The sales force at a certain company successfully closed 94 out of 200 sales calls. What was their percent success rate?

The linear equation from the given statement is the N + F+11 = 2F.

According to the statement

We have to write the linear equation.

So, For this purpose, we know that the

The definition of a linear equation is an algebraic equation in which each term has an exponent of one and the graphing of the equation results in a straight line.

From the given information:

David has 11 shirts to fold. Let N be the number of shirts he would have left to fold after folding F of them. Write an equation relating and 2F.

Then

The number of shirts left = N

The number of the shirts which are folded = F+11

The total number of shirts = 2F

And then

The linear equation becomes :

N + F+11 = 2F

This the linear equation for the given statement.

So, The linear equation from the given statement is the N + F+11 = 2F.

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b. Linear programming model is the correct option.

A linear programming model is a mathematical technique used to find the best outcome in a given set of constraints. In this case, Manders Manufacturing Corporation is trying to determine the optimal product mix for its two products, metal (M) and scrap metal (S), based on certain constraints. The objective is to maximize the profit, represented by the function Z = $30M + $70S.

The constraints are represented by the inequalities:

3M + 2S ≤ 15

2M + 4S ≤ 18

These constraints define the limitations on the production of metal and scrap metal. The model aims to find values of M and S that satisfy these constraints while maximizing the objective function.

Using linear programming techniques, the corporation can solve this model to find the optimal values for M and S that will maximize their profit. This approach allows them to make data-driven decisions and allocate their resources efficiently. By formulating the problem as a linear programming model, Manders Manufacturing Corporation can make informed choices about the optimal product mix to achieve their business objectives.

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SOLUTION

We want to use the information in the diagram to prove that

Now, we have been given for number 1

2.

3.

4.

5.

6.

7.

8.

9. and 10. is good (correct)

11.

12.

13.

14.

Let's solve your inequality step-by-step.

5m<6m+6

Step 1: Subtract 6m from both sides.

5m−6m<6m+6−6m

−m<6

Step 2: Divide both sides by -1.

−m / −1 < 6 / −1

m>−6

Answer:

m>−6

Answer:

Slope = 2

Y intercept = 4

Step-by-step explanation:

This is of the form y = mx + k

where m is the slope

K = y intercept

Hello! (:

y=2x+4

This equation is written in slope-intercept form:

y=mx+b

m is the slope (2) and b is the y-intercept (4)

Hope it helps!

If you have any question or query, feel free to ask! (:

~An excited gal

\(SparklingFlower\)

Given the parameters in the diagrams, we have;

4. ∆ABC ≈ ∆DEF by ASA

5. UW ≈ XZ by CPCTC

6. QR ≈ TR by CPCTC

4. The given parameters are;

<B = <E = 90°

AB = DE Definition of congruency

<A = <D Definition of congruency

Therefore;

5. Given;

XY is perpendicular to WZ

UV is perpendicular to WZ

VW = YZ

<Z = <W

Therefore;

∆UVW ≈ ∆XYZ by Angle-Side-Angle, ASA, congruency postulate

Which gives;

6. Given;

PQ is perpendicular to QT

ST is perpendicular to QT

PQ ≈ ST

From the diagram, we have;

<SRR ≈ <PRQ by vertical angles theorem;

Therefore;

∆QRP ≈ ∆TRS by Side-Angle-Angle, SAA, congruency postulate

Which gives;

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To find all of the cube roots of ii and write the answers in rectangular form, we need to first express ii in polar form. To do this, we can convert ii to its polar form by writing it as a complex number in the form r(cosθ + isinθ), where r is the magnitude and θ is the argument.

In this case, we have ii = 1(cos(π/2) + isin(π/2)).  The magnitude of ii is 1, and the argument is π/2.  Now, to find the cube roots, we need to find the numbers that, when raised to the power of 3, give us ii. To find the cube roots, we can use De Moivre's theorem, which states that for any complex number z = r(cosθ + isinθ), the nth roots of z can be found by taking the nth root of the magnitude and dividing the argument by n.

In this case, we have n = 3, r = 1, and θ = π/2.  Taking the cube root of the magnitude 1 gives us 1^(1/3) = 1. Dividing the argument π/2 by 3 gives us (π/2) / 3 = π/6. So, the first cube root is 1(cos(π/6) + isin(π/6)). To find the other cube roots, we can add multiples of 2π/3 to the argument. Adding 2π/3 to π/6 gives us π/6 + 2π/3 = π/2. So, the second cube root is 1(cos(π/2) + isin(π/2)), which is equal to ii. Adding another 2π/3 gives us π/2 + 2π/3 = 7π/6. So, the third cube root is 1(cos(7π/6) + isin(7π/6)). Therefore, the cube roots of ii in rectangular .

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A and B are vertical angles. If angle A=(4x13) ∘and B=(7x4) ∘ then the value of x is 3.

Since A and B are vertical angles, they must and should have equal measures. Therefore, we can set the two expressions equal to each other and solve for x:

4x + 13 = 7x + 4

Subtracting 4 from both sides:

4x + 9 = 7x

Subtracting 4x from both sides:

9 = 3x

Dividing both sides by 3:

x = 3

So the value of x is 3.

After solving the x value, we should subtract 4 from both sides of the equation, which results in 4x + 9 = 7x. Then, we subtract 4x from both sides, then we get 9 = 3x.

Finally, we divide both sides of the equation by 3 to find that x = 3.

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In triangle ABC with ∠C as a right angle and given b = 8 and c = 17, the remaining sides and angles would be approximately:
a ≈ 15
A ≈ 28.1°
B ≈ 61.9°

In triangle ABC, ∠C is a right angle. We are given two measures: b = 8 and c = 17. To find the remaining sides and angles, we can use the Pythagorean theorem and trigonometric ratios.

1. Use the Pythagorean theorem to find side a:
  The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b).
  Therefore, we have:
  a^2 + b^2 = c^2
  a^2 + 8^2 = 17^2
  a^2 + 64 = 289
  a^2 = 289 - 64
  a^2 = 225
  a = √225
  a = 15

2. Use trigonometric ratios to find the remaining angles:
  We can use the sine, cosine, or tangent ratios to find the angles.
  Let's use the sine ratio for angle A:
  sin(A) = opposite/hypotenuse
  sin(A) = b/c
  sin(A) = 8/17
  A ≈ sin^(-1)(8/17)
  A ≈ 28.1°

  To find angle B, we can use the fact that the sum of the angles in a triangle is 180°:
  B = 180° - A - 90°
  B = 180° - 28.1° - 90°
  B ≈ 61.9°

So, in triangle ABC with ∠C as a right angle and given b = 8 and c = 17, the remaining sides and angles are approximately:
a ≈ 15
A ≈ 28.1°
B ≈ 61.9°

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Using proportions, it is found that he would have to ride his bike 3 miles a day to meet his goal.

A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.

He has already ridden the bike for 6 miles, and needs to run 21 - 6 = 15 miles in 5 days, hence the average is given by:

x = 15/5 = 3 miles a day.

He would have to ride his bike 3 miles a day to meet his goal.

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In order to convert centimeters (cm) into inches, we can use the conversion factor of 1 inch = 2.54 cm. So, 100 cm is equal to 39.37 inches.

To convert 100 cm into inches, we can use this conversion factor by dividing the number of centimeters by 2.54.

100 cm ÷ 2.54 = 39.37 inches

So, 100 cm is equal to 39.37 inches.

It's important to note that this conversion factor is based on the international standard for length measurements, known as the International System of Units (SI). This system is widely used around the world, but it's important to be aware that some countries may use different units of measurement.

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the range of values of y for which the binomial expression 5y - 7 is in the interval (-5, 13) is:

2/5 < y < 4

To find the range of values of y that satisfy this condition, we can set up an inequality:

-5 < 5y - 7 < 13

Adding 7 to all parts of the inequality, we get:

2 < 5y < 20

Dividing by 5, we get:

2/5 < y < 4

Therefore, the range of values of y for which the binomial expression 5y - 7 is in the interval (-5, 13) is:

2/5 < y < 4
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Answer:

The answer is 12. Hope this helped :-)

Step-by-step explanation:

60% of 20

6.2=12

The equation of the line that passes through point (-1, 3) and parallel to line y = 3x + 2 is

As a parallel line part of the qualities include that the slopes of the lines  are equal  

The equation of line is y = 3x + 2

The slope intercept form of the form as

y = mx + c

where

m = slope

c = intercept

x = input variables

y = output variables

Line has slope, m = 3, a new parallel line of slope 3 passing through point  (-1, 3)

(y - y₁) = m  (x - x₁)

y - 3 = 3 (x - -1)

y = 3x + 1 + 3

y = 3x +  4

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Answer: It's a right triangle

Answer: It is a right triangle.

the attachment shows the graphed triangle.

Step-by-step explanation:  The slope of the line between coordinates (-2,-3) and (2,1) is +1  rise/run is 4/4

The slope of the line between points (2,1) and (5,-2) is -1 rise/run -3/3

These slopes are perpendicular to each other, so they form the right angle of this triangle.

The required answer is the volume of the sphere is approximately 65 cubic inches.

To find the volume of the sphere inscribed in a cube with a volume of 125 cubic inches,  the formula for the volume of a sphere.

The volume of a sphere is given by the formula V = (4/3) * π * r^3, where r is the radius of the sphere.

In this case, since the sphere is inscribed in the cube, the diameter of the sphere is equal to the side length of the cube. the side length of the cube as s.

Since the volume of the cube is 125 cubic inches, we have s^3 = 125.

Taking the cube root of both sides gives us s = 5.

Therefore, the diameter of the sphere is 5 inches, and the radius is half of the diameter, which is 2.5 inches.

Plugging the value of the radius into the volume formula, we get V = (4/3) * π * (2.5)^3.

Evaluating this expression gives us V ≈ 65.4 cubic inches.

Rounding this answer to the nearest whole number, the volume of the sphere is approximately 65 cubic inches.

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B AND C

Step-by-step explanation:

B

AREA OF SQUARE =L²

= 7²

= 49cm²

C..

area of a rectangle Base × height

= 14 × 3

= 42cm²

The circle centered at C(-5,4) intersects the line y = 3x + 2 at the point Q, with coordinates (-1/10, 17/10). This point Q serves as the tangent point between the line and the circle.

To find the coordinates of the point Q where the line y = 3x + 2 is tangent to the circle with center C(-5,4), we can use the concept of the slope of a tangent line.

First, we need to find the slope of the tangent line. The slope of the line y = 3x + 2 is 3. For a tangent line to a circle, the radius drawn from the center of the circle to the point of tangency is perpendicular to the tangent line. Since the slope of the radius is the negative reciprocal of the tangent line's slope, the slope of the radius is -1/3.

Next, we find the equation of the radius line passing through the center C(-5,4) with a slope of -1/3. Using the point-slope form, we have:

y - 4 = (-1/3)(x + 5)

To find the point of tangency, we solve the system of equations formed by the line y = 3x + 2 and the radius line:

y = 3x + 2

y - 4 = (-1/3)(x + 5)

Substituting the value of y from the first equation into the second equation:

3x + 2 - 4 = (-1/3)(x + 5)

3x - 2 = (-1/3)x - 5/3

3x + (1/3)x = 5/3 - 2

(10/3)x = -1/3

x = -1/10

Substituting this value of x back into the first equation:

y = 3(-1/10) + 2

y = -3/10 + 20/10

y = 17/10

Therefore, the coordinates of the point Q, where the line y = 3x + 2 is tangent to the circle with center C(-5,4), are (-1/10, 17/10)

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The elastic potential energy in the spring is 0.81Joules

Hooke's law states that if the elastic limit of an elastic material is not exceed the extension is directly proportional to the applied force or load.

Hooke sought to demonstrate the relationship between the forces applied to a spring and its elasticity.

F= ke

where k is the force constant

and e is the extension caused by the load

the potential elastic energy in an elastic material is I/2fe

= 1/2× 13.5×0.12

= 0.81J

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Answer:

10,8,12

Step-by-step explanation:

Answer:

y=2x+3

Step-by-step explanation:

in third line x = 0 y=2×0+3 =3

Step-by-step explanation:

To find the times when the temperature of the water is 60 degrees or cooler, we need to solve the equation:

0.2x² - 6x + 79 = 60

Subtracting 60 from both sides, we get:

0.2x² - 6x + 19 = 0

We can solve this quadratic equation using the quadratic formula:

x = (-b ± sqrt(b² - 4ac)) / 2a

where a = 0.2, b = -6, and c = 19.

Plugging in these values, we get:

x = (-(-6) ± sqrt((-6)² - 4(0.2)(19))) / 2(0.2)

x = (6 ± sqrt(16.4)) / 0.4

Simplifying, we get:

x = 9.9 or 3.6

or

x = 32.9 or 26.4

or

x = 39.9

These are the four times when the temperature of the water is 60 degrees or cooler. To find the time the scientist has to conduct her experiment, we need to take the difference between the two smallest times or the two largest times:

30 - 2.9 = 27.1

or

39.9 - 32.9 = 7

Therefore, the scientist has about 7 to 27.1 minutes to conduct her experiment, depending on which two times she chooses to use.

Answer:

4ln x +ln 3-lnx

4ln x -ln x+ln3

3ln x+ln 3

ln(3x+3)is equivalent.

Answer:

Consistent

Step-by-step explanation:

The shortest possible height at which the two stacks will be level with one another as required is; 360 cm.

It follows from the task content that the height at which the two stacks are level is to be determined.

On this note, since there are 120 cm and 90 cm stacks, it follows that the least common multiple of 90 and 60 represents the height in discuss.

Multiples of 90: 90, 180, 270, 360....

Multiples of 120; 120, 240, 360 .....

On this note, since the LCM is; 360, the shortest possible height for the two stacks to be level is; 360cm.

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