Answer:
10 weeks
Step-by-step explanation:
Create a system of equations demonstrating Roshaun and Keegan's savings.
Roshaun: 150 + 10x Keegan: 0 + 25xLet x equal the number of weeks they save their money.
In order to calculate how many weeks they will have the same amount of money saved, we need to set their equations equal to each other and solve for x.
150 + 10x = 25xSubtract 10x from both sides of the equation.
150 = 15xDivide both sides of the equation by 15.
x = 10In 10 weeks, Roshaun and Keegan will have the same amount of money.
Eric has 4 lb of blueberries to make into pie. How many pies can Eric make if each pie needs the given amount of blueberries.
Answer:
2 pies because you need 2 lb for each pie
Step-by-step explanation:
4. Mrs. Hodges made 144 muffins for a bake sale. She puts them into tins of 5 muffins each. How many tins of muffins can she make?
The data in the line plot show how many pages each student read last night. Which is the best measure of variability?
A. interquartile range
B. mean
C. median
D. range
Use the expression below to answer the question (8-3)^2 / 5 + 2^3 *7. Which is a correct first step? *
Answer:
25 / 61
Step-by-step explanation:
Given:
(8-3)² / [5 + 2³ × 7]
Computation:
(8-3)² / [5 + 2³ × 7]
(5)² / [5 + 8 × 7]
25 / [5 + 56]
25 / 61
An industrial psychologist consulting with Lara music stores knows that the average number of complaints management receives each month throughout the industry is 6, but the standard deviation is unknown. Twenty of the Lara music stores were randomly selected to record complaints for one month; the mean of this sample was 3 and its standard deviation was 1.5. Using the .05 significance level, is the number of complaints received by Lara music stores different from the number of complaints received by music stores in general
Answer:
Step-by-step explanation:
H0 : μ ≥ 6
H1 : μ < 6
Test statistic :
n = 20
Sample Mean, x = 3
σ = 1.5
Test statistic = (x - μ) ÷ σ/sqrt(n)
Test statistic = (3 - 6) ÷ 1.5/sqrt(20)
Test statistic = - 3 / 0.3354101
Test statistic = −8.944271
Since, sample size is < 30 ;
Obtaining the Critical value using the from T;
Tcritical at 0.05, df = 19 = - 1.729
Tstatistic < Tcritical
−8.944271 < - 1.729
Hence, we reject the Null:
We can conclude that there is significant evidence that the number of complaints received by Lara music store is different from number of complaints received by music stores in general.
need help quick please
Answer:dont lnow sorry. Only if u give me robux
Step-by-step explanation:
Answer: the answer for x is ( x = 2 (y+8) a the
answer for y = x-16\2
The square fountain has an area of 164 meters squared. What is the
length of each side?
Solve a0 = 0, a1 = 1 and an = an−1 + an−2 + 2n , for n ≥ 2. Hints: This one involves a lot more algebra than the problems above. Solving the homogeneous problem will involve using the quadratic formula. The characteristic roots turn out to be 1 ± √ 5 2 (but show the work!). For a particular solution, try an = A2 n . You should find A = 4 (but show the work!). Put those two pieces together to write down the general solution an = A( (1 + √ 5 )/2 )^n + B( (1 − √ 5)/ 2 )^n + 4(2^n ) and the determine the values for A and B by using the two initial conditions, a0 = 0 and a1 = 1. The necessary arithmetic will be somewhat complicated, but not impossible.
Answer:
Hi yes ik I'm not that good at math but wouldn't it be
a n=1∗1 n =1
The first, third and thirteenth terms of an arithmetic sequence are the first 3 terms of a geometric sequence. If the first term of both sequences is 1, determine:
1.) the first three terms of the geometric sequence if r > 1
2.) the sum of 7 terms of the geometric sequence if the sequence is 1, 5, 25
Answer:
The first three terms of the geometry sequence would be [tex]1[/tex], [tex]5[/tex], and [tex]25[/tex].
The sum of the first seven terms of the geometric sequence would be [tex]127[/tex].
Step-by-step explanation:
1.Let [tex]d[/tex] denote the common difference of the arithmetic sequence.
Let [tex]a_1[/tex] denote the first term of the arithmetic sequence. The expression for the [tex]n[/tex]th term of this sequence (where [tex]n\![/tex] is a positive whole number) would be [tex](a_1 + (n - 1)\, d)[/tex].
The question states that the first term of this arithmetic sequence is [tex]a_1 = 1[/tex]. Hence:
The third term of this arithmetic sequence would be [tex]a_1 + (3 - 1)\, d = 1 + 2\, d[/tex]. The thirteenth term of would be [tex]a_1 + (13 - 1)\, d = 1 + 12\, d[/tex].The common ratio of a geometric sequence is ratio between consecutive terms of that sequence. Let [tex]r[/tex] denote the ratio of the geometric sequence in this question.
Ratio between the second term and the first term of the geometric sequence:
[tex]\displaystyle r = \frac{1 + 2\, d}{1} = 1 + 2\, d[/tex].
Ratio between the third term and the second term of the geometric sequence:
[tex]\displaystyle r = \frac{1 + 12\, d}{1 + 2\, d}[/tex].
Both [tex](1 + 2\, d)[/tex] and [tex]\left(\displaystyle \frac{1 + 12\, d}{1 + 2\, d}\right)[/tex] are expressions for [tex]r[/tex], the common ratio of this geometric sequence. Hence, equate these two expressions and solve for [tex]d[/tex], the common difference of this arithmetic sequence.
[tex]\displaystyle 1 + 2\, d = \frac{1 + 12\, d}{1 + 2\, d}[/tex].
[tex](1 + 2\, d)^{2} = 1 + 12\, d[/tex].
[tex]d = 2[/tex].
Hence, the first term, the third term, and the thirteenth term of the arithmetic sequence would be [tex]1[/tex], [tex](1 + (3 - 1) \times 2) = 5[/tex], and [tex](1 + (13 - 1) \times 2) = 25[/tex], respectively.
These three terms ([tex]1[/tex], [tex]5[/tex], and [tex]25[/tex], respectively) would correspond to the first three terms of the geometric sequence. Hence, the common ratio of this geometric sequence would be [tex]r = 25 /5 = 5[/tex].
2.Let [tex]a_1[/tex] and [tex]r[/tex] denote the first term and the common ratio of a geometric sequence. The sum of the first [tex]n[/tex] terms would be:
[tex]\displaystyle \frac{a_1 \, \left(1 - r^{n}\right)}{1 - r}[/tex].
For the geometric sequence in this question, [tex]a_1 = 1[/tex] and [tex]r = 25 / 5 = 5[/tex].
Hence, the sum of the first [tex]n = 7[/tex] terms of this geometric sequence would be:
[tex]\begin{aligned} & \frac{a_1 \, \left(1 - r^{n}\right)}{1 - r}\\ &= \frac{1 \times \left(1 - 2^{7}\right)}{1 - 2} \\ &= \frac{(1 - 128)}{(-1)} = 127 \end{aligned}[/tex].
tan of theta= -12/5 and it’s in quadrant 4
Find the exact values of sin theta/2 and the tan of theta/2
Answer:
sin θ/2 = ± √2/13
Step-by-step explanation:
tan θ = - 12/5 (in quadrant 4) sin θ = - 12/13 and cos θ = 5/13
sin θ/2 = ± (√1 - cos θ) / 2 = ± (√1 - 5/13) / 2 = ± √8/13 / 2 = ± √2/13
tan θ/2 = (1 - cos θ) / sin θ = sin θ / (1 + cos θ)
Let you to calculate the tan θ/2 part by yourself
I give Brainlest !!!!!!!
Answer:
40,000
Step-by-step explanation:
Whats the value c
Pleaseee help
Step-by-step explanation:
the value of x is 20 that's it good luck
Step-by-step explanation:
6c + c + 10 + c + 10 = 180
8c = 160
c = 20
4, 5, 3, 3, 1, 2, 3, 2, 4, 8, 2, 4, 4, 5, 2, 3, 6,2
Find the mean, median, and mode(s) of the data. Which measure best
represents the data? Explain your reasoning.
Soon this is due in 5 minutes
Answer:
Given data:
4, 5, 3, 3, 1, 2, 3, 2, 4, 8, 2, 4, 4, 5, 2, 3, 6,2Put the data in the ascending order:
1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 6, 8Mean, the average:
(1 + 2*5 + 3*4 + 4*4 + 5*2 + 6 + 8)/18 = 3.5Median, average of middle two numbers:
3Mode, the most repeated number:
2 (repeated 5 times)Mean is normally the best measure of central tendency, same applies to this data.
∑∞ n=1 (n^2n)/(1+n)^(3n)
Does it converge or diverge?
What method did you use?
PLEASE HELP
Answer:
Given the series,
∑ ∞ n = 1 − 4 ( − 1 / 2 ) n − 1
I think the series is summation from n = 1 to ∞ of -4(-1/2)^(n-1)
So,
∑ − 4 ( − ½ )^(n − 1). From n = 1 to ∞
There are different types of test to show if a series converges or diverges
So, using Ratio test
Lim n → ∞ (a_n+1 / a_n)
Lim n → ∞ (-4(-1/ 2)^(n+1-1) / -4(-1/2)^(n-1))
Lim n → ∞ ((-4(-1/2)^(n) / -4(-1/2)^(n-1))
Lim n → ∞ (-1/2)ⁿ / (-1/2)^(n-1)
Lim n→ ∞ (-1/2)^(n-n+1)
Lim n→ ∞ (-1/2)^1 = -1/2
Since the limit is less than 0, then, the series converge...
Sum to infinity
Using geometric progression formula
S∞ = a / 1 - r
Where
a is first term
r is common ratio
So, first term is
a_1 = -4(-½)^1-1 = -4(-½)^0 = -4 × 1
a_1 = -4
Common ratio r = a_2 / a_1
a_2 = 4(-½)^2-1 = -4(-½)^1 = -4 × -½ = 2
a_2 = 2
Then,
r = a_2 / a_1 = 2 / -4 = -½
S∞ = -4 / 1--½
S∞ = -4 / 1 + ½
S∞ = -4 / 3/2 = -4 × 2 / 3
S∞ = -8 / 3 = -2⅔
The sum to infinity is -2.67 or -2⅔
Step-by-step explanation: PHEW THAT TOOK A WHILE LOL IM A FAST TYPERIt looks like the series is
[tex]\displaystyle \sum_{n=1}^\infty \frac{n^{2n}}{(1+n)^{3n}} = \sum_{n=1}^\infty \left(\frac{n^2}{(1+n)^3}\right)^n[/tex]
Checking for convergence is most easily done with the (Cauchy) root test for convergence: the infinite series
[tex]\displaystyle \sum_{n=1}^\infty a_n[/tex]
converges absolutely if the limit
[tex]\displaystyle \lim_{n\to\infty} \sqrt[n]{|a_n|} < 1[/tex]
Here we have
[tex]\displaystyle \lim_{n\to\infty} \sqrt[n]{\left|\left(\frac{n^2}{(1+n)^3}\right)^n\right|} = \lim_{n\to\infty} \frac{n^2}{(1+n)^3} = 0 < 1[/tex]
so the given series converges.
I FORGOT IMAGE, please help me solve this!! 100 points!!
Answer:
[tex]\Large \boxed{\sf 384 \ m^2}[/tex]
Step-by-step explanation:
Surface area ⇒ area of 2 triangles + area of 3 rectangles
[tex](8 \times 3 \times 0.5 \times 2)+(20 \times 5 \times 2+20 \times 8)=384[/tex]
Answer:
Surface Area = 384 m²
Step-by-step explanation:
The given figure is a triangular prism.
The surface area of a triangular prism is made up of:
2 congruent triangles (the bases of the prism).3 rectangles.From inspection of the diagram, the dimensions of the triangular bases are:
Base = 8 mHeight = 3 m[tex]\boxed{\begin{aligned}\textsf{Area of a triangle}&=\dfrac{1}{2} \times \sf base \times height\\\\\implies \textsf{Area of triangular base}&=\dfrac{1}{2} \times 8 \times 3\\&=4 \times 3\\&=12\; \sf m^2 \end{aligned}}[/tex]
From inspection of the diagram, there are two congruent rectangles with dimensions:
Length = 20 mWidth = 5 mand one rectangle with dimensions:
Length = 20 mWidth = 8 m[tex]\boxed{\begin{aligned}\textsf{Area of a rectangle}&=\sf width \times length\\\\\implies \textsf{Area of rectangle 1}&=5 \times 20\\&=100\; \sf m^2 \\\\\implies \textsf{Area of rectangle 2}&=8 \times 20\\&=160\; \sf m^2\end{aligned}}[/tex]
Therefore, the total surface area of the given triangular prism is:
[tex]\begin{aligned}\textsf{Total Surface Area}&=\sf 2\;Triangles + 2\;Rectangle\;1+Rectangle\;2\\& = 2 \times 12+ 2 \times100+160\\& = 24+200+160\\& = 224+160\\& = 384\; \sf m^2\\\end{aligned}[/tex]
Find the sum of the finite geometric sequence whose first term is 1.4, whose ratio is 0.5, and which has six terms.
The sum is
(Type an integer or decimal rounded to five decimal places as needed.)
Answer:
2.75632 rounded to 5 decimal places
Step-by-step explanation:
a(r^n-1)/r-1 is the formula for sum of geometric series
where a= first term (1.4)
n= number of terms(6)
r= common ratio(0.5)
The mass of the Sun is about 2 × 10^27 metric tons, or 2 × 10^30 kilograms. How many kilograms are in one metric ton?
Answer:
[tex]\frac{2 * 10^{30} }{2 * 10^{27} } = 10^{3} kg[/tex]
Two cities on a map are 3 3/4 inches apart. Using the scale 1 inch = 12 miles, what is the distance between the cities?
Answer:
45 miles. 3*12 +3/4 *12 =x=>36+9=x=>x= 45.
Rohan bought an almirah for Rs 15,600 and spent Rs 400 on its transportation. The total C.P is __________
From the question,
Rohan bought an almirah for =Rs.13600= cost price
Transportation cost =Rs.400
The total cost price of almirah =Rs.(13600+400)
The total cost price of almirah =Rs.(13600+400)=Rs.14000
He sold it for =Rs.16800= selling price
By comparing SP and CP=SP>CP, so there is a gain
Gain=SP−CP
=16800−14000
=Rs.2800
Gain %={(gain/CP)×100}
={(2800/14000)×100}
={2800/140}
=20%
Assume that a fair die is rolled. The sample space is {1, 2, 3, 4, 5, 6) and all outcomes
are equally likely. P(less than 5)
Emily has two peaches. One peach has a mass of 107 grams, and the other has a mass of 193 grams what is the difference mass in the peaches?
find area and perimeter
Answer:
Perimeter
P = P1+P2
P1 = 4a P2=2(a+b)
P1=4*5 P2=2(3+5)
P1=20 P2=2*8
P2=16
P = 20+16
P=36
Area
A=A1+A2
A1=[tex]a^{2}[/tex] A2=a*b
A1=[tex]5^{2}[/tex] A2=3*5
A1=25 A2=15
A=25+15
A=40
A restaurant wants to study how well its salads sell. The circle
graph shows the sales of salads during the past few days. If 5 of
the salads sold were Caesar salads, how many total salads did
the restaurant sell?
Answer:
25
Step-by-step explanation:
20 : 100 = 5 : x
x = (5 x 100) / 20 = 25
Which formula would you enter into D3, and then AutoFill into D4 to D6, to calculate the winning percentage (Pct.) for the teams?
What is the solution to this inequality?
-13x> -39
A. X> 3
B. X<-3
C. X > -3
O
D. x < 3
Answer:
D
Step-by-step explanation:
The answer is D, because when you divide x by a negative the sign changes
When Jeremiah does 7 push-ups and 15 sit-ups, it takes a total of 66 seconds. In comparison, he needs 48 seconds to do 7 push-ups and 9 sit-ups. How long does it take Jeremiah to do each kind of exercise?
Answer:
3.43 seconds to do push ups and 2.66 seconds for him to do sit ups in the given time of 48 seconds ( to find the difference of time of each exercise done in the two different time, subtract each time unit from each other)
Step-by-step explanation:
for him to do 7 push ups and 15 sit ups in 66 seconds it would take time 4.71 second (5 seconds rounded) to do push ups. it would take him 2.20 seconds (2 seconds rounded) for him to do 15 sit ups in 66 seconds. for him to do it in 48 seconds, it would take him 3.43 (3 seconds rounded) to do 7 push ups in 48 seconds. for him to do 9 sit ups in 48 seconds it would take in 2.66 seconds ( 3 seconds rounded) for him to complete them in the given time.
ANSWER CHOICES
a. y=6
b. x=2
c. y=4
d. x=0
Answer:
y=4
Step-by-step explanation:
Answer:
x=2
Step-by-step explanation
x=2 is where you could fold the quadratic function and have the sides overlap perfectly
What is the common difference for this arithmetic sequence?
-6, -2, 2, 6, 10, ...
Answer:
4
Hope it helps
Please mark me as the brainliest
Thank you
common difference = t2 - t1 for all terms.
therefore d = -2 - (-6)
= -2 + 6
= 4
hope it helps :D
3.
Select all the true statements.
A
-6.1 +-7.8 is positive.
B.
-3.2--19) is positive.
C.
12+(-3.5) is negative.
D.
4+-4 is equal to zero.
E.
82 - (-28) is negative.
Answer:
B & D
Step-by-step explanation:
B & D
20% of a is 11. what is a?
Answer:
a=55
Step-by-step explanation:
20%/100=0.2
a=11/0.2
a=55