Answer:
2580 ft-lb
Step-by-step explanation:
Water leaks out of the bucket at a rate of [tex]\frac{0.15 \mathrm{lb} / \mathrm{s}}{1.5 \mathrm{ft} / \mathrm{s}}=0.1 \mathrm{lb} / \mathrm{ft}[/tex]
Work done required to pull the bucket to the top of the well is given by integral
[tex]W=\int_{a}^{b} F(x) dx[/tex]
Here, function [tex]F(x)[/tex] is the total weight of the bucket and water [tex]x[/tex] feet above the bottom of the well. That is,
[tex]F(x)=4+(42-0.1 x)[/tex]
[tex]=46-0.1x[/tex]
[tex]a[/tex] is the initial height and [tex]b[/tex] is the maximum height of well. That is,
[tex]a=0 \text { and } b=60[/tex]
Find the work done as,
[tex]W=\int_{a}^{b} F(x) d x[/tex]
[tex]=\int_{0}^{60}(46-0.1 x) dx[/tex]
[tex]&\left.=46x-0.05 x^{2}\right]_{0}^{60}[/tex]
[tex]=(2760-180)-0[[/tex]
[tex]=2580 \mathrm{ft}-\mathrm{lb} [/tex]
Hence, the work done required to pull the bucket to the top of the well is [tex]2580 \mathrm{ft}- \mathrm{lb}[/tex]
A manufacturer of banana chips would like to know whether its bag filling machine works correctly at the 409 gram setting. It is believed that the machine is underfilling the bags. A 42 bag sample had a mean of 404 grams. Assume the population standard deviation is known to be 24. A level of significance of 0.01 will be used. Find the P-value of the test statistic. You may write the P-value as a range using interval notation, or as a decimal value rounded to four decimal places.
Answer:
[tex]z=\frac{404-409}{\frac{24}{\sqrt{42}}}=-1.35[/tex]
The p value for this case is given by:
[tex]p_v =P(z<-1.35)=0.0885[/tex]
For this case the p value is higher than the significance level given so we have enough evidence to FAIL to reject the null hypothesis and we can't conclude that the true mean is significantly less than 409
Step-by-step explanation:
Information given
[tex]\bar X=404[/tex] represent the sample mean
[tex]\sigma=24[/tex] represent the population standard deviation
[tex]n=42[/tex] sample size
[tex]\mu_o =409[/tex] represent the value to verify
[tex]\alpha=0.01[/tex] represent the significance level for the hypothesis test.
z would represent the statistic (variable of interest)
[tex]p_v[/tex] represent the p value
Hypothesis to test
We want to verify if the true mean is less than 409, the system of hypothesis would be:
Null hypothesis:[tex]\mu \geq 409[/tex]
Alternative hypothesis:[tex]\mu < 409[/tex]
The statistic for this case is given by:
[tex]z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}[/tex] (1)
Replacing the info we got:
[tex]z=\frac{404-409}{\frac{24}{\sqrt{42}}}=-1.35[/tex]
The p value for this case is given by:
[tex]p_v =P(z<-1.35)=0.0885[/tex]
For this case the p value is higher than the significance level given so we have enough evidence to FAIL to reject the null hypothesis and we can't conclude that the true mean is significantly less than 409
A nationwide survey of seniors by the University of Michigan reveals that almost 18.0% disapprove of daily pot smoking. If 8 seniors are selected at random, what is the probability that at least 2 disapprove of daily pot smoking.
Answer:
[tex] P(X\geq 2)=1- P(X<2)= 1-[P(X=0) +P(X=1)][/tex]
And using the probability mass function we can find the individual probabilities:
[tex]P(X=0)=(8C0)(0.18)^0 (1-0.18)^{8-0}=0.2044[/tex]
[tex]P(X=1)=(8C1)(0.18)^1 (1-0.18)^{0-1}=0.3590[/tex]
And replacing we got:
[tex] P(X\geq 2)=1 -[0.2044 +0.3590]= 0.4366[/tex]
Then the probability that at least 2 disapprove of daily pot smoking is 0.4366
Step-by-step explanation:
Let X the random variable of interest "number of seniors who disapprove of daily smoking ", on this case we now that:
[tex]X \sim Binom(n=8, p=0.18)[/tex]
The probability mass function for the Binomial distribution is given as:
[tex]P(X)=(nCx)(p)^x (1-p)^{n-x}[/tex]
Where (nCx) means combinatory and it's given by this formula:
[tex]nCx=\frac{n!}{(n-x)! x!}[/tex]
And we want to find this probability:
[tex] P(X\geq 2)=1- P(X<2)= 1-[P(X=0) +P(X=1)][/tex]
And using the probability mass function we can find the individual probabilities:
[tex]P(X=0)=(8C0)(0.18)^0 (1-0.18)^{8-0}=0.2044[/tex]
[tex]P(X=1)=(8C1)(0.18)^1 (1-0.18)^{0-1}=0.3590[/tex]
And replacing we got:
[tex] P(X\geq 2)=1 -[0.2044 +0.3590]= 0.4366[/tex]
Then the probability that at least 2 disapprove of daily pot smoking is 0.4366
A video game requires at least 4 points to advance. Each solved puzzle is worth two points. Each solved riddle is worth 1 point. If x is the number of solved puzzles and y is the number of solved riddles, which graph represents the overall equation represented by this scenario (all points may not apply to the scenario)? On a coordinate plane, a solid straight line has a negative slope and goes through (0, 2) and (4, 0). Everything below the line is shaded. On a coordinate plane, a solid straight line has a negative slope and goes through (0, 2) and (4, 0). Everything above the line is shaded. On a coordinate plane, a solid straight line has a negative slope and goes through (0, 4) and (2, 0). Everything to the left of the line is shaded. On a coordinate plane, a solid straight line has a negative slope and goes through (0, 4) and (2, 0). Everything to the right of the line is shaded.
Answer:
Its D The Last Graph
Step-by-step explanation:
it just is my guy
Teresa's parents are getting phones that each and 64 GB of storage how many bits of storage come with each phone answer both in scientific in standard notation
Answer:
5.12 x 10¹¹ bit
Step-by-step explanation:
1GB = 8 x 10⁹ bits
so 64gb = 64 x 8 x 10⁹
= 512 x 10⁹
= 5.12 x 10¹¹ bits
scientific notation = 5.12 x 10¹¹ bits
standard Notation = 512 ,000,000,000 bits.
The length of a rectangle is 9 more than the width. The area is 162 square centimeters. Find the length and width of the rectangle.
Answer:
Length: 18
Width: 9
Step-by-step explanation:
Denote the width as x, hence the length is x+9. As a result, you can create the equation x(x+9) = 162. Solving, you find x = 9.
A financial advisor is analyzing a family's estate plan. The amount of money that the family has invested in different real estate properties is normally distributed with a mean of $225,000 and a standard deviation of $50,000. Use a calculator to find how much money separates the lowest 80% of the amount invested from the highest 20% in a sampling distribution of 10 of the family's real estate holdings.
Answer:
The amount of money separating the lowest 80% of the amount invested from the highest 20% in a sampling distribution of 10 of the family's real estate holdings is $238,281.57.
Step-by-step explanation:
Let the random variable X represent the amount of money that the family has invested in different real estate properties.
The random variable X follows a Normal distribution with parameters μ = $225,000 and σ = $50,000.
It is provided that the family has invested in n = 10 different real estate properties.
Then the mean and standard deviation of amount of money that the family has invested in these 10 different real estate properties is:
[tex]\mu_{\bar x}=\mu=\$225,000\\\\\sigma_{\bar x}=\frac{\sigma}{\sqrt{n}}=\frac{50000}{\sqrt{10}}=15811.39[/tex]
Now the lowest 80% of the amount invested can be represented as follows:
[tex]P(\bar X<\bar x)=0.80\\\\\Rightarrow P(Z<z)=0.80[/tex]
The value of z is 0.84.
*Use a z-table.
Compute the value of the mean amount invested as follows:
[tex]\bar x=\mu_{\bar x}+z\cdot \sigma_{\bar x}[/tex]
[tex]=225000+(0.84\times 15811.39)\\\\=225000+13281.5676\\\\=238281.5676\\\\\approx 238281.57[/tex]
Thus, the amount of money separating the lowest 80% of the amount invested from the highest 20% in a sampling distribution of 10 of the family's real estate holdings is $238,281.57.
Consider the equation below. (If an answer does not exist, enter DNE.) f(x) = x4 ln(x) (a) Find the interval on which f is increasing. (Enter your answer using interval notation.) Find the interval on which f is decreasing. (Enter your answer using interval notation.) (b) Find the local minimum and maximum values of f. local minimum value local maximum value (c) Find the inflection point. (x, y) = Find the interval on which f is concave up. (Enter your answer using interval notation.) Find the interval on which f is concave down. (Enter your answer using interval notation.)
Answer: (a) Interval where f is increasing: (0.78,+∞);
Interval where f is decreasing: (0,0.78);
(b) Local minimum: (0.78, - 0.09)
(c) Inflection point: (0.56,-0.06)
Interval concave up: (0.56,+∞)
Interval concave down: (0,0.56)
Step-by-step explanation:
(a) To determine the interval where function f is increasing or decreasing, first derive the function:
f'(x) = [tex]\frac{d}{dx}[/tex][[tex]x^{4}ln(x)[/tex]]
Using the product rule of derivative, which is: [u(x).v(x)]' = u'(x)v(x) + u(x).v'(x),
you have:
f'(x) = [tex]4x^{3}ln(x) + x_{4}.\frac{1}{x}[/tex]
f'(x) = [tex]4x^{3}ln(x) + x^{3}[/tex]
f'(x) = [tex]x^{3}[4ln(x) + 1][/tex]
Now, find the critical points: f'(x) = 0
[tex]x^{3}[4ln(x) + 1][/tex] = 0
[tex]x^{3} = 0[/tex]
x = 0
and
[tex]4ln(x) + 1 = 0[/tex]
[tex]ln(x) = \frac{-1}{4}[/tex]
x = [tex]e^{\frac{-1}{4} }[/tex]
x = 0.78
To determine the interval where f(x) is positive (increasing) or negative (decreasing), evaluate the function at each interval:
interval x-value f'(x) result
0<x<0.78 0.5 f'(0.5) = -0.22 decreasing
x>0.78 1 f'(1) = 1 increasing
With the table, it can be concluded that in the interval (0,0.78) the function is decreasing while in the interval (0.78, +∞), f is increasing.
Note: As it is a natural logarithm function, there are no negative x-values.
(b) A extremum point (maximum or minimum) is found where f is defined and f' changes signs. In this case:
Between 0 and 0.78, the function decreases and at point and it is defined at point 0.78;After 0.78, it increase (has a change of sign) and f is also defined;Then, x=0.78 is a point of minimum and its y-value is:
f(x) = [tex]x^{4}ln(x)[/tex]
f(0.78) = [tex]0.78^{4}ln(0.78)[/tex]
f(0.78) = - 0.092
The point of minimum is (0.78, - 0.092)
(c) To determine the inflection point (IP), calculate the second derivative of the function and solve for x:
f"(x) = [tex]\frac{d^{2}}{dx^{2}}[/tex] [[tex]x^{3}[4ln(x) + 1][/tex]]
f"(x) = [tex]3x^{2}[4ln(x) + 1] + 4x^{2}[/tex]
f"(x) = [tex]x^{2}[12ln(x) + 7][/tex]
[tex]x^{2}[12ln(x) + 7][/tex] = 0
[tex]x^{2} = 0\\x = 0[/tex]
and
[tex]12ln(x) + 7 = 0\\ln(x) = \frac{-7}{12} \\x = e^{\frac{-7}{12} }\\x = 0.56[/tex]
Substituing x in the function:
f(x) = [tex]x^{4}ln(x)[/tex]
f(0.56) = [tex]0.56^{4} ln(0.56)[/tex]
f(0.56) = - 0.06
The inflection point will be: (0.56, - 0.06)
In a function, the concave is down when f"(x) < 0 and up when f"(x) > 0, adn knowing that the critical points for that derivative are 0 and 0.56:
f"(x) = [tex]x^{2}[12ln(x) + 7][/tex]
f"(0.1) = [tex]0.1^{2}[12ln(0.1)+7][/tex]
f"(0.1) = - 0.21, i.e. Concave is DOWN.
f"(0.7) = [tex]0.7^{2}[12ln(0.7)+7][/tex]
f"(0.7) = + 1.33, i.e. Concave is UP.
MAN IF U ANSWER THIS QUESTION U ENDED 2020 Which of the following is equal to the square root of the cube root of 6? 6 to the power of one sixth 6 to the power of one third 6 to the power of two thirds 6 to the power of three halves
Answer:
6 to the power of 1/6
Step-by-step explanation:
In general, a root is the same as a fractional power. That is, ...
[tex]\sqrt[n]{x}=x^{\frac{1}{n}}[/tex]
So, the square root of a cube root is ...
(6^(1/3))^(1/2)
According to the rules of exponents, a power of a power is ...
(a^b)^c = a^(bc)
so, the above root of a root is ...
(6^(1/3))^(1/2) = 6^((1/3)(1/2)) = 6^(1/6)
The square root of the cube root of 6 is 6 to the power of 1/6.
Answer:
A) 6^1/6 or 6 to the power of 1 sixth
The percent defective for parts produced by a manufacturing process is targeted at 4%. The process is monitored daily by taking samples of sizes n = 160 units. Suppose that today’s sample contains 14 defectives. Determine a 88% confidence interval for the proportion defective for the process today. Place your LOWER limit, rounded to 3 decimal places, in the first blank. For example, 0.123 would be a legitimate answer. Place your UPPER limit, rounded to 3 decimal places, in the second blank. For example, 0.345 would be a legitimate entry.
Answer:
The 88% confidence interval for the proportion of defectives today is (0.053, 0.123)
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
For this problem, we have that:
[tex]n = 160, \pi = \frac{14}{160} = 0.088[/tex]
88% confidence level
So [tex]\alpha = 0.12[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.12}{2} = 0.94[/tex], so [tex]Z = 1.555[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.088 - 1.555\sqrt{\frac{0.088*0.912}{160}} = 0.053[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.088 + 1.555\sqrt{\frac{0.088*0.912}{160}} = 0.123[/tex]
The 88% confidence interval for the proportion of defectives today is (0.053, 0.123)
For the dilation, DO, K = (10, 0) → (5, 0), the scale factor is equal to _____.
Answer:
[tex] \frac{1}{2} [/tex]
Step-by-step explanation:
[tex]scale \: factor = \frac{5}{10} = \frac{1}{2} \\ [/tex]
5. Joan sold half of her comic books and then bought 8 more. She now has 14.how many did she
begin with?
Answer:
Dear ishika
Answer to your query is provided below
She begin with 12 comic books.
Step-by-step explanation:
After reading question , you will get that she sell half of comic books ; that is (12/2) = 6
And
Bought = 8 books
And
now have 14 books
Verify =
14 = 6+8
Point P is the center of dilation. Triangle A B C is dilated to create triangle A prime B prime C prime. The length of P A is 2 and the length of P B is 3. The Length of A A prime is 4 and the length of B B prime is 5. Is triangle A'B'C' a dilation of triangle ABC? Explain. Yes, it is an enlargement with a scale factor of 3. Yes, it is an enlargement with a scale factor of Eight-thirds. No, it is not a dilation because the points of the image are not moved away from the center of dilation proportionally. No, it is not a dilation because the sides of the image are proportionally reduced from the pre-image.
Answer:
C. No, it is not a dilation because the points of the image are not moved away from the center of dilation proportionally.
Step-by-step explanation:
Dilation is the process in which the size i.e dimensions of a given figure is either increased or decreased by a scale factor, without changing the shape of the figure.
Given that: PA = 2, PB = 3, A[tex]A^{I}[/tex] = 4, B[tex]B^{I}[/tex] = 5.
So that: P[tex]A^{I}[/tex] = 6, P[tex]B^{I}[/tex] = 8.
Therefore, triangle A'B'C' is not an exact dilation of triangle ABC. So that the correct option is; No, it is not a dilation because the points of the image are not moved away from the center of dilation proportionally.
Answer:
the answer is c
Step-by-step explanation:
what 826,497 in standard form answer
Answer:8.2 x 10^5
Step-by-step explanation:
what is the sum of 4m(m-6) and 8(m-4)?
Step-by-step explanation:
4m2 - 24m + 8m - 32
4m2 - 16m - 32
What is the common difference of the sequence 20, 17, 14, 11, 8.... ?
Answer:
-3
Step-by-step explanation:
every sequence goes down by -3
Answer:
take away 3. the common difference is 3
Step-by-step explanation:
take away 3
>
3. Express or-a-7
80X-9=7
Answer:
x = 1/5
Step-by-step explanation:
Step 1: Add 9 to both sides
80x = 16
Step 2: Divide both sides by 80
x = 16/80
Step 3: Simplify by dividing top and bottom by 16
x = 1/5
And we have our final answer!
Answer:
x = 1/5
Step-by-step explanation:
80x - 9 = 7
Add 9 into both sides.
80x = 7 + 9
80x = 16
Divide 80 into both sides.
x = 16/80
Simplify.
x = 1/5
The price-earnings ratios of a sample of stocks have a mean value of 13.5 and a standard deviation of 2. If the ratios have a bell-shaped distribution, what can be said about the proportion of ratios that fall between 11.5 and 15.5
Answer:
[tex]P(11.5<X<15.5)=P(\frac{11.5-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{13.5-\mu}{\sigma})=P(\frac{11.5-13.5}{2}<Z<\frac{15.5-13.5}{2})=P(-1<z<1)[/tex]
And we can find the probability with this difference
[tex]P(-1<z<1)=P(z<1)-P(z<-1)[/tex]
And we can use the normal standard distribution or excel and we got:
[tex]P(-1<z<1)=P(z<1)-P(z<-1)=0.841-0.159=0.682[/tex]
So then we expect a proportion of 0.682 between 11.5 and 13.5
Step-by-step explanation:
Let X the random variable that represent the price earning ratios of a population, and for this case we know the distribution for X is given by:
[tex]X \sim N(13.5,2)[/tex]
Where [tex]\mu=13.5[/tex] and [tex]\sigma=2[/tex]
We want to find the following probability
[tex]P(11.5<X<15.5)[/tex]
And we can use the z score formula given by:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
Using this formula we got:
[tex]P(11.5<X<15.5)=P(\frac{11.5-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{13.5-\mu}{\sigma})=P(\frac{11.5-13.5}{2}<Z<\frac{15.5-13.5}{2})=P(-1<z<1)[/tex]
And we can find the probability with this difference
[tex]P(-1<z<1)=P(z<1)-P(z<-1)[/tex]
And we can use the normal standard distribution or excel and we got:
[tex]P(-1<z<1)=P(z<1)-P(z<-1)=0.841-0.159=0.682[/tex]
So then we expect a proportion of 0.682 between 11.5 and 13.5
The volume of a trianglular prism is 54 cubic units. What is the value of x?
3
5
7
9
Answer:
X is 3 units.
Step-by-step explanation:
Volume of prism is cross sectional area multiplied by length. So 1/2 ×2× x ×2 into 3x, which is equal to 6x^2. So, 6x^2=54. Therefore, x=3.
D
С
Micaela tried to rotate the square 180° about the origin.
Is her rotation correct? If not, explain why.
O No, she translated the figure instead of rotating it.
O No, she reflected the figure instead of rotating it.
O No, the vertices of the image and pre-image do not
correspond.
Yes, the rotation is correct.
cu
Answer:
it’s C
Step-by-step explanation:
No, the vertices of the image and pre-image do not correspond
No, the vertices of the image and pre-image do not correspond, Micaela tried to rotate the square 180° about the origin. Hence, option C is correct.
What is rotation about the origin?A figure can be rotated by 90 degrees clockwise by rotating each vertex of the figure 90 degrees clockwise about the origin.
Let's take the vertices of a square with points at (+1,+1), (-1,+1), (-1,-1), and (+1,-1), centered at the origin, can be found in the following positions after rotation:
The vertex (+1,+1) would be rotated to the point (-1,-1).The vertex (-1,+1) would be rotated to the point (+1,-1).The vertex (-1,-1) would be rotated to the point (+1,+1).The vertex (+1,-1) would be rotated to the point (-1,+1).Micaela's rotation must be accurate if it led to the same points. Her rotation is incorrect if the points are different, though.
It is impossible to tell if Micaela's rotation is accurate without more details or a diagram.
Thus, option C is correct.
For more information about rotation about the origin, click here:
https://brainly.com/question/30198965
#SPJ7
what is the answer to the equation -(-(-(-2)))
Answer:
2
Step-by-step explanation:
Since there are four negative signs, we have -1 multiplying each other 4 times, multiplying by positive 2. This is then 1 * 2, which is 2.
Answer:
+2
Step-by-step explanation:
=> -(-(-(-2))))
=> -(-(+2))
=> -(-2)
=> +2
You are interested in estimating the the mean age of the citizens living in your community. In order to do this, you plan on constructing a confidence interval; however, you are not sure how many citizens should be included in the sample. If you want your sample estimate to be within 5 years of the actual mean with a confidence level of 97%, how many citizens should be included in your sample
Question:
You are interested in estimating the the mean age of the citizens living in your community. In order to do this, you plan on constructing a confidence interval; however, you are not sure how many citizens should be included in the sample. If you want your sample estimate to be within 5 years of the actual mean with a confidence level of 97% , how many citizens should be included in your sample? Assume that the standard deviation of the ages of all the citizens in this community is 18 years.
Answer:
61.03
Step-by-step explanation:
Given:
Standard deviation = 18
Sample estimate = 5
Confidence level = 97%
Required:
Find sample size, n.
First find the Z value. Using zscore table
Z-value at a confidence level of 97% = 2.17
To find the sample size, use the formula below:
[tex] n = (Z * \frac{\sigma}{E})^2[/tex]
[tex] n = ( 2.17 * \frac{18}{5})^2 [/tex]
[tex] n = (2.17 * 3.6)^2 [/tex]
[tex] n = (7.812)^2 [/tex]
[tex] n = 61.03 [/tex]
Sample size = 61.03
Tasha wants to take money out of the ATM for a taxi fare. She wants to do a quick estimate to see if taking $120 out of her bank account will overdraw it. She knows she had $325 in the account this morning when she checked her balance. Today she bought lunch for $19, a dress for $76, a pair of shoes for $53, and a necklace for $23. She also saw a movie with a friend for $12. Rounding each of her expenses to the nearest tens place, estimate how much money Tasha has left in her account before she goes to the ATM. Do not include the $ in your answer.
Answer:145
Step-by-step explanation: $19=20 76=80 53=50 23=20 12=10 total = 180 325-180 =145
A sample of 1500 people from a certain industrial community showed that 800 people suffered from a lung disease. A sample of 1000 people from a rural community showed that 300 suffered from the same lung disease. Assume these two proportions give good estimates of population proportions, respectively. Find the probability that the difference of the proportions (industrial - rural) is greater than 0.2 if two samples of size 150 and 100 are drawn from the two populations, respectively.
Answer:
The probability that the difference of the proportions (industrial - rural) is greater than 0.2 is 0.7054
Step-by-step explanation:
Solution
Given that:
n₁ = 1500
x₁ = 800
p₁ =800/1500 =0.533
q₁ = 1- 0.533 = 0.467
Thus,
n₂ =1000
x₂ = 300
p₂ = 300/1000 = 0.3
q₂ = 1-0.3 =0.7
So,
p₁ - p₂ = 0.533 - 0.3
=0.233
Now,
SE (p₁ - p₂ ) =√0.533 * 0467/150 + 0.3 * 0.7/1000
=0.0613
So,
p ( p₁ - p₂ > 0.2
= p ( Ƶ > 0.2 - 0.233/0.0613
p = ( Ƶ > - 0.54)
= 0.7054
Simplify 8x + 10y + 9x - 3y by identifying and combining like terms. A. 17x + 13y B.24y C.17x+7 D.17x + 7y
Answer:
17x +7y
Step-by-step explanation:
8x + 10y + 9x - 3y
Combine like terms
8x+ 9x + 10y - 3y
17x +7y
8x+9x are like terms and 10y -3y are like terms
Answer:
17x + 7y
Step-by-step explanation:
8x + 10y + 9x - 3y
Rearrange.
8x + 9x + 10y - 3y
Factor out x and y.
x (8 + 9) + y (10 - 3)
Add or subtract.
x (17) + y (7)
17x + 7y
Luther evaluated 2 to the power of 3 as 9 and wade evaluated 3 to the power of 2 as 9 are both students correct explain why or why not
Answer:
Luther is wrong
Wade is right
Step-by-step explanation:
Luther's case 2^3 = 2x2x2 = 8
Wade's case 3^3 = 3 x 3 = 9
Answer:
Luther is incorrect, while Wade is correct. (2)(2)(2)=8, not 9. (3)(3)= 9.
Step-by-step explanation:
I put that as my answer and it was counted as right.
Subtract -6 4/9-3 2/9-8 2/9
Answer:
[tex]-\frac{161}{9}=\\or\\-16\frac{8}{9}[/tex]
Step-by-step explanation:
[tex]-6\frac{4}{9}-3\frac{2}{9}-8\frac{2}{9}=\\\\-\frac{58}{9}-\frac{29}{9}-\frac{74}{9}=\\\\-\frac{161}{9}=\\\\-16\frac{8}{9}[/tex]
How would plot y=1/4x-4 on graph
Answer:
________________________
if rectangle ABCD was reflected over the y-axis, reflected over x axis, and rotated 180°, where would point A' lie?
Answer:
Option C (-4,-1) (In Quadrant III)
Step-by-step explanation:
Coordinate = (-4,1)
=> Reflecting over y-axis will make the coordinate (4,1)
=> Reflecting across x-axis will make the coordinate (4,-1)
=> Rotating 180 will make it (-4,-1)
Use the given degree of confidence and sample data to construct a confidence interval for the population mean μ. Assume that the population has a normal distribution. Thirty randomly selected students took the calculus final. If the sample mean was 95 and the standard deviation was 6.6, construct a 99% confidence interval for the mean score of all students.
A. 91.68
Answer:
B) 92.03 < μ < 97.97
99% confidence interval for the mean score of all students.
92.03 < μ < 97.97
Step-by-step explanation:
Step(i):-
Given sample mean (x⁻) = 95
standard deviation of the sample (s) = 6.6
Random sample size 'n' = 30
99% confidence interval for the mean score of all students.
[tex]((x^{-} - Z_{0.01} \frac{S}{\sqrt{n} } , (x^{-} + Z_{0.01} \frac{S}{\sqrt{n} })[/tex]
step(ii):-
Degrees of freedom
ν = n-1 = 30-1 =29
[tex]t_{0.01} = 2.462[/tex]
99% confidence interval for the mean score of all students.
[tex]((95 - 2.462 \frac{6.6}{\sqrt{30} } , 95 + 2.462\frac{6.6}{\sqrt{30} } )[/tex]
( 95 - 2.966 , 95 + 2.966)
(92.03 , 97.97)
Final answer:-
99% confidence interval for the mean score of all students.
92.03 < μ < 97.97
What is the slope and y-intercept of the equation on the graph?
A. M=3/2,y-int=-3
B.m=3/2,y-int=3
C.m=2/3,y-int=-3
D.m=2/3,y-int=4
Answer:
m = 3/2, y intercept = 3
Step-by-step explanation:
The y intercept is where it crosses the y axis. It crosses at 3
The slope is found by using two points on the line
(-2,0) and (0,3)
m= (y2-y1)/(x2-x1)
= (3-0)/(0- -2)
= 3 / +2
=3/2