Therefore, 0.4854 to 0.5546 is the 95% confidence range for the percentage of businesses that are anticipated to need greater employee payments for health insurance coverage in 2009.
A. Computation the margin of error
First step is to calculate the Confidence level using this formula
Confidence level= 1 -α
Where,
α=0.95
Let's enter the formula.
Level of confidence = 1-0.95
Level of confidence = 0.05
The following step is to use this formula to get Z.
Zα/2
Let's enter the formula.
Z= 0.05/2
Z=0.025
Finding the Z score of Z=0.025 is the third stage.
Zα/2=1.96
Let's now use this approach to calculating the margin of error.
Margin of error=Zα/2√p(1-p)/n
Where,
Zα/2=1.96
p=0.52
n=800
Let plug in the formula
Margin of error=1.96√0.52(1-0.52)/800
Margin of error=1.96√0.52(0.48)/800
Margin of error=1.96√0.2496/800
Margin of error=1.96√0.000312
Margin of error=0.0346
Therefore Margin of error will be 0.0346
B. Calculating the proportion of businesses anticipated to demand greater employee payments for health insurance coverage in 2009 with a 95% confidence interval
computation for the confidence interval's outer limits
p- Zα/2√p(1-p)/n
Where,
Zα/2=1.96
p=0.52
n=800
Let plug in the formula
Confidence interval=0.52-1.96√0.52(1-0.52)/800
Confidence interval=0.52-1.96√0.52(0.48)/800
Confidence interval=0.52-1.96√0.2496/800
Confidence interval=-0.52-1.96√0.000312
Confidence interval=0.4854
Computation for the boundaries of confidence interval
Using this formula
p+ Zα/2√p(1-p)/n
Where,
Zα/2=1.96
p=0.52
n=800
Let plug in the formula
Confidence interval=0.52+1.96√0.52(1-0.52)/800
Confidence interval=0.52+1.96√0.52(0.48)/800
Confidence interval=0.52+1.96√0.2496/800
Confidence interval=-0.52+1.96√0.000312
Confidence interval=0.5546
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Alexandra is fishing from a small boat. A fish swimming at the same depth as the hook
at the end of her fishing line is 5 meters away from the hook. If Alexandra is 13 meters away
from the fish, how far below Alexandra is the hook?
Answer:
12 m
Step-by-step explanation:
Here's a picture to show the problem.
boat
--------------------------------------------
~~~~~~~~~~~\ /~~~~~~~~~~~~~~~~~~~~~~~~
\-----------Alexandra ---------/ surface of the water
|\
| \
| \
| \
d | \ 13 m
| \
| \
| \
| --- rt < \
hook -----|------------------------------ fish
5 m
There is a right angle at the hook. We have a right triangle with leg d, the distance we need to find, leg 5 m, and hypotenuse 13 m.
a² + b² = c²
5² + b² = 13²
25 + b² = 169
b² = 144
b = √144
b = 12
Answer: 12 m
find the roots of the factored polynomial. (x 1)2(x 2) write your answer as a list of values separated by commas.
The (x-1)2(x+2) factored polynomial has roots of 5 and -2. In mathematics, a polynomial is a statement with variables.
what are polynomial ?A polynomial is a mathematical expression that solely uses additions, subtractions, multiplications, and powers of positive integer variables. It is composed of coefficients and uncertainty. A single indeterminate x polynomial is indicated by the expression x2 4x + 7. In mathematics, a polynomial is a mathematical equation made up of variables (sometimes called indeterminates) and coefficients that can be added, subtracted, multiplied, and raised to negative integer powers of non-variables. A polynomial is a statement in mathematics involving variables and coefficients. The only operations that can be included in an expression are addition, subtraction, multiplication, and non-negative integer exponents. These formulas are known as polynomials.
given
(x - 5)(x + 2) = 0
Using the 0 product property:
Case 1
x - 5 = 0
x = 5
Case 2
x + 2= 0
x = -2
The (x-1)2(x+2) factored polynomial has roots of 5 and -2. In mathematics, a polynomial is a statement with variables.
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8 ÷ 28 *has to be in decimal form*
Answer: 0.28571428571
Step-by-step explanation: 8 dived by 28
alex thinks $163$ degree angles are neat. what is the maximum number of interior angles of a convex polygon that can have measure $163$ degrees?
The maximum number of interior angles of a convex polygon would be 7.
Imagine operating a small vehicle on a track with a polygonal shape. Your compass is handy (directional, not one for drawing circles). The automobile concludes the lap in the same direction as it began. If there was a compass, it has completed one full rotation.
180 - 131 = 49°
360/49 = 7.346938775510204
So 7 interior angles max
A convex polygon's outside angles add up to 360 degrees.
131 degrees for the inside angles and 49 degrees for the outside angles. The vehicle is capable of seven rotations at 49 degrees and one turn at 17 degrees, for a total of 360 degrees in one lap.
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The question is wrong the correction:
Alex thinks 131 degrees are neat. What is the maximum number of interior angles of a convex n-gon that can measure 131 degrees?
the ratio of boys to girls in ms.cano's class is 7 to 21. there are 49 girls in the class. what is the total number of students in mr.cano's class?
The ratio of boys to girls in Ms. Cano's class is 7 to 21, there are 49 girls in the class. The total number of students in Mr. Cano's class is 196
Ratio:
In mathematics, ratios indicate the number of times one number contains another number. For example, if you have 8 oranges and 6 lemons in your fruit bowl, the ratio of oranges to lemons is 8 to 6 (that is, a ratio of 8:6, or 4:3). Similarly, the ratio of lemons to oranges is 6:8 (or 3:4) and the ratio of oranges to whole fruit is 8:14 (or 4:7). Ratios can be given by giving both constituent numbers written "a to b" or "a : b", or by giving only the value of their quotient a/b.
When comparing one data point (A) to another data point (B), the formula is A/B. That is, divide information A by information B. For example, if A is 5 and B is 10, the ratio is 5/10. Solve the equation. Divide data A by data B to get the ratio.
According to the Question:
Given:
The ratio of boys to girls is 7: 21,
and there are 49 boys,
Let number of boys be x and number of girls be y.
49/7 × 11 = 77 girls
Therefore,
Total number of boys and girls in the classroom is
77 + 49 = 126.
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Solve the word problem below using the steps given in the lesson above. Show your equation and each step you take to solve it. Neil and Tom love to collect baseball cards. Neil has 83 more baseball cards than Tom. Neil has 517 baseball cards. How many baseball cards does Tom have
In linear equation , the number of baseball cards Tom has is 434.
What in mathematics is a linear equation?
A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.
Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.
We need to find the amount of cards Tom has.
The number of cards Tom has is 434.
Let the number of baseball cards Tom has be X .
Neil has 83 more baseball cards than Tom so
X + 83 is the number of baseball cards that Neil has.
The number of baseball cards Neil has is 517
So,
x + 83 = 517
x = 517 - 83
x = 434
Hence, the number of baseball cards Tom has is 434.
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An astronaut on the moon throws a baseball upward. The astronaut is 6 ft, 6 in. talk and the initial velocity of the ball is 40 ft per sec. The height s of the hall in feet is given by the equation s=-2.7t^2 + 40t+6.5 , where the number of seconds after the ball was thrown. After how many seconds in the ball 22ft above the moons surface?
Answer:
Step-by-step explanation:
Using the given equation, we can solve for t when s is equal to 22.
22 = -2.7t^2 + 40t + 6.5
Subtracting 6.5 from both sides, we get:
15.5 = -2.7t^2 + 40t
Adding 2.7t^2 to both sides, we get:
18.2t^2 = 15.5 + 40t
Subtracting 40t from both sides, we get:
18.2t^2 - 40t = 15.5
Dividing both sides by 18.2, we get:
t^2 - 2.2t = 0.855
Factoring, we get:
(t - 1)(t - 0.855) = 0
Setting each factor equal to 0 and solving, we get:
t = 1 and t = 0.855
Therefore, the ball will reach a height of 22ft after 1 second and 0.855 seconds.
ABCD is a regular tetrahedron. MandN are the mid points of the edges AB and CD. It the length of AB is a, then |MN|^2 = ...?
4/3 is the valve of |MN| ^2 of a given tetrahedron in which M AND N are the mid points of the edges AB and CD . is explained below:
on observing the diagram we can estimate that image of point D in the plane is given by ABC is [tex](2\sqrt{2} , 0 , -2 )[/tex] and volume of tetrahedron ACBM is 4/3
AB=BC=CD=AD =a
hence a =[tex]2\sqrt{2}[/tex] then MA =2 ; 2b^2 =4 ; therefore , b=[tex]\sqrt{2}[/tex]
then value of B ([tex](\sqrt{2} ,\sqrt{2}, 0 )[/tex] then according to the theorem we get as
[tex]MA^{2} + MB^{2} = AB^{2}[/tex] we have condition by diagram as MA ⊥ MB similarly
MA ⊥ MC , MB ⊥ MC hence , MA.MC =-2z =0
hence MB.MC= [tex]\sqrt{2x} +\sqrt{2y} =0[/tex] therefore we get y=-x and z=0 hence the coordinates for C(x ,-x ,0)
and also MC^2 =2x^2=MA^2 =4 ; x=[tex]\sqrt{2}\\[/tex] (x>0)
hence C[tex](\sqrt{2} ,\sqrt{2}, 0 )[/tex] hence
|MN|^2 = [tex]\frac{1}{6} |MA| . |MB| . |MC| = \frac{4}{3}[/tex]
hence the value of |MN|^2 = 4/3
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in a jar containing dry beans, the ratio of white beans to kidney beans is 5:4. if 30 white beans were replaced with 30 kidney beans, the ratio would be 1:1. how many more white beans are there than kidney beans?
As per the unitary method, the amount of white beans are there than kidney beans are 30.
The term unitary method is known as a technique for solving a problem by first finding the value of a single unit and then finding the necessary value by multiplying the single unit value.
Here we have given that in a jar containing dry beans, the ratio of white beans to kidney beans is 5:4.
And we also know that if 30 white beans were replaced with 30 kidney beans, the ratio would be 1:1.
Here we have consider that let the number of pinto beans be x and that is the number of white beans will be x + 30
In which means the total number of beans in the jar will be written as,
=> x + x + 30 = 2x + 30
Here we know that the Total ratio is calculated as,
=> 5 + 4 = 9
In order to find the number of pinto beans then it can be calculated as,
=> ratio of pinto beans / Total ratio X Total number of beans
Which can be written as.
=> (2x + 30) = x
When we simplify this one then we get the value of x as,
=> x = 30.
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a company produces steel rods. the lengths of the steel rods are normally distributed with a mean of 97-cm and a standard deviation of 1-cm. for shipment, 15 steel rods are bundled together. find the probability that the average length of a randomly selected bundle of steel rods is less than 97.1-cm.
The most typical or average value among a group of numbers is called the mean. It is a statistical measure of a probability distribution's central tendency along the median and mode. It also goes by the name "anticipated value."
Steel rods are produced by a firm. The lengths of the steel rods have a mean of 97 cm and a standard deviation of 1 cm, and they are regularly distributed. 15 steel rods are packaged together for shipping. determine the likelihood that the average length of a bundle of steel rods chosen at random is less than 140.7 cm.
mean is N (M) (109,1.6)
Looking for P(M 108.7) to P(z ???) conversion utilizing N(0,1) z-statistic transformation
P(z [M - population mean]/[SD/square root(sample size)]) = P(z [108.7-109)/[1.6/sqrt(27)] = P(z -0.974] = 0.165.
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You pick a card at random. 2 3 4 5 What is P(3)?
If you picked a card at random, then the probability of picking a three is 1 / 4 or 25 %.
How to find the probability ?The probability of an event occurring is defined by probability. There are many instances in real life where we may need to make predictions about how something will turn out. The outcome of an event may be known to us or unknown to us. When this happens, we say that there is a chance that the event will happen or not. In general, probability has many wonderful uses in games, in business to make forecasts based on likelihood, and in this emerging branch of artificial intelligence.
The probability that an event will occur is determined by the probability formula. The ratio of positive outcomes to all possible outcomes is used as the formula to determine an event's probability.
The probability that you can pick a three out of the cards given is:
= Number of cards of 3 / Number of total cards
= 1 / 4
= 25 %
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31. Grace solved the equation 2 1/2y = 5/8. Her steps for the solution are shown in the table but are all mixed up. Write her steps I. The correct order on the right side of the table
The correct steps in the solution of the fraction are;
Step 1 ; 2 1/2y = 5/8Step 2 ; 5/2 y = 5/8Step 3 ; y = 5/8 . 2/5Step 4 ; y = 10/40 or 1/4What are the steps in the solution?We know that when we talk about a fraction what we mean is just a part of a whole. There are some steps that we would need in the solution of the question and the steps have not been arranged in the proper order in the image that is attached here.
The task that we have then is to be able to arrange the steps that we need to take in the proper order and as such, we are going to have that;
Step 1 ; 2 1/2y = 5/8
Step 2 ; 5/2 y = 5/8
Step 3 ; y = 5/8 . 2/5
Step 4 ; y = 10/40 or 1/4
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Elena is designing a logo in the shape of a triangle. She wants the logo to have an area of 12 square inches. She draws bases of different lengths and tries to compute the height for each base. Write an equation that Elena can use to find the height, h, for a base that is b inches long.
An equation that Elena can use to find the height 'h' is h = 24/b.
What is a triangle?A triangle is a three-sided closed-plane figure formed by joining three noncolinear points. Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.
We know the area of a triangle is (1/2)×base×height.
Given, Elena is designing a logo in the shape of a triangle having an area of 12 square inches.
Therefore,
(1/2)×base×height = 12.
b×h = 12×2.
b×h = 24.
So, Elena can use the following equation to get the height 'h',
h = 24/b.
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(Graphing Linear Equations MC)
A eyeglasses store is checking their inventory. The table shows the relationship between the number of days since the opening of the eyeglasses store and the total amount of sunglasses in their inventory.
Sunglasses Inventory
Number of Days Total Amount of Sunglasses
2 54
5 48
7 44
10 38
Which of the following graphs shows the relationship given in the table?
graph with the x axis labeled number of days and the y axis labeled total amount of sunglasses and a line going from the point 0 comma 52 through the point 1 comma 50
graph with the x axis labeled number of days and the y axis labeled total amount of sunglasses and a line going from the point 0 comma 52 through the point 1 comma 49
graph with the x axis labeled number of days and the y axis labeled total amount of sunglasses and a line going from the point 0 comma 58 through the point 1 comma 56
graph with the x axis labeled number of days and the y axis labeled total amount of sunglasses and a line going from the point 0 comma 58 through the point 1 comma 55
The solution is Option C.
The equation of line is given by y = -2x + 58
What is an Equation of a line?The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation of line be represented as A
Now , the value of A is
Let the first point be P ( 2 , 54 )
Let the second point be Q ( 5 , 48 )
The slope of the line between the points m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Substituting the values in the equation , we get
Slope m = ( 54 - 48 ) / ( 2 - 5 )
On simplifying the equation , we get
Slope m = 6 / -3
Slope m = -2
Now , the equation of line is y - y₁ = m ( x - x₁ )
Substituting the values in the equation , we get
y - 54 = -2 ( x - 2 )
On simplifying the equation , we get
y - 54 = 2x + 4
Adding 54 on both sides of the equation , we get
y = -2x + 58
Therefore , the graph is plotted through the points ( 0 , 58 ) , ( 1 , 56 )
Hence , the equation of line is y = -2x + 58
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Determine the number of positive integers n that satisfy 1/2 < n/(n +1) < 99/101. Do any negative integers satisfy this inequality? Hint: Tackle 1/2 < n/(n + 1) and n/(n +1) < 99/101 separately.
Answer:
No
Step-by-step :
n/n + 1 > 1/2, (n + 1)/n < 2, (n+1)/n - 2 < 0, [(n + 1) - 2n]/n < 0, (1 - n)/n < 0, n > 0, 1 - n < 0, n > 1
n/n + 1 < 99/101, (n + 1)/n > 101/99, [99(n+1)]/n > 101, [(99n + 99)]/n > 101, [(99n + 99)]/n - 101 > 0, (99n + 99 - 101n)/n > 0
(99 - 2n)/n > 0, n > 0, 99 - 2n > 0, 2n < 99, n < 99/2
1 < n < 49.5
Allie is creating an art project using pieces of paper that are each 8. 06 inches long. If she tapes 5. 4 pieces together end-to-end, what will the total length be?
According to the formula of area of rectangle, the length of each piece is 1.49 inches.
The formula to calculate the area of the rectangle is written as,
A = l x b
where l refers the length and b refers the breadth of the rectangle.
Here we have know that Allie is creating an art project using pieces of paper that are each 8. 06 inches long.
Here we also know that she tapes 5. 4 pieces together end-to-end.
Here the value 8.06 refers the total area of the paper and the value 5.4 refers the breadth of the paper.
Then according to the formula, the length is calculated as,
=> l = 8.06/5.4
=> 1.49
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Find the value of 2π√l /g
when π=3⅐, l= 98 and g = 32
Answer:
Step-by-step explanation:
2π√l/g = (2*3.14*sqrt(98))/32 = 10.945
use the row of numbers shown below to generate 12 random numbers between 01 and 99. 78038 18022 84755 23146 12720 70910 49732 79606 Starting at the beginning of the row, what are the first 12 numbers between 01 and 99 in the sample?
The first 12 numbers between 01 and 99 in the sample are: 99, 25, 68, 17, 9, 89, 56, 97, 43, 28, 3, 66.
The formula to generate random numbers between 01 and 99 is (number*99/max_number)+1.
For the first number in the row, 78038, the calculation would be (78038*99/78038)+1 = 99.
For the second number in the row, 18022, the calculation would be (18022*99/78038)+1 = 25.
For the third number in the row, 84755, the calculation would be (84755*99/78038)+1 = 68.
For the fourth number in the row, 23146, the calculation would be (23146*99/78038)+1 = 17.
For the fifth number in the row, 12720, the calculation would be (12720*99/78038)+1 = 9.
For the sixth number in the row, 70910, the calculation would be (70910*99/78038)+1 = 89.
For the seventh number in the row, 49732, the calculation would be (49732*99/78038)+1 = 56.
For the eighth number in the row, 79606, the calculation would be (79606*99/78038)+1 = 97.
The first 12 numbers between 01 and 99 in the sample are: 99, 25, 68, 17, 9, 89, 56, 97, 43, 28, 3, 66.
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there are 260 plants in a garden. 2/20 are flowers. how many plants are not flowers?
Answer:
To find out how many plants are not flowers, we need to subtract the number of flowers from the total number of plants.
We know that 2/20 of the plants are flowers, and we can use this information to find out how many plants are flowers. To do this, we can multiply the total number of plants (260) by the fraction of plants that are flowers (2/20).
260 x (2/20) = 260 x 0.1 = 26
So there are 26 plants that are flowers.
To find the number of plants that are not flowers, we subtract the number of flower plants from the total number of plants:
260 - 26 = 234
So there are 234 plants that are not flowers.
the seller of a loaded die claims that it will favor the outcome 6. we don't believe that claim, and roll the die 200 times to test an appropriate hypothesis. our p-value turns out to be 0.03. which conclusion is appropriate? explain. a) there's a 3% chance that the die is fair. b) there's a 970/0 chance that the die is fair. c) there's a 3% chance that a loaded die could randomly produce the results we observed, so it's reasonable to conclude that the die is fair.
It is plausible to assume that the die is fair because there is a 3% possibility that a loaded die might randomly yield the outcomes that we saw.
The appropriate conclusion is that there is a 3% chance that a loaded die could randomly produce the results we observed. We tested this hypothesis by rolling the die 200 times and our p-value turned out to be 0.03. This means that there is only a 3% chance that the results we observed could have been produced randomly by a loaded die, so it is reasonable to conclude that the die is fair. This is because a p-value of 0.03 is considered to be statistically significant, which indicates that the results we observed are unlikely to have been due to chance. Therefore, we can conclude that the seller's claim that the die will favor the outcome 6 is likely false.
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Question 9(Multiple Choice Worth 1 points)
(02.05 MC)
What are the vertex and range of y = x + 21-6?
O(-2,-6); -6 ≤ y ≤0⁰
O(-2,-6); -
O(2,-6): -6 ≤ y
O(2,-6); -
The vertex and range of y = |x + 2| - 6 are: A. (-2, -6); -6 ≤ y < ∞.
What is an absolute value function?Generally speaking, the vertex points of an absolute value function occurs when the absolute values are equal to zeros. Therefore, we would equate the x-values of this absolute value function to zero as follows;
y = |x + 2| - 6
|x + 2| = 0
x + 2 = 0
x = -2
When x = -2, the value of y for this absolute value function is given by;
y = |x + 2| - 6
y = |-2 + 2| - 6
y = 0 - 6
y = -6
Therefore, the vertex is (-2, -6).
Since |x + 2| ≥ 0, we would add -6 to both sides of the inequality in order determine the range as follows;
|x + 2| - 6 ≥ -6
y = f(x) ≥ -6
Therefore, the range of this absolute value function is defined for all real numbers that are greater than or equal to -6 i.e -6 ≤ y < ∞.
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Complete Question:
What are the vertex and range of y = |x + 2| - 6?
ABCD i a trapezoid. = 1 cm and = 5 cm, and the area = 7. 5 cm2. What i the altitude of the trapezoid?
The required altitude of the trapezoid ABCD is 2.5 cm.
What is trapezoid?The Greek roots of the term trapezoid are trapeza, which means "table," and -oeides, which means "formed." A trapezoid is shaped like a table. It has two parallel sides, which are often referred to as the figure's bases. Take the average of the bases and multiply it by the height to determine the area of a trapezoid.
According to question:Here, we must utilise the area of a trapezoid formula, which is
where h is the height or altitude and b1 and b2 are the two bases.
[tex]Area =\frac{ (b_{1}+b_{2})h}{2}[/tex]
Given are the values of Area = 7.5, b1 = 1, b2 = 5, and h is unknown.
Then,
7.5 = (1+5)h/2
7.5 = 3h
h = 2.5cm
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which angles must be less than 146 degrees? please list both angles and support your answer by stating the theorem that will support your conclusion.
Any two angles whose sum is 146 degrees must both be less than 146 degrees. This can be supported by the Triangle Sum Theorem, which states that the sum of the measure of the interior angles of a triangle is 180 degrees.
The Triangle Sum TheoremThe Triangle Sum Theorem states that the sum of the measure of the interior angles of a triangle is always 180 degrees. Therefore, if two angles add up to 146 degrees, then both of those angles must be less than 146 degrees. This is because the remaining angle must make up the difference to reach the total of 180 degrees.
For example, if two angles measure 80 degrees and 66 degrees, then the third angle must measure 34 degrees in order to sum up to 180 degrees.Therefore, any two angles whose sum is 146 degrees must both be less than 146 degrees.
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In an AP, a1,a2,a3,.....an, where a1 represents first term and an represents nth term, what is the common difference d?
Answer:
a2 - a1
Step-by-step explanation:
Tn= a+(n-1)d
Tn = a1 (an -1) a2-a1
Last month the average price of gas was $2.20 per gallon. This month, the average price has increased by 75%. What is the average price of gas per gallon this month?
The average price of gas per gallon this month is
(don't forget $)
The average price of gas per gallon this month: $3.85 per gallon.
Define the term percentage increase?The degree, intensity, extent, or value of a variable can change to a greater or lesser extent as measured by percent rise and percent decrease. By comparing the original (or before) as well as final (or after) amounts in accordance with a predetermined formula, the figures are derived.For the stated question-
Average price of gas last month = $2.20 per gallon.
Percentage increase = 75%.
75% of 2.20 = 75*2.20 / 100
= 1.65
Average price of gas this month = $2.20 + $1.65 per gallon
= $3.85 per gallon
Thus, the average price of gas per gallon this month: $3.85 per gallon.
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19. Two consecutive odd numbers are such that the difference of twice the larger number and twice the smaller number is 21. Find the product of the numbers.
There are no two consecutive odd numbers that satisfy the given condition.
What are the consecutive numbers?
Numbers that follow each other continuously in the order from smallest to largest are called consecutive numbers. For example 1, 2, 3, 4, 5, 6, and so on are consecutive numbers.
consecutive numbers are defined as numbers that follow each other in the natural sequence of numbers either from largest to smallest or from smallest to largest.
Let x be the smaller odd number and y be the larger odd number. Since y is larger than x, we know that y = x + 2.
The problem states that:
2y - 2x = 21
We can substitute in the value of y:
2(x + 2) - 2x = 21
Solving for x:
2x + 4 - 2x = 21
4 = 21
This is a contradiction, so there are no two consecutive odd numbers that satisfy the given condition.
Hence, there are no two consecutive odd numbers that satisfy the given condition.
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find the volume of the largest right circular cylinder (in units^3) that fits in a sphere of radius 4 units.
The volume of the largest right circular cylinder (in cubic units) that fits in a sphere of radius 4 units is 154.7 cubic units.
First, draw a diagram. The diagram shows the cylinder inscribed in the sphere. Given that in the diagram the height, h, we can find the radius of the cylinder in terms of r using the Pythagorean Theorem.
h represents half of the total height of the cylinder. choose h instead of h² to simplify things better.
To find the volume of the cylinder, we need to multiply the area of the top by the total height of the cylinder. In other words;
V = π(radius of cylinder)²(height of cylinder)
V = π(√r²−h²)²(2h)
V = 2πh(r²−h²)
V = 2π(r²h−h³)
d/dxV(h) = 2π(r²−3h²) = 0
The 2π divides out and we are left with;
r²−3h² = 0
After some rearranging;
h² = r²/3
Take the square root of both sides.
h = r/√3
To find the volume, we need to put this into the volume equation.
V = 2πh(r²−h²) = 2π(r/√3){r²−(r/√3)²}
V = (2πr/√3)(r²−r²/3)
V = (2πr/√3){(3r²−r²)/3}
V = (2πr/√3)(2r²/3)
V = 4πr³/3√3
V = 4√3πr³/9
Now, put the value of r in the above equation, and we get
V = 4√3π(4)³/9
V = 256√3π/9
V = 154.7 cubic units
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Conditional statements: MELTS IN YOUR MOUTH , NOT IN YOUR HAND!
Converse:
Inverse:
Contrapositve:
dont forget to use If and Then
If something melts in your mouth and not in your hand, then it must be something that has a low melting point.
Converse,Inverse and Contrapositve
If it melts in your hand, then it does not melt in your mouth.Inverse: If it does not melt in your mouth, then it does not melt in your hand.Contrapositive: If it does not melt in your hand, then it does not melt in your mouth.This could be something like chocolate, marshmallows, or even butter.The inverse of this statement is if something does not melt in your mouth but does in your hand, then it must have a high melting point.This could be something like metal or plastic. The contrapositive of this statement is if something does not melt in your hand, then it will not melt in your mouth either.This could be something like a rock or a piece of ice. All of these statements apply when discussing the melting temperature of different materials. Therefore, when it comes to melting, it all depends on the temperature of the material and whether it is safe to put in your mouth.To learn more about Converse,Inverse and Contrapositve refer to:
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write 6x^5/8 in radical form
the radial form is, 6 times the eight root of x to the fifth power.
What is radical form?Radical - The √ symbol that is used to denote square root or nth roots. Radical Expression - A radical expression is an expression containing a square root.
here, given that,
6x^5/8
now,
the radial form is,
6 times the eight root of x to the fifth power.
Hence, the radical form is, 6 times the eight root of x to the fifth power.
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what is 4 2/3 - 3 1/3
Answer:
1.33333333333
Step-by-step explanation:
1.33333333333
