In ΔA B C, ∠B is a right angle, A B=30 , and secA= 5/3 . Find each value in fraction and in decimal form.
tan C
Answers
\(\sec A=\frac{AC}{AB} \implies \frac{AC}{30}=\frac{5}{3} \implies AC=50\)
By the Pythagorean theorem, \(BC=\sqrt{50^2-30^2}=40\).
So, it follows that:
\(\tan C=\frac{AB}{BC}=\frac{30}{40}=\boxed{\frac{3}{4}}\)
Related Questions
Please help i'm struggling with this!It's urgent!
Answers
Hope this helps you. If available please give me a branliest. It is much appreciated. It would also help me answer more questions! Goodluck.
- Mathhotdog •~•
help please. what does x equal.
Answers
The answer would be 53
A bookstore decides to divide its space into three sections: nonfiction books, novels, and stationery. The bookstore wants to devote 1/6 of its space to stationery. If the total area of the bookstore is 288 square feet, and the stationery section will be 12 feet long, how wide will the stationery section be?
Answers
Answer:
Stationery section will be 4 feet wide.
Step-by-step explanation:
Total area of bookstore = 288 sq ft
Area to be devoted to stationery = \(\frac{1}6\) of total area = \(\frac{1}{6} \times 288 = 48\ sq\ ft\)
Length of stationery section = 12 ft
To find:
Width of stationery section = ?
Solution:
First of all, let us have a look at the area of rectangle:
\(A = Length \times Width\)
Here, we are given the length for stationery section and area of stationery section has been calculated above.
And we have to find the Width of stationery section.
So, let us put the two values to find the third value.
\(\Rightarrow 48 = 12 \times Width\\\Rightarrow Width = \dfrac{48}{12}\\\Rightarrow \bold{Width = 4\ ft}\)
So, the answer is:
Stationery section will be 4 feet wide.
How will you describe the graph of exponential function?
Answers
The graph of exponential function, is described below.
What is an exponential function?
The mathematical formula f(x) = e^x stands for the exponential function. The term, unless specifically stated otherwise, generally refers to the positive-valued function of a real variable, though it can be extended to the complex numbers or generalized to other mathematical objects like matrices or Lie algebras.
The formula for an exponential growth function is y = ab^x, where a > 0 and b > 1. As can be seen in the example of f(x) = 2x below, the graph will ascend. The numbers get smaller as x gets closer to negative infinity, as you can see.
If b > 1 , then the graph's slope is positive and exponential growth is depicted. The value of y approaches infinity as x rises. The value of y approaches zero as x falls.
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Let's say someone is conducting research on whether people in the community would attend a pride parade. Even though the population in the community is 95% straight and 5% lesbian, gay, or some other queer identity, the researchers decide it would be best to have a sample that includes 50% straight and 50% LGBTQ+ respondents. This would be what type of sampling?
A. Disproportionate stratified sampling
B. Availability sampling
C. Snowball sampling
D. Simple random sampling
Answers
The type of sampling described, where the researchers intentionally select a sample with 50% straight and 50% LGBTQ+ respondents, is known as "disproportionate stratified sampling."
A. Disproportionate stratified sampling involves dividing the population into different groups (strata) based on certain characteristics and then intentionally selecting a different proportion of individuals from each group. In this case, the researchers are dividing the population based on sexual orientation (straight and LGBTQ+) and selecting an equal proportion from each group.
B. Availability sampling (also known as convenience sampling) refers to selecting individuals who are readily available or convenient for the researcher. This type of sampling does not guarantee representative or unbiased results and may introduce bias into the study.
C. Snowball sampling involves starting with a small number of participants who meet certain criteria and then asking them to refer other potential participants who also meet the criteria. This sampling method is often used when the target population is difficult to reach or identify, such as in hidden or marginalized communities.
D. Simple random sampling involves randomly selecting individuals from the population without any specific stratification or deliberate imbalance. Each individual in the population has an equal chance of being selected.
Given the description provided, the sampling method of intentionally selecting 50% straight and 50% LGBTQ+ respondents represents disproportionate stratified sampling.
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Which best explains whether a triangle with side lengths 2 in., 5 in., and 4 in. is an acute triangle?
The triangle is acute because 22 + 52 > 42.
The triangle is acute because 2 + 4 > 5.
The triangle is not acute because 22 + 42 < 52.
The triangle is not acute because 22 < 42 + 52.
Answers
Answer:
The second one. (The triangle is not acute because 2+4>5)
Step-by-step explanation:
If you try to make the triangle, one angle would be obtuse so it's not acute.
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What is the error in the solution of the proportion shown at the right?
A. The second line should be 2x + 18 = 3x making the final answer 18 = x
B. The second line should be 2x + 27 = 3x making the final answer 27= x
C. The second line should be 3x + 9 = 2x making the final answer 9 = x
D. There is no error
Answers
The error in the proportion is the second line should be 2x + 18 = 3x making the final answer 18 = x
The error in the solution of the proportion shown can be calculated as follows:
Therefore, let's solve the equation to know the error made.
2 / 3 = x / x + 9
cross multiply
2(x + 9) = 3x
open the brackets
2x + 18 = 3x
subtract 2x from both sides of the equation
2x + 18 = 3x
2x - 2x + 18 = 3x - 2x
x = 18
Therefore, he made mistake in the second line, it should be 2x + 18 = 3x making the final answer 18 = x
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problem 2. (1 point) you are hosting a party with 80 fellow students from uci (including yourself the number of students is 81). as the party organizer, you shake hands with every guest to welcome them. moreover, there are a lot handshakes among the guests as well (e.g., to say hello or introduce themselves). if you do not know the total number of handshakes, can you be certain that there are at least two guests who had the same number of handshakes?
Answers
Yes, you can be certain that there are at least two guests who had the same number of handshakes. This is due to the Pigeonhole Principle.
As the party organizer, you shake hands with all 80 guests, which means you have 80 handshakes. The guests can have a minimum of 0 handshakes (if they don't shake hands with anyone except you) and a maximum of 79 handshakes (if they shake hands with everyone except themselves). There are 80 guests (excluding yourself), so there are 80 "pigeonholes" for the number of handshakes. The range of possible handshakes among the guests is from 0 to 79, which creates 80 possible outcomes or "pigeons."
According to the Pigeonhole Principle, if there are n pigeonholes and n+1 pigeons, at least one pigeonhole must contain at least two pigeons. In this case, there are 80 pigeonholes (guests) and 80 pigeons (possible handshakes). Therefore, at least two guests must have had the same number of handshakes.
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A movie with an aspect ratio of 1.85:1 is shown as a letterboxed image on a newer 50-inch 16:9 television. Calculate the height of the image, the height of each barely visible black bar at the top and bottom of the screen, and the percent of the screen’s area that is occupied by the image. Use a variety of representations to justify your response.
Answers
The aspect ratio of a Television is the ratio of the width to the height of the television.
The height of image on the 50-inch television is 24.48 inchesThe height of each black bar is 23.52 inchesThe percentage of the screen area occupied is 96.08%The size of a TV is calculated using Pythagoras theorem. Assume the length ratio of the new 50-inch 16:9 TV is x.
The ratio is represented as:
\(Width : Height = 16 : 9\)
Using Pythagoras theorem, we have:
\((16x)^2 + (9x)^2 = 50^2\)
\(256x^2 + 81x^2 = 2500\)
\(337x^2 = 2500\)
Divide both sides by 337
\(x^2 = 7.42\)
Take square roots of both sides
\(x = \sqrt{7.42\)
\(x = 2.72\)
So, the width of the image is:
\(Width = 16x\)
\(Width = 16 \times 2.72\)
\(Width = 43.52\)
The height of the image is then calculated as:
\(Height = 9x\)
\(Height = 9 \times 2.72\)
\(Height = 24.48\)
The height of the image is 24.48 inches
The height of each black bar is calculated as follows:
\(Width : Height = 1.85 : 1\)
Express as fraction
\(\frac{Height}{Width}= \frac{1}{1.85}\)
Make Height the subject
\(Height = \frac{1}{1.85}\times Width\)
Substitute \(Width = 43.52\)
\(Height = \frac{1}{1.85}\times 43.52\)
\(Height = 23.52\)
The height of each black bar is 23.52 inches
Lastly, the percentage of the screen’s area that is occupied by the image
First, we calculate the area of the bars
\(A_1 = Height \times Width\)
Where:
\(Height = 23.52\) and \(Width = 43.52\)
So:
\(A_1 = 23.52 \times 43.52\)
\(A_1 = 1023.59\)
Next, calculate the area of the 50-inch TV
\(A_2 = Height \times Width\)
Where
\(Width = 43.52\) and \(Height = 24.48\)
So:
\(A_2 = 24.48 \times 43.52\)
\(A_2 = 1065.37\)
So, the percentage occupied on the screen area is:
\(\% Screen = \frac{A_1}{A_2} \times 100\%\)
\(\% Screen = \frac{1023.59}{1065.37} \times 100\%\)
\(\% Screen = \frac{102359}{1065.37} \%\)
\(\% Screen = 96.08 \%\)
Hence, the percentage of the screen area occupied is 96.08%
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When solving for a variable in an equation, what must be achieved as a final answer?
A
More than one variable on both sides.
B
Coefficient one one side; formula on the other.
C
Variables and numbers on both sides.
D
Variable on one side; formula on the other.
Answers
Answer:
D is the correct answer.
Hope it helps!!
Answer:
im not sure but i think its b
These box plots show the basketball scores for two teams.
Which statement is the most appropriate comparison of the spreads?
Answers
Answer: The interquartile range (1QR) for the Bulldogs, 20, is less than the IQR for the Wolverines , 30.
Step-by-step explanation:
identify the proportional relationship.
1. y = x + 2
2. y = -x
3. x = 2
4. y = -2x - 1
Answers
Answer:
y = -x
Step-by-step explanation:
Answers 1 and 4 have an offset (+2 and -1) that interferes. x = 2 is not a proportion. It is simply a statement that x = 2. It is not allowed in the high stakes room.
The cost of a cake is twice that of a cup of tea.
1 cake and 5 cups of tea cost £21.
How much does a cake cost?
Answers
Answer:
The cake cost $6.00
Step-by-step explanation:
Let c = the cost of the cake
Let t = the cost of the tea
c = 2t
c + 5t = 21 Substitute 2t for c
2t + 5t = 21 Combine like terms
7t = 21 Divide both sides by 7
\(\frac{7t}{7}\) = \(\frac{21}{7}\)
t = 3
A cup of tea costs $3.00
c = 2t Substitute 3 for t
c = 2(3)
c = 6
A cake costs $6.00
Answer:
Cake: £6
Step-by-step explanation:
1c = 2t Eq. 1
1c + 5t = 21 Eq. 2
c = cost of a cake
t = cost of a cup of tea
Replacing Eq. 1 in Eq 2:
2t + 5t = 21
7t = 21
t = 21/7
t = 3
From Eq. 1:
c = 2t
c = 2*3
c = 6
Check:
From Eq. 2:
c + 5t = 21
6 + 5*3 = 21
6 + 15 = 21
1
Select the correct answer from each drop-down menu.
The function ($) = 38 has been transformed, resulting in function h.
h(s) = -(* + 2) - 4
To create function h function was translated 2 units
V, translated 4 units
and reflected across the
Reset
Next
Answers
Answer: up
Step-by-step explanation: good
Which expression is equivalent to 5 a + 20?
5 (5 a + 4)
5 (a + 4)
5 (a + 20)
5 (a + 1)
Answers
Answer:
It's B
Step-by-step explanation:
I took the quiz and I'm just good at math.
PLEASE HELP SOMEONE NEED TO DRAW A NUMBER LINE!!!
Answers
Answer=30 I think
Step-by-step explanation:
Blue card chances: 5/25=%20 Afterwards: 4/25=%16/2=%8
Red card chances: 12/25=%48 Afterwards: 11/25=%44/2=%22
Green card chances: 8/25=%32
Red and Blue card chances: %68
Answer=30 I think
For any events A and B with P(B)>0, show that P(A∣B)+P(A
′
∣B)=1 (Hint: use the conditional probability formula, distributive law and axiom 3 of probability)
Answers
To prove the statement using the given hint, we'll use the conditional probability formula and the properties of probability axioms. Let's proceed with the proof:
1. Conditional Probability Formula:
The conditional probability of event A given event B is defined as:
P(A|B) = P(A ∩ B) / P(B)
2. Law of Total Probability:
According to the Law of Total Probability, for any two events A and B:
P(A) = P(A ∩ B) + P(A ∩ B')
3. Axiom 3 of Probability:
The probability of the sample space Ω is 1, i.e., P(Ω) = 1.
Now, let's proceed with the proof:
We need to show that P(A|B) + P(A'|B) = 1.
Using the conditional probability formula:
P(A|B) = P(A ∩ B) / P(B) ---(1)
P(A'|B) = P(A' ∩ B) / P(B) ---(2)
Using the Law of Total Probability:
P(A) = P(A ∩ B) + P(A ∩ B') ---(3)
From equation (3), we can rewrite P(A ∩ B') as:
P(A ∩ B') = P(A) - P(A ∩ B)
Now, substituting this value in equation (2):
P(A'|B) = (P(A' ∩ B)) / P(B)
= (P(A) - P(A ∩ B)) / P(B) ---(4)
Adding equations (1) and (4), we have:
P(A|B) + P(A'|B) = (P(A ∩ B) / P(B)) + ((P(A) - P(A ∩ B)) / P(B))
= (P(A ∩ B) + P(A) - P(A ∩ B)) / P(B)
= P(A) / P(B)
Now, using the Axiom 3 of Probability:
P(A) / P(B) = P(A) / (P(B) + P(B')) ---(5)
Using the Law of Total Probability:
P(B) + P(B') = P(Ω) = 1
Substituting this value in equation (5):
P(A) / (P(B) + P(B')) = P(A) / 1 = P(A)
Therefore, we have:
P(A|B) + P(A'|B) = P(A)
Since the sum of the probabilities of mutually exclusive events is 1, we can conclude that:
P(A|B) + P(A'|B) = 1
Hence, the statement is proven.
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If 25 gallons of gasoline has been used after driving 700 miles,how many gallons of gasoline would be used after driving 1,000 miles?
Answers
six upright dominos of increasing height are lined up to be knocked down.The dominos sre numbered 0 to 5.The smallest domino number 0 is 5.00 cm tall and will be toppled by a person to start the chain reaction.Each subsequent domino 13% taller than the one before what is the height of domino number 5?
Answers
Answer:
Approximately 9.23 cm
Step-by-step explanation:
We can start by finding the height of each domino in the chain, starting with domino 0, which is 5.00 cm tall.
Let h be the height of domino 5. Then we can express the height of each domino in terms of h as follows:
Domino 0: 5.00 cm
Domino 1: 1.13 * 5.00 = 5.65 cm
Domino 2: 1.13 * 5.65 = 6.38 cm
Domino 3: 1.13 * 6.38 = 7.21 cm
Domino 4: 1.13 * 7.21 = 8.16 cm
Domino 5: 1.13 * 8.16 = h cm
Since we know that domino 5 is the tallest domino and is number 5 in the sequence, we can set the height of domino 5 equal to h and solve for h:
h = 1.13 * 8.16
h ≈ 9.23 cm
Therefore, the height of domino 5 is approximately 9.23 cm.
help pls m? find the QW
Answers
Answer:42
Step-by-step explanation:eh i just eyeballed it
Answer:
The answer is d, 23. This is because the whole line is 65, and the part that QW is not is 42. If you want to find QW, subtract 42 from 65, which is 23.
Step-by-step explanation:
find the area under the standard normal curve over the interval specified below to the right of z=3
Answers
The standard normal curve, also known as the standard normal distribution or the z-distribution, is a specific probability distribution that follows a bell-shaped curve. The area under the standard normal curve to the right of z = 3 is approximately 0.0013.
For the area under the standard normal curve to the right of z = 3, we need to calculate the cumulative probability from z = 3 to positive infinity.
The standard normal distribution, also known as the z-distribution, has a mean of 0 and a standard deviation of 1. It is a symmetric bell-shaped curve that represents the distribution of standard scores or z-scores.
Using statistical tables or software, we can find the cumulative probability associated with z = 3, which represents the area under the curve to the left of z = 3.
The cumulative probability for z = 3 is approximately 0.9987.
For the area to the right of z = 3, we subtract the cumulative probability from 1.
Therefore, the area to the right of z = 3 is approximately 1 - 0.9987 = 0.0013.
In conclusion, the area under the standard normal curve to the right of z = 3 is approximately 0.0013.
This means that the probability of randomly selecting a value from the standard normal distribution that is greater than 3 is approximately 0.0013 or 0.13%.
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Identify the cross section that results from slicing the three-dimensional figure.
A) pyramid
B) prism
C) square
D) triangle
Answers
For cross-sectional slicing of the three-dimensional figure is that is a square. Thus option C is correct.
What is cross-section slicing ?As per the figure, cross-sectional slicing means the division of the three-dimension into half and they are divided into the 3D view thus forming a square.
All the 3 dimension figures include the cone, rectangle, and triangle. The volume of space that the cross-section of the plane makes tells us about the figure.
Hence the options square is correct as it makes the 3D view from the base of the triangle figure.
Find out more information about the cross-section.
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what is 2 + 2 plssssssssssssssss i need help itsso hard my brain broken and cannot do it so good so sory guys i cannot do it sory
Answers
Answer:
2+2 is 4
Step-by-step explanation:
2
+2
___
4
Answer:
4
2 is the same 1+1
1 + 1 + 1 + 1 =4
Hope this helps!
if the population average is 45, the sample mean is 50, and the standard error of the mean is 5, what is the observed z value?a. 0b. -1c. 1d. 2
Answers
The observed z value is 1. Therefore, the given option that falls under the criteria of the correct answer is Option C.
To find the observed z value we have to use the principles to create a formula.
The formula for finding the value of z is
z = ( x - μ)/(σ/√n)
here,
x = sample mean
μ = population mean
σ = standard deviation of the population
n = sample size
for the given question the values are
x = 50
μ = 45
σ = 5
n = 1
staging the values in the formula
z = (50-45)/(5/√1)
z = 1
The observed z value is 1. Therefore, the given option that falls under the criteria of the correct answer is Option C.
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What is the slope of the line that passes through the points (3,-1) and (-2. -5)?
A -5/4
B -4/5
C 4/5
D 5/4
Answers
Answer:
Step-by-step explanation:
2222222
Answer:
Brainliest???
C 4/5
Step-by-step explanation:
Positive slope b/c it goes up
Used rise over run
Select the sequences that are geometric.
18, 36, 54, 72, …
4.1, 8.2, 16.4, 32.8, …
–7, 14, –28, 56, …
980, 784, 627.2, 501.76, …
5, 2, –1, –4, …
Answers
Answer:
BCD
Step-by-step explanation:
Answer: B,C & D
Step-by-step explanation:
Which of the following statements about frequency polygons are true? Multiple Choice a. Frequency polygons do not show the shape of a distribution b. A frequency polygon is a graph of a bar chart c. The frequencies of each class are graphed at the midpoint of each class d. Frequency polygons represent each class as a rectangle
Answers
Statements A and C are true about frequency polygons, while statements B and D are false.
Frequency polygons are a type of graph that displays frequency data in a series of data points. Frequency polygons are also known as line graphs. Below are the following true statements about frequency polygons:
Statement C is correct. The frequencies of each class are graphed at the midpoint of each class. This is the most essential feature of frequency polygons. The midpoints are joined by straight lines. The horizontal axis represents the variable being measured, and the vertical axis represents the frequency of occurrence. In this sense, frequency polygons are similar to histograms.Statement A is false. The shape of a distribution can be easily seen on a frequency polygon. The jagged shape of the polygon illustrates the skewness or normalcy of the distribution. The distribution's form can be determined using this chart, making it an essential data analysis tool.
Statement B and D are false. A frequency polygon is not a graph of a bar chart, and it does not represent each class as a rectangle. The bars are replaced with straight lines that connect points. The distance between the points represents the class width, whereas the height represents the frequency of the class.
To conclude, statements A and C are true about frequency polygons, while statements B and D are false.
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5,678.321 what is the place value of the 2
Answers
Answer:
20
Step-by-step explanation:
Answer:
Step-by-step explanation:
Hundredths
Solve the equation t - 8 = -3.
Answers
Answer: \(t=5\)
Add 8 to both sides
\(t-8+8=-3+8\\t=5\)
Answer:
The correct answer is t = 5.
Step-by-step explanation:
To solve this question, we must first recognize that our goal is to get the variable t by itself. To do this, we should add 8 to both sides of the equation to get rid of the -8 on the left side of the equation. This is modeled below:
t - 8 = - 3
t - 8 + 8 = -3 + 8
t = 5
Therefore, the correct answer is t = 5.
If we want to check our answer, we can plug in 5 for t in the original equation. If we do this, we get: 5 - 8 = -3, which is a true statement, so we know that we did the problem correctly.
Hope this helps!
a class rolled number cubes. their results are shown in the table. what is the experimental probability of rolling the number 3? round your answer to the nearest tenth.
Answers
The experimental probability of rolling the number 3 is approximately 0.2
Experimental probability is the ratio of the number of times an event occurs to the total number of trials or observations conducted in an experiment or a trial. It is an estimate of the probability of an event based on the actual outcome of a series of trials or experiments.
To find the experimental probability of rolling the number 3, we need to divide the number of times the number 3 occurred by the total number of rolls.
From the table, we can see that the number 3 occurred 45 times. The total number of rolls is
42 + 44 + 45 + 44 + 47 + 46 = 268
So, the experimental probability of rolling the number 3 is
45/268 = 0.168 (rounded to the nearest tenth)
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The given question is incomplete, the complete question is:
A class rolled number cubes. their results are shown in the table. what is the experimental probability of rolling the number 3? round your answer to the nearest tenth.
