Evaluate the mean of each data set mentally:

27, 30, 33

61, 71, 81, 91, 101

0, 100, 100, 100, 100

0, 5, 6, 7, 12

Answer:

35

Step-by-step explanation:

Substitute x in the equation for 10

x/2 = 10/2

+ 3x = + 3(10)

10/2 = 5

+ 3(10) = + 30

5 + 30 = 35

The approximate height of the boat ramp is 21 feet.

sin(20°) = height / 60 feet

To find the height, multiply both sides of the equation by 60 feet:

height = 60 feet * sin(20°)

Using a calculator to find the sine of 20°:

height ≈ 60 feet * 0.342

height ≈ 20.52 feet

So the approximate height of the boat ramp is 20.52 feet.

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Answer:

There are two. <CEB and <AED. You could put either one.

Step-by-step explanation:

There are two. <CEB and <AED. You could put either one.

Person's diastolic blood pressure at 6:00am is  94.5 mmHg.

Diastolic blood pressure is the lower number in a blood pressure reading. It indicates the pressure in the arteries when the heart muscle is resting between beats and refilling with blood. A normal diastolic blood pressure is between 80 and 90 mmHg (millimeters of mercury).

For example, if a person's blood pressure reading is 120/80 mmHg, the diastolic blood pressure is 80 mmHg. This means that the pressure in the arteries when the heart is at rest is 80 mmHg. High diastolic blood pressure (greater than 90 mmHg) is a risk factor for heart attack, stroke, and other cardiovascular problems.

The formula for diastolic blood pressure at time t is given by B(t) = 90 + 9 sin(t/12). To find the diastolic blood pressure at 6:00am, need to plug in t = 6 into the formula.

B(6) = 90 + 9 sin(6/12) = 90 + 9 sin(0.5) = 90 + 9(0.4794) = 94.5 mmHg.

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ANSWER

5 hours

EXPLANATION

Let h be the number of hours per labor. We know that they charge $48 per hour of labor, so for h hours, the cost is $48h.

In this case, the total cost of parts was $265 and that plus the h hours of labor resulted in a bill for a total of $505,

We have to solve this equation for h. First, subtract 265 from both sides,

And then divide both sides by 48,

Hence, you were charged for 5 hours of labor.

The turning points of the function y = x³ - 3x² - 9x + 4 are (3, -23) and (-1, 9).

To determine the turning points of the given function y = x³ - 3x² - 9x + 4, we need to find the critical points where the derivative of the function is equal to zero.

1. Find the derivative of the function:

  y' = 3x² - 6x - 9

2. Set the derivative equal to zero and solve for x:

  3x² - 6x - 9 = 0

3. Factorize the quadratic equation:

  3(x² - 2x - 3) = 0

4. Solve the quadratic equation by factoring or using the quadratic formula:

  (x - 3)(x + 1) = 0

  This gives us two possible values for x: x = 3 and x = -1.

5. Substitute these critical points back into the original function to find the corresponding y-values:

  For x = 3:

  y = (3)³ - 3(3)² - 9(3) + 4

    = 27 - 27 - 27 + 4

    = -23

  For x = -1:

  y = (-1)³ - 3(-1)² - 9(-1) + 4

    = -1 - 3 + 9 + 4

    = 9

6. Therefore, the turning points are (3, -23) and (-1, 9).

Note: It appears that there was a typo in the original equation, where the term "-9x" should have been "-3x²". The above solution assumes the corrected equation.

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Answer: 12 x 6

Step-by-step explanation:

36/2=18

3x=18

x equal 6

6x2=12 as it is two times

Answer:

17/20

Step-by-step explanation:

Total no. of beads = 6 + 3 + 11 = 20

We need RED or GREEN bead .

So no. of beads needed = 6 + 11 = 17

So probability of getting GREEN or RED beads = 17/20

The length AC in the kite is 8.7 cm.

A kite is a quadrilateral that has two pairs of consecutive equal sides and

perpendicular diagonals. Therefore, let's find the length AC in the kite.

Hence, using Pythagoras's theorem, let's find CE.

Therefore,

7² - 4² = CE²

CE = √49 - 16

CE = √33

CE = √33

Let's find AE as follows:

5²- 4² = AE²

AE = √25 - 16

AE = √9

AE = 3 units

Therefore,

AC = √33 + 3

AC = 5.74456264654 + 3

AC = 8.74456264654

AC = 8.7 units

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Answer:

There are two equivalent formulas to choose from when solving work-rate problems. If two people are working together on a job then their work rates add and they can perform the job working together in a shorter amount of time. If we let x = the time it takes a person to complete a task then his work rate is 1/x. In other words, he can complete the 1 job in x number of hours. If we let y = the time it takes a second person to complete the task and t = the time it takes for both people working together we get the following work-rate formulas:

Answer:

Wind speed = 40 km/hr

Speed of the plane in still air = 280km/hr

Step-by-step explanation:

Formula to use

Distance = Rate multiplied by Time

D = R × T

Speed of the plane in still air = a

Speed of the wind = b

Plane with the wind (tailwind) is a + b where the time = 3hours

Plane against the wind is a - b, where the time = 4hours

This would give us 2 equations

3 × (a+ b) = 960

3a + 3b = 960 ...... Equation 1

4 × (a- b) = 960

4a - 4b = 960 ........ Equation 2

Solve this like you would with system of equations:

We solve the equation using elimination method.

Mulitply equation 1 by 4 and equation 2 by -3

4 × (3a + 3b = 960)

12a + 12b = 3840 ..... Equation 4

-3 × (4a- 4b = 960)

-12a + 12b= -2880 ........ Equation 5

Therefore we have

12a + 12b = 3840 ..... Equation 4

-12a + 12b= -2880 ........ Equation 5

24b = 960

b = 960÷ 24

b = 40

Wind Speed = 40km/hr

To find the speed of air, we use equation 2

4a - 4b = 960 ........ Equation 2

Substituting 40 which is wind of speed for b in equation 2 we would have

4a - 4(40) = 960

4a - 160 = 960

4a = 960 + 160

4a = 1120

a = 1120 ÷ 4

a = 280

The speed of the small plane in still air is 280 km/hr

Note that:

 a) 1 unit  of   agricultural production required to obtain 1 agricultural product.

b) 200,000 units of agricultural production are required to obtain 1 of agricultural product.

c) 22,727 units of agricultural production are required to obtain 50,000 units of energy.

d) we need 27,825 units of energy to produce 50,000 units of agricultural products.

a) According to the table, the coefficient of production for agriculture is 0.293, that is

0.293 units of agricultural production = a unit of agricultural product.

b) To obtain 200,000 units of agricultural products we say

0.293 x 200,000,=  58,600 units of agricultural production.

c) the coefficient of production for energy with respect to agriculture is 0.044,

that is ,

0.044 units of agricultural production = a unit of energy.

So

50,000 units of energy,=

0.044 by 50,000,

= 2,200 units of agricultural production.

d) To obtain 50,000 units of agricultural products

use the Leontief inverse of the input-output table, which is simply the inverse of the coefficient matrix.

      [ 3.4175  -0.2345  -0.5565 ]

       [-0.1894   4.8264  -0.2114 ]

       [-0.3074   0.1772   4.8324 ]

       [ (3.4175  x0) +   (-0.2345 x 0) + (-0.5565  x 50,000)  ]

       [ (-0.1894   x0) + (4.8264x 0) + (-0.2114  x50,000) ]

       [ (-0.3074   x0) + (0.1772  x0) + (4.8324  x50,000) ]

       [ -27,825 ]

       [ -10,570 ]

       [ 241,620 ]

Thus, we need 27,825 units of energy to produce 50,000 units of agricultural products.

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Answer:

19.625

Step-by-step explanation:

Area is pi x \(r^{2}\) so 3.14 x \(2.5^{2}\) = 19.625

Answer:

C

Step-by-step explanation:

simply add all the terms and simplify

3^x + 10x + 4x - 2

3^x + 14x - 2

Answer:

50

Step-by-step explanation:

the formula for Pythagorean theorem is A^2+B^2=C^2

14 squared is 196 48 squared is 2304 add them together u get 2500 and u have u get the sqrt of 2500 which is 50.

Answer:c

Step-by-step explanation:

Step-by-step explanation:

To determine the type of triangle formed by the three roads, we need to use the Triangle Inequality Theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Let's check if this theorem holds true for the three sides:

- 15 + 18 > 20 (True)

- 15 + 20 > 18 (True)

- 18 + 20 > 15 (True)

Since the sum of the lengths of any two sides is greater than the length of the third side, we can conclude that a triangle can be formed.

To determine the type of triangle, we can use the Pythagorean Theorem, which states that in a right triangle, the sum of the squares of the two shorter sides equals the square of the longest side.

Let's check if this theorem holds true for the three sides:

- 15² + 18² = 225 + 324 = 549

- 20² = 400

Since 15² + 18² is less than 20², we can conclude that the triangle is not a right triangle.

Next, we can use the Law of Cosines to determine the type of triangle. The Law of Cosines states that in a triangle with side lengths a, b, and c, and angles A, B, and C opposite those sides, the following equation holds true:

c² = a² + b² - 2ab cos(C)

Let's calculate the cosine of each angle:

- cos(A) = (18² + 20² - 15²) / (2 * 18 * 20) = 0.425

- cos(B) = (15² + 20² - 18²) / (2 * 15 * 20) = 0.3

- cos(C) = (15² + 18² - 20²) / (2 * 15 * 18) = 0.208

Using these values, we can calculate the value of c² for each angle:

- c² = 18² + 20² - 2(18)(20)(0.425) = 344.4

- c² = 15² + 20² - 2(15)(20)(0.3) = 331

- c² = 15² + 18² - 2(15)(18)(0.208) = 304.68

Since none of these values equals the sum of the squares of the other two sides, we can conclude that the triangle is not a right triangle either.

To determine the type of triangle, we can look at the values of the cosine of each angle. If the cosine of an angle is greater than 0, the angle is acute. If the cosine of an angle is less than 0, the angle is obtuse. If the cosine of an angle is equal to 0, the angle is a right angle.

From the values we calculated above, we can see that the cosine of each angle is positive, which means that all angles are acute. Therefore, the answer is:

D: acute triangle.

The base case in a recursive solution to the problem of finding the factorial of a number is n = 0 .

Given :

the base case in a recursive solution to the problem of finding the factorial of a number. recall that the factorial of a non-negative whole number is defined as n! .

Base case :

The base case is the condition to stop the recursion. The recursive case is the part where the function calls on itself .

we know that ,

def func ( n ) :

     if   n == 0 :

return 1

Here the base case is clearly n = 0

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These values represent the petrol consumption in gallons for the given distances traveled by the milk van. To complete the table, we need to find the corresponding values of petrol (gallon) for the given distances (km) based on the information provided.

From the given data, we can observe that the milk van used 3 gallons of petrol for a distance of 60 km. To find the petrol consumption for other distances, we can use the ratio of petrol consumption to distance.

Let's calculate the values for the missing entries in the table:

For the distance of 300 km:

Using the ratio, we can set up a proportion:

60 km / 3 gallons = 300 km / x gallons

Cross-multiplying and solving for x, we get:

x = (300 km * 3 gallons) / 60 km = 15 gallons

For the distance of 500 km:

Using the same proportion:

60 km / 3 gallons = 500 km / x gallons

Cross-multiplying and solving for x, we get:

x = (500 km * 3 gallons) / 60 km = 25 gallons

Th completed table would look like this:

Distance (km) Petrol (gallon)

60 3

300 15

500 25

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Answer:

a) 0.23x+0.21y=75

b) (For the Graph see the attached picture).

A possible solution for the inequality \(0.23x+0.21y\leq75\) would be any point inside the shaded region of the graph. For example (150,175) This is 150 minutes to the United Kingdom and 175 minutes to France.

\(0.23x+0.21y\leq75\)

\(0.23(150)+0.21(175)\leq75\)

\(34.5+36.75\leq75\)

\(71.25\leq 75\)

this inequality is true, so the number of minutes used for the United Kingdom and to France is valid.

Step-by-step explanation:

a)

In order to solve this problem, we must first set our variables:

x= Minutes to the United Kingdom.

y= Minutes to France

The greatest amount of money you can spend is $75 and each minute will cost $0.23 when calling to the United Kingdom and $0.21 when calling to France. So we can use this information to build our equation:

0.23x+0.21y=75.

b) So first, we need to convert our equation into an inequality where the total amount of money spent must be less than $75, so our inequality is:

[tex}0.23x+0.21y\leq75\)

so now we can proceed and graph. This is graphed exactly as you would graph a regular linear equation. You need to find two points on the graph that will satisfy the equation. Plot them and then connect them with a straight line. For example:

First, let's solve the equation for y:

0.23x+0.21y=75

we start by moving the 0.23x to the other side of the equation so we get:

0.21y=-0.23x+75

and next we divide both sides of the equation into 0.21 so we get:

\(y=\frac{-0.23x+75}{0.21}\)

which yields:

y= -1.095x+357.14

next we need to pic an x-value so we can find the first ordered pair. Let's say I pick x=0. So we get:

y= -1.095x+357.14

y= -1.095(0)+357.14

y=357.14

so our first point is (0, 357.14)

And we can follow the same procedure for the second point. Let's say I pick x=1. In that case our second point is (1, 354.04). We can now plot them. Once the graph is drawn, we need to shade it, for which we will pick an ordered pair to the left and an ordered pair to the right of the line. For the left region let's pick the point (0,0) and for the right of the graph, let's pick the point (150,357).

So let's test the inequality for these two points:

First, let's use the point (0,0)

\(0.23x+0.21y\leq75\)

\(0.23(0)+0.21(0)\leq75\)

\(0\leq75\)

This proves that the left side of the graph is the side to be shaded. We can still use the other point and see what we qet:

(150, 357) and let's use it on our inequality:

\(0.23x+0.21y\leq75\)

\(0.23(150)+0.21(357)\leq75\)

\(109.47\leq75\)

Is a false statement, so only the region on the left will contain the possible number of minutes to do the phone calls to the UK and France.

A possible solution for the inequality \(0.23x+0.21y\leq75\) would be any point inside the shaded region of the graph. For example (150,175) This is 150 minutes to the United Kingdom and 175 minutes to France.

\(0.23x+0.21y\leq75\)

\(0.23(150)+0.21(175)\leq75\)

\(34.5+36.75\leq75\)

\(71.25\leq 75\)

This is a true statement so the possible solution is correct.

The true statements are:

√(-1) is an imaginary number.

There are no real numbers that satisfy the equation  x = √-1.

A number that produces a negative square root is referred to as an imaginary number. An imaginary number, which has no real-world equivalent, is essentially the square root of a negative number.

Given:

We know that the value of √(-1) is i (iota) which is imaginary number.

So, √(-1) is an imaginary number.

Now, Negative numbers don't have real square roots since a square is either positive or 0.

So, x = √-1 have no real solution.

Now, x² = -1 again have no real solution because

x = √-1 and , Negative numbers don't have real square roots.

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Answer:x^1/2 • 1/3 x^1/2 + 1/3

Step-by-step explanation:

The equivalent expressions are,

C) x⁻² = 1/x²

E) (2x²y⁵)³ = 8x⁶y¹⁵

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Now, We can all the expression as,

A) (x²)⁵ = x⁷

LHS, (x²)⁵ = x¹⁰

               ≠ x⁷

B) x⁹ ÷ x⁴ = x¹³

LHS, x⁹ ÷ x⁴ = x ⁹⁻⁴

                  = x⁵

                  ≠ x¹³

C) x⁻² = 1/x²

LHS, x⁻² = 1/x²

             = 1/x²

D) (2x²y⁵)³ = 2x⁵y⁸

LHS, (2x²y⁵)³ = 8x⁶y¹⁵

                   ≠ 2x⁵y⁸

E) (2x²y⁵)³ = 8x⁶y¹⁵

LHS, 2x²y⁵)³ = 8x⁶y¹⁵

Thus, The equivalent expressions are,

C) x⁻² = 1/x²

E) (2x²y⁵)³ = 8x⁶y¹⁵

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The first quantity (45g) as 60 percentage of second (75g).

A part of whole expressed in Hundredth. Percentage is a fraction of a number out of 100%. It can be in fraction or in decimal.

To convert the given percentage value in decimal, divide the given value by 100.

For example:

1. 50% in decimal or fraction will be 50/100 = 0.5.

2. 20% in decimal or fraction will be 20/100 = 0.2.

1. Finding the total amount from which we need to find the percent.

2. Dividing the required amount to find the percentage by total amount.

3. Multiply it by 100.

For example:

1. It rained 10 of the 30 days in April.

Percentage will be 10/30 = (1/3) x 100

Percentage = 33.33%

Here, we have given that:

Total amount = 75g

Required amount for percent = 45g

Now, to find the percentage:

Percentage = 45/75

Percentage = 0.6 x 100

Percentage = 60%

Hence,

The first quantity (45g) as 60 percentage of second (75g).

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Step-by-step explanation:

72km/h = 72,000m/3,600s = 20m/s.

Using Kinematics, we have

v = u + at

= (20m/s) + (-2m/s²)(5s)

= 10m/s.

Hence the velocity will be 10m/s. (or 36km/h)

The monthly PMI Payment for Christina's loan is $37.50.The correct answer is option B.

To determine Christina's monthly PMI (Private Mortgage Insurance) payment, we need to find the corresponding interest rate for her loan-to-value (LTV) ratio. The LTV ratio is calculated by dividing the loan amount by the property value.

The loan amount can be calculated by subtracting the down payment from the property value:

Loan amount = Property value - Down payment

           = $170,000 - $20,000

           = $150,000

Now we can calculate the LTV ratio:

LTV ratio = Loan amount / Property value * 100

         = $150,000 / $170,000 * 100

         = 88.24%

Since Christina is obtaining a 30-year mortgage, we need to look at the interest rates for LTV ratios between 85.01% and 90%. According to the table, the interest rate for this range is 0.30%.

To calculate the PMI payment, we multiply the loan amount by the PMI rate and divide it by 12 months:

PMI payment = (Loan amount * PMI rate) / 12

           = ($150,000 * 0.30%) / 12

           = $450 / 12

           = $37.50

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The Probable question may be:
Christina is buying a $170,000 home with a 30-year mortgage. She makes a $20,000 down payment.

Use the table to find her monthly PMI payment

Base to loan% = 95.01% to 97%,90.01% to 95%,85.01% to 90%,80.01% to 85%.

30-year fixed-rate loan = 0.55%,0.41%,0.30%,0.19%

15-year fixed-rate loan = 0.37%,0.28%,0.19%,0.17%.

A. $51.25

B. $37.50

C. $23.75

D. $42.50

Equating the expressions, if Li Wei can read 30 pages in an hour and Colleen Henry 24 pages an hour, they will be on the same page in 6 hours.

Equivalent expressions are two or more algebraic expressions that have the same value when the variables are substituted with real numbers.

In this situation, we can determine the time that Li Wei and Colleen Henry can be on the same page by equating the expressions representing their reading rates.

The number of pages Li Wei can read in a week = 90

The number of pages Collen can read in a week = 126

Li Wei's reading rate per hour = 30 pages

Collen's reading rate per hour = 24 pages

Let the hours that Li Wei and Colleen can be on the same page= x

The total number of pages Li Wei can read = 90 + 30x

The total number of pages Colleen can read = 126 + 24x

For Li Wei and Colleen to be on the same, the two expressions are equated.

90 + 30x = 126 + 24x

6x =  36

x = 6

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Answer: The area and perimeter of the square whose length of one side is of p cm are p^2 square cm and 4p cm respectively.

Step-by-step explanation: We know,

Area of the square = p^2 where p is the side of the square.

The perimeter of the square = 4p cm where p is the side of the square.

thus, The area and perimeter of the square whose length of one side is of p cm are p^2 square cm and 4p cm respectively.

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The equation of the linear function is y=8x+(-8).

What do you mean by equation?

A mathematical statement with two expressions that have the same value and the sign "equal to" between them is called an equation. Take the example of 3x + 5 = 15. Equations can be of several sorts, including linear, quadratic, cubic, and others.

According to data in the given question,

We have points (0,-8) and (1,0), thus

\(m=\frac{y_{2} -y_{1} }{x_{2} -x_{1} } \\=\frac{(0-(-8))}{1-0} \\=8\)

Then

y=8x+b

Points (0,-8) means that when x=0, y=-8 and we use this to find b,

y=8x+b

-8=8(0)+b

-8=0+b

b=-8

So, y=8x+(-8)

Therefore, the equation of the linear function is y=8x+(-8).

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Answer:

1/12. Larger the disparity between numerator and the denominator (with the denominator the larger), the smaller the fraction!

Answer:

if it says 12x = 7

the u will divide the 12 on both sides and x will equal to 7/12,,

if it simply says 12 = 7 then put false cause that's not true!!