Find all angles θ between 0° and 180° satisfying the given equation. round your answer to one decimal place. (enter your answers as a comma-separated list.) sin(θ) = 3 4
We are given the equation:
sin θ = 3 / 4
To find for the value of θ, simply compute using the calculator:
θ = sin^-1 (3 / 4)
θ = 48.60° = θ1
To find for the other value, subtract the answer from 180°, so:
θ2 = 180° - 48.60°
θ2 = 131.40°
So the angles are 48.60° and 131.40°
The angles θ for which sin(θ) equals 3/4 between 0° and 180° are approximately 48.6° and 131.4°.
Explanation:The student's question relates to the topic of trigonometry. Specifically, finding the angles θ for which the sine equals 3/4. To answer this, in the first quadrant, we can use the arcsin function to get θ = arcsin(3/4). Using a calculator, θ ≈ 48.6°. In the second quadrant, the sine is still positive, so θ = 180° - arcsin(3/4) ≈ 131.4°. Thus, the solution is 48.6°, 131.4°. It's worth noting that using a calculator's arcsin function usually gives a result in the first quadrant (0° - 90°) so we have to calculate the second quadrant angle ourselves.
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At the bookstore checkout, you watch as the register rings up your purchases and coupons.
The prices were as follows:
$1.85
$8.56
$6.30
$2.73
$5.25
$4.09
$7.95
– $0.85 (coupon)
– $2.10 (coupon)
The register gives your total bill as $41.44. Estimate the total amount of the bill, by rounding
each value to the nearest dollar, and use your answer to determine whether the total on the register is reasonable.
12 out of 142 people standing in line for tickets were going to see the movie in theater
a. if there were a total of 1704 tickets sold, predict how many people were going to see the movie in theater a?
The _______ represents the expected proportion of intervals that will contain the parameter if a large number of different samples of size n is obtained. it is denoted _______.
The concept referred to in the question is the 'confidence interval', which represents the estimated range that will contain the parameter in the event of obtaining a large quantity of different samples of size n. The denoted term '____' is the standard error (SE), which describes the standard deviation of these sample means distribution. As the number of samples increases, according to the central limit theorem, these sample sums or means tend towards a normal distribution.
Explanation:The portion of the question, 'The _______ represents the expected proportion of intervals that will contain the parameter if a large number of different samples of size n is obtained...' refers to the confidence interval. The confidence interval is a range of values, derived from statistical analysis, that is likely to contain the parameter of interest. For instance, a 0.95 confidence interval stands for a 95% probability that the population parameter will fall within this range.
The second fill-in-the-blank part of the question, 'it is denoted _______.' refers to the standard error. The standard error denoted as SE or rarely s.e., represents the standard deviation of the sampling distribution of the mean or in simpler words, it highlights how much our sample mean might differ from the actual population mean.
As the number of different samples (n) gets larger, the sampling distribution of the sum, ΣX, or the mean, X, tends towards the normal distribution, according to the central limit theorem. This feature is harnessed in diverse areas such as probability theory and statistics.
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Which expression represents the phrase "one third the sum of 12 and a number"?
A.) 1/3+12+x
B.) 1/3(12+x)
C.) 1/3x+12
D.) 1/3(12)+x
The expression that represents the phrase 'one third the sum of 12 and a number' is B.) 1/3(12+x).
To represent the phrase "one third the sum of 12 and a number", we can break it down into two parts:
1. The sum of 12 and a number
2. One third of that sum
The expression for the sum of 12 and a number is (12 + x). Then, one third of that sum is [tex]\(\frac{1}{3}(12 + x)\).[/tex]
So, the correct expression is:
[tex]B.) \(\frac{1}{3}(12 + x)\)[/tex]
solve the given problem 7y-84=2y+61
A(n) __________ transformation preserves the size and shape of an object's original image; the image is congruent to the pre-image.
A. dilation
B. isometric
C. scale
D. non-isometric
The correct transformation that preserves the size and shape of an object, resulting in congruent images, is an isometric transformation. Examples include translation, rotation, and reflection, all of which maintain the object's proportions and dimensions.
A transformation that preserves the size and shape of an object's original image, such that the image is congruent to the pre-image, is known as an isometric transformation. This transformation includes operations like translation (a shift from one place to another), rotation (turning around a center), and reflection (flipping over a line). All these transformations keep the object's dimensions and proportions unchanged. The key property of isometric transformations is that they maintain congruency and preserve distances and angles.
An example of an isometric transformation is when a square is rotated 90 degrees around its center. The square's shape and size remain the same, even though its orientation has changed. This contrasts with dilation, which changes the size of the object, and affine transformations, which can alter both shape and size, such as through stretching or skewing. The correct answer to the student's question is B. isometric.
Solve the inequality: -1+4y < 31
-1 +4y < 31
add 1 to each side:
4y < 32
divide both sides by 4
y<32/4
y<8
Name the property of equality that justifies this statement if p=q then p+s=q+s
Answer:
Addition property of equality that justifies this statement if p=q then p+s=q+s
Step-by-step explanation:
Addition property of equality states that you add the same number to both sides of an equation.
For example
If a = b then;
a+c = b+c
As per the statement:
if p=q
then;
p+s=q+s
⇒Addition property of equality justifies this statement.
There are three pieces of pizza how many 1/4 pieces of pizza can be sliced from the 3 pieces
Vicky ran 5⁄14 of a mile and walked 1⁄7 of a mile. how much further did vicky run than walk?
List at least three (3) characteristics of carbon that make it a unique element.
Answer: Carbon occurs as a solid, liquid, and gas.
Carbon is found everywhere.
Carbon is versatile and easily combines with other elements.
Carbon bonds with other elements to form macromolecules.
McDonald's has sold more than a billion hamburgers. If it were possible to eat a hamburger every minute of everyday (day and night) without stopping, how many years would it take to eat a billion hamburgers?
Use the vertical line test to determine whether the relation is a function ((-6,-2)
Solve for x and y. What is m
Multiply -2x^(-3) y (5yx^(5)+8xy-4y^(2) x(2) ).
Final answer:
The original equation, after multiplication and simplification, results in -10x^2y^2 - 16y^2 + 8x^-1y^3. This process demonstrates the use of the distributive property and exponent rules in algebra.
Explanation:
The question requires us to multiply -2x-3y by (5yx5+8xy-4y2x2). Proceed by applying the distributive property, which involves multiplying each term inside the parentheses by -2x-3y. Here are the steps:
Multiply -2x-3y by 5yx5 to get -10x2y2.
Multiply -2x-3y by 8xy to get -16y2.
Multiply -2x-3y by -4y2x2 to get 8x-1y3.
Therefore, the final result of the multiplication is -10x2y2 - 16y2 + 8x-1y3.
The result is [tex]\[ -10yx^2 - 16y^2x^{-2} + 8x^{-1}y^3 \][/tex].
To multiply [tex]\(-2x^{-3} y\) by \(5yx^5 + 8xy - 4y^2x^2\)[/tex], we distribute [tex]\(-2x^{-3} y\)[/tex] to each term inside the parentheses.
[tex]\[ -2x^{-3} y (5yx^5) + (-2x^{-3} y)(8xy) + (-2x^{-3} y)(-4y^2x^2) \][/tex]
Simplify each term:
[tex]\[ = -10yx^2 + (-16)x^{-2}y^2x + 8x^{-1}y^3 \][/tex]
[tex]\[ = -10yx^2 - \frac{16y^2}{x^2} + 8x^{-1}y^3 \][/tex]
[tex]\[ = -10yx^2 - 16y^2x^{-2} + 8x^{-1}y^3 \][/tex]
Thus, the final result of the multiplication is [tex]\[ -10yx^2 - 16y^2x^{-2} + 8x^{-1}y^3 \][/tex].
This expression cannot be further simplified, as it represents the result of multiplying each term in the first expression by each term in the second expression and then combining like terms.
Therefore, the correct option is B. [tex]\[ -10yx^2 - 16y^2x^{-2} + 8x^{-1}y^3 \][/tex].
Complete Question:
The quotient of a number r and 7 is no more than 18. I cant find the equation part or the inequality
Answer:
The inequality would be r/7 ≤ 18 and the solution would be r ≤ 126
Step-by-step explanation:
We start by writing the inequality
r/7 ≤ 18
We know to use division between r and 7 since it asks for the quotient and we know to use a ≤ sign since it says "is no more than"
To solve, simply multiply both sides by 7
r ≤ 126
The inequality will be r/7 ≤ 18
Since it's a quotient, we'll need to divide the expression and this will be:
= r/7 ≤ 18
Now the value of r will be gotten thus:
r/7 ≤ 18
Cross multiply.
r ≤ 18 × 7
r ≤ 126
Therefore, this mean that the value of r will be 126 or numbers lower than 126
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answer to #10 and #13. can’t figure out how to use interval notation to write domain and range for graphs.
I NEED HELP QUICK, PLEASE!
A hair salon charges a fixed rate of $25.00 for a haircut and then an additional $15 for any other services. Write a function to model the cost of services there and then determine how many services you had if you were charged $115
A) f(x) = 15x + 25; f(6) = 115
B) f(x) = 25x + 15; f(6) = 165
C) f(x) = 15x + 25; f(6) = 125
D) f(x) = 15x + 25; f(115) = 1750
A) f(x) = 15x + 25; f(6) = 115
Use the graphing calculator to graph the quadratic function y = x2 − 5x − 36. Which value is a solution of 0 = x2 − 5x − 36?
Answer:
B) −4
Step-by-step explanation:
Your friend has $90 when he goes to the fair. he spends $5 to enter the fair and $15 on food. rides at the fair cost $1.50 per ride. which function can be used to determine how much money he has left over after x rides? (1 point)
how can you interpret the independent or conditional probability of two events
1. Independent probability of A and B occurring together (drawing a red queen): [tex]\( \frac{1}{26} \)[/tex]
2. Conditional probability of A given B (drawing a red card given that a queen was drawn): [tex]\( \frac{1}{2} \)[/tex]
- Independent probability: This is the probability of two events occurring together, assuming that one event's occurrence does not affect the other. Mathematically, if A and B are independent events, then [tex]\( P(A \cap B) = P(A) \times P(B) \).[/tex]
- Conditional probability: This is the probability of an event occurring given that another event has already occurred. Mathematically, if A and B are events with[tex]\( P(B) > 0 \)[/tex], then the conditional probability of A given B is [tex]\( P(A|B) = \frac{P(A \cap B)}{P(B)} \).[/tex]
Let's illustrate these concepts with an example:
Suppose we have a deck of cards (52 cards total), and we're interested in two events:
A: Drawing a red card
B: Drawing a queen
First, let's find the independent probabilities:
1. Probability of A (drawing a red card):
- There are 26 red cards out of 52 total cards, so [tex]\( P(A) = \frac{26}{52} = \frac{1}{2} \).[/tex]
2. Probability of B (drawing a queen):
- There are 4 queens out of 52 total cards, so[tex]\( P(B) = \frac{4}{52} = \frac{1}{13} \).[/tex]
Now, let's find the probability of both events occurring together (A and B):
3. Probability of A and B (drawing a red queen):
- There are 2 red queens (hearts and diamonds) out of 52 total cards, so [tex]\( P(A \cap B) = \frac{2}{52} = \frac{1}{26} \).[/tex]
For independent events,[tex]\( P(A \cap B) = P(A) \times P(B) \):[/tex]
[tex]\[ \frac{1}{26} = \frac{1}{2} \times \frac{1}{13} \][/tex]
Now, let's find the conditional probability of A given B:
[tex]\[ P(A|B) = \frac{P(A \cap B)}{P(B)} = \frac{\frac{1}{26}}{\frac{1}{13}} = \frac{1}{2} \][/tex]
1. Independent probability of A and B occurring together (drawing a red queen): [tex]\( \frac{1}{26} \)[/tex]
2. Conditional probability of A given B (drawing a red card given that a queen was drawn): [tex]\( \frac{1}{2} \)[/tex]
In summary, we first calculated the independent probabilities of A and B, then found the probability of A and B occurring together, and finally calculated the conditional probability of A given B using the given formulas and calculations.v
complete question
how can you interpret the independent or conditional probability of two events
Graph y≤1−3x .
Number graph x axis ranging from negative one to five, and y axis ranging from negative four to two. A solid line with arrows at both ends passing through the y axis at one and the x axis at point three. The graph is shaded below the line.
A graph with y axis ranging from negative 4 to 2 and x axis ranging from negative 1 to 4. A dotted line with arrows at both ends passing through the y axis at one and the x axis at point 3. The graph is shaded above the line.
Number graph with y axis ranging from negative 4 to 2, and x axis ranging from negative 2 to 6. A solid line with arrows at both ends passing through the y axis at one and the x axis at point three. The graph is shaded above the line.
Number graph with x axis ranging from negative one to five, and y axis ranging from negative four to two. A dotted line with arrows at both ends passing through the y axis at one and the x axis at point three. The graph is shaded below the line.
To graph the inequality y ≤ 1 - 3x, we can start by graphing the equation y = 1 - 3x. The graph should be a solid line passing through the y-axis at 1 and the x-axis at 1/3. The shaded region below the line represents the solution set.
Explanation:The given inequality is y ≤ 1 - 3x. To graph this inequality, we can start by graphing the equation y = 1 - 3x. This equation represents a line with a y-intercept of 1 and a slope of -3. We can plot the y-intercept at (0, 1) and use the slope to find additional points on the line.
For example, if we increase x by 1, y will decrease by 3. So, when x = 1, y = -2. By connecting these points and extending the line, we can have a line passing through the y-axis at 1 and the x-axis at 1/3.
To graph the inequality y ≤ 1 - 3x, we shade the region below the line because any point in this region will satisfy the inequality.
Therefore, the graph should be a solid line with arrows at both ends, passing through the y-axis at 1 and the x-axis at 1/3, and the region below the line shaded.
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Correct & best answer ill get brainliest.
1. Find the zeros of the function.
f(x) = 9x2 + 6x - 8 (2 points)
a) -2 and 4
b) Negative two divided by three. and Four divided by three.
c) Two divided by three. and Negative four divided by three.
d) 2 and -4
2. Find the zeros of the function.
f(x) = 9x3 - 45x2 + 36x (2 points)
a) 0, 1, and 4
b) -1 and -4
c) 1 and 4
d) 0, -1, and -4
3. Find the zeros of the polynomial function and state the multiplicity of each.
f(x) = 4(x + 7)2(x - 7)3 (2 points)
a) 4, multiplicity 1; -7, multiplicity 3; 7, multiplicity 3
b) -7, multiplicity 3; 7, multiplicity 2
c) 4, multiplicity 1; 7, multiplicity 1; -7, multiplicity 1
d) -7, multiplicity 2; 7, multiplicity 3
4. Find a cubic function with the given zeros. (2 points)
Square root of five. , - Square root of five. , -7
a) f(x) = x3 - 7x2 - 5x - 35
b) f(x) = x3 + 7 x2 - 5x + 35
c) f(x) = x3 + 7x2 - 5x - 35
d) f(x) = x3 + 7x2 + 5x - 35
5. Expand the following using either the Binomial Theorem or Pascal's Triangle. You must show your work for credit.
(2x + 4)3
Don't Put a Bad Words on your answer and you get a warning and report.
One of the rows in the table has an error and does not have the same ratio as the other rows.
Conversion Chart
Feet
Inches
Row 1
3
36
Row 2
6
72
Row 3
7
94
Row 4
9
108
Which explains how to correct the error in the table?
A.Row 1 should show 3 feet is equivalent to 32 inches.
B.Row 2 should show 6 feet is equivalent to 66 inches.
C.Row 3 should show 7 feet is equivalent to 84 inches.
D.Row 4 should show 9 feet is equivalent to 104 inches.
Complete the following theorem.
If two angles in a triangle are congruent to two angles in another triangle, then the ______________ angles are also congruent.
What compound inequality has all real numbers that are less than than -3 or greater than or equal to 5?
Answer:
less than -3 and greater than 5
Step-by-step explanation:
1 cubic meter of concrete has a wight of 2400 kg. 15% of the concrete is water. The rest of the ingredients are cerment, sand and stone. The weights are in a ratio of 1:2:5. Work out the weight of cement, sand and stone in the 1 cubic meter of concrete
Help me please i have a test coming up
Answer:
Step-by-step explanation:
2400 × 0.15 = 360
2400 - 360 = 2040
2040 × 1/8 = 255 kg of Cement
2040 × 2/8 = 510 kg of Sand
2040 × 5/8 = 1275 kg of Stone
To check if it is right
255 + 510 + 1275 = 2040 kg
1 cubic meter of concrete the weight of water is 360 Kg, the weight of cement is 255 Kg, the weight of sand is 510 Kg and the weight of stone is 1275 Kg and this can be determine by forming the linear equation in one variable.
Given :
1 cubic meter of concrete has a wight of 2400 kg.15% of the concrete is water.The rest of the ingredients are cement, sand and stone. The weights are in a ratio of 1:2:5.The weight of the water in the concrete will be:
[tex]= 2400\times \dfrac{15}{100}[/tex]
= 360 Kg
Let x be the weight in Kg. Then the combine weight of stone, cement and sand will be:
[tex]8x = 2400 - 360[/tex]
8x = 2040
x = 255 Kg
Then the weight of the cement will be = 255 Kg.
The weight of the sand will be = [tex]\rm 255\times 2 = 510\; Kg[/tex].
The weight of the stone will be = [tex]\rm 255\times 5 = 1275\; Kg[/tex].
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Help?
The coordinates of the vertices of a polygon are (−2, −2) , (−2, 3) , (2, 4) , (3, 1) , and (0, −2) .
What is the perimeter of the polygon?
Enter your answer as a decimal, rounded to the nearest tenth of a unit, in the box.