It is demonstrated that log3 (7) is irrational using unique factorization for integers theorem and the definition of logarithm.
Explain the term unique factorization theorem?Every integer bigger than 1 is either a prime number by itself or the result of a singular combination of prime numbers, based on the fundamental theorem of arithmetic (FTA), Often known as the unique factorization theorem or even the unique-prime-factorization theorem.If a contradiction is rational, then log3(7) = a/b for some a,b∈R .
In which, b≠0 will be true.
As a result, 7 = 3ᵃ/ᵇ according to the definition of logarithms.
7 = 1*7 is unique according to the unique factorization theorem.
Thus, it is demonstrated that log3 (7) is irrational using unique factorization for integers theorem and the definition of logarithm.
To know more about the unique factorization theorem, here
https://brainly.com/question/12971919
#SPJ4
Question
What is the net signed area between f(x) = 2x-6 and the x-axis over the interval [-8,5]? Do not include any units in
your answer
Provide your answer below:
The net signed area of f(x) = 2x - 6 on the interval [-8, 5] is - 21 units.
What is the net signed area?The definite integral can be used to calculate the net signed area, which is the area above the x-axis less the area below the x-axis.
Given, f(x) = 2x - 6 and the x-axis over the interval [-8 , 5].
∴ The net signed area is,[tex]\[ \int_{-8}^{5} 2x -6 \,dx \][/tex].
[tex]= \[ \int_{-8}^{5} 2x \,dx \ - \ \int_{-8}^{5} 6 \,dx \][/tex].
= (5)² - (-8)² - {(5×6) - (-8×6)}.
= 25 - 64 - 30 + 48.
= - 21 units.
learn more about net signed area here :
https://brainly.com/question/22867526
#SPJ1
A can of campbell's chicken Noodles Soup has a diameter of 30 millimeters and a height of 5 inches Find the volume of the can in cubic millimeters
The volume of the can of campbell's chicken Noodles Soup in cubic millimeters is 89,725.5 cubic millimeters
What is the volume of the can?Volume of a cylinder = πr²h
Convert inch to millimeters:
1 inch = 25.4 millimeters5 inch = 127 millimetersHeight of the cylinder = 5 inches = 127 millimeters
Radius = diameter / 2
= 30 millimeters / 2
= 15 millimeters
Volume of a cylinder = πr²h
= 3.14 × 15² × 127
= 3.14 × 225 × 127
= 89,725.5 cubic millimeters
Consequently, the can of campbell's chicken Noodles Soup has a volume of 89,725.5 cubic millimeters
Read more on volume of a cylinder:
https://brainly.com/question/9554871
#SPJ1
Elizaveta painted 35 m2 of wall space. This represents 20% of the total area.
What is the total area of the walls to be painted?
The total area of the space will be equal to 175 square meters.
What is the percentage?The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.
Given that Elizaveta painted 35 square meters of wall space. This represents 20% of the total area.
The total area will be calculated as,
20% of area = 35 square meters
100% of the area = ( 35 x 100) / 20
100% of the area = 175 square meters
Therefore, the total area of the space will be equal to 175 square meters.
To know more about percentages follow
https://brainly.com/question/24304697
#SPJ1
Elizaveta painted 35 m2 of wall space. This represents 20% of the total area.
What is the total area of the walls to be painted?f ^(4) 2
Which expression is equivalent to (3+4i)(2−3i)
The expression that is equivalent to the given value would be = 18-i . That is option C.
What is an equivalent expression?An equivalent expression is defined as the type of expression that is similar to a given value when simplified.
The given expression = ( 3 + 4i) ( 2 - 3i)
Expand the given expression by removing the brackets as follows:
= =2(3+4i)−3i(3+4i)
=(6+8i)−(9i−12)
= (6+12)+i(8−9)
=18−i.
Learn more about multiplication equation here:
https://brainly.com/question/28552292
#SPJ1
Please help me I just look at the photo I am so confused
Answer:
Grandma=P
Wagon=TH
Library= PL
Step-by-step explanation:
its pretty simple
A series of rigid motions maps ANEM onto ACDE. Based on this information, which of the following is a true statement? OA) There isn't enough information to make a statement about ANEM and ACDE B) ACDE is half the area of ANEM. C) All corresponding pairs of angles and sides of ANEM and ACDE are congruent. OD) The corresponding pairs of angles of ANEM and ACDE are congruent, but the corresponding sides aren't. Question 9 (5 points)
All the corresponding pairs of angles and sides of ΔNEM and ΔCDE are congruent.
What is rigid motion?
A geometric figure is moved by rigid motions, but its size and shape remain unchanged. It generates visuals that make sense.
Rigid transformation comes in four different varieties.
1. translate 2. reflect. 3. Rotation 4. Gliding reflection
Here,
We have a series of rigid motion maps ΔNEM onto ΔCDE.
We have to find the correct statement, so we concluded that all the corresponding pairs of angles and sides of ΔNEM and ΔCDE are congruent.
Hence, ΔNEM and ΔCDE are congruent.
To learn more about the rigid motion from the given link
https://brainly.com/question/25965367
#SPJ1
Ver en español
The volume of this cylinder is 1,570 cubic inches. What is the radius?
Use ≈ 3.14 and round your answer to the nearest hundredth.
Therefore ,the radius of the given cylinder is 10 inches
What is volume ?A three-dimensional space's occupied volume is measured. It is frequently expressed as a numerical value using SI-derived units, other imperial units, or US customary units. Volume definition and length definition are connected.
Here,
The volume of the cylinder is 1570 cubic inches
Volume of the cylinder = 1570 cubic inches
Volume of cylinder = π[tex]r^{2}[/tex]h
Where r is the radius of cylinder
h is the height of cylinder
So,
Volume of the cylinder = 1570 cubic inches
=> 1570 = π[tex]r^{2}[/tex]h
=> 1570 = 3.14*[tex]r^{2}[/tex]*5
=> 1570/3.14 = [tex]r^{2}[/tex]*5
=> 500=[tex]r^{2}[/tex] *5
=> 500/5 =[tex]r^{2}[/tex]
=>100 =[tex]r^{2}[/tex]
=>r=10 inches
Therefore the radius of the given cylinder is 10 inches.
To know more about Volume , visit
https://brainly.com/question/23477586
#SPJ1
test the pair of events b and d for independence based on the following table. a b c total d 0.12 0.04 0.24 0.40 e 0.09 0.03 0.18 0.30 f 0.09 0.03 0.18 0.30 total 0.30 0.10 0.60 1.00 Are A and D independent or dependent and why? Select the correct answer below and fill in the answer boxes to complete your choice. A) A and D are dependent because P(AnD) equals P(A)P(D): P(AOD) = and P(AJP(D) = B) A and D are dependent because P(AnD) does not equal P(A)P(D): P(AnD) = and P(A)P(D) = C) A and D are independent because P(AnD) does not equal P(A)P(D): P(AnD) = and P(A)P(D) = D) A and D are independent because P(AOD) equals P(A)P(D): P(AnD) = and P(A)P(D) =
There must be no chance that d and e will happen. If the two occurrences cannot coexist, we can infer that they are not independent.
What is probability?Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.
What is the probability formula?P(A) = n(A)/n(S)
Where P(A) is the likelihood that an event "A" will occur and n(A) is the number of positive outcomes. The total number of occurrences in the sample space is denoted by n(S).
We must have a similar probability for both events in order for them to be independent. Because of the table, we may test for independence by knowing the likelihood that e and d will occur. When we are told that occurrences d and e are mutually exclusive, the entire table of values becomes somewhat of a red herring. The chance of d given e and the probability of d given d are both equal to zero if two events are mutually incompatible. There must be no chance that d and e will happen. If the two occurrences cannot coexist, we can infer that they are not independent. There is a chance for it.
to learn more about probability visit:
https://brainly.com/question/29381779
#SPJ4
Suppose a triangle with the vertices (-1, 4), (-1, -2) and (2, -2) were dilated, with the center of dilation at the origin and with a scale factor of 2. Which of these would be a vertex of the dilated figure? Select the three correct answers. A. (-2, -4) B. (-2, 8) C. (-1, -4) D. (-1, 4) E.
New coordinates become (-2,8) (-2,-4) and (4,-4)
What do you mean by scale factor?
Magnification is defined as the scale ratio of a given original object and a new object that is a representation of it but of a different size (larger or smaller).
The new figure obtained is similar to the original figure
The expansion description should state how much the shape was expanded.
Suppose a triangle with the vertices (-1, 4), (-1, -2) and (2, -2) were dilated, with the center of dilation at the origin and with a scale factor of 2.
As we know, if (x,y) point dilated by scale factor a then new coordinates become (ax, ay)
So, if triangle having vertices (-1, 4), (-1, -2) and (2, -2) were dilated, with the center of dilation at the origin and with a scale factor of 2 then new coordinates become (-2,8) (-2,-4) and (4,-4)
Therefore, new coordinates become (-2,8) (-2,-4) and (4,-4)
To learn more about the scale factor from the given link.
https://brainly.com/question/25722260
#SPJ1
10.
A
group of friends went to lunch. The bill,/before)
sales tax and tip, was $37.50. A sales tax of 8%
was added. The group then tipped 18% on the
amount after the sales tax was added.
What was
the amount, in dollars, of the sales tax?
What was the total amount the group paid,
including tax and tip?
Answer:
The total amount of the sales tax: $3.00
The total amount paid: $47.25
Step-by-step explanation:
Tip (In $): 6.75
Sales tax: 3.00
The total amount of food (before additional fees): 37. 50
So, to find the amount (in dollars) of the sales tax and tip, we must use this formula:
Amount = whole number * part percent/100
So, plugging in the numbers to the formula, it would look like this:
37.50 * 18 / 100
That is how to find the tip, you would do the same to find the sales tax. Then, when you get both amounts, you add them to 37.50 (the total before the fees) and get $47.25.
Question 1
Match the sample description with the type of sample that was taken.
Names of all high school students are placed on slips of paper in a box and 10 are chosen.________
Fifteen students are randomly selected from each grade level.______
A high school is divided into classrooms and one classroom is selected._______
All high school students eating lunch at 11 am.______
All students in the school are listed in alphabetical order and every 50th name is chosen._______
The sampling types in this problem are given as follows:
Names of all high school students are placed on slips of paper in a box and 10 are chosen -> Random.Fifteen students are randomly selected from each grade level -> Stratified.A high school is divided into classrooms and one classroom is selected -> Cluster.All high school students eating lunch at 11 am -> Convenient.All students in the school are listed in alphabetical order and every 50th name is chosen -> Systematic.What are the sampling types?The sampling types used in this problem are defined as follows:
Random: all options are listed as options and then some are selected.Convenient: all the options are at some place such as the cafeteria then some are selected.Systematic: one of each n elements is chosen.Cluster: options are divided into groups, and then one group is selected.Stratified: options are divided into groups, and then a proportion of each group is chosen.More can be learned about the types of sampling at https://brainly.com/question/9910540
#SPJ1
In how many ways can a committee of five Democrats and four
Republicans be formed from a group of twelve Democrats and twelve
Republicans?
Answer:
392040 ways------------------------------
Find the combination of 4 of 12 and 5 of 12:
C(12, 4) × C(12, 5) = 12!/(4!8!) × 12!/(5!7!) = 495 × 792 = 392040At the local bunny-hop, Mr. Meyering jumps 20 inches on his first jump and then 10 inches with his second jump. If the distances form a geometric sequence, what is the total distance Mr. Meyering jumps if he completes infinitely many jumps?
Hint: Use S= a1/1- r and remember that |r| must be less than 1.
At the local bunny-hop, the sum of geometric sequences showing the jumps performed by Mr. Meyering is 40
How to find the sum of the jumping records of Mr. MeyeringThe Sequences of the jump include
20, 10, ...
The common ratio, r is calculated from
first term, a * common ratio, r = second term
20 * r = 10
20r = 10
r = 10/20
r = 1/2
hence r < 1
The sum of gp to infinity for r < 1 is
Sum = a/ (1 - r)
Sum = 20 / (1 - 1/2)
Sum = 20 / 1/2
Sum = 20 * 2
Sum = 40
Learn more about geometric sequences at:
https://brainly.com/question/24643676
#SPJ1
For each system of equations, which operation will eliminate one of the variable? 2x+7y=32 and 2x+y=8
By subtraction, the variable x will eliminate and we will find out the value of y in the given system of equations.
What is the equation?There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.
The equation must be constrained with some constraints.
As per the given system of equations,
2x + 7y = 32 and 2x + y = 8
Subtract both equations from each other,
(2x + 7y) - (2x + y) = 32 - 8
2x + 7y - 2x - y = 24
2x - 2x + 7y - y = 24
6y = 24
y = 4
Hence "By subtraction, the variable x will eliminate and we will find out the value of y in the given system of equations".
For more about the equation,
brainly.com/question/10413253
#SPJ1
You want to buy a $181,000 home. You plan to pay 15% as a down payment, and take out a 30 year fixed loan for the rest.
Round all answers to the nearest cent as needed.
a) How much is the loan amount going to be?
$
b) What will your monthly payments be if the interest rate is 4.5%?
$
c) What will your monthly payments be if the interest rate is 5.5%?
$
Submit QuestionQuestion 4
Answer:
a) $153,850
b) $779.54
c) $873.54
Step-by-step explanation:
Part a)[tex]\begin{aligned}\textsf{Loan amount}&=\textsf{Cost of property}-\textsf{Down payment}\\&=181000-(181000 \times 0.15)\\&=181000-27150\\&=153850\end{aligned}[/tex]
Therefore, the loan amount is $153,850.
Part b)[tex]\boxed{\begin{minipage}{8.5 cm}\underline{Monthly Payment Formula}\\\\$PMT=\dfrac{Pi\left(1+i\right)^n}{\left(1+i\right)^n-1}$\\\\where:\\\\ \phantom{ww}$\bullet$ $P =$ loan amount \\\phantom{ww}$\bullet$ $i =$ interest rate per month (in decimal form) \\\phantom{ww}$\bullet$ $n =$ term of the loan (in months) \\\end{minipage}}[/tex]
Given:
P = $153,850i = 0.045 per year = 0.045/12 per monthn = 30 years = 360 monthsSubstitute the given values into the Monthly Payment formula and solve for PMT:
[tex]\implies \sf PMT=\dfrac{153850 \cdot \frac{0.045}{12}\left(1+\frac{0.045}{12}\right)^{360}}{\left(1+\frac{0.045}{12}\right)^{360}-1}[/tex]
[tex]\implies \sf PMT=\dfrac{153850 \cdot 0.00375\left(1.00375\right)^{360}}{\left(1.00375\right)^{360}-1}[/tex]
[tex]\implies \sf PMT=779.5353492[/tex]
Therefore, the monthly payments would be $779.54.
Part c)Given:
P = $153,850i = 0.055 per year = 0.055/12 per monthn = 30 years = 360 monthsSubstitute the given values into the Monthly Payment formula and solve for PMT:
[tex]\implies \sf PMT=\dfrac{153850 \cdot \frac{0.055}{12}\left(1+\frac{0.055}{12}\right)^{360}}{\left(1+\frac{0.055}{12}\right)^{360}-1}[/tex]
[tex]\implies \sf PMT=873.5433786[/tex]
Therefore, the monthly payments would be $873.54.
(4, -22) and (9,-57)
what is 122222×2222221÷12
Answer:
The result of the calculation is approximately 22535940185.17
Step-by-step explanation:
To solve this problem, we can use the order of operations. First, we perform the multiplication:
122222 * 2222221 = 2704312822242
Then, we perform the division:
2704312822242 / 12 = 22535940185.17
CAN SOMEONE HELP WITH THIS QUESTION?✨
The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.
The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.
The equation of the form y = A[tex]2^x[/tex] + K from the graph above is
y = (-5/3) . [tex]2^x[/tex] - (2/3)
What are coordinates in a graph?The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.
The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.
We have,
y = [tex]2^x[/tex]
From the graph, we see that,
x = 0, y = -1
x = 1, y = -4
Now,
The equation in the form of y = A.[tex]2^x[/tex] + K can be written as,
Taking (0, -1) we get,
-1 = A x 1 + K
-1 = A + K ______(1)
Now,
Taking (1, -4) we get,
-4 = A x 2 + K
-4 = 2A + K _____(2)
From (1) and (2) we get,
A = K - 1 putting in (2) we get,
-4 = 2(K - 1) + K
-4 = 2K - 2 + K
-4 = 3K - 2
3K = -4 + 2
3K = -2
K = -2/3
Now,
A = K - 1
A = -2/3 - 1
A = (-2 - 3) / 3
A = -5/3
Now,
The equation is y = (-5/3) . [tex]2^x[/tex] - (2/3)
Thus,
The equation of the form y = A[tex]2^x[/tex] + K from the graph above is
y = (-5/3) . [tex]2^x[/tex] - (2/3)
Learn more about coordinates here:
https://brainly.com/question/13118993
#SPJ1
Combine the radicals
The combination of radical 5√27 - 17√3 is -2 √3, so option D is correct.
What are radicals?The opposite of an exponent, denoted by the symbol "√" and also known as the root, is a radical. The number before the symbol or radical is regarded as an index number or degree.
Given:
5√27 - 17√3
Simplify the value under roots,
5√(3 × 3 × 3) - 17√3
5 × 3 √3 - 17√3
√3 (15 - 17)
-2 √3
Therefore, the combination of radical 5√27 - 17√3 is -2 √3.
To know more about Radicals:
https://brainly.com/question/8020018
#SPJ1
For what value of X is the parallelogram a rhombus?
Answer:
x = 8
Step-by-step explanation:
a rhombus has all equal sides so this means that you must set them equal to each other
8x - 5 = 5x + 19
now subtract 5x to both sides
3x = 24
x = 8
that is your answer
10. A bag contains marbles: 5 purple, 6 blue, 8 yellow, 1 green. You will draw a
marble, keep it, and then draw another. What is the probability that you will
draw a purple and a green? SHOW YOUR WORK. Make sure to simplify your
answer if using a fraction. If using a percent, round to the nearest hundredth
after you change it to a percent.
Answer:
1st darw
[tex] p(purple)= \frac{5}{20} \\ = \frac{1}{4} [/tex]
[tex]p(green) = \frac{1}{20} [/tex]
2nd draw
[tex]p(purple) = \frac{4}{18} \\ = \frac{2}{9} [/tex]
[tex]p(green) = 0[/tex]
Graham Auto Parts has current sales of $42,700, EBIT of $9,700, net income of $6,600, interest expense of $1,360, and dividends paid of $1,925. Assume the net profit margin, debt-equity ratio, and dividend payout ratio are held constant. Sales are expected to increase by $8,000 next year. What is the projected change to retained earnings for next year?
Retained profits for the upcoming year: 5551.
Retained earnings: What is it?The amount of profit a business keeps after paying all of its direct and indirect expenses, income taxes, and dividends to shareholders is known as retained profits. This is the percentage of the company's equity that may be utilized, for example, to fund the purchase of new machinery, research and development, and marketing.
RE=[tex]RE_{0}[/tex]-NI-D
Reserved Earnings
RE stands for initial retained income.
Net income is referred to as NI.
the dividend D
Graham Auto Parts now has $42,700 in sales, $9,700 in EBIT, $6,600 in net income, $1,360 in interest expenditure, and $1,925 in dividends paid. and a $8,000 rise in revenue is anticipated for the following year.
8000/42700 = 0.1873536 is the sales growth rate as a result. Its proportion is 18.73536%.
Now project net income = 6600 * 1.1873536
7837
dividends = 1925*1.1873536 = 2286
7837 - 2286 = 5551
retained earnings for next year 5551
To know more about retained earnings click the link:
brainly.com/question/28495052
#SPJ1
Every day a school bus driver passes the same traffic light twice, once before school and once after. Each time he passes the light, he records If it is red, green, or yellow.
Here is a summary of the data he got after 200 days.
Traffic light before school Traffic light after school Number of day
red red 25
red green 21
red yellow 17
green red 16
green green 31
green yellow 27
yellow red 22
yellow green 28
yellow yellow 13
Suppose the driver will continue recording the colors for 150 more days.
In how many of these 150 days will the light be red exactly once? Use the data to make a prediction.
Answer:
Step-by-step explanation: the amswer is B trust me
zero and negative exponents result from applying properties of exponents. for example, zero indicates that the same number of repeated factors of a non-zero base was found in both the numerator and denominator of an expression.
The question is incomplete , I am answering it with my general knowledge,
Zero exponent
Simplifying an expression with a 0 as the exponent does not need consideration of the base value.
Any non-zero number multiplied by 0 has the value 1.
x0 = 1, where x = 0 and x = 1, 2, 3, and so forth.
Negative exponent
For any positive integer m and non-zero number a,
a⁻ⁿ=1/a⁻ⁿ
This rule states that if the exponent is negative, it can be made positive by writing the same number in the denominator and writing one for the numerator.
When a number is positive, the exponent shows how many times it has been multiplied by itself.
On the other hand, the negative exponent indicates how many times we must divide the base number. The negative exponent, then, tells us how many times to multiply the reciprocal of the base, to put it another way.
To learn more about exponents
brainly.com/question/26659533
#SPJ4
What is the domain of the graph? *
{-5,-4,-3,-1,0,2,4}
All real numbers
{-5,-4,-3,-1}
{-4,0,2,4}
The domain of the graph is {-5,-4,-3,-1}.
How can I determine a graph's domain?
Graphs can be used as another tool for determining the domain and range of functions. The domain of a graph is made up of all the input values displayed on the x-axis since the term "domain" refers to the set of potential input values. The y-axis on a graph represents the possible output values, or range.Consider the function y = f(x), which has the independent variable x and the dependent variable y. A value for x is said to be in the domain of a function f if it successfully allows the production of a single value y using another value for x.To know more about domain check the below link:
https://brainly.com/question/26098895
#SPJ4
The length and width of a rectangle are consecutive integers. The perimeter of the
rectangle is 86 inches. Find the length and width of the rectangle.
The rectangle has the consecutive integers of 21 inches and 22 inches for its width and length respectively.
What are consecutive integersConsecutive integers are numbers that follow in a particular order, usually just one after the for example, 1, 2, 3,... and so on.
Let the width of the rectangle be represented by x so that the length will be x + 1 as they consecutive integers
The perimeter of the rectangle will have the equation;
x + x + x + 1 + x + 1 = 86 inches
4x + 2 = 86 inches {collect like terms}
4x = (86 - 2) inches {subtract 2 from both sides of the equation}
4x = 84 inches
x = (84/4) inches {divide through by the coefficient of x}
x = 21 inches
Therefore, the rectangle has width of 21 inches and length of 21 + 1 = 22inches.
Learn more about rectangle here:https://brainly.com/question/19819849
#SPJ1
19) A parking garage charges the rates in the table below. What is the rate of change? Don't forget your units.
The rate of change is not constant.
What is rate of change ?
A rate of change is a measurement of how one quantity alters in proportion to another. The dependent variable y must be present if independent variable x is. rate of change = y-to-x conversion of change. Change rates may be positive or negative.
We know that the rate of change in a function is given by :-
(change in dependent variable) / (change in independent variable)
Let x denotes the Number of hours and y denotes the Cost of parking .
Here , x- independent variable
y- dependent variable
Now, rate of change = ( change in y) / ( change in x)
= (14-10)/(3-1) = 2
Here , the rate of change = $ 2 per hour.
Again rate of change = ( change in y) / ( change in x)
= (16-14)/(5-3) = 1
Here , the rate of change = $ 1 per hour.
Since both rate of changes are not equal , it means the rate of change is not constant.
To learn more about the rate of change from the given link
https://brainly.com/question/25184007
#SPJ4
what is the value of p?
The value of p, using the exterior angle property is 53°.
What is the exterior angle property of a triangle?
The exterior angle property of a triangle states that the sum of the measures of the two non-adjacent angles of a triangle is equal to the measure of the exterior angle of the triangle. This means that if a triangle has three interior angles, the measure of any non-adjacent angle of the triangle must be equal to the measure of the exterior angle of the triangle. This property is useful in solving for unknown angles when the measures of two angles are known. For example, if two angles of a triangle measure 30° and 45°, then the measure of the third angle must be 105°, which is the same measure of the exterior angle.
The Exterior angle is = Sum of the Interior opposite angles.
By using the exterior angle property, we can get the following:
p+p-13°=p+40°
=>p=40°+13°
=>p=53°
The value of p is 53°
To learn more about the exterior angle property of the triangle, visit the link below:
https://brainly.com/question/14256482
#SPJ1
Find the average rate of change of g(x) = 3x² - 8x from x= 1 to x = 6.
Simplify your answer as much as possible.
The average rate of change of g(x) = 3x² - 8x from x= 1 to x = 6 is 13.
What is the average?The middle number, which is obtained by dividing the sum of all the numbers by the variety of numbers, is the average value in a set of numbers. To calculate the average of a set of data, add up all the values and divide the result by the total number of values.
Given:
g(x) = 3x² - 8x
The intervals, x = 1 to x = 6
Calculate the values of g(6) and g(1) as shown below,
g(6) = 3 × 6² - 8 × 6
g(6) = 3 × 36 - 48
g(6) = 108 - 48
g(6) = 60
And, g(1) = 3 × 1² - 8 × 1
g(1) = 3 - 8
g(1) = -5
Calculate the average rate of change as shown below,
The average rate of change = [g(6) - g(1)] / x₂ - x₁
The average rate of change = [60 - (-5)] / 6 - 1
The average rate of change = 65 / 5
The average rate of change = 13
To know more about average:
https://brainly.com/question/28123159
#SPJ1
What is the probability that out of 125 babies born, at least 50 will be girls? Assume that boys and girls are equally probable, and round your answer to the nearest tenth of a percent.
When boys and girls are equally likely, the likelihood that at least 50 of 125 infants born will be females is 0.40.
What is probability?Probability is an area of mathematics that deals with numerical representations of how probable an event is to occur or how likely a statement is to be true. The probability of an occurrence is a number between 0 and 1, where 0 denotes the event's impossibility and 1 represents certainty. A probability is a number that represents the possibility or chance that a specific event will occur. Probabilities can be stated as proportions ranging from 0 to 1, as well as percentages ranging from 0% to 100%.
Here,
total number of sample=125
number of girls=50
Probability that out of 125 babies born, at least 50 will be girls,
=50/125
=0.40
The probability that out of 125 babies born, at least 50 will be girls is 0.40 when boys and girls are equally probable.
To know more about probability,
https://brainly.com/question/11234923
#SPJ1