Answer:
The answer is 20 and 200.
Step-by-step explanation:
Write the expression as a monomial in standard form.
(−3xy^2)^3 · (-2/3x^2y^3)^4
Answer:
It would be -16/13x^11y^18.
The standard form of the expression as a monomial [tex]&\left(-3 x y^2\right)^3\left(\frac{-2}{3 x^2 y^3}\right)^4 \\[/tex]is
-16 /3[tex]$ x^5y^6[/tex]
What is meant by standard form?A number in standard form in mathematics. Standard decimal numbers are the easiest to read and write. For example, the standard form of the decimal number 0.007 is 7 10-3. It can be difficult to read or write very large or very small numbers. As a result, we write them in standard format. Any number that can be written as a decimal number between 1.0 and 10.0 multiplied by a power of ten is said to be in standard form.An equation is written in standard form as Ax + By = C, where A, B, and C are all integers. This form of the equation is especially useful for calculating the x- and y-intercepts.Given,
[tex]&\left(-3 x y^2\right)^3\left(\frac{-2}{3 x^2 y^3}\right)^4 \\[/tex]
Simplify
[tex]\left(-3 x y^2\right)^3:-27 x^3 y^6 \\[/tex]
[tex]&=-27 x^3 y^6\left(\frac{-2}{3 x^2 y^3}\right)^4 \\[/tex]
Simplify
[tex]\left(\frac{-2}{3 x^2 y^3}\right)^4: \frac{16}{81 x^8 y^{12}} \\[/tex]
[tex]&=-27 x^3 y^6 \frac{16}{81 x^8 y^{12}}[/tex]
Apply the fraction rule:
[tex]$\quad a \cdot \frac{b}{c}=\frac{a \cdot b}{c}$[/tex]
∴ [tex]=-\frac{27 x^3 y^6 \cdot 16}{81 x^8 y^{12}}[/tex]
Factor the number: 81 = 27.3
[tex]=-\frac{27 x^3 y^6 \cdot 16}{27 \cdot 3 x^8 y^{12}}[/tex]
Cancel the common factor: 27
[tex]=-\frac{x^3 y^6 \cdot 16}{3 x^8 y^{12}}$$[/tex]
Simplify
[tex]$\frac{x^3}{x^8}: \frac{1}{x^5}$[/tex]
∴ [tex]=-\frac{y^6 \cdot 16}{3 x^5 y^{12}}[/tex]
Simplify the equation,
[tex]$\frac{y^6}{y^{12}}: \frac{1}{y^6}$[/tex]
then we get,
[tex]=-\frac{16}{3 x^5 y^6}[/tex]
Hence, The standard form of the expression as a monomial [tex]&\left(-3 x y^2\right)^3\left(\frac{-2}{3 x^2 y^3}\right)^4 \\[/tex]is -16 /3[tex]$ x^5y^6[/tex]
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A researcher wants to determine if birthweights of children born to U.S. mothers is affected in any way when large megadoses of caffeine are consumed routinely by the mother during pregnancy. It is known that the birthweights are normally distributed with mean 7.5 pounds and standard deviation 1 pound. When drawing a sample of size 40 from such a population, and computing the mean birthweight in the sample, use the Central Limit Theorem to find the 2.5-th percentile of the distribution of sample means.
Answer:
7.19
Step-by-step explanation:
A pizza delivery company classifies its customers by gender and location of residence. The research department has gathered data from a random sample of 1664 customers. The data is summarized in the table below.
Gender and Residence of Customers
Males Females
Apartment 206 149
Dorm 295 276
With Parent(s) 55 68
Sorority/Fraternity House 132 204
Other 180 99
What is the probability that a customer is female and lives in a dorm or is female and lives in 'Other'? Express your answer as a fraction or a decimal number rounded to four decimal places.
Answer: 0.2254
Step-by-step explanation:
Let E= Event of getting of female lives in a dorm.
F = Event of getting of female lives in a 'Other'.
From the table , n(E) = 276 and n(F) = 99
and n(E∩F) = 0 [E and F are Mutually exclusive]
Now, n(E∪F)= n(E) + n(F) - n(E∩F)
= 276+99-0
= 375
also, n(S) =1664 (Sample size)
Required probability : [tex]P(E\cup F)=\dfrac{n(E\cup F)}{n(S)}[/tex]
[tex]=\dfrac{375}{1664}\approx0.2254[/tex]
Hence, the probability that a customer is female and lives in a dorm or is female and lives in 'Other' = 0.2254
Customers arrive to a bank according to a Poisson process having a rate of 8.6 customers per hour. Suppose we begin observing the bank at some point in time. (a) What is the probability that 3 customers arrive in the first 30 minutes
Answer:
The value is [tex]P(X = 3) = 0.1798[/tex]
Step-by-step explanation:
From the question we are told that
The rate is [tex]\lambda = 8.6 \ hr ^{-1}[/tex]
General probability distribution for Poisson distribution is mathematically represented
[tex]P(X = x) = \frac{(\lambda * t)^{x} }{x!} * e^{-\lambda * t}[/tex]
Given that is in per hour then the unit of t is in hours
Generally 30 minutes = [tex]0.5 \ hours[/tex]
Generally the probability that 3 customers arrive in the first 30 minutes is mathematically represented
[tex]P(X = 3) = \frac{( 8.6 * 0.5 )^{3} }{3!} * e^{-8.6 * 0.5 }[/tex]
=> [tex]P(X = 3) = 0.1798[/tex]
Find the value of x in the triangle shown below. x = 56° 99°
Answer:
x = 25 degrees
Step-by-step explanation:
All angles in a triangle should add up to 180 degrees. So to solve for x, set up an equation where all three angles added up equals 180.
180 = 99 + 56 + x
180 = 155 + x
25 = x
The unknown angle is equal to 25 degrees.
What is the length of a segment with endpoints at F(6, 4) and G(14, 19)? Round to the nearest whole number.
Answer:
17
Step-by-step explanation:
d = √( (x₂ - x₁)² + (y₂ - y₁)² )
= √( (14 - 6)² + (19 - 4)² )
= √( 8² + 15² )
= √( 64 + 225 )
= [tex]\sqrt{289}[/tex]
= 17
The number of chocolate chips in a bag of chocolate chip cookies is approximately normally distributed with a mean of 1262 chips and a standard deviation of 117 chips. (a) Determine the 28th percentile for the number of chocolate chips in a bag. (b) Determine the number of chocolate chips in a bag that make up the middle 97% of bags. (c) What is the interquartile range of the number of chocolate chips in a bag of chocolate
Answer:
Using z score formula:
X = z ∂ + µ
= 157.833
Step-by-step explanation:
Solution:
Mean = µ = 1262
Standard deviation = ∂ = 117
(a) 28th percentile for the number of chocolate chip.
P( z < z) = 28%
= 0.28
P( z<- 0.58) = 0.28
Z = -0.58
By using z score formula:
Z = x - µ /∂
-0.58= x – 117 / 1262
X = (- 0.58)(117) + (1262)
= 1194.14
(b) Middle 97% of bag.
P(-z < z < z) = 97%
= 0.97
P( z < z) – p(z < -z) = 0.97
2p(z < z) -1 = 0.97
2p (z < z) = 1 + 0.97
P(z < z) = 1.97 / 2
= 0.99
P(z < 2.33) = 0.99
Z ± 2.33
By using z score formula:
Z = x - µ / ∂
X = z ∂ + µ
= - 2.33 x 117 + 1262
=989.39
Z = 2.33
X = z ∂ + µ
= 2.33 x 117 + 1262
=1533.61
(c) What is the interquartile range of the number of chocolate chips in a bag of chocolate.
By using standard normal table,
The z dist’n formula:
P(z < z ) = 25%
=0.25
P(z < -0.6745) = 0.25
Z = 0.6745
Using z score formula:
X = z∂ + µ
= - 0.6745 x 117 + 1262
= 1183.0835
First quartile = Q1 =1183.0835
The third quartile is:
P(z<z) = 75%
= 0.75
P(z < 0.6745) = 0.75
Z = 0.6745
Using z score formula:
X = z ∂ + µ
= 0.6745 x 117 + 1262
= 1340.9165
IQR = Q3 – Q1
= 1340.9165 – 1183.0835
= 157.833
i have another one sry out fated meme but i need 1-1 is it 0? or is it -1
Answer:
It is 0
Step-by-step explanation:
Answer:
1-1 is 0 if it was 1-2 it would be -1
Step-by-step explanation:
PLEASE HELP I CANT DO MATH
Answer:
c
Step-by-step explanation:
the number line says less than 4 so if you solce for all the equations c will be x<4
A quadrilateral with 90 degree angles is shown. The lengths of the left and right sides are 10 and 2 y + 4. The lengths of the top and bottom sides are 18 and 10 + 2 x. What is the value of y? 3 4 5 6
Answer: y=3
Step-by-step explanation:
Since the quadrilateral has 90 degree angles, it must be a a square or a rectangle. This means the measure of sides left and right are the same and the measure of sides top and bottom are the same.
To get the measure of y, you can use left and right or top nd bottom.
I'll use left and right. 10=2y+4 => 10-4=2y => 6=2y => y=3
You can check it by substituting. 2(3)+4=10 The answer is the measure of the right side, which is the same as the measure of the left side.
I hope this helps you!
Answer:
3
Step-by-step explanation:
Sophia says that you can solve the problem in the Example by multiplying both quantities in the ratio 60:36 by one-sixth. Is Sophia correct?
Answer:
Sophia is not correct
Step-by-step explanation:
The given situation represent the problem of a ratio and it is predicted to do the simplify the ratio by determining the smallest possible values
Here it can be presented 60:36 as a fraction i.e. [tex]\frac{60}{36}[/tex]
Now the fraction should be fall by dividing both the numerator and denominator by a common factor i.e. 6
Now after dividing it, the fraction would be [tex]\frac{10}{6}[/tex]
Now it can be further reduced by a common factor i.e. 2
So now the fraction is [tex]\frac{5}{2}[/tex]
Thus, the ratio is 5:2
Hence, she is not correct
Does anyone know this stuff? Im bad at it
Answer:
6
Step-by-step explanation:
Rewrite each of the following numbers
as a square or a cube of some other
number.
0.064
Confused on this please help
Answer: it would be half the size
Step-by-step explanation:
You are planning to evaluate the mean of a single continuous variable from a study with a sample of n =10 using the t statistic. What are the degrees of freedom for the sample?a. 11b. 9c. 10d. 8With another study, where you also plan on evaluating a mean using the t statistic, you have sample of n =31 that has as SS of 120. What is the variance for the sample?a. 10.95b. 14,400c. 4d. 2.00For a sample of n =25 that has a sample variance of 400, what is the estimated standard error for the sample?a. 16b. 17c. 4.08d. 4
Answer:
a) b. 9
b) c. 4
c) d. 4
Step-by-step explanation:
You are planning to evaluate the mean of a single continuous variable from a study with a sample of n =10 using the t statistic. What are the degrees of freedom for the sample?a. 11 b. 9 c. 10 d. 8
The formula for degree of freedom
= n - 1
n = 10
Degrees of freedom for the sample = 10 - 1
= 9
Option b is correct.
b) With another study, where you also plan on evaluating a mean using the t statistic, you have sample of n =31 that has as SS of 120.
What is the variance for the sample?a. 10.95 b. 14,400 c. 4 d. 2.00
The formula for Variance of a samples = SS(Sum of squares) /n - 1
n = 31
Variance of samples = 120/31 - 1
= 120/30
= 4
Option c is correct
c) For a sample of n =25 that has a sample variance of 400, what is the estimated standard error for the sample?a. 16 b. 17 c. 4.08 d. 4
The formula for standard error =
Standard deviation/√n
We are given Sample variance.
Standard deviation = √400
= 20
Hence, Standard Error = 20/√25
= 20/5
= 4
Option d is correct.
a) The degrees of freedom for the sample is option b. 9.
b) The variance is option c. 4.
c) The standard error is option d. 4.
Calculation of the degree of freedom, variance, and the standard error:a.
The formula for degree of freedom
= n - 1
n = 10
Now
Degrees of freedom for the sample should be
= 10 - 1
= 9
b) The variance should be
Since
n = 31
So,
Variance of samples = 120/31 - 1
= 120/30
= 4
c.
The formula for standard error is
= Standard deviation/√n
Here,
Standard deviation = √400
= 20
so, Standard Error = 20/√25
= 20/5
= 4
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Let A and B be events with P(A) = 0.7 and P(A ∩ B) = 0.3. For what value of P(B) will A and B be independent?
Answer:
The value of P(B) for independent events = 0.429
Step-by-step explanation:
Given;
P(A) = 0.7
P(A ∩ B) = 0.3
A and B will be independent if event A will occur and B will also occur, ie A and B will occur independently.
P(A) and P(B) = P(A ∩ B)
[tex]P(B) = \frac{ P(A\ n\ B) }{P(A)}\\\\ P(B) = \frac{0.3}{0.7}\\\\P(B) = 0.429[/tex]
Therefore, the value of P(B) for independent events = 0.429
Please solve and explain this...
Answer:
Correct option: c. 8
Step-by-step explanation:
One-sided Limit
Given a piecewise function, we can find the limit when the variable approaches a specific value in the boundary of two pieces.
Special care must be taken to determine what function will be used to calculate the limit according to the conditions of the independent variable.
The given function p(t) has 3 pieces or subfunctions according to different conditions of t. We need to calculate:
[tex]\lim _{x\to 2^{-}}p(t)[/tex]
We must find the subfunction where a value of t is close to 2 but is less than 2.
The correct subfunction is
[tex]p(t)=t^3\qquad -2\le t\le 2[/tex]
Taking the limit:
[tex]\lim _{x\to 2^{-}}p(t)=\lim _{x\to 2}t^3=2^3=8[/tex]
Correct option: c. 8
The body temperatures of a group of healthy adults have a bell-shaped distribution with a mean of 98.18 F and a standard deviation of 0.65 F. Using the empirical rule, find each approximate percentage below.
a.
What is the approximate percentage of healthy adults with body temperatures within 3 standard deviation of the mean, or between 96.23 F and100.3 F?
Answer:
99.7%
Step-by-step explanation:
Empirical rule formula states that:
• 68% of data falls within 1 standard deviation from the mean - that means between μ - σ and μ + σ.
• 95% of data falls within 2 standard deviations from the mean - between μ – 2σ and μ + 2σ.
• 99.7% of data falls within 3 standard deviations from the mean - between μ - 3σ and μ + 3σ.
From the question, we have mean of 98.18 F and a standard deviation of 0.65 F
The approximate percentage of healthy adults with body temperatures between 96.23 F and100.13 F is
μ - 3σ
= 98.18 - 3(0.65)
= 98.18 - 1.95
= 96.23 F
μ + 3σ.
98.18 + 3(0.65)
= 98.18 + 1.95
= 100.13 F
Therefore, the approximate percentage of healthy adults with body temperatures between 96.23 F and 100.13 F which is within 3 standard deviations of the mean is 99.7%
Use the measurements of the original figure and the scale drawing to calculate the scale factor and missing measures.
What is the scale factor?
What is the length of A?
What is the length of B?
Answer:
Step-by-step explanation: scale factor is 1/10 the length of a is 1 the length of b is 8.5
The scale factor is 1/10, the length of A is 1 cm and the length of B is 8.5 cm.
What is scale factor?A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size (bigger or smaller).
The basic formula to find the scale factor of a figure is expressed as,
Scale factor = Dimensions of the new shape ÷ Dimensions of the original shape.
From the given figure,
Scale factor = 6.2/62
= 1/10
The length of A = 1/10 ×10 cm
= 1 cm
The length of B = 1/10 ×85 cm
= 8.5 cm
Therefore, the scale factor is 1/10, the length of A is 1 cm and the length of B is 8.5 cm.
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6x(24÷2) equals what?
Answer:
72
Step-by-step explanation:
do 24/2=12x6=72
gimme stuff to improve on or just things to draw :)
Answer:
draw your representation of a 4 characters depicting each Hogwarts house?
Answer:
hmm you are already really good, I'm not sure if you have already but try drawing different perspectives of the head/ neck :)
The Daily Info charges a fee of $650 plus $80 per week to run an add. The People's Paper charges $145 per week. For how many weeks must an ad run for the total cost at the Daily Info to be less expensive than the cost at the People's Paper?
Answer:
10 weeksStep-by-step explanation:
let the total cost be y
and let the number of weeks be x
Daily Info charges
y=650+80x---------1
People's Paper charges
y=145x---------------2
equating 1 and 2 to solve for x we have
650+80x=145x
650=145x-80x
650=65x
x=650/65
x=10
Therefore the answer is 10 weeks
The output from the machine depends on the input to to
A.
B.
C.
D.
Answer:
i think its B
Step-by-step explanation:
A short quiz has two true-false questions and one multiple-choice question with four possible answers. A student guesses at each question. Assuming the choices are all equally likely and the questions are independent of each other, the following is the probability distribution of the number of answers guessed correctly. What is the Probability of two or more questions right? X 0 1 2 3 P(X) .1875 .4375 .3125 .0625
Answer:
[tex]P(X\geq 2) = 0.375[/tex]
Step-by-step explanation:
Given
X ------0 --------1 -------- 2--------- 3
P(X) --.1875 -.4375 ---.3125 --- .0625
Required
Determine [tex]P(X\geq 2)[/tex]
This is calculated as:
[tex]P(X\geq 2) = P(X = 2) + P(X = 3)[/tex]
[tex]P(X\geq 2) = 0.3125 + 0.0625[/tex]
[tex]P(X\geq 2) = 0.375[/tex]
Bailey had 35.78 Elena have 39.51 how many seconds bailey could have won by
Answer:
the answer would be 3.73
Step-by-step explanation:
all you gotta do is subtract 39.51 and 35.78 and you get your answer
Suppose that diameters of a new species of apple have a bell-shaped distribution with a mean of 7.45cm and a standard deviation of 0.4cm. Using the empirical rule, what percentage of the apples have diameters that are greater than 7.85cm? Please do not round your answer.
Answer:
The percentage is 68.26%
Step-by-step explanation:
Before we use the empirical rule , we need to find the value of the z-score
Mathematically;
z-score = (x - mean)/SD
Thus;
z-score = (7.85 - 7.45)/0.4 = 0.4/0.4 = 1
So the percentage we want to calculate now is the percentage of values within 1 standard deviation of the mean
According to the empirical rule, 68.26% of values are within 1 standard deviation of the mean
the list price of a fan is Rupees 1500 If the shopkeeper allows 20% is ground how much to the customer pay for it with a 10% vat
Answer:
450
Step-by-step explanation:
First we have to find the discount
20% of 1500 = 300
if you search up 20 x 1500/100, it would say 300
you can do that same equation in your maths book, and also by canceling out
10% vat tax
so 10% of 1500 = 150
since it is tax, we have to add it to our discount
300 + 150 = 450
450 is the answer
Solve for x , Help asap
Answer:
x = -3.5
Step-by-step explanation:
Mark brainliest please!!
Rewrite the following without an exponent:
4^-4. (-4 is the exponent).
Thank you!
Answer:
[tex]\frac{1}{256}[/tex]
Step-by-step explanation:
The [tex]4^{-4}[/tex] without exponents is 1/256.
Given,
[tex]4^{-4}[/tex]
We need to write the given expression without exponents.
What are exponents?
Exponents are power to a base value.
Example:
a² and b³
a and b are base
2 and 3 are exponents.
We can a fraction into an exponents form and vice versa.
Example:
1/a = [tex]a^{-1}[/tex]
We have,
[tex]4^{-4}[/tex]
Changing into a fraction form
= 1/[tex]4^{4}[/tex]
Find [tex]4^{4}[/tex].
[tex]4^{4}[/tex] = 4 x 4 x 4 x 4 = 16 x 16 = 256
Now,
= [tex]4^{-4}[/tex]
= 1/[tex]4^{4}[/tex]
= 1/256
We get,
= 1/256
Thus the [tex]4^{-4}[/tex] without exponents is 1/256.
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Can someone help me with number 1 and 2