Answer: C. 225
Step-by-step explanation:
To get the total population (x), we will take the 40% of the total population and equate to 90
40%× x = 90
40/100 × x = 90
40x/100= 90
Cross multiplying,
40x = 100 × 90.
x = 9000/40
x =225 C
Carol put some green and red unit cubes in a box. The ratio of the number of red cubes is 2:1. She adds 12 more red cubes in the box and the ratio becomes 4:5. A) how many green cubes are there in the box B) how many red cubes does carol have in the end
Final answer:
Carol has 10 green cubes in the box. After adding 12 more red cubes, she ends up with 32 red cubes.
Explanation:
To solve this problem, we can use the concept of ratios and equations. First, we know that the initial ratio of red to green cubes is 2:1. Let's represent the number of red cubes as 2x and green cubes as x. We then are told that Carol adds 12 more red cubes and the ratio becomes 4:5. If we let the number of green cubes remain as x, we have that the new number of red cubes is 2x + 12.
We can set up the following proportion to represent the new situation:
(2x + 12) / x = 4 / 5
By cross-multiplying, we can solve for x to find the quantity of green cubes:
5(2x + 12) = 4x
10x + 60 = 4x
6x = 60
x = 10
Therefore, there are 10 green cubes in the box (as x represents the number of green cubes).
To find out how many red cubes are there in the end, we add 12 to the initial amount of red cubes (2 times the number of green cubes):
Initial red cubes = 2x = 2(10) = 20
Final red cubes = 20 + 12 = 32 cubes
So, Carol has 32 red cubes in the end.
A ________ is a numerical quantity computed from the data of a sample and is used in reaching a decision on whether or not to reject the null hypothesis.
1. significance level2. critical value3. test statistic4. parameter
Answer:
3. Test Statistic
A test statistic is a numerical quantity computed from the data of a sample and is used in reaching a decision on whether or not to reject the null hypothesis.
The numerical quantity computed from the data of a sample and used in reaching a decision on whether or not to reject the null hypothesis is called; 3.Test statistic.
When we are dealing with hypothesis testing, it is pertinent to note that we have terms like sample size, sample mean, population size, population mean, test statistic, significance level, critical value, standard deviation e.t.c.Now, among all those terminologies, the one that we always calculate first after defining the hypothesis is the test statistic. The test statistic is the one that is computed from which we will get the p-value to know whether to reject the null hypothesis or not.Read more about test statistic at; https://brainly.com/question/15980493
f the line passing through the points (1, a) and (5, −2) is parallel to the line passing through the points (2, 8) and (−5, a + 7), what is the value of a?
Answer:
[tex]a=-6[/tex]
Step-by-step explanation:
Line 1: (1, a) and (5, −2)
slope of the line is
[tex]slope = \frac{y_2-y_1}{x_2-x_1} =\frac{-2-a}{5-1} =\frac{-2-a}{4}[/tex]
Line 2: (2, 8) and (−5, a + 7)
slope of the line is
[tex]slope = \frac{y_2-y_1}{x_2-x_1} =\frac{a+7-8}{-5-2} =\frac{a-1}{-7}[/tex]
when the lines are parallel then slopes are equal
[tex]\frac{a-1}{-7} =\frac{-2-a}{4}[/tex]
cross multiply it
[tex]4(a-1)=-7(-2-a)[/tex]
[tex]4a-4=14+7a[/tex]
subtract 4a from both sides
[tex]-4=14+3a[/tex]
[tex]-18=+3a[/tex]
divide both sides by 3
[tex]a=-6[/tex]
A restaurant offers a medium pizza for $8. If a person can choose from one of eleven toppings, one of four cheeses, one of four kinds of sauce, and one of five type of crust, how many different pizzas are possible if a pizza must have a topping, cheese, sauce. And crust?
1) you first add up all of the amount of ingredients you have
2)you the take the total and divide your total up by the 4 ingredients you currently have
3)that is your total
11+4++4+5=24
24/4=6
answer= 6
There are 880 different pizzas are possible if a pizza must have a topping, cheese, sauce and crust.
What is Multiplication?
To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
Given that;
A restaurant offers a medium pizza for $8.
And, A person can choose from one of 11 toppings, one of 4 cheeses, one of 4 kinds of sauce, and one of 5 type of crust.
Now,
Since, A person can choose from one of 11 toppings, one of 4 cheeses, one of 4 kinds of sauce, and one of 5 type of crust.
So, We get;
The different ways for a pizza must have a topping, cheese, sauce. And crust = 11 x 4 x 4 x 5
= 880
Thus, There are 880 different pizzas are possible if a pizza must have a topping, cheese, sauce and crust.
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the mean of a sample size n=35 is 1860. the standard deviation of the sample is 102 and the population is normally distributed. construct a 99% confidence interval estimate of the mean of the population.
Answer: (1812.967, 1907.033)
Step-by-step explanation:
The confidence interval for population mean is given by :-
[tex]\overline{x}\pm t_{df,\ \alpha} \dfrac{s}{\sqrt{n}}[/tex]
, where [tex]\overline{x}[/tex] = Sample mean
n= Sample size.
s = Sample standard deviation
[tex]t_{df,\ \alpha}[/tex] = Critical t-value for degree of freedom(n-1).
As per given , we have
n= 35
[tex]\overline{x}=1860[/tex]
s=102
Significance level : [tex]\alpha=0.01[/tex]
By t- distribution table , for degree of freedom 43 and [tex]\alpha=0.01[/tex] , we have
[tex]t_{df,\ \alpha}=t_{34,\ 0.005} =2.728[/tex]
Substitute all the values in the above formula , we will get
[tex]1860\pm (2.728)\dfrac{102}{\sqrt{35}}[/tex]
[tex]=1860\pm (2.728)(17.2411)[/tex]
[tex]=1860\pm47.034[/tex]
[tex]=(1860-47.033\ 1860+47.033)= (1812.967,\ 1907.033)[/tex]
Hence, the 99% confidence interval estimate of the mean of the population is (1812.967, 1907.033).
Final answer:
To construct a 99% confidence interval for the population mean with a known standard deviation, calculate the standard error, find the appropriate z-score for 99% confidence, and apply the formula Sample mean ± z * SEM. The 99% confidence interval for the given sample data is approximately (1811.26, 1908.74).
Explanation:
A student asked how to construct a 99% confidence interval estimate for the mean of the population given that the mean of a sample of size n=35 is 1860 with a standard deviation of 102, and the population is normally distributed.
To construct a 99% confidence interval, we proceed by calculating the standard error of the mean (SEM), which is the standard deviation divided by the square root of the sample size:
SEM = σ / √n = 102 / √35 ≈ 17.25
We then find the z-score that corresponds to a 99% confidence level. For a two-tailed test, which is relevant here, this value is approximately 2.576.
The confidence interval is then calculated by:
Sample mean ± z * SEM = 1860 ± 2.576 * 17.25
Lower limit: 1860 - (2.576 * 17.25) ≈ 1811.26
Upper limit: 1860 + (2.576 * 17.25) ≈ 1908.74
Hence, the 99% confidence interval estimate for the population mean is approximately (1811.26, 1908.74).
PLEASE HELP!!!
Find MG.
∆EGF~∆EML.
Answer:
[tex]MG=56\ units[/tex]
Step-by-step explanation:
step 1
Find the value of x
we know that
If two triangles are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent
In this problem we have that
∆EGF~∆EML
so
[tex]\frac{EG}{EM}=\frac{EF}{EL}[/tex]
substitute the given values
[tex]\frac{5x+2}{16}=\frac{126}{28}[/tex]
solve for x
[tex]5x+2=\frac{126}{28}(16)[/tex]
[tex]5x+2=72\\5x=70\\x=14[/tex]
[tex]EG=5x+2=5(14)+2=72\ units[/tex]
step 2
Find MG
we know that
[tex]MG=EG-EM[/tex]
substitute
[tex]MG=72-16=56\ units[/tex]
True or False. The larger the distance between two adjacent numbers in the five‑number summary, the more spread out the data in that interval.
Answer: Its True
Step-by-step explanation:
The statement is true because the Percentages are preferred and also they are easier to compare than counts.
Find the value of x please help.
Answer:
x=11
Step-by-step explanation:
[tex]\frac{5x}{3x-3} =\frac{44}{24} =\frac{11}{6} \\33x-33=30x\\33x-30x=33\\3x=33\\x=11[/tex]
Identify the constant of proportionality in each group and use it as an equation in the form y= kx
Answer:
Step-by-step explanation:
5.
y=kx
when x=4,y=5
5=4k
k=5/4
y=5/4 x
or y=1.25 x
6.
y=kx
when x=4,y=9
9=4k
k=9/4
y=9/4 x
or y=2.25 x
A train drove the distance of 440 feet in 20 seconds. Select ALL the unit rates that are equivalent to the speed of the model airplane. (Use page 26 unit of measure chart to help.)
Answer:
yo is ya boi Nick you already know what it is yeah big daddy nick
A Sociology student investigated the association between a country’s Literacy Rate and Life Expec- tancy, and then drew the conclusions listed below. Explain why each statement is incorrect. (Assume that all the calculations were done properly.)
a) The determines 64% of the Life Expectancy for a country.
b) The slope of the line shows that an increase of 5% in will produce a 2-year improvement in
Answer:
Step-by-step explanation:
(a) R2 does not determine the level of correlation between two variables in statistics but rather it is used to determine the level of variance in a dependent variable that is explained by an independent variable. It is also known as coefficient of determination.
Pearson's correlation coefficient (r) will better explain a direct relationship between a country's literacy rate and life expectancy and the value obtained will better explain option a
(b) The slope of the line can predict an improvement in life expectancy but cannot guarantee this improvement. And as such, the use of the word "will" suggests a form of guarantee which is wrong in interpreting slopes.
There was a sample of
600
milligrams of a radioactive substance to start a study. Since then, the sample has decayed by
7.9%
each year.
Let
t
be the number of years since the start of the study. Let
y
be the mass of the sample in milligrams.
Write an exponential function showing the relationship between
y
and
t
Answer: y(t) = 600(0.921)^t
Step-by-step explanation:
Given:
Percentage yearly reduction = 7.9%
Initial mass m = 600 mg
time in years = t
An exponential function with yearly decay rate to determine the final mass of the substance is given as:
y(t) = m(f)^t
y(t) = final mass in milligram
m = 600
f = final mass fraction = 1 - 0.079 = 0.921
f = 0.921
Therefore, the exponential function is given as;
y(t) = 600(0.921)^t
An equilateral triangle has a height of 10 feet. How long is one of its sides? (Note: In an equilateral triangle, all sides have the same length.)
Answer:
side length is [tex]\frac{20\sqrt{3} }{3}[/tex] feet
Step-by-step explanation:
An equilateral triangle has a height of 10 feet. the height of the triangle is the perpendicular bisector to the base
so it forms a two right angle triangle
the triangle formed is a 30-60-90 degree triangle
the diagram is attached below
Let x be the side if the equilateral triangle
sin(theta)=opposite by hypotenuse
[tex]sin(60)=\frac{10}{x}[/tex]
[tex]\frac{\sqrt{3}}{2} =\frac{10}{x}[/tex]
cross multiply
[tex]\sqrt{3} x=20[/tex]
[tex]x=\frac{20}{\sqrt{3} } =\frac{20\sqrt{3} }{3}[/tex]
The length of the side of an equilateral triangle with a height of 10 feet is approximately 11.54 feet. This is determined by applying the properties of a 30-60-90 triangle which is a half of an equilateral triangle.
Explanation:The problem is asking to solve for the side (s) of an equilateral triangle given the height (h). An equilateral triangle can be divided into two 30-60-90 right triangles. In such a triangle, the ratio between the hypotenuse (which is the side of the equilateral triangle) and the longer leg (which is half of the height) is 2:√3. Therefore, if the height is 10 feet, then the side length would be (2/√3)*h.
Step 1: Recognize that the triangle is a 30-60-90 triangle.
Step 2: Apply the ratio between the sides in a 30-60-90 triangle, 2:√3.
Step 3: Multiply the height by 2/√3 to get the length of one side which equals about 11.5 feet.
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Pam brought water to the soccer game.She had 12 containers.She put 4 liters of water in each container.How many liters of water did Pam bring to the soccer game?
Answer:
48 liters
Step-by-step explanation:
You should multiply the number of containers by the number of liters in each container.
12 x 4 = 48
Pam brought 48 liters of water to the soccer game.
A large company wants to admiister a satisfaction survey to its current customers. using their customer database the company radoml selects 60 customers and asks them about their elvel of satifcation with the company. What type of sampling is used?
Answer:
The sampling used is simple random sampling.
Step-by-step explanation:
Consider the provided information.
Types:
Simple random sample is a subset of the population chosen from a larger set. Every person is selected by chance and randomly.Systematic sampling: list of elements is counted off.Convenience sampling: data which is readily available is used. That is, the first people are running into by the surveyor.Cluster sampling: divide the population into groups, usually geographically.Stratified sampling: divide population into groups called strata. but this time population might be separated into males and females.Here, randomly selected 60 customers, Thus, the sampling used is simple random sampling.
Flight 725 left New York at 10:28 a.m. flying north. Flight 245 left from the same airport at 11:18 a.m. flying south at one hundred twenty kph less than three times the speed of flight 725. At 1:06 p.m. they are 1,030 kilometers apart. What is the average rate of speed for Flight 245?
A) 165 kph
B) 395 kph
C) 365 kph
D) 345 kph
E) 155 kph
F) 175 kph
Answer:
Step-by-step explanation:
Let x represent the average speed of flight 725.
Flight 725 left New York at 10:28 a.m. flying north.
Flight 245 left from the same airport at 11:18 a.m. flying south at one hundred twenty kph less than three times the speed of flight 725. This means that the speed of flight 245 is
3x - 120
At 1:06 p.m. they are 1,030 kilometers apart. This means that total distance travelled by both planes would be 1030
Between 10:28am and 1:06pm, the number of hours would be 2hr 38 minutes = 2 + 38/60 = 2.63 hours
Distance = speed × time
Total distance travelled by flight 725 = x × 2.63 = 2.63x
Between 11:18am and 1:06pm, the number of hours would be 1hr 48 minutes = 1 + 48/60 = 1.8 hours
Distance = speed × time
Total distance travelled by flight 245 = x × 1.8 = 1.8(3x - 120)
5.4x - 216 + 2.63x = 1030
8.03x = 1030 + 216 = 1246
x = 1246/8.03 = 155 kph
A shipment of computer monitors, some weighing 25lb and the others weighing 40lb each, has a total weight of 680lb. If there are 20 monitors altogether, how many weigh 40lb?
Answer:
The answer to your question is 12 monitors
Step-by-step explanation:
Data
v = monitors weighing 25 lb
f = monitors weighing 40 lb
Total weight = 680 lb
Total monitors = 20
Process
1.- Write equations
v + f = 20 ------------------ (l)
25v + 40f = 680 -----------------(II)
2.- Solve the system by elimination
Multiply equation l by -25
-25v - 25f = - 500
25v + 40f = 680
0 + 15 f = 180
Solve for f
f = 180 / 15
f = 12
3.- Find the value of v
v + 12 = 20
v = 20 - 12
v = 8
4.- Conclusion
There are 12 monitors weighing forty lb
There are 8 monitors weighing 25 lb
What type of pay is modeled below?
A) commission pay. B) hourly pay with a bonus. C) hourly pay without a bonus. D) piece rate.
The model shown in the graph describes a piece rate. Correct option is D.
Let us take a point (3, 60) in the given graph.
The function which model this is y=kx.
Let us plug in y as 60 and x as 3.
60=3k
Divide both sides by 3:
k=20
So, y=20x.
The model is proportional function, if the x value increases then y value increases.
Similarly, if x value decreases the y value decreases.
Hence, the model shown in the graph describes a piece rate. option D is correct.
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Answer:
Hourly pay without a bonus
Step-by-step explanation:
I just took the test
Andy and Diane want to buy a new van. They are allowed $5,500 for their present car. They also made a down payment of $2,300. They still owe 40% of the regular price of the car. What is the regular price of the car
Answer:
The regular price of the car is $13,000.
Step-by-step explanation:
i) let the price of the van Andy and Diane want to buy be $x.
ii) they get $5,500 for their present car
iii) they also make a down payment of $2,300.
iv) therefore $x = $0.4x + $5,500 + $2,300
therefore $0.6x = $7,800
therefore $x = $[tex]\frac{7800}{0.6}[/tex] = $13,000
The regular price of the car is $13,000.
The price of milk has been increasing over the last month. Audrey believes there is a positive correlation between the number of predicted storms and the price of milk.
Number of Storms Predicted Milk Price
1 $2.70
3 $2.89
4 $3.50
6 $3.88
7 $3.91
Use the table to determine the average rate of change from 3 to 6 storms.
Answer:
0.33
Step-by-step explanation:
So we find the difference between the price of milk at 6 storms and the price of milk at 3 storms.
3.88 - 2.89= 0.99
Then we divide the difference by 3 to find the average rate of change for each storm between 3 to 6.
0.99 ÷3= 0.33
So the answer is 0.33.
The average rate of change from 3 to 6 storms is 0.33
What is Correlation?A correlation exists as a statistical measurement that expresses the extent to which two variables are linearly related (suggesting they change together at a constant rate). It's a familiar tool for defining simple relationships without making a statement about cause and effect.
To solve this example use this rule :
Δx/Δy
x exists the amount that changed. so Δx=0,99.
The storm stands to 3 to 6 so find the difference for x: for the 3rd and 6th members of the table... 3.88-2.89=0.99
Now,
0.99/Δy
Because require to find from 3 to 6, Δy=3,
When finding both, rate of change with :
0.99/3=0.33.
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Peanuts cost $1.50 per pound. how much does 2 pounds of Peanuts cost?
Answer:
$3.00
Step-by-step explanation:
If you wanna buy 2 pounds, just time it by 2! $1.50*2=$3.00!
If peanuts cost $1.50 per pound, the cost of 2 pounds of peanuts would be equal to $3.0.
Given the following data:
Cost of peanut = $1.50 per pound.Quantity of peanuts = 2 pounds.How to calculate the cost of 2 pounds?In order to determine the cost of 2 pounds of peanuts, we would set up a direct proportion equation as follows:
1 pounds = 1.50 dollars.
2 pounds = X dollars.
Cross-multiplying, we have:
X = 2 × 1.5
X = $3.0
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Charles Miller invested his textbook royalty income in two accounts, one paying 3% annual simple interest and the other paying 2% interest. He earned a total of $11 interest. If he invested three times as much in the 3% account as he did in the 2% account how much did he invest at each rate
Answer:
The amount invested at 3% is 300 &
The amount invested at 2% is 100.
Step-by-step explanation:
Total yearly interest for the two accounts is: $11
Let x be the amount invested at 3%
& y be the amount invested at 2%
From the question we can get 2 equations as;
x = 3y --------------------------Equation 1
0.03x + 0.02y = 11 ----------Equation 2
Substitute for x in Equation 2 we get;
0.03 (3y) + 0.02y = 11
0.09y + 0.02y = 11
0.11y = 11
Divide the above equation by 0.11, we get;
y = [tex]\frac{11}{0.11}[/tex]
y = 100
Let us substitute the value of y in Equation 1 we get;
x = 3(100)
x = 300
Now to check our answer let us put in the simple interest formula. If we get the sum of the two interests equal to 11 then our answers are correct:
0.03 x 300 + 0.02 x 100
= 9 + 2
= 11
Hence the amount invested at 3% is 300 and the amount invested at 2% is 100.
Why wont anybody help me :(
PLEASE MARK BRAINLIEST!
Answer:
Don't worry friend! I am here to help you!
Step-by-step explanation:
I tried answering as many questions as I could, but the ones I didn't answer, I didn't know how to solve.
Please understand that I am here to help you and others on brainly!
I hope this makes you feel better!
- sincerelynini
wo crafty bacteria fall into a pot of milk which has recently been sterilized. They reproduce at a rate of 4% per day. Determine how many bacteria will be present after 100 days.
Final answer:
After 100 days, there will be approximately 7.18 bacteria present.
Explanation:
To determine the number of bacteria that will be present after 100 days, we need to calculate the exponential growth of the bacteria. The bacteria reproduce at a rate of 4% per day, which means the population will double every 25 days (since 100 divided by 4 is 25).
To calculate the final population, we can use the formula N = N₀ * [tex](1 + r/100)^t[/tex], where N is the final population, N₀ is the initial population, r is the growth rate, and t is the time in days.
In this case, the initial population is 2 (assuming there are initially only two bacteria), the growth rate is 4%, and the time is 100 days.
Plugging in these values,
we get [tex]N = 2 * (1 + 4/100)^{100} = 2 * (1.04)^{100}[/tex]nal population of approximately 7.18 bacteria. Therefore, there will be approximately 7.18 bacteria present after 100 days.
The test scores on the Chapter 10 mathematics test have a mean of 52 and a standard deviation of 10. Andrea scored 76 on the test. How many standard deviations from the mean is that?
Final answer:
Andrea's score of 76 is 2.4 standard deviations above the mean test score of 52 with a standard deviation of 10.
Explanation:
The question is how many standard deviations from the mean Andrea's score of 76 is on the mathematics test where the mean is 52 and the standard deviation is 10. To find this, you would use the formula for calculating a z-score:
Z = (X - μ) / σ
Where:
Z is the z-score
X is the value of the score
μ is the mean of the scores
σ is the standard deviation of the scores
For Andrea's score, the calculation would be:
Z = (76 - 52) / 10 = 24 / 10 = 2.4
Therefore, Andrea's score is 2.4 standard deviations above the mean. This indicates that her score was significantly higher than the average test score.
A football player completes a pass 69.4% of the time. Find the probability that (a) the first pass he completes is the second pass, (b) the first pass he completes is the first or second pass, and (c) he does not complete his first two passes.
The student asked for the calculations of probabilities concerning a football player's passes. The answers are: (a) 21.18%, (b) 90.58%, (c) 8.68%. This involves the use of probability rules and calculations carried out to two decimal places.
Explanation:The subject of this question is probability, particularly in the context of repeated independent trials. The football player has a 69.4% chance of completing a pass, so we can use this information to answer the questions.
The first pass he completes is the second pass: This means that he fails the first pass and succeeds on the second. Both of these are independent events. So, we multiply the probabilities: (1 - 0.694) * 0.694 = 0.2118 or 21.18%.The first pass he completes is the first or second pass: We've already calculated the probability for the second pass. The probability for the first pass is simply his success rate, 0.694 or 69.4%. To find the probability of either event occurring, we add the two probabilities together: 0.2118 + 0.694 = 0.9058 or 90.58%.He does not complete his first two passes: This means he fails both passes. Since these are independent events, we multiply the probabilities: (1 - 0.694) * (1 - 0.694) = 0.0868 or 8.68%.Learn more about Probability here:https://brainly.com/question/22962752
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(a) The probability that the first pass he completes is the second pass is [tex]$\frac{3099}{10000}$[/tex].
(b) The probability that the first pass he completes is the first or second pass is [tex]$\frac{3499}{5000}$[/tex].
(c) The probability that he does not complete his first two passes is [tex]$\frac{9826}{2500}$[/tex].
To solve this problem, we will use the given completion rate of 69.4% and convert it into a fraction to make the calculations easier. The completion rate is equivalent to [tex]$\frac{694}{1000}$[/tex] or [tex]$\frac{347}{500}$[/tex].
(a) To find the probability that the first pass he completes is the second pass, we need to consider two events: he must fail the first pass and then succeed on the second pass. The probability of failing the first pass is [tex]$1[/tex] - [tex]\frac{347}{500}$[/tex], and the probability of succeeding on the second pass is [tex]$\frac{347}{500}$[/tex]. Multiplying these two probabilities gives us the desired probability:
[tex]$$ \left(1 - \frac{347}{500}\right) \times \frac{347}{500} = \frac{153}{500} \times \frac{347}{500} = \frac{3099}{25000}. $$[/tex]
Simplifying this fraction by dividing both the numerator and the denominator by 4, we get:
[tex]$$ \frac{3099}{25000} = \frac{77475}{62500} = \frac{3099}{10000}. $$[/tex]
(b) To find the probability that the first pass he completes is the first or second pass, we need to consider the probability of completing the first pass and the probability of failing the first pass but completing the second pass. We add these two probabilities because they are mutually exclusive events. The probability of completing the first pass is [tex]$\frac{347}{500}$[/tex], and the probability of failing the first pass but completing the second pass is the same as calculated in part (a), [tex]$\frac{3099}{10000}$[/tex]. Adding these probabilities gives us:
[tex]$$ \frac{347}{500} + \frac{3099}{10000} = \frac{694}{1000} + \frac{3099}{10000} = \frac{3499}{5000}. $$[/tex]
(c) To find the probability that he does not complete his first two passes, we need to consider the probability of failing both passes. The probability of failing one pass is [tex]$1[/tex]- [tex]\frac{347}{500}$[/tex], so for two consecutive failures, we square this probability:
[tex]$$ \left(1 - \frac{347}{500}\right)^2 = \left(\frac{153}{500}\right)^2 = \frac{23409}{25000}. $$[/tex]
Simplifying this fraction by dividing both the numerator and the denominator by 4, we get:
[tex]$$ \frac{23409}{25000} = \frac{585025}{62500} = \frac{9826}{2500}. $$[/tex]
These calculations provide the probabilities for each of the specified events.
Buthaina is thinking of a number.The number is greater than two hundred twenty-five. Her number is less than 2 hundreds,2 tens, and 7 ones.What is Buthaina's number?
Answer:
The number is 226.
Step-by-step explanation:
Let the number be x.
Given:
The number is greater than two hundred twenty-five.
So we can say that;
[tex]x>225[/tex] equation 1
Also Given:
Her number is less than 2 hundreds,2 tens, and 7 ones.
Now we can say that 2 hundreds,2 tens, and 7 ones is equal to 227
So now the number is less than 227.
[tex]x<227[/tex] equation 2
From equation 1 and equation 2 we can say that;
[tex]225<x<227[/tex] equation 3
Also,
[tex]225<226<227[/tex] equation 4
Comparing equation 3 and 4 we get;
[tex]x=226[/tex]
Hence The number is 226.
Which is an example of continuous data? A) number of people wearing a team jersey B) temperature during the game on Saturday C) number of innings played in a baseball game D) number of home runs hit by a player during a game
Answer:
B)temperature during the game on Saturday
Step-by-step explanation:
In a state lottery, four digits are drawn at random one at a time with replacement from 0 to 9. Suppose that you win if any permutation of your selected integers is drawn. Give the probability of winning if you select
The probability of winning in the state lottery is 0.24%.
Explanation:Probability of Winning in the State LotteryTo calculate the probability of winning, we need to consider the total number of possible outcomes and the number of favorable outcomes. In this case, there are 10 choices for each digit, so the total number of possible outcomes is 10 x 10 x 10 x 10 = 10,000. Since any permutation of the selected integers counts as a win, we have 4! = 4 x 3 x 2 x 1 = 24 favorable outcomes.
Therefore, the probability of winning is 24/10,000 = 0.0024, or 0.24%.
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The probability of winning by selecting unique digits is 0.0024 or 24/10,000.
We first determine the total number of possible outcomes when drawing four digits. Since the digits range from 0 to 9, there are 10 possible choices for each digit.
Total outcomes = 10 choices for the first digit * 10 choices for the second digit * 10 choices for the third digit * 10 choices for the fourth digit
= 10⁴ = 10,000.
Now, if you select four specific digits, we need to consider the number of ways these digits can be arranged, which is calculated using permutations. If all selected digits are unique, the number of permutations is 4! = 24.
If you select digits with repetitions, the calculation varies. For example, if you select 1, 2, 2, and 3, the permutations would be 4! / 2! = 12.
Assuming you selected four unique digits, the probability of winning is given by the number of favorable outcomes divided by the total outcomes. Thus, the probability of winning with unique digits is:
Probability = Number of favorable outcomes / Total outcomes
= 24 / 10,000
= 0.0024.
Brooklyn has a combination of dimes and nickels in her wallet she has three times as many nickels as she does dimes and the total value of the coins is 4.00 how many does she have of each coin
Answer: she has 16 dimes and 48 nickels
Step-by-step explanation:
The worth of a dime is 10 cents. Converting to dollars, it becomes
10/100 = $0.1
The worth of a nickel is 5 cents. Converting to dollars, it becomes
5/100 = $0.05
Let x represent the number of dimes that she has in her wallet.
Let y represent the number of nickels that she has in her wallet.
she has three times as many nickels as she does dimes. This means that
y = 3x
the total value of the coins is $4.00. This means that
0.1x + 0.05y = 4 - - - - - - - - - - - 1
Substituting y = 3x into equation 1, it becomes
0.1x + 0.05 × 3x = 4
0.1x + 0.15x = 4
x = 4/0.25 = 16
y = 3x = 3 × 16
y = 48