The angle that the ramp makes with the ground rounded off to two decimal places is 10.48°.
What is trigonometry?
The study of the relationship between the sides and angles of the right-angle triangle is essentially the focus of the field of mathematics known as "trigonometry". Therefore, employing trigonometric formulas, functions, or trigonometric identities can be helpful in determining the missing or unknown angles or sides of a right triangle. Angles in trigonometry can be expressed as either degrees or radians.
Given, the length of the ramp = h = 17 feet
Height at which ramp is placed on truck = p = 4 feet
Let the angle that the ramp makes with the ground = ∅
Taking the length and height of ramp as basis, on assuming a right triangle with the length as hypotenuse and the height as perpendicular, we have:
sin ∅ = Perpendicular/Hypotenuse = h / p = 17/4 = 4.25
⇒ ∅ = sin⁻¹ (4.25) ⇒ ∅ = 10.48°
Thus, the angle that the ramp makes with the ground rounded off to two decimal places is 10.48°.
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Using your academic vocabulary and writing at least 5-7 sentences, give the (x, y) solution to the system and explain how to
solve it using the SUBSTITUTION METHOD. If your explanation uses any other method (graphing calculator or linear combination), you will not receive credit for this writing assignment.
y - 3x + 7
5x-y-5
Why are most streets designed in a way that they are perpendicular or parallel to each other? ...
The simple reason why streets are usually designed parallel or perpendicular to each other is because that pattern makes it easy for users to connect people easily.
What is meant by perpendicular and parallel streets?A perpendicular street can simply be defined as a street which intersect another streets. However, on the other end, two streets are said to be parallel to each other when they are in the same distance apart. The same is applicable in mathematics as a perpendicular line intercept another line and parallel lines don't meet.
That being said, when streets are parallel or perpendicularly designed, residents of the environment find it easy to communicate with each other. Business owners use this easy accessibility to easily describe their addresses to customers.
So therefore, it can be deduced from the given explanation above that when streets are designed with good planning, it makes people access it easily.
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The graph of a quadratic function with vertex (-3,1) is shown in the figure below. Find the range and the domain
The domain of the given quadratic function is { -3 }
and range is { 1 }
What is a domain and range ?A function's domain is the set of values that can be plugged into it. This set symbolizes the x values in a function like f. (x). Additionally, we can deduce that a function's range refers to the set of values it can accept. There are values in this set that the function returns when we enter an x value.
The domain of the given quadratic function is { -3 }
and range is { 1 }
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suppose that people's heights (in centimeters) are normally distributed, with a mean of 170 and a standard deviation of 5. we find the heights of 60 people. (you may need to use the standard normal distribution table. round your answers to the nearest whole number.) (a) how many would you expect to be between 165 and 175 cm tall? people (b) how many would you expect to be taller than 167 cm?
The expected number of people between 165 and 175 is 41.
The expected number of people taller than 168 is 39.
Given that the mean and standard deviation of people's heights (measured in centimeters) are 170 and 5 respectively. The heights of 60 people are revealed.
μ = 170
σ = 5
n = 60
(a) The probability would you expect to be between 165 and 175 cm tall;
P( 165 < x < 175 ) = P( (165 - 170)/5 < z < (175 - 170)/5 )
= P( -1 < z < 1 )
= P( z < 1) - P( z < -1 )
= 0.8413 - 0.1587
= 0.6826
Expected number of people between 165 and 175 = n * p
= 60 * 0.6826
= 40.956
≅ 41
(b) The probability would you expect to be taller than 167 cm;
P( x > 167 ) = P( z > (167 - 170)/5 )
= P( z > -0.6 )
= 0.7257
Expected number of people taller than 168 = n * p
= 60 * 0.7257
= 43.542
≅ 39
Hence,
The expected number of people between 165 and 175 is 41.
The expected number of people taller than 168 is 39.
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Find the equation of a line parallel to 3x+3y=6 that passes through the point (7,-1)
The equation of the line parallel to 3x+3y=6 that passes through the point (7,-1) is y = -x + 8
How to find equation of a line?The equation of a line can be represented as follows:
y = mx + b
where
m = slopeb = y-interceptThe lines that are parallel have the same slopes.
Therefore, let's find the slope of the equation 3x+3y=6.
3x + 3y = 6
3y = - 3x + 6
divide through by 3
y = - x + 2
Therefore, the slope is - 1.
Let's find the y-intercept of the equation using (7, 1)
y = - x + b
1 = - 7 + b
b = 8
Therefore, the equation of the line is y = -x + 8
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a high school theater club has 40 student, 6 of whom are left handed. two student will be selected at random, one at a time without replacement. what is the pobability that the 2 student selected will both be left-handed/
1.92% is the probability .
Describe probability using an example?
By dividing the number of preferable possibilities by the total number of potential outcomes, probability, which measures the likelihood that an event will occur, is obtained. The most basic illustration is a coin toss. There are only two outcomes that can occur when you flip a coin: either heads or tails.The probability of an event is the ratio of the size of the event space to the size of the sample space.
The size of the sample space is the total number of possible outcomes
The event space is the number of outcomes in the event you are interested in.
so
Let
x------> size of the event space
y-----> size of the sample space
so
P = x/y
Find out the probability that the first student selected will be left-handed
we have
x = 6
y = 40
substitute
P = 6/40
Simplify
P = 3/20
the probability that the second student selected will be left-handed
we have
x = 6 - 1 = 4
y = 40 -1 = 39
substitute
P = 5/39
the probability that the 2 students selected will both be left-handed
Multiply the probabilities
P = 3/20(5/39) = 15/780
Convert to percentage
Multiply by 100
15/780 * 100 = 1.92%
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a random variable is normally distributed with a mean of 25 and a standard deviation of 5. if an observation is randomly selected from the distribution, what value will 15% of the observations be below?
the 2 values X(19.8,30.2) is value will 15% of the observations be below .
by hypothesis .
What is hypothesis ?
A hypothesis is an assertion, a notion put up for the purpose of debating and then examined to discover if it might be true. Prior to conducting any relevant research, other than a brief background review, the hypothesis is developed using the scientific method.Here, Mean(\mu) and Standard Deviation (\sigma)= 5. You need to find the 2 values of which the smallest has 15% of the values below it i.e (Z<x)= 0.15 and the largest has 15% of the values above it i.e(Z>y)= 0.15.
Now we need to refer to the Z tables and see which value of x corresponds to 0.15, and we see that -1.04 is = 0.149 \sim 0.15
Now we know that the Z value is given by Z = X - μ/σ
Substituting we get
-1.04= (X-25)/5
therefore -5.2= X-25 or X= 19.8
Now let us get the value of X for (Z>y)=0.15`. Since Z tables give values for Z<a only, hence we can write that
Z>y=0.15 is the same as Z<y= 1-0.15= 0.85. We now check the Z tables and see which value of Z corresponds to 0.85, and we get 0.850 = +1.04
Again, substituting Z in the equation Z = X - μ/σ
we get
+1.04= (X-25)/5
Therefore 5.2= X-25, therefore X= 30.2
From the 2 values X(19.8,30.2)
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Help me please ill add more points than usual!
Answer: how
Step-by-step explanation: love
A square painting has a side length of 17 inches.
What is the area of the painting?
The area of the painting is 289 [tex]inches^{2}[/tex].
Given:
A square painting has a side length of 17 inches.
we know that,
Area of square = side * side.
= 17 inches * 17 inches
= 289 [tex]inches^{2}[/tex].
Therefore the area of the painting is 289 [tex]inches^{2}[/tex].
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Enter all real solutions to $(m-4)^4 = \left(\frac 1{16}\right)^{-1}$.
The value of m is 8.
What is Exponents and powers?The amount of times a number has been multiplied by itself is shown by its exponent. The result of multiplying 8 by itself n times is represented as follows:
8 x 8 x 8 x 8 x …..n times = [tex]8^n[/tex]
Given:
[tex]$(m-4)^4 = \left(\frac 1{16}\right)^{-1}$.[/tex]
Now, solving for m
[tex](m-4)^4[/tex] = 16
[tex](m-4)^4[/tex] = [tex]4^4[/tex]
Taking the quad root we have
m -4 = 4
m = 4+ 4
m = 8
Hence, the value of m is 8.
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An 80 kg jumper in flight accelerates at a rate of 8 m/s^2. What is the force of the long jumper? F = ma
By taking the product between the mass and the acceleration, we will see that the force is:
F = 640 N
What is the force of the long jumper?
By the second Newton's law, we know that a force can cause motion on a body by accelerating it, such that the force is equal to the product between the mass of the object and the acceleration.
F = m*a
F = forcem = massa = acceleration.Here we know that:
m = 80kg
a = 8 m/s^2
Replacing that we get:
F = (80 kg)*( 8 m/s^2) = 640 N
Where N is the unit Newton.
1 N = 1 kg*m/s^2
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A marathon is 26.2 miles long. There is a water station every 1 31/100 miles along the race route. Which expression represents the total number of water stations?
The expression that represents the total number of water stations is 26.2 ÷ 1.31
What is an expression?An expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.
It's important to note as an illustration, the expression x + y has the terms x and y with an addition operator between them.
In this case, the marathon is 26.2 miles long and there is a water station every 1 31/100 miles along the race route. The expression will be:
= 26.2 ÷ 1 31/100
= 26.2 ÷ 1.31
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Whose limeade has a weaker like flavor?
well, your proportion setup is good, let's simply use that then
[tex]\stackrel{Jaylan}{\cfrac{~~ \frac{ 3}{4 } ~~}{\frac{1}{5}}}\implies \cfrac{3}{4}\cdot \cfrac{5}{1}\implies \cfrac{15}{4}\implies \cfrac{3\frac{3}{4}}{1}~\frac{water}{lime} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{Wanchen}{\cfrac{~~ \frac{ 2}{3 } ~~}{\frac{1}{6}}}\implies \cfrac{2}{3}\cdot \cfrac{6}{1}\implies \cfrac{12}{3}\implies \cfrac{4}{1}~\frac{water}{lime}[/tex]
well, the one with the lesser lime flavor will be the one that put too much water in the drink, the more water the less the fruit mix, the more waterdowned the drink is, well hell who put more water per lime? well Wanchen, shame on you.
A skydiver fell toward Earth at a steady speed for 10.0 seconds. He fell 593 meters in that
time. What was his speed?
Answer:
59.3 meters/second
Step-by-step explanation:
593 / 10 = 59.3
assume the state of arkansas placed a tax on playing cards of 6 cents per pack. if the state generated $48600 in revenue, how many packs of cards were sold?
The number of pack of cards sold at the state of Arkansas is 8100.
Describe the term division?Multiplication is the complete reverse of division. If participants of 4 add up to 12, then 12 divided into three classes of equally sized results in 4 in each group.For the values given in question.
The tax on playing card in state of Arkansas = 6 cents per pack.
Total revenue generated = $48600.
Divide total revenue by one pack price to get the number of packs.
Number of pack = Total revenue/price of each pack
Number of pack = $48600/6
$48600.Number of pack = 8100
Thus, the number of pack of cards sold at the state of Arkansas is 8100.
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pls hurry and thanks 40 pts
The angle of x in the triangle is 75 degrees.
How to find the angles of triangle?The sum of angles in a triangle is 180 degrees. The triangle is a an isosceles triangle.
An isosceles triangle is a triangle that has any two sides equal in length and angles opposite to equal sides are equal in measure.
Therefore, the base angles are equal.
The third angle of the triangle is 30 degrees(vertically opposite angles)
Hence,
x + x + 30 = 180
2x + 30 = 180
2x = 180 - 30
2x = 150
x = 150 / 2
x = 75 degrees
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A shop is having a sale.
All items are reduced by 25%
Work out the sale price of an item normally priced at £90
The sale price of an item normally priced at £90 is £67.5
What is the percentage?
A percentage in mathematics is a figure or ratio that is stated as a fraction of 100.
Given :
A shop is having a sale. all items are reduced by 25%.
To Find:
Work out the sale price of an item normally priced at £90.
Price of an item = £90
Price is reduced by 25%
Reduction in price = 25%*90=25/100= 22.5
Reduced price = 90-22.5=67.5
Hence, the sale price of an item normally priced at £90 is £67.5
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Select the graph that can be used to find the solution(s) of the system of equations:
y = |x| – 3
y = –x2 + 9
Answer:
(3,0) (-3,0)
Step-by-step explanation:
ask:))
Some doctors recommend that men drink 3 liters of water every day. there are approximately 29.6 milliliters in 1 fluid ounce. which measurement is closest to the number of fluid ounces in 3 liters? responses 89 fl oz 89 fl oz 10 fl oz 10 fl oz 101 fl oz 101 fl oz 33 fl oz 33 fl oz
The measurement closest to the number of fluid ounces there are in 3 liters is 101 fl oz.
In mathematics, conversion is the process of changing the value of one form or unit to another. It can be changing ones unit of length, weight, volume or even currency to another.
If there are approximately 29.6 milliliters in 1 fluid ounce, then divide 3 liters by 29.6 milliliters to get the amount of fluid ounces it has.
29.6 milliliters = 1 fluid ounce
3 liters = 3000 milliliters
3000 milliliters / 29.6 milliliters = 101 fluid ounce
Hence, 3 liters ≈ 101 fluid ounces.
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if a peregrine falcon dove at its maximum speed for half a mile to catch prey, how many seconds would the dive take? (round your answer to the nearest second.)
The time taken by peregrine falcon dove at its maximum speed to cover half a mile is 9 sec.
Who is peregrine falcon dove?It can be found with in Arctic tundra of North America and Greenland, and it migrates to Central and South American countries as during winter.The peregrine falcon is the world's swiftest bird, diving to acquire its prey at speeds of over 321 kph (200 mph). They are also among the most tolerant species and can flourish in populated places.For the given question;
The maximum speed of peregrine falcon dove is 200 mph.
Time of travel = 0.5 miles.
The relation of distance and speed is;
speed = distance/time
200 mph = 0.5 miles / time
Time = 0.5 miles / 200 mph
Time = 0.5 × 60 × 60 miles / 200 m/ sec
Time = 9 sec
Thus, time taken by peregrine falcon dove at its maximum speed to cover half a mile is 9 sec.
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Elon is paid by the hour. He earned $50 for a 4 hour workday. How much
does he earn in one hour?
Answer:
$12.50 per hour
Step-by-step explanation:
Elon is paid by the hour. He earned $50 for a 4 hour workday. How much does he earn in one hour?
50 / 4 = $12.50 per hour
A triangle has sided with lengths of 20 miles, 25 miles, and 30 miles. Is it a right triangle ?
Answer:
No
Step-by-step explanation:
Answer:
No
Step-by-step explanation:
For a Triangle to be a Right-Angled Triangle, should follow the Pythagoras Theorem which states that
If a is the larger side and b , c are the lengths of the other two sides
Then [tex]a^{2} =b^{2} +c^{2}[/tex]
Here a=30 , Then [tex]a^{2}=30^{2} =900[/tex]
and b=20 , c=25 , Then [tex]b^{2} +c^{2} =20^{2} +25^{2} =1025[/tex]
Since [tex]a^{2} \neq b^{2} +c^{2}[/tex]
Then the Triangle is not Right Triangle
What is the side length of the smaller square in the diagram?
The side length of the smaller square is 3 cm.
Given that:-
Length of the larger square = [tex]3\sqrt{2}[/tex] cm.
We have to find the length of the smaller square.
As the length of the larger square is equal to the diameter of the circle
Hence,
Diameter of the circle = [tex]3\sqrt{2}[/tex] cm
Now,
The diameter of the circle is equal to the diagonal of the square.
Hence, diagonal of the square = [tex]3\sqrt{2}[/tex] cm
Let the length of the square be x cm.
Hence, by pythagoras theorem, we can write,
[tex]x^2+x^2=(3\sqrt{2} )^2\\x^2+x^2=18\\2x^2=18\\x^2=9\\[/tex]
x = 3 cm
Hence, the length of the smaller square is 3 cm.
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Be Precise: Yesterday, Noah ran 2½ miles in 3/5 hour. Emily ran 3 3/4 miles in 5/6 hour. Anna ran 3 1/2 miles in hour. How fast, in miles per hour, did each person run? Who ran the fastest? Help pleaseeee
Answer:
Step-by-step explanation:
Noah- 4 1/6 miles/hour
Emily- 8 1/10 miles/hour
Anna- 3 1/2 miles/ hour
Emily ran the quickest.
Answer:
Anna was the fastest.
Step-by-step explanation:
Following are the steps we take to determine each one's speed:
speed=distance/time
Noah went 4 1/6 miles an hour, Emily went 4 1/2 miles an hour, and Anna went 5 5/9 miles an hour. Therefore, Anna was the fastest.
What is the perimeter of the figure?
32.0cm
51.0cm
19.0cm
63.0cm
The perimeter of the figure is 32 cm
How to determine the perimeter of the shape?The figure represents the given parameters
On the figure, we have the lengths of the side lengths to be:
Lengths = 7 cm, 5 cm, 3 cm, 4 cm, 4 cm, 9 cm
To determine the perimeter of the shape, we simply add the side lengths
Mathematically, this can be represented as
Perimeter = Sum of side lengths
Substitute the known values in the above equation So, we have the following equation
Perimeter = 7 cm + 5 cm + 3 cm + 4 cm + 4 cm + 9 cm
Evaluate the sum
Perimeter = 32 cm
Hence, the perimeter is 32 cm
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If the taxi company only has $10.50 to spend, what value does this represent?
The statement "If the taxi company only has $10.50 to spend" represents that the maximum amount to spend is $10.50.
Amount to spend by the taxi driver ≤ 10.50.
What is inequality?It shows a relationship between two numbers or two expressions.
There are commonly used four inequalities:
Less than = <
Greater than = >
Less than and equal =
Greater than and equal=
We have,
The taxi company only has $10.50 to spend.
This means that,
The maximum amount to spend is $10.50.
We can also represent as:
Amount to spend by the taxi driver ≤ 10.50.
Thus,
The statement "If the taxi company only has $10.50 to spend" represents that the maximum amount to spend is $10.50.
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Evaluate the expression and enter your answer in the box below.
|34|
Answer:
34
Step-by-step explanation:
Absolute value means the distance from 0. So the absolute value of 34 is just 34.
Complete the table. Round percent change to the nearest tenth of a percent.
Please find attached the completed table of the percentage changes on the amounts drawn with MS Word.
What is the percentage change on an amount?The percentage change on an amount is found by finding ratio of the change in the amount to the original amount then multiplying the obtained ratio by 100.
The percentage change formula is presented as follows;
[tex]\%C = \dfrac{x_2-x_1}{x_1} \times 100[/tex]Where;
%C = The percentage changex₂ = The new amountx₁ = the initial amountMaking each of the variables the subject, indicates;
The new amount, [tex]x_2 = \dfrac{\%C \times x_1}{100} + x_1[/tex]
[tex]\%C \times x_1+100\cdot x_1 = 100\cdot x_2[/tex]
[tex]x_1\cdot (\%C+100) = 100\cdot x_2[/tex]
The original amount, [tex]x_1 = \dfrac{100\cdot x_2}{(\%C+100)}[/tex]
The percentage change, [tex]\%C = \dfrac{c}{x_1} \times 100[/tex]
The original amount, [tex]x_1 = \dfrac{c}{\%C} \times 100[/tex]
Using the above formulas, the completed table is created with MS Excel and is presented as follows;
Original amount Change Percent Change New Amount
68 [tex]{}[/tex] 15 22.1 83
590 [tex]{}[/tex] -40 -6.8 550
115 [tex]{}[/tex] 20 17.4 135
120[tex]{}[/tex] -33 -27.5 87
125[tex]{}[/tex] -39 -31.2 86
163 [tex]{}[/tex] 47 28.8 210
274[tex]{}[/tex] 145.22 17.4 419.22
70 [tex]{}[/tex] -15.4 -27.5 54.6
1400[tex]{}[/tex] -1050 22.1 350
1250[tex]{}[/tex] -25 -2.0 1225
0.24[tex]{}[/tex] 0.3 125.0 0.54
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Please help! This makes no sense to me
Geometry A
Brainliest for correct answer!!
a standard deck of 52 cards is acquired. for those who do not know, a deck of cards contains 4 suits (hearts, diamonds, clubs, and spades). hearts and diamonds are red, clubs and spades are black. there are 13 denominations of cards (2, 3, 4, 5, 6, 7, 8, 9, 10, jack, queen, king, and ace). if you select two cards (without replacement), what is the probability that you select a black card and a red card?
The probability that you select a black card and a red card is 26/51 as per the condition mentioned "choosing two cards (without replacement )".
What is probability?The area of mathematics known as probability studies potential outcomes of events as well as their relative probabilities and distributions. Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of various outcomes. Statistics is the study of events that follow a probability distribution.
Here,
Since we have not mentioned the order,
so it can black-red or red-black,
=26/52*26/51+26/52*26/51
=2*26/52*26/51
=26/51
Assuming you choose two cards (without replacement), there is a 26/51 chance that you will choose a black card and a red card.
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