Answer:
99.7% of the confidence intervals we could construct after repeated sampling would go from 12.64 cm to 14.44 cm.
True that's the correct interpretation for this case since if we repeat the measures with this sample size we will got a similar result.
Step-by-step explanation:
For this case we need to remember that the confidence interval for the true mean is given by this formula:
[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex]
And for this case the 99.7 % confidence interval for the true mean is (12.64cm , 14.44cm) we analyze one by one the possible options in order to select one:
99.7% of the confidence intervals we could construct after repeated sampling would go from 12.64 cm to 14.44 cm.
True that's the correct interpretation for this case since if we repeat the measures with this sample size we will got a similar result.
There's a 99.7% chance that any particular frog I catch can jump between 12.64 cm and 14.44 cm.
False the confidence interval can't be interpreted as a chance
There's a 99.7% chance that the the mean length of frog jumps falls between 12.64 cm and 14.44 cm.
False the confidence interval can't be interpreted as a chance
If we were to repeat this sampling many times, 99.7% of the confidence intervals we could construct would contain the true population mean.
False always the confidence interval contain the mean since is the middle value.
Final answer:
The correct interpretation of a 99.7% confidence interval for mean length of frog jumps is that if we repeat the sampling many times, 99.7% of the constructed confidence intervals would contain the true population mean. This emphasizes the methodology's reliability over repeated sampling rather than assuring specifics of individual outcomes.
Explanation:
The correct interpretation of a 99.7% confidence interval, like the one provided for the mean length of frog jumps (12.64 cm, 14.44 cm), is that if we were to repeat this sampling process many times, 99.7% of the confidence intervals we construct would contain the true population mean. The other statements provided misinterpret the concept of confidence intervals by implying a probability about individual measurements or the certainty of the mean falling within a specific interval, which is not accurate.
Confidence intervals are about the process of estimation rather than specifics about single outcomes. They provide a range in which we are certain to a specified level (in this case, 99.7%) that the true population mean lies, assuming the sampling and calculations are correct. The correct interpretation underscores the reliability of the methodology over repeated sampling rather than guaranteeing specifics of individual outcomes or the exact location of the population mean.
What’s the correct answer for this?
Answer:
D
Step-by-step explanation:
Because their slopes are equal. Rest of the step-by-step explanation is in the attached file!!
Which graph shows the solution set for Negative 4.4 greater-than-or-equal-to 1.6 x minus 3.6?
A number line going from negative 3 to positive 3. A closed circle is at negative 0.5. Everything to the left of the circle is shaded.
A number line going from negative 3 to positive 3. A closed circle is at negative 0.5. Everything to the right of the circle is shaded.
A number line going from negative 7 to negative 1. A closed circle is at negative 5. Everything to the left of the circle is shaded.
A number line going from negative 7 to negative 1. A closed circle is at negative 5. Everything to the right of the circle is shaded.
Answer:
A number line going from negative 7 to negative 1. A closed circle is at negative 5. Everything to the right of the circle is shaded.
Step-by-step explanation:
-4.4 ≥ 1.6 x - 3.6
Solving for the value of x,
1.6 x ≤ -4.4 + 3.6
1.6 x ≤ - 0.8
Dividing 1.6 from both sides to know value of x
x ≤ - 0.5
Answer:
the answer is a
Step-by-step explanation:
Edenuity
Which is the correct calculation for the volume of the
pyramid?
(36)(7)= 84 units
(36)(7) = 126 units
36(7) = 252 units
3617)(3) = 756 units
Answer:
(A)One-third(36)(7)= 84 cubic units
Step-by-step explanation:
Volume of a Pyramid = [tex]\frac{1}{3}X$Base Area X Height[/tex]
The base is a rectangle
Base Area = 9 X 4=36 Square Units
Height =7 Units
Therefore:
Volume [tex]=\frac{1}{3}(36)(7)[/tex]
=84 Cubic Units
Answer:
Step-by-step explanation:
Andre drew a plan of a courtyard at a scale of 1 to 60. On his drawing, one side of the courtyard is 2.75 inches. if Andre made another courtyard scale drawing at a scale of 1 to 12, would this drawing be smaller or larger than the first drawing? explain your reasoning
Answer: The new drawing would be larger than the first drawing.
Step-by-step explanation:
A scale factor greater that one is an enlargement, but one smaller than one is a reduction
The second drawing will be 5 times bigger than the first one.
What is the scale factor?You must specify the extent of the shape's enlargement when describing one.
The scale factor is the ratio of two dimensions such that one figure is large and another is small.
The scale factor is done due to the unpractical measurement of any figure.
Given in the first drawing scale factor is 1:60
So Andre takes 60 units as 1
For example, it is 60 inches to 1 inch.
In the second drawing, Andre took 1:12
So he took 12 units as 1
For example 12 inches to 1
Now multiply by 5 then 5:60
So 60 inches to 5 inches means the second drawing is 5 times bigger the first one.
Hence "The second drawing will be 5 times bigger than the first one".
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A baker has 6.8 kilograms of flour. She buys another 1.5 kilograms of flour. She uses 1.2 kilograms to make cupcakes and 0.8 kilograms to make cookies.
How much flour does the baker have left?
Answer:6.3
Step-by-step explanation: 6.8 +1.5 -1.2 -0.8=6.3
The amount of flour left is 6.3 kg.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Total flour = 6.8 + 1.5 = 8.3 kg
Amount of flour used = 1.2 + 0.8 = 2 kg
The amount of flour left.
= 8.3 - 2
= 6.3 kg
Thus,
6.3 kg of flour is left.
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find the zeros of the polynomial 12x^2+31x+20
Answer:
-5/4; -4/3
Step-by-step explanation:
12x^2 + 31x + 20 =
(4x + 5)(3x + 4) -->
x = -5/4 OR -4/3
Do you want brainlyest
Answer:
I mean I guess sure
Step-by-step explanation:
Anyway hope you have a good day!!
ig..
Problem:
An old coin is kept in a cubic box in such a way that the outline of the coin touches the 4 walls of the box, if the base of the box has a 24 cm perimeter, what is the area of the coin?
Answer:
28.27 cm^2 (2 decimal places)
Step-by-step explanation:
side of box = 24/4 = 6
diameter of coin would be 6 too
area of coin = pi x (6/2)^2 = 28.2743
Name four possible solutions to the inequality; X > -1
Final answer:
Four possible solutions to the inequality X > -1 are 0, 1, 2, and 2.5, as each of these values is greater than -1. The solution set in interval notation is (-1, ∞).
Explanation:
The inequality in question is X > -1. To provide four possible solutions, we are essentially looking for any four numbers that are greater than -1. Remember, there are an infinite number of solutions since X can be any value greater than -1, but here are four specific examples:
0122.5Each of these values satisfies the inequality X > -1, because they are all greater than -1. It is important to note that solutions to inequalities like this one are often represented in interval notation, in this case, it would be (-1, ∞), meaning any number greater than -1 but less than infinity.
Please help me with this 15+0.50=25+0.25 *
Answer:
15.50=25.25
Step-by-step explanation:
15+0.50=15.50
25+0.25=25.25
So 15+0.50=25.25 = 9.75 because you subract 25.25-15.50=9.75
Hope this helps
What is the surface area of the triangular prism shown
Answer:
C
Step-by-step explanation:
A. 558 m2
B. 976 m2
C. 1,680 m2
D. 1,750 m2
Answer:
1064.64
Step-by-step explanation:
What is a food that provides energy to perform activitie in a food chain
Answer: The Sun is the major source of energy for organisms and the ecosystems of which they are a part. Producers such as plants, algae, and cyanobacteria use the energy from sunlight to make organic matter from carbon dioxide and water. This establishes the beginning of energy flow through almost all food webs.
Hope you understood : )Scores of an IQ test have a bell-shaped distribution with a mean of 100 and a standard deviation of 11. Use the empirical rule to determine the following. (a) What percentage of people has an IQ score between 67 and 133? (b) What percentage of people has an IQ score less than 89 or greater than 111? (c) What percentage of people has an IQ score greater than 111?
Answer:
(a) The percentage of people having an IQ score between 67 and 133 is 99.73%.
(b) The percentage of people having an IQ score less than 89 or greater than 111 is 31.73%.
(c) The percentage of people having an IQ greater than 111 is 15.87%.
Step-by-step explanation:
The random variable X can be defined as the scores of an IQ test.
The random variable X is normally distributed with parameters μ = 100 and σ = 11.
(a)
Compute the probability of people who has an IQ score between 67 and 133 as follows:
[tex]P(67<X<133)=P(\frac{67-100}{11}<\frac{X-\mu}{\sigma}<\frac{133-100}{11})\\\\=P(-3<Z<3)\\\\=P(Z<3)-P(Z<-3)\\\\=0.99865-0.00135\\\\=0.9973[/tex]
The percentage is, 0.9973 × 100 = 99.73%.
Thus, the percentage of people having an IQ score between 67 and 133 is 99.73%.
(b)
Compute the probability of people having an IQ score less than 89 or greater than 111 as follows:
[tex]P(X<89\ \cup\ X>111)=1-P(89<X<111)\\\\=1-P(\frac{89-100}{11}<\frac{X-\mu}{\sigma}<\frac{111-100}{11})\\\\=1-P(-1<Z<1)\\\\=1-[P(Z<1)-P(Z<-1)]\\\\=1-[0.84134-0.15866]\\\\=0.31732\\\\\approx 0.3173[/tex]
The percentage is, 0.3173 × 100 = 31.73%.
Thus, the percentage of people having an IQ score less than 89 or greater than 111 is 31.73%.
(c)
Compute the probability of people having an IQ score greater than 111 as follows:
[tex]P(X>111)=P(\frac{X-\mu}{\sigma}>\frac{111-100}{11})\\\\=P(Z>1)\\\\=1-P(Z<1)\\\\=1-0.84134\\\\=0.15866\\\\\approx 0.1587[/tex]
The percentage is, 0.1587 × 100 = 15.87%.
Thus, the percentage of people having an IQ greater than 111 is 15.87%.
The % of people having an IQ score between the 67 and the 133 is 99.73%. The % of people having an IQ score less than the 89 or greater than 111 is 31.73%. The % of people having an IQ greater than 111 is 15.87%.
What is the percentage of the scope of the IQ test.?As per the IQ test which is done to check the intelligent quotient of a score that s derived from a standard sets of tests. They are made to test human intelligence. The IQ score falls in a bell-shaped curve with the distortion of 100 and SD of 11.
The percentage of the people having a score between the 67 and 133 was 099.7% and those between the 89 of more 111 is 31.7% and those having a greater IQ of 111 are 15.8 % that is declining to the top.
Find out more information about the IQ test.
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Anna invests $7,000 in an account that compounds interest continuously and earns 7.5%. How long will it take for her
money to reach $105,000? Round to the nearest tenth of a year.
In need of help !!
Answer:
It will take 36.1 years for her money to reach $105,000.
Step-by-step explanation:
The amount of money earned after t years in continuous interest is given by:
[tex]P(t) = P(0)e^{rt}[/tex]
In which P(0) is the initial investment and r is the interest rate, as a decimal.
Anna invests $7,000 in an account that compounds interest continuously and earns 7.5%.
This means that [tex]P(0) = 7000, r = 0.075[/tex]
How long will it take for her money to reach $105,000?
This is t for which P(t) = 105000.
[tex]P(t) = P(0)e^{rt}[/tex]
[tex]105000 = 7000e^{0.075t}[/tex]
[tex]e^{0.075t} = \frac{105000}{7000}[/tex]
[tex]e^{0.075t} = 15[/tex]
[tex]\ln{e^{0.075t}} = \ln{15}[/tex]
[tex]0.075t = \ln{15}[/tex]
[tex]t = \frac{\ln{15}}{0.075}[/tex]
[tex]t = 36.1[/tex]
It will take 36.1 years for her money to reach $105,000.
Let the abbreviation PSLT stand for the percent of the gross family income that goes into paying state and local taxes. Suppose one wants to estimate the mean PSLT for the population of all families in New York City with gross incomes in the range $35.000 to $40.000. If sigma equals 2.0, how many such families should be surveyed if one wants to be 90% sure of being able to estimate the true mean PSLT within .5?
Answer:
Number of families that should be surveyed if one wants to be 90% sure of being able to estimate the true mean PSLT within 0.5 is at least 43.
Step-by-step explanation:
We are given that one wants to estimate the mean PSLT for the population of all families in New York City with gross incomes in the range $35.000 to $40.000.
If sigma equals 2.0, we have to find that how many families should be surveyed if one wants to be 90% sure of being able to estimate the true mean PSLT within 0.5.
Here, we will use the concept of Margin of error as the statement "true mean PSLT within 0.5" represents the margin of error we want.
SO, Margin of error formula is given by;
Margin of error = [tex]Z_(_\frac{\alpha}{2}_ ) \times \frac{\sigma}{\sqrt{n} }[/tex]
where, [tex]\alpha[/tex] = significance level = 10%
[tex]\sigma[/tex] = standard deviation = 2.0
n = number of families
Now, in the z table the critical value of x at 5% ( [tex]\frac{0.10}{2} = 0.05[/tex] ) level of significance is 1.645.
SO, Margin of error = [tex]Z_(_\frac{\alpha}{2}_ ) \times \frac{\sigma}{\sqrt{n} }[/tex]
0.5 = [tex]1.645 \times \frac{2}{\sqrt{n} }[/tex]
[tex]\sqrt{n} =\frac{2\times 1.645 }{0.5}[/tex]
[tex]\sqrt{n} =6.58[/tex]
n = [tex]6.58^{2}[/tex]
= 43.3 ≈ 43
Therefore, number of families that should be surveyed if one wants to be 90% sure of being able to estimate the true mean PSLT within 0.5 is at least 43.
Which scenarios have a negative correlation? Check all that apply. the number of calories consumed and the amount of weight lost by a person the temperature outside and the number of pool guests the number of children assigned to a class and the number of desks the price of rice and the number of penguins at the South Pole the thickness of the ice on a lake and the likelihood of falling through the ice
answer:
the first one and the last one
The correlation coefficient helps us to know how strong is the relation between two variables. The situations in which there exists a negative relationship are A and E.
What is the correlation coefficient?The correlation coefficient helps us to know how strong is the relation between two variables. Its value is always between +1 to -1, where, the numerical value shows how strong is the relation between them and, the '+' or '-' sign shows whether the relationship is positive or negative.
1 indicates a strong positive relationship.-1 indicates a strong negative relationship.A result of zero indicates no relationship at all, therefore, independent variable.A negative correlation is a relation in which as one variable increases the other decreases, therefore, there exists an inverse relationship between the two varibles.
A.) The number of calories consumed and the amount of weight lost by a person
It is known that if a person consumes more calories then he will gain more weight, therefore, the number of calories consumed and the amount of weight lost by a person have a negative correlation.
B.) The temperature outside and the number of pool guests.
If the temperature outside is more, more people will come to visit the pool. Thus, there exists a positive correlation.
C.) The number of children assigned to a class and the number of desks
The more the number of students, the more desk will be needed for them. Thus, there exists a positive correlation.
D.) The price of rice and the number of penguins at the South Pole.
The price of rice and the number of penguins at the south pole are two completely independent variables, therefore, there exists zero correlation.
E.)The thickness of the ice on a lake and the likelihood of falling through the ice.
If the thickness of the ice on a lake is more, there will be less likelihood of falling through the ice. Therefore, there exists a negative correlation.
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coles buys a new laptop for 335 he makes a down payment of 50$ and pays the rest in 6 equal monthly payments p what equation represent the relationship between the cost of the laptopand cole payment
Answer:
335 = 50 + 6p
Step-by-step explanation:
50 +6p=335
subtract from both sides
-50 -50
6p=285
/6p /6p
divide both sides
p=47.5
A math class has 3 girls and 9 boys in the seventh grade and 7 girls and 3 boys in the eighth grade. The teacher randomly selects a seventh grader and an
eighth grader from the class for competition. What is the probability that the students she selects are both girls?
Write your answer as a fraction in simplest form.
Final answer:
To calculate the probability that both a seventh grader and an eighth grader selected at random are girls, multiply the probability of selecting a girl from each grade. For the seventh grade, it's 1/4, and for the eighth grade, it's 7/10. The overall probability of both being girls is therefore 7/40.
Explanation:
The question involves determining the probability that both students selected for a competition from different grades are girls. To find this, we need to consider the number of girls in each of the two grades separately.
In the seventh grade, there are 3 girls out of 12 students. So, the probability of selecting a girl from the seventh grade is 3/12, which simplifies to 1/4. In the eighth grade, there are 7 girls out of 10 students. Therefore, the probability of selecting a girl from the eighth grade is 7/10.
To find the overall probability of selecting girls from both grades, we multiply the probabilities of each event since they are independent: (1/4) * (7/10) = 7/40.
Thus, the probability that both selected students are girls is 7/40.
a single number between 0 and 9 occurring either alone or in a larger number is called a _________
Answer:
The answer is digit
Step-by-step explanation:
A single number between 0 and 9 is a digit, which often makes up larger numbers.
Is 80 a multiple of 10 why or why not
Answer:
Yes because 10 times 8 is 80.
Step-by-step explanation:
Answer: 80 IS a multiple of 10 because 8 times 10 is 80.
Step-by-step explanation:
Equation to 2 cups peaches to 3 cups cherries to make 60 cups how many cups of peaches would i need
Answer:
90
Step-by-step explanation:
2*30= 60
3*30= 90
Olivia has taken an initial dose of a prescription medication.
The relationship between the elapsed time T, in hours, since she took the first dose, and the amount of medication M(t), in milligrams (mg), remaining in her bloodstream is modeled by the following function.
M(t)=50 (e^-0.75t)
How many milligrams of the medication will be remaining in Olivia's bloodstream after 6 hours?
Round your answer, if necessary, to the nearest hundredth.
Answer:
0.56 mg
Step-by-step explanation:
Put 6 where t is and do the arithmetic.
M(6) = 50(e^(-0.75·6)) = 50e^-4.5 ≈ 0.56
Olivia will have about 0.56 mg of medication remaining in her blood.
6th grade math please help ! c;
Answer:
$19.99
Step-by-step explanation:
Take the price for 2 pairs and divide by 2 to get the price for one pair
39.98 /2
19.99 for one pair
Suppose that 20% of the residents in a certain state support an increase in the property tax. An opinion poll will randomly sample 900 state residents and will then compute the proportion in the sample that support a property tax increase. How likely is the resulting sample proportion to be within .02 of the true proportion (i.e., between .18 and .22)? (Hint: Use the sampling distribution of the sample proportion in this case.)
Answer:
86.64% probability that the resulting sample proportion is within .02 of the true proportion.
Step-by-step explanation:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
For the sampling distribution of a sample proportion p in a sample of size n, we have that [tex]\mu = p, \sigma = \sqrt{\frac{p(1-p)}{n}}[/tex]
In this problem:
[tex]\mu = 0.2, \sigma = \sqrt{\frac{0.2*0.8}{900}} = 0.0133[/tex]
How likely is the resulting sample proportion to be within .02 of the true proportion (i.e., between .18 and .22)?
This is the pvalue of Z when X = 0.22 subtracted by the pvalue of Z when X = 0.18.
X = 0.22
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{0.22 - 0.2}{0.0133}[/tex]
[tex]Z = 1.5[/tex]
[tex]Z = 1.5[/tex] has a pvalue of 0.9332.
X = 0.18
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{0.18 - 0.2}{0.0133}[/tex]
[tex]Z = -1.5[/tex]
[tex]Z = -1.5[/tex] has a pvalue of 0.0668
0.9332 - 0.0668 = 0.8664
86.64% probability that the resulting sample proportion is within .02 of the true proportion.
A researcher studying public opinion of proposed Social Security changes obtains a simple random sample of 35 adult Americans and asks them whether or not they support the proposed changes. To say that the distribution of the sample proportion of adults who respond yes, is approximately normal, how many more adult Americans does the researcher need to sample in the following cases?
(a) 20% of all adult Americans support the changes(b) 25% of all adults Americans support the changes
To determine the number of adult Americans needed for the distribution of the sample proportion to be approximately normal, we can use the formula n = (Z/E)^2 * p * (1-p).
Explanation:To determine the number of adult Americans needed for the distribution of the sample proportion to be approximately normal, we need to calculate the minimum sample size n required. We can use the formula:
n = (Z₃/E)^2 * p * (1-p)
Where Z₃ is the critical value, E is the maximum error tolerance (which is half the width of the confidence interval), and p is the estimated proportion of adult Americans who support the changes.
For part (a), where 20% of all adult Americans support the changes, the estimated proportion p is 0.20. Plugging in the values for Z₃ and E, we can solve for n. Similarly, for part (b), where 25% of all adult Americans support the changes, the estimated proportion p is 0.25. Plugging in the values for Z₃ and E, we can solve for n.
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(a) The researcher needs to sample 15 more adult Americans if 20% support the changes.
(b) The researcher needs to sample 5 more adult Americans if 25% support the changes.
To determine how many more adult Americans the researcher needs to sample for the distribution of the sample proportion to be approximately normal, we need to use the Central Limit Theorem (CLT).
According to the CLT, the sampling distribution of the sample proportion [tex]\(\hat{p}\)[/tex] is approximately normal if both [tex]\(n \hat{p} \geq 10\)[/tex] and [tex]\(n (1 - \hat{p}) \geq 10\)[/tex], where n is the sample size and [tex]\(\hat{p}\)[/tex] is the sample proportion.
Let's find the required sample size for both cases:
Case (a): 20% of all adult Americans support the changes
Given [tex]\(\hat{p} = 0.20\),[/tex]
To ensure normality:
[tex]\[n \hat{p} \geq 10 \quad \text{and} \quad n (1 - \hat{p}) \geq 10\][/tex]
1. [tex]\( n \hat{p} \geq 10 \)[/tex]
[tex]\[ n \times 0.20 \geq 10 \implies n \geq \frac{10}{0.20} = 50 \][/tex]
2. [tex]\( n (1 - \hat{p}) \geq 10 \)[/tex]
[tex]\[ n \times 0.80 \geq 10 \implies n \geq \frac{10}{0.80} = 12.5 \][/tex]
The stricter condition is [tex]\( n \geq 50 \).[/tex]
Since the researcher already has a sample size of 35, the additional number of adults needed is:
[tex]\[50 - 35 = 15\][/tex]
Case (b): 25% of all adult Americans support the changes
Given [tex]\(\hat{p} = 0.25\),[/tex]
To ensure normality:
[tex]\[n \hat{p} \geq 10 \quad \text{and} \quad n (1 - \hat{p}) \geq 10\][/tex]
1. [tex]\( n \hat{p} \geq 10 \)[/tex]
[tex]\[ n \times 0.25 \geq 10 \implies n \geq \frac{10}{0.25} = 40 \][/tex]
2. [tex]\( n (1 - \hat{p}) \geq 10 \)[/tex]
[tex]\[ n \times 0.75 \geq 10 \implies n \geq \frac{10}{0.75} = 13.33 \][/tex]
The stricter condition is [tex]\( n \geq 40 \).[/tex]
Since the researcher already has a sample size of 35, the additional number of adults needed is:
[tex]\[40 - 35 = 5\][/tex]
Each of six jars contains the same number of candies. Alice moves half of the candies from the first jar to the second jar. Then Boris moves half of the candies from the second jar to the third jar. Then Clara moves half of the candies from the third jar to the fourth jar. Then Dara moves half of the candies from the fourth jar to the fifth. Finally, Ed moves half of the candies from the fifth jar to the sixth jar. At the end, 30 candies are in the fourth jar.
How many candies are now in the sixth jar?
Answer:
The number of candies in the sixth jar is 42.
Step-by-step explanation:
Assume that there are x number of candies in each of the six jars.
⇒ After Alice moves half of the candies from the first jar to the second jar, the number of candies in the second jar is:
[tex]\text{Number of candies in the 2nd jar}=x+\fracx}{2}=\frac{3}{2}x[/tex]
⇒ After Boris moves half of the candies from the second jar to the third jar, the number of candies in the third jar is:
[tex]\text{Number of candies in the 3rd jar}=x+\frac{3x}{4}=\frac{7}{4}x[/tex]
⇒ After Clara moves half of the candies from the third jar to the fourth jar, the number of candies in the fourth jar is:
[tex]\text{Number of candies in the 4th jar}=x+\frac{7x}{4}=\frac{15}{8}x[/tex]
⇒ After Dara moves half of the candies from the fourth jar to the fifth jar, the number of candies in the fifth jar is:
[tex]\text{Number of candies in the 5th jar}=x+\frac{15x}{16}=\frac{31}{16}x[/tex]
⇒ After Ed moves half of the candies from the fifth jar to the sixth jar, the number of candies in the sixth jar is:
[tex]\text{Number of candies in the 6th jar}=x+\frac{31x}{32}=\frac{63}{32}x[/tex]
Now, it is provided that at the end, 30 candies are in the fourth jar.
Compute the value of x as follows:
[tex]\text{Number of candies in the 4th jar}=40\\\\\frac{15}{8}x=40\\\\x=\frac{40\times 8}{15}\\\\x=\frac{64}{3}[/tex]
Compute the number of candies in the sixth jar as follows:
[tex]\text{Number of candies in the 6th jar}=\frac{63}{32}x\\[/tex]
[tex]=\frac{63}{32}\times\frac{64}{3}\\\\=21\times2\\\\=42[/tex]
Thus, the number of candies in the sixth jar is 42.
There are now 33.75 candies in the sixth jar.
Let's denote:
- x as the initial number of candies in each jar.
After Alice moves half of the candies from the first jar to the second jar, the number of candies in the first jar becomes [tex]\( \frac{x}{2} \)[/tex], and the number of candies in the second jar becomes [tex]x + \frac{x}{2} = \frac{3x}{2} \)[/tex] .
After Boris moves half of the candies from the second jar to the third jar, the number of candies in the second jar becomes [tex]\( \frac{3x}{4} \)[/tex], and the number of candies in the third jar becomes [tex]x + \frac{x}{2} = \frac{3x}{2} \)[/tex] .
After Clara moves half of the candies from the third jar to the fourth jar, the number of candies in the third jar becomes [tex]\( \frac{x}{2} \)[/tex], and the number of candies in the fourth jar becomes [tex]x + \frac{x}{2} = \frac{3x}{2} \)[/tex] .
After Dara moves half of the candies from the fourth jar to the fifth jar, the number of candies in the fourth jar becomes [tex]\( \frac{3x}{4} \)[/tex], and the number of candies in the fifth jar becomes [tex]\( \frac{3x}{4} + \frac{3x}{8} = \frac{9x}{8} \).[/tex]
Finally, after Ed moves half of the candies from the fifth jar to the sixth jar, the number of candies in the fifth jar becomes [tex]\( \frac{9x}{16} \)[/tex], and the number of candies in the sixth jar becomes [tex]\( \frac{9x}{16} + \frac{9x}{32} = \frac{27x}{32} \).[/tex]
Given that 30 candies are now in the fourth jar, we can set up the equation:
[tex]\[ \frac{3x}{4} = 30 \][/tex]
Solving for x :
[tex]\[ x = \frac{4 \times 30}{3} = 40 \][/tex]
Now, we can find the number of candies in the sixth jar:
[tex]\[ \frac{27 \times 40}{32} = \frac{1080}{32} = 33.75 \][/tex]
So, there are now 33.75 candies in the sixth jar.
Of the 300 students at your middle school, only 15% attended this field trip. How many students need to make it to the boat to be rescued?
Final answer:
45 students need to make it to the boat to be rescued.
Explanation:
The question asks us to calculate how many students attended a field trip, given that 15% of the 300 students at a middle school attended.
To find the number of students who attended the field trip, we use the percentage formula: number of students = total students × percentage attending.So, the calculation would be: 300 students × 15% = 300 × 0.15.This equals 45 students.Therefore, 45 students need to make it to the boat to be rescued.
Jennifer scores a 77 on her algebra 2 test. The mean on the test was 73. The standard deviation on the test was 5. What was her Z-score
Answer:
0.80
Step-by-step explanation:
The z-score is found from the formula ...
Z = (X -μ)/σ
Z = (77 -73)/5 = 4/5 = 0.80
Jennifer's Z-score was 0.80.
Carlos used 6 boards to build 2/3 of a front porch. How many boards will Carlos use to build the whole porch? Express your answer in simplest form.
Answer:
9 boards
Step-by-step explanation:
2/3 of the porch= 6 boards
so to figure out how much one third of the porch needs you find half of what it takes to fill in 2/3 of the porch and you get 3.
so 3=1/3 of the porch
then you simply do 3times 3 or 3+3+3 and you get 9
so it takes 9 boards to fill the whole porch
An inequality represents an infinite amount of numbers larger than-5. Which inequality represents the situation?
OX<-5
Ox>-5
O x>-4
OX<-4
Answer:
b) x > - 5
Step-by-step explanation:
x > - 5
x ∈ (- 5 ; + oo)
Answer:
B
Step-by-step explanation:
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