Answer:
15/72
Step-by-step explanation:
15/36 ÷ 2. First Make 2 into a fraction, which is 2/1. Now we have 15/36 ÷ 2/1. Turn the division into multiplication. And switch 2/1 into 1/2. 15/36 x 1/2 is 15/72.
The triangles shown below must be congruent.
151-
80⁰
10
O A. True
OB. False
51
80⁰
10
Answer:
false
Step-by-step explanation:
Put the following ORIGINAL values in order from least to greatest: 4⁻² -4², (-4)². 4⁰
The ordered exponential values, from least to greatest, are given as follows
-4², 4^(-2), 4^0, (-4)²
How to order the exponential values?An exponential value is defined as follows:
y = a^x.
In which the base and the exponent are given as follows:
a is the base.x is the exponent.When two numbers have the same base, we order them according to the exponent, the lowest the exponent, the lowest the number, hence they are ordered as follows:
4^(-2), 4^0, (-4)²
As:
2 > 0 > -2.
The smallest number is -4², as the exponential has precedence over the negative, hence the value is of -4² = -(16) = -16.
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Which linear system is Mcq? A : y [ n ] = x [ n ] x x [ n - 1]
B : y [ n ] = x [ n ] + x [ n - 10]
C : y [ n ] = x 2 [ n ]
D : (a) and (c)
Only, Option B: y [ n ] = x [ n ] + x [ n - 10] forms a linear system.
A linear system is a mathematical model that represents a relationship between input and output using linear equations.
A: y [ n ] = x [ n ] x x [ n - 1]: This is not a linear system because it includes a product of two input signals x[n] and x[n-1], which makes the system non-linear.
B: y [ n ] = x [ n ] + x [ n - 10]: This is a linear system because it includes only one input signal x[n] and one delayed input signal x[n-10], which are added together. It's a linear combination of input signals and it's a linear system.
C: y [ n ] = x 2 [ n ]: This is not a linear system because it includes the square of the input signal x[n] which makes the system non-linear.
D : (a) and (c): Only option B is a linear system.
It's worth noting that linear systems are characterized by the linearity property, which means that the input-output relationship is a linear combination of the inputs.
Therefore, Option B: y [ n ] = x [ n ] + x [ n - 10] forms a linear system.
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Joe rides a bicycle in a straight line for 15 minutes with an average velocity of 9.0 m/s south, how far have they ridden.(convert 15 min into units of seconds)
Answer:We can use the formula:
Distance = Velocity x Time
To find out how far Joe has ridden on the bicycle.
First, we need to convert 15 minutes into seconds. 1 minute is equal to 60 seconds. So 15 minutes is equal to 15*60 = 900 seconds.
So the distance Joe has ridden is:
Distance = Velocity x Time
Distance = 9.0 m/s x 900 sec
Distance = 8100 meters.
Joe has ridden 8100 meters in a straight line for 15 minutes with an average velocity of 9.0 m/s south.
Step-by-step explanation:
What is the derivative of sin0?
The derivative of sin0 is cos0. We take the derivative of the inner function, which is 0, and then multiply it by the derivative of the outer function, which is the sine function. The derivative of the sine function is the cosine function.
The derivative of sinθ is cosθ.
When θ is 0, the derivative of sin0 is cos0.
The derivative of the sine function is the cosine function. This can be expressed mathematically as the derivative of sinθ equals cosθ. This means that the rate of change of the sine of an angle is equal to the cosine of that same angle. In other words, the derivative of sin0 is equal to cos0. To calculate the derivative of sin0, we can use the chain rule and the basic derivative rules. First, we identify the base function, which is sin0. Then, we differentiate the base function by applying the chain rule. We take the derivative of the inner function, which is 0, and then multiply it by the derivative of the outer function, which is the sine function. The derivative of the sine function is the cosine function. Therefore, the derivative of sin0 is cos0.
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Cesium-137 has a half-life of approximately 30 years. How much of a 40 g sample would be left after 90 years?
40 grams of sample would be left 5 grams after 90 years.
What is an exponential function?Mathematical functions with exponents include exponential functions. f(x) = bˣ, where b > 0 and b 1, is a fundamental exponential function.
Given:
Cesium-137 has a half-life of approximately 30 years.
The amount of 40 g sample would be left after 90 years,
= 40 x (1/2[tex])^{90/30}[/tex]
= 40 x (1/2)³
= 5
Therefore, 5 grams would be left.
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A 50 foot ladder is set against the side of a house so that it reaches up 48 feet. If Jack grabs the ladder at its base and pulls it 4 feet farther from the house, how far up the side of the house will the ladder reach now? (The answer is not 44 ft.) Round to the nearest tenth of a foot
Check the picture below.
before Jack moved the ladder
[tex]\textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \sqrt{c^2 - b^2}=a \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases} \\\\\\ \sqrt{50^2 - 48^2}=x\implies \sqrt{196}=x\implies \boxed{14=x}[/tex]
after Jack pulled the ladder
[tex]\textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \sqrt{c^2 - a^2}=b \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases} \\\\\\ \sqrt{50^2 - (x+4)^2}=y\implies \sqrt{50^2 - (14+4)^2}=y \\\\\\ \sqrt{50^2 - 18^2}=y\implies \sqrt{2176}=y\implies \boxed{46.6\approx y}[/tex]
Mr. Grant wants to tile a 27 - square - foot area with square tiles. let s = the side length, in feet, of a square tile. Use the expression 27 divided by s2 to find the number of tiles Mr. Grant needs to buy
The expression for the number of tiles will be 27 / ( s² ).
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that Mr. Grant wants to tile a 27 - square - foot area with square tiles. let s = the side length, in feet, of a square tile.
The number of tiles will be calculated as,
Number = Total area / Area of tile
Number = 27 / s²
Hence, the number of tiles will be calculated by the formula Number = 27 / s².
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4x - 10
40
120°
115°
24
24
Find the range of possible values for x
Inequalities in two triangles
Therefore , the solution of the given problem of inequality comes out to be x = 12.5°.
What exactly is inequality?An inequality in mathematics is a linear relationship or a set of integers even without equal sign. Equilibrium follows equity ineluctably. Inequality exists between two variables when they are not equal. There are distinctions between equality and inequality. I've selected the most prevalent symbol because when variables aren't identical or comparable (). Any number of inequalities, no matter how little or large, can be used to compare values.
Here,
Given :4x -10 = 40
=> 4x = 40 + 10
=> 4x =50
=> x =50/4
=>x= 12.5°
Therefore , the solution of the given problem of inequality comes out to be x = 12.5°.
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I need answers please
Answer:The graph of the equation that is a line that slants to the left would be (B) y = 2x+3
Step-by-step explanation:
The slope of the line in figure 3c-1a is (A) positive slope.
The y-intercept of the line in figure 3c-1b is (A) -3.
The trend of the graph of the line in figure 3c-1a is (B) increasing.
Please note that the above answers are based on the information provided, but since we do not have any information about figure 3c-1, it is not possible for me to confirm that the answers are accurate.
It is important to have more context and information to fully understand and answer the questions.
CC.3 Solve a system of equations by graphing: word problems W9J or For her parents' anniversary party, Kira is considering using one of two venues. A hotel in Stamford will cost $200 for a reservation, plus $50 per person. A restaurant in the same city will cost $75 per person, in addition to $150 for the reservation. In order to make the best decision, Kira figures out how many attendees it would take to have the venues cost the same amount. How many attendees would that be? Write a system of equations, graph them, and type the solution.
Tanya is training a turtle for a turtle race. For every 1/3 of an hour that the turtle is crawling, he can travel 1/8 of a mile. At what unit rate is the turtle crawling?
Enter the value of p so that the expression 2(n+7) is equivalent to (n+p)2
33. Jamal organizes an annual recycling drive to recycle cardboard. A recycling company
pays him for the cardboard he collects. The table shows the numbers of pounds of
cardboard and amounts of money collected in previous years of the recycling drive.
Recycling Drive Data
Pounds of Amount of
Cardboard Money Collected
1,630
$96
2,7
$110
3,220
$160
Part A
Use the data in the table to write an equation that can be used to find the amount of
money collected, y, for x pounds of cardboard.
From the table which shows numbers of pounds of cardboard and amounts of money collected in previous years of recycling drive , then equation to find amount of money collected is y = 0.0126x + 75.462 .
From the table ,
we get the data that ,
amount paid for 1630 pounds of card board is = $96 ;
the amount paid for 2740 pounds of card board is = $110 ;
let the amount of money be denoted as = y ;
the amount of cardboard collected be denoted as = x ;
we get the two set of points as (1630 , 96) and (2740 , 110) ;
the equation is ⇒ [tex](y-96) = (\frac{110-96}{2740-1630}) \times (x-1630)[/tex] ;
solving further ,
we get ;
⇒ [tex](y-96) = (\frac{14}{1110}) \times (x-1630)[/tex]
⇒ [tex](y-96) = 0.0126 \times (x-1630)[/tex]
⇒ [tex]y-96 = 0.0126x-20.538[/tex]
⇒ [tex]y = 0.0126x-20.538 +96[/tex]
⇒ y = 0.0126x + 75.462 ;
Therefore , the equation find the amount of money collected (y) , for "x" pounds of cardboard is y = 0.0126x + 75.462 .
The given question is incomplete , the complete question is
Jamal organizes an annual recycling drive to recycle cardboard. A recycling company pays him for the cardboard he collects. The table shows the numbers of pounds of cardboard and amounts of money collected in previous years of the recycling drive.
Pounds of Amount of Cardboard Money Collected
1630 $96
2740 $110
3220 $160
Use the data in the table to write an equation that can be used to find the amount of money collected "y" , for "x" pounds of cardboard.
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there are 57 grains of salt in a container of salt. if a large store has 54 containers of salt, how many grains of salt do they have? leave the answer in exponent form.
They have a total of 5¹¹ grains of salt in the large store.
Before solving this Question we must know an important result,
a^(m) × a^(n) = a^(m + n)
We know that,
1 container contains 5⁷ grains of salt
also, there are 5⁴ containers in the store
Thus,
Total grains of salt in all the container = 5⁷ × 5⁴
Hence, from the above result,
5⁷ × 5⁴ = 5^(7 + 4)
= 5¹¹ grains of salt
Thus,
They have a total of 5¹¹ grains of salt in the large store.
Now, just for your information, (this is not a part of the Answer and is not required in Answer)
This is just for you to know the magnitude of salt grains,
5¹¹ = 48,828,125 grain of salt were there in the store
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Convert the degree measure below to radians.
1230°= ? radians
Answer:
41/6 n
Step-by-step explanation:
Given
1230°
Find
Convert degree to radians
Explanation
To convert a degree measurement to radians we use the following formula:
Substitute the value of 1230°:
Simplify:
Answer:
41/6 nLook at this diagram:
If TV and WY are parallel lines and m
If TV and WY are parallel lines, then m∠VUX = 53°.
What are parallel lines?
Lines that are parallel to one another on a plane do not intersect or meet at any point. They are always equidistant from one another and parallel. Non-intersecting lines are parallel lines. Parallel lines intersect at infinity is another way to put it.
It is given that line segment TV and WY are parallel to each other.
A line ZS intersect the parallel lines.
The measure of m∠TUS = 53°.
The measure of m∠VUX = m∠TUS as they are both vertically opposite angles and hence they are same.
Therefore, m∠VUX = 53°.
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select all the pairs of ratios that form a proportion Pick two
1/6, 4/20
7/9, 28/36
14/18, 21/27
30, 6/18
Answer:Answer for the first one is just 7/9, 28/36Second one is 9/14, 3/4For the third one you multiply 12.50 by 5 which gives you 62.5
Step-by-step explanation:
Which statement best explains whether the following table represents a linear or nonlinear function?
x −2 −1 0 1 2
y −4 −2 0 2 4
The table represents a nonlinear function because there is not a constant rate of change in the input values.
The table represents a nonlinear function because there is not a constant rate of change in the output values.
The table represents a linear function because there is a constant rate of change in the input and output values.
The table represents a linear function because there is not a constant rate of change in the input and output values.
Answer:
its C; or their is a constat change in the output values and it is non linear
Step-by-step explanation:
this is because we can see that 0/0 match each other. There is a constamt chage in the imput valu.
I NEED HELP PLEASE!!! Select the correct systems of equations.
Which systems of equations intersect at point A in this graph?
Answer: Number 2
Step-by-step explanation:
Substitute (-2, 1) into (x, y) into each equation and see if it works.
Pls help me evaluate 252.7 divided by 19
Answer:
Step-by-step explanation:
Answer: 13.3
252.7 divided by 19
A LOT OF POINTS
The table shows a comparison between EU and USA shoe sizes:
USA (Men's)
7
8
9
EU
40
41
42
(a) Develop a linear model to find the EU shoe size given the USA shoe size.
(b) Use your model to predict the EU shoe size for a USA Men's shoe
size of 12.
(c) Use your model to predict the USA Men's shoe size for an EU shoe size of 44.
(d) Interpret the gradient of your model in context.
(e) Given that USA Men's shoe sizes typically run from 6 to 16, calculate
a reasonable domain and range for your model.
Between men's and women's sizes, there is a roughly 1.5 size difference. Men's sizes apply to the unisex fashions. For women, go down 1.5 sizes.
What size is EUR 40 41 in US men?( a ) By adding 33 to your current US size, you may convert a men's US shoe size to an EU size with ease. For illustration, if you are a US men's size 9, your EU size is 42. There are centimeter-based shoe sizes throughout Europe.
( b ) European Size 40.=25,3 cm. EU Size 41.=26.0 cm Size 42 in EU.
( c ) By adding 33 to your current US size, you may convert a men's US shoe size to an EU size with ease.
( d ) US to EU and EU to US shoe size conversion for Euro shoes. According to the ISO standard, an EU Size 40 is equivalent to a US women's shoe size 9.
( e ) By adding 33 to your men's US shoe size, you can convert to Euro Sizing.
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Please help i need the wright answer please
Tadeo volunteered for 2 hours, and Dylan volunteered for 12 hours.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
Tadeo volunteered at the library 6 times as many hours over the weekend as Dylan. Together, they volunteered a total of 14 hours.
Let x represent Dylan's hours and y represents Tadeo's hours. Then the equations are given as,
y = 6x ...1
x + y = 14 ...2
From equations 1 and 2, then we have
x + 6x = 14
7x = 14
x = 2
Then the value of 'y' is given as,
2 + y = 14
y = 12
Tadeo volunteered for 2 hours, and Dylan volunteered for 12 hours.
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What is the form of the Pythagorean triple generator?
O A. (x² + y²)² = (x² - y²)² + (2xy)²
O B. (x² + y²)² = (x² + y²)² + (2xy)²
O C. (x² + y²)² = (x² - y²)² - (2xy)²
O D. (x² - y²)² = (x² + y²)²-(2xy)²
The form of the Pythagorean triple generator is (x² + y²)² = (x² - y²)² + (2xy)²
What is Pythagorean triple generator?A collection of three natural integers f, g, and h is referred to as a Pythagorean triple if f2 + g2 = h2. If a valid result is obtained when three numbers are entered into the Pythagorean Theorem formula, then three numbers DO form a Pythagorean triple. Neither two even numbers nor one odd number can ever be used to create a Pythagorean triple. This is accurate since an even number's square is an even number, and an odd number's square is an odd number. Pythagorean triples consist of the three positive numbers a, b, and c, where a2+b2 = c2. The symbols for these triples are (a,b,c). Here, a represents the right-angled triangle's hypotenuse, b its base, and c its perpendicular.To learn more about Pythagorean triple generator refer to:
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What is distance Class 9 formula?
Distance is the total movement of an object without any regard to direction. We can define distance as to how much ground an object has covered despite its starting or ending point.
The complete length of the path between any two points is called the distanceDistance is a scalar quantity as it only depends upon the magnitude and not the directionThe distance can only have a positive valueWhile distance and displacement appear to have the same meaning, they actually have very different definitions and implications. Displacement is the measurement of "how far an object is out of place," whereas distance refers to "how much ground an object has covered during its motion." Let's examine the distinction between distance and displacement in this post.
Distance refers to the actual length of the object's route. The shortest distance between an object's original and final positions is called displacement. It has a scalar value. A vector quantity, that is. A body can never travel a distance of zero.
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A box of 8 ice cream cones costs $5.34. A box of 10
ice cream cones costs $6.80. Which box costs less per
cone? Show your work.
00S
Answer: The box of 8 cones costs less per cone. The cost per cone is $0.67.
Step-by-step explanation:
To find the cost per cone, we need to divide the total cost by the number of cones.
8 cones box: $5.34 / 8 = $0.67 per cone
10 cones box: $6.80 / 10 = $0.68 per cone
Therefore, the box of 8 cones costs less per cone. The cost per cone is $0.67.
since the heights of people in usa is normally distributed, what is the probability that an individual is two standard deviations ( 2) from the norm?
Z score is used to get by how many standard deviations the raw score is higher or minimum the mean. The z score is given by:
z = (x - μ)/σ
where x is the raw score, μ is the mean and σ is the standard deviation.
In a normal distribution, data is uniform distributed with no skew. When plotted on a graph, the data accompany a bell shape, with maximum values clustering around a central region and tapering off as they go far away from the center.
Normal distributions have key attribute that are easy to spot in graphs:
1. The median, mean, and mode are exactly the same.
2. The distribution is symmetric about the mean half the data fall below the mean and half greater the mean.
3. The distribution can be narrated by two values: the standard deviation and the mean.
The mean determines where the top of the curve is centered.
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Select the correct answer. What is the value of x in the equation ln (x + 6) – ln (2x – 1) = 1? A. -0.21 B. 0.74 C. 1.35 D. 1.97
Answer: 6!
Step-by-step explanation: Isolate the variables. In order to do that you have to divide each side by factors that don't contain the variables.
Answer: Correct option is (D) 1.97
Step-by-step explanation:
According to question,
ln (x + 6) – ln (2x – 1) = 1.....(i)
Now by using log rule
Log(a) – Log(b)= Log(a/b)
Equation (i) becomes
Log((x + 6) / (2x - 1)) = 1
Taking anti log on both sides
((x + 6) / (2x - 1)) = e1
We know that
e1 = 2.72
Therefore,
((x + 6) / (2x - 1)) ≈ 2.72
(x + 6) = 2.72 (2x - 1)
x + 6 = 2.72 (2x) - 2.72 (1)
x + 6 = 5.44x - 2.72
8.72 = 4.44x
By cross multiplication we get,
x = 8.72 / 4.44
x = 1.97
Hence the correct value of x is 1.97
Why are the trigonometric ratios the same for all 30 60 90 triangles?
Sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant are the six trigonometric ratios (sec). A branch of mathematics called trigonometry in geometry deals with the sides and angles of a right-angled triangle. Trig ratios are therefore assessed in relation to sides and angles.
The trigonometric ratios (sine, cosine, and tangent) are the same for all 30-60-90 triangles because these triangles have a unique set of properties that make them special. Specifically, all 30-60-90 triangles have a right angle, and the angle measures are in a ratio of 1:2:3. Because of these properties, the length of the hypotenuse is always twice the length of the shorter leg, and the length of the longer leg is always equal to the square root of 3 times the length of the shorter leg. This allows us to determine the exact values of the trigonometric ratios for all 30-60-90 triangles, regardless of their size.
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The first and second terms of an exponential sequence (G.P) are respectively the first and third terms of a linear sequence (A.P). The fourth term of the linear sequence is 10 and sum of its first five terms is 60. find (a) the first five terms of the linear sequence and the sum of the first n terms. (b) the sum Sn of the first n terms of the exponential sequence. (c) the limit of Sn for large value of n
Answer:
a) To find the first five terms of the linear sequence and the sum of the first n terms, we can use the following formulas:
The common difference of an A.P is (an - a1) / (n - 1)
The sum of the first n terms of an A.P is (n/2)(2a1 + (n-1)d)
Let the first term of the linear sequence be a1 and the common difference be d. Since the first and second terms of the exponential sequence are the first and third terms of the linear sequence, we can write:
a1 = a and a3 = ar^2
Given that the fourth term of the linear sequence is 10, we can write:
a1 + 3d = 10
Given that the sum of the first five terms of the linear sequence is 60, we can write:
(5/2)(2a1 + (5-1)d) = 60
Solving these two equations for a1 and d gives:
a1 = 2, d = 2
Therefore, the first five terms of the linear sequence are 2, 4, 6, 8, 10, and the sum of the first n terms is (n/2)(2a1 + (n-1)d) = (n/2)(2*2 + (n-1)2) = n2
b) To find the sum of the first n terms of the exponential sequence, we can use the following formula:
Sn = a(1 - r^n) / (1 - r)
where a is the first term and r is the common ratio.
Given that a1 = a and a3 = ar^2, we can write:
a = a1 and r^2 = a3/a1
Substituting these values into the formula for Sn gives:
Sn = a(1 - r^n) / (1 - r) = a1(1 - (a3/a1)^n) / (1 - (a3/a1)^(1/2))
c) As n tends to infinity, the limit of Sn is a1/(1-(a3/a1)^(1/2))
So the first five terms of the linear sequence are 2, 4, 6, 8, 10, the sum of the first n terms is 2n and the limit of Sn for large value of n is a1/(1-(a3/a1)^(1/2))
Step-by-step explanation: