jane's salary is increased by 2% to £39474. how much is her salary before the rise?
Phillip watched a beach volleyball game from 1:45pm to 2:00pm.how many degrees did the minutes hand turn?
Answer:
90 degrees
Step-by-step explanation:
A cone and a cylinder have the same base and height, as shown below.
(please see attached picture)
The volume of the cylinder is 84(3.14) in^2 What can be concluded about the volume of the cone? Check all that apply.
The volume of the cone is 1/3 the volume of the cylinder.
The volume of the cylinder is 2 times the volume of the cone.
The volume of the cone is less than the volume of the cylinder.
The expression 84(3.14)/3 finds the volume of the cone.
The expression 84 (3.14)/2 finds the volume of the cone.
Answer with Step-by-step explanation:
We know that volume of a cylinder with radius r and height h is:
πr²h
and volume of cone with radius r and height h is:
πr²h/3
Volume of cone=Volume of cylinder/3 < Volume of cylinder
Volume of cylinder=84π in² where π=3.14
Volume of cone=84π/3 in²
= 84(3.14)/3 in²
Hence, correct options are:
The volume of the cone is 1/3 the volume of the cylinder.
The volume of the cone is less than the volume of the cylinder.
The expression 84(3.14)/3 finds the volume of the cone.
the answer is: A, C, and D
How do you simplify x^2+y^2?
If I’m 17 1/2 do I still have to wait a year to get my provisional license after I get my permit in Florida
solve for y. triangle PQR is congruent to triangle DEF, PQ= 15, QR= 10, RP=8, and EF = 6y +4
A summer camp manager wants to order 500 bag lunches for a field trip. Each lunch will have a piece of fruit. The manager is deciding on ordering apples, oranges, bananas, or plums. The camp manager surveys 50 random campers, and the results are given in this table.
Based on the results, which fruit should the manager order?
A- Apples
B- Oranges
C- Plums
D- Bananas
16. Supposes that y varies inversely with x and that y-10 whenx-7. Which of the following equations models this relationship?
A. Y=70x
B. Y=-10x
C. Y=x/70
D. Y=70/x
The equation that models this relation is y = 70/x. So, option (D) is the correct answer.
What is constant of proportionality?The constant of proportionality is the ratio of two proportional values at a constant value. Two variable values have a proportional relationship when either their ratio or their product gives a constant.
For the given situation,
The values are y = 10 and x = 7
y varies inversely with x.
⇒ [tex]y[/tex] ∝ [tex]\frac{1}{x}[/tex]
To remove proportionality we introduce a constant 'k'.
⇒ [tex]y=\frac{k}{x}[/tex]
Substitute the values of x and y,
⇒ [tex]10=\frac{k}{7}[/tex]
⇒ [tex]k=70[/tex]
Now substitute the value of k = 70 in y,
⇒ [tex]y = \frac{70}{x}[/tex]
Hence we can conclude that the equation that models this relation is y = 70/x. So, option (D) is the correct answer.
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If I get 3 problems wrong on a 12 question math paper, what grade would I get?
If you got 3 questions wrong on a 12 problem math paper, to figure out how many you got right you must subtract the number you got incorrect (3) from the total number (12).
12-3=9
To figure out your grade, you have to divide how many you got correct (9-see above) by the total number of questions (12).
9/12 = 0.75
If you multiply this decimal by 100, you get the equivalent percentage of 75%.
Therefore, you would have gotten a 75% on the paper.
Hope this helps!
A waitress works 1.75 hours less in the afternoon than in the evening. If she works 5 1/8
hours in the afternoon, how many hours does she work in the evening?
Answer: The waitress works:[tex]\[{6 \frac{7}{8}}[/tex] hours in the evening
Let us denote the number of hours the waitress works in the evening as E and the number of hours she works in the afternoon as A.
Given that:
[tex]\[A = 5 \frac{1}{8} \text{ hours}\][/tex]
We can convert the mixed number to an improper fraction:
[tex]\[5 \frac{1}{8} = 5 + \frac{1}{8} = \frac{40}{8} + \frac{1}{8} = \frac{41}{8}\][/tex]
So, [tex]\( A = \frac{41}{8} \)[/tex] hours.
The waitress works 1.75 hours less in the afternoon than in the evening. Thus, we have:
[tex]\[A = E - 1.75\][/tex]
[tex]\[\frac{41}{8} = E - 1.75\][/tex]
Converting 1.75 to a fraction:
[tex]\[1.75 = \frac{7}{4} = \frac{14}{8}\][/tex]
Now, the equation becomes:
[tex]\[\frac{41}{8} = E - \frac{14}{8}\][/tex]
[tex]\[E = \frac{41}{8} + \frac{14}{8}\]\[E = \frac{41 + 14}{8} = \frac{55}{8}\][/tex]
Convert the improper fraction back to a mixed number:
[tex]\[\frac{55}{8} = 6 \frac{7}{8}\][/tex]
Therefore, the waitress works:
[tex]\[{6 \frac{7}{8}}[/tex] hours in the evening
if you enjoy math and science, the career cluster that might be best for you is
Information Technology and Engineering
Step-by-step explanation:Mathematics is also a branch of Science. A person who is good in mathematics can take the analytical view of anything and convert ideas into practical form by using mathematical models. There are a lot of applications that can be used for converting analog models into digital models by using mathematics. So all of these models require mathematical backgrounds and engineers are the people who bring ideas to reality. The same is applied on IT field too.
Doug can paint the living room in 4 hours. it would take elaine 6 hours to paint the same room. how long would it take doug and elaine, working together, to paint the living room?
Use the following information to answer the next two questions
Subtract 8 + 7i from 4 − 16i. -4 − 23i 4 − 23i 4 + 9i 4 − 11i
Answer:
-4-23i
Step-by-step explanation:
Above answer didn't quite understand what the question was asking. It's asking to SUBTRACT 8+7i from 4-16i. So it would be written like this:
(4-16i) - (8+7i).
Simplify it from there and you'd get -4-23i
To subtract 8 + 7i from 4 - 16i, subtract the real parts and the imaginary parts separately, resulting in -4 - 23i.
Explanation:To subtract 8 + 7i from 4 − 16i, you treat the real and imaginary parts separately.
Subtract the real parts: 4 − 8 = −4.
Subtract the imaginary parts: (−16i) − (7i) = −16i − 7i = −23i.
Combine the results to get the final answer: −4 − 23i.
Therefore, subtracting 8 + 7i from 4 − 16i gives −4 − 23i.
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You have a bag of chocolate candy. Ten of them are red, 7 are brown, 12 are green, and 9 are blue. What is the probability that you pick a red candy, given that you have already picked a red candy and have not replaced it?
9/37 is the correct answer.
The number of tropical fish that an aquarium can hold depends on the volume of the fish tank. the interior dimensions of the fish tank are 25 cm, 30 cm, and 39 cm. each fish requires 10,000 cubic centimeters of water. how many tropical fish will this fish tank hold?
Circle 1 is center at (-4,5) and has a radius of 2 centimeters. Circle 2 is centered at (2,1) and has a radius of 6 centimeters. What transformations can be applied to Circle 1 to prove the circles are similar?
Two mechanics worked on a car. the first mechanic worked for 20 hours, and the second mechanic worked for 15 hours. together they charged a total of $1775 . what was the rate charged per hour by each mechanic if the sum of the two rates was $100 per hour?
The perimeter of a rectangular garden is 100 feet (ft). the area of the rectangular garden area is 600 ft2. find the length and width of the garden. let the length of the garden be the shorter side, of necessary.
The length of the garden is 20 feet and the width is 30 feet.
To solve this problem, we will use the formulas for the perimeter and area of a rectangle. The perimeter (P) of a rectangle is given by the formula P = 2(l + w), where l is the length and w is the width. The area (A) of a rectangle is given by the formula A = lw.
Given the perimeter of the garden is 100 feet, we can set up the following equation:
[tex]\[ 2(l + w) = 100 \][/tex]
[tex]\[ l + w = 50 \][/tex]
[tex]\[ w = 50 - l \][/tex]
This equation relates the length and width of the garden.
Next, we are given that the area of the garden is 600 square feet:
[tex]\[ lw = 600 \][/tex]
Substituting the expression for w from the first equation into the area equation, we get:
[tex]\[ l(50 - l) = 600 \][/tex]
[tex]\[ 50l - l^2 = 600 \][/tex]
Rearranging the terms, we have a quadratic equation:
[tex]\[ l^2 - 50l + 600 = 0 \][/tex]
To solve this quadratic equation, we can factor it:
[tex]\[ (l - 20)(l - 30) = 0 \][/tex]
This gives us two possible solutions for the length: l = 20 feet or l = 30 feet.
Since we are asked to let the length be the shorter side, if necessary, we choose the smaller value for the length:
[tex]\[ l = 20 \text{ feet} \][/tex]
Now we can find the width by substituting the length back into the equation for the perimeter:
[tex]\[ w = 50 - l \][/tex]
[tex]\[ w = 50 - 20 \][/tex]
[tex]\[ w = 30 \text{ feet} \][/tex]
Therefore, the length of the garden is 20 feet and the width is 30 feet.
A large truck and a small car have a head-on collision. Which scenario is true?
A) The truck has the greater acceleration because it has the greater mass
B) The car has the greater acceleration because it has the smaller mass
C) Both the truck and car have the same magnitude of acceleration
(Edit: This was meant to go in the Physics section, I'm so sorry about this, if anyone here could still answer that's be amazing)
In a collision, both the car and truck experience the same force due to Newton's Third Law. However, due to Newton's Second Law, the car, with its smaller mass, experiences a greater acceleration.
Explanation:According to Newton's Third Law of Motion, 'for every action, there is an equal and opposite reaction', both the truck and the car would experience the same magnitude of force. However, let's recall Newton's Second Law, 'force equals mass times acceleration' (F=ma). Using these physics principles, we can deduce that the car with the smaller mass would experience a greater acceleration, and the large truck would experience a lesser acceleration. This is because when the same force is applied to both objects, an object with a smaller mass will have a greater acceleration compared to an object with a larger mass. Hence, option B) 'The car has the greater acceleration because it has the smaller mass' would be the correct answer based on Newton's laws of motion.
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8 MIN LEFT anyone know this?
An in-ground pond has the shape of a rectangular prism. The pond has a depth of 24 inches and a volume of 72,000 cubic inches. The length of the pond is two times its width. Find the length and width of the pond to the nearest tenth.
The length of the pond is 77.4 inches, and the width of the pond is 38.7 inches.
What is the rectangular prism?In geometry, a rectangular prism can be defined as a 3-dimensional solid shape that has six faces that are rectangles. A rectangular prism is also a cuboid.
Let,a be the length of the pond and b be the width of the pond.
The volume of the pond is;
[tex]\rm Volume \ of \ the \ pond= Area\ of\ the\ base\times deep\\\\Area\ of\ the\ base=\dfrac{Volume \ of \ the \ pond}{base}\\\\Area\ of\ the\ base=\dfrac{72000}{24}\\\\Area\ of\ the\ base=3000 in^2[/tex]
The length of the pond is two times its width.
a = 2b
The area of the base = a × b
3000 = ab
ab = 3000
Substitute the value of a in equation 2
[tex]\rm ab=3000\\\\2b \times b = 3000\\\\b^2=\dfrac{3000}{2}\\\\b^2=1500\\\\b=38.7[/tex]
Substitute the value of b in equation 1
[tex]\rm a=2b\\\\a=2 \times 38.7\\\\a=77.4[/tex]
Hence, the length of the pond is 77.4 inches, and the width of the pond is 38.7 inches.
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The width of the pond is approximately 38.7 inches and the length is approximately 77.4 inches.
Explanation:To find the length and width of the pond, we can use the formula for the volume of a rectangular prism: length × width × depth. We are given that the depth is 24 inches and the volume is 72,000 cubic inches.
Let's denote the width as w.
Since the length is two times the width, we can express the width as w and the length as 2w.
Therefore, the equation for the volume becomes:
2w × w × 24 = 72,000
48w^2 = 72,000
w^2 = 1,500
w ≈ 38.7
Therefore, the width is approximately 38.7 inches and the length is approximately 77.4 inches.
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Zack borrowed $1,087 for 12 months at 11 percent interest. If he must pay 11.00 per $100, what is Zack's monthly payment?
The sales tax in the city of Taxemalot is 8.1%. What is the growth factor for any item purchased at your local Tarmart? a.8.1 c.1.081 b.0.81 d.81
Calculate the area of the shaded sector in square inches.
Chris took a vacation trip to maine, where sales tax on taxable items is 5%. in maine, prepared food and lodging are taxed an additional 2%, for a total of 7% tax, while auto rentals are taxed an additional 5%, for a total of 10% tax.chris bought $70 worth of souvenirs, taxable at the general rate. he also spent $580 on prepared food and lodging and $620 for a rental car, all before tax. how much did he spend in total after tax was included?
a.$1333.50
b.$1316.10
c.$1270.00
d.$1376.10
For anyone with the “TRICIA” problem: $1202.30
What is the center of the circle with the equation (x-1)2 + (y-3)2= 9?
a store is selling uniform shirts for 18.95 each. if samuel has a coupon for 1/4 off the price, how much would he pay for the shirt, excluding tax??
Please help:
In a right triangle ABC, tan(A) = 3/4. Find sin(A) and cos(A).
In a right triangle ABC with angle A equal to 90 degrees, find angle B and C so that sin(B) = cos(B).
PLEASE HELP ME!!!! Thank you