The length of the arc is 5½ units
What is length of an arc?The length of an arc is the distance covered at a particular angle on the circumference of a circle.
A circumference is the external body of a circle. it is also called the perimeter of a circle
Length of an arc is given as :
l = 2 π r × (θ/360°)
where θ = angle subtended
therefore l = 45/360 × 2 × 22/7 ×7
dividing through by 45
= 1/8× 2 × 22/7 ×7
dividing through by 7
= 1/8 × 2 × 22
= 44/8
dividing through by 4
= 11/2
therefore l = 5 ½ units
This means that the length of the arc is 5 ½ unit
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Given f(x) = 2x - 3, find f(3).
Answer:
f(3) = 3
Step-by-step explanation:
f(x) = 2x - 3
f(3) = 2(3) - 3
f(3) = 6 - 3
f(3) = 3
Use a system of equations to solve the following problem.
The sum of three integers is 45. The sum of the first and second integers exceeds the third by 69. The third integer is 65 less than the first. Find the three integers.
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
Mr. Luthi is taking his 30 passing students on a field trip to the aquatic center. They will all get a ticket to
enter and swim as well as a serving of pizza and ice cream that costs $3 per student. Ms. Byer's is taking her
12 passing students on a field trip to the museum. Their tickets cost twice as much and they all get a
souvenir t-shirt for $10. Ms. Byers and Mr. Luthi paid the same amount for their field trips. How much did
tickets to each field trip cost?
The total trip cost approx $140
What is the unitary method?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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A particle moves along a line so that its velocity is given by v(t)=-t^3+2t^2+2^-t for t>0. For what values of t is the speed of the particle increasing? The answer is (0.177,1.256) and (2.057, infinity).
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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oes the name describe the quadrilateral? Choose yes or no.
A quadrilateral has two pairs of opposite sides and no right angles. The opposite sides are parallel and equal in length, but adjacent sides are not the same length.
parallelogram
Choose...
trapezoid
Choose...
rhombus
Choose...
rectangle
Choose...
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 to the graph ok
Answer:
(4,-3)
Step-by-step explanation:
The point at which the line’s cross is the solution
Question 6(Multiple Choice Worth 2 points)
(Linear Relationships LC)
Which of the following tables represents a linear relationship that is also proportional?
x y
0 0
4 2
8 4
x y
0 1
2 3
4 5
x y
0 2
3 5
6 8
x y
0 3
6 5
12 7
Table 1 is the correct answer.
What are linear equations?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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Please help I don’t understand!
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.
Describe equation.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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A college student plans to use a credit card to cover the cost of purchasing a $3,200 campus meal plan. If the credit card has annual interest rate of 12.99% compounded continuously and the student plans to pay off the loan in 15 months, how much interest will be owed? $739.25 $688.41 $588.69 $564.16
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.
How to find the interest amount?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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according to the u.s. census bureau, 23.5% of people in the united states are under the age of 18. in a random sample of 250 residents of a small town in ohio, 28% of the sample was under 18. which one of the following statements is true?
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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1/4 cup are in 4 cups
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.
What does a mathematical inequality equation mean?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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Let's be any real number such that 4 < √ s <9. Which of the following is a possible value of s?
A. 2.5
B. 7.6
C. 12.7
D. 39.3
E. 82.4
The possible real number for the variable s is 39.3 (letter D).
Power and Square RootsIt 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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The following data represent the weight of a child riding a bike and the rolling distance achieved after going down a hill without pedaling. 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 Can it be concluded at a 0.05 level of significance that there is a linear correlation between the two variables?
It can be concluded that there is a significant linear relationship between weight and rolling distance at a 0.05 level of significance.
How to determine the true statementFrom 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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What is the probability that a test correctly rejects a false null hypothesis called? Choose the correct answer below. A. P-value B. power of the test C. Type II error D. significance level
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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The definition of the absolute value of a number is its magnitude, or distance, from zero. How do these two definitions connect?
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.
What is absolute value ?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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1 2 3 4 5 6 7 8 9 10 A graph has quantity on the x-axis and price on the y-axis. Demand curve points are at (20, 70), (40, 40), (60, 10).A graph has quantity on the x-axis and price on the y-axis. A demand line goes through (20, 70), (40, 80), (60, 90). Based on the demand graph and the supply graph shown above, what is the price at the point of equilibrium? a. 100 b. 70 c. 40 d. There is not enough information given to determine the point of equilibrium. Please select the best answer from the choices provided A B C D Mark this and return
Answer:
B) 70
Step-by-step explanation:
Solve the system of equations by graphing.
y = -2
y = -3
2
x + 4
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.
Using the slope and y-intercept, graph an equation as follows:The equation y = mx + b's y-intercept can be found.Determine the y-intercept. The purpose will be (0, b).The slope=m of the equation y = mx + b can be found.Run from the slope while taking a single step using the rise.Your line should join those two spots.This is how the equation can be solved-
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Given polynomials p(x), q(x), and r(x), p(x) + ( q(x) + r(x) ) = ( p(x) + q(x) ) + r(x)
To verify the associative property of addition, begin by finding the sum of the polynomials:
(3x + 4) + ((5x2 - 1) + (2x + 6))
Associative property of addition is applied in adding the polynomials to give
5x² + 5x + 9
What is associative property of addition?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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Confusing question:
Please help quickly!
The value of angle x based on the information given is 45°.
How to determine the value of angle x?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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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.
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.
Please help me solve this question
Answer:
Hope this helped thanks
Consider the function f(x) = x ^ x + 5 with domain x >= 0 , and its Inverse , f ^ - 1 * (x) = sqrt(x) - 5 What are the domain and range of f(x) and f ^ - 1 * (x) Express the domain and range as Inequalities
Regardless of the sign of the inequality, the domain and range of a linear inequality are always all real numbers.
How do you find the domain of an inequality?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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Students in jakes class were numbered in order from 1 to 24 jake was asked to choose classmates numbered with multiples of 5 to be in his group which number could be the number of a classmate in his group
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.
Find an angle θ conterminal −464 ° , where 0 degree ≤θ<360 °
Thank you!
The coterminal angles of -464° are -104° and -824°.
What are coterminal angles?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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1) In the given figure, name (a) the vertex opposite A to side AB (b) the angle opposite to side AC (c) the angle made by the sides CB and CA.
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.
What is vertex in angle ABC?The vertex and arm of the provided ABC must be found in this question. Vertex information is required for this puzzle. Angles are formed when two rays share a terminal. The vertex is the term for the shared endpoint. Alternatively, vertex refers to the shared terminal point where two rays converge to form an angle. Likewise, we must understand what an angle's arm is. An angle's arm is made up of the two rays that unite to make it. Here, an angle of ABC was provided. Specifically, we must identify the angle's vertex and arm.The arms of the ABC formula are represented by AB and AC, two rays that unite to make an angle.The vertex of ABC is the common terminal point where rays converge to form an angle. In this case, B is the vertex.AB and AC make up the arms of ABC, and B serves as the vertex.To Learn more About vertex of angle Refer To:
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The volume of fuel in a tank changes at a rate given by the equation:
V′(t)=4t/√(t^2+33_, t≥0. At t=√7 hours the tank holds 9.3 gallons. What is the volume of fuel in the tank after 6 hours?
Round answer to one decimal place.
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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Glen is asked to convert 21 feet to yards he knows that 3 feet = 1 yard his work is shown explain glens error and show how to use a rate to find the correct solution
Answer:
Step-by-step explanation:
the answer if 7 yards because 21 feet divided by 3feet per yard you would get 7 yards
in order to graph your solutions solve for the variable be sure to show your work
Variable x isb5 is the answer to the equation 6 is 3x - 9 in the given situation.
The equation is what?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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Use the distributive property to write an equivalent expression. Then
evaluate the expression
3(2+12)
Equivalent Expression
=
John has 37 marbles for his collection. He gives 17 marbles to his friend Zach. How many marbles does he have left?
Answer:
20
I wish you good luck on your assignments.