Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).
A right triangle ABC has complementary angles A and C.
Answers
Using a right-angled triangle the value of Cos C is 24/25 and Sin A is 20/29.
What are trigonometric identities?Trigonometric identities are the functions that include trigonometric functions such as sine, cosine, tangents, secant, and, cot.
A right triangle ABC has complementary angles A and C.
Using a right-angled triangle if Sin A = 24/25 then the other side =7
Therefore Cos C = 24/25
Similarly,
Using a right-angled triangle if Cos C = 20/29 then the other side =21
Therefore Sin A = 20/29
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Related Questions
Need help ASAP!
I have no idea how to do this
Answers
Answer:
the last one 3(x+4) = 3x + 12
Step-by-step explanation:
TIME REMAINING
44:54
The table below shows the number of cars sold each month for 5 months at two dealerships.
Cars Sold
Month
Admiral Autos
Countywide Cars
Jan
4
9
Feb
19
17
Mar
15
14
Apr
10
10
May
17
15
Which statements are supported by the data in the table? Check all that apply.
The mean number of cars sold in a month is the same at both dealerships.
The median number of cars sold in a month is the same at both dealerships.
The total number of cars sold is the same at both dealerships.
The range of the number of cars sold is the same for both dealerships.
The data for Admiral Autos shows greater variability.
Answers
The statements supported by the data in the table are:
The mean number of cars sold in a month is the same at both dealerships.
The total number of cars sold is the same at both dealerships.
The data for Admiral Autos shows greater variability.
To determine which statements are supported by the data in the table, let's analyze the given information:
The mean number of cars sold in a month is the same at both dealerships.
To calculate the mean, we need to find the average number of cars sold each month at each dealership.
For Admiral Autos:
(4 + 19 + 15 + 10 + 17) / 5 = 65 / 5 = 13
For Countywide Cars:
(9 + 17 + 14 + 10 + 15) / 5 = 65 / 5 = 13
Since both dealerships have an average of 13 cars sold per month, the statement is supported.
The median number of cars sold in a month is the same at both dealerships.
To find the median, we arrange the numbers in ascending order and select the middle value.
For Admiral Autos: 4, 10, 15, 17, 19
Median = 15
For Countywide Cars: 9, 10, 14, 15, 17
Median = 14
Since the medians are different (15 for Admiral Autos and 14 for Countywide Cars), the statement is not supported.
The total number of cars sold is the same at both dealerships.
To find the total number of cars sold, we sum up the values for each dealership.
For Admiral Autos: 4 + 19 + 15 + 10 + 17 = 65
For Countywide Cars: 9 + 17 + 14 + 10 + 15 = 65
Since both dealerships sold a total of 65 cars, the statement is supported.
The range of the number of cars sold is the same for both dealerships.
The range is determined by subtracting the lowest value from the highest value.
For Admiral Autos: 19 - 4 = 15
For Countywide Cars: 17 - 9 = 8
Since the ranges are different (15 for Admiral Autos and 8 for Countywide Cars), the statement is not supported.
The data for Admiral Autos shows greater variability.
To determine the variability, we can look at the range or consider the differences between each data point and the mean.
As we saw earlier, the range for Admiral Autos is 15, while for Countywide Cars, it is 8. Additionally, the data points for Admiral Autos are more spread out, with larger differences from the mean compared to Countywide Cars. Therefore, the statement is supported.
Based on the analysis, the statements supported by the data are:
The mean number of cars sold in a month is the same at both dealerships.
The total number of cars sold is the same at both dealerships.
The data for Admiral Autos shows greater variability.
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Solve for f.
f 3 = 8
f =
Answers
Work:
3f = 8
3 f = 8
—- —-
3 3
(3/3 cancels out)
So, 8/3 = 2.6666
Rounded = 2.7
f = 2.7
find the y intercept of the line on the graph
Answers
Answer:
(0, -4) or just -4
Step-by-step explanation:
The y-intercept is where a line intersects with the y-axis. The line hits the y-axis at the point (0, -4). That's why the y-intercept is -4.
:3))
PLEASE HELP!! 35 POINTS!!!
ignore my writing if it’s wrong
Answers
Answer: sin(x)=5/11
Step-by-step explanation:
For #7, the hypotenuse is always the longest side of a triangle and in right triangles it's always the side that's opposite the right angle. MO, the side thats 11, is the hypotenuse in this triangle and not the adjacent side which would be NM. Therefore, you need to use sin=opp/hyp and get sin(x)=5/11
An antique chair was purchased in the year 2013 for $500. At the time of purchase, an appraiser estimated that
the value would increase by 10% every year. Which of the following functions can be used to model the
estimated dollar value of the chair years after purchase?
(A) f(t) = 500(0.1)
(B) f(t) = 500(0.9)
(C) f(t) = 500(1.1)
(D) f(t) = 500(10)
(E) f(t) = 510+
Answers
Answer:
A
Step-by-step explanation:
To find 10% of 500 you would multiply 500 by 0.1
At 3pm corettas shadow is 1.03 meters long. Her height is 1.65 meters at the same time, a trees shadow is 5.57 meters long. How tall is the tree
Answers
I am greater than 320. You say my number if you start at 324 and count from 10 to 10. I have the same number of tens and ones.
Answers
Answer:
344
Step-by-step explanation:
Um..... sorta confusing, but I think you are only allowed to increase by 10 each time, so then you need to add 20 to make 344, where the units digit and tens digit are the same
The x and y intercepts for the linear equation x – 2y = -8 is
Answers
Answer:
x- intercept = - 8 , y- intercept = 4
Step-by-step explanation:
to find the x- intercept let y = 0 in the equation and solve for x
x - 2(0) = - 8
x - 0 = - 8
x = - 8 ← y- intercept
to find the y- intercept let x = 0 in the equation and solve for y
0 - 2y = - 8
- 2y = - 8 ( divide both sides by - 2 )
y = 4 ← y- intercept
Which graph shows the image of AABC after a rotation about the origin?
10
8
10 8 6 4 2
O A.
6
2
2
-4
66
8
-10
B
A
C
2
4
10-8-6-4
6
10
B
8 10
8
2 4
6 8 10
Answers
The coordinates of the vertices of a triangle that is rotated 270° clockwise are -
A(x₁, y₁) → A'(y₁, - x₁)
B(x₂, y₂) → B'(y₂, - x₂)
C(x₃, y₃) → C'(y₃, - x₃)
What is rotation of image?The rotation of a figure is defined as the angle about a point by which a image is rotated such that the image and the figure remains similar.
Given is triangle ΔABC.
The images of the vertices of triangle ABC after the composition is applied is -
A(0.5x₁ - 4, 0)
B(0.5x₂ - 4, 0)
C(0.5x₃ - 4, 0)
What is algebraic expression?An algebraic expression is a combination of terms both constants and variables. For example -
2x + 3y + z
3x + y
Given are the vertices of the triangle ABC as -
A(x₁, y₁)
B(x₂, y₂)
C(x₃, y₃)
The algebraic rule for a figure that is rotated 270° clockwise about the origin is (y, -x). So, we can write the new coordinates as -
A(x₁, y₁) → A'(y₁, - x₁)
B(x₂, y₂) → B'(y₂, - x₂)
C(x₃, y₃) → C'(y₃, - x₃)
Therefore, the coordinates of the vertices of a triangle that is rotated 270° clockwise are -
A(x₁, y₁) → A'(y₁, - x₁)
B(x₂, y₂) → B'(y₂, - x₂)
C(x₃, y₃) → C'(y₃, - x₃)
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22. A liver cell is about 20 um in diameter. How many liver cells would it take to form an end to end chain 10 in long?
Answers
The number of liver cells it would take to form an end to end chain 10 in long is 12,700 liver cells
Calculating quantityFrom the question, we are to determine how many liver cells it would take to form an end to end chain 10 in long
First, we will convert 10 in to meters
1 inch = 0.0254
∴ 10 inches = 0.254 m
From the giving information,
A liver cell is about 20 μm in diameter
∴ The number of liver cells it would take to form an end to end chain 10 in long = 0.254 m / 20 μm
= 0.254 m / (20 ×10⁻⁶) m (NOTE: 1μm = 10⁻⁶m)
= 12700
Hence, the number of liver cells it would take to form an end to end chain 10 in long is 12,700 liver cells
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how many ft is equal to 1.66m
Answers
Answer:
5.44 meters
Step-by-step explanation:
We Know
0.3048 meter = 1 ft
How many ft makes a height of 1.66m?
We Take
1.66 ÷ 0.3048 ≈ 5.44 meters
So, the answer is 5.44 meters.
Michael is working two summer jobs, making $19 per hour lifeguarding and making
$14 per hour clearing tables. In a given week, he can work at most 17 total hours and
must earn a minimum of $280. If a represents the number of hours lifeguarding and
y represents the number of hours clearing tables, write and solve a system of
inequalities graphically and determine one possible solution.
Answers
The possible solutions are 8 hours and 9 hours.
The number of hours for lifeguarding is 8 hours.
The number of hours for clearing tables is 9 hours.
What is inequality?It shows a relationship between two numbers or two expressions.
There are commonly used four inequalities:
Less than = <
Greater than = >
Less than and equal = ≤
Greater than and equal = ≥
We have,
Two summer jobs:
Lifeguarding.
x = number of hours
= $19 per hour
Cleaning tables.
y = number of hours
=$14 per hour
Total hours in a week = 17 hours
Minimum earning = $280
The inequality represents the above situation.
x + y ≥ 17
19x + 14y ≥ 280
Solving for x and y.
x + y = 17 _____(1)
x = 17 - y
19x + 14y = 280 ______(2)
Putting (1) in (2) we get,
19(17 - y) + 14y = 280
323 - 19y + 14y = 280
323 - 5y = 280
323 - 280 = 5y
43 = 5y
y = 43/5
y = 8.6
y = 9
Now,
x = 17 - y
x = 17 - 8.6
x = 8.4
x = 8
Thus,
The possible solutions are 8 hours and 9 hours.
The number of hours for lifeguarding is 8 hours.
The number of hours for clearing tables is 9 hours.
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The equation of line is 2y = -3x + 4 .
What is the y-intercept of line L?
Answers
Answer:
y-intercept=2
Step-by-step explanation:
2y=-3x+4
divide both sides by 2
y=-1.5x+2
y=mx+c
'c' is the y-intercept so '2' is the answer.
Answer:
= -3/2
Step-by-step explanation:
The equation of the line = 2y = -3x + 4
2y = -3x + 4
2y = -3x + 4
2 2 2
y intercept of the line = -3/2.
Describe two different ways to translate a figure that result in the same image. Justify your answer.
Answers
The ways to translate the figure include:
It doesn't change its orientation.
It also doesn't change its size or shape.
How to illustrate the information?When a geometric figure glides up, down, left, or right on the coordinate plane, this is referred to as translation. The figure changes its location but not its orientation. It also retains its size and shape. When you translate a figure, you slide it left or right, up or down.
When you translate a figure, you slide it left or right, up or down. This indicates that the coordinates for the figure's vertices will vary on the coordinate plane. To graph a, make the same modification at each point. The variations in coordinates of a reflection can be used to identify it.
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positive.
an remove
3√5a-8√/35a2
Answers
3√(5a) - 8√(a) / 35a^2
To simplify this expression, we can first separate the two terms in the numerator:
3√(5a) / 35a^2 - 8√(a) / 35a^2
We can then simplify each term separately. For the first term:
3√(5a) / 35a^2 = √(5a) / (35a^2/3)
We can simplify the denominator by using the rule that (a^m)^n = a^(mn):
35a^2/3 = (5a^2/3) * 7 = (a^(2/3))^5 * 7
So the first term simplifies to:
√(5a) / (a^(2/3))^5 * 7
For the second term:
8√(a) / 35a^2 = 8a^(1/2) / (35a^2)
We can simplify the denominator by using the rule that a^-m = 1/a^m:
35a^2 = 5 * 7 * a^2 = a^-2 * 5 * 7
So the second term simplifies to:
8a^(1/2) / (a^-2 * 5 * 7)
Now we can combine the two terms by finding a common denominator:
√(5a) / (a^(2/3))^5 * 7 - 8a^(1/2) / (a^-2 * 5 * 7)
The common denominator is (a^(2/3))^5 * 5 * 7:
√(5a) * 5 * 7 / (a^(2/3))^5 * 5 * 7 - 8a^(1/2) * (a^(2/3))^5 * 5 * 7 / (a^-2 * 5 * 7) * (a^(2/3))^5 * 5 * 7
Simplifying each term, we get:
35√(5a) / 5a^2 - 40a^(5/2) / 5a^3
Now we can simplify further by factoring out a common factor of 5a^(5/2):
5a^(5/2) * (7√(5a) - 8) / 5a^3
The 5's cancel out, and we can remove the common factor of 5a^(5/2) to get:
(7√(5a) - 8) / a^(3/2)
So the simplified expression is:
(7√(5a) - 8) / a^(3/2)
at school there are 8 students who only play violin, 10 students who only play guitar, 3 students who play both, and 12 students who don't play any instrument at all. if a student is randomly selected from this school, what is the probability that they play violin or guitar
Answers
Answer:
\(\frac{7}{11}\)Step-by-step explanation:
\(\frac{21}{33}\) simplified would be \(\frac{7}{11}\)
The probability that they play violin or guitar is 7/11 .
What is Probability ?Probability is the likeliness of an event to occur.
It is given that
The number of students who only play violin is 8
The number of students who only play guitar is 10
The number of Students who play both is 3
The number of students who don't play either is 12
Total Students = 8+10+3+12 = 33
Total favorable outcomes (violin or guitar) = 8 + 10 +3
Probability = Total favorable outcomes / Total outcomes
Probability = 21 / 33
Probability = 7/11
Therefore the probability that they play violin or guitar is 7/11 .
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The table shows claims and their
probabilities for an insurance
company.
Amount of claim
(to the nearest $20,000)
$0
$20,000
$40,000
$60,000
$80,000
$100,000
Probability
0.70
0.16
0.09
0.03
0.01
0.01
Answers
Answer:
Step-by-step explanation:
This is an equation! Solutions: x=1.
Graphical form: Equation 3%2Ax-x%2B2=4 was fully solved.
Text form: 3*x-x+2=4 simplifies to 0=0
Cartoon (animation) form: simplify_cartoon%28+3%2Ax-x%2B2=4+%29
For tutors: simplify_cartoon( 3*x-x+2=4 )
If you have a website, here's a link to this solution.
make e the subject
e-5=2f
Answers
Answer:
e-5=2f
take '-5' to the other side where '2f' is
e=2f+5
In the states of Florida and Colorado, veterinarians investigating obesity in dogs obtained random samples of pet medical records and recorded the weights of the dogs in the samples. A test was conducted of H0 : p1= p2 versus Ha : p1 ≠ p2, where p1 represents the proportion of all overweight dogs in Florida and p2 represents the proportion of all overweight dogs in Colorado. The resulting test statistic for a two-sample z-test for a difference between proportions was 1.85. At the significance level α = 0.05, which of the following is a correct conclusion?
A
There is not sufficient statistical evidence to conclude that the proportion of all overweight dogs in Florida is different from the proportion of all overweight dogs in Colorado because the p-value is greater than 0.05.
B
There is not sufficient statistical evidence to conclude that the proportion of all overweight dogs in Florida is different from the proportion of all overweight dogs in Colorado because the z-test statistic is greater than 0.05.
C
There is sufficient statistical evidence to conclude that the proportion of all overweight dogs in Florida is different from the proportion of all overweight dogs in Colorado because the p-value is greater than 0.05.
D
There is sufficient statistical evidence to conclude that the proportion of all overweight dogs in Florida is different from the proportion of all overweight dogs in Colorado because the p-value is less than 0.05.
E
There is sufficient statistical evidence to conclude that the proportion of all overweight dogs in Florida is greater than the proportion of all overweight dogs in Colorado because the z-test statistic is positive.
Answers
The correct statement regarding the conclusion of the test of the hypothesis is given as follows:
A. There is not sufficient statistical evidence to conclude that the proportion of all overweight dogs in Florida is different from the proportion of all overweight dogs in Colorado because the p-value is greater than 0.05.
What is the relation between the p-value and the conclusion of the test hypothesis?Depends on if the p-value is less or more than the significance level:
If it is more, the null hypothesis is not rejected, meaning that the research study is not statistically significant.If it is less, it is rejected, meaning that the research study is statistically significant.We have a two-tailed test in this problem, as we are testing if the proportions is different.
A p-value of 0.05 is achieved with z = 1.96, hence, as the test statistic is less than 1.96, the p-value is greater than 0.05, and option A is correct.
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What is the median of this set of data:593,588,540,434,420,398,390,375
Answers
Answer:
427
Step-by-step explanation:
d = √(x2 - x1)2 + (y2 - y1)2, what is the distance between point (3, 2) and point (5, 4) rounded to nearest 10th
Answers
add. simplify the answer and write it as a mixed number 2/15+3/10+4/5
Answers
Answer:
1 7/30
Step-by-step explanation:
First find common denominator then solve
\(\frac{2}{15} + \frac{3}{10} + \frac{4}{5}\\\\\frac{4+9+24}{30} = \frac{37}{30} = 1\frac{7}{30}\)
Fill in the blank with either "edge" or "vertex" to make a true statement.
A Hamiltonian circuit uses each once and only once.
An Euler circuit uses each once and only once.
Answers
9514 1404 393
Answer:
H: vertexE: edgeStep-by-step explanation:
A Hamiltonian circuit uses each vertex once and only once. (may repeat edges)
An Euler circuit uses each edge once and only once. (may repeat vertices)
Suppose you start with one liter of vinegar and repeatedly remove 0.14 L, replace with water, mix, and repeat. a. Find a formula for the concentration after n steps. b. After how many steps does the mixture contain less than 9% vinegar?
Answers
Formula for the concentration after n steps is \(C(n) = C(0) * (0.86)^n\) and
after 11 steps, the mixture contains less than 9% vinegar.
What is concentration?
Concentration in science refers to the amount of a particular substance (the solute) that is dissolved in a given amount of a solution. It is typically expressed in units of moles per liter (M or mol/L) or as a percentage or fraction of the total solution.
a. Let C(n) be the concentration of vinegar after n steps. At each step, we remove 0.14 L of the mixture, which contains C(n) liters of vinegar. So we are left with (1 - C(n)) liters of water. We then add back 0.14 L of water, giving us a total volume of 1 liter. Therefore, the concentration after one step is:
\(C(1) = C(0) * \frac{1 - 0.14}{1}\)
where C(0) is the initial concentration of vinegar, which is 1 liter per liter or 100%. After two steps, we repeat the process:
C(2) = C(1) * \(\frac{1 - 0.14}{1}\)
Substituting the formula for C(1), we get:
C(2) = C(0) * \((\frac{1 - 0.14}{1}) * (\frac{1 - 0.14}{1})\)
or, more generally:
\(C(n) = C(0) * (0.86)^n\)
b. We want to find the smallest integer n such that C(n) < 0.09 or 9%. Substituting the formula from part (a), we get:
\(C(0) * (0.86)^n < 0.09\)
Dividing both sides by C(0), we get:
\((0.86)^n < 0.09\)
Taking the natural logarithm of both sides, we get:
n * ln(0.86) < ln(0.09)
Dividing both sides by ln(0.86), we get:
n > ln(0.09) / ln(0.86)
Using a calculator, we get:
n > 10.7
Since n must be an integer, the smallest possible value of n is 11. Therefore, after 11 steps, the mixture contains less than 9% vinegar.
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Lines A and B are parallel <5 = [???]
![Lines A and B are parallel <5 = [???]](https://i5t5.c14.e2-1.dev/h-images-qa/contents/attachments/z6kv2gShCissDkznCRtXXDTw9Eyfb9oS.png)
Answers
Answer:
∠ 5 = 130°
Step-by-step explanation:
∠ 5 and 130° are corresponding angles and are congruent . so
∠ 5 = 130°
8 – 3x = 20
A.
x = 4
B.
x = 9.33
C.
x = –4
D.
x = –9.33
Please select the best answer from the choices provided
A
B
C
D
Answers
Answer:
The answer is option C.
I don’t understand, please help
Answers
Answer:
cosA=root8/3 is the answer
Given that the mass, m g, of a sphere is directly
proportional to the cube of its radius, r cm, copy
and complete the table.
r
m
0.2
0.25
0.7
1.5
6.75
11.664
Answers
I need help asap please!!!
Answers
The values of the angles given are: 0,90,180,240,270,360,420,480,540,600,630,660,720 and
What is sine of angles?he sine of an angle is the trigonometric ratio of the opposite side to the hypotenuse of a right triangle containing that angle. It is defined as the length of the opposite side divided by the length of the hypotenuse
The given angles are: 0,30,45,90,120,135,180,210,225,240,270,300,315,330,360
2∅ 2*∅ = 0, 90,180,240,270,360,420,480,540,600,630,660,720
sin 2∅ = sin0 = 0; Sin90=1; sin180=0; sin240= -0.8660; sin270 = -1;
Each angle is multiplied by sine sine360 =1; sin420 = 0.8660; sin480= 0.9848; sin540=1; sin600=-0.8660; sin630=-1; sin660=0.8660; sin720= 0.9397
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