The value of the logarithmic function log₄7 = 1.404, when the values of the logarithmic functions log₄3 = 0.792 and log₄21 = 2.196.
We are given the logarithmic functions:
log₄3 = 0.792 ,,, (i), and log₄21 = 2.196 ... (ii),
and we are asked to find the value of the logarithmic function log₄7.
On subtracting (i) from (ii), we get:
log₄21 - log₄3 = 2.196 - 0.792.
Using the quotient law of logarithms, according to which:
logₓa - logₓb = logₓ(a/b), we can write the above equation as:
log₄(21/3) = 1.404,
or, log₄7 = 1.404.
Therefore, the value of the logarithmic function log₄7 = 1.404, when the values of the logarithmic functions log₄3 = 0.792 and log₄21 = 2.196.
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Answer:
A.
1.404
Step-by-step explanation:
Given f of x is equal to the quantity 8x plus 1 end quantity divided by the quantity 2x minus 9 end quantity, what is the end behavior of the function? As x → -∞, f(x) → 9 ; as x → ∞, f(x) → 9. As x → -∞, f(x) → -9; as x → ∞, f(x) → -9. As x → -∞, f(x) → -4; as x → ∞, f(x) → -4. As x → -∞, f(x) → 4; as x → ∞, f(x) → 4.
Using limits, it is found that the end behavior of the function is given as follows:
As x → -∞, f(x) → 4; as x → ∞, f(x) → 4.
How to find the end behavior of a function f(x)?The end behavior of a function f(x) is given by the limit of f(x) as x goes to infinity.
In this problem, the function is:
[tex]f(x) = \frac{8x - 1}{2x - 9}[/tex]
Considering that x goes to infinity, for the limits, we consider only the terms with the highest exponents in the numerator and denominator, hence:
[tex]\lim_{x \rightarrow -\infty} f(x) = \lim_{x \rightarrow -\infty} \frac{8x}{2x} = \lim_{x \rightarrow -\infty} 4 = 4[/tex].[tex]\lim_{x \rightarrow \infty} f(x) = \lim_{x \rightarrow \infty} \frac{8x}{2x} = \lim_{x \rightarrow \infty} 4 = 4[/tex].Hence the correct statement is:
As x → -∞, f(x) → 4; as x → ∞, f(x) → 4.
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Answer:
D
Step-by-step explanation:
does this table represent a function? why or why not x:2,2,3,4,5 y:1,4,4,2,5
Answer:
No, the table does not represent a function.
Step-by-step explanation:
By definition, a function will not have 2 or more results for the same input.
The table shows two values of y for the same x: (2,1) and (2,4). The same input, 2, results in two different values, 1 and 4.
See attached image.
Given that the expression “p dollars for every q items” describes a unit price, which statement must be true?
The complete question is
"Given that the expression “p dollars for every q items” describes a unit price, which statement must be true?
p = 1
p = q
q = 1
pq = 1"
The statement that must be true would be from option D; pq = 1.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
Given that the expression “p dollars for every q item” describes a unit price,
So, the equation will be formed as
p x q = 1
pq = 1
Hence, the statement that must be true would be from option D; pq = 1.
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Find the slope of the line on the graph.
Write your answer as a fraction or a whole
number, not a mixed number or decimal.
Answer:
3/2
Step-by-step explanation:
Solve the equation for 0 <= x < 2pi.
(2sin x - 1)(2cos^2 x - 1) = 0
If
(2 sin(x) - 1) (2 cos²(x) - 1) = 0
then either
2 sin(x) - 1 = 0 or 2 cos²(x) - 1 = 0
sin(x) = 1/2 or cos(2x) = 0
The first equation gives two families of solutions,
x = arcsin(1/2) + 2nπ = π/6 + 2nπ
x = π - arcsin(1/2) + 2nπ = 5π/6 + 2nπ
where n is any integer; we get the solutions x = π/6 and x = 5π/6 in the interval 0 ≤ x < 2π when n = 0.
The second equation also gives two families of solutions,
2x = arccos(0) + 2nπ = π/2 + 2nπ
2x = -arccos(0) + 2nπ = -π/2 + 2nπ
Divide both sides by 2 :
x = π/4 + nπ
x = -π/4 + nπ
Then the solutions we want are x = π/4 and x = 5π/4 (when n = 0 and 1 in the first family, respectively) and x = 3π/4 and x = 7π/4 (when n = 1 and 2 in the second family).
We have 6 solutions, so A is the correct choice.
Can I get some help with this please?
Answer:
c =2.5
Step-by-step explanation
1.5×1.5=2.25
2×2=4
4+2.25=6.25
√6.25=2.5
c=2.5
Simplify the expression below. How many digits are in the answer?
2.784 - 3.00079 + 10.671 x 1.0798
Answer:
11.3057558
Step-by-step explanation:
Find the measure of ZDCF. C F mDF = 49 G E MEG = 127 Find the measure of angle DCF
Answer:
Step-by-step explanation:
Comment
If two secants intersect outside a circle (as these two do) then the angle at which they meet is 1/2 the difference between the intersected arcs. Put much simpler <DCF = 1/2 (arc EG - arc DF)
Givens
Arc EG = 127
Arc DF = 49
Solution
<DCF = 1/2(127 - 49)
<DCF = 1/2(78)
<DCF = 39
Which ordered pair would form a proportional relationship with the point graphed below?
On a coordinate plane, a line goes through points (0, 0), (10, 40) and (negative 10, negative 40).
(40, 10)
(–5, –10)
(5, 20)
(–10, –20)
Answer:
(5,20)
Step-by-step explanation:
divide both sides of (10, 40) by the same number 2 and you will get (5,20). The points should all lie on the same straight line to form a proportional relationship.
Answer: 5,20
Step-by-step explanation:
Having exactly the same shape and size
Answer:
If two things have the same shape and size then they are congruent to one another. If they are only the same shape but not size, then they are similar.
If two things have the same shape and size then they are congruent to one another.
If they are only the same shape but not size, then they are similar.
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Which is not a characteristic of the absolute value parent function?
Answer:
B
Step-by-step explanation:
the range of y=|x| is not all real numbers its [0,inf)
sign - ...
Zekrom
A group of people were given a personality test to determine if they were Type A or Type B. The results are shown in the table below:
Answer choices:
Compare P(Male or Type B) with P(Male | Type B). (5 points)
P(Male or Type B) > P(Male | Type B)
P(Male or Type B) = P(Male | Type B)
P(Male or Type B) < P(Male | Type B)
There is not enough information.
The option third "P(Male or Type B) < P(Male | Type B)" is correct because 0.575 < 0.76
What is probability?It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.
P(Male or Type B) = (number of male + number of type B - number that are both)/total population
[tex]\rm = \dfrac{103 + 50- 38}{200 }[/tex]
= 0.575
P(Male | Type B) = (number of male people inside the type B)/(number of Type B people)
= 38/(38 + 12)
= 0.76
0.575 < 0.76
P(Male or Type B) < P(Male | Type B)
Thus, the option third "P(Male or Type B) < P(Male | Type B)" is correct because 0.575 < 0.76
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Round to 2 decimal places 8.041
Answer:
8.04
Step-by-step explanation:
If the last digit in 8.041 is less than 5, then remove the last digit.
I hope this helps!
Shape x is translated by 4 units to the right and 1 unit down, what are the coordinates of c'
A coordinate system in geometry is a system that employs one or more integers, or coordinates, to define the position of objects. The coordinates of c' are (a+4, b-1).
What are coordinates?A coordinate system in geometry is a system that employs one or more integers, or coordinates, to define the position of points or other geometric components on a manifold such as Euclidean space.
Let the coordinates of c be represented by (a,b). Now, if the shape x is translated by 4 units to the right and 1 unit down. Then, the coordinates of c' are:
c = (a, b)
c' = (a+4, b-1)
Hence, the coordinates of c' are (a+4, b-1).
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HELPPPP PLEASEE DUEE SOONNN
(A) n=w by the corresponding angles theorem.
(B) This is the correct answer. n=s by the vertical angles theorem and s and x are supplementary by the same-side interior angles theorem. Thus, n and x are supplementary, and are not always equal.
(C) n=z by the alternate exterior angles theorem.
(D) s=w, so (s+w)/2 = (s+s)/2 = s. Since n=s by the vertical angles theorem, n=s.
(E) n and w are equal by the corresponding angles theorem, and w and y are supplementary as they form a linear pair. Thus, n+y=180, and it follows n=180-y.
The exchange rate of Mexican pesos for US dollars is approximately 19 pesos for 1 dollar if Lynn exchanges 4,000 pesos for US dollars what was the approximate value in US dollars
Unit conversion is a way of converting some common units into another without changing their real value. The approximate value in US dollars is $210.53.
What is unit conversion?Unit conversion is a way of converting some common units into another without changing their real value. for, example, 1 centimetre is equal to 10 mm, though the real measurement is still the same the units and numerical values have been changed.
The exchange rate of Mexican pesos for US dollars is approximately 19 pesos for 1 dollar. Therefore, we can write,
19 pesos = 1 dollar
1 pesos = 1/19 dollar
if Lynn exchanges 4,000 pesos for US dollars, then the approximate value in US dollars will be,
4,000 pesos = 4000/19 = 210.53 dollars
Hence, the approximate value in US dollars is $210.53.
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Find the midpoint of the line segment with end coordinates of:
(-1,7) and (3,-2)
Give coordinates as decimals where appropriate.
Answer:
(1,2.5)
Step-by-step explanation:
On the graph, the (-1,7) lies in the top right grid. The (3,-2) lies in the bottom left grid. If you use a graphing calculator, the middle is hard to find but you will find (1, 2.5) or (1, 5/2).
Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options.
x < 5
–6x – 5 < 10 – x
–6x + 15 < 10 – 5x
A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right.
A number line from negative 3 to 3 in increments of 1. An open circle is at negative 5 and a bold line starts at negative 5 and is pointing to the left.
The correct simplified inequality is - 6x + 15 < 10 - 5x and the number line representation is "an open circle is at 5 and a bold line starts at 5 and is pointing to the right".
The given inequality is -3(2x - 5) < 5(2 - x)
We need to simplify the inequality.
What is inequality?In mathematics, inequality is a statement of an order relationship greater than, greater than or equal to, less than, or less than or equal to between two numbers or algebraic expressions.
Consider LHS and simplify -3(2x - 5) = -3(2x)-5(-3)
⇒ -3(2x - 5) = - 6x + 15 [∵(-)(-) = (+)]
Consider RHS and simplify 5(2 - x) = 5(2) + 5(-x)
⇒5(2 - x) = 10 - 5x [∵(+)(-) = (-)]
Now, - 6x + 15 < 10 - 5x
By subtracting 15 from both sides, we get
- 6x < -5 - 5x
By adding 5x to both sides, we get - x < - 5
The coefficient of x is -1. So, divide both sides by -1
Then we get x > 5
Hence, the correct simplified inequality is - 6x + 15 < 10 - 5x and the number line representation is "an open circle is at 5 and a bold line starts at 5 and is pointing to the right".
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A (-2, 1) B (3,6) Find the gradient of the line
Step-by-step explanation:
A (-2,1) B (3,4) find the gradient of the line
m = -1
we know that=
m/y2 - y 1) / (x2-1)
= (-4-1)/{3-(-2)
=-5/(3+2)
=5/5
= 1
The radius of the ring is 0.25 cm. Find the circumference of the ring.
Answer: circumference 1.5714
Answer:
Circumference formula: 2πr
2π(0.25) = 0.5π or 1.57
Circle A has a diameter of 8 inches, a circumference of 25.12 inches, and an area of 50.24 square inches. The diameter of circle B is 3 inches, the circumference is 9.42 inches, and the area is 7.065 square inches.
Part A: Using the formula for circumference, solve for the value of pi for each circle. (4 points)
Part B: Use the formula for area and solve for the value of pi for each circle. (4 points)
Part C: What observation can you make about the value of pi for circles A and B? (2 points)
I just need the equations and answer for each part please
The value of pi determined is same when used the circumference formula and the formula of area.
What is Circle ?A circle is a round shaped figure , whose all the point lie on same plane.
It is given that
The value of pi is about 3.14, and it is the same when using both the area and circumference.
The circumference is found by
Circumference = π * diameter
For circle A:
25.12 = π * 8
π = 3.14
For circle B:
9.42 = π * 3
π = 3.14
The area is given by
Area = π * diameter² / 4
For circle A:
50.24 = π * (8²)/4
π = 3.14
For circle B:
7.065 = π * (3²)/4
π = 3.14
The value of pi is about 3.14,
The value of pi determined is same when used the circumference formula and the formula of area.
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Select from the drop-down menu to create a statistical question Susan could ask her friends in a survey.
How many
pushups can you do
days does melanie exercise
bones are in the human body
pounds are in a kilogram
The statistical question that Susan could ask her friends in a survey is that How are push-ups important for the body?
What are statical questions?It should be noted that statistical or research questions are the questions that an individual seeks answers to.
In this case, the statistical question that Susan could ask her friends in a survey is that How are push-ups important for the body?
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Answer: 2. How many pushups can you do
I got 100% on my online homework and here is proof.
Please mark me brainliest : D
The loudness, L, measured in decibels (Db), of sound intensity, I, measured in watts per square meter, is defined as L = 10 log StartFraction I Over I 0 EndFraction, where I 0 = 10 Superscript negative 12 and is the least intense sound a human ear can hear. What is the approximate loudness of a dinner conversation with a sound intensity of 10–7?
The correct option is Option D: the approximate loudness of a dinner conversation will be 50Db with a sound intensity 10⁻⁷.
The loudness L, ( which is measured in decibels (Db)), of the sound of the intensity I, can be calculated in watts per square meter,
L = 10 log(I/I₀)
where I₀ = 10⁻¹² which is the least intensity that a human can hear.
The sound intensity of a dinner conversation= I= 10⁻⁷
Loudness L of that conversation = 10 log (10⁻⁷/10⁻¹²)
= 10 log(10⁻⁷⁻⁽⁻¹²⁾)
= 10 log(10⁻⁷⁺¹²)
= 10 log(10⁵)
= 10*5
= 50 Db
Therefore the correct option is Option D: the approximate loudness of a dinner conversation will be 50Db with a sound intensity 10⁻⁷.
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Which statement is true regarding the graphed functions?
Answer:
4th option
Step-by-step explanation:
the solution is at the point of intersection of the 2 lines, that is
(- 2, 4 ) where x = - 2 , then
f(- 2) = g(- 2)
Answer: D. or f(–2) = g(–2)
Step-by-step explanation:
In the given graph, the two lines intersects at x = -2
And intersection point is that point, where the y values of the two graphs are equal.
That is: f(x) = g(x)
And at x=-2, the y values are equal. So:
f(-2) = g(-2)
The graph of quadratic function f has zeros of -8 and 4 and a maximum at (-2,18). What is the value of a in the function’s equation?
To find the equation of a parabola given the vertex and the zeroes, we can use the intercept form equation to help us:
[tex]y=a(x-r)(x-s)[/tex]
r and s = intercepts/zeros of the graphSolving the QuestionWe're given:
Zeros: -8, 4Maximum: (-2, 18)[tex]y=a(x-r)(x-s)[/tex]
⇒ Plug in the given information:
[tex]y=a(x-(-8))(x-4)\\18=a(-2-(-8))(-2-4)\\18=a(-2+8)(-2-4)\\18=a(6)(-6)\\18=a(-36)\\1=-2a\\\\a=-\dfrac{1}{2}[/tex]
Answer[tex]a=-\dfrac{1}{2}[/tex]
A pet store has 10 puppies, including 3 poodles, 4 terriers, and 3 retrievers. if rebecka and aaron, in that order, each select one puppy at random without replacement (they may both select the same one), find the probability that they both select a poodle
Step-by-step explanation:
the problem description is seemingly contradicting itself.
"without replacement" means that you don't put the picked item back into the bag or "pool" of items.
and that means that after Rebecka picked a puppy, Aaron CANNOT pick the same one at all.
but then it says that they both may select the same one. which means it is WITH replacement.
so, what is it now ?
I have to give you both answers, and you will have to clarify with your original question or directly with your teacher what is the true condition.
in any case, a probability is always
desired cases / total possible cases.
WITH replacement (they can both pick the same puppy) :
there are 10 puppies, from which 3 are poodles.
so, total possible cases = 10, desired cases = 3
the probability to pick a poodle at the 1st pick = 3/10.
the picked puppy goes back.
the probability to pick a poodle at the 2nd pick = 3/10.
the probability that both picks are poodles is
3/10 × 3/10 = 9/100 = 0.09
WITHOUT replacement :
the first picked puppy is not returned to the group of 10 puppies, so, it can't be picked again, and the number of available puppies gets less as each puppy is removed. this changes the probabilities.
at the beginning we have 10 puppies, from which 3 are poodles.
the probability to pick a poodle at the 1st pick = 3/10.
the picked puppy does NOT go back.
now we have 9 puppies for Aaron to pick from. and for our desired cases for the second pick we have to combine it with the outcome, that the first pick was a poodle.
that means we have only 2 poodles left in the group of 9 puppies.
the probability to pick a poodle at the 2nd pick = 2/9.
the probability that both picks are poodles is therefore
3/10 × 2/9 = 6/90 = 1/15 = 0.066666666...
Question 3
In Question 1, what do you notice about the x-coordinates before and after a horizontal stretch? What do you notice about the y-coordinates
before and after a vertical stretch? Express your answer in terms of Nx and Ny
The y coordinates doesn't change under a horizontal stretch while the x coordinates do not change under a vertical stretch.
How to depict the coordinate?It should be noted that coordinates are vital in determine the position of an object or points.
In this case, the y coordinates doesn't change under a horizontal stretch while the x coordinates do not change under a vertical stretch.
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Answer:
The y-coordinates do not change under a horizontal stretch. The x-coordinates do not change under a vertical stretch.
Step-by-step explanation:
What is the slope of the line represented by the equation y = -x + 1/2x+1/4
- 1/2
- 1/4
1/4
1/2
find the five ratoinal numbers between -2/3 and -1
Answer:
-31/30, -32/30, -33/30, -45/30, -49/30.
Step-by-step explanation:
-2/3 and -1 make denominators 30
-60/30 and -30/30
put any five
NEED HELP ASAP! ITS IN THE IMAGE BELOW.
i’ve done the graph which is part a and b but i need help in part c and d, help will be appreciated!
Answer:
(a) see below
(b) see attached
(c) (15, 180) is not on the line
(d) a = -40
Step-by-step explanation:
Given equation:
[tex]y = 10x+20[/tex]
Part (a)
To complete the table of values, simply substitute each value of x into the given equation:
[tex]x=-3 \implies y=10(-3)+20=-10[/tex]
[tex]x=-1 \implies y=10(-1)+20=10[/tex]
[tex]x=0 \implies y=10(0)+20=20[/tex]
[tex]x=1 \implies y=10(1)+20=30[/tex]
[tex]x=3 \implies y=10(3)+20=50[/tex]
[tex]\large \begin{array}{| c | c | c | c | c | c | c | c |}\cline{1-8} x & -3 & -2 & -1 & 0 & 1 & 2 & 3\\\cline{1-8} y & -10 & 0 & 10 & 20 & 30 & 40 & 50\\ \cline{1-8} \end{array}[/tex]
Part (b)
Plot 2 points from the table and draw a straight line through them.
Part (c)
To determine if (15, 180) is on the line, substitute x = 15 into the given equation of the line:
[tex]\begin{aligned} x=15 \implies y & =10(15)+20\\& = 150 + 20\\& = 170\end{aligned}[/tex]
Therefore (15, 180) is not on the line
Part (d)
If (-6, a) is on the line, substitute x = -6 and y = a into the equation and solve for a:
[tex]\begin{aligned} y & = 10x+20\\\implies a & = 10(-6)+20\\a & = -60 + 20\\a & = -40\end{aligned}[/tex]
Therefore, a = -40