Answer:
The value of given expression is [tex]-\frac{\sqrt{2}-\sqrt{6}}{4}[/tex].
Step-by-step explanation:
The given expression is
[tex]\cos\left(\dfrac{19\pi}{12}\right)[/tex]
The trigonometric ratios are not defined for [tex]\dfrac{19\pi}{12}[/tex].
[tex]\dfrac{19\pi}{12}[/tex] can be split into [tex]\frac{5\pi}{4}+\frac{\pi}{3}[/tex].
[tex]\cos\left(\dfrac{19\pi}{12}\right)=\cos (\frac{5\pi}{4}+\frac{\pi}{3})[/tex]
Using the addition formula
[tex]\cos (A+B)=\cos A\cos B-\sin A\sin B[/tex]
[tex]\cos (\frac{5\pi}{4}+\frac{\pi}{3})=\cos( \frac{\pi}{3})\cdot \cos (\frac{5\pi}{4})-\sin( \frac{\pi}{3})\cdot \sin (\frac{5\pi}{4})[/tex]
We know that, [tex]\cos(\frac{\pi}{3})=\frac{1}{2}[/tex] and [tex]\sin (\frac{\pi}{3})=\frac{\sqrt{3}}{2}[/tex]
[tex]\cos\left(\dfrac{19\pi}{12}\right)=\frac{1}{2}\cdot \cos (\frac{5\pi}{4})-\frac{\sqrt{3}}{2}\cdot \sin (\frac{5\pi}{4})[/tex]
[tex]\frac{5\pi}{4}[/tex] lies in third quadrant, by using reference angle properties,
[tex]\cos(\frac{5\pi}{4})=-\cos(\frac{\pi}{4})=-\frac{\sqrt{2}}{2}[/tex]
[tex]\sin(\frac{5\pi}{4})=-\sin(\frac{\pi}{4})=-\frac{\sqrt{2}}{2}[/tex]
[tex]\cos\left(\dfrac{19\pi}{12}\right)=\frac{1}{2}\cdot (-\frac{\sqrt{2}}{2})-\frac{\sqrt{3}}{2}\cdot (-\frac{\sqrt{2}}{2})[/tex]
[tex]\cos\left(\dfrac{19\pi}{12}\right)=-\frac{\sqrt{2}}{4}+\frac{\sqrt{6}}{4}[/tex]
[tex]\cos\left(\dfrac{19\pi}{12}\right)=-\frac{(\sqrt{2}-\sqrt{6})}{4}[/tex]
Therefore the value of given expression is [tex]-\frac{\sqrt{2}-\sqrt{6}}{4}[/tex].
Final answer:
To find [tex]\(\cos(\frac{19\pi}{12})\),[/tex] we express the angle as the sum of [tex]\(\frac{4\pi}{3}\) and \(\frac{\pi}{4}\)[/tex] and then use the cosine addition formula. Calculating the values of cosine and sine for these angles gives us the exact value of [tex]\(\cos(\frac{19\pi}{12})\) as \(\frac{\sqrt{6} - \sqrt{2}}{4}\).[/tex]
Explanation:
To find [tex]\(\cos\left(\frac{19\pi}{12}\right)\)[/tex] using an angle addition or subtraction formula, let's break down the angle [tex]\(\frac{19\pi}{12}\)[/tex] into the sum or difference of angles whose cosine values we know. We can express[tex]\(\frac{19\pi}{12}\) as \(\frac{16\pi}{12} + \frac{3\pi}{12}\)[/tex] which simplifies to[tex]\(\frac{4\pi}{3} + \frac{\pi}{4}\).[/tex] Now we use the cosine addition formula [tex], \(\cos(a+b) = \cos a \cos b - \sin a \sin b\)[/tex], to find the answer:
[tex]\(\cos\left(\frac{19\pi}{12}\right) = \cos\left(\frac{4\pi}{3} + \frac{\pi}{4}\right) = \cos\left(\frac{4\pi}{3}\right)\cos\left(\frac{\pi}{4}\right) - \sin\left(\frac{4\pi}{3}\right)\sin\left(\frac{\pi}{4}\right)\)[/tex]
[tex]\(= (-\frac{1}{2})\cdot(\frac{\sqrt{2}}{2}) - (-\frac{\sqrt{3}}{2})\cdot(\frac{\sqrt{2}}{2})\)[/tex]
[tex]\(= -\frac{\sqrt{2}}{4} + \frac{\sqrt{6}}{4}\)[/tex]
Combining these, we get:
[tex]\(\cos\left(\frac{19\pi}{12}\right) = \frac{\sqrt{6} - \sqrt{2}}{4}\)[/tex]
A restaurant offers a $12 dinner special that has 6 choices for an appetizer, 12 choices for an entrée, and 3 choices for a dessert. How many different meals are available when you select an appetizer, an entrée, and a dessert?
There are 216 different meals available when you select an appetizer, an entrée, and a dessert from the restaurant's menu.
Given that there are 6 choices for the appetizer, 12 choices for the entrée, and 3 choices for the dessert.
Total number of choices:
6 (choices for appetizer) × 12 (choices for entrée) × 3 (choices for dessert) = 216 different meals
Therefore, there are 216 different meals available when you select an appetizer, an entrée, and a dessert from the restaurant's menu.
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There are 216 possible meals. This answer is obtained by applying the counting principle in mathematics, which multiplies together the choices for each part of the meal (appetizer, entrée, dessert).
Explanation:This problem regards the counting principle in mathematics, which is a way of finding the total number of possible outcomes for a series of events. In this case, the events are choosing an appetizer, entrée, and dessert. The counting principle tells us that we can find the total number of possible meals by multiplying together the number of choices for each part of the meal.
Thus, we can solve this problem as follows:
Select an appetizer: 6 choices.Select an entrée: 12 choices.Select a dessert: 3 choices.By the counting principle, we multiply these together to get the total number of possible meals: 6 * 12 * 3 = 216 meals.
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You want to put a 5 inch thick layer of topsoil for a new 16 ft by 34 ft garden. The dirt store sells by the cubic yards. How many cubic yards will you need to order? The store only sells in increments of 1/4 cubic yards.
Answer: About 8.5 cubic yards
Step-by-step explanation:
Given : The length of the garden = 16 ft.
The width of the garden = 34 ft.
The depth of the thick layer of topsoil on the garden = 5 inch
=[tex]\dfrac{5}{12}\text{ ft.}[/tex] [Since 1 foot = 12 inches]
The volume of a rectangular prism :-
[tex]V=l*w*h[/tex], where l is length , w is width and h is height.
The number of cubic feet of topsoil required will be
[tex]V=16\times34\times\dfrac{5}{12}=\dfrac{680}{3}\text{cubic feet}[/tex]
Since 1 yard = 3 feet
[tex]1\text{ foot}=\dfrac{1}{3}\text{ yard}[/tex]
[tex]V=\dfrac{680}{3}\times\dfrac{1}{3}\times\dfrac{1}{3}\times\dfrac{1}{3}=8.3950617284\approx8.50\text{cubic yards}[/tex]
Initially, there were only 197 weeds at a park. The weeds grew at a rate of 25% each week. The following function represents the weekly weed growth: f(x) = 197(1.25)x. Rewrite the function to show how quickly the weeds grow each day and calculate this rate as a percentage.
A.) f(x) = 197(1.25)^7x; grows at a rate of approximately 2.5% daily
B.) f(x) = 197(1.25^7)^x; grows at a rate of approximately 4.77% daily
C.) f(x) = 197(1.03)^x; grows at a rate of approximately 0.3% daily
D.) f(x) = 197(1.03)^7x; grows at a rate of approximately 3% daily
Answer:
D.) f(x) = 197(1.03)^(7x); grows at a rate of approximately 3% daily
Step-by-step explanation:
The growth equation can be written in terms of a rate compounded 7 times per week:
f(x) = 197×1.25^x = 197×(1.25^(1/7))^(7x)
f(x) ≈ 197×1.0324^(7x) . . . . x represents weeks, a daily growth factor is shown
The daily growth rate as a percentage is the difference between the daily growth factor and 1, expressed as a percentage:
(1.0324 -1) × 100% = 3.24%
The best match is choice D:
f(x) ≈ 197(1.03^(7x)); grows approximately 3% daily
The correct answer to this question is D
given the expression (7-4i)-(2+6i), perform the indicated operation and write the answer in the form a+bi
Answer:
[tex]5-10i[/tex]
Step-by-step explanation:
we know that
To subtract two complex number, subtract the real parts and subtract the imaginary parts
so
[tex](a+bi)-(c+di)=(a-c)+(b-d)i[/tex]
we have
[tex](7-4i)-(2+6i)[/tex]
so
[tex](7-4i)-(2+6i)=(7-2)+(-4-6)i=5-10i[/tex]
URGENT!! Offering 39 Points
The solution to this system of equations lies between the x-values -2 and -1.5. At which x-value are the two equations approximately equal?
Answer:
D. -1.8
Step-by-step explanation:
A graphing calculator can show you this easily, as can any calculator or spreadsheet that helps you evaluate the functions at different values of x.
The graphs cross at approximately x = -1.8.
Answer:
Step-by-step explanation:
d
In a right triangle the lengths of the legs are a and b. Find the length of the hypotenuse, if: a=3/7, b=4/7
Answer:
5/7
Step-by-step explanation:
We need the Pythagorean Theorem here.
If you have a right triangle, you can use the equation a^2+b^2=c^2 where a and b are legs and c is the hypotenuse.
Plug in your information.
(3/7)^2+(4/7)^2=c^2
Simplify what you can.
9/49+16/49=c^2
25/49=c^2
Square root both sides.
5/7=c
Answer:
5/7.
Step-by-step explanation:
Let the hypotenuse = h , then:
h^2 = (3/7)^2 +(4/7)^2 ( By the Pythagoras Theorem).
h^2 = 9/49 + 16/49
h^2 = 25/49
h = 5/7.
URGENT!! Offering 50 Points
Approximate the solution to the equation using three iterations of successive approximation. Use the graph below as a starting point.
Answer:
B. x ≈ 13/8
Step-by-step explanation:
We assume that one iteration consists of determining the midpoint of the interval known to contain the root.
The graph shows the functions intersect between x=1 and x=2, hence our first guess is x = 3/2.
Evaluation of the difference between the left side expression and the right side expression for x = 3/2 shows that difference to be negative, so we can narrow the interval to (3/2, 2). Our 2nd guess is the midpoint of this interval, so is x = 7/4.
Evaluation of the difference between the left side expression and the right side expression for x = 3/4 shows that difference to be positive, so we can narrow the interval to (3/2, 7/4). Our 3rd guess is the midpoint of this interval, so is x = 13/8.
_____
The sign of the difference at this value of x is still negative, so the next guess would be 27/16. It is a little hard to tell what the question means by "3 iterations." Evaluating the function for x=13/8 will be the third evaluation, so the determination that x=27/16 will be the next guess might be considered to be the result of the 3rd iteration.
Answer:
B. x=13/8
Step-by-step explanation:
#platofam
A rectangle is 5 times as long as it is wide. The perimeter is 70 cm. Find the dimensions of the rectangle. Round to the nearest tenth if necessary. a. 14 cm by 70 cm c. 11.7 cm by 29.2 cm b. 5.8 cm by 64.2 cm d. 5.8 cm by 29.2 cm
Let the width = X, then the length would be 5x ( 5 times as long as the width).
The perimeter is adding the 4 sides.
x + x + 5x + 5x = 70
Combine the like terms:
12x = 70
Divide both sides by 12:
x = 70/12
x = 5.83
The width = 5.83 cm.
The length = 5 x 5.83 = 29.15
Now round each length to the nearest tenth:
5.8 and 29.2 cm.
The answer is d.
Can someone also help me on this one!!
The change in the X values is in multiples of 2.
The change in the h(x) values need to be: -0.3 x 2 = -0.6
Now find the h(x) values that have a difference of -0.6
A negative value is a decrease.
2 to 4 is an increase.
4 to 6 is an increase.
6 to 8 is an increase.
8 to 10 is an increase.
10 to 12 = 20-19.8 = 0.2
12 to 14 = 19.8 - 19.2 = 0.6
The two columns are 12 and 14
Find the coefficient to the x4 term in the expansion of (x + 4) 6.
Answer:
240
Step-by-step explanation:
The x^k term will be ...
(6Ck)(x^k)(4^(6-k))
For k=4, this is ...
(6C4)(x^4)(4^2) = 15·16·x^4 = 240x^4
The coefficient of x^4 is 240.
_____
nCk = n!/(k!(n-k)!)
A level of measurement describing a variable whose attributes are rank-ordered and have equal distancesbetween adjacent attributes are _____ measures. interval ratio nominal theoretical ordinal
Answer: ordinal
Step-by-step explanation:
There are 4 levels of measurements scales :-
1. Nominal scale : It is used when we categorize the data on the basis of the characteristic such as Religion, Gender , etc.
2. Ordinal scale : It is used when we can order attributes according to their ranks. For example : First > Second > Third and so on.
3. Interval scale : It provides the characteristic of the difference between any two categories. For example : Fahrenheit scale to measure temperature.
4. Ratio scale : It has all the qualities of nominal, ordinal, and interval measures and in addition a "true zero" point. For example : Age.
From the above definitions , A level of measurement describing a variable whose attributes are rank-ordered and have equal distances between adjacent attributes are ordinal measures.
Identify the area of ⊙M in terms of π. HELP ASAP!!
Answer:
A = 196 pi m^2
Step-by-step explanation:
The area of a circle is given by
A = pi * r^2
The radius is 14
A = pi *14^2
A = 196 pi m^2
Answer:
196π m2
Step-by-step explanation:
Sabra went for a long hike and burned 845 calories in 3 1/4 hours.Nelson decided to go for a bike ride. He burned 1,435 calories in 4 7/8 hours.Who burned the most calories per hour?
Answer:
Nelson burned the most calories per hour
Explanation:
To solve this question, we will get the amount calories burned by each in one hour and then compare the two values
To do this, we will divide the total amount of calories burned by the total time
1- For Sabra:
We are given that she burnt 845 calories in [tex]3\frac{1}{25}[/tex] (which is equivalent to 3.25) hours
Therefore:
Calories burnt in an hour = [tex]\frac{845}{3.25}=260[/tex] calories/hour
2- For Nelson:
We are given that he burnt 1435 calories in [tex]4\frac{7}{8}[/tex] (which is equivalent to 4.875) hours
Therefore:
Calories burnt in an hour = [tex]\frac{1435}{4.875}=294.36[/tex] calories/hour
3- Comparing the two values:
From the above calculations, we can deduce that Nelson burned the most calories per hour
Hope this helps :)
Answer:
Nelson burned more cal/hr than Sabra at a rate of 294.36 cal/hr.
Step-by-step explanation:
To find out how many calories per hour each person burned, divide the amount of calories they burned by the amount of hours they spent exercising.
Sabra: 845 cal / 3.25 hr = 260 cal/hr
Nelson: 1435 cal / 4.875 hr = 294.36 cal/hr
260 < 294.36, so Nelson burned more calories/hour than Sabra.
Geometry question, (photo inside)
Simplify the polynomial expression given below.
(2x − 1)(2x2 + 5x + 3) + (3x + 6)
Answer:
[tex]4x^{3}+8x^{2} +4x+3[/tex]
Step-by-step explanation:
Hello
To simplify the polynomial we must eliminate the parentheses
by definition
[tex]ax^{n}*bx^{m} =abx^{n+m}[/tex]
[tex](2x-1)(2x^{2} +5x+3)+(3x+6)\\(4x^{3} +10x^{2} +6x-2x^{2} -5x-3)+(3x+6)\\\\We\ add\ the\ similar\ terms\\\\(4x^{3}+8x^{2} +x-3)+(3x+6)\\\\4x^{3}+8x^{2} +4x+3[/tex]
I hope it helps
Have a great day
Answer:
Its A
Step-by-step explanation:
Just took it.
PLEASE HELP I PUT ALOT OF POINTS INTO THIS AND I WILL GIVE BRAINLIEST
Using the graph of f(x) and g(x), where g(x) = f(k⋅x), determine the value of k.
A.) 3
B.) 1/3
C.) -1/3
D.) -3
Answer:
3
Step-by-step explanation:
The points they have in bold is probably a hint to the problem.
The points they have in bold are (1,2) on curve g which means g(1)=2
and (3,2) on curve f which means f(3)=2.
g(x)=f(kx)
We know g(1)=2 so if we replace the x's with 1, we get:
g(1)=f(k*1)
g(1)=f(k)
2=f(k).
Now we just need to solve f(k)=2 for k.
We know the point (3,2) is on f so f(3)=2.
If you compare:
f(k)=2
and
f(3)=2
then you should see that k=3.
Identify the number as real, complex, pure imaginary, or nonreal complex. (more than one of these descriptions may apply.)−7
Answer:
-7 is real and complex
Step-by-step explanation:
Every number is complex.
Complex numbers are in the form of a+bi where a and b are real numbers.
Pure imaginary are complex numbers with a being 0.
Real numbers are complex number with b being 0.
-7 is a real number and a complex number.
(It doesn't have an imaginary part)
-7 is a real and complex number.
What are the different types of numbers?A real number is a value of a continuous quantity that can represent a distance along a line.The real numbers include all the rational numbers (positive, negative, fraction -4,-3,2,3,4/3,-6/7, etc)The real numbers are all irrational numbers, such as square root, cube root, etc.Real numbers are complex numbers with 0.Pure imaginary numbers are complex numbers with a being 0.Complex numbers are in the form of (x+yi) where a and b are real numbers.Every number is a complex number.Learn more about numbers here:-https://brainly.com/question/148825
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Please help question attached
Answer:
a = sqrt( 3x+1)
Step-by-step explanation:
f(x) = sqrt(x-1)
g(x) = 3x+2
(f°g)(x) means replace g(x) in f(x) every place you see an x
(f°g)(x) = sqrt( g(x) -1)
= sqrt( 3x+2 -1)
Simplifying
=sqrt( 3x+1)
HELLP!!
Drag the signs and values to the correct locations on the image. Each sign and value can be used more than once, but not all signs and values will be used.
Complete the standard form of the equation of the ellipse represented by the equation 9x2 + 4y2 − 36x + 8y + 4 = 0.
Answer:
(x - 2)²/2² + (y + 1)²/3² = 1 ⇒ The bold values and signs are the answers
Step-by-step explanation:
* Lets revise the equation of the ellipse
- The standard form of the equation of an ellipse with center (h , k)
and major axis parallel to x-axis is (x - h)²/a² + (y - k)²/b² = 1
- The coordinates of the vertices are (h ± a , k)
- To change the form of the equation of the ellipse to standard form we
will using the completing square
∵ The equation of the ellipse is 9x² + 4y² - 36x + 8y + 4 = 0
- Lets collect x in bracket and y in bracket
∴ (9x² - 36x) + (4y² + 8y) + 4 = 0
- We will take a common factor 9 from the bracket of x and 4 from the
bracket of y
∴ 9(x² - 4x) + 4(y² + 2y) + 4 = 0
- Lets make 9(x² - 4x) a completing square
∵ √x² = x ⇒ the 1st term in the bracket
∵ 4x ÷ 2 = 2x ⇒ the product of the 1st and 2nd terms
∵ 2x ÷ x = 2 ⇒ the 2nd term in the bracket
∴ The bracket is (x - 2)²
∵ (x - 2)² = x² - 4x + 4 ⇒ we will add 4 in the bracket and subtract 4
out the bracket
∴ 9[(x² - 4x + 4) - 4] = 9[(x - 2)² - 4]
- Lets make 4(y² + 2y) a completing square
∵ √y² = y ⇒ the 1st term in the bracket
∵ 2y ÷ 2 = y ⇒ the product of the 1st and 2nd terms
∵ y ÷ y = 1 ⇒ the 2nd term in the bracket
∴ The bracket is (y + 1)²
∵ (y + 1)² = y² - 2y + 1 ⇒ we will add 1 in the bracket and subtract 1
out the bracket
∴ 4[(y² + 2y + 1) - 1] = 4[(y + 1)² - 1]
- Lets write the equation with the completing square
∴ 9[(x - 2)² - 4] + 4[(y + 1)² - 1] + 4 = 0 ⇒ simplify
∴ 9(x -2)² - 36 + 4(y + 1)² - 4 + 4 = 0 ⇒ add the numerical terms
∴ 9(x - 2)² + 4(y + 1)² - 36 = 0 ⇒ add 36 to both sides
∴ 9(x - 2)² + 4(y + 1)² = 36 ⇒ divide both sides by 36
∴ (x - 2)²/4 + (y + 1)²/9 = 1
∵ 4 = 2² and 9 = 3²
∴ (x - 2)²/2² + (y + 1)²/3² = 1
* The standard form of the equation of the ellipse is
(x - 2)²/2² + (y + 1)²/3² = 1
Answer: (x - 2)²/2² + (y + 1)²/3² = 1
Step-by-step explanation:
Answer the following questions, using the chart and graph from above (see attached).
c. What type of patterns do you notice? Explain
Answer:
f(x) appears to be match the trig function sin(x)
Step-by-step explanation:
The function is an odd function that is periodic with a period of 2π. It is symmetrical about either of ±π/2. It matches sin(x) in every detail shown.
The director of a daycare center noticed that the infants were getting more diaper rashes than usual in the summer time. The policy of the center was to change the diapers on a schedule every three hours. The director wanted to find out if adjusting the diaper-changing schedule to every two hours would significantly reduce the number of diaper rashes. Since some of the infants seemed to have more sensitive skin, she decided to directly compare the number of diaper rashes for each individual infant when the diaper was changed every three hours versus every two hours. For the first week, the daycare center changed the diapers as usual every three hours and noted the number of days that each infant had symptoms of a diaper rash. During the second week, the teachers changed diapers every two hours and recorded the number of days with symptoms of a diaper rash. At the end of the two weeks, they compared for each individual infant the number of days with symptoms of a diaper rash when the diapers were changed every three hours versus every two hours.Let μ 1 and μ 2 represent the mean number of days with symptoms of a diaper rash when diapers were changed every three hours and two hours, respectively, and let μ d be the mean of the differences in thenumber of days with symptoms of a diaper rash (diaper rash days when changed every three hours minus diaper rash days when changed every two hours).What is the appropriate null and alternative hypotheses?
Answer:
Let μ1 and μ2 represent the mean number of days with symptoms of a diaper rash when diapers were changed every three hours and two hours, respectively.
Let μd be the mean of the differences in the number of days with symptoms of a diaper rash.
The null hypothesis and alternative hypotheses are two mutually exclusive things about any population. The null hypothesis is that, which is to be actually tested but an alternative hypothesis gives an alternative to the null hypothesis.
Here the appropriate null and alternative hypotheses will be :
H0: μd=0 (null)
Ha: μd>0 (alternative)
This given study is a matched pair design study, so we are using μd : the mean of the differences.
Also, here we are testing if the number of diaper rashes are more when they are changed every 3 hours than 2 hours. This is why we chose the above hypothesis H0: μd = 0 and Ha: μd > 0.
Answer:
Let μ1 and μ2 represent the mean number of days with symptoms of a diaper rash when diapers were changed every three hours and two hours, respectively.
Let μd be the mean of the differences in the number of days with symptoms of a diaper rash.
The null hypothesis and alternative hypotheses are two mutually exclusive things about any population. The null hypothesis is that, which is to be actually tested but an alternative hypothesis gives an alternative to the null hypothesis.
Here the appropriate null and alternative hypotheses will be :
H0: μd=0 (null)
Ha: μd>0 (alternative)
This given study is a matched pair design study, so we are using μd : the mean of the differences.
Also, here we are testing if the number of diaper rashes are more when they are changed every 3 hours than 2 hours. This is why we chose the above hypothesis H0: μd = 0 and Ha: μd > 0.
Carol uses this graduated tax schedule to determine how much income tax she owes.If Carol’s taxable income is $89,786, how much income tax does she owe, to the nearest dollar?
If Carol’s taxable income is $89,786, how much income tax does she owe, to the nearest dollar?
a.
$25,140
b.
$12,654
c.
$19,636
d.
$37,626
Answer:
C
Step-by-step explanation:
The answer is C
Answer:
Your answer would be C
Step-by-step explanation:
I got it right on edge <3
From Tony's seat in the classroom, his eyes are 1.0 m above ground. On the wall 4.2 m away, he can see the top of a blackboard that is 2.1 m above ground. What is the angle of elevation, to the nearest degree, to the top of the blackboard from Tony's eyes?
The answer is 27 degrees but i dont know how to get that. can someone show me the steps please. will give BRAINLIEST.
Answer:
15 degrees
Step-by-step explanation:
Draw a horizontal segment approximately 4 inches long. Label the right endpoint A and the left endpoint C. Label the length of AC 4.2 meters. That is the horizontal distance between the eye and the blackboard.
At the right endpoint, A, draw a vertical segment going up, approximately 1 inch tall. Label the upper point E, for eye. Label segment EA 1 meter since the eye is 1 meter above ground.
At the left endpoint of the horizontal segment, point C, draw a vertical segment going up approximately 2 inches. Label the upper point B for blackboard. Connect points E and B. Draw one more segment. From point E, draw a horizontal segment to the left until it intersects the vertical segment BC. Label the point of intersection D.
The angle of elevation you want is angle BED.
The length of segment BC is 2.1 meters. The length of segment CD is 1 meter. That means that the length of segment BD is 1.1 meters.
To find the measure of angle BED, we can use the opposite leg and the adjacent leg and the inverse tangent function.
BD = 1.1 m
DE = 4.2 m
tan <BED = opp/adj
tan <BED = 1.1/4.2
m<BED = tan^-1 (1.1/4.2)
m<BED = 15
Answer: 15 degrees
The tangent or tanθ in a right-angle triangle is the ratio of its perpendicular to its base. The angle of elevation is 15°.
What is Tangent (Tanθ)?The tangent or tanθ in a right-angle triangle is the ratio of its perpendicular to its base. it is given as,
[tex]\rm Tangent(\theta) = \dfrac{Perpendicular}{Base}[/tex]
where,
θ is the angle,
Perpendicular is the side of the triangle opposite to the angle θ,
The base is the adjacent smaller side of the angle θ.
Given that Tony's seat in the classroom, his eyes are 1.0 m above ground. On the wall 4.2 m away, he can see the top of a blackboard that is 2.1 m above ground. Therefore, The angle of elevation,
tan(x) = (2.1 - 1.0)/4.2
x = tan⁻¹ (1.1/4.2)
x = 14.68° ≈ 15°
Hence, the angle of elevation is 15°.
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A magazine provided results from a poll of 2000 adults who were asked to identify their favorite pie. Among the 2000 respondents, 13% chose chocolate pie, and the margin of error was given as + or -4 percentage points. Given specific sample data, which confidence interval is wider: the 95% confidence interval or the 80% confidence interval? Why is it wider?
Answer:
95%
Step-by-step explanation:
For a given sample data, the width of the confidence interval would vary directly with the confidence level i.e. more the confidence level, wider will be the confidence interval.
This is because the critical value associated with the confidence level(e.g z value) becomes larger as the confidence level is increased which results in an increased interval.
The confidence interval for a population proportion is given by the formula:
[tex]p \pm z\sqrt{\frac{pq}{n} }[/tex]
So, for a fixed value of p,q and n, the larger the value of z the wider will be the confidence interval.
Hence 95% confidence interval will be wider than 80% confidence interval.
The 95% confidence interval is wider than the 80% confidence interval because it includes a larger area under the curve of a normal distribution, offering a higher level of confidence the true population parameter falls within this range.
Explanation:In statistical analysis, especially for polls like the one mentioned about favorite pies, the confidence interval plays a significant role in interpreting the reliability of the results. The 95% confidence interval is wider than the 80% confidence interval. This is because a higher confidence level, in this case 95%, means we are more sure that the actual population parameter lies within the interval, but in order to gain this certainty, the interval necessarily needs to be wider.
This can also be understood in the context of a normal distribution. For a 95% confidence interval, we are including a larger area under the curve of the distribution, thus the interval has to be wider than the one for the 80% confidence interval, which covers a smaller area.
It's important to note, however, that a wider confidence interval doesn't necessarily imply better predictability. It simply means there's a higher level of confidence that the true population parameter falls within the specified range.
Learn more about Confidence Interval here:https://brainly.com/question/34700241
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A regular hexagonal prism has a height of 12 cm and base edge length of 10 cm. Identify its lateral area and surface area.
L = 620 cm2 ; S = 942.6 cm2
L = 720 cm2 ; S = 1239.6 cm2
L = 720 cm2 ; S = 1759.2 cm2
Answer:
L = 720 cm² ; S = 1239.6 cm²
Step-by-step explanation:
The area of a hexagon is given by the formula ...
A = (3/2)√3·s²
where s is the side length. Then the area of the two hexagonal bases will be ...
base area = 3√3·(10 cm)² ≈ 519.6 cm²
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The lateral area is the product of the perimeter of the base and the height of the prism:
L = 6×(10 cm)×(12 cm)
L = 720 cm²
The totals surface area is the sum of lateral area and base area:
S = L + base area = (720 +519.6) cm²
S = 1239.6 cm²
Answer:
L = 720 cm2 ; S = 1239.6 cm2
Step-by-step explanation:
Got lucky ('<')
Mrs. Herby bought some carrots. She put 2/5 of them on a platter and the rest in a plastic bag. If there were 8 carrots on the platter, how many carrots were there in the plastic bag?
Answer:
5
Step-by-step explanation:
2/5 = 40%
40% of 8 Carrots = 3.2
3 Carrots on Platter
5 Carrots in Plastic Bag
Answer:
12 carrots
Step-by-step explanation:
To get the answer, you need to multiply and divide.
x ÷ 3 · 2 = 8
Now, we need to do the equation backwards to find x.
8 ÷ 2 · 3 = 4 · 3 = 12 carrots
Mayra did not have a date on a Friday night so she decided to mix solutions that she obtained from her garage. She has 9 liters of a 4% -saline solution that must be mixed with a 10% solution to get a 6% solution. How many liters of the 10% solution are needed?
Let [tex]x[/tex] be the number of liters of the 10% solution she needs to use. She'd end up with a 6% solution with a volume of [tex]9+x[/tex] liters. The starting solution contains 0.04*9 = 0.36 liter of salt. Each liter of the 10% solution contributes 0.1 liter of salt, so that
[tex]0.36+0.1x=0.06(9+x)[/tex]
Solve for [tex]x[/tex]:
[tex]0.36+0.1x=0.54+0.06x[/tex]
[tex]0.04x=0.18[/tex]
[tex]x=4.5[/tex]
so Mayra needs to add 4.5 liters of the 10% solution.
Find x [Angles and Segment]
Answer:
8.3 cm
Step-by-step explanation:
The product of lengths to the near and far point of intersection with the circle is the same in all cases:
(7 cm)(7 cm) = (y)(11 cm +y) = (4 cm)(4 cm +x)
Since we're only interested in x, we can divide by 4 and subtract 4:
49 cm² = (4 cm)(4 cm +x)
(49/4) cm = 4 cm +x . . . . . . divide by 4 cm
8.25 cm = x . . . . . . . . . . . . . subtract 4 cm
To the nearest tenth, x = 8.3 cm.
_____
For a tangent segment, the two points of intersection with the circle are the same point, so the product of lengths is the square of the length.
___
The angles depend on the size of the circle, which is not given.
Every year, roughly 25,000,000 kg of hair is cut in the United States. Each kilogram of hair contains about 0.0002 kg of zinc, and each kilogram of zinc is worth about $444. How many dollars worth of zinc is contained in hair cut in the United States every year?
The dollars worth of zinc which is contained in hair cut in the United States every year is:
$ 2,220,000
Step-by-step explanation:The total kilograms of hair that are cut in the United States are: 25,000,000 kg
Also, the amount of zinc present in 1kg of hair is: 0.0002 kg
Hence, the amount of zinc present in 25,000,000 kg of hair is:
25,000,000×0.0002=5,000 kg
Also, cost of 1 kg of zinc= $ 444
Hence, cost of 5,000 kg of zinc will be: 5,000×444
Hence, cost of 5,000 kg of zinc=$ 2,220,000
Answer:
20,000
Step-by-step explanation:
25,000,000 * 0.0002 =5,000
5,000 * 4 = 20,000
Can someone help me with this! I don’t understand
Answer:
B
Step-by-step explanation:
We are given:
[tex]y=4x[/tex]
[tex]2x^2-y=0[/tex]
We are going to put 4x in place of the second y since the first y equaled it:
[tex]2x^2-4x=0[/tex]
So we can factored this equation:
[tex]2x(x-2)=0[/tex]
This implies 2x=0 or x-2=0.
2x=0
Divide both sides by 2:
x=0
x-2=0
Add 2 on both sides:
x=2
If x=0 and y=4x, then y=4(0)=0 so we have (0,0) is an intersection.
If x=2 and y=4x, then y=4(2)=8 so we have (2,8) is an intersection.
Answer:
the answer to the problem given is b