The expression 1 + 3² can be evaluated as follows:
First, we calculate 3², which is equal to 9.
Then, we add 1 to 9, which gives us 10.
Therefore, 1 + 3² = 10.
Answer:
Step-by-step explanation:
1 +[tex]3^{2}[/tex]
= 1 + (3*3)
= 1 + 9
= 10
What is sin in terms of the sides
The correct option is A.
Describe Right Triangle?A right triangle is a type of triangle in which one of its angles measures exactly 90 degrees (π/2 radians). This angle is called the right angle, and it is located opposite to the longest side of the triangle, which is called the hypotenuse. The other two sides are called the legs of the triangle.
The Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs, is one of the most important properties of right triangles. This theorem can be written algebraically as:
a^2 + b^2 = c^2
where a and b are the lengths of the legs, and c is the length of the hypotenuse.
Right triangles also have several other important properties, including:
The acute angles (those that are not the right angle) are complementary, which means that their sum is equal to 90 degrees.
The side opposite the right angle is always the longest side (the hypotenuse).
The legs are always perpendicular to each other.
The altitude (height) from the right angle to the hypotenuse divides the triangle into two smaller triangles that are similar to the original triangle and to each other.
Right triangles are used in many areas of mathematics and science, including trigonometry, calculus, geometry, physics, and engineering. They are also used in practical applications, such as in construction, surveying, and navigation.
In a right triangle EFG, where angle EFG = θ, the sine of θ is defined as the ratio of the length of the side opposite θ (EF) to the length of the hypotenuse (EG). Therefore, the answer is:
A. sin(θ) = EF/EG
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LESSON 20 • QUIZ
Name:
The price of a ticket to a play is $50 per person. On Monday afternoons, the
theater reduces the ticket price to $35 per person. Students receive an additional
$5 discount on all tickets. What is the percent discount for a student ticket to a
Monday afternoon performance?
A 20%
B 30%
С 40%
D 60%
The percent discount for a student ticket is C. 40%
What is Percent Discount?Percent Discount is a kind of discount that is offered on a product or service in the form of an amount per hundred.
How to determine the percentage discountFrom the question, we have the following parameters that can be used in our computation:
Original price of the ticket = $50
Price of ticket on Monday = $35
Additional discount = $5
To determine the percentage discount, we make use of the following equation
Discount = 1 - (Price of ticket on Monday - Additional discount)/Original price of the ticket * 100%
Substitute the known values in the above equation, so, we have the following representation
Discount = 1 - (35 - 5)/50 * 100%
Evaluate
Discount = 40%
Hence, the percentage discount is 40%
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Writing Prompt: Being very detailed, explain how to solve the following problem to a friend that needs help?
Make sure to use complete sentences
5 minimum sentences
What is the volume of the triangular prism?
The volume of the triangular prism is 144 cm³.
What is the volume of the triangular prism?
We know that the volume of the prism = base area × Length of the prism. Therefore, the volume of the prism, in this case, is calculated using the same formula, Volume of triangular prism = (1/2) bh × L.
We have given:
b = 8cm,
h = 3 cm
l = 12 cm
So, the Volume of the triangular prism = (1/2) bh × L.
= (1/2) 8*3 × 12.
= 12 * 12
= 144
Hence, the volume of the triangular prism is 144 cm³.
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Naylar spent 1 hour and 40 minutes listening to music on her headphones.
If she started at 1:40, what time was it when she finished?
Answer: 3:20
Step-by-step explanation:
Answer: She will be finished by 3:20.
Step-by-step explanation: The time at which she started = 1:40
Adding 1 hour 40 minutes to the given time = 1:40 + 1:00 = 2:40
Adding 20 minutes to it, time becomes = 3:00
Adding 20 more minutes (20+20 =40), final time = 3:20.
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pls help with this question
a. Line A represents Duncan's wages. b. We can determine this by equation of the line. Luke's equation of line has an additional constant and thus it starts from the point 30 above from the origin.
What are variables?In mathematics, a variable is a symbol that designates a mathematical object (from the Latin variabilis, "changeable"). Any number, vector, matrix, function, function argument, set, or set element can be represented by a variable.
A variety of issues are resolved by algebraic calculations that treat variables like explicit integers in a single computation. The quadratic formula, for instance, can be used to solve any quadratic equation by exchanging the variables in the quadratic formula for the numerical values of the coefficients in the equation.
Let us suppose number of hours worked = x.
Given that,
Duncan gets paid R8,50 per hour. His equation of line is:
D = 850x
Luke gets R30 and R450 per hour. His equation of line is:
L = 450x + 30
a. From the graph we see that line A represents Duncan's wages.
b. We can determine this by looking at the equation of the line. Luke's equation of line has an additional constant and thus it starts from the point 30 above from the origin.
c. For x = 2 hours.
L = 450(2) + 30
L = 900 + 30 = R930
d. For D = 1000:
1000 = 850x
x = 1.17 hours.
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A plane is 105 mi north and 196 mi east of an airport. Find x, the angle the pilot should turn in order to fly directly to the airport. Round your answer to
the nearest tenth of a degree.
The angle that the pilot should turn in order to fly directly to the airport is given as follows:
x = 28.2º.
What are the trigonometric ratios?The three trigonometric ratios are defined as follows:
Sine of angle = length of opposite side divided by the length of the hypotenuse.Cosine of angle = length of adjacent side divided by the length of the hypotenuse.Tangent of angle = length of opposite side divided by the length of the adjacent side.For the angle x, we have that:
The adjacent side is of 196 mi.The opposite side is of 105 mi.Hence the angle is obtained applying the tangent as follows:
tan(x) = 105/196
x = arctan(105/196)
x = 28.2º.
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ann and sarah are icing cupcakes. ann can ice a cupcake in 30 seconds. sarah can ice a cupcake in 40 seconds. how many seconds will it take them, working together, to ice all 35 cupcakes
it will take them both 600 seconds to ice 35 cupcakes.
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Here, Ann can ice a cupcake in 30 seconds,
Then, the total number of cupcakes iced by Ann is,
t/30 cupcakes
Similarly, If Sarah can ice a cupcake in 40 seconds,
Then, the total number of cupcakes iced by Sarah is
t/40 cupcakes,
Hence, For them to ice 35 cupcakes together, then;
t/30 + t/40 = 35
where t is the times taken by both of them to ice 35cupcakes
40t+30t/1200 = 35
70t/1200 = 35
7t/120 = 35
t/120 = 5
t = 600
Thus, This shows that it will take them both 600seconds to ice 35 cupcakes.
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Isabella recently opened her online candle shop, Spectacular Scents. Her sales in the first week were $86. After advertising her new shop on social media, her sales increased by 20% the following week and continued to increase at that rate
The exponential equation can be written as y = 84.3(1.02)ˣ.
What are Exponential Equations?Exponential equations are equations where the independent variable, x is in the exponent.
Given that,
Sale in the first week after opening her shop = $86
After advertising her new shop on social media, her sales increased by 20% the following week and continued to increase at that rate.
Percentage increase each week = 20%
Exponential equation will be of the form,
y = a (b)ˣ
where a is the initial sale.
b is the increase in sale.
Initial sale = $86
Sale in the second week = $86 + (20% of $86)
= 86 + (0.2 × 86)
= 86 (1 + 0.2)
Sale in the third week = [86 (1 + 0.2)] + [0.2 × 86 (1 + 0.2)]
= [86 (1 + 0.2)] [ 1 + 0.2]
= 86 (1 + 0.2)²
This goes on.
So sale after x weeks = 86 (1 +0.2)ˣ⁻¹
= 86 (1.02)ˣ⁻¹
= 86 (1.02)ˣ (1.02)⁻¹
= 84.3(1.02)ˣ
Hence the function can be modeled as 84.3(1.02)ˣ.
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Your question is incomplete. The complete question is given below.
Isabella recently opened her online candle shop, Spectacular Scents. Her sales in the first week were $86. After advertising her new shop on social media, her sales increased by 20% the following week and continued to increase at that rate.
Write an exponential equation in the form y = a (b)ˣ that can model Isabella's weekly sales, y , x weeks after opening her shop.
The probability that a continuous random variable equals a certain value is 0: Does that apply to finding even/odd values?
No, the probability that a continuous random variable equals a certain value is zero does not imply that the probability of finding even or odd values is also zero.
The reason for this is that even and odd values are not specific points in the continuous probability distribution, but rather sets of points. For example, if we consider a uniform distribution over the interval [0, 1], the probability of any particular point in the interval is zero, including both even and odd values. However, the probability of finding an even value in the interval is 1/2, since half of the values in the interval are even. Similarly, the probability of finding an odd value is also 1/2. Therefore, the fact that the probability of a continuous random variable taking a certain value is zero does not imply anything about the probability of finding even or odd values.
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When (2x-3) squared is subtracted from 5x squared, what is the result
The outcome of removing (2x-3)2 from 5x2 is therefore x2 + 12x - 9.
What does subtract go by?Therefore, it can be expressed as Minuend Subtrahend = Differential. As a result, the number being removed is known as Barely heard, and the number being deducted is known as Minuend. As a result, the amount that is being removed from is known as the minuend, and the number being deducted from is known as the subtrahend.
To answer this question, we need to expand (2x-3)² and then subtract it from 5x².
(2x-3)² means (2x-3) multiplied by itself:
(2x-3)² = (2x-3) × (2x-3)
The first term in the first parentheses can be multiplied by both terms in the second parentheses using the distributive property, and the second term in the first parentheses can be multiplied by both terms in the second parentheses using the distributive property:
(2x-3) × (2x-3) = 2x × (2x-3) - 3 × (2x-3)
Simplifying each of the two terms:
= 4x² - 6x - 6x + 9
= 4x² - 12x + 9
Now we can subtract this expression from 5x²:
5x² - (4x² - 12x + 9)
Distributing the negative sign:
5x² - 4x² + 12x - 9
Combining like terms:
x² + 12x - 9
Therefore, the result of subtracting (2x-3)² from 5x² is x² + 12x - 9.
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$18 an hour is how much a year
The rate of $18 an hour will be approximately $157248 for a year .
In order to find how much $18 an hour is in a year,
We need to know how many hours are present in a year.
The number of weeks in 1 year is = 52 weeks ;
and 1 week consists of 168 hours , as 1 week has 7 days and 1 day has 24 hours .
So , 1 year (52 weeks) is = 52 × 168 = 8736 hours .
We get that 1 year consists of 8736 hours ,
Now , multiplying the number of hours by $18 ,
We get ,
⇒ 8736 × 18 = $157248 .
Therefore , $18 an hour will be $157248 for a year .
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Ben reached into his wallet without looking it took out two bills. What is the probability that each bill would be worth less $10
In existence, there is the 1 dollar, 5, 10, 20, 50, and 100. The only way he could take out two different dollar bills and it be worth less than 10 bucks is if he pulls out a 1 and a 5. In these odds, it would be 2 / 12 chance of pulling out two dollar bills and it being worth less than 10 bucks.
Determine the equation of the ellipse with center (6, -6), a vertex at (13, -6), and a co-vertex at (6, 0).
The equation of the ellipse is equal to (x - 6)² / 49 + (y + 6)² / 36 = 1.
How to derive of the equation of an ellipse
In this problem we must derive the equation of an ellipse based on information about the center, a vertex and a co-vertex thereof. The vertex represents the end of the major semiaxis that lies on the curve and co-vertex is the end of the minor semiaxis that lies on the curve. The major semiaxis is parallel with x-axis and the minor semiaxis is parallel with y-axis.
The standard form of the ellipse is shown below:
(x - h)² / a² + (y - k)² / b² = 1
Where:
(h, k) - Center of the ellipsea - Length of the major semiaxis.b - Length of the minor semiaxis.Now we proceed to derive the equation of the ellipse:
Major semiaxis:
A = (13, - 6) - (6, - 6)
A = (7, 0)
a = 7
Minor semiaxis:
B = (6, 0) - (6, - 6)
B = (0, 6)
b = 6
Equation of the elipse:
(x - 6)² / 49 + (y + 6)² / 36 = 1
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simplify and distribute 5h^3(4h^2-7h)
20h⁵ - 35h⁴ is the simplified and dispersed expression.
What does math's distribution mean?
Something is divided, shared, or given away when it is "distributed." What does this mean for the distributive property of mathematics? Basic arithmetic operations like addition and subtraction are used to divide the results of multiplication according to the distributive property of the law of multiplication.
We may utilize the distributive property of multiplication, which asserts that a(b + c) = ab + ac, to distribute and simplify 5h³(4h² - 7h).
The 5h³ is first distributed to both words inside of the parenthesis as follows:
5h³(4h² - 7h) is equal to 5h³ * 4h² - 5h³ * 7h.
Secondly, by multiplying the coefficients and adding the exponents, we simplify each term:
20:5 + 5:3 + 4:2 + 5:3 + 7:4 = 35:4
When we add everything together, we get the following: 5h³(4h² - 7h) = 20h⁵- 35h⁴.
Hence, 20h⁵ - 35h⁴ is the simplified and dispersed expression.
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Please look at the screenshot and help with the problem. Will be giving 15 points.
Answer:-1
Step-by-step explanation:
When you multiply exponents that have the same bases you add the exponent. You subtract the exponents when you divide.
x^9=x^y*x^10 the blank box is -1.
what is 57 feet in cm?
According to the concept of unit conversion, 57 feet is equal to 1737.36 centimeters.
Unit conversion is an essential skill to have in science, engineering, and everyday life. It allows us to convert between different units of measurement and compare them easily.
To convert 57 feet to centimeters, we need to know the conversion factor between these two units. One foot is equal to 30.48 centimeters. So, we can multiply the given number of feet by this conversion factor to get the equivalent number of centimeters.
57 feet x 30.48 cm/ft = 1737.36 cm
In unit conversion, it is important to keep track of the units and make sure they cancel out correctly. In this case, the feet unit cancels out with the feet unit in the conversion factor, leaving us with only the centimeter unit.
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Line Plots
4
This data gives the width, in yards, of several drawers.
Width (yd):16 16
23
7 1 11 3 3 1
Create a line plot to display this data.
To create a line plot, hover over each number on the number line. Then click and drag up to plot the
16 2 16 16 16 16
3 LIELI
7 3
Drawer's Width
3
Answer:
i have no clue whats going on sorry i cant help
Step-by-step explanation:
Molly si selling bracelets and necklace at a crack fair . The cost of 4 bracelets and 3 neckclace is 23.50. The cost of 5 bracelets and 2 necklace is 21.50. A custumer bought 1 bracelet and 1 necklace. How Mich money did the custumer spend?
Word problems
Simultaneous equation
4b + 3n = $23.50 x2
5b + 2n = $21.50 x3
We solve this equation using the elimination method. By removing necklaces, we can find the cost of a bracelet.
8b + 6n = $47 --- eqn 1
15b + 6n = $64.5 --- eqn 2
Subtract eqn 1 from eqn 2
7b = 17.5
1b = 17.5/7
1b = $2.50
Substitute the value of bracelet into eqn 1 to find the cost of 1 necklace
8(2.5) + 6n = $47
20 + 6n = $47
6n = 47 -20
6n = 27
1n = 27/6
1n = $4.5
1b + 1n = ?
2.50 + 4.50 = $7
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Someone answer please appreciate it
Answer:
$4
Step-by-step explanation:
A recent Gallup Poll found that 61% of American adults are "satisfied with their personal life."
Suppose you take a random sample of 5 Americans and ask each one if they are "satisfied with their
personal life and record the number who report personal life satisfaction. Use this experiment to answer
the following questions. Round solutions to four decimal places, if necessary.
Binomial probability distribution of the given experiment is as follows 0.00902, 0.07056, 0.22073, 0.34524, 0.26999, 0.08446. its mean is 3.05 and standard deviation is 0.53196.
What is binomial probability distribution?The binomial distribution is a type of probability distribution that models the probability of one of two outcomes given a set of parameters. It summarizes the number of trials with the same chance of producing the same result. The value of a binomial is determined by multiplying the number of independent trials by the number of successes.
Given : n = 5
P = satisfied Americans = 61/100
Q = 1 – P = 1 – 61/100 = 39/100
Binomial distribution formula P(x) = ⁿCₓ . Pˣ . Qⁿ⁻ˣ
ⁿCₓ = n!/ x! (n-x)!
a) Binomial table
P(x) = P(0) = ⁵C₀ . (61/100)⁰. (39/100)⁵ = 0.00902
P(x) = P(1) = ⁵C₁ . (61/100)¹ . (39/100)⁴ = 0.07056
P(x) =P(2) = ⁵C₂ . (61/100)² . (39/100)³ = 0.22073
P(x) = P(3) = ⁵C₃ . (61/100)³ . (39/100)² = 0.34524
P(x) = P(4) = ⁵C₄ . (61/100)⁴ . (39/100)¹ = 0.26999
P(x) = P(5) = ⁵C₅ . (61/100)⁵ . (39/100)⁰ = 0.08446
b) mean of binomial distribution = np
= 5 * 61/100
= 5 * 0.61
= 3.05
c) Standard deviation of binomial distribution = √nPQ
=√5 * 0.61 * 0.39
= 0.53196
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two tickets are drawn without replacement from the following box of tickets: 1, 1, 1, 2, 2, 3, 4, 5. find the probability that the second ticket is 2, given that the first ticket is 5. express your answer as a fraction.
The probability of drawing a ticket with value 2 when the first ticket drawn is 5 is 2/7.
What is probability tree?The tree diagram makes it easier to arrange and see all of the potential possibilities. The tree's branches and ends are its two primary locations. On each branch is written the probability, and the ends hold the results in the end. To determine when to multiply and when to add, use tree diagrams.
Let A be an event: the first ticket extracted was the 5.
Let B be an event: the second ticket is 2.
The probability for the following is given as:
P (B/ A) = 2/7
Hence. the probability of drawing a ticket with value 2 when the first ticket drawn is 5 is 2/7.
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Let the graph of g be a vertical stretch by a factor of 4 and a reflection in the x-axis of the graph of f(x) =x^2-3. Write a rule for g
The rule for the graph of g is g(x) = -4(x^2-3). This graph is a vertical stretch by a factor of 4 and a reflection in the x-axis of the graph of f(x) = x^2-3.
The value where the histogram balances when supported at that point is called ____.
The value where the histogram balances when supported at that point is called the mode of the distribution.
The mode of distribution is the value that appears most frequently in the data set. It is often used as a measure of central tendency, along with the mean and median. The mode is especially useful when dealing with categorical or discrete data, where the possible values are limited and well-defined.
For example, the mode of a list of test scores might be the score that occurs most frequently, indicating the most common level of performance. In a histogram, the mode is the value where the distribution is highest, or where the histogram balances when supported at that point.
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i don’t know how to do it
For the given graph we have:
Domain [-4, 7]
Range [-5, 7]
How to find the domain and range?For a function y = f(x) we define the domain as the set of the inputs and the range as the set of the outputs.
To identify the domain on a graph we need to see the horizontal axis, here we can see that the graph starts at x = -4 and ends at x = 7, then the domain is [-4, 7]
For the rangewe need to look at the vertical axis, here we can see that it starts at y = -5 and ends at y = 7
Then the range is [-5, 7]
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. Find the area of the shaded region.
What is the most precise term for quadrilateral ABCD with vertices A(4, 4), B(5, 8), C(8, 8),
and D(8, 5)?
square
rhombus
kite
Parallelogram
The most precise term for quadrilateral ABCD with vertices A(4, 4), B(5, 8), C(8, 8) is a kite.
Option C is the correct answer.
What is a kite?A kite is a quadrilateral where the adjacent sides are equal which means there are two pairs of equal sides.
We have,
Quadrilateral ABCD:
A = (4, 4)
B = (5, 8)
C = (8, 8)
D = (8, 5)
Now,
A__________B
| |
| |
| |
D_________ C
We see the distance between the two points.
AB = √(8 - 4)² + (5 - 4)² = √(4² + 1) = √17
AD = √(5 - 4)² + (8 - 4)² = √(1² + 4²) = √17
AB = AD
BC = √(8 - 8)² + (8 - 5)² = √9 = 3
CD = √(5 - 8)² + (8 - 8)² = √9 = 3
BC = CD
AB and AC are adjacent sides.
CD and DB are adjacent sides.
So,
The quadrilateral ABCD is a kite.
Thus,
The quadrilateral ABCD is a kite.
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how to convert miliseconds to seconds
We can convert milliseconds to seconds using the formula 1 millisecond = 10⁻³ seconds.
The second is the unit of time. A millisecond is likewise a time unit, however it is a smaller unit.
We already know Milli is equivalent to 10⁻³.
As a consequence, we may use the unit conversion concept to describe the connection.
One millisecond is equivalent to 10⁻³ seconds.
For instance, 6 milliseconds is equal to 6 x 10⁻³ seconds.
As a result, we now have a standard formula for calculating the value of time in milliseconds to seconds and seconds to milliseconds.
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Drag the red and blue dots along the x-axis and y-axis to graph 2x-2y=20
Answer:
Blue dot: (0,10)
red dot: (1,-9) or (2,-8)
Step-by-step explanation:
2x-2y=20-2y=-2x+202y=2x-20y=x-10The equation is y=x-10
what is quart to ml?
The relationship between quart to ml is that 1 quart is equal to 946.6 mililitres.
Quart and ml both are the unit of volume. ml is abbreviated form of mililitres and the two units are related together. Here is how they are related -
1 quart is equal to 946.6 mililitres.
Thus, in this method we can simply relate and calculate the quart amount of liquid in mililitres. Let us interpret the above mentioned statement through example. For instance, we need to know the mililitres in 0.25 quart. Here is how we will solve this.
Quantity in mililitres = quantity in quart × amount of mililitres in one quart
Quantity of mentioned liquid in mililitres = 0.25 × 946.4
Performing multiplication on Right Hand Side of the equation
Quantity of mentioned liquid in mililitres = 236.6 mililitres
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Verify the identity (cos x )(tan x + sin x cot x) = sin x + cos2 x. Show all work for full credit.
Answer:
Step-by-step explanation:
Starting with the left-hand side (LHS) of the identity:
(cos x)(tan x + sin x cot x)
We can simplify using trigonometric identities. First, we can rewrite tan x as sin x/cos x and cot x as cos x/sin x:
(cos x)(sin x/cos x + sin x(cos x/sin x))
Simplifying, we get:
(sin x + cos2 x)/sin x
Next, we can multiply the numerator and denominator by the conjugate of sin x + cos2 x, which is sin x - cos2 x:
[(sin x + cos2 x)/(sin x + cos2 x)] * [(sin x - cos2 x)/(sin x - cos2 x)]
Expanding and simplifying, we get:
[(sin x)(sin x - cos2 x) + (cos2 x)(sin x - cos2 x)] / [(sin x)(sin x - cos2 x) + (cos2 x)(sin x + cos2 x)]
Simplifying further, we get:
(sin2 x - cos2 x + cos2 x sin x - cos4 x) / (sin2 x + cos2 x)
Using the identity sin2 x + cos2 x = 1 and simplifying, we get:
(sin x - cos2 x) / 1
Finally, using the identity cos2 x = 1 - sin2 x, we can simplify to:
(sin x - (1 - sin2 x)) / 1
Simplifying further, we get:
2 sin x - 1
So the left-hand side is equal to 2 sin x - 1.
Now, let's simplify the right-hand side (RHS) of the identity:
sin x + cos2 x
Using the identity cos2 x = 1 - sin2 x, we can rewrite the RHS as:
sin x + 1 - sin2 x
Simplifying further, we get:
1 - sin2 x + sin x
Finally, using the identity sin2 x + cos2 x = 1, we can rewrite as:
cos2 x + sin x
So the right-hand side is equal to cos2 x + sin x.
Since the left-hand side is equal to 2 sin x - 1 and the right-hand side is equal to cos2 x + sin x, the identity is not true in general. Therefore, the given identity does not hold true.
hope this helps