The unknown measures and angle measures are:
A. LH ≈ 45.68; m∠K ≈ 55°; m∠L ≈ 35°
How to find the unknown measures of the triangle?Trigonometry deals with the relationship between the ratios of the sides of a right-angled triangle with its angles.
The unknown measures of the triangle can be founding as follow:
LH² = 56² - 32.4² (Pythagoras Theorem)
LH = √(56²- 32.4²)
LH = 45.68 units
sin K = 45.68/56
K = sin⁻¹(45.68/56)
K ≈ 55°
Thus, m∠K ≈ 55°
sin L = 32.4/56
L = sin⁻¹( 32.4/56)
L ≈ 35°
Thus, m∠L ≈ 35°
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Triangle ABC was dilated with the origin as the center of dilation to create triangle A'B'C'. Write the rule that best represents the dilation that was applied to triangle ABC to create triangle A'B'C'. -10-9-S A B C
The rule of dilation is a dilation by a scale factor of 2
Determining the rule of dilationFrom the question, we have the following parameters that can be used in our computation:
ABC with vertices at A(1, 1)A'B'C' with vertices at A'(2, 2)The scale factor is calculated as
Scale factor = A'/A
Substitute the known values in the above equation, so, we have the following representation
Scale factor = (2, 2)/(1, 1)
Evaluate
Scale factor = 2
Hence, the rule of dilation is (2x, 2y)
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ASSAAP NEED HELPPPPPPPPP
The translation is of 5 units to the right and 3 units down, it can also be written as:
(x, y) ---> (x + 5, y - 3)
Which is the translation from F to G?To study the translation, just look at some vertex in both figures.
The top left vertex of F is at (2, 7)
And the top left vertex at G is (7, 4)
Taking the difference between these, we will get:
(7, 4) - (2, 7) = (5,, - 3)
Then the translation from F to G can be defined as:
(x, y) ---> (x + 5, y - 3)
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find the polynomial M if 2x^2 - 1/3ax + by - M = 0
Polynomial M is 2(x - [tex](\frac{1}{12}a)^{2}[/tex] - (1/72)[tex]a^{2}[/tex] + by
To find the polynomial M, we need to rearrange the equation given to us. We can start by adding M to both sides of the equation to isolate the constant term. This gives us:
2[tex]x^{2}[/tex] - (1/3)ax + by = M
Now, we have the polynomial M in terms of x, a, b, and y. However, this is not in its simplest form yet. We can simplify this further by factoring out the coefficient of x. This gives us:
2([tex]x^{2}[/tex] - (1/6)ax) + by = M
Now, we can complete the square inside the brackets to get a perfect square trinomial. This means taking half of the coefficient of x, squaring it, and adding it and subtracting it inside the brackets. This gives us:
2((x - [tex](\frac{1}{12}a)^{2}[/tex] - (1/144)[tex]a^{2}[/tex]) + by = M
Simplifying this further, we get:
2(x - [tex](\frac{1}{12}a)^{2}[/tex] - (1/72[tex]a^{2}[/tex] + by = M
Therefore, the polynomial M is given by:
M = 2(x - [tex](\frac{1}{12}a)^{2}[/tex] - (1/72)[tex]a^{2}[/tex] + by
This is the final answer for the polynomial M.
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What is the surface area of the triangular prism?
10 cm
5 cm
5 cm
5 cm
4 cm
The surface area of the triangular prism is 120 sq cm
What is the surface area of the triangular prism?From the question, we have the following parameters that can be used in our computation:
Dimensions = 10 cm 5 cm 5 cm 5 cm and 4 cm
Using the formula of the surface area of the triangular prism, we have
Surface area = bh + (l1 + l2 + l3) * h
Substitute the known values in the above equation, so, we have the following representation
Surface area = 10 * 5 + (5 + 5 + 4) * 5
Evaluate
Surface area = 120
Hence, the surface area is 120 sq cm
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A small sleepy town in California has been losing population since 1993. In 1993 the population was 10500 but it has been decreasing by about 5.2% per year.
If this trend continues, predict the population in 2018. Round your answer to the nearest integer.
The population of the town in 2018 will be 5,040.
To predict the population in 2018, we need to use the following formula:
Population in 2018 = Population in 1993 × (1 - rate of decrease)[tex].^n[/tex]
Here, the population in 1993 is 10,500, the rate of decrease is 5.2% or 0.052 (in decimal form), and the number of years from 1993 to 2018 is 25.
Substituting these values, we get:
Population in 2018 = 10,500 × (1 - 0.052)^25
= 10,500 × 0.480
= 5,040
Rounding this answer to the nearest integer, we get a predicted population of 5,040 in 2018.
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Mason is ordering a one-topping pizza. He can get either thin crust or hand tossed and can choose from 15 toppings. How many different pizzas can Mason order?
A. 15
B. 17
C. 7
D. 30
A teacher has a box of 100 pencils and wants to divide it equally among 25 students what fraction of the box of pencils would each student get
Answer:1/25
Step-by-step explanation:100/25=4. So 1/25 of the box.
Assume that adults have IQ scores that are normally distributed with a mean of 100 and a standard deviation 15. Find the probability that a randomly selected adult has an IQ between 85 and 115. Question content area bottom Part 1 The probability that a randomly selected adult has an IQ between and is enter your response here. (Type an integer or decimal rounded to four decimal places as needed.)
The requried probability that a randomly selected adult has an IQ between 85 and 115 is also 0.6827.
Standardize 85 and 115 using the formula:
z = (x - μ) / σ
where x is the value we want to standardize, μ is the mean, and σ is the standard deviation.
For 85:
z = (85 - 100) / 15 = -1
For 115:
z = (115 - 100) / 15 = 1
So we want to find the probability that a standard normal random variable Z is between -1 and 1. Using a standard normal distribution table or a calculator, we can find that this probability is 0.6827.
Since IQ scores are normally distributed with a mean of 100 and a standard deviation of 15, the probability that a randomly selected adult has an IQ between 85 and 115 is also 0.6827.
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The mean score on the Stats exam was 75 points with a standard deviation of 5 points, and Gregor’s z-score was -3 . How many points did he score?
A. 75
B. 90
C. 65
D. 60
Answer:
The answer is D. 60
Step-by-step explanation:
We can use the formula for calculating z-score to find out how many points Gregor scored on the Stats exam. The z-score formula is:
z = (x - μ) / σ
where x is the raw score, μ is the population mean, and σ is the population standard deviation.
We know that the population mean (μ) is 75 points and the population standard deviation (σ) is 5 points. We also know that Gregor's z-score (z) is -3. Substituting these values into the formula, we get:
-3 = (x - 75) / 5
Simplifying the equation, we get:
-15 = x - 75
Adding 75 to both sides, we get:
x = 60
Therefore, Gregor scored 60 points on the Stats exam. The answer is (D) 60.
You are performing a study about weekly per capita milk consumption. A previous study found weekly per capita milk consumption to be normally distributed, with a mean of 45.6 fluid ounces and a standard deviation of 11.1 fluid ounces. You randomly sample 30 people and record the weekly milk consumptions shown below.
37 55 30 38 43 46 32 63 34 47
40 27 34 54 43 44 40 47 50 51
36 28 22 42 58 43 48 41 56 37
A graph is a visual representation or diagram that shows facts or values in an ordered way. The only graph that satisfies the above shape is the third one.
In mathematics, a graph is a visual representation or diagram that shows facts or values in an ordered way. The relationships between multiple items are frequently represented by the points on a graph. The term "pictograph" refers to the visual depiction of information. Each graphic represents a specified number of objects. The only graph that satisfies the above shape is the third one.
Therefore, the correct option is option C.
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Your question is incomplete but most probably your full question was,
please help me, quick and right answers only algebra :)
The slope of f(x) is less than the slope of g(x).
How to compare the slopes of the lines?A general linear equation is written as:
y = a*x + b
Where a is the slope and b is the y-intercept.
If we know two points on a line, then the slope is equal to the quotient between the difference of the y-values and the difference of the x-values.
So the slope of f(x) is:
a = (3 - 0)/(0 + 2) = 3/2
And g(x) = (4/5)*x - 2
So here the slope is 4/5
We can see that clearly the slope of g(x) is larger.
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Last one that’s due 200 pts
The concentration (C) in ounces of sugar per ounce of milk will be C = 10/(10/t + 1) + 1
The domain is all real numbers except t = 0.
How to calculate the valueThe concentration (C) in ounces of sugar per ounce of milk will be
C = S/M
C = (10 + 10t)/(10 + t)
C = 10/(10/t + 1) + 1
The concentration after five minutes, will be:
C = 10/(10/5 + 1) + 1
C = 10/3
C ≈ 3.33 ounces of sugar per ounce of milk
The time it takes to reach a concentration of 8 ounces of sugar per ounce of milk, will be:
8 = 10/(10/t + 1) + 1
7 = 10/(10/t)
70/t = 10
t = 7 minutes
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10/(x-2)=7/(x+2) what is the solution?
Answer:
-34/3
Step-by-step explanation:
I've provided the explanation from my e-board in a picture below
Jenny mixed 4 kg of mixed nuts containing 16% peanuts with 12 kg of mixed nuts containing 40% peanuts. What percent of the new mixture if peanuts?
A. 34%
B. 17%
C. 13%
D. 26%
The new mixture contains 34% peanuts. The correct option is A
To solve this problemThe idea of weighted averages can be applied.
First, let's determine the mixture's entire weight:
Total weight = 4 kg + 12 kg = 16 kg
We can now calculate how many peanuts there are overall in the mixture:
Total weight in kilograms is = (4 kg) (0.16) + (12 kg) (0.40)
= 0.64 kg + 4.80 kg
= 5.44 kg.
Finally, we can find the percentage of peanuts in the mixture:
Percent of peanuts = (Total amount of peanuts / Total weight) x 100%
= (5.44 kg / 16 kg) x 100
= 34%
Therefore, the new mixture contains 34% peanuts, which is option A.
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-
93 log d +65, where d is the distance, in
The wind speed near the center of a tornado is represented by the equation S
miles, that the tornado travels and S is the wind speed, in miles per hour.
If a tornado traveled 55 miles, what was its wind speed, in miles per hour? Round your answer to the nearest tenth.
Answer: 55/60
Step-by-step explanation:
Brenda is a metalsmith who makes custom signs out of different types of metals. She sold 10
signs this week in the following metals:
copper, silver, brass, silver, aluminum, copper, brass, copper, silver, copper
Based on the data, estimate how many of the next 40 signs Brenda sells will be made of
brass.
If necessary, round your answer to the nearest whole number.
Answer:
8
Step-by-step explanation:
Brenda sold 2 brass signs of the 10 signs she sold this week. You want an estimate of the number of brass signs she will sell out of the next 40.
ProportionWe expect the proportion of brass signs to remain the same, so the number (x) of brass signs in the next 40 signs is expected to be ...
x/40 = 2/10
x = 40(2/10) = 8
We estimate Brenda will sell 8 brass signs out of the next 40 signs she sells.
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2. The Party Place also sells edible fruit arrangements. The number of
arrangements sold each day is shown in the list below.
12, 9, 4, 16, 5, 6, 15, 3, 19, 5, 12, 8, 4, 13, 5, 14, 15, 17, 11, 10
A. If a frequency table displays the data in 4 intervals, what are the
intervals that could be used?
First interval: 0-
Second interval: B -18
Third interval:
-
Fourth interval:
161
B. Use your intervals from Part A to complete the frequency table.
Interval
Frequency
C. If you drew a histogram for the data, which interval would be the
tallest bar?
The intervals that could be used based on the information will be:
First interval: 0-3Second interval: 4-7Third interval: 8-11Fourth interval: 12-16How to explain the dataThe frequency distribution will be:
Interval Frequency
0-3. 2
4-7. 6
8-11. 4
12-16 8
Lastly, it should be noted that to work out which bar is the tallest, we must compare the frequencies of all the intervals. In our case here, the interval with a frequency of 8, 12-16, has the highest value and therefore its bar will be the tallest in the histogram.
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Which of the following is the graph of the inverse of the function shown below? (1 point)
The graph of the inverse of the function is shown below.
What is an inverse function?In Mathematics, an inverse function simply refers to a type of function that is obtained by reversing the mathematical operation in a given function (f(x)).
From the information provided, we can logically deduce the following ordered pairs from the graph of the parent function:
x, f(x) = {(-2, 5), (-1, 1), (1, 2), (2, 3)}
In order to determine the inverse of this function f(x), we would interchange (swap) both the input value (x) and output value (y) as follows:
Inverse of f(x) = {(5, -2) (1, -1), (2, 1), (2, 3)}
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please help with this semi circle !! Radius circumference
The radius of the circle is 6 inches and the circumference is 30.84 in
How to find the circumference?For a circle of radius R, the circumference is given by:
C = (pi*R + 2*R)
Where pi = 3.14
For the given semicircle, we can see that the diameter is 12 inches. Then the radius is half of that, we will get.
R = D/2 = 12in/2 = 6 inches.
Now we can replace that in the circumference formula to get.
C = (3.14*6in + 2*6in)
C = 30.84 in
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Below is a picture of a Table Runner. The Table Runner has an overall length of 72" and a width of 13", as seen in
the diagram below. What is the total area of the table runner in square inches?
60"
O 858 sq in
036 sq in
O 810 sq in
O 700 sq in
13"
72"
The total area of the table runner is 858 square inches
Given that Table Runner has an overall length of 72" and a width of 13",
Area = length ×width
=60×13
=780 sq in
Area of triangle = 1/2×base ×height
=1/2×13×6
=39
There are two triangles so area is 2(39) = 78
Total area is 936+78
=858 square inches
Hence, the total area of the table runner is 858 square inches
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Find the slope of the line shown in the graph below.
Answer:
Step-by-step explanation:
Points on line= (-4,5) and (1,2)
use slope formula: M= y2-y1 divided by X2-X1
Filling into the formula: M=2-5 divided by 1+4
M (slope) = -3/5
Use the image to determine the type of transformation shown.
Image of polygon ABCD and a second polygon A prime B prime C prime D prime below.
Reflection across the x-axis
180° counterclockwise rotation
Horizontal translation
Vertical translation
The type of transformation shown is vertical translation. That is option D.
What is Transformation in geometry?Transformation of geometrical figures or points is the manipulation of a given figure to take the same shape but with different direction of its original angles.
Different types of transformations are Rotation, Reflection, Glide reflection, Translation and Dilation.
Given a polygon ABDC.
It is transformed to another polygon with the same size A'B'D'C'.
Here the polygon ABDC is just moved downwards as it is and mark is as A'B'D'C'.
In rotation or reflection transformation, the points will change it's correspondent place.
Translation is a type of transformation where the original figure is shifted from a place to another place without affecting it's size.
Since the shifting is done vertically, it is vertical translation.
Hence the transformation is vertical translation.
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find the measure of each numbered angle:
(Also, can you explain how you got one of the answers just so i know)
Answer:
A. 115
B. 65
C. 115
D. 65
E. 115
F. 665
G. 115
Step-by-step explanation:
a straight line is a 180 degree angle. If one of 2 angles is 65 degrees the other angle will be 115 because 180-65= 115
since both lines on the graph are parallel the angles will be coresponding.
1. Write the following number in scientific notation: 0.000089
O 89 x 106
8.9 x 105
89 x 10-6
8.9 x 10-5
Answer:
To write the number 0.000089 in scientific notation, we need to move the decimal point to the right until there is only one non-zero digit to the left of the decimal point, and count the number of places we moved the decimal point. In this case, we need to move the decimal point 5 places to the right:
0.000089 = 8.9 × 10^(-5)
Therefore, the number 0.000089 in scientific notation is 8.9 × 10^(-5).
an airplane is climbing 500 feet for every 700 feet it travels. estimat the airplane's climb angle while this is happeing.
The value of airplane's climb angle while this is happening is,
⇒ 35.53 degree
We have to given that;
An airplane is climbing 500 feet for every 700 feet it travels.
Hence, We can formulate;
The value of airplane's climb angle while this is happening is,
⇒ tan x = 500 / 700
⇒ tan x = 0.714
⇒ x = 35.53 degree
Thus, The value of airplane's climb angle while this is happening is,
⇒ 35.53 degree
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Mr. Martin traveled to a city 310 miles from his home to attend a meeting. Due to car trouble, his average speed returning was 7 mph less than his speed going. If the
total time for the round trip was 12 hours, at what rate of speed did he travel to the city? (Round your answer to the nearest tenth.)
Step-by-step:
ANALYSIS:
From the question, we know that...
• 310m from his home to the meeting
• Average speed RETURNING: 7 mph LESS than the speed he went on
• Total time = 12 hours
• Rate of speed = ?
-Round off to the nearest TENTH-
EXPLANATION:
Speed = Distance / Time
• S = 310/12
• S = 25.83333... mph
• S = 25.83 (round off)
Then it says that speed returning is -7 from the speed he went on, so...
• 25.83 - 7 = 18.83 mph
Rounding off to the nearest TENTH:
18.83 = 18.8 mph
Final Answer : 18.8 mph
Two boxes are shaped as right rectangular prisms. The larger box is has a length of 24 cm, a width of 10 cm, and a height of 30 cm
The dimensions of the smaller box are half the dimensions of the larger box.
What is the volume of the smaller box?
Enter your answer in the box.
cm³
The volume of the smaller box is 900 cm³.
We have,
The dimensions of the smaller box are half the dimensions of the larger box.
Length = 24/2 = 12 cm
Width = 10/2 = 5 cm
Height = 30/2 = 15 cm.
The volume of the smaller box is the product of these dimensions:
Volume = length × width × height
= 12 cm × 5 cm × 15 cm
= 900 cm³
Therefore,
The volume of the smaller box is 900 cm³.
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Mei Mei bought 15 chicken wings for $28.50. If Mei Mei spent $34.20, how many chicken wings did she buy?
Answer:18 wings
Step-by-step explanation: 28.50 divided by 15 is 1.9 so if you do 1.9 x 18 you get 34.2
Answer:
18 wings
Step-by-step explanation:
Use a proportion.
15/$28.5 = x/$34.2
28.5x = 15 × 34.2
28.5x = 513
x = 18
Answer: 18 wings
[tex]x^{2} -6x=7[/tex]
The solutions to the equation [tex]x^{2}[/tex] - 6x = 7 are x = 7 and x = -1.
To solve the equation [tex]x^{2}[/tex] - 6x = 7, we need to first bring all the terms to one side, so subtracting 7 from both sides gives us [tex]x^{2}[/tex] -6x - 7 = 0.
Next, we can use the quadratic formula, which is x = (-b ± [tex]\sqrt{b^{2}-4ac}[/tex]) / 2a, where a, b, and c are the coefficients of the quadratic equation a[tex]x^{2}[/tex]+bx+c=0.
In this case, a=1, b=-6, and c=-7, so plugging these values into the formula gives us x = (6 ± [tex]\sqrt{6^{2}-4(1)(-7) }[/tex]) / 2(1).
Simplifying further, we get x = (6 ± [tex]\sqrt{64}[/tex]) / 2, which can be written as x = 3 ± [tex]\sqrt{16}[/tex].
Therefore, the solutions to the equation [tex]x^{2}[/tex]-6x=7 are x = 3 + [tex]\sqrt{16}[/tex] = 3 + 4 = 7 and x = 3 - [tex]\sqrt{16}[/tex] = 3 - 4 = -1.
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c) The NY Knicks won 35 games out of 65 games. What is the probability that they win the next game?
d) Find the experimental probability of a player on the New York Liberty being over 73 inches
The probability that they win the next game and player on the New York Liberty being over 73 inches is 53% and 50%
We are given that;
Games= 35/35
Now,
We can use the past performance of the Knicks as an estimate of their probability of winning a game. They won 35 games out of 65 games, so their probability of winning a game is:
P(win) = 35/65 P(win) = 0.538
To find the experimental probability of a player being over 73 inches, we need to count how many players are over 73 inches and divide by the total number of players. There are six players who are over 73 inches, so the experimental probability is:
P(over 73 inches) = 6/12 P(over 73 inches) = 0.5
Therefore, by probability the answer will be 53% and 50%.
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