Answer:
1) For every copy she sells, her pay increases by $110
2) Her total pay is 2300
Step-by-step explanation:
1) X is the number of copies she sells. In the equation 110X+ 2300 = Y, X will determine how many times 110 is multiplied. So, for every increase by one in X, Y will also go up by 110
eg.
110(50) + 2300 = 7800 -- if she sells 50 copies
110(51) + 2300 = 7910 -- if she sells 51 copies,
2) If she doesn't sell any copies, the equation becomes 110 * 0 + 2300. Anything multiplied by 0 equals 0, so the equation equals 0 + 2300 = 2300 = Y
Therefore, if she doesn't sell any copies, she will get a pay of $2300
A 95% confidence interval indicates that:
A. 95% of the intervals constructed using this process based on samples from this population will
include the population mean
B. 95% of the time the interval will include the sample mean
C. 95% of the possible population means will be included by the interval
D. 95% of the possible sample means will be included by the interval
95% interval would be 95% of the population mean.
The answer should be:
A. 95% of the intervals constructed using this process based on samples from this population will
include the population mean
Answer:
A
Step-by-step explanation:
A 95% confidence interval indicates that 95% of the intervals constructed using this process based on samples from this population will
include the population mean
PLEASE HELP FOR 70 POINTS!!!!!! Maria and Jackson like in adjacent neighborhoods. If they superimpose a coordinate grid on the map of their neighborhoods, Maria lives at (–9, 1) and Jackson lives at (5, –4). Each unit on the grid is equal to approximately 0.132 mile. 8. How far apart do Maria and Jackson live to the nearest thousandth? 9. If April lives equidistant to both Maria and Jackson, at what coordinate on the grid would she live? 10. How far apart would Maria and April live to the nearest thousandth?
Answer:
8) 1.962 miles
9) (-2, -1.5)
10) 0.515 miles
Step-by-step explanation:
√(-9 - 5)² + (1 - -4)² = 14.866
14.866 x .132 = 1.962
(-9+5)/2, (1 + -4)/2
-4/2, -3/2
-2, -3/2
√(-2 - 1)² + (-3/2 - -4)² = 3.905
3.905 x .132 = 0.515 miles
Given that −4i is a zero, factor the following polynomial function completely. Use the Conjugate Roots Theorem, if applicable. f(x)=x4−2x3+x2−32x−240
Answer:
[tex]\large \boxed{\sf \bf \ \ f(x)=(x-4i)(x+4i)(x+3)(x-5) \ \ }[/tex]
Step-by-step explanation:
Hello, the Conjugate Roots Theorem states that if a complex number is a zero of real polynomial its conjugate is a zero too. It means that (x-4i)(x+4i) are factors of f(x).
[tex]\text{Meaning that } (x-4i)(x+4i) =x^2-(4i)^2=x^2+16 \text{ is a factor of f(x).}[/tex]
The coefficient of the leading term is 1 and the constant term is -240 = 16 * (-15), so we a re looking for a real number such that.
[tex]f(x)=x^4-2x^3+x^2-32x-240\\\\ =(x^2+16)(x^2+ax-15)\\\\ =x^4+ax^3-15x^2+16x^2+16ax-240[/tex]
We identify the coefficients for the like terms, it comes
a = -2 and 16a = -32 (which is equivalent). So, we can write in [tex]\mathbb{R}[/tex].
[tex]\\f(x)=(x^2+16)(x^2-2x-15)[/tex]
The sum of the zeroes is 2=5-3 and their product is -15=-3*5, so we can factorise by (x-5)(x+3), which gives.
[tex]f(x)=(x^2+16)(x^2-2x-15)\\\\=(x^2+16)(x^2+3x-5x-15)\\\\=(x^2+16)(x(x+3)-5(x+3))\\\\=\boxed{(x^2+16)(x+3)(x-5)}[/tex]
And we can write in [tex]\mathbb{C}[/tex]
[tex]f(x)=\boxed{(x-4i)(x+4i)(x+3)(x-5)}[/tex]
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
what are the like terms of the expression.
3x+8x+y+x+8
Answer:
the like terms are:
3x+8x+x+y+8
12x+y+8
Answer:
The like terms are
3x, 8x, x
Step-by-step explanation:
3x+8x+y+x+8
The like terms are
3x, 8x, x
They are the terms that are in terms of the first power of x
When x=5 what would the value of expression
Answer:
46
Step-by-step explanation:
6 more than the product of 8 and a number x
6 more means 6+
product of 8 and a number x means 8x
6+8x
when x=5
6+8(5)=6+40=46
plz someone help me with this question
Answer:
(x+3)^2=-4(y-3)
Step-by-step explanation:
(x-h)^2 = 4p(y-k)
P is the distance between the focus and vertex
P = 1 --> used distance formula for the points of -3,2 -3,3
Vertex is -3,3 --> according to picture
(x+3)^2=-4(y-3)
P is negative since it goes downwards in the picture.
Help please!!! Tyyyyy
Answer:
D) 60 degree
Step-by-step explanation:
Let's connect the remaining diagonal, which forms a triangle containing angle x.
As a property of regular hexagon, all diagonals are equal.
=> The formed triangle is a regular triangle and it has three equal angles, which are 60 degrees.
Find the volume of the cylinder. Round your answer to the nearest tenth.
Answer:
716.75 m^3
Step-by-step explanation:
Volume of a cylinder:
=> PI x R^2 x H
H = Height
R = Radius
=> PI x 3.9^2 x 15
=> PI x 15.21 x 15
=> PI x 228.15
=> 228.15 PI
or
=> 228.15 x 3.14159
=> 716.75 m^3
Which quadratic equation would be used to solve for the unknown dimensions?
0 = 2w2
512 = w2
512 = 2w2
512 = 2l + 2w
Answer:
C
Step-by-step explanation:
Answer:
C: 512 = 2w2
Step-by-step explanation:
on edge
Jury Duty Three people are randomly selected from voter registration and driving records to report for jury duty. The gender of each person is noted by the county clerk.
a. Define the experiment.
b. List the simple events in S.
c. If each person is just as likely to be a man as a woman, what probability do you assign to each simple event?
d. What is the probability that only one of the three is a man?
e. What is the probability that all three are women?
Answer:
(a) The experiment defined here is a random variable that includes the selecting of 3 people from the set of voter registration and driving records.
(b) The simple events in sample space, S = (M, M, M), (M, F, M), (M, M, F), (F, M, M), (F, M, F), (F, F, M), (M, F, F), and (F, F, F).
(c) If each person is just as likely to be a man as a woman, then the probability for each of the simple event can be assigned as [tex]0.5 \times 0.5 \times 0.5 = 0.125[/tex].
(d) The probability that only one of the three is a man is 0.375.
(e) The probability that all three are women is 0.125.
Step-by-step explanation:
We are given that three people are randomly selected from voter registration and driving records to report for jury duty. The gender of each person is noted by the county clerk.
(a) The experiment defined here is a random variable that includes the selecting of 3 people from the set of voter registration and driving records.
(b) As we know that the gender of each person is noted by the county clerk, which means one is male and another female.
So, the simple events in sample space, S = (M, M, M), (M, F, M), (M, M, F), (F, M, M), (F, M, F), (F, F, M), (M, F, F), and (F, F, F).
Here, M is denoted for male and F for female.
(c) If each person is just as likely to be a man as a woman, then the probability for each of the simple event can be assigned as [tex]0.5 \times 0.5 \times 0.5 = 0.125[/tex].
Because there is 50-50 chance of selecting males or females.
(d) The probability that only one of the three is a man is given by;
The total cases in the sample space = 8
Number of cases of only one man out of three = 3
So, the required probability = [tex]\frac{3}{8}[/tex] = 0.375.
(e) The probability that all three are women is given by;
The total cases in the sample space = 8
Number of cases of all three are women = 1
So, the required probability = [tex]\frac{1}{8}[/tex] = 0.125.
Which is greater 9/20 or 60%
Answer:
60%
Step-by-step explanation:
9/20 is 45%
Answer:
60 %
Step-by-step explanation: If you divide 9/20, it equals to 0.45, makes it 45% and the number 45 in general is smaller than 60. Thus, 60% is greater than 9/20. I hope this helps.
If Company X has 1600 employees and 80% of those employees have attended the warehouse training course how many employees have yet to attend?
Answer:
320
Step-by-step explanation:
Total no of employees = 1600
% of employees attended the training = 80%
no. of employee who attended the training = 80/100* 1600 = 1280
No. of employees who are yet to attend the training = Total no of employees - no. of employee who attended the training = 1600-1280 = 320
Thus, 320 employees have yet to attend the training
How many pencils are in a bundle of 10
if they're in a bundle of 10 then theres 10 pencils
woman has 7 coworkers' man. How many different possible groups of four people could do the project, if one out of three is women? g
Answer: 24ways
Step-by-step explanation:
Given data:
No of men in the workplace = 7
No of women in the workplace = 1
How many ways can a group of 4 people carry out a project if on out of the 3 must be a woman.
Solution.
A group of 4 can carry out the project with one be a woman
This means there must be 3 males and 1 female in the group
= 4p3
= 24ways
The project can be carried out by 4 groups in 24 ways
Question on Statistics and Confidence Intervals
A field test for a new exam was given to randomly selected seniors. The exams were graded, and the sample mean and sample standard deviation were calculated. Based on the results, the exam creator claims that on the same exam, nine times out of ten, seniors will have an average score within 5% of 75%.
Is the confidence interval at 90%, 95%, or 99%? What is the margin of error? Calculate the confidence interval and explain what it means in terms of the situation. (10 points)
The phrasing "nine times out of ten" means 9/10 = 0.90 = 90% is the confidence level. We're confident 90% of the time that the confidence interval captures the population parameter we're after (in this case mu = population mean)
The portion "have an average score within 5% of 75%" means that 75% = 0.75 is the center of the confidence interval, and it goes as low as 0.75 - 0.05 = 0.70 and as high as 0.75 + 0.05 = 0.80
This confidence interval is from 70% to 80%, meaning that nine times out of ten, we're confident that the average score is between 70% and 80%
We write the confidence interval as (0.70, 0.80). It's common to use the notation (L, U) to indicate the lower (L) and upper (U) boundaries. You might see the notation in the form L < mu < U. If so, then it would be 0.70 < mu < 0.80; either way they mean the same thing.
The margin of error is 0.05 as its the 5% radius of the interval. It tells us how far the most distant score is from the center (75%)
=========================================
In summary, we have these answers
confidence level = 90%margin of error = 5% = 0.05confidence interval = (0.70, 0.80)interpretation = We're 90% confident that the average exam score is between 0.70 and 0.80Help us plazz this is mathematics IGCSE fast as you can
Answer:
Step-by-step explanation:
y varies direcrtly with √(x+5) wich can be expressed mathematically as:
● y = k*√(x+5)
Let's calculate k khowing that y=4 and x=-1
● 4 = k*√(-1+5)
● 4 = k*√(4)
● 4 = k * 2
● k = 4/2
● k = 2
■■■■■■■■■■■■■■■■■■■■■■■■■■
Let's calculate y khowing that x = 11
● y = k*√(x+5)
● y = 2×√(11+5)
● y = 2× √(16)
● y = 2× 4
● y = 8
Answer:
The value of y is 8.
Step-by-step explanation:
Given that y is directly proportional to √(x+5) so the equation is y = k√(x+5) where k is constant. First, you have to find the value of k with given values :
[tex]y = k \sqrt{x + 5} [/tex]
[tex]let \: x = - 1,y = 4[/tex]
[tex]4 = k \sqrt{ - 1 + 5} [/tex]
[tex]4 = k \sqrt{4} [/tex]
[tex]4 = k(2)[/tex]
[tex]4 \div 2 = k[/tex]
[tex]k = 2[/tex]
So the equation is y = 2√(x+5). In order to find the value of y, you have to substitute x = 11 into the equation :
[tex]y = 2 \sqrt{x + 5} [/tex]
[tex]let \: x = 11[/tex]
[tex]y = 2 \sqrt{11 + 5} [/tex]
[tex]y = 2 \sqrt{16} [/tex]
[tex]y = 2(4)[/tex]
[tex]y = 8[/tex]
Cesium-137 has a half-life of about 30 years. A) Find the annual decay rate and round final result to 4 decimal places. B) Find the continuous decay rate and round final result to 4 decimal places. C) How long will it take for a 10 gram sample to decay to 1 gram? Round to nearest year and interpret your result with a complete sentence. D) Complete this statement: as x goes to infinity, y goes to ___.
Answer:
0.02280.0231100 years0Step-by-step explanation:
The exponential equation for the fraction remaining after x years can be written as ...
y = (1/2)^(x/30)
A) For x=1, the fraction remaining is ...
y = (1/2)^(1/30) ≈ 0.97716 = 1 - 0.0228
Of the original amount, 0.0228 decays each year.
__
B) The continuous decay rate is the natural log of the growth factor, so is ...
ln(0.97716) = -0.0231
The continuous decay rate is 0.0231 of the present amount (per year).
__
C) For y=.10 (1/10 of the original amount) we find x to be ...
.1 = .5^(x/30)
ln(.1) = (x/30)ln(.5) . . . . . take the natural log
30ln(0.1)/ln(0.5) = x ≈ 100 . . . years
It will take 100 years for a 10-gram sample to decay to 1 gram.
__
D) As x goes to infinity, y goes to zero.
_____
The relationship between growth rate and growth factor is ...
growth factor = 1 + growth rate
When the growth rate is negative, it is called a decay rate.
What number must be added to the expression below to complete the square? x2-5x
Answer:
6.25
Step-by-step explanation:
(x-a)^2=x^2-2ax+a^2
2a=5
a=2.5
2.5 ^ 2 = 6.25
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 118 chips.
Required:
a. Determine the 26th percentile for the number of chocolate chips in a bag.
b. Determine the number of chocolate chps in a bag that make up the middle 96% of bags.
Answer:
(a) The 26th percentile for the number of chocolate chips in a bag is 1185
(b) The number of chocolate chips in a bag that makes up the middle 96% of the bags is between 1020 and 1504
Step-by-step explanation:
From the question, we have the following values:
μ =1262 and σ =118
(a) Let the value of x represents the 26th percentile. So the 26th percentile means 26% data is less than x. We can use the standard normal table to get the particular z-value that corresponds to this percentile.
P( Z<-0.65 )=0.2578 which is approximately 0.26
So for 26th percentile z-score will be -0.65.
Mathematically;
z-score = (x-mean)/SD
-0.65 = (x-1262)/118
-76.7 = x -1262
x = 1262-76.7 = 1185.3
This value is approximately 1,185
(b) Using a graph of standard normal distribution curve, if middle is 96% , then at both tails 2% each.
From z-table, we can find the closest probability;
P(-2.05<z<2.05) = 0.96
So we have two x values to get from the individual z-scores
-2.05 = (x-1262)/118
x = 1020(approximately)
For 2.05, we have
2.05 = (x-1262)/118
x = 1262 + 2.05(118) = 1504 (approximately)
The data set {3, 7, 5, 4, 1} consists of the lengths, in minutes, of a sample of speeches at an awards banquet. Use a formula to find the standard deviation of the sample, and label it with the correct variable.
Answer:
Standard deviation = 2.2360679774998
Step-by-step explanation:
We are asked to find the Standard deviation of a samples of speeches as an awards.
The formula for sample standard deviation is given as:
√[(x - μ)²/N - 1 ]
Step 1
We find the mean (μ)
The mean of the sample =>
= Sum of term/ Number of terms
= (3 + 7 + 5 + 4 + 1)/5
= 20/5
= 4
Step 2
Find the Standard deviation of the sample
√[(x - μ)²/N - 1 ]
N = number of samples or terms = 5
= √[(3 - 4) ² + (7 - 4)² + (5 - 4)² +(4 - 4)² +(1 - 4)²/ 4]
= √ (1 ² + 3² + -1² + 0² + -3²/4)
= √( 1 + 9 + 1 + 0 + 9/4)
= √20/5 - 1
= √5
= 2.2360679774998
The standard deviation of the sample = 2.2360679774998
A rectangular city is 3 miles long and 10 miles wide. What is the distance between opposite corners of the city? The exact distance is ______ miles How far is it to the closest tenth of a mile? Answer: The distance is approximately ______ miles.
Answer:
The exact distance is [tex]\sqrt{109}[/tex] miles.
The distance is approximately 10.4 miles.
Step-by-step explanation:
It is given that a rectangular city is 3 miles long and 10 miles wide. So,
Length = 3 miles
Width = 10 miles
We need to find the distance between opposite corners of the city. It means, we need to find the length of the diagonal of the rectangle.
Using Pythagoras theorem, the length of diagonal is
[tex]d=\sqrt{l^2+w^2}[/tex]
where, l is length and w is width.
Substitute l=3 and w=10.
[tex]d=\sqrt{(3)^2+(10)^2}[/tex]
[tex]d=\sqrt{9+100}[/tex]
[tex]d=\sqrt{109}[/tex]
The exact distance is [tex]\sqrt{109}[/tex] miles.
Now,
[tex]d=\sqrt{109}[/tex]
[tex]d=10.4403065[/tex]
[tex]d\approx 10.4[/tex]
The distance is approximately 10.4 miles.
Jesse bought 3 T-shirts for $6 each and 4 T-shirts for $5 each. What expression can you use to describe what Jesse bought?
Can someone please help me ASAP:(
Answer:
3 =x
Step-by-step explanation:
(segment piece) x (segment piece) = (segment piece) x (segment piece)
3x(x+1) = 4x*x
Divide each side by x
3(x+1) = 4x
Distribute
3x+3 = 4x
Subtract 3x from each side
3x-3x +3 = 4x-3x
3 =x
To the nearest tenth, what is the value of P(C|Y)? 0.4 0.5 0.7 0.8
Answer:
P(C|Y) = 0.5.
Step-by-step explanation:
We are given the following table below;
X Y Z Total
A 32 10 28 70
B 6 5 25 36
C 18 15 7 40
Total 56 30 60 146
Now, we have to find the probability of P(C/Y).
As we know that the conditional probability formula of P(A/B) is given by;
P(A/B) = [tex]\frac{P(A \bigcap B)}{P(B)}[/tex]
So, according to our question;
P(C/Y) = [tex]\frac{P(C \bigcap Y)}{P(Y)}[/tex]
Here, P(Y) = [tex]\frac{30}{146}[/tex] and P(C [tex]\bigcap[/tex] Y) = [tex]\frac{15}{146}[/tex] {by seeing third row and second column}
Hence, P(C/Y) = [tex]\frac{\frac{15}{146} }{\frac{30}{146} }[/tex]
= [tex]\frac{15}{30}[/tex] = 0.5.
Answer: 0.5
Step-by-step explanation:
edge
in the diagram, POS,QOT and UOR are straight lines. Find the value of y.
Answer:
y = 15°
Step-by-step explanation:
Since ∠QOR and ∠UOT are vertical, they are congruent so ∠UOT = 5y. Since POS is a straight line (which has a measure of 180°) and ∠POS = ∠POU + ∠UOT + ∠TOS, we can write:
5y + 5y + 2y = 180
12y = 180
y = 15°
If “n” is a positive integer divisible by 3 and n is less than or equal to 44, then what is the highest possible value of n?
Answer:
Step-by-step explanation:
positive integer divisible by 3 includes
3,6,9,12,15,18,21,24,27,30,33,36,39,42,45...
less than highest possible value is 42
point estimate A sample of 81 observations is taken from a normal population with a standard deviation of 5. The sample mean is 40. Determine the 95% confidence interval for the population mean
Answer:
The 95 percent Confidence Interval is for the population is (38.911 , 41.089)
Step-by-step explanation:
To solve the above question, we would be making use of the confidence interval formula:
Confidence Interval = Mean ± z score × σ/√n
In the above question,
Mean = 40
σ = Standard deviation = 5
n = number of samples = 81
Confidence Interval = 95%
The z score for a 95% confidence interval = 1.96
Therefore, the confidence interval =
= 40 ± 1.96 (5/√81)
= 40 ± 1.96(5/9)
= 40 ± 1.0888888889
Confidence Interval
a)40 + 1.0888888889
= 41.0888888889
Approximately = 41.089
b ) 40 - 1.0888888889
= 38.911111111
Approximately = 38.911
Therefore, the 95 percent Confidence Interval is for the population is (38.911 , 41.089)
20 liters of mixture contain milk nad water in the ratio 5:3 of 4 liters of the mixture are replaced by 4 liters of milk find the new ratio of milk to water
Answer:
7:3
Step-by-step explanation:
5 + 3 = 8
The ratio is
5 milk : 3 water : 8 total
Milk is 5/8 of the total.
Water is 3/8 of the total.
The 20-liter mixture contains:
5/8 * 20 = 12.5 liters of milk, and
3/8 * 20 = 7.5 liters of water
4 liters of the mixture contain:
5/8 * 4 = 2.5 liters of milk, and
3/8 * 4 = 1.5 liter of water
When you remove 4 liters of the mixture from 20 liters of the mixture, you end up with
12.5 L - 2.5 L = 10 L milk, and
7.5 L - 1.5 L = 6 L water
Now you add 4 liters of milk. Now you have
10 L + 4 L = 14 L milk
6 L water
The new ratio of milk to water is 14:6 = 7:3
Answer
Step-by-step explanation:
sum of ratio=5+3=8
In a recent survey of drinking laws, a random sample of 1000 women showed that 65% were in favor of increasing the legal drinking age. In a random sample of 1000 men, 60% favored increasing the legal drinking age. Test the claim that the percentage of men and women favoring a higher legal drinking age is different at (alpha 0.05).
Answer:
Step-by-step explanation:
Given that:
Let sample size of women be [tex]n_1[/tex] = 1000
Let the proportion of the women be [tex]p_1[/tex] = 0.65
Let the sample size of the men be [tex]n_2[/tex] = 1000
Let the proportion of the mem be [tex]p_2[/tex] = 0.60
The null and the alternative hypothesis can be computed as follows:
[tex]H_0: p_1 = p_2[/tex]
[tex]H_0a: p_1 \neq p_2[/tex]
Thus from the alternative hypothesis we can realize that this is a two tailed test.
However, the pooled sample proportion p = [tex]\dfrac{p_1n_1+p_2n_2 } {n_1 +n_2}[/tex]
p =[tex]\dfrac{0.65 * 1000+0.60*1000 } {1000 +1000}[/tex]
p = [tex]\dfrac{650+600 } {2000}[/tex]
p = 0.625
The standard error of the test can be computed as follows:
[tex]SE = \sqrt{p(1-p) ( \dfrac{1} {n_1}+ \dfrac{1}{n_2} )}[/tex]
[tex]SE = \sqrt{0.625(1-0.625) ( \dfrac{1} {1000}+ \dfrac{1}{1000} )}[/tex]
[tex]SE = \sqrt{0.625(0.375) ( 0.001+0.001 )}[/tex]
[tex]SE = \sqrt{0.234375 (0.002)}[/tex]
[tex]SE = \sqrt{4.6875 * 10^{-4}}[/tex]
[tex]SE = 0.02165[/tex]
The test statistics is :
[tex]z =\dfrac{p_1-p_2}{S.E}[/tex]
[tex]z =\dfrac{0.65-0.60}{0.02165}[/tex]
[tex]z =\dfrac{0.05}{0.02165}[/tex]
[tex]z =2.31[/tex]
At level of significance of 0.05 the critical value for the z test will be in the region between - 1.96 and 1.96
Rejection region: To reject the null hypothesis if z < -1.96 or z > 1.96
Conclusion: Since the value of z is greater than 1.96, it lies in the region region. Therefore we reject the null hypothesis and we conclude that the percentage of men and women favoring a higher legal drinking age is different.
Find the value of x to the nearest tenth. A) 5 B) 9.2 C) 3.3 D) 2.9
Answer:
B) 9.2
Step-by-step explanation:
tan(57)=x/6 multiply 6 on both sides
6.tan(57)=x use calculator to find answer
9.2 rounded
Answer:9.2 is correct
Step-by-step explanation:
