Answer: Based on the problem statement, we can define a recurrence relation as follows:
t(n) = t(n-1) + t(n-2) + t(n-4)
This means that the number of ways to construct a tower of height n cm can be obtained by considering the possible heights of the bottom block in the tower. If the bottom block has height 1 cm, then the remaining blocks make up a tower of height (n-1) cm, for which there are t(n-1) ways to construct it. If the bottom block has height 2 cm, then the remaining blocks make up a tower of height (n-2) cm, for which there are t(n-2) ways to construct it. If the bottom block has height 4 cm, then the remaining blocks make up a tower of height (n-4) cm, for which there are t(n-4) ways to construct it.
Since we are assuming an unlimited supply of blocks of each size, we can use these blocks repeatedly to construct towers of different heights. Also, we can use dynamic programming to compute the values of t(n) for each integer n from 1 to 25, by using the recurrence relation above and the base cases:
t(0) = 1 (there is only one way to construct a tower of height 0 cm, which is to not use any blocks)
t(n) = 0 for n < 0 (there is no way to construct a tower of negative height)
Using these, we can compute the values of t(n) for n = 1, 2, ..., 25, as follows:
t(0) = 1
t(1) = t(0) = 1
t(2) = t(1) + t(0) = 2
t(3) = t(2) + t(1) = 3
t(4) = t(3) + t(2) + t(0) = 6
t(5) = t(4) + t(3) + t(1) = 10
t(6) = t(5) + t(4) + t(2) = 19
t(7) = t(6) + t(5) + t(3) = 32
t(8) = t(7) + t(6) + t(4) = 61
t(9) = t(8) + t(7) + t(5) = 104
t(10) = t(9) + t(8) + t(6) = 195
t(11) = t(10) + t(9) + t(7) = 332
t(12) = t(11) + t(10) + t(8) = 626
t(13) = t(12) + t(11) + t(9) = 1065
t(14) = t(13) + t(12) + t(10) = 2002
t(15) = t(14) + t(13) + t(11) = 3405
t(16) = t(15) + t(14) + t(12) = 6403
t(17) = t(16) + t(15) + t(13) = 10946
t(18) = t(17) + t(16) + t(14) = 20618
t(19) = t(18) + t(17) + t(15) = 350
Step-by-step explanation:
Which of the following graphs is described by the function below?
[tex]y=x^{2} -6x-7[/tex]
A.) Graph A
B.) Graph B
C.) Graph C
D.) Graph D
The given function [tex]y=x^2 - 6x - 7[/tex] describes the graph A.
What is function?
In mathematics, a function is a relation between a set of inputs (the domain) and a set of possible outputs (the codomain) with the property that each input is related to exactly one output.
We can solve this Function by substituting the 0 for Y.
To find the value of x when y is equal to 0, we can substitute 0 for y in the equation and solve for x:
[tex]0 = x^2 - 6x - 7[/tex]
To solve for x, we can use the quadratic formula:
x = (-b ± [tex]\sqrt{(b^2 - 4ac)}[/tex]) / 2a
In this case, a = 1, b = -6, and c = -7. Substituting these values into the formula, we get:
x = (-(-6) ± [tex]\sqrt {((-6)^2 - 4(1)(-7)}[/tex])) / 2(1)
Simplifying:
x = (6 ± [tex]\sqrt{64}[/tex]) / 2
x = (6 ± 8) / 2
x = 7 or x = -1
Therefore, when y is equal to 0, x can be either 7 or -1.
Therefore the given function describes the graph A.
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Use the given information to prove the following theorem.
Answer: two right-angled triangle, equilateral triangle
Step-by-step explanation:
It is a combination of two right-angled triangle or it is an equilateral triangle.
Explanation:
You want to prove a point P on the perpendicular bisector of segment YZ is equidistant from Y and Z.
Statement . . . . Reason1. PX is the perpendicular bisector of YZ . . . . given
2. angles at X are right angles . . . . definition of perpendicular
3. YX = XZ . . . . definition of bisector
4. PX = PX . . . . reflexive property of congruence
5. ∆PXY ≅ ∆PXZ . . . . LL congruence theorem
6. YP ≅ ZP . . . . CPCTC
The area of a rectangular garden is 6298 m². If the length of the garden is 94 m, what is its width?
Answer:Your answer is 67.
Step-by-step explanation:Your very welcome! :D
hope im right. Good luck acing your quiz!
21 x 8 ÷ 12 as a equivalent ratio?
Answer:
There are many options, like:
14/1 or 28/2...
Step-by-step explanation:
First write the system:
(21 x 8) / 12
Then simplify the brackets:
(168) / 12
= 14
Then you can put 14 over 1 as an example of proportionality:
14/1 : (21 x 8) / 12
Or multiply it by 2, 3 etc.:
42/3 : (21 x 8) / 12.
Compute the interest on 250000 at a 7. 5% interest rates for half a year
the interest earned on 250000 at a 7.5% interest rate for half a year is 4687.50. This means that after half a year, the total amount that you would have is the sum of the principal and the interest, which is 254687.50.
To calculate the interest on 250000 at a 7.5% interest rate for half a year, we first need to determine the annual interest rate, as most interest rates are quoted on an annual basis. To do this, we can divide the annual interest rate of 7.5% by 2 to get the half-yearly interest rate, which is 3.75%.
Next, we can use the formula for simple interest to calculate the interest earned over half a year. Simple interest is calculated by multiplying the principal amount (in this case, 250000) by the interest rate (3.75%) and the time period (0.5 years).
So, the interest earned would be:
Interest = Principal x Rate x Time
= 250000 x 0.0375 x 0.5
= 4687.50
Therefore, the interest earned on 250000 at a 7.5% interest rate for half a year is 4687.50. This means that after half a year, the total amount that you would have is the sum of the principal and the interest, which is 254687.50.
It's worth noting that this calculation assumes that the interest is simple interest, which means that the interest earned is not reinvested. If the interest is compounded (i.e., the interest earned is reinvested), then the interest earned would be higher.
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what is the probability that 356 randomly selected children will have a proportion of nearsightedness of at least 9% ?
The accurate solution is that the probability of the proportion of nearsightedness of at least 0.09 is approximately 0.0324 or 3.24%.
There are a few steps to answer this question about probability with the proportion of nearsightedness:
1. Define the variable: Let p be the true proportion of children with nearsightedness.
2. Check the conditions for using the normal approximation to the binomial distribution: np = 356 × 0.09 = 32.04 and n(1 - p) = 356 × 0.91 = 323.96, both greater than or equal to 10.
3. Calculate the z-score using the formula: z = (x - np) / √(np(1 - p)), where x = 0.09 × 356 = 32.04.
4. Find the probability using a calculator.
The probability that 356 randomly selected children will have a proportion of nearsightedness of at least 9% is approximately 0.0324, or 3.24%.
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What is the area of circle Q?
Q14
A. 28п
B. 28п²
С. 49п
D. 49п²
Answer:
Step-by-step explanation:
The area of a circle is pi times the radius squared (A = π r²).
Harold will drive 330 more miles at the same rate how long will it take care old to drive 330 miles
Assuming he drives at a speed of 60 miles per hour, it will take him 5.5 hours to drive the 330 miles.
How long does it takes him to drive the 330 miles?If Harold drives 330 more miles at the same rate of 60 miles per hour, we can use the formula:
distance = rate x time
Let t be the time in hours it takes to drive the additional 330 miles. Then we have:
330 = 60t
Solving for t, we get:
t = 330/60
t ≈ 5.5 hours
Therefore, it takes approximately 5.5 hours to drive the additional 330 miles at a rate of 60 miles per hour.
Full question "Harold will drive 330 more miles at the same rate. Assume he drives at a speed of 60 miles per hour, how long does it take to drive the 330 miles?'
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Suppose records indicate that the length of voicemails (in seconds) between a group of friends is normally distributed with a mean of 40 seconds and standard deviation of 10 seconds. Find the probability that a given voicemail is between 10 to 20 or 30 to 40 seconds
Hence, there's a 36.41 percent chance that a voicemail will be between 10 and 20 or 30 and 40 seconds in length.
What are examples and probability?It is based on the possibility that something will actually happen. The basis for theoretical probability is the justification for probability. For example, the theoretical probability of getting a head when flipping a coin is ½.
Calculating the area underneath the normal curve of distribution between the two iterations will allow us to determine the likelihood that a specific voicemail will last between 10 and 20 or 30 and 40 seconds.
The intervals must first be standardized by transforming it into z-scores using following formula:
z = (x - μ) / σ
Where x is the value, we want to convert, μ is the mean of the distribution, and σ is the standard deviation.
For the period of 10 to 20 seconds:
z1 = (10 - 40) / 10 = -3
z2 = (20 - 40) / 10 = -2
For the interval 30 to 40 seconds:
z3 = (30 - 40) / 10 = -1
z4 = (40 - 40) / 10 = 0
The region of the curve between such z-scores can now be calculated or found using a calculator and a standard normally distributed table. As an alternative, we can employ the normal distribution's CDF, or cumulative distribution function.
P(10 ≤ x ≤ 20 or 30 ≤ x ≤ 40) = P(10 ≤ x ≤ 20) + P(30 ≤ x ≤ 40)
P(10 ≤ x ≤ 20) = P(-3 ≤ z ≤ -2) ≈ 0.0228
P(30 ≤ x ≤ 40) = P(-1 ≤ z ≤ 0) ≈ 0.3413
As a result, the likelihood that a voicemail will be between 10 and 20 or 30 and 40 seconds is:
P(10 ≤ x ≤ 20 or 30 ≤ x ≤ 40) ≈ 0.0228 + 0.3413 ≈ 0.3641
A voicemail that is between 10 and 20 or 30 to 40 seconds in length has a 36.41% chance of being left.
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Chanda gets a new puppy and purchases supplies that cost $52.00. The sales tax is 5.5%. What is the total cost of Chanda's purchase? (label!)
Answer:
$54.86
Step-by-step explanation:
The tax is 5.5%. Convert to decimals --> .055
Multiply .055 x 52 = $2.86 in tax
Add $2.86 + 52 = $54.86 total
Factorise p²q-pr²-pq+r²
Target is selling a speaker for $166.50. It is at Costco for $90. What percentage did
Target markup the speaker?
Answer:
45.6%
Step-by-step explanation:
166.50 minus 45.6% equals 90 dollars
Cora painted for three fifths of an hour. Her friend painted for 7 times as long. How many hours did Cora's friend paint in total? four fifths of an hour 3 hours sixteen fifteenths or three and one fifth hours twenty-one fifths or four and one fifth hours
The number of hours Cora's friend paint in total is found to be - twenty-one fifths.
Explain the term fraction of the number?The components of a whole or group of items are represented by fractions. A fraction consists of two components. The numerator is the figure at the top on the line.
The denominator is the figure that appears below the line. It shows either the overall number of identical objects in either a collection or the actual number of equal sections the entire thing is divided into.The following are examples of the types of adverbs that can be used to describe the meaning of a word. The numerator and indeed the denominator are the two main components of a fraction. These can be used to define various fraction types.Three-fifths of an hour was spent by Cora painting.
= 3/5 of hour
Her companion spent seven times as long painting.
= 7 * 3/5 of hour
= 21 /5 of hour
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What are all of the constants in the equation n + 6 = 30?
Answer:
Simple and best practice solution for n/6=30= equation. Check how easy it is, ... n-30*6=0. We add all the numbers together, and all the variables n-180=0
when trevor graduated high school, he put his pirating cds behind him and got a job at a clothing store to save money for college.
When Trevor graduated high school, he put his pirating CDs behind him and got a job at a clothing store to save money for college. Saving money is an essential part of financing college.
A student can achieve their dream of attending college by following the steps below.
Step 1: Create a budget. Creating a budget is the first step in saving for college. The budget should include all expenses, such as tuition, room and board, books, and other fees.
Step 2: Find ways to save money. Save money by finding ways to reduce spending on non-essentials such as entertainment, dining out, and shopping. Every little bit counts, and the savings can be put toward college.
Step 3: Explore scholarships and financial aid. Apply for financial aid and scholarships to help pay for college. Grants, loans, and scholarships are available from federal, state, and private sources.
Step 4: Consider community college or online education. Consider community college or online education as an affordable way to earn college credit and save money.
Step 5: Work and save Continue working and saving money during college. A part-time job or paid internship can help cover expenses and reduce student loan debt.
These are the essential steps for saving money for college. A student can explore these options and make smart financial decisions to achieve their dream of attending college.
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2 3/5 as an improper fraction
give your answer in its lowest terms
Answer:
13/5
Step-by-step explanation:
2*5=10
3+10=13
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathtt{2\dfrac{3}{5}}\\\\\mathtt{= \dfrac{2\times5 + 3}{5}}\\\\\mathtt{= \dfrac{10 + 3}{5}}\\\\\mathtt{= \dfrac{13}{5}}\\\\\\\huge\text{Therefore your answer should be:}\\\\\huge\boxed{\mathtt{\dfrac{13}{5}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
At a basketball game, a team made 53 successful shots. They were a combination of 1- and 2-point shots. The team scored 90 points in all. Write and solve a system of equations to find the number of each type of shot.
Answer: the team amassed 88i points total, by shooting t two-point baskets and u 1-point free throws.
t+u = 53
total is: 2t + u = 88.
Step-by-step explanation:
hope i makes sense
you randomly select 15 cards from a deck of 52 cards. what is the probability that it contains exactly one queen given that it contains exactly two aces?
The probability that the 15 cards contain exactly one queen given that they contain exactly two aces is approximately 0.060 or 6.0%.
We can use conditional probability. Let A be the event that the 15 cards contain exactly two aces, and B be the event that they contain exactly one queen. Then we want to find the conditional probability P(B|A).
First, let's find the probability of A. There are C(4,2) ways to choose the two aces out of four, and C(48,13) ways to choose the other 13 cards out of the remaining 48 cards. So the total number of ways to choose 15 cards with exactly two aces is:
C(4,2) × C(48,13) ≈ 4.57 × 10^12
Next, let's find the probability of both A and B. There are C(4,2) ways to choose the two aces out of four, C(4,1) ways to choose one queen out of four, and C(47,12) ways to choose the other 12 cards out of the remaining 47 cards. So the total number of ways to choose 15 cards with exactly one queen and exactly two aces is:
C(4,2) × C(4,1) × C(47,12) ≈ 2.76 × 10^11
Finally, we can use the formula for conditional probability:
P(B|A) = P(A and B) / P(A)
P(B|A) = (C(4,2) × C(4,1) × C(47,12)) / (C(4,2) × C(48,13))
P(B|A) ≈ 0.060
Therefore, the probability is approximately 0.060 or 6.0%.
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What is the volume of the prism?
in.³.
Answer:18
Step-by-step explanation:
Volume prism is equal to product of width, length and height of prism which is in this case:
[tex]V=4*2*2\frac{1}{4}=8*\frac{9}{4}=18[/tex]
midazolam 9 mg im now is ordered. the nurse has the following vial of midazolam. how many milliliters will the nurse administer? enter only the numeral (not the unit of measurement) in your answer.
1.8 ml (milliliters) the nurse will administer the vial of the Midazolam of ordered 9mg.
The formula of calculating this is D/H × Q = x
where x = Desired dose amount, D = ordered Dose amount, H = amount on hand and Q = quantity.
From the following questions we have.
9mg = order dose, 5mg = amount on hand and 1ml quantity.
x = 9/5 × 1
= 1.8 ml.
Midazolam is administered carefully .it is used for sedation and anesthesia before surgical procedure. Midazolam is a short acting drug under benzodiazepines which have sedation power, so use or administered carefully before surgical procedure.
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4. Davie has sent the following number of text messages in the past 7 days: 10, 2, 5, 22, 19, 11, 8. (1 point)
Gabby has sent the following number of text messages in the past 7 days: 19, 15, 25, 24, 20,
29, 21. Using IQR, who has had a higher variability of text messages per day?
ODavie had a higher variability because his IQR is 8 more than Gabby's.
OGabby had a higher variability because her IQR is 7 more than Davie's.
ODavie had a higher variability because his IQR is 6 more than Gabby's.
OGabby had a higher variability because her IQR is 6 more than Davie's.
Answer:
Step-by-step explanation:
4. The cοrrect οptiοn is A) David had a higher variability because his IQR is 8 mοre than Gabrielle
6. The cοrrect οptiοn is D) The IQR For both sets is 8.
What is the descriptive statistics?Descriptive statistics is a branch οf statistics that invοlves the cοllectiοn, presentatiοn, and characterizatiοn οf a set οf data.
4) Given
1. Number οf text messages frοm David 10, 2, 5, 22, 19, 11, 8
2. Number οf text messages frοm Gabrielle 19, 15, 25, 24, 20, 29, 21
Find the median fοr the data οf David
10, 2, 5, 22, 19, 11, 8
Arrange in ascending οrder
2, 5, 8, 10, 11, 19, 22
Median οf the data is (n + 1)/2
= (7 + 2)/2
= 4
= 4th term = 10
Nοw Find Q1 and Q3
Q1 = 5 and Q3= 19
IQRD=Q3−Q1
IQRD=19−5
IQRD=14 Equatiοn (1)
Find the median fοr the data οf Gabrielle
19, 15, 25, 24, 20, 29, 21
Arrange in ascending οrder
15, 19, 20, 21, 24, 25, 29
Median οf the data is 4th term 21
Nοw Find Q1 and Q3
Q1=19 and Q3=25
IQRG=Q3−Q1
IQRG=25−19
IQRG=6 Equatiοn (2)
Frοm equatiοn 1 and 2 we can say that
David had a higher variability because his IQR is 8 mοre than Gabrielle.
Hence, The cοrrect οptiοn is A) David had a higher variability because his IQR is 8 mοre than Gabrielle.
5) Seventh grade = 6 10 14 18 22 26
Median = 4th value = (18 + 14)/2 = 16
Q1=10 and Q3=22
IQR = 22 - 14 = 8
Eighth grade = 22 26 30 34 38
Median (n + 1)/2 = 3rd value = 30
Q1=22 and Q3=38
IQR = 34 - 26 = 8
Thus, The IQR For both sets is 8.
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please help asap im begging
Answer:
The diameter of the circle is 12 inches, which means the radius of the circle is half of the diameter, or 6 inches.
The formula for the area of a circle is:
A = πr^2
where A is the area of the circle and r is the radius.
Plugging in the value for the radius, we get:
A = π(6 in)^2
A = π(36 in^2)
A = 113.1 in^2 (rounded to one decimal place)
Therefore, the area of the circle is approximately 113.1 square inches.
Find m∠AZJ using the figure below
In Linear pair, 52° is the value ∠AZJ .
What is Linear pairs?
When two lines meet at a single point, a pair of linear angles is created. If, following the junction of the two lines, the angles are next to one another, they are said to be linear. A linear pair's total angles are always equal to 180 degrees.
A pair of adjacent angles is said to be a linear pair if the total of the two angles' (measured) angles is 180°. This means that a linear pair of angles always adds up to 180°. The linear pair of 30°, for instance, is 150°; the linear pair of 70°, 110°; etc.
∠JZF or ∠HZG
Linear pairs form supplementary angles.
∠AZJ = ∠AZH - ∠HZA
= 90° - 38°
∠AZJ = 52°
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Find the value of each variable and show work step by step please. Thank you I appreciate it! Also Ramadan Mubarak to anyone who is Muslim seeing this
Note that the angles above are marked to be similar hence, one half of the base has a length of 16 units.
What is the explanation for the above response?
To solve this problem, we can use the fact that the line bisecting the angle at the top of a triangle also bisects the base. This means that the two halves of the base are equal in length.
Let's call the length of one half of the base "z". Then, the length of the other half of the base is also "z". The total length of the base is 32 units, so we can set up an equation:
z + z = 32
Simplifying this equation, we get:
2z = 32
Dividing both sides by 2, we get:
z = 16
So one half of the base has a length of 16 units.
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the volume of a cube (in cubic inches) plus three times the total length of its edges (in inches) is equal to twice its surface area (in square inches). how many inches long is its long diagonal? express your answer as where is a prime number. find .
The length of the long diagonal of the cube is 3sqrt(3) inches.
Let's denote the length of one side of the cube as "a". Then the cube has a volume of a^3, a surface area of 6a^2 (since a cube has 6 faces with side length a), and a total edge length of 12a (since each face has 4 edges of length a).
Using the given equation, we can write
a^3 + 3(12a) = 2(6a^2)
Simplifying this equation, we get
a^3 + 36a = 12a^2
a^3 - 12a^2 + 36a = 0
a(a^2 - 12a + 36) = 0
a(a - 6)^2 = 0
The only positive solution for "a" is a = 6 (since a cannot be zero or negative). Therefore, the cube has a side length of 6 inches.
To find the length of the long diagonal of the cube, we can use the Pythagorean theorem. The long diagonal passes through the center of the cube and connects two opposite corners. The distance from the center to a corner is half the length of the long diagonal. Let's call this distance "d".
Using the Pythagorean theorem, we can write
d^2 = (6/2)^2 + (6/2)^2 + (6/2)^2
d^2 = 3(6^2)/4
d = (sqrt(3)×6)/2
d = 3sqrt(3) inches
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if all multiples of 3 and all multiples of 4 are removed from the list of whole numbers 1 through 100, then how many whole numbers are left?
Answer:
The lowest common multiple 3 and 4 is 12.
Step-by-step explanation:
The total multiples of both 3 and 4 between 1 - 100 are 100/12 = 8 4/12 i.e. 8.
If Planet I is 32. 6 million miles farther from the sun than Planet II, then Planet III is 26. 3 million miles farther from the sun than Planet I. When the total of the distances for these three planets from the sun is 190. 5
million miles, how far away from the sun is Planet II?
Rewrite 6x2 + 3xy + 4x + 2y in factored form.
(2x + 2)(3x + y)
(2x + 2y)(3x + 1)
(2x + y)(2x + 3)
(2x + y)(3x + 2)
The factorised form of the given expression would be = (3x+2)(2x+y). That is option D.
How to factorised an expression?Factorisation is when a number is written as a product of several other numbers.
The given expression is as follows:
6x² + 3xy + 4x + 2y
Insert bracket to simplify the above expression;
(6x² + 3xy) (4x + 2y)
Factorise the expressions one after the other;
3x(2x+y) +2( 2x+ y)
The factorised form = (3x+2)(2x+y). This is soo because when multiplied will give the same expression such as 6x² + 3xy + 4x + 2y .
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Answer:
D. (2x + y)(3x + 2)
Step-by-step explanation:
i took the test :)
Written as a simplified polynomial in standard form, what is the result when
(x+4)² is subtracted from 8?
The simplified form of the polynomial expression in standard form is: - x² - 8x - 8
How to express the polynomial in standard form?The standard form of a polynomial is usually expressed by writing the highest degree of terms first then the next degree and so on. The standard form of polynomial is given by, f(x) = aⁿxⁿ + aⁿ⁻¹xⁿ⁻¹ + aⁿ⁻²xⁿ⁻² + ... + a₁x + a₀, where x is the variable and a_i are coefficients.
The polynomial expression is given as (x+4)² is subtracted from 8. Thus, we have:
8 - (x+4)²
Expanding gives:
8 - (x² + 8x + 16)
= 8 - x² - 8x - 16
= - x² - 8x - 8
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how many???? help brainliest
Answer:
First figure:
Faces--5
Edges--8
Vertices--5
Type--pyramid
Second figure:
Faces--6
Edges--12
Vertices--8
Type--rectangular prism