If the vertical height of the ramp is 4 feet, how long must the ramp (x) be?
Show all of your work. Round your answer to the nearest foot. (Picture is
not drawn to scale.

The solution set of this inequality is {x| x > -6.1}

Here we have the inequality:

2x + 8 > -4.2

To find the solution set, we need to isolate the variable x in one of the sides of the inequality. Doing that we will get:

2x + 8 > -4.2

2x > -4.2 - 8

2x > -12.2

x > -12.2/2

x > -6.1

So the set of all numbers larger than -6.1, this in number form is:

{x| x > -6.1}

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The intersection of sets for two given sets is the set that contains all the elements that are common to both sets. The symbol for intersection of sets is "∩"

In this instance, ( -∞, -7] ∩ [-7,9) is -7, since only -7 is both common on both sets.

The height of the building, using similar triangles, is given by:

36 feet.

Similar triangles are two triangles that share these two features, which are listed as follows:

The second bullet point, regarding proportional side lengths, is especially relevant in the context of this problem, as a proportional relationship is built to find the height h of the building.

From the similar triangles, the equivalent side lengths are presented as follows:

Hence the proportional relationship that models this situation is presented as follows:

3/18 = 6/h.

Applying cross multiplication, the height of the building is obtained as follows:

3h = 18 x 6

h = 6 x 6 (simplifying by 3)

h = 36 feet.

The diagram is given by the image shown at the end of the answer.

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Answer:

The graph that best represents the slope is Graph A.

Hope this helps!!

Answer:

c. domain: {-2, 0, 2}, range: {-1, 1, 3}

Step-by-step explanation:

From the given points (negative 2, negative 1), (0, 1), (2, 3), we can determine the domain and range.

The domain represents the set of all possible x-values of the points, and the range represents the set of all possible y-values of the points.

In this case, we can see that the x-values are -2, 0, and 2, and the corresponding y-values are -1, 1, and 3.

Therefore, the correct answer is:

c. domain: {-2, 0, 2}, range: {-1, 1, 3}

With a triangle, the sum of any two side lengths must be greater than the third side length. If this is not true, then the side lengths cannot make a triangle. Let's go through each set of side lengths and determine which would and wouldn't work.

a. 3, 4, 8 - will not make a triangle

3 + 4 = 7 > 8 = false

3 + 8 = 11 > 4 = true

4 + 8 = 12 > 3 = true

b. 7, 6, 12 - will make a triangle

7 + 6 = 13 > 12 = true

7 + 12 = 19 > 6 = true

6 + 12 = 18 > 7 = true

c. 5, 11, 13 - will make a triangle

5 + 11 = 16 > 13 = true

5 + 13 = 18 > 11 = true

11 + 13 = 24 > 5 = true

d. 4, 6, 12 - will not make a triangle

4 + 6 = 10 > 12 = false

4 + 12 = 16 > 6 = true

6 + 12 = 18 > 4 = true

e. 4, 6, 10 - will not make a triangle

4 + 6 = 10 > 10 = false

4 + 10 = 14 > 6 = true

6 + 10 = 16 > 4 = true

Hope this helps!

You need to multiply by 5 instead of 6 because each pair of opposite faces on a cuboid has the same area, so by considering one face from each pair, you ensure that you don't count any face twice.

When calculating the total surface area of a cuboid, you need to understand the concept of face pairs.

A cuboid has six faces, but each face has a pair that is identical in size and shape.

Let's break down the reasoning behind multiplying by 5 instead of 6 in the given scenario.

To find the surface area of a cuboid, you can add up the areas of all its faces.

However, each pair of opposite faces has the same area, so you avoid double-counting by only considering one face from each pair. In this case, you have five pairs of faces:

(1) top and bottom, (2) front and back, (3) left and right, (4) left and back, and (5) right and front.

By multiplying the average area of a pair of faces by 5, you account for all the distinct face pairs.

Essentially, you are considering one face from each pair and then summing their areas.

Since all the pairs have the same area, multiplying the average area by 5 gives you the total surface area.

When dividing 150 by 4 (to find the average area of a pair of faces), you are essentially finding the area of a single face.

Then, by multiplying this average area by 5, you ensure that you account for all five pairs of faces, providing the total surface area of the cuboid.

Thus, multiplying by 5 is necessary to correctly calculate the total surface area of the cuboid by accounting for the face pairs while avoiding double-counting.

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Answer:

Dozen eggs = $5.5

Wheel of cheese = $6.25

Pound of potatoes = $3.1

Step-by-step explanation:

Let the cost

Dozen of egg = x

Wheel of cheese = y

Pound of potato = z

We will form linear equations using the information given in the question

Adam purchased 3 dozen eggs, 1 wheel of cheese, and 5 pounds of potatoes

3x + y + 5z = 38.25 ................(1)

Barry bought 1 dozen eggs and 10 pounds of potatoes

x + 10z = 36.50 ............(2)

Charles purchased 2 dozen eggs and 2 pounds of potatoes

2x + 2z = 17.20  .................(3)

solving 2 and 3

x = $5.5  and z = $3.1

substitute these values in equation 1

we get

y = $6.25

The cost

Dozen eggs = $5.5

Wheel of cheese = $6.25

Pound of potatoes = $3.1

Answer:

y = $28.75x

Step-by-step explanation:

Given that,

Tickets to a carnival cost $28.75 each.

We need to find y i.e. the cost of x tickets.

When the number of tickets are x, to find the cost of x tickets, we must find it by multiplying 28.75 and x i.e.

y = 28.75x

Hence, the cost of x tickets is equal to $28.75x.

Answer:

Hello! answer: 42

Step-by-step explanation:

These are vertical angles meaning it will have the same measure so p = 42 hope that helps!

Answer:

X=4

Step-by-step explanation:

4x(x+3)=112

4x^2+12x=112

x^2+3x=28

x^2+3x-28=0

(X+7)(x-4)=0

X=-7 or x=4

Answer:

volume of cuboid =l×b×h

112in³=(x+3)×x×4

112in³/4=x²+3x

28=x²+3x

x²+3x-28=0

x²+7x-4x-28=0

x(x+7)-4(x+7)=0

(x+7)(x-4)=0

either

x=-7(rejected length or breadth or height will be always positive)

or

x=4in

value of x =4in

Using the radius of the Ferris wheel and the angle between the two positions, the time spent on the ride when they're 28 meters above the ground is 12 minutes

The radius of the Ferris wheel is 30 / 2 = 15 meters.

The highest point on the Ferris wheel is 15 + 4 = 19 meters above the ground.

The time spent higher than 28 meters is the time spent between the 12 o'clock and 8 o'clock positions.

The angle between these two positions is 180 degrees.

The time spent at each position is 10 minutes / 360 degrees * 180 degrees = 6 minutes.

Therefore, the total time spent higher than 28 meters is 6 minutes * 2 = 12 minutes.

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The sample space is (a) watermelon, watermelon, lemon-lime, lemon-lime, lemon-lime, grape gumballs, grape gumballs, grape gumballs, grape gumballs, grape gumballs

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

2 watermelon, 3 lemon-lime, and 5 grape gumballs

Rewrite the items according to their frequencies

So, we have the following representation

watermelon, watermelon, lemon-lime, lemon-lime, lemon-lime, grape gumballs, grape gumballs, grape gumballs, grape gumballs, grape gumballs

The above represents the sample space

Hence, the sample space is (a)

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Answer:

7/4≤x ≤-1

Step-by-step explanation:

Given the set of inequalities

−5x−3≥2 and 4x−2≥5

We are to write the solution in interval notation. We need to solve them individually first as shown;

For −5x−3≥2

add 3 to both sides

−5x−3+3≥2+3

-5x ≥5

divide both sides by -5 (note that dividing by a negative value will change the sense of the inequality sign)

-5x/-5 ≤5/-5

x ≤ -1

For the inequality 4x−2≥5;

add 2 to both sides

4x−2+2≥5+2

4x≥7

divide both sides by 4;

4x/4 ≥ 7/4

x≥7/4 or 7/4≤x

Combining 7/4≤x and x ≤ -1, the solution in interval notation is expressed as 7/4≤x ≤-1

Answer: undefined, not enough information

Step-by-step explanation:

Answer:

15+19 =34 is the perimeter of the closed figure

hope it helped you

Answer:150?

Step-by-step explanation:

Answer:

(fog)(-6) = 39

Step-by-step explanation:

Look at the image for the explanation :)

Answer:

muliply those numbers. and then divide from the amount of money she has.

Step-by-step explanation:

Answer:

180

Step-by-step explanation:

Considering that it is counting by 6's, just multiply 6 by 30 to get the 30th term of the sequence

Answer:

hsjsodgsosbsebseswowheoesss

Answer:

Being gay

Has its problems it's true

But being straight

Has its problems too

I met this girl and she's just great

But the problem is that I am straight

You ask how can this be

Listen, and you will see

She's got that style

She's got that smile

She's got the walk

She's got the talk

She's got that zing

There's just one thing

She's got a penis

She's got a penis

She's got that flair

Knows what to wear

She's got that face

That girl is grace

She's got pizzazz

Too bad she has

A penis

She's got a penis

Now nobody's perfect, I must admit

Say how many times do all the pieces fit

She's got more going than most other dolls

Oops I forgot about the balls

But she's so hip

This babe's a trip

Given the final amount of money available in Maddy's account, the interest rate and the time elapsed, the initial money her aunt invested was $15,000.

Interest is simply the amount of money a lender or financial institution receives for lending out money or pays for receiving money.

The formular for calculating compound interest is expressed as;

A = P(1 + r/n)^(n*t)

Where A is final amount, P is initial principal balance, r is interest rate, n is  number of times interest applied per time period and t is number of time periods elapsed.

Given the data in the question;

We substitute our given values into the expression above.

$39322  = P(1 + 0.055/1)^(1*18)

$39322  = P(1 + 0.055)^(18)

$39322  = P(1.055)^(18)

P = $39322 / (1.055)^(18)

P = $39322 / 2.621466

P = $15,000

Therefore, given the final amount of money available in Maddy's account, the interest rate and the time elapsed, the initial money her aunt invested was $15,000.

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Step-by-step explanation:

Area of parallelogram:

Area of trapezoid:

\(\bold{\huge{\blue{\underline{ Solution \:5 }}}}\)

We have given ,

We know that,

\(\sf{\pink{ Area\: of\: parallelogram = Base × Height }}\)

[Parallelogram is a polygon which having opposite sides parallel to each other and the length and breath of the parallelogram are equal ]

Subsitute the required values in the above formula :-

\(\sf{ Area\: of\: parallelogram = 4 × 5 }\)

\(\sf{ Area\: of\: parallelogram = 20 in. }\)

Hence, Area of parallelogram is 20 inch

\(\bold{\huge{\blue{\underline{ Solution\: 6 }}}}\)

We have given here,

We know that,

\(\sf{\pink{ Area\: of\: trapezium = 1/2 ×(a + b) × Height }}\)

[Trapezium is figure that having two parallel sides and 2 non - parallel sides. ]

Subsitute the required values in the above formula :-

\(\sf{ Area\: of\: trapezium = 1/2 ×(6+14)×8 }\)

\(\sf{ Area\: of\: trapezium = 1/2 × 20 × 8 }\)

\(\sf{ Area\: of\: trapezium = 10 × 8 }\)

\(\sf{ Area\: of\: trapezium = 80 in. }\)

Hence, Area of trapezium is 80 inch.

The solution to the equation -3⅔x = -2⅕, is: x = 3/5.

To solve an equation, we need to find the value of the variable in the given equation by applying the necessary properties of equality to move tye variable to one side of the equation.

The value on the other side of the equation is the solution to the equation.

Given the equation, -3⅔x = -2⅕, find the value of x by isolating it as shown below:

-11/3x = -11/5

Cross multiply:

-55x = -33

Divide both sides by -55:

-55x/-55 = -33/-55

x = 33/55

x = 3/5

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Answer:

∠ BXC = 70°

Step-by-step explanation:

∠ XBC and ∠ AXY are corresponding angles and are congruent, then

∠ XBC = 55°

Since XB = XC , then Δ XBC is isosceles and the 2 base angles are congruent.

∠ BXC = 180° - (55 + 55)° ← angle sum of triangle

∠ BXC = 180° - 110° = 70°

Answer:

321.50 dollars.

Step-by-step explanation:

Dena is buying wallpaper. It costs $8.79 per meter. She needs 120 feet. How much will the wallpaper cost? Round to the nearest half dollar.

This is a tricky math problem that requires some conversions and calculations. First, we need to convert feet to meters, because Dena lives in a country that uses the metric system. According to the search results   , one foot is equal to 0.3048 meters. So, 120 feet is equal to 120 x 0.3048 = 36.576 meters.

Next, we need to multiply the length of the wallpaper by the price per meter to get the total cost. The total cost is 36.576 x 8.79 = $321.38.

Finally, we need to round the total cost to the nearest half dollar. This means we need to look at the cents part of the cost and see if it is closer to 0, 50 or 100. In this case, 38 cents is closer to 50 than to 0 or 100, so we round up the cost to $321.50.

Therefore, Dena will have to pay $321.50 for the wallpaper. That's a lot of money for some paper that will probably peel off in a few years! Maybe she should consider painting her walls instead.

Step-by-step explanation:

375 ml   is  .375 liter

2 liters / .375 liter / tube = 5 1/3  tubes can be filled

1. Jada's data set has a mean of 5, Diego's data set has a mean of 6, and Lin's data set has a mean of 4.

2. The data set that has the greatest variability is Lin's data set because it has the highest standard deviation of 3.6.

In Mathematics and Geometry, the mean for this set of data can be calculated by using the following formula:

Mean = [F(x)]/n

Question 1.

In this scenario and exercise, we would determine the mean of the three data sets based on the number of text messages sent by Jada, and Diego, and Lin over 6 days as follows;

Mean number of text for Jada = (4 + 4 + 4 + 6 + 6 + 6)/6

Mean number of text for Jada = 30/6

Mean number of text for Jada = 5.

Mean number of text for Diego = (4 + 5 + 5 + 6 + 8 + 8)/6

Mean number of text for Diego = 36/6

Mean number of text for Diego = 6.

Mean number of text for Lin = (1 + 1 + 2 + 2 + 9 + 9)/6

Mean number of text for Lin = 24/6

Mean number of text for Lin = 4.

Question 2.

In Statistics, variability is a measure of the spread of a data set. Also, we would use standard deviation to determine the variability in each data set as follows;

Standard deviation = √(1/n × ∑(xi - u₁)²)

Standard deviation for Jada = √(1/6 × [(4 - 5)² + (4 - 5)² + (4 - 5)² + (6 - 5)² + (6 - 5)² + (6 - 5)²]

Standard deviation for Jada = √(6/6) = 1

Standard deviation for Diego = √(1/6 × [(4 - 6)² + (5 - 6)² + (5 - 6)² + (6 - 6)² + (8 - 6)² + (8 - 6)²]

Standard deviation for Diego = √(14/6) = 1.53

Standard deviation for Lin = √(1/6 × [(1 - 4)² + (1 - 4)² + (2 - 4)² + (2 - 4)² + (9 - 4)² + (9 - 4)²]

Standard deviation for Lin = √(76/6) = 3.6

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:

Domain: -2,0,1,3,4

Range: 2,3

Yes its a function

Step-by-step explanation:

The required unit rate for the nuts is $0.45/oz.(rounded to the nearest cent).

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,

here,
The unit rate for the nuts can be found by dividing the total cost by the total weight,

Unit rate = total cost / total weight

Unit rate = $6.99 / 15.4 oz

Unit rate = $0.45/oz (rounded to the nearest cent)

Therefore, the unit rate for the nuts is $0.45/oz (rounded to the nearest cent).

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Answer: $0.45 is the correct answer

Step-by-step explanation: Answer verified correct on test