The cofunction of cos is sin(90-x)
90 degrees is equal to PI/2
The cofunction becomes sin(PI/2 - 2PI/9)
Rewrite both fractions to have a common denominator:
PI/2 = 9PI/18
2PI/9 = 4PI/18
Now you have sin(9PI/18 - 4PI/18)
Simplify:
Sin(5PI/18)
The cofunction of cos 2pi/9 is sin(pi/2 - 2pi/9), which is a basic concept in trigonometry.
Explanation:The student is asking about the cofunction of
cos 2pi/9
. In trigonometry, the cofunction of a function is basically the complementary function of 90 degrees minus the original function. In this case, the cofunction of cos is sin, so to find the cofunction of cos 2pi/9, you need to find sin(90 - 2pi/9). However, since we are dealing with radians here, rather than degrees, we will be using pi/2 instead of 90 degrees. Therefore, the cofunction of cos 2pi/9 is
sin(pi/2 - 2pi/9)
.
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a cube has a volume of 125 in3. find the side length of this cube in inches.
Answer:
5 inches
Step-by-step explanation:
The formula for a cube's volume is its side length cubed. So to get the side length when given the volume, you can take the cube root of the volume. [tex]\sqrt[3]{125} = 5[/tex] inches.
5. A car wash uses 50 gallons of water every
40 seconds. How much water does it use per
second?
Answer:
1.25 gallons per second
Step-by-step explanation:
To figure this out divide 50 by 40
I don't know how to explain this further, hope this is good enough.
- Que
Answer:
It use 1.25 gallons of water per second
Step-by-step explanation:
Amount of water used for car wash in 40 seconds = 50 gallons
Amount of water used for car wash in 1 seconds = [tex]\frac{50}{40}[/tex]
Amount of water used for car wash in 1 seconds = [tex]1.25[/tex]
So, Amount of water used in 1 second is 1.25 gallons
So, Unit rate = 1.25 gallons per second
Hence it use 1.25 gallons of water per second
What is the area of a figure that is formed using a parallelogram with base 5.2 meters and height 3 meters, and a semicircle with a radius of 4 meters. Round to the nearest tenth, if necessary.
Question 1 options:
40.7 m2
40.733 m2
33.3 m2
28.2 m2
Answer:
40.7m^2
Step-by-step explanation:
Base×Height= 5.2m×3=15.6m2
Area of semicircle= Pie r^2= Pie×4^2=16×pie
pie×16÷2=8×pie
8×3.14=25.12m2
15.6m2+25.12m2=40.72m2
rounded to nearest tenth=40.7m2
Answer: [tex]40.7\ m^2[/tex]
Step-by-step explanation:
Given : A parallelogram has base 5.2 meters and height 3 meters, and a semicircle with a radius of 4 meters.
Area of parallelogram is given by :-
[tex]A_p=b\times h[/tex] , where b is base and h is height of parallelogram.
[tex]=5.2\times3=15.6\ m^2[/tex] (1)
Area of semicircle :-
[tex]A_s=\dfrac{\pi r^2}{2}[/tex], where r is radius.
[tex]=\dfrac{3.14\times4^2}{2}=25.12[/tex] (2)
Now from (1) and (2),. the area of the combined figure will be :-
[tex]A=A_p+A_s\\\\=15.6+25.12=40.72\approx40.7\ m^2[/tex]
Find the prime factors of all the numbers from 21 to 30
Answer:
21: 7*3
22: 11*2
23: prime
24: 2^3 * 3
25: 5^2
26: 13*2
27: 3^3
28: 2^2*7
29: prime
30: 3*2*5
Abc is a straight line. The length of AB is four times bigger than BC.
AC=75
Answer:
AB=15 BC=60
Step by step:
AB+BC=AC
AC=75
Plug in AC to the equation: AB+BC=75
BC=4(ab)
Plug in BC into the equation: AB+4(AB)=75
Simplify: 5AB=75
Divide each side by 5: AB=15
BC=4(15)=60
Answer: AB = 60, BC = 15
Step-by-step explanation:
AB is 4 times bigger than BC ⇒ AB = 4BC
Use the Segment Addition Property: AB + BC = AC
and substitution (replace AB with 4BC) and (AC with 75) to solve for BC
4BC + BC = 75
5BC = 75
BC = 15
AB = 4BC
= 4(15)
= 60
Function g is defined as g(x)=f(-x)
The function g(x) = f(-x) represents a reflection of the graph of f(x) across the y-axis. This transformation swaps the values of the function for positive and negative x values, creating a mirror image. So since the max of f was when x = 2, the max of g will be when x = -2.
Understanding the Transformation of Function g(x) = f(-x)
function g(x) = f(-x).
This indicates a transformation where the function f(x) is reflected across the y-axis.
To put it simply, the graph of y = f(-x) is the mirror image of the graph of y = f(x) across the y-axis.
f g(x) = f(-x), the graph of g looks like a mirror image of f, where the y-axis is the mirror.
For example, g(1) will be what f's value at -1 was (-1). g(2) = f(-2) = -3. g(3) = f(-3) = -1. etc.
So since the max of f was when x = 2, the max of g will be when x = -2.
Here’s an example to illustrate:
Suppose f(x) = x².
The graph of y = f(x) is a parabola facing upwards.
For y = f(-x), or y = (-x)²,
the graph will still be a parabola facing upwards.
Since g(x) = f(-x), the absolute values are not changed but the sign change in x reflects each point across the y-axis.
This reflection happens because negating the independent variable x means we swap the values of the function at positive and negative x values.
Question:
If the function g is defined so that g(x)=f(-x), then for what value of x does g attain its maximum value?
You pay $22 to rent 6 video games. The store charges $4 for new games and $2 for older games. How many new games did
you rent?
How many new games
Final answer:
To find the number of new games rented, set up an equation using the given information. Assume all 6 games rented were new games, and solve for the number of new games.
Explanation:
To find the number of new games rented, we can set up an equation using the information given.
Let x represent the number of new games rented and y represent the number of older games rented.
We know that the total cost of renting 6 games is $22. Therefore, we can write the equation:
4x + 2y = 22
To find the number of new games rented, we want to solve for x. We can do this by substituting a value for y and solving for x.
Let's assume all 6 games rented were new games, so y = 0.
Substituting this value into the equation gives:
4x + 2(0) = 22
Simplifying, we get:
4x = 22
Dividing both sides by 4, we find that x = 5.5.
Since we can't rent a fractional number of games, the student rented 5 new games.
Rainfall collected in a rain gauge was found to be 2.3 cm when rounded to the nearest tenth of a centimeter.
a. Circle all the measurements below that could be the actual measurement of the rainfall.
2.251 cm
2.349 cm
2.352 cm
2.295 cm
b. Convert the rounded measurement to meters. Write an equation to show your work.
Answer:
A.2.251 cm , 2.349 cm, 2.295 cm
B. 0.023 meters.
Step-by-step explanation:
a. The possible actual measurements are 2.251 cm, 2.349 cm and 2.295 cm.
b. Rounded measurement in meters is 0.023 meters
a. To determine which measurements could be the actual measurement of the rainfall, we need to consider how rounding works.
When rounding to the nearest tenth of a centimeter, any measurement with a hundredth digit of 5 or greater rounds up, and any measurement with a hundredth digit less than 5 rounds down.
Given that the rounded measurement is 2.3 cm, let's evaluate the measurements:
2.251 cm: Rounds down to 2.3 cm
2.349 cm: Rounds up to 2.3 cm
2.352 cm: Rounds up to 2.4 cm
2.295 cm: Rounds down to 2.3 cm
So, the possible actual measurements are 2.251 cm, 2.349 cm and 2.295 cm.
b. To convert the rounded measurement to meters, we need to divide it by 100, since there are 100 centimeters in a meter.
Rounded measurement: 2.3 cm
Conversion to meters: 2.3 cm / 100 = 0.023 meters
Equation: Rounded Measurement (in meters) = Rounded Measurement (in centimeters) / 100
Rounded Measurement (in meters) = 2.3 cm / 100
= 0.023 meters
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The total area of Ohio is 4.5 * 10^4 square miles.The total area of Ohio is about how many times the total area of Rhode Island?
Answer:
The total area of Ohio is about 30 times the total area of Rhode Island
Step-by-step explanation:
Let
x -----> the total area of Ohio in square miles
y -----> the total area of Rhode Island in square miles
we know that
[tex]x=4.5*10^{4}\ mi^{2}[/tex]
[tex]y=1.5*10^{3}\ mi^{2}[/tex] (searched in Google)
To find out approximately how many times the total area of Ohio is compared to the area of Rhode Island, divide the area of Ohio by the area of Rhode Island
[tex]\frac{x}{y}[/tex]
substitute the values
[tex]\frac{4.5*10^{4}}{1.5*10^{3}}=(\frac{4.5}{1.5})( 10^{4-3}) =3*10^{1}=30[/tex]
therefore
The total area of Ohio is about 30 times the total area of Rhode Island
Ohio is approximately 37.5 times larger than Rhode Island.
To find out how many times larger Ohio is compared to Rhode Island, we need to know the area of both states and then divide the area of Ohio by the area of Rhode Island.
The total area of Ohio is given as[tex]\( 4.5 \times 10^4 \)[/tex]square miles.
The area of Rhode Island is approximately[tex]\( 1.2 \times 10^3 \)[/tex] square miles.
Now, we divide the area of Ohio by the area of Rhode Island to find the factor by which Ohio is larger:
[tex]\[ \frac{\text{Area of Ohio}}{\text{Area of Rhode Island}} = \frac{4.5 \times 10^4}{1.2 \times 10^3} \][/tex]
[tex]\[ = \frac{4.5}{1.2} \times \frac{10^4}{10^3} \][/tex]
[tex]\[ = 3.75 \times 10 \][/tex]
[tex]\[ = 37.5 \][/tex]
The statement "The measure of an angle is equal to itself is true because of what property?
Property of Equality
Reflective
Symmetric
Transitive
The measure of an angle being equal to itself is an example of the Reflexive Property, which states that any quantity is equal to itself.
Explanation:The statement "The measure of an angle is equal to itself" is true because of the Reflexive Property. This property states that any quantity is equal to itself, which is a fundamental idea in mathematics and logic. In the context of geometry and angles, it means that an angle is always equal to its measure. So, if θ represents the measure of an angle, then we could say θ = θ, which demonstrates the Reflexive Property.
The other properties listed—the Property of Equality, Symmetric, and Transitive—are also important in the realms of algebra and geometry but do not directly apply to the fact that an entity is equal to itself. Instead, these properties involve the relationship between different entities or the equality between them derived from other equalities.
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10% of what number is 81
The answer is 810
10% of a number is 81.
All you need to do is multiply 81 by 10 (810) to see that 10% of 810 is 81.
Best of luck
Answer:
810
Step-by-step explanation:
Multiply 81 by 100 (8,100).
The decimal for 10% is 0.10.
Then multiply 8,100 by 0.10.
If the sides of a square are increased by 3m, the area becomes 64 m. Find the lenght of a side of the original square
Final answer:
To find the side length of the original square, we formed a quadratic equation based on the given information and solved it to get a side length of 5 meters.
Explanation:
The question asks us to find the length of a side of the original square when the sides are increased by 3 meters and the new area becomes 64 square meters. First, let's denote the side length of the original square as x. If each side of the square is increased by 3 meters, then the new side length is x + 3 meters. The area of the new square is given to be 64 m², which can be represented as the square of the new side length, so the equation becomes:
(x + 3)²= 64
This simplifies to:
x² + 6x + 9 = 64
Subtracting 64 from both sides:
x² + 6x - 55 = 0
This is a quadratic equation that we can solve by factoring or using the quadratic formula. In this case, the equation factors to:
(x + 11)(x - 5) = 0
This gives us two possible solutions for x: -11 or 5. Since a side length cannot be negative, we disregard the -11 and conclude that the side length of the original square is 5 meters.
“Fine the slope of each line usin two methods
Check the picture below.
there are 3 squares in each row how many squares are in 5 rows
Answer: 15
Step-by-step explanation:
3x5 is 15
To find the total number of squares in 5 rows, multiply the number of squares in each row, which is 3, by the number of rows, which is 5.
To find the total number of squares in 5 rows, we need to multiply the number of squares in each row by the number of rows. Since there are 3 squares in each row, we can multiply 3 by 5 to get the answer.
Step 1: Multiply the number of squares in each row, which is 3, by the number of rows, which is 5: 3 x 5 = 15.
Step 2: Therefore, there are 15 squares in 5 rows.
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point p’(-6,-4) is the image point P(-2,3) under translation T. what is the image of (5,-1) under the same translation
Answer:
(1, - 8 )
Step-by-step explanation:
We have P(- 2, 3 ) → P'(- 6, - 4 )
The image coordinates are 4 less than the original x- coordinate and 7 less than the original y- coordinate, thus the translation rule is
T : (x, y ) → (x - 4, y - 7 ), thus
(5, - 1 ) → (5 - 4, - 1 - 7 ) → (1, - 8 )
Maria has a bag with 6 red marbles, 6 blue marbles, and 4 green marbles. Without looking, Maria picks one marble. She does not replace it, and she picks up another one. On the first pick, Maria gets a green marble. What is the probability that she gets a red marble on her second pick? A. 4/15
B. 3/8
C. 2/5
D. 5/8
Answer: Hello there!
initially Maria has 6 red marbles, 6 blue marbles, and 4 green marbles.
You know that in the first pick, Maria gets a green marble ( this means that now there are 3 green marbles left)
Now we want to know the probability that she gets a red marble on the second pick.
Now there are 6 + 6 + 3 = 15 marbles in the bag, and 6 of them are red ones. Then the probability of getting one red is the number of red ones divided by the total amount ( which is the ratio of red marbles to total marbles)
this is 6/15.
now you can see that there is no 6/15 in the options, so we need to see which one is equivalent.
if we took the option C, 2/5, and multiply both denominator and numerator by 3, we get (3*2)/(3*5) = 6/15, then 2/5 and 6/15 are equivalents.
Then the correct answer is C.
The probability that she gets a red marble on her second pick is 2/5.
What is the probability?Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.
The probability that she gets a red marble on her second pick = [number of red marbles / (total number of marbles - 1)]
6 / 15 = 2/5
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an=7+(n-1)2 is the general rule for the nth term of the arithmetic sequence 7,9,11,13,15 ... true or false ?
Answer:
True
Step-by-step explanation:
The n th term rule for an arithmetic sequence is
[tex]a_{n}[/tex] = a + (n - 1)d
where a is the first term and d the common difference
here d = 9 - 7 = 2 and a = 7, thus
[tex]a_{n}[/tex] = 7 + 2(n - 1)
What is 3,920,000,000,000 in scientific notation? 3.92×1010 3.92×1012 3.92×10−10 3.92×10−12
Writing in scientific notation is writing in power form.
Writing in power form is usually in the form:
X.y × 10ⁿ
We now write 3 920 000 000 000 in this form.
3.92 × 10¹²
Answer :
3.92 × 10¹²
This is the scientific notation.
Hope I helped :)
3,920,000,000,000 in scientific notation is 3.92×10^12.
Explanation:To express a large number in scientific notation, we need to move the decimal point to the right until there is only one non-zero digit to the left of the decimal point. In this case, we start with the number 3.92 and move the decimal point to the right 10 places.
Therefore, 3,920,000,000,000 in scientific notation is written as 3.92×1012.
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Which of the following equations have no solutions? Choose all answers that apply: Choose all answers that apply: (Choice A) A 14x-23=14x-2314x−23=14x−2314, x, minus, 23, equals, 14, x, minus, 23 (Choice B) B -23x-14=14x-23−23x−14=14x−23minus, 23, x, minus, 14, equals, 14, x, minus, 23 (Choice C) C 14x+23=14x-2314x+23=14x−2314, x, plus, 23, equals, 14, x, minus, 23 (Choice D) D -14x+23=14x-23−14x+23=14x−23
Answer:
The Correct answer:
CORRECT (SELECTED)
14x+23=14x-23
Step-by-step explanation:
We are given four equations and are asked to identify which has no solutions. By isolating the variable 'x' in each equation, we can see that the only equation without a solution is Choice C: 14x+23=14x-23 because it results in an incorrect statement.
Explanation:The subject of this question is about identifying which equations have no solutions. To find the solution of an equation, you need to isolate the variable, here, it is 'x'. Let's evaluate the provided choices:
Choice A: 14x-23=14x-23. In this case, both sides of the equation are identical, suggesting that there is an infinite number of solutions - any value of x will make the equation correct.Choice B: -23x-14=14x-23. We can rearrange this equation to form 37x = 9, which implies x=9/37, thus this equation has a solution.Choice C: 14x+23=14x-23. When we try to isolate x, we will get 23 = -23 which is an incorrect statement. Therefore, this equation has no solutions.Choice D: -14x+23=14x-23. If we rearrange this equation, we get 28x = 46, which got x=46/28 or x=23/14, thus, this equation has a solution.Thus, only equation Choice C: 14x+23=14x-23 has no solutions.
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What is the slope of the line in the graph?
Answer:
1
Step-by-step explanation:
Starting from the y-intercept of [0, 1], you do rise\run by either moving one block south over one block west or one block north over one block east. Either way, you will still get a rate of change [slope] of 1.
I am joyous to assist you anytime.
Write 0.6 repeating as a fraction???
Answer: 0.6666666
Step-by-step explanation:
Answer:
0.6 repeatedly. as a fraction is 2/3
The area of a certain desert (Desert 1) is four times the area of another desert (Desert 2). If the sum of their areas is 25,000
desert.
What is the area of Desert 1?
What is the area of Desert 2?
Write the equation. kate has a seashell. Collection. She has 35shells in all. This is five times morethan her brother. How many shells does her brother have.
Rewrite the function f of x equals 7 times one half to the 3 times x power using the properties of exponents.
f of x equals 7 times three sixths to the x power
f of x equals 7 times one eighth to the x power
f of x equals 21 times three sixths to the x power
f of x equals 343 times one eighth to the x power
Answer:
f of x equals 7 times one eighth to the x power
Step-by-step explanation:
Given phrase,
function f of x equals 7 times one half to the 3 times x power,
[tex]\implies f(x) = 7(\frac{1}{2})^{3x}[/tex]
By the power to power property of exponent,
That is,
[tex](a^m)^n=a^{m.n}[/tex]
[tex]f(x) = 7((\frac{1}{2})^3)^x[/tex]
[tex]f(x) = 7(\frac{1}{8})^x[/tex]
= f of x equals 7 times one eighth to the x power
Which of the following numbers is NOT in
scientific notation?
A 4.5 X 10-12
B 3.025 X 10-9
C 0.21 X 107
D 1.1 X 1010
Answer: c
Step-by-step explanation: because the first number has to be greater then 1 less then 10
Option C (0.21 X 10^7) is not in scientific notation.
Explanation:The number that is NOT in scientific notation is 0.21 X 10^7 (option C).
A: 4.5 X 10^-12 - This is in scientific notation, represented as a decimal number multiplied by 10 raised to a negative power.B: 3.025 X 10^-9 - This is also in scientific notation, represented as a decimal number multiplied by 10 raised to a negative power.C: 0.21 X 10^7 - This is the only option that is not in scientific notation. Scientific notation requires the coefficient (0.21) to be greater than or equal to 1 and less than 10, so it should be written as 2.1 X 10^6 instead.D: 1.1 X 10^10 - This is in scientific notation, represented as a decimal number multiplied by 10 raised to a positive power.Learn more about Scientific Notation here:https://brainly.com/question/2005529
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You work for a large farm with many fields of corn. You are investigating the mass of a sample of ears of corn. You gather the following data and enter it into your spreadsheet:
Mass(g) of ears of corn:
12.8, 13.0, 13.5, 15.0, 15.0, 15.1, 15.2, 15.5, 15.6, 16.4, 16.6, 17.7, 18.3, 19.1, 19.3, 19.6, 20.5, 21.0, 26.2, 27.8, 33.5
Checksum: 405.5
Some of the masses in the sample seem much larger than the rest. You decide to make several calculations describing the “spread” of the data set. You hope to use them to help in the search for outliers. Round answers to 2 decimal places.
Start with the IQR:
a. IQR = ?
Apply the 1.5 IQR rule to search for outliers. Report the lower and upper cutoffs.
b. Lower: ?
c. Upper: ?
d. Are there any outliers by the 1.5 IQR rule? (Enter “yes” or “no”): ?
The IQR is a measure of data distribution and used in outlier detection. The IQR is calculated by subtracting Q1 from Q3. After calculating the IQR, the lower and upper cut-offs can be calculated and data points below or above these cut-offs are considered as outliers.
Explanation:The interquartile range (IQR) is a measure of statistical dispersion, and it can be useful in identifying 'outliers' in data. The IQR is calculated by subtracting the first quartile (Q1) from the third quartile (Q3) in a data set.
For the provided data set, to find the IQR, it should be sorted in ascending order and then Q1 and Q3 should be calculated. In your case, the sorted data set is: 12.8, 13.0, 13.5, 15.0, 15.0, 15.1, 15.2, 15.5, 15.6, 16.4, 16.6, 17.7, 18.3, 19.1, 19.3, 19.6, 20.5, 21.0, 26.2, 27.8, 33.5.
After finding Q1 and Q3, subtract Q1 from Q3 to get IQR (a.). Then, find the lower and upper cut-offs by subtracting 1.5 times of IQR from Q1 (b.) and adding 1.5 times of IQR to Q3 (c.), respectively. Any data points below the lower cut-off or above the upper cut-off are considered as outliers (d.).
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What are the output for an input of x=5 given functions defined by following formulas: y=2 to the power of x can someone please help me and no wrong answers or I will report u
Answer:
input x = 5, output y = 32Step-by-step explanation:
[tex]y=2^x\\\\\text{Put}\ x=5\ \text{to the equation of the function:}\\\\y=2^5=2\cdot2\cdot2\cdot2\cdot2=32[/tex]
The output, or the result when we input x=5 into the function y=2^x, is 32. This is found by substituting the given input into the function.
Explanation:The function you've provided is y=2 to the power of x . It is an exponential function. The output for a function is simply the result you get when you substitute a given input into the function. In this case, the function is defined as y = 2^x. To find the output when x=5, replace x in the function with 5. So y = 2^5 = 32. Therefore, the output for an input of x=5 in your function is 32.
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what is the mean of 8,7,5,7,4,7,6,7,8,8,8,6
Answer:
6,75
Step-by-step explanation:
It's necessary the addition of all numbers, divided between the number of the numbers. It means: 8 +7 +5 +7 +4 +7 +6 +7 +8 +8 +8 +6 = 81, then we'll divide 81 between 12 (because there are 12 numbers), and the result is 6,75
Mean = ∑numbers/n numbers
a bus drives 66km at an average speed of 24 km/h. How long does the journey take?
Answer:
66 km ÷ 24 km/h = 2 3/4 hours =
2 hours, 45 minutes
What is the equation of the parabola with focus (3, 0) and directrix x = –3?
Answer:
x = [tex]\frac{1}{12}[/tex] y²
Step-by-step explanation:
Any point (x, y ) on the parabola is equidistant from the focus and the directrix
Using the distance formula, then
[tex]\sqrt{(x-3)^2+(y-0)^2}[/tex] = | x + 3 |
Squaring both sides
(x - 3)² + y² = (x + 3)² ← expanding both sides
x² - 6x + 9 + y² = x² + 6x + 9 ← subtract x² + 6x + 9 from both sides
- 12x + y² = 0 ( subtract y² from both sides )
- 12x = - y² ( divide both sides by - 12 )
x = [tex]\frac{1}{12}[/tex] y²
Answer:
y²-12x = 0
Step-by-step explanation:
The formula for calculating the equation of a parabola is y² = 4ax
and x = a
To find the equation of the parabola with focus (3, 0) and directrix x = –3,
The point given (x,y) = (3,0) and x = -3
From the data given, it can be seen that a = -3 by simply comparing x = a with x = -3
Similarly, x = 3 from the given point.
Substituting the value of x = -3 in the formula for equation of a parabola gives;
y² = 4(-3)x
y²= -12x
y²-12x = 0