The volume the rest of the items in the box take up (in cubic inches) is (x-3240) cu in.
What is volume?
Volume is a mathematical term that describes how much three-dimensional space an object or closed surface occupies. Volume is measured in cubic units like m^3, cm^3, in3, etc.Volume is sometimes referred to as capacity. For instance, a cylindrical jar's volume can be used to calculate how much water it can hold.The area that any three-dimensional solid occupies is known as its volume. These solids can take the form of a cube, cuboid, cone, cylinder, or sphere.Various forms have various volumes.Let the volume of the full box be = x cu in
The volume of the computer box = 9 in. x 18 in. x 20 in. = 3240 cu in
Volume the rest of the items in the box take up (in cubic inches)
= x cu in - 3240 cu in = (x-3240) cu in
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At midnight, the temperature was -5°C.
By 9 am the next morning, the temperature had increased by 3°C .
Work out the temperature at 9 am the next morning.
Explanation:
Draw a vertical number line as shown below.
Plot -5 on the number line which is 5 units below 0.
Then move up 3 units to arrive at -2
This shows us that -5+3 = -2
Describe the graph of y = -|x + 4| - 5
Trigonometry is the study of angles and the angular relationships between planar and three-dimensional shapes. The cosecant, cosine, cotangent, secant, sine, and tangent are among the trigonometric functions (also known as the circle functions) that make up trigonometry.
What is y =-(x 5)+4's vertex? Y = | X is it linear?Examples of algebra. Discover the vertex of absolute value. The vertex in this instance for y=|x5|+4 y = | x - 5 | + 4 is (5,4). Set the interior of the absolute value x5 x - 5 equal to 0 0 to determine the vertex's x x coordinate.
Examples of Algebra The degree of variable y in this instance is 1, which means that the degrees of the variables in the equation violate the definition of a linear equation, indicating that the equation is not a linear equation.
Pick a few x values and look for some ordered pairings to graph an absolute value function. Connect the points by plotting them on a coordinate plane. The graph has a V form, as you can see. (1) The graph's vertex is (0,0).
Obtain the equation y = ax2 + bx + c.
Determine -b / 2A. The vertex's x-coordinate is given here.
Simply enter the value of -b / 2a into the equation for x and solve for y to obtain the vertex's y-coordinate. The vertex's y-coordinate is given here.
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Which segments are skewed
Answer:
AB, DC, ED, GA
Step-by-step explanation:
You want to identify the segments that are skew to edge FH of cuboid ABCDEFGH.
Skew linesTwo lines are skew when no plane exists that can contain them both. That is, skew lines are not parallel and do not intersect.
Cuboid ABCDEFGH has 12 edges. Of those, 3 are parallel to FH, and 4 intersect FH. The remaining edges are skew to FH:
AB, DC, ED, GA . . . . . segments skew to FH
a bag contains 10 white, 12 blue, 13 red, 7 yellow, and 8 green wooden balls. a ball is selected from the bag and kept. you then draw a second ball and keep it also. what is the probability of selecting one white ball and one blue ball? round your answer to four decimal places.
Answer:0.096
here this is your answer
on Friday, 280 Fry Middle school students purchase pizza in the cafeteria.
What is your answer?
Write an equation for the intervals of a parabola with x-intercepts at (3,0) and (9,0) that passes through the point (10,-7).
Help is always greatly appreciated.
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad\displaystyle \tt \rightarrow \: y= - {x}^{2} +12x - 27[/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
The values of x where a parabola cuts the x - axis (y = 0) are the roots of the quadratic equation.
I.e 3 and 9 for the given problem.
and the equation can be represented as :
[tex]\qquad\displaystyle \tt \rightarrow \: y = a(x - x1)(x- x2)[/tex]
where, x1 and x2 are the roots of the quadratic equation, a is a constant value (depicting strech in curve)
Now, plug in the values :
[tex]\qquad\displaystyle \tt \rightarrow \: y= a(x- 3)(x - 9)[/tex]
[tex]\qquad\displaystyle \tt \rightarrow \: y = a( {x}^{2} -9x - 3x +27)[/tex]
[tex]\qquad\displaystyle \tt \rightarrow \: y= a( {x}^{2} -12 +27)[/tex]
Now, we need to find the value of a, for that let's use the coordinates of a point lying on the curve (10 , -7)
[tex]\qquad\displaystyle \tt \rightarrow \: - 7= a( {10}^{2} -12(10) +27)[/tex]
[tex]\qquad\displaystyle \tt \rightarrow \: - 7= a(100- 120+27)[/tex]
[tex]\qquad\displaystyle \tt \rightarrow \: - 7= a( 7)[/tex]
[tex]\qquad\displaystyle \tt \rightarrow \: a = ( - 7) \div ( 7)[/tex]
[tex]\qquad\displaystyle \tt \rightarrow \: a = -1[/tex]
Now, we got all required values. let's plug the value of a in equation, and we will get the required equation of parabola.
[tex]\qquad\displaystyle \tt \rightarrow \: y= -( {x}^{2} -12x +27)[/tex]
[tex]\qquad\displaystyle \tt \rightarrow \: y= - {x}^{2} +12x - 27[/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
Answer:
[tex]y=-x^2+12x-27[/tex]
Step-by-step explanation:
Intercept form of a quadratic equation
[tex]\boxed{y=a(x-p)(x-q)}[/tex]
where:
p and q are the x-intercepts.a is some constant.Given x-intercepts:
(3, 0)(9, 0)Substitute the given x-intercepts into the formula:
[tex]\implies y=a(x-3)(x-9)[/tex]
To find a, substitute the given point (10, -7) into the equation and solve for a:
[tex]\implies a(10-3)(10-9)=-7[/tex]
[tex]\implies a(7)(1)=-7[/tex]
[tex]\implies 7a=-7[/tex]
[tex]\implies a=-1[/tex]
Therefore, the equation of the function in factored form is:
[tex]\implies y=-(x-3)(x-9)[/tex]
Expand the brackets:
[tex]\implies y=-(x^2-9x-3x+27)[/tex]
[tex]\implies y=-(x^2-12x+27)[/tex]
[tex]\implies y=-x^2+12x-27[/tex]
Therefore, the equation of the function in standard form is:
[tex]\boxed{y=-x^2+12x-27}[/tex]
What is the slope of the line that passes through the points (0, -10)
and (-4,-11)?
Answer: - 4 /1 x -10
Step-by-step explanation:
the rise is -4
the run is -1
the y intesept is -10
Convert into a mixed number.
19/01
7
Answer: 2 3/7
Step-by-step explanation:
Determine the rate of change on the graphs below
Answer:
a. 3
b. -3/2
c. 4/3
d. -5/3
e. 0
f. undefined
Step-by-step explanation:
Please help me with this.
least common mutiple of...
6 and 8: 24
8 and 12: 24
12 and 9: 36
6 and 9: 18
Arthur crafts miniature chocolate dollhouses which he sells for $24 each. arthur has calculated the breakeven level of revenues for his business at $1,720 of sales. the dollhouses have a variable cost of $12 to produce per unit. what are arthur's fixed costs?
Answer: you mom loves your neighbor
Step-by-step explanation: because the do things together
While sorting some change into piggy banks, Kyle put 4 coins in the first piggy bank, 6 coins in the second piggy bank, 9 coins in the third piggy bank, 13 coins in the fourth piggy bank, and 18 coins in the fifth piggy bank. If this pattern continues, how many coins will Kyle put in the sixth piggy bank?
Answer:24
Step-by-step explanation:4+2=6,6+3=9,9+4=13,13+5=18,18+6=24
Answer:
24
Step-by-step explanation:
because in first piggy bank has 4 coins and second has 6 . difference=6-4=2
second has 6 coins and third has 9 . difference= 9 - 6 = 3 third has 9 coins and fourth has 13 . difference=13-9=4
fourth has 13 and fifth has 18 coins difference is 18 -13 =5
then,sixth has 24 because all have 2 3 4 5 difference then six has 6
a credit score is used by credit agencies (such as mortgage companies and banks) to assess the creditworthiness of individuals. values range from 300 to 850, with a credit score over 700 considered to be a quality credit risk. according to a survey, the mean credit score is . a credit analyst wondered whether high-income individuals (incomes in excess of $100,000 per year) had higher credit scores. he obtained a random sample of high-income individuals and found the sample mean credit score to be with a standard deviation of . conduct the appropriate test to determine if high-income individuals have higher credit scores at the level of significance.
There is insufficient evidence to conclude that those with the high incomes are the ones that have the more credit scores.
How to carry out the hypothesis testWe have the bar x = 705.9
The value of n = 34
mean = 724 . 1
standard deviation = 83.4
the level of significance = 5 percent level
The Hypothesis formulation
The null hypothesis H0 = u 705.9
alternative hypothesis = H1 u > 705.9
The t test is given as x - u / s /√n
= (724.1 - 705.9) / (83.4 / √34)
= 1.2725
The degree of freedom = 34 - 1 = 33
The test that we have here is a right tailed test
The p value for the test is given as probability of p (t33 > t)
= 0.1064
From the solution that we have here, we can see that the p value that has been calculated is greater than the level of significance.
Given that this is the case, the decision rule would be for us not to reject the null hypothesis.
There is insufficient evidence to the claim that the high income persons have the greater credit scores.
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The volume, V, of a container is directly proportional to the cube of its height, h. When its height
is 4 cm, its volume is 48 cm3.
1.What is the volume if the height is 3 cm?
2.If the height is doubled to 6 cm, how many times bigger will the volume be?
Answer:
see explanation
Step-by-step explanation:
given that V is directly proportional to h³ , then the equation relating them is
V = kh³ ← k is the constant of proportion
to find k use the condition V = 48 when h = 4 , then
48 = k × 4³ = 64k ( divide both sides by 64 )
[tex]\frac{48}{64}[/tex] = k , then k = 0.75
V = 0.75h³ ← equation of proportion
1
when h = 3 , then
V = 0.75 × 3³ = 0.75 × 27 = 20.25 cm³
2
when h = 6 , then
V = 0.75 × 6³ = 0.75 × 216 = 162 cm³
then
162 ÷ 20.25 = 8
the volume will be 8 times bigger
7.25 to the nearest tenth
Answer:
7.3
Step-by-step explanation:
Above 5- round up
below 5- round down
One employee of a computer store is paid a base salary of 2000 a month plus an 8% commision on all sales over 7000 during the month. how much must the employee sell in one month to earn a total of 4000 for the month
According to this, the answer is that the employee must sell $32,000 in one month to earn a total of $4,000 for the month.
From the information given, the equation would indicate that the total salary is equal to the base salary plus the result of subtracting $7,000 from the amount of sales for 8%:
2000+(x-7,000)*0.08=4,000, where x is the amount of sales
Now, you can solve for x:
2,000+0.08x-560=4,000
0.08x+1440=4,000
0.08x=4,000- 1440
x=2,560/0.08
x=32,000
According to this, the answer is that the employee must sell $32,000 in one month to earn a total of $4,000 for the month.
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Find the value of x in the triangle below:
X =
55°
Blank 1:
X
please hurry
Answer:
35
Step-by-step explanation:
90-55= 35 degress
the length of a rectangle is increasing at a rate of 5 cm/s and its width is increasing at a rate of 7 cm/s. when the length is 11 cm and the width is 9 cm, how fast is the area of the rectangle increasing (in cm2/s)?
The area of the rectangle is increasing at a rate of 122cm²/s if the length of the rectangle is 11 cm and the width is 9 cm.
The area of a rectangle can be described as the product of the length and width of that rectangle, therefore;
Area = L × W
Here L represents length and W represents the width
Now by differentiating using the product rule;
dA/dt = (dL/dt)(W) + (dW/dt)(L)
As the length is 11 cm and the width is 9 cm and the length is increasing at a rate of 5 cm/s and its width is increasing at a rate of 7 cm/s; substituting these values in the equation;
dA/dt = (5)(9) + (7)(11)
dA/dt = 45 + 77
dA/dt = 122
Hence, the area of the rectangle is increasing at the rate of 122cm²/s.
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question 5 (10 points)
What numbers are equivalent to 4/8?
Answer:numbers that are equal to 4/8 would be 2/4 and 1/2 and are you multiplying up?
Step-by-step explanation:
How many twelfths are in 3 2/3?
To make a mixed number from an improper fraction, divide the numerator by the denominator then there exists eight twelfths in two-thirds.
How to convert mixed numbers to improper fraction?Multiply the full number by the denominator to convert a mixed number to an improper fraction. Include it in the numerator. Add that total to the denominator from the beginning.
To make a mixed number from an improper fraction, divide the numerator by the denominator. After division, the mixed number is produced in such a way that the obtained quotient becomes the entire number, the remainder becomes the new numerator, and the denominator remains constant.
Let the value be [tex]$3 \frac{2}{3}$[/tex].
Convert mixed numbers to improper fraction:
[tex]$a \frac{b}{c}=\frac{a \cdot c+b}{c}$[/tex]
substitute the values in the above equation, we get
[tex]$&3 \frac{2}{3}=\frac{3 \cdot 3+2}{3}=\frac{11}{3} \\[/tex]
Therefore, there exists eight twelfths in two-thirds.
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The rectangle below has an area of 70y^8+30y^670y
8
+30y
6
70, y, start superscript, 8, end superscript, plus, 30, y, start superscript, 6, end superscript.
The width of the rectangle is equal to the greatest common monomial factor of 70y^870y
8
70, y, start superscript, 8, end superscript and 30y^630y
6
30, y, start superscript, 6, end superscript.
What is the length and width of the rectangle?
\text{Width} =Width=start text, W, i, d, t, h, end text, equals
\text{Length} =Length=start text, L, e, n, g, t, h, end text, equals
The width of the rectangle with area 70y⁸+ 30y⁶ is; 10y⁶.
Then the length of the rectangle with area 70y⁸+ 30y⁶ is; (7y² + 3).
What are the dimensions of the rectangle?
The area of a rectangle is given by;
Area = Length× width
Given that;
The area of the rectangle = 70y⁸ + 30y⁶
Now, 70y⁸ can be broken down to; 7×5×2×y×y×y×y×y×y×y×y
And 30y⁶ can be broken down to; 5×3×2×y×y×y×y×y×y
The common factors of 70y⁸ and 30y⁶ are = 5,2,y,y,y,y,y,y
Thus, the greatest common factor of 70y⁸ and 30y⁶ is;
5×2×y×y×y×y×y×y = 10y⁶
Therefore our area 70y⁸+ 30y⁶ can be factorized to get;
A = 10y⁶(7y² + 3)
The greatest common monomial of 70y⁸+ 30y⁶ is 10y⁶ which is the width of the rectangle.
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If tomorrow is Friday, then today is Thursday.
The coordinates of the vertices of quadrilateral JKLM are J(-4,
1), K(2, 3), L(5,
3), and M(0,
5)
Drag and drop the choices into each box to correctly complete the sentences.
Answer:
Slope:
JK = (1/3)
LK = (-2)
ML = (2/5)
MJ = (-3/2)
Quadrilateral JKLM is not a parallelogram because the slopes don't match.
Step-by-step explanation:
Slope = m
JK = (-4, 1), (2, 3)
(x₁, y₁) (x₂, y₂)
y₂ - y₁ 3 - 1 2 2 1
m = ------------ = ------------- = ---------- = --------- = -------
x₂ - x₁ 2 - (-4) 2 + 4 6 3
----------------------------------------------------------------------------------------------------------
LK = (5, -3), (2, 3)
(x₁, y₁) (x₂, y₂)
y₂ - y₁ 3 - (-3) 3 + 3 6
m = ------------ = ------------- = ---------- = --------- = -2
x₂ - x₁ 2 - 5 -3 -3
----------------------------------------------------------------------------------------------------------
ML = (0, -5), (5, -3)
(x₁, y₁) (x₂, y₂)
y₂ - y₁ -3 - (-5) -3 + 5 2
m = ------------ = ------------- = ---------- = ---------
x₂ - x₁ 5 - 0 5 5
----------------------------------------------------------------------------------------------------------
MJ = (0, -5), (-4, 1)
(x₁, y₁) (x₂, y₂)
y₂ - y₁ 1 - (-5) 1 + 5 6 -3
m = ------------ = ------------- = ---------- = --------- = -------
x₂ - x₁ -4 - 0 -4 -4 2
----------------------------------------------------------------------------------------------------------
I hope this helps!
I need the symetry so please be correct
Answer:
The Point of symmetry is (5, 6) and not (-5, -6).
Bruno works for Poseidon Pool Service. He needs to drain a 38,000-gallon pool so that he can repair the cracked plaster. The Pool drains 12 gallons per minute.
Write an equation to represent the pool draining in slope-intercept form.
How long will it take for the pool to fully drain? Explain using numbers and words
Bruno needs to refill the pool now that the plaster is repaired. The Pool fills 16 gallons per minute.
Write an equation in slope intercept form to represent the pool filling back up.
*
How long will it take for the pool to fill back up? Explain using words and numbers..
*
The equation representing the pool draining in slope-intercept form is y = -12x + 38000 and the time for the pool to fully drain is 3167 minutes.
What is a linear equation?It is described as the relationship between two variables, and a straight line results from plotting the graph of the linear equation.
The equation is referred to as a linear equation in one variable if just one variable is contained in the linear equation.
As we know,
The standard form of the straight line is:
y = mx + b
The slope in this case is m, and the y-intercept is b.
From the data given:
y = -12x + 38000
Plug y = 0 to find how long it will take for the pool to fully drain:
0 = -12x + 38000
x = 3167 minutes
To fill it back up, the y-intercept is 0.
The slope is given M = 16
y = 16x
Now plug y = 38000 to find how long it will take for the pool to fill back up
38000 = 16x
x = 2375 minutes
Thus, the equation representing the pool draining in slope-intercept form is y = -12x + 38000 and the time for the pool to fully drain is 3167 minutes.
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Label the points, lines, and planes to show AB and line n perpendicular to each other in plane R at point B, plane R
(
AB both perpendicular to line p and intersecting line m at point A.
intersecting plane S in line p, and
R
Answer:
sorry i don't know it to should have listened to your teacher
Step-by-step explanation:
Label the points,lines,and planes to show AB and line in perpendicular
to each other in plane R to point B, plane R
Derek says the dilation was a reductionDelilah says the dilation was an enlargement who is correct and why
Delilah is correct; it is
Here, we want to check who was right
Mathematically, we can dilate a figure by reduction or enlargement by the use of a specific scale factor
When the scale factor is less than 1, it is a reduction
However, if the scale factor is greater than 1, it is an enlargement
The original point is (x,y)
From the image coordinates given, we see that the scale factor is 6/5 which is greater than 1
Thus, the dilation is an enlargement and Delilah was right
Help!! Me! Please
(You don’t have to answer all)
1. Which kind of model do you think best represents the profit for each business?
2. Find a function that models the profit you can expect, based on your projections, for each business. You can round your values to the nearest thousandth, as needed.
Answer:
Please see below for answers and explanation and attachments
Step-by-step explanation:
These models are best figured out using regression analysis which is a rather complicated computation but luckily there are calculators that can solve
1. The best way to approach this problem is to plot the values and see whether the model is a linear equation or a higher degree equation.
For all three cases it appears that the equations are not linear which would have suggested a model of the form y = mx + b where y = profit in $, x = hours, m is the slope (rate of increase in profit) and b a constant, the y-intercept
For example if you look at the data for the dog walker table, the increase in $ for every additional hour of service is not constant eliminating a linear model. For the first hour, the increase is $7, the second hour it is $11, the third it is $27
So i assumed a quadratic model of the form y = ax² + bx + c where y = profit in $ and x is the number of hours of service for all three businesses
There are plenty of online calculators out there which can rapidly compute the quadratic regression model parameters fitting the data and provide a level of goodness of fit of the equation through a statistic known as the correlation coefficient, r
I entered the data for all 3 rows and came up with the following results
In all the equations, y represents the profit in $ and x the hours
I have also attached screenshots of the computation results which should be self explanatory
Dog Walker
Equation:
y = 1.05357x² + 8.3964x - 6.7
Correlation Coefficient r:
0.9913546 (pretty high goodness of fit)
House Sitter
Equation:
[tex]y = 1.482x^2 + 1.396x + 9.3[/tex]
Correlation Coefficient r:
0.99556069
Lawn Care
Equation:
y = -5.875x² + 30.582143x + 116.9
Coefficient of Correlation r:
0.9794537681
The attached screenshots will provide all necessary info.
I hope that helps ya out :)
Use the figure shown. Let point D be at (-4,1) . Use the sides of triangle BDA to find the slope of the line.
The slope of the line shown in the figure having equation x + 2y = 0 is 1/2.
The point A is at ( -2 , 1 ), point B is at ( -4 , 2 ) and Point C is at ( -2 , 2 ).
Let point D be at ( -4 , 1 ).
Now the new triangle is ΔBDA and the corner points are A is at ( -2 , 1 ), point B is at ( -4 , 2 ) and point D is at ( -4 , 1 ).
The equation of line passing through two points is given by:
[tex](y-y_{1} ) = (\frac{y_{2}-y_{1} }{x_{2} - x_{1} })(x - x_{1} )[/tex]
The equation of line passing through two points A( -2 , 1 ) and B( -4 , 2 ) IS
y - 1 = ((2-1)/(-4-(-2))) (x-(-2))
y - 1 = (1/(-2)) (x+2)
2y -2 = -x -2
x + 2y = 0
The equation of straight line is x + 2y = 0
The equation in slope intercept form can be written as,
y = x/2 + 0
Slope = m = 1/2
Intercept = c = 0
So, we can conclude that 1/2 is the slope of the line .
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