In the given right triangle, the angle opposite the side of length 16 units has a measure of 49.6 degrees.
We have a right triangle with an unknown angle θ (measured in degrees), the opposite side length of 16 units, and a hypotenuse length of 21 units. We're given the formula for calculating the sine of an angle:
sin(θ) = opposite / hypotenuse
By substituting the values we know, we get:
sin(x) = 16 / 21
x = sin⁻¹(16 / 21)
x ≈ 49.6°
Therefore, in the given right triangle, the angle opposite the side of length 16 units has a measure of 49.6 degrees.
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Answers for these test question
The missing lengths and angles in the geometric systems are listed below:
Case 8: x = 60
Case 9: x = 48
Case 10: x = 5.535
Case 11: x = 5.665
Case 12: x = 9.103
Case 13: θ = 60°
Case 14: θ = 23.025°
How to find missing lengths and angles in triangles
In this problem we find two cases of geometric systems formed by triangles:
Systems of two similar triangles with a common unknown side.A triangle with an unknown side or an unknown angle.First case is analyzed by means of proportionality ratios and second case done by trigonometric functions:
Case 8
100 / x = x / 36
x² = 3600
x = 60
Case 9
x / 36 = 64 / x
x² = 36 · 64
x = 48
Case 10
x = 17 · sin 19°
x = 5.535
Case 11
x = 11 · cos 59°
x = 5.665
Case 12
x = 13 · tan 35°
x = 9.103
Case 13
cos θ = 7 / 14
cos θ = 1 / 2
θ = 60°
Case 14
tan θ = 17 / 40
θ = 23.025°
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7.35 km = _______ mm
Answer: 7.35 km = 7350000 mm
Step-by-step explanation:
Multiply km by 1000000
7.35 * 1000000 = 7350000 mm
full method please
-6+28÷(-4)
Answer:
-13
Step-by-step explanation:
To add fractions, find the lowest common denominator and then combine
Can I get some help in this question?
What value of x satisfies the equation (7q^3x)^3=343q^36
4 is the value of the variable x.
What is algebraic Expression?Any mathematical statement that includes numbers, variables, and an arithmetic operation between them is known as an expression or algebraic expression. In the phrase 4m + 5, for instance, the terms 4m and 5 are separated from the variable m by the arithmetic sign +.
We can simplify the left side of the equation by using the properties of exponents:
[tex](7q^{3x})^3 = 7^3 * (q^{3x})^3 = 343q^{9x}\\\\343q^{9x} = 343q^{36}\\\\q^{9x} = q^{36[/tex]
Now we can use the property that if [tex]a^b = a^c[/tex], then b = c. Therefore:
9x = 36
Dividing both sides by 9, we get:
x = 4
Therefore, the value of x that satisfies the equation is 4.
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Let u = -2i+9j, v = 2i- j, and w= -4i. Find 3u - (2v-w).
3u - (2v-w) =
(Type your answer in terms of i and j.)
The value of 3u - (2v-w) is -6i + 25j.
We have,
u = -2i+9j, v = 2i- j, and w= -4i.
Now, 3u - (2v - w)
= 3(-2i + 9j) - [ 2(2i - j) - (-4i)]
= -6i + 27j - [4i - 2j + 4i]
= -6i + 27j - 4i - 2j + 4i
= -6i + 25j
Thus, the value of 3u - (2v-w) is -6i + 25j.
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Find the area of the composite figure.
2 ft
F
4.5 ft
K
6.5 ft
1 ft
1 ft
Answer:
The area is 13 feet squared.
Step-by-step explanation:
To find the area, first separate the composite figure into two shapes: a rectangle and a triangle.
Find the area of each shape separately, and then add the areas together.
First, the rectangle:
length= 4.5 feet
width = 2 feet
[tex]2*4.5=9 ft^{2}[/tex]
The area of the rectangle is 9 feet squared.
Next, the triangle:
The base is 2 feet + 1 foot + 1 foot = 4 feet
The height is 6.5 feet - 4.5 feet = 2 feet
The formula to find the area of a triangle is [tex]\frac{h*b}{2}[/tex] (height times base over two)
[tex]\frac{2*4}{2}=4ft^{2}[/tex]
the area of the triangle is 4 feet squared.
Add the two areas together to find the total area of the composite figure:
[tex]9ft^{2} +4ft^{2}=13ft^{2}[/tex]
The area is 13 feet squared.
The radius, R, of a sphere is 9.5cm . Calculate the sphere's volume,V . Use the value 3.14 for , and round your answer to the nearest tenth. (Do not round any intermediate computations.)
The volume of a sphere of radius 9.5 cm is approximately 3589.5 cm³
Calculating the volume of a sphereFrom the question, we are to calculate the volume of a sphere
The volume of a sphere is given by the formula
V = 4/3 πr³
Where V is the volume of the sphere
and r is the radius of the sphere
From the given information,
r = 9.5 cm
Thus,
Volume of the sphere = 4/3 × π × 9.5³
Put π = 3.14
Volume of the sphere = 4/3 × 3.14 × 9.5³
Volume of the sphere = 3589.54333 cm³
Volume of the sphere ≈ 3589.5 cm³
Hence,
The volume of the sphere is 3589.5 cm³
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I need help as soon as possible please??
Answer:
4x² - 11xy - 3y²
Step-by-step explanation:
(4x + y)(x - 3y) =
Multiply each term of the first binomial by each term of the second binomial.
= 4x² - 12xy + xy - 3y²
Now combine like terms.
= 4x² - 11xy - 3y²
If Ton spend $76.25 on food for a party. And he is having 4 friends over what average amount of money he will spent for food per person?
Answer: He would be spending $15.25 for each person including himself
Step-by-step explanation:
step 1. you need to find out how many people are getting food
step 2. divide that number (5) by how much the total cost is ($76.25) to get 15.25
If m/8 = 133°, find m/1.
Answer:
1064
Step-by-step explanation:
If m/8 = 133°, find m/1.
m/1 = m (Any number, except zero, divided by itself is 1)
m : 8 = 133 : 1
m = 8 * 133 : 1
m = 1064
----------------------
check
1064 : 8 = 133 : 1
133 = 133
the answer is good
Need help pls and thank u!
Answer:
[tex]\sqrt[]{72}[/tex]
6.3141414141414...
[tex]\sqrt[4]{64}[/tex]
8.121 121 112 111...
Step-by-step explanation:
irrational numbers are real numbers that cannot be expressed as a ratio of integers.
example of irrational number [tex]\sqrt[]{2}[/tex]
example of rational number 2, 3, -4, etc.
A country recently had a GDP of $1000 billion. Its consumption expenditures were $650 billion, its government spent $250 billion, and it had domestic investment of $150 billion. What was the value of this country’s net capital outflow?
The value of this country's net capital outflow is $200 billion.
We have,
The formula for net capital outflow (NCO) is:
NCO = Domestic Investment - Foreign Investment
Since the problem only gives us information about domestic investment, we need to use another formula to calculate foreign investment.
The formula for national saving (S) is:
S = GDP - Consumption Expenditures - Government Spending
We can rearrange this formula to solve for foreign investment:
Foreign Investment = GDP - Consumption Expenditures - Government Spending - Domestic Investment
Substituting the given values, we get:
Foreign Investment = $1000 billion - $650 billion - $250 billion - $150 billion
Foreign Investment = $1000 billion - $1050 billion
Foreign Investment = -$50 billion
The negative sign indicates that there is a net capital inflow (i.e., foreign investment is greater than domestic investment).
Therefore, the value of this country's net capital outflow is:
NCO = Domestic Investment - Foreign Investment
NCO = $150 billion - (-$50 billion)
NCO = $150 billion + $50 billion
NCO = $200 billion
Thus,
The value of this country's net capital outflow is $200 billion.
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For a population growing at 3% a year, what is the yearly growth factor?
(Identifying Transformations LC)
Use the image to determine the type of transformation shown.
Preimage of polygon ABCD. A second image, polygon A prime B prime C prime D prime to the right of the first image with all points in the same position.
Horizontal translation
Vertical translation
Reflection across the x-axis
90° clockwise rotation
If the polygon A, B, C, D is transformed to polygon A', B', C', D' to the right of the first image with all points in the same position, then the transformation is a horizontal translation.
Option A is the correct answer.
We have,
A horizontal translation moves every point of a figure the same distance in the same direction.
In this case, since the second polygon is to the right of the first one, we know that every point of the polygon has been translated to the right by the same amount.
A vertical translation would move every point of the figure the same distance in the same direction, but vertically instead of horizontally.
A reflection across the x-axis would flip the figure over the x-axis, so points that were above the x-axis would end up below it and vice versa.
A 90° clockwise rotation would rotate the figure 90 degrees to the right.
Thus,
If the polygon A, B, C, D is transformed to polygon A', B', C', D' to the right of the first image with all points in the same position, then the transformation is a horizontal translation.
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A towns government is looking into its residences opinion on rebuilding the boardwalk on the coast line.
two representatives from the town visit the existing boardwalk and randomly survey 50 people to see whether they support the new boardwalk, they find that 60% of those surveyed support the construction of the new boardwalk and conclude with 90% confidence the majority of residents support its construction, what aspects of the scenario brings the validity of this conclusion into doubt
The aspects of the scenario that bring the validity of the conclusion made by the representatives of the government would be:
Small sample sizeSampling biasWhat reduced the validity of the sample ?The sample size used by the representatives in the survey was only 50 individuals, which might not be sufficient to represent the views of the entire town's population accurately. A more extensive sample size would provide a more precise approximation of the public opinion.
Moreover, the conductance of the survey on the existing boardwalk presents the possibility of sampling bias since those who visit the boardwalk could hold different opinions towards the new construction than those that do not visit.
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find the area of the figure (hint don’t forget units!)
5.2 ft 3 ft 2.4
Answer:
A = 11.4 ft²
Step-by-step explanation:
the area (A) of a trapezium is calculated as
A = [tex]\frac{1}{2}[/tex] h (b₁ + b₂ )
where h is the height between the bases
here h = 3 , b₁ = 2.4 , b₂ = 5.2 , then
A = [tex]\frac{1}{2}[/tex] × 3 × (2.4 + 5.2) = 1.5 × 7.6 = 11.4 ft²
Please help solve for x image attached!
Answer:
7 should go in the green blank.
10/x = x/7
Determine the value of y, if x is 3.
y = x² + 11
Answer:
20
Step-by-step explanation:
just a substitute 3 in x so 3x3=9
11+9=20
David is trying to pick out an outfit for the first day of school. He can choose from 8 pairs of pants, 8 t-shirts, 4 sweaters or hoodies, and 3 pairs of shoes. How many different outfits does David have to choose from?
The number of the different outfits do David have to choose is 768.
Here we will use the concept of Combinations,
Combinations are the way of selecting objects or elements from a group of objects or collections, in such a way the order of the objects does not matter.
Different outfits do Damian have to choose, will be;
⇒ 8C₁×4C₁×8C₁×3C₁
⇒ 8×4×8×3
⇒ 768
Hence, the number of the different outfits do David have to select is 768.
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A boat heading out to sea starts out at Point A, at a horizontal distance of 1035 feet from a lighthouse/the shore. From that point, the boat’s crew measures the angle of elevation to the lighthouse’s beacon-light from that point to be 8°. At some later time, the crew measures the angle of elevation from point B to be 5°. Find the distance from point A to point B. Round your answer to the nearest foot if necessary.
Note that given the angle of elevation, the distance from pont A to Point B is approximately 627.6ft.
See the attached image.
As shown in the attached figure:
L = AO Tan 8°
L = 1035 * Tan 8°
L = 1035 * 0.14054083470239144683811769343281
L = 1035 * 0.14054083470239144683811769343281
L = 145.46 Feet
BO = L/Tan 5°
BO = 145.459763917 / 0.08748866352592400522201866943496
BO = 1662.61270952
BO = 1662.6 Feet
Since AB = BO-AO
AB = 1662.6-1035
AB = 627.6 Ft.
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Try it
Mrs. Chauvet has an unfair number cube that lands with 6 For how many of the outcomes does X = 0, meaning
facing up 40% of the time.
the outcome has no 6s?
Let X = the number of times that she rolls a 6 among 3
trials.
For how many of the outcomes does X = 1, meaning
the outcome has exactly one 6?
For how many of the outcomes does X=2, meaning
the outcome has exactly two 6s?
For how many of the outcomes does X=3, meaning
the outcome has exactly three 6s?
Answer:
The problem describes rolling an unfair number cube which lands with 6, and asks for the number of outcomes where X=0, X=1, X=2, and X=3.
X can be 0, 1, 2, or 3 if X equals the number of times she rolls a 6 over the course of three tries.
We must count the instances where none of the three trials yields a six in order to determine the number of occurrences where X = 0. Since there is a 0.4 percent chance that the cube will fall on 6, there is a 0.6 percent chance that it won't. Therefore, there are 0.6 * 3 = 0.216, or 21.6%, of outcomes where X = 0.
To find the number of outcomes where X=1, we need to count the number of outcomes where exactly one of the three trials results in a 6. There are three ways to choose which trial will result in a 6, and each of the other two trials must not result in a 6. Therefore, the number of outcomes where X=1 is 3 × 0.4 × 0.6^2 = 0.432 or 43.2%.
We must count the outcomes where precisely two out of the three trials yield a six in order to determine the number of events where X=2. There are three options for selecting the two trials that will end in a 6, and the third trial cannot also end in a 6. The proportion of outcomes where X=2 is therefore 3 0.4 2 0.6 = 0.288 or 28.8%.
Finally, to find the number of outcomes where X=3, we need to count the number of outcomes where all three trials result in a 6. This occurs with probability 0.4^3 = 0.064 or 6.4%.
Therefore, the number of outcomes where X = 0 is 21.6%, X=1 is 43.2%, X=2 is 28.8%, and X=3 is 6.4%.
How many times greater is the
value of the 4 in 2,849 than the
value of the 4 in 3,824?
Answer:
The value of the 4 in 2,849 is 4 x 100 = 400, while the value of the 4 in 3,824 is 4 x 10 = 40. Therefore, the value of the 4 in 2,849 is 400/40 = 10 times greater than the value of the 4 in 3,824.
Step-by-step explanation:
i need help with this prblem
Answer:
y = x + 2
Step-by-step explanation:
y = mx + b
Point (0, 2) shows that the y-intercept is 2, so b = 2.
y = mx + 2
Now we find the slope using the 2 points, (0, 2) and (2, 4).
m = (4 - 2)/(2 - 0) = 1
y = x + 2
Ayuda por favor es para mañana, fracciones equivalentes. Doy coronita
These fractions are equivalent fractions by algebraic property:
Case 1: YES
Case 2: NO
Case 3: YES
Case 4: NO
Case 5: YES
Case 6: YES
Case 7: NO
Case 8: YES
Case 9: YES
Case 10: YES
Case 11: NO
Case 12: YES
Case 13: NO
Case 14: YES
Case 15: YES
Case 16: YES
Case 17: NO
Case 18: YES
How to determine if two fractions are equivalent
In this question we must check 18 cases of equivalent fractions, two fractions are equivalent if the following algebraic property is met:
a / b = (a · c) / (b · c), where a, b, c are integers and c is nonzero.
Now we proceed to determine if each pair is equivalent:
Case 1
2 / 3 = (2 · 2) / (3 · 2)
2 / 3 = 4 / 6 (YES)
Case 2
2 / 6 = (2 · 3) / (6 · 3)
2 / 6 = 6 / 18 (NO)
Case 3
9 / 9 = (9 · 4) / (9 · 4) = 36 / 36 (YES)
Case 4
3 / 11 = (3 · 3) / (11 · 3) = 9 / 33 (NO)
Case 5
7 / 8 = (7 · 2) / (8 · 2) = 14 / 16 (YES)
Case 6
4 / 6 = (4 · 5) / (6 · 5) = 20 / 30 (YES)
Case 7
5 / 6 = (5 · 2) / (6 · 2) = 10 / 12 (NO)
Case 8
2 / 7 = (2 · 4) / (7 · 4) = 8 / 28 (YES)
Case 9
6 / 12 = (6 · 2) / (12 · 2) = 12 / 24 (YES)
Case 10
4 / 9 = (4 · 5) / (9 · 5) = 20 / 45 (YES)
Case 11
9 / 10 = (9 · 3) / (10 · 3) = 27 / 30 (NO)
Case 12
1 / 5 = (1 · 5) / (5 · 5) = 5 / 25 (YES)
Case 13
12 / 12 = (12 · 3) / (12 · 3) = 36 / 36 (NO)
Case 14
8 / 11 = (8 · 4) / (11 · 4) = 32 / 44 (YES)
Case 15
5 / 5 = (5 · 4) / (5 · 4) = 20 / 20 (YES)
Case 16
6 / 9 = (6 · 4) / (9 · 4) = 24 / 36 (YES)
Case 17
3 / 7 = (3 · 8) / (7 · 8) = 24 / 56 (NO)
Case 18
10 / 12 = (10 · 4) / (12 · 4) = 40 / 48 (YES)
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Vanilla rent increased by 5%. The increase was $82. What was the original amount of Pavati's rent?
if f(x)=x³-1 and g(x)=x²
find (gof) ( x) and (fog) (x)
Answer:
(x²)³ - 1 = x^6 - 1
Step-by-step explanation:
To find (gof)(x), we first need to evaluate g(x), which is x², and then use the result as input to f(x), giving us f(g(x)).
So, we have:
g(x) = x²
f(g(x)) = f(x²) = (x²)³ - 1 = x^6 - 1
Therefore, (gof)(x) = g(f(x)) = (f(x))² = (x³ - 1)² = x^6 - 2x^3 + 1.
To find (fog)(x), we first need to evaluate f(x), which is x³ - 1, and then use the result as input to g(x), giving us g(f(x)).
So, we have:
f(x) = x³ - 1
g(f(x)) = g(x³ - 1) = (x³ - 1)² = x^6 - 2x^3 + 1
Therefore, (fog)(x) = f(g(x)) = (x²)³ - 1 = x^6 - 1.
What is the value of x in this triangle?
Enter your answer as a decimal in the box. Round only your final answer to the nearest hundredth.
Answer:
58.85°
Step-by-step explanation:
You want to know the measure of the angle in the right triangle that has hypotenuse 29 and adjacent side 15.
CosineThe cosine function relates angles and sides by ...
Cos = Adjacent/Hypotenuse
cos(x) = 15/29
The inverse function is used to find the angle value:
x = arccos(15/29) ≈ 58.85°
The value of x is about 58.85°.
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A student takes a multiple-choice test that has 10 questions. Each question has four choices. The student guesses randomly at each answer. Let X be the number of questions answered correctly. Find P (4) and Find P (More than 2)
Probability of answering exactly 4 questions correctly = 0.206
P (More than 2) = 0.475
How to solve for the probability1.
ind P(4): Probability of answering exactly 4 questions correctly.
P(X=4) = (10C4) * (0.25^4) * (0.75^6)
10C4 = 10! / (4! * (10-4)!) = 210
P(X=4) = 210 * (0.25^4) * (0.75^6)
= 0.206
2. P(More than 2):P(X=0) = (10C0) * (0.25^0) * (0.75^10) ≈ 0.056
P(X=1) = (10C1) * (0.25^1) * (0.75^9) ≈ 0.187
P(X=2) = (10C2) * (0.25^2) * (0.75^8) ≈ 0.282
Now, calculate P(X>2):
P(X>2)
= 1 - (P(X=0) + P(X=1) + P(X=2))
= 1 - (0.056 + 0.187 + 0.282)
= 1 - 0.525
= 0.475
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A virus takes 5 days to grow from 180 to 230. How many days will it take to grow from 180 to 260? Round to the nearest whole number.
It will take approximately 8 days for the virus to grow from 180 to 260.
We can set up a proportion to solve this problem. Let "x" represent the number of days it will take for the virus to grow from 180 to 260.
The proportion can be set up as follows;
(Change in value) / (Time taken) = (Change in value) / (Time taken)
Using the given information, we have;
(260 - 180) / x = (230 - 180) / 5
Simplifying the fractions on both sides of the equation, we get:
80 / x = 50 / 5
Cross-multiplying, we have;
80 × 5 = 50 × x
400 = 50x
Dividing both sides of the equation by 50, we get;
x = 400 / 50
x = 8
Therefore, it will take 8 days.
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Please help on this asap!! 65 Points
No, It is not possible for 75% of the people surveyed at the park to purchase any two combination of the treats unless 14 people from the 'No preference group" decide to pick a treat. The two best frozen treat to pick will be Ice-cream sandwich and frozen fruit bar. With these two, 174 people are guaranteed to purchase the product.
How do we find the 75% chance of people surveyed buying any two combination of frozen treats?To find the 75% chance of people surveyed buying any two combination we say
58 + 95 + 79 + 17 = 250
75% of 250 = 187.5 which is 188
We need to see if 188 of people will pick up a treat based on the survey
58 + 95 = 153 < 188
95 + 79 = 174 < 188 however, if 14 people from no preference group purchase, then, this is the best combination.
58 + 79 = 137 < 188
The answer provided is based on the question below as seen in the picture;
Is it possible to select a combination of two frozen treats so that 75% of the people surveyed would be able to purchase their favorite? If so, which two types of frozen treats should you select? Use words and numbers to justify your answer
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