Answers
Answer:
x = 31.8°
Step-by-step explanation:
Applying the Law of Sines, we have:
[tex] \frac{sin(x)}{12} = \frac{sin(75)}{22} [/tex]
Multiply both sides by 12
[tex] \frac{sin(x)}{12} \times 12 = \frac{sin(75)}{22} \times 12 [/tex]
[tex] sin(x) = \frac{sin(75) \times 12}{22} [/tex]
[tex] sin(x) = 0.5269 [/tex]
[tex] x = sin^{-1}(0.5269) [/tex]
x = 31.8° (nearest tenth)
Related Questions
Show that the two-variable function f given by f(x, y) = 2x^2 − xy is
differentiable at any point (a, b). What is the derivative of f at (a, b)?
Answers
The derivative of f at (a, b) is the gradient vector [4a - b, -a].
How to determine the derivative of f at (a, b)From the question, we have the following parameters that can be used in our computation:
f(x, y) = 2x^2 − xy
The two-variable function f(x, y) = 2x^2 - xy is differentiable at any point (a, b) if its partial derivatives exist and are continuous at that point.
This is represented as
∂f/∂x = 4x - y
∂f/∂y = -x
The derivative of f at (a, b) can be calculated by evaluating the partial derivatives of f at (a, b):
∂f/∂x(a, b) = 4a - b
∂f/∂y(a, b) = -a
Hence, the derivative of f is [4a - b, -a].
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What is the slope of the line that contains the points negative 3, negative seven halves and (2, −4)?
Answers
Answer: -1/10
Step-by-step explanation:
The sum of three times a number and seven is greater than twice the number -4
Answers
Answer: x > -11
Step-by-step explanation:
3x + 7 > 2x - 4
First, we can simplify the right side of the equation by combining like terms:
3x + 7 > 2x - 4
then we can subtract 2x from both sides of the equation:
3x + 7 - 2x > -4
This gives us:
x+7 > -4
then we can add 4 to both sides of the equation:
x + 7 + 4 > 0
This gives us:
x + 11 > 0
then we can subtract 11 from both sides of the equation:
x + 11 - 11 > 0 - 11
This gives us:
x > -11
so the number is greater than -11.
what is the distributive property and how do I find it
Answers
Answer: The distributive property is a property where there is a coefficient/number, that is being multiplied to a group of numbers enclosed in parentheses. The coefficient can be distributed/multiplied to the numbers in the parentheses individually or after solving the expression in it.
Step-by-step explanation:
You can spot when the distributive property is used when you see a number in front of a group of numbers, such as these examples (in bold):
1. 4(5 + 6) = 46 , in this problem you can solve 5+6 before multiplying it by 4, or multiply 4*5 and 4*6 and then add it.
2. 2(x-3) = 12 , in this situation x is the unknown variable so you must distribute the 2 individually, so the result would look like: (2*x) + (2*-3) -> 2x - 6 = 12
ignore text just answer ty <3
Answers
The histogram shows the distribution of the annual hours of commuting delay per traveler for 46 small and medium urban areas, fewer than one million in population. Kebay 5 10 15 20 hours Which of the following must be true?
a. The mean is greater than the median.
b. The mean is less than the median.
c. The mean is the same as the median.
Answers
In this problem the statement that the mean is greater than the median is true. So, the correct answer is option(a).
We have a histogram which shows the distribution of the annual hours of commuting delay per traveler for 46 small, medium and urban areas, fewer than one million in population. See the diagram carefully and try to draw the conclusion. The shape of the histogram showing that positive skewed or right skewed distribution since Curve increases fastly and decreases slowly. A positive skewed distribution is a type of distribution where most of the values are concentrated in the left tail of the distribution and the right tail of the distribution is longer. In positive skewed distribution,
i) Mean > Median
ii) (Q₃ - Q₂) > (Q₂ - Q₁)
iii) Sqrt(β₁) >0
Hence, The mean is greater than the median is true.
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A clothing store is going out of business. To sell their remaining inventory, the managers drop the price of each item $5 at the end of each week until the item sells. Write the equation of this being shown.
Answers
The equation to represented the situation of drop the price of each item $5 at the end of each week until the item sells as used by the manager of the clothing store is
y = c - $5xHow to write the equation as used by the managerInformation given in the problem include
the managers drop the price of each item $5 at the end of each week
until the item sells
let c represent the cost of the item at the beginning
;et x represent the number of weeks
let y represent the cost at the end of each week
The equation is modeled as follows
the present cost c will drop by $5 each week
c - $5x
The cost after the drop that is at the end of the week
y = c - $5x
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The graph below shows f(x), which represents a parent function, and g(x), which represents a translation of that function.
On a coordinate plane, 2 exponential functions are shown. f (x) decreases in quadrant 2 and approaches y = 0 in quadrant 1. It goes through (negative 3, 8) and crosses the y-axis at (0, 0.5). g (x) decreases in quadrant 2 and approaches y = 0 in quadrant 1. It goes crosses the y-axis at (0, 14) and goes through (1, 5) and (2, 2).
Which statements about the functions are true? Check all that apply.
f(x) = (one-half) Superscript x
g(x) = (one-half) Superscript x + 4 – 2
The ranges of both functions are the same.
The domains of both functions are the same.
The translation from f(x) to g(x) is right 4 units and down 2 units.
Answers
The statements about the functions are true A. f(x) = 1/2ˣ
D. The domains of both functions are the same.E. The translation from f(x) to g(x) is right 4 units and down 2 units.What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s range(involving values of y) or in it’s domain(involving values of x).
We are given that On a coordinate plane, 2 exponential functions are shown. f (x) decreases in quadrant 2 and approaches y = 0 in quadrant 1.
When evaluated in zero we have:
f(0) = 2(1/2)^0 = 2
So it crosses through the point (0, 2).
And when evaluated in x = 1, then
f(1) = 2(1/2)^1 = 1
Then it also passes through (1, 1). It goes crosses the y-axis at (0, 14) and goes through (1, 5) and (2, 2).
The answers are A, D, and E
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Answer:a,d,e
Step-by-step explanation:
i took the test
PLEASE HELP MEEEEEE IM STRUGGLING
Answers
Answer:
Step-by-step explanation: i can't see the lab top
Please as soon as possible,
I’ll give brainliest
Answers
1. The average rate of range for 3 to 4 days is -3.9.
2. Approximate rate of range for 3 days is 34.8.
How is the instantaneous rate of change estimated?Adding a very small increment, for example, can help us approximate the instantaneous rate of change at x = a.
The instantaneous rate of change is equal to the slope of the tangent line at a given location. The slope of secant lines can be used to calculate the slope at a point as each secant line's "run" gets closer to zero (the slope of the tangent line).
You can find the instantaneous rate of change of a function by computing the derivative at a specific point and then entering the point's x-value.
The speed at which that function changes right now.
IROC = f(a + 0.001) - f(a) / 0.001 f(a) = 0.1
1.
[tex]$$\begin{aligned}& \text { A.R.C }=\frac{\mathrm{A}(4)-\mathrm{A}(3)}{4-3} \\& \mathrm{~A}(4)=100(0.5)^{\frac{4}{15}} \\& \mathrm{~A}(4)=83.12378 \\& \mathrm{~A}(3)=100(0.5)^{\frac{3}{16}} \\& \mathbf{A}(3)=87.05505\end{aligned}$$A. R. C $=\frac{83.12378-87.05505}{1}$$$=-3.93127$$A. R. $\mathrm{C}=-3.9$[/tex]
2. it can be obtained by takibg derivative with respect 't';
[tex]$\mathrm{A}^{\prime}(\mathrm{t})=100\left(\frac{\mathrm{t}}{15}\right)(0.5)^{\left(\frac{t}{15}\right)-1}$\\rate of change in 3 days:$$\begin{aligned}& \mathrm{A}^{\prime}(3)=100\left(\frac{3}{15}\right)(0.5)^{\left(\frac{3}{15}\right)-1} \\& \mathrm{~A}^{\prime}(3)=34.82202\end{aligned}$$Approximate rate of change;$$\mathrm{A}^{\prime}(3) \approx 34.8$$[/tex]
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what si the mad of the numbers: 240, 225, 227, 227, 228, 230, 230, 231, 238, 240
Answers
The MAD of the given set of numbers is 4.64.
What is MAD?The mean absolute deviation (MAD) is a variability metric that indicates the average distance between observations and their mean. MAD interprets the data in its original units. Larger values indicate that the data points are further apart from the mean. Lower values, on the other hand, represent data points clustering closer to it. The average absolute deviation is also known as the mean deviation.
The mean absolute deviation is defined in the same way as the standard deviation (SD). While they both measure variability, their calculations differ. Some proponents of MAD have suggested that it replace SD as the primary measure in recent years because it is a simpler concept that is more applicable in real life.
Lets find the mean of given data set:
240+ 225+ 227+ 227+ 228+ 230+ 230+ 231+ 238+ 240
= 2316
⇒ 2316/10 = 231.6
Find the distances of the mean
240 - 231.6 = 8.4
225 - 231.6 = 6.6
227 - 231.6 = 4.6
227 - 231.6 = 4.6
228 - 231.6 = 3.6
230 - 231.6 = 1.6
230 - 231.6 = 1.6
231 - 231.6 = 0.6
238 - 231.6 = 6.4
240 - 231.6 = 8.4
Add the distances
8.4+ 6.6+ 4.6 + 4.6 + 3.6 + 1.6 + 1.6 + 0.6 + 6.4 + 8.4 = 46.4
Divide the sum by the number of data points.
46.4/10 = 4.64
Thus, The Mad of the given set of numbers is 4.64.
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Can someone help me? I'm confused
Answers
Match the word to its definition or symbol.
1. ∈ element
2. { } braces representing a set with no elements
3. C subset
4. {whole numbers] finite set
5. ∅ symbol for the empty set or null set
6. A set limited by definition - infinite set
7. ∉ not an element
What is a set in math?In mathematics, a set is a logically arranged group of items that can be represented in either set-builder or roster form.
Curly brackets are typically used to represent sets.
Sets with a finite/countable number of members are referred to as finite sets. Due to their ability to count, finite sets are often referred to as countable sets.
A set with an infinite number of elements is one that cannot be numbered. Any set that has no last element is said to be infinite Set
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Find two fractions with a sum of but with neither denominator equal to 3.
Answers
Answer:
2/6 +2/6= 4/6 and 4/6 reduced down is 2/3
Step-by-step explanation:
hope this helps
f(0) = 2 , f(-2) = -2 Write a linear function f with the given values.
Answers
The linear function f with the given values is f(x) = 2x + 2
How to determine the linear function f with the given values.From the question, we have the following parameters that can be used in our computation:
f(0) = 2 , f(-2) = -2
A linear equation can be represented as
f(x) = mx + c
Substitute the known values in the above equation, so, we have the following representation
m * 0 + c = 2
m * -2 + c = -2
Solving 0 * x + c = 2, we have
c = 2
So, we have
m * -2 + c = -2
This gives
-2 * m + 2 = -2
Evaluate
-2m = -4
Evaluate
m = 2
So, we have
f(x) = 2x + 2
Hence, the function is f(x) = 2x + 2
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Una deuda de $1500 se cancelará a un plazo de 6 trimestres con una tasa del 5% compuesto mensual. Determine:
a) El valor final que termina cancelando por la deuda contraída.
b) Calcule el tiempo (trimestres) que se demora el mismo préstamo inicial tomando como referencia una tasa del 12% anual compuesta.
Answers
a) Una deuda total de $ 4837.65 en un período de amortización debe ser pagada en seis trimestres.
b) Se requiere aproximadamente 42 trimestres para pagar la misma deuda.
¿Cómo determinar el valor final a pagar y el tiempo requerido de amortización?En este problema tenemos dos casos de préstamos bajo un modelo de interés compuesto, léase un caso acumulativo de intereses en el tiempo, en función de períodos definidos. La persona que recibe el préstamo se hace acreedora de una deuda, la cual debe ser amortizada en el tiempo. Ahora, bien, el modelo de interés compuesto se describe bajo la siguiente fórmula:
D' = D · (1 + r / 100)ˣ
Donde:
D - Deuda inicial, en unidades monetarias.D' - Deuda final, en unidades monetarias.r - Tasa de interés, en porcentaje.x - Número de períodos de amortización, en unidades de tiempo.a) Si sabemos que D = 1500, r = 5 y x = 24, entonces:
D' = 1500 · (1 + 5 / 100)²⁴
D' = 4837.65
La persona debe pagar una deuda total de $ 4837.65 en un período de amortización de seis trimestres (nótese que un año tiene cuatro trimestres).
b) Es preciso determinar el período equivalente para una tasa de interés compuesta anual de 12 %, esto es:
D' = D · (1 + r /100)ˣ
㏒ (D' / D) = x · ㏒ (1 + r / 100)
㏒ D' - ㏒ D = x · ㏒ (1 + r / 100)
x = (㏒ D' - ㏒ D) / [㏒ (1 + r / 100)]
x = (㏒ 4837.65 - ㏒ 1500) / [㏒ (1 + 12 / 100)]
x = 10.332 años (aprox. 42 trimestres)
El período de amortización es de aproximadamente 42 trimestres.
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7(3x+3) as an algebraic expression
Answers
Answer: 21x + 21
Step-by-step explanation:
Simply multiply 7 to 3x and 3 respectively.
Please help!
Graph y = 5/3x - 9.
Answers
Answer:
I have graphed it and attached an image in the explanation.
Step-by-step explanation:
If Gerry is approved for a $150,000 mortgage at 7.5 percent interest for a 30-year loan, what would the
monthly payment be?
$1081.96
$1069.58
$1032.32
$1048.82
Answers
Answer:
One can use the formula for a compound annuity
A = (1 - (1 + i)^-n) / i
n = payments = 360 (12/yr * 30 yr)
i - interest rate = .075 / 12 = .00625
The formula tells you what $1 / mo will be worth after 360 mos
A = (1 - 1.00625^-360) / .00625 = (1 - .10362) / .00625
A = 143.02
To have 150,000 after 30 yrs the monthly payment needs to be
150000 / 143.02 = 1048.82
The discount price of socks are $21. What is the regular price
Answers
Answer: To help you with this problem, I need to know the discount percentage.
Step-by-step explanation:
Solve the following radical equation.
6y2−22y+16⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯√+4=4y
Write your answer(s) beginning with the first answer box. If applicable, the second answer box may be left blank.
Answers
The solution to the radical equation is 2/5
How to determine the solutionFrom the question, we have the following radical equation
6y2−22y+16⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯√+4=4y
Complete the equation
So, we have the following representation
6√y² − 22y + √16 + 4 = 4y
Evaluate the radicals
The equation becomes
6y - 22y + 4 + 4 = 4y
So, we have
6y - 22y + 8 = 4y
Evaluate the like terms
So, we have the following
20y = 8
Divide both sides by 20
y = 2/5
Hence, the solution is 2/5
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determine the constant rate of change (slope) of the linear function. a high school basketball team notices that attendance at its games changes at a constant rate based on the number of losses the team has suffered. when the team had lost seven games, 295 people attended the next game. when the team had lost 13 games, 199 people attended the next game.
Answers
The team loses 20 people/audience with each loss.
The slope formula defines to the formula used to calculate the steepness of a line and determines how much it's inclined. To calculate the slope of the lines, the x and y coordinates of the points lying on the line can be used.
The formula to calculate slope is:
m = (y2 - y1)/(x2 - x1) = Δy/Δx
When the team lost eight games, 295 people attended the next game.
When the team lost 13 games, 199 people attended the next game.
Slope = 295-199/8-13
slope=100/-5
slope=-20
Therefore, the team loses 20 people/audience with each loss.
And the attendance loss is 20 times as great as the number of games lost/losses
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93 divided by 585.9 steps to solve?
Answers
A simple random sample of size n is drawn from a population that is normally distributed. The sample mean, x, is found to be 113, and the sample standard deviation, s, is found to be 10.
(a) Construct a 95% confidence interval about μ if the sample size, n, is 26.
(b) Construct a 95% confidence interval about μ if the sample size, n, is 15.
(c) Construct a 90% confidence interval about μ if the sample size, n, is 26.
(d) Could we have computed the confidence intervals in parts (a)-(c) if the population had not been normally distributed?
Answers
a) The 95% confidence interval about μ with n = 26 is given as follows: (109, 117).
b) The 95% confidence interval about μ with n = 15 is given as follows: (107.5, 118.5).
c) The 90% confidence interval about μ with n = 26 is given as follows: (109.7, 116.3).
d) The intervals could not have been computed if the population was not normally distributed, as the sample size is less than 30.
What is a t-distribution confidence interval?The t-distribution is used when the standard deviation for the population is not known, and the bounds of the confidence interval are given according to the following rule:
[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]
In which the variables of the equation are presented as follows:
[tex]\overline{x}[/tex] is the sample mean.t is the critical value.n is the sample size.s is the standard deviation for the sample.The sample mean and standard deviation for this problem are given as follows:
[tex]\overline{x} = 113, s = 10[/tex]
The critical values are given as follows:
95% confidence, 25 df: 2.0595.95% confidence, 14 df: 2.1448.90% confidence, 25 df: 1.7081.The bounds of the interval for item a are given as follows:
[tex]113 - 2.0595\frac{10}{\sqrt{26}} = 107.5[/tex][tex]113 + 2.0595\frac{10}{\sqrt{26}} = 118.5[/tex]The bounds of the interval for item b are given as follows:
[tex]113 - 2.1448\frac{10}{\sqrt{15}} = 109[/tex][tex]113 + 2.1448\frac{10}{\sqrt{15}} = 117[/tex]The bounds of the interval for item c are given as follows:
[tex]113 - 1.7081\frac{10}{\sqrt{26}} = 109.7[/tex][tex]113 + 1.7081\frac{10}{\sqrt{26}} = 116.3[/tex]The Central Limit Theorem states that the intervals can only be calculated for non-normal populations if the sample size is greater than 30.
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Solve this please i will mark brainlest and give 5 hearts
Answers
Answer: 5.75pi(yards)
Step-by-step explanation: We know the radius is 3 so the area is 9pi. The shaded area has an angle of 230 and the total angle of a circle is 360. We multiply the area by the fraction of the angle which is 230/360(9pi).
Please help I will give all stars!! I have a text on this tomorrow!!
Answers
5x - 3y = 7 is in slope intercept form is y = 5/3x - 7/3
How do you write slope intercept form?When you know the slope of the line to be investigated and the given point is also the y intercept, you can utilise the slope intercept formula, y = mx + b. (0, b). The y value of the y intercept point is denoted by the symbol b in the formula.
You can utilize two different versions of a line's general form to figure out its equation.
These are the formulas:
1) (y - y1) = m (x – x1), the Point-Slope Formula
2) The formula for slope-intercept, y = mx + b
The form you use depends on the information you are provided at the beginning, as the names suggest.
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Solve each expression using the order of operations.
64 ÷ 8 × 2 + 2 × 4 – 4 × 5
(3 + 9) × 2 ÷ 4
Answers
Answer:
64 ÷ 8 × 2 + 2 × 4 – 4 × 5= 4 (3 + 9) × 2 ÷ 4= 6
Which is the joint relative frequency for teachers who teach math and not English? Round the answer to the nearest percent.
Answers
The required percentage of teachers who teach math but not English is 21%. Option B is correct.
What is the percentage?The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.
here,
Total teachers = 104
A number of teachers teach math but not English = 22
Percentage = 22 / 104 × 100%
Percentage = 21%
Thus, the required percentage of teachers who teach math but not English is 21%. Option B is correct.
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We need to assume the sample was randomly selected because we are making inferences about _____________
Answers
We need to assume the sample was randomly selected because we are making inferences about parameters.
In mathematics, the parameter is a variable for which the range of possible values identifies a collection of distinct cases in a problem. Any equation expressed in terms of parameters is a parametric equation. The general equation of a straight line in slope-intercept form, y = mx+b, in which m and b are parameters, is an example of a parametric equation.
In statistics, the parameter in a function is a variable whose value is sought by means of evidence from samples. The resulting assigned value is the estimate or statistic.
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Find the domain and range for the function shown in the graph given below.
What is the domain?
what is the range?
(Type your answer in interval notation.)
Answers
Answer:
Step-by-step explanation:
y axis range is 35
What is the solution to the equation below?
12+v1 – 5x = 18
A. x = -7
B. x = 7
C. x = 1
D. x = -1
Answers
Solving given algebra problem, value of x is equal to -1. It is the area of mathematics that uses arithmetic to manipulate or operate abstract symbols rather than actual numbers.
In algebra, how do you solve square roots?Isolate the squared term and the constant term on the opposite sides of the equation to solve quadratic equations using the square root method. After that, take the square root of both sides, plus or minus the side with the constant term.
Given equation,
[tex]12+\sqrt{1-5x} =18\\\sqrt{1-5x}=18-12\\ \sqrt{1-5x}=6\\\\square\\ case1\\1-5x=64x=-1\\case2\\1-5x=-6\\x=7/5[/tex]
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