Answer:
A. If you send me an e-mail message, then I will remember to send you the address.
B. If you were born in the United States, then you can be a citizen of the United States.
C. If you keep your textbook, then it will be a useful reference in your future courses.
D. If the Red Wings’s goalie plays well, then they will win the Stanley Cup.
E. If you get the job, then you had the best credentials.
F. If there is a storm, then beach erodes.
G. If you can log on to the server, then you must have a valid password.
H. If you begin your climb too late, then you will not reach the summit
Step-by-step explanation:
The statement which is written in the form, "if p, then q" symbolized by p-->q is known as a conditional statement. p is known as the hypothesis, while q is the conclusion. In such statements, the hypothesis and the conclusion may or may not have a correlation. But for the statement to be true, the conclusion must be true even if the hypothesis is wrong.
In statements A, the condition for sending the address is if I receive an email message.
In statement B, the condition for being a citizen is if one is born in the United States.
In statement C, the condition for my books to be a useful reference is if I keep them.
In statement D, the condition for winning the Stanley Cup by the Red Wings is if their Goalie plays well.
In statement E, the condition I get the job is if I had the best credentials.
In statement F, the condition for the beach eroding is if there's a storm.
In statement G, the only way I can log on to the server is if I have the correct password. In each of these statements, the conclusions correlates with the hypothesis. The conditions in the hypothesis need to be met for the conclusion to be true.
Statement H gives a conclusion which depends on not meeting the conditions of the hypothesis which is that if I don't start climbing the mountain early (if I start late), I will not reach the summit.
The average retirement age for a certain country was reported to be 56.4 years according to an international group dedicated to promoting trade and economic growth. With the pension system operating with a deficit, a bill was introduced by the government during the summer to raise the minimum retirement age from 60 to 62. Suppose a survey of 40 retiring citizens is taken to investigate whether the new bill has raised the average age at which people actually retire. Assume the standard deviation of the retirement age is 55 years. Using α=0.10
Required:
Calculate the probability of a Type II error occurring if the actual population age is 57.5 years old.
Answer:
|Z| = |-0.126| = 0.126 < 1.645
Null hypothesis is accepted
The retiring citizens is taken to investigate whether the new bill has raised the average age at which people actually retire.
μ = 57.5
Step-by-step explanation:
Explanation:-
The average retirement age for a certain country was reported to be 56.4 years
The mean of the sample x⁻ = 56.4
The standard deviation of the Population 'σ'= 55 years
The mean of the population μ = 57.5
Null hypothesis: H₀:The retiring citizens is taken to investigate whether the new bill has raised the average age at which people actually retire.
μ = 57.5
Alternative Hypothesis : H₁: μ ≠57.5
Test statistic
[tex]Z = \frac{x^{-}-mean }{\frac{S.D}{\sqrt{n} } }[/tex]
critical value:
[tex]Z_{\frac{\alpha }{2} } = Z_{0.05} =1.645[/tex]
[tex]Z = \frac{56.4-57.5 }{\frac{55}{\sqrt{40} } } = -0.126[/tex]
|Z| = |-0.126| = 0.126 < 1.645
The null hypothesis is accepted
Conclusion:-
The retiring citizens is taken to investigate whether the new bill has raised the average age at which people actually retire.
μ = 57.5
Round 5 to the nearest ten.Enter your answer in the box below.
Answer:
[tex]10[/tex]
Step-by-step explanation:
[tex]05[/tex]
If the units place is higher than 5, then add 1 to the tens place.
How do you solve this problem? population proportion is to be estimated from a sample of 400 with a sample proportion of 0.1. Approximate the 95% confidence interval of the population proportion
Answer:
(0.0706, 0.1294)
Step-by-step explanation:
Confidence interval of a proportion is:
CI = p ± CV × SE
where p is the proportion,
CV is the critical value (z score or t score),
and SE is the standard error.
The sample is large enough to estimate as normal. For 95% confidence level, CV = z = 1.96.
Standard error for a proportion is:
SE = √(pq/n)
SE = √(0.1 × 0.9 / 400)
SE = 0.015
The confidence interval is:
CI = 0.1 ± (1.96)(0.015)
CI = (0.0706, 0.1294)
Round as needed.
Autism is a serious and lifelong disability that is characterized by a severely decreased ability to engage in communication and social interaction. In 1998 citizens in a New Jersey town were concerned about the number of children diagnosed with autism, and a study was undertaken to establish the prevalence in the community. Data from the study are reported below:
Numbers of Children Diagnosed with Autistic Disorder
Age Category (y) Diagnosed with Autistic Disorder Number of Children in Population
3-5 19 3479
6-10 17 5417
Required:
a. Calculate the prevalence rate of autism for these children for the two age categories.
b. Convert the prevalence rate to a rate per 1,000
Answer:
a. Calculate the prevalence rate of autism for these children for the two age categories.
3-5: prevalence rate = 0.55%6-10: prevalence rate = 0.31%b. Convert the prevalence rate to a rate per 1,000
3-5: prevalence rate = 5.5 per thousand6-10: prevalence rate = 3.1 pér thousandStep-by-step explanation:
Generally prevalence is calculated using the following formula:
(number of people with autism / number of people measured) x 100%
age category
3-5: prevalence rate = (19/3,479) x 100% = 0.55%
6-10: prevalence rate = (17/5,417) x 100% = 0.31%
if you want to convert to a rate per 1,000, allyou need to do is multiply by 1,000 instead of 100
3-5: prevalence rate = (19/3,479) x 1,000 = 5.5
6-10: prevalence rate = (17/5,417) x 1,000 = 3.1
laura quiere cúbrir con papel de china una puerta como la que se muestran el dibujo cuánto centímetros cuadrados es la que tendra que cubrir con papel de china
Answer:
Necesita cubrir 4800 cm^2.
Step-by-step explanation:
La pregunta está incompleta:
Laura quiere cubrir con papel de china una puerta como la que se muestra en el dibujo. Las medidas son 80 cm de largo y 60 cm de ancho.
Tenemos que calcular la superficie de la puerta, cuyas medidas son 80 cm de largo y 60 cm de ancho.
Para calcular el área simplemente multiplicamos las medidas de ambos lados:
[tex]A=80\,cm\cdot 60\,cm=4800\,cm^2[/tex]
18x-5x=13+20 what is the answer
Answer:
3.3
Step-by-step explanation:
18x-5x=13+20
13x=33
x=2.5
You are playing a game called cornhole and let’s assume that you are reallygood at it with the winning probability is 0.8. For the following parts, find (a) the name ofthe appropriate probability distribution and correct parameters, (b) the expected value and (c) the variance of Y.
A. Y = the number of games it takes you to lose one time.
B. Y = the number of games it takes you to lose four times.
C. Y the number of times you win out of 100 games.
Answer:
Step-by-step explanation:
Given that :
The probability of winning is 0.8
i.e P(winning) = 0.8
Then P(losing) = 0.2
a) Y ~ Geometric distribution
[tex]P = P(loose) =0.2 \\ \\ \mu_{\delta} = \dfrac{1}{P}= \dfrac{1}{0.2}\\ \\ = 5.0 \\ \\ \\ \dfrac{\sigma ^2 }{\delta } = \dfrac{1-P}{P^2} \\ \\ =\dfrac{0.8}{0.04} \\ \\ = 20[/tex]
b) Y ~ Negative Binomial Distribution
[tex]P = P (loose) =0.2 \\ \\ \delta = number \ of \ loss = 4 \\ \\ \mu_{\delta} = \dfrac{\delta}{P} \\ \\ =\dfrac{4}{0.2} \\ \\ = 20 \\ \\ \\ \sigma ^2_{\delta} = \dfrac{\delta (1-P)}{P^2} \\ \\ = \dfrac{4*0.8}{0.04}\\ \\ = 80[/tex]
c) Y ~ Binomial Distribution;
n = 100 ; P = 0.8
[tex]\mu_{\delta} = nP \\ \\ = 100*0.8 \\ \\ = 80 \\ \\ \\ \sigma_{\delta}^2 = nP(1-P) \\ \\ =80*0.2 \\ \\ = 16[/tex]
winnie and kevin like to create their own triathlon courses to challenge each other. last weekend, winnie created a course that included a swim of 3/4 of a mile, a bike ride of 57/4 miles and a run of 13/4 miles. how long was the course winnie created?
a boat operator in a boat can travel 15m/sec in still water he tries to cross a river which is flowing at 5 m/sec south. A) what is the resultant velocity of the boat? B) The takes exactly 55 seconds to cross the river in the resulting velocity, how many meters did the boat travel?
Answer:
a) 15.8 ms-1
b)869 m
Step-by-step explanation:
We have to obtain the resultant velocity by the Pythagorean theory;
R^2= V1^2 + V2^2
Where
R= resultant velocity of the boat
V1= velocity of the boat
V2= velocity of the flowing river
Thus;
R= √V1^2 + V2^2
R= √15^2 + 5^2
R= √225 + 25
R= √250
R= 15.8 ms-1
B) from
v= s/t
Where
v= velocity (resultant velocity in this case)
s= distance
t= time (55 secs)
s= vt
s= 15.8×55
s= 869 m
Robin read somewhere that adding salt to water while heating it will raise the temperature of
the water causing it to boil faster. To test this claim, she filled 30 identical pots with one quart
of water. She randomly selected 15 of the pots and added 1 teaspoon of salt. She then placed
each pot on identical burners set to the highest setting. She measured the water temperature
In each pot after 5 minutes.
Is Robin's research method an example of an observational study experiment, or
simulation?
b
If Robin does find that there is a difference between the water temperatures in the pots
with salt compared to those without can she conclude that the salt caused the
difference in temperature?
Answer:
a. An experiment
b. No
Step-by-step explanation:
a. Robin's research method can be concluded to be an experiment because she has a testable group (pots of water with salt) and a control group (pots of water without salt).
2. Based on this alone, she cannot conclude that the salt caused the
difference in temperature because she has not set some appropriate conditions which are to be met for this test.
Determine the least number of patties that will share equally among groups og 6, 9, 12
Answer:
72.
Step-by-step explanation:
Given a group of 6, 9 and 12.
We are to determine the least number of patties that will be shared equally among the groups.
This we do by determine the Least common multiple of the three numbers.
[tex]6=2 X 3\\9 = 3 X 3\\12 =2 X 2 X 2\\L.C.M.=2^3X3^2=72[/tex]
Therefore, the least number of patties that can be shares equally among groups of 6, 9 and 12 is 72.
4x2 - 14x + 6
x3 - 7x2 + 12x
What is the GCF of the terms in the numerator and denominator? Rewrite the expression by factoring out any common
factors.
Answer:
Answer is given below.
Step-by-step explanation:
let us solve the numerator first
=4x²-14x+6
=2(2x²)+2(-7x)+2(3)
= GCF of the terms of the numerator is 2.
denominator
x³-7x²+12x
x(x²)+x(-7x)+x(12)
GCF of the terms of the denominator is x.
factorise the numerator
4x²-14x+6
4x²-2x-12x + 6 (by splitting the middle term; the numbers should produce the product 4*6 and when the no.s are added they should give -14)
(4x²-2x) + (-12x+6)
2x(2x-1) -6(2x-1)
(2x-6)(2x-1)
factors are
(2x-6), (2x-1)
denominator
this can also be done by splitting the middle term
x³-7x²+12x
x³-3x²-4x²+12x
(x³-3x²) + (-4x²+12x)
x²(x-3) -4x(x-3)
(x²-4x)(x-3)
factors are
(x²-4x), (x-3)
Suppose an All Greens store in Sonoma, California, wants to estimate a range of advertising costs appropriate to its store. If it spends too little on advertising, it will not reach enough customers. However, it does not want to overspend on advertising for this type and size of store. At this store, x1 = 163, x2 = 2.4, x3 = 188, x5 = 6.6, and x6 = 10. Use these data to predict x4 (advertising costs) and find an 80% confidence interval for your prediction. (Use 2 decimal places.)
Answer:
The advertising cost, X₄ = 5.626 million
The 80% confidence limits for X₄ is (5.041 , 6.100)
The 80% prediction limits for X₄ is (4.048 , 7.094)
Step-by-step explanation:
Using MINITAB
The regression equation is X₄ = 4.14 + 0.0431 X₁ - 0.800 X₂ + 0.00059 X₃ - 0.661 X₅ + 0.057 X₆
Predictor Coef SE Coef T P
Constant 4.142 1.626 2.55 0.019
X₁ 0.043089 0.009466 4.55 0.000
X₂ -0.7998 0.2515 -3.18 0.005
X₃ 0.000590 0.004221 0.14 0.890
X₅ -0.6606 0.1542 -4.28 0.000
X₆ 0.0574 0.1254 0.46 0.652
S = 1.07911 R-Sq = 93.4% R-Sq(adj) = 91.8%
Analysis of Variance
Source DF SS MS F P
Regression 5 345.966 69.193 59.42 0.000
Residual Error 21 24.454 1.164
Total 26 370.420
Source DF Seq SS
X₁ 1 309.464
X₂ 1 8.699
X₃ 1 5.994
X₅ 1 21.566
X₆ 1 0.244
Unusual Observation
Obs X₁ X₄ Fit SE Fit Residual St Resid
17 398 5.500 7.714 0.641 -2.214 -2.55 R
27 400 7.000 7.366 1.025 -0.336 -1.00 X
Where R is observation with a large standardized residual.
Where X is observation whose X values give it large influence.
Predicted values for new Observations
New
Obs Fit SE Fit 80% Cl 80% Pl
1 5.571 0.400 (5.041 , 6.100) (4.048 , 7.094)
Values of Predictors for New Observations
New
Obs X₁ X₂ X₃ X₅ X₆
1 163 2.40 188 6.60 10.0
∴ The advertising cost, X₄ = 5.626 million, The 80% confidence limits for X₄ is (5.041 , 6.100), and The 80% prediction limits for X₄ is (4.048 , 7.094)
A student is getting ready to take an important oral examination and is concerned about the possibility of having an "on" day or an "off" day. He figures that if he has an on day, then each of his examiners will pass him, independently of one another, with probability 0.8, whereas if he has an off day, this probability will be reduced to 0.4. Suppose that the student will pass the examination if a majority of the examiners pass him. If the student believes that he is twice as likely to have an off day as he is to have an on day, should he request an examination with 3 examiners or with 5 examiners?
Answer:
The students should request an examination with 5 examiners.
Step-by-step explanation:
Let X denote the event that the student has an “on” day, and let Y denote the
denote the event that he passes the examination. Then,
[tex]P(Y)=P(Y|X)P(X)+P(Y|X^{c})P(X^{c})[/tex]
The events ([tex]Y|X[/tex]) follows a Binomial distribution with probability of success 0.80 and the events ([tex]Y|X^{c}[/tex]) follows a Binomial distribution with probability of success 0.40.
It is provided that the student believes that he is twice as likely to have an off day as he is to have an on day. Then,
[tex]P(X)=2\cdot P(X^{c})[/tex]
Then,
[tex]P(X)+P(X^{c})=1[/tex]
⇒
[tex]2P(X^{c})+P(X^{c})=1\\\\3P(X^{c})=1\\\\P(X^{c})=\frac{1}{3}[/tex]
Then,
[tex]P(X)=1-P(X^{c})\\=1-\frac{1}{3}\\=\frac{2}{3}[/tex]
Compute the probability that the students passes if request an examination with 3 examiners as follows:
[tex]P(Y)=P(Y|X)P(X)+P(Y|X^{c})P(X^{c})[/tex]
[tex]=[\sum\limits^{3}_{x=2}{{3\choose x}(0.80)^{x}(1-0.80)^{3-x}}]\times\frac{2}{3}+[\sum\limits^{3}_{x=2}{{3\choose x}(0.40)^{3}(1-0.40)^{3-x}}]\times\frac{1}{3}[/tex]
[tex]=0.715[/tex]
The probability that the students passes if request an examination with 3 examiners is 0.715.
Compute the probability that the students passes if request an examination with 5 examiners as follows:
[tex]P(Y)=P(Y|X)P(X)+P(Y|X^{c})P(X^{c})[/tex]
[tex]=[\sum\limits^{5}_{x=3}{{5\choose x}(0.80)^{x}(1-0.80)^{5-x}}]\times\frac{2}{3}+[\sum\limits^{5}_{x=3}{{5\choose x}(0.40)^{x}(1-0.40)^{5-x}}]\times\frac{1}{3}[/tex]
[tex]=0.734[/tex]
The probability that the students passes if request an examination with 5 examiners is 0.734.
As the probability of passing is more in case of 5 examiners, the students should request an examination with 5 examiners.
Please answer this correctly
Answer:
10.71
Step-by-step explanation:
The arc length is
2*3*3.14/4 = 4.71
Add to the two side lengths to get the perimeter
4.71+3+3 = 10.71
[tex]answer = 10.71 \: millimeters \\ solution \\ radius = 3 \: millimeters \\ perimeter \: of \:quarter \: circle \\ = \frac{2\pi \: r}{4} + 2r \\ = \frac{2 \times 3.14 \times 3}{4} + 2 \times 3\\ = \frac{18.84}{4} + 6 \\ = \frac{18.84 + 6 \times 4}{4} \\ = \frac{18.84 + 24}{4} \\ = \frac{42.84}{4} \\ = 10.71 \: millimeters \\ hope \: it \: helps[/tex]
A game is played using one die. If the die is rolled and shows 1, the player wins $5. If the die shows any number other than 1, the player wins nothing. If there is a $1 charge to play the game, what is the game’s expected value?
Answer:
1/5
Step-by-step explanation:
i had a similar question
For each roll you start with paying 2 dollars and you only with 10 dollars one out of 6 rolls (on average).
So the cost for one play is 2 dollars and your win is 10/6.
Value is -2+10/6=-1/3 dollars
So you lose 1/3 dollars on average with each game
since you have no limited rolls u put 1/5
this from another question but both same just different numbers
Many traffic experts argue that the most important factor in accidents is not the average speed of cars but the amount of variation. Suppose that the speeds of a sample of 200 cars were taken over a stretch of highway that has seen numerous accidents. Compute the standard deviation of the speeds in Excel file Q-14.xlsx.
Answer and Step-by-step explanation: Standard Deviation is the measure of how diferent a number is from the mean of the data set. It is the spread of a data set. To calculate it manually:
1) Find the mean of the data set. Mean, represented by μ, is the sum of all the values divided by the total number of elements forming the set;
2) Subtract each number with the Mean and square the result;
3) Add the differences and divide it by the total number of elements of the set;
4) Take the square root of the result and that is the Standard Deviation.
The calculations can be done by a calculator like Excel:
1) In each cell of a same column, write the data you want to know the deviation.
2) On the last cell, write: =stdev.p(A1:A10) or =stdev.s(A1:A10).
3) Press Enter. The deviation will appeared on the same cell.
The function STDEV.P is used when the data represents the entire population, whereas STDEV.S is used when the data is for a sample of the population. Inside the parenthesis, put the cells where your data is. For example, if you put your data in the column A, from cell 1 to cell 10, you write like it's written above.
Question 2 of 10
2 Points
What is the sum of the rational expressions below?
2x+3/3x+x/x+1
Answer:
5x^2+5x+3/3x^2+3x
Step-by-step explanation:
You are renting a car that charges a $30 fee plus 40 cents a mile. The rate of change
is $30.
True
False
Answer:
true
is the answer
Your local school board wants to determine the proportion of people who plan on voting for the school levy in the upcoming election. They conduct a random phone poll, where they contact 150 individuals and ask them whether or not they plan on voting for the levy. Of these 150 respondents, 78 people say they plan on voting for the levy. The school board wants to determine whether or not the data supports the idea that more than 50% of people plan on voting for the levy. Conduct a hypothesis test at the 0.10 significance level to test this claim.
Answer:
There is not enough evidence to conclude that the data supports the idea that more than 50% of people plan on voting for the levy
Step-by-step explanation:
Sample size, n = 150
Number of people that plan on voting for the levy, X = 78
Proportion of people that plan on voting for the levy:
[tex]\bar{p} = X/n\\\bar{p} = 78/150\\\bar{p} = 0.52[/tex]
The study is to determine whether or not the data supports the idea that more than 50%(0.5) of people plan on voting for the levy
The null and alternative hypotheses are:
[tex]H_0: p \leq 0.5\\H_a: p > 0.5[/tex]
Calculate the test statistics:
[tex]t_s = \frac{\bar{p} - p}{\sqrt{\frac{p(1-p)}{n} } } \\t_s = \frac{0.52-0.5}{\sqrt{\frac{0.5(1-0.5)}{150} } } \\t_s = 0.49[/tex]
For a test statistic [tex]t_s = 0.49[/tex], the p-value = 0.3121
The significance value, [tex]\alpha = 0.10[/tex]
Since the p-value(0.3121) is greater than α(0.10), the null hypothesis [tex]H_0[/tex] will be accepted.
This means that there is not enough evidence to conclude that the data supports the idea that more than 50% of people plan on voting for the levy
Need help ASAP please
Answer:
r = l / π/180× θ
11.6 cm
Step-by-step explanation:
l = π/180 × r × θ
r = l / π/180× θ
r = 12.5 / π/180× 62
r = 11.55156845
Consider the scatterplot above. Write a sentence explaining the meaning of the value of the slope for this linear model. The is an average of per year .
Answer:
Slope: The percent that voted falls by 0.1271 units per year.
Step-by-step explanation:
The slope of a regression line represent the average rate of change in the dependent variable (y) based upon the changes in the independent variable (x).
In this case the regression equation provided is:
y = -0.1271 x + 307.53
The slope of the line is -0.1271.
The dependent variable is the percent that voted and the independent variable is the year.
The slope of -0.1271 indicates that every year, on average, the percent that voted decreases by 0.1271 units.
Or the percent that voted falls by 0.1271 units per year.
Sam colors each tile in a 4 by 4 grid white or black. A coloring is called rotationally
symmetric if the grid can be rotated 90, 180, or 270 degrees to achieve the same pattern.
Two colorings are called rotationally distinct if neither can be rotated to match the
other. How many rotationally distinct ways are there for Sam to color the grid such
that the colorings are not rotationally symmetric?
Answer:
65,280
Step-by-step explanation:
Consider the 4×4 grid ...
[tex]\left[\begin{array}{cc}a&b\\d&c\end{array}\right][/tex]
where each of a, b, c, d is a 2×2 array of tiles. Let's use the notation a' to represent the 2×2 array "a" rotated right 1/4 turn. For 90° rotational symmetry, we must have b=a', c=b'=a'', d=c'=b''=a'''. That is, once "a" is determined, the rest of the grid is determined. Since "a" consists of 4 tiles, each of which can be black or white, there are 2^4 = 16 patterns that have 90° rotational symmetry.
The same will be true of 270° rotational symmetry, for the same reason.
__
For 180° rotational symmetry, we must have c=a'' and d=b''. Then the combination of "a" and "b" together fully determines the grid. Together, "a" and "b" consist of 8 tiles, so there are 2^8 = 256 ways to pattern the grid so it will have 180° rotational symmetry. (Of those, 16 have 90° symmetry, and 16 have 270° symmetry. The sets are overlapping.)
__
The 16 tiles of the grid can be colored 2^16 = 65,536 different ways. As we have seen, 256 of those colorings result in 180° rotational symmetry. Then the number of colorings that have no rotational symmetry is ...
65,536 -256 = 65,280 . . . . colorings not rotationally symmetric
Complete the following subtraction exercises.
10 – 2 =
14 – 6 =
15 – 9 =
17 – 8 =
13 – 5 =
11 – 8 =
20 – 8 =
16 – 7 =
12 – 9 =
21 – 9 =
11 – 6 =
5 – 5 =
4 – 0 =
16 – 8 =
10 – 5 =
18 – 7 =
13 – 8 =
12 – 4 =
Answer:
Below
Step-by-step explanation:
8,8,6,9,8,3,12,9,3,12,5,0,4,8,5,11,5,8. Answers are in order from the first to the last
how do you find the zero(s) of a polynomial function
Answer:
by using the quadratic formula
Step-by-step explanation:
negative b plus or minus the square root of b squared minus 4ac, then all divided by 2a
What is the area of a rectangle that is 4 1/2 cm long and 2 5/9 cm wide? Solution: Answer: What is the area of a square that has a side of 4 3/5 cm?
Answer:
1) 23/2
2) 529/25
Step-by-step explanation:
Transformation:
[tex]4\frac{1}{2} = \frac{(2*4) + 1}{2} = \frac{9}{2}[/tex]
[tex]2\frac{5}{9} = \frac{(9*2) + 5}{9} = \frac{23}{9}[/tex]
A = [tex]\frac{9}{2} * \frac{23}{9} = \frac{23}{2}[/tex]
-----------------------------
Transformation:
[tex]4\frac{3}{5} = \frac{(5*4) + 3}{5} = \frac{23}{5}[/tex]
A = [tex](\frac{23}{5})^{2} = \frac{529}{25}[/tex]
What is the measure of <6?
Answer: Choice B. 54degrees
Step-by-step explanation:
Angles 1 4 5 8 are equal and angles 2 3 6 7 are also equal. These two sets of angles of supplementary(you‘d get 180 by adding them).
so
13x+9=180-(5x+9)
by simplifying the equation youll get
18x+18=180
x=9
so angle 7(and therefore angle 6) equals
5*9+9=54
In an aquarium, there are 4 large fish and 16 small fish. Half of the small fish are blue. One fish is selected at random. Find the probability that it is a small, blue fish. Write your answer as a fraction in simplest form.
Answer:
2/5
Step-by-step explanation:
There are 20 fish, 8 of which are small and blue. Therefore, the probability of randomly selecting a small blue fish is 8/20 = 2/5.
How much money does the average professional hockey fan spend on food at a single hockey game? That question was posed to 10 randomly selected hockey fans. The sampled results show that sample mean and standard deviation were $ 18.00 and $ 2.75, respectively. Use this information to create a 90% confidence interval for the mean. Express the answer in the form x overbar plus or minus t Subscript alpha divided by 2 Baseline (s divided by StartRoot n EndRoot ).
Answer:
Now we have everything in order to replace into formula (1):
[tex]18-2.262\frac{2.75}{\sqrt{10}}=16.03[/tex]
[tex]18+2.262\frac{2.75}{\sqrt{10}}=19.97[/tex]
Step-by-step explanation:
Information given
[tex]\bar X=18[/tex] represent the sample mean
[tex]\mu[/tex] population mean (variable of interest)
s=2.75 represent the sample standard deviation
n=10 represent the sample size
Confidence interval
The confidence interval for the mean is given by the following formula:
[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex] (1)
The degrees of freedom are given by:
[tex]df=n-1=10-1=9[/tex]
The Confidence is 0.90 or 90%, the significance is [tex]\alpha=0.1[/tex] and [tex]\alpha/2 =0.05[/tex], and the critical vaue would be [tex]t_{\alpha/2}=2.262[/tex]
Now we have everything in order to replace into formula (1):
[tex]18-2.262\frac{2.75}{\sqrt{10}}=16.03[/tex]
[tex]18+2.262\frac{2.75}{\sqrt{10}}=19.97[/tex]
The function f(x) = −x2 + 16x − 60 models the daily profit, in dollars, a shop makes for selling candles, where x is the number of candles sold. Determine the vertex, and explain what it means in the context of the problem. (6, 10); The vertex represents the maximum profit. (6, 10); The vertex represents the minimum profit. (8, 4); The vertex represents the minimum profit. (8, 4); The vertex represents the maximum profit.
Answer:
A.
f is a quadratic function, which means it's graph is a parabola.
Notice that the coefficient of is negative, so the parabola opens downwards.
the x-coordinate of a parabola is always determined by the formula:
where a is coefficient of the term, and b is the coefficient of the x term.
Thus, x-coordinate of the vertex of the graph of f is :
the y-coordinate of the vertex is f(8)=-8*8+16*8-60=4.
The vertex is (8, 4).
This means that the maximum daily profit is when exactly 8 candles are sold.
B.
The x-intercepts are the values of x such that f(x)=0,
so to find these values we solve:
complete the square:
so x-8=2 or x-8=-2
the roots are x=10 and x=6, are the roots.
This means that when the shop sells exactly 6 or 10 candles, it makes no profit.
Answer: d (8, 4); The vertex represents the maximum profit.
Explanation: i got it right on the test