Write each number in scientific notation

Answer:

To find the derivative of the given function, we will use the product rule and the chain rule of differentiation.

Let u = 4x² and v = (5-7x)^8. Then, we have:

y = u * v

Using the product rule, we have:

y' = u' * v + u * v'

To find u' and v', we use the power rule and the chain rule:

u' = d/dx (4x²) = 8x

v' = d/dx (5-7x)^8 = 8(5-7x)^7 * (-7)

Now, we can substitute these values into the product rule formula:

y' = u' * v + u * v'

= 8x * (5-7x)^8 + 4x² * 8(5-7x)^7 * (-7)

Simplifying this expression, we get:

y' = 8x(5-7x)^7 * (40-56x-28x+49x)

= 8x(5-7x)^7 * (-14x+40)

Therefore, the derivative of the function y = 4x² (5-7x)^8 is y' = 8x(5-7x)^7 * (-14x+40).

The complete proof to show that ∠HIJ ≅ ∠EFG is:

Statement                                         Reason

FG ⊥ EF                                             Given

HI ⊥ IJ                                                Given

m ∠EFG = 90°                                    Definition of perpendicular lines  

m ∠HIJ = 90°                                     Definition of perpendicular lines

∠HIJ ≅ ∠EFG                                    Substitution property

From the question, we to prove that the given angles are congruent.

The given angles are ∠HIJ and ∠EFG

To prove that angle HIJ is congruent to angle EFG we will complete the given table.

The given table is

Statement                                         Reason

FG ⊥ EF                                             Given

HI ⊥ IJ                                                Given

m ∠EFG = 90°                                    Definition of perpendicular lines  

m ∠HIJ = 90°                                     Definition of perpendicular lines

Now, we will complete the proof by adding the last statement and its reason

Statement                                         Reason

FG ⊥ EF                                             Given

HI ⊥ IJ                                                Given

m ∠EFG = 90°                                    Definition of perpendicular lines  

m ∠HIJ = 90°                                     Definition of perpendicular lines

∠HIJ ≅ ∠EFG                                    Substitution property

Hence,

We have completed the proof by using the substitution property

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The area of the shaded region is  π(R + 3)² - 9π where R is teh radius of the outer circle

The circumference of the inner circle is 18.84 feet

So, we have

2πr = 18.84

Divide by 2π

r = 18.84/2π

Evaluate

r = 3.0

So, the area of the inner circle is

A = πr²

This gives

A = π * 3²

Evaluate

A = 9π

The shaded area is

Area of big - Area of inner circle

So, we have

Shaded area = π(R + 3)² - 9π where R is teh radius of the outer circle

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If a  sports ball has a diameter of 11cm then the volume of the ball is 696.5 cubic centimeters

The volume of a sphere can be calculated using the formula:

V = (4/3)πr³

where V is the volume of the sphere, r is the radius of the sphere, and π is a constant equal to approximately 3.14159.

Since the diameter of the sports ball is given as 11 cm, we can find the radius by dividing the diameter by 2:

r = 11 cm / 2 = 5.5 cm

Now we can substitute this value of r into the formula and calculate the volume:

V = (4/3)π(5.5 cm)³

V = (4/3)π(166.375 cm³)

V = 696.5 cm³

Therefore, the volume of the sports ball is 696.5 cubic centimeters (cm³).

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Answer:

Charles Baudelaire recommended that artists paint scenes of modern life.

Charles Baudelaire was the one who recommended that artists paint scenes of modern life.

The perimeter of the quadrilateral is  b + 2c - 2 inches

To determine the value of the perimeter, we need to know the properties of a quadrilateral.

These properties includes;

The perimeter of a quadrilateral is expressed as;

Perimeter = A + B + C + D

add the values of the sides

Substitute the values, we have;

Perimeter = b + c + b - 2 + c - b

collect the like terms

Perimeter = b + 2c - 2

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The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.

We have,

Equation of circle: x²+ y² – 2x – 8 = 0

The standard equation of a circle is

x² + y² + 2gx + 2fy + C= 0

where Centre is (-g, -f)

and, radius = √g²+f²-C

from given equation the center is

2gx = -2x

x= -1

and,  2fy = 0

f = 0

So, the Centre = (-(-1), 0) = (1, 0)

Now, r = radius = √g²+f²-C

r= √1²+0²-(-8)

r=√9

r = 3 units

Hence, the radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.

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The coordinates of Y' are (6, 4) and the coordinates of Z' are (5, -1).

Here, we have,

To find the coordinates of Y' and Z', we need to apply the same translation that maps X to X'.

We know that the vector that connects X to X' is (3 - (-1), 1 - 0) = (4, 1).

So, to translate Y to Y', we add the vector (4, 1) to the coordinates of Y:

Y' = Y + (4, 1)

= (2, 3) + (4, 1)

= (6, 4)

Similarly, to translate Z to Z', we add the vector (4, 1) to the coordinates of Z:

Z' = Z + (4, 1)

= (1, -2) + (4, 1)

= (5, -1)

Therefore, the coordinates of Y' are (6, 4) and the coordinates of Z' are (5, -1).

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Answer: A. 102

Step-by-step explanation:

1,125 divided by 11 is 102.2727... so only 102 full goodie bags can be made.

The height of the building, found using the equivalent ratios of the corresponding sides of the similar triangles formed by Rob, the building and the shadows is 90 feet

Similar triangles are triangles that have the same shape but may have different sizes.

The length of the shadow cast by the building = 30 feet

Rob's height = 6 feet

The length of Rob's shadow = 2 feet long

The height of the building can be found from the similar right triangles formed by the building and the building's shadow and the triangle formed by Rob and Rob's shadow as follows;

Let h represent the height of the building, we get;

h/30 = 6/2 = 3

h = 30 × 3 = 90

The height of the building is 90 feet tall

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The level of significance based on the information will be:

a. F = 4.11, with 3 df between and 30 df within - < 0.05

b. F = 1.12, with 5 df between and 83 df within - > 0.05

c. F = 2.28, with 4 df between and 42 df within - > 0.05

The likelihood of rejecting the null hypothesis when it is true, or the alpha level, is used in statistical tests to evaluate statistical significance.

The significance level, or alpha, for this example is set at 0.05 (5%). This was accurately illustrated above

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For each relation, we would determine whether or not it is a function as follows;

Relation 1 is: B. not a function

Relation 2 is: A. function.

Relation 3 is: B. not a function

Relation 4 is: A. a function.

In Mathematics and Geometry, a function is generally used for uniquely mapping an independent value (domain or input variable) to a dependent value (range or output variable).

This ultimately implies that, an independent value (domain) represents the value on the x-coordinate of a cartesian coordinate while a dependent value (range) represents the value on the y-coordinate of a cartesian coordinate.

Based on relations 1 and 3, we can logically deduce that they do not represent a function because their independent value (domain) has more than one dependent value (range).

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the answer is B

B

because the answer B make the most sense to me and hopefully this helps

Pythagoras theorem: In a right triangle, if the hypotenuse, perpendicular, and base are its sides, then as per the theorem, the square of the hypotenuse side is equal to the sum of the square of the base and the square of the perpendicular. Hence, if we know any two sides, then we can easily find the third side of the triangle.

C. 20 ft, 20 ft, 50 ft correct?

The quadratic regression equation for the data is given as follows:

y = 2.4x² - 14.4x + 46.8.

To find the quadratic regression equation, we need to insert the points (x,y) into a quadratic regression calculator.

The points for this problem are taken from the table, as follows:

(1, 35), (2, 27), (3, 24), (4, 28), (5, 33).

Inserting these points into a calculator, the equation is given as follows:

y = 2.4x² - 14.4x + 46.8.

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Answer:

plein-air. Is the correct answer

Claude Monet's Impression: Sunrise (1872) is considered a plein-air painting because it was completed out-of-doors.

The statement that is not true is (c) The measure of ∠R is the same as ∠N.

We have,

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

The coordinates of ΔRGB are R(‒3, 2), G(3, 4) and B(1, 1).

The coordinates of ΔUNA are U(2, ‒3), N(‒4, ‒3) and A(‒1, ‒1).

Looking at the above coordinates, we can see that the transformation rule is (x, y) = (-x, -y)

This is a rigid transformation

And so, the side lengths and the corresponding angle measures are equal

However, angles R and N are not corresponding angles

So, the false statement is (c) The measure of ∠R is the same as ∠N.

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The probability of passing the quiz by randomly guessing answers is very low, approximately 0.02%.

To pass the quiz with a minimum passing grade of 60%, a person needs to answer at least 12 questions correctly out of the 20 total questions.

If a person is making random guesses for all of the answers, the probability of guessing one question correctly is 1/4, since there are 4 possible answers for each question. The probability of guessing one question incorrectly is 3/4.

Using the binomial probability formula, we can find the probability of passing the quiz by correctly guessing at least 12 questions:

P(X >= 12) = 1 - P(X < 12)

where X is the number of questions answered correctly.

P(X < 12) = sum of the probabilities of getting 0, 1, 2, ..., or 11 questions correct:

P(X < 12) = C(20,0)(1/4)⁰(3/4)²⁰ + C(20,1)(1/4)¹(3/4)¹⁹ + ... + C(20,11)(1/4)¹¹(3/4)⁹

where C(20,0), C(20,1), ..., C(20,11) are the binomial coefficients.

We can use a calculator or a computer to evaluate this sum of probabilities, or we can use a normal approximation to the binomial distribution if we assume that np = 20(1/4) = 5 and n x (1-p) = 20 x (3/4) = 15 are both greater than 10.

Using the normal approximation, we can find the mean and standard deviation of the binomial distribution:

mean = np = 20(1/4) = 5

Standard deviation = √(np(1-p)) = √(20*(1/4) x (3/4)) = √(15/2) = 1.94 (rounded to 2 decimal places)

Then, we can standardize the distribution by subtracting the mean and dividing by the standard deviation:

z = (12 - 5) / 1.94 = 3.61 (rounded to 2 decimal places)

Using a standard normal distribution table or a calculator, we can find the probability of getting a z-score greater than 3.61:

P(Z > 3.61) = 0.0002 (rounded to 4 decimal places)

Therefore, the probability of passing the quiz by randomly guessing answers is very low, approximately 0.02%.

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Answer:

There are 300 students at East High School.

Step-by-step explanation:

East High School has 1/10 as many students as West High School, which means that the number of students at East High School is equal to 1/10 of the number of students at West High School.

To find out how many students are at East High School, we can multiply the number of students at West High School by 1/10:

East High School = West High School x 1/10East High School = 3000 x 1/10East High School = 300

Therefore, there are 300 students at East High School.

Answer:

East High School has 1/10 × 3,000 = 300 students.

The error in this derivation in step 3 will be cos2(x) – 1 – cos2(x) should be cos2(x) – 1 + cos2(x).

The trigonometric identities are given as,

sin²x + cos²x = 1

cos 2x = cos²x - sin²x

A 2-column table with 4 rows.

Column 1                      Column 2

    1                      cos 2x = cos²x – sin²x

   2                                  = cos²x – (1 – cos²x)

   3                                  = cos²x – 1 – cos²x

   4                                  = 2 cos²x – 1

The error in this derivation in step 3 will be cos2(x) – 1 – cos2(x) should be cos2(x) – 1 + cos2(x).

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The values AB² + BC² ≠ AC², triangle ABC is not a right triangle.

A mathematical notion known as the Pythagorean theorem explains how a right triangle's sides relate to one another. It asserts that the square of the hypotenuse's (the triangle's longest side) length equals the product of the squares of the other two sides (the adjacent and opposite sides).

To find the length of AB, we use the distance formula:

AB = √[(x2 - x1)² + (y2 - y1)²]

AB = √[(1 - (-9))² + ((-1) - (-3))²]

AB = √[10² + 2²]

AB = √104

To find the length of BC, we use the distance formula:

BC = √[(x2 - x1)² + (y2 - y1)²]

BC = √[(-3 - 1)² + ((-7) - (-1))²]

BC = √[(-4)² + (-6)²]

BC = √52

To find the length of AC, we use the distance formula:

AC = √[(x₂ - x₁)² + (y₂ - y₁)²]

AC = √[(-3 - (-9))² + ((-7) - (-3))²]

AC = √[6² + (-4)²]

AC = √52

Using the Pythagorean Theorem, we can determine if triangle ABC is a right triangle. If a triangle is a right triangle, then the sum of the squares of the lengths of the two shorter sides will equal the square of the length of the longest side. So, we need to check if:

AB² + BC² = AC²

(√104)² + (√52)² = (√52)²

104 + 52 = 52

156 ≠ 52

Since AB² + BC² ≠ AC², triangle ABC is not a right triangle.

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Her rate loss in pounds per week is given as follows:

3.75 pounds per week.

Her rate loss in pounds per week is obtained applying the proportions in the context of the problem.

A proportion is applied as the rate loss is given by the division of the loss by the number of weeks.

The parameters are given as follows:

Hence the rate loss is given as follows:

r = 60/16

r = 3.75 pounds per week.

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Answer: there were 190 children, 140 parents, and 70 grandparents in attendance at the family reunion.

Step-by-step explanation: Let's denote the number of children, parents, and grandparents as "c", "p", and "g", respectively.

We are given three pieces of information:

The total number of people in attendance is 400:

c + p + g = 400

There were twice as many parents as grandparents:

p = 2g

There were 50 more children than parents:

c = p + 50

We can use this system of equations to solve for the unknown variables.

First, we can use equation (2) to express "p" in terms of "g":

p = 2g

Next, we can substitute this expression for "p" into equation (3) to get:

c = 2g + 50

Now, we can use equations (1) and (4) to eliminate "p" and "c" from the system and express "g" in terms of only known quantities:

c + p + g = 400

2g + 50 + p + g = 400 (substituting c=2g+50)

3g + p = 350 (simplifying)

We can then substitute the expression for "p" from equation (2) into this last equation to obtain:

3g + 2g = 350

Simplifying:

5g = 350

Solving for "g", we get:

g = 70

Now, we can use equation (2) to find "p":

p = 2g = 2(70) = 140

Finally, we can use equation (3) to find "c":

c = 2g + 50 = 2(70) + 50 = 190

Therefore, there were 190 children, 140 parents, and 70 grandparents in attendance at the family reunion.

The standard deviation of the sum S = I + O is [tex]$1,508.48[/tex]. The Option C is correct.

In order to calculate standard deviation of the sum S = I + O on the information given from the question, we can use this formula: "SD(S) = sqrt[SD(I)^2 + SD(O)^2 + 2Cov(I,O)]".

Details:

SD(I) & SD(O) means standard deviations of in-state and out-of-state tuition.

Cov(I,O) means covariance between the two variables.

The two variables I and O are independent

Their covariance is zero

Now, we can solve the S.D. using the formula. The SD(S):

= sqrt[SD(I)^2 + SD(O)^2]

= sqrt[(1003.25)^2 + (1126.50)^2]

= sqrt[1006510.5625 + 1269002.25]

= sqrt[2275512.8125]

= 1508.48029901

= $1508.48

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The solution to the given inequality is −1.26354284<x<1.75564007 or x>4.50790277.

The given inequality is x³-5x²+10>0.

Solve for x by simplifying both sides of the inequality, then isolating the variable.

Inequality Form: −1.26354284<x<1.75564007 or x>4.50790277

Interval Notation:(−1.26354284,1.75564007)∪(4.50790277,∞)

Therefore, the solution to the given inequality is −1.26354284<x<1.75564007 or x>4.50790277.

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After 20 years, the initial investment of $650 will have grown to $2,386.10

Now, let's consider the problem at hand: a $650 investment at 6.5% interest compounded continuously for 20 years. To calculate the final amount of the investment, we can use the formula:

A = P[tex]e^{rt}[/tex]

where A is the final amount, P is the initial investment, e is the mathematical constant approximately equal to 2.71828, r is the interest rate (in decimal form), and t is the time (in years).

Plugging in the values given in the problem, we get:

A = 650 x [tex]e^{0.065 \times 20}[/tex]

Simplifying this expression, we get:

A = 650 x [tex]e^{1.3}[/tex]

Using a calculator, we can find that  [tex]e^{1.3}[/tex] is approximately 3.6693. Therefore, the final amount of the investment is:

A = 650 x 3.6693

A = $2,386.10

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The number of children, parents, and Grandparents that were in attendance are:

First, we should come up with equations that relate the number of children, parents, and Grandparents, given the information we know. The equations would have C for children, P for parents, and G for grandparents.

Total number of people:

C + P + G = 400

Parents to grandparents:

P = 2G

Children to parents:

C = P + 50

Substituting gives:

( P + 50 ) + P + ( P / 2 ) = 400

P + 50 + P + P / 2 = 400

(5 / 2) P + 50 = 400

(5 / 2 )P = 350

P = 140 parents

The children would be:

C = P + 50

= 140 + 50

= 190 children

The grandparents:

G = P/2

= 140/2

= 70 grandparents

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The value of x in the equation  27=−5x+3 is -24/5

The given equation is 27=−5x+3

We have to find the value of x

Subtract 3 from both sides

27-3=-5x

24=-5x

Divide both sides by 5

x=-24/5

Hence, the value of x in the equation  27=−5x+3 is -24/5

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