Answer:
Step-by-step explanation:the first one
Find the values of the variable y, for which:
the difference between the fractions y+12/y-4 and y/y+4 is equal to their product
Answer:
y = 12
Step-by-step explanation:
Ordinarily, in math, when we say "the difference between ..." we mean the second listed item is subtracted from the first. (In English, we often mean "the positive difference between ..." so the order doesn't matter.)
We'll assume we are only interested in the case where the difference is in the order listed.
[tex]\dfrac{y+12}{y-4}-\dfrac{y}{y+4}=\dfrac{y+12}{y-4}\cdot\dfrac{y}{y+4}\\\\\dfrac{(y+12)(y+4)-(y-4)(y)}{y^2-16}=\dfrac{(y+12)(y)}{y^2-16}\\\\0=\dfrac{y^2-8y-48}{y^2-16}=\dfrac{(y-12)(y+4)}{(y-4)(y+4)}=\dfrac{y-12}{y-4}\qquad\text{$y\ne -4$}\\\\\boxed{y=12}[/tex]
There is one solution.
_____
Comment on the solution
If you were to "clear fractions" by multiplying the equation by (y^2-16), you would also obtain the extraneous solution y=-4. That is why we did not solve it that way.
What is the area of this parallelogram
Answer:
27
Step-by-step explanation:
The area of this parallelogram is its base times height. 6x4.5 is 27.
Hope this helps! (please mark me brainliest)
What is the volume of this triangular prism?:HURRY:
Answer:
195 m3
Step-by-step explanation:
Answer:195 m^3
Step-by-step explanation:
volume of triangular prism=base area x height
height=h=5m
Base area=0.5 x 13 x 6
Base area=39
Volume of triangular prism=39 x 5
Volume of triangular prism=195m^3
Put in order from greatest to svllems 12 1/2, 12.09,. 12 2/5,12.8
Answer:
12.8
12 1/2
12 2/5
12.09
The owner of an automobile repair shop studied the waiting times for customers who arrive at the shop for an oil change. The following data with waiting times in minutes were collected over a one-month period. 2 5 10 12 4 4 5 17 11 8 9 8 12 21 6 8 7 13 18 3 (a) Develop a frequency distribution using classes of 0-4, 5-9, 10-14, 15-19, and 20-24.
Answer:
Step-by-step explanation:
Developing a frequency distribution of the ungrouped data simply means creating a structure (table) for the data. It is a method of converting an ungrouped data into a grouped data for proper analysis of the data.
The table will contain the values, their frequency (this means the number of times individual values occurs based on the classes) and the tally.
Check the attachment for the table.
Given the ungrouped data 2 5 10 12 4 4 5 17 11 8 9 8 12 21 6 8 7 13 18 3. The total number of data collected is 20. From the frequency distribution table, it can be seen that the total frequency is 20 which shows that all the values have been catered for.
Find the area of the regular polygon.
Round your answer to the
nearest tenth if necessary.
Answer:
See Explanation
Step-by-step explanation:
The question is incomplete as the dimension of the polygon is not given.
However, I'll give a general explanation of how to calculate the area of a regular polygon.
If you follow these simple steps, you'll arrive at your answer.
The area of a polygon is calculated as thus;
A = ½(nbh)
Where A represent the area
n represents the number of sides
b represents the length of the base
h represent the height of the polygon
Take for instance, the polygon is a regular pentagon.
This means n = 5.
Also assume that the base and the height are 5cm and 7cm respectively.
This means that
Area = ½ * (5 * 5 * 7)
Area = ½ * 175
Area = 87.5cm²
Hence, the area of the polygon is 87.5cm²
Which line is parallel to y = 1/2x -5
Answer:
Any line with a slope of 1/2 would be parallel to that line.
Step-by-step explanation:
A line is parallel when the slopes are the same, causing the situation where the lines will never intercept. The line in the question has a slope of 1/2, so a parallel line must have that same slope.
help help help please
Answer:
to add to the table, continue the arithmetic sequence in each columnto use the table, extend the third column to 45, or multiply the first row by 9Step-by-step explanation:
The numbers in the first column are an arithmetic sequence with a common difference of 2. The next few numbers will be 6, 8, 10, ...
The numbers in the second column are an arithmetic sequence with a common difference of 3. The next few numbers will be 9, 12, 15, ...
The numbers in the third column are an arithmetic sequence with a common difference of 5. The next few numbers will be 15, 20, 25, ...
To use the table, Mark can extend each sequence until he has a row with 45 in the third column, or he can multiply or add rows to give a result of 45 in the third column. For example, multiplying the first row by 9 gives 18:27:45 meaning that Mark needs 18 liters of blue and 27 liters of yellow to make 45 liters of green paint.
Professor Isaac Asimov was one of the most prolific writers of all time. Prior to his death, he wrote nearly 500 books during a 40-year career. In fact, as his career progressed, he became even more productive in terms of the number of books written within a given period of time. The data given in increments of 100:
Number of books, x: 100 200 300 400 500
Time in months, y: 237 350 419 465 507
a. Assume that the number of books x and the time in months y are linearly related. Find the least-squares line relating y to x.
b. Plot the time as a function of the number of books written using a scatterplot, and graph the least-squares line on the same paper. Does this seem to provide a good fit to the data points?
c. Construct the ANOVA table for the linear regression.
Answer:
Step-by-step explanation:
n = sample size = 5
a) Let us determine the sum
[tex]\sum x_i= 100+200+300+400+490=1490[/tex]
[tex]\sum x_i^2= 100^2+200^2+300^2+400^2+490^2=540100[/tex]
[tex]\sum y_i = 237+350+419+465+507=1978[/tex]
[tex]\sum y_i^2= 237^2+350^2+419^2+465^2+507^2=827504[/tex]
[tex]\sum x_i y_i=100 \times 237 + 200\times350+300 \times 419 + 400 \times 465 + 490 \times 507=653830[/tex]
Now we can determine [tex]S_x_x, S_x_y, S_y_y[/tex]
[tex]S_x_x = \sum x_i^2-\frac{(\sum x_1)^2}{n} \\= 540100 - \frac{1490^2}{5} \\= 96080[/tex]
[tex]S_x_y = \sum x_i y_i -\frac{(\sum x_i)(\sum y_i) }{n} \\\\[/tex]
[tex]653830 - \frac{1490 \times 1978 }{5} = 64386[/tex]
[tex]S_y_y = \sum y_i^2-\frac{(\sum y_i)^2 }{n} = 82750-\frac{1978^2}{5} \\\\= 45007.2[/tex]
The estimate b of the slope β is the ratio of [tex]S_x_y[/tex] and [tex]S_x_x[/tex]
[tex]b = \frac{S_x_y}{S_x_x}[/tex]
[tex]\frac{64386}{96080} = 0.67[/tex]
The mean is the sum of all value divide by number of values
[tex]\bar x= \frac{\sum x_i}{n} \\\\= \frac{100+200+300+400+490}{5} \\\\= \frac{1490}{5} = 298[/tex]
[tex]\bar y= \frac{\sum y_i}{n} \\\\= \frac{237+350+419+465+507}{5} \\\\= \frac{1978}{5} = 395.6[/tex]
The estimate a of the intercept is
[tex]a = \bar y - b \bar x[/tex]
[tex]= 395.6 - 0.69 \times 298\\= 195.9[/tex]
General least square equation;
[tex]\bar y = \alpha + \beta x[/tex]
replace alpha by a = 3 and beta by b = 0.67 in general least equation
y = a + bx
195.9 + 0.67x
b)
Scatter plot is shown in the attached file
x is on the horizontal axis
y is n the vertical axis
The degree of freedom of regression is 1
because we use one variable s predictor variable
[tex]d_f_R = 1[/tex]
The degree of freedom of error is the sample size n decrease by 2
[tex]d_f_E =n-2= 5 - 2=3[/tex]
Total df is equal to the sum of seperate degree of freedom dfR and dfE
total df = 1 +3 4
[tex]SSR = \frac{(S_x_y)^2}{S_x_x} = \frac{64386^2}{96080} \\\\= 43146.9296[/tex]
Total SS =Syy= 45007.2
SSE + Total SS = SSR
= 45007.2 - 43146.9296
= 1860.2705
Suppose you had to
guess on a four-choice
multiple-choice test and
were given four questions.
Find the binomial
probability distribution.
( + ) ℎ =
4 = 0.25
Answer:
For 0 correct answer [tex]^4c_0p^0q^{4-0}[/tex]
For 1 correct answer [tex]^4c_1p^1q^{4-1}[/tex]
For 2 correct answer [tex]^4c_2p^0q^{4-2}[/tex]
For 3 correct answer [tex]^4c_3p^1q^{4-3}[/tex]
For 4 correct answer [tex]^4c_4p^1q^{4-4}[/tex]
Step-by-step explanation:
It is given that there are 4 questions n = 4
Number of choices is 4
So probability of getting correct answer [tex]=\frac{1}{4}[/tex]
Probability of getting incorrect answer [tex]=1-\frac{1}{4}=\frac{3}{4}[/tex]
Probability distribution is given by [tex]^nc_rp^rq^{n-r}[/tex]
Therefore probability distribution of 0 correct answer
[tex]^4c_0p^0q^{4-0}[/tex]
Therefore probability distribution of 1 correct answer
[tex]^4c_1p^1q^{4-1}[/tex]
Therefore probability distribution of 2 correct answer
[tex]^4c_2p^0q^{4-2}[/tex]
Therefore probability distribution of 3 correct answer.
[tex]^4c_3p^1q^{4-3}[/tex]
Therefore probability distribution of 4 correct answer.
[tex]^4c_4p^1q^{4-4}[/tex]
Triangle ABC is rotated 180º using the origin as the center of rotation.
On a coordinate plane, triangle A B C has points (negative 4, negative 3), (negative 5, negative 2), (negative 3, negative 2). Triangle A prime B prime C prime has points (4, 3), (5, 2), (3, 2).
Which sequence of transformations will produce the same result?
a
a reflection over the x-axis and then a reflection over the y-axis
b
a translation up 4 and then a translation right 6
c
a translation up 4 and then a reflection over the y-axis
d
a translation right 6 and then a reflection over the x-axis
Answer:
a. a reflection over the x-axis and then a reflection over the y-axis
Step-by-step explanation:
If you plot it on a graph (you can use Desmos), you can see the triangles and only a. a reflection over the x-axis and then a reflection over the y-axis makes sense.
Answer:
thats c
Step-by-step explanation:
Can someone help ??
Answer:
A. is 10/12 B. is 8/28 C. is 20/45
Step-by-step explanation:
I think
1).
A) supplementary
B) complementary
C) comesponding
D) alternate interior
Please solve this in a paper and send the answers with steps.
*marking as brainlist.
Answer: 2. 121 could be the dividend and 11 will be the quotient. 3) 35 could be the dividend and -5 could be the divisor.
4) 256 could be the dividend and -16 would be the quotient. 5) 12 could be the divisor and 144 could be the dividend. 6) 17 could be the divisor and and 9 could be the quotient.
Step-by-step explanation:
2. 121/11= 11
3. 35/-5= -7
4.256/-16 =-16
5.144/12= 12
6.153/17=9
Audrey collected 4⁄5 pint of blueberries. Addison collected 12 times as many pints of blueberries as Audrey. How many pints of blueberries did Addison collect?
Answer:
48/5≈ 9 3/5
Step-by-step explanation:
12 is the same thing as 12/1
so your multiply fractions
4/5 times 12/1
numerator=top
denominator=bottom
so to multiply a fraction you multiply the numerator times the numerator
so in that case your multiplying 4 times 12
=48
to find the bottom half you multiply the denominator times the denominator
in that case is 5 times 1
=5
numerator/denominator
48/5
if you want to simplify it further simply divide 48/5
5 goes into 48 about 9 times
and were left with 3/5
so 9 and 3/5
pls mark me brainliest
Write the following equation in standard form.
y=-4/5x-2
Answer:
4x+5y=-2
Step-by-step explanation:
y=-4/5x-2
5y=-4x-2
4x+5y=-2
What is the height?
4m
3m
2m
find area
Answer:
I think the area is 24
Step-by-step explanation:
A company makes cones out of solid foam. Each cone has a height of 9 inches, and its base has a diameter of 5 inches. How much foam is needed to make 120 cones?
Answer: 2250 pi
Step to do:
where is the volume of the cone, is the radius of the base, and is the height of the cone.
In the given problem, we know that and . Using this, we can find the volume of a single cone:
Since the problem asks how much foam is needed to make 120 cones, we can multiply this result to get our answer:
Write the slope-intercept form of the equation of the line through (-1,4) and parallel to x=5
Answer:
x = -1
Step-by-step explanation:
When lines are parallel, they have the same slope
x = 5 means the line is a vertical line going through x=5
The new line is a vertical line
We have a point (-1,4)
It will need to go through the x point of -1 and be a vertical line ( which is in the form x= )
x=-1
PLEASE HELP WITH THIS EASY QUESTION!! EXPLANATION NEEDED!!
Answer:
100
Step-by-step explanation:
(b/2)^2
b= -20
(-20/2)^2
(-10)^2
100
The altitude of an airplane is decreasing at a rate of 44 feet per second. What is the change in altitude of the airplane over a period of 34 seconds?
Answer:
1320 feet
Step-by-step explanation:
All we have to do is multiply the rate of change of altitude by the time it took the altitude to change.
The altitude of an airplane is decreasing at a rate of 44 feet per second. After 30 seconds, the change is altitude is:
44 * 30 = 1320 feet
The altitude of the airplane has changed by 1320 feet.
The scatter plot for which type of data is most likely to suggest a linear association between
the two variables?
ages and heights of a group of dogs
time working out and strength of muscles
level of water in a reservoir each day and the day's date during one month
number of books returned to the library each day and the day's date over a period of one week
Plzzzz help
Answer:
level of water in a reservoir each....
Step-by-step explanation:
The scatter plot
A scatter plot is like a scatter chart or graph that uses the dots for representing the values of two different numeric variables. The horizontal value indicates the individual point data. Thus is used for observing the realtisohips between the variables.
This the answer is level of the water in a dam each day and date during 1 month.
The scatter plot can tell you the values for the set of data. The points may be given in different sizes, colors, and shapes. The data is displayed in points. The values are shown on the vertical axis. The relationship of the data can positive, negative, and neutral. The scatter plot can display a mosaic and a fluctuational diagram.Hence the option C is correct.Learn more about the which type of data.
brainly.com/question/22485501.
g(x) = 9x plug in g(9)
Answer:
81
Step-by-step explanation:
replace x with 9 so it's 9x9 which is 81
Answer:
g(9) = 81
Step-by-step explanation:
g(x) = 9x
g(9) = 9(9) = 81
Find the slope, if it exists, of the line containing the points (-1,-15) and (-17,-20)
The slope is _____________________
brainliest quick!
Aiden wanted to model -15 + 15 = 0 on the number line. He first drew an arrow 15 units long starting from zero that pointed to the left. He then draws another arrow 15 units long starting from zero that points to the right. What error did Aiden make?
A. The first arrow he drew should have pointed to the right to represent -15.
B. The second arrow he drew should have pointed to the left to represent 15.
C. The first arrow he drew should have started at -15 instead of 0.
D. The second arrow he drew should have started at -15 instead of 0.
Answer:
c
Step-by-step explanation:
Answer:
it's D
Step-by-step explanation:
The number never goes over 0 so there is no need to put anything above 0
Four students attempt to register online at the same time for an Introductory Statistics class that is full. Two are psychology majors and two are biology majors. They are put on a wait list. Prior to the start of the semester, two enrolled students drop the course, so the professor randomly selects two of the four wait list students and gives them seats in the class.What is the probability that both students selected have different majors?
Answer:
2/3
Step-by-step explanation:
If all outcomes are listed,
{P1P2, P1B1, P1B2, P2B1, P2B2, B1B2}
then 4/6 of the outcomes have different majors.
this can be simplified to 2/3.
The probability that both students selected have different majors is 2/3
What is probability?Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.
Here, given that,
Four students attempt to register online.
The professor randomly selects two of the four wait list students and gives them seats in the class.
Then, the all outcomes are listed,
{P1P2, P1B1, P1B2, P2B1, P2B2, B1B2}
And, 4/6 of the outcomes have different majors
Let, A = the event of having different majors
We get, n(S)= 6
n(A)= 4
i.e. P(A)= n(A)/n(S) = 4/6 =2/3
Hence, required probability = 2/3.
To learn more on probability click:
brainly.com/question/11234923
#SPJ5
WILL RATE BRAINLIEST PLZ HELP
Answer:
if your question is to find the vertical height of D, ans is 5
Step-by-step explanation:
100 POINTS!!
PLEASE PROVIDE STEPS
Answer:
a = 2
not continuous
Step-by-step explanation:
In order for f(x) to have a limit at 0, f(0) from the left must equal f(0) from the right.
f(0⁺) = f(0⁻)
-2 + a = a sin(0)
-2 + a = 0
a = 2
If f(x) is continuous at x = 0, f'(0) from the left must equal f'(0) from the right.
f(x) = 0 for x > 0, so f'(x) = 0 for x > 0.
f(x) = 2 sin x for x < 0, so f'(x) = 2 cos x for x < 0.
f'(0⁺) = f'(0⁻)
0 = 2 cos 0
0 = 2
f(x) is not continuous at x = 0.
Answer:
a = 2
Step-by-step explanation:
PLZ HELP WILL RATE BRAINLIEST REMEMBER IT HAS 5 DIGITS
Answer:
The number: 13,226
Step-by-step explanation:
1. The smallest 5-digit number possibile is: 10,000
2. The smallest 5-digit number being odd should be: 10,001
3. All factors of 6 are {1, 2, 3, 6} so that the smallest possible way to arrange these numbers would be: 11,236
4. Now this number contains 3 prime numbers, 2 being {2 and 3}. If we were to consider another prime number, still being a factor of 6, that would be: 2. That would mean instead of the 1 being the second digit of the value 11,236 it could be 2: 12,236.
5. The digit in the thousands place (2) should be greater than the digit in the tens place (3). Let's swap these digits for now so that condition is satisfied: 13,226. 2 is the only number that has a number greater than it, besides 1, but 1 can't be a digit in the tenth place as it would make a greater 5 digit-number. Thus, provided the conditions are still satisfied, the number 13,226 is the smallest number possible.
Raven is four years younger than her brother, Eddie (x)which equation and graph best represents Raven's age (y)
Answer:
the equation is
[tex]x - 4 = y[/tex]