The critical value of p in a test to determine if a filling system under-fills less than 10% of all boxes, with a significance level of 0.10 and a random sample of size 200, is -1.28.
Assuming that the filling system under-fills with probability p, the null hypothesis is:
H0: p >= 0.10
Ha: p < 0.10 (one-tailed test)
To find the critical value of p, we need to use the inverse cumulative distribution function (ICDF) of the standard normal distribution.
At a significance level of 0.10, the critical value is the value z such that P(Z <= z) = 0.10, where Z is a standard normal random variable. We can find this value using a standard normal table or calculator, or by using the function norm.inv(0.10) in Microsoft Excel, which gives the result -1.28 (rounded to two decimal places).
Since the sample size is large (n = 200), we can use the normal approximation to the binomial distribution to test the null hypothesis. The test statistic is:
z = (x/n - p0) / √(p0*(1-p0)/n)
where x is the number of boxes that under-fill, n is the sample size, and p0 is the null hypothesis value of the proportion. We want to reject the null hypothesis if the test statistic is less than the critical value of -1.28.
Since we do not have any information about the sample proportion, we can use the null hypothesis value of p0 = 0.10. Then the critical value of the test statistic is:
z_critical = -1.28
Substituting the values into the test statistic formula, we get:
z = (x/200 - 0.10) / √(0.10*(1-0.10)/200)
Simplifying, we get:
z = (x - 20) / 4.24
To reject the null hypothesis at the 0.10 significance level, we need the test statistic z to be less than -1.28. Therefore, we can write the rejection region as:
z < -1.28
Substituting this inequality into the test statistic formula, we get:
(x - 20) / 4.24 < -1.28
Solving for x, we get:
x < 14.5
Therefore, if the number of boxes that under-fill is less than or equal to 14 (out of 200), we reject the null hypothesis at the 0.10 significance level and conclude that there is sufficient evidence to suggest that the filling system under-fills less than 10% of all boxes.
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what type of graph is best suited for displaying the number of hours spent watching television by people from different age ranges?
A bar graph or a histogram is best suited for displaying the number of hours spent watching television by people from different age ranges.
What is a bar graph?
A bar graph is a type of graph that uses bars or rectangles to represent data, with the height or length of each bar proportional to the value it represents.
Both types of graphs can easily show the distribution of data across different age groups and allow for easy comparison of the number of hours spent watching television.
The choice between a bar graph or a histogram depends on the nature of the data and the desired level of detail.
A bar graph is appropriate when the data is categorical (e.g., age ranges) while a histogram is used when the data is continuous (e.g., number of hours).
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AD and EC are diameters of 0. OB is a radius. Classify each statement as true or false. AOE = 50
Applying the definition of a diameter, we can conclude that m<AOE = 80 degrees. Therefore, m<AOE = 50 is FALSE.
What is a Diameter and a Radius?The diameter is the longest chord passing through the center of a circle, while the radius is the distance from the center to any point on the circumference. The diameter forms two semicircles or divides the circle into two halves.
We are given that AD and EC are diameters of the circle O. This means that EOC is a straight angle or semicircle, which is equal to 180 degrees. Therefore:
m<EOC - m<AOB - m<BOC = m<AOE
Substitute:
180 - 50 - 50 = m<AOE
80 = m<AOE
m<AOE = 80°
Therefore, the statement, m<AOE = 50 is FALSE.
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Question 6, 1.6.75 Solve the absolute value equation or indicate that th |7x-4|+5=5
x = -1/7.
To solve the absolute value equation or indicate that th |7x-4|+5=5, you should follow the steps given below:Step 1: Write the absolute value equation as two separate equations, one with a positive argument and one with a negative argument. |7x - 4| + 5 = 5, can be written as:7x - 4 + 5 = 5 or 7x - 4 - 5 = -5Step 2: Simplify both equations.7x = 4 or 7x = -1Step 3: Solve for x by dividing both sides by the coefficient of x.7x = 4 → x = 4/7 or7x = -1 → x = -1/7Therefore, the solution of the absolute value equation |7x-4|+5=5 is x = 4/7 and x = -1/7.
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all the whole numbers that re greater than -4 but less than 3
Answer: -3, -2, -1, 0, 1 and 2
Answer:
0, 1, and 2
Step-by-step explanation:
A whole number is any number that does not contain a fraction, decimal, or negative value. For example, 1, 25, and 365 are whole numbers. Whereas the values of -3, 100.01, 365 ¼, and 2006.3 are not.
If QS = 7, what is TU?
[tex]TU = 2QS = 2(7)[/tex]
[tex]\implies \bf TU = 14[/tex]
At the Great Lakes Medieval Faire, 12% of the entertainers have red hair. If there are a total of 150 entertainers, how many of them do NOT have red hair?
HeLP Im iN cLAsS
There are 132 entertainers who do not have red hair.
What is Percentage?
Percentage is a way of expressing a number or quantity as a fraction of 100. It is represented by the symbol "%". Percentages are commonly used to express the proportion or ratio of one quantity to another.
Percentages are widely used in many fields, including mathematics, science, finance, and economics, among others. They are a convenient way to express a relative quantity or change in quantity, and are easy to compare and interpret.
If 12% of the entertainers have red hair, then 100% - 12% = 88% do not have red hair.
To find out how many entertainers do not have red hair, we can calculate 88% of the total number of entertainers:
88% = 88/100 = 0.88
Number of entertainers without red hair = 0.88 x 150 = 132
Therefore, 132 entertainers do not have red hair.
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Calculate the perimeter of the following.
The perimeter of the figure is 52 cm
How to determine the perimeter of the figureFrom the question, we have the following parameters that can be used in our computation:
The composite figure
The perimeter of the figure is the sum of the side lengths of the figure
So, we start by calculating the missing lengths as follows
Missing = 12 cm/4
Missing = 3 cm
Using the above as a guide, we have the following:
Perimeter = 12 + 9 + 3 + 3 + 3 + 3 + 3 + 3 + 7 + 9 - 3
Evaluate
Perimeter = 52
Hence, the perimeter is 52 cm
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Mark horneó 195 galletas y las dividió en partes iguales en 13 paquetes. ¿Cuántas galletas puso Mark en cada paquete?
Answer:
Para saber cuántas galletas puso Mark en cada paquete, podemos dividir el número total de galletas por el número de paquetes:
195 galletas ÷ 13 paquetes = 15 galletas por paquete
Por lo tanto, Mark puso 15 galletas en cada paquete.
¡Espero que esto haya ayudado! Si no es así, lo siento. Si necesitas más ayuda, ¡pregúntame! :]
If the correlation coefficient r is equal to 0.521,
find the coefficient of nondetermination.
a) 0.729
b) 0.720
c) 0.396
d) 0.271
The correct option is d. If the correlation coefficient r is equal to 0.521, the coefficient of non-determination is 0.271.
Correlation is a term used to describe the relationship between two variables in a statistical context. The correlation coefficient is a measure of the strength and direction of the relationship between two variables.
The coefficient of non-determination is used in statistics to refer to the proportion of variability in one variable that is not accounted for by another variable. It is equal to 1 - r², where r is the correlation coefficient between the two variables.
So, the coefficient of non-determination can be found using the formula:
Coefficient of non-determination = 1 - r²Given that the correlation coefficient, r = 0.521, substitute the value in the formula to find the coefficient of non-determination:
Coefficient of non-determination = 1 - (0.521)²= 1 - 0.271 = 0.729
Hence, the answer is (a) 0.729.
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Play the game Karappan Poochi: Algebra vs The Cockroaches
get to level six take a snip shop and post it in the comments
please help me
The solution to the equation x² + 2x = 18 is x = 4 ± √19.
Karappan Poochi: Algebra vs The Cockroaches is a math-based game designed to help students learn and practice algebra. The objective of the game is to help Karappan, a character in the game, solve algebraic equations. Players must solve equations by manipulating the variables and constants to reach the correct answer. To reach level six, the player must solve six equations correctly.
The equation for level six is x² + 2x = 18. To solve this equation, the player must first recognize that it is a quadratic equation and can be solved using the quadratic formula. The formula is: x = [-b ± √(b²-4ac)]/2a. For this equation, a = 1, b = 2, and c = -18. Plugging these values in, the player gets: x = [-2 ± √(2²-4(1)(-18))]/2(1). This simplifies to x = [-2 ± √76]/2, which simplifies to x = [8 ± √76]/2. Therefore, the solution to this equation is x = 4 ± √19.
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One year, the population of a city was 181,000. Several years later it was 150,230. Find the percent decrease.
Answer:
17%
Step-by-step explanation:
Calculate the difference in the population
181,000 - 150,230 = 30,770
Decrease is 30,770
Perecentage decrease = Decrease/ original population x 100%
30770/ 181,000 x 100 = 0.17 x 100
= 17%
Check 17% of 181,000
Deduct from 181,000 and you will get 150,230
Suppose you want to purchase a house. Your take-home pay is $3160 per month, and you wish to stay within the recommended guidelines for mortgage amounts by only spending 1414 of your take-home pay on a house payment. You have $16,400 saved for a down payment and you can get an APR from your bank of 4.35%, compounded monthly. What is the total cost of a house you could afford with a 15-year mortgage? Round your answer to the nearest cent, if necessary.
The total cost of the house we can afford is $242,139.78.
What is compound interest?
Compound interest is when you earn interest on both the money you've saved and the interest you earn.
First, we need to determine the maximum monthly payment we can afford based on the recommended guidelines. If we can only spend 1414 of our take-home pay on a house payment, then:
Monthly payment = 0.45 × take-home pay
1414 = 0.45 × 3160
1414 = 1422
Therefore, we can afford a maximum monthly payment of $1422.
Next, we can use the present value formula to find the maximum loan amount we can afford:
Loan amount = (monthly payment / monthly interest rate) × (1 - (1 + monthly interest rate)^(-n))
where monthly interest rate = 4.35% / 12 = 0.003625, and n = 15 years × 12 months/year = 180 months.
Substituting the values, we get:
Loan amount = (1422 / 0.003625) × (1 - (1 + 0.003625)^(-180))
Loan amount = $225,739.78
Therefore, the maximum cost of the house we can afford with a 15-year mortgage is $225,739.78 + $16,400 (down payment) = $242,139.78. Rounded to the nearest cent, the total cost of the house we can afford is $242,139.78.
Hence, the total cost of the house we can afford is $242,139.78.
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i think of a number ,i double it,and subtract two.I get nine
What is the number?
let the number be x, next perform calculations on it
double : 2x
subtract 2 : 2x - 2
2x - 2 = 9
2x = 9 + 2
x = 11 ÷ 2 = 5.5
so the number is 5.5
6 poini(s) The geomerric mean ral places as necimal ped tho The value of this stock at cent as nee ded (Round to the nearest c. Compare the rese correct answ choos chour choice. A. The value c. Compare the result of (b) to the value of the $1,000 of the social media stock, Choose the correct answer below and fill in the answer box to complete your choice. (Round to the nearest cent as needed. A. The value of the $1,000 invested in the conglomerate corporation's stock in 2014 was greater than that of the value of the $1,000 invested in the social media stock. The conglomerate corporation's stock would earn \$ more than the social media's stock. B. The value of the $1,000 invested in the conglomerate corporation's stock in 2014 was less than that of the value of the $1,000 invested in the social media stock. The social media stock would earn $ more than the conglomerate corporation's stock.
The social media stock would earn $ more than the conglomerate corporation's stock.
When answering questions on Brainly, it is important to always be factually accurate, professional, and friendly, be concise and not provide extraneous amounts of detail, repeat the question in your answer, provide a step-by-step explanation in your answer, and use the following terms in your answer: geometric, Compare, invested.The value of a conglomerate corporation's stock was $1,145 in 2014.
If $1,000 were invested in this stock, what would its value be in 2017 if the stock had increased 3.5% annually?The solution to the given problem is as follows:Calculate the value of the stock when $1,000 was invested in 2014.Using the geometric mean formula,$\text{Geometric mean} = \sqrt[n]{a_1a_2a_3\cdots a_n}$Here, $n = 3$ since the value is given for the years 2014, 2015, and 2016. $a_1 =$ the value of the stock in 2014, $a_2 =$ the value of the stock in 2015, and $a_3 =$ the value of the stock in 2016.
We have to find $a_1$.Solve for $a_1:$\[a_1 = \frac{\text{Geometric mean}}{\sqrt[n-1]{a_2a_3\cdots a_n}} = \frac{\sqrt[3]{1145}}{\sqrt[2]{1.035^2}} \approx 1042.97\]Therefore, the value of the stock when $1,000$ was invested in 2014 was approximately $1,042.97$.
Calculate the value of the stock in 2017.Using the same formula as before, we have:\[\text{Geometric mean} = \sqrt[3]{1042.97 \cdot 1.035 \cdot 1.035} \approx 1,124.54\]Therefore, the value of the stock in 2017 would be approximately $1,124.54$ dollars.Compare the results obtained from the above two parts to the value of $1,000$ of the social media stock.
The value of $1,000$ of the social media stock after three years with a 7% annual increase is given by:\[\text{Social media stock} = 1000 \cdot (1 + 0.07)^3 \approx 1225.04\]Therefore, we can compare the results obtained from the two previous parts to see which one is greater. It is clear that the social media stock value of $1,000$ is greater than that of the conglomerate corporation's stock. Therefore, the correct answer is:The value of the $1,000 invested in the conglomerate corporation's stock in 2014 was less than that of the value of the $1,000 invested in the social media stock. The social media stock would earn $ more than the conglomerate corporation's stock.
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The coordinates of the point M are (4, -8) and the coordinates of point N
are (-8,-8). What is the distance, in units, between the point M and point
N?
The distance between point M and point N is 12 units.
What are coordinates?Coordinates are a set of numbers or vaIues that describe the position or Iocation of a point in space. In two-dimensionaI space (aIso known as the Cartesian pIane), coordinates are typicaIIy represented by two vaIues, usuaIIy denoted as (x, y), that describe the horizontaI and verticaI position of a point reIative to a set of axes.
What is distance formuIa?The distance formuIa is a mathematicaI formuIa used to find the distance between two points in a two- or three-dimensionaI space.
d = √[(x₂ - x₁)² + (y₂ - y₁)²]
The distance formuIa is based on the Pythagorean theorem, which states that in a right triangIe, the square of the Iength of the hypotenuse (the side opposite the right angIe) is equaI to the sum of the squares of the Iengths of the other two sides.
In the given question,
We can use the distance formuIa to find the distance between point M and point N:
d = √[(x₂ - x₁)²+ (y₂ - y₁)²]
where (x₁, y₁) are the coordinates of point M and (x₂, y₂) are the coordinates of point N.
PIugging in the given vaIues, we have:
d = √[(-8 - 4)² + (-8 - (-8))²]
d = √[(-12)² + 0²]d = √[144]
d = 12
Therefore, the distance between point M and point N is 12 units.
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What is the area of this trapezoid? Enter your answer in the box. Ft²
Trapezoid with parallel sides labeled 13 feet and 31 feet. The dashed perpendicular
segment between them is labeled 16 feet
The area of the given trapezoid would be 176 feet² with the length of the parallel sides of the trapezoid is 13 feet and 31 feet respectively and the height of the trapezoid given is 16 feet.
Given that,
The length of the parallel sides of the trapezoid is 13 feet and 31 feet
The height of the trapezoid given is 16 feet.
We know that area of trapezoid is (a+b)×h/2
Where, (a) and (b) are Length of the parallel sides of trapezoid and h is the height of trapezoid.
Thus, Area = (13+31) × 16/2
Area = 22×8
Area = 176 feet²
Hence the area of the given trapezoid would be 176 feet² with the length of the parallel sides of the trapezoid is 13 feet and 31 feet respectively and the height of the trapezoid given is 16 feet.
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what is 10 divided by 1/5
A kite is flying 85 ft off the ground, and its string is pulled taut. The angle of elevation of the kite is 58 . Find the length of the string. Round your answer to the nearest tenth.
The length of the string which is pulled taut as described in the task content is; 100.2 ft.
What is the length of the string?As evident in the task content; the kite is flying 85 ft off the ground, and the angle of elevation is; 58°.
It therefore, follows from trigonometric ratios that the ratio which holds true is;
sin (58°) = 85 / l
where l = Length of the string.
Therefore;
Multiply both sides by l;
l sin (58) = 85
Divide both sides by sin (58);
l = 85 / sin (58)
I = 100.2 ft (nearest tenth)
Ultimately, the length of the string as described in the task content is; 100.2 ft.
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Your math teacher is planning a test for you. The test will have 30 questions. Some of the questions will be worth 3 points and the others will be worth 4 points. The total number of points on the test will be 100 points. How many 3-point questions and how many 4-point questions will be on the test?
Identify the problem: _______
a.Do I know the material?
b.How many 3-point questions and how many 4 point questions will be on the test?
c.Did I study?
d.What will my score be?
Answer:
B
Step-by-step explanation:
This is just the prosses of elmiation. How is A even possablie, C doesnt make sense, and D is also a non logical or solvable question. Thus its b.
Which is the difference in price?? Please help
Answer:
the left one is cheaper, the difference is 4.2 pounds cheaper
Step-by-step explanation:
the length of a rectangle is increasing at a rate of 5 cm/s and its width is increasing at a rate of 4 cm/s. when the length is 13 cm and the width is 4 cm, how fast is the area of the rectangle increasing (in cm2/s)?
The rate of increasing the area of the rectangle is 72cm²/s
We have, The length of a rectangle is increasing at a rate of 5 cm/s and its width is increasing at a rate of 4 cm/s. When the length is 13 cm and the width is 4 cm, we have to find how fast is the area of the rectangle increasing.
The area of a rectangle is given by, A = l × w
Where l is the length and w is the width.
Now we will differentiate the equation with respect to time t.
dA/dt = d/dt (l × w)
dA/dt = l(dw/dt) + w(dl/dt)
We can use this formula to calculate how fast the area of the rectangle increases when the length is 13 cm and the width is 4 cm.
Substituting the given values, l = 13 cm and dl/dt = 5 cm/s w = 4 cm and dw/dt = 4 cm/s
dA/dt = 13(4) + 4(5)
dA/dt = 72 cm²/s
Therefore, the area of the rectangle increasing at a rate of 72 cm²/s.
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unit 10 m homework 1 parts of a circle
1. The parts of the circle identified are as explained below. 2. Area = 153.94 m²; Circumference ≈ 43.98 m; 3. Area ≈ 706.86 ft²; Circumference ≈ 94.25 ft; 4. Area ≈ 326.85 in.; Circumference = 64.09 in.
What is a Circle?A circle is a closed two-dimensional shape that consists of points that are equidistant from a central point called the center.
1. An example of each part using the diagram of the circle given would be:
a. a center is K
b. One radius is JK
c. A chord is JL
d. Diameter is JI
e. Secant is GI
f. Tangent is GJ
g. Point of tangency is J
h. A minor arc is IL
i. A major arc is HIL
j. Semicircle is JLI
k. A central angle is <JKL
l. An inscribed angle is <HIJ
Use the area and circumference formula to calculate each required measure for each circle.
2. Area = πr² = π*7² = 153.94 m²
Circumference = 2πr = 2·π·7 ≈ 43.98 m
3. Area = πr² = π·15² ≈ 706.86 ft²
Circumference = 2·π·15 ≈ 94.25 ft
4. Area = πr² = π·10.2² ≈ 326.85 in.²
Circumference = 2·π·10.2 ≈ 64.09 in.
5. Area = πr² = π·9² ≈ 254.47 mm²
Circumference = 2·π·9 ≈ 56.55 mm
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Use the dot plots below----What is the mean height at Camp 1 (round to the nearest tenth) ?
The mean height of camp 1 is 2.5.
Define the term dοt plοts?A dοt plοt is a type οf graphical display that shοws the distributiοn οf a set οf data values. In a dοt plοt, each data pοint is represented by a dοt that is placed abοve its cοrrespοnding value οn a number line οr axis. The dοts are stacked οn tοp οf each οther tο shοw the frequency οr density οf the data at each value οr range οf values.
Dοt plοts are useful fοr visualizing small tο mοderate-sized data sets and fοr identifying patterns, οutliers, and gaps in the data. They are alsο easy tο cοnstruct and interpret, making them a pοpular tοοl fοr explοratοry data analysis.
Mean height of club fit = (2 + 2 + 3 + 5 + 3 + 3 + 1 + 1)/8
= 2.5
Thus, The mean height of camp 1 is 2.5.
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Complete question:
Please help me answer my homework in the image
Answer:
C) Both pairs of opposite sides are parallel because mPN = mLM = (1/2) and mPL = mMN = - 2.
Step-by-step explanation:
The corners of a rectangle are all right angles. The two sets of sides are parallel. In this example:
PL ║ MN and
LM ║ NP
To prove that the corners are all right angles, we could compre the slopes of the two lines that form each corner. They will be perpendicular if they are 90°.
In this example:
PL ⊥ LM and
MN ⊥ NP
So one approach Sherry may have taken is to compare the slopes of all four lines. To prove the object is a rectangle she could show that:
1. The sets of parallel lines have equal slopes, and
2. The sets of perpendicular lines have slopes that are the negative inverse of each other. (e.g., if a line has slope 5, a perpendicular line will have slope -(1/5))
To prove these points, Sherry probably used a spreadsheet to calculate each line's slopes. See the attached spreadsheet for how she may have set up the calculations. The slopes are the Rise/Run for each line. Rise is the change in y and x is the change in x between the two points.
Note the green cells. These are the slopes. Sherry found that:
a) PL ║ MN and LM ║ NP, since PL and MN both have slopes of -2; and LM and NP both have slopes of -0.5
b) PL ⊥ LM and MN ⊥ NP, since PL and LM and MN and NP both have slopes that are the negative inverse of each other (-2 and -(1/-2) or 0.5)
These are the two conditions Sherry originally established as proof of a rectangle.Without having checked whether any of the other answer options are viable options, Sherry will likely have seen, and done, enough to have chosen option C as proof that quadrilateral PLMN is a rectangle.
On a standardized test with a normal distribution the mean score was 67. 2. The standard deviation was 4. 6. What percent of the data fell between 62. 6 and 71. 8?
Question 2 options:
95%
68%
4. 6%
13. 2%
The total percent of the data falling between 62. 6 and 71. 8 is around 68%
Mean score = 67.2
Standard deviation = 4.6
Standardizing the values of interest by converting them into z-scores by -
z = (x - μ) / σ
where x is the score, μ is the mean, and σ is the standard deviation.
Calculating for the lower bound of 62.6:
z1
= (62.6 - 67.2) / 4.6
= - 4.6/4.6
= -1
Similarly,
Calculating for the upper bound of 71.8:
z2
= (71.8 - 67.2) / 4.6
= 4.6/4.6
= 1
Getting the area under curve between these two z-scores using a table of common normal probability. The normal distribution is symmetric, thus, the area between z1 and z2, can be then subtracted from the area to the left of z2. The Left of z1 is an area of 0.1587 and the left of z2 is an area of 0.8413. Therefore, the area between z1 and z2 is:
= 0.8413 - 0.1587
= 0.6826
Converting this area to a percentage -
0.6826 × 100%
= 68.26%
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I need help with this question if anyone knows it?
Answer:
the answer is 13700m²
Step-by-step explanation:
cut this shape in two parts namely
A and B
from my view it could be cut into 1. two triangles or 2. a triangle and a rectangle
I will pick 2 because it seems much more simpler
let the triangle be A
let the rectangle be B
firstly you have to cut it then separate the shape with name given when dis is done you'll have
for ∆A=length=170-70=100m
but in B the small place is 110m,but the bigger one is 160
so to find height of triangle we say
160m-110m=50m for h of A
so for B we have
length=160m, width of breath=70m
Area of the total shape=area of A + area of B
=1/2(b×h) + (L×B)
=1/2×100×50 + (160×70)
=50m×50m+11200m²
=2500+11200
=13700m²
Given: ABCD is a parallelogram, E is the midpoint of overline AB and F is the midpoint of overline DC. Prove: overline DE ≌ overline FB.
Therefore , the solution of the given problem of parallelograms comes out to be s intended, overline DE and overline FB are congruent.
How do parallelograms function?In Euclidean mathematics, a simple quadrilateral of two sets of equal distances is referred to as a parallelogram. In a specific kind of quadrilateral known as a parallelogram, both set of opposite sides are straight and equal. There are four types of parallelograms, 3 of which are each mutually exclusive. Rhombuses, parallelograms, squares, but also rectangles are the four distinct shapes.
Here,
We can use the midpoint theorem and the fact that the opposing sides of a parallelogram are parallel and congruent to demonstrate that overline DE is congruent with overline FB.
The midpoint theory tells us that DE EA because we first know that E is the midpoint of overline AB.
The midpoint theory tells us that BF FC because we also know that F is the midpoint of overline DC.
As a result, overline DE and overline BC are parallel, and overline BF and overline AD are parallel.
DE EA and BF FC resulted in:
=> FC = EA Plus DE (Preserving equality by adding identical lengths)
If we replace FC with EA and DE with BF, we get:
=> BF + FC = DE + DE
If we simplify, we get:
=> 2DE = 2BF
When you divide both parts by 2, you get:
=> DE = BF
We have thus demonstrated that, as intended, overline DE and overline FB are congruent.
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What is the following product?
Solve the quadratics attached using the quadratic formula or completing the square
[tex]n^2+9n+18[/tex]
Answer:
n = -3 or n = -6
Step-by-step explanation:
Solve for n over the real numbers:
n^2 + 9 n + 18 = 0
Subtract 18 from both sides:
n^2 + 9 n = -18
Add 81/4 to both sides:
n^2 + 9 n + 81/4 = 9/4
Write the left-hand side as a square:
(n + 9/2)^2 = 9/4
Take the square root of both sides:
n + 9/2 = 3/2 or n + 9/2 = -3/2
Subtract 9/2 from both sides:
n = -3 or n + 9/2 = -3/2
Subtract 9/2 from both sides:
Answer: n = -3 or n = -6
Find the difference quotient of \( f \); that is, find \( \frac{f(x+h)-f(x)}{h}, h \neq 0 \), for the following function. Be sure to simplify. \[ f(x)=\frac{9}{x^{2}} \] The difference quotient for \(
The difference quotient of the given function is\[\frac{f(x+h) - f(x)}{h} = \frac{-2x - h}{x^2(x+h)^2}\]The given function is\[f(x) = \frac{9}{x^2}\]
Now we have to find the difference quotient of this function, which is given as\[\frac{f(x+h) - f(x)}{h}\]
We are given that \(h ≠ 0\).
So, first let's find \(f(x+h)\).\[f(x+h) = \frac{9}{(x+h)^2}\]
Now we can put both the values of \(f(x+h)\) and \(f(x)\) in the difference quotient.
\[\frac{f(x+h) - f(x)}{h} = \frac{\frac{9}{(x+h)^2} - \frac{9}{x^2}}{h}\]
Let's put the LCM of \((x+h)^2\) and \(x^2\) which is \(x^2(x+h)^2\) in the numerator.
\[\frac{\frac{9x^2 - 9(x+h)^2}{x^2(x+h)^2}}{h}\]
Now, simplify the numerator.
\[\frac{9x^2 - 9(x^2 + 2xh + h^2)}{x^2(x+h)^2h}\]\[\frac{9x^2 - 9x^2 - 18xh - 9h^2}{x^2(x+h)^2h}\]
Now we can cancel out the common factor of 9 from both numerator and denominator.
\[\frac{-2xh - h^2}{x^2(x+h)^2h}\]
Now cancel out h from both numerator and denominator.
\[\frac{-2x - h}{x^2(x+h)^2}\]
So, the difference quotient of the given function is\[\frac{f(x+h) - f(x)}{h} = \frac{-2x - h}{x^2(x+h)^2}\]
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