Answer:
To find the Maclaurin series for $f(x) = xe^x$, we can use the formula for the Maclaurin series of $e^x$ and differentiate the product term by term:
$$e^x = \sum_{n=0}^\infty \frac{x^n}{n!}$$
$$xe^x = x \sum_{n=0}^\infty \frac{x^n}{n!} = \sum_{n=0}^\infty \frac{x^{n+1}}{n!}$$
So the first few terms of the Maclaurin series for $f(x)$ are:
$$f(x) = xe^x = x + x^2 + \frac{x^3}{2} + \frac{x^4}{3} + \frac{x^5}{24} + \cdots$$
To find the radius of convergence, we can use the ratio test:
$$\lim_{n\to\infty} \left| \frac{a_{n+1}}{a_n} \right| = \lim_{n\to\infty} \left| \frac{x^{n+2}/(n+1)!}{x^{n+1}/n!} \right| = \lim_{n\to\infty} \frac{|x|}{n+1} = 0$$
Since the limit is less than 1 for all values of $x$, the Maclaurin series converges for all values of $x$, and the radius of convergence is infinite.
Tom spent 2/3 of his pocket money to buy apples and spent 1/4 of the remaining money to buy some bananas. It cost Tim 45 dollars to buy the fruits. How many money did he have at first
Tom had 60 dollars as his pocket money initially.
Let's assume that Tom had x dollars as his pocket money.
He spent 2/3 of his pocket money on apples, which means he spent (2/3)x dollars on apples.
He had 1/3 of his pocket money left after buying the apples.
Out of the remaining money, he spent 1/4 on bananas, which means he spent (1/4)(1/3)x = (1/12)x dollars on bananas.
The total amount spent on apples and bananas is given as $45. So, we can write the equation:
(2/3)x + (1/12)x = 45
Multiplying both sides by 12 to get rid of the fractions:
8x + x = 540
Simplifying, we get:
9x = 540
Dividing both sides by 9:
x = $60
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A plane traveled 630 kilometers each way to Toronto and back. The trip there was with the wind. It took 7 hours. The trip back was into the wind. The trip back took 15 hours. What is the
speed of the plane in still air? What is the speed of the wind?
A plane traveled 630 kilometers each way to Toronto and back. The trip there was with the wind. It took 7 hours. The trip back was into the wind. The trip back took 15 hours. The speed of the plane in still air is 66 km/h, and the speed of the wind is 24 km/h.
Let's use the following variables:
Let's call the speed of the plane in still air "p"Let's call the speed of the wind "w"When the plane is flying with the wind, its effective speed is p + w. When it is flying against the wind, its effective speed is p - w.
We know that the distance to Toronto and back is 630 km each way, for a total of 1260 km. We also know that the time it took to fly to Toronto with the wind was 7 hours, and the time it took to fly back against the wind was 15 hours.
Using the formula distance = speed x time, we can set up the following equations:
630 = (p + w) x 7 (equation 1)
630 = (p - w) x 15 (equation 2)
We now have two equations with two unknowns. We can solve for either p or w in terms of the other variable. Let's solve for p in terms of w.
From equation 1, we get:
p + w = 90
From equation 2, we get:
p - w = 42
Adding the two equations, we get:
2p = 132
So,
p = 66 km/h
Now we can use either equation 1 or equation 2 to solve for w. Let's use equation 1:
630 = (66 + w) x 7
Simplifying this equation, we get:
90 = 66 + w
w = 24 km/h
Therefore, the speed of the plane in still air is 66 km/h, and the speed of the wind is 24 km/h.
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If you were to have a data set of the heights of all 12-year-old boys who live on a given street in the city of Grand Rapids, this would be a perfect example of a normal distribution. True or false
False. A data set of the heights of 12-year-old boys would not necessarily follow a normal distribution pattern as it may be skewed or not evenly distributed around the mean.
False. A normal distribution is a type of probability distribution that takes the shape of a bell curve. It is characterized by having an equal number of values on either side of the mean, with the values in the middle being more numerous than those on the outside. A data set of the heights of all 12-year-old boys who live on a given street in the city of Grand Rapids would not necessarily fit this pattern. It is possible that the data set may be skewed in one direction or the other, depending on the height of the tallest and shortest boys in the group. It is also likely that the data will not be evenly distributed around the mean, as some boys may be taller or shorter than others.
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can yall help me again i still don't understand this
Answer:
52.
Step-by-step explanation:
So 143 members represent 100% of the population of the problem. A ratio of 4:7 similarly represent 100%. First, you need to get the value of 4:7 in a representation of 100%. You can do that by adding the two (4+7=11) and then dividing it by each value of it. So 7 divided by 11 is .6363, or 63.63% of the whole. Then 4 divided by 11 is .3636, or 36.36% of the whole. After getting this, seeing that the ratio for union members to non union members is 4 union members to 7 nonunion members, and there are 143 employees in total, just get the value of 36.36% of 143; in this case, it's 51.99 - rounded off to 52 employees.
Answer:
52 members
Step-by-step explanation:
Proportional setup.
(4/11)=(x/143)
In a state's Pick 3 lottery game, you pay $1.33 to select a sequence of three digits (from 0 to 9), such as 333. If you select the same sequence of three digits that are drawn, you win and collect $477.38. Complete parts (a) through (e). a. How many different selections are possible? b. What is the probability of winning? (Type an integer or a decimal.) c. If you win, what is your net profit? s ] (Type an integer or a decimal.) d. Find the expected value. (Round to the nearest hundredth as needed.) e. If you bet $1.33 in a certain state's Pick 4 game, the expected value is $0.85. Which bet is better, a $1.33 bet in the Pick 3 game or a $1.33 bet in the Pick 4 game? Explain.
a. There are 1,000 different possible selections. b. The probability of winning is 1/1,000, or 0.001. c. If you win, your net profit is $476.05. d. The expected value is $0.476. e. The Pick 4 game is better.
a. There are 1,000 different possible selections (000 to 999).
b. The probability of winning is 1/1,000, or 0.001.
c. If you win, your net profit is $476.05. This can be calculated by,
$477.38 - $1.33 = $476.05
d. The expected value is $0.476. This can be calculated by,
$476.05 * 0.001 = $0.476
e. The Pick 4 game is better.
The expected value of a Pick 3 bet is $0.476, while the expected value of a Pick 4 bet is $0.85. The Pick 4 bet is better because it has a higher expected value. This is because the Pick 4 game has more possible selections, meaning the odds of winning are lower than the Pick 3 game, but the prize is larger. So, the expected value for Pick 4 is larger than Pick 3. The expected value of a bet is the amount of money you can expect to win if you make the same bet over and over again, so a higher expected value means you have a better chance of making a profit in the long run.
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HELP PLEASE
Determined to fill her water balloons before Diego, Lin fills her balloons at a rate of 1/3 ounce per second. She has already filled balloons with 8 ounces of water
Diego has filled balloons with 6 ounces of water. He continues to fill balloons at a rate of 2/3 an ounce per second.
1. Write an equation for Lin
2. Write and equation for Diego
3. What is the intersection point of the solution tell us about this situation?
1. An equation for Lin is y = 1/3x + 8.
2. An equation for Diego is y = 2/3x + 6.
3. The intersection point of the solution is (6, 10).
Let there have total number of balloons are y.
Lin fills her balloons at a rate of 1/3 ounce per second.
So she filled 1/3 x balloons.
She has already filled balloons with 8 ounces of water.
So the required equation is;
y = 1/3x + 8.................(1)
Diego fills her balloons at a rate of 2/3 ounce per second.
So he filled 2/3 x balloons.
He has already filled balloons with 6 ounces of water.
So the required equation is;
y = 2/3x + 6.................(2)
To determine the intersecting point we solve the both equation.
Subtract equation 1 and 2, we get
1/3x + 8 - 2/3x - 6 = 0
-1/3x + 2 = 0
Subtract 2 on both side, we get
-1/3x = -2
Multiply by -3 on both side, we get
x = 6
Now put the value of x in equation 1
y = 1/3 × 6 + 8
y = 10
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9. In a recent taste test, 1017 out of 1250 people could not tell the difference between a popular soda's original flavor and the new calorie-fre
difference. Find a test statistic for the proportion.
z = 2.21
z = 1.38
z = 1.20
z = 0.39
Answer:
z=1.20
Step-by-step explanation:
Just Took Test
The table shows the consolidated government fiscal framework for 2020/21- 2022/23 financial year in billions, the total amount collected by government from taxpayers (Revenue), the total amount spent by government (Expenditure), and the Budget Balance thereof. Consolidated Government Fiscal Framework 2020/21-2022/23 1 p9) 2020/21 outcome R billion Revenue Expenditure Budget Balance (Adapted from: http://www.sars.gov.za/home.asp?pid=63430;chapter 1.1 1.2 2021/22 Estimate 666.9 832.5 -165.6 Use the table above to answer the following questions: 761.0 904.1 -143.1 2022/23 843.0 977.2 -134.2 Write down the tax estimated to be collected by government during the financial year 2020/21? Write the amount in 1.1 in billions numerically (2)
the tax estimated to be collected by the government during the financial year 2020/21 is 666.9 billion rands.
why it is and what is a financial year?
The tax estimated to be collected by the government during the financial year 2020/21 is not explicitly given in the table. However, the total revenue collected by the government during the financial year 2020/21 is given, which is:
666.9 billion rands
Therefore, the tax estimated to be collected by the government during the financial year 2020/21 is 666.9 billion rands.
A financial year (also known as fiscal year) is a period of 12 months that a company or government uses for financial reporting and accounting purposes. It does not necessarily correspond to the calendar year, which is a period of 12 months starting on January 1st and ending on December 31st.
The financial year is important because it helps organizations to keep track of their financial performance over a consistent period of time, which facilitates comparison of financial results from year to year. The financial year is often chosen to align with a company's operational cycle, which may be seasonal or have other considerations that affect the timing of revenues and expenses.
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Compare the area of this parallelogram
to the area of a rectangle with a length
of 7 cm and a width of 4.5 cm. Explain.
The area of the parallelogram will equal to Area of the rectangle
Area of parallelogram:
The area of a parallelogram is given by the formula:
A = b × hWhere A is the area of the parallelogram,
b is the length of the base of the parallelogram,
h is the height of the parallelogram.
Area of Rectangle:The area of a rectangle is given by the formula:
A = l × wWhere A is the area of the rectangle
l is the length of the rectangle
w is the width of the rectangle.
Here we have a Parallelogram
Where the height of the parallelogram is 4.5 cm and the length is 7 cm
Using the formula,
Area of parallelogram = 4.5 cm × 7 cm = 31.5 cm²
From the data,
The length of a rectangle is 7 cm and width is 4.5 cm
Using the formula,
Area of the rectangle = 7 cm × 4.5 cm = 31.5 cm²
Therefore,
The area of the parallelogram will equal to Area of the rectangle
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The complete question is given in the picture
I need help with this please can you help me
The answer of the given question based on the following equations are the order of the variables from least to greatest is c, a, b, since c = 18 is the smallest, followed by a = 36, and b = 72 is the largest.
What is Variable?A variable is symbol or letter used to represent value that can change or vary. Variables are commonly used in the algebra and other branches of mathematics to represent the unknown quantities, as well as in a scientific and engineering applications to represent the physical parameters and measurements.
In algebra, variables are typically represented by the letters such as x, y, z, a, b, c, etc.
To solve this problem, we first need to solve each equation for its respective variable, a, b, and c.
a - 5 = 31
Adding 5 to both sides, we get:
a = 36
1/2b - 5 = 31
Adding 5 to both sides and multiplying by 2, we get:
b = 2(31 + 5) = 72
2c - 5 = 31
Adding 5 to both sides and dividing by 2, we get:
c = (31 + 5)/2 = 18
Therefore, the order of the variables from least to greatest is c, a, b, since c = 18 is the smallest, followed by a = 36, and b = 72 is the largest.
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Your retail garden store buys 500 plants at $2.49 each from the wholesaler. You plan to sell 75% of the plants to customers for the full retail price of $5.00. Ten percent will be sold to employees at a 20% markdown, and the final 15% will be sold on sale for 25% off at the end of the season. In the end, how much will the store make in net profits?
The store will make a net profit of $1,111.25 from selling the plants.
To find how much will the store make in net profits?
The first step is to calculate the total revenue from selling the plants:
Total revenue = (75% of 500) x $5.00 + (10% of 500) x $4.00 + (15% of 500) x $3.75Total revenue = 375 x $5.00 + 50 x $4.00 + 75 x $3.75Total revenue = $1,875 + $200 + $281.25Total revenue = $2,356.25Next, we need to calculate the cost of buying the plants from the wholesaler:
Cost of plants = 500 x $2.49
Cost of plants = $1,245.00
The net profit is then the difference between the total revenue and the cost of buying the plants:
Net profit = Total revenue - Cost of plants
Net profit = $2,356.25 - $1,245.00
Net profit = $1,111.25
Therefore, the store will make a net profit of $1,111.25 from selling the plants.
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Use the distributive property to simplify
12 • 3 3/4
Answer:
We can first write 3 3/4 as an improper fraction:3 3/4 = 15/4Then, using the distributive property, we get:12 • 3 3/4 = 12 • (3 + 3/4) = 12 • 3 + 12 • 3/4 = 36 + 9 = 45Therefore, 12 • 3 3/4 simplifies to 45.
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathtt{12\times 3\dfrac{3}{4}}[/tex]
[tex]\mathtt{= 12 \times \dfrac{3\times4+3}{4}}[/tex]
[tex]\mathtt{= 12\times\dfrac{12 + 3}{4}}[/tex]
[tex]\mathtt{= 12\times\dfrac{15}{4}}[/tex]
[tex]\mathtt{= \dfrac{12}{1}\times\dfrac{15}{4}}[/tex]
[tex]\mathtt{= \dfrac{12\times15}{4\times1}}[/tex]
[tex]\mathtt{= \dfrac{180}{4}\rightarrow 180\div4 \rightarrow \bold{12(3 + \dfrac{3}{4}})\rightarrow 12(3) + 12(\dfrac{3}{4})\rightarrow 36 + 9}[/tex]
[tex]\mathtt{= 45}[/tex]
[tex]\huge\text{Therefore your answer should be:}[/tex]
[tex]\huge\boxed{\mathtt{12(3 + \dfrac{3}{4})\ which\ gives\ you\ \bf 45}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
Devon measures and records his height every year. This year, as a fifth grader, his height is 423 feet. He has grown 116 feet since he was in second grade. What was Devon’s height when he was in second grade? Responses 213 feet 2 and 1 third feet 313 feet 3 and 1 third feet 312 feet 3 and 1 half feet 356 feet 3 and 5 sixths feet
Devon's height when he was in second grade was 312 feet 3 and 1 half feet.
The proper explanation of this answer is given below. Devon's height .
To arrive at this answer, we must subtract 116 feet from 423 feet, which is the height that Devon is currently measuring as a fifth grader. 423 feet - 116 feet = 307 feet. However, we know that his height was 312 feet 3 and 1 half feet, which is 5 feet more than 307 feet. Therefore, we can add 5 feet to 307 feet to get the answer, 312 feet 3 and 1 half feet.
The height that Devon is now measuring as a fifth grader is 423 feet, so we must subtract 116 feet from that measurement to get this answer. 307 feet Equals 423 feet minus 116 feet. Yet, we are aware of his height, which was 312 feet 3 and a half feet, or 5 feet taller than 307 feet. In order to obtain the solution, 312 feet 3 and a half feet, we can add 5 feet to 307 feet.
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c) when x is divided by 5 the result is 20
Answer:
x= 100
Step-by-step explanation:
x/5 = 20
multiply both the sides by 5 we get
5× x/5 = 20×5
x = 100
A designer has designed different tops, pants, and jackets to create outfits. How many different outfits can the models wear if she has designed the following pieces? six tops, three pants, two jackets There are a total of □ different outfits.
There are 36 different outfits that can be created using six tops, three pants, and two jackets.
Combinations:Combinations refer to the ways in which a set of objects or items can be arranged or chosen without regard to their order.
In mathematics, a combination is a selection of objects from a larger set, where the order of the selected objects does not matter.
Here we have
A designer has designed different tops, pants, and jackets to create outfits.
Number of options for tops = 6
Number of options for pants = 3
Number of options for jackets = 2
Here,
The total number of different outfits that can be created = (No of options for tops) × (No of options for pants) × (No of options for jackets)
= 6 × 3 × 2
Therefore,
There are 36 different outfits that can be created using six tops, three pants, and two jackets.
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For rhombus EFGH diagonals eg and fh intersect at k. The diagonals have lengths of EG = 36 and FH=14. What is the measure of
Therefore, the measure of the area of rhombus EFGH is 252 square units.
What is rhombus?A rhombus is a four-sided geometric shape that has the following properties:
All four sides are of equal length.
Opposite sides are parallel to each other.
The angles formed between adjacent sides are equal (i.e., they are all congruent).
The diagonals of a rhombus bisect each other at right angles, meaning they intersect at a 90-degree angle. Additionally, the length of one diagonal is equal to the product of the length of the other diagonal and the sine of one of the angles formed by adjacent sides.
by the question.
[tex]EK^2 = EG^2/4 + KH^2 (where KH is half the length of FH)EK^2 = 36^2/4 + (14/2)^2EK^2 = 324 + 49EK^2 = 373EK = sqrt(373)[/tex]
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Find the perimeter of a square if the length of its diagonal is 14.
? square root of ?
Answer:
28√2 units.
Step-by-step explanation:
Let's denote the length of a side of the square as "s". We know that the diagonal of the square is √2 times the length of a side, so we can write:
√2 s = 14
Solving for "s", we can divide both sides by √2:
s = 14 / √2
To simplify this expression, we can rationalize the denominator by multiplying both the numerator and denominator by √2:
s = (14 / √2) x (√2 / √2) = 14√2 / 2 = 7√2
Now we can find the perimeter of the square by adding up the lengths of all four sides:
Perimeter = 4s = 4(7√2) = 28√2
Therefore, the perimeter of the square is 28√2 units.
Are the triangles similar? If yes, write a similarity statement and explain how you know they are similar
Yes, the triangles ∆AOR and ∆EOD are similar. By Angle-Angle similarity rule, triangle AOR is similar to triangle EOD.
See the above figure, it consists two triangles say ∆AOR and ∆EOD. Now, we check whether both of triangles are similar or not. Similar triangles are are the triangles that have corresponding sides in ratio to each other and corresponding angles equal to each other. It's time to check the similarity property in ∆AOR and ∆EOD.
In ∆AOR, measure of angle R = 105°
In ∆EOD, measure of angle D = 35°
measure of angle DOE = 40°
Sum of interior angles of triangle = 180°
so, measure of angle E = 180° - 35° - 40°
= 105°
Now, in ∆AOR and ∆EOD,
Measure of angle R = measure of angle E = 105° ( since equal angles)
Measure of angle AOR = measure of angle EOD ( corresponding angles)
Thus, two angles of triangle EOD are congruent or equal to the corresponding angles of another triangle, AOR. So, by Angle-Angle ( AA) congruence rule, ∆AOR is similar to the ∆EOD.
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Complete question:
See the above figure, Are the triangles similar? If yes, write a similarity statement and explain how you know they are similar.
what is the equation of the line that is perpendicular to line m and passes through the point (3,2)
The equation of the line that is perpendicular to line m and passes through the point (3, 2) is y = (2/5)x + 4/5.
How to Find the Equation of Perpendicular Lines?To find the equation of a line that is perpendicular to line m, we need to know the slope of line m.
The slope of line m can be found using the two given points on the line, (0, -3) and (-2, 2):
slope of line m = (change in y) / (change in x) = (2 - (-3)) / (-2 - 0) = 5 / (-2) = -5/2
A line perpendicular to m will have a slope that is the negative reciprocal of -5/2. The negative reciprocal is obtained by flipping the fraction and changing its sign.
slope of line perpendicular to m = -1 / (-5/2) = 2/5
Now we have the slope of the line perpendicular to m and a point that it passes through, (3, 2). We can use the point-slope form of the equation of a line to find its equation:
y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope.
Substituting in the values we have:
y - 2 = (2/5)(x - 3)
Simplifying:
y - 2 = (2/5)x - (6/5)
y = (2/5)x - (6/5) + 2
y = (2/5)x + 4/5
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x power 4 -8 x power 2 y power 2+ 16 y power 4 -289
The values of x = 17 and y = 0.
Define quadratic equation?
A quadratic equation is a second-degree polynomial equation in one variable of the form a + b + c = 0, where a, b, and c are constants and x is the variable. The term "quadratic" comes from the Latin word "quadratus", which means square.
Given:
[tex]x^{4} - 8x^{2} y^{2} +16y^{4} -289[/tex] equals to 0
[tex]x^{4} - 8x^{2} y^{2} +16y^{4} -289 = 0[/tex]
[tex]x^{4} - 8x^{2} y^{2} +16y^{4} =289[/tex]
We know that [tex](x-b)^{2} =x^{2} -2xy +y^{2}[/tex]
Compare it: [tex](x^{2} -4y^{2} )^{2} = x^{4} - 8x^{2} y^{2} +16y^{4}[/tex]
So, [tex](x^{2} -4y^{2} )^{2} = 289[/tex]
[tex](x^{2} -4y^{2} ) = 17[/tex]
We know that [tex](x^{2} -b^{2} ) = (x+y)(x-y)[/tex]
So, [tex](x +2y)(x-2y) =17[/tex]
If we solve two equations that is:
(x+2y) = 17 and (x-2y) = 17
Simplification, x = 17 and y = 0
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The balance in an account earning simple interest varies jointly with principal (the amount invested), the annual interest rate, and time measured in years with a constant of proportionality of 1. If you receive $10,000 from a rich uncle for a graduation gift and invest it in a certificate of deposit that pays 5% simple interest for 50 years (approximately the number of years before you retire), how much will the account then be worth?
After 50 years, the certificate of deposit will be worth
Answer: $100,000
Step-by-step explanation:
$100,000. This is because the balance in the account varies jointly with principal, the annual interest rate, and time measured in years with a constant of proportionality of 1. Therefore, the balance in the account at the end of 50 years is 10,000 × 1 × (1 + 0.05)50, which is equal to $100,000.
Answer:
$35000
Step-by-step explanation:
account worth = deposit + simple interest
/ 100
intrest = deposit x year x simple interest
10000×50×5/100=25000
account worth = deposit + simple interest
= 10000 + 25000
= $ 35000
What happens to the mode of the data set shown below if the number 8 is added to the data set?
A. There is no mode.
B. The mode will not change.
C. There will be two modes.
D. The mode increases by 6.
8. In a drawing of the solar system, the scale is 1 mm = 500 km. For a planet with a diameter of (1 point)
7,000 km, what should be the diameter of the drawing of the planet?
3,500,000 mm
140 mm
14 mm
7,000 mm
Answer: The diameter of the drawing of the planet= 14 mm
Step-by-step explanation:
Given: In a drawing of the solar system the scale is 1 mm = 500 km
which means [tex]1 \ km=\frac{1}{500}mm[/tex] on the drawing.
The diameter of planet =7000 kilometers.
Then the diameter of the drawing of the planet [tex]=\frac{7000}{500}=14[/tex]
Therefore, the diameter of the drawing of the planet= 14 mm.
This shape has been made from two identical isosceles triangles. Work out the size of angle x.
Angles - 25, x
The size of angle x is equal to 100°.
How to determine the value of x?Based on the identical isosceles triangles ΔABD and ΔACD, we can logically deduce the following:
m∠DAB = 25°
AD = BD = CD
In triangle ΔABD, we have:
AD = BD (Given)
m∠DBA = ∠DAB (Angle opposite to equal sides are congruent)
m∠DBA = 25°.
Next, we would determine the measure of m∠ADB;
m∠DBA + m∠DAB + m∠ADB = 180° (Sum of angle in a triangle)
25° + 25° + m∠ADB = 180°
m∠ADB = 180° - 50°
m∠ADB = 130°.
Since ΔABD and ΔACD are two identical isosceles triangles, we have:
m∠DCA = m∠DBA
m∠DCA = 25°
Similarly, we have:
m∠DAC = m∠DAB = 25°
m∠ADC = m∠ADB = 130°
Generally speaking, we know that a complete revolution (circle) is equal to 360°:
m∠ADC + m∠ADB + m∠CDB = 360°
130° + 130° + x = 360°
x = 360° - 260°
x = 100°.
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could you help me out with this question?
simplify the square root of 10 divided by square root 8
A large retailer wants to estimate the proportion of Hispanic customers in a particular state. How large a sample size (of the retailer’s customers) do you need to estimate this proportion to within 0.04 accuracy and with 99% confidence? Assume there is no planning value for p* available. The sample size required is:......
To estimate the proportion of Hispanic customers in a particular state to within 0.04 accuracy and with 99% confidence, you need a sample size of 397 customers.
To accurately estimate the proportion of Hispanic customers in a particular state to within 0.04 accuracy and with 99% confidence, you will need a sample size of 397 customers. To calculate this, you will need to use the formula:
n = ( 2z × p* × q*) / e2
Where:
- n is the sample size
- z is the Z-score associated with the confidence level (in this case, it is 2.58 for 99%)
- p* is the planning value for the population proportion (in this case, it is not known, so it should be set to 0.5)
- q* is the compliment of p* (in this case, q* = 1 - 0.5 = 0.5)
- e is the desired accuracy (in this case, e = 0.04).
Substituting the values into the formula:
n = (2.582 × 0.5 × 0.5) / 0.042 = 397.
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A pediatrician randomly selected 50 six-month-old boys from her practice's database and recorded an average weight of 15.7 pounds with a standard deviation of 0.42 pounds. She also recorded an average length of 27.6 inches with a standard deviation of 0.28 inches. Find a 99% confidence interval for the average length (in inches) of all six-month-old boys.
27.25 in. to 27.95 in.
27.32 in. to 27.98 in.
27.50 in. to 27.70 in.
27.74 in. to 27.98 in.
The 99% confidence interval for the average length (in inches) of all six-month-old boys is 27.74 in. to 27.98 in. The correct answer is E
This is calculated using the average length (27.6 in.) and standard deviation (0.28 in.) recorded by the pediatrician. To calculate the confidence interval, you need to calculate the margin of error. The margin of error is found using the following formula:
ME = (Critical Value) x (Standard Deviation/√Sample Size)
For a 99% confidence interval, the critical value is 2.58. Therefore, the margin of error for this sample is (2.58) x (0.28/√50) = 0.24 in. This means that the 99% confidence interval for the average length of all six-month-old boys is 27.6 in. ± 0.24 in., or 27.74 in. to 27.98 in. The correct answer is E
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what is 17 minus 2x equals 4x plus 5
Answer:
x=2
Step-by-step explanation:
Answer:
x=2
Step-by-step explanation:
What are the solutions to this equation?
1
-1
√17
-√17
There are no solutions.
Answer:
1 and -1
Step-by-step explanation:
[tex]5 - \sqrt[3]{( {x}^{2} - 9 } = 7[/tex]
[tex] - \sqrt[3]{( {x}^{2} - 9} = 7 - 5[/tex]
[tex]- \sqrt[3]{( {x}^{2} - 9} = 2[/tex]
[tex] \sqrt[3]{( {x}^{2} - 9} = - 2[/tex]
Cube both sides of the equation:
[tex] {x}^{2} - 9 = { - 2}^{3} [/tex]
[tex] {x}^{2} - 9 = - 8[/tex]
[tex] {x}^{2} = - 8 + 9[/tex]
[tex] {x}^{2} = 1[/tex]
[tex] {x}^{2} - 1 = 0[/tex]
[tex](x - 1)(x + 1) = 0[/tex]
[tex]x = 1 \: \: or \: \: x = - 1[/tex]
[tex]5-\sqrt[3]{x^2-9}=7\implies 5=\sqrt[3]{x^2-9}+7\implies -2=\sqrt[3]{x^2-9} \\\\\\ (-2)^3=(\sqrt[3]{x^2-9})^3\implies -8=x^2-9\implies 1=x^2 \\\\\\ \pm\sqrt{1}=x\implies \pm 1 = x[/tex]