After evolution of log_6(36) value obtain is 2..
What is Logarithm?
The logarithm is exponentiation's opposite function in mathematics. This indicates that the exponent to which b must be raised in order to obtain a number x is the logarithm of x to the base b. For instance, because 1000 = 103, the logarithm of 1000 in base 10 is 3, or log10 = 3.
Given that;
log6 36
Formula we used to solve this logarithm equation is :
logb(x) = y, if b^y = x
So,
y = log6 36
= log6 62
= 2 log6 6 = 2 x 1
log6 36 = 2
Hence ,the value log6(36) is 2.
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Consider the absolute value function
f(x) = x + 21-1.
a. Graph the function.
b. What are the domain and range of the
function?
c. What are the x-intercept(s) and y-intercept of
the function?
d. Describe the symmetry of the graph.
(a) Graph of the function is given below.
(b) The domain of the function is, - ∞ < x < ∞.
The range of the function is, -1 ≤ ∞.
(c) The x - intercepts are, (-3, 0), (-1, 0) and the y - intercept is, (0, 1).
(d) The graph is symmetric about the vertical line y = -2.
What is absolute value function?
The non-negative value of x, regardless of its sign, is referred to in mathematics as the absolute value or modulus of the real number x, symbolized by the symbol |x|. Specifically, |x| = x if x is a positive number, |x| = -x if x is a negative number, and |0| = 0.
Given: f(x) = | x + 2 | - 1.
(a) The graph of the function is attached below.
(b) As the function is absolute function, so the function is defined for all the real numbers.
Hence, the domain is, - ∞ < x < ∞.
The function has all y - values from -1.
Hence, range of the function is, -1 ≤ y.
(c) Now to find the x - intercepts and the y - intercepts.
Let, y = | x + 2| - 1
To find x - intercept plug y = 0
⇒ 0 = |x + 2| - 1
⇒ |x + 2| = 1
⇒ -(x + 2) = 1, (x + 2) = 1
⇒ -x - 2 = 1, x + 2 = 1
⇒ x = -3, x = -1
Therefore, the x - intercepts are (-3, 0) and (-1, 0).
To find y - intercept plug x = 0 in the above equation.
y = |0 + 2| - 1
y = 2 - 1
y = 1
Therefore, the y - intercept is, (0, 1).
(d) From the graph we can see that, the symmetry of the graph is about the vertical line x = -2.
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if there are 20 apples and 40 bananas for a fruit basket, fill out all of the possible ratios of apples to bananas that could be made.
Answer:
Step-by-step explanation:
Michael is going to invest in an account paying an interest rate of 6.7% compounded
continuously. how much would michael need to invest, to the nearest dollar, for the
value of the account to reach $100,000 in 14 years?
Answer:
P≈39141 ENTER 39141
Step-bystep explanation:
Source TRUST ME BRO
If the figure on the left is the base of a right prism that is 8 feet high, how many
sugar cubes that measure 1 foot on a side will the solid hold? What is the
surface area of the prism? Dimensions are in feet. All angles are right angles.
Number of sugar cubes hold the sugar cube = 768÷1 = 768 unit
Surface area of the prism = 8×8 + 6×8 + 4×8 + 4×8 + 4×8 + 4×8 + 8×8+ 14×8 + 8×8 + 4×4 + 4×8 = 512 sqft
Divide the base area of figure into three parts
Area of the 1st part = 8×6 = 48 sqft
Area of the 2nd part = 4×4 = 16 sqft
Area of the 3rd part = 4×8 = 32 sqft
Height of the prism is 8 ft
So the total volume of the prism ,
Volume = 8×( 6×8 + 4×4 + 4×8 )
= 8×( 48 + 16 + 32 )
= 8×96 = 768 cubic feet
1 feet side sugar cube solid holds a volume = 1×1×1 = 1 cubic feet
Number of sugar cubes hold the solid prism = volume of prism / volume of sugar cube
Number of sugar cubes hold the sugar cube = 768÷1 = 768 unit.
Surface area of the prism =( lateral surface area) + (top surface area)
Lateral surface area = 8×8 + 6×8 + 4×8 + 4×8 + 4×8 + 4×8 + 8×8+ 14×8 = 416 sqft
Top surface area = 8×8 + 4×4 + 4×8 = 96 sqft
Surface area of the prism = 8×8 + 6×8 + 4×8 + 4×8 + 4×8 + 4×8 + 8×8+ 14×8 + 8×8 + 4×4 + 4×8 = 512 sqft
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What is 23a 76b - 17a 42b
Factor completely 3x4 – 30x³ +75x². (1 point)
O3(x - 5)²
3x²(x - 5)²
3x²(x²-10x+25)
3x²(x + 5)(x - 5)
Answer: 3x²(x - 5)²
Step-by-step explanation:
Factoring out 3x² of each term leaves you with 3x²(x² - 10x +25)
We can still factor out (x² - 10x +25) to (x-5)(x-5), which is simply (x-5)².
This will leave you with 3x²(x - 5)².
A line that intersects two or more lines in a plane at different points is called a.
A line that intersects two or more lines in a plane at different points is called a transversal line.
A line is a geometrical figure that has length and can be extended in both directions.
Line is of two types: Straight and curved.
There are other types of lines also:
1. Parallel lines: Regardless of the length of the lines, two lines that run parallel to one another and are separated by the same distance but do not intersect are known as parallel lines.
2. Perpendicular lines: When two non-parallel lines cross at a place, they are said to be intersecting. The point of intersection is the solitary intersection of two lines.
3. Transversal lines: A straight line called a transversal cuts two or more lines, some of which may or may not be parallel. In the idea of geometry, a transversal line intersects two lines in the same plane at two different locations.
Hence, A line that intersects two or more lines in a plane at different points is called a transversal line.
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Identify the type of transformation.
The type of transformation is translation
How to determine the type of transformation?The figures represent the given parameters
On the figure, we can see that:
Both shapes have the same size
This means that none of the shapes is dilated
Also, the orientation of the shapes are the same
This implies that the shapes are not rotated or reflected
So, the closest transformation is translation
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Anita works 31 hours next week, What is her gross
pay, total amount of deductions, and net pay,
assuming the same percentage is taken out for each
of her deductions during the next pay period?
What formula will we use to calculate her gross pay:
Answer:
In order to answer this question, the amount she makes must be provided.
The radius of a circle is 1. What is the measure, in radians, of the angle subtended by an arc 13 18 long?
The measure of the arc 13cm long with a radius = 1 is 13rad
What is an arc of a circle?The arc of a circle is defined as the part or segment of the circumference of a circle. A straight line that could be drawn by connecting the two ends of the arc is known as a chord of a circle. If the length of an arc is exactly half of the circle, it is known as a semicircular arc.
Length of an arc = ∅/360 x 2πr
where ∅ = subtended angle in degree
r = 1 = radius of the complete circle
length = 13
13 = ∅ /360 x 2 x π x 1
but 2π rad = 360 degrees
substitute 2π rad for 360 into the equation
13 = ∅/2π rad x 2 x π x 1
By cross multiplying
∅ = 13 x 2π rad / 2 x π
∅ = 13 rad
In conclusion, the angle subtended by the arc in radians is 13 rad.
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Can someone help me ?
Answer:
2
Step-by-step explanation:
2 [tex]\frac{3}{5}[/tex] ÷ 1 [tex]\frac{3}{10}[/tex]
[tex]\frac{13}{5}[/tex] ÷ [tex]\frac{13}{10}[/tex]
[tex]\frac{13}{5}[/tex] x [tex]\frac{10}{13}[/tex] = 2
(03.02 LC)
A turtle is 6 feet below the surface of the sea. If his position can be recorded as −6 feet, what would the position of 0 represent?
Group of answer choices
A.) 6 feet in the sea
B.) 6 feet above the water
C.) At the bottom of the sea
D.) On the surface of the sea
Option (D) is the correct option and
The position of 0 represents on the surface of the sea.
Given, a turtle is 6 feet below the surface of the sea.
And his position can be recorded as −6 feet.
Now, if his position is recorded as -6 feet, then
according to the cartesian plane
0 represents the origin i.e. the surface of the sea.
Hence, Option (D) is the correct option and
The position of 0 represents on the surface of the sea.
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When 5 is added to 1/2 of a number, the result is 6 less than the number. Find the number.
Answer:
5 - 1/2x = x - 6
Step-by-step explanation:
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campus residence office receives 120 applications for ra from students. assuming that these applicants can be viewed as a random sample of all such students, what is the probability that between 35% and 45% of them are women if 40% of all students are women? round your answer to 3 decimal places.
The probability to have women applications between 35% to 45% is 1.
Here we are given that the sample number of applications received was 120.
Also, 40% of total applications are of women.
Hence this is clearly a Binomial Distribution with,
n = 120
p= 0.4
We need to find the probability that the sample applications have women applicants between 35% to 45%. For this, we need to use the method of Normal Approximation
Now,
np = 120 X 0.4
= 48
Since np > 10,
We can use Normal approximation here, with
mean = np = 48
Variance = np(1 - p)
= 48 X 0.6
= 28.8
35% of applicants = 42
45% of applicants = 54
Hence we need to find
P(42<X<54)
P(a<X<b)
= P(X<b) - P(X<a)
Therefore we get
P(X < 54) - P(X<42)
Now subtracting it with its mean and dividing it by its standard deviation we get
P(X < (54 - 48)/5.3666) - P(X < (42- 48)/5.3666)
= P(X < 1.1180) - P(X < -1.1180)
= 0.86650 - 0.13350
= 1
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Mr. Brian is planning a staff party. Plates come in packs of 8 and napkins come in packs of 12. Mr. Brian wants to buy the same number of napkins and plates. What is the smallest number of plates Mr. Brian can buy?
Solving inequalities
Solve -2x-6>x+9.
The solution for the given inequality is x < -5.
What is inequality in mathematics?
An inequality in mathematics is a relationship that makes a non-equal comparison between two numbers or other mathematical expressions. It is most commonly used to compare the sizes of two numbers on a number line.
The given inequality is -2x - 6 > x + 9
Subtract x from both sides.
-2x -6 -x > x + 9 -x
-3x - 6 > 9
Add 6 to both sides, and we get
-3x - 6 + 6 > 9 + 6
-3x > 15
Divide both sides by -3
⇒ x < -5
Hence, the solution for the given inequality is x < -5.
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At a butcher hop, Hildabought beef and pork. She left with pound of meat. Expre the number of pound of pork he bought uing a decimal
Using conversion of improper fraction to a decimal, we find that she bought 18.32 pounds of meat, which is a terminating decimal.
What is unitary method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units. What can be values and units.Let's say you go to the store to buy six apples. You are informed by the shopkeeper that he is offering 10 apples for Rs 100. In this instance, the value and the units are the price of the apples.Recognizing the units and values is crucial when using the unitary technique to a problem.Always write the items that need to be computed on the right side and the things that are known on the left side to simplify things. We are aware of the quantity of apples and the amount of money in the aforesaid problem.acc to our question-
The amount of mean she left, in pounds, was of:We want to convert the improper fraction to decimal, which is made adding the decimal fraction to the integer part, that is:The division of 800 by 25 is exact(32), thus terminating decimal, and she bought 18.32 pounds.learn more about unitary method click here:
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Help would be much appreciated
Answer:
[tex]r(t)=\dfrac{1}{t}\ln \left(\dfrac{A}{P}\right)[/tex]
Step-by-step explanation:
Given function:
[tex]A(t)=Pe^{rt}[/tex]
Divide both sides by P:
[tex]\implies \dfrac{A}{P}=e^{rt}[/tex]
Take natural logs of both sides of the equation:
[tex]\implies \ln \left(\dfrac{A}{P}\right)=\ln e^{rt}[/tex]
[tex]\textsf{Apply the power law}: \quad \ln x^n=n \ln x[/tex]
[tex]\implies \ln \left(\dfrac{A}{P}\right)=rt\ln e[/tex]
Apply the natural log law: ln (e) = 1
[tex]\implies \ln \left(\dfrac{A}{P}\right)=rt[/tex]
Divide both sides by t:
[tex]\implies r=\dfrac{1}{t}\ln \left(\dfrac{A}{P}\right)[/tex]
Solve the inequality.
6(4q − 8) > 8(3q + 2)
The inequality 6(4q − 8) > 8(3q + 2) have no solution.
How to solve inequalities?The inequality can be solved as follows:
An inequality is an expression that has <, >, ≤ and ≥ symbols.
Therefore,
6(4q − 8) > 8(3q + 2)
open the bracket on both sides of the inequality
6(4q − 8) > 8(3q + 2)
24q - 48 > 24q + 16
add 48 to both sides of the inequality
24q - 48 > 24q + 16
24q - 48 + 48 > 24q + 16 + 48
24q > 24q + 64
Subtract 24 q from both sides of the inequality
24q > 24q + 64
24q - 24q > 24q - 24q + 64
0 > 64
The inequality cannot be solved
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2/5 of what number is 44
Answer:
110
Step-by-step explanation:
2/5=44/x
Cross multiply
2x=44(5)
2x=220
/2. /2
x=110
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a parallelogram has a 5-inch side and an 8-inch side that make a 50-degree angle. find the area of the parallelogram and the lengths of its diagonals.
For the given parallelogram of 5-inch side and an 8-inch side with an angle of 50-degree , the area of the parallelogram is equal to 30.64 square inches and the lengths of its diagonals are 11.85inches and 6.13 inches.
As given in the question,
Side lengths of the parallelogram are :
From the attached diagram we have,
Side AC = 5 inches
Side CD = 8 inches
Angle ACD = 50°
Draw altitude 'h' from vertex A to the base CD at point E.
Length of CE = x inches
In ΔACE,
sin 50° = h / 5
⇒ h = 5 sin 50°
⇒ h = 5 (0.766)
⇒ h = 3.83 inches
cos 50° = x/ 5
⇒ x = 5 cos 50°
⇒ x = 5 ( 0.6428)
⇒ x = 3.214 inches
Length of diagonal BC
BC = √ h² + ( 8 + x )²
= √(3.83)² + ( 8 + 3.214)²
= √140.422696
≈ 11.85 inches
Length of diagonal AD
AD = √ h² + ( 8 -x )²
= √(3.83)² + ( 8 - 3.214)²
=√37.574696
≈ 6.13 inches
Area of a parallelogram ABCD
= height × corresponding base
= 3.83 × 8
= 30.64 square inches
Therefore, for the given parallelogram of 5-inch side and an 8-inch side with an angle of 50-degree , the area of the parallelogram is equal to 30.64 square inches and the lengths of its diagonals are 11.85inch and 6.13 inch.
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(x + 2)(x - 1)(x - 2) = 0
polynomial equations
Answer:
∴ (x + 2)(x - 1)(x - 2) = x³- x² - 4x + 4
Step-by-step explanation:
(x + 2)(x - 1)(x - 2) = (x² + 2x - x - 2)(x - 2)
= (x² + x - 2)(x - 2)
= (x³ + x² - 2x - 2x² - 2x + 4)
= x³ - x² - 4x + 4
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The percentage error of Bob’s measurement is 3.87%
The percentage error is The difference between the estimated value and the actual value in relation to the actual value is given as a percentage. Analyst use this formula to determine how big is the error in a relation to true value.
Percentage error can be calculated by the given formula
percentage error=((Exprimental value-Actual value))/(Actual value)∙100
Here, given that
The experimental volume of liquid is 18.8 ml, and the actual volume of liquid is 18.1 ml
i.e. exprimental volume=18.8 mL
and, actual volume=18.1 mL
Now, we will calculate the percentage error
So,
percntage error=((18.8-18.1))/18.1∙100
percentage error=0.7/18.1∙100
percentage error=0.0387∙100
percentage error=3.87%
Hence,
We got percentage error of 3.87% in measurement
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Please help due tonight.
Answer:
A
Step-by-step explanation:
Why is the formula for a triangle 1 2BH?.
By using the rectangle, we proved that area of triangle is half the area of rectangle that is 1/2 (base×height).
Some properties of rectangle are ?The opposite sides are parallel and equally spaced apart, and each internal angle is 90 degrees.360 degrees are equal to the total of all internal angles.Both of the diagonals are identical in length and parallel to one another.A rectangle's perimeter is equal to 2a+2b units if its sides are of lengths a and b.A rectangle with sides that are a and b long has an area that is equal to ab sin 90 square units.Diagonally is the diameter of the circumference of a rectangle.To Prove:- Area of a triangle= 1/2 (base×height)
Diagonals of a rectangle divide it into two parts of equal parts that is area
.
Let ABCD be a rectangle.
In ΔABC and ΔADC,
AC=AC
By Alternate Interior Angles:
∠BAC=∠CAD
∠BCA=∠CDA
Hence, ΔABC≅ΔACD
∴ar(ΔABC) =ar(ΔACD)
Let ΔABC,
We draw a line AD perpendicular to BC, line EF parallel to BC passing through A and lines BE and CF , perpendicular to BC passing through B and C respectively.
In rectangle ADBE,
we get,
ar(ΔABE)=ar(ΔADB)
Similarly, in rectangle ADCF,
ar(ΔADC)=ar(ΔACF)
Now, area of rectangle BCFE, from axiom,
=(length)⋅(breadth)
=AB⋅BC
=AD⋅BC
Also,
ar(BCFE)
=ar(ADBE)+ar(ADCF)
=2⋅ar(ΔADC)+2⋅ar(ΔADB)
=2(ar(ΔADC)+ar(ΔADC)
=2(ar(ΔABC))
From (1) and (2),
2(ar(ΔABC))=AD⋅BC
ar(ΔABC)=1/2AD⋅BC
ar(ΔABC)=1/2(base)⋅(height)
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Adaim ha a goal to reach 70 mile. If he hike 8 mile per day, how long will it take him to hike all 70 mile?
It will take at least 9 days for adaim to reach his goal of 70 miles.
Given that,
The 70-mile mark is Adaim's objective. He can hike 8 miles every day.
To find : How long will he need to hike the entire 70 miles?
Therefore, your main task will be to find X.
X times 8 equals 70.
Dividing both sides by 8 yields X on its own.
X therefore equals 70/8.
In the event that your teacher prefers a decimal, you would convert that to 8.75 and round to 9 because it is a day.
Therefore, It will take atleast 9 days for adaim to reach his goal of 70 miles.
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what is the probability that when drawing 2 cards without replacement from a standard 52 card deck that the second is an ace given that the first is a 10
The probability is 1/3 of the given event .
What is probability ?Probability turned into added into arithmetic to are expecting the possibility of an occasion occurring. Probability essentially approach how in all likelihood it's miles that some thing will happen. This is the fundamental principle of possibility and is likewise utilized in possibility distributions to examine feasible consequences of random experiments.
CalculationThere are 52×51 outcomes when you draw 2 cards one after another without returning the first drawn card to the deck.
There are 48×4 outcomes when the first card is not Ace and the second card is Ace. There are 4×3 outcomes when both cards are Ace. The total outcomes are 48×4+4×3=51×4.
The probability is 51×452×51=51/52×4/51=4/52=1/3.
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Ian is bisecting line segment cd. First, ian places the compass on point d and opens it to a width larger than half of the segment. What is the next step?.
The next step to bisect the line segment CD is to make an arc above the line as well as an arc below the line.
How to cut a line segment in half is as follows:
• Place the compass at point D.
• Set the compass to be just a little bit longer than half the length of the line segment.
• Draw arcs above and below the line.
• Do the same thing by keeping the compass at C point while maintaining the same compass width.
• Draw the line segment that passes through the points where both arcs crosses each other.
Hence, after keeping compass on point D, the next step will be to draw an arc above and below the line segment.
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The points (2,-20) and (r,-5) lie on a line with slope 5/4. Find the missing coordinate r.
Answer: 14
Step-by-step explanation:
The formula for slope in this problem is:
[tex]\frac{-5-(-20)}{r-2}=\frac{5}{4}[/tex]
[tex]\frac{15}{r-2} = \frac{5}{4}[/tex] (cross multiply)
60 = 5(r-2)
60 = 5r - 10
70 = 5r
14 = r
Check: (2, -20) (14, -5)
[tex]\frac{-5-(-20)}{14-2}[/tex]
[tex]\frac{15}{12}[/tex]
[tex]\frac{5}{4}[/tex]
I took a picture because it may be a little difficult to understand if I wrote it in text. Hope this helps.
no contestant received the same score on two different days. if a contestant is selected at random, what is the probability that the selected contestant received a score of 555 on day 222 or day 333, given that the contestant received a score of 555 on one of the three days?
The probability that the selected contestant received a score of 555 on day 222 or day 333 is 5/7.
If it is given that on day 222 the no of contestants received a score of 555 is 2 and no of contestants received a score of 555 on day 222 is 3.
Given:
It is given that no contestant received the same score on two different days. So, we have 7 days in a week which means there are 7 contestants only who could be chosen and have a score of 555.
So, the contestants who received a score of 555 on any day = 7.
Now, the contestant received a score of 555 on day 222 is 2 and on day 333 is 3.
Probability = No of favorable outcomes/Total no. of outcomes
Probability = (2 + 3)/7 = 5/7
The probability that the selected contestant received a score of 555 on day 222 or day 333 is 5/7.
If it is given that on day 222 the no of contestants received a score of 555 is 2 and no of contestants received a score of 555 on day 222 is 3.
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