The value of [tex]\(\log 12\)[/tex] is approximately 1.0792 based on the given logarithmic values. Option B [tex]$\approx 1.0791$[/tex]
Let's evaluate the logarithmic expression [tex]\(\log 12\)[/tex]. We'll use the given logarithmic values:
1. Recall that [tex]\(\log 12\)[/tex] represents the common logarithm (base 10 logarithm) of the number 12.
2. Apply the change of base formula:
[tex]\[ \log 12 = \frac{\log 12}{\log 10} \][/tex]
Given values:
[tex]- \(\log 12 \approx 2.4849\) (from \(\log 12\))[/tex]
[tex]- \(\log 10 \approx 2.3026\) (from \(\log 10\))[/tex]
Now calculate:
[tex]\[ \log 12 \approx \frac{2.4849}{2.3026} \][/tex]
[tex]\[ \log 12 \approx 1.0792 \][/tex]
Therefore, the value of [tex]\(\log 12\)[/tex] is approximately 1.0792.
The correct answer is b. [tex]\(\approx 1.0791\)[/tex].
The correct question is:
Use the laws of logarithms and the values given below to evaluate the logarithmic expression.
[tex]$$\begin{array}{ll}\log 7=0.8451 & \log 5=0.6990 \\\log 3=0.4771 & \log 2=0.3010\end{array}$$[/tex]
[tex]$\log 12$[/tex]
a. [tex]$\approx-1.0791$[/tex]
b. [tex]$\approx 1.0791$[/tex]
c. [tex]$\approx 3.0234$[/tex]
d. [tex]$\approx-3.0234$[/tex]
Combine the like terms to create an equivalent expression:
- k + 3k
Answer:
2k
Step-by-step explanation:
- k + 3k
3k - k
2k
Which expression is a factor of x2 – 9x + 14?
A not factorable
B (x + 2)(x - 7)
C (x-2)(x + 7)
D (x-2)(x - 7)
Answer:
x² - 9x + 14 = (x - 2)(x - 7)
The correct answer is D.
A rectangular prism has a volume of 3995 cubic inches. Its base measures 5 in by 17 in. What is the height of the rectangular prism? You must show all work to receive credit.
Answer:
47 inches.
I hope this helped!! :3
Edit- to find the height of a rectangular prism with a known volume, use the formula
V= AH.
3995= lwH
3995= 85h
If you don’t have the area, multiply the width and the length of one side to get that value.
Find the length of arc AB. leave your answers in terms of pi
Answer:
arc AB = 60°
Step-by-step explanation:
The diameter splits the circle into two semi circles.
in the semicircle above the diameter, you can do 180° - 120° = 60°
so arc AB = 60°
( I'm sorry; I'm not sure how to get the answer in terms of pi. )
i need help please for this picture
Answer:
3,500
Step-by-step explanation:
Factor completely 3x2 − x + 5.
The function f (x) = -x^2 + 4x - 3 is graphed in the xy-coordinate plane as shown based on the graph of the function which of the following statements are true. Select all that apply
Answer:
In the picture attached, the function f(x) = -x² + 4x - 3 is shown.
Based on the graph of the function, the following statements are true:
f(x) < 0 on the interval x < 0f(x) < 0 on the interval 0 < x < 1f(x) > 0 on the interval 1 < x < 3f(x) < 0 on the interval x > 3Choose four endpoints and connect them to make a trapezoid with only 1 pair of opposite sides that are paraell
we can;t answer question that need a graph without you showing the graph
A chef keeps track of the temperature of his refrigerator in degrees Celsius. What is the level of measurement of data?
Answer:
interval level of measurement
Step-by-step explanation:
Interval level of measurement is numeric and allows for mathematical operations like mean. It is quantitative and in fixed units, i.e changes in values are as a result of a phenomenon. It does not have a zero point i.e a value of zero does not mean what you are measuring is absent, for example a temperature of 0°C do not mean there is no heat applied. It specifies the distance between intervals.
32. What is the degree of the monomial?
7x^8
A-7
B-8
C-15
D-56
Answer:
B - 8
Step-by-step explanation:
The answer is 8 because when determining the degree of any polynomial you find the sum of all the exponents that are attached to variables.
Since there's only one variable then you only have to take the number attached to the variable "x" which is 8.
given f(x)=2x^2-3 and g(x) = x+4 What is (fg)(x)?
Answer: [tex]f(g(x))=2x^2+16x+29[/tex]
Step-by-step explanation:
[tex]f(x)=2x^2-3\\g(x)=x+4[/tex]
f of g of x means "function f, replace x by the value of g of x"
[tex]f(g(x))=2x^2-3\\f(g(x))=2(x+4)^2-3\\f(g(x))=2(x^2+8x+16)-3\\f(g(x))=2x^2+16x+32-3\\f(g(x))=2x^2+16x+29[/tex]
Answer:
2x^3+8x^2−3x−12
Step-by-step explanation:
Given f(x)=2x^2−3 and g(x)=x+4.
What is (fg)(x)?
2x^3+8x^2−3x−12
What is the solution of the system of equations shown in the graph below?
Find the slope of the line that goes through the points (-3, -4) and (0, -1).
A. LaTeX: \frac{4}{3}4 3
B. -1
C. LaTeX: \frac{3}{4}3 4
D. 1
Answer:
D
Step-by-step explanation:
The slope is the change in y-coordinates divided by the change in x-coordinates.
Here, the y-coordinates are -4 and -1, and the x-coordinates are -3 and 0, so:
slope = m = (-4 - (-1)) / (-3 - 0) = -3 / -3 = 1
The slope is thus 1, so the answer is D.
We can use the points (-3, -4) and (0, -1) to solve.
Slope formula: y2-y1/x2-x1
= -1-(-4)/0-(-3)
= 3/3
= 1 (Option D)
Best of Luck!
Compare the two figures. How many times bigger or smaller is the cone to
the pyramid? Round your answer to the nearest tenth. Explain how you
found your answer and show your work. Write your answer in the space
provided and explain your answer in relation to the problem.
Answer:
The proportion of the volume of the cone to the volume of the pyramid is: 3.14 times bigger.
Step-by-step explanation:
Given the information of the cone:
The height: 12 inchesThe radius of the base is : 10/2= 5 inches=> the volume of the cone
= 1/3π[tex]r^{2} *h[/tex]
= 1/3*3.14*[tex]5^{2} *12[/tex]
= 314 cubic inches
Given the information of the pyramid:
the height: 12 inchesThe base is a suqare with a side lengh = 5 inches=> the volume of the pyramid:
= 1/3*Bh (where B is the area of the base)
= 1/3*5*5*12
= 100 cubic inches
The proportion of the volume of the cone to the volume of the pyramid is:
= 314 /100
= 3.14 times bigger.
Hope it will find you well
Compare the period of y = 2x with the period of y= sin x
Final answer:
The function y = 2x is linear and without a period, whereas the function y = sin x is periodic with a period of 2π radians.
Explanation:
The period of a function is the length of the interval over which it repeats.
The function y = 2x is a linear function, not a periodic function, and thus does not have a period.
In contrast, the function y = sin x is a periodic function and has a period of 2π radians.
This means that the sine function repeats its values every 2π radians.
Therefore, when comparing the period of these two functions, we can conclude that y = 2x does not have a defined period, while y = sin x has a period of 2π radians.
Simplify to create an equivalent expression
8k - 5(-5k + 3
Choose 1 answer:
A.33k +15
B.33k – 15
C.3k +3
D.3k-3
A school buys pens and pencils from a supplier. The supplier charges $0.05 for each pencil and $0.25 for each pen. The school pays $400 for the pens and pencils. If the school bought 1500 pencils, how many pens did the school buy?
Answer:
1460 pens
Step-by-step explanation:
What is the mean price for the sneakers?
Answer:
38
Step-by-step explanation:
You need to add all of numbers together and then divide by the total number of numbers.
Can someone help me with this question?
I have been struggling to answer it.
The question is about the difficulty in satisfying multiple chemical conditions at once, particularly kinetically favorable conditions and thermodynamically stable conditions, which is a complex task often tested in advanced placement chemistry exams.
Explanation:The question pertains to the challenges associated with satisfying multiple conditions simultaneously in the context of a Chemistry Advanced Placement (AP) Examination. Students often find it difficult to address complex problems where multiple variables must be considered and optimized at the same time. In chemistry, achieving this can involve understanding and balancing various principles such as reaction rates, equilibrium positions, and thermodynamic stability.
In reference to the AP Chemistry exam, students might come across questions that require not just recall of facts or formulas but also the application of these in dynamic scenarios. For instance, satisfying both the kinetic and thermodynamic requirements in a chemical reaction is often challenging. This is because conditions favorable for kinetics, which may involve higher temperatures to increase reaction rates, might adversely affect the thermodynamics by shifting the equilibrium away from the desired products. On the other hand, conditions that favor thermodynamic stability might result in slower reaction rates. Therefore, finding a balance where both kinetics and thermodynamics conditions are optimized is a complex task and is a concept featured in advanced placement chemistry content.
The examination of such complex issues can involve analyzing various aspects and outcomes of a reaction, predicting how changes in conditions could influence the course of the reaction, and understanding the conceptual underpinnings that govern these processes. It is a clear representation of the depth and detail expected at the college level of chemistry education, particularly AP level studies.
Mia has a rectangle shaped brownie brownie. She cuts the brownie into 3 equal pieces.Which sentence is true? The whole brownie is 1/3. The whole brownie is 3/3. The whole brownie is 2/3. The whole brownie is 3/2.
Answer:
The whole brownie is 3/3
Step-by-step explanation:
She cut it into 3 equal pieces out of the whole brownie so it would be 3/3
The community center has a pottery class each month. Each student pays $15 for the class and $27 for materials. This month the pottery class brought in a total of $714. How many students are in the class this month?
Answer:
17
Step-by-step explanation:
$15+$27=$42
$712 divided by $42 is 17 meaning there are 17 kids in the class.
please help!!
58
72
55
65
70
81
66
Consider the speed in miles per hour that Officer Williams clocked the last seven drivers at with his radar. Find the interquartile range of the speeds.
Answer:
Answer: 14
Step-by-step explanation:
14
interquartile range = upper quartile - lower quartile
first, order the scores from least to greatest
55, 58, 65, 66, 70, 72, 81
thus, UQ = 72 and LQ = 58
IQR = UQ - LQ = 72 - 58 = 14
Solve for x 7(x - 9) = 8x - 6
Answer:
x= -57
Step-by-step explanation:
7x-63+8x-6
-x-63-7
-x=57
x=-57
Answer:
x = -57
Step-by-step explanation:
Simplify both sides of the equation:
Distribute:
(7)(x) + (7)(-9) = 8x + -6
7x + -63 = 8x -6
7x - 63 = 8x - 6
Subtract 8x from both sides
7x−63−8x=8x−6−8x
−x − 63 = −6
Add 63 to both sides
−x − 63 + 63 = −6 + 63
-x = 57
Divide both sides by -1
-x / -1 = 57 / -1
Therefore, you get x = -57
If you were a college professor taking a survey of how many hours of
homework students were assigned, which visual tool would you use if you
organized students in hour ranges?
A. Line plot
B. Bar graph
C. Frequency table
D. None of the above
If I were a college professor taking a survey of how many hours of homework students were assigned and I wanted to organize the data by hour ranges, the visual tool that I would use is C) a frequency table.
Explanation:A frequency table would be the best visual tool to organize students in hour ranges for a survey of how many hours of homework students were assigned.
A frequency table is a way to organize data into different intervals, or ranges, and count how many data points fall into each interval. In this case, I would create intervals such as 0-1 hour, 1-2 hours, 2-3 hours, and so on, and then count the number of students assigned homework in each interval. This would give me a clear picture of the distribution of homework hours among the students. Therefore the correct answer is C) a frequency table.
A jar contains 20 yellow marbles, 55 green marbles, and 25 purple marbles. You pick one marble from the jar at random. What is the theoretical probability of picking a green or yellow marble? 75% 55% 20% 25%
Answer:
75%
Step-by-step explanation:
20+55=75
so 75/100 or 75%
hope this helped! :)
Answer:
it's 75%
Step-by-step explanation:
(ANSWER ALL QUESTIONS FOR 60 POINTS AND BRAINLYEST)
Question 1 (1 point)
The coordinate (0,0) is a point on the graph y = 2x.
Question 1 options:
True
False
Question 2 (1 point)
The coordinate (1,2) is a point on the graph of y = 2x.
Question 2 options:
True
False
Question 3 (1 point)
Which coordinate is a point on the graph of y = 2x + 2
Question 3 options:
(2,4)
(0,0)
(1, 3)
(2,6)
Question 4 (1 point)
Which equation has the coordinate (0, 2) as a point on its graph?
Question 4 options:
y = x - 2
y = x + 2
y = 2
y = 2x
Question 5 (1 point)
In slope intercept form, y = mx + b.
Which variable represents the slope of this equation's graph?
Question 5 options:
b
x
m
y
Answer:
answer to q1= True
q2= true
q3= x2y6
q4= y+x+2
q5= y
Answer:
Answer to question 1. True
Answer to question 2. True
Answer to question 3. 2,6
Answer to question 4. I think it is y=x+2
Answer to question 5. I'm pretty sure it is M
I hope this helped if they were wrong I'm sorry.
How did you use similarity to find the areas and circumferences of circles? How are the radius and diameter of a circle related?
To find areas and circumferences of circles using similarity, we scale proportions from known circles to unknown circles. The diameter is twice the radius (d = 2r), allowing us to use formulas C = 2πr for circumference and A = πr^2 for area.
To determine the area and circumference of circles using similarity, we can scale up or down from a known circle to an unknown one. The relationships between circles of different sizes but with proportional radii allow us to use the similarity concept. For example, if a small circle has a radius that is half the radius of a larger circle, the area and circumference will also be in proportion to the squares and the linear dimensions, respectively.
The radius (r) and diameter (d) of a circle are directly related by the equation d = 2r. This means that diameter is twice the radius. Given the radius, we can determine the circumference of a circle (C = 2πr) and its area (A = πr2) easily. The role of π (approximately 3.14159) is critical as it provides the constant of proportionality in these equations.
An adult takes 400mg of vitamin c. Each hour, the amount of vitamin c in the person’s system decreases by about 29%. How much vitamin c is left after 6 hours?
Answer:
1
Step-by-step explanation:
Answer:
51.24 mg
Step-by-step explanation:
400 x (0.71^6) = 51.24
What is the distance, rounded to the nearest tenth, between the points (-5,3) and (1,-1)? Enter the answer in the box.
units
Final answer:
The distance between the points (-5,3) and (1,-1) is found using the distance formula and is approximately 7.2 units when rounded to the nearest tenth.
Explanation:
To find the distance between two points (-5,3) and (1,-1), we can use the distance formula: √((x2 - x1)² + (y2 - y1)²). Plugging in our values, we get the distance as √((1 - (-5))² + (-1 - 3)²) = √(6² + (-4)²) = √(36 + 16) = √52. To round to the nearest tenth, we calculate √52 and find it is approximately 7.2. Therefore, the distance between the points, rounded to the nearest tenth, is 7.2 units.
You flip a fair coin.
What is \text{P(tails})P(tails)start text, P, left parenthesis, t, a, i, l, s, end text, right parenthesis?
If necessary, round your answer to 222 decimal places.
Question:
You flip a fair coin. What is P(tails)?
If necessary, round your answer to 2 decimal places.
Answer:
P(tail) = 0.5
Step-by-step explanation:
Given:
A fair die
Required
P(Tails)
A fair die has 2 sides, the head and the tail; each of the sides have equal probability.
The number of head in a die is 1 and the number of a tail in a die is 2.
Let P(tail) represent the probability of obtaining a tail.
P(tail) is calculated by number of tail divided by number of sides of a die.
Hence, P(tail) = ½
P(tail) = 0.50
"The probability of getting tails when flipping a fair coin is [tex]\(\frac{1}{2}\)[/tex] or 0.5.
A fair coin has two equally likely outcomes: heads or tails. Since a fair coin has no bias towards either side, the probability of landing on tails is the same as the probability of landing on heads.
The probability of an event E, denoted as P(E), is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. In this case, the event E is getting tails. There is one favorable outcome for getting tails, and there are two possible outcomes in total (heads or tails).
Therefore, the probability of getting tails, P(tails), is given by:
[tex]\[ P(\text{tails}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} = \frac{1}{2} \][/tex]
This fraction simplifies to 0.5, which is the correct probability of getting tails when flipping a fair coin. There is no need to round to 222 decimal places as the probability is exact.