The large solid below is made from small cubes. Each has a side length of 1/5. Answer the questions below. Write your answers in simplest form. (c) What is the volume of the large solid?
Answers
The volume of the large solid is equal to 8/25 cm³.
How to calculate the volume of a cube?In Mathematics, the volume of a cube can be calculated by using the following formula:
V = m³
Where:
V represents the volume of a cube.m is the side lengths of a cube.By substituting the given points into the formula for the volume of a cube, we have the following;
Volume of cube, V = m³
Volume of cube, V = (1/5)³
Volume of cube, V = 1/125 cm³.
For the volume of the large solid, we have:
Volume of large solid = 5 × 2 × 4 × 1/125
Volume of large solid = 8/25 cm³.
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
Related Questions
Lesson 6.04
Comparing Data
Questions/Main Idea Notes
List the steps to compare two
representations of data
Example: use an example to show how to
compare data in two-line plots
Example: use an example to show how to
compare data displayed in a box plot
Example: use an example to show how to
compare data displayed in histograms
List the steps to create a back-to-back
stem-and-leaf plot
Include any examples here from the
lesson, that you would like.
Vocabulary Review:
Measures of center
Measures of variability
spread
Answers
Compare the data by observing the shape, center, and spread of the data in both representations.
1. Understand the data: Before comparing two representations of data, it is important to understand what the data represents and its context.
2. Identify the type of data: Identify the type of data represented in each representation to ensure the data is comparable.
3. Plot the data: Plot the data in each representation, such as a line plot, box plot, or histogram.
4. Compare the data: Compare the data by looking at the shape, center, and spread of the data in both representations.
Example: To compare data in two-line plots, plot the data as two lines on the same graph. Observe the difference in the shape of the two lines, the difference in center (the average value of the data), and the difference in spread (the range of the data).
Example: To compare data displayed in a box plot, plot the data as two box plots side by side. Observe the difference in the shape of the two box plots, the difference in center (the median value of the data), and the difference in spread (the interquartile range of the data).
Example: To compare data displayed in histograms, plot the data as two histograms side by side. Observe the difference in the shape of the two histograms, the difference in center (the mean value of the data), and the difference in spread (the standard deviation of the data).
List the steps to create a back-to-back stem-and-leaf plot:
1. Organize the data: Organize the data into two sets of numerical data.
2. Create stems: Create a stem for each set of data by dividing the values by a common multiple.
3. Create leaves: Create leaves for each set of data by recording the remainder of the original values after dividing them by the common multiple.
4. Plot the data: Arrange the stems and leaves into a back-to-back stem-and-leaf plot.
5. Compare the data: Compare the data by observing the shape, center, and spread of the data in both representations.
Therefore, compare the data by observing the shape, center, and spread of the data in both representations.
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Consider the parabola given by the equation:
f
(
x
)
=
−
2
x
2
−
8
x
+
14
Find the following for this parabola:
A) The value of
f
(
−
5
)
:
B) The vertex = (
,
)
C) The
y
intercept is the point (0,
)
D) Find the two values of
x
that make
f
(
x
)
=
0
. Round your answers to two decimal places. Write the values as a list, separated by commas:
x
=
Answers
Answer:
Sure, here are the answers to your questions:
**A) The value of $f(-5)$ is $-2$.**
To find the value of $f(-5)$, we can simply substitute $x=-5$ into the equation $f(x)=-2x^2-8x+14$. This gives us:
$$f(-5)=-2(-5)^2-8(-5)+14=-2(25)+40+14=-50+54=4$$
**B) The vertex of the parabola is $(2,6)$.**
To find the vertex of the parabola, we can complete the square. This involves adding and subtracting $\left(\dfrac{{b}}{2}\right)^2$ to both sides of the equation, where $b$ is the coefficient of the $x$ term. In this case, $b=-8$, so we have:
$$\begin{aligned}f(x)&=-2x^2-8x+14\\\\ f(x)+20&=-2x^2-8x+14+20\\\\ f(x)+20&=-2(x^2+4x)\\\\ f(x)+20&=-2(x^2+4x+4)\\\\ f(x)+20&=-2(x+2)^2\end{aligned}$$
Now, if we subtract 20 from both sides, we get the equation of the parabola in vertex form:
$$f(x)=-2(x+2)^2-20$$
The vertex of a parabola in vertex form is always the point $(h,k)$, where $h$ is the coefficient of the $x$ term and $k$ is the constant term. In this case, $h=-2$ and $k=-20$, so the vertex of the parabola is $(-2,-20)$. We can also see this by graphing the parabola.
[Image of a parabola with vertex at (-2, -20)]
**C) The $y$-intercept is the point $(0,14)$.**
The $y$-intercept of a parabola is the point where the parabola crosses the $y$-axis. This happens when $x=0$, so we can simply substitute $x=0$ into the equation $f(x)=-2x^2-8x+14$ to find the $y$-intercept:
$$f(0)=-2(0)^2-8(0)+14=14$$
Therefore, the $y$-intercept is the point $(0,14)$.
**D) The two values of $x$ that make $f(x)=0$ are $2.5$ and $-3.5$.**
To find the values of $x$ that make $f(x)=0$, we can set the equation $f(x)=-2x^2-8x+14$ equal to zero and solve for $x$. This gives us:
$$-2x^2-8x+14=0$$
We can factor the left-hand side of the equation as follows:
$$-2(x-2)(x-3)=0$$
This means that either $x-2=0$ or $x-3=0$. Solving for $x$ in each case gives us the following values:
$$x=2\text{ or }x=3$$
However, we need to round our answers to two decimal places. To do this, we can use the calculator. Rounding $x=2$ and $x=3$ to two decimal places gives us the following values:
$$x=2.5\text{ and }x=-3.5$$
Therefore, the two values of $x$ that make $f(x)=0$ are $2.5$ and $-3.5$.
the permieter of object A is 94cm. What the value of x
Answers
The value of x if the object is a square with a perimeter of 94 cm is 23.5 cm
Calculating the value of xFrom the question, we have the following parameters that can be used in our computation:
The permieter of object A is 94cm
Assuming the object is a square
So, we have
4x = 94
Divide both sides by 4
So, we have
x = 94/4
Evaluate
x = 23.5
Hence, the value of x is 23.5cm
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10 points. please answer
Answers
The measure of the angles for the similar triangles are ∠G = 105°; ∠H = 55° and ∠I = 20°
What are similar triangles?Two triangles are said to be similar if the ration of their corresponding sides are in the same proportion. Also, all their corresponding angles are congruent with each other.
From the diagram shown:
∠X + ∠Y + ∠Z = 180° (sum of angles in a triangle)
20 + 105 + ∠Z = 180
∠Z = 55°
Since triangle XYZ and triangle GHI are similar, hence:
∠X = ∠G = 105°; ∠Z = ∠H = 55° and ∠Y = ∠I = 20°
The measure of the angles are ∠G = 105°; ∠H = 55° and ∠I = 20°
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Evaluate 6×[2−(4)×(–8)]
Answers
Answer:204
Step-by-step explanation:
pemdas
6x[2--32]=6×[34]=204
How many solutions does this equation have 10+ 6k6k
Answers
Answer:
10 + 36k²
Step-by-step explanation:
considering that it is not an equation but an algebraic expression we solve it like this
10 + 6k6k =
10 + 36k²
One month Eric rented 3 movies and 5 video games for a total of $34. The next month he rented 9 movies and 7 video games for a total of $56. Find the rental
cost for each movie and each video game.
Rental cost for each movie:
Rental cost for each video game:
G
O
G
Answers
movies 1.75 each
games 5.75 each
In an online game, you receive –3 points for every banana your character slips on during a race. The total points from slipping on bananas during one race were at most –27. When the character slips, it takes 2 seconds for him to resume the race. Write an inequality to find the least number of bananas your character slipped on.
Answers
An inequality to find the least number of bananas your character slipped on: -3x ≤ -27
And the least amount of race time character took to slip on bananas = 18 seconds.
Let us assume that x represents the number of bananas your character slipped on.
Here, based on the informtaion we get an inequality to find the least number of bananas your character slipped on -3x ≤ -27
We solve this inequality to find the least number of seconds of race time.
-3x ≤ -27
⇒ x ≥ 9
When the character slips, it takes 2 seconds for him to resume the race.
Therefore, the least amount of race time your character took to slip on bananas would be,
9 × 2 = 18 seconds
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The complete question is:
In an online game, you receive -3 points for every banana your character slips on during a race. The total points from slipping on bananas during one race were at most -27. When the character slips, it takes 2 seconds for him to resume the race. Write and solve an inequality to find the least number of bananas your character slipped on. At least how many seconds of race time
-2 square root of 2r +5=6
Answers
Evaluating the square root expression -2√(2r + 5) = 6 gives r = 2
Evaluating the square root expressionFrom the question, we have the following expression that can be used in our computation:
-2 square root of 2r +5=6
Express properly
So, we have
-2√(2r + 5) = 6
Divide by -2
√(2r + 5) = -3
So, we have
2r + 5 = 9
Subtract 5 from both sides
2r = 4
Divide
r = 2
Hence, the solution is 2
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Abi takes out a loan that gathers compound interest. The table below shows the value of the loan over time. a) What is the rate of interest per annum? Give your answer as a percentage to 1 d.p. b) Work out the value of the loan 10 years after it starts. Give your answer in pounds (£) to the nearest 1p. Start After 1 year After 2 years £2500.00 £2645.00 £2798.41
Answers
Using the table, we can see that the loan increases by a factor of 1.058 after 1 year and by a factor of 1.058/1.045 = 1.0124 after 2 years. Thus, we have:
1.058 = (1 + r/n)^(n*1)
1.0124 = (1 + r/n)^(n*2)
Dividing the second equation by the first, we get:
1.0124/1.058 = (1 + r/n)^(n*1)
Taking the nth root of both sides, we get:
(1 + r/n) = (1.0124/1.058)^(1/n)
Solving for r, we get:
r = n * [(1.0124/1.058)^(1/n) - 1]
We don't know the value of n, but we can make an educated guess that it's either 1 or 2, since the loan is increasing by roughly 5.8% per year. If we try n = 1, we get:
r = 1 * [(1.0124/1.058)^(1/1) - 1] = -0.0427
This is clearly not the correct answer, since the interest rate cannot be negative. If we try n = 2, we get:
r = 2 * [(1.0124/1.058)^(1/2) - 1] = 0.0574
This is a reasonable answer, since it's close to the observed increase in the loan value of 5.8% per year. Therefore, the rate of interest per annum is 5.7% to 1 d.p.
(b) Using the formula for compound interest, we can find the value of the loan 10 years after it starts:
A = P * (1 + r/n)^(n*t) = 2500 * (1 + 0.0574/1)^(1*10) = £4,745.60 (to the nearest 1p
Answer:
25000
Step-by-step explanation:
PLEASE HELP (WILL GIVE BRAINLIEST)
Answers
Answer:
V = 3 × 2 × 6 = 36 cubic centimeters
Help I need to finish this before midnight
Answers
The correct statement regarding the graph is given as follows:
C. The graph is non-proportional and has the equation y = -2x + 18.
How to define a linear function?The slope-intercept representation of a linear function is given by the equation presented as follows:
y = mx + b
The coefficients of the function and their meaning are described as follows:
m is the slope of the function, representing the change in the output variable y when the input variable x is increased by one.b is the y-intercept of the function, which is the initial value of the function, i.e., the numeric value of the function when the input variable x assumes a value of 0. On a graph, it is the value of y when the graph of the function crosses the y-axis.The slope and the intercept of the line in this problem are given as follows:
m = -2, as when x increases by 2, y decays by 4, m = -4/2 = -2.b = 18, as when x = 0, y = 18.Thus the equation is:
y = -2x + 18.
The equation is non-proportional, as it has an intercept which is different of zero.
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The wind speed near the center of a tornado is represented by the equation S = 93 log d +65, where d is the distance, in
miles, that the tornado travels and S is the wind speed, in miles per hour.
If the wind speed was 130 miles per hour, which equation could be used to find the distance that the tornado traveled?
Select the correct answer below:
Answers
The equation that could be used to find the distance that the tornado traveled is: log d = 0.7
How to change the subject of the equation?We are told that The wind speed near the center of a tornado is represented by the equation S = 93 log d + 65,
where:
d is the distance, in miles, that the tornado travels.
S is the wind speed, in miles per hour.
When S = 130, we have:
130 = 93 log d + 65
93 log d = 130 - 65
93 log d = 65
log d = 65/93
log d = 0.7
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Solve equation by using the quadratic formula. 15 x squared + 13 x = 0
Answers
Answer:
x= -13/15
Step-by-step explanation:
x(15x +13)
x =0
15x + 13 = 0
15x = -13
x =-13/15
Use the diagram of the right triangle above and round your answer to the nearest hundredth.
If Measure of angle B = 60 degreesº and a = 10 meters, find b.
a.17.32 m
b6.93 m
c.14 m
d.9.99 m
Answers
The calculated value of the side length b is 17.32 meters
Finding the side length bFrom the question, we have the following parameters that can be used in our computation:
Angle B = 60 degrees
Length a = 10 meters
The side length b is calculated as
tan(60) = b/a
So, we have
tan(60) = b/10
Make b the subject
b = 10 * tan(60)
Evaluate
b = 17.32
Hence, the side length b is 17.32 meters
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Look at the picture
Answers
Answer: 84 in
Step-by-step explanation:
A = h(b)/2
h= 7
b= 24
24x7= 168
168/2= 84
84 inch !!!!!!!!!!!!!!!!
Complete the sentences to compare the intervals for which each function is decreasing
Answers
The intervals for which each function is decreasing are f(x) = [0, ∝) and g(x) = (-∝, ∝)
Completing the sentences to compare the intervalsFrom the question, we have the following parameters that can be used in our computation:
The functions f(x) and g(x)
From the graph of the functions, we can see that
The function g(x) decreases all through because it is a linear function with a negative slopeThe function f(x) decreases at [0, ∝) because it a quadratic function with a maximum vertex at (0, 5)Read more about functions at
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The growth of an investment is given by the formula A = 1200 × 1.3 n , where A is the amount the investment is worth and n is the number of years. Estimate how many days it would take for the investment to be valued at £3,800.
Answers
The number of days it would take for the investment to be valued at £3,800 is 4.4 days
Estimate the number of days it would takeFrom the question, we have the following parameters that can be used in our computation:
A = 1200 × 1.3^n
For the investment to be valued at £3,800, the value of A would be
A = 3800
Substitute the known values in the above equation, so, we have the following representation
1200 × 1.3^n = 3800
Divide both sides by 1200
1.3^n = 3800/1200
So, we have
n = ln(3800/1200)/ln(1.3)
Evaluate the quotient
n = 4.4
Hence, it would take 4.4 days
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The vertices of a quadrilateral are listed below.
Answers
The strongest classification of the quadrilateral with the given vertices is rhombus.
The vertices of the quadrilateral is given as,
E(5, 4), F(9, 2), G(5, 0) and H(1, 2).
Find the adjacent sides EF and FG whether they are equal.
Using the distance formula,
EF = √(9 - 5)² + (2 - 4)² = √(16 + 4) = √20
FG = √(5 - 9)² + (0 - 2)² = √(16 + 4) = √20
Adjacent sides are equal.
So they are either square or rhombus.
Find the lengths of the diagonals whether they are equal.
EG = √(5 - 5)² + (0 - 4)² = √(0 + 16) = 4
FH = √(1 - 9)² + (2 - 2)² = √(64 + 0) = 8
Diagonals are not equal.
So it is a rhombus.
Hence the quadrilateral is a rhombus.
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Abbie needs to cover square pyramids with fabric. The dimensions of each pyramid are shown in the table. If the fabric costs $0.001 per square millimeter, what is the surface area and cost to cover each pyramid, rounded to the nearest whole cent?
PLEASE HELP !!!
Answers
The surface area of each square pyramid, we used the formula Surface Area = Base Area + 4 x (1/2 x Base x Height of Face) is 1049.2, 1285.8 and 2100mm². The cost to cover each pyramid was $1.05, $1.29 and $2.10
To calculate the surface area of each pyramid, we need to use the formula
Surface Area = Base x Height of face + 2 x ((Base/2) x Slant Height)
For the small pyramid, we have
Surface Area = 20 x 25 + 2 x ((20/2) x 26.46)
Surface Area = 500 + 2 x 10 x 26.46
Surface Area = 1049.2 mm²
Cost to cover the small pyramid
Cost = Surface Area x 0.001
Cost = 1049.2 x 0.001
Cost = $1.05
For the medium pyramid, we have
Surface Area = 20 x 40 + 2 x ((20/2) x 42.43)
Surface Area = 800 + 2 x 10 x 42.43
Surface Area = 1285.8 mm²
Cost to cover the medium pyramid
Cost = Surface Area x 0.001
Cost = 1285.8 x 0.001
Cost = $1.29
For the large pyramid, we have
Surface Area = 30 x 40 + 2 x ((30/2) x 50)
Surface Area = 1200 + 2 x 15 x 50
Surface Area = 2100 mm²
Cost to cover the large pyramid
Cost = Surface Area x 0.001
Cost = 2100 x 0.001
Cost = $2.10
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can u please help me with number 3 the graph
Answers
This prompt has to do with the analysis of random outcomes. See the attached tables and graphs accordingly.
What are random outcomes?An exhaustive depiction of all possible marble combinations that may arise out of a chance experiment involving two random selections has been depicted in this table.
The table enlists five different-colored marbles available in a bag and elaborates its varying conclusions based on two distinct selections.
The columns indicate colors, whereas each result depicts two correlated choices made during an experiment's progression to illustrate randomness accurately.
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Convert 135° from degrees to radians.
Answers
Answer: 2.35619
Step-by-step explanation: Hope this helps! :)
The Jackson Hole Aerial Tram takes passengers from an elevation of 6311 ft to an elevation of 10,450 ft up the slope of Rendezvous Mountain in Wyoming. If the tram runs on a cable measuring 12,463 ft in length, what is the angle of incline of the tram to he nearest tenth of a degree?
Answers
The angle of incline of the tram is 19.4 degree.
According to the question:
h=(10450-6311)ft
= 4139 ft
We know that, sinθ=Opposite/Hypotenuse
So, sinθ=h/12463
sinθ= 4139/12463
sinθ= 0.3321
Solve the trigonometric equation by isolating the function and then taking the inverse. Use the period to find the full set of all solutions.
θ=19.39
θ≈19.4°
Therefore, the angle of incline of the tram is 19.4 degree.
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6. Teachers' Salaries New York and Massachusetts lead the list of average teacher's
salaries. The New York average is $76,409 while teachers in Massachusetts make an
average annual salary of $73,195. Random samples of 45 teachers from each state
yielded the following.
Answers
Step-by-step explanation:
Need help now please!
Answers
The exact value of tan2θ in simplest radical form is -21/√7.
What is the value of tan2θ?The value of tan2θ at the given quadrant is calculated as follows;
From Pythagorean identity, we know that;
sin² θ + cos² θ = 1
cos² θ is calculated as follows;
(3/4)² + cos² θ = 1
9/16 + cos² θ = 1
cos² θ = 1 - 9/16
cos² θ = 7/16
cos θ = √(7/16)
The value of tan θ is calculated as follows;
tan θ = sin θ / cos θ = 3/4 x 4/√7 = 3/√7
Now, we will find tan 2θ;
tan 2θ = 2tan θ / (1 - tan² θ)
tan 2θ = 2(3/√7) / (1 - (3/√7)²)
tan 2θ = (6/√7) / (-2/7)
tan 2θ = -21/√7
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perimeter of a tabe is 228 inches and the length is 18 inches which is more than twice the width. How do I find the length and width of the worktable
Answers
The length of the worktable is 82 inches and the width is 32 inches.
To find the length and width of the worktable, we can use a system of equations. Let's denote the width of the table by w.
Since the length is 18 inches more than twice the width, we can write:
Length = 2w + 18
The perimeter of the table is the sum of all its sides, which in this case is the sum of the length and the width, each multiplied by 2:
Perimeter = 2(length + width)
Perimeter = 2(2w + 18 + w)
Perimeter = 2(3w + 18)
Perimeter = 6w + 36
We know that the perimeter is 228 inches, so we can set up an equation:
6w + 36 = 228
Solving for w, we get:
w = 32
Now that we know the width, we can use the equation for the length to find:
Length = 2w + 18
Length = 2(32) + 18
Length = 82
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Rectangle ABCD is shown on the coordinate plane below. What is the perimeter of rectangle ABCD? If necessary, round your answer to the nearest tenth.
Answers
The area of the given rectangle is 34 squared units.
How to find the area of the rectangleDetermining the area of a rectangle with the coordinates
A(-5, 3), B(3, 5), C(4, 1), and D(-4, -1)can be achieved through using the distance formula to calculate the magnitude of its sides and then applying the formula for the area pf rectangle we find the area.
Length of Side AB:
= square root of [(3 - (-5))^2 + (5 - 3)^2]
= square root of 68
Length of Side BC:
= square root of [ (4-3)^2 + (1 - 5)^2]
= square root of 17
Area of this rectangle
= side AB × Side BC
= square root[68] x square root[17]
= square root of [68 times 17]
= square root of 1156
= 34 Square Units
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Round to the nearest whole number, then find the sum. 15.43 + 12.85 + 21.3 = ___ pls i will give 60 points!!!!!!!!!!
Answers
Answer:
15.43 + 12.85 + 21.3 = 49.58
Rounding to the nearest whole number, the sum is 50.
Step-by-step explanation:
Answer:
15.43 + 12.85 + 21.3 = 49.58
Step-by-step explanation:
I need help with these problems??
Answers
The value of the variable x;
1. x = -4, BC = 4x + 3 = -13
2. x = 72 degrees
3. x = 5/2, SV = 6.5, ZU = 6.4
4. x = 4
5. x = 5
6. x = 3
What are tangent lines?Tangent are simply described as any straight line that is drawn from the curve at a point but never reaches the center of the circle.
It is also important to note that tangent segments of a circle are equal.
From the information given, we have that;
1. The tangents are;
4x + 1 = 5x - 3
collect the like terms
-x = 4
x = -4
Then BC = 4x + 3 = -13
2. 2x - 1 = 143
collect the like terms
2x = 143 + 1
2x = 144
x = 72 degrees
3. 3x - 1 = 5x - 6
collect the like terms
-2x = -5
x = 5/2
Then,
SZ = ZU = 3(5/2) - 1 = 15/2 - 1 = 6.5
4. 5x² + 10 = x² + 74
collect the like terms
4x² = 64
x² = 16
x = 4
5. 2x + 7 = 5x - 8
collect the like terms
-3x = -15
divide the values
x = 5
6. 3x - 1.2 = 2x + 1.8
x = 3
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Katherine is going to invest in an account paying an interest rate of 5.8%
compounded monthly. How much would Katherine need to invest, to the nearest ten
dollars, for the value of the account to reach $960 in 16 years?
Answers
The amount that Katherine, who is going to invest in an account paying an interest rate of 5.8% compounded monthly, would need to invest, to the nearest ten dollars for the future value of the account for the account to reach $960 in 26 years, is $380 (present value).
What is the difference between the future value and the present value?The future value is the present value compounded at an interest rate.
The present value is the future value discounted at an interest rate.
The future value and the present value can be computed using an online finance calculator.
N (# of periods) = 192 months (16 years x 12)
I/Y (Interest per year) = 5.8%
PMT (Periodic Payment) = $0
FV (Future Value) = $960
Results:
Present Value (PV) = $380.38
Total Interest = $579.62
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