Answer:
Total Distance = 20km = 20 × 1000 = 20,000 m
Distance walked = 800m
Distance travelled by cycle = 20,000 - 800 = 19,200m
Percentage of journey by cycle = (distance travelled by cycle ÷ total distance) × 100
Percentage of journey by cycle = (19200 / 20000) * 100
Percentage of journey by cycle = 96%
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
Write 2^60 the expression as a exponent with the base of 4
Answer:
Step-by-step explanation:
Answer:
Step-by-step explanation:
[tex]2^{60} =2^{2 \times 30} =(2^{2} )^{30}=4^{30}[/tex]
if the lines 3x+2ky=0 and 2x+5y+1=0 are parallel, then what is the value of k?
Answer:
k = 15/4
Step-by-step explanation:
Slope of a line = -a/b
slope of the first line = -3/2k
slope of the second line = -2/5
the slope of two parallel lines are congruent
-3/2k = -2/5
-15 = -4K
k = 15/4
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
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
Two complex numbers have a sum of 14 and a product of 74. Write either of the two numbers.
Answer:
Hello,
Step-by-step explanation:
The 2 numbers are roots of the equation:
U²-14U+74=0
Discriminant=14²-4*74=-100
U=7-5i or U=7+5i
9514 1404 393
Answer:
7 +5i or 7 -5i
Step-by-step explanation:
If the two numbers are represented by x and y, then ...
x+y = 14
xy = 74
Substituting for y, we have ...
x(14 -x) = 74
x^2 -14x +49 = -74 +49 . . . . . multiply by -1, complete the square
(x -7)^2 = -25 . . . . . . . . . . . write as a square
x -7 = ±√(-25) = ±5i . . . . take the square root
x = 7 ± 5i . . . . . . . . . . . add 7
One of the numbers is 7 +5i.
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).
Can anybody help me with this one plz.
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]
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 consistent system of equations is a system with __________.
Select one:
a. the same line
b. parallel lines
c. intersecting lines and lines that have the same slope
d. intersecting lines and lines that have the same equation
the answer is d. my shlime
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.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
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
Change the following expression involving addition and subtraction into one only involving addition
7-3+8-2-6+1-(-3)
please help me with this function problem
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!
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
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]
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:
m1=28 degrees, m6=65 degrees, m5=65 degrees. Find mMAX.
Answer:
D. 93
Step-by-step explanation:
Given:
m<1 = 28°
m<6 = 65°
m<5 = 65°
Required:
m<MAX
Solution:
m<MAX = m<1 + m<5 (angle addition postulate)
Substitute
m<MAX = 28° + 65°
m<MAX = 93°
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)
Define percent in terms of ratios
Find f(0) and then find the equation of the given linear function.
x 1 2 3 4
f(x) 6 10 14 18
f(0) =
f(x) =
Answer:
f(0) = 2
f(x) = 4x + 2
Step-by-step explanation:
You can see that the consecutive x-values are producing y-values that increase by 4 each time. Since the change in y is the same every time, we know this is a linear graph because in a continuous linear graph the slope does not change.
We can use the equation for a line: y = mx + b,
where m is the slope and b is the y-intercept.
The slope [m] is calculated by [change in y]/[change in x]. The y-values are increasing by 4 each time x increases by 1. m = 4/1 = 4.
Once we have found the slope, we can find the value for f(0). The line graph has a positive slope, so to find the value at x=0, we would subtract 4, moving backwards along the line.
6-4 = 2
The y-intercept on a line is the y-value for which x = 0. In this case we have already solved for the y-intercept, f(0) = 2.
Now plug the values into the formula.
y = mx + b
The value of f(0) is 2.
The equation of this linear function is y = 4x + 2
What is a function?A function is defined as a relation between a set of inputs having one output each.
The inputs are called domain of the function.
The outputs are called the range of the function.
We have,
x = 1, 2, 3, 4
f(x) = 6, 10, 14, 18
The f(x) values are the values we get when we substitute x values.
There is a difference of 4 in the f(x) values.
10 - 6 = 4
14 - 10 = 4
18 - 14 = 4
Since the difference between the values of f(x) is same, the given function is a linear function.
The equation of this linear function will be in the form of:
y = mx + c
m = slope
c = y-intercept
Find m.
Choose any two points as: (1, 6) and (2, 10)
m = 10-6 / 2-1 = 4/1= 4
Find c.
x = 0 in y-intercept and choosing any point = (1, 6)
So,
6 = 4 + c
c = 6 - 4 = 2
Now,
The equation of this linear function:
y = 4x + 2
f(0) = 4 x 0 + 2 = 0 + 2 = 2
Thus,
The value of f(0) is 2.
The equation of this linear function is y = 4x + 2
Learn more about functions here:
brainly.com/question/17440903
#SPJ2
Brenda wants to buy a sweater that costs 138 Croatian kuna (form of money in Croaita). She has $20.
$1 = 6 Croatian kuna
Fill in the blank.
$20 = (blank) Croatian kuna
Does Brenda have enough money to buy the sweater?
Answer:
She only has 120 croat
Step-by-step explanation:
We can use a ratio to solve
She only has 20 dollars
1 dollar 20 dollars
---------- = --------------
6 croat x croat
6*20 = x
120 =x
120croat
She does not have enough money
She needs 138 croat
Answer:
120 croatian kuna
Step-by-step explanation:
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.
PLEASE HELP ME AND PLEASE BE CORRECT
TELL ME WHERE TO PUT THE POINT
LOOK AT THE BOTTOM
Answer:
hi what is your name and place
Pls help with this question. No links.
Answer:
i hope it's helpful for youThe time for a visitor to read health instructions on a Web site is approximately normally distributed with a mean of 10 minutes and a standard deviation of 2 minutes. Suppose 64 visitors independently view the site. Determine the following: a. The expected value and the variance of the mean time of the visitors. b. The probability that the mean time of the visitors is within 15 seconds of 10 minutes c. The value exceeded by the mean time of the visitors with probability 0.01.
Answer:
a) The mean is 10 and the variance is 0.0625.
b) 0.6826 = 68.26% probability that the mean time of the visitors is within 15 seconds of 10 minutes.
c) 10.58 minutes.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score 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 p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Normally distributed with a mean of 10 minutes and a standard deviation of 2 minutes.
This means that [tex]\mu = 10, \sigma = 2[/tex]
Suppose 64 visitors independently view the site.
This means that [tex]n = 64, = \frac{2}{\sqrt{64}} = 0.25[/tex]
a. The expected value and the variance of the mean time of the visitors.
Using the Central Limit Theorem, mean of 10 and variance of (0.25)^2 = 0.0625.
b. The probability that the mean time of the visitors is within 15 seconds of 10 minutes.
15 seconds = 15/60 = 0.25 minutes, so between 9.75 and 10.25 seconds, which is the p-value of Z when X = 10.25 subtracted by the p-value of Z when X = 9.75.
X = 10.25
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{10.25 - 10}{0.25}[/tex]
[tex]Z = 1[/tex]
[tex]Z = 1[/tex] has a p-value of 0.8413.
X = 9.75
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{9.75 - 10}{0.25}[/tex]
[tex]Z = -1[/tex]
[tex]Z = -1[/tex] has a p-value of 0.1587.
0.8413 - 0.1587 = 0.6826.
0.6826 = 68.26% probability that the mean time of the visitors is within 15 seconds of 10 minutes.
c. The value exceeded by the mean time of the visitors with probability 0.01.
The 100 - 1 = 99th percentile, which is X when Z has a p-value of 0.99, so X when Z = 2.327.
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]2.327 = \frac{X - 10}{0.25}[/tex]
[tex]X - 10 = 2.327*0.25[/tex]
[tex]X = 10.58[/tex]
So 10.58 minutes.
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
