This data is going to be plotted on a scatter graph.
Length(cm) 103 129 99 82 110
Mass(kg) 4.1 2.6 5.7 1.9 2.8
The length axis is shown below
Choose the best scale for this axis
What should the values of A and B be

Answer:

in 25 weeks the stalk grew to 4 inches - false

the stalk grew to a height of 25 inches in 4 weeks - true

each bag can hold 25 cornstalks - cannot be determined

the stalk grew at a rate of 6.25 inches each week - true (25/4 = 6.25)

the quotient 25/4 equals the growth rate of the stalks each week - true

We can conclude that the central angle C and inscribed angle S intersect the same arc, and their measures are related as follows:

Measure of Central Angle C = Measure of Intersected Arc

Measure of Inscribed Angle S = 1/2 * Measure of Intersected Ar

Central angle C and inscribed angle S intersect the same arc. Therefore, we can determine their relationship based on the properties of angles formed by intersecting chords, tangents, or secants.

When two angles intersect the same arc of a circle, the following relationships hold true:

1. Central Angle (C): A central angle is an angle whose vertex is at the center of the circle, and its arms extend to the endpoints of an arc. The measure of a central angle is equal to the measure of the intercepted arc.

2. Inscribed Angle (S): An inscribed angle is an angle formed by two chords in a circle, and its vertex is on the circle. The measure of an inscribed angle is half the measure of the intercepted arc.

Therefore, we can conclude that the central angle C and inscribed angle S intersect the same arc, and their measures are related as follows:

Measure of Central Angle C = Measure of Intersected Arc

Measure of Inscribed Angle S = 1/2 * Measure of Intersected Arc

In summary, the central angle C and inscribed angle S have a relationship where the measure of the central angle is equal to the measure of the intercepted arc, while the measure of the inscribed angle is half the measure of the intercepted arc.

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After finding the sides of the triangle using sine law, we found that the height of the flagpole is found to be 110.89 ft.

What is meant by sine law?

The law of sines specifies how many sides there are in a triangle and how their individual sine angles are equal. The sine law, sine rule, and sine formula are additional names for the sine law.

The side or unknown angle of an oblique triangle is found using the law of sine. Any triangle that is not a right triangle is referred to as an oblique triangle. At least two angles and their corresponding side measurements should be used at once for the sine law to function.

Given,

 The distance between two observers = 600 ft

The angle of elevation of the first observer = 19°

The angle of elevation of the second observer = 21°

We are asked to find the height of the flagpole.

The figure is given below.

There are 2 right triangles, ΔABD and ΔCBD.

We will start with ΔABC.

∠B = 180 - (∠A+∠C) = 180 - (21+19) = 140

Now using sine law, we can find lengths a and b.

According to sine law,

b/sin21 = a/sin 19 = 600/sin 140

From this,

b/sin 21 = 600/sin 140

b/0.36 = 933.43

b = 336.03ft

Also,

a/sin 19 = 600/sin 140

a/0.33 = 933.43

a = 308.03ft

Now using ΔABD,

sin 21  =h/a

0.36 = h/308.03

h = 110.89 ft

Therefore after finding the sides of the triangle using sine law, we found that the height of the flagpole is found to be 110.89 ft.

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Answer:

D) 2

Step-by-step explanation:

Use the following slope formula:

m (slope) = (y₂ - y₁)/(x₂ - x₁)

Let:

(x₁ , y₁) = (4 , 1)

(x₂ , y₂) = (1 , -5)

Plug in the corresponding numbers to the corresponding variables:

m = (-5 - 1)/(1 - 4)

Simplify. Remember to follow PEMDAS. First subtract, then divide:

m = (-5 - 1)/(1 - 4)

m = (-6)/(-3)

m = 2

D) 2 is your answer.

~

Answer:

18.8

Step-by-step explanation:

Surface area=2*pi*r*(r+h)=2*pi*1*(3)=18.8

The equation that will make a system with infinite solutions is the third option.

y = 2x + 6

A system of linear equations will have infinite solutions only if the two equations represent the same line.

Here we know that one of the linear equations of the system is:

2y - 4x = 12

If we now divide the whole equation by 2, we will get:

(2y - 4x)/2 = 12/2

y - 2x = 6

Now we can move the "2x" term to the right side, then we will get.

y = 2x + 6

So the equations:

y = 2x + 6

2y - 4x = 12

Represent the same line, then that system will have infinite solutions.

Finally, the correct option is the third one.

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Answer: the diagonals of a trapezoid do not bisect each other.

Step-by-step explanation:

We're going to prove that the diagonals of a trapezoid do not bisect each other. But instead of just straight up telling you the proof, we're going to do it using something called an indirect proof. This means we're going to assume that the diagonals do bisect each other and then show that this leads to a contradiction.

So, let's assume that the diagonals of our trapezoid, call them d1 and d2, do bisect each other. That means that they cut each other in half. Now, since a trapezoid has exactly one pair of parallel sides, we know that the midpoint of d1 and d2 must also be the midpoint of the parallel sides.

But here's the catch: the midpoint of a line segment is the same distance from both ends of the segment. So, if the midpoint of d1 is the same as the midpoint of d2, that means that d1 and d2 are the same length! And that's a contradiction, because we know that the diagonals of a trapezoid are not the same length.

So, by assuming that the diagonals of a trapezoid bisect each other, we've shown that it leads to a contradiction. And that means that our assumption was wrong, which means that the diagonals of a trapezoid do not bisect each other.

Answer:

y = -2x + 4

Step-by-step explanation:

slope intercept form:

y = mx + b

m = slope = -2

b = y-intercept

x = x = 3

y = y = -2

Plug in the corresponding numbers to the corresponding variables:

-2 = (-2) * (3) + b

Simplify. First, multiply:

-2 = (-6) + b

Next, isolate the b. Note the equal sign, what you do to one side, you do to the other. Add 6 to both sides of the equation:

-2 (+6) = -6 (+6) + b

b = -2 + 6

b = 4

Plug in 4 for b in the equation:

y = mx + b

y = -2x + 4

~

Answer:

two times a number

Step-by-step explanation:

(a) The company's break-even point in total sales dollars is $69,249,800. At the break-even point, the sales mix is as follows: Sale of mail pouches and small boxes: $55,399,840 and Sale of non-standardized boxes: $13,849,960

(b) If the company shifts its sales mix so that 60% of its revenue comes from the delivery of non-standardized boxes, the new break-even sales would be $46,166,533. The amount of sales provided by each service type would be as follows:

Sale of mail pouches and small boxes: $18,466,613

Sale of non-standardized boxes: $27,699,920

Explanation and Calculation:

(a) To calculate the company's break-even point, we use the weighted-average contribution margin ratio to find the total sales dollars at which the company's total contribution margin equals its fixed costs. The contribution margin ratio for mail pouches and small boxes is 20% (0.20), and for non-standardized boxes, it is 70% (0.70).

Let X be the total break-even sales, Y be the sales of mail pouches and small boxes, and Z be the sales of non-standardized boxes.

Based on the given information, we set up the following equations:

0.20Y + 0.70Z = X (equation 1) [Total contribution margin equals fixed costs]

Y + Z = X (equation 2) [Total sales dollars equals X]

From equation 2, we get:

Y = X - Z

Substituting Y = X - Z into equation 1, we have:

0.20(X - Z) + 0.70Z = X

0.20X - 0.20Z + 0.70Z = X

0.50Z = 0.80X

Z = 1.6X

Substituting Z = 1.6X into equation 2, we get:

Y + 1.6X = X

Y = -0.6X

Since Y represents the sales of mail pouches and small boxes, which cannot be negative, we ignore the negative solution and take Y = 0. Therefore, Z = X.

Substituting Z = X into equation 2, we find the break-even point:

Y + X = X

Y = 0

Thus, at the break-even point, the sales of mail pouches and small boxes are $0, and the sales of non-standardized boxes are equal to the total break-even sales, X.

(b) To find the break-even sales with the new sales mix, where 60% of the revenue comes from the delivery of non-standardized boxes and the remainder from mail pouches and small boxes, we can calculate the sales dollars based on the weighted-average contribution margin ratio.

Let Y2 be the new break-even sales, and let Y3 be the sales of mail pouches and small boxes with the new sales mix.

Using the weighted-average contribution margin ratio, we have:

0.60(0.70)Y2 + 0.40(0.20)Y2 = 13,824,900

0.42Y2 + 0.08Y2 = 13,824,900

0.50Y2 = 13,824,900

Y2 = 27,649,800

Therefore, the company's break-even sales with the new sales mix would be $27,649,800. The amount of sales provided by each service type would be:

Sale of mail pouches and small boxes: 40% of 27,649,800 = $11,059,920

Sale of non-standardized boxes: 60% of 27,649,800 = $16,589,880

Conclusion:

(a) The company's break-even point in total sales dollars is $69,249,800. At the break-even point, the sales mix is as follows:

Sale of mail pouches and small boxes: $55,399,840

Sale of non-standardized boxes: $13,849,960

(b) If the company shifts its sales mix so that 60% of its revenue comes from the delivery of non-standardized boxes, the new break-even sales would be $46,166,533. The amount of sales provided by each service type would be as follows:

Sale of mail pouches and small boxes: $18,466,613

Sale of non-standardized boxes: $27,699,920

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Answer:

C.

Step-by-step explanation:

X is down and up and Y is left to right. the all all have a center point of 0. Having Y at zero going down will make it a negitive number to subtract 2 from 0 and you just went 2 units down. For X going to the left is counting backwards, So subtract 7 and you 7 units the the left there for making it C.

Answer:

Option D, 4

Step-by-step explanation:

2 pizzas x 6 slices per pizza = 12 slices of pizza

12 slices of pizza divided by 3 friends eating equal slices = 4 slices per friend

Option D, 4, is your answer

The bending moment is the algebraic sum of the moments about the section of all external forces that act either to the left or to the right of the section under consideration.

The generalized numerical formula for the shear force at a point x along the beam is

V = (5x + 1/12 x^2)/2, w

The bending moment is the algebraic sum of the moments about the section of all external forces that act either to the left or to the right of the section under consideration. The shear force at any section of the beam is equal to the rate of change of bending moment with respect to the length of the beam, that is,

V = dm/dx.

Here, the bending moment of a 12-m beam is

M(x) = 5x + 1/12x.

The objective is to determine the generalized numerical formula for calculating the shear force of a beam at length x using a 2-m interval.

To estimate the shear force for each 2-m segment of the beam, differentiate the moment equation with respect to x.

dM/dx = d/dx

(5x + 1/12 x) = 5 + 1/12.

Therefore, the shear force at any point x along the beam can be obtained by integrating dM/dx over a given length from the start of the beam.
∫(5 + 1/12)dx

= (5x + 1/12 x^2)/2 + C.

We can determine the constant of integration C by using the boundary condition that the shear force is zero at the start of the beam.

V(0) = 0

= (5*0 + 1/12 * 0^2)/2 + C.

Therefore, C = 0.

Hence the generalized numerical formula for the shear force at a point x along the beam is

V = (5x + 1/12 x^2)/2, w

here x is the length of the beam from the start.

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Answer:

25.2

Step-by-step explanation:

To find tax you simply multiply the original price by the tax(make sure to turn it into a decimal) so,

420 x 0.06 = 25.2

Answer:

$29.20

Step-by-step explanation:

Multiply $420 by 6% (or .06) and you get 2920. Because we multiplied it by .06, count two to the left and you get $29.20. Hope this helps!

Answer:

The answer is above. Numbers 2 and 3

Answer:

£1,614.06

Step-by-step explanation:

Increase £854 by 89%

89% = 0.89

£854  * 1.89 = £1,614.06

Answer: 7.62

Step-by-step explanation:

\(AB=\sqrt{(-2-1)^{2}+(-3-4)^{2}}=\sqrt{9+49}=\sqrt{58} \approx 7.62\)

The measure of side P to the nearest degree is 79 degrees.

Given:

ΔOPQ ,

O = 700 cm,

P = 840cm

Q = 620cm.

To find:

The measure of angle P.

According to the Law of Cosines:

In trigonometry, the law of cosines relates the lengths of the sides of a triangle to the cosine of one of its angles. The law of cosines states:

                                   \(cos A = b^{2} +c^{2} - a^{2} / 2bc\)

Using Law of Cosines ΔOPQ, we get,

           cos P = o² +q²- p² / 2oq

       ⇒ cos P = (700)² + (620)² -(840)² /2×700×620

       ⇒ Cos P = 490000 + 384400 - 705600 / 868000

       ⇒ Cos P = 168800/868000

on further simplification, we get,

Cos P = 0.19447

P = Cos⁻¹ (0.19447)

P = 78.786236

P = 79.

∴ the measure of angle P is 79 degrees.

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Therefore, the measure of angle P is 79 degrees.

If a biologist measures the offspring of the surviving finches and finds that their mean beak depth is 13 mm, the heritability (h2) of beak depth, to two decimal places is -0.33.

The heritability of a trait refers to the proportion of the variation in that trait within a population that can be attributed to genetic factors. In this case, the heritability of beak depth can be estimated using the following formula:

h2 = (response to selection) / (selection differential)

where the response to selection is the difference between the mean value of the trait in the next generation and the mean value in the current generation.

The selection differential is the difference between the mean value of the trait in the current generation of individuals that survive and reproduce and the mean value in the entire population.

Using the given data, the response to selection is 13 - 12 = 1 mm, and the selection differential is 12 - 15 = -3 mm. Therefore, the heritability of beak depth can be calculated as:

h2 = (1/-3) = -0.33

The negative value obtained here suggests that there may have been some measurement error or other factors influencing the results. It is important to note that heritability estimates are subject to various assumptions and limitations and should be interpreted with caution.

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The volume of the box with an open top, constructed by cutting squares of side x cm from each corner of a rectangular piece of cardboard with dimensions 5 cm by 12 cm, is given by V = x(12 - 2x)(5 - 2x) cm³.

To find the volume, we need to consider the dimensions of the box. By cutting squares of side x cm from each corner, the length of the box becomes (12 - 2x) cm, the width becomes (5 - 2x) cm, and the height becomes x cm. Multiplying these dimensions together gives us the volume of the box.

Thus, the volume can be calculated as V = x(12 - 2x)(5 - 2x) cm³.

Simplifying this expression, we get V = 4x³ - 34x² + 60x cm³.

Therefore, the volume of the box with an open top, constructed by cutting squares of side x cm from each corner of a rectangular piece of cardboard with dimensions 5 cm by 12 cm, is given by V = 4x³ - 34x² + 60x cm³.

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Answer:

b

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

I did this.

Answer:

5/8+1/6= 19/24

24/24-19/24= 5/24

5/24 of her money is left

Step-by-step explanation:

Step-by-step explanation: 5/8 =30/48 + the 8/48 she spent = 38/48 .... 48/48 - 38/48= 10/48. that simplifies to 5/24

Answer:

144 square feet of carpet

We know that the area of square = (side)²

So , the area of the bedroom = (12)²

Simplify it

The area of the bedroom = 12 × 12 = 144 ft²

To solve the equation x² - 4 = -3x by factoring, we first rearrange the equation and factor it. The solutions obtained are then checked by substituting them back into the original equation.

We start by rearranging the equation to bring all terms to one side:

x² + 3x - 4 = 0.

Next, we attempt to factor the quadratic expression on the left side of the equation. We look for two numbers that multiply to give -4 and add up to 3. The numbers that satisfy this condition are -1 and 4. Therefore, we can factor the equation as follows:

(x - 1)(x + 4) = 0.

Now, we can set each factor equal to zero and solve for x:

x - 1 = 0 or x + 4 = 0.

Solving these equations gives us the solutions:

x = 1 or x = -4.

To check our answers, we substitute these values back into the original equation:

For x = 1: (1)² - 4 = -3(1) → 1 - 4 = -3 → -3 = -3 (True).

For x = -4: (-4)² - 4 = -3(-4) → 16 - 4 = 12 → 12 = 12 (True).

Both solutions satisfy the original equation, confirming that x = 1 and x = -4 are the correct solutions to the equation x² - 4 = -3x when factored.

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The solutions to the equation are x = -4 and x = 1 obtained by factoring and satisfy the equation by substitution.

To solve the equation x² + 3x - 4 = 0 by factoring, we need to find two numbers whose sum is -3 and whose product is 4. These numbers are 1 and -4. Therefore, we can rewrite the equation as (x + 4)(x - 1) = 0.

Setting each factor equal to zero, we have two equations: x + 4 = 0 and x - 1 = 0. Solving these equations, we find x = -4 and x = 1 as the solutions to the original equation.

To check our answers, we substitute x = -4 and x = 1 back into the original equation x² + 3x - 4 = 0.

For x = -4, we have:

4² + 3(-4) - 4

= 16 - 12 - 4

= 0

Similarly, for x = 1, we have

(1)² + 3(1) - 4

= 1 + 3 - 4

= 0

Hence, both x = 3 and x = -1 satisfy the equation x² - 4x - 3 = 0, confirming our solutions.

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Answer:

32 million / x million year 3 * 100%

Step-by-step explanation:

Since they mention that the total value of azco sales remain the same as year 2, therefore the earnings for year 2 and 3 are the same.

Which means that the percentage of sales profits would be 32 million dollars divided by the profits of year 3, which we do not know because the statement does not tell them but they tell us that they do not change with respect to year 2.

Therefore the percentage would be:

32 million / x million year 3 * 100%

Answer:

- 16k + 28

Step-by-step explanation:

3 - 2(k - 2) - 7(2k - 3) ← distribute parenthesis

= 3 - 2k + 4 - 14k + 21 ← collect like terms

= - 16k + 28

Answer:28−16k

Step-by-step explanation:

3−2(k−2)−7(2k−3)

Use the distributive property to multiply −2 by k−2.

3−2k+4−7(2k−3)

Add 3 and 4 to get 7.

7−2k−7(2k−3)

Use the distributive property to multiply −7 by 2k−3.

7−2k−14k+21

Combine −2k and −14k to get −16k.

7−16k+21

Add 7 and 21 to get 28.

28−16k