According to recent studies, there is a notable difference in credit scores between those over the age of 55 and those between the ages of 18-24.
On average, individuals over the age of 55 tend to have higher credit scores than those in the 18-24 age range. This is primarily due to the fact that older individuals have had more time to establish and build their credit history, whereas younger individuals are just starting out and may not have had the opportunity to establish credit yet.
Additionally, older individuals tend to have more stable financial situations and may have less debt compared to younger individuals who may be dealing with student loans or other types of debt.
However, it's important to note that credit scores can vary greatly between individuals, regardless of age, and there are many factors that contribute to credit score, such as payment history, credit utilization, and length of credit history.
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Consider the series Σ(1) с (where c is a constant). For which values of c will the series converge, and for which it diverge? Justify your answer, and show all your work. (Hint: Use the root test)
To determine whether the series Σ(1) с converges or diverges, we can use the root test. The root test states that if the limit of the absolute value of the nth root of the terms of the series approaches a value less than 1, then the series converges. If the limit approaches a value greater than 1, the series diverges. If the limit equals 1, the test is inconclusive and another test should be used.
Using the root test, we have:
lim┬(n→∞)〖|1^(1/n) c| = lim┬(n→∞)|c| = |c|〗
If |c| < 1, then the limit approaches a value less than 1 and the series converges. If |c| > 1, then the limit approaches a value greater than 1 and the series diverges. If |c| = 1, then the test is inconclusive.
Therefore, the series Σ(1) с converges if |c| < 1, and diverges if |c| > 1. If |c| = 1, then another test should be used to determine convergence or divergence.
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Can you use addition or mulipulcation for solving 100000 x 1/100000
Using multiplication to solve 100000 x 1/100000, the answer would be 1.
You should use multiplication to solve the problem 100000 x 1/100000.
When you multiply 100000 by 1/100000, you're essentially multiplying 100000 by a fraction that represents "one part out of 100000.". The step by step explanation is:
1. Write down the given problem: 100000 x 1/100000
2. Perform the multiplication: 100000 x (1/100000)
3. Simplify the expression: 1
Mathematically, this can be written as:
So, 100000 x 1/100000 equals 1.
You wouldn't typically use addition to solve this particular problem, as it involves multiplication of a fraction rather than adding two numbers together. However, you could use addition to solve related problems.
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the diagram shows a polygon composed of rectangles
Answer:
210 feet
Step-by-step explanation:
Refer the attached figure
LK = 22 ft
KH=JI = 18 ft.
HG=14 ft.
CD=FE=16 ft.
AL=15 ft.
GF=CB = 5ft.
KJ=HI=10 ft.
CF=CB+BG+GF=5+15+5=25 ft. =DE
AB= LK+KH+HG=22+18+14= 54 ft.
Perimeter of polygon = Sum of all sides
Perimeter of polygon=AL+LK+KJ+JI+HI+HG+GF+FE+DE+CD+CB+BA
=15+22+10+18+10+14+5+16+25+16+5+54
=210
Hence the perimeter of the polygon is 210 feet.
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Find the measure of the question marked arc (view photo )
The arc angle indicated with ? is derived as 230° using the angle between intersecting tangents.
What is an angle between intersecting tangentsThe angle between two tangent lines which intersect at a point is 180 degrees minus the measure of the arc between the two points of tangency.
angle G = 180° - arc angle HF
arc angle HF = 180° - 50°
arc angle HF = 130°
so the arc angle indicated with ? is;
? = 360° - 130°
? = 230°
Therefore, using the angle between the intersecting tangents, the arc angle indicated with ? is 230°.
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Which shows 71. 38 in word form? O A seventy-one thirty-eighths O B. Seventy-one and thirty eighths O c. Seventy-one and thirty-eight tenths D. Seventy-one and thirty-eight hundredths E seventy-one and thirty-eight thousands
The number 71.38 can be written in word form as "seventy-one and thirty-eight hundredths." The correct answer is option D.
In decimal notation, the number 71.38 can be broken down into its whole number and decimal parts. The whole number part is 71, and the decimal part is 0.38.
In a decimal number, the digits to the right of the decimal point represent fractions of a whole. Each digit to the right of the decimal point has a place value that is a power of 10.
In word form, the decimal part 0.38 is read as "thirty-eight hundredths." Therefore, when combined with the whole number 71, the correct word form is "Seventy-one and thirty-eight hundredths."
Therefore option D is the correct answer.
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Tell which property the statement illustrates.
(x + 2) + 5 = x + (2 + 5)
The given statement:
(x + 2) + 5 = x + (2 + 5)
illustrates the associative property of addition.
There are three properties of addition : Associative, commutative and identity.
The associative property of addition states that : (a+b)+c = a + (b+c)
The commutative property of addition states that : a + b = b + a
The identity property of addition states that : a + 0 = a.
Therefore, the statement is illustrating the associative property of addition.
Consider the following planes. 5x - 3y + z = 2, 3x + y - 5z = 4 Find parametric equations for the line of intersection of the planes. (Use the parameter t.) (x(t), y(t), z(t)) = Find the angle between the planes. (Round your answer to one decimal place.)
the cross product of the normal vectors of the planes will give you the direction vector of the line.
(5,−3,1)×(3,1,−5)=(14,28,14)
Which we can scale down to (1,2,1)
Now we need a point on the line. By inspection we can see that (1,1,0) lies in both planes.
Sometimes it it not that easy. But it is usually pretty easy to find a point in at least one plane and then travel along some line in that plane until we intersect the line in question.
Vector form of the line L:(x,y,z)=(1,2,1)t+(1,1,0)
In parametric form x=t+1,y=2t+1,z=t
The parametric equations are (x(t), y(t), z(t)) = (17/34 + 11t/34, 22/34 - 5t/34, 57/34 + 7t/34), where t is a parameter. The angle between the planes is 93.7 degrees.
To find the line of intersection of the planes, we can set the two equations equal to each other and solve for x, y, and z in terms of a parameter t. We can begin by eliminating one variable, say z.
From the first equation, we have z = 2 - 5x + 3y, and substituting this into the second equation gives 3x + y - 5(2 - 5x + 3y) = 4. Simplifying this equation, we get 22x - 14y - 23 = 0. Solving for y in terms of x, we get y = (22/14)x - (23/14).
Substituting this into the first equation and solving for z, we get z = (17/14)x + (57/14). Therefore, we have x = (17/22) + (11/22)t, y = (22/14) - (5/14)t, and z = (17/14)x + (57/14) + (7/22)t. These are the parametric equations for the line of intersection of the planes.
To find the angle between the planes, we can find the angle between their normal vectors.
The normal vector to the plane 5x - 3y + z = 2 is (5, -3, 1), and the normal vector to the plane 3x + y - 5z = 4 is (3, 1, -5). Using the dot product formula, we have cosθ = (5)(3) + (-3)(1) + (1)(-5) / sqrt(5² + (-3)² + 1²) sqrt(3² + 1² + (-5)²), which simplifies to cosθ = -19/34.
Taking the inverse cosine of this value, we get θ = 93.7 degrees, rounded to one decimal place. Therefore, the angle between the planes is approximately 93.7 degrees.
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The buying and selling rate of U. S. Doller ($) in a day are Rs 115. 25 and Rs 116. 5 respectively. How many dollar should be bought and sold to have the profit of $ 10 ? Find it
To earn a profit of $10, we need to buy and sell 10 dollars.
The difference between the buying and selling rates is the profit margin for the currency exchange. Here, the profit margin is 116.5 - 115.25 = 1.25 Rs per dollar.
To make a profit of $10, we need to buy and sell enough dollars to earn a profit of 1.25*10 = 12.5 Rs.
Let's assume we buy and sell x dollars. Then the cost of buying x dollars is 115.25x Rs, and the revenue from selling x dollars is 116.5x Rs.
So, the profit from buying and selling x dollars is (116.5x - 115.25x) = 1.25x Rs.
We need to find x such that 1.25x = 12.5, which gives x = 10.
Therefore, we need to buy and sell 10 dollars to earn a profit of $10.
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I need help ASAP (will give brainliest)
Answer:
92°
Step-by-step explanation:
All angles should add up to 360°
Opposite angles are equal so that means two angles are 88°
88+88=176
360 - 176 = 184
184 / 2 = 95
Measure of angle A is 92°
b) During the first market day, Fatuma bought 30 oranges and 12 mangoes and paid Ksh. 936 for all the fruits. In the second market day, the price of an orange increased by 20% while that of a mango reduced in the ratio 3:4. Fatuma bought 15 oranges and 20 mangoes and paid Ksh. 780 for all the fruits. Given that the cost of an orange and that of a mango during the first market day was Ksh. x and Ksh. y respectively: (i) Write down simultaneous equations to represent the information above. (2 marks) (ii) Use matrix in (a) above to find the cost of an orange and that of a mango in the first market day. (4 marks) (iii) Fatuma sold all the fruits bought on the second market day at a profit of 10% per orange and 15% per mango. Calculate the total amount of money realized for the sales. (2 marks)
Answer:Let the cost of an orange and that of a mango during the first market day be Ksh. x and Ksh. y respectively.
From the first market day:
30x + 12y = 936
From the second market day:
15(1.2x) + 20(3/4y) = 780
Simplifying the second equation:
18x + 15y = 780
(ii) Using matrix to find the cost of an orange and that of a mango in the first market day:
Rewriting the equations in matrix form:
|30 12| |x| |936|
|18 15| x |y| = |780|
Multiplying the matrices:
|30 12| |x| |936|
|18 15| x |y| = |780|
|30x + 12y| |936|
|18x + 15y| = |780|
Using matrix inversion:
| x | |15 -12| |936 12|
| y | = | -18 30| x |780 15|
|x| |270 12| |936 12|
| | = |-360 30| x |780 15|
|y|
Simplifying the matrix multiplication:
|x| |1194| |12|
| | = | 930| x |15|
|y|
Therefore, the cost of an orange in the first market day was Ksh. 39 and the cost of a mango in the first market day was Ksh. 63.
(iii) Calculation of the total amount of money realized for the sales:
On the second market day, Fatuma bought 15 oranges and 20 mangoes.
Cost of 15 oranges = 15(1.2x) = 18x
Cost of 20 mangoes = 20(3/4y) = 15y
Total cost of fruits bought on the second market day = 18x + 15y = 18(39) + 15(63) = Ksh. 1629
Profit earned on 15 oranges at 10% = 1.1(1.2x)(15) - (1.2x)(15) = 0.18x(15) = 2.7x
Profit earned on 20 mangoes at 15% = 1.15(3/4y)(20) - (3/4y)(20) = 0.15y(20) = 3y
Total profit earned = 2.7x + 3y
Total amount of money realized for the sales = Total cost + Total profit
= Ksh. 1629 + 2.7x + 3y.
Step-by-step explanation:
LA and LB are vertical angles. If mLA=(x+21)° and mLB=(4x-30)°, the find then measure of LB
Answer:
38 degrees
Step-by-step explanation:
Vertical angles are congruent(equal measures), so mLA = mLB
STEP 1:
Let's use some simple substitution.
mLA = mLB
mLA = x+21, mLB = 4x-30
You plug these two in and get:
x+21 = 4x-30
This is your equation.
STEP 2:
Let's solve our equation!
x+21 = 4x-30
(add 30 to both sides)
x+51 = 4x
(subtract x from both sides)
51 = 3x
(switch order for comprehension)
3x = 51
(divide both sides by 3)
x = 17
Ta-da! You get the measure of x = 17 degrees.
STEP 3:
Let's plug in our value of x to get the value of LB.
mLB = 4x - 30
mLB = 4(17) - 30
mLB = 68 - 30
mLB = 38
This is your answer.
Is the expression (x + 18) a factor of x² - 324?
Answer: We can check whether the expression (x + 18) is a factor of x² - 324 by dividing x² - 324 by (x + 18) using polynomial long division or synthetic division.
Using polynomial long division:
x + 18 │x² + 0x - 324
-x² - 18x
----------
18x - 324
18x + 324
----------
0
Since there is no remainder, we can see that (x + 18) is indeed a factor of
x² - 324.
If a sample of 32 runners is taken from a population of 201 people what if the means of how many runners times
201 could refer to the mean of how many runners' times. The Option C is correct.
Could sample refer to the mean of runner times?The sample of 32 runners, as given, does not refer to the mean of how many runners' times. The sample size refers to the number of individuals selected from the population while population size refers to the total number of individuals in the population.
Data:
The population of 201 people is given.
The sample of 32 runners is taken from the population.
So, the mean of the runners' times would be calculated using all 201 runners in the population, not just the 32 in the sample. Therefore, the Option C is correct.
Full question "If a sample of 32 runners were taken from a population of 201 runners, could refer to the mean of how many runners' times ? A. Both 32 and 201 B. Neither 32 nor 201 C. 201 D. 32"
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5. this prism has a right triangle for a base. the volume of the prism is 54 cubic units.
what is the value of h?
The value of h is 6 units.
The volume of the prism is given by the formula V = 1/3 x (base area) x height. Since the base of the prism is a right triangle, the area of the base is given by A = 1/2 x base x height of the triangle. Therefore, the volume of the prism can be written as V = 1/3 x 1/2 x base x height of the triangle x height of the prism.
Simplifying this expression, we get V = 1/6 x base x height^2. Given that the volume of the prism is 54 cubic units, and substituting the value of the base which is not given as per the formula we get, 54 = 1/6 x base x h^2. Solving for h, we get h = 6 units. Therefore, the value of h is 6 units.
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SOMEONE HELPP , giving brainlist to anyone who answers
Answer:
[tex]2( {3}^{x} ) = 258280326[/tex]
[tex] {3}^{x} = 129140163[/tex]
[tex]x = \frac{ ln(129140163) }{ ln(3) } = 17[/tex]
n = 17 + 1 = 18
[tex]s = \frac{2( 1 - {3}^{18} )}{1 - 3} = 387420488[/tex]
The sum of this finite geometric series is 387,420,488.
36 A bicycle rental company charges a fixed rental fee for the first
30 minutes and a cost per minute for each additional minute. The
table shows the linear relationship between the total cost in dollars
to rent a bicycle and the number of additional minutes a bicycle
is rented.
Bicycle Rental
Number of Additional Minutes Total Cost (dollars)
15
3.05
20
$0.17 per min
$0.35 per min
$0.07 per min
$0.56 per min
35
55
3.40
4.45
5.85
What is the rate of change of the total cost in dollars with respect to
the number of additional minutes?
Answer:
C
Step-by-step explanation:
Since the rate is linear, we can subtract a larger amount of minutes by a smaller one and a larger cost by a smaller one.
For example:
20 - 15 = 5
3.40 - 3.05 = 0.35
Since you want to find the amount it takes per minute, you divide the 5 by 5 to make it one minute. You also divide the 0.35 by 5 in which you get 7.
What is the area of the following circle?
Either enter an exact answer in terms of π or use 3.14 for π and enter your answer as a decimal.
The area of the circle whose diameter is 14 is approximately 153.94 square units or 49π square units..
The area of a circle is given by the formula A = πr², where r is the radius of the circle. Since the diameter of the circle is given as d = 14, we know that the radius is half of the diameter, which is r = d/2 = 7.
Substituting the value of the radius in the formula, we get:
A = πr² = π(7)² = π(49) ≈ 153.94 (rounded to two decimal places using 3.14 for π)
Therefore, the area of the circle is approximately 153.94 square units. Alternatively, the exact answer can be left in terms of π, which would be A = 49π square units.
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which of the following groups of numbers is ordered from least to greatest?
A. 1/5, 3/8, 4/10, 0.45, 0.6
B. 1/5, 3/8, 0.45, 4/10, 0.6
C. 0.6, 0.45, 4/10, 3/8, 1/5
D. 0.6, 4/10, 0.45, 1/5, 3/8
ans.(a) is correct
only in option (a) numbers are arranged from least to greatest.
John has a pepper shaker in the shape of a cylinder. It has a radius of 9 mm and a height of 32 mm. John wants to cover the pepper shaker with tape, How much tape is needed? Round to the hundredths
John needs approximately 1,814.4 mm² of tape to cover the pepper shaker. Rounded to the hundredths, the answer is 1,814.40 mm².
To calculate the amount of tape needed to cover the pepper shaker, we need to find the lateral area of the cylinder. This is given by the formula L = 2πrh, where r is the radius and h is the height.
Substituting the values given, we get L = 2π(9 mm)(32 mm) = 1,814.4 mm².
Therefore, John needs approximately 1,814.40 mm² of tape to cover the pepper shaker.
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Let the function f be defined by
f(x) = x² + 28. If f(3y) = 2f(y), what is the one possible
value of y?
A) -1
B) 1
C) 2
D) -3
The one possible value of y, will be 2. Option C is correct.
We have f(x) = x² + 28, and f(3y) = 2f(y). Substituting 3y for x in the definition of f, we get;
f(3y) = (3y)² + 28 = 9y² + 28
Substituting y for x in the definition of f, we get;
f(y) = y² + 28
Using the given equation, we have;
2(y² + 28) = 9y² + 28
Expanding and simplifying, we get;
0 = 7y² - 56
Dividing by 7, we get:
y² - 8 = 0
Factoring, we get;
(y + 2)(y - 2) = 0
So y = -2 or y = 2. Since we are looking for only one possible value of y is 2.
Hence, C. is the correct option.
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The berry-picking boxes at bingo berry farm have square bottoms that are 8 centimeters on each side. mateo fills his box with raspberries to a height of 6 centimeters. what is the volume of raspberries in mateo's box?
The volume of raspberries in Mateo's box is 384 cubic centimeters.
To calculate the volume of raspberries in Mateo's box, we need to use the formula for the volume of a rectangular prism, which is length x width x height. In this case, the length and width are both 8 centimeters, as the box has a square bottom. The height is 6 centimeters, as Mateo fills the box to that height with raspberries.
So, the volume of raspberries in Mateo's box is:
Volume = length x width x height
Volume = 8 cm x 8 cm x 6 cm
Volume = 384 cubic centimeters
Therefore, the volume of raspberries in Mateo's box is 384 cubic centimeters. This calculation assumes that the raspberries are tightly packed in the box, without any gaps or air pockets. In reality, the actual volume of raspberries may be slightly less than this, depending on how they are arranged in the box. Nonetheless, this calculation provides a reasonable estimate of the amount of raspberries that Mateo is able to pick and fit in the box.
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when rounding to the nearest hundred what is the greatest whole number that rounds to 500?
Answer:
499
Step-by-step explanation:
A rectangle with length n is inscribed in a circle of radius 9. Find an expression for the area of the rectangle in terms of n
Using pythagorean theorem the area of the rectangle in terms of n is given by A = n√(324 - n^2).
In the given scenario, we have a circle with a diameter that is twice the length of the radius, which is stated as 18. The diagonal of the rectangle is also the diameter of the circle, so it measures 18. Let's assume the width of the rectangle as 'w'. By applying the Pythagorean theorem, we can establish the following relationship:[tex]n^2 + w^2 = 18^2[/tex] = 324, where 'n' represents the length of the rectangle.
To solve for 'w', we rearrange the equation: [tex]w^2 = 324 - n^2.[/tex] This equation allows us to calculate the width 'w' of the rectangle when we know the length 'n'.
The area of the rectangle, denoted as 'A', is given by the formula A = nw, where 'n' is the length and 'w' is the width of the rectangle. By substituting the expression for w^2, we obtain: A =[tex]n\sqrt(324 - n^2).[/tex]
This equation represents the relationship between the length 'n' and the area 'A' of the rectangle, taking into account the given information about the diameter of the circle, which is also the diagonal of the rectangle. By solving for 'n' and substituting it into the formula, we can determine the area of the rectangle.
Let the width of the rectangle be w, then by the Pythagorean theorem, we have:
[tex]n^2 + w^2 = 18^2[/tex] = 324
Solving for w, we get: [tex]w^2 = 324 - n^2[/tex]
The area of the rectangle is given by:
A = nw
Substituting the expression for w^2, we get:
A =[tex]n\sqrt(324 - n^2)[/tex]
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Only a small percentage of Americans owned cars before the 1940s. By 2017, there were nearly 250 million vehicles for 323 million people, significantly increasing the need for roadways. In 1960, the United States had about 16,000 km of interstate highways. Today, the interstate highway system includes 77,000 km of paved roadways. What percent increase does this represent?
A. 381 percent
B. 792 percent
C. 38 percent
D. 79 percent
The percent increase in the interstate highway system from 1960 to now is 381%.
option A.
What is the percent increase?The percent increase from 16,000 km to 77,000 km is difference between the old value and new value divided by the old value expressed in 100%.
percent increase = 100% x (new value - old value) / old value
percent increase = 100% x (77,000 - 16,000) / 16,000
percent increase = 100% x 61,000 / 16,000
percent increase = 381.25%
Thus, the percent increase in the interstate highway system from 1960 to now is approximately 381%, which is option A.
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A consumer group is investigating two brands of popcorn, R and S. The population proportion of kernels that will pop for Brand R is 0. 90. The population proportion of kernels that will pop for Brand S is 0. 85. Two independent random samples were taken from the population. The following table shows the sample statistics. Number of Kernels in Samples Proportion from Sample that Popped Brand R 100 0. 92 Brand S 200 0. 89 The consumer group claims that for all samples of size 100 kernels from Brand R and 200 kernels from Brand S, the mean of all possible differences in sample proportions (Brand R minus Brand S) is 0. 3. Is the consumer group’s claim correct? Yes. The mean is 0. 92−0. 89=0. 3. Yes. The mean is 0. 92 minus 0. 89 equals 0. 3. A No. The mean is 0. 92+0. 892=0. 905. No. The mean is the fraction 0. 92 plus 0. 89 over 2 equals 0. 905. B No. The mean is 0. 92−0. 892=0. 15. No. The mean is the fraction 0. 92 minus 0. 89 over 2 equals 0. 15. C No. The mean is 0. 90+0. 852=0. 875. No. The mean is the fraction 0. 90 plus 0. 85 over 2 equals 0. 875. D No. The mean is 0. 90−0. 85=0. 5
The mean of all possible differences in sample proportions (Brand R minus Brand S) is given by:
mean = pR - pS,
where pR is the population proportion of kernels that will pop for Brand R, and pS is the population proportion of kernels that will pop for Brand S.
Substituting the given values, we get:
mean = 0.90 - 0.85 = 0.05
However, the consumer group claims that the mean of all possible differences in sample proportions is 0.3. This claim is not supported by the calculations above.
Therefore, the correct answer is:
C) No. The mean is 0.90+0.85/2=0.875. No. The mean is the fraction 0.90 plus 0.85 over 2 equals 0.875.
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Which name best describes the polygon with
vertices (0,0), (4,8), (12,8), and (16,0)?
The polygon described by the given vertices is a trapezoid.
Why is the polygon is given vertices a trapezoid?
A trapezoid is a quadrilateral with at least one pair of parallel sides. In this case, the sides with endpoints (0,0) and (16,0) are parallel to each other, and the sides with endpoints (4,8) and (12,8) are parallel to each other. Therefore, the polygon described by the given vertices is a trapezoid.
In addition to having parallel sides, a trapezoid can have various other properties, such as being isosceles (having two equal sides) or having perpendicular diagonals. However, based solely on the given vertices, we can determine that the polygon is a trapezoid.
A trapezoid has various properties, including having one pair of parallel sides, having one pair of non-parallel sides, and having two pairs of adjacent angles that add up to 180 degrees. It can also be isosceles if the non-parallel sides are equal in length.
The trapezoid is a commonly studied shape in geometry because of its simple properties and its appearance in many real-world applications, such as in architecture and engineering. Trapezoids are used in the design of roofs, bridges, and other structures that require stable, load-bearing shapes.
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Find the missing parts of the triangle. Round to the nearest tenth when necessary or to the nearest minute as appropriate.
a = 8. 0 in.
b = 13. 7 in.
c = 16. 7 in.
A = 26. 4°, B = 54. 5°, C = 99. 1°
A = 28. 4°, B = 54. 5°, C = 97. 1°
A = 30. 4°, B = 52. 5°, C = 97. 1°
No triangle satisfies the given conditions
The missing parts of the triangle are:
Angle A ≈ 28.4°Angle B ≈ 52.5°Angle C ≈ 99.1°How to find the missing parts of the triangle?To find the missing parts of the triangle, we can use the Law of Sines and Law of Cosines.
First, we can use the Law of Cosines to find angle A:
cos(A) = (b² + c² - a²) / (2bc)
cos(A) = (13.7² + 16.7² - 8²) / (2 * 13.7 * 16.7)
cos(A) = 0.773
A = [tex]cos^-^1^(^0^.^7^7^3^)[/tex]
A ≈ 28.4°
Next, we can use the fact that the sum of the angles in a triangle is 180° to find angles B and C:
B = 180° - A - C
B = 180° - 28.4° - 99.1°
B ≈ 52.5°
C = 180° - A - B
C = 180° - 28.4° - 52.5°
C ≈ 99.1°
Therefore, the missing parts of the triangle are:
Angle A ≈ 28.4°Angle B ≈ 52.5°Angle C ≈ 99.1°Learn more about triangle
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Find the interval of convergence of the power series. (Be sure to include a check for convergence at the endpoints of the interval. If the interval of convergence is an Interval, enter your answer using interval notation. If the Interval of convergence is a finite set, enter your answer using set notation.)
Sum = (n!(x+5)^n) / 1 . 3 . 5 ...... (2n-1)
To find the interval of convergence of the power series, we can use the ratio test:
lim (n->inf) |((n+1)!(x+5)^(n+1)) / (1.3.5....(2n+1))| / |(n!(x+5)^n) / (1.3.5....(2n-1))|
= lim (n->inf) |(x+5)(2n+1)| / (2n+2) = |x+5| lim (n->inf) (2n+1)/(2n+2) = |x+5|
So the series converges if |x+5| < 1, and diverges if |x+5| > 1. Thus the interval of convergence is (-6, -4).
To check for convergence at the endpoints, we can use the limit comparison test with the divergent series:
1/1.3 + 1/1.3.5 + 1/1.3.5.7 + ... = sum (2n-1) terms = inf
At x = -6, we have:
sum (n=0 to inf) (n!(-1)^n)/(1.3.5....(2n-1)) = 1/1 - 1/1.3 + 1/1.3.5 - 1/1.3.5.7 + ... = inf
Since the series diverges at x = -6, the interval of convergence is (-6, -4] using set notation.
At x = -4, we have:
sum (n=0 to inf) (n!(1)^n)/(1.3.5....(2n-1)) = 1/1 - 1/1.3 + 1/1.3.5 - 1/1.3.5.7 + ... = 1 - 1/3 + 1/15 - 1/105 + ...
This is an alternating series that satisfies the conditions of the alternating series test, so it converges. Thus the interval of convergence is (-6, -4] using set notation, or [-6, -4) using interval notation.
To find the interval of convergence of the power series, we'll use the Ratio Test, which states that if the limit L = lim(n→∞) |aₙ₊₁/aₙ| < 1, then the series converges. Here, the series is given by:
Σ(n!(x+5)^n) / 1 . 3 . 5 ... (2n-1)
Let's find the limit L:
L = lim(n→∞) |(aₙ₊₁/aₙ)|
= lim(n→∞) |((n+1)!(x+5)^(n+1))/(1 . 3 . 5 ... (2(n+1)-1)) * (1 . 3 . 5 ... (2n-1))/(n!(x+5)^n)|
Now, simplify the expression:
L = lim(n→∞) |(n+1)(x+5)/((2n+1))|
For the series to converge, we need L < 1:
|(n+1)(x+5)/((2n+1))| < 1
As n approaches infinity, the above inequality reduces to:
|x+5| < 1
Now, to find the interval of convergence, we need to solve for x:
-1 < x + 5 < 1
-6 < x < -4
The interval of convergence is given by the interval notation (-6, -4). To check the endpoints, we need to substitute x = -6 and x = -4 back into the original series and use other convergence tests such as the Alternating Series Test or the Integral Test. However, the power series will diverge at the endpoints, as the terms do not approach 0. Therefore, the interval of convergence remains (-6, -4).
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how would you work the image attached out
The ratio of a : b : c : d is 3 : 7 : 2 : 7.
What are the ratios?The ratios are determined as follows from the data given.
The given data is:
7a = 2b
b = (7/2)a.
a and b have no common factors, thus a must be even and b must be odd.
c : d is 2 : 7
For an integer x, c = 2x and d = 7x
a : d is 3 : 1
So for an integer y, a = 3y and d = y
Substituting into 7a = 2b:
7(3y) = 2(7/2)y a
21y = 7y * b
b = 3a
Substituting these expressions for a and b into c : d = 2:7, we get:
2x : 7x = 3 : 1
2x = 3y and 7x = y
y = 14x/3
a : b : c : d = 3y : 7y : 2x : 7x
a : b : c : d = 3(3y) : 3(7y) : 3(2x) : 3(7x)
a : b : c : d = 9y : 21y : 6x : 21x
a : b : c : d = 3 : 7 : 2 : 7
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What is the slope of the linear function that models the data in the table?
The slope of the linear function that models the data in the table is -1.5. It was calculated by using the formula for slope (change in y divided by change in x) and plugging in the given coordinates. This means that for every increase of 2 in the x-value, the y-value decreases by 3.
To find the slope of the linear function that models the data in the table, we can use the slope formula
slope = (change in y)/(change in x)
We can choose any two points from the table to calculate the slope. Let's choose the points (-2,6) and (0,3)
change in y = 3 - 6 = -3
change in x = 0 - (-2) = 2
So the slope is
slope = (-3)/(2) = -1.5
Therefore, the slope of the linear function that models the data in the table is -1.5.
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--The given question is incomplete, the complete question is given
" What is the slope of the linear function that models the data in the table? "--
