Question 8 of 10
In order to apply the law of cosines to find the measure of an interior angle, it
is enough to know which of the following?
A. The lengths of all three sides of the triangle
B. The area of the triangle
C. At least two of the angles of the triangle and the length of one of
its sides
SUBMIT

A sample size of 5 is required to estimate the population mean with a 98% confidence level and a margin of error of 5.

To determine the sample size required to estimate a population mean with a 98% confidence level and a margin of error of 5, we need to use the formula:

n = (z^2 * σ^2) / E^2

where:
- n is the sample size
- z is the z-score associated with the confidence level (in this case, 2.33 for a 98% confidence level)
- σ is the population standard deviation (0. given in the question)
- E is the margin of error (5 in this case)

Plugging in the values, we get:

n = (2.33^2 * 0.^2) / 5^2
n = 4.8556

Since we cannot have a fraction of a sample, we round up to the nearest whole number. Therefore, a sample size of 5 is required to estimate the population mean with a 98% confidence level and a margin of error of 5.

It is important to note that this formula assumes that the population is normally distributed. If this assumption is not met, the sample size calculation may need to be adjusted. Additionally, this formula only estimates the minimum sample size required and does not take into account factors such as cost and feasibility of obtaining the sample.

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Answer:

a) 10 per for 4 min means 150 per hour. so more hamburgers are sold per hour.

b) see attachment

True, The objective function in linear programming is formulated to either maximize or minimize a specific value or quantity.

The goal of linear programming is to optimize this objective function by finding the optimal values for the decision variables within the given constraints. Whether it is maximizing profit, minimizing cost, maximizing production, or minimizing waste, the objective function is designed to achieve the desired optimization outcome.

The objective function in linear programming serves as the goal or target to be achieved. It can involve maximizing profits, minimizing costs, maximizing efficiency, minimizing waste, or any other measurable quantity. The objective function guides the optimization process by defining the objective to be pursued in the linear programming problem.

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Answer: I'll explain.

Step-by-step explanation:

A factor is a number that divides that into another number without leaving a remainder                                                                                                                    A solution is a assignment of values to the unknown variables that amke the equality in the equation true

The absolute maximum is -2 at x = 4, and the absolute minimum is -9 at x = -3.

To find the absolute extrema of f(x) on the interval [-3, 4), we need to first find the critical points and endpoints of the function. The critical points are the points where the derivative of the function is equal to 0 or undefined.

1. Find the derivative of f(x): f'(x) = 1

Since the derivative is a constant, there are no critical points.

2. Evaluate the function at the endpoints of the interval:

f(-3) = -3 - 6 = -9
f(4) = 4 - 6 = -2

3. Compare the values to determine the maximum and minimum:

The maximum value of f(x) on the interval is -2 at x = 4: f(4) = -2.
The minimum value of f(x) on the interval is -9 at x = -3: f(-3) = -9.

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Answer:

Volume: 762 in³

LA: 448 in²

SA: 544 in²

Step-by-step explanation:

So first, the volume, the formula to find the area is base x height, so we have to find the base first:

8 x 12 ÷ 2 = 48

48 x 14  = 672

So the volume of the prism is 762 in³

Now, the lateral area, which is basically the surface area without the bases, or, in this case, the triangles:

10 x 14 = 140 x 2 = 280

12 x 14 = 168

168 + 280 = 448

So the LA = 448 in²

Now, for the surface area:

12 x 8 = 96 (usually, it would then be ÷ 2, but because there are two triangles, it isn't necessary)

96 + 448 (the LA) = 544

So the SA = 544 in²

hope this is right:)

The reciprocal of the fraction is 14/-t is -t/14.

To find the reciprocal of a fraction, we simply switch the numerator and the denominator.

In this case, we are given the fraction 14/-t. To find its reciprocal, we switch the numerator and the denominator:

Reciprocal = -t/14

Therefore, the reciprocal of the fraction 14/-t is -t/14.

To find the reciprocal of a fraction, we switch the numerator and the denominator. In this case, we are given the fraction 14/-t.

To find its reciprocal, we switch the numerator and the denominator.

Therefore, the reciprocal of 14/-t is -t/14.

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The equation that has no solution is "112 + 25 – 45m = –50m + 60". The presence of contradictory terms involving the variable "m" on both sides of the equation makes it impossible to find a value that satisfies the equation.

In this equation, we have variables on both sides of the equation and constants on both sides.

To solve the equation, we need to simplify and combine like terms. However, when we simplify the equation, we end up with contradictory terms.

The variable "m" appears on both sides with different coefficients, which means that there is no value of "m" that can satisfy the equation.

In other words, no matter what value we assign to "m", the equation will not hold true.

This is why this equation has no solution. It indicates that there is no value of "m" that would make the equation balanced and true.

In summary, the equation "112 + 25 – 45m = –50m + 60" has no solution.

The presence of contradictory terms involving the variable "m" on both sides of the equation makes it impossible to find a value that satisfies the equation.

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see the attached figure below to better understand the problem

Remember that in a unit circle the radius r=1

so

Applying the Pythagorean Theorem in the right triangle

Solve for y

Answer:

60-32

Step-by-step explanation:

i had the same thing

Simplification of the expression gives 2a + c = -24

4+4-3-4-2-5-1-8-9-0=a +c + a

First, let's add

\(8 -3 -4-2-5-1-8-9-0 = a+ c + a\)

Then, let's substract

\(-24 = a + c + a\)

\(-24 = 2a + c\)

We then have,

\(2a + c = -24\)

Thus, simplification of the expression gives 2a + c = -24

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Answer:

The answer is b

Step-by-step explanation:

here you go mate'

step 1

12-c  equation

step 2

12-(5)  insert 5 to the equation

step 3

12+(-5)  subtract the numbers

answer

7

mind if i get brainliest?

The running time wοrst case οf deleting a minimum element frοm a (min) binary heap with N elements is O(lοgN). Therefοre, the cοrrect answer is c. O(lοgN).

When deleting the minimum element frοm a binary heap, the heap needs tο be restructured tο maintain its heap prοperty. This restructuring prοcess invοlves mοving elements within the heap and pοtentially swapping elements tο maintain the heap's structure and οrdering.

Since a binary heap is a cοmplete binary tree and has a height οf lοgN, the wοrst-case running time fοr deleting the minimum element is prοpοrtiοnal tο the height οf the heap, which is O(lοgN). This is because the number οf cοmparisοns and swaps required during the restructuring prοcess is dependent οn the height οf the heap.

Therefοre, the cοrrect answer is c. O(lοgN).

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The most appropriate method for creating an estimate of the percent of district residents who support the building of a new middle school would be  v. A one-sample z-interval for a population proportion.

In this case, the superintendent wants to estimate the proportion (percentage) of district residents who support the building of a new middle school. To achieve this, a random sample of district residents can be selected, and the proportion of residents in the sample who support the new middle school can be calculated.

Since the sample size is relatively large (as it is a large school district), the sampling distribution can be assumed to follow a normal distribution. Therefore, a one-sample z-interval for a population proportion is suitable for estimating the proportion of district residents who support the new middle school.

Using this method, a confidence interval can be constructed around the sample proportion, providing an estimate of the true proportion of district residents who support the new middle school, along with a measure of uncertainty.

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The solution of the given formula s = (1/2)gt² for the indicated variable g is g = 2s/t².

According to the given question.

We have a formula.

s = (1/2)gt²

Since, we have to solve this given formula s = (1/2)gt² for the variable g.

Which means we have to write separate variable g to one side from the other variables which are in the given formual s = (1/2)gt² .

Thereofre, the solution of the given formula for the variable g is given by

s = (1/2)gt²

⇒ 2s = gt²               (multipling both the sides by 2)

⇒2s/t² = g               (dividing both the sides by t²)

⇒ g = 2s/t²

Hence, the solution of the given formula s = (1/2)gt² for the indicated variable g is g = 2s/t².

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Answer:

.1km

Step-by-step explanation:

The tractor can move .01 km in a second so 10 times .01 is .1

so the tractor can move .1km every 10 seconds

1 hour = 3600 seconds

10 seconds is 10/3600 = 1/360 of an hour

36 km per hour x 1/360 of an hour = 0.1 km (100 meters)

If g(2) = 12 and g'(x) ≥ 1/2 for 2 ≤ x ≤ 6, the smallest value g(6) can be g(6) ≥ 14.

g(2) = 12 and g'(x) ≥ 1/2 for 2 ≤ x ≤ 6.

From the mean value theorem we know that if at [2, 6] g(x) is continuous as well as differentiable then there exists (2, 6) as

{g(6) - g(2)}/(6 - 2) = g'(x)

As we know that g'(x) ≥ 1/2, so

{g(6) - g(2)}/(6 - 2) ≥ 1/2

Now simplify

{g(6) - g(2)}/4 ≥ 1/2

As g(2) = 12, now put the value

{g(6) - 12}/4 ≥ 1/2

Multiply by 4 on both side, we get

g(6) - 12 ≥ 2

Add 12 on both side, we get

g(6) ≥ 14

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Answer: The required ratio is PT:TR  = 1:2.

Step-by-step explanation:

Given: In triangle PQR, ST || QR, PT = 4cm, TR = 8cm, area of PQR = 90 cm².

To find : PT:TR

.i.e. Ratio of PT to TR.

Here, PT:TR\(=\dfrac{PT}{TR}\)

\(=\dfrac{4\ cm}{8\ cm}\)

Divide numerator and denominator by 4 , we get

\(\dfrac{1}{2}\)

Therefore, the required ratio is PT:TR  = 1:2.

This value represents the greatest distance between the particle and the origin during the time interval [0, 3].

To find the greatest distance between the particle and the origin during the time interval [0, 3], we need to find the position function of the particle, differentiate it to find the velocity function and analyze the critical points.

Let x(t) be the position function of the particle. Unfortunately, you haven't provided the specific position function, so I will use a generic one: x(t) = at^3 + bt^2 + ct + d. You'll need to substitute your given function here.

Step 1: Find the velocity function by differentiating the position function with respect to time:
v(t) = dx(t)/dt = 3at^2 + 2bt + c

Step 2: Find the critical points by setting the velocity function equal to zero and solving for t:
0 = 3at^2 + 2bt + c      
   
Step 3: Analyze the critical points and endpoints of the given interval [0, 3] by plugging them into the position function x(t):
x(0), x(t1), x(t2), and x(3) (where t1 and t2 are the critical points found in step 2)

Step 4: Determine which of these values corresponds to the greatest distance from the origin. Remember that distance is always positive, so take the absolute value of the positions if necessary.

The answer will be the largest absolute value among the positions x(0), x(t1), x(t2), and x(3). This value represents the greatest distance between the particle and the origin during the time interval [0, 3].

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The exact trigonometric ratios for the angle x is second quadrant.

Given Radian equals to θ = 27π / 4, we need to find all the Trigonometric ratios for the same -

Lets calculate the value of θ first.

We know π equals 180 degree angle and 2π equals 360 degree, hence with each 2π the radian moves back to zero degree. Which means

θ = 27π / 4 can be reduced to θ = 3π / 4

Hence θ = 135 degree which can be represented as below -

As This lies in second quadrant, hence  on x-axis (Value of base , needs to be taken as -1)

sin θ = 1/√2                            cosec θ = √2

cos θ = -1/√2                          sec θ = - √2

tan θ = -1                               cot θ = - 1

Trigonometric ratios are based on the value of the ratio of sides of a right-angled triangle and contain the values of all trigonometric functions. The trigonometric ratios of a given acute angle are the ratios of the sides of a right-angled triangle with respect to that angle.

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Answer:

y = -1

Step-by-step explanation:

1y + 14 = -4y + 9

Isolate the variable, y. Note the equal sign, what you do to one side, you do to the other. Add 4y and subtract 14 from both sides:

1y (+4y) + 14 (-14) = -4y (+4y) + 9 (-14)

1y + 4y = 9 - 14

5y = -5

Divide 5 from both sides:

(5y)/5 = (-5)/5

y = -5/5 = -1

-1 is your answer for y.

~

The value of the double integral is  \(I = \int\limits^{\pi/2}_{\pi/4} \int\limits^{3/sin0}_{r=0} r^{2}cos0drd0\).

Let z* be the common (finite) optimal value of P and D.

Given integral is

\(I = \int\limits^3_{y = 0} \int\limits^y_{x=0} {x} \, dxdy\)

The region of integration lies between

y = 0, y = 3, x = 0 & x = y

Let x = rcosθ, y = rsinθ,

\(x^{2} +y^{2}= r^{2}\)

At y = 3, rsinθ = 3

Thus r varies from 0 to 3/sinθ

θ varies from π/4 to π/2

Now, dxdy ----> rdrdθ

Therefore,

\(I = \int\limits^{\pi/2}_{\pi/4} \int\limits^{3/sin0}_{r=0} r^{2}cos0drd0\)

Hence the answer is The value of the double integral is  \(I = \int\limits^{\pi/2}_{\pi/4} \int\limits^{3/sin0}_{r=0} r^{2}cos0drd0\).

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Answer:

C

Step-by-step explanation:

Plug in the points to see which equation is true

Answer:

15 pizzas.

Step-by-step explanation:

The rate is 3 pizzas for every 7 people. If there are 35 people at the party (7 times 5), the amount of pizzas you should buy is 15 pizzas (3 times 5). Hope I  explained that well (^^'')

Answer:

180 ft^3

Step-by-step explanation:

volume=lwh

15 * 2* 6 = 180 ft^3

*change 24 inches to 2 feet*

Answer:

180 ft³

Step-by-step explanation:

To find the volume of a right rectangular prism, the equation is length x width x height. So, you would do 2 x 6 x 15, because 24 inches is 2 feet and the rest is given. And so, 2 x 6 x 15 = 180, so your answer is 180 ft³.

(hope this helps :P)

Step-by-step explanation:

Equation 1: \(3x^{2} +7x-6\)

Step 1: Write a quadratic equation in standard form choosing your own coefficients and constant.

Conditons that need to be satisfied: B can be 0 in only one question, parabola should open up and have a negative y intercept.

1. The parabola should open upwards: a> 0

2. \(3x^2+7x-6\) (a>0), y-int is negative (0s for x's)

                     3(0)^2 + 7(0) -6

                                   y= -6

Step 2:

1. Factor the original equation: (3x-2)(x+3)

x=2/3, -3

2. Strategy used (factor by grouping)

Equation 2: -\(x^{2}\) + 3x - 6

Equation 2 should represent a parabola that opens down and has a negative y-intercept.

Parabola that opens down = a<0

Ax^2 + Bx + C

-\(x^{2}\) + 3x - 6

Negative y-intercept: -(0)^2 +3(0) -6 = y= -6

Strategy to solve: Quadratic formula

Why? - This equation doesn't factor cleanly.

Show your work:

a= -1 b= 3 c= -6

Write the quadratic formula down (\(x= \frac{-b + \sqrt{b^{2} - 4ac } }{2a}\)) ± not just +

Show step, solve.

x​= 1.5 + 1.9365i

Equation 3:

Sorry, I can't do this.

Equation 4 :\(x^{2} -1\)

You decide.

Alright, easy parabola.

1. Does parabola open up or down. UP

2. Is there a vertical stretch or compression? NO

3. What is the y-intercept- (0,-1)

\(x^{2} -1\)

Strategy: Simple factoring patterns (Difference of squares) -

(x+1)(x-1)

x = + 1

Show work: x^2 is square of x,

Equation 5: \(x^{2} -3x+15\)

x^2−3x+15

a=1 b= -3 c=15

(\(x= \frac{-b + \sqrt{b^{2} - 4ac } }{2a}\)) ± not just +

Good luck! Sorry that I couldn't do equation 3, vertical stretches are not my thing.

The limit of the given expression as x approaches 1 from the right is 1.8.

To evaluate the limit of the given expression:

\(lim_{x - > 1} + [ln(x ^ 9 - 1) - ln(x ^ 5 - 1)]\)

We can start by directly substituting x = 1 into the expression:

[ln(1⁹ - 1) - ln(1⁵ - 1)]

= [ln(0) - ln(0)]

However, ln(0) is undefined, so this approach doesn't provide a meaningful answer.

To apply L'Hôpital's Rule, we need to rewrite the expression as a fraction and differentiate the numerator and denominator separately. Let's proceed with this approach:

\(lim_{x - > 1}\)+ [ln(x⁹ - 1) - ln(x⁵ - 1)]

= \(lim_{x - > 1}\)+ [ln((x⁹ - 1)/(x⁵ - 1))]

Now, we can differentiate the numerator and denominator with respect to x:

Numerator:

d/dx[(x⁹ - 1)] = 9x⁸

Denominator:

d/dx[(x⁵ - 1)] = 5x⁴

Taking the limit again:

\(lim_{x - > 1}\)+ [9x⁸ / 5x⁴]

= \(lim_{x - > 1}\)+ (9/5) * (x⁸ / x⁴)

= (9/5) * \(lim_{x - > 1}\)+ (x⁸ / x⁴)

Now, we can substitute x = 1 into the expression:

(9/5) * \(lim_{x - > 1}\)+ (1⁸ / 1⁴)

= (9/5) * \(lim_{x - > 1}\)+ 1

= (9/5) * 1

= 9/5

= 1.8

The complete question is:

Find the limit. Use l'Hospital's Rule where appropriate. If there is a more elementary method, consider using it. \(lim_{x - > 1} + [ln(x ^ 9 - 1) - ln(x ^ 5 - 1)]\)

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The three greatest consecutive prime numbers where the sum is a multiple of 5 are 3, 5, and 7.

We have,

To find the three consecutive prime numbers with a sum that is a multiple of 5 and each less than 100, start by listing the prime numbers less than 100:

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97

Check each combination:

(2, 3, 5): Sum = 2 + 3 + 5 = 10 (which is a multiple of 5)

(3, 5, 7): Sum = 3 + 5 + 7 = 15 (which is a multiple of 5)

(5, 7, 11): Sum = 5 + 7 + 11 = 23 (not a multiple of 5)

(7, 11, 13): Sum = 7 + 11 + 13 = 31 (not a multiple of 5)

(11, 13, 17): Sum = 11 + 13 + 17 = 41 (not a multiple of 5)

(13, 17, 19): Sum = 13 + 17 + 19 = 49 (which is not a multiple of 5)

(17, 19, 23): Sum = 17 + 19 + 23 = 59 (not a multiple of 5)

(19, 23, 29): Sum = 19 + 23 + 29 = 71 (not a multiple of 5)

(23, 29, 31): Sum = 23 + 29 + 31 = 83 (not a multiple of 5)

(29, 31, 37): Sum = 29 + 31 + 37 = 97 (not a multiple of 5)

(31, 37, 41): Sum = 31 + 37 + 41 = 109 (which is not a multiple of 5)

(37, 41, 43): Sum = 37 + 41 + 43 = 121 (which is not a multiple of 5)

(41, 43, 47): Sum = 41 + 43 + 47 = 131 (not a multiple of 5)

(43, 47, 53): Sum = 43 + 47 + 53 = 143 (which is not a multiple of 5)

(47, 53, 59): Sum = 47 + 53 + 59 = 159 (which is not a multiple of 5)

(53, 59, 61): Sum = 53 + 59 + 61 = 173 (not a multiple of 5)

(59, 61, 67): Sum = 59 + 61 + 67 = 187 (not a multiple of 5)

(61, 67, 71): Sum = 61 + 67 + 71 = 199 (not a multiple of 5)

(67, 71, 73): Sum = 67 + 71 + 73 = 211 (not a multiple of 5)

(71, 73, 79): Sum = 71 + 73 + 79 = 223 (not a multiple of 5)

(73, 79, 83): Sum = 73 + 79 + 83 = 235 (which is a multiple of 5)

(79, 83, 89): Sum = 79 + 83 + 89 = 251 (not a multiple of 5)

(83, 89, 97): Sum = 83 + 89 + 97 = 269 (not a multiple of 5)

Thus,

The three greatest consecutive prime numbers where the sum is a multiple of 5 are 3, 5, and 7.

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Answer

x = 3 ± i

x = (3 + i)

OR

x = (3 - i)

Explanation

To solve this, we need to note that √(-1) = i

So, for this simplification

√(36 - 40) = √(-4) = √[(4)(-1)] = 2i

We can now fully simplify the expression given

x = 3 ± i

x = (3 + i)

OR

x = (3 - i)

Hope this Helps!!!