The second ramp needs to have an angle of 20° from the ground to achieve the overall angle of 35° for the car to drive off smoothly and reach the desired height.
Here,
To find the angle measure the second ramp needs to have, we can use the concept of angles of elevation and depression.
When the car drives off the first ramp, it will be going at an angle of 15° from the ground, and the angle of elevation from the ground to the car will also be 15°.
This is because the angle of elevation is the angle between the horizontal line and the line of sight from the ground to an object above the ground.
Now, when the car reaches the top of the first ramp, it will be at the same level as the second ramp.
At this point, the car needs to continue its ascent with an additional angle of 20° (35° - 15°) to reach the desired angle of 35° from the ground.
So, the second ramp needs to have an angle of 20° from the ground to achieve the overall angle of 35° for the car to drive off smoothly and reach the desired height.
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The sale price of ground beef at a local grocery store is $1.49 for the first pound and $1.09 for each additional pound. Which function rule shows how the cost of ground beef, y depends on the number of pounds, x?
Answer:
y=1.09x+0.4
Step-by-step explanation:
Let's assume that the price of beef stays the same for every pound of beef (the first pound is also $1.09)
Then, the equation would be, it y was the cost, and x was pounds:
y=1.09x
But, the price of beef is not the same for the first pound.
The first pound costs an extra 1.49-1.09=0.4 dollars a pound, so we will add that to the equation.
y=1.09x+0.4
What is the sum of the geometric series 2+6+18+...+486?
Answer:
728
Step-by-step explanation:
2+6+18+...+486
a=2
r=6/2=3
[tex]a_{n}=ar^{n-1}\\486=2(3)^{n-1}\\3^{n-1}=486/2=243=3^5\\n-1=5\\n=5+1=6\\S_{6}=2\frac{3^6-1}{3-1} \\=2\frac{729-1}{2}\\=728[/tex]
Consider this right triangle with the given measures.
A triangle has side lengths 5 inches and 12 inches. The hypotenuse is unknown.
What is the length of the hypotenuse?
1. 52 + 122 =c2
2. 25 + 144 =c2
3. 169=c2
c=
Answer:
c=13
Step-by-step explanation:
You then square root both sides of the equation and the square root of 169 is 13.
Hope this helps! :)
Answer:
c is 13
Step-by-step explanation:
trust me bro
Which is a name for the angle shown? Select all that apply
Answer:
D
Step-by-step explanation:
Well, the angle is an acute angle and <CDE is what would connect to make an acute angle. Easy.The name for the angle shown is ∠D and ∠CDE.
What is Coordinate system?A coordinate system is a system that uses one or more numbers, or coordinates, to uniquely determine the position of the points or other geometric elements on a manifold such as Euclidean space.
An angle is formed when two straight lines or rays meet at a common endpoint.
An angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle.
Angles formed by two rays lie in the plane that contains the rays.
Angles are also formed by the intersection of two planes.
The name of the angle are ∠D and ∠CDE.
Hence, the name for the angle shown is ∠D and ∠CDE.
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The radius of a cylindrical water tank is 6.5 ft, and its height is 11 ft. What is the volume of the tank? Use the value 3.14 for pie, and round your answer to the nearest whole number. Be sure to include the correct unit in your answer.
Answer:
Step-by-step explanation:Idon't say you have to mark my ans as brainliest but my friend if it has helped you don't forget to thank me...
The volume of the cylindrical water tank with the given value of radius and height to the nearest whole number is 1459ft³.
What is a cylinder?
A cylinder is simply a 3-dimensional shape having two parallel circular bases joined by a curved surface.
The volume of a cylinder is expressed as;
V = π × r² × h
Where r is radius of the circular base, h is height and π is constant pi ( π = 3.14 )
Given the data in the question;
Radius r = 6.5ftHeight h = 11ftConstant pi π = 3.14Volume of the cylindrical water tank V = ?We substitute our values into the expression above.
V = π × r² × h
V = 3.14 × (6.5ft)² × 11ft
V = 3.14 × 42.25ft² × 11ft
V = 1459ft³
The volume of the cylindrical water tank with the given value of radius and height to the nearest whole number is 1459ft³.
Learn more on volume of cylinder here: brainly.com/question/16788902
A cylinder and it’s dimensions are diameter 8.4cm and height 10.9cm. Which measurement is closest to the lateral surface area of the cylinder in square centimeters
Answer:
287.64
Step-by-step explanation:
2πrh is the formula you use for the lateral surface area.
to get radius, we know its half of the diameter so 4.2.
plug them in and you get your answer :)
Eric created a rectangular patio 1 ft.² paving stones which are sold in batches by a dozen the patio measures 7‘ x 8‘ how many batches of Pavingstone did Eric need
Answer:
The number of batches of paving stones Eric needs is 5 batches
Step-by-step explanation:
Here we have the size of of one paving stone = 1 ft²
The dimensions, size, of one patio = 7 ft × 8 ft = 56 ft²
Therefore, the number of paving stones Eric needs per patio is given by the relation;
[tex]Number\, of\ paving\ stones \ required =\frac{size\, of \, one\, patio}{size \, of \, one\, paving\, stone} = \frac{56 \, ft^2}{1 ft^2/(paving \, stone)} = 56 \, paving \, stones[/tex]
Since the paving stones are sold in batches of one dozen, we have ;
4 batches = 48 paving stones and 5 batches = 60 paving stones
Therefore, the number of batches of paving stones Eric needs = 5 batches.
Simplify the following expression (6x2 + 8x - 3) - (3x2 - 6)
Answer:
3x^2 +8x +3
Step-by-step explanation:
(6x^2 + 8x - 3) - (3x^2 - 6)
Distribute the minus sign
(6x^2 + 8x - 3) - 3x^2 + 6
Combine like terms
3x^2 +8x +3
A hemisphere has a diameter of 48 inches. What is the volume of the
hemisphere? Use 3.14 for and round to the nearest tenth.
Answer:
9,216π or 28,938.2 meters³
Step-by-step explanation:
Given: diameter 48 inches
Radius 24 inches
Note:
Volume of hemisphere = volume of sphere / 2
Volume of hemisphere = 1/2 • 4/3 • πr³
= 1/2• 4/3×π×24³
= 1/2•18432π
= 9,216π
= 28,938.2 meters³
What is the answer? Plz need help
30x and 12 have a common factor of 6. So yes, this might have been the result of distributing the 6 in
6(5x - 2)
Answer:
30x - 12 = 2(15x - 6)
30x - 12 = 3(10x - 4)
30x - 12 = 6(5x - 2)
Step-by-step explanation:
30 and 12 have these factors in common: 2, 3, 6
There are three possible answers.
30x - 12 = 2(15x - 6)
30x - 12 = 3(10x - 4)
30x - 12 = 6(5x - 2)
Kristen made sails for a model boat. She cut along the diagonal of a rectangular piece of cloth to make two sails, shown.
A) 2 1/3 ft
B) 2 7/12 ft
C) 4 2/3 ft
D) 9 1/3 ft
Answer:
2 1/3 ft^2
Step-by-step explanation:
Take the area of the rectangle
A = l *w
4 * 1 1/6
4 * 7/6
28/6
Divide this in half since the rectangle is cut in half by using the diagonal
28/6 *1/2
28/12
7/3
Changing to a mixed number
2 1/3
Find the area of the following trapezoid
The formula to calculate the area of a trapezoid is as follow:
4 * (8 + 16) * 1/2
Answer:
trapezoid area :(a+b)/2 ×h
(16+ 8)/2 ×4
=48
Today, everything at a store is on sale. The store offers a 20% discount.If the regular price of an item is x dollars, what is the discount price in dollars? Type the correct expression in the box below.
Answer:
0.80x dolllars
Step-by-step explanation:
20% discount of the total amount is
0.20 * x dolllars
So if you start with x dollars you need to subtract the discount to get the new (lower ) price.
x - (0.20 * x) dolllars
1* x - 0.20 * x
x * 1 - 0.20 * x
x * ( 1 - 0.20 )
x * ( 0.80 )
0.80x dolllars
1. Express as a unit rate
a) Serena walks 4 km in 1 h.
Answer:
Step-by-step explanation:
Serena walks 4 km in 1 h.
That means:
1) She walks 4 km per hour.
2) She spends 1/4 = 0.25 hour per mile.
Have a good day.
We can write this as:
4 kilometers/1 hour
The unit rate is already simplified so there is nothing else to do.
Answer: 4km/1hr
Best of Luck!
Question 2 of 10
2 Points
What is the location of the point on the number line that is of the way from
A = 37 to B = 13?
A 19
B. 28
C. 31
D. 25
Answer:
31
Step-by-step explanation:
Please answer me<br />bis two fifths of c.<br />4a = 30<br />Work out the ratio a:b:c<br />Give your answer in its simplest form where a, b and c are integers.
b is two fifths of c, so we make this a ratio with c = 1.
The ratio of b:c is 2/5 : 1
We also have 4a = 3c, rewrite this ratio so c is 1 by dividing both sides by 4,
so we get the ratio of a to c as 3/4 : 1
Now we get the a:b:c ratio of 3/4 : 2/5 : 1 now we can change the fractions to whole numbers, first by multiplying the 3 numbers by 4 to get get rid of the denominator of 4 in a:
3 : 8/5 : 4
Now multiply the 3 numbers by 5 to remove the denominator of 5 in b:
15 : 8 : 20
Now we can check using the equations:
b is 2/5 of c: 20 x 2/5 = 40/5 = 8 This is true.
4a = 3c: 4(15) = 3(20) = 60 = 60, this is also true.
The ratios is 15 : 8: 20
The answer to 7/12 divided by 2
Answer: 7/24
Step-by-step explanation: Think of the 2 as 2/1.
When dividing by a fraction, we can simply change, we can simply change the multiplication sig to division and take the reciprocal of the second fraction or flip the second fraction.
So our problem can be rewritten as [tex](\frac{7}{12})[/tex] [tex]x[/tex] [tex](\frac{1}{2})[/tex].
Now multiplying across the top and bottom we get 7/24.
Answer:
7/24
Step-by-step explanation:
the guy was right! (also khan said so)
Angela works 18 hours a week for 12 weeks in the summer at the local swimming pool as a life guard. she earns $13 per hour. her employer takes 15 percent out of her check for federal income tax withholding and 6.2 percent for social security and 1.45 percent for medicare. she will receive 12 paychecks, one for each week she works. calculate angela’s weekly gross pay: calculate the amount taken out of angela’s check for federal income tax withholding: calculate the amount taken out of angela’s check for social security taxes: calculate the amount taken out of angela’s check for medicare taxes: calculate angela’s net paycheck using the calculations above: calculate angela’s total gross pay for all 12 weeks: calculate angela’s total net pay for all 12 weeks:
Answer:
Gross pay per week = $234
Federal income tax = $421.2
Social security = $174.96
Medicare =$40.71
net pay per week = $181
Total gross pay = $2,808
Total net pay = $2172
Step-by-step explanation:
Hi, to answer this question, first, we have to calculate Angela gross income per week:
18 hours per week x $13 per hour = $234 per week (gross)
234 x 12 =2,808
Amount taken ; multiply weekly gross pay by each percentage discount in decimal form (divided by 100)
Federal income tax = 234 x (15/100) = $35.1 (in 12 weeks = 35.1 x 12 = $421.2)
Social security = 234 x (6.2/100)= $14.508 (in 12 weeks = 14.5 x 12 = $174.96)
Medicare = 234 x (1.45/100)=$3.393 (in 12 weeks = 3.39x 12 = $40.71)
Total amount taken (per week)= 35.1+14.508+3.393=$53.001
Net pay per week = 234-53 = $181
For the total gross pay we have to multiply the weekly gross pay by the number of weeks (12)
Total gross pay = 234 x 12 =$2,808
Total net pay = 181 x 12 = 181 per week x 12 = $2172
Need help ASAP. WILL MARK BRAINLIEST.
Answer:
Circumference = 2 x 3.14 x radius = 27 (in)
=> radius = 27/(2 x 3.14) = 4.3 (in)
=> Area = 3.14 x radius^2 = 3.14 x 4.3^2 = 58.1 (in2)
Answer:
58 inches^2
Step-by-step explanation:
The formula for the area of a circle is [tex]\pi *radius^{2}[/tex]
To work out the area of this circle you would first need to divide the circumference of 27 by pi, this gives you 8.594. This is because the formula for the circumference is: [tex]\pi *diameter\\[/tex] and so by dividing the circumference by pi we are isolating the value of the diameter.
Then now that we have worked out the diameter we can now begin to work out the area, however in order to work out the area we must work out the radius. You can do this by dividing the diameter by 2, which gives you 4.297.
Then to work out the area you would multiply pi by the radius of 4.297 squared, this gives you 58.01 [tex]inches^{2}[/tex].
The next step is to round it to the nearest whole number, this gives you 58.
1) Divide 27 by pi.
[tex]27/\pi =8.594[/tex]
2) Divide 8.594 by 2.
[tex]8.594/2=4.297[/tex]
3) Multiply pi by 4.297 squared.
[tex]\pi *4.297^{2} =58.01[/tex]
4) Round to the nearest whole number.
58 square inches
* Approximate the value of V5 to the nearest hundredth.
Answer:
2.24
Step-by-step explanation:
If you mean sqrt(5), then the answer is 2.236, which rounds to 2.24
I'm going to assume you mean √5.
√5 is not a perfect square but it can evaluated into a non-terminating decimal.
√5 = 2.23606797...
Round to the nearest hundredth.
2.23606797... → 2.24
Therefore, the answer is 2.24
Best of Luck!
The area of a garden is 30 square feet. The perimeter is 26 feet. What are the measurements of each side?
Please help this question is fustrating
Answer: 3 feet by 10 feet rectangle
===========================================================
Explanation:
Assuming this garden is a rectangle, it has dimensions L and W which are the length and width respectively.
perimeter of rectangle = 2*(length+width)
P = 2*(L+W)
26 = 2(L+W) ... plug in given perimeter
26/2 = L+W .... divide both sides by 2
13 = L+W
13-W = L .... isolate L by subtracting W from both sides
L = 13-W
------
Area of rectangle = Length*Width
A = L*W
A = (13-W)W .... replace L with 13-W
A = W(13-W)
A = 13W - W^2 ..... distribution
30 = 13W - W^2 .... plug in given area A = 30
W^2 - 13W + 30 = 0 ... get everything to one side
(W - 10)(W - 3) = 0 ...... factor
W-10 = 0 or W-3 = 0 ...... zero product property
W = 10 or W = 3
----------
If the width is W = 10, then
L = 13-W
L = 13-10
L = 3 is the length
Or if the width is W = 3, then
L = 13-W
L = 13-3
L = 10 is the length
Either way, this is a 3 ft by 10 ft rectangle
--------
Check:
Area = length*width = 10*3 = 30 square feet
perimeter = 2(length+width) = 2*(10+3) = 2*13 = 26 feet
or you could say
perimeter = L+W+L+W = 10+3+10+3 = 13+13 = 26 feet
we get the correct area and perimeter, so this confirms our answer.
A basketball has a circumference of 31.4 inches. Using 3.14 as an approximation for pie, what is the basketball's volume to the nearest cubic inch?
Answer:
0.52 cubic inches
Step-by-step explanation:
Given: circumference of a basketball is 31.4 inches.
[tex]\pi =3.14[/tex]
To find: basketball's volume to the nearest cubic inches
Solution:
circumference of a basketball (sphere) = 6.28(radius)
Also, circumference of a basketball = 31.4 inches.
So, 6.28(radius) = 3.14
radius = [tex]\frac{3.14}{6.28}=\frac{1}{2}[/tex] inch
Volume of the basketball (sphere) = [tex]\frac{4}{3}(\pi )(radius)^3=\frac{4}{3}(3.14)(\frac{1}{2})^3=0.52\,\,cubic\,\,inches[/tex]
please please help me
Answer:
a) 22, b) i. 5/11, ii. 5/11, iii. 7/11
Step-by-step explanation:
a) 3+6+3+5+4+1 = 22 total number of students
b)
i. Number of girl/total number of students= 10/22 = 5/11
ii. blond hair/total number of students = 10/22 = 5/11
iii.
Number of girl/total number of students= 10/22 = 5/11
red hair/total number of students = 4/22 = 2/11
P(a girl or red hair) = 5/11 + 2/11 = 7/11
Evaluate the expression 3 x
{10 +1} +5.
Answer:
38
Step-by-step explanation:
3 x {10 +1} +5.
PEMDAS
Parentheses first
3 x {11} +5.
Then multiply and divide
33+5
38
Answer:
38
Step-by-step explanation:
3 x {10 +1} +5 Following PEMDAS, solve in the parentheses
3 x 11 + 5 Multiply 3 x 11
33 + 5 Add
38
A factory uses 3/4 of a barrel of raisins in each batch of granola bars. Yesterday, the factory
used 1 1/2 barrels of raisins. How many batches of granola bars did the factory make
yesterday?
Answer:
Step-by-step explanation:
3/4 * 2 = 1 1/2
The factory made two batches of granola bars.
what is the slope of the line that passes through the points (-4,-4) and (-4,-9)? Write your answer in simplest form
Answer:
undefined
Step-by-step explanation:
We can find the slope of a line using two points by
m = (y2-y1)/(x2-x1)
= (-9- -4)/(-4 - -4)
= (-9+4)/(-4+4)
= -5/0
When we divide by zero, our solutions is undefined
The slope is undefined
You're playing a game where you defend your village from an orc invasion. There are 3 characters (elf, hobbit, or human) and 555 defense tools (magic, sword, shield, slingshot, or umbrella) to pick from.
If you randomly choose your character and tool, what is the probability that you won't be a hobbit or use an umbrella?
Answer:
There is a 1/3 chance of getting a hobbit, and a 0.1/11 chance of getting an umbrella.
13th term of 2, 10, 18, 26
Answer:
192
Step-by-step explanation:
Add 8 started from 2 and keep going till you hit 192.
Answer:
a1 = 2 d = 8
n = 13
an = a1 + d(n-1)
a(13) = 2 + 8(13-1)
2 + 8(12)
2 + 96 = 98
Step-by-step explanation:
1. identify the terms
2. write down the arithmetic sequence formula and then replace the letters with their values.
3. do parenthesis first, then multiply by d.
4. add them together to get the 13th term
Measure of angle r is 22. Find the measure of angle 0
Can someone please help me? I keep losing points...
CORRECT ANSWERS ONLY PLEASE!!!!
Use the formula i = prt, where i is the interest earned, p is the principal (starting amount), r is the interest rate expressed as a decimal, and t is the time in years.
Answer:
$93,996
Step-by-step explanation:
i = prt
i = ($53,712)(.15)(5)
i = $40, 284
$40, 284 + $53,712
$93,996
Answer:
$92996
Step-by-step explanation:
Using the given formula :
I = P × R × T
I = 53712 × 15/100 × 5
I = $40284
He has = 40284 + 53712 = $93996
