13) A cutlery manufacturer packs 200 teaspoon into boxes holding either 4 spoons or six spoons.there are 48 full boxes.
are 48 full boxes,
a) If there are a four-spoon boxes and y six spoons boxes use the information to find two equations relating to x and y
relating x and y.
b) How many boxes hold four spoons

Answer: We can use the formula for compound interest to calculate the total amount in each account after 2 years.

Account 1: A = P * (1 + r/n)^(nt)

where P = $1,200, r = 2.7%, n = 365 (days/year), t = 2 years.

Substituting the values into the formula, we get:

A = $1,200 * (1 + 0.027/365)^(365 * 2) = $1,200 * (1.0007365)^(365 * 2)

Account 2: A = P * (1 + r)^t

where P = $1,000, r = 3.9%, t = 2 years.

Substituting the values into the formula, we get:

A = $1,000 * (1 + 0.039)^2 = $1,000 * (1.039)^2

Comparing the two amounts, we see that Account 1 has a higher return. The final amount in Account 1 is $1,268.27 and the final amount in Account 2 is $1,079.61.

Step-by-step explanation:

The solution is, Total estimated living expenses = $53,900.

In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.

here, we have,

Estimated expenses for next 2 years:

Rent = 1100 * 12 * 2 = 26,400

Gym membership = 450 * 2 = 900

Gym monthly fee = 40 * 12 * 2 = 960

Renter's insurance = 60 * (12 * 2 / 6) = 240

Groceries = 300 * 12 * 2 = 7200

Eating out & entertainment = 175 * 52 * 2 = 18,200

Total estimated living expenses = $53,900

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The sum of the first 4 terms of the binomial expansion of (0.9 + 0.081)³ is approximately 0.9441.

The binomial expansion formula is given by:

[tex](a + b)^n = nC_0 \times a^n \times b^0 + nC_1 \times a^{(n-1)} \times b^1 + nC_2 \times a^{(n-2)} \times b^2 + ... + nC_n \times a^0 \times b^n[/tex]

where nCk is the binomial coefficient, which is equal to n! / (k! * (n-k)!) for k = 0, 1, 2, ..., n.

Here, we have a = 0.9 and b = 0.081, and we want to find the sum of the first 4 terms, which means we need to find:

(0.9 + 0.081)⁰ + (0.9 + 0.081)¹ + (0.9 + 0.081)² + (0.9 + 0.081)³

Using the binomial expansion formula with n = 3, we get:

(0.9 + 0.081)³ = 3C0 x 0.9³ x 0.081^0 + 3C1 x 0.9² x 0.081¹ + 3C2 x 0.9¹ x 0.081² + 3C3 x 0.9⁰ x 0.081³

Simplifying each term, we get:

1 x 0.729 x 1 + 3 x 0.81 x 0.081 + 3 x 0.9 x 0.006561 + 1 x 0.000531441

= 0.729 + 0.19683 + 0.0177117 + 0.000531441

= 0.944076141

Therefore, the sum of the first 4 terms of the binomial expansion of (0.9 + 0.081)³ is approximately 0.9441 (rounded to 4 decimal places).

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D i.e. {C, T, U, -, *} is the minimal complete set of relational algebra operations.

What is relational algebra?

Relational Algebra is a query language that takes a Relation as input and returns another Relation as output. Relational algebra provides the theoretical basis for relational databases and SQL. The necessary column data for a relation is projected via projection.

Now,

As Five basic operations in relational algebra are : Selection, Projection, Cartesian product, Union, and Set Difference and all these are present in

{C, T, U, -, *}.

Hence,

            D i.e. {C, T, U, -, *} is the minimal complete set of relational algebra operations.

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Answer:

See below

Step-by-step explanation:

The derivative function f' is the slope of the function at any given 'x'

A) f ' = 8 x^3 - 24 x^2

B ) put in x = -1 and compute   8 ( -1)^3 -24(-1)^2 = -8 - 24 = - 32 slope

C)  we know the slope (-32) and the x coordinate (-1)   put this value of x into the original equation to find y = 2(1^4) - 8(-1)^3 + 6 = 16

   so point slope form of the line is

       y - 16 = -32 (x - -1)    re-arrange:

       y = -32x -16

D) where slope (f ') = 0 the slope is 0 and thus the tangent line is horizontal      8x^3 - 24x^2 = 0    

                         8x^3 = 24x^2

                           8x = 24

                             x = 3  

The measures of the angles are:

n = q = j = 57°

m = l = p = k = 123°

Remember that vertical angles have the same measure, then:

n = 57°

And if the two horizontal lines are parallel, then the values in the correspondent quadrants are the same ones, then:

q = 57°

j = 57°

And adjacent angles add up to 180°, them:

57° + m = 180°

m = 180° - 57°

m = 123°

Then:

m = l = p = k = 123°

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Answer:

1960g remaining

Step-by-step explanation:

2kg=total amount of tea

40g=amount of tea taken

Thus, covert 2kg to gram

2×1000=2000g

amount of tea remaining=total amount of tea –amount of tea taken

x=2000–40

x=1960g remaining

P(Female) = 111, P(Car) = 132, P(Female | truck) = 19 P(Truck | female)

Probability is a branch of math which deals with finding out the likelihood of the occurrence of an event. Probability measures the chance of an event happening.

From the image in the question,

P(Female) = 92 + 19

= 111

P(Car) = 40 + 92

= 132

P(Female | truck) = 19

P(Truck | female) = 19

The events "Female" and "Truck" are dependent

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Answer:

Step-by-step explanation:

To calculate the rate at which the water level drops, we need to find the volume of water being lost per second and convert that to a height change. The volume of water being lost is given as 0.05 liters per second. The volume of a cylinder with height h and radius r is given by the formula:

V = πr^2h

We can rearrange this formula to solve for h:

h = V / (πr^2)

Substituting the given values, we get:

h = 0.05 / (π * 20^2) = 0.05 / (π * 400) = 0.05 / 1257.0796

So the rate at which the water level is dropping is approximately 0.04 cm per second.

In a case whereby It was recently estimated that domestic vehicles out number foreign vehicles by about seven to five. If there are 4152 vehicles in a county, the number of them that are domestic is 2422  domestic vehicles.

The concept that will be used here is simplification.

From the question, we were told that there are 7x domestic vehicles  as well as 5x foreign vehicle.

We can see that the x is the unknown number, which we need to find out,  

Then  we can make an equation as:

7x + 5x =  4152

12x= 4152

x=4152/12

=346

Hence we can say that there are  7*346 = 2422  domestic vehicles

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Answer:

PR = 288.75 feet

Step-by-step explanation:

There are two triangles that we need to consider:
ΔPRE and ΔPOC

These triangles are similar since
m∠PRE = m∠POC = 90°
∠PRE ≅ ∠POC

∠RPE ≅  ∠OPC (common angle)

AA Similarity theorem..
If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.  

∴ ΔPRE ≅ ΔPOC

If two triangles are similar, the ratios of the corresponding sides must be equal

⇒ [tex]\dfrac{PO}{PR} = \dfrac{OC}{PE}\\\\[/tex]    (1)

PO = PR + RO
PR is the width of the river that is to be determined
Let PR = x

Then
PO = x + 165

OC = 330, RE = 210

[tex]\dfrac{PO}{PR} = \dfrac{OC}{PE}\\\\\Rightarrow \dfrac{x + 165}{165} = \dfrac{330}{210}\\\\[/tex]

Left side:
[tex]\dfrac{x+165}{x} = \dfrac{x}{x} + \dfrac{165}{x} = 1 + \dfrac{165}{x}[/tex]

Simplify  [tex]\dfrac{330}{210}[/tex]   by dividing both numerator and denominator by 30

=>
[tex]\dfrac{330}{210} = \dfrac{11}{7}\\\\[/tex]

Therefore
[tex]\dfrac{PO}{PR} = \dfrac{OC}{PE}\\\\\Rightarrow 1 + \dfrac{165}{x} = \dfrac{11}{7}\\[/tex]

Subtract 1 from both sides:
[tex]\dfrac{165}{x} = \dfrac{11}{7} - 1\\\\\dfrac{165}{x} = \dfrac{4}{7}\\\\[/tex]

Cross-multiply
[tex]165 \times 7 = 4x\\\\\Rightarrow 4x = 165 \times 7\\\\\Rightarrow x = \dfrac{165 \times 7 }{4} = 288.75\;feet[/tex]

Answer:

aaaaaæaaaaaaaaaaaaaaaaaaaaaa

The value of the side x is 6. Option D

It is important that we know the six different trigonometric identities in mathematics.

These identities are;

We have the sides are;

Hypotenuse side = x

Opposite side = y

Angle = 30

Adjacent side = 3

Then,

cos 60 = 3/x

Find the value

x = 6

Hence, the value is 6

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Answer:8

Step-by-step explanation:

100*0.08

you would buy 8 cupcakes

timer--;  //This statement uses the auto-decrement operator to decrease the value of the variable timer by 1.

The auto-decrement operator -- is used to decrease the value of a variable by 1. In this case, the variable is called timer. The statement which uses the auto-decrement operator is timer--;. This statement will take the current value of the timer variable and decrease it by 1. For example, if the current value of timer is 5, the statement timer--; will decrease the value to 4. This is a very useful and efficient way to decrease a variable's value by 1. It is also much shorter than having to write out a statement such as timer = timer - 1;. The auto-decrement operator can be used with other types of variables as well, such as strings or characters.

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Answer:

(a) 44%

(b) 32%

Step-by-step explanation:

(a) In order to find the percentage of students that prefer comedies, we can add up divide the sum of the total number of students who prefer comedies (Twice/month or less + Thrice/month or more) by the total number of students.  

Then, we can multiply this number by 100 to find the percentage:

[tex](\frac{45+21}{150})*100\\ (\frac{66}{150})*100\\ 44[/tex]

(b) To find the percentage of students who visit the movies three times a month or more, we can divide the sum of the total number of students who visit the movies three times a month or more by the total number of students.

Like before, we can multiply this number by 100 to find the percentage:

[tex](\frac{21+27}{150})*100 \\(\frac{48}{150})*100\\ 32[/tex]

Answer:

ok

Step-by-step explanation:

later

Answer: 20% of the class is girls.

6/30 = 0.2

0.2=20%

Federal Deposit Insurance Corporation, programs were parts of FDR's New Deal.

Social security is the protection that a society provides to individuals and households to ensure access to health care and to guarantee income security, particularly in cases of old age, unemployment, sickness, invalidity, work injury, maternity or loss of a breadwinner.

here, we have,

One of Franklin D. Roosevelt's most well-known and widespread programmers, Social Security was first introduced in 1935. One of the New Deal initiatives that helped the nation emerge from the Great Depression and recover its assets and wealth as well as give the economy new life was Social Security.

In order to help the aged and disabled better support themselves while they were unable to work, Social Security established safety net protections.

The Social Security programmed and Fannie Mae, or The Federal National Mortgage Association, both still exist today, despite the fact that the majority of the New Deal policies were abandoned when the United States entered World War II. After World War II, Fannie Mae contributed to funding and fueling the housing boom for soldiers coming home.

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Answer:

see explanation

Step-by-step explanation:

(a)

let ∠ QRS = x then ∠ PQR = x and

∠ QPS = [tex]\frac{6}{7}[/tex] x and ∠ PSR = [tex]\frac{4}{7}[/tex] x

the sum of the 4 angles in a quadrilateral = 360°

sum the 4 angles and equate to 360

x + x + [tex]\frac{6}{7}[/tex] x + [tex]\frac{4}{7}[/tex] x = 360 ( multiply through by 7 to clear the fractions )

7x + 7x + 6x + 4x = 2520

24x = 2520 ( divide both sides by 24 )

x = 105

then

∠ QRS = 105° , so

∠ PSR = [tex]\frac{4}{7}[/tex] × 105° = 4 × 15° = 60°

(b)

∠ QPS = [tex]\frac{6}{7}[/tex] × 105° = 6 × 15° = 90° ← a right angle

On solving the provided question we can say that by percentage y = $1900(77/100)t

A percentage in mathematics is a figure or ratio that is stated as a fraction of 100. The abbreviations "pct.," "pct," and "pc" are also occasionally used. It is frequently denoted using the percent symbol "%," though. The amount of percentages has no dimensions. With a denominator of 100, percentages are basically fractions. To show that a number is a percentage, place a percent symbol (%) next to it. For instance, if you correctly answer 75 out of 100 questions on a test (75/100), you receive a 75%. To compute percentages, divide the amount by the total and multiply the result by 100. The percentage is calculated using the formula (value/total) x 100%.

In 2005, a laptop computer was purchased for 81900. Each year since, the resale value has decreased by 23%. Let t be the number of years since Let Y be the value of the laptop computer, in dollars. Write an exponential function showing the relationship between Y and

t. value of laptop in 2005 81900 decrease in resale \/aIUe each year

23 77% resale value of laptop after each year = 100

resale value after one x $1,900

Now, Hence relation between value of the laptop computer and time is

y = $1900(77/100)t

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Answer:

C

Step-by-step explanation:

Supplementary angles are two angles that equal 180 degrees. An angle is 180 degrees when it's a straight line. As you see, the line with E, A, P, and B is a straight line, making A and B supplementary.

Answer: Supplementary angles because the 2 angles when they are joined they both add up to 180 degrees

Step-by-step explanation:

Answer:

z=0.13 or z=-2/15

Step-by-step explanation:

First you must simply the fraction into a decimal, leaving us with 1.2 and 1.3. Then you subtract 1.3 from 1.2. Leaving us with z=0.13 or in fraction form,

z= -2/15

Answers in bold

[tex]\begin{array}{|c|c|} \cline{1-2}\text{Term} & \text{Coefficient}\\\cline{1-2}\text{x}^2 & \boldsymbol{1}\\\cline{1-2}\boldsymbol{-3\textbf{x}} & -3\\\cline{1-2}2 & \boldsymbol{2}\\\cline{1-2}\end{array}[/tex]

Explanation:

The given expression [tex]\text{x}^2-3\text{x}+2[/tex] is the same as [tex]\text{x}^2+(-3\text{x})+2[/tex]

This leads to the three terms as shown in the table above. Each term is separated by a plus sign.

The coefficient is the number to the left of the variable. Think of [tex]\text{x}^2[/tex] as [tex]1\text{x}^2[/tex] and think of [tex]2[/tex] as [tex]2\text{x}^0[/tex]

In other words, [tex]\text{x}^2-3\text{x}+2[/tex] is the same as [tex]1\text{x}^2+(-3\text{x})+2\text{x}^0[/tex]

Using the box method, the expression is solved as: 4x³ + 8y² - 19y - 35 (see image below).

The box method, also known as the grid method or area model, is a visual technique for multiplying two expressions or expanding algebraic expressions. Here are the steps to expand an algebraic expression using the box method:

The box method shows how the expression has been expanded, thus, combining like terms, we have:

4x³ + 8y² - 19y - 35

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With a constant speed Robert took 20 minutes paddle.

The speed formula can be defined as the rate at which an object covers some distance. Speed can be measured as the distance travelled by a body in a given period of time. The SI unit of speed is m/s.

Given that, Robert paddled at a constant speed and travels 3/4 of a mile in 15 minutes.

We know that, Speed = Distance/Time

Speed = 3/4 ÷15/1

= 3/4 × 1/15

= 1/20 miles per minutes

Now, distance = 1 mile and speed =1/20 miles per minutes

1/20 = 1/Time

Time = 20 minutes

Therefore, with a constant speed Robert took 20 minutes paddle.

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The page numbers of the book are 147 and 148.

Consecutive numbers are numbers that follow each other in order. They have a difference of 1 between every two numbers.

In a set of consecutive numbers,the mean and the median are Equal. If n is a number, then n, n+1, and n+2 would be consecutive numbers.

Given,

Left and right page numbers of a book are consecutive integers.

Sum of both integers = 295

Let x is left integer then right integer is x + 1

Equation becomes

x + x + 1 = 295

2x + 1 = 295

2x = 295 - 1

x = 294/2

x = 147

Left integer = 147,

Right integer = 147 + 1 = 148

Hence, 147 and 148 are the page numbers of the book.

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The terms a0, a1, a2, and a3 of the sequence {an} in each case are as follows:

a. a0 = 0, a1 = 3, a2 = 6, a3 = 9

b. a0 = 0, a1 = 2, a2 = 12, a3 = 72

c. a0 = 0, a1 = 0.5, a2 = 1, a3 = 1.5

d. a0 = 0, a1 = 1, a2 = 2, a3 = 3

a. 2n + n

a0 = 2*0 + 0 = 0

a1 = 2*1 + 1 = 3

a2 = 2*2 + 2 = 6

a3 = 2*3 + 3 = 9.

b. n(n+1)!

a0 = 0(0+1)! = 0

a1 = 1(1+1)! = 2

a2 = 2*(2+1)! = 12

a3 = 3(3+1)! = 72

c. [n/2]

a0 = [0/2] = 0

a1 = [1/2] = 0.5

a2 = [2/2] = 1

a3 = [3/2] = 1.5

d. [n/2] + [n/2]

a0 = [0/2] + [0/2] = 0

a1 = [1/2] + [1/2] = 1

a2 = [2/2] + [2/2] = 2

a3 = [3/2] + [3/2] = 3

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