You are creating a model of a bookcase for a dollhouse.
The actual bookcase is 48 inches tall and 32 inches wide.
If you plan to make the model 3 inches tall, how wide do
you have to make the model if you want the rectangular
shapes of the bookcases to be similar figures?

A cylindrical can is to be made to hold 1 l of oil. Then the dimensions that will minimize the cost of metal to manufacture the can is r = h = \(\sqrt[3]{\frac{500}{\pi }}\) i.e. radius(r) and h both are equal.

In the given question, a cylindrical can is to be made to hold 1 l of oil.

We have to find the dimensions that will minimize the cost of metal to manufacture the can.

The volume of cylinder = 1 l

Now converting l in cm.

As we know that 1 l = 1000 cm^3

As we know that the volume of cylinder = πr^2h

So, πr^2h = 1000

h = 1000/πr^2

Metal required to manufacture the can = Surface area of the can (assuming lid is there)

Metal required to manufacture the can = 2πr(r+h)

Metal required to manufacture the can = 2πr^2 + 2000/r

Use derivative test

S'(r) = 4πr-2000/r^{2}

S"(r) = 4π +4000/r^{3} > 0

Set first derivative equal to 0

4πr = 2000/r^2

Or r = \(\sqrt[3]{\frac{500}{\pi }}\)

h = 1000/πr^2

h = \(\sqrt[3]{\frac{500}{\pi }}\) i.e. radius and h are equal.

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the answer is correct.x= -7

Answer:

Nonrefundable deposit: y = 30x + 150

Refundable deposit:  y = 30x

In both cases, the slope is 30.

Step-by-step explanation:

The equation is:

y = 30x + 150

[Total Cost is equal to the rate per hour times the number of hours, plus the $150 deposit]

The slope is 30 [30x]

It doesn't say if the deposit will be refunded.  If it is, then the total cost is:  y = 30x.

The value of x is 21.29 degrees.

The figure given is a circle. A circle is a bounded figure which points from its center to its circumference is equidistant. The circle has been divided into segments.

Given the information the in the question segment DEF :

152 = 7x + 3

In order to determine the value of x, take the following steps:

Combine similar terms: 152 - 3 = 7x

Add similar terms together: 149 = 7x

Divide both sides of the equation by 7: x = 149 / 7

x = 21.29°

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The value of n corresponding to AIG = 11.6 and i = 7%, compounded annually, using the given known points (n, A/G) (all at i = 7%) is 41 years.

Given Points are as follows:(35, 10.6687), (40, 11.4234), (45,12.0360)Here, we have to find the value of "n" such that A/G = 11.6A/G is given by the following formula:A/G = (1 - (1+i)^-n)/i * (F/A, i, n)

By substituting the values of the above given points in the formula, we get:(35, 10.6687)  => A/G = 10.6687 = (1 - (1+0.07)^-35)/0.07 * (F/A, 0.07, 35) (1)(40, 11.4234) => A/G = 11.4234 = (1 - (1+0.07)^-40)/0.07 * (F/A, 0.07, 40) (2)(45, 12.0360) => A/G = 12.0360 = (1 - (1+0.07)^-45)/0.07 * (F/A, 0.07, 45) (3)Now, we will use the value of equation (2) and (3) to get the value of "n".

Equation (2) => 11.4234 = (1 - (1+0.07)^-40)/0.07 * (F/A, 0.07, 40) => (F/A, 0.07, 40) = 11.4234 * 0.07 / (1 - (1+0.07)^-40)Equation (3) => 12.0360 = (1 - (1+0.07)^-45)/0.07 * (F/A, 0.07, 45) => (F/A, 0.07, 45) = 12.0360 * 0.07 / (1 - (1+0.07)^-45)

Now, using the above value of (F/A, 0.07, 40) and (F/A, 0.07, 45) in equation (1)10.6687 = (1 - (1+0.07)^-35)/0.07 * (11.4234 * 0.07 / (1 - (1+0.07)^-40)) => n = 40 years11.4234 = (1 - (1+0.07)^-40)/0.07 * (12.0360 * 0.07 / (1 - (1+0.07)^-45)) => n = 41 years12.0360 = (1 - (1+0.07)^-45)/0.07 * (11.4234 * 0.07 / (1 - (1+0.07)^-40)) => n = 43 years

Therefore, the value of n corresponding to AIG = 11.6 and i = 7%, compounded annually, using the given known points (n, A/G) (all at i = 7%) is 41 years.

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Answer:

9.42

Step-by-step explanation:

Breaking the phrase down:

'Nine' would be the number 9 in the ones place.

'And' represents the decimal in a number. ('.')

'Forty-Two Hundredths" is 0.42.

So, "nine and forty-two hundredths" would be 9.42.

Hope this helps.

x² + 6x + 5 = 0

To find the solution, we can use the quadratic formula.

The solutions are (-1, 0) and (-5, 0)

If f is an increasing function and g is a decreasing function, then fog will be a decreasing function (option b).

The behavior of the composite function fog when f is an increasing function and g is a decreasing function. To answer this question, let's examine the properties of fog.

1. f is an increasing function: This means that if x1 < x2, then f(x1) < f(x2).
2. g is a decreasing function: This means that if y1 < y2, then g(y1) > g(y2).

Now, let's analyze the behavior of fog(x):

fog(x) = f(g(x))

Let's consider two points x1 and x2 such that x1 < x2.

Since g is a decreasing function, we have:
g(x1) > g(x2)

Now, as f is an increasing function, when we apply f to both sides, we get:
f(g(x1)) > f(g(x2))

This translates to:
fog(x1) > fog(x2)

Since x1 < x2, and fog(x1) > fog(x2), we can conclude that the composite function fog is a decreasing function.

So, the answer to your question is: If f is an increasing function and g is a decreasing function, then fog will be a decreasing function (option b).

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Answer:

  9/4

Step-by-step explanation:

You want to know the value required to complete the square in the equation 1 = x² -3x.

Your picture shows the required value: (-3/2)² = 9/4.

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The space C1(S1) is a Banach space, which means it is a complete normed vector space, equipped with the norm ||f|| = sup{|f(θ)| + |f'(θ)| : θ ∈ S1}.

The space C1(S1) is the space of continuously differentiable real-valued functions defined on the unit circle S1, which is a subset of the complex plane given by the equation |z| = 1, where z is a complex number.

Specifically, a function f: S1→R belongs to C1(S1) if it has a continuous first derivative f': S1→R that also belongs to C(S1), the space of continuous real-valued functions defined on S1.

Formally, we can define the space C1(S1) as follows:

C1(S1) = {f: S1→R | f is continuously differentiable on S1 and f' belongs to C(S1)}

Here, f' denotes the first derivative of f, which is defined as the limit:

f'(θ) = lim [f (θ + h) - f(θ)]/h

h→0

for all θ in S1

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There is no rate of increase as the graph shows a decrease in the amount of water, Since the specific values for the graph are not provided, I cannot give you the exact rate in liters per minute.

(a) 270 liters reach 0 liters at 60 minutes.
(b) As time increases, the amount of water in the aquarium decreases.
The rate at which the amount of water is decreasing is 4.5 liters per minute.
There is no rate of increase as the graph shows a decrease in the amount of water.

Based on the information provided,
(a) The time at which the amount of water reaches 0 liters is not provided in the question. However, you can determine it by finding the point on the graph where the amount of water is 0 liters.

(b) The statement that best describes how time and amount of water are related is: "As time increases, the amount of water in the aquarium decreases."

To find the rate at which the amount of water is decreasing, you'll need to examine the graph and calculate the slope of the line, which represents the rate of change. The slope (rate) can be calculated as:

(rate) = (change in water amount) / (change in time)

Since the specific values for the graph are not provided, I cannot give you the exact rate in liters per minute.

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The equations in options B and D are the polynomials other equations are not polynomial.

Polynomial is an expression of more than two algebraic terms, especially the sum of several terms that contain different powers of the same variable(s).

The exponent of the polynomial should be always a whole number like {0,1,2,3,4,5,6,.........}

Here in the option, only two equations are polynomials that are

(2/3)x²+x+1  and   x³+2x+√2

Hence the equations in options B and D are the polynomials other equations are not polynomial.

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Answer: 3.579 × 10^5

Step-by-step explanation:

The standard deviation of a set of seventeen numbers described by Σx=272 Σx² = 11849​ is 21.

The term "standard deviation"  refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.

We have Σx=272 and Σx² = 11849​.

n= 17

So, the Variance of the Data

= Σx²/n - (Σx/ n)²

= 11849 / 17 - (272/17)²

= 697 - 256

= 441

Then, the Standard deviation is

= √Variance

= √441

= 21

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Answer:

15 items Emma packed in the bag .

#Hope it helps!!

Answer: 50 items

Step-by-step explanation: 2x5=10+3x5=15+3x5=15+2x5=10

10+15+15+10=50

Answer:

4,000 dollars i think

Step-by-step explanation:

because in this case you have have to divide and multiply 20/5 and 4x5

The mean amount of snow per day is equal to 19 cm snow per day.

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

Mean = [F(x)]/n

For the total amount of snow based on the frequency, we have;

Total amount of snow (s cm), F(x) = 5(8) + 15(10) + 25(7) + 35(2) + 45(3)

Total amount of snow (s cm), F(x) = 40 + 150 + 175 + 70 + 135

Total amount of snow (s cm), F(x) = 570

Now, we can calculate the mean amount of snow as follows;

Mean = 570/30

Mean = 19 cm snow per day.

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Missing information:

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

Answer:

slope m = - 8

Step-by-step explanation:

the equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b ) a point on the line

y + 3 = - 8(x - 4) ← is in point- slope form

with slope m = - 8

The slope is :

Solution:

Given: \(\bf{y+3=-8(x-4)}\)

To determine the slope, it's important to know the form of the equation first.

There are 3 forms that you should be familiar with.

The three forms of equations of a straight line are:

This equation matches point slope perfectly.

The question becomes, how do you work with point slope to find slope?

In point slope, m is the slope and (x₁, y₁) is a point on the line.

Similarly, the slope of \(\bf{y+3=-8(x-4)}\) is -8.

Using inferential statistics, it is found that the option that is best surveyed from the collected in the survey is given by:

D. The Number of students who prefer cookies and cream is higher than the number of those who prefer chocolate and those who prefer strawberry.

An inferential statistic is one that makes inference or predictions about a population based on a sample.

From the table, we have that cookies and cream is the most popular flavor, hence the correct option is:

D. The Number of students who prefer cookies and cream is higher than the number of those who prefer chocolate and those who prefer strawberry.

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Answer:

Remaining cups = 10/3 cups

Step-by-step explanation:

Given:

Total amount of broccoli = 4 cup

Amount of broccoli used = 2/3 cup

Find:

Remaining cups

Computation:

Remaining cups = Total amount of broccoli - Amount of broccoli used

Remaining cups = 4 - 2/3

Remaining cups = (12-2) / 3

Remaining cups = 10/3 cups

The linear function decreases when x is between –6 and 0.

An equation can be represented by a linear function. The standard form for the linear equation is: y= mx+b , for example, y=5x+2. Where:

m= the slope.

b= the constant term that represents the y-intercept.

For the given example: m=5 and b=2.

A function can be classified as:

From the graph is possible to see that the function decreases when x is between –6 and 0 because the values of y decrease with the increasing of x-values.

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Answer:

can u just post a question pls

Answer:

2 pie r is the measure of its circumference.

Answer:

you need to know the value of the radius in order to work out the circumfrance. do you have a picture of the math question?

Answer:

1. this is alwas true since points x and y are in plane z the line cntatining

Answer: 74.61 ft^3

Step-by-step explanation:

Answer:

x=13

Step-by-step explanation:

See attached image. If you have any questions, let me know!

Answer:

Step-by-step explanation:

Given that:

cos(x) = x³

f(x) = cos (x) - x³

f(x) is continuous on the interval (0, 1)

when;

f(0) = cos (0) - (0)

f(0) = 1 - 0

f(0) = 1 > 0

f(1)  = cos (1) - 1³

f(1) = 0.5403 - 1

f(1) = -0.4597

f(1) = - 0.46

f(1) = - 0.46 < 0

Since, 1 > 0 > -0.46, thus there is a number ''c" in (0,1)

such that f(c) = 0

By applying the Intermediate Value Theorem, there is a root of the equation in the interval (0,1)

b) Given that:

The interval length = 0.01; this implies that it is 0.005 length from its root.

f(0.865) = 0.0014

f(0.87) = - 0.013

The solution to the interval lies between 0.865 , 0.87 by using a calculator at length 0.01.