-67/50 + 1.5 - 100% =
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The probability that 40 randomly selected buckets will provide enough coating to cover the tank is 0.5000 or 0.5000 (approx) or 0.5000

Given: The surface area of the tank is 80,000 square feet. The coating comes in five-gallon buckets. The area that the coating in one randomly selected bucket can cover varies, with a mean of 2000 square feet and a standard deviation of 100 square feet.

The probability that 40 randomly selected buckets will provide enough coating to cover the tank. (If it matters, you may assume that the selection of any given bucket is independent of the selection of any and all other buckets.)

The area covered by one bucket follows a normal distribution, with a mean of 2000 and a standard deviation of 100. So, the area covered by 40 buckets will follow a normal distribution with a mean μ = 2000 × 40 = 80,000 and a standard deviation σ = √(40 × 100) = 200.

The probability of the coating provided by 40 randomly selected buckets will be enough to cover the tank: P(Area covered by 40 buckets ≥ 80,000).

Z = (80,000 - 80,000) / 200 = 0.

P(Z > 0) = 0.5000 (using the standard normal table).

Therefore, the probability that 40 randomly selected buckets will provide enough coating to cover the tank is 0.5000 or 0.5000 (approx) or 0.5000 (rounded to four decimal places).

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The gradient vector field of function f(x,y) is given as follows:

grad(f(x,y)) = (1 + 3xy)e^(3xy) i + 3x²e^(3xy) j.

Suppose that we have a function defined as follows:

f(x,y).

The gradient function is defined considering the partial derivatives of function f(x,y), as follows:

grad(f(x,y)) = fx(x,y) i + fy(x,y) j.

In which:

The function in this problem is defined as follows:

f(x,y) = xe^(3xy).

Applying the product rule, the partial derivative relative to x is given as follows:

fx(x,y) = e^(3xy) + 3xye^(3xy) = (1 + 3xy)e^(3xy).

Applying the chain rule, the partial derivative relative to y is given as follows:

fy(x,y) = 3x²e^(3xy).

Hence the gradient vector field of the function is defined as follows:

grad(f(x,y)) = (1 + 3xy)e^(3xy) i + 3x²e^(3xy) j.

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Las soluciones de las ecuaciones lineales por propiedades algebraicas se listan a continuación:

7) x = 7

8) x = 16 / 7

9) x = - 1 / 4

10) x = 1 / 5

En este caso tenemos cuatro casos de ecuaciones lineales, cuya variable x debe ser despejada mediante propiedades algebraicas. A continuación, se procede a determinar las soluciones correspondientes a cada expresión:

Caso 7:

2 · (x - 1) - 5 = 14 - x

2 · x - 2 - 5 = 14 - x

2 · x - 7 = 14 - x

3 · x = 21

x = 7

Caso 8:

15 · x + 10 = 6 · x - 2 · (x - 7) + 3 · (1 - x)

15 · x + 10 = 6 · x - 2 · x + 14 + 3 - 3 · x

15 · x + 10 = x + 17

14 · x = 32

x = 32 / 14

x = 16 / 7

Caso 9:

x + 3 · (x - 1) = 6 - 4 · (2 · x + 3)

x + 3 · x - 3 = 6 - 8 · x - 12

4 · x - 3 = - 6 - 8 · x

12 · x = - 3

x = - 1 / 4

Caso 10:

6 - 3 · (x + 1) = 4 · x + 2 · (1 - x)

6 - 3 · x - 3 = 4 · x + 2 - 2 · x

3 - 3 · x = 2 · x + 2

- 5 · x = - 1

x = 1 / 5

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Answer:

by game 3(at 1:00 p.m.)

temperature increases to 5 degrees at 1:00 p.m

The answer to this question is none of the given options (A, B, C, D, or E).To find the maximum perimeter of a square that can fit inside a circle of radius 5 cm, we need to consider that the diameter of the circle is equal to the diagonal of the square.

This means that the side of the square will be equal to the radius of the circle multiplied by the square root of 2 (since the diagonal of a square is the side length times the square root of 2).

So, the side length of the square will be 5 cm x √2 = 7.07 cm. And since a square has four sides of equal length, the perimeter of the square will be 4 x 7.07 cm = 28.28 cm.

However, this perimeter is greater than the circumference of the circle with radius 5 cm, which is 2 x π x 5 cm = 31.42 cm. This means that the square cannot fit entirely inside the circle.

Therefore, the answer to this question is none of the given options (A, B, C, D, or E).

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Answer: x=5

Step-by-step explanation: isolate the variable by dividing each side by factors that don't contain the variable

Answer:

x=5

i don't know why the "infinite solution" is in the question but there is one solution.

Step-by-step explanation:

-3x+5 = -2(x+7)+2x+4

Distribute

-3x+5 = -2x-14+2x+4

Combine like terms

-3x+5 = -10

Apply inverse operations

-3x = -15

x=5

Answer:

See Explanation

Step-by-step explanation:

Incomplete question, as the number line is not attached. However, the solution is as follows:

Let y be the absolute value of -1/2 So:

\(y = |-\frac{1}{2}|\)

The absolute sign removes all negation. So:

\(y = \frac{1}{2}\)

This means that the point at the label \(\frac{1}{2}\) or \(0.5\) is the solution to the question.

Take for instance, the attached image has point Q at \(\frac{1}{2}\).

Hence, Q is the absolute value of -1/2

Answer:

3 Years old

Step-by-step explanation:

Let Jake be x

Let Jenny be y

x-5=5(y-5)

x+4=2(y+4)

x+4=2y+8

x-5=5y-25

x=5y-20

5y-16=2y+8

3y=24

y=3

Answer:

The surface area is 70 yards

Step-by-step explanation:

The formula for surface area is (SA)=2lw+2lh+2hw. Meaning it would be 2 times (8 times 3 + 8 times 1 + 3 times 1) which equals 70 yards.

Answer:

56 ounces

Step-by-step explanation:

The number of ounces of apples she buys with 3 1/2 pounds per pie will be the multiplication of 3 1/2 with 16, which will equal 56 ounces.

Multiplication is the general procedure in mathematics in which we multiply two or more numbers.

Multiplication gives us a resultant number that will be very big as compared to the number which is going to be multiplied if and only if the number which is going to be multiplied is more than one.

As per the given,

Angie bought 3 1/2 pounds of apples

Number of ounces = 16 in one pound

Multiplication of 16 with = 3 /12

16 x 3 1/2 = 56

Hence "The number of ounces of apples she buys with 3 1/2 pounds per pie will be the multiplication of 3 1/2 with 16, which will equal 56 ounces".

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The perimeter of the triangle is C. 16.7 units.

We can calculate the perimeter of a triangle by adding up all of the given sides. First, we are given the length of the base which is 4.9. Now we have to find the length of the remaining two sides. For the hypotenuse, we use:

Cos 45° - 4.9/r

0.707r = 4.9

r = 4.9/0.707

r = 6.93

Then we find the length of the opposite side to be 4.9

On adding all of the sides, we will have:

6.93 + 4.9 +4.9 = 16.7 units.

This is the perimeter of the triangle.

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Answer:

C. 16.7 units.

Step-by-step explanation:

Answer:

The third expression: (2x)^3

Step-by-step explanation:

Plug in 3 for x in each expression

2x^3

2(3)^3

Use PEMDAS

2 (3 × 3 × 3)

2 (9 × 3)

2 (27)

54

2x^3 + 5

(The last expression told us 2x^3 = 54 so feel free to use this information to make life easier)

54 + 5

59

(2x)^3

(2 × 3)^3

Use PEMDAS

6^3

6 × 6 × 6

36 × 6

216

(x - 1)^3

(3 - 1)^3

Use PEMDAS

2^3

2 × 2 × 2

4 × 2

8

216 is the greatest value so the third expression is the answer

The range of this data set include the following: D. 6.

In Mathematics and Geometry, a range is the set of all real numbers that connects with the elements of a domain.

Furthermore, the vertical extent of any graph of a function represents all range values and they are always read and written from smaller to larger numerical values, and from the bottom of the graph to the top.

By critically observing the graph (dot plot) shown in the image attached above, we can reasonably and logically deduce the following range:

Range = {18, 19, 20, 21, 22, 24} = 6.

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Sonny get 240=240 because  the cross products of the proportion are equal.

Proportion : Two ratios are said to be in proportion when the two ratios are equal.

For Example , If Smith walks 5 km in 1 hour then he will walk 25 km in 5 hours. denoted by

\(\frac{5}{1} =\frac{25}{5} \\ \\ 5=5\).

According to the given question the equation can be written as

\(\frac{16}{x} =\frac{48}{15}\)

Sonny substituted 5 for x in the proportion , the equation can be written as

\(\frac{16}{5} =\frac{48}{15} \\ \\ Doing .the .cross.product\\ \\ 16*15=48*5\\ \\ 240=240\)

Therefore , Sonny get 240=240 because  the cross products of the proportion are equal.

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Answer:(8,15)

Step-by-step explanation:

your linear equations are y=2x+15

Y=x+7

Answer:

60°

140°

Step-by-step explanation:

From the given figures,

 a. we use the concept of alternate angles.

   Two parallel lines cut by a transversal will have equal alternate angles;

  So;

       6x + 12 = 7x + 4

    collect like terms and solve for x;

     6x - 7x = 4 - 12

         -x = -8

         x = 8

Now, 6x + 12 = 6(8) + 12

                     = 48 + 12

                     = 60°

b. Here we use alternate angles and angles on a line;

     4x is an alternate angle to that angle to the left of 13x + 10

And sum of angles on a line = 180

    4x + 13x + 10 = 180

        17x = 170

          x = 10

Now,  13x + 10 = 13(10) + 10 = 140°

Answer:

2000 = 24x + 20y (x represents hours and y represents money per sale)

she must make 88 sales

Step-by-step explanation:

2000 = 24(10) + 20y

2000 = 240 + 20y

-240  = -240

1760 = 20y

/20   = /20

88 = y

Answer:

10500 \(mm^{3}\)

Step-by-step explanation:

h = Perpendicular height of the cylinder

  = 52 mm

r = Base radius

 = \(\frac{Diameter}{2}\)

 = \(\frac{16}{2}\) mm

 = 8 mm

Volume of a cylinder = Base Area × h

                                   = (Area of circle) × h

                                   = \(\pi r^{2} h\)

                                   = \(\pi (8 mm)^{2} (52 mm)\)

                                   = 10455.22 \(mm^{3}\)

                                   ≈ 10500 \(mm^{3}\) (Rounded to 3 significant figures)

Given:

Using synthetic division we get,

Hence, the answer is,

Answer:

Rs 6900

Step-by-step explanation:

To calculate the tax amount the girl should pay in a year, we need to determine the taxable income and then apply the corresponding tax rates.

The taxable income is calculated by subtracting the tax-free allowance from the girl's early income:

Taxable Income = Early Income - Tax-Free Allowance

Taxable Income = 150,000 - 100,000

Taxable Income = 50,000

Now, we can calculate the tax amount based on the given tax rates:

For the first 20,000 rupees, the tax rate is 12%:

Tax on First 20,000 = 20,000 * 0.12

Tax on First 20,000 = 2,400

For the remaining taxable income (30,000 rupees), the tax rate is 15%:

Tax on Remaining 30,000 = 30,000 * 0.15

Tax on Remaining 30,000 = 4,500

Finally, we add the two tax amounts to get the total tax she should pay in a year:

Total Tax = Tax on First 20,000 + Tax on Remaining 30,000

Total Tax = 2,400 + 4,500

Total Tax = 6,900

Therefore, the girl should pay 6,900 rupees in tax in a year.

Answer:

To calculate the volume of a triangular pyramid, we can use the formula:

V = (1/3) * B * h

where V is the volume, B is the area of the base, and h is the height of the pyramid.

Since the base of the pyramid is a right-angled triangle, we can use the Pythagorean theorem to find the length of the other two sides, which are the legs of the triangle. The hypotenuse is 6 cm and the angle opposite to the hypotenuse is 30°, so we can use the sine function to find the length of the other leg:

sin(30) = opposite / hypotenuse

opposite = (sin(30) * hypotenuse) = (1/2 * 6) = 3

Now we can use the area formula for a right-angled triangle:

B = (1/2) * base * height = (1/2) * 3 * 6 = 9

To find the height of the pyramid, we can use the fact that all side faces form an angle of 60° with the base. We can use the sine function to find the height of the pyramid:

sin(60) = opposite / hypotenuse

opposite = (sin(60) * hypotenuse) = (√3/2 * 6) = 3√3 cm

Now we can substitute the values of B and h into the volume formula:

V = (1/3) * B * h = (1/3) * 9 * 3√3 = 3√3 cm³

So the exact volume of the triangular pyramid is 3√3 cm³.

Step-by-step explanation:

Approximately 1.5% of computer programmers make over $97,800.

The average salary of computer programmers is $71,800 with a standard deviation of $13,000. To determine the percentage of programmers making over $97,800, we need to find the area under the normal distribution curve to the right of this value.

Using the z-score formula, we can find the z-score corresponding to $97,800: z = (x - μ) / σ = (97800 - 71800) / 13000 ≈ 2.145.

Looking up the z-score in a standard normal distribution table, we find that approximately 1.5% of programmers make over $97,800.

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Answer:

(1)

x = 128/3

y = 52/3

(2)

x=3

Step-by-step explanation:

(1)

x+y=60 => 3y=52 => y=52/3 => x=128/3

x=2y+8

(2)

M1V1 + M2V2 = MV

x × 10 + x × 70 = 6 × 40

80x = 240

x = 3

The value of 'x' is 5/2  

An exponent is a number that is written in superscript (above and to the right of another number) and indicates how many times that number should be multiplied by itself.    

Exponents are used in many areas of mathematics and science, including algebra, calculus, physics, and chemistry.  

Here we have

\(3^{x+1} - 3^{x-1} = 24\sqrt{3}\)      

Can be solved as follows

=>  \(3^{x} \times 3^{1} - 3^{x} \times 3^{-1} = 24\sqrt{3}\)  

=>  \(3^{x} [ 3^{1} - 3^{-1}] = 24\sqrt{3}\)  

=>  \(3^{x} [ 3 - \frac{1}{3} ] = 24\sqrt{3}\)  

=>   \(3^{x} [ \frac{9- 1}{3} ] = 24\sqrt{3}\)  

=>  \(3^{x} [ 8 ] = 3 \times 24\sqrt{3}\)  

=>  \(3^{x} = 3 \times 3\sqrt{3}\)  

=>  \(3^{x} = 3^{2} \sqrt{3}\)    

=>  \(3^{x} = 3^{2 + \frac{1}{2} }\)    

=> x = 5/2

Therefore,

The value of 'x' is 5/2  

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Answer:

A. To find a linear equation that models the temperature T when crickets are chirping at x chirps per minute, we need to use two points that are known. In this case, we are given that a cricket produces 120 chirps per minute at 70 degrees F and 168 chirps per minute at 80 degrees F. We can use these two points to find the slope and y-intercept of the line.

The slope of a line can be found using the formula: m = (y2 - y1) / (x2 - x1)

In this case, we can substitute the given values to get:

m = (168 - 120) / (80 - 70) = 48/10 = 4.8

The y-intercept of a line can be found using the formula: b = y - mx

We can use the point (70, 120) and the slope that we found to get:

b = 120 - (4.8 * 70) = -264

So the linear equation that models the temperature T when crickets are chirping at x chirps per minute is:

T = 4.8x - 264

B. If the crickets are chirping at 150 chirps per minute, we can substitute this value for x in the equation we found above to estimate the temperature:

T = 4.8x - 264

T = 4.8(150) - 264 = 720 - 264 = 456

So the estimated temperature is 456 degrees F.

C. The y-intercept of the line is -264, it represents the temperature when x (chirps per minutes) is zero. In this case it represents the temperature when the cricket is not chirping which is impossible, so it doesn't have any physical meaning.

If Pharma Plus wants to achieve the optimal staffing level, they need to hire 5 additional pharmacists and 16 additional technicians, which would increase the payroll cost by $9,576 per hour.

a) To determine a minimum-cost staffing plan for Pharma Plus,

we have the following optimization problem:

Min 48P + 12T

Subject to:

P + T > 251 (Employees required)

2P - T > 0 (Service quality guideline)

P > 90 (Pharmacists employed)

Using the graphical method, we can graph the lines of each constraint:

Figure 1 From Figure 1, we can see that the feasible region is the shaded region above the blue line (P + T = 251) and

to the right of the orange line (2P - T = 0),

and to the right of the green line (P = 90).

To obtain the optimal solution, we need to find the intersection point of two lines, where the total cost is minimized.

However, this region has infinite intersection points, which makes it difficult to find the optimal solution.

To overcome this challenge, we use the corner-point method, where we evaluate the objective function at each corner point and select the one that yields the lowest cost.

In this case, the corner points are A (90, 161), B (115, 136), and C (165.5, 85.5).

Using the objective function, we obtain the following values:

At point A: 48(90) + 12(161)

= $3,624

At point B: 48(115) + 12(136)

= $4,008

At point C: 48(165.5) + 12(85.5)

= $7,308

Hence, the optimal solution is at point A (90, 161), where the total cost is $3,624 per hour.

Therefore, Pharma Plus needs at least 90 pharmacists and 161 technicians to minimize the total payroll cost to $3,624 per hour.

b) Given the current staffing levels and expected attrition, Pharma Plus has 85 pharmacists and 175 technicians.

To reach the level recommended in part (a), they need 5 additional pharmacists and 16 additional technicians.

The additional cost of payroll is the difference between the cost at current staffing levels and the cost at the optimal solution.

Using the average salary for licensed pharmacists and technicians, we have the following calculations:

The payroll cost using the current levels of 85 pharmacists and 175 technicians is $60 x 85 + $12 x 175

= $13,200 per hour.

The payroll cost using the optimal solution in part (a) is $48 x 90 + $12 x 161 = $3,624 per hour.

The increase in payroll cost is $9,576 per hour.

Therefore, if Pharma Plus wants to achieve the optimal staffing level, they need to hire 5 additional pharmacists and 16 additional technicians, which would increase the payroll cost by $9,576 per hour.

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Answer:

x=1.25

y=1.75

Step-by-step explanation:

please don’t quote me on this I don’t normally do triangles like this

7/7+y=8/10

7(10)=8(7+y)

70=56+8y

-56 -56

14=8y

/8 /8

1.75=y

5/5+x=8/10

5(10)=8(5+x)

50=40+8x

10=8x

/8 /8

1.25=x

Answer:

Descriptive statistics

Step-by-step explanation:

Descriptive statistics is a branch of statistics that collects, analyzes, and characterizes a set of data.

If you can please give me a Brainliest, thank you, and have a good day!

Reporting frequencies of sample data, such as eye color, ethnicity, grade point average, and height is done by using descriptive statistics.

Answer:

2

Step-by-step explanation:

The average rate of change of f(x) in the closed interval [ a, b ] is

\(\frac{f(b)-f(a)}{b-a}\)

Here [ a, b ] = [ - 5, - 1 ] , thus

f(b) = f(- 1) = - (- 1)² - 4(- 1) + 6 = - 1 + 4 + 6 = 9

f(a) = f(- 5) = - (- 5)² - 4(- 5) + 6 = - 25 + 20 + 6 = 1 , then

average rate of change = \(\frac{9-1}{- 1-(-5)}\) = \(\frac{8}{4}\) = 2