Answer: -0.6
Step-by-step explanation:
First thing to do is to solve for θ and ϕ from the given information
tan(θ) = 4/3,
θ = tan-¹4/3,
θ = 53.1°
Since tan is positive in quadrant III, θ = 53.1°
Also,
sin(ϕ) = − 10/10 ,
ϕ = sin-¹-1
ϕ = 270°
If ϕ is in the fourth quadrant, that gives 360 - ϕ i.e 360 - 270 = 90°
Substituting the values of θ and ϕ into sin(θ − ϕ), we have;
Sin(53.1 - 90)
= sin (-36.9°)
= -0.6
The given expression sin(θ - ϕ), with tan(θ) = 4/3, θ in Quadrant III, sin(ϕ) = -10/10, and ϕ in Quadrant IV, is evaluated by using trigonometric principles and identities. Upon calculations, sin(θ - ϕ) comes out to be -3/5.
Explanation:The question is asking us to evaluate the expression sin(θ − ϕ), given that tan(θ) = 4/3, θ is in Quadrant III, sin(ϕ) = -10/10, and ϕ is in Quadrant IV. In trigonometry, tan θ = sin θ/cos θ. We have tan θ = 4/3 and we know that in Quadrant III, tangent is positive but sine and cosine are negative. So, we can make a right triangle where the opposite side is 4 (basing this on the absolute value of the tan θ) and the adjacent side is 3. The hypotenuse then, by using Pythagoras theorem, comes out to be 5. Then sin θ = -4/5 and cos θ = -3/5.
For sin(ϕ), we are given that it equals -1. In Quadrant IV, sine is negative and cosine is positive, so cos ϕ = √(1 - (-1)^2) = 0.
Finally, utilizing the formula sin (a ± ß) = sin a cos ß ± cos a sin ß, we plug in our values to come to the solution sin(θ - ϕ) = (sin θ cos ϕ) - (cos θ sin ϕ) = ((-4/5)*0) - ((-3/5)*-1) = -3/5
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If a dice is rolled one time, find the probability of getting a number less than 5
Total Outcomes = {1,2,3,4,5,5}
Less than 5 = {1,2,3,4}
P(less than 5) = 4/6 = 2/3
Jenna brought in $25,000 to her startup firm at the beginning of the year. During the year, she withdrew $2,500 for her personal expenses. The business earned $10,000 at the end of the accounting period after paying off all its expenses. What is the value of Jenna’s capital account at the end of the accounting year?
A. $25,000
B. $22,500
C. $35,000
D. $32,500
➷ 25,000 - 2500 = 22500
22500 + 10,000 = 32,500
The correct answer would be option D. $32,500
✽➶ Hope This Helps You!
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➶ Have A Great Day ^-^
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Answer:
Step-by-step explanation:
I would have to go with D. The 25,000 is what you start with minus the 2,500 she withdrew which would leave her at 22,500. She then receives 10,000 for the business leaving her with 32,500
(50 Points & Brainliest)
A group of students plotted the number of hours they spent cycling and the number of hours they spent playing football in a week.
Which statement best describes the relationship between the number of hours spent cycling and the number of hours spent playing football?
A) Fewer hours cycled, fewer hours spent playing football
B) Greater hours cycled, greater hours spent playing football
C) Fewer hours cycled, greater hours spent playing football
D) There is no relationship between hours spent cycling and hours spent playing football.
Answer:
Answer: There is no relationship between hours spent cycling and hours spent playing football. I did flvs and I got this question correct.
Step-by-step explanation:
Answer:
D) There is no relationship between hours spent cycling and hours spent playing football.
Step-by-step explanation:
As we can see that the scatter plot dots are distributed very randomly and we cannot form any relation between both conditions. Rather to easily compare both conditions we need two plots with respect to time. So, we can compare the hours spent in cycling and hours spent in playing football.
So, the correct answer would be - There is no relationship between hours spent cycling and hours spent playing football.
If 28 dog biscuits weigh 12 1/4
A) 3/7 of an ounce
B) 4/5 of an ounce
C) 7/16 of an ounce
D) 7/28 of an ounce
Divide total weight by number of treats:
12 1/4 / 28 = 7/16
The answer is C.
Answer:
[tex]\large\boxed{C)\ \dfrac{7}{16}\ of\ an\ ounce}[/tex]
Step-by-step explanation:
Divide the weight by the number of dog biscuits:
[tex]\left(12\dfrac{1}{4}\right):28=\dfrac{12\cdot4+1}{4}:28=\dfrac{49}{4}:28=\dfrac{1}{28\!\!\!\!\!\diagup_4}\cdot\dfrac{49\!\!\!\!\!\diagup^7}{4}=\dfrac{1}{4}\cdot\dfrac{7}{4}=\dfrac{7}{16}[/tex]
Find approximate solution for the equation in the interval -π
tan x= 2 csc x
Answer:
Option a.
-1.144 , 1.144
Step-by-step explanation:
Since we are dealing with trascendental equations, it is best if we solve the problem graphically with the help of a calculator or any plotting tool.
Please, see attached image
We graph both equations and find the intersection between them in the interval from -pi to pi
This will give the solution to the equation
tan(x) = 2* csc(x)
The answer is
x = -1.144
x = 1.144
The question requires solving a trigonometric equation tan x = 2 csc x by using trigonometric identities to express it in terms of sine and cosine and then finding the approximate solutions within the interval -π to π.
Explanation:The student is asking for an approximate solution for a trigonometric equation within a specified interval. The equation given is tan x = 2 csc x. To solve this trigonometric equation, you need to use trigonometric identities to express both sides of the equation in terms of a single trigonometric function and then find the values of x that satisfy the equation within the given interval.
To start with, we can use the identity csc x = 1/sin x and then rewrite the equation as tan x = 2/sin x. Since tan x = sin x/cos x, we can now express the equation purely in terms of sine and cosine:
sin x/cos x = 2/sin x
Multiplying both sides by sin x cos x, we obtain sin2 x = 2 cos x. From here, we can use numerical methods or graphing techniques to find an approximate solution for x within the interval -π to π.
A study looked at n=238 adolescents, all free of severe illness.23 Subjects wore a wrist actigraph, which allowed the researchers to estimate sleep patterns. Those subjects classified as having low sleep efficiency had an average systolic blood pressure that was 5.8 millimeters of mercury (mm Hg) higher than that of other adolescents. The standard deviation of this difference is 1.4 mm Hg. Based on these results, test whether this difference is significant at the 0.01 level.
Answer:
Step-by-step explanation:
Since n < 30, we will find the t-score and compare that to the t-score of a significance level of 1%.
Since they are asking if the difference is significant, we will have a two tailed test, with degree of freedom being 22, so our critical values are
t < -2.704 and t > 2.704
Our t-value for this situation is
t = ([µ + 5.8] - µ)/(1.4/√23)
It's µ + 5.8 because the problem told us that their levels are 5.8 mm higher than the average, so it's the average, plus 5.8
Simplify the equation...
t = 5.8/(1.4/√23)
t = 19.868
19.868 > 2.704, the evidence supports that there is significant difference between the sample and the population
There is a significant difference between the sample and the population.
What is standard deviation?A standard deviation (or σ) indicates how dispersed the data is in relation to the mean.
What is t-distribution?The t-distribution indicates the standardized distances of sample means to the population mean when the population standard deviation is not known, and the observations come from a normally distributed population.
What is t-score?A t-score is the number of standard deviations away from the mean of the t-distribution.
How to find whether the difference is significant at the 0.01 level?Here n < 30.So, we will find the t-score and compare that to the t-score of a significance level of 1%.Here the degree of freedom is 22 and so the critical values are:
t < -2.704 and t > 2.704
In the problem, it is given that those subjects classified as having low sleep efficiency had an average systolic blood pressure that was 5.8 millimeters of mercury (mm Hg) higher than that of other adolescents∴ The t-value for this situation is
t = ([µ + 5.8] - µ)/(1.4/√23)
⇒ t = 5.8/(1.4/√23)
⇒t = 19.868
Now, 19.868 > 2.704So, we can say that there is significant difference between the sample and the population.
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DESCRIBE HOW TO USE THE SCALE FACTOR TO DILATE A POLYGON ON THE COORDINATE PLANE.
Answer:
Multiply the original points by the fraction or ratio of the dilution needed
Step-by-step explanation:
I'm less confident in this answer, but Scale factor is the ration between two geometric figures, like 1:2 is for every one unit on one figure is two on the other, so to dilute a figure, you multiply the points by 1/2 to make a smaller figure, or by 2 to get a bigger one. Plot the given answers and you have diluted :) Hope this helps!
A single die is rolled twice. the 36 equally-likely outcomes are shown to the right. find the probability of getting two numbers whose sum is 7
Answer:
1/6
Step-by-step explanation:
When a die is rolled twice the possible outcomes are:
Here the first value represents the first outcome and the second value represents the second outcome.
S = { (1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (2,1), (2,2), (2,3),(2,4), (2,5),(2,6),(3,1),(3,2),(3,3),(3,4),(3,5),(3,6), ( 4,1), (4,2), (4,3), (4,4), (4,5), (4,6), (5,1), (5,2), (5,3), (5,4), (5,5), (5,6), (6, 1), (6, 2), (6,3), (6,4), (6,5), (6,6)}
Total outcomes = n(S) = 36
Let A be the event that the sum of both outcomes is 7.
A = {(1, 6) , (2,5), (3,4) , (4,3), (5,2), (6,1)}
n(A) = 6
So, P(A) = n(A)/n(S)
= 6/36
= 1/6
In this scenario, there are 36 potential outcomes when rolling a die twice. Six of these outcomes would lead to a sum of 7. Therefore, the probability of rolling two numbers whose sum is 7 is 1/6.
Explanation:When rolling a single six-sided die twice, the sample space consists of 36 outcomes (since each roll can result in one of six possible outcomes, so 6 outcomes for the first roll times 6 outcomes for the second roll gives 36 total). Now, we need to find the probabilities that would result in a sum of 7. These are: 1 and 6, 2 and 5, 3 and 4, 4 and 3, 5 and 2, 6 and 1. These are 6 possible outcomes. Hence, the probability of getting the two numbers whose sum is 7 is 6 out of 36, or 1/6 when simplified.
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Find the greatest common factor of 270 and 360. (Give the answer in the numerical form in the top box and i exponential form by filing in the boxes for exponents)
the answer is 90 because 360/90=4 270/90=3
Given the system of equations, what is the solution?
x + 2y = 7
x - 2y = -1
{(-8, -12)}
{(3, 2)}
{(-4, 6)}
Answer:
[tex]\large\boxed{x=3\ and\ y=2\to(3,\ 2)}[/tex]
Step-by-step explanation:
[tex]\underline{+\left\{\begin{array}{ccc}x+2y=7\\x-2y=-1\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad2x=6\qquad\text{ivide both sides by 2}\\.\qquad x=3\\\\\text{Put the value of x to the first equation:}\\\\3+2y=7\qquad\text{subtract 3 from both sides}\\\\2y=4\qquad\text{divide both side by 2}\\\\y=2[/tex]
The solution to the given system of linear equations is (3, 2), which is found by eliminating y and solving for x, then substituting back to find y.
Given the system of equations:
x + 2y = 7
x - 2y = -1
To find the solution to the system, we can add the two equations to eliminate y:
(x + 2y) + (x - 2y) = 7 + (-1)
2x = 6
x = 3
Substituting x = 3 into the first equation:
3 + 2y = 7
2y = 4
y = 2
So, the solution to the system of equations is (3, 2). None of the other provided options, {(-8, -12)} or {(-4, 6)}, match this solution.
Solve for w
-4w+(2/5)=-(7/2)w-(3/2)
Answer:
-(19/5) or -3.8
Step-by-step explanation:
In this case we put the like terms together as follows
-4w+(7/2)w=(-3/2)-(2/5) note the change of signs when the equal sign. + changes to - and -changes to +.
Therefore -(1/2)w=-(19/10)
dividing both of the equal sign by -(1/2) gives:
w=-(19/10)/-(1/2)
w=-(19/5) or -3.8
Ken drinks 2/7 of a carton of milk each day. How much milk does he drink in 3 days. Be sure to show your work or explain your reasoning
Answer:
6/7 of a carton
Step-by-step explanation:
Option 1:
add: 2/7+2/7+2/7 = 6/7
Option 2:
multiply 2/7 * 3/1 = 6/7
The milk he drinks in 3 days should be 6 by 7.
Given information:Ken drinks 2/7 of a carton of milk each day.
Calculation of milk:Here we have to add [tex]2 \div 7[/tex] three times so it gives [tex]6 \div 7[/tex]
Now the milk should be
[tex]= 2\div 7 \times 3\div 1 \\\\= 6\div 7[/tex]
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Find the value of x and y.
A) x=109, y=108
B) x=108, y=109
C) x=108, y=108
D) x=109, y=109
Answer:
B
Step-by-step explanation:
Since a quadrilateral has an angle sum of 360 degrees you just add the three angle measures together and subtract them from 360 leaving you with 108.
The angle which is outside is supplementary which means it adds to 180 degrees. All you have to do here is subtract 71 from 180 which gives you 109.
It’s B) x=108,y=109
Es la respuesta
What are the ratios for sin A and cos A? The triangle is not drawn to scale.
Answer:
[tex]SinA = \frac{84}{85}[/tex] and [tex]CosA=\frac{13}{85}[/tex]
Step-by-step explanation:
The ratios of sine and cos are defined as follows:
[tex]Sin A = \frac{Opposite}{Hypotenuse}[/tex] , and
[tex]CosA = \frac{Adjacent}{Hypotenuse}[/tex]
The hypotenuse is always the side opposite of the 90 degree angle (for the given triangle, the hypotenuse is 85)
Since we are looking at the angle A, the opposite side with respect to A would be the side length of 84. That leaves the side 13 as the adjacent side.
Thus, we can now write:
[tex]Sin A = \frac{Opposite}{Hypotenuse}\\SinA = \frac{84}{85}[/tex]
[tex]CosA = \frac{Adjacent}{Hypotenuse}\\CosA=\frac{13}{85}[/tex]
The correct answer is the first answer choice.
How much fabric is needed to make a tent in the shape of a triangular prism with the following measures?
273 ft 2
329 ft 2
294 ft 2
266 ft 2
The total fabric required to make a tent in the shape of a triangular prism with the given measures is 1162 square feet.
Explanation:To calculate the amount of fabric required to make a tent in the shape of a triangular prism, we need to calculate the surface area, which is essentially the sum of the areas of all the faces.
The measures provided are presumably the areas of each of the faces of the triangular prism (273 ft^2, 329 ft^2, 294 ft^2, and 266 ft^2). In which case, we simply add these areas together:
273 ft^2 + 329 ft^2 + 294 ft^2 + 266 ft^2 = 1162 ft^2
Therefore, the total fabric required is 1162 square feet.
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To calculate the amount of fabric needed for a triangular prism-shaped tent, find the area of each face and add them together.
Explanation:To find the amount of fabric needed to make a triangular prism-shaped tent, we need to calculate the surface area of all the faces. A triangular prism has two triangular bases and three rectangular faces. First, find the area of each face: base = 273 ft2, height = 329 ft2, and second base = 294 ft2. Then, calculate the area of the three rectangular faces: length = height of the triangular face = 329 ft2, and the other two lengths are the same as the base or second base.
So, the total fabric needed is the sum of the areas of all the faces. Add the areas of the two triangular faces and the three rectangular faces to find the final answer.
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Could you please help me?
Answer:
x = 31
Step-by-step explanation:
AC=BD
3x+7 = 131-x
Subtract 7 from both sides
3x = 124-x
Add x to 3x
4x = 124
Divide by 4
x = 31
Check:
3(31)+7 = 131 - 31
Mulitply 3 times 31 / subtract 131 and 31
93+7 = 100
Add 93 to 7
100 = 100
What is the degree measure of the angle formed by the hands of a clock when the time is 12:00
Answer:
0 degrees
Step-by-step explanation:
when it is hour 12 and 0 minutes, the hour and minute hand will be on top of each other, so therefore it does not form an angle
how would you solve 200 x 30/100? Please give instructions in how you did so.
Answer:
Well first you multiple 200 by 30 which equals 6,000 and then divide it by 100 which then leads you to the answer of 60. Hope I helped. :)
Step-by-step explanation:
The expression (x-9)(2x^2-6x+3) can be rewritten as which of the following?
a. x(2x^2-6x+3)-9(2x^2-6x+3)
b. 2x^3+54x-27
c. x(2x^2-6x+3)+9(2x^2-6x+3)
d. 2x^3-6x^2-27
Answer:
A
Step-by-step explanation:
An equivalent expression is an expression which is equal to (x-9)(2x^2-6x+3). You can expand or simplify an expression to make an equivalent expression. Apply the distributive property to form a new equivalent expression by multiplying (x-9) separately into the factor in parenthesis.
(x-9)(2x^2-6x+3) = x(2x^2-6x+3) - 9(2x^2-6x+3)
(4Q) If c < d and x > 1, which of the following must be true?
Use the rule to change the base
[tex]\log_a(b) = \dfrac{\log_c(b)}{\log_c(a)}[/tex]
To express both logarithms in terms of the natural logarithm (for example, any common base would be fine:
[tex]\log_c(x) = \dfrac{\ln(x)}{\ln(c)},\quad \log_d(x) = \dfrac{\ln(x)}{\ln(d)}[/tex]
Since the natural logarithm is an increasing function, we have
[tex]c<d\implies \ln(c)>\ln(d)[/tex]
which implies
[tex]\dfrac{\ln(x)}{\ln(c)}=\log_c(x)<\log_d(x)=\dfrac{\ln(x)}{\ln(d)}[/tex]
Given the following functions f(x) and g(x), solve f over g (−5) and select the correct answer below:f(x) = 2x − 20g(x) = x − 1a. -5b. 5c. 1/6d. 30
Answer:
(f/g)(-5) = 5
Step-by-step explanation:
You mean, "determine the value of (f/g)(x) at x = -5."
That would be:
f(x) 2x - 20
------- = ------------ and we now substitute -5 for x:
g(x) x - 1
2(-5) - 20 -30
(f/g)(-5) = --------------- = -------- = 5
-5 -1 -6
Rewrite the expression 5(10+12) using the disruptive of multiplication over addition
Answer:
5·10 + 5·12
Step-by-step explanation:
The distributive property of multiplication over addition says the factor outside parentheses can be applied to each of the terms inside parentheses:
5(10 + 12) = 5·10 + 5·12
___
Of course, this can be simplified further if you like, to 50+60 = 110. But we already knew the value of the expression is 5·22 = 110.
Which of the following is not a commonly used practice? Choose the correct answer below. A. If the original population is normally distributed, then for any sample size n, the sample means will be normally distributed. B. If the distribution of the sample means is normally distributed, and ngreater than30, then the population distribution is normally distributed. C. The distribution of sample means gets closer to a normal distribution as the sample size n gets larger. D. If the original population is not normally distributed and ngreater than30, the distribution of the sample means can be approximated reasonably well by a normal distribution.
Answer:
. B. If the distribution of the sample means is normally distributed, and greater than30, then the population distribution is normally distributed
Using the Central Limit Theorem, it is found that the statement which does not represent a commonly used practice is:
B. If the distribution of the sample means is normally distributed, and n greater than 30, then the population distribution is normally distributed.
The Central Limit Theorem establishes that, for a normally distributed random variable X, the sampling distribution of the sample means with size n can be approximated to a normal distribution. For a skewed variable, the Central Limit Theorem can also be applied, as long as n greater than 30.From this, we have that no matter the distribution, for samples of at least 30, the distribution of the sample means is normal. If the underlying distribution is normal, the sample size is not important.However, we cannot infer anything about the population given the distribution of the sample means, thus, statement B is false.A similar problem is given at https://brainly.com/question/4086221
Please answer this multiple choice question, will give brainliest!!
Answer:
C. 4.3 cm
Step-by-step explanation:
Since it is a right triangle you can use a²+b²=c² to solve this. Then you subtract 2 from the AC to get AD.
Answer: I think its 4.3 if its not then its 4.0
What is the surface area of this cylinder?
A) 6.4 m2.
B) 25.1 m2.
C) 37.7 m2.
D) 62.8 m2.
Answer:
it is c
Step-by-step explanation:
During his science experiment, Yuri measured the temperature of a water sample as 24 degrees Celsius. To determine the temperature in degrees Fahrenheit, he used the formula , where F is the temperature in degrees Fahrenheit and C is the temperature in degrees Celsius. Which is a correct step in the process Yuri should take to convert the temperature? Check all that apply.
Substitute 24 for F.Substitute 24 for C.Add 32 to C before multiplying by .Multiply the value of C by before adding 32.
The correct steps to take are substitute 24 for C, Multiply the value of C by 9/5 before adding 32.
Conversion of celsius to FahrenheitThe formula for converting celsius to Fahrenheit is expressed as shown below;
(T°C * 9/5) + 32 = T°F
Given the following
T°C = 24°C
Substitute
(24 * 9/5) + 32 = T°F
multiply the value of C by 9/5
43.2 + 32 = T°F
Then add 32
T°F = 74.2°F
Hence the correct steps to take are substitute 24 for C, Multiply the value of C by 9/5 before adding 32.
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Answer:The correct steps to take are substitute 24 for C, Multiply the value of C by 9/5 before adding 32.
Step-by-step explanation:
Conversion of celsius to Fahrenheit
The formula for converting celsius to Fahrenheit is expressed as shown below;
(T°C * 9/5) + 32 = T°F
Given the following
T°C = 24°C
Substitute
(24 * 9/5) + 32 = T°F
multiply the value of C by 9/5
43.2 + 32 = T°F
Then add 32
T°F = 74.2°F
Hence the correct steps to take are substitute 24 for C, Multiply the value of C by 9/5 before adding 32.
Find the measure of Arc AB.
Answer:
The measure of arc AB is [tex]88\°[/tex]
Step-by-step explanation:
we know that
The inscribed angle measures half that of the arc comprising
so
[tex]m<ACB=\frac{1}{2}(arc\ AB)[/tex]
we have
[tex]m<ACB=44\°[/tex]
substitute
[tex]44\°=\frac{1}{2}(arc\ AB)[/tex]
[tex]88\°=arc\ AB[/tex]
rewrite
[tex]arc\ AB=88\°[/tex]
The measure of arc AB is 88°
The inscribed angle measures half that of the arc comprising
so
[tex]m < ACB=(1)/(2)(arc\ AB)[/tex]
we have
[tex]m < ACB=44°[/tex]
substitute
[tex]44\°=(1)/(2)(arc\ AB)[/tex]
[tex]88\°=arc\ AB[/tex]
rewrite
[tex]arc\ AB=88\°[/tex]
Fiona ran 6 laps around a track each lap was 500 meters how far did Fiona run? Circle all that apply
A. 30 kilometers
B. 3 kilometers
C. 3,000 meters
D. 300 meters
the answer to this question is d
14.3 rounded to the nearest one
Answer:
14
Step-by-step explanation:
To round 14.3 to the nearest one, we round down because the digit to the right of the decimal point is less than 5. Therefore, the answer is 14.
Explanation:To round 14.3 to the nearest one, we look at the digit to the right of the decimal point, which is 3. Since 3 is less than 5, we round down. Therefore, 14.3 rounded to the nearest one is 14.
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Need help picture below is ez like crazy i just need help on it AND 22 POINT FOR IT DO YOUR BEST
A. Explain the error and redo the problem showing the correct answer. *
B. Are both of the boys correct? If not who is correct and explain your answer. *
Answer:
I know a is because he added 0.2 instead of still decreasing since its subtraction in negatives
and b : since -0.2 - -0.3 is -0.5 so neither are correct