Arrange the following decimals in ascending order.
4. 7569 ; 47. 569 ; 4.9675 ; 4.0007 ; 47. 965 ; 47.005 ; 4.5

Answer:

If the repayment period is the same length for both loans, the interest option that will result in the least amount of interest added to the loan is B. Option A will have the least amount of interest because simple interest generates earnings from principal only.

What is the simple interest?

The simple interest is the interest system that does not compute interest on accumulated interest.

Unlike simple interest, compound interest charges interest on accumulated interest.

Thus, the simple interest system applies the interest rate on the principal only for each period to determine the amount of interest.

Step-by-step explanation:

Have a nice day

The value of gravitational force between two masses is,

⇒ Gravitational force (F) = 3

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

Two masses are,

m₁ = 6

m₂ = 8

d = 4

Now, We know that;

Gravitational force (F) = m₁ m₂ / d²

Substitute all the values we get;

Gravitational force (F) = m₁ m₂ / d²

Gravitational force (F) = 6 × 8 / 4²

Gravitational force (F) = 48/16

Gravitational force (F) = 3

Thus, The value of gravitational force between two masses is,

⇒ Gravitational force (F) = 3

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Answer:

[tex]\huge\boxed{\sf (x - 9)(x + 2)}[/tex]

Step-by-step explanation:

x² + 7x - 18

Using mid-term break formula.

So,

= x² - 9x + 2x - 18

Now, take x from (x² - 9x) and 2 from (2x - 18) common

= x(x - 9) + 2(x - 9)

Take (x - 9) common

[tex]\rule[225]{225}{2}[/tex]

The result is (x + 8).

Polynomial is an equation written with terms of the form kx^n.

where k and n are positive integers.

There are quadratic polynomials and cubic polynomials.

Example:

2x³ + 4x² + 4x + 9 is a cubic polynomial.

4x² + 7x + 8 is a quadratic polynomial.

We have,

x² + 12x + 32 and g(x) = x + 4.

Now,

(f/g)(x)

= (x² + 12x + 32) / (x + 4) _____(1)

Now,

We can factorize x² + 12x + 32.

x² + 12x + 32

= x² + (8 + 4)x + 32

= x² + 8x + 4x + 32

= x(x + 8) + 4(x + 8)

= (x + 4) (x + 8) ______(2)

From (1) and (2),

(f/g)(x)

= (x² + 12x + 32) / (x + 4)

=  (x + 4) (x + 8) / (x + 4)

= x + 8

Thus,

The result is (x + 8).

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(A) The scale factor of the dilation that transforms Triangle PQR to Triangle P'Q'R'  is 1/2

(B) Coordinates of Δ P"Q"R"

P" (-4,0)

Q"(-3,1)

R"(1,-2)

(C) Triangles PQR and P"Q"R" are not congruent.

Given

ΔPQR is transformed into ΔP'Q'R'

Coordinates of P, Q, R are

P (8,0),

Q(6,2)

R(-2,-4)

Coordinates of P'Q'R' are

P′(4, 0)

Q′(3, 1)

R′(−1, −2)

(A) By Distance formula we can find the distance between P Q and P'Q'

Distance formula = [tex]D = \sqrt{(x2-x1)^{2} +(y2-y1)^{2} }[/tex]

Where D = Distance between two points

from distance formula we can write that

PQ = [tex]\sqrt{(6-8)^{2} +(2-0)^{2} } = \sqrt{4+4} =2 \sqrt{2}[/tex]

Similarly

P'Q'= √2

PQ /P'Q' = 2

hence the scale factor of dilation is 1/2 (Compression)

(B )The Coordinates of Reflection about y axis can be written for a point

(x,y) as (-x,y)

So the Coordinated of Δ P"Q"R" can be written as

P" (-4,0)

Q"(-3,1)

R"(1,-2)

(C) ΔPQR  and ΔP"Q"R" are similar triangles but they are not  congruent because their sides  are not equal in size.

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The amount ali paid in tax is $1.71.

Suppose that we have to measure the rate of change of y as x changes, then we have:

[tex]Rate = \dfrac{y_2 - y_1}{x_2 - x_1}[/tex]

where we have

[tex]\rm when \: x=x_1, y = y_1\\when\: x = x_2, y= y_2[/tex]

Remember that, we divide by the change in independent variable so that we get some idea of how much the dependent quantity changes as we change the independent quantity by 1 unit.

(5 change per 3 unit can be rewritten as 5/3 change per 1 unit)

We are given that;

Cost of coat=$38

Rate= 4.5%

Now,

To find out how much Ali paid in sales tax, we need to multiply the purchase price by the sales tax rate:

Sales tax amount = Purchase price x Sales tax rate

Sales tax rate = 4.5% = 0.045 (in decimal form)

Purchase price = $38

Sales tax amount = $38 x 0.045 = $1.71

Therefore, by the given rate Ali paid $1.71 in sales tax.

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Answer:

  BC = 100°

Step-by-step explanation:

You want the measure of arc BC formed by two chords that intersect at 85° and intercept an opposite arc of 70°.

The angle formed by crossing chords is the average of the angles they intercept. Here, that means ...

  85° = (? +70°)/2 . . . . the crossing angle is 85°

  170° = ? +70° . . . . . . multiply by 2

  100° = ? . . . . . . . . . subtract 70°

The intercepted arc BC is 100°.

The value that should go on the flyer from the environmental group can be found to be 60, 000 m ².

The reason why the building developer chose a different unit from the environmental group is to try to understate the amount of land they would be building on.

The conversion factor for square kilometers and meters squared is :

1 km ² = 100, 000 m²

0. 06 km ² would then be :

= 0. 6 x 100, 000

= 60, 000 m ²

The building developer chose to use square kilometers to make it seem as though the amount of land they were using was little so as not to have people being angry with the amount of land they would use. The environmental group chose meters squared for the opposite effect to make it seem like a lot of land was to be used.

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The valid inferences are (a) and (c)

From the data in the table, we can make the following valid inferences:

Using the above as a guide, we have the following:

Other inferences are invalid

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The height of the  building which casts a 103-foot shadow is 95.5 foot.

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.

Given that building casts a 103-foot shadow at the same time that a 32-foot flagpole casts as 34.5-foot shadow

We need to find the height of the building.

Let us consider x be the height of building.

Form a proportional equation.

x/103=32/34.5

Apply cross multiplication

34.5x=32×103

34.5x=3296

Divide both sides by 34.5

x=3296/34.5

x=95.5

Hence, 95.5 foot be the height of the  building which casts a 103-foot shadow.

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The missing numbers for the respective rows are:

row 1: 4/5

row 2: -4/5 and -2/5

row 3: -3/5 and 6/5

Missing number for row 1(top row):

1 - 1/5 = 4/5

Missing number for row 2 (2nd number for last column):

3/5 - 1 = -2/5

Missing number for row 2 (1st number for first column):

-2/5 - 2/5 = -4/5

Missing number for row 3 (1st number for first column):

1/5 + (-4/5) = -3/5

Missing number for row 3 (2nd number for second column):

4/5 + 2/5 = 6/5

Therefore, row 1 have the missing number; 4/5. Row 2 missing numbers from left; -4/5 and -2/5. Row 3 missing number from left; -3/5 and 6/5

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Possible question:

If the sum of the first two numbers in row 1 is equal to 1 and the sum of the first two in last column to the right is equal to 3/5. Find the missing numbers.

The side lengths form a proportional relationship, and the ratios are;

17.955/11.97 = 14.565/9.71 = 5.415/3.61.

Similar triangles are triangles that share these two features presented as follows:

First is Congruent angle measures, then Proportional side lengths.

Here, the triangles are similar, because they have the same angle measures.

17.955/11.97 = 14.565/9.71

= 5.415/3.61.

Thus, the side lengths form a proportional relationship, have a ratio of 1.5.

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Answer:

the solution to the equation 2x^+4=8^x is x = 1.

Step-by-step explanation:

To solve the equation 2x^+4=8^x, we can start by simplifying both sides of the equation.

First, we can rewrite 8^x as (2^3)^x, using the property that 8 is equal to 2 raised to the power of 3.

So, the equation becomes:

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

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

Next, we can rewrite 2x^+4 as 2^2 * 2^x, using the property that a^b * a^c = a^(b+c).

So, the equation becomes:

2^2 * 2^x = 2^(3x)

2^(x+2) = 2^(3x)

Now, we can equate the exponents on both sides of the equation:

x + 2 = 3x

2x = 2

x = 1

Therefore, the solution to the equation 2x^+4=8^x is x = 1.

Answer:

Below

Step-by-step explanation:

2  x^4  =  8^x        <====not sure syntax is correct(?)

Solving GRAPHICALLY shows x = - .61181

Answer:

decay

Step-by-step explanation:

Because you are dying every second of the day and are growing only when your body is resting

Answer:

hey, good morning! the answer to this equation is growth!

Step-by-step explanation:

because if you figure out what 115% is as a decimal which is 1.15. and this decimal is above 1.

good luck!

Answer:  20:12

Step-by-step explanation:

Answer:

15:9

Step-by-step explanation:

multiply both by 3,4,5,6,7,8,9,etc.

Answer:

Step-by-step explanation:1/3

The measurement of the line segment to the nearest 1 / 4 inch is C. 5 ³ / ₄ inches.

To measure the line segment, you should look at the length of the line segment, while taking into account the measurements between the integrals.

There are 3 sections between each integral, with the suceeding integral being the 4 the section. Seeing as there are 4 sections therefore, it means that each section accounts for :

= 1 / 4 inches

The last integral is 5 inches and then there are 3 section after that. The measurement of the line segment then is:

= 5 + ( 3 x 1 / 4 )

= 5 + 3 / 4

= 5 ³ / ₄ inches

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The question is:

Measure the line segment

Prove by contradiction that in a right triangle with integer sides, the two shorter sides cannot both be odd.

Assume that the two shorter sides, a and b, of a right triangle are both odd integers. Then the hypotenuse, c, must also be an integer. From the Pythagorean theorem, we know that c2 = a2 + b2. We can rewrite this as c2 = (2m + 1)2 + (2n + 1)2, where m and n are integers. We can expand the left-hand side of the equation to get c2 = 4m2 + 4n2 + 4m + 4n + 1. Since c2 is an even integer, 4m2 + 4n2 must be an even integer as well. But, since 4m + 4n + 1 is odd, the only way to make the left-hand side of the equation an even integer is if 4m2 + 4n2 is an odd integer, which is impossible.

Therefore, our initial assumption that a and b are both odd integers is false. Thus, in a right triangle with integer sides, the two shorter sides cannot both be odd.

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The correct answer is: 2.8 is greater than 2.58.

A decimal value is a number expressed in the decimal system, which is based on the number ten. It includes a decimal point that separates the whole number part from the fractional part. The digits to the left of the decimal point represent whole numbers, and the digits to the right of the decimal point represent fractional parts of a whole number, which are expressed in powers of ten (tenths, hundredths, thousandths, etc.). For example, in the decimal value 3.14, the digit 3 represents the whole number part, and the digits 1 and 4 represent the tenths and hundredths parts, respectively. Decimal values are commonly used in mathematics, science, and everyday life to represent quantities that are not whole numbers, such as measurements, percentages, and money values.

Given by the question.

because the digit in the tenths place is larger in 2.8 than in 2.58. In decimal notation, the digit immediately to the right of the decimal point represents tenths, and larger values in this place indicate a larger overall value. In this case, 2.8 has a digit of 8 in the tenths place, while 2.58 has a digit of 5 in the tenths place. Therefore, 2.8 is greater than 2.58. The location of the numbers on a number line is not relevant for comparing decimal values, unless they have the same digit in the tenths.

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The amount of urea per square meter in form of fraction will be 6/29 ounce/meter².

What exactly is a fraction?

In mathematics, a fraction is used to represent a piece or part of a whole. It symbolises the equal pieces of the whole. A fraction is made up of two parts: the numerator and the denominator. The top number is known as the numerator, while the bottom number is known as the denominator. The denominator describes the total number of equal parts in a whole, whereas the numerator defines the number of equal parts taken.

5/10, for example, is a fraction.

In this case, 5 is the numerator and 10 is the denominator.

Now,

Given that Total area=58 square meter

Total Urea used=12 ounce

then urea used for 1 square meter=12/58

=6/29 ounce/meter².

Hence,

          The amount of urea per square meter in form of fraction will be 6/29 ounce/meter².

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The required value of the scooter after 5 years will be $1,120.

Percentage is a way of expressing a number as a fraction of 100. It is often denoted by the symbol "%". For example, if there are 20 students in a class and 5 of them are boys, the percentage of boys in the class can be calculated as follows:

Percentage of boys = (Number of boys / Total number of students) x 100%

After 5 years, the scooter will depreciate by 65%, which means its value will be reduced to 35% of its original value.

35% of $3,200 = 0.35 x $3,200 = $1,120

Therefore, the value of the scooter after 5 years will be $1,120.

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You only showed one btw.

75%=3/4

Answer:

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

Step-by-step explanation:

A percentage is a ratio or a number expressed in the form of a fraction of 100. Percentages are often used to express a part of a total.

If we know that percentages are fractions of 100, we know that 75% is equivalent to [tex]\frac{75}{100}[/tex].

Simplifying [tex]\frac{75}{100}[/tex]:

Therefore, 75% as a simplified fraction is [tex]\frac{3}{4}[/tex].

The volume of the new box is 30 units³.

We can infer the roots are rational integers from the response options, thus this polynomial ought to be simple to factor. The coefficients of x must multiply by 10, hence they must be in some sequence of 5, 2, 1 or 10, 1. Since we can try each one separately, we can express the factored form as follows:

                                      (5x-p)(2x-q)(x-r)

Due to the fact that p, q, and r must multiply to 6, they must be either 3, 2, 1 or 6, 1, 1 in some sequence. Once more, we may test each one in a different place to determine if they multiply properly.

When we multiply the x-terms and attempt (5x - 2)(2x - 1)(x - 3), the answer is 29. Try adding the x² terms together, they equal -39. Consequently, the roots are 2/5, 1/2 and 3 Now if you add 2 to each root, you get the volume is

= 12/5 × 5/2 × 5 = 30 units³

Therefore, The volume of the new box is 30 units³.

The question is incomplete. The complete question is:

"the roots of the polynomial 10x³ - 39x² + 29x - 6 are the height, length, and width of a rectangular box (right rectangular prism). a new rectangular box is formed by lengthening each edge of the original box by 2 units. what is the volume of the new box?"

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Answer: 266256π

Step-by-step explanation:

♡ Hope this helps ♡

Answer:

Step-by-step explanation:

a) The area covered by algae 10 days after it was first spotted is approximately 32.64 square meters.

b) We can find the area covered by algae one day after it was first spotted by multiplying [tex]12.5^{1/7}[/tex] by 2.

An equation contains one or more terms with variables connected by an equal sign.

Example:

2x + 4y = 9 is an equation.

2x = 8 is an equation.

We have,

a.

To find the area covered by algae 10 days after it was first spotted, we need to convert 10 days into weeks, since the growth rate is given in terms of weekly doubling.

There are 7 days in a week,

So 10 days are approximately 1.43 weeks (10/7).

Let A be the area covered by algae in square meters after n weeks.

Then we can use the formula for exponential growth:

A = 12.5 x [tex]2^n[/tex]

Substituting n = 1.43, we get:

A = 12.5 x [tex]26^{1.43}[/tex]

A ≈ 32.64

Therefore,

The area covered by algae 10 days after it was first spotted is approximately 32.64 square meters.

b.

We know that the area covered by algae doubles each week.

One week is equivalent to 7 days, so after one week, the area covered by algae will be twice the initial area of 12.5 square meters, or 25 square meters.

We can represent this mathematically as:

A = 12.5 x [tex]2^1[/tex]

Now, let's consider what happens after two weeks, or 14 days.

The area covered by algae will double again, so it will be four times the initial area of 12.5 square meters or 50 square meters.

We can represent this mathematically as:

A = 12.5 x 2²

Using the same reasoning, we can find that after three weeks (21 days), the area covered by algae will be eight times the initial area or 100 square meters:

A = 12.5 * 2³

In general, we can see that after n weeks, the area covered by algae will be 2^n times the initial area of 12.5 square meters. This can be written as:

A = 12.5 x [tex]2^n[/tex]

If we want to find the area covered by algae after one day, we can use the fact that one day is equivalent to 1/7 of a week.

So, after one day, the area covered by algae will be:

A = 12.5 x [tex]2^{1/7}[/tex]

Simplifying this expression using the laws of exponents, we get:

A = [tex]12.5^{1/7}\times2[/tex]

Therefore,

We can find the area covered by algae one day after it was first spotted by multiplying [tex]12.5^{1/7}[/tex] by 2.

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The probability of obtaining a z-value less than 1.5 is 0.8531 or 85.31% using normal distribution table.

The probability of obtaining a z-value less than 1.5 can be calculated using the standard normal distribution table or by using software like Excel or statistical calculators.

The standard normal distribution is a probability distribution with a mean of zero and a standard deviation of one. It is denoted by the letter Z and is used to standardize normal random variables. The standard normal distribution table provides the probabilities for different values of Z, ranging from -3.4 to 3.4.

To find the probability of obtaining a z-value less than 1.5, we need to look up the value of 1.5 in the standard normal distribution table. The table provides the area under the standard normal curve to the left of a given Z-value.

Looking at the table, we find that the probability of obtaining a z-value less than 1.5 is 0.8531, which means that approximately 85.31% of the area under the standard normal curve is to the left of 1.5.

This means that if we have a normally distributed variable with a mean of zero and a standard deviation of one, there is a 85.31% chance that the z-value will be less than 1.5.

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Answer:

Step-by-step explanation:

Y is 2 when X is 6

The ratio of the short side to the long side is 9/4 and the ratio of the hypotenuse to the long side is 5/4.

What is triangle ?

A triangle is a two-dimensional shape with three straight sides and three angles. It is one of the most basic and important shapes in geometry.

The three sides of a triangle can be of different lengths, or they can be of the same length, in which case it is called an equilateral triangle. The angles of a triangle can also vary, and they always add up to 180 degrees. Triangles can have acute angles (less than 90 degrees), right angles (exactly 90 degrees), or obtuse angles (greater than 90 degrees).

According to given information :

Ratio of short to long sides:

x/9 = 9/4

To solve for x, we can cross-multiply:

4x = 9 * 9

4x = 81

x = 81/4

So the ratio of the short side to the long side is:

x/9 = (81/4) / 9 = 81/36 = 9/4

Ratio of hypotenuse to long sides:

y/9 = 15/12

To solve for y, we can cross-multiply:

12y = 9 * 15

12y = 135

y = 135/12 = 45/4

So the ratio of the hypotenuse to the long side is:

y/9 = (45/4) / 9 = 45/36 = 5/4

Therefore, the ratio of the short side to the long side is 9/4 and the ratio of the hypotenuse to the long side is 5/4.

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