The measure of <1 is 31°.
What are vertical angles?Two angles are said to be vertical angles when they are formed by two straight lines intersecting at a point. This produces a series of angles of which some are vertical, thus they have equal measure.
In the information given in the question, it was given that <1 and <2 are vertical angles. This implies that they have equal measure, such that;
<2 = 31° (given)
So that;
<1 = <2 = 31°
Thus,
<1 = 31°
Therefore, it can be concluded that the measure of <1 is 31°.
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Lisa is putting 11 colored light bulbs into a string of lights. There are 3 red light bulbs, 2 yellow light bulbs, and 6 pink light bulbs. How many distinct orders of light bulbs are there if two light bulbs of the same color are considered identical (not distinct)?
We can see here that the distinct orders of light bulbs that are there if two light bulbs of the same color are considered identical is: 4,620.
How we arrived to the solution?We can see here that in order to find the solution, we use the permutation with repetition formula:
n! / (n1! × n2! x ... × nk!)
In order to adjust for overcounting, we divide by 3! because of the 3 red light bulbs we have. For the 2 yellow light bulbs, we divide with 2!. For the 6 pink light bulbs, we divide by 6!. This is because we are treating lights bulbs of the same color which are identical.
Therefore, the total number of distinct orders of bulbs will be:
11! / (3! × 2! × 6!) = 4,620
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What is the domain of the function y=tan (x/8)
The domain can be written as follows:
R - {x = n*12pi or m*4pi | n, m ∈ Z}
where pi = 3.14 and R is the set of real numbers.
What is the domain of the function?Here we want to find the domain of the function:
y = tan(x/8)
The tangent is the quotient between the cosine and the sine, then we will get:
sin(x/8)/cos(x/8)
The problems of the tangent are all the values that make the denominator equal to zero, then we need to remove these.
The zeros are:
cos(x/8) = 0
We know that cos(pi/2) = cos(3pi/2) = 0
Then:
x/8 = pi/2
x = 4pi
x/8 = 3pi/2
x = 12pi
So the domain is the set of all real numbers except the ones in the next set:
{x = n*12pi or m*4pi | n, m ∈ Z}
Where Z is the set of integers.
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One number is 10 more than fifteen times another. Their sum is 42. Find the numbers.
Answer:
40, 2
Step-by-step explanation:
x = number 1
y = number 2
x = 15y + 10
x + y = 42
we use the first in the second equation and get
15y + 10 + y = 42
16y = 32
y = 32/16 = 2
x + y = 42
x + 2 = 42
x = 40
Determine if triangle RQP is similar to triangle YXW. If they are similar enter the scale factor from triangle YXW to triangle RQP
The triangles are similar, and the scale factor is given as follows: k = 0.8.
What are similar triangles?Similar triangles are triangles that share these two features listed as follows:
Congruent angle measures, as both triangles have the same angle measures.Proportional side lengths, which helps us find the missing side lengths.The sum of the measures of the internal angles of a triangle is of 180º, hence the measure of the missing angle is given as follows:
x + 114 + 24 = 180
x + 138 = 180
x = 42º.
Which is equals to the measure on the second triangle, hence they are similar.
The scale factor is given as follows:
k = 16/20 = 36/45 = 0.8.
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Use the relationship given in the right triangle and the inverse sine, cosine, and tangent functions to write 0 as a function of x in three different ways. It is not
necessary to rationalize the denominator.
a
-√√81-x²³.c-9
The measure of inverse of sinθ is c/√ (c² - a²)..
What is the measure of inverse of sinθ?The measure of inverse of sinθ is calculated by applying trigonometry identities for right triangles.
Mathematically, the trig identities are represented using the following method;
SOH CAN TOA
SOH is for sine θ
CAH is fof cos θ
TOA is for tan θ
From the diagram we need find the value of the opposite side;
b = √ (c² - a²)
Sin θ = b/c
The inverse of b/c = c/b
1/sinθ = c/b = c/√ (c² - a²).
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Here is question 3 of 6. Thank you for the help
Yes, data provide convincing evident that contest has increased participation.
We have,
H₀: p = 0.12
Hₐ: p > 0.12
So, z = (p' - p)/ (√pq/n)
z = 1/6 - 0.2/ √(0.12 x 0.88) /210
z= 2.08
The test is right tailed.
So, P value = P( z> 2.08) = 0.0188
and, P- value < α, Reject H₀
Yes, data provide convincing evident that contest has increased participation.
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a. The following is the input/output table for two industries X and Y. The values are in million of rupees.
Producers
X
Y
X
14
7
Users
Y
6
Final Demand
8
Total Output
28
18
11
36
Determine the outputs if the final demand changes to 20 for X and 30 for Y.
[3]
The outputs for industries X and Y will be 31 million and 43.2 million, respectively supposedly the final demand changes to 20 for X and 30 for Y.
How do we calculate?We will start with industry X.
The final demand for X hade an increment from 14 million to 20 million with an increase of 6 million, hence the final output of X must also increase by 6 million to make up for demand.
Users Final Producers
Demand X Y
X 14 7
Y 6 18
Total 20 25
The table tells us that for every additional million of final demand for X, the producers in industry X need to produce 0.5 million of output.
So the new total output for industry X is 28 + 3 = 31 million.
For industry Y
The same scenario occurred for Industry Y which had final output of 12 in order to meet the demand increment.
So the new total output for industry Y is 36 + 7.2 = 43.2 million.
In conclusion, the outputs for industries X and Y will be 31 million and 43.2 million, respectively, if the final demand changes to 20 for X and 30 for Y.
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What is the answer to this question
Answer:
The height of the kite is 63.40 feet.
Trigonometric ratio is used to show the relationship between the sides of a triangle and its angles.
Let h represent the height of the kite. Hence, using trigonometric ratios:
sin(30) = h / 95
h = 47.5 feet
Therefore the height of the kite is 63.40 feet.
For the polynomial 11x4 + 8x2 + x which represents how much Patrick won from Michael, find the degree of each term. Then find the degree of the polynomial.
The degree of the polynomial 11x⁴ + 8x² + x is 4, which is the highest degree among its terms. The degrees of the terms are 4, 2, and 1 for the first, second, and third terms, respectively.
The degree of a term in a polynomial is the exponent of its variable.
In the polynomial 11x⁴ + 8x² + x, the degree of the first term 11x⁴ is 4, the degree of the second term 8x² is 2, and the degree of the third term x is 1.
The degree of the polynomial is the highest degree among its terms. In this case, the highest degree is 4, which is the degree of the first term. Therefore, the degree of the polynomial is 4.
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Help much needed pls and thank you.
Answer:
Step-by-step explanation:
A full revolution on a circle/radians is 2[tex]\pi[/tex], so keep adding or subtracting 2[tex]\pi[/tex] til you get a base angle, that's when the sign changes. Then decide which quadrant your in.
For this one the equivalent of 2[tex]\pi[/tex] is [tex]6\pi /3[/tex]
-29[tex]\pi[/tex]/3 + [tex]6\pi /3[/tex]
= -23[tex]\pi[/tex]/3 + [tex]6\pi /3[/tex]
= -17[tex]\pi[/tex]/3 + [tex]6\pi /3[/tex]
= -11[tex]\pi[/tex]/3 + [tex]6\pi /3[/tex]
= -5[tex]\pi[/tex]/3 + [tex]6\pi /3[/tex]
= 1[tex]\pi[/tex]/3 sign changed it's equavalent to [tex]\pi /3[/tex] Which is in the first quadrant. See unit circle.
-5[tex]\pi[/tex]/6 + [tex]12\pi /6[/tex]
=[tex]7\pi /6[/tex] third quadrant, i count quadrants by know [tex]\pi[/tex]/6 is 30°, so every 30° line is 1/6 of the unit circle. when i count 7 of them that's in the 3rd quadrant. Don't forget to count the axis's
2[tex]\pi[/tex]/3 is in the 2nd quadrant. Count my pi/3's which is 60°
45[tex]\pi[/tex]/7 - 14[tex]\pi[/tex]/7
= 31[tex]\pi[/tex]/7 - 14[tex]\pi[/tex]/7
=17[tex]\pi[/tex]/7 - 14[tex]\pi[/tex]/7
=3[tex]\pi[/tex]/7 - 14[tex]\pi[/tex]/7
= -11[tex]\pi[/tex]/7 1/7th's is not your typical unit circle angle
This one i think of logically. this is -1 4pi/7
1 pi going backwards is 180
keep going backards 4/7 is bigger than 1/2 so it's in the 1st quadrant
Graph the relationship with the greater rate of change on the coordinate grid.
• It takes Jason 2 hours to travel 180 miles to reach his destination.
.
Isaiah travels from Nashville to Atlanta. The equation below shows y as the number of miles traveled and x as the number of
hours he traveled.
y = 80x
SOMONE please tel me where to put the slope !!!‼️‼️
help
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helphelp
helphelp
helphelp
helphelp
helphelp
helphelp
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help
The volume of the solid is 1922.7 in³.
How to find the volume of a solid?The volume of a solid can be found by adding the volume of the shapes that make the solid. In this case:
Volume of solid = volume of hemisphere + volume of cylinder
Volume = 2/3πr³ + πr²h
where r = 12/2 = 6 in
height of cylinder (h) = 13 - 6 = 7 in
Volume = (2/3 * π * 6³) + (π * 6² * 13)
Volume = 1922.7 in³
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The area of a large parking space is 162 square feet. If the width of the parking space is 9 feet, what is the length?
A 12 feet
B 14 feet
C 16 feet
D 18 feet
Please help me answer this question
The quadratic polynomial with integer as coefficients that has four real roots including these conjugates is a² + b² - 2ab - 20a - 20b + 88 ≥ 0
Here is how to derive the polynomialOne possible quartic polynomial with integer coefficients that has four real roots, including the conjugates 5+√3 and 5-√3, is:
(x - 5 - √3)(x - 5 + √3)(x - a)(x - b)
where a and b are the remaining two roots.
Expanding the first two factors using the difference of squares formula, we get:
(x - 5)² - 3
Expanding the last two factors, we get:
x² - (a + b)x + ab
Putting it all together, the quartic polynomial is:
a² + b² - 2ab - 20a - 20b + 88 ≥ 0
To ensure that a and b are also real, we can use the fact that the discriminant of a quadratic equation ax² + bx + c = 0 with real coefficients is b² - 4ac ≥ 0. Applying this to the quadratic factor in the above polynomial, we get:
(a + b)² - 4ab ≥ 0
Expanding and simplifying, we get:
a² + b² - 2ab - 20a - 20b + 88 ≥ 0
To simplify the problem, we can set a = b, since the polynomial is symmetric with respect to the roots. Then, the inequality becomes:
2a² - 40a + 88 ≥ 0
Dividing by 2 and factoring, we get:
(a - 10)² - 12 ≥ 0
This inequality is always true for real values of a, so we can choose any real value for a and set b = a to obtain a quartic polynomial with integer coefficients that has four real roots, including the conjugates 5+√3 and 5-√3.
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List at least five combinations of nickels and dimes such that the number of nickels is double the number of dimes.
2 nickels and 1 dime
4 nickels and 2 dimes
6 nickels and 3 dimes
8 nickels and 4 dimes
10 nickels and 5 dimes
Simplify. (5 x sqrt 2 - 1)^2
FOR 20 POINTS!!!
(Look at picture)
Answer:
Kenyon could make a total of 7 bouquets.
Step-by-step explanation:
To find the greatest number of bouquets we need to find GCF.
We need to find GCF for 21 and 28.
The factors of 21 are: 1,3,7, and 21.
The factors of 28 are: 1,2,4,7,14, and 28
1 and 7 are the common factors between 21 and 28.
From the factors, the greatest common factor is 7.
Malick is forming clay blocks in the shape of rectangular prisms.
Two faces of the blocks are squares.
First, find the missing length of the clay block. Then, find the volume.
The missing length is 4 in.
The volume of a rectangular prism is 32 in³.
We have,
Since the two faces of the blocks are squares.
The face that has the missing length can be considered as a square face.
i.e
The front and back faces are squares.
So,
The missing length is 4 in.
Now,
The volume of a rectangular prism.
= length x width x height
= 4 x 2 x 4
= 32 in³
Thus,
The missing length is 4 in.
The volume of a rectangular prism is 32 in³.
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find the distance between the two points in simplest radical form (9,2) (4,-7)
Answer:
√50
Step-by-step explanation:
To solve, use distance formula.
√(9-4)^2 + (2-(-7))^2=
√5^2+5^2=
√50
Two machines, X and Y, produce earbuds. Let X represent the diameter of an earbud produced by machine X, and let
Y represent the diameter of an earbud produced by machine Y. X has a mean of 14 mm with a standard deviation of
0.6 mm, and Y has a mean of 15.2 mm with a standard deviation of 0.2 mm. Which answer choice correctly calculates
and interprets the mean of the difference, D = X-Y?
OD=-1.2; earbud manufacturers can expect the difference in the diameter of earbuds produced from machines X
and Y, on average, to be -1.2 mm.
OH = 0.4; earbud manufacturers can expect the difference in the diameter of earbuds produced from machines X and
Y, on average, to be 0.4 mm.
O = 1.2; earbud manufacturers can expect the difference in the diameter of earbuds produced from machines X and
Y, on average, to be 1.2 mm.
OD = 29.2; earbud manufacturers can expect the difference in the diameter of earbuds produced from machines X
and Y, on average, to be 29.2 mm.
-1.2, earbud manufacturers can expect the difference in the diameter of earbuds produced from machines X
Given that two machines, X and Y, produce earbuds
Let X represent the diameter of an earbud produced by machine X, and
let Y represent the diameter of an earbud produced by machine Y. X has a mean of 14 mm with a standard deviation of 0.6 mm
Y has a mean of 15.2 mm with a standard deviation of 0.2 mm.
The mean of the difference, D = X - Y, can be calculated as:
mean(D) = mean(X) - mean(Y)
= 14 - 15.2
= -1.2
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Larry cut a ribbon into 8 equal pieces. If the ribbon was 26 m long, how many meters long was each piece?
As per the unitary method, each piece is 3.25 meters long by dividing the total length of the ribbon by the number of pieces.
Larry has cut a ribbon into 8 equal pieces. The total length of the ribbon is 26 m. We need to find out the length of each piece of the ribbon.
To do this, we can use the unitary method. We know that the ribbon is divided into 8 equal pieces, so each piece is 1/8th of the total length of the ribbon.
Therefore, we can find the length of each piece by dividing the total length of the ribbon by 8:
Length of each piece = Total length of ribbon / Number of pieces
Length of each piece = 26 m / 8
Length of each piece = 3.25 m
So, each piece of the ribbon is 3.25 meters long.
We used the unitary method by finding the value of one unit (1/8th of the ribbon) and then using it to calculate the value of other units (the length of each piece).
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Paola has enough mulch to cover 48 square feet. She wants to use it to make three square vegetable gardens of equal sizes. Solve the equation 3s2 = 48 to find s, the length of each garden side (in feet).
The length of each garden side is 4 ft.
Given that, Paola has 48 ft² of mulch, she wants to make three square vegetable gardens of equal sizes, we need to find the length of each garden side.
Let s be the length of the side of the gardens,
Since, she need 3 gardens,
So,
3 × side² = 48
3s² = 48
s² = 16
s = 4
Hence, the length of each garden side is 4 ft.
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In circle V, VW = 8 and the area of shaded sector = 167. Find the length of
WY X. Express your answer as a fraction times .
W
The length of m∠WYX is equal to 12π units.
How to calculate the area of a sector?In Mathematics and Geometry, the area of a sector can be calculated by using the following formula:
Area of sector = θπr²/360
Where:
r represents the radius of a circle.θ represents the central angle.By substituting the given parameters into the area of a sector formula, we have the following;
Area of sector = θπr²/360
16π = θ(π/360) × 8²
Central angle, θ = 0.5π
m∠WYX = 2π - m∠WX
m∠WYX = 2π - 0.5π
m∠WYX = 1.5π
Length of m∠WYX = (1.5π)/2π × 2πr
Length of m∠WYX = (1.5π)/2π × 2π(8)
Length of m∠WYX = 12π units.
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Let f(t) be the sales of a gaming product, in thousands of units, after t months.
The sales after 5 months is 36,000 units (since f(t) is given in thousands of units).
The given function f(t) represents the sales of a gaming product in thousands of units after t months. To find the sales after 5 months, we need to substitute t = 5 in the function f(t) and evaluate the expression. f(5) = 5(5) + 11
= 25 + 11
= 36
Therefore, the sales of the gaming product after 5 months is 36 thousand units. This means that the company has sold 36 thousand units of the gaming product within the first 5 months since the launch of the product. It also indicates that the sales are increasing by 5 thousand units every month.
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-- The given question is incomplete, the complete question is
"Let f(t) be the sale of a gaming product in thousand of units after t months f(t)=5t+11. Find the sales after 5 months."
A plane takes off at a 10 degree angle. How far away is the plane (ground distance) once it reaches an altitude (height) of 30,000 feet?
We are missing a side or and angle? Regular or Inverse Trig?
The ground distance of the plane is 170,138.5 ft.
What is the ground distance of the plane?
The ground distance of the plane is calculated by applying trigonometry ratio as shown below;
SOH CAH TOA
SOH = sin θ = opposite /hypothenuse side
TOA = tan θ = opposite side / adjacent side
CAH = cos θ = adjacent side / hypothenuse side
The height attained by the plane is the opposite side, while the ground distance is the adjacent side
tan (10) = 30,000 ft/d
d = 30,000 ft/tan(10)
d = 170,138.5 ft
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What is the solution to this system?
(1, 0)
(1, 6)
(8, 26)
(8, –22)
Math Algebra Help needed
You can use functions to complete the table as follow:
x f(g(x))
4 2
10 4
20 6
34 8
52 10
How to use functions to complete the table?A function is an expression that shows the relationship between the independent variable and the dependent variable. A function is usually denoted by letters such as f, g, etc.
We have:
f(x) = √(x+1)
g(x) = 2x - 5
When x = 4:
f(g(x)) = f(g(4))
f(g(4)) = f(2*4 - 5)
f(g(4)) = f(3)
f(g(4)) = √(3+1) [Remember f(x) = √(x+1)]
f(g(4)) = 2
When x = 10:
f(g(10)) = f(2*10 - 5)
f(g(10)) = f(15)
f(g(10)) = √(15+1)
f(g(10)) = 4
When x = 20:
f(g(20)) = f(2*20 - 5)
f(g(20)) = f(35)
f(g(20)) = √(35+1)
f(g(20)) = 6
When x = 34:
f(g(34)) = f(2*34 - 5)
f(g(34)) = f(63)
f(g(34)) = √(63+1)
f(g(34)) = 8
When x = 52:
f(g(34)) = f(2*52 - 5)
f(g(34)) = f(99)
f(g(34)) = √(99+1)
f(g(34)) = 10
Thus, fill the values into the table to complete it.
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PLEASE HELP ( WILL GIVE BRAINLIEST)
Answer: Option C.
The volume of a cylinder is given by the formula V = πr^2h, where r is the radius and h is the height.
Given that the diameter of the container is 24 ft, the radius (r) would be half of that, which is 12 ft.
The depth of the container (h) is given as 4 ft.
Plugging in these values into the formula, we get:
V = π(12^2)(4)
V = 3.14(144)(4)
V = 1808.6 cubic feet (rounded to the nearest tenth)
So, the storage container can hold approximately 1808.6 cubic feet of wood, rounded to the nearest tenth.
Step-by-step explanation:
What is 2 plus 2 please tell me
Answer:
Step-by-step explanation: The answer is 4 all u do is add 2 to 2
Answer: 2+2=4
Step-by-step explanation: The sum of two and two results in a value of four in a quantitative analysis.
Helppp please it’s due tomorrow
The total number of cups of grapes and raisins include the following: 5/6 cups of grapes and raisins.
How to determine the total number of cups of grapes and raisins?In Mathematics and Geometry, a fraction is a numerical quantity (number or numeral) that is typically expressed as a quotient (ratio) or not expressed as a whole number. This ultimately implies that, a fraction simply refers to a part of a whole number.
Based on the information provided above, the total number of cups of grapes and raisins can be calculated as follows;
Fraction = 1/2 + 2/3
Fraction = (3 + 2)/6
Fraction = 5/6 cups of grapes and raisins.
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