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Final answer:

To find the number of different ways Jacob can arrange 3 books on a single bookshelf out of 12 books, we use the concept of permutations. The number of arrangements is 1320.

Explanation:

To find the number of different ways Jacob can arrange 3 books on a single bookshelf out of 12 books, we use the concept of permutations. Permutations calculate the number of ways to arrange objects in a specific order. In this case, we need to find the number of permutations of 3 books out of 12, which can be calculated using the formula:

P(n, r) = n! / (n - r)!

Where n is the total number of books (12) and r is the number of books to be arranged (3).

Substituting the values into the formula, we get:

P(12, 3) = 12! / (12 - 3)! = 12! / 9!

Calculating the factorial, we have:

12! = 12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 479,001,600

9! = 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 362,880

Now, dividing the factorial values, we can calculate the number of arrangements:

P(12, 3) = 479,001,600 / 362,880 = 1320

Therefore, Jacob can arrange 3 books on a single bookshelf in 1320 different ways.

Answer:

199 square feet

Step-by-step explanation:

Given:

Trace needs a new carpet for her house.

Dimension of dining room = 6 feet by 4 feet.

Dimension of sitting area = 10 feet by 15 feet.

Dimension of breakfast nook = 5 feet by 5 feet.

Question asked:

How many square feet of carpet does she need ?

Solution:

First of all we will calculate the area of each part of the house and then add up.

[tex]Area \ of \ dining\ room=length\times width[/tex]

                                  [tex]=6\times4\\ \\ =24\ square\ feet[/tex]

[tex]Area \ of \ sitting\ part=length\times width[/tex]

                                  [tex]=15\times10\\ \\ =150\ square\ feet[/tex]

[tex]Area \ of \ breakfast\ nook=(side)^{2}[/tex]

                                       [tex]=5^{2} =25\ square\ feet[/tex]

Total carpet needed will be needed = For dining + For sitting area + For breakfast nook

                                              = 24 + 150 + 25

                                              = 199 square feet

Therefore, she needs 199 square feet of a new carpet for her house.

Answer:

x=-80

Step-by-step explanation:

Answer:

[tex]x=-80[/tex]

Step-by-step explanation:

[tex]a) (-4)x=320\\\\x=\frac{320}{-4} \\\\x=-80[/tex]

Step-by-step explanation:

Speakers =£ 31.5

Headphones =£ 4.8

Book =£ 3.85

Mobile phone =£ 36

mouse = £12.75

DVD =£ 10.2

Hope it will help you :)

Answer:

The probability that none will have high blood pressure is 0.0281

Step-by-step explanation:

The correct question is as follows;

Twenty percent of Americans ages 25 to 74 have high blood pressure. If 16 randomly selected Americans ages 25 to 74 are selected, find each probablility. a. None will have high blood pressure

This is a binomial problem. We shall solve in that line

The probability of success is 20% or 0.2 [(Americans ages 25 to 74 have high blood pressure)] p = 0.2

The probability of failure q is thus 1-p = 1-0.2 = 0.8

The probability of none is thus;

P(X= 0) = 16C0 p^0 q^16

= 16C0 * 0.2^0 * 0.8^16 = 0.0281

Answer:

The consumers in that commercial area create the demand for coffee shops. However, Jeff is the consumer for coffee shop employees.

Step-by-step explanation:

The consumers in that commercial area create the demand for coffee shops.

Jeff creates the demand for coffee shop employees.

Demand is an economic term that refers to the number of products or services that consumers wish to purchase at any given price level. The mere desire of a consumer for a product is not demand. Demand includes the purchasing power of the consumer to acquire a given product at a given period.

Supply is the number of goods an individual or business provides to the market which refers to the amount they produce at a specific point in time. For example, if Apple manufactures 100 iPhones, then this is the supply that is brought to the market.

Learn more about demand here https://brainly.com/question/1245771

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Answer:

h=0.748

Step-by-step explanation:

The value of x that corresponds to this point on the phase shift is 0.748.

The phase shift simply means when the graph of the sine and cosine function is shifted from their usual position.

The phase shift, is any value of x that occurs at the beginning of a cycle. In this case, value of x that corresponds to this point on the phase shift is 0.748.

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Answer: The probability is zero.

Step-by-step explanation:

The labels on the 4 cards are 1, 3, 5 and 7. Because the cards are equal, the probability of dragging at random each one of them is equal to 1/4 = 0.25.

Now, the probability that Tim selects a card labeled with a 4 is equal to the number of cards labeled with a 4, divided the total number of cards.

We do not have cards labeled with a 4, so the probability is:

p = 0/4 = 0

because we do not have any card labeled with a 4, the probability of selecting one at random is equal to zero.

Final Answer:

The probability is zero.

Explanation:

The labels on the 4 cards are 1, 3, 5 and 7. Because the cards are equal, the probability of dragging at random each one of them is equal to 1/4 = 0.25.

Now, the probability that Tim selects a card labeled with a 4 is equal to the number of cards labeled with a 4, divided the total number of cards.

We do not have cards labeled with a 4, so the probability is:

p = 0/4 = 0

because we do not have any card labeled with a 4, the probability of selecting one at random is equal to zero.

Answer:

y = 6+3x

Step-by-step explanation:

If y = f(x), it means y is depending on x. This shows that y is the independent variable and x is the dependent variable.

y variable will be the output depending on the input variable x.

According to the function rule, “The output is 6 greater than three times the input." This can be expressed mathematically as 3x+6 (x being the input)

Three times the input = 3x

6 greater than three times the input = 6+3x

Since y is output then;

y = 6+3x

The function rule is [tex]\boldsymbol{y=6+3x}[/tex].

A function rule is an equation that represents the relationship of the dependent and independent variables.

[tex]\boldsymbol{x}[/tex] is the independent variable.

[tex]\boldsymbol{y}[/tex] is the dependent variable.

The output is [tex]6[/tex] greater than three times the input.

[tex]y=6+3x[/tex].

So, the function rule is [tex]\boldsymbol{y=6+3x}[/tex].

Find out more information about function here:

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Answer:

4 × 10/9 = 40/9 is the solution

Answer: the first one

Step-by-step explanation:

Answer:

A or the first one on the left

Answer:

As the size of a school building increases, the number of student musicians increases because the scatterplot has a cluster that increases from left to right.

Step-by-step explanation:

Answer:

a is the answer

Step-by-step explanation:

Answer:

[tex]\frac{20}{9}[/tex] square feet

Step-by-step explanation:

We are given that

Side of square tile=[tex]\frac{1}{3} foot[/tex]

Total number of tiles used in rectangular floor=20

Area of square=[tex](Side)^2[/tex]

Area of square tile=[tex](\frac{1}{3})^2=\frac{1}{9}[/tex]square feet

Area of rectangular floor covered by square tiles =Area of 20 square tiles

Area of rectangular floor covered by square tiles=[tex]20\times \frac{1}{9}[/tex] square feet

Area of rectangular floor covered by square tiles=[tex]\frac{20}{9}[/tex] square feet

Hence, the area of rectangular floor covered by square tiles=[tex]\frac{20}{9}[/tex] square feet

Answer:

Mean (Average) 3.7777777777778

Median 4

Range 7

Mode 1, appeared 3 times

Geometric Mean 2.8976123026694

Largest 8

Smallest 1

Sum 34

Count 9

Step-by-step explanation:

Im bored so i gave you everything

Answer:

8/125 ft

Step-by-step explanation:2/5 x 2/5 x 2/5 = 8/125

Answer:

The answer to your question is Volume of a cube = 8/125 ft³

Step-by-step explanation:

Data

length of a side = 2/5 ft

Formula

Volume of a cube = side x side x side

Substitution

Volume of a cube = 2/5 x 2/5 x 2/5

-Just multiply the numerator and multiply the denominators

-Simplification

The Volume of a cube = 8/125 ft³

Answer: 16 pints

Step-by-step explanation:

There are 8 pints in a gallon so 8*2=

16 pints

Answer:

16 pints.

Step-by-step explanation:

Hello there!

There are 8 pints in a US gallon, so:

8x2=16 pints

Answer:

Therefore the rate change of distance between the car and the person at the instant, the car is 24 m from the intersection is 12 m/s.

Step-by-step explanation:

Given that,

A person stand 10 meters east of an intersection and watches a car driving towards the intersection from the north at 13 m/s.

From Pythagorean Theorem,

(The distance between car and person)²= (The distance of the car from intersection)²+ (The distance of the person from intersection)²+

Assume that the distance of the car from the intersection and from the person be x and y at any time t respectively.

∴y²= x²+10²

[tex]\Rightarrow y=\sqrt{x^2+100}[/tex]

Differentiating with respect to t

[tex]\frac{dy}{dt}=\frac{1}{2\sqrt{x^2+100}}. 2x\frac{dx}{dt}[/tex]

[tex]\Rightarrow \frac{dy}{dt}=\frac{x}{\sqrt{x^2+100}}. \frac{dx}{dt}[/tex]

Since the car driving towards the intersection at 13 m/s.

so,[tex]\frac{dx}{dt}=-13[/tex]

[tex]\therefore \frac{dy}{dt}=\frac{x}{\sqrt{x^2+100}}.(-13)[/tex]

Now

[tex]\therefore \frac{dy}{dt}|_{x=24}=\frac{24}{\sqrt{24^2+100}}.(-13)[/tex]

               [tex]=\frac{24\times (-13)}{\sqrt{676}}[/tex]

               [tex]=\frac{24\times (-13)}{26}[/tex]

               = -12 m/s

Negative sign denotes the distance between the car and the person decrease.

Therefore the rate change of distance between the car and the person at the instant, the car is 24 m from the intersection is 12 m/s.

The rate of change of the distance between the car and the person is [tex]\(-\frac{65}{12}\)[/tex] meters per second, indicating decreasing distance.

To find the rate of change of the distance between the car and the person at the given instant, we can use the concept of related rates. We'll use the Pythagorean theorem to relate the distances involved.

Step 1:

Establish variables.

Let (x) represent the distance the car has traveled north from the intersection, and let (y) represent the distance between the car and the person.

Step 2:

Formulate the equation using the Pythagorean theorem.

[tex]\[x^2 + y^2 = 24^2\][/tex]

Step 3:

Differentiate both sides of the equation with respect to time.

[tex]\[2x\frac{dx}{dt} + 2y\frac{dy}{dt} = 0\][/tex]

Step 4:

Plug in the given values and solve for [tex]\(\frac{dy}{dt}\)[/tex].

Given that the car is traveling north, [tex]\(\frac{dx}{dt} = 13\)[/tex]m/s.

When the car is 10 meters east, [tex]\(x = 10\).[/tex]

At that instant, when the car is 24 meters from the intersection, [tex]\(y = 24\).[/tex]

[tex]\[2(10)(13) + 2(24)\frac{dy}{dt} = 0\]\[260 + 48\frac{dy}{dt} = 0\]\[\frac{dy}{dt} = -\frac{260}{48} = -\frac{65}{12}\][/tex]

The rate of change of the distance between the car and the person at that instant is [tex]\(\boxed{-\frac{65}{12}}\)[/tex] meters per second. The negative sign indicates that the distance is decreasing.

Answer:

3 people

Step-by-step explanation:

$51/$17 = 3 people

- We know to start with $51 dollars because that is the total price of the meal.

- We also know each meal costs $17.

- Next, ask youself what we are trying to find? We are trying to find how many people are eating.

- Therefore to find that we need to take our starting amount $51 divided by $17 because that is the cost of 1 meal.

- $51/$17 = 3 people (whole cost/individual cost = # of people)

- To check this take 3 x 17 = 51 (Now we know it is correct)

- If you would like a further explanation please let me know.

Answer:

B

Step-by-step explanation:

Answer: B

Step-by-step explanation:

If you have a negative exponent its like you divide it

10^-2 = 0.01 then multiply it by 5 = 0.01 x 5 = 0.05

Answer:

22.36

Step-by-step explanation:

20*.86=17.2

12 *.43= 5.16

Final answer:

To find the total amount Rosa spent on the chocolate and candy, multiply the cost of a box of chocolate by 20 and the cost of a bag of candy by 12. Then, add the two amounts together.

Explanation:

To find the total amount Rosa spent on the chocolate and candy, we need to calculate the cost of each item and then add them together.

Given that a bag of candy costs $0.43 and a box of chocolate costs twice as much as a bag of candy, we can calculate:

The cost of a box of chocolate = $0.43 x 2 = $0.86

Rosa bought 20 boxes of chocolate, so the total cost of the boxes of chocolate = 20 x $0.86 = $17.20

Rosa also bought 12 bags of candy, so the total cost of the bags of candy = 12 x $0.43 = $5.16

Finally, to find the total amount Rosa spent, we add the cost of the boxes of chocolate and the bags of candy together:

Total spent on chocolate and candy = $17.20 + $5.16 = $22.36

The cost for making the sign is $812.38

Step-by-step explanation:

Radius = 28 cm

Cost of aluminum per square cm = $0.33

Area of the sign = π(r x r)

= (3.14) (28 x 28)

= (3.14) (784)

= 2461.76 square cm

Total cost to make the sign = 2461.76 x 0.33

= 812.38

The cost for making the sign is $812.38

To find the cost of making the circular aluminum sign, first calculate the area of the circle, then multiply the area by the cost per square centimeter. The total cost is $812.65.

To determine the cost to make a circular aluminum sign with a radius of 28 centimeters, we first need to find the area of the circle. The formula for the area of a circle is:

→ A = πr²

Given:

→ Radius, r = 28 cm

→ π ≈ 3.14

We can now calculate the area:

→ A = 3.14 × (28 cm)²

→ A = 3.14 × 784 cm²

→ A = 2,462.56 cm²

Next, we calculate the cost of the aluminum sheet:

→ Cost = Area × Price per cm²

→ Cost = 2,462.56 cm² × $0.33/cm²

→ Cost = $812.65

Therefore, it will cost $812.65 to make the circular aluminum sign.

Answer:

-47b + 19

Step-by-step explanation:

Answer:

Combine like terms is the first step.

Step-by-step explanation:

Subtract '122-7' on both sides and that gives you [tex]2x^2=-115[/tex]

Which equation represents a proportional relationship?

C. y=1/2x+3

Answer:

$4.90 per towel

Step-by-step explanation

If each towel costs and equal amount, you divide the full amount of the pack, $19.60, by the number of towels, which is 4, which gives you $4.90 as the answer.

Answer:

The answer for this question is 4.

Step-by-step explanation:

2+2=4

Answer: perimeter = 96mm, Area = 564mm².

Step-by-step explanation:

From the diagram, it is a trapezium, it has a rectangle joined together by a right angled triangle. Now to find the perimeter, we add all the dimensions together. To get the other side of the rectangle, which is also the perpendicular height of the figure, we take the Pythagoras. Let the perpendicular height = x

Therefore,

25² = ײ + 7²

625 = x² + 49

x² = 625 - 49

x² = 576

x. = √576

= 24.

Now the perimeter

= 20 + 25 + 7 + 20 + 24

= 96mm.

Area of the figure will be

= 1/2( a + b )h

Where a = 20, b = 20 + 7 = 27 and h = 24, now substitute for the values

( 20 + 27) x 24

---------------------

2

= 47 x 24/2

= 47 x 12

= 564mm²