The value of trigonometric function sin(x-y) = -44/125
Given ,
cos x = 3/5
sin y = 24/25
Sin( x - y) = sin(x)cos(y) - sin(y)cos(x)
substituting the values,
=> sin(x)cos(y) - sin(y)cos(x)
=> sin(x)cos(y) - (24/25)(3/5) ------(1)
As we know ,
sin(x) = √(1 - cos²x)
sin x = √(1 - (3/5)²)
=> sin x = √1 -9/25
=> sin x = √16/25
=> sin x = 4/5
Again ,
cos y = √(1 - sin²y)
=> cos y = √(1 - (24/25)²
=> cos y = √1 - 576/625
=> cos y = √49/625
=> cos y = 7/25
Substituting the values of sin x and cos y in equation (1)
=> sin(x - y) = (4/5)(7/25) - (24/25)(3/5)
=> sin(x - y) = (28 / 125) - (72 / 125)
=> sin(x - y) = -44/125
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Find the residual if you know the actual number is 3 and the predicted value is 1. 6.
For the actual number 3 and the predicted value 1.6 the residual is equal to 1.4.
As given in the question,
The actual number is equal to 3
The predicted value is equal to 1.6
The residual is the difference between actual number and predicted value.
Formula for the residual is:
Residual = Actual number - Predicted value
Substitute the value of the actual number and the predicted value in the formula ,
⇒ Residual = 3 - 1.6
⇒ Residual = 1.4
Therefore, the residual for the given the actual number and the predicted value is given by 1.4.
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Mathew drives m miles in x hours. How many hours would he save if he drove the same distance at k miles per hour
The time saved will be: x - m/k This is a simple exercise in manipulating symbols. Let's take a look at the problem and break it down. "Stanley drives m miles in x hours" This statement immediately gives us 2 variables; "m" to represent how many miles the trip is and "x" for the number of hours it took Stanley to drive that far. Now let's look at the next statement. "How many hours would he save if he drove the same distance at k miles per hour?" This statement gives us another variable "k" for a new speed and gives us the question to answer. How many hours would Stanley save if he made the trip at a different speed. Since we're interested in hours saved, we need 2 different time values. They are 1. How much time did Stanley originally take? 2. How much time will the new speed make Stanley take? Looking at m, x, and k. We can immediately see that x is the original time that Stanley took. So we have that value. But we don't have any value for how long will it take at a new speed. But can we calculate it? And the answer to that is YES. The time it will take is the distance divided by the new speed. And that would be m/k. And since we're looking for savings, we just need to subtract the two time values. So our equation becomes x - m/k where x = original time taken m = distance of trip k = new speed to drive at.
An artist used 6 tubes of red paint, 2 tubes of yellow paint, 13tubes of white paint, and 9 tubes of blue paint for a mural.
What is the ratio of tubes of blue paint to all of the tubes of paint used?
The ratio of tubes of blue paint to all of the tubes of paint used is 3/10
In this question, we have been given an artist used 6 tubes of red paint, 2 tubes of yellow paint, 13 tubes of white paint, and 9 tubes of blue paint for a mural.
Total number of the tubes of paint used = 6 + 2 + 13 + 9
= 30
the ratio of tubes of blue paint to all of the tubes of paint used would be,
9/30 = 3/10
Therefore, the ratio of tubes of blue paint to all of the tubes of paint used is 3/10
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what is 41616125671617152751278 times a44
Answer:
1.8311095e+24
Step-by-step explanation:
41616125671617152751278 x 44 = the number above
why..
7 girls : 2 boys is equivalent to what ratio?
Answer:7:2 or 7 to 2
Step-by-step explanation:
Answer:
7 : 2 7/2 we can use two
Step-by-step explanation:
7 : 2 can't simplified
4 friend buy cinema ticket uing the offer
Buy 3 ticket and get a ticket free
Tey EACH pay £6. 15
How much doe a ticket cot
One ticket will cost you £8.20.
What is an example of a unitary method?
A single or distinct unit is referred to by the word unitary. Therefore, the goal of this strategy is to establish values in reference to a single unit. The unitary method, for instance, can be used to calculate how many kilometers a car will travel on one litre of gas if it travels 44 km on two litres of fuel.
Explanation
Suppose a single ticket costs = [tex]x[/tex]
They actually need to pay for 3 tickets because the promotion reads "purchase 3 tickets and receive one free."
so, the total price of three tickets = [tex]3x[/tex]
Four buddies each pay £6.15, making a total of £24.60 between them.
The equation will therefore be.....
[tex]3x = 24.60\\x = \frac{24.60}{3} = 8.20[/tex]
Consequently, a single ticket will cost £8.20.
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Using technology, determine the present value given that you make quarterly payments of $1,635 at 4.2% compouded quarterly over a 3 year period. Round your answer to the nearest cent. a. $15,168.06 c. $19,180.84 b. $19,188.94 d. $18,344.05
Present value of the quarterly payments of $1,635 at 4.2% compounded quarterly over a 3 year period is $18,344
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
The present value of the quarterly payments of $1,635 at 4.2% compounded quarterly over a 3 year period is calculated as follows:
Present Value = $1,635 × PVIFA ( 4.2%/4 ,3 Years)
Present Value = $1,635 × PVIFA (1.05% ,12)
= $1,635 × 11.21960
= $18,344
The present value of the quarterly payments of $1,635 at 4.2% compounded quarterly over a 3 year period is $18,344
Hence, present value of the quarterly payments of $1,635 at 4.2% compounded quarterly over a 3 year period is $18,344
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Use two unit multipliers to convert 300 inches to meters.
Answer: 7.62m
Step-by-step explanation:
[tex]300in(\frac{2.54cm}{1in})( \frac{0.01m}{1 cm} )[/tex]
[tex]7.62m[/tex]
Two friends, Karen and Jodi, work different shifts for the same ambulance service. They wonder if the different shifts average different numbers of calls. Looking at past records, Karen determines from a random sample of 37 shifts that she had a mean of 4.5 calls per shift. She knows that the population standard deviation for her shift is 1.1 calls. Jodi calculates from a random sample of 32 shifts that her mean was 5.3 calls per shift. She knows that the population standard deviation for her shift is 1.5 calls. Test the claim that there is a difference between the mean numbers of calls for the two shifts at the 0.05 level of significance. Let Karen's shifts be Population 1 and let Jodi's shifts be Population 2. Step 2 of 3 : Compute the value of the test statistic. Round your answer to two decimal places
The Test value for difference between the mean numbers of calls for the two shifts at the 0.05 level of significance is 31.94
According to the question,
Karen's data:
Sample size : n₁ = 37
Sample mean = 4.5
Sample standard deviation : s₁ = 1.1
Jodi's data ,
Sample size : n₂ = 32
Sample mean = 5.3
Sample standard deviation : s₂ = 1.5
To calculate significance difference between two means we use t-test
t = difference of mean / √(pooled variance / n₁ + n₂)
Pooled Standard deviation = [tex]\sqrt(\frac{(n_1 - 1)s_1^{2} + (n_2 - 1)s_2^{2})}{n_1 + n_2 -2}[/tex]
=> [tex]\sqrt(\frac{(37 - 1)1.21+ (32 - 1)2.25)}{37 + 32 -2}[/tex]
=> [tex]\sqrt(\frac{(43.56+ 69.75)}{67}[/tex]
=>[tex]\sqrt(\frac{(113.31)}{67}[/tex]
=> √1.6911
t = 37 - 32 / (√1.6911/37+32)
=> 5 / √0.0245
=> 31.94 is test value
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The function c represents the cost in dollars of renting a car and driving d
miles.
c(d) =0.24d + 34
What is the cost of renting the car and driving 206 miles?
Round answer to nearest cent (2 decimal places).
83.44
Answer:
$83.44=======================
GivenFunction c(d):
c(d) = 0.24d + 34Find the value of c(d) when d = 206:
c(206) = 0.24*206 + 34 = 49.44 + 34 = 83.44Answer:
Cost = $83.44
Step-by-step explanation:
The given equation is,
→ c(d) = 0.24d + 34
Now the required cost will be,
→ c(d) = 0.24d + 34
→ c(206) = 0.24(206) + 34
→ c(206) = 49.44 + 34
→ c(206) = $83.44
Hence, the cost is $83.44.
Alinethatincludesthepoint(–6, –4)hasaslopeof1
. What
isitsequationin
slope -intercept
form
Answer:
(y – 4) = 1(x +6)
Step-by-step explanation:
y – y₁ = m(x – x₁)
(y – 4) = 1(x –(–6))
(y – 4) = 1(x +6)
Choose which line represents the line of best fit.
A. There is no line of best fit for this data.
B. Line C
C. Line B
D. Line A
A line which represents the line of best fit is: C. Line B.
What is a line of best fit?A line of best fit is sometimes referred to as a trend line and it can be defined as a statistical or analytical tool that is commonly used in conjunction with a scatter plot, in order to determine whether or not there is any form of association and correlation between a data set.
The characteristics of a line of best fit.In Mathematics, there are different characteristics that are used for determining the line of best fit on a scatter plot and these include the following:
The line should be very close to the data points as much as possible.The number of data points that are above the line should be equal to the number of data points that are below the line.By critically observing the scatter plot using the aforementioned characteristics, we can reasonably and logically deduce that line B represents the line of best fit because the data points are in a linear pattern.
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Points G (-5,-8) and H (3,7) are plotted on a coordinate grid. Point J is plotted so that GH is the hypotenuse of the right triangle formed by joining the three points. What are the coordinates of point J? Select all that are possible.
(-3,-8)
(5,-7)
(-3,8)
(-5,7)
(3,8)
(5,7)
(-5,-7)
(3,-8)
(question 5.)
The coordinates of point J so that GH is the hypotenuse of the right triangle formed by joining the three points will be (3,-8).
What is a right-angle triangle?It is a triangle in which one of the angles is 90 degrees and the other two are sharp angles. The sides of a right-angled triangle are known as the hypotenuse, perpendicular, and base.
Given is a coordinate grid with the points G (-5, -8) and H (3, 7) plotted on it. In order for GH to be the hypotenuse of the right triangle created by joining the three points, point J is plotted.
Thus, the coordinates of point J so that GH is the hypotenuse of the right triangle formed by joining the three points will be (3,-8).
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true or false? there are in total 24 ways to arrange 2 out of 5 books (a, b, c, d, and e) on a shelf, if the order of each arrangement does matter.
Answer:True
Step-by-step explanation:
Students in the HC States Advisory are covering one of their homeroom walls with wallpaper. The wall is rectangular and has a perimeter of 408 ⅜ inches. The students are using square stickers with a side length of 2 ⅜ inches to cover the wall. If they need exactly 18 stickers to completely cover the width of the wall, how many whole stickers can they fit across the length of the wall?
Answer:
cm2 to inch2 conversion. Conversion square centimeters to square inches, cm2 to inch2. The conversion factor is 0.15500031000062; so 1 square centimeter ...
Step-by-step explanation:
A rectangle is a two-dimensional shape where the length and width are different.
The area of a rectangle is given as:
Area = Length x width
The perimeter of a rectangle.
= 2 ( length + width)
The number of 2(3/8) inches tickets to fit into the length of the wall is
154 tickets.
What is a rectangle?A rectangle is a two-dimensional shape where the length and width are different.
The area of a rectangle is given as:
Area = Length x width
We have,
The perimeter of a rectangle.
= 2 ( length + width)
The wall is rectangular and has a perimeter of 408 ⅜ inches.
This means,
408 (3/8) = 2 (length + width)
3267/8 = 2 (length + width) _____(1)
Now,
The total width of the wall.
= 2 width
Now,
Length of the square stickers = 2 (3/8) inches = 19/8 inches
The number of stickers needed to cover the width of the wall = 18
2 width = 18 x 19/8 inches.
2width = 18 x 19/8
width = 171/8 inches
Now,
From (1) we get,
3267/8 = 2 (length + width)
3267/8 = 2 (length + 171/8)
3267/8 - 342/8 = 2 length
2925/(8 x 2) = length
2length = 2925/(8 x 2)
2length = 2925/8
The number of stickers to cover the total length.
= 2925/8 ÷19/8
= (2925 x 8)/ (19 x 8)
= 154
Thus,
The number of 2(3/8) inches tickets to fit into the length of the wall is
154 tickets.
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how do you subtract mixed fractions?
Answer: Making them into improper fractions will really help you with subtracting mixed fractions! For example 2[tex]\frac{1}{5} \\[/tex] - 1[tex]\frac{1}{4}[/tex].
Making them into improper fractions will turn the expression into [tex]\frac{11}{5}[/tex] - [tex]\frac{5}{4}[/tex].
Turn the denominators into the greatest common multiple, so the greatest common multiple of 5 and 4 is 20. Meaning you multiply [tex]\frac{11}{5}[/tex] by 4 and [tex]\frac{5}{4}[/tex] by 5.
You now have [tex]\frac{44}{20} -\frac{25}{20}[/tex], which is much easier to work with. Simply subtract the numerators, and you should get [tex]\frac{19}{20}[/tex].
Hope this helps :)
13. LMN-QMP. Find the length of LM
Answer:
LM = 18
Step-by-step explanation:
since the triangles are similar then the ratios of corresponding sides are in proportion, that is
[tex]\frac{LM}{QM}[/tex] = [tex]\frac{LN}{QP}[/tex] ( substitute values )
[tex]\frac{LM}{12}[/tex] = [tex]\frac{15}{10}[/tex] ( cross- multiply )
10 LM = 180 ( divide both sides by 10 )
LM = 18
Find the value of x *
2x - 12
2
1
3
This is triangle proportional theorem and I need help
Answer:
2x2+1+3-12
4+1+3-12
5+3-12
8-12
-4x
GCF (96,144).............................
Answer:
The LCM of 96 and 144 is 288.
Step-by-step explanation:
Please give the brainliest, really appreciated.
Factor the expression 16a4 − b4 using the polynomial identity (x2 − y2) = (x − y)(x + y)
The factorization of given expression would be,
(4a^2)^2 - (b^2)^2= (4a^2 + b^2)(4a^2 - b^2)
In this question, we have been given an expression 16a^4 − b^4
We need to factor given expression using the polynomial identity
(x^2 - y^2) = (x − y)(x + y)
We write given expression as,
16a^4 − b^4 = (4a^2)^2 - (b^2)^2
Using the above polynomial identity,
16a^4 − b^4
= (4a^2)^2 - (b^2)^2
= (4a^2 + b^2)(4a^2 - b^2)
Therefore, the factorization of given expression would be,
(4a^2)^2 - (b^2)^2= (4a^2 + b^2)(4a^2 - b^2)
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n C (x) = 0.6x² − 168x+17,507. What is the minimum unit cost?
-
Step-by-step explanation:
Answer:
Minimum Unit Cost = $14,362
Step-by-step explanation:
The standard form of a quadratic is given by:
ax^2 + bx + c
So for our function, we can say,
a = 0.6
b = -108
c = 19,222
We can find the vertex (x-coordinate where minimum value occurs) by the formula -b/2a
So,
-(-108)/2(0.6) = 108/1.2 = 90
Plugging this value into original function would give us the minimum (unit cost):
The distance of 2 laps around a park is 2.5 miles. Walking 5 laps around the same park is 6.25 miles.
Complete the table to show the relationship between the number of laps and the number of miles. Enter the answers in the boxes.
Answer:
Each lap is 1.25 miles, so multiply the number of laps with 1.25 to get your answer.
Step-by-step explanation:
1 lap = 1.25 miles
2 laps = 2.5 miles
3 laps = 3.75 miles
4 laps = 5 miles
5 laps = 6.25 miles
6 laps = 7.5 miles
7 laps = 8.75 miles
8 laps = 10 miles
9 laps = 11.25 miles
10 laps = 12.5 miles
Solve for Y. X=2/3(Y+Z)
Y=3X/2-Z for the equation X=2/3(Y+Z)
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The given equation is
X=2/3(Y+Z)
x equal to two by three times of y plus z
Apply distributive property on RHS
X=2Y/3+2/3Z
Now Subtract 2/3Z on both sides
X-2/3Z=2/3Y
Divide both sides by 2/3
3/2X-Z=Y
Hence Y=3X/2-Z for the equation X=2/3(Y+Z)
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25.75x + 22.00 = 19.50x+47.00
The value of x for the given expression 25.75x + 22.00 = 19.50x+47.00 will be 4.
What is an expression?A mixture of variables, numbers, addition, subtraction, multiplication, and division are called expressions.
An expression is a mathematical proof of the equality of two mathematical expressions.
A statement expressing the equality of two mathematical expressions is known as an equation.
As per the given expression,
25.75x + 22.00 = 19.50x+47.00
25.75x - 19.50x = 47.00 - 22.00
6.25x = 25
x = 4
Hence "The value of x for the given expression 25.75x + 22.00 = 19.50x+47.00 will be 4".
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f(x) = 0.5x-3 into the graph g? Use the graph and the given equation to describe the transformation. g(x)=f(x) + k
The values of k are as follows when using translational ideas:
7. k = 3
A translation is what?
A change in the function graph, as defined by operations like multiplication or sum/subtraction, represents a translation.
How do you describe a change?
A metamorphosis is an indicate higher in look or form. Your life may change as a result of a significant occasion like earning your driver's license, enrolling in college, or getting married. An dramatic, drastic shift is called a metamorphosis.
In this problem:
g(x) is a 3 unit shift up of f(x), therefore k = 3.
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A third pistachio farm, Top Choice Farms, intends to set up shop next weekend at the Farmer’s Market. In order to immediately win over all the customers who shop there, Top Choice Farms promises their pistachios will cost 20% less than the next-cheapest farm. It will cost Top Choice Farms $125 to rent a booth at the Farmer’s Market. If Top Choice Farms sells out of their full 3,520 ounces of pistachios at their promised low, low price, how much profit will they make after paying for the Farmer’s Market booth?
Answer:
$648
Step-by-step explanation:
[100 Points]'m stuck on this answer and I don't know it. So it says I need to Determine whether side-angle-angle (AAA) is a valid means for establishing triangle congruence. In this case, you know the measure of a side, an adjacent angle, and the angle opposite to the side.
Answer:
each side has to be the same for the triangle to be congruent
Answer:
In this case SAA is a valid means for establishing triangle congruence. You can see in the following image. The triangles are the same, SAA is a valid means for establishing triangle congruence. You can see in the following image. The triangles are the same, in other words congruent. How I figured it out was by making a random triangle (ABC) then finding the lengths and angles. From there, I picked a random side (AB) and angles (A) and (B) after I transferred the information I had and put it into a new triangle. Using this formula to determine the third angle: 3rd angle (C = 45*) = 180* - angle A (45*) - angle B (90*). From there, I looked for where line (BC) and (CA) would connect. Leaving me with two congruent triangles.
(ﾉ◕ヮ◕)ﾉ*:･ﾟ✧
what is the answer for 1/5 (3x + 4) = 3
Answer:
11/3
Step-by-step explanation:
3x+4=15
3x=11
x=11/3
if your model performs great on the training data but generalizes poorly to new instances, what is happening? discuss two possible solutions.
Increasing data collection and streamlining the model are the answers to overfitting.
Given statement;
If your model performs great on the training data but generalizes poorly to new instances.
The possible solutions for the given condition is,
A model is probably overfitting the training data if it performs well on the training data but poorly on new examples (or we got extremely lucky on the training data). Obtaining more data, simplifying the model (choosing a simpler technique, reducing the amount of parameters or features utilized, or regularizing the model), or lowering the noise in the training data are all potential remedies for overfitting.
Hence, the solutions to overfitting are getting more data, simplifying the model.
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What is the first step that should be taken to solve the equation 5 - 2 (1x +3) = 12.
(A) Divide both sides of the equation by 5
(B) Add 1x + 3 inside the parenthesis
(C) Distribute -2 to (1x +3)
(D) Rewrite 5 - 2 as 3
Answer:
B
Step-by-step explanation: Good luck on your test
