We find the sine and cosine of an acute angle by taking the ratio of the length of the side opposite to the angle with respect to the length of the side adjacent to the acute angle.
What is the tangent of the angle?
The ratio of the right-angle triangle's base or perpendicular is known as the tangent of the angle.
The ratio of two of the right-angled triangle's three sides is used to define the sine, cosine, and tangent of an acute angle.
Here,
We have to find out how is a right triangle used to find the sine and cosine of an acute angle is there a unique right triangle that must be used.
We concluded that a right triangle can be used to determine the tangent of any acute angle, by taking the ratio of the length of the side opposite to the angle with respect to the length of the side adjacent to the acute angle.
Hence, we find the sine and cosine of an acute angle by taking the ratio of the length of the side opposite to the angle with respect to the length of the side adjacent to the acute angle.
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How do you know if its logarithmic or exponential?
The difference between logarithmic and exponential functions can be determined by looking at the form of the equation and by performing a calculation.
A logarithmic equation is written as log_b(x) = y, where b is the base and x and y are variables. An exponential equation is written as b^x = y, where b is the base and x and y are variables.
To determine if an equation is logarithmic or exponential, begin by comparing the form of the equation to the two equations above. If the equation is written in the form of log_b(x) = y, then it is a logarithmic equation. If the equation is written in the form of b^x = y, then it is exponential.
To perform a calculation, plug in a known value for x and then solve for y. For example, if the equation is log_2(x) = 4, then plug in x = 8. The calculation would then be:
log_2(8) = 4
This is a logarithmic equation, as the form of the equation matches log_b(x) = y.
If the equation is b^x = 16, then plug in x = 4. The calculation would then be:
2^4 = 16
This is an exponential equation, as the form of the equation matches b^x = y.
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State your conclusion to the following hypothesis test.
A certain academic program boasts that 87% of their graduates find full-time employment in their field within the first year of graduation. The academic director is concerned that market factors may have adversely affected the full-time placement rate and decides to perform a Hypothesis Test to see if her concern is warranted.
The hypothesis test is performed at a 5% significance level and the resulting p-value is 0.07.
Assume that all conditions for testing have been met and choose the statement that contains the correct conclusion.
Question 11 options:
a.there is not sufficient sample evidence to conclude that the full-time placement rate is now less than 87% because the p-value is greater than 0.05.
b.there is sufficient sample evidence to conclude that the full-time placement rate is now less than 87% because the p-value is greater than 0.05.
c.there is sufficient sample evidence to conclude that the full-time placement rate is 87% because the p-value is greater than 0.05.
c.there is not sufficient sample evidence to conclude that the full-time placement rate is 87% because the p-value is greater than 0.05.
Construct the equation of the regression line.
An editing firm compiled the following table which lists the number of pages contained in a piece of technical writing and the cost of proofreading and correcting them (in dollars). Assume there is a significant linear relationship between X and Y and construct the equation of the linear regression line.
Number of Pages, x
7
12
4
14
25
30
Cost, y
128
213
75
250
446
540
Question 28 options:
yˆ=17.9(x)+1.6
yˆ=15.4(x)+7.1
yˆ=1.6(x)+17.9
yˆ=7.1(x)+15.4
Use the model to make the appropriate prediction.
A sociologist wanted to determine whether there was a relation between a state's poverty rate (x) and its teen pregnancy rate (y). Data from all 50 states produced the regression model:
yˆ=4.3+1.4(x)
What does the model suggest for the poverty rate of Florida, which has a poverty rate of 16.6?
Answer:
Part A
a. There is not sufficient sample evidence to conclude that the full-time placement rate is now less than 87% because the p-value is greater than 0.05
Part B
[tex]\hat Y[/tex] = 17.9·(x) + 1.6
Part C
The teen pregnancy rate in Florida is 6.54
Step-by-step explanation:
The percentage of graduates that find full-time employment in their fields within the first year of graduation = 87%
The significant level of the hypothesis test = 5% = 0.05
The p-value = 0.07
Given that the testing conditions are met, we have;
The p-value is larger than the significant level of 0.05, therefore, it cannot be concluded that there is significant difference between the two rates
Therefore;
There is not enough statistical evidence available to come to a conclusion that the placement rate of full-time students has reduced below the given 87% because from the statistics, the p-value is larger than 0.05.
Part B
Number of Pages, x; 7, 12, 4, 14, 25, 30
Cost, y; 128, 213, 75, 250, 446, 540
The regression analysis formula is;
Y = a + b·X
We have;
[tex]b = \dfrac{N\sum XY - \left (\sum X \right )\left (\sum Y \right )}{N\sum X^{2} - \left (\sum X \right )^{2}}[/tex]
∴ b = (6×34602-92×1652)/(6×1930 - 92²) ≈ 17.852
[tex]a = \dfrac{\sum Y - b\sum X}{N}[/tex]
a = (1652 - 17.852 × 92)/6 ≈ 1.6
∴ Y ≈ 17.9·(x) + 1.6
Part C
The given regression model is y = 4.3 + 1.4(x)
Therefore, at x = 1.6, we get;
y = 4.3 + 1.4 × 1.6 = 6.54
The suggests that the teen pregnancy rate in Florida is 6.54.
Identify like terms
24a - 12b + 4 - 8a
Answer:
The like terms in this expression are 24a and -8a, and -12b and 12b.
Step-by-step explanation:
The like terms 24a and -8a can be combined by adding the coefficients and the variables, which gives us 24a - 8a = 16a.
The like terms -12b and 12b can be combined by adding the coefficients and the variables, which gives us -12b + 12b = 0.
So the like terms in this expression are 24a, -8a, and -12b, 12b.
Choose the system of linear equations that represents the mapping diagrams.
Answer:
A
Step-by-step explanation:
If you substitute each x value from the input boxes into the equations, you can find your answer.
The first input value is 1, and the output value is 12, so plug those into the first equation in the answer options.
y = 4x + 8
(12) = 4(1) + 8
12 = 4 + 8
12 = 12
Because the simplified equation ended in a true equality statement, that pair works with the equation.
The next x value is 3 and the y value is 20:
y = 4x + 8
(20) = 4(3) + 8
20 = 12 + 8
20 = 20
Again, it ends in true equality statement, so it also works with the equation.
(28) = 4(5) + 8 = 28 so that one works as well.
Then check the second equation with the second set of input and output values.
(2) = -7(-1) - 5 = 2
The first x and y values of that system work.
(9) = -7(-2) - 5 = 9
The second one works as well.
(16) = -7(-3) - 5 = 16
The last one is equal as well.
So the equations in A, or the first option, work with all of the inputs and outputs.
Which bag of potatoes is the better deal?
Answer:
5 kg.
Step-by-step explanation:
2 kg for $0.96 is more expensive than 5 kg for $1.95
The conversion of a temperature from Celsius to Fahrenheit is represented by the expression below, where C is the temperature in degrees Celsius. Use the expression to find the Fahrenheit temperature equivalent to 15° C.
The expression to convert celcius to Fahrenheit isn't given.
Answer:
59°F
Step-by-step explanation:
However, the expression required for the conversion is :
Temperature (°F) = [Temperature (°C) * 1.8] + 32
Therefore, using the expression, we can convert a celcius temperature of 15°C to Fahrenheit ;
Temperature (°F) = (15 * 1.8) + 32
Temperature °F = 27 + 32
Temperature °F = 59°F
A) A sequence is defined using this term-to-term rule.
Un+1 = 2un+ 20
If uy = 8, find u2
b) Another sequence is defined using this term-to-term rule,
unty = ku,+r
where k and rare constants.
Given that u, = 37, uz = 188 and ug = 943, find the value of k and
the value of r.
The Value of the two constants K and R are 5 and 3 respectively.
a) To find u2, you can substitute u1 = 8 into the term-to-term rule to get:
u2 = 2u1 + 20 = 2(8) + 20 = 36
So u2 = 36.
b) To find the values of k and r, you can use the given values of u1, u2, and u3 to set up a system of equations. Using the term-to-term rule:
u2 = ku1 + ru3 = ku2 + rSubstituting in the given values:
u2 = 188 = k(37) + ru3 = 943 = k(188) + rSolving for r and k, we get:
k = 5 and r = 3.
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pls help!!! asap!! will give brainliest NO LINKS
Answer:
it's -63
good luck if you want explanation comment
Answer: 63
Step-by-step explanation:
All triangles' angles added up should be 180 degrees, so 70+47=117 and 180-117=63.
180 = a+b+c
180 = 47 + 70 + c
180 - 47 - 70 = c
or,
180 - (47+70) = c
The area of a square is 275 square meters and one side length is 55 meters. What is the perimeter of the square?
Answer:
220 meter
Step-by-step explanation:
According to the scenario, computation of the given data are as follows,
Area of square = 275 square meters
Side length (a) = 55 meters
We can calculate the perimeter of square by using following formula,
Perimeter of square = 4a
By putting the value, we get
Perimeter of square = 4 × 55 mt
= 220 meter
Hence, the perimeter of the square is 220 meter.
find the output, g, when the input, r is 3
g= -5 + 13
The output of function g(r) = -5x + 13 when r is 3 is -2.
What is a function?A function is a relationship between inputs where each input is related to exactly one output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
g(r) = -5r + 13
Input r = 3
g(3)
= -5 x 3 + 13
= -15 + 13
= - 2
Thus,
The output is -2.
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PLZ HELP DESPERATE NO LINKs! Will mark brainliest
Answer:
Step-by-step explanation:
y is 40 and x is 21
so xy=61
Answer:
Y=40
X=21
XY=61
I hope you have a spectacular day and take mental health breaks!
Find the slope of a line that passes through the given two points using ratio method
The slope formula, or the ratio of the change in the y values to the change in the x values, is m=(y2-y1)/(x2-x1).
What is slope ?A line's steepness and direction are measured by the line's slope.
Without actually using a compass, determining the slope of lines in a coordinate plane can assist in forecasting whether the lines are parallel, perpendicular, or none at all.
A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes.
The y coordinate's net change is y, and the x coordinate's net change is x.
Hence, The slope formula, or the ratio of the change in the y values to the change in the x values, is m=(y2-y1)/(x2-x1).
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A set of data has the trend line modeled by the equation Y =1.5x + 11. What value of X corresponds to y =56?
Answer:
x = 30
Step-by-step explanation:
Plug in 56 in place of y, then solve for x.
56 = 1.5x + 11
Subtract 11.
45 = 1.5x
Divide both sides by 1.5.
45/1.5 = x
30 = x
Answer:202
Step-by-step explanation:
I did it
what is the volume of a cylinder in cubic feet with a height of 12 feet in a base diameter of 12 feet
Answer:
1357.17 cubic feet
Step-by-step explanation:
The volume of a cylinder is
[tex]\pi {r}^{2} h[/tex]
We know the height is 12, and the radius is simply half our diameter, which in this case is
[tex] \frac{12}{2} = 6[/tex]
plug these two numbers into our formula and we have found our volume.
How do you find the 3rd side of a triangle?
The third side of a triangle, the following formula can be used c² = a² + b² - 2abcos(C)
To calculate the third side of a triangle, first find the lengths of the other two sides and the angle opposite the third side. Then plug these values into the formula above and solve for c.
Where c is the third side of the triangle, a and b are the other two sides, and C is the angle between them.
For example, for a triangle with two sides of length 4 and 6, and an angle between them of 75 degrees, the formula would look like this:
c² = 42 + 62 - 2(4)(6)cos(75)
Solving for c yields a third side length of 8.4.
To solve for c, first square the two side lengths: 42 = 16 and 62 = 36. Then, multiply the two side lengths together and multiply by the cosine of the angle between them: 2(4)(6)cos(75) = 43.9. Finally, add the two squared values together and subtract the result of the multiplication: 16 + 36 - 43.9 = 8.1. Then, take the square root of this result to get the length of the third side: √8.1 = 8.4.
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What is horizontal give example?
A horizontal line is a line extending from left to right. When you look at the sunrise over the horizon you are seeing the sunrise over a horizontal line. The x-axis is an example of a horizontal line.
Now, According to the question:
What is a Horizontal Line?
Horizontal lines are also known as sleeping lines. In coordinate geometry, horizontal lines are those lines that are parallel to the x-axis. In geometry, we can find horizontal line segments in many shapes, such as quadrilaterals, 3d shapes, etc. In real life, we can find horizontal lines on the steps of the staircase, planks on the railway tracks, etc.
The x-axis is an example of a horizontal line.
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a rectangular picture frame has dimensions of 2 feet by 3 feet.
I dont know
I would just pick c
please help me outt the image is below
Answer:
ggjhh
Step-by-step explanation:
gf Dayanand on fall in didn't you
If there are 1000 meters in one kilometer, how many kilometers are in 4230 meters?
A nail salon raises their price for nails from $25 to $30. What is the percent increase?
Answer:
17%
Step-by-step explanation:
5 out of 30 is 17%
5/30 = 5 ÷ 30 = .16. rounds to .17 =17%
find the mean,median and mode for x,2x,3x,4x,5x
Answer:
Mean: 3x
Median: 3x
Mode: None
Step-by-step explanation:
The mean is the sum of all the numbers divided by how many there are.
x + 2x + 3x + 4x + 5x = 15x and 15x/5 = 3x. So the mean is 3x.
The median is the number in the middle when the values are in order from least to greatest. The median is 3x.
The mode is the number that appears most often in the data set. In this case, the mode is none because no number appears more than the other numbers.
can y’all help me please
Answer: we need more information to solve
Step-by-step explanation:
In the diagram below, line f is parallel to line g, and line l intersects them as shown.
If m 2 is increased by moving line l, which statement is true?
A. m 8 would increase
B. m 6 would decrease
C. m 4 would remain the same
D. m 3 would increase
Answer:
m 8 would increase, or A
Step-by-step explanation:
Max bought a 5 kg cake for his birthday party. After eating 1 3 of it, he cut the remaining cake into pieces of 1 6 kg each. How many pieces of cake did Max cut?
Answer:
10
Step-by-step explanation:
Cake remaiing after eating 1/3 = 1/3 x 5 = 5/3 kg
let x = pieces he divided the cake into
5/3 ÷ x = 1/6
1/ x = 3/5 x 1/6 = 1/10
x = 10
PLEASE ANWSER!!!
PICTURE
Answer:
The 4th would be 0.25
Step-by-step explanation:
Could someone help!
How much of your data would be included within 2 standard deviations of the mean?
A) 68%
B) 95%
C) 97%
D) 99.7%
c.) Find the Surface Area of the Regular Pyramid. Surface Area: Volume: 24 yds 20 yds
¿Cuántos decimetros hoy en un metro?
Q 9-1 Pythagorean Theorem and Trig
A girl is 20 ft. east of her school and her bike is 21 ft. south of the school. How far is she from her bike? Round to the nearest hundredth.
Answer: 29 ft
Step-by-step explanation:
Based on the description we are given. we know that we can form a right triangle, where 20 and 21 are the legs. The length from the girl to the bike would be the hypotenuse. To do this, we need to use the Pythagorean Theorem, which is [tex]a^2+b^2=c^2[/tex], where a and b are legs, and c is hypotenuse. We can go ahead and plug them in.
[tex]20^2+21^2=c^2[/tex] [exponent]
[tex]400+441=c^2[/tex] [add]
[tex]841=c^2[/tex] [square root both sides]
[tex]c=29[/tex]
Therefore, the distance from the girl to the bike is 29 ft.
Mrs. Remeto separate would like to buy a television TV set payable for 6 months starting at the end of the month how much is the cost at the TV set if her monthly payment is P3,000 and interest is 9% compounded semi annually?
If her monthly payment is P3,000 and interest is compounded semi-annually at 9%, the cost of the TV set comes to P17,545.08.
What is compound interest?Compound interest, also known as interest on principal and interest, is the practice of adding interest to the principal amount of a loan or deposit.
It occurs when interest is reinvested, or added to the loaned capital rather than paid out, or when the borrower is required to pay it, so that interest is generated the next period on the principal amount plus any accumulated interest.
In finance and economics, compound interest is common.
In contrast to simple interest, which does not compound since past interest is not added to the principal for the current period, compound interest allows interest to build over time.
The interest per period multiplied by the number of periods in a year yields the simple annual interest rate.
According to our question-
9% = 0.09 / 2
=0.045 + 1 =1.045^(1/6)
=1.00736312 - 1 x 12 x 100
=8.836%
PV=0;
PMT=3000;
R=0.08836/12; N=6; PV
=PMT*(((1 + R)^N - 1)*((1 + R)^-N)* R^-1)
PV==17,545.08
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