At a grocery store, three- dozen cookies costs $9.00. What would it cost for one cookie

Using the relationship of permutation and combination, we can say that the relation [tex]${ }^n p_r=(n-\Gamma+1)^n p_{r-1}$[/tex] holds true.

What is Permutation?

The process of placing all the components of a set into a certain sequence or order is known as permutation in mathematics. In other terms, the process of permuting is the reordering of the components of a set if the set is already ordered. Nearly all areas of mathematics include permutations in some form or another. They frequently appear when various orderings on certain finite sets are taken into account.

What is Combination?

Contrary to permutations, the order of selection is irrelevant when choosing elements from a collection using the combination method. The number of combinations may be counted in simpler situations. The combination is the taking together of n items, k at a time, without repetition. The words k-selection or k-combination with repetition are frequently used to describe combinations when repetition is permitted.

In the given question:

To proof:

[tex]${ }^n p_r=(n-\Gamma+1)^n p_{r-1}$[/tex].

Let's Proof the relation:

Using the basic relation of permutation and combination, we have;

[tex]$\begin{aligned}(n-r+1){ }^n P_{r-1} &=(n-r+1) \frac{n !}{(n-r+1) !} \\ &=(n-r+1) \frac{n !}{(n-r+1)(n-r) !} \\ &=\frac{n !}{(n-r) !}={ }^n P_r \end{aligned}$[/tex]

Hence, Proved.

Therefore, we can say that the relation [tex]${ }^n p_r=(n-\Gamma+1)^n p_{r-1}$[/tex] holds true.

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Answer: 63 inches

Step-by-step explanation:

Answer:

63 inches

Hope this helps :)

Answer:

Maximum height of 32 feet after 1.25s

Step-by-step explanation:

The number of kilometers in 5 square gigameters is  5. 0 × 10^18

Proportion can be described as an expression or equation in which two ratios are made equal to each other.

It is also known as the mathematical comparison between two numbers or elements.

From the information given, we have;

1 gigameter = 1.0×10^6 kilometers

But,

5 square gigameters = 5. 1.0×10^6 . 1.0×10^6

Add the powers

5 square gigameters = 5..0×10^12

If 1 gigameter = 1.0×10^6 kilometers

Then 5. 1.0×10^12 gigameter = x

cross multiply

x = 5.0×10^12 ×  1.0×10^6

x = 5. 0 × 10^18 kilometers

Hence, the value is 5. 0 × 10^18 kilometers

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Triangle AEM is congruent to triangle DEN by SAS congruence criterion.

What do you mean by congruence of triangle?

Triangle congruence: If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent. Slide, twist, flip, and turn these triangles to create an identical appearance. If moved, they coincide with one other. The sign of congruence is’ ≅’. After proving triangles congruent, the remaining dimension can be predicted without actually measuring the sides and angles of a triangle.

In triangle AEM and triangle DEN

AE = DE (Given)

ME = NE (As In triangle MEN , angle M = angle N and sides opposite to equal angles are equal)

angle MEA = angle NED (Vertically opposite angles)

Triangle AEM ≅ Triangle DEN (By SAS congruence criterion)

Therefore, both the trinagles are congruent by SAS congruence criterion.

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In a multiple regression problem involving two independent variables, if b1 is computed to be 2.0, it means that For every unit increase in x1, the predicted mean of Y rises by 2 units holding [tex]x_{2}[/tex] constant.

Given data,

Slope b1 = +2

Mutiple regression which means,

Use multiple linear regression to determine the relationship between two or more independent variables and one dependent variable.

The value of the dependent variable at a specific level of the independent variables (For instance, the crop's anticipated yield at specific levels of temperature, rainfall, and fertilizer application).

[tex]y = b_{0} +b_{1}x_{1}+b_{2}x_{2}+b_{3}x_{3}+....[/tex]

[tex]b_{1}[/tex]=2 means

The estimated mean of Y increases by 2 units for each increase of 1 unit of [tex]x_{1}[/tex], holding [tex]x_{2}[/tex] constant.

Hence, the expected mean of Y increases by two units for every unit increase in x1.

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The coordinates of the centroid of a triangle with vertices X(−4, 0) , Y(−1, 4) , and Z(2, 2) is; (x, y) = (-1, 2)

Centroid of a Triangle states that  the center of the triangle can be calculated as the point of intersection of all the three medians of that same triangle, and that this median is a line drawn right from the midpoint of one side to the opposite vertex.

We are given the coordinate of the vertices of the triangle as;

X(−4, 0) , Y(−1, 4) , and Z(2, 2)

Now, the formula to find the coordinates of the centroid of the triangle is; (x, y) = (x₁ + x₂ + x₃)/3, (y₁ + y₂ + y₃)/3

Thus, the coordinates of the Centroid is;

(x, y) = (-4 + (-1) + (2))/3, (0 + 4 + 2)/3

(x, y) = (-1, 2)

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From a set of whole numbers less than 25, the probability of getting a number either divisible by 5 or divisible by 3 is 11/25

The set of whole numbers = {0, 1,2,3,4,5.....}

The set of whole numbers less than 25 = {0,1,2,3,4,......,24}

The numbers divisible by 5 = {5, 10, 15, 20}

The numbers divisible by 3 = {3, 6, 9, 12, 15, 18, 21, 24}

The common term is 15

The probability = Number of favorable outcomes /  Total number of outcomes

The number of favorable outcome = 11

Total number of outcomes = 25

Substitute the values in the equation

The probability = 11/25

Hence, from a set of whole numbers less than 25, the probability of getting a number either divisible by 5 or divisible by 3 is 11/25

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Based on the image attached, the relationship are:

a). AB and BC - Both the segments are said to be perpendicular and they are intersecting at the point B.

b). AE and BF - Both segments are said to be parallel

c). EF and ED - Both are skew

d). Plane ABC and plane ABF - Both of the planes do  intersect at point AB

e). Plane AED and plane BFC - Both of the given planes are known to be parallel

if the ratio equality is accurate, parallel. If the lines are not parallel or if you can solve them as a system of simultaneous equations, the lines will intersect. If two crossing lines have a zero dot product, they are perpendicular.

If the lines are not parallel or intersecting, they are said to skew. Lines that are parallel never cross.

Therefore,

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The use of prime factorization to find the exponents of the given numbers gives  625 = 5⁴, 343 = 7³, 216 = 6³,  169 = 13², 256 = 4⁴; 256 =  2⁸ and 729 = 9³; 729 = 3⁶

When a number is written as a product of its prime factors, we have the prime factorization of the number e.g 8 = 2×2×2

An exponent is defined as a way of expressing large numbers in terms of powers e.g 81 = 3×3×3×3 = 3⁴

Thus, you can use prime factorization to find the exponent of the given numbers as follows:

625 as a power of 5

625 = 5×5×5×5 = 5⁴

343 as a power of 7

343 = 7×7×7 = 7³

216 as a power of 6

216 =  6×6×6 = 6³

169 as a power of 13

169 = 13×13 = 13²

256 as a power of 4; as a power of 2

256 = 4×4×4×4 = 4⁴

256 = 2×2×2×2× 2×2×2×2 = 2⁸

729 as a power of 9; as a power of 3

729 = 9×9×9 = 9³

729 = 3×3×3×3×3×3 = 3⁶

Therefore, 625 as a power of 5, 343 as a power of 7, 216 as a power of 6, 169 as a power of 13, 256 as a power of 4; as a power of 2 and  729 as a power of 9; as a power of 3 are 5⁴, 7³, 6³, 13², 4⁴; 2⁸ and 9³; 3⁶ respectively

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The mean of the distribution of sample means is 100.

Considering the values provided in the question,

Population mean = 100

We know that,

The sample mean is a reliable indicator of the population mean.

That is, E( sample mean)=Mean(sample mean)= population mean

Here population mean is 100, therefore mean of distribution of sample means is also 100.

The total of all the values in a sample is known as the Sample Mean. It is a statistical metric used to examine different variables throughout time. It is calculated by statisticians and researchers by dividing the total sum of all data fragment values by the total number of data sets.

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Answer: D

Step-by-step explanation: Took the test

Answer:

1.) 150/512 in.  

2.) 64/125 in.

Step-by-step explanation:

1.) V = l x w x h                That's the formula to find the volume of a rectangle

V = 6/8 x 5/8 x 5/8 in.    Plug in the numbers

V = 150/512 in.                Multiply

V = 75/256 in.                 Simplify

Since you're asked to not reduce don't write this answer. I only put it to show that it can be simplified.

2.) V = l^3                       This is the formula to find the volume of a cube

V = (4/5)^3 in.                 Plug in the numbers

V = 64/125 in.                 Miltuply

The value of x is 15

If two angles sum to 90 degrees, they are said to be complimentary angles. In other terms, a right angle is created when two complementary angles are combined (90 degrees). If the sum of angles 1 and 2 equals 90 degrees (i.e., angle 1 plus angle 2 = 90°), then the angles are complementary and are referred to as one another's complements.

∠1 and ∠2 are complementary angles i.e the sum of ∠1 and ∠2 is 90° .

Thus

∠1 + ∠2 = 90°

x° + (3x+30)° = 90°

x + 3x + 30 = 90

4x = 90-30

4x = 60

x = 15

Therefore the value of x is 15.

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Answer:

$24,067.32

Step-by-step explanation:

If you look up a compound interest calculator and put in the data correctly you should get $24,067.32

Answer:

(2x)-8 is the correct answer

Step-by-step explanation:

Hope this helps

With the help of some mathematical operations, we can conclude that after 42 months, coach will have a total amount of $8,356 in his bank account.

So, we know that coach gets 2.3% simple interest monthly.

Now, calculate the total amount after 42 months as follows:

Then, on monthly basis, the coach gets $97.75 as interest.

Then, for 42 months:

Hence, the total amount after 42 months:

Therefore, with the help of some mathematical operations, we can conclude that after 42 months, coach will have a total amount of $8,356 in his bank account.

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Correct question:

Coach deposits $4250 in the bank and gets 2.3% simple interest monthly. He keeps the money in the bank for 42 months without any deposits or withdrawals. How much money will he have in the bank after 42 months? Round to the nearest cent.

Answer:

y = x - 3

Step-by-step explanation:

Consider the equation "y = mx + b" :

y = mx + b

Since the slope is 1, you could input that into the equation:

y = (1)x + b

The variable "b" represents the y-intercept, therefore, to find the y - intercept, you would have to subtract 7 from each side of the coordinate points to get 0 as the x - coordinate to find the y - intercept:

(7    4)

-7 || -7

(0, -3)

Therefore, the y - intercept would be -3 and the equation would be:

y = x - 3

Answer:

Completely satisfied with their car:  60.00%

Step-by-step explanation:

I'll assume that "180 percent of people not satisfied . ." is meant to read "180 people not satisfied . . ."

Add the people in the groups to find a total.  Then divide the numeber of people in each group by the total.  This will provide a decimal number which can be multiplies by 100% to give the breakdown requested.

   Group              Count   Percent(%)

Not S.                      180        7.20

Somewhat S.          820      32.80

Completely S.       1500       60.00

Total People:       2500      100.00%

Answer:

5.68 ft

Step-by-step explanation:

12 inches = 1 feet

[tex]68 \: inches \: *\: \frac{1 feet}{12 \: inches} =\frac{68}{12} \: feet= 5.6777...\\\\68 \: inches \approx 5.68 \: feet[/tex]

Answer:

Step-by-step explanation:

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

Let the Beth deposite is x.Here r and n will be 1.

A=x(1+1/1)^5

Similarly
B=2x(1+1/n)^nt

B=2x(1+1/1)^5

There combined interest is:
A+B=x(1+1/1)^5+2x(1+1/1)^5

21=32x+64x

21=96x

x=21/96 is the beth deposite.

2x=2*21/96 is the Reena deposite

The value of x in the given triangle is x = 12  .

Angle Sum Property of the Triangle states that the sum of measure of all three sides of the triangle is 180° .

In the question ,

a triangular figure is given

in which , the measure of angle A is (6x - 19)°

the measure of angle B is [tex]=[/tex] 84°

the measure of angle C is [tex]=[/tex] (3x + 7)°

So , By Angle sum property ,

we get

∠A + ∠B + ∠C [tex]=[/tex] 180°

substituting the values of angle A, B and C ,

we get

(6x - 19)° [tex]+[/tex] 84° + (3x + 7)° [tex]=[/tex] 180°

6x - 19 [tex]+[/tex] 84 [tex]+[/tex] 3x + 7 [tex]=[/tex] 180

9x + 72 = 180

9x = 180 - 72

9x = 108

x = 108/9

x = 12

Therefore , the value of x is [tex]=[/tex] 12

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This comes to $141, indicating that Ms. Patel spent that money on four sets of pliers, two wrench sets, and a chisel set.

The given condition states that;

Make a ratio first.

This ratio might be expressed as 4:2:1 (in pliers, wrenches, and chisels).

Then, multiply every one of these sums by their respective prices before adding them all up.

Pliers : 4 times 17.50 equals $70

Wrenches : $2 x $21.5 = $43

Chisels : 1 x 28 equals $28

Thus,

Sum = $70 + $43 + $28

Sum = $141

This amounts to $141, proving that she purchased a chisel set, two wrench sets, and four pairs of pliers.

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The equation in standard form is x - y = 9

From the question, we have the following parameters that can be used in our computation:

Points = (8, –1) and (2, –5)

Point-slope form is y + 1 = (x – 8).

Recall that the point-slope form is y + 1 = (x – 8).

So, we have

y + 1 = (x – 8)

Open the brackets

y + 1 = x – 8

Subtract 1 from both sides

y = x - 9

Rewrite as

-x + y = -9

Multiply through by -1

x - y = 9

Hence, the equation is x - y = 9

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The total amount Joh spend when he was in the river for 4(1/2) hours is 29.865.

Given, Joh rent a kayak at a nearby state park.

He pay a fee of 12.99 plus 3. 75 for each hour that he spend in the water.

We have to find the amount he spend when he was in the water for 4(1/2) hours.

Total amount = 12.99 + hourly amount

Hourly amount = 3.75×4(1/2)

Hourly amount = 3.75×9/2

Hourly amount = 16.875

Total amount = 12.99 + 16.875

Total amount = 29.865

Hence, the total amount Joh spend when he was in the river for 4(1/2) hours is 29.865.

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Answer: By compare the graph of -6 ≤ x ≤-4 with the graph of x ≤-6 or x ≥-4 we can see that in first graph value is x belongs to [-6,-4] and in second graph we can see that x belongs to (-∞,-6] ∪ [-4,∞)

What does a coordinate mean in math?

a pair of values used to specify a point's position on a coordinate plane using the horizontal and vertical breakups from the two reference axes. typically represented by the pair of x-values and y-values (x,y).

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The perimeter of the given figure is 89.12 inches.

Given that, the shape is made up of one half-circle attached to a square with side lengths 16 inches.

The perimeter of a shape is defined as the total distance around the shape. It is the length of the outline or boundary of any two-dimensional geometric shape. The perimeter of different figures can be equal in measure depending upon the dimensions.

We know that, the perimeter of square is 4a, where a is side of a square.

When, a=16

The perimeter of square =4×16

= 64 inches

We have circumference of circle = 2πr

Circumference of a semi circle= πr

Here, radius(r)=8 inches

= 3.14×8

= 25.12 inches

Total perimeter = 64+25.12

= 89.12 inches

Therefore, the perimeter of the given figure is 89.12 inches.

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Answer: 3

I used PEMDAS in this explanation: Parenthesis, Exponents, Multiplication, Division, Addition, Subtraction. Also known as the order of operations

Step-by-step explanation:

-5 + (5+3) :

First, add 5+3 =8

-5+8

When adding a negative to a positive, first, switch the -5 and 8 around like so.

8 + (-5)

then turn the -5 into it's opposite and subtract ---> 5

8-5=3

Unworded explanation:

-5 + (5+3) :

-5 + 8

8 + (-5)

8-5 = 3

Answer:

b = 8 ft

Step-by-step explanation:

Formula we use,

→ (AC)² = (BC)² + (AB)²

Now the value of a will be,

→ (10)² = b² + (6)²

→ 100 = b² + 36

→ b² = 100 - 36

→ b = √64

→ [ b = 8 ft ]

Hence, value of b is 8 ft.