Which equation would help find the measure of

Answer:

2/3

Step-by-step explanation:

Which equation represents a proportional relationship?

C. y=1/2x+3

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:

For a $45 purchase the discount would be $-4.5

the sales price $40.5

For a $110 purchase the discount is  $-11

The sales price $99

Step-by-step explanation:

To find the discount on an item first multiply the original cost of the item by the percentage discounted. in this case,

$45 × 0.10 = $4.5

$110 × 0.10 =$11

$4.5 and $11 are respective discount amounts

now simply subtract the amount of the discount from the original price

$110 - $11 = $99

$45 - $4.5 =  $40.5

These are your final sale prices after discount.

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:

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:

The events a) and c) are mutually exclusive.

Step-by-step explanation:

a) This is mutually exclusive, each card has a unique value between 2 and 10, or it is a jack, queen, king, or an Ace. A single card cant have two different values at the same time.

b) This is not mutually exclusive, since you can get a king of clubs. Each card can have any combination of one suit and one value.

c) A face card is either a Jack, a Queen or a King, it is not an Ace. For the same argument of a), a card cant have two different values, therefore this event is mutually exclusive.

d) This is not mutually exclusive, since a card can have any suit independently of the value it has (same argument than b), therefore, a card can be a face card and a spade at the exact time.

Therefore, events a and c are mutually exclusive.

a)    Getting a 7 and getting a jack: Mutually exclusive events

b)    Getting a club and getting a king: Not mutually exclusive events

c)    Getting a face card and getting an ace: Mutually exclusive events

d)    Getting a face card and getting a spade: Not mutually exclusive events

A standard deck of cards has 52 cards having 13 ranks each of 4 suites. The 13 ranks are

[tex]\text{Ranks}=\{Ace,2,3,4,5,6,7,8,9,10,Jack,Queen,King\}[/tex]

and the suites are

[tex]Suites=\{Clubs,Diamonds,Hearts,Spades\}[/tex]

a)    Getting a 7 and getting a jack:

Since a 7 and a Jack are different rank elements, you either pick a 7 of a suite, or a Jack of a suite, but never both. So, the events are mutually exclusive.

b)    Getting a club and getting a king:

Since a Club is a suite and a King is a Rank, the sample space will have a King of Clubs card. So, the events are not mutually exclusive.

c)    Getting a face card and getting an ace:

A face card is a card with a face on it. Faces are Ranks, but an Ace is also a Rank. The sample space contains cards with only one Rank per card. So, the events are mutually exclusive.

d)    Getting a face card and getting a spade:

Faces are Ranks, and a Spade is a suite. The sample space will contain face cards for the Spade suite of cards. So, the events are not mutually exclusive.

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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:

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:

-47b + 19

Step-by-step explanation:

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:

[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:

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

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.

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Answer:

4 × 10/9 = 40/9 is the solution

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: 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:

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:

12,000 people were present

Step-by-step explanation:

In this question, we are asked to calculate the number of people in a park on an afternoon given the measurements of the park and its population density.

Firstly, we calculate the area of the park.

Mathematically the area is the product of the length and width = 0.5 * 2.5 = 1.25 square miles

Let’s convert this to acres. From the question, we know that one square mile is 640 acres, this mean that 1.25 square mile would be 1.25 * 640 = 800 acres

Now let’s consider the population density of 15 people per acre, the number of people present is thus 800 * 15 = 12,000 people

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:

  125

Step-by-step explanation:

The volume scale factor is the cube of the scale factor of linear dimensions:

  5³ = 125

The volume scale factor is 125.

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].

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Answer:N10500

Step-by-step explanation:

10%of 14000=1400

20%=1400x2=2800

5%=1400 divided by 2=700

25%=2800+700=3500

14000-3500=10500

hope this helps

Answer:

4

Step-by-step explanation:

If you prime factorization both

for 16 you get 2^4= 2^2*2^2

for 44 you get 2^2*11

they both have 2^2 so 4

Look at the attached picture⤴

Hope it will help u...

Answer:

40%

Step-by-step explanation:

Total Number of Students in Introductory Physics Course =100

Number of Math Majors = 60

Number of Science Majors = 40

Relevant Facts

Therefore, there is a 40 out of 100 chance that Sarah is a science major.

Expressed in percentage, there is a 40% chance that Sarah is a science major.

There is a 40% chance that Sarah is a science major.

To determine the probability that Sarah is a science major, we use the information given about the composition of the student group. There are 100 students in total, 60 of whom are math majors, and 40 are science majors.

To find the probability that Sarah is a science major, we simply take the number of science majors and divide it by the total number of students. Therefore, the probability (P) is calculated as:

So, there is a 40% chance that Sarah is a science major.

Answer:

Stacey is 16 miles far from the beginning of the trail.

Step-by-step explanation:

Given:

Stacey's total hike journey to NCT, Colorado = 18 miles

Distance covered by her to, a resting spot = 4 miles

We have to find:

How far from the beginning of the trail is Stacey [tex]6[/tex] hours after leaving the resting spot.

According to the question.

Distance remaining = [tex](18-4) = 14[/tex] miles

Time taken = [tex]6[/tex] hours    Speed maintained = [tex]2[/tex] mph

After leaving the resting spot she has covered a distance :

⇒ [tex]Distance = speed\times time[/tex]

⇒ [tex]Distance = 2\times 6[/tex]

⇒ [tex]Distance = 12[/tex] miles.

In [tex]6[/tex] hours she has covered [tex]12[/tex] miles and also she has covered [tex]4[/tex] miles before stopping here.

From the beginning she has covered :

⇒ [tex]Total\ distance =(4+12)[/tex]

⇒ [tex]Total\ distance = 16[/tex] miles.

Stacey is 16 miles far from the beginning of the trail.

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