Answer:
The sum of the first 70 terms of the sequence [tex]-6, -3,0,3,6, ...[/tex] is 6825.
Step-by-step explanation:
A sequence is a set of numbers that are in order.
In an Arithmetic Sequence the difference between one term and the next is a constant.
[tex]-6, -3,0,3,6, ...[/tex] This sequence has a difference of 3 between each number.
The sum of an arithmetic series is found by multiplying the number of terms times the average of the first and last terms.
[tex]S_n=\frac{n}{2}(2a_1+(n-1)d)[/tex]
where [tex]n[/tex] = the number of terms, [tex]a_1[/tex] = the first term, and [tex]d[/tex] = the common difference.
For our arithmetic sequence, the values of a, d and n are:
[tex]a_1 =-6[/tex][tex]d=3[/tex][tex]n = 70[/tex]So:
[tex]S_{70}=\frac{70}{2}(2(-6)+(70-1)3)\\\\S_{70}=35\left(3\left(70-1\right)-2\cdot \:6\right)=35\left(207-12\right)=35\cdot \:195)=6825[/tex]
Shira packs 170 lemon bars in boxes for the bake sale. Each box holds 8 lemon bars. She takes home the lemon bars tha are leg over after she has filled as many boxes as possible. Ahora use partial quotients to find how many boxes of lemon bars she can fill to sell at the bake sale. She finds only two partial quotients when she divides. Use the numbers in the box to answer the questions
1 2 7 8 20 21 23 27 29
Question:
1. How many full boxes of lemon bars can Shira fill?
2. How many delicious lemon bars will she be taking home?
Answer:
1. Number of filled box = 21
2. Number of take home = 2
Step-by-step explanation:
Given
Number of lemon bars = 170
Each bar contains 8 lemon bars
Required
(1) & (2)
To calculate the number of boxes Shira can fill, we simply divide the total number of bars by constituents of each bar .
i.e.
Number of filled box = 170/8
Number of filled box = 21.25
But here, we only need the quotient of the division because it represents the filled boxed.
So,
Number of filled box = 21
Calculating the number of take home.
We'll follow the same steps as (1) above but here, we only need the remainder of the division.
When 170 is divided by 8, the remainder is 2.
So, number of boxes she'll take home is 2.
See calculation below
Number of take home = 170 % 8
Number of take home = 2
What is the equation of the line passing through the points two (2,-1) and (5,-10) in slope intercept form
Answer:
y=-3x+b
Step-by-step explanation:
Find slope
-1-(-10)/2-5
9/-3
-3 is slope
y=-3x+b
substitute (2,-1)
-1=6+b
b=-7
y=-3x-7
A rectangular poster has a length of 24 inches , and it’s width is 12 inches. What is the perimeter of the poster.
Answer:
(24 + 12) x 2 = 72 inches
An mp3 player is on sale for 30% off the regular price of $39.98. How much is the discount?
Answer:
$27.98
Step-by-step explanation:
100 - 30 in price %=70%
Price will be 70% of original regular price
$39.98 * .7 = answer
Answer:
Discount is $11.99
Total is now $27.99
Step-by-step explanation:
To find the discount, you find out what 30% is of 39.98, so you multiply
39.98 x 30%(or .3) = 11.994
39.98- 11.99= 27.99
what does linear regression represent
Step-by-step explanation:
In statistics, linear regression is a linear approach to modeling the relationship between a scalar response (or dependent variable) and one or more explanatory variables (or independent variables). The case of one explanatory variable is called simple linear regression. ... Linear regression has many practical uses.
ead the question and type your response in the box provided. Your response will be saved automatically.
Two expressions are below.
M = 4(2x + 6)
N = 8x + 10
Part A:
Apply the distributive property to write an expression that is equivalent to expression M.
Part B:
Explain whether or not expressions M and N are equivalent for any value of x.
Label your answers to both parts of the problem in the response box.
Answer:
Part A: 8x + 24
Part B: Expressions M and N are not equivalent for any value of x because if you do 8x + 24 = 8x + 10, the 8x will cancel out from both sides and you are left with 24 = 10, which is not true, and therefore has no solution.
Step-by-step explanation:
For Part A, to apply the Distributive Property, you multiple the 4 with both terms in the parentheses. So, you do 4(2x) + 4(6). This expression is equal to 8x + 24.
Hope this helped! :)
Which expression shows a way to find 25% of 1000?
Answer:
25% of 1000 is 250
Step-by-step explanation:
(25 ÷ 100) × 1000
Divide the numbers
0.25 × 1000
0.25 × 1000
Multiply the numbers
250
250
Answer:250
Step-by-step explanation:
25% of 1000
25/100 x 1000
(25x1000)/100
25000/100=250
why isn’t anyone helping me with my worksheet :(
Answer:
because it looks terrifying:( i feel so bad 4 u
please ASAP , giving BRAINLIEST if correct.
Answer:
B. -3(4x + 1) (x - 4)
Step-by-step explanation:
Out of the other answer choices, "B," is the only that factorizes correctly and ends up with the correct factorization (It already gives you the break-down of the trinomial).
However, if you're unsure about the answer, you can always take the end result: -3(4x + 1) (x - 4), and multiply it together to see if you can end up with the original trinomial: [tex]-12x^2 + 45x + 12[/tex]
6³=216. Using exponents, write three expressions whose value is 216.
Please help I don't understand.
9514 1404 393
Answer:
216 = 2³·3³ = 8·3³ = 27·2³
Step-by-step explanation:
6³ = 2·2·2·3·3·3
The string of factors can be grouped however you like, and any repeated factors in the group can be expressed using an exponent.
= 2·2²·3³
= 8·3³
= 6·2²·3²
= 6·6²
= 27·2³
Can somebody please solve this? I'm confused
Answer:
9
Step-by-step explanation:
Not sure if it is right, don't at me :)
what is the value of the rational expression below when x is equal to 4? x+20/x+4
Answer:
3
Step-by-step explanation:
All we need to do here is plug in the number 4 for the variable x. Wherever there's an x, kidnap it and replace it with a 4!
[tex]\frac{x + 20}{x + 4}[/tex]
x = 4
[tex]\frac{4 + 20}{4 + 4}[/tex]
Do the addition.
4 + 20 = 24
4 + 4 = 8
[tex]\frac{24}{8}[/tex]
We can simplify this! What is 24 divided by 8?
24/8 = 3
The answer is 3!
Pls help me I give brainliest y’all thank you
Answer:
V= a^3 = 53 = 125m³
Step-by-step explanation:
Answer:
125 m cubed
Step-by-step explanation:
because length x width x height
* If k, m, and n are all prime numbers, list all factors of k∙m∙n.
Answer:
1 and kmn
Step-by-step explanation:
Prime numbers are numbers that are divisible by themselves only.
Example:
k- 1 and k are the factors
Answer:
1,
k*m*n,
k*m,
m*n,
k*n,
k,
m,
n
Step-by-step explanation:
Based on historical data, your manager believes that 45% of the company's orders come from first-time customers. A random sample of 166 orders will be used to estimate the proportion of first-time-customers. What is the probability that the sample proportion is between 0.24 and 0.35?
Answer: 0.00494.
Step-by-step explanation:
Given : The proportion of the company's orders come from first-time customers. [tex]p=0.45[/tex]
Sample size : n= 166
Now , the probability that the sample proportion is between 0.24 and 0.35 would be :-
[tex]P(0.24<p<0.35)=P\left({\dfrac{0.24-0.45}{\sqrt{\dfrac{0.45(1-0.45)}{166}}}<\dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}}<\dfrac{0.35-0.45}{\sqrt{\dfrac{0.45(1-0.45)}{166}}}}\right)\\\ \ \left[\because z=\dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}}\right][/tex]
[tex]=P(-5.44<z<-2.58)=P(z<-2.58)-P(z<-5.44)\\\\=1-P(z<2.58)-(1-P(z<5.44))\\\\=P(z<5.44)-P(z<2.58)\\\\=1-0.99506\ [\text{By z-value table}]\\\\=0.00494[/tex]
Hence, the probability that the sample proportion is between 0.24 and 0.35 is 0.00494.
5.75 - 1
2
(20 ÷ 2.5) ÷ 2 + 6
Answer:
-48.25
Step-by-step explanation:
You will start by using PEMDAS- Parenthesis-Exponent-Multiplication-Division- Addition-Subtraction
[tex]5.75-12(20/2.5)/2+6\\5.75-12(8)/2+6\\5.75-96/2+6\\5.75-48+6\\5.75-54= -48.25[/tex]
Answer:
48.25 or 9.75
Step-by-step explanation:
5.75-54=48.25
ESSON 3 REFINE
The rectangular prism shown below has a volume of 42 cubic
meters. What is the length of the prism? Show your work
What dim
labeled
prisma
3 m
2 m
Answer:
The length of the prism = 3m
See below for explanation
Step-by-step explanation:
The question is incomplete without the diagram stated in the question.
Since the diagram is missing, I'll show you how you can determine the length of a prism.
Volume of prism = length × width × height = l×w×h
Find attached below the diagram used in solving the question.
From the diagram,
height = 7m
Width = 2m
Given that the volume of prism = 42 cubic meters = 42m³
Length of prism = ?
Inserting the values of the variables:
42 = l×2×7
42 = 14×l
l = 42/14
l = 3
The length of the prism = 3m
find the missing measurement lesson 13.1, 13.2 A=62.5 length is 14 and width is 11 what is the highth.
Answer:
11.36
Step-by-step explanation:
A=1/2*b*h
62.5=1/2*11*x(height)
62.5= 1/2*11*x
62.5=5.5*x
X=62.5/5.5
=11.36
Which statement describes a cause of screwed data
a sample that excludes subjects that are not part of the population being measured.
I don’t understand it
Answer:39.6x + 26.4
Step-by-step explanation:
length=3x+2
Width=13.2
area of rectangle=length x width
area of rectangle=(3x+2) x 13.2
area of rectangle=13.2(3x+2)
area of rectangle=39.6x + 26.4
Answer:
39.6x + 26.4
Step-by-step explanation:
13.2 (3x + 2)
Multiply each term in the parentheses by 13.2.
13.2 × 3x + 13.2 × 2
Multiply the numbers.
39.6x + 13.2 × 2
39.6x + 26.4
39.6x + 26.4
Find the area of the shape
Consider the following proposed proof, which claims to show that every nonnegative integer power of every nonzero real number is 1.
Let r be any nonzero real number, and let P(n) be the equation r ^n = 1.
Show that P(0) is true : P(0) is true because r^0 = 1 by definition of zeroth power.
Show that for every integer k >= 0, if P(i) is true for each integer i from 0 through k, then P(k + 1) is also true:
Let k be any integer with k >= 0 and suppose that r^ i = 1 for each integer i from 0 through k. This is the inductive hypothesis. We must show that r^ k + 1 = 1. Now
r^ k + 1 = r^ k + k - (k - 1) because k + k - (k - 1) = k + 1
r ^k * r^ k / r^ k - 1 by the laws of exponents
1*1 / 1 by inductive hypothesis
=1
Thus r^ k + 1 = 1 [as was to be shown].
[Since we have proved the basis step and the inductive step of the strong mathematical induction, we conclude that the given statement is true.]
Question:
a) Identify the error(s) in the above "proof."
Answer:
The statement is not true. There is an error in the following step:
[tex]\frac{r^{k} * r^{k} }{r^{(k-1)} } = \frac{1 * 1}{1}[/tex]
Step-by-step explanation:
Here is the complete proof:
[tex]r^{k + 1} = r^{k + k - (k - 1)}[/tex] (because k + k - (k - 1) = k + 1)
[tex]= \frac{r^{k} * r^{k} }{r^{(k-1)} }[/tex] (By laws of exponent)
[tex]= \frac{r^{k} * r^{k} }{r^{k} * r^{-1} } }[/tex]
[tex]= \frac{r^{k} * r^{k} * r^{1} }{r^{k}} }[/tex] (Since the power of r is a negative integer i.e. -1 it will shift to the numerator)
[tex]= r^{k} * r^{1}[/tex] (We get this equation after canceling out the similar terms in numerator and denominator in previous step)
[tex]= r^{k + 1} \neq 1[/tex] (Provided r > 1 or r < -1)
Q2:
The figure below is the net of a three-dimensional figure.
If the net is folded along the dashed lines, what three-dimensional figures would it form?
A
rectangular prism
B
cube
C
triangular prism
D
rectangular pyramid
Answer: rectangular prism
Step-by-step explanation:
K.Brew sells a wide variety of outdoor equipment and clothing. The company sells both through mail order and via the internet. Random samples of sales receipts were studied for mail-order sales and internet sales, with the total purchase being recorded for each sale. A random sample of 18 sales receipts for mail-order sales results in a mean sale amount of $74.90 with a standard deviation of $21.75. A random sample of 9 sales receipts for internet sales results in a mean sale amount of $87.30 with a standard deviation of $19.75. Using this data, find the 95% confidence interval for the true mean difference between the mean amount of mail-order purchases and the mean amount of internet purchases. Assume that the population variances are not equal and that the two populations are normally distributed.
Step 1 of 3: Find the point estimate that should be used in constructing the confidence interval.
Step 2 of 3: Find the margin of error to be used in constructing the confidence interval. Round your answer to six decimal places.
Step 3 of 3: Construct the 95% confidence interval. Round your answers to two decimal places.
Answer:
Step-by-step explanation:
Step 1. The point estimate is the difference between the the mean amount of mail-order purchases and the mean amount of internet purchases. It becomes
74.9 - 87.3 = - 12.4
Step 2. The formula for determining margin of error is expressed aa
Margin of error = z√(s1²/n1 + s2²/n2)
Where
z = z score
s1 = sample standard deviation for data 1
s2 = sample standard deviation for data 2
n1 = number of samples in group 1
n2 = number of samples in group 2
For a 95% confidence interval, the z score is 1.96
From the information given,
s1 = 21.75
n1 = 18
s2 = 19.75
n2 = 9
z√(s1²/n1 + s2²/n2) = 1.96√(21.75²/18 + 19.75²/9) = 1.96 × 8.343
= 16.35
Step 3. Confidence interval = (x1 - x2) ± z√(s²/n1 + s2²/n2)
95% Confidence interval = - 12.4 ± 16.35
a hiking trail is 3 4/5 miles long. terence 5/8 of the trail how many miles does terence walk
Answer:
[tex]2.375\,\,miles[/tex]
Step-by-step explanation:
Given: Length of a hiking trail is [tex]3\frac{4}{5}\,\,miles[/tex]
Terence travels [tex]\frac{5}{8}[/tex] of the length of a hiking trail
To find: Distance travelled by Terence
Solution:
Whole numbers refer to natural numbers together with 0.
A fraction represents a part of a whole.
A whole number and a fraction combined into mixed fraction.
Distance travelled by Terence = [tex]\frac{5}{8}(3\frac{4}{5})=\frac{5}{8}(\frac{19}{5})=\frac{19}{5}=2.375\,\,miles[/tex]
Triangle R S T is shown. The length of R S is 9, the length of S T is 8, and the length of R T is s. Angle R S T is 111 degrees. Law of cosines: a2 = b2 + c2 – 2bccos(A) What is the value of s to the nearest whole number? 10 12 13 14
Answer:
bro I think its 14
Step-by-step explanation:
si paps
The length of RT is 14 cm. Therefore, option D is the correct answer.
Given that, RS=9, ST=8, RT=s and ∠RST=111°.
How do you solve cosine rules?The cosine formula to find the side of the triangle is given by: c = √[a²+ b²– 2ab cos C] Where a,b and c are the sides of the triangle.
Here, given a²= b²+ c²– 2bc cos A.
s²= 9²+ 8²– 2×9×8 cos111°
⇒s²=81+64+51.552
⇒s²=197.552
⇒s=14.05≈14 cm
Therefore, option D is the correct answer.
To learn more about cosine rule visit:
https://brainly.com/question/20839703.
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Alex and Annie each have 3 boxes of crayons. each box has 10 crayons. how many crayons do Alex and Annie have in all?
Answer:
60
Step-by-step explanation:
they each have 3 boxes, so you can multiply 3 by 2 to get 6. if each box has 10 crayons, then multiply 6 by 10 to get 60.
The total number of crayons that Alex and Annie have in all will be 30 crayons.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
Alex and Annie each have 3 boxes of crayons. Each box has 10 crayons. Then the total number of crayons is given as,
Total = 3 x 10
Total = 30
The total number of crayons that Alex and Annie have in all will be 30 crayons.
More about the Algebra link is given below.
https://brainly.com/question/953809
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What is the value of LaTeX: 4^{-3}
4
−
3
?
Answer:
1/64
Step-by-step explanation:
[tex]4^{-3}=\dfrac{1}{4^3}=\dfrac{1}{4\cdot 4\cdot 4}=\boxed{\dfrac{1}{64}}[/tex]
Answer:
13
Step-by-step explanation:
=4^-3 . 4 - 3
= 4^-3+1 -3
= 4^-2 -3
= 16-3
= 13
I WILL GIVE BRAINLIEST PLEASE HELP!! Determine whether the given sequence could be geometric, arithmetic, or neither. If possible, identify either the common ratio or the common difference.
−1280, −320, −80, −20, −5, ....
Answer:
geometric, 1/4
Step-by-step explanation:
An arithmetic sequence will have a common difference. A geometric sequence will have a common ratio. If neither of those describes the sequence, it is "neither."
Obviously the difference between numbers in this sequence is decreasing, so this is not an arithmetic sequence.
__
The ratios of adjacent terms are ...
-320/-1280 = -80/-320 = -20/-80 = -5/-20 = 1/4
The sequence is a geometric sequence with a common ratio of 1/4.
16. Each of a group of sealed opaque envelopes contains eight bills. One envelope contains eight $1 bills, one envelope contains eight $5 bills, and one envelope contains four $1 bills and four $5 bills. An envelope is selected at random, and a bill is taken from the envelope at random. If it is a $5 bill, what is the probability that the rest of the bills in the envelope are also $5 bills
Answer:
probability = 1/2
Step-by-step explanation:
Ok probability is the possibility of something happening.
So let's check the chance of $5 appearing according to how it appeared before.
4 envelopes are opened and 8 bills are inside . So total bills are 32 bills
Out of 24 bills 12 are 1$ bill
12 are $ 5 bill.
So it's a fifty fifty chance.
So the probability is 1/2
