Scale factor for the dimensions of the gymnasium on the blue print will be represented by the expression,
Scale factor = [tex]\frac{\text{Dimension of the blueprint}}{\text{Dimension of the original}}[/tex]
Length of the gymnasium = [tex]96[/tex] feet
Length of the gymnasium on the blueprint = [tex]5.5[/tex] inches
Therefore, scale factor for the blueprint = [tex]\frac{5.5}{96}[/tex]
= [tex]0.0573[/tex]
If the width of the gymnasium = [tex]75[/tex] feet
For the width on the blueprint,
[tex]0.0573=\frac{\text{Width on the blueprint}}{75}[/tex]
Width on the blueprint = [tex]4.29[/tex]
≈ [tex]4.3[/tex] inches
Therefore, width of the gymnasium on the blueprint will be [tex]4.3[/tex] inches.
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How do you work out the size of angle x ?
Answer:
117°
Step-by-step explanation:
Angle of straight line is 180°
Angles in a triangle add up to 180°
starting at right
180 - 101 = 79° at right side angle in triangle
now solving left side angle
180 - 38 - 79 = 63°
now solving x using left side angle, must add to 180°
x + 63 = 180°
x = 117°
x is an exterior angle of the triangle and its measure is 117 degrees.
Given,
Triangle with interior and exterior angles.
Linear pair : ∠x + ∠y = 180 degrees.
Angle of straight line is 180°(Linear pair).
180 - 101 = 79°
Angle sum property: Sum of all the angles in a triangle add up to 180° .
So,
180 - 38 - 79 = 63°
Now solving x,
Angles must add to 180° in a straight line.
x + 63 = 180°
x = 117°
Therefore measure of angle x in the triangle is 117 degrees.
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Which expression is equal to c2−4c+412c3+30c2÷c2−46c4+15c3?
Answer
A: c (c-2)/ 2 (c +2)
Step-by-step explanation:
Which is equal to c^2-4c+4/ 12c^3+ 30c^2 divided by c^2-4/ 6c^4 +15c^3?
A: c (c-2)/ 2 (c +2)
B: 2 (c-2)/ c(c+2)
C: 2 (c+2)/ c(c-2)
D: c(c+2)/ 2(c-2)
[c^2 - 4c + 4] / [12×(c^3) + 30×(c^2)] ÷ [c^2 - 4] / [6×(c^4) +15×(c^3)]
Expand the expression
= [c^2 - 2×2×c + 2^2] / [6×(c^2)×(2c + 5)] ÷ [c^2 - 2^2] / [3×(c^3)×(2c +5)]
Factorize the expression
= [(c-2)^2] / [6×(c^2)×(2c + 5)] ÷ [(c-2)(c+2)] / [3×(c^3)×(2c +5)]
Multiply by interchanging the numerator and denominator of the divisor
= [(c-2)^2] / [6×(c^2)(2c + 5)] × [3(c^3)(2c +5)] / [(c-2)(c+2)]
= [(c-2)×3(c^3)] / [6×(c^2)×(c+2)]
= [c×(c-2)] / [2×(c+2)]
= c(c - 2) / 2(c + 2)
[c^2 - 4c + 4] / [12×(c^3) + 30×(c^2)] ÷ [c^2 - 4] / [6×(c^4) +15×(c^3)] = c(c - 2) / 2(c + 2)
Answer:
A: [tex]\frac{c(c-2)}{2(c+2)}[/tex]
Step-by-step explanation:
[tex]\frac{c^{2} -4c+4}{12c^{3} + 30c^{2}}[/tex] ÷ [tex]\frac{c^{2} -4}{6c^{4} + 15c^{3}}[/tex]
expand.
= [c^2 - 2×2×c + 2^2] / [6×(c^2)×(2c + 5)] ÷ [c^2 - 2^2] / [3×(c^3)×(2c +5)]
factorize.
= [(c-2)^2] / [6×(c^2)×(2c + 5)] ÷ [(c-2)(c+2)] / [3×(c^3)×(2c +5)]
multiply by the reciprocal.
= [(c-2)^2] / [6×(c^2)(2c + 5)] × [3(c^3)(2c +5)] / [(c-2)(c+2)]
= [(c-2)×3(c^3)] / [6×(c^2)×(c+2)]
= [c×(c-2)] / [2×(c+2)]
= A: [tex]\frac{c(c-2)}{2(c+2)}[/tex]
A ruler cost x pence a pen costs 10 pence more than the ruler write an expression in terms of x for the cost of the pen
Answer:
(A ruler) = X (a pen) = Y
y = x+10
Step-by-step explanation:
Answer:
A ruler cost x pence.
Let the cost of the ruler be x pencePen costs 10 pence more than the ruler
Therefore, the pen cost (x+10) pence(x+10) is the right answer.- Find the probability of rolling a divisor of 15.
Answer:
1/3
Step-by-step explanation:
if you're excluding 1 you can only role 3 and 5, which are divisors of 15. so that is 2 of 6 sides 2/6=1/3
X3 + 2x + 3 =18
What is x?
Answer:
x=3
Step-by-step explanation:
Assuming X3 means 3x, then you would have:
5x+3 = 18, 5x = 15, x=3
Use an inverse function to write o
function of
X+1
Answer:
it is e hope it helps :)
Step-by-step explanation:
27.) Find the sum of the length of line segments EF and CD
Answer:
5√10
Step-by-step explanation:
The distance between two points A([tex]x_1,y_1[/tex]) and B([tex]x_2,y_2[/tex]) on the coordinate plane is given by:
[tex]|AB|=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2 }[/tex]
From the image attached the coordinates of the points are E(-1, -1), F(8, -4), C(-7, -4) and D(-1, 2).
Hence the lengths of the line segment EF and CD are:
[tex]|EF|=\sqrt{(8-(-1))^2+(-4-(-1))^2} =\sqrt{90}=3\sqrt{10} \\\\CD=\sqrt{(-1-(-7))^2+(-2-(-4))^2}=\sqrt{40} =2\sqrt{10} \\\\Therefore:\\\\|EF|+|CD|=3\sqrt{10} +2\sqrt{10} =5\sqrt{10}[/tex]
00:00
What quotient does the model Nestor made represent?
0 3.21 + 3 = 1.07
0 1.47 + 7 = 0.27
0.21 + 7 = 0.03
0.81 - 3 = 0.27
Answer:
0.81-3=0.27
Step-by-step explanation:
0.81-3=0.27 it
It is similar to 3.21÷3=1.07 this is division
Please help me with this
Answer:
Option 2 Andrew and Jason rode bikes to the park after Andrew finished his morning chores
What is the slope of the line?
-3, 3
-4, -1
9514 1404 393
Answer:
4
Step-by-step explanation:
Assuming the given numbers are supposed to be (x, y) ordered pairs, the slope can be found using the slope formula:
m = (y2 -y1)/(x2 -x1)
m = (-1 -3)/(-4 -(-3)) = -4/-1 = 4
The slope of the line through the points (-3, 3) and (-4, -1) is 4.
Which expression is equivalent to the given expression?
6y−12
Answer:
it is 6(y-2)
Step-by-step explanation:
Find the quotient. Use a model to help you divide. 6.15 divided by 5
Answer:
The answer for this question is 1.23
i am even number smaller than 48 but not greater than 30 i am multiple of 6 and factor of 72 what number i am
Answer:
36Step-by-step explanation:
Even number smaller than 48 but not greater than 30 i am multiple of 6:
30, 36, 42Factor of 72:
2, 3, 6, 8, 9, 12, 24, 36, 72So the number is 36
Tony bought 8 books about plants and 3
books about fish. He also bought 7
science magazines. Each book cost $6
and each magazine cost $5. How much
did Tony spend in all?
Answer:
Tony spent $101.
Step-by-step explanation:
11*6 = 66
7*5 = 35
66+35 = 101
4. After Lin makes her way down the hallway, will locker 56 have no stickers, 1 point 1 sticker or 2 stickers? Explain how you know. * 1 sticker
Answer:1 sticker
Step-by-step explanation:because 56 is not a multiple of 6
Determine how (if possible) the triangles are similar?
How much is 10% of 10 liters of milk
Answer:
1 liters
Step-by-step explanation:
simplyfy 0.064/0.84 and leave the answer in standard form
Answer:
0.07619047619.
Answer:7.619 x 10 -2
Step-by-step explanation
Standard form :)
Find the surface area and volume of a rectangular prism formed by the net below. The length is 10 inches,
the width is 4 inches and the height is 5 inches.
h
W
Step-by-step explanation:
Surface area of rectangular prism
= 2lw + 2lh + 2wh
= 2(10)(4) + 2(10)(5) + 2(4)(5)
= 80 + 100 + 40 = 220 square inches.
Volume of rectangular prism
= lwh
= (10)(4)(5)
= 200 cubic inches.
express 20.025m in centimeters
Answer:
20025
Step-by-step explanation:
the answer is
20.025 m
= 20.025×1000 cm
= 20025 cm
If k is a constant, what is the value of k such that the polynomial 2ky^-kx-8 is divisible by (x-2)
Answer:we have that
k² x³-6kx+9
we know that
The Remainder Theorem says: If the polynomial f(x) is divisible by a bynomial (x-a) then the number "a" is a root of the polynomial f(x)
so
x=1 is a root of the polynomial
therefore
for x=1
k² x³-6kx+9=0--------> k² (1)³-6k(1)+9=0-----> k²-6k+9=0
using a graph tool------> to resolve the second order equation
the solution is
k=3
k=3
k²-6k+9=0---------> (k-3)²=0
the answer is
k=3
Answer:
Ok so if I did this right the answer will be 2ky^kx-8 / x -2
will someone help with this
Answer:
When rotating a point 180 degrees counterclockwise about the origin
(1,0)→(-1,0)
Step-by-step explanation:
Explanation:-
When rotating a point 180 degrees counterclockwise about the origin
(x,y) →(-x,-y)
Given point ( x,y) = (1,0)
When rotating a point 180 degrees counterclockwise about the origin
(1,0)→ (-1,-0)
(1,0)→(-1,0)
What are the mean,median,mode and range of 59,63,63,72,72,72,72,72,76,81,83,84,84,93.
Answer:
mean 74.714285714286
median 72
mode 72
range 34
Step-by-step explanation:
Answer:
Mean: 74.71
Median: 72
Mode: 72
Range: 34
Step-by-step explanation:
First, let's define what each of these terms mean:
Mean: the average of the data
Median: the number in the middle after being put in ascending order
Mode: the number listed the most
Range: the highest number minus the smallest number
To find the mean, just add up all the numbers and divide by how many there are. First, add up all the numbers in the set. This should give you 1,046. Next, divide by how many terms there are. Since there are 14 terms in this set, we'll be dividing 1,046 by 14. This will give us a mean of 74.71 or 75 if you're rounding up.
To find the median, you'll first need to put the terms in ascending order, meaning from lowest to highest. Luckily, the set is already in ascending order, so that step is not necessary here. Next, you're going to find the number in the middle of the set. However, since there are an even number of terms, we have two numbers in the middle: 72 and 72. To find the median with two numbers in the middle, just add both terms up and divide by 2. However, since both terms are 72, this step is also not necessary. Our median is simply 72.
To find the mode, you're just looking for the number that appears the most. In this case, it would be 72 since it appears more than any other number in the set (5 times.)
Last, to find the range, just subtract the lowest number from the highest number in the set. With the highest number being 93 and the lowest being 59, just do 93 - 59 for a range of 34. Please let me know if you have any further questions!
-4 = r/20 -5
Solve for r. Show your steps
Answer:
r = 20
Explanation:
-4 = r/20 - 5
Simplify both sides of the equation-4 = r/20 - 5
-4 = 1/20r + -5
-4 = 1/20r - 5
Flip the equation1/20r - 5 = -4
Add 5 to both sides1/20r - 5 + 5 = -4 + 5
1/20r = 1
Multiply both sides of the equation by 20(20)1/20r = 1(20)
r = 20Towns a and b are 10km apart. Uncle bill wants a new house at least 5km away from town b
Students obtained a mean score of 400 and standard deviation of 40 in a test with a bell-shaped distribution. What approximate percentage of the students above 520
The percentage of students who scored above 520 is 0.13%.
Given data:
To determine the approximate percentage of students who scored above 520, use the concept of standard deviations.
Given that the mean score is 400 and the standard deviation is 40, calculate the z-score for the value of 520 using the formula:
z = (x - mean) / standard deviation
where x is the value of interest.
So, x = 520, mean = 400, and standard deviation = 40. Plugging in these values:
z = (520 - 400) / 40
z = 120 / 40
z = 3
The z-score of 3 represents a value that is 3 standard deviations above the mean.
To find the approximate percentage of students above 520, we can refer to the standard normal distribution table (also known as the Z-table). Looking up the z-score of 3 in the table, the area to the left of this z-score is approximately 0.9987.
To find the percentage above 520, subtract this value from 1 to find the area to the right of the z-score:
1 - 0.9987 = 0.0013
Hence, approximately 0.13% of students scored above 520 in the test.
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angela bought a pair of shoes at 12% off and receive an additional membership discount of 70 pesos if the pair of shoes cost her 1866 pesos what was the original price of the shoes
Answer:
The original price of the shoes was of 2200 pesos
Step-by-step explanation:
She bought the shoes for 1866 pesos.
She receibed a discount of 70 pesos, so the cost, with the discount, is 1866 + 70 = 1936 pesos.
The pair was bought at 12% off, that is, 1936 pesos is 100 - 12 = 88% of the original price. Then
[tex]0.88x = 1936[/tex]
[tex]x = \frac{1936}{0.88}[/tex]
[tex]x = 2200[/tex]
The original price of the shoes was of 2200 pesos
Solve the following equation algebraically
2x2 = 98
a. x =7
b. x +49
c. x=+7
d. x=49
The difference of two complementary angles is 20. Find the measure of each angle
Answer:
35° , 55°
Step-by-step explanation:
Let one angle be x.
It's complementary angle is = (90 - x)°
According to the question ,
[tex]x - (90 - x) = 20[/tex]
[tex]=> x - 90 + x = 20[/tex]
[tex]=> 2x = 90 - 20 = 70[/tex]
[tex]=> x = \frac{70}{2} = 35[/tex]
The cost of tools for building the wind chimes is 130$ the costs of materials are 10$ Per wind chime what is the total cost to make 100 wind chimes
Step-by-step explanation:
Total cost
= Cost of tools + Cost of materials
= $130 + 100 * $10
= $1,130.