Answer:
[tex]I_2=9[/tex]
Step-by-step explanation:
We have been told that the ratios are inversely proportional in our given problem. We are asked to find the missing value.
We know that two inversely proportional quantities are in form [tex]y=\frac{k}{x}[/tex], where, y is inversely proportional to x and k is the constant of proportionality.
Let us find constant of proportionality using [tex]R_1 = 6[/tex] and [tex]I_1 = 12[/tex] in above equation.
[tex]6=\frac{k}{12}[/tex]
[tex]6*12=\frac{k}{12}*12[/tex]
[tex]72=k[/tex]
Now, we will use [tex]72=k[/tex] and [tex]R_2 = 8[/tex] in our equation to find [tex]I_2[/tex] as:
[tex]8=\frac{72}{I_2}[/tex]
[tex]I_2=\frac{72}{8}[/tex]
[tex]I_2=9[/tex]
Therefore, the value of [tex]I_2[/tex] is 9.
The question is about the mathematical concept of inverse proportionality. The missing value of [tex]I_2[/tex] is found by applying the property of inversely proportional quantities, yielding the result [tex]I_2 = 9[/tex].
In an inverse proportionality relationship, the product of the values in one set is equal to the product of the corresponding values in the other set. This can be represented as:
[tex]\[R_1 \cdot I_1 = R_2 \cdot I_2\][/tex]
Given that [tex]\(R_1 = 6\)[/tex], [tex]\(R_2 = 8\)[/tex], and [tex]\(I_1 = 12\)[/tex], you can solve for [tex]\(I_2\)[/tex]:
[tex]\[6 \cdot 12 = 8 \cdot I_2\][/tex]
Now, simplify the equation:
[tex]\[72 = 8 \cdot I_2\][/tex]
To isolate [tex]\(I_2\)[/tex], divide both sides by 8:
[tex]\[I_2 = \frac{72}{8}\][/tex]
[tex]\[I_2 = 9\][/tex]
So, the value of [tex]\(I_2\)[/tex] is 9. In this inverse proportionality relationship, when [tex]R_1[/tex] is 6, [tex]\(R_2\)[/tex] is 8, and [tex]\(I_1\)[/tex] is 12, [tex]\(I_2\)[/tex] is 9. This means that as one variable increases, the other variable decreases in such a way that their product remains constant.
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Please answer with how you did it
Answer:
B) 0.11
Step-by-step explanation:
Use the conditional probability formula.
P(transfer | never graduated) = P(transfer & never graduated) / P(never graduated)
__
Denominator
But the P(never graduated) is made of two parts:
P(never graduated) = P(transfer & never graduated) + P(freshman & never graduated)
= (1 -0.80)×(1 -0.85) + (0.80)×(1 -0.70)
= (0.20)(0.15) + (0.80)(0.30)
= 0.0300 +0.2400 = 0.2700
__
Numerator
The numerator of our fraction is one of the components we just calculated:
P(transfer & never graduated) = (1 -0.80)×(1 -0.85) = 0.0300
__
Conditional Probability
So ...
P(transfer | never graduated) = 0.0300/0.2700 = 1/9 ≈ 0.11
Julia is going to the store to buy candies. Small candies cost $4 and extra-large candies cost $12.She needs to purchase at least 20 candies, but she cannot spend any more than$180.
Answer:
Small candies [tex]=9[/tex]
Extra large candies [tex]=12[/tex]
Step-by-step explanation:
Let small candies [tex]=x[/tex]
Extra large candies [tex]=y[/tex]
the number of candies is at least [tex]20[/tex].
[tex]x+y\geq20[/tex]
Cost of [tex]1[/tex] small candy [tex]=\$4[/tex]
Cost of [tex]1[/tex] extra large candy [tex]=\$12[/tex]
but she has only [tex]\$180[/tex] to spend
[tex]4x+12y\leq180[/tex]
Solve for
[tex]x+y=20.......(1)\\4x+12y=180.....(2)\\eqn(2)-eqn(1)\times4\\8y=100\\y=\frac{100}{8} \\y=\frac{25}{8} \\from\ eqn(1)\\x+\frac{25}{2}=20\\ x=20-\frac{25}{2} \\x=\frac{15}{2}[/tex]
Since number of candies should be integer.
let [tex]x=7,y=13[/tex]
total spend [tex]4\times7+12\times13=184 [/tex] which is more than [tex]\$180[/tex], so this combination is not possible.
[tex]let\ x=8,y=12\\8\times4+12\times12=176<180[/tex]
She has [tex]\$4[/tex] more so she can buy [tex]1[/tex] more small candy.
Hence small candy [tex]=9[/tex]
extra large candy [tex]=12[/tex]
Evaluate.
43 – 4:25
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This is an improper. Perhaps you can fix it, so that I can assist you with it? I apologise.
30 Points!!
Juan solves the system of equations by forming a matrix equation.
−4x+y=9
3x+2y=7
He multiplies the left side of the coefficient matrix by the inverse matrix.
How does he proceed to the solution?
Answer:
multiply the left side of the constant vector by the inverse matrix
Step-by-step explanation:
The matrix equation ...
AX = B
is solved by left-multiplying by the inverse of A:
A⁻¹AX = A⁻¹B
IX = A⁻¹B . . . . . the result of multiplying A⁻¹A is the identity matrix
X = A⁻¹B . . . . . B needs to be multiplied by the inverse matrix
[tex]\left[\begin{array}{c}x&y\end{array}\right] = \left[\begin{array}{cc}-4&1\\3&2\end{array}\right]^{-1}\left[\begin{array}{c}9&7\end{array}\right]=\dfrac{1}{11}\left[\begin{array}{cc}-2&1\\3&4\end{array}\right]\left[\begin{array}{c}9&7\end{array}\right]=\left[\begin{array}{c}-1&5\end{array}\right][/tex]
Answer:
I used the above answer and got it wrong. Hope this helps! (Sorry it looks a little weird... just look at whta is in the boxes)
Step-by-step explanation:
PLZZ HELPP!!! WILL GIVE BRAINLIEST!!!
Let f(x) = 8x^3 + 18x^2 − 10 and g(x) = 4x + 1. Find f(x)/g(x).
A. 2x^2 + 4x - 1 + 9/4x + 1
B. 2x^2 + 4x - 1 - 9/4x + 1
C. 2x^2 + 4x + 1 + 9/4x + 1
D. 2x^2 + 4x + 1 - 9/4x + 1
Answer:B. 2x^2 + 4x - 1 - 9/4x + 1
Step-by-step explanation:
f(x) = 8x^3 + 18x^2 − 10
g(x) = 4x + 1
We want to determine f(x)/g(x). We would apply the long division method. The steps are shown in the attached photo.
The correct answer is
2x^2 + 4x - 1 - 9/4x + 1
Answer:
[tex]\text{B. }2x^{2} - 4x - 1 - \dfrac{9}{4x + 1}[/tex]
Step-by-step explanation:
One way is to use long division.
2x² + 4x - 1
4x + 1) 8x³ + 18x² - 10
8x³ + 2x²
16x²
16x² + 4x
-4x - 10
-4x - 1
- 9
[tex]\dfrac{8x^{3} + 18x^{2} - 10} {4x+1} = 2x^{2} - 4x - 1 - \dfrac{9}{4x + 1}[/tex]
An introductory psychology class has 9 freshman males, 15 freshman females, 8 sophomore males, and 12 sophomore females. A random sample of n = 2 students is selected from the class. If the first student in the sample is a male, what is the probability that the second student will also be a male?
a. 16/43
b. 16/44
c. 17/43
d. 17/44
Answer:
The probability is [tex]\frac{16}{43}[/tex]
Step-by-step explanation:
The psychology class has 9 freshman male, 15 freshman females, 8 sophomore male and 12 sophomore female.
Total population constitution of the class=
17 males and 27 females and 44 students in total.
If on selecting on the first attempt, a male has been picked up then the number of males for the picking up in the second attempt has to decrease by one.
Also, the total number of students from which it has to be selected also decreases by 1, because one child has already been selected.
Therefore for Second Attempt, Total 43 students and 16 males.
Probability=[tex]\frac{No.OfFavorableOutcomes}{TotalNo.OfOutcomes}[/tex]
Probability=[tex]\frac{16}{43}[/tex]
Final answer:
The probability that the second student will also be a male, given that the first student is a male, is 16/43.
Explanation:
To find the probability that the second student will also be a male, given that the first student is a male, we need to determine the number of males left in the sample space after choosing the first male student. In the class, there are 9 freshman males and 8 sophomore males, making a total of 17 males. However, since we are choosing 2 students, the total sample space decreases by 1 after choosing the first male student.
Therefore, the probability of choosing a male as the second student, given that the first student is a male, is:
P(second student is male | first student is male) = (number of males left in sample space after choosing first male) / (total sample space after choosing first male)
P(second student is male | first student is male) = 16/43
WILL GIVE BRAINLIEST
1. Given the function P(x)= (x+3)^2 +2 Write the new function after a translation of 3 units UP. Q(x)= ___
Answer:
Q(x) = [tex](x+3)^{2}+5[/tex] is the final equation.
Step-by-step explanation:
By translation of the graph 3 units upward direction, it means that the y-value of the function is increased by 3 unit at each value of x.
Given , P(x) = [tex](x+3)^{2}+2[/tex]
We can actually translate the graph in any direction, and for that we have to make the necessary changes. If we translate the graph in the positive x direction, then we have to substitute (x - 3) instead of x in the equation.
Since we are translating the graph upwards ,
Q(x) = [tex](x+3)^{2}+2[/tex] + 3
Q(x) = [tex](x+3)^{2}+5[/tex]
This is the final equation of the graph after translation.
What time is it?
A. 11:10
B. 9:11
C. 11:09
D. 10:55
E. 9:55
Answer:
10:55
Step-by-step explanation:
Hour hand is at the 10, minute hand at the 11 (which means 11 * 5 = 55)
Two identical rubber balls are dropped from different heights. Ball 1 is dropped from a height of 115 feet, and ball 2 is dropped from a height of 269 feet. Use the function f(t)= -16t^2 + h to determine the current height, f(t), of a ball dropped from a height h, over the given time t.
Write a?function for the height of ball 2
h_2(t)= ____
Answer:
[tex]h_2(t)=-16t^2+269[/tex]
Step-by-step explanation:
Put the initial height of ball 2 into the given formula. The problem statement tells you "h" stands for the initial height, and that height is 269 feet.
[tex]h_2(t)=-16t^2+269[/tex]
Your mother takes you to your grandparents house for dinner. She drives 60 minutes at a constant speed of 40 miles per hour. She reaches the highway, quickly speeds up, and drives another 30 minutes at constant speed for 70 miles per hour. How far did you and your mother travel altogether? How long did the trip take?
Answer:
Step-by-step explanation:
We will separate our trips as "slow" and "fast". Filling in a motion table:
d = r x t
slow
fast
We know that the slow rate is 40 mph and the time is, in hours (because the time has to match the rate. We can't say "40 mph" and then state the time in minutes), 1 hour.
We know that the fast rate is 70 mph and the time in hours is .5 hours.
If distance = rate times time, then the distance traveled at the slow speed is 40 * 1 = 40 miles
The distance traveled at the fast speed is 70 * .5 = 35 miles.
The trip was 40 + 35 = 75 miles total, and the time it took was 1 + .5 = 1.5 hours.
True or False: The following pair of ratios are equivalent ratios.8/9 and 72/81
A farmer uses a lever to move a large rock. The force required to move the rock varies inversely with the distance from the pivot to the point the force is applied. A force of 50 pounds applied to the lever 36 inches from the pivot point of the lever will move the rock. Which function models the relationship between f, the amount of force applied to the lever and d the distance of the applied force from the pivot point?
Final answer:
The relationship between the force applied to the lever and the distance from the pivot point can be modeled using an inverse variation function. The function that models this relationship is f = 1800/d.
Explanation:
The relationship between the force applied to the lever and the distance from the pivot point can be modeled using an inverse variation function. In this case, the force required to move the rock varies inversely with the distance. Let's denote the force as f and the distance as d. The inverse variation function is given by f = k/d, where k is a constant.
To find the value of k, we can use the given information. When a force of 50 pounds is applied 36 inches from the pivot point, the rock is moved. Plugging these values into the inverse variation equation, we have 50 = k/36. Solving for k, we get k = 50 x 36 = 1800.
Therefore, the function that models the relationship between the force applied to the lever (f) and the distance of the applied force from the pivot point (d) is f = 1800/d.
The function that models the relationship between the force (f) applied and the distance (d) from the pivot point is:
[tex]f(d) = \frac{1800}{d}[/tex]
To model the relationship between the force (f) applied to the lever and the distance (d) from the pivot point, we need to understand that the force varies inversely with the distance. This means that as the distance increases, the force required decreases, and vice versa.
The mathematical model for such a relationship is given by the equation:
[tex]f = \frac{k}{d}[/tex]
Here, k is a constant that we need to determine using the given information. We know that a force of 50 pounds is applied to the lever 36 inches from the pivot point. Plug these values into the equation to find the value of k:
[tex]50 = \frac{k}{36}[/tex]
To solve for k, multiply both sides by 36:
[tex]k = 50 \times 36[/tex]
[tex]k = 1800[/tex]
Now, we substitute the value of k back into the equation to get the final model:
[tex]f = \frac{1800}{d}[/tex]
.
What is the twentieth term of the arithmetic sequence 21, 18, 15, 12, ... ?
78
-39
-36
1
Answer:
-36.
Step-by-step explanation:
First term a1 = 21.
Common difference d = 18 - 21 = -3 (15-18 = -3)
nth term an = a1 + (n - 1)d
So 20th term = 21 + (20-1) -3
= 21 - 3 * 19
= 21 - 57
= -36.
The 20th term of the arithmetic sequence will be -36.
The nth teem of an arithmetic sequence is calculated by using the formula: a + (n - 1) d.
The 20th term will be:
= a + (n - 1) d.
= a + (20 - 1)d
= a + 19d
where,
a = first term = 21
d = common difference = 2nd term - 1st term = 18 - 21 = -3
Therefore, 20th term will be:
= a + 19d
= 21 + 19(-3)
= 21 - 57
= -36
Therefore, the 20th term is -36
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Graph the system of linear equations. negative StartFraction one-half EndFraction y equals StartFraction one-half EndFraction x plus 5 and y equals 2 x plus 2.y = x + 5 and y = 2x + 2. The solution to the system is (, ).
Answer:
It is (-4,-6)
Step-by-step explanation:
I just did it on E2020 ur welcome
To graph a system of linear equations, start at the y-intercept and use the slope to plot the next points. The solution to the system of equations is the point where the lines intersect, and can be found by setting the equations equal to each other and solving.
Explanation:The problem involves graphing a system of linear equations, which are y = x + 5 and y = 2x + 2.
Each equation is in the form of y = mx + b, where m is the slope and b is the y-intercept. For the first equation, the slope is 1 and the y-intercept is 5. For the second equation, the slope is 2 and the y-intercept is 2.
To graph these, you typically start at the y-intercept (where the line crosses the y-axis) and use the slope to determine the next points on the graph - you rise/run according to the slope.
The solution to the system of equations is the point where the two lines intersect. To find this point, you need to solve the system of equations either graphically or algebraically. This would involve setting the equations equal to each other and solving for x, and then substituting that value of x into either of the original equations to solve for y.
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PLEASE HELP WILL MARK AS BRAINLIEST 50 POINTS
After sales tax your brand new car is $17,300. What is the total price of the car with DMV fees of 1.25% of the purchase price of the car?
A. $261.25
B. $17,516.25
C. $216.25
D. $17,561.25
Answer:B
Step-by-step explanation:
17, 300+ 1.25% You can take the decimal and move it to the other side then start doing the math
Answer:
C; 21625
Step-by-step explanation:
Logan borrowed some money from his friend in order to help buy a new video game system and agreed to pay the friend back a constant amount each week. Logan originally borrowed $40 from his friend and after 7 weeks, he still owed his friend $26. Write an equation for the function L(t),L(t),representing the amount Logan owes his friend after tt weeks.
Answer:L(t) = 40 - 2t
Step-by-step explanation:
Total amount of money that Logan borrowed from his friend to buy the video game system is $40
Let x represent the constant amount that he agreed to pay the friend back each week.
After 7 weeks, he still owed his friend $26. This means that the amount that he paid in 7 weeks is 7×x = $7x
He still owed his friend $26.
This means that amount paid in 7 weeks would be 40 - 26 = $14
Therefore
7x = 14
x = 14/7 = 2
He pays $2 each week.
Let t represent the number of weeks, the equation for the function L(t),representing the amount Logan owes his friend after t weeks would be
L(t) = 40 - 2t
A reciepe uses 1 1/4 cups of milk to make 10 servings. If the same amount of milk is used for each serving, how many servings can you use for 1 gallon of milk?
Answer:
128 servings
Step-by-step explanation:
16 cups in a gallon
16/1.25 = 12.8
12.8 * 10 = 128
128 servings
Write an equation of the line containing the given point and perpendicular to the given line:
(7,- 4); 9x+7y=4
Answer:
Step-by-step explanation:
The equation of a straight line can be represented in the slope intercept form as
y = mx + c
Where
m = slope = (change in the value of y in the y axis) / (change in the value of x in the x axis)
The equation of the given line is
9x+7y=4
7y = - 9x + 4
y = -9x/7 + 4/7
Comparing with the slope intercept form, slope = - 9/7
If the line passing through the given point is perpendicular to the given line, it means its slope is the negative reciprocal of the slope of the given line.
Therefore, the slope of the line passing through (7,-4) is 7/9
To determine the intercept, we would substitute m = 7/9, x = 7 and y = -4 into y = mx + c. It becomes
- 4 = 7/9×7 + c = 49/9 + c
c = - 4 - 49/9 = -85/9
The equation becomes
y = 7x/9 - 85/9
Answer:
Step-by-step explanation:
any eq. of line perpendicular to 9x+7y=4 is
7x-9y=a
it passes through (7,-4)
7(7)-9(-4)=a
49+36=a
a=85
reqd. eq. is 7x-9y=85
Let f be the function given by the sum of the first three nonzero terms of this series. The maximum value of |lnx-f(x)| for .3<=x<=1.7 is:__________
Answer:
Step-by-step explanation:
f(x) = sin(4x)f' = 4 cos(4x)f'' = -16 sin(4x)f''' = -64 cos(4x)f⁽⁴⁾ = 256 sin(4x)f⁽⁵⁾ = 1024 cos(4x)The 4-th order Taylor series expansion isf(x+h) = f(x) + hf'(x) + (h²/2!)f''(x) + (h³/3!)f'''(x) + (h⁴/4!)f⁽⁴⁾(x) + ...The Maclaurin series is obtained by setting x = 0.Note that sin(0) = 0 and cos(0) = 1.The non zero terms aref(h) = 4h - (4h)³/3! + (4h)⁵/5! - (4h)⁷/7! + ...Answer: f(x) =4x- 4/3+4x/5+4x7
HOPE THIS HELPED ;3 please mark Brainliest
A fair coin is tossed 10 times. What is the probability that two heads do not occur consecutively?
Answer:
0.140625
Step-by-step explanation:
Total numbers of possible combinations for a coin = 2^n
If the coin is tossed 10 times, we have 2^10 = 1024
If the coin is tossed once, we have 2^1 = 2 outcomes.
The possible outcomes are H, T.
We have 2 outcomes with no two consecutive head.
If the coin is tossed twice, we have 2^2 = 4 outcomes.
The possible outcomes are HH, HT, TH, TT
We have 1 outcome with two consecutive heads and 3 outcomes without two consecutive heads.
If the coin is tossed thrice, we have 2^3 = 8 outcomes.
The possible outcomes are HHH, HHT, HTH, HTT, TTH, THT, THH and TTT
We have 3 outcomes with two consecutive head and 5 outcomes without two consecutive heads.
Comparing the results from the outcomes of the coin,we have 2,3,5,......
This looks like a financial sequence. For the next 10 tosses, we have
2,3,5,8,13,21,34,55,89,144
We have 144 outcomes without two consecutive heads if the coin is tossed 10 times
Pr(number of two consecutive Heads in 10 tosses) = 144/1024
= 0.140625
The probability that two heads do not occur consecutively in 10 coin tosses is 45/512 or approximately 0.0879.
Explanation:In order to calculate the probability that two heads do not occur consecutively in 10 coin tosses, we can use the concept of permutations with restrictions. Let's consider the possibilities:
When choosing a head, there are 10 possibilities for the first head (H) and 9 possibilities for the second head.
This gives us a total of 10 * 9 = 90 possibilities.
When choosing tails (T), there are 2 possibilities for each toss, giving us a total of 2^10 = 1024 possibilities.
Therefore, the probability that two heads do not occur consecutively is 90/1024, which simplifies to 45/512 or approximately 0.0879.
The manager of a supermarket wants to obtain information about the proportion of customers who dislike a new policy on cashing checks. How many customers should he sample if he wants the sample fraction to be within .15 of the true fraction, with probability .98
Answer:
n = 61 costumers
Step-by-step explanation:
For calculating the number of costumers he should sample we use the next equation:
[tex]n = \frac{z_{1-\alpha/2}^{2}p(1-p)}{E^{2} }[/tex]
Where E is the error that we are prepared to accept, in this case E = 0.15
How we don't know the value of p, we can estimate it like p = 0.5
∝ = 1-0.98 = 0.02
1-∝/2 = 0.99
[tex]z_{0.99} = 2.33[/tex]
[tex]n = \frac{(2.33^{2})(0.5)(1-0.5)}{0.15^{2} }[/tex]
n = 60.32 costumers
n ≈ 61 costumers
Final answer:
To determine the sample size needed for the proportion of customers who dislike the new policy on cashing checks, we can use the formula: n = (Z^2 * p' * (1-p')) / E^2. The manager wants a sample fraction within 0.15 of the true fraction with a probability of 0.98.
Explanation:
To determine the sample size needed for the proportion of customers who dislike the new policy on cashing checks, we can use the formula:
n = (Z^2 * p' * (1-p')) / E^2
Where:
n is the sample size
Z is the z-score corresponding to the desired confidence level
p' is the estimated proportion
E is the maximum error or margin of error
In this case, the manager wants a sample fraction within 0.15 of the true fraction with a probability of 0.98. Assuming p' is 0.5, we can calculate the required sample size.
Determine whether the following statement regarding the hypothesistest for two population proportions is true or false.
However small the difference between two population proportion ,for sufficiently large sample size, the null hypothesis of equalpopulation proportions is likely to be rejected.
The statement is true; as sample size increases, even small differences between two population proportions can lead to the rejection of the null hypothesis. The decreasing standard error with larger samples increases the test statistic, leading to smaller p-values. However, practical significance should also be considered alongside statistical significance.
Explanation:The statement regarding the hypothesis test for two population proportions is true. As the sample size increases, even a very small difference between the two population proportions becomes significant. This is because with larger sample sizes, the standard error of the difference between the two proportions decreases, which increases the test statistic used in hypothesis testing. As a result, we are more likely to reject the null hypothesis of equal population proportions if the sample size is sufficiently large, assuming there is indeed a small actual difference.
The null hypothesis typically states that there is no effect or no difference, and in the case of two population proportions, it states that the proportions are equal. When we conduct a hypothesis test, we calculate the probability of observing our sample data, or something more extreme, given that the null hypothesis is true. This probability is known as the p-value. A small p-value indicates that the observed data is unlikely under the null hypothesis, leading to its rejection.
However, it's important to note that the ability to detect small differences with large samples does not imply that those differences are practically significant, only statistically so. Therefore, in addition to hypothesis testing, it's essential to consider effect size and practical significance when interpreting results.
Suppose that in the maintenance of a large medical-records file for insurance purposes the probability of an error in processing is 0.0010, the probability of an in filing is 0.0009, the probability of an error in retrieving is 0.0012, the probability of an error in processing as well as filing is 0.0002, the probability of an error in processing as well as retrieving is 0.0003, and the probability of an error in processing and filing as well as retrieving is 0.0001. What is the probability of making at least one of these errors? (P(R intersection F)=0.0002) Be sure to draw a Venn diagram.
Answer:
The probability of making at least one of these errors is 0.0025
Step-by-step explanation:
Consider the provided information.
Let P represents the error in processing.
Let F represents the error in filling.
Let R represents the error in retrieving.
The probability of an error in processing is 0.0010: P(P) = 0.0010
The probability of an in filing is 0.0009: P(F) = 0.0009
The probability of an error in retrieving is 0.0012: P(R) = 0.0012,
The probability of an error in processing as well as filing is 0.0002:
P(P∩F) = 0.0002
The probability of an error in processing as well as retrieving is 0.0003,
P(P∩R) = 0.0003
The probability of an error in processing and filing as well as retrieving is 0.0001.
P(P∩F∩R)=0.0001
P(R∩F)=0.0002
The probability of at least one is:
P(P∪F∪R)=P(P)+P(R)+P(F)-P(P∩F)-P(P∩R)-P(R∩F)+P(P∩F∩R)
P(P∪F∪R)=0.0010+0.0009+0.0012-0.0002-0.0002-0.0003+0.0001
P(P∪F∪R)=0.0025
Hence, the probability of making at least one of these errors is 0.0025
The required diagram is shown below.
A circle is shown. Secants E G and D G intersect at point G outside of the circle. Secant E G intersects the circle at point F and secant D G intersects the circle at point H. The length of E F is x, the length of F G is 6, the length of D H is x + 3, and the length of H G is 5. What is the length of line segment DG? 4 units 7 units 12 units 23 units
Answer:
Step-by-step explanation:
The formula we need here is
[tex]6(6+x)=5(5+x+3)[/tex]
which simplifies to
[tex]6(6+x)=5(8+x)[/tex]
which simplifies to
36 + 6x = 40 + 5x and
x = 4
So DG = 5 + 4 + 3 which is 12
Answer:
The correct answer is C. 12
Step-by-step explanation:
I just took the test
After sales tax your brand new car is $17,300. What is the total price of the car with DMV fees of 1.25% of the purchase price of the car?
A. $261.25
B. $17,516.25
C. $216.25
D. $17,561.25
The right answer is Option B.
Step-by-step explanation:
Given,
Purchase price of car = $17,300
DMV fees = 1.25% of purchase price
DMV fees = [tex]\frac{1.25}{100}*17300=\frac{21625}{100}[/tex]
DMV fees = $216.25
Total price of car = Purchase price + DMV fees
Total price of car = 17300 + 216.25 = $17516.25
The total price of car is $17,516.25
The right answer is Option B.
Keywords: percentage, division
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A student wanted to estimate the number of chocolate chips in a commercial brand of cookie. He sampled 100 cookies and found an average of 10.5 chips per cookie. If we assume the standard deviation is 8, what is a 99% confidence interval for the average number of chips per cookie?A. (8.4,12.6)B. (8.9,12.1)C. (5.3,10.7)
Answer:
The 99% confidence interval is given by (8.4;12.6)
A. (8.4,12.6)
Step-by-step explanation:
1) Notation and definitions
n=100 represent the sample size
[tex]\bar X= 10.5[/tex] represent the sample mean
[tex]\sigma=8[/tex] represent the population standard deviation assumed
m represent the margin of error
Confidence =99% or 0.99
A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".
The margin of error is the range of values below and above the sample statistic in a confidence interval.
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
2) Calculate the critical value zc
On this case we can to use the z distribution. Since our interval is at 99% of confidence, our significance level would be given by [tex]\alpha=1-0.99=0.01[/tex] and [tex]\alpha/2 =0.005[/tex]. The degrees of freedom are given by:
We can find the critical values in excel using the following formulas:
"=NORM.INV(0.005,0,1)" for [tex]z_{\alpha/2}=-2.58[/tex]
"=NORM.INV(1-0.005,0,1)" for [tex]z_{1-\alpha/2}=2.58[/tex]
The critical value [tex]zc=\pm 2.74[/tex]
3) Calculate the margin of error (m)
The margin of error for the sample mean is given by this formula:
[tex]m=z_c \frac{\sigma}{\sqrt{n}}[/tex]
[tex]m=2.58 \frac{8}{\sqrt{100}}=2.064[/tex]
4) Calculate the confidence interval
The interval for the mean is given by this formula:
[tex]\bar X \pm z_{c} \frac{\sigma}{\sqrt{n}}[/tex]
And calculating the limits we got:
[tex]10.5 - 2.58 \frac{8}{\sqrt{100}}=8.4[/tex]
[tex]10.5 + 2.58 \frac{8}{\sqrt{100}}=12.6[/tex]
The 99% confidence interval is given by (8.4;12.6)
A. (8.4,12.6)
Kevin and Mark took a random sample of 100 pieces of trail mix to determine the number of peanuts, raisins, and almonds in a container. If each container of trail mix is known to have 40% peanuts, 40% almonds, and 20% raisins, which sample is a better representation of the actual population?
Answer:
Marks answer is more representative
Step-by-step explanation:
The number of peanuts is 40, the number of almonds is 40 and the number of raisins is 20.
What is the percentage?The percentage is defined as representing any number with respect to 100. It is denoted by the sign %. The percentage stands for "out of 100." Imagine any measurement or object being divided into 100 equal bits.
Given that Kevin and Mark took a random sample of 100 pieces of trail mix to determine the number of peanuts, raisins, and almonds in a container. If each container of trail mix is known to have 40% peanuts, 40% almonds, and 20% raisins.
The number will be calculated as,
40% peanut = 100 x 40 / 100 = 40
40% almonds = 100 x 40 / 100 = 40
20 % raisins = 100 x 20 /100 = 20
Therefore, the number of peanuts is 40, the number of almonds is 40 and the number of raisins is 20.
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A line passes through the points
(P,a) and (P,-a) where p and a are real numbers and p=/0.
Describe each of the following and explain your reasoning please.
1. slope of the line
2. equation of the line
3. Y-intercept
4. slope of a line perpendicular to the given line
Answer:
Step-by-step explanation:
Slope, m =change in value of y on the vertical axis / change in value of x on the horizontal axis
change in the value of y = y2 - y1
Change in value of x = x2 -x1
y2 = final value of y
y 1 = initial value of y
x2 = final value of x
x1 = initial value of x
From the information given,
y2 = - a
y1 = a
x2 = 0
x1 = 0
Slope = (- a - a)/0-0 = -2a/0 = 0
2) equation of the line is represented in the slope intercept form as y = mx + c
Where
m = slope
c = intercept.
To determine c, we would substitute y = a, x = p and m = 0 into y= mx + c. It becomes
a = 0×p + c
c = a
The equation becomes
y = a
3) y intercept,c = a
4) the slope of a line perpendicular to the given line is a negative reciprocal of the slope of the given line. Therefore,
Slope = - 0 = 0
Assuming that the roots of the given qudratic equation are a,b find the sum and product of the roots.
Answer: Sum of root a+b = -c/d
Product of root ab= e/d
Step-by-step explanation:
Let the general quadratic equation be dx² + cx + e = 0
And the root of the equation be
'a' and 'b'
Using the general formula to find the solution to the quadratic equation
a = -c+√c²- 4de/2d
b = -c-√c²- 4de/2d
Taking the sum of the roots
a+b = (-c+√c²- 4de/2d) + (-c-√c²- 4de/2d)
a+b = (-c-c+√c²- 4de/2d - √c²- 4de/2d)/2d
a+b = -2c/2d
a+b = -c/d
The sum of the root of the quadratic equation will be -c/d
Product of roots
ab = (-c+√c²- 4de/2d)(-c-√c²- 4de/2d)
= {c² +(c√c²- 4de)- (c√c²- 4de) -(c²-4de)}/4d²
= {c²-c²+4de}/4d²
= 4de/4d²
= e/d
The product of the above quadratic equation will be e/d
Reggie ate 31 raisins. Which correctly describes 31 as a prime or a composite number and tells the number of factor pairs 31 has? You're choices are: A-31 is a prime number because it has 0 factor pairs. B-31 is a prime because it has 1 factor pair. C-31 is a composite number because it has 1 factor pair. D-31 is a composite number because it has 2 factor pairs.
The number 31 is a prime number and has exactly one factor pair which is 1 and the number itself, so the correct answer is option B.
Explanation:The value 31 is considered a prime number.
A prime number is a number that only two distinct positive divisors: 1 and itself. Therefore, every prime number has exactly one factor pair, which is 1 and the number itself.
So, option B-31 is a prime because it has 1 factor pair is the correct answer. This means that the factors of 31 are simply 1 and 31.
so the correct answer is option B.
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Final answer:
The number 31 is a prime number because it is only divisible by 1 and itself, hence it has one factor pair, which is (1, 31). The correct answer to the question is B - 31 is a prime because it has 1 factor pair.
Explanation:
The question is asking whether the number 31 is a prime number or a composite number and to identify the number of factor pairs it has. A prime number is a number that has only two factors, 1 and the number itself. In contrast, a composite number is a number that has more than two factors.
For the number 31, we can confirm that it is not divisible by any integers other than 1 and 31 without a remainder. Therefore, 31 is a prime number, and it has only one factor pair, which is (1, 31). There are no other pairs of numbers that multiply together to give the product of 31. Thus, the correct choice is B - 31 is a prime because it has 1 factor pair.