If all other factors are held constant, decreasing the significance level results in an increase in the probability of a type II error. This is true. we can say that the probability of making a type II error increases when the significance level is lowered.
What is a type II error? In hypothesis testing, a type II error occurs when a false null hypothesis is not rejected. When there is a real effect and the null hypothesis is false, this happens. It's a mistake that occurs when a researcher fails to reject a false null hypothesis.
A false negative is another term for a type II error. The power of the test, the size of the sample, the confidence level, and the effect size are all factors that influence the probability of making a type II error. Only if we decrease the significance level can the probability of a type II error be increased.
What is the significance level? The significance level is also known as alpha. It is the probability of rejecting a null hypothesis when it is true. It is represented by α. It is usually set at 0.05 or 0.01 in most studies. When the significance level is lowered, the probability of making a type I error decreases, but the probability of making a type II error increases. Therefore, we can say that the probability of making a type II error increases when the significance level is lowered.
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A 20ft ladder is leaning against the roof of a house that is 18ft high. How far away is the ladder from the house?
Therefore, the ladder is approximately 8.72 feet away from the house.
What is Pythagoras theorem?Pythagoras' theorem is a fundamental theorem in mathematics that states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. In equation form, it can be written as:
c² = a² + b²
where c is the length of the hypotenuse, and a and b are the lengths of the other two sides of the right triangle.
Here,
We can use the Pythagorean theorem to solve this problem. Let x be the distance from the base of the ladder to the house.
In equation form, it can be written as:
c² = a² + b²
where c is the length of the hypotenuse, and a and b are the lengths of the other two sides of the right triangle.
Then we have:
x² + 18² = 20²
Simplifying and solving for x, we get:
x² = 20² - 18²
=400 - 324
= 76
x = √(76)
= 8.72 (rounded to two decimal places)
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1.3. The Dow Jones average (a stock market share index) dropped from 12 837 to 12 503 in one week in July 2012. 1.3.1. Calculate the drop in the share index. 1.3.2. If the price continued to drop at the same rate, calculate the Dow Jones average after 4 more weeks.
The Dow Jones average after 4 more weeks of the same rate of drop would be 11,167.
What is average?
Average, also known as mean, is a measure of central tendency that represents the typical or common value in a set of data. It is calculated by adding up all the values in a data set and then dividing the sum by the total number of values.
To calculate the drop in the Dow Jones average, we subtract the initial value from the final value:
Drop = Final Value - Initial Value
Drop = 12,503 - 12,837
Drop = -334
So the Dow Jones average dropped by 334 points in one week.
If the price continued to drop at the same rate for 4 more weeks, then the total drop after 5 weeks would be:
Total Drop = 5 x Drop
Total Drop = 5 x (-334)
Total Drop = -1670
To calculate the Dow Jones average after 4 more weeks, we need to subtract the total drop from the initial value:
New Dow Jones Average = Initial Value - Total Drop
New Dow Jones Average = 12,837 - 1,670
New Dow Jones Average = 11,167
Therefore, the Dow Jones average after 4 more weeks of the same rate of drop would be 11,167.
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will give 25 points!!!! please help!!
Consider the marked interior angles in the regular pentagon and the concave pentagon in the following image, and then answer the questions below.
a. After looking at the sum of the angle measures of these polygons, what would you guess would be the sum of the interior angles of a
17-gon? Explain your reasoning.
b. What would you guess would be the sum of the interior angles of a
concave 17-gon? Explain your reasoning.
c. In your own words, explain why the sum of the exterior angles of any
convex polygon always equals 360°.
d. What would you guess would be the sum of the exterior angles of a
concave polygon? Explain your reasoning.
Answer:
a. The sum of the interior angles of a regular polygon with n sides can be found using the formula (n-2) x 180 degrees. Using this formula, we know the sum of the interior angles of a pentagon is (5-2) x 180 = 540 degrees. Since the sum of the interior angles of a polygon increases by 180 degrees for each additional side, we can guess that the sum of the interior angles of a 17-gon would be (17-2) x 180 = 2700 degrees.
b. For concave polygons, the sum of the interior angles may not follow the same pattern as that of regular polygons. It is possible for the sum of the interior angles of a concave polygon to be greater or less than the sum of the interior angles of a regular polygon with the same number of sides. So, it is difficult to make an accurate guess without more information about the specific shape of the concave 17-gon.
c. The sum of the exterior angles of any convex polygon always equals 360 degrees because each exterior angle is supplementary to its adjacent interior angle. In other words, the exterior angle and the adjacent interior angle form a straight line, which is 180 degrees. Since there are n exterior angles in an n-sided polygon, the sum of all the exterior angles is n x 180 degrees. However, each exterior angle is counted once for each vertex, and there are n vertices, so we need to divide by n to get the total sum of exterior angles, which is (n x 180) / n = 180 degrees.
d. For a concave polygon, the sum of the exterior angles may be greater than or less than 360 degrees, depending on the shape of the polygon. In a concave polygon, some of the exterior angles will be greater than 180 degrees, which means that their adjacent interior angles will be less than 180 degrees. Since the sum of the exterior angles is equal to the sum of the adjacent interior angles, some of the exterior angles will need to be subtracted from 360 degrees to get the total sum of exterior angles. However, without more information about the specific shape of the concave polygon, it is difficult to make an accurate guess.
Answer:
a. The sum of the angle measures of the regular pentagon is 540 degrees, and the sum of the angle measures of the concave pentagon is 720 degrees. Both of these polygons have five sides. If we assume that the sum of the angle measures of a polygon with n sides is proportional to n, we can use the ratios of the number of sides in each polygon to make an estimate for the sum of the interior angles of a 17-gon. The ratio of the number of sides in a 17-gon to the number of sides in a regular pentagon is 17/5. If we multiply the sum of the angle measures of the regular pentagon by this ratio, we get an estimate for the sum of the angle measures of a 17-gon:
540 * (17/5) = 1836 degrees.
So, we would guess that the sum of the interior angles of a 17-gon is 1836 degrees.
b. We can use a similar reasoning as in part (a) to estimate the sum of the interior angles of a concave 17-gon. The ratio of the number of sides in a concave pentagon to the number of sides in a concave 17-gon is 5/17. If we multiply the sum of the angle measures of the concave pentagon by this ratio, we get an estimate for the sum of the angle measures of a concave 17-gon:
720 * (5/17) = 211.76 degrees.
So, we would guess that the sum of the interior angles of a concave 17-gon is 211.76 degrees.
c. The sum of the exterior angles of a convex polygon always equals 360 degrees because the exterior angle at each vertex of the polygon is equal to the sum of the two adjacent interior angles. If we add up all of the exterior angles of a polygon, we are essentially adding up all of the vertex angles twice (once for each adjacent exterior angle). Therefore, the sum of the exterior angles of a convex polygon is equal to 2 times the sum of the interior angles. Since the sum of the interior angles of any n-sided polygon is (n-2)*180 degrees, the sum of the exterior angles is:
2 * (n-2) * 180 = 360(n-2) degrees.
d. It is not possible to make a generalization about the sum of the exterior angles of a concave polygon, because the sum of the exterior angles of a concave polygon can be greater than, less than, or equal to 360 degrees, depending on the polygon's shape. The sum of the exterior angles of a concave polygon can be greater than 360 degrees if the polygon has one or more reflex angles, which are angles greater than 180 degrees. In this case, the exterior angle at each vertex is less than the adjacent interior angle, so the sum of the exterior angles is greater than 360 degrees. On the other hand, if a concave polygon has no reflex angles, the sum of the exterior angles will be less than 360 degrees.
Step-by-step explanation:
simplest form please
hmmm what we do is firstly make the recurring part a variable, then we multiply it such that, the recurring digits move over from the decimal point to the left, so we'd multiply it by some power of 10, in this case power of 3, because we have three digits to move, 246, so let's do all that
[tex]0.\overline{246}\hspace{5em}x=0.\overline{246}\hspace{5em} \begin{array}{llll} 1000x&=&246.\overline{246}\\\\ &&246+0.\overline{246}\\\\ &&246+x \end{array} \\\\[-0.35em] ~\dotfill\\\\ 1000x=246+x\implies 999x=246\implies x=\cfrac{246}{999}\implies x=\cfrac{82}{333}[/tex]
Help me help me help me help me help me
Answer: cab
Step-by-step explanation:
you start with the last point and move up
please can someone help me with this question?
Answer:
a) Equation B is correct
b) u = 5.2 m
Step-by-step explanation:
Trigonometry ratios:[tex]\sf Sin \ \theta = \dfrac{opposite \ side \ \angle64^\circ}{hypotenuse}\\\\\\Sin \ 64^\circ = \dfrac{u}{5.8}\\\\\\0.8987 = \dfrac{u}{5.8}[/tex]
0.8987 * 5.8 = u
u = 5.2 m
a group of students form a circle in a game. Th circumferrence of the circle was about 37.68 feet and the diamator of the circle was about 12 feet
Please find the solution asap
A 37.68/12
B 37.68/6
C 12/37.68
D` 6/37.68
Answer:
B
Step-by-step explanation:
given,
circumference of circle= 37.68ft
diameter of circle= 12ft
now,
circumference of circle = 2πr
37.68=2πr
37.68/2=πr
18.84 = 22/7 × r
radius (r) = 6ft
according to question, we have
number of students that can fit on circle = circumference/ radius
which is
37.68/6 ft
At the age of 30, Jasmine started a retirement account with $50,000 which compounded interest semi-annually with an interest rate of 1. 75%. She made no further deposits. After 25 years, she decided to withdraw 50% of what had accumulated in the account so that she could con- tribute towards her grandchild's college education. She had to pay a 10% penalty on the early withdrawal. What was her penalty?
Jasmine's penalty for the early withdrawal from her retirement account was approximately $3,702.50.
The formula to calculate the compound interest is:
[tex]A = P(1 + r/n)^{n \times t}[/tex]
Where:
A = the final amount after t years
P = the principal amount (initial investment) ($50,000 in this case)
r = the annual interest rate (1.75% in decimal form, so 0.0175)
n = the number of times interest is compounded per year (semi-annually, so 2)
t = the number of years (25 years in this case)
Let's calculate the final amount accumulated in the account:
[tex]A = 50000 \times (1 + 0.0175/2)^{2\times 25}[/tex]
[tex]A = 50000 \times (1.00875)^{50}[/tex]
A = 50000 × 1.481
A = $74,050
After 25 years, Jasmine has approximately $74,050 in her retirement account.
Now, she decides to withdraw 50% of that amount:
Withdrawal Amount = 0.5 × $74,050
Withdrawal Amount = $37,025
Finally, she had to pay a 10% penalty on the early withdrawal:
Penalty = 0.10×$37,025
Penalty = $3,702.50
So, Jasmine's penalty for the early withdrawal from her retirement account was approximately $3,702.50.
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the following data represent the number of songs downloaded per month by people of various ages. a researcher wants to determine whether the age of the person downloading songs helps predict the number of songs downloaded. age 15 17 18 19 23 27 48 number of songs downloaded 34 33 38 27 21 16 6 the calculated correlation coefficient is r= -0.898. Would you say the correlation is weak, moderate, or strong?
The correlation coefficient r=-0.898. From this, we can conclude that the correlation is strong.
The researcher wants to determine whether the age of the person downloading songs helps predict the number of songs downloaded. The age and the number of songs downloaded per month data are as follows:
Age Number of Songs Downloaded153433183827192116486
The researcher can use the correlation coefficient to measure the correlation between the two variables. The correlation coefficient is denoted by r. It lies between -1 and +1. Here's what it means: If r is close to -1, then there is a strong negative correlation between the two variables. If r is close to +1, then there is a strong positive correlation between the two variables. If r is close to 0, then there is no correlation between the two variables.
The calculated correlation coefficient is r=-0.898. This indicates that there is a strong negative correlation between the age of the person downloading songs and the number of songs downloaded. Therefore, we can say that the correlation is strong.
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Adam spent $25 for 5 pizzas how much money does he need to buy 7 pizzas
$35
He would need $35 to buy 7 pizzas because if you divide 25 and 5, you would get 5.
5+5+5+5+5+5+5=35
5x7=35
Answer:
$35
Step-by-step explanation:
So basically to find the unit price we need to craft an equation. Lets imagine one pizza is p.
We can craft this equation:
5p = 25
Divide both sides by 5
p = 5
How we just multiply that unit price by 7 to get 35, which is the answer
I put a lot of thought and effort into my answers, so I would really appreciate a Brainliest!
Problem 13.3 Use the power method to determine the lowest eigenvalue and corresponding eigenvector for the system from Prob. 13.2. Problem 13.2 Use the power method to determine the highest eigenvalue and corresponding eigenvector for |2-x 8 10|
|8 4-x 5 |
|10 5 7-x|
In problem 13.2, we can use the power method to determine the highest eigenvalue and corresponding eigenvector for the matrix:
|2-x 8 10|
| 8 4-x 5 |
|10 5 7-x|
We start by assuming a random initial vector, say v0, and then repeatedly multiplying it by the matrix A and normalizing the resulting vector, until the vector converges to the eigenvector corresponding to the highest eigenvalue.
For problem 13.3, we can use a similar approach to determine the lowest eigenvalue and corresponding eigenvector. However, instead of multiplying by A, we multiply by A^-1. This is because the lowest eigenvalue is the reciprocal of the highest eigenvalue, and the corresponding eigenvector remains the same.
Both problems require us to perform the power method until the resulting vector converges to the desired eigenvector. The number of iterations required for convergence depends on the matrix A and the initial vector v0.
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How do you find the volume under the surface and above the rectangle?
To find the volume under a surface and above a rectangle, use a double integral. Integrate the surface function over the rectangle and approximate using Riemann sums or numerical methods to obtain an estimate of the volume
To find the volume under a surface and above a rectangle in three-dimensional space using a double integral, we can follow these steps:
Determine the limits of integration for x and y based on the rectangle R. Write the function f(x,y) that defines the surface. Set up the double integral with the limits of integration and the function f(x,y). Evaluate the integral using appropriate integration techniques.To learn more about volume of three-dimensional space:
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the six trigonometric functions are not invertible what has to be done make them invertible
Can you post the image in your question.
The coefficient of variation is a better measure of risk than the standard deviation if the expected returns of the securities being compared differ significantly.
A. True
B. False
True. The coefficient of variation is a better measure of risk than the standard deviation if the expected returns of the securities being compared differ significantly.
The coefficient of variation (CV) is a relative measure of risk that takes into account the standard deviation and the mean of a distribution. It is a better measure of risk than the standard deviation when comparing securities with significantly different expected returns because it adjusts for the differences in the means.
The CV is calculated as the ratio of the standard deviation to the mean, and it allows for the comparison of the risk of investments with different expected returns on a standardized basis. Therefore, it is a useful tool for investors who want to compare the risk of investments that have different levels of expected returns. However, it should be noted that the CV has limitations and should not be the sole measure of risk used in investment analysis.
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Use a triple integral to find the volume of the given solid The tetrahedronenclosed by the coordinate planes and the plane 10x y z 4
The volume of the tetrahedron is 1.0667 cubic units.
The tetrahedron is enclosed by the coordinate planes and the plane 10x + y + z = 4.
To find the volume of the tetrahedron using a triple integral, we can use the following bounds:
0 ≤ z ≤ 4 - 10x - y
0 ≤ y ≤ 4 - 10x
0 ≤ x ≤ 0.4
This is because the tetrahedron is bound by the coordinate planes, so x, y, and z all must be positive, and the plane 10x + y + z = 4 sets the upper bound for z and y, and the upper bound for x is simply where the plane intersects the x-axis (which can be found by setting y and z equal to 0 and solving for x).
The triple integral to find the volume of the tetrahedron is then:
V = ∫∫∫ dV = ∫0^0.4 ∫0^(4-10x) ∫0^(4-10x-y) dz dy dx
Evaluating this integral, we get:
V = ∫0^0.4 ∫0^(4-10x) (4-10x-y) dy dx
= ∫0^0.4 [4y - 10xy - (1/2)y^2]0^(4-10x) dx
= ∫0^0.4 [4(4-10x) - 10x(4-10x) - (1/2)(4-10x)^2] dx
= ∫0^0.4 (-25x^2 + 20x + 8) dx
= [-25/3 x^3 + 10 x^2 + 8x]0^0.4
= 1.0667
Therefore, the volume of the tetrahedron is approximately 1.0667 cubic units.
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The spinner above is used in a game. What is the theoretical probability of the given event with one spin?
P (5)
Answer:
B
Step-by-step explanation
so there is 8 numbers so when you spin you have a 1/8 chance of spinning the numberThe segment of a circle of radius 14 cm has an angle of 135° at the centre. Calculate its perimeter.
Answer: 61
Step-by-step explanation:
explination in image
Write a quadratic equation that goes through the points (0,5), (2,1), and (1,2). y = ax^2 + bx + c
The number of bacteria in a culture is growing at a rate of 3,000e^(2t/5) per unit of time t. At t=0, the number of bacteria present was 7,500. Find the number present at t=5.a. 1.200 e^2b. 3,000 e^2c. 7,500 e^2d. 7,500 e^5e. 15.000/7 e^7
The number of bacteria present with the given growth rate at t=5 is [tex]N(5) = 7,500 * e^2[/tex] and option x is the correct answer.
What is exponential growth?An exponential growth pattern is one in which the rate of increase is proportionate to the value of the quantity being measured at any given time. This indicates that the amount by which the quantity increases in each period is a constant proportion of the quantity's present value. Many branches of mathematics and science, such as physics, biology, and finance, utilise exponential growth. Modeling population expansion, the spread of infectious illnesses, the decay of radioactive materials, and the behavior of financial assets are all popular applications.
Given that, the number of bacteria present was 7,500.
The exponential growth is given by the formula:
[tex]N(t) = N(0) * e^{(kt)}[/tex]
Substituting the values N(0) = 7,500 and the growth rate is k = 2/5 we have:
[tex]N(5) = 7,500 * e^{(2/5 * 5)}\\N(5) = 7,500 * e^2[/tex]
Hence, the number of bacteria present at t=5 is [tex]N(5) = 7,500 * e^2[/tex] and option x is the correct answer.
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A grocer has two kinds of candy: one sells for 90 cents per pound, and the other sells for 40 cents per pound. How many pounds of each kind must he use to make 50 pounds that he can sell of 85 cents per pound?
The grocer must use 45 pounds of each kind of candy
How to calculate the number of pounds that the grocer requires?A grocer has two kinds of candy
The first type of candy sells for 90 cents per pound
The second type of candy sells for 40 cents per pound
The number of pounds needed to make each kind of candy if he uses 50 pounds can be calculated as follows
The first step is to multiply 50 by 85%
50(85/100)
= 50(0.85)
= 42.5
Let y represent the unknown
y(90/100) + (50-y)(40/100)
0.9y + 0.4(50-y)
0.9y + 20-0.4y
0.9y-0.4y+20
0.5y+20(equate this value with 42.5)
0.5y+20= 42.5
collect the like terms
0.5y= 42.5-20
0.5y= 22.5
y= 22.5/0.5
y= 45
Hence the grocer needs 45 pounds for each kind of candy
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A solid square-based pyramid 1 is divided into two parts: a square-based pyramid 2 and a frustum 3.
Pyramid 1 has a base of side length 8 cm.
Pyramid 2 has a base of side length 2 cm.
The perpendicular height of pyramid 1 is 10 cm.
Frustum 3 is made from a material with a density of 4.2g/cm^3
Work out the mass of the frustum,
The mass of the frustum is 784kg
What is a frustum?Remember that a frustum is a unique 3D object that is derived by cutting the apex of a cone or a pyramid.
We should know that since pyramid 1 and pyramid 2 are similar,
The perpendicular height of pyramid 2 is 10*4/8 = 5cm
So the volume of [pyramid 1 is =V₁ = 1/3*8²*10 = 640/3 cm³
The voluume of pyramid 2 V₂ = 1/3*4²*5 = 40/3 cm³
So the volume of frustum is 640/3 cm³ - 40/3 cm³ = 560/3 cm³
Recall mass = density*volume
So the mass is = 560/3 * 42 = 784g
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Assume that different groups of couples use a particular method of gender selection and each couple gives birth to one baby. This method is designed to increase the liklihood that each baby will be a girl?
This method is designed to increase the likelihood that each baby will be a 15 girls is above 12.6 so it is significant high. It seems that method is effective.
Here we have
n=17, p=0.5
(a)
The mean is
np=17*0.5=8.5
The standard deviation is
[tex]\sigma=\sqrt{ np(1-p) } = 2.1[/tex]
(b)
Significantly low:
[tex]\mu[/tex] - 2[tex]\sigma[/tex] = 8.5 – 2* 2.1 = 4.4
Significantly high:
[tex]\mu[/tex] + 2[tex]\sigma[/tex] = 8.5+2 * 2.1 = 12.6
(c)
Since 15 girls is above 12.6 so it is significant high. It seems that method is effective.
Standard deviation is a statistical measure that describes the amount of variation or dispersion of a set of data from its mean or average value. In other words, it measures how much the data is spread out from the central tendency. It is calculated as the square root of the variance, which is the average of the squared differences between each data point and the mean.
The standard deviation is expressed in the same units as the data and is typically denoted by the symbol σ. A small standard deviation indicates that the data points are clustered around the mean, while a large standard deviation indicates that the data points are widely spread out from the mean.
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Complete Question: -
Assume that different groups of couples use a particular method of gender selection and each couple gives birth to one baby. This method is designed to increase the likelihood that each baby will be a girl, but assume that the method has no effect, so the probability of a girl is 0.5. Assume that the groups consist of 17 couples. Complete parts (a) through (c) below.
a. Find the mean and the standard deviation for the numbers of girls in groups of 17 births.
The value of the mean is μ=_____ (Type an integer or a decimal. Do not round.)
The value of the standard deviation is σ=____(Round to one decimal place as needed.)
b. Use the range rule of thumb to find the values separating results that are significantly low or significantly high.
Values of ___ girls or fewer are significantly low. (Round to one decimal place as needed.)
Values of ___ girls or greater are significantly high. (Round to one decimal place as needed.)
c. Is the result of 15 girls a result that is significantly high? What does it suggest about the effectiveness of the method?
The result ____ is not. is. significantly high, because 15 girls is greater than. less than. equal to _______ __ girls. A result of 15 girls would suggest that the method _______ is effective. is not effect.
Which scenario shows a value of 0. 4? select all that apply
Options B and C, Utilizing basic fractions, the qualities scenario displays a result of 0. 4 Jesse completed 40 out of 100 arithmetic problems and rode his bike for 4 of the 10 kilometers.
We are seeking a scenario that corresponds to a value of 0.4 or 40% among the possibilities mentioned, which represent various sections or fractions of a total.
Jesse rode his bike 4 out of the 10 miles in option B, which is equal to 0.4 or 40%.
Similarly, Jesse completed 40 of the 100 arithmetic problems in option C, which is likewise 0.4 or 40%. The other choices don't correspond to a 0.4 value.
A fraction of 2/3, or 0.666, is represented by choice A, a fraction of 4/100, or 0.04, by option D, and a fraction of 1/2, or 0.5, by option E.
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The question is -
Which of the following scenarios shows a value of 0.4? Select all that apply.
A. Jesse sold 40 out of 60 items at a garage sale.
B. Jesse rode 4 out of 10 miles on his bike.
C. Jesse finished 40 out of 100 math problems.
D. Jesse ate 4 out of 100 jellybeans.
E. Jesse returned 4 out of 8 library books.
In a candy factory, each bag of candy contains 300 pieces. The bag can be off by 10 pieces.
Write an absolute value inequality that displays the possible number of candy pieces that a bag contains.
Answer:
[tex] |x - 300| \leqslant 10[/tex]
find the values of a and b such that
x^2- +5=(x-a)^2+b
The value οf a = 1/2 and b = 19/4 in the equatiοn x² - x + 5 = (x-a)² + b.
What dο yοu mean by algebra?The part οf mathematics in which letters and οther general symbοls are used tο represent numbers and quantities in fοrmulae and equatiοn is called algebra.
x² - x + 5 = (x-a)² + b
x² - x + 5 = x² + a² - 2xa + b
-x + 5 = -2xa + a² + b
By matching cοrrespοnding terms,
2a = 1 and a²+ b = 5
a= 1/2 and a²+ b = 5
Substituting value οf "a"
(1/2)² + b = 5
1/4 + b = 5
b = 5- 1/4
b = 19/4
Thus, a = 1/2 and b = 19/4.
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Which is an equivalent fraction for 2/3
Answer:
2/3 is equivalent to the fraction 2/6
For triangles ABC and DEF, ∠A ≅ ∠D and B ≅ ∠E. Based on this information, which statement is a reasonable conclusion?
a. ∠C ≅ ∠D because they are corresponding angles of congruent triangles.
b. CA ≅ FD because they are corresponding parts of congruent triangles.
c. ∠C ≅ ∠F because they are corresponding angles of similar triangles.
d. AB ≅ DE because they are corresponding parts of similar triangles.
the triangles are similar, corresponding parts of the triangles are equal in measure. Thus, it is reasonable to conclude that [tex]AB ≅ DE.[/tex]
It is reasonable to conclude that [tex]AB ≅ DE[/tex]because triangles ABC and DEF are similar.
This means that corresponding parts of the two triangles are equal in measure. Specifically, ∠A and ∠D are equal in measure, as are ∠B and ∠E.
Therefore, the corresponding sides AB and DE are equal in measure.
A way to show that the two triangles are similar is by using the AA Similarity Postulate.
This postulate states that if two angles of one triangle are equal in measure to two angles of a second triangle, then the two triangles are similar. In this case, [tex]∠A ≅ ∠D and B ≅ ∠E[/tex], which means the two triangles are similar.
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are these equivalent
10-2x -2x10
A square yellow rug has a orange square in the center. The side length of the orange square is x inches. The width of the yellow band that surrounds the orange square is 5 in. What is the area of the yellow band?
The yellow band has a surface area of 20x + 100 square inches.
The area of the yellow band is the difference between the area of the yellow square and the area of the orange square.
The yellow square has a side length of (x + 10) inches, where 10 inches is the sum of the widths of the two yellow bands that border the orange square.
So the area of the yellow square is:
A_ yellow = (x + 10)²
The orange square has a side length of x inches, so its area is:
A_ orange = x²
The area of the yellow band is the difference between these two areas:
A_ band = A_ yellow - A_ orange
= (x + 10)² - x²
= x² + 20x + 100 - x²
= 20x + 100
Therefore, the area of the yellow band is 20x + 100 square inches.
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The distance between new orleans and houston is 353 miles. At 12:20pm, a bus leaves houston for new orleans at a speed of 60mph. 45 minutes late, a motorcycle leaves new orleans for houston at a speed of 72mph. At what time will the bus and the motorcycle pass each other if neither stops or changes speed?
As per the given distance, the bus and the motorcycle will pass each other at 4:50 pm.
Now, let's find the distance the bus travels during that time. We know the speed of the bus is 60 mph, so we can use the formula distance = speed x time. Thus, the distance the bus travels is:
distance = speed x time
distance = 60 x t
Next, let's find the distance the motorcycle travels during the same time. The speed of the motorcycle is 72 mph, so we can use the same formula to find the distance the motorcycle travels:
distance = speed x time
distance = 72 x (t - 3/4)
Here, we subtract 3/4 from the time because the motorcycle leaves 45 minutes later than the bus. Remember, we need to convert 45 minutes to hours by dividing it by 60. Therefore, 45 minutes is equal to 3/4 of an hour.
Now that we have both distances, we can set them equal to each other since the bus and the motorcycle will meet at the same point in time:
60t = 72(t - 3/4)
Let's simplify and solve for "t":
60t = 72t - 54
12t = 54
t = 4.5
Therefore, it will take 4.5 hours for the bus and the motorcycle to meet each other. But, we need to find out what time that will be. We know the bus left at 12:20 pm, so we add 4.5 hours to that time:
12:20 pm + 4.5 hours = 4:50 pm
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