The area of a triangle is 6 square feet. The base is 3 times its height. What is the base of the triangle?
Area=1/2 bh
6=1/2bh
12=bh
height is x, base 3x
12=3x^2
x^2=4
x=2
height = 2 feet
base = 3*2 = 6 feet
A factory employs 3 full-time workers and 6 part-time workers; the amount earned by each is: $36,000 for the production supervisor; $27,000 for the machine operator; $21,000 for the general assistant; a total of $50,000 for part-time staff. How much was the wage bill for the 3 full-time staff?
The total wage for full-time workers is 84000$.
What is simplification?Simplifying a value simply means finding it in its most basic form. To simplify the problem, we use a number of approaches, including PEMDAS and BODMAS. Aside from the value, the variables must also be made simpler.
Given, A factory employs 3 full-time workers and 6 part-time workers; the amount earned by each is $36,000 for the production supervisor; $27,000 for the machine operator; $21,000 for the general assistant; a total of $50,000 for part-time staff.
The Total wage for the full-time staff = 36000 + 27000 + 21000
The total wage for the full-time staff = 84000
Therefore 84000$ was the wage bill for the 3 full-time staff.
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the selling price of a house dropped from 250,000 to 210,000 over a period of five years. By what percentage didnthe sellling price decrease?
The selling price of the house decreased by 16%.
Explanation:To find the percentage decrease in the selling price of the house, we need to calculate the difference between the initial selling price and the final selling price, and then divide that by the initial selling price. Finally, we multiply the result by 100 to get the percentage decrease.
Difference = Initial Selling Price - Final Selling Price = $250,000 - $210,000 = $40,000Percentage decrease = (Difference / Initial Selling Price) x 100 = ($40,000 / $250,000) x 100 = 16%Therefore, the selling price of the house decreased by 16%.
The selling price of the house decreased by 16%.
Explanation:To find the percentage decrease in the selling price of the house, we can use the following formula:
Percentage decrease = ((Initial price - Final price) / Initial price) x 100
In this case, the initial price is $250,000 and the final price is $210,000. Plugging these values into the formula, we get:
((250,000 - 210,000) / 250,000) x 100 = (40,000 / 250,000) x 100 = 0.16 x 100 = 16%
Therefore, the selling price of the house decreased by 16%.
The highest score that is a record for a particular video game is 19,749 points. The lowest score on record for the same video game is 176 points. Which of the following inequalities best shows the range of scores recorded on the game?
Carmen buys 153 shares of Cawh Consolidated Banks, each of which pays a constant yearly dividend of $7.14. After six years, how much has Carmen received in dividends?
Answer: $6554.52
Step-by-step explanation:
Total number of shares bought by Carmen =153
A constant yearly dividend paid by each share=$7.14
Thus, 153 shares pays yearly dividend =[tex]153\times7.14=\$1092.42[/tex]
After 6 years, total dividend received by Carmen=[tex]6\times1092.42=\$6,554.52[/tex]
Hence, The total dividend received by Carmen in 6 years = $6554.52
Which expression will equal a rational product even though it is multiplying an irrational number times another irrational number?
Answer:
Which expression will equal a rational product even though it is multiplying an irrational number times another irrational number?
A
math question down below
You are watching your favorite soccer player on TV. Statistics show that he has a 37% chance of scoring a goal each time he shoots. He shoots twice. What is the probability that he scores a goal both times?
I draw a card 50 times from a standard 52 deck and gets a heart 8 times what's the probability that I draw a heart on the next draw
To solve this problem, let us first define what probability is. By standard definition, probability is the ratio of how many times a selected event occurred over the total number of events which occurred. Hence:
Probability = number of times a selected event occurred / total number of events
In this case, our selected event is the drawing of a heart which occurred 8 times. While our total event is the total number of drawing of cards which occurred 50 times. Hence, the probability is:
Probability = 8 / 50
Probability = 4 / 25 = 0.16 = 16%
Therefore there is a 4/25 or 0.16 or 16% chance that the next draw will be a heart.
7.06) If the greatest value the variable m can be is less than 9, which of the following inequalities best shows all the possible values of m? m < 9 m > 9 m ≤ 9 m ≥ 9
Hello,
The correct answer is A) m < 9
Hope this helps!!!! Happy Holidays!!!! (:
How to solve: (looking for b)
y =mx+b
"Exponents and Multiplication- Simplify. Your answer should only contain positive exponents." Please help quickly !!
plz help you have to turn your phone to the side
Seth is trying to find the unit price for a package of blank discs on sale at 10 for 5.49, his answer was $1.82 per disc is he correct?
The area of a triangle is 6.75m2. If the base of the triangle is 3 m, what is the height of the triangle?
what is 7a + 10 = 2a
Find the greatest number
0.9,0.91,9/10
What is p−m ⋅ pn equal to?
A ladder that is 14 feet long is placed against a building. The bottom of the ladder is 6 feet from the base of the building.
In feet, how high up the side of the building is the top of the ladder? Round to the nearest tenth of a foot
The height of the building from the top of the ladder is 12.6 ft
The situation forms a right angle triangle.
Right angle triangle:A right angle triangle is a triangle that has one of its sides as 90 degrees.
Therefore,
The length of the ladder is the hypotenuse side.
The bottom of the ladder distance from the base of the building is the adjacent side of the triangle. Therefore,
The height of the building from the top of the ladder is the opposite sides. Therefore, using Pythagoras theorem.
c² = a² + b²
14² - 6² = b²
b² = 196 - 36
b² = 160
b = √160
b = 12.6491106407
b = 12.6 ft
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What is the equation of the line that is parallel to y = -2x + 4 and goes through the point (1,7)
Jaidee made her trip to the train station and back. The trip there took two hours and the trip back took five hours. She averaged 30 mph faster on the trip there than on the return trip. What was Jaidee's average speed on the outbound trip?
How do you do solve this question?
From the side view, a gymnastics mat forms a right triangle with other angles measuring 60° and 30°. The gymnastics mat extends 5 feet across the floor. How high is the mat off the ground?
To find the height of the mat off the ground, we can use trigonometry.
Explanation:To find the height of the mat off the ground, we can use trigonometry. Since the angles of the right triangle formed by the mat are 60° and 30°, we can determine the height using the sine function. The sine of an angle is equal to the length of the side opposite the angle divided by the length of the hypotenuse.
In this case, the side opposite the 30° angle is the height of the mat, and the hypotenuse is the length of the mat, which is 5 feet. So, we have sin(30°) = height/5. Solving for the height, we get height = 5 * sin(30°) = 5 * 0.5 = 2.5 feet.
Therefore, the mat is 2.5 feet off the ground.
The correct answer is option B. The height of the gymnastics mat off the ground is [tex]\frac{5\sqrt{3}}{3}}[/tex] feet.
Given that the gymnastics mat extends 5 feet across the floor, this length corresponds to the side opposite the 60° angle in the right triangle.
Let's denote the length of the side opposite the 30° angle as [tex]$x$[/tex].
According to the properties of a 30-60-90 triangle, the side opposite the 60° angle is [tex]\sqrt{3}[/tex] times the side opposite the 30° angle, so we have:
[tex]\[ 5 = x\sqrt{3} \][/tex]
To find [tex]$x$[/tex], we divide both sides of the equation by [tex]$\sqrt{3}$[/tex]:
[tex]\[ x = \frac{5}{\sqrt{3}} \][/tex]
To rationalize the denominator, we multiply the numerator and the denominator by [tex]$\sqrt{3}$[/tex]:
[tex]\[ x = \frac{5\sqrt{3}}{3} \][/tex]
The complete question is:
From the side view, a gymnastics mat forms a right triangle with other angles measuring 60° and 30°. The gymnastics mat extends 5 feet across the floor. How high is the mat off the ground?
A. [tex]\frac{5}{2}[/tex] ft.
B. [tex]\frac{5\sqrt{3}}{3}[/tex] ft.
C. [tex]5\sqrt{3}}[/tex] ft.
D. 10 ft.
Rewrite the set M by listing its elements. Make sure to use the appropriate set notation
M= {x | x is an integer and -2 < x < 1}
Can some one please help me ?
110% =1.10
multiply the old price by that
2.85 *1.10 = 3.135
round to 3.14
new price is $3.14
Simplify (9.5)(−2)(−5).
An arrow is shot upward with a velocity of 64 feet per second. Using the formula h(t)=64t-16t^2, how long after the arrow is released does it hit the ground?
Answer:
After the 4 second arrow is released, it will hit the ground.
Step-by-step explanation:
Consider the provided formula.
[tex]h(t)=64t-16t^2[/tex]
We need to find how long after the arrow is released does it hit the ground.
If the arrow hit the ground that means the value of h(t)=0.
Substitute the value of h(t)=0 and solve the equation as shown.
[tex]64t-16t^2=0[/tex]
[tex]16t(4-t)=0[/tex]
Now use zero product rule: If ab=0 then either a=0 or b=0
[tex]16t=0\ or\ 4-t=0[/tex]
[tex]t=0\ or\ -t=-4[/tex]
[tex]t=0\ or\ t=4[/tex]
Hence, after the 4 second arrow is released, it will hit the ground.
Which of the sets of ordered pairs represents a function?
A = {(−5, 5), (−2, 2), (2, −2), (5, −5)}
B = {(4, 2), (3, −2), (9, 4), (11, −3)}
The baker pays $0.80 per pound for sugar and $1.25 per pound for butter. Write an expression that shows how much the baker will spend if he buys 6 pounds of butter and 20 pounds of sugar.
Answer:
$0.80x + $1.25y = z
Step-by-step explanation:
the total money spent if the Baker bought 6 pounds of butter and 20 pounds of sugar would be $23.50.
The total money spent if the Baker bought 6 pounds of butter and 20 pounds of sugar would be $23.50.
What is Expression?An expression is combination of variables, numbers and operators.
Given,
The baker pays $0.80 per pound for sugar
The baker pays $1.25 per pound for butter.
We need to write expression that shows how much the baker will spend if he buys 6 pounds of butter and 20 pounds of sugar.
Let x be the pounds for sugar
x be the pounds for butter
20x+6y=Total
As x=0.80 and y=1.25
20(0.80)+6(1.25)
16+7.5
23.5
Hence, the total money spent if the Baker bought 6 pounds of butter and 20 pounds of sugar would be $23.50.
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A water tower is used to store fire fighting water at an industrial plant. The tank on top of the tower is in the shape of a cylinder with a height of 15 feet and a diameter of 7 feet. One cubic foot is approximately 7.5 gallons. how many gallons are in the tank if its 55% full?