The image coordinates of N'M'O' are (−9, −2), (−6, −1), and (−9, −5).
Translating the triangle 5 units leftTo translate the preimage 5 units to the left, we need to subtract 5 from the x-coordinates of all three vertices.
So the new coordinates of N', M', and O' will be:
N'((-4)-5, (-2)) = (−9, −2)
M'((-1)-5, (-1)) = (−6, −1)
O'((-4)-5, (-5)) = (−9, −5)
Therefore, the image coordinates of N'M'O' are (−9, −2), (−6, −1), and (−9, −5).
So the correct answer is N′(−9, −2), M′(−6, −1), O′(−9, −5).
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3. The t test for two independent samples - Two-tailed example
“Bullying,” according to noted expert Dan Olweus, “poisons the educational environment and affects the learning of every child.” Bullying and victimization are evident as early as preschool, with the problem peaking in middle school. Suppose you are interested in the emotional well-being of not only the victims but also bystanders, bullies, and those who bully but who are also victims (bully-victims). You decide to measure depression in a group of victims and a group of bully-victims using a 26-item, 3-point depression scale. Assume scores on the depression scale are normally distributed and that the variances of the depression scores are the same among victims and bully-victims.
The group of 30 victims scored an average of 21.5 with a sample standard deviation of 10 on the depression scale. The group of 27 bully-victims scored an average of 25.8 with a sample standard deviation of 9 on the same scale. You do not have any presupposed assumptions about whether victims or bully-victims will be more depressed, so you formulate the null and alternative hypotheses as:
H0
: μvictims
– μbully-victims
= 0
H1
: μvictims
– μbully-victims
≠ 0
You conduct an independent-measures t test. Given your null and alternative hypotheses, this is a test. To use the Distributions tool to find the rejection region, you first need to set the degrees of freedom. The degrees of freedom is .
The critical t-scores that form the boundaries of the rejection region for α = 0.01 are ± .
In order to calculate the t statistic, you first need to calculate the standard error under the assumption that the null hypothesis is true. In order to calculate the standard error, you first need to calculate the pooled variance. The pooled variance is s2p
= . The standard error is s(M1 – M2)
= .
The t statistic is .
The t statistic in the rejection region. Therefore, the null hypothesis is . You conclude that victims have a different mean depression score than bully-victims. Thus, it can be said that these two means are different from one another.
The test statistics do not lie in the rejection so the null hypothesis does not reject.
How to solveHere we have the following information:
[tex]\bar{x}_{1}=25.3, n_{1}=25, s_{1}=9, \bar{x}_{2}=20.5, n_{2}=23, s_{2}=8[/tex]
Here degree of feedom will be
[tex]df=n_{1}+n_{2}-2=25+23-2=46[/tex]
The critical values of t are: +/- 2.687
Rejection region:
If t < -2.687 and t > 2.687, reject H0
Pooled variance is :
[tex]s^{2}_{p}=\frac{(n_{1}-1)s_{1}^{2}+\left ( n_{2}-1 \right )s_{2}^{2}}{n_{1}+n_{2}-2}=72.8696[/tex]
The standard error is
[tex]s_{M_{1}-M_{2}}=s_{p}\sqrt{\frac{1}{n_{1}}+\frac{1}{n_{2}}}=2.4664[/tex]
and t-statistics will be
[tex]t=\frac{\bar{x}_{1}-\bar{x}_{2}}{s_{p}\sqrt{\frac{1}{n_{1}}+\frac{1}{n_{2}}}}=1.946[/tex]
The test statistics do not lie in the rejection so the null hypothesis does not reject.
You cannot conclude...
not
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Write three dollars and 65 cents
as an improper fraction (and then reduce).
Answer:
300/65
Step-by-step explanation:
Answer:
3 65/100 then the simplified version is 13/20
Step-by-step explanation:
Read the following text from a student essay. How can the writer best improve his or
her organization?
Ponies are a type of horse, but there are significant differences between ponies and
horses. Ponies are generally shorter than horses. Ponies also tend to live longer than
horses. Horses are considered to be over fifty-eight inches tall, and ponies are less
than that. Horses usually live to be twenty-five to thirty years old. Most ponies live
to be thirty-five or even forty.
by adding missing commas
moving the first sentence to the end of the paragraph
by moving the first sentence to the second paragraph
by reordering sentences to keep the related ideas together
The writer can best improve their organization by reordering sentences to keep related ideas together.
Who is called writer?
Writers are individuals who use written words to communicate ideas, stories, or information to a particular audience. They may work in various fields such as journalism, creative writing, copywriting, technical writing, or academic writing. Writers can be novelists, poets, essayists, screenwriters, playwrights, and more, and their work can take many forms, such as books, articles, blogs, scripts, and speeches. Writing is a skill that can be developed and honed through practice, and good writers are able to engage and captivate their readers with their words.
Here,
The writer can best improve their organization by reordering sentences to keep related ideas together. Here's a possible reorganization of the text:
Ponies and horses have significant differences. Horses are considered to be over fifty-eight inches tall and usually live to be twenty-five to thirty years old. In contrast, ponies are generally shorter than horses, with a height of less than fifty-eight inches, and they tend to live longer, often up to thirty-five or even forty years.
This revision keeps the sentences that relate to each other together, creating a clear and logical progression of ideas. Additionally, it removes the redundant statement of defining ponies as a type of horse, which is already well-known information.
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ΔQRS is an isosceles triangle. What is the length of RT¯¯¯¯¯
R
T
? Round to the nearest hundredth. Enter your answer in the box.
[tex]\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies o=\sqrt{c^2 - a^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{11}\\ a=\stackrel{adjacent}{6}\\ o=\stackrel{opposite}{RT} \end{cases} \\\\\\ RT=\sqrt{ 11^2 - 6^2}\implies RT=\sqrt{ 121 - 36 } \implies RT=\sqrt{ 85 }\implies RT\approx 9.22[/tex]
Hurit Imala works 40 hours a week as a clerk in a local store. She earns $8.50 an hour. Assuming she is paid for 52 weeks annually, what is her gross annual pay?
Answer:
Hurit Imala's gross annual pay is $17,680
Step-by-step explanation:
Hurit Imala works 40 hours a week, so her weekly pay would be:
40 hours/week x $8.50/hour = $340/week
To find her annual pay, we need to multiply her weekly pay by the number of weeks in a year:
$340/week x 52 weeks/year = $17,680/year
Therefore, Hurit Imala's gross annual pay is $17,680.
Given the parent function f(x)=√x and a new function g(x)=√x+6+3.
Select from the drop-down menus to correctly describe the changes on the graph from f(x) to g(x)
1. The graph will shift 6 units ___
UP , DOWN , LEFT , RIGHT
2. and 3 units ____
UP , DOWN , LEFT , RIGHT
Answer:
up down
Step-by-step explanation:
NEED HELP!! 9.1 Puzzle Time
What Do You Get When You Cross a Computer With a Lifeguard?
6. Using Pythagoras Theorem the value of x = 99. 7, The value of x is 102.56. 8. The triangle is a right triangle. 9. The triangle is acute. 10. The triangle is acute. 11. The value of x is 32.28. 12. The value of x is 40.
What is Pythagoras Theorem?The relationship between the sides of a right triangle is explained by the Pythagorean theorem, a fundamental mathematical theorem. The square of the hypotenuse's length, the longest side in a right triangle, is said to be equal to the sum of the squares of the lengths of the other two sides.
6. For a = 20, b = 99 using the Pythagoras Theorem we have:
x² = a² + b²
x² = 20² + 99²
x² = 9801
x = 99
7. For a = 60, b = 91 we have:
x² = 60² + 91²
x² = 10521
x ≈ 102.56
8. To determine whether the triangle is acute, obtuse, or right we check for using the Pythagoras Theorem.
a = 20, b = 21, and c = 29
Here,
20² + 21² = 841
29² = 841
Hence, the triangle is right.
9. For a = 15, b = 19, and c = 24. We have:
15² + 19² = 556
24² = 576
The triangle is acute.
10. For a = 11, b = 23, and c = 26. We have:
11² + 23² = 650
26² = 676
The triangle is acute.
11. Using the Pythagoras Theorem we have:
x² = 53² - 45²
x² = 1044
x ≈ 32.28
The value of x is 32.28
12. x² = 41² - 9²
x² = 1600
x = 40
The value of x is 40.
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Answer:
Step-by-step explanation:
Knowing that the given sides are congruent, find the perimeter of the
triangle. *Congruent is EQUAL
9x-3
4x+7
Answer:
Step-by-step explanation:
9x-3=4x+7
+3
9x=4x+10
-4x=-4x
5x=10
divide the 5 by 10 which equals 2.
x=2
Find the value of x:
With regards to the above geometry problems the value of x are given below.
a) Here x = 15
b) here x = 28
These are solved using proportions.
How does proportion help to solve the above problems?Proportion helps to solve the above problems by setting two ratios equal to each other and cross-multiplying to solve for the unknown variable, which satisfies the ratio relationship between the two quantities.
a)
To solve for x, we can cross-multiply the fractions and simplify:
x/20 = 9/12
Cross-multiply:
12x = 9 * 20
Simplify:
12x = 180
x = 15
Therefore, the solution to the equation x/20 = 9/12 is x = 15.
b)
To solve for x, we can cross-multiply the fractions and simplify:
15/(x-3) = 18/(x+2)
Cross-multiply:
15(x+2) = 18(x-3)
Simplify:
15x + 30 = 18x - 54
Subtract 15x from both sides:
30 = 3x - 54
Add 54 to both sides:
84 = 3x
Divide both sides by 3:
x = 28
Therefore, the solution to the equation 15/(x-3) = 18/(x+2) is
x = 28.
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The question is In the image
the probability of the marble landing on either a 00 or black slot is 19/38 or approximately 0.5.
how to solve probability?
There are 38 possible outcomes for a single spin of the American roulette wheel. Out of these 38 slots, two are labeled 0 and 00, and half of the remaining 36 slots are red and half are black.
Therefore, the probability of the marble landing on a black slot is 18/38 or 9/19. This is because there are 18 black slots out of a total of 38 slots.
Similarly, the probability of the marble landing on a 00 slot is 1/38.
To find the probability of the marble landing on either a 00 or black slot, we can add the probabilities of these two events. That is,
P(00 or black) = P(00) + P(black)
= 1/38 + 9/19
= (1 + 18)/38
= 19/38
Therefore, the probability of the marble landing on either a 00 or black slot is 19/38 or approximately 0.5.
It is important to note that while the probability of winning on a single bet in roulette may seem attractive, the game has a high house edge, meaning that the odds are in favor of the casino. Therefore, it is important to gamble responsibly and within one's means.
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find the products AB and BA to determine whether B is the multiplicative inverse of A.
B is not the multiplicative inverse of A.
Multiplicative inverse matrix:The multiplicative inverse matrix, also known as the inverse matrix or simply the inverse, is a matrix that when multiplied by a given matrix, results in the identity matrix. The identity matrix is a square matrix with ones on the diagonal and zeros elsewhere.
Here we have
[tex]A = \left[\begin{array}{cc}3&-2&\\0&-3&\end{array}\right][/tex] [tex]B = \left[\begin{array}{cc}-1&2&\\0&-4&\end{array}\right][/tex]
Product of A and B
[tex]AB = \left[\begin{array}{cc}3&-2&\\0&-3&\end{array}\right] \times \left[\begin{array}{cc}-1&2&\\0&-4&\end{array}\right][/tex]
[tex]AB = \left[\begin{array}{cc}3(-1) + (-2)(0) &3(2) + (-2)(-4)&\\0 + 0 &0 +(-3)(-4)&\end{array}\right][/tex]
[tex]AB = \left[\begin{array}{cc}-3 &14&\\0 &12&\end{array}\right][/tex]
Product of B and A
[tex]BA = \left[\begin{array}{cc}-1&2&\\0&-4&\end{array}\right] \times \left[\begin{array}{cc}3&-2&\\0&-3&\end{array}\right][/tex]
[tex]BA = \left[\begin{array}{cc}1(3) + 2(0)&-1(-2)+2(-3)\\0(3)+0 &0(-2)+(-4)(-3) \end{array}\right][/tex]
[tex]BA = \left[\begin{array}{cc}-3&-4\\0&12\end{array}\right][/tex]
Here AB ≠ BA ≠ I
Therefore,
B is not the multiplicative inverse of A.
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Complete Question given in the picture
State the amplitude, period, midline and an equation involving the sine function for the
graph shown below using a horizontal shift between 0 and 2pi
Amplitude:
Period:
Midline: y =
f(x) =
The amplitude is 2 units.
The period is 2π units.
f(x) = 2 sin(x - π/2)
What is sine function?An oscillation that repeats itself repeatedly in many natural events is described by the sine function, which is a mathematical function. It is described as the proportion of a right triangle's hypotenuse to the side that faces an angle. The typical notation for the sine function is sin(x), where x represents the angle.
Amplitude:
The distance between the graph's midline and its maximum or minimum point is known as the amplitude. The midline in the following graph is located at y=0, midway between the greatest value of 2, and the minimum value of -2. The amplitude is therefore 2 units.
Period:
The distance among two consecutive graph points with the same value and direction is known as the period. The above graph repeats itself every 2π units of x and has one complete cycle between x=0 and x=2π. The duration is therefore 2π units.
Midline:
The midline, also referred to as the average of the highest and minimum values, traverses the graph's centre horizontally. The x-axis or the line y=0 serves as the midline in the presented graph.
It is possible to write the sine function equation for the provided graph with a horizontal shift between 0 and 2 as:
f(x) = 2 sin(x - π/2)
The graph fluctuates up and down near the midline, hence the sine function is utilised. The highest value occurs at x=π/2, which is π/2 units to the right of x=0, and the graph continues every 2π units of x, therefore the horizontal shift is π/2. The sine function multiplies the amplitude of two units.
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A line has a slope of -2 and passes through the point (-2, -3). Write its equation in slope-
intercept form.
The slope-intercept form of a line's equation is y = mx + b, where m is the slope of the line and b is the y-intercept. We can use the given slope and point to solve for the y-intercept and write the equation in slope-intercept form.
Given: Slope (m) = -2 and point (-2, -3)
Step 1: Use the point-slope form of a line's equation to find the equation of the line in point-slope form:y - y1 = m(x - x1) (where x1,y1 are the coordinates of the given point)y - (-3) = -2(x - (-2))y + 3 = -2(x + 2)Step 2: Simplify the equation by distributing the -2:y + 3 = -2x - 4Step 3: Solve for y by subtracting 3 from both sides of the equation:y = -2x - 7Therefore, the equation of the line in slope-intercept form is y = -2x - 7.Mary is planning to buy a mobile phone that costs $500. She can choose any of five different payment plans with varying simple interest rates and periods:
plan 1: 6% for 10 months
plan 2: 8% for 12 months
plan 3: 10% for 14 months
plan 4: 12% for 18 months
plan 5: 14% for 12 months
Which plan offers the lowest monthly payments?
As a result, Plan 4's $38.89 monthly premium is the lowest.
How to find the lowest monthly payments ?The monthly premium you pay for health insurance. You typically have to pay additional fees for your health care in addition to your premium, such as a deductible, copayments, and coinsurance.
(P + Simple Interest) / (500 + 58.33) / 14 = $42.02 is the formula for the monthly payment.
Plan 4: P = $500
t = 18/12 years, and r = 0.12
Simple interest equals $500 * 0.12/* (18/12) = $90.
(P + Simple Interest) / t = ($500 + $90) / 18 = $38.89 is the monthly payment.
Plan 5: P = $500
t = 12/12 years, and r = 0.14.
Simple interest is equal to $500 * 0.14 * (12/12) = $70.
(P + Simple Interest) / t = ($500 + $70) / 12 = $47.50 is the amount due each month.
As a result, Plan 4's $38.89 monthly premium is the lowest.
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The vertices of a rectangle are plotted.
A graph with both the x and y axes starting at negative 8, with tick marks every one unit up to 8. The points negative 5 comma 2, 4 comma 2, negative 5 comma negative 4, and 4 comma negative 4 are each labeled.
What is the area of the rectangle?
15 square units
30 square units
45 square units
54 square units
The area of the rectangle is d. 54 square units.
What is rectangle?A rectangle is a closed two-dimensional geometry with four sides, four corners, and four right angles (90°). A rectangle's opposite sides are equal and parallel. Because a rectangle is a 2-D form, it has two dimensions: length and width. The length of the rectangle is the longer side, while the width is the shorter side.
The rectangle has two pairs of parallel sides, so its area can be calculated by multiplying the length of one pair of parallel sides by the length of the other pair of parallel sides.
From the given points, we can see that the length of one pair of parallel sides of the rectangle is:
4 - (-5) = 9 units
And the length of the other pair of parallel sides of the rectangle is:
2 - (-4) = 6 units
Therefore, the area of the rectangle is:
9 units × 6 units = 54 square units.
So the area of the rectangle is d. 54 square units.
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Geometry task!!!
Please help for all three , a) , b) , and c)
The power emitted by the star's surface is much greater than the power generated by its interior.
How to explain the informationa) The power generated by the star's interior can be calculated using the formula for the volume of a sphere:
V = (4/3)πr³
V = (4/3)π(7x10^8)³ ≈ 1.41x10^27 cm³
Multiplying this volume by the power generated per cubic centimeter, we get:
P(interior) = 3x10^-7 watts/cm^3 x 1.41x10^27 cm^3 = 4.23x10^20 watts
The power emitted by the star's surface can be calculated using the formula for the surface area of a sphere:
A = 4πr²
Substituting r = 7x10^8 cm, we get:
A = 4π(7x10^8)^2 ≈ 6.16x10^18 cm^2
Multiplying this area by the power emitted per square centimeter, we get:
P(surface) = 6,000 watts/cm² x 6.16x10^18 cm^2 = 3.70x10^22 watts
We can see that the power emitted by the star's surface is much greater than the power generated by its interior.
b) Following the same process as in part (a), we get:
V = (4/3)π(5x10^12)³ = 5.24x10^38 cm³
P(interior) = 3x10^-7 watts/cm^3 x 5.24x10^38 cm^3 = 1.57x10^32 watts
A = 4π(5x10^12)^2 ≈ 3.14x10^26 cm²
P(surface) = 6,000 watts/cm^2 x 3.14x10^26 cm^2 = 1.88x10^30 watts
Again, we see that the power emitted by the star's surface is much greater than the power generated by its interior. However, the difference between the two quantities is much smaller in this case compared to the previous case.
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the lenghth of a picture frame is 7 inches more than th width. For what values of x is the perimeter of the picture frame greater than 154 inches
Answer:
x > 35
Step-by-step explanation:
Let's denote the width of the picture frame as "x" inches.
According to the problem, the length of the picture frame is 7 inches more than the width, so it can be expressed as "x + 7" inches.
The perimeter of the picture frame can be found by adding up the lengths of all four sides, which is given by:
Perimeter = 2*(length + width)
Substituting the values of length and width in terms of x, we get:
Perimeter = 2*(x + 7 + x)
Perimeter = 4x + 14
Now we can set up an inequality to find the values of x for which the perimeter is greater than 154 inches:
4x + 14 > 154
Subtracting 14 from both sides, we get:
4x > 140
Dividing both sides by 4, we get:
x > 35
Therefore, the values of x for which the perimeter of the picture frame is greater than 154 inches are x > 35.
Suppose a researcher is trying to understand whether people who purchase fast-food hamburgers would be willing to pay more if the hamburger comes with a free whistle. Prior research suggests the mean amount customers say they are willing to pay for a hamburger is μ = 3.68 and σ = 0.70. The researcher plans to conduct a study very similar to the prior research by selecting a sample of customers and asking them how much they are willing to pay for the hamburger. Before asking, however, she will tell the customer about the free whistle that will come with the hamburger. The researcher’s null hypothesis is that the mean amount the customers are willing to pay when they are told about the free whistle is no different than the amount customers are willing to pay when they are not told they will receive a free whistle. The researcher’s sample of 49 customers has a sample mean of M = 4.04. The test statistic for this sample mean is 3.60. Using a significance level of α = .05, which of the following is the most appropriate statement of the result?
a. Telling customers they will receive a free cookie with their hamburger had a significant effect on the amount they say they are willing to pay for a hamburger, z = 3.68, p < .05.
b. Telling customers they will receive a free cookie with their hamburger did not have a significant effect on the amount they say they are willing to pay for a hamburger, z = 4.04, p > .05.
c. Telling customers they will receive a free cookie with their hamburger had a significant effect on the amount they say they are willing to pay for a hamburger, z = 3.60, p < .05.
d. Telling customers they will receive a free cookie with their hamburger did not have a significant effect on the amount they say they are willing to pay for a hamburger, z = 3.60, p < .05
Compute the estimated Cohen’s d to measure the size of the treatment effect.
Note: Cohen’s d is always reported as a positive value and reflects the proportion of the standard deviation that is affected by the treatment.
Estimated Cohen’s d =
Using Cohen’s criteria, the estimated Cohen’s d indicates that telling customers they will receive a free whistle is associated with a in the amount they are willing to pay for the hamburger.
The correct answer is option c: Telling customers they will receive a free whistle with their hamburger had a significant effect on the amount they say they are willing to pay for a hamburger, z = 3.60, p < .05.
What is standard deviation?A statistical measure known as the standard deviation depicts how variable or dispersed a set of data is. It is determined by taking the square root of the variance, which is the sum of the squared deviations from the data set mean. While a large standard deviation suggests that the data points are more dispersed, a small standard deviation suggests that the data points tend to be close to the mean. It can be used to assess the variability between different data sets and is frequently used as a gauge of a data set's consistency or reliability.
Given, level of significance = 0.05.
n = 49 and sample > 30
Thus, using z-score we have:
z = 4.04 - 3.68 / (0.70/7) = 3.60
Now, p-value = 0.000318
Now, for P < 0.05 we have:
cohens D = 4.04 - 3.67 / 0.70 = 0.51
This shows a medium increase.
Hence, the correct answer is option c: Telling customers they will receive a free whistle with their hamburger had a significant effect on the amount they say they are willing to pay for a hamburger, z = 3.60, p < .05.
The estimated Cohen’s d is given as:
Cohen’s d = (M - μ) / σ
The sample standard deviation is not given, so we cannot calculate the exact value of Cohen's d.
The sample standard deviation will determine the estimated Cohen's d in this situation, although if it is greater than 0.2, it might be regarded as having a small effect size.
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find the values of X and Y
The values of x and y for the right triangle are 4 and 7.21
How to evaluate for the values of x and y for the triangleThe perpendicular height of the right triangle divides the triangle in two triangles with the same proportions as the original triangle.
by Pythagoras, the hypotenuse for the bigger of the two triangles is calculated as;
√(6² + 9²) = 10.82
the angle opposite the side length 6 for triangle with hypotenuse 10.82 and the angle opposite the side length x for triangle with hypotenuse y are the same by proportion, so:
x/6 = 6/9 {opposite/adjacent}
x = 36/9 {cross multiplication}
x = 4
also;
4/y = 6/10.52 {opposite/hypotenuse}
y = 42.08/6
y = 7.21
Therefore, the values of x and y for the right triangle are 4 and 7.21
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A central angle of a circle whose radius is 14 centimeters subtends an arc whose length is 7pi/15 centimeters. What is the radian measure of the central angle?
π/30 R is the radian measure of the central angle.
What is a circle, exactly?
The collection of all points in the plane that make up a circle are all equally spaced from a certain point known as the "centre," making the form a closed two-dimensional shape.
The reflection symmetry line is created by all lines that traverse the circle. Additionally, it is symmetrical in rotation around the centre at all angles.
Total circle circumference would be π d = 28 π
this arc is a fraction of the total
7π/15 / 28π x 2π = π/30 R
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At West Point School District, enrollment increased from 320 students in 2019 to 225 students in 2020. What is the percent of change in enrollment? Round to the nearest percent.
Answer:95
Step-by-step explanation: cause 320 - 225 = 95
11. A local grocery store has 7 different kinds of hot sauce that you would love try.
However, you only have enough money to purchase 5 of the different flavors. How
many of the flavors of hot sauce are possible for you to purchase?
we are selecting 5 flavors out of 7 without regard to order. The number of combinations of 7 things taken 5 at a time is given by: C(7,5) = 21
what is combinations ?
Combinations, on the other hand, refer to the selection of objects from a set without considering their order. For example, the combinations of 2 letters from the set "ABC" are "AB", "AC", and "BC". The order of the letters in each combination does not matter, so "AB" and "BA" are considered the same combination.
In the given question,
This is a combination problem, since we are selecting 5 flavors out of 7 without regard to order. The number of combinations of 7 things taken 5 at a time is given by:
C(7,5) = 7! / (5! * 2!) = (76543) / (54321) = 21
Therefore, you can purchase 21 different combinations of 5 flavors of hot sauce
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URGENT - A triangle is shown in the imagine below. Answer the questions related to it.
Answer:
a) sin(β) = 7/6 is false for any β
b) angle β is not a real angle
Step-by-step explanation:
You want to use the Sine Law to show that a triangle with sides of lengths 6 and 10 and a smallest angle of 44.5° is impossible.
a) BetaThe Sine Law tells you side lengths are proportional to the sines of their opposite angles.
sin(β)/10 = sin(44.5°)/6
sin(β) = 10(0.7)/6
sin(β) = 7/6
The angle β does not exist. The maximum value of the sine function is 1. There are no angles for which the sine is greater than 1.
b) ImpossibleThe triangle is impossible because angle β cannot exist.
In effect, the angle 44.5° is too large, or side 10 is too long, or side 6 is too short for the figure to be a triangle.
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Additional comment
In the realm of complex numbers, β ≈ π/2 -0.569618i radians, about (90 -32.64i)°. You cannot draw this complex angle with your real pencil.
a) For any, sin(β) = 1.17 is false.
b) Angle (β) is not a true angle.
What is trigonometry?In the branch of mathematics known as trigonometry, the relationships between the sides and angles of triangles are examined.
It involves the study of trigonometric functions like sine, cosine, tangent, cotangent, secant, and cosecant that describe the connections between the sides and angles of a right triangle.
(a) Using the Sine Law, we have:
sin(β)/10 = sin(44.5°)/6
Multiplying both sides by 10, we get:
sin(β) = (10/6)sin(44.5°)
sin(β) = 1.17
However, this is impossible since the sine of an angle can never be greater than 1. Therefore, there is no value of β that satisfies the equation, and we cannot find the value of B.
(b) The fact that the sine of β is greater than 1 means that there is no angle whose sine is equal to that value.
Therefore, there is no possible angle for β that can satisfy the given conditions of the triangle.
This means that the triangle is impossible and cannot exist with the given side lengths and angle measures.
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A boat is heading towards a lighthouse, where Lamonte is watching from a vertical distance of 141 feet above the water. Lamonte measures an angle of depression to the boat at point � A to be 21 ∘ ∘ . At some later time, Lamonte takes another measurement and finds the angle of depression to the boat (now at point � B) to be 57 ∘ ∘ . Find the distance from point � A to point � B. Round your answer to the nearest foot if necessary.
The distance from point A to point B is 812 feet.
What is triangle?
A triangle is a form of polygon with three sides; the intersection of the two longest sides is known as the triangle's vertex. There is an angle created between two sides. One of the crucial elements of geometry is this.
Certain fundamental ideas, including the Pythagorean theorem and trigonometry, rely on the characteristics of triangles. The angles and sides of a triangle determine its kind.
Here lines AC and ED are parallel. So alternate angles are equal. Now the corresponding angles in triangle ADC and BDC.
In Δ ADC ,
=> tan 9 = opposite / adjacent = 141/AC
=> AC = 141/ tan9= 890.2389.
Now In ΔBDC,
=> tan 61 = 141/BC
=> BC = 141/tan 61 = 78.1575
Now distance AB = AC - BC = 890.2389 - 78.1575 = 812 feet.
Hence the distance from point A to point B is 812 feet.
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The following are equivalent radicals
3√3 = √27
-
3√6 = √54
3√7 = √63
What would be an equivalent form of 3√11 ? Explain
how you know.
Debbie saves $900 each summer with her summer job. She plans to work the same job for the next four summers. She wants to save money from her summer job to pay for her first year of college. She's thinking of attending a college that costs $8,500 for one year's tuition. Her parents have said that they will pay for half of her tuition. How much more money will Debbie need by her freshman year of college to afford her first year's tuition?
Step-by-step explanation:
If Debbie saves $900 each summer for four summers, she will have saved a total of:
$900 x 4 = $3600
Her parents have agreed to pay half the tuition, which is $8,500 / 2 = $4250.
Therefore, Debbie will need to come up with the remaining amount:
$8,500 - $4,250 = $4,250
Since Debbie will have saved $3,600 from her summer job, she will need an additional:
$4,250 - $3,600 = $650
Debbie will need $650 more to afford her first year's tuition.
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You made $75 an hour with your commission pay. This month I want to increase that by 20% so that I make
Task 1abcd: Suppose we have n = 60 puppies (across several litters from these two dogs). For the sample, we have the (previously observed) sample proportion
= 0.3833.
Suppose we wanted to use this sample to determine if there is evidence that p = the population proportion of puppies who are spotted is greater than 0.25.
a. State the hypotheses about the population proportion p.
H0:
H1:
H0 is the null hypothesis stating with that the population proportion of
puppies who are spotted is less than or equal to 0.25,
H0: p <= 0.25
H1: p > 0.25
Why do you use the term "hypothesis"?In a scientific setting, a hypothesis (plural: hypotheses) is a tested
claim regarding the causal connection between two or more variables
or a suggested explanation for a phenomenon that has been
observed.
where H0 is the null hypothesis stating that the population proportion
of puppies who are spotted is less than or equal to 0.25, and H1 is the
alternative hypothesis stating that the population proportion of puppies
who are spotted is greater than 0.25.
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Simplify each complex fractions. Assume no denominators are 0
The complex fractions are simplified to;
60. 3/2062. xy.64. (x² + x + 1)/[2x³(x-1)].How to calculate complex fractions?(1/4 - 1/5)/(1/3)
To simplify this complex fraction, first simplify the numerator by finding a common denominator:
(1/4 - 1/5) = (5/20 - 4/20) = 1/20
Then, we can divide by the denominator by multiplying by its reciprocal:
1/20 ÷ (1/3) = 1/20 × (3/1) = 3/20
Therefore, the simplified complex fraction is 3/20.
(x-y)/(x⁻¹ - y⁻¹)
To simplify this complex fraction, use the formula for the difference of squares on the denominator:
x⁻¹ - y⁻¹ = (x - y)/(xy)
Then, we can rewrite the complex fraction as a division of two fractions:
(x-y)/(x⁻¹ - y⁻¹) = (x-y) × (xy)/(x - y) = xy
Therefore, the simplified complex fraction is xy.
((2x + 1)/(x- (1/x)) - (1/x))/(2x + (2x)/(1-1/x))
To simplify this complex fraction, first simplify each of the two fractions in the numerator and denominator separately:
(2x + 1)/(x- (1/x)) = [(2x² + x)/x]/[(x² - 1)/x] = (2x² + x)/(x² - 1)
(1/x) = (x⁻¹)
(2x + (2x)/(1-1/x)) = (2x + (2x)/(x-1))
= [(2x(x-1) + 2x)/ (x-1)] / [(x-1)/(x-1)]
= (2x² - 2x + 2x)/(x-1)
= (2x²)/(x-1)
Substituting these simplified fractions back into the original complex fraction:
[(2x² + x)/(x² - 1) - x⁻¹] ÷ [(2x²)/(x-1)]
= [(2x² + x)/(x² - 1) - (1/x)] × [(x-1)/(2x²)]
= [(2x² + x) - (x² - 1)]/[x(x² - 1)] × [(x-1)/(2x²)]
= (x² + x + 1)/[2x³(x-1)]
Therefore, the simplified complex fraction is (x² + x + 1)/[2x³(x-1)].
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Image transcribed:
60. (1/4 -1/5)/(1/3)
62. (x-y)/(x⁻¹ - y⁻¹)
64. ((2x 1)/(x- (1/x)) - (1/x))/(2x + (2x)/(1-1/x)
Answer:
60. 3/20
62. -xy
64. (2x³ -x² +1)/(4x⁴ +2x³ -2x²)
Step-by-step explanation:
You want the simplified form of various complex fractions.
SimplificationFractions are added and divided in the usual ways:
a +b/c = (ac +b)/c
a/b +c/d = (ad +bc)/(bd)
(a/b)/(c/d) = (ad)/(bc)
60.(1/4 -1/5)/(1/3) = (5 -4)/(5·4)·(3/1) = 3/20
62.(x -y)/(1/x -1/y) = (x -y)/((y -x)/(xy)) = xy(x -y)/(y -x) = -xy
64.[tex]\dfrac{\dfrac{2x}{x-\dfrac{1}{x}}-\dfrac{1}{x}}{2x+\dfrac{2x}{1-\dfrac{1}{x}}}=\dfrac{\dfrac{2x^2}{x^2-1}-\dfrac{1}{x}}{2x+\dfrac{2x^2}{x-1}}=\dfrac{(2x^3-x^2+1)(x-1)}{x(x^2-1)(2x^2-2x+2x^2)}\\\\=\dfrac{2x^3-x^2+1}{2x^2(x+1)(2x-1)}=\boxed{\dfrac{2x^3-x^2+1}{4x^4+2x^3-2x^2}}[/tex]
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Additional comment
The factored form in 64 is useful for many purposes. "Simplified" usually means that factors are multiplied out. Note that we used (x²-1) = (x-1)(x+1).
If you were to describe the domain of the expression in 64, it would exclude x=1 as well as those values of x that make the remaining denominator factors zero.
Solve the equation
x^2 + 11x - 26 = 0
The two solutions of the quadratic equation x² + 11x - 26 = 0 are x = 2 and x = -13
How to solve the quadratic equation?Here we have the quadratic equation:
x² + 11x - 26 = 0
A quadratic equation is a second-degree polynomial equation in one variable, where the highest power of the variable is two.
To solve it we need to use the quadratic formula, it will give:
[tex]x = \frac{-11 \pm \sqrt{11^2 - 4*1*-26} }{2*1}[/tex]
Now we can simplify that and we will get two solutions, these are:
[tex]x = \frac{-11 \pm \sqrt{11^2 - 4*1*-26} }{2*1}\\\\x = \frac{-11 \pm15}{2}[/tex]
Then the two solutions of the quadratic equation are:
x+ = (-11 + 15)/2 = 4/2 = 2
x- = (-11 - 15)/2 = -26/2 = -13
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