Given:
Length of side = 2.8 in
Let's find the volume of the cube.
To find the volume of a cube, apply the formula:
[tex]V=a^3[/tex]Where:
a is the side length = 2.8 in
Hence, to find the volume, we have:
[tex]\begin{gathered} V=2.8^3 \\ \\ V=2.8*2.8*2.8 \\ \\ V=21.952\approx22.0\text{ in}^3 \end{gathered}[/tex]Therefore, the volume of the cube is 22.0 cubic inch.
ANSWER:
22.0 in³
Pizza House offers 4 different salads, 5 different kinds of pizza, and 3 different desserts. How many different three course meals can be ordered?...Question content area rightPart 1How many different meals can be ordered?enter your response here
A three-course meal will contain 1 pizza, 1 salad, and 1 dessert.
The question tells us that there are 4 different salads, 5 different pizzas, and 3 different desserts.
Therefore, the total number of possible ways a three-course meal can be served is calculated as the product of all the numbers. This is shown below:
[tex]\Rightarrow4\times5\times3=60[/tex]60 different meals can be ordered.
Carla has a music box that has a base area of 9 1/2 in² and a height of 3 1/5 inches.What is the volume of the music box?
Given in the question:
a.) Base area of music box = 9 1/2 in²
b.) Height of music box = 3 1/5 in.
Let's recall the formula for getting the volume of a rectangular prism:
[tex]\text{ Volume = Length x Width x Height or Base Area x Height}[/tex]Before we plug in the values, let's first transform the mixed numbers into improper fractions.
[tex]\text{ 9 }\frac{1}{2}\text{ = }\frac{1\text{ + (2 x 9)}}{2}\text{ = }\frac{1\text{ + 18}}{2}\text{ = }\frac{19}{2}[/tex][tex]\text{ 3 }\frac{1}{5}\text{ = }\frac{1\text{ + (3 x 5)}}{5}\text{ = }\frac{1\text{ + 15}}{5}\text{ = }\frac{16}{5}[/tex]Let's now plug in the values to get the volume of the music box.
[tex]\text{ Volume = Base Area x Height}[/tex][tex]=\text{ 9 }\frac{1}{2}\text{ x 3 }\frac{1}{5}\text{ = }\frac{19}{2}\text{ x }\frac{16}{5}\text{ = }\frac{304}{10}\text{ }[/tex][tex]\frac{304}{10}\text{ = }\frac{\frac{304}{2}}{\frac{10}{2}}=\frac{152}{5}\text{ or 30 }\frac{2}{5\text{ }}in.^3[/tex]Therefore, the volume of the music box is 30 2/5 in.^3.
Find the solution of this system of linearequations. Separate the x- and y- values with acomma. Enclose them in a pair of parantheses. System of equations4x + 8y = 838x + 7y = 76- 8x - 16y = -1668x + 7y = 76
Given,
System of equation is,
[tex]\begin{gathered} 4x+8y=83\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots(i) \\ 8x+7y=76\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots(ii) \end{gathered}[/tex]Taking the equation (i) as,
[tex]\begin{gathered} 4x+8y=83 \\ 4x=83-8y \\ x=\frac{83-8y}{4} \end{gathered}[/tex]Substituting the value of x in equation (ii) then,
[tex]\begin{gathered} 8x+7y=76 \\ 8(\frac{83-8y}{4})+7y=76 \\ 664-64y+28y=304 \\ 36y=360 \\ y=10 \end{gathered}[/tex]Substituting the value of y in above equation then,
[tex]\begin{gathered} x=\frac{83-8\times10}{4} \\ x=\frac{3}{4} \end{gathered}[/tex]Hence, the value of x is 3/4 and y is 10. (3/4, 10)
System of equation is,
[tex]\begin{gathered} -8x-16y=-166\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots(i) \\ 8x+7y=76\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots(ii) \end{gathered}[/tex]Taking the equation (i) as,
[tex]\begin{gathered} -8x-16y=-166 \\ 8x+16y=166 \\ 4x+8y=83 \\ 4x=83-8y \\ x=\frac{83-8y}{4} \end{gathered}[/tex]Substituting the value of x in equation (ii) then,
[tex]\begin{gathered} 8x+7y=76 \\ 8(\frac{83-8y}{4})+7y=76 \\ 664-64y+28y=304 \\ 36y=360 \\ y=10 \end{gathered}[/tex]Substituting the value of y in above equation then,
[tex]\begin{gathered} x=\frac{83-8\times10}{4} \\ x=\frac{3}{4} \end{gathered}[/tex]Hence, the value of x is 3/4 and y is 10. (3/4, 10)
y+2=−3(x−4)y, plus, 2, equals, minus, 3, left parenthesis, x, minus, 4, right parenthesis Complete the missing value in the solution to the equation.
The required equation is 11y = 3x + 2.
What is equation?
An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.
Given y+2=−3(x−4)y .....................(1)
Simplifying (1) and we get
y+2=−3x + 12y
=> 3x + y - 12y + 2 = 0
=> 3x -11y + 2 = 0
=> 3x - 11y = -2
=> 11y - 3x = 2
=> 11y = 3x + 2
Therefore, the required equation is 11y = 3x + 2.
To learn more about equation from the given link
https://brainly.com/question/25896797
#SPJ9
#8 help with algebra 2 question. That’s the only picture I have. I tried writing it out.
Solution:
Given a cosine function graph;
The general cosine function is
[tex]y=A\cos(Bx-C)+D[/tex]Where
[tex]\begin{gathered} A\text{ is the amplitude} \\ Period=\frac{2\pi}{B} \\ C\text{ is the phase shift} \\ D\text{ is the vertical shift} \end{gathered}[/tex]From the graph,
The midline is y = 1
The amplitude, A, is
[tex]\begin{gathered} A=4-1=3 \\ A=3 \end{gathered}[/tex]The amplitude, A is 3
Where,
[tex]\begin{gathered} Period=12 \\ Period=\frac{2\pi}{B} \\ 12=\frac{2\pi}{B} \\ Crossmultiply \\ 12B=2\pi \\ Duvide\text{ both sides by 12} \\ \frac{12B}{12}=\frac{2\pi}{12} \\ B=\frac{\pi}{6} \end{gathered}[/tex]The phase shift, C = 0, and the vertical, D, is 1
Thus, the equation of the graph is
[tex]\begin{gathered} y=A\cos(Bx-C)+D \\ Where \\ A=3 \\ B=\frac{\pi}{6} \\ C=0 \\ D=1 \\ y=3\cos(\frac{\pi}{6}x)+1 \end{gathered}[/tex]The graph is shown below
Hence, the equation is
[tex]y=3\cos(\frac{\pi}{6}x)+1[/tex]Use the given rounded values, the properties of logsand your knowledge of logarithmic functions to find thevalue of each log expression. Show your work.
We want to find the value for
[tex]\log _425[/tex]To do that, first let's rewrite this expression as
[tex]\log _425=\log _45^2[/tex]Using the following property
[tex]\log _ab^c=c\log _ab[/tex]We can rewrite our expression as
[tex]\log _45^2=2\log _45[/tex]Using the given value on the text, we get our answer
[tex]\log _425=2\log _45=2\cdot1.2=2.4[/tex]40.0 Reyna runs a textile company that manufactures T-shirts. The profit, p, made by the company is modeled by the function p=s2+95-142, where s is the number of T-shirts sold. How many T-shirts should be sold to earn a profit of more than $2,000?
But cannot be negative, hence s= 42. This implies that 42 shirts will be sold to make a profit of exactly $2000.
To earn a profit of more than $2000, then s must be greater than 42
This makes the answer to be s > 42
The correct answer is the second option
HELP ASAP MATH PRE CALC
The values for the dimensions of the open box are L = (30 - x)inches, W = (30 - x)inches, and H = (x)inches.
The cube as a three dimensional shapes.A cube is 3- dimensional shape with 6 equal sides, 6 faces, and 6 vertices. Each face of a cube is a square. In there dimension, the cube's sides are; the L = length, W = width, and H = height.
From question, squares of equal sides x are cut out of each corner of the metal sheet, hence the dimension for the height of the box is equal to x.
So; H = (x) inches,
L = (30 - x)inches, and
W = (30 - x)inches.
Therefore, the dimensions of the box that can maximize the volume of the metal sheet of 30inches by 30inches are L = (30 - x)inches, W = (30 - x)inches, and H = (x)inches.
Know more 3-dimensional shapes here: https://brainly.com/question/326906
#SPJ1
in two or more complete sentences, compare the slopes of the two functions. in your comparison, include which function has the greatest slope.
Slope of g (x) : ZERO. The slope of any horizontal line is zero, 0.
Slope of f (x) :
let's take the points ( -4, 7) and (-2, 5) from the table
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{5-7}{-2-(-4)}=\frac{-2}{-2+4}=\frac{-2}{2}=-1[/tex]Answer: The slope of g (x ) is zero since it is a horizontal line while the slope of f (x) is -1. The slope of g(x) i greater than the slope of f(x).
Please help, will give brainliest!!!!
i am asked to find the range of this, (of the possible third angle)
Answer:
rage=<C-<B
=101°-70°
=30°
1
Pratap Puri rowed 26 miles down a river in 2 hours, but the return trip took him 6; hours. Find the rate Pratap can row
in still water and find the rate of the current. Let x=rate Pratap can row in still water and y = rate of the current.
What is the rate that Pratap rows in still water?
Pratap can row at a rate of
(Type an integer or a decimal.)
in still water.
The speed of current will be "4.5 mph" and the rate Pratap can row in still water will be "8.5 mph".
What does "speed" mean in mathematics?
Speed is what it means. the speed of a change in an object's location in any direction. Speed is defined as the ratio of distance to the amount of time it took to cover that distance. Speed is a scalar quantity because it just has a direction and no magnitude.Given:
Distance "26 miles" in time "2 hours".
Let,
Speed of water = y
Pratap speed when rowing in still water = x
As we know,
Speed = distance/time
then,
x + y = 26/2
x + y = 13
x = 13 - y
In return trip took him time "6.5 hours",
x - y = 26/6.5
x - y = 4
By substituting the value of "x", we get
13 - y - y = 4
13 - 2y = 4
2y = 13 - 4
2y = 9
y = 9/4 = 4.5 mph (Rate of the current)
By substituting the value of "y", we get
x = 13 - a
x = 13 - 4. 5 = 8.5 mph (Pratap can row in still water)
Learn more about speed
brainly.com/question/28224010
#SPJ13
Which equation could be represented by the number line? O A. -5 + 7 = 2 O.B. -3+(-4)= -7 O C. 4+ (-7)=-3 O D.7+(-6) = 1 SURAT E PREVIOUS
C. 4 + (-7) = -3
C. 4 + (-7) = -3 could represent by the number line because no other equation has reflected the lines' displacement of 7 grid from a certain point going to the left which is equivalent to -7.
The rest of the choices is not a possible equation to the line.
A. -5 + 7 = Displacement of 7 Grid to the Right from Point -5
B. -3 - 4 = Displacement of 4 Grid to the Left from Point -3
D. 7 - 6 = Displacement of 6 Grid to the Left from Point 7
Forproblems 5-10, determine what type of symmetry each figure has. If the figure has line symmetry, determine how many lines of symmetry the figure has. If the figure has rotational symmetry, determine the angle of rotational symmetry and if the figure also has point symmetry. (A figure can have both line and rotational symmetries or neither of these symmetries)
7. The figure has line and rotational symmetries. There are 2 lines of symmetry. The angle of symmetry is 180°
8. The figure has no symmetry
How to graph this and how to solve the equation
SOLUTION:
Step 1:
In this question, we are given the following:
Step 2:
The details of the solution are as follows:
The graphs of the two equations:
[tex]\begin{gathered} y=\text{ }\frac{-1}{5}x\text{ - 6} \\ y=\text{ }\frac{3x}{5}-\text{ 2} \end{gathered}[/tex]is as follows:
CONCLUSION:
From the graphs above, we can see that the solution to the graphs is:
[tex](x,\text{ y \rparen = \lparen - 5, - 5\rparen}[/tex]Help meeeeeeeee
ASAP
Deena works at a customer service call center. She fields an average of 7 calls per hour. Employees are encouraged to field more than 280 calls per week. Deena has already fielded 112 calls this week.
How many more hours, x, does Deena need to work this week to reach the weekly goal of fielded calls if she continutes to field an average of 7 calls per hour? Select the inequality that includes the fewest number of hours Deena can work this week and still reach the weekly goal.
A.
x > 24
B.
x > 40
C.
x > 3
D.
x > 31
Allen's goal is to have between 1,500 and 1,600 bottles in his collection. Write and solve a compound inequality to determine the number of weeks it will take Allen to reach his goal.
The compound inequality is 1500 < 300 + 25x < 1600, the solution is 48 < x < 52 and the number of weeks to reach his goal 48 to 52 weeks
How to determine the compound inequality?The given parameters from the question are
Existing collection = 300
Rate = 25 bottles each week
Represent the number of weeks by x and the total number of bottles with y
So, we have the following equation
y = Existing collection + Rate * x
This gives
y = 300 + 25x
Also, we have
The goal is to have between 1,500 and 1,600 bottles in his collection.
This means that
1500 < Total < 1600
So, we have
1500 < 300 + 25x < 1600
Evaluate the like terms
1200 < 25x < 1300
Divide by 25
48 < x < 52
Hence, the number of weeks is 48 to 52 weeks
Read more about inequality at
https://brainly.com/question/2262197
#SPJ1
Possible question
Allen wants to add to his existing collection of 300 bottles. Starting today, he will collect 25 bottles each week.
Allen's goal is to have between 1,500 and 1,600 bottles in his collection. Write and solve a compound inequality to determine the number of weeks it will take Allen to reach his goal.
H.O.T. FOCUS ON HIGHER ORDER THINKING 20. Communicate Mathematical Ideas Explain how to graph the inequality 8≥ y.
Given the inequality:
8 ≥ y
Let's graph the inequality.
To graph the inequality, take the following steps:
Step 1.
Rewrite the inequality for y and slip the inequality.
[tex]y\le8[/tex]Step 2.
Draw a solid horizontal line at y = 8.
Since the y is less than or equal to 8, shade the region below the boundary line.
Thus, we have the graph of the inequality below:
divide the sum of z and 3 by 7
Answer:
4 divide the sum of z and 3 by 7
Step-by-step explanation:
z+3=7
or,z=7-3
or,z=4
A number between 280 and 380 when rounded to the nearest hundred is 45 less than the original number what number is the original number
If the unknown number is an integer between 280 and 349;
When rounded to the nearest hundred, the unknown number is 300.
If the unknown number is an integer from 350-380;
When rounded to the nearest hundred, the unknown number is 400.
If the approximation is 45 less than the original number, thus it cant be in the range of 350-380.
But;
[tex]300+45=345[/tex]When 345 is rounded to the nearest hundred, it is 300.
And the difference between the approximated value and the original value is 45.
Hence, 345 is the original number.
CORRECT ANSWER: 345
sketch the graph of and identify the axis of symmetry
Given the following equation:
[tex]y=(x-1)^2+2[/tex]We will sketch the graph and identify the axis of symmetry.
the given function is a quadratic function with a vertex at (1, 2)
the graph of the function will be as follows:
As shown, the graph of the function has an axis of symmetry at x = 1
So, the answer will be option 3) x = 1
translate the inequality into a sentence. ten subtracted from the product of 9 and a number is at most -17. use x for unknown number
find the measure of each segment
The value of each line segment is found as 26 units.
What is defined as the mid point?A midpoint is a point in the center of a line connecting two points. The two points of reference are the line's endpoints, and the midpoint is located between the two. The midpoint splits the line connecting such two points in half. Furthermore, a line drawn to bisect the line connecting these two points passes through midpoint.For the given question.
The line is given as DE and the mid point of line is D.
Thus,
CD = DE .....eq 1
The value of each term are given as;
CD = 2x + 7
DE = 4(x - 3)
Put the value in equation 1.
2x + 7 = 4(x - 3)
2x + 7 = 4x - 12
Bring variables and constants on the different sides.
4x - 2x = 7 + 12
2x = 19
x = 9.5
Put the value in each side;
CD = 2×9.5 + 7 = 26 unitsDE = 4(9.5 - 3) = 26 unitsThus, the value of each line segment is found as 26 units.
To know more about the mid point, here
https://brainly.com/question/12223533
#SPJ13
The 3D object above is sliced parallel to the base. What shape is formed? triangle octagon rectangle hexagon
When a 3D object is sliced such that the top is parallel to the base, then the top and the base formed same shape.
The shape formed at the base;
It is a six-sided shape. A six-sided polygon is called HEXAGON
What are the solutions to the equation (x − 21)2 = 25?x= x=
SOLUTION:
Case: Quadratics equation
Method:
[tex]\begin{gathered} (x-21)^2=25 \\ TakeSquarerootsOfBothSides \\ x-21=\sqrt{25} \\ x-21=\pm5 \\ x=21\pm5 \\ x=21+5\text{ }or\text{ }x=21-5 \\ x=26\text{ }or\text{ }x=16 \end{gathered}[/tex]Final answer:
x= 16
x= 26
1. Write the value of the digit in the hundreds place and the value of the digit in the tens place in 440. What is the relationship between the values of those two digits? The ___ in the in the hundreds place has a value _____ times as great as the____in the ____ place.
The ___ in the in the hundreds place has a value _____ times as great as the____in the ____ place.
• We have 440
,• 400 + 40
,• Four hundreds + four tens
The relationship between the values of these two digits is that they are the same, but the four in the hundreds place has a value ten times as great as the four in the tens place.
The graph of F(x), shown below, resembles the graph of G(x) = x^2 but it hasbeen stretched somewhat and shifted. Which of the following could be theequation of F(x)?
Solution
The final answer
Option C
kindly asking for help to clarify this question and mathematical problem .
As you can see the options A and B are decreasing, D is constant, therefore, the only increasing relationship is the option C
a) Reflection, then translationb) Rotation, then translationc) Reflection, then rotationd) Rotation, then reflection
We have the following:
Therefore we can conclude that from step 1 to step 2, it is a rotation because it moves on its own axis and from step 2 to 3, it is a reflection
Alan is putting money into a savings account. He starts with $550 in the savings account, and each week he had $70. Let S represent the total amount of money in the savings account in dollars, and let W represent the number of weeks Allen has been adding money. Write an equation relating S to W. Then use this equation to find the total amount of money in the savings account after 18 weeks.
Equation: S = $70·W + $550
Amount of manoey after 18 weeks: $1810
To solve this, we have two variables, the amount of weeks (W) and savings (S)
Each week, $70 dolars are added to the account. Then we can write this as: $70·W.
Now there is an initial amount of $550. Then we must add that mount to the previous calculation: $70·W + $550
This give us the savings on each week. THen THe complete equation is S = $70·W + $550
Now, to know the savings after 18 weeks, we can replace W = 18 and solve:
[tex]\begin{gathered} S=$70\cdot W+$550 \\ S=70\cdot18+550 \\ S=1260+550=1810 \end{gathered}[/tex]Thus, the savings after 18 weeks is $1810
[tex]3 - \frac{1}{2} = 3 + n[/tex]what is nthank you