An iron rod of length 10.38 ft is bent to form a circle. What is the radius of the circle?

The equivalent expression for the given expression is 1/2⁹⁸.

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.

The given expression is (2⁻¹⁰/4²)⁷.

Now, (2⁻¹⁰/(2²)²)⁷

= (2⁻¹⁰/2⁴)⁷

= (1/2¹⁰×2⁴)⁷

= (1/2¹⁰⁺⁴)⁷

= (1/2¹⁴)⁷

= 1/2⁹⁸

Therefore, the equivalent expression for the given expression is 1/2⁹⁸.

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The simplification of the logarithm expression are as shown below

A logarithm expression is a mathematical statement that involves logarithms. It is an expression that contains logarithmic functions, such as log, ln, logₐ, etc. These expressions can include logarithms with different bases, numbers in logarithm form, and exponents.

The logarithm expressions can be simplified as follow:

1. since logₐa = 1,

log₄4 = 1

2. Since logₐ1 = 0,

log₁₀1 = 0

3.  since logₐ(M × N) =  logₐM -  logₐN and logₐa = 1

log₃4 × 3 = log₃4 + log₃3 = log₃4 + 1

4. since logₐxⁿ = n logₐx and logₐa = 1

log₄4³ = 3 log₄4 = 3 × 1 = 3

5. since logₐxⁿ = n logₐx and logₐa = 1

logₓx⁰ = 0 logₓx = 0 × 1 = 0

6. since logₐxⁿ = n logₐx and logₐa = 1

logₓx³ =  3 logₓx = 3 × 1 = 3

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Check the picture below.

Answer:

x = greater than or equal to 3.5         x = 3≥

Step-by-step explanation:

any number that is greater than or is 3.5 will make 2x greater than 5 + 2 which equals 7

Answer:2.75 (or 11/4, they are equal).

Step-by-step explanation: The graph of f(x) is continuous on the closed interval and differentiable on the open interval. Now we need to find the average slope over the interval, which is [0-3]/[5-(-4)] = -3/9 = -1/3. The goal is to find a place where f'(c) = -1/3, so basically anywhere where the derivative equals -1/3. First we need to find the derivative of the function which can be rewritten as (5-x)^(1/2). Differentiating this using the chain rule gives you -1/(2*sqrt(5-x)). Set this equal to -1/3. The numerator is -1, so really we just need to find where the denominator, 2sqrt(5-x), is equal to 3. Divide by 2 and get sqrt(5-x) = 3/2. Square both sides and get 5-x = 9/4. Subtract 5 and get -x = -2.75, so x = 2.75. This means c = 2.75.

If each child consumed the same quantity, then each would need to drink (63)x(4/n) of a gallon.

The US fluid ounce is equal to 1/128 of a US gallon since there are four quarts in a gallon, two pints in a quart, and 16 US fluid ounces in a US pint. The US gallon is accepted to be equivalent to around 3.785 L or 231 in inches, but the Imperial gallon is accepted to be equal to 4.54609 L. The liter is the unit of volume used by the great majority of people in the world. a volume measurement equal to eight pints.

An imperial gallon (Britain, Canada) is exactly 4.54609 liters. (US) 3.785 liters or around 231 cubic inches for liquids (a "U.S. liquid gallon")

Here gallon of lemonade to share = 63

let each children has 1 gallon of lemonade

so gallon=63

so portion =63/1

Formula = gallon to share x (4 parts of gallon shape / number of gallon)

which means if each one have n gallon then portion = (63)x(4/n)

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Each child would need to eat 63*4/n of a gallon if they all consumed the same amount.

Since there are four quarts in a gallon, two pints in a quart, and 16 US fluid ounces in a US pint, one US fluid ounce is equivalent to 1/128 of a US gallon. The Imperial gallon is acknowledged to be equal to 4.54609 L, but the US gallon is accepted to be about 3.785 L or 231 in. The vast majority of people in the world measure volume in litres. a volume that is eight pints in size.

In Britain and Canada, an imperial gallon equals precisely 4.54609 litres. 3.785 litres (US) or around 231 cubic inches (a "U.S. liquid")

Here, six thirty kids were sharing a gallon of lemonade.

each youngster should drink a gallon of lemonade.

Gallon = 63.

Hence part = 63/1

It indicates that the fraction is equal to 63*4/n if each has n gallons.

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Note: The complete question would be as bellow,

six thirty children had gallon of lemonade to share. if each child had the same amount, what portion of the gallon did each child have to drink?

The equivalent expression is 1 divided by 5 raised to the fourteenth power 5^14. Option B

The index form of a number is described as the number written as an exponential expression, or even a single number that is raised to another number.

This exponent, or index form, of an exponential expression tells us the number of multiple times to multiply the base by itself to simply the expression.

Other names for index forms are scientific notation or standard forms.

From the information given, we have that;

This is represented as;

5⁻¹⁰/5⁴ × 5⁰

Any number raised to zero = 1

5⁻¹⁰/5⁴

subtract the exponents

5⁻¹⁰⁻⁴

5⁻¹⁴

Hence, the value is 5⁻¹⁴

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The formula would you put in cell location h10 to find the numerical derivative at position 10 of column k of the data found in j is =DERIVXY(h10, k10, j)

The term called derivative is defined as the process to determine the rate of change of a quantity with respect to another changing quantity

Here we have to write the formula for the cell location h10 to find the numerical derivative at position 10 of column k of the data found in j.

As from the definition, the general form derivative function is written as,

=> =DERIVXY(x, y, p, [options])

where x a vector of the points x-coordinates and y corresponding vector of the points y-values and p the point at which to compute the derivative.

Here we have the values of x as h10, y as k10 and p as j

Then the formula is written as,

=> =DERIVXY(h10, k10, j)

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Estimation done by Mia is not accurate, as the accurate estimated sum of the given expression 5/8 + 1/9  is equal to ( 1/2).

Estimation done by Mia is not accurate:

Replaced 5 /8 with 1.

But accuracy represents:

0 < (1 /4 ) < ( 1 /2 ) < (5 /8 ) < ( 3 / 4 ) < 1

( 5 / 8 ) is more close to ( 1 /2 ).

Estimated value of ( 5 / 8 ) is ( 1 / 2 )

0 < ( 1 / 9 ) < ( 1 / 4 )

So , estimated value of ( 1 / 9 ) is 0

Estimated sum = ( 1 / 2 ) + 0

                         = ( 1 / 2 )

                         ≠ 1

Therefore, accurate estimated sum of 5/8 + 1/9  is equal to ( 1 /2 ).

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Answer:

the average height is 5 feet 0 inches

Step-by-step explanation:

To find the average height of Maria, Marla, Mandy and Marilyn, we need to add up their individual heights and divide by the number of people in the group.

First, we need to convert all the heights to a common unit of measurement. Since inches are the smallest unit of measurement, we will convert all the heights to inches.

Maria: 5 feet 3 inches = 63 inches

Marla: 4 feet 11 inches = 59 inches

Mandy: 5 feet 2 inches = 62 inches

Marilyn: 4 feet 8 inches = 56 inches

Now we can add up the heights:

63 inches + 59 inches + 62 inches + 56 inches = 240 inches

To find the average, we divide the total height by the number of people:

240 inches / 4 people = 60 inches

So the average height of these four friends is 60 inches or 5 feet, which is the same as 5 feet 0 inches.

Therefore, the average height of these four friends is 5 feet 0 inches.

The area of the plate of the microscope with a circumference of

100mm is 2500/π mm².

A circle is simply a closed 2-dimensional curved shape with no corners or edges.

The area of a circle is expressed mathematically as;

A = πr²

The circumference of a circle is expressed as 2πr.

Given the data in the question;

First, we determine the radius of the plate.

Circumference C = 2πr

100 = 2πr

r = 100/2π

r = 50/π

Now, calculate the area of the plate.

A = πr²

A = π ( 50/π )²

A = π × 2500/π²

A = 2500π / π²

A = 2500/π mm²

Therefore, the area of the plate is 2500/π mm².

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If m∠DAC = 65°, m∠DAC and m∠BCA can be classified as alternate interior angles. And m∠BCA = 65°.

Alternate interior angles of a rectangle are congruent, which implies they are equal in measure and are formed by the intersection of the opposite sides of the rectangle.

Considering the diagonal AC from one corner of the rectangle to the opposite corner, the angles formed at the intersection of the non-parallel sides will be congruent

Therefore, the angles m∠DAC and m∠BCA are alternate interior and m∠DAC = m∠BCA, which makes m∠BCA = 65°

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The two consecutive numbers whose cubes differ by 217 are n=-9 or n=8.

The concept that will be used here is factorization. Consecutive numbers are those that follow one another continually, from lowest to largest. For instance, the numbers 1, 2, 3, 4, 5, and so on are all consecutive.

The number can be arranged as

(n+1)^3 -n^3=217

We can simplified this as:

[n^3+3n^2 +3n+1 -n^3]=217

3n^2+3n+1=217

This can be simplified as :

3n^2+3n-216=0

This can be factorized as

(n+9)(n-8)=0

n=-9 or n=8

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Answer:

83.7

Step-by-step explanation:

Substitute v = 3 and w = 4:

[tex]\displaystyle{12.3 \cdot 3 + 11.7 \cdot 4}\\\\\displaystyle{= 36.9 + 46.8}\\\\\displaystyle{= 83.7}[/tex]

Therefore, the value is 83.7

The solution of the given expression is -13. The correct option is A.

PEMDAS stands for the sequence of operations for multi-step mathematical expressions. The letters PEMDAS stand for parentheses, exponents, multiplication, division, addition, and subtraction.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication and division.

Given the expression is −8+(6+4)÷(−2). The expression by using the PEMDAS will be solved as below,

E = −8+(6+4)÷(−2)

First, solve the bracket and then division,

E = -8 + ( 10 ) ÷ (−2)

E = -8 - 5

E = -13

Hence, the solution is -13.

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The mileage rate of 75 miles per gallon is equal to 19.8 miles/liter or 31.9 km/liter. The result is obtained by converting the value of each unit.

The conversion value of

Some hybrids achieve mileage ratings as high as 75 miles per gallon of gasoline. Determine that quantity in:

Multiply the number with the conversion value of each!

In miles per liter,

75 miles/gallon = 75 × 1/3.785 miles/liter

75 miles/gallon = 19.8 miles/liter

In kilometers per liter,

75 miles/gallon = 75 × 1.609 × 1/3.785 km/liter

75 miles/gallon = 31.9 km/liter

Hence, 75 miles per gallon is equal to 19.8 miles/liter or 31.9 km/liter.

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Answer:

Step-by-step explanation:The exponent of a number shows how many times the number is multiplied by itself.

According to the rules of exponents,

We know that, am ÷ an = am − n

(5m ÷ 5−3) = 55

5m−(−3) = 55

5m + 3 = 55

The bases are the same on both the sides, so their exponents must be equal.

∴ m + 3 = 5

⇒ m = 5 − 3

⇒ m = 2

The area of triangle A(F) D is 42.44 units²

The formula to calculate the area of a triangle with base b and height h is given by:

Area = 1/2(bh)

In ΔA(F) D, the base is (F)D and A(F) is the height

Using trigonometric ratio:

sin 30° = A(F) /AD  (opposite/hypotenuse)

0.5 = A(F) /14

A(F)  = 7 units

(F)D = √(14²-7²) = 7√3 units (Pythagoras theorem)

Area of  ΔA(F) D = 1/2 × (F) D × A(F)

Area of  ΔA(F) D = 1/2 × 7√3 × 7

Area of  ΔA(F) D = (49√3)/2

Area of  ΔA(F) D = 42.44 units²

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Answer:

-13F

Step-by-step explanation:

since its negative, you could find the answer by doing 35-22

then, just adding a negative symbol in front!

this is because you are finding the difference by subtracting, and by doing this i find it a lot easier to get your answer

so, 35-22 is equal to 13. so, 22-35 is -13

i hope that makes sense

honestly, you can just use a calculator to figure it out too! just put 22-35

The linear equations for the graph is obtained to be option D: y = x + 2 and y = -x - 4.

What is a linear equation?

A linear equation is one that has a degree of 1 as its maximum value. No variable in a linear equation, thus, has an exponent greater than 1. A linear equation's graph will always be a straight line.

The graph of two lines are given.

For the first line going from top left corner to bottom right corner, the point of coordinates are (-5, 1) and (-3,-1).

The slope-intercept form of an equation/function is - y = mx + b

To find the slope m use the formula -

(y2 - y1)/(x2 - x1)

Substituting the values in the equation -

[-1 - 1]/[-3 - (-5)]

(-2)/(2)

-1

So, the slope point is obtained as m = -1.

The equation becomes - y =-x + b

To find the value of b substitute the values of x and y in the equation -

-1 = -(-3) + b

-1 = 3 + b

b = -1 - 3

b = -4

So, the value for b is -4.

Now, the equation becomes -

y = -x - 4

Now, for the second line going from bottom left corner to top right corner, the point of coordinates are (-1, 1) and (-3,-1).

The slope-intercept form of an equation/function is - y = mx + b

To find the slope m use the formula -

(y2 - y1)/(x2 - x1)

Substituting the values in the equation -

[-1 - 1]/[-3 - (-1)]

(-2)/(-2)

1

So, the slope point is obtained as m = 1.

The equation becomes - y = x + b

To find the value of b substitute the values of x and y in the equation -

-1 = (-3) + b

-1 = -3 + b

b = -1 + 3

b = 2

So, the value for b is 2.

Now, the equation becomes -

y = x + 2

Therefore, the two equations are y = -x - 4 and y = x + 2.

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Answer: a ≥ -1/3

Step-by-step explanation:

If we want the result of the expression to end up as a real number, the fraction under the square root cannot be negative.

Therefore, we can make an equation like this:

(1+3a) / 25 ≥ 0

Multiply by 25

1 + 3a ≥ 0

Subtract 1

3a ≥  -1

Divide by 3

a ≥  -1/3

Answer:

50/3

Step-by-step explanation:

5 5/7 divided by 1 3/5 times 4 2/3

5 5/7 = 40/7

1 3/5 = 8/5

4 2/3 = 14/3

40/7 divided by 8/5 = 40/7 times 5/8 = 200/56

200/56 times 14/3 = 2800/168 = 400/24 = 100/6 = 50/3

So, the answer is 50/3

According to the area of circle, the area covers the dartboard in which you can land is 254.34 square inches.

In math the term called area of circle is defined as the process of π multiplied by the square of the radius and area of a circle(A) when the radius 'r' is given is πr² here the value of π is approx. 3.14 or 22/7.

Here we know that the dartboard has a radius of 9 inches.

And the value of area covers the dartboard in which you can land is calculated as,

Where the value of r is 9, then the area is calculated as,

=> A = π(9)²

When we expand the terms, then we get,

=> A = π x 81

Apply the value of π as 3.14, then we get,

=> A = 3.14 x 81

=> A = 254.34

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The Angel read 5/12 of the book at night if Angel read 1/3 of a book in the morning, and he read some more at night. By the end of the day, he still had 1/4 of the book left to read.

What is ratio ?

Ratio can be defined as the given value divided by the total value.

The easiest thing to do first is convert all of these fractions to common denominators, and figure out the rest of the problem from there.

So the common denominator between 1/3 and 1/4 is 12, so convert these to fractions to /12 and continue on.

Think of the whole book being 12/12, and Sarah read 4/12 of it in the morning, so we know she has 8/12 left of it. Since we know she still has 3/12 left to read by the end of the day, we can subtract 8/12 - 3/12 to find out how much she read at night, which is 5/12. This makes sense because when we add all the fractions up (4/12 + 3/12 + 5/12) it comes out to 12/12, which is the whole book.

Therefore, The Angel read 5/12 of the book at night if Angel read 1/3 of a book in the morning, and he read some more at night. By the end of the day, he still had 1/4 of the book left to read.

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Answer:

x= 3x/7 - 10/7

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

Answer:

Step-by-step explanation:

x+2=4(2x + 3)-3

x+2=8x+9

2=8x+9−x

2=7x+9

2-9=7x

-7=7x

-7/-7=7x/-7

-1 = x

x=-1

Answer: 31

Step-by-step explanation:

4 3/7 = 31/7

31 × 7 = 217

7 × 1 = 7

217/7 = 31

The difference in average birthweight between smoking mothers and non- smoking mothers is, mothers who smoke cigarettes during pregnancy have, on average, lower birthweight children.

When cigs=0, the bwght is 119.77 ounces.

The average birth weight of the baby when the mother is not a smoker is 119.77 ounces.

When cigs=20,

bwght = 119.77 − 0.514(20) = 109.49,

The bwght is 109.49 ounces.

However, as more cigarettes are smoked, the birthweight of the baby decreases at the rate of 0.5138 ounce for every additional cigarette smoked per day.

Obviously, mothers who smoke cigarettes during pregnancy have, on average, lower birthweight children.

So, The difference in average birthweight between smoking mothers and non- smoking mothers is, mothers who smoke cigarettes during pregnancy have, on average, lower birthweight children.

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The value of the equation is A = √ ( -6 + x )

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

A = √ - ( 6 - x )    be equation (1)

On simplifying the equation , we get

Remove the parentheses for addition or subtraction

A = √ ( -6 + x )

when the value of A = 0

√ ( -6 + x ) = 0

Taking squares on both sides of the equation , we get

-6 + x = 0

Adding 6 on both sides of the equation , we get

x = 6

Therefore , the value of x is 6

Hence , the equation is A = √ ( -6 + x )

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Answer: 4-6 inches

Step-by-step explanation: Hope this helps

Answer:

Feathers are 214 in or less

Step-by-step explanation: