After the 4th cut, we will have 1,296 pieces and after the nth cut, we will have [tex]6^{n}[/tex] pieces.
Here, we are given that a sheet of paper is cut into 6 same-size parts. Each of the parts is then cut into 6 same-size parts and so on.
Thus, after one cut we will have 6 pieces
After second cut, we will have 6*6 = 36 pieces
After the third cut, we will have 36*6 = 216 pieces
After the fourth cut, we will have 216*6 = 1,296 pieces
Now, we can clearly see a pattern here. The number of pieces follow a geometric progression with a common ratio of 6.
Thus, after the nth cut, the number of pieces will be-
a[tex]r^{n-1}[/tex]
where a = first term which is 6
and r = common ratio which is also 6
⇒ 6*[tex]6^{n-1}[/tex]
= [tex]6^{n}[/tex]
Thus, after the 4th cut, we will have 1,296 pieces and after the nth cut, we will have [tex]6^{n}[/tex] pieces.
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1. A local zoo had 750 visitors on Saturday. If
20% of the guests traveled from out of town,
how many local guests visited the zoo on
Saturday?
The percentage is calculated by dividing the required value by the total value and multiplying by 100.
Required percentage value = a
total value = b
Percentage = a/b x 100
The number of local guests who visited the zoo is 600.
What is a percentage?
The percentage is calculated by dividing the required value by the total value and multiplying by 100.
Example:
Required percentage value = a
total value = b
Percentage = a/b x 100
Example:
50% = 50/100 = 1/2
25% = 25/100 = 1/4
20% = 20/100 = 1/5
10% = 10/100 = 1/10
We have,
Total number of visitors = 750
The percentage that visited the zoo.
= 100% - 20%
= 80%
Now,
The number of local guests who visited the zoo.
= 80% of 750
= 80/100 x 750
= 600
Thus,
The number of local guests who visited the zoo is 600.
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5 years ago muskam was twice as old as sesay .if the sum of their ages is 100 find sesay present age
The present age of Sesay is found as the 35 years.
Explain the term twice of the number?The term "twice" simply implies "multiply by two." Typically, when working with numbers in algebra, we don't know their values; instead, we only refer to them as variables and express them with letters. The quantity in question in this instance is x. Similar to how twice 3 is written as 23,For the stated question;
Let the age of Sesay five years ago be 'x'.
Then, the age of Muskam is twice of Sesay be '2x'.
The sum of their present ages after 5 years is;
(x + 5) + (2x + 5) = 100
3x + 10 = 100
3x = 90
x = 30 (Age of Sesay 5 years ago)
Present age of Sesay = x + 5 = 30 + 5 = 35 years.
Thus, the present age of Sesay is found as the 35 years.
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The difference of 11y from 12y is −4
translate into an equation
then solve for y
What is the Factor of 30 and 45?
What is the Factor of 3 and 8?
Answer:
1. The GCF is 15 and the LCF is 1.
There are 4 common factors: 1, 3, 5, 15
2. The GCF and LCF is 1. This is the only common factor.
Step-by-step explanation:
To find common factors, think about what two numbers you can multiply to get the desired values. The numbers that are the same for both desired values are going to be factors.
dg's plumbing and heating charges $50 plus $60 per hour for emergency service. bill remembers being billed just over $400 for an emergency call. how long to the nearest hour was the plumber at bill's house?
Answer:
6 hours
Step-by-step explanation:
dg's plumbing and heating charges $50 plus $60 per hour for emergency service. bill remembers being billed just over $400 for an emergency call. how long to the nearest hour was the plumber at bill's house?
60h + 50 > 400
subtract 50 from both sides:
60h > 350
divide both sides by 60:
h > 5.8333
rounded: 6 hours
what is the area of rectangular region r ? each diagonal of r has length 5. the perimeter of r is 14.
The area of rectangular region r is = 12.
Given:
each diagonal of r has length 5. the perimeter of r is 14.
Let l and b be the length and breadth of a rectangle.
we know that
perimeter of rectangle = 2 ( l + b )
2 ( l + b ) = 14
divide by 2 on both sides
( l + b ) = 14/2
l + b = 7
l = 7 - b
l^2 + b^2 = d^2
( 7 - b )^2 + b^2 = 5^2
7^2 + b^2 - 2 * 7 * b + b^2 = 25
49 + 2b^2 - 14b = 25
2b^2 - 14b + 24 = 0
on solving b = 4,3
Take any one value
b = 4
l = 7 - 4
l = 3
Area of rectangle = l * b
= 4 * 3
= 12
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What is the distance between the points (11,19) and (11,-6) in the coordinate plane?
Answer: 25 units
Step-by-step explanation:
distance with negatives is still an addition but you have to turn the negative into a positive to get the answer.
576,000 in science notation
Answer: 5.76 x 10 to the 5th
at what speed, as a fraction of c , will a moving rod have a length 60% that of an identical rod at res
As a fraction of c, the length will be 60% at v/c = 0.76
The length of the moving rod = 60%
Using the formula for length contraction-
L = L_o(√(1 - (v²/c²))
Where;
v = The speed of the object
c = The speed of light
L = The length of the object at a moving speed
L_o = The length of the object at rest
Thus,
L = 65%
L_o = 0.65
Substituting the values -
0.65L_o = L_o[√(1 - (v²/c²))]
Dividing both sides by L_o -
0.65 = √(1 - (v²/c²))
Squaring both sides -
0.65² = (1 - (v²/c²))
v²/c² = 1 - 0.65²
v²/c² = 0.5775
Taking the square root of both sides gives;
v/c = 0.76
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an auditor selects a sample from the file of shipping documents to determine whether invoices were prepared for this sample. this test is to satisfy the audit objective of
An auditor selects a sample of shipping documents to examine whether invoices were created for this sample. The fundamental objective of the audit, Completeness, will be satisfied by this test.
Given,
An auditor picks a sample of shipping papers to examine if the related sales invoices were produced.
We need to determine what kind of audit aim will be the focus of this test's evidence gathering;
Audit purpose;
An audit's objective is to form an unbiased evaluation of the entity's financial statements. It is a component of the opinion if the financial statements give a true and fair picture and have been accurately prepared in accordance with accounting rules.
Here,
The audit objective completion test was carried out by the auditor to acquire proof.
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The question is incomplete. Completed question is given below;
An auditor selects a sample of shipping documents in order to determine if the related sales invoices were prepared. This test would gather evidence concerning which audit objective?
A) Completeness
B) Detail tie-in
C) Occurrence
D) Realizable value
we want to construct a 99% confidence interval for the proportion of people who will vote 'yes' on a ballot question in the next election. how many people should we sample to construct such an interval with a margin of error of 3%?
The sample size should be 1843 at 99% confidence level with margin of error of 3%.
What is Inferential statistics?
By studying the samples that were drawn from the population data, inferential statistics aids in the development of a solid knowledge of the data. By utilising numerous analytical techniques, it aids in the creation of population-level generalisations.
Given, Margin of error (m) = 0.03
z (at 99% confidence level)=2.576
We know that, Sample size(n) = (z/m)^2 p (1-p)
In order to find the sample size, we must know the value of proportion.
here, the value of proportion is missing so, in the absence of proportion, we will consider it as 0.5.
Now, we've p = 0.5
∴ Sample size = (z/m)^2 p (1-p)
= (2.576/0.03)^2 × 0.5 × (1-0.5)
= 1843 (approx).
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for each of the following implications, state the converse, inverse, and contrapositive. a. if a quadrilateral is a parallelogram, then its opposite sides are congruent. b. if two lines do not intersect, then they are parallel. c. if the sky does not look blue, then it is not night time. d. if a rectangle is a parallelogram, then it is not a quadrilateral.
A statement in the form p→q has three related implications that are called converse, inverse, and contrapositive.
A statement in the form p→q has three related implications.
Statement: If p then q (p→q)
Converse: If q then p (q→p)
Inverse: If not p then not q (-p → -q)
Contrapositive: If not q then not p (-q → -p)
For the given implications, its converse, inverse, and contrapositive can be written as.
Given statement:
(a) If a quadrilateral is a parallelogram, then its opposite sides are congruent then its converse, inverse, and contrapositive are:
Converse: If a quadrilateral has opposite sides that are congruent then it's a parallelogram.
Inverse: If a quadrilateral is not a parallelogram then its opposite sides are not congruent.
Contrapositive: If a quadrilateral has opposite sides that are not congruent then it's not a parallelogram.
(b) If two lines do not intersect, then they are parallel:
Converse: If the two lines do not intersect in the same plane, then they are parallel.
Contrapositive: If the two lines intersect in the same plane, then they are not parallel.
(c) If the sky does not look blue, then it is not nighttime:
Converse: If it is not nighttime, then the sky looks blue.
Inverse: If the sky does not look blue then it is nighttime.
Contrapositive: If it is nighttime then the sky does not look blue.
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a computer software developer would like to use the number of downloads (in thousands) for the trial version of his new shareware to predict the amount of revenue (in thousands of dollars) he can make on the full version of the new shareware. attached below is the output from a simple linear regression along with the residual plot and normal probability plot obtained from a data set of 30 different sharewares that he has developed. what is the correct null hypothesis for testing whether there is a linear relationship between revenue and the number of downloads?
We can say that there is sufficient evidence that revenue and the number of downloads are linearly related.
What is the null hypothesis?
The null hypothesis is a common statistical theory that asserts that no statistical relationship or significance exists between two sets of observed data and measured phenomena based on a single observed variable.
Hypothesis:
[tex]H_0:\rho_1=0\\H_1:\rho\neq0[/tex]
Test statistic:
[tex]t=r\times\sqrt{\frac{n-2}{1-r^2} }\\\\ t=(0.8691)\times\sqrt{\frac{30-2}{(1-0.8691)^2} } \\\\t=9.2974[/tex]
D.F. = n - 2 = 28
P-value = P-value at t = 9.2974, ∝=0.05, 28 d.f. is
P-value = 0.000
Conclusion: Since. P-value < ∝=0.05, so we have to reject the null hypothesis.
Hence, we can say that there is sufficient evidence that revenue and the number of downloads are linearly related.
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what is the remainder when the positive integer n is divided by the positive integer k, where k > 1 ? (1) n
n=(K+1)^3 the remainder when the positive integer n is divided by the positive integer k, where k > 1
What is Remainder?
The value remaining after division is known as the Remainder. After division, we are left with a value if a number (dividend) cannot be divided entirely by another number (divisor). The remaining is the name for this amount.
For instance, 10 is not precisely divisible by 3. We can calculate 3 x 3 = 9 because that is the closest value.
As a result, 10 3 3 R 1, where 1 is the remainder and 3 is the quotient.
As we are aware:
Dividend: Divisor x Quotient + Remainder
Therefore,
Dividend - Remainder (Divisor x Quotient)
The formula for the remainder is as follows.
[tex]n=(k+1)^3\\\\=k^3+3k^2+3k+1\\\\=k(k^2+3k+3)+1=(k+1)^3\\\\=k^3+3k^2+3k+1=k(k2+3k+3)+1 \\\\[/tex]
[tex]k(k^2+3k+3)[/tex] is clearly divisible by k, because 1 divided by k gives 1 as the result (since k > 1).
The remainder will be n= (K+1)^3
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A
Given:
O HA
ZC, ZF are rt. Z's; AC= DF, BC= EF
O LA
OLL
B D.
OHL
F
E
Answer: your question is not very clear
Step-by-step explanation:
Two angles are
complementary. One angle is six more than
twice the other. What is the measure of each
angle?
Answer:
Step-by-step explanation:
1st angle = (2x+6)° = (56 + 6)°= 62°. 2nd angle = x = 28°. Thus, 62° and 28° are the required angles. Answer.
A researcher wants to test the hypothesis that on average girls perform better on standardized tests than boys. Since it is true that some boys do better than girls and some girls do better than boys, the researcher must use a two tailed test.
True OR False
The statement of the given hypothesis condition is False.
What is hypothesis testing?
A type of statistical inference known as hypothesis testing uses data from a sample to make inferences about a population parameter or population probability distribution.
Given this, A researcher wants to test the hypothesis that on average girls perform better on standardized tests than boys.
i.e. [tex]\mu_{1} > \mu_{2}[/tex]
">" sign implies that right-tailed test i.e. one-tailed right-sided.
Hence, the given statement is FALSE.
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if 17% of men are bald, what is the probability that at most 140 in a random sample of 900 men are bald? use normal to binomial
If 17% of men are bald, then the probability that at most 140 in a random sample of 900 men are bald, is 0.1335.
In the given question, if 17% of men are bald, then we have to find the probability that at most 140 in a random sample of 900 men are bald.
As given that; 17% of men are bald.
So,p=0.17
Let X=Number of men that are bald
Sample size, n=900
Here X follows binomial distribution with parameters n= 900 and p =0.17
Since np≥5 and n(1-p)≥5, We can use normal approximation to the binomial with continuity correction.
So,Binomial can be approximated to normal with;
mean, μ=np
μ = 900*0.17
μ = 153
Standard deviation, σ = √np(1-p)
σ = √900*0.17*(1-0.17)
σ = √153*0.83
σ = √126.99
σ = 11.269
So, X→Normal (μ = 153, σ = 11.269)
Then, X= (X-μ)/σ
X=(X-153)/11.269
We need to find the probability that at most 140 in a random sample of 900 men are bald i.e. we need to find P(X≤140)
P(X≤140) =P(X<140+0.5) [using continuity correction factor]
P(X≤140) =P(X<140.5)
P(X≤140) =P(z<(X-153)/11.269)
P(X≤140) =P(z<(140.5-153)/11.269)
P(X≤140) =P(Z<-1.11) [z score rounded to 2 decimal places]
P(X≤140) =0.1335
Hence, if 17% of men are bald, then the probability that at most 140 in a random sample of 900 men are bald, is 0.1335.
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if a population begins with 25 individuals and grows exponentially for 20 generations with an r value of 0.2, then the greatest percentage increase will occur: please choose the correct answer from the following choices, and then select the submit answer button. answer choices from generation 11 to 12. from generation 5 to 6. from generation 1 to 2. from generation 19 to 20.
Answer: from generation 19 to 20.
Step-by-step explanation:
The greatest percentage increase will occur from generation 19 to 20 as the exponential power will be highest.
What is exponential growth?
Exponential growth happens once the larger in size you're the quicker you grow that causes you to even larger in size. it's the expansion characterised by interest, or growth. it's known as exponential growth as a result of it will solely be delineate mathematically by inserting time within the exponent or power of the bottom. Population then is adequate to the population at the current times some discretional range to the facility of the expansion rate times the time. The discretional range is sometimes two then the expansion rates is given because the reciprocal of the doubling time.
Main body:
initial population = 25
Total generation = 20
growth rate = 0.2
General formula of exponential function = aˣ
here a = 25 and x = 0.2
⇒25⁰°²
= 1.9
hence total population = 25+2 = 27
So it is clear that in 19 to 20 generation , growth will be highest.
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an srs of 28 students at uh gave an average height of 5.9 feet and a standard deviation of .1 feet. construct a 90% confidence interval for the mean height of students at uh.
The 90% confidence interval for the mean height of students at UH is (5.885,5.915) feet.
We have given that, an srs of 28 students at UH gave an average height of 5.9 feet and a standard deviation of 0.1 feet.
i.e n = 28
x = 5.9 feet
s = 0.1 feet
and we have to construct a 90% confidence interval for the mean height of students at UH.
The level of significance, α = 1 - 0.9 = 0.1
The value of 0.9 in z-table is 0.816.
The formula for confidence interval is,
CI = x ± z* (s/[tex]\sqrt{n}[/tex])
Substituting the values,
CI = 5.9 ± (0.816) (0.1/√28 )
= 5.9 ± (0.816)(0.1/5.291)
= 5.9 ± (0.816)(0.0189)
CI = 5.9 ± 0.015
CI = 5.9 + 0.015 = 5.915
CI = 5.9 - 0.015 = 5.885
Therefore 90% confidence interval for the mean height of students at UH is 5.885 feet to 5.915 feet.
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The following data set represents the ages of all six grandchildren in a family. Find the variance for this data set of ages: 6,3,14,11,14,6 round the final answer to one decimal place.
The variance for the data set is 18.
What is a variance?
The term variance refers to a statistical measurement of the spread between numbers in a data set. More specifically, variance measures how far each number in the set is from the mean (average), and thus from every other number in the set.
Here we have to find the variance for this data set.
Given data:
The age of six grandchildren in a family is = 6, 3, 14, 11, 14, 6
The mean = 6+3+14+11+14+6/ 6
= 9
The variance = (6-9)² + (3-9)² + (14-9)² +(11-9)² + (14-9)² + (6-9)²/ 6
= 9+36+25+4+25+9/ 9
= 18
Therefore the variance is 18.
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Is the following relation a function?
Answer:
Yes
Step-by-step explanation:
Given the following: f(x)=x^2-8x+4;\;g(x)=4x+3;\;and\;h(x)=x+2.f(x)=x
2
−8x+4;g(x)=4x+3;andh(x)=x+2.
What is the result of the following: \left(\frac{\mathrm{h}}{\mathrm{g}}\right)(x)(
g
h
)(x)
The result of the following: [tex]\left(\frac{\mathrm{h}}{\mathrm{g}}\right)(x)[/tex] is (x+2)/( 4x+3).
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Given the following function:
[tex]f(x)=x^2-8x+4;\;g(x)=4x+3;\;and\;h(x)=x+2.[/tex]
We need to find the result of the following: [tex]\left(\frac{\mathrm{h}}{\mathrm{g}}\right)(x)[/tex]
Therefore,
g(x)=4x+3
h(x)=x+2
[tex]\left(\frac{\mathrm{h}}{\mathrm{g}}\right)(x)[/tex] =(x+2)/( 4x+3)
Hence, the result of the following: [tex]\left(\frac{\mathrm{h}}{\mathrm{g}}\right)(x)[/tex] is (x+2)/( 4x+3).
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a ship leaves port at noon and has a bearing of s 23° w. the ship sails at 10 knots. (a) how many nautical miles south and how many nautical miles west will the ship have traveled by 6:00 p.m.? (round your answers to two decimal places.) miles south miles west (b) at 6:00 p.m., the ship changes course to due west. find the ship's bearing and distance from port at 7:00 p.m. (round your answers to one decimal place.) s ° w nautical miles
(a) 52.475nm many nautical miles south and 29.09nm many nautical miles west will the ship have traveled by 6:00 p.m.
(b) at 6:00pm the ship changes course to due west when 36.68° the ship's bearing and distance from port at 7:00 p.m.
Given that,
A ship sets out from port at noon with a bearing of s 23° west and a speed of 10 knots.
We have to find
(a) By the time it gets dark at six o'clock, how far south and west will the ship have sailed? The ship alters its course to head due west at 6:00 p.m. miles south miles west
(b). at 7:00 p.m., determine the ship's bearing and distance from the port. nautical miles in s.
We know that,
(a) For 6:00 p.m
Sin(θ)=opposite/ hypothesis
θ=29
Opposite=west
Hypothesis =60
Sin(29°)=w/60
w=29.09nm
West= 29.09nm
Cos(θ)=adjacent/ hypothesis
θ=29
Adjacent= south
Hypothesis =60
Cos(29°)= south/60
south=52.475nm
Therefore, 52.475nm many nautical miles south and 29.09nm many nautical miles west will the ship have traveled by 6:00 p.m.
(b) tan(θ)=opposite/adjacent
Opposite=29.09nm
Adjacent= 52.475nm
Tan(θ)=29.09nm/52.475nm
θ=36.68°
Therefore, at 6:00pm the ship changes course to due west when 36.68° the ship's bearing and distance from port at 7:00 p.m.
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Tom wants to rent a truck for two days and pay no more than $300. How far can he drive the truck if the truck rental cost $49 a day plus $0.40 a mile?
A) 490
B) 505
C) 520
D) 535
Answer:
B
Step-by-step explanation:
for 2 days it's 98
then 300-90=202
202÷0.40=505
a number line going from 0 to 4. numbers 0, 1, 2, 3, and 4 are marked on the line. marks divide the spaces between each number into 2 equal parts. ms. cole has 4 yards of string. she cuts the string into pieces that are each 1 2 yard long. how many pieces of string does ms. cole have? one-eighth one-fourth 2 8
Ms. Cole have the 8 pieces of string.
Given,
In the question:
A number line going from 0 to 4. numbers 0, 1, 2, 3, and 4 are marked on the line. marks divide the spaces between each number into 2 equal parts. Ms. Cole has 4 yards of string. she cuts the string into pieces that are each 1 2 yard long.
To find the how many pieces of string does Ms. Cole have?
Now, According to the question:
Total yards of string = 4
Length in yard of each string = 1/2 yards
Number of pieces of string Ms. Cole has :
Total. Yards of string / length in yard of each string
=> 4 / (1/2)
=> 4 * (2 /1)
=> 8/1
=> 8 pieces of string.
Hence, Ms. Cole have the 8 pieces of string.
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If rs=12, rt=5, st=7, and points r, s, and t are collinear, what is the relationship between collinear points r, s, and t?.
Answer: The relationship between points R , S , and T is that the sum of the RS and RT will be equal to RT that is RT=RS+ST
Step-by-step explanation:
Donnie, Karim, and Shawn run on the cross-country team. At yesterday’s practice, Donnie ran 200% as far as Karim. The ratio of the distance that Karim ran to the distance that Shawn ran is 4 : 3.
If you add the distance that all three boys ran, you get a sum of 45 miles. How far did each boy run individually?
this is ratio problem
The distance that each boy ran is as follows:
Donnie = 24 miles
Karim = 12miles
Shawn = 9 mile.
What is ratio?Ratio is defined as an expression that is used to represent the part of a whole entity or structure.
The total distance covered by the three boys = 46miles.
Distance covered by Donnie = 200% of Karim (ratio 4)
That is;
200/100×4 = 8
Now the ratio of the three boys = 8:4:3
To calculate the distance of each boy is by finding the total ratio of the whole boys such as:
= 8+4+3 = 15
For Donnie = 8/15×45 = 24 miles
For Karim = 4/15×45 = 12 miles
For Shawn = 3/15 × 45 = 9 miles
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A factory makes components used in jet engines, including reinforced steel washers. The washers are required to have a very precise thickness. The thickness of the washers follow a normal distribution with mean 1. 59 millimeters and standard deviation 0. 042 millimeters. A technician randomly samples washers and calculates the mean of their thicknesses, which is. What is the probability that ?.
The probability that [tex]\bar{x}[/tex] < 1.57 for the given mean, standard deviation , and samples is equal to 0.0162.
As given in the question,
Normal distribution with mean 'μ' = 1.59 millimeters
Standard deviation 'σ' = 0.042 millimeters
Sample size 'n' = 20
standard error = σ /√n
= 0.042 / √20
= 0.00933
Probability that [tex]\bar{x}[/tex] < 1.57 is
X = 1.57
s = 0.0093
P( X < 1.57)
= P[ (X -μ)/s < ( 1.57 - 1.59)/ 0.0093]
= P ( z < -2.14 )
Using z - table p value is
= 0.01617
= 0.0162
Therefore, the probability for the [tex]\bar{x}[/tex] < 1.57 is equal to 0.0162.
The complete question is :
A factory makes components used in jet engines, including reinforced steel washers. the washers are required to have a very precise thickness. the thickness of the washers follow a normal distribution with mean 1.59 millimeters and standard deviation 0.042 millimeters. a technician randomly samples n = 20 washers and calculates the mean of their thicknesses, which is x¯. what is the probability that x¯<1.57?
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Equations with variables on both sides that equal 19
An equation with variables on both sides that equal 19 is x - 2 = 17.
What is an equation?An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario. It is vital to note that an equation is a mathematical statement which is made up of two expressions that are connected by an equal sign
Based on the information, the equation will be:
x - 2 = 17
Collect like terms
x = 17 + 2
x = 19
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