Answer:
555
Step-by-step explanation:
Answer:
the edges only would be 16 pieces.
Step-by-step explanation:
Think of it as a square. The top row is 5 pieces, bottom row is 5 pieces.
The left vertical side is 3 and the right vertical side is 3. Because the corner pieces are already there, you don't count them twice.
Write a polynomial equation of degree 4 that has the following roots : -1 repeated three times and 4.
Answer:
p(x) = x^4 - x^3 - 9x^2 - 11x - 4
Step-by-step explanation:
You are saying there are 3 roots of x = -1 and one x = 4 root
so...
p(x) = [(x + 1)^3 ] * (x - 4)
p(x) = (xxx + 3xx + 3x + 1 )*(x- 4)
p(x) = x^4 + 3 x^3 + 3x^2 + x - 4x^3 - 12xx - 12x - 4
p(x) = x^4 - x^3 - 9x^2 - 11x - 4
Answer: yes
Step-by-step explanation:
do u by chance still have access to those units on odyssey would love to get the answers lol.
My locker combination has three digits. None of the digits are 0. What is the probability that the first digit of my locker combination is less than 3? A. 1/3 B. 1/2 C. 2/9 D. 3/10
The probability that the first digit of a three-digit locker combination is less than 3 is 2/9, because there are 2 favorable digits (1 and 2) out of 9 possible non-zero digits, option C.
The question is asking about the probability that the first digit of a three-digit locker combination is less than 3, given that none of the digits can be 0. Since the digits can range from 1 to 9 (inclusive), there are a total of 9 possible digits for the first position. We are interested in the digits 1 and 2, which are the only digits less than 3. Therefore, there are 2 favorable outcomes.
To calculate the probability, we use the formula:
Probability = Number of favorable outcomes / Total number of possible outcomes
In this case, the probability is 2 (favorable outcomes) divided by 9 (possible outcomes), which simplifies to:
Probability = 2/9, option C.
free round trip tickets Hawaii were given to 0.4% of the people staying at a hotel. Larry says that tickets were given to 4/10 of the people at the hotel.
Answer: He is badly mistaken! It's 4/1000
Larry needs to learn how to read percentages!
Step-by-step explanation:
4/10 would be 40% For every 100 guests, 40 free tickets would be given away. A very popular offer, but the hotel will soon be out money, and out of business!
0.4% is less than 1% . As a decimal it is 0.004. That is Four thousandths!
Only 4 out of every 1000 people were given free round trip tickets to Hawaii.
A candidate for one of Ohio's two U.S. Senate seats wishes to compare her support among registered voters in the northern half of the state with her support among registered voters in the southern half of the state. A random sample of 2000 registered voters in the northern half of the state is selected, of which 1062 support the candidate. Additionally, a random sample of 2000 registered voters in the southern half of the state is selected, of which 900 support the candidate.
A 95% confidence interval for the difference in proportion of registered voters that support this candidate between the northern and southern halves of the state is
A. 0.050 to 0.112.
B. 0.035 to 0.127.
C. 0.040 to 0.122.
D. 0.037 to 0.119.
Answer:
[tex](0.531-0.45) - 1.96 \sqrt{\frac{0.531(1-0.531)}{2000} +\frac{0.45(1-0.45)}{2000}}=0.050[/tex]
[tex](0.531-0.45) + 1.96 \sqrt{\frac{0.531(1-0.531)}{2000} +\frac{0.45(1-0.45)}{2000}}=0.112[/tex]
And the best option for this case would be:
A. 0.050 to 0.112.
Step-by-step explanation:
Data given
[tex]p_A[/tex] represent the real population proportion of who support the cnadite for the northern half state
[tex]\hat p_A =\frac{1062}{2000}=0.531[/tex] represent the estimated proportion of who support the candidate for the northern half state
[tex]n_A=2000[/tex] is the sample size required the northern half state
[tex]p_B[/tex] represent the real population proportion of who support the candidate for the southern half state
[tex]\hat p_B =\frac{900}{2000}=0.45[/tex] represent the estimated proportion of people who support the candidate for the southern half state
[tex]n_B=2000[/tex] is the sample size for the northern half state
[tex]z[/tex] represent the critical value
The confidence interval for the difference of two proportions would be given by this formula
[tex](\hat p_A -\hat p_B) \pm z_{\alpha/2} \sqrt{\frac{\hat p_A(1-\hat p_A)}{n_A} +\frac{\hat p_B (1-\hat p_B)}{n_B}}[/tex]
For the 95% confidence interval the value of [tex]\alpha=1-0.95=0.05[/tex] and [tex]\alpha/2=0.025[/tex], with that value we can find the quantile in the normal standard distribution and we got.
[tex]z_{\alpha/2}=1.96[/tex]
Replacing into the formula we got:
[tex](0.531-0.45) - 1.96 \sqrt{\frac{0.531(1-0.531)}{2000} +\frac{0.45(1-0.45)}{2000}}=0.050[/tex]
[tex](0.531-0.45) + 1.96 \sqrt{\frac{0.531(1-0.531)}{2000} +\frac{0.45(1-0.45)}{2000}}=0.112[/tex]
And the best option for this case would be:
A. 0.050 to 0.112.
Nadia is making a rectangular moisac out of 1/2 -inch by 1/2 -inch tiles. The rectangle is 12 inches long and 3 1/2 inches wide. How many tiles will nadia use to cover the rectangle completely
Answer:
168
Step-by-step explanation:
GIVEN: Nadia is making a rectangular moisac out of [tex]\frac{1}{2}[/tex] inch by [tex]\frac{1}{2}[/tex] inch tiles. The rectangle is [tex]12[/tex] inches long and [tex]3\frac{1}{2}[/tex] inches wide.
TO FIND: How many tiles will Nadia use to cover the rectangle completely.
SOLUTION:
Area of rectangular moisac[tex]=\text{length}\times\text{width}[/tex]
[tex]=12\times3\frac{1}{2}=\frac{12\times7}{2}[/tex]
[tex]=42 \text{ inch}^2[/tex]
Area of one tile [tex]=\text{side}^2[/tex]
[tex]=\frac{1}{2}\times\frac{1}{2}=\frac{1}{4}\text{ inch}^2[/tex]
According to question
Total tiles required [tex]=\frac{\text{Area of rectangular moisac}}{\text{Area of one tile}}[/tex]
[tex]=\frac{42}{\frac{1}{4}}=42\times4[/tex]
[tex]=168[/tex] tiles
Hence, 168 tiles are required to completely cover the rectangular moisac.
A regular heptagon has a side of 13.9 and an apothem of 14.4. Find the area of the heptagon. Round your answer to the nearest WHOLE NUMBER.
Answer:
Step-by-step explanation:
Given that,
A regular heptagon, a heptagon has 7 sides and since it is a regular heptagon, then, it has equal sides
n = 7, number of sides
Each sides of the heptagon has a length of 13.9
s= 13.9
The apothem is 14.4
Apothem is a line from the centre of a regular polygon at right angles to any of its sides.
r = 14.4
The area of a regular heptagon can be calculated using
Area = ½ n•s•r
Where n is the number of sides
s- is the length of the sides
r Is the apothem
Then,
A = ½ × 7 × 13.9 × 14.4
A = 700.56 square units
To the nearest whole number, I.e no decimal points
A = 701 Square units
How many minutes does it take 7people to paint 4 walls ?
Bruh. More information is needed to answer that question. We need to know the rate of change.
Chapin Manufacturing Company operates 24 hours a day, five days a week. The workers rotate shifts each week. Management is interested in whether there is a difference in the number of units produced when the employees work on various shifts. A sample of five workers is selected and their output recorded on each shift.
Units Produced
Employee Day Afternoon Night
Skaff 38 24 34
Lum 35 23 37
Clark 28 26 38
Treece 35 26 23
Morgan 22 23 24
1. At the 0.01 significance level, can we conclude there is a difference in the mean production rate by shift or by employee?
Answer:
The answer is there is a difference in the mean production rate by shift
Step-by-step explanation:
The level of significance is actually very low since the same production level is maintained for each of the 5 workers at the same time in the afternoon.
As for the other shifts, that is, the day shift and the night shift, the level of significance varies according to the production established by each worker.h
A 5-card hand is dealt from a perfectly shuffled deck. Define the events: A: the hand is a four of a kind (all four cards of one rank plus a 5th card). B: at least one of the cards in the hand is an ace Are the events A and B independent? Prove your answer by showing that one of the conditions for independence is either true or false.
In a hand of 5 cards, you want 4 of them to be of the same rank, and the fifth can be any of the remaining 48 cards. So if the rank of the 4-of-a-kind is fixed, there are [tex]\binom44\binom{48}1=48[/tex] possible hands. To account for any choice of rank, we choose 1 of the 13 possible ranks and multiply this count by [tex]\binom{13}1=13[/tex]. So there are 624 possible hands containing a 4-of-a-kind. Hence A occurs with probability
[tex]\dfrac{\binom{13}1\binom44\binom{48}1}{\binom{52}5}=\dfrac{624}{2,598,960}\approx0.00024[/tex]
There are 4 aces in the deck. If exactly 1 occurs in the hand, the remaining 4 cards can be any of the remaining 48 non-ace cards, contributing [tex]\binom41\binom{48}4=778,320[/tex] possible hands. Exactly 2 aces are drawn in [tex]\binom42\binom{48}3=103,776[/tex] hands. And so on. This gives a total of
[tex]\displaystyle\sum_{a=1}^4\binom4a\binom{48}{5-a}=886,656[/tex]
possible hands containing at least 1 ace, and hence B occurs with probability
[tex]\dfrac{\sum\limits_{a=1}^4\binom4a\binom{48}{5-a}}{\binom{52}5}=\dfrac{18,472}{54,145}\approx0.3412[/tex]
The product of these probability is approximately 0.000082.
A and B are independent if the probability of both events occurring simultaneously is the same as the above probability, i.e. [tex]P(A\cap B)=P(A)P(B)[/tex]. This happens if
the hand has 4 aces and 1 non-ace, orthe hand has a non-ace 4-of-a-kind and 1 aceThe above "sub-events" are mutually exclusive and share no overlap. There are 48 possible non-aces to choose from, so the first sub-event consists of 48 possible hands. There are 12 non-ace 4-of-a-kinds and 4 choices of ace for the fifth card, so the second sub-event has a total of 12*4 = 48 possible hands. So [tex]A\cap B[/tex] consists of 96 possible hands, which occurs with probability
[tex]\dfrac{96}{\binom{52}5}\approx0.0000369[/tex]
and so the events A and B are NOT independent.
The events A and B in the given scenario are not independent. This determination is based on the principle of sampling without replacement, where drawing a four of a kind is likely to influence the probability of drawing an ace.
Explanation:Two events A: the hand is a four of a kind, and B: at least one of the cards in the hand is an ace, are defined in a situation where a 5-card hand is dealt from a perfectly shuffled 52-card deck. To determine if these events are independent, we need to check if the occurrence of event A affects the occurrence of event B.
In sampling with replacement, each member of a population is replaced after it is picked. However, dealing a 5-card hand from a deck of cards is an example of sampling without replacement, meaning that each card may only be chosen once, causing the events to be considered as not independent.
It is highly probable that drawing a four of a kind will influence the likelihood of drawing an ace. Hence, the events A and B are not independent.
Learn more about Independent Events here:https://brainly.com/question/30905572
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Consider the following least squares specification between test scores and the student - teacher ratio: TestScore = 557.8 + 36.42 In (Income). According to this equation, a 1% increase income is associated with an increase in test scores of :A. 36.42 points B. cannot be determined from the information given here C. 0.36 points D. 557.8 points
Answer:
[tex] Test score_i= 557.8 +36.42 Income[/tex]
If we increase the income by 1% that means that the new income would be 1.01 the before one and if we replace this we got:
[tex] Test score_f = 557.8 + (36.42* 1.01 Income)= 557.8 +36.7842 Income[/tex]
And the net increase can be founded like this:
[tex] Test score_f -Tet score_i = 557.8 +36.7842 Income- [557.8 +36.42 Income] = 36.7842 Income -36.42 Income = 0.3642[/tex]
So then the net increase would be:
C. 0.36 points
Step-by-step explanation:
For this case we have the following linear relationship obtained from least squares between test scores and the student-teacher ratio:
[tex] Test score_i= 557.8 +36.42 Income[/tex]
If we increase the income by 1% that means that the new income would be 1.01 the before one and if we replace this we got:
[tex] Test score_f = 557.8 + (36.42* 1.01 Income)= 557.8 +36.7842 Income[/tex]
And the net increase can be founded like this:
[tex] Test score_f -Tet score_i = 557.8 +36.7842 Income- [557.8 +36.42 Income] = 36.7842 Income -36.42 Income = 0.3642[/tex]
So then the net increase would be:
C. 0.36 points
For a 1% increase in income, the test scores would increase by approximately 0.36 points based on the given regression equation. This is calculated by multiplying the coefficient of the natural logarithm of income, 36.42, with the decimal value of the percent change in income, which is 0.01.
Explanation:The equation provided is a linear regression equation where the dependent variable, TestScore, is predicted based on the natural logarithm of the independent variable, Income. The coefficient of 36.42 in front of the natural logarithm indicates how much the dependent variable changes for a 1% change in the independent variable. To find the contribution to the test scores for a 1% increase in income, we need to use the fact that the derivative of the natural logarithm, Ln(x), with respect to x is 1/x, which means a change in income translates directly to the change in test score when multiplied by the coefficient.
So, for a small percentage change in income, approximately 1%, the corresponding change in TestScore is 36.42 multiplied by the percentage change in decimal form. Specifically, 0.01 × 36.42 = 0.3642 or approximately 0.36 points.
He takes a random sample of 49 recent charterholders and computes a mean salary of $172,000 with a standard deviation of $35,000. Use this sample information to determine the 90% confidence interval for the average salary of a CFA charterholder.
Answer:
the 90% of confidence intervals for the average salary of a CFA charter holder
(1,63,775 , 1,80,000)
Step-by-step explanation:
Explanation:-
random sample of n = 49 recent charter holders
mean of sample (x⁻) = $172,000
standard deviation of sample( S) = $35,000
Level of significance α= 1.645
90% confidence interval
[tex](x^{-} - Z_{\alpha } \frac{s}{\sqrt{n} } , x^{-} + Z_{\alpha } \frac{s}{\sqrt{n} })[/tex]
[tex](172000 - 1.645 \frac{35000}{\sqrt{49} } , 172000 +1.645 \frac{35000}{\sqrt{49} })[/tex]
on calculation , we get
(1,63,775 , 1,80,000)
The mean value lies between the 90% of confidence intervals
(1,63,775 , 1,80,000)
whats the slope of the graph -4, 5 1,-7.5
Answer:
Slope (m)= -12.5/5= -2.5
-12.5/5 in fraction form
or
-2.5 in decimal form
Step-by-step explanation:
slope (m)= -12.5/5= -2.5
the points belong as a decreasing linear function
equation: y= -2.5x-5
Just the distributive property to write an expression that is equivalent to 10 + 15x
Answer:
5 ( 2 + 3x )
Step-by-step explanation:
1st step: Take the GCF of the equation 10+15x
2nd step: GCF means, taking the Greatest Common Factor out of BOTH the numbers in an equation. (GCF is 5 in this case.)
3rd step: Divide by the GCF that you got. (In this case, you have 10 +15x. You need to do 10/5, and 15x /5. (Note that ANYTHING multiplied by "x" can also be divided just like a regular number.)
4th step: Put the the number that you divided with for both numbers OUTSIDE parentheses. (Note in this case it is common.)
5th step: Check your work. PLEASE DO THIS STEP.
Check: 5( 2 + 3x )
5 x 2 = 10
5 x '3x' = 15x
So, the answer for this problem is: 5 ( 2 +3x )
Answer: 5( 2 + 3x)
Hope this helped you understand the basics of disributive property. And if you have another problem just like this, you can use the same rule as shown above. :)
Final answer:
Use the distributive property to factor out a common factor in 10 + 15x to get an equivalent expression.
Explanation:
To write an expression equivalent to 10 + 15x using the distributive property, you can factor out a common factor. Here’s how:
Factor out 5 from 10 and 15x: 10 + 15x = 5(2 + 3x)
Apply the distributive property to get the equivalent expression: 5(2 + 3x) = 5*2 + 5*3x = 10 + 15x
find slope of P(0,0), Q(10,8)
Answer:
4/5
Step-by-step explanation:
We can find the slope when given two points by using
m= (y2-y1)/(x2-x1)
= (8-0)/(10-0)
=8/10
= 4/5
Answer:
4/5
Step-by-step explanation:
Crash testing is a highly expensive procedure to evaluate the ability of an automobile to withstand a serious accident. A simple random sample of 12 small cars were subjected to a head-on collision at 40 miles per hour. Of them 8 were "totaled," meaning that the cost of repairs is greater than the value of the car. Another sample of 15 large cars were subjected to the same test, and 5 of them were totaled. Find a 95% confidence interval for the difference in the prop
Answer:
95% confidence interval for the difference in the proportion is [-0.017 , 0.697].
Step-by-step explanation:
We are given that a simple random sample of 12 small cars were subjected to a head-on collision at 40 miles per hour. Of them 8 were "totaled," meaning that the cost of repairs is greater than the value of the car.
Another sample of 15 large cars were subjected to the same test, and 5 of them were totaled.
Firstly, the pivotal quantity for 95% confidence interval for the difference between population proportion is given by;
P.Q. = [tex]\frac{(\hat p_1-\hat p_2)-(p_1-p_2)}{\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+\frac{\hat p_2(1-\hat p_2)}{n_2} } }[/tex] ~ N(0,1)
where, [tex]\hat p_1[/tex] = sample proportion of small cars that were totaled = [tex]\frac{8}{12}[/tex] = 0.67
[tex]\hat p_2[/tex] = sample proportion of large cars that were totaled = [tex]\frac{5}{15}[/tex] = 0.33
[tex]n_1[/tex] = sample of small cars = 12
[tex]n_2[/tex] = sample of large cars = 15
[tex]p_1[/tex] = population proportion of small cars that are totaled
[tex]p_2[/tex] = population proportion of large cars that were totaled
Here for constructing 95% confidence interval we have used Two-sample z proportion statistics.
So, 95% confidence interval for the difference between population population, ([tex]p_1-p_2[/tex]) is ;
P(-1.96 < N(0,1) < 1.96) = 0.95 {As the critical value of z at 2.5% level
of significance are -1.96 & 1.96}
P(-1.96 < [tex]\frac{(\hat p_1-\hat p_2)-(p_1-p_2)}{\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+\frac{\hat p_2(1-\hat p_2)}{n_2} } }[/tex] < 1.96) = 0.95
P( [tex]-1.96 \times {\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+\frac{\hat p_2(1-\hat p_2)}{n_2} } }[/tex] < [tex]{(\hat p_1-\hat p_2)-(p_1-p_2)}[/tex] < [tex]1.96 \times {\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+\frac{\hat p_2(1-\hat p_2)}{n_2} } }[/tex] ) = 0.95
P( [tex](\hat p_1-\hat p_2)-1.96 \times {\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+\frac{\hat p_2(1-\hat p_2)}{n_2} } }[/tex] < [tex]p_1-p_2[/tex] < [tex](\hat p_1-\hat p_2)+1.96 \times {\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+\frac{\hat p_2(1-\hat p_2)}{n_2} } }[/tex] ) = 0.95
95% confidence interval for [tex]p_1-p_2[/tex] = [[tex](\hat p_1-\hat p_2)-1.96 \times {\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+\frac{\hat p_2(1-\hat p_2)}{n_2} } }[/tex] , [tex](\hat p_1-\hat p_2)+1.96 \times {\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+\frac{\hat p_2(1-\hat p_2)}{n_2} } }[/tex]]
= [[tex](0.67-0.33)-1.96 \times {\sqrt{\frac{0.67(1-0.67)}{12}+\frac{0.33(1-0.33)}{15} } }[/tex] , [tex](0.67-0.33)+1.96 \times {\sqrt{\frac{0.67(1-0.67)}{12}+\frac{0.33(1-0.33)}{15} } }[/tex]]
= [-0.017 , 0.697]
Therefore, 95% confidence interval for the difference between proportions l and 2 is [-0.017 , 0.697].
The data shows the weights of 2 groups of house cats in pounds.
Group 1
Group 2
6
8
8
10
8
10
9
11
10
12
14
15
15
15
18 20
15 21
Which statistic has a greater value for Group 1 than Group 2?
A
Mean
B. Range
C. Mode
D. Median
Reset
Final answer:
Upon calculating the mean, range, mode, and median for both groups of house cats, we found that none of the statistics have greater values for Group 1 than for Group 2.
Explanation:
To determine which statistic has a greater value for Group 1 than Group 2 in a dataset containing the weights of house cats, we first need to calculate the mean, range, mode, and median for both groups.
Calculations for Group 1:
Mean: (6+8+8+9+10+14+15+15+18+15) / 10 = 118 / 10 = 11.8 poundsRange: 18 - 6 = 12 poundsMode: 8 and 15 (Most frequent)Median: (10 + 14) / 2 = 24 / 2 = 12 pounds (since there's an even number of data points, we take the average of the two middle values)Calculations for Group 2:
Mean: (8+10+10+11+12+15+15+20+21) / 9 = 122 / 9 = 13.56 poundsRange: 21 - 8 = 13 poundsMode: 10 and 15 (Most frequent)Median: 12 pounds (since there's an odd number of data points, the median is the middle value)When comparing the statistics, we can see that the range of Group 1 is smaller than that of Group 2, and the mean and median for Group 1 are also smaller than those for Group 2. The mode for both groups is the same with two values that repeat the most. Therefore, none of the statistics have greater values for Group 1 than for Group 2.
More on the Leaning Tower of Pisa. Refer to the previous exercise. (a) In 1918 the lean was 2.9071 meters. (The coded value is 71.) Using the least-squares equation for the years 1975 to 1987, calculate a predicted value for the lean in 1918. (Note that you must use the coded value 18 for year.)
Answer:
2.9106
Step-by-step explanation:
According to the information of the problem
Year 75 76 77 78 79 80 81 82 83 84 85 86 87
Lean 642 644 656 667 673 688 696 698 713 717 725 742 757
If you use a linear regressor calculator you find that approximately
[tex]y = 9.318 x - 61.123[/tex]
so you just find [tex]x = 18[/tex] and then the predicted value would be 106mm
therefore the predicted value for the lean in 1918 was 2.9106
Which of the following is an example of a subjective probability? A. Although College A has never played College B in basketball, a sports analyst believes there is a 0.8 probability that A will beat B in their upcoming game. B. Based on many years of data, an automobile insurance company estimates the probability that a randomly chosen 20-year old driver will have an accident during his 20th year as 0.001. C. After examining a deck of cards to determine that there are 52 cards of the correct suits and values, a card player says the probability of drawing the 7 of hearts is 1/52. D. After examining a coin to determine that it is an unaltered coin produced by the U.S. Mint, a gambler says the probability of a coin flip coming up heads is 1/2.
Answer:
The answer is option A.
Step-by-step explanation:
Subjective probability is defined as a probability which is derived from a person's own experience or belief without relying on any data or scientific calculation.
In the question, the situation given in option A is an example of subjective probability because the analyst is giving a probability based on his or her own belief without using any data at all.
The other options clearly state the probability is being calculated by relying on observations and data.
I hope this answer helps.
A subjective probability example is the belief of a sports analyst in the probability of one college team beating another, without prior data. This contrasts with objective probabilities based on statistical analysis or historical evidence.
Explanation:The example of a subjective probability among the options given is when a sports analyst believes there is a 0.8 probability that College A will beat College B in their upcoming basketball game, despite there being no previous encounters between the two teams to base this on. This type of probability, which includes personal belief or judgment rather than empirical evidence and statistical analysis, contrasts with objective probabilities that rely on historical data, such as the probability of a 20-year old driver having an accident or the probability of drawing a specific card from a standard deck.
Subjective probability is used in situations where there is a lack of historical data or when assessing future events, making it a personal estimation. This approach is different from calculating probabilities based on observed outcomes and statistical independence, where the probability of events is determined through analysis and empirical evidence.
Richie Rich started his day with 12 bucks. Richie Rich ended his day with a dozen bucks. A. How many bucks did Richie Rich share today? B. Explain your answer.
Answers and Step-by-step explanations:
A. He shared $0.
B. Richie Rich started out with $12. He ended his day with a dozen bucks. However, notice that a dozen is the same as 12, so he still has $12. In other words, he didn't share any money today, so he shared $0.
Hope this helps!
Answer:
A. 0
B. No difference in starting and ending amounts
Step-by-step explanation:
12 = 1 dozen
12 bucks is equal to 1 dozen bucks, which means he didn't spend/share any
Miguel buys textbook with a listed price of $81. Miguel uses
a discount that provides 10% off. What is the total final
price Miguel pays?
Answer:
$72
Step-by-step explanation:
Answer:
72.9 (mark me brainleist pls )
Step-by-step explanation:
81 x 0.10 = 8.1
81 - 8.1 = 72.9
. If $200 is invested at the end of each month into an account that has an APR of 3.4% compounded monthly, what will the balance be after 15 years?
Answer:
$332.82
Step-by-step explanation:
We will use the compound interest formula provided to solve this:
[tex]A=P(1+\frac{r}{n} )^{nt}[/tex]
P = initial balance
r = interest rate (decimal)
n = number of times compounded annually
t = time
First, we change 3.4% into a decimal:
3.4% -> [tex]\frac{3.4}{100}[/tex] -> 0.034
Since the interest is compounded monthly, we will use 12 for n. Lets plug in the values now:
[tex]A=200(1+\frac{0.034}{12})^{12(15)}[/tex]
[tex]A=332.82[/tex]
Your balance after 15 years will be $332.82
The manager of a grocery store has taken a random sample of 100 customers. The average length of time it took the customers in the sample to check out was 3.1 minutes. The population standard deviation is known to be 0.5 minute. We want to test to determine whether or not the mean waiting time of all customers is significantly more than 3 minutes.
Answer:
The mean waiting time of all customers is significantly more than 3 minutes, at 0.05 significant level
Step-by-step explanation:
Step 1: State the hypothesis and identify the claim.
[tex]H_0:\mu=3\\H_1:\mu\:>\:3(claim)[/tex]
Step 2: We calculate the critical value. Since we were not given any significant level, we assume [tex]\alpha=0.05[/tex], and since this is a right tailed test, the critical value is z=1.65
Step 3: Calculate the test statistic.
[tex]Z=\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }=\frac{3.1-3}{\frac{0.5}{\sqrt{100} } }=2[/tex]
Step 4:Decide. Since the test statistic , 2 s greater than the critical value, 1.65, and it is in the critical region, the decision is to reject the null hypothesis.
Step 5: Conclusion, there is enough evidence to support the claim that the mean is greater than 3
Find the exact circumference of a circle with the given radius.
7 feet
C=
75 ft.
145 ft.
275 ft.
Answer:
the answer is 44
you don't have the answer choice
Find the area of the region under the graph of the function f on the interval [4, 8].
f(x) = 10/x^2
If you could show the steps and the answer, I would really appreciate it!
Answer:
[tex]\displaystyle \int\limits^8_4 {\frac{10}{x^2}} \, dx = \frac{5}{4}[/tex]
General Formulas and Concepts:
Calculus
Integration
IntegralsIntegration Rule [Reverse Power Rule]: [tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]
Integration Rule [Fundamental Theorem of Calculus 1]: [tex]\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)[/tex]
Integration Property [Multiplied Constant]: [tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]
Area of a Region Formula: [tex]\displaystyle A = \int\limits^b_a {[f(x) - g(x)]} \, dx[/tex]
Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle f(x) = \frac{10}{x^2} \\\left[ 4 ,\ 8 \right][/tex]
Step 2: Find Area
Substitute in variables [Area of a Region Formula]: [tex]\displaystyle \int\limits^8_4 {\frac{10}{x^2}} \, dx[/tex][Integral] Rewrite [Integration Property - Multiplied Constant]: [tex]\displaystyle \int\limits^8_4 {\frac{10}{x^2}} \, dx = 10 \int\limits^8_4 {\frac{1}{x^2}} \, dx[/tex][Integral] Integrate [Integration Rule - Reverse Power Rule]: [tex]\displaystyle \int\limits^8_4 {\frac{10}{x^2}} \, dx = 10 \bigg( \frac{-1}{x} \bigg) \bigg| \limits^8_4[/tex]Evaluate [Integration Rule - Fundamental Theorem of Calculus 1]: [tex]\displaystyle \int\limits^8_4 {\frac{10}{x^2}} \, dx = 10 \bigg( \frac{1}{8} \bigg)[/tex]Simplify: [tex]\displaystyle \int\limits^8_4 {\frac{10}{x^2}} \, dx = \frac{5}{4}[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Integration
The head of maintenance at XYZ Rent-A-Car believes that the mean number of miles between services is 2643 miles, with a standard deviation of 368 miles. If he is correct, what is the probability that the mean of a sample of 44 cars would differ from the population mean by less than 51 miles
Final answer:
To find the probability that the mean of a sample of 44 cars would differ from the population mean by less than 51 miles, use the Central Limit Theorem to approximate the distribution of sample means. Calculate the standard error using the formula: standard error = population standard deviation / sqrt(sample size). Then, standardize the sample mean using the z-score formula. Finally, find the probability using a standard normal distribution table or a calculator.Therefore, the probability that the mean of a sample of 44 cars would differ from the population mean by less than 51 miles is approximately 0.3595, or 35.95%.
Explanation:
To find the probability that the mean of a sample of 44 cars would differ from the population mean by less than 51 miles, we can use the Central Limit Theorem. According to the Central Limit Theorem, the distribution of sample means approximates a normal distribution, regardless of the shape of the population distribution, as long as the sample size is large enough (typically n ≥ 30).
First, we need to calculate the standard error, which is the standard deviation of the sampling distribution of the sample mean. The standard error is given by the formula: standard error = population standard deviation / sqrt(sample size). In this case, the population standard deviation is 368 miles, and the sample size is 44. Therefore, the standard error = 368 / sqrt(44) = 55.354 miles.
Next, we use the z-score formula to standardize the sample mean. The z-score = (sample mean - population mean) / standard error. Plugging in the given values, we get: z-score = (51 - 2643) / 55.354 = -0.3668.
Finally, we need to find the probability that the standardized sample mean (z-score) is less than -0.3668. We can use a standard normal distribution table or a calculator to find the corresponding probability. From the standard normal distribution table, we find that the probability corresponding to a z-score of -0.3668 is approximately 0.3595. Therefore, the probability that the mean of a sample of 44 cars would differ from the population mean by less than 51 miles is approximately 0.3595, or 35.95%.
UCF believes that the average time someone spends in the gym is 56 minutes. The university statistician takes a random sample of 32 gym goers and finds the average time of the sample was 50 minutes. Assume it is known the standard deviation of time all people spend in the gym is 8 minutes. What conclusion can the university statistician make?
Answer:
We conclude that the average time someone spends in the gym is different from 56 minutes.
Step-by-step explanation:
We are given that UCF believes that the average time someone spends in the gym is 56 minutes.
The university statistician takes a random sample of 32 gym goers and finds the average time of the sample was 50 minutes. Assume it is known the standard deviation of time all people spend in the gym is 8 minutes.
Let [tex]\mu[/tex] = population average time someone spends in the gym
SO, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] = 56 minutes {means that the average time someone spends in the gym is 56 minutes}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu\neq[/tex] 56 minutes {means that the average time someone spends in the gym is different from 56 minutes}
The test statistics that will be used here is One-sample z test statistics as we know about the population standard deviation;
T.S. = [tex]\frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] ~ N(0,1)
where, [tex]\bar X[/tex] = sample average time someone takes in the gym = 50 min
[tex]\sigma[/tex] = population standard deviation = 8 minutes
n = sample of gym goers = 32
So, test statistics = [tex]\frac{50-56}{\frac{8}{\sqrt{32} } }[/tex]
= -4.243
Since in the question we are not given the level of significance so we assume it to b 5%. Now at 5% significance level, the z table gives critical value between -1.96 and 1.96 for two-tailed test. Since our test statistics does not lie within the range of critical values of z so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region.
Therefore, we conclude that the average time someone spends in the gym is different from 56 minutes.
Suppose that the population of the scores of all high school seniors that took the SAT-M (SAT math) test this year follows a Normal distribution, with mean μ and standard deviation σ = 100. You read a report that says, "On the basis of a simple random sample of 100 high school seniors that took the SAT-M test this year, a confidence interval for μ is 512.00 ± 25.76." The confidence level for this interval is
Answer:
The confidence level for this interval is 99%.
Step-by-step explanation:
The margin of error M has the following equation.
[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
z is related to the confidence level.
In this problem:
[tex]M = 25.76, \sigma = 100, n = 100[/tex]
So
[tex]25.76 = z*\frac{100}{\sqrt{100}}[/tex]
[tex]10z = 25.76[/tex]
[tex]z = 2.576[/tex]
Looking at the z table, [tex]z = 2.576[/tex] has a pvalue of 0.995.
So the confidence level is:
[tex]1 - 2(1 - 0.995) = 1 - 0.01 = 0.99[/tex]
The confidence level for this interval is 99%.
PLEASE HURRY!! The pictures Please!!!
Which inequality is represented by this graph?
A. 0>x
B. x>0
C.0>_x
D. 0>_0
X > 0
sdjkfgsdjfjkdfnejnwsfjdnsk it made me write more
Since the blue line points to numbers more positive then 0, it would be a greater then. Since the dot is open it would be greater then and not equal to.
Therefore the answer is B, x > 0
Which expression is equivalent to 8-(6r+2)?
Answer:
6(1-r)
Step-by-step explanation:
8-6r+2
=6-6r
=6(1-r)
PLLLLZZZ HELP ME. Given the function f(x)=3x^2-2x-5 : What are the zeros for this function? 5 extra credit points for an exact answer. 30 points if you get the exact answer and its 100% Correct.
Answer:
The zeros for this function are x = -1 and x = 1.67
Step-by-step explanation:
Solving a quadratic equation:
Given a second order polynomial expressed by the following equation:
[tex]ax^{2} + bx + c, a\neq0[/tex].
This polynomial has roots [tex]x_{1}, x_{2}[/tex] such that [tex]ax^{2} + bx + c = (x - x_{1})*(x - x_{2})[/tex], given by the following formulas:
[tex]x_{1} = \frac{-b + \sqrt{\bigtriangleup}}{2*a}[/tex]
[tex]x_{2} = \frac{-b - \sqrt{\bigtriangleup}}{2*a}[/tex]
[tex]\bigtriangleup = b^{2} - 4ac[/tex]
In this question:
[tex]f(x) = 3x^{2} - 2x - 5[/tex]
The zeros of the function are the values of x for which
[tex]f(x) = 0[/tex]
Then
[tex]3x^{2} - 2x - 5 = 0[/tex]
This means that [tex]a = 3, b = -2, c = -5[/tex]
Then
[tex]\bigtriangleup = (-2)^{2} - 4*3*(-5) = 64[/tex]
[tex]x_{1} = \frac{-(-2) + \sqrt{64}}{2*3} = 1.67[/tex]
[tex]x_{2} = \frac{-(-2) - \sqrt{64}}{2*3} = -1[/tex]
The zeros for this function are x = -1 and x = 1.67