Based on the figure, select all true equations.
Answer:
B, C, E, F
Step-by-step explanation:
Solve for the missing angle first (which is 42°)
Listing all of the basic trig ratios (sohcahtoa):
sin x = opp/hyp
cos x = adj/hyp
tan = opp/adj
sin 48° = a/c
cos 48° = b/c
tan 48 = a/b
sin 42° = b/c
cos 42° = a/c
tan 42° = b/a
a ball is dropped from a height of 16 feet. each time it drops feet, it rebounds feet. (a) find the total vertical distance traveled by the ball
The total distance travelled by the ball after dropping from a height of 16 feet and rebounds 0.81 feet is equal to 168.4 feet.
Balls from a height = 16 feet
Rebounds = 0.81feet
It form a geometric progression pattern :
16 + 16(0.81) + 16(0.81)² + 16(0.81)³ + ......+ ∞
Using sum of geometric progression :
S = a / 1 - r
here a = 16
r = 0.81
S represents the sum .
The total distance travelled by the ball is double of the sum .
S = 16 / ( 1 - 0.81 )
= 16 / ( 0.19)
= 84.2 feet
Total distance travelled by the ball = 2 × 84.2 feet
= 168.4 feet
Therefore, the total distance travelled by the ball as per given situation is equal to 168.4 feet.
The above question is incomplete, the complete question is:
A ball is dropped from a height of 16 feet. Each time it drops h feet, it rebounds 0.81h feet. Find the total distance traveled by the ball .
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assuming we know σ=5.5, construct a 85.0 percent confidence interval for the true population mean, μ, given that a random sample of 94 values was noted to have x¯=85.0.
The confidence interval is (84.41, 85.59), meaning that we are 85.0% confident that the true population mean, μ, lies between 84.41 and 85.59
How to construct the confidence intervalA 85.0% confidence interval for the true population mean, μ, can be constructed using the following formula:
x¯ ± (Zα/2 * σ/√n)
where
x¯ is the sample mean (85.0), Zα/2 is the critical value for a given confidence level σ is the population standard deviation (5.5)n is the sample size (94).Using the Z-score table for a confidence level of 0.85, we have
Zα/2 = 1.040.
Substitute the known values in the above equation, so, we have the following representation
CI = 85.0 ± (1.040 * 5.5/√94)
Evaluate
CI = 85.0 ± 0.59
This gives
CI = 84.41 to 85.59
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Leander, his brother, and a friend are sharing 36
dollars equally. How much money will each one get? What fractional part of the
$36 did each person get? * Write an equivalent fraction that represent the amount
each person received.
The amount of money each person gets is $12.
For a total amount of $36, each person gets a fraction of 1/3 of the whole amount.
What is fraction?
In mathematics, a fraction is used to denote a portion or component of the whole. It stands for the proportionate pieces of the whole. Numerator and denominator are the two components that make up a fraction. The numerator is the number at the top, and the denominator is the number at the bottom.
The number of people are = 3
The amount of money to be shred equally is = $36
Let the amount of money each person gets be = x
Then for 3 people the amount will be = 3x.
The formula to find the value of x is -
3x = 36
x = 36/3
x = 12
Therefore, each person get $12.
The fraction that represents the amount will be -
share of each person / total amount
Substitute the value into the expression -
12/36 = 1/3
Therefore, each person shares 1/3 of the money.
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PLEASE HELP! Based on the graph shown, which of the following statements is true?
Median is defined as the middle value in a given set of numbers or data. ... defined by a median. The repeated value of the given data is defined by mode.
Define median?
The median is the value that's exactly in the middle of a dataset when it is ordered. It's a measure of central tendency that separates the lowest 50% from the highest 50% of values. The steps for finding the median differ depending on whether you have an odd or an even number of data points.The median is the value in the middle of a data set, meaning that 50% of data points have a value smaller or equal to the median and 50% of data points have a value higher or equal to the median. For a small data set, you first count the number of data points (n) and arrange the data points in increasing order.Find n/2. Then find the class whose cumulative frequency is greater than and nearest to n/2. This is the median class.To learn more about median refers to:
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Correct option is C, The median 300, is the middle number.
The x-axis in the graph below depicts the numbers, and the y-axis the frequency.
Total = 72
The most frequent number is called the mode. The frequency that appears most frequently in the table above is 18 at 300. As a result, the data's mode is 300.
The frequency sum is 72, an even number.
N/2th term median
Mean = 72 / 2
average 36th term
We need to identify the number whose cumulative frequency is greater than 36 but less than 36 before it.
The graph's median value is 300.
Since the values of the median and mode are equal, median equals mode.
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however sums between 10 and 19 inclusive are forbidden
The result is true, the number is forbidden.
This rule can be expressed mathematically as:
10 ≤ x < 19
This statement is saying that any number x must be greater than or equal to 10, but less than 19. So if x is set to any number between 10 and 19, the statement will be false. For example, if x is set to 15, the statement becomes:
10 ≤ 15 < 19
Which is false. So any number between 10 and 19 is forbidden.
This can be calculated by first subtracting 10 from the number. For example, if the number is 17, we would subtract 10 to get 7. Since 7 is less than 19, the number is forbidden. We can also use this equation to check any given number:
x − 10 < 19
If the result is true, then the number is forbidden. For example, if x is set to 17, the equation becomes:
17 - 10 < 19
Which is true, so 17 is forbidden.
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Complete question:
What is the sum of any two numbers between 10 and 19?
Select the correct answer from each drop-down menu.
A company manufactures CD drives that theoretically experience disc-read errors 1.2% of the time.
If a CD drive is tested for 250 read operations and fails 4 times, the empirical probability that a CD drive will fail is 0.016%
If the theoretical model is valid, the company would expect the empirical probability to decrease as the number of read operations
decreases
increases
Reset
Next
Does it increase or decrease
When the empirical probability that a CD drive would fail is 0.016%, there are four possible failures.
what is probability ?The probability that a happening will occur or a claim will be true is measured by probability theory, a branch of mathematics. The probability of an occurrence is a value between 0 and 1 and 1, where about 0 represents how likely something event is always to occur and 1 represents certainty. A probabilities is a numerical illustration of the possibility that a specific occurrence will take place. Probabilities can also be expressed as percentages ranging from 0% to 100percentage or from 0 to 1. the ratio of the number of outcomes to the proportion of occurrences in a whole set of fairly probable options that lead to a specific occurrence.
given
Let n = number of operations and P = error.
P = .016
n = 250
Increase P and n.
.016 (250) = 4
When the empirical probability that a CD drive would fail is 0.016%, there are four possible failures.
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5. Number of cars of a particular model produced by a factory between 2006 and 2010 2006 35,000 2007 40,000 2008 45,000 2009 30,000 2010 35,000 2012
Answer:
The number of cars of a particular model produced by the factory between 2006 and 2010 are:
2006: 35,000
2007: 40,000
2008: 45,000
2009: 30,000
2010: 35,000
No data is available for 2012.
The drama club is selling tickets to their play to raise money for the show's expenses. Each student ticket sells for $7 and each adult ticket sells for $9. There was a total of $543 in revenue from the sale of 67 total tickets. Write a system of equations that could be used to determine the number of student tickets sold and the number of adult tickets sold. Define the variables that you use to write the system.
The system of equations that can find the number of student tickets sold is:
7x + 9y = 543
x + y = 67
Defining the variables that helped write the system are:
Let x be the number of student tickets sold
Let y be the number of adult tickets sold.
How to come up with the system of equations ?First, define the variables. In this case, we can say that x will be the number of student tickets while also making y the number of adult tickets.
The first equation would be:
Revenue of student tickets sold + Revenue of adult tickets = Total revenue
7x + 9 y = 543
The second equation is:
Number of student tickets + Number of adult tickets = Number of total tickets
x + y = 67
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Answer: The answer is 7x + 9y = 543x + y = 67.
Step-by-step explanation: Please give Brainlist.
Hope this helps!!!!
Simplify the following using trigonometric identities:
( - tan² (x) + sec² (x) ) - sin² (x)
Answer:
cos^2 (x)
Step-by-step explanation:
Use two of the Pythagorean Identities. See image.
You can rearrange the Pyth Identities. Like subtract the same thing from both sides.
Your question simplifies in just two steps. See image.
Convert the following decimal number to a fraction or mixed number: 6.4
Answer:
Step-by-step explanation:
well 6.4 converted to a fraction is 32/5 so i hope this helps.
Amir buys a car for £15095 which depreciates in value at a rate of 2.75% per year
Work out how much Amir's car will be worth in 4 years.
Answer: £13,741.69 will be the value in 4 years
Step-by-step explanation:
formula: present value * (1-depreciation rate)^years
15095*(1-0.0275)^4
=13,741.69
Please help me on this question.
For what value of x is line m parallel to line n?
Answer:
x=42
Step-by-step explanation:
Step 1) 105=3x-21
Step 2) 126= 3x
Step 3) 42=x
write a function if the input value is 5 then the output should be 5,7,9,11,13
f(x)= x+2 a function if the input value is 5 then the output should be 5,7,9,11,13
g is a transformation f the function f.
We have to figure out the transformation and write the equation of g with respect to f.
g is (with respect to the function f):
• reflected upside down [reflected about x-axis]
• translated 3 units left
Reflection with respect to x-axis makes the function negative, so:
f(x) would be -f(x)
Then,
Translation "a" units to the left, makes a function f(x) into f(x+a), thus:
f(x) would be -f(x+3)
hence f(x)= x+2 a function if the input value is 5 then the output should be 5,7,9,11,13
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how many times greater is 6 x 10^6 than 4 x 10^4?
Answer:
Step-by-step explanation:
We have two values i.e., 6*10^6 and 4*10^4
we divide both of them
i.e., =6*10^6/4*10^4
we shift the 10^4 to the numerator which becomes 10^-4.
=6*10^6*10^-4/4
=6*10^2/4
=600/4
=150
so, 6*10^6 is 150 times greater than 4*10^4
Determine all intervals on which the graph of f is decreasing.
f′(x) < 0 at each point in an interval I, then the function is said to be decreasing on I.
How do you find the decreasing interval on a graph?To find when a function is decreasing, you must first take the derivative, then set it equal to 0, and then find between which zero values the function is negative. Now test values on all sides of these to find when the function is negative, and therefore decreasing.
The derivative of a function may be used to determine whether the function is increasing or decreasing on any intervals in its domain. If f′(x) > 0 at each point in an interval I, then the function is said to be increasing on I. f′(x) < 0 at each point in an interval I, then the function is said to be decreasing on I.
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if the variable num contains a positive integer, what are the only two possible results of the expression num % 2? 0 and 2 0 and 1 -1 and 1 1 and 2
The only two possible results of the expression num % 2 if the variable num contains a positive integer is 0 and 1.
Variables include effects like height, age, income, fiefdom of birth, academy grades, and kind of dwelling. There are two introductory types of variables order and numeric. also, each order is divided into two subcategories separate or nonstop for numeric variables, and nominal or ordinal for categorical variables. In this section, these orders are compactly described.
A quantifiable property with numerical values is known as a numeric variable( also known as a quantitative variable)( except figures which are canons standing up for orders). Both nonstop and separate numerical variables are possible.
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Express tan
I as a fraction in simplest terms.
The tangent of the corners of this right-angle triangle is 4/3.
What is the Pythagorean Theorem?The Pythagorean theorem states, "In a right triangle, the square of the hypotenuse equals the sum of the squares of the other two sides." The sides of this triangle were called the perpendicular, the base, and the hypotenuse.
The tangent of a right triangle angle is equal to the ratio of the opposite side to the adjacent side. So if we call the other side "x", we can set the following formula:
tan(θ) = 8/x
where θ is the angle from height 8. We can find the value of x using the Pythagorean theorem.
[tex]x^2 + 8^2 = 10^2\\x^2 = 100 - 64\\x^2 = 36\\x = 6[/tex]
So the tangent values are:
tan(θ) = 8/6 = 4/3
Therefore, the tangent of the corners of this right triangle is 4/3.
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Which of the following can you use to justify the statement VWX~AZYX?
1. AA
2.SAS
3.SSS
4. Not similar
ΔVWX ≅ ΔZYX, to justify the statement SAS property is used.
Correct option is: 3
What is the SAS property in triangle?Congruent triangles exist if its two sides and also included angles are identical to that of other triangle's two sides and also included angle.
The triangles are considered to be congruent when all three pairs of matching sides are. Side-side-side is the name of this congruence shortcut (SSS). Side-angle-side (SAS) is an alternative simplification if two sets of side as well as the angles between them is known to just be congruent.
When determining if a collection of triangles is congruent, the Side-Angle-Side rule is utilized. According to the SAS rule, two sides and the included angle of one triangle must equal two sides and the included angle of another triangle in order for the two triangles to be considered congruent. An angle produced by two specified sides is called an included angle.
Correct option: 3
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Y= 2x + 1
y =x - 2
identify the point of intersection of a pair functions
Answer:
(-3,-5)
Step-by-step explanation:
2x+1=x-2
subtract 3 from both sides
x=(-3)
sub the value of x back into one of the equations
y=2(-3) + 1=-5
if i subtract 20 from my number, then square the result, i get the same answer as, if i square my number, then subtract 20 from the result
Answer:
The number is 10.5.
Step-by-step explanation:
Let x be your number.
"i subtract 20 from my number,:" (x-20)
"square the result" : (x-20)^2
-------
"i square my number": x^2
"subtract 20 from the result": x^2 - 20
-----
The results are equal:
(x-20)^2 = x^2 - 20
x^2 -40x + 400 = x^2 - 20
-40x = -420
x = 10.5
==================
CHECK:
1) (x-20)^2 = ?
(10.5-20)^2 = 90.25
2) x^2 - 20 = ?
(10.5)^2 - 20 = 90.25
x=10.5 is correct
Answer:
[tex]\textrm{The number is: }\\\\\\ \rm{\boxed{\dfrac{21}{2}}\; or\; \boxed{10.5} \;in \;decimal}}[/tex]
Step-by-step explanation:
Let x be the number we have to determine
From the question description
[tex]\left(x-20\right)^2=\:x^2-20[/tex]
[tex]\mathrm{Expand\:}\left(x-20\right)^2:\quad x^2-40x+400[/tex]Answer:
[tex]\rm{\boxed{x = \dfrac{21}{2}}\; or\; \boxed{x = 10.5} \;in \;decimal}}[/tex]
Find the surface area of the equilateral triangular pyramid base is 16 height is 20
The surface area of a pyramid with a base equilateral triangle is 480 + 100√3 square inches.
What is the surface area of a pyramid?The total surface area (S) of a regular pyramid is given by the formula as
1/2 Pl + B ...... (i)
Here, p represents the perimeter of the base, l is the slant height, and B is the base area of the pyramid.
As per the question, we have
Side of equilateral triangle = 20 inches
The slant height of the pyramid(l) = 16 inches.
First, we have to determine the perimeter and Area of the base pyramid.
The perimeter of an equilateral triangle (p):
= 3 × side
= 3×(20)
= 60 inches
Area of an equilateral triangle (B):
= (√3/4) × side²
= (√3/4) × (20)²
= 100√3 square inches.
Substitute the above values in equation (i), and we get
The total surface area (S):
= 1/2 x 60 x 16 + 100√3
= 480 + 100√3 square inches
Hence, the surface area of the given pyramid is 480 + 100√3 square inches.
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Maggie reads 1/3 of a book every 3/4 of a Week. How manny books does Maggie read?
Answer:
4/9
Step-by-step explanation:
If Maggie reads 1/3 of a book in 3/4 weeks, you want to know how many books per week Maggie reads.
Books per weekTo find Maggie's reading rate in books per week, divide books by weeks:
(1/3 book)/(3/4 week) = (1/3)/(3/4) book/week
= (1/3) · (4/3) book/week = 4/9 book per week
Maggie reads 4/9 books per week.
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Express 220 as the product of its prime factors write the prime factors in ascending order and give your answer in ascending order
Answer:
Below
Step-by-step explanation:
220 = 2 x 110
= 2 x 2 x 55
= 2 x 2 x 5 x 11
increase £102 by 15%
£117.3
Step-by-step explanation:To increase an amount by a certain percentage, you can use the following formula:
New amount = original amount + (percentage increase x original amount)/100
In this case, to increase £102 by 15%:
New amount = 102 + (15/100) x 102 = 102 + 15.3 = £117.3
yeah that's it...
102 + 102 × 15/100 = £117.3
Solve 7(x + 3) = 2x + 1.
A. x = 3
B. x = 2
C. x = -4
D. x = -6
Answer:
C
Step-by-step explanation:
7(x + 3) = 2x + 1 ← distribute parenthesis on left side by 7
7x + 21 = 2x + 1 ( subtract 2x from both sides )
5x + 21 = 1 ( subtract 21 from both sides )
5x = - 20 ( divide both sides by 5 )
x = - 4
Answer:
x=-4
Step-by-step explanation:
7(x+3)=2x+1
distribute 7
7x+21=2x+1
subtract 1 from both sides
7x+20=2x
subtract 7x from both sides
20=-5x
divide both sides by -5
x=-4
you have 10 pairs of socks, five black and five blue, but they are not paired up. instead, they are all mixed up in a drawer. it's early in the morning, and you don't want to turn on the lights in your dark room. q1.1 sock drawer i 5 points grading comment: how many socks must you pull out to guarantee that you have a pair of one color?
The number of socks you pull out to have two black socks is 3 socks
Total number of pairs of socks in a drawer = 10
Number of black pairs of socks = 5
Number of blue pairs of socks = 5
A. If you picked 2 socks [black] and [blue] 3rd pick guarantees you will have one pair of either blue or black
The number of socks you pull out to guarantee that you have a pair of one color is 3 socks
B. If you want to pick 2 good pairs and your 6 picks are the worst case, so 7th pick of the socks will give you good pair of two colors.
The number of socks you pull out to have two good pairs is 7 socks
C. If you want to have a pair of black socks your worst case will be you pick all 10 blue socks so another 2 socks must be black.
Therefore, the number of socks you pull out to have two black socks is 12 socks.
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T varies s/t when
S =36, t =16, T=18
Find T when s=33, t=18
Answer:
Step-by-step explanation:
We are given that T varies as the square root of the ratio of s and t, and we are trying to find the value of T when s=33 and t=18.
The relationship between T, s and t can be represented by the following equation:
T = k * √(s/t)
Where k is a constant.
We are given that when S=36, t=16, T=18. We can use this information to find the value of k.
We know that T = k * √(s/t)
and, T = 18 when s=36, t=16.
So we can substitute these values in the equation
18 = k * √(36/16)
Solving for k, we get:
k = 18/2 = 9
Now that we know the value of k, we can use it to find the value of T when s=33 and t=18.
T = k * √(s/t) = 9 * √(33/18) = 9 * √(11/6) = 9 * √(11/6)
The value of T when s=33, t=18 is 9 * √(11/6),
It is not possible to give the exact value of T because the value of the square root of (11/6) is not a whole number.
in exercises 35–38, are and parallel? and if so, do they point in the same direction?
Yes, the lines AB and PQ are parallel lines and have same direction.
Coordinates of the line AB and PQ :
A = (1, 1), B = (3, 4), P = (1, 1), Q = (7, 10)
Slope = (y₂ - y₁)/ (x₂ -x₁)
Substitute the value in the formula:
Slope of the line AB = ( 4 - 1 )/ ( 3 - 1 )
⇒ Slope of the line AB = 3 /2
Slope of the line PQ = ( 10 - 1 )/ ( 7 - 1 )
⇒ Slope of the line PQ = 9 /6
⇒ Slope of the line PQ = 3 /2
Slope of line AB and PQ are equal it implies they are parallel lines.
Therefore, both the lines AB and PQ are parallel lines to each other and are in the same direction.
The above question is incomplete , the complete question is:
Are lines AB and PQ parallel? And if so, do they point in the same direction? A = (1, 1), B = (3, 4), P = (1, 1), Q = (7, 10)
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Can anyone solve these equations?
The equation can be factorized as (x + 4/3) (x + 3/2).
The expression 2x² + bx - 9 will be prime for the the values of b = 18, 12, and -1.
What are Quadratic Expressions?Quadratic expressions are polynomial expressions of second degree.
The general form of a quadratic expression is ax² + b x + c.
18. The zeroes of the expression ax² + b x + c can be found by,
x = [-b ± √(b² - 4ac)] / 2a
The given expression is 6x² + 17x + 12.
We have to factorize the expression.
x = [-17 ± √(17² - 4×6×12)] / [2 × 6]
= [-17 ± √(289 - 288)] / 12
= (-17 ± 1) / 12
x = -16/12 = -4/3 and x = -18/12 = -3/2
The expression can be factorized as (x + 4/3) (x + 3/2).
19. The expression is non factorable if the value of the discriminant is neither zero nor a positive perfect square.
For ax² + b x + c, Discriminant = b² - 4ac
The expression given is 2x² + bx - 9.
Discriminant = b² - (4 × 2 × -9) = b² + 72
When b = 18, b² + 72 = 396, not a perfect square root
When b = 3, b² + 72 = 81, a perfect square root
When b = 12, b² + 72 = 216, not a perfect square root
When b = -3, b² + 72 = 81, a perfect square root
When b = -7, b² + 72 = 121, a perfect square root
When b = -1, b² + 72 = 73, not a perfect square root
When b = 17, b² + 72 = 361, a perfect square root
So when b = 3, -3, -7 and 17, the expression is factorable.
When b = 18, 12, and -1, the expression is prime.
Hence the expression 2x² + bx - 9 is prime when the values of b are 18, 12, and -1.
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