the breadth of the river is [tex]20\sqrt{3} m[/tex] or 34.614 m
as per given in the question ,
the length of the tower (l) = 20m
the angle of elevation of the top of the tower from the opposite bank
[tex]\theta[/tex] = [tex]30^{0}[/tex]
the breadth of the river should be found
let the breadth of the river be x,
to find breadth,
[tex]tan\theta=\frac{opposite\ side}{adjacent\ side}[/tex] ----(1)
the opposite side will be the length of the pole i.e, 20m
the adjacent side will be the breadth of the river i.e, x
now substitute all the values in equation (1)
[tex]tan\theta=\frac{20}{x}[/tex]
=> [tex]tan 30^0= \frac{20}{x}[/tex] ( the value of [tex]tan30^0 =\frac{1}{\sqrt{3} }[/tex] )
=> [tex]\frac{1}{\sqrt{3} } =\frac{20}{x}[/tex]
=> [tex]x=20\sqrt{3}m[/tex]
so,
the breadth of the river is [tex]20\sqrt{3} m[/tex] or we can write 34.614m
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if 47200 dollar is invested at an interest rate of 10 percent per ayear.Find the value o the investment at the end of 5years for the following compunding method,to the nesrset cen.
(a) anually?
(b) semi anual?
(c)monthly?
(d)daily?
Answer:
a. annually
Step-by-step explanation:
anually means yearly, semi anual means twice a year
A technician is setting up a router and would like to increase the security level. Which of the following actions will achieve this? A. Increasing transmission power B. Changing the default admin password C. Installing anti-malware on the router D. Configuring multifactor logon authentication
changing the default admin password will achieve the security level.
What is a router ?
An networking device called a router is used to forward data packets between computer networks. On the worldwide Internet and between networks, routers handle traffic directing. Data packets are the unit of data delivered via a network, such as an email or a web page. An internetwork (such as the Internet) is made up of networks, and a packet is normally passed from one router to another router over those networks until it reaches its destination node.
Default admin password can be known for many people and they can use the internet.
So, changing the default admin password will achieve the security level.
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given the triangle below, select all true statements
Answer:
first and fourth statements are true
Step-by-step explanation:
the sum of the 3 angles in a triangle = 180° , so
2x + 1 + x + x + 15 = 180 , that is
4x + 16 = 180 ( subtract 16 from both sides ) ← True
4x = 164 ( divide both sides by 4 )
x = 41 ≠ 49
then
∠ A = 2x + 1 = 2(41) + 1 = 82 + 1 = 83° ≠ 99°
∠ C = x + 15 = 41 + 15 = 56° ← True
what is the slope of a line perpendicular to the following line
y=1/3x-2
Answer:
The slope of a line perpendicular to the line y=1/3x-2 is the negative reciprocal of the slope of that line. The slope of the line y=1/3x-2 is 1/3, so the slope of a line perpendicular to it is -3.
Compensation to find 37×4 please broken down showing work
The product of two given numbers 37 and 4 using distributive property is 148.
What is the distributive property?The distributive property states that an expression which is given in form of A (B + C) can be solved as A × (B + C) = AB + AC.
Given that, 37×4.
Using distributive property, we can find the product of two given numbers
That is 37×4
= (30+7)4
= 30×4+7×4
= 120+28
= 148
Therefore, the product of two given numbers using distributive property is 148.
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The price of a stock steadily decreased by a total of $159 over the past 14 months. Which expression shows the change in the stock's value?
The expression that shows the change in the stock's value is -159 * 14
How to determine the expression that shows the change in the stock's value?From the question, we have the following parameters that can be used in our computation:
Rate of decrement = $159
Duration = 14 months
Using the above as a guide, we have the following:
The expression that shows the change in the stock's value is
Expression = Rate of decrement * Duration
Substitute the known values in the above equation, so, we have the following representation
Expression = -159 * 14
Evaluate the products
Expression = -2226
Hence, the required expression is -159 * 14
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Two sides of a triangle measure 15 inches and 18 inches, respectively. Which of these is NOT a possible length for the third side of the triangle? Responses 36 in. StartFragment, 36 in., 24 in. StartFragment, 24 in., 18 in. StartFragment, 18 in., 4 in.
Answer:.
Step-by-step explanation:
If LM bisects JK at point P, which statements must be true? Select all the true statements.
10. en Vision STEM Sound travels in
waves. In dry air at 20° Celsius, sound
travels about 343 meters in one second
How many meters will sound travel in
7 seconds?
In 2401 meters will sound travel in 7 seconds if In dry air at 20° Celsius, sound travels about 343 meters in one second.
Define distance.The length of the line connecting two places represents the distance between them. Subtracting the different coordinates will reveal the distance if the two points are on the same horizontal or vertical line. Distance is the sum of an object's movements, regardless of direction. Distance can be defined as the amount of space an object has covered, regardless of its starting or ending position.
Given
Speed = 343 m
Time = 7 seconds
For distance,
Distance = Time × Speed
Distance = 343 × 7
Distance = 2401
In 2401 meters sound will travel in 7 seconds if In dry air at 20° Celsius, sound travels about 343 meters in one second.
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is this right
aww we fast
(algebra)
Which of the following terms are equivalent to the slope in a proportional relationship? Select all that apply.
a.) Constant Rate of Change
b.) origin
c.) Change in y / Change in x
d.) rise/run
e.) inverse
Answer:
a.) Constant Rate of Change - yes
b.) origin - yes
c.) Change in y / Change in x - yes
d.) rise/run - yes
e.) inverse - Not apply
What is the difference between rate of change and slope coefficient?
The terms rate of change, gradient, slope coefficient, and rise over run are all equivalent to the slope in a proportional relationship. The slope of a line describes the rate at which a variable changes in relation to another variable. Rate of change is the same concept, but it is more general and can be applied to any relationship, not just linear. Gradient is another term for the slope of a line, which is the change in one variable compared to the change in another variable. Slope coefficient is a mathematical term for the slope of a line, which is the ratio of the vertical change to the horizontal change. Rise over run is another term for the slope of a line, which describes the rate of change by measuring the vertical change (rise) over the horizontal change (run). All of these terms describe the same concept, which is the rate of change in a proportional relationship.
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-9k+7>=16 and 5-k<=13
The solution to the inequality -9k + 7 ≥ 16 and 5 - k ≤ 13 is -8 ≤ k ≤ -1
How to determine the solution to the inequality?The complete question is added at the end of this solution
From the question, we have the following parameters that can be used in our computation:
-9k+7>=16 and 5-k<=13
Rewrite the above inequality expressions
So, we have the following representation
-9k + 7 ≥ 16 and 5 - k ≤ 13
Evaluate the like terms in the above inequality expressions
So, we have the following representation
-9k ≥ 9 and - k ≤ 8
Divide both sides of the above inequality expressions by the coefficient of x
So, we have the following representation
k ≤ -1 and k ≥ -8
When the solution is merged, we have
-8 ≤ k ≤ -1
Hence, the solution is -8 ≤ k ≤ -1
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Complete question
Solve for k in -9k+7>=16 and 5-k<=13
Which two values of x are roots of the polynomial below?
x^2+ 5x + 9
The two values of x that are roots of the polynomial are:
x = -5 + i√11/2
x = -5 - i√11/2
What is a polynomial?Polynomial is an equation written as the sum of terms of the form kx^n.
where k and n are positive integers.
We have,
x² + 5x + 9 = 0
It is in the form of ax² + bx + c
a = 1
b = 5
c = 9
Using the determinant.
x = -b ± √(b² - 4ac) / 2a
x = -5 ± √(25 - 36) / 2
x = -5 ± √-11 / 2
x = -5 ± i√11/2
Where i = √-1
Thus,
The roots of the polynomial are:
x = -5 + i√11/2 and x = -5 - i√11/2
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Gianna is taking a walking tour in her city. the entire tour is 10 1/10 kilometers long. According to an app on her phone, Gianna's average walking rate is 1.6 meters per second.
Part (A) How many meters does Gianna walk each hour?
Part (B) How many kilometers does Gianna walk each hour?
The distances travelled in each hour for both part are given as 5760 m and 5.76 km respectively.
What is the application ratio and proportion?A ratio is the relation between two numbers as a / b. A proportion is the equality of two ratios as a / b = c / d.
Ratio and proportion can be applied to solve Mathematical problems dealing with unit values of the quantities.
The given problem can be solved by ratio method as follows,
(A) The average walking rate is 1.6 m/s
The speed in meter per hour is calculated as,
1 second = 1/3600 hour
Take the ratio of 1.6 and 1/3600 as follows,
1.6 ÷ 1/3600
= 3600 × 1.6
= 5760
(B) The average walking rate is 1.6 m/s
It implies that 1.6 m in 1 second.
Now, 1 m = 1/1000 km
=> 1.6 m = 1.6/1000 km
And, 1 second = 1/3600 hour
Thus, the distance travelled in kilometer per hour can be evaluated by taking the ratio as follows,
1.6/1000 ÷ 1/3600
= (3600 × 1.6)/1000
= 5.76
Hence, the distances travelled per hour in meter and kilometer are given as 5760 m and 5.76 km respectively.
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Professor Conner recorded a base hit 2 times in his 11 at bats. He is not happy about this. What percentage of the time will he record a base hit?
Round to the nearest whole number.
Remember: this is a percentage, not a proportion. Just type the number. You do not need to type the percentage sign.
Percentage of the time will he record a base hit is 18.
To find the percentage of times that Professor Conner recorded a base hit, you need to divide the number of times he recorded a base hit by the total number of at bats, and then multiply by 100%.
In this case, the percentage of times that Professor Conner recorded a base hit would be
= (2 base hits / 11 at bats) * 100%
= 18.2%.
After Rounding off to nearest whole number it becomes 18%.
What is a Base Hit?
A fair ball hit in such a way that the hitter can reach a base safely without a fielding error by the other side.
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Percentage of the time will he record a base hit is 18.
To find the percentage of times that Professor Conner recorded a base hit, you need to divide the number of times he recorded a base hit by the total number of at bats, and then multiply by 100%.
In this case, the percentage of times that Professor Conner recorded a base hit would be
= (2 base hits / 11 at bats) * 100%
= 18.2%.
After Rounding off to nearest whole number it becomes 18%.
What is a Base Hit?A fair ball hit in such a way that the hitter can reach a base safely without a fielding error by the other side.
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Matthew invests $8,586 in a retirement account with a fixed annual interest rate of 5%
compounded continuously. How long will it take for the account balance to reach $23.457"
For each $23.457" borrowed, you would pay about a year $8,586 in interest, as in the case of a credit card with an APR of 5%.
What does annual interest rate mean?An estimate of the annual cost of borrowing money is the annual percentage rate (APR), which is expressed as a percentage of the principal loan amount. An accurate representation of how much borrowing money will cost is sought after by the annual percentage rate (APR) on a credit card or loan. In a different method, the annual percentage rate (APR) of a given loan is the total annual interest payments divided by the loan's outstanding balance. Assuming a credit card with a 10% APR, you would pay $8,586 in interest for every $23.457" borrowed over the course of a year.To learn more about Annual percentage rate (APR) refer to:
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5) An 8-inch dinner knife is sitting on a circular plate so that its ends are on the edge of the plate. If the central angle made by the knife measures 120°, what is the diameter of the plate? Show all work.
6) If the area of a circumscribed square is 324 square feet, then
The diameter of the plate. show all work. will be 9.24 inches. The diameter is double of the hypotenuse.
What is the diameter?
A diameter is a line that travels through the center of an object and intersects the circumference at opposing ends. It measures twice as long as the object's radius.
The radius of the circle becomes the hypotenuse when a right triangle is formed by joining the edge of the knife to the center of the circle and the center of the knife to the center of the circle.
With the help of the trigonometric function, the value of the hypotenuse is found as;
sin60 = 8/h
h = 4.62 inches
The diameter of the plate is double the hypotenuse in the given figure;
D = 2 X h
D = 2 X 4.6
D = 9.8
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Ivanna is draining an aquarium. The graph shows the amount of water (in liters) in the aquarium versus time (in minutes).
(a) At what time does the amount of water in the aquarium reach 0 liters?
minutes
(b) Choose the statement that best describes how the time and amount of water are related. Then fill in the blank.
As time increases, the amount of water in the aquarium decreases.
At what rate is the amount of water decreasing?
liters per minute
As time increases, the amount of water in the aquarium increases.
At what rate is the amount of water increasing?
liters per minute
A linear function gives us the following:
a) At 0 seconds, there are 300 liters of water in the aquarium.
b) The amount of water is losing volume at a rate of 60 liters per minute as time goes on.
Given,
Linear function;-
Modeling a linear function involves:
y = ax + b
That where:
The rate of change, or a, is the slope, or how much y changes when x changes by one.B is the y-intercept, which is also known as the function's starting point and is the value of y at x = 0.The y-intercept in this problem is 300, hence 300 liters of water are present in the tank at 0 seconds.
The quantity drops by 60 liters each minute, so:
Water is losing volume at a rate of 60 liters per minute as time goes on.
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There are 20 cards labeled from 1 to 20 in a bag. A card is randomly selected from the bag.
What is the probability of getting an even number or a 1?
The probability of getting an even number or a 1 is 11/20
What is probability?
Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics is the study of events subject to probability.
Given that there are 20 cards numbers 1,2... 20.
A card is randomly drawn.
We have to find the probability of drawing either 1 or even card.
P(drawing even card) = no of even cards/total cards = 10/20= 0.5
P(drawing one) = no of 1's/total cards = 1/20 = 0.05
P(drawing both one and even card) = 0 (since impossible)
Hence P(drawing even or one) =0.5+0.05-0
=0.55
= 11/20
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8. Jay pays a flat fee each month for basic cable service. He also pays $ 3.50 for each movie he orders during the month. Last month, he ordered 5 movies and his total bill came to $ 54.
a. Write an equation in point-slope form that b. What is the monthly flat fee Jay pays represents the total bill, y, in terms of the number each month? of movies, x Then simplify it to slope-intercept form.
c. Next month, Jay plans to order 7 movies.
d. This month, Jay's total bill is $ 78.50.
What will be his total bill for the month?
How many movies did he order this month?
Answer:
y=f+3.5x
Step-by-step explanation:
Let the total bill be y
and let the number of movies be x
let the flat fee be f
given that he pays $3.5 per movie
and his total bill is $54
The expression is given bellow for his total bill
y=f+3.5x
For 5 movies his total bill is $54
54=f+3.5(5)
54=f+17.5
54-17.5=f
f=36.5
Therefore the flat fee is $36.5
A kiddie pool holds 16 gallons of water. How many pints of water is this equal
The kiddie pool can hold 128 pints of water which is equivalent to 16 gallons.
What is a unitary method?A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.
We know 1 gallon is equal to 8 pints.
So, To obtain the number of pints in 16 gallons of water we have to multiply the total no.of gallons with a unitary pint value of 1 gallon which is,
= (16×8) pints.
= 128 pints.
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Answer: 128 pints
Step-by-step explanation:
1 gallon is 8 pints, 8 multiplied by 16 equals 128
Help please, what is the slope and y intercept
slpoe is -1/2 and y-intercept is 2
A social security number contains nine digits, such as 952-56-7606. How many different social security numbers can be formed?
First spot: 9 choices (0-9)
Second spot: 9 choices (0-9)
Third spot: 9 choices (0-9)
.
.
.
Ninth spot: 9 choices (0-9)
There are 9 choices for each digit, meaning we need to compute 9^9 to figure out how many possible social security numbers there are.
Explination:
9^9 = 387420489 possible social security numbers
If the perimeter of a trapezium is 68cm, its non -parallel sides are equal to 12cm each and its altitude is 4cm. The area of the trapezium is
Answer:
88 cm²
Step-by-step explanation:
Area of trapezium = [tex]\frac{1}{2}[/tex](a + b)h
12 * 2 = 24
68 -24 = 44
44 is (a + b) as they are the sum of the parallel sides of the trapezium.
h (altitude) = 4
[tex]\frac{1}{2}[/tex](44)(4) = 88 cm²
Answer:
88 cm², hope it helps.
What is the slope of -15x + 10y = 50?
m = 15
m = 2/3
m = 5
m = 1
m = 3/2
Answer:
[tex] \huge{ \boxed{m = \frac{3}{2} }}[/tex]
Step-by-step explanation:
[tex] - 15x + 10y = 50[/tex]
Equation of a line is given by
[tex] \bold{y = mx + c}[/tex]
where
m is the slope
c is the y intercept
To find the slope, we must first rewrite the equation in the given form y = mx + c and compare both equations.
[tex] - 15x + 10 y = 50 \\ \\ 10y = 15x + 50 \\ \\ \frac{10y}{10} = \frac{15}{10} x + \frac{50}{10} \\ \\ y = \frac{3}{2} x + 5[/tex]
Comparing it with the general equation y=mx + c,
[tex]m = \frac{3}{2} \\ [/tex]
For the following set of data, find the percentage of data within 1
population standard deviation of the mean, to the nearest percent.
58, 58, 50, 64, 59, 62, 58
The percentage of data within 1 population standard deviation of the mean, to the nearest percent is; 71%
How to find the mean and standard deviation?The mean of a data sample is defined as the average of that data sample. The formula for the mean is;
μ= ∑x/n
Thus;
μ = (58 + 58 + 50 + 64 + 59 + 62 + 58)/7
μ = 409/7
μ = 58.429
The standard deviation is defined as a measure of how dispersed the data is in relation to the mean. It is gotten from the formula;
σ = √[Σ(xi - μ)²/N]
Solving this with a standard deviation calculator gives;
σ = 4.065
Thus, 1 standard deviation from the mean is;
58.429 ± 1(4.065)
= (54.364, 62.494)
The values that fall in this range from the given data set are;
58, 58, 59, 62, 58
They are 5 in number out of 7 and so the percentage = (5/7) * 100%
= 71.43%
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FOR BRAINLIEST Jada's pet turtle walked 10 feet, and then half that length again. b, C. d. Jada's baby brother walked 3 feet, and then half that length again.
Jadas hamster walked 4.5 feet and then half length That again
Jadas robot walked 1 foot then half that length again
a person walked x feet then half that length again
Answer:
a walked x feet then half that length again-step explanation:
50 POINTS ASAP!!!!!!!!!!!!!!!! 50 POINTS ASAP!!!!!50 POINTS ASAP!!!!!50 POINTS ASAP!!!!!!!!!!!!!!!! 50 POINTS ASAP!!!!!50 POINTS ASAP!!!!!
Quadrilateral A'B'C'D' is a translation of quadrilateral ABCD. What is the length of A'B' ?
Answer:
7
Step-by-step explanation:
A'B' should be equal to AB, as AB corresponds to A'B' in the second image attached. Since AB = 7, A'B' will also equal to 7.
Answer:
Answer A
Step-by-step explanation:
7 units
The side lengths of a 30-60-90 triangle are in the ratio 1: √3:2. What is
cos 60°?
The value of cos60° is 1/2.
What is a 30-60-90 triangle?It is a triangle with constant angles of 30, 60, and 90. This triangle is always a right triangle, as one of the angles is 90 degrees. Thus, a right-angled triangle is formed by these angles. Additionally, the right angle is equal to the sum of two acute angles, which will have a 1: 2 or 2: 1 ratio.
We know,
For a 30-60-90 triangle, the sides opposite to 30° is a, the side opposite to 60° is √3a and the side opposite to 90° is 2a.
Therefore,
If a = 1,
The sides are where,
perpendicular = 1
Base = √3
Hypotenuse = 2
We know cosΦ = Base/ Hypotenuse
But in the case of cos60°, we have to take base as 1 and hypotenuse as 2, that is the angle has to be at base.
Base = 1
Hypotenuse = 2
Therefore,
cos60° = Base/ Hypotenuse
cos60° = 1/2
Therefore, the cos60° = 1/2.
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Let f(x)=3x-4 and g(x)=x/2+1. Find f(g(x)) of f o g
Answer:
f(g(x)) = 1.5x - 1------------------------------------------
Given functionsf(x) = 3x - 4 and g(x) = x/2 + 1Find f(g(x))Substitute g(x) into x of f and evaluate:
f(g(x)) = f(x/2 + 1) = 3(x/2 + 1) - 4 = 3/2x + 3 - 4 = 1.5x - 1