Answer:
$70 per year
Step-by-step explanation:
Answer: can you please give me answer choices
Step-by-step explanation:
A boat heading out to sea starts out at Point A, at a horizontal distance of 1083 feet
from a lighthouse/the shore. From that point, the boat's crew measures the angle of
elevation to the lighthouse's beacon-light from that point to be 8°.At some later
time, the crew measures the angle of elevation from point B to be 4°. Find
distance from point A to point B. Round your answer to the nearest
the
tenth of a foot if
necessary.
The distance between point A and point B is 75.6 feet.
Let's set up a right triangle with the lighthouse at the top and the boat at points A and B at the bottom, with the base of the triangle being the horizontal distance between the two points.
We can then use the trigonometric function tangent to solve for the vertical distance between points A and B, which is given by the formula:
tan(angle of elevation) = vertical distance / horizontal distance
For point A, the angle of elevation is 8° and the horizontal distance is 1083 feet. So, the vertical distance from point A to the lighthouse is given by:
tan(8°) = vertical distance / 1083 feet
Solving for the vertical distance gives us:
vertical distance = tan(8°) * 1083 feet
For point B, the angle of elevation is 4° and the horizontal distance is still 1083 feet. So, the vertical distance from point B to the lighthouse is given by:
tan(4°) = vertical distance / 1083 feet
Solving for the vertical distance gives us:
vertical distance = tan(4°) * 1083 feet
Now we can find the distance between points A and B by subtracting the vertical distance from point A to the lighthouse from the vertical distance from point B to the lighthouse. This gives us:
distance between point A and point B = (tan(8°) * 1083 feet) - (tan(4°) * 1083 feet)
Plugging in the numerical values, we get:
Distance between point A and point B = (0.1403 * 1083 feet) - (0.0698 * 1083 feet)
Simplifying, we get: distance between point A and point B = 75.6083 feet
Therefore, the distance between point A and point B is 75.6 feet.
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ZEFH = 127°. Solve for mzGFH.
E
F
mZGFH =
(8x - 4)º
(5x + 14)°
G
H
The value of ∠GFH=59°, in the given question.
What do you mean by angle?
Two straight lines or rays intersect at a same terminus to make an angle. The vertex of an angle is the point at which all points meet.
According to the data in the given question,
We have :
∠EFH=127°
∠EFG=(8x-4)°
∠GFH=(5x+14)°
Now, we have to solve the value of ∠GFH,
∠EFG+∠GFH=∠EFH
Putting the values given and solve for x,
(8x-4)°+(5x+14)°=127°
8x°-4°+5x°+14°=127°
13x°+10°=127°
13x°=127°-10°
13x°=117°
x=9
Then, putting the value of x in ∠GFH,
∠GFH=(5x+14)°
=(5(9)+14)°
=(45+14)°
=59°
Therefore, the value of ∠GFH=59°.
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true or false? the solutions for y>x+3 are all in the points in the shaded half plane but does not include points on the line y=x+3
When we have an inequality with the symbols < or >, the boundary line of the solution area will not be included in the solution of the inequality, then in this case that we have y>x+3 the solution set are all the points in the shaded half-plane but does not include points on the line y=x+3, and the answer is true
Three Albany Middle Schools raised money to buy new computers.EON raised $286.00 Hackett raised $192.84 Myers raised $113.25 more than Hackett. What is the total amount of money raised by all three schools
We have to find the amount of money raised by all three schools.
The first school: EON, raised $286.00
The second school: Hackett raised $192.84
The third school: Myers raised $113.25 more than Hackett
To calculate the amount that the third school raised, we add $113.25 to the amount that the second school raised $192.84:
[tex]192.84+113.25=306.09[/tex]Myers raised $306.09
Finally, we add the money that the three schools raised to find the total:
[tex]286.00192.84+306.09=784.93[/tex]The total amount of money raised was $784.93
Answer:
$784.93
Solve x^2+5x=-6
A)x=5 and x=1
B)x=-5 and x=-1
C)x=3 and x =2
D)x=-3 and x=-2
Answer:
C
Step-by-step explanation:
x²+5x=-6
Collect like terms
x²+5x+6=0
Factors that when multiplied will give us 6 and when added will give us 5 are 2 and 3.
Therefore,
x²+5x+6=0
x²+2x+3x+6=0
Factorizing;
x(x+2)+3(x+2)=0
Pick one (x+2)
(x+2)(x+3)=0
x+2=0 x+3=0
x=2 and x=3
Which expression is equivalent to -2(5x + 3y)?
A. 3y(5x - 2)
B. 5x(-2 + 3y)
C. -10x - 6y
D. -10x + 3y
Answer:
C. -10x - 6yStep-by-step explanation:
[tex]\sf -2(5x + 3y)[/tex]
Apply the Distributive Property:-
[tex]\sf -2\left(5x+3y\right)[/tex]
[tex]\sf -2\times\:5x-2\times\:3y[/tex]
[tex]\sf -2\times\:5x=\bf -10x[/tex]
[tex]\sf 2\times\:3y=\bf 6y[/tex]
[tex]\sf -10x-6y[/tex]
Therefore, your answer is C. -10x - 6y!!
_______________________
Hope this helps you!
Have a great day!
A school's administration needs to buy benches and chairs for the gymnasium. They have a total budget of $1,500 and each bench, x, costs $100 while each chair, y, costs $50. Which graph shows an inequality that describes the possible number of benches and chairs the administration can buy?
The required graph shows the inequality that describes the possible number of benches and chairs the administration can buy is graph A. Option A is correct.
Here,
According to the question,
cost of the benches = 100x
cost of the chairs = 50y,
the total cost would exceed $1500
So,
the inequality can be formed,
100x + 50y ≤ 1500
Graph A shows the above inequality.
Thus, the required graph shows the inequality that describes the possible number of benches and chairs the administration can buy is graph A. Option A is correct.
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A quarter weights approximately 5.7 grams and dimes weights approximately 2.3 grams. a bag of 18 quarters and some dimes weights 141.7 grams. how many dimes are in the bag?
No. of dimes in the bag will be = 17
What is linear equation ?In the algebraic form y=mx+b, where m denotes the slope and b the y-intercept, a linear equation is defined as a first-order (linear) term plus a constant. When x and y are the variables, the previous statement is occasionally referred to as a "linear equation of two variables."
Calculation5.7 grams -------> one quarter
2.3 grams -------> one dimes
5.7 q + 2.3 d = 141.7
given q = 18
5.7 * 18 + 2.3 d = 141 .7
2.3d = 141.7 - 102.6
2.3 d = 39.1
d = 39.1 / 2.3
d = 17
therefore , no. of dimes in the bag will be = 17
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Khan Academy
Graph the equation.
y = 2(x-4)² + 5
Answer: 4,5
Step-by-step explanation
please help!!!
A handicapped ramp is being constructed for the front entrance of First National Bank in Springfield. ADA guidelines requires a rise angle from the foot of the ramp (point furthest from the entrance) not to exceed 4.8 degrees. This means the vertical to horizontal ratio cannot exceed 1:12. If the handicapped ramp must start 15 feet away from the front entrance, contractors estimate the rise to be about 3 feet.
Part A: Explain thoroughly whether or not these ramp dimensions meet the ADA guidelines.
Part B: If the rise estimate does not meet ADA requirements, provide a measurement that would meet the guidelines.
Part A; The vertical to horizontal ratio of the ramp in the question of 3:15 does not meet the ADA guideline of a vertical to horizontal ratio of 1:12
Part B; The measurement of the ramp that would meet ADA guideline is a vertical to horizontal ratio of 3 feet to 36 feet.
The front entrance of the ramp should therefore be 36 feet away
What is a ratio in mathematics?A ratio is an indication of the number of times one quantity is contained in another quantity.
The ADA guidelines requires that the rise angle ≤ 4.8°
The vertical ratio of the ramp ≤ 1:12
The distance the handicapped ramp must start = 15 feet from the front entrance
The rise of the ramp estimated by the contractors = 3 feet
Part A; The vertical to horizontal ratio of the ramp in the question = 3/15, which is 1:5
Therefore, the ramp does not meet ADA guidelines that requires a vertical to horizontal ratio of less than or equal to 1:12
Part B:
The ramp can be made to meet ADA guideline, whereby the horizontal distance from the entrance can be be adjusted as follows;
Let d represent the required horizontal distance of the front entrance, we get;
3:d = 1:12
From which we get;
[tex]\dfrac{3}{d} =\dfrac{1}{12}[/tex]
3 × 12 = 1 × d
d = 36
The horizontal distance of the front entrance of the ramp should be 36 feet away.
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What is the equation for this please help
Answer:
the equation would be 1.67x+0
A population of values has a normal distribution with μ = 159.8 and σ = 59.5 . If a random sample of size n = 13 is selected, Find the probability that a single randomly selected value is greater than 156.5. Round your answer to four decimals. P(X > 156.5) = Find the probability that a sample of size n = 13 is randomly selected with a mean greater than 156.5. Round your answer to four decimals. P(M > 156.5) =
In a population of values having a normal distribution with (μ = 159.8) and (σ = 59.5), if a random sample of size (n = 13) is selected, then the probability that a single randomly selected value is greater than 156.5 will be 0.52.
As per the question statement, a population of values has a normal distribution with (μ = 159.8) and (σ = 59.5) and a random sample of size (n = 13) is selected,
Then we are required to calculate the probability that a single randomly selected value is greater than 156.5.
To solve this question, let us assume that, a random variable "X" follows normal distribution with mean (μ = 159.8), standard deviation (σ = 59.5) and a sample size of (n = 13).
Then the probability that a single randomly selected value is greater than 156.5 can be calculated as follows:
P (X > 156.5) = [1 - P(X < 156.5)]
= [1 - P{(X - μ)/σ < (156.5- 159.8)/59.5}]
= [1 - P{Z < (-0.0554)}]
= (1 - 0.477885127828 )...[Using Excel Function "NORMSDIST (-0.0554)]
= 0.522114872172
≈ 0.52
Probability: Probability is the branch of mathematics that deals with the numerical descriptions on the extent to which an event is likely to occur, or how likely it is, that a proposition is true, being calculated by the ratio of the favorable cases to the total number of cases possible.To learn more about Samples and Probability, click on the link below.
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I can enter the problem here so ill add a picture, sorry for the inconvenience
Given two numbers a and b
Their Arithmetic mean (A), Geometric mean (G) and Harmonic mean (H) are given below,
[tex]\begin{gathered} A=\frac{a+b}{2} \\ G=\sqrt[]{ab} \\ G=\sqrt[]{AH} \end{gathered}[/tex]To find the formula that correctly relates H, a and b,
Relating the last two equations, i.e the geometric and harmonic mean below,
[tex]\begin{gathered} G=\sqrt[]{ab} \\ G=\sqrt[]{AH} \\ \text{relating both equations} \\ \sqrt[]{ab}=\sqrt[]{AH} \\ \text{Square both sides } \\ (\sqrt[]{AH})^2=(\sqrt[]{ab})^2 \\ AH=ab \\ \text{Make H the subject},\text{ by dividing both sides by A} \\ \frac{AH}{A}=\frac{ab}{A} \\ H=\frac{ab}{A} \end{gathered}[/tex]Substituting for A into the above expression,
[tex]\begin{gathered} \text{recall A=}\frac{a+b}{2} \\ H=\frac{ab}{A}=\frac{ab}{\frac{a+b}{2}} \\ H=(2\times\frac{ab}{a+b})=\frac{2ab}{a+b} \\ H=\frac{2ab}{a+b} \end{gathered}[/tex]Hence, A is the correct option.
Which two angles are supplementary?23 degrees and 147 degrees45 degrees and 145 degrees30 degrees and 60 degrees41 degrees and 139 degrees
The population of rabbits on an island is growing exponentially. In the year
2010, the population of rabbits was 9400, and by 2012 the population had
grown to 11500. Predict the population of rabbits in the year 2021, to the
nearest whole number.
The population of the rabbit in 2009
Given that the population of rabbits on an island which is growing exponentially
So let the population be as P = P₀ [tex]e^{bt}[/tex]
where P₀ and b are constants and t = current year - 1994
In 1994, time is equal to 0
the population of rabbit , P = 9,600
so thus the expression becomes
P₀ = 9,600
and in 2000 , t = 2000 - 1994 thus time = 6 years and population of the rabbit is 18,400
[tex]18400 = 9600[/tex] × [tex]e^{b 6}[/tex]
18400 / 9600 = [tex]e^{b 6}[/tex]
23/ 12 = [tex]e^{b 6}[/tex]
Taking log on both sides
ln 1.92/ 6 = b
b = 0.109
On putting the value of P₀ and b the population of the rabbit after t years from 1994 is
P = 9600 × [tex]e^{0.109}[/tex] [tex]^{t}[/tex]
In 2009, t = 2009 - 1994 = 15 years
So, the population of the rabbit in 2009
thus P= 49243
Hence we can say that the population of the rabbit in 2009
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Answer:
It's 28495
Step-by-step explanation:
May you please help me solve the answer to this problem step by step, please?
Given:
As angle N is 90 degree.
[tex]\begin{gathered} \angle N=44^{\circ}+\angle n \\ \angle n=90^{\circ}-44^{\circ} \\ \angle n=46^{\circ} \end{gathered}[/tex]To find the bearing of flight from Elgin to Canton.
Use the sin ratio,
[tex]\begin{gathered} \frac{\sin c}{510}=\frac{\sin n}{720} \\ \frac{\sin c}{510}=\frac{\sin46^{\circ}}{720} \\ \sin c=\frac{\sin46^{\circ}}{720}\times510 \\ \sin c=0.4995 \\ c=\sin ^{-1}(0.5095) \\ c=30.63^{\circ} \end{gathered}[/tex]The bearing angle ( clockwise from north ) can be calculated by subtracting the above angle from the west bearing angle of 270 degree.
[tex]270^{\circ}-30.63^{\circ}=239.37^{\circ}[/tex]Answer: 239.37 degree
Select all units that can be used for surface area. Explain why the others cannot be
used for surface area.
motera
A square meters
B. feet
C. centimeters
D. cubic inches
E.square inches
F. square feet
Answer: A, E, F
Step-by-step explanation:
The area answers always need to have a square in the unit so B & C are wrong.
D is wrong because it is a unit for volume. So A, E, and F are the right answers.
If a watch costs $40 and you must pay 6.5 % sales tax, how much will the tax be?
Dado la siguiente información de un triángulo, encuentre B,C y cB=_______. A = 36° , a = 8 , b = 5C=_______c=_______
Usa la ley de seno para hallar la medida del angulo B:
[tex]\frac{a}{\sin A}=\frac{b}{\sin B}[/tex][tex]\begin{gathered} \sin B(\frac{a}{\sin A})=b \\ \\ \sin B=b\cdot\frac{\sin A}{a} \\ \\ B=\sin ^{-1}(b\cdot\frac{\sin A}{a}) \\ \\ B=\sin ^{-1}(5\cdot\frac{\sin 36}{8}) \\ \\ B\approx21.55 \end{gathered}[/tex]Como la suma de los angulos interiores de un triangulo siempre es 180°, usa la medida del angulo A y angulo B para hallar la medida del angulo C:
[tex]\begin{gathered} A+B+C=180 \\ C=180-A-B \\ C=180-36-21.55 \\ C=122.45 \end{gathered}[/tex]Usa la ley de seno para hallar la medida del lado c:
[tex]\begin{gathered} \frac{c}{\sin C}=\frac{a}{\sin A} \\ \\ c=\frac{a}{\sin A}\cdot\sin C \\ \\ c=\frac{8}{\sin36}\cdot\sin 122.45 \\ \\ c\approx11.48 \end{gathered}[/tex]Entonces, las medidas que tenias que hallar so;
B=21.55°
C=122.45°
c=11.48
15x -2 = 3 ( 5x + 7)
We have the following:
[tex]15x-2=3\cdot(5x+7)[/tex]solving for x:
[tex]\begin{gathered} 15x-2=15x+7 \\ 15x-15x=2+7 \\ 0=9 \end{gathered}[/tex]Therefore, the system has no solution
c to the fifth power squared
Answer: c to the power of 25
Step-by-step explanation: c can stay on its on 5 squared is 25 so the answer is c *25
Determine if it’s true or false based on the figure shown
Answer:
True is the correct answer for this
Melina is hiking and is at en elevation of 2000 feet. If she descends by 500 feet. What is her elevation now?
Please help! I need this asap. P.S.- I'm in class. Thanks!
The elevation of Melina when she descends by 500 feet is 1500 feet.
What is an elevation?An elevation simply means the height above a particular place. It is usually referenced as the sea level.
In this situation, Melina is hiking and is at en elevation of 2000 feet. If she descends by 500 feet. It should be noted that since she descend, we will have to subtract 500 from the initial value that was given as 2000. feet.
Therefore, the calculation will be illustrated through subtraction. This will be:
= 2000 - 500
= 1500 feet.
This implies that when Melina descends, the elevation that she'll be at that point in time is 1500 feet.
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Read the following statement: Line segment CD is congruent to line segment EF. Which of the following is an equivalent statement? (5 points) CD overbar similar to EF overbar CD overbar equal to EF overbar CD overbar element to EF overbar CD overbar congruent to EF overbar
An equivalent statement is CD overbar congruent to EF overbar.
What is a line segment?
The line segment has two fixed-length endpoints, A and B. The distance between this line segment's endpoints A and B is its length.
Here,
Line segment CD is congruent to line segment EF and in geometry, an overbar represents a line segment.
So, we can say that the CD overbar means line segment CD and the EF overbar means line segment EF.
Hence, An equivalent statement is CD overbar congruent to EF overbar.
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Which of the following is the equivalent mathematical symbol of the expression, "A book of stamps at the post office has less than 10 stamps in it"? * b. s > 10 a. s < 10 d. s is greater than or equal to 10 c. s is less than or equal to 10
ANSWER
s < 10
EXPLANATION
With the 'less than' or 'greater than' symbol we can see that it's like an equal sign that has been shrinked on one end. In the smallest end we have to write the smallest expression or number and in the largest end we have to write the greatest expression or number.
For example: 5 < 10 is the same as 10 > 5, because the smallest number (5) is in the smallest end of the sign and the greatest number (10) is in the largest end of the sign in both expressions.
If 's' is the number of stamps, the expression says that there are 'less than' 10 stamps at the post office, so 's' has to be in the smallest end of the sign.
Determine the exact surface area of the cylinder in terms of π.
cylinder with radius labeled 1 and one fourth centimeters and a height labeled 2 and three fourths centimeters
6 and 9 over 16 times pi square centimeters
10 times pi square centimeters
15 and 15 over 16 times pi square centimeters
19 and three eighths times pi square centimeters
A right circular cylinder is a three dimensional geometric figure with its top and bottom as circle. The exact surface area for the given cylinder is 10π square cm.
What is a cylinder?A cylinder is a three dimensional geometric figure.
The volume of a cylinder is given as πr²h, where r is the radius and h is the height of the cylinder.
Given that,
The radius of cylinder r = 1 and one fourth cm
= 1 + 1 / 4 cm
= 5 / 4 cm
The height of cylinder h = 2 and three fourth cm
= 2 + 3 / 4 cm
= 11 / 4 cm.
Since the exact surface area of cylinder is given by 2πr(h+ r), the exact surface area for the given cylinder is given as,
= 2π × (5 / 4 ) × ((11 / 4) + ( 5 / 4))
= 2π × (5 / 4 ) × 4
= 10π
Hence, the exact surface area for the given cylinder is 10π square cm.
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the price of a computer component is decreasing at a rate of 9% per year. if the component costs $60today ,what will it cost in there years ?
The exponential decay formula is:
[tex]y=a(1-r)^t[/tex]where y is the final cost, a is the initial cost, r is the annual decreasing rate (as a decimal), and t is the time in years.
Substituting with a = $60, r = 0.09, and t = 3 years, we get:
[tex]\begin{gathered} y=60\cdot(1-0.09)^3 \\ y=60\cdot(0.91)^3 \\ y=60\cdot0.75 \\ y=45.21 \end{gathered}[/tex]It will cost $45.21 in 3 years
Abelita and franco had great service during the meal. they would like to tip the server 20 percent. which of these expressions would find the total bill, including tax and gratuity? check all that apply
The tip is 20%. Franco and Abelita want to quit the server.
How do I just specify percentages?In mathematics, a number or ratio that can be expressed as a fraction of 100 is known as a percentage. In order to calculate a percentage of a number, we must divide it by 100 and then multiply the resulting number by 100. The percentage thus denotes a component per 100. Percentage refers to a division by 100. The letter "%" stands for it.
Total Amount of Bill=11.72 is an expression that will equal the full amount, including tax and gratuity.
=11.72+11.72×20/100
=11.72+{(0.2)×11.72}
=11.72×(1+0.2)
11.72×1.02
Option C→11.72+0.2×(11.72)
And Option D→11.72×(1.02)
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On a road map, the distance from City A to City B is 4 inches. The map scale is 1 inch = 20 miles. What is the actual distance, in miles, between City A and City B? A. 5 miles B. 24 miles C. 48 miles D. 80 miles
Answer: D. 80 miles
Step-by-step explanation:
if 1 inch is 20 miles, then 4 inches is 4 x 20 = 80 miles what is real distance between City A and City B
1 inch = 20 miles4 inch = 4 x 1 inch = 4 x 20 miles = 80 milesAnswer:
D. 80 miles
Step-by-step explanation:
If the map distance between Cities A and B is 4 in, and the map scale is 1 in = 20 mi, then the actual distance between Cities A and B is:
[tex]\frac{4\text{ in}}{1}\times\frac{20\text{ mi}}{1\text{ in}}=\frac{80\text{ mi}}{1}=80\text{ mi}[/tex]
In other words, every one inch on the map equates to 20 miles in actual distance. Therefore, 4 inches equates to 80 miles.
A diagram is shown, where kill and Move statements and reasons to the table to provem is a transversal.that 21 25.mReasonsStatements1. kl-K2.1. Given2. Corresponding anglesare congruent.3.253763.4. 215 254.A <10 -2 B-1u23C218 24 D-2013E-2014 F-2025 G229 26 1723324I 23:25 J24325 R-4826L_Transitive property Msymmetric propertyN Vertical angles are congruent.Straight angles form a linear pair.P Corresponding angles are congruent.Q Alternate exterior angles are congruent.
Given:- The triangle with dimensions in it.
To find:- Which triangle is congruent to triangle MNO.
Solution:-
As we know that two triangles are congruent only when they satisfy one of the given rules.
1. SSS (Side-side-side) congruency rule.
2. SAS (side-angle-side) congruency rule.
3. ASA (Angle-Side-Angle) congruency rule.
4. AAS (Angle-Angle-Side) congruency rule
5. RHS (Right angle-Hypotenuse-Side) congruency rule.
So, check one by one option.
Option A:-
One side is 4.6 cm, another side is 4.99 cm and one angle is 60 degrees.
But it does not satisfy any of the congruency rules because there are 2 sides and then one angle.
So, option A is incorrect.
Option B:-
In option B there are three angles given 70 degrees, 60 degrees and 50 degrees. But to prove that the triangle is congruent we need at least one side.
So, Option B is incorrect.
Option C:-
In option C, there are only two sides given as 4.07 cm and 4.99 cm and to prove that the triangles are congruent we need at least three measurements of the triangle.
So, option C is incorrect.
Option D:-
In option D, there is one side of 4.07 cm, then one angle of 60 degrees and then one side of 4.99 cm. And we can observe that there is an angle between the two sides.
So, it follows SAS (side-angle-side) congruency rule.
So, Option D is correct.
Final answer:-
Therefore, the answer is option D.