Using proportions, it is found that the floor space occupied by each machine is of 6.5 ft².
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
In this problem, five identical machines cover a total of 32 1/2 ft² = 32.5 ft², hence the space occupied by each machine is given as follows, applying the proportion:
32.5 ft²/5 = 6.5 ft².
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A
ABCD FECG
2
B
F
6
4
5
E
100°
120°
G
W
D
w = [?]°
5
60°
C
Answer:
120
Step-by-step explanation:
Corresponding angles of similar figures are congruent.
The measure for w is 120 degree.
We have ABCD ~ FECG
If two quadrilaterals are similar, it means that their corresponding angles are congruent, and their corresponding sides are proportional.
Then, we can write as
AB/ FE = CB/ EC = CD/ CD = AD/ FG
and, <A= <F,
<B = <E,
<C= <C,
<D= <G
So, the measure for w is same as angle G.
Thus, the measure for w is 120 degree.
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1) Write an equation in point slope form
that passes through the point (1, 2) & slope
of -5
Answer:
y - 2 = -5 (x - 1)
Step-by-step explanation:
Formula for point-slope equation :
y - y₁ = m (x - x₁)
============================================================
Given :
⇒ Point (x₁, y₁) = (1, 2)
⇒ Slope (m) = -5
=============================================================
Solving :
⇒ y - 2 = -5 (x - 1)
[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]
Equation of line can be written in point - slope form as :
[tex]\qquad \sf \dashrightarrow \:y - y_1 = m(x - x_1)[/tex]
y1 = y - coordinate of point = 2 x1 = x - coordinate of point = 1m = slope = -5So, required equation is ~
[tex]\qquad \sf \dashrightarrow \:y - 2 = - 5(x - 1)[/tex]
Eugene and three of his friends went out to eat. They decided to split the bill evenly. Each person paid $11. What was the total bill?
Answer:
Step-by-step explanation:
Je calcule la facture totale
11x4=44
La facture totale d'Eugène et ses trois amis était de 11$
4,5,5,6,10,11,12,13 mode
Answer: 5 is the mode
Step-by-step explanation: The mode is the number that is appeared most often in the data, so the mode in this case (4, 5, 5, 6, 10, 11, 12, 13) is 5.
The outside of a rectangular picture frame has length 4x + 5 centimeters and width 2x + 3 centimeters. The picture window inside the frame is a rectangle that is 4x - 2 centimeters long and x + 1 centimeters wide.
a. Write a polynomial to describe the area (in square centimeters) of the picture window.
b. The picture frame, not including the window, is made of flat pieces of wood. Write a polynomial that describes the area (in square centimeters) of the wooden part of the frame. Explain your reasoning
The area of the wooden part of the frame is 4x² +20x +17 sq.cm , Area of a Rectangle is 4x² +2x-2 sq.cm .
What is a Rectangle ?A rectangle is a polygon with four sides . The opposite sides are parallel and equal.
It is given that the outside length and breadth is 4x + 5 centimeters and width 2x + 3 centimeters.
inside the frame has length and breadth 4x - 2 centimeters long and x + 1 centimeters wide.
The polynomial to describe the area of the picture window
The dimension of the inner picture frame is the dimension of the picture window
Area of a Rectangle = Length * Breadth
Area of a Rectangle = (4x-2) (x+1) = 4x² +4x -2x-2 = 4x² +2x-2 sq.cm
The picture frame area without the window =
Area of the total picture frame - Area of the inner picture frame
= (4x+5)(2x+3) - (4x-2)(x+1)
= 8x² + 12x +10x+15 -4x²-2x +2
= 4x² +20x +17
The area of the wooden part of the frame is 4x² +20x +17 .
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Celia simplified the expression Negative 4 x (1 minus 3) minus (2 x + 2). She checked her work by letting x = 5 in both expressions. Her work for the original expression is shown below.
Negative 4 x (1 minus 3) minus (2 x + 2) = negative 4 (5) (1 minus 3) minus (2 (5) + 2) = negative 20 (negative 2) minus 12 = 40 minus 12 = 28.
Celia knows that the simplified expression should also equal 28 when x = 5. Which shows Celia’s simpllifed expression?
–6x – 1
–6x + 2
6x + 1
6x – 2
Answer:
6x-2
Step-by-step explanation:
-4x(1-3)-(2x+2)
= 4x+12x-2x-2
6x-2
(simplify)
Answer:
6x - 2
Step-by-step explanation:
Edge
Help asap immediately
[tex] \frac{9}{8 \: } = 1 \frac{1}{8} [/tex]
HOPE THIS HELPS :)[tex] \sf \frac{9}{8} [/tex]
Step-by-step explanation:
[tex] \sf9 \div 8 = 1(1left)[/tex]
[tex]1 \frac{1}{8} [/tex]
#Hopethishelp
_______
Moumocl!
3 (without using trig table) evaluate
It tan 60 x tan 30 divided by
Tan 60 + tan 30
Answer:
[tex]1.25332[/tex]
Step-by-step explanation:
[tex] tan(30 times tan(60 ) \div \tan(60 \div + 30) [/tex]
pls help me this is important
Using the Charles law, the following are the solutions to the problems;
1) 16 dm3
2) 170 K
3) 2.4 L
What is Charles law?Charles law states that, the volume of a given mass of gas is directly proportional to the temperature at constant pressure.
For problem 1;
T1 = 20 + 273 = 293 K
V1 = 15 dm3
T2 = 318 K
V2 = ?
V1/T1 = V2/T2
V1T2 =V2T1
V2 = V1T2/T1
V2 = 15 dm3 * 318 K/293 K
V2 = 16 dm3
Problem 2
V1 = 250cm3
T1 = 10 + 273 = 283 K
V2 = 150cm3
T2= ?
T2 = V2T1/ V1
T2 = 150cm3 * 283 K/250cm3
T2 = 170 K
Problem 3
V1 = 2.3 L
T1 = 25 + 273 = 298K
V2 = ?
T2 = 40 + 273 = 313 K
V2 = V1T2/T1
V2 = 2.3 L * 313 K/298K
V2 = 2.4 L
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What are the sides of (triangle)PQR?
OA. ZP, ZQ, and ZR
OB. None of these
OC. PQ, QR, and PR
OD. P. Q. and A
A triangle is a three-edged polygon with three vertices. The correct option is C.
What is a triangle?A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. The sum of all the angles of a triangle is always equal to 180°.
The sides of the triangle PQR are PQ, QR, and PR. Thus, the correct option is C.
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A dentist has 420 male and female patients that range in ages from 10 years old to 50 years old and up as shown in the table.
What is the experimental probability that the next patient will be female and in the age range 22-39?
The experimental probability that the next patient will be female and in the age range 22-39 is 56/420
What is the experimental probability?Probability is the odds that a random event would happen. The odds usually lie between 0 and 1.
The experimental probability = number of female in the age range 22-39 / total number of patients
= 56/420
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X÷ 5+1 = 11
X =
What does X =
Answer:
x = 2
Step-by-step explanation:
x/5 + 1 = 11
x/5 = 10
x = 50
I NEED HELP ASAP!!!
Amalia and Alec are studying the growth of a plant over time. They measure the height of the plant at the end of each week for several weeks and display the data in a scatter plot. They then find the equation for the best-fit line to be y=2.5 + 1.25rMULTIPLE CHOICE Question 7 Amalia and Alec are studying the growth of a plant over time. They measure the height of the plant at the end of each week for several weeks and display the data in a scatter plot. They then find the equation for the best-fit line to be y= 2.5 + 1.25x
X = the number of weeks that have passed
= the height of the plant
They want to use the equation to estimate when the height of the plant will be 10
Amalia's estimate is after 6 weeks.
Alec's estimate is after Week 15.
Is either student correct?
Amalia would be correct. They are guessing when the height would be 10, and you are given an equation that will 'predict' that. Height is y, so substitute 10 in the equation and solve for x. You will get x=6
willams bought piece of woods that is 3 feet long.he cuts it in to two pieces.one piece is 14 in long how long is the other piece
Answer:
22 inches
Step-by-step explanation:
3 feet = 36 inches
36-14=22
The other half is 22 inches long
Without plotting the function
y = f(x) on a graph paper, find the coordinates of the common points of the axes when
a) f(x) = 4x² - 25
b) f(x) = 3x² - 5x
Question 2: Find the equation of the line that has an x intercept of 2 and a y intercept of -6
Answer:
[tex]y = 3x - 6[/tex]
Step-by-step explanation:
Hello!
With an x - intercept of 2, the coordinate is (2, 0). With a y - intercept of -6, the coordinate is (0, -6).
We have to find the equation of the line that goes through these points.
The equation of a line is written in slope-intercept format: [tex]y = mx + b[/tex]
y = ordinate, y - valuem = slope, rate of changex = abscissa, x - valueb = y-interceptSlopeFirst let's find the slope using the slope formula: [tex]\frac{y_2 - y_1}{x_2 - x_1}[/tex]. Remember that a coordinate is written in (x, y) format.
[tex]\frac{-6 - 0}{0 - 2}[/tex][tex]\frac{-6}{-2}[/tex][tex]3[/tex]So, we have the slope and the y - intercept. We can plug those into the equation.
[tex]y = mx + b[/tex][tex]y = 3x - 6[/tex]The equation of the line is [tex]y = 3x - 6[/tex]
110- (5x) 70, 110- What is the value of x? 14 15 16 17
The value of x is 14 because the sum of all angles in kite is 360 degree option first 14 is correct.
What is linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
The question is incomplete.
The question is in the picture please refer to the attached picture.
We know the sum of all angles in a kite is 360 degree
110 + (5x) + 110 + 70 = 360
290 + 5x = 360
5x = 70
x = 14
Thus, the value of x is 14 because the sum of all angles in kite is 360 degree option first 14 is correct.
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The table shows the change in the price of a stock. At the end of the week, the price is $17.17.
The price of the stock after the change in price on Thursday is $16.76.
The price of the stock at the beginning of the week is $16.81.
What are the price changes?The price at the end of the week is a function of the total changes in price and the price at the beginning of the week.
$17.17 = beginning price + 0.21 + 0.09 - 0.03 - 0.02 + 0.11
$17.17 = beginning price + 0.36
Beginning price = $17.17 - 0.36 = $16.81
Price on Thursday = $16.81 + 0.21 + 0.09 - 0.03 - 0.02 = $16.76
Here are the questions:
What was the price of the stock after the change in price on Thursday?
What was the price of the stock at the beginning of the week?
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Select the correct answer. Which expression is equivalent to the complex number 10 + 3i?
The expression that is equivalent to the complex number 10 + 3i is (4+7i)-2i(2+3i)
Complex numbersComplex numbers are square root of negative numbers. They are expressed as a + bi
Using the expression
(4+7i)-2i(2+3i)
Expand
4 + 7i - 4i -2i(3i)
4 + 3i - 2(-3)
4 + 6 + 3i
10 + 3i
Hence the expression that is equivalent to the complex number 10 + 3i is (4+7i)-2i(2+3i)
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The annual profits for a company are given in the following table, where x represents the number of years since 2014, and y represents the profit in thousands of dollars. Write the linear regression equation that represents this set of data, rounding all coefficients to the nearest tenth. Using this equation, estimate the calendar year in which the profits would reach 144 thousand dollars.
The linear regression equation that represents this data set is equal to y = 11.7x + 48.2 and an estimate of the calendar year is 2022.
How to write the linear regression equation?First of all, we would determine the slope of the given data set by using this formula:
[tex]Slope = \frac{\sum (x-\bar x)(y-\bar y)}{\sum (x-\bar x)^2}[/tex]
For the sample mean (years), we have:
∑x = 0 + 1 + 2 + 3
∑x = 6.
∑x² = 0² + 1² + 2² + 3²
∑x² = 14.
For the sample mean (profits), we have:
∑y = 46 + 57 + 84 + 76
∑y = 263.
∑xy = (0 × 46) + (1 × 57) + (2 × 84) + (3 × 76)
∑xy = 453.
Now, we can determine the slope:
[tex]Slope = \frac{4(453) - 6(263)}{4(14) - 6^2} \\\\Slope = \frac{234}{20}[/tex]
Slope, m = 11.7.
For the intercept, we have:
[tex]Intercept = \frac{14(263) - 6(453)}{4(14) - 6^2} \\\\Intercept = \frac{964}{20}[/tex]
Intercept, c = 48.2.
Therefore, the linear regression equation is given by:
y = 11.7x + 48.2.
Since the profit would reach 144,000 dollars, the calendar year would be calculated as follows:
144 = 11.7x + 48.2
11.7x = 144 - 48.2
11.7x = 95.8
x = 95.8/11.7
x = 8.2.
For the calendar year, we have:
Year = 2014 + 8.2
Year = 2022.2 ≈ 2022.
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A certain species of animal can has varying fur color. The probability that the animal will have orange fur is 0.7, the probability of brown fur is 0.11 and the probability of grey fur is 0.19. The animal also occasionally will have stripes. If the animal is orange the probability of stripes is 0.16, if the animal is brown the probability of stripes is 0.3, and if the animal is grey the probability of stripes is 0.4.
What is the probability an animal has stripes?
(Round answer to three decimal places)
What is the probability an animal is orange given it does NOT have stripes?
(Round answer to three decimal places)
The probability that an animal has stripes will be 0.86.
How to calculate the probability?The probability that an animal has stripes will be:
= Orange stripes + Brown stripes + Grey stripes
= 0.16 + 0.3 + 0.4
= 0.86
The probability that an animal doesn't have stripes will be:
= 1 - 0.86
= 0.14
Therefore, the probability that an animal doesn't have stripes is 0.14.
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Please solve these questions!! preferrably today since the quarter locks today!!
Answer:
131
Step-by-step explanation:
What is the volume of the solid?
Answer:
V≈314
Step-by-step explanation:
* means times
volume of a cone
it's a right circular cone
formula
volume =
π * radius squared * (height ÷ 3)
π * 5 squared * (12 ÷ 3)
π * 25 * (4)
π * 100
3.14 * 100 = 314
factoid
pi or π in fraction form is 22/7
5 and 12 means the length of that
cone is 13
because it's a right circular cone
that means there's a right triangle
one of the special triangles is a
5,12,13 right triangle where
13 is the hypotenuse
moomoomath
F(x)=x^2 + 4x + 12 what is the vertex form of f(x)? What is the minimum value of f(x)?
the equation of f(x) which is "x" terms is the equation of a vertical parabola that is opening upwards like a bowl, the minimum will be at its vertex
[tex]\textit{vertex of a vertical parabola, using coefficients} \\\\ y=\stackrel{\stackrel{a}{\downarrow }}{1}x^2\stackrel{\stackrel{b}{\downarrow }}{+4}x\stackrel{\stackrel{c}{\downarrow }}{+12} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right) \\\\\\ \left(-\cfrac{ 4}{2(1)}~~~~ ,~~~~ 12-\cfrac{ (4)^2}{4(1)}\right) \implies \left( - \cfrac{ 4 }{ 2 }~~,~~12 - \cfrac{ 16 }{ 4 } \right) \\\\\\ (-2~~,~~12-4)\implies \stackrel{minimum}{(-2~~,~~\stackrel{\downarrow }{8})}[/tex]
Which of the following solutions to the inequality -7x+14>-3x -6? Select all that apply
-10
10
-5
5
-3
3
0
I went thru it and im pretty sure that only these work
-10
-5
-3
Suppose a nuclear power plant disaster occurs. How could GDP be a "false beacon" in this case?
If there was a nuclear plant disaster, then GDP would be a false beacon because it would account for government spending but not for the pollution caused.
Why would GDP be a false beacon?Two of the components of GDP are government spending and private investment.
If there is a nuclear plant disaster, either the government will spend a lot to clean it up, or a private company will depending on if the plant is public or private.
GDP would therefore increase.
This would be a false beacon however, because this increase would not take into account the nuclear pollution that would have occurred that would negatively impact future production.
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using the digits 4,5,6,and 7,write the greatest 4 digit number you can without repeating any of the digits.
Answer:
7,654
Step-by-step explanation:
Arrange the digits in order to create the highest possible number.
7000 + 600 + 50 + 4 = 7654
The first three terms of a sequence are given. Round to the nearest thousandth (if
necessary).
36, 27,
81
4
Find the 10th term.
Answer:
T10=108
Step-by-step explanation:
TN=bn+c
27,36,81=constant difference is 9
Tn=bn+c
Tn=9n+18
T10=9(10)+18
T10=90+18
T10=108.
hope it helps.
Answer: 2.703
Step-by-step explanation:
Building A is 875 feet tall and contains 71 stories. Building B contains 109 stories. If the two buildings have the same number of feet per floor, approximate the height of building B rounded to the nearest foot.
Answer:
Approx. 1343 feet
Step-by-step explanation:
Building A is 71 stories at 875 feet tall. Since the two buildings have the same number of feet per floor, we can divide building A's stories to find the height of 1 story, and then multiply by the stories of building B.
Building A
71 ÷ 71 = 1 story
875 ÷ 71 = 12.32 feet
Each story is approximately 12.32 feet tall
Building B
1 story × 109 = 109 stories
12.32 feet × 109 = 1343.31 feet
Rounded to the nearest foot is 1343 feet.
Determine the probability of the treatment group’s mean being greater than the control group’s mean by 8 points or more. Then complete the statements.
The significance level is set at 5%, and the probability of the result is
%, which is
the significance level. The result is
.
The probability of the treatment group’s mean being greater than the control group’s mean by 8 points or more is 0.036.
How to calculate the probability?The probability of the treatment group’s mean being greater than the control group’s mean by 8 points or more will be:
= (26 + 8 + 2)/1000
= 36/1000
= 0.036
The significance level is set at 5%, and the probability of the result is statistically significant because the probability of the difference is less than 5% significance level.
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