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:
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
What is the height?
4m
3m
2m
find area
Answer:
I think the area is 24
Step-by-step explanation:
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 length of the right triangle’s other leg. Round to the nearest tenth.
leg = 10 ft
hypotenuse = 12 ft
Answer: 17.32
Step-by-step explanation:
subtract 6066 from 294
Answer:
-5772
Step-by-step explanation:
294-6066=-5772
Answer:
The answer would be 2,772
Step-by-step explanation:
6,066 - 294 = 2,272
I hope that helps!!:)
donovan bought 5.5 kilograms of flour for $8.25. how much does 1 kilogram of flour cost?
Answer:
$1.50
Step-by-step explanation:
Answer:$1.5
Step-by-step explanation:
5.5kg cost $8.25
1kg cost __
1kg cost 8.25/5.5
1kg cost $1.5
Please help asap! Will give brainliest! Please read the question then answer correctly! No guessing.
Answer:D
Step-by-step explanation:
(4/5)^0
(4^0)/(5^0)=1/1=1
ILL GIVE YOY BRAINLIST *have to get it right * What is the slope of the line shown in the graph?
Answer:
A
Step-by-step explanation:
3 over 2 down.
Four people—Rob, Sonja, Jack, and Ang—enter their names into a drawing. The winner receives either a t-shirt or a mug, and which prize they receive is randomly selected.
What is the probability that either Ang wins and is given a mug, or Jack wins (and is given either prize)? Give the answer as a percent.
Answer:
3.125%Step-by-step explanation:
It is assumed the first winner is part of the second drawing as well
There are 4 people and two prizes
The probability of each person to win is 1/4
The first winner has 1/2 probability to get a mug
P(win and a mug) = 1/4*1/2 = 1/8 for AngThe second winner, if it is Jack, gets either prize
P(win and either prize) = 1/4The combined probability is:
1/8*1/4 = 1/32 = 0.03125 = 3.125%Answer:
The probability is 37.5%
Step-by-step explanation:
There are eight total outcomes, but we only need to focus on three. Ang winning a mug and Jack winning either a t-shirt or a mug, that makes three. Write that as a fraction: 3/8, and then divide. 3 divided by 8 gives us 0.375. But we need a percent so multiply that by 100, that now gives us 37.5.
So, the probability that either Ang wins and is given a mug, or Jack wins is 37.5%. If it makes you feel more confident in this, I put the same exact answer for my assessment and I got it correct.
Also, “The monks named me aOng.”
Which figure below has point symmetry
Answer:
Figure D
Step-by-step explanation:
Point Symmetry is when every part has a matching part: the same distance from the central point. but in the opposite direction. Hope this helps! :)
Find the area of the shaded region.
You do not need to include units.
21 in
20 in
Answer: about 450.52
Use Pythagorean Theorem to find the diameter of the circle. Divide the diameter by 2 to find the radius, and solve for the area of the circle (πr^2). Then, solve for the area of the triangle (bh/2). Subtract the area of the triangle from the area of the circle.
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.
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
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 slope, if it exists, of the line containing the points (-1,-15) and (-17,-20)
The slope is _____________________
13x=-21-6y and -8x=36+6y
Answer:
[tex]x=3\\y=-10[/tex]
Step-by-step explanation:
[tex]13x=-21-6y\\-8x=36+6y[/tex]
Let's take one of the equations and solve for x. I'll take the first one.
[tex]13x=-21-6y[/tex]
Divide by 13.
[tex]x=\frac{-21-6y}{13}[/tex]
Now replace x in the second equation.
[tex]-8x=36+6y\\-8(\frac{-21-6y}{13} )=36+6y[/tex]
Distribute -8
[tex]\frac{168+48y}{13}=36+6y[/tex]
Break down the fraction.
[tex]\frac{168}{13}+\frac{48}{13}y=36+6y[/tex]
Subtract [tex]\frac{168}{13}[/tex]
[tex]\frac{48}{13}y=36+6y-\frac{168}{13}[/tex]
Subtract 6y
[tex]\frac{48}{13}y-6y=36-\frac{168}{13}[/tex]
Combine like terms;
[tex]\frac{48-13*6}{13}y=\frac{36*13-168}{13}[/tex]
Solve;
[tex]\frac{48-78}{13}y=\frac{468-168}{13}[/tex]
Keep solving;
[tex]\frac{-30}{13}y=\frac{300}{13}[/tex]
Multiply by the negative reciprocal of the fraction next to y.
[tex](-\frac{13}{30} )\frac{-30}{13}y=\frac{300}{13}(-\frac{13}{30} )[/tex]
On the right side; 13 and 13 become 1. 300/30 = 30/3 = 10
[tex]y=-10[/tex]
After having found y, replace it in any of the equations to find x.
[tex]13x=-21-6y\\13x=-21-6(-10)\\13x=-21+60\\13x=39\\x=\frac{39}{13}\\ x=3[/tex]
Answer:
x=3
y=-10
Step-by-step explanation:
13x=-21-6y...............(1)
-8x=36+6y................(11)
Add (11) to (1)
5x=15-6y+6y
5x=15
Divide both sides by 5
5x/5=15/5
x=3
Substitute x=3 in 13x=-21-6y
13(3)=-21-6y
39=-21-6y
Collect like terms
39+21=-6y
60=-6y
Divide both sides by -6
60/-6=-6y/-6
-10=y
y=-10
Oswaldo is cooking a big dinner. He buys 301230\dfrac{1}{2}302130, start fraction, 1, divided by, 2, end fraction ounces of sweet potatoes, 131413\dfrac{1}{4}134113, start fraction, 1, divided by, 4, end fraction ounces of asparagus and 201420\dfrac{1}{4}204120, start fraction, 1, divided by, 4, end fraction ounces of squash.
How many pounds of vegetables did Oswaldo buy altogether?
Answer:
4
Step-by-step explanation:
30 + 20 + 13 = 63, + fractions = 64. But you have to divide to get to pounds. So 64 / 16 = 4
YAY
help please quick 29 points please answer
Answer:
Step-by-step explanation:
It costs $7 for 1 baseball and Mrs.Weeks is buying 36 baseballs, that would be: $7 X 36 = $252
It costs $5 for 1 softball and Mrs.Weeks is buying 24 softballs that would be:
$5 X 24 = $120
$252 + $120 = $372 for the baseballs and softballs
Mrs.Weeks gives the cashier four $100 bills that is $400 dollars.
so $400 - $372 = $28 (Mrs.Weeks change)
Greatest common factor for 30 abd 42
Answer:
6
Step-by-step explanation:
Because you are familiar with your times tables, you know that ...
30 = 6·5
42 = 6·7
The greatest common factor is 6.
Prove that line RT⟂ line SU.
Answer:
1. Statement: ∠RVS ≅ ∠SVT
2. Statement: m∠RVS + m∠SVT = 180°
3. Statement: m∠RVS + m∠RVS = 180°
4. Statement: m∠RVS = 90°
5. Statement: Line RT ⊥ Line SU
1. Reason: Given
2. Reason: Angles forming a linear pair sum of 180°
3. Reason: Substitution
4. Reason: Algebra
5. Reason: Defintion of perpendicular lines
Step-by-step explanation:
First, write the given (line 1).
Next, use the fact that angles forming a linear pair sum to 180° to show m∠RVS + m∠SVT = 180° (line 2).
Next, substitute m∠RVS for m∠SVT in m∠RVS + m∠SVT=180° (line 3).
Next, use algebra to show m∠RVS = 90° (line 4).
Finally, use the definition of perpendicular lines to prove that Line RT ⊥ Line SU (line 5).
Hope this helps :D
Answer:
1. Statement: ∠RVS ≅ ∠SVT
2. Statement: m∠RVS + m∠SVT = 180°
3. Statement: m∠RVS + m∠RVS = 180°
4. Statement: m∠RVS = 90°
5. Statement: Line RT ⊥ Line SU
1. Reason: Given
2. Reason: Angles forming a linear pair sum of 180°
3. Reason: Substitution
4. Reason: Algebra
5. Reason: Defintion of perpendicular lines
In his statistics class, Sam said, “Linear regression model is a tool to predict the relationship between the dependent variable, and independent variable. So, there will be one specific linear regression model that I can use to know the relationship of variables. I decided to use ordinary least square to have the best estimates for linear regression model parameters because ordinary lease square makes me find the linear regression equation with minimum average of difference between actual dependent variable and the value predicted by linear regression model.” Is Sam correct? If not, how do we need to fix his idea?
Answer:
Yes, Sam is correct and there is no need to fix his idea.
Step-by-step explanation:
Linear Regression model is one of the Important model that is been used in statistics especially in statistics which actively involved data analysis of dependent variable and an independent variable. Between these two that is dependent variable and an independent variable, the application of Linear Regression model is used in showing the relationships between the two variables.
Just like Sam said in the question above, '' “Linear regression model is a tool to predict the relationship between the dependent variable, and independent variable...'', that is what linear regression is used for.
Answer:
Yes, obviously Sam is correct
Step-by-step explanation:
Linear regression model is a tool to predict the relationship between the dependent variable, and independent variable
Linear Regression model is one of the Important model that is been used in statistics involved data analysis of dependent variable and an independent variable. Between these two that is dependent variable and an independent variable, the application of Linear Regression model is used in showing the relationships between the two variables.
determine the sample space of all of the possible outcomes of choosing a card numbered 1,2,3, or 4 and a blue, green, or yellow marble. how many outcomes involve choosing a blue marble
Answer:
a) Sample Space = {(1,blue), (1, green), (1, yellow), (2,blue), (2, green), (2, yellow), (3,blue), (3, green), (3, yellow), (4,blue), (4, green), (4, yellow)}
b) 4 outcomes involve choosing blue marble.
Step-by-step explanation:
a) FOR SAMPLE SPACE:
No. of options for choosing card = 4
No. of options for choosing marble = 3
No. of options for choosing a card and a marble = (3)(4) = 12
Therefore,
Sample Space = {(1,blue), (1, green), (1, yellow), (2,blue), (2, green), (2, yellow), (3,blue), (3, green), (3, yellow), (4,blue), (4, green), (4, yellow)}
b) CHOOSING BLUE MARBLE:
It is evident from the sample space that, there are only 4 outcomes, which involve choosing a blue marble.
Those 4 outcomes are as follows:
(1, blue), (2, blue), (3, blue), (4, blue)
Answer:
12
Step-by-step explanation:
Please help ASAP! I will mark Brainliest! Please READ the question THEN answer CORRECTLY! No guessing!
Answer:
a
Step-by-step explanation:
Answer:
A.
Step-by-step explanation:
Firstly, [tex]x^{-y} = \frac{1}{x^y}[/tex], so in this case, you multiply [tex](6^{-8})^4[/tex], which equals [tex]6^{-32}[/tex]. Then, plug it into [tex]x^{-y} = \frac{1}{x^y}[/tex] and you get
[tex]6^{-32} = \frac{1}{6^{32}}[/tex], so it's [tex]\boxed{A.}[/tex]
please help me with this question
Answer: yes
Step-by-step explanation:
Answer:
Step-by-step explanation:
A = 3
B = 5.5
C = 11
simplify 36ab divided by 40ab
Simon knows that 25% of the people at a movie theater are seeing a romantic comedy. How many people are at the movie theater if 55 people are seeing a romantic comedy?
Answer:
220
Step-by-step explanation:
Number of people in theater = x
25% * x = 55
x = 55 / 25% = 55 / 25 * 100 = 55 * 4 = 220
Which of the following values of t will result in a true statement when substituted into the given equation? A. t = 8 B. t = -8 C. t = 11 D. t = -12
Answer:
B
Step-by-step explanation:
Answer:
The answer is B
Step-by-step explanation:
19/20 into a percentage
Answer:
it will be 95%
hope that helps
Answer:
95 percent
Step-by-step explanation:
Since 20 is 1/5 of 100, one number is equivalent to 5 percent.
Multiply 5 by 19.
You will get your percentage.
The median and mode of this set of data (23,13,17,11,11)
Answer:
Mode: 11
Median: 13
Answer:
(23, 13, 17, 11, 11):
Median: 13
Arithmetic mean: 15
Geometric mean: 14.380735416546
Harmonic mean: 13.848764056076
Mode: 11
Standard deviation: 4.5607017003966
Variance: 20.8
Mean Absolute Deviation: 4
Range: 12
Interquartile range: 9
Lower quartile: 11
Upper quartile: 20
Quartile deviation: 4.5
Population size:5
