Answers
9514 1404 393
Answer:
-1
Step-by-step explanation:
We notice that we want term a1 and have terms a17 and a33. These terms (every 16-th term) form an arithmetic sequence. The middle term (a17) is the average of the other two, so we have ...
a17 = (a1 +a33)/2
2a17 -a33 = a1 = 2(10) -21 = -1
a1 = -1
_____
Additional comment
You could go to the trouble to find the general term of the sequence.
an = a1 +d(n -1)
a17 = a1 + d(17 -1) = 10
a33 = a1 + d(33 -1) = 21
Subtracting the first equation from the second, we have ...
16d1 = 11
d1 = 11/16
Using the first equation, we find ...
a1 +(11/16)(17 -1) = 10
a1 = 10 -11 = -1 . . . . same as above.
Related Questions
According to the number line, what is the distance between points A and B?
А
B
VX
- 16 - 14 -12 -10 -8 -6 4-2
0 2
4
6
8 10 12 14 16
U6 units
X 7 units
12 units
14 units
Answers
Answer:
Below!
Step-by-step explanation:
Please provide the two points (A & B) so I can help you out with the question or...
use the distance formula: [tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
where the first point = [tex](x_1,y_1)[/tex] & the second point: [tex](x_2,y_2)[/tex]
Please help me guys :)
Question:
In exercises 1 through 4, find the one-sided limits lim x->2(left) f(x) and limx-> 2(right) from the given graph of f and determine whether lim x->2 f(x) exists.
Answers
Step-by-step explanation:
For a left-hand limit, we start at the left side and move right, and see where the function goes as we get close to the x value.
For a right-hand limit, we start at the right side and move left, and see where the function goes as we get close to the x value.
If the two limits are equal, then the limit exists. Otherwise, it doesn't.
1. As we approach x = 2 from the left, f(x) approaches -2.
lim(x→2⁻) f(x) = -2
As we approach x = 2 from the right, f(x) approaches 1.
lim(x→2⁺) f(x) = 1
The limits are not the same, so the limit does not exist.
lim(x→2) f(x) = DNE
2. As we approach x = 2 from the left, f(x) approaches 4.
lim(x→2⁻) f(x) = 4
As we approach x = 2 from the right, f(x) approaches 2.
lim(x→2⁺) f(x) = 2
The limits are not the same, so the limit does not exist.
lim(x→2) f(x) = DNE
3. As we approach x = 2 from the left, f(x) approaches 2.
lim(x→2⁻) f(x) = 2
As we approach x = 2 from the right, f(x) approaches 2.
lim(x→2⁺) f(x) = 2
The limits are equal, so the limit exists.
lim(x→2) f(x) = 2
4. As we approach x = 2 from the left, f(x) approaches 2.
lim(x→2⁻) f(x) = 2
As we approach x = 2 from the right, f(x) approaches infinity.
lim(x→2⁺) f(x) = ∞
The limits are not the same, so the limit does not exist.
lim(x→2) f(x) = DNE
Solve 2 - (7x + 5) = 13 - 3x (make sure to type the number only)
Answers
Answer:
x = -4
Step-by-step explanation:
2 - (7x + 5) = 13 - 3x
add the binomial (7x +5) to both sides
2 = (7x + 5) + 13 - 3x
combine like terms
2 = 4x + 18
subtract 18 from both sides
-16 = 4x
divide by 4
x = -4
Answer:
-4
Step-by-step explanation:
Distribute the negative signs to the values in the parentheses
2 -7x - 5 = 13 - 3x
Add like terms:
-7x - 3 = 13 - 3x
Add 3x to both sides:
-4x - 3 = 13
Add 3 to both sides:
-4x = 16
Divide both sides by -4:
x = -4
NO LINKS OR ANSWERING QUESTIONS YOU DON'T KNOW!!! PLEASE answer thoroughly. Chapter 9 part 2
4. How can you determine the maximum number of solutions for a polynomial? How are these counted on the graph?
Answers
9514 1404 393
Answer:
a) the degree of the polynomial
b) count the x-intercepts, with attention to multiplicity
Step-by-step explanation:
The Fundamental Theorem of Algebra tells you the number of zeros of a polynomial is equal to the degree of the polynomial. That is, for some polynomial p(x), the number of solutions to p(x)=0 will be the degree of p.
__
On a graph, a real zero of the polynomial will be an x-intercept. The "multiplicity" of a zero is the degree of the factor giving rise to that zero. When the multiplicity is even, the graph does not cross the x-axis at the x-intercept. The greater the multiplicity, the "flatter" the graph is at the x-intercept.
If all solutions (zeros) are distinct, then the number of real solutions can be found by counting the number of x-intercepts of the graph.
_____
By way of illustration, the attached graph is of a 6th-degree polynomial with 6 real zeros. From left to right, they are -1 (multiplicity 1), 1 (multiplicity 2), 4 (multiplicity 3). The higher multiplicities are intended to show the flattening that occurs at the x-intercept, and the fact that the graph does not cross the x-axis where the multiplicity is even.
WHY CAN'T ANYONE HELP ME PLEASE?A 40% solution of fertilizer is to be mixed with a 80% solution of fertilizer in order to get 80 gallons of a 70% solution. How many gallons of the 40% solution and 80% solution should be mixed? 40% solution =? gallons, 80% solution =? gallons
Answers
Answer:
40% solution = 20 gallons
80% solution = 60 gallons
Step-by-step explanation:
x = gallons of 40% solution
y = gallons of 80% solution
Total volume is:
x + y = 80
Total amount of fertilizer is:
0.40 x + 0.80 y = 0.70 (80)
Solve by substitution.
0.40 x + 0.80 (80 − x) = 0.70 (80)
0.40 x + 64 − 0.80 x = 56
0.40 x = 8
x = 20
y = 60
Hey guys! I have this problem and I dont really understand how to solve it, could you guys help me? :' )
Answers
Answer:
Step-by-step explanation:
Answer:
-7
Step-by-step explanation:
There are 25,400,000 nanometers in an inch. What is this number written in scientific notation?
Answers
Answer:
254 x 10^5
Step-by-step explanation:
Hope this helps :)
If anything is misunderstood plz comment and I will change to the answer which you give me thank you very much :)
Answer:
2.54 x 10^5
hope this answer helps u ._.
PLEASE HELP!!!!!! TIMED QUESTION!!!! FIRST CORRECT ANSWER WILL GET BRAINLIEST....PLEASE ANSWER NOW!!!!
The bar graph shows the number of students who earned each letter grade on an
exam, which statement about the graph is true?
1)
1/5 of the students earned a C
2)
3% more students earned an A then B
3)
20% of the students earned a D
4)
1/4 of the class earned a B
Answers
Answer:
Option (3)
Step-by-step explanation:
From the picture attached,
Bar graph sketched shows the grades earned by the students in an exam.
Number of students who achieved the grade A = 17
Number of students who achieved grade B = 14
Number of students with grade C = 5
Number of students with grade D = 9
Total students who took the exam = 17 + 14 + 5 + 9 = 45
Option (1)
"[tex]\frac{1}{5}[/tex] of the students earned a C"
Fraction of students who earned C = [tex]\frac{\text{Students who earned C}}{\text{Total students}}[/tex]
= [tex]\frac{5}{45}[/tex]
= [tex]\frac{1}{9}[/tex]
Therefore, this option is incorrect.
Option (2)
"3% more students earned an A then B"
Percentage of students who earned A = [tex]\frac{\text{Students got A}}{\text{Total students who took the exam}}\times 100[/tex]
= [tex]\frac{17}{45}\times 100[/tex]
= 37.78%
Percentage of students who earned B = [tex]\frac{\text{Students got B}}{\text{Total students who took the exam}}\times 100[/tex]
= [tex]\frac{14}{45}\times 100[/tex]
= 31.11%
Difference in percentage = 37.78 - 31.11
= 6.67%
Therefore, this option is not correct.
Option (3)
"20% of the students earned a D"
Percentage of students who earned D = [tex]\frac{\text{Students got D}}{\text{Total students who took the exam}}\times 100[/tex]
= [tex]\frac{9}{45}\times 100[/tex]
= 20%
Option (3) is the correct option.
Option (4)
" [tex]\frac{1}{4}[/tex] of the class earned a B"
Fraction of class who earned B = [tex]\frac{\text{Students got B}}{\text{Total students who took the exam}}[/tex]
= [tex]\frac{14}{45}[/tex]
Therefore, Option (4) is not correct.
(-3.8)+(-21.14)+(-0.55)
Answers
please mark this answer as brainlist
[PLEASE HELP] Consider this function, f(x) = 2X - 6.
Match each transformation of f (x) with its descriptions..
Answers
Answer:
Find answer below
Step-by-step explanation:
f(x)=2x-6
Domain of 2x-6: {solution:-∞<x<∞, interval notation: -∞, ∞}
Range of 2x-6: {solution:-∞<f(x)<∞, interval notation: -∞, ∞}
Parity of 2x-6: Neither even nor odd
Axis interception points of 2x-6: x intercepts : (3, 0) y intercepts (0, -6)
inverse of 2x-6: x/2+6/2
slope of 2x-6: m=2
Plotting : y=2x-6
Suppose that 67.2% of all adults with type 2 diabetes also suffer from hypertension. After developing a new drug to treat type 2 diabetes, a team of researchers at a pharmaceutical company wanted to know if their drug had any impact on the incidence of hypertension for diabetics who took their drug. The researchers selected a random sample of 500 participants who had been taking their drug as part of a recent large-scale clinical trial and found that 317 suffered from hypertension.
The researchers want to use a one‑sample z ‑test for a population proportion to see if the proportion of type
2 diabetics who have hypertension while taking their new drug, p, is different from the proportion of all type
2 diabetics who have hypertension. They decide to use a significance level of ???? = 0.05.
A. Determine the p value for this test.
B. Determine the value of the z test statistic.
Answers
Answer: A. p-value = 0.04
B. z = - 1.77
Step-by-step explanation: To calculate z test statistic or z-score for a population proportion, first find the proportion (p-hat):
[tex]p_{hat}[/tex] = [tex]\frac{317}{500}[/tex] = 0.634
Then determine the standard deviation:
[tex]\sigma = \sqrt{\frac{p_{hat}(1-p_{hat})}{n} }[/tex]
[tex]\sigma = \sqrt{\frac{0.634(0.366)}{500} }[/tex]
[tex]\sigma = \sqrt{0.00046 }[/tex]
[tex]\sigma[/tex] = 0.0215
Calculating z-score:
[tex]z=\frac{p_{hat}-p}{\sigma}[/tex]
[tex]z=\frac{0.634-0.672}{0.0215}[/tex]
[tex]z=-1.77[/tex]
Z-test for the population proportion is z = - 1.77
P-value is the probability describing the data if null hypothesis is true, i.e.:
P(z< -1.77)
Using z-score table, the probability is:
P(z< -1.77) = 0.04
p-value = 0.04
P-value for this test is p-value = 0.04.
what is 2x2x2x3x3 please give me answer
Answers
Answer:
The answer is 72.
I am right .
Hope your day is good
2 time 2 is 4
4 times 2 is 8
8 times 2 is 16
16 times 3 is 48
48 times 3 is 144
144 is your answer
Hope this helps *smiles*
Christina's time for a race was 22.3 seconds. Another runner's time was 4.41 seconds faster. Write and evaluate an equation with a variable to find the difference between Christina's time and the other runner's time.
Answers
Answer:
[tex]Difference = 4.41[/tex]
Step-by-step explanation:
Given
Represent Christina's time with C and the other runner's time with R
C = 22.3
R = 4.41 + C
Required
Determine the difference using an equation
The difference between both runner's time is as follows;
[tex]Difference = R - C[/tex]
Substitute 4.41 + C for R
[tex]Difference = 4.41 + C - C[/tex]
[tex]Difference = 4.41[/tex]
Hence, the difference is 4.41 seconds
Find the particular solution to a differential equation whose general solution and initial condition are given. (C is the constant of integration.) x(t)
Answers
To divide a whole number or decimal by 10, move the decimal point
place(s) to the left.
Answers
Answer:
you simply have to move one left. It thats decimal you can simply remove one zero
Answer:
You just have to move to the left once
Step-by-step explanation:
pLEASE help best and right answer gets brainliest
Answers
2) is 2
Absolute value of a number is the distance a number is from 0.
Step-by-step explanation:
| - 5 | + | - 4 |
5 + 4
= 9
| - 6| - 4
6 - 4
2
I hope this answers your question.
Suppose log subscript a x equals 3, log subscript a y equals 7, and log subscript a z equals short dash 2. Find the value of the following expression. log subscript a open parentheses fraction numerator x cubed y over denominator z to the power of 4 end fraction close parentheses
Answers
Answer:
24Step-by-step explanation:
Given the following logarithmic expressions [tex]log_ax = 3, log_ay = 7, log_az = -2[/tex], we are to find the value of [tex]log_a(\frac{x^3y}{z^4} )[/tex]
[tex]from\ log_ax = 3, x = a^3\\\\from\ log_ay = 7,y = a^7\\\\from\ log_az = -2, z = a^{-2}[/tex]Substituting x = a³, y = a⁷ and z = a⁻² into the log function [tex]log_a(\frac{x^3y}{z^4} )[/tex] we will have;
[tex]= log_a(\frac{x^3y}{z^4} )\\\\= log_a(\dfrac{(a^3)^3*a^7}{(a^{-2})^4} )\\\\= log_a(\dfrac{a^9*a^7}{a^{-8}} )\\\\= log_a\dfrac{a^{16}}{a^{-8}} \\\\= log_aa^{16+8}\\\\= log_aa^{24}\\\\= 24log_aa\\\\= 24* 1\\\\= 24[/tex]
Hence, the value of the logarithm expression is 24
URGENT!! (Picture included)
Answers
Answer:
-85
Step-by-step explanation:
You can use calculator for this question
How many different 6-digit phone numbers do not contain the digit 8? Assume that any digit in the phone number can be any of the remaining numbers.
Answers
The following data shows the number of home runs hit by the top 12 home run hitters in Major League Baseball during the 2011 season.
43 41 39 39 38 37 37 36 34 33 33 32
The lower limit for determining outliers for a box-and-whisker plot is______.
a. 23.75.
b. 20.0.
c. 22.5.
d. 25.25.
Answers
Answer:
d. 25.25.
Step-by-step explanation:
A whisker plot is a type of box plot which is graphical representation of five number summary. It is used for explanatory data analysis. The baseball league has data set whose median is 45. When the outliner are present in data set the median measures central tendency.
the value of 2√4-3√27+√16+√225 is
Answers
Answer:
hope this help you
sorry if it is mistake
find the slope of the joining pairs of points (1/a, 1/b) (b,a)
Answers
Answer: m = 1/b
Step-by-step explanation: Unfortunately, I can't give you a picture of the slope, but take that formula I gave you and enter it into a graphing calculator and it will show you the slope. I recommend desmos online calculator, good luck
1/b i believe
Write the null and alternative hypotheses you would use to answer this question. Are Americans getting fatter? Researchers interested in this question take a random sample of 500 people and record an average weight of 190 pounds. Ten years ago, the average weight was 185 pounds.
Answers
Answer:
H0: u = 185 against Ha: u > 185
or
H0: u ≤ 185 against Ha: u > 185
Step-by-step explanation:
The null and alternative hypotheses for this experiment would be
H0: u = 185 against Ha: u > 185
or
H0: u ≤ 185 against Ha: u > 185
This is a one tailed test .
If the results are such that we reject the null hypothesis and accept the alternative hypothesis it means that the Americans are getting fatter as the mean weight is increasing day by day.
The null hypothesis deals with all the values equal to or less than 185 pounds and the alternative with all the values greater than 185 pounds.
Which of the following theorems verifies that ANPO- AXYZ?
Answers
If A = { 10, 30,} B = { 10, 20, 30, 40, 50, 60, 70, 80,90} find A ∩ B There are options. Choose one option only: A- { 30 ,10} B- { 90 ,30 ,10} C- { 90 } D- { 80, 70, 60, 50, 40, 20 }
Answers
[tex]A \cap B=\{10,30\}[/tex]
Answer:
[tex] \boxed{ \purple{10 \: , 30}}[/tex]Option A is the correct option
Step-by-step explanation:
[tex] \mathrm{Given}[/tex]
A = { 10 , 30 }
B = { 10 , 20 , 30 , 40 , 50 , 60 , 70 , 80 , 90 }
Now, let's find A ∩ B
A ∩ B = { 10 , 30 } ∩ { 10 , 20 , 30 , 40 , 50 , 60 , 70 , 80 , 90 }
The intersection of sets A and B is the set of all elements which belong to both A and B
A ∩ B = { 10 , 30 }
The intersection of sets A and B is denoted by ( A ∩ B ) and read as A intersection B.
Hope I helped!
Best regards!
Harrison has 20 tasks on to do list he has completed 5%. How many tasks has he completed?
Answers
Answer:
1 task
Step-by-step explanation:
100%=20 tasks
5%=1 task
NEED HELP ASAP!! Angles of Elevation and Despression! Need to find y! Round to the nearest tenth!!
Answers
Answer:
y = 178.3 ftStep-by-step explanation:
Since the above figure is a right angled triangle we can use trigonometric ratios to find y
To find y we use tan
tan∅ = opposite/ adjacent
From the question
the opposite is y
the adjacent is 350 ft
Substitute the values into the above formula
That's
[tex] \tan(27) = \frac{y}{350} [/tex]
y = 350 tan 27
y = 178.3339
We have the final answer as
y = 178.3 ft to the nearest tenthHope this helps you
how many feet is in one centimeter and how many inches is in 1 feet?
Answers
Answer:
12 inches r in a foot
0 feet r in a centimeter
Step-by-step explanation:
Answer:
0.032 feet in a centimeter and 12 inches in 1 foot
Step-by-step explanation:
hope it helps pls mark as brainliest!
What unit of measurement would you use to measure the capacity of a juice box?
Answers
Juice in a juice box is usually measured in ounces.
You drive 15 miles in 0.1hours . How fast did you travel if 8=d/t
Answers
Answer:
150Step-by-step explanation:
[tex]distance = 15 miles\\time = 0.1 hours\\\\Speed = \frac{Distance}{time}\\ Speed = \frac{15}{0.1}\\ Speed =150[/tex]
Answer:
[tex]150mph[/tex]
Step-by-step explanation:
Given:
s=15miles
t=0.1hours
Required:
v=?
Formula:
[tex]v = \frac{s}{t} [/tex]
Solution:
[tex]v = \frac{s}{t} = \frac{15m}{0.1h} = \frac{150m}{1h} = 150mph[/tex]
Hope this helps ;) ❤❤❤