A set of blocks contains blocks of heights 1, 2, and 4 centimeters. Imagine constructing towers by piling blocks of different heights directly on top of one another. (A tower of height 6 cm could be obtained using six 1 cm blocks, three 2 cm blocks, one 2 cm block with one 4 cm block on top, one 4 cm block with one 2 cm block on top, and so forth.) Lett, be the number of ways to construct a tower of height n cm using blocks from the set. (Assume an unlimited supply of blocks of each size.) Use recursive thinking to obtain a recurrence relation for ty, ty, tzo Imagine a tower of height k cm. Either the bottom block has height 1 cm or it has height 2 cm or it has height cm. If the bottom block has height 1 cm, then the remaining blocks make up a tower of height x cm. By definition of t, there are tk-1 such towers. If the bottom block has height 2 cm, then the remaining blocks make up a tower of height x cm. By definition of there are x cm, then the remaining blocks make tx-2 such towers. If the bottom block has height such towers up a tower of height x cm. By definition of there are 1 Select X Therefore, for each integer, n 25,

Hence, there's a 36.41 percent chance that a voicemail will be between 10 and 20 or 30 and 40 seconds in length.

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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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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Assuming he drives at a speed of 60 miles per hour, it will take him 5.5 hours 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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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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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

Answer:

Step-by-step explanation:

The area of a circle is pi times the radius squared (A = π r²).

Answer:

45.6%

Step-by-step explanation:

166.50 minus 45.6% equals 90 dollars

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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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.

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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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

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.

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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Note that the angles above are marked to  be similar hence, one half of the base has a length of 16 units.

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 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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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.

1. 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

Answer:Your answer is 67.

Step-by-step explanation:Your very welcome! :D

hope im right. Good luck acing your quiz!

The number of hours Cora's friend paint in total is found to be - twenty-one fifths.

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.

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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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.

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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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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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

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]

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.

Answer:

First figure:

Faces--5

Edges--8

Vertices--5

Type--pyramid

Second figure:

Faces--6

Edges--12

Vertices--8

Type--rectangular prism

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]

The simplified form of the polynomial expression in standard form is: - x² - 8x - 8

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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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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The factorised form of the given expression would be = (3x+2)(2x+y). That is option D.

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 :)