Answer:
Slopes of parallel lines are equal
Step-by-step explanation:
On a coordinate plane, quadrilateral ABCD is shown. Point A is at (-2, -2), point B is at (-3, 4), point C is at (2, 2), and point D is at (3, -4).
The slope of the line segment BC is:
[tex]\dfrac{4-2}{-3-2} =-\dfrac{2}{5}[/tex]
The slope of the line segment AD is:
[tex]\dfrac{-4-(-2)}{3-(-2)} =\dfrac{-4+2}{3+2}=-\dfrac{2}{5}[/tex]
The slope of the line segment CD is:
[tex]\dfrac{2-(-4)}{2-3} =\dfrac{2+4}{2-3}=\dfrac{6}{-1}=-6[/tex]
The slope of the line segment BA is:
[tex]\dfrac{4-(-2)}{-3-(-2)} =\dfrac{4+2}{-3+2}=\dfrac{6}{-1}=-6[/tex]
Because the slopes of parallel lines are equal. Therefore, ABCD is a parallelogram because both pairs of opposite sides are parallel.
Answer:
c.) on edg.
Step-by-step explanation:
got it right :)
Please answer this correctly without making mistakes as my work is due today
Answer:
2
Step-by-step explanation:
Arranging them in ascending order we have the scores as;
[tex]2, 3, 3, 4, 4, 6, 8, 9, 9, 9[/tex]
The median is the average of the 5th and 6th scores.
[tex] \frac{4 + 6}{2} \\ \frac{10}{2} \\ 5[/tex]
The new set of scores become
[tex]2,3,3,4,6,8,9,9,9,9[/tex]
The median is;
[tex] \frac{6 + 8}{2} \\ \frac{14}{2} \\ 7[/tex]
The difference is
[tex]7 - 5 = 2[/tex]
Hope it helps! Vote for brainliest!
Kinda been stuck on this one, someone pls let me know
Answer:
255
Step-by-step explanation:
use calculator
Answer:
255
Step-by-step explanation:
∑ᵢ₌₁⁸ 2ⁱ⁻¹
Using brute force method:
S = 2⁰ + 2¹ + 2² + 2³ + 2⁴ + 2⁵ + 2⁶ + 2⁷
S = 1 + 2 + 4 + 8 + 16 + 32 + 64 + 128
S = 255
Using formula:
S = a₁ (1 − rⁿ) / (1 − r)
S = 1 (1 − 2⁸) / (1 − 2)
S = 255
A common inhabitant of human intestines is the bacterium Escherichia coli. A cell of this bacterium in a nutrient-broth medium divides into two cells every 20 minutes. The initial population of a culture is 58 cells. (a) Find the relative growth rate. (Assume t is measured in hours.) k = Correct: Your answer is correct. (b) Find an expression for the number of cells after t hours. P(t) = Correct: Your answer is correct. (c) Find the number of cells after 8 hours. 973078528 Correct: Your answer is correct. cells (d) Find the rate of growth after 8 hours. (Round your answer to three decimal places.) billion cells per hour (e) When will the population reach 20,000 cells? (Round your answer to two decimal places.) 2.81 Correct: Your answer is correct. hr
Answer:
The E. Coli will grow at a rate of approximately 800% an hour.
3. Students arrive at an ATM machine in a random pattern with an average inter-arrival time of 3 minutes. The length of transactions at the ATM machine is exponentially distributed with an average of 2 minutes. (a) What is the probability that a student arriving at the ATM will have to wait
Answer:
The probability that a student arriving at the ATM will have to wait is 67%.
Step-by-step explanation:
This can be solved using the queueing theory models.
We have a mean rate of arrival of:
[tex]\lambda=1/3\,min^{-1}[/tex]
We have a service rate of:
[tex]\mu=1/2\,min^{-1}[/tex]
The probability that a student arriving at the ATM will have to wait is equal to 1 minus the probability of having 0 students in the ATM (idle ATM).
Then, the probability that a student arriving at the ATM will have to wait is equal to the utilization rate of the ATM.
The last can be calculated as:
[tex]P_{n>0}=\rho=\dfrac{\lambda}{\mu}=\dfrac{1/3}{1/2}=\dfrac{2}{3}=0.67[/tex]
Then, the probability that a student arriving at the ATM will have to wait is 67%.
What is the radius of a sphere with a surface area of 100Ttcm??
10 cm
3 cm
5 cm
25 cm
Consider the function represented by 9x + 3y = 12 with x as the independent variable. How can this function be written using
function notation?
Fly) = -
f(x) = - 3x + 4
f(x) =
FCV) = -3y+ 4
Answer:
f(x) = -3x + 4
Step-by-step explanation:
Step 1: Write it in slope-intercept form
9x + 3y = 12
3y = -9x + 12
y = -3x + 4
Step 2: Replace y with f(x)
f(x) = -3x + 4
In math, function f(x) is equal to the variable y.
78% of U.S. adults think that political correctness is a problem in America today. You randomly select six U.S. adults and ask them whether they think that political correctness is a problem in America today. The random variable represents the number of U.S. adults who think that political correctness is a problem in America today. Answer the questions below.
1. Find the mean of the binomial distribution (Round to the nearest tenth as needed.)
2. Find the variance of the binomial distribution. (Round to the nearest tenth as needed.)
3. Find the standard deviation of the binomial distribution. (Round to the nearest tenth as needed.)
4. Most samples of 6 adults would differ from the mean by no more than nothing. (Type integers or decimals rounded to the nearest tenth as needed.)
Answer:
Step-by-step explanation:
Let x be a random variable representing the number of U.S. adults who think that political correctness is a problem in America today. This is a binomial distribution since the outcomes are two ways. The probability of success, p = 78/100 = 0.78
The probability of failure, q would be 1 - p = 1 - 0.78 = 0.22
n = 6
a) Mean = np = 6 × 0.78 = 4.68
b) Variance = npq = 6 × 0.78 × 0.22 = 1.0
c) Standard deviation = √npq = √(6 × 0.78 × 0.22) = 1.0
d) The standard deviation is used to express the spread of the data from the mean. Therefore, most samples of 6 adults would differ from the mean by no more than 1.0
If the legs of a right triangle are 10 and 24, then the
hypotenuse is
26.
Step-by-step explanation:
To figure out the missing side of a right triangle, we will use the Pythagorean theorem. This is...
[tex]a^2+b^2=c^2[/tex]
With this Pythagorean theorem, a and b will always be the legs and the c will always be the hypotenuse, no matter what. Now knowing this, we can plug the legs into the equation.
[tex]10^2+24^2=c^2[/tex]
[tex]100+576=c^2[/tex]
Add the legs together.
[tex]676=c^2[/tex]
Now, since c is squared we will have to find the square root of 676.
[tex]\sqrt{676}[/tex]
= 26
The graph of linear function f passes through the point (1, −9) and has a slope of −3.
Answer:
Equation of a line y = mx + c
m = slope
Using point (1,-9) and slope -3
y + 9 = -3(x - 1)
y + 9 = -3x + 3
y = -3x + 3 - 9
y = -3x - 6
Hope this helps.
The average amount of water in randomly selected 16-ounce bottles of water is 16.15 ounces with a standard deviation of 0.45 ounces. If a random sample of thirty-five 16-ounce bottles of water are selected, what is the probability that the mean of this sample is less than 15.99 ounces of water? Answer: (round to 4 decimal places)
Answer:
0.0179 = 1.79% probability that the mean of this sample is less than 15.99 ounces of water.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal probability distribution
When the distribution is normal, we use 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.
Central Limit Theorem
The Central Limit Theorem estabilishes 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.
In this question, we have that:
[tex]\mu = 16.15, \sigma = 0.45, n = 35, s = \frac{0.45}{\sqrt{35}} = 0.0761[/tex]
What is the probability that the mean of this sample is less than 15.99 ounces of water?
This is the pvalue of Z when X = 15.99. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{15.99 - 16.15}{0.0761}[/tex]
[tex]Z = -2.1[/tex]
[tex]Z = -2.1[/tex] has a pvalue of 0.0179
0.0179 = 1.79% probability that the mean of this sample is less than 15.99 ounces of water.
Urgent need help immediately please !
Answer:
D
Step-by-step explanation:
the ratio of men to women in a village is 12: 25. if there are 120men, (a)how many women are there ?, (b) what is the total number of men to women
Answer:
a) 250 women
b) 370 in total
Step-by-step explanation:
Men : Women
12 : 25
120 : 250
a) If there are 120 men that means 12 was multiplied 10 times to get 120 so to get the amount for women we multiply 25 ten times which will give 250.
b) the sum will be 120 + 250 = 370
Does the equation Axequalsb have a solution for each b in set of real numbers RSuperscript 4? A. No, because A has a pivot position in every row. B. Yes, because the columns of A span set of real numbers RSuperscript 4. C. Yes, because A does not have a pivot position in every row. D. No, because the columns of A do not span set of real numbers R
Answer:
C. Yes, because A does not have a pivot position in every row.
Step-by-step explanation:
The pivot position in the matrix is determined by entries in non zero rows. The pivot position may be in the row or a column. By Invertible Matrix Theorem the equation Axequalsb has non trivial solution. A has fewer pivot positions therefore A is not invertible. Ax will map RSuperscript into real numbers for n times. A has pivot position if left parenthesis bold x right parenthesis.
Taylor Swift wants to know the proportion of her fans who listened to her new single ME! within the first hour of it being released. In order to estimate this, she takes a sample of 150 of her fans and asks them if they listened to the song in this time period. Of the 150 fans, 135 of them (90%) responded that they did listen to the song during this time period. What is the parameter and what is its value
Answer:
The parameter is the population proportion of fans who listened to her new single and has an estimated value of 90%.
Step-by-step explanation:
The parameter is a value that corresponds to a population, while an a value that corresponds to a sample is know as statistic.
She takes a sample to estimate, with a point estimate and probably with a confidence interval around this point estimate, the true proportion of fans who listened to her new single.
This is the paramater: the population proportion of fans who listened to her new single.
Its value comes from an estimation based on the sample proportion (point estimate).
The sample proportion is 90%, so we can estimate, as there is no bias, that the population proportion is also 90%.
At what point will the graph of the equations 3x +y =7&
y=1 intersect?
=======================================================
Work Shown:
Substitute y = 1 into the first equation. Basically we replace every y with 1. From here we solve for x
3x+y = 7
3x+1 = 7
3x+1-1 = 7-1 .... subtracting 1 from both sides
3x = 6
3x/3 = 6/3 .... dividing both sides by 3
x = 2
We have x = 2 pair up with y = 1. The two equations intersect at (2,1)
As a check, plugging (x,y) = (2,1) into the first equation should lead to a true statement
3x+y = 7
3(2)+1 = 7
6+1 = 7
7 = 7 and it does lead to a true statement
The graph is shown below.
To express the polynomial 4a^3 + a^2 - 6a^5 + 2a^3 - 4a + 1 in standard form, which terms should be combined?
Answer:
Step-by-step explanation:
-6a^5+6a^3+a^2-4a+1
Answer:
4a^3 and 2a^3
Step-by-step explanation:
you always start by combining like terms
i dont understand, help?
Help me please thank u
Answer:
160cm
74mm
3.6km is 3600m
Step-by-step explanation:
1. 6 x 100= 160cm
7.4cm x 10 =74mm
3.6 x 1000= 3600m
A problem requires finding the distance traveled in miles. Which would not be a reasonable answer? Justify your response. A. minus10 B. 1.8 C. 10 and one half D. 50
Answer:
A. minus 10,
Step-by-step explanation:
The distance travelled must be positive.
Therefore minus 10 would not be a reasonable answer.
The two figures are similar. Write a proportion to find the missing measure. Then find the value of x.
Answer:
First option is the right choice.
Step-by-step explanation:
x/95 = 15/19
x = 75
Best Regards!
Answer:
Option A
Step-by-step explanation:
Triangle ABC and DEF are similar.
Taking proportion of their sides to find the value of the unknown.
=> x/15 = 95/19
Cross Multiplying
=> 19x = 1425
Dividing both sides by 9
=> x = 75
Which best compares the slope and y-intercepts of the linear functions f and g where f= 1/3 x + 3 and g is shown in the table? X =0,1,2,3 and g(x) =3,6,9,12
Answer:
different slope same intercept
Step-by-step explanation:
g(x)= 3x+3
this means they both intercept the y axis at 3 but the incline of g is much greater then f since the slope is much larger.Hope this is what you were looking for
20 Find the area of the rectangle given that
the perimeter is 50 cm.
3m + 2
m - 5
F 32
G 7
H 46
J 9
Answer: H - 46
Step-by-step explanation:
Primeter = 2(l + w)
50 = 2{(3m+2) + (m-5)}
25 = 3m+2 +m -5
25 = 4m -3
m = 28/4 = 7
l = 3m+2 = 23 cm
w = m-5 = 2 cm
Area = l x b
= 23 x 2 = 46 sq. cm.
parallelogram JKLM is shown on the coordinate plane below
Answer: c) K' = (6, 4) L' = (3, 3)
Step-by-step explanation:
The simplest way to find the coordinates is to rotate the graph 3 times.
Rotate 1 time to the left (counterclockwise) = 90°
Rotate 2 times to the left (counterclockwise) = 180°
Rotate 3 times to the left (counterclockwise) = 270°
see image for 3 times to the left = 270°
Consider the ski gondola from Question 3. Suppose engineers decide to reduce the risk of an overload by reducing the passenger capacity to a maximum of 15 skiers. Assuming the maximum load limit remains at 5,000 lb, what is the probability that a group of 15 randomly selected skiers will overload the gondola
Answer:
The probability that a group of 15 randomly selected skiers will overload the gondola = (3.177 × 10⁻⁵¹)
(almost zero probability showing how almost impossible it is to overload the gondola, therefore showing how very safe the gondola is)
Step-by-step explanation:
Complete Question
A ski gondola carries skiers to the top of the mountain. If the Total weight of an adult skier and the equipment is normally distributed with mean 200 lb and standard deviation 40 lb.
Consider the ski gondola from Question 3. Suppose engineers decide to reduce the risk of an overload by reducing the passenger capacity to a maximum of 15 skiers. Assuming the maximum load limit remains at 5,000 lb, what is the probability that a group of 15 randomly selected skiers will overload the gondola.
Solution
For 15 people to exceed 5000 lb, each person is expected to exceed (5000/15) per skier.
Each skier is expected to exceed 333.333 lb weight.
Probability of one skier exceeding this limit = P(x > 333.333)
This becomes a normal distribution problem with mean = 200 lb, standard deviation = 40 lb
We first standardize 333.333 lbs
The standardized score for any value is the value minus the mean then divided by the standard deviation.
z = (x - μ)/σ = (333.333 - 200)/40 = 3.33
To determine the required probability
P(x > 333.333) = P(z > 3.33)
We'll use data from the normal distribution table for these probabilities
P(x > 333.333) = P(z > 3.33) = 1 - P(z ≤ 3.33)
= 1 - 0.99957
= 0.00043
So, the probability that 15 people will now all be above this limit = (probability of one person exceeding the limit)¹⁵ = (0.00043)¹⁵
= (3.177 × 10⁻⁵¹)
(almost zero probability showing how almost impossible it is to overload the gondola, therefore showing how very safe the gondola is)
Hope this Helps!!!
Please answer this correctly
Answer:
The correct answer is
Fact
a thing that is known or proved to be true
Hope this helps
- Quinn
Translate to an algebraic expression.
28 more than d
Answer: d + 28
Step-by-step explanation:
Answer:
d+28
Step-by-step explanation:
it is easier to remeber that you should always flip the wording so for this on "d" would be first then add the 28
1/4 ÷ 3/8 Please show work
Answer:
2/3
Step-by-step explanation:
Reciprocal and it becomes multiplication.
1/4 × 8/3
Multiply.
8/12
Simplify.
2/3
Answer:
2/3
Step-by-step explanation:
you can also make them both the same denominator and divide them or easier just multiply and them simplify
Please answer this correctly
Answer:
The median would change the most
Step-by-step explanation:
The mode will not change, because the only duplicate number is 20
The mean will change from 53.22 to 55.2 when you put 73 into the set
and the median will change from 67 to 70 when you put 73 into it
Answer:
Median
Step-by-step explanation:
Mean:
Mean of 9 numbers = 477/9 = 53
Mean of 10 numbers = 550/10 = 55
Mode:
Mode for the set of 9 numbers: 20
Mode for the setof 10 numbers when 73 is included = 20
Median:
Set of 9 numbers:
10, 20, 20 , 32, 67, 74, 76, 84, 94
Median = 67
Set of 10 numbers:
10, 20, 20 , 32, 67, 73, 74, 76, 84, 94
Median = 67+73/2 = 140/2 = 70
find the mean of x,2x,3x,4x,5
Answer:
Mean = 3x
Step-by-step explanation:
Mean = [tex]\frac{SumOfObservations}{TotalNumberOfObservations}[/tex]
Mean = [tex]\frac{x+2x+3x+4x+5x}{5}[/tex]
Mean = [tex]\frac{15x}{5}[/tex]
Mean = [tex]\frac{15x}{5}[/tex]
Mean = 3x
If the difference between two numbers is 7 and their product is 137 what is the sum of squares if the numbers?
Answer:
323
Step-by-step explanation:
a-b= 7
ab= 137
a²+b²= ?
---------
Since (a-b)²= a²-2ab +b²
⇒ a²+b²= (a-b)² + 2ab= 7² + 2*137= 323