Answer:
1. Yes, there is sufficient evidence to support the claim that student cars are older than faculty cars.
2. The 98% confidence interval for the difference between the two population means is [1.432 years, 3.968 years].
Step-by-step explanation:
We are given that randomly selected 110 student cars to have ages with a mean of 8 years and a standard deviation of 3.6 years, while randomly selected 75 faculty cars to have ages with a mean of 5.3 years and a standard deviation of 3.7 years.
Let [tex]\mu_1[/tex] = mean age of student cars.
[tex]\mu_2[/tex] = mean age of faculty cars.
So, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu_1 \leq \mu_2[/tex] {means that the student cars are younger than or equal to faculty cars}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu_1>\mu_2[/tex] {means that the student cars are older than faculty cars}
(1) The test statistics that will be used here is Two-sample t-test statistics because we don't know about the population standard deviations;
T.S. = [tex]\frac{(\bar X_1-\bar X_2)-(\mu_1-\mu_2)} {s_p \times \sqrt{\frac{1}{n_1}+\frac{1}{n_2} } }[/tex] ~ [tex]t_n_1_+_n_2_-_2[/tex]
where, [tex]\bar X_1[/tex] = sample mean age of student cars = 8 years
[tex]\bar X_2[/tex] = sample mean age of faculty cars = 5.3 years
[tex]s_1[/tex] = sample standard deviation of student cars = 3.6 years
[tex]s_2[/tex] = sample standard deviation of student cars = 3.7 years
[tex]n_1[/tex] = sample of student cars = 110
[tex]n_2[/tex] = sample of faculty cars = 75
Also, [tex]s_p=\sqrt{\frac{(n_1-1)\times s_1^{2}+(n_2-1)\times s_2^{2} }{n_1+n_2-2} }[/tex] = [tex]\sqrt{\frac{(110-1)\times 3.6^{2}+(75-1)\times 3.7^{2} }{110+75-2} }[/tex] = 3.641
So, the test statistics = [tex]\frac{(8-5.3)-(0)} {3.641 \times \sqrt{\frac{1}{110}+\frac{1}{75} } }[/tex] ~ [tex]t_1_8_3[/tex]
= 4.952
The value of t-test statistics is 4.952.
Since the value of our test statistics is more than the critical value of t, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region.
Therefore, we support the claim that student cars are older than faculty cars.
(2) The 98% confidence interval for the difference between the two population means ([tex]\mu_1-\mu_2[/tex]) is given by;
98% C.I. for ([tex]\mu_1-\mu_2[/tex]) = [tex](\bar X_1-\bar X_2) \pm (t_(_\frac{\alpha}{2}_) \times s_p \times \sqrt{\frac{1}{n_1}+\frac{1}{n_2} })[/tex]
= [tex](8-5.3) \pm (2.326 \times 3.641 \times \sqrt{\frac{1}{110}+\frac{1}{75} })[/tex]
= [tex][2.7 \pm 1.268][/tex]
= [1.432, 3.968]
Here, the critical value of t at a 1% level of significance is 2.326.
Hence, the 98% confidence interval for the difference between the two population means is [1.432 years, 3.968 years].
a company needs to refill printing paper. each one of printing paper costs $30 and a delivery fee of $10. write an equation to find the total cost of purchasing x number of boxes of printing paper.
Answer:
Cost in $= x(y(30))+10
Step-by-step explanation:
a company needs to refill printing paper. each one of printing paper costs $30 and a delivery fee of $10.
Let y be the number of paper in a box
Let x be the number of box to be purchased.
So it means for each x box, there are y paper costing $30 and a delivery fee for the box is $10
Cost in $= x(y(30))+10
Arthur, Yusuf, and Bill had some stamps in the ratio 3: 5: 6. When Yusuf gave some stamps to Arthur and Bill gave Arthur 42 stamps more than what Yusuf gave Arthur, they all had the same number of stamps each. How many stamps did Yusuf have at first?
Answer:
210 stamps
Step-by-step explanation:
Given:
Arthur ⇒ a = 3 kYusuf ⇒ y = 5kBill ⇒ b = 6kYusuf gave x stamps to Arthur, then:
y = 5k -xa = 3k + xBill gave Arthur 42 stamps more than Yusuf gave to Arthur, then:
b = 6k - (x+42)a = 3k + x + x + 42Now all 3 have same amount of stamps:
5k -x = 6k - x - 42 = 3k + 2x + 42From the first part of the equation we get:
6k - 5k = 42 + x - xk = 42How many stamps did Yusuf have at first?
y = 5k y =5*42 y = 210 stampsYusuf had 210 stamps at first
True or false: the coordinate grid below shows the triangle transformed following the rule : (x,y)-> (x-4,y+3)
Answer: True
Step-by-step explanation:
Answer:
True
Step-by-step explanation:
Step 1: Find the Coordinates of the Original Triangle
(2, -2)
(6, -3)
(5, 2)
Step 2: Apply the Transformation to the Coordinates
(2-(4),-2+(3)) -> (-2, 5)
(6-(4),-3+(3)) -> (2, 0)
(5-(4),2+(3)) -> (1, 5)
Step 3: Compare the points on the red triangle with the points you got
(-2, 5) = (-2, 5)
(2, 0) = (2, 0)
(1, 5) = (1, 5)
Because the coordinates are the same we can conclude that the triangle was transformed with the rule: (x,y)-> (x-4,y+3)
the question is below:
Answer:
x = 19.5, RQS=43
Step-by-step explanation:
It is important to note that RQS and TQS are supplementary, meaning their angles will add up to 180. Knowing this, we can create and solve the equation to find x..
(2x+4) + (6x+20) = 180
8x + 24 = 180
8x = 156
x = 19.5
Now that we know the value of x, we can substitute it into the equation for RQS, 2x+4.
2(19.5)+4
39+4
43
Hope this helped!
Answer:
[tex]x=19.5^o[/tex]
[tex]\angle RQS=43^o[/tex]
Step-by-step explanation:
Notice that the addition of these two angles give you and angle of [tex]180^o[/tex], therefore we can write the following equation to represent such addition:
[tex](2x+4)^o + (6x+20)^o=180^o\\2x+6x+4^o+20^o=180^o\\8\,x+24^o=180^o\\8\,x=180^o-24^o\\8\,x=156^o\\x=156^o/8\\x=19.5^o[/tex]
Therefore, the value of the angle RQS is:
[tex]\angle RQS=(2\,x+4)^o=(2\,*\,19.5^o)+4^o=43^o[/tex]
Which tables display linear functions?Check all that apply
Please help me!!!!!
Answer:
The first one and the last one. A and D.
Step-by-step explanation:
A linear equation is and equation where the line is going up on a graph. In order for that to happen, y must always be bigger than x. The first and last chart all the way to the right is the only one that has that trait. :)
The price of an item was reduced 25% to $30 what was the original price of the item
Answer:
$40
Step-by-step explanation:
Let the original price of the item be x.
From the first statement, the price of the item was reduced 25% to $30. This means that new price of the item is now 75% (0.75) of the original price(x), and this new price is equal to $30. i.e
0.75x = 30
Now, let's solve for x.
0.75x = 30 [divide both sides by 0.75]
[tex]\frac{0.75x}{0.75}[/tex] = [tex]\frac{30}{0.75}[/tex]
x = 40.
Therefore, the original price of the item was $40
Step-by-step explanation:
40 is the answer for your question
pls helpppp c=30m+50 and c=20m+100. solve for c and show your work.
Answer:c=200
Step-by-step explanation:
30(5) + 50 = 200
20(5) + 100 = 200
-------------------------------|
100 30m
- 50 - 20m
——— ———
50 10m 50/10 = 5 [m=5]
Find the equation of the line that contains the point (7.9) and is perpendicular to the line 5x + 3y = 4. Write the equation in the form
y = mx + band identify m and b
Answer:
[tex]y = \frac{3}{5} x + \frac{24}{5} [/tex]
m= 3/5
b= 24/5
The area of a rectangular piece of land J is 220 square metres.Its width is 12.5.what is the perimeter of the land ?
Answer:
60.2m
Step-by-step explanation:
area =breadth × width
220m^2 = x × 12.5
x = 17.6
perimeter = 2(a+b)
perimeter = 2(12.5+17.6)
perimeter = 60.2m
AB = 5 units and CD = 5 units, what is the length of your new segment, AD?
Answer:
New segment AD = 10 units
Step-by-step explanation:
Given:
AB = 5 units
CD = 5 units
Find:
New segment AD.
Computation:
⇒ New segment AD = AB + CD
⇒ New segment AD = 5 units + 5 units
⇒ New segment AD = 10 units
In which of these situations would it be more appropriate to use a probability model rather than a regression/data-mining approach?
a. Predicting when the customer will make her next purchase.
b. Predicting which customer is most likely to churn in the next year.
c. Predicting the brand that the customer will buy during her next category purchase.
d. Predicting whether the customer will buy the brand at least once in the next year.
e. Predicting whether the customer will churn in the next year
Answer:
The correct options are b, c and d.
Step-by-step explanation:
The regression or data mining approach is used to predict the future value of the variable under study.
Whereas the probability model is used to predict the chances or likelihood of an event taking place.
Predicting which customer is most likely to churn in the next year.To predict which customer is most likely to churn in the next year, we need to compute the probability for customers who are likely to churn in the next year.
Thus, a probability model would be used.
Predicting the brand that the customer will buy during her next category purchase.Each brand has a specific probability of being purchased by a customer.
Thus, a probability model would be used.
Predicting whether the customer will buy the brand at least once in the next year.In this case also we need to compute the probability of a customer buying the brand at least once in the next year.
The correct options are b, c and d.
What value does the 1 represents in the number 4,105.8
Answer:
the 1 represents the value of 100 of one-hundreth place
Step-by-step explanation:
Two rectangles have equal areas. If the base and altitude of one are 12mm and 8mm, and the base of the other is 16mm, what is the altitude of the second rectangle?
Answer:
6mm
Explanation:
since the area of both rectangle is equal, therefore :
Arectangle 1= Arectangle 2
base 1*altitude 1 =base 2*altitude 2
12mm*8mm = 16mm* altitude 2
96mm²= 16mm* altitude 2
96mm²/16mm = altitude 2
6mm = altitude 2
4. A recent poll of 1079 adults finds that 55% of Americans support a more stringent immigration law. Construct a 99% confidence interval of the proportion of the population that will support such a law.
Answer:
0.5306[tex]<\mu<[/tex]0.5694
Step-by-step explanation:
USing the formuls for calculating the confidence interval for the population proportion;
CI = p±Z*√[p(1-p)/n]
p is the percentage proportion of the population 55%
Z is the z-score at 99% confidence interval = 2.576
n is the sample size = 1079
CI = 0.55 ± 2.576*[0.55(1-0.55)/√1079]
CI = 0.55 ± 2.576*[0.55(0.45)/√1079]
CI = 0.55 ± 2.576*[0.2475/√1079]
CI = 0.55 ± 2.576*[0.2475/32.85]
CI = 0.55 ± 2.576*[0.00753]
CI = 0.55 ±0.0194
CI =(0.55-0.0194, 0.55+0.0194)
CI = (0.5306, 0.5694)
Hence, a 99% confidence interval of the proportion of the population that will support such a law is 0.5306[tex]<\mu<[/tex]0.5694
If the length of the legs of a right triangle are 18 and 34, what is the length of the hypotenuse? Round your
answer to the nearest tenth, if necessary.
Answer:
The answer is 38.5Step-by-step explanation:
Since we have been given the legs of the right angled triangle we can use Pythagoras theorem to find the hypotenuse
That's
[tex] {h}^{2} = {b}^{2} + {c}^{2} [/tex]
where
h is the hypotenuse
The legs of the triangle are 18 and 34 so the hypotenuse is
[tex] {h}^{2} = {18}^{2} + {34}^{2} [/tex]
[tex]h = \sqrt{324 + 1156} \\ h = \sqrt{1480} \\ h = 2 \sqrt{370} [/tex]
h = 38.47076
We have the final answer as
h = 38.5 to the nearest tenthHope this helps you
Answer:
38.5
Step-by-step explanation:
Hello!
To find the length of a missing side of a right triangle we use the equation
[tex]a^{2} +b^{2} =c^{2}[/tex]
a is a leg
b is the other leg
c is the hypotenuse
Put in what we know
[tex]18^{2} +34^{2}= c^{2}[/tex]
Simplify
[tex]324+1156 = c^{2}[/tex]
Simplify
[tex]1480 = c^{2}[/tex]
Take the square root of both sides
38.470 = c
Round to the nearest tenth
38.5 = c
Hope this helps!
Over 4 days the temperature was 4, 6, -12, and -5 degrees. What was the average temperature?
Answer:
-1.75
Step-by-step explanation:
add -12 and -5, you get -17, and 4 and 6, get 10, add -17 and 10 to get -7, and divide by 4 and get -1.75
1 way ANOVA analysis was used to test the effectiveness of 3 kinds of headache medicines (Advil, Tylenol, and Excedrin). The analysis involved 21 people (7 per group), and used an alpha level of 0.01. What is the Critical Value
Answer:
The critical region is F >F ₀.₀₁ (2,18) = 6.01
Step-by-step explanation:
For 1 way ANOVA the degrees of freedom Between Samples would 2 and within Samples would be 18 .
Alpha is given to be = 0.01
v1 = k-1 and v2 = n-k
Where k is the number of rows and n is the total number of values
v1= 3-1= 2 and v2 = 21-3= 18
So if we look up the table we find the values of the critical region to be 6.01
Hence the critical region is less and equal to 6.01
The critical region is F >F ₀.₀₁ (2,18) = 6.01
Monica Ramirez works at the hospital as a nursing assistant. She works 15 hours per week and earns $8.50 per hour. What is Monica’s straight-time pay for each week? *
1 point
$120.00
$127.00
$127.50
$120.50
Answer:
Answer:
C. She makes $127.50 a week
Step-by-step explanation:
Since we are looking for how much she makes every week, we need to multiply her number of hours by the pay. She makes 8.50 per hour and works 15 hours.
8.5x15=127.5
She makes $127.50 a week
Step-by-step explanation:
The solution is Option C.
The total amount of straight time pay of Monica for the week is $ 127.50
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
Let the total number of hours worked in the week by Monica be = T
The value of T = 15 hours
Let the earnings per hour of Monica be = $ 8.50
Now , the equation will be
Total straight line pay for Monica = number of hours worked in the week by Monica x earnings per hour of Monica
Substituting the values in the equation , we get
Total straight line pay for Monica A = 15 x 8.50
Total straight line pay for Monica A = $ 127.50
Therefore , the value of A is $ 127.50
Hence , The total amount of earnings of Monica for the week is $ 127.50
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30 POINTS! 3 questions! EASY 1. Jason is 22, which is 6 years older than twice his sister Taylor’s age.How old is Taylor? Enter your answer in the box.
2. Each month, Sal must pay for car insurance and fuel to drive a vehicle. Sal's parents agree to pay p percent of his car expenses. The cost of car insurance is the same every month, but the cost of fuel depends on d, the number of miles Sal drives. The expression (1−p)(0.10d+60) represents how much Sal must pay toward his monthly car expenses. Which part of the expression represents the percentage of the monthly expenses that Sal must pay?
A. 0.10d + 60
B. 1−p
C. 60
D. 0.10d
3. Which equation represents this sentence? Twenty-eight is the product of four and a number.
A. 28=4n
B. 28=4+n
C. 28=4n
D. 28=4n
Answer:
question 1: she is 8 years old Question 2: C-60
Step-by-step explanation:
Write an algebraic expression for the word expression.
the sum of 9 and a number x
The expression is ___
Answer: 9 + x
The word "sum" indicated that we are adding the two numbers, so we put the number and the variable in an expression that adds them together. There is no indication that there is anything else we need to add to this expression, so this is all you need. (The "x" is a variable, which can represent any number.)
The algebraic expression for the word expression is the sum of 9 and a number x will be 9 + x.
What is an expression?An expression is a combination of some mathematical symbol such that an arithmetic operator and variable such that all are constrained and create an equation.
In other meaning, expression is very useful to determine the end or root value of constraint.
As per the given phrase,
The sum of 9 and the number x.
The sum is an addition and represents by the symbol "+".
Therefore, 9 + x
Hence "The algebraic expression for the word expression is the sum of 9 and a number x will be 9 + x".
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A party planner is going to use an arch of balloons for a parade of recent graduates. The estimated curve the
balloons will create is modeled by the function given in the table, where x represents the distance in feet along
the ground from the start and f(x) represents the height in feet above the ground.
The planner needs a clearance of 9 feet under the arch. Has the planner met the minimum height?
No, because the width of the arch is 8 feet
Yes, because the width of the arch is 9.6 feet
No, because the maximum height of the arch is 8 feet
Yes, because the maximum height of the arch is 9.6
feet
Answer:
Option (4)
Step-by-step explanation:
Party planner has used an arc of balloons for the parade.
This arc starts from x = 0 along the ground and f(x) defines the height of the arch.
From the table attached, it is clear that at x = 4 maximum height of the arch is 9.6 feet.
Therefore, clearance space below the arc is 9.6 feet which is greater than 9 feet, minimum height required for the clearance of the parade.
Option (4) will be the answer.
Answer:
D. yes, because the maximum height of the arch is 9.6 feet
Step-by-step explanation:
EDGE 2020 :)
1440 men had sufficent food for 32 days in a camp
Answer:
the boy is gay
Step-by-step explanation:
kkkjssjska
A rectangle has a width of 55 centimeters and a perimeter of 224 centimeters. What is the rectangle's length
The length is
cm.
Answer:
[tex]as \: we \: know \: perameter \: of \: rectngle = 2(length \ + beadth)[/tex]
[tex]and \: also \: perimeter \: = 224cm[/tex]
[tex]therefore \: we \: can \: write \: that 2(length + bredth) = 224cm [/tex]
let the length be l
and breadth is 55 cm
[tex]2(l + 55) = 224[/tex]
[tex]l + 55 = \frac{224}{2} [/tex]
[tex]l + 55 = 112[/tex]
[tex]l = 112 - 55[/tex]
[tex]l = 57[/tex]
so the length of rectangle is 57 cm
(10+i)^2 = (in form a+bi)
Answer:
99+20i
Step-by-step explanation:
(10+i)^2
➡
(10 + i) × (10 + i) = 100 + 10i + 10i + i^2 add like terms
100 + 20i + i^2 since i^2 = -1 we can write the expression like this
99 + 20i
Show all work to identify the asymptotes and zero of the function f of x equals 5 x over quantity x squared minus 25.
Answer:
asymptotes: x = -5, x = 5zero: x = 0Step-by-step explanation:
The function of interest is ...
[tex]f(x)=\dfrac{5x}{x^2-25}=\dfrac{5x}{(x-5)(x+5)}[/tex]
The asymptotes are found where the denominator is zero. It will be zero when either factor is zero, so at x = 5 and x = -5
__
The zeros are found where the numerator is zero. It will be zero for x = 0.
The asymptotes are x=-5, x=5; the zero is x=0.
Answer:
The asymptotes are x=-5, x=5; the zero is x=0.
Step-by-step explanation:
Consider the system of equations. y = −2x + 4 y = − 1/3x − 1
Hey there! I'm happy to help!
We have two values for y. Since y=y, this means that −2x + 4 and − 1/3x − 1 are equal as well, so we can put them in an equation and solve for x.
−2x + 4 = − 1/3x − 1
We subtract 4 from both sides.
-2x=-1/3x-5
We add 1/3 x to both sides.
-5/3x=-5
We divide both sides by -1 2/3.
x=3
Now, we plug this into one of the original equations to find y.
y=-2(3)+4
y=-6+4
y=-2
Therefore, the solution is (3,-2) or x=3 and y=-2.
I hope that this helps! Have a wonderful day! :D
the first three terms of an arithmetic progression is (x + 1), (4 x - 2) and 6 x - 3 if the last term is 18 find the value of x
Answer:
2
Step-by-step explanation:
Since it is AP, the common difference is same for any term:
(4x - 2) - (x + 1) = (6x - 3) - (4x - 2)3x - 3 = 2x -13x - 2x = 3 - 1x= 2The first 3 terms are:
3, 6, 9Since the last term is 18, it means this AP has 6 terms:
{3, 6, 9, 12, 15, 18}Answer: as we need to find the value of x only, it is = 2
A function is defined as (f of x) = -3^4√x-9. Evaluate (f of x) at x=81 A. -36 B. -18 C. -27 D. -12
Answer:
F(x) = -3^(27)
According to the way the question was arranged, the answer above is the answer.
But the options given none of them matches my answer.
Step-by-step explanation:
A function is defined as (f of x)
= -3^4√x-9.
F(x)= -3^(4√x-9) at x= 81
√x= √81
√x= 9
F(x)= -3^(4(9)-9)
F(x) = -3^(36-9)
F(x) = -3^(27)
A 1,000 ohm resistor has a tolerance of 20%. This means that the resistor actual value can be +-20%. What's the acceptable range of values for this resistor
Answer:
[800, 1200]
Step-by-step explanation:
We need to calculate the acceptable range of values for this resistor. The center point would be the nominal resistance: 1000 ohms.
20% above that would be 1.20(1000 ohms) = 1200 ohms, and 20% below would be (0.80)(1000 ohms) = 800 ohms.
Thus, the acceptable resistance range in ohms is [800, 1200]
if 5 lbs cost 9 dollars how much does 1 lbs cost
Answer: $1.80
Step-by-step explanation:
9=5x
9/5= 1.8