σ\)

Wherez is the Z-score of the given data point x is the data point

μ is the mean weight of the oranges

σ is the standard deviation

Now, let's plug in the given values.

\(z = (4 - 8) / 2= -2\)

The area under the standard normal distribution curve to the left of a Z-score of -2 can be found using the standard normal distribution table. It is 0.0228. This means that 0.0228 of the oranges in the batch are expected to weigh less than 4 oz.

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Exact value of the definite integral is 320. Comparing the results: Exact value of the definite integral = 320, Trapezoidal Rule approximation (n = 4) = 340, Simpson's Rule approximation (n = 4) ≈ 246.6667.

What is trapezoid?

A trapezoid is a quadrilateral (a polygon with four sides) that has one pair of parallel sides. The parallel sides are called the bases of the trapezoid, while the non-parallel sides are called the legs.

To approximate the value of the definite integral ∫[0, 4] 5x * x^2 dx using the Trapezoidal Rule and Simpson's Rule, we need to specify the value of n, which represents the number of subintervals.

Let's calculate the approximations using n = 4 for both methods:

Trapezoidal Rule:

Using n = 4, we divide the interval [0, 4] into four subintervals of equal width: h = (4 - 0) / 4 = 1.

The approximated value using the Trapezoidal Rule is given by:

\(T_4 = (h/2) * [f(x_0) + 2f(x_1) + 2f(x_2) + 2f(x_3) + f(x_4)]\)

Plugging in the values:

\(T_4 = (1/2) * [f(0) + 2f(1) + 2f(2) + 2f(3) + f(4)]\\\\= (1/2) * [5(0)(0^2) + 2(5)(1)(1^2) + 2(5)(2)(2^2) + 2(5)(3)(3^2) + 5(4)(4^2)]\\\\= (1/2) * [0 + 10 + 80 + 270 + 320]\\\\= (1/2) * 680\\\\= 340\)

Simpson's Rule:

Using n = 4, we divide the interval [0, 4] into four subintervals of equal width: h = (4 - 0) / 4 = 1.

The approximated value using Simpson's Rule is given by:

\(S_4 = (h/3) * [f(x_0) + 4f(x_1) + 2f(x_2) + 4f(x_3) + f(x_4)]\)

Plugging in the values:

\(S_4 = (1/3) * [f(0) + 4f(1) + 2f(2) + 4f(3) + f(4)]\\\\= (1/3) * [5(0)(0^2) + 4(5)(1)(1^2) + 2(5)(2)(2^2) + 4(5)(3)(3^2) + 5(4)(4^2)]\\\\= (1/3) * [0 + 20 + 40 + 360 + 320]\\\\= (1/3) * 740\\\\= 246.6667\)

Exact value of the definite integral:

∫[0, 4] 5x * \(x^2\) dx = [(5/4) * \(x^4\)] evaluated from 0 to 4

\(= (5/4) * 4^4 - (5/4) * 0^4\\\\= (5/4) * 256 - (5/4) * 0\\\\= 320 - 0\\\\= 320\)

Comparing the results:

Exact value of the definite integral = 320

Trapezoidal Rule approximation (n = 4) = 340

Simpson's Rule approximation (n = 4) ≈ 246.6667

As we can see, the Trapezoidal Rule approximation is slightly greater than the exact value, while Simpson's Rule approximation is less than the exact value.

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Answer:

The vertex is option C: (-6, -2)

Step-by-step explanation:

The equation for a parabola is y = a(x – h)² + k where h and k are the y and x coordinates of the vertex, respectively. Thus, the vertex is (-6,2)

Pls mark brainliest.

Answer:

Consider x^ {2}-4x+3. Factor the expression by grouping. First, the expression needs to be rewritten as x^ {2}+ax+bx+3. To find a and b, set up a system to be solved. a=-3 b=-1. Since ab is positive, a and b have the same sign. Since a+b is negative, a and b are both negative. The only such pair is the system so

Step-by-step explanation:

9514 1404 393

Answer:

Step-by-step explanation:

Just as you find it easiest to ask someone else to find the roots for you, I find it easiest to use a graphing calculator to find the roots. It shows the roots to be ...

If you're searching for roots by hand, the usual process is to make a guess based on Descartes' Rule of Signs, and the Rational Root Theorem. Then factor out that root using synthetic division or long division to reduce the polynomial degree.

__

This has 3 sign changes, so 1 or 3 positive real roots. If odd-degree terms change signs, there is one sign change, indicating 1 negative real root. The Rational root theorem tells you the rational roots will be divisors of 4:

  ±1, ±2, ±4

Both even-degree terms and odd-degree terms have coefficients that sum to zero. This indicates that 1 and -1 are both roots of the equation. Factoring those out gives ...

  (x -1)(x +1)(x^2 -4x +4) = 0

The quadratic is a perfect square, so the full factorization is ...

  (x +1)(x -1)(x -2)² = 0

Roots are -1, 1, and 2 (multiplicity 2).

__

The rule of signs tells you there is one positive real root and 0 or 2 negative real roots. The rational roots will be divisors of 105, so will be any of ...

  ±1, ±3, ±5, ±7, ±15, ±21, ±35, ±105

Various other ways of estimating roots suggest the magnitudes will be less than ∛105 +√1 +9 ≈ 14.7. The sum of coefficients tells you the positive root is greater than 1. Trying x=3 shows that to be the positive real root. Factoring it out gives ...

  (x -3)(x² +12x +35) = 0

The quadratic can be further factored, so we have ...

  (x -3)(x +5)(x +7) = 0

Roots are -7, -5, and 3.