Answer:
4 by 5 inch rectangle
Step-by-step explanation:
Answer:
4 by 5 inch rectangle
Step-by-step explanation:
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y=2x+2 y+4=2(x-3)
What is the solution of the system of equations?
Answer: y = 2x + 2
y + 4 = 2 (x − 3)
Note sure but hope this helped!!!
Show that the sum of the first 2n natural numbers is n(2n+1)
Not really sure if there’s a typo in my book or not
Answer:
This sum is the sum of an arithmetic sequence. There is a formula for the sum of an arithmetic sequence which can be looked up or derived by a variety of means.
A nice approach for this sequence is the following. Notice that the sum of first and last number in the sequence is the same as the sum of the second and second last, and also the same as the sum of the third and third last, and so on.
There are n of these pairs. So the desired sum is n x (first number + last number). But the first number is 1 and the last on is 2n. Thus the desired sum is n(1 + 2n).
Hope this helps!!
Mark Brainleast!!!!!!!!!!!
Consider the set {1, 2, 3, 4, ..., m} where m is some natural number, i.e. a positive whole number.
Now let's say we wanted to add everything in that set.
What we can do is write out the terms
1, 2, 3, 4, ..., m
then just underneath, we write the reverse of that set
m, ..., 4, 3, 2, 1
Here's an example of what I mean. I'll use m = 7
\(\begin{array}{|c|c|c|c|c|c|c|} \cline{1-7}1 & 2 & 3 & 4 & 5 & 6 & 7\\\cline{1-7}7 & 6 & 5 & 4 & 3 & 2 & 1\\\cline{1-7}\end{array}\)
For each column, add straight down
The third row will be nothing but 8's
\(\begin{array}{|c|c|c|c|c|c|c|} \cline{1-7}1 & 2 & 3 & 4 & 5 & 6 & 7\\\cline{1-7}7 & 6 & 5 & 4 & 3 & 2 & 1\\\cline{1-7}8 & 8 & 8 & 8 & 8 & 8 & 8\\\cline{1-7}\end{array}\)
We can see there are seven copies of '8' being added here, so the sum of all the numbers in the set {1,2,3,4,5,6,7} is 8*7 = 56. But wait, we double-counted each item when we formed the second row. So we must divide by 2 to fix the double-counting error.
Therefore, 1+2+3+4+5+6+7 = 56/2 = 28 instead.
-----------------------------
That previous example showed that adding from 1 to 7 means we have 7 copies of (1+7). In other words, 7 copies of 8 being added.
We could write that as 7(1+7)
Then divide that by 2 to fix the double-counting error.
We have 7(1+7)/2
Now imagine that we applied all of what was mentioned to the set {1,2,3,4,5,6,7,8}. Instead of 7's, we use 8's this time to get 8(1+8)/2
Then we can extend it out to the set {1,2,3,4,..., m} and we get the formula m(1+m)/2
We have m copies of (1+m) being added; hence the m(1+m). Don't forget to divide by 2 to fix the double-counting error.
-----------------------------
The key takeaway here is that summing 1+2+3+4+...+m gets us m(1+m)/2
In this case, m = 2n because we want the first 2n natural numbers.
Therefore,
m(1+m)/2
2n(1+2n)/2
n(1+2n)
n(2n+1)
represents the sum 1+2+3+...+n+...+2n
-----------------------------
Try out a value like n = 5 to find that 2n = 2*5 = 10, and,
1+2+3+4+5+6+7+8+9+10 = 55
also
n(2n+1) = 5(2*5+1) = 5*(11) = 55
Showing that the formula works for n = 5. I'll let you try other values of n.
researchers wanted to know whether it is better to give the diphtheria, tetanus and pertussis (dtap) vaccine in the thigh or the arm. they collected data by gender. what would be the best statistical test for them to utilize?
The best statistical test for them to utilize is two sample chi square test
Given that,
Diphtheria, tetanus, and pertussis (DTaP) vaccination administration in the thigh vs. arm was the topic of a study. By gender, data was gathered.
To find: Which statistical test would be the most appropriate for them to use
As here there are two independent samples in which each sample represent severe reactions to vaccine based on if shot is on thigh or the arm.
What is two sample chi square test?
Based on binned data, the chi-square two sample test is used. The binning for both data sets should be the same, it should be noted. The chi-square two sample test's fundamental premise is that if the two data samples are drawn from similar distributions, then there should be a similar number of observed points in each bin (adjusted for different sample sizes).
Therefore, two sample chi square test of independence would be best.
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Which ordered pair is the best estimate for the solution of the
system of equations?
y=-1/5x+1
y=x+4
O (-2.25, 1.75)
O (-2.75, 1.25)
O(-2.75, 1.75)
O (-2.5,1.5)
Given y1(t) = t^2 is a solution to: t^2y'' - 4ty' + 6y = 0, t > 0 find another solution using the method of reduction of order.
For a second order differential equation t²y'' - 4ty' + 6y = 0, general solution is of the form y(t) = c₁t² + c₂t³, so another solution other than y₁(t) = t² is y₂(t) = t³.
Given solution to t²y'' - 4ty' + 6y = 0 is
y₁(t) = t²
Using the method of reduction of order, let us assume, y₂(t) = v(t)y₁(t) is a solution to t²y'' - 4ty' + 6y = 0 for suitable choice of v(t). So,
y₂ = vt²
y₂' = 2vt + t²v'
y₂'' = 2v + 2tv' + 2tv' + t²v''
y₂'' = 2v + 4tv' + t²v''
Substituting this
t²×( 2v + 4tv' + t²v'') - 4t×(2vt + t²v') + 6×(vt²) = 0
t⁴v'' = 0
v'' = 0
v' = c, c is a constant
v = ct
Therefore, y₂(t) = ct×t²
y₂ (t) = ct³
Therefore general solution will be y(t) = c₁t² + c₂t³
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what is4=3a-14? .....
Answer:
a=6
Step-by-step explanation:
-3a=-14-4
-3a=-18
a=6
Answer:
The answer is a=6
Step-by-step explanation:
How can you identify and write equivalent expressions?
You can identify equivalent expressions if one of the expressions can be written like the other and it is usually written by combining any like terms on each side of the equation such as x-terms with x-terms and constants with constants.
What is an Equivalent expression?These are the type of expressions that have similar value or worth but do not look the same.
This type of expression can be identified if one of the expressions can be written like the other and example can be seen below:
3(x + 3) and 3x + 9
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Scarlett tried to shade all the factors of 15 on the hundred chart.What mistake did Scarlett make? A.Scarlett shaded the factors of 5 instead of the factors of 15. B.Scarlett did not make a mistake. C.Scarlett shaded the multiples instead of the factors of 15. D.Scarlett shaded 15, but factors are always less than the number.
Answer:
C. Scarlett shaded the multiples instead of the factors of 15
Step-by-step explanation:
Scarlett tried to shade all the factors of 15 on the hundred chart 15,45,75,30,60,90 What mistake did she make
She shaded 15,45,75,30,60,90 on the chart
Factors of 15 are 1, 3, 5 and 15
15, 45, 75, 30, 60, 90 are multiples of 15
That is,
15 × 1 = 15
15 × 3 = 45
15 × 5 = 75
15 × 2 = 30
15 × 4 = 60
15 × 6 = 90
Therefore Scarlett's mistake is:
C. Scarlett shaded the multiples instead of the factors of 15
Geometry, Help Please hurry!!!
In the diagram, ABCD is Similar EFGH. Find the following,
4. Scale Factor
5. EH
6. AB
Scale Factor is equal to \(\frac{2}{3}\). Length of EH is equal to 16 units and length of AB is equal to 9.
4. A scale factor is the ratio of the scales of an original object and a new object.
Scale factor = Ordinated dimension / original dimension
Scale factor = \(\frac{10}{15}\)
Scale factor = \(\frac{2}{3}\) (or) 0.67
5. Length of EH
Scale factor = \(\frac{EH}{AD}\)
\(\frac{EH}{AD}\) = \(\frac{2}{3}\)
\(\frac{EH}{24} = \frac{2}{3}\)
EH = 2 * 8
EH = 16 units
6. Length of AB
Scale factor = \(\frac{EF}{AB}\)
\(\frac{EF}{AB}\) = \(\frac{2}{3}\)
\(\frac{6}{AB} = \frac{2}{3}\)
AB = 3 * 3
AB = 9 units.
Therefore, Scale Factor is equal to \(\frac{2}{3}\). Length of EH is equal to 16 units and length of AB is equal to 9.
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Clara and Toby are telemarketers. Yesterday, Clara reached 4 people in 10 phone calls, while Toby reached 3 people in 8 phone calls. If they continue at those rates, who will reach more people in 40 phone calls? Use the drop-down menu to show your answer.
Answer:
Clara will reach 16 people while Toby will reach 15 calls.
4 out of ten=16 out of 40
3 out of 8=15 out of 40
3х
(2x + 16)
Solve for x
Answer:
16
Step-by-step explanation:
Step 1:
3x = 2x + 16 Equation
Step 2:
3x - 2x = 16 Subtract 2x on both sides
Answer:
x = 16
Hope This Helps :)
the larger of two numbers js 11 more than twice the smaller number. the sum of the number is 1 less than 7 times the smaller number. find the numbers
Answer:
smaller: 3
larger: 27
Step-by-step explanation:
Hope this helps!
of 34 cars in a parking lot 20 are green 8 are gold and the rest are black what are the odds against the next car leaving the lot being black
Answer:
3/17=.18
Step-by-step explanation:
There is a .18 or 3/17 chance that a car leaving will be black.
Please help!
which triangle is similar to ΔABC? and why?
Answer:
neither. one of them is a right triangle, the other lacks and angle of ∆ABC
Step-by-step explanation:
Which statement is true?
A probability of − 1 indicates an event will likely happen.
A probability of 0.4 indicates an event will never happen.
A probability of 0.9 indicates an event will probably not happen.
A probability of 1 indicates an event will definitely happen.
Answer:
Its d
Step-by-step explanation:A probability of 1 indicates an event will definitely happen.
The true statement is D; probability of 1 indicates an event will definitely happen.
What is the probability?Probability refers to a possibility that deals with the occurrence of random events. The probability of all the events occurring need to be 1.
P(E) = Number of favorable outcomes / total number of outcomes
Probability theory, a subfield of mathematics, gauges the likelihood of an occurrence . An event's probability is a number between 0 and 1, where approximately 0 indicates how unlikely the event is to occur and 1 indicates certainty.
It is a numerical representation of the likelihood or likelihood that a particular event will occur, Alternative ways to express probabilities are as percentages from 0% to 100% or from 0 to 1.
The correct statement is D; A probability of 1 indicates an event will definitely happen.
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Find the limit of the function by using direct substitution. Limit as x approaches zero of quantity x squared plus ten. Answer Choices: A) -10 B) Does not exist C) 0 D) 10
Answer:
D
Step-by-step explanation:
So we are given the limit:
\(\lim_{x \to 0} (x^2+10)\)
To figure out this limit, we can use direct substitution. Simply substitute 0 for x and then simplify. Therefore:
\(\lim_{x \to 0} (x^2+10)\\=(0)^2+10\\=0+10\\=10\)
Therefore, the limit equals 10.
FACTORIZE
A(X)=(x+2)^2(-x+2)(2x-1)
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On average, Shawnte drinks of a -ounce glass of water in hour. How much water
does she drink in an hour?
Answer:
a- ounce glass of water.
What is the addition and subtraction rule with significant figures? Please give some specific examples.
When adding or subtracting numbers with significant figures, the result should be rounded to the least precise decimal place of the measurements involved.
How do you round the result when adding or subtracting significant figures?When performing addition or subtraction operations with numbers that have different levels of precision, it is important to ensure that the result is reported with the appropriate number of significant figures.
The rule states that the result should be rounded to the least precise decimal place among the measurements involved in the calculation.
For example, consider the addition of 53.5 and 46.5. Both numbers have one decimal place, so the sum should also be reported with one decimal place.
Adding the numbers gives us 100, but when applying the rule, we round the result to 100.0 to reflect the precision of the original measurements.
Similarly, if we subtracted 46.5 from 53.5, the result would still have one decimal place: 7.0.
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incy length
The pregnancy length in days for a population of new mothers can be approximated by a normal distribution with a mean of 270 days and a standard deviation of 9
days
(a) What is the minimum pregnancy length that can be in the top 12% of pregnancy lengths?
(b) What is the maximum pregnancy length that can be in the bottom 6% of pregnancy lengths?
egnancy len
ution with a
incy length
mean = = 26
(a) The minimum pregnancy length is days
(Round to one decimal place as needed)
(b) The maximum pregnancy length is days.
(Round to one decimal place as needed)
egnancy len
ution with a
ancy length
wer
egnancy len
ution with a
ancy lenath
Enter your answer in each of the answer boxes
e
r
we
DHE
PEEL
S:06 PM
Answer:
(a) 259.5 days
(b) 284 days
Step-by-step explanation:
Let X represent the pregnancy length in days.
It is provided that \(X\sim N(270,9^{2})\).
(a)
Let a represent the minimum pregnancy length that can be in the top 12% of pregnancy lengths.
Then,
P (X < a) = 0.12
⇒ P (Z < z) = 0.12
The corresponding z-score is, z = -1.17.
*Use a z-table.
Compute the value of x as follows:
\(z=\frac{x-\mu}{\sigma}\\\\-1.17=\frac{a-270}{9}\\\\z=270-(9\times 1.17)\\\\z=259.47\\\\z\approx 259.5\)
Thus, the minimum pregnancy length that can be in the top 12% of pregnancy lengths is 259.5 days.
(b)
Let b be the maximum pregnancy length that can be in the bottom 6% of pregnancy lengths.
Then,
P (X > b) = 0.06
⇒ P (X < b) = 0.94
⇒ P (Z < z) = 0.94
The corresponding z-score is, z = 1.56.
*Use a z-table.
Compute the value of x as follows:
\(z=\frac{x-\mu}{\sigma}\\\\1.56=\frac{b-270}{9}\\\\z=270+(9\times 1.56)\\\\z=284.04\\\\z\approx 284\)
Thus, the maximum pregnancy length that can be in the bottom 6% of pregnancy lengths is 284 days.
√2x+27-4 = 1
Solve for x
Answer:
x = -1
Step-by-step explanation:
You want the solution to √(2x +27) -4 = 1.
Radical equationIn general, a radical equation is solved by isolating the radical, then raising the equation to a power that makes the radical disappear. Here, that means we will want to square both sides of the equation after we add 4.
\(\sqrt{2x+27}-4=1\\\\\sqrt{2x+27}=5\qquad\text{add 4}\\\\2x+27=25\qquad\text{square both sides}\\\\2x=-2\qquad\text{subtract 27}\\\\\boxed{x=-1}\qquad\text{divide by 2}\)
The value of x that makes this true is -1.
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18 students are going on a field trip the bus can fit 14 so four of them will have to ride in a car and how many ways can we choose the four students who must ride in the car
Answer:
Number of ways we can choose the four students who must ride in the car = 3060 ways
Step-by-step explanation:
This is a combination question.
The number of selections of "r" objects from the given "n" objects is denoted by;
C(n,r), and is given by;
C(n, r) = n!/[r!(n - r)!]
In this question, n = 18 and r = 4
Thus;
C(18, 4) = 18!/[4!(18 - 4)!]
C(18,4) = 3060
Number of ways we can choose the four students who must ride in the car = 3060 ways
am i right?? this is a graded assignment and no links!!
Answer:
yes
Step-by-step explanation:
an initial population of 765 quail increases at an annual rate of 16%. write an exponential function to model the quail population. what will the approximate population be after 4 years?
An exponential function to model the quail population is y = 765(1+0.16)ⁿ and the approximate population be after 4 years is 1384.65 quails.
Population growth is seen to increase at an exponential rate. We use the following to model this growth.
y = A₀(1 + r)ⁿ
where
y = value at time
A₀ = original value
r = rate of growth
n = time elapsed
An exponential function that models the quail population is set up like:
y = 765(1+0.16)ⁿ
so that, for example, if we wanted to figure out the population at time (4 years), then we would set up the function as follows,
y = 765(1+0.16)⁴
y = 765(1.16)⁴
y = 765* 1.81
to get
y = 1384.65 quails after 4 year has elapsed.
Hence, an exponential function to model the quail population is y = 765(1+0.16)ⁿ and the approximate population be after 4 years is 1384.65 quails.
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Suppose that when your friend was born, your friend's parents deposited $4000 in an account paying 5.4% interest compounded quarterly. What will the account balance be after 13 years?
The balance after 13 years will be $_
(Round to the nearest cent as needed.)
Suppose that when your friend was born, your friend's parents deposited $4000 in an account paying 5.4% interest compounded quarterly therefore the account balance after 13 years will be $8033.
What is Compound interest?This is referred to as the interest on savings calculated on both the initial principal and the accumulated interest from previous periods.
A = P(1 + r/n)^nt.
Amount = $4000 ( 1 + .054/4)^ 4 × 13.
= $4000 (1.0135) ^ 52
= $8033
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Make the mathematical expressions. Simplify them and find the correct answers. a) The total cost of 4 pens at Rs 20 each, 5 pencils at Rs 5 each and 2 boxes at Rs 60 each.
Answer:
Step-by-step explanation:
Cost of 1 pen = 20 rupees
Cost of 4 pens = 20 x 4 = 80 rupees
Cost of 1 pencil = 5 rupees
Cost of 5 pencils = 5 x 5 = 25 rupees
Cost of 1 box = 60 rupees
Cost of 2 boxes = 60 x 2 = 120 rupees
therefore, total cost = 80 + 25 + 120 = 225 rupees
base area - 20 cm
Among these figures, figure
and figure
have the same volume.
It can be inferred that C and D have the same volume.
How to explain the volume?For figures such as B, C, and D, with the top area is the same as the bottom area, the volume is the product of the base area and the height.
The base area of all these figures is the same, so those (among B, C, and D) with the same height have the same volume.
Here, C and D both have a base area of 20 cm² and a height of 5 cm, so both have the same volume.
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A
X
Find the value of x.
B
X+2
D
x = [?]
3
E
2
C
Answer:
Step-by-step explanation:
The segments formed by the parallel lines are proportional segments.
Is dividing by 0.5 the same as dividing by 2?
The dividing by 0.5 is not the same as dividing by 2 , because 0.5 and 2 are different numbers .
Let us understand the Division with the help of example ;
let the number be 10 ;
first we divide the number 10 by 0.5 ;
this can be written mathematically as ⇒ \(\frac{10}{0.5}\) ;
⇒ \(\frac{10}{\frac{1}{2} }\) = \(10\times2\) = 20 ;
So , on dividing 10 by 0.5 , we get the answer as 20 .
Second , the number 10 is divided by 2 ;
this can be written mathematically as ⇒ \(\frac{10}{2}\) ;
⇒ \(\frac{10}{2 }\) = 5 ;
So , on dividing 10 by 2 , we get the answer as 5 .
Therefore , dividing by 0.5 is not same as dividing by 2 .
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Find the period of the function f(x) = cos(2.22x+0.19). Provide four decimal places. Answer:______ Find the period of the function f(x) = sin(1.05x). Provide four decimal places. Answer:______
The period of the function f(x) = cos(2.22x+0.19) is 2.8323 and the period of the function f(x) = sin(1.05x) is 5.9834
The period of a trigonometric function, we use the formula:
Period = 2π/|B|
where B is the coefficient of x in the function.
For the first function, f(x) = cos(2.22x+0.19), the coefficient of x is 2.22. Therefore, the period is:
Period = 2π/|2.22| ≈ 2.8323
For the second function, f(x) = sin(1.05x), the coefficient of x is 1.05. Therefore, the period is:
Period = 2π/|1.05| ≈ 5.9834
So, the period of the first function is 2.83 and the period of the second function is 5.98. Both answers are rounded to four decimal places.
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