Answer:
The first term is 6; the common difference in 0.8.
Step-by-step explanation:
The nth term is:
[tex] a_n = a_1 + (n - 1)d [/tex]
The sum of the first n terms is:
[tex] S_n = \dfrac{n(a_1 + a_n)}{2} [/tex]
[tex] a_{n} = a_1 + (n - 1)d [/tex]
[tex] a_{11} = a_1 + (11-1)d [/tex]
[tex] a_1 + 10d = 14 [/tex] Equation 1
[tex] S_n = \dfrac{n(a_1 + a_n)}{2} [/tex]
[tex] S_{26} = \dfrac{26(a_1 + a_{26})}{2} [/tex]
[tex] \dfrac{26(a_1 + a_1 + 25d}{2} = 416 [/tex]
[tex] \dfrac{52a_1 + 650d)}{2} = 416 [/tex]
[tex] 26a_1 + 325d = 416 [/tex] Equation 2
Equation 1 and Equation 2 form a system of equations in 2 unknowns.
To eliminate a_1, subtract 26 times Eq. 1 from Eq. 2.
[tex] 65d = 52 [/tex]
[tex] d = \dfrac{52}{65} [/tex]
[tex] d = \dfrac{4}{5} = 0.8 [/tex]
[tex] a_1 + 10d = 14 [/tex]
[tex] a_1 + 10 \times 0.8 = 14 [/tex]
[tex] a_1 + 8 = 14 [/tex]
[tex] a_1 = 6 [/tex]
Answer:
The first term is 6; the common difference in 0.8.
Two different formulas of an oxygenated motor fuel are being tested to study their road octane numbers. The variance of road octane number for formula 1 is σ12=1.5, and for formula 2 it is σ22=1.2. Two random samples of size n1=15 and n2=20 are tested, and the mean octane numbers observed are x¯1=89.0 fluid ounces and x¯2=92.2 fluid ounces. Assume normality.
a. Test the hypothesis that the formulations are equal versus the hypothesis that formulation 2 produces a higher mean road octane number than formulation 1. Calculate z0=
b. Calculate a 95% two-sided confidence interval on the mean difference road octane number.
Answer:
Step-by-step explanation:
a)
zo=(89.0-92.2)/sqrt((1.5/15)+(1.2/20))
zo=-8.00
p-value=0.0000
Reject the null hypothesis.
b)
95% confidence interval for difference
=(89-92.2)+/-1.96*sqrt((1.5/15)+(1.2/20))
=-3.2+/-0.78
=(-3.98, -2.42)
Find the solution for this system of equations.
2x + 4y = 8
x = 3y − 6
Answer:
[tex]{ \tt{2x + 4y = 8 - - - (a)}} \\ { \tt{x = 3y - 6 - - - (b)}} [/tex]
Substitute for x in equation (a) :
[tex]{ \tt{2(3y - 6) + 4y = 8}} \\ { \tt{6y - 12 + 4y = 8}} \\ { \tt{10y = 20}} \\ y = 2[/tex]
Substitute for y in equation (b) :
[tex]{ \tt{x = (3 \times 2) - 6}} \\ x = 0[/tex]
2x+4y =8
x=3y-6 ——> x–3y=–6
x–3y = – 6 ] ×(–2) ——> –2x +6y=12
2x+4y=8
–2x+6y =12
__o_o____
0+10y=20 —> 10y= 20 —> y= 20/10 —> y= 2
2x+4y=8 —> 2x + 4(2) = 8 —> 2x + 8=8 —> 2x = 0 —> x=0
(x,y) —> (0,2)
if 8km=5miles.how many miles are in 56m?
Answer:
89.6 miles
Step-by-step explanation:
[tex]\frac{8}{5}[/tex] = [tex]\frac{x}{56}[/tex]
5x = 448
x=89.6
Step-by-step explanation:
if 8km=5
x =56km
5x=8×56
5x=448
x=89.6 miles
Find the value of x in each case:
A line contains the points (3,1) and (-6,4) what is the equation for this line in slope intercept form
Answer:
y = (-1/3)x + 2
Step-by-step explanation:
Since points (3,1) and (-6,4) lie on y = (-1/3)x + c , it should satisfy the this equation. Thus, intercept is 2.
Answer:
m = -⅓
Step-by-step explanation:
m = (y2- y1)/(x2 - x1)
m = (4 -1)/(-6-3)
m = -⅓
alvin is 5 years older than elga. the sum of their age is 85. what is elga age
Answer:
40 years old.
Step-by-step explanation:
We can let Elga's age equal [tex]x[/tex]. Alvin's age can be equal to [tex]y[/tex]. We can make several equations from the information we know. We know that Elga's age plus five equal's Alvin's age.
[tex]x+5=y[/tex]
We also know that the sum of their ages is 85.
[tex]x+y=85[/tex]
We can substitute [tex]x+5[/tex] for [tex]y[/tex] in the second equation since [tex]x+5=y[/tex], so we have the following equation:
[tex]x+(x+5)=85[/tex]
We can combine like terms to get
[tex]2x+5=85[/tex]
Subtracting 5 from both sides results in
[tex]2x=80[/tex]
After that, we can divide both sides by 2 to get
[tex]x=40[/tex]
Thus, Elga is 40 years old.
Answer:
e = 40
a=45
Step-by-step explanation:
a + e = 85
a = e+5
e + 5 + e = 85
2e = 80
e = 40
a=45
A movie theater has a seating capacity of 283. The theater charges $5.00 for children, $7.00 for students, and $12.00 of adults. There are half as many adults as there are children. If the total ticket sales was $ 2060 on a sold out night, how many children, students, and adults attended
Answer: adults = 79
children = 158
student = 46
Step-by-step explanation:
Let a = adults
Let c = children
Let s = student
From the information given,
a + c + s = 283 ....... i
c/a = 2, c = 2a ....... ii
5c + 7s + 12a = 2060 ...... iii
Put the value of c = 2a into equation i
a + c + s = 283
a + 2a + s = 283
3a + s = 283
s = 283 - 3a
Note that c = 2a
From equation iii
5c + 7s + 12a = 2060
5(2a) + 7(283 - 3a) + 12a = 2060
10a + 1981 - 21a + 12a = 2060
10a + 12a - 21a = 2060 - 1981
a = 79
Note c = 2a
c = 2 × 79 = 158
Since a + c + s = 283
79 + 158 + s = 283
s = 283 - 237
s = 46
adults = 79
children = 158
student = 46
PLEASE HELP ME ASAP GIVING 10+ POINTS
The actual height of the building shown in the model is 150 feet What is the actual width of the building shown in the model?
Answer:
60 ft
Step-by-step explanation:
The answer has to be in feet units
Now that we know the height is 5 cm equivalent to 150 feet, what is the width of the building in feet units
5 cm = 150 ft
Rule: multiply cm by 30 to get the ft
2 cm = ?
2 cm × 30 = 60 ft
2 cm = 60 ft
Suppose these data show the number of gallons of gasoline sold by a gasoline distributor in Bennington, Vermont, over the past 12 weeks.
Week Sales (1,000s of gallons)
1 17
2 22
3 20
4 24
5 18
6 17
7 21
8 19
9 23
10 21
11 16
12 23
(a) Using a weight of
1
2
for the most recent observation,
1
3
for the second most recent observation, and
1
6
for third most recent observation, compute a three-week weighted moving average for the time series. (Round your answers to two decimal places.)
Compute four-week and five-week moving averages for the time series.
Week Time Series Moving
Value Average Forecast
1 17
2 22
3 20
4 24
5 18
6 17
7 21
8 19
9 23
10 21
11 16
12 23
(b) Compute the MSE for the four-week moving average forecasts. (Round your answer to two decimal places.)
Compute the MSE for the five-week moving average forecasts. (Round your answer to two decimal places.)
(c) What appears to be the best number of weeks of past data (three, four, or five) to use in the moving average computation? MSE for the three-week moving average is 11.12.
Answer:
Use suitable identity to find the product (3-2x)(3+2x).Find the remainder when x³+ 3x²+3x+1 is divided by x+1.On a plane surface we can find straight lines.8√15 + 2√3The decimal form of 36 100(a-b)³ = a ³- ........ 3 + 3ab²-b³In the Cartesian plane the horizontal line is called .........The coefficient of x² in 2-x²+ x³ is -1.√225 is an irrational number.The coordinates of a point on x-axis is (y, 0).The coordinates of a point on x-axis is (y, 0).The coordinates of a point on x-axis is (y, 0).The coordinates of a point on x-axis is (y, 0).
On dividing 12x³ by 4x the quotient is …..
Answer:
12x^3 is equivalent to
12x*12x*12x which if we multiply is
1728x
we divide by 4x
1728x divided by 4x=432x
Hope This Helps!!!
Answer:
3x^2
Step-by-step explanation:
when u divide 12x^3/4x....u divide 12/4=3 along with the x also..tat is x^3/x=x^2
PLEASE HELP I DONT NEED EXPLANATION JUST THE EQUATION IM IN A TEST RN HELP ASAP THANK YOU SO MUCH :)))
Answer:
[tex]-x^{2}[/tex]
Step-by-step explanation:
It simple really its just a reflection over the x-axis making it a negative towards the parent function
Answer:
The answer is -x²
Step-by-step explanation:
Hope this helps :)
what's the value of the function f(x)= 2x+5 if x=3
Answer:
f(x) = 2(3) + 5
= 6 + 5 = 11
y = 11
x = 3
hope it helps.
Also, I think that Brainly is an awesome app, but there's an app which is doing great work for me in maths, named Gauthmath. I will suggest it. Video concepts and answers from real tutors.
Which of the following expressions is not equivalent to the others?
Answer:
Im going to guess the second one
Step-by-step explanation:
It's the only one that does not have more than one negative fraction.
What is the distance between -10.2 and 5.7?
Answer:
15.9
Step-by-step explanation:
The distance between -10.2 and 5.7 is 15.9 after plotting the points on a number line.
What is a number line?It is defined as the representation of the numbers on a straight line that goes infinitely on both sides.
It is given that:
Two numbers on a number line:
-10.2 and 5.7
As we know, a number is a mathematical entity that can be used to count, measure, or name things. For example, 1, 2, 56, etc. are the numbers.
Indicating the above numbers on a number line:
= 5.7 -(-10.5)
The arithmetic operation can be defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.
= 5.7 + 10.5
= 15.9
Thus, the distance between -10.2 and 5.7 is 15.9 after plotting the points on a number line.
Learn more about the number line here:
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Ernest bought t T-shirts. The shirts came in 6 packages. Write an expression that shows how many T-shirts were in each package.
Type an asterisk ( * ) if you want to use a multiplication sign and a forward slash ( / ) if you want to use a division sign.
Answer:
t / 6 = # of shirts in each package.
Step-by-step explanation:
total amount of shirts / total packages = # of shirts in each package
insert a digit in a place of each "..." to make numbers that are divisible by 6 if it is possible: 4...6
Answer:
1 There is no number that make it divisible by 6 with no decimals
2 1,4,7
Step-by-step explanation:
2 23718/6= 3953
23748/6= 3958
23778/6= 3963
X+ 1
If g(x)=
X-2 and h(x) = 4 – x, what is the value of (g•)(-3)?
ola Mo Nional
15
2
18
An arch is in the form of a parabola given by the function h = -0.06d^2 + 120, where the origin is at ground level, d meters is the horizontal distance and h is the height of the arch in meters.
Graph this function on your graphing calculator then complete the following statements.
The height of the arch is: ------- m
The width to the nearest meter, at the base of the arch is ------ m
Answer:
See attachment for graph
The height of the arch is: 120 m
The width to the nearest meter, at the base of the arch is 22 m
Step-by-step explanation:
Given
[tex]h = -0.06d^2 + 120[/tex]
Solving (a): The graph
See attachment for graph
Variable h is plotted on the vertical axis while variable d is plotted on the horizontal axis.
Solving (b): The height
The curve of [tex]h = -0.06d^2 + 120[/tex] opens downward. So, the maximum point on the vertical axis represents the height of the arch,
Hence:
[tex]height = 120[/tex]
Solving (c): The width
The curve touches the horizontal axis at two different points.
[tex]x_1 = -11[/tex]
[tex]x_2 = 11[/tex]
The absolute difference of both points represents the width.
So:
[tex]Width = |x_2 - x_1|[/tex]
[tex]Width = |11 - -11|[/tex]
[tex]Width = |11 +11|[/tex]
[tex]Width = |22|[/tex]
Hence:
[tex]Width = 22[/tex]
PLEASE HELP THIS IS MY LAST QUESTIONNNN
- The electric company charges Dalton a monthly service fee of $30 plus $0.15 per kilowatt-hour of electricity used. This month, Dalton's bill is $105.
- How many kilowatt-hours of electricity did Dalton use?
500 kwh
$105 - $30 = $75
$75 / $0.15 = 500
Answer:
$105-$30 service fee, this leaves only the electricity used. $75. now to find how many kilowatt hours used you divide $75/.15=500 answer 500 kilowatt hours.
Step-by-step explanation:
see above
Assuming the probability of a single sample testing positive is 0.15, find the probability of a positive result for two samples combined into one mixture. Is the probability low enough so that further testing of the individual samples is rarely necessary?
Answer:
[tex]P(Positive\ Mixture) = 0.2775[/tex]
The probability is not low
Step-by-step explanation:
Given
[tex]P(Single\ Positive) = 0.15[/tex]
[tex]n = 2[/tex]
Required
[tex]P(Positive\ Mixture)[/tex]
First, we calculate the probability of single negative using the complement rule
[tex]P(Single\ Negative) = 1 - P(Single\ Positive)[/tex]
[tex]P(Single\ Negative) = 1 - 0.15[/tex]
[tex]P(Single\ Negative) = 0.85[/tex]
[tex]P(Positive\ Mixture)[/tex] is calculated using:
[tex]P(Positive\ Mixture) = 1 - P(All\ Negative)[/tex] ---- i.e. complement rule
So, we have:
[tex]P(Positive\ Mixture) = 1 - 0.85^2[/tex]
[tex]P(Positive\ Mixture) = 1 - 0.7225[/tex]
[tex]P(Positive\ Mixture) = 0.2775[/tex]
Probabilities less than 0.05 are considered low.
So, we can consider that the probability is not low because 0.2775 > 0.05
Suppose 46% of politicians are lawyers. If a random sample of size 662 is selected, what is the probability that the proportion of politicians who are lawyers will differ from the total politicians proportion by less than 4%
Answer:
0.9606 = 96.06% probability that the proportion of politicians who are lawyers will differ from the total politicians proportion by less than 4%
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score 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 p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]
Suppose 46% of politicians are lawyers.
This means that [tex]p = 0.46[/tex]
Sample of size 662
This means that [tex]n = 662[/tex]
Mean and standard deviation:
[tex]\mu = p = 0.46[/tex]
[tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.46*0.54}{662}} = 0.0194[/tex]
What is the probability that the proportion of politicians who are lawyers will differ from the total politicians proportion by less than 4%?
p-value of Z when X = 0.46 + 0.04 = 0.5 subtracted by the p-value of Z when X = 0.46 - 0.04 = 0.42. So
X = 0.5
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.5 - 0.46}{0.0194}[/tex]
[tex]Z = 2.06[/tex]
[tex]Z = 2.06[/tex] has a p-value of 0.9803
X = 0.42
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{0.42 - 0.46}{0.0194}[/tex]
[tex]Z = -2.06[/tex]
[tex]Z = -2.06[/tex] has a p-value of 0.0197
0.9803 - 0.0197 = 0.9606
0.9606 = 96.06% probability that the proportion of politicians who are lawyers will differ from the total politicians proportion by less than 4%
How to answer this question
Answer:
(0.3049 ; 0.3751)
Step-by-step explanation:
The confidence interval for proportion can be obtained using the relation :
Phat ± Zcritical * [√phat(1-phat) / n]
phat = x / n
Sample size, n = 700
x = 238
phat = 238/700 = 0.34
Zcritical at 95% = 1.96
C.I = 0.34 ± 1.96 * [√0.34(1-0.34) / 700]
C.I = 0.34 ± 1.96 * 0.0179045
C. I = 0.34 ± 0.0350928
Lower boundary = 0.34 - 0.0350928 = 0.3049
Upper boundary = 0.34 + 0.0350928 = 0.37509
(0.3049 ; 0.3751)
This Bar Chart shows the number of DVDs sold at a local music store during one week.
Which measure(s) of central tendency can be used to determine the average number of DVDs sold each day?
A. the median
B. the mean
C. the mean and the median
D. the mode
Answer:
B. the mean
Step-by-step explanation:
According to the Bar Chart shown, the number of DVDs sold at a local music store during one week are displayed.
Therefore, the measure(s) of central tendency that can be used to determine the average number of DVDs sold each day is the mean.
This is because the mean is the sum total of the number of DVDs sold, divided by the number, which gives the average.
Answer:
The Mean
Step-by-step explanation:
I took the test
Can someone help me with this problem?
An 8-oz bottle of hair spray costs $4.46. Find the unit price in cents per ounce
Answer:
55.75 cents per ounce
Step-by-step explanation:
Take the cost and divide by the number of ounces
We want cents per ounce so change dollars to cents
446 / 8
55.75 cents per ounce
Classify the following polynomials. Combine any
like terms first.
x^2+3x + 2x - 2x^2
X^3+ 4x - 4x - 4x^2
X^3+2x - X^3- 2x^2+ 3
First simplify all polynomials and rewrite them in descending exponent order.
1. [tex]-x^2+2x[/tex]
2. [tex]x^3-4x^2[/tex]
3. [tex]-2x^2+2x+3[/tex]
Now observe the terms with highest exponents in each expression, in particularly focus on their exponent value,
[tex]-x^2[/tex] with value of 2
[tex]x^3[/tex] with value of 3
[tex]-2x^2[/tex] with value of 2
The value is also known as order of polynomial and it is a way to classify polynomials.
Every order creates a family of polynomials determined by the order (which is always greater than -1)
A polynomial such as (1) and (3) have an orders of 2, which is often called quadratic order and thus the polynomials (1), (3) are classified in the same family of quadratic polynomials, these are polynomials with order of 2.
Polynomial (2) however has an order of 3, which is called cubic order. This polynomial (2) is classified in the family of cubic polynomials.
There are of course many other families, in fact, infinitely many of them because you have order 0, 1, 2, 3, and so on there are precisely [tex]\aleph_0+1[/tex] read as "aleph 0 + 1" (the number of natural numbers + 1 (because 0 is not a natural number)) of polynomial families.
The first few have these fancy names, for example:
order 0 => constant polynomial
order 1 => linear polynomial
order 2 => quadratic polynomial
order 3 => cubic polynomial
order 4 => quartic polynomial
and so on.
Hope this helps!
what are the coordinates of the point that is 1/6 of the way from a(14 -1) to b(-4 23)
9514 1404 393
Answer:
(11, 3)
Step-by-step explanation:
That point is ...
P = a + (1/6)(b -a) = (5a +b)/6
P = (5(14, -1) +(-4, 23))/6 = (70-4, -5+23)/6 = (11, 3)
The point of interest is (11, 3).
Answer:
The coordinates of the point that is 1/6 of the way from a to b is thus (11, 3)
Step-by-step explanation:
Let's look first at the x coordinates of the two given points: 14 and -4. From 14 to -4 is a decrease of 18. Similarly, from y = -1 to y = 23 is an increase of 24.
Starting at a(14, -1) and adding 1/6 of the change in x, which is -18, we get the new x-coordinate 14 + (1/6)(-18), or 14 - 3, or 11. Similarly, adding 1/6 of the increase in y of 24 yields -1 + 4, or 3.
The coordinates of the point that is 1/6 of the way from a to b is thus (11, 3)
Pls answer? Last one for today!
Step-by-step explanation:
You look for the common factor of both of them which in this case is 5, therefore it's
5(x+7)..just divide 5 in 5x and in 35
Jerome is cooking dinner. He needs 8 ounces of broccoli for each person. Part A: Jerome is not sure how many people will come to dinner. Write an expression with a variable that represents the amount of broccoli Jerome needs for dinner. Identify what the variable represents. Part B: If Jerome has 32 ounces of broccoli, how many people can he feed? Create an equation and show all work to solve it.
Answer:
A. 8x = amount of broccoli needed
B. 4 people; 32÷8=4
Step-by-step explanation:
A. the variable (x) represents the amount of people.
B. 32 ounces divided by 8 ounces is enough for four people.
Find the measure of angle C of a triangle ABC, if angle A=a and angle B= 2a.
*The answer is not 180-3a
The angle C of the triangle ABC is ( π - 3a ).
What is an angle?The angle is defined as the span between two intersecting lines or surfaces at or close to the point where they meet.
The angle will be calculated as follows:-
We know that the sum of the angles of the triangle is 180 degrees or π in radians.
∠A + ∠B + ∠C = π
a + 2a + ∠C = π
∠C = π - a - 2a
∠C = π - 3a
Therefore angle C of the triangle ABC is ( π - 3a ).
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