Find all the angles in the interval 0 to 360 degrees that satisfy the following condition. Round theanswer to the nearest hundredth of a degree.tan(x) = 13/25
Answers
To find the angles, we first solve the equation:
\(\begin{gathered} \tan x=\frac{13}{25} \\ x=\tan ^{-1}(\frac{13}{25}) \\ x=27.47 \end{gathered}\)Now, since the tangent has a period of 180 this means that, in the interval given, two angles will fullfil the condition given; to find the second angle we just add 180 to the x we found.
Therefore, in the interval from 0 to 360, the angles 27.47 and 207.47 will fulfill the condition given.
Related Questions
You start at (0,-4). You move left 1 unit and right 4 units. where do you end?
Answers
If you start at (0,-4) and you move left 1 unit and right 4 units, you end at (3, -4)
Calculating the endpoint of the pointFrom the question, we have the following parameters that can be used in our computation:
Start = (0, -4)
Also, we have
You move left 1 unit and right 4 units
Mathematically, this can be expressed as
(x, y) = (x - 1 + 4, y)
Substitute the known values in the above equation, so, we have the following representation
Endpoint = (0 - 1 + 4, -4)
Evaluate the expression
Endpoint = (3, -4)
Hence, the endpoint is (3, -4)
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A specimen of 100 mm length along the stroke of a shaper is machined with 15° rake angle tool. Determine the shear plane angle and chip thickness if uncut chip thickness is 1.5 mm and chip length obtained is 40 mm.
Answers
The shear plane angle is approximately 84.3°, and the chip thickness is approximately 15.1 mm.
What is the shear plane angle?To determine the shear plane angle and chip thickness in the given scenario, we can use the following formulas:
Shear Plane Angle (α):
tan(α) = tan(β - φ)
where β is the inclination angle of the machined surface (rake angle) and φ is the friction angle.
Chip Thickness (t):
t = tc / cos(α)
where tc is the uncut chip thickness.
Given:
Uncut chip thickness (tc) = 1.5 mm
Chip length (lc) = 40 mm
Length of the specimen (L) = 100 mm
Rake angle (β) = 15°
First, we need to calculate the shear plane angle (α):
tan(α) = tan(β - φ)
Since the friction angle (φ) is not given, we will assume a typical value of 5°.
tan(α) = tan(15° - 5°)
tan(α) = tan(10°)
α ≈ 84.3° (rounded to two decimal places)
Next, we can calculate the chip thickness (t):
t = tc / cos(α)
t = 1.5 mm / cos(84.3°)
t ≈ 15.1 mm (rounded to two decimal places)
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In the data set below, what is the value of the 1st quartile?
(6,7,8,9,10,12,14)
Answers
Answer: 7 is the first quartile
Step-by-step explanation:
method to find quartile
Order your data set from lowest to highest values
Find the median. This is the second quartile Q2.
At Q2 split the ordered data set into two halves.
The lower quartile Q1 is the median of the lower half of the data.
The upper quartile Q3 is the median of the upper half of the data.
If the size of the data set is odd, do not include the median when finding the first and third quartiles.
If the size of the data set is even, the median is the average of the middle 2 values in the data set. Add those 2 values, and then divide by 2. The median splits the data set into lower and upper halves and is the value of the second quartile Q2.
What is the area of the figure?
Answers
Answer: 23.76 sq yds
Step-by-step explanation:
0.5*9.9*4.7=23.76
Area of triangle: 0.5*b*h
The starting salaries of individuals with an MBA degree are normally distributed with a mean of $40,000 and a standard deviation of $5,000. Refer to Exhibit 6-4. What is the random variable in this experiment? a. Normal distribution b. $40,000 C. Starting salaries d. $5,000
Answers
The random variable in this experiment is the starting salaries of individuals with an MBA degree. Therefore, the answer is option C, "Starting salaries".
The random variable is the quantity that is being measured or observed in a statistical experiment. In this case, the statistical experiment involves measuring the starting salaries of individuals with an MBA degree.
The random variable in this experiment is "starting salaries", as it is the variable of interest that is being measured. The starting salaries are assumed to follow a normal distribution with a mean of $40,000 and a standard deviation of $5,000.
It is important to identify the random variable in a statistical experiment in order to understand what is being measured and to appropriately interpret the results of any statistical analysis. In this case, knowing that the random variable is the starting salaries of individuals with an MBA degree allows us to make inferences about the population of individuals with MBAs and their potential earning potential.
The random variable in this experiment is the starting salaries of individuals with an MBA degree, denoted by X.
X ~ N(40,000, 5,000)
where "~" means "is distributed as", "N" means "normal distribution", 40,000 is the mean of the distribution, and 5,000 is the standard deviation of the distribution.
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A hallow sphere sits snugly inside a foam cube so that the sphere touches all sides. Find the volume of the foam. Round answer to nearest tenth.
Answers
Answer:
5832
Step-by-step explanation:
How do you convert 72 kilograms to pounds? show the mathmatical steps
Answers
1 kilogram = 2.20462 pounds
To convert 72 kilograms to pounds, you can multiply 72 by 2.20462 as follows:
72 kilograms = 72 x 2.20462 pounds
72 kilograms = 158.73264 pounds (rounded to five decimal places)
Therefore, 72 kilograms is equal to approximately 158.73264 pounds.
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A. A manufacturer knows that their items have a normally distributed length, with a mean of 19.7 inches, and standard deviation of 4 inches.
If 25 items are chosen at random, what is the probability that their mean length is less than 17.4 inches?
Round to 4 decimal places
A manufacturer knows that their items have a normally distributed lifespan, with a mean of 12.1 years, and standard deviation of 1.9 years.
If you randomly purchase 12 items, what is the probability that their mean life will be longer than 11 years?
Round to 4 decimal places.
B. A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 98.4-cm and a standard deviation of 0.9-cm. For shipment, 15 steel rods are bundled together.
Find the probability that the average length of the rods in a randomly selected bundle is between 97.9-cm and 98.6-cm.
P(97.9-cm < X¯¯¯ < 98.6-cm) = Round to 4 decimal places.
Answers
The probability that their mean length is less than 17.4 inches is 28.26%
Given :
A manufacturer knows that their items have a normally distributed length, with a mean of 19.7 inches, and standard deviation of 4 inches , If 25 items are chosen at random .
z = ( X - μ ) / σ, where X = date , μ = mean , σ = standard deviation .
substitute the values
z = 17.4 - 19.7 / 4
= -2.3 / 4
= -0.575
P - value at z = -0.575 is 0.2826
Converting into percentage :
= 0.2826 * 100%
= 28.26 %
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What is rhombus and formula?
Answers
A rhombus is a quadrilateral with four equal-length sides. The term equilateral quadrilateral refers to the fact that all of its sides are the same length.
What is rhombus ?A rhombus is a subset of a parallelogram. The opposite sides of a rhombus are parallel, and the opposite angles are equal. Furthermore, all of the sides of a rhombus are the same length, and the diagonals intersect at right angles. A rhombus is also referred to as a diamond or rhombus diamond.In terms of geometry, The opposite sides of a rhombus are parallel to each other, and the opposite angles are equal. All the sides of the rhombus are the same in length. The diagonals of the rhombus meet at a 90° angle. The sum of the rhombus's interior angles equals 360°.Rhombus Area Calculation Formulas Diagonals are used. A = ½ × d1 × d2. Making use of Base and Height. A = b × h.The opposite angles of a rhombus are equal. In addition, the sum of adjacent angles in a rhombus is supplementary, i.e. (∠B + ∠C = 180°).To learn more about rhombus refer :
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100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!
Answers
Answer:
\(BC=5.1\)
\(B=23^{\circ}\)
\(C=116^{\circ}\)
Step-by-step explanation:
The diagram shows triangle ABC, with two side measures and the included angle.
To find the measure of the third side, we can use the Law of Cosines.
\(\boxed{\begin{minipage}{6 cm}\underline{Law of Cosines} \\\\$c^2=a^2+b^2-2ab \cos C$\\\\where:\\ \phantom{ww}$\bullet$ $a, b$ and $c$ are the sides.\\ \phantom{ww}$\bullet$ $C$ is the angle opposite side $c$. \\\end{minipage}}\)
In this case, A is the angle, and BC is the side opposite angle A, so:
\(BC^2=AB^2+AC^2-2(AB)(AC) \cos A\)
Substitute the given side lengths and angle in the formula, and solve for BC:
\(BC^2=7^2+3^2-2(7)(3) \cos 41^{\circ}\)
\(BC^2=49+9-2(7)(3) \cos 41^{\circ}\)
\(BC^2=49+9-42\cos 41^{\circ}\)
\(BC^2=58-42\cos 41^{\circ}\)
\(BC=\sqrt{58-42\cos 41^{\circ}}\)
\(BC=5.12856682...\)
\(BC=5.1\; \sf (nearest\;tenth)\)
Now we have the length of all three sides of the triangle and one of the interior angles, we can use the Law of Sines to find the measures of angles B and C.
\(\boxed{\begin{minipage}{7.6 cm}\underline{Law of Sines} \\\\$\dfrac{\sin A}{a}=\dfrac{\sin B}{b}=\dfrac{\sin C}{c} $\\\\\\where:\\ \phantom{ww}$\bullet$ $A, B$ and $C$ are the angles. \\ \phantom{ww}$\bullet$ $a, b$ and $c$ are the sides opposite the angles.\\\end{minipage}}\)
In this case, side BC is opposite angle A, side AC is opposite angle B, and side AB is opposite angle C. Therefore:
\(\dfrac{\sin A}{BC}=\dfrac{\sin B}{AC}=\dfrac{\sin C}{AB}\)
Substitute the values of the sides and angle A into the formula and solve for the remaining angles.
\(\dfrac{\sin 41^{\circ}}{5.12856682...}=\dfrac{\sin B}{3}=\dfrac{\sin C}{7}\)
Therefore:
\(\dfrac{\sin B}{3}=\dfrac{\sin 41^{\circ}}{5.12856682...}\)
\(\sin B=\dfrac{3\sin 41^{\circ}}{5.12856682...}\)
\(B=\sin^{-1}\left(\dfrac{3\sin 41^{\circ}}{5.12856682...}\right)\)
\(B=22.5672442...^{\circ}\)
\(B=23^{\circ}\)
From the diagram, we can see that angle C is obtuse (it measures more than 90° but less than 180°). Therefore, we need to use sin(180° - C):
\(\dfrac{\sin (180^{\circ}-C)}{7}=\dfrac{\sin 41^{\circ}}{5.12856682...}\)
\(\sin (180^{\circ}-C)=\dfrac{7\sin 41^{\circ}}{5.12856682...}\)
\(180^{\circ}-C=\sin^{-1}\left(\dfrac{7\sin 41^{\circ}}{5.12856682...}\right)\)
\(180^{\circ}-C=63.5672442...^{\circ}\)
\(C=180^{\circ}-63.5672442...^{\circ}\)
\(C=116.432755...^{\circ}\)
\(C=116^{\circ}\)
\(\hrulefill\)
Additional notes:
I have used the exact measure of side BC in my calculations for angles B and C. However, the results will be the same (when rounded to the nearest degree), if you use the rounded measure of BC in your angle calculations.
A caterer for a wedding reception wants to use a recipe for eggplant salad that recommends using 0.7 kg of eggplant for guests. However, in her area, eggplant is only sold by the pound. If 70 guests are expected, how many pounds of eggplant should the caterer purchase?
Answers
By performing a change of units, we will see that the caterer should purchase 107.8 lb
How many pounds of eggplant should the caterer purchase?First, let's find how many kilograms are needed. We know that the recipe recomends using 0.7kg per person, and there are 70 guests, so an estimate of the mass needed is:
M = 70*0.7kg = 49 kg
Now weneedto do a change of units, we know that:
1 kg = 2.2 lb
Then we can rewrite:
49 kg = 49*(2.2 lb) = 107.8 lb
The caterer should purchase 107.8 pounds
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Help asap tor point abs brainliest
Answers
Answer:
D. -2/3x - 2
Step-by-step explanation:
Slope is rise/run. In this situation, we drop 2, and run 3 to get to an even point. This means our slope is -2/3. Now that we know our slope, we just need to find an answer with -2/3, which would be D.
Write the phrase as an expression.
the total of 6 and 10
An expression is:
Answer:
Answers
Answer:
16
Step-by-step explanation:
6+10 (TOTAL) is another word to compromise addition. So 6+10 = 16 cheonman- eyo
please help me, i dont understand
Answers
Answer:
OK so we can see that when x increases y does too. The answer is C
Given the vertex of a quadratic function, find the axis of symmetry.
Answers
(i) The equation of the axis of symmetry is x = - 5.
(ii) The coordinates of the vertex of the parabola are (h, k) = (4, - 18). The x-value of the vertex is 4.
(iii) According to the vertex form of the quadratic equation, the parabola opens down due to negative lead coefficient and has a vertex at (2, 4), which is a maximum.
How to analyze and interpret quadratic functions
In this question we must find and infer characteristics from three cases of quadratic equations. (i) In this case we must find a formula of a axis of symmetry based on information about the vertex of the parabola. Such axis passes through the vertex. Hence, the equation of the axis of symmetry is x = - 5.
(ii) We need to transform the quadratic equation into its vertex form to determine the coordinates of the vertex by algebraic handling:
y = x² - 8 · x - 2
y + 18 = x² - 8 · x + 16
y + 18 = (x - 4)²
In a nutshell, the coordinates of the vertex of the parabola are (h, k) = (4, - 18). The x-value of the vertex is 4.
(iii) Now here we must apply a procedure similar to what was in used in part (ii):
y = - 2 · (x² - 4 · x + 2)
y - 4 = - 2 · (x² - 4 · x + 2) - 4
y - 4 = - 2 · (x² - 4 · x + 4)
y - 4 = - 2 · (x - 2)²
According to the vertex form of the quadratic equation, the parabola opens down due to negative lead coefficient and has a vertex at (2, 4), which is a maximum.
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If ABCD is a square where A(-4;2) B(-2;-1) C(1;1) , determine the coordinates of of D
Answers
Answer:
(4;-1)
Step-by-step explanation:
A(-4;2)
B(-2;-1)
C(1;1)
D(-4;-1)
Answer:
-1;4
Step-by-step explanation:
karla is offered a job as parking lot attendant. the job will pay 2400 per month, paid biweekly. along with the base salary, the company offers to pay half the cost of medical insurance and will match karlas contribution to a retirment plan up to a total of 1500. if the full cost of the medical insurance is 450 a month and karla plans to contribute the full 1500 every year tpa retirement plan, what is the actual annual value of this job to karla?
Answers
The actual annual value of this job to Karla is 33000.
What are arithmetic operations?
Arithmetic operations is a branch of mathematics that studies numbers and the operations on numbers that are useful in all other branches of mathematics. It consists primarily of operations like addition, subtraction, multiplication, and division.
We have,
the job will pay 2400 per month,
if the full cost of the medical insurance is 450 a month and Karla plans to contribute the full 1500 every year tpa retirement plan,
the actual annual value of this job to Karla is:
2400 per month
annual value = 2400 * 12 = 28,800
the medical insurance is 450 a month
half the cost of medical insurance is 225 a month
annual value = 225 * 12 = 2700
the full 1500 every year tpa retirement plan,
So, the total value is:
= 28,800 + 2700 + 1500
= 33000
Hence, the actual annual value of this job to Karla is 33000.
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A school holds a pairs running
competition. In Team A, Finn runs 33 km
and his team-mate Jake runs 3 km.
Team B runs a total of 7 km.
5
9
10
a) Which team runs further?
b) How much further, in kilometres (km),
does that team run? Give your answer in
its simplest form.
Answers
Answer:
Step-by-step explanation:
(a) Step 1
Distance ran by Finn = 3.2
Distance ran by Jake = 3.9
Total Distance of team A = 7.1
Step 2
Distance ran by team B = 7.2
Hence team B ran further
(b) Difference in distances ran by team A and B = 7.2 -7.1
= 0.1 km
Hence team B ran 0.1 km more than team A
Type your answers into the boxes.
The ratio of men to women in a gym is 7 : 5
What fraction of the gym members are women?
Answers
Answer:
\( \frac{5}{12} \)
Step-by-step explanation:
\( \frac{5}{7 + 5} \)
I'm not sure about the answer. Sorry if it's wrong.
MISTERBRAINLYY!!
The paint in a certain container is sufficient to paint an area equal to 9.375m2. How many bricks of dimensions 22.5cm×10cm×7.5cm can be painted out of this container?
Answers
There are three area options for the number of bricks:
4165551250How many bricks can be painted out of a container?
The number of bricks that can be painted out is equal to the paint area (A), in square centimeters, divided to the area of a brick (A'), in square centimeters. That is:
n = A / A'
A' = w · h
Where:
w - Width of the brick, in centimeters.h - Height of the brick, in centimeters.There are three possible answers:
Case 1: A = 93750 cm², w = 22.5 cm, h = 10 cm
A' = 22.5 · 10
A' = 225
n = 93750 / 225
n = 416.667
n = 416
Case 2: A = 93750 cm², w = 22.5 cm, h = 7.5 cm
A' = 22.5 · 7.5
A' = 168.75
n = 93750 / 168.75
n = 555.556
n = 555
Case 3: A = 93750 cm², w = 10 cm, h = 7.5 cm
A' = 10 · 7.5
A = 75
n = 93750 / 75
n = 1250
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Graph y = - 1/2x + 3 use the line tool and select two points on the line
Answers
The points to be graphed are (6, 0) and (0, 3). The graph of the equation is shown in the attached image
How to graph the equation of a line?y = - 1/2x + 3
In order to graph the equation of the line:
First, find the value of x when y = 0:
y = - 1/2x + 3 , when y = 0:
0 = - 1/2x + 3
1/2x = 3
x = 3 × 2
x = 6
Also, find the value of y when x = 0:
y = - 1/2x + 3, when x = 0:
y = - 1/2(0) + 3
y = 3
Therefore, the values to be plotted on our graph are (6, 0) and (0, 3). The image of the graph is attached
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2b -7 ≥ 2 (-7+b) what is the answer
Answers
Answer: No solution/Empty Set
Step-by-step explanation: When you factor the 2(-7+b), you get 2b, which when moved to the other side cancels out the variable
What type of transformation
has this figure made
Answers
Answer:
translation
Step-by-step explanation:
a rotation would make it horizontal which it is not
reflection would flip it its not fliped.
There for its translation
hope this helps
Which one is it
a
b
c
d
Answers
The solution is b. (-3,0).
What is a system of equations?
Two or more equations in algebra must be solved jointly (i.e., the solution must satisfy all the equations in the system). The number of equations must match the number of unknowns for a system to have a singular solution. A solution is not assured even then.
The given system of equations is:
y=x+3...................(1)
2x+y=-6...............(2)
We will substitute (1) in two to find the solution for the given system of equations.
2x+x+3=-6
3x=-9
x=-3
Now we will substitute x=-3 in (1), and we will get y=-3+3=0
so y=0
Therefore the solution is b. (-3,0).
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The PTO is selling raffle tickets to raise money for
classroom supplies. A raffle ticket costs $3.00. There is 1
winning ticket out of the 280 tickets sold. The winner gets
a prize worth $90.00.
What is the expected value (to you) of one raffle ticket?
The expected value (to you) of one raffle ticket is _________.
Calculate the expected value (to you) if you purchase 8
raffle tickets.
The expected value (to you) if you purchase 8 raffle
tickets is __________.
What is the expected value (to the PTO) of one raffle ticket?
The expexted value (to the PTO) of one raffle ticket is_________.
If the PTO sells all 280 raffle tickets, how much money can
they expect to raise for the classroom supplies?
The PTO can expect to raise_________ from selling all 280 tickets.
Answers
Answer:
The expected value (to you) of one raffle ticket is -$0.15.
Explanation: The probability of winning is 1/280, so the expected value of winning is (1/280) * $90 = $0.32. The expected value of losing is (279/280) * (-$3) = -$2.97. So, the expected value (to you) of one raffle ticket is $0.32 - $2.97 = -$0.15.
The expected value (to you) if you purchase 8 raffle tickets is -$1.20.
Explanation: The expected value (to you) of one raffle ticket is -$0.15, so the expected value (to you) of eight raffle tickets is -$0.15 * 8 = -$1.20.
The expected value (to the PTO) of one raffle ticket is $0.05.
Explanation: The expected value (to the PTO) of one raffle ticket is the difference between the price of the ticket ($3) and the expected cost of the prize, which is (1/280) * $90 = $0.32. So, the expected value (to the PTO) of one raffle ticket is $3 - $0.32 = $2.68.
The PTO can expect to raise $840 from selling all 280 tickets.
Explanation: The total revenue from selling 280 raffle tickets is 280 * $3 = $840.
Find the slope-intercept equation of the line that has the given characteristics.
Slope 7 and y-intercept (0,3)
Answers
The required slope-intercept equation of the line is y = 7x + 3.
Given that,
Slope of the line = m = 7,
The Y-intercept of the line = (0, 3)
To find the slope-intercept equation of the line
A line can be defined by the shortest distance between two points is called a line.
Here,
The slope-intercept form of the line is given as,
y = mx + c - - - - - (1)
Now put m and coordinate of y-intercept in the above equation in order to get c
3 = 7 * 0 + c
c = 3
Now put this c and m in equation 1
y = 7x + 3
Thus, the required slope-intercept equation of the line is y = 7x + 3.
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A student ran out of time on a multiple-choice exam and randomly guessed the answers for two problems. Each problem had 4 answer choices –a,b,c,d – and only one correct answer. What is the probability that he answered both of the problems correctly?
Do not round your answer.
Answers
\({\huge{\fbox{\tt{\blue{ANSWER}}}}}\)
______________________________________
The probability of answering a single problem correctly by randomly guessing is 1/4, since there are 4 answer choices and only one correct answer. Since the student randomly guessed the answer to both problems, the probability of answering both problems correctly is:
(1/4) x (1/4) = 1/16
Therefore, the probability that the student answered both problems correctly is 1/16.
In △ABC, AB=5, BC=4, and AC=3. The triangle is translated left 2 units and up 6 units to △A′B′C′. What is the length of segment A′C′?
A′C′=6
cap A prime cap c prime is equal to 6
A′C′=3
cap A prime cap c prime is equal to 3
A′C′=4
cap A prime cap c prime is equal to 4
A′C′=2
Answers
Answer:
3
Step-by-step explanation:
The entire triangle shifts 2 to the left and up 6, the lengths of the sides remain the same, therefore:
AC = A'C' = 3
estimate the population in the year 2040
Answers
well, in 2007 it was 12000, so initially that's what it was, and in 2019 it went to 23000, so that's 12 years later, and in 2040, that'll be 33 years later.
\(\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$ 23000\\ P=\textit{initial amount}\dotfill &12000\\ r=rate\to r\%\to \frac{r}{100}\\ t=years\dotfill &12\\ \end{cases} \\\\\\ 23000 = 12000(1 + \frac{r}{100})^{12}\implies \cfrac{23000}{12000} =\left(1+ \cfrac{r}{100} \right)^{12} \\\\\\ \cfrac{23}{12}=\left(\cfrac{100+r}{100} \right)^{12}\implies \sqrt[12]{\cfrac{23}{12}}=\cfrac{100+r}{100}\)
\(100\sqrt[12]{\cfrac{23}{12}}=100+r\implies 100\sqrt[12]{\cfrac{23}{12}}-100=r\implies \boxed{5.57\approx r} \\\\[-0.35em] ~\dotfill\\\\ \qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &12000\\ r=rate\to 5.57\%\to \frac{5.57}{100}\dotfill &0.0557\\ t=years\dotfill &\stackrel{year~2040 }{33}\\ \end{cases} \\\\\\ A \approx 12000(1 + 0.0557)^{33} \implies \boxed{A \approx 71782}\)
At the organic produce store you can buy 3 bags of sweet potatoes for $20.07.
How much would it cost if you were to buy only 2 bags.
Answers
Answer:
$13.38
Step-by-step explanation:
Use proportions to solve this problem:
$20.07 / 3 bags = X / 2 bags
multiply both sides by "2 bags" to isolate the unknown X
$20.07 * 2 / 3 = X
Therefore, X = $13.38