Answer:
The correct 90% confidence interval for the difference between women and men in the average number of hours of personal time taken per year is
contained by the interval (0.54 , 5.18)
Step-by-step explanation:
Given that:
for women
sample size = n₁ = 16
sample mean [tex](\bar X_1)[/tex] = 24.75
standard deviation s₁ = 2.84
for men
sample size for men = n₂ = 7
sample mean [tex](\bar X_2)[/tex] = 21.89
standard deviation s₂ = 3.29
degree of freedom = [tex](n_1 + n_2 )-2[/tex]
= 16 + 7 -2
= 21
The critical value for [tex]\alpha = 0.1 \ and \ df \ of \ 21 \ is :[/tex]
[tex]t_{0.005;21}= 1.721[/tex]
The pooled standard deviation can be calculated as follows since the population variances are assumed to be equivalent.
[tex]s_p = \sqrt{\dfrac{(n_1 -1)s_1^2+(n_2-1)s_2^2}{n_1+n_2-2}}[/tex]
[tex]s_p = \sqrt{\dfrac{(16 -1)2.84^2+(7-1)3.29^2}{16+7-2}}[/tex]
[tex]s_p = \sqrt{\dfrac{(15)8.0656+(6)10.8241}{21}}[/tex]
[tex]s_p = 2.976[/tex]
The standard error is estimated as follow:
[tex]se = s_p\sqrt{\dfrac{1}{n_1} + \dfrac{1}{n_2}}[/tex]
[tex]se = 2.976\sqrt{\dfrac{1}{16} + \dfrac{1}{7}}[/tex]
se = 1.348
Finally, the confidence interval [tex]C.I = ( x_1 -x_2 -t_c \times se \ \ ; \ \ x_1-x_2 +t_c \times se)[/tex]
[tex]=(24.75 - 21.89 -1.721 \times 1.348 \ \ , \ \ 2475 - 21.89 + 1.721 \times 1.348) \\ \\ \mathbf{ = (0.54 \ \ , \ \ 5.18)}[/tex]
Question 1
10 pts
The vertices of a triangle are P(4,7), Q(-1,7) and R(4,-5). What is the
perimeter of triangle PQR?
Answer:
30
Step-by-step explanation:
This problem can be done without the Distance Formula (which is a way to find the distance between any two points in the plane).
The attached image shows the points and segments joining them.
PQ = 5 because the points are on the same horizontal line, and you can count spaces between them (or subtract x-coordinates: 4 - (-1) = 5).
PR = 12 because the points are on the same vertical line; count spaces or subtract y-coordinates, 7 - (-5) = 12.
The triangle is a right triangle, so the Pythagorean Theorem can be used to find the length of the hypotenuse.
[tex](\text{leg})^2+(\text{leg})^2=(\text{hypotenuse})^2[/tex]
[tex](QR)^2=5^2+12^2=25+144=169\\QR=\sqrt{169}=13[/tex]
The perimeter of the triangle is 5 + 12 + 13 = 30
Graph the equation.
y-3= -5(x-1)
Step-by-step explanation:
First you gotta write it in standard form
y - 3 = -5(x-1)
distribute -5(x-1) = -5x + 5
y - 3 = -5x + 5
+3 +3
y = -5x + 8
I used desmos graphing caculator to graph
Choose all of the shapes that are used to create the net of a cylinder. circle triangle wedge rectangle
Answer:
trianglw
Step-by-step explanation:
Answer:
Two circles and a rectangle will make up a cylander.
Step-by-step explanation:
Have a good day! :)
1. In the diagram below, the length of the legs AC and BC of right triangle ABC are 6 cm and 8 cm,
respectively. Altitude CD is drawn to the hypotenuse of AABC. What is the length of AD to the nearest tenth
of a centimeter?
Answer:
Note that ABC is a 6 - 8 -10 right triangle with AB = 10
Also note that triangle ADC is similar to triangle ACB
Therefore
AD/ AC = AC / AB so
AD / 6 = 6/ 10 cross-multiply
10*AD = 6 * 6
810*AD = 36
AD = 36 / 10 = 3.6 = x
I hope this helps a little bit.
The amount of flight time between failures of an airplane engine is exponentially distributed with mean 900 hours. If the engine is inspected every 600 hours of flight time, what is the probability that the engine will fail before it is inspected
Answer:
0.4866 = 48.66% probability that the engine will fail before it is inspected
Step-by-step explanation:
Exponential distribution:
The exponential probability distribution, with mean m, is described by the following equation:
[tex]f(x) = \mu e^{-\mu x}[/tex]
In which [tex]\mu = \frac{1}{m}[/tex] is the decay parameter.
The probability that x is lower or equal to a is given by:
[tex]P(X \leq x) = \int\limits^a_0 {f(x)} \, dx[/tex]
Which has the following solution:
[tex]P(X \leq x) = 1 - e^{-\mu x}[/tex]
The probability of finding a value higher than x is:
[tex]P(X > x) = 1 - P(X \leq x) = 1 - (1 - e^{-\mu x}) = e^{-\mu x}[/tex]
Exponentially distributed with mean 900 hours.
This means that [tex]m = 900, \mu = \frac{1}{900}[/tex]
If the engine is inspected every 600 hours of flight time, what is the probability that the engine will fail before it is inspected?
This is [tex]P(X \leq 600)[/tex], which is:
[tex]P(X \leq 600) = 1 - e^{-\frac{600}{900}} = 0.4866[/tex]
0.4866 = 48.66% probability that the engine will fail before it is inspected
6. What is the circumference of a circle at the right in terms of it
Answer:
The perimeter or circumference of the circle can be found using the equation C=2π(r), where r= the radius of the circle.
Step-by-step explanation:
The vertex of a parabola is at the origin, and its focus is at . Which function does the graph with these attributes represent?
A.
B.
C.
D.
Answer:
ANSWER
step explanation:
The vertex of the parabola below is at the point (2,4), and the point (3,6) is on the parabola. What is the equation of the parabola? 10 (3,6) (2,4) TO 10 10 A. y= 2(x - 2)2 + 4 B. x = 4(y - 3)2 + 1 C. y= 6(x - 2)2 + 4 D. y = 3(x - 4)2 + 2
What is the length,in meters,of VX?
Answer:
C) [tex]\sqrt{90}[/tex]
Step-by-step explanation:
VY = base and leg
XY = height and leg
VX = hypotenuse (c)
VY:
9 - 6 = 3
Solving for VX(c):
a² + b² = c²
3² + 9² = c²
9 + 81 = c²
c² = 90
c = [tex]\sqrt{90}[/tex]
Answer:The answer would be C 90
Step-by-step explanation:
In a fruit cocktail, for every 12ml of orange juice you need 8ml of apple juice and 50ml of coconut milk. What is the ratio of apple juice to coconut milk to orange juice expressed in its simplest form
Answer:
4:25:6 would be the simplest form
B.Exercise 1: Directions: Write TRUE if the given answer is correct and False if it is not, give the answer. ______1. Mary bought a magazine for Php 135.00, and 2 bottles of nail polish. Give an expression to represent the total amount she spent. Given answer: 2xp+135 or 2p + 135
Answer:
Verdader
o
Step-by-step explanation:
FOR BRAINLIST!!
While building the White House model for the
iconic movie Independence day the movie makers
had to use a scale drawing in which the height of
the scale was 2 feet and the actual height of the
White house was 70 feet. If the actual length of the
white house is 168 feet, what is the length of the
scale model in feet?
А.
4.8 ft
B.
1.2 ft
5 ft
58.8 ft
Answer:
4.8
Step-by-step explanation:
Since the scale is 2 feet and the real is 70 to find the cale factor you do 70/2. Since the answer to that is 35 the scale factor is 35. SO to find tha drawing scale factor in feet you do 168/35 to get 4.8,
Need help on iready you get 13 points :)
Answer:
4 x 10
Step-by-step explanation:
4 x 2 x 5
4 x 2 = 8
8 x 5 = 40
4 x 10 = 40
Select the correct answer. Consider functions fand g. f(x) = -3x^2 + 4x + 4 g(x) = x(-7x – 7) Which expression is equal to f(x) + g(x)? A. 4x2 – 3x + 4 B. -10r2 + 41 – 3 C. -10,2 – 3x + 4 D. –332 – 3x - 3
Answer:
Correct Answer:
Option (B) -10r2 + 41 - 3
Step-by-step explanation:
#platolivesmatter
Hope this helped :)
Comment for more help, I respond very fast ;)
The expression is equal to f(x) + g(x) is -10x^2 - 3x + 4, the correct option is C.
What is an expression?Expression in mathematics is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division. An equation is an expression that shows the relationship between two or more numbers and variables.
A mathematical equation is a statement with two equal sides and an equal sign in between. An equation is, for instance, 4 + 6 = 10. Both 4 + 6 and 10 can be seen on the left and right sides of the equal sign, respectively.
We are given that;
The expression f(x) = -3x^2 + 4x + 4 g(x) = x(-7x – 7)
Now,
To find f(x) + g(x), you can add the two functions term by term. This gives you:
f(x) + g(x) = (-3x^2 + 4x + 4) + (x(-7x – 7))
f(x) + g(x) = -3x^2 + 4x + 4 - 7x^2 - 7x
f(x) + g(x) = -10x^2 - 3x + 4
Therefore, by the given expression the answer will be -10x^2 - 3x + 4.
To know more about an expression follow;
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Which is equal to the cos ÐR?
PLEASE HELP ME
Answer: 4/5 = .8
cos adj/hyp of r is .8
HOWEVER...
I’m assuming it’s talking about angle R...
PLEASE HELP!!! Needed asappp!
Step-by-step explanation:
Add the corresponding sides of the two equations
1.
2x=6
x=3
substitute for x
3+y=-1
y=-4
4.
5x=10
x=2
substitute for x
2(2)+2y=-2
2y=-6
y=-3
5.
12y=24
y=2
substitute for y
6x+5(2)=4
6x+10=4
x=-6
x=-1
Answer:
Q3. x = 3, y = -4
Q4. x = 2, y = -3
Q5. x = -1, y = 2
Step-by-step explanation:
Since the question is asking us to solve the system using elimination/adding, that's what I'll do.
To solve by adding, we add the like terms of both equations together.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
1st question:
x + y = -1
x - y = 7
We add the first term together.
x + x = 2x
Then the second term.
y + -y = y - y = 0
Then the last term.
-1 + 7 = 6
Which becomes:
2x = 6
Then we solve the linear equation.
2x = 6
÷ 2 ÷ 2
x = 3
From the x value, we can then find y.
We can use either equation. In this example, I'll choose the first one.
x + y = -1
Substitute x = 3
3 + y = -1
-3 -3
y = -4
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
2nd question:
2x + 2y = -2
3x - 2y = 12
We add the first term together.
2x + 3x = 5x
Then the second term.
2y + - 2y = 2y - 2y = 0
Then the last term.
-2 + 12 = 10
Which becomes:
5x = 10
Then we solve the linear equation.
5x = 10
÷5 ÷5
x = 2
From the x value, we can then find y.
We can use either equation. In this example, I'll choose the first one.
2x + 2y = -2
Substitute x = 2
4 + 2y = -2
-4 -4
2y = -6
÷2 ÷2
y = -3
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
3rd question:
6x + 5y = 4
-6x + 7y = 20
We add the first term together.
6x + -6x = 6x - 6x = 0
Then the second term.
5y + 7y = 12y
Then the last term.
4 + 20 = 24
Which becomes:
12y = 24
Then we solve the linear equation.
12y = 24
÷12 ÷12
y = 2
From the x value, we can then find y.
We can use either equation. In this example, I'll choose the first one.
6x + 5y = 4
Substitute y = 2
6x + 10 = 4
-10 -10
6x = -6
÷6 ÷6
x = -1
Baseball statisticians studied how often triples (a certain event in a baseball game) occurred in professional games played between 1947 and 2017. A 98 percent confidence interval to estimate the slope of the linear regression line relating the year, x, and the mean number of triples per game, y, yielded (−0.006,−0.002). A check shows that the conditions necessary for inference for the slope of the regression line are met.
Based on the confidence interval, which of the following claims is supported?
A. The mean number of triples per game is between 0.002 and 0.006.
B. The number of triples per game has increased, on average, per year.
C. There is no linear relationship between the mean number of triples per game and year.
D. There is a negative linear relationship between the mean number of triples per game and year.
E. A conclusion cannot be made about the relationship between year and mean number of triples per game because the values are close to 0.
Answer: D. There is a negative linear relationship between the mean number of triples per game and year.
Step-by-step explanation: This claim is supported by the interval. The interval contains plausible values for the slope of the linear regression line relating year and mean number of triples per game. Since all the values in the interval are negative, the interval supports the claim that increases in the year are associated with decreases in the mean number of triples per game.
plz plz plz help me ill give brainliest i just really need help
Which rectangular prism has a surface area of 62 square units? [Note: Art is not drawn to scale.]
A rectangular prism with a length of 5, width of 3, and height of 1.
A rectangular prism with a length of 2, width of 2, and height of 6.
A rectangular prism with a length of 5, width of 3, and height of 2.
A rectangular prism with a length of 6, width of 2, and height of 4.
Answer:
C. when L =5, W = 3, H = 2
Step-by-step explanation:
2(wl + hl + hw)
2(15+5+3) = 46
2(4+12+12) = 56
2(15+10+6) = 62
What value of x makes the equation –7x + 4 – 3x = –2x – 12 true?
Answer:
x=2
Step-by-step explanation:
To solve this equation combine like terms and move all like terms to the same side. Then, isolate the variable.
First, combine like terms that are on the same side,
-10x+4=-2x-12
Next, move -10x to the other side by adding it to both sides,
4=8x-12
Then, add 12 to both sides as well,
16=8x
Finally, isolate x by dividing the whole equation by 8,
2=x
Answer:
x=2
Step-by-step explanation:
I know the answer is x=2.
First, I set up the equation.
-7x+4-3x=-2x-12
Next, I added like values on each side.
-10x+4=-2x-12
Then, I added 10x to both sides.
4=8x-12
Then, I added 12 to both sides.
16=8x
Next, I divided 8 on both sides.
2=x
To make sure 2 is the true value of x, I inserted 2 to all values of x in the equation. -7(2)+4-3(2)=-2(2)-12. Both sides of the equation are -16. So, 2 is the real value of x in this equation.
what is the slope for this graph ?
Answer:
um 6/1?
Step-by-step explanation:
Answer:
2
Step-by-step explanation:
The slope of a line is the change in the line. It is often referred to as the ([tex]\frac{rise}{run}[/tex]), the slope of the line can be found using the following formula,
[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
The graph of the given line gives one the points (7, 2), (9, 6). Substitute these points into the given formula and solve for the slope,
[tex]\frac{6 - 2}{9 - 7}[/tex]
Simplify,
[tex]=\frac{4}{2}[/tex]
[tex]=2[/tex]
NeverReady batteries has engineered a newer, longer-lasting AAA battery. The company claims this battery has an average life span of 17 hours with a standard deviation of 0.8 hours. Your statistics class questions this claim. You randomly select 30 batteries and find that the sample mean life span is 16.7 hours. If the process is working properly,
Answer:
the probability is 0.0202
Step-by-step explanation:
The computation is shown below:
Given that
The Average life span = 17 hours
Standard deviation = 0.8 hours
Sample = 30 batteries
Sample mean = 16.7 hours
Now based on the above information
The probability is
[tex]P (\bar x \leq 16.7) = P (\frac{\bar x - \mu}{(\frac{\sigma }{\sqrt{n} } )} \leq (\frac{16.7 - \mu}{(\frac{\sigma }{\sqrt{n} } )}\\\\= P(z\leq \frac{16.7-17}{\frac{0.8}{\sqrt{30} } } )\\\\= P(\leq -2.05)\\\\= 0.0202[/tex]
Hence, the probability is 0.0202
Oridinary interest method to find the rate of interest that make over photo pays on a loan of $8,000 for 285 days. If the amount of interest is $590.
Answer:
The correct answer is "9.3%".
Step-by-step explanation:
The given values are:
Amount of interest,
= $590
Principle,
= $8,000
Time:
= 285
Let the interest rate will be "x".
Now,
⇒ [tex]Amount \ of \ interest=Principle\times Interest \ rate\times \frac{time}{No. \ of \ days \ in \ year}[/tex]
On substituting the values, we get
⇒ [tex]590=8000\times x\times \frac{285}{360}[/tex]
⇒ [tex]590=6333.33\times x[/tex]
⇒ [tex]x=\frac{590}{6333.33}[/tex]
⇒ [tex]=9.3157 \ percent[/tex]
or,
⇒ [tex]=9.3[/tex]%
Find the reference angle in radians: 7pi over 12
Answer:
5π/12
Step-by-step explanation:
5 pie / 12
(hope this helps can i plz have brainlist :D hehe)
Four students, Kaylee, Xavier, Ruby, and Brandon, line up one behind the other. How many different ways can they stand in line?
40 points && brainliest! pls help.
Four students, Kaylee, Xavier, Ruby, and Brandon, line up one behind the other. So, there are 24 different ways they can stand in line.
How does factorial work?Factorial of a positive integer is the result of the repeated multiplication of all the integers from 1 till that considered integer.
Thus, if we want to take the factorial of 'n',(n being a positive integer), then:
[tex]n! = 1 \times 2 \times \cdots \times (n-1) \times n[/tex]
Four students, Kaylee, Xavier, Ruby, and Brandon, line up one behind the other.
The different ways they can stand in line = 4!
[tex]= 4 \times 3 \times 2 \times 1\\\\= 12 \times 2\\\\24[/tex]
So, there are 24 different ways they can stand in line.
Learn more about factorials here:
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|y-x|, if y>x PLZ HELP
Answer:
56tt8989899999999×-×554545--455356788:988
Which of the following shows the correct first step to solve x^2-16x=-21 by completing the square? I'll give brainiest ASAP
`
An expression is defined as a set of numbers, variables, and mathematical operations. The correct option is C.
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
The perfect square of the given expression can be created by adding 36 to the expression, then the expression will reduce to,
(x-6)² = x² - 12x + 36
Hence, the correct option is C.
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5.3d = 42.4
pls help
Answer:
Step-by-step explanation:
Divide both sides by 5.3 and you get d = 8. You can use a calculator for this or just do division by hand.
2-An 83cm piece is cut from a length of ribbon measuring 1.3 metres. What length is left?
Answer:
81.7cm is the length left behind
Step-by-step explanation:
83 -1.3 =81.7
6
Uzupełnij zdania, wykorzystując podane
w nawiasach wyrazy w odpowiedniej formie.
Nie zmieniaj kolejności podanych wyrazów,
jednak - jeżeli jest to konieczne - dodaj
inne wyrazy. W każdą lukę możesz wpisać
maksymalnie cztery słowa, wliczając w to
wyrazy już podane.
1 We couldn't make an omelette because we
(have /no/egg)
2 You cooked a delicious meal, so let (1 / wash/
dish)
3 My uncle is a chef, so everyone (listen / he /
advice)
about cooking.
4 Claire is trying (not/ eat / sweet)
5 I only (drink/bit)
the coffee because it was too strong.
Answer:
This is an english server?
Step-by-step explanation:
A new car battery is sold with a two-year warranty whereby the owner gets the battery replaced free of cost if it breaks down during the warranty period. Suppose an auto store makes a net profit of $20 on batteries that stay trouble-free during the warranty period; it makes a net loss of $10 on batteries that break down. The life of batteries is known to be normally distributed with a mean and a standard deviation of 40 and 16 months, respectively.
Required:
a. What is the probability that a battery will break down during the warranty period?
b. What is the expected profit of the auto store on a battery?
c. What is the expected monthly profit on batteries if the auto store sells an average of 500 batteries a month?
Answer:
a) 0.1587 = 15.87% probability that a battery will break down during the warranty period.
b) The expected profit of the auto store on a battery is of $15.239.
c) The expected monthly profit on batteries if the auto store sells an average of 500 batteries a month is of $7,619.50.
Step-by-step explanation:
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
The life of batteries is known to be normally distributed with a mean and a standard deviation of 40 and 16 months, respectively.
This means that [tex]\mu = 40, \sigma = 16[/tex]
a. What is the probability that a battery will break down during the warranty period?
Two year warranty, that is, 24 months. This probability is the pvalue of Z when X = 24. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{24 - 40}{16}[/tex]
[tex]Z = -1[/tex]
[tex]Z = -1[/tex] has a pvalue of 0.1587.
0.1587 = 15.87% probability that a battery will break down during the warranty period.
b. What is the expected profit of the auto store on a battery?
1 - 0.1587 = 0.8413 probability of a profit of $20.
0.1587 probability of a loss of $10. So
[tex]E = 0.8413*20 - 0.1587*10 = 15.239[/tex]
The expected profit of the auto store on a battery is of $15.239.
c. What is the expected monthly profit on batteries if the auto store sells an average of 500 batteries a month?
Multiplying the average for a battery by 500. So
15.239*500 = $7,619.50
The expected monthly profit on batteries if the auto store sells an average of 500 batteries a month is of $7,619.50.
I have 48 candys for 50cents each, how much total will I have after I sell all 48 candies?
Answer:
the answer is 2400 cents
Step-by-step explanation:
if you have 48 candies and each cost 50 cents so u meltiply 48 with 50. so if u mutiply them u get 2400cents, but if u want them in dollar then 1 dollar is 100 cent so if 1 dollar = 100 cent
? = 2400 cent
you criss -cross them so when u do 2400 multiplyed by 1 is 2400 and 100 multiplyed by ? is 100?
so your going to get this
2400 = 100?
so u divide both sides by 100 because u want "?" alone. so when u do 100 will vanish because you divided both sides with 100
so it will look something like this
2400/100 = ?
when u divide 2400 with 100 u get 24.
what does that mean? it mean 2400 cents are 24 dollars
do you get it?