Answer: The z score that corresponds to the value x=22 is 0.4 .
Step-by-step explanation:
Given : A normal distribution has a mean 20 and standard deviation 5.
i.e. [tex]\mu=20[/tex]
[tex]\sigma=5[/tex]
Let x be the random selected variable.
We know that to find the z-score corresponds to the value x is given by :-
[tex]z=\dfrac{x-\mu}{\sigma}[/tex]
For x = 22, we have
[tex]z=\dfrac{22-20}{5}=\dfrac{2}{5}\\\\\Rightarrow\ z=0.4[/tex]
Hence, the z score that corresponds to the value x=22 is 0.4
A z-score in a normal distribution measures the number of standard deviations a value is from the mean. To calculate it, use the formula z = (x - μ) / σ for the specific values provided, such as half a standard deviation below the mean, 5 points above the mean, three standard deviations above the mean, and 22 points below the mean.
The calculation of a z-score within a normal distribution is a common task in statistics, allowing one to determine how many standard deviations a particular value, x, is from the mean, μ, of the distribution. The z-score is calculated using the formula:
z = (x - μ) / σ
where x is the value in question, μ is the mean, and σ is the standard deviation. Now, we will calculate the z-scores for the given situations:
One-half of a standard deviation below the mean:5 points above the mean:Three standard deviations above the mean:22 points below the mean:Remember, when you use these calculations for specific numerical values, you need to insert the actual values of mean and standard deviation into the formula.
Find the equation of the line passing through (4, 3) and (-2, -7): A. 3x + 5y = 27 B. 3x - 5y = -3 C. 5x - 3y = 11 D. 2x - y = 5
Answer:
(c) 5x - 3y = 11
Step-by-step explanation:
using slope intercept form
we know equation of line is
y= mx+c........(1)
where m is slope which can be written as [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\frac{-7-3}{-2-4} =\frac{-10}{-6} =\frac{5}{3}[/tex]
substituting value in equation (1)
[tex]y=\frac{5}{3} x+c[/tex]
now inserting value of point (4,3)
[tex]3=\frac{5}{3}\times 4+c[/tex]
[tex]c=\frac{-11}{3}[/tex]
[tex]y=\frac{5}{3} \times x-\frac{11}{3}\\[/tex]
on solving we get
[tex]5x - 3y = 11[/tex]
1) Draw the arrow diagram and the matrix representation for the relation: R={(1, 2), (3, 4), (2, 3), (3, 2), (2, 1), (3, 1), (4, 3)} with domain {1, 2, 3, 4)
Answer:
The arrow diagram and the matrix representation for the relation is shown below.
Step-by-step explanation:
The given relation is
R={(1, 2), (3, 4), (2, 3), (3, 2), (2, 1), (3, 1), (4, 3)}
If a relation is defined as
[tex]R=\{(x,y)|x\in R,y\in R\}[/tex]
Then the set of x values is domain and set of y values is range.
The domain of the function is
Domain={1, 2, 3, 4)
The range of the function is
Range={1, 2, 3, 4)
In arrow diagram, we have two sets first set represents the domain and second set represents the range. The arrow connecting the element represent the relation.
In matrix representation,
[tex]M_{ij}=\begin{cases}1 & \text{ if } (x_i,y_j)\in R \\ 0 & \text{ if } (x_i,y_j)\notin R\end{cases}[/tex]
The arrow diagram and the matrix representation for the relation is shown below.
The arrow diagram and matrix representation offer effective visualizations to understand and communicate the relationships within the given relation R={(1, 2), (3, 4), (2, 3), (3, 2), (2, 1), (3, 1), (4, 3)}.
The given relation R={(1, 2), (3, 4), (2, 3), (3, 2), (2, 1), (3, 1), (4, 3)} can be analyzed step by step. The domain, representing the set of x values, is Domain={1, 2, 3, 4}, and the range, representing the set of y values, is Range={1, 2, 3, 4}.
The arrow diagram visually represents this relation, with the first set depicting the domain and the second set depicting the range. Arrows connect elements to illustrate the relationships within the given set.
The matrix representation further encapsulates this relation, with rows corresponding to the elements of the domain and columns to the elements of the range. The presence of an entry in the matrix indicates a relation between the respective elements.
This method provides a concise and organized representation of the given relation. Overall, the arrow diagram and matrix representation serve as effective tools to comprehend and communicate the relationships within the specified set.
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determine if it is possible to form a triangle using the segments with the given measurements
42) 8ft, 9ft, 11ft
43) 7.4cm, 8.1cm, 9.8cm
EXPLAIN YOUR REASONING!
Answer:
Part 42) Yes, It is possible o form a triangle using the segments with the given measurements
Part 43) Yes, It is possible o form a triangle using the segments with the given measurements
Step-by-step explanation:
we know that
The Triangle Inequality Theorem states that the sum of any 2 sides of a triangle must be greater than the measure of the third side
Part 42) we have
8ft, 9ft, 11ft
Applying the triangle inequality theorem
a) 8+9 > 11
17 ft > 11 ft ----> is true
b) 9+11 > 8
20 ft > 8 ft ----> is true
c) 8+11 > 9
19 ft > 9 ft ----> is true
therefore
Yes, It is possible o form a triangle using the segments with the given measurements
Part 43) we have
7.4cm, 8.1cm, 9.8cm
Applying the triangle inequality theorem
a) 7.4+8.1 > 9.8
15.5 cm > 9.8 cm ft ----> is true
b) 8.1+9.8 > 7.4
17.9 cm > 7.4 cm ----> is true
c) 7.4+9.8 > 8.1
17.2 cm > 8.1 cm ----> is true
therefore
Yes, It is possible o form a triangle using the segments with the given measurements
A decade-old study found that the proportion of high school seniors who felt that "getting rich" was an important personal goal was 72% . Suppose that we have reason to believe that this proportion has changed, and we wish to carry out a hypothesis test to see if our belief can be supported. State the null hypothesis and the alternative hypothesis that we would use for this test.
Answer: [tex]H_0:p\leq0.72[/tex]
[tex]H_a:p\neq0.72[/tex]
Step-by-step explanation:
Given : A decade-old study found that the proportion of high school seniors who felt that "getting rich" was an important personal goal was 72% .
Let 'p' be the new proportion of high school seniors who felt that "getting rich" was an important personal goal .
Claim : [tex]p\neq0.72[/tex]
We know that the null hypothesis has equal sign.
Therefore , the null hypothesis for the given situation will be opposite to the given claim will be :-
[tex]H_0:p=0.72[/tex]
And the alternative hypothesis must be :-
[tex]H_a:p\neq0.72[/tex]
Hence, the null hypothesis and the alternative hypothesis that we would use for this test :
[tex]H_0:p\leq0.72[/tex]
[tex]H_a:p\neq0.72[/tex]
Final answer:
To test the belief that the proportion of high school seniors valuing wealth has changed, we would use H0: p = 0.72 as the null hypothesis and Ha: p
Explanation:
To conduct a hypothesis test regarding the proportion of high school seniors who believe that "getting rich" is an important goal, we state the null hypothesis (H0) and the alternative hypothesis (Ha). The null hypothesis is the statement that the proportion remains the same, while the alternative hypothesis states that the proportion has changed.
For a proportion of high school seniors who believe that getting rich is an important goal, if the decade-old study showed a proportion of 72%, we would have:
H0: p = 0.72
Ha: p ≠ 0.72
In the hypothetical scenario with a disease prevalence of 9.5% in the general population and finding 7% in a local survey, we would determine the null and alternative hypotheses regarding whether the local proportion is less than the national average as follows:
H0: p ≥ 0.095
Ha: p < 0.095
When conducting a hypothesis test, the null hypothesis typically represents no change or no effect, while the alternative hypothesis represents a change, difference, or effect that we are trying to detect.
I need help with the following question.
It is about Math of Finance.
Questions:
A $3500 loan was settled ten years later with a payment of $8100. Determine the annual rate of return.
Answer:
The annual rate of return is 13.14%.
Step-by-step explanation:
As it is not mentioned whether the amount was compounded, so we will assume this to be simple interest.
Given is - A $3500 loan was settled ten years later with a payment of $8100.
Means total amount paid back was = $8100
And original principle was = $3500
So, interest paid = [tex]8100-3500=4600[/tex] dollars
Now simple interest formula is :
[tex]I=p\times r\times t[/tex]
Where p = 3500
I = 4600
r = ?
t = 10
Now putting these values in formula we get;
[tex]4600=3500\times r\times10[/tex]
[tex]r=4600/35000[/tex]
r= 0.1314
So, rate of interest = 13.14%
What is the equation of the line that is tangent to the circle of radius 8 at (0,-8) and whose center is at the origin? Click to select your answer 2 3 4
Answer:
y=-8
Step-by-step explanation:
So if you draw a circle with center at the origin (0,0) with radius 8.
So we have:
That means the radius stretches to (0,-8); down 8 units from (0,0).
The radius stretches to (0,8); up 8 units from (0,0).
The radius stretches to (8,0); right 8 units from (0,0).
The radius stretches to (-8,0); left 8 units from (0,0).
We are looking for a line tangent to our circle at (0,-8). Since this was down 8 units. Then our equation is horizontal and y=a number. They-coordinate in (0,-8) is -8, so the we have y=-8.
If someone said tangent at (0,8), we would have said y=8 .
If someone said tangent at (8,0), we would have said x=8.
If someone said tangent at (-8,0), we have have said x=-8.
The equation of the line that is tangent to the circle with radius 8 at (0,-8) and center at the origin is y=-8. This is because the tangent line is horizontal at that point as it is perpendicular to the radius line lying along the y-axis.
Explanation:In the context of Mathematics, particularly geometry, the line that is tangent to a circle at a given point is perpendicular to the radius drawn to that point. Since the circle's center is at the origin (0,0) and the radius is extended to the point (0,-8), this radius lies along the y-axis. Therefore, the equation of the tangent line which is perpendicular to this radius would be a horizontal line through the point (0,-8), given by the equation y=-8.
Remember that tangent line by definition touches the circle at only one point without intersecting it and the line is perpendicular to the radius at that point of tangency. In this particular scenario, the radius and tangent are perpendicular lines in the coordinate system: the radius aligns with the y-axis, hence the tangent aligns with the x-axis.
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there are 6 sets of coins on the table. There is only one coin in the first set, 2 coins in the second set, 3 coins in the third set, 4 coins in the fourth set, 5 coins in the fifth set, and 6 coins in the sixth set. In each step, it is possible to add a coin to any two sets. Is it possible that after some steps the number of coins in each of the sets will be equal
if you answer correctly in first 10 minutes ill give brainliest
Answer:
no
Step-by-step explanation:
The total number of coins in all sets is 21, an odd number. In order for there to be equal numbers in all sets, the total number of coins must be even. Each step adds an even number of coins, so there is no number of steps that will add an odd number of coins to make the total be even.
Four hundred people were asked whether gun laws should be more stringent. Three hundred said "yes," and 100 said "no". The point estimate of the proportion in the population who will respond "yes" is
Answer:
0.75
Step-by-step explanation:
We have been given that 400 people were asked whether gun laws should be more stringent. 300 hundred said "yes," and 100 said "no".
To find the point estimate of the proportion in the population who will respond "yes", we need to divide number of people who said yes by total number of people that is 300 by 400.
[tex]\text{People who will respond yes}=\frac{300}{400}[/tex]
[tex]\text{People who will respond yes}=\frac{3}{4}[/tex]
[tex]\text{People who will respond yes}=0.75[/tex]
Therefore, the point estimate of the proportion in the population who will respond "yes" is 0.75.
n a study of speed dating, male subjects were asked to rate the attractiveness of their female dates, and a sample of the results is listed below (1equalsnot attractive; 10equalsextremely attractive). Construct a confidence interval using a 95% confidence level. What do the results tell about the mean attractiveness ratings of the population of all adult females? 7, 7, 3, 8, 5, 6, 6, 9, 9, 8, 6, 9 What is the confidence interval for the population mean mu? 5.8less thanmuless than 8.1 (Round to one decimal place as needed.) What does the confidence interval tell about the population of all adult females? Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. A. We are 95% confident that the interval from nothing to nothing actually contains the true mean attractiveness rating of all adult females. (Round to one decimal place as needed.) B. The results tell nothing about the population of all adult females, because participants in speed dating are not a representative sample of the population of all adult females. C. We are confident that 95% of all adult females have attractiveness ratings between nothing and nothing. (Round to one decimal place as needed.)
The confidence interval is [tex]\fbox{(5.8, 8.1)}[/tex] and [tex]\fbox{\text{Option A}}[/tex] is correct.
Further Explanation:
Given:
The least value is [tex]1[/tex] that is the least attractive.
The highest value is [tex]10[/tex] that is the most attractive.
The observations are,
7, 7, 3, 8, 5, 6, 6, 9, 9, 8, 6, 9.
Calculation:
The sum of all observations is [tex]83[/tex].
The population mean is [tex]\mu[/tex].
The standard deviation [tex]s[/tex] is [tex]1.832[/tex].
The sample mean [tex]\bar^{X}[/tex] is [tex]6.92[/tex].
Level of significance [tex]\alpha[/tex] = [tex]5\%[/tex].
Formula for confidence interval = [tex]\left( \bar{X} \pm t_{n-1, \frac{\alpha}{2}\%} \frac{s}{\sqrt{n}} \right)[/tex]
Confidence interval =[tex]\left( 6.92 \pm t_{12-1, \frac{5}{2}\%} \frac{1.832}{\sqrt{12}} \right)[/tex]
The value of [tex]t_{11, \frac{5}{2}\%[/tex]=[tex]2.201[/tex]
Confidence interval = [tex]( 6.92 \pm 2.201}\times \frac{1.832}{\sqrt{12}}) \right)[/tex]
Confidence interval = [tex]( 6.92 - 2.201}\times 0.5288 ,6.92 + 2.201}\times \0.5288) \right)[/tex]
Confidence interval = [tex](6.92-1.1639,6.92+1.1639)[/tex]
Confidence interval = [tex]\fbox{(5.8, 8.1)}[/tex]
The [tex]95\%[/tex] confidence interval gives us an idea that [tex]95\%[/tex] chances of the true mean or population mean lies in the interval.
A. We are [tex]95\%[/tex] confident that the interval from [tex]5.8[/tex] to [tex]8.1[/tex] actually contains the true mean of attractiveness rating of all adult females.
B. The results tell nothing about the population of all adult females, because participants in speed dating are not a representative sample of the population of all adult females.
C. We are confident that [tex]95\%[/tex] of all adult females have attractiveness ratings between [tex]5.8[/tex] and [tex]8.1[/tex].
[tex]\fbox{\text{Option A}}[/tex] is Correct as we are [tex]95\%[/tex] confident that the interval from [tex]5.8[/tex] to [tex]8.1[/tex] actually contains the true mean of attractiveness rating of all adult females.
Option B is not correct as the confidence interval tells us about the population mean.
Option C is not correct as the individual rating can be more than [tex]5.8[/tex] or less than the [tex]8.1[/tex].
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Answer Details:
Grade: College Statistics
Subject: Mathematics
Chapter: Confidence Interval
Keywords:
Probability, Statistics, Speed dating, Females rating, Confidence interval, t-test, Level of significance , Normal distribution, Central Limit Theorem, t-table, Population mean, Sample mean, Standard deviation, Symmetric, Variance.
The confidence interval for the population mean attractiveness rating of all adult females is 5.8 to 8.1, and we are 95% confident that this interval contains the true mean attractiveness rating.
In this study of speed dating, male subjects were asked to rate the attractiveness of their female dates on a scale from 1 (not attractive) to 10 (extremely attractive). A sample of attractiveness ratings was provided: 7, 7, 3, 8, 5, 6, 6, 9, 9, 8, 6, 9. The objective is to construct a confidence interval with a 95% confidence level to estimate the true mean attractiveness rating of all adult females.
The calculated confidence interval is 5.8 to 8.1. This means that we are 95% confident that the interval from 5.8 to 8.1 contains the true mean attractiveness rating of all adult females. The margin of error, represented by the range of the interval, provides a level of precision in our estimation.
The confidence interval suggests that the true mean attractiveness rating for all adult females falls within the specified range. It does not provide an exact value for the mean, but it indicates a plausible interval within which the true mean is likely to be found. Additionally, the confidence interval does not imply a causal relationship, but rather a statistical estimate based on the observed sample.
Problem 2 Previous Problem Problem List Next Problem (1 point) Determine ifv is an eigenvector of the matrix A No 1 5 0 0 7 0 -2 0 5 A = ,v= 5 2 0 1 No 2. 0 -4-8 -1 2 8 4 C A = ,v= -4 -4-4 -1 3. Yes -1 2 0 8 0 -3 0 5 A = -6 2 5 1 Note: You can earn partial credit on this problem. Submit Answers Preview My Answers You have attempted this problem 1 time. Your overall recorded score is 33%. You have 1 attempt remaining.
Problem 4 Previous Problem Problem List Next Problem (1 point) The matrix -6 A = -9 -5 k has two distinct real eigenvalues if and only if k
Analyze the diagram below and complete the instructions that follow.
Find the value of x and the value of y.
A. x=4, y=8
B. x=7 , y=4√2
C. x=4√3 , y= 7√2
D. x=7√3 , y=4√2
Answer:
D. x=7√3 , y=4√2
Step-by-step explanation:
Step 1: Lets assume an imaginary line from A to B to make the triangle ABC( (refer to the attached image).
AB = 4
BD = 3
Step 2: Find the value of y by the sin formula.
opposite = 4
adjacent = BC
hypotenuse = AC
sin (angle) = opposite/hypotenuse
sin (45) = 4/AC
√2/2 = 4/AC
AC = y = 4√2
Step 3: Find the value of x
Tan (45) = opposite/adjacent
1 = 4/CB
CB = 4
x = CB + BD
x = 4 + 3
x = 7
Therefore, the answer is D where x = 7 and y = 4√2
!!
According to the data reported by the New York State Department of Health regarding West Nile Virus for the years 2000-2004, the least squares line equation for the number of reported dead birds (x) versus the number of human West Nile virus cases (y) is ŷ = −10.2638 + 0.0491x. If the number of dead birds reported in a year is 844, how many human cases of West Nile virus can be expected? (Round your answer to the nearest whole number.)
Final answer:
Using the least squares line equation given, by substituting 844 for the number of reported dead birds, we calculate an expected number of approximately 31 human cases of West Nile virus.
Explanation:
To estimate the number of human cases of West Nile virus based on the number of reported dead birds using the least squares line equation ŷ = −10.2638 + 0.0491x, we need to substitute x with the number of reported dead birds. In this case, x = 844.
The calculation would be:
ŷ = −10.2638 + (0.0491 × 844)
This simplifies to:
ŷ = −10.2638 + 41.4474
Which further simplifies to:
ŷ = 31.1836
After rounding the result to the nearest whole number, we get that approximately 31 human cases of West Nile virus can be expected.
The expected number of human cases of West Nile virus when 844 dead birds are reported is approximately 31, calculated using the given least squares line equation.
To predict the number of human West Nile virus cases when 844 dead birds are reported, we use the least squares line equation:
Y = -10.2638 + 0.0491xHere, x represents the number of dead birds, which is 844.
We substitute x into the equation:Y = -10.2638 + 0.0491 * 844
First, calculate the product:0.0491 * 844 = 41.4404
Next, add the product to the intercept:Y = -10.2638 + 41.4404
Y = 31.1766
Rounding to the nearest whole number, the expected number of human cases of West Nile virus is 31.
A company provided the following data: Selling price per unit: 60 Variable cost per unit 20 Total fixed costs 400,000 HOw many units must be sole to earn a profit of $40,000?
Answer:
The company needs to sell 9000 units in order to turn a profit of $40,000
Step-by-step explanation:
Hello, great question. These types are questions are the beginning steps for learning more advanced Algebraic Equations.
From the question we can get some important hints before creating our formula. First the Selling Price will be profit so it will be a positive number, but both unit cost and fixed costs are losses so they will be negative values in our formula. Also our formula will depend on the amount sold which we can represent as the variable x. With these hints we can create our formula as the following
[tex](60x-20x)-400,000 = y[/tex]
Where:
x is the amount of units created and soldy is the total profit after selling x-unitsNow that we have our formula the question asks how many units need to be sold in order to earn a profit of $40,000. We can calculate this by replacing the $40,000 with y and solving for x like so,
[tex](60x-20x)-400,000 = 40,000[/tex] .... add 400,000 on both sides
[tex]40x= 360,000[/tex] ... divide both sides by 40
[tex]x= 9000[/tex]
The company needs to sell 9000 units in order to turn a profit of $40,000
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Please help me with this
Answer:
Yes, the triangles are congruent by Hypotenuse angle congruence
Step-by-step explanation:
we know that
The Hypotenuse-Angle Congruence states that If the hypotenuse and an acute angle of a right triangle are congruent to the hypotenuse and corresponding acute angle of another right triangle, then the triangles are congruent.
In this problem
The hypotenuse and an acute angle of the right triangle in the left are congruent to the hypotenuse and corresponding acute angle of the right triangle in the right
therefore
The triangles are congruent by Hypotenuse angle congruence
Problem Page
A ball is thrown vertically upward. After t seconds, its height h (in feet) is given by the function h(t) = 120t - 16t^2 . After how long will it reach its maximum height?
Do not round your answer.
Answer: After 3.75 seconds
Step-by-step explanation:
For a Quadratic function in the form [tex]f(x)=ax^2+bx+c[/tex], if [tex]a<0[/tex] then the parabola opens downward.
Rewriting the given function as:
[tex]h(t) = - 16t^2+120t[/tex]
You can identify that [tex]a=-16[/tex]
Since [tex]a<0[/tex] the the parabola opens downward.
Therefore, we can conclude that the x-coordinate of the vertex is the time in seconds in which the ball will reach the maximum height. You can find it with this formula:
[tex]t=\frac{-b}{2a}[/tex]
Substitute values, we get
[tex]t=\frac{-120}{2(-16)}=3.75\ seconds[/tex]
Final answer:
The time at which the ball reaches its maximum height is calculated using the vertex formula for a quadratic equation. In this case, the ball achieves maximum height after 3.75 seconds.
Explanation:
The function given is a quadratic equation in the form h(t) = 120t - 16t2, representing the height of a ball thrown vertically upward after t seconds. To find the time when the ball reaches its maximum height, we need to determine the vertex of the parabola represented by this equation.
The standard form of a quadratic equation is ax2 + bx + c. In this form, the time to reach the maximum height occurs at t = -b/(2a). Applying this to our equation, where a = -16 and b = 120, we calculate t = -120/(2*(-16)) = 120/32 = 3.75 seconds. Therefore, the ball reaches its maximum height after 3.75 seconds.
You deposit $400 each month into an account earning 5% interest compounded monthly. a. How much will you have in the account in 30 years? b. How much total money will you put into the account? c. How much total interest will you earn?
a) After 30 years, the amount in the account will be approximately $499,355.18.
b) The total money deposited over 30 years will be $144,000.
c) The total interest earned over 30 years will be approximately $355355.18.
We have,
Given:
Monthly deposit: $400
Interest rate: 5% (expressed as a decimal, 0.05)
Time: 30 years (in months, 30 * 12 = 360 months)
a.
To calculate the amount in the account after 30 years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = Amount in the account
P = Initial deposit (first deposit)
r = Annual interest rate
n = Number of times interest is compounded per year
t = Time in years
In this case:
P = $400 x 360 = $144000
r = 0.05
n = 12 (compounded monthly)
t = 30
Substituting the values into the formula:
A = 144000(1 + 0.05/12)^(12 * 30)
A ≈ $499,355.18
b.
The total money deposited can be calculated by multiplying the monthly deposit by the number of months:
Total Money Deposited = Monthly deposit * Number of months
Total Money Deposited = $400 * 360
Total Money Deposited = $144,000
c.
The total interest earned can be calculated by subtracting the total money deposited from the amount in the account:
Total Interest Earned = Amount in the account - Total Money Deposited
Total Interest Earned = $499,355.18 - $144,000
Total Interest Earned ≈ $355355.18
Therefore,
After 30 years, the amount in the account will be approximately $499,355.18.
The total money deposited over 30 years will be $144,000.
The total interest earned over 30 years will be approximately $355355.18.
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To find the future value of the account after 30 years, use the compound interest formula. Multiply the monthly deposit by the number of months to find the total money put into the account. The total interest earned is found by subtracting the total money put into the account from the future value.
Explanation:To calculate the future value of the account, we can use the formula for compound interest: A = P(1 + r/n)^(nt), where A is the future value, P is the principal (initial deposit), r is the interest rate in decimal form, n is the number of times interest is compounded per year, and t is the number of years.
a. Plugging in the values, we have [tex]A = 400(1 + 0.05/12)^(12*30)[/tex]. Using a calculator, the future value after 30 years will be approximately $1000.40.
b. To find the total money put into the account, we multiply the monthly deposit by the number of months. In this case, it will be $[tex]400 * 12 * 30 = $144,000.[/tex]
c. The total interest earned can be found by subtracting the total money put into the account from the future value. In this case, it will be $[tex]1000.40 - $144,000 = -$143,999.60.[/tex]
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Find the remainder when a is divided by m
a = 207^321 + 689! ; m=7
Answer with explanation:
⇒689!=689×688×687×686×........×7×6×5×4×3×2×1
So, 689! is divisible by 7.
We have to find the remainder when,
[tex]\frac{a}{m}=\frac{207^{321}+689!}{7}\\\\=\frac{207^{321}}{7}+\frac{689!}{7}\\\\=\frac{(210-3)^{321}}{7}+0\\\\=\frac{_{0}^{321}\textrm{C}\times (210)^{321}\times (3)^{0} -_{1}^{321}\textrm{C}\times (210)^{320}\times (3)^{1}+_{2}^{321}\textrm{C}\times (210)^{319}\times (3)^{2}-----(-1)\times _{321}^{321}\textrm{C}\times (321)^{0}\times (3)^{321}}{7}\\\\ \text{As ,210 is divisible by 7}\\\\=\frac{ (3)^{321}}{7}[/tex]
⇒[tex]3^7[/tex] ,when divided by 7, gives remainder 3.
[tex]\frac{ (3)^{321}}{7}=\frac{ (3)^{45\times 7+6}}{7}\\\\=3+\frac{3^6}{7}\\\\=3+1\\\\=4[/tex]
So,Remainder when
[tex]\frac{207^{321}+689!}{7}[/tex] is 4.
A coin is tossed four times What is the probability of getting four heads? (1 mark) a) b) What is the probability of getting exactly work. (2 marks) two heads? Be sure to show your What is the probability of not getting two heads? Be sure to show your work.
1. A coin is tossed four times. What is the probability of getting four heads?
Each toss has a 1/2 chance of getting a head.
So the chance of getting all four heads can be calculated as :
[tex]1/2\times1/2\times1/2\times1/2=1/16[/tex]
2. A coin is tossed four times. What is the probability of getting two heads?
Each toss can have 2 results, so 4 flips will have [tex]2^{4}[/tex] or 16 results.
Getting two heads means getting two tails also. So, we can get the number of times two heads come = [tex]\frac{4!}{2!2!}[/tex] = 6
We can write the groups like - {HHTT,HTHT,HTTH,THHT,THTH,TTHH}
So, the required probability is : 6/16 or 3/8.
3. Not getting two heads means getting 3 tails and 1 head or all tails.
Probability of having all tails = [tex]1/2\times1/2\times1/2\times1/2=1/16[/tex]
Probability of one head(1st trial) and three tails = 1/16
Probability of one head (2nd trial) and three tails (the 1st, 3rd and 4th trials) = 1/16
Probability of one head (3rd trial) and three tails (the 1st, 2nd and 4th trials) = 1/16
Probability of one head (4th trial) and three tails (the 1st, 2nd and 3rd trials) = 1/16
So, the total probability showing only one or none head and at least three tails = [tex]1/16+1/16+1/16+1/16+1/16=5/16[/tex]
According to the label, a can of soup holds an average of 307 grams, with a standard deviation of 4.1 grams. Assuming a normal distribution, what is the probability that a can will be sold that holds more than 308 grams?
Answer: 0.4052
Step-by-step explanation:
Given : Mean : [tex]\mu=\text{307 grams}[/tex]
Standard deviation : [tex]\sigma = \text{4.1 grams}[/tex]
The formula for z -score :
[tex]z=\dfrac{x-\mu}{\sigma}[/tex]
For x=308 ,
[tex]z=\dfrac{308-307}{4.1}=0.24390\approx0.24[/tex]
The p-value = [tex]P(z>0.24)=1-P(z<0.24)[/tex]
[tex]=1-0.5948348= 0.4051652\approx0.4052[/tex]
Hence, the probability that a can will be sold that holds more than 308 grams =0.4052.
Which philosophical assumptions are reflected in quantitative research designs? a. transformative b. constructivist c. postpositivist d. pragmatist
Answer:
postpositivist
Step-by-step explanation:
Of the all four options "post positivist" philosophical assumption are reflected in quantitative research designs
"post positivist" believes that, theory, hypothesis, background knowledge,believes and values of researchers can alter the actual observations. Post positivist consider both quantitative and qualitative methods to be a valid form of approaches unlike "positivist" which emphasize only on quantitative methods.
The philosophical assumption reflected in quantitative research designs is postpositivist. Postpositivism believes in the existence of an objective reality that can be studied through empirical observation and measurement.
Explanation:The philosophical assumption reflected in quantitative research designs is postpositivist. Postpositivism is a philosophical stance that believes in the existence of an objective reality that can be studied through empirical observation and measurement. Quantitative research designs aim to gather numerical data that can be analyzed statistically to uncover patterns and relationships in the data. A postpositivist approach to research values objectivity, generalizability, and the use of rigorous methodologies.
Learn more about Philosophical assumptions in quantitative research designs here:https://brainly.com/question/13012373
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The time between unplanned shutdowns of a power plant has an exponential distribution with a mean of 30 days. Find the probability that the time between two unplanned shutdowns is between 18 and 24 days.
The probability that the time between two unplanned shutdowns of a power plant is between 18 and 24 days, following an exponential distribution with a mean of 30 days, is approximately 0.0033.
For an exponential distribution, the probability density function (PDF) is given by:
[tex]\[ f(x) = \lambda e^{-\lambda x} \][/tex]
where [tex]\( \lambda \)[/tex] is the rate parameter, and for an exponential distribution, [tex]\( \lambda = \frac{1}{\text{mean}} \)[/tex].
Given a mean of 30 days, [tex]\( \lambda = \frac{1}{30} \)[/tex].
Now, to find the probability that the time between two unplanned shutdowns is between 18 and 24 days, integrate the PDF over this interval:
[tex]\[ P(18 < X < 24) = \int_{18}^{24} \lambda e^{-\lambda x} \, dx \]\[ P(18 < X < 24) = \int_{18}^{24} \frac{1}{30} e^{-\frac{x}{30}} \, dx \][/tex]
Let's complete the calculations step by step.
[tex]\[ P(18 < X < 24) = \int_{18}^{24} \frac{1}{30} e^{-\frac{x}{30}} \, dx \]\[ P(18 < X < 24) = -\frac{1}{30}e^{-\frac{x}{30}} \Big|_{18}^{24} \][/tex]
Now, evaluate the integral at the upper and lower limits:
[tex]\[ P(18 < X < 24) = -\frac{1}{30} \left(e^{-\frac{24}{30}} - e^{-\frac{18}{30}}\right) \]\[ P(18 < X < 24) = -\frac{1}{30} \left(e^{-0.8} - e^{-0.6}\right) \][/tex]
Using a calculator:
[tex]\[ P(18 < X < 24) \approx -\frac{1}{30} \left(0.44933 - 0.54881\right) \]\[ P(18 < X < 24) \approx -\frac{1}{30} \times (-0.09948) \]\[ P(18 < X < 24) \approx 0.003316 \][/tex]
Therefore, the probability that the time between two unplanned shutdowns is between 18 and 24 days is approximately 0.0033 (rounded to four decimal places).
It is given that y is directly proportional to x.
What is the constant of variation?
Answer:
The constant of variation is -4
Step-by-step explanation:
If y is directly proprtional to x, then we write:
[tex]y \propto \: x[/tex]
If we introduce the constant of proportionality or variation k, then we obtain:
[tex]y = kx[/tex]
When x=1, y=-4 (We can choose any ordered pair from the table)
[tex] - 4 = k(1)[/tex]
[tex]k = - 4[/tex]
Therefore the constant of variation is -4.
Answer:
-4
Step-by-step explanation:
Find the coordinates of the vertex for the parabola defined by the given quadratic function f(x) = (x + 2)^2 + 2 a) (0,2) b) (2.0) c) (-2.2) d) (-2,-2) e) none
Answer:
(-2,2)
Step-by-step explanation:
Let's find the answer.
Because a tangent line for a parabola function is equal to 0 only at its vertex then:
[tex]f(x)=(x+2)^{2}+2[/tex]
[tex]f'(x)=2*(x+2)[/tex]
[tex]f'(x)=2x+4[/tex] so then:
[tex]f'(x)=0[/tex] when
[tex]0=2x+4[/tex]
[tex]-2=x[/tex]
For x=-2 f(x) is:
[tex]f(x)=(x+2)^{2}+2[/tex]
[tex]f(1)=(-2+2)^{2}+2[/tex]
[tex]f(x)=2[/tex]
In conclusion, the vertex of the given parabola is (-2,2), so the answer is C. Although in your answer is reported as (-2.2) but I think was a typing mistake.
4. Without performing the divisions, determine whether the integers 176521221 and 149235678 are divisible by 9 or 11. - Obtain the following aralization . The int e nted
Final answer:
By using the divisibility rules for 9 and 11, we can conclude that the integer 176521221 is divisible by 9 but not by 11, and the integer 149235678 is divisible by 9 but not by 11.
Explanation:
To determine whether the integers 176521221 and 149235678 are divisible by 9 or 11 without performing the division, we can use divisibility rules:
Divisibility by 9: Add up all the digits in the number. If the sum is divisible by 9, then the original number is also divisible by 9.
Divisibility by 11: Take the alternating sum of the digits. If the result is divisible by 11 (including 0), the original number is divisible by 11.
Divisibility of 176521221 by 9
1+7+6+5+2+1+2+2+1 = 27; Since 27 is divisible by 9, 176521221 is also divisible by 9.
Divisibility of 176521221 by 11
(1-7+6-5+2-1+2-2+1) = -3; Since -3 is not divisible by 11, 176521221 is not divisible by 11.
Divisibility of 149235678 by 9
1+4+9+2+3+5+6+7+8 = 45; Since 45 is divisible by 9, 149235678 is also divisible by 9.
Divisibility of 149235678 by 11
(1-4+9-2+3-5+6-7+8) = 9; Since 9 is not divisible by 11, 149235678 is not divisible by 11.
A market research firm conducts telephone surveys with a 41% historical response rate. a. What is the probability that in a new sample of 400 telephone numbers, at least 135 individuals will cooperate and respond to the questions? In other words, what is the probability that the sample proportion will be at least 135/400 = 0.3375?
Answer:
probability is 0.778
Step-by-step explanation:
Given data in question
success of probability (p) = 41% = 0.41
no of sample (n) = 400
individual = 150
to find out
probability that the sample proportion will be at least 135/400
solution
first we calculate the mean i.e
mean = p × n
mean = 400 × 0.41
mean = 164
now we calculate standard deviation = [tex]\sqrt{400(0.41) 0.59}[/tex]
standard deviation = 9.83666
we know P(X ≥ 135) = P(Z ≥ (150 - 164)/9.83666)
P(X ≥ 135) = P(Z ≥ (-1.42324)
from table 1 find corresponding probability
P(X ≥ 135) = 1 - P(Z ≥ (-1.42324)
= 1 - 0.9222 = 0.778
probability is 0.778
A car's velocity changes at a rate of 36 miles per hour in 0.5 hour.
What is its acceleration, in miles/hour2?
(Note: Do not specify units in your answer. Your answer must be only a number.)
Answer:
72
Step-by-step explanation:
In order to find the acceleration we need first to defined it, so:
acceleration=((final velocity)-(initial velocity))/time interval
[tex]a=(vf-vi)/dt[/tex]
But (vf-vi) actually represents the velocity change, so (vf-vi)/dt represents the velocity change rate. This means that in our case:
[tex]a=(36miles/hour)/(0.5hours)[/tex]
[tex]a=72miles/hour^2[/tex]
In conclusion the acceleration is [tex]a=72miles/hour^2[/tex], without units just 72.
Use a truth table to determine which of the following is true for this proposition:
(p & (q v p)) → ~p
Question 1 options:
The proposition is never true.
The proposition is false when p is false.
The proposition is false if p is true.
The proposition is always true.
Answer:
The proposition is false if p is true.
Step-by-step explanation:
I made the truth table in the picture, to fill it you need to know:
v : only is false when both propositions are false.
^ : only is true when both propositions are true.
⇒: only is false when the left proposition is true and the right proposition is false.
So, the answer is the third option.
The truth table analysis shows that the proposition (p & (q \/ p)) → ~p is a tautology, meaning it is always true regardless of the truth values of p and q.
To determine the truth value of the proposition (p & (q \/ p)) \/ ~p, we need to construct a truth table and evaluate the proposition for all possible truth values of p and q.
Truth Table Construction
Let's go step by step:
Construct two initial columns for the variables p and q with their possible truth values.
Create a column for the sub-proposition (q \/ p), which is true if either q or p (or both) is true.
Construct the column for the main proposition (p & (q \/ p)) which is true if both p is true and the previous sub-proposition is true.
Determine the negation of p (~p), which is true when p is false.
Finally, combine the results to evaluate the column for the entire proposition (p & (q \/ p)) \/ ~p, using the implication operator (→), whose result is only false when the antecedent is true and the consequent is false.
After evaluating, we find that the proposition is always true, making it a tautology. Therefore, the original proposition (p & (q \/ p)) → ~p is always true irrespective of the truth values of p and q.
Which type of conic section is described by the following equation?
Answer:
C. Hyperbola opening up and down
Step-by-step explanation:
A graph tells the tale.
___
The term with the positive coefficient identifies the axis along which the hyperbola opens. Here, that is the y-axis, so the figure opens up and down.
The minus sign between the squared terms indicates it is a hyperbola, rather than a closed curve (ellipse or circle). The fact that both terms are squared indicates it is not a parabola.
Find an equation of the line that passes through the given points. (Let x be the independent variable and y be the dependent variable.) (3, 9) and (4, 14)
Answer:
y=5x-6
Step-by-step explanation:
Hello
let´s see , we have P1(3,9) and P2(4.14)
first let's find its slope
[tex]m=\frac{y2-y1}{x2-x1} = \frac{14-9}{4-3}[/tex]
[tex]m=\frac{5}{1} \\m=5[/tex]
the slope is 5.
[tex]y-y_{0} = m(x-x_{0} )\\\\using P1\\\\ y-9 = 5(x-3)\\\\y=5x-15+9\\\\y=5x-6[/tex]
where x is the independent variable and y is the dependent variable
Have a great day.
To find the equation of the line that passes through (3, 9) and (4, 14), calculate the slope and use the point-slope form, resulting in the equation y = 5x - 6 in slope-intercept form.
To find an equation of the line that passes through the points (3, 9) and (4, 14), we will first calculate the slope (m) of the line using the formula: m = (y2 - y1) / (x2 - x1). Substituting the given points into the formula, we have m = (14 - 9) / (4 - 3) = 5. With the slope known, we can use one of the points and the slope to write the equation in point-slope form, which is y - y1 = m(x - x1). Using the point (3, 9), the equation becomes y - 9 = 5(x - 3). To put this into slope-intercept form, we simplify to get y = 5x - 6.
An exam worth 269 points contains 36 questions. Some questions are worth 7 points, and the others are worth 8 points. How many 7 point and 8 point questions are on the test?
Answer:
There are 19 questions worth 7 points.
There are 17 questions worth 8 points.
Step-by-step explanation:
Assign variables:
Let x = number of questions worth 7 points.
Let y = number of questions worth 8 points.
First we deal with the number of questions.
There are 36 questions, so our first equation is:
x + y = 36
Now we deal with the points.
x questions worth 7 points each are worth 7x points.
y questions worth 8 points each are worth 8y points.
The total worth of all the questions is 7x + 8y.
The total worth of the exam is 269, so our second equation is
7x + 8y = 269
We have a system of 2 equations in 2 variables.
x + y = 36
7x + 8y = 269
Let's use the substitution method to solve the system of equations.
Solve the first equation for x.
x + y = 36
x = 36 - y
Substitute 36 - y in for x in the second equation.
7x + 8y = 269
7(36 - y) + 8y = 269
Distribute the 7.
252 - 7y + 8y = 269
Combine like terms.
252 + y = 269
Subtract 252 from both sides.
y = 17
There are 17 questions worth 8 points.
x + y = 36
x + 17 = 36
x = 19
There are 19 questions worth 7 points.
Check:
What does 19 questions at 7 points each and 17 questions at 8 points each add to?
19 * 7 + 17 * 8 = 133 + 136 = 269
The points add to 269, so our answer is correct.