The length and width is 32 inches and 10 inches.
Let us assume the width of rectangle be w. So, length of rectangle = 3w + 2. As per the known fact, the length and width of rectangle for perimeter is related as - Perimeter = 2 (length + width)
Keep the values in formula to find the value of width
84 = 2 (3w + 2 + w)
Performing addition in bracket
84 = 2 (4w + 2)
Performing multiplication
84 = 8w + 4
8w = 84 - 4
Performing subtraction
8w = 80
w = 80 ÷ 8
Performing division
w = 10 inches
Finding length now -
Length = 3×10 + 2
Length = 30 + 2
Length = 32 inches
Hence, the length and width is 32 inches and 10 inches.
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A sprinkler rotates 360° to water a circular region. If the total area watered is approximately 171 yd^2, determine the radius of the region (the radius is the length of the stream of water). Round the answer to the nearest yard.
The radius is approximately ___ yd.
The radius of the sprinkler is approximately 7 yards.
How long is the arm of the sprinkler?
In this situation we find the case of a sprinkler that rotates until a complete revolution is done, that is, the area of complete circle is covered due to the rotation. That area can be found by using this formula:
A = (θ / 360) · π · r²
Where:
A - Area of rotation, in square yards.θ - Angle of rotation, in degrees.r - Radius of the sprinkler, in yards.If we know that A = 171 yd² and θ = 360°, then the radius is approximately:
171 = π · r²
r = √(171 / π)
r ≈ 7.378 yd (approx. 7 yd)
The radius of the sprinkler is approximately 7 yards.
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At the grocery store, Mr. Arnett allowed each of his
children to fill their own bag with trail mix for their hike.
The table shows the amount of trail mix for each child.
Child
Ava
Grayson
Mason
Tyler
Amount of
Trail Mix (oz)
15
14
10
17
The trail mix costs $4.50 per pound. How much will Mr.
Arnett pay for all the trail mix?
The temperature is-2°C. if the temperature reses by 15°C, what is the new temperature?
Explanation:
Draw a vertical number line (see below). Mark -2 on it. Then move up 2 units to arrive at 0. Move up the remaining 13 units to arrive at 13
This shows that -2+15 = 13
The table shows the percent of each type of doughnut sold at a bakery. A store clerk put all of the cream filled and powered sugar doughnuts on a display in the front of the store. Both of these types of doughnuts completely sold out on Tuesday morning. If the clerk put 108 doughnuts in front of the store, how many doughnuts were there in all at the beginning of the day on Tuesday.
Using proportions, it is found that 240 doughnuts were there in all at the beginning of the day on Tuesday.
What is the missing information?The percentages are missing and are given in the graph at the end of the answer.
What is a proportion?A proportion is a fraction of a total amount, and equations can be built to find the desired measures using the unit rates and operations such as multiplication and division.
One example of application of proportions is for percentage problems, as the decimal equivalent of the percentages are used to find either the equivalent amount or the total amount, by multiplication operations.
The percentages of doughnuts displayed are given as follows:
Cream filled: 20%.Powdered sugar: 25%.Hence 45% of the total amount is equivalent to 108 doughnuts, hence:
0.45n = 108.
n = 108/0.45
n = 240.
Which is the number of doughnuts that were there in all at the beginning of the day on Tuesday.
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In the diagram m∠ACB=25° and CE bisects ∠DCF. explain how to find m∠DCE
The measure of ∠ DCE is equal to 57.5° by using the property of bisectors and vertically opposite angles.
We are given a ray diagram.
In the diagram, the measure of angles are given as:
∠ ACB = 25°
∠ ACG = 90°
We need to find the measure of angle ∠ DCE when CE bisects ∠ DCEF.
Now, we know that:
∠ BCG = ∠ DCF ( Vertically opposite angles.) … (1)
Now,
∠ BCG = ∠ ACB + ∠ ACG
∠ BCG = 25° + 90°
∠ BCG = 115° … (2)
∠ DCF = ∠ DCE + ∠ CEF
∠ DCF = ∠ DCE + ∠DCE ( as ∠ DCE = ∠ CEF since CE bisects them)
∠ DCF = 2 ∠ DCE … (3)
Now, put (2) and (3) in (1), we get that:
115° = 2 ∠ DCE
∠ DCE = 115 / 2°
∠ DCE = 57.5°
Therefore, we get that, the measure of ∠ DCE is equal to 57.5° by using the property of bisectors and vertically opposite angles.
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5. Write the letter of the correct explanation next to each step in the chart. (Each blank is worth
2 points)
A. Distributive property
B. Simplify using addition
C. Add 9 to each side and simplify
D. Use multiplication to simplify
+
E. Multiply each side by
Steps
-
and simplify
Explanation
-(x + 4) - 6 = 54 Original equation
-(x) (4) - 6 = 54
-(x) + (-3) - 6 = 54
- (x) - 9 = 54
-(x) = 63
x=- 84
The solution to the equation and the explanation for each step is given below.
How to Solve an Equation?Given the equation, -3/4(x + 4) - 6 = 54, the steps to find the value of x is given below:
-3/4(x + 4) - 6 = 54 [given]
-3/4(x) -3/4(4) - 6 = 54 [Distributive property]
-3/4x + (-3) - 6 = 54 [Use multiplication to simplify]
-3/4x - 9 = 54 [Simplify using addition]
-3/4x = 63 [Add 9 to each side and simplify]
x = -84 [Multiply each side by -4/3 and simplify]
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Use the number line to answer the following 2 questions
Answer:
for first question the answer will be .. 5
Step-by-step explanation:
easily,
[tex] \frac{1}{5} \times 5 = 1 [/tex]
There are [tex]6\frac{1}{4}[/tex] groups of 1/5 in 5.
The simplified value of 5 ÷ 4/5 is also [tex]6\frac{1}{4}[/tex].
What is a number line?A number line is a one-dimensional horizontal line where we can represent any real number. The origin of the number line is represented by zero left to it are all negative real numbers and right to it are all positive real numbers.
From the bar given above the number line, each group has subgroups of 4.
Therefore, The number of groups of (1/5) in 5 is [tex]6\frac{1}{4}[/tex] groups.
We know when a fraction is in the division we can reciprocate the fraction and the division changes to multiplication,
Therefore, 5 ÷ 4/5 = 5×5/4 = 25/4 = [tex]6\frac{1}{4}[/tex]
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HELP QUICK I WILL GIVE BRAINLIEST ANSWER! In the diagram, line m intersects line n. A two-column proof shows that vertical angles 21 and 23 are
congruent. What should be the statement and justification for step 3?
Answer:
Option A=============================
The missing statement is:
∠1 + ∠2 = 180°∠2 + ∠3 = 180°Justification is:
Angles that form a linear pair have measures that sum to 180°.All the other options have mismatching or wrong statements or justifications:
B) Wrong statement, the angles are not congruent.C) Wrong justification, angles are not vertical.D) Wrong justification, not matching the statement.how can you make the equation true?
111+222=
Answer: 111 + 222 = 333
Douglas Noel went to Home Depot and bought thirteen doors at $43.44 each and six bags of fertilizer at $8.71 per bag.
Round your answers to 2 decimal places.
What was the total cost to Douglas?
If Douglas had $660 in his pocket, what does he have left to spend?
The total cost is $616.98.
The amount he has left to spend is $43.02.
What is the total cost?The total cost to Douglas is the sum of the total cost of the thirteen doors and the sum of the six bags of fertilizers
The total cost of the thirteen doors = (cost of one door x total number of doors that would be bought)
$43.44 x 13 = $564.72
The total cost of six bags of fertilizers = (cost of one bag x total number of bags)
$8.71 X 6 = $52.26
Total cost = $564.72 + $52.26 = $616.98
Amount he has left to spend = $660 - $616.98 = $43.02
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Westside Energy charges its electric customers a base rate of $8.00 per month, plus 12¢ per kilowatt-hour (kWh) for the first 300 kWh used and 4¢ per kWh for all usage over 300 kWh. Suppose a customer uses x kWh of electricity in one month. Express the monthly cost E as a piecewise defined function of x. (Assume E is measured in dollars.)
The linear function that gives the monthly cost E for x > 300 is given by:
E(x) = 44 + 0.04x.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.When x > 300, we have that:
The base rate of $8.00 was paid.The 12 cents for each kWh up to 300 was paid.Hence the intercept is given by:
b = 8 + 0.12 x 300 = 44.
The slope is the cost per kWh of 4 cents, hence the function is:
E(x) = 44 + 0.04x.
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PLEASE HELP FAST I ONLY HAVE ONE HOUR!!!!!!
The height of the density curve is 1/5
How to determine the height of the density curve?From the graph, we have the following parameter
Base = 5 units
As a general rule, the area under the density curve must have a value of 1
This means that
Area = 1
So, we have
Area = Base * Height
So, we have
1 = 5 * Height
Evaluate
Height = 1/5
Hence, the height of the density curve is 1/5
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Puja claims that any fraction can be thought of as a division problem and any
division problem can be thought of as a fraction. Is Puja's claim true? Give two
examples-one division problem as a fraction and one fraction as a division
problem to explain your answer.
Puja is not right to claim that any fraction can be thought of as a division problem and any division problem can be thought of as a fraction.
What is a fraction and division problem?Any number of equal parts is represented by a fraction, which also represents a portion of a whole. Represented as [tex]\frac{a}{b}[/tex].A division problem has three primary components: the dividend, the divisor, and the quotient. The amount that will be divided is the dividend. The quantity of "people" among whom the number is divided is referred to as the divisor. The answer is the quotient.As seen by the definition of fraction, in terms of division problem, it involves only the the dividend and the divisor and not the quotient.
Hence, the two cannot be used inter-changeably, i.e., a fraction is not a division problem and vice versa.
Hence, Puja is not right to claim that any fraction can be thought of as a division problem and any division problem can be thought of as a fraction.
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Answer:
Step-by-step explanation:
yesterday
HURRY IM TIMED Which benchmark fraction is closest to 9/10-3/10 A. 3/4 B. 1/2 C. 1/4 D. 4/4
Answer:
I am pretty sure it is a i think.
Step-by-step explanation:
just subtract the fractions and you will get 6\10 and the you will simplify and get 3\5. so 3\4 is closest to 3\5.
It takes 3 people 4 hours to paint a wall. Assume that all people paint at the same rate. How long would it take 5 people to paint the same wall?
Answer:
2 [tex]\frac{2}{5}[/tex] hours or 2.4 hours or 2 hours and 24 minutes
Step-by-step explanation:
A formula for v is given as v=u+ 9.8t The value for u after truncation to 2 decimal places is 4.7 Given also that t, measured to the nearest whole number is 17, calculate the smallest possible value for V
Answer:
V = 86.06
Step-by-step explanation:
V = u + 9.8t
V = 4.7 + 9.8(17)
V = 86.06
PLS HELP FAST!! 20 POINTS!!
Overall, the river festival made £12 858.56. The organisers spent £6429.28 running the festival. How much was the profit, as a percentage of the total money made?
Step-by-step explanation:
it made £12,858.56.
the costs were £6,429.28
so, the profit was
12,858.56 - 6,429.28 = £6,429.28
since cost and profit are equal, that means they are both exactly half of the total income.
and half means 50%.
formally, to do the full % calculation :
100% = 12,858.56
1% = 100%/100 = 12,858.56/100 = 128.5856
how many % are 6,429.28 ?
as many % as times that 1% fits into 6,429.28 :
6,429.28 / 128.5856 = 50
so, it is 50%.
I am stuglling please someone help me
76 degrees n 83 degrees it's div
A parking garage charges $2.00 for the first hour and $0.75 for each additional hour. If a customer gave the parking attendant $35 for parking from 10 AM to 3 PM, how much did the garage charge?
Which piece of information is not necessary to solve the problem?
$2.00 parking charges for the first hour
$0.75 parking charges for each additional hour
O
Amount of time the customer was parked
$35 the customer gave the parking attendant
None of the information provided
How much did the garage charge?
Answer:
The information that I do not need is how much the customer gave the parking attendant.
The garage charged $5.00
Step-by-step explanation:
2 + .75h h stands for the number of hours the car was parked.
2 + .75 (4)
2 + 3 = 5
pls help 50 if corrret
Answer:
-4.2
Step-by-step explanation:
Check the attached photo for work.
convert 1100 feet per second into miles per hour
Answer: 0.681818
Hope this helps!
A cookie recipe requires 4 2/3 cups of flour. If a person only wanted to make 3/4 of a batch, how many cups of flour would they need? (Do not add the label)
[tex]\begin{array}{ccll} \stackrel{recipe}{batch}&\stackrel{recipe}{flour}\\ \cline{1-2} 1&4\frac{2}{3}\\[1em] \frac{3}{4}&f \end{array}\implies \cfrac{1}{ ~~ \frac{3}{4}~~ }~~ = ~~\cfrac{ ~~ 4\frac{2}{3} ~~ }{f}\implies \cfrac{4}{3}~~ = ~~\cfrac{ ~~ \frac{4\cdot 3+2}{3}~~ }{f}\implies \cfrac{4}{3}=\cfrac{ ~~ \frac{14}{3} ~~ }{f} \\\\\\ \cfrac{4}{3}=\cfrac{14}{3f}\implies 12f=42\implies f=\cfrac{42}{12}\implies f=\cfrac{7}{2}\implies f=3\frac{1}{2}[/tex]
Use the map shown below to find the distance between cities A and B to the nearest tenth.
Check the picture below.
[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ B(\stackrel{x_1}{-3}~,~\stackrel{y_1}{6})\qquad A(\stackrel{x_2}{0}~,~\stackrel{y_2}{0})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ BA=\sqrt{(~~0 - (-3)~~)^2 + (~~0 - 6~~)^2} \implies BA=\sqrt{(0 +3)^2 + (0 -6)^2} \\\\\\ BA=\sqrt{( 3 )^2 + ( -6 )^2} \implies BA=\sqrt{ 9 + 36 } \implies BA=\sqrt{ 45 }\implies BA\approx 6.7[/tex]
The probability of passing the math class of Professor Goodrum is 59%, the probability of passing Professor Cruise's physics
class is 26%, and the probability of passing both is 17%. What is the probability of passing one or the other?
(Give your answer as a whole percent number.)
probability of passing one or the other:
Answer:
51%
Step-by-step explanation:
Given P(passing math) = 59%, P(passing physics) = 26%, and P(passing both) = 17%, you want to find the probability of passing only one of the courses.
Probability relationsWe can record the given probabilities in a 2-way table (values shown in blue). The table is completed by making sure the totals add up (values shown in black).
The probability of passing one course and failing the other is the sum of the probabilities with a yellow background:
42% +9% = 51%
The probability of passing one or the other is 51%.
__
Additional comment
We can also get there using the relation ...
P(A+B) = P(A) +P(B) -P(AB)
The union of A and B also includes their overlap:
P(A+B) = P(AB') +P(A'B) +P(AB)
In other words, the probability of interest is ...
P(AB') +P(A'B) = P(A) +P(B) -2×P(AB) = 59% +26% -2(17%)
P(AB') +P(A'B) = 51%
Vincent earns $892 on Monday and he earns $711 on Tuesday. How much total money does Vincent
earn?
Please help
(100 Points)
Answer:
Equation: (14.71-4.48) [divided by] 3 =x
"Answer x": 3.41
Explanation:
14.71-4.48=10.23
10.23/3 = 3.41
3.41
what is the value of x?!?
please help!
Answer:
x = 25
Step-by-step explanation:
The given angles, x° and (6x+5)° form a linear pair. You want the value of x.
Linear pairTwo angles that together form a straight line are called a linear pair. A linear pair of angles has a total measure of 180°.
x° +(6x +5)° = 180°
7x +5 = 180 . . . . . . . . . divide by °, collect terms
7x = 175 . . . . . . . . . . subtract 5
x = 25 . . . . . . . . . . divide by 7
The value of x is 25.
Robert buys last year's best-selling novel, in hardcover, for $22.40. This is with a 20% discount from the original price. What was the original price of the novel?
Answer:
$28.00
Step-by-step explanation:
Set up an equation:
$22.40 = y(1 - 0.20)
Solve the contents of the parentheses first:
$22.40 = y(0.80)
Divide by 0.80 on both sides to isolate y:
($22.40)/0.80 = y
Solve:
$22.40 / 0.80 = $28.00
A 17 foot ladder is leaning on a wall. the bottom of the ladder on the ground is at a distance of 3 feet from the base of the wall.
What is the distance, in feet, between the griund and the top of the ladder? round your answer to the nearest tenth
The distance in feet between the ground and the top of the ladder is 16.7 feet.
Let the distance in feet between the ground and the top of the ladder be x.
According to the given question.
Length of the ladder = 17 foot
The distance of the ladder from the base of the wall is 3 feet.
From the given data we can say that we have a right angle triangle in which the hypotenuse is the length of the ladder, base is the distance between the ladder and wall. And the distance between ground and ladder is our perpendicular.
Now according to the Pythagoras theorem,the sum of the areas of the two squares on the legs (a and b) equals the area of the square on the hypotenuse (c).
Therefore,
17^2 = 3^2 + x^2
⇒ 289 = 9 + x^2
⇒ 280 = x^2
⇒ x = 16.7 feet
Hence, the distance in feet between the ground and the top of the ladder is 16.7 feet.
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During a science experiment Mary found the mass of two rocks to be 36.81 grams and 52.4 grams what is the total mass of these two rocks
Answer: 89.21g
Step-by-step explanation:
36.81g + 52.40g = 89.21g