The sum of the length of all the ten movies is [tex]\fbox{\begin\\\ 780\text{ minutes}\\\end{minispace}}[/tex].
Step-by-step explanation:
It is given that a new movie is released each year for [tex]10[/tex] consecutive years so there are total number of [tex]10[/tex] movies released in [tex]10[/tex] years.
The movie released in first year is [tex]60\text{ minutes}[/tex] long and each movie released in the successive year is [tex]4\text{ minutes}[/tex] longer than the movie released in the last year.
So, as per the above statement movie released in first year is [tex]60[/tex] minutes long, movie released in second year is [tex]64[/tex] minutes long, movie released in third year is [tex]68[/tex] minutes long and so on.
The sequence of the length of the movie formed is as follows:
[tex]\fbox{\begin\\\ 60,64,68,72...\\\end{minispace}}[/tex]
The sequence formed above is an arithmetic sequence.
An arithmetic sequence is a sequence in which the difference between the each successive term and the previous term is always constant or fixed throughout the sequence.
The general term of an arithmetic sequence is given as
[tex]\fbox{\begin\\\math{a_{n} =a+(n-1)d}\\\end{minispace}}[/tex]
The sequence formed for the length of the movie is an arithmetic sequence in which the first term is [tex]60[/tex] and the common difference is [tex]4[/tex].
The arithmetic series corresponding to the arithmetic sequence of length of the movie is as follows:
[tex]\fbox{\begin\\\ 60+64+68+72+...\\\end{minispace}}[/tex]
The arithmetic series formula to obtain the sum of the above series is as follows:
[tex]\fbox{\begin\\\math{S_{n} =(n/2)(2a+(n-1)d)}\\\end{minispace}}[/tex]
In the above equation [tex]n[/tex] denotes the total number of terms, a denotes the first term, d denotes the common difference and Sn denotes the sum of n terms of the series.
Substitute [tex]\fbox{\begin\\\math{a}=60\\\end{minispace}}[/tex],[tex]\fbox{\begin\\\math{n}=10\\\end{minispace}}[/tex] and [tex]\fbox{\begin\\\math{d}=4\\\end{minispace}}[/tex] in the equation [tex]\fbox{\begin\\\math{S_{n} =(n/2)(2a+(n-1)d)}\\\end{minispace}}[/tex]
[tex]S_{10} =(10/2)(120+36) \\S_{10} =780[/tex]
Therefore, the length of the all [tex]10[/tex] movies as calculated above is [tex]\fbox{\begin\\\ 780\text{ minutes}\\\end{minispace}}[/tex]
Learn more:
A problem to complete the square of quadratic function brainly.com/question/12992613A problem to determine the slope intercept form of a line brainly.com/question/1473992Inverse function brainly.com/question/1632445Answer details
Grade: Middle school
Subject: Mathematics
Chapter: Arithemetic preogression
Keywords: Sequence, series, arithmetic , arithmetic sequence, arithmetic series, common difference, sum of series, pattern, arithmetic pattern, progression, arithmetic progression, successive terms.
Answer:
The total length of all 10 movies is 780 minutes.
Further Explanation:
Arithmetic Sequence: A sequence of numbers in which difference of two successive numbers is constant.
The sum of n terms of an arithmetic sequence is given by the formula,
[tex]S_n=\dfrac{n}{2}[2a+(n-1)d][/tex]
Where,
a is the first term of the sequence. d is a common difference.n is number of terms[tex]S_n[/tex] is sum of n terms of the sequence.The first movie is 60 minutes long. This would be the first term of the sequence.
Thus, First term, a= 60 minutes
A new movie is released each year for 10 years. In 10 years total 10 movies will released.
Thus, Number of terms, n=10
Each movie is 4 minutes longer than the last released movie. It means the difference of length of two successive movie is 4 minutes.
Thus, Common difference, d=4
Using the sum of arithmetic sequence formula, the total length of all 10 movies is,
[tex]S_{10}=\dfrac{10}{2}[2\cdot 60+(10-1)\cdot 4][/tex]
[tex]S_{10}=\dfrac{10}{2}[2\cdot 60+9\cdot 4][/tex] [tex][\because 10-1=9][/tex]
[tex]S_{10}=\dfrac{10}{2}[120+36][/tex] [tex][\because 2\cdot 60=120\text{ and }9\cdot 4=36][/tex]
[tex]S_{10}=\dfrac{10}{2}\times 156[/tex] [tex][\because 120+36=156][/tex]
[tex]S_{10}=5\times 156[/tex] [tex][\because 10\div 2=5][/tex]
[tex]S_{10}=780[/tex] [tex][\because 5\times 156=780][/tex]
Therefore, The total length of all 10 movies is 780 minutes
Learn more:
Find nth term of series: https://brainly.com/question/11705914
Find sum: https://brainly.com/question/11741302
Find sum of series: https://brainly.com/question/12327525
Keywords:
Arithmetic sequence, Arithmetic Series, Common difference, First term, AP progression, successive number, sum of natural number.
[tex] \frac{7}{15 \frac{17}{22} \frac{22}{37} \frac{5}{17} [/tex]
greatest to least
first off, is noteworthy that on the denominators, 17 and 37 are prime numbers, so we can't quite factor them, and denominators of 15 and 22, have no common factors so the LCD of all denominators is simply their product, 15*22*37*17.
what we do is, turn all fractions with the same denominator, so they all represent the same division of the whole, and from there we can simply look at which numerator is larger or smaller to sort them.
we'll do so by using the LCD of all denominators, and dividing the LCD by each denominator, our quotient we'll use to multiply the fraction, let's do so
[tex]\bf \cfrac{7}{15} \qquad \cfrac{17}{22}\qquad \cfrac{22}{37} \qquad \cfrac{5}{17}~\hspace{5em} \stackrel{\textit{so the LCD for those denominators is}}{15\cdot 22\cdot 37\cdot 17\implies 207570} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf \stackrel{207570\div 15 ~=~ 13838}{\cfrac{7\cdot 13838}{15\cdot 13838}}\qquad \stackrel{207570\div 22 ~=~ 9435}{\cfrac{17\cdot 9435}{22\cdot 9435}}\qquad \stackrel{207570\div 37 ~=~ 5610}{\cfrac{22\cdot 5610}{37\cdot 5610}}\qquad \stackrel{207570\div 17 ~=~ 12210}{\cfrac{5\cdot 12210}{17\cdot 12210}} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf \cfrac{96866}{207570}\qquad \cfrac{160395}{207570}\qquad \cfrac{123420}{207570}\qquad \cfrac{61050}{207570} \\\\\\ \stackrel{\textit{and if we sort them from greatest to least}}{\cfrac{160395}{207570}\qquad \cfrac{123420}{207570}\qquad \cfrac{96866}{207570}\qquad\cfrac{61050}{207570}}[/tex]
One-fourth of the 48 people at the pool had on blue swimsuits. How many people had on blue swimsuits?
Answer:
12
Step-by-step explanation:
48 x 1/4
Multiply the total number of people by 1/4:
48 x 1/4 = 48/4
Simplify by dividing 48 by 4:
48 / 4 = 12
12 people had blue swimsuits.
Write an equation and solve. Round to the nearest hundredth where necessary.
ssential
44 is 11% of what number?
44 is 11% of 400. To find the number that 44 is 11% of, you divide 44 by 0.11.
The question asks for an equation to represent the scenario where 44 is 11% of a number. In algebraic terms, this is represented as:
44 = 0.11 times x
To find x, divide both sides of the equation by 0.11:
x = 44 / 0.11
Calculating this gives us x = 400, which means that 44 is 11% of 400.
For certain workers, the mean wage is $5.00/hr, with a standard deviation of $0.25. If a worker is chosen at random, what is the probability that the workers wage is between $4.25-$5.75. Assume a normal distribution of wages.
Answer:
The probability is 0.9973 or 99.73%
Step-by-step explanation:
* Lets explain how to solve the problem
- For the probability that a < X < b (X is between two numbers, a and b),
convert a and b into z-scores and use the table to find the area
between the two z-values.
- Lets revise how to find the z-score
- The rule the z-score is z = (x - μ)/σ , where
# x is the score
# μ is the mean
# σ is the standard deviation
* Lets solve the problem
- For certain workers, the mean wage is $5.00/hr, with a standard
deviation of $0.25
∴ μ = 5 and σ = 0.25
- The worker wage is between $4.25 and $5.75
∴ 4.25 < X < 5.75
∵ z = (x - μ)/σ
∴ z = (4.25 - 5)/0.25 = -0.75/0.25 = -3
∴ z = (5.75 - 5)/0.25 = 0.75/0.25 = 3
- Use the z table to find the corresponding area
∵ P(z > -3) = 0.00135
∵ P(z < 3) = 0.99865
∴ P(-3 < z < -2) = 0.99865 - 0.00135 = 0.9973
∵ P(4.25 < X < 5.75) = P(-3 < z < 3)
∴ P(4.25 < X < 5.75) = 0.9973 = 99.7%
* The probability is 0.9973 or 99.73%
Using the z-score method, we found that there is approximately a 99.74% chance that a randomly chosen worker's wage is between $4.25 and $5.75, given the wages follow a normal distribution.
To determine the probability that a randomly chosen worker's wage is between $4.25 and $5.75 when the mean wage is $5.00/hr with a standard deviation of $0.25, we'll use the properties of the normal distribution. First, we need to convert the wages into z-scores, which are measures of how many standard deviations away from the mean a value is.
To find the z-score for $4.25: Z = (4.25 - 5.00) / 0.25 = -3. To find the z-score for $5.75: Z = (5.75 - 5.00) / 0.25 = 3. Using these z-scores, we can look up the corresponding probabilities in a standard normal distribution table or use a calculator equipped with a normal distribution function.
The probability of a z-score between -3 and 3 is approximately 0.9974, meaning there is about a 99.74% chance that a randomly chosen worker's wage is between $4.25 and $5.75, given the distribution of wages is normal.
A recipe calls for 2/3 of a cup of milk. Zeinab wants to make 1/4 of the original recipe. How many cups of milk does Zeinab need?
Answer:
1/6 of a cup of milk. Or at least that's my answer.
Step-by-step explanation:
Okay, we need to find out 25% of 2/3.
25% of 2/3 is 1/6.
To find out how much milk Zeinab needs for 1/4 of the original recipe, multiply 2/3 of a cup by 1/4. The answer is 1/6 of a cup of milk.
Detailed Explanation:
To find out how much milk Zeinab needs, we need to calculate 1/4 of the original amount of milk. The original recipe requires 2/3 of a cup of milk.
Start with the original amount: 2/3 of a cup of milk.
Multiply this amount by 1/4 to find the reduced quantity:
Multiply the fractions: 2/3 * 1/4
Simplify the result, which is 1/6 of a cup of milk.
So, Zeinab needs 1/6 of a cup of milk to make 1/4 of the original recipe.
Hence 1/6 of a cup of milk is required
What is the midpoint of the segment shown below?
Answer:
D. (-7/2, 3/2)
Step-by-step explanation:
x = (-6+(-1))/2 = -7/2
y = (-2+5)/2 = 3/2
Answer: D.
[tex](\dfrac{-7}{2},\ \dfrac{3}{2})[/tex]
Step-by-step explanation:
The coordinates of mid point (x,y) of a line joining points [tex](x_1 , y_1)[/tex] and [tex](x_2, y_2)[/tex] is given by :-
[tex]x=\dfrac{x_1+x_2}{2},\ y=\dfrac{y_1+y_2}{2}[/tex]
From the given graph , we can see that the line is joining two points (-6,-2) and (-1,5) .
Then, the mid point of the line is given by :-
[tex]x=\dfrac{-6+(-1)}{2},\ y=\dfrac{-2+5}{2}[/tex]
[tex]x=\dfrac{-6-1}{2},\ y=\dfrac{5-2}{2}[/tex]
[tex]x=\dfrac{-7}{2},\ y=\dfrac{3}{2}[/tex]
Hence, the midpoint of the given segment = [tex](\dfrac{-7}{2},\ \dfrac{3}{2})[/tex]
The system of equations y = –2x + 1 and y = x + 5 is shown on the graph below. Which statement is true about the solution to the system of equations?
A. The x-value is between –1 and –2, and the y-value is between 3 and 4.
B. The x-value is between 3 and 4 , and the y-value is between –1 and –2.
C. The x-value is between 1 and 2, and the y-value is between –3 and –4.
D.The x-value is between –3 and –4, and the y-value is between 1 and 2.
Answer:
the answer is a
Step-by-step explanation:
y = -2x +1
y = x + 5
-2x+1=x+5
-3x = 4
x= -4/3
y = -1 1/3 + 5= 3 2/3
What is the range of the function f(x) = 4x + 9, given the domain D = {4, -2, 0, 2}?
O A. R = {-17, -9, -1, 17)
OB. R= {1, 7, 9, 17)
C. R=17, -1, 9, 17)
OD. R= {-7, 1, 9, 17}
For this case we have that by definition, the domain of a function is given by all the values for which the function is defined.
While the range of the function is the set of all the values that [tex]f (x)[/tex] takes.
We have the following function:
[tex]f (x) = 4x + 9[/tex]
We evaluate in the domain:
[tex]f (-4) = 4 (-4) + 9 = -16 + 9 = -7\\f (-2) = 4 (-2) + 9 = -8 + 9 = 1\\f (0) = 4 (0) + 9 = 0 + 9 = 9\\f (2) = 4 (2) + 9 = 8 + 9 = 17[/tex]
ANswer:
{-7,1,9,17}
Please help!!! How do I solve questions 4 and 5?
Answer:
[tex]\large\boxed{4.\ V=\dfrac{33.64\pi x}{3}\approx35.21x}\\\boxed{5.\ V=21\ cm^3}[/tex]
Step-by-step explanation:
4.
The formula of a volume of a cone:
[tex]V=\dfrac{1}{3}\pi r^2H[/tex]
r - radius
H - height
We have
[tex]2r=11.6\to r=5.8,\ H=x[/tex]
Substitute:
[tex]V=\dfrac{1}{3}\pi(5.8^2)x=\dfrac{1}{3}\pi(33.64)x=\dfrac{33.64\pi x}{3}[/tex]
[tex]\pi\approx3.14[/tex]
[tex]V\approx\dfrac{(33.64)(3.14)x}{3}\approx35.21x[/tex]
5.
The formula of a volume of a pyramid:
[tex]V=\dfrac{1}{3}BH[/tex]
B - base area
H - height
In the base we have the square. The formula of an area of a square with side s:
[tex]A=s^2[/tex]
We have
[tex]s=3cm,\ H=7\ cm[/tex]
[tex]B=3^2=9\ cm^2[/tex]
[tex]V=\dfrac{1}{3}(9)(7)=(3)(7)=21\ cm^3[/tex]
Solve this inequality
[tex]3b-7<32\\3b<39\\b<13[/tex]
Elen deposited $2,500 into a savings account that earns 5% interest per year. Her friend's bank offerS a 6% annual interest rate. How much more money would Ellen's money have earned in one year if she had deposited her money at her friend's bank?
Answer:
Ellen's money would have earned $25 more than her money at her account
Step-by-step explanation:
* Lets explain how to solve the problem
- The simple Interest Equation (Principal + Interest) is:
A = P(1 + rt) , Where
# A = Total amount (principal + interest)
# P = Principal amount
# r = Rate of Interest per year in decimal r = R/100
# t = Time period involved in months or years
* Lets solve the problem
- Ellen deposited $2,500 into a savings account that earns 5% interest
per year
- Her friend's bank offers a 6% annual interest rate
* Lets calculate her money after 1 year in each account
# Her account
∵ P = $2500
∵ r = 5/100 = 0.05
∵ t = 1
∵ A = P(1 + rt)
∴ A = 2500(1 + 0.05 × 1) = 2500 (1.05) = 2625
* Her money would be $2625 in one year
# Her friend's account
∵ P = $2500
∵ r = 6/100 = 0.06
∵ t = 1
∵ A = P(1 + rt)
∴ A = 2500(1 + 0.06 × 1) = 2500 (1.06) = 2650
* Her money would be $2650 in one year
∵ 2650 - 2625 = 25
∴ Ellen's money would have earned $25 more than her money at her
account
if squar root of x-5 is 15 what is the value of x
Answer:
x = 230
Step-by-step explanation:
Given
[tex]\sqrt{x-5}[/tex] = 15 ( square both sides )
x - 5 = 15² = 225 ( add 5 to both sides )
x = 230
What is the base length of a parrellelogram with an area of 33.75 square meters and a height of 3 meters
Answer:
b = 11.25m
Step-by-step explanation:
The base length of a parrellelogram with an area of 33.75 square meters and a height of 3 meters is 11.25 meters.
Answer:
11.25 m
Step-by-step explanation:
area of parallelogram = base x height
so base = area/height
we substitute the values :
base = 33.75/3
= 11.25
quick!!!
The admission fee to a zoo is $1.20 for children and twice as much for
adults. If twice as many adults as children visited the zoo and the total
admission fee collected was $1 944, how many people visited the zoo?
Answer:
324 children, and648 adults.That's 972 people in total.
Step-by-step explanation:
Here's how to solve this problem by setting up an equation with a single unknown.
Let the number of children that visited the zoo be [tex]x[/tex].
There are twice as many adults as children. So the number of adults will be [tex]2x[/tex].
Each child's ticket costs [tex]\$1.20[/tex]. The [tex]x[/tex] children will contribute a total of [tex]1.20 x[/tex] dollars to the total admission fee.
Each adult's ticket costs twice as much as a child's ticket. That's [tex]2\times \$1.20 = \$2.40[/tex]. The [tex]2x[/tex] adults will contribute a total of [tex]2.40\times 2x =4.80x[/tex] dollars to the total admission fee.
However,
[tex]\begin{aligned}&\text{Admission fee from children} \\+&\text{Admission fee from adults} \\ = &\text{Total Admission fee collected}\end{aligned}[/tex].
In other words,
[tex]1.20x + 4.80x = 1944[/tex].
[tex]6x = 1944[/tex].
[tex]\displaystyle x = \frac{1944}{6} = 324[/tex].
In other words, [tex]324[/tex] children visited the zoo. Twice as many adults visited the zoo. That's [tex]2x = 648[/tex] adults. [tex]324 + 648 = 972[/tex] people visited the zoo in total.
NEED HELP WITH THIS ASAP
Answer:
First one.
Step-by-step explanation:
You don't need the diagram.
You need the congruence statement.
In a congruence statement, it tells you the correspond parts (the congruent parts).
Angle T = Angle L because T and L are both in 2nd position.
Segment TD=Segment SG is false because while D and G share the same position, T and S don't.
Segment MT=Segment GL is false because M and G do not share the same position while T an L do.
Use the order. The order does matter.
Answer:
Step-by-step explanation:First one.
Step-by-step explanation:
You don't need the diagram.
You need the congruence statement.
In a congruence statement, it tells you the correspond parts (the congruent parts).
Angle T = Angle L because T and L are both in 2nd position.
Segment TD=Segment SG is false because while D and G share the same position, T and S don't.
Segment MT=Segment GL is false because M and G do not share the same position while T an L do.
Use the order. The order does matter.
Read more on Brainly.com - https://brainly.com/question/12951285#readmore
what is the equation of a line that contains the points 5,0 and 5, -2
x=5
x=0
y=0
y=5
Check the picture below.
Answer: X=5
Step-by-step explanation: i took the FLVS test
A couch regularly sells for $840. The sales price is $714. Find the percent decrease of the sales price from the regular price. Work out the problem plz
Answer: 15%
Step-by-step explanation: i just subtracted 714 from 840 then i started by multiplying by 10% and increasing until it gave me 126 which is what you get from subtracting 714 from 840
A given data set has a symmetrical shape.
Which statement is true about the data set?
It cannot be determined if the mean is greater than, less than, or equal to the median.
The mean is less than the median.
The mean is greater than the median.
The mean is equal to the median.
Answer:
The mean is equal to the median.
Step-by-step explanation:
Median is the middle value of a given data set. In a symmetric distribution, the data on the left side of the median is equal to the data on the right side of the median. Therefore, the mean of that data is equal to the median of the symmetric distribution.
Answer:
the mean is less than the explanation
Step-by-step explanation:
I just checked
Which graph is the graph of this fucntion
Graph C
Step-by-step explanation:This is a piecewise-defined function because it is defined by two equations over a specified domain and this domain is [tex][0,5][/tex]. The first function comes from the pattern of the square root function [tex]f(x)=\sqrt{x}[/tex] and the second one is a linear function.
The graph of [tex]3\sqrt{x+1}[/tex] has been shifted one unit to the left of [tex]f(x)=\sqrt{x}[/tex] and stretched vertically where each y-value is multiplied by 3.
Moreover, we can prove that:
The graph of [tex]3\sqrt{x+1}[/tex] passes through points (0,3) and (3,6):
[tex]y= 3\sqrt{x+1} \\ \\ \\ \bullet \ (0,3): \\ \\ let \ x=0: \\ \\ y= 3\sqrt{0+1} \therefore y=3\sqrt{1} \therefore y=3(1) \therefore y=3 \\ \\ \\ \bullet \ (3,6): \\ \\ let \ x=3: \\ \\ y= 3\sqrt{3+1} \therefore y=3\sqrt{4} \therefore y=3(2) \therefore y=6[/tex]
It passes through these points.
The graph of [tex]5-x[/tex] passes through points (5,0) and (3,2):
[tex]y=5-x \\ \\ \\ \bullet \ (5,0): \\ \\ let \ x=5: \\ \\ y=5-0 \therefore y=5 \\ \\ \\ \bullet \ (3,2): \\ \\ let \ x=3: \\ \\ y=5-3 \therefore y=2[/tex]
It passes through these points.
____________________
Finally, the graph is shown bellow and matches Graph C.Let p: x<-3
Let q: x > 3
What is represented by p V q?
The symbol [tex]\lor[/tex], from the latin "vel", which means "or", is indeed the logical "or" operator.
This operator puts together two statements A and B, and [tex]A\lor B[/tex] is true whenever at least one between A and B is true.
So, in this case, [tex]p \lor q[/tex] is true whenever either p is true, or q is true, or both are true.
So, every number which is less than -3 or more than 3 makes [tex]p \lor q[/tex] true.
Mathematically, this is the same as claiming that [tex]|x|>3[/tex]
A pair of parallel lines is cut by a transversal:
What is the measure of angle x?
Answer:
40 degrees
Step-by-step explanation:
The alternate interior angles are equal when parallel lines are cut by transversal.
Basically the angle 70 would be equal to the 2 angles (x and 30). Thus we can say:
70 = 30 + x
x = 70 -30
x = 40
Hence x is 40 degrees
I need help with letters (D) and (E). My model equation from letter (C) is: P = -55/4 t+ 340.
Answer:
(a) The two ordered pairs are (0 , 340) and (4 , 285)
(b) The slope is m = -55/4
The slope means the rate of decreases of the owl population was 55/4
per year (P decreased by 55/4 each year)
(c) The model equation is P = -55/4 t + 340
(d) The owl population in 2022 will be 216
(e) At year 2038 will be no more owl in the park
Step-by-step explanation:
* Lets explain how to solve the problem
- The owl population in 2013 was measured to be 340
- In 2017 the owl population was measured again to be 285
- The owl population is P and the time is t where t measure the numbers
of years since 2013
(a) Let t represented by the x-coordinates of the order pairs and P
represented by the y-coordinates of the order pairs
∵ t is measured since 2013
∴ At 2013 ⇒ t = 0
∵ The population P in 2013 was 340
∴ The first order pair is (0 , 340)
∵ The time from 2013 to 2013 = 2017 - 2013 = 4 years
∴ At 2017 ⇒ t = 4
∵ The population at 2017 is 285
∴ The second order pair is (4 , 285)
* The two ordered pairs are (0 , 340) and (4 , 285)
(b) The slope of any lines whose endpoints are (x1 , y1) and (x2 , y2)
is [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
∵ (x1 , y1) is (0 , 340) and (x2 , y2) is (4 , 285)
∴ x1 = 0 , x2 = 4 and y1 = 340 , y2 = 285
∴ [tex]m = \frac{285-340}{4-0}=\frac{-55}{4}[/tex]
* The slope is m = -55/4
∵ The slope is negative value
∴ The relation is decreasing
* The slope means the rate of decreases of the owl population was
55/4 per year (P decreased by 55/4 each year)
(c) The linear equation form is y = mx + c, where m is the slope and c is
the value of y when x = 0
∵ The population is P and represented by y
∵ The time is t and represented by t
∴ P = mt + c , c is the initial amount of population
∵ m = -55/4
∵ The initial amount of the population is 340
∴ P = -55/4 t + 340
* The model equation is P = -55/4 t + 340
(d) Lets calculate the time from 2013 to 2022
∵ t = 2022 - 2013 = 9 years
∵ P = -55/4 t + 340
∴ P = -55/4 (9) + 340 = 216.25 ≅ 216
* The owl population in 2022 will be 216
(e) If the model is accurate , then the owl population be be zero after
t years
∵ P = -55/4 t + 340
∵ P = 0
∴ 0 = -55/4 t + 340
- Add 55/4 t to both sides
∴ 55/4 t = 340
- Multiply both sides by 4
∴ 55 t = 1360
- Divide both sides by 55
∴ t = 24.7 ≅ 25 years
- To find the year add 25 years to 2013
∵ 2013 + 25 = 2038
* At year 2038 will be no more owl in the park
Classify this polynomial 5x^2 +3
Answer:
Degree is 2 so it is a quadratic.
The number of terms is 2 so it is a binomial.
It is a binomial quadratic.
Step-by-step explanation:
Let's find the degree of the polynomial first. I'm going to consider first the degrees of 5x^2 and 3.
The degree of the monomial 5x^2 is 2 because x is the only variable and it's exponent is 2.
The degree of the monomial 3 is 0 because there is no variable.
The degree of 5x^2+3 is therefore 2 because that is the highest degree of the monomials contained with in this polynomial 5x^2+3.
Degree 2 has a special name.
The special name for a degree 2 polynomial is quadratic.
Let's look at the number of terms in 5x^2+3.
Terms are separated by addition and subtraction symbols so there are two terms.
There is a special name for a two-termed polynomial, it is binomial.
So this is the following information I collected on our given polynomial:
Degree is 2 so it is a quadratic.
The number of terms is 2 so it is a binomial.
It is a binomial quadratic.
The question asks, "Find the equation of the ellipse with the following properties.
The ellipse with x-intercepts (5, 0) and (-5, 0); y-intercepts (0, 3) and (0, -3)."
I know that the equation for an ellipse is x^2/a^2+ y^2/b^2=1 but I have no idea how to create the equation given x-intercepts and y-intercepts. Please help! Thank you.
Answer:
x^2 / 25 + y^2 / 9 = 1
Step-by-step explanation:
The major axis is along the x axis and the minor axis is on the y axis.
Major axis = 2a = 5--5 =10 so a = 5 and a^2 = 25.
Similarly b^2 = 3^2 = 9.
Answer:
[tex]\frac{x^2}{25}+\frac{y^2}{9}=1[/tex]
Step-by-step explanation:
Equation of ellipse is of form [tex]\frac{x^2}{a^2}+\frac{y^2}{b^2}=1[/tex] where [tex](a,0) , (-a,0)[/tex] are the x-intercepts and [tex](0,b) , (0,-b)[/tex] are the y-intercepts . If [tex]a > b[/tex] then it is a horizontal ellipse and if [tex]a < b[/tex] then it is a vertical ellipse .
For horizontal axis ,
Here, [tex](a,0) , (-a,0)[/tex] are known as the vertices of ellipse and [tex](0,b) , (0,-b)[/tex] are the co-vertices of ellipse .
Horizontal axis is known as the major axis and vertical axis is known as the minor axis .
Here, x-intercepts are [tex](5,0) , (-5,0)[/tex] , take a = 5
y-intercepts are [tex](0,3) , (0,-3)[/tex] , take b = 3
As [tex]a > b[/tex] , it is a horizontal ellipse .
On putting a = 5 and b = 3 , we get equation as
[tex]\frac{x^2}{5^2}+\frac{y^2}{3^2} =1\\ \frac{x^2}{25}+\frac{y^2}{9} =1[/tex]
21,42,126,504 If it is a geometric sequence, choose the common ratio. If it is not a geometric sequence, choose "not geometric.
Answer:
Not geometric
Step-by-step explanation:
In a geometric sequence, each term is multiplied by a common ratio to get the next term.
So if this is a geometric sequence, then dividing each term by the one before it should result in the same common ratio.
42 / 21 = 2
126 / 42 = 3
504 / 126 = 4
The ratios are different. This is not a geometric sequence.
Answer:
Some tips for the future, when trying to find if its arithmetic or geometric sequence we can do this to find the common ratio. Arithmetic; subtraction test Geometric; division test
Ex; 19, 25, 31, 37
Subtract-
37-31= 6
31-25= 6
25-19= 6
6 is the common difference for this arithmetic sequence
Ex; 4, 8, 16, 32
Divide-
32/16= 2
16/8= 2
8/4= 2
The common ratio for the geometric sequence is 2
Step-by-step explanation:
21, 42, 126, 504
504/126= 4
126/42= 3
42/21= 2
This is not a geometric sequence, there is no common ratio.
What is the slope shown in the graph (-3,2) (-1,-1)
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\text{The formula is:}\dfrac{\huge\text{y}_2-\text{y}_1}{\text{x}_2-\text{x}_1}[/tex]
[tex]\huge\text{y}_2\huge\text{ = -1}\\\\\huge\text{y}_1\huge\text{ = 2}[/tex]
[tex]\huge\text{x}_2\huge\text{ = -1}\\\\\huge\text{x}_1\huge\text{ = -3}[/tex]
[tex]\dfrac{-1 -2 }{-1 - (-3)}[/tex]
[tex]\huge\text{-1 - 2 = -3}[/tex]
[tex]\huge\text{-1 - (-3) = 2 }[/tex]
[tex]\boxed{\boxed{\huge\text{Answer: }\dfrac{-3}{2}}}\huge\checkmark[/tex]
[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{LoveYourselfFirst:)}[/tex]
ABC paint company needs to paint the outside of the building shown. They will also need to paint the roof. What is the surface area that needs to be painted?
3,100 ft^2
4,600 ft^2
4,100 ft^2
4,300 ft^2
Answer:
3,100 ft^2
Step-by-step explanation:
Answer:
3,100 ft^2
Step-by-step explanation:
I am having trouble with this question, can anyone help? This is for Geometry.
Answer:
by geometry rules
for a triangle
external angle of a triangle is equal to the sum of two internal angle of the triangle ( other than external adjacent angle)
m<1= sum of m<2 and m<3
m<1= m<1+<2
m<1 = 31+72
m<1= 103
hope you are clear now !
Answer:
The correct answer is last option. 103
Step-by-step explanation:
Points to remember
Sum of any two angles of a triangle is equal to the exterior angle of the third angle
To find the measure of <1
It is given that m<2 = 31° and m< 3 = 72°
From the figure we can see that <2 and <3 are two angles of a triangle. And <1 is the exterior angle of third angle of same triangle.
Therefore we can write,
m<2 + m<3 = m<1
m<1 = 31 + 72
= 103°
Therefore the correct answer is last option. 103
Calculate 6.7 x 108 times 6.1 x 106 by using scientific notation and the product rule.
Express your answer in scientific notation with the proper number of significant figures.
Write and solve an equation using the constant of proportionality to answer each question.
The ratio between the number of children (c) on a field trip and number of teachers (t) on the trips is 14/3. There are 70 children on the field trip.how many teachers are on the trip?
Answer:
15 teachers
Step-by-step explanation:
Given:
number of children is c
number of teachers is t
[tex]\frac{c}{t}[/tex] = [tex]\frac{14}{3}[/tex] (rearrange)
t = [tex]\frac{3}{14}[/tex] x C
When C = 70,
t = [tex]\frac{3}{14}[/tex] x 70
t = 15 teachers
Answer:
[tex] \frac{c}{t } = \frac{14}{3} [/tex]
as c=70 so put value of c in above formula we get
[tex] \frac{70}{t} = \frac{14}{3} [/tex]
by cross multiplication
[tex]70 \times 3 = 14t[/tex]
[tex]210 = 14t[/tex]
[tex] \frac{210}{14} = t[/tex]
t=15
i hope u will understand