Round to 2 decimal places *

1 point

An architect is designing a building topped with a hemispherical dome. She

creates a scale model of the building using a scale of 0. 25 inch : 1 foot. In

the scale model, the diameter of the dome is 23. 75 inches.

What will be the circumference, in feet, of the actual dome?

This graph represents a function Because it passes the vertical line test.

Let us first understand the Vertical Line Test.

In this test, we draw a few random vertical lines on a graph and check whether any one or more than one lines intersect the graph, no matter once or more.

If there exists a line that intersects the graph, we say the graph passes the vertical line test.

The vertical line test is a visual way to determine if a curve is a graph of a function or not. A function can only have one output, y, for each unique input, x.

Hence this graph passes the vertical line test because there are many vertical lines that intersect it.

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These numbers represent the distribution of preferences among the surveyed respondents for different types of food.

The given survey results provide the count or frequency of respondents who identified each type of food as their favorite. Here's an explanation of the results:

Italian food: 10 respondents

This means that out of the total number of respondents surveyed, 10 individuals specified Italian food as their favorite.

Mexican food: 20 respondents

Similarly, 20 respondents, out of the total surveyed, mentioned Mexican food as their favorite.

Chinese food: 30 respondents

For Chinese food, 30 respondents favored it as their preferred cuisine among those surveyed.

Anything else: 40 respondents

The category "Anything else" indicates that 40 respondents had a favorite food other than Italian, Mexican, or Chinese cuisine.

Overall, these numbers represent the distribution of preferences among the surveyed respondents for different types of food.

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Answer:

It should be c.

Step-by-step explanation:

Answer: I think it’s c

Step-by-step explanation:

We need to find the first partial derivative of the function f(x, y) = x^9y with respect to x and y.

To find the first partial derivatives of the function, we differentiate the function with respect to each variable while treating the other variable as a constant.

Taking the partial derivative with respect to x, we treat y as a constant:

∂f/∂x = \(9x^8y\).

Next, taking the partial derivative with respect to y, we treat x as a constant:

∂f/∂y = \(x^9\).

Therefore, the first partial derivatives of the function f(x, y) = \(x^9y\) are:

∂f/∂x = \(9x^8y,\)

∂f/∂y = \(x^9\).

These partial derivatives give us the rate of change of the function with respect to each variable. The first partial derivative with respect to x represents how the function changes as x varies while keeping y constant, and the first partial derivative with respect to y represents how the function changes as y varies while keeping x constant.

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Answer:

Numbers are 29 and 34

Step-by-step explanation:

Let x = one number

let y = second number

x + y = 63

x - y = 5

substitution method, x = 5 + y

5 + y + y = 63

2y + 5 = 63

2y = 58

y = 29

Find value of x:  x - 29 = 5

x = 34

Answer:

a) Upwards

b) x = -1

c) (-1,-9)

d) x intercepts; (2,0) and (-4,0)

y intercept is (0,-8)

Step-by-step explanation:

a) As we can see, the parabola faces upwards

b) To find the axis of symmetry equation, we look at the plot of the graph and see the point through the vertex of the parabola that exactly divides the parabola into two equal parts

The x-value that the line passes through here is the point x = -1 and that is the equation of the axis of symmetry

c) The vertex represents the lowest point of the circle here,

As we can see, this is the point through which the axis of symmetry passes through to make a symmetrical division of the parabola

We have the coordinates of this point as

(-1,-9)

d) The intercepts

The x-intercept are the two points in which the parabola crosses the x-axis

We have this point as 2 and -4

The x-intercepts are at the points (2,0) and (-4,0)

For the y-intercept; it is the y-coordinate of the point at which the parabola crosses the y-axis and this is the point (0,-8)

The fall in the level of oil is 1.4147 cm when the total volume of oil consumed is 1 liter.

We assume the drop in the level of water to be d cm.

Since the container is cylindrical in shape, its volume is given as:

V = πr²h, where V is the volume, r is the radius, and h is the height.

In the question, we are given that the diameter of the can is 30 cm.

Hence its radius = 30/2 = 15 cm.

The capacity of the container is given to be 30 liters or 30*1000 = 30000 cm³.

The volume of the oil used = 1 liter or 1*1000 = 1000 cm³.

Thus, substituting V = 1000, r = 15, and h = d, in the formula of the volume, V = πr²h, we get:

1000 = π(15)²(d),

or, d = 1000/(225π) = 1.4147.

Thus, the fall in the water level is 1.4147 cm.

Therefore, the fall in the level of oil is 1.4147 cm when the total volume of oil consumed is 1 liter.

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Answer:

Answer

2x+3y=14,2x−3y=2

Adding :

2x+3y=14

2x−3y=2

__________

4x=16

x=4

∴xy=4×2

=8

2×4+3y=14

8+3y=14

3y=6

y=2

Step-by-step explanation:

here you go

Answer: The y-intercept is found by substituting known values for x and y in the equation and solving for b. the known values are (x,y) = (2,8.4) Equation of y = 4.2*x + b becomes 8.4 = 4.2*2 + b

Step-by-step explanation:

Yes, the point (1, -4) is a solution to the given system of equations.

To determine if the point (1, -4) is a solution to the system of equations, we substitute the values of x and y into each equation and check if both equations are satisfied.

Given equations:

y = -4x    ... (1)

y = x - 5  ... (2)

Substituting x = 1 and y = -4 into equation (1):

-4 = -4(1)

-4 = -4

The equation is true when x = 1 and y = -4 in equation (1).

Substituting x = 1 and y = -4 into equation (2):

-4 = 1 - 5

-4 = -4

The equation is also true when x = 1 and y = -4 in equation (2).

Since both equations are satisfied when x = 1 and y = -4, the point (1, -4) is indeed a solution to the given system of equations.

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Jeremy paid $20.40 for a box of 15 pens.

The cost of one pen can be calculated by dividing the total cost by 15. This is shown below:

Hence, each pen costs $1.36.

The cost of each pen is $1.36.

We will use the formula:

Cost of one pen = total amount/number of pens

Given in the question,

Total amount = $20.40

Number of pens = 15

Now, we will put the values in the above formula,

Cost of one pen = 20.40 / 15

= $1.36

Therefore, the cost of each pen is $1.36.

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Using the concept of application of derivative it is concluded that the rate of change in the area of square tile is 94.25 cm²/hour.

The area of the square is defined as the square of its sides.

Let the side of the square is a then its area will be a².

Area of square figure = Side².

Let the side of the square is x= 29cm.

It is given that the side 29 cm tile is growing by 1.625 cm per hour on heating.

And the rate of change in side of square dx/dt = 1.625 cm/hour

We have to calculate the rate of change in an area of the square (A).

hen, area A = x²

On differentiating A with respect to time(t) we get a rate of change in area

dA/dt = d(x²)/dt

= 2x dx/dt

= 2×29×1.625

= 94.25 cm²/hour

Hence, the rate of change in the area of the square tile is 94.25 cm²/hour.

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Answer:

1.44

Step-by-step explanation:

1 box 18 candy bars each box 12.49

18 divide by 12.49 equals 1.44 each candy bars

Answer:

x = 24

Step-by-step explanation:

if a and b are parallel then

62 and 5x - 2 are same- side interior angles and sum to 180° , that is

5x - 2 + 62 = 180

5x + 60 = 180 ( subtract 60 from both sides )

5x = 120 ( divide both sides by 5 )

x = 24

thus for a to be parallel to b , then x = 24

The mass of the planet Mercury is 1.74 × 10⁻⁴ kg time the mass of the planet Jupiter.

Mass of Mercury = 3.3 × 10²³ kg

Mass of Jupiter = 1.9 × 10²⁷ kg

We need to find that how many times the mass of Mercury is the mass

of Jupiter.

For this, we will divide the mass of mercury with the mass of Jupiter.

So, we get that:

= ( 3.3 × 10²³ kg ) ÷ ( 1.9 × 10²⁷ kg )
Solving the expression by using the properties of exponents, we get that:

= 1.74 × 10⁻⁴ kg.

Therefore, we get that, the mass of the planet Mercury is 1.74 × 10⁻⁴ kg time the mass of the planet Jupiter.

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Answer:

4

Step-by-step explanation:

m = 4

Answer:

Step-by-step explanation:

Let's try all of them one by one.

Our equation is 4x + 2y + 3 = 19.

A:

20 + 6 + 3 = 19

Not quite!

B:

16 + 10 + 3 = 19

Still not it!

C:

12 + 4 + 3 = 19

We got it!

But still, we check D.

8 + 10 + 3 = 21

Nope.

C (or the 3rd option) is our answer.

I hope this helped.

Answer:

96 yards^2

Step-by-step explanation:

When you are looking for square yards, that is the area you are calculating. The area of a rectangle is length×width.

Area = 12 ×

= 96

There are 96 square yards in a 12 by 8 rectangle. Hope this helps!

The length of the building should be measured in meters, as that is the most appropriate unit.

The most suitable unit to measure the length of the building will be measuring the length of the building in meters.

Therefore, the length of the building should be measured in meters, as that is the most appropriate unit.

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Answer:

(0,21)

Step-by-step explanation:

when you want to find the x intercept make y=0

to find the y intercept make x=0

If both p and 2p+1 are prime, then 2p+1 is a safe prime and p is a Sophie Germain prime.

Sophie Germain was a French mathematician who used these primes to investigate Fermat's Last Theorem, a famous mathematical conjecture that was finally proved in 1994 by Andrew Wiles. A safe prime is a prime number of the form 2p+1, where p is also a prime number, and it is called "safe" because it has some cryptographic properties that make it useful in certain encryption schemes.                                                                                                                                          In number theory, Fermat's Last Theorem (sometimes called Fermat's conjecture, especially in older texts) states that no three positive integers a, b, and c satisfy the equation an + bn = cn for any integer value of n greater than 2. The cases n = 1 and n = 2 have been known since antiquity to have infinitely many solutions.

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Answer:

91.42 crates

Step-by-step explanation:

Let

Greatest Number of 140kg crates = x

weight of crate = 140-kilogram

Weight of other shipment = 13200 kilograms

greatest weight of container = 26000 kilograms

Weight of other shipment + (weight of crate * number of crates) ≤ greatest weight of container

13,200 + 140x ≤ 26,000

140x ≤ 26,000 - 13,200

140x ≤ 12,800

x ≤ 12,800/140

x ≤ 91.42 kilograms

Greatest Number of 140kg crates = 91.42 crates

A basic feasible solution to a linear program refers to a solution that satisfies all the constraints of the problem and lies on one of the extreme points of the feasible region.

To describe all descent directions from this point, we need to consider the gradient of the objective function. A descent direction is any direction along which the objective function decreases. Mathematically, the descent directions can be obtained by considering the null space of the constraint matrix.

The null space of the constraint matrix represents all the directions in which the constraints are satisfied. In other words, any linear combination of the vectors in the null space would not violate any of the constraints. Therefore, these vectors represent feasible descent directions.

However, not all descent directions are feasible descent directions. A feasible descent direction is one that not only decreases the objective function, but also satisfies all the constraints. The feasible descent directions can be obtained by intersecting the null space with the feasible region.

The simplex method, which is commonly used to solve linear programs, does not always move in a descent direction. In some cases, the simplex method may move in a direction that increases the objective function temporarily before eventually finding a better solution. This is because the simplex method explores different vertices of the feasible region in search of the optimal solution.

The descent directions from a basic feasible solution can be obtained by considering the null space of the constraint matrix. Feasible descent directions are those that not only decrease the objective function but also satisfy all the constraints. The simplex method does not always move in a descent direction as it may explore different vertices in search of the optimal solution.

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Answer:

True

Step-by-step explanation:

1) Add up the cost of all items.

11+4.50+2.95=18.45

2) Compare with 18.

18.45>18

Therefore, Abdurrahman got what he asked for.

Answer:

\(\dfrac{2m -1}{5}\)

Step-by-step explanation:

Since we have common denominators inside the parentheses, we can combine the denominators. Then, we get the following expression:

\(2\huge\text{(}\dfrac{1}{5} m - \dfrac{2}{5} \huge\text{)} + \dfrac{3}{5}\)

\(2\huge\text{(}\dfrac{m - 2}{5} \huge\text{)} + \dfrac{3}{5}\)

Now, we can multiply the expression inside the parentheses by 2.

\(\huge\text{(}\dfrac{2m - 4}{5} \huge\text{)} + \dfrac{3}{5}\)

Since the expression inside the parentheses cannot be simplified further, we can open the parentheses and simplify the expression.

\(\dfrac{2m - 4}{5} + \dfrac{3}{5}\)

We can combine the denominators as the denominators are the same.

\(\dfrac{2m - 4 + 3}{5}\)

Finally, we can simplify -4 + 3.

\(\dfrac{2m -1}{5}\)

Therefore, the simplified expression is (2m - 1)/5.

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Answer:

Work shown below!

Step-by-step explanation:

(a + 3)(a + 5) = \(a^{2} +5a+3a+15=a^{2}+8a+15\)

a) The average selling price in Bloomington is $301,596.27.

b) The average and standard deviation of the square footage of houses in Bloomington are 2,164.57 sqft and 954.61 sqft, respectively.

c) There are 98 houses made primarily of brick and 102 not.

d) There is a positive moderate relationship between selling price and square footage of houses in Bloomington.

e) On average, houses in newer neighborhoods have a higher selling price than more traditional ones.

The descriptive analysis in Bloomington has given the following insights: The average selling price in Bloomington is $301,596.27. The average and standard deviation of the square footage of houses in Bloomington are 2,164.57 sqft and 954.61 sqft, respectively. There are 98 houses made primarily of brick and 102 not. There is a positive moderate relationship between selling price and square footage of houses in Bloomington. On average, houses in newer neighborhoods have a higher selling price than more traditional ones.

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Answer:

first angle is 95

second angle is 95

third angle is 95

the sum of angle in a quadrilateral is 360

therefore 95+95+95°=285

to get the fourth angle=360-285=75

therefore the fourth angle is 75°

The total amount of rainwater collected in the next 6 hours will be equal to 1.5 cm.

The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or even more items.

Included in them is the study of integers, especially the order of operations, which is important for all other areas of mathematics, notably algebra, data management, and geometry.

As per the data mentioned in the question,

Rainwater in the bucket from last night = 3 cm

Night = 12 hours

Then, rainwater collected per hour = 3/12 = 0.25 cm per hour.

Then, the total amount of water in the next 6 hours will be,

0.25 × 6 = 1.5 cm.

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