Rewrite (2+3)+4 using the Associative Law of Addition

The temperature on the Fahrenheit scale is 107.6°F and Kelvin scale is 315.15K. The solution has been obtained by unit conversion.

What is unit conversion?

The same attribute is expressed using a unit conversion, but in a different unit of measurement. For instance, instead of using hours to represent time, you might use minutes, or you could use feet instead of miles to express distance. Measurements are frequently offered in one set of units, like feet, but are required in another set, like chains.

We are given the melting point of an unknown solid to be 42.0°C.

For converting the given temperature in Fahrenheit, we use the given formula:

⇒(Temperature in Celsius × 9/5) + 32 = Temperature in Fahrenheit

So,

⇒(42°C × 9/5) + 32 = x°F

⇒(42°C × 9/5) + 32 = 107.6°F

Now, for converting the given temperature in Kelvin, we use the given formula:

⇒Temperature in Celsius  +  273.15 = Temperature in Kelvin

This is because 0°C = 273.15 K

So, 42°C + 273.15 = 315.15K

Hence, the temperature on the Fahrenheit scale is 107.6°F and Kelvin scale is 315.15K.

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The interest rate of the bank R is 2.5% and interest rate of the bank Q is 3%.

What is compound interest?

Compound interest is calculated on the principal as well as the interest accumulated over the previous period. It differs from simple interest in that interest is not added to the principal when calculating interest for the following period.

Here the given equation represents the amount in compound interest.

Using compound interest formula then

=> A = P[tex](1+\frac{R}{100})^n[/tex]

According to the question the equation for trust bank is

=> R =350 [tex](1+0.025)^n[/tex]

comparing with compound interest formula then

=> [tex]\frac{R}{100}= 0.025[/tex]

=> R = 0.025× 100 =2.5%

Now the equation of other bank is

=> Q = 350[tex](1+0.03)^n[/tex]

Comparing with compound interest formula then

=> [tex]\frac{R}{100}= 0.03[/tex]

=> R = 0.03×100 = 3%

Hence the interest rate of the bank R is 2.5% and interest rate of the bank Q is 3%.

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A researcher plans to use a random sample of n = 500 families to estimate the mean monthly family income for large population. A 99% confidence interval based on the sample would be  wider and would involve a smaller risk of being incorrect  than a 90$ confidence interval.

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Answer:

9

Step-by-step explanation:

The Total surface area of a pyramid formula = ½ pl + B, Where 'p' is the perimeter of the base and 'l' is the slant height of the pyramid and B is the area of the base.

A pyramid's volume can be calculated by multiplying the base area by the height, then dividing the result by three. The formula V=13Bh, where B is the area of the pyramid's base and h is its height, is used to express this product.

A triangular pyramid, for instance, has a base area of 20 cm2 and a height of 9 cm. The formula V = (1/3) Bh, where "B" stands for the base area and "h" for the height of the pyramid, is used to calculate the volume of a pyramid.

We can use the formulas for the area of polygons to calculate "B" because we know that the base of a pyramid can be any polygon. A pyramid with a triangle base is referred to as a triangular pyramid. 

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The value of x is 2, when the volume of pyramid is 125 cm³ which is equal to [tex]\mathrm{5^{\tfrac{x}{6}} }[/tex].

A pyramid's volume can be calculated by multiplying the base area by the height, then dividing the result by three. The formula V=1/3Bh, where B is the area of the pyramid's base and h is its height, is used to express this product.

We know that pyramid's volume is

[tex]\mathrm{{\textstyle V={\tfrac {1}{3}}Bh}}[/tex]

B = base area = [tex]25^{1/4} \times25^{1/4}[/tex]

= [tex]\sqrt[4]{25} \times \sqrt[4]{25}[/tex]

= [tex]\sqrt[4]{25}^2[/tex]

= [tex]\sqrt[2]{25}[/tex]

= 5 cm²

and

h = 75 cm

[tex]$\mathrm{{\textstyle V={\dfrac {1}{3}} \times5 \times 75}}[/tex]

V = 125 cm³

Now it is given that  [tex]\mathrm{5^{\tfrac{x}{6}} = 125 }[/tex]

So,

[tex]\mathrm{5^{\tfrac{x}{6}} = 125 }[/tex]

[tex]\mathrm{5^{\tfrac{x}{6}} = \sqrt[3]{5} }[/tex]

[tex]\mathrm{5^{\tfrac{x}{6}} = 5^{\tfrac{1}{3}} }[/tex]

[tex]\dfrac{x}{6} = \dfrac{1}{3}[/tex]

3x = 6

x = 6/3

x = 2

Thus, the value of x is 2, when the volume of pyramid is 125 cm³ which is equal to [tex]\mathrm{5^{\tfrac{x}{6}} }[/tex].

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16 is  Median a sample with data values .

What is the mathematical median?

The middle number, or median, is obtained by sorting all of the data points and choosing the center one (or if there are two middle numbers, taking the mean of those two numbers).

                                 Example: Because the number 4 is in the middle when the numbers are ordered (1, 4, 7), it is the median of 4, 1, and 7.

Mean = Total of values/ Total number of observations

Total of values = 10+20+12+17+16 = 75

Total number of observations = 5

Mean = 75/5 = 15

Median:

Arrange in ascending order = 10, 12,16,17,20

Median = [n+1] / 2

N = number of observation = 5

Median = [5+1]/2 = 3rd observation

Median = 16

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The value of the expression 84.7 divided by 14 will be 6.05.

It is important to note that an expression is simply used to show the relationship between the variables that are provided or the data given regarding an information.

In this case, it is vital to note that they have at least two terms which have to be related by through an operator. Some of the mathematical operations that are illustrated in this case include addition, subtraction, etc.

The value of the expression 84.7 divided by 14 will be:

= 84.7 / 14

= 6.05

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Answer: The width of the floor space covered by 38 boards with 7 3/4-in exposed surface each is 298 inches.

To find this, you would multiply the number of boards (38) by the width of the exposed surface of each board (7 3/4 inches).

38 x 7.75 = 298 inches.

Step-by-step explanation:

The proportion of voters who favor stem cell research can be estimated by taking a survey and calculating (Number of voters who favor stem cell research / Total Number of voters) x 100.

Proportion of favor stem cell research = (Number of voters who favor stem cell research / Total Number of voters) x 100

In order to estimate the proportion of voters who favor stem cell research, a survey has to be taken. Suppose the survey results indicate that out of a total of 500 voters, 300 of them favor stem cell research. Then, the proportion of favor stem cell research would be calculated as follows: Proportion of favor stem cell research = (300/500) x 100 = 60%. This means that 60% of the total voters favor stem cell research.

The proportion of voters who favor stem cell research can be estimated by taking a survey and calculating (Number of voters who favor stem cell research / +++Total Number of voters) x 100.

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The biggest angle in the triangle is opposite the largest side, which is how they actually relate to one another. The right answer is D.

A triangle's characteristics are:

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Line segment AB is congruent to line segment CD, ∠A ≡ ∠C, BE is congruent to DE and AE is congruent to CE in triangle ABE and triangle CDE. So all the first four options are corresponding parts of the two congruent triangles.

Therefore, the answer is e. None of the above.

Corresponding parts of congruent triangles are any pair of matching or identical elements in two congruent triangles. These can include:

Sides, such as line segment AB being congruent to line segment CD

Angles, such as ∠A being congruent to ∠C

Vertices, such as point E being the intersection of segments BD and AC in both triangles

Any other element that is identical in both triangles, like height, medians, circumcenters, etc.

In triangle ABE ≡ triangle CDE, congruent sides are

AB ≡ CD

BE ≡ DE

AE ≡ CE

Congruent angles are

∠A and ∠C

∠B and ∠D

∠BEA and ∠DEC

--The question is not readable, answering to the question below--

"Which of the following are not corresponding parts of the congruent triangles, triangle ABE and triangle CDE? Segments BD and AC intersect at point E to form one vertex and two sides of each triangle.

a. line segment AB is congruent to line segment CD

b. ∠A ≡ ∠C

c. BE is congruent to DE

d. AE is congruent to CE

e. None of the above"

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By completing squares we will see that the solutions of the quadratic equations is:

x = -4 ± √10

Here we want to solve the quadratic equation:

x^2 + 8x + 6 = 0

Remember the perfect square trinomial:

(a + b)^2 = a^2 + 2ab + b^2

We can rewrite the quadratic equation as:

x^2 + 2*4x + 6 = 0

To complete squares we need to add 4^2 = 16 in both sides, then we will get:

x^2 + 2*4x + 16 + 6 = 16

(x + 4)^2 + 6 = 16

(x + 4)^2 = 16 - 6

(x + 4)^2 = 10

x = -4 ± √10

That is the solution.

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As a result, the angle's measure is 135° and its supplement is 45°.

Two angles are referred to as supplementary angles when the sum of their measures is 180 degrees.

For instance, 70 degrees and 110 degrees complement one another.

Two angles are said to be supplementary if their sums total 180 degrees.

A linear pair's two angles, are always supplementary.

Let x be the angle's measurement. If so, (180x) is the size of its supplementary angle.

Now, calculate:

180 - x = 1/3x

3(180 - x) = x

4x = 540

x = 135

Supplementary angle = 180 - 135 = 45°

Therefore, as a result, the angle's measure is 135° and its supplement is 45°.

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Step-by-step explanation:

The correct option is A

Because,

A Binomial is defined as a polynomial containing 2 terms in it.

In option c there are three terms they are x, 2[tex]y^{2}[/tex], -7

In option A There are only two terms That satisfy the definition of binomial.

The walkway encircling the garden has a 64-square-foot area.

The area is the entire amount of space occupied by a flat (2-D) surface or an object's form. On a sheet of paper, draw a square using a pencil. It has two dimensions. The area of a form on paper is the area that it occupies.

Given, A garden is rectangular with a width of 7 feet in a length of 9 feet.

From the general formula of Area:

Area = Length * width

Area of garden = 7 * 9

Area of garden = 63 Square feet

Perimeter of garden = 2(length * width)

Perimeter of garden = 2(7 + 9)

Perimeter of garden = 32

Since a 2 feet wide rectangular sidewalk is made surrounded the garden So, the area of the walkway will be

Area of walkway = perimeter * width

Area of walkway = 32 * 2 = 64

Therefore, the area of the walkway surrounding the garden is 64 square feet.

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The area of R can be calculated using the definite integral of the function y = 2x^2 -6x +4 and  between g(x ) = cos1/4 and x = 4.

The integral expression is ∫(2x^2)-6x+4dx = ∫e^u du = e^u + C = e^(2x-x^2) + C. Evaluating the integral between x = 0 and x = 1 gives the area of R as e^2 - 1.

(b) The area of S can be calculated using the definite integral of the function y = e^(2x-x^2) between x = 0 and x = 1, minus the integral of the function y = 1 between x = 0 and x = 1. The integral expression for S is ∫e^(2x-x^2)dx - ∫1dx = ∫e^u du - x = e^u + C - x = e^(2x-x^2) + C - x. Evaluating the integral between x = 0 and x = 1 gives the area of S as e^2 - 1 - 1.

(c) The volume of the solid generated when R is rotated about the horizontal line y = 1 can be found using the integral expression ∫2πx(e^(2x-x^2) - 1)dx. This expression represents the area of the circular cross-sections of the solid multiplied by 2πx, which is the circumference of the circle. When evaluated between x = 0 and x = 1, this integral gives the volume of the solid generated when R is rotated about the horizontal line y = 1.

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Answer:

see i have a same solution not exactly though

Step-by-step explanation:

so check and solve good luck

Answer:

c

Step-by-step explanation:

because y = 0 when x = 2 and y = -4 when x =0

Time intervals that t will occur using the mean value theorem of calculus are (4,5) and (5,6)

What is mean value theorem ?

The Mean Value Theorem states that if a function f is continuous on the closed interval [a,b] and differentiable on the open interval (a,b), then there exists a point c in the interval (a,b) such that f'(c) is equal to the function's average rate of change over [a,b].

The property of derivative  : r'(t) is the rate of change of water flow.

Justification :

r(s) - r(4) = r'(3) (5-4)

        - 5 = r(3)

In (4,5) , r(t) decreasing , so there are value of 3 and r'(3) > 0 , r'(3) = -5.

r(6) - r(5) = r'(3) (6-5)

          4  = r'(3)

In (5,6), r(t) increasing , so there are values of 3 and r'(3) > 0, r'(3) = 4.

∴ Time intervals that t will occur using the mean value theorem of calculus are (4,5) and (5,6)

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The complete question is :

Water is flowing into a tank at a rate of r(t) where t is measured in seconds. Is there ever a time where the r'(t) = 0? If so, what time interval does t occur in? Justify your answer using the Mean Value Theorem.

In given word problem the possibility for 3 non repeating digits followed by # sign is 720 ways.

What is word problem?

Word problems are often described verbally as instances where a problem exists and one or more questions are posed, the solutions to which can be found by applying mathematical operations to the numerical information provided in the problem statement. Determining whether two provided statements are equal with respect to a collection of rewritings is known as a word problem in computational mathematics.

Here the gate code at your apartment complex is three numerical digits followed by the "#"sign.

There are 10 digits (0 to 9)

Compute the number of possible gate codes if each code contains non repeating digits as follows,

The first 3 place in the code must be filled by three non-repeating digits.

So, there are 10 possibility for first  digit and 9 possibility for second digit and 8 possibility for third digit.

Hence the 3 non repeating digits can occur un 10×9×8 ways.

The three non repeating digit followed by #. Then sign # can occur in only way, then,

Total possibility = 10×9×8×1 = 720 ways.

Hence the possibility for 3 non repeating digits followed by # sign is 720 ways.

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Answer:

$80.56

Step-by-step explanation:

First determine the cost of the bat after the discount.

20% of 95 = .20x 95 = 19

95-19= $76

Next, you will calculate the additional cost of sales tax.

Sales tax rate = Sales tax percent / 100 (6/100) = .06

Sales tax = List price x Sales tax rate (76 x .06) = 4.56

Total tax equals $4.56

76+4.56= $80.56

R13 fiberglass batt insulation, typically used in walls and floors, is 3 5/8 inches thick, according to Energy.gov.

To determine the number of insulation batts required, first determine the area to be insulated in square meters (m2). Calculating the square metre (m2) area of your walls is actually fairly simple; simply multiply the length by the breadth.

To assess the cost of cellulose insulation for your project, first decide how much insulation you would require. To do so, divide the square footage of the space by the depth or the desired R-value. R-25 EcoTouch insulation is designed to fit snugly between outside wall wood studs. After installing cover material on one side of the cavity, friction-fit unfaced insulation between studs.

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The area of shaded region from the given figure is 278.64 when the diameter of the circle is 36m.

What is area of circle ?

area of circle can be defined as the product of pi and square of radius

and here the value of pi is 22/7 or 3.14

Given in the figure,

a circle is within square with diameter 36m .

So, we have to find the

area of a shaded region  = area of square - area of circle .

radius = d/2

radius = 36/2

radius = 18 .

= 36*36 - 3.14 * 18*18

= 1296 - 1017.36

= 278.64

Hence, The area of shaded region from the given figure is 278.64 when the diameter of the circle is 36m.

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Part (a)

[tex]42^{\circ}[/tex] since the angle intercepted by a central angle is the same as the measure of the arc.

Part (b)

[tex]21^{\circ}[/tex] by the inscribed angle theorem.

The probability that the favorite team of a randomly selected person in the group is the New York Mets is 1 / 5.

Probability is defined as the ratio of the number of favorable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.

Probability = Number of favorable outcomes / Number of samples

Given that 25 people gathered to watch a baseball game while talking they realized that 5 of them were New York Mets fans.

The probability will be calculated as:-

Probability = 5 / 25

Probability = 1 / 5

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The area of the shaded triangles is nearest to 10

The total area of the shaded triangles can be calculated using the following equation:

[tex]Total Area = (AC∧2)÷2 × (2∧n)[/tex]

Where AC is the length of the original triangle's hypotenuse and n is the number of iterations.

Given that AC = 6 and n = 100, the equation becomes

[tex]Total Area = (6^2)/2 × (2^100)[/tex]

Total Area = 18 × (2^100)

Total Area = 18 × 1.26 x 10^31

Total Area ≈ 10

Therefore, the total area of the shaded triangles is nearest to 10

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Answer:

20 for both

Step-by-step explanation:

hope this helps

The correct conversion factor is B: 5280 ft / 1 mi.

Option (B) is correct.

What is unit conversion?

Unit conversion is the process of changing a measurement from one unit to another. For example, converting meters to feet, or kilometers to miles. In order to convert from one unit to another, you need to know the conversion factor between the units, which is the ratio of equivalent values in the two units.

When converting a distance in miles to feet, you need to multiply the distance in miles by the number of feet in a mile. The conversion factor that is commonly used to convert miles to feet is 1 mi = 5280 ft.

The correct conversion factor to convert a distance of 12 mi to feet is therefore:

12 mi x (5280 ft / 1 mi) = 12 x 5280 ft

Hence, the correct conversion factor is B: 5280 ft / 1 mi.

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Answer:

WU=4.8

Step-by-step explanation:

put it in the box WU =4.8

The formula for the average hourly compensation of production workers in manufacturing is C = 40.25x + $6.81.

For example, in 1975 (x = 5), the average hourly compensation of production workers in manufacturing was calculated using the formula as follows:

C = 40.25(5) + $6.81

C = $202.81

Therefore, the average hourly compensation of production workers in manufacturing in 1975 was $202.81. The same formula can be used to calculate the average hourly compensation of production workers in manufacturing for any year since 1970.

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