sum of first n terms of an ap sequance is 3n2+5n.what is the sum of its first n+1 terms.find the sum of its first 10 terms.
Answer:
a) 3n^2 + 11n + 8
b) 350
Step-by-step explanation:
10) 3(10^2)+ 5*10 = 350
n+1) 3(n+1)^2 + 5(n+1)
3(n^2 + 2n + 1) + 5n+5
3n^2 + 6n+3 + 5n + 5
3n^2 + 11n + 8
f(x) = 2x + 9
f^-1(x)= ??
Step-by-step explanation:
Given
f(x) = 2x + 9
f^-1 (x) = ?
Let
y = f(x)
y = 2x + 9
Interchanging the roles of x and y we get
x = 2y + 9
2y = x - 9
y = ( x - 9) / 2
Therefore
⏩f^-1(x) = (x-9)/2
Hope it will help :)
express the ratio as a fraction in it's lowest term.2mm:100cm
Answer:
2/1000 broken down to 1/500
Step-by-step explanation:
convert 100cm to mm
10mm-1cm
x-100
x=1000mm
since the question says as a fraction
2mm/1000mm
1mm/500mm
The ratio [tex]2mm:100cm[/tex] expressed as a fraction in its lowest term is [tex]\frac{1 mm}{500mm}[/tex].
To express the ratio 2mm:100cm as a fraction in its lowest term, we need to convert both measurements to the same unit.
Since 1cm is equal to 10mm, we can convert the ratio as follows:
[tex]2mm:100cm[/tex]
[tex]= 2mm : (100cm \times 10mm/cm)[/tex]
[tex]= 2mm : 1000mm[/tex]
Now, we can write the ratio as a fraction: [tex]\frac{2mm}{1000mm}[/tex]
To simplify the fraction, we can divide both the numerator and denominator by their greatest common divisor, which is 2:
[tex]\frac{2mm}{1000mm}[/tex]
= [tex]\frac{1 mm}{500mm}[/tex]
Therefore, the ratio [tex]2mm:100cm[/tex] expressed as a fraction in its lowest term is [tex]\frac{1 mm}{500mm}[/tex].
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can someone tell me where i can get a graph that shows this:
Weight Not Over (lbs.) Price
0 $0
1 $2.69
2 $3.17
3 $3.65
4 $4.13
5 $4.61
6 $5.09
7 $5.57
8 $6.03
9 $6.49
10 $6.95
Answer:
Note: See the attached photo for the graph showing Weight Not Over (lbs.) vs Price($). The attached excel file also shows the same graph with the data used to draw it in the excel.
Step-by-step explanation:
In the attached graph, Weight Not Over (lbs.) is on the horizontal axis while Price ($) is on the vertical axis.
From the attached, it can be observed that the graph shows an upward trend. That implies that there is a positive relation between Weight Not Over (lbs.) and Price. That is, as Weight Not Over (lbs.) rises, the Price also rises.
The annual demand for a product is 16,400 units. The weekly demand is 315 units with a standard deviation of 90 units. The cost to place an order is $31.00, and the time from ordering to receipt is four weeks. The annual inventory carrying cost is $0.20 per unit.
a. Find the reorder point necessary to provide a 95 percent service probability.
b. Suppose the production manager is asked to reduce the safety stock of this item by 55 percent. If she does so, what will the new service probability be?
Answer:
a) The reorder point necessary to provide a 95 percent service probability is 1557 units.
b) The Z value of 0.74 corresponds to 77% service probability.
Step-by-step explanation:
Average weekly demand (d) = 315 units
The standard deviation of weekly demand (\sigmad) = 90 units
Lead time (L) = 4 weeks
At 95% service level value of Z = 1.65
Reorder point = d x L + safety stock
[tex]= d \times L + (Z \times \sigma d \times \sqrt L)\\\\= 315 x 4 + (1.65 x 90 x \sqrt 4)\\\\= 1260 +(1.65 x 90 x 2)\\\\= 1260 + 297\\\\= 1557 units[/tex]
b) Earlier the safety stock was 297 units(calculated in part a)
Now the safety stock is reduced to 55%.so,55% of 297 = 163.35 units
So the new safety stock = 297 - 163.35 = 133.65
[tex]Safety stock = Z \times \sigma d \times \sqrt L\\133.65 = Z x 90 x 2\\133.65 = 180Z\\ Z = 133.65/180\\Z = 0.74[/tex]
The Z value of 0.74 corresponds to 77% service probability.
Convert the equation (y + 2) = –1/3(x – 4) to the point-slope form. Then fill in the blanks below to describe how to graph the equation. Plot the point _______, move _______ unit(s) down, and _______ unit(s) over to find the next point on the line.
A. (–2, 4), one, three
B. (4, –2), one, three
C. (2, 4), one, three
D.(4, –2), three, one
Answer:
A. (–2, 4), one, three
Step-by-step explanation:
For a linear equation:
y = a*x + b
the point-slope form is:
(y - y₁) = m*(x - x₁)
Where we know that this line has the slope m, and passes through the point (x₁, y₁)
In this case, the equation:
(y + 2) = –1/3(x – 4)
is already in the point-slope form.
here we have:
y₁ = -2
x₁ = 4
then the point is (-2, 4)
m = -(1/3)
m = -1/3 means that when we move 3 units to the right, we need to move one unit down. (or the inverse, we can move one unit down and 3 to the right)
So, to complete the statement we have:
plot the point (-2, 4), move one unit down, and three units over to find the next point on the line.
The correct option is A.
Find the critical point for f and then use the second derivative test to decide whether the critical point is a relative maximum or a relative minimum.f(x)=-x^2-2x-9
Answer:the answer is 9
Step-by-step explanation:
what much is 1/2 - 1/4
Answer:
1/4
Step-by-step explanation:
The answer is 1/4.
1/2 is equivalent to 2/4.
2/4-1/4=1/4
Find the interquartile range of the data set represented by this box plot.
25
20
45
35
Answer:
25
Step-by-step explanation:
im pretty sure i think only ok i think no saying bad things in the comment
define saturated and unsaturated fats
Answer:
A saturated fat is a type of fat in which the fatty acid chains have all or predominantly single bonds. A fat is made of two kinds of smaller molecules: glycerol and fatty acids. Fats are made of long chains of carbon atoms. Some carbon atoms are linked by single bonds and others are linked by double bonds.
Saturated fats: a type of fat containing a high proportion of fatty acid molecules without double bonds, considered to be less healthy in the diet than unsaturated fat
Unsaturated fats: a type of fat containing a high proportion of fatty acid molecules with at least one double bond, considered to be healthier in the diet than saturated fat.
what's the difference between both?: saturated fats Contains a single bond, Excessive consumption leads to heart diseases,High melting point and Solid state in room temperature. While Unsaturated Contains at least one double bond, Good for consumption, but excessive may increase cholesterol,Low melting point and Liquid state in room temperature.
The sum of four consecutive odd integers is –72. Write an equation to model this situation, and find the values of the four integers.
9514 1404 393
Answer:
(x -3) +(x -1) +(x +1) +(x +3) = -72-21, -19, -17, -15Step-by-step explanation:
Let x represent the even integer between the middle two odd integers. Then the sum of the four odd integers is ...
(x -3) +(x -1) +(x +1) +(x +3) = -72
4x = -72
x = -18
The four integers are -21, -19, -17, -15.
_____
Additional comment
You could let x represent one of the integers. Often, people choose to let it represent the least of them. Then the equation becomes x +(x+2) +(x+4) +(x+6) = -72, so 4x = -84 and x = -21. This introduces a "subtract 12" step in the solution process that is unnecessary if x is chosen to be the average of the integers.
As the average, x is the sum divided by the number of them, so you know x=-72/4 = -18 immediately. Then you just have to find the nearest two odd integers below and above -18. You can do the whole problem mentally.
In the figure, ∆ABD ≅ ∆CBD by Angle-Side-Angle (ASA). Which segments are congruent by CPCTC?
Answer:
[tex]\angle ADB \cong \angle CDB[/tex]
[tex]\angle DBA \cong \angle DBC[/tex]
[tex]BD = BD[/tex]
Step-by-step explanation:
Given
[tex]\triangle ABD \cong \triangle CBD[/tex]
Required
The congruent segments by CPCTC
From the question, we have:
[tex]\angle ADB \cong \angle CDB[/tex] --- given
[tex]\angle DBA \cong \angle DBC[/tex] --- given
Both triangles share a common side (length BD);
So, we have:
[tex]BD = BD[/tex]
Hence, the congruent segments are:
[tex]\angle ADB \cong \angle CDB[/tex]
[tex]\angle DBA \cong \angle DBC[/tex]
[tex]BD = BD[/tex]
What is the equation of the line graphed below?
5
- 5
5
(3,-1)
1
-5
O A. y=-3x
1
O B. y = -
O c. y =
C. 5
-X
What is the equation of the line graphed below
A person is standing close to the edge on a 56 foot building and throws the ball vertically upward. The quadratic function h(t)=-16^2+104t+56 models the balls height above the ground,h(t),in feet, T seconds after it was thrown
what is the maximum height of ball.=
How many seconds did it take to hit the ground=
Please help!
Answer:
Part 1)
225 feet.
Part 2)
7 seconds.
Step-by-step explanation:
The height h(t) of the ball above the ground after t seconds is modeled by the function:
[tex]h(t)=-16t^2+104t+56[/tex]
Part 1)
We want to determine the maximum height of the ball.
Notice that the function is a quadratic with a negative leading coefficient, so its maximum will be at its vertex point.
The vertex of a parabola is given by:
[tex]\displaystyle \text{Vertex} = \left(-\frac{b}{2a}, f\left(-\frac{b}{2a}\right)\right)[/tex]
In this case, a = -16, b = 104, and c = 56.
Find the x- (or rather t-) coordinate of the vertex. So:
[tex]\displaystyle t=-\frac{(104)}{2(-16)}=\frac{104}{32}=\frac{13}{4}=3.25\text{ seconds}[/tex]
In other words, the ball reaches its maximum height after 3.25 seconds.
To find the maximum height, substitute this value back into the function. Hence:
[tex]\displaystyle h(3.25)=-16(3.25)^2+104(3.25)+56=225\text{ feet}[/tex]
The maximum height of the ball is 225 feet in the air.
Part 2)
We want to find the amount of time it took for the ball to hit the ground.
When the ball hit the ground, its height above the ground is zero. Therefore, we can set h(t) to 0 and solve for t:
[tex]0=-16t^2+104t+56[/tex]
We can simplify a bit. Divide both sides by -8:
[tex]0=2t^2-13t-7[/tex]
We can factor. Find two numbers that multiply to 2(-7) = -14 and add to -13.
-14 and 1 works! Therefore, split the second term into -14 and 1:
[tex]\displaystyle 0=2t^2-14t+t-7[/tex]
Factor out a 2t from the first two terms and group the last two terms:
[tex]0=2t(t-7)+(t-7)[/tex]
Factor by grouping:
[tex]0=(2t+1)(t-7)[/tex]
Zero Product Property:
[tex]2t+1=0\text{ or } t-7=0[/tex]
Solve for each case:
[tex]\displaystyle t=-0.5\text{ or } t=7[/tex]
Since time cannot be negative, we can ignore the first case.
Therefore, it takes seven seconds for the ball to hit the ground.
Suppose a life insurance company sells a $240,000 one-year term life insurance policy to a 19-year-old female for $240. The probability that the female survives the year is 0.999578. Compute and interpret the expected value of this policy to the insurance company. The expected value is $ (Round two decimal places as needed.)
Answer:
$138.72
Step-by-step explanation:
(1-0.999578)*$240,000 = $101.28
$240 - $101.28 = $138.72
Solve this:
A woman was 39years old when she gave birth to a pair of twins.12 years ago,she was twice as old as the sum of the ages of the twins put together.Find their present ages.
Answer:
woman =39years
twins 0year each since 12 years ago they were not yet born
If someone can pls give the answer with steps that would be greatly appreciated :)
Answer:
1.Sentence examples for that would be greatly appreciated from inspiring English sources. If Norton or Symantec or anyone else can provide any info that would be greatly appreciated!! In all sincerity, if Hillary supporters at The Daily Beast and Daily Banter can enlighten us, that would be greatly appreciated.Hope It helps
Question 4*
4. Sam's goal is to exercise for 400 minutes each
week. This week, he reached 128% of his goal.
How many minutes did he exercise?
Answer: Get at least 150 minutes of moderate aerobic activity or 75 minutes of vigorous aerobic activity a week, or a combination of moderate and vigorous activity. The guidelines suggest that you spread out this exercise during the course of a week. Greater amounts of exercise will provide even greater health benefit.
Step-by-step explanation:
If Sam reached 128% of his goal to exercise each week, he would have exercised for 512 minutes.
How many minutes did Sam exercise this week?Given the parameters:
Sam's goal is to exercise for 400 minutes each week.
This week, he reached 128% of his goal.
The number of minutes =?
To determine how many minutes Sam exercised this week, we simply calculate 128% of his goal.
Number of minutes = 128% × Sam's goal of exercise
Number of minutes = 128% × 400 minutes
Note that: 128% = 128/100
Number of minutes = 128/100 × 400 minutes
Number of minutes = 128 × 4 minutes
Number of minutes = 512 minutes
Therefore, Sam exercised for 512 minutes this week.
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how do we get 24 using 3,3,7 and7
Answer:
2 Answers. #1. +11. [3+(3/7)] times 7 is 24. DarkBlaze347 May 1, 2015. +5. Good job, DB! civonamzuk May 1, 2015.
35 Online Users.
Step-by-step explanation:
brainliest please and follow:D
Which statement about y=x^2-12x+35 is true?
A. The zeros are 7 and 5, because y=(x-7)(x-5)
B. The zeros are 7 and -5, because y=(x+7)(x-5)
c. The zeros are -7 and -5, because y=(x+7)(x+5)
D. The zeros are -7 and -5, because y=(x-7)(x-5)
Answer:The zeros are 7 and 5, because y=(x-7)(x-5)
Step-by-step explanation:
Can someone please help me with this math problem.
Answer:
8 + 30 ÷ 2 + 4 = 27
8 + 30 ÷ (2 + 4 ) = 13
(8 + 30) ÷ 2 + 4 = 23
Step-by-step explanation:
simplify 2x²y²÷m³×m²÷2xy
Which one is a better deal?
paying $2.88 for a 12 roll package of toilet paper
paying $1.20 for a 6 roll package of toilet paper
Answer:
paying $1.20 for a 6 roll package of toilet paper
Step-by-step explanation:
to find the answer, double 6 to equal 12 and double the price as well. therefore, it is 2.40. since 2.40 is cheaper than 2.88, it is a better deal.
Please hlep x^2+6x+1=0
Answer:
Substitute into the quadratic formula
-6 ± √32 / 2
= -3 ± √16
= 1 and -1 are the answer
Answer:
x = - 3 ± 2[tex]\sqrt{2}[/tex]
Step-by-step explanation:
Given
x² + 6x + 1 = 0 ( subtract 1 from both sides )
x² + 6x = - 1
Using the method of completing the square
add/ subtract ( half the coefficient of the x- term)² to both sides
x² + 2(3)x + 9 = - 1 + 9
(x + 3)² = 8 ( take the square root of both sides )
x + 3 = ± [tex]\sqrt{8}[/tex] = ± 2[tex]\sqrt{2}[/tex] ( subtract 3 from both sides )
x = - 3 ± 2[tex]\sqrt{2}[/tex]
Then
x = - 3 - 2[tex]\sqrt{2}[/tex] , x = - 3 + 2[tex]\sqrt{2}[/tex]
The durations (minutes) of 26 electric power outages in Shah Alam over the past five years are shown below. 32 44 25 66 27 12 62 9 51 4 17 50 35 99 30 21 12 53 25 2 18 24 84 30 17 17 (a) Find the mean, median and mode.
Answer:
Mean = 33.31
Median = 26
Mode = 17
Step-by-step explanation:
Given the data:
32 44 25 66 27 12 62 9 51 4 17 50 35 99 30 21 12 53 25 2 18 24 84 30 17 17
Reordered data : 2, 4, 9, 12, 12, 17, 17, 17, 18, 21, 24, 25, 25, 27, 30, 30, 32, 35, 44, 50, 51, 53, 62, 66, 84, 99
The mean, xbar = Σx / n = 866 /26 = 33.31
The median = 1/2(n+1)th term
Median = 1/2(27)th term = 13.5th term
Median = (13 + 14)th / 2
Median = (25 + 27) / 2 = 26
The mode = 17 (highest frequency)
HELP ME ASAP a is the blue line. B is the purple line. C is the orange line. And D is the green line
Answer: D (Green)
Step-by-step explanation:
Answer:
Step-by-step explanation:
There should be three others
<DPB
<APC
And the acute angle at D going up and to the right. It's not lettered so I can give it as an answer. I have no idea what the colors mean.
Feedback:Correct answer
Question 2 of 10
10.0 Points
3
Find the interquartile range for a data set having the five-number
summary: 4.6, 14.3, 19.7, 26.1, 31.2
A. 26.6
B. 11.8
C. 11.5
D. 15.1
A sprinkler releases water st a rate of 150 liters per hour. If the sprinkler operated for 80 minutes how many liters of water will be released
The amount of water released from the sprinkler for 80 minutes is 200 L
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the amount of water from the sprinkler for 80 minutes be = A
Now , the value of A is given by the equation
A sprinkler releases water st a rate of 150 liters per hour
So , 60 minutes = 150 Liters of water
80 minutes = 1/60 hours
80 minutes = 1.333 hours
The amount of water released for 1.333 hours A = 150 x 1.333
On simplifying the equation , we get
The amount of water released for 1.333 hours A = 200 L
Therefore , the value of A is 200 L
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By visual inspection, determine the best-fitting regression model for the
scatterplot.
X
10
.
-10
A. No pattern
B. Exponential
C. Quadratic
D. Linear
Answer:
The answer is B since the chance is expontential since it gets bigger over time and each one is farther apart
The best-fitting regression model for the scatterplot is Exponential, the correct option is B.
What is fitting of curve for a data plot?When the data shows some trend, either linear (making a line), or non-linear (a predictable curve), we fit a mathematical curve(exponential) on that data set, as a representative of the pattern in that data set, to predict the output based on the inputs.
We are given;
The graph representation
Now,
By visual inspection of the scatterplot, we can see that the points do not follow a clear pattern that suggests an exponential or quadratic relationship. However, there appears to be a linear relationship between the variables.
Therefore, the answer will be exponential.
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A university dean is interested in determining the proportion of students who receive some sort of financial aid. Rather than examine the records for all students, the dean randomly selects 200 students and finds that 118 of them are receiving financial aid. If the dean wanted to estimate the proportion of all students receiving financial aid to within 1% with 90% reliability, how many students would need to be sampled
Answer:
6546 students would need to be sampled.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].
The margin of error is:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
The dean randomly selects 200 students and finds that 118 of them are receiving financial aid.
This means that [tex]n = 200, \pi = \frac{118}{200} = 0.59[/tex]
90% confidence level
So [tex]\alpha = 0.1[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.1}{2} = 0.95[/tex], so [tex]Z = 1.645[/tex].
If the dean wanted to estimate the proportion of all students receiving financial aid to within 1% with 90% reliability, how many students would need to be sampled?
n students would need to be sampled, and n is found when M = 0.01. So
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.01 = 1.645\sqrt{\frac{0.59*0.41}{n}}[/tex]
[tex]0.01\sqrt{n} = 1.645\sqrt{0.59*0.41}[/tex]
[tex]\sqrt{n} = \frac{1.645\sqrt{0.59*0.41}}{0.01}[/tex]
[tex](\sqrt{n})^2 = (\frac{1.645\sqrt{0.59*0.41}}{0.01})^2[/tex]
[tex]n = 6545.9[/tex]
Rounding up:
6546 students would need to be sampled.
