In the simple random sample, the probability that at least half of the students have brown eyes is 0.400
How to calculate probability of an event at a particular time?Probability is defined as the chance of occurrence of an event.
Probability is defined as follows:
P(E)=[tex]\frac{no of required outcome}{total of possible outcomes}[/tex]
The given parameters are:
The sample size= 30 students
Number with brown eye=40%
40% x 30 = [tex]\frac{40}{100} * 30[/tex]
=12
This means that there 12 students out of 30 that have brown eyes.
Applying the probability formula
[tex]\frac{12}{30}[/tex]= 2/5
In conclusion 0.400 of the students have brown eyes.
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Y-2=1/3(x+6) write in standard form
Answer:
2x+3y = -15
Step-by-step explanation:
Consider a rectangle that is inscribed with its base on the x-axis and its upper corners on the parabola y=C−x2, with C>0. What are the width and height that maximize the area of this rectangle? What is that maximal area?
The width of the rectangle that maximizes the area is C/2 and the height of the rectangle that maximizes the area is C/2. The maximal area of the rectangle is C2/4.
How do you determine a maximum area?The gap between a rectangle's length and width must be as small as possible for its area to be as large as possible. Therefore, the length in this scenario must be ceiling (perimeter / 4) and the width will be floor (perimeter /4). The greatest size of a rectangle with a given perimeter is therefore equal to ceiling(perimeter/4) * floor(perimeter/4)
What does "maximum area" mean?The average of the maximum areas of land planted to a specific crop over the Relevant Period is referred to as the "maximum area for a particular crop."
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Show that if f is a function from S to T, where S and T are finite sets with |S| > |T |, then there are elements s₁ and s₂ in S such that f(s₁) = f(s₂), or in other words, f is not one-to-one.
The function f : S--> T is not a one to one function
Given :
f : S --> T
S and T are finite sets with |S| > |T|
To proof : f is not one-one function
Let us assume for the sake of contradiction that f is one to one function
Let n and m be positive integers such that |S| = n and |T| = m.
Note that these integers need to exist as S and T are finite sets
n > m
Let S = {s1 , . . . , sn} and T = { t1 , . . . , tm}
Without loss of generality , we can assume that f(si) = ti , for i = 1, 2, 3 ....
as each element needs to have a unique image ( since , f is one to one ) and we can rename the element t1 , . . . , tm if the order of the elements didnt match up the images.
Since , n > m we have a term sm+1 while we do not have a term t m+1 .
This implies that sm+1 needs to have a same image as some sk
f(sm+1) = f(sk) = tk
However , f(sm+1) = f(sk) = tk is then in contradiction with the fact that f is one-to-one.
Since , we derive a contradiction our assumption that f is one-to-one is incorrect and thus f is not one-to-one
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Find the value of x. Hint: use the Exterior Angle Theorem
The value of x using Exterior Angle Theorem is 9.
What is the exterior angle of theorem?
The measure of an exterior angle is equal to the sum of the measures of the two opposite(remote) interior angles of the triangle, according to the external angle theorem. A triangle contains three internal angles, all of which add up to 180 degrees. This theorem is applied to each of the outer angles, which total six. As they constitute a linear pair of angles, take note that an exterior angle is supplementary to the neighbouring interior angle. Exterior angles are those that are created between a polygon's side and its extended neighbouring side.Interior 2 angle = exterior angle
32° + (6x -2)° = 9x + 3
32° + 6x -2° = 9x + 3
30° - 3° = 9x - 6x
3x = 27°
x = 9
Hence, the value of x using Exterior Angle Theorem is 9.
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If AC=26, find BC. in simplest radical from
BC=
The simplest radical from BC = 2/3.
Step by Step Explanation:AC = 26 and BC = 10.
Therefore, BC = 26 - 10 = 14.
we need to find the simplest radical from BC = 14. A simple radical is a fraction with no common factors other than 1 and itself. The simplest radical from BC = 14 is 2/3
What is simplest radical ?Simply put, simplifying a radical eliminates the need to find any further square roots, cube roots, fourth roots, etc. Additionally, it entails eliminating any radicals from a fraction's denominator.
The radical consists of three separate parts:
RadicandDegree SymbolThe Complete Question is :
AC = 26 and BC = 10 find the simplest radical from BC =
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Solve for Input of Function Given Output
Given } h(x)=-3 x-5 solve for x when } h(x)=-2
Step-by-step explanation:
put the value of h(x) in the function like in the above figure.
Consider the following inequality:
−2(2z−3)≥2z+24
Step 1 of 2 : Write the solution using interval notation.
The required solution of the given inequality is z ≤ 9.
Given that,
To determine the solution of the inequality −2(2z−3)≥2z+24.
Inequality can be defined as the relation of the equation containing the symbol of ( ≤, ≥, <, >) instead of the equal sign in an equation.
Here,
−2(2z−3)≥2z+24
-4z + 6 ≥ 2z + 24
-2z ≥ 18
z ≤ 9
Thus, the required solution of the given inequality is z ≤ 9.
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Find the 10th term of the geometric sequence whose common ratio is 1/3 and whose first term is 7.
The 10th term of the geometric sequence whose common ratio is 1/3 and whose first term is 7 is [tex]\frac{7}{19683}[/tex].
What is geometric sequence?
A unique kind of sequence is a geometric sequence. Every term in the series (apart from the first term) is multiplied by a fixed amount to determine the following term. In other words, we multiply the current phrase in the geometric sequence by a constant term (called the common ratio), and then divide the current term in the geometric sequence by the same common ratio to discover the previous term in the geometric sequence.
nth term of geometric series
a(n) = a(1) * r^(n-1)
You are given a(1) = 7, r = 1/3 and n = 10.
a(10) = 7 * 1/3^(10-1)
[tex]7\left(\frac{1}{3}\right)^{10-1}$$[/tex]
Apply exponent rule: [tex]$\left(\frac{a}{b}\right)^c=\frac{a^c}{b^c}$[/tex]
[tex]$$\begin{aligned}& \left(\frac{1}{3}\right)^{10-1}=\frac{1^{10-1}}{3^{10-1}} \\& =7 \times \frac{1^{10-1}}{3^{10-1}}\end{aligned}$$[/tex]
[tex]$$\begin{aligned}& 1^{10-1}=1 \\& =7 \times \frac{1}{3^{10-1}} \\& 3^{10-1}=19683 \\& =7 \times \frac{1}{19683}\end{aligned}$$[/tex]
Convert element to fraction: [tex]$\quad 7=\frac{7}{1}$[/tex]
[tex]=\frac{7}{1} \times \frac{1}{19683}$$[/tex]
Apply the fraction rule: [tex]$\frac{a}{b} \times \frac{c}{d}=\frac{a \times c}{b \times d}$[/tex]
[tex]=\frac{7 \times 1}{1 \times 19683}$$[/tex]
Multiply the numbers: [tex]$7 \times 1=7$[/tex]
[tex]=\frac{7}{1 \times 19683}$$[/tex]
Multiply the numbers: [tex]$1 \times 19683=19683$[/tex]
[tex]=\frac{7}{19683}[/tex]
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1. A basketball player made 12 out of 15 free throws she attempted. She wants to know how many consecutive free throws she would have to make to raise the percent of successful free throws to 85%. (a) Write an equation to represent this situation. (b) Solve the equation. How many consecutive free throws would she have to make to raise her percent to 85%? Answer:
Basketball player have to make 5 successful consecutive throws to make to raise her percent to 85%.
What is percentage?Percentage is a part of the whole number. It is denoted by % sign.
1 %= 1/100.
Given that,
Basketball player makes 12 out of 15 free throws she attempted.
The percentage of successful throws = (12/15)x100 = 75%
Let n consecutive free throws she has to make to increase the percentage of successful throws to 85%,
Implies that,
(12+n)/ (15+n) = 85/100
(12+n)/ (15+n) = 17 /20
240 + 20n = 255 + 17n
3n = 15
n = 5
Basketball player have to make 5 successful consecutive throws to make to raise her percent to 85%.
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Teacher's Salary The average teacher's salary in a particular state is $54,137.
If the standard deviation is $10,450, find the salaries corresponding to the following z scores.
The salary corresponding to z=1 is $64587 if the average teacher's salary in a particular state is $54,137.
What is z-score?A Z-score is a metric that quantifies the connection between a value and the mean of a set of values. The Z-score is measured as the standard deviations from the mean. If the Z-score is 0, A data point's score is the same as the mean score. In statistics, a raw score's value that deviates or surpasses the mean of the phenomenon being observed or measured is referred to as the standard score. Raw scores above the mean are given positive standard scores, whilst raw values below the mean are given negative standard ratings.
The pay is 1 standard deviation above the mean, according to a z score of 1.
Therefore, the salary for a z-score of 1 is:
$54,137 + 1($10,450) = $64587
Therefore, the salary corresponding to z=1 is $64587
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PLEASE ASAP HURRY PLEASE
Mario set a goal to run 170 miles this month to prepare for a marathon. So far this month, he has run 85 miles. Write and solve an equation to show how many miles Mario has left to run this month to reach his goal.
A. m over 85 equals 170; m = 14,450 miles
B. m − 85 = 170; m = 255 miles
C. m + 85 = 170; m = 85 miles
D. 85m = 170; m = 2 miles
The equation to show how many miles Mario has left to run this month to reach his goal is C. m + 85 = 170; m = 85 miles.
How to illustrate the equation?An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario. It is vital to note that an equation is a mathematical statement
In this situation, Mario set a goal to run 170 miles this month to prepare for a marathon and far this month, he has run 85 miles.
Let the remaining miles be m.
This will be illustrated as:
m + 85 = 170
Collect like terms
m = 170 - 85
m = 85
In conclusion, the correct option is C
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A standard normal distribution has the following characteristics O the mean and the variance are both equal to 1 O the mean and the variance are both equal to 0 O the mean is equal to the variance the mean is equal to 0 and the variance is equal to 1 the mean is equal to the standard
A standard normal distribution's characteristics are its mean is equal to 0 and the standard deviation is 1. Thus, the variance is equal to 1.
What is a standard normal distribution?A normal distribution that has a mean value of 0 and a standard deviation or a variance of 1 is said to be a standard normal distribution.
I.e., μ = 0 and σ² = 1
This is also called z-distribution.
Calculation:A standard normal distribution has μ = 0 and σ² = 1.
So, the probability of a normal random variable is calculated by using a z-score.
The z-score value is calculated by the formula
z = (X - μ)/σ
Where mean (μ) and standard deviation (σ) for the variable X
By using the standard normal distribution tables with the z-score and probabilities, the required values are calculated.
So, we can conclude that the major characteristics of a standard normal distribution are mean = 0 and variance = 1.
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For each of the statements below, is it true with Correlation, Regression, Both, or Neither? Please explain. Thank You!
1. Requires a measure for both variables'individual variances
2. Can be tested for statistical significance
3. Provides a way to predict a specific value of one variable (such as weight) from the value of another variable (such as height)
1. Correlation is a bivariate analysis that measures the strength of association between two variables and the direction of the relationship. Regression is a statistical method to determine the strength and character of the relationship between one dependent variable and a series of other variables (known as independent variables). So, both correlation and regression require a measure for both variables individual variances.
2. We can test for the statistical significance of a correlation coefficients by performing a hypothesis test on the correlation coefficients. And it's also possible to perform hypothesis tests on the regression slope on the values which is being estimated using a regression analysis. So, both correlation and regression can be tested for statistical significance.
3. Correlation helps us to test the strength of association between two variables. But regression helps us to predict one of the variables from the other. So, it is true for a regression. It is only regression which provides a way to predict a specific value of one variable from the value of another variable.
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Which of the following conclusions do you draw if the p-value is not small enough to convincingly rule out chance?
a. We cannot reject the null hypothesis.
b. We accept the null hypothesis.
c. We are convinced that chance alone produced the observed results.
d. We accept the alternative hypothesis.
The conclusion is option A, we cannot reject the null hypothesis.
What is hypothesis?An assumption or concept is given as a hypothesis for the purpose of debating it and testing if it might be true.
The null hypothesis cannot be rejected for the entire population if your sample is not sufficiently incompatible with it, which can be determined if your P value is small enough.
Therefore, we can not reject the hypothesis.
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Stephen's current average weekly net pay is $354.76. The van he wants to purchase has monthly payments of $325.00. Which inequality correctly shows the comparison between 15% of Stephen's average monthly net pay and the monthly van payment? (4 points)
$212.86 ≥ $325.00
$212.86 ≤ $325.00
$230.59 ≤ $325.00
$230.59 ≥ $325.00
Stephen's current average weekly net pay is $354.76. The van he wants to purchase has monthly payments of $325.00. the inequality that correctly shows the comparison between 15% of Stephen's average monthly net pay and the monthly van payment is $212.86 ≤ $325.00
How to find the inequalityInformation given in the question
Stephen's current average weekly net pay is $354.76
The van he wants to purchase has monthly payments of $325.00.
the inequality that compares 15% of Stephen's average monthly net pay and the monthly van payment = ?
A weekly pay of $354.76 getting the monthly pay is
= 4 * $354.76
= $1419.04
15% of the monthly pay
= 0.15 * $1419.04
= 212.856
= $212.86
This amount is less than $325.00 which is monthly payment for the van hence $212.86 ≤ $325.00
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can yall help me with this question
A barn is in the shape of a pentagonal prism with the dimensions shown. The volume of the barn is 9072 cubic feet. Find the dimensions of each half of the roof.
(Help I cannot solve this-)
According to the given information the dimensions of each of the roof is 12 feet.
Mathematical concepts include volume.The amount the three-dimensional space that's also occupied is measured in volume. To define it quantitatively, a variety of imperial either Us or metric system, in addition to SI-derived units such as the cubic meter but instead liter), are widely utilized. A symbiotic relationship exists between volume and length (cubed).
What does mathematic volume mean?Mathematics refers to volume as the measurement of internal space in a specific 3D object. A fish tank, for instance, is three feet long, one foot broad, and two feet high. Expanding the length, that width, and the height results in the volume, which is equal to six when 3x1x2 is used. Consequently, the fish tank can hold 6 cubic feet of water.
Briefing:According to the given picture
a = 18 ft,
b = 8ft,
c = 36ft and h = x
[tex]\begin{matrix}V=a\times b\times c+\frac{a\times h}{2}\times c\\\9072=18\times8\times36+\frac{18\times x}{2}\times36\\9072=5184+324\times x\\\x=12\\\end{matrix}[/tex]
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Answer: 15
Step-by-step explanation: I submitted 12 and that was wrong, answer is 15
What is the percent of increase from 24 to 42?
Write your answer using a percent sign (%).
Submit
Answer:
42.86%
Explanation:
First, we subtract the two numbers.
42 - 24 = 18
Now we divide this to the original number.
18 / 42 = 0.4285714286
Multiply by 100:
42.85714286
So, the percent increase is approximately 42.86%
what is the rate of change of the function y=7/4x-2
Answer:
7/4
Step-by-step explanation:
The rate of change is the slope or the change in y over the change in x.
Mariam has $520 to spend at a bicycle store for some new gear and biking outfits. Assume all prices listed include tax.
She buys a new bicycle for $311.60.
She buys 4 bicycle reflectors for $7.18 each and a pair of bike gloves for $19.94.
She plans to spend some or all of the money she has left to buy new biking outfits for $76.57 each.
What is the greatest number of outfits Mariam can buy with the money that's left over?
Answer: 2
Step-by-step explanation:
a varies inversely as the square of b. If a is 1 when b is 3, find a when b is 5
The distance it takes to stop a car varies directly as the square of the speed of the car. If it takes 112 feet for a car traveling at 40 miles per hour to stop, what distance is required for a speed of 65 miles per hour?
*
a. The inverse variation relationship between a and b can be expressed as a = k/b^2, where k is a constant. We are given that a is 1 when b is 3, so we can substitute these values into the equation to find k: 1 = k/(3^2). Solving for k, we get k = 9.
Substituting this value of k back into the equation a = k/b^2, we can find a when b is 5: a = 9/(5^2) = 9/25 = 0.36. Therefore, a is 0.36 when b is 5.
b. To find the distance it takes for a car traveling at 65 miles per hour to stop, we can use the equation for direct variation: d = kv^2, where d is the distance, v is the speed, and k is a constant. We are given that it takes 112 feet for a car traveling at 40 miles per hour to stop, so we can substitute these values into the equation to find k: 112 = k(40^2). Solving for k, we get k = 0.0056.
Substituting this value of k back into the equation d = kv^2, we can find the distance it takes for a car traveling at 65 miles per hour to stop: d = 0.0056(65^2) = 2256 feet. Therefore, it takes 2256 feet for a car traveling at 65 miles per hour to stop.
Hannah wants to have $ 5500 to help pay for a new deck in 10 years. If she wants to put her money into an account earning 5.5% interest compounded continuously, how much should she invest now, so that she will have $ 5500 in 10 years?
Payment amount =
[tex]~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$5500\\ P=\textit{original amount deposited}\\ r=rate\to 5.5\%\to \frac{5.5}{100}\dotfill &0.055\\ t=years\dotfill &10 \end{cases} \\\\\\ 5500=Pe^{0.055\cdot 10} \implies \cfrac{5500}{e^{0.055\cdot 10}}=P\implies 3173.22\approx P[/tex]
what is the answer to this? solve for x
4x+4=24
Answer: x=5
Step-by-step explanation:
4x+4-4=24-4
4x=20
x=5
Answer…………………………………….
What is the answers to this?
Answer:
5x^2
4x
-20x
Step-by-step explanation:
5x(x) = 5x^2
4(x)= 4x
5x(-4)= -20x
a plumber cuts 2 3/4 feet from pipe. The pipe is now 13 1/4 feet long. Write and solve an equation of to determine the original length if the pipe
Answer:
x - 2 [tex]\frac{3}{4}[/tex] = 13 [tex]\frac{1}{4}[/tex]
x = 16
Step-by-step explanation:
x - 2 [tex]\frac{3}{4}[/tex] = 13 [tex]\frac{1}{4}[/tex]
x - [tex]\frac{11}{4}[/tex] = [tex]\frac{53}{4}[/tex] Add [tex]\frac{11}{4}[/tex] to both sides
x = [tex]\frac{53}{4}[/tex] + [tex]\frac{11}{4}[/tex]
x = [tex]\frac{64}{4}[/tex]
x = 16
Answer:
[tex]x-2 \frac{3}{4}=13 \frac{1}{4}[/tex]
(where x is the original length of the pipe).
Original length of the pipe = 16 feet
Step-by-step explanation:
Let x be the original length of the pipe.
Given a plumber cuts 2 3/4 feet from a pipe and now has a pipe that is 13 1/4 feet long, the equation that models this is:
[tex]\boxed{ x-2 \frac{3}{4}=13 \frac{1}{4}}[/tex]
To determine the length of the original pipe, solve the equation for x.
Add 2 3/4 to both sides of the equation:
[tex]\implies x-2 \frac{3}{4}+2 \frac{3}{4}=13 \frac{1}{4}}+2 \frac{3}{4}[/tex]
[tex]\implies x=13 \frac{1}{4}}+2 \frac{3}{4}[/tex]
When adding mixed numbers, partition the mixed numbers into fractions and whole numbers, and add them separately:
[tex]\implies x=13 +\dfrac{1}{4}}+2 +\dfrac{3}{4}[/tex]
[tex]\implies x=13 +2 +\dfrac{1}{4}}+\dfrac{3}{4}[/tex]
[tex]\implies x=15 +\dfrac{1+3}{4}[/tex]
[tex]\implies x=15 +\dfrac{4}{4}[/tex]
[tex]\implies x=15 +1[/tex]
[tex]\implies x=16[/tex]
Therefore, the original length of the pipe was 16 feet.
Here is a data set:
1 2 3 3 4 4 4 4 5 5 6 7
What happens to the mean and standard deviation of the data set when the 7 is changed to a 70?
The mean of the dataset increases and the standard deviation of the data set increases when the 7 is changed to a 70
How to determine the effect of changing a data element?From the question, we have the following parameters that can be used in our computation:
Dataset: 1 2 3 3 4 4 4 4 5 5 6 7
As a general rule:
When a data item is changed (increased), the mean is increasedWhen a data item is changed (increased), the standard deviation is increasedWhen a data item is changed (decreased), the mean is decreasedWhen a data item is changed (decreased), the standard deviation is decreasedTo prove the above statements, the mean and the standard deviations are calculated using online calculators
So, we have
Original dataset
1, 2, 3, 3, 4, 4, 4, 4, 5, 5, 6, 7
Mean = 4
Standard deviation = 1.58
New dataset
1, 2, 3, 3, 4, 4, 4, 4, 5, 5, 6, 70
Mean = 9.25
Standard deviation = 18.36
This means that changing 7 to 70 would increase the mean and the standard deviation
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An architect is designing a home and needs to create a rectangular bedroom. The bedroom must be 425 ft2 and must be 8 ft longer than it is wide. What are the width and length of the bedroom?
The width of the bedroom is 17 feet. The length of the bedroom is 17 + 8 = 25 feet.
What is the area of the rectangle?
The area of the rectangle is length x breadth. The diagonals of the rectangle divide it into two equivalent right-angled triangles. Therefore, the area of the rectangle will be equal to the sum of the area of these two triangles.
Let w be the width of the bedroom and l be the length of the bedroom.
The width of the bedroom is 8 feet shorter than the length, so the length is w + 8.
The area of the bedroom is the product of its width and length, or w * (w + 8).
We can set up the equation 425 = w * (w + 8) and solve for w.
First, we can rewrite the equation as 425 = w^2 + 8w.
Then, we can complete the square by adding (8/2)^2 = 16 to both sides:
425 + 16 = w^2 + 8w + 16
441 = w^2 + 8w + 16
We can rewrite the left side of the equation as (w + 4)^2, which gives us:
(w + 4)^2 = 441
Taking the square root of both sides gives us:
w + 4 = 21
Subtracting 4 from both sides gives us:
w = 17
Therefore, the width of the bedroom is 17 feet. The length of the bedroom is 17 + 8 = 25 feet.
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Help! Write the slope-intercept form given the graph. PLEASE I NEED A ANSWER
The linear equation written in the slope-intercept form is:
y = (-3/5)*x
The correct option is C.
How to write the line on the graph?A general linear equation is written as:
y = a*x + b
Where a is the slope and b is the y-intercept.
Here we can see that the line crosses through the poin (0, 0), so the y-intercept is 0.
b = 0
y = a*x + 0
y = a*x
To find the value of a, we can use another point on the graph.
We can see that the linear equation passes through (5, - 3), replacing these values:
-3 = a*5
-3/5 = a
Then the linear equation is just:
y = (-3/5)*x
The correct option is C.
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give the component from the following vectors shown
Answer:
[tex](-3, 4)[/tex]
Step-by-step explanation:
The horizontal component is [tex]-3[/tex] and the vertical component is [tex]4[/tex]
The component (-3, 4) from the given vectors are shown in the graph.
What are vectors linearly independent and dependent?Let A = v 1, v 2,..., v r be a collection of vectors from Rn. If r > 2 and at least one of the vectors in A can be expressed as a linear combination of the others, A is said to be linearly dependent. The rationale for this description is straightforward: at least one of the vectors is dependent (linearly) on the others. If no vector exists in A, the set is said to be linearly independent. It is also usual to state "the vectors are linearly dependent (or independent)" rather than "the set comprising these vectors is linearly dependent (or independent)."
We have been given that the graph in the question
Here v = -3i + 4j
This means the component (-3, 4) of the provided vectors.
Therefore, the required component (-3, 4) from the provided vectors are depicted in the graph.
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