Find the length of an arc on a circle of radius 7 corresponding to an angle of 45∘.
Arc length =

Give an exact answer as a fraction, not a decimal approximation.

The volume of fuel in the tank after 6 hours is 97.5 gallons.

To find the volume of fuel in the tank after 6 hours, we need to integrate the rate of change of the volume, given by V′(t)=4t/√(t^2+33), with respect to time from the initial time of t=√7 hours to t=6 hours.

The integral of V′(t) with respect to t is V(t)= 2/3 (t^3 + 33t) + C

We know that when t = √7 hours, the volume of fuel in the tank is 9.3 gallons. So we can use that information to find the value of the constant C.

9.3 = 2/3 (√7^3 + 33√7) + C

C = 9.3 - 2/3 (7^3/2 + 337^1/2)

C = 9.3 - 2/3 (343/2 + 337^1/2)

C = 9.3 - 2/3 (343/2 + 231)

C = 9.3 - 2/3 (574)

C = 9.3 - 382 = 5.5

Now we can substitute t = 6 into the equation for V(t) to find the volume of fuel in the tank after 6 hours.

V(6) = 2/3 (6^3 + 33*6) + 5.5

V(6) = 2/3 (216 + 198) + 5.5

V(6) = 2/3 (414) + 5.5

V(6) = 276/3 + 5.5

V(6) = 92 + 5.5 = 97.5

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Answer:

f(3) = 3

Step-by-step explanation:

f(x) = 2x - 3

f(3) = 2(3) - 3

f(3) = 6 - 3

f(3) = 3

The value of angle x based on the information given is 45°.

Geometry is a branch of mathematics that deals with shapes, angles, dimensions and sizes of different things we see in everyday life

From the image ∠BEC = 160°, ∠FED = 115° and ∠AEF = x°

∠AEC = 180 - 160 = 20° (sum of angles on a straight line)

∠DEB = ∠AEC (vertically opposite angles)

∠DEB = 20°

It should be noted that vertically opposite angles are equal just as denoted above.

x = 180 - ∠DEB - ∠FED  (sum of angles on a straight line)

It should be noted that the sum of angles that are on a straight line is 180°.

x = 180 - 20 - 115

x = 45°

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In this case, the arms of $angle ABC$ are represented by AB and AC, which are two rays that unite to make an angle. The vertex of angle $angle ABC$ is B in this case. It is the common terminal point where rays meet to form an angle.

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Answer:

20

I wish you good luck on your assignments.

If a college student plans to use a credit card to cover the cost of purchasing a $3,200 campus meal plan. The amount of interest that will be owed is: D. $564.16.

Using this formula to

I=   Pe^rt - P

Where:

I = Interest amount = ?

P = Principal = $3,200

e = Exponential

r = Rate = 12.99% or 0.1299

T =Time = 15 months/12 = 1.25

Let plug in the formula

Interest amount = ( $3,200e^0.1299× 1.25) - $3200

Interest amount = ( $3,200e^0.162375) -  $3,200

Interest amount =  $3,764.16 -$3,200

Interest amount = $564.16

Therefore we can conclude that the correct option is D.

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The coterminal angles of -464° are -104° and -824°.

Coterminal angles are the angles that have the same initial side and terminal sides.

To find the coterminal angle we add or subtract 360° from the given angle.

We have,

Angle = -464°

The coterminal angles of -464°.

(-464 + 360)° and (-464 - 360)°

Now,

(-464 + 360)° = -104°

(-464 - 360)° = 824°

Thus,

The coterminal angles are -104° and -824°.

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Table 1 is the correct answer.

Linear equations help in representing the relationship between variables such as x, y, and z, and are expressed in exponents of one degree. In these linear equations, we use algebra, starting from the basics such as the addition and subtraction of algebraic expressions.

Given: Table 1

x y

0 0

4 2

8 4

Clearly here x=2y which is proportional equation with 2 being the constant with x varying directly with the value of y

Hence, Table 1 is the correct answer.

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The percentage of people under 18 in the sample of 250 people from Ohio is higher than the percentage of people under 18 in the United States.

This can be demonstrated mathematically using the following formula: (28/250)*100 = 11.2%. This is higher than the US percentage of 23.5%, which indicates that the sample of 250 people from Ohio had a higher proportion of people under 18 than the US population as a whole. To calculate this, we can use the formula to find the difference between the two percentages: (28% - 23.5%) = 4.5%. This means that the small town in Ohio has a higher percentage of people under 18 than the national average. Therefore, it is true that the percentage of people under 18 in the small town in Ohio is higher than the national average.

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Answer:

Step-by-step explanation:

the answer if 7 yards because 21 feet divided by 3feet per yard you would get 7 yards

Answer: x < 5 and –6x + 15 < 10

Step-by-step explanation:

Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options. x < 5 –6x – 5 < 10 – x –6x + 15 < 10 – 5x A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right. A number line from negative 3 to 3 in increments of 1. An open circle is at negative 5 and a bold line starts at negative 5 and is pointing to the left.

The correct answer is B. power of the test

The probability that a test correctly rejects a false null hypothesis is referred to as the power of the test. It is a statistical measure that helps us to determine the effectiveness of a test in detecting a real difference or effect when it exists. The power of the test is generally represented by the Greek letter beta (β) and is calculated as 1-β.

A test with a high power value is more likely to correctly reject a false null hypothesis, which means it is better at detecting the real difference or effect when it exists. On the other hand, a test with a low power is more likely to fail to reject a false null hypothesis, which means it is not as effective in detecting the real difference or effect. The p-value and significance level are also statistical measures used in hypothesis testing, but they are not directly related to the power of the test.

P-value refers to the probability of observing a test statistic as extreme or more extreme as the one observed, given that the null hypothesis is true. Significance level refers to the threshold of p-value beyond which the null hypothesis will be rejected.

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Answer:

the possible classmates numbered with multiples of 5 that Jake can choose are 5,10,15,20.

Step-by-step explanation:

Multiples of 5 are numbers that are obtained by multiplying 5 by any whole number. So, to find the classmates numbered with multiples of 5, we can start by multiplying 5 by 1, then by 2, 3, and so on. The first few multiples of 5 are 5, 10, 15, 20, 25 and so on. Since the students are numbered from 1 to 24, only students whose numbers are less than or equal to 24 can be chosen.

So the possible classmates numbered with multiples of 5 that Jake can choose are 5,10,15,20.

Therefore , we can conclude from answering the given question of equation that dy/dx =2t² = > dy/dxat (5,3) = -2 is the solution to the following problem.

An equation is an mathematical formula that joins two statements with the equivalent symbol = to express equality. In algebra, an equation is defined as a formula that asserts that two formulae are equivalent. For instance, an equal sign separates the components three times + 5 and 14 in the equations 3x + 5 = 14. In mathematical formulas, especially equations, the equal sign is a necessary varaibles. Equations frequently make use of algebra. When we don't have a precise quantity to compute in math, algebra is used.

Here,

In this instance,

x=5 + In(t)

=>y=t² + 2

=> dx/dt=1/t

=>dy/dt=2t

=>dy/dx=2t²

=> dy/dx at (5,3) = -2

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The possible values for the number of hours lifeguarding, is 5,4 hours  and the number of hours tutoring, is 5,6 hours that Brianna inequality equation  can work in a given week.

In Algebra, an inequality is a mathematical statement that uses the inequality symbol to depict the relationship between two expressions. An inequality sign has non-equal expressions on both sides.

Use these steps to resolve an inequality: Eliminate fractions in Step 1 by multiplying all terms by the total fractions' lowest common denominator. On both sides of the inequality, combine like phrases to simplify in Step 2. To get the unknown on one side and the numbers on the other, add or subtract the appropriate amounts.

16h + 11t ≥ 130

16*5=80, 16*4=64

11*5=55, 11*6=66

80x+55y>130

64x+66y>130

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Answer:

1) parallelogram: Yes

2) trapezoid: No

3) rhombus: No

4) rectangle: No

Step-by-step explanation:

1) A parallelogram has two pairs of opposite sides and no right angles. The opposite sides are parallel and equal in length, but the adjacent sides are not the same length.

2) A trapezoid's opposite sides are parallel but not equal.

3) All sides of a rhombus are equal.

4) The four sides of a rectangle are right-angled.

Answer:

B) 70

Step-by-step explanation:

Answer:

Hope this helped thanks

The way that the definitions of the absolute value of a number, connect is that the absolute value of a number is the positive representation of the number's distance from zero.

The absolute value of a number is the numerical value of a real number without regard to its sign. In other words, the absolute value of a number is the number's distance from zero on the number line. The absolute value of a number is always positive or zero, and is written as the number inside of absolute value notation, which is two vertical lines on either side of the number, like so: |number|. For example, the absolute value of -5 is 5, and the absolute value of 5 is also 5.

The distance from zero is the same as the magnitude of a number, and the absolute value of a number is a non-negative representation of its magnitude. So, in other words, the absolute value of a number is its distance from zero on the number line. The two definitions are connected because the absolute value of a number is a positive representation of its distance from zero.

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Regardless of the sign of the inequality, the domain and range of a linear inequality are always all real numbers.

Regardless of the inequality's sign, the domain and range of a linear inequality always include all real numbers. The vertex will determine the scope of the absolute value inequality. Intervals of the x values derived from zeros will decide the domain and range for polynomial inequalities.

The domain of the function is all values of x that are larger than or equal to zero, and we would write Read as an inequality if it were a mathematical statement. Inequalities is a good place to learn more about them. The identical function has a domain of in 'interval notation'. This is used to define the range of numbers from 0 to positive infinity.

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Answer:

53, 4, -12

Step-by-step explanation:

Let the first, second, and third integers be a, b, and c, respectively.

a + b + c = 45

a + b = c + 69

c = a - 65

Using the third equation, substitute the value of c, a - 65, for c in the first two equations.

a + b + a - 65 = 45

a + b = a - 65 + 69

2a + b = 110

b = 4

2a + 4 = 110

2a = 106

a = 53

c = a - 65

c = 53 - 65

c = -12

a = 53; b = 4; c = -12

Answer: 53, 4, -12

For the values running between (0, 0.177) ∩ (2.057, ∝) the speed of the particle moving with velocity v(t)=-t³+2t²+2^(-t) will be increasing.

Here we are given an equation of the velocity of the particle to be

v(t)=-t³+2t²+2^(-t)

Now taking the first derivative of v(t) and equating it to 0 we get

v'(t) = -3t² + 4t - 2^(-t)log2 = 0

Using Shreedharachara's method of solving quadratic equations we get the values of t to be

1.25635 and 0.17634

Now these 2 values are the points of inflexion, hence we will now take values a little lesser and greater than these 2 values to determine the increasing points of the function

Let's consider 0.16, 0.18, and 1.3

v'(0.16) = -0.0572

v'(0.18) = 0.0109

v'(1.3) = -0.152

Hence here we see that the values of the first derivative will be negative

for (0, 0.177) ∩ (2.057, ∝)

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It can be concluded that there is a significant linear relationship between weight and rolling distance at a 0.05 level of significance.

From the question, we have the following parameters that can be used in our computation:

Weight (lbs.) Rolling Distance (m.)

59 26

84 43

97 48

56 20

103 59

87 44

88 48

92 46

53 28

66 32

71 39

100 49

Using a graphing calculator, we have the following summary:

t = 2.739

df = 10

p-value = 0.0208

The p value is less than 0.5

So, we accept the alternative hypothesis

Hence, there is a significant relationship

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The possible real number for the variable s is 39.3 (letter D).

It is common in math solutions, you multiply a number by itself.  See the examples below.

2 x 2 =4

3 x 3 = 9

4 x 4 = 16

In math, you can use the power to represent a multiply a number by itself using the operation power. Let's consider the previous example for a better understanding.

2 x 2 = 2²

3 x 3 = 3²

4 x 4 = 4²

Therefore, the power represents the number of times the numeral repeats in a product. It is important to know that the inverse operation of power is the root. Thus,

2²=4 and [tex]\sqrt{4}[/tex]= 2

The question asks you the possible value of s.

If  [tex]4 < \sqrt{s}[/tex], you can apply power operation on both sides, for eliminating the root.

[tex](4)^2 < (\sqrt{s})^2\\ \\ 16 < s[/tex]

Another inequality is [tex]\sqrt{s} < 9[/tex]. Then, one more time you will apply power operation on both sides, for eliminating the root.

[tex](\sqrt{s})^2 < (9)^2 \\ \\ s < 81[/tex]

Combining the intervals you have: 16< s< 81.  Now, let's analyze the given options.

A. 2.5  - It is not contained in the given range 16< s< 81.

B. 7.6  - It is not contained in the given range 16< s< 81.

C. 12.7 - It is not contained in the given range 16< s< 81.

D. 39.3 -  It is contained in the given range 16< s< 81.

E. 82.4 - It is not contained in the given range 16< s< 81.

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Answer:

(4,-3)

Step-by-step explanation:

The point at which the line’s cross is the solution

Associative property of addition is applied in adding the polynomials to give

5x² + 5x + 9

According to the associative property of addition, altering how the addends are grouped has no effect on the sum.

This is applied in the addition of the given polynomial (3x + 4) + ((5x² - 1) + (2x + 6))

Addition of the polynomial

= (3x + 4) + ((5x² - 1) + (2x + 6))

= (3x + 4) + (5x² + 2x + 5)

= 5x² + 2x + 3x + 5 + 4

= 5x² + 5x + 9

altering the addends

= (5x² - 1) + ((3x + 4) + (2x + 6))

= (5x² - 1) + (3x + 4 + 2x + 6)

= 5x² - 1 + 5x + 10

= 5x² + 5x + 9

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Variable x isb5 is the answer to the equation 6 is 3x - 9 in the given situation.

A mathematical statement is considered to be an equation if it contains at least two terms with equal amounts of variables or integers.

We can start by focusing on the variable on one side of equation 6 = 3x - 9 in order to find a solution. We may accomplish this by adding 9 to both sides, giving us:

6 + 9 = 3x

Simply put, this means:

15 = 3x

The next step is to divide the equation's two sides by 3, which will yield the answer to the question "what is x?"

15/3 = 3x/3

We obtain 5 = x by simplifying.

Consequently, x = 5 is the answer to the variable.

The complete question is,

Locate the answer to the variable in the following equation. Use entire sentences to describe the problem-solving procedure you used to come up with a solution, and be sure to present all of your efforts. Include two words from the word bank at the very least.

6 = 3 x - 9.

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The total trip cost approx $140

The unitary method is a method in which you find the value of a unit and then the value of a required number of units.

Given here: Mr. Luthi took 30 passing students and they each get a pizza and a ice cream. let the cost of the ticket be t then we have

Cost = 30t+90

Similarly for Mr. Byers students the total cost is=12t+120

Now as per question they paid the same amount for the field trips '

Thus we have, 30t+90= 12t+120

                         18t=30

                             t=$1.66

Thus 12t+120= 140(approx)

Hence, The total trip cost approx $140

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The system of graphs is a very unique concept which helps to understand various concepts in a visual way.

How does this occur?

The two lines intersect at (-3, -4), which is the system of equations' solution.

This is how the equation can be solved-

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