The type of function for f(x) = 2 · ㏒₅ (3 · x) is a logarithmic function. (Correct choice: B)
What kind of function is a given expression?
In this problem we must check the characteristics of an expression and conclude what kind of function is. First, we need to find if any trascendent operator, it not, then the function may be either polynomial or rational. If the function has a trascendent operator, then we must check if it is logarithmic or exponential.
At first glance, we see that the function includes only one trascendent operator, a "log" operator that creates a function of the form f(x) = A · ㏒ₙ (B · x). Therefore, the type of function for f(x) = 2 · ㏒₅ (3 · x) is a logarithmic function. (Correct choice: B)
RemarkThe statement is poorly formatted, correct form is shown below:
What type of function is f(x) = 2 · ㏒₅ (3 · x)? a) Exponential, b) Logarithmic, c) Polynomial, d) Rational.
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Answer: Logarithmic
Step-by-step explanation: Got the question right on test.
In the circle below, if < B = 39 °, what is the measure of arc AB?
From my analysis, the answer is likely to be D. I don't have a formula to prove it though.
Answer: 78 degrees.
Step-by-step explanation:
The other guy is wrong don't listen to him.
Find the area of the base of a drum if it needs 88 m long rope to tie twice it around.
solve with full solutions!
Answer:
[tex]154 $\ m^2[/tex]
Step-by-step explanation:
If 88 m of long rope is wrapped twice around the base of the drum, the circumference of the drum is 44m. We can use this information to find the radius of the base.
Find the RadiusThe equation for circumference is [tex]C=2\pi r[/tex]. We can substitute the value we found for circumference into the equation:
[tex]44=2\pi r[/tex]
Divide both sides by 2
[tex]22=\pi r[/tex]
Divide both sides by π
[tex]r=\frac{22}{\pi}[/tex]
Use the Radius to find the AreaThe area of a circle is [tex]A=\pi r^2[/tex]. We can substitute the value we found for the radius into the equation:
[tex]A=\pi (\frac{22}{\pi})^2\\[/tex]
[tex]A=\pi (\frac{22}{\pi})(\frac{22}{\pi})[/tex]
[tex]A=22*\frac{22}{\pi}[/tex]
[tex]A=\frac{484}{\pi}[/tex]
[tex]A\approx154[/tex]
The table lists the speeds of the fastest roller coasters in North America and Asia.
Roller Coaster Speeds in North America
(miles/hour) Roller Coaster Speeds in Asia
(miles/hour)
128
149.1
120
106.9
100
95
93
83
92
80.8
90
80.3
85
78.3
82
71.5
80
69.6
77
68.4
The difference of the means of the two data sets is .
The mean absolute deviation of the roller coaster speeds in North America is .
The mean absolute deviation of the roller coaster speeds in Asia is .
The difference of the means of the two data sets is = 4.57
The mean absolute deviation of the roller coaster speeds in North America is 13.3
The mean absolute deviation of the roller coaster speeds in Asia is 16.8
How to solve for the meansFirst we have to start with the data for North America
128, 120, 100, 93, 92, 80.8, 85, 82, 80, 77
To get the mean you have to sum up the values and divide through by the total number 10
937.8/10
Mean = 93.78
Mean Absolute Deviation = (128 - 93.78) + ( 120 - 93.78) + ( 100 - 93.78) + ( 93 - 93.78) + ( 92 - 93.78) + ( 80.8 - 93.78) + ( 85 - 93.78) + ( 82 - 93.78) + ( 80 - 93.78) + ( 77 - 93.78) / 10
133.32/10 = 13.3
For Asia, we have the data as
149.1, 106.9, 95, 83, 90, 80.3, 78.3, 71.5, 69.6, 68.4
Mean for Asia = 892.1/10
= 89.21
Mean Absolute Deviation = (149.1 - 89.21) + ( 106.9 - 89.21) + ( 95 - 89.21) + ( 83 - 89.21) + ( 90 - 89.21) + ( 80.3 - 89.21) + ( 78.3 - 89.21) + ( 71.5 - 89.21) + ( 69.6 - 89.21) + ( 68.4 - 89.21) / 10
= 168.32/10
16.8
The difference in the means = 93.78 -89.21
= 4.57
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4y^5-6y+8y^2-1 for y = -1
Answer:9
Step-by-step explanation:
A monkey has a strict banana eating
schedule. On a sunny day it eats 20
bananas and on a rainy day it eats 12
bananas. In 8 consecutive days it eats
112 bananas. Question: how many
sunny days are there in these 8 days?
Solve the system of equations
ax+y=2a
x+ay=1+a^2
Answer:
x = 1; y = a
Step-by-step explanation:
ax+y=2a
x+ay=1+a^2
-a²x-ay=-2a²
x+ay=1+a^2
(1 - a²)x = 1 - a²
x = (1 - a²)/(1 - a²)
x = 1
a + y = 2a
1 + ay = 1 + a²
a = y
x = 1; y = a
5. On the way to the museum, 50% of the students rode on the first bus.
What fraction of the students rode on the second bus? Show your work
in the space below. Remember to check your solution.
Answer:
1/2
Step-by-step explanation:
50% = 50/100 = 1/2
1/2 of the students rode the first bus.
1 - 1/2 = 1/2
1/2 of the students rode the second bus.
The x component of vector is 5.3 units, and its y component is -2.3 units. The angle that vector makes with the x-axis is closest to?
The angle that vector makes with the x-axis is closest to [tex]340^\circ[/tex].
What is a vector?
An item with both magnitude and direction is referred to be a vector. A vector can be visualized geometrically as a directed line segment, with an arrow pointing in the direction and a length equal to the magnitude of the vector. The vector points in a direction from its tail to its head.
If the magnitude and direction of two vectors match, they are the same vector. This indicates that if we take a vector and move it to a different point (without rotating it), the vector we finish up with is the same vector we started with.
Given,
[tex]x[/tex]-component of vector = 5.3
[tex]y[/tex]-component of vector = -2.3
angle = [tex]tan^{-1}(\frac{y}{x})[/tex]
angle = [tex]tan^{-1}(\frac{-2.3}{5.3} )[/tex]
angle = [tex]340^\circ[/tex]
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When Kenny's electricity went out one night, his clock stopped at 8:39 p.m. when Kenny woke up the next morning his power was back on and his clock read 5:34 a.m. When he called the time services, the time was actually 7:11 a.m. How long was his electricity off?
Answer:
Step-by-step explanation:
Let's look at this in this perspective. There are 60 minutes in 1 hour. What I would do first is get rid of the 39 minutes at the end of 8:39. Now you have 8:00. Count until you get to 7 AM. 9, 10, 11, 12, 1, 2, 3, 4, 5, 6, 7. That's 11 hours from 8 PM to 7 AM. 60 x 11 = 660. Now, there are 11 minutes more on that 7-o clock and the 39 minutes we got rid of in the beginning. 11 + 39 = 40. 660 + 40 = 700.
Answer: Kenny's energy was off for 700 minutes, or 11 hours and 40 minutes.
(2x+1)/(x²-3) simplified
The simplified expression of (2x+1)/(x²-3) is 2x/(x²-3) + 1/(x²-3)
How to simplify the expression?The expression is given as:
(2x+1)/(x²-3)
The above expression is a fraction and the numerator has 2 terms
For a fraction
A + B)/x
The fraction can be split as
A/x + B/x
Using the above as a guide, we have:
(2x+1)/(x²-3) = 2x/(x²-3) + 1/(x²-3)
Hence, the simplified expression of (2x+1)/(x²-3) is 2x/(x²-3) + 1/(x²-3)
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PLEASE HELP IN STUCK
Simplify these expressions
4. 9a+7-2a+13=
5. 21-3b+5b-7=
6.3c squared + 8c squared - 15=
Answer:
4) 7a+20
5) 14+2b
6) 25c² - 15
Step-by-step explanation:
4) 9a+7-2a+13= 9a-2a+7+13 = 7a+20
5) 21-3b+5b-7= 21-7+5b-3b = 14+2b
6) (3c)² + (8c)² - 15 = 9c² + 16c² - 15 = 25c² - 15
Solve the equation 3x² = 108.
Answer:
x = 6
Step-by-step explanation:
First we divide both sides by 3 :
x² = 108 ÷ 3
x² = 36
Now we square root both sides :
x = √36
x = 6
Hope this helped and have a good day
Answer:
x = ± 6
Step-by-step explanation:
Quick steps
[tex]3x^{2} =108[/tex]
[tex]x=\sqrt{\frac{108}{3} } =\sqrt{36}[/tex]
[tex]x=[/tex] ±6
A (positive) number has two square roots; one positive and one negative
Hope this helps
5x(3x-10) + (2x-6)(3x+8)
Answer: 21[tex]x^{2}[/tex] - 52x - 48
Step-by-step explanation:
Using the expanding rule we get
5x * 3x - 5x * 10 + (6[tex]x^{2}[/tex] - 18x + 16x -48)
15[tex]x^{2}[/tex] - 50x + 6[tex]x^{2}[/tex] - 2x - 48
21[tex]x^{2}[/tex] - 52x - 48
Answer:
21x^2-52x-48
Step-by-step explanation:
5x(3x-10) + (2x-6)(3x+8)
Distribute
5x^2 -50x+6x^2-2x-48
Combine like terms
21x^2-50x-2x-48
21x^2-52x-48
What would cause an Inequality sign in an equation to flip?
a.) When dividing both sides by a negative.
b.) When adding a negative to both sides.
c.) When multiplying a fraction by both sides.
d.) When subtracting a negative to both sides.
Answer:
When dividing both sides by a negative.
Step-by-step explanation:
When dividing OR multiplying both sides by a negative, we need to flip the inequality signs.
PLS HELP ME WITH THIS
Using it's concept, the experimental probability of getting an odd number and a number greater than 6 is given by:
1/5.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes. An experimental probability is calculated considering the results of previous trials.
In this problem, there are 10 trials, and of those, 2 of them, trial 8 and trial 10, resulted in an odd number and a number greater than 6, hence the probability is:
p = 2/10 = 1/5.
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How do you solve this geometry question?
The statement that <A > <C and <B > <D has been proved
How to prove that <A > <C and <B > <D?In geometry, the side length opposite the largest angle is the longest side.
Similarly, the side length opposite the smallest angle is the shortest side.
From the given figure of quadrilateral, we have the following sides in increasing order:
Side length ABSide length BCSide length ADSide length CDThe angles opposite the side lengths are:
Angle DAngle BAngle CAngle AThis means that:
<A > <C and <B > <D
Hence, the statement that <A > <C and <B > <D has been proved
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3 cm ▼ 2 cm The diagram shows a prism. Work out the volume of the prism. 4 cm 1 cm 12 cm
Write the point where the linear equation 3x + 4y = 12 cuts the x-axis.
Answer:
When the eqn cuts the x-axis , y=0
3x=12
x=12/3
x=4
So,at x=4 is the point at which the linear equation cuts the x-axis
Answer:
collect like terms
12xy=12
xy=1
A con is tossed n times. How many difference sequences of head and tails can you get?
Answer:
2^n
Step-by-step explanation:
So whenever you flip a coin, you can see it as 2 nodes branching off of each existing node. so for example when you flip a coin once you're going to have 2 sequences initially H and T, now when you flip a coin again for each of those 2 sequences 2 are going to branch off of that, making the total sequences 4, and the next flip 2 sequences are going to branch off each of the 4 sequences and so on. this can generally be described as: 2^n
I attached an image describing this a bit better but the bottom line is that for each 'end node'/sequence you're going to have 2 branch off of it, thus for each coin flip the number of sequences multiplies by 2
Answer:
2^n
Step-by-step explanation:
dont worry bout it ur welcome
Solve the equation in the image (yr 8 math, 40pt)
Answer:
a = 3
Step-by-step explanation:
4(2a - 3) = -2(a - 9)
8a - 12 = -2a + 18
10a = 30
a = 3
Let's check if we got it correct by substituting 3 for a in the original equation.
4(2*3 - 3) = -2(3 - 9)
4(6 - 3) = -2(-6)
4(3) = 12
12 = 12
What order will result in a final output of - 31 when the initial input is 0?? Someone please please helpoo
The order that will result in a final output of -31 when the first input is 0 is as follows; Third → Second → Fourth → First
How to find the order?First gives;
y = -2·x + 34 = 18
Second gives;
y = -x/3 - 10 = -38/3
Third gives;
= -24
Fourth gives;
y = (x - 2)² = 36
We have after several iterations;
Third gives,
= -24
Next we input into the second to get,
y = -(-24)/3 - 10 = 24/3 - 10 = 8 - 10 = -2
Next we input into the fourth to get,
y = ((-2) - 2)² = (-4)² = 16
Next we input into the first to get,
y = -2×16 + 34 = -32 + 34 = 2
Which gives the order as follows;
Third → Second → Fourth → First
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.
An unbiased number cube is rolled 24 times and lands on an even number 10 times. What is the approximate difference between the
theoretical and experimental probabilities for rolling an even number?
12%
17%
8%
2%
Answer:
8%
Step-by-step explanation:
The approximate difference between the theoretical and experimental probabilities for rolling an even number is 8%
Theoretical probability is what we expect to happen, whereas experimental probability is what actually happens when we try it out. The probability is still calculated the same way, using the number of possible ways an outcome can occur divided by the total number of outcomes. As more trials are conducted, the experimental probability generally gets closer to the theoretical probability.
Theoretical probability of rolling a cube and getting a even number is 1/2 or 50% as number of odd numbers and number of even numbers are equal.
Experimental probability = Favorable outcomes/Total outcomes
Experimental probability = 10/24 = 5/12 ≅ 42%
Thus approximate difference between these two equals 50% - 42% = 8%
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thu gọn biểu thức : (x-5)(x+5)-(x+1)^2
[tex](x-5)(x+5)-(x+1)^2\\=x^2 -25-(x^2+2x +1)\\=x^2 -25-x^2-2x -1\\=-2x-26[/tex]
ANSWER: -2x -26
Ok done. Thank to me :3
PLS HELP OR ILL FAIL MY CLASSES I RLLY NEED HELP PLEASE + 30 POINTS + BRAINLIST
PLS HELP
PLS
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I NEED HELP
HELP
I’ll appreciate it so much please don’t skip and read this please
Answer:
See the attached picture.
Step-by-step explanation:
Myra is 555 years younger than her sister Talat. Myra wants to write an equation for her own age (m)(m)left parenthesis, m, right parenthesis given Talat's age (t)(t)left parenthesis, t, right parenthesis.
The equation that represents the Myra's age given Talat age is as follows:
t = m + 5
How to represent an equation?Myra is 5 years younger than her sister Talat
Myra age is represented by m while Talat age is represented by t.
Hence,
m = age of Myra
t = age of Talat
Myra is 5 years younger than Talat. This means Talat is 5 years older than Myra.
Therefore, the equation that represents the Myra's age given Talat age is as follows:
t = m + 5
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Answer:
[tex]m=t-5[/tex]Step-by-step explanation:
give me brainiest if I'm correct2x+3≥7 OR 2x+9>1
Please help me
Answer:
x > -4
Step-by-step explanation:
[tex]2x+3 \geq 7 \\ \\
2x \geq 4 \\ \\
x \geq 2[/tex]
[tex]2x+9>1 \\ \\ 2x>-8 \\ \\ x>-4[/tex]
So, the union of these solutions is x > -4.
Anna wanted to buy a camera. The first discount store sold her favorite camera for $95. The second store sold the same camera for $115, but it was on sale for 20% off. The third store carried the camera for $105 but offered it at 10% off with a coupon. which store had the better buy?
Answer: third store
Step-by-step explanation:
1
First store: 95
Second store: 0.8*115=92
Third store: 0.9*105=94.5
Suppose a normal distribution has a mean of 98 and a standard deviation of 6. What is P(x<110)? (The greater than sign is actually greater than or equal to)
A. 0.975
B. 0.025
C. 0.16
D. 0.84
Using the normal distribution, the probability that x is less than 110 is:
A. 0.975.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.The mean and the standard deviation are given as follows:
[tex]\mu = 98, \sigma = 6[/tex]
The probability is the p-value of Z when X = 110, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{110 - 98}{6}[/tex]
Z = 2
Z = 2 has a p-value of 0.975.
Hence option A is correct.
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A trapezoid is shown. The lengths of the bases K L and J M are 10 feet and 5 feet. The length of side L M is 6 feet. An altitude is drawn from point K to a point on side J M.
A plot of land has an area of 33.75 square feet. Jackson wants to put a 4-foot by 4-foot shed on the land. He can only do this if the height of the trapezoid is at least 4.5 feet. What is the height of the trapezoid?
feet
The given height of this trapezoid is given to be 4.5m
How to solve for the height of the trapezoidWe have to solve for this by making use of the height of a trapezoid. The height is given as
A = (1/2) h (b1 + b2)
The variables here are
h = height
b1 = lenght at base 1
b2 = length at base 2
If the trapezoid that we have is a isosceles triangle, then base 1 is going to be the same length as that of the first base
b1 = 4 ft is the area. Given that the height has to be at least 4.5feet, then this would ensure that the trapezoid would be able to hold the shed.
Hence the height would begiven as 4.5 ft
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Answer: 4.5
Step-by-step explanation: