. the salaries of physicians in a certain speciality are approximately normally distributed. if 25 percent of these physicians earn less than $180,000 and 25 percent earn more than $320,000, approximately what fraction earn (a) less than $200,000? (b) between $280,000 and $320,000?
When 25 percent of doctors make less than $180k and 25% make more than $320k, a. Approximately 13.14% of physicians earn less than $200,000. and b. Approximately 7.75% of physicians earn between $280,000 and $320,000.
a. The fraction of physicians who earn less than $200,000 can be estimated using the given information as follows:
Let's denote the mean salary of physicians in this specialty by μ and the standard deviation by σ. Since the salaries are approximately normally distributed, we can use the properties of the standard normal distribution to solve this problem.
We know that 25% of the physicians earn less than $180,000, which means that their z-score (number of standard deviations from the mean) is: z = (180,000 - μ) / σ
Using a calculator, we can find the z-score corresponding to the 25th percentile, which is approximately -0.674. Therefore: -0.674 = (180,000 - μ) / σ
Similarly, we know that 75% of the physicians earn more than $180,000, which means that their z-score is: z = (320,000 - μ) / σ
Using the calculator, we can find the z-score corresponding to the 75th percentile, which is approximately 0.674. Therefore: 0.674 = (320,000 - μ) / σ
Solving these two equations simultaneously, we can find μ and σ:
μ = $250,000
σ = $53,333
Now, to find the fraction of physicians who earn less than $200,000, we need to calculate the z-score corresponding to this salary: z = (200,000 - μ) / σ = -1.125
Using the calculator, we can find that the fraction of physicians who earn less than $200,000 is approximately 0.1314.
b. The fraction of physicians who earn between $280,000 and $320,000 can be estimated using the same method as above. We need to calculate the z-scores corresponding to these salaries:
z1 = (280,000 - μ) / σ = 0.596
z2 = (320,000 - μ) / σ = 0.674
Using the calculator, we can find the area between these two z-scores, which represents the fraction of physicians who earn between $280,000 and $320,000. This area is approximately 0.0775.
To know more about percent, refer here:
https://brainly.com/question/29014288#
#SPJ11
-5x+4y=3 what is the total of x
Answer:
x= -3/5+4y/5
x= -3/5 or -0.6 in decimal form
Step-by-step explanation:
I hope this helps :)
Rewrite the following polynomial in standard form. -x^5+\frac{1}{5}+x^3 −x 5 + 5 1 +x 3
The given polynomial is x⁵ + (1/5)x³ - x⁵ - x + 5 + x³, Combining the like terms, we get: 2x⁵ + (6/5)x³ - x + 5 This is the polynomial in standard form.
To rewrite the given polynomial in standard form, we first need to combine the like terms. The polynomial can be simplified by adding the coefficients of the same degree terms. After combining like terms, we get -2x⁵ + (6/5)x³ - x + 5. This is the standard form of the polynomial, where the terms are arranged in descending order of degree, and each term has a coefficient multiplied by a power of x. In this case, the highest degree term is -2x⁵, followed by (6/5)x³, -x, and finally, the constant term 5.
To learn more about polynomial click here
brainly.com/question/11536910
#SPJ1
Complete Question
Rewrite the following polynomial in standard form. -x⁵ + (1/5)x³ - x⁵ - x + 5 + x³
Rewrite sin^2 (x) cos^2 (x) in expanded form, with no powers, parentheses or products.
cos^2(x) - cos^4(x)
sin^2 (x) cos^2 (x) can be written as sin^2 (x) cos^2 (x) = (1-cos^2(x)) cos^2(x)Expanding (1-cos^2(x)) cos^2(x) gives - cos^4(x) + cos^2(x)Therefore, sin^2 (x) cos^2 (x) in expanded form, with no powers, parentheses or products is cos^2(x) - cos^4(x).
Learn more about cosine
brainly.com/question/29114352
#SPJ4
simone is designing a piece of artwork in the shape of a square pyramid for a hotel. she wants to cover the pyramid with decorative glass. how many square feet of glass does simone need to cover the entire pyramid?
Simone will need approximately 429.4 square feet of glass to cover the entire pyramid.
Calculating the surface area of a square pyramid
The surface area of a square pyramid can be calculated by using the following formula: S = l² + 2lw
where, S = surface areal = length of one side of the bases = 10 feet
w = slant height of the pyramid
We need to find the slant height of the pyramid to calculate the surface area of the pyramid.
The slant height of the square pyramid can be calculated using the Pythagorean theorem. We can draw a triangle by joining the midpoint of one of the sides of the base and the apex of the pyramid.
This will divide the pyramid into two right triangles. Using the Pythagorean theorem, we have; l² + h² = sl²
where, h = height of the pyramid = 14 feet
l = half the length of one of the sides of the base = 5 feet
Substituting the given values into the above formula, we get;
5² + 14² = s²
25 + 196 = s²
221 = s²s = √221 ≈ 14.87 feet
Now that we have the slant height of the pyramid, we can substitute the values into the surface area formula we had earlier: S = l² + 2lw
S = 10² + 2(10)(14.87)S ≈ 429.4 square feet
Therefore, Simone will need approximately 429.4 square feet of glass to cover the entire pyramid.
To know more about pyramid: https://brainly.com/question/18994842
#SPJ11
7/8/2+3 1/12
please answer who ever answer first will get brainliest
Find a function r(t) that describes the following curve. A circle of radius 6 centered at (4,3,0) that lies in the plane y = 3 Choose the correct answer below. O A. r(t) = (4 cos t,3 sin t,6), for Osts 21 OB. r(t) = (4 + 6 cos t,3,6 sin t), for Osts 21 O c. r(t) = (6 cost +4,6 sint +3,0), for Osts 21 OD. r(t) = (4 cost+6,3, sin t+6), for Osts 21 +
Function describing following curve in which a circle of radius 6 centered at (4,3,0) that lies in the plane y = 3 is [tex]r(t) = (6 cos t +4,6 sin t +3,0)[/tex], for Osts 21. Therefore the correct answer is Option c.
A circle of radius 6 centered at (4,3,0) that lies in the plane y = 3 can be described by the following function:
[tex]r(t) = (6 cost +4,6 sint +3,0), for Osts 21[/tex]
This function describes the position of a point on the circle at any given time t.
The x and z coordinates are determined by the cosine and sine function, respectively, with a radius of 6. The y coordinate is constant at 3, since the circle lies in the plane y = 3. The center of the circle is shifted by adding 4 to the x coordinate and 3 to the y coordinate.
Therefore, the correct answer is Option c. [tex]r(t) = (6 cost +4,6 sint +3,0),[/tex] for Osts 21.
Know more about coordinate here:
https://brainly.com/question/16634867
#SPJ11
Question 1 A horizontal or vertical line segment with a length of 12 units has one endpoint at (-2,-7). Identify the ordered pairs of three points that could each be the other endpoint of the line segment. Use the coordinate plane if needed. Answer format: (x,y)
the ordered pairs of three points that could each be the other endpoint of the line segment are (10,-7) or (-14,-7) and (-2,5) or (-2,-19)
Define Line segment
A line segment in geometry contains two different points on it that called its boundaries. A line segment is sometimes called as a section of a line that links two places.
Given
One end point=(-2,-7)
Length of the line segment=12unit
Line segment is horizontal
Ordered pair that will be other end of the line segment=(-2+12,-7) or(-2-12,-7)
=(10,-7) or (-14,-7)
Line segment is Vertical
Ordered pair that will be other end of the line segment=(-2,-7+12) or(-2,-7-12)
=(-2,5) or (-2,-19)
To know more about endpoint , visit
https://brainly.com/question/29164764
#SPJ1
Assume that the masses of adult men can be modelled by the Normal
distribution with mean 75 kg and standard deviation 5 kg.
The probability that an adult man, chosen at random, will have a mass greater
than 77. 5 kg is
(4 d. P. )
The probability that an adult man, chosen at random, will have a mass between
76. 6 kg and 83. 5 kg is
(4 d. P. )
62% of adult men have a mass greater than
kg (1 d. P. )
The interquartile range for the masses of adult men is
kg (1 d. P. )
The interquartile range for the masses of adult men is 6.75 kg (1 decimal place).
The probability that an adult man, chosen at random, will have a mass greater than 77.5 kg is 0.4 (4 decimal places). The probability that an adult man, chosen at random, will have a mass between 76.6 kg and 83.5 kg is 0.2366 (4 decimal places). 62% of adult men have a mass greater than 78.45 kg (1 decimal place).
Let X be the mass of an adult man, then X ~ N(75, 5^2).
P(X > 77.5) = P(Z > (77.5 - 75) / 5) where Z is the standard normal random variable.
P(Z > 0.5) = 1 - P(Z ≤ 0.5) ≈ 0.3085
Therefore, the probability that an adult man, chosen at random, will have a mass greater than 77.5 kg is approximately 0.3085.
P(76.6 < X < 83.5) = P[(76.6 - 75) / 5 < Z < (83.5 - 75) / 5]
P(1.32 < Z < 1.7) = P(Z < 1.7) - P(Z < 1.32) ≈ 0.0932
Therefore, the probability that an adult man, chosen at random, will have a mass between 76.6 kg and 83.5 kg is approximately 0.0932.
Let p be the proportion of adult men with a mass greater than some value x, then we want to find x such that p = 0.62.
By standardizing and using the standard normal distribution table, we get:
P(Z > (x - 75) / 5) = 0.62
P(Z < (75 - x) / 5) = 0.38
Using the standard normal distribution table, we find that Z ≈ 0.2533
Therefore, (x - 75) / 5 ≈ 0.2533
x ≈ 76.267 kg (rounded to 1 decimal place)
Therefore, 62% of adult men have a mass greater than 76.3 kg.
The interquartile range (IQR) is a measure of spread and is defined as the difference between the 75th percentile and the 25th percentile of the distribution. For a normal distribution, the IQR is approximately 1.35 times the standard deviation.
IQR ≈ 1.35 * 5 ≈ 6.75 kg (rounded to 1 decimal place)
To learn more about Interquartile range :
https://brainly.com/question/4102829
#SPJ11
Assignment Scoring Your last submission is used for your score. 1. + -/1 points SPreCalc7 3.7.033. My Notes Solve the inequality. (Enter your answer using interval notation.) 72 - 72 > 1 X-1 X Need Help? Read It Talk to a Tutor 2. + -/1 points SPreCalc7 3.7.037. My Notes Find all values of x for which the graph of Flies above the graph of g. (Enter your answer using interval notation.) f(x) = x2; 9(x) = 2x + 48 Need Help? Read It Talk to a Tutor 3. -/1 points SPreCalc7 3.7.041. My Notes Find the domain of the given function. (Enter your answer using interval notation.) f(x) = 72 + x - x2
domain of the function is (-∞, ∞)
When answering questions on the Brainly platform, it is important to always be factually accurate, professional, and friendly. In addition, you should be concise and provide a step-by-step explanation in your answer. Irrelevant parts of the question should be ignored, and the following terms should be used in your answer.To solve the inequality 72 - 72 > 1 X-1 X, we need to simplify the inequality as shown below:72 - 72 > 1 X-1 X0 > X - 1Since we want to get X alone on one side of the inequality, we need to add 1 to both sides:0 + 1 > X - 1 + 1X > 0Thus, the solution to the inequality 72 - 72 > 1 X-1 X is (0, ∞).To find all values of x for which the graph of f(x) = x² flies above the graph of g(x) = 2x + 48, we need to solve the inequality:f(x) > g(x)x² > 2x + 48We can rearrange this inequality as follows:x² - 2x > 48Now, we need to factor the left-hand side of the inequality:x(x - 2) > 48The inequality will be satisfied if x > 0 and x - 2 > 0 (i.e. x > 2), so the solution to the inequality is x > 2.The domain of the given function f(x) = 72 + x - x² is all real numbers, since there are no restrictions on the input value x. Therefore, the domain of the function is (-∞, ∞).
Learn more about Function
brainly.com/question/12431044
#SPJ4
In the diagram below, \triangle EFD\sim \triangle GHD△EFD∼△GHD. Which ratio is equivalent to tan FF?
The equivalent ratio to tan F in right angles triangle, △EFD is tan F = DE / DF.
Explain about the similar triangles?Identical triangles differ in size but have the same shape. Corresponding angles are identical in similar triangles. Similar triangles have corresponding sides that have the same ratio. The ratio of a square of any two of their corresponding sides to any identical triangle's area is the same.For the stated question:
△EFD∼△GHD
So, in right angles triangle, △EFD
Sin Ф = perpendicular / hypotenuse.
Sin E = DF / EF
And,
The ratio is equivalent to tan F = perpendicular / base
tan F = DE / DF
Thus, the equivalent ratio to tan F in right angles triangle, △EFD is tan F = DE / DF.
Know more about similar triangles
https://brainly.com/question/14285697
#SPJ9
The complete question is attached:
Which linear function can be used to model the line on the graph?
Option (a) [tex]y=\frac{3x}{2} -5[/tex] can be used as a the model line on the graph for the Linear function.
What is Linear function?A linear function in mathematics is one that has either one or two variables but no exponents. It is a function with a straight line as its graph.
A straight line on the coordinate plane is described by a linear function.
Option (a) [tex]y=\frac{3x}{2} -5[/tex] satisfy with all point as below,
If we take, x = 0, we get y = -5
If we take, x = 2, we get y = -2
If we take, x = 4, we get y = 1
If we take, x = 6, we get y = 4
If we take, x = 8, we get y = 7
So, here we see all the value are match according to the graph.
Therefore, [tex]y=\frac{3x}{2} -5[/tex] can be used as a the model line on the graph for the Linear function.
To learn more about Linear function, visit:
https://brainly.com/question/2408815
#SPJ1
Determine the equation of the circle with radius 5 and center (-5.-6).
The equatiοn οf the circle is [tex](x + 5)^2 + (y + 6)^2 = 25[/tex].
The standard fοrm equatiοn οf a circle with radius "r" and center (a, b) is:
[tex](x - a)^2 + (y - b)^2 = r^2[/tex]
In this case, the center is (-5, -6) and the radius is 5. Sο, we can substitute these values intο the standard fοrm equatiοn and get:
[tex](x - (-5))^2 + (y - (-6))^2 = 5^2[/tex]
Simplifying the equatiοn, we get:
[tex](x + 5)^2 + (y + 6)^2 = 25[/tex]
Therefοre, the equatiοn οf the circle is [tex](x + 5)^2 + (y + 6)^2 = 25.[/tex]
To learn more about circles, from the link given.
https://brainly.com/question/29142813
#SPJ1
Giving 50 points
Solve for x.
x² = 144
Enter your answers in the boxes. Enter the smaller answer first.
x = and x =
Answer:
x = -12 and x = 12.
Step-by-step explanation:
To solve for x, we need to take the square root of both sides of the equation:
x² = 144
√(x²) = √144
since sqaure root gives both positive and neagtive value, so
x = ±12
So the solutions for x are x = -12 and x = 12.
For the right triangles below, find the exact values of the side lengths b and d.
If necessary, write your responses in simplified radical form.
The side of the right triangle can be found as follows:
b = 4√2 units
d = 7√3 / 2 units
How to find the side of a right triangle?A right triangle is a triangle that has one of its angles as 90 degrees. The sum of angles in a triangle is 180 degrees.
Therefore, let's use trigonometric ratios to find the side of the right triangle as follows;
Let's find b as follows:
sin 45 = opposite / hypotenuse
sin 45° = b / 8
cross multiply
b = 8 sin 45
b = 8 × √2 / 2
b = 8√2 / 2
b = 4√2 units
Let's find d as follows:
sin 60° = d / 7
cross multiply
d = 7 sin 60
d = 7 × √3 / 2
d = 7√3 / 2 units
learn more on right triangles here: https://brainly.com/question/28696213
#SPJ1
Write the 5 number summary for the set of data.
42,58,67,55,40,69,66,51,46,48,68
minimum ___
quartile 1__
quartile 2___
quartile3___
Maximum____
The 5 number summary for the given dataset (40, 42, 46, 48, 51, 55, 58, 66, 67, 68, 69) is: Minimum: 40, Q1: 47, Median (Q2): 55, Q3: 66.5, Maximum: 69.
What is statistics ?
Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of data. It involves the use of quantitative methods to gather, describe, and draw inferences from data, which can be used to make decisions, predictions, or conclusions about a population or a phenomenon.
To find the 5 number summary, we need to find the minimum, maximum, and the three quartiles of the given dataset:
The minimum value is 40.
To find the quartiles, we first need to sort the data in ascending order:
40, 42, 46, 48, 51, 55, 58, 66, 67, 68, 69
The median (quartile 2) is the middle value of the dataset, which is 55.
Quartile 1 (Q1) is the median of the lower half of the dataset, which includes the values 40, 42, 46, 48, and 51. The median of this lower half is (46+48)/2 = 47.
Quartile 3 (Q3) is the median of the upper half of the dataset, which includes the values 58, 66, 67, 68, and 69. The median of this upper half is (66+67)/2 = 66.5.
The maximum value is 69.
Therefore, the 5 number summary for the given dataset is:
Minimum: 40
Q1: 47
Median (Q2): 55
Q3: 66.5
Maximum: 69
Therefore, the 5 number summary for the given dataset (40, 42, 46, 48, 51, 55, 58, 66, 67, 68, 69) is: Minimum: 40, Q1: 47, Median (Q2): 55, Q3: 66.5, Maximum: 69.
To know more about statistics visit :
https://brainly.com/question/15525560
#SPJ1
2. a researcher wants to know how often children push other children onto the ground. to study this, she watches children on the playground for 10 minutes and records the number of pushes. what kind of sampling is she not doing?
The researcher is not conducting non-random sampling.
Random sampling is a sampling technique in which every individual or element of the population of interest has an equal opportunity of being selected for the sample. Each member of the population has an equal chance of being selected for the sample. Random sampling helps to ensure that the sample is representative of the population.
Non-random sampling, on the other hand, is a sampling technique in which the individuals or elements of the population of interest are not randomly selected. In other words, not every member of the population has an equal chance of being selected. This sampling method is biased and can lead to an unrepresentative sample.
The researcher is not conducting a non-random sampling technique because she is observing every child in the population of interest. The population of interest, in this case, is the children on the playground.
What kind of sampling is the researcher not doing?The researcher is not conducting non-random sampling because random sampling is a sampling technique in which every individual or element of the population of interest has an equal opportunity of being selected for the sample.
To know more about "non-random sampling": https://brainly.com/question/24466382
#SPJ11
How will the product change if it be number is decreased by a factor of two and the other is decreased by a factor of eight?
Answer:
Assuming you're referring to a product of two numbers, if one number is decreased by a factor of two and the other is decreased by a factor of eight, the overall effect on the product will depend on the relative values of the two numbers.
Let's say the product is given by P = a * b, where a and b are the two numbers. If we decrease one number by a factor of two, we can write it as 0.5a. Similarly, if we decrease the other number by a factor of eight, we can write it as 0.125b. So the new product, P', can be written as:
P' = (0.5a) * (0.125b)
= 0.0625ab
So the new product will be 1/16th (0.0625) of the original product. This means that the product will be decreased by a factor of 16.
In other words, if you decrease one number by a factor of two and the other by a factor of eight, the resulting product will be 16 times smaller than the original product.
A family buys 4 airline tickets online. The family buys travel insurance that costs $19 per ticket. The total cost is $724. Let x represent the price of one ticket. Write an equation for the total cost. Then find the price of one ticket.
Answer:
total cost equation = ( 9+x) times 4 = 724. Total,price of a ticket is 162$
Step-by-step explanation:
Since insurance for each ticket costs 19$ and the family bought four and the ticket itself costs x, the costs of the four tickets is (19+x) times 4. If thr total cost is 724 then we can take 19 times4 and subtract that from it because 19times 4 + x times 4 is the same as (19+x) times 4. From this we fet 648. Now we have x4 or x times 4 = 648 leftover, so divided 648 by 4 to get one x out of it since it is made up of four x. You get 162 from this, so the price of a ticket without insurance is 162$
Which of the following situations can be modeled with a periodic function?
the height of a football after it has been thrown
the height of a person riding on an escalator
the height of a building after it has been constructed
the height of a pebble stuck in the tread of a tire
The correct situation which can be modeled with a periodic function is,
⇒ The height of a pebble stuck in the tread of a tire.
What is mean by Function?A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Now, The situations that can be modeled with a periodic function is that,
The height of a pebble stuck in the tread of a tire.
And, A function is said to be periodic if it gives same value after a same period. And functions which are not periodic are called aperiodic.
Thus, The correct situation which can be modeled with a periodic function is,
⇒ The height of a pebble stuck in the tread of a tire.
Learn more about the function visit:
https://brainly.com/question/11624077
#SPJ5
Determine the number of ways to perform the task described.
Three-players are to be selected from a 13-player baseball team to visit schools to support a summer reading program. In how many ways can this selection be made.
There are ____ different ways 3 players can be selected from a 13 player baseball toam. (Simplify your answer. Type a whole number)
There are 286 different ways to select 3 players from a 13-player baseball team to visit schools to support a summer reading program.
This is a combination problem, where we want to select 3 players from a team of 13 players, without regard to order.
The number of ways to select r items from a set of n distinct items is given by the combination formula:
C(n, r) = n! / (r!(n-r)!)
where n is the total number of items and r is the number of items to be selected.
In this case, we want to select 3 players from a team of 13 players, so we can use the combination formula:
C(13, 3) = 13! / (3!(13-3)!) = (13 x 12 x 11) / (3 x 2 x 1) = 286
Learn more about combination here: brainly.com/question/11732255
#SPJ1
A town has 2 fire engines operating independently. The probability that a specific fire engine is available when needed is 0.96.a) What is the probability that neither is available when needed?b) What is the probability that a fire engine is available when needed?
a) The probability that neither fire engine is available when needed is 0.0016. b) The probability that a fire engine is available when needed is 0.9984.
The probability of an event occurring is the likelihood that it will happen. In this case, we are looking at the probability of a specific fire engine being available when needed.
The probability that neither fire engine is available when needed can be found by multiplying the probabilities of each fire engine not being available. The probability of a specific fire engine not being available is [tex]1 - 0.96 = 0.04[/tex]. So the probability that neither is available is [tex]0.04 * 0.04 = 0.0016.[/tex]
The probability that a fire engine is available when needed can be found by subtracting the probability that neither is available from 1. So the probability that a fire engine is available when needed is[tex]1 - 0.0016 = 0.9984.[/tex]
Know more about probability here:
https://brainly.com/question/30034780
#SPJ11
fsThe cuboid below is made of lead and has a mass of 339 g. Calculate its density, in g/cm³. If your answer is a decimal, give it to 1 d.p.
The density of the lead cuboid is approximately 11.3 g/cm³.
What is density?
Density is a physical property of matter that describes how much mass is contained within a certain volume. It is defined as the amount of mass per unit of volume, and is typically measured in grams per cubic centimeter (g/cm³) or kilograms per cubic meter (kg/m³).
The formula for density is:
density = mass / volume
where mass is the amount of matter in an object, and volume is the amount of space that the object occupies.
The volume of the cuboid can be calculated using the formula V = lwh, where l, w, and h are the length, width, and height of the cuboid, respectively.
Given that the length (l) of the cuboid is 5cm, the width (w) is 3cm, and the height (h) is 2cm, we can calculate the volume as:
V = lwh = 5cm x 3cm x 2cm = 30 cm³
The density (ρ) of an object is defined as its mass (m) per unit volume (V), or ρ = m/V.
Given that the mass of the cuboid is 339 g and its volume is 30 cm³, we can calculate the density as:
ρ = m/V = 339 g / 30 cm³ ≈ 11.3 g/cm³ (to 1 decimal place)
Therefore, the density of the lead cuboid is approximately 11.3 g/cm³.
To know more about density visit:
brainly.com/question/29775886
#SPJ1
What is the acceleration of a bus his speech changes from 126M/S to 3097 m/s over a period of three seconds
The acceleration of a bus his speech changes from 126M/S to 3097 m/s over a period of three seconds is 990. 3 m/s^2
What is acceleration?Acceleration is can be defined as the rate of change of the velocity of an object with respect to time.
It is also defined as the rate at which velocity changes with time, that is, in both speed and direction.
Accelerations are vector quantities because they are known to have both magnitude and direction.
The orientation of an object's acceleration is determined by the configuration of the net force acting on that object.
The formula for acceleration is given as;
Acceleration = change in velocity/time
Substitute the values
Acceleration = 3097 - 126 (m/s)/3 s
Divide the values
Acceleration = 990. 3 m/s^2
Learn about acceleration at: https://brainly.com/question/605631
#SPJ1
Rita is proving that the following trigonometric identity is true: cos(−θ)sin(−θ)=−1tanθ which step would be the first line of her proof?
Hence, in answering the stated question, we may say that We may now trigonometry compare the two sides and observe that they are equal, demonstrating the provided identity.
what is trigonometry?Trigonometry is the field of mathematics that explores the connection between triangle side lengths and angles. Owing to the application of geometry in astronomical research, the topic originally originated in the Hellenistic era, beginning in the third century BC. The subject of mathematics known as exact techniques is concerned with certain trigonometric functions and their possible applications in calculations. Trigonometry contains six commonly used trigonometric functions. Their separate names and acronyms are sine, cosine, tangent, cotangent, secant, and cosecant (csc). Trigonometry is the study of triangle characteristics, particularly those of right triangles. As a result, geometry is the study of the properties of all geometric forms.
The first stage in Rita's evidence would be determined by the method she uses to verify her identity. Nonetheless, one alternative method to begin the proof is to use the trigonometric identities:
sin(-θ) = -sin(θ) and cos(-θ) = cos(θ)
Applying these identities, we can rewrite the given equation's left side as:
sin(-) cos(-) = cos() (-sin())
After that, we may employ the following identity:
tan( ) = sin( )/cos( )
to rewrite the following equation's right side as:
-1 tan() = -sin()/cos()
We may now compare the two sides and observe that they are equal, demonstrating the provided identity.
To know more about trigonometry visit:
https://brainly.com/question/29002217
#SPJ1
Select the correct answer. What is the solution to the equation? -2x - 5 - 4 =z A. -7 and -3 B. 3 and 7 C. -3 D. 7
The solution to the equation √(-2x - 5) - 4 = x are x = -7 and x = -3
How to determine the solution to the equationFrom the question, we have the following parameters that can be used in our computation:
√(-2x - 5) - 4 = x
So, we have
-2x - 5 = x + 4
Take the square of both sides
so, we have the following representation
x² + 8x + 16 = -2x - 5
Evalyate the like terms
x² + 10x + 21 = 0
When factorized, we have
(x + 7)(x + 3) = 0
This means that
x = -7 and x = -3
Hence, the solutions are x = -7 and x = -3
Read more about equations at
https://brainly.com/question/18831322
#SPJ1
Melvin Small typed 485 business letters. The cost of writing these letters was estimated to be $3,455. 25. What was the average cost of a letter to the nearest cent
The average cost of a letter was 7.11.
The average cost of a letter can be calculated using the following formula:
Average cost per letter = Total Cost / Number of Letters
In this instance, the average cost of a letter is 7.11 (rounded to the nearest cent):
Average cost per letter = 3,455 / 485
Average cost per letter = 7.11
To calculate the average cost of a letter, we used a simple formula. The total cost was divided by the total number of letters to get the average cost per letter. This amount was then rounded to the nearest cent to get the final answer of 7.11.
Learn more about average cost here:
https://brainly.com/question/2192893
#SPJ4
Given △PQR ~ △STU, find the missing measures in △STU. Triangles P Q R and S T U. Side P Q has length 14, side Q R has length 28, and side R P has length 21. Angle P has measure 70 degrees and angle R has measure 46 degrees. In triangle S T U, side U S has length 6. No other measures are given. SU ST TU m∠S m∠T m∠U 6
Answer:
The missing measures in triangle STU are:
SU = 14, ST = (2/3)TU, TU = (4/3)ST, m∠S = 70 degrees, m∠T = 64 degrees, m∠U = 46 degrees.
Step-by-step explanation:
Since triangles PQR and STU are similar, their corresponding sides are in proportion, and their corresponding angles are congruent. We can use this information to find the missing measures in triangle STU:
Since side PQ corresponds to side ST, we have:
ST/PQ = TU/PR
Substituting the given values, we get:
ST/14 = TU/21
Cross-multiplying, we get:
ST × 21 = 14 × TU
ST = (14/21)TU
Simplifying, we get:
ST = (2/3)TU
Since side QR corresponds to side TU, we have:
TU/QR = ST/RP
Substituting the given values, we get:
TU/28 = ST/21
Cross-multiplying, we get:
TU × 21 = 28 × ST
TU = (28/21)ST
Simplifying, we get:
TU = (4/3)ST
Since angle P corresponds to angle S, we have:
m∠S = m∠P = 70 degrees
Since angle R corresponds to angle U, we have:
m∠U = m∠R = 46 degrees
To find m∠T, we can use the fact that the angles in a triangle add up to 180 degrees:
m∠S + m∠T + m∠U = 180
Substituting the given values, we get:
70 + m∠T + 46 = 180
Simplifying, we get:
m∠T = 64 degrees
To find SU, we can use the fact that the corresponding sides are in proportion:
SU/PR = ST/PQ
Substituting the given values, we get:
SU/21 = (2/3)
Cross-multiplying, we get:
SU = 14
Therefore, the missing measures in triangle STU are:
SU = 14
ST = (2/3)TU
TU = (4/3)ST
m∠S = 70 degrees
m∠T = 64 degrees
m∠U = 46 degrees.
Hope this helps! Sorry if it doesn't. If you need more help, ask me! :]
due in 5 minutes -3x-24≤-36
Answer:
x ≥ 4
Step-by-step explanation:
HI, PLEASE HELP IM STRUGGLING SO MUCH! thank you!
A restaurant makes smoothies in batches of 6.4 litres.
The smoothies are made from ice cream and a mixed fruit juice in the ratio 5:3. 35% of the juice is lime juice.
Work out the maximum number of batches of smoothie that can be made from 42 litres of lime juice.
If a restaurant makes smoothies in batches of 6.4 litres. the maximum number of batches of smoothie that can be made from 42 litres of lime juice is 50.
What is the maximum number of batches of smoothie?If the ratio of ice cream to mixed fruit juice is 5:3, then,
Fraction of the smoothie that is ice cream =5/(5+3) = 5/8
Fraction that is mixed fruit juice = 3/(5+3) = 3/8
If 35% of the mixed fruit juice is lime juice, then,
Fraction of the mixed fruit juice that is lime juice= 35/100 = 7/20
Fraction of the smoothie that is lime juice = (3/8) x (7/20) = 21/160
To make one batch of smoothie, we need 6.4 litres of mixed fruit juice, of which (21/160) x 6.4 = 0.84 litres is lime juice.
To make 42 litres of lime juice, we nee:
42/0.84 = 50 batches of smoothie.
Therefore, the maximum number of batches of smoothie that can be made from 42 litres of lime juice is 50.
Learn more about maximum number of batches of smoothie here:https://brainly.com/question/29213047
#SPJ1