Answer:
157 is the 24th term.
Step-by-step explanation:
We are given that in an arithmetic sequence, -4 is the first term and 10 is the third term. And we want to find the term number of 157.
Recall that the direct formula for an arithmetic sequence is given by:
[tex]\displaystyle x_n=a+d(n-1)[/tex]
Where n is the nth term, a is the initial term, and d is the common difference.
We know that the initial term a is -4. Hence:
[tex]x_n= -4 + d(n-1)[/tex]
Since 10 is the third term, n = 3:
[tex]\displaystyle x_{3}=10=-4+d(3-1)[/tex]
Solve for the common difference:
[tex]14=2d\Rightarrow d=7[/tex]
Hence, our direct formula is:
[tex]\displaystyle x_n=-4+7(n-1)[/tex]
To find the term number of 157, let 157 equal xₙ and solve for n. Hence:
[tex]\displaystyle (157)=-4+7(n-1)[/tex]
Therefore:
[tex]\displaystyle \begin{aligned} 161 &= 7(n-1) \\ 23 & = n-1 \\ n &= 24\end{aligned}[/tex]
157 is the 24th term.
The length of a ladder leaning against a building is 60 feet. The ladder hits the building at the top of the building. The distance to the building from where the ladder touches the ground is 15 feet. What is the height of the building to the nearest foot?
A. 38ft
B. 48ft
C. 58ft
D. 68ft
Answer:
C. 58ft
Step-by-step explanation:
An imaginary triangle is described here. The hypotenuse is 60, and one of the other sides is 15.
60*60=3600
15*15=225
3600-225=3375
sqrt3375=58.09
round that to get 58ft
What is 10+2
Please I need help
Answer: 12
Step-by-step explanation:
Answer:
12
Step-by-step explanation:
Check the picture below
A manager records the repair cost for 14 randomly selected dryers. A sample mean of $88.34 and standard deviation of $19.22 are subsequently computed. Determine the 90% confidence interval for the mean repair cost for the dryers. Assume the population is approximately normal. Step 1 of 2 : Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places.
Answer:
Hence the 90% confidence interval estimate of the population mean is [tex](79.24 , 97.44)[/tex]
Step-by-step explanation:
Given that,
Point estimate = sample mean = [tex]\bar x[/tex] = 88.34
sample standard deviation = s = 19.22
sample size = n = 14
Degrees of freedom = df = n - 1 = 13
Critical value =[tex]t\alpha /2,[/tex] df = 1.771
Margin of error
[tex]E = t\alpha/2,df \times (\frac{s}{\sqrt{n} } )\\= 1.771 \times (19.22 / \sqrt 14)[/tex]
Margin of error = E = 9.10
The 90% confidence interval estimate of the population mean is,
[tex]\bar x - E < \mu < \bar x + E\\\\88.34 - 9.10 < \mu < 88.34 + 9.10\\\\79.24 < \mu < 97.44\\(79.24 , 97.44)[/tex]
n-1 increased by 110%
Answer:
2.1n-2.1
Step-by-step explanation:
The increase is
1.10 (n-1)= 1.1n -1.1
Add this to the original amount
(n-1) + 1.1n - 1.1
2.1n-2.1
Wilbur spent $27 on a magazine and some notepads. If the magazine cost $3 and
each notepad cost $3, then how many notepads did he buy?
A) 11
B) 9
C) 8
D)12
Answer:
d 12
Step-by-step explanation:
27-3=24÷3=12 do the mathssssss
Answer:
If it was 11, it would be 33 dollars which is over the total so its not a.
It can't be b because that would be 27, and that would be on just notebooks not magazine
24 is correct because he baught one magazine so + 3 which is the total so it is C
Step-by-step explanation:
25% of £90
Work it out
Answer:
22.5
Step-by-step explanation:
percent is any number over 100, so 25% is 25 over 100, this means that 25% can be written as:
25100
Now, any number in fractional form (a number over a number) is the same as division so 25% can also be written as a decimal, we just move the decimal point 2 places to the right of 25, like this:
25100=0.25
Now we have two ways that we can solve this problem! I'll start with the fractional method of solving.
Alonzo finish history assignment and 5/8 hours then he completed his math assignment and 1/3 hours what was the total amount of time allowed to spend doing these two assignments
Step-by-step explanation:
The answer is 5/8 + 1/3
Answer = 5*3 /(8*3) +8/24 =23/24
Answer = 23/24
Use a calculator to find the mean of the data. {21.8, 23.3, 18.9, 22.9, 19.4, 23.7, 21.8, 22.8, 20.9, 21.1, 21.5, 22.9, 18.8, 22.6, 22.3, 20.8, 20.3, 19.1, 23.3, 18.8, 19.8, 24.2}
Answer:
The mean of the data is 21.41
Step-by-step explanation:
To find the mean of a data set you must...
Add up all data values to get the sum
Count the number of values in your data set
Divide the sum by the count
The mean of the data set 21.8, 23.3, 18.9, 22.9, 19.4, 23.7, 21.8, 22.8, 20.9, 21.1, 21.5, 22.9, 18.8, 22.6, 22.3, 20.8, 20.3, 19.1, 23.3, 18.8, 19.8, 24.2 is 21.41 the asnwer is 21.41.
What is mean?It is defined as the single number that represents the mean value for the given set of data or the closed value for each entry given in the set of data.
We have a data set:
{21.8, 23.3, 18.9, 22.9, 19.4, 23.7, 21.8, 22.8, 20.9, 21.1, 21.5, 22.9, 18.8, 22.6, 22.3, 20.8, 20.3, 19.1, 23.3, 18.8, 19.8, 24.2}
As we know from the definition of the mean:
The mean can be calculated using the formula:
Mean = sum of the data set/number of the data in the data set
Mean = 471/22
Mean = 21.409 ≈ 21.41
Thus, the mean of the data set 21.8, 23.3, 18.9, 22.9, 19.4, 23.7, 21.8, 22.8, 20.9, 21.1, 21.5, 22.9, 18.8, 22.6, 22.3, 20.8, 20.3, 19.1, 23.3, 18.8, 19.8, 24.2 is 21.41 the asnwer is 21.41.
Learn more about the mean here:
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triangle ABC is reflected about the line Y equals negative X to give triangle ABC with vertices A (-1, 1), B (-2, -1), C (-1,0). What are the vertices of triangle ABC?
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Answer:
A'(-1, 1)B'(1, 2)C'(0, 1)Step-by-step explanation:
Reflection across the line y = -x is accomplished by the transformation ...
(x, y) ⇒ (-y, -x)
Then the images of the given points are ...
A(-1, 1) ⇒ A'(-1, 1) . . . . this point is on the line of reflection, so doesn't move
B(-2, -1) ⇒ B'(1, 2)
C(-1, 0) ⇒ C'(0, 1)
A canoeist traveling with the current traveled the 24 miles between two riverside campsites in 2 hours. The return trip against the current took 3 hours. Find the speed of the canoeist in still water and the speed of the current, both in miles per hour.
Answer:
Speed of canoiest is 10 miles/hour.
Speed of current is 2 miles/hour.
Step-by-step explanation:
Let the speed of canoiest is v and the speed of current is u.
distance = speed x time
24 = (v + u ) x 2
v + u = 12 ..... (1)
Now
24 = (v- u) x 3
v - u = 8 .... (2)
By solving (1) and (2)
2 v = 20
v = 10 miles/hour
u = 2 miles/hour
HELP ME PLS!!!!!
Which of the following is | 5-12i |?
A) -√119
B) √119
C) −13
D)13
Answer:
D) 13
[tex]\sqrt{169} = 13[/tex]
Step-by-step explanation:
Critical Thinking: Empirical/Quantitative Skills
United flight 15 from New York's JFK to San Francisco uses a Boeing 757-200 with 180 seats. Because some
people with tickets don't show up. United will overbook by selling more than 180 tickets. If the flight is not
overbooked, the airline will lose revenue due to empty seats, but if too many tickets are sold and some
passengers are denied seats, the airline loses money from the compensation that must be given to bumped
passengers. Assume that there is a 0.905 probability that a passenger with a ticket will show up for the
flight. Also assume that the airline sells 200 tickets for the 180 seats that are available.
1. When 200 tickets are sold, calculate the probability that exactly 180 passengers show up for the flight.
Show your calculation (i.e. what you put in the calculator) and round to 4 decimals.
2. When 200 tickets are sold, calculate the probability that at most 180 passengers show up for the flight.
Show your calculation (ie. what you put in the calculator) and round to 4 decimals.
3. When 200 tickets are sold, calculate the probability that more than 180 passengers show up for the flight.
Show your calculation (i.e. what you put in the calculator) and round to 4 decimals.
Answer:
1. 0.0910 = 9.10% probability that exactly 180 passengers show up for the flight.
2. 0.4522 = 45.22% probability that at most 180 passengers show up for the flight.
3. 0.5478 = 54.78% probability that more than 180 passengers show up for the flight.
Step-by-step explanation:
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
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].
Assume that there is a 0.905 probability that a passenger with a ticket will show up for the flight.
This means that [tex]p = 0.905[/tex]
Also assume that the airline sells 200 tickets
This means that [tex]n = 200[/tex]
Question 1:
Exactly, so we can use the P(X = x) formula, to find P(X = 180).
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 180) = C_{200,180}.(0.905)^{180}.(0.095)^{20} = 0.0910[/tex]
0.0910 = 9.10% probability that exactly 180 passengers show up for the flight.
2. When 200 tickets are sold, calculate the probability that at most 180 passengers show up for the flight.
Now we have to use the approximation.
Mean and standard deviation:
[tex]\mu = E(X) = np = 200*0.905 = 181[/tex]
[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{200*0.905*0.095} = 4.15[/tex]
Using continuity correction, this is [tex]P(X \leq 180 + 0.5) = P(X \leq 180.5)[/tex], which is the p-value of Z when X = 180.5. Thus
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{180.5 - 181}{4.15}[/tex]
[tex]Z = -0.12[/tex]
[tex]Z = -0.12[/tex] has a p-value of 0.4522.
0.4522 = 45.22% probability that at most 180 passengers show up for the flight.
3. When 200 tickets are sold, calculate the probability that more than 180 passengers show up for the flight.
Complementary event with at most 180 passengers showing up, which means that the sum of these probabilities is 1. So
[tex]p + 0.4522 = 1[/tex]
[tex]p = 1 - 0.4522 = 0.5478[/tex]
0.5478 = 54.78% probability that more than 180 passengers show up for the flight.
Is the answer right?
Answer:
one solution.. your answer is correct
Step-by-step explanation:
discriminate = 900 - (4*9*25) = 0
thus only one solution
Write the sum using summation notation, assuming the suggested pattern continues.
2, -10, 50, -250, +…
Is this sequence arithmetic or geometric? How do you know?
Answer:
[tex]\sum_{n = 1} 2*(-5)^{n-1}[/tex]
Step-by-step explanation:
An arithmetic sequence is of the form:
[tex]A_n = A_{n-1} + d[/tex]
While a geometric sequence is of the form:
[tex]A_n = A_{n-1}*r[/tex]
notice that first, we have a change of sign in our sequence, so we already can discard the arithmetic sequence.
In fact, the pattern is kinda easy to see.
The first term is:
A₁ = 2
the second term is:
A₂ = -10
notice that:
A₂/A₍ = r = -10/2 = -5
The third term is:
A₃ = 50
the quotient between the third term and the second term is:
A₃/A₂ = 50/-10 = -5
Whit this we can already conclude that the n-th term of our sequence will be:
[tex]A_n = A_{n-1}*(-5)[/tex]
Then the summation will be something like:
[tex]\sum_{n = 1} A_n = A_1 + A_2 + A_3 + ... = 2 - 10 + 50 - ...[/tex]
We can write:
[tex]A_n = A_{n-1}*(-5) = (A_{n-2}*(-5))*(-5)) = A_1*(-5)^{n-1} = 2*(-5)^{n-1}[/tex]
Then the summation is just:
[tex]\sum_{n = 1} 2*(-5)^{n-1}[/tex]
Which word phrases represent the variable expression m – 11? Choose all answers that are correct. A. 11 more than a number B. the difference of a number and 11 C. the quotient of a number and 11 D. 11 less than a number
Answer: D
Step-by-step explanation:
m – 11
A. 11 more than a number ( m+11 )
B. the difference of a number and 11 ( 11/m )
C. the quotient of a number and 11 ( m/11 )
D. 11 less than a number ( m-11 )
This is the question I am stuck on
Answer:
a^ 8 / b^12
Step-by-step explanation:
We know that x^y / x^z = x^ (y-z)
a^-5 b^-4
----------------
a^ -13 b^8
a^ (-5 - -13) b ^ (-4 -8)
a^ (-5+13) b^ (-4-8)
a^ 8 b^ (-12)
We know that x ^ - y = 1/ x^y
a^ 8 / b^12
A triangular patch of grass in a park is bordered by walking paths. The longest path bordering the patch of grass measures 110 feet. The smallest path bordering the patch of grass measures 55 feet. The smallest angle formed by the paths bordering the patch of grass measures 29º.
What is the measure of the largest angle of the triangular patch of grass? Round your answer to the nearest
degree. Show all your work.
Answer:
76 degrees
Step-by-step explanation:
First, we can draw a picture. Two of the sides are 110 feet and 55 feet. In a triangle, the smallest angle is opposite the smallest side and vice versa. Therefore, if I have my triangle arranged in the way shown, the smallest angle of 29 degrees will be opposite of the smallest side of 55 feet.
The law of sines states that a/sinA=b/sinB=c/sinC , with corresponding angles being opposite of its corresponding side. Therefore, we can say that
55 feet/ sin(29 degrees) = 110 / sin(largest angle).
If we say that the largest angle is equal to x, we can say
55 / sin(29°) = 110/sin(x)
multiply both sides by x to remove a denominator
55 * sin(x)/ sin(29°) = 110
multiply both sides by sin(29°) to remove the other denominator
55 * sin(x) = 110 * sin(29°)
divide both sides by 55 to isolate the sin(x)
sin(x) = 110 * sin(29°) / 55
For an angle, if sin(x) = y, we can say that arcsin(y) = x. Therefore, we can say
x = arcsin(110 * sin(29°)/55)
x ≈ 76 degrees
Expand the following: 4(a + 3b - 5c).
Please help, I'm really struggling with expanding equations
Answer:
4a+12b-20c
Step-by-step explanation:
Use the distributive property, multiply the number on the outside to everythign on the inside.
4*a=4a
4*3b=12b
-5c*4=-20c
11 + box equals 19 find box
Answer:
8
Step-by-step explanation:
11 + x = 19
Subtract 11 from each side
11+x -11 = 19-11
x = 8
Answer:
8
Step-by-step explanation:
11 + box = 19
=> box = 19 - 11
.°. box = 8
Help with this please!
Answer:
A
Step-by-step explanation:
The correct answer is A
One month Ivanna rented 7 movies and 9 video games for a total of $80. The next month she rented 5 movies and 3 video games for a total of $34. Find the rental cost for each movie and each video game.
Answer:
each movie costs $2.75, each video game costs $6.75
Step-by-step explanation:
x = movies, y = video games
7x + 9y = 80
5x + 3y = 34
simplified to
x = 11/4 , y = 27/4
REVISED 2/3/
the following using the picture below.
4
a) Two pairs of supplementary angles:
b) A pair of complementary angles:
Please explain this! Thank you!
Supplementary angles are those angles which make a sum of 180°.
Complementary angles are those angles which make a sum of 90°.
The supplementary angles are given by the straight lines making angles of 180°.
There are two straight lines CB and DE
The angles DAF and FAE are the two angles making a straight line DE
The angles CAF and FAB are the two angles making a straight line CB
The complementary angles are given by angles formed between the perpendicular lines making angles of 90°.
Angle BAF is formed by angle BAE and angle AEF
Supplementary Angle given by the straight line DE is formed by the angles DAF and FAE.
Complementary Angle BAF is formed by angle BAE and angle AEF.
https://brainly.com/question/12919120
Plz help, fill in the blanks in order
A telephone pole has a wire attached to its top that is anchored to the ground. The distance from the bottom of the pole to the anchor point is 49 feet less than the height of the pole. If the wire is to be 14 feet longer than the height of the pole, what is the height of the pole?
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Answer:
105 ft
Step-by-step explanation:
Let x represent the height of the pole. Then (x -49) is the distance from the pole to the anchor point, and (x+14) is the length of the wire from the top of the pole to the anchor point.
The Pythagorean theorem gives us the relation ...
(x +14)² = x² +(x -49)²
x² +28x +196 = x² +x² -98x +2401 . . . . eliminate parentheses
x² -126x +2205 = 0 . . . . . . . . put in standard form
x² -126x +3969 -1764 = 0 . . . . "complete the square)
(x -63) = ±√1764 . . . . . . add 1764, take the square root
x = 63 +42 = 105 . . . . . . highest value root. The pole must be higher than 49 feet
The height of the pole is 105 feet.
In 5 days she made 80 sandcastles. Each day she made 4 fewer castles than the day before. How many castles did she make each day?
Answer:
Castles made: N day 1
N - 4 day 2
N - 8 day 3
N - 12 day 4
N - 16 day 5
Total 5 N - 40 = 80
N = 24 total castles day 1
Total castles = 24 + 20 + 16 + 12 + 8 = 80
f(x) = x2
g(x) = (x +4)^2 - 1
We can think of g as a translated (shifted) version of f.
Hurry I am in summer school and almost done I need help ASAP!
Answer:
down by 1 unit and left by 4 units
Step-by-step explanation:
Given f(x) then f(x) + c is a vertical translation of f(x)
• If c > 0 then a shift up of c units
• If c < 0 then a shift down of c units
Given f(x) then f(x + a) is a horizontal translation of f(x)
• If a > 0 then a shift left of a units
• If a < 0 then a shift right of a units
Then
g(x) = (x + 4)² - 1
is f(x) shifted down by 1 unit and shifted left by 4 units
A scientist has acid solutions with concentrations of 4% and 15%. He wants to mix some of each solution to get 44 milliliters of solution with a 12% concentration. How many milliliters of each solution does he need to mix together?
Let x and y be the amounts (in mL) of the 4% and 15% solutions, respectively, that the scientist needs to use.
He wants to end up with a 44 mL solution, so
x + y = 44 mL
Each milliliter of 4% solution contains 0.04 mL of acid, while each mL of 15% contains 0.15 mL of acid. The resulting solution should have a concentration of 12%, so that each mL of it contains 0.12 mL of acid. Then the solution will contain
0.04x + 0.15y = 0.12 × (44 mL) = 5.28 mL
of acid.
Solve for x and y. In the first equation, we have y = 44 mL - x, and substituting into the second equation gives
0.04x + 0.15 (44 mL - x) = 5.28 mL
0.04x + 6.6 mL - 0.15x = 5.28 mL
1.32 mL = 0.19x
x ≈ 6.95 mL
==> y ≈ 37.05 mL
f(x) = −16x2 + 24x + 16
what is the vertex
Answer:
VERTEX: (0.75,25)
Step-by-step explanation:
the vertex will be at [-b/2a, f(-b/2a)]
−16x2 + 24x + 16
4(-4x^2 + 6x +4)
a = -4, b=6,c=4
-6/-8 = 3/4
f(3/4) = 25
Evaluate the given expression for x = 5 and y=5. 6x2 + 7xy + 3y?
Step-by-step explanation:
Given, x = 5
y = 5
= 6(5)^2 +7(5)(5) +3(5)
= 6(25)+7(25) +15
= 150+175 + 15
= 150 + 190
=340
Answer:
x = 12 y = 7
Step-by-step explanation:
6x^2 + 7xy + 3y
6(5)^2+ 7(5) + 7(8)y
6(5+5)+25+35 + 7(8)-7y
60+25+35+ 56-7y
y - 5 = 120 + 35 - 5 (+49y)
sqrt 150 + sqrt 49
x = 12 y = 7
Please Help!! much appreciated! :D
Find the value of y.
In the largest triangle, the missing side has length
√((11 + 5)² - x ²) = √(256 - x ²)
But it's also the hypotenuse of the triangle with side lengths 11 and y, so that its length can also be written as
√(11² + y ²) = √(121 + y ²)
so that
√(256 - x ²) = √(121 + y ²)
or, by taking the squares of both sides,
256 - x ² = 121 + y ²
y ² = 135 - x ²
In the smallest triangle, you have
5² + y ² = x ² ==> x ² = 25 + y ²
Substitute this into the previous equation and solve for y :
y ² = 135 - (25 + y ²)
y ² = 110 - y ²
2y ² = 110
y ² = 55
y = √55
