Evaluate each expression for the given value of the variable. 3(2 a+5)+2(3-a) ; a=4

The diameter of the trunk of a tree is 5 times larger than the diameter of the trunk of a bush.

Given data

diameter of the trunk of a bush is 7.62 × 10^-2 meter

diameter of the trunk of a tree is 3.81 × 10^–1 meter

To achieve the comparison we divide the diameter of the trunk of a tree with the  diameter of the trunk of a bush, as follows:

= 3.81 × 10^–1 meter ÷  7.62 × 10^-2 meter

= 5

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Answer:

x= -(2y+7)/(4)

Step-by-step explanation:

4x+2y=7

4x = -2y+7

x= -(2y+7)/(4)

Answer:

x = [tex]\frac{7-2y}{4}[/tex]

Step-by-step explanation:

4x + 2y = 7 ( subtract 2y from both sides )

4x = 7 - 2y ( divide both sides by 4 )

x = [tex]\frac{7-2y}{4}[/tex]

Answer:

hii

Step-by-step explanation:

18.75 answer

is

correct

Triangle classification will always help us to prove congruency in triangle. Each of the three angles in an acute triangle is acute. One right angle and two acute angles make up a right triangle. Additionally, an obtuse triangle has two acute angles and one obtuse angle.

The triangles are congruent when two sets of corresponding sides and the corresponding angles between them are in agreement. Two triangles that have a congruent angle in the middle and two congruent sides.

Instead of using the unit measure, it is based on the proportion of the side lengths to one another. As a result, triangles are categorized according to how many of their sides are the same length as one another or not at all equal.

Angles are another way to categorize triangles. Each of the three angles in an acute triangle is acute (less than 90 degrees). One right angle and two acute angles make up a right triangle. Additionally, an obtuse triangle has two acute angles and one obtuse angle (greater than 90 degrees).

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Answer: 97.7 F 32.54 F

Step-by-step explanation:

So the equation to go from Celsius to Fahrenheit is 9/5(C)+32

So it would be 9/5(36.5)+32=97.7 F

And 9/5(0.3)+32=32.54 F

The new mean is 97.7 F and new standard deviation is 32.54 C.

The term "standard deviation" (or "") refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.

The average degree of variability in your data set is represented by the standard deviation. It reveals the average deviation of each score from the mean.

Given:

Mean = 36.5 C

Standard deviation = 0.3 C

Now, converting Celsius to Fahrenheit as

= 9/5(C)+32

So, the new mean is

=9/5(36.5)+32

=97.7 F

and, new standard deviation is

= 9/5(0.3)+32

=32.54 F

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Using technology, the weighted average ROR of the investment, rounded to the nearest tenth of a percent is 2.1%

What is the weighted average ROR?

The weighted average ROR means the rate of return of the four investments combined together to give a single return, which is computed as the sum of the RORs multiplied by the percentage of total portfolio invested in each security.

total investment=$2600+$3700+$575+$1225

total investment=$8100

% invested in each security=amount invested in each security/total investment

weighted average ROR=(1.7%*$2600/$8100)+(3.2%*$3700/$8100)+(12.9%*$575/$8100)+(-5.6%*$1225/$8100)

weighted average ROR=2.1%

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Answer: 216, 36, 6, 1, 1/6, ...

Step-by-step explanation:

216, 36, 6, ...

[tex]b_1=216\\b_2=36\\b_3=6\\\displaystyle\\q=\frac{b_2}{b_1} \\\\q=\frac{36}{216} \\\\q=\frac{1}{6} \\\\q=\frac{b_3}{b_2} \\\\q=\frac{6}{36} \\\\q=\frac{1}{6} \\\\Hence,\\\\b_n=b_1q^{n-1}\\\\b_5=216*(\frac{1}{6})^{5-1}\\\\b_5=216*(\frac{1}{6} )^4\\\\b_5=216*\frac{1}{6^4}\\\\b_5=6^3 *\frac{1}{6^4} \\\\b_5=\frac{6^3}{6^4} \\\\b_5=6^{3-4}\\\\b_5=6^{-1}\\\\b_5=\frac{1}{6}[/tex]

Answer: coordinates would be 0,1 and 3,-3

Step-by-step explanation:

The infinite geometric series has the general form a1 + a1r + a1r² + a1r³ +…, where r is the common ratio and a1 is the first term. The common ratio of the geometric sequence 64, 48, 36,.... is 3/4.

The result of an endless geometric sequence exists an infinite geometric series. There would be no conclusion to this series. There would be no conclusion to this series. The infinite geometric series has the general form a1 + a1r + a1r² + a1r³ +…, where r is the common ratio and a1 is the first term.

The equation be S = a1/(1-r), where s is the total, a1 is the series's first term, and r is the common ratio, is a general formula for calculating the sum of an infinite geometric series. The formula a2/a1, where a2 is the second term in the series and a1 is the first term in the series, can be used to determine the common ratio.

Given: a1 = 64 and a2 = 48

The common ratio(r) is:

r = a2/a1 = 48/64

r = 6/8 = 3/4

Therefore, the common ratio of the geometric sequence 64, 48, 36,.... is 3/4.

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 The complete expression of the given quadratic function is:

x² + 14x + 49

   An algebraic expression is a set of numbers and letters that make up an expression that has a meaning, the letters are variables and the numbers are coefficients or independent terms, algebraic expressions can be part of an equation and model mathematical processes.

   To solve this problem we must complete square in the expression, it is necessary to note that perfect square trinomial has the form of:

(a + b)² = a² + 2ab + b²

x² + 14x + ?

where:

Substitute and find b

14x = 2xb

2b = 14

b = 7

   Let's complete the square

x² + 14x + 7²

x² + 14x + 49  

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1. Average rate of change = -1/3

2. Average rate of change = 4/3

Average rate of change = change in y /change in x.

1. Average rate of change from x = 1 to x = 4

When x = 1, y = 5

When x = 4, y = 4

Average rate of change = (4 - 5)/(4 - 1)

Average rate of change = -1/3

2. Average rate of change from x = 2 to x = 5

When x = 2, y = 3

When x = 5, y = 7

Average rate of change = (7 - 3)/(5 - 2)

Average rate of change = 4/3

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Answer:

x = 3.6

Step-by-step explanation:

since the 2 figures are similar then the ratios of corresponding sides are in proportion, that is

[tex]\frac{AD}{EH}[/tex] = [tex]\frac{AB}{EF}[/tex] ( substitute values )

[tex]\frac{x}{2.4}[/tex] = [tex]\frac{3}{2}[/tex] ( cross- multiply )

2x = 7.2 ( divide both sides by 2 )

x = 3.6

The simplified form of the expression (( 1 + 1/3 )² - 2/9) is 14/9.

Given the expression in the question;

( 1 + 1/3 )² - 2/9

Add the two terms inside the parenthesis

( (3+1)/3 )² - 2/9

( 4/3 )² - 2/9

Apply product rule to 4/3

4²/3² - 2/9

Raise 4 and 3 to the power of 2

16/9 - 2/9

Combine the numerators over common denominator

( 16 - 2 ) / 9

14/9

Therefore, the simplified form of the expression (( 1 + 1/3 )² - 2/9) is 14/9.

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Let's say 125 / 5

5 can't go into 1 so we move on to 12(if it doesn't work for twelve you move on to the next number). 5 goes into 12 twice because 5*2=10.

So the first number to our answer is 2 and we do 12-10=2. Then we bring down the 5 in 125 to make 25(from 12-10=2).

Since we are dividing by 5, 5 goes into 25 five times, so the next number to our answer is 5. 25-25=0 which means we can't divide by 5 any further so our answer is 25.

I think it's confusing but just for the points :)

Answer:

50 red apples

Step-by-step explanation:

If the ratio is 2:5

20 tomatoes ( 2 ratio)

20 ÷ 2 = 10 ( 1 ratio)

5 x 10 = 50 (5 ratio)

then there would be 50 red apples.

(o´▽`o)ﾉ x

Answer:

50 red apples

Step-by-step explanation:

the 2 part of the ratio applies to tomatoes of which there are 20, then

20 ÷ 2 = 10 ← value of 1 part of the ratio, then

5 parts = 5 × 10 = 50 red apples

The required value of x is 4 by using constant of proportion.

What is the constant of proportion?

A constant of proportion is illustrated as the ratio which relates two given quantities with each other in the relationship of proportion. Constant of proportion is also called constant variation, rate of change, and constant ratio.

Solving for the value of y

When a quantity varies directly with others, then we have a relation, y = kx, where k is the constant of the proportion      —-- 1

Now, find k for given x = 2 and y = 6, we need to put these values in equation 1, i.e.

6 = k(2)

k = 6/2

k = 3

Further calculate x for given y = 12 and constant of variation = 3 i.e.

12 = (3)x

x = 4

Hence, the required value of x is 4.

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The slope of the line that passes through the given points,

(1,3) and (6,1)= -0.4

How slope is calculated?

              [tex]\text{slope of a line between }(x_{1} ,y_{1} ) \text{ and } (x_{2} ,y_{2})=\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

             [tex]\text{slope of a line between }(1,3 ) \text{ and } (6,1)=\frac{1-3}{6-1}=-\frac{2}{5}=-0.4[/tex]

What is a slope?

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The correct option out of all these is option B: Econometrics.

Now to clear our confusion further, we will look at the basic definitions of these concepts,

A confidence interval in statistics is the probability that a population parameter falls within a range of values ​​for a specified percentage of the time.

Variance and standard deviation are very different measures from the mean, so we expect to see significant differences in how they are estimated.

Econometrics is a statistical and mathematical analysis of economic relations and is often the basis for economic forecasting. Governments may use such information to set economic policies and private companies to support pricing, inventory, and production decisions. However, economists mainly use it to study relationships between economic variables.

So, option B is Correct Econometrics.

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The first five terms of an arithmetic sequence with first term 3 and common difference 7 are 3, 10, 17, 24, 31

The given parameters:

a₁ = 3, d = 7

d is the common difference, hence, the given sequence is an arithmetic sequence.

In an arithmetic sequence, the formula for the nth term is given by:

      a(n) = a(1) + (n - 1) . d

We can also find the terms using recursive formula. The nth term of an arithmetic sequence is equal to the (n-1)th term plus the common difference, d. Mathematically,

      a(n) = a(n -1) + d

Let us start from n = 1

a(1) = 3  (given)

a(2) = a(1) + d = 3 + 7 = 10

a(3) = a(2) + d = 10 + 7 = 17

a(4) = a(3) + d = 17 + 7 = 24

a(5) = a(4) + d = 24 + 7 = 31

Thus, the first five terms are 3, 10, 17, 24, 31

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Answer:

5

Step-by-step explanation:

it's because one shelf is 40 then the second shelf is 80 and then the third is 5.

Answer:

1)  y = 6

2) Paul has 20 quarters

Step-by-step explanation:

After calculating we have come to find that  [tex]\frac{1 + 2 \sqrt3 }{2}[/tex]  is the rationalized form of the expression 1/2 + √3

Rationalizing is the process of multiplying one surd by another similar surd to produce a rational number. The rationalizing factor is the surd used to multiply (RF).

We rationalize the denominator to make it easier to perform any calculation on the rational number. When we rationalize the denominator of a fraction, we remove any radical expressions from the denominator, such as square roots and cube roots.

We have been asked to rationalize 1/2 + √3

⇒ 1/2 + √3

=  [tex]\frac{1 + 2 \sqrt3 }{2}[/tex]

As the denominator is a rational number  1/2 + √3 has been rationalized

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Answer:

276

Step-by-step explanation:

so since there is 3 section we know that it will be the same answer for the three sections then if it's 8 rows with 8 in each it would be 8x8=64 then since it's three sections 64 x 3= 192 that's the total of band then you repeat the process with dancers with will give you the total of 276

Given the area, the equation that Noor should use to determine the width of pen is x² + 3x = 70.

The length and width of the rectangular pen are 10m and 7m respectively.

The area of a rectangle is expressed as;

A = l × w

Where l is length and w is width.

Given the data in the question;

Let the width of the rectangular pen be 'x'

To determine the equation that Noor will use to find the width of the pen, plug the values into the equation above.

A = l × w

70 = (x+3) × x

70 = x² + 3x

x² + 3x = 70

We can go further and solve for the width of the pen.

x² + 3x = 70

x² + 3x - 70 = 0

Factor sing AC method; find two integer whose addition gives 3 and multiplication gives -70.

-7 and 10

(x-7) (x+10) = 0

x - 7 = 0, x + 10 = 0

x = 7, x = -10

But the dimension of the width can not be negative.

Hence

x = 7

Width = x = 7m

Length x + 3 = 7 + 3 = 10m

Given the area, the equation that Noor should use to determine the width of pen is x² + 3x = 70.

The length and width of the rectangular pen are 10m and 7m respectively.

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Answer:

B. will take 7.5 more days

Answer:

There is nothing to answer.