Answer:
Average Rate of Change
Functions are relationships that exist between two variables. Graphing them allows us to observe and predict their behavior. The graph of a function is a line or curve where we can determine random values directly and identify a set of results through it.
The rate of change is one of the calculations we can determine from a graph. It is the change of the function per unit. It is deriving from the slope of the line formed in the interval. The formula for determining the rate of change is:
r
c
=
y
2
−
y
1
x
2
−
x
1
P
1
=
(
−
1
,
0
)
P
2
=
(
3
,
12
)
We use the average exchange rate formula:
r
c
=
y
2
−
y
1
x
2
−
x
1
We substitute the values, obtaining:
r
c
=
12
−
0
3
−
(
−
1
)
Solving, we obtain:
r
c
=
12
4
=
3
The average rate of change of
g
when
x
varies from
−
1
to
3
is:
R
c
=
3
a test consists of 10 true/false questions. if a student guesses on each question, what is the probability that thestudent will answer at least7questions correctly.
The probability that the student will answer at least7questions correctly then the probability is = [tex]\frac{120}{128}[/tex]
A probability is a number that reflects the chance or likelihood that a particular event will occur. Probabilities can be expressed as proportions that range from 0 to 1, and they can also be expressed as percentages ranging from 0% to 100%.
Given that,
A test consists of 10 true/false questions.
If a student guesses on each question
The probability that the student will answer at least7questions correctly.
The probability that the student answers each question correctly is 1/2, and
The probability that the student answers each question correctly is also 1/2
{Bernoalli trail}
Bernoalli trail for at least 7 times,
Probability P = [tex]C7_{10} (\frac{1}{2}) ^{7} (\frac{1}{2}) ^{7}[/tex]
Using the formula nCr = n!(n−r)!r!
= 10!(10−7)!7!
Subtract 7 from 10.
= 10!(3)!7!
Simplify 10!(3)!7!.
Rewrite 10! as (10⋅9⋅8⋅7!)
= (10⋅9⋅8⋅7! / (3)!7!)
Cancel the common factor of 7!.
Cancel the common factor.
= 10⋅9⋅8⋅7! / (3)!7!
Rewrite the expression.
= 10⋅9⋅8 / (3)!
Multiply 10 by 9.
= 90⋅8 / (3)!
Multiply 90 by 8.
= 720 / (3)!
Expand (3)! to 3⋅2⋅1.
= 720 / 3⋅2⋅1
Multiply 3 by 2.
= 720 / 6⋅1
= 720 / 6
Divide 720 by 6
= 120
So,
We can write,
P = [tex]\frac{120}{2^{7} }[/tex]
P = [tex]\frac{120}{128}[/tex]
Therefore,
The probability that the student will answer at least7questions correctly then the probability is = [tex]\frac{120}{128}[/tex]
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Billy’s mom bought pizza for 4 boys. The boys ate 3 pizzas. If each boy ate the same amount, how much did each eat
Answer:
If there are 4 boys and they ate 3 pizzas, and each boy ate the same amount, then each boy ate 3/4 of a pizza. If you want to express this as a fraction, it would be 3/4 of a pizza per boy. If you want to express it as a decimal, it would be 0.75 pizzas per boy. If you want to express it as a percentage, it would be 75% of a pizza per boy.
Let g(x) be a horizontal compression of f(x) = -x + 4 by a factor of 0.5. Write the
rule for g(x).
g(x) = 4x+4
g(x)=x-4
g(x)=0.5x-4
g(x)=-2x+4
1 pts
There is no correct answer given.
Horizontal compression of f(x) = -x + 4 by a factor of 0.5 will be -2x + 4.
What is a horizontal function?A horizontal line that a function's graph looks to coincide with but does not really do so is said to be its horizontal asymptote. The final behavior of the function is determined using the horizontal asymptote.
Given, g(x) is a horizontal compression of function f(x) = - x + 4 by a factor of 0.5. Hence,
g(x) = -x / 0.5 + 4
g(x) = -2x + 4
Therefore, By a factor of 0.5, the horizontal compression of the function (f(x)) is -x + 4 will result in -2x + 4.
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There are 35 questions total that will be posted in mathematics as this is Algebra I!
Whoever answers correctly and with an explanation will receive Brainliest when the option shows up on my end!
PLEASE ANSWER ASAP!!
Answer: x=5
Step-by-step explanation:
Answer:
(x - 1)² = 16
Step-by-step explanation:
x² - 2x - 15 = 0
x² - 2x + 1 = 15 + 1
(x - 1)² = 16
Herb and Marci Jordan obtained an installment loan that has a 10% APR to purchase a dishwasher that sells for $699. 95. They agree to make a down payment of 20% and to make 12 monthly payments. What is the finance charge?
$699.95×20%=$139.99, is the finance charge.
What is finance charge?A finance charge is any fee that reflects the cost of credit or borrowing under American law.
Some forms of credit have fees and interest that accrue over time. [1] In addition to interest, it also includes additional costs, like those for financial transactions.
The Truth-in-Lending Act and Regulation Z, which were issued by the Statutory Reserve Board, contain information about the federal definition of a finance charge.
A financing charge in personal finance is just the cash amount paid to borrow money, whereas interest is the amount paid as a percentage, such as the annual percentage rate (APR).
Compared to standard dictionary definitions or accounting definitions, these definitions are more specific.
Lenders and creditors both calculate finance charges in different ways. a majority.
Hence, $699.95×20%=$139.99, is the finance charge.
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Prove that tan(A+B)
cot(A−B)
=
2−2
2−2�
Triagonometric function tan(A+B)/cot(A−B) is tan²A-tan²B/1-tan²Atan²B
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
Given,
tan(A+B)/cot(A-B)
tan(A+B)/1/tan(A-B)
(tanA+tanB/1-tanAtanB)/1/(tanA-tanB/1+tanAtanB)
tanA+tanB/1-tanAtanB)×tanA-tanB/1+tanAtanB
We know algebraic identity
(a+b)(a-b)=a²-b²
(tanA+tanB/1-tanAtanB)×(tanA-tanB/1+tanAtanB)
tan²A-tan²B/1-tan²Atan²B
Hence, triagonometric function tan(A+B)/cot(A−B) is tan²A-tan²B/1-tan²Atan²B
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4. The Johnsons' bill at a restaurant is $124.00. How much money should the Johnsons leave if they plan to tip their waiter 15%?
Answer:
142.6
Step-by-step explanation:
100% + 15% = 115%
115÷100 = 1.15
1.15 x 124 = 142.6
Hope that helped
PLEASE HELP!!!!!! It’s algebra
When the cost of a gallon of milk increases from $2.81 to $3.48 over a period of 10 years the annual inflation rate is 2.15 percent.
What is a annual inflation rate?
A percentage is used to represent the inflation rate. For instance, a yearly inflation rate of 2% indicates that the cost of products and services as a whole has increased by 2%. As an illustration, a product that cost $10 last year will cost $10.20 this year.
Here, we have
Given
The cost of the gallon of milk earlier was $2.81
The cost of a gallon of milk now is $3.48.
The total time period is 10 years.
r = (F/P)ⁿ⁻¹ - 1
r = {(3.48/2.81)^(1/10) - 1}×100
r = {(1.238)^(1/10) - 1}×100
r = 0.0215 ×100
r = 2.15
Hence, when the cost of a gallon of milk increases from $2.81 to $3.48 over a period of 10 years the annual inflation rate is 2.15 percent.
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Karima made 9 pairs of earrings in 9 hours. At this rate: How long will it take Karima to make 12 pairs of earrings?
Answer:
12 hours
Step-by-step explanation:
1 pair per hour ?
A railroad's track can be determined using the following graph.
Linear function increasing from the left in quadrant 3 passing through the point negative 8 comma 0 and 0 comma 5.
Several different roadways are in the same region as the railroad.
Part A: A highway's path can be found using the equation 2x − 3y = 21. Use the graphs of the functions to determine the number of intersections there will be between the railroad and the highway, and explain completely. (5 points)
Part B: A turnpike's route is determined by the equation y equals one third times x squared period Prove algebraically how many intersections there will be between the railroad and the turnpike, showing all necessary work. (5 points)
a) The number of intersections between the railroad and the highway is of: One.
b) The number of intersections between the railroad and the turnpike is of: Two.
How to define the linear function?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which the parameters are listed as follows:
m is the slope, representing by how much y changes when x is increased by one.b is the intercept, representing the value of y when x = 0.The points for the railroad are given as follows:
(-8, 0) and (0,5).
When x = 0, y = 5, hence the intercept is of:
b = 5.
When x increases by 8, y increases by 5, hence the slope is of:
m = 5/8.
Thus the equation for the railroad is of:
y = 5/8x + 5.
Then the number of intersections with the highway is of one, as they are linear functions with different slopes.
With the turnpike, the intersection is given as follows:
5/8x + 5 = x²/3
x² -1.875x - 15 = 0.
The discriminant is of:
(-1.875)² - 4(1)(-15) = 63.5.
Which is positive, hence they have two intersections.
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The choices below are data sets. In the choices, w is a constant. Each choice has the same mean.
Which choice has the greatest standard deviation?
A.)
w-2, w-1, w, w + 1, w+ 2
B.)
w-2, w-2, w, w + 2,w+2
C.)
w-3, w-1, w, w + 1, w+3
D.)
w-3, w, w, w, w +3
Answer:
C)w-3, w-1, w, w + 1, w+3
Step-by-step explanation:
I'm not great with standard deviation, but I know that the greater the standard deviation, the more spread out the data is.
C) is the correct answer, the data points do not repeat and are spread out more than A.
You can check this by calculated each standard deviation (but only if you are crazy ;] )
Hope this helps,
:]
to avoid a possible collision with a manned airplane, you estimate that your small ua climbed to an altitude greater than 600 feet agl. to whom must you report the deviation? group of answer choices
We must report the deviation to Upon request of the Federal Aviation Administration.
What is Deviation?
The deviation is a metric used to determine the discrepancy between an observed variable's value and its predicted value. The deviation can be defined as the distance from the centre point.
Concept:
Each remote PIC who deviates from a Part 107 rule shall, upon request from the FAA administrator, submit a written report of such deviation.
Who is in charge of providing the participants with information on emergency procedures while utilising a small unmanned airplane in a commercial operation? The commander of the remote pilot. A person may fly an unmanned aerial system for profit even without a Part 107 remote pilot certificate: under the immediate control of a Remote PIC.
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The formula K=1/2mv² is used to find the kinetic energy of an object in
motion using its mass, m, and its velocity (speed), v. Solve the equation
for the mass, m.
What is the Equation?
Is it: m = K/2v²
Answer:
m = 2k/v²
Step-by-step explanation:
K = ½mv²
multiply both sides by 2
2 × k = ² × ½mv²
2k = mv²
divide both sides by (v²)
m = 2k/v²
i hope this helped
explain the process of the square root of 80n3
The square root of 80 is 4√5 ≅ 8.92.
What is a square root of a number?
In mathematics, the square root of a number is a value that gives the original number on multiplication by itself. The positive number, when multiplied by itself, represents the square of the number. Thus, the square root of the square of a positive number gives the original number.
Using Prime Factorization:
The first step in this method is to find the prime factors of 80.
80 = 2 × 2 × 2 × 2 × 5
To find the root from here, we can simplify this to
√80 = √(2 × 2 × 2 × 2 × 5)
√80 = 4√5
We can either leave it at this or find the root of 5 which is 2.23 and simplify further.
Hence, Square Root of 80 = 4√5 ≅ 8.92.
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Punch recipe. Orange juice, 3, 1/3. Grape juice six and 1/2. Cherry juice. 4 and 1/8. Club soda, one and 1/4. About how much fruit juice,(orange, grape, and cherry) is used in the punch.
answers.
11 cups
12 cups
13 cups
14 cups
Answer:
14 cups
Step-by-step explanation:
3 + 6 = 9
9 + 4 = 13
13 + 1 = 14
14 plus fraction
Write the
equation
of the line In
Slope-Intercept
Form.
Type your
answer here.
Answer:y=2x+3
Step-by-step explanation:
The slope intercept form is y=mx+b
m equals to slope
b equals the y-intercept
the slop of this equation is 2
The y-intercept is at (0, 3)
y=2x+3
3(2x+4) = 6x + 8
3(2x + 4) = 6x + 8
6x + 12 = 6x + 8
-6x -6x
12 = 8
no solution??
Answer: no solution
Step-by-step explanation:
Correct, there is no solution as any values of x and y will make the equation false
A company manufactures water bottles. The list below describes the number of water bottles manufactured in three months.
• February: 4, 100 water bottles
• March: 7% more water bottles in February
• April: 500 more water bottles in March
What is the percent change, to the nearest percent, in the number water bottles the company manufactured from February to April. show your work
Answer:
19%
Step-by-step explanation:
You want the change from February to April if 4100 bottles were manufactured in February, 7% more were manufactured in March, and 500 more were manufactured in April.
ChangeThe change from February to March is given as 7%.
The change from March to April is 500 bottles. In terms of the February quantity, this is ...
500/4100 × 100% ≈ 12.2%
Then the total of changes from February to April is ...
change = 7% +12.2% = 19.2% ≈ 19%.
The number of bottles manufactured increased by about 19% from February to April.
__
Additional comment
When working with percentages, one must always be aware of the base amount—what it is that represents 100%. Here, we know the 7% number for March uses the February value as its base.
Since we want a percent change from the February base, we can use that same base to find the percent difference from March to April. Then the total difference from February is the difference to March plus the difference from March to April.
<95141404393>
would somebody be nice enough to help me with this? i’m confused
The triangles ΔPQR ~ ΔPXY are similar by using the AA test for the similarity of triangles.
What is the Angle-Angle similarity theorem of triangles?
The AA Similarity Theorem states: If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.
In the given figure,
In ΔPQR and ΔPXY
∠P ≅ ∠P ----- Common Angle
∠PQR ≅ ∠PXY ----Corresponding angles.
So, ΔPQR ~ ΔPXY -----(AA test)
Hence, the triangles ΔPQR ~ ΔPXY are similar by using the AA test for the similarity of triangles.
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Which table of values represents the equation y = 7x - 3?
The table of values which represent the equation y = 7x - 3 is: table D.
What is an ordered pair?In Mathematics, an ordered pair can be defined as a pair of two (2) elements or points that are commonly written in a fixed order within parentheses as (x, y), which represents the x-coordinate or x-axis (abscissa) and the y-coordinate or y-axis (ordinate) on the coordinate plane of any graph.
In order to determine the true ordered pair that is a solution for the given linear equation, we would have to test the ordered pair contained in each table by substituting it into the linear equation as follows;
For ordered pair (-2, -1), we have:
y = 7x - 3
-1 = 7(-2) - 3
-1 = -14 - 3
-1 = -17 (False).
For ordered pair (-2, -19), we have:
y = 7x - 3
-19 = 7(-2) - 3
-19 = -14 - 3
-19 = -17 (False).
For ordered pair (-2, -15), we have:
y = 7x - 3
-15 = 7(-2) - 3
-15 = -14 - 3
-15 = -17 (False).
For ordered pair (-2, -17), we have:
y = 7x - 3
-17 = 7(-2) - 3
-17 = -14 - 3
-17 = -17 (True).
In this context, we can logically deduce that all of the coordinates in table D represents the equation y = 7x - 3.
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What is the term to term rule for this sequence ? 625,125,25,5,1
The required expression for the term of the given sequence is aₙ = 625 × (1/5)ⁿ⁻¹.
How to know whether a given sequence is geometric?In order to check a geometric sequence, find the ratios of the consecutive terms of the given sequence. If they are equal, the given sequence is geometric.
The given sequence is as follows,
625, 125, 25, 5, 1
The first term is given as a₁ = 625
And, the ratio of the consecutive terms are,
125/625 = 1/5
25/125 = 1/5
Since the ratio of two consecutive terms are equal, the given sequence is a geometric sequence.
The nth term of a geometric sequence is given as aₙ = a₁rⁿ⁻¹.
Thus, the expression for the given sequence is aₙ = 625 × (1/5)ⁿ⁻¹.
Hence, the term for the given sequence can be written in general form as aₙ = 625 × (1/5)ⁿ⁻¹.
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Four boards were given to Sam to build a triangular picture frame for a large painting.
32 feet
21 feet
8 feet
12 feet
Which of these boards could be used for his project?
The sum of any two sides of a triangle must be greater than the other thus 32 feet,21 feet, and 12 feet will be the correct so options (A),(B), and (D) are correct.
What is a triangle?A triangle is a 3-sided shape that is occasionally referred to as a triangle. There are three sides and three angles in every triangle, some of which may be the same.
As per the given,
To be a triangle of three side polygon the sum of any two sides must be greater than the third side.
If we take 32 feet,21 feet, and 8 feet.
21 + 8 = 29 < 32 so it will not form any triangle.
Thus, 8 cannot be taken. now let's take 32,21 and 12 here 21 + 12 = 33 > 32 so it will form a triangle this will be used for the project.
Hence "The right answer will be 32 feet, 21 feet, and 12 feet because the sum of any two sides of a triangle must be bigger than the other".
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Diego is also training for the tournament. The graph shows the relationship between the time in the distant he rows how many meters does Diego Roper minute
Diego rows 300 meters per minute
How to determine the the number of rows per minuteInformation given in the question include
The graph shows the relationship between the time in the distant, Diego rows
The data is plotted as a linear function
A linear function consists of functions where the variables has exponents of 1. The graph of linear functions is a straight line graph and the relationship is expressed in the form.
y = mx + c
The slope is represented as m, The slope by definition is the change of the output values to the input values
the slope, m calculating using the points on the graph (1, 300) and (2, 600)
m = (y₀ - y₁) / (x₀ - x₁)
m = (600 - 300) / (2 - 1)
m = 300 / (1)
m = 300
The number of meters Diego rows per minute is solved to be 300
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Find the 56th term of the following arithmetic sequence 7,10,13,16
The 56th term of the following arithmetic sequence 7,10,13,16 is 172.
What is the arithmetic sequence?
A series of numbers called an arithmetic progression or arithmetic sequence has a constant difference between the terms.
Here, we have
Given
Arithmetic sequence 7,10,13,16.
We have to find the 56th term.
The common difference between terms: 10 - 7 = 3
Using the arithmetic progression formula:
nth term = first term + (n-1)* common difference
56th term = 7 +(56-1) 3
56th term = 7 + 55×3
56th term = 7 + 165
56th term = 172
Hence, the 56th term of the following arithmetic sequence 7,10,13,16 is 172.
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While looking at some reports, a store manager notes that televisions that retail for $475 and up costing customers $513 once the sales tax is ended, what is the sales tax percentage?
The sales tax percentage of the store manager report is 7.41%
How to solve for the sales tax percentageCustomers are subject to a charge known as sales tax when they buy goods and services.
It is a pass-through tax, which means you must collect it from clients and send the money to your state or local government. the seller do not contribute sales tax.
The sales tax is first calculated by
= price after tax - price before tax
= 513 - 475
= 38
sales tax percentage is calculated using the formula
= (Tax amount / Price before tax) × 100%
= (38 / 513) * 100
= 7.4074
= 7.41%
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Which of the following is a point on the line defined by the parametric equations below?
[x(t)=t+7
y(t) = 5-2t
○ (3,10)
○ (7,0)
O (8,3)
O (2,1)
The following are five different examples of parametric models: exponential distributions, poisson distributions, normal distributions, the Weibull distribution, and linear regressions.
What is an example of a parametric equation?Well, a parametric equation is an equation where the variables (usually x and y) are expressed in terms of a third parameter, usually expressed as t. For example: Consider the equation of a circle with radius r and center at (0,0) : x2+y2=r2 x 2 + y 2 = r 2 .parametric equation, a type of equation that employs an independent variable called a parameter (often denoted by t) and in which dependent variables are defined as continuous functions of the parameter and are not dependent on another existing variable. More than one parameter can be employed when necessary.If there are m free variables in the homogeneous equation, the solution set can be expressed as the span of m vectors: x = s1v1 + s2v2 + ··· + smvm. This is called a parametric equation or a parametric vector form of the solution.Types of Parametric test–
Two-sample t-test.Paired t-test.Analysis of variance (ANOVA)Pearson coefficient of correlation.To learn more about parametric refer to:
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What is the value of x?
Enter your answer in the box.
The value of x in the intersecting line is 54.
How to find angles in intersected lines?When lines intersect, angle relationships are formed such as vertically opposite angles, linear angles angles on a straight lines.
Therefore, angle 2x + 2 is vertically opposite to the angle 3x - 52 .
Vertically opposite angles are congruent to each other.
Vertical Angles are the angles opposite each other when two lines cross. in other words, vertical angles are formed when two lines meet each other at a point.
Hence,
2x + 2 = 3x - 52
2x - 3x = -52 - 2
- x = -54
Therefore,
x = 54
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To find the area of a square,
use the formula A = s2. If the side of
a square is b5, what is the area of
the square?
Answer:
25
Step-by-step explanation:
When you're figuring out the area of a square, you're measuring the size of its surface. You can think of it as finding how many square units make up the entire surface. For squares, the formula for determining area is A = s2, or A = side x side.=
The residents of a city voted on whether to raise property taxes. The ratio of yes votes to no votes was 5 to 3. If there were 4296 total votes, how many no votes were there?
Answer: 1611 no votes
Explanation:
4296/8=537
537*3=1611
0=x2+18x+45
I need help with this place
The factorise quadratic equation x² + 18x + 45 = 0 is (x + 3)(x + 15)
How to factorise quadratic equation?A quadratic equation is a polynomial equation that contains the second degree, but no higher degree, of the variable.
Therefore, quadratic equation can be represented as follows:
ax² + bx + c
where
a, b and c are constantHence, let's factorise x² + 18x + 45 = 0
x² + 18x + 45 = 0
Let's find the two numbers to add to get 18 and multiply to get 45
Therefore, the numbers are 3 and 15
x² + 18x + 45 = 0
x² + 3x + 15x + 45 = 0
x(x + 3) + 15(x + 3) = 0
(x + 3)(x + 15) = 0
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