Find the area of the triangle ABC. C = 133.9°, a = 45.9 ft and b=35.9 ft

Answer:

Step-by-step explanation:

R40×5%=2

R40-2=R38

40%×38=R15,2

15,2+40=55,2

55,2÷50=R1,10

i didnt do the radio sum...

Answer:

see below

Step-by-step explanation:

1. 6 and 6sqrt(2)

2. 5 and 5sqrt(3)

3. 3 and 3

4. 12 and 6sqrt(3)

5. 2 and 2

6. 4 and 8

7. 6/sqrt(2) and 6/sqrt(2)

8. 9/sqrt(3) and 18/sqrt(3)

9.4/sqrt(2) and 4/sqrt(2)

10. 3 and 3sqrt(3)

11. 5 and 5sqrt(2)

12. 12/sqrt(3) and 24/sqrt(3)

Answer:

$105

Step-by-step explanation:

20 × 5 = 100

5% Increase = 105% of Original

100/100 × 105 = 105

The changes in weights (b) did not affect the decision as Worldwide Delivery remained the most suitable provider. However, the increase in ratings for Overnight Shipping (c) resulted in it becoming the most suitable outsourcing provider according to the given criteria.

1) Factor rating
2) Outsourcing provider
3) Logistics services
4) Weights
5) Ratings

a) Factor rating is a method used to evaluate and select an outsourcing provider based on predetermined criteria. In this case, Fernando Garza's firm wants to select a logistics services provider using factor rating. The table provided includes the weights assigned to different criteria (quality, delivery, and cost) and the ratings of three potential providers (Overnight Shipping, Worldwide Delivery, and United Freight).

To make his decision, Garza needs to multiply the weight of each criterion by the rating of each logistics provider and sum up the results. The highest sum indicates the most suitable outsourcing provider. Let's calculate the results:

Overnight Shipping:
Quality: 5 (weight) x 90 (rating) = 450
Delivery: 3 (weight) x 70 (rating) = 210
Cost: 2 (weight) x 70 (rating) = 140
Total: 450 + 210 + 140 = 800

Worldwide Delivery:
Quality: 5 (weight) x 80 (rating) = 400
Delivery: 3 (weight) x 85 (rating) = 255
Cost: 2 (weight) x 80 (rating) = 160
Total: 400 + 255 + 160 = 815

United Freight:
Quality: 5 (weight) x 75 (rating) = 375
Delivery: 3 (weight) x 70 (rating) = 210
Cost: 2 (weight) x 95 (rating) = 190
Total: 375 + 210 + 190 = 775

Based on these calculations, Worldwide Delivery has the highest total score of 815, making it the most suitable outsourcing provider according to the given criteria.

b) Garza decides to increase the weights for quality, delivery, and cost to 10, 6, and 4, respectively. This change means that Garza now considers quality to be twice as important as before, delivery to be 1.5 times as important, and cost to be twice as important.

Let's recalculate the results with the updated weights:

Overnight Shipping:
Quality: 10 (weight) x 90 (rating) = 900
Delivery: 6 (weight) x 70 (rating) = 420
Cost: 4 (weight) x 70 (rating) = 280
Total: 900 + 420 + 280 = 1600

Worldwide Delivery:
Quality: 10 (weight) x 80 (rating) = 800
Delivery: 6 (weight) x 85 (rating) = 510
Cost: 4 (weight) x 80 (rating) = 320
Total: 800 + 510 + 320 = 1630

United Freight:
Quality: 10 (weight) x 75 (rating) = 750
Delivery: 6 (weight) x 70 (rating) = 420
Cost: 4 (weight) x 95 (rating) = 380
Total: 750 + 420 + 380 = 1550

With the updated weights, the new results show that Worldwide Delivery still has the highest total score of 1630, making it the most suitable outsourcing provider.

c) If Overnight Shipping's ratings for each of the factors increase by 10%, we need to recalculate the results while considering these changes.

Overnight Shipping:
Quality: 10 (weight) x (90 + 10% of 90) = 990
Delivery: 6 (weight) x (70 + 10% of 70) = 462
Cost: 4 (weight) x (70 + 10% of 70) = 308
Total: 990 + 462 + 308 = 1760

With the increased ratings, Overnight Shipping now has the highest total score of 1760, making it the most suitable outsourcing provider.

In summary, the changes in weights (b) did not affect the decision as Worldwide Delivery remained the most suitable provider. However, the increase in ratings for Overnight Shipping (c) resulted in it becoming the most suitable outsourcing provider according to the given criteria.

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Step-by-step explanation:

To find the vector parametric equation for the parabola from the origin to a point P, we need to express the position vector of P as a function of a parameter. Let's assume the coordinates of P are (x, y).

(a) Vector Parametric Equation for the Parabola: We can represent the position vector of P as a linear combination of two vectors. The first vector will point from the origin to P, and the second vector will be perpendicular to it.

Let's consider the vector from the origin to P as OP. Since P lies on the parabola, the magnitude of OP is given by the equation y = x^2. Therefore, the magnitude of OP is √(x^2 + (x^2)^2) = √(x^2 + x^4).

The unit vector in the direction of OP can be found by dividing OP by its magnitude: u = OP / √(x^2 + x^4).

To find a perpendicular vector, we can take the cross product of u with the vector (0, 0, 1) (which is perpendicular to the xy-plane). This will give us a vector perpendicular to the plane containing the parabola.

Let's call the perpendicular vector v. The cross product of u and (0, 0, 1) is given by: v = u × (0, 0, 1).

Finally, the vector parametric equation for the parabola from the origin to P is given by: r(t) = tu + tv, where t is the parameter ranging from 0 to 1.

(b) Line Integral along the Parabola: To find the line integral of a vector field F along the parabola from the origin to P, we need to evaluate the line integral: ∫(F · dr) from 0 to 1, where F is the vector field, dr is the differential vector along the parabola, and the integral is taken with respect to t.

The line integral can be calculated as follows: ∫(F · dr) = ∫(F · (du/dt) dt), where du/dt is the derivative of the unit vector u with respect to t.

Substituting r(t) = tu + tv into the above expression, we can find the line integral.

Please provide the vector field F so that I can assist you further in evaluating the line integral.

Rectangle ABCD is a square.

Relation between rectangle and square?

Squares and rectangles each have four straight sides. However, a square's and a rectangle's mathematical characteristics are very dissimilar. For instance, a common distinction is that squares have equal sides on each side, whereas only the opposite sides of a rectangle are equal.

Radius of circle R = 4cm

let sides of rectangle is a,b

let rectangle be ABCD in which AB =CD= a , AC=BD=b

ACD is right angled triangle on C.

Then,

\(AD^{2} =AC^{2} +CD^{2} \\\\8^{2} =b^{2} +a^{2} \\\\64=b^{2} +a^{2} \\\\b^{2} =\sqrt{64-a^{2} }\)------(1)

Area of rectangle = Area of ΔACD + ΔABD

                             = \(\frac{1}{2} \times a\times b + \frac{1}{2} \times a\times b\)

Area of rectangle = a×b

by eqn (1)

             Area = \(a\times (\sqrt{64-a^{2} } )\)

For maximum area

\(\frac{dA}{da} =0\\\\a \times \frac{1}{\sqrt{64-a^{2} } } (-a)+(\sqrt{64-a^{2} } )\times(1)=0\)

\(\sqrt{64-a^2} -\frac{a^2}{\sqrt{64-a^2} } =0\\\\\frac{64-a^2-a^2}{\sqrt{64-a^2} } =0\\\\64-2a^2=0\\\\a^2=32\\\\a=\sqrt{32} \\\\In (1) eqn\\b=\sqrt{64-a^2} \\\\b=\sqrt{64-32} \\\\b=32\)

So, a=b

Means Rectangle ABCD is a square.

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1) (a) The transformations that occur from the parent function are horizontal translation of 2 units to the left and vertical translation of 4 units to the down.

(b) (-2, -4)

(c) Graph is given below.

1) Given a function,

g(x) = (x + 2)² - 4

(a) Given a parent function p(x) = x².

We can write g(x) as,

g(x) = p(x + 2) - 4

So the transformation is horizontal translation of 2 units to the left and vertical translation of 4 units to the down.

(b) Vertex formula of a parabola is,

y = a (x - h)² + k, where (h, k) is the vertex.

Comparing the given function with vertex form,

Vertex of the parabola = (-2, -4)

(c) Graph of g(x) will be a parabola with vertex at (-2, -4).

It is given below.

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Based on the z-score, an Endure All battery selected at random has a 10.56% chance of lasting more than 550 hours.

How closely a value relates to the mean of a set of values is expressed by a Z-score.

The Z-score is created using standard deviations from the mean.

A data point's total value is equal to the mean value when the Z-score of the data point is equal to 0.

So, in order to determine how far the raw score deviates from the mean, the Z score is used.

The following steps are used to determine the Z score:

z = (x - μ)/σ

We know that:  x > 550 and μ = 500, σ = 40

z = 550 - 500 / 40

z = 1.25

The graph of the normal distribution indicates:

P(z > 1.25) = 1 - P(z < 1.25)

P(z > 1.25) = 1 - 0.8944

P(z > 1.25) = 0.1056

Therefore, based on the z-score, an Endure All battery selected at random has a 10.56% chance of lasting more than 550 hours.

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Answer:

input 4y into x

then square 4y

answer is 48y²-2

Answer:

x=6

Step-by-step explanation:

(5x+30)+80=140

5x+110=140

5x=30

x=6

answer: B

The interest after three years is $117.711 and new balance after three years is $1347.711

Simple interest is a type of interest calculated on the initial principal or starting amount of a loan or investment.

The formula for simple interest is:

I = PRT/100

Where:

I = Interest

P = Principal or starting amount

R = Interest rate

T = Time

a. Interest after three years:

I = PRT/100

P = $1,230, R = 3.19% and T = 3 years

I = (1,230 ×3.19 × 3)/100

I =  $117.711

b.  New balance after three years:

New balance = P + I

New balance =  $1,230 + $117.711 = $1347.711

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The value of x is 2.045 by simple algebra.

Use the time formula, t = d/s, which states that time is equal to distance divided by speed, to solve for time. Time is a function of both speed and distance.

Until it reaches its destination 200 miles distant, a car is driving on a little highway at either 55 or 35 miles per hour, depending on the posted speed restrictions.

x is the duration, in hours, that the vehicle is travelling at 55 mph.

Y is the duration, in hours, that the vehicle is travelling at 35 mph.

55x + 35y = 200 is the equation defining the relationship.

We must locate:

If the trip takes the car 2.5 hours at 35 miles per hour, how long does it take to travel at 55 miles per hour?

∵ 55x + 35y = 200

The drive takes the car 2.5 hours at a speed of 35 mph.

Y shows the duration of time for an automobile travelling at 35 mph.

∴ y = 2.5

- To obtain the value of x, substitute the value of y into the equation.

∴ 55x + 35(2.5) = 200

∴ 55x + 87.5 = 200

- Take 87.5 off of both sides.

∴ 55x = 112.5

- Subtract 55 from both sides.

x equals 2.045 hours.

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Q.2: A review of the t-test on the significance of individual independent variable suggests that, based on the p-values. None of the independent variables could be retained. This is because if the p-value is high, it means the significance is low.

Q3: Choose the right option below. Based on the full regression model involving all of the independent variables. VIF for Size = 5.3352, VIF for Fireplace = 10.1873, VIF for bedrooms = 2.7885.

Q.4: Based on VIF values, there is concern for collinearity in this dataset. True

Q5: Based on the normal probability plot, the normality assumption seems to be met. True

Q7: Based on conducting residual analysis the model seems. Adequate.

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Answer:

-2x+y+4<0

Step-by-step explanation:

y=mx+b

(m) slope is 2 (4/2)

(b) intercept is -4

y=2x-4

-2x+y+4=0

Plug in the origin for x and y (0,0)

4=0

since we do not want the side of the graph shaded to include the origin, the sign needs to be <

-2x+y+4<0

Answer:

PT = 11

Step-by-step explanation:

In a parallelogram, the diagonals bisect each other. So, QS cuts PR in half so that PT = TR

PT + TR = PR = 22

2 * PT = 22

PT = 11

Answer:

PT = 11

Step-by-step explanation:

Theorem:  The diagonals of a parallelogram bisect each other.

So, if PR = 22, then PT = 11

See how easy that is if you know the theorem.

The statement "If |x| = 6, then x can only be equal to 6" is false.

The absolute value of a number represents its distance from zero on the number line.

The expression |x| = 6 means that the distance of x from zero is 6. Therefore, x can be either positive or negative 6.

In this case, x can be either 6 or -6 because both numbers have an absolute value of 6.

Hence, x is not limited to being equal to only 6.

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To ensure that a sample proportion (0.1) equals a population proportion (0.01), the required sample size depends on the desired level of confidence and the acceptable margin of error.

Determining the appropriate sample size involves considering factors such as the desired level of confidence, the acceptable margin of error, and the estimated population proportion. In this case, the desired level of confidence is not specified, so we will assume a commonly used level of 95% confidence. The margin of error is the maximum allowable difference between the sample proportion and the population proportion. To calculate the required sample size, we can use the formula:

n = (Z^2 * p * (1-p)) / E^2

where:

n represents the required sample size

Z is the Z-score associated with the desired level of confidence (for 95% confidence, Z ≈ 1.96)

p is the estimated population proportion (0.01 in this case)

E is the desired margin of error

Since the goal is for the sample proportion to equal the population proportion (0.1 = 0.01), the estimated population proportion would be 0.01. The margin of error, E, would be 0.1 - 0.01 = 0.09. Plugging these values into the formula, we get:

n = (1.96^2 * 0.01 * (1-0.01)) / 0.09^2 ≈ 43,279

Therefore, a sample size of approximately 43,279 would be required to ensure that the sample proportion equals the population proportion with a 95% confidence level and a margin of error of 0.09. It's important to note that these calculations assume a simple random sample and other statistical assumptions hold true.

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Answer:

20 /_<<&&&&^%%^^$^&&//>&^=^^^^

Step-by-step explanation:

^=%&&%^&%

Answer:

-21

Step-by-step explanation:

The level of significance that would indicate the company is packaging less than the required average and being most restrictive is \(\alpha = 0.025 = 2.5\%\)

There are two hypotheses. First one is called null hypothesis and it is chosen such that it predicts nullity or no change in a thing. It is usually the hypothesis against which we do the test. The hypothesis which we put against null hypothesis is alternate hypothesis.

Null hypothesis is the one which researchers try to disprove.

For this case, we have:

Hypotheses:

Since sample size = 20 < 30, thus, we will use t-test.

The value of t test statistic is calculated as:

\(t = \dfrac{\overline{x} - \mu}{\sigma/\sqrt{n}}\)

Thus, we get:

\(t = \dfrac{298.4 - 300}{3/\sqrt{20}} \approx 2.385\)

The degree of freedom is n - 1 = 20 - 1 = 19

The p-value for this is  0.0138 = 1.38%

This is less than 2.5%, 5% and 10% but bigger than 1%

For showing that company is manufacturing less than needed, we need p value to be smaller than level of significance, so that we can reject null-hypothesis and accept the alternate hypothesis.

Thus, only 2.5%, 5% and 10% as level of significance would be helpful.

Now, the most restricting one is 2.5% as it is closest to 1.38%.

Thus, the level of significance that would indicate the company is packaging less than the required average and being most restrictive is \(\alpha = 0.025 = 2.5\%\)

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Answer:

B

Step-by-step explanation:

Answer:

If Bryan can run 2 miles in 20 minutes, he can run 10 miles in 100 minutes.

Step-by-step explanation:

To determine the answer to this problem, we can first find how many minutes it takes Bryan to run one mile. Because it takes him twenty minutes to run two miles, it must take Bryan ten minutes to run one mile.

1 mile = 10 minutes

Multiply this by ten to find how many miles Bryan runs in 100 minutes.

10 miles = 100 minutes

Bryan can run 10 miles in 100 minutes.

Answer: 10 miles

Step-by-step explanation: They’re equivalent to the minutes. 20 minutes 2 miles, 40 minutes 4 miles and so on.

a. the equilibrium price is $52 per bushel and the equilibrium quantity is 20 bushels.

b. the new equilibrium price is $42 per bushel and the new equilibrium quantity is 15 bushels.

Equilibrium price and quantity:

The equilibrium is the point where the supply and demand curve intersect each other. The point where the demand and supply curve intersect each other, P and Q determine the equilibrium price and quantity respectively.

The given equations for demand and supply of the bananas in Binghamton are:

P = 92 - 2QP = 12 + 2QThe equilibrium price and quantity can be obtained by equating the demand and supply equations,92 - 2Q = 12 + 2Q⇒ Q = 20P = 92 - 2(20)⇒ P = 52

Therefore, the equilibrium price is $52 per bushel and the equilibrium quantity is 20 bushels.

The given equations for demand and supply of the bananas in Binghamton are:

P = 92 - 2QP = 12 + 2QThe demand for bananas increases due to the National Institutes of Health’s study, which shows that bananas reduce the risk of cancer.

The new demand equation is given by:

P = 132 - 2QAt the original equilibrium price ($52), the quantity demanded exceeds the quantity supplied.

Therefore, there is a shortage.

The shortage can be calculated as follows:

Quantity demanded at equilibrium price (P = $52) = Quantity supplied at equilibrium price (P = $52)Qd = 92 - 2(20) = 52 bushels Qs = 12 + 2(20) = 52 bushels Shortage = Qd - Qs= 52 - 52 = 0

Therefore, the shortage is 0 bushels.

c.  Show graphically.

The new demand equation is given by:

P = 132 - 2QTo find the new equilibrium price and quantity, we need to equate the new demand equation with the original supply equation,P = 12 + 2Q (original supply equation)P = 132 - 2Q (new demand equation)⇒ 12 + 2Q = 132 - 2Q⇒ 4Q = 60⇒ Q = 15P = 12 + 2(15)⇒ P = 42

Therefore, the new equilibrium price is $42 per bushel and the new equilibrium quantity is 15 bushels.

The graphical representation is given below:

Graphical representation of new equilibrium price and quantity.

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Answer:

119

Step-by-step explanation:

So 45+24=69 (haha nice)

So he owes -69.

-69+119=50$.

The right answer is B. It is not applicable when data are continuous, is not a characteristic of the standard deviation.

The statement "It is not applicable when data are continuous" is not a characteristic of the standard deviation.

The standard deviation is a measure of the dispersion or variability of a dataset. It quantifies how spread out the values are from the mean. Explanation for other parts are as follows:

A. It can be calculated when the data contain negative or zero values:

This is true. The standard deviation can be calculated for datasets that contain negative or zero values. It considers the deviations from the mean, regardless of their sign.

C. It is always the square root of the variance:

This is true. A quadrilateral with exactly two sets of congruent following sides is called a kite. The variance is the average of the squared deviations from the mean.

D. Its physical interpretation is not as easy as the MAD:

This is a subjective statement. The physical interpretation of the standard deviation depends on the context and the familiarity of the user with the concept. However, it is often considered a more widely used and understood measure of dispersion compared to the Mean Absolute Deviation (MAD).

The statement "It is not applicable when data are continuous" is incorrect. The standard deviation can be calculated for both discrete and continuous data. The other options provided (A, C, and D) correctly describe characteristics of the standard deviation.

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Answer:

2 real and irrational roots

Step-by-step explanation:

given a quadratic equation in standard form

ax² + bx + c = 0 ( a ≠ )

then the nature of the roots can be determined using the discriminant

Δ = b² - 4ac

• if b² - 4ac > 0 then 2 real and irrational roots

• if b² - 4ac > 0 and a perfect square then 2 real and rational roots

• if b² - 4ac = 0 then 2 real and equal roots

• if b² - 4ac < 0 then 2 complex roots

- 6x² + 7x + 3 = 0 ← is in standard form

with a = - 6 , b = 7 , c = 3

b² - 4ac = 7² - (4 × - 6 × 3) = 49 - (- 72) = 49 + 72 = 121

since b² - 4ac > 0 then the equation has 2 real and irrational roots

Quadratic equation -

\(\: \:\:\:\: \small \underline{ \boxed{ \sf{ -6x^2 +7x+3 =0}}}\\\)

Where-

To find the Discriminant of this equation is given by -

\(\longrightarrow\underline\purple{\boxed{\pmb{D = b^2-4ac}}}\)

On substituting the values -

\( \: \:\:\:\: \longrightarrow\sf { D = \bigg(7\bigg)^2 - 4\times -6\times 3}\\\)

\( \: \:\:\:\: \longrightarrow\sf { D = 49+72}\\\)

\( \: \:\:\:\: \longrightarrow\pmb{ \underline{\purple{D =121}}}\\\)

Since, D>0 hence, this equation has two distinct real roots.

Answer:

See below

Step-by-step explanation:

See graph below

just an addition to the great reply above by jsimpson11000

Check the picture below.