9514 1404 393
Answer:
9 days
Step-by-step explanation:
Divide quantity by rate to find time.
(3 cups)(1/3 cup/day) = 3/(1/3) days = 3(3/1) days = 9 days
Vector wants to create a new box he wants the new box to be 2 inches wide the length and volume is 4 and 64. How tall should he make the new box?
9514 1404 393
Answer:
8 inches
Step-by-step explanation:
The product of length, width, and height is the volume.
V = LWH
H = V/(LW) = 64/(2·4) = 8
The height of the new box should be 8 inches.
To create a box that is 2 inches wide, 4 inches long, and has a volume of 64 cubic inches, the box should be made 8 inches tall.
The question asks how tall a new box should be if it is 2 inches wide, has a length of 4 inches, and must have a volume of 64 cubic inches. To find the height of the box, we use the formula for the volume of a rectangular prism (box), which is Volume = length × width × height.
Given the volume (V) is 64 cubic inches, the width (w) is 2 inches, and the length (l) is 4 inches, we can rearrange the formula to solve for the height (h):
h = V / (l × w)
= 64 / (4 × 2)
= 64 / 8
= 8 inches
Therefore, to create a new box with the specified dimensions and volume, Vector should make the box 8 inches tall.
When rolling two fair 6 sided dice, what is the probability that the difference between the scores is more than 3?
Answer:
[tex]1/6[/tex]
Step-by-step explanation:
When we say, the difference of scores should be more than 3 it means that the difference can be 4 or 5.
Case 1: The difference of scores is 4.
The possible outcomes can be [tex](1,5), (5,1), (2,6) \text{ and }(6,2).[/tex] i.e. 4 number of cases are possible.
Case 2: The difference of scores is 5.
The possible outcomes can be [tex](1,6) \text{ and } (6,1)[/tex]. i.e. 2 number of cases.
Here, total number of favorable cases are 4 + 2 = 6.
Total number of cases, when two fair dice are rolled, are 36.
These cases are:
[tex][(1,1),(1,2),(1,3),(1,4),(1,5),(1,6),\\ (2,1),(2,2),(2,3),(2,4),(2,5),(2,6),\\..\\(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)]}[/tex]
Formula:
[tex]\text{Probability of an event = } \frac{Number\ of\ favorable\ cases}{Total\ number\ of\ cases}[/tex]
Hence, the probability that the difference of scores is more than 3, at the roll of 2 dice, is [tex]\frac{6}{36}[/tex] i.e. [tex]\frac{1}{6}[/tex].
Hence, the required probability is [tex]\frac{1}{6}[/tex].
Sunnyside Middle School wanted to add a new school sport, so they surveyed the students to determine which sport is most popular. Students were able to choose among soccer, football, lacrosse, or swimming. The same number of students chose lacrosse and swimming. The number of students who chose soccer was double the number of students who chose lacrosse. The number of students who chose football was triple the number of students who chose swimming. If 434 students completed the survey, how many students chose each sport?
Answer:
Lacrosse = 62 students
Swimming = 62 students
Soccer = 124 students
Football = 186 students
Step-by-step explanation:
Based on the information, we can draw some equations
1. Lacrosse = Swimming
2. Soccer = 2 * Lacrosse
3. Football = 3 * Swimming
4. Football + Soccer + Swimming + Lacrosse = 434
Lets solve for once sport at a time, I will start with Football.
I will put equation 1, 2 and 3 into equation 4
3Sw + 2L + L + L = 434
We can now again put equation 1 into the new equation 4
3L + 2L + L + L = 434
Simplify
7L = 434
L = 434 ÷ 7
L = 62 students
Since L = Sw, 62 students did swimming also
We can put L into equation 2 to solve for So
So = 2 * 62
So = 124 students
And now we can put Sw into equation 3 to solve for F
F = 3 * 62
F = 186 students
Please help me with this question:(((((
Answer:
see below
Step-by-step explanation:
The component form of the polar coordinate pair (r, θ) is ...
(r, θ) ⇔ (r·cos(θ), r·sin(θ))
Then your point (2, 60°) translates to ...
(2, 60°) ⇔ (2·cos(60°), 2·sin(60°)) = (2(1/2), 2(√3)/2) = (1, √3)
Find the area of the circle d=10 in 62.80 in^2 ,15.70^2, 314.00in ^2, 78.50in^2, 31.40 in2
Step-by-step explanation:
In order to find the area, we need to find the radius. In order to find the radius, we need to divide 10 by 2 because the radius is half of the diameter.
10 ÷ 2 = 5
[tex]A=r^2\pi[/tex]
[tex]A=(5)^2\pi[/tex]
[tex]A=25\pi[/tex]
[tex]A=78.5[/tex]
So, the area of the circle (given that the diameter is 10) is 78.50 in².
An angle has a reference angle measuring 35º and its terminal side lies in Quadrant IV. What are possible positive and negative measures for the angle?
Answer:
Step-by-step explanation:
Given that,
The reference angle is 35°
It lies in the fourth quadrant.
The reference angle is the positive acute angle that can represent an angle of any measure.
The reference angle must be < 90∘.
In radian measure, the reference angle must be < π/ 2.
Basically, any angle on the x-y plane has a reference angle, which is always between 0 and 90 degrees. The reference angle is always the smallest angle that you can make from the terminal side of an angle (ie where the angle ends) with the x-axis. A reference angle always uses the x-axis as its frame of reference.
Since the reference angle is less than 35°, then, the reference angle is positive,
The negative angle is 360 - 35 = 325°
So, the positive reference angle is 35° and the negative reference angle is 325°
This question is based on concept of reference angle.Therefore, the positive measures for the angle would be 35° and the negative would be 325°.
Given:
The reference angle is 35º and its terminal side lies in [tex]\bold{4^{th}}[/tex] Quadrant .
By the definition of reference angle,
An angle's reference angle is the measure of the smallest, positive, acute angle formed by the terminal side of the angle and the horizontal axis.
Thus, positive reference angles have terminal sides that lie in the first quadrant and can be used as models for angles in other quadrants.
The reference angle is acute angle.Therefore, it must be < 90°.
In radian measure, it must be less than [tex]\bold{\dfrac{\pi }{2}}[/tex].
Therefore, the reference angle is less than 35°. So, reference angle is positive.And the negative angle is 360 - 35 = 325°.
Therefore, the positive measures for the angle would be 35° and the negative would be 325°.
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Mia used 4.5 cups of orange juice in a punch that serve 6 people. Isaac used 2.75 cups of orange juice in a punch that serves 5 people. How much more orange juice is in one serving of mias punch
Answer:
0.2 Cup per serving
Step-by-step explanation:
Mia used 4.5 cups of orange juice in a punch that serve 6 people.
Mia's Serving of orange juice per serving=4.5/6=0.75 cup per serving
Isaac used 2.75 cups of orange juice in a punch that serves 5 people.
Isaac's Serving of orange juice per serving=2.75/5=0.55 cup per serving
Difference of orange juice in cup per serving=0.75-0.55=0.2 cup per serving
There was 0.2 cup more orange juice in one serving of Mia's punch.
Answer:
0.2 is the correct answer
Step-by-step explanation:
What is the area? i need help please im timed and don't know how to do this
Answer:
This is what it looks like and also so Regretfulderey can get brainliest
Answer:
Step
[tex] \frac{1}{2} \times (4 + 12) \times 5[/tex]
there
Find the dot product of the given vectors.
u=9i+4j
v=3i−j
The dot product of u = 9i+4j and v = 3i- j is 23.
Explanation:The dot product of two vectors can be calculated by multiplying their corresponding components and then summing them up. In this case, the dot product of u = 9i+4j and v = 3i- j is:
u · v = (9)(3) + (4)(-1) = 27 - 4 = 23
So, the dot product of u and v is 23.
Deborah hikes due south for 3 miles. She then turns due west and hikes 4 miles. What is the shortest distance between the starting point and the ending point? 1 mile 2 miles 5 miles 6 miles
Answer:
5 miles
Step-by-step explanation:
The two legs of Deborah's hike form the right-angle legs of a right triangle. The shortest distance is then the hypotenuse of that triangle, found using the Pythagorean theorem.
d^2 = 3^2 + 4^2 = 9 +16 = 25
d = √25 = 5
Deborah ends 5 miles from her start.
Suppose that every student at a university is assigned a unique 8-digit ID number. For i ∈ {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}, define the set Ai to be the set of currently enrolled students whose ID number begins with the digit i. For each digit, i, there is at least one student whose ID starts with i. Do the sets A0, …, A9 form a partition of the set of currently enrolled students?
Answer:
Yes, they form a partition
Step-by-step explanation:
For a group of sets to be considered a partition of set A (currently enrolled students), all of the elements in set A must be contained in the subsets that form the partition and no individual element can be present in more than one subset.
In this situation, take set A0 for instance, all students whose ID numbers begin with 0 will be in this set and in this set alone. The same can be said for Ai where i ∈ {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}. Since no other possible value can be assigned for the first digit of an student ID, it is correct to affirm that sets A0, …, A9 form a partition of the set of currently enrolled students.
Final answer:
The sets A0, A1, ..., A9, where each set consists of students whose ID starts with a specific digit, form a partition of the set of all currently enrolled students because each set is non-empty, the sets are mutually exclusive, and their union represents the entire set of students.
Explanation:
To understand if the sets A0, A1, ..., A9, form a partition of the set of currently enrolled university students based on their 8-digit ID numbers starting with digits 0 through 9, three conditions must be met: each set must be non-empty, the sets must be mutually exclusive, and their union must form the entire set of currently enrolled students.
Non-empty Sets: Given that for each digit i, there is at least one student whose ID starts with i, all sets A0 through A9 meet the criterion of being non-empty.Mutually Exclusive: Since each student is assigned a unique 8-digit ID, and an ID can only start with one digit, the sets are mutually exclusive; a student whose ID starts with a 1, for example, cannot also be in the set of IDs beginning with 2.Union Forms the Entire Set: Because all possible ID numbers will begin with a digit from 0 to 9, the union of sets A0 through A9 covers every currently enrolled student making them a partition of the set of all students.Thus, the sets A0 through A9 form a partition of the set of all currently enrolled students.
Find the slope of the line. Y=2x-9
Answer:
Slope is 2
Step-by-step explanation:
The number before x is the slope value.
[tex]\dotfill[/tex]
We want to find the slope for the following line:
[tex]\bf y=2x-9[/tex]
First, notice the form of the given equation is in slope intercept (y=mx+b) form. In this formula, m is the slope and b is the y-intercept. So to find the value of m, compare the equation to the slope int. formula.
[tex]\sf y=mx+b[/tex] ← formula
[tex]\sf y=2x-9[/tex] ← the slope is 2
>>> Therefore, the slope is 2.
Find the volume of a right circular cone that has a height of 11.1 in and a base with a circumference of 17.6 in. Round your answer to the nearest tenth of a cubic inch.
Answer:
91.2
Step-by-step explanation:
use formula v=1/3 by pie r squared then the hieght
Final answer:
To calculate the volume of a cone given its height and the circumference of its base, first find the radius using the circumference formula, then apply the volume formula for a cone. In this case, the volume is approximately 92.4 cubic inches.
Explanation:
To find the volume of a right circular cone with a height of 11.1 inches and a base circumference of 17.6 inches, we first need to calculate the radius of the base. The formula for the circumference of a circle is C = 2πr. We can solve for r (radius) by rearranging the formula: r = C / (2π). Plugging in the given circumference, we get r = 17.6 / (2π) ≈ 2.8 inches.
Next, we use the formula for the volume of a cone, which is V = (1/3)πr²h. Substituting in our values for r (2.8 inches) and h (11.1 inches), we obtain V = (1/3)π(2.8)²(11.1) ≈ 92.4 cubic inches.
Therefore, the volume of the right circular cone is approximately 92.4 cubic inches, rounding to the nearest tenth.
Linda invests $3000 in a bond trust that pays 8% interest compounded monthly. Her friend Lyla invests $3000 in a certificate of deposit that pays 7.75% compounded continuously. For Linda: a. State which formula should be used to solve this problem. _____________________ b. Write the function for Linda. _____________________ c. Determine how much Linda would have in her account after 20 years
Answer:
a) The interest is compounded monthly, so should use the compound interest formula.
b) [tex]A(t) = 3000(1.0067)^{12t}[/tex]
c) Linda would have $14898.33 in her account after 20 years.
Step-by-step explanation:
Compound Interest Formula:
[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]
Where A(t) is the amount of money after t years, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per year and t is the number of years for which the money is invested.
Continuous Interest Formula:
[tex]P(t) = P(0)e^{rt}[/tex]
In which P(0) is the initial amount invested and r is the interest rate, as a decimal.
For Linda: a. State which formula should be used to solve this problem.
The interest is compounded monthly, so should use the compound interest formula.
b. Write the function for Linda.
Invests 3000, so [tex]P = 3000[/tex]
8% interest, so [tex]r = 0.08[/tex]
Compounded monthly. An year has 12 months, so [tex]n = 12[/tex]
Then
[tex]A = P(1 + \frac{r}{n})^{nt}[/tex]
[tex]A = 3000(1 + \frac{0.08}{12})^{12t}[/tex]
[tex]A = 3000(1.0067)^{12t}[/tex]
c. Determine how much Linda would have in her account after 20 years
This is A(20)
[tex]A = 3000(1.0067)^{12*20} = 14898.33[/tex]
Linda would have $14898.33 in her account after 20 years.
For Linda the formula that would be used to solve this problem is: FV = A (1 + r)^nm
For Linda, the function is: $3000(1.0067)^12n.
The amount Linda would have in her account after 20 years is $14,780.41.
The formula for determining the future value of an amount of money is: FV = A (1 + r)^nm
Where:
FV = Future value A = Amount deposited R = interest rate = 8%/12 = 0.067 m = number of compounding = 12 N = number of years = 20Value after 20 years $3000(1.0067)^(12 x 20) = $14,780.41.
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Maya mowed 4 lawns in 12 hours. What was her rate of mowing in hours per lawn?
Answer:
1 Lawn per 3 Hours
Step-by-step explanation:
In 'Lawns : Hours' the work that she has done = 4 : 12 = 1 : 3
With this workout, we can conclude that Maya mowed 1 Lawn every 3 Hours.
Maya's rate of mowing is 3 hours per lawn, calculated by dividing the total time spent (12 hours) by the number of lawns mowed (4 lawns).
Maya mowed 4 lawns in 12 hours, so to find her rate of mowing in hours per lawn, we divide the total hours by the number of lawns mowed. The calculation is 12 hours / 4 lawns, which equals 3 hours per lawn. Therefore, Maya's mowing rate is 3 hours per lawn.
When engaging in weight-control (fitness/fat burning) types of exercise, a person is expected to attain approximately 60% of his or her maximum heart rate. For 20-year-olds, this rate is approximately 120 bpm. A simple random sample of thirty 20-year-olds was taken, and the sample mean was found to be 107 bpm, with a standard deviation of 45 bpm. Researchers wonder if this is evidence to conclude that the expected level is actually lower than 120 bpm. Report a 95% confidence region for the mean level of heart rate for this group. the mean level of heart rate is greater than 117.67 the mean level of heart rate is lower than 120.96 the mean level of heart rate is lower than 114.47 the mean level of heart rate is greater than 114.47
Answer:
Check the explanation
Step-by-step explanation:
Kindly check the attached image below to see the step by step explanation to the question above.
The following measurements were recorded for the drying time, in hours, of a certain brand of latex paint: 3.4, 2.5, 4.8, 2.9, 3.6, 2.8, 3.3, 5.6, 3.7, 2.8, 4.4, 4.0, 5.2, 3.0, 4.8. Assuming that the measurements represent a random sample from a normal population, find a 95% prediction interval for the drying time for the next trial of the paint.
Answer:
The 95% confidence interval for the mean is (3.249, 4.324).
We can predict with 95% confidence that the next trial of the paint will be within 3.249 and 4.324.
Step-by-step explanation:
We have to calculate a 95% confidence interval for the mean.
As the population standard deviation is not known, we will use the sample standard deviation as an estimation.
The sample mean is:
[tex]M=\dfrac{1}{15}\sum_{i=1}^{15}(3.4+2.5+4.8+2.9+3.6+2.8+3.3+5.6+3.7+2.8+4.4+4+5.2+3+4.8)\\\\\\ M=\dfrac{56.8}{15}=3.787[/tex]
The sample standard deviation is:
[tex]s=\sqrt{\dfrac{1}{(n-1)}\sum_{i=1}^{15}(x_i-M)^2}\\\\\\s=\sqrt{\dfrac{1}{14}\cdot [(3.4-(3.787))^2+(2.5-(3.787))^2+(4.8-(3.787))^2+...+(4.8-(3.787))^2]}\\\\\\[/tex][tex]s=\sqrt{\dfrac{1}{14}\cdot [(0.15)+(1.66)+(1.03)+...+(1.03)]}[/tex]
[tex]s=\sqrt{\dfrac{13.197}{14}}=\sqrt{0.9427}\\\\\\s=0.971[/tex]
We have to calculate a 95% confidence interval for the mean.
The population standard deviation is not known, so we have to estimate it from the sample standard deviation and use a t-students distribution to calculate the critical value.
The sample mean is M=3.787.
The sample size is N=15.
When σ is not known, s divided by the square root of N is used as an estimate of σM:
[tex]s_M=\dfrac{s}{\sqrt{N}}=\dfrac{0.971}{\sqrt{15}}=\dfrac{0.971}{3.873}=0.2507[/tex]
The t-value for a 95% confidence interval is t=2.145.
The margin of error (MOE) can be calculated as:
[tex]MOE=t\cdot s_M=2.145 \cdot 0.2507=0.538[/tex]
Then, the lower and upper bounds of the confidence interval are:
[tex]LL=M-t \cdot s_M = 3.787-0.538=3.249\\\\UL=M+t \cdot s_M = 3.787+0.538=4.324[/tex]
The 95% confidence interval for the mean is (3.249, 4.324).
To estimate a 95% prediction interval, calculate the sample mean and standard deviation, then use the t-distribution to apply the formula that includes the t-value for 95% confidence level and the sample size.
Explanation:To find a 95% prediction interval for the drying time for the next trial of latex paint, we need to use the measurements provided with the assumption that they represent a random sample from a normally distributed population.
However, before we can provide the prediction interval, we must first calculate the sample mean and the sample standard deviation from the given data. With those, we can then use the t-distribution to find the prediction interval, which will take the form of:
Sample Mean ± (t-value * Sample Standard Deviation * √(1 + 1/n))
Where 'n' is the number of observations and the t-value is determined from the t-distribution table for (n-1) degrees of freedom at the 95% confidence level.
Once calculated, this interval estimates the range within which we can expect the drying time for the next trial of paint to fall, with 95% confidence.
The solution is (3, –2). Verify the solution. Which true statement appears in your check? 4 = 4 –2 = –2 –1 = –1 –3 = –3
Answer:
b.) -2= -2
Step-by-step explanation:
i got it correct
Answer:
-2=-2
Step-by-step explanation:
Point A is located at 11 on the number line. Point B is 5 less than Point A, where on the number line is Point B
Answer:
11-5 = 6
Step-by-step explanation:
Solve the following equation X = 2 and y = 4
3x + 2y + 4 =?
Answer:
18
Step-by-step explanation:
3(2)+2(4)+4=
6+8+4=18
The solution to the equation 3x + 2y + 4 when x = 2 and y = 4 is 18.
Explanation:In the equation given, we are asked to find the value of 3x + 2y + 4 when x = 2 and y = 4.
First, let's substitute these values into the equation. We get 3×2 + 2×4 + 4, which simplifies to 6 + 8 + 4.
Adding these together gives us a total of 18. Therefore, the solution to the following equation is 18.
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What is the equation of the line that is perpendicular to the line y = 6 and passes through the point (-4, -3)?
A.) x=-4. B.) x=-3. C.) x= -1/6. D.) x=6
Maricopa's Success scholarship fund receives a gift of $ 185000. The money is invested in stocks, bonds, and CDs. CDs pay 5 % interest, bonds pay 5.5 % interest, and stocks pay 11.3 % interest. Maricopa Success invests $ 30000 more in bonds than in CDs. If the annual income from the investments is $ 13115 , how much was invested in each account?
Maricopa Success invested $ ____ in stocks.
Maricopa Success invested $ ____ in bonds.
Maricopa Success invested $ _____ in CDs.
Answer:
Maricopa Success invested $55,000 in stocks
Maricopa Success invested $80,000 in bonds
Maricopa Success invested $50,000 in CDs
Step-by-step explanation:
Let S denotes stocks, B denotes bonds and C denotes CDs.
Maricopa's Success scholarship fund receives a gift of $185,000 which she invests in stocks. bonds, and CDs.
Mathematically,
S + B + C = 185,000 eq. 1
Money is invested in stocks at interest = 11.3% = 0.113
Money is invested in bonds at interest = 5.5% = 0.055
Money is invested in CDs at interest = 5% = 0.05
Annual income from the investments is $13,115
Mathematically,
0.113S + 0.055B + 0.05C = 13,115 eq. 2
Maricopa Success invests $30,000 more in bonds than in CDs.
Mathematically,
B = C + 30,000 eq. 3
Substitute the eq. 3 into eq. 1
S + B + C = 185,000
S + (C + 30,000) + C = 185,000
S + 2C + 30,000 = 185,000
S + 2C = 185,000 - 30,000
S + 2C = 155000 eq. 4
Substitute the eq. 3 into eq. 2
0.113S + 0.055B + 0.05C = 13,115
0.113S + 0.055(C + 30,000) + 0.05C = 13,115
0.113S + 0.055C + 1650 + 0.05C = 13,115
0.113S + 0.105C + 1650 = 13,115
0.113S + 0.105C = 13,115 - 1650
0.113S + 0.105C = 11,465 eq. 5
Now we have to equations and two unknowns
S + 2C = 155,000 eq. 4
0.113S + 0.105C = 11,465 eq. 5
Multiply eq. 4 by 0.113 and subract it from eq. 5
0.113S + 0.226C = 17,515
subtract it from eq. 5
0.113S + 0.105C = 11,465 eq. 5
0.113S + 0.226C = 17,515
-0.121C = -6050
0.121C = 6050
C = 6050/0.121
C = 50,000
Substitute the value of C into eq. 3
B = C + 30,000
B = 50,000 + 30,000
B = 80,000
Substitute the value of B and C into eq. 1
S + B + C = 185,000
S + 80,000 + 50,000 = 185,000
S = 185,000 - 80,000 - 50,000
S = 55,000
Therefore,
Maricopa Success invested $55,000 in stocks
Maricopa Success invested $80,000 in bonds
Maricopa Success invested $50,000 in CDs
Verification:
S + B + C = 185,000 eq. 1
55,000 + 80,000 + 50,000 = 185,000
185,000 = 185,000 (satisfied)
0.113S + 0.055B + 0.05C = 13,115 eq. 2
0.113(55,000) + 0.055(80,000) + 0.05(50,000) = 13,115
6215 + 4400 + 2500 = 13,115
13,115 = 13,115 (satisfied)
B = C + 30,000 eq. 3
80,000 = 50,000 + 30,000
80,000 = 80,000 (satisfied)
Order the steps to solve the equation
log(x2 – 15) = log(2x) form 1 to 5.
x2 - 2x - 15 = 0
Potential solutions are -3 and 5
x2 - 15 = 2x
X-5 = 0 or x + 3 = 0
(x - 5)(x + 3) = 0
Answer:
x2 - 15 = 2x
x2 - 2x -15 = 0
(x - 5)(x + 3) = 0
X-5 = 0 or x + 3 = 0
Potential solutions are -3 and 5
Answer:
2
5
1
4
3
p-by-step explanation:
did the assignment
what is the y -value of the point where they intersect
Help please little I try my best
Mr. Good Wrench advertises that a customer will have to wait no more than 30 minutes for an oil change. A sample of 26 oil changes had a standard deviation of 4.8 minutes. Use this information to calculate a 90% confidence interval for the population standard deviation waiting time for an oil change.
Answer:
The 90% confidence interval for the population standard deviation waiting time for an oil change is (3.9, 6.3).
Step-by-step explanation:
The (1 - α)% confidence interval for the population standard deviation is:
[tex]CI=\sqrt{\frac{(n-1)s^{2}}{\chi^{2}_{\alpha/2, (n-1)}}}\leq \sigma\leq \sqrt{\frac{(n-1)s^{2}}{\chi^{2}_{1-\alpha/2, (n-1)}}}[/tex]
The information provided is:
n = 26
s = 4.8 minutes
Confidence level = 90%
Compute the critical values of Chi-square as follows:
[tex]\chi^{2}_{\alpha/2, (n-1)}=\chi^{2}_{0.10/2, (26-1)}=\chi^{2}_{0.05, 25}=37.652[/tex]
[tex]\chi^{2}_{1-\alpha/2, (n-1)}=\chi^{2}_{1-0.10/2, (26-1)}=\chi^{2}_{0.95, 25}=14.611[/tex]
*Use a Chi-square table.
Compute the 90% confidence interval for the population standard deviation waiting time for an oil change as follows:
[tex]CI=\sqrt{\frac{(n-1)s^{2}}{\chi^{2}_{\alpha/2, (n-1)}}}\leq \sigma\leq \sqrt{\frac{(n-1)s^{2}}{\chi^{2}_{1-\alpha/2, (n-1)}}}[/tex]
[tex]=\sqrt{\frac{(26-1)\times 4.8^{2}}{37.652}}\leq \sigma\leq \sqrt{\frac{(26-1)\times 4.8^{2}}{14.611}}\\\\=3.9113\leq \sigma\leq 6.2787\\\\\approx 3.9 \leq \sigma\leq6.3[/tex]
Thus, the 90% confidence interval for the population standard deviation waiting time for an oil change is (3.9, 6.3).
explain a advantage and disadvantage for paying with a debit card
I need help please it is just one question and can you explain how u did it thx please look at the picture thx
Answer:
112
Step-by-step explanation:
A supplementary angle is 1 or more angles that add up to 180 degrees. So, the 2 angles we have are 2x and 3x + 10, and those add up to 180.
In order to make an equation for this, we need to add 2x and 3x + 10 and equal it to 180.
5x + 10 = 180
Now that we have our equation, the goal is to isolate the variable. The most immediate step I see is to subtract 10 from both sides so 5x will be alone on one side of the equation.
5x = 170
Now, to ultimately isolate the variable, we must divide both sides by 5 so that x will be alone.
170 / 5 is 34
5x / 5 is x
x = 34
Now, we plug in our value of x into 3x + 10 to find out what the measurement is equal to.
3(34) + 10 = y
102 + 10 = y
112 = y
3x + 10 is equal to 112.
Use Random number generator and simulate 1000 long columns, for each of the three cases. Example: for the Car type 1, use Number of variables=1, Number of random numbers=1000, Distribution=Normal, Mean=520 and Standard deviation=110, and leave random Seed empty. Next: use either sorting to construct the appropriate histogram or rule of thumb to answer the questions: 13. What is approximate probability that Car Type 3 has annual cost less than $550?
Answer:
Step-by-step explanation:
The question is incomplete since they do not give information about the Car type 3.
We will do it in a generic way, we will say that the Car type 3 has a mean of M and a standard deviation SD.
We would be:
P (CT3 <550) = P [z <(550 - X) / SD]
Now if we give it values, for example that X = 600 and SD = 120
It would remain:
P (CT3 <550) = P [z <(550 - 600) / 120]
P (CT3 <550) = P [z <-0.42]
We look for this value in the normal distribution table (attached) and it shows us that the probability is approximately 0.3372, that is, 33.72%
What you need to do is replace the X and SD values of theCar type 3 in the equation above how I just did and you will get the result.
Can someone help me, im really stuck.
Answer:
(x/4) +1 OR (4/x)+1
Step-by-step explanation: