Answer:
4
Step-by-step explanation:
4-0=4
Answer:
4 left
Step-by-step explanation:
then you have 4 apples
Which rule yields the dilation of the figure KLMN centered at the origin? Responses A (x, y) → (x + 0. 5, y + 0. 5)(x, y) → (x + 0. 5, y + 0. 5) B (x, y) → (0. 5x, 0. 5y)(x, y) → (0. 5x, 0. 5y) C (x, y) → (x + 2, y + 2)(x, y) → (x + 2, y + 2) D (x, y) → (2x, 2y)(x, y) → (2x, 2y)
The rule that yields the dilation of the figure KLMN centered at the origin is (x, y) → (2x, 2y). So, the correct answer D).
In this question, we are looking for the rule that yields the dilation of the figure KLMN centered at the origin. Option D, (x, y) → (2x, 2y), represents a dilation by a scale factor of 2, which means that the image will be twice as large as the original figure. Thus, option D is the correct answer.
This rule doubles the distance of each point from the origin and results in an image that is twice as large as the original figure. Rule A translates the figure up and to the right, while Rule B halves the coordinates of each point, resulting in an image that is half as large. Rule C translates the figure to the right and up by 2 units.
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At noon, a barista notices that she has $10 in her tip jar. If she makes an average of $0. 75 from
each customer, how much will she have in her tip jar if she serves more customers during her
shift?
The total amount of money she would have at the end of her shift would be 0.75x + 10
If the barista makes an average of $0.75 from each customer and she has $10 in her tip jar at noon, we can use this information to estimate how much money she will have at the end of her shift if she serves more customers.
Let's assume that the barista serves "x" more customers during her shift, and that each customer gives her an average of $0.75 in tips. The total amount of money she would make from the tips of these "x" customers would be 0.75x.
Adding the $10 she already has in her tip jar, the total amount of money she would have at the end of her shift would be:
Total = 0.75x + 10
The amount of money the barista would have at the end of her shift would depend on the number of customers she serves after noon. For instance, if she serves 20 more customers after noon, then the total amount of money she would have at the end of her shift would be:
Total = 0.75(20) + 10 = $25
Therefore, the amount of money the barista would have in her tip jar at the end of her shift depends on the number of customers she serves and the amount of money each customer gives her in tips.
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if your math class had a greater standard deviation for the first quiz of the unit than they did for the second quiz of the unit, what would this tell you?
A greater standard deviation for scores on the first quiz than on the second quiz would state that the results were less consistent on the first quiz than on the second quiz.
How to calculate the mean and the standard deviation of the data-set?The mean of a data-set is given by the sum of all observations in the data-set divided by the number of observations, which is also called the cardinality of the data-set.The standard deviation of a data-set is given by the square root of the sum of the differences squared between each observation and the mean, divided by the cardinality of the data-set.The standard deviation of a data-set measures the consistency of the data-set, and the higher the standard deviation, the less consistent the data-set is.
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please answer this .............
he coordinates of three corners of a square are (–2, 0), (1, 0), and (1, –3). Use this information to complete the following tasks.
Graph the three points given.
Determine the coordinates of the fourth corner of the square.
Draw the square.
Determine the perimeter of the square.
The coordinates of point D on the graph are (2,-2). the square has a surface area of 25 square units. The perimeter of the square p is 20 units.
How to plot the coordinate on the graph?A (2,3), B (-3, 3), and C (-3, -2) are the given points.
In the graph below, the points are plotted.
The coordinates of point D on the graph are (2,-2).
In this case, AB = 5 units [from the graph].
The square's area = side * side
ABCD's square area = AB *AB
= 5×5
= 25 square units.
As a result, the square has a surface area of 25 square units.
The perimeter of the square p = 4 * side
p = 4 *5 = 20 units.
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Similar question:
The three vertices of a square are A (2,3), B(-3, 3), and C (-3, -2). Plot these points on graph paper and
hence use it to find the coordinates of the fourth vertex. Also, find the area and perimeter of the square.
what is the surface area of a composite figure (square pyramid and rectangular prism) with the dimensions length 6 width 6 height 12 triangle height 4 slant height 5
The total surface area to paint is 22000 sq. ft.
What is surface area?Surface area is the measurement of the outer surface of an object. It is often used to calculate the area of a three-dimensional object, such as a cube, cylinder, or sphere, and is also used to calculate the area of the faces of a solid object. Surface area is measured in square units such as square centimeters (cm2), square meters (m2), or square inches (in2).
Surface Area = 2(lw + lh + wh)
Surface Area = 2((100' x 50') + (100' x 40') + (50' x 40'))
Surface Area = 2(5000' + 4000' + 2000')
Surface Area = 2(11000')
Surface Area = 22000 sq. ft.
Answer: The total surface area to paint is 22000 sq. ft.
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Answer:
2200
Step-by-step explanation:
students conducted a survey and found out that 18% of their peers on campus go home every weekend but only 3% rides the public transportation. if 100 students were surveyed, can these students use the normal approximation to study the proportion of students in the population who go home every weekend?
To determine whether the normal approximation can be used to study the proportion of students in the population who go home every weekend, we need to check if the sample size is large enough and if the success-failure condition is met.
Sample size: A commonly used rule of thumb is that the sample size should be at least 10 times the number of successes and failures combined. In this case, the number of students who go home every weekend in the sample is 18, and the number who do not is 82. So the sample size is 100, which is greater than 10 times the number of successes and failures combined.
Success-failure condition: Another assumption for the normal approximation is that the sample proportion is not too close to 0 or 1. In this case, the sample proportion of students who go home every weekend is 18/100 = 0.18, and the proportion who do not is 0.82. Both proportions are between 0.1 and 0.9, so the success-failure condition is met.
Therefore, we can use the normal approximation to study the proportion of students in the population who go home every weekend.
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Use the following data to answer questions 1-2.
1. Find the median, mean, and range of the elephant ages.
a) Median:.
b) Mean:,
Ages of 10 elephants (in years) living in zoos:
28, 14, 19, 20, 21, 28, 33, 36, 41
c) Range:.
years
years
years
Answer:
median - 28
mean - 26.6 (6 repeating)
range - 27
Step-by-step explanation:
The elephant ages would go in the order of 14, 19, 20, 21, 28, 28, 33, 36, 41. To find the median, you need to look for the center of the numbers, which would be 28, since 28 is the middle number. To find the mean, you add all the numbers up and divide them by however many numbers there are, in this case, they add up to 240, and there is 9 numbers, so you would do 240 divided by 9 = 26.66 (repeating so a line over the 6's after the decimal) and to find the range you subtract the highest number and the lowest, which is 41 and 14 and that would give you 27.
I'M SO SORRY IF THIS DIDN'T MAKE SENSE!
The Wigwam Motel in Holbrook, Arizona is famous for its large tepees, which are shaped like cones. Each of these units has a base diameter of 14 feet and a height of 32 feet. (a) What is the slant height of the Teepees at the Wigwam Motel? Please make sure to use the Pythagorean Theorem and show your work. (b) (1. 5 pts) For extra credit, how much floor space, in square units, is available inside each tepee?
The Wigwam Motel in Holbrook, Arizona is famous for its large tepees shaped like cones. the floor space inside each tepee is approximately 153.94 square feet.
(a) To find the slant height of the tepee, we can use the Pythagorean theorem. The slant height is the hypotenuse of a right triangle with the height and the radius of the base as the legs.
The radius of the base is half of the diameter, so r = 14/2 = 7 feet. The height of the tepee is 32 feet. Let's call the slant height "s".
Using the Pythagorean theorem, we have:
s² = r² + h²
s² = 7² + 32²
s² = 49 + 1024
s² = 1073
s = sqrt(1073)
s ≈ 32.77 feet
Therefore, the slant height of the tepee is approximately 32.77 feet.
(b) To find the floor space inside the tepee, we need to calculate the area of the circular base. The formula for the area of a circle is A = πr², where A is the area and r is the radius.
A = π(7)²
A = 49π
A ≈ 153.94 square feet
Therefore, the floor space inside each tepee is approximately 153.94 square feet.
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HELPP
Find the area of this shape:
Answer:
67 [tex]ft^{2}[/tex]
Step-by-step explanation:
Divide the shape into more recognizable shapes.
5*7 = 35
7*4 = 28
35+28
67
The graph below does not represent a function because it fails the vertical-line test. Which is the best explanation of why a graph that fails the vertical line test does not represent a function? A. If a vertical line intersects a graph more than once, this indicates that there are multiple points with the same y-value. A function cannot have repeated y-values. B. On a vertical line, one x-value is paired with many y-values. A function cannot have one x-value paired with different y-values, so a vertical line is not a function. C. The points where a vertical line intersects a graph have the same x-value but different y-values. The graph of a function cannot have points with the same x-value but different y-values. D. The relation represented by a vertical line maps many x-values to the same y-value. This kind of mapping is not a function. So if a graph intersects a vertical line more than once, that graph is not a function either.
As a result, choice B adequately justifies why a graph that fails the vertical line test cannot be used to represent a function.
what is a function?A function in mathematics is a rule or association that gives each input value a distinct output value. A function, then, is a collection of ordered pairs, each pair consisting of an input value (also known as an argument or predictor variable) and the control signal value (also known as the value or dependent variable). The output value for each given input value can be found using the formula or graph of a function.
Option B provides the justification for why a graph that fails the vertical line test cannot be used to represent a function: One x-value is coupled with numerous y-values on a vertical line.
A vertical line is not a function since a function cannot have one x-value associated with multiple separate y-values.
To ascertain whether a graph accurately depicts a function, use the vertical line test.
Each vertical line that crosses the graph more than once has an x value and several y values, which is against the definition of a function.
As a result, choice B adequately justifies why a graph that fails the vertical line test cannot be used to represent a function.
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Sandy used a virtual coin toss app to show the results of flipping a coin 100 times, 500 times, and 1,000 times. Explain what most likely happened in
Sandy's experiment.
O Sandy's experimental probability was closest to the theoretical probability in the experiment with 100 flips.
O Sandy's experimental probability was closest to the theoretical probability in the experiment with 500 flips.
O Sandy's experimental probability was closest to the theoretical probability in the experiment with 1,000 flips.
Sandy's experimental probability was exactly the same as the theoretical probability for all three experiments.
And please give me the answer
Answer: option C - Sandy's experimental probability was closest to the theoretical probability in the experiment with 1,000 flips, is the most likely scenario.
Step-by-step explanation:
Based on the Law of Huge Numbers, the more times a coin is flipped, the closer the test likelihood will be to the hypothetical likelihood of 0.5 for heads and 0.5 for tails. In this manner, Sandy's exploratory likelihood is most likely to be closest to the hypothetical likelihood within the test with 1,000 flips.
In spite of the fact that it is conceivable that Sandy's exploratory likelihood might be near to the hypothetical likelihood within the explore with 100 flips or 500 flips, it is more likely that the bigger test measure of 1,000 flips will result in a more precise representation of the hypothetical likelihood.
select all that applywith weighted moving averages, how are the weights selected?multiple select question.trial and errorfitting to a regression lineguessingexperience
The weights in a weighted moving average are selected by: Trial and error, Fitting to a regression line, Guessing, Experience.
The methods for selecting weights in weighted moving averages are trial and error, fitting to a regression line, and experience.
When selecting weights for weighted moving averages, the following methods can be used:
Trial and error:
Testing different weight combinations to find the best fit for the data.
Fitting to a regression line:
Analyzing the relationship between the data points and assigning weights accordingly.
Experience:
Using prior knowledge and understanding of the data or similar situations to determine appropriate weights.
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Trial and error fitting, fitting to a regression line, and experience are the methods that can be used to select weights in a weighted moving average.
With weighted moving averages, the weights can be selected using various methods. Here are the applicable methods from your given options:
1. Trial and error fitting: Weights can be selected by testing different combinations of weights and observing their impact on the accuracy of the model.
2. Fitting to a regression line: Weights can be determined by fitting a regression line to the data and using the coefficients of the regression line as the weights.
3. Experience: Domain knowledge or past experience with similar data can help in selecting appropriate weights.
In summary, trial and error fitting, fitting to a regression line, and experience are the methods that can be used to select weights in a weighted moving average.
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Complete the table for factoring the trinomial −+x squared , minus 7 x plus 12
The factored form of the trinomial x² - 7x + 12 is (x - 3)(x - 4).The involved trinomial is x² - 7x + 12.
How to calculate the factored form of trinomial?Here is a detailed explanation:
a = 1 (coefficient of x²),
b = -7 (co - efficient of x), and
c = 12 are the trinomial's coefficients and constant (constant term).
Step 2: Find two numbers that multiply to a*c (1*12) and add up to b (-7).
The two numbers are -3 and -4.
Step 3: Modify the middle word as x²- 3x - 4x + 12 using the two integers
Step 4: Factor by grouping. Group the first two terms and the last two terms separately: (x² - 3x) + (-4x + 12).
Step 5: Factor out the greatest common factor (GCF) from each group: x(x - 3) - 4(x - 3).
Step 6: Factor out the common binomial (x - 3) from both terms: (x - 3)(x - 4).
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Can someone check if I’m right on all of these!?
If not please correct me, I have a test tomorrow :( thank youuu <3
Results from the Simple Interest:
1. The amount Tucker will receive in interest after 5 years = $1,165.50.
2 The simple interest rate Wilson would need to make his $9,000 grow to $85,000 in 16 years = 53%.
3. The number of years it will take for $7,000 to double in an account with 2.8% simple interest = ≈36 years.
4. The ending balance after 6 years = $25,472.
How to calculate Simple interest?Using Simple interest formula: S.I. = P × R × T
Simple interest (SI) formular = Interest (I) = Principal (P) * Rate (R) * Time(T)
Given:
P= $7,400
R = 3.15% or 0.0315
T = 5 years
Plugging in the values:
Interest = ($7,400 * 0.0315 * 5)
Interest = $1,165.50
2) Using SI formular: I = P* R * T
Given:
P = $9,000
I = $85,000 - $9,000 = $76,000 (as the total cost is the principal plus interest)
T = 16 years
Plugging in the values:
$76,000 = $9,000 * Rate * 16
R = $76,000 / ($9,000 * 16)
To convert to percentage, we multiply by 100:
Rate = 0.531 * 100
Rate = 53.1%.
3) Using SI formular: I = P* R * T
Given:
P = $7,000
R = 2.8%
I = P
T = ?
Plugging in the values and solving for Time (T):
$7,000 = $7,000 * 0.028 * T
T = $7,000 / ($7,000 * 0.028) = 35.7
T ≈36 years
4. Using SI formular: I = P* R * T
Given:
P = $20,000
R = 4.56%
T = 6 years
Plugging in the values:
P = $20,000
R = 4.56% or 0.0456
T = 6 years
Ending Balance (EB) = P + (Pl * R * T)
EB = $20,000 + ($20,000 * 0.0456 * 6)
EB = $20,000 + $5,472
EB = $25,472
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Solve: 11x - 24 = 7x + 76
Answer:
[tex] \sf \: x = 25[/tex]
Step-by-step explanation:
Now we have to,
→ Find the required value of x.
The equation is,
→ 11x - 24 = 7x + 76
Then the value of x will be,
→ 11x - 24 = 7x + 76
→ 11x - 7x = 76 + 24
→ 4x = 100
→ x = 100 ÷ 4
→ [ x = 25 ]
Hence, the value of x is 25.
Hello and greetings Brainly users.
Answer:Therefore, the solution to the equation is x = 25.Step-by-step explanation:It is an exercise of linear equations with one variable is a fundamental topic in the study of algebra. These types of equations are characterized by being first-degree polynomials in one variable, and can be found in various contexts, such as physics, economics, engineering, among others. Therefore, the ability to solve these equations is essential in the training of any mathematics student and in the development of their ability to solve problems in real life situations.
A linear equation with a variable can be solved by means of a series of algebraic operations that allow us to simplify the expression and clear the variable to be solved. These operations include adding, subtracting, multiplying, and dividing, always maintaining equality between both sides of the equation. The ultimate goal is to find the numerical value that satisfies the equation, that is, the value that makes the equality true.
Solving linear equations with one variable is an important skill not only for mathematics students, but also for professionals in various fields. For example, in engineering, linear equations are used to model physical systems and phenomena, and their resolution is necessary to perform calculations and make informed decisions. In the economy, they are used to analyze the behavior of financial variables and make projections for the future.
Now we solve our exercise:
To solve the equation 11x - 24 = 7x + 76 we need to isolate the variable x on one side of the equation.
First, we can simplify both sides of the equation by combining like terms:
11x - 7x = 76 + 24
Which gives us
4x = 100
Next, we can solve for x by dividing both sides of the equation by 4:
4x/4 = 100/4
x = 25
Therefore, the solution to the equation is x = 25.
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A florist wants to determine if a new additive would help extend the life of cut flowers longer than the original additive. The florist randomly selects 20 carnations and randomly assigns 10 to the new additive and 10 to the original additive. After three weeks, 6 carnations placed in the new additive still looked healthy and 2 carnations placed in the original additive still looked healthy. The difference in proportions (new – original) for the carnations that still looked healthy after three weeks was 0. 4. Assuming there is no difference in the additives, 200 simulated differences in sample proportions are displayed in the dotplot. Using this dotplot and the difference in proportions from the samples, is there convincing evidence that the new additive was more effective?
A Yes, because a difference in proportions of 0. 4 or more occurred 7 out of 200 times, meaning the difference is statistically significant and the new additive is more effective.
B Yes, because a difference in proportions of 0. 4 or less occurred 193 out of 200 times, meaning the difference is statistically significant and the new additive is more effective.
C No, because a difference in proportions of 0. 4 or more occurred 7 out of 200 times, meaning the difference is not statistically significant and the new additive is not more effective.
D No, because a difference in proportions of 0. 4 or less occurred 193 out of 200 times, meaning the difference is not statistically significant and the new additive is not more effective
Yes, since the new additive is more efficient and a proportional difference of 0.4 or more occurred 7 times out of 200, making the difference statistically significant. The correct answer is A) .
The dotplot can be used to determine whether the 0.4 observed proportional difference is statistically significant. Few dots are at or above 0.4 in any direction, as can be seen by looking at the dotplot. In particular, it appears that there are no dots to the left of the observed difference and only roughly 7 dots that are at or beyond 0.4. Therefore, at the 5% level of significance, the observed proportional difference of 0.4 is statistically significant. Hence the correct answer is option: A.
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Tangent ratios can be greater than or equal to 1 because...
Tangent ratios can be greater than or equal to 1 because acute angle is between 45 degrees and 90 degrees.
If the opposite side is longer than the adjacent side, then the tangent ratio will be greater than 1.
Similarly, if the opposite side is equal in length to the adjacent side, then the tangent ratio will be equal to 1.
In general, the tangent ratio can be greater than or equal to 1 when the opposite side is longer or equal in length to the adjacent side. This occurs when the acute angle is between 45 degrees and 90 degrees.
It is important to note that when the acute angle is less than 45 degrees, the tangent ratio will always be less than 1. Conversely, when the acute angle is greater than 90 degrees, the tangent ratio will be negative and less than 1.
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The Grandview high school band plans to play six pieces of music in their upcoming concert. How many ways can they manage the order of their performance?
There are 720 ways the Grandview high school band can manage the order of their performance of six pieces of music
To determine the number of ways the Grandview high school band can manage the order of their performance of six pieces of music, we need to find the number of permutations of six objects taken six at a time.
The following is the formula for the number of permutations of n objects taken r at a time:
P(n, r) = n! / (n - r)!
In this case, we need to find P(6, 6), which is:
P(6, 6) = 6! / (6 - 6)!
= 6! / 0!
= 6 x 5 x 4 x 3 x 2 x 1
= 720
Therefore, there are 720 ways the Grandview high school band can manage the order of their performance of six pieces of music.
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4 times 1/6 in fraction.
Answer:
4/6 or 2/3 simplified
Step-by-step explanation:
4 ⋅ 1/6=4/6
multiply numerators together and denominators together
4/6
simplify
2/3
Hope this helps :)
Destiny's mother started a college fund when Destiny was born. She deposited $9,300 into a CD (certicate of deposit) that yields an interest rate of 0.46%
compounded annually. How much money will the CD be worth when Destiny turns 16 years old?
Answer:
Step-by-step explanation:
$10,008.61
pls help asap!! Algebra 2 unit test on edge
The value of cotθ given that cscθ = 8/7 using trigonometric identities is √(15)/7.
To find the value of cotθ given cscθ = 8/7, we can use the relationship between trigonometric functions:
cscθ = 1/sinθ and cotθ = cosθ/sinθ
First, we can find the value of sinθ by using the definition of cscθ:
cscθ = 1/sinθ
8/7 = 1/sinθ
sinθ = 7/8
Next, we can use the value of sinθ to find the value of cosθ using the Pythagorean identity:
sin²θ + cos²θ = 1
cos²θ = 1 - sin²θ
cos²θ = 1 - (7/8)²
cos²θ = 1 - 49/64
cos²θ = 15/64
Taking the square root of both sides, we get:
cosθ = ±√(15)/8
Since cscθ is positive and cotθ is positive, we need to take the positive square root:
cosθ = √(15)/8
Finally, we can use the definition of cotθ to find the value of cotθ:
cotθ = cosθ/sinθ
cotθ = (√(15)/8) / (7/8)
cotθ = √(15)/7
In conclusion, to find the value of cotθ given cscθ, we can use the relationship between trigonometric functions and the Pythagorean identity to find the values of sinθ and cosθ, and then use the definition of cotθ to find its value.
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The words per and each are associated with ___________________
Answer:
The words "per" and "each" are associated with quantity and division. They are used to express the ratio or rate of one thing in relation to another. For example, "The cost is $10 per pound" or "Each student receives one book."
Answer:
The words per and each are associated with Division.
Step-by-step explanation:
Think of the words "percent". We can divide the word into two easier terms, "per" and "cent". Per means for each. Dividing also means for each.
I'm trying my best without an answer key to help me see what you want to be answered, let me know if there is something specific you would like to know. :)
-a friendly 8th grader :D
PLEASE ANSWER QUICK!!! 20 POINTS!!!!1
Suppose the length of voicemails (in
seconds) is normally distributed with a mean
of 40 seconds and standard deviation of 10
seconds. Find the probability that a given
voicemail is between 20 and 50 seconds.
10
20
30
40
P = [?]%
Hint: use the 68 - 95 - 99.7 rule.
50 60
70
Enter
Answer:
P=9600000000
Step-by-step explanation:
1 point is =0.150119
40x10=400x20=8000x50x400000x10=400000x20=800000x30=240000000x40=9600000000
given that tanα=4/3 (α is in Q1) and cosβ= -4/5 (β is in Q3), find cos(α+β)
Answer:
We can use the following formula for the cosine of the sum of two angles:
cos(α + β) = cos(α)cos(β) - sin(α)sin(β)
To use this formula, we need to find the values of cos(α), sin(α), cos(β), and sin(β).
Since tan(α) = 4/3 and α is in the first quadrant, we can use the Pythagorean identity to find sin(α) and cos(α):
tan^2(α) + 1 = sec^2(α)
(4/3)^2 + 1 = sec^2(α)
16/9 + 1 = sec^2(α)
25/9 = sec^2(α)
sec(α) = 3/5
cos(α) = 1/sec(α) = 5/3
sin(α) = tan(α) * cos(α) = (4/3) * (5/3) = 20/9
Since cos(β) = -4/5 and β is in the third quadrant, we can use the Pythagorean identity again to find sin(β):
sin^2(β) + cos^2(β) = 1
sin^2(β) = 1 - cos^2(β)
sin(β) = -√(1 - cos^2(β)) (since sin(β) is negative in Q3)
sin(β) = -√(1 - (-4/5)^2) = -√(1 - 16/25) = -√(9/25) = -3/5
Now we can substitute these values into the formula for cos(α+β):
cos(α + β) = cos(α)cos(β) - sin(α)sin(β)
cos(α + β) = (5/3) * (-4/5) - (20/9) * (-3/5)
cos(α + β) = -4/3 + 4/3
cos(α + β) = 0
Therefore, cos(α+β) = 0.
when flipping a coin 4 times. How many favorable outcomes are there for two heads and two tails (in any order)?
There are 6 ways to get two heads and two tails (in any order) when flipping a coin 4 times.
How many favorable outcomes are there for heads and tailsWhen flipping a coin 4 times, there are 2 possible outcomes (heads or tails) for each flip.
Therefore, there are a total of 2^4 = 16 possible outcomes for 4 coin flips.
To find the number of favorable outcomes for getting two heads and two tails (in any order), we can use combinations.
We need to choose 2 coin flips out of 4 to be heads, which can be done in C(4,2) = 6 ways.
Once we have chosen the positions for the heads, the remaining positions must be tails.
So there are 6 ways to get two heads and two tails (in any order) when flipping a coin 4 times.
These outcomes are:
HH-TT
HT-HT
TH-HT
TT-HH
HT-TH
TH-HT
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ABC is a right triangle.
AC = 12
CB = 9
Blank #1 Find AB Do not label
Blank #2. Find ∠A Round your answer to the nearest whole number. Do not include a degree sign
Blank #3 Find ∠C Round your answer to the nearest whole number. Do not include a degree sign.
Blank #4 Find ∠B Round your answer to the nearest whole number. Do not include a degree sign
a) The length of the hypotenuse AB is 15.
b) The angle ∠A is approximately 53 degrees.
c) The angle ∠C is 90 degrees.
d) The angle ∠B is approximately 37 degrees.
a) To find the length of the hypotenuse AB, we can use the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the legs is equal to the square of the hypotenuse. In this case, we have:
AB² = AC² + CB²
AB² = 12² + 9²
AB² = 144 + 81
AB² = 225
AB = √225
AB = 15
Therefore, the length of the hypotenuse AB is 15.
b) To find the angle ∠A, we can use trigonometry. The sine of an angle is the ratio of the opposite side to the hypotenuse. In this case, we have:
sin(∠A) = AC/AB
sin(∠A) = 12/15
sin(∠A) = 0.8
Taking the inverse sine of 0.8, we get:
∠A = sin⁻¹(0.8)
∠A ≈ 53
Therefore, the angle ∠A is approximately 53 degrees.
c) Since angle ∠C is the right angle, its measure is 90 degrees.
d) To find the angle ∠B, we can use the fact that the sum of the angles in a triangle is 180 degrees. Therefore:
∠B = 180 - ∠A - ∠C
∠B = 180 - 53 - 90
∠B ≈ 37
Therefore, the angle ∠B is approximately 37 degrees.
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Abiola left for work at 7.30a.m. On her way she wasted 20 minutes waiting for her friend and finally got to work at 8.20a.m. The work closes at 4p.m., but she stayed at work for 1 hou watching African Magic film on DSTV channel, and got back home at 6p.m. For how long did she stay at work?
Answer:
Abiola stayed at work for 8 hours and 40 minutes.
Step-by-step explanation:
Abiola wasted 20 minutes waiting for her friend, so she actually left for work at 7:50 am (7:30 am + 20 minutes).
She arrived at work at 8:20 am, so she spent 30 minutes (8:20 am - 7:50 am) traveling to work.
Abiola worked from 8:20 am to 4:00 pm, which is a total of 7 hours and 40 minutes (4:00 pm - 8:20 am).
She then stayed at work for an additional 1 hour to watch African Magic, so in total, she was at work for 8 hours and 40 minutes (7 hours and 40 minutes of work + 1 hour of watching African Magic).
Therefore, Abiola stayed at work for 8 hours and 40 minutes.
The Volume of a Rectangular prism is given by the expression LWH, What is its volume if L=1.2, W=3, H=2.5?
What solution please
an a normal distribution be used to approximate the distribution of the random variable x that counts the number of adults who have not visited a dentist in the last two years?
Yes, a normal distribution can be used to approximate the distribution of the random variable X, which counts the number of adults who have not visited a dentist in the last two years. This approximation can be done using the Central Limit Theorem (CLT), which states that if you have a large enough sample size, the distribution of the sample means will approach a normal distribution, regardless of the original distribution's shape.
To use a normal distribution for this approximation, you need to meet the following criteria:
1. The sample size (n) should be large enough, typically n > 30.
2. The random variable X should have a known mean (μ) and standard deviation (σ).
If these criteria are met, you can use the normal distribution to approximate the distribution of X by calculating the standard error (SE), which is equal to σ / √n. This will help you estimate probabilities and analyze the data for the number of adults who have not visited a dentist in the last two years.
In summary, using a normal distribution to approximate the distribution of the random variable X is possible through the Central Limit Theorem, as long as the sample size is large enough and the mean and standard deviation are known.
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