Please answer with the work shown

Please Answer With The Work Shown

Answers

Answer 1

The perimeter first figure that is made of a square and equilateral triangle is 52 cm.

What exactly are squares?

A square is a two-dimensional planar shape with four equal sides and four 90-degree angles. The features of a rectangle are similar to those of a square, but the distinction is that a rectangle has just its opposing sides equal.

A square's most significant qualities are

The four inner angles are 90 degrees.The four sides of the square are congruent, or equal.The square's opposing sides are parallel.The diagonals of the square intersect at 90°.The square's two diagonals are equal to each other.

The diagonal of a square is divided into two isosceles triangles.

Square area=(side)²

Square perimeter=4*side

Now,

For first figure given that

sides of square are 14 cm in length

and length of side of equilateral triangle are=5 cm

but for finding perimeter of the figure only 3 sides of square and 2 sides of triangle are needed.

So, perimeter=3*14+2*5

=42+10

=52 cm

hence,

         The perimeter first figure 52 cm.

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Related Questions

solve
(2x-3) (x2+4x-5)

Answers

Answer: 2x^3 + 5x^2 - 10x + 15

Step-by-step explanation:

To multiply two polynomials, you can use the distributive property and multiply each term of one polynomial by each term of the other. In this case, the two polynomials are (2x - 3) and (x^2 + 4x - 5), so we have:

(2x - 3) * (x^2 + 4x - 5) =

2x * x^2 + 2x * 4x - 2x * 5 +(-3) * x^2 + (-3) * 4x - (-3) * 5

Expanding the products, we get:

2x^3 + 8x^2 - 10x - 3x^2 - 12x + 15

Combining like terms, we get: 2x^3 + 5x^2 - 10x + 15

What is X and Z. please tell me

Answers

x = 5

z = 118°

Step-by-step explanation:

opposite angles are equal

(6x + 32)° = 62°

6x = 62° - 32°

6x = 30°

x = 5°

angles on a straight line add up to 180

180° = 62° + z

z = 180° - 62°

z = 118°

PLEASE HELP 25 POINTS!! NO LINKS

Answers

Answer:

C i think

Step-by-step explanation:

A cylinder-shaped scoop has a base radius of 2 centimeters and a height of 5 centimeters. The scoop has a mass of 14.9 grams when empty. The scoop is completely filled with water. One cubic centimeter of water has a mass of one gram. What is the mass of the scoop of water in grams, including the mass of the scoop? Describe how you found your answer. Round to the nearest tenth.

Answers

Answer:

  77.7 g

Step-by-step explanation:

You want the mass of a cylindrical scoop of radius 2 cm and height 5 cm when it is filled with water at 1 g/cm³, and has an empty mass of 14.9 g.

Water

The mass of the water will be the product of its volume and its density. The volume is that of a cylinder with radius 2 cm and height 5 cm. That volume is given by the formula ...

  V = πr²h = π(2 cm)²(5 cm) ≈ 62.83 cm³

The mass of the water is then ...

  (62.83 cm³) × (1 g/cm³) = 62.83 g

Total mass

The total mass of the water-filled scoop is the sum of its empty mass and the mass of the water:

  scoop + water = 14.9 g + 62.8 g = 77.7 g

The mass of the scoop and water is 77.7 grams.

An online app charges $0.99 to download a song and $7.99 membership fee. (A)Write an expression that gives the total cost in dollars to download “s” songs. (B)Then, find the cost of downloading 12 songs. Incorrect work/solutionCorrect work/solution (A) s(0.99 + 7.99) = 0.99s + 7.99s = 8.98s = (B) 8.98(12) = 8.98 x 12 = $107.76 for 12 songs Part A:Explain what this student did incorrectly.

Answers

Answer: The student correctly wrote an expression to find the total cost of downloading "s" songs. The expression is: 0.99s + 7.99. However, they made a mistake when they simplified the expression to 8.98s. The expression should have remained as 0.99s + 7.99, because the $7.99 membership fee does not change regardless of how many songs are downloaded.

In Part B, the student correctly used the expression to find the cost of downloading 12 songs. They multiplied 8.98 by 12 and got the correct answer of 107.76.

Step-by-step explanation:

Raul is wrapping a cylindrical package with wrapping paper. He has two different packages to choose from:
Package A has a radius of 1.5 inches and a height of 6 inches
Package B has radius of 2 inches and a height of 3 inches

He has 70 in2 of wrapping paper and he will need to cover all sides of the package.

Using the formula SA = 2π
rh + 2π
r2, determine which of the following packages Raul will have enough wrapping paper to cover.

Package A has a surface area of
Choose...
in2. Package B has a surface area of
Choose...
in2.

Raul will have enough paper to wrap
Choose...

Answers

The package that will have enough wrapping paper to cover is package B

Package A has a surface area of 70. 65 in²

Package B has a surface area of 62. 8 in²

How to determine the surface area

The formula for the surface area of a cylinder is expressed as;

SA = 2πrh + 2π

Given that the parameters are;

r is the radiush is the height of the cylinder

For Package A, substitute the values

= 2 × 3.14 × 1.5 × 6 + 2 × 3.14 × (1.5)²

Multiply the values, we have;

= 70. 65 in²

For package B, substitute the values, we get;

= 2 × 3.14 × 2 × 3 + 2× 3.14 × (2)²

Multiply the values

= 62. 8 in²

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You must spend at least $10 at the grocery store to get a free greeting card

Answers

Answer:

I spent 13.32 at the store the other day...?

Step-by-step explanation:

What is the question.

Go to the dollar section and pick out 10 things and then get the gift card

The table below shows the ratios of black to white keys on pianos of various sizes.


Black A 18 45 72
White 13 B 65 C


Determine which table has the correct values for A, B, and C.

Black 8 18 45 72
White 13 25 65 105

Black 9 18 45 72
White 13 26 65 104

Black 9 18 45 72
White 13 39 65 117

Black 1 18 45 72
White 13 26 65 104

Answers

Using the given ratios found the values of A, B and C, and completed the table as follows:

Black   9   18       45     72

White  13   26     65    104

What is meant by the ratio?

A ratio in mathematics demonstrates how many times one number is present in another. A ratio is what a fraction looks like when it is written as a:b. A ratio is the comparative or condensed version of two quantities of the same type.

Given the table:

Black   A   18   45   72

White  13   B    65    C

The table represents the ratios of black keys to white keys on pianos of various sizes.

The ratio of keys of the piano always remains constant.

So we can write as follows:

A/13 = 18/B = 45/65 = 72/C

To find A, we take the following ratios.

A/13 = 45/65

On solving, we get

A = 45 * 13 / 65 = 585/65 = 9

To find B, we take the following ratios.

18/B = 45/65

B = 18 * 65 / 45 = 1170/45 = 26

To find C,  we take the following ratios.

72/C = 45/65

C = 72 * 65 / 45 = 104

Therefore using the given ratios we can complete the table using the values of A, B and C,

Black   9   18       45     72

White  13   26     65    104

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Need help, please, thanks!

Answers

The earnings in the simple interest and compound interest for a 5 year period is in the table below where S is for Suzanne and D is for Derrick

            S - annual interest  S - Balance   D - annual interest   D - Balance

Year 1                 147                   3147                      147                    3147

Year 2                294                  3294                     301.2                 3301.2

Year 3                441                   3441                      462.96              3462.96

Year 4                588                  3588                     632.65              3632.65

Year 5                735                   3735                     810.65               3810.65

How to solve simple interest

Simple interest is calculated by the formula

principal x time x rate / 100

In the problem

Principal = $3000

rate = 4.9%

time is varying from 1 to 5

For the first year we have

= 3000 * 1 * 4.9 / 100

= 147

Compound interest the formula is

Principal(1 + rate)^(year) - 1)

For the first year, (the rate is already divided by 100 to get 0.049) we have

= 3000(1 + 0.049)^(1) - 1)

= 147

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HELP PLSS I NEED HELPPPPP

Answers

The required measures of length are, as follows:

GF = 11, GE = 28, DF = 28, HF = 14, and DG = 25.75.

What is a rectangle?

A rectangle is defined as a four-sided shape with opposite sides that are equal in length and parallel to each other.

The lengths are given in the question, as follows:

DE = 11

GH = 14

Since DE and GF are opposite sides then both are equal.

So GF = 11

Here GH and HF are equal,

HF = 14

∵ GE = GH + HE = 14 + 14 = 28

As we know that the two lengths of the diagonals are equal in the rectangle.

So GE = DF

So DF = 28

Using the Pythagorean theorem, we have

DG² + GF² = DF²

DG² + 11² = 28²

DG² + 121 = 784

DG² = 663

DG = 25.75

Thus, the measures are, as follows:

GF = 11, GE = 28, DF = 28, HF = 14, and DG = 25.75.

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Penny is vacationing at the beach and decides to purchase a pair of swim goggles and a
sand bucket which she randomly selects off the shelf. When she realizes that they are
both green, she states that "because she selected a green pair of swim goggles, she was
more likely to select a green sand bucket." Do you agree or disagree with Penny's
statement? Justify your thinking

Answers

Answer: I disagree with Penny's statement. The probability of her selecting a green pair of swim goggles and then a green sand bucket is the product of their individual probabilities. The fact that she selected a green pair of swim goggles does not change the probability of selecting a green sand bucket. Each selection is independent of the other, and the probabilities of each event remain the same. So, Penny's statement that "because she selected a green pair of swim goggles, she was more likely to select a green sand bucket" is not valid.

Step-by-step explanation:

what is c over 2 < -0.75=

Answers

The value of c lies in the interval [tex](-\infty, -1.5)[/tex]

What is inequality?

Inequality is a statement that shows the relationships the two expressions are not equal. It is defined by the symbols like <, >, ≤, ≥.

[tex]\frac{c}{2} < -0.75[/tex]

To find the value of c:

[tex]\frac{c}{2} < -0.75[/tex]

Multiply both sides by 2 we get,

[tex]2\frac{c}{2} < (-0.75)*2[/tex]

⇒c < -1.5

Therefore c<-1.5 is the solution for the given inequality.

It can also be represented in the interval form.

This is given in the interval notation [tex](-\infty, -1.5)[/tex]

Hence, the value of c lies in the interval [tex](-\infty, -1.5)[/tex]

Complete question:

What is the values that c can take when  [tex]\frac{c}{2} < (-0.75)[/tex]?

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Two important ingredients for baking bread are
yeast and flour. To make a loaf of bread of at
most
30 servings, maintain a yeast to
flour ratio of 1:200. If you're making a loaf of more than 30
servings, use a ratio of 1:180.
If you're making 30 servings
of bread and using 0.25 oz of yeast, how many ounces of flour do you
need?
If you're making 60 servings of bread and using 540 oz of flour, how many ounces of yeast do you
need?
NOTE: Enter only numerals for each of your answers.

Answers

If you're making 60 servings of bread and using 540 oz of flour, then the number of ounces of yeast you need is 3 oz.

What are proportions?

Proportion, in general, is referred to as a part, share, or number considered in comparative relation to a whole. Proportion definition says that when two ratios are equivalent, they are in proportion. It is an equation or statement used to depict that two ratios or fractions are equal.

Given that, to make a loaf of bread of at most 30 servings, maintain a yeast to flour ratio of 1:200. If you're making a loaf of more than 30 servings, use a ratio of 1:180.

If you're making 30 servings of bread and using 0.25 oz of yeast, then

0.25/Flour = 1/200

Flour = 50 oz

If you're making 60 servings of bread and using 540 oz of flour, then

Yeast/540 = 1/180

Yeast = 3 oz

Therefore, if you're making 30 servings of bread and using 0.25 oz of yeast, then the number of ounces of flour you need is 50 oz.

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x^2+y^2=100 is it a function?

Answers

The equation x^2+y^2=100 is not a function

How to determine if it is a function

From the question, we have the following parameters that can be used in our computation:

x^2 + y^2 = 100

The above equation is a circle equation

As a general rule, we have

Circle equations are not functions and they do not represent a function on a graph

Hence, x^2+y^2=100 is not a function

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Suppose that n 0 and n 1. Show that the substitution v = y^1-n transforms the Bernoulli equation dy/dx + P (x) y = Q(x) y^n into the linear equation dy/dx +(1-n)p(x)v(x)=(1-n)q(x).

Answers

The substitution, transforms the Bernoulli equation dy/dx + P(x)y = Q(x)y^n into the linear equation dv/dx+(1-n)P(x)v(x) = (1 - n)Q(x). It is done as:

The equation is in the form  

dy/dx +P(x)y=Q(x)yⁿ,  where P and Q are functions of x or constants, this is called Bernoulli's equation.

Now, we have to substitution using 

[tex]v = {y}^{1 - n} [/tex]

Differentiating both side with respect to 'x'

[tex]v' = (1 - n) {y}^{ - n} y' \\ \frac{dx}{dy} = \frac{1}{1 - n} {y}^{n} v'[/tex]

we get,

[tex]= \frac{1}{1 - n} {y}^{n} v' + p(x)y \\ = q(x) {y}^{n} \\ = v' + (1 - n)p(x) {y}^{1 - n} \\ = (1 - n)q(x)[/tex]

Now, by using 

[tex]v' = {y}^{1 - n} [/tex]

The given equation is expressed as:

[tex]v + (1 - n)p(x)v = (1 - n)q(x)[/tex]

or dv/dx + (1-n)P(x)v(x) = (1 - n)Q(x)

The Bernoulli equation simply states that total energy per unit mass of flowing fluid, at any point in the subsurface, is the sum of the kinetic, potential, and fluid-pressure energies and is equal to a fixed value. The Bernoulli Equation can be viewed as a statement of the conservation of energy principle applicable to flowing fluids.

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What is the degree of 7c3d2

Answers

The degree of the expression 7c³d² is 2

How to determine the degree

From the question, we have the following parameters that can be used in our computation:

Expression = 7c³d²

The degree of an expression is the highest power in the expression

In this case,

7c³ =  Constant

d² = Variable

The highest power of the variable is 2

Hence, the degree is 2

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can someone explain the questions attached? thanks

Answers

The probability of landing on the head side of coin and rolling a 3 on the die is found as 1/12.

Explain about the term sample space?A sample space is a set of potential results from a random experiment. The letter "S" is used to denote the sample space. Events are the subset of feasible experiment results. Depending on the experiment, a sample area could contain a variety of results.

Sample space for tossing a coin: (H,T)

P(head) = 1/2

Sample space for tossing a dice : (1, 2, 3, 4, 5, 6)

P(3) = 1/6

So,

Probability of head with 3 on the die = 1/ 2* 1/6 = 1/ 12

Thus, the probability of landing on the head side of the coin and rolling a 3 on the die is found as 1/12.

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The correct question is-

A coin is tossed and a single 6-sided die is rolled. Find the probability of landing on the head side of the coin and rolling a 3 on the die.

Enter your answer as a fraction in the form a/b (for example 2/3, 5/7) or as an integer.

From the top of a 450-foot cliff, a hiker looks down at a river below. Her angle of
depression to the near and far banks of the river are 80° and 50° respectively, as
shown in the picture. Based on this information, how wide is the river?

Answers

The width of the river is calculated by the tangent of the angle will be 293 feet.

What is a right-angle triangle?

It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometry function.

Observing a river below from the top of a 450-foot cliff, a hiker. Her depression lies at an angle of 80° to the near bank and 50° to the far bank of the river.

The horizontal distance when the angle is 80° is given as,

tan 80° = 450 / x₁

x₁ = 84.64 feet

The horizontal distance when the angle is 50° is given as,

tan 50° = 450 / x₂

x₂ = 377.59 feet

The width of the river is given as,

W = x₂ - x₁

W = 377.59 - 84.64

W = 292.95

W ≈ 293 feet

The width of the river is calculated by the tangent of the angle will be 293 feet.

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If you take - 3/10 of a number and add 1, you get 10. Write an equation to represent the situation. What is the original number

Answers

Answer: -30

Let's call the original number "x". Then, we can write the equation as follows:

-3/10 x + 1 = 10

To find the original number, we can isolate x by subtracting 1 from both sides and then multiplying both sides by 10/3:

-3/10 x = 9

x = (9 * 10)/(-3)

x = -30

So, the original number is -30.

8 A crystal paperweight
is shaped like a cylinder with a star-shaped hole. The
top of the star-shaped hole is shaped like a square with four points that are
identical equilateral triangles. The height of the cylinder is 3 centimeters. Find
the volume of the paperweight.


Please Help ASAP!!!

Answers

The volume of the paperweight is 79.3 cm³.

What is a cylindrical shape?

A cylinder is a three-dimensional solid object with two bases that are identically circular and are connected by a curving surface that is located at a specific height from the center.

Examples of cylinders are toilet paper rolls and cold beverage cans.

The volume of a cylinder is πr²h.

Curved surface area = 2πrh.

Total surface area = 2πr(h + r).

From the given information, The area of the star-shaped cutout is,

A square has a side length of 2 cm, and four equilateral triangles have a side and a height of 2 cm.

So, The area of the star-shaped cutout is,

= (2×2) + 4×(1/2)×2×2.

= 4 + 8.

= 12 cm.

Now, The volume of the star-shaped cut-out is,

= 12×height,

= 12×3.

= 36 cm³.

And the volume of the cylinder is,

= π(1 + 2 + 0.5)²×3.

= π(3.5)²×3.

= 115.4 cm³

Therefore, The volume of the paperweight is,

= 115.4 - 36 cm³.

= 79.3 cm³.

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Solve for x . circles tangent 1 A. 12 B. 10 C. 42 D. 9

Answers

8 is the measure if the angle x in the given diagram.

Circle geometry

The point where two lines meet is known as an angle. The given diagram is a circle geometry.

Using the theorem, angle at the arc is twice the angle at the vertex, we will have:

80 = 2(4x + 8)

80/2 = 8x + 8

40 = 4x + 8

4x = 40 - 8

4x = 32

x = 32/4

x = 8

Hence the value of x from the diagram given is 8

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One way to establish validity of a questionnaire is my measuring:A) The correlation between the score on the questionnaire and another measure of the same conceptB) The alpha value of the reliability coefficientC) How well sunjects perform on the questionnaire at one time compared to another timeD) The consistency by which multiple sunjects are able to complete the questionnaire without error

Answers

The correct option is Option D) The consistency with which several individuals can complete the questionnaire without making an error is one technique to determine a questionnaire validity.

A questionnaire is a sort of research tool used to collect data from respondents for a survey or statistical analysis. It consists of a collection of questions (or other forms of prompts). Typically, a research questionnaire will have both closed-ended and open-ended questions. Long-term, open-ended inquiries provide the respondent the chance to go into more detail. The Statistical Society of London created the research questionnaire in 1838. Despite the fact that surveys are frequently created so that the answers may be statistically analyzed. Consequently, it may not be practical to conduct a survey using a questionnaire for some demographic groups.

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[tex]1\frac{1}{3} :2\frac{1}{3}[/tex]

Answers

Answer:

Given: [tex]1\frac{1}{3} :2\frac{1}{3}[/tex]

To simplify this ratio, convert the mixed fractions into improper fractions:

[tex]\frac{4}{3}[/tex] : [tex]\frac{7}{3}[/tex]

Then to divide ( because ratio = division ) turn around [tex]\frac{7}{3}[/tex] and multiply:

[tex]\frac{4}{3} * \frac{3}{7}[/tex]

Then multiply:

[tex]\frac{12}{21}[/tex]

Finally simplify this fraction by dividing the denominator & numerator by 3:

= [tex]\frac{4}{7}[/tex]

...

Convert 2 pints into milliliters. Round your answer to the nearest whole number.

Answers

Answer: 946 ml

Step-by-step explanation: 1 pint= 473.2

2*

473.2= 946.4

=946 ml

Simplify the following by rationalizing the denominator. need rightnow pahelp.

Answers

Answer:

Step-by-step explanation:

Multiply the numerator and denominator by the conjugate.

Exact Form:

3√2+2

    7

Decimal Form:

0.89180581

-3x² + 2x-5 = y
-x+2=-y

Answers

Answer:     \left(h,\:k\right)=\left(\frac{1}{3},\:\frac{14}{3}\right),\:p=\frac{1}{12\

Step-by-step explanation:

a || b and p is a transversal. If m 1 = 140°, find the
measure of each angle giving one reason for each answer.
(The first one is done for you.)

Answers

Answer:

Angle 4 = 140

Angle 3= 40

Angle 5=140

angle 6=40

angle 7=40

Step-by-step explanation:

Adjacent angles are congruent. Thats how I can tell angle 4 is 140. And also how i can tell angle 3 is 40. Any questions?

im not explaining the rest im too tired

btw I also do 8th math lol it stinks.

A car is bought for £8500
In it's first year it's price reduces by 10%
Each year after that it decreases by 5%
What is the price after 3 years?

Answers

Answer: The price after 3 years is £6904.15

Step-by-step explanation:

After 1 year,  8500*0.9= 7650

7650*0.95=7267.5

7267.5*0.95=6904.125

The price after 3 years is £6904.15

PLEASE ANSWER ASAP THANKS

Answers

The value of x is 97.

What are corresponding angles?

The angles that are in the same position on a given two parallel lines intersected by a transversal line are called the corresponding angles.

Corresponding angles are always equal.

We can also have alternate angles which are always equal.

We can also have alternate interior and exterior angles which are equal.

The angles on the same side make upto 180 degrees

We have,

From the figure,

(x - 5) and (x - 9) forms a straight angle.

This means,

x - 5 + x - 9 = 180

Solve for x.

2x - 14 = 180

2x = 180 + 14

2x = 194

x = 97

Thus,

The value of x is 97.

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1. Arturo earns n dollars per hour. Next month
he will receive a 2% raise in pay per hour. The
expression n +0.02n is one way to represent
Arturo's pay per hour after the raise. Write
an equivalent simplified expression that will
represent his pay per hour after the raise.

Answers

The equivalent simplified expression is 1.02n.

What is an equivalent expression?

Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value for the variable.

Given that, Arturo earns n dollars per hour. Next month he will receive a 2% raise in pay per hour.

The expression n +0.02n is one way to represent Arturo's pay per hour after the raise.

Here, the equivalent expression is n +0.02n= 1.02n

Therefore, the equivalent simplified expression is 1.02n.

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PLS HELP ME THIS IS HARD in the selection from life on the mississippi, what main character flaw does twain reveal in himself as a boy? what is organic chemistry excess reactant ? what is the generic name of Tylenol? The most recent financial statements for Williamson, Inc., are shown here (assuming no income taxes):Income Statement ($) Balance Sheet ($)Sales 8,400 Assets 14,000 Debt 6,000Costs 6,390 Equity 8,000Net Income 2,010 Total 14,000 Total 14,000Assets and costs are proportional to sales. Debt and equity are not. No dividends are paid. Next year's sales are projected to be $9,996. What is the external financing needed? An abnormally high engine oil temperature indication may be caused bya) the oil level being too lowb) operating with a too high viscosity oilc) operating with an excessively rich mixture what number is greater than 7/2 If a squirrel cage induction motor draws 2A of current at 240V and is connected for use on 480V, the amperage will be ___. 1A. Of the following motors, the one most likely to have 15 or 18 motor leads is the _____. 2,400V three-phase motor. The main purpose of motor overload protection is to protect the motor ____. occurs when two patent holders license each other to use their patents only on the condition that neither licenses anyone else to use his or her patent without the other's consent. what is the ph of a solution that contains 11.7g of nacl for every 200 ml of solution? what is the content of the godfather quotes On the first day it was posted online, a music video got 2000 views. The number of views that the video got on the second day was 2400. On the third day the video got 2880 views and so on. Write the explicit formula for the number of views on the nth day What are the disadvantages of a pooled trust? which band released the studio album goats head soup? Why is pH of a soil would not be constant? Phlebotomy certification is often required at ---- blood ---- and independent ----- PLEASE HELP Identify the schwa sounds in the following words by writing them in capitals. Some of the words may contain more than one schwa sound. Which of the following has contributed to Tesla's competitive advantage in terms of stock appreciation?A. reinvesting profits continually design and produce better electric vehiclesB. keeping its proprietary secretC. copying the most popular features of competitors' vehiclesD. using inexpensive materials to keep costs low What is the importance of design cycle? Which statement is correct regarding the distinction between prokaryotic and eukaryotic gene expression?Prokaryotes regulate gene expression at the level of transcription whereas eukaryotes regulate at multiple levels including epigenetic, transcriptional and translational.Prokaryotes regulate gene expression at the level of translation whereas eukaryotes regulate at the level of transcription to manipulate protein levels.Prokaryotes regulate gene expression with the help of repressors and activators whereas eukaryotes regulate expression by degrading mRNA transcripts, thereby controlling protein levels.Prokaryotes control protein levels using epigenetic modifications whereas eukaryotes control protein levels by regulating the rate of transcription and translation.