Answer:
7000
Step-by-step explanation:
If the hundreds place is higher than 5, then add 1 to the thousands place.
Use any method to multiply (-14ab)(a + 3b - 4c).
Answer:
-14a^2b-42ab^2+56abc
Step-by-step explanation:
You can use the FOIL method
multiply the first numbers
then inner
then outer
then last
= [70 + (-30)] + [2 + (-9)] + [0.3 + (-0.10]
Answer:
33.2
Step-by-step explanation:
70−30+2−9+0.3−0.1
=40+2−9+0.3−0.1
=40+−7+0.3−0.1
=33+0.3−0.1
=33+0.2
=33.2
Answer:
33.2
Step-by-step explanation
If we start from the left and work our way right:
70+(-30) is the same as 70-30 which would give 40
2+(-9) is the same as 2-9 which would give -7
0.3(-0.1) is the same as 0.3-0.1 which would give 0.2
now if you put them together
40-7+.2 gives 33.2
The amount of pollutants that are found in waterways near large cities is normally distributed with mean 9 ppm and standard deviation 1.5 ppm. 38 randomly selected large cities are studied. Round all answers to 4 decimal places where possible.
1. What is the distribution of XX? XX ~ N(,)
2. What is the distribution of ¯xx¯? ¯xx¯ ~ N(,)
3. What is the probability that one randomly selected city's waterway will have more than 9.6 ppm pollutants?
4. For the 37 cities, find the probability that the average amount of pollutants is more than 9.6 ppm.
5. For part d), is the assumption that the distribution is normal necessary? YesNo
6. Find the IQR for the average of 37 cities.
Q1 = ppm
Q3 = ppm
IQR: ppm
Answer:
Step-by-step explanation:
Hello!
There are two values of n in the text, I'll use the one that appears in all the questions.
The variable of interest is
X: pollutants found in waterways near large cities. (ppm)
This variable has a normal distribution with parameters μ= 9ppm and σ= 1.5ppm
1) X~N(μ;σ²)
X~N(9;2.25)
2) The distribution of the sample mean is X~N(μ;σ²/n)
σ²/n= 2.25/37= 0.06
X~N(9;0.06)
3) P(X>9.6)
To calculate this probability you have to use the standard normal distribution. Using the population parameters, you can calculate the corresponding Z value:
Z= (X-μ)/σ= (9.6-9)/1.5= 0.4
P(Z>0.4)= 1-P(Z≤0.4)= 1 - 0.65542= 0.34458
The probability of selecting a city at random and finding 9.6ppm pollutants.
4) In this item, instead of calculating the probability of one value of the variable you have to calculate the probability of the sample average taking a determined value. Because of this, you have to work using the distribution of the sample mean, instead of the distribution of the variable.
P(X[bar]>9.6)
Z= (X[bar]-μ)/(σ/√n)= (9.6-9)/√0.06= 2.45
P(Z>2.45)= 1 - P(Z≤2.45)= 1 - 0.99286= 0.00714
5) The assumption of a normal distribution is not necessary for item 4. Since the sample size is large enough (greater than 30) you can apply the central limit theorem and approximate the distribution of the sample mean to normal, regarding the distribution of the original variable.
6)
In this case, you have to work starting with the standard normal distribution and then "translate" the Z values into values of the average amount of pollutants.
The first quartile divides the bottom 25% of the distribution from the top 75%, symbolically:
P(Z≤z₁)= 0.25
z₁= -0.674
z₁= (X[bar]-μ)/(σ/√n)
z₁*(√n/σ)=X[bar]-μ
X[bar]=z₁*(√n/σ)+μ
X[bar]=(-0.674)*(√37/1.5)+9= 6.27ppm
The third quartile divides the bottom 75% of the distribution from the top 25%, symbolically:
P(Z≤z₂)= 0.75
z₂= 0.674
z₂= (X[bar]-μ)/(σ/√n)
z₂*(√n/σ)=X[bar]-μ
X[bar]=z₂*(√n/σ)+μ
X[bar]=(0.674)*(√37/1.5)+9= 11.7.3ppm
IQR= Q₃-Q₁= 11.73-6.27= 5.46ppm
I hope this helps!
Which point is an x-intercept of the quadratic function f(x) = (x + 6)(x – 3)? (0,6) (0,–6) (6,0) (–6,0)
Answer: (-6, 0)
Step-by-step explanation:
X-intercepts of equations are any points on the equation that lie on the x-axis, or the horizontal line "y = 0".
In order to find the x-intercept of an equation, find the points that will satisfy the equation "y = 0":
y = (x + 6)(x - 3)
y = 0
(x + 6)(x - 3) = 0
With this equation, you can find which points lie on the x-axis.
When x = -6, the equation is: 0 * -9 = 0, which is correct.
When x = 3, the equation is 9 * 0 = 0, which is correct.
Make sure you're picking the correct coordinate out of the answer choices.
The x-coordinates are -6 and 3, and the y-coordinates are 0, because the points lie on the x-axis.
The correct answer is (-6, 0).
(3, 0) is also correct, but the question does not require it.
Answer:
D
Step-by-step explanation:
Please help ASAP thank you
Answer:
q
Step-by-step explanation:
Since AB is a transversal of the two parallel lines, the angle with measure 135 degrees and angle q are vertical angles. Therefore, their measure must be equal.
Hope this helps!
Can anyone help???????
Answer:
80
Step-by-step explanation:
For every additional 10 hrs, you get 200 more dollars.
I’ll give the bralyist to the first correct answer
Let f be defined as shown.
What is f1 (-7)?
Answer:
The answer is 2
From the function when the input is 2 the output is -7. The inverse reverses the order so the input will be -7 and the output will be 2.
What is true about this system of equations {2x-y=5 , x=4
Answer: The systems of equations have only one solution because if x 4 then y is equal to 3 which proves it that is a one solution graph.
Step-by-step explanation:
2(4)- y = 5
8 - y= 5
-8 -8
-1y= -3
y= 3
The function s(t) represents the position of an object at time t moving along a line. Suppose s (1 )equals 62 and s (5 )equals 102. Find the average velocity of the object over the interval of time [1 comma 5 ].
Answer:
v = 10
the average velocity of the object over the interval of time [1, 5 ] is 10 units per unit time
Step-by-step explanation:
Given;
function s(t) represents the position of an object at time t moving along a line.
s(1) = 62 at t1 = 1
s(5) = 102 at t5 = 5
Velocity v = distance/time
Average velocity v over time t is;
v = ∆s/∆t
v = [s(5) - s(1)]/[t5 - t1]
Substituting the given values;
v = (102 - 62)/(5 - 1)
v = 10
the average velocity of the object over the interval of time [1, 5 ] is 10 units per unit time
The price of a ring was increased by 9% to £1800. What was the price before the increase? Give your answer to the nearest penny.
Answer:
1651
Step-by-step explanation:
let s say that the price before the increase is x
to apply an increase of 9% it does x + x*0.09 = x*(1+0.09)=x*1.09
and we know that this value is 1800
so
x*1.09=1800
<=>
x = 1800/1.09=1651.376147
to the nearest penny it gives 1651
Answer:
Hello!
Answer: 1651
I hope that was correct. Please let me know, thank you!
Step-by-step explanation:
The students in Mrs. Willow's reading class are all reading the same novel independently. Four students create a graph of their reading rates, in words per minute, as shown below. Which student reads the fastest? A. Mason B. RIley C. Sarah D. Charlie
Answer:
Mason reads the fastest
Answer:
c
Step-by-step explanation:
try to see how much every person reads every one or two minutes.
Charlie: 350 in two min
Mason :400 in two min
Sarah: 450 in two min (the middle of 300-600 is 450)
so between the three Sarah wins.
now Reilly is a bit more difficult but you can see that she read 4000 in 20 min. so if we divide it by 10 we can see she reads 400 in 2 min. and therefore Sarah os the winner.
The Tennessean, an online newspaper located in Nashville, Tennessee, conducts a daily poll to obtain reader opinions on a variety of current issues. In a recent poll, readers responded to the following question: "If a constitutional amendment to ban a state income tax is placed on the ballot in Tennessee, would you want it to pass? Possible responses are yes or no,or not sure.
Required:
a. What was the sample size for this poll?
b. Are the data categorical or quantitative?
c. Would it make more sense to use averages or percentages as a summary of the data for this question?
d. Of the respondents, 67% said Yes, they would want it to pass. How many individuals provided this response?
Answer:
Step-by-step explanation:
a. The sample size for the poll would be at most 10% of the total readers of the tennessean.
b. Categorical data...data collected in groups or categories.
c. Yes it would make more sense to use percentages as this gives a better estimate for proportion.
d. The number of individual that provided this response is 67% of the sample size (which is at most 10% of the total population of readers of the online newspaper).
The amount of coffee that people drink per day is normally distributed with a mean of 17 ounces and a standard deviation of 4 ounces. 15 randomly selected people are surveyed. Round all answers to 4 decimal places where possible.
a) What is the distribution of XX? XX ~ N(,)
b) What is the distribution of ¯xx¯? ¯xx¯ ~ N(,)
c) What is the probability that one randomly selected person drinks between 15.5 and 18 ounces of coffee per day?
d) For the 15 people, find the probability that the average coffee consumption is between 15.5 and 18 ounces of coffee per day.
e) For part d), is the assumption that the distribution is normal necessary? YesNo
f) Find the IQR for the average of 15 coffee drinkers.
Q1 = ounces
Q3 = ounces
IQR: ounces
Answer:
Step-by-step explanation:
(a)
The distribution of X is Normal Distribution with mean [tex]= \mu =17[/tex] and Variance [tex]= \sigma^{2} = 16 \ i.e., X \sim N (17, 16),[/tex]
(b)
The distribution of [tex]\bar{x}[/tex] is Normal Distribution with mean [tex]= \mu =17[/tex] and Variance = [tex]\sigma^{2}/n = 16/15= 1.0667[/tex].i.e., [tex]\bar{x}\sim N(17,1.0667)[/tex]
c)
To find P(15.5 < X < 18):
Case 1: For X from 15.5 to mid value:
Z = (15.5 - 17)/4 = - 0.375
Table of Area Under Standard Normal Curve gives area = 0.1480
Case 2: For X from mid value to 18:
Z = (18 - 17)/4 = 0.25
Table of Area Under Standard Normal Curve gives area = 0.0987
So,
P(15.5 < X< 18) = 0.1480 +0.0987 = 0.2467
So,
Answer is:
0.2467
(d)
[tex]SE = \sigma/\sqrt{n}\\\\= 4/\sqrt{15}[/tex]
= 1.0328
To find [tex]P(15.5 < \bar{x}< 18):[/tex]
Case 1: For [tex]\bar{x}[/tex] from 15.5 to mid value:
Z = (15.5 - 17)/1.0328 = - 1.4524
Table of Area Under Standard Normal Curve gives area = 0.4265
Case 2: For X from mid value to 18:
Z = (18 - 17)/1.0328 = 0.9682
Table of Area Under Standard Normal Curve gives area = 0.3340
So,
[tex]P(15.5 < \bar{x}< 18) = 0.4265 + 0.3340 = 0.7605[/tex]
So,
Answer is:
0.7605
(e)
Correct option:
No
because Population SD is provided.
(f)
(i)
Q1 is given by:
[tex]- 0.6745 = (\bar{x} - 17)/1.0328[/tex]
So,
X = 17 - (0.6745 * 1.0328) = 17 - 0.6966 = 16.3034
So,
Q1 = 16.3034
(ii)
Q3 is given by:
[tex]0.6745 = (\bar{x} - 17)/1.0328[/tex]
So,
X = 17 + (0.6745 * 1.0328) = 17 + 0.6966 = 17.6966
So,
Q3= 17.6966
(iii)
IQR = Q3 - Q1 = 17.6966 - 16.3034 = 1.3932
So
Answers are:
Q1 = 16.3034 ounces
Q3 = 17.6966 Ounces
IQR = 1.3932 Ounces
Which one of the following is always true?a. The coefficient of variation measures variability in a positively skewed data set relative to the size of the median.b. None of the suggested answers are correctc. The coefficient of variation is a measure of relative dispersion that expresses the standard deviation as a percentage of the mean, for any data on a ratio scale and an interval scale.d. The interquartile range is very unique in the sense that it is a measure of central tendency as well as a measure of dispersion.e. The coefficient of variation should only be used to compare positive data on an interval scale.
Answer:
C. The coefficient of variation is a measure of relative dispersion that expresses the standard deviation as a percentage of the mean, for any data on a ratio scale and an interval scale
Step-by-step explanation:
Th Coefficient of Variance is a measure of dispersion that can be calculated using the formula:
[tex]CV = \frac{\sigma_{x} }{\mu_{x} } * 100%[/tex]
Where [tex]\sigma{x}[/tex] is the Standard Deviation
and [tex]\mu_{x}[/tex] is the sample mean
From the formula written above, it is shown that the Coefficient of Variation expresses the Standard Deviation as a percentage of the mean.
Coefficient of variation can be used to compare positive as well as negative data on the ratio and interval scale, it is not only used for positive data.
The Interquartile Range is not a measure of central tendency, it is a measure of dispersion.
Are You Ready for More?: Two raised to the 12th power is equal to 4,096. How many other
whole numbers can you raise to a power and get 4,096? Explain or show your reasoning.
(1 Point)
2^12 = 4096
Answer:
4, 8, 16,64 and 4096.
Step-by-step explanation:
We are already given: [tex]4096=2^{12}[/tex]
To determine other whole numbers that can be raised to a power to obtain 4096, we apply the product rule of indices.
Product Rule of Indices: [tex]a^{xy}=(a^x)^y[/tex]
Now 12 can be factored in the following ways where one of the terms must be a perfect square:
12=2 X 612 =6 X 212 =3 X 412 =4 X 312=1 X 12[tex]2^{12}=(2^2)^6=4^6\\\\2^{12}=(2^6)^2=64^2\\\\2^{12}=(2^4)^3=16^3\\\\2^{12}=(2^3)^4=(8^2)^2=8^{2*2}=8^4\\\\2^{12}=(2^{12})^1=4096^1 $(This is the trivial case)[/tex]
Therefore, the other whole numbers that can be raised tp a power to obtain 4096 are: 4, 8, 16, 64 and 4096.
Simplify the following:
(4x^3+2x) + (8x^3 -5x + 4)
Answer:
12x^3 - 3x + 4
Im 100% percent sure and if you are kind enough, I’d love a BRAINLIEST :)
Rectangle WXYZ was dilated to create W'X'Y'Z'. Point G is the center of dilation. Rectangle W X Y Z was dilated to create smaller rectangle W prime X prime Y prime Z prime. The length of G Z prime is 1.5. The length of Z prime Z is 7.5. Side W X is 3 units and side X Y is 6 units. What is W'X'? 0.5 units 1.2 units 1.5 units 1.8 units
Answer:
0.5 units
Step-by-step explanation:
The dilation factor is ...
(GZ')/(GZ) = (GZ')/(GZ' +Z'Z) = 1.5/(1.5 +7.5) = 1/6
Side WX is 3 units, so side W'X' is (1/6)(3 units) = 1/2 units
W'X' is 0.5 units.
Answer:
It is .5 on edge
Step-by-step explanation:
I took the test
What is a word problem for 15-28?
Answer:
valarie had 28 pencils , she gave 15 pencils away to people. How many pencils will she have left?
Step-by-step explanation:
hope this helps:)
How do I explain this answer
Answer:
199
Step-by-step explanation:
i dont know
An appliance repairman charges $25 plus $40 per hour for house calls. Write the rule as an equation that relates hours worked x and his fee y.
To get the total fee, you need to multiply the hourly rate by number of hours worked and add that to the flat fee of $25.
The equation would be y = 40x + 25
A local store developed a multiplicative time-series model to forecast its revenues in future quarters, using quarterly data on its revenues during the 5-year period from 2008 to 2012. The following is the resulting regression equation: log10 = 6.102 + 0.012 X - 0.129 Q1 - 0.054 Q2 + 0.098 Q3 where is the estimated number of contracts in a quarter X is the coded quarterly value with X = 0 in the first quarter of 2008 Q1 is a dummy variable equal to 1 in the first quarter of a year and 0 otherwise Q2 is a dummy variable equal to 1 in the second quarter of a year and 0 otherwise Q3 is a dummy variable equal to 1 in the third quarter of a year and 0 otherwise To obtain a fitted value for the fourth quarter of 2009 using the model, which of the following sets of values should be used in the regression equation?1. In testing the significance of the coefficient of X in the regression equation (0.012) which has a p-value of 0.02. Which of the following is the best interpretation of this result? a. The quarterly growth rate in revenues is significantly different from 0%. b. The quarterly growth rate in revenues is not significantly different from 0%. c. The quarterly growth rate in revenues is significantly different from 1.2%. d. The quarterly growth rate in revenues is not significantly different from 1.2%. e. The quarterly growth rate in revenues is significantly different from 1.2% 2. using the regression equation, the forecast for the revenues in the fourth quarter of 2004 is:______ a. 6,426 b. 2,666,858 c. 6,638 d. 2,741,574 e. 6,414
Answer:
The quarterly growth rate in revenues is significantly different from 1.2%.
b. 2,666,858
Step-by-step explanation:
Given that:
The regression equation can be represented as :
[tex]log_{10} \hat Y= 6.102+0.012 X - 0.129 Q_1 - 0.054 Q_2 + 0.098 Q_3[/tex]
In testing the significance of the coefficient of X in the regression equation (0.012) which has a p-value of 0.02.
The null and alternative hypothesis can be stated as;
[tex]H_0:[/tex] The quarterly growth rate in revenues is not significantly different from 1.2%.
[tex]H_a:[/tex] The quarterly growth rate in revenues is significantly different from 1.2%.
The decision rule is to reject the null hypothesis if the p-value is less than 0.05.
From above ; the p-value = 0.02 which is less than 0.05.
Conclusion:
Thus; we reject the null hypothesis and accept the alternative hypothesis. i.e
The quarterly growth rate in revenues is significantly different from 1.2%.
b.
Since [tex]Q_1=Q_2=Q_3 = 0[/tex] ; X = 27
Thus ;
[tex]log_{10} \hat Y= 6.102+0.012 X - 0.129 Q_1 - 0.054 Q_2 + 0.098 Q_3[/tex]
[tex]log_{10} \hat Y= 6.102+0.012 (27)[/tex]
[tex]\hat Y=10^{ 6.102+0.012 (27) }[/tex]
[tex]\hat Y =[/tex] 2666858.665
[tex]\hat Y =[/tex] 2,666,858
Find the range of the set of numbers shown by the box-and-whisker plot.
6
6
7
8
9
10
11
12
13
14
16
16
17
18
19
20
21
22
Answer:
16
Step-by-step explanation:
The range is the difference between the highest and lowest number of a data set. 22-6=16
Please answer this correctly
Answer:
The answer is 2.5ft².
Step-by-step explanation:
Given that the area of trapezoid formula is A = 1/2×(a+b)×h where a and b is the length and h is the height. Then substitute the following values into the formula :
[tex]area = \frac{1}{2} \times (a + b) \times h[/tex]
Let a = 1.2,
Let b = 0.8,
Let c = 2.5,
[tex]area = \frac{1}{2} \times (1.2 + 0.8) \times 2.5[/tex]
[tex]area = \frac{1}{2} \times 2 \times 2.5[/tex]
[tex]area = 2.5 {feet}^{2} [/tex]
What is the area of the obtuse triangle below?
A. 90 sq units
B. 23 sq units
C. 18 sq units
D. 45 sq units
Answer:
A. 90 sq. units
Step-by-step explanation:
5(18) = 90
What is the solution set of the quadratic inequality x2+x-2
Answer:
The solution set is x = 1 and x = -2
Step-by-step explanation:
Use the given information to find the P-value. Also, use a 0.05 significance level and state the conclusion about the null hypothesis (reject the null hypothesis or fail to reject the null hypothesis). The test statistic in a left-tailed test is z = -1.63.
a. 0.1032; fail to reject the null hypothesis
b. 0.0516; reject the null hypothesis
c. 0.9484; fail to reject the null hypothesis
d. 0.0516; fail to reject the null hypothesis
Answer:
Option d
Step-by-step explanation:
The p-value is 0.0516 which is not statistically significant to reject the null hypothesis. Thus we will fail to reject the null hypothesis.
I need this question today. Pls help
[tex]answer \\ = 2 , 4 , 5 \\ additional \: information \\ let \: r \: be \: a \: relation \: a \: to \: b. \: then \: the \: set \\ of \: first \: components \: or \: the \: set \: of \: \\ elements \: of \: a \: are \: called \: domain \\ and \: the \: set \: of \: second \: components \\ or \: the \: set \: of \: elements \: of \: b \: are \: called \: the \: range. \\ hope \: it \: helps[/tex]
You have 10 shirts 2 of them are black what is the probability of not choosing a black shirt.
Answer:
80% or 4/5
Step-by-step explanation:
the probability of not choosing a black shirt
P = number of shirts that are not black ÷ total number of shirts
Total number of shirts = 10
Number of black shirts = 2
Number of shirts that are not black = 10-2 = 8
P = 8/10 = 4/5 or 80%
PLEASE HELP QUICKLY AS POSSIBLE THANK YOU :)
Answer:
Option (B).
Step-by-step explanation:
From the table shown in the figure attached,
There is a common difference of 5 in every successive and previous term, so the relation is a linear relation.
Let the equation representing the relation is,
y - y' = m(x - x')
where m = slope of the line
Now we choose two ordered pairs from the table,
Let the points are (10, 54) and (11, 59)
Slope = [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
m = [tex]\frac{59-54}{11-10}[/tex]
m = 5
Now the equation of of the line passing through (10, 54) and slope = 5
y - 54 = 5(x - 10)
y - 54 = 5x - 50
y = 5x - 50 + 54
y = 5x + 4
By substituting the values of x and y from the ordered pairs given in the options we find option B satisfies the equation.
For (2, 14),
14 = 5×2 + 4
14 = 14 [True]
For (3, 19),
19 = 5×3 + 4
19 = 19 [True]
Therefore, option (B) will be the answer.
Help! Please do a,b,c and d with explanation
Answer:
a. 235°
b. 146.03 km
c. 105 km
d. 193 km
Step-by-step explanation:
a. The bearing of E from A is given as 55°. The bearing in the opposite direction, from E to A, is this angle with 180° added:
bearing of A from E = 55° +180° = 235°
__
b. The internal angle at E is the difference between the external angle at C and the internal angle at A:
∠E = 134° -55° = 79°
The law of sines tells you ...
CE/sin(∠A) = CA/sin(∠E)
CE = CA(sin(∠A)/sin(∠E)) = (175 km)·sin(55°)/sin(79°) ≈ 146.03 km
CE ≈ 146 km
__
c. The internal angle at C is the supplement of the external angle, so is ...
∠C = 180° -134° = 46°
The distance PE is opposite that angle, and CE is the hypotenuse of the right triangle CPE. The sine trig relation is helpful here:
Sin = Opposite/Hypotenuse
sin(46°) = PE/CE
PE = CE·sin(46°) = 146.03 km·sin(46°) ≈ 105.05 km
PE ≈ 105 km
__
d. DE can be found from the law of cosines:
DE² = DC² +CE² -2·DC·CE·cos(134°)
DE² = 60² +146.03² -2(60)(146.03)cos(134°) ≈ 37099.43
DE = √37099.43 ≈ 192.6 . . . km
DE is about 193 km
