What is the rate of 5 pounds

Answer:

∠ GRS = 74°

Step-by-step explanation:

∠ GRS + ∠ QRG = ∠ QRS , that is

∠ GRS + 105° = 179° ( subtract 105° from both sides )

∠ GRS = 74°

Answer:

75°

Step-by-step explanation:

While it may appear that QRS is a straight line, it is not so since m∠QRS = 179° and if it was a straight line, it would be 180°

The figure actually represents three rays with endpoint at R

The three rays are RQ, RS and RG

Draw another ray RT with endpoint at R and opposite to ray RG. Opposite rays have angles that add up to 180°

Therefore m∠GRT = 180°

m∠SRT = m∠QRG since they are opposite angles

Since m∠QRG = 105°, therefore m∠SRT = 105°

m∠GRS + m∠SRT=180° since these angles are formed by two opposite rays

Substituting we get
m∠GRS + 105 = 180

m∠GRS = 180-105 = 75°

The quadratic equation 2a^2 = -6 + 8a has two solutions: a = 3 and a = 1.

To solve the quadratic equation 2a^2 = -6 + 8a, we need to rearrange it into standard quadratic form, which is ax^2 + bx + c = 0, where a, b, and c are coefficients.

Step 1: Move all the terms to one side of the equation to set it equal to zero:

2a^2 - 8a + 6 = 0

Step 2: The equation is now in standard quadratic form, so we can apply the quadratic formula to find the solutions for 'a':

a = (-b ± √(b^2 - 4ac))/(2a)

Comparing with our equation, we have:

a = (-(-8) ± √((-8)^2 - 4(2)(6)))/(2(2))

Simplifying further:

a = (8 ± √(64 - 48))/(4)

a = (8 ± √16)/(4)

a = (8 ± 4)/(4)

Now, we can calculate the two possible solutions:

a1 = (8 + 4)/(4) = 12/4 = 3

a2 = (8 - 4)/(4) = 4/4 = 1

Therefore, the quadratic equation 2a^2 = -6 + 8a has two solutions: a = 3 and a = 1.

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Answer:

Step-by-step explanation:

The answer is 4

Answer:

72r^3t^4

Step-by-step explanation:
* and x = times tables btw

First you'll want to rewrite the equation:
12r^3
18r^2t
24t^4

Then factor the monomial, 12r^3=2*2*3*r*r*r
18r^2t
24t^4

Finding the lease common multiple of the expressions, write the product of all factors the greatest number of times they appear in factorization.

12r^3=2*2*3*r*r*r
18r^2t=2*3*3*r*r*t
24t^4=2*2*2*3*t*t*t*t
Your answer is
2 x 2 x 2 x 3 x 3 x r x r x r x t x t x t
simplify it and you get
72r^3t^4

The minimal amount of work the bird can expend to break open a whelk shell can be found by minimizing the function 27 + 1)hw(h) = -0.51.

To find the minimal value, we need to find the minimum value of the function w(h). Since no specific equation for w(h) is provided, we can assume that w(h) is a linear function of h.

Let's rewrite the given equation in a more simplified form:

w(h) = -0.51 / (27 + 1)h

To find the minimum value of w(h), we need to find the maximum value of the denominator, (27 + 1)h.

The maximum value of the denominator occurs when h is at its highest possible value. However, no information about the maximum height is given in the problem.

Therefore, without further information about the range of values for h, we cannot determine the minimal amount of work the bird can expend to break open a whelk shell.

As a result, none of the options provided (28.7, 25.5, 34.9, 16.6) can be conclusively determined to be the minimal amount of work.

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Answer:

Below

Step-by-step explanation:

Slope, m, is  rise (80 ft ) / run (15 ft ) =   80 /15 = 5.33

Answer:

c)$73

Step-by-step explanation:

You just have to substitute 4 in for h because h stands for how many hows. They're renting it for 4 hours.

Answer:

c) 73

Step-by-step explanation:

c=12(4 hours) + 25

c=48 + 25

c=73

Answer:

she needs 8

Step-by-step explanation:

12-4=8

The three double-angle identities are :

1.\($\cos(2\theta) = \cos^2\theta - \sin^2\theta$\)

2. \($\sin(2\theta) = 2\sin\theta\cos\theta$\)

3. \($\tan(2\theta) = \frac{2\tan\theta}{1-\tan^2\theta}$\)

The three double angle identities are equations that relate the cosine, sine, and tangent of twice an angle to the cosine, sine, and tangent of the original angle. these identities are useful in trigonometry, as they make it possible to express a double angle in terms of its simpler  angle components.

The first identity states that the cosine of twice an angle is equal to the square of the cosine of the original angle, minus the square of the sine of the original angle. the second identity, states that the sine of twice an angle is equal to twice the product of the sine and cosine of the original angle.

The third  identity states that the tangent of twice an angle is equal to twice the tangent of the original angle, over one minus the square of the tangent of the original angle,

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Answer: the answer would be 16

Step-by-step explanation:

it’s because the volume is V = 1/3 Bh and B is the area of the base and h is the height.

Answer:

80

Step-by-step explanation:

The velocity of the velociraptor is 0.4 m/s [E] - 0.8 m/s [W] + 0.3 m/s [S] and  the speed of the velociraptor is 2 m/s.

To calculate the speed of the velociraptor, we need to divide the total distance traveled by the total time taken:

Total distance = 5m + 10m + 3m + 2m = 20m

Total time = 10 seconds

Speed = Total distance / Total time

     = 20m / 10s

     = 2m/s

To calculate the velocity of the velociraptor, we need to consider both the magnitude of its speed and its direction. We can calculate the displacement by subtracting the final position from the initial position:

Displacement = (5m [E] + 10m [W] + 3m [S] + 2m [W])

           = (5m [E] - 8m [W] + 3m [S])

           = 5m [E] - 8m [W] + 3m [S]

Note that we have used negative sign for the distance traveled towards the west.

The time taken is 10 seconds.

Velocity = Displacement / Time taken

        = (5m [E] - 8m [W] + 3m [S]) / 10s

        = 0.4 m/s [E] - 0.8 m/s [W] + 0.3 m/s [S]

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Answer - the answer should be:

-3x+4

down below is how i did it,

Step-by-step explanation:

use the formula mx+b=y

y is f(x)

m = -3

x = x

b = 4

so,

mx+b is -3x+4

Answer:

f(x)=-3x+4

Step-by-step explanation:

Slope= -3

(1-(-2))/(1-2)=3/-1= -3

Y-intercept= 4

Answer:

Step-by-step explanation:

c)18

Answer:

Step-by-step explanation:

According  to Euler's formula:

Substitute known values and solve for E:

Correct choice is B

Total Total revenues will exceed = 8782.01

What is Total Revenue?

Total revenue is the overall sum of money received by a business through the sale of its products and services. Based on demand and price, it measures how successfully a company is generating revenue from its main operations.

Let x - normal (101.15 ,12.15)

where µ = 101.15

σ = 12.15

Mean for 85 customers

µ = 85 * 101.15 =8597.75

standard deviation for 85 customers

σ = \(\sqrt{85}\) * 12.15 = 112.017

P ( x >x₁ ) = 0.05

P ( x-µ/ σ > x₁-8597.75/112.017) = 0.05

P (Z >Z₁) = 0.05

Where

Z₁ = x- 8597.75/112.017

Z₁ = 1.645

Then x = 112.017 *1.645 +8597.75

x = 8782.01

Total total revenues will exceed = 8782.01

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The concept of the oldest prime numbers is an ancient one and has been known since ancient times. The ancient Greeks were the first to systematically study prime numbers

The largest and oldest data collection in mathematics is prime numbers. What is it about them that has intrigued mathematicians for millennia?

They were very much aware of the existence of prime numbers and the fundamental theorem of arithmetic, the statement that every positive integer greater than 1 can be represented uniquely as the product of primes. So, it is hard to determine the oldest prime number known, but it's been studied throughout human history.

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The median age of the 120 people seated in the first five rows of the concert was 31.

What is value?
Value is an important concept in economics and business. It is the worth of goods, services, or assets that is determined by the market or by an individual. It can be measured in terms of money, time, or effort. Value is also used to describe a person’s sense of worth or importance. Values can be seen as the principles, standards, or goals that guide an individual’s actions and decisions. Ultimately, value is subjective and is held by each person and can change over time.

The box and whisker plot provided by the sponsor shows the ages of the 120 people seated in the first five rows of the concert. The box and whisker plot shows a minimum value of 18, a maximum value of 45, a median of 31, a first quartile of 24, and a third quartile of 37. This indicates that 50% of the 120 people in the first five rows had an age of 31 or below, and 50% of the 120 people had an age of 37 or above. The median age of the 120 people seated in the first five rows of the concert was 31.

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Answer:

x = 1

Y = 1

Step-by-step explanation:

A. 3(2x-3y= - 1)

6x-9y=- 3

B. -2(3x-4y= - 1)

- 6x+8y=2

Add both equations:

(6x-9y= - 3) + (- 6x+8y=2)

-y= - 1

3x - 4(1) = - 1

3x-4= - 1

3x = 4 - 1

= 3/3 = 1

The length of side BD which is the altitude of the triangle is 2√(70)

The length of BD is solved using similar triangles. This is defined by triangles formed from triangle ABC and they include

Let the altitude be h, hence we have the formula of the proportions as

AD / h = h / DC

plugging the values gives

20 / h = h / 14

h^2 = 20 * 14

h = √(20 * 14 )

h = √(280)

h = 2√(70)

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Answer:

3

Step-by-step explanation:

18: 1, 2, 3, 6, 9, 18

39: 1, 3, 13, 39

18: 1, 2, 3, 6, 9, 18

39: 1, 3, 13, 39

3

The artificial variables is x1 ≥ 0, x2 ≥ 0, x3 ≥ 0, A1 ≥ 0, A2 ≥ 0

To reformulate the given problem as a convenient artificial problem for preparing to apply the simplex method, we introduce artificial variables. The steps to reformulate the problem are as follows:

1. Introduce the artificial variables. For each inequality constraint, introduce an artificial variable by subtracting a slack variable from the left-hand side of the inequality.

The problem can be reformulated as follows:

Minimize Z = 2x1 + x2 + 3x3

subject to:

5x1 + 2x2 + 7x3 + A1 = 420    (Equation 1)

3x1 + 2x2 + 5x3 + A2 = 280    (Equation 2)

where A1 and A2 are the artificial variables.

2. Rewrite the problem with the added artificial variables. The reformulated problem becomes:

Minimize Z = 2x1 + x2 + 3x3 + 0A1 + 0A2

subject to:

5x1 + 2x2 + 7x3 + A1 = 420    (Equation 1)

3x1 + 2x2 + 5x3 + A2 = 280    (Equation 2)

x1 ≥ 0, x2 ≥ 0, x3 ≥ 0, A1 ≥ 0, A2 ≥ 0

By introducing the artificial variables, we have transformed the original problem into a convenient artificial problem that can be solved using the simplex method.

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The complete question is:

Consider the following problem.

Minimize

Z = 2x_{1} + x_{2} + 3x_{3}

x_{3} >= 0

subject to

5x_{1} + 2x_{2} + 7x_{3} = 420

3x_{1} + 2x_{2} + 5x_{3} >= 280

and

x_{1} >= 0

x_{2} >= 0

Introduce artificial variables to reformulate this problem as a convenient artificial problem for preparing to apply the simplex method.

There are \(\frac{60!}{57!}\) ways we can do it.

Since organization has 60 members from which we haveto pick one person at random to be the president, another person to be the vice president and a third person to be the transformer,

the president can be select in 60c1 = \(\frac{60!}{1! 59!}\)

                                                           = \(\frac{60 *59!}{1*59!}\)

                                                           = 60 ways

After this for vice president we have 59 members from which vice president can be select in 59c1 = 59 ways.

and for treasure we have 58 members from which treasure can be select in 58c1 = 58 ways.

∴ No. of ways in which we can select president, vice president and treasure = 60 × 59 × 58

              =  \(\frac{60 * 59 * 58 * 57!}{57!}\)

              =  \(\frac{60!}{57!}\)

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The value of cos2x when sine of x equals negative 15 over 17 and cos x > 0 is -161/289.

The ratio of the neighboring side's length to the longest side, or hypotenuse, in a right triangle is known as the cosine. Let's say that the hypotenuse of a triangle ABC is written as AB, and the angle between the hypotenuse and base is written as.

It's interesting to see that cos's value varies depending on the quadrant. As observed in the above table, cos 0°, 30°, etc. have positive values while cos 120°, 150°, and 180° have negative values. Cos will have a good value in the first and fourth quadrants.

Given that, sin x equals negative 15 over 17.

Using the Pythagoras theorem we have:

(17)² = (- 15)² + y²

y = 8

The value of cos x = 8/17

Then the value of cos2(x) is calculated using the formula:

cos2x = cos²x - sin²x

cos2x = (8/17)² - (15/17)²

cos2x = -161/289

Hence, the value of cos2x when sine of x equals negative 15 over 17 and cos x > 0 is -161/289.

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Answer:

w = 4

Step-by-step explanation:

distribute 10(w+3)=70

10w + 30 = 70

subtract 30

10w = 40

divide by 10

w = 4

Answer: w=7

Step-by-step explanation: 10 times what equals 70? 10 times 7 equals 10. So 3 plus 4 equals 7.

10(7+3)=70

Answer:

3:2

Step-by-step explanation:

2/5 are terriers which means 3/5 of them are dalmations

Answer:

2xy and 5xy are like terms

Step-by-step explanation:

Like terms have the same number, and variables.

A is correct since it has one number and two variables of x and y.

B is wrong since 7 doesn’t have xy at the end like 2xy does.

C is wrong since -3 doesn’t have xy at the end like 5xt does.

D is right since 7 and -3 are by themselves with no variables.

Best of Luck!

The vector orthogonal for both vectors is \((20, -10, -4) / \sqrt{444}\) = (\(20 / \sqrt{444}\), \(-10 / \sqrt{444}\), \(-4 / \sqrt{444}\))

What is an orthogonal vector?

An orthogonal vector is a vector that is perpendicular to another vector in a given space. In other words, two vectors are orthogonal if their dot product is equal to zero.

To find a vector orthogonal to both 2, 2, 0 and 0, 2, 5 of the form 1, we can take the cross product of the two vectors, which results in a vector that is orthogonal to both. The cross product of 2, 2, 0 and 0, 2, 5 is given by:

(2, 2, 0) x (0, 2, 5) = (20, -10, -4)

So, a vector orthogonal to both 2, 2, 0 and 0, 2, 5 is given by (20, -10, -4). We can normalize this vector by dividing it by its magnitude, which is equal to sqrt(20^2 + (-10)^2 + (-4)^2) = sqrt(444). The normalized vector will be of the form 1:

\((20, -10, -4) / \sqrt{444}\) = (\(20 / \sqrt{444}\), \(-10 / \sqrt{444}\), \(-4 / \sqrt{444}\))

Hence, the vector orthogonal for both vectors is \((20, -10, -4) / \sqrt{444}\) = (\(20 / \sqrt{444}\), \(-10 / \sqrt{444}\), \(-4 / \sqrt{444}\)).

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James needs to make a cut that is 18 inches long along the median to cut the tiles in half and create two congruent triangles. The correct answer is: D. 18 inches

To cut the tiles along the median, James needs to make a cut that divides the trapezoid into two congruent triangles. The median of a trapezoid is the line segment that connects the midpoints of the non-parallel bases.

In this case, the top base of the trapezoid is 15 inches, and the bottom base is 21 inches. To find the length of the median, we can take the average of the lengths of the top and bottom bases.

Median = (15 + 21) / 2

Median = 36 / 2

Median = 18 inches

The correct answer is: D. 18 inches

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The hospital must cut the number of overtime hours by approximately 2.91% in order to stay within budget.

To determine the required percentage reduction in overtime hours, we need to consider the impact of the nurses' hourly rate increase and the limited budget increase for overtime wages.

Let's assume the current budget for nurses' overtime wages is denoted by B, and the total number of overtime hours worked is denoted by H. The current overtime rate per hour is R.

With the 5% hourly rate increase, the new overtime rate per hour becomes 1.05R. Considering the limited budget increase of 3%, the new budget for overtime wages is 1.03B.

To calculate the required percentage reduction in overtime hours, we can set up the following equation:

(1.05R) * (1 - x) * H = 1.03B

where x represents the required percentage reduction in overtime hours.

Simplifying the equation, we have:

(1 - x) * H = (1.03B) / (1.05R)

Now, let's solve for x:

1 - x = (1.03B) / (1.05R * H)

x = 1 - [(1.03B) / (1.05R * H)]

Here, we can see that the required percentage reduction in overtime hours, represented by x, depends on the values of B, R, and H.

It's important to note that without knowing the specific values of B, R, and H, we cannot calculate the exact percentage reduction. However, based on the provided information, we can determine the maximum percentage reduction that the hospital must make to stay within budget.

By assuming that B, R, and H are constant, we can use the given constraints to calculate an approximate percentage reduction. Based on the constraints of a 3% budget increase and a 5% hourly rate increase, the hospital would need to reduce the number of overtime hours by approximately 2.91% to maintain a balanced budget.

Please keep in mind that this approximation may vary depending on the specific values of B, R, and H.

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Answer:

see below

Step-by-step explanation:

h(t) = –gt^2 + v0t + h

where g is 1/2 the gravity constant and v0 is the initial velocity and h is the initial height

h(t) = –16t^2 +49t + 0

h(t) = –16t^2 +49t

Factor out t

0 = t(-16t+49)

The zeros are at

t= 0 and   -16t = -49

                      t = 49/16

The vertex  (or max) is 1/2 way between the zeros

(0+ 49/16)  /2 = 49/32  =1.53125

Round to the nearest hundredth

x = 1.53

The height is

h(1.53) = 1.53(-16 * 1.53 +49)

          37.5156

To the nearest hundredth

           37.52

The range is the values that height can take

0 ≤h≤37.52

There is a maximum height because eventually the effects of gravity going down outweigh the effects of the initial velocity going up