What is the sum rule in integration?.

The statement about the relationship of the data in the table is indicated in the option;

A proportional relationship is one in which one variable (the output variable) is a constant multiple of the input variable, such that a point on the graph of ordered pairs of variable is the point (0, 0), which is the origin.

The points on the graph are; (1, 3.5), (2, 4.5), (3, 5,5)

The slope of the graph is therefore; (4.5 - 3.5)/(2 - 1) = 1

The equation in point-slope form is therefore; y - 3.5 = x - 1

y = x - 1 + 3.5 = x + 2.5

y = x + 2.5

The equation is a linear relationship. The equation is in the form; y = m·x + c, with the slope m = 1 and a y-intercept, c = 2.5

The y-intercept is 2,5, therefore, the graph does not pass through the origin.

The relationship of the line passing through the points, is a linear relationship. The line passing through the points does not pass through the origin, therefore the relationship is not a proportional relationship

The correct option is therefore; It cannot be a proportional because the straight line through the points does not go through the origin.

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The total amount Rita spend on the mall for 2 items is $77.12.

Given that,

The expression of amount spend on the first store = 13.06b + 29

The amount spend on the second store =  22

Total amount Rita spends=  13.06b + 29 + 22

= 13.06b + 51

Then to estimate the amount Rita spent if she had bought 2 items.

Now, we have the value of b = 2.

So by substituting,

= 13.06 x 2 + 51

= 77.12

Therefore the total amount Rita spend on the mall is $77.12.

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a. the difference in the two data provided =31072940 - 24658823 = 6414117

b. the sum of the two data to the nearest thousand hundred = 31072940 - 24658823 = 55731763

nearest to Thousand hundred = 55730000

Julio needs to prove that two sides of the two triangles are congruent, in addition to the hypotenuse and one set of legs that are already congruent, to use the SAS Triangle Congruence Theorem.

Julio needs to prove that the two triangles have congruent sides in order to use the SAS Triangle Congruence Theorem. This means that he needs to show that one side of one triangle is congruent to a corresponding side of the other triangle and the same applies to the other two sides. This can be done by using methods such as measuring the sides, using algebraic equations, or using geometric constructions.

According to Julio statement, he has already constructed two right triangles to have congruent hypotenuses and one set of congruent legs, which means he has already proved that one side of one triangle is congruent to a corresponding side of the other triangle (hypotenuse) and one set of legs are congruent.

Therefore, Julio need to prove the remaining side of the triangle congruent to the corresponding side of the other triangle. Once he proves this, he can use the SAS Triangle Congruence Theorem to state that the two triangles are congruent.

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The probability that Marshall wins a prize on his second spin =  0.1875

Consider an event X = the number of spins until Marshall wins a prize.

Given that a prize wheel with 4 segments of equal size, one of which is labeled winner.

So, the sample space n = 4

For given event x, the possible outcomes = 1

Using the formula of probability,

p = x/n

p = 1/4

p = 0.25

So, the probability of success p = 0.25

q = 1 - p

q = 1 - 0.25

q = 0.75

To find the probability that Marshall wins a prize on his 2nd spin.

Using formula, [tex]P(X = k) = (1 - p)^{k-1}p[/tex]

For  k = 2,

[tex]P(X = 2) = (1 - 0.25)^{2-1}\times 0.25[/tex]

P(X = 2) = 0.75 × 0.25

P(X = 2) = 0.1875

Thus, the required probability is  0.1875

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Answer:

2 in

Step-by-step explanation:

If im not wrong, each side should be 2 inches, as it would have to be 2x2x2 for a volume of 8 inches cubed

Answer: 2/3

Step-by-step explanation:

To find the probability of A or B, we can use the formula: P(A or B) = P(A) + P(B) - P(A ∩ B)

Plugging in the given values:

P(A or B) = 1/2 + 1/3 - 1/4

To solve this, we must find a common denominator in order to add the fractions:

P(A or B) = 3/6 + 2/6 - 1/6

Simplifying:

P(A or B) = 4/6 = 2/3

So the value of P(A or B) is 2/3

Yes, it is possible for a negative number to be an exponential function.

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Answer:

= -13/6 OR -2.1667

Step-by-step explanation:

1 1/2 - 3 2/3

=3/2 - 11/3

LCM of 2 and 3 is 6

3/2 - 11/3

= 9 - 22

6

= - 13/6 OR -2.5

Answer: is it  

-2 1/6

Step-by-step explanation:

Rewriting our equation with parts separated

=1+12−3−23

Solving the whole number parts

1−3=−2

Solving the fraction parts

12−23=?

Find the LCD of 1/2 and 2/3 and rewrite to solve with the equivalent fractions.

LCD = 6

36−46=−16

Combining the whole and fraction parts

−2−16=−216

Simple bro

Fast food chains that use plastic or styrofoam containers in selling their products are contributing to the global plastic pollution crisis. Styrofoam and plastic containers, which are not biodegradable, take up to 1000 years to decompose.

Every year, an estimated 8 million metric tons of plastic end up in the ocean, and the majority of it is from single-use plastic products such as those used by fast food chains. This plastic pollution is having a devastating effect on the environment, with marine life ingesting and becoming entangled in the plastic. In addition, the production of styrofoam and plastic containers is highly energy intensive and contributes to the emission of greenhouse gases. This is a problematic situation that needs to be addressed urgently.

The energy intensity of production for styrofoam and plastic containers can be calculated using the formula:

Energy Intensity (EI) = Energy Used (EU) / Output (O)

For example, if it takes 50 kWh of energy to produce a unit of output, the energy intensity of production would be 50 kWh/unit. This highlights the environmental impact of styrofoam and plastic containers, and the urgent need to reduce their use in fast food chains.

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Answer:

ff(x)=9x-48

Step-by-step explanation:

f(x)=3x-12

ff(x)=f(3x-12)

=3(3x-12)-12

= 9x-36-12

= 9x-48

Answer:

9

Step-by-step explanation:

2x + 3y - 2

Putting x=1; y=3

(2x1) + (3x3) - 2

2 + 9 - 2

Now, according to BODMAS, we shall add first.

11 - 2

9

The value of angle x is 45°. Thus, option B is correct.

A corner is an angle if it forms a projecting part or a partially enclosed space. An angle is a figure made up of two lines that extend from the same point. a measurement of an angle or the amount of turning required to align or make parallel two lines or planes.

step1:

o is center

JK is a tangent

so <OKJ =90°

<OKM=90°-30°=60°

OM=OK=><OMK=60°

step2:

because LO=LO, LM=LK, ON=OK

So Triangle OLM ≅ Triangle OLK => <LOM=<LOK

so <LOM=150° => <LMO =15°

so  60° +15° =30°+x°=>x= 45

so the answer is B. 45°

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The solution to the equation 7x - 9 = 16 is x = 25/7. This can be achieved by using the addition property of equality and simplifying the equation.

The equation 7x - 9 = 16 can be solved by using The equation's solution can be changed by adding the same amount to either side of the equation, according to the addition property.

To both sides of the equation, add 9.

7x - 9 + 9 = 16 + 9

Simplify the equation.

7x = 25

Divide both sides of the equation by 7.

7x/7 = 25/7

Simplify the equation.

x = 25/7

Therefore, the solution to the equation 7x - 9 = 16 is x = 25/7.

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Henry could only see one line since both lines had the same slope, which means that the graphs of both equations will be identical and hence overlap.

Linear equations in a system 3x + 2y = 4, and 9x + 6y = 12

We must demonstrate why Henry could only make out one line when he plotted the equations 3x-2y=4 and 9x-6y=12 on a graph.

Take the provided linear equation system into consideration.

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

9x - 6y = 12 ..................(2)

Due to the fact that equation (2) is a multiple of equation (1), 3 (3x - 2y = 4) = 9x - 6y = 12

The slopes of the provided equations are also same.

Difference with regard to x for equation (1) yields,

additional to equation (2),

With regard to x, we can differentiate to get,

The graphs of both equations will overlap since both lines have the same slope and hence have the same appearance on the graph.

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Answer: we would need 7 bags of fertilizer to cover the area of the triangle.

Step-by-step explanation:

To find the area of a triangle, we can use Heron's formula. Heron's formula states that the area of a triangle can be found by taking the square root of the semi-perimeter multiplied by the difference of the semi-perimeter and each side length.

The semi-perimeter of the triangle is (2.1+1.8+2.7)/2 = 2.7

The area of the triangle is sqrt(2.7*(2.7-2.1)(2.7-1.8)(2.7-2.7)) = sqrt(2.70.60.9*0) = 1.35

Each bag of fertilizer covers 0.2 square miles, so we need to divide the area of the triangle by the area covered by each bag to find how many bags are needed: 1.35 / 0.2 = 6.75

Rounding up to the nearest whole number, we would need 7 bags of fertilizer to cover the area of the triangle.

The Law of Sines says that in any given triangle, the ratio of any side length to the sine of its opposite angle is the same for all three sides of the triangle. This is true for any triangle, not just right triangles.

The law of sines relates the ratios of side lengths of triangles to their respective opposite angles. This ratio remains equal for all three sides and opposite angles. We can therefore apply the sine rule to find the missing angle or side of any triangle using the requisite known data.

The ratio of the side and the corresponding angle of a triangle is equal to the diameter of the circumcircle of the triangle. The sine law is can therefore be given as,

[tex]\frac{a}{sin A} = \frac{b}{sin B} = \frac{c}{sin C}[/tex]

In a right triangle, the sine of an angle is the ratio of the length of the opposite side divided by the length of the hypotenuse.

The Law of Sines says that in any given triangle, the ratio of any side length to the sine of its opposite angle is the same for all three sides of the triangle. This is true for any triangle, not just right triangles.

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So, each platter will have 25 legs and 25 wings.

To determine the greatest number of platters the kitchen staff can make, you need to find the least common multiple of 25 and 50. This is because each platter must have the same number of legs and wings, so you need to find the smallest number of legs and wings that can be divided evenly into both 25 legs and 50 wings.

The least common multiple (LCM) of 25 and 50 is 50. This means that the greatest number of platters the kitchen staff can make is 50/25 = 2 platters.

Therefore, each platter will have 25 legs and 25 wings.

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Find the least frequent multiple of 25 and 50 to determine the maximum number of platters the kitchen staff can produce. Finding the fewest number of legs and wings that can be equally divided into 25 legs and 50 wings is necessary because each platter must have the same number of legs and wings.

25 and 50 have a least common multiple (LCM) of 50. The maximum amount of platters the kitchen staff is capable of producing is 50/25, or 2 platters.

Therefore, there will be 25 legs and 25 wings on each plate.

1/6 of the whole garden is planted in cucumber.

What is cucumber ?

Cucumber is a type of vegetable that belongs to the cucurbit family, which also includes melons, squash and gourds. They are typically long, cylindrical in shape, and have a green skin that is typically eaten raw.

The proportion of the garden planted in cucumber is 1/3 of the vegetable part of the garden. To find out what proportion of the entire garden is planted in cucumber, we can use this proportion and multiply it by the proportion of the garden that is planted in vegetables.

Half of the garden is planted in vegetables, so the proportion of the garden planted in vegetables is 1/2.

1/3 of the vegetable part of the garden is planted in cucumber, so the proportion of the garden planted in cucumber is ,

(1/2) x (1/3) = 1/6

So, 1/6 of the whole garden is planted in cucumber.

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Half of the garden is planted in vegetables, so the proportion of the garden planted in vegetables is 1/2.

1/3 of the vegetable part of the garden is planted in cucumber, so the proportion of the garden planted in cucumber is ,

(1/2) x (1/3) = 1/6

1/6 of the whole garden is planted in cucumber

Answer:

10 1/8

Step-by-step explanation:

25 3

8

+

-15 1

4

=  (25 + -15) + (

3

8

+

-1

4

)

=  10 +

3

8

+

-1 × 2

4 × 2

=  10 +

3

8

+

-2

8

=  10 +

3 + -2

8

=  10 +

1

8

=  

10 1

8

Answer:

75+(4²- 6²) +12= 67

15³- 16 × 2+28=3371

Answer:

V = 10 km/h

Step-by-step explanation:

Formula for speed --> V = X/t being X  equal to space and t the time wasted.

X = 30 km

t = 3 hours

then,

V = 30/3

V = 10 km/h

The length x will be 23.994615468 ft or rounded approximately 24 feet.

The length x is the distance from the center of the roof to the edge of the roof.

        x = 15 + (15 * tan(25°)) + 1

        tan(25°) = 0.466307658

        x = 15 + (15 * 0.466307658) + 1

        x = 15 + 6.994615468 + 1

        x = 23.994615468 ft

So, the length x = 23.994615468 ft, or approximately 24 feet.

The problem is about finding the length x, which is the distance from the center of the roof to the edge of the roof of a grain bin with a radius of 15 ft and a recommended slant of 25° for the roof. The roof is also required to overhang the edge of the bin by 1 ft. The length x was calculated using trigonometry and found to be approximately 24 feet.

Complete Problems (Question):

Carlos plans to build a grain bin with a radius of 15 ft. The suggested slant of the roof is 25°. He wants the roof to overhang the edge of the bin by 1 ft. What should the length x be? Give your answer in feet and inches.

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Answer:

The value of x is -19.

Step-by-step explanation:

Given that ZA and B are vertical angles and m/A = (2x +20)°, and m/B = (3x + 1)°, we know that ZA and B are congruent, meaning they have the same measure. We can set the two given equations equal to each other: m/A = (2x + 20)° = m/B = (3x + 1)°. Then, by isolating x on one side of the equation, we subtract 20 from both sides of the equation, then subtract 2x from both sides of the equation, which gives us x = -19, thus the value of x is -19.

Answer:

x = 19

Step-by-step explanation:

since vertical angles are equal we can set the value of angles A and B equal and solve for 'x'

2x + 20 = 3x + 1

20 = x + 1

19 = x

Answer:

B)  (-∞, 2)

Step-by-step explanation:

Given functions:

[tex]f(x)=x-3[/tex]

[tex]g(x)=-0.5x[/tex]

To find the interval for which (f - g)(x) is negative, set (f - g)(x) less than zero and solve for x:

[tex]\begin{aligned}(f-g)(x)& < 0\\f(x)-g(x)& < 0\\(x-3)-(-0.5x)& < 0\\x-3+0.5x& < 0\\1.5x-3& < 0\\1.5x& < 3\\x& < 2\end{aligned}[/tex]

Therefore, the interval for which the composite function (f - g)(x) is negative is:

To show that one value is greater than another, use the "greater than" symbol (>). It can be used to express a comparison between two values in mathematical operations, programming, and other forms of notation.

   For instance, the "greater than" symbol can be used to compare integers in mathematical operations. For instance, you would write "x > y" to indicate that x is greater than y. This can alternatively be understood as "x exceeds y."

  Other comparison symbols, such as "less than," "greater than," and "less than or equal to," can be used in addition to the "greater than" symbol. These symbols can be used to describe many forms of value comparisons in programming and mathematical processes.

  The word "greater than" is represented by the symbol ">," therefore to write "greater than 4" you would write ">4".

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Answer:

The correct statements describing the process of converting z = 2 + 3i to polar coordinates using technology are:

Write the complex number as a point in the complex plane: (2, 3i)

Substitute a = 2 and b = 3 for the real and imaginary parts respectively.

Using radians for θ, record the result as r = 3.606 and θ = 0.983 as your answer in polar coordinate form: (3.606, 0.983).

To convert a complex number in the form of z = a + bi to polar coordinates using technology, we can use the following steps:

Write the complex number as a point in the complex plane, with the real part as the x-coordinate and the imaginary part as the y-coordinate.

Substitute a for the real part and b for the imaginary part.

Using the Pythagorean theorem, we can find the distance from the origin to the point, which is the magnitude or modulus of the complex number, represented by r.

Using the tangent function, we can find the angle of the point from the positive x-axis, which is the argument or phase of the complex number, represented by θ.

Record the result in polar coordinates as (r, θ), where r is the magnitude and θ is the argument, given in radians.

It's also worth noting that polar coordinates can also be represented in the form of (r, θ ) or (r, arg(z)) or (r, angle(z))

Answer:

z = 2 + 3i

Step-by-step explanation:

Two term polynomial called as a binomial .

An algebraic equation that has more than two terms, particularly the accumulation of numerous phrases that each include a different power of the same variables known as polynomial.

But when we reduce more than two terms into only two terms we get binomial.

A formula in algebra that expresses the difference or sum of two terms is known as binomial.

For example:

[tex]x^{4} + x y^{2} +x^{2} + x[/tex] is polynomial because it has more than two separate terms which are [tex]x^{4}[/tex] , [tex]x y^{2}[/tex] , [tex]x^{2}[/tex] and [tex]x[/tex]

[tex]x^{2} + y^{2}[/tex] is binomial because it has only two separate terms which are [tex]x^{2}[/tex] and [tex]y^{2}[/tex].

[tex]4x+6y[/tex] is also binomial because it has also only two separate terms which are [tex]4x[/tex] and [tex]6y[/tex]

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