Ms. Francis is planning a birthday party for her daughter. There will be 22 children at the party, and in order to seat them all she needs to rent square card tables. Only 1 child can sit at each side of a card table.

Ms. Francis wants to arrange the tables in a rectangular shape so they look like one large table. The room is large enough that

the rectangle can be made with more than one row of tables.

Part A: How many different arrangements can Ms. Francis make to seat all 22 children?

Part B: What is the smallest number of tables that Ms. Francis needs to rent?

DIRECTIONS: To solve the problem, apply the steps of the Mathematical Problem-Solving Routine.

Understand

1. Try to visualize the situation. Consider drawing a diagram

2. State the problem in your own words.

3. What is the important information in the problem?

Plan

4. What strategy will you use to solve the problem? Why?​

Answer:

B or 3.5 if you meant 1/2 as many small wreaths as medium wreaths

Step-by-step explanation:

(Keep in mind you wouldn't write 1x where I wrote it, but just x instead, I just wrote 1x to make it easier to understand)

You have 1x medium wreaths to start with.

You have twice as many large wreaths as medium wreaths.

1x ⋅ 2 = 2x

So you have 1x medium wreaths and 2x large wreaths.

Lastly, it says you have 1/2 as many small wreaths as medium wreaths.

1x ⋅ 1/2 = 1/2x

So you have

1x + 2x + 1/2x = 3 1/2x wreaths, which is answer B.

Answer:

9.047619047619048

Step-by-step explanation:

The  answer is distance from P to l. is equal to square root of 2

Line I contains points (0, -3) and (7,4). Point P has coordinates (4,3)

Find the slope of line l we have the points (0, -3) and (7,4)

m=(4+3)/(7-0) m=7/7 m=1

Find the equation of the line perpendicular to the line l that passes through the point P

Remember that

If two lines are perpendicular, then the product of their slopes is equal to -1, the slope of the perpendicular line is

m=-1 .Find the equation in point slope form

y-y1=m(x-x1)

(x1,y1)=P(4,3)

substitute

y-3=-1(x-4)

y-3=-x+4

y=-x+7

m=1 (see the step 1)

and we have the point (0,-3) -----> y-intercept

so the equation of the line l is

y=x-3

Find the intersection point line l and its perpendicular line

y=x-3 ------> equation A

y=-x+7 -----> equation B

solve the system of equations

Adds equation A and equation B

2y=-3+7

2y=4

y=2

substitute in equation A

2=x-3 x=2+3 x=5

the intersection point is (5,2)

Find the distance between point (5,2) and point P(4,3)

Remember that, this distance is the distance from P to l.

the formula to calculate the distance between two points is equal to

we have

(x1,y1)=(5,2)

(x2,y2)=(4,3)

substitute in the formula

therefore

The  answer is distance from P to l. is equal to square root of 2

To learn more about point slope refer:

brainly.com/question/24907633

#SPJ1

Answer:

True

Step-by-step explanation:

3x5=15

15+8=23

23=23

Answer:

True

Step-by-step explanation:

3 x 5 = 15

15 + 8 = 23

Answer: $23,896

Step-by-step explanation:

In the year 2030, the number of years since the investment would be;

= 2030 - 2012

= 18 years.

As the question does not mention that the interest paid is compounded, simple interest will be used;

= Amount + (Amount * interest rate * number of years).

= 14,500 + ( 14,500 * 0.036 * 18)

= $23,896

We will have the following:

First, we see the approximate or exact decimal forms then we arrange them, that is:

Now, we arrange them:

Answer:

  5.793 s

Step-by-step explanation:

On average she swam 1/10 the distance in 1/10 the time.

She took an average of 5.793 seconds to swim 10 m.

___

10 m is 1/10 of 100 m

Choice D is correct

Every point on circle is equidistant from the point at its centre and that fixed distance = radius of that circle.

The joint probability mass function given by PX, Y(a, b) = {1/4a, for 1≤ b≤a≤4, otherwise is indeed a joint probability mass function because the sum of all the joint probabilities is equal to 1.

To find the marginal probability mass function of X, we need to sum the joint probabilities over all possible values of Y:

PX(a) = ∑ PX, Y(a,b) = ∑ (1/4a) = 1/4

To find the marginal probability mass function of Y, we need to sum the joint probabilities over all possible values of X:

PY(b) = ∑ PX, Y(a,b) = ∑ (1/4a) = 1/4

To find P(X = Y + 1), we need to find the joint probability of X = a and Y = a-1, where a = 2,3.

P(X = Y + 1) = PX, Y(2,1) + PX, Y(3,2) = (1/42) + (1/43) = 1/4 + 3/12 = 5/12

So the probability that X is one more than Y is 5/12.

It's important to note that the given joint probability mass function is valid as it satisfies the non-negativity and the condition of summing to 1.

For more questions like Joint probability click the link below:

https://brainly.com/question/29582649

#SPJ4

Using the percentages we know that the required sales tax percentage in the given situation is 1%.

A sales tax is a fee that is paid to the government when specified goods and services are sold. T

Typically, laws permit the vendor to charge the customer the tax at the time of purchase.

When a tax on goods or services is paid to a governing body directly by a customer, it is commonly called a usage tax.

The sale and use tax is frequently exempted for some goods and services, including food, education, and medical.

A sales tax is similar to a value-added tax (VAT) that is levied on products and services.

Key distinctions can be found in the comparison with sales tax.

So, the sales tax percentage would be:

= 0.55/55*100

= 0.01

= 1%

Therefore, using the percentages we know that the required sales tax percentage in the given situation is 1%.

Know more about the sales tax percentage here:

https://brainly.com/question/9437038

#SPJ1

Answer:

B

Step-by-step explanation:

Answer: is A

Step-by-step explanation:

Start at 555 on the number line and move 888 to the left.

The angle (off of a north-south line) at which a navy carrier needs to travel to sail straight to the submarine is 53.843°.

The trigonometric function gives the ratio of different sides of a right-angle triangle.

\(\rm Sin \theta=\dfrac{Perpendicular}{Hypotenuse}\\\\\\Cos \theta=\dfrac{Base}{Hypotenuse}\\\\\\Tan \theta=\dfrac{Perpendicular}{Base}\)

where perpendicular is the side of the triangle which is opposite to the angle, and the hypotenuse is the longest side of the triangle which is opposite the 90° angle.

The Navy carrier, Mercy, is sailing in the Pacific Ocean. The ship is in the sea, 4,365 miles south of a city. On radar, they notice a submarine is 7,390 miles away from them and north-west of their current position.

Therefore, the angle at which the Carrier needs to move to reach the submarine is,

Cosθ = 4365/7390

θ = Cos⁻¹ (0.59)

θ = 53.843°

Hence, the angle (off of a north-south line) at which a navy carrier needs to travel to sail straight to the submarine is 53.843°.

Learn more about Trigonometric functions:

https://brainly.com/question/6904750

#SPJ1

Multiply weeks by minutes per week:

52 x 205 = 10,660 total minutes per year

Work Shown:

205 minutes: 1 week

52*(205 minutes) : 52*(1 week)

10660 minutes : 52 weeks

10660 minutes : 1 year

Answer: x=35

Step-by-step explanation:

The missing values in the quantitative reasoning given are : -2, 13 and 9

Given the rule :

We can deduce that :

For the left circle :

circle = -6 - (-4) = -6 + 4 = -2

For the right circle :

circle = 11 - (-2) = 11 + 2 = 13

For the left square :

square = 13 + (-4)

square = 13 -4 = 9

Therefore, the missing values are : -2, 13 and 9

Learn more on puzzle: https://brainly.com/question/27645967

#SPJ1

Answer:

\(10 = 2x - 20 \\ 10 + 20 = 2x \\ \frac{30}{2} = \frac{2x}{2} \\ 15 = x\)

Answer:

B) 9.2

Step-by-step explanation:

tan(57)=x/6 multiply 6 on both sides

6.tan(57)=x use calculator to find answer

9.2 rounded

Answer:9.2 is correct

Step-by-step explanation:

Answer:

the iqr is 42

Step-by-step explanation:

Answer:

Sin A= − 12/37

Step-by-step explanation:

tan ⁡ A = − 12/35

Reason for minus sign is because of it's in the fourth quadrant.

12 = opposite

35 = adjacent

? = Hypotenuse

12² + 35² = hypotenuse ²

1369 = hypotenuse ²

hypotenuse = √1369

hypotenuse= 37

Sin = -12/37

Reason for minus sign is because of it's in the fourth quadrant.

Answer:

IV

Step-by-step explanation:

Answer:

The Quadrent it would be in would be the bottom right.

Step-by-step explanation:

Go over 6 units on the x axis, then go down 4 (because it is a negative).

75% is the missing percentage in x% of 1000000 = 750000.

A fraction of a number in hundredths, or fractions with a denominator of 100 (such as 5/100), can be expressed as a percentage, also known as a %. The Latin phrase per centum, which means "per hundred," or the French word pour cent, which has a similar meaning to the Latin word, may have been the source of the word %. A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion therefore refers to a component per hundred. Percent is a unit of measurement.

Given,

Let x be the missing percentage,

x% of 1000000 = 750000

Dividing,

x% = 750000/1000000

x/100 = 0.75

Cross multiplying,

x = 75

75% is the missing percentage in x% of 1000000 = 750000.

To learn more about percentage, visit:

https://brainly.com/question/28269290

#SPJ1

The expression 4(30+5) rewritten using the distributive property of multiplication over addition is 4(30) + 4(5).

The correct answer choice is option C

The distributive property states that multiplying the sum of two or more addends by a number gives equal result as multiplying each addend individually by the number and then adding the products together.

4(30 + 5)

= 120 + 20

= 140

4(30) + 4(5)

= 120 + 20

= 140

Therefore, 4(30) + 4(5) is equivalent to 4(30 + 5) using distributive property.

Read more on distributive property:

https://brainly.com/question/4077386

#SPJ1

(x² - 6 ) ( x + 3 ) is the completely factored form of this polynomial .

What is polynomial in maths?

= x³+3x² - 6x-18

= x² ( x + 3 ) - 6( x + 3 )

= (x² - 6 ) ( x + 3 )

Learn more about polynomial

brainly.com/question/11536910

#SPJ13

Answer:

Me: 60

Zayn and Attia: 6

Step-by-step explanation:

12 = 2 × 2 × 3

20 = 2 × 2 × 5

LCM of 12 and 20 = 2 × 2 × 3 × 5 = 60

My number is 60.

Zayn's and Attia's numbers are 6.

Answer:

Deepak have taken 5 days leave from the start of the work.

The unit rate of computers per day using the graph is that 12 computers are made per day.

The unit rate is how many units of quantity correspond to the single unit of another quantity. We say that when the denominator in rate is 1, it is called unit rate. Unit rates is said to be the amount of something in each unit or per unit.

To obtain the unit rate of computers sold per day using the graph, we need to obtain the slope of the graph, which is the change in y per change in x

So, it is given by:

\(\text{Slope} = \dfrac{\text{change in y}}{\text{change in x}}\)

\(\text{Slope} = \dfrac{\text{y}_2-\text{y}_1}{\text{x}_2-\text{x}_1}\)

\(\text{y}_2 = 60 , \ \text{y}_1 = 36 , \ \text{x}_2 = 5, \ \text{x}_1 = 3.\)

\(\text{Slope} = \dfrac{(60 - 36)}{(5 - 3)} = \dfrac{24}{2} = 12\)

\(\bold{Slope = 12}\)

Unit rate = 12 computers per day.

The attachment of the graph is given below.

Therefore, the unit rate of computers per day is 12.

Learn more about the unit rate at:

https://brainly.com/question/28572142

For the expression \(x^64 + ax^b + 25\) to be a perfect square for all integer values of x, b must be 64, and a must be a perfect square, written as a = \(y^2.\)

To determine the values of a and b such that the expression\(x^64 + ax^b\) + 25 is a perfect square for all integer values of x, we need to analyze the properties of perfect squares.

A perfect square is an expression that can be written as the square of another expression. In this case, we want the given expression to be in the form of\((x^n)^2,\) where n is an even integer.

Let's examine the given expression: \(x^64 + ax^b\) + 25

For it to be a perfect square, the quadratic term \(ax^b\)must have the same exponent as the leading term\(x^6^4.\) This means b must be equal to 64.

So we have:\(x^64 + ax^64 + 25\)

Now, we can rewrite this as:\((x^32)^2 + 2(x^32) (\sqrt{a}) + (\sqrt{25})^2\)

By comparing this with the standard form of a perfect square, (\(x^n +\sqrt{k} )^2\), we can deduce that √a must be equal to x^32 and \(\sqrt{25}\) must be equal to \(\sqrt{k.}\)

Therefore, we have: \(\sqrt{a} = x^3^2\)and\(\sqrt{25} = \sqrt{k}\)

From the second equation, we know that k = 25.

Now, substituting the value of k back into the first equation, we have: \(\sqrt{a} = x^3^2\)

To satisfy this equation for all integer values of x, a must be a perfect square. Therefore, we can express a as a =\(y^2\), where y is an integer.

For more such information on: expression

https://brainly.com/question/1859113

#SPJ8

Answer:

if angle dfb and angle cea measure something other than 90degrees, then line we is not equal to line bf. in this case, line and and line cd intersect at a single point.

Answer:

b= 49 degrees

Step-by-step explanation:

That is a 90 degree angle. And 90-41 is 49

Answer: acute

Step-by-step explanation:did the test