The approximate value of log₈1000 is 0.30.
What are logarithms?The inverse of power is a logarithm. When you take the log of a number, you reverse the exponent.Logarithms normally use a base of 10 (but a different value can be provided), whereas natural logs always use a base of e. Use the following calculation to convert between logarithms and natural logs.[tex]log_{10}x[/tex] [tex]= ln(x) / ln(10)[/tex]
The given values are:
In 8 ≈ 2.08 and In 1000 ≈ 6.91
To find the approximate value of log₈1000,
log₈1000 = In 8/In 1000
= 2.08/6.91
≅ 0.30
Therefore, the approximate value of log₈1000 is 0.30.
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please answer the question below the top question. on both.
The value of x is 6 degrees.
It is given in the question that:-
HI is parallel to JK and FG is the transversal intersecting HI at L and JK at M.
∠LMK = 115 degrees
∠MLI = (8x + 17) degrees
We have to find the value of x.
We know that,
Angles on the same side of the transversal sum up to 180 degrees.
Hence, we can write,
∠LMK + ∠MLI = 180 degrees.
115 + (8x + 17) = 180 degrees
8x + 132 = 180 degrees
8x = 180 - 132
8x = 48 degrees
x = 48/8 degrees
x = 6 degrees
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A cylinder with radius r and height h is inscribed in a cone with radius of 4m and height of 10m. Express the volume V of the cylinder as a function of h.
The volume of the cylinder is 502.4m³
Volume of the cylinder:
Volume of the cylinder can be calculated by the product of the area of base and height.
For any cylinder with base radius ‘r’, and height ‘h’, the volume will be base times the height.
V = πr²h cubic units.
Given,
A cylinder with radius r and height h is inscribed in a cone with radius of 4m and height of 10m.
Here we need to find the volume of the cylinder,
We know that the values of,
Radius = 4m
height = 10m.
Now we have to apply the value on the formula, then we get,
V = π x (4)² x 10
Apply the value of π as 3.14 then we get,
V = 3.14 x 16 x 10
V = 502.4
Therefore, the volume of the cylinder is 502.4 m³.
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find the indicated sum in each sequence 7,10,17,27,44,71,115...,a10
The sequence of numbers, 7, 10, 17, 27, 44, 71, 115... in which each new term is given by the sum of the previous two terms, gives the sum of the first 10 terms as 1,265
What is a sequence of numbers?A number sequence consists of a listing of numbers that are connected to each other by a rule.
The given sequence is presented as follows;
7, 10, 17, 27, 44, 71, 115..., [tex] a_{10}[/tex]
From the given sequence, we have;
a_n = a_{(n-1)} + a_{(n-2)}
The first 10 terms of the sequence is therefore;
7, 10, 17, 27, 44, 71, 115, (71+115), (115+(71+115)), ((71+115)+(115+(71+115)))
Which gives;
7, 10, 17, 27, 44, 71, 115, 186, 301, 487
The sum of the first 10 terms of the sequence is therefore;
7 + 10 + 17 + 27 + 44 + 71 + 115 + 186 + 301 + 487 = 1265
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on a bike trip across the united states rodney notes that he covers about 190 miles every 4 if he continues at this rate use a ratio table to determine about how man miles he could bike in 6 days
In 6 days 285 miles can be travelled.
What is proportion?In general, the term "proportion" refers to a part, share, or amount that is compared to a total.
According to the concept of proportion, two ratios are in proportion when they are equal.
A mathematical comparison of two numbers is called a proportion. According to proportion, two sets of provided numbers are said to be directly proportional to one another if they increase or decrease in the same ratio. "::" or "=" are symbols used to indicate proportions.
Given:
190 miles cover in 4 days.
let x miles travelled in 6 days
So, using proportion
190/4 = x/6
190 x 6 = 4x
4x= 1440
x= 285 miles.
Hence, in 6 days 285 miles can be travelled.
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-4(w + 5) + 5w simplify use distributive property
Answer:
w - 20
Step-by-step explanation:
Simplifying the expression:Remove the parenthesis by multiplying each term of (w + 5) by (-4)
-4(w + 5) + 5w = -4*w + 5*(-4) + 5w
= -4w - 20 + 5w
= -4w + 5w - 20
Combine like terms. Like terms have same variable with same power.
= w - 20
Solve the inequality.8(x-1) >12(x-2)
SOLUTION
Solve the inequality.
[tex]8(x-1)>12(x-2)[/tex][tex]\begin{gathered} 8(x-1)>12(x-2) \\ 8x-8>12x-24 \\ 8x-12x>-24+8 \\ -4x>-16 \end{gathered}[/tex]divide both sides by -4
[tex]\begin{gathered} -4x>-16 \\ x<\frac{16}{4} \\ x<4 \end{gathered}[/tex]In the problems below, copy the problems and the picture, mark the givens, and prove the statements.
Answer:
Step-by-step explanation:
Givens
OF = RF
OU = UR
Draw a line from U to F
UF = UF Reflexive property.
Solution
ΔOUF = ΔRUF SSS
<O = < R Congruent parts are congruent when the triangles are congruent.
Add parentheses to make true3 + 4 × 2 = 1472 ÷ 12 - 6 = 12
We want to find where to put the parentheses on each expression to make the expression true.
First, we identify the symbols +, x, / and - to identify the pairs of numbers. For example, in the expression
[tex]3+4\cdot2[/tex]we have two symbols (+, *).
Now, this would give us two pairs of expression where we can put the parentheses. That is, one possibility per symbol. So we have
[tex](3+4)[/tex]and
[tex](4\cdot2)[/tex]Now, let us try the first choice. Remember that first we have to evaluate what is inside the parentheses. This would give us
[tex](3+4)\cdot2=7\cdot2=14[/tex]which coincides to the value we wanted.
In the second case, we have the following symbols / and -
This would give us two pairs for grouping, namely
[tex](72/12)[/tex]and
[tex](12\text{ -6)}[/tex]as before, we will first evaluet the first option
[tex](\frac{72}{12})\text{ - 6=6 -6 =0}[/tex]If we try the second option, we woud get
[tex]\frac{72}{(12\text{ -6)}}=\frac{72}{6}=12[/tex]which would give us the correct value.
One card is drawn from a standard deck of 52 cards. Find the probability of drawing the following. an eight or a diamond
The probability of a simple event to occur is this:
[tex]P(x)=\frac{\text{total number of favorable outcomes}}{\text{total }number\text{ of possible outcomes}}[/tex]In the question given, the favorable outcomes are either 8 or diamond.
In a deck of cards, there are 13 diamond cards and 4 eights however one of the diamond cards is also 8. Therefore, total favorable outcome is 13 + 4 - 1 = 16.
Of course, the total number of possible outcomes is 52. So, the probability of getting an eight or a diamond is:
[tex]p(x)=\frac{16}{52}=\frac{4}{13}\approx0.3077[/tex]The probability, in fraction, is 4/13.
In decimal form, it is 0.3077.
In percentage form, it is 30.77%
What is the equation of the graph?
The required equation of the graph is y = x - 1.
How can we define the slope for a given line?
A line's slope in mathematics is defined as the ratio of the change in the y coordinate to the change in the x coordinate. Both the net change in the y-coordinate and the net change in the x-coordinate are denoted by y and x, respectively. Therefore, the relationship between the change in the y-coordinate and the change in the x-coordinate is provided by the formula m = change in y/change in x = Δy/Δx, where "m" is the slope of a line.
Mathematically, slope of a line = m = (y₂ - y₁)/(x₂ - x₁)
What is the y-intercept for a given line?
When a graph crosses the y-axis, that location is known as the y-intercept. It is, in other words, the value of y at x=0.
What is the general equation of a line?
The equation for a standard line is y = mx + c, where m is the slope and c is the y-intercept.
Given, the line passes through the points (-1, 0) and (0, 1).
Also, the y-intercept for the line = c = -1
Now, using the formula established in the literature, we get:
slope = m = (y₂ - y₁)/(x₂ - x₁) = (1 - 0)/(0 - (-1)) = 1/1 = 1
y-intercept = c = -1
Therefore, equation of the standard line is y = mx + c, thus y = (1*x) + (-1)
Thus, the required equation of the graph is y = x - 1.
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Please answer if blurry let me know
Answer:
[tex]P'(-6,4)[/tex]
Step-by-step explanation:
P(x,y) -> rotate 90 degrees -> P'(-y,x)
P'(-6,4)
:]
(Brainliest would be greatly appreciated :] )
the group u(49) is cyclic. using only the sage commands described previously, use sage to find a generator for this group. now using only theorems about the structure of cyclic groups, describe each of the subgroups of u(49) by specifying its order and by giving an explicit generator. do not repeat any of the subgroups — in other words, present each subgroup exactly once
then the generator is the element which can generate whole set
therefore U(49) has 12 generator
What is meant by cyclic group?
A cyclic group is a group that can be generated by a single element. (the group generator). Cyclic groups are Abelian.
the group u(49) is cyclic. using only the sage commands described previously, use sage to find a generator for this group.
elements of U(49) are {1,2,3,5,,7,11,,13,17,19,23,29,31,37,39,,41,47}
then the generator is the element which can generate whole set
therefore U(49) has 12 generator
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solve for t
300,000 = 300 (1+.0375/12) ^ (12t) / (.0375/12)
If the equation be [tex]$300000=\frac{300\left(1+\frac{0.0375}{12}\right)^{(12 t)}}{\left(\frac{0.0375}{12}\right)}$$[/tex]then the value of t = 30.43236.
How to estimate the value of t?Let the equation be
[tex]$300000=\frac{300\left(1+\frac{0.0375}{12}\right)^{(12 t)}}{\left(\frac{0.0375}{12}\right)}$$[/tex]
Multiply both sides by 0.0375 / 12, and we get
[tex]$300000 \cdot \frac{0.0375}{12}=\frac{300\left(1+\frac{0.0375}{12}\right)^{12 t}}{\frac{0.0375}{12}} \cdot \frac{0.0375}{12}$$[/tex]
Simplifying the above equation, we get
[tex]$\frac{1875}{2}=300\left(1+\frac{0.0375}{12}\right)^{12 t}$$[/tex]
Switch sides of the equation,
[tex]$300\left(1+\frac{0.0375}{12}\right)^{12 t}=\frac{1875}{2}$$[/tex]
Divide both sides by 300, and we get
[tex]$\frac{300\left(1+\frac{0.0375}{12}\right)^{12 t}}{300}=\frac{\frac{1875}{2}}{300}$$[/tex]
Simplifying the above equation, we get
[tex]$\left(1+\frac{0.0375}{12}\right)^{12 t}=\frac{25}{8}$$[/tex]
Apply exponent rules, then
[tex]$12 t \ln \left(1+\frac{0.0375}{12}\right)=\ln \left(\frac{25}{8}\right)$$[/tex]
Solving the above equation, then
[tex]$12 t \ln \left(1+\frac{0.0375}{12}\right)=\ln \left(\frac{25}{8}\right): \quad t=\frac{\ln \left(\frac{25}{8}\right)}{12 \ln \left(\frac{12.0375}{12}\right)}$[/tex]
[tex]$t=\frac{\ln \left(\frac{25}{8}\right)}{12 \ln \left(\frac{12.0375}{12}\right)}$$[/tex]
simplifying the above value of t, we get
t = 30.43236.
If the equation be [tex]$300000=\frac{300\left(1+\frac{0.0375}{12}\right)^{(12 t)}}{\left(\frac{0.0375}{12}\right)}$$[/tex]then the value of t = 30.43236.
Therefore, the value of t = 30.43236.
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The current population of a city is about 2,130,000 people, and it's increasing at a rate of 10 percent per year. Arrange the steps in the correct order to
show how to determine the population of the city in five years.
The population of the city in 5 years is 3430386 as the population is increasing 10% per year
What is percentage and how to calculate?
Percentage is the ratio which can be expressed as fraction of 100. And to calculate percentage we multiply by 100.
We are given that population of a city is 2130000
And the population is increasing at a rate of 10%
We are asked to find the population after 5 years
The equation can be given as (1.1)^x*2130000
We put x =5
We get
[tex](1.1)^5*2130000\\1.61051*2130000\\=3430386[/tex]
Hence the population will be 3430386 after 5 years at a rate of 10% increase per year
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The diameter of a basketball rim is 18 inches. What is the circumference of the rim? Write your answer using pi. Show your work.
Answer:
18 pi
Step-by-step explanation:
2xpixr d divided by 2 equals 9 pi x 2 x 9 =18
Consider the chart of millionaires and population
The number of millionaires Los Angeles should have will be equal to 5,065 millionaires.
Proportion may be defined as part or share of a complete unit compared with respect to the whole unit. A proportion is basically the equality of ratios. Two different ratios can be treated as equals if they are in proportion to each other. Now, the number of millionaires in Los Angeles will be equal to the Proportion of Millionaires in Dubai multiplied by the Population of Los Angeles that is
= 0.00124 × 4,085,014
= 5,065 millionaires
The Data and Calculations will be given as:
City Millionaires Population Proportion
Los Angeles 11,560 4,085,014 0.00283 (11,560/4,085,014)
Casablanca 6,900 3,752,357 0.00184 (6,900/3,752,357)
Berlin 6,750 3,562,038 0.00189 (6,750/3,52,038)
Dubai 3,570 2,878,344 0.00124 (3,570/2,878,344)
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Complete Question:
City Millionaires Population
Los Angeles 11,560 4,085,014
Casablanca 6,900 3,752,357
Berlin
6,750
3,562,038
Dubai
3,570
2,878,344
Consider the chart of Millionaires and Population. If Los Angeles were
proportional to Dubai with respect to population, how many millionaires
should we expect Los Angeles to have? Round your answer to a whole number.
PLEASE HELP ME IT WOULD MAKE MY MONTH!!! ILYSM
How many pounds of apples will he get if he goes to David’s orchard?
Answer:
David's orchid: 20 +x
Pam's orchid: 25 + 0.75x
Step-by-step explanation:
Framing linear equations:
David's apple orchid:Cost of first 10 pounds = 10 * 2 = $ 20
Let the weight of additional apples picked = x pounds
Cost of 'x' pounds = 1 * x = $ x
Total cost = cost of first 10 pounds + cost of additional 'x' pounds
= 20 + x
Pam's orchid:Entry fee = $ 10
Cost of first 10 pounds = 10 * 1.50 = $ 15
Cost of 'x' pounds = 0.75*x = 0.75x
Total cost = Entry fee + cost of first 10 pounds + cost of additional 'x' pounds
= 10 + 15 + 0.75x
= 25 + 0.75x
What common factor of 10 and 14 can you use to write in simpler form?
Answer:
1 and 2
and the greatest common divisor is 2
I have no idea what I’m doing And could use help! Anyone who takes time out of their day to help I appreciate you!!
Answer: It is impossible for two obtuse angles to be a straight angle
Step-by-step explanation:
Definition of a straight angle: An angle that is exactly 180 degrees
Definition of obtuse angle: An angle that is more than 90 degrees
1) X = obtuse angle
x > 90
Set minimum to test:
x = 91
2) Set up the question
(<= less than or equal to)
2x <= 180
3) Sub the first equation
2(91) <= 180
182 <= 180
4) Answer the question
It is impossible for two obtuse angles to be a straight angle
A model car has a list price of $46.20. The model is on
sale at 15% off. Find the total cost to the nearest cent
after a 4.5% sales tax is added to the sale price.
Answer:The total cost is $41.04
Step-by-step explanation:
Which method can't you use to solve this problem? x^2 + 7x =0
A) Factoring
B) Square roots
C) Quadratic formula
the head of institutional research at a university believed that the mean age of full-time students was declining. in 1995, the mean age of a full-time student was known to be 27.4 years. after looking at the enrollment records of all 4934 full-time students in the current semester, he found that the mean age was 27.1 years, with a standard deviation of 7.3 years. he conducted a hypothesis of : 27.4 years versus : 27.4 years and obtained a p-value of 0.0020. he concluded that the mean age of full-time students did decline. is there anything wrong with his research?
No, there is nothing wrong in the research that is done by the head of the institution. He said correct that the mean age of the full time students has declined.
Given above that a university's director of institutional research thought that the average age of full-time students was lowering. The average age of a full-time student in 1995 was 27.4 years old.
He registered all 4934 pupils for this and the average age was 27.1 years.
The fact that the inquiry concerns the average age of a full-time student makes this situation ideal. This is a trustworthy approach when the mean is calculated after accounting for all full-time students at the university.
Given that this is a left-tailed test, the hypothesis is also correct.
He rejected the null hypothesis because p = 0.0020.05.
The average age did decrease, in conclusion. The situation is ideal.
Therefore his hypothesis is absolutely correct. There is nothing wrong with it.
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Using the graph, determine the coordinates of the x-intercepts of the parabola.
Answer:
2 points
Step-by-step explanation:
According to the graph, the parabola has two x-intercept, where is (0,-2) and (0,-8).
Carlos sold half of his comic books then bought 14 more. He now has 33 comics books. How many did he start with?
Answer: Carlos started with 38 comic books.
Step-by-step explanation:
33 - 14 = 19
19 x 2 = 38
Evaluate. Write your answer as a whole number or as a simplified fraction.
Answer:
1000
Step-by-step explanation:
Hello!
Use the Quotient Property of Exponents to evaluate the expression:
[tex]\frac{a^b}{a^c} = a^{b-c[/tex]
In this case, a is 10, b is 5, and c is 2.
Evaluate:[tex]\frac{10^5}{10^2}[/tex][tex]10^{5-2}[/tex][tex]10^3[/tex]If we simplify 10³, we should get 1000.
According to the Empirical Rule, what percent of values in a normal distribution will fall between 1 standard deviations above the mean and 3 standard deviations above the mean?
According to the Empirical Rule, 99.7% percent of values in a normal distribution will fall between 1 standard deviations above the mean and 3 standard deviations above the mean.
What is the Empirical Rule?The Empirical Rule is also referred to as the 68-95-99.7 rule and it can be defined as a statistical rule which states that:
The middle 68% of a normal distribution would be within one (1) standard deviation of its mean.The middle 95% of a normal distribution would be within two (2) standard deviations of its mean.The middle 99.7% of a normal distribution would be within three (3) standard deviations of its mean.In this context, we can reasonably infer and logically deduce that 99.7% of a normal distribution would fall within three (3) standard deviations of its mean in accordance with the Empirical Rule.
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PLEASE HELP QUICK. NOW NEEDED
pls tell me u understand the drawing
Determine the minimum sample size required when you want to be % confident that the sample mean is within one unit of the population mean and. Assume the population is normally distributed.
The minimum sample size of the given condition is 89.
In given condition,
For 95% confidence level, critical value of z is z* = 1.96
The margin of error given is E = 1
Standard deviation ( α ) = 4.8
Final required sample size is;
n = [tex](\frac{z*\alpha }{E} )^{2}[/tex]
= [tex](\frac{1.96 * 4.8}{1} )^2[/tex]
= 88.51
n ≅ 89
The minimum sample size of the given condition is 89.
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Factor by Grouping.. I know there is no common GCF but i don't know how to continue!
xy^2 − 3xy − 6y + 18
Answer:
(xy-6)(y-3)
Step-by-step explanation:
i don't know if you needed this, but if you need this i can explain step by step
xy(y-3)-6(y-3). we take the common ones out and than simplify as:. (xy-6)(y-3)
Need help! Finding Missing Angles !
Step-by-step explanation:
Since right angles are 90°
11 = 90°
12 = 90°
13 = 90°