Answer:
i hope it's helpful for youWhat is the true solution to the equation below? 2 lne^ln2x-lne^ln10x=ln30
It looks like the equation is
[tex]2\ln\left(e^{\ln(2x)}\right)-\ln\left(e^{\ln(10x)}\right) = \ln(30)[/tex]
Right away, we notice that any solution to this equation must be positive, so x > 0.
For any base b, we have [tex]b^{\log_b(a)}=a[/tex], so we can simplify this to
[tex]2\ln(2x)-\ln\left(10x\right) = \ln(30)[/tex]
Next, [tex]\ln(a^b)=b\ln(a)[/tex], so that
[tex]\ln(2x)^2-\ln\left(10x\right) = \ln(30)[/tex]
[tex]\ln\left(4x^2\right)-\ln\left(10x\right) = \ln(30)[/tex]
Next, [tex]\ln\left(\frac ab\right)=\ln(a)-\ln(b)[/tex], so that
[tex]\ln\left(\dfrac{4x^2}{10x}\right) = \ln(30)[/tex]
For x ≠ 0, we have [tex]\frac xx=1[/tex], so that
[tex]\ln\left(\dfrac{2x}5\right) = \ln(30)[/tex]
Take the antilogarithm of both sides:
[tex]e^{\ln\left((2x)/5\right)} = e^{\ln(30)}[/tex]
[tex]\dfrac{2x}5 = 30[/tex]
Solve for x :
[tex]2x = 150[/tex]
[tex]\boxed{x=75}[/tex]
Please help asap please
Answer:
12.9 miles
Step-by-step explanation:
Formula: (x/360)×dπ(circumference)
90/360=1/4
1/4×16.4π
1/4×51.496
12.874
Answer:
[tex]m JM=90 =\Theta[/tex]
[tex]Radius=dimeter/2=16.4/2[/tex]
[tex]\longrightarrowr=8.2[/tex]
The length of arc JM=
[tex]=\frac{\Theta }{360} \times\pi r[/tex]
[tex]=\frac{90}{360} \times2\times\ 3.14\times 8.2[/tex]
[tex]=12.874[/tex]
[tex]\approx 12.9 \; miles[/tex]
[tex]OAmalOHopeO[/tex]
125. Albert surveyed a class of 25 students on sports. 5 kids love baseball. 7 kids love basketball. 10 kids
love football. How many students did not like baseball, basketball, or football?
25 students
12 students
22 students
3 students
Answer:
3 students
Step-by-step explanation:
since the total number of students is 25,when you add those that like baseball, basketball and football the total number must be 25 but in this case it's 22 meaning 2 student liked neither.
7+5+10+x=25
x=25-22
=3
I hope this helps
Write the point-slope form of an equation of the line through the points (-2, 6) and (3,-2).
Answer:
[tex]y-6=-\frac{\displaystyle 8}{\displaystyle 5}(x+2)[/tex]
OR
[tex]y+2=-\frac{\displaystyle 8}{\displaystyle 5}(x-3)[/tex]
Step-by-step explanation:
Hi there!
Point-slope form: [tex]y-y_1=m(x-x_1)[/tex] where [tex](x_1,y_1)[/tex] is a point and [tex]m[/tex] is the slope
1) Determine the slope
[tex]m=\frac{\displaystyle y_2-y_1}{\displaystyle x_2-x_2}[/tex] where two given points are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]
Plug in the given points (-2, 6) and (3,-2):
[tex]m=\frac{\displaystyle -2-6}{\displaystyle 3-(-2)}\\\\m=\frac{\displaystyle -8}{\displaystyle 3+2}\\\\m=-\frac{\displaystyle 8}{\displaystyle 5}[/tex]
Therefore, the slope of the line is [tex]-\frac{\displaystyle 8}{\displaystyle 5}[/tex]. Plug this into [tex]y-y_1=m(x-x_1)[/tex]:
[tex]y-y_1=-\frac{\displaystyle 8}{\displaystyle 5}(x-x_1)[/tex]
2) Plug in a point [tex](x_1,y_1)[/tex]
[tex]y-y_1=-\frac{\displaystyle 8}{\displaystyle 5}(x-x_1)[/tex]
We're given two points, (-2, 6) and (3,-2), so there are two ways we can write this equation:
[tex]y-6=-\frac{\displaystyle 8}{\displaystyle 5}(x-(-2))\\\\y-6=-\frac{\displaystyle 8}{\displaystyle 5}(x+2)[/tex]
OR
[tex]y-(-2)=-\frac{\displaystyle 8}{\displaystyle 5}(x-3)\\y+2=-\frac{\displaystyle 8}{\displaystyle 5}(x-3)[/tex]
I hope this helps!
I need help ASAP please no links
Answer: D' = (1, -1)
Step-by-step explanation:
When dilating by a 1/2 you take a point and divide the x and y of the point in half. So D before is (2,-2) and then divide that by a 1/2, which gives us our answer (1, -1).
Find the sum of the geometric series given a1=−2, r=2, and n=8.
A. -510
B. -489
C. -478
D. 2
Answer:
A. -510
Step-by-step explanation:
We are given the variable values:
a = -2r = 2n = 8Geometric series formula:
[tex]s = \frac{a( {r}^{n} \times - 1) }{r - 1} [/tex]
Plugging in values we have:
[tex]s = \frac{ - 2( {2}^{8} - 1) }{2 - 1} [/tex]
Simplifying the equation we are left with:
[tex] \frac{ - 2(255)}{1} = - 510[/tex]
Determine the probability of landing on tails at most 33 times if you flip a fair coin 80 times. Round your answer to the nearest tenth.
Answer:
0.0728177272
Step-by-step explanation:
Given :
Number of flips = 80
Probability of landing on tail at most 33 times ;
Probability of landing on tail on any given flip = 1 / 2 = 0.5
This a binomial probability problem:
Hence ;
P(x ≤ 33) = p(x=0) + p(x=1) +... + p(x = 33)
Using a binomial probability calculator :
P(x ≤ 33) = 0.0728177272
You wish to create a 5 digit number from all digits; 0 1 2 3 4 5 6 7 8 9
Repetition is not allowed
* 0 cannot be first as it does not count as a place value if it is first. Ie. 027 is a 2 digit number
How many even numbers can you have?
Answer:
10234
Step-by-step explanation:
one is the smallest number so its first
and then you can place zero
after that just place the second smallest number
and so on
Last year Diana sold 800 necklaces. This year she sold 1080 necklaces. what is the percentage increase of necklaces she sold?
Answer:
13.5% is the increase in percentage
Answer:
74%
Step-by-step explanation:
To get the answer, divide 800 by 1080, and you will get a decimal. That decimal is 0.74074074074. Then, move the decimal point two times two the right, so you should have 074.074074074. Ignore everything after the decimal point as well as the 0 before the decimal point, and if done correctly, it should be 74%.
So, the final answer would be 74%.
Hope this helped!
Simplify
x * x^5 / x^2 * x
PLS
Write the equation of the piecewise function that is represented by its graph.
IS IT A, B, C, OR D
9514 1404 393
Answer:
a) domain bounds are -1 ≤ x ≤ 1, x > 1
Step-by-step explanation:
In considering the definition of any piecewise function, the domain descriptions in the function definition must match the pieces shown in the graph.
Here, the right segment has no upper bound, so x > 1 is an appropriate description of its domain.
The left segment has the points at x=-1 and x=1 included, so the appropriate domain description for that is -1 ≤ x ≤ 1.
The one answer choice that combines these domain descriptions is ...
[tex]\displaystyle f(x)=\begin{cases}x^2,&\text{if }-\!1\le x\le1\\\sqrt{x},&\text{if }x>1\end{cases}[/tex]
construct an angle that bisect 90°
Answer:
We can construct a 90º angle either by bisecting a straight angle or using the following steps.
Step 1: Draw the arm PA.
Step 2: Place the point of the compass at P and draw an arc that cuts the arm at Q.
Step 3: Place the point of the compass at Q and draw an arc of radius PQ that cuts the arc drawn in Step 2 at R.
Step-by-step explanation:
As part of a statistics project, a teacher brings a bag of marbles containing 500 white marbles and 400 red marbles. She tells the students the bag contains 900 total marbles, and asks her students to determine how many red marbles are in the bag without counting them. A student randomly draws 100 marbles from the bag. Of the 100 marbles, 45 are red. The data collection method can best be described as
Answer:
Survey
Step-by-step explanation:
During data collection for a particular study, reaching all target Population might seem illogical or impossible. Therefore, a subset of the population of interest is chosen and the outcome used to infer about the population. This procedure could be referred to a a SURVEY. In the scenario samples drawn from the population of interest is used to make inference on population. During a survey, selected data ponuts or subjects must be drawn at random in other to ensure that it is representative of the larger population data.
The product of two numbers is 50 and there sum is 15. Find the number.
Answer: the numbers are 10 and 5
Step-by-step explanation:
10 times 5 is 50
10 plus 5 is 15
Hari earns Rs 4300 per month. He spends 80% from his income. How much amount does he save in a year?
Answer:
Hari saves $ 10,320 in a year.
Step-by-step explanation:
Given that Hari earns $ 4300 per month, and he spends 80% from his income, to determine how much amount does he save in a year, the following calculation must be performed:
100 - 80 = 20
4300 x 0.20 x 12 = X
860 x 12 = X
10320 = X
Therefore, Hari saves $ 10,320 in a year.
calculate the resistance if V = 220V and I = 3.6amp
Step-by-step explanation:
V= IR --> R = V/I = (220 V)/(3.6 A) = 61.1 ohms
Answer:
61.11 ohms
Step-by-step explanation:
R=V/I
R=220/3.6
R=61.11 ohms
Please helppppppppp!!!!
Terminal point for 4π/3
(cos4π/3 ,sin4π/3)
{cos(π+π/3) ,sin(π+π/3)}= (-cosπ/3 ,-sinπ/3)
or ,(- 1/2, -√3/2)
OPTION C
Reasoning by induction
Question 1 options:
1)
develops a general conclusion based on observations of cases.
2)
develops a general conclusion based on given information.
3)
starts with assumptions that are known to be valid to draw another new truths.
4)
uses patterns to create logical proofs.
Answer:
1because the occasion of cases
A political party wishes to estimate the proportion of voters that support the party in a particular state. The party will poll a random sample of n voters from the state. Which of the following is likely to result in the largest margin of error?
a. n = 500, confidence level 95%
b. n = 500, confidence level = 99%
c. n = 500, confidence level = 90%
d. n= 300, confidence level 95%
e. n = 300, confidence level = 90%
Answer:
Option D
Step-by-step explanation:
Generally the equation for Margin of Error is mathematically given by
[tex]M.E=Z*sqrt{\frac{p*(1-p)}{n}}[/tex]
Condition for Largest M.E
n has to be smallest and Z value has to be largest.
Where
From options
Smallest [tex]n=300[/tex]
Largest Z value respects to [tex]\alpha=95\%[/tex]
Therefore
n= 300, confidence level 95%
Option D
Based on this example, make a
generalization about the acute angles
formed when two parallel lines are
cut by a transversal.
Answer:
Step-by-step explanation:
There are 4 of them (acute angles that is)Those 4 are less than 90 degrees.They have supplementary angles which are greater than 90 degrees.There are 4 of them also.The total number of angles should be 8 if there are 2 parallel lines and 1 transversal.The function f(x)=log4x is dilated to become g(x)=f(13x).
What is the effect on f(x)?
Answer:
f(x) is compressed horizontally
Step-by-step explanation:
Given
[tex]f(x) = \log(4x)[/tex]
[tex]g(x) = f(13x)[/tex]
Required
The effect on f(x)
[tex]g(x) = f(13x)[/tex] implies that f(x) is horizontally compressed by 13.
So, we have:
[tex]f(13) = \log(4 * 13x)[/tex]
[tex]f(13) = \log(52x)[/tex]
So:
[tex]g(13) = \log(52x)[/tex]
Describe the system of equations
How many solutions does this system have.
Answer:
Step-by-step explanation:
One solution, at the point of intersection, (3,3)
Consider the phrase "the sum of 3 times a number and the quotient of the number and 4." Let’s break it down. You want the sum of two values. The first value is 3 times a number. What expression represents 3 times a number?
9514 1404 393
Answer:
3x
Step-by-step explanation:
If x represents the number, then "3 times a number" is 3x.
__
Additional comment
"The quotient of the number and 4" is x/4.
The sum of those two expressions is ...
3x + x/4
Define percent in terms of ratios
If (-3)^-5 = 1/x, what is the value of x?
Answer:
-243
Step-by-step explanation:
(-3) (-3) (-3) (-3) (-3) = - 243
[tex]\frac{1}{-243 }[/tex]
someone please help
Answer:
28
Step-by-step explanation:
78
AABC-AXYZ. What's the scale factor from
AABC to AXYZ?
9514 1404 393
Answer:
(d) 1/4
Step-by-step explanation:
The scale factor is the ratio of lengths of corresponding sides:
XZ/AC = 3/12 = 1/4
_____
Additional comment
I find the wording of the question a bit ambiguous. To transform ΔABC to ΔXYZ, every linear dimension of ΔABC is multiplied by 1/4. This is the sense of "ΔABC to ΔXYZ" that is used in the above answer.
On the other hand, one of the ways ratios are written is using the word "to," as in "12 to 3". Using this idea, we might interpret the question to be asking for ...
ΔABC to ΔXYZ = AC to XZ = 12 to 3 = 12/3 = 4
One of the problems encountered by corporations in America is finding an adequate number of employees who want to move into management. Recent surveys of workers in America taken by the Department of Labor in Washington D. C. revealed that only 20% of employees would like to move into management and be the boss. Suppose that a random sample of 75 U.S. workers was taken and each person was asked whether or not they would like to move into management. Find the probability that at least 18 of the 75 sampled employees would like to move into management.
Answer:
0.2358 = 23.58% probability that at least 18 of the 75 sampled employees would like to move into management.
Step-by-step explanation:
Binomial probability distribution
Probability of exactly x successes on n repeated trials, with p probability.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
Normal probability distribution
Problems of normally distributed distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].
20% of employees would like to move into management and be the boss.
This means that [tex]p = 0.2[/tex]
Sample of 75:
This means that [tex]n = 75[/tex]
Mean and standard deviation:
[tex]\mu = E(X) = np = 75(0.2) = 15[/tex]
[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{75*0.2*0.8} = 3.4641[/tex]
Find the probability that at least 18 of the 75 sampled employees would like to move into management.
Using continuity correction, this is [tex]P(X \geq 18 - 0.5) = P(X \geq 17.5)[/tex], which is 1 subtracted by the p-value of X = 17.5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{17.5 - 15}{3.4641}[/tex]
[tex]Z = 0.72[/tex]
[tex]Z = 0.72[/tex] has a p-value of 0.7642.
1 - 0.7642 = 0.2358
0.2358 = 23.58% probability that at least 18 of the 75 sampled employees would like to move into management.
The population, P(t), in millions, of a country, in year t, is given by the formula P(t) = 24 + 0.4t. What are the values of the population for t = 10, 20,
and 30?
Answer:
B. 28, 32, 36 millions
Step-by-step explanation:
Given:
P(t) = 24 + 0.4t
Where,
P(t) = population in millions
t = number of years
✔️Value of the population when t = 10:
Plug in t = 10 into P(t) = 24 + 0.4t
P(t) = 24 + 0.4(10)
P(t) = 24 + 4
P(t) = 28 million
✔️Value of the population when t = 20:
Plug in t = 20 into P(t) = 24 + 0.4t
P(t) = 24 + 0.4(20)
P(t) = 24 + 8
P(t) = 32 million
✔️Value of the population when t = 30:
Plug in t = 30 into P(t) = 24 + 0.4t
P(t) = 24 + 0.4(30)
P(t) = 24 + 12
P(t) = 36 million
If 4 gallons of gasoline cost $13.76, how much will 11 gallons of gasoline cost?
Answer:
x=37.84
Step-by-step explanation:
We can write a ratio to solve
4 gallons 11 gallons
--------------- = ----------------
13.76 x dollars
Using cross products
4x = 11*13.76
4x=151.36
Divide by 4
4x/4 = 151.36/4
x=37.84