Answers
The Volume of the composite figure = Volume of the rectangular prism + Volume of the square pyramid = 4,050 ft³.
How to Find the Volume of a Composite Figure?The composite figure shown is composed of a square pyramid and a rectangular prism. To find the volume of the composite figure, find the volume of the square pyramid and the volume of the rectangular prims respectively.
Volume of the square pyramid = 1/3(B)(h), where:
Base area (B) = (l)(w) = (15)(15)
Base area (B) = (l)(w) = 225 ft³.
h = 9 ft
Volume of the square pyramid = 1/3(225)(9)
Volume of the square pyramid = 675 ft³.
Volume of the rectangular prism = (length)(width)(height)
Volume of the rectangular prism = (15)(15)(15)
Volume of the rectangular prism = 3,375 ft³.
The Volume of the composite figure = Volume of the rectangular prism + Volume of the square pyramid
The Volume of the composite figure = 3,375 + 675
The Volume of the composite figure = 4,050 ft³.
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Related Questions
The next number in the series 0,7, 26, 63 is?
Answers
Answer:
124
Step-by-step explanation:
1^3-1=0
2^3-1=7
3^3-1=26
4^3-1=63
5^3-1=124
Hence the next one in the pattern is 124.
0 , 7 , 26 , 63 , … 1 3 − 1 = 0 2 3 − 1 = 7 3 3 − 1 = 26 4 3 − 1 = 63 5 3 − 1 = 124 Hence, the answer is 124.
Alexander Efland has a savings account that earns 5.5% interest compounded daily. On May 5, the amount in the account was $28,214.35. How much interest will the money earn in the next 90 days?
Answers
Using compound interest, it is found that $390.6 was earned in interest in the next 90 days.
What is compound interest?The amount of money earned, in compound interest, after t years, is given by:
[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]
In which:
A(t) is the amount of money after t years. P is the principal(the initial sum of money). r is the interest rate(as a decimal value). n is the number of times that interest is compounded per year.In this problem, the parameters are:
P = 28214.35, r = 0.055, n = 365, t = 3/12 = 0.25.
Hence the amount after 90 days is:
[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]
[tex]A(90) = 28214.35\left(1 + \frac{0.055}{365}\right)^{365 \times 0.25}[/tex]
A(90) = $28,604.95
28604.95 - 28214.35 = $390.6 was earned in interest in the next 90 days.
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cting Polynomials: Practice
Question 1 of 5
Select the correct answer.
Let p(x) be a polynomial as shown below, and let b be an integer.
p(=) = a₁ + a₁ + a₂=² + ... + an In
Which of the following is true regarding the sum and difference of p(x) and b?
O
The sum-and difference of p(x) and b are integers.
The sum and difference of p(x) and b are polynomials.
The sum of p(x) and b is a polynomial, and the difference is an integer.
The sum of plx) and b is an integer, and the difference is a polynomial.
Submit
Reset
Answers
The option that's true regarding the sum and difference of the polynomial p(x) and b is B. The sum and difference of p(x) and b are polynomials.
How to illustrate the information?From the information given, it was stated that p(x) is a polynomial and is given as p(=) = a₁ + a₁ + a₂=² + ... + an.
In this case, it should be noted that the sum and difference of p(x) and b are polynomials.
They can't be integers as the function given is represented as a polynomial.
In conclusion, the correct option is B.
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4. The following set of points belong to a specific function: {(-3,0)(-2,4), (-1,0 ), (0,-6),(1,-8), (2,0),(3,24)} Based on the set of points answers the following questions:
a) What type of function does the set of points produce? Justify your answer.
b) Write an equation for this function based on the set of points that have been given.
Answers
The type of function that these sets of points are known to produce is the cubic function.
What is a cubic function?This is a function that is known to be a polynomial of degree 3. This type of polynomial is one that the coefficients are known to be complex numbers.
This is a cubic function given that the x axis is known to go through these points (-3,0), (-1,0), (2,0).
b. Given the sets of pints that we have, we have the equation
f(x) = a(x+3)(x+1)(x-2)
Such that
f = -2 =
4 = a x 1 x -1 x -4
4 = 4a
a = 1
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Assume that P(E) = 0.471 and P(F) = 0.595. If E and F are independent, find P(E and F)
Answers
The value of the probability P(E and F) is 0.2802
Independent probabilityEvents are known to be independent if the occurrence of one does not affect the other.
Given the following parameters
P (E) =0.471
P(F) = 0.595
If E and F are independent, then;
P(E and F) = P(E)P(F)
P(E and F) = 0.471 * 0.595
P(E and F) = 0.2802
Hence the value of the probability P(E and F) is 0.2802
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A square has a perimeter of 12x+25 units. Which expression represents the side length of a square and units
Answers
Answer:
3x+13 units
Step-by-step explanation:
square perimeter of 12x +52 units
perimeter= 12x +52
12x + 52= 4(sides)
divide both sides by 4 = 12x/4 + 52/4= 3x+13
which give you 3x +13 units
Hi- I need help please to get my HS diploma...did not graduate :(
For the inequality y+4x≤x2+2, where is the graph shaded and is the curve solid or dotted?
Answers
Answer:
B
Step-by-step explanation:
first for the easy one : the curve line is dotted, if the line points are NOT part of the solution. and it is solid, if the points are included.
you know what the curve line indicates ? it indicates the points for which there is equality.
so, if there is a ">=" or "<=" relation, then that includes equality, and the curve is solid.
if there is only a true inequality ("<", ">"), then the curve is dotted, as the equality is not included.
so, I how this is now really clear.
in our case here (I suspect it really looks like this)
y + 4x <= x² + 2
we have a "<=" sign, so, the curve is ..., well ? ... well ? ...
well ? ... well ? ... solid !
and we still treat inequalities as much as possible as regular equalities.
so,
y <= x² - 4x + 2 (after subtracting 4x from both sides).
and now you see it, right ?
all y values that are smaller or equal to the quadratic expression.
SMALLER ! so, BELOW the curve (as the smaller y values are represented by the lower part of the y-axis).
4. A triangle has vertices A(4, 2), B(3, 7), and C(–4, –5).
a) Explain HOW you would draw the median of the triangle from vertex A. Then draw it on the grid provided.
B). Calculate the length of the median from C to AB
Answers
To draw the median of the triangle from vertex A, the mid point of BC must be determined. The median of the vertex A is given at (-1/2, 1). See explanation below.
How you would draw the median of the triangle from vertex A?Recall that B = (3, 7)
and C = (-4, -5).
Note that when you are given coordinates in the format above, B or C = (x, y)Hence the mid point of line BC is point D₁ which is derived as:D₁ [tex][ (\frac{3-4}{2})[/tex] , [tex](\frac{7-5}{2}) ][/tex]hence, the Median of the Vertex A = (-1/2, 1).
Connecting D' and A gives us the median of the vertex A. See attached graph.
What is the length of the median from C to AB?
Recall that
A → (4, 2); and
B → (3, 7)
Hence, the Midpoint will be
[tex][(\frac{4+3}{2} )[/tex], [tex](\frac{2+7}{2} )][/tex]
→ [tex](\frac{7}{2}, \frac{9}{2} )[/tex]
Recall that
C → (-4, 5)
Hence,
[tex]\overline{C D_{2} }[/tex] = [tex]\sqrt{[(-4 -\frac{7}{2} })^{2} + (-5-\frac{9}{2} )^{2} ][/tex]
Simplified, the above becomes
= √(586)/2)
= 24.2074/2
= 12.1037
The length of the Median from C to AB ≈ 12
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Use the function below to find F(3).
)(
F(x)=(1/4)^x
Answers
Answer:
1/64
Step-by-step explanation:
F(3) means to use 3 in place of x in the given equation.
f(x) = (1/4)^x
f(3) = (1/4)^3
Either use exponents rules:
= 1^3 / 4^3
= 1 / 64
or just use the meaning of exponents
= 1/4 × 1/4 × 1/4
= 1/64
what is the value of h(2)
a) -2
b) -1
c) 0
d) 3
Answers
Answer:
(c) 0
Step-by-step explanation:
The answer to this question requires that you read a graph.
How to read a graphFinding the value of h(2) means finding the value of "y" that corresponds to x=2.
The x-axis of this graph is identified by the "x" at the right side, under the arrow at the end of the x-axis. The y-axis is similarly identified by the "y" to the right of the y-axis at the top of the graph.
Each axis is labeled with numbers.
To find the y-value associated with x=2, first find the vertical line labeled 2 on the x-axis. It is 2 grid squares to the right of the y-axis.
Follow this vertical line until you reach the point where it intersects the line segment(s) representing h(x). At one of these, you encounter a solid dot. At the other point of intersection, you see an open circle (empty dot). The open circle means the point is not included in the function graph.
The value of h(2) is the y-value at the point where the vertical line x=2 meets the defined point on the function graph, the solid dot. The y-value is found by following the horizontal grid line to the y-axis, and reading the y-value there.
The point on this graph where the axes cross, the "origin," has no markings indicating the x- and y-values are zero there. You must infer that from the markings that are shown.
Value of h(2)The point on the graph where x=2 lies on the horizontal line y=0. That is ...
h(2) = 0
Identify the underline place 75.733
Answers
Answer: Digit Place Value
7 Tens
5 Ones
.
7 Tenths
3 Hundredths
3 Thousandths
Step-by-step explanation: this should help its not the answer but it's support
In which quadrants do solutions for the inequality y≤x-4 exist?
OI, III, and IV
OI, II, and III
OI and IV
All four quadrants
Answers
Answer:
(a) I, III, and IV
Step-by-step explanation:
We want to identify areas on a graph where the solutions to an inequality might be found.
Boundary lineThe boundary line for the inequality y ≤ 2/3x -4 has a positive slope and a negative y-intercept. That means it must pass through quadrants I, III, and IV.
Solution setQuadrant II is above the line, but the y ≤ () inequality tells you the shading is below the line, where y-values are less than those on the line. There can be no solutions in quadrant II.
Solutions are found in quadrants I, III, and IV.
___
For reference, the second attachments shows the quadrant numbering.
Here are the ages (in years) of 10 professors at a college. 49, 43, 53, 41, 33, 67, 55, 34, 75, 55 What is the percentage of these professors who are younger than 55?
Answers
Answer:
60%
Step-by-step explanation:
There are 6 professors younger than 55 (49, 43, 53, 41, 33, 34).
6/10 = 60%
Kelli swam upstream for some distance in one hour. She then swam downstream the same river for the same distance in only 6 minutes. If the river flows at 5 km/hr, how fast can Kelli swim in still water?
Choose the most logical value for the variable to represent.
Let x = .
3m = 15
9 + 15m = 12m – 1
3m = 18
9 + 6 – 15 = 15m – 12m
Answers
By solving a system of equations, we conclude that Kelli's speed on still water is 6.1km/h
How fast can Kelli swim in still water?Let's say that the speed of Kelli in still water is S. And we know that the speed of the river is 5km/h.
When she swims upstream, her velocity is:
(S - 5km/h)
When she swims downstream, her velocity is:
(S + 5km/h)
With the given information, we can write for a distance D:
(S - 5km/h)*1h = D
(S + 5km/h)*6min = D
First, let's rewrite 6 minutes into hours.
1 hour = 60min
6 min = 6/(60) hours = 0.1 hours
Then the system of equations that we need to solve is:
(S - 5km/h)*1h = D
(S + 5km/h)*0.1h = D
D is the same distance in both cases, then we can write:
(S - 5km/h)*1h = (S + 5km/h)*0.1h
Now we can solve this for S.
S*1h - 5km = S*0.1h + 0.5km
S*1h - S*0.1h = 5km + 0.5km
S*(0.9h) = 5.5km
S = 5.5km/0.9h = 6.1km/h
Kelli's speed on still water is 6.1km/h
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If xm/x5=x7 and (x)=x¹2, then the value of m-r= A. 3 B. 4 C. 8 D. 12 If xm / x5 = x7 and ( x ) = x¹2 , then the value of m - r = A. 3 B. 4 C. 8 D. 12
Answers
The difference between m and r from the given expressions is 8
Indices and exponentsGiven the following exponents
x^m/x^5=x^7
x^m = x^5 * x^7
x^m = x^12
Equate the powers
m = 12
For the expression
(x^r)³ = x^12
x^3r = x^12
3r = 12
r = 4
Take the difference
m - r = 12 - 4
m - r = 8
Hence the difference between m and r is 8
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A bus can reach from Kathmandu to Lumbini in 15 hours when the speed is 40 km per hour. I how many hours it reaches when the speed of the bus is 50 km per hour.
Answers
Answer:
12 hours
Step-by-step explanation:
1) Find the distance using: Distance = speed × time.
Distance = 40 × 15
= 600 km
2) Use the time formula to find the time taken. The formula is Time = distance / speed.
Time = 600 / 50
= 12 hours
The fine schedule for overdue books at the county library is modeled by the values in the table.
Library Fines for Overdue Books
Days overdue
Amount of fine
0
0 ¢
2
5 ¢
4
10 ¢
6
15 ¢
8
20 ¢
10
25 ¢
Which equation best models the fine schedule for overdue books?
Answers
Thus, the required equation is given by Y = 5/2X.
Given data can tabulate is
Days overdue(x) = 0 2 4 6 8 10
Amount of fine(y) = 0 5 10 15 20 25
What is equation?equation is the relationship between variable and represented as is example of polynomial equation.
Since, the as for every value of x, y grows linerely.
Equation can be given as for every 2 step of x, y increase 5 steps
therefore, y = 5/2x
Thus, The required equation is given by y = 5/2x
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What is the measure of 2 if 1 is (4x - 4) and 2 is (4x)?
Answers
The measure of <2 is 92 degrees
How to solve for 2?The complete question is in the attached image
The angles are given as:
<1 = 4x - 4
<2 = 4x
The sum of angles on a straight line is
<1 + <2 = 180
So, we have:
4x - 4 + 4x = 180
Evaluate the like terms
8x = 184
Divide by 8
x = 23
Substitute x = 23 in <2 = 4x
<2 = 4 * 23
Evaluate
<2 = 92
Hence, the measure of <2 is 92 degrees
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John and 2 friends are going out for pizza for lunch. They split one pizza and 3 large drinks. The pizza cost $14.00. After using a $7.00 gift certificate, they spend a total of $12.10. Write an equation to model this situation, and find the cost of one large drink.
Answers
Answer:
$2.55
Step-by-step explanation:
2d + $14.00 – $7.00 = $12.10; $2.55
Solve the following equation:
30= |- 4y + 2|
Answers
Suppose [tex]-4y+2\ge0[/tex]. Then by definition of absolute value,
[tex]|-4y+2| = -4y+2 \implies 30 = -4y+2 \implies -4y = 28 \implies \boxed{y=-7}[/tex]
On the other hand, suppose [tex]-4y+2<0[/tex]. Then
[tex]|-4y+2| = -(-4y+2) \implies 30 = 4y - 2 \implies 4y = 32 \implies \boxed{y=8}[/tex]
Recall the definition,
[tex]|x| = \begin{cases} x & \text{if } x \ge 0 \\ -x & \text{if } x < 0 \end{cases}[/tex]
The doctor tells Evelyn that she needs to exercise enough to burn at least 700 calories each day. She prefers practicing yoga or jogging. While practicing yoga she burns 5 calories per minute, and while jogging she burns 8 calories per minute. Let x be the number of minutes she spend practicing yoga and let y be the number of minutes she spends jogging. Write an inequality that models this situation.
Answers
The inequality that can be used to model Evelyn situation is
x + y = 60
x + y = 605x + 8y ≥ 700
Inequalityx = number of minutes she spend practicing yogay = number of minutes she spends joggingCalories burnt practicing yoga = 5Calories burnt jogging = 8The inequality
x + y = 60
5x + 8y ≥ 700
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Analyze the diagram below and complete the instructions that follow.
Find m
A. 15°
B. 30°
C. 75°
D. 150°
Please select the best answer from the choices provided
A
B
C
D
Answers
Answer:
I believe the answer to be c 75°
Step-by-step explanation:
a 4 sided shape is 360 total degrees
The Customer Service Center in a large New York department store has determined that the amount of time spent with a customer about a complaint is normally distributed, with a mean of 8.9 minutes and a standard deviation of 2.8 minutes. What is the probability that for a randomly chosen customer with a complaint, the amount of time spent resolving the complaint will be as follows. (Round your answers to four decimal places.)
(a) less than 10 minutes
(b) longer than 5 minutes
(c) between 8 and 15 minutes
Answers
Using the normal distribution, the probabilities are given as follows:
a) 0.6517 = 65.17%
b) 0.0823 = 8.23%.
c) 0.6109 = 61.09%.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.The mean and the standard deviation are given, respectively, by:
[tex]\mu = 8.9, \sigma = 2.8[/tex]
Item a:
The probability is the p-value of Z when X = 10, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{10 - 8.9}{2.8}[/tex]
Z = 0.39
Z = 0.39 has a p-value of 0.6517.
0.6517 = 65.17% probability that the time is less than 10 minutes.
Item b:
The probability is the one subtracted by the p-value of Z when X = 5, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{5 - 8.9}{2.8}[/tex]
Z = -1.39
Z = -1.39 has a p-value of 0.0823.
0.0823 = 8.23% probability that the time is more than 5 minutes.
Item c:
The probability is the p-value of Z when X = 15 subtracted by the p-value of Z when X = 8, hence:
X = 15:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{15 - 8.9}{2.8}[/tex]
Z = 2.18
Z = 2.18 has a p-value of 0.9854.
X = 8:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{8 - 8.9}{2.8}[/tex]
Z = -0.32
Z = -0.32 has a p-value of 0.3745.
0.9854 - 0.3745 = 0.6109 = 61.09%.
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Solve for x
x - 20 + 2x = 35
Answers
[tex] \sf{\red{ANSWER \: \: :}}[/tex]
x = 18 1/3
[tex] \sf{\purple{EXPLANATION \: \: :}}[/tex]
x - 20 + 2x = 35
- 20 + 3x = 35
3x = 35 + 20
3x = 55
x = 55/3
x = 18 1/3
Find the sum of the measures of the interior angles of the figure.
Answers
Answer:
[tex]\huge\boxed{\sf 900}[/tex]
Step-by-step explanation:
Sides of the figure = n = 7
Formula for measuring the interior angles of a polygon:(n - 2)×180
Where n is the number of sides in the polygon
So,
Measure of interior angles in the figure:= (n - 2) × 180
= (7 - 2) × 180
= 5 × 180
= 900
[tex]\rule[225]{225}{2}[/tex]
Answer: 720°
Step-by-step explanation:
- Assuming this is a regular hexagon, all the sides are equal and all the angles are equal
- One of the properties of a regular hexagon is that the sum of all the interior angles is 720°
- Since the sum of all the interior angles is 720°, this means each interior angle is 120°
hope this helps :)
write the equation of the line that is parallel to the y-axis and passes through the point (7,0)
Answers
The equation of the line is x = 7 which is parallel to the y-axis and passes through the point (7,0)
What is a straight line?A straight line is a combination of endless points joined on both sides of the point.
The slope 'm' of any straight line is given by:
[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]
We have:
The line that is parallel to the y-axis and passes through the point (7,0)
As we know the line equation:
Parallel to the y-axis
x = c
Passes through the point (7,0)
x = 7
Thus, the equation of the line is x = 7 which is parallel to the y-axis and passes through the point (7,0)
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Consider the relationship 3r+8t=3
Answers
The function r =f(t) is f(t) = 1 - 8t/3
How to evaluate the function?The function is given as:
3r + 8t = 3
Make r the subject
3r = 3 - 8t
Divide by 3
r = 1 - 8t/3
This means that:
f(t) = 1 - 8t/3
To calculate f(-3), we have:
f(3) = 1 - 8 * 3/3
Evaluate
f(3) = -7
Also, we have:
1 - 8t/3 = 2
Add 2 to both sides
-8t/3 = 3
Solve for t
t = -9/8
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Complete question
Consider the relationship 3r+8t=3
Write the relationship as a function r = f(t)
Evalute f(-3)
Solve for f(t) = 2
PLEASE FIND THE COORDINATES!!!
Answers
The graph of the given equation is given below.
We have given the equation of the line is f(x)=-1/5x+4f(x)
We have to determine the coordination.
What are the coordinates of the line?line coordinates are used to specify the position of a line just as point coordinates (or simply coordinates) are used to specify the position of a point.
Therefore we get f(x)=y
y=-1/5x+4....(1)
Plug x=0 in (1) then y=4
Plug x=5 in (1) then
y=-1/5(5)+4
=-1+4
=3
Therefore we get the coordinates (0,4) and (5,3)
Therefore the graph is given below,
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In 2011, the maximum amount that you could have contributed to your RRSP (Registered Retirement Savings Plan) was
the lesser of $22,450 or 18% of your earned income from the previous year. How much income do you need to claim a
$22,450 contribution in 2011?
Answers
Using proportions, it is found that you need an income of $124,722.22 to claim a $22,450 contribution in 2011.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
To claim a $22,450 contribution in 2011, this amount has to be 18% of your income, hence:
0.18x = 22450
x = 22450/0.18
x = $124,722.22.
You need an income of $124,722.22 to claim a $22,450 contribution in 2011.
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Which of the following is a valid probability distribution? Probability distribution A is shown. The probabilities of 1, 2, 3, 4, 5 and 6 are all 0.2. Probability distribution B is shown. The probability of 1 is 0.1; 2 is 0.2; 3 is 0.3; 4 is 0.3; 5 is 0.2; 6 is 0.1. Probability distribution C is shown. The probability of 1 is 0.1; 2 is 0.2; 3 is 0.4; 5 is 0.1; 6 is 0.1. Probability distribution D is shown. The probability of 1 is 0.2; 2 is 0.1; 3 is 0.1; 4 is 0.5; 5 is 0.1.
Answers
Considering the given probability distribution, distribution D is valid.
When a probability distribution is valid?A probability distribution is valid if:
There are no negative probabilities.,The sum of all probabilities is of 1.In this problem:
For distribution A, the sum is of 1.2, hence it is not valid.For distribution B, the sum is of 1.2, hence it is not valid.For distribution C, the sum is of 0.9, hence it is not valid.For distribution D, the sum is of 1, hence it is valid.More can be learned about probability distributions at https://brainly.com/question/23670007
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