The prime number 7 is the average of which two different numbers?

The indefinite integral is [tex]$\\{\frac{(2 x+5)^{10}}{40}-\frac{5}{36}(2 x+5)^9+C}{}$$[/tex].

The indefinite integral is [tex]& \int x(2 x+5)^8 d x[/tex]

u=2x+5

du=(2)dx.

[tex]& x=\frac{u-5}{2} \\[/tex]

An integral which is not having any upper and lower limit is known as an indefinite integral.

Mathematically, if F(x) is any anti-derivative of f(x) then the most general antiderivative of f(x) is called an indefinite integral and denoted,

Where,

Anti derivatives or integrals of the functions are not unique. There exist infinitely many antiderivatives of each of certain functions, which can be obtained by choosing C arbitrarily from the set of real numbers. For this reason, C is customarily referred to as an arbitrary constant. C is the parameter by which one gets different antiderivatives (or integrals) of the given function.

[tex]& \Rightarrow \int\left(\frac{u-5}{2}\right) u^8\left(\frac{1}{2}\right) d u \text {. } \\[/tex]

[tex]& \Rightarrow \quad \frac{1}{4} \int\left(u^9-5 u^8\right) d u \\\\& \Rightarrow \quad \frac{1}{4}\left[\frac{u^{10}}{10}-\frac{5 u^9}{9}\right] \\&[/tex]

Then differentiative u=2x+5  is

[tex]$\\{\frac{(2 x+5)^{10}}{40}-\frac{5}{36}(2 x+5)^9+C}{}$$[/tex]

Therefore, the integral is [tex]$\\{\frac{(2 x+5)^{10}}{40}-\frac{5}{36}(2 x+5)^9+C}{}$$[/tex]

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Answer:

Step-by-step explanation:

lol

Answer:

[tex]x^{4}[/tex] + 2x²y² + [tex]y^{4}[/tex]

Step-by-step explanation:

(x² - y²)² + 4x²y²

= (x² - y²)(x² - y²) + 4x²y²

= x²(x² - y²) - y²(x² - y²) + 4x²y² ← distribute parenthesis

= [tex]x^{4}[/tex] - x²y² - x²y² + [tex]y^{4}[/tex] + 4x²y² ← collect like terms

= [tex]x^{4}[/tex] - 2x²y² + [tex]y^{4}[/tex] + 4x²y²

= [tex]x^{4}[/tex] + 2x²y² + [tex]y^{4}[/tex]

Based on the given function, the average temperature in the town between 3 A.M. (t= 3) and 6 A M. (t = 6), in degrees Fahrenheit is 57.797°. (Option B)

The temperature, in degrees Fahrenheit, in a small-town t hours after midnight (t 0) is modeled by the function g(t)= 65 - 8 sin (πt/12). Hence, the average temperature in the town between 3 A.M. (t= 3) and 6 A M. (t = 6), in degrees Fahrenheit is given by:

1/((6-3)) ∫_3^6▒〖(65-8 sin⁡(πt/12)dt〗

65/3 t+  32/π  cos⁡(πt/12)

(65π-16√2)/π

57.797

Note: The question is incomplete. The complete question probably is: On a certain day, the temperature, in degrees Fahrenheit, in a small-town t hours after midnight (t 0) is modeled by the function g(t)= 65 - 8 sin (πt/12). What is the average temperature in the town between 3 A.M. (t= 3) and 6 A M. (t = 6), in degrees Fahrenheit? A) 57.609° B) 57.797° C) 58.172° D) 59.907°.

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Answer:

[tex]1.\ (x - 1)^2 + (y + 4)^2 = 4\\2.\ (x + 2)^2 + (y -5)^2 = 36[/tex]

[tex]\textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \hspace{5em}\stackrel{center}{(\underset{1}{h}~~,~~\underset{-4}{k})}\qquad \stackrel{radius}{\underset{2}{r}} \\\\[-0.35em] ~\dotfill\\\\ ( ~~ x - 1 ~~ )^2 ~~ + ~~ ( ~~ y-(-4) ~~ )^2~~ = ~~2^2\implies {\large \begin{array}{llll} (x-1)^2+(y+4)^2=4 \end{array}}[/tex]

now as for the 2nd one, we know the center and a point on it, well, what's the radius?  well, recall that for a circle the radius is simply the distance from the center to the circle in proper, so the distance between those two points is the radius

[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ C(\stackrel{x_1}{-2}~,~\stackrel{y_1}{5})\qquad P(\stackrel{x_2}{-2}~,~\stackrel{y_2}{-1})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ CP=\sqrt{(~~-2 - (-2)~~)^2 + (~~-1 - 5~~)^2} \implies CP=\sqrt{(-2 +2)^2 + (-1 -5)^2} \\\\\\ CP=\sqrt{( 0 )^2 + ( -6 )^2} \implies CP=\sqrt{ 0 + 36 } \implies CP=\sqrt{ 36 }\implies \stackrel{radius}{CP=6}[/tex]

so we're really looking for the equation of a circle with a center at (-2 , 5) with a radius of 6

[tex]\textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \hspace{5em}\stackrel{center}{(\underset{-2}{h}~~,~~\underset{5}{k})}\qquad \stackrel{radius}{\underset{6}{r}} \\\\[-0.35em] ~\dotfill\\\\ ( ~~ x - (-2) ~~ )^2 ~~ + ~~ ( ~~ y-5 ~~ )^2~~ = ~~6^2\implies {\large \begin{array}{llll} (x+2)^2+(y-5)^2=36 \end{array}}[/tex]

Answer:

x = 9

Step-by-step explanation:

The exterior angle of a triangle is equal to the sum of the opposite interior angles.

<3  = <1 + <2

5x+4 = x+1   + 39

Combine like terms

5x+4=x+40

Subtract x from each side

5x-x+4=x-x+40

4x+4 = 40

Subtract 4 from each side

4x+4-4 = 40-4

4x = 36

Divide by 4

4x/4 = 36/4

x = 9

Answer:

x = 12

Step-by-step explanation:

We know that,

The exterior angle of a triangle equals to the sum of opposite interior angles.

Accordingly,

[tex] \angle \: 1 + \angle \: 2 = \angle \:3[/tex]

That is,

x + 13 + 39 = 5x + 4

Combine like terms.

x + 52 = 5x + 4

Subtract x from both sides.

52 = 5x - x + 4

52 = 4x + 4

Subtract 4 from both sides.

52 - 4 = 4x

48 = 4x

Divide both sides by 4.

12 = x

Use the equation area = 1/2 * base * height to get a triangle's surface area. Decide which side will serve as the triangle's base, and then calculate the triangle's height from that base.

Calculating the area of triangles. Use the equation area = 1/2 * base * height to determine the area of a triangle. Determine the triangle's height from the base by picking a side to serve as the base.

The space encircled by a triangle's three sides is known as its area. According to the type of triangle, it is computed using a variety of formulas and expressed in square units like cm2, inches2, and so on.

If the base and height of the triangle are known, the area of the triangle may be computed. The area of a triangle is calculated using the following fundamental formula: Area of triangle = 1/2 (base height).

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The total number of dried fruits are 21, while the total number of nuts are 33 and the total pieces are 18.

As per the given data in the question, there are 54 total fruits in the bag, mixed in a ratio of 11 to 7.

Here we have to determine the total number of dried fruits and total number of nuts.

First, we have to find the percentage of nut or dried fruit present.

The ratio of fruits to nuts be 7 : 11.

The total pieces are:

7 + 11 = 18

This means that the percentage would be

[tex]\frac{7}{18}[/tex] = 38.889%

[tex]\frac{11}{18}[/tex] = 61.111%

This is the ratio in which they are shared. Then we move on to calculate the final contents of the bag.

[tex]\frac{7}{18}[/tex]  × 54 = 21 fruits

[tex]\frac{11}{18}[/tex]  × 54 = 33 nuts

This means that there are 33 nuts in the bag, to 21 dried fruits.

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Ren has a bag of trail mix made of 54 total pieces of nut or dried fruit. There are 11 nuts for every 7 fruits. Calculate the total number of dried fruits, the total number of nuts and the total pieces?

There are 77 number of nuts in the bag.

To find the number of nuts in the bag of trail mix, we must first calculate the total number of fruits in the bag. Since the bag contains 54 pieces of nuts or dried fruits, and there are 11 nuts for every 7 fruits, we can divide 54 by 7 to find the number of fruits. This yields 7.714, which, when rounded to the nearest whole number, is 8. We then multiply 8 by 11 to find the number of nuts in the bag. 8 x 11 = 88. Thus, there are 77 nuts in the bag.

Fruits = 54 / 7  = 7.714 (rounded to 8)

Nuts = 8 x 11 = 88

the complete questiion is : Ren has a bag of trail mix made of 54 total pieces of nut or dried fruit. There are 11 nuts for every 7 fruits. How many nuts are in the bag?

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The requried simplified value of the given expression is,
(A) 4
(B) No solution,

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

here,
Simplifying the expression, in order to get the solution,

(A)
[tex]= log_3(81)\\=log_3(3)^4\\= 4log_33 \ \ \ \ \ \ \ \{log_ee = 1}\\=4\times 1\\= 4[/tex]

(B)

[tex]2^x = 1/32x\\2^x\times 32 = x\\x = 2^x \times 2^5\\x = 2^{x + 5}\\[/tex]
A solution for this equation is not possible,

Thus, the requried simplified value of the given expression is,
(A) 4
(B) No solution,

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The value of  f(a+2) = (5 + a) / (a - 1). so the correct option is B.

In mathematics, a function is an expression, rule, or law that describes the relationship between one variable (the independent variable) and another variable (the dependent variable) (the dependent variable). In mathematics and the physical sciences, functions are indispensable for formulating physical relationships.

Now we directly substitute the a + 2 to the all the x's in the function such that,

f(a + 2) = (3 + a + 2) / (a + 2 - 3)

Then Simplifying the function generated above,

f(a + 2) = (5 + a) / (a - 1)

The correct option is B.

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Answer:

6^-14

Step-by-step explanation:

Using laws of indices you'll add the denominators power to account for multiplication

then substract it from the numerators power to get an answer which is 6×10^-14

The amount of rotation that is required to bring one side of an angle to the same position as the other is what is referred to as the measure of an angle. Degrees (°) are used as the unit of measurement for angles. One complete turn encompasses all 360 possible degrees.

There are several ways to find the measure of an angle in 8th grade geometry:

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The age of the 3 members who left the team is 65 years.

Let "x" be the age of the 3 team members who left the team.

The mean age of all the 10 members was 58 years. So, the total sum of all the 10 members ages was 580 years.

Now, the mean age of the remaining 7 members after the leaving of 3 members is 55 years. So, the total sum of the 7 remaining members ages is 385 years.

Therefore, the total sum of the 3 members who left the team is (580-385) = 195 years.

Since the 3 members are of the same age, the age of each member is (195/3) = 65 years.

Hence, the age of the 3 members who left the team is 65 years.

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The Percentage of error of the measurement is 5.1 %

The formula of percentage of error

[tex]\delta = \left| \frac{v_A - v_E}{v_E} \right| \cdot 100\%[/tex]

where

[tex]\delta[/tex] is the percent error

Va is the actual value observed

Ve is the expected value of the measurement

The percent error is the distinction between the estimated value and the actual value in relation to the actual value. In other words, the relative error or expected error is multiplied by 100 to calculate the percent error.

the percent error is

((Estimated Number - Actual Number)/ Actual number) x 100 equals percentage error.

[tex]\delta = \left| \frac{4.1- 3.9}{3.9} \right| \cdot 100\%[/tex]

=> 0.2 / 3.9 x 100

=> 0.0512 x 100

=> 5.12%

The percentage error in the measurement is 5.1%

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The percent error of the measurement is 5.1%, to the nearest tenth of a percent.

To calculate the percent error of the measurement, the formula is:

(|Actual Value - Measured Value|/Actual Value) * 100 = Percent Error

In this case, the actual value is 4.1 inches and the measured value is 3.9 inches. So the calculation is:

(|4.1 - 3.9|/4.1) * 100 = 5.1%

Therefore, the percent error of the measurement is 5.1%, to the nearest tenth of a percent.

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Answer:

Step-by-step explanation:

is that the question? what do you mean by 3

Answer:

998

Step-by-step explanation:

The possibility of three people being chosen to give a random presentation as calculated from the given data is 1 / 12.

There are 10 possibilities of selecting the required  3 people.

Using combination we can find the required probability as ,

10c3

= 10 ! / 7! x 3 !

= 10 x 9 x 8 / 3 x 2

= 120

Thus, the probability is equal to 10 / 120 = 1 / 12 .

Combination is a way of combining things in the desired manner . Other than probability we also have permutation which tells about the possibility.

Probability refers to the possibility of occurrence of an event. It is used in industries such as weather forecast.

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(111)₂ = (12)₅

The base of a number system refers to the total number of digits that are actually used in the given number system. The number system that has the base 'b' consists of its digits in the [0, b-1] range. This base of the number system is also known as the radix of a number system.

Given,

number 111 with base 2

To convert it into base 5 number we need to first convert it into decimal

(111)₂ = 1×2²+1×2¹+1×2⁰

(111)₂ = 4+2+1

(111)₂ = (7)₁₀

Now converting decimal to base 5, converting decimal numbers to base 5 is nearly as simple: just divide by 5.

(111)₂ = (12)₅

Hence, the number becomes (12)₅.

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The total members of the chess club at the school, given the number of teachers, can be found to be 25 students.

When the teachers joined the members of the chess club for a tournament, the number of members that Alan counted was 31 people which means that the number of members in the chess club would be this number, less the number of teachers.

The number of chess club students is therefore :

= Number of people counted by Alan - Number of teachers

= 31 - 6

= 25 members

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The element in the domain has image 6 under the function g(x) = 2x ÷ 3​ is 9.

The collection of possible input values is referred to as the domain, and the domain of a graph is made up of all the input values displayed on the x-axis. The collection of potential output values that make up the range is represented by the y-axis.

Given:

g(x) = 2x ÷ 3​

The image is 6,

g(x) = 6  (Given)

Calculate the value of the domain as shown below,

6 = 2x / 3

6 × 3 = 2x

x = 18 / 2

x = 9

Thus, the domain is 9.

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The area of the triangle is 6 ft^2.

What is the area of the triangle?

In a two-dimensional plane, a triangle's area is the area that it completely encloses. A triangle is a closed shape with three sides and three vertices, as is common knowledge. The entire area occupied by a triangle's three sides is referred to as its area. Half of the product of the triangle's base and height provides the general formula for calculating the area of the triangle.

The values of base (b) and height (h) of triangle is given as -

h=4 ft

b=3 ft

The formula for area of triangle is -

A = hb/2

Plugging in the values in the equation -

A = (4 x 3)/2

A = 12/2

A = 6 ft^2

Therefore, the area of the triangle is obtained as 6 ft^2.

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To find the missing side of an AAS triangle, use the Pythagorean Theorem and the known lengths of the other two sides to calculate the length of the missing side.

An AAS triangle (angle-angle-side) is a triangle where two angles and one side length are known. To find the missing side, the Pythagorean Theorem must be used. The Pythagorean Theorem states that in a right triangle, the sum of the squares of the two sides must equal the square of the hypotenuse. To use this theorem, the two known sides must be squared and added together. The resulting number must then be equal to the square of the missing side. Once the result is equal, the square root of the result will give you the length of the missing side. For example, if two sides of a triangle are given as 3 and 4, the Pythagorean Theorem can be used to calculate the missing side. Squaring and adding the two sides together (3^2 + 4^2) will result in 25. Taking the square root of this result will give you the length of the missing side, which is 5.

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The actual distances, considering the scale 4 inches = 30 miles, are given as follows:

A. 2 inches = 15 miles.

B. 7 inches = 52.5 miles.

C. 5.5 inches = 41.25 miles.

D. 10 inches = 75 miles.

The scale given is a proportion, which represents the relation between the represented distance and the actual distance.

The scale is given as follows:

4 inches = 30 miles

Meaning that each inch in the drawing represents an actual distance of 7.5 miles, as 30/4 = 7.5.

Then the actual distances for each item, in miles, are found multiplying the given distances in inches by 7.5, which is the scale factor of the scale.

For example, in item a, we have that:

2 inches = 2 x 7.5 = 15 miles.

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Using division, the length of the sandwich each friends got was 1.02083ft

Division is a mathematical operation that divides one number (the dividend) by another (the divisor) to find the answer (the quotient). It is one of the four basic operations in mathematics, along with addition, subtraction, and multiplication.

To determine the size each one got, we have to divide the total length of the sandwich by the number of friends.

We need to convert the mixed fraction into improper fraction or decimal

6 1/8 = 49/8 = 6.125

Now, let's divide this by 6

6.125 / 6 = 49/48 = 1.02083

The length each of her friends will get is 1.02083ft

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Answer:

18 pieces

Step-by-step explanation:

78 pieces to start with and she kept 24 to herself which means that she has 54 pieces of candy remaining. Assuming she gave an equal amount to each friend, the answer would be 54/3=18. So she gave 18 pieces to each friend.

Answer:The  ratios are equivalent to 8 : 12 are A 4 : 6 , D 24 : 36 and E 56 : 84.Those expressions who might look different but their simplified forms are same expressions are called equivalent expressions.What is the ratio of two quantities?Suppose that we've got two quantities with measurements as 'a' and 'b'Then, their ratio(ratio of a to b) a:bWe usually cancel out the common factors from both the numerator and the denominator of the fraction we obtained. Numerator is the upper quantity in the fraction and denominator is the lower quantity in the fraction).Suppose that we've got a = 8, and b= 12, So, the  ratios are equivalent to 8 : 12A 4 : 6D 24 : 36E 56 : 84

Step-by-step explanation:

carry on learning

You can find the equation of a dilated line by using the formula (x – m)/k = (y – n)/k

There are some steps you can take in order to find the equation of a dilated line. First, you will need to identify the coordinates of the line’s endpoints.

Then, you will need to find the midpoint of the line and the scale factor of the dilation. Once you have those two pieces of information, you can use the formula for a dilated line to find the equation.

Specifically, the equation will be (x – m)/k = (y – n)/k, where m and n are the coordinates of the midpoint and k is the scale factor.

With this formula, you can find the equation of any dilated line.

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we need for 500 grams of sugar, we can plug 500 into the equation for our value of s. This gives us f = 300 * 500/200 = 750 grams.

1. f = 300s/200

2. f = 300 * 500/200 = 750 grams

1. To write the equation, we can set up a ratio that compares the number of grams of flour to the number of grams of sugar. Since the recipe calls for 300 grams of flour for every 200 grams of sugar, we can set up the equation as f = 300s/200, where f is the number of grams of flour and s is the number of grams of sugar.

2. To find out how many grams of flour we need for 500 grams of sugar, we can plug 500 into the equation for our value of s. This gives us f = 300 * 500/200 = 750 grams.

To write the equation, we can set up a ratio that compares the number of grams of flour to the number of grams of sugar. Since the recipe calls for 300 grams of flour for every 200 grams of sugar, we can set up the equation as f = 300s/200, where f is the number of grams of flour and s is the number of grams of sugar.

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Answer:
750

Equation:
f = 3/2s

Wendel has left 144 nickels and 48 dimes to pay for a bus ticket back home.

An equation is an expression that shows the relationship between two or more numbers and variables.

Let x represent the number of nickels and y represent the number of dimes.

Each nickel is 5 cents (0.05) and each dime is 10 cents (0.1). Hence:

Wendell has $12 in nickels and dimes, hence:

0.05x + 0.1y = 12  

0.1y = 12 - 0.05x

y = 120 - 0.5x    (1)

Wendell has 3 times as many nickels as dimes, hence:

x = 3y   (2)

Using substitution method:

Substituting y = 120 - 0.5x in eqn 2 gives:

x = 3(120 - 0.5x)

x = 360 - 1.5x

x = 144

y = 120 - 0.5(144) = 48

Wendel has 144 nickels and 48 dimes.

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