The exact value for cos (α+β) is √21/25- 4√2/15, for the given quadrants II and IV
we know that cos (α+β)) = cos α cos β - sin α sin β, we are given the values of sin α=2/5 and cos β= 1/3 ( both are positive for quadrant 2 and 3). Since we know cos² a + sin² a = 1
for α, cos² α + sin² α = 1
=> cos² α = 1 - sin² α
=> cos² α = 1 - 4/25
=> cos α = √21/25
same for β, cos² β + sin² β = 1
=> sin² β = 1 -cos² β
=> sin² β = 1 -1/9
= 8/9
=2√2/3
substituting the known values in the above formula for cos (α+β)
=>cos α cos β - sin α sin β
=√21/25 *1/3- 2/5*2√2/3
=√21/25- 4√2/15
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Answer:
d. [tex]\frac{4\sqrt{2}-\sqrt{21} }{15}[/tex]
Step-by-step explanation:
The lovely person in the comments was correct on Edge so i decided to put it as an answer in case anyone was looking for it!
Have a lovely day!
the coded values for a measure of brightness in paper (light reflectivity), prepared by two different processes, are as shown in the accompanying table for samples of size 9 drawn randomly from each of the two processes. do the data present sufficient evidence to indicate a difference in locations of brightness measurements for the two processes? give the attained significance level.
The level can be attained by light reflections.
What are light reflections?The law of reflection states that objects can either be observed through the light they emit or, more frequently, through the light they reflect. The law of reflection, which states that the angle of incidence and reflection must be equal, is observed by reflected light.The transition known as reflection flips a shape in a mirror line, also known as a line of reflection, such that each point is at the same distance from the mirror line as its reflected point.n mathematics, a reflection (also spelled reflexion) is a mapping from a Euclidean space to itself that is an isometry with a hyperplane as a set of fixed points; this set is called the axis (in dimension 2) or plane (in dimension 3) of reflectionlearn more about reflections here:
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a positive integer divisor of 12! is chosen at random. the probability that the di-visor chosen is a perfect square can be expressed asmn, wheremandnare relativelyprime positive integers. what ism n?
The probability that the divisor chosen is a perfect square is found to be 1/22 which is m:n.
What exactly is meant by probability?Probability is synonymous with possibility. It is a mathematical branch that deals with the occurrence of a random event. The value ranges from zero to one. Probability has been introduced in mathematics to predict the likelihood of events occurring.Given: Randomly, a positive integer divisor of 12! is selected.
Prime factorization of 12! = 2¹⁰ × 3⁵ × 5² × 7¹ × 11
Total divisors of 12! = 11 × 6 × 3 × 2 × 2
Each number in the prime factorization must have an even exponent in order to construct a perfect square divisor. In the prime factorization, the divisor cannot have any factors of 7 and 11 because there is only one of each in 12!. There are 6 × 3 × 2 perfect squares as a result.The probability that the divisor chosen is a perfect square is given as:
(6 × 3 × 2)/(11 × 6 × 3 × 2 × 2)
= 1/22
=m/n
Therefore, the probability that the divisor chosen is a perfect square is found to be 1/22 which is m:n.
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There are 728 calories in eight ounces of a certain ice cream. How many calories are there in two pounds? \text{1 pound}=\text{16 ounces} 1 pound=16 ounces Before you try that problem, answer the question below. How many ounces will you need to find the number of calories for?
Answer:
Step-by-step explanation:
author link
adioabiola
Ace
12K answers
42.2M people helped
Answer:
1,008 calories
Step-by-step explanation:
504 calories in eight ounces
How many calories are there in one pound
1 pound = 16 ounces
504 calories = 8 ounces
x calories = 1 pound
Recall, 1 pound = 16 ounces
504 calories : 8 ounces = x calories : 16 ounces
504 / 8 = x / 16
Cross Multiply
504 * 16 = 8 * x
8,064 = 8x
Divide both sides by 8
x = 8,064 / 8
= 1,008
x = 1,008 calories
Therefore, there are 1,008 calories in one pound
It is 5:15 now. What time was it 9 hours and 15 minutes ago?
Answer:
8:00
Step-by-step explanation:
Calculate time
It is 5:15 now.
Subtract 15 minutes
5:00
Subtract 9 hours
subtract 5 hours
12:00
Then subtract 4 hours
8:00
Given the equation negative 28 equals y over 7, solve for y.
196
4
−4
−196
please help me.
The linear equation:
-28 = y/7
Can be solved by multiplying both sides by 7, to get y = -196
How to solve the equations?Here we want to solve the equation:
-28 = y/7
And we want to solve this for the variable y.
To do so, we need to isolate said variable in one side of the equation, now remember that we can multiply both sides of the equation by the same number.
Then we can multiply both sides by 7 so we get:
-28*7 = (y/7)*7
-196 = y
The correct option is the last one.
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The measure of two remote interior angles of a triangle are x - 10 and 4x + 4 The exterior angle of the triangle measures 3x + 54 Solve for the measure of the exterior angle .
The measure of the exterior angle of the triangle is 144 degrees.
How to solve angles of a triangle?The exterior angle theorem states that the measure of an exterior angle is equal to the sum of the measures of the two remote interior angles of the triangle.
Therefore, the measure of the two remote interior angles of a triangle are x - 10 and 4x + 4. The exterior angle of the triangle measures 3x + 54 .
Let's solve for the exterior angle.
x - 10 + 4x + 4 = 3x + 54
5x - 6 = 3x + 54
5x - 3x = 54 + 6
2x = 60
x = 60 / 2
x = 30
Therefore,
exterior angle = 3x + 54 = 3(30) + 54 = 90 + 54 = 144 degrees
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which is a perfect square 20 13 25 24 14 10 7 11 8
HELPPPP PLSPLSPPSPPPLSPSLPLLSLPSLP
Answer: What do those numbers mean
Step-by-step explanation:
What is 27/31 in its simplest form
Answer:
27/31
Step-by-step explanation:
line bd is tangent to a circle with diameter ab. explain why the measure of angle bca must equal the measure of angle abd.
The measures of the angles BCA and ABD are equal because they are both right angles.
The line segment BD is a tangent to the circle with diameter AB. We need to find out the reason why the measure of angle BCA must be equal to the measure of angle ABD. The diagram is attached below.
Since AB is the diameter of the circle, it makes an angle equal to 180 degrees at the center of the circle. So the measure of the angle BCA is half of the angle produced by the diameter.
∠BCA = (1/2)×180° = 90°
Since the line BD is tangent to the circle, it will be perpendicular to the diameter. Hence, the angle formed by the diameter and the tangent must be the right angle.
∠ABD = 90°
Hence, both the angles are equal to each other.
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It is given that AC ≅ AD and ∠CAB ≌ ∠DAB
Part A Write a paragraph proof to prove ABC ≌ ABD. Explain in complete sentences each statement and reason. Be sure to give the reason the two triangles are congruent.
Part B Now that you have proven the two triangles are congruent, can you show that ∠CBA ≌ ∠DBA? Explain your reasoning in a complete sentence.
Step-by-step explanation:
the triangle above is an isosceles triangle,
two sides and angles are equal
AC=AD
triangle ACB=triangle ABD(because it is an isosceles triangle )
c.) In a class of 28 sophomores and juniors, 16 are
juniors. What percent of the class are sophomores?
The percent of the sophomores in the class of 28 sophomores and juniors is 42.86%.
According to the question,
We have the following information:
Total number in a class including sophomores and juniors = 28
Number of juniors in the class = 16
Now, we have the number of sophomores in this class:
Total number in the class- Number of juniors in the class
28-16
12
Now, we can easily find the percent of sophomores in the class by following the given steps:
Number of sophomores*100/Number of sophomores and juniors
1200/28
42.86%
Hence, the percent of the sophomores in the class of 28 sophomores and juniors is 42.86%.
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You deposit $3000 in an account that
earns simple interet at an annual rate of
5%. How long must you leave the money
in the account to earn $500 in interest?
Answer:
3 ¹/₃ years
Step-by-step explanation:
Simple Interest Formula
I = Prt
where:
I = Total interest.P = Principal amount.r = Annual interest rate (in decimal form).t = Time (in years).Given:
I = $500P = $3,000r = 5% = 0.05Substitute the given values into the formula and solve for t:
[tex]\sf \implies 500=3000 \times 0.05 \times t[/tex]
[tex]\sf \implies 500=150t[/tex]
[tex]\sf \implies t=\dfrac{500}{150}[/tex]
[tex]\implies \sf t=3\frac{1}{3}[/tex]
Therefore, the money must be left in the account for 3 ¹/₃ years for the account to earn $500 interest.
Does the diagram contain enough information to prove that line segment JK is parallel to line segment ML? Explain your answer.
I think so ya is does you just need to tell your teacher if you don't understand
A short-wave radio antenna is supported by two guy wires, 150 ft and 180 ft long. Each wire is attached to the top of the antenna and anchored to the ground at two anchor points on opposite sides of the antenna. The shorter wire makes an angle of 65° with the ground. How far apart are the anchor points? (Round your answer to the nearest foot.)
The distance between the anchor points of the two guy wires holding radio antenna is 181 feet (to the nearest foot)
How to determine the distance between the two anchor points of the guy wireThe problem will be solved using SOH CAH TOA
let the distance between the 150 ft long guy wire and the radio antenna be x
let the distance between the 180 ft long guy wire and the radio antenna be y
cos 65° = x / 150
x = cos 65° * 150
x = 63.39 ft
The height of the antenna
sin 65° = height of antenna / 150
height of antenna = sin 65 * 150
height of antenna = 135.95
using Pythagoras theorem
(length of guy wire)² = (height of the antenna)² + (anchor distance)²
(anchor distance)² = 180² - 135.95²
anchor distance = √(180² - 135.95²)
anchor distance = 117.97
The anchor points distance apart
= 63.39 + 117.97
= 181 (to the nearest foot)
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an airplane ticket has a perimeter of 58 cm and an area of 198 square cm. What are the dimensions of the ticket
The dimensions of the ticket are width is 11 cm and length is 18 cm.
What is the perimeter of the rectangle?The perimeter of a rectangle is defined as the addition of the lengths of the rectangle's four sides.
An airplane ticket has a perimeter of 58 cm and an area of 198 square cm.
Let W is the width of the ticket and L is the length of the ticket
The area of a credentials= L × W
198 = L × W ...(i)
The perimeter of a ticket = 2(L+W)
58 = 2(L+W)
29 = L + W
L = 29 - W ...(ii)
Substitute the value of L = 99 - W in equation (i)
198 = (29 - W) × W
198 = 29W - W²
0 = W² - 29W + 198
[tex]0=\left(W^2-11W\right)+\left(-18W+198\right)[/tex]
[tex]0=W\left(W-11\right)-18\left(W-11\right)[/tex]
[tex]0=\left(W-11\right)\left(W-18\right)[/tex]
W = 18 or 11
Substitute the value of W = 11 in equation (ii)
L = 29 - 11
L = 18
Thus, the dimensions of the ticket are width is 11 cm and length is 18 cm.
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Pls help/ A function (x) is graphed on the coordinate plane.
What is the function rule in slope-intercept form?
Enter your answer in the box.
f(x)=
The function rule in slope-intercept form is y = -4x - 2
How to calculate the slope-intercept form of this function?Mathematically, the slope-intercept form of a straight line can be calculated by using this equation:
y = mx + c
Where:
m represents the slope.x and y are the points.c represents the intercept.From the graph of this line, we have the following data points:
Point (x, y) = (-1, 2)
Point (x, y) = (0, -2)
In Mathematics, the slope of any straight line can be calculated by using this formula;
Slope, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope, m = (y₂ - y₁)/(x₂ - x₁)
Slope, m = (-2 - 2)/(1 - 0)
Slope, m = -4/-1
Slope, m = -4
Note: The y-intercept occurs at the point where the x-value is equal to zero (0).
Now, we can write the function rule for this line in slope-intercept form as follows:
y = mx + c
y = -4x - 2
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For every 8 candles that you sell, you raise $96. You raise $288.
How many candles did you sell?
Answer:
24
Step-by-step explanation:
Start by finding the unit price. Unit price is the term for finding the price of one unit of an item, often used in word problems. We find this by dividing the cost of an item after a certain amount is sold, by that amount.
[tex]96/8 = \$12[/tex]
Now, we know the unit price is 12. Divide the end value of everything you sold by the unit price, 12.
[tex]288/12 = 24[/tex]
Therefore, you sold 24 candles.
Hope this helps!
2 1/2 divided by 2 1/4
Answer:
Step-by-step explanation:
(2 1/2) : (1/4) = 10/1 =10
3. Martin finishes a swim race in 78.934 seconds. His teammate, Abby finishes the race in 83.978 seconds and their last teammate finishes the race in 84.765 seconds.
If the teammates were to have a combined time of less than 250 seconds to qualify to the next round, did they qualify or not? How do you know?
help me please i really need help!
Does this scatter plot show a linear association explain yes or no
No, The scatter plot does not show a linear association
What is graph?A graph is way of presenting data used by several disciplines.
There are many types of graphs and scatter plot is one of them.
scatter plot can be defined as set of dots plotted on a horizontal and vertical axis.
scatter plots can demonstrate the degree of connection, if any, between the values of observed quantities or events, they are crucial in statistics
The scatter plot does not show a straight line graph or a linear function. tracing the line shows a inverted shape of "s" which is not associated with linear functions.
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The linear equation y = negative 2 x + 4 is represented on the graph below.
On a coordinate plane, a line goes through (0, 4) and (2, 0).
A second linear equation is represented by the data in the table.
x
y
–4
–3
0
–1
2
0
6
2
What is the solution to the system of equations?
(2, 0)
(0, 4)
(0, –1)
(4, –4)
The solution to the system of equations will be;
⇒ (2, 0)
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.
Given that;
The first equation is,
y = - 2x + 4
And, A line goes through (0, 4) and (2, 0).
Now,
For the second linear equation;
The coordinates are,
(-4, -3) (0, -1) , (2, 0) , (6, 2)
Hence, The equation of line passes through the points (-4, -3) and (0, -1).
So, We need to find the slope of the line.
Hence, Slope of the line is,
m = (y₂ - y₁) / (x₂ - x₁)
m = (- 1 - (-3)) / (0 - (-4))
m = 2 / 4
m = 1/2
Thus, The equation of line with slope 1/2 is,
⇒ y - (-3)= 1/2 (x - (-4))
⇒ y + 3 = 1/2 (x + 4)
⇒ y = 1/2x + 2 - 3
⇒ y = 1/2x - 1
Now, We find the value of system of equations;
y = - 2x + 4
y = 1/2x - 1
Solve both above equation, we get;
1/2x - 1 = - 2x + 4
1/2x + 2x = 4 + 1
5/2x = 5
x = 2
And, y = 1/2 (2) - 1 = 0
Thus, The solution to the system of equations will be;
⇒ (2, 0)
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Answer:
A
Step-by-step explanation:
Here is a correlation, does it also represent causation? Explain you answer.
The number of additional calories consumed and the amount of weight gained.
Yes, there is causation between the two given variables, as the weight is related at some point with the amount of calories consumed.
What does correlation and causation mean?
For two variables x and y, we say that there is causation when, if we modify one of the variables, the other changes in response.
Correlation just means that the variables are related in some way (maybe both have a causation relationship with the same other variable)
So causation implies correlation.
Correlation does not imply causation.
In this case, we have the example:
x = The number of additional calories consumed
y = amount of weight gained.
Clearly, we have causation between x and y as larger is the value of x, larger will be the value of x.-
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valuerelative frequency 10.15 20.30 30.45 40.10 if there are a total of 40 data values, with what frequency does the data value 1 occur?
The frequency of data value 1 that is 10 will be 6 as "Dividing each frequency by the total number of data values gives the relative frequency. So multiplying the relative frequency by the total number of data values gives the frequency."
What is relative frequency?The proportion of outcomes where a specific event occurs to all trials, not in a hypothetical sample space but in a real experiment, is known as the empirical probability, relative frequency, or experimental probability of an event. The relative frequency is calculated by dividing each frequency by the total number of data values. Therefore, the frequency is calculated by multiplying the relative frequency by the total number of data values.
Here,
Value Relative frequency
10 0.15
20 0.30
30 0.45
40 0.10
data 1 value=10
Dividing each frequency by the total number of data values gives the relative frequency.
So, multiplying the relative frequency by the total number of data values gives the frequency.
40*0.15=6
Since "multiplying the relative frequency by the total number of data values gives the frequency," the frequency of the data value 1 that is 10 will be 6.
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A skydiver fell toward Earth at a steady speed for 10.0 seconds. He fell 593 meters in that
time. What was his speed?
Answer:
59.3 meters/second
Step-by-step explanation:
593 / 10 = 59.3
- Use the rules of measurement to subtract:
123.9 g - 56.041 g
Answer:
67.859 g
Step-by-step explanation:
123.9 g - 56.041 g
= 123.900 g - 56.041 g
= 67.859 g
Answer:
Step-by-step explanation:
67.859
When using re-grouping to solve 21 x 43, what are the four products that would be calculated and then added?
800 + 40 + 6 + 3
80 + 40 + 60 + 3
800 + 40 + 60 + 3
800 + 3
Using re-grouping to solve 21 x 43, the four products that would be calculated and then added is: 800 + 40 + 60 + 3.
How to find the products?Given data:
21 x 43
Now let make use of re-group to find the for product
21 x 43
So,
20 +1 = 21
40 + 3 =43
Hence,
(20+1) × (40+3)
Expand
(20 × 40) + (1 × 40) + (20 ×3) + (1 ×3)
800 + 40 + 60 + 3
= 903
Check:
21 x 43 = 903
800 + 40 + 60 + 3 =903
Therefore the correct option is C.
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according to money magazine, maryland had the highest mean annual household income of any state in at (time website). assume that annual household income in maryland follows a normal distribution with a mean of and standard deviation of . a. what is the probability that a household in maryland has an annual income of or more (to 4 decimals)?
The probability that a household in Maryland has an annual income of 100000 or more is 0.2373
Given Data;
Maryland had the greatest mean yearly household income of any state, according to Money magazine (time website). Consider a normal distribution with a mean of 75847 and a standard deviation of 33800 for the annual household income in Maryland.
Population Mean (μ) = 75847
Population Standard Deviation (σ) = 33800
'X' follows a normal distribution with a population mean and population standard deviation.
Here,
X ~ N ( μ = 75847 ,σ = 33800 )
Z =(X - μ)/σ
To get the probability that a household in Maryland has an annual income of 100000 or more.
Now, we have to compute P (X > 100000)
P (X > 100000) = 1 - P( (X-μ)/σ < (100000-75847)/33800 )
= 1 - p(z < 0.715 )
= 1 - 0.7627
= 0.2373
The required probability is 0.2373
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help meeeeeeeeeeee pleaseeeeeeeeeee rn rnnnnnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeeeeee pleaseeeeeeeeeee rn rnnnnnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Dimensions of the area enclosed is 800 * 800 and the maximum area = 6,40,000 square yards.
Given:
Liana has 3200 yards of fencing to enclose a rectangular area.
Let l and b be the length and width.
we know that:
perimeter of rectangle = 2(l+b)
2l + 2b = 3200
l+b = 1600
b = 1600 - l
Area of rectangle A = lb
= l*1600-l
= 1600 l - l^2
Apply derivative:
dA/dl = 1600 - 2l
1600 - 2l = 0
1600 = 2l
l = 1600/2
l = 800
l+b = 1600
b = 1600 - 800
= 800
Area = 800*800
= 6,40,000
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a pair of shoes is on sale, the original price is $150.99 and they are 30% whats a new price after the discount?
Answer:
Price after discount is $105.69Step-by-step explanation:
It is assumed 30% is the discount.
Original price is $150.99, discount is 30%, sale price is:
150.99 - 30% = 150.99 × (1 - 0.3) = 150.99 × 0.7 = 105.69 (rounded)ADDITION AND SUBTRACT OF RATIONAL ALGEBRAIC EXPRESSION WITH UNLIKE DENOMINATORS. (See the picture)
The evaluation of the rational algebraic expression are presented as follows;
1. [tex]\dfrac{1}{3} +\dfrac{2}{5} = \dfrac{11}{15}[/tex]
2. [tex]\dfrac{x + y}{x} + \dfrac{x + y}{y} = \dfrac{x^2 + 2\cdot x \cdot y + y^2}{x \cdot y}[/tex]
3. [tex]\dfrac{3 \cdot x + 1}{x^2+2\cdot x +1} +\dfrac{5}{2\cdot x + 8} =\dfrac{11\cdot x^2 +36\cdot x +13}{2\cdot x^3 + 12\cdot x^2 + 18\cdot x+ 8}[/tex]
What is a rational algebraic expression?
A rational algebraic expression is an algebraic expression that consists of a quotient and divisor that consists of variables and numbers.
1. [tex]\dfrac{1}{3} + \dfrac{2}{5}[/tex]
[tex]\dfrac{1}{3} + \dfrac{2}{5} = \dfrac{5\times 1 + 2 \times 3}{3\times 5} =\dfrac{5 + 6}{15}[/tex]
[tex]\dfrac{5 + 6}{15} = \dfrac{11}{15}[/tex]
Therefore, we get;
[tex]\dfrac{1}{3} +\dfrac{2}{5} = \dfrac{11}{15}[/tex]
2. [tex]\dfrac{x + y}{x} + \dfrac{x + y}{y}[/tex]
[tex]\dfrac{x + y}{x} + \dfrac{x + y}{y} = \dfrac{y\times (x + y) + x\times (x+ y)}{x\cdot y}[/tex]
[tex]\dfrac{y\times (x + y) + x\times (x+ y)}{x\cdot y}= \dfrac{x^2+ 2\cdot y \cdot x +y^2 }{x \cdot y}[/tex]
Therefore;
[tex]\dfrac{x + y}{x} + \dfrac{x + y}{y} = \dfrac{x^2+ 2\cdot y \cdot x +y^2 }{x \cdot y}[/tex]
3. [tex]\dfrac{3 \cdot x + 1}{x^2 + 2\cdot x + 1} + \dfrac{5}{2 \cdot x + 8}[/tex]
[tex]\dfrac{3 \cdot x + 1}{x^2 + 2\cdot x + 1} + \dfrac{5}{2 \cdot x + 8} = \dfrac{(3 \cdot x + 1) \times (2\cdot x + 8) + 5 \times (x^2 + 2\cdot x + 1) }{(x^2 + 2\cdot x + 1) \times (2\cdot x + 8)}[/tex]
[tex]\dfrac{(3 \cdot x + 1) \times (2\cdot x + 8) + 5 \times (x^2 + 2\cdot x + 1) }{(x^2 + 2\cdot x + 1) \times (2\cdot x + 8)} = \dfrac{11\cdot x^2+ 36\cdot x+ 13}{2\cdot x^3 + 12\cdot x^2+18\cdot x+ 8}[/tex]
[tex]\dfrac{3 \cdot x + 1}{x^2 + 2\cdot x + 1} + \dfrac{5}{2 \cdot x + 8}=\dfrac{11\cdot x^2+ 36\cdot x+ 13}{2\cdot x^3 + 12\cdot x^2+18\cdot x+ 8}[/tex]
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