The angle of elevation of the ramp to the nearest degree is 34°.
we can use trigonometry to determine the angle of elevation of the ramp.To begin, we need to draw a diagram to visualize the problem.
Let's assume that the height of the end of the ramp is h, and the horizontal distance from the bottom of the ramp to the building is d.
From the diagram, we can see that we have a right-angled triangle where the height of the triangle is h, the base of the triangle is d, and the hypotenuse of the triangle is the length of the ramp.
Using the tangent ratio, we can write:
tanθ = opposite/adjacent
where opposite is the height of the triangle, and adjacent is the base of the triangle. Substituting the values we have, we get:
tanθ = h/d
Rearranging this formula, we can write:
θ = tan⁻¹(h/d)
Substituting the values we have, we get:θ = tan⁻¹(10/15)θ = 33.69°
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suppose 42% of the population has myopia. if a random sample of size 442 is selected, what is the probability that the proportion of persons with myopia will differ from the population proportion by less than 3% ? round your answer to four decimal places.
0.7994 portion of persons with myopia will differ from the population portion by less than 3%.
Here we have to implement the central limit theorem,
therefore,
the formula is Z = x- a /s where, a = mean , d= standard deviation
let us consider that 42% has myopia
then p = 0.42
size of random sample given is 442
therefore, n = 442
then, a = p = 0.42
standard deviation is
s = [tex]\sqrt{p(1-p)/n}[/tex]
=[tex]\sqrt{0.42* 0.58/442}[/tex]
=0.0235
portion between 0.42 +0.03 = 0.45 and 0.42 - 0.03 = 0.39
there for there are two values of X = 0.45 , X = 0.39
when X = 0.45Z = X - a/s
Z = 0.45 - 0.42 / 0.0235
Z = 1.28 have a p-value of 0.8997
when X = 0.39Z = X - a /s
Z = 0.39 - 0.42 / 0.0235
Z = -1.28 have a p-value of 0.1003
0.8997 - 0.1003 = 0.7994
0.7994 portion of persons with myopia will differ from the population portion by less than 3%.
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Which equations represent the line that is parallel to 3x − 4y = 7 and passes through the point (−4, −2)? select two options. y = â€"three-fourthsx 1 3x − 4y = −4 4x − 3y = −3 y â€" 2 = â€"three-fourths(x â€" 4) y 2 = three-fourths(x 4)
Two equations that represent the line that is parallel to 3x - 4y = 7 and passes through the point (-4,-2) are [tex]y + 2 = (\frac{3}{4})(x + 4)[/tex] and [tex]y = (\frac{3}{4})x - 5[/tex]. So, option A and D are correct.
We know that a line parallel to 3x - 4y = 7 will have the same slope as the given line. So, we can rearrange the equation 3x - 4y = 7 into slope-intercept form y = mx + b to find the slope:
3x - 4y = 7
-4y = -3x + 7
[tex]y = (\frac{3}{4}) x - \frac{7}{4}[/tex]
Therefore, the slope of the line is 3/4.
Now, we can use the point-slope form of the equation of a line to write the equations of the line that is parallel to 3x - 4y = 7 and passes through the point (-4,-2):
[tex]y - (-2) = \frac{3}{4} *(x - (-4))[/tex] or [tex]y - (-2) = \frac{3}{4} x - 3[/tex]
Simplifying these equations, we get:
[tex]y + 2 = (\frac{3}{4})(x + 4)[/tex] or [tex]y = (\frac{3}{4})x - 5[/tex].
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Caden’s school is due west of his house and due south of his friends Eva’s house. The distance between the school and Eva’s house is 5 kilometers and the straight-line distance between Caden’s house and Eva’s house is 13 kilometers. How far is Caden’s house from school?
Thus, the distance between Caden’s house and school is found as: 12 km.
Define about the Pythagorean theorem:Pythagoras theorem triangles are right triangles that adhere to the Pythagoras theorem. Pythagorean triples are the name given to the three sides that make up this triangle.
The axiom that the hypotenuse's square in a right triangle equals the sum of its squares on the other sides (c² = a² + b²)
Given data:
From the attached diagram for question:
Distance between Caden’s house and Eva’s house CA = 13 kilometers.
Distance between school and Eva’s house CB = 5 kilometers.
using Pythagorean theorem:
CA² = CB² + BA²
BA² = CA² - CB²
BA² = 13² - 5²
BA² = 169 - 25
BA = 12
Thus, the distance between Caden’s house and school is found as: 12 km.
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sam buys a laptop for R6 840 (including VAT). Determine the price of the laptop
without VAT (excluding VAT). VAT = 15%
the price of the laptop without VAT (excluding VAT) is R5 814.
Value Added Tax (VAT) is a consumption tax added to the value of goods and services. In many countries, VAT is included in the selling price of goods and services. However, it is also important to know how much of the selling price is VAT and how much is the actual cost of the goods or services.
In this problem, Sam bought a laptop for R6 840, which includes VAT of 15%. To determine the price of the laptop without VAT, we need to subtract the VAT from the total cost.
The VAT amount can be found by multiplying the total cost by the VAT rate. In this case, the VAT rate is 15%, so the VAT amount is:
VAT = 15/100 * R6 840
VAT = R1 026
To find the price of the laptop without VAT, we need to subtract the VAT amount from the total cost:
Price without VAT = Total cost - VAT
Price without VAT = R6 840 - R1 026
Price without VAT = R5 814
Therefore, the price of the laptop without VAT (excluding VAT) is R5 814.
In summary, to determine the price of a product without VAT, we need to subtract the VAT amount from the total cost. The VAT amount can be found by multiplying the total cost by the VAT rate. Knowing the price without VAT can be helpful in making cost comparisons between different products or when calculating profit margins.
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a train, an hour after starting, meets with an accident which detains it a half hour, after which it proceeds at of its former rate and arrives hours late. had the accident happened miles farther along the line, it would have arrived only hours late. the length of the trip in miles was:
The total distance of the trip is 600 km if a train meet with an accident and then proceed further with its former speed.
Normal time be x for remaining distance, but time taken = 4x/3
Difference in time = (1+1/2+4x/3)−(1+x)=72
x=9
2nd case of going further 90 km which lessens the difference by 1/2
If it loses 90 km in 1/2 hr.
Total difference was 3 + 1/2 out of which 1/2 was for repair
Difference in travelling is 3+1/2-1/2=3 hrs
It will lose 3 hrs in 90 x 6=540 km
Now it travelled for 10 hr hours, which is 1 hr + 540 km
So 540 in 9hr
So 60 km per hour
Total distance = 540+60=600km
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-- The given question is incomplete, the complete question is
"A train, an hour after starting, meet with an accident which delays it for half an hour and after this, it proceeds at 3/4th of its former rate and arrives 3.5 hrs late. Had the accident happened 90 km farther along the line, it would have arrived only 3 hour late. What is the length of trip in km?" --
you want to obtain a sample to estimate a population mean. based on previous evidence, you believe the population standard deviation is approximately . you would like to be 98% confident that your estimate is within 2 of the true population mean. how large of a sample size is required?
The required sample size is 108, to estimate the population mean with a 98% confidence level.
The following formula can be used to determine the required sample size.
n = ((z*σ) / E)^2
where:
n = sample size
z = z-score corresponding to desired confidence level (98% = 2.33 for two-sided test)
σ = population standard deviation (specified in the problem)
E = tolerance (2 for the problem)
After plugging in the values it looks like this:
n = ((2.33*) / 2)^2
n=107.13
Rounding up to the nearest integer, the required sample size is 108.
Therefore, a sample size of at least 108 is required to estimate the population mean with a 98% confidence level and a margin of error of 2, taking the population standard deviation as approximate.
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The volume of a cylinder is 1540cm^3 and the difference of its height and radius is 3cm then, find the total surface area of the cylinder.
The formula for the volume of a cylinder is [tex]r^{2}[/tex]h, where r is the radius and h is the height. To solve for h, h = r + 3, and to find the total surface area, lateral surface area = 2rh, top and bottom areas = 2[tex]r^{2}[/tex], and total surface area = 826.59 [tex]cm^{2}[/tex].
What is the total surface area of the cylinder?Let's calculate for the radius and height using the cylinder's volume formula:
Volume = π[tex]r^2h[/tex], where r is the radius and h is the height.
We have Volume = 1540 [tex]cm^3[/tex], so we can write:
1540 = π[tex]r^2h[/tex]
Also, we know that the difference between the height and radius is 3 cm:
h - r = 3
We can solve for h in terms of r by rearranging the above equation:
h = r + 3
Now we can substitute this into the formula for volume:
1540 = π[tex]r^2(r + 3)[/tex]
Simplifying and solving for r:
1540 = π[tex]r^3[/tex] + 3π[tex]r^2[/tex]
π[tex]r^3[/tex] + 3π[tex]r^2[/tex] - 1540 = 0
r ≈ 7.38 cm
Using the equation h = r + 3, we can find the height:
h = 7.38 + 3 = 10.38 cm
Now we can use the formulas for the lateral surface area and the top and bottom areas to find the total surface area of the cylinder:
Lateral surface area = 2πrh
Top and bottom areas = 2π[tex]r^2[/tex]
Substituting in the values we found, we get:
Lateral surface area = 2π(7.38)(10.38) ≈ 483.87 [tex]cm^2[/tex]
Top and bottom areas = 2π[tex](7.38)^2[/tex] ≈ 342.72 [tex]cm^2[/tex]
Total surface area = Lateral surface area + Top and bottom areas
Total surface area ≈ 826.59 [tex]cm^2[/tex]
Therefore, the total surface area of the cylinder is approximately 826.59 [tex]cm^2[/tex].
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5. A soccer team played 32 games. If they won 25% of
them, how many games did the team win?
To find out how many games the soccer team won, we need to multiply the total number of games they played by the percentage of games they won.
25% of 32 games can be calculated as:
0.25 x 32 = 8
Therefore, the soccer team won 8 games out of 32.
Please help solve this
Angles are measured in degrees and radians, and can be created by joining the extremities of two rays. The joint vertex is the common terminal of the two beams. Thus, ∠SRT = 38.16°.
What are angles?An angle is the result of the intersection of two lines.
An "angle" is the length of the "opening" between these two beams.
Angles are commonly measured in degrees and radians, a measurement of circularity or rotation.
In geometry, an angle can be created by joining the extremities of two rays. These rays are intended to represent the angle's sides or limbs.
The two primary components of an angle are the limbs and the vertex.
The joint vertex is the common terminal of the two beams.
According to our question,
6x-66°+5x-26°+70°+x+70°=360°
6x+5x+x+ 66°+140°=360°
12x+ 206°=360°
12x=360°-206°
12x= 154°
x= 154/12°
Hence, ∠SRT = 5x - 26°
= 5 * 154/12° - 26°
= 770/12° - 26°
= 64.16° - 26°
= 38.16°
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Hey could someone help me with this?
Step-by-step explanation:
30% of 500 voted for Sycamore
30% x 500 = .30 * 500 = 150 votes
Fox Glen got the most votes
can yall pls help me with this?
The value of the given linear equation to satisfied the given expression of the equation is = [tex]\frac{-9}{10}[/tex]
What about linear equation?
A linear equation is a mathematical equation that represents a straight line in a Cartesian coordinate system. It is an algebraic equation in which the highest power of the variable is 1.
The general form of a linear equation in one variable is:
ax + b = 0 where "a" and "b" are constants and "x" is the variable. The solution to this equation is: x = -b/a
The general form of a linear equation in two variables is:
ax + by + c = 0
Define equation:
An equation is a mathematical statement that asserts that two expressions are equal. It typically consists of variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. Equations can be used to represent a wide range of relationships between variables.
According to the given information:
Here, the value of x and y are given
Put the value of x and y in the given expression we have that,
⇒ 4y - x
⇒ 4 x [tex]\frac{-3}{20}[/tex] - [tex](\frac{3}{10} )[/tex]
⇒ [tex]\frac{-12}{20}[/tex] - [tex](\frac{3}{10} )[/tex]
⇒ [tex]\frac{-18}{20}[/tex]
⇒ [tex]\frac{-9}{10}[/tex]
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you want to save $12,000 for a downpayment on a house. how much should be put into an account that pays 3.95% interest compounded continuously for 5 years
The formula for continuous compounding is given by:
A = Pe^(rt)
where:
A = final amount
P = principal amount (initial investment)
e = 2.71828 (constant)
r = annual interest rate (as a decimal)
t = time in years
We can solve for P as follows:
P = A/e^(rt)
We know that we want to save $12,000, the interest rate is 3.95%, and the time is 5 years. Substituting these values into the formula, we get:
P = 12000/e^(0.0395*5)
P = 12000/e^0.1975
P = 12000/1.2183
P = 9854.16
Therefore, Max should put $9,854.16 into the account that pays 3.95% interest compounded continuously for 5 years.
a circle has an area of 78.5 units2 and a circumference of 31.4 units. if the radius is 5 units, what can be said about the relationship between the area and the circumference? (use 3.14 for .)
Step-by-step explanation:
give atleast 2 situations,in which you would store the data on cloud storage
Relationship between the area and the circumference of the circle is that they are proportional to each other.
The relationship between the area and the circumference of a circle with a radius of 5 units that has an area of 78.5 units² and a circumference of 31.4 units can be expressed as follows:
Area = πr²
where r is the radius of the circle.
Area = π(5)² = 78.5 units²
Therefore, the area of the circle is 78.5 units².
Circumference = 2πr,
where r is the radius of the circle.
2πr = 31.4 units
Therefore, 2π(5) = 31.4 units
Therefore, the circumference of the circle is 31.4 units.
Since the radius is the same, the relationship between the area and the circumference of the circle is that they are proportional to each other.
Area : Circumference
πr² : 2πr
r : 2
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Whose work is correct? Elise’s work Jake’s work Malik’s work Xiao’s work
Answer: Without further context, it is impossible to determine whose work is correct. (Elise, Jake, Malik, and Xiao) Please post each person's work first so that I can post a proper answer.
Solve.
3/4 + (1/3 divided by 1/6) - (-1/2) =
Which one of the following is not equal reast
A 2 of 15
B 3/2 of 400
C 5% of60
D 6 of 50%
please help will give brainliest
The area of the space devoted to paintings is: 600 ft²
How to find the area of the triangle?The formula for the area of a triangle is expressed as:
A = ¹/₂ * b * h
where:
A is area
b is base
h is height
From the 7th grade painting, we see that each box of 1 unit represents 10 ft actually.
Thus, area of space devoted to paintings is:
Area = ¹/₂ * 40 * 30
= 600 ft²
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In ΔMNO, the measure of ∠O=90°, MO = 8, ON = 15, and NM = 17. What ratio represents the sine of ∠M?
The ratio representing the sine of angle ∠M in triangle MNO, where ∠O = 90°, MO = 8, ON = 15, and NM = 17, is 17/8.
In a right triangle, the sine of an angle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse. In this problem, we are given a right triangle MNO, with a right angle at O. The side opposite angle M is MN, and the hypotenuse is MO.
To find the sine of angle M, we use the formula sin(M) = opposite/hypotenuse, where the opposite side is MN and the hypotenuse is MO.
Using the Pythagorean theorem, we can find the length of side MN:
[tex]MN^2 = MO^2 + ON^2[/tex]
[tex]MN^2 = 8^2 + 15^2[/tex]
[tex]MN^2[/tex] = 289
MN = 17
Therefore, the sine of angle M is:
sin(M) = MN/MO
sin(M) = 17/8
The ratio that represents the sine of angle M is 17/8.
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BRAINLIEST TO WHOEVER IS RIGHT
There are 13 possible toppings at the local ice cream shop. You can have 3 toppings on a large sundae. How many combinations of ice cream toppings are possible?
plsss i need this done yall! help a girl out!
Answer: 286 toppings
Step-by-step explanation:
true or false: to calculate the value of the 50th term, you could assume 5 is g(1). then, using the growth factor of 3, use g(n)
The given statement " to calculate the value of the 50th term, you could assume 5 is g(1). then, using the growth factor of 3, use g(n) = 5*3^n-1 with n = 50 to find g(50)" is true. Assuming that 5 is g(1), we can use the growth factor of 3 to find the value of g(50) using the formula g(n) = 5*3^(n-1).
Assuming that 5 is the first term of the sequence g(n), we can use the formula g(n) = 53^(n-1) to find any term of the sequence. This formula gives us the value of the nth term in the sequence, where n is any positive integer.
For example, if we want to find the 50th term of the sequence, we simply substitute n = 50 into the formula and calculate g(50) = 53^(50-1) = 5*3^49. Therefore, we can use this formula to find any term of the sequence, given the first term and the growth factor. so, the given statement is true.
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--The given question is incomplete, the complete question is given
" true or false: to calculate the value of the 50th term, you could assume 5 is g(1). then, using the growth factor of 3, use g(n) = 5*3^n-1 with n = 50 to find g(50)."--
A yoga studio offers one option for a monthly membership of $120 for unlimited classes. A second option is to pay a monthly fee of $30 plus $5 per class. A new customer is deciding between the two options. If the customer chooses the second option, which
best describes how many classes they can take to spend less than the unlimited membership fee?
Answer: 17
Step-by-step explanation:
First, you would subtract 30 from 120 to see how much money is left over for the classes, which is 90. Now you would divide 90 by 5 to see how many classes you can go to with the leftover money, which is 18. But since this is the same as the 120, just take away one lesson so it's sum would be less than 120, which would be 17. Hope this helps
The LIDAR camera displays a beam of light to determine the speed of the car is going. Light travels at 9.84 x 10^8 ft/sec. If it takes the beam 4.5 x 10^-7 to reach the car and return. How far away is the car? (remember divide by 2)
For exercises 5 and 6, find the measures and length of each arc. Express the answer in terms of pi
5) The measure of arc BC is 1.14π radians and the length of arc BC is 2.86π units.
6) The measure of arc ABC is 1.99π radians and the length of arc ABC is 3.14π units.
What is an arc?An arc is a curved line that is a portion of a circle.
It is formed by connecting two points on the circumference of the circle with a curve.
5) BC: To find the measure of arc BC, we need to find the measure of angle BAC.
angle BAC = angle AOC
angle BAC = 129 degrees
Therefore, the measure of arc BC is:
arc BC = (129/360) x (2π x 4)
arc BC = 1.14π radians
To find the length of arc BC, we need to find the measure of angle BAC.
angle BAC = angle AOC
angle BAC = 129 degrees
Therefore, the length of arc BC is:
arc BC = (129/360) x (2π x 4)
arc BC = 2.86π
6) ABC: To find the measure of arc ABC, we need to find the measure of angle BOC.
angle BOC = 360 - angle AOB - angle AOC
angle BOC = 360 - 51 - 83
angle BOC = 226 degrees
Therefore, the measure of arc ABC is:
arc ABC = (226/360) x (2π x 4)
arc ABC = 1.99π radians
To find the length of arc ABC, we need to find the measure of angle BOC.
angle BOC = 360 - angle AOB - angle AOC
angle BOC = 360 - 51 - 83
angle BOC = 226 degrees
Therefore, the length of arc ABC is:
arc ABC = (226/360) x (2π x 4)
arc ABC = 3.14π
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The complete question is -
y=xto the power of 2+4x-12
The equation [tex]y = x^2 + 4x - 12[/tex] represents a parabolic curve in a 2D coordinate system.
What is graph?
A graph is a concept in mathematics and computer science that involves a set of nodes or vertices, linked together by edges to depict the interconnections between objects. Graphs are a powerful method for examining complex relationships within diverse systems, including communication networks, transportation systems, and social networks.
To graph this equation, you can follow these steps:
Choose a range of values for x that you want to plot. For example, you might choose x values from -6 to 2.
For each x value, calculate the corresponding y value by plugging it into the equation. For example, if x = -6, then y = [tex](-6)^2[/tex] + 4(-6) - 12 = 0.
Plot each (x, y) pair on the graph.
Connect the plotted points with a smooth curve to represent the parabolic shape of the equation.
Using these steps, you can graph the equation [tex]y = x^2 + 4x - 12[/tex] to visualize its shape and better understand its behavior.
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[tex]\sqrt{2+-7+2=-3[/tex]
It has been proved from the given equation that (2 + -7 + 2 = -3)
How to solve Rational Equations?A rational equation is defined as an equation that containins at least one fraction whose numerator and denominator are polynomials. These fractions may be on one or both sides of the equation.
Now, we are given the rational expression as:
√(2 + -7 + 2 = -3)
In order words, we want to prove that:
(2 + -7 + 2 = -3)
The left hand side, when we multiply + and - sign, we have negative sign and as such we will have:
2 - 7 + 2
= 4 - 7
= -3
This is same as the right hand side of the original equation
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If f varies inversely as g, find f when g= -6
f= 15 when g= 9
The value of f is -10.
What is an inverse function?
An inverse in mathematics is a function that "undoes" another part. In other words, if f(x) produces y, y entered into the inverse of f producing x. An invertible function has an inverse, and the inverse is represented by the symbol f1.
Here, we have
Given: If f varies inversely as g, and when g = -6, f = 15.
We have to find the value of f.
f ∝ 1/g
f₁ ×g₁ = f₂ ×g₂
Let the required value of f = x
Inserting in equation (1) and we get
15 × (-6) = x × 9
-90/9 = x
x = -10
Hence, the value of f is -10.
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g lemon and pepper are in very posh luxury cars. pepper starts at a point 30 miles north of where lemon starts. pepper starts driving east at 25 miles per hour and lemon starts driving north at 40 miles per hour. how fast is the distance between them changing after 15 minutes? is the distance increasing or decreasing?
To solve this problem, you will need to use the Pythagorean theorem. According to this theorem, a^2 + b^2 = c^2, where a and b are the two sides of a right-angled triangle and c is the hypotenuse or the longest side. In this case, the two sides are the distance traveled by Pepper and Lemon respectively, and the hypotenuse is the distance between them.
Distance between Lemon and Pepper. Let's say that after 15 minutes, Lemon has traveled a distance of d1, and Pepper has traveled a distance of d2. Since they are moving in perpendicular directions, we can say that the distance between them is the hypotenuse of the right-angled triangle formed by their paths.
Using the Pythagorean theorem, we can write this as:d^2 = d1^2 + d2^2Distance traveled by LemonIn 15 minutes, Lemon travels a distance of 40 x 15/60 = 10 miles.Distance traveled by PepperIn 15 minutes, Pepper travels a distance of 25 x 15/60 = 6.25 miles.Distance between Lemon and Pepper. Using the Pythagorean theorem, we can find the distance between Lemon and Pepper:d^2 = 10^2 + 6.25^2d^2 = 100 + 39.0625d^2 = 139.0625d = sqrt(139.0625)d = 11.7858 miles.
Differentiating this expression with respect to time (t), we get:d/dt (d^2) = d/dt (d1^2 + d2^2)2d * (dd/dt) = 2d1 * (dd1/dt) + 2d2 * (dd2/dt)(dd/dt) = (d1 * dd1/dt + d2 * dd2/dt)/dd/dt = (10 * 40/60) + (6.25 * 25/60)dd/dt = 6.25 + 2.6042dd/dt = 8.8542 miles per hourThe distance between Lemon and Pepper is increasing at a rate of 8.8542 miles per hour. Therefore, the answer is that the distance between them is increasing.
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The boiling point of water is 212°F at sea level. Andres lives at an elevation of
7,500 ft and finds that water boils at 198°F. What is the percent decrease in
the boiling point of water from sea level to 7,500 ft? Give your answer to the
nearest tenth of a percent. Show your work.
Step-by-step explanation:
The decrease from 212 to 198 is 14 degrees
14 degrees is what percent of 212 degrees?
14 / 212 x 100% = 6.6 % decrease
Factor the polynomial
HELPPP I NEED THIS DUE ASAP
Answer:
Tony is not correct because 3(x^2-25) can be factored further. The final answer is 3(x+5)(x-5)
Step-by-step explanation:
1/4 divided by 3/2 as a fraction
Answer:
1/6
Step-by-step explanation:
1/4 divided by 3/2 as a fraction
1/4 : 3/2 = (flip 3/2 and change the sign from division to multiplication)
1/4 × 2/3 (semplify)
1/2 × 1/3 = (solve)
1/6
Answer:
= 1/6
Step-by-step explanation:
(1/4) ÷ (3/2) = (1*2) ÷ (4*3) = 2/12
= 1/6