Add all of the numbers together and then divide that by how many numbers there are.
Mean mode formula - Mean = {Sum of Observation} ÷ {Total numbers of Observations}
What does the mode mean?
By summing all the numbers in a data collection and dividing by the total number of values in the set, the mean (average) of the data set can be determined.
A data collection is ordered from least to largest, and the median is the midpoint number. A data set's mode is the number that appears the most frequently.
What are the mean, median, and example?
The most frequent number, or the one that happens the most frequently, is known as the mode. Example: Since the number 2 appears three times, more than any other number, it is the mode of the numbers 4, 2, 4, 3, and 2.
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How do you calculate full height in Class 8?
Due to the closing of a growth plates in bones, the majority of people's height would not increase after the ages of 18 to 20. The average human height is about 6 feet, but some individuals can reach heights of more than 9 feet.
What is termed as the full height of a person?Your height varies slightly throughout the day as a result of the decompression and compression of a discs in your spine.
Adolescence is the stage of development when the body goes through changes that prepare it for sexual maturity. Adolescence typically starts at age 11 and lasts until age 18 or 19. Because they range in age from 13 to 18 or 19 years old, adolescents are sometimes referred to as teenagers. •Puberty: The stage of adolescence during which teenage sexual maturation and childbearing potential occur.Thus, the formula for finding the height is -
Full height = Present height/% of full height at present x 100
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7.
Shino typed
-4²
into a calculator and got -16. Then Shino
typed
(-4)²
into a calculator and got 16. Can you
explain to Shino why she got two
different answers?
Type a response
Answer:
order of operations
Step-by-step explanation:
You want to know why -4² = -16 and (-4)² =16.
Order of operationsThe calculator properly applied the order of operations to -4². In evaluating, this expression, the exponentiation operation is performed first. That means this is evaluated as ...
-4² = -(4×4) = -16
When the parentheses include the minus sign, as in the second expression, the squaring operation is applied to -4, not to 4:
(-4)² = (-4)×(-4) = 16
A model rocket is shot upward at a rate of 230 ft/sec. The height of the rocket, in feet, after t seconds
is given by the formula h=16t² + 230t. Answer the following question and round to the nearest tenth where applicable. Be sure to show all of your algebraic work and formulas.
When will the rocket reach its highest point?
Answer:
Step-by-step explanation:
given the formula
[tex]h(t)=16t^{2}+230t[/tex]
Find the axis of symmetry
[tex]t=\frac{-b}{2a}[/tex]
Notice the function is of the form
[tex]h(t)=at^{2}+bt[/tex]
where
[tex]a=16, b=230[/tex]
To find the time at which the rocket reached its highest point, use the formula for the axis of symmetry. Substitute 16 for a and 230 for b. This gives you,
[tex]t=\frac{-(230)}{2(16)}[/tex]
simplify the arithmetic expression..
[tex]t=\frac{-230}{32}[/tex]
[tex]t[/tex]≈-7.2 seconds
I THINK the answer should be -7.2 seconds but I do not know how this would really play into the problem being that seconds should be positive, not negative... hope this helps!
Please describe what the absolute value inequality | x-0 |
What is the equation of the line that passes through the point (8, -3) and has a slope of 1/4?
Answer:
y=1/4x-5
Step-by-step explanation:
y=mx+b is slope intercept form
m is slope
b is y intercept
we know m is 1/4 so we fill it in
y=1/4x+b
fill is the coordinates to find b
-3=1/4(8)+b
-3=2+b
-2. -2
-5=b
place b in
y=1/4x-5
hopes this helps
Answer:y=1/4x-5
Step-by-step explanation:
Your point was (8,-3) and your rise is 1 and your run is 4 so if you want to get from 0 to 8 and count by 4 you need to move twice, and if you established that you will move twice then you need a number that you add 2 to that will give you -3. And that number is -5 so your y-intercept is
What are asymptotes example?
An asymptote is a line that a curve approaches but never touches. There are two types of asymptotes: horizontal and vertical. Few examples of asymptotes are f(x) = 1/x, f(x) = 1/x² + 1 and f(x) = 1/(x-3).
Here are some examples of functions with horizontal asymptotes:
The function f(x) = 1/x has a horizontal asymptote at y = 0.
f(x) = 1/x
As x gets larger and larger, the value of the function approaches 0, but never quite reaches it. This means that the horizontal line y = 0 is an asymptote for the function f(x) = 1/x.
The function f(x) = 1/x² + 1 has a horizontal asymptote at y = 1.
f(x) = 1/x² + 1
As x gets larger and larger, the value of the function approaches 1, but never quite reaches it. This means that the horizontal line y = 1 is an asymptote for the function f(x) = 1/x² + 1.
Here is an example of a function with a vertical asymptote:
The function f(x) = 1/(x-3) has a vertical asymptote at x = 3.
f(x) = 1/(x-3)
As x gets closer and closer to 3, the value of the function approaches infinity, but never quite reaches it. This means that the vertical line x = 3 is an asymptote for the function f(x) = 1/(x-3).
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What is the nature of the roots of x2 6x 9 0?
The value of the Discriminant is 0 so we have equal roots = b/2a = 6/2 = 3
The given equation is a quadratic equation.
x^2+6x+9 = 0.
To tell the nature of the roots we have to understand how to find the root of a quadratic equation.
The roots of a quadratic equation are the values of the variables that fulfil the equation. In other words, if f(α) = 0, then x = α is a root of the quadratic equation f(x).
The term Discriminant is used in quadratic equations.
The discriminant of a quadratic equation is the expression [tex](b^2 - 4ac)[/tex] in the quadratic formula. A quadratic equation's discriminant shows the nature of roots.
Discriminant important thing is that it is used to find the nature of roots.
x^2+6x+9 = 0. a =1, b = 6, c=9
discriminant d = b^2 - 4*a*c = 36-4*1*9 = 36-36 = 0
So the value of the discriminant is 0 so we have equal roots = b/2a = 6/2 = 3
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Your school plans to give the freshman class a pizza party if they spend a total of at least $7,000 on
yearbooks and class rings. Each yearbook costs $35 and each class ring costs $60.
Part A: Write an inequality in slope intercept form that best represents this scenario. Make sure to create your
KEY!
Considering the definition of an inequality, the inequality that best represents this scenario is 35x + 60y≥ 7000
Definition of inequalityAn inequality is the existing inequality between two algebraic expressions, connected through the signs:
greater than >.less than <.less than or equal to ≤.greater than or equal to ≥.Solving an inequality consists of finding all the values of the unknown for which the inequality relation holds.
Inequality in this caseIn this case, you know that:
They spend a total of at least $7,000 on yearbooks and class rings. Each yearbook costs $35 and each class ring costs $60.Being:
"x" the number of yearbook."y" the number of class ring.the inequality that expresses the scenario is
35x + 60y≥ 7000
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If a train leaves New York at 10am (est) going 90mph and a train leaves Los Angeles at 8am (pst) going 60 mph, at what time will the trains meet if the total distance is 3000 miles?
Answer:
Therefore for this distance combined speed is to be taken. Time taken to cover 2800 miles = 2800/(60+40) = 28 hours.
Step-by-step explanation:
We can assume that B leaves Los Angeles not at noon but at 2pm Eastern Time, so 5 hours later than A leaves New York.
In 5 hours A covers 5*40=200 miles. So, A and B together should cover 3,000-200=2,800 miles.
Combined rate = 40 + 60 = 100 miles per hour.
To cover 2,800 miles they'll need 2,800/100=28 hours.
2pm Eastern Time on Monday + 28 hours = 6pm Eastern Time on Tuesday
these are two separate questions, please answer both. Thank youuu !!
Answer:
answers are T,F,T
Step-by-step explanation:
Just had this worksheet
PLEASE I REALLY NEED HELP THE BRAINLIST ANSWER WILL GET MARKED!!!!
Students in a class were asked to tell their favorite color.
a. What percent said red, blue, or yellow?
__ % said red, blue, or yellow.
b. How many times more students said red than yellow? __ times more students said red than yellow.
c. Use two methods to find the percent of students who said green. green: __%
Which method do you prefer? Explain.
Answer: a = 70%
b 6.5 times
c green = 16%
2. ????? Very poorly worded question
2. a 54%
b. 46%
c. 70%
d. 27%
Step-by-step explanation:
Students in a class were asked to tell their favorite color.
a. What percent said red, blue, or yellow? __% said red, blue, or yellow.
red is .26
blue is .40
yellow is .04
---------------------
.70 = 70 %
b. How many times more students said red than yellow?
red .26
yellow is .04
.26/.04 = 6.5 times
c. What percent of students said green? __% said green.
The circle must total 100 %
Red + blue + yellow + purple + green = 100
26+ 40 + 4 + 14 + green = 100
84 + green = 100
Subtract 84 from each side
84-84 + green = 100-84
green = 16
2. Which two methods could be used to find the percent of students who said green?
We can either convert the percents to decimals or the decimals to percents
The total percents must equal 100%
The total decimal must equal 1
a. Find the sum of the percents given in the circle graph.
If they only want the ones written on the graph as percents
(14+40) = 54%
b. Find the sum of the percent forms of the numbers given in the circle graph. Subtract the result from 100%.
100 - 54% = 46%
c. Find the sum of the decimal forms of the numbers given in the circle graph. Subtract that sum from 1. Change the result to a percent.
.26+.04 = .3
1-.3 = .7
70%
d. Find the sum of half of the percents given in the circle graph. Subtract that total from 50%.
1/2 (46%) = 23%
50 -23 = 27%
How do I notify SSS for EC sickness benefit?
The claim for the EC sickness benefit are filed at any SSS branch or representative office nearest the member's residence or place of work.
Here we need to find the way to notify SSS for EC sickness benefit.
In order to find the solution, we must know that what is meant by SSS for EC sickness benefit.
The term SSS for EC sickness benefit is defined as the benefits under the EC program may be enjoyed simultaneously with benefits under the social security program effective June 1984.
Based on the definition, we have identified that the notification process is done through the E-Services tab and click on "Submit SS Sickness Benefit Reimbursement Application (SBRA)."
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How do you know if two figures are similar by transformations?
Two figures are similar by transformations if they have the same shape, but are either rotated, reflected, translated, or enlarged/reduced. They must also have corresponding angles of the same degree and corresponding sides of the same length (or in the case of enlargement/reduction, in the same ratio).
Transformations – what are they?Four distinct approaches to modify the position and/or shape of a point, line, or geometric figure are collectively referred to as transformations. The Pre-Image of the object is its initial shape, while the Image, after transformation, is the final shape and location of the thing.
Describe a transformation example.A drastic change in shape or appearance is called a transformation. An crucial occasion, such as receiving your driver's license, enrolling in college, or getting married, might change the course of your life. Extreme, dramatic change is what we refer to as transformation.
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How do you solve a quadrilateral problem?
Answer:
It depends on what the question is.
Step-by-step explanation:
What is the vertical asymptote of X 4?
The vertical asymptote of X 4 is x = 4, which means that as x approaches 4, the function approaches infinity.
The vertical asymptote of a function is an x-value at which the function tends to approach infinity. In the case of X 4, the vertical asymptote is x = 4. This means that as x approaches 4, the function X 4 approaches infinity. This can be seen by examining the function. As x approaches 4 from the left, the denominator of X 4 becomes increasingly small while the numerator remains constant. This means that the function's value becomes increasingly large as x approaches 4, eventually resulting in an infinite value. In the same way, as x approaches 4 from the right, the denominator of X 4 becomes increasingly large while the numerator remains constant. This means that the function's value becomes increasingly small, eventually resulting in an infinite value. Thus, the vertical asymptote of X 4 is x = 4.
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Which of the following equations has the sum of its roots as 3 a 2x² 3x 6 0 B X² 3x 3 0 C √ 2x² 3 √ 2x 1 0 D 3x² 3x 3 0?
The equation x² + 3x - 3 = 0 has the sum of its roots as 3. This can be found by using the quadratic formula, which gives us two roots x1 and x2. Their sum is x1 + x2 = 3, which is the sum of the roots of the equation.
The correct answer is B: x² + 3x - 3 = 0
The equation has the form of ax² + bx + c = 0.
a = 1, b = 3, c = -3
The sum of the roots can be found using the quadratic formula:
x = (-b ± √(b² - 4ac))/2a
x = (-3 ± √(9 - 4*1*(-3))/(2*1)
x = (-3 ± √15)/2
x = (-3 ± 3√5)/2
x1 = (3 - 3√5)/2
x2 = (3 + 3√5)/2
The sum of the roots is x1 + x2 = 3.
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Convert 140 kilograms to pounds. (1 kilogram = 2.204 pounds)
310.76 pounds
308.56 pounds
63.52 pounds
15.74 pounds
Converting 140 kilograms to pounds is: 308.56 pounds.
Here, we have,
given that,
Convert 140 kilograms to pounds.
now, we know that,
1 kilogram = 2.204 pounds
so, we get,
we would multiply 140 by 2.204
i.e.
140 × 2.204 = 308.56
which would give the answer which is 308.56 pounds.
Hence, Converting 140 kilograms to pounds is: 308.56 pounds.
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Is 2 a factor of 36?
The factors of the number 36 will be 2, 2, 3, and 3. So, yes, 2 is the factor of 36.
What is factorization?It is a method for dividing a polynomial into pieces that will be multiplied together. At this moment, the polynomial's value will be zero.
It is also known as the product. If the object n is given to m times then we just simply multiply them.
The number is given below.
⇒ 36
The factor of the number 36 is given below.
36 = 2 x 2 x 3 x 3
The factors of the number 36 will be 2, 2, 3, and 3. So, yes, 2 is the factor of 36.
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Graph g(x)=2x2−4x−16 Use the parabola
The parabola Refer the attached figure, x- intercepts are (4,0) and (-2,0)
Quadratic function = f(x) = 2x²-4x-16.
To find: The graph of the quadratic function using parabola tool?
First we find the vertex form of the equation.
f(x) = 2x²-4x-16
Where, a=2 ,b=-4 , c=-16
Vertex is V,
[tex]v=\frac{-b}{2a} , f(\frac{-b}{2a})\\\\\frac{-b}{2a} = \frac{4}{4} =1\\\\f(\frac{-b}{2a})=f(1)\\\\=-10[/tex]
So, The vertex of the equation is (1,-10).
Now, we find y- intercept by putting x=0 in the equation
[tex]y=2(0)^{2} -4(0)-16\\\\y=-16[/tex]
y- intercept (0,-16)
Now, we find x- intercept by putting y=0 in the equation.
[tex]2x^{2} -4x-16=0\\\\x^{2} -2x-8=0\\\\x^{2} -4x+2x-8=0\\\\x=4 \ and \ x=-2[/tex]
x- intercepts are (4,0) and (-2,0)
Placing all the points and plot a graph.
Refer the attached figure below.
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The temperature in Mexico City is 43 degrees Celsius. What is the corresponding temperature in Fahrenheit
Answer:109.4 Fahrenheit
Step-by-step explanation:
A rectangle of the same size is divided by 5 squares in length and 4 in bredth. The measure of the sides of these smaller squares is an integer. One of the following numbers cannot be the perimeter of the rectangle. Which one?
A. 261
B.270
C.918
D.1782
E.2016
Please help me with the explanation!
Answer: 270 is the answer
Step-by-step explanation:
What is the equation of a line having a slope of 5 and whose y-intercept is 8?
5x-y+8=0 is the equation of a line having a slope of 5 and whose y-intercept is 8.
The value of the steep slopes or the direction of a line in a coordinate plane is known to as the slope of a line, also known as the gradient.
A straight line's general equation is y = mx + c, where m denotes the gradient and y = c denotes the point at which the line crosses the y-axis. Mostly on y-axis, this value c is referred to as the intercept. Y = mx + c represents the equation of a straight line with gradient m and intercept c on the y-axis.
given information like Slope=m=5 and Y intercept equals c=8,
A line's equation is y=mx+c.
As a result of the information provided, the equation for a line is y=5x+8.
A line must have the equation 5x-y+8=0.
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If truth values of p be F and q be T. Then, truth value of ∼(∼p∨q) is
a. T
b. E
c. Either T or F
d. Neither T not F
If truth values of p be F and q be T. Then, truth value of ∼(∼p∨q) is F.
Describe truth value.A proposition's characteristic indicating whether it is true or false is the definition of a truth value. For instance, the truth value for "7 is odd" is true and can be represented by the letter T. "1 + 1 = 3" has a false truth value, which can be represented by the letter F. Truth is crucial. People's plans can be ruined and their lives could be in danger if they believe something that is false. Legal and societal repercussions may occur from telling lies. The excellent historian, good investigator, and good scientist, on the other hand, are committed to the search of truth.
Given
If truth values of p be F and q be T. Then, truth value of ∼(∼p∨q) is
b. F
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The acceleration of segment d is m/s2. rank segments a, b, and c from least acceleration to greatest acceleration. least: greatest:
Calculating acceleration involves dividing the change in velocity by the change in time.. The equation is a = (v-u)/t, where a is acceleration, v is the final velocity, u is the initial velocity, and t is the time.
Acceleration is the rate of change in velocity over time. To calculate acceleration, you need to know the initial velocity (u), the final velocity (v), and the time (t) of the motion. The formula for calculating acceleration is a = (v-u)/t. To use this formula, subtract the initial velocity from the final velocity and divide by the time. This will give you the acceleration. For example, if the initial velocity is 10 m/s, the final velocity is 20 m/s, and the time is 2s, then the acceleration is (20-10)/2 = 10 m/s2. This means that the velocity has increased by 10 m/s every second.If the initial velocity is 10 m/s, the final velocity is 20 m/s, and the time is 2s, then the acceleration is (20-10)/2 = 10 m/s2.
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Answer:
1st Q: -20
2nd Q: C,B,A
Step-by-step explanation:
Its correct
answer for the page?
Answer:
(9) x = 9
(10) I cannot see the image clearly, sorry :(
(11) x = 54
(12) I cannot see the image clearly, sorry :(
(13) ∠P = 64°
(14) ∠Q = 26°
(15) ∠U = 47°
(16) ∠W = 43°
Step-by-step explanation:
(9)
To find an unknown side length in a right triangle, we need to use a trigonometric function.
⭐ What is a trigonometric function?
A trigonometric function is the ratio of two side lengths for a certain angle, where one of the side lengths is unknown and denoted by a variable (x)⭐ What are the trigonometric functions?
sin(θ) = opposite/hypotenusecos(θ) = adjacent/hypotenusetan(θ) = opposite/adjacentθ = an angle measure that isn't the 90 degrees angle.To determine which trigonometric function to use, we need to see which type of side lengths we are given (hypotenuse/opposite/adjacent).
We are given side length x, which is opposite of the 37 degrees, and side length 15, which is the hypotenuse of the triangle. Therefore, we will use sin(θ).
Substitute the angle measure we are given and the side lengths into sin(θ).
[tex]sin(37) = \frac{x}{15}[/tex]
[tex]15sin(37) = x[/tex]
Compute this equation into a scientific calculator. I recommend using the Desmos Scientific Calculator.
[tex]9.0 = x[/tex]
(10) I'd need to see x clearly to solve.
(11) To find an unknown side length in a right triangle, we need to use a trigonometric function.
⭐ What is a trigonometric function?
A trigonometric function is the ratio of two side lengths for a certain angle, where one of the side lengths is unknown and denoted by a variable (x)⭐ What are the trigonometric functions?
sin(θ) = opposite/hypotenusecos(θ) = adjacent/hypotenusetan(θ) = opposite/adjacentθ = an angle measure that isn't the 90 degrees angle.To determine which trigonometric function to use, we need to see which type of side lengths we are given (hypotenuse/opposite/adjacent).
We are given side length x, which is the hypotenuse of the triangle, and side length 14, which is adjacent to the 75 degrees. Therefore, we will use cos(θ).
Substitute the angle measure we are given and the side lengths into cos(θ).
[tex]cos(75) = \frac{14}{x}[/tex]
[tex]\frac{14}{cos(75)} = x[/tex]
Compute this equation into a scientific calculator. I recommend using the Desmos Scientific Calculator.
[tex]54 = x[/tex]
(12) I'd need to see x clearly to solve.
(13) To find the angle measure of an angle in a right angle triangle, we need to use the inverses of the trigonometric functions.
⭐ What are the inverses of the trigonometric functions?
[tex]sin^-1(opposite/hypotenuse) =[/tex][tex]cos^-1(adjacent/hypotenuse) =[/tex][tex]tan^-1(opposite/adjacent)[/tex]First, we need to see the type of side lengths we are given (adjacent/hypotenuse/opposite) to determine which inverse trigonometric function we use for each angle.
∠P is adjacent to side length 8, and side length 18 is the hypotenuse of the triangle. Therefore, we will use [tex]cos^-1(adjacent/hypotenuse) =[/tex].
Substitute the side lengths and compute using a scientific calculator. I recommend using the Desmos Scientific Calculator.
[tex]cos^-1(\frac{8}{18})[/tex]
∴ ∠P = 64°
(14) To find the angle measure of an angle in a right angle triangle, we need to use the inverses of the trigonometric functions.
∠Q is opposite of side length 8, and side length 18 is the hypotenuse of the triangle. Therefore, we will use [tex]sin^-1(opposite/hypotenuse) =[/tex].
Substitute the side lengths and compute using a scientific calculator.
[tex]sin^-1(\frac{8}{18})[/tex]
∴ ∠Q = 26°
(15) To find the angle measure of an angle in a right angle triangle, we need to use the inverses of the trigonometric functions.
∠U is opposite of side length 11, and side length 15 is the hypotenuse of the triangle. Therefore, we will use [tex]sin^-1(opposite/hypotenuse) =[/tex].
Substitute the side lengths and compute using a scientific calculator.
[tex]sin^-1(\frac{11}{15})[/tex]
∴ ∠Q = 47°
(16) To find the angle measure of an angle in a right angle triangle, we need to use the inverses of the trigonometric functions.
∠W is adjacent to side length 11, and side length 15 is the hypotenuse of the triangle. Therefore, we will use [tex]cos^-1(adjacent/hypotenuse) =[/tex].
Substitute the side lengths and compute using a scientific calculator.
[tex]cos^-1(\frac{11}{15})[/tex]
∴ ∠W = 43°
What is the coefficient of x² in 3x²?
The coefficient of the variable x² in the expression 3x² is 3
Given that,
The expression is 3x²
To find : The coefficient of the variable x² in the expression
Coefficient is the number that is beside the variable in the equation.
The coefficient of x in 3x² is 3
A number multiplied by a variable is referred to as the coefficient of a number. For instance, the x2 coefficient in the formula 6x2+99 is 6
As we can see that the term that is in multiplication with x² is 3.
Hence, the coefficient of x² in the equation 3x² is 3.
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A baseball is hit upwards with a velocity of 60 feet per second. The height of the ball above the ground, in feet, at time t seconds is given by h(t)=-18t^2+60t+4. How long after the ball is hit does it strike the ground?
The ball is hits the ground after 3.4 seconds it strike s
How to determine how long after the ball is hit does it strike the ground?From the question, we have the following parameters that can be used in our computation:
h(t)=-18t^2+60t+4.
Rewrite as
h(t) = -18t² + 60t + 4
When the ball hits the ground, we have
h(t) = 0
So, the equation becomes
-18t² + 60t + 4 = 0
Divide through by 2
-9t² + 30t + 2 = 0
So, we have
9t² - 30t - 2 = 0
Using a graphing tool, we have
t = 3.4
Hence, the time is 3.4 seconds
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Is 16 a multiple of 3 yes or no?
No, 16 is not a multiple of 3 as they leave some reminder.
What are the multiples of 3?A multiple in mathematics is created when an integer and any quantity are combined. It can be argued that b is a multiple of a given quantity an if and only if b = na for some integer n, known as the multiplier.A is referred to as a divisor of b if both a and b are integers and b is a multiple of a. 16, 12, 22, 28, 31, 33, and 42 are on the list. The numbers that are precisely divisible by three are known as the multiples of three. However, due to the leftover value they leave, the numbers 16, 22, 28, and 31 are not multiples of 3.Hence, No, 16 is not a multiple of 3 as they leave some reminder.
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5/8 subtracted by 3/4
Answer:
Step-by-step explanation:
[tex]x_{123} \sqrt{x} x^{2} \alpha \int\limits^a_b {x} \, dx \lim_{n \to \infty} a_n \lim_{n \to \infty} a_n x_{123} \frac{x}{y} \sqrt[n]{x} \sqrt[n]{x} \alpha \sqrt{x} 5#\left[\begin{array}{ccc}1&2&3\\4&5&6\\7&8&9\end{array}\right] \alpha[/tex]√β⇄ΜΒΑςΘPlease help I will give brainliest
Answer:
1. ∠YZX = 37°
2. ∠YXZ = 53°
3. XZ = 30 meters
Step-by-step explanation:
1. To solve for an unknown angle, we need to utilize the inverse of a trigonometric function.
⭐What are the inverses of the trigonometric functions?
[tex]sin^-1 (opposite/hypotenuse)[/tex][tex]cos^-1 (adjacent/hypotenuse)[/tex][tex]tan^-1(opposite/adjacent)[/tex]To know which inverse of the trigonometric functions we use, we have to see the type of side lengths we are given (opposite, adjacent, or hypotenuse)
We are given side length XY, which is opposite of ∠YZX, and we are given side length YZ, which is adjacent to ∠YZX. Therefore, we will use [tex]tan^-1 (opposite/adjacent) =[/tex]
Substitute the values we are given into the function:
[tex]tan^-1 (18/24) =[/tex]
Compute this equation using a scientific calculator. I recommend using the Desmos Scientific Calculator:
[tex]= 37[/tex]
∴ ∠YZX = 37°
2. We already know 2 angles (∠YZX = 37°, and ∠ZYX = 90°) Therefore, to find ∠YXZ, we have to utilize the triangle sum theorem.
⭐ What is the triangle sum theorem?
[tex]angle_1 + angle_2 +angle_3 = 180[/tex]The sum of all angles in a triangle is 180°Substitute the angles we know already (∠YZX and ∠ZYX), and solve for ∠YXZ.
[tex]< YZX + < ZYX + < YXZ = 180[/tex]
[tex]37 + 90 + YXZ = 180[/tex]
[tex]127 + YXZ = 180[/tex]
[tex]< YXZ = 53[/tex]
∴ ∠YXZ = 53°
3. We already know 2 side lengths (ZY = 24 meters, and XY = 18). Therefore, to find XZ, we have to utilize the Pythagoras' theorem.
⭐ What is the Pythagoras' theorem?
[tex](C)^2 = (A)^2 + (B)^2[/tex]C is the hypotenuse of the triangle, A is a leg of the triangle, and B is another leg of the trianglePythagoras' theorem can only be used on right trianglesSubstitute the values of the side lengths into the formula:
[tex](XZ)^2 = (XY)^2 + (ZY)^2[/tex]
[tex](XZ)^2 = 18^2 + 24^2[/tex]
Solve for XZ:
[tex](XZ)^2 = 324 + 576[/tex]
[tex](XZ)^2 = 900[/tex]
[tex]\sqrt{(XZ)^2} = \sqrt{900}[/tex]
[tex]XZ = 30[/tex]
∴ XZ = 30 meters