What is the value of cos(15°)?
StartFraction StartRoot 6 EndRoot minus StartRoot 2 EndRoot Over 2 EndFraction
StartFraction StartRoot 6 EndRoot minus StartRoot 2 EndRoot Over 4 EndFraction
StartFraction StartRoot 6 EndRoot + StartRoot 2 EndRoot Over 4 EndFraction
StartFraction StartRoot 6 EndRoot + StartRoot 2 EndRoot Over 2 EndFraction
we know that,
[tex] \sf \dashrightarrow \: cos(a - b) = cos a \times cos b + sin a \times sin b[/tex]
Therefore,
[tex] \sf \leadsto \: cos \: 15 \degree[/tex]
[tex] \sf \leadsto \: cos \: (45 \degree - 30 \degree)[/tex]
[tex] \sf \leadsto \: cos \: 45 \degree . \: cos \: 30 \degree + \: sin \: 45 \degree . \: sin \: 30 \degree[/tex]
[tex] \sf \leadsto \: \frac{1}{ \sqrt{2} } \: . \: \frac{ \sqrt{3} }{2} + \: \frac{1}{ \sqrt{2} } \: . \: \: \frac{1}{2} \\ [/tex]
[tex] \sf \leadsto \: \frac{1. \: \sqrt{3} }{ \sqrt{2} \: . \: 2} \: + \: \frac{1 \: .\: 1}{ \sqrt{2} \: .\: 2} \\ [/tex]
[tex] \sf \leadsto \: \frac{ \: \sqrt{3} }{ 2\sqrt{2} \: } \: + \: \frac{1}{ 2\sqrt{2} \: } \\ [/tex]
[tex] \sf \leadsto \: \frac{ \: \sqrt{3} + 1 }{ 2\sqrt{2} \: } \: \\ [/tex]
Therefore Value of cos 15° is [tex] \sf \: \frac{ \: \sqrt{3} + 1 }{ 2\sqrt{2} \: } \: [/tex]
For each SSA case below, i) solve by the law of cosines, (ii) solve by the law of sines; use degrees for angles, and round each answer to its nearest 100th:
The values of the angles will be 6.67°, 156.78° Be 29.93° and the sides will be 10.01, 34 and 43.
How to explain the angleSSA stands for side side angle postulate. In this postulate of congruence, we say that if two sides and an angle not included between them are respectively equal to two sides and an angle of the other triangle then the two triangles are equal.
By sine rule,
Y = sin156.78 × 44 / 34
= 29
sin Y = 0.499
Y = 29.93°
By the angle sum property. The last angle will be:
180 - 156.78 - 29.93
= 6.67°
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A sidewalk in front of Kathy’s house is in the shape of a rectangle four feet wide by 45 feet long. Find the perimeter and the area
Answer:
Parameter= 98ft
Area=180ft^2
Step-by-step explanation:
Parameter= Length times 2 plus width times 2 or
L2+W2=P 4(2)+45(2)=8+90=98
Area= LxW=A^2
4x45=180^2
ASAP Scott and Lana booked a cruise that departs from Seward, Alaska, but their flight flew into Anchorage, Alaska. The couple decided to travel from Anchorage to Seward on the Alaska Railroad's non-stop Coastal Classic route to enjoy the 117 miles of beautiful scenery. If the train had traveled 13 miles in 30 minutes, how long, in hours, was the non-stop train ride from Anchorage to Seward?
A. 4.5 hours
B. 18 hours
C. 3 hours
D. 9 hours
Answer:
A. 4.5 hours
Step-by-step explanation:
We can use a proportion to solve this problem. Let x be the total time in hours for the train ride from Anchorage to Seward. We know that the train traveled 117 miles in x hours, and it traveled 13 miles in 0.5 hours (30 minutes). Therefore:
117 miles / x hours = 13 miles / 0.5 hours
We can cross-multiply to get:
117 miles * 0.5 hours = 13 miles * x hours
Simplifying:
58.5 = 13x
x = 58.5 / 13
x = 4.5 hours
Therefore, the non-stop train ride from Anchorage to Seward took 4.5 hours. Answer: A.
Hope this helps!
Answer:
A. 4.5 hours
Step-by-step explanation:
We can use a proportion to solve this problem. Let x be the total time in hours for the train ride from Anchorage to Seward. We know that the train traveled 117 miles in x hours, and it traveled 13 miles in 0.5 hours (30 minutes). Therefore:
117 miles / x hours = 13 miles / 0.5 hours
We can cross-multiply to get:
117 miles * 0.5 hours = 13 miles * x hours
Simplifying:
58.5 = 13x
x = 58.5 / 13
x = 4.5 hours
Therefore, the non-stop train ride from Anchorage to Seward took 4.5 hours. Answer: A.
Hope this helps!
Jen works for a cellular phone company. She earns a salary of $250 per
week plus a bonus of 10% of the value of any phones and accessories
that she sells. In the past four weeks, Jen sold $312 worth of phones
and accessories.
Circle the amount that correctly completes the statement.
In the past four weeks, Jen earned a total income of $
1,031.20
562.00
312.00
281.20
31.20
Okay, here are the steps to solve this problem:
* Jen earns a weekly salary of $250
* She gets a 10% bonus on any sales
* In the past 4 weeks, she sold $312 worth of phones and accessories
* 10% of $312 is $31.20
* So in 4 weeks, her bonus would be $31.20 * 4 = $124.80
* Her weekly salary is $250
* So in 4 weeks, her salary would be $250 * 4 = $1000
* Her total income over 4 weeks is $1000 + $124.80 = $1124.80
* The choices are:
** $1,031.20 ** $562.00 ** $312.00 ** $281.20 ** $31.20
So the correct choice is $1,031.20.
What is the midpoint of the line segment graphed below?
The midpoint of the line joining the endpoints (-1, 5) and (-8, -4) will be (-4.5, 0.5).
Given that:
Endpoints, (-1, 5) and (-8, -4)
The coordinate of the mid-point of the line segment is given as,
(x, y) = [(x₁ + x₂) / 2, (y₁ + y₂) / 2]
The midpoint is calculated as,
(x, y) = [(-1 - 8) / 2, (5 - 4) / 2]
(x, y) = (-9 / 2, 1 / 2)
(x, y) = (-4.5, 0.5)
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riangle ABC with vertices at A(−3, −3), B(3, 3), C(0, 3) is dilated to create triangle A′B′C′ with vertices at A′(−9, −9), B(9, 9), C(0, 9). Determine the scale factor used.
6
one sixth
3
Graph the equation y=-x^2+12x−35 on the accompanying set of axes. You must plot 5 points including the roots and the vertex.
Answer:
To graph the equation y=-x^2+12x-35, we need to find the vertex and the roots of the equation.
The equation can be written in vertex form as y=-(x-6)^2+1, where the vertex is (6,1).
To find the roots, we need to set y=0 and solve for x:
0=-x^2+12x-35
x^2-12x+35=0
(x-5)(x-7)=0
x=5 or x=7
So the roots are (5,0) and (7,0).
The vertex is at (6,1) and the roots are at (5,0) and (7,0). The curve is a downward-facing parabola.
Of the following Z-score values, which one represents the location closest to the mean?
A. Z=+0.5
B. Z=+1,0
C. Z=-1.5
D. Z=-0.3
Z=+0.5, which has an absolute value of 0.5 and is the closest Z-score to the mean so option A is correct.
What is?In mathematics, the absolute value (also known as modulus) of a real number is its distance from zero on the number line. It is denoted by enclosing the number between two vertical bars, such as |x|.
For example, the absolute value of 5 is 5, because 5 units to the right of zero on the number line is at a distance of 5 units from zero. Similarly, the absolute value of -5 is also 5, because 5 units to the left of zero on the number line is at a distance of 5 units from zero.
According to the given informationTo determine which Z-score represents the location closest to the mean, we need to know the sign of each Z-score, as well as the absolute value of each Z-score.
The sign of the Z-score indicates whether the location is above (+) or below (-) the mean. The absolute value of the Z-score indicates how far away the location is from the mean, measured in standard deviations.
Looking at the options provided, we see that:
A. Z=+0.5 is positive, indicating a location above the mean, and has an absolute value of 0.5.
B. Z=+1.0 is positive, indicating a location above the mean, and has an absolute value of 1.0.
C. Z=-1.5 is negative, indicating a location below the mean, and has an absolute value of 1.5.
D. Z=-0.3 is negative, indicating a location below the mean, and has an absolute value of 0.3.
Since we want to find the Z-score closest to the mean, we should look for the option with the smallest absolute value. Therefore, the answer is A. Z=+0.5, which has an absolute value of 0.5 and is the closest Z-score to the mean.
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PLEASE HELP ME!!! Unit 10 Circles Homework Inscribed Angles questions 15 and 17
Applying the inscribed angle theorem, we have the missing measures as: 15. m<DEF = 127° 16. m(PL) = 62°
How to Apply the Inscribed Angle Theorem?15. Angle DEF is an inscribed angle while arc FGD is the intercepted arc. Thus, according to the inscribed angle theorem, we have:
m<DEF = 1/2(m(FGD)
Plug in the values:
6x + 37 = 1/2(19x - 31)
2(6x + 37) = 19x - 31
12x + 74 = 19x - 31
12x - 19x = -74 - 31
-7x = -105
x = 15
m<DEF = 6x + 37 = 6(15) + 37 = 127°
16. m<LMP = m<LNP
Plug in the values:
5x - 19 = 2x + 11
5x - 2x = 19 + 11
3x = 30
x = 10
m(PL) = 2(LMP) [based on the inscribed angle theorem]
Plug in the values:
m(PL) = 2(5x - 19)
Plug in the value of x:
m(PL) = 2(5(10) - 19)
m(PL) = 62°
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A person invests 8000 dollars in a bank. The bank pays 4.75% interest compounded daily. To the nearest tenth of a year, how long must the person leave the money in the bank until it reaches 20400 dollars?
To the nearest tenth of a year, the person must leave the money in the bank for 15.5 years.
How long must the person leave the money in the bank until it reaches 20400 dollars?We can use the formula for compound interest:
A = P[tex](1 + r/n)^{nt}[/tex]
where A is the final amount, P is the principal (initial investment), r is the annual interest rate (as a decimal), n is the number of times the interest is compounded per year, and t is the time in years.
We know P = 8000, r = 0.0475, and we want A = 20400. We also know that the interest is compounded daily, so n = 365.
Let's solve for t:
20400 = 8000[tex](1 + 0.0475/365)^{(365t)}[/tex]
2.55 = [tex](1.00013)^{(365t)}[/tex]
Taking the natural logarithm of both sides, we get:
after solving
Using a calculator, we find:
t ≈ 15.5
So, to the nearest tenth of a year, the person must leave the money in the bank for 15.5 years.
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$550 is deposited in an account with 8.5%
interest rate, compounded continuously.
What is the balance after 6 years?
F = $[?]
the balance after 6 years is approximately $926.45.
What is Continuous compounding ?
Continuous compounding is the process of calculating interest and reinvesting it into an account's balance over an infinite number of periods.
We can use the formula for continuous compounding to find the balance after 6 years:
[tex]F = Pe^{(rt)}[/tex]
where F is the future value, P is the present value, e is the mathematical constant e (approximately 2.71828), r is the annual interest rate, and t is the time in years.
In this problem, P = $550, r = 8.5% = 0.085 (note that we need to use the decimal form of the interest rate), and t = 6 years.
[tex]F = 550e^{(0.085*6)}[/tex]
F ≈ $926.45
Therefore, the balance after 6 years is approximately $926.45.
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For what values of x and y are the triangles to the right congruent by HL?
The values of x and y that make the triangles congruent by HL are:
x = 3 and y = 1
Congruent triangles: Calculating the values of x and yFrom the question, we are to determine the values of x and y that make the triangles congruent by HL.
Two triangles are said to be congruent if all three corresponding sides are equal and all the three corresponding angles are equal in measure.
Thus,
For the triangles to be right congruent by HL
x = y + 2
and
x + 1 = 4y
Solve the equations simultaneously
Substitute x = y + 2 in the second equation
x + 1 = 4y
y + 2 + 1 = 4y
y + 3 = 4y
3 = 4y - y
3 = 3y
Divide both sides by 3
3/3 = 3y/3
1 = y
Therefore,
y = 1
Substitute the value of y into the first equation
x = y + 2
x = 1 + 2
x = 3
Hence,
The values are:
x = 3 and y = 1
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Will give brainliest if you get correctly!
Guessing = Report
Answer:
Step-by-step explanation:
The solids are similar.
Find the surface area of
solid B to the nearest
hundredth.
Cylinder A
24 mm
S = 594 mm²
Cylinder B
16 mm
The surface area of solid B is
square millimeters.
Answer:
264π
Step-by-step explanation:
A scatter plot is shown on the coordinate plane. scatter plot with points at 1 comma 8, 2 comma 5, 4 comma 7, 5 comma 2, 7 comma 6, 8 comma 2, 10 comma 1, and 10 comma 4 Which of the following graphs shows a line on the scatter plot that fits the data? scatter plot with points at 1 comma 8, 2 comma 5, 4 comma 7, 5 comma 2, 7 comma 6, 8 comma 2, 10 comma 1, and 10 comma 4, with a line passing through the coordinates 2 comma 5, 8 comma 2, and 10 comma 1 scatter plot with points at 1 comma 8, 2 comma 5, 4 comma 7, 5 comma 2, 7 comma 6, 8 comma 2, 10 comma 1, and 10 comma 4, with a line passing through the coordinates 4 comma 7, and 10 comma 4 scatter plot with points at 1 comma 8, 2 comma 5, 4 comma 7, 5 comma 2, 7 comma 6, 8 comma 2, 10 comma 1, and 10 comma 4, with a line passing through the coordinates 1 comma 8, and 10 comma 1 scatter plot with points at 1 comma 8, 2 comma 5, 4 comma 7, 5 comma 2, 7 comma 6, 8 comma 2, 10 comma 1, and 10 comma 4, with a line passing through the coordinates 4 comma 5.33, and 6 comma 4.33 Question 11(Multiple Choice Worth 5 points) (Scatter Plots MC) A large retailer calculated the average hourly wage of employees over 6 years. The following table shows the years since 2016 and the average hourly wage of an employee at that time. Years (since 2016) 0 1 2 3 4 5 6 Hourly Wage (in dollars) 10 10.5 11 11.5 12 13 14 Which of the following representations is most appropriate for showing the change in the average hourly wage each year? scatter plot with the title average hourly wage and the x axis labeled years since 2016 and the y axis labeled hourly wage in dollars, with points at 0 comma 10, 1 comma 10 and a half, 2 comma 11, 3 comma 11 and a half, 4 comma 12, 5 comma 13, 6 comma 14 scatter plot with the title average hourly wage and the x axis labeled hourly wage in dollars and the y axis labeled years since 2016, with points at 10 comma 0, 10 and a half comma 1, 11 comma 2, 11 and a half comma 3, 12 comma 4, 13 comma 5, and 14 comma 6 line graph with the title average
Rajindri, a physician assistant who works in an emergency room, earns $163 for every two hours that she works.
Which equation represents the relationship between d, the number of dollars Rajindri earns, and t, the amount of time Rajindri works, in hours?
A. d= 163 + t
B. d= 163/2 × t/2
C. d= 163t
D. d= 81.50t
Answer:
b but I'm not exactly sureb
It is possible to select 3 restraunts in how many different ways?
There are 1140 different possible ways to select 3 restaurants out of 20 for the promotional program.
In mathematics, what are a permutation and combination?Combination and permutation are two alternative strategies in mathematics to divide up a collection of components into subsets. The subset's components can be listed in any order when combined. The components of the subset are listed in a permutation in a certain order.The combination formula, which is: can be used to resolve this issue.
n C r = r! * (n-r)!
where r is the number of restaurants to be chosen, and n is the total number of restaurants (20 in this case). (3 in this case).
By replacing these values, we obtain:
20 C 3 = 20! / (3! * (20-3)!) = 20! / (3! * 17!) = (20 * 19 * 18) / (3 * 2 * 1) = 1140
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Can someone actually help me with this!!!! please do A through D, I attached the picture. BRAINLIEST!!!!!
which average is the most representative of the data
The median is the average that is most representative of the data.
How to obtain the median of a data-set?The median of a data-set is the middle value of a data-set, the value of which 50% of the measures are less than and 50% of the measures are greater than. Hence, the median also represents the 50th percentile of a data-set.
In this problem, we have that smaller values have a higher number of observations, meaning that the data-set is not symmetric.
As the data-set is not symmetric, it means that the median is the average that is most representative of the data.
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HELP PLEASE
Solve by graphing g(x)=lx-4l+3
Please refer to the attachment
Diane is a camp counselor she did signs in new obstacle course and tested course with three friends the Doppler shows the time it takes to complete the obstacle course. What is the mean absolute deviation(MAD)of the times.
Therefore, the mean absolute deviation of the times taken to complete the obstacle course is 0.3125 minutes.
What is mean absolute deviation?Mean absolute deviation (MAD) is a statistical measure that calculates the average distance between each data point in a dataset and the mean or median of that dataset. It measures the dispersion or variability of the data points in relation to the central tendency of the dataset.
To calculate the MAD, you first find the mean or median of the dataset, and then you calculate the absolute difference between each data point and the mean or median. The absolute differences are then averaged to give the mean absolute deviation.
MAD is expressed in the same units as the original data and is commonly used in finance, economics, and other fields to measure the variability of financial returns, economic indicators, or other datasets. MAD is a robust measure of dispersion that is less sensitive to extreme values or outliers compared to other measures of dispersion such as standard deviation.
Let's say the times taken by the four people are:
Diane: 2 minutes
Friend 1: 1.5 minutes
Friend 2: 2.5 minutes
Friend 3: 1.75 minutes
The mean of these times is:
Mean = (2 + 1.5 + 2.5 + 1.75) / 4 = 1.9375 minutes
Next, we need to find the absolute deviations of each time from the mean. To do this, we subtract the mean from each time and take the absolute value of the result:
|2 - 1.9375| = 0.0625
|1.5 - 1.9375| = 0.4375
|2.5 - 1.9375| = 0.5625
|1.75 - 1.9375| = 0.1875
Then, we find the mean of these absolute deviations:
MAD = (0.0625 + 0.4375 + 0.5625 + 0.1875) / 4 = 0.3125 minutes
Therefore, the mean absolute deviation of the times taken to complete the obstacle course is 0.3125 minutes.
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,Kofi, Adoma and Esenam are three siblings, Kofi is x years older than Adoma and Adoma is y years older than Esenam. a. How much older than Esenam is Kofi ? b. If Esenam is 5 years old, how old is (i) Adoma (ii)Kofi
a. K = E + (x + y). This implies that Kofi is (x + y) older than Esenam.
b. (i) Adoma = (5 + y) years
(ii) Kofi = (5 + (x+y)) years
What is a word problem?Word problem is a topic that requires the transformation of a mathematical statement into an equation, such that the variable is to be determined.
In the given question, we have;
Let the age of Kofi, Adoma, and Esenam be represented by K, A and E respectively. So that;
K = A + x ...... i
A = E + y........ ii
substitute i into ii
K = (E + y) + x
= E + (x + y)
K = E + (x + y) ........ iii
Thus,
a. From equation iii, we can deduce that Kofi is (x + y) years older than Esenam.
b. The age of Adoma = 5 + y years
ii. The age of Kofi = 5 + (x + y) years
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URGENT!! ILL GIVE
BRAINLIEST! AND 100 POINTS
Answer:
The y-intercept represents Adam's base salary
Step-by-step explanation:
Since it's y = 0.28x + 38,000, when x is 0, the salary is 38,000 without commission.
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Find the sum of the interior angles of the following polygon:
115⁰
4
130⁰
115
95⁰
Sum of interior angles =
Part 2:
Find the measure of x:
degrees.
degrees.
The Sum of interior angles of the given polygon is: 540°
The value of the angle x is: 85°
What is the interior angle of the polygon?The interior angle-sum formula for an irregular polygon is the same as the sum of interior angle in a regular polygon.
Sum of interior angles in a n-sided polygon is:
Sum = (n - 2)180
where:
n is the number of sides of the irregular polygon.
This is a 5-sided irregular polygon
Thus:
Sum = (5 - 2)180
Sum = 540°
Thus:
x + 115 + 115 + 130 + 95 = 540
x + 455 = 540
x = 540 - 455
x = 85°
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Richard is saving money for a down payment on a car. He opens a savings account at his local bank and deposits $500. He models his savings plan with the equation y = 200x + 500 based on his current monthly savings rate. What does the y-intercept of linear model represent?
Question 8 options:
The date the savings account was started.
The starting amount in his savings account.
The date when he will have enough money.
The largest amount that he can save.
In a case whereby Richard is saving money for a down payment on a car He models his savings plan with the equation y = 200x + 500 based on his current monthly savings rate y-intercept of linear model represent B. The starting amount in his savings account.
How can the linear model be interpreted?It should be noted that in a linear equation the y intercept can be seen as one that is starting point whereby x is zero, which implkies that starting balance he had is 1000 in the bank.
Therefore, from the equation y = 200x + 500, the y-intercept of linear model serves as the starting amount in his savings account.
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if you rotate cars tires at 10,000 miles, if a car tire has 25,200 rotations per day, how many weeks will it be until you rotate the tires
It will take 4. 09 weeks for the tires to be rotated at the current rate.
How to find the time till rotation ?When rotating a car's tires every 10,000 miles, each tire must complete this distance before being moved.
25, 200 rotations / day x 7 days / week = 176, 400 rotations per week
To solve this predicament, dividing 10,000 miles by the number of rotations/mile (which equates to the tire's circumference) is necessary. The formula for calculating a tire's circumference can aid in obtaining this number along with the weeks required to perform the rotation process:
C = 2πr
Rotation per mile is:
1 mile / 87.96 inches / rotation = 72.26 rotations / mile
Number of weeks:
10, 000 miles x 72. 26 rotations / mile = 722, 600 rotations
722, 600 rotations / 176, 400 rotations/week = 4.09 weeks
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Write an equation in the form y = mx +b of the line that is described.
The line rises from left to right. It passes through the origin and a second point with equal x and y
coordinates.
The equation of the line is y Write your response here...
Answer:
I have my answer in the picture i will upload
please check the below pictures.
Consider a rectangle with width of x units and an area of 10 square units. The length l of the rectangle can be modeled by the function f (x) = 10\x. Suppose the width of the rectangle increases 1 unit, while the area remains constant. Which graph models the length of the new rectangle?
please explain the answer step by step and explain why you chose the option you chose.
In linear equation, The graph in option 3 models the length of the new rectangle.
What is a linear equation in mathematics?
A linear equation in algebra is one that only contains a constant and a first-order (direct) element, such as y = mx b, where m is the pitch and b is the y-intercept.
Sometimes the following is referred to as a "direct equation of two variables," where y and x are the variables. Direct equations are those in which all of the variables are powers of one. In one example with just one variable, layoff b = 0, where a and b are real numbers and x is the variable, is used.
According to the problem,
width of the rectangle is x units
Area of the rectangle is 10 square units
Length of the rectangle is given by f(x) = 10/x
Now if width becomes (x+1) units
∴ Length will be represented as 10/(x+1)
Now from the given options we need to find the exact graph of f(x) = 10/(x +1)
Here if x = 4 , y =2
So the point (4 , 2) is satisfied which is only happening in the graph of option 3
Option 3 represents the correct graph.
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Find the measure of each indicated side. Round your answer to the nearest tenth.
Answer:
m∠R = 78.9°------------------------------
We are given three sides and need to find one of angles.
Use the law of cosines:
[tex]cos(A) = \cfrac{ b^2 + c^2 - a^2}{2bc}[/tex]
Here we are given:
R - angle A, a = 59.7, b = 52, c = 41Substitute above values into the given equation:
[tex]cos(R) = \cfrac{ 52^2 + 41^2 - 59.7^2}{2*52*41} =0.1925[/tex]
Find m∠R:
m∠R = arccos (0.1925), use calculatorm∠R = 78.9° (rounded to the nearest tenth)