The angle of elevation that the instruments have to record to be at the correct height is given as 79°
How to solve for the angle of elevationWe have 2x + 70 = 180
We have to find the value of x
2x = 110
x = 55
y/sin x = 225/sin70
This is the use of sine rule
From here we would have
y = 225(sinx/sin70)
Remember x = 55
y = 225(sin55/sin70)
y = 196.1378
tanθ = 1000/y
tan θ = 1000/196.1378
tanθ = 5.098
θ = tan⁻¹5.098
= 78.90°
Hence the conclusion is that the angle of elevation has to be 78.9 degrees for it to be at the correct height.
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Express in standard form :
42634.7
Answer:
ans is 42635 when expressed in standard form
Step-by-step explanation:
Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes
respectively: (a) 3 /2 and 5
The quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively as 3 /2 and 5 is 2x² - 3x + 10
What is a quadratic polynomial?A quadratic polynomial is a polynomial of the form ax² + bx + c
How to find the quadratic polynomial?For any given quadratic polynomial we have
x² - (sum of zeros)x + (products of zeros) = 0
Given that the sum and product of its zeroes respectively 3/2 and 5,
We have that
sum of zeroes = 3/2 and product of zeros = 5Substituting the values of the variables into the equation, we have
x² - (sum of zeros)x + (products of zeros) = 0
x² - (3/2)x + (5) = 0
x² - (3/2)x + (5) = 0
Multiplying through by 2, we have
2 × x² - 2 × (3/2)x + 2 × (5) = 0 × 2
2x² - 3x + 10 = 0
So, the quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively as 3/2 and 5 is 2x² - 3x + 10
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Help help help help help just need answer
Answer:
25 miles
Step-by-step explanation:
2 inches represents 10 miles ( divide both parts by 2 )
1 inch represents 5 miles , then
5 inches represents 5 × 5 = 25 miles
What effect does 'h' have on the graph of a parabola?
Vertical stretch
Vertical compression
Vertical shift
Horizontal shift
The effect that 'h' have on the graph of a parabola is Horizontal shift or translation .
What is translation?A translation is the movement of a shape up, down , this can also be movement from side to side.
Even though there is movement, its appearance remains the same in any other way, hence, h values cause left or right movement with respect to the graph.
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A couple purchased a home and signed a mortgage contract for $900,000 to be paid with half-yearly payments over a 25-year period. the interest rate applicable is j2 = 5.5% p.a. applicable for the rst ve years, with the condition that the interest rate will be increased by 12% every 5 years for the remaining term of the loan.
A mortgage payment is typically made up of four components: principal, interest, taxes, and insurance. The Principal portion is the amount that pays down your outstanding loan amount. Interest is the cost of borrowing money. The amount of interest you pay is determined by your interest rate and your loan balance.
The term “loan” can be used to describe any financial transaction where one party receives a lump sum and agrees to pay the money back. A mortgage is a type of loan that's used to finance a property. A mortgage is a type of loan, but not all loans are mortgages. Mortgages are “secured” loans.
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HURRY PLS 15 MINS LEFT!!
Answer:
y is less than or equal to 2/3x + 1/5
Step-by-step explanation:
Which equations could be used to solve for the unknown lengths of △ABC? Check all that apply.
sin(45°) = StartFraction B C Over 9 EndFraction
sin(45°) = StartFraction 9 Over B C EndFraction
9 tan(45°) = AC
(AC)sin(45°) = BC
cos(45°) = StartFraction B C Over 9 EndFraction
Applying the trigonometric ratios, the equations that can be used are:
sin 45 = BC/9
cos 45 = BC/9
How to Apply the Trigonometric Ratio?In the given image below, to find the unknown lengths of the triangle, we would apply the following trigonometric ratios:
To find AC, use the cosine ratio, CAH.
To find BC, use the sine ratio, SOH.
sin 45 = opp/hyp = BC/9
sin 45 = BC/9
cos 45 = adj/hyp = BC/9
cos 45 = BC/9
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Answer: A, E
Step-by-step explanation: Sin(45)=BC/9 ; cos(45)=Bc/9
can someone please help mee
Answer:
5/13
Step-by-step explanation:
sine=opposite/hypotenuse
cosine=adjacent/hypotenuse
opposite=-12 (I know that this is not possible)
hypotenuse=13
These are ratios, not real lengths
using the Pythagorean theorem, the other leg is 5
cos (theta)=5/13
How many solutions does this nonlinear system of equations have? NEED HELP ASAP!
Answer:
Step-by-step explanation:
two
Write an expression, of the type A log(x B), for the transformed logarithmic function shown below:
The equation of the logarithmic function is y = log(x - 1)
How to write the equation of the transformed function?The points are given as:
(0,3) and (2,0)
The equation is represented as:
y = A log(x + B)
Substitute (2,0) in y = A log(x + B)
y = A log(x + B)
This means that:
0 = A log(2 + B)
This means that:
A = 0 or log(2 + B) = 0
Take the antilog of both sides of log(2 + B) = 0
2 + B = 1
Solve for B in 2 + B = 1
B = -1
Substitute B = -1 in y = A log(x + B)
y = A log(x - 1)
Substitute (0,3) in y = A log(x - 1)
3 = A log(0 - 1)
So, we have:
3 = A log(-1)
The above equation is undefined.
Hence, the equation of the logarithmic function is y = log(x - 1)
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Complete question
Write an expression, of the type A log(x + B), for the transformed logarithmic function shown below:
(0,3) and (2,0)
The diameter of a semicircle is 26 meters. What is the semicircle's perimeter? Use 3.14 for .
The perimeter of the semicircle is 66. 846 meters
How to find the perimeterThe formula for finding the perimeter of a semicircle is
Perimeter = πr + 2r
We were given diameter = 26meters
Radius, r = diameter/2
radius = 26/ 2 = 13 meters
π = 3. 142
Substitute value into the formula
Perimeter = 3. 142 × 13 + 2 × 13
Perimeter = 40. 846 + 26
Perimeter = 66. 846 meters
Thus, the perimeter of the semicircle is 66. 846 meters
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A motorcycle travels 20 miles west and then turns and goes 52° north of west another 38 miles. How far is the motorcycle from its starting point?? Round your answer to the nearest tenth
__ miles
Answer:
52.7 miles
Step-by-step explanation:
Please refer to attached photo. (Apologies for the terrible drawing).
We can deduce from A to B the distance is 20 miles, therefore no calculations is required.
However, from B to C, we will have to find the horizontal and vertical distances.
Horizontal Distance B > C = = hBC = [tex]BCcos(52)[/tex] = [tex]38cos(52) miles[/tex]
Vertical Distance B > C = vBC = [tex]BCsin(52)[/tex] = [tex]38sin(52)miles[/tex]
Here you can see the whole diagram is a right angle triangle. Which means, we can use Pythagoras' Theorem to find AC.
By Pythagoras Theorem,
[tex]c^{2} =a^{2}+b^{2}[/tex]
[tex]AC^{2} = (AB + hBC)^{2} + vBC^{2} \\AC^{2} = (20+38cos(52))^{2} +(38sin(52))^{2} \\AC = \sqrt{(20+38cos(52))^{2} +(38sin(52))^{2} } \\AC = 52.7 miles[/tex](nearest tenth)
5.5(x+6 1/2)-(x+9 1/3)-(19-x)
The simplified form of the expression [5.5(x+6 1/2)-(x+9 1/3)-(19-x)] is 11x/2 + 89/12
What is the simplified form of the expressionGiven the expression;
5.5(x+6 1/2) - (x+9 1/3) - (19-x)
First, we convert 6 1/2, 9 1/3 and 5.5 to an improper fraction
6 1/2 = 13/2, 9 1/3 = 28/3 and 5.5 = 11/2
So, we have
(11/2)( x + 13/2 ) - ( x + 28/3 ) - ( 19 - x )
Next, we remove the parentheses
11x/2 + 143/4 - x - 28/3 - 19 + x
11x/2 + 143/4 - 28/3 - 19
11x/2 + 317/12 - 19
11x/2 + 89/12
Therefore, the simplified form of the expression [5.5(x+6 1/2)-(x+9 1/3)-(19-x)] is 11x/2 + 89/12.
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pls help me on 109 I got it wrong :c
Answer:
30
Step-by-step explanation:
Let's start by multiplying the equation through bt the least common denominator so that we can clear the denominator:
[tex]\frac{2}{5}x+\frac{1}{3}y=1[/tex]
The least common of 3 and 5 is 15, so we can multiply through by 15:
[tex]15(\frac{2}{5}x+\frac{1}{3}y)=15(1)\\6x+5y=15[/tex]
We want the left side of the equation to be 12x + 10y. We can get this if we multiply the expression we currently have (6x + 5y) by 2. However, if we multiply the left side by 2, we must also multiply the right side by 2 to balance out the equation. If we do this, we will get our answer:
[tex]2(6x+5y)=2(15)\\12x+10y=30[/tex]
On the right side, we get 30. Therefore, the answer is 30
Complete the following conversions. i) 1 mm = m ii) mm = 1 m iii) 1 cm = m iv) cm = 1 m v) 1 km = m vi) km = 1 m vii) 1 cm = mm viii) cm = 1 mm
The unit conversion for the given values are explained below.
What is unit conversion?Unit conversion is the process of changing a quantity's measurement between different units, frequently using multiplicative conversion factors.
The following measurements: length, weight, capacity, temperature, and speed are all measured in units.
Some basic unit conversions are-
1 Km = 1000 m1 m = 100 cm1 m = 1000 mm1 cm = 10 mmThere are two methods to convert the units
To convert smaller unit into larger divide the number by conversion factor.To convert larger value into smaller value multiply by the conversion factor.The unit conversion for the following factors are-
i) 1 mm = _ m
Here, conversion is from smaller to larger. So, divide by conversion factor.
1 mm = (1/100)m
ii) _ mm = 1 m
Here, conversion is from larger to smaller. So, multiply with conversion factor.
1000 mm = 1 m
iii) 1 cm = _ m
Here, conversion is from smaller to larger. So, divide by conversion factor.
1 cm = (1/100)m
iv) _ cm = 1 m
Here, conversion is from larger to smaller. So, multiply with conversion factor.
100 cm = 1 m
v) 1 km = _m
Here, conversion is from larger to smaller. So, multiply with conversion factor.
1 km = 1000 m.
vi) _ km = 1 m
Here, conversion is from smaller to larger. So, divide by conversion factor.
(1/1000) km = 1 m.
vii) 1 cm = _mm
Here, conversion is from larger to smaller. So, multiply with conversion factor.
1 cm = 10 mm
viii) _cm = 1 mm
Here, conversion is from smaller to larger. So, divide by conversion factor.
(1/10) cm = 1 mm.
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Part a: is the probability of hitting the black circle inside the target closer to 0 or 1? explain your answer and show your work. (5 points) part b: is the probability of hitting the white portion of the target closer to 0 or 1? explain your answer and show your work. (5 points)
The probability of hitting the black circle inside the target is close to 0, and the probability of hitting the white portion is close to 1.
Given:
The square's length is 10 units.
The circle's diameter is equal to two units.
To Determine:
It is necessary to determine the probability that the target's white section and black circle will both be hit.
Solution:
The square's area is 10 x 10 or 100 units.
The shaded circle's area is given by πr² = 3.14 (1)² = 3.14 units.
The white area has a surface area of (100 - 3.14) = 96.86 units.
Probability of an event = The number of favorable events /Total number of events
The probability that it will occur in the shaded area = 3.14/100 = 0.0314 (The probability is close to 0).
The probability of hitting the white section is equal = 96.86/100= 0.9686.
(The probability is quite near to 1)
Hence, the probability of hitting the black circle inside the target is close to 0, and the probability of hitting the white portion is close to 1.
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PLS HELP ASAP
42. Use the graph below to answer all questions. Assume the graph is incremented by one.
Does the graph represent a function? How do you know?
What is the domain?
What is the range?
What is the maximum?
What is the minimum?
Identify the intervals where the graph is increasing. What does this mean in the context of the problem?
Identify the intervals where the graph is decreasing. What does this mean in the context of the problem?
See below for the solution to each question
Is the graph a function?Yes, the graph is a function.
This is because all x values have different y values
The domainThis is the set of input values of the graph.
From the graph, we have
x = 0 to x = 17
Hence, the domain is [0, 17]
The rangeThis is the set of output values of the graph.
From the graph, we have
y = 0 to y = 10
Hence, the range is [0, 10]
The maximumThis is the maximum point on the graph.
From the graph, we have
Maximum = (12, 10)
The minimumThis is the minimum point on the graph.
From the graph, we have
Minimum = (0, 0)
The increasing intervalsThese are the intervals where the y values increase as x increase.
From the graph, we have
Increasing intervals = (0, 5) ∪ (10, 12) ∪ (14, 15)
The decreasing intervalsThese are the intervals where the y values decrease as x increase.
From the graph, we have
Decreasing intervals = (7, 10) ∪ (12, 14) ∪ (15, 17)
The constant intervalsThese are the intervals where the y values remain unchanged as x changes.
From the graph, we have
Constant intervals = (5, 7)
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help please much appreciated if you attempt to help
196 36 correct answer is 232
Answer:
728 cm²
Step-by-step explanation:
the surface area is the area of the 6 faces.
the opposite rectangular faces are congruent , then
SA = front/ back + sides + top/ bottom
= 2(14 × 14) + 2(6 × 14) + 2(14 × 6)
= 2 × 196 + 2 × 84 + 2 × 84
= 392 + 168 + 168
= 728 cm²
JJ decided to leave a tip that is 15% of the original price for his meal. How much should he leave as tip for the $5.50 cheeseburger and $2.50 milkshake? Express you answer to the hundreaths place.
If JJ decided to leave a tip that is 15% of the original price for his meal, he should leave $1.2 as tip for the $5.50 cheeseburger and $2.50 milkshake.
How to calculate discount?According to this question, JJ bought a $5.50 cheeseburger and a $2.50 milkshake.
This means that in total, JJ purchased $5.50 + $2.50 = $8 worth of meal.
If he decided to leave a tip that is 15% of the original price of his meal, hence,
15/100 × $8 = $1.2
Therefore, if JJ decided to leave a tip that is 15% of the original price for his meal, he should leave $1.2 as tip for the $5.50 cheeseburger and $2.50 milkshake.
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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, 14​% chose chocolate​ pie, and the margin of error was given as 4 percentage points. Given specific sample​ data, which confidence interval is​ wider: the 90​% confidence interval or the ​80% confidence​ interval? Why is it​ wider?
Between 95% confidence interval and 80% confidence interval, 95% confidence interval is wider than 80% confidence interval.
Given two confidence interval 95% and 80%.
For a given sample data, each confidence interval have different width.
This is because the critical value associated with the confidence level becomes larger as the confidence level is increased which results in an increased interval.
Confidence interval is the range of estimate.
The confidence interval for a population proportion can be found by the following formula:
p±[tex]\sqrt{(pq)/n}[/tex]
The value of z will be wider if the value of p,q are greater.
Hence 95% confidence interval will be wider than 80% confidence interval.
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Alcohol is a major contributor to high percentages of academic problems and college dropouts. question: alcohol is a major contributor to high percentages of academic problems and college dropouts. true false not sure increasing alcohol consumption lowers gpas. question: increasing alcohol consumption lowers gpas. true false not sure students who drink more heavily miss classes at the same rate as other students. question: students who drink more heavily miss classes at the same rate as other students. true false not sure students who drink more study less. question: students who drink more study less. true false not sure students with a 2.0 gpa (c) consume twice as many drinks on average than students with a 4.0 gpa (a).
The correct decision for the statements are
True--->Alcohol is a major contributor to high percentages of academic problems and college dropouts. True--->Increasing alcohol consumption lower GPAs. False--->Students who drink more heavily miss classes at the same rate as other students.True----> Students who drink more study less. False----> Students with a 2.0 GPA (C) consume twice as many drinks on average than students with a 4.0 GPA (A).This is further explained below.
What is Alcohol?Generally, alcohol is a colorless liquid that is volatile and combustible. It is created during the natural fermentation of carbohydrates and is the component that gives wine, beer, spirits, and other beverages their intoxicating properties. Additionally, alcohol is utilized as an industrial solvent and as fuel.
In conclusion, The appropriate response for each of the statements is
Alcohol is a significant factor in the large percentage of students who struggle academically and drop out of college, which is true. It's true that drinking more alcohol brings a drop in GPA. Students who consume more alcohol miss the same number of courses as students who consume less alcohol. This statement is false. Students who drink more spend less time studying, which is true. Students with a grade point average of 2.0 (C) drink on average two times as much alcohol as students with a grade point average of 4.0 (A) (A).
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If B P ⊥ P C , what is m B C ^ ? 180 90 60
The measure of angle BC (m ∠BC) is 90°
Perpendicular linesFrom the question, we are to determine the measure of angle BC
From the given information, we have that
B P ⊥ P C
This means line BP is perpendicular to line PC
The angle between two perpendicular lines is 90°
Hence, the measure of angle BC (m ∠BC) is 90°.
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pls help me w this, i need it answred asap
Answer:
A
Step-by-step explanation:
As angles in a triangle add to 180 degrees, angle C measures 35 degrees.
Therefore, the answer is A, since thr triangles will be similar by AA.
What numbers are zeros of g(x) = x^2 - 2x - 4? take your time if you need to!
Answer:
[tex]x = 1 + \sqrt5, x = 1 - \sqrt5[/tex]
Step-by-step explanation:
Hello!
We can solve the quadratic by using the quadratic formula.
Standard form of a quadratic: [tex]ax^2 + bx + c = 0[/tex]
Quadratic Formula: [tex]x = \frac{-b\pm\sqrt{b^2 - 4ac}}{2a}[/tex]
Given our Equation: [tex]g(x) = x^2 - 2x - 4[/tex]
a = 1b = -2c = -4Plug the values into the equation and solve.
Solve[tex]x = \frac{-b\pm\sqrt{b^2 - 4ac}}{2a}[/tex][tex]x = \frac{-(-2)\pm\sqrt{(-2)^2 - 4(1)(-4)}}{2(1)}[/tex][tex]x = \frac{2\pm\sqrt{4 +16}}{2}[/tex][tex]x = \frac{2\pm\sqrt{20}}{2}[/tex][tex]x = \frac{2\pm\sqrt{4 * 5}}{2}[/tex][tex]x = \frac{2\pm(\sqrt4 * \sqrt5)}{2}[/tex][tex]x = \frac{2\pm2\sqrt5}{2}[/tex][tex]x = 1 + \sqrt5, x = 1 - \sqrt5[/tex]HELPP A PERSON OUT PLSS! i dont really understand how to do ittt!!
giving you all my points so help pleaseeee
Four pounds of apples cost $5 How much would 10 pounds o apples cost?
Answer:
Step-by-step explanation:
plus all of them 5times 10
how many cards from a standard deck must be drawn to guarantee atleast 3 cards of the same suit have been drawn, pidgeon hole
The number of cards which must be drawn from the standard deck is 12.
Given a standard deck of cards.
We have to find the number of cards to be drawn so that we will get atleast 3 cards from each suit. Because they have used atleast in the question so the cards can be more also so we have to reach at minimum level of cards to be drawn to guarantee atleast 3 cards of the same suit.
Number of suits in a standard deck= 4 (Clubs, Hearts, Diamond, Spades)
Cards in 1 suit=13
We need atleast 3 cards of the same suit so we need atleast 3*4=12 cards. (3 from each suit)
Hence the minimum cards which must be drawn to get atleast 3 cards of the same suit is 12.
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The director of research and development is testing a new drug. She wants to know if there is evidence at the 0.01 level that the drug stays in the system for more than 377 minutes. After performing a hypothesis test, she decides to reject the null hypothesis. What is the conclusion
Here null hypothesis is rejected in this problem.
According to the statement
We have a given that the evidence at alpha level is 0.02, ANd the sample size n is 67. And mean time equal to 330 minutes and the variance that is the sigma square is equal to 529 point.
And We have to make the decision to reject or feel fail to reject the null hypothesis to solve this problem.
Firstly we solve alternative and null hypothesis
So, the null hypothesis h naught will be that mu is less than equal to 327 point and alternative hypothesis ha will be.
That mu is greater than 327 point now. This alternative hypothesis is claimed.
Next we will find the value of s which is given by sigma divided by under root n.
So, s = 67/ (529)^1/2
s = 2.8099.
Now we find the value of Z
So, Z = 327 - 330 / 2.8099
Z = 1.0677
Now the critical value of z is 2.05
Critical, we can say fail to reject the null hypothesis, and this is the result from the null hypothesis test.
With this test, we can conclude that the the data do not support that. There is evidence at 0.02 level that the drug stays in the system for more than 327 minutes. So this is the conclusion for the test for the hypothesis test and the answer to the problem.
So, Here null hypothesis is rejected in this problem.
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This is the graph of f(x). What is the value of f(3)?
10+
2
-5
C
A. 5
B. 3
C. 6
D. 8
5
X
The value of f(3) is 8
Given Circle G with radius r, what is the formula for the area of the segment (unshaded region)
Answer:
Option D
Step-by-step explanation:
The triangle ABJ is equitorial
So area
√3/4r²Then mBJ is a arc which is 1/6th of circle
Area.
π/6r²So area of unshaded region
πr²/6-√3/4r²r²(π/6-√3/4)Answer:
[tex]\textsf{d.} \quad r^2\left(\dfrac{\pi}{6}- \dfrac{\sqrt{3}}{4}\right)[/tex]
Step-by-step explanation:
To find the area of the unshaded region, subtract the area of ΔJGB from the area of sector JGB.
The measure of an arc is equal to its corresponding central angle measure. Therefore, the central angle of sector JGB is 60°.
As the two sides of ΔJGB adjacent the central angle are the radii of the circle (and therefore equal in length), ∠GJB = ∠GBJ.
Interior angles of a triangle sum to 180°. Therefore, all interior angles of ΔJGB are 60° which makes it an equilateral triangle.
Area of an equilateral triangle:
[tex]\sf A=\dfrac{\sqrt{3}}{4}a^2 \quad \textsf{(where a is the side length)}[/tex]
As the side length of the given equilateral triangle is the radius (r):
[tex]\implies \sf Area\:of\:triangle=\dfrac{\sqrt{3}}{4}r^2[/tex]
To find the area of the sector, first convert degrees to radians by multiplying the degrees by π/180 :
[tex]\implies 60^{\circ}=60 \times \dfrac{ \pi}{180}=\dfrac{\pi}{3}\:\:\sf radians[/tex]
Area of a sector of a circle
[tex]\textsf{A}=\dfrac12 r^2 \theta \quad \textsf{(where r is the radius and the angle }\theta \textsf{ is in radians)}[/tex]
Substituting the angle in radians, the area of the sector is:
[tex]\implies \sf A=\dfrac{1}{2}r^2\left(\dfrac{\pi}{3}\right)[/tex]
[tex]\implies \sf A=\dfrac{\pi}6}r^2[/tex]
Area of the unshaded region:
[tex]\begin{aligned}\textsf{Area of unshaded region} & =\textsf{Area of sector} - \textsf{Area of triangle}\\\\& = \dfrac{\pi}{6}r^2 - \dfrac{\sqrt{3}}{4}r^2\\\\& = r^2\left(\dfrac{\pi}{6}- \dfrac{\sqrt{3}}{4}\right)\end{aligned}[/tex]
Therefore, the solution is option D.