Answer:
(195 - 286) ± 1.992 * sqrt((46^2/45) + (58^2/40))
Step-by-step explanation:
Given that:
NEWER CARS:
Sample size = n1 = 45
Standard deviation s1 = 46
Mean = m1 = 195
OLDER CARS:
Sample size = n2 = 40
Standard DEVIATION s2 = 58
Mean = m2 = 286
Confidence interval at 95% ; α = 1 - 0.95 = 0.05 ; 0.05 / 2 = 0.025
Confidence interval is calculated thus : (newer--older)
(m1 - m2) ± Tcritical * standard error
Mean difference = m1 - m2; (195 - 286)
Tcritical = Tn1+n2-2, α/2 = T(45+40)-2 = T83, 0.025 = 1.99 (T value calculator)
Standard error (E) = sqrt((s1²/n1) + (s2²/n2))
E = sqrt((46^2/45) + (58^2/40))
Hence, confidence interval:
(195 - 286) ± 1.992 * sqrt((46^2/45) + (58^2/40))
The 95% confidence interval for estimating the difference in the mean dollar cost of the routine maintenance between newer and older cars is given by:
[tex]CI=(\overline{x_1} - \overline{x_2}) \pm t_{critical} \sqrt{\dfrac{s_1^2}{n_1} + \dfrac{s_2^2}{n_2}}[/tex]
Given that:The first sample consists of owners of newer cars
First sample's size = [tex]n_1 =45[/tex]First sample's mean = [tex]\overline{x_1}=\$195[/tex]First sample's standard deviation = [tex]s_1 = \$46[/tex]The second sample consists of owner of older cars.
Second sample's size = [tex]n_2 = 40[/tex]Second sample's mean = [tex]\overline{x_2}=\$286[/tex]Second sample's standard deviation = [tex]s_2 = \$58[/tex]To find:95% confidence interval for difference between both samples' means.
Calculations and Explanations:Since the sample sizes are > 30, thus we can use the z table for finding the Confidence interval.
The CI is given as:
[tex]CI=(\overline{x_1} - \overline{x_2}) \pm t_{critical} \sqrt{\dfrac{s_1^2}{n_1} + \dfrac{s_2^2}{n_2}}[/tex]
For 0.95 probability confidence, we have t at 40+45-3= t at 83 at 0.05/2 is 1.992 (from T tables)
Thus,
[tex]CI=(195-268) \pm 1.992 \sqrt{\dfrac{46^2}{45} + \dfrac{58^2}{40}}[/tex]
Learn more about confidence interval here:
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8. Lisa types 6 pages in 36 minutes. Frank types 5 pages in 30 minutes. Do they type at the same rate? Use a proportion to explain.
Answer:
Yes
Step-by-step explanation:
Lisa and Frank type at the same rate.
They both type 1 page every six minutes.
Lisa types 6 pages every 36 minutes, and if we divide the minutes by the pages, we get
[tex]\frac{36}{6} = 6[/tex]
And Frank types 5 pages ever 30 minutes, when we divide we get
[tex]\frac{30}{5} = 6[/tex]
y = -8x – 3
x+y=7
Is (3, 4) a solution of the system?
Answer: the answer is no :)
The ratio of pies to cakes in Susan's bakery is 3:1. Choose ALL statements that correctly show this relationship.
A)
For each pie, there are three cakes.
B)
For each cake, there are three pies.
C)
For every three cakes, there is one pie.
D)
For every three pies, there is one cake.
E)
For every three pies there are three cakes.
Help asap if you get it right ill give 30 points no cap. Zach created a blueprint using only similar parallelograms.
Which statement about the parallelograms must be true?
The parallelograms have corresponding angles that are not congruent.
The parallelograms have corresponding sides that are congruent.
The parallelograms have proportional corresponding sides.
The parallelograms all have congruent sides and angles.
Answer: Hello!
Step-by-step explanation:
Your answer would be D :)
Data on investments in the high-tech industry by venture capitalists are compiled by a corporation. A random sample of 18venture-capital investments in a certain business sector yielded the accompanying data, in millions of dollars. Determine and interpret a 95%confidence interval for the mean amount, mu,of all venture-capital investments in this business sector. Assume that the population standard deviation is $1.70million. (Note: The sum of the data is $102.52million.)
Answer:
$4.911 million or $6.481 million
Thus, we are 95% confident that the mean amount of all venture-capital investments in the high-tech industry is somewhere between $4.911 million and $6.481 million.
Step-by-step explanation:
Given that:
sample size n = 18
standard deviation σ = 1.70
confidence interval = 95%
Sample mean [tex]\overline x =\dfrac{ \sum x }{n}[/tex]
[tex]\overline x =\dfrac{ 102.52 }{18}[/tex]
[tex]\overline x =[/tex] 5.696
The level of significance = 1 - C.I
= 1 - 0.95
= 0.05
The critical value of [tex]Z_{\alpha/2} = Z_{0.025} = 1.960[/tex] from the Z tables
The 95% C.I for the mean is;
[tex]= \overline x \pm Z_{\alpha/2} \times \dfrac{\sigma}{\sqrt{n}}[/tex]
[tex]=5.696 \pm 1.960 \times \dfrac{1.70}{\sqrt{18}}[/tex]
[tex]=5.696 \pm 1.960 \times \dfrac{1.70}{4.243}[/tex]
[tex]=5.696 \pm 1.960 \times 0.4007[/tex]
= 5.696 ± 0.785372
= (5.696 - 0.785372 , 5.696 + 0.785372 )
= ( 4.910628 , 6.481372 )
≅ $4.911 million or $6.481 million.
Thus, we are 95% confident that the mean amount of all venture-capital investments in the high-tech industry is somewhere between $4.911 million and $6.481 million.
the product of a number and -8 is 72
Answer:
-9.
The product of -9 and -8 is 72.
Step-by-step explanation:
Product means the answer of a multiplication, so we're given 72 and -8.
We can solve this by using inverse operations.
The inverse operation of multiplication is division, so we divide 72÷ -8
This will give us -9.
2x squared times 6 =
A:10x squared
B:8x squared
C:12x squared
Answer:
C: 12x squared
Step-by-step explanation:
the equation would look like [tex]2x^{2}[/tex] · [tex]6[/tex] or [tex]6(2x^{2})[/tex]
you only multiply the coefficients, leave the exponent alone for this one
so 2 times 6 would be 12 and the [tex]x^{2}[/tex] remains the same giving you [tex]12x^{2}[/tex]
If a=5 what is the value of the card 4a-2
Answer:
18
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightStep-by-step explanation:
Step 1: Define
4a - 2
a = 5
Step 2: Evaluate
Substitute in a: 4(5) - 2Multiply: 20 - 2Subtract: 18Answer:
The card "4a-2" is equal to 18
4a-2 = 18
Step-by-step explanation:
#1. Replace a with 5 and Your equation should look like the following:
4(5)-2
#2. Now Simplify, we all know that multiplication goes before subtraction or addition:
20-2
#3. Celebrate:
18
Woohoo
Hope this helps!
Have a nice day!
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Solve for M in the formula S= C+M.
A. M= S+ C
B. M= S - C
C. M= SC
D. M= s/c
Answer:
im pretty sure its a
Step-by-step explanation:
WILL GIVE BRAINLIEST TO WHOEVER ANSWERS FASTEST!
Answer:
speed i answerd first U.U
Step-by-step explanation:
An elevator is traveling underground at a constant rate. The equation y= -2x - 10 can be used to represent this situation, where y is the position of the elevator underground in feet and x is the number of seconds the elevator has been traveling Which statement best describes the position of the elevator, given this equation?
O From a starting position of 2 feet underground, the elevator is descending 10 feet per second
O From a starting position of 10 feet underground, the elevator is descending 2 feet per second
O From a starting position of 2 feet underground, the elevator is ascending 10 feet per second
O From a starting position of 10 feet underground, the elevator is ascending 2 feet per second
4 is correct
reason is because the number next to x is the constant number and the end number is where you started
Which of the following linear equations passes through points (2,0) and (5,-3)?
y = -x + 2
O y= x-2
y = x + 2
None of these choices are correct.
O y=-x-2
Which of the following would you expect to find on a monthly account statement? a. A new set of checks and deposit slips for the coming month. b. A list of credits and debits made during the period. c. A comparison of ending balances for the past 12 months. d. A tally of all credits and debits in the account’s history.
Answer:
b. A list of credits and debits made during the period.
Step-by-step explanation:
Edge 2021
On a monthly account statement, what you are expected to find is a A list of credits and debits made during the period.
What is a monthly account statement?This can be referred to as a statement of the debits and the credits that occurred in a given period of one month.
The account statement is a statement of the transactions that have occurred in an establishment over a period.
Read more on account statements here:
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Reid's Hardware discounts all riding lawnmowers 9% to customers paying in cash. If Trey paid $1,390.49 in cash for a riding lawnmower, which of the following equations can be used to determine the original price of the lawnmower?
Answer:
The original price of the lawnmower is $ 1,528.
Step-by-step explanation:
If Reid's Hardware makes a 9% discount on cash payments, and Trey paid $ 1,390.49 for his lawnmower, to determine the initial cost of the same, the following calculation must be performed:
100 - 9 = 91
91 = 1,390.49
100 = X
(100 x 1,390.49) / 91 = X
139.049 / 91 = X
1.528 = X
Thus, the original price of the lawnmower is $ 1,528.
can someone help me with this
Answer:0.98
hope this helps have a good day
Step-by-step explanation:
Pls answer this is very easy
Answer:
A and B
Step-by-step explanation:
The original equation simplifies down to -4m - 2
Answer A and B also simplify down to -4m -2, and therefor are equivalent
A: -2(4m + 1) + 4m
-8m - 2 + 4m
-4m - 2
B: 2(2m - 1) - 8m
4m - 2 - 8m
-4m - 2
Each week, Tasha saves 80% of the money she earns babysitting and spends the rest. This week she earned $80.00.
How much more money did she save than spend this week?
Answer:
48$
Step-by-step explanation:
80% of 80 is 64 which means she spent 16$ and saved 64$
so 64-16=48$
answer = 48$
Please help I don’t under
Answer:
x=30
Step-by-step explanation:
set the sum of both equal to 180 bc it makes a straight line
(x-1)+(5x+1)=180
add and subtract 1 from each side
x+5x=180
add like terms
6x=180
divide by 6
x=30
Answer:
D: x=30
Step-by-step explanation:
(x-1)⁰+ (5x+1)⁰=180⁰
x-1+5x+1=180
x+5x-1+1=180
6x=180
x=30
Write a function formula for g using the function f.
g(x)=
Write a function formula for f using the function g.
f(x)=
9514 1404 393
Answer:
g(x) = f(x -2) -1
Step-by-step explanation:
The transformation g(x) = f(x -h) +k causes the graph of function f(x) to be translated h units to the right and k units up. Here, g is translated 2 units right and 1 unit down, so (h, k) = (2, -1). The translated function is ...
g(x) = f(x -2) -1
The Quality Control Department employs five technicians during the day shift Listed below is the number of times each technician instructed the production foreman to shut down the manufacturing process last week.
Technician Shutdown
Taylor 4
Hurley 3
Gupta 5
Rousche 6
Huang 3
Required:
a. How many samples, without replacement, of size two are possible?
b. Compute the mean of the sample means and compare it to the population mean. (Round your answers to 1 decimal place.)
Solution :
Number of different samples of two technicians possible is = 10, as 2 technicians are to be chosen from a total of 5 technicians.
a). Therefore, 10 different samples are possible of size two.
b).
Sample Shut down Mean
1. Taylor, Hurley 4, 3 3.5
2. Taylor, Gupta 4, 5 4.5
3. Taylor, Rousche 4,6 5
4. Taylor, Huang 4, 3 3.5
5. Hurley, Gupta 3,5 4
6. Hurley, Rousche 3,6 4.5
7. Hurley, Huang 3,3 3
8. Gupta, Rousche 5,6 5.5
9. Gupta, Huang 5,3 4
10. Rousche, Huang 6,3 4.5
42
Now mean of sample means [tex]$=\frac{42}{10}$[/tex] = 4.2
Mean of population is = [tex]$\frac{4+3+5+6+3}{5}$[/tex] = 4.2
Thus both the means are equal.
Helppp asappp I need help with 4
Answer:
Step-by-step explanation:
1. Write the equation in point slope form. Remember, point slope form looks like this: y-y1=m(x-x1), with m representing slope. With this equation, you plug in the y coordinate for y1 and the x coordinate for x1. So, it will look like this
y+6=2/3(x+5)
2. Then, convert that into slope intercept form, which is y=mx+b.
y+6=2/3x+10/3 (2/3 * 5)
y= 2/3x - 8/3 (10/3 - 6)
Therefore, your slope-intercept form of the equation is: y=2/3x - 8/3
3. From there, you can graph the line. See the graph in the image attached.
Jose uses the pattern in rows 1 and 8 in the multiplication table below to find ratios that are equivalent to 1:8.
A multiplication table. In the row labeled 1, the numbers 1, 2, 3, 4, 5, 6, 7, 8 and 9 are highlighted. In the row labeled 8, the numbers 8, 16, 24, 32, 40, 48, 56, 64, and 72 are highlighted.
If Jose extends the pattern in the highlighted rows to include a ratio that has a first term of 10, what would be the second term of the ratio?
10
20
80
90
Answer:
10Step-by-step explanation:
Answer:
Your answer would be 20 not 10
Step-by-step explanation:
trust me i took the test
(7+ 1 4) + 6 = 7 ( ■ + 1 6)
Need help! Which matrix equation represents the system of equations?
[2x+ y =5
[5x+3y -12
Step-by-step explanation:
The given equations are :
2x+ y =5 ....(1)
5x+3y = 12
We need to find the matrix equation that represents the system of equations.
[tex][A]=\left[\begin{array}{cc}2&1&\\5&3\end{array}\right][/tex]
[tex][B]=\left[\begin{array}{cc}5\\12\end{array}\right][/tex]
And
[tex][X]=\left[\begin{array}{cc}x\\y\end{array}\right][/tex]
Hence, the matrix equation is :
[tex]\left[\begin{array}{cc}2&1&\\5&3\end{array}\right] \left[\begin{array}{cc}x\\y\end{array}\right]=\left[\begin{array}{cc}5\\12\end{array}\right][/tex]
Hence, the correct option is (b).
PLEASE HELP ME
(a) Find m
(b) Find AB
-10x-3y=-18
-7x-8y=11 solve system using elimination
Answer:
(-7) (-10x - 3y = -18)
(10) (-7x - 8x = 11)
--------------------------
70x + 21y = 126
+ -70 - 80x = 110
---------------------------
-59x = 236
x = -4
Answer
[tex] \huge{ \boxed{ \text{(3 \:, - 4)}}}[/tex]
✑ [tex] \underline{ \underline{ \text{First ,\: let's \: know \: about \: elimination \: method}}}[/tex] :
☇ In this method , we add or subtract the given equations to eliminate one of the two variables by making their coefficients equal. Then , a single equation with one variable so obtained is solved to find the value of the variable. The value of the variable is substituted to any one equation to find the value of the eliminated variable.
☯ [tex] \underline{ \underline{ \text{Let's \: solve}}} : [/tex]
[tex] \underline{ \text{Original \: system}} : [/tex]
[tex] \text{ - 10x - 3y = - 18 - - - - Equation\: (i)}[/tex]
[tex] \text{ - 7x - 8y = 11 - - - - Equation \: (ii)}[/tex]
[tex] \text{Step \: 1} : [/tex] Take L.C.M ( Lowest Common Multiple ) of 10 and 7. For this , find the prime factors of each number. Then, take out the common prime factors and other remaining prime factors and multiply them.
prime factors of 10 = 1 × 2 × 5prime factors of 7 = 1 × 7L.C.M = Common factors × Remaining Factors
= 1 × 2 × 5 × 7
= 70
[tex] \text{Step \: 2} : [/tex] Multiply equation ( i ) by 7
[tex] \text{7( - 10x - 3y ) = - 18 * 7}[/tex]
⇢ [tex] \text{ - 70x - 21y = - 126 - - - - equation \: (iii)}[/tex]
[tex] \text{Step \: 3} : [/tex]Multiply equation ( ii ) by 10
[tex] \text{10( - 7x - 8y) = 11 \: * \: 10}[/tex]
⇢ [tex] \text{ - 70x - 80y = 110 - - - - equation \: (iv)}[/tex]
[tex] \text{Step \: 4} : [/tex] Subtract equation ( iv ) from equation ( iii ) :
Also Remember that while subtracting , sign of each term of the second equation changes. Here , we are eliminating x . So to make the coefficient of y same , equation ( i ) is multiplied by 7 and equation ( ii ) is multiplied by 10.⇩
[tex] \text{ - 70x - 21y = - 126}[/tex]
[tex]\text{+70x + 80y = - 110}[/tex]
___________________
[tex] \text{ \: \: \: \: \: \: 59y = - 236}[/tex]
Solve :
⇢ [tex] \text{59y/59 = - 236/59}[/tex]
⇢ [tex] \boxed{ \bold{ \text{y = - 4}}}[/tex]
[tex] \text{Step \: 5} : [/tex]
Substitute the value of y into equation ( iii ) , we get :
[tex] \text{ - 70x - 21y = - 126}[/tex]
➳ [tex] \text{ - 70x - 21( - 4) = - 126} [/tex]
➳ [tex] \text{ - 70x - ( - 84) = - 126} [/tex]
➳ [tex] \text{ - 70x + 84 = - 126}[/tex]
➳ [tex] \text{ - 70x = - 126 - 84}[/tex]
➳ [tex] \text{ - 70x = - 210}[/tex]
➳ [tex] \text{ - 70x/ - 70 = - 210/ - 70}[/tex]
➳ [tex] \boxed{ \bold{ \text{x = 3}}}[/tex]
[tex] \bold{ \underline{ \text{Hence ,\: x = 3 \: and \: y = - 4}}}[/tex]
Hope I helped!
♡ Have a wonderful day / night ツ
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please help me solve this anyone! plz don’t guess just for points this was due a few weeks ago and i have to have good grade
Answer:
[tex] - 23[/tex]
Step-by-step explanation:
Substitute -3 for X in the expression then solve.
Answer:
-23
Step-by-step explanation:
They give us the variable's value, which is [tex]x=-3[/tex]. All we have to do from here is plug it into the expression that they gave us!
So, let's do exactly that! The expression that they gave us is [tex]5x-8[/tex], and we know the value of x because they gave it to us!
Let's plug it in.:
[tex]5(-3)-8[/tex]
Let's follow P.E.M.D.A.S. and our order of operations to determine what to do first. Since we have multiplication going on within parenthesis, let's do that first.
[tex]5(-3)=-15[/tex] because a negative number times a positive number equates to a negative number. Now, we have the following expression: [tex]-15-8[/tex]
Let's subtract this now! Remember, subtracting a number from another number is basically adding the opposite of the second number; essentially, you're following keep, change, flip. You keep the first number without doing anything to it, you change the sign of the operation, and you flip the sign of the 2nd number. Let's revise this problem now with these rules.: [tex]-15 + (-8)[/tex], now we have something that we can work with! Since both numbers are negative and are being added, we keep the sign, and just add their absolute value, leaving us with the expression being -23.
$1,580 at 10% for 8 years
complete the table of values for y=2-x
x= -1, 0, 1, 2, 3, 4,
y= , , , , -1, ,
Answer:
x = -1, 0, 1, 2, 3, 4
y = 3, 2, 1, 0, -1, -2
Answer:
x = -1, 0, 1, 2, 3, 4
y = 3, 2, 1, 0, -1, -2
What is 3/8 equal to in decimals..?
Answer:
.375
Step-by-step explanation:
Answer: 0.375
Step-by-step explanation:
Hey there! If you have any questions feel free to leave them in the comments below.
To find the answer you would divide the numerator by the denominator. [tex]\frac{3}{8}[/tex] would be equal to 0.375
~I hope I helped you :)~