what is the correct factorization of 33^3x39x4^11
The correct factorization of 33³ × 39 × 4¹¹ = 2²² × 3⁴ × 11³ × 13
What is factorization?Factorization is the collecting together of the common terms of an expression so as to have it in simpler form.
How to find the correct factorization of the expression 33³ × 39 × 4¹¹?To find the correct factorization of 33³ × 39 × 4¹¹, we write out each term in terms of its common factors.
so, we have that the factorization of the first term is 33³ = (3 × 11)³ = 3³ × 11³
Also, we have that the factorization of the second term is 39 = 3 × 13
Finally, we have that the factorization of the last term is 4¹¹ = (2²)¹¹ = 2²²
So, we have that 33³ × 39 × 4¹¹ = 3³ × 11³ × 3 × 13 × 2²²
= 3³ × 3 × 13 × 11³ × 2²²
= 2²² × 3⁴ × 11³ × 13
So, the correct factorization is 2²² × 3⁴ × 11³ × 13
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95 POINTS!!! To increase business, the owner of a shoe store is running a promotion in which a customer's bill can be selected at random to receive a discount. When a customer's bill is printed, a program in the cash register determines randomly whether the customer will receive a discount on the bill. The program was written to generate a discount with a probability of 0.15; that is, 15% of the bills get a discount in the long run. However, the owner is concerned the program is incorrect and is not generating the intended long-run proportion of 0.15.
The owner selects a random sample of bills and finds that only 12% of them received a discount. A confidence interval for p, the proportion of bills that will receive a discount in the long run, is 0.12 ± 0.05, and all conditions for inference are met.
Consider the confidence interval 0.12 ± 0.05.
Part A: Does the confidence interval provide convincing statistical evidence that the program is not working as intended? Justify your answer. (3 points)
Part B: Does the confidence interval provide convincing statistical evidence that the program generates the discount with a probability of 0.15? Justify your answer. (2 points)
Part C: A second random sample of bills is taken that is six times the size of the original sample. In the second sample, 12% of the bills received the discount. Determine the value of the margin of error based on the second sample of bills used to compute an interval for p with the same confidence level as that of the original interval. (2 points)
Part D: Based on the margin of error in part C that was obtained from the second sample, is the program working as intended? Justify your answer.
An area surrounding a measurement that indicates how accurate it is called a confidence interval.
Let X = The proportion of n randomly selected consumers who receive the discount. So, X = B(n, p), where p is the likelihood that a consumer will receive the discount.
Back-up Theory 100(1 - α) % Confidence Interval for the population proportion, p is:
p ± Zα/2[√{P(1 –p)/n}] ……(1)
where
Zα/2 is the upper (α/2)% point of N(0, 1),
pcap = sample proportion, and
n = sample size.
One can conclude with 100(1 - )% confidence that the population proportion, p, is p if a 100(1 - )% Confidence Interval for p holds a specific hypothesized value of p…………. (2)
Now to work out the solution,
The given confidence interval is: 0.12 ± 0.05 i.e., [0.07, 0.17] or [7%, 17%]……………………. (3)
for Part (a)
equation (2) and (3), [7%, 17%] holds 15%. Hence the statement is NOT valid.
for Part (b)
equation(2) and (3), [7%, 17%] holds 15%. Hence the statement is valid.
For Part (c)
Margin of error is: Zα/2[√{P(1 –P)/n}]
If the sample sizes under Part (c) and (a) are respectively, n2 and n1, the ratio of respective margin of errors would be
[Zα/2.√t{P(1 –P)/n2}]/[Zα/2√{P(1 –P)/n1}]
= √(n1/n2)
= 1/√6 [given the second sample size is 6 times the first sample size]
= 0.4082
= > the margin of error under Part (c) = the margin of error under Part (c) x 0.4082
= 0.05 x 0.4082
= 0.020.
Thus, the margin of error when the sample size if 6-fold is 0.020.
For Part (d)
The revised Confidence Interval from Part (c) is 0.12 ± 0.02 or [0.10, 0.14], which does not hold 0.15 as a result, according to (2), the program is NOT operating as anticipated.
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you plan to mark up your taco prices by 15%, of your original prices are 4.50, 2.25, and 3.00 what would be the new prices?
Answer:
Step-by-step explanation:
$4.50 + $4.50(0.15) = $5.18
$2.25 + $2.25(0.15) = $2.59
$3.00 + $3.00(0.15) = $3.45
Complete this table so it shows a relation that is not a function.
X
2
-4
-3
y
3
1
7
-5
If we remove the ordered pair in Table 1 and either the value of (3,7) or (3,-2) we have the relation as a function.
what is function ?Mathematics encompasses the study of numbers, formulas and related structures, shapes and the spaces in which they exist, quantities and their variations, and spaces in which they exist. A function is an association between a set of inputs, each of which has an output. Simply described, a function is a relationship between inputs and outputs, where each input results in a single, distinct output. Each function has a domain and a codomain, often known as a scope. Typically, the letter f is used to denote functions (x). is the input. There are four different categories of functions. based on one-to-one functions, many-to-one functions, on functions, within functions, and one-to-one functions.
given
Table 1:
x 0 -4 3 -2 9 3
y 5 8 7 8 5 -2
No, Table 1 is not a function.
Since there are two images of element '3'.
i.e. 3 is mapped to 7 and -2.
Table 2:
x 2 -7 5 1 -6 3
y 5 8 -6 8 5 7
Yes, this relation is a function.
Because corresponding to each x there is a single image.
If we remove the ordered pair in Table 1 and either the value of (3,7) or (3,-2) we have the relation as a function.
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A square pryamid have a total surface area of 1,477,500ft² and need to find the slant length. The length is 750ft. Find the slant length.
A.) 610in
B.) 610ft
C.) 3,050ft
D.) 3,050in
pls help I have a hundred points for someone who answers
957÷3=319 this divide answer i hope help you
Select the correct answer from each drop-down menu. A bag contains one green ball, one yellow ball, one red ball, and one blue ball. Jerome picks a ball from the bag, replaces it, and then picks another ball. The sample space for this situation is listed. Fill in the missing values in the list.
G-Y Y-Y R-__ B-Y
G-__Y-R R-R B-R
G-B Y-__ R-B B-B
G-G Y-G R-G B-__
Answer:Y, R, B, G
Step-by-step explanation:
Order matters since the ball is being replaced each time. This is all the possible combinations to take 2 balls with replacement, so you can look at the list and see that RR, RB, and RG are listed. The only other combination when choosing a red first would be to pick a yellow, so RY. This is the same pattern for the others also. Look at the list and see what combinations are already listed.
This is the correct answer;
Please leave a Thanks!
It helps!
What add up to -3 and multiples to -70
We add (x +7 ) (x - 10) up to -3 and multiply to -70.
What is a quadratic equation?
Any equation in algebra that can be written in the standard form where x denotes an unknown value and a, b, and c denote known numbers, where a 0 is a quadratic equation.
Here,
We illustrate and prove that -9 and 10 multiply to -90 and add up to 1:
7 × -10 = -70
-10 + 7 = -3
We are trying to determine how to factor the following quadratic equation.
x² -3 x - 70 = 0
If so, the solution to factor the quadratic equation above is:
(x +7 ) (x - 10)
To summarize, -10 and 7 multiplied by -70 and add up to -3, you know that the following is true:
x² -3x - 70
= (x +7 ) (x - 10)
Hence, we add (x +7 ) (x - 10) up to -3 and multiply by -70.
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Given that f(x)=√x, describe the function of g(x)
shown on the graph.
The function is represented by the equation
g(x)=√x +
The function g(x) has a domain x²
The function g(x) has a range y ≥
Answer: It's not possible to accurately describe the function g(x) without more information about the equation or the graph. The equation provided is g(x)=√x + , which is incomplete, it does not have a value assigned for the "+" operator, it could be added to any number, for example, g(x)= √x + 1, or g(x)= √x+5, and so on.
Additionally, the statement that the function g(x) has a domain x² and range y ≥ , is not a valid mathematical notation or statement. The domain of a function is the set of all input values (x-values) for which the function is defined, it's usually a set of real numbers or interval, like [-∞,+∞], (a,b) or [a,b], for example.
And range is the set of all output values (y-values) of a function, it's also usually a set of real numbers or interval.
I would suggest if you can provide me with the complete function of g(x) and more detailed information about the graph. I can help you better understand its features and properties.
Step-by-step explanation:
SOMEONE PLEASE HELPPP
The values of the [tex]\bar x[/tex] (x-bar) (the mean) and the median of the dataset in the question are;
[tex]\bar {x}[/tex] ≈ 13.05
Median = 13.60
What is the mean and median of a dataset?The mean and the median are descriptive statistical values that provides a description of the data that can be found in the dataset.
The mean is the average value of the data in the dataset, and the median is the middle value of the set of data arranged in an order of increasing values.
The mean is the average value of the set of data which is obtained by dividing the sum of the data points by the number of the datapoints, we get;
The number of data points = 28
The sum of the data is; (4.7 + 12.6 + 3.6 + 16.1 + 2.3 + 28.2 + 2.2 + 16.9 + 10.7 + 19.5 + 11.4 + 27.9 + 11 + 15 + 4.2 + 15.8 + 15.9 + 17.3 + 24.9 + 10.8 + 16.4 + 7.3 + 3.2 + 14.6 + 2.6 + 8.4 + 21.2 + 20.8) = 365.5
The average is the mean is therefore; [tex]\bar x[/tex] = 365.5 ÷ 28 ≈ 13.05
The median is the value of the number in the middle when the numbers are arranged in increasing order as follows;
2.2, 2.3, 2.6, 3.2, 3.6, 4.2, 4.7, 7.3, 8.4, 10.7, 10.8, 11, 11.4, 12.6, 14.6, 15, 15.8, 15.9, 16.1, 16.4, 16.9, 17.3, 19.5, 20.8, 21.2, 24.9, 27.9, 28.2
The numbers at the middle of the set of numbers are 14th and 15th numbers, which are 12.6 and 14.6, which indicates that the median is the average of the two numbers, which is therefore;
Median = (12.6 + 14.6)/2 = 13.60
The median is 13.60
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The length of a rectangle is 4 feet more than twice the width. The perimeter is 116. Find the dimensions of the rectangle
The dimensions of the rectangle are 40 and 18 units respectively
What is the area and perimeter of the rectangle?The formula for area is equal to the product of the length and breadth of the rectangle. Whereas when we speak about the perimeter of a rectangle, it is equal to the sum of all its four sides.
Given here: The length of a rectangle is 4 feet more than twice the width.
Then let the width be x then length is equal to 2x+4 and therefore the perimeter is 2(2x+4+x)=116
3x+4 = 58
3x = 54
x = 18
Hence, the dimensions of the rectangle are 40 and 18 units respectively.
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use demoivre's theorem to evaluate the expression (3(cos cos(5pie/6)+isin(5pie/y))))^4 write the answer in rectangular form.
By DeMoivre's theorem,
(3 (cos(5π/6) + i sin(5π/6)))⁴ = 3⁴ (cos(4×5π/6) + i sin(4×5π/6))
… = 81 (cos(20π/6) + i sin(20π/6))
… = 81 (cos(10π/3) + i sin(10π/3))
… = 81 (cos(-2π/3) + i sin(-2π/3))
… = 81 (cos(2π/3) - i sin(2π/3))
… = 81 (-1/2 + √3/2 i )
… = -81/2 + 81√3/2 i
(Don’t send me a link pls just answer!) First 3 people to answer get lots of points pls do it by friday!
Answer:
8835.73ft^3
Step-by-step explanation:
First:
Find area of the base circle.
Diameter is 15, so radius is 7.5
Area of the base circle is 56.25pi (use formula: A=pi(r)^2 ) (also ill convert pi into decimals only later)
next find the volume of the cylinder
height is 40 so volume = 56.25pi*40 = 2250pi
next find the volume of the dome at the top.
you know the radius is 7.5
Use volume of sphere formula below :
4 /3πr^3
=1767.15
alright now add the two bolded values
1767.15+2250pi
= 8835.73
hope this helps
ln cos2y + xy + 5x² = 5, find dy/dx. HELP PLEASE!!!
shown below. Which of the triangle congruence theorems could be used to prove the triangles congruent without establishing any additional information? FA 20 20 in 14 m A SSA B SSS CHL D SAS 14 in
The right triangles are congruent by HL theorem.
What are congruent triangles?The triangles having congruent corresponding parts are called congruent triangles.
Given are two right triangles, with equal hypotenuse and one of the bases.
The question is by which theorem do they are congruent,
HL theorem :-
The HL Postulate states that if the hypotenuse and leg of one right triangle are congruent to the hypotenuse and leg of another right triangle, then the two triangles are congruent.
Since, we know that, when two right triangles have congruent hypotenuse and one of their legs are also congruent, then both are congruent by HL theorem of congruence.
Here, both the right triangles are following the condition of the HL theorem.
Hence, the correct option is HL.
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22 Points For The First Person To Get It Correct.
Answer:
8×5= 40 is the answer .......
One pitcher serves 8 people, so to figure out how many 5 pitchers would serve you would do 8×5 which is 40. 5 pitchers would serve 40 people. I hope this helps!
Which equation is equivalent to 16^2p=32^p+3?
Answer:
C. 2^8p=2^5p+15
:D
W is greater than or equal to -2 and less that or equal to 5, write the following as an inequality.
Answer:
Step-by-step explanation:
w≥-2
or -2 ≤w≤5
What is the value of 6(2b-4) when b=5?
[tex]6(2b - 4)[/tex]
Expanding the terms,
[tex](6 \times 2b) - (6 \times 4) \\ = 12b - 24[/tex]
Plugging in our value b,
[tex]b = 5 \\ 12b - 24 = 12(5) - 24 = 36[/tex]
So the answer is,
[tex]36[/tex]
Answer:
Given expression: 6(2b - 4)
To find the value of 6(2b - 4) at b= 5, we need to substitute the b=5 in the expression, we get
6(2(5) - 4)
= 6(10 - 4)…[solve parentheses]
= 6(6)
6 * 6 = 36
=> 6(2(5) - 4) = 36
Therefore, the value of 6(2b - 4) is 36, when b=5.
i need help right freaking now
Answer:
a. x^4 - 12x^3 + 2x^2 - 2x + 4
Degree: 4
b. x^4 - 2x^2 - 2x - 4
Degree: 4
Step-by-step explanation:
For part a, all you are doing is adding the polynomials together. They already set up the boxes in standard form, so all you need to do is add each like term as I wrote out in the answer. The degree is then going to be the first exponent that you see once the polynomial is in standard form, which is 4.
For part b, you are now subtracting the polynomials. Again, it is set up for you in standard form. There is no x^3 terms because they cancel out, but you basically subtract each like term from another, and remember to distribute the subtraction sign (it acts as a -1) across the parenthesis. The degree is the first exponent you see, and that is 4.
Explain why the figure is a parallelogram…. Please I need help ASAP.
Answer:
In Euclidean geometry, a parallelogram is a simple (non-self-intersecting) quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure.
Step-by-step explanation:
6 cm
To the nearest cubic centimeter, what is the volume of the regular
hexagonal prism?
17 cm
5.2 cm
The volume of the regular hexagonal prism is about cm3.
Answer:
1,590.02
just round it to the nearest centimeter
Step-by-step explanation:
Can y’all help me on question 19?!
Answer: 178.31
Step-by-step explanation: subtract 574.54 by 396.23
Fractional index
Without using mathematical table simplify the following
(16/81)^-3/4
Answer:
[tex]\frac{27}{8}[/tex]
Step-by-step explanation:
using the rules of exponents/ radicals
• [tex](\frac{a}{b}) ^{-m}[/tex] = [tex](\frac{b}{a}) ^{m}[/tex]
• [tex]a^{\frac{m}{n} }[/tex] = [tex](\sqrt[n]{a}) ^{n}[/tex]
then
[tex](\frac{16}{81}) ^{-\frac{3}{4} }[/tex]
= [tex](\frac{81}{16}) ^{\frac{3}{4} }[/tex]
= [tex]\frac{(\sqrt[4]{81})^3 }{(\sqrt[4]{16})^3 }[/tex]
= [tex]\frac{3^3}{2^3}[/tex]
= [tex]\frac{27}{8}[/tex]
Find the LCM of 7xy and 6y2
Step-by-step explanation:
lcm = hcf × remaining expressions
7xy= 7 × x × y
6y² = 6 × y × y
here only y is common in both. so y is the hcf. now, without hcf, the remaining expressions are : 7x and 6y.
so LCM = hcf × remaining expressions
= y × 7x × 6y
= 42xy²
What is the volume, in cubic inches, of a rectangular prism with a height of 6 inches, a width of 15 inches, and a length of 16 inches?
Answer:
1,440 inches^3
Step-by-step explanation:
First, remember the formula for volume is v = l x w x h
Next, sub in your values for your prism 6 x 15 x 16 = 1,440in^3
So, the final answer is 1,440 inches^3
A normal distribution of scores has a standard deviation of 10. Find the z-scores
corresponding to each of the following values:
Answer:
Yes
Step-by-step explanation:
A random sample of 250 campers at a summer camp were surveyed to see what water activities they were most interested in participating in. The study found that 110 campers were not interested in paddleboarding. The study also showed that 64 of the campers who were interested in paddleboarding were also interested in waterskiing and 90 of the students were not interested in waterskiing. Based on the given information, which of the following relative frequency tables summarizes the data?
The relative frequency table that summarizes the data is given by the image at the end of the answer.
What is Relative frequency?The number of desired experiment results divided by the total number of experiment results is used to compute the relative frequency of an event in an experiment.
Given:
The percentage of people interested in waterskiing
= 90/250 x 100
= 36%.
Thus, the percentage of people that was not interested in waterskiing is
=100-36
= 64%
Now, the percentages related to paddle boarding are :
Yes: 72/250 = 28.8%.
No: 18/250 = 7.2%.
Of those not interested in waterskiing, the percentages related to paddle boarding are
Yes: 112/250 = 44.8%.
No: (120 - 72)/250 = 19.2%.
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The circle graph shows how a family budgets its annual income. If the total annual income is $100,000, what amount is budgeted for Clothing?
Answer:
where is the circle graph
A concave lear of focal length of 20cm forms an image 1/2 the size of the object .The object distance?
Answer:
60cm
Step-by-step explanation:
given:
focal length (f) = 20cm
image height (v) = ½u
object height (u) = ?
(1÷v) + (1÷u) = (1÷20)
(1÷(½u)) + (1÷u) = (1÷20)
(2÷u) + (1÷u) = (1÷20)
(3÷u) = (1÷20)
u = 20 × 3
u = 60cm